blead is upstream for Math-BigInt

60 files changed, 23305 insertions, 0 deletions

diff --git a/dist/Math-BigInt/lib/Math/BigFloat.pm b/dist/Math-BigInt/lib/Math/BigFloat.pm
new file mode 100644
index 0000000000..27d60b3143
--- /dev/null
+++ b/dist/Math-BigInt/lib/Math/BigFloat.pm
@@ -0,0 +1,4402 @@
+package Math::BigFloat;
+
+# 
+# Mike grinned. 'Two down, infinity to go' - Mike Nostrus in 'Before and After'
+#
+
+# The following hash values are internally used:
+#   _e	: exponent (ref to $CALC object)
+#   _m	: mantissa (ref to $CALC object)
+#   _es	: sign of _e
+# sign	: +,-,+inf,-inf, or "NaN" if not a number
+#   _a	: accuracy
+#   _p	: precision
+
+$VERSION = '1.60';
+require 5.006;
+
+require Exporter;
+@ISA		= qw/Math::BigInt/;
+@EXPORT_OK	= qw/bpi/;
+
+use strict;
+# $_trap_inf/$_trap_nan are internal and should never be accessed from outside
+use vars qw/$AUTOLOAD $accuracy $precision $div_scale $round_mode $rnd_mode
+	    $upgrade $downgrade $_trap_nan $_trap_inf/;
+my $class = "Math::BigFloat";
+
+use overload
+'<=>'	=>	sub { my $rc = $_[2] ?
+                      ref($_[0])->bcmp($_[1],$_[0]) : 
+                      ref($_[0])->bcmp($_[0],$_[1]); 
+		      $rc = 1 unless defined $rc;
+		      $rc <=> 0;
+		},
+# we need '>=' to get things like "1 >= NaN" right:
+'>='	=>	sub { my $rc = $_[2] ?
+                      ref($_[0])->bcmp($_[1],$_[0]) : 
+                      ref($_[0])->bcmp($_[0],$_[1]);
+		      # if there was a NaN involved, return false
+		      return '' unless defined $rc;
+		      $rc >= 0;
+		},
+'int'	=>	sub { $_[0]->as_number() },		# 'trunc' to bigint
+;
+
+##############################################################################
+# global constants, flags and assorted stuff
+
+# the following are public, but their usage is not recommended. Use the
+# accessor methods instead.
+
+# class constants, use Class->constant_name() to access
+# one of 'even', 'odd', '+inf', '-inf', 'zero', 'trunc' or 'common'
+$round_mode = 'even';
+$accuracy   = undef;
+$precision  = undef;
+$div_scale  = 40;
+
+$upgrade = undef;
+$downgrade = undef;
+# the package we are using for our private parts, defaults to:
+# Math::BigInt->config()->{lib}
+my $MBI = 'Math::BigInt::FastCalc';
+
+# are NaNs ok? (otherwise it dies when encountering an NaN) set w/ config()
+$_trap_nan = 0;
+# the same for infinity
+$_trap_inf = 0;
+
+# constant for easier life
+my $nan = 'NaN'; 
+
+my $IMPORT = 0;	# was import() called yet? used to make require work
+
+# some digits of accuracy for blog(undef,10); which we use in blog() for speed
+my $LOG_10 = 
+ '2.3025850929940456840179914546843642076011014886287729760333279009675726097';
+my $LOG_10_A = length($LOG_10)-1;
+# ditto for log(2)
+my $LOG_2 = 
+ '0.6931471805599453094172321214581765680755001343602552541206800094933936220';
+my $LOG_2_A = length($LOG_2)-1;
+my $HALF = '0.5';			# made into an object if nec.
+
+##############################################################################
+# the old code had $rnd_mode, so we need to support it, too
+
+sub TIESCALAR   { my ($class) = @_; bless \$round_mode, $class; }
+sub FETCH       { return $round_mode; }
+sub STORE       { $rnd_mode = $_[0]->round_mode($_[1]); }
+
+BEGIN
+  {
+  # when someone sets $rnd_mode, we catch this and check the value to see
+  # whether it is valid or not. 
+  $rnd_mode   = 'even'; tie $rnd_mode, 'Math::BigFloat';
+
+  # we need both of them in this package:
+  *as_int = \&as_number;
+  }
+ 
+##############################################################################
+
+{
+  # valid method aliases for AUTOLOAD
+  my %methods = map { $_ => 1 }  
+   qw / fadd fsub fmul fdiv fround ffround fsqrt fmod fstr fsstr fpow fnorm
+        fint facmp fcmp fzero fnan finf finc fdec ffac fneg
+	fceil ffloor frsft flsft fone flog froot fexp
+      /;
+  # valid methods that can be handed up (for AUTOLOAD)
+  my %hand_ups = map { $_ => 1 }  
+   qw / is_nan is_inf is_negative is_positive is_pos is_neg
+        accuracy precision div_scale round_mode fabs fnot
+        objectify upgrade downgrade
+	bone binf bnan bzero
+	bsub
+      /;
+
+  sub _method_alias { exists $methods{$_[0]||''}; } 
+  sub _method_hand_up { exists $hand_ups{$_[0]||''}; } 
+}
+
+##############################################################################
+# constructors
+
+sub new 
+  {
+  # create a new BigFloat object from a string or another bigfloat object. 
+  # _e: exponent
+  # _m: mantissa
+  # sign  => sign (+/-), or "NaN"
+
+  my ($class,$wanted,@r) = @_;
+
+  # avoid numify-calls by not using || on $wanted!
+  return $class->bzero() if !defined $wanted;	# default to 0
+  return $wanted->copy() if UNIVERSAL::isa($wanted,'Math::BigFloat');
+
+  $class->import() if $IMPORT == 0;             # make require work
+
+  my $self = {}; bless $self, $class;
+  # shortcut for bigints and its subclasses
+  if ((ref($wanted)) && UNIVERSAL::can( $wanted, "as_number"))
+    {
+    $self->{_m} = $wanted->as_number()->{value}; # get us a bigint copy
+    $self->{_e} = $MBI->_zero();
+    $self->{_es} = '+';
+    $self->{sign} = $wanted->sign();
+    return $self->bnorm();
+    }
+  # else: got a string or something maskerading as number (with overload)
+
+  # handle '+inf', '-inf' first
+  if ($wanted =~ /^[+-]?inf\z/)
+    {
+    return $downgrade->new($wanted) if $downgrade;
+
+    $self->{sign} = $wanted;		# set a default sign for bstr()
+    return $self->binf($wanted);
+    }
+
+  # shortcut for simple forms like '12' that neither have trailing nor leading
+  # zeros
+  if ($wanted =~ /^([+-]?)([1-9][0-9]*[1-9])$/)
+    {
+    $self->{_e} = $MBI->_zero();
+    $self->{_es} = '+';
+    $self->{sign} = $1 || '+';
+    $self->{_m} = $MBI->_new($2);
+    return $self->round(@r) if !$downgrade;
+    }
+
+  my ($mis,$miv,$mfv,$es,$ev) = Math::BigInt::_split($wanted);
+  if (!ref $mis)
+    {
+    if ($_trap_nan)
+      {
+      require Carp;
+      Carp::croak ("$wanted is not a number initialized to $class");
+      }
+    
+    return $downgrade->bnan() if $downgrade;
+    
+    $self->{_e} = $MBI->_zero();
+    $self->{_es} = '+';
+    $self->{_m} = $MBI->_zero();
+    $self->{sign} = $nan;
+    }
+  else
+    {
+    # make integer from mantissa by adjusting exp, then convert to int
+    $self->{_e} = $MBI->_new($$ev);		# exponent
+    $self->{_es} = $$es || '+';
+    my $mantissa = "$$miv$$mfv"; 		# create mant.
+    $mantissa =~ s/^0+(\d)/$1/;			# strip leading zeros
+    $self->{_m} = $MBI->_new($mantissa); 	# create mant.
+
+    # 3.123E0 = 3123E-3, and 3.123E-2 => 3123E-5
+    if (CORE::length($$mfv) != 0)
+      {
+      my $len = $MBI->_new( CORE::length($$mfv));
+      ($self->{_e}, $self->{_es}) =
+	_e_sub ($self->{_e}, $len, $self->{_es}, '+');
+      }
+    # we can only have trailing zeros on the mantissa if $$mfv eq ''
+    else
+      {
+      # Use a regexp to count the trailing zeros in $$miv instead of _zeros()
+      # because that is faster, especially when _m is not stored in base 10.
+      my $zeros = 0; $zeros = CORE::length($1) if $$miv =~ /[1-9](0*)$/; 
+      if ($zeros != 0)
+        {
+        my $z = $MBI->_new($zeros);
+        # turn '120e2' into '12e3'
+        $MBI->_rsft ( $self->{_m}, $z, 10);
+        ($self->{_e}, $self->{_es}) =
+	  _e_add ( $self->{_e}, $z, $self->{_es}, '+');
+        }
+      }
+    $self->{sign} = $$mis;
+
+    # for something like 0Ey, set y to 1, and -0 => +0
+    # Check $$miv for being '0' and $$mfv eq '', because otherwise _m could not
+    # have become 0. That's faster than to call $MBI->_is_zero().
+    $self->{sign} = '+', $self->{_e} = $MBI->_one()
+     if $$miv eq '0' and $$mfv eq '';
+
+    return $self->round(@r) if !$downgrade;
+    }
+  # if downgrade, inf, NaN or integers go down
+
+  if ($downgrade && $self->{_es} eq '+')
+    {
+    if ($MBI->_is_zero( $self->{_e} ))
+      {
+      return $downgrade->new($$mis . $MBI->_str( $self->{_m} ));
+      }
+    return $downgrade->new($self->bsstr()); 
+    }
+  $self->bnorm()->round(@r);			# first normalize, then round
+  }
+
+sub copy
+  {
+  # if two arguments, the first one is the class to "swallow" subclasses
+  if (@_ > 1)
+    {
+    my  $self = bless {
+	sign => $_[1]->{sign}, 
+	_es => $_[1]->{_es}, 
+	_m => $MBI->_copy($_[1]->{_m}),
+	_e => $MBI->_copy($_[1]->{_e}),
+    }, $_[0] if @_ > 1;
+
+    $self->{_a} = $_[1]->{_a} if defined $_[1]->{_a};
+    $self->{_p} = $_[1]->{_p} if defined $_[1]->{_p};
+    return $self;
+    }
+
+  my $self = bless {
+	sign => $_[0]->{sign}, 
+	_es => $_[0]->{_es}, 
+	_m => $MBI->_copy($_[0]->{_m}),
+	_e => $MBI->_copy($_[0]->{_e}),
+	}, ref($_[0]);
+
+  $self->{_a} = $_[0]->{_a} if defined $_[0]->{_a};
+  $self->{_p} = $_[0]->{_p} if defined $_[0]->{_p};
+  $self;
+  }
+
+sub _bnan
+  {
+  # used by parent class bone() to initialize number to NaN
+  my $self = shift;
+  
+  if ($_trap_nan)
+    {
+    require Carp;
+    my $class = ref($self);
+    Carp::croak ("Tried to set $self to NaN in $class\::_bnan()");
+    }
+
+  $IMPORT=1;					# call our import only once
+  $self->{_m} = $MBI->_zero();
+  $self->{_e} = $MBI->_zero();
+  $self->{_es} = '+';
+  }
+
+sub _binf
+  {
+  # used by parent class bone() to initialize number to +-inf
+  my $self = shift;
+  
+  if ($_trap_inf)
+    {
+    require Carp;
+    my $class = ref($self);
+    Carp::croak ("Tried to set $self to +-inf in $class\::_binf()");
+    }
+
+  $IMPORT=1;					# call our import only once
+  $self->{_m} = $MBI->_zero();
+  $self->{_e} = $MBI->_zero();
+  $self->{_es} = '+';
+  }
+
+sub _bone
+  {
+  # used by parent class bone() to initialize number to 1
+  my $self = shift;
+  $IMPORT=1;					# call our import only once
+  $self->{_m} = $MBI->_one();
+  $self->{_e} = $MBI->_zero();
+  $self->{_es} = '+';
+  }
+
+sub _bzero
+  {
+  # used by parent class bone() to initialize number to 0
+  my $self = shift;
+  $IMPORT=1;					# call our import only once
+  $self->{_m} = $MBI->_zero();
+  $self->{_e} = $MBI->_one();
+  $self->{_es} = '+';
+  }
+
+sub isa
+  {
+  my ($self,$class) = @_;
+  return if $class =~ /^Math::BigInt/;		# we aren't one of these
+  UNIVERSAL::isa($self,$class);
+  }
+
+sub config
+  {
+  # return (later set?) configuration data as hash ref
+  my $class = shift || 'Math::BigFloat';
+
+  if (@_ == 1 && ref($_[0]) ne 'HASH')
+    {
+    my $cfg = $class->SUPER::config();
+    return $cfg->{$_[0]};
+    }
+
+  my $cfg = $class->SUPER::config(@_);
+
+  # now we need only to override the ones that are different from our parent
+  $cfg->{class} = $class;
+  $cfg->{with} = $MBI;
+  $cfg;
+  }
+
+##############################################################################
+# string conversation
+
+sub bstr 
+  {
+  # (ref to BFLOAT or num_str ) return num_str
+  # Convert number from internal format to (non-scientific) string format.
+  # internal format is always normalized (no leading zeros, "-0" => "+0")
+  my ($self,$x) = ref($_[0]) ? (undef,$_[0]) : objectify(1,@_);
+
+  if ($x->{sign} !~ /^[+-]$/)
+    {
+    return $x->{sign} unless $x->{sign} eq '+inf';      # -inf, NaN
+    return 'inf';                                       # +inf
+    }
+
+  my $es = '0'; my $len = 1; my $cad = 0; my $dot = '.';
+
+  # $x is zero?
+  my $not_zero = !($x->{sign} eq '+' && $MBI->_is_zero($x->{_m}));
+  if ($not_zero)
+    {
+    $es = $MBI->_str($x->{_m});
+    $len = CORE::length($es);
+    my $e = $MBI->_num($x->{_e});	
+    $e = -$e if $x->{_es} eq '-';
+    if ($e < 0)
+      {
+      $dot = '';
+      # if _e is bigger than a scalar, the following will blow your memory
+      if ($e <= -$len)
+        {
+        my $r = abs($e) - $len;
+        $es = '0.'. ('0' x $r) . $es; $cad = -($len+$r);
+        }
+      else
+        {
+        substr($es,$e,0) = '.'; $cad = $MBI->_num($x->{_e});
+        $cad = -$cad if $x->{_es} eq '-';
+        }
+      }
+    elsif ($e > 0)
+      {
+      # expand with zeros
+      $es .= '0' x $e; $len += $e; $cad = 0;
+      }
+    } # if not zero
+
+  $es = '-'.$es if $x->{sign} eq '-';
+  # if set accuracy or precision, pad with zeros on the right side
+  if ((defined $x->{_a}) && ($not_zero))
+    {
+    # 123400 => 6, 0.1234 => 4, 0.001234 => 4
+    my $zeros = $x->{_a} - $cad;		# cad == 0 => 12340
+    $zeros = $x->{_a} - $len if $cad != $len;
+    $es .= $dot.'0' x $zeros if $zeros > 0;
+    }
+  elsif ((($x->{_p} || 0) < 0))
+    {
+    # 123400 => 6, 0.1234 => 4, 0.001234 => 6
+    my $zeros = -$x->{_p} + $cad;
+    $es .= $dot.'0' x $zeros if $zeros > 0;
+    }
+  $es;
+  }
+
+sub bsstr
+  {
+  # (ref to BFLOAT or num_str ) return num_str
+  # Convert number from internal format to scientific string format.
+  # internal format is always normalized (no leading zeros, "-0E0" => "+0E0")
+  my ($self,$x) = ref($_[0]) ? (undef,$_[0]) : objectify(1,@_);
+
+  if ($x->{sign} !~ /^[+-]$/)
+    {
+    return $x->{sign} unless $x->{sign} eq '+inf';      # -inf, NaN
+    return 'inf';                                       # +inf
+    }
+  my $sep = 'e'.$x->{_es};
+  my $sign = $x->{sign}; $sign = '' if $sign eq '+';
+  $sign . $MBI->_str($x->{_m}) . $sep . $MBI->_str($x->{_e});
+  }
+    
+sub numify 
+  {
+  # Make a number from a BigFloat object
+  # simple return a string and let Perl's atoi()/atof() handle the rest
+  my ($self,$x) = ref($_[0]) ? (undef,$_[0]) : objectify(1,@_);
+  $x->bsstr(); 
+  }
+
+##############################################################################
+# public stuff (usually prefixed with "b")
+
+sub bneg
+  {
+  # (BINT or num_str) return BINT
+  # negate number or make a negated number from string
+  my ($self,$x) = ref($_[0]) ? (undef,$_[0]) : objectify(1,@_);
+
+  return $x if $x->modify('bneg');
+
+  # for +0 dont negate (to have always normalized +0). Does nothing for 'NaN'
+  $x->{sign} =~ tr/+-/-+/ unless ($x->{sign} eq '+' && $MBI->_is_zero($x->{_m}));
+  $x;
+  }
+
+# tels 2001-08-04 
+# XXX TODO this must be overwritten and return NaN for non-integer values
+# band(), bior(), bxor(), too
+#sub bnot
+#  {
+#  $class->SUPER::bnot($class,@_);
+#  }
+
+sub bcmp 
+  {
+  # Compares 2 values.  Returns one of undef, <0, =0, >0. (suitable for sort)
+
+  # set up parameters
+  my ($self,$x,$y) = (ref($_[0]),@_);
+  # objectify is costly, so avoid it
+  if ((!ref($_[0])) || (ref($_[0]) ne ref($_[1])))
+    {
+    ($self,$x,$y) = objectify(2,@_);
+    }
+
+  return $upgrade->bcmp($x,$y) if defined $upgrade &&
+    ((!$x->isa($self)) || (!$y->isa($self)));
+
+  if (($x->{sign} !~ /^[+-]$/) || ($y->{sign} !~ /^[+-]$/))
+    {
+    # handle +-inf and NaN
+    return undef if (($x->{sign} eq $nan) || ($y->{sign} eq $nan));
+    return 0 if ($x->{sign} eq $y->{sign}) && ($x->{sign} =~ /^[+-]inf$/);
+    return +1 if $x->{sign} eq '+inf';
+    return -1 if $x->{sign} eq '-inf';
+    return -1 if $y->{sign} eq '+inf';
+    return +1;
+    }
+
+  # check sign for speed first
+  return 1 if $x->{sign} eq '+' && $y->{sign} eq '-';	# does also 0 <=> -y
+  return -1 if $x->{sign} eq '-' && $y->{sign} eq '+';	# does also -x <=> 0
+
+  # shortcut 
+  my $xz = $x->is_zero();
+  my $yz = $y->is_zero();
+  return 0 if $xz && $yz;				# 0 <=> 0
+  return -1 if $xz && $y->{sign} eq '+';		# 0 <=> +y
+  return 1 if $yz && $x->{sign} eq '+';			# +x <=> 0
+
+  # adjust so that exponents are equal
+  my $lxm = $MBI->_len($x->{_m});
+  my $lym = $MBI->_len($y->{_m});
+  # the numify somewhat limits our length, but makes it much faster
+  my ($xes,$yes) = (1,1);
+  $xes = -1 if $x->{_es} ne '+';
+  $yes = -1 if $y->{_es} ne '+';
+  my $lx = $lxm + $xes * $MBI->_num($x->{_e});
+  my $ly = $lym + $yes * $MBI->_num($y->{_e});
+  my $l = $lx - $ly; $l = -$l if $x->{sign} eq '-';
+  return $l <=> 0 if $l != 0;
+  
+  # lengths (corrected by exponent) are equal
+  # so make mantissa equal length by padding with zero (shift left)
+  my $diff = $lxm - $lym;
+  my $xm = $x->{_m};		# not yet copy it
+  my $ym = $y->{_m};
+  if ($diff > 0)
+    {
+    $ym = $MBI->_copy($y->{_m});
+    $ym = $MBI->_lsft($ym, $MBI->_new($diff), 10);
+    }
+  elsif ($diff < 0)
+    {
+    $xm = $MBI->_copy($x->{_m});
+    $xm = $MBI->_lsft($xm, $MBI->_new(-$diff), 10);
+    }
+  my $rc = $MBI->_acmp($xm,$ym);
+  $rc = -$rc if $x->{sign} eq '-';		# -124 < -123
+  $rc <=> 0;
+  }
+
+sub bacmp 
+  {
+  # Compares 2 values, ignoring their signs. 
+  # Returns one of undef, <0, =0, >0. (suitable for sort)
+  
+  # set up parameters
+  my ($self,$x,$y) = (ref($_[0]),@_);
+  # objectify is costly, so avoid it
+  if ((!ref($_[0])) || (ref($_[0]) ne ref($_[1])))
+    {
+    ($self,$x,$y) = objectify(2,@_);
+    }
+
+  return $upgrade->bacmp($x,$y) if defined $upgrade &&
+    ((!$x->isa($self)) || (!$y->isa($self)));
+
+  # handle +-inf and NaN's
+  if ($x->{sign} !~ /^[+-]$/ || $y->{sign} !~ /^[+-]$/)
+    {
+    return undef if (($x->{sign} eq $nan) || ($y->{sign} eq $nan));
+    return 0 if ($x->is_inf() && $y->is_inf());
+    return 1 if ($x->is_inf() && !$y->is_inf());
+    return -1;
+    }
+
+  # shortcut 
+  my $xz = $x->is_zero();
+  my $yz = $y->is_zero();
+  return 0 if $xz && $yz;				# 0 <=> 0
+  return -1 if $xz && !$yz;				# 0 <=> +y
+  return 1 if $yz && !$xz;				# +x <=> 0
+
+  # adjust so that exponents are equal
+  my $lxm = $MBI->_len($x->{_m});
+  my $lym = $MBI->_len($y->{_m});
+  my ($xes,$yes) = (1,1);
+  $xes = -1 if $x->{_es} ne '+';
+  $yes = -1 if $y->{_es} ne '+';
+  # the numify somewhat limits our length, but makes it much faster
+  my $lx = $lxm + $xes * $MBI->_num($x->{_e});
+  my $ly = $lym + $yes * $MBI->_num($y->{_e});
+  my $l = $lx - $ly;
+  return $l <=> 0 if $l != 0;
+  
+  # lengths (corrected by exponent) are equal
+  # so make mantissa equal-length by padding with zero (shift left)
+  my $diff = $lxm - $lym;
+  my $xm = $x->{_m};		# not yet copy it
+  my $ym = $y->{_m};
+  if ($diff > 0)
+    {
+    $ym = $MBI->_copy($y->{_m});
+    $ym = $MBI->_lsft($ym, $MBI->_new($diff), 10);
+    }
+  elsif ($diff < 0)
+    {
+    $xm = $MBI->_copy($x->{_m});
+    $xm = $MBI->_lsft($xm, $MBI->_new(-$diff), 10);
+    }
+  $MBI->_acmp($xm,$ym);
+  }
+
+sub badd 
+  {
+  # add second arg (BFLOAT or string) to first (BFLOAT) (modifies first)
+  # return result as BFLOAT
+
+  # set up parameters
+  my ($self,$x,$y,@r) = (ref($_[0]),@_);
+  # objectify is costly, so avoid it
+  if ((!ref($_[0])) || (ref($_[0]) ne ref($_[1])))
+    {
+    ($self,$x,$y,@r) = objectify(2,@_);
+    }
+ 
+  return $x if $x->modify('badd');
+
+  # inf and NaN handling
+  if (($x->{sign} !~ /^[+-]$/) || ($y->{sign} !~ /^[+-]$/))
+    {
+    # NaN first
+    return $x->bnan() if (($x->{sign} eq $nan) || ($y->{sign} eq $nan));
+    # inf handling
+    if (($x->{sign} =~ /^[+-]inf$/) && ($y->{sign} =~ /^[+-]inf$/))
+      {
+      # +inf++inf or -inf+-inf => same, rest is NaN
+      return $x if $x->{sign} eq $y->{sign};
+      return $x->bnan();
+      }
+    # +-inf + something => +inf; something +-inf => +-inf
+    $x->{sign} = $y->{sign}, return $x if $y->{sign} =~ /^[+-]inf$/;
+    return $x;
+    }
+
+  return $upgrade->badd($x,$y,@r) if defined $upgrade &&
+   ((!$x->isa($self)) || (!$y->isa($self)));
+
+  $r[3] = $y;						# no push!
+
+  # speed: no add for 0+y or x+0
+  return $x->bround(@r) if $y->is_zero();		# x+0
+  if ($x->is_zero())					# 0+y
+    {
+    # make copy, clobbering up x (modify in place!)
+    $x->{_e} = $MBI->_copy($y->{_e});
+    $x->{_es} = $y->{_es};
+    $x->{_m} = $MBI->_copy($y->{_m});
+    $x->{sign} = $y->{sign} || $nan;
+    return $x->round(@r);
+    }
+ 
+  # take lower of the two e's and adapt m1 to it to match m2
+  my $e = $y->{_e};
+  $e = $MBI->_zero() if !defined $e;		# if no BFLOAT?
+  $e = $MBI->_copy($e);				# make copy (didn't do it yet)
+
+  my $es;
+
+  ($e,$es) = _e_sub($e, $x->{_e}, $y->{_es} || '+', $x->{_es});
+
+  my $add = $MBI->_copy($y->{_m});
+
+  if ($es eq '-')				# < 0
+    {
+    $MBI->_lsft( $x->{_m}, $e, 10);
+    ($x->{_e},$x->{_es}) = _e_add($x->{_e}, $e, $x->{_es}, $es);
+    }
+  elsif (!$MBI->_is_zero($e))			# > 0
+    {
+    $MBI->_lsft($add, $e, 10);
+    }
+  # else: both e are the same, so just leave them
+
+  if ($x->{sign} eq $y->{sign})
+    {
+    # add
+    $x->{_m} = $MBI->_add($x->{_m}, $add);
+    }
+  else
+    {
+    ($x->{_m}, $x->{sign}) = 
+     _e_add($x->{_m}, $add, $x->{sign}, $y->{sign});
+    }
+
+  # delete trailing zeros, then round
+  $x->bnorm()->round(@r);
+  }
+
+# sub bsub is inherited from Math::BigInt!
+
+sub binc
+  {
+  # increment arg by one
+  my ($self,$x,@r) = ref($_[0]) ? (ref($_[0]),@_) : objectify(1,@_);
+
+  return $x if $x->modify('binc');
+
+  if ($x->{_es} eq '-')
+    {
+    return $x->badd($self->bone(),@r);	#  digits after dot
+    }
+
+  if (!$MBI->_is_zero($x->{_e}))		# _e == 0 for NaN, inf, -inf
+    {
+    # 1e2 => 100, so after the shift below _m has a '0' as last digit
+    $x->{_m} = $MBI->_lsft($x->{_m}, $x->{_e},10);	# 1e2 => 100
+    $x->{_e} = $MBI->_zero();				# normalize
+    $x->{_es} = '+';
+    # we know that the last digit of $x will be '1' or '9', depending on the
+    # sign
+    }
+  # now $x->{_e} == 0
+  if ($x->{sign} eq '+')
+    {
+    $MBI->_inc($x->{_m});
+    return $x->bnorm()->bround(@r);
+    }
+  elsif ($x->{sign} eq '-')
+    {
+    $MBI->_dec($x->{_m});
+    $x->{sign} = '+' if $MBI->_is_zero($x->{_m}); # -1 +1 => -0 => +0
+    return $x->bnorm()->bround(@r);
+    }
+  # inf, nan handling etc
+  $x->badd($self->bone(),@r);			# badd() does round 
+  }
+
+sub bdec
+  {
+  # decrement arg by one
+  my ($self,$x,@r) = ref($_[0]) ? (ref($_[0]),@_) : objectify(1,@_);
+
+  return $x if $x->modify('bdec');
+
+  if ($x->{_es} eq '-')
+    {
+    return $x->badd($self->bone('-'),@r);	#  digits after dot
+    }
+
+  if (!$MBI->_is_zero($x->{_e}))
+    {
+    $x->{_m} = $MBI->_lsft($x->{_m}, $x->{_e},10);	# 1e2 => 100
+    $x->{_e} = $MBI->_zero();				# normalize
+    $x->{_es} = '+';
+    }
+  # now $x->{_e} == 0
+  my $zero = $x->is_zero();
+  # <= 0
+  if (($x->{sign} eq '-') || $zero)
+    {
+    $MBI->_inc($x->{_m});
+    $x->{sign} = '-' if $zero;				# 0 => 1 => -1
+    $x->{sign} = '+' if $MBI->_is_zero($x->{_m});	# -1 +1 => -0 => +0
+    return $x->bnorm()->round(@r);
+    }
+  # > 0
+  elsif ($x->{sign} eq '+')
+    {
+    $MBI->_dec($x->{_m});
+    return $x->bnorm()->round(@r);
+    }
+  # inf, nan handling etc
+  $x->badd($self->bone('-'),@r);		# does round
+  } 
+
+sub DEBUG () { 0; }
+
+sub blog
+  {
+  my ($self,$x,$base,$a,$p,$r) = ref($_[0]) ? (ref($_[0]),@_) : objectify(1,@_);
+
+  return $x if $x->modify('blog');
+
+  # $base > 0, $base != 1; if $base == undef default to $base == e
+  # $x >= 0
+
+  # we need to limit the accuracy to protect against overflow
+  my $fallback = 0;
+  my ($scale,@params);
+  ($x,@params) = $x->_find_round_parameters($a,$p,$r);
+
+  # also takes care of the "error in _find_round_parameters?" case
+  return $x->bnan() if $x->{sign} ne '+' || $x->is_zero();
+
+  # no rounding at all, so must use fallback
+  if (scalar @params == 0)
+    {
+    # simulate old behaviour
+    $params[0] = $self->div_scale();	# and round to it as accuracy
+    $params[1] = undef;			# P = undef
+    $scale = $params[0]+4; 		# at least four more for proper round
+    $params[2] = $r;			# round mode by caller or undef
+    $fallback = 1;			# to clear a/p afterwards
+    }
+  else
+    {
+    # the 4 below is empirical, and there might be cases where it is not
+    # enough...
+    $scale = abs($params[0] || $params[1]) + 4;	# take whatever is defined
+    }
+
+  return $x->bzero(@params) if $x->is_one();
+  # base not defined => base == Euler's number e
+  if (defined $base)
+    {
+    # make object, since we don't feed it through objectify() to still get the
+    # case of $base == undef
+    $base = $self->new($base) unless ref($base);
+    # $base > 0; $base != 1
+    return $x->bnan() if $base->is_zero() || $base->is_one() ||
+      $base->{sign} ne '+';
+    # if $x == $base, we know the result must be 1.0
+    if ($x->bcmp($base) == 0)
+      {
+      $x->bone('+',@params);
+      if ($fallback)
+        {
+        # clear a/p after round, since user did not request it
+        delete $x->{_a}; delete $x->{_p};
+        }
+      return $x;
+      }
+    }
+
+  # when user set globals, they would interfere with our calculation, so
+  # disable them and later re-enable them
+  no strict 'refs';
+  my $abr = "$self\::accuracy"; my $ab = $$abr; $$abr = undef;
+  my $pbr = "$self\::precision"; my $pb = $$pbr; $$pbr = undef;
+  # we also need to disable any set A or P on $x (_find_round_parameters took
+  # them already into account), since these would interfere, too
+  delete $x->{_a}; delete $x->{_p};
+  # need to disable $upgrade in BigInt, to avoid deep recursion
+  local $Math::BigInt::upgrade = undef;
+  local $Math::BigFloat::downgrade = undef;
+
+  # upgrade $x if $x is not a BigFloat (handle BigInt input)
+  # XXX TODO: rebless!
+  if (!$x->isa('Math::BigFloat'))
+    {
+    $x = Math::BigFloat->new($x);
+    $self = ref($x);
+    }
+  
+  my $done = 0;
+
+  # If the base is defined and an integer, try to calculate integer result
+  # first. This is very fast, and in case the real result was found, we can
+  # stop right here.
+  if (defined $base && $base->is_int() && $x->is_int())
+    {
+    my $i = $MBI->_copy( $x->{_m} );
+    $MBI->_lsft( $i, $x->{_e}, 10 ) unless $MBI->_is_zero($x->{_e});
+    my $int = Math::BigInt->bzero();
+    $int->{value} = $i;
+    $int->blog($base->as_number());
+    # if ($exact)
+    if ($base->as_number()->bpow($int) == $x)
+      {
+      # found result, return it
+      $x->{_m} = $int->{value};
+      $x->{_e} = $MBI->_zero();
+      $x->{_es} = '+';
+      $x->bnorm();
+      $done = 1;
+      }
+    }
+
+  if ($done == 0)
+    {
+    # base is undef, so base should be e (Euler's number), so first calculate the
+    # log to base e (using reduction by 10 (and probably 2)):
+    $self->_log_10($x,$scale);
+
+    # and if a different base was requested, convert it
+    if (defined $base)
+      {
+      $base = Math::BigFloat->new($base) unless $base->isa('Math::BigFloat');
+      # not ln, but some other base (don't modify $base)
+      $x->bdiv( $base->copy()->blog(undef,$scale), $scale );
+      }
+    }
+ 
+  # shortcut to not run through _find_round_parameters again
+  if (defined $params[0])
+    {
+    $x->bround($params[0],$params[2]);		# then round accordingly
+    }
+  else
+    {
+    $x->bfround($params[1],$params[2]);		# then round accordingly
+    }
+  if ($fallback)
+    {
+    # clear a/p after round, since user did not request it
+    delete $x->{_a}; delete $x->{_p};
+    }
+  # restore globals
+  $$abr = $ab; $$pbr = $pb;
+
+  $x;
+  }
+
+sub _len_to_steps
+  {
+  # Given D (digits in decimal), compute N so that N! (N factorial) is
+  # at least D digits long. D should be at least 50.
+  my $d = shift;
+
+  # two constants for the Ramanujan estimate of ln(N!)
+  my $lg2 = log(2 * 3.14159265) / 2;
+  my $lg10 = log(10);
+
+  # D = 50 => N => 42, so L = 40 and R = 50
+  my $l = 40; my $r = $d;
+
+  # Otherwise this does not work under -Mbignum and we do not yet have "no bignum;" :(
+  $l = $l->numify if ref($l);
+  $r = $r->numify if ref($r);
+  $lg2 = $lg2->numify if ref($lg2);
+  $lg10 = $lg10->numify if ref($lg10);
+
+  # binary search for the right value (could this be written as the reverse of lg(n!)?)
+  while ($r - $l > 1)
+    {
+    my $n = int(($r - $l) / 2) + $l;
+    my $ramanujan = 
+      int(($n * log($n) - $n + log( $n * (1 + 4*$n*(1+2*$n)) ) / 6 + $lg2) / $lg10);
+    $ramanujan > $d ? $r = $n : $l = $n;
+    }
+  $l;
+  }
+
+sub bnok
+  {
+  # Calculate n over k (binomial coefficient or "choose" function) as integer.
+  # set up parameters
+  my ($self,$x,$y,@r) = (ref($_[0]),@_);
+
+  # objectify is costly, so avoid it
+  if ((!ref($_[0])) || (ref($_[0]) ne ref($_[1])))
+    {
+    ($self,$x,$y,@r) = objectify(2,@_);
+    }
+
+  return $x if $x->modify('bnok');
+
+  return $x->bnan() if $x->is_nan() || $y->is_nan();
+  return $x->binf() if $x->is_inf();
+
+  my $u = $x->as_int();
+  $u->bnok($y->as_int());
+
+  $x->{_m} = $u->{value};
+  $x->{_e} = $MBI->_zero();
+  $x->{_es} = '+';
+  $x->{sign} = '+';
+  $x->bnorm(@r);
+  }
+
+sub bexp
+  {
+  # Calculate e ** X (Euler's number to the power of X)
+  my ($self,$x,$a,$p,$r) = ref($_[0]) ? (ref($_[0]),@_) : objectify(1,@_);
+
+  return $x if $x->modify('bexp');
+
+  return $x->binf() if $x->{sign} eq '+inf';
+  return $x->bzero() if $x->{sign} eq '-inf';
+
+  # we need to limit the accuracy to protect against overflow
+  my $fallback = 0;
+  my ($scale,@params);
+  ($x,@params) = $x->_find_round_parameters($a,$p,$r);
+
+  # also takes care of the "error in _find_round_parameters?" case
+  return $x if $x->{sign} eq 'NaN';
+
+  # no rounding at all, so must use fallback
+  if (scalar @params == 0)
+    {
+    # simulate old behaviour
+    $params[0] = $self->div_scale();	# and round to it as accuracy
+    $params[1] = undef;			# P = undef
+    $scale = $params[0]+4; 		# at least four more for proper round
+    $params[2] = $r;			# round mode by caller or undef
+    $fallback = 1;			# to clear a/p afterwards
+    }
+  else
+    {
+    # the 4 below is empirical, and there might be cases where it's not enough...
+    $scale = abs($params[0] || $params[1]) + 4;	# take whatever is defined
+    }
+
+  return $x->bone(@params) if $x->is_zero();
+
+  if (!$x->isa('Math::BigFloat'))
+    {
+    $x = Math::BigFloat->new($x);
+    $self = ref($x);
+    }
+  
+  # when user set globals, they would interfere with our calculation, so
+  # disable them and later re-enable them
+  no strict 'refs';
+  my $abr = "$self\::accuracy"; my $ab = $$abr; $$abr = undef;
+  my $pbr = "$self\::precision"; my $pb = $$pbr; $$pbr = undef;
+  # we also need to disable any set A or P on $x (_find_round_parameters took
+  # them already into account), since these would interfere, too
+  delete $x->{_a}; delete $x->{_p};
+  # need to disable $upgrade in BigInt, to avoid deep recursion
+  local $Math::BigInt::upgrade = undef;
+  local $Math::BigFloat::downgrade = undef;
+
+  my $x_org = $x->copy();
+
+  # We use the following Taylor series:
+
+  #           x    x^2   x^3   x^4
+  #  e = 1 + --- + --- + --- + --- ...
+  #           1!    2!    3!    4!
+
+  # The difference for each term is X and N, which would result in:
+  # 2 copy, 2 mul, 2 add, 1 inc, 1 div operations per term
+
+  # But it is faster to compute exp(1) and then raising it to the
+  # given power, esp. if $x is really big and an integer because:
+
+  #  * The numerator is always 1, making the computation faster
+  #  * the series converges faster in the case of x == 1
+  #  * We can also easily check when we have reached our limit: when the
+  #    term to be added is smaller than "1E$scale", we can stop - f.i.
+  #    scale == 5, and we have 1/40320, then we stop since 1/40320 < 1E-5.
+  #  * we can compute the *exact* result by simulating bigrat math:
+
+  #  1   1    gcd(3,4) = 1    1*24 + 1*6    5
+  #  - + -                  = ---------- =  --                 
+  #  6   24                      6*24       24
+
+  # We do not compute the gcd() here, but simple do:
+  #  1   1    1*24 + 1*6   30
+  #  - + -  = --------- =  --                 
+  #  6   24       6*24     144
+
+  # In general:
+  #  a   c    a*d + c*b 	and note that c is always 1 and d = (b*f)
+  #  - + -  = ---------
+  #  b   d       b*d
+
+  # This leads to:         which can be reduced by b to:
+  #  a   1     a*b*f + b    a*f + 1
+  #  - + -   = --------- =  -------
+  #  b   b*f     b*b*f        b*f
+
+  # The first terms in the series are:
+
+  # 1     1    1    1    1    1     1     1     13700
+  # -- + -- + -- + -- + -- + --- + --- + ---- = -----
+  # 1     1    2    6   24   120   720   5040   5040
+
+  # Note that we cannot simple reduce 13700/5040 to 685/252, but must keep A and B!
+
+  if ($scale <= 75)
+    {
+    # set $x directly from a cached string form
+    $x->{_m} = $MBI->_new(
+    "27182818284590452353602874713526624977572470936999595749669676277240766303535476");
+    $x->{sign} = '+';
+    $x->{_es} = '-';
+    $x->{_e} = $MBI->_new(79);
+    }
+  else
+    {
+    # compute A and B so that e = A / B.
+ 
+    # After some terms we end up with this, so we use it as a starting point:
+    my $A = $MBI->_new("90933395208605785401971970164779391644753259799242");
+    my $F = $MBI->_new(42); my $step = 42;
+
+    # Compute how many steps we need to take to get $A and $B sufficiently big
+    my $steps = _len_to_steps($scale - 4);
+#    print STDERR "# Doing $steps steps for ", $scale-4, " digits\n";
+    while ($step++ <= $steps)
+      {
+      # calculate $a * $f + 1
+      $A = $MBI->_mul($A, $F);
+      $A = $MBI->_inc($A);
+      # increment f
+      $F = $MBI->_inc($F);
+      }
+    # compute $B as factorial of $steps (this is faster than doing it manually)
+    my $B = $MBI->_fac($MBI->_new($steps));
+    
+#  print "A ", $MBI->_str($A), "\nB ", $MBI->_str($B), "\n";
+
+    # compute A/B with $scale digits in the result (truncate, not round)
+    $A = $MBI->_lsft( $A, $MBI->_new($scale), 10);
+    $A = $MBI->_div( $A, $B );
+
+    $x->{_m} = $A;
+    $x->{sign} = '+';
+    $x->{_es} = '-';
+    $x->{_e} = $MBI->_new($scale);
+    }
+
+  # $x contains now an estimate of e, with some surplus digits, so we can round
+  if (!$x_org->is_one())
+    {
+    # raise $x to the wanted power and round it in one step:
+    $x->bpow($x_org, @params);
+    }
+  else
+    {
+    # else just round the already computed result
+    delete $x->{_a}; delete $x->{_p};
+    # shortcut to not run through _find_round_parameters again
+    if (defined $params[0])
+      {
+      $x->bround($params[0],$params[2]);		# then round accordingly
+      }
+    else
+      {
+      $x->bfround($params[1],$params[2]);		# then round accordingly
+      }
+    }
+  if ($fallback)
+    {
+    # clear a/p after round, since user did not request it
+    delete $x->{_a}; delete $x->{_p};
+    }
+  # restore globals
+  $$abr = $ab; $$pbr = $pb;
+
+  $x;						# return modified $x
+  }
+
+sub _log
+  {
+  # internal log function to calculate ln() based on Taylor series.
+  # Modifies $x in place.
+  my ($self,$x,$scale) = @_;
+
+  # in case of $x == 1, result is 0
+  return $x->bzero() if $x->is_one();
+
+  # XXX TODO: rewrite this in a similiar manner to bexp()
+
+  # http://www.efunda.com/math/taylor_series/logarithmic.cfm?search_string=log
+
+  # u = x-1, v = x+1
+  #              _                               _
+  # Taylor:     |    u    1   u^3   1   u^5       |
+  # ln (x)  = 2 |   --- + - * --- + - * --- + ... |  x > 0
+  #             |_   v    3   v^3   5   v^5      _|
+
+  # This takes much more steps to calculate the result and is thus not used
+  # u = x-1
+  #              _                               _
+  # Taylor:     |    u    1   u^2   1   u^3       |
+  # ln (x)  = 2 |   --- + - * --- + - * --- + ... |  x > 1/2
+  #             |_   x    2   x^2   3   x^3      _|
+
+  my ($limit,$v,$u,$below,$factor,$two,$next,$over,$f);
+
+  $v = $x->copy(); $v->binc();		# v = x+1
+  $x->bdec(); $u = $x->copy();		# u = x-1; x = x-1
+  $x->bdiv($v,$scale);			# first term: u/v
+  $below = $v->copy();
+  $over = $u->copy();
+  $u *= $u; $v *= $v;				# u^2, v^2
+  $below->bmul($v);				# u^3, v^3
+  $over->bmul($u);
+  $factor = $self->new(3); $f = $self->new(2);
+
+  my $steps = 0 if DEBUG;  
+  $limit = $self->new("1E-". ($scale-1));
+  while (3 < 5)
+    {
+    # we calculate the next term, and add it to the last
+    # when the next term is below our limit, it won't affect the outcome
+    # anymore, so we stop
+
+    # calculating the next term simple from over/below will result in quite
+    # a time hog if the input has many digits, since over and below will
+    # accumulate more and more digits, and the result will also have many
+    # digits, but in the end it is rounded to $scale digits anyway. So if we
+    # round $over and $below first, we save a lot of time for the division
+    # (not with log(1.2345), but try log (123**123) to see what I mean. This
+    # can introduce a rounding error if the division result would be f.i.
+    # 0.1234500000001 and we round it to 5 digits it would become 0.12346, but
+    # if we truncated $over and $below we might get 0.12345. Does this matter
+    # for the end result? So we give $over and $below 4 more digits to be
+    # on the safe side (unscientific error handling as usual... :+D
+
+    $next = $over->copy->bround($scale+4)->bdiv(
+      $below->copy->bmul($factor)->bround($scale+4), 
+      $scale);
+
+## old version:    
+##    $next = $over->copy()->bdiv($below->copy()->bmul($factor),$scale);
+
+    last if $next->bacmp($limit) <= 0;
+
+    delete $next->{_a}; delete $next->{_p};
+    $x->badd($next);
+    # calculate things for the next term
+    $over *= $u; $below *= $v; $factor->badd($f);
+    if (DEBUG)
+      {
+      $steps++; print "step $steps = $x\n" if $steps % 10 == 0;
+      }
+    }
+  print "took $steps steps\n" if DEBUG;
+  $x->bmul($f);					# $x *= 2
+  }
+
+sub _log_10
+  {
+  # Internal log function based on reducing input to the range of 0.1 .. 9.99
+  # and then "correcting" the result to the proper one. Modifies $x in place.
+  my ($self,$x,$scale) = @_;
+
+  # Taking blog() from numbers greater than 10 takes a *very long* time, so we
+  # break the computation down into parts based on the observation that:
+  #  blog(X*Y) = blog(X) + blog(Y)
+  # We set Y here to multiples of 10 so that $x becomes below 1 - the smaller
+  # $x is the faster it gets. Since 2*$x takes about 10 times as
+  # long, we make it faster by about a factor of 100 by dividing $x by 10.
+
+  # The same observation is valid for numbers smaller than 0.1, e.g. computing
+  # log(1) is fastest, and the further away we get from 1, the longer it takes.
+  # So we also 'break' this down by multiplying $x with 10 and subtract the
+  # log(10) afterwards to get the correct result.
+
+  # To get $x even closer to 1, we also divide by 2 and then use log(2) to
+  # correct for this. For instance if $x is 2.4, we use the formula:
+  #  blog(2.4 * 2) == blog (1.2) + blog(2)
+  # and thus calculate only blog(1.2) and blog(2), which is faster in total
+  # than calculating blog(2.4).
+
+  # In addition, the values for blog(2) and blog(10) are cached.
+
+  # Calculate nr of digits before dot:
+  my $dbd = $MBI->_num($x->{_e});
+  $dbd = -$dbd if $x->{_es} eq '-';
+  $dbd += $MBI->_len($x->{_m});
+
+  # more than one digit (e.g. at least 10), but *not* exactly 10 to avoid
+  # infinite recursion
+
+  my $calc = 1;					# do some calculation?
+
+  # disable the shortcut for 10, since we need log(10) and this would recurse
+  # infinitely deep
+  if ($x->{_es} eq '+' && $MBI->_is_one($x->{_e}) && $MBI->_is_one($x->{_m}))
+    {
+    $dbd = 0;					# disable shortcut
+    # we can use the cached value in these cases
+    if ($scale <= $LOG_10_A)
+      {
+      $x->bzero(); $x->badd($LOG_10);		# modify $x in place
+      $calc = 0; 				# no need to calc, but round
+      }
+    # if we can't use the shortcut, we continue normally
+    }
+  else
+    {
+    # disable the shortcut for 2, since we maybe have it cached
+    if (($MBI->_is_zero($x->{_e}) && $MBI->_is_two($x->{_m})))
+      {
+      $dbd = 0;					# disable shortcut
+      # we can use the cached value in these cases
+      if ($scale <= $LOG_2_A)
+        {
+        $x->bzero(); $x->badd($LOG_2);		# modify $x in place
+        $calc = 0; 				# no need to calc, but round
+        }
+      # if we can't use the shortcut, we continue normally
+      }
+    }
+
+  # if $x = 0.1, we know the result must be 0-log(10)
+  if ($calc != 0 && $x->{_es} eq '-' && $MBI->_is_one($x->{_e}) &&
+      $MBI->_is_one($x->{_m}))
+    {
+    $dbd = 0;					# disable shortcut
+    # we can use the cached value in these cases
+    if ($scale <= $LOG_10_A)
+      {
+      $x->bzero(); $x->bsub($LOG_10);
+      $calc = 0; 				# no need to calc, but round
+      }
+    }
+
+  return if $calc == 0;				# already have the result
+
+  # default: these correction factors are undef and thus not used
+  my $l_10;				# value of ln(10) to A of $scale
+  my $l_2;				# value of ln(2) to A of $scale
+
+  my $two = $self->new(2);
+
+  # $x == 2 => 1, $x == 13 => 2, $x == 0.1 => 0, $x == 0.01 => -1
+  # so don't do this shortcut for 1 or 0
+  if (($dbd > 1) || ($dbd < 0))
+    {
+    # convert our cached value to an object if not already (avoid doing this
+    # at import() time, since not everybody needs this)
+    $LOG_10 = $self->new($LOG_10,undef,undef) unless ref $LOG_10;
+
+    #print "x = $x, dbd = $dbd, calc = $calc\n";
+    # got more than one digit before the dot, or more than one zero after the
+    # dot, so do:
+    #  log(123)    == log(1.23) + log(10) * 2
+    #  log(0.0123) == log(1.23) - log(10) * 2
+  
+    if ($scale <= $LOG_10_A)
+      {
+      # use cached value
+      $l_10 = $LOG_10->copy();		# copy for mul
+      }
+    else
+      {
+      # else: slower, compute and cache result
+      # also disable downgrade for this code path
+      local $Math::BigFloat::downgrade = undef;
+
+      # shorten the time to calculate log(10) based on the following:
+      # log(1.25 * 8) = log(1.25) + log(8)
+      #               = log(1.25) + log(2) + log(2) + log(2)
+
+      # first get $l_2 (and possible compute and cache log(2))
+      $LOG_2 = $self->new($LOG_2,undef,undef) unless ref $LOG_2;
+      if ($scale <= $LOG_2_A)
+        {
+        # use cached value
+        $l_2 = $LOG_2->copy();			# copy() for the mul below
+        }
+      else
+        {
+        # else: slower, compute and cache result
+        $l_2 = $two->copy(); $self->_log($l_2, $scale); # scale+4, actually
+        $LOG_2 = $l_2->copy();			# cache the result for later
+						# the copy() is for mul below
+        $LOG_2_A = $scale;
+        }
+
+      # now calculate log(1.25):
+      $l_10 = $self->new('1.25'); $self->_log($l_10, $scale); # scale+4, actually
+
+      # log(1.25) + log(2) + log(2) + log(2):
+      $l_10->badd($l_2);
+      $l_10->badd($l_2);
+      $l_10->badd($l_2);
+      $LOG_10 = $l_10->copy();		# cache the result for later
+					# the copy() is for mul below
+      $LOG_10_A = $scale;
+      }
+    $dbd-- if ($dbd > 1); 		# 20 => dbd=2, so make it dbd=1	
+    $l_10->bmul( $self->new($dbd));	# log(10) * (digits_before_dot-1)
+    my $dbd_sign = '+';
+    if ($dbd < 0)
+      {
+      $dbd = -$dbd;
+      $dbd_sign = '-';
+      }
+    ($x->{_e}, $x->{_es}) = 
+	_e_sub( $x->{_e}, $MBI->_new($dbd), $x->{_es}, $dbd_sign); # 123 => 1.23
+ 
+    }
+
+  # Now: 0.1 <= $x < 10 (and possible correction in l_10)
+
+  ### Since $x in the range 0.5 .. 1.5 is MUCH faster, we do a repeated div
+  ### or mul by 2 (maximum times 3, since x < 10 and x > 0.1)
+
+  $HALF = $self->new($HALF) unless ref($HALF);
+
+  my $twos = 0;				# default: none (0 times)	
+  while ($x->bacmp($HALF) <= 0)		# X <= 0.5
+    {
+    $twos--; $x->bmul($two);
+    }
+  while ($x->bacmp($two) >= 0)		# X >= 2
+    {
+    $twos++; $x->bdiv($two,$scale+4);		# keep all digits
+    }
+  # $twos > 0 => did mul 2, < 0 => did div 2 (but we never did both)
+  # So calculate correction factor based on ln(2):
+  if ($twos != 0)
+    {
+    $LOG_2 = $self->new($LOG_2,undef,undef) unless ref $LOG_2;
+    if ($scale <= $LOG_2_A)
+      {
+      # use cached value
+      $l_2 = $LOG_2->copy();			# copy() for the mul below
+      }
+    else
+      {
+      # else: slower, compute and cache result
+      # also disable downgrade for this code path
+      local $Math::BigFloat::downgrade = undef;
+      $l_2 = $two->copy(); $self->_log($l_2, $scale); # scale+4, actually
+      $LOG_2 = $l_2->copy();			# cache the result for later
+						# the copy() is for mul below
+      $LOG_2_A = $scale;
+      }
+    $l_2->bmul($twos);		# * -2 => subtract, * 2 => add
+    }
+  
+  $self->_log($x,$scale);			# need to do the "normal" way
+  $x->badd($l_10) if defined $l_10; 		# correct it by ln(10)
+  $x->badd($l_2) if defined $l_2;		# and maybe by ln(2)
+
+  # all done, $x contains now the result
+  $x;
+  }
+
+sub blcm 
+  { 
+  # (BFLOAT or num_str, BFLOAT or num_str) return BFLOAT
+  # does not modify arguments, but returns new object
+  # Lowest Common Multiplicator
+
+  my ($self,@arg) = objectify(0,@_);
+  my $x = $self->new(shift @arg);
+  while (@arg) { $x = Math::BigInt::__lcm($x,shift @arg); } 
+  $x;
+  }
+
+sub bgcd
+  {
+  # (BINT or num_str, BINT or num_str) return BINT
+  # does not modify arguments, but returns new object
+
+  my $y = shift;
+  $y = __PACKAGE__->new($y) if !ref($y);
+  my $self = ref($y);
+  my $x = $y->copy()->babs();			# keep arguments
+
+  return $x->bnan() if $x->{sign} !~ /^[+-]$/	# x NaN?
+	|| !$x->is_int();			# only for integers now
+
+  while (@_)
+    {
+    my $t = shift; $t = $self->new($t) if !ref($t);
+    $y = $t->copy()->babs();
+    
+    return $x->bnan() if $y->{sign} !~ /^[+-]$/	# y NaN?
+     	|| !$y->is_int();			# only for integers now
+
+    # greatest common divisor
+    while (! $y->is_zero())
+      {
+      ($x,$y) = ($y->copy(), $x->copy()->bmod($y));
+      }
+
+    last if $x->is_one();
+    }
+  $x;
+  }
+
+##############################################################################
+
+sub _e_add
+  {
+  # Internal helper sub to take two positive integers and their signs and
+  # then add them. Input ($CALC,$CALC,('+'|'-'),('+'|'-')), 
+  # output ($CALC,('+'|'-'))
+  my ($x,$y,$xs,$ys) = @_;
+
+  # if the signs are equal we can add them (-5 + -3 => -(5 + 3) => -8)
+  if ($xs eq $ys)
+    {
+    $x = $MBI->_add ($x, $y );		# a+b
+    # the sign follows $xs
+    return ($x, $xs);
+    }
+
+  my $a = $MBI->_acmp($x,$y);
+  if ($a > 0)
+    {
+    $x = $MBI->_sub ($x , $y);				# abs sub
+    }
+  elsif ($a == 0)
+    {
+    $x = $MBI->_zero();					# result is 0
+    $xs = '+';
+    }
+  else # a < 0
+    {
+    $x = $MBI->_sub ( $y, $x, 1 );			# abs sub
+    $xs = $ys;
+    }
+  ($x,$xs);
+  }
+
+sub _e_sub
+  {
+  # Internal helper sub to take two positive integers and their signs and
+  # then subtract them. Input ($CALC,$CALC,('+'|'-'),('+'|'-')), 
+  # output ($CALC,('+'|'-'))
+  my ($x,$y,$xs,$ys) = @_;
+
+  # flip sign
+  $ys =~ tr/+-/-+/;
+  _e_add($x,$y,$xs,$ys);		# call add (does subtract now)
+  }
+
+###############################################################################
+# is_foo methods (is_negative, is_positive are inherited from BigInt)
+
+sub is_int
+  {
+  # return true if arg (BFLOAT or num_str) is an integer
+  my ($self,$x) = ref($_[0]) ? (undef,$_[0]) : objectify(1,@_);
+
+  (($x->{sign} =~ /^[+-]$/) &&			# NaN and +-inf aren't
+   ($x->{_es} eq '+')) ? 1 : 0;			# 1e-1 => no integer
+  }
+
+sub is_zero
+  {
+  # return true if arg (BFLOAT or num_str) is zero
+  my ($self,$x) = ref($_[0]) ? (undef,$_[0]) : objectify(1,@_);
+
+  ($x->{sign} eq '+' && $MBI->_is_zero($x->{_m})) ? 1 : 0;
+  }
+
+sub is_one
+  {
+  # return true if arg (BFLOAT or num_str) is +1 or -1 if signis given
+  my ($self,$x,$sign) = ref($_[0]) ? (undef,@_) : objectify(1,@_);
+
+  $sign = '+' if !defined $sign || $sign ne '-';
+
+  ($x->{sign} eq $sign && 
+   $MBI->_is_zero($x->{_e}) &&
+   $MBI->_is_one($x->{_m}) ) ? 1 : 0; 
+  }
+
+sub is_odd
+  {
+  # return true if arg (BFLOAT or num_str) is odd or false if even
+  my ($self,$x) = ref($_[0]) ? (undef,$_[0]) : objectify(1,@_);
+  
+  (($x->{sign} =~ /^[+-]$/) &&		# NaN & +-inf aren't
+   ($MBI->_is_zero($x->{_e})) &&
+   ($MBI->_is_odd($x->{_m}))) ? 1 : 0; 
+  }
+
+sub is_even
+  {
+  # return true if arg (BINT or num_str) is even or false if odd
+  my ($self,$x) = ref($_[0]) ? (undef,$_[0]) : objectify(1,@_);
+
+  (($x->{sign} =~ /^[+-]$/) &&			# NaN & +-inf aren't
+   ($x->{_es} eq '+') &&	 		# 123.45 isn't
+   ($MBI->_is_even($x->{_m}))) ? 1 : 0;		# but 1200 is
+  }
+
+sub bmul
+  { 
+  # multiply two numbers
+  
+  # set up parameters
+  my ($self,$x,$y,@r) = (ref($_[0]),@_);
+  # objectify is costly, so avoid it
+  if ((!ref($_[0])) || (ref($_[0]) ne ref($_[1])))
+    {
+    ($self,$x,$y,@r) = objectify(2,@_);
+    }
+
+  return $x if $x->modify('bmul');
+
+  return $x->bnan() if (($x->{sign} eq $nan) || ($y->{sign} eq $nan));
+
+  # inf handling
+  if (($x->{sign} =~ /^[+-]inf$/) || ($y->{sign} =~ /^[+-]inf$/))
+    {
+    return $x->bnan() if $x->is_zero() || $y->is_zero(); 
+    # result will always be +-inf:
+    # +inf * +/+inf => +inf, -inf * -/-inf => +inf
+    # +inf * -/-inf => -inf, -inf * +/+inf => -inf
+    return $x->binf() if ($x->{sign} =~ /^\+/ && $y->{sign} =~ /^\+/);
+    return $x->binf() if ($x->{sign} =~ /^-/ && $y->{sign} =~ /^-/);
+    return $x->binf('-');
+    }
+  
+  return $upgrade->bmul($x,$y,@r) if defined $upgrade &&
+   ((!$x->isa($self)) || (!$y->isa($self)));
+
+  # aEb * cEd = (a*c)E(b+d)
+  $MBI->_mul($x->{_m},$y->{_m});
+  ($x->{_e}, $x->{_es}) = _e_add($x->{_e}, $y->{_e}, $x->{_es}, $y->{_es});
+
+  $r[3] = $y;				# no push!
+
+  # adjust sign:
+  $x->{sign} = $x->{sign} ne $y->{sign} ? '-' : '+';
+  $x->bnorm->round(@r);
+  }
+
+sub bmuladd
+  { 
+  # multiply two numbers and add the third to the result
+  
+  # set up parameters
+  my ($self,$x,$y,$z,@r) = (ref($_[0]),@_);
+  # objectify is costly, so avoid it
+  if ((!ref($_[0])) || (ref($_[0]) ne ref($_[1])))
+    {
+    ($self,$x,$y,$z,@r) = objectify(3,@_);
+    }
+
+  return $x if $x->modify('bmuladd');
+
+  return $x->bnan() if (($x->{sign} eq $nan) ||
+			($y->{sign} eq $nan) ||
+			($z->{sign} eq $nan));
+
+  # inf handling
+  if (($x->{sign} =~ /^[+-]inf$/) || ($y->{sign} =~ /^[+-]inf$/))
+    {
+    return $x->bnan() if $x->is_zero() || $y->is_zero(); 
+    # result will always be +-inf:
+    # +inf * +/+inf => +inf, -inf * -/-inf => +inf
+    # +inf * -/-inf => -inf, -inf * +/+inf => -inf
+    return $x->binf() if ($x->{sign} =~ /^\+/ && $y->{sign} =~ /^\+/);
+    return $x->binf() if ($x->{sign} =~ /^-/ && $y->{sign} =~ /^-/);
+    return $x->binf('-');
+    }
+
+  return $upgrade->bmul($x,$y,@r) if defined $upgrade &&
+   ((!$x->isa($self)) || (!$y->isa($self)));
+
+  # aEb * cEd = (a*c)E(b+d)
+  $MBI->_mul($x->{_m},$y->{_m});
+  ($x->{_e}, $x->{_es}) = _e_add($x->{_e}, $y->{_e}, $x->{_es}, $y->{_es});
+
+  $r[3] = $y;				# no push!
+
+  # adjust sign:
+  $x->{sign} = $x->{sign} ne $y->{sign} ? '-' : '+';
+
+  # z=inf handling (z=NaN handled above)
+  $x->{sign} = $z->{sign}, return $x if $z->{sign} =~ /^[+-]inf$/;
+
+  # take lower of the two e's and adapt m1 to it to match m2
+  my $e = $z->{_e};
+  $e = $MBI->_zero() if !defined $e;		# if no BFLOAT?
+  $e = $MBI->_copy($e);				# make copy (didn't do it yet)
+
+  my $es;
+
+  ($e,$es) = _e_sub($e, $x->{_e}, $z->{_es} || '+', $x->{_es});
+
+  my $add = $MBI->_copy($z->{_m});
+
+  if ($es eq '-')				# < 0
+    {
+    $MBI->_lsft( $x->{_m}, $e, 10);
+    ($x->{_e},$x->{_es}) = _e_add($x->{_e}, $e, $x->{_es}, $es);
+    }
+  elsif (!$MBI->_is_zero($e))			# > 0
+    {
+    $MBI->_lsft($add, $e, 10);
+    }
+  # else: both e are the same, so just leave them
+
+  if ($x->{sign} eq $z->{sign})
+    {
+    # add
+    $x->{_m} = $MBI->_add($x->{_m}, $add);
+    }
+  else
+    {
+    ($x->{_m}, $x->{sign}) = 
+     _e_add($x->{_m}, $add, $x->{sign}, $z->{sign});
+    }
+
+  # delete trailing zeros, then round
+  $x->bnorm()->round(@r);
+  }
+
+sub bdiv 
+  {
+  # (dividend: BFLOAT or num_str, divisor: BFLOAT or num_str) return 
+  # (BFLOAT,BFLOAT) (quo,rem) or BFLOAT (only rem)
+
+  # set up parameters
+  my ($self,$x,$y,$a,$p,$r) = (ref($_[0]),@_);
+  # objectify is costly, so avoid it
+  if ((!ref($_[0])) || (ref($_[0]) ne ref($_[1])))
+    {
+    ($self,$x,$y,$a,$p,$r) = objectify(2,@_);
+    }
+
+  return $x if $x->modify('bdiv');
+
+  return $self->_div_inf($x,$y)
+   if (($x->{sign} !~ /^[+-]$/) || ($y->{sign} !~ /^[+-]$/) || $y->is_zero());
+
+  # x== 0 # also: or y == 1 or y == -1
+  return wantarray ? ($x,$self->bzero()) : $x if $x->is_zero();
+
+  # upgrade ?
+  return $upgrade->bdiv($upgrade->new($x),$y,$a,$p,$r) if defined $upgrade;
+
+  # we need to limit the accuracy to protect against overflow
+  my $fallback = 0;
+  my (@params,$scale);
+  ($x,@params) = $x->_find_round_parameters($a,$p,$r,$y);
+
+  return $x if $x->is_nan();		# error in _find_round_parameters?
+
+  # no rounding at all, so must use fallback
+  if (scalar @params == 0)
+    {
+    # simulate old behaviour
+    $params[0] = $self->div_scale();	# and round to it as accuracy
+    $scale = $params[0]+4; 		# at least four more for proper round
+    $params[2] = $r;			# round mode by caller or undef
+    $fallback = 1;			# to clear a/p afterwards
+    }
+  else
+    {
+    # the 4 below is empirical, and there might be cases where it is not
+    # enough...
+    $scale = abs($params[0] || $params[1]) + 4;	# take whatever is defined
+    }
+
+  my $rem; $rem = $self->bzero() if wantarray;
+
+  $y = $self->new($y) unless $y->isa('Math::BigFloat');
+
+  my $lx = $MBI->_len($x->{_m}); my $ly = $MBI->_len($y->{_m});
+  $scale = $lx if $lx > $scale;
+  $scale = $ly if $ly > $scale;
+  my $diff = $ly - $lx;
+  $scale += $diff if $diff > 0;		# if lx << ly, but not if ly << lx!
+
+  # already handled inf/NaN/-inf above:
+
+  # check that $y is not 1 nor -1 and cache the result:
+  my $y_not_one = !($MBI->_is_zero($y->{_e}) && $MBI->_is_one($y->{_m}));
+
+  # flipping the sign of $y will also flip the sign of $x for the special
+  # case of $x->bsub($x); so we can catch it below:
+  my $xsign = $x->{sign};
+  $y->{sign} =~ tr/+-/-+/;
+
+  if ($xsign ne $x->{sign})
+    {
+    # special case of $x /= $x results in 1
+    $x->bone();			# "fixes" also sign of $y, since $x is $y
+    }
+  else
+    {
+    # correct $y's sign again
+    $y->{sign} =~ tr/+-/-+/;
+    # continue with normal div code:
+
+    # make copy of $x in case of list context for later reminder calculation
+    if (wantarray && $y_not_one)
+      {
+      $rem = $x->copy();
+      }
+
+    $x->{sign} = $x->{sign} ne $y->sign() ? '-' : '+'; 
+
+    # check for / +-1 ( +/- 1E0)
+    if ($y_not_one)
+      {
+      # promote BigInts and it's subclasses (except when already a BigFloat)
+      $y = $self->new($y) unless $y->isa('Math::BigFloat'); 
+
+      # calculate the result to $scale digits and then round it
+      # a * 10 ** b / c * 10 ** d => a/c * 10 ** (b-d)
+      $MBI->_lsft($x->{_m},$MBI->_new($scale),10);
+      $MBI->_div ($x->{_m},$y->{_m});	# a/c
+
+      # correct exponent of $x
+      ($x->{_e},$x->{_es}) = _e_sub($x->{_e}, $y->{_e}, $x->{_es}, $y->{_es});
+      # correct for 10**scale
+      ($x->{_e},$x->{_es}) = _e_sub($x->{_e}, $MBI->_new($scale), $x->{_es}, '+');
+      $x->bnorm();		# remove trailing 0's
+      }
+    } # ende else $x != $y
+
+  # shortcut to not run through _find_round_parameters again
+  if (defined $params[0])
+    {
+    delete $x->{_a}; 				# clear before round
+    $x->bround($params[0],$params[2]);		# then round accordingly
+    }
+  else
+    {
+    delete $x->{_p}; 				# clear before round
+    $x->bfround($params[1],$params[2]);		# then round accordingly
+    }
+  if ($fallback)
+    {
+    # clear a/p after round, since user did not request it
+    delete $x->{_a}; delete $x->{_p};
+    }
+
+  if (wantarray)
+    {
+    if ($y_not_one)
+      {
+      $rem->bmod($y,@params);			# copy already done
+      }
+    if ($fallback)
+      {
+      # clear a/p after round, since user did not request it
+      delete $rem->{_a}; delete $rem->{_p};
+      }
+    return ($x,$rem);
+    }
+  $x;
+  }
+
+sub bmod 
+  {
+  # (dividend: BFLOAT or num_str, divisor: BFLOAT or num_str) return reminder 
+
+  # set up parameters
+  my ($self,$x,$y,$a,$p,$r) = (ref($_[0]),@_);
+  # objectify is costly, so avoid it
+  if ((!ref($_[0])) || (ref($_[0]) ne ref($_[1])))
+    {
+    ($self,$x,$y,$a,$p,$r) = objectify(2,@_);
+    }
+
+  return $x if $x->modify('bmod');
+
+  # handle NaN, inf, -inf
+  if (($x->{sign} !~ /^[+-]$/) || ($y->{sign} !~ /^[+-]$/))
+    {
+    my ($d,$re) = $self->SUPER::_div_inf($x,$y);
+    $x->{sign} = $re->{sign};
+    $x->{_e} = $re->{_e};
+    $x->{_m} = $re->{_m};
+    return $x->round($a,$p,$r,$y);
+    } 
+  if ($y->is_zero())
+    {
+    return $x->bnan() if $x->is_zero();
+    return $x;
+    }
+
+  return $x->bzero() if $x->is_zero()
+ || ($x->is_int() &&
+  # check that $y == +1 or $y == -1:
+    ($MBI->_is_zero($y->{_e}) && $MBI->_is_one($y->{_m})));
+
+  my $cmp = $x->bacmp($y);			# equal or $x < $y?
+  return $x->bzero($a,$p) if $cmp == 0;		# $x == $y => result 0
+
+  # only $y of the operands negative? 
+  my $neg = 0; $neg = 1 if $x->{sign} ne $y->{sign};
+
+  $x->{sign} = $y->{sign};				# calc sign first
+  return $x->round($a,$p,$r) if $cmp < 0 && $neg == 0;	# $x < $y => result $x
+  
+  my $ym = $MBI->_copy($y->{_m});
+  
+  # 2e1 => 20
+  $MBI->_lsft( $ym, $y->{_e}, 10) 
+   if $y->{_es} eq '+' && !$MBI->_is_zero($y->{_e});
+ 
+  # if $y has digits after dot
+  my $shifty = 0;			# correct _e of $x by this
+  if ($y->{_es} eq '-')			# has digits after dot
+    {
+    # 123 % 2.5 => 1230 % 25 => 5 => 0.5
+    $shifty = $MBI->_num($y->{_e}); 	# no more digits after dot
+    $MBI->_lsft($x->{_m}, $y->{_e}, 10);# 123 => 1230, $y->{_m} is already 25
+    }
+  # $ym is now mantissa of $y based on exponent 0
+
+  my $shiftx = 0;			# correct _e of $x by this
+  if ($x->{_es} eq '-')			# has digits after dot
+    {
+    # 123.4 % 20 => 1234 % 200
+    $shiftx = $MBI->_num($x->{_e});	# no more digits after dot
+    $MBI->_lsft($ym, $x->{_e}, 10);	# 123 => 1230
+    }
+  # 123e1 % 20 => 1230 % 20
+  if ($x->{_es} eq '+' && !$MBI->_is_zero($x->{_e}))
+    {
+    $MBI->_lsft( $x->{_m}, $x->{_e},10);	# es => '+' here
+    }
+
+  $x->{_e} = $MBI->_new($shiftx);
+  $x->{_es} = '+'; 
+  $x->{_es} = '-' if $shiftx != 0 || $shifty != 0;
+  $MBI->_add( $x->{_e}, $MBI->_new($shifty)) if $shifty != 0;
+  
+  # now mantissas are equalized, exponent of $x is adjusted, so calc result
+
+  $x->{_m} = $MBI->_mod( $x->{_m}, $ym);
+
+  $x->{sign} = '+' if $MBI->_is_zero($x->{_m});		# fix sign for -0
+  $x->bnorm();
+
+  if ($neg != 0)	# one of them negative => correct in place
+    {
+    my $r = $y - $x;
+    $x->{_m} = $r->{_m};
+    $x->{_e} = $r->{_e};
+    $x->{_es} = $r->{_es};
+    $x->{sign} = '+' if $MBI->_is_zero($x->{_m});	# fix sign for -0
+    $x->bnorm();
+    }
+
+  $x->round($a,$p,$r,$y);	# round and return
+  }
+
+sub broot
+  {
+  # calculate $y'th root of $x
+  
+  # set up parameters
+  my ($self,$x,$y,$a,$p,$r) = (ref($_[0]),@_);
+  # objectify is costly, so avoid it
+  if ((!ref($_[0])) || (ref($_[0]) ne ref($_[1])))
+    {
+    ($self,$x,$y,$a,$p,$r) = objectify(2,@_);
+    }
+
+  return $x if $x->modify('broot');
+
+  # NaN handling: $x ** 1/0, x or y NaN, or y inf/-inf or y == 0
+  return $x->bnan() if $x->{sign} !~ /^\+/ || $y->is_zero() ||
+         $y->{sign} !~ /^\+$/;
+
+  return $x if $x->is_zero() || $x->is_one() || $x->is_inf() || $y->is_one();
+  
+  # we need to limit the accuracy to protect against overflow
+  my $fallback = 0;
+  my (@params,$scale);
+  ($x,@params) = $x->_find_round_parameters($a,$p,$r);
+
+  return $x if $x->is_nan();		# error in _find_round_parameters?
+
+  # no rounding at all, so must use fallback
+  if (scalar @params == 0) 
+    {
+    # simulate old behaviour
+    $params[0] = $self->div_scale();	# and round to it as accuracy
+    $scale = $params[0]+4; 		# at least four more for proper round
+    $params[2] = $r;			# iound mode by caller or undef
+    $fallback = 1;			# to clear a/p afterwards
+    }
+  else
+    {
+    # the 4 below is empirical, and there might be cases where it is not
+    # enough...
+    $scale = abs($params[0] || $params[1]) + 4; # take whatever is defined
+    }
+
+  # when user set globals, they would interfere with our calculation, so
+  # disable them and later re-enable them
+  no strict 'refs';
+  my $abr = "$self\::accuracy"; my $ab = $$abr; $$abr = undef;
+  my $pbr = "$self\::precision"; my $pb = $$pbr; $$pbr = undef;
+  # we also need to disable any set A or P on $x (_find_round_parameters took
+  # them already into account), since these would interfere, too
+  delete $x->{_a}; delete $x->{_p};
+  # need to disable $upgrade in BigInt, to avoid deep recursion
+  local $Math::BigInt::upgrade = undef;	# should be really parent class vs MBI
+
+  # remember sign and make $x positive, since -4 ** (1/2) => -2
+  my $sign = 0; $sign = 1 if $x->{sign} eq '-'; $x->{sign} = '+';
+
+  my $is_two = 0;
+  if ($y->isa('Math::BigFloat'))
+    {
+    $is_two = ($y->{sign} eq '+' && $MBI->_is_two($y->{_m}) && $MBI->_is_zero($y->{_e}));
+    }
+  else
+    {
+    $is_two = ($y == 2);
+    }
+
+  # normal square root if $y == 2:
+  if ($is_two)
+    {
+    $x->bsqrt($scale+4);
+    }
+  elsif ($y->is_one('-'))
+    {
+    # $x ** -1 => 1/$x
+    my $u = $self->bone()->bdiv($x,$scale);
+    # copy private parts over
+    $x->{_m} = $u->{_m};
+    $x->{_e} = $u->{_e};
+    $x->{_es} = $u->{_es};
+    }
+  else
+    {
+    # calculate the broot() as integer result first, and if it fits, return
+    # it rightaway (but only if $x and $y are integer):
+
+    my $done = 0;				# not yet
+    if ($y->is_int() && $x->is_int())
+      {
+      my $i = $MBI->_copy( $x->{_m} );
+      $MBI->_lsft( $i, $x->{_e}, 10 ) unless $MBI->_is_zero($x->{_e});
+      my $int = Math::BigInt->bzero();
+      $int->{value} = $i;
+      $int->broot($y->as_number());
+      # if ($exact)
+      if ($int->copy()->bpow($y) == $x)
+        {
+        # found result, return it
+        $x->{_m} = $int->{value};
+        $x->{_e} = $MBI->_zero();
+        $x->{_es} = '+';
+        $x->bnorm();
+        $done = 1;
+        }
+      }
+    if ($done == 0)
+      {
+      my $u = $self->bone()->bdiv($y,$scale+4);
+      delete $u->{_a}; delete $u->{_p};         # otherwise it conflicts
+      $x->bpow($u,$scale+4);                    # el cheapo
+      }
+    }
+  $x->bneg() if $sign == 1;
+  
+  # shortcut to not run through _find_round_parameters again
+  if (defined $params[0])
+    {
+    $x->bround($params[0],$params[2]);		# then round accordingly
+    }
+  else
+    {
+    $x->bfround($params[1],$params[2]);		# then round accordingly
+    }
+  if ($fallback)
+    {
+    # clear a/p after round, since user did not request it
+    delete $x->{_a}; delete $x->{_p};
+    }
+  # restore globals
+  $$abr = $ab; $$pbr = $pb;
+  $x;
+  }
+
+sub bsqrt
+  { 
+  # calculate square root
+  my ($self,$x,$a,$p,$r) = ref($_[0]) ? (ref($_[0]),@_) : objectify(1,@_);
+
+  return $x if $x->modify('bsqrt');
+
+  return $x->bnan() if $x->{sign} !~ /^[+]/;	# NaN, -inf or < 0
+  return $x if $x->{sign} eq '+inf';		# sqrt(inf) == inf
+  return $x->round($a,$p,$r) if $x->is_zero() || $x->is_one();
+
+  # we need to limit the accuracy to protect against overflow
+  my $fallback = 0;
+  my (@params,$scale);
+  ($x,@params) = $x->_find_round_parameters($a,$p,$r);
+
+  return $x if $x->is_nan();		# error in _find_round_parameters?
+
+  # no rounding at all, so must use fallback
+  if (scalar @params == 0) 
+    {
+    # simulate old behaviour
+    $params[0] = $self->div_scale();	# and round to it as accuracy
+    $scale = $params[0]+4; 		# at least four more for proper round
+    $params[2] = $r;			# round mode by caller or undef
+    $fallback = 1;			# to clear a/p afterwards
+    }
+  else
+    {
+    # the 4 below is empirical, and there might be cases where it is not
+    # enough...
+    $scale = abs($params[0] || $params[1]) + 4; # take whatever is defined
+    }
+
+  # when user set globals, they would interfere with our calculation, so
+  # disable them and later re-enable them
+  no strict 'refs';
+  my $abr = "$self\::accuracy"; my $ab = $$abr; $$abr = undef;
+  my $pbr = "$self\::precision"; my $pb = $$pbr; $$pbr = undef;
+  # we also need to disable any set A or P on $x (_find_round_parameters took
+  # them already into account), since these would interfere, too
+  delete $x->{_a}; delete $x->{_p};
+  # need to disable $upgrade in BigInt, to avoid deep recursion
+  local $Math::BigInt::upgrade = undef;	# should be really parent class vs MBI
+
+  my $i = $MBI->_copy( $x->{_m} );
+  $MBI->_lsft( $i, $x->{_e}, 10 ) unless $MBI->_is_zero($x->{_e});
+  my $xas = Math::BigInt->bzero();
+  $xas->{value} = $i;
+
+  my $gs = $xas->copy()->bsqrt();	# some guess
+
+  if (($x->{_es} ne '-')		# guess can't be accurate if there are
+					# digits after the dot
+   && ($xas->bacmp($gs * $gs) == 0))	# guess hit the nail on the head?
+    {
+    # exact result, copy result over to keep $x
+    $x->{_m} = $gs->{value}; $x->{_e} = $MBI->_zero(); $x->{_es} = '+';
+    $x->bnorm();
+    # shortcut to not run through _find_round_parameters again
+    if (defined $params[0])
+      {
+      $x->bround($params[0],$params[2]);	# then round accordingly
+      }
+    else
+      {
+      $x->bfround($params[1],$params[2]);	# then round accordingly
+      }
+    if ($fallback)
+      {
+      # clear a/p after round, since user did not request it
+      delete $x->{_a}; delete $x->{_p};
+      }
+    # re-enable A and P, upgrade is taken care of by "local"
+    ${"$self\::accuracy"} = $ab; ${"$self\::precision"} = $pb;
+    return $x;
+    }
+ 
+  # sqrt(2) = 1.4 because sqrt(2*100) = 1.4*10; so we can increase the accuracy
+  # of the result by multipyling the input by 100 and then divide the integer
+  # result of sqrt(input) by 10. Rounding afterwards returns the real result.
+
+  # The following steps will transform 123.456 (in $x) into 123456 (in $y1)
+  my $y1 = $MBI->_copy($x->{_m});
+
+  my $length = $MBI->_len($y1);
+  
+  # Now calculate how many digits the result of sqrt(y1) would have
+  my $digits = int($length / 2);
+
+  # But we need at least $scale digits, so calculate how many are missing
+  my $shift = $scale - $digits;
+
+  # This happens if the input had enough digits
+  # (we take care of integer guesses above)
+  $shift = 0 if $shift < 0; 
+
+  # Multiply in steps of 100, by shifting left two times the "missing" digits
+  my $s2 = $shift * 2;
+
+  # We now make sure that $y1 has the same odd or even number of digits than
+  # $x had. So when _e of $x is odd, we must shift $y1 by one digit left,
+  # because we always must multiply by steps of 100 (sqrt(100) is 10) and not
+  # steps of 10. The length of $x does not count, since an even or odd number
+  # of digits before the dot is not changed by adding an even number of digits
+  # after the dot (the result is still odd or even digits long).
+  $s2++ if $MBI->_is_odd($x->{_e});
+
+  $MBI->_lsft( $y1, $MBI->_new($s2), 10);
+
+  # now take the square root and truncate to integer
+  $y1 = $MBI->_sqrt($y1);
+
+  # By "shifting" $y1 right (by creating a negative _e) we calculate the final
+  # result, which is than later rounded to the desired scale.
+
+  # calculate how many zeros $x had after the '.' (or before it, depending
+  # on sign of $dat, the result should have half as many:
+  my $dat = $MBI->_num($x->{_e});
+  $dat = -$dat if $x->{_es} eq '-';
+  $dat += $length;
+
+  if ($dat > 0)
+    {
+    # no zeros after the dot (e.g. 1.23, 0.49 etc)
+    # preserve half as many digits before the dot than the input had 
+    # (but round this "up")
+    $dat = int(($dat+1)/2);
+    }
+  else
+    {
+    $dat = int(($dat)/2);
+    }
+  $dat -= $MBI->_len($y1);
+  if ($dat < 0)
+    {
+    $dat = abs($dat);
+    $x->{_e} = $MBI->_new( $dat );
+    $x->{_es} = '-';
+    }
+  else
+    {    
+    $x->{_e} = $MBI->_new( $dat );
+    $x->{_es} = '+';
+    }
+  $x->{_m} = $y1;
+  $x->bnorm();
+
+  # shortcut to not run through _find_round_parameters again
+  if (defined $params[0])
+    {
+    $x->bround($params[0],$params[2]);		# then round accordingly
+    }
+  else
+    {
+    $x->bfround($params[1],$params[2]);		# then round accordingly
+    }
+  if ($fallback)
+    {
+    # clear a/p after round, since user did not request it
+    delete $x->{_a}; delete $x->{_p};
+    }
+  # restore globals
+  $$abr = $ab; $$pbr = $pb;
+  $x;
+  }
+
+sub bfac
+  {
+  # (BFLOAT or num_str, BFLOAT or num_str) return BFLOAT
+  # compute factorial number, modifies first argument
+
+  # set up parameters
+  my ($self,$x,@r) = (ref($_[0]),@_);
+  # objectify is costly, so avoid it
+  ($self,$x,@r) = objectify(1,@_) if !ref($x);
+
+  # inf => inf
+  return $x if $x->modify('bfac') || $x->{sign} eq '+inf';	
+
+  return $x->bnan() 
+    if (($x->{sign} ne '+') ||		# inf, NaN, <0 etc => NaN
+     ($x->{_es} ne '+'));		# digits after dot?
+
+  # use BigInt's bfac() for faster calc
+  if (! $MBI->_is_zero($x->{_e}))
+    {
+    $MBI->_lsft($x->{_m}, $x->{_e},10);	# change 12e1 to 120e0
+    $x->{_e} = $MBI->_zero();		# normalize
+    $x->{_es} = '+';
+    }
+  $MBI->_fac($x->{_m});			# calculate factorial
+  $x->bnorm()->round(@r); 		# norm again and round result
+  }
+
+sub _pow
+  {
+  # Calculate a power where $y is a non-integer, like 2 ** 0.3
+  my ($x,$y,@r) = @_;
+  my $self = ref($x);
+
+  # if $y == 0.5, it is sqrt($x)
+  $HALF = $self->new($HALF) unless ref($HALF);
+  return $x->bsqrt(@r,$y) if $y->bcmp($HALF) == 0;
+
+  # Using:
+  # a ** x == e ** (x * ln a)
+
+  # u = y * ln x
+  #                _                         _
+  # Taylor:       |   u    u^2    u^3         |
+  # x ** y  = 1 + |  --- + --- + ----- + ...  |
+  #               |_  1    1*2   1*2*3       _|
+
+  # we need to limit the accuracy to protect against overflow
+  my $fallback = 0;
+  my ($scale,@params);
+  ($x,@params) = $x->_find_round_parameters(@r);
+    
+  return $x if $x->is_nan();		# error in _find_round_parameters?
+
+  # no rounding at all, so must use fallback
+  if (scalar @params == 0)
+    {
+    # simulate old behaviour
+    $params[0] = $self->div_scale();	# and round to it as accuracy
+    $params[1] = undef;			# disable P
+    $scale = $params[0]+4; 		# at least four more for proper round
+    $params[2] = $r[2];			# round mode by caller or undef
+    $fallback = 1;			# to clear a/p afterwards
+    }
+  else
+    {
+    # the 4 below is empirical, and there might be cases where it is not
+    # enough...
+    $scale = abs($params[0] || $params[1]) + 4; # take whatever is defined
+    }
+
+  # when user set globals, they would interfere with our calculation, so
+  # disable them and later re-enable them
+  no strict 'refs';
+  my $abr = "$self\::accuracy"; my $ab = $$abr; $$abr = undef;
+  my $pbr = "$self\::precision"; my $pb = $$pbr; $$pbr = undef;
+  # we also need to disable any set A or P on $x (_find_round_parameters took
+  # them already into account), since these would interfere, too
+  delete $x->{_a}; delete $x->{_p};
+  # need to disable $upgrade in BigInt, to avoid deep recursion
+  local $Math::BigInt::upgrade = undef;
+ 
+  my ($limit,$v,$u,$below,$factor,$next,$over);
+
+  $u = $x->copy()->blog(undef,$scale)->bmul($y);
+  $v = $self->bone();				# 1
+  $factor = $self->new(2);			# 2
+  $x->bone();					# first term: 1
+
+  $below = $v->copy();
+  $over = $u->copy();
+
+  $limit = $self->new("1E-". ($scale-1));
+  #my $steps = 0;
+  while (3 < 5)
+    {
+    # we calculate the next term, and add it to the last
+    # when the next term is below our limit, it won't affect the outcome
+    # anymore, so we stop:
+    $next = $over->copy()->bdiv($below,$scale);
+    last if $next->bacmp($limit) <= 0;
+    $x->badd($next);
+    # calculate things for the next term
+    $over *= $u; $below *= $factor; $factor->binc();
+
+    last if $x->{sign} !~ /^[-+]$/;
+
+    #$steps++;
+    }
+  
+  # shortcut to not run through _find_round_parameters again
+  if (defined $params[0])
+    {
+    $x->bround($params[0],$params[2]);		# then round accordingly
+    }
+  else
+    {
+    $x->bfround($params[1],$params[2]);		# then round accordingly
+    }
+  if ($fallback)
+    {
+    # clear a/p after round, since user did not request it
+    delete $x->{_a}; delete $x->{_p};
+    }
+  # restore globals
+  $$abr = $ab; $$pbr = $pb;
+  $x;
+  }
+
+sub bpow 
+  {
+  # (BFLOAT or num_str, BFLOAT or num_str) return BFLOAT
+  # compute power of two numbers, second arg is used as integer
+  # modifies first argument
+
+  # set up parameters
+  my ($self,$x,$y,$a,$p,$r) = (ref($_[0]),@_);
+  # objectify is costly, so avoid it
+  if ((!ref($_[0])) || (ref($_[0]) ne ref($_[1])))
+    {
+    ($self,$x,$y,$a,$p,$r) = objectify(2,@_);
+    }
+
+  return $x if $x->modify('bpow');
+
+  return $x->bnan() if $x->{sign} eq $nan || $y->{sign} eq $nan;
+  return $x if $x->{sign} =~ /^[+-]inf$/;
+  
+  # cache the result of is_zero
+  my $y_is_zero = $y->is_zero();
+  return $x->bone() if $y_is_zero;
+  return $x         if $x->is_one() || $y->is_one();
+
+  my $x_is_zero = $x->is_zero();
+  return $x->_pow($y,$a,$p,$r) if !$x_is_zero && !$y->is_int();		# non-integer power
+
+  my $y1 = $y->as_number()->{value};			# make MBI part
+
+  # if ($x == -1)
+  if ($x->{sign} eq '-' && $MBI->_is_one($x->{_m}) && $MBI->_is_zero($x->{_e}))
+    {
+    # if $x == -1 and odd/even y => +1/-1  because +-1 ^ (+-1) => +-1
+    return $MBI->_is_odd($y1) ? $x : $x->babs(1);
+    }
+  if ($x_is_zero)
+    {
+    return $x if $y->{sign} eq '+'; 	# 0**y => 0 (if not y <= 0)
+    # 0 ** -y => 1 / (0 ** y) => 1 / 0! (1 / 0 => +inf)
+    return $x->binf();
+    }
+
+  my $new_sign = '+';
+  $new_sign = $MBI->_is_odd($y1) ? '-' : '+' if $x->{sign} ne '+';
+
+  # calculate $x->{_m} ** $y and $x->{_e} * $y separately (faster)
+  $x->{_m} = $MBI->_pow( $x->{_m}, $y1);
+  $x->{_e} = $MBI->_mul ($x->{_e}, $y1);
+
+  $x->{sign} = $new_sign;
+  $x->bnorm();
+  if ($y->{sign} eq '-')
+    {
+    # modify $x in place!
+    my $z = $x->copy(); $x->bone();
+    return scalar $x->bdiv($z,$a,$p,$r);	# round in one go (might ignore y's A!)
+    }
+  $x->round($a,$p,$r,$y);
+  }
+
+sub bmodpow
+  {
+  # takes a very large number to a very large exponent in a given very
+  # large modulus, quickly, thanks to binary exponentation. Supports
+  # negative exponents.
+  my ($self,$num,$exp,$mod,@r) = objectify(3,@_);
+
+  return $num if $num->modify('bmodpow');
+
+  # check modulus for valid values
+  return $num->bnan() if ($mod->{sign} ne '+'           # NaN, - , -inf, +inf
+                       || $mod->is_zero());
+
+  # check exponent for valid values
+  if ($exp->{sign} =~ /\w/)
+    {
+    # i.e., if it's NaN, +inf, or -inf...
+    return $num->bnan();
+    }
+
+  $num->bmodinv ($mod) if ($exp->{sign} eq '-');
+
+  # check num for valid values (also NaN if there was no inverse but $exp < 0)
+  return $num->bnan() if $num->{sign} !~ /^[+-]$/;
+
+  # $mod is positive, sign on $exp is ignored, result also positive
+
+  # XXX TODO: speed it up when all three numbers are integers
+  $num->bpow($exp)->bmod($mod);
+  }
+
+###############################################################################
+# trigonometric functions
+
+# helper function for bpi() and batan2(), calculates arcus tanges (1/x)
+
+sub _atan_inv
+  {
+  # return a/b so that a/b approximates atan(1/x) to at least limit digits
+  my ($self, $x, $limit) = @_;
+
+  # Taylor:       x^3   x^5   x^7   x^9
+  #    atan = x - --- + --- - --- + --- - ...
+  #                3     5     7     9 
+
+  #               1      1         1        1
+  #    atan 1/x = - - ------- + ------- - ------- + ...
+  #               x   x^3 * 3   x^5 * 5   x^7 * 7 
+
+  #               1      1         1            1
+  #    atan 1/x = - - --------- + ---------- - ----------- + ... 
+  #               5    3 * 125     5 * 3125     7 * 78125
+
+  # Subtraction/addition of a rational:
+
+  #  5    7    5*3 +- 7*4
+  #  - +- -  = ----------
+  #  4    3       4*3
+
+  # Term:  N        N+1
+  #
+  #        a             1                  a * d * c +- b
+  #        ----- +- ------------------  =  ----------------
+  #        b           d * c                b * d * c
+
+  #  since b1 = b0 * (d-2) * c
+
+  #        a             1                  a * d +- b / c
+  #        ----- +- ------------------  =  ----------------
+  #        b           d * c                b * d 
+
+  # and  d = d + 2
+  # and  c = c * x * x
+
+  #        u = d * c
+  #        stop if length($u) > limit 
+  #        a = a * u +- b
+  #        b = b * u
+  #        d = d + 2
+  #        c = c * x * x
+  #        sign = 1 - sign
+
+  my $a = $MBI->_one();
+  my $b = $MBI->_copy($x);
+ 
+  my $x2  = $MBI->_mul( $MBI->_copy($x), $b);		# x2 = x * x
+  my $d   = $MBI->_new( 3 );				# d = 3
+  my $c   = $MBI->_mul( $MBI->_copy($x), $x2);		# c = x ^ 3
+  my $two = $MBI->_new( 2 );
+
+  # run the first step unconditionally
+  my $u = $MBI->_mul( $MBI->_copy($d), $c);
+  $a = $MBI->_mul($a, $u);
+  $a = $MBI->_sub($a, $b);
+  $b = $MBI->_mul($b, $u);
+  $d = $MBI->_add($d, $two);
+  $c = $MBI->_mul($c, $x2);
+
+  # a is now a * (d-3) * c
+  # b is now b * (d-2) * c
+
+  # run the second step unconditionally
+  $u = $MBI->_mul( $MBI->_copy($d), $c);
+  $a = $MBI->_mul($a, $u);
+  $a = $MBI->_add($a, $b);
+  $b = $MBI->_mul($b, $u);
+  $d = $MBI->_add($d, $two);
+  $c = $MBI->_mul($c, $x2);
+
+  # a is now a * (d-3) * (d-5) * c * c  
+  # b is now b * (d-2) * (d-4) * c * c
+
+  # so we can remove c * c from both a and b to shorten the numbers involved:
+  $a = $MBI->_div($a, $x2);
+  $b = $MBI->_div($b, $x2);
+  $a = $MBI->_div($a, $x2);
+  $b = $MBI->_div($b, $x2);
+
+#  my $step = 0; 
+  my $sign = 0;						# 0 => -, 1 => +
+  while (3 < 5)
+    {
+#    $step++;
+#    if (($i++ % 100) == 0)
+#      {
+#    print "a=",$MBI->_str($a),"\n";
+#    print "b=",$MBI->_str($b),"\n";
+#      }
+#    print "d=",$MBI->_str($d),"\n";
+#    print "x2=",$MBI->_str($x2),"\n";
+#    print "c=",$MBI->_str($c),"\n";
+
+    my $u = $MBI->_mul( $MBI->_copy($d), $c);
+    # use _alen() for libs like GMP where _len() would be O(N^2)
+    last if $MBI->_alen($u) > $limit;
+    my ($bc,$r) = $MBI->_div( $MBI->_copy($b), $c);
+    if ($MBI->_is_zero($r))
+      {
+      # b / c is an integer, so we can remove c from all terms
+      # this happens almost every time:
+      $a = $MBI->_mul($a, $d);
+      $a = $MBI->_sub($a, $bc) if $sign == 0;
+      $a = $MBI->_add($a, $bc) if $sign == 1;
+      $b = $MBI->_mul($b, $d);
+      }
+    else
+      {
+      # b / c is not an integer, so we keep c in the terms
+      # this happens very rarely, for instance for x = 5, this happens only
+      # at the following steps:
+      # 1, 5, 14, 32, 72, 157, 340, ...
+      $a = $MBI->_mul($a, $u);
+      $a = $MBI->_sub($a, $b) if $sign == 0;
+      $a = $MBI->_add($a, $b) if $sign == 1;
+      $b = $MBI->_mul($b, $u);
+      }
+    $d = $MBI->_add($d, $two);
+    $c = $MBI->_mul($c, $x2);
+    $sign = 1 - $sign;
+
+    }
+
+#  print "Took $step steps for ", $MBI->_str($x),"\n";
+#  print "a=",$MBI->_str($a),"\n"; print "b=",$MBI->_str($b),"\n";
+  # return a/b so that a/b approximates atan(1/x)
+  ($a,$b);
+  }
+
+sub bpi
+  {
+  my ($self,$n) = @_;
+  if (@_ == 0)
+    {
+    $self = $class;
+    }
+  if (@_ == 1)
+    {
+    # called like Math::BigFloat::bpi(10);
+    $n = $self; $self = $class;
+    # called like Math::BigFloat->bpi();
+    $n = undef if $n eq 'Math::BigFloat';
+    }
+  $self = ref($self) if ref($self);
+  my $fallback = defined $n ? 0 : 1;
+  $n = 40 if !defined $n || $n < 1;
+
+  # after 黃見利 (Hwang Chien-Lih) (1997)
+  # pi/4 = 183 * atan(1/239) + 32 * atan(1/1023) – 68 * atan(1/5832)
+  #	 + 12 * atan(1/110443) - 12 * atan(1/4841182) - 100 * atan(1/6826318)
+
+  # a few more to prevent rounding errors
+  $n += 4;
+
+  my ($a,$b) = $self->_atan_inv( $MBI->_new(239),$n);
+  my ($c,$d) = $self->_atan_inv( $MBI->_new(1023),$n);
+  my ($e,$f) = $self->_atan_inv( $MBI->_new(5832),$n);
+  my ($g,$h) = $self->_atan_inv( $MBI->_new(110443),$n);
+  my ($i,$j) = $self->_atan_inv( $MBI->_new(4841182),$n);
+  my ($k,$l) = $self->_atan_inv( $MBI->_new(6826318),$n);
+
+  $MBI->_mul($a, $MBI->_new(732));
+  $MBI->_mul($c, $MBI->_new(128));
+  $MBI->_mul($e, $MBI->_new(272));
+  $MBI->_mul($g, $MBI->_new(48));
+  $MBI->_mul($i, $MBI->_new(48));
+  $MBI->_mul($k, $MBI->_new(400));
+
+  my $x = $self->bone(); $x->{_m} = $a; my $x_d = $self->bone(); $x_d->{_m} = $b;
+  my $y = $self->bone(); $y->{_m} = $c; my $y_d = $self->bone(); $y_d->{_m} = $d;
+  my $z = $self->bone(); $z->{_m} = $e; my $z_d = $self->bone(); $z_d->{_m} = $f;
+  my $u = $self->bone(); $u->{_m} = $g; my $u_d = $self->bone(); $u_d->{_m} = $h;
+  my $v = $self->bone(); $v->{_m} = $i; my $v_d = $self->bone(); $v_d->{_m} = $j;
+  my $w = $self->bone(); $w->{_m} = $k; my $w_d = $self->bone(); $w_d->{_m} = $l;
+  $x->bdiv($x_d, $n);
+  $y->bdiv($y_d, $n);
+  $z->bdiv($z_d, $n);
+  $u->bdiv($u_d, $n);
+  $v->bdiv($v_d, $n);
+  $w->bdiv($w_d, $n);
+
+  delete $x->{_a}; delete $y->{_a}; delete $z->{_a};
+  delete $u->{_a}; delete $v->{_a}; delete $w->{_a};
+  $x->badd($y)->bsub($z)->badd($u)->bsub($v)->bsub($w);
+
+  $x->bround($n-4);
+  delete $x->{_a} if $fallback == 1;
+  $x;
+  }
+
+sub bcos
+  {
+  # Calculate a cosinus of x.
+  my ($self,$x,@r) = ref($_[0]) ? (ref($_[0]),@_) : objectify(1,@_);
+
+  # Taylor:      x^2   x^4   x^6   x^8
+  #    cos = 1 - --- + --- - --- + --- ...
+  #               2!    4!    6!    8!
+
+  # we need to limit the accuracy to protect against overflow
+  my $fallback = 0;
+  my ($scale,@params);
+  ($x,@params) = $x->_find_round_parameters(@r);
+    
+  #         constant object       or error in _find_round_parameters?
+  return $x if $x->modify('bcos') || $x->is_nan();
+
+  return $x->bone(@r) if $x->is_zero();
+
+  # no rounding at all, so must use fallback
+  if (scalar @params == 0)
+    {
+    # simulate old behaviour
+    $params[0] = $self->div_scale();	# and round to it as accuracy
+    $params[1] = undef;			# disable P
+    $scale = $params[0]+4; 		# at least four more for proper round
+    $params[2] = $r[2];			# round mode by caller or undef
+    $fallback = 1;			# to clear a/p afterwards
+    }
+  else
+    {
+    # the 4 below is empirical, and there might be cases where it is not
+    # enough...
+    $scale = abs($params[0] || $params[1]) + 4; # take whatever is defined
+    }
+
+  # when user set globals, they would interfere with our calculation, so
+  # disable them and later re-enable them
+  no strict 'refs';
+  my $abr = "$self\::accuracy"; my $ab = $$abr; $$abr = undef;
+  my $pbr = "$self\::precision"; my $pb = $$pbr; $$pbr = undef;
+  # we also need to disable any set A or P on $x (_find_round_parameters took
+  # them already into account), since these would interfere, too
+  delete $x->{_a}; delete $x->{_p};
+  # need to disable $upgrade in BigInt, to avoid deep recursion
+  local $Math::BigInt::upgrade = undef;
+ 
+  my $last = 0;
+  my $over = $x * $x;                   # X ^ 2
+  my $x2 = $over->copy();               # X ^ 2; difference between terms
+  my $sign = 1;                         # start with -=
+  my $below = $self->new(2); my $factorial = $self->new(3);
+  $x->bone(); delete $x->{_a}; delete $x->{_p};
+
+  my $limit = $self->new("1E-". ($scale-1));
+  #my $steps = 0;
+  while (3 < 5)
+    {
+    # we calculate the next term, and add it to the last
+    # when the next term is below our limit, it won't affect the outcome
+    # anymore, so we stop:
+    my $next = $over->copy()->bdiv($below,$scale);
+    last if $next->bacmp($limit) <= 0;
+
+    if ($sign == 0)
+      {
+      $x->badd($next);
+      }
+    else
+      {
+      $x->bsub($next);
+      }
+    $sign = 1-$sign;					# alternate
+    # calculate things for the next term
+    $over->bmul($x2);					# $x*$x
+    $below->bmul($factorial); $factorial->binc();	# n*(n+1)
+    $below->bmul($factorial); $factorial->binc();	# n*(n+1)
+    }
+
+  # shortcut to not run through _find_round_parameters again
+  if (defined $params[0])
+    {
+    $x->bround($params[0],$params[2]);		# then round accordingly
+    }
+  else
+    {
+    $x->bfround($params[1],$params[2]);		# then round accordingly
+    }
+  if ($fallback)
+    {
+    # clear a/p after round, since user did not request it
+    delete $x->{_a}; delete $x->{_p};
+    }
+  # restore globals
+  $$abr = $ab; $$pbr = $pb;
+  $x;
+  }
+
+sub bsin
+  {
+  # Calculate a sinus of x.
+  my ($self,$x,@r) = ref($_[0]) ? (ref($_[0]),@_) : objectify(1,@_);
+
+  # taylor:      x^3   x^5   x^7   x^9
+  #    sin = x - --- + --- - --- + --- ...
+  #               3!    5!    7!    9!
+
+  # we need to limit the accuracy to protect against overflow
+  my $fallback = 0;
+  my ($scale,@params);
+  ($x,@params) = $x->_find_round_parameters(@r);
+    
+  #         constant object       or error in _find_round_parameters?
+  return $x if $x->modify('bsin') || $x->is_nan();
+
+  return $x->bzero(@r) if $x->is_zero();
+
+  # no rounding at all, so must use fallback
+  if (scalar @params == 0)
+    {
+    # simulate old behaviour
+    $params[0] = $self->div_scale();	# and round to it as accuracy
+    $params[1] = undef;			# disable P
+    $scale = $params[0]+4; 		# at least four more for proper round
+    $params[2] = $r[2];			# round mode by caller or undef
+    $fallback = 1;			# to clear a/p afterwards
+    }
+  else
+    {
+    # the 4 below is empirical, and there might be cases where it is not
+    # enough...
+    $scale = abs($params[0] || $params[1]) + 4; # take whatever is defined
+    }
+
+  # when user set globals, they would interfere with our calculation, so
+  # disable them and later re-enable them
+  no strict 'refs';
+  my $abr = "$self\::accuracy"; my $ab = $$abr; $$abr = undef;
+  my $pbr = "$self\::precision"; my $pb = $$pbr; $$pbr = undef;
+  # we also need to disable any set A or P on $x (_find_round_parameters took
+  # them already into account), since these would interfere, too
+  delete $x->{_a}; delete $x->{_p};
+  # need to disable $upgrade in BigInt, to avoid deep recursion
+  local $Math::BigInt::upgrade = undef;
+ 
+  my $last = 0;
+  my $over = $x * $x;			# X ^ 2
+  my $x2 = $over->copy();		# X ^ 2; difference between terms
+  $over->bmul($x);			# X ^ 3 as starting value
+  my $sign = 1;				# start with -=
+  my $below = $self->new(6); my $factorial = $self->new(4);
+  delete $x->{_a}; delete $x->{_p};
+
+  my $limit = $self->new("1E-". ($scale-1));
+  #my $steps = 0;
+  while (3 < 5)
+    {
+    # we calculate the next term, and add it to the last
+    # when the next term is below our limit, it won't affect the outcome
+    # anymore, so we stop:
+    my $next = $over->copy()->bdiv($below,$scale);
+    last if $next->bacmp($limit) <= 0;
+
+    if ($sign == 0)
+      {
+      $x->badd($next);
+      }
+    else
+      {
+      $x->bsub($next);
+      }
+    $sign = 1-$sign;					# alternate
+    # calculate things for the next term
+    $over->bmul($x2);					# $x*$x
+    $below->bmul($factorial); $factorial->binc();	# n*(n+1)
+    $below->bmul($factorial); $factorial->binc();	# n*(n+1)
+    }
+
+  # shortcut to not run through _find_round_parameters again
+  if (defined $params[0])
+    {
+    $x->bround($params[0],$params[2]);		# then round accordingly
+    }
+  else
+    {
+    $x->bfround($params[1],$params[2]);		# then round accordingly
+    }
+  if ($fallback)
+    {
+    # clear a/p after round, since user did not request it
+    delete $x->{_a}; delete $x->{_p};
+    }
+  # restore globals
+  $$abr = $ab; $$pbr = $pb;
+  $x;
+  }
+
+sub batan2
+  { 
+  # calculate arcus tangens of ($y/$x)
+  
+  # set up parameters
+  my ($self,$y,$x,@r) = (ref($_[0]),@_);
+  # objectify is costly, so avoid it
+  if ((!ref($_[0])) || (ref($_[0]) ne ref($_[1])))
+    {
+    ($self,$y,$x,@r) = objectify(2,@_);
+    }
+
+  return $y if $y->modify('batan2');
+
+  return $y->bnan() if ($y->{sign} eq $nan) || ($x->{sign} eq $nan);
+
+  # Y X
+  # 0 0 result is 0
+  # 0 +x result is 0
+  # ? inf result is 0
+  return $y->bzero(@r) if ($x->is_inf('+') && !$y->is_inf()) || ($y->is_zero() && $x->{sign} eq '+');
+
+  # Y    X
+  # != 0 -inf result is +- pi
+  if ($x->is_inf() || $y->is_inf())
+    {
+    # calculate PI
+    my $pi = $self->bpi(@r);
+    if ($y->is_inf())
+      {
+      # upgrade to BigRat etc. 
+      return $upgrade->new($y)->batan2($upgrade->new($x),@r) if defined $upgrade;
+      if ($x->{sign} eq '-inf')
+        {
+        # calculate 3 pi/4
+        $MBI->_mul($pi->{_m}, $MBI->_new(3));
+        $MBI->_div($pi->{_m}, $MBI->_new(4));
+        }
+      elsif ($x->{sign} eq '+inf')
+	{
+        # calculate pi/4
+        $MBI->_div($pi->{_m}, $MBI->_new(4));
+	}
+      else
+        {
+        # calculate pi/2
+        $MBI->_div($pi->{_m}, $MBI->_new(2));
+        }
+      $y->{sign} = substr($y->{sign},0,1); # keep +/-
+      }
+    # modify $y in place
+    $y->{_m} = $pi->{_m};
+    $y->{_e} = $pi->{_e};
+    $y->{_es} = $pi->{_es};
+    # keep the sign of $y
+    return $y;
+    }
+
+  return $upgrade->new($y)->batan2($upgrade->new($x),@r) if defined $upgrade;
+
+  # Y X
+  # 0 -x result is PI
+  if ($y->is_zero())
+    {
+    # calculate PI
+    my $pi = $self->bpi(@r);
+    # modify $y in place
+    $y->{_m} = $pi->{_m};
+    $y->{_e} = $pi->{_e};
+    $y->{_es} = $pi->{_es};
+    $y->{sign} = '+';
+    return $y;
+    }
+
+  # Y X
+  # +y 0 result is PI/2
+  # -y 0 result is -PI/2
+  if ($x->is_zero())
+    {
+    # calculate PI/2
+    my $pi = $self->bpi(@r);
+    # modify $y in place
+    $y->{_m} = $pi->{_m};
+    $y->{_e} = $pi->{_e};
+    $y->{_es} = $pi->{_es};
+    # -y => -PI/2, +y => PI/2
+    $MBI->_div($y->{_m}, $MBI->_new(2));
+    return $y;
+    }
+
+  # we need to limit the accuracy to protect against overflow
+  my $fallback = 0;
+  my ($scale,@params);
+  ($y,@params) = $y->_find_round_parameters(@r);
+    
+  # error in _find_round_parameters?
+  return $y if $y->is_nan();
+
+  # no rounding at all, so must use fallback
+  if (scalar @params == 0)
+    {
+    # simulate old behaviour
+    $params[0] = $self->div_scale();	# and round to it as accuracy
+    $params[1] = undef;			# disable P
+    $scale = $params[0]+4; 		# at least four more for proper round
+    $params[2] = $r[2];			# round mode by caller or undef
+    $fallback = 1;			# to clear a/p afterwards
+    }
+  else
+    {
+    # the 4 below is empirical, and there might be cases where it is not
+    # enough...
+    $scale = abs($params[0] || $params[1]) + 4; # take whatever is defined
+    }
+
+  # inlined is_one() && is_one('-')
+  if ($MBI->_is_one($y->{_m}) && $MBI->_is_zero($y->{_e}))
+    {
+    # shortcut: 1 1 result is PI/4
+    # inlined is_one() && is_one('-')
+    if ($MBI->_is_one($x->{_m}) && $MBI->_is_zero($x->{_e}))
+      {
+      # 1,1 => PI/4
+      my $pi_4 = $self->bpi( $scale - 3);
+      # modify $y in place
+      $y->{_m} = $pi_4->{_m};
+      $y->{_e} = $pi_4->{_e};
+      $y->{_es} = $pi_4->{_es};
+      # 1 1 => +
+      # -1 1 => -
+      # 1 -1 => -
+      # -1 -1 => +
+      $y->{sign} = $x->{sign} eq $y->{sign} ? '+' : '-';
+      $MBI->_div($y->{_m}, $MBI->_new(4));
+      return $y;
+      }
+    # shortcut: 1 int(X) result is _atan_inv(X)
+
+    # is integer
+    if ($x->{_es} eq '+')
+      {
+      my $x1 = $MBI->_copy($x->{_m});
+      $MBI->_lsft($x1, $x->{_e},10) unless $MBI->_is_zero($x->{_e});
+
+      my ($a,$b) = $self->_atan_inv($x1, $scale);
+      my $y_sign = $y->{sign};
+      # calculate A/B
+      $y->bone(); $y->{_m} = $a; my $y_d = $self->bone(); $y_d->{_m} = $b;
+      $y->bdiv($y_d, @r);
+      $y->{sign} = $y_sign;
+      return $y;
+      }
+    }
+
+  # handle all other cases
+  #  X  Y
+  # +x +y 0 to PI/2
+  # -x +y PI/2 to PI
+  # +x -y 0 to -PI/2
+  # -x -y -PI/2 to -PI 
+
+  my $y_sign = $y->{sign};
+
+  # divide $x by $y
+  $y->bdiv($x, $scale) unless $x->is_one();
+  $y->batan(@r);
+
+  # restore sign
+  $y->{sign} = $y_sign;
+
+  $y;
+  }
+
+sub batan
+  {
+  # Calculate a arcus tangens of x.
+  my ($x,@r) = @_;
+  my $self = ref($x);
+
+  # taylor:       x^3   x^5   x^7   x^9
+  #    atan = x - --- + --- - --- + --- ...
+  #                3     5     7     9 
+
+  # we need to limit the accuracy to protect against overflow
+  my $fallback = 0;
+  my ($scale,@params);
+  ($x,@params) = $x->_find_round_parameters(@r);
+    
+  #         constant object       or error in _find_round_parameters?
+  return $x if $x->modify('batan') || $x->is_nan();
+
+  if ($x->{sign} =~ /^[+-]inf\z/)
+    {
+    # +inf result is PI/2
+    # -inf result is -PI/2
+    # calculate PI/2
+    my $pi = $self->bpi(@r);
+    # modify $x in place
+    $x->{_m} = $pi->{_m};
+    $x->{_e} = $pi->{_e};
+    $x->{_es} = $pi->{_es};
+    # -y => -PI/2, +y => PI/2
+    $x->{sign} = substr($x->{sign},0,1);		# +inf => +
+    $MBI->_div($x->{_m}, $MBI->_new(2));
+    return $x;
+    }
+
+  return $x->bzero(@r) if $x->is_zero();
+
+  # no rounding at all, so must use fallback
+  if (scalar @params == 0)
+    {
+    # simulate old behaviour
+    $params[0] = $self->div_scale();	# and round to it as accuracy
+    $params[1] = undef;			# disable P
+    $scale = $params[0]+4; 		# at least four more for proper round
+    $params[2] = $r[2];			# round mode by caller or undef
+    $fallback = 1;			# to clear a/p afterwards
+    }
+  else
+    {
+    # the 4 below is empirical, and there might be cases where it is not
+    # enough...
+    $scale = abs($params[0] || $params[1]) + 4; # take whatever is defined
+    }
+
+  # 1 or -1 => PI/4
+  # inlined is_one() && is_one('-')
+  if ($MBI->_is_one($x->{_m}) && $MBI->_is_zero($x->{_e}))
+    {
+    my $pi = $self->bpi($scale - 3);
+    # modify $x in place
+    $x->{_m} = $pi->{_m};
+    $x->{_e} = $pi->{_e};
+    $x->{_es} = $pi->{_es};
+    # leave the sign of $x alone (+1 => +PI/4, -1 => -PI/4)
+    $MBI->_div($x->{_m}, $MBI->_new(4));
+    return $x;
+    }
+  
+  # This series is only valid if -1 < x < 1, so for other x we need to
+  # to calculate PI/2 - atan(1/x):
+  my $one = $MBI->_new(1);
+  my $pi = undef;
+  if ($x->{_es} eq '+' && ($MBI->_acmp($x->{_m},$one) >= 0))
+    {
+    # calculate PI/2
+    $pi = $self->bpi($scale - 3);
+    $MBI->_div($pi->{_m}, $MBI->_new(2));
+    # calculate 1/$x:
+    my $x_copy = $x->copy();
+    # modify $x in place
+    $x->bone(); $x->bdiv($x_copy,$scale);
+    }
+
+  # when user set globals, they would interfere with our calculation, so
+  # disable them and later re-enable them
+  no strict 'refs';
+  my $abr = "$self\::accuracy"; my $ab = $$abr; $$abr = undef;
+  my $pbr = "$self\::precision"; my $pb = $$pbr; $$pbr = undef;
+  # we also need to disable any set A or P on $x (_find_round_parameters took
+  # them already into account), since these would interfere, too
+  delete $x->{_a}; delete $x->{_p};
+  # need to disable $upgrade in BigInt, to avoid deep recursion
+  local $Math::BigInt::upgrade = undef;
+ 
+  my $last = 0;
+  my $over = $x * $x;			# X ^ 2
+  my $x2 = $over->copy();		# X ^ 2; difference between terms
+  $over->bmul($x);			# X ^ 3 as starting value
+  my $sign = 1;				# start with -=
+  my $below = $self->new(3);
+  my $two = $self->new(2);
+  delete $x->{_a}; delete $x->{_p};
+
+  my $limit = $self->new("1E-". ($scale-1));
+  #my $steps = 0;
+  while (3 < 5)
+    {
+    # we calculate the next term, and add it to the last
+    # when the next term is below our limit, it won't affect the outcome
+    # anymore, so we stop:
+    my $next = $over->copy()->bdiv($below,$scale);
+    last if $next->bacmp($limit) <= 0;
+
+    if ($sign == 0)
+      {
+      $x->badd($next);
+      }
+    else
+      {
+      $x->bsub($next);
+      }
+    $sign = 1-$sign;					# alternate
+    # calculate things for the next term
+    $over->bmul($x2);					# $x*$x
+    $below->badd($two);					# n += 2
+    }
+
+  if (defined $pi)
+    {
+    my $x_copy = $x->copy();
+    # modify $x in place
+    $x->{_m} = $pi->{_m};
+    $x->{_e} = $pi->{_e};
+    $x->{_es} = $pi->{_es};
+    # PI/2 - $x
+    $x->bsub($x_copy);
+    }
+
+  # shortcut to not run through _find_round_parameters again
+  if (defined $params[0])
+    {
+    $x->bround($params[0],$params[2]);		# then round accordingly
+    }
+  else
+    {
+    $x->bfround($params[1],$params[2]);		# then round accordingly
+    }
+  if ($fallback)
+    {
+    # clear a/p after round, since user did not request it
+    delete $x->{_a}; delete $x->{_p};
+    }
+  # restore globals
+  $$abr = $ab; $$pbr = $pb;
+  $x;
+  }
+
+###############################################################################
+# rounding functions
+
+sub bfround
+  {
+  # precision: round to the $Nth digit left (+$n) or right (-$n) from the '.'
+  # $n == 0 means round to integer
+  # expects and returns normalized numbers!
+  my $x = shift; my $self = ref($x) || $x; $x = $self->new(shift) if !ref($x);
+
+  my ($scale,$mode) = $x->_scale_p(@_);
+  return $x if !defined $scale || $x->modify('bfround'); # no-op
+
+  # never round a 0, +-inf, NaN
+  if ($x->is_zero())
+    {
+    $x->{_p} = $scale if !defined $x->{_p} || $x->{_p} < $scale; # -3 < -2
+    return $x; 
+    }
+  return $x if $x->{sign} !~ /^[+-]$/;
+
+  # don't round if x already has lower precision
+  return $x if (defined $x->{_p} && $x->{_p} < 0 && $scale < $x->{_p});
+
+  $x->{_p} = $scale;			# remember round in any case
+  delete $x->{_a};			# and clear A
+  if ($scale < 0)
+    {
+    # round right from the '.'
+
+    return $x if $x->{_es} eq '+';		# e >= 0 => nothing to round
+
+    $scale = -$scale;				# positive for simplicity
+    my $len = $MBI->_len($x->{_m});		# length of mantissa
+
+    # the following poses a restriction on _e, but if _e is bigger than a
+    # scalar, you got other problems (memory etc) anyway
+    my $dad = -(0+ ($x->{_es}.$MBI->_num($x->{_e})));	# digits after dot
+    my $zad = 0;				# zeros after dot
+    $zad = $dad - $len if (-$dad < -$len);	# for 0.00..00xxx style
+   
+    # p rint "scale $scale dad $dad zad $zad len $len\n";
+    # number  bsstr   len zad dad	
+    # 0.123   123e-3	3   0 3
+    # 0.0123  123e-4	3   1 4
+    # 0.001   1e-3      1   2 3
+    # 1.23    123e-2	3   0 2
+    # 1.2345  12345e-4	5   0 4
+
+    # do not round after/right of the $dad
+    return $x if $scale > $dad;			# 0.123, scale >= 3 => exit
+
+    # round to zero if rounding inside the $zad, but not for last zero like:
+    # 0.0065, scale -2, round last '0' with following '65' (scale == zad case)
+    return $x->bzero() if $scale < $zad;
+    if ($scale == $zad)			# for 0.006, scale -3 and trunc
+      {
+      $scale = -$len;
+      }
+    else
+      {
+      # adjust round-point to be inside mantissa
+      if ($zad != 0)
+        {
+	$scale = $scale-$zad;
+        }
+      else
+        {
+        my $dbd = $len - $dad; $dbd = 0 if $dbd < 0;	# digits before dot
+	$scale = $dbd+$scale;
+        }
+      }
+    }
+  else
+    {
+    # round left from the '.'
+
+    # 123 => 100 means length(123) = 3 - $scale (2) => 1
+
+    my $dbt = $MBI->_len($x->{_m}); 
+    # digits before dot 
+    my $dbd = $dbt + ($x->{_es} . $MBI->_num($x->{_e}));
+    # should be the same, so treat it as this 
+    $scale = 1 if $scale == 0; 
+    # shortcut if already integer 
+    return $x if $scale == 1 && $dbt <= $dbd; 
+    # maximum digits before dot 
+    ++$dbd;
+
+    if ($scale > $dbd) 
+       { 
+       # not enough digits before dot, so round to zero 
+       return $x->bzero; 
+       }
+    elsif ( $scale == $dbd )
+       { 
+       # maximum 
+       $scale = -$dbt; 
+       } 
+    else
+       { 
+       $scale = $dbd - $scale; 
+       }
+    }
+  # pass sign to bround for rounding modes '+inf' and '-inf'
+  my $m = bless { sign => $x->{sign}, value => $x->{_m} }, 'Math::BigInt';
+  $m->bround($scale,$mode);
+  $x->{_m} = $m->{value};			# get our mantissa back
+  $x->bnorm();
+  }
+
+sub bround
+  {
+  # accuracy: preserve $N digits, and overwrite the rest with 0's
+  my $x = shift; my $self = ref($x) || $x; $x = $self->new(shift) if !ref($x);
+
+  if (($_[0] || 0) < 0)
+    {
+    require Carp; Carp::croak ('bround() needs positive accuracy');
+    }
+
+  my ($scale,$mode) = $x->_scale_a(@_);
+  return $x if !defined $scale || $x->modify('bround');	# no-op
+
+  # scale is now either $x->{_a}, $accuracy, or the user parameter
+  # test whether $x already has lower accuracy, do nothing in this case 
+  # but do round if the accuracy is the same, since a math operation might
+  # want to round a number with A=5 to 5 digits afterwards again
+  return $x if defined $x->{_a} && $x->{_a} < $scale;
+
+  # scale < 0 makes no sense
+  # scale == 0 => keep all digits
+  # never round a +-inf, NaN
+  return $x if ($scale <= 0) || $x->{sign} !~ /^[+-]$/;
+
+  # 1: never round a 0
+  # 2: if we should keep more digits than the mantissa has, do nothing
+  if ($x->is_zero() || $MBI->_len($x->{_m}) <= $scale)
+    {
+    $x->{_a} = $scale if !defined $x->{_a} || $x->{_a} > $scale;
+    return $x; 
+    }
+
+  # pass sign to bround for '+inf' and '-inf' rounding modes
+  my $m = bless { sign => $x->{sign}, value => $x->{_m} }, 'Math::BigInt';
+
+  $m->bround($scale,$mode);		# round mantissa
+  $x->{_m} = $m->{value};		# get our mantissa back
+  $x->{_a} = $scale;			# remember rounding
+  delete $x->{_p};			# and clear P
+  $x->bnorm();				# del trailing zeros gen. by bround()
+  }
+
+sub bfloor
+  {
+  # return integer less or equal then $x
+  my ($self,$x,$a,$p,$r) = ref($_[0]) ? (ref($_[0]),@_) : objectify(1,@_);
+
+  return $x if $x->modify('bfloor');
+   
+  return $x if $x->{sign} !~ /^[+-]$/;	# nan, +inf, -inf
+
+  # if $x has digits after dot
+  if ($x->{_es} eq '-')
+    {
+    $x->{_m} = $MBI->_rsft($x->{_m},$x->{_e},10); # cut off digits after dot
+    $x->{_e} = $MBI->_zero();			# trunc/norm	
+    $x->{_es} = '+';				# abs e
+    $MBI->_inc($x->{_m}) if $x->{sign} eq '-';	# increment if negative
+    }
+  $x->round($a,$p,$r);
+  }
+
+sub bceil
+  {
+  # return integer greater or equal then $x
+  my ($self,$x,$a,$p,$r) = ref($_[0]) ? (ref($_[0]),@_) : objectify(1,@_);
+
+  return $x if $x->modify('bceil');
+  return $x if $x->{sign} !~ /^[+-]$/;	# nan, +inf, -inf
+
+  # if $x has digits after dot
+  if ($x->{_es} eq '-')
+    {
+    $x->{_m} = $MBI->_rsft($x->{_m},$x->{_e},10); # cut off digits after dot
+    $x->{_e} = $MBI->_zero();			# trunc/norm	
+    $x->{_es} = '+';				# abs e
+    $MBI->_inc($x->{_m}) if $x->{sign} eq '+';	# increment if positive
+    }
+  $x->round($a,$p,$r);
+  }
+
+sub brsft
+  {
+  # shift right by $y (divide by power of $n)
+  
+  # set up parameters
+  my ($self,$x,$y,$n,$a,$p,$r) = (ref($_[0]),@_);
+  # objectify is costly, so avoid it
+  if ((!ref($_[0])) || (ref($_[0]) ne ref($_[1])))
+    {
+    ($self,$x,$y,$n,$a,$p,$r) = objectify(2,@_);
+    }
+
+  return $x if $x->modify('brsft');
+  return $x if $x->{sign} !~ /^[+-]$/;	# nan, +inf, -inf
+
+  $n = 2 if !defined $n; $n = $self->new($n);
+
+  # negative amount?
+  return $x->blsft($y->copy()->babs(),$n) if $y->{sign} =~ /^-/;
+
+  # the following call to bdiv() will return either quo or (quo,reminder):
+  $x->bdiv($n->bpow($y),$a,$p,$r,$y);
+  }
+
+sub blsft
+  {
+  # shift left by $y (multiply by power of $n)
+  
+  # set up parameters
+  my ($self,$x,$y,$n,$a,$p,$r) = (ref($_[0]),@_);
+  # objectify is costly, so avoid it
+  if ((!ref($_[0])) || (ref($_[0]) ne ref($_[1])))
+    {
+    ($self,$x,$y,$n,$a,$p,$r) = objectify(2,@_);
+    }
+
+  return $x if $x->modify('blsft');
+  return $x if $x->{sign} !~ /^[+-]$/;	# nan, +inf, -inf
+
+  $n = 2 if !defined $n; $n = $self->new($n);
+
+  # negative amount?
+  return $x->brsft($y->copy()->babs(),$n) if $y->{sign} =~ /^-/;
+
+  $x->bmul($n->bpow($y),$a,$p,$r,$y);
+  }
+
+###############################################################################
+
+sub DESTROY
+  {
+  # going through AUTOLOAD for every DESTROY is costly, avoid it by empty sub
+  }
+
+sub AUTOLOAD
+  {
+  # make fxxx and bxxx both work by selectively mapping fxxx() to MBF::bxxx()
+  # or falling back to MBI::bxxx()
+  my $name = $AUTOLOAD;
+
+  $name =~ s/(.*):://;	# split package
+  my $c = $1 || $class;
+  no strict 'refs';
+  $c->import() if $IMPORT == 0;
+  if (!_method_alias($name))
+    {
+    if (!defined $name)
+      {
+      # delayed load of Carp and avoid recursion	
+      require Carp;
+      Carp::croak ("$c: Can't call a method without name");
+      }
+    if (!_method_hand_up($name))
+      {
+      # delayed load of Carp and avoid recursion	
+      require Carp;
+      Carp::croak ("Can't call $c\-\>$name, not a valid method");
+      }
+    # try one level up, but subst. bxxx() for fxxx() since MBI only got bxxx()
+    $name =~ s/^f/b/;
+    return &{"Math::BigInt"."::$name"}(@_);
+    }
+  my $bname = $name; $bname =~ s/^f/b/;
+  $c .= "::$name";
+  *{$c} = \&{$bname};
+  &{$c};	# uses @_
+  }
+
+sub exponent
+  {
+  # return a copy of the exponent
+  my ($self,$x) = ref($_[0]) ? (ref($_[0]),$_[0]) : objectify(1,@_);
+
+  if ($x->{sign} !~ /^[+-]$/)
+    {
+    my $s = $x->{sign}; $s =~ s/^[+-]//;
+    return Math::BigInt->new($s); 		# -inf, +inf => +inf
+    }
+  Math::BigInt->new( $x->{_es} . $MBI->_str($x->{_e}));
+  }
+
+sub mantissa
+  {
+  # return a copy of the mantissa
+  my ($self,$x) = ref($_[0]) ? (ref($_[0]),$_[0]) : objectify(1,@_);
+ 
+  if ($x->{sign} !~ /^[+-]$/)
+    {
+    my $s = $x->{sign}; $s =~ s/^[+]//;
+    return Math::BigInt->new($s);		# -inf, +inf => +inf
+    }
+  my $m = Math::BigInt->new( $MBI->_str($x->{_m}));
+  $m->bneg() if $x->{sign} eq '-';
+
+  $m;
+  }
+
+sub parts
+  {
+  # return a copy of both the exponent and the mantissa
+  my ($self,$x) = ref($_[0]) ? (ref($_[0]),$_[0]) : objectify(1,@_);
+
+  if ($x->{sign} !~ /^[+-]$/)
+    {
+    my $s = $x->{sign}; $s =~ s/^[+]//; my $se = $s; $se =~ s/^[-]//;
+    return ($self->new($s),$self->new($se)); # +inf => inf and -inf,+inf => inf
+    }
+  my $m = Math::BigInt->bzero();
+  $m->{value} = $MBI->_copy($x->{_m});
+  $m->bneg() if $x->{sign} eq '-';
+  ($m, Math::BigInt->new( $x->{_es} . $MBI->_num($x->{_e}) ));
+  }
+
+##############################################################################
+# private stuff (internal use only)
+
+sub import
+  {
+  my $self = shift;
+  my $l = scalar @_;
+  my $lib = ''; my @a;
+  my $lib_kind = 'try';
+  $IMPORT=1;
+  for ( my $i = 0; $i < $l ; $i++)
+    {
+    if ( $_[$i] eq ':constant' )
+      {
+      # This causes overlord er load to step in. 'binary' and 'integer'
+      # are handled by BigInt.
+      overload::constant float => sub { $self->new(shift); }; 
+      }
+    elsif ($_[$i] eq 'upgrade')
+      {
+      # this causes upgrading
+      $upgrade = $_[$i+1];		# or undef to disable
+      $i++;
+      }
+    elsif ($_[$i] eq 'downgrade')
+      {
+      # this causes downgrading
+      $downgrade = $_[$i+1];		# or undef to disable
+      $i++;
+      }
+    elsif ($_[$i] =~ /^(lib|try|only)\z/)
+      {
+      # alternative library
+      $lib = $_[$i+1] || '';		# default Calc
+      $lib_kind = $1;			# lib, try or only
+      $i++;
+      }
+    elsif ($_[$i] eq 'with')
+      {
+      # alternative class for our private parts()
+      # XXX: no longer supported
+      # $MBI = $_[$i+1] || 'Math::BigInt';
+      $i++;
+      }
+    else
+      {
+      push @a, $_[$i];
+      }
+    }
+
+  $lib =~ tr/a-zA-Z0-9,://cd;		# restrict to sane characters
+  # let use Math::BigInt lib => 'GMP'; use Math::BigFloat; still work
+  my $mbilib = eval { Math::BigInt->config()->{lib} };
+  if ((defined $mbilib) && ($MBI eq 'Math::BigInt::Calc'))
+    {
+    # MBI already loaded
+    Math::BigInt->import( $lib_kind, "$lib,$mbilib", 'objectify');
+    }
+  else
+    {
+    # MBI not loaded, or with ne "Math::BigInt::Calc"
+    $lib .= ",$mbilib" if defined $mbilib;
+    $lib =~ s/^,//;				# don't leave empty 
+    
+    # replacement library can handle lib statement, but also could ignore it
+    
+    # Perl < 5.6.0 dies with "out of memory!" when eval() and ':constant' is
+    # used in the same script, or eval inside import(). So we require MBI:
+    require Math::BigInt;
+    Math::BigInt->import( $lib_kind => $lib, 'objectify' );
+    }
+  if ($@)
+    {
+    require Carp; Carp::croak ("Couldn't load $lib: $! $@");
+    }
+  # find out which one was actually loaded
+  $MBI = Math::BigInt->config()->{lib};
+
+  # register us with MBI to get notified of future lib changes
+  Math::BigInt::_register_callback( $self, sub { $MBI = $_[0]; } );
+
+  $self->export_to_level(1,$self,@a);		# export wanted functions
+  }
+
+sub bnorm
+  {
+  # adjust m and e so that m is smallest possible
+  my ($self,$x) = ref($_[0]) ? (undef,$_[0]) : objectify(1,@_);
+
+  return $x if $x->{sign} !~ /^[+-]$/;		# inf, nan etc
+
+  my $zeros = $MBI->_zeros($x->{_m});		# correct for trailing zeros
+  if ($zeros != 0)
+    {
+    my $z = $MBI->_new($zeros);
+    $x->{_m} = $MBI->_rsft ($x->{_m}, $z, 10);
+    if ($x->{_es} eq '-')
+      {
+      if ($MBI->_acmp($x->{_e},$z) >= 0)
+        {
+        $x->{_e} = $MBI->_sub ($x->{_e}, $z);
+        $x->{_es} = '+' if $MBI->_is_zero($x->{_e});
+        }
+      else
+        {
+        $x->{_e} = $MBI->_sub ( $MBI->_copy($z), $x->{_e});
+        $x->{_es} = '+';
+        }
+      }
+    else
+      {
+      $x->{_e} = $MBI->_add ($x->{_e}, $z);
+      }
+    }
+  else
+    {
+    # $x can only be 0Ey if there are no trailing zeros ('0' has 0 trailing
+    # zeros). So, for something like 0Ey, set y to 1, and -0 => +0
+    $x->{sign} = '+', $x->{_es} = '+', $x->{_e} = $MBI->_one()
+     if $MBI->_is_zero($x->{_m});
+    }
+
+  $x;					# MBI bnorm is no-op, so dont call it
+  } 
+ 
+##############################################################################
+
+sub as_hex
+  {
+  # return number as hexadecimal string (only for integers defined)
+  my ($self,$x) = ref($_[0]) ? (ref($_[0]),$_[0]) : objectify(1,@_);
+
+  return $x->bstr() if $x->{sign} !~ /^[+-]$/;  # inf, nan etc
+  return '0x0' if $x->is_zero();
+
+  return $nan if $x->{_es} ne '+';		# how to do 1e-1 in hex!?
+
+  my $z = $MBI->_copy($x->{_m});
+  if (! $MBI->_is_zero($x->{_e}))		# > 0 
+    {
+    $MBI->_lsft( $z, $x->{_e},10);
+    }
+  $z = Math::BigInt->new( $x->{sign} . $MBI->_num($z));
+  $z->as_hex();
+  }
+
+sub as_bin
+  {
+  # return number as binary digit string (only for integers defined)
+  my ($self,$x) = ref($_[0]) ? (ref($_[0]),$_[0]) : objectify(1,@_);
+
+  return $x->bstr() if $x->{sign} !~ /^[+-]$/;  # inf, nan etc
+  return '0b0' if $x->is_zero();
+
+  return $nan if $x->{_es} ne '+';		# how to do 1e-1 in hex!?
+
+  my $z = $MBI->_copy($x->{_m});
+  if (! $MBI->_is_zero($x->{_e}))		# > 0 
+    {
+    $MBI->_lsft( $z, $x->{_e},10);
+    }
+  $z = Math::BigInt->new( $x->{sign} . $MBI->_num($z));
+  $z->as_bin();
+  }
+
+sub as_oct
+  {
+  # return number as octal digit string (only for integers defined)
+  my ($self,$x) = ref($_[0]) ? (ref($_[0]),$_[0]) : objectify(1,@_);
+
+  return $x->bstr() if $x->{sign} !~ /^[+-]$/;  # inf, nan etc
+  return '0' if $x->is_zero();
+
+  return $nan if $x->{_es} ne '+';		# how to do 1e-1 in hex!?
+
+  my $z = $MBI->_copy($x->{_m});
+  if (! $MBI->_is_zero($x->{_e}))		# > 0 
+    {
+    $MBI->_lsft( $z, $x->{_e},10);
+    }
+  $z = Math::BigInt->new( $x->{sign} . $MBI->_num($z));
+  $z->as_oct();
+  }
+
+sub as_number
+  {
+  # return copy as a bigint representation of this BigFloat number
+  my ($self,$x) = ref($_[0]) ? (ref($_[0]),$_[0]) : objectify(1,@_);
+
+  return $x if $x->modify('as_number');
+
+  if (!$x->isa('Math::BigFloat'))
+    {
+    # if the object can as_number(), use it
+    return $x->as_number() if $x->can('as_number');
+    # otherwise, get us a float and then a number
+    $x = $x->can('as_float') ? $x->as_float() : $self->new(0+"$x");
+    }
+
+  my $z = $MBI->_copy($x->{_m});
+  if ($x->{_es} eq '-')			# < 0
+    {
+    $MBI->_rsft( $z, $x->{_e},10);
+    } 
+  elsif (! $MBI->_is_zero($x->{_e}))	# > 0 
+    {
+    $MBI->_lsft( $z, $x->{_e},10);
+    }
+  $z = Math::BigInt->new( $x->{sign} . $MBI->_num($z));
+  $z;
+  }
+
+sub length
+  {
+  my $x = shift;
+  my $class = ref($x) || $x;
+  $x = $class->new(shift) unless ref($x);
+
+  return 1 if $MBI->_is_zero($x->{_m});
+
+  my $len = $MBI->_len($x->{_m});
+  $len += $MBI->_num($x->{_e}) if $x->{_es} eq '+';
+  if (wantarray())
+    {
+    my $t = 0;
+    $t = $MBI->_num($x->{_e}) if $x->{_es} eq '-';
+    return ($len, $t);
+    }
+  $len;
+  }
+
+1;
+__END__
+
+=head1 NAME
+
+Math::BigFloat - Arbitrary size floating point math package
+
+=head1 SYNOPSIS
+
+  use Math::BigFloat;
+
+  # Number creation
+  my $x = Math::BigFloat->new($str);	# defaults to 0
+  my $y = $x->copy();			# make a true copy
+  my $nan  = Math::BigFloat->bnan();	# create a NotANumber
+  my $zero = Math::BigFloat->bzero();	# create a +0
+  my $inf = Math::BigFloat->binf();	# create a +inf
+  my $inf = Math::BigFloat->binf('-');	# create a -inf
+  my $one = Math::BigFloat->bone();	# create a +1
+  my $mone = Math::BigFloat->bone('-');	# create a -1
+
+  my $pi = Math::BigFloat->bpi(100);	# PI to 100 digits
+
+  # the following examples compute their result to 100 digits accuracy:
+  my $cos  = Math::BigFloat->new(1)->bcos(100);		# cosinus(1)
+  my $sin  = Math::BigFloat->new(1)->bsin(100);		# sinus(1)
+  my $atan = Math::BigFloat->new(1)->batan(100);	# arcus tangens(1)
+
+  my $atan2 = Math::BigFloat->new(  1 )->batan2( 1 ,100); # batan(1)
+  my $atan2 = Math::BigFloat->new(  1 )->batan2( 8 ,100); # batan(1/8)
+  my $atan2 = Math::BigFloat->new( -2 )->batan2( 1 ,100); # batan(-2)
+
+  # Testing
+  $x->is_zero();		# true if arg is +0
+  $x->is_nan();			# true if arg is NaN
+  $x->is_one();			# true if arg is +1
+  $x->is_one('-');		# true if arg is -1
+  $x->is_odd();			# true if odd, false for even
+  $x->is_even();		# true if even, false for odd
+  $x->is_pos();			# true if >= 0
+  $x->is_neg();			# true if <  0
+  $x->is_inf(sign);		# true if +inf, or -inf (default is '+')
+
+  $x->bcmp($y);			# compare numbers (undef,<0,=0,>0)
+  $x->bacmp($y);		# compare absolutely (undef,<0,=0,>0)
+  $x->sign();			# return the sign, either +,- or NaN
+  $x->digit($n);		# return the nth digit, counting from right
+  $x->digit(-$n);		# return the nth digit, counting from left 
+
+  # The following all modify their first argument. If you want to preserve
+  # $x, use $z = $x->copy()->bXXX($y); See under L<CAVEATS> for why this is
+  # necessary when mixing $a = $b assignments with non-overloaded math.
+ 
+  # set 
+  $x->bzero();			# set $i to 0
+  $x->bnan();			# set $i to NaN
+  $x->bone();                   # set $x to +1
+  $x->bone('-');                # set $x to -1
+  $x->binf();                   # set $x to inf
+  $x->binf('-');                # set $x to -inf
+
+  $x->bneg();			# negation
+  $x->babs();			# absolute value
+  $x->bnorm();			# normalize (no-op)
+  $x->bnot();			# two's complement (bit wise not)
+  $x->binc();			# increment x by 1
+  $x->bdec();			# decrement x by 1
+  
+  $x->badd($y);			# addition (add $y to $x)
+  $x->bsub($y);			# subtraction (subtract $y from $x)
+  $x->bmul($y);			# multiplication (multiply $x by $y)
+  $x->bdiv($y);			# divide, set $x to quotient
+				# return (quo,rem) or quo if scalar
+
+  $x->bmod($y);			# modulus ($x % $y)
+  $x->bpow($y);			# power of arguments ($x ** $y)
+  $x->bmodpow($exp,$mod);	# modular exponentation (($num**$exp) % $mod))
+  $x->blsft($y, $n);		# left shift by $y places in base $n
+  $x->brsft($y, $n);		# right shift by $y places in base $n
+				# returns (quo,rem) or quo if in scalar context
+  
+  $x->blog();			# logarithm of $x to base e (Euler's number)
+  $x->blog($base);		# logarithm of $x to base $base (f.i. 2)
+  $x->bexp();			# calculate e ** $x where e is Euler's number
+  
+  $x->band($y);			# bit-wise and
+  $x->bior($y);			# bit-wise inclusive or
+  $x->bxor($y);			# bit-wise exclusive or
+  $x->bnot();			# bit-wise not (two's complement)
+ 
+  $x->bsqrt();			# calculate square-root
+  $x->broot($y);		# $y'th root of $x (e.g. $y == 3 => cubic root)
+  $x->bfac();			# factorial of $x (1*2*3*4*..$x)
+ 
+  $x->bround($N); 		# accuracy: preserve $N digits
+  $x->bfround($N);		# precision: round to the $Nth digit
+
+  $x->bfloor();			# return integer less or equal than $x
+  $x->bceil();			# return integer greater or equal than $x
+
+  # The following do not modify their arguments:
+
+  bgcd(@values);		# greatest common divisor
+  blcm(@values);		# lowest common multiplicator
+  
+  $x->bstr();			# return string
+  $x->bsstr();			# return string in scientific notation
+
+  $x->as_int();			# return $x as BigInt 
+  $x->exponent();		# return exponent as BigInt
+  $x->mantissa();		# return mantissa as BigInt
+  $x->parts();			# return (mantissa,exponent) as BigInt
+
+  $x->length();			# number of digits (w/o sign and '.')
+  ($l,$f) = $x->length();	# number of digits, and length of fraction	
+
+  $x->precision();		# return P of $x (or global, if P of $x undef)
+  $x->precision($n);		# set P of $x to $n
+  $x->accuracy();		# return A of $x (or global, if A of $x undef)
+  $x->accuracy($n);		# set A $x to $n
+
+  # these get/set the appropriate global value for all BigFloat objects
+  Math::BigFloat->precision();	# Precision
+  Math::BigFloat->accuracy();	# Accuracy
+  Math::BigFloat->round_mode();	# rounding mode
+
+=head1 DESCRIPTION
+
+All operators (including basic math operations) are overloaded if you
+declare your big floating point numbers as
+
+  $i = new Math::BigFloat '12_3.456_789_123_456_789E-2';
+
+Operations with overloaded operators preserve the arguments, which is
+exactly what you expect.
+
+=head2 Canonical notation
+
+Input to these routines are either BigFloat objects, or strings of the
+following four forms:
+
+=over 2
+
+=item *
+
+C</^[+-]\d+$/>
+
+=item *
+
+C</^[+-]\d+\.\d*$/>
+
+=item *
+
+C</^[+-]\d+E[+-]?\d+$/>
+
+=item *
+
+C</^[+-]\d*\.\d+E[+-]?\d+$/>
+
+=back
+
+all with optional leading and trailing zeros and/or spaces. Additionally,
+numbers are allowed to have an underscore between any two digits.
+
+Empty strings as well as other illegal numbers results in 'NaN'.
+
+bnorm() on a BigFloat object is now effectively a no-op, since the numbers 
+are always stored in normalized form. On a string, it creates a BigFloat 
+object.
+
+=head2 Output
+
+Output values are BigFloat objects (normalized), except for bstr() and bsstr().
+
+The string output will always have leading and trailing zeros stripped and drop
+a plus sign. C<bstr()> will give you always the form with a decimal point,
+while C<bsstr()> (s for scientific) gives you the scientific notation.
+
+	Input			bstr()		bsstr()
+	'-0'			'0'		'0E1'
+   	'  -123 123 123'	'-123123123'	'-123123123E0'
+	'00.0123'		'0.0123'	'123E-4'
+	'123.45E-2'		'1.2345'	'12345E-4'
+	'10E+3'			'10000'		'1E4'
+
+Some routines (C<is_odd()>, C<is_even()>, C<is_zero()>, C<is_one()>,
+C<is_nan()>) return true or false, while others (C<bcmp()>, C<bacmp()>)
+return either undef, <0, 0 or >0 and are suited for sort.
+
+Actual math is done by using the class defined with C<with => Class;> (which
+defaults to BigInts) to represent the mantissa and exponent.
+
+The sign C</^[+-]$/> is stored separately. The string 'NaN' is used to 
+represent the result when input arguments are not numbers, as well as 
+the result of dividing by zero.
+
+=head2 C<mantissa()>, C<exponent()> and C<parts()>
+
+C<mantissa()> and C<exponent()> return the said parts of the BigFloat 
+as BigInts such that:
+
+	$m = $x->mantissa();
+	$e = $x->exponent();
+	$y = $m * ( 10 ** $e );
+	print "ok\n" if $x == $y;
+
+C<< ($m,$e) = $x->parts(); >> is just a shortcut giving you both of them.
+
+A zero is represented and returned as C<0E1>, B<not> C<0E0> (after Knuth).
+
+Currently the mantissa is reduced as much as possible, favouring higher
+exponents over lower ones (e.g. returning 1e7 instead of 10e6 or 10000000e0).
+This might change in the future, so do not depend on it.
+
+=head2 Accuracy vs. Precision
+
+See also: L<Rounding|Rounding>.
+
+Math::BigFloat supports both precision (rounding to a certain place before or
+after the dot) and accuracy (rounding to a certain number of digits). For a
+full documentation, examples and tips on these topics please see the large
+section about rounding in L<Math::BigInt>.
+
+Since things like C<sqrt(2)> or C<1 / 3> must presented with a limited
+accuracy lest a operation consumes all resources, each operation produces
+no more than the requested number of digits.
+
+If there is no gloabl precision or accuracy set, B<and> the operation in
+question was not called with a requested precision or accuracy, B<and> the
+input $x has no accuracy or precision set, then a fallback parameter will
+be used. For historical reasons, it is called C<div_scale> and can be accessed
+via:
+
+	$d = Math::BigFloat->div_scale();		# query
+	Math::BigFloat->div_scale($n);			# set to $n digits
+
+The default value for C<div_scale> is 40.
+
+In case the result of one operation has more digits than specified,
+it is rounded. The rounding mode taken is either the default mode, or the one
+supplied to the operation after the I<scale>:
+
+	$x = Math::BigFloat->new(2);
+	Math::BigFloat->accuracy(5);		# 5 digits max
+	$y = $x->copy()->bdiv(3);		# will give 0.66667
+	$y = $x->copy()->bdiv(3,6);		# will give 0.666667
+	$y = $x->copy()->bdiv(3,6,undef,'odd');	# will give 0.666667
+	Math::BigFloat->round_mode('zero');
+	$y = $x->copy()->bdiv(3,6);		# will also give 0.666667
+
+Note that C<< Math::BigFloat->accuracy() >> and C<< Math::BigFloat->precision() >>
+set the global variables, and thus B<any> newly created number will be subject
+to the global rounding B<immediately>. This means that in the examples above, the
+C<3> as argument to C<bdiv()> will also get an accuracy of B<5>.
+
+It is less confusing to either calculate the result fully, and afterwards
+round it explicitly, or use the additional parameters to the math
+functions like so:
+
+	use Math::BigFloat;	
+	$x = Math::BigFloat->new(2);
+	$y = $x->copy()->bdiv(3);
+	print $y->bround(5),"\n";		# will give 0.66667
+
+	or
+
+	use Math::BigFloat;	
+	$x = Math::BigFloat->new(2);
+	$y = $x->copy()->bdiv(3,5);		# will give 0.66667
+	print "$y\n";
+
+=head2 Rounding
+
+=over 2
+
+=item ffround ( +$scale )
+
+Rounds to the $scale'th place left from the '.', counting from the dot.
+The first digit is numbered 1. 
+
+=item ffround ( -$scale )
+
+Rounds to the $scale'th place right from the '.', counting from the dot.
+
+=item ffround ( 0 )
+
+Rounds to an integer.
+
+=item fround  ( +$scale )
+
+Preserves accuracy to $scale digits from the left (aka significant digits)
+and pads the rest with zeros. If the number is between 1 and -1, the
+significant digits count from the first non-zero after the '.'
+
+=item fround  ( -$scale ) and fround ( 0 )
+
+These are effectively no-ops.
+
+=back
+
+All rounding functions take as a second parameter a rounding mode from one of
+the following: 'even', 'odd', '+inf', '-inf', 'zero', 'trunc' or 'common'.
+
+The default rounding mode is 'even'. By using
+C<< Math::BigFloat->round_mode($round_mode); >> you can get and set the default
+mode for subsequent rounding. The usage of C<$Math::BigFloat::$round_mode> is
+no longer supported.
+The second parameter to the round functions then overrides the default
+temporarily. 
+
+The C<as_number()> function returns a BigInt from a Math::BigFloat. It uses
+'trunc' as rounding mode to make it equivalent to:
+
+	$x = 2.5;
+	$y = int($x) + 2;
+
+You can override this by passing the desired rounding mode as parameter to
+C<as_number()>:
+
+	$x = Math::BigFloat->new(2.5);
+	$y = $x->as_number('odd');	# $y = 3
+
+=head1 METHODS
+
+Math::BigFloat supports all methods that Math::BigInt supports, except it
+calculates non-integer results when possible. Please see L<Math::BigInt>
+for a full description of each method. Below are just the most important
+differences:
+
+=head2 accuracy
+
+        $x->accuracy(5);                # local for $x
+        CLASS->accuracy(5);             # global for all members of CLASS
+                                        # Note: This also applies to new()!
+
+        $A = $x->accuracy();            # read out accuracy that affects $x
+        $A = CLASS->accuracy();         # read out global accuracy
+
+Set or get the global or local accuracy, aka how many significant digits the
+results have. If you set a global accuracy, then this also applies to new()!
+
+Warning! The accuracy I<sticks>, e.g. once you created a number under the
+influence of C<< CLASS->accuracy($A) >>, all results from math operations with
+that number will also be rounded.
+
+In most cases, you should probably round the results explicitly using one of
+L<round()>, L<bround()> or L<bfround()> or by passing the desired accuracy
+to the math operation as additional parameter:
+
+        my $x = Math::BigInt->new(30000);
+        my $y = Math::BigInt->new(7);
+        print scalar $x->copy()->bdiv($y, 2);           # print 4300
+        print scalar $x->copy()->bdiv($y)->bround(2);   # print 4300
+
+=head2 precision()
+
+        $x->precision(-2);      # local for $x, round at the second digit right of the dot
+        $x->precision(2);       # ditto, round at the second digit left of the dot
+
+        CLASS->precision(5);    # Global for all members of CLASS
+                                # This also applies to new()!
+        CLASS->precision(-5);   # ditto
+
+        $P = CLASS->precision();        # read out global precision
+        $P = $x->precision();           # read out precision that affects $x
+
+Note: You probably want to use L<accuracy()> instead. With L<accuracy> you
+set the number of digits each result should have, with L<precision> you
+set the place where to round!
+
+=head2 bexp()
+
+	$x->bexp($accuracy);		# calculate e ** X
+
+Calculates the expression C<e ** $x> where C<e> is Euler's number.
+
+This method was added in v1.82 of Math::BigInt (April 2007).
+
+=head2 bnok()
+
+	$x->bnok($y);		   # x over y (binomial coefficient n over k)
+
+Calculates the binomial coefficient n over k, also called the "choose"
+function. The result is equivalent to:
+
+	( n )      n!
+	| - |  = -------
+	( k )    k!(n-k)!
+
+This method was added in v1.84 of Math::BigInt (April 2007).
+
+=head2 bpi()
+
+	print Math::BigFloat->bpi(100), "\n";
+
+Calculate PI to N digits (including the 3 before the dot). The result is
+rounded according to the current rounding mode, which defaults to "even".
+
+This method was added in v1.87 of Math::BigInt (June 2007).
+
+=head2 bcos()
+
+	my $x = Math::BigFloat->new(1);
+	print $x->bcos(100), "\n";
+
+Calculate the cosinus of $x, modifying $x in place.
+
+This method was added in v1.87 of Math::BigInt (June 2007).
+
+=head2 bsin()
+
+	my $x = Math::BigFloat->new(1);
+	print $x->bsin(100), "\n";
+
+Calculate the sinus of $x, modifying $x in place.
+
+This method was added in v1.87 of Math::BigInt (June 2007).
+
+=head2 batan2()
+
+	my $y = Math::BigFloat->new(2);
+	my $x = Math::BigFloat->new(3);
+	print $y->batan2($x), "\n";
+
+Calculate the arcus tanges of C<$y> divided by C<$x>, modifying $y in place.
+See also L<batan()>.
+
+This method was added in v1.87 of Math::BigInt (June 2007).
+
+=head2 batan()
+
+	my $x = Math::BigFloat->new(1);
+	print $x->batan(100), "\n";
+
+Calculate the arcus tanges of $x, modifying $x in place. See also L<batan2()>.
+
+This method was added in v1.87 of Math::BigInt (June 2007).
+
+=head2 bmuladd()
+
+	$x->bmuladd($y,$z);		
+
+Multiply $x by $y, and then add $z to the result.
+
+This method was added in v1.87 of Math::BigInt (June 2007).
+
+=head1 Autocreating constants
+
+After C<use Math::BigFloat ':constant'> all the floating point constants
+in the given scope are converted to C<Math::BigFloat>. This conversion
+happens at compile time.
+
+In particular
+
+  perl -MMath::BigFloat=:constant -e 'print 2E-100,"\n"'
+
+prints the value of C<2E-100>. Note that without conversion of 
+constants the expression 2E-100 will be calculated as normal floating point 
+number.
+
+Please note that ':constant' does not affect integer constants, nor binary 
+nor hexadecimal constants. Use L<bignum> or L<Math::BigInt> to get this to
+work.
+
+=head2 Math library
+
+Math with the numbers is done (by default) by a module called
+Math::BigInt::Calc. This is equivalent to saying:
+
+	use Math::BigFloat lib => 'Calc';
+
+You can change this by using:
+
+	use Math::BigFloat lib => 'GMP';
+
+B<Note>: General purpose packages should not be explicit about the library
+to use; let the script author decide which is best.
+
+Note: The keyword 'lib' will warn when the requested library could not be
+loaded. To suppress the warning use 'try' instead:
+
+	use Math::BigFloat try => 'GMP';
+
+If your script works with huge numbers and Calc is too slow for them,
+you can also for the loading of one of these libraries and if none
+of them can be used, the code will die:
+
+        use Math::BigFloat only => 'GMP,Pari';
+
+The following would first try to find Math::BigInt::Foo, then
+Math::BigInt::Bar, and when this also fails, revert to Math::BigInt::Calc:
+
+	use Math::BigFloat lib => 'Foo,Math::BigInt::Bar';
+
+See the respective low-level library documentation for further details.
+
+Please note that Math::BigFloat does B<not> use the denoted library itself,
+but it merely passes the lib argument to Math::BigInt. So, instead of the need
+to do:
+
+	use Math::BigInt lib => 'GMP';
+	use Math::BigFloat;
+
+you can roll it all into one line:
+
+	use Math::BigFloat lib => 'GMP';
+
+It is also possible to just require Math::BigFloat:
+
+	require Math::BigFloat;
+
+This will load the necessary things (like BigInt) when they are needed, and
+automatically.
+
+See L<Math::BigInt> for more details than you ever wanted to know about using
+a different low-level library.
+
+=head2 Using Math::BigInt::Lite
+
+For backwards compatibility reasons it is still possible to
+request a different storage class for use with Math::BigFloat:
+
+        use Math::BigFloat with => 'Math::BigInt::Lite';
+
+However, this request is ignored, as the current code now uses the low-level
+math libary for directly storing the number parts.
+
+=head1 EXPORTS
+
+C<Math::BigFloat> exports nothing by default, but can export the C<bpi()> method:
+
+	use Math::BigFloat qw/bpi/;
+
+	print bpi(10), "\n";
+
+=head1 BUGS
+
+Please see the file BUGS in the CPAN distribution Math::BigInt for known bugs.
+
+=head1 CAVEATS
+
+Do not try to be clever to insert some operations in between switching
+libraries:
+
+	require Math::BigFloat;
+	my $matter = Math::BigFloat->bone() + 4;	# load BigInt and Calc
+	Math::BigFloat->import( lib => 'Pari' );	# load Pari, too
+	my $anti_matter = Math::BigFloat->bone()+4;	# now use Pari
+
+This will create objects with numbers stored in two different backend libraries,
+and B<VERY BAD THINGS> will happen when you use these together:
+
+	my $flash_and_bang = $matter + $anti_matter;	# Don't do this!
+
+=over 1
+
+=item stringify, bstr()
+
+Both stringify and bstr() now drop the leading '+'. The old code would return
+'+1.23', the new returns '1.23'. See the documentation in L<Math::BigInt> for
+reasoning and details.
+
+=item bdiv
+
+The following will probably not print what you expect:
+
+	print $c->bdiv(123.456),"\n";
+
+It prints both quotient and reminder since print works in list context. Also,
+bdiv() will modify $c, so be careful. You probably want to use
+	
+	print $c / 123.456,"\n";
+	print scalar $c->bdiv(123.456),"\n";  # or if you want to modify $c
+
+instead.
+
+=item brsft
+
+The following will probably not print what you expect:
+
+	my $c = Math::BigFloat->new('3.14159');
+        print $c->brsft(3,10),"\n";	# prints 0.00314153.1415
+
+It prints both quotient and remainder, since print calls C<brsft()> in list
+context. Also, C<< $c->brsft() >> will modify $c, so be careful.
+You probably want to use
+
+	print scalar $c->copy()->brsft(3,10),"\n";
+	# or if you really want to modify $c
+        print scalar $c->brsft(3,10),"\n";
+
+instead.
+
+=item Modifying and =
+
+Beware of:
+
+	$x = Math::BigFloat->new(5);
+	$y = $x;
+
+It will not do what you think, e.g. making a copy of $x. Instead it just makes
+a second reference to the B<same> object and stores it in $y. Thus anything
+that modifies $x will modify $y (except overloaded math operators), and vice
+versa. See L<Math::BigInt> for details and how to avoid that.
+
+=item bpow
+
+C<bpow()> now modifies the first argument, unlike the old code which left
+it alone and only returned the result. This is to be consistent with
+C<badd()> etc. The first will modify $x, the second one won't:
+
+	print bpow($x,$i),"\n"; 	# modify $x
+	print $x->bpow($i),"\n"; 	# ditto
+	print $x ** $i,"\n";		# leave $x alone 
+
+=item precision() vs. accuracy()
+
+A common pitfall is to use L<precision()> when you want to round a result to
+a certain number of digits:
+
+	use Math::BigFloat;
+
+	Math::BigFloat->precision(4);		# does not do what you think it does
+	my $x = Math::BigFloat->new(12345);	# rounds $x to "12000"!
+	print "$x\n";				# print "12000"
+	my $y = Math::BigFloat->new(3);		# rounds $y to "0"!
+	print "$y\n";				# print "0"
+	$z = $x / $y;				# 12000 / 0 => NaN!
+	print "$z\n";
+	print $z->precision(),"\n";		# 4
+
+Replacing L<precision> with L<accuracy> is probably not what you want, either:
+
+	use Math::BigFloat;
+
+	Math::BigFloat->accuracy(4);		# enables global rounding:
+	my $x = Math::BigFloat->new(123456);	# rounded immediately to "12350"
+	print "$x\n";				# print "123500"
+	my $y = Math::BigFloat->new(3);		# rounded to "3
+	print "$y\n";				# print "3"
+	print $z = $x->copy()->bdiv($y),"\n";	# 41170
+	print $z->accuracy(),"\n";		# 4
+
+What you want to use instead is:
+
+	use Math::BigFloat;
+
+	my $x = Math::BigFloat->new(123456);	# no rounding
+	print "$x\n";				# print "123456"
+	my $y = Math::BigFloat->new(3);		# no rounding
+	print "$y\n";				# print "3"
+	print $z = $x->copy()->bdiv($y,4),"\n";	# 41150
+	print $z->accuracy(),"\n";		# undef
+
+In addition to computing what you expected, the last example also does B<not>
+"taint" the result with an accuracy or precision setting, which would
+influence any further operation.
+
+=back
+
+=head1 SEE ALSO
+
+L<Math::BigInt>, L<Math::BigRat> and L<Math::Big> as well as
+L<Math::BigInt::BitVect>, L<Math::BigInt::Pari> and  L<Math::BigInt::GMP>.
+
+The pragmas L<bignum>, L<bigint> and L<bigrat> might also be of interest
+because they solve the autoupgrading/downgrading issue, at least partly.
+
+The package at L<http://search.cpan.org/~tels/Math-BigInt> contains
+more documentation including a full version history, testcases, empty
+subclass files and benchmarks.
+
+=head1 LICENSE
+
+This program is free software; you may redistribute it and/or modify it under
+the same terms as Perl itself.
+
+=head1 AUTHORS
+
+Mark Biggar, overloaded interface by Ilya Zakharevich.
+Completely rewritten by Tels L<http://bloodgate.com> in 2001 - 2006, and still
+at it in 2007.
+
+=cut
diff --git a/dist/Math-BigInt/lib/Math/BigInt.pm b/dist/Math-BigInt/lib/Math/BigInt.pm
new file mode 100644
index 0000000000..9f1f983ae3
--- /dev/null
+++ b/dist/Math-BigInt/lib/Math/BigInt.pm
@@ -0,0 +1,5115 @@
+package Math::BigInt;
+
+#
+# "Mike had an infinite amount to do and a negative amount of time in which
+# to do it." - Before and After
+#
+
+# The following hash values are used:
+#   value: unsigned int with actual value (as a Math::BigInt::Calc or similiar)
+#   sign : +,-,NaN,+inf,-inf
+#   _a   : accuracy
+#   _p   : precision
+#   _f   : flags, used by MBF to flag parts of a float as untouchable
+
+# Remember not to take shortcuts ala $xs = $x->{value}; $CALC->foo($xs); since
+# underlying lib might change the reference!
+
+my $class = "Math::BigInt";
+use 5.006;
+
+$VERSION = '1.89_01';
+
+@ISA = qw(Exporter);
+@EXPORT_OK = qw(objectify bgcd blcm); 
+
+# _trap_inf and _trap_nan are internal and should never be accessed from the
+# outside
+use vars qw/$round_mode $accuracy $precision $div_scale $rnd_mode 
+	    $upgrade $downgrade $_trap_nan $_trap_inf/;
+use strict;
+
+# Inside overload, the first arg is always an object. If the original code had
+# it reversed (like $x = 2 * $y), then the third paramater is true.
+# In some cases (like add, $x = $x + 2 is the same as $x = 2 + $x) this makes
+# no difference, but in some cases it does.
+
+# For overloaded ops with only one argument we simple use $_[0]->copy() to
+# preserve the argument.
+
+# Thus inheritance of overload operators becomes possible and transparent for
+# our subclasses without the need to repeat the entire overload section there.
+
+use overload
+'='     =>      sub { $_[0]->copy(); },
+
+# some shortcuts for speed (assumes that reversed order of arguments is routed
+# to normal '+' and we thus can always modify first arg. If this is changed,
+# this breaks and must be adjusted.)
+'+='	=>	sub { $_[0]->badd($_[1]); },
+'-='	=>	sub { $_[0]->bsub($_[1]); },
+'*='	=>	sub { $_[0]->bmul($_[1]); },
+'/='	=>	sub { scalar $_[0]->bdiv($_[1]); },
+'%='	=>	sub { $_[0]->bmod($_[1]); },
+'^='	=>	sub { $_[0]->bxor($_[1]); },
+'&='	=>	sub { $_[0]->band($_[1]); },
+'|='	=>	sub { $_[0]->bior($_[1]); },
+
+'**='	=>	sub { $_[0]->bpow($_[1]); },
+'<<='	=>	sub { $_[0]->blsft($_[1]); },
+'>>='	=>	sub { $_[0]->brsft($_[1]); },
+
+# not supported by Perl yet
+'..'	=>	\&_pointpoint,
+
+'<=>'	=>	sub { my $rc = $_[2] ?
+                      ref($_[0])->bcmp($_[1],$_[0]) : 
+                      $_[0]->bcmp($_[1]); 
+		      $rc = 1 unless defined $rc;
+		      $rc <=> 0;
+		},
+# we need '>=' to get things like "1 >= NaN" right:
+'>='	=>	sub { my $rc = $_[2] ?
+                      ref($_[0])->bcmp($_[1],$_[0]) : 
+                      $_[0]->bcmp($_[1]);
+		      # if there was a NaN involved, return false
+		      return '' unless defined $rc;
+		      $rc >= 0;
+		},
+'cmp'	=>	sub {
+         $_[2] ? 
+               "$_[1]" cmp $_[0]->bstr() :
+               $_[0]->bstr() cmp "$_[1]" },
+
+'cos'	=>	sub { $_[0]->copy->bcos(); }, 
+'sin'	=>	sub { $_[0]->copy->bsin(); }, 
+'atan2'	=>	sub { $_[2] ?
+			ref($_[0])->new($_[1])->batan2($_[0]) :
+			$_[0]->copy()->batan2($_[1]) },
+
+# are not yet overloadable
+#'hex'	=>	sub { print "hex"; $_[0]; }, 
+#'oct'	=>	sub { print "oct"; $_[0]; }, 
+
+# log(N) is log(N, e), where e is Euler's number
+'log'	=>	sub { $_[0]->copy()->blog($_[1], undef); }, 
+'exp'	=>	sub { $_[0]->copy()->bexp($_[1]); }, 
+'int'	=>	sub { $_[0]->copy(); }, 
+'neg'	=>	sub { $_[0]->copy()->bneg(); }, 
+'abs'	=>	sub { $_[0]->copy()->babs(); },
+'sqrt'  =>	sub { $_[0]->copy()->bsqrt(); },
+'~'	=>	sub { $_[0]->copy()->bnot(); },
+
+# for subtract it's a bit tricky to not modify b: b-a => -a+b
+'-'	=>	sub { my $c = $_[0]->copy; $_[2] ?
+			$c->bneg()->badd( $_[1]) :
+			$c->bsub( $_[1]) },
+'+'	=>	sub { $_[0]->copy()->badd($_[1]); },
+'*'	=>	sub { $_[0]->copy()->bmul($_[1]); },
+
+'/'	=>	sub { 
+   $_[2] ? ref($_[0])->new($_[1])->bdiv($_[0]) : $_[0]->copy->bdiv($_[1]);
+  }, 
+'%'	=>	sub { 
+   $_[2] ? ref($_[0])->new($_[1])->bmod($_[0]) : $_[0]->copy->bmod($_[1]);
+  }, 
+'**'	=>	sub { 
+   $_[2] ? ref($_[0])->new($_[1])->bpow($_[0]) : $_[0]->copy->bpow($_[1]);
+  }, 
+'<<'	=>	sub { 
+   $_[2] ? ref($_[0])->new($_[1])->blsft($_[0]) : $_[0]->copy->blsft($_[1]);
+  }, 
+'>>'	=>	sub { 
+   $_[2] ? ref($_[0])->new($_[1])->brsft($_[0]) : $_[0]->copy->brsft($_[1]);
+  }, 
+'&'	=>	sub { 
+   $_[2] ? ref($_[0])->new($_[1])->band($_[0]) : $_[0]->copy->band($_[1]);
+  }, 
+'|'	=>	sub { 
+   $_[2] ? ref($_[0])->new($_[1])->bior($_[0]) : $_[0]->copy->bior($_[1]);
+  }, 
+'^'	=>	sub { 
+   $_[2] ? ref($_[0])->new($_[1])->bxor($_[0]) : $_[0]->copy->bxor($_[1]);
+  }, 
+
+# can modify arg of ++ and --, so avoid a copy() for speed, but don't
+# use $_[0]->bone(), it would modify $_[0] to be 1!
+'++'	=>	sub { $_[0]->binc() },
+'--'	=>	sub { $_[0]->bdec() },
+
+# if overloaded, O(1) instead of O(N) and twice as fast for small numbers
+'bool'  =>	sub {
+  # this kludge is needed for perl prior 5.6.0 since returning 0 here fails :-/
+  # v5.6.1 dumps on this: return !$_[0]->is_zero() || undef;		    :-(
+  my $t = undef;
+  $t = 1 if !$_[0]->is_zero();
+  $t;
+  },
+
+# the original qw() does not work with the TIESCALAR below, why?
+# Order of arguments unsignificant
+'""' => sub { $_[0]->bstr(); },
+'0+' => sub { $_[0]->numify(); }
+;
+
+##############################################################################
+# global constants, flags and accessory
+
+# These vars are public, but their direct usage is not recommended, use the
+# accessor methods instead
+
+$round_mode = 'even'; # one of 'even', 'odd', '+inf', '-inf', 'zero', 'trunc' or 'common'
+$accuracy   = undef;
+$precision  = undef;
+$div_scale  = 40;
+
+$upgrade = undef;			# default is no upgrade
+$downgrade = undef;			# default is no downgrade
+
+# These are internally, and not to be used from the outside at all
+
+$_trap_nan = 0;				# are NaNs ok? set w/ config()
+$_trap_inf = 0;				# are infs ok? set w/ config()
+my $nan = 'NaN'; 			# constants for easier life
+
+my $CALC = 'Math::BigInt::FastCalc';	# module to do the low level math
+					# default is FastCalc.pm
+my $IMPORT = 0;				# was import() called yet?
+					# used to make require work
+my %WARN;				# warn only once for low-level libs
+my %CAN;				# cache for $CALC->can(...)
+my %CALLBACKS;				# callbacks to notify on lib loads
+my $EMU_LIB = 'Math/BigInt/CalcEmu.pm';	# emulate low-level math
+
+##############################################################################
+# the old code had $rnd_mode, so we need to support it, too
+
+$rnd_mode   = 'even';
+sub TIESCALAR  { my ($class) = @_; bless \$round_mode, $class; }
+sub FETCH      { return $round_mode; }
+sub STORE      { $rnd_mode = $_[0]->round_mode($_[1]); }
+
+BEGIN
+  { 
+  # tie to enable $rnd_mode to work transparently
+  tie $rnd_mode, 'Math::BigInt'; 
+
+  # set up some handy alias names
+  *as_int = \&as_number;
+  *is_pos = \&is_positive;
+  *is_neg = \&is_negative;
+  }
+
+############################################################################## 
+
+sub round_mode
+  {
+  no strict 'refs';
+  # make Class->round_mode() work
+  my $self = shift;
+  my $class = ref($self) || $self || __PACKAGE__;
+  if (defined $_[0])
+    {
+    my $m = shift;
+    if ($m !~ /^(even|odd|\+inf|\-inf|zero|trunc|common)$/)
+      {
+      require Carp; Carp::croak ("Unknown round mode '$m'");
+      }
+    return ${"${class}::round_mode"} = $m;
+    }
+  ${"${class}::round_mode"};
+  }
+
+sub upgrade
+  {
+  no strict 'refs';
+  # make Class->upgrade() work
+  my $self = shift;
+  my $class = ref($self) || $self || __PACKAGE__;
+  # need to set new value?
+  if (@_ > 0)
+    {
+    return ${"${class}::upgrade"} = $_[0];
+    }
+  ${"${class}::upgrade"};
+  }
+
+sub downgrade
+  {
+  no strict 'refs';
+  # make Class->downgrade() work
+  my $self = shift;
+  my $class = ref($self) || $self || __PACKAGE__;
+  # need to set new value?
+  if (@_ > 0)
+    {
+    return ${"${class}::downgrade"} = $_[0];
+    }
+  ${"${class}::downgrade"};
+  }
+
+sub div_scale
+  {
+  no strict 'refs';
+  # make Class->div_scale() work
+  my $self = shift;
+  my $class = ref($self) || $self || __PACKAGE__;
+  if (defined $_[0])
+    {
+    if ($_[0] < 0)
+      {
+      require Carp; Carp::croak ('div_scale must be greater than zero');
+      }
+    ${"${class}::div_scale"} = $_[0];
+    }
+  ${"${class}::div_scale"};
+  }
+
+sub accuracy
+  {
+  # $x->accuracy($a);		ref($x)	$a
+  # $x->accuracy();		ref($x)
+  # Class->accuracy();		class
+  # Class->accuracy($a);	class $a
+
+  my $x = shift;
+  my $class = ref($x) || $x || __PACKAGE__;
+
+  no strict 'refs';
+  # need to set new value?
+  if (@_ > 0)
+    {
+    my $a = shift;
+    # convert objects to scalars to avoid deep recursion. If object doesn't
+    # have numify(), then hopefully it will have overloading for int() and
+    # boolean test without wandering into a deep recursion path...
+    $a = $a->numify() if ref($a) && $a->can('numify');
+
+    if (defined $a)
+      {
+      # also croak on non-numerical
+      if (!$a || $a <= 0)
+        {
+        require Carp;
+	Carp::croak ('Argument to accuracy must be greater than zero');
+        }
+      if (int($a) != $a)
+        {
+        require Carp;
+	Carp::croak ('Argument to accuracy must be an integer');
+        }
+      }
+    if (ref($x))
+      {
+      # $object->accuracy() or fallback to global
+      $x->bround($a) if $a;		# not for undef, 0
+      $x->{_a} = $a;			# set/overwrite, even if not rounded
+      delete $x->{_p};			# clear P
+      $a = ${"${class}::accuracy"} unless defined $a;   # proper return value
+      }
+    else
+      {
+      ${"${class}::accuracy"} = $a;	# set global A
+      ${"${class}::precision"} = undef;	# clear global P
+      }
+    return $a;				# shortcut
+    }
+
+  my $a;
+  # $object->accuracy() or fallback to global
+  $a = $x->{_a} if ref($x);
+  # but don't return global undef, when $x's accuracy is 0!
+  $a = ${"${class}::accuracy"} if !defined $a;
+  $a;
+  }
+
+sub precision
+  {
+  # $x->precision($p);		ref($x)	$p
+  # $x->precision();		ref($x)
+  # Class->precision();		class
+  # Class->precision($p);	class $p
+
+  my $x = shift;
+  my $class = ref($x) || $x || __PACKAGE__;
+
+  no strict 'refs';
+  if (@_ > 0)
+    {
+    my $p = shift;
+    # convert objects to scalars to avoid deep recursion. If object doesn't
+    # have numify(), then hopefully it will have overloading for int() and
+    # boolean test without wandering into a deep recursion path...
+    $p = $p->numify() if ref($p) && $p->can('numify');
+    if ((defined $p) && (int($p) != $p))
+      {
+      require Carp; Carp::croak ('Argument to precision must be an integer');
+      }
+    if (ref($x))
+      {
+      # $object->precision() or fallback to global
+      $x->bfround($p) if $p;		# not for undef, 0
+      $x->{_p} = $p;			# set/overwrite, even if not rounded
+      delete $x->{_a};			# clear A
+      $p = ${"${class}::precision"} unless defined $p;  # proper return value
+      }
+    else
+      {
+      ${"${class}::precision"} = $p;	# set global P
+      ${"${class}::accuracy"} = undef;	# clear global A
+      }
+    return $p;				# shortcut
+    }
+
+  my $p;
+  # $object->precision() or fallback to global
+  $p = $x->{_p} if ref($x);
+  # but don't return global undef, when $x's precision is 0!
+  $p = ${"${class}::precision"} if !defined $p;
+  $p;
+  }
+
+sub config
+  {
+  # return (or set) configuration data as hash ref
+  my $class = shift || 'Math::BigInt';
+
+  no strict 'refs';
+  if (@_ > 1 || (@_ == 1 && (ref($_[0]) eq 'HASH')))
+    {
+    # try to set given options as arguments from hash
+
+    my $args = $_[0];
+    if (ref($args) ne 'HASH')
+      {
+      $args = { @_ };
+      }
+    # these values can be "set"
+    my $set_args = {};
+    foreach my $key (
+     qw/trap_inf trap_nan
+        upgrade downgrade precision accuracy round_mode div_scale/
+     )
+      {
+      $set_args->{$key} = $args->{$key} if exists $args->{$key};
+      delete $args->{$key};
+      }
+    if (keys %$args > 0)
+      {
+      require Carp;
+      Carp::croak ("Illegal key(s) '",
+       join("','",keys %$args),"' passed to $class\->config()");
+      }
+    foreach my $key (keys %$set_args)
+      {
+      if ($key =~ /^trap_(inf|nan)\z/)
+        {
+        ${"${class}::_trap_$1"} = ($set_args->{"trap_$1"} ? 1 : 0);
+        next;
+        }
+      # use a call instead of just setting the $variable to check argument
+      $class->$key($set_args->{$key});
+      }
+    }
+
+  # now return actual configuration
+
+  my $cfg = {
+    lib => $CALC,
+    lib_version => ${"${CALC}::VERSION"},
+    class => $class,
+    trap_nan => ${"${class}::_trap_nan"},
+    trap_inf => ${"${class}::_trap_inf"},
+    version => ${"${class}::VERSION"},
+    };
+  foreach my $key (qw/
+     upgrade downgrade precision accuracy round_mode div_scale
+     /)
+    {
+    $cfg->{$key} = ${"${class}::$key"};
+    };
+  if (@_ == 1 && (ref($_[0]) ne 'HASH'))
+    {
+    # calls of the style config('lib') return just this value
+    return $cfg->{$_[0]};
+    }
+  $cfg;
+  }
+
+sub _scale_a
+  { 
+  # select accuracy parameter based on precedence,
+  # used by bround() and bfround(), may return undef for scale (means no op)
+  my ($x,$scale,$mode) = @_;
+
+  $scale = $x->{_a} unless defined $scale;
+
+  no strict 'refs';
+  my $class = ref($x);
+
+  $scale = ${ $class . '::accuracy' } unless defined $scale;
+  $mode = ${ $class . '::round_mode' } unless defined $mode;
+
+  if (defined $scale)
+    {
+    $scale = $scale->can('numify') ? $scale->numify() : "$scale" if ref($scale);
+    $scale = int($scale);
+    }
+
+  ($scale,$mode);
+  }
+
+sub _scale_p
+  { 
+  # select precision parameter based on precedence,
+  # used by bround() and bfround(), may return undef for scale (means no op)
+  my ($x,$scale,$mode) = @_;
+  
+  $scale = $x->{_p} unless defined $scale;
+
+  no strict 'refs';
+  my $class = ref($x);
+
+  $scale = ${ $class . '::precision' } unless defined $scale;
+  $mode = ${ $class . '::round_mode' } unless defined $mode;
+
+  if (defined $scale)
+    {
+    $scale = $scale->can('numify') ? $scale->numify() : "$scale" if ref($scale);
+    $scale = int($scale);
+    }
+
+  ($scale,$mode);
+  }
+
+##############################################################################
+# constructors
+
+sub copy
+  {
+  # if two arguments, the first one is the class to "swallow" subclasses
+  if (@_ > 1)
+    {
+    my  $self = bless {
+	sign => $_[1]->{sign}, 
+	value => $CALC->_copy($_[1]->{value}),
+    }, $_[0] if @_ > 1;
+
+    $self->{_a} = $_[1]->{_a} if defined $_[1]->{_a};
+    $self->{_p} = $_[1]->{_p} if defined $_[1]->{_p};
+    return $self;
+    }
+
+  my $self = bless {
+	sign => $_[0]->{sign}, 
+	value => $CALC->_copy($_[0]->{value}),
+	}, ref($_[0]);
+
+  $self->{_a} = $_[0]->{_a} if defined $_[0]->{_a};
+  $self->{_p} = $_[0]->{_p} if defined $_[0]->{_p};
+  $self;
+  }
+
+sub new 
+  {
+  # create a new BigInt object from a string or another BigInt object. 
+  # see hash keys documented at top
+
+  # the argument could be an object, so avoid ||, && etc on it, this would
+  # cause costly overloaded code to be called. The only allowed ops are
+  # ref() and defined.
+
+  my ($class,$wanted,$a,$p,$r) = @_;
+ 
+  # avoid numify-calls by not using || on $wanted!
+  return $class->bzero($a,$p) if !defined $wanted;	# default to 0
+  return $class->copy($wanted,$a,$p,$r)
+   if ref($wanted) && $wanted->isa($class);		# MBI or subclass
+
+  $class->import() if $IMPORT == 0;		# make require work
+  
+  my $self = bless {}, $class;
+
+  # shortcut for "normal" numbers
+  if ((!ref $wanted) && ($wanted =~ /^([+-]?)[1-9][0-9]*\z/))
+    {
+    $self->{sign} = $1 || '+';
+
+    if ($wanted =~ /^[+-]/)
+     {
+      # remove sign without touching wanted to make it work with constants
+      my $t = $wanted; $t =~ s/^[+-]//;
+      $self->{value} = $CALC->_new($t);
+      }
+    else
+      {
+      $self->{value} = $CALC->_new($wanted);
+      }
+    no strict 'refs';
+    if ( (defined $a) || (defined $p) 
+        || (defined ${"${class}::precision"})
+        || (defined ${"${class}::accuracy"}) 
+       )
+      {
+      $self->round($a,$p,$r) unless (@_ == 4 && !defined $a && !defined $p);
+      }
+    return $self;
+    }
+
+  # handle '+inf', '-inf' first
+  if ($wanted =~ /^[+-]?inf\z/)
+    {
+    $self->{sign} = $wanted;		# set a default sign for bstr()
+    return $self->binf($wanted);
+    }
+  # split str in m mantissa, e exponent, i integer, f fraction, v value, s sign
+  my ($mis,$miv,$mfv,$es,$ev) = _split($wanted);
+  if (!ref $mis)
+    {
+    if ($_trap_nan)
+      {
+      require Carp; Carp::croak("$wanted is not a number in $class");
+      }
+    $self->{value} = $CALC->_zero();
+    $self->{sign} = $nan;
+    return $self;
+    }
+  if (!ref $miv)
+    {
+    # _from_hex or _from_bin
+    $self->{value} = $mis->{value};
+    $self->{sign} = $mis->{sign};
+    return $self;	# throw away $mis
+    }
+  # make integer from mantissa by adjusting exp, then convert to bigint
+  $self->{sign} = $$mis;			# store sign
+  $self->{value} = $CALC->_zero();		# for all the NaN cases
+  my $e = int("$$es$$ev");			# exponent (avoid recursion)
+  if ($e > 0)
+    {
+    my $diff = $e - CORE::length($$mfv);
+    if ($diff < 0)				# Not integer
+      {
+      if ($_trap_nan)
+        {
+        require Carp; Carp::croak("$wanted not an integer in $class");
+        }
+      #print "NOI 1\n";
+      return $upgrade->new($wanted,$a,$p,$r) if defined $upgrade;
+      $self->{sign} = $nan;
+      }
+    else					# diff >= 0
+      {
+      # adjust fraction and add it to value
+      #print "diff > 0 $$miv\n";
+      $$miv = $$miv . ($$mfv . '0' x $diff);
+      }
+    }
+  else
+    {
+    if ($$mfv ne '')				# e <= 0
+      {
+      # fraction and negative/zero E => NOI
+      if ($_trap_nan)
+        {
+        require Carp; Carp::croak("$wanted not an integer in $class");
+        }
+      #print "NOI 2 \$\$mfv '$$mfv'\n";
+      return $upgrade->new($wanted,$a,$p,$r) if defined $upgrade;
+      $self->{sign} = $nan;
+      }
+    elsif ($e < 0)
+      {
+      # xE-y, and empty mfv
+      #print "xE-y\n";
+      $e = abs($e);
+      if ($$miv !~ s/0{$e}$//)		# can strip so many zero's?
+        {
+        if ($_trap_nan)
+          {
+          require Carp; Carp::croak("$wanted not an integer in $class");
+          }
+        #print "NOI 3\n";
+        return $upgrade->new($wanted,$a,$p,$r) if defined $upgrade;
+        $self->{sign} = $nan;
+        }
+      }
+    }
+  $self->{sign} = '+' if $$miv eq '0';			# normalize -0 => +0
+  $self->{value} = $CALC->_new($$miv) if $self->{sign} =~ /^[+-]$/;
+  # if any of the globals is set, use them to round and store them inside $self
+  # do not round for new($x,undef,undef) since that is used by MBF to signal
+  # no rounding
+  $self->round($a,$p,$r) unless @_ == 4 && !defined $a && !defined $p;
+  $self;
+  }
+
+sub bnan
+  {
+  # create a bigint 'NaN', if given a BigInt, set it to 'NaN'
+  my $self = shift;
+  $self = $class if !defined $self;
+  if (!ref($self))
+    {
+    my $c = $self; $self = {}; bless $self, $c;
+    }
+  no strict 'refs';
+  if (${"${class}::_trap_nan"})
+    {
+    require Carp;
+    Carp::croak ("Tried to set $self to NaN in $class\::bnan()");
+    }
+  $self->import() if $IMPORT == 0;		# make require work
+  return if $self->modify('bnan');
+  if ($self->can('_bnan'))
+    {
+    # use subclass to initialize
+    $self->_bnan();
+    }
+  else
+    {
+    # otherwise do our own thing
+    $self->{value} = $CALC->_zero();
+    }
+  $self->{sign} = $nan;
+  delete $self->{_a}; delete $self->{_p};	# rounding NaN is silly
+  $self;
+  }
+
+sub binf
+  {
+  # create a bigint '+-inf', if given a BigInt, set it to '+-inf'
+  # the sign is either '+', or if given, used from there
+  my $self = shift;
+  my $sign = shift; $sign = '+' if !defined $sign || $sign !~ /^-(inf)?$/;
+  $self = $class if !defined $self;
+  if (!ref($self))
+    {
+    my $c = $self; $self = {}; bless $self, $c;
+    }
+  no strict 'refs';
+  if (${"${class}::_trap_inf"})
+    {
+    require Carp;
+    Carp::croak ("Tried to set $self to +-inf in $class\::binf()");
+    }
+  $self->import() if $IMPORT == 0;		# make require work
+  return if $self->modify('binf');
+  if ($self->can('_binf'))
+    {
+    # use subclass to initialize
+    $self->_binf();
+    }
+  else
+    {
+    # otherwise do our own thing
+    $self->{value} = $CALC->_zero();
+    }
+  $sign = $sign . 'inf' if $sign !~ /inf$/;	# - => -inf
+  $self->{sign} = $sign;
+  ($self->{_a},$self->{_p}) = @_;		# take over requested rounding
+  $self;
+  }
+
+sub bzero
+  {
+  # create a bigint '+0', if given a BigInt, set it to 0
+  my $self = shift;
+  $self = __PACKAGE__ if !defined $self;
+ 
+  if (!ref($self))
+    {
+    my $c = $self; $self = {}; bless $self, $c;
+    }
+  $self->import() if $IMPORT == 0;		# make require work
+  return if $self->modify('bzero');
+  
+  if ($self->can('_bzero'))
+    {
+    # use subclass to initialize
+    $self->_bzero();
+    }
+  else
+    {
+    # otherwise do our own thing
+    $self->{value} = $CALC->_zero();
+    }
+  $self->{sign} = '+';
+  if (@_ > 0)
+    {
+    if (@_ > 3)
+      {
+      # call like: $x->bzero($a,$p,$r,$y);
+      ($self,$self->{_a},$self->{_p}) = $self->_find_round_parameters(@_);
+      }
+    else
+      {
+      $self->{_a} = $_[0]
+       if ( (!defined $self->{_a}) || (defined $_[0] && $_[0] > $self->{_a}));
+      $self->{_p} = $_[1]
+       if ( (!defined $self->{_p}) || (defined $_[1] && $_[1] > $self->{_p}));
+      }
+    }
+  $self;
+  }
+
+sub bone
+  {
+  # create a bigint '+1' (or -1 if given sign '-'),
+  # if given a BigInt, set it to +1 or -1, respectively
+  my $self = shift;
+  my $sign = shift; $sign = '+' if !defined $sign || $sign ne '-';
+  $self = $class if !defined $self;
+
+  if (!ref($self))
+    {
+    my $c = $self; $self = {}; bless $self, $c;
+    }
+  $self->import() if $IMPORT == 0;		# make require work
+  return if $self->modify('bone');
+
+  if ($self->can('_bone'))
+    {
+    # use subclass to initialize
+    $self->_bone();
+    }
+  else
+    {
+    # otherwise do our own thing
+    $self->{value} = $CALC->_one();
+    }
+  $self->{sign} = $sign;
+  if (@_ > 0)
+    {
+    if (@_ > 3)
+      {
+      # call like: $x->bone($sign,$a,$p,$r,$y);
+      ($self,$self->{_a},$self->{_p}) = $self->_find_round_parameters(@_);
+      }
+    else
+      {
+      # call like: $x->bone($sign,$a,$p,$r);
+      $self->{_a} = $_[0]
+       if ( (!defined $self->{_a}) || (defined $_[0] && $_[0] > $self->{_a}));
+      $self->{_p} = $_[1]
+       if ( (!defined $self->{_p}) || (defined $_[1] && $_[1] > $self->{_p}));
+      }
+    }
+  $self;
+  }
+
+##############################################################################
+# string conversation
+
+sub bsstr
+  {
+  # (ref to BFLOAT or num_str ) return num_str
+  # Convert number from internal format to scientific string format.
+  # internal format is always normalized (no leading zeros, "-0E0" => "+0E0")
+  my ($self,$x) = ref($_[0]) ? (undef,$_[0]) : objectify(1,@_); 
+
+  if ($x->{sign} !~ /^[+-]$/)
+    {
+    return $x->{sign} unless $x->{sign} eq '+inf';	# -inf, NaN
+    return 'inf';					# +inf
+    }
+  my ($m,$e) = $x->parts();
+  #$m->bstr() . 'e+' . $e->bstr(); 	# e can only be positive in BigInt
+  # 'e+' because E can only be positive in BigInt
+  $m->bstr() . 'e+' . $CALC->_str($e->{value}); 
+  }
+
+sub bstr 
+  {
+  # make a string from bigint object
+  my ($self,$x) = ref($_[0]) ? (undef,$_[0]) : objectify(1,@_); 
+
+  if ($x->{sign} !~ /^[+-]$/)
+    {
+    return $x->{sign} unless $x->{sign} eq '+inf';	# -inf, NaN
+    return 'inf';					# +inf
+    }
+  my $es = ''; $es = $x->{sign} if $x->{sign} eq '-';
+  $es.$CALC->_str($x->{value});
+  }
+
+sub numify 
+  {
+  # Make a "normal" scalar from a BigInt object
+  my $x = shift; $x = $class->new($x) unless ref $x;
+
+  return $x->bstr() if $x->{sign} !~ /^[+-]$/;
+  my $num = $CALC->_num($x->{value});
+  return -$num if $x->{sign} eq '-';
+  $num;
+  }
+
+##############################################################################
+# public stuff (usually prefixed with "b")
+
+sub sign
+  {
+  # return the sign of the number: +/-/-inf/+inf/NaN
+  my ($self,$x) = ref($_[0]) ? (undef,$_[0]) : objectify(1,@_); 
+  
+  $x->{sign};
+  }
+
+sub _find_round_parameters
+  {
+  # After any operation or when calling round(), the result is rounded by
+  # regarding the A & P from arguments, local parameters, or globals.
+
+  # !!!!!!! If you change this, remember to change round(), too! !!!!!!!!!!
+
+  # This procedure finds the round parameters, but it is for speed reasons
+  # duplicated in round. Otherwise, it is tested by the testsuite and used
+  # by fdiv().
+ 
+  # returns ($self) or ($self,$a,$p,$r) - sets $self to NaN of both A and P
+  # were requested/defined (locally or globally or both)
+  
+  my ($self,$a,$p,$r,@args) = @_;
+  # $a accuracy, if given by caller
+  # $p precision, if given by caller
+  # $r round_mode, if given by caller
+  # @args all 'other' arguments (0 for unary, 1 for binary ops)
+
+  my $c = ref($self);				# find out class of argument(s)
+  no strict 'refs';
+
+  # convert to normal scalar for speed and correctness in inner parts
+  $a = $a->can('numify') ? $a->numify() : "$a" if defined $a && ref($a);
+  $p = $p->can('numify') ? $p->numify() : "$p" if defined $p && ref($p);
+
+  # now pick $a or $p, but only if we have got "arguments"
+  if (!defined $a)
+    {
+    foreach ($self,@args)
+      {
+      # take the defined one, or if both defined, the one that is smaller
+      $a = $_->{_a} if (defined $_->{_a}) && (!defined $a || $_->{_a} < $a);
+      }
+    }
+  if (!defined $p)
+    {
+    # even if $a is defined, take $p, to signal error for both defined
+    foreach ($self,@args)
+      {
+      # take the defined one, or if both defined, the one that is bigger
+      # -2 > -3, and 3 > 2
+      $p = $_->{_p} if (defined $_->{_p}) && (!defined $p || $_->{_p} > $p);
+      }
+    }
+  # if still none defined, use globals (#2)
+  $a = ${"$c\::accuracy"} unless defined $a;
+  $p = ${"$c\::precision"} unless defined $p;
+
+  # A == 0 is useless, so undef it to signal no rounding
+  $a = undef if defined $a && $a == 0;
+ 
+  # no rounding today? 
+  return ($self) unless defined $a || defined $p;		# early out
+
+  # set A and set P is an fatal error
+  return ($self->bnan()) if defined $a && defined $p;		# error
+
+  $r = ${"$c\::round_mode"} unless defined $r;
+  if ($r !~ /^(even|odd|\+inf|\-inf|zero|trunc|common)$/)
+    {
+    require Carp; Carp::croak ("Unknown round mode '$r'");
+    }
+
+  $a = int($a) if defined $a;
+  $p = int($p) if defined $p;
+
+  ($self,$a,$p,$r);
+  }
+
+sub round
+  {
+  # Round $self according to given parameters, or given second argument's
+  # parameters or global defaults 
+
+  # for speed reasons, _find_round_parameters is embeded here:
+
+  my ($self,$a,$p,$r,@args) = @_;
+  # $a accuracy, if given by caller
+  # $p precision, if given by caller
+  # $r round_mode, if given by caller
+  # @args all 'other' arguments (0 for unary, 1 for binary ops)
+
+  my $c = ref($self);				# find out class of argument(s)
+  no strict 'refs';
+
+  # now pick $a or $p, but only if we have got "arguments"
+  if (!defined $a)
+    {
+    foreach ($self,@args)
+      {
+      # take the defined one, or if both defined, the one that is smaller
+      $a = $_->{_a} if (defined $_->{_a}) && (!defined $a || $_->{_a} < $a);
+      }
+    }
+  if (!defined $p)
+    {
+    # even if $a is defined, take $p, to signal error for both defined
+    foreach ($self,@args)
+      {
+      # take the defined one, or if both defined, the one that is bigger
+      # -2 > -3, and 3 > 2
+      $p = $_->{_p} if (defined $_->{_p}) && (!defined $p || $_->{_p} > $p);
+      }
+    }
+  # if still none defined, use globals (#2)
+  $a = ${"$c\::accuracy"} unless defined $a;
+  $p = ${"$c\::precision"} unless defined $p;
+ 
+  # A == 0 is useless, so undef it to signal no rounding
+  $a = undef if defined $a && $a == 0;
+  
+  # no rounding today? 
+  return $self unless defined $a || defined $p;		# early out
+
+  # set A and set P is an fatal error
+  return $self->bnan() if defined $a && defined $p;
+
+  $r = ${"$c\::round_mode"} unless defined $r;
+  if ($r !~ /^(even|odd|\+inf|\-inf|zero|trunc|common)$/)
+    {
+    require Carp; Carp::croak ("Unknown round mode '$r'");
+    }
+
+  # now round, by calling either fround or ffround:
+  if (defined $a)
+    {
+    $self->bround(int($a),$r) if !defined $self->{_a} || $self->{_a} >= $a;
+    }
+  else # both can't be undefined due to early out
+    {
+    $self->bfround(int($p),$r) if !defined $self->{_p} || $self->{_p} <= $p;
+    }
+  # bround() or bfround() already callled bnorm() if nec.
+  $self;
+  }
+
+sub bnorm
+  { 
+  # (numstr or BINT) return BINT
+  # Normalize number -- no-op here
+  my ($self,$x) = ref($_[0]) ? (undef,$_[0]) : objectify(1,@_);
+  $x;
+  }
+
+sub babs 
+  {
+  # (BINT or num_str) return BINT
+  # make number absolute, or return absolute BINT from string
+  my ($self,$x) = ref($_[0]) ? (undef,$_[0]) : objectify(1,@_);
+
+  return $x if $x->modify('babs');
+  # post-normalized abs for internal use (does nothing for NaN)
+  $x->{sign} =~ s/^-/+/;
+  $x;
+  }
+
+sub bneg 
+  { 
+  # (BINT or num_str) return BINT
+  # negate number or make a negated number from string
+  my ($self,$x) = ref($_[0]) ? (undef,$_[0]) : objectify(1,@_);
+  
+  return $x if $x->modify('bneg');
+
+  # for +0 dont negate (to have always normalized +0). Does nothing for 'NaN'
+  $x->{sign} =~ tr/+-/-+/ unless ($x->{sign} eq '+' && $CALC->_is_zero($x->{value}));
+  $x;
+  }
+
+sub bcmp 
+  {
+  # Compares 2 values.  Returns one of undef, <0, =0, >0. (suitable for sort)
+  # (BINT or num_str, BINT or num_str) return cond_code
+  
+  # set up parameters
+  my ($self,$x,$y) = (ref($_[0]),@_);
+
+  # objectify is costly, so avoid it 
+  if ((!ref($_[0])) || (ref($_[0]) ne ref($_[1])))
+    {
+    ($self,$x,$y) = objectify(2,@_);
+    }
+
+  return $upgrade->bcmp($x,$y) if defined $upgrade &&
+    ((!$x->isa($self)) || (!$y->isa($self)));
+
+  if (($x->{sign} !~ /^[+-]$/) || ($y->{sign} !~ /^[+-]$/))
+    {
+    # handle +-inf and NaN
+    return undef if (($x->{sign} eq $nan) || ($y->{sign} eq $nan));
+    return 0 if $x->{sign} eq $y->{sign} && $x->{sign} =~ /^[+-]inf$/;
+    return +1 if $x->{sign} eq '+inf';
+    return -1 if $x->{sign} eq '-inf';
+    return -1 if $y->{sign} eq '+inf';
+    return +1;
+    }
+  # check sign for speed first
+  return 1 if $x->{sign} eq '+' && $y->{sign} eq '-';	# does also 0 <=> -y
+  return -1 if $x->{sign} eq '-' && $y->{sign} eq '+';  # does also -x <=> 0 
+
+  # have same sign, so compare absolute values. Don't make tests for zero here
+  # because it's actually slower than testin in Calc (especially w/ Pari et al)
+
+  # post-normalized compare for internal use (honors signs)
+  if ($x->{sign} eq '+') 
+    {
+    # $x and $y both > 0
+    return $CALC->_acmp($x->{value},$y->{value});
+    }
+
+  # $x && $y both < 0
+  $CALC->_acmp($y->{value},$x->{value});	# swaped acmp (lib returns 0,1,-1)
+  }
+
+sub bacmp 
+  {
+  # Compares 2 values, ignoring their signs. 
+  # Returns one of undef, <0, =0, >0. (suitable for sort)
+  # (BINT, BINT) return cond_code
+  
+  # set up parameters
+  my ($self,$x,$y) = (ref($_[0]),@_);
+  # objectify is costly, so avoid it 
+  if ((!ref($_[0])) || (ref($_[0]) ne ref($_[1])))
+    {
+    ($self,$x,$y) = objectify(2,@_);
+    }
+
+  return $upgrade->bacmp($x,$y) if defined $upgrade &&
+    ((!$x->isa($self)) || (!$y->isa($self)));
+
+  if (($x->{sign} !~ /^[+-]$/) || ($y->{sign} !~ /^[+-]$/))
+    {
+    # handle +-inf and NaN
+    return undef if (($x->{sign} eq $nan) || ($y->{sign} eq $nan));
+    return 0 if $x->{sign} =~ /^[+-]inf$/ && $y->{sign} =~ /^[+-]inf$/;
+    return 1 if $x->{sign} =~ /^[+-]inf$/ && $y->{sign} !~ /^[+-]inf$/;
+    return -1;
+    }
+  $CALC->_acmp($x->{value},$y->{value});	# lib does only 0,1,-1
+  }
+
+sub badd 
+  {
+  # add second arg (BINT or string) to first (BINT) (modifies first)
+  # return result as BINT
+
+  # set up parameters
+  my ($self,$x,$y,@r) = (ref($_[0]),@_);
+  # objectify is costly, so avoid it 
+  if ((!ref($_[0])) || (ref($_[0]) ne ref($_[1])))
+    {
+    ($self,$x,$y,@r) = objectify(2,@_);
+    }
+
+  return $x if $x->modify('badd');
+  return $upgrade->badd($upgrade->new($x),$upgrade->new($y),@r) if defined $upgrade &&
+    ((!$x->isa($self)) || (!$y->isa($self)));
+
+  $r[3] = $y;				# no push!
+  # inf and NaN handling
+  if (($x->{sign} !~ /^[+-]$/) || ($y->{sign} !~ /^[+-]$/))
+    {
+    # NaN first
+    return $x->bnan() if (($x->{sign} eq $nan) || ($y->{sign} eq $nan));
+    # inf handling
+    if (($x->{sign} =~ /^[+-]inf$/) && ($y->{sign} =~ /^[+-]inf$/))
+      {
+      # +inf++inf or -inf+-inf => same, rest is NaN
+      return $x if $x->{sign} eq $y->{sign};
+      return $x->bnan();
+      }
+    # +-inf + something => +inf
+    # something +-inf => +-inf
+    $x->{sign} = $y->{sign}, return $x if $y->{sign} =~ /^[+-]inf$/;
+    return $x;
+    }
+    
+  my ($sx, $sy) = ( $x->{sign}, $y->{sign} ); 		# get signs
+
+  if ($sx eq $sy)  
+    {
+    $x->{value} = $CALC->_add($x->{value},$y->{value});	# same sign, abs add
+    }
+  else 
+    {
+    my $a = $CALC->_acmp ($y->{value},$x->{value});	# absolute compare
+    if ($a > 0)                           
+      {
+      $x->{value} = $CALC->_sub($y->{value},$x->{value},1); # abs sub w/ swap
+      $x->{sign} = $sy;
+      } 
+    elsif ($a == 0)
+      {
+      # speedup, if equal, set result to 0
+      $x->{value} = $CALC->_zero();
+      $x->{sign} = '+';
+      }
+    else # a < 0
+      {
+      $x->{value} = $CALC->_sub($x->{value}, $y->{value}); # abs sub
+      }
+    }
+  $x->round(@r);
+  }
+
+sub bsub 
+  {
+  # (BINT or num_str, BINT or num_str) return BINT
+  # subtract second arg from first, modify first
+  
+  # set up parameters
+  my ($self,$x,$y,@r) = (ref($_[0]),@_);
+
+  # objectify is costly, so avoid it
+  if ((!ref($_[0])) || (ref($_[0]) ne ref($_[1])))
+    {
+    ($self,$x,$y,@r) = objectify(2,@_);
+    }
+
+  return $x if $x->modify('bsub');
+
+  return $upgrade->new($x)->bsub($upgrade->new($y),@r) if defined $upgrade &&
+   ((!$x->isa($self)) || (!$y->isa($self)));
+
+  return $x->round(@r) if $y->is_zero();
+
+  # To correctly handle the lone special case $x->bsub($x), we note the sign
+  # of $x, then flip the sign from $y, and if the sign of $x did change, too,
+  # then we caught the special case:
+  my $xsign = $x->{sign};
+  $y->{sign} =~ tr/+\-/-+/; 	# does nothing for NaN
+  if ($xsign ne $x->{sign})
+    {
+    # special case of $x->bsub($x) results in 0
+    return $x->bzero(@r) if $xsign =~ /^[+-]$/;
+    return $x->bnan();          # NaN, -inf, +inf
+    }
+  $x->badd($y,@r); 		# badd does not leave internal zeros
+  $y->{sign} =~ tr/+\-/-+/; 	# refix $y (does nothing for NaN)
+  $x;				# already rounded by badd() or no round nec.
+  }
+
+sub binc
+  {
+  # increment arg by one
+  my ($self,$x,$a,$p,$r) = ref($_[0]) ? (ref($_[0]),@_) : objectify(1,@_);
+  return $x if $x->modify('binc');
+
+  if ($x->{sign} eq '+')
+    {
+    $x->{value} = $CALC->_inc($x->{value});
+    return $x->round($a,$p,$r);
+    }
+  elsif ($x->{sign} eq '-')
+    {
+    $x->{value} = $CALC->_dec($x->{value});
+    $x->{sign} = '+' if $CALC->_is_zero($x->{value}); # -1 +1 => -0 => +0
+    return $x->round($a,$p,$r);
+    }
+  # inf, nan handling etc
+  $x->badd($self->bone(),$a,$p,$r);		# badd does round
+  }
+
+sub bdec
+  {
+  # decrement arg by one
+  my ($self,$x,@r) = ref($_[0]) ? (ref($_[0]),@_) : objectify(1,@_);
+  return $x if $x->modify('bdec');
+  
+  if ($x->{sign} eq '-')
+    {
+    # x already < 0
+    $x->{value} = $CALC->_inc($x->{value});
+    } 
+  else
+    {
+    return $x->badd($self->bone('-'),@r) unless $x->{sign} eq '+'; 	# inf or NaN
+    # >= 0
+    if ($CALC->_is_zero($x->{value}))
+      {
+      # == 0
+      $x->{value} = $CALC->_one(); $x->{sign} = '-';		# 0 => -1
+      }
+    else
+      {
+      # > 0
+      $x->{value} = $CALC->_dec($x->{value});
+      }
+    }
+  $x->round(@r);
+  }
+
+sub blog
+  {
+  # calculate $x = $a ** $base + $b and return $a (e.g. the log() to base
+  # $base of $x)
+
+  # set up parameters
+  my ($self,$x,$base,@r) = (undef,@_);
+  # objectify is costly, so avoid it
+  if ((!ref($_[0])) || (ref($_[0]) ne ref($_[1])))
+    {
+    ($self,$x,$base,@r) = objectify(1,ref($x),@_);
+    }
+
+  return $x if $x->modify('blog');
+
+  $base = $self->new($base) if defined $base && !ref $base;
+
+  # inf, -inf, NaN, <0 => NaN
+  return $x->bnan()
+   if $x->{sign} ne '+' || (defined $base && $base->{sign} ne '+');
+
+  return $upgrade->blog($upgrade->new($x),$base,@r) if 
+    defined $upgrade;
+
+  # fix for bug #24969:
+  # the default base is e (Euler's number) which is not an integer
+  if (!defined $base)
+    {
+    require Math::BigFloat;
+    my $u = Math::BigFloat->blog(Math::BigFloat->new($x))->as_int();
+    # modify $x in place
+    $x->{value} = $u->{value};
+    $x->{sign} = $u->{sign};
+    return $x;
+    }
+  
+  my ($rc,$exact) = $CALC->_log_int($x->{value},$base->{value});
+  return $x->bnan() unless defined $rc;		# not possible to take log?
+  $x->{value} = $rc;
+  $x->round(@r);
+  }
+
+sub bnok
+  {
+  # Calculate n over k (binomial coefficient or "choose" function) as integer.
+  # set up parameters
+  my ($self,$x,$y,@r) = (ref($_[0]),@_);
+
+  # objectify is costly, so avoid it
+  if ((!ref($_[0])) || (ref($_[0]) ne ref($_[1])))
+    {
+    ($self,$x,$y,@r) = objectify(2,@_);
+    }
+
+  return $x if $x->modify('bnok');
+  return $x->bnan() if $x->{sign} eq 'NaN' || $y->{sign} eq 'NaN';
+  return $x->binf() if $x->{sign} eq '+inf';
+
+  # k > n or k < 0 => 0
+  my $cmp = $x->bacmp($y);
+  return $x->bzero() if $cmp < 0 || $y->{sign} =~ /^-/;
+  # k == n => 1
+  return $x->bone(@r) if $cmp == 0;
+
+  if ($CALC->can('_nok'))
+    {
+    $x->{value} = $CALC->_nok($x->{value},$y->{value});
+    }
+  else
+    {
+    # ( 7 )    7!          7*6*5 * 4*3*2*1   7 * 6 * 5
+    # ( - ) = --------- =  --------------- = ---------
+    # ( 3 )   3! (7-3)!    3*2*1 * 4*3*2*1   3 * 2 * 1 
+
+    # compute n - k + 2 (so we start with 5 in the example above)
+    my $z = $x - $y;
+    if (!$z->is_one())
+      {
+      $z->binc();
+      my $r = $z->copy(); $z->binc();
+      my $d = $self->new(2);
+      while ($z->bacmp($x) <= 0)		# f < x ?
+        {
+        $r->bmul($z); $r->bdiv($d);
+        $z->binc(); $d->binc();
+        }
+      $x->{value} = $r->{value}; $x->{sign} = '+';
+      }
+    else { $x->bone(); }
+    }
+  $x->round(@r);
+  }
+
+sub bexp
+  {
+  # Calculate e ** $x (Euler's number to the power of X), truncated to
+  # an integer value.
+  my ($self,$x,@r) = ref($_[0]) ? (ref($_[0]),@_) : objectify(1,@_);
+  return $x if $x->modify('bexp');
+
+  # inf, -inf, NaN, <0 => NaN
+  return $x->bnan() if $x->{sign} eq 'NaN';
+  return $x->bone() if $x->is_zero();
+  return $x if $x->{sign} eq '+inf';
+  return $x->bzero() if $x->{sign} eq '-inf';
+
+  my $u;
+  {
+    # run through Math::BigFloat unless told otherwise
+    require Math::BigFloat unless defined $upgrade;
+    local $upgrade = 'Math::BigFloat' unless defined $upgrade;
+    # calculate result, truncate it to integer
+    $u = $upgrade->bexp($upgrade->new($x),@r);
+  }
+
+  if (!defined $upgrade)
+    {
+    $u = $u->as_int();
+    # modify $x in place
+    $x->{value} = $u->{value};
+    $x->round(@r);
+    }
+  else { $x = $u; }
+  }
+
+sub blcm 
+  { 
+  # (BINT or num_str, BINT or num_str) return BINT
+  # does not modify arguments, but returns new object
+  # Lowest Common Multiplicator
+
+  my $y = shift; my ($x);
+  if (ref($y))
+    {
+    $x = $y->copy();
+    }
+  else
+    {
+    $x = $class->new($y);
+    }
+  my $self = ref($x);
+  while (@_) 
+    {
+    my $y = shift; $y = $self->new($y) if !ref ($y);
+    $x = __lcm($x,$y);
+    } 
+  $x;
+  }
+
+sub bgcd 
+  { 
+  # (BINT or num_str, BINT or num_str) return BINT
+  # does not modify arguments, but returns new object
+  # GCD -- Euclids algorithm, variant C (Knuth Vol 3, pg 341 ff)
+
+  my $y = shift;
+  $y = $class->new($y) if !ref($y);
+  my $self = ref($y);
+  my $x = $y->copy()->babs();			# keep arguments
+  return $x->bnan() if $x->{sign} !~ /^[+-]$/;	# x NaN?
+
+  while (@_)
+    {
+    $y = shift; $y = $self->new($y) if !ref($y);
+    return $x->bnan() if $y->{sign} !~ /^[+-]$/;	# y NaN?
+    $x->{value} = $CALC->_gcd($x->{value},$y->{value});
+    last if $CALC->_is_one($x->{value});
+    }
+  $x;
+  }
+
+sub bnot 
+  {
+  # (num_str or BINT) return BINT
+  # represent ~x as twos-complement number
+  # we don't need $self, so undef instead of ref($_[0]) make it slightly faster
+  my ($self,$x,$a,$p,$r) = ref($_[0]) ? (undef,@_) : objectify(1,@_);
+ 
+  return $x if $x->modify('bnot');
+  $x->binc()->bneg();			# binc already does round
+  }
+
+##############################################################################
+# is_foo test routines
+# we don't need $self, so undef instead of ref($_[0]) make it slightly faster
+
+sub is_zero
+  {
+  # return true if arg (BINT or num_str) is zero (array '+', '0')
+  my ($self,$x) = ref($_[0]) ? (undef,$_[0]) : objectify(1,@_);
+  
+  return 0 if $x->{sign} !~ /^\+$/;			# -, NaN & +-inf aren't
+  $CALC->_is_zero($x->{value});
+  }
+
+sub is_nan
+  {
+  # return true if arg (BINT or num_str) is NaN
+  my ($self,$x) = ref($_[0]) ? (undef,$_[0]) : objectify(1,@_);
+
+  $x->{sign} eq $nan ? 1 : 0;
+  }
+
+sub is_inf
+  {
+  # return true if arg (BINT or num_str) is +-inf
+  my ($self,$x,$sign) = ref($_[0]) ? (undef,@_) : objectify(1,@_);
+
+  if (defined $sign)
+    {
+    $sign = '[+-]inf' if $sign eq '';	# +- doesn't matter, only that's inf
+    $sign = "[$1]inf" if $sign =~ /^([+-])(inf)?$/;	# extract '+' or '-'
+    return $x->{sign} =~ /^$sign$/ ? 1 : 0;
+    }
+  $x->{sign} =~ /^[+-]inf$/ ? 1 : 0;		# only +-inf is infinity
+  }
+
+sub is_one
+  {
+  # return true if arg (BINT or num_str) is +1, or -1 if sign is given
+  my ($self,$x,$sign) = ref($_[0]) ? (undef,@_) : objectify(1,@_);
+    
+  $sign = '+' if !defined $sign || $sign ne '-';
+ 
+  return 0 if $x->{sign} ne $sign; 	# -1 != +1, NaN, +-inf aren't either
+  $CALC->_is_one($x->{value});
+  }
+
+sub is_odd
+  {
+  # return true when arg (BINT or num_str) is odd, false for even
+  my ($self,$x) = ref($_[0]) ? (undef,$_[0]) : objectify(1,@_);
+
+  return 0 if $x->{sign} !~ /^[+-]$/;			# NaN & +-inf aren't
+  $CALC->_is_odd($x->{value});
+  }
+
+sub is_even
+  {
+  # return true when arg (BINT or num_str) is even, false for odd
+  my ($self,$x) = ref($_[0]) ? (undef,$_[0]) : objectify(1,@_);
+
+  return 0 if $x->{sign} !~ /^[+-]$/;			# NaN & +-inf aren't
+  $CALC->_is_even($x->{value});
+  }
+
+sub is_positive
+  {
+  # return true when arg (BINT or num_str) is positive (>= 0)
+  my ($self,$x) = ref($_[0]) ? (undef,$_[0]) : objectify(1,@_);
+
+  return 1 if $x->{sign} eq '+inf';			# +inf is positive
+ 
+  # 0+ is neither positive nor negative
+  ($x->{sign} eq '+' && !$x->is_zero()) ? 1 : 0;	
+  }
+
+sub is_negative
+  {
+  # return true when arg (BINT or num_str) is negative (< 0)
+  my ($self,$x) = ref($_[0]) ? (undef,$_[0]) : objectify(1,@_);
+  
+  $x->{sign} =~ /^-/ ? 1 : 0; 		# -inf is negative, but NaN is not
+  }
+
+sub is_int
+  {
+  # return true when arg (BINT or num_str) is an integer
+  # always true for BigInt, but different for BigFloats
+  my ($self,$x) = ref($_[0]) ? (undef,$_[0]) : objectify(1,@_);
+  
+  $x->{sign} =~ /^[+-]$/ ? 1 : 0;		# inf/-inf/NaN aren't
+  }
+
+###############################################################################
+
+sub bmul 
+  { 
+  # multiply the first number by the second number
+  # (BINT or num_str, BINT or num_str) return BINT
+
+  # set up parameters
+  my ($self,$x,$y,@r) = (ref($_[0]),@_);
+  # objectify is costly, so avoid it
+  if ((!ref($_[0])) || (ref($_[0]) ne ref($_[1])))
+    {
+    ($self,$x,$y,@r) = objectify(2,@_);
+    }
+
+  return $x if $x->modify('bmul');
+
+  return $x->bnan() if (($x->{sign} eq $nan) || ($y->{sign} eq $nan));
+
+  # inf handling
+  if (($x->{sign} =~ /^[+-]inf$/) || ($y->{sign} =~ /^[+-]inf$/))
+    {
+    return $x->bnan() if $x->is_zero() || $y->is_zero();
+    # result will always be +-inf:
+    # +inf * +/+inf => +inf, -inf * -/-inf => +inf
+    # +inf * -/-inf => -inf, -inf * +/+inf => -inf
+    return $x->binf() if ($x->{sign} =~ /^\+/ && $y->{sign} =~ /^\+/); 
+    return $x->binf() if ($x->{sign} =~ /^-/ && $y->{sign} =~ /^-/); 
+    return $x->binf('-');
+    }
+
+  return $upgrade->bmul($x,$upgrade->new($y),@r)
+   if defined $upgrade && !$y->isa($self);
+  
+  $r[3] = $y;				# no push here
+
+  $x->{sign} = $x->{sign} eq $y->{sign} ? '+' : '-'; # +1 * +1 or -1 * -1 => +
+
+  $x->{value} = $CALC->_mul($x->{value},$y->{value});	# do actual math
+  $x->{sign} = '+' if $CALC->_is_zero($x->{value}); 	# no -0
+
+  $x->round(@r);
+  }
+
+sub bmuladd
+  { 
+  # multiply two numbers and then add the third to the result
+  # (BINT or num_str, BINT or num_str, BINT or num_str) return BINT
+
+  # set up parameters
+  my ($self,$x,$y,$z,@r) = (ref($_[0]),@_);
+  # objectify is costly, so avoid it
+  if ((!ref($_[0])) || (ref($_[0]) ne ref($_[1])))
+    {
+    ($self,$x,$y,$z,@r) = objectify(3,@_);
+    }
+
+  return $x if $x->modify('bmuladd');
+
+  return $x->bnan() if  ($x->{sign} eq $nan) ||
+			($y->{sign} eq $nan) ||
+			($z->{sign} eq $nan);
+
+  # inf handling of x and y
+  if (($x->{sign} =~ /^[+-]inf$/) || ($y->{sign} =~ /^[+-]inf$/))
+    {
+    return $x->bnan() if $x->is_zero() || $y->is_zero();
+    # result will always be +-inf:
+    # +inf * +/+inf => +inf, -inf * -/-inf => +inf
+    # +inf * -/-inf => -inf, -inf * +/+inf => -inf
+    return $x->binf() if ($x->{sign} =~ /^\+/ && $y->{sign} =~ /^\+/); 
+    return $x->binf() if ($x->{sign} =~ /^-/ && $y->{sign} =~ /^-/); 
+    return $x->binf('-');
+    }
+  # inf handling x*y and z
+  if (($z->{sign} =~ /^[+-]inf$/))
+    {
+    # something +-inf => +-inf
+    $x->{sign} = $z->{sign}, return $x if $z->{sign} =~ /^[+-]inf$/;
+    }
+
+  return $upgrade->bmuladd($x,$upgrade->new($y),$upgrade->new($z),@r)
+   if defined $upgrade && (!$y->isa($self) || !$z->isa($self) || !$x->isa($self));
+ 
+  # TODO: what if $y and $z have A or P set?
+  $r[3] = $z;				# no push here
+
+  $x->{sign} = $x->{sign} eq $y->{sign} ? '+' : '-'; # +1 * +1 or -1 * -1 => +
+
+  $x->{value} = $CALC->_mul($x->{value},$y->{value});	# do actual math
+  $x->{sign} = '+' if $CALC->_is_zero($x->{value}); 	# no -0
+
+  my ($sx, $sz) = ( $x->{sign}, $z->{sign} ); 		# get signs
+
+  if ($sx eq $sz)  
+    {
+    $x->{value} = $CALC->_add($x->{value},$z->{value});	# same sign, abs add
+    }
+  else 
+    {
+    my $a = $CALC->_acmp ($z->{value},$x->{value});	# absolute compare
+    if ($a > 0)                           
+      {
+      $x->{value} = $CALC->_sub($z->{value},$x->{value},1); # abs sub w/ swap
+      $x->{sign} = $sz;
+      } 
+    elsif ($a == 0)
+      {
+      # speedup, if equal, set result to 0
+      $x->{value} = $CALC->_zero();
+      $x->{sign} = '+';
+      }
+    else # a < 0
+      {
+      $x->{value} = $CALC->_sub($x->{value}, $z->{value}); # abs sub
+      }
+    }
+  $x->round(@r);
+  }
+
+sub _div_inf
+  {
+  # helper function that handles +-inf cases for bdiv()/bmod() to reuse code
+  my ($self,$x,$y) = @_;
+
+  # NaN if x == NaN or y == NaN or x==y==0
+  return wantarray ? ($x->bnan(),$self->bnan()) : $x->bnan()
+   if (($x->is_nan() || $y->is_nan())   ||
+       ($x->is_zero() && $y->is_zero()));
+ 
+  # +-inf / +-inf == NaN, reminder also NaN
+  if (($x->{sign} =~ /^[+-]inf$/) && ($y->{sign} =~ /^[+-]inf$/))
+    {
+    return wantarray ? ($x->bnan(),$self->bnan()) : $x->bnan();
+    }
+  # x / +-inf => 0, remainder x (works even if x == 0)
+  if ($y->{sign} =~ /^[+-]inf$/)
+    {
+    my $t = $x->copy();		# bzero clobbers up $x
+    return wantarray ? ($x->bzero(),$t) : $x->bzero()
+    }
+  
+  # 5 / 0 => +inf, -6 / 0 => -inf
+  # +inf / 0 = inf, inf,  and -inf / 0 => -inf, -inf 
+  # exception:   -8 / 0 has remainder -8, not 8
+  # exception: -inf / 0 has remainder -inf, not inf
+  if ($y->is_zero())
+    {
+    # +-inf / 0 => special case for -inf
+    return wantarray ?  ($x,$x->copy()) : $x if $x->is_inf();
+    if (!$x->is_zero() && !$x->is_inf())
+      {
+      my $t = $x->copy();		# binf clobbers up $x
+      return wantarray ?
+       ($x->binf($x->{sign}),$t) : $x->binf($x->{sign})
+      }
+    }
+  
+  # last case: +-inf / ordinary number
+  my $sign = '+inf';
+  $sign = '-inf' if substr($x->{sign},0,1) ne $y->{sign};
+  $x->{sign} = $sign;
+  return wantarray ? ($x,$self->bzero()) : $x;
+  }
+
+sub bdiv 
+  {
+  # (dividend: BINT or num_str, divisor: BINT or num_str) return 
+  # (BINT,BINT) (quo,rem) or BINT (only rem)
+  
+  # set up parameters
+  my ($self,$x,$y,@r) = (ref($_[0]),@_);
+  # objectify is costly, so avoid it 
+  if ((!ref($_[0])) || (ref($_[0]) ne ref($_[1])))
+    {
+    ($self,$x,$y,@r) = objectify(2,@_);
+    } 
+
+  return $x if $x->modify('bdiv');
+
+  return $self->_div_inf($x,$y)
+   if (($x->{sign} !~ /^[+-]$/) || ($y->{sign} !~ /^[+-]$/) || $y->is_zero());
+
+  return $upgrade->bdiv($upgrade->new($x),$upgrade->new($y),@r)
+   if defined $upgrade;
+   
+  $r[3] = $y;					# no push!
+
+  # calc new sign and in case $y == +/- 1, return $x
+  my $xsign = $x->{sign};				# keep
+  $x->{sign} = ($x->{sign} ne $y->{sign} ? '-' : '+'); 
+
+  if (wantarray)
+    {
+    my $rem = $self->bzero(); 
+    ($x->{value},$rem->{value}) = $CALC->_div($x->{value},$y->{value});
+    $x->{sign} = '+' if $CALC->_is_zero($x->{value});
+    $rem->{_a} = $x->{_a};
+    $rem->{_p} = $x->{_p};
+    $x->round(@r);
+    if (! $CALC->_is_zero($rem->{value}))
+      {
+      $rem->{sign} = $y->{sign};
+      $rem = $y->copy()->bsub($rem) if $xsign ne $y->{sign}; # one of them '-'
+      }
+    else
+      {
+      $rem->{sign} = '+';			# dont leave -0
+      }
+    $rem->round(@r);
+    return ($x,$rem);
+    }
+
+  $x->{value} = $CALC->_div($x->{value},$y->{value});
+  $x->{sign} = '+' if $CALC->_is_zero($x->{value});
+
+  $x->round(@r);
+  }
+
+###############################################################################
+# modulus functions
+
+sub bmod 
+  {
+  # modulus (or remainder)
+  # (BINT or num_str, BINT or num_str) return BINT
+  
+  # set up parameters
+  my ($self,$x,$y,@r) = (ref($_[0]),@_);
+  # objectify is costly, so avoid it
+  if ((!ref($_[0])) || (ref($_[0]) ne ref($_[1])))
+    {
+    ($self,$x,$y,@r) = objectify(2,@_);
+    }
+
+  return $x if $x->modify('bmod');
+  $r[3] = $y;					# no push!
+  if (($x->{sign} !~ /^[+-]$/) || ($y->{sign} !~ /^[+-]$/) || $y->is_zero())
+    {
+    my ($d,$r) = $self->_div_inf($x,$y);
+    $x->{sign} = $r->{sign};
+    $x->{value} = $r->{value};
+    return $x->round(@r);
+    }
+
+  # calc new sign and in case $y == +/- 1, return $x
+  $x->{value} = $CALC->_mod($x->{value},$y->{value});
+  if (!$CALC->_is_zero($x->{value}))
+    {
+    $x->{value} = $CALC->_sub($y->{value},$x->{value},1) 	# $y-$x
+      if ($x->{sign} ne $y->{sign});
+    $x->{sign} = $y->{sign};
+    }
+   else
+    {
+    $x->{sign} = '+';				# dont leave -0
+    }
+  $x->round(@r);
+  }
+
+sub bmodinv
+  {
+  # Modular inverse.  given a number which is (hopefully) relatively
+  # prime to the modulus, calculate its inverse using Euclid's
+  # alogrithm.  If the number is not relatively prime to the modulus
+  # (i.e. their gcd is not one) then NaN is returned.
+
+  # set up parameters
+  my ($self,$x,$y,@r) = (undef,@_);
+  # objectify is costly, so avoid it
+  if ((!ref($_[0])) || (ref($_[0]) ne ref($_[1])))
+    {
+    ($self,$x,$y,@r) = objectify(2,@_);
+    }
+
+  return $x if $x->modify('bmodinv');
+
+  return $x->bnan()
+        if ($y->{sign} ne '+'                           # -, NaN, +inf, -inf
+         || $x->is_zero()                               # or num == 0
+         || $x->{sign} !~ /^[+-]$/                      # or num NaN, inf, -inf
+        );
+
+  # put least residue into $x if $x was negative, and thus make it positive
+  $x->bmod($y) if $x->{sign} eq '-';
+
+  my $sign;
+  ($x->{value},$sign) = $CALC->_modinv($x->{value},$y->{value});
+  return $x->bnan() if !defined $x->{value};		# in case no GCD found
+  return $x if !defined $sign;			# already real result
+  $x->{sign} = $sign;				# flip/flop see below
+  $x->bmod($y);					# calc real result
+  $x;
+  }
+
+sub bmodpow
+  {
+  # takes a very large number to a very large exponent in a given very
+  # large modulus, quickly, thanks to binary exponentation. Supports
+  # negative exponents.
+  my ($self,$num,$exp,$mod,@r) = objectify(3,@_);
+
+  return $num if $num->modify('bmodpow');
+
+  # check modulus for valid values
+  return $num->bnan() if ($mod->{sign} ne '+'		# NaN, - , -inf, +inf
+                       || $mod->is_zero());
+
+  # check exponent for valid values
+  if ($exp->{sign} =~ /\w/) 
+    {
+    # i.e., if it's NaN, +inf, or -inf...
+    return $num->bnan();
+    }
+
+  $num->bmodinv ($mod) if ($exp->{sign} eq '-');
+
+  # check num for valid values (also NaN if there was no inverse but $exp < 0)
+  return $num->bnan() if $num->{sign} !~ /^[+-]$/;
+
+  # $mod is positive, sign on $exp is ignored, result also positive
+  $num->{value} = $CALC->_modpow($num->{value},$exp->{value},$mod->{value});
+  $num;
+  }
+
+###############################################################################
+
+sub bfac
+  {
+  # (BINT or num_str, BINT or num_str) return BINT
+  # compute factorial number from $x, modify $x in place
+  my ($self,$x,@r) = ref($_[0]) ? (undef,@_) : objectify(1,@_);
+
+  return $x if $x->modify('bfac') || $x->{sign} eq '+inf';	# inf => inf
+  return $x->bnan() if $x->{sign} ne '+';			# NaN, <0 etc => NaN
+
+  $x->{value} = $CALC->_fac($x->{value});
+  $x->round(@r);
+  }
+ 
+sub bpow 
+  {
+  # (BINT or num_str, BINT or num_str) return BINT
+  # compute power of two numbers -- stolen from Knuth Vol 2 pg 233
+  # modifies first argument
+
+  # set up parameters
+  my ($self,$x,$y,@r) = (ref($_[0]),@_);
+  # objectify is costly, so avoid it
+  if ((!ref($_[0])) || (ref($_[0]) ne ref($_[1])))
+    {
+    ($self,$x,$y,@r) = objectify(2,@_);
+    }
+
+  return $x if $x->modify('bpow');
+
+  return $x->bnan() if $x->{sign} eq $nan || $y->{sign} eq $nan;
+
+  # inf handling
+  if (($x->{sign} =~ /^[+-]inf$/) || ($y->{sign} =~ /^[+-]inf$/))
+    {
+    if (($x->{sign} =~ /^[+-]inf$/) && ($y->{sign} =~ /^[+-]inf$/))
+      {
+      # +-inf ** +-inf
+      return $x->bnan();
+      }
+    # +-inf ** Y
+    if ($x->{sign} =~ /^[+-]inf/)
+      {
+      # +inf ** 0 => NaN
+      return $x->bnan() if $y->is_zero();
+      # -inf ** -1 => 1/inf => 0
+      return $x->bzero() if $y->is_one('-') && $x->is_negative();
+
+      # +inf ** Y => inf
+      return $x if $x->{sign} eq '+inf';
+
+      # -inf ** Y => -inf if Y is odd
+      return $x if $y->is_odd();
+      return $x->babs();
+      }
+    # X ** +-inf
+
+    # 1 ** +inf => 1
+    return $x if $x->is_one();
+    
+    # 0 ** inf => 0
+    return $x if $x->is_zero() && $y->{sign} =~ /^[+]/;
+
+    # 0 ** -inf => inf
+    return $x->binf() if $x->is_zero();
+
+    # -1 ** -inf => NaN
+    return $x->bnan() if $x->is_one('-') && $y->{sign} =~ /^[-]/;
+
+    # -X ** -inf => 0
+    return $x->bzero() if $x->{sign} eq '-' && $y->{sign} =~ /^[-]/;
+
+    # -1 ** inf => NaN
+    return $x->bnan() if $x->{sign} eq '-';
+
+    # X ** inf => inf
+    return $x->binf() if $y->{sign} =~ /^[+]/;
+    # X ** -inf => 0
+    return $x->bzero();
+    }
+
+  return $upgrade->bpow($upgrade->new($x),$y,@r)
+   if defined $upgrade && (!$y->isa($self) || $y->{sign} eq '-');
+
+  $r[3] = $y;					# no push!
+
+  # cases 0 ** Y, X ** 0, X ** 1, 1 ** Y are handled by Calc or Emu
+
+  my $new_sign = '+';
+  $new_sign = $y->is_odd() ? '-' : '+' if ($x->{sign} ne '+'); 
+
+  # 0 ** -7 => ( 1 / (0 ** 7)) => 1 / 0 => +inf 
+  return $x->binf() 
+    if $y->{sign} eq '-' && $x->{sign} eq '+' && $CALC->_is_zero($x->{value});
+  # 1 ** -y => 1 / (1 ** |y|)
+  # so do test for negative $y after above's clause
+  return $x->bnan() if $y->{sign} eq '-' && !$CALC->_is_one($x->{value});
+
+  $x->{value} = $CALC->_pow($x->{value},$y->{value});
+  $x->{sign} = $new_sign;
+  $x->{sign} = '+' if $CALC->_is_zero($y->{value});
+  $x->round(@r);
+  }
+
+sub blsft 
+  {
+  # (BINT or num_str, BINT or num_str) return BINT
+  # compute x << y, base n, y >= 0
+ 
+  # set up parameters
+  my ($self,$x,$y,$n,@r) = (ref($_[0]),@_);
+  # objectify is costly, so avoid it
+  if ((!ref($_[0])) || (ref($_[0]) ne ref($_[1])))
+    {
+    ($self,$x,$y,$n,@r) = objectify(2,@_);
+    }
+
+  return $x if $x->modify('blsft');
+  return $x->bnan() if ($x->{sign} !~ /^[+-]$/ || $y->{sign} !~ /^[+-]$/);
+  return $x->round(@r) if $y->is_zero();
+
+  $n = 2 if !defined $n; return $x->bnan() if $n <= 0 || $y->{sign} eq '-';
+
+  $x->{value} = $CALC->_lsft($x->{value},$y->{value},$n);
+  $x->round(@r);
+  }
+
+sub brsft 
+  {
+  # (BINT or num_str, BINT or num_str) return BINT
+  # compute x >> y, base n, y >= 0
+  
+  # set up parameters
+  my ($self,$x,$y,$n,@r) = (ref($_[0]),@_);
+  # objectify is costly, so avoid it
+  if ((!ref($_[0])) || (ref($_[0]) ne ref($_[1])))
+    {
+    ($self,$x,$y,$n,@r) = objectify(2,@_);
+    }
+
+  return $x if $x->modify('brsft');
+  return $x->bnan() if ($x->{sign} !~ /^[+-]$/ || $y->{sign} !~ /^[+-]$/);
+  return $x->round(@r) if $y->is_zero();
+  return $x->bzero(@r) if $x->is_zero();		# 0 => 0
+
+  $n = 2 if !defined $n; return $x->bnan() if $n <= 0 || $y->{sign} eq '-';
+
+   # this only works for negative numbers when shifting in base 2
+  if (($x->{sign} eq '-') && ($n == 2))
+    {
+    return $x->round(@r) if $x->is_one('-');	# -1 => -1
+    if (!$y->is_one())
+      {
+      # although this is O(N*N) in calc (as_bin!) it is O(N) in Pari et al
+      # but perhaps there is a better emulation for two's complement shift...
+      # if $y != 1, we must simulate it by doing:
+      # convert to bin, flip all bits, shift, and be done
+      $x->binc();			# -3 => -2
+      my $bin = $x->as_bin();
+      $bin =~ s/^-0b//;			# strip '-0b' prefix
+      $bin =~ tr/10/01/;		# flip bits
+      # now shift
+      if ($y >= CORE::length($bin))
+        {
+	$bin = '0'; 			# shifting to far right creates -1
+					# 0, because later increment makes 
+					# that 1, attached '-' makes it '-1'
+					# because -1 >> x == -1 !
+        } 
+      else
+	{
+	$bin =~ s/.{$y}$//;		# cut off at the right side
+        $bin = '1' . $bin;		# extend left side by one dummy '1'
+        $bin =~ tr/10/01/;		# flip bits back
+	}
+      my $res = $self->new('0b'.$bin);	# add prefix and convert back
+      $res->binc();			# remember to increment
+      $x->{value} = $res->{value};	# take over value
+      return $x->round(@r);		# we are done now, magic, isn't?
+      }
+    # x < 0, n == 2, y == 1
+    $x->bdec();				# n == 2, but $y == 1: this fixes it
+    }
+
+  $x->{value} = $CALC->_rsft($x->{value},$y->{value},$n);
+  $x->round(@r);
+  }
+
+sub band 
+  {
+  #(BINT or num_str, BINT or num_str) return BINT
+  # compute x & y
+ 
+  # set up parameters
+  my ($self,$x,$y,@r) = (ref($_[0]),@_);
+  # objectify is costly, so avoid it
+  if ((!ref($_[0])) || (ref($_[0]) ne ref($_[1])))
+    {
+    ($self,$x,$y,@r) = objectify(2,@_);
+    }
+  
+  return $x if $x->modify('band');
+
+  $r[3] = $y;				# no push!
+
+  return $x->bnan() if ($x->{sign} !~ /^[+-]$/ || $y->{sign} !~ /^[+-]$/);
+
+  my $sx = $x->{sign} eq '+' ? 1 : -1;
+  my $sy = $y->{sign} eq '+' ? 1 : -1;
+  
+  if ($sx == 1 && $sy == 1)
+    {
+    $x->{value} = $CALC->_and($x->{value},$y->{value});
+    return $x->round(@r);
+    }
+  
+  if ($CAN{signed_and})
+    {
+    $x->{value} = $CALC->_signed_and($x->{value},$y->{value},$sx,$sy);
+    return $x->round(@r);
+    }
+ 
+  require $EMU_LIB;
+  __emu_band($self,$x,$y,$sx,$sy,@r);
+  }
+
+sub bior 
+  {
+  #(BINT or num_str, BINT or num_str) return BINT
+  # compute x | y
+  
+  # set up parameters
+  my ($self,$x,$y,@r) = (ref($_[0]),@_);
+  # objectify is costly, so avoid it
+  if ((!ref($_[0])) || (ref($_[0]) ne ref($_[1])))
+    {
+    ($self,$x,$y,@r) = objectify(2,@_);
+    }
+
+  return $x if $x->modify('bior');
+  $r[3] = $y;				# no push!
+
+  return $x->bnan() if ($x->{sign} !~ /^[+-]$/ || $y->{sign} !~ /^[+-]$/);
+
+  my $sx = $x->{sign} eq '+' ? 1 : -1;
+  my $sy = $y->{sign} eq '+' ? 1 : -1;
+
+  # the sign of X follows the sign of X, e.g. sign of Y irrelevant for bior()
+  
+  # don't use lib for negative values
+  if ($sx == 1 && $sy == 1)
+    {
+    $x->{value} = $CALC->_or($x->{value},$y->{value});
+    return $x->round(@r);
+    }
+
+  # if lib can do negative values, let it handle this
+  if ($CAN{signed_or})
+    {
+    $x->{value} = $CALC->_signed_or($x->{value},$y->{value},$sx,$sy);
+    return $x->round(@r);
+    }
+
+  require $EMU_LIB;
+  __emu_bior($self,$x,$y,$sx,$sy,@r);
+  }
+
+sub bxor 
+  {
+  #(BINT or num_str, BINT or num_str) return BINT
+  # compute x ^ y
+  
+  # set up parameters
+  my ($self,$x,$y,@r) = (ref($_[0]),@_);
+  # objectify is costly, so avoid it
+  if ((!ref($_[0])) || (ref($_[0]) ne ref($_[1])))
+    {
+    ($self,$x,$y,@r) = objectify(2,@_);
+    }
+
+  return $x if $x->modify('bxor');
+  $r[3] = $y;				# no push!
+
+  return $x->bnan() if ($x->{sign} !~ /^[+-]$/ || $y->{sign} !~ /^[+-]$/);
+  
+  my $sx = $x->{sign} eq '+' ? 1 : -1;
+  my $sy = $y->{sign} eq '+' ? 1 : -1;
+
+  # don't use lib for negative values
+  if ($sx == 1 && $sy == 1)
+    {
+    $x->{value} = $CALC->_xor($x->{value},$y->{value});
+    return $x->round(@r);
+    }
+  
+  # if lib can do negative values, let it handle this
+  if ($CAN{signed_xor})
+    {
+    $x->{value} = $CALC->_signed_xor($x->{value},$y->{value},$sx,$sy);
+    return $x->round(@r);
+    }
+
+  require $EMU_LIB;
+  __emu_bxor($self,$x,$y,$sx,$sy,@r);
+  }
+
+sub length
+  {
+  my ($self,$x) = ref($_[0]) ? (undef,$_[0]) : objectify(1,@_);
+
+  my $e = $CALC->_len($x->{value}); 
+  wantarray ? ($e,0) : $e;
+  }
+
+sub digit
+  {
+  # return the nth decimal digit, negative values count backward, 0 is right
+  my ($self,$x,$n) = ref($_[0]) ? (undef,@_) : objectify(1,@_);
+
+  $n = $n->numify() if ref($n);
+  $CALC->_digit($x->{value},$n||0);
+  }
+
+sub _trailing_zeros
+  {
+  # return the amount of trailing zeros in $x (as scalar)
+  my $x = shift;
+  $x = $class->new($x) unless ref $x;
+
+  return 0 if $x->{sign} !~ /^[+-]$/;	# NaN, inf, -inf etc
+
+  $CALC->_zeros($x->{value});		# must handle odd values, 0 etc
+  }
+
+sub bsqrt
+  {
+  # calculate square root of $x
+  my ($self,$x,@r) = ref($_[0]) ? (undef,@_) : objectify(1,@_);
+
+  return $x if $x->modify('bsqrt');
+
+  return $x->bnan() if $x->{sign} !~ /^\+/;	# -x or -inf or NaN => NaN
+  return $x if $x->{sign} eq '+inf';		# sqrt(+inf) == inf
+
+  return $upgrade->bsqrt($x,@r) if defined $upgrade;
+
+  $x->{value} = $CALC->_sqrt($x->{value});
+  $x->round(@r);
+  }
+
+sub broot
+  {
+  # calculate $y'th root of $x
+ 
+  # set up parameters
+  my ($self,$x,$y,@r) = (ref($_[0]),@_);
+
+  $y = $self->new(2) unless defined $y;
+
+  # objectify is costly, so avoid it
+  if ((!ref($x)) || (ref($x) ne ref($y)))
+    {
+    ($self,$x,$y,@r) = objectify(2,$self || $class,@_);
+    }
+
+  return $x if $x->modify('broot');
+
+  # NaN handling: $x ** 1/0, x or y NaN, or y inf/-inf or y == 0
+  return $x->bnan() if $x->{sign} !~ /^\+/ || $y->is_zero() ||
+         $y->{sign} !~ /^\+$/;
+
+  return $x->round(@r)
+    if $x->is_zero() || $x->is_one() || $x->is_inf() || $y->is_one();
+
+  return $upgrade->new($x)->broot($upgrade->new($y),@r) if defined $upgrade;
+
+  $x->{value} = $CALC->_root($x->{value},$y->{value});
+  $x->round(@r);
+  }
+
+sub exponent
+  {
+  # return a copy of the exponent (here always 0, NaN or 1 for $m == 0)
+  my ($self,$x) = ref($_[0]) ? (ref($_[0]),$_[0]) : objectify(1,@_);
+ 
+  if ($x->{sign} !~ /^[+-]$/)
+    {
+    my $s = $x->{sign}; $s =~ s/^[+-]//;  # NaN, -inf,+inf => NaN or inf
+    return $self->new($s);
+    }
+  return $self->bone() if $x->is_zero();
+
+  # 12300 => 2 trailing zeros => exponent is 2
+  $self->new( $CALC->_zeros($x->{value}) );
+  }
+
+sub mantissa
+  {
+  # return the mantissa (compatible to Math::BigFloat, e.g. reduced)
+  my ($self,$x) = ref($_[0]) ? (ref($_[0]),$_[0]) : objectify(1,@_);
+
+  if ($x->{sign} !~ /^[+-]$/)
+    {
+    # for NaN, +inf, -inf: keep the sign
+    return $self->new($x->{sign});
+    }
+  my $m = $x->copy(); delete $m->{_p}; delete $m->{_a};
+
+  # that's a bit inefficient:
+  my $zeros = $CALC->_zeros($m->{value});
+  $m->brsft($zeros,10) if $zeros != 0;
+  $m;
+  }
+
+sub parts
+  {
+  # return a copy of both the exponent and the mantissa
+  my ($self,$x) = ref($_[0]) ? (undef,$_[0]) : objectify(1,@_);
+
+  ($x->mantissa(),$x->exponent());
+  }
+   
+##############################################################################
+# rounding functions
+
+sub bfround
+  {
+  # precision: round to the $Nth digit left (+$n) or right (-$n) from the '.'
+  # $n == 0 || $n == 1 => round to integer
+  my $x = shift; my $self = ref($x) || $x; $x = $self->new($x) unless ref $x;
+
+  my ($scale,$mode) = $x->_scale_p(@_);
+
+  return $x if !defined $scale || $x->modify('bfround');	# no-op
+
+  # no-op for BigInts if $n <= 0
+  $x->bround( $x->length()-$scale, $mode) if $scale > 0;
+
+  delete $x->{_a};	# delete to save memory
+  $x->{_p} = $scale;	# store new _p
+  $x;
+  }
+
+sub _scan_for_nonzero
+  {
+  # internal, used by bround() to scan for non-zeros after a '5'
+  my ($x,$pad,$xs,$len) = @_;
+ 
+  return 0 if $len == 1;		# "5" is trailed by invisible zeros
+  my $follow = $pad - 1;
+  return 0 if $follow > $len || $follow < 1;
+
+  # use the string form to check whether only '0's follow or not
+  substr ($xs,-$follow) =~ /[^0]/ ? 1 : 0;
+  }
+
+sub fround
+  {
+  # Exists to make life easier for switch between MBF and MBI (should we
+  # autoload fxxx() like MBF does for bxxx()?)
+  my $x = shift; $x = $class->new($x) unless ref $x;
+  $x->bround(@_);
+  }
+
+sub bround
+  {
+  # accuracy: +$n preserve $n digits from left,
+  #           -$n preserve $n digits from right (f.i. for 0.1234 style in MBF)
+  # no-op for $n == 0
+  # and overwrite the rest with 0's, return normalized number
+  # do not return $x->bnorm(), but $x
+
+  my $x = shift; $x = $class->new($x) unless ref $x;
+  my ($scale,$mode) = $x->_scale_a(@_);
+  return $x if !defined $scale || $x->modify('bround');	# no-op
+  
+  if ($x->is_zero() || $scale == 0)
+    {
+    $x->{_a} = $scale if !defined $x->{_a} || $x->{_a} > $scale; # 3 > 2
+    return $x;
+    }
+  return $x if $x->{sign} !~ /^[+-]$/;		# inf, NaN
+
+  # we have fewer digits than we want to scale to
+  my $len = $x->length();
+  # convert $scale to a scalar in case it is an object (put's a limit on the
+  # number length, but this would already limited by memory constraints), makes
+  # it faster
+  $scale = $scale->numify() if ref ($scale);
+
+  # scale < 0, but > -len (not >=!)
+  if (($scale < 0 && $scale < -$len-1) || ($scale >= $len))
+    {
+    $x->{_a} = $scale if !defined $x->{_a} || $x->{_a} > $scale; # 3 > 2
+    return $x; 
+    }
+   
+  # count of 0's to pad, from left (+) or right (-): 9 - +6 => 3, or |-6| => 6
+  my ($pad,$digit_round,$digit_after);
+  $pad = $len - $scale;
+  $pad = abs($scale-1) if $scale < 0;
+
+  # do not use digit(), it is very costly for binary => decimal
+  # getting the entire string is also costly, but we need to do it only once
+  my $xs = $CALC->_str($x->{value});
+  my $pl = -$pad-1;
+
+  # pad:   123: 0 => -1, at 1 => -2, at 2 => -3, at 3 => -4
+  # pad+1: 123: 0 => 0,  at 1 => -1, at 2 => -2, at 3 => -3
+  $digit_round = '0'; $digit_round = substr($xs,$pl,1) if $pad <= $len;
+  $pl++; $pl ++ if $pad >= $len;
+  $digit_after = '0'; $digit_after = substr($xs,$pl,1) if $pad > 0;
+
+  # in case of 01234 we round down, for 6789 up, and only in case 5 we look
+  # closer at the remaining digits of the original $x, remember decision
+  my $round_up = 1;					# default round up
+  $round_up -- if
+    ($mode eq 'trunc')				||	# trunc by round down
+    ($digit_after =~ /[01234]/)			|| 	# round down anyway,
+							# 6789 => round up
+    ($digit_after eq '5')			&&	# not 5000...0000
+    ($x->_scan_for_nonzero($pad,$xs,$len) == 0)		&&
+    (
+     ($mode eq 'even') && ($digit_round =~ /[24680]/) ||
+     ($mode eq 'odd')  && ($digit_round =~ /[13579]/) ||
+     ($mode eq '+inf') && ($x->{sign} eq '-')   ||
+     ($mode eq '-inf') && ($x->{sign} eq '+')   ||
+     ($mode eq 'zero')		# round down if zero, sign adjusted below
+    );
+  my $put_back = 0;					# not yet modified
+	
+  if (($pad > 0) && ($pad <= $len))
+    {
+    substr($xs,-$pad,$pad) = '0' x $pad;		# replace with '00...'
+    $put_back = 1;					# need to put back
+    }
+  elsif ($pad > $len)
+    {
+    $x->bzero();					# round to '0'
+    }
+
+  if ($round_up)					# what gave test above?
+    {
+    $put_back = 1;					# need to put back
+    $pad = $len, $xs = '0' x $pad if $scale < 0;	# tlr: whack 0.51=>1.0	
+
+    # we modify directly the string variant instead of creating a number and
+    # adding it, since that is faster (we already have the string)
+    my $c = 0; $pad ++;				# for $pad == $len case
+    while ($pad <= $len)
+      {
+      $c = substr($xs,-$pad,1) + 1; $c = '0' if $c eq '10';
+      substr($xs,-$pad,1) = $c; $pad++;
+      last if $c != 0;				# no overflow => early out
+      }
+    $xs = '1'.$xs if $c == 0;
+
+    }
+  $x->{value} = $CALC->_new($xs) if $put_back == 1;	# put back, if needed
+
+  $x->{_a} = $scale if $scale >= 0;
+  if ($scale < 0)
+    {
+    $x->{_a} = $len+$scale;
+    $x->{_a} = 0 if $scale < -$len;
+    }
+  $x;
+  }
+
+sub bfloor
+  {
+  # return integer less or equal then number; no-op since it's already integer
+  my ($self,$x,@r) = ref($_[0]) ? (undef,@_) : objectify(1,@_);
+
+  $x->round(@r);
+  }
+
+sub bceil
+  {
+  # return integer greater or equal then number; no-op since it's already int
+  my ($self,$x,@r) = ref($_[0]) ? (undef,@_) : objectify(1,@_);
+
+  $x->round(@r);
+  }
+
+sub as_number
+  {
+  # An object might be asked to return itself as bigint on certain overloaded
+  # operations. This does exactly this, so that sub classes can simple inherit
+  # it or override with their own integer conversion routine.
+  $_[0]->copy();
+  }
+
+sub as_hex
+  {
+  # return as hex string, with prefixed 0x
+  my $x = shift; $x = $class->new($x) if !ref($x);
+
+  return $x->bstr() if $x->{sign} !~ /^[+-]$/;	# inf, nan etc
+
+  my $s = '';
+  $s = $x->{sign} if $x->{sign} eq '-';
+  $s . $CALC->_as_hex($x->{value});
+  }
+
+sub as_bin
+  {
+  # return as binary string, with prefixed 0b
+  my $x = shift; $x = $class->new($x) if !ref($x);
+
+  return $x->bstr() if $x->{sign} !~ /^[+-]$/;	# inf, nan etc
+
+  my $s = ''; $s = $x->{sign} if $x->{sign} eq '-';
+  return $s . $CALC->_as_bin($x->{value});
+  }
+
+sub as_oct
+  {
+  # return as octal string, with prefixed 0
+  my $x = shift; $x = $class->new($x) if !ref($x);
+
+  return $x->bstr() if $x->{sign} !~ /^[+-]$/;	# inf, nan etc
+
+  my $s = ''; $s = $x->{sign} if $x->{sign} eq '-';
+  return $s . $CALC->_as_oct($x->{value});
+  }
+
+##############################################################################
+# private stuff (internal use only)
+
+sub objectify
+  {
+  # check for strings, if yes, return objects instead
+ 
+  # the first argument is number of args objectify() should look at it will
+  # return $count+1 elements, the first will be a classname. This is because
+  # overloaded '""' calls bstr($object,undef,undef) and this would result in
+  # useless objects being created and thrown away. So we cannot simple loop
+  # over @_. If the given count is 0, all arguments will be used.
+ 
+  # If the second arg is a ref, use it as class.
+  # If not, try to use it as classname, unless undef, then use $class 
+  # (aka Math::BigInt). The latter shouldn't happen,though.
+
+  # caller:			   gives us:
+  # $x->badd(1);                => ref x, scalar y
+  # Class->badd(1,2);           => classname x (scalar), scalar x, scalar y
+  # Class->badd( Class->(1),2); => classname x (scalar), ref x, scalar y
+  # Math::BigInt::badd(1,2);    => scalar x, scalar y
+  # In the last case we check number of arguments to turn it silently into
+  # $class,1,2. (We can not take '1' as class ;o)
+  # badd($class,1) is not supported (it should, eventually, try to add undef)
+  # currently it tries 'Math::BigInt' + 1, which will not work.
+
+  # some shortcut for the common cases
+  # $x->unary_op();
+  return (ref($_[1]),$_[1]) if (@_ == 2) && ($_[0]||0 == 1) && ref($_[1]);
+
+  my $count = abs(shift || 0);
+  
+  my (@a,$k,$d);		# resulting array, temp, and downgrade 
+  if (ref $_[0])
+    {
+    # okay, got object as first
+    $a[0] = ref $_[0];
+    }
+  else
+    {
+    # nope, got 1,2 (Class->xxx(1) => Class,1 and not supported)
+    $a[0] = $class;
+    $a[0] = shift if $_[0] =~ /^[A-Z].*::/;	# classname as first?
+    }
+
+  no strict 'refs';
+  # disable downgrading, because Math::BigFLoat->foo('1.0','2.0') needs floats
+  if (defined ${"$a[0]::downgrade"})
+    {
+    $d = ${"$a[0]::downgrade"};
+    ${"$a[0]::downgrade"} = undef;
+    }
+
+  my $up = ${"$a[0]::upgrade"};
+  # print STDERR "# Now in objectify, my class is today $a[0], count = $count\n";
+  if ($count == 0)
+    {
+    while (@_)
+      {
+      $k = shift;
+      if (!ref($k))
+        {
+        $k = $a[0]->new($k);
+        }
+      elsif (!defined $up && ref($k) ne $a[0])
+	{
+	# foreign object, try to convert to integer
+        $k->can('as_number') ?  $k = $k->as_number() : $k = $a[0]->new($k);
+	}
+      push @a,$k;
+      }
+    }
+  else
+    {
+    while ($count > 0)
+      {
+      $count--; 
+      $k = shift;
+      if (!ref($k))
+        {
+        $k = $a[0]->new($k);
+        }
+      elsif (!defined $up && ref($k) ne $a[0])
+	{
+	# foreign object, try to convert to integer
+        $k->can('as_number') ? $k = $k->as_number() : $k = $a[0]->new($k);
+	}
+      push @a,$k;
+      }
+    push @a,@_;		# return other params, too
+    }
+  if (! wantarray)
+    {
+    require Carp; Carp::croak ("$class objectify needs list context");
+    }
+  ${"$a[0]::downgrade"} = $d;
+  @a;
+  }
+
+sub _register_callback
+  {
+  my ($class,$callback) = @_;
+
+  if (ref($callback) ne 'CODE')
+    { 
+    require Carp;
+    Carp::croak ("$callback is not a coderef");
+    }
+  $CALLBACKS{$class} = $callback;
+  }
+
+sub import 
+  {
+  my $self = shift;
+
+  $IMPORT++;				# remember we did import()
+  my @a; my $l = scalar @_;
+  my $warn_or_die = 0;			# 0 - no warn, 1 - warn, 2 - die
+  for ( my $i = 0; $i < $l ; $i++ )
+    {
+    if ($_[$i] eq ':constant')
+      {
+      # this causes overlord er load to step in
+      overload::constant 
+	integer => sub { $self->new(shift) },
+      	binary => sub { $self->new(shift) };
+      }
+    elsif ($_[$i] eq 'upgrade')
+      {
+      # this causes upgrading
+      $upgrade = $_[$i+1];		# or undef to disable
+      $i++;
+      }
+    elsif ($_[$i] =~ /^(lib|try|only)\z/)
+      {
+      # this causes a different low lib to take care...
+      $CALC = $_[$i+1] || '';
+      # lib => 1 (warn on fallback), try => 0 (no warn), only => 2 (die on fallback)
+      $warn_or_die = 1 if $_[$i] eq 'lib';
+      $warn_or_die = 2 if $_[$i] eq 'only';
+      $i++;
+      }
+    else
+      {
+      push @a, $_[$i];
+      }
+    }
+  # any non :constant stuff is handled by our parent, Exporter
+  if (@a > 0)
+    {
+    require Exporter;
+ 
+    $self->SUPER::import(@a);			# need it for subclasses
+    $self->export_to_level(1,$self,@a);		# need it for MBF
+    }
+
+  # try to load core math lib
+  my @c = split /\s*,\s*/,$CALC;
+  foreach (@c)
+    {
+    $_ =~ tr/a-zA-Z0-9://cd;			# limit to sane characters
+    }
+  push @c, \'FastCalc', \'Calc'			# if all fail, try these
+    if $warn_or_die < 2;			# but not for "only"
+  $CALC = '';					# signal error
+  foreach my $l (@c)
+    {
+    # fallback libraries are "marked" as \'string', extract string if nec.
+    my $lib = $l; $lib = $$l if ref($l);
+
+    next if ($lib || '') eq '';
+    $lib = 'Math::BigInt::'.$lib if $lib !~ /^Math::BigInt/i;
+    $lib =~ s/\.pm$//;
+    if ($] < 5.006)
+      {
+      # Perl < 5.6.0 dies with "out of memory!" when eval("") and ':constant' is
+      # used in the same script, or eval("") inside import().
+      my @parts = split /::/, $lib;             # Math::BigInt => Math BigInt
+      my $file = pop @parts; $file .= '.pm';    # BigInt => BigInt.pm
+      require File::Spec;
+      $file = File::Spec->catfile (@parts, $file);
+      eval { require "$file"; $lib->import( @c ); }
+      }
+    else
+      {
+      eval "use $lib qw/@c/;";
+      }
+    if ($@ eq '')
+      {
+      my $ok = 1;
+      # loaded it ok, see if the api_version() is high enough
+      if ($lib->can('api_version') && $lib->api_version() >= 1.0)
+	{
+	$ok = 0;
+	# api_version matches, check if it really provides anything we need
+        for my $method (qw/
+		one two ten
+		str num
+		add mul div sub dec inc
+		acmp len digit is_one is_zero is_even is_odd
+		is_two is_ten
+		zeros new copy check
+		from_hex from_oct from_bin as_hex as_bin as_oct
+		rsft lsft xor and or
+		mod sqrt root fac pow modinv modpow log_int gcd
+	 /)
+          {
+	  if (!$lib->can("_$method"))
+	    {
+	    if (($WARN{$lib}||0) < 2)
+	      {
+	      require Carp;
+	      Carp::carp ("$lib is missing method '_$method'");
+	      $WARN{$lib} = 1;		# still warn about the lib
+	      }
+            $ok++; last; 
+	    }
+          }
+	}
+      if ($ok == 0)
+	{
+	$CALC = $lib;
+	if ($warn_or_die > 0 && ref($l))
+	  {
+	  require Carp;
+	  my $msg = "Math::BigInt: couldn't load specified math lib(s), fallback to $lib";
+          Carp::carp ($msg) if $warn_or_die == 1;
+          Carp::croak ($msg) if $warn_or_die == 2;
+	  }
+        last;			# found a usable one, break
+	}
+      else
+	{
+	if (($WARN{$lib}||0) < 2)
+	  {
+	  my $ver = eval "\$$lib\::VERSION" || 'unknown';
+	  require Carp;
+	  Carp::carp ("Cannot load outdated $lib v$ver, please upgrade");
+	  $WARN{$lib} = 2;		# never warn again
+	  }
+        }
+      }
+    }
+  if ($CALC eq '')
+    {
+    require Carp;
+    if ($warn_or_die == 2)
+      {
+      Carp::croak ("Couldn't load specified math lib(s) and fallback disallowed");
+      }
+    else
+      {
+      Carp::croak ("Couldn't load any math lib(s), not even fallback to Calc.pm");
+      }
+    }
+
+  # notify callbacks
+  foreach my $class (keys %CALLBACKS)
+    {
+    &{$CALLBACKS{$class}}($CALC);
+    }
+
+  # Fill $CAN with the results of $CALC->can(...) for emulating lower math lib
+  # functions
+
+  %CAN = ();
+  for my $method (qw/ signed_and signed_or signed_xor /)
+    {
+    $CAN{$method} = $CALC->can("_$method") ? 1 : 0;
+    }
+
+  # import done
+  }
+
+sub from_hex
+  {
+  # create a bigint from a hexadecimal string
+  my ($self, $hs) = @_;
+
+  my $rc = __from_hex($hs);
+
+  return $self->bnan() unless defined $rc;
+
+  $rc;
+  }  
+
+sub from_bin
+  {
+  # create a bigint from a hexadecimal string
+  my ($self, $bs) = @_;
+
+  my $rc = __from_bin($bs);
+
+  return $self->bnan() unless defined $rc;
+
+  $rc;
+  }  
+
+sub from_oct
+  {
+  # create a bigint from a hexadecimal string
+  my ($self, $os) = @_;
+
+  my $x = $self->bzero();
+  
+  # strip underscores
+  $os =~ s/([0-7])_([0-7])/$1$2/g;	
+  $os =~ s/([0-7])_([0-7])/$1$2/g;	
+  
+  return $x->bnan() if $os !~ /^[\-\+]?0[0-7]+\z/;
+
+  my $sign = '+'; $sign = '-' if $os =~ /^-/;
+
+  $os =~ s/^[+-]//;						# strip sign
+  $x->{value} = $CALC->_from_oct($os);
+  $x->{sign} = $sign unless $CALC->_is_zero($x->{value}); 	# no '-0'
+  $x;
+  }
+
+sub __from_hex
+  {
+  # internal
+  # convert a (ref to) big hex string to BigInt, return undef for error
+  my $hs = shift;
+
+  my $x = Math::BigInt->bzero();
+  
+  # strip underscores
+  $hs =~ s/([0-9a-fA-F])_([0-9a-fA-F])/$1$2/g;	
+  $hs =~ s/([0-9a-fA-F])_([0-9a-fA-F])/$1$2/g;	
+  
+  return $x->bnan() if $hs !~ /^[\-\+]?0x[0-9A-Fa-f]+$/;
+
+  my $sign = '+'; $sign = '-' if $hs =~ /^-/;
+
+  $hs =~ s/^[+-]//;						# strip sign
+  $x->{value} = $CALC->_from_hex($hs);
+  $x->{sign} = $sign unless $CALC->_is_zero($x->{value}); 	# no '-0'
+  $x;
+  }
+
+sub __from_bin
+  {
+  # internal
+  # convert a (ref to) big binary string to BigInt, return undef for error
+  my $bs = shift;
+
+  my $x = Math::BigInt->bzero();
+
+  # strip underscores
+  $bs =~ s/([01])_([01])/$1$2/g;	
+  $bs =~ s/([01])_([01])/$1$2/g;	
+  return $x->bnan() if $bs !~ /^[+-]?0b[01]+$/;
+
+  my $sign = '+'; $sign = '-' if $bs =~ /^\-/;
+  $bs =~ s/^[+-]//;						# strip sign
+
+  $x->{value} = $CALC->_from_bin($bs);
+  $x->{sign} = $sign unless $CALC->_is_zero($x->{value}); 	# no '-0'
+  $x;
+  }
+
+sub _split
+  {
+  # input: num_str; output: undef for invalid or
+  # (\$mantissa_sign,\$mantissa_value,\$mantissa_fraction,\$exp_sign,\$exp_value)
+  # Internal, take apart a string and return the pieces.
+  # Strip leading/trailing whitespace, leading zeros, underscore and reject
+  # invalid input.
+  my $x = shift;
+
+  # strip white space at front, also extranous leading zeros
+  $x =~ s/^\s*([-]?)0*([0-9])/$1$2/g;   # will not strip '  .2'
+  $x =~ s/^\s+//;                       # but this will
+  $x =~ s/\s+$//g;                      # strip white space at end
+
+  # shortcut, if nothing to split, return early
+  if ($x =~ /^[+-]?[0-9]+\z/)
+    {
+    $x =~ s/^([+-])0*([0-9])/$2/; my $sign = $1 || '+';
+    return (\$sign, \$x, \'', \'', \0);
+    }
+
+  # invalid starting char?
+  return if $x !~ /^[+-]?(\.?[0-9]|0b[0-1]|0x[0-9a-fA-F])/;
+
+  return __from_hex($x) if $x =~ /^[\-\+]?0x/;		# hex string
+  return __from_bin($x) if $x =~ /^[\-\+]?0b/;		# binary string
+  
+  # strip underscores between digits
+  $x =~ s/([0-9])_([0-9])/$1$2/g;
+  $x =~ s/([0-9])_([0-9])/$1$2/g;		# do twice for 1_2_3
+
+  # some possible inputs: 
+  # 2.1234 # 0.12        # 1 	      # 1E1 # 2.134E1 # 434E-10 # 1.02009E-2 
+  # .2 	   # 1_2_3.4_5_6 # 1.4E1_2_3  # 1e3 # +.2     # 0e999	
+
+  my ($m,$e,$last) = split /[Ee]/,$x;
+  return if defined $last;		# last defined => 1e2E3 or others
+  $e = '0' if !defined $e || $e eq "";
+
+  # sign,value for exponent,mantint,mantfrac
+  my ($es,$ev,$mis,$miv,$mfv);
+  # valid exponent?
+  if ($e =~ /^([+-]?)0*([0-9]+)$/)	# strip leading zeros
+    {
+    $es = $1; $ev = $2;
+    # valid mantissa?
+    return if $m eq '.' || $m eq '';
+    my ($mi,$mf,$lastf) = split /\./,$m;
+    return if defined $lastf;		# lastf defined => 1.2.3 or others
+    $mi = '0' if !defined $mi;
+    $mi .= '0' if $mi =~ /^[\-\+]?$/;
+    $mf = '0' if !defined $mf || $mf eq '';
+    if ($mi =~ /^([+-]?)0*([0-9]+)$/)		# strip leading zeros
+      {
+      $mis = $1||'+'; $miv = $2;
+      return unless ($mf =~ /^([0-9]*?)0*$/);	# strip trailing zeros
+      $mfv = $1;
+      # handle the 0e999 case here
+      $ev = 0 if $miv eq '0' && $mfv eq '';
+      return (\$mis,\$miv,\$mfv,\$es,\$ev);
+      }
+    }
+  return; # NaN, not a number
+  }
+
+##############################################################################
+# internal calculation routines (others are in Math::BigInt::Calc etc)
+
+sub __lcm 
+  { 
+  # (BINT or num_str, BINT or num_str) return BINT
+  # does modify first argument
+  # LCM
+ 
+  my ($x,$ty) = @_;
+  return $x->bnan() if ($x->{sign} eq $nan) || ($ty->{sign} eq $nan);
+  my $method = ref($x) . '::bgcd';
+  no strict 'refs';
+  $x * $ty / &$method($x,$ty);
+  }
+
+###############################################################################
+# trigonometric functions
+
+sub bpi
+  {
+  # Calculate PI to N digits. Unless upgrading is in effect, returns the
+  # result truncated to an integer, that is, always returns '3'.
+  my ($self,$n) = @_;
+  if (@_ == 1)
+    {
+    # called like Math::BigInt::bpi(10);
+    $n = $self; $self = $class;
+    }
+  $self = ref($self) if ref($self);
+
+  return $upgrade->new($n) if defined $upgrade;
+
+  # hard-wired to "3"
+  $self->new(3);
+  }
+
+sub bcos
+  {
+  # Calculate cosinus(x) to N digits. Unless upgrading is in effect, returns the
+  # result truncated to an integer.
+  my ($self,$x,@r) = ref($_[0]) ? (undef,@_) : objectify(1,@_);
+
+  return $x if $x->modify('bcos');
+
+  return $x->bnan() if $x->{sign} !~ /^[+-]\z/;	# -inf +inf or NaN => NaN
+
+  return $upgrade->new($x)->bcos(@r) if defined $upgrade;
+
+  require Math::BigFloat;
+  # calculate the result and truncate it to integer
+  my $t = Math::BigFloat->new($x)->bcos(@r)->as_int();
+
+  $x->bone() if $t->is_one();
+  $x->bzero() if $t->is_zero();
+  $x->round(@r);
+  }
+
+sub bsin
+  {
+  # Calculate sinus(x) to N digits. Unless upgrading is in effect, returns the
+  # result truncated to an integer.
+  my ($self,$x,@r) = ref($_[0]) ? (undef,@_) : objectify(1,@_);
+
+  return $x if $x->modify('bsin');
+
+  return $x->bnan() if $x->{sign} !~ /^[+-]\z/;	# -inf +inf or NaN => NaN
+
+  return $upgrade->new($x)->bsin(@r) if defined $upgrade;
+
+  require Math::BigFloat;
+  # calculate the result and truncate it to integer
+  my $t = Math::BigFloat->new($x)->bsin(@r)->as_int();
+
+  $x->bone() if $t->is_one();
+  $x->bzero() if $t->is_zero();
+  $x->round(@r);
+  }
+
+sub batan2
+  { 
+  # calculate arcus tangens of ($y/$x)
+ 
+  # set up parameters
+  my ($self,$y,$x,@r) = (ref($_[0]),@_);
+  # objectify is costly, so avoid it
+  if ((!ref($_[0])) || (ref($_[0]) ne ref($_[1])))
+    {
+    ($self,$y,$x,@r) = objectify(2,@_);
+    }
+
+  return $y if $y->modify('batan2');
+
+  return $y->bnan() if ($y->{sign} eq $nan) || ($x->{sign} eq $nan);
+
+  # Y    X
+  # != 0 -inf result is +- pi
+  if ($x->is_inf() || $y->is_inf())
+    {
+    # upgrade to BigFloat etc.
+    return $upgrade->new($y)->batan2($upgrade->new($x),@r) if defined $upgrade;
+    if ($y->is_inf())
+      {
+      if ($x->{sign} eq '-inf')
+        {
+        # calculate 3 pi/4 => 2.3.. => 2
+        $y->bone( substr($y->{sign},0,1) );
+        $y->bmul($self->new(2));
+        }
+      elsif ($x->{sign} eq '+inf')
+        {
+        # calculate pi/4 => 0.7 => 0
+        $y->bzero();
+        }
+      else
+        {
+        # calculate pi/2 => 1.5 => 1
+        $y->bone( substr($y->{sign},0,1) );
+        }
+      }
+    else
+      {
+      if ($x->{sign} eq '+inf')
+        {
+        # calculate pi/4 => 0.7 => 0
+        $y->bzero();
+        }
+      else
+        {
+        # PI => 3.1415.. => 3
+        $y->bone( substr($y->{sign},0,1) );
+        $y->bmul($self->new(3));
+        }
+      }
+    return $y;
+    }
+
+  return $upgrade->new($y)->batan2($upgrade->new($x),@r) if defined $upgrade;
+
+  require Math::BigFloat;
+  my $r = Math::BigFloat->new($y)->batan2(Math::BigFloat->new($x),@r)->as_int();
+
+  $x->{value} = $r->{value};
+  $x->{sign} = $r->{sign};
+
+  $x;
+  }
+
+sub batan
+  {
+  # Calculate arcus tangens of x to N digits. Unless upgrading is in effect, returns the
+  # result truncated to an integer.
+  my ($self,$x,@r) = ref($_[0]) ? (undef,@_) : objectify(1,@_);
+
+  return $x if $x->modify('batan');
+
+  return $x->bnan() if $x->{sign} !~ /^[+-]\z/;	# -inf +inf or NaN => NaN
+
+  return $upgrade->new($x)->batan(@r) if defined $upgrade;
+
+  # calculate the result and truncate it to integer
+  my $t = Math::BigFloat->new($x)->batan(@r);
+
+  $x->{value} = $CALC->_new( $x->as_int()->bstr() );
+  $x->round(@r);
+  }
+
+###############################################################################
+# this method returns 0 if the object can be modified, or 1 if not.
+# We use a fast constant sub() here, to avoid costly calls. Subclasses
+# may override it with special code (f.i. Math::BigInt::Constant does so)
+
+sub modify () { 0; }
+
+1;
+__END__
+
+=pod
+
+=head1 NAME
+
+Math::BigInt - Arbitrary size integer/float math package
+
+=head1 SYNOPSIS
+
+  use Math::BigInt;
+
+  # or make it faster with huge numbers: install (optional)
+  # Math::BigInt::GMP and always use (it will fall back to
+  # pure Perl if the GMP library is not installed):
+  # (See also the L<MATH LIBRARY> section!)
+
+  # will warn if Math::BigInt::GMP cannot be found
+  use Math::BigInt lib => 'GMP';
+
+  # to supress the warning use this:
+  # use Math::BigInt try => 'GMP';
+
+  # dies if GMP cannot be loaded:
+  # use Math::BigInt only => 'GMP';
+
+  my $str = '1234567890';
+  my @values = (64,74,18);
+  my $n = 1; my $sign = '-';
+
+  # Number creation	
+  my $x = Math::BigInt->new($str);	# defaults to 0
+  my $y = $x->copy();			# make a true copy
+  my $nan  = Math::BigInt->bnan(); 	# create a NotANumber
+  my $zero = Math::BigInt->bzero();	# create a +0
+  my $inf = Math::BigInt->binf();	# create a +inf
+  my $inf = Math::BigInt->binf('-');	# create a -inf
+  my $one = Math::BigInt->bone();	# create a +1
+  my $mone = Math::BigInt->bone('-');	# create a -1
+
+  my $pi = Math::BigInt->bpi();		# returns '3'
+					# see Math::BigFloat::bpi()
+
+  $h = Math::BigInt->new('0x123');	# from hexadecimal
+  $b = Math::BigInt->new('0b101');	# from binary
+  $o = Math::BigInt->from_oct('0101');	# from octal
+
+  # Testing (don't modify their arguments)
+  # (return true if the condition is met, otherwise false)
+
+  $x->is_zero();	# if $x is +0
+  $x->is_nan();		# if $x is NaN
+  $x->is_one();		# if $x is +1
+  $x->is_one('-');	# if $x is -1
+  $x->is_odd();		# if $x is odd
+  $x->is_even();	# if $x is even
+  $x->is_pos();		# if $x >= 0
+  $x->is_neg();		# if $x <  0
+  $x->is_inf($sign);	# if $x is +inf, or -inf (sign is default '+')
+  $x->is_int();		# if $x is an integer (not a float)
+
+  # comparing and digit/sign extraction
+  $x->bcmp($y);		# compare numbers (undef,<0,=0,>0)
+  $x->bacmp($y);	# compare absolutely (undef,<0,=0,>0)
+  $x->sign();		# return the sign, either +,- or NaN
+  $x->digit($n);	# return the nth digit, counting from right
+  $x->digit(-$n);	# return the nth digit, counting from left
+
+  # The following all modify their first argument. If you want to preserve
+  # $x, use $z = $x->copy()->bXXX($y); See under L<CAVEATS> for why this is
+  # necessary when mixing $a = $b assignments with non-overloaded math.
+
+  $x->bzero();		# set $x to 0
+  $x->bnan();		# set $x to NaN
+  $x->bone();		# set $x to +1
+  $x->bone('-');	# set $x to -1
+  $x->binf();		# set $x to inf
+  $x->binf('-');	# set $x to -inf
+
+  $x->bneg();		# negation
+  $x->babs();		# absolute value
+  $x->bnorm();		# normalize (no-op in BigInt)
+  $x->bnot();		# two's complement (bit wise not)
+  $x->binc();		# increment $x by 1
+  $x->bdec();		# decrement $x by 1
+  
+  $x->badd($y);		# addition (add $y to $x)
+  $x->bsub($y);		# subtraction (subtract $y from $x)
+  $x->bmul($y);		# multiplication (multiply $x by $y)
+  $x->bdiv($y);		# divide, set $x to quotient
+			# return (quo,rem) or quo if scalar
+
+  $x->bmuladd($y,$z);	# $x = $x * $y + $z
+
+  $x->bmod($y);		   # modulus (x % y)
+  $x->bmodpow($exp,$mod);  # modular exponentation (($num**$exp) % $mod))
+  $x->bmodinv($mod);	   # the inverse of $x in the given modulus $mod
+
+  $x->bpow($y);		   # power of arguments (x ** y)
+  $x->blsft($y);	   # left shift in base 2
+  $x->brsft($y);	   # right shift in base 2
+			   # returns (quo,rem) or quo if in scalar context
+  $x->blsft($y,$n);	   # left shift by $y places in base $n
+  $x->brsft($y,$n);	   # right shift by $y places in base $n
+			   # returns (quo,rem) or quo if in scalar context
+  
+  $x->band($y);		   # bitwise and
+  $x->bior($y);		   # bitwise inclusive or
+  $x->bxor($y);		   # bitwise exclusive or
+  $x->bnot();		   # bitwise not (two's complement)
+
+  $x->bsqrt();		   # calculate square-root
+  $x->broot($y);	   # $y'th root of $x (e.g. $y == 3 => cubic root)
+  $x->bfac();		   # factorial of $x (1*2*3*4*..$x)
+
+  $x->bnok($y);		   # x over y (binomial coefficient n over k)
+
+  $x->blog();		   # logarithm of $x to base e (Euler's number)
+  $x->blog($base);	   # logarithm of $x to base $base (f.i. 2)
+  $x->bexp();		   # calculate e ** $x where e is Euler's number
+  
+  $x->round($A,$P,$mode);  # round to accuracy or precision using mode $mode
+  $x->bround($n);	   # accuracy: preserve $n digits
+  $x->bfround($n);	   # $n > 0: round $nth digits,
+			   # $n < 0: round to the $nth digit after the
+			   # dot, no-op for BigInts
+
+  # The following do not modify their arguments in BigInt (are no-ops),
+  # but do so in BigFloat:
+
+  $x->bfloor();		   # return integer less or equal than $x
+  $x->bceil();		   # return integer greater or equal than $x
+  
+  # The following do not modify their arguments:
+
+  # greatest common divisor (no OO style)
+  my $gcd = Math::BigInt::bgcd(@values);
+  # lowest common multiplicator (no OO style)
+  my $lcm = Math::BigInt::blcm(@values);	
+ 
+  $x->length();		   # return number of digits in number
+  ($xl,$f) = $x->length(); # length of number and length of fraction part,
+			   # latter is always 0 digits long for BigInts
+
+  $x->exponent();	   # return exponent as BigInt
+  $x->mantissa();	   # return (signed) mantissa as BigInt
+  $x->parts();		   # return (mantissa,exponent) as BigInt
+  $x->copy();		   # make a true copy of $x (unlike $y = $x;)
+  $x->as_int();		   # return as BigInt (in BigInt: same as copy())
+  $x->numify();		   # return as scalar (might overflow!)
+  
+  # conversation to string (do not modify their argument)
+  $x->bstr();		   # normalized string (e.g. '3')
+  $x->bsstr();		   # norm. string in scientific notation (e.g. '3E0')
+  $x->as_hex();		   # as signed hexadecimal string with prefixed 0x
+  $x->as_bin();		   # as signed binary string with prefixed 0b
+  $x->as_oct();		   # as signed octal string with prefixed 0
+
+
+  # precision and accuracy (see section about rounding for more)
+  $x->precision();	   # return P of $x (or global, if P of $x undef)
+  $x->precision($n);	   # set P of $x to $n
+  $x->accuracy();	   # return A of $x (or global, if A of $x undef)
+  $x->accuracy($n);	   # set A $x to $n
+
+  # Global methods
+  Math::BigInt->precision();	# get/set global P for all BigInt objects
+  Math::BigInt->accuracy(); 	# get/set global A for all BigInt objects
+  Math::BigInt->round_mode();	# get/set global round mode, one of
+				# 'even', 'odd', '+inf', '-inf', 'zero', 'trunc' or 'common'
+  Math::BigInt->config();	# return hash containing configuration
+
+=head1 DESCRIPTION
+
+All operators (including basic math operations) are overloaded if you
+declare your big integers as
+
+  $i = new Math::BigInt '123_456_789_123_456_789';
+
+Operations with overloaded operators preserve the arguments which is
+exactly what you expect.
+
+=over 2
+
+=item Input
+
+Input values to these routines may be any string, that looks like a number
+and results in an integer, including hexadecimal and binary numbers.
+
+Scalars holding numbers may also be passed, but note that non-integer numbers
+may already have lost precision due to the conversation to float. Quote
+your input if you want BigInt to see all the digits:
+
+	$x = Math::BigInt->new(12345678890123456789);	# bad
+	$x = Math::BigInt->new('12345678901234567890');	# good
+
+You can include one underscore between any two digits.
+
+This means integer values like 1.01E2 or even 1000E-2 are also accepted.
+Non-integer values result in NaN.
+
+Hexadecimal (prefixed with "0x") and binary numbers (prefixed with "0b")
+are accepted, too. Please note that octal numbers are not recognized
+by new(), so the following will print "123":
+
+	perl -MMath::BigInt -le 'print Math::BigInt->new("0123")'
+	
+To convert an octal number, use from_oct();
+
+	perl -MMath::BigInt -le 'print Math::BigInt->from_oct("0123")'
+
+Currently, Math::BigInt::new() defaults to 0, while Math::BigInt::new('')
+results in 'NaN'. This might change in the future, so use always the following
+explicit forms to get a zero or NaN:
+
+	$zero = Math::BigInt->bzero(); 
+	$nan = Math::BigInt->bnan(); 
+
+C<bnorm()> on a BigInt object is now effectively a no-op, since the numbers 
+are always stored in normalized form. If passed a string, creates a BigInt 
+object from the input.
+
+=item Output
+
+Output values are BigInt objects (normalized), except for the methods which
+return a string (see L<SYNOPSIS>).
+
+Some routines (C<is_odd()>, C<is_even()>, C<is_zero()>, C<is_one()>,
+C<is_nan()>, etc.) return true or false, while others (C<bcmp()>, C<bacmp()>)
+return either undef (if NaN is involved), <0, 0 or >0 and are suited for sort.
+
+=back
+
+=head1 METHODS
+
+Each of the methods below (except config(), accuracy() and precision())
+accepts three additional parameters. These arguments C<$A>, C<$P> and C<$R>
+are C<accuracy>, C<precision> and C<round_mode>. Please see the section about
+L<ACCURACY and PRECISION> for more information.
+
+=head2 config()
+
+	use Data::Dumper;
+
+	print Dumper ( Math::BigInt->config() );
+	print Math::BigInt->config()->{lib},"\n";
+
+Returns a hash containing the configuration, e.g. the version number, lib
+loaded etc. The following hash keys are currently filled in with the
+appropriate information.
+
+	key		Description
+			Example
+	============================================================
+	lib		Name of the low-level math library
+			Math::BigInt::Calc
+	lib_version 	Version of low-level math library (see 'lib')
+			0.30
+	class		The class name of config() you just called
+			Math::BigInt
+	upgrade		To which class math operations might be upgraded
+			Math::BigFloat
+	downgrade	To which class math operations might be downgraded
+			undef
+	precision	Global precision
+			undef
+	accuracy	Global accuracy
+			undef
+	round_mode	Global round mode
+			even
+	version		version number of the class you used
+			1.61
+	div_scale	Fallback accuracy for div
+			40
+	trap_nan	If true, traps creation of NaN via croak()
+			1
+	trap_inf	If true, traps creation of +inf/-inf via croak()
+			1
+
+The following values can be set by passing C<config()> a reference to a hash:
+
+	trap_inf trap_nan
+        upgrade downgrade precision accuracy round_mode div_scale
+
+Example:
+	
+	$new_cfg = Math::BigInt->config( { trap_inf => 1, precision => 5 } );
+
+=head2 accuracy()
+
+	$x->accuracy(5);		# local for $x
+	CLASS->accuracy(5);		# global for all members of CLASS
+					# Note: This also applies to new()!
+
+	$A = $x->accuracy();		# read out accuracy that affects $x
+	$A = CLASS->accuracy();		# read out global accuracy
+
+Set or get the global or local accuracy, aka how many significant digits the
+results have. If you set a global accuracy, then this also applies to new()!
+
+Warning! The accuracy I<sticks>, e.g. once you created a number under the
+influence of C<< CLASS->accuracy($A) >>, all results from math operations with
+that number will also be rounded. 
+
+In most cases, you should probably round the results explicitly using one of
+L<round()>, L<bround()> or L<bfround()> or by passing the desired accuracy
+to the math operation as additional parameter:
+
+        my $x = Math::BigInt->new(30000);
+        my $y = Math::BigInt->new(7);
+        print scalar $x->copy()->bdiv($y, 2);		# print 4300
+        print scalar $x->copy()->bdiv($y)->bround(2);	# print 4300
+
+Please see the section about L<ACCURACY and PRECISION> for further details.
+
+Value must be greater than zero. Pass an undef value to disable it:
+
+	$x->accuracy(undef);
+	Math::BigInt->accuracy(undef);
+
+Returns the current accuracy. For C<$x->accuracy()> it will return either the
+local accuracy, or if not defined, the global. This means the return value
+represents the accuracy that will be in effect for $x:
+
+	$y = Math::BigInt->new(1234567);	# unrounded
+	print Math::BigInt->accuracy(4),"\n";	# set 4, print 4
+	$x = Math::BigInt->new(123456);		# $x will be automatically rounded!
+	print "$x $y\n";			# '123500 1234567'
+	print $x->accuracy(),"\n";		# will be 4
+	print $y->accuracy(),"\n";		# also 4, since global is 4
+	print Math::BigInt->accuracy(5),"\n";	# set to 5, print 5
+	print $x->accuracy(),"\n";		# still 4
+	print $y->accuracy(),"\n";		# 5, since global is 5
+
+Note: Works also for subclasses like Math::BigFloat. Each class has it's own
+globals separated from Math::BigInt, but it is possible to subclass
+Math::BigInt and make the globals of the subclass aliases to the ones from
+Math::BigInt.
+
+=head2 precision()
+
+	$x->precision(-2);	# local for $x, round at the second digit right of the dot
+	$x->precision(2);	# ditto, round at the second digit left of the dot
+
+	CLASS->precision(5);	# Global for all members of CLASS
+				# This also applies to new()!
+	CLASS->precision(-5);	# ditto
+
+	$P = CLASS->precision();	# read out global precision 
+	$P = $x->precision();		# read out precision that affects $x
+
+Note: You probably want to use L<accuracy()> instead. With L<accuracy> you
+set the number of digits each result should have, with L<precision> you
+set the place where to round!
+
+C<precision()> sets or gets the global or local precision, aka at which digit
+before or after the dot to round all results. A set global precision also
+applies to all newly created numbers!
+
+In Math::BigInt, passing a negative number precision has no effect since no
+numbers have digits after the dot. In L<Math::BigFloat>, it will round all
+results to P digits after the dot.
+
+Please see the section about L<ACCURACY and PRECISION> for further details.
+
+Pass an undef value to disable it:
+
+	$x->precision(undef);
+	Math::BigInt->precision(undef);
+
+Returns the current precision. For C<$x->precision()> it will return either the
+local precision of $x, or if not defined, the global. This means the return
+value represents the prevision that will be in effect for $x:
+
+	$y = Math::BigInt->new(1234567);	# unrounded
+	print Math::BigInt->precision(4),"\n";	# set 4, print 4
+	$x = Math::BigInt->new(123456);		# will be automatically rounded
+	print $x;				# print "120000"!
+
+Note: Works also for subclasses like L<Math::BigFloat>. Each class has its
+own globals separated from Math::BigInt, but it is possible to subclass
+Math::BigInt and make the globals of the subclass aliases to the ones from
+Math::BigInt.
+
+=head2 brsft()
+
+	$x->brsft($y,$n);		
+
+Shifts $x right by $y in base $n. Default is base 2, used are usually 10 and
+2, but others work, too.
+
+Right shifting usually amounts to dividing $x by $n ** $y and truncating the
+result:
+
+
+	$x = Math::BigInt->new(10);
+	$x->brsft(1);			# same as $x >> 1: 5
+	$x = Math::BigInt->new(1234);
+	$x->brsft(2,10);		# result 12
+
+There is one exception, and that is base 2 with negative $x:
+
+
+	$x = Math::BigInt->new(-5);
+	print $x->brsft(1);
+
+This will print -3, not -2 (as it would if you divide -5 by 2 and truncate the
+result).
+
+=head2 new()
+
+  	$x = Math::BigInt->new($str,$A,$P,$R);
+
+Creates a new BigInt object from a scalar or another BigInt object. The
+input is accepted as decimal, hex (with leading '0x') or binary (with leading
+'0b').
+
+See L<Input> for more info on accepted input formats.
+
+=head2 from_oct()
+
+	$x = Math::BigInt->from_oct("0775");	# input is octal
+
+=head2 from_hex()
+
+	$x = Math::BigInt->from_hex("0xcafe");	# input is hexadecimal
+
+=head2 from_bin()
+
+	$x = Math::BigInt->from_oct("0x10011");	# input is binary
+
+=head2 bnan()
+
+  	$x = Math::BigInt->bnan();
+
+Creates a new BigInt object representing NaN (Not A Number).
+If used on an object, it will set it to NaN:
+
+	$x->bnan();
+
+=head2 bzero()
+
+  	$x = Math::BigInt->bzero();
+
+Creates a new BigInt object representing zero.
+If used on an object, it will set it to zero:
+
+	$x->bzero();
+
+=head2 binf()
+
+  	$x = Math::BigInt->binf($sign);
+
+Creates a new BigInt object representing infinity. The optional argument is
+either '-' or '+', indicating whether you want infinity or minus infinity.
+If used on an object, it will set it to infinity:
+
+	$x->binf();
+	$x->binf('-');
+
+=head2 bone()
+
+  	$x = Math::BigInt->binf($sign);
+
+Creates a new BigInt object representing one. The optional argument is
+either '-' or '+', indicating whether you want one or minus one.
+If used on an object, it will set it to one:
+
+	$x->bone();		# +1
+	$x->bone('-');		# -1
+
+=head2 is_one()/is_zero()/is_nan()/is_inf()
+
+  
+	$x->is_zero();			# true if arg is +0
+	$x->is_nan();			# true if arg is NaN
+	$x->is_one();			# true if arg is +1
+	$x->is_one('-');		# true if arg is -1
+	$x->is_inf();			# true if +inf
+	$x->is_inf('-');		# true if -inf (sign is default '+')
+
+These methods all test the BigInt for being one specific value and return
+true or false depending on the input. These are faster than doing something
+like:
+
+	if ($x == 0)
+
+=head2 is_pos()/is_neg()/is_positive()/is_negative()
+	
+	$x->is_pos();			# true if > 0
+	$x->is_neg();			# true if < 0
+
+The methods return true if the argument is positive or negative, respectively.
+C<NaN> is neither positive nor negative, while C<+inf> counts as positive, and
+C<-inf> is negative. A C<zero> is neither positive nor negative.
+
+These methods are only testing the sign, and not the value.
+
+C<is_positive()> and C<is_negative()> are aliases to C<is_pos()> and
+C<is_neg()>, respectively. C<is_positive()> and C<is_negative()> were
+introduced in v1.36, while C<is_pos()> and C<is_neg()> were only introduced
+in v1.68.
+
+=head2 is_odd()/is_even()/is_int()
+
+	$x->is_odd();			# true if odd, false for even
+	$x->is_even();			# true if even, false for odd
+	$x->is_int();			# true if $x is an integer
+
+The return true when the argument satisfies the condition. C<NaN>, C<+inf>,
+C<-inf> are not integers and are neither odd nor even.
+
+In BigInt, all numbers except C<NaN>, C<+inf> and C<-inf> are integers.
+
+=head2 bcmp()
+
+	$x->bcmp($y);
+
+Compares $x with $y and takes the sign into account.
+Returns -1, 0, 1 or undef.
+
+=head2 bacmp()
+
+	$x->bacmp($y);
+
+Compares $x with $y while ignoring their. Returns -1, 0, 1 or undef.
+
+=head2 sign()
+
+	$x->sign();
+
+Return the sign, of $x, meaning either C<+>, C<->, C<-inf>, C<+inf> or NaN.
+
+If you want $x to have a certain sign, use one of the following methods:
+
+	$x->babs();		# '+'
+	$x->babs()->bneg();	# '-'
+	$x->bnan();		# 'NaN'
+	$x->binf();		# '+inf'
+	$x->binf('-');		# '-inf'
+
+=head2 digit()
+
+	$x->digit($n);		# return the nth digit, counting from right
+
+If C<$n> is negative, returns the digit counting from left.
+
+=head2 bneg()
+
+	$x->bneg();
+
+Negate the number, e.g. change the sign between '+' and '-', or between '+inf'
+and '-inf', respectively. Does nothing for NaN or zero.
+
+=head2 babs()
+
+	$x->babs();
+
+Set the number to its absolute value, e.g. change the sign from '-' to '+'
+and from '-inf' to '+inf', respectively. Does nothing for NaN or positive
+numbers.
+
+=head2 bnorm()
+
+	$x->bnorm();			# normalize (no-op)
+
+=head2 bnot()
+
+	$x->bnot();			
+
+Two's complement (bitwise not). This is equivalent to
+
+	$x->binc()->bneg();
+
+but faster.
+
+=head2 binc()
+
+	$x->binc();			# increment x by 1
+
+=head2 bdec()
+
+	$x->bdec();			# decrement x by 1
+
+=head2 badd()
+
+	$x->badd($y);			# addition (add $y to $x)
+
+=head2 bsub()
+
+	$x->bsub($y);			# subtraction (subtract $y from $x)
+
+=head2 bmul()
+
+	$x->bmul($y);			# multiplication (multiply $x by $y)
+
+=head2 bmuladd()
+
+	$x->bmuladd($y,$z);
+
+Multiply $x by $y, and then add $z to the result,
+
+This method was added in v1.87 of Math::BigInt (June 2007).
+
+=head2 bdiv()
+
+	$x->bdiv($y);			# divide, set $x to quotient
+					# return (quo,rem) or quo if scalar
+
+=head2 bmod()
+
+	$x->bmod($y);			# modulus (x % y)
+
+=head2 bmodinv()
+
+	num->bmodinv($mod);		# modular inverse
+
+Returns the inverse of C<$num> in the given modulus C<$mod>.  'C<NaN>' is
+returned unless C<$num> is relatively prime to C<$mod>, i.e. unless
+C<bgcd($num, $mod)==1>.
+
+=head2 bmodpow()
+
+	$num->bmodpow($exp,$mod);	# modular exponentation
+					# ($num**$exp % $mod)
+
+Returns the value of C<$num> taken to the power C<$exp> in the modulus
+C<$mod> using binary exponentation.  C<bmodpow> is far superior to
+writing
+
+	$num ** $exp % $mod
+
+because it is much faster - it reduces internal variables into
+the modulus whenever possible, so it operates on smaller numbers.
+
+C<bmodpow> also supports negative exponents.
+
+	bmodpow($num, -1, $mod)
+
+is exactly equivalent to
+
+	bmodinv($num, $mod)
+
+=head2 bpow()
+
+	$x->bpow($y);			# power of arguments (x ** y)
+
+=head2 blog()
+
+	$x->blog($base, $accuracy);	# logarithm of x to the base $base
+
+If C<$base> is not defined, Euler's number (e) is used:
+
+	print $x->blog(undef, 100);	# log(x) to 100 digits
+
+=head2 bexp()
+
+	$x->bexp($accuracy);		# calculate e ** X
+
+Calculates the expression C<e ** $x> where C<e> is Euler's number.
+
+This method was added in v1.82 of Math::BigInt (April 2007).
+
+See also L<blog()>.
+
+=head2 bnok()
+
+	$x->bnok($y);		   # x over y (binomial coefficient n over k)
+
+Calculates the binomial coefficient n over k, also called the "choose"
+function. The result is equivalent to:
+
+	( n )      n!
+	| - |  = -------
+	( k )    k!(n-k)!
+
+This method was added in v1.84 of Math::BigInt (April 2007).
+
+=head2 bpi()
+
+	print Math::BigInt->bpi(100), "\n";		# 3
+
+Returns PI truncated to an integer, with the argument being ignored. This means
+under BigInt this always returns C<3>.
+
+If upgrading is in effect, returns PI, rounded to N digits with the
+current rounding mode:
+
+	use Math::BigFloat;
+	use Math::BigInt upgrade => Math::BigFloat;
+	print Math::BigInt->bpi(3), "\n";		# 3.14
+	print Math::BigInt->bpi(100), "\n";		# 3.1415....
+
+This method was added in v1.87 of Math::BigInt (June 2007).
+
+=head2 bcos()
+
+	my $x = Math::BigInt->new(1);
+	print $x->bcos(100), "\n";
+
+Calculate the cosinus of $x, modifying $x in place.
+
+In BigInt, unless upgrading is in effect, the result is truncated to an
+integer.
+
+This method was added in v1.87 of Math::BigInt (June 2007).
+
+=head2 bsin()
+
+	my $x = Math::BigInt->new(1);
+	print $x->bsin(100), "\n";
+
+Calculate the sinus of $x, modifying $x in place.
+
+In BigInt, unless upgrading is in effect, the result is truncated to an
+integer.
+
+This method was added in v1.87 of Math::BigInt (June 2007).
+
+=head2 batan2()
+
+	my $x = Math::BigInt->new(1);
+	my $y = Math::BigInt->new(1);
+	print $y->batan2($x), "\n";
+
+Calculate the arcus tangens of C<$y> divided by C<$x>, modifying $y in place.
+
+In BigInt, unless upgrading is in effect, the result is truncated to an
+integer.
+
+This method was added in v1.87 of Math::BigInt (June 2007).
+
+=head2 batan()
+
+	my $x = Math::BigFloat->new(0.5);
+	print $x->batan(100), "\n";
+
+Calculate the arcus tangens of $x, modifying $x in place.
+
+In BigInt, unless upgrading is in effect, the result is truncated to an
+integer.
+
+This method was added in v1.87 of Math::BigInt (June 2007).
+
+=head2 blsft()
+
+	$x->blsft($y);		# left shift in base 2
+	$x->blsft($y,$n);	# left shift, in base $n (like 10)
+
+=head2 brsft()
+
+	$x->brsft($y);		# right shift in base 2
+	$x->brsft($y,$n);	# right shift, in base $n (like 10)
+
+=head2 band()
+
+	$x->band($y);			# bitwise and
+
+=head2 bior()
+
+	$x->bior($y);			# bitwise inclusive or
+
+=head2 bxor()
+
+	$x->bxor($y);			# bitwise exclusive or
+
+=head2 bnot()
+
+	$x->bnot();			# bitwise not (two's complement)
+
+=head2 bsqrt()
+
+	$x->bsqrt();			# calculate square-root
+
+=head2 broot()
+
+	$x->broot($N);
+
+Calculates the N'th root of C<$x>.
+
+=head2 bfac()
+
+	$x->bfac();			# factorial of $x (1*2*3*4*..$x)
+
+=head2 round()
+
+	$x->round($A,$P,$round_mode);
+	
+Round $x to accuracy C<$A> or precision C<$P> using the round mode
+C<$round_mode>.
+
+=head2 bround()
+
+	$x->bround($N);               # accuracy: preserve $N digits
+
+=head2 bfround()
+
+	$x->bfround($N);
+
+If N is > 0, rounds to the Nth digit from the left. If N < 0, rounds to
+the Nth digit after the dot. Since BigInts are integers, the case N < 0
+is a no-op for them.
+
+Examples:
+
+	Input		N		Result
+	===================================================
+	123456.123456	3		123500
+	123456.123456	2		123450
+	123456.123456	-2		123456.12
+	123456.123456	-3		123456.123
+
+=head2 bfloor()
+
+	$x->bfloor();			
+
+Set $x to the integer less or equal than $x. This is a no-op in BigInt, but
+does change $x in BigFloat.
+
+=head2 bceil()
+
+	$x->bceil();
+
+Set $x to the integer greater or equal than $x. This is a no-op in BigInt, but
+does change $x in BigFloat.
+
+=head2 bgcd()
+
+	bgcd(@values);		# greatest common divisor (no OO style)
+
+=head2 blcm()
+
+	blcm(@values);		# lowest common multiplicator (no OO style)
+ 
+head2 length()
+
+	$x->length();
+        ($xl,$fl) = $x->length();
+
+Returns the number of digits in the decimal representation of the number.
+In list context, returns the length of the integer and fraction part. For
+BigInt's, the length of the fraction part will always be 0.
+
+=head2 exponent()
+
+	$x->exponent();
+
+Return the exponent of $x as BigInt.
+
+=head2 mantissa()
+
+	$x->mantissa();
+
+Return the signed mantissa of $x as BigInt.
+
+=head2 parts()
+
+	$x->parts();		# return (mantissa,exponent) as BigInt
+
+=head2 copy()
+
+	$x->copy();		# make a true copy of $x (unlike $y = $x;)
+
+=head2 as_int()/as_number()
+
+	$x->as_int();	
+
+Returns $x as a BigInt (truncated towards zero). In BigInt this is the same as
+C<copy()>. 
+
+C<as_number()> is an alias to this method. C<as_number> was introduced in
+v1.22, while C<as_int()> was only introduced in v1.68.
+  
+=head2 bstr()
+
+	$x->bstr();
+
+Returns a normalized string representation of C<$x>.
+
+=head2 bsstr()
+
+	$x->bsstr();		# normalized string in scientific notation
+
+=head2 as_hex()
+
+	$x->as_hex();		# as signed hexadecimal string with prefixed 0x
+
+=head2 as_bin()
+
+	$x->as_bin();		# as signed binary string with prefixed 0b
+
+=head2 as_oct()
+
+	$x->as_oct();		# as signed octal string with prefixed 0
+
+=head2 numify()
+
+	print $x->numify();
+
+This returns a normal Perl scalar from $x. It is used automatically
+whenever a scalar is needed, for instance in array index operations.
+
+This loses precision, to avoid this use L<as_int()> instead.
+
+=head2 modify()
+
+	$x->modify('bpowd');
+
+This method returns 0 if the object can be modified with the given
+peration, or 1 if not.
+
+This is used for instance by L<Math::BigInt::Constant>.
+
+=head2 upgrade()/downgrade()
+
+Set/get the class for downgrade/upgrade operations. Thuis is used
+for instance by L<bignum>. The defaults are '', thus the following
+operation will create a BigInt, not a BigFloat:
+
+	my $i = Math::BigInt->new(123);
+	my $f = Math::BigFloat->new('123.1');
+
+	print $i + $f,"\n";			# print 246
+
+=head2 div_scale()
+
+Set/get the number of digits for the default precision in divide
+operations.
+
+=head2 round_mode()
+
+Set/get the current round mode.
+
+=head1 ACCURACY and PRECISION
+
+Since version v1.33, Math::BigInt and Math::BigFloat have full support for
+accuracy and precision based rounding, both automatically after every
+operation, as well as manually.
+
+This section describes the accuracy/precision handling in Math::Big* as it
+used to be and as it is now, complete with an explanation of all terms and
+abbreviations.
+
+Not yet implemented things (but with correct description) are marked with '!',
+things that need to be answered are marked with '?'.
+
+In the next paragraph follows a short description of terms used here (because
+these may differ from terms used by others people or documentation).
+
+During the rest of this document, the shortcuts A (for accuracy), P (for
+precision), F (fallback) and R (rounding mode) will be used.
+
+=head2 Precision P
+
+A fixed number of digits before (positive) or after (negative)
+the decimal point. For example, 123.45 has a precision of -2. 0 means an
+integer like 123 (or 120). A precision of 2 means two digits to the left
+of the decimal point are zero, so 123 with P = 1 becomes 120. Note that
+numbers with zeros before the decimal point may have different precisions,
+because 1200 can have p = 0, 1 or 2 (depending on what the inital value
+was). It could also have p < 0, when the digits after the decimal point
+are zero.
+
+The string output (of floating point numbers) will be padded with zeros:
+ 
+	Initial value   P       A	Result          String
+	------------------------------------------------------------
+	1234.01         -3      	1000            1000
+	1234            -2      	1200            1200
+	1234.5          -1      	1230            1230
+	1234.001        1       	1234            1234.0
+	1234.01         0       	1234            1234
+	1234.01         2       	1234.01		1234.01
+	1234.01         5       	1234.01		1234.01000
+
+For BigInts, no padding occurs.
+
+=head2 Accuracy A
+
+Number of significant digits. Leading zeros are not counted. A
+number may have an accuracy greater than the non-zero digits
+when there are zeros in it or trailing zeros. For example, 123.456 has
+A of 6, 10203 has 5, 123.0506 has 7, 123.450000 has 8 and 0.000123 has 3.
+
+The string output (of floating point numbers) will be padded with zeros:
+
+	Initial value   P       A	Result          String
+	------------------------------------------------------------
+	1234.01			3	1230		1230
+	1234.01			6	1234.01		1234.01
+	1234.1			8	1234.1		1234.1000
+
+For BigInts, no padding occurs.
+
+=head2 Fallback F
+
+When both A and P are undefined, this is used as a fallback accuracy when
+dividing numbers.
+
+=head2 Rounding mode R
+
+When rounding a number, different 'styles' or 'kinds'
+of rounding are possible. (Note that random rounding, as in
+Math::Round, is not implemented.)
+
+=over 2
+
+=item 'trunc'
+
+truncation invariably removes all digits following the
+rounding place, replacing them with zeros. Thus, 987.65 rounded
+to tens (P=1) becomes 980, and rounded to the fourth sigdig
+becomes 987.6 (A=4). 123.456 rounded to the second place after the
+decimal point (P=-2) becomes 123.46.
+
+All other implemented styles of rounding attempt to round to the
+"nearest digit." If the digit D immediately to the right of the
+rounding place (skipping the decimal point) is greater than 5, the
+number is incremented at the rounding place (possibly causing a
+cascade of incrementation): e.g. when rounding to units, 0.9 rounds
+to 1, and -19.9 rounds to -20. If D < 5, the number is similarly
+truncated at the rounding place: e.g. when rounding to units, 0.4
+rounds to 0, and -19.4 rounds to -19.
+
+However the results of other styles of rounding differ if the
+digit immediately to the right of the rounding place (skipping the
+decimal point) is 5 and if there are no digits, or no digits other
+than 0, after that 5. In such cases:
+
+=item 'even'
+
+rounds the digit at the rounding place to 0, 2, 4, 6, or 8
+if it is not already. E.g., when rounding to the first sigdig, 0.45
+becomes 0.4, -0.55 becomes -0.6, but 0.4501 becomes 0.5.
+
+=item 'odd'
+
+rounds the digit at the rounding place to 1, 3, 5, 7, or 9 if
+it is not already. E.g., when rounding to the first sigdig, 0.45
+becomes 0.5, -0.55 becomes -0.5, but 0.5501 becomes 0.6.
+
+=item '+inf'
+
+round to plus infinity, i.e. always round up. E.g., when
+rounding to the first sigdig, 0.45 becomes 0.5, -0.55 becomes -0.5,
+and 0.4501 also becomes 0.5.
+
+=item '-inf'
+
+round to minus infinity, i.e. always round down. E.g., when
+rounding to the first sigdig, 0.45 becomes 0.4, -0.55 becomes -0.6,
+but 0.4501 becomes 0.5.
+
+=item 'zero'
+
+round to zero, i.e. positive numbers down, negative ones up.
+E.g., when rounding to the first sigdig, 0.45 becomes 0.4, -0.55
+becomes -0.5, but 0.4501 becomes 0.5.
+
+=item 'common'
+
+round up if the digit immediately to the right of the rounding place
+is 5 or greater, otherwise round down. E.g., 0.15 becomes 0.2 and
+0.149 becomes 0.1.
+
+=back
+
+The handling of A & P in MBI/MBF (the old core code shipped with Perl
+versions <= 5.7.2) is like this:
+
+=over 2
+
+=item Precision
+
+  * ffround($p) is able to round to $p number of digits after the decimal
+    point
+  * otherwise P is unused
+
+=item Accuracy (significant digits)
+
+  * fround($a) rounds to $a significant digits
+  * only fdiv() and fsqrt() take A as (optional) paramater
+    + other operations simply create the same number (fneg etc), or more (fmul)
+      of digits
+    + rounding/truncating is only done when explicitly calling one of fround
+      or ffround, and never for BigInt (not implemented)
+  * fsqrt() simply hands its accuracy argument over to fdiv.
+  * the documentation and the comment in the code indicate two different ways
+    on how fdiv() determines the maximum number of digits it should calculate,
+    and the actual code does yet another thing
+    POD:
+      max($Math::BigFloat::div_scale,length(dividend)+length(divisor))
+    Comment:
+      result has at most max(scale, length(dividend), length(divisor)) digits
+    Actual code:
+      scale = max(scale, length(dividend)-1,length(divisor)-1);
+      scale += length(divisor) - length(dividend);
+    So for lx = 3, ly = 9, scale = 10, scale will actually be 16 (10+9-3).
+    Actually, the 'difference' added to the scale is calculated from the
+    number of "significant digits" in dividend and divisor, which is derived
+    by looking at the length of the mantissa. Which is wrong, since it includes
+    the + sign (oops) and actually gets 2 for '+100' and 4 for '+101'. Oops
+    again. Thus 124/3 with div_scale=1 will get you '41.3' based on the strange
+    assumption that 124 has 3 significant digits, while 120/7 will get you
+    '17', not '17.1' since 120 is thought to have 2 significant digits.
+    The rounding after the division then uses the remainder and $y to determine
+    wether it must round up or down.
+ ?  I have no idea which is the right way. That's why I used a slightly more
+ ?  simple scheme and tweaked the few failing testcases to match it.
+
+=back
+
+This is how it works now:
+
+=over 2
+
+=item Setting/Accessing
+
+  * You can set the A global via C<< Math::BigInt->accuracy() >> or
+    C<< Math::BigFloat->accuracy() >> or whatever class you are using.
+  * You can also set P globally by using C<< Math::SomeClass->precision() >>
+    likewise.
+  * Globals are classwide, and not inherited by subclasses.
+  * to undefine A, use C<< Math::SomeCLass->accuracy(undef); >>
+  * to undefine P, use C<< Math::SomeClass->precision(undef); >>
+  * Setting C<< Math::SomeClass->accuracy() >> clears automatically
+    C<< Math::SomeClass->precision() >>, and vice versa.
+  * To be valid, A must be > 0, P can have any value.
+  * If P is negative, this means round to the P'th place to the right of the
+    decimal point; positive values mean to the left of the decimal point.
+    P of 0 means round to integer.
+  * to find out the current global A, use C<< Math::SomeClass->accuracy() >>
+  * to find out the current global P, use C<< Math::SomeClass->precision() >>
+  * use C<< $x->accuracy() >> respective C<< $x->precision() >> for the local
+    setting of C<< $x >>.
+  * Please note that C<< $x->accuracy() >> respective C<< $x->precision() >>
+    return eventually defined global A or P, when C<< $x >>'s A or P is not
+    set.
+
+=item Creating numbers
+
+  * When you create a number, you can give the desired A or P via:
+    $x = Math::BigInt->new($number,$A,$P);
+  * Only one of A or P can be defined, otherwise the result is NaN
+  * If no A or P is give ($x = Math::BigInt->new($number) form), then the
+    globals (if set) will be used. Thus changing the global defaults later on
+    will not change the A or P of previously created numbers (i.e., A and P of
+    $x will be what was in effect when $x was created)
+  * If given undef for A and P, B<no> rounding will occur, and the globals will
+    B<not> be used. This is used by subclasses to create numbers without
+    suffering rounding in the parent. Thus a subclass is able to have its own
+    globals enforced upon creation of a number by using
+    C<< $x = Math::BigInt->new($number,undef,undef) >>:
+
+	use Math::BigInt::SomeSubclass;
+	use Math::BigInt;
+
+	Math::BigInt->accuracy(2);
+	Math::BigInt::SomeSubClass->accuracy(3);
+	$x = Math::BigInt::SomeSubClass->new(1234);	
+
+    $x is now 1230, and not 1200. A subclass might choose to implement
+    this otherwise, e.g. falling back to the parent's A and P.
+
+=item Usage
+
+  * If A or P are enabled/defined, they are used to round the result of each
+    operation according to the rules below
+  * Negative P is ignored in Math::BigInt, since BigInts never have digits
+    after the decimal point
+  * Math::BigFloat uses Math::BigInt internally, but setting A or P inside
+    Math::BigInt as globals does not tamper with the parts of a BigFloat.
+    A flag is used to mark all Math::BigFloat numbers as 'never round'.
+
+=item Precedence
+
+  * It only makes sense that a number has only one of A or P at a time.
+    If you set either A or P on one object, or globally, the other one will
+    be automatically cleared.
+  * If two objects are involved in an operation, and one of them has A in
+    effect, and the other P, this results in an error (NaN).
+  * A takes precedence over P (Hint: A comes before P).
+    If neither of them is defined, nothing is used, i.e. the result will have
+    as many digits as it can (with an exception for fdiv/fsqrt) and will not
+    be rounded.
+  * There is another setting for fdiv() (and thus for fsqrt()). If neither of
+    A or P is defined, fdiv() will use a fallback (F) of $div_scale digits.
+    If either the dividend's or the divisor's mantissa has more digits than
+    the value of F, the higher value will be used instead of F.
+    This is to limit the digits (A) of the result (just consider what would
+    happen with unlimited A and P in the case of 1/3 :-)
+  * fdiv will calculate (at least) 4 more digits than required (determined by
+    A, P or F), and, if F is not used, round the result
+    (this will still fail in the case of a result like 0.12345000000001 with A
+    or P of 5, but this can not be helped - or can it?)
+  * Thus you can have the math done by on Math::Big* class in two modi:
+    + never round (this is the default):
+      This is done by setting A and P to undef. No math operation
+      will round the result, with fdiv() and fsqrt() as exceptions to guard
+      against overflows. You must explicitly call bround(), bfround() or
+      round() (the latter with parameters).
+      Note: Once you have rounded a number, the settings will 'stick' on it
+      and 'infect' all other numbers engaged in math operations with it, since
+      local settings have the highest precedence. So, to get SaferRound[tm],
+      use a copy() before rounding like this:
+
+        $x = Math::BigFloat->new(12.34);
+        $y = Math::BigFloat->new(98.76);
+        $z = $x * $y;                           # 1218.6984
+        print $x->copy()->fround(3);            # 12.3 (but A is now 3!)
+        $z = $x * $y;                           # still 1218.6984, without
+                                                # copy would have been 1210!
+
+    + round after each op:
+      After each single operation (except for testing like is_zero()), the
+      method round() is called and the result is rounded appropriately. By
+      setting proper values for A and P, you can have all-the-same-A or
+      all-the-same-P modes. For example, Math::Currency might set A to undef,
+      and P to -2, globally.
+
+ ?Maybe an extra option that forbids local A & P settings would be in order,
+ ?so that intermediate rounding does not 'poison' further math? 
+
+=item Overriding globals
+
+  * you will be able to give A, P and R as an argument to all the calculation
+    routines; the second parameter is A, the third one is P, and the fourth is
+    R (shift right by one for binary operations like badd). P is used only if
+    the first parameter (A) is undefined. These three parameters override the
+    globals in the order detailed as follows, i.e. the first defined value
+    wins:
+    (local: per object, global: global default, parameter: argument to sub)
+      + parameter A
+      + parameter P
+      + local A (if defined on both of the operands: smaller one is taken)
+      + local P (if defined on both of the operands: bigger one is taken)
+      + global A
+      + global P
+      + global F
+  * fsqrt() will hand its arguments to fdiv(), as it used to, only now for two
+    arguments (A and P) instead of one
+
+=item Local settings
+
+  * You can set A or P locally by using C<< $x->accuracy() >> or
+    C<< $x->precision() >>
+    and thus force different A and P for different objects/numbers.
+  * Setting A or P this way immediately rounds $x to the new value.
+  * C<< $x->accuracy() >> clears C<< $x->precision() >>, and vice versa.
+
+=item Rounding
+
+  * the rounding routines will use the respective global or local settings.
+    fround()/bround() is for accuracy rounding, while ffround()/bfround()
+    is for precision
+  * the two rounding functions take as the second parameter one of the
+    following rounding modes (R):
+    'even', 'odd', '+inf', '-inf', 'zero', 'trunc', 'common'
+  * you can set/get the global R by using C<< Math::SomeClass->round_mode() >>
+    or by setting C<< $Math::SomeClass::round_mode >>
+  * after each operation, C<< $result->round() >> is called, and the result may
+    eventually be rounded (that is, if A or P were set either locally,
+    globally or as parameter to the operation)
+  * to manually round a number, call C<< $x->round($A,$P,$round_mode); >>
+    this will round the number by using the appropriate rounding function
+    and then normalize it.
+  * rounding modifies the local settings of the number:
+
+        $x = Math::BigFloat->new(123.456);
+        $x->accuracy(5);
+        $x->bround(4);
+
+    Here 4 takes precedence over 5, so 123.5 is the result and $x->accuracy()
+    will be 4 from now on.
+
+=item Default values
+
+  * R: 'even'
+  * F: 40
+  * A: undef
+  * P: undef
+
+=item Remarks
+
+  * The defaults are set up so that the new code gives the same results as
+    the old code (except in a few cases on fdiv):
+    + Both A and P are undefined and thus will not be used for rounding
+      after each operation.
+    + round() is thus a no-op, unless given extra parameters A and P
+
+=back
+
+=head1 Infinity and Not a Number
+
+While BigInt has extensive handling of inf and NaN, certain quirks remain.
+
+=over 2
+
+=item oct()/hex()
+
+These perl routines currently (as of Perl v.5.8.6) cannot handle passed
+inf.
+
+	te@linux:~> perl -wle 'print 2 ** 3333'
+	inf
+	te@linux:~> perl -wle 'print 2 ** 3333 == 2 ** 3333'
+	1
+	te@linux:~> perl -wle 'print oct(2 ** 3333)'
+	0
+	te@linux:~> perl -wle 'print hex(2 ** 3333)'
+	Illegal hexadecimal digit 'i' ignored at -e line 1.
+	0
+
+The same problems occur if you pass them Math::BigInt->binf() objects. Since
+overloading these routines is not possible, this cannot be fixed from BigInt.
+
+=item ==, !=, <, >, <=, >= with NaNs
+
+BigInt's bcmp() routine currently returns undef to signal that a NaN was
+involved in a comparison. However, the overload code turns that into
+either 1 or '' and thus operations like C<< NaN != NaN >> might return
+wrong values.
+
+=item log(-inf)
+
+C<< log(-inf) >> is highly weird. Since log(-x)=pi*i+log(x), then
+log(-inf)=pi*i+inf. However, since the imaginary part is finite, the real
+infinity "overshadows" it, so the number might as well just be infinity.
+However, the result is a complex number, and since BigInt/BigFloat can only
+have real numbers as results, the result is NaN.
+
+=item exp(), cos(), sin(), atan2()
+
+These all might have problems handling infinity right.
+ 
+=back
+
+=head1 INTERNALS
+
+The actual numbers are stored as unsigned big integers (with seperate sign).
+
+You should neither care about nor depend on the internal representation; it
+might change without notice. Use B<ONLY> method calls like C<< $x->sign(); >>
+instead relying on the internal representation.
+
+=head2 MATH LIBRARY
+
+Math with the numbers is done (by default) by a module called
+C<Math::BigInt::Calc>. This is equivalent to saying:
+
+	use Math::BigInt try => 'Calc';
+
+You can change this backend library by using:
+
+	use Math::BigInt try => 'GMP';
+
+B<Note>: General purpose packages should not be explicit about the library
+to use; let the script author decide which is best.
+
+If your script works with huge numbers and Calc is too slow for them,
+you can also for the loading of one of these libraries and if none
+of them can be used, the code will die:
+
+	use Math::BigInt only => 'GMP,Pari';
+
+The following would first try to find Math::BigInt::Foo, then
+Math::BigInt::Bar, and when this also fails, revert to Math::BigInt::Calc:
+
+	use Math::BigInt try => 'Foo,Math::BigInt::Bar';
+
+The library that is loaded last will be used. Note that this can be
+overwritten at any time by loading a different library, and numbers
+constructed with different libraries cannot be used in math operations
+together.
+
+=head3 What library to use?
+
+B<Note>: General purpose packages should not be explicit about the library
+to use; let the script author decide which is best.
+
+L<Math::BigInt::GMP> and L<Math::BigInt::Pari> are in cases involving big
+numbers much faster than Calc, however it is slower when dealing with very
+small numbers (less than about 20 digits) and when converting very large
+numbers to decimal (for instance for printing, rounding, calculating their
+length in decimal etc).
+
+So please select carefully what libary you want to use.
+
+Different low-level libraries use different formats to store the numbers.
+However, you should B<NOT> depend on the number having a specific format
+internally.
+
+See the respective math library module documentation for further details.
+
+=head2 SIGN
+
+The sign is either '+', '-', 'NaN', '+inf' or '-inf'.
+
+A sign of 'NaN' is used to represent the result when input arguments are not
+numbers or as a result of 0/0. '+inf' and '-inf' represent plus respectively
+minus infinity. You will get '+inf' when dividing a positive number by 0, and
+'-inf' when dividing any negative number by 0.
+
+=head2 mantissa(), exponent() and parts()
+
+C<mantissa()> and C<exponent()> return the said parts of the BigInt such
+that:
+
+        $m = $x->mantissa();
+        $e = $x->exponent();
+        $y = $m * ( 10 ** $e );
+        print "ok\n" if $x == $y;
+
+C<< ($m,$e) = $x->parts() >> is just a shortcut that gives you both of them
+in one go. Both the returned mantissa and exponent have a sign.
+
+Currently, for BigInts C<$e> is always 0, except +inf and -inf, where it is
+C<+inf>; and for NaN, where it is C<NaN>; and for C<$x == 0>, where it is C<1>
+(to be compatible with Math::BigFloat's internal representation of a zero as
+C<0E1>).
+
+C<$m> is currently just a copy of the original number. The relation between
+C<$e> and C<$m> will stay always the same, though their real values might
+change.
+
+=head1 EXAMPLES
+ 
+  use Math::BigInt;
+
+  sub bint { Math::BigInt->new(shift); }
+
+  $x = Math::BigInt->bstr("1234")      	# string "1234"
+  $x = "$x";                         	# same as bstr()
+  $x = Math::BigInt->bneg("1234");   	# BigInt "-1234"
+  $x = Math::BigInt->babs("-12345"); 	# BigInt "12345"
+  $x = Math::BigInt->bnorm("-0.00"); 	# BigInt "0"
+  $x = bint(1) + bint(2);            	# BigInt "3"
+  $x = bint(1) + "2";                	# ditto (auto-BigIntify of "2")
+  $x = bint(1);                      	# BigInt "1"
+  $x = $x + 5 / 2;                   	# BigInt "3"
+  $x = $x ** 3;                      	# BigInt "27"
+  $x *= 2;                           	# BigInt "54"
+  $x = Math::BigInt->new(0);       	# BigInt "0"
+  $x--;                              	# BigInt "-1"
+  $x = Math::BigInt->badd(4,5)		# BigInt "9"
+  print $x->bsstr();			# 9e+0
+
+Examples for rounding:
+
+  use Math::BigFloat;
+  use Test;
+
+  $x = Math::BigFloat->new(123.4567);
+  $y = Math::BigFloat->new(123.456789);
+  Math::BigFloat->accuracy(4);		# no more A than 4
+
+  ok ($x->copy()->fround(),123.4);	# even rounding
+  print $x->copy()->fround(),"\n";	# 123.4
+  Math::BigFloat->round_mode('odd');	# round to odd
+  print $x->copy()->fround(),"\n";	# 123.5
+  Math::BigFloat->accuracy(5);		# no more A than 5
+  Math::BigFloat->round_mode('odd');	# round to odd
+  print $x->copy()->fround(),"\n";	# 123.46
+  $y = $x->copy()->fround(4),"\n";	# A = 4: 123.4
+  print "$y, ",$y->accuracy(),"\n";	# 123.4, 4
+
+  Math::BigFloat->accuracy(undef);	# A not important now
+  Math::BigFloat->precision(2); 	# P important
+  print $x->copy()->bnorm(),"\n";	# 123.46
+  print $x->copy()->fround(),"\n";	# 123.46
+
+Examples for converting:
+
+  my $x = Math::BigInt->new('0b1'.'01' x 123);
+  print "bin: ",$x->as_bin()," hex:",$x->as_hex()," dec: ",$x,"\n";
+
+=head1 Autocreating constants
+
+After C<use Math::BigInt ':constant'> all the B<integer> decimal, hexadecimal
+and binary constants in the given scope are converted to C<Math::BigInt>.
+This conversion happens at compile time. 
+
+In particular,
+
+  perl -MMath::BigInt=:constant -e 'print 2**100,"\n"'
+
+prints the integer value of C<2**100>. Note that without conversion of 
+constants the expression 2**100 will be calculated as perl scalar.
+
+Please note that strings and floating point constants are not affected,
+so that
+
+  	use Math::BigInt qw/:constant/;
+
+	$x = 1234567890123456789012345678901234567890
+		+ 123456789123456789;
+	$y = '1234567890123456789012345678901234567890'
+		+ '123456789123456789';
+
+do not work. You need an explicit Math::BigInt->new() around one of the
+operands. You should also quote large constants to protect loss of precision:
+
+	use Math::BigInt;
+
+	$x = Math::BigInt->new('1234567889123456789123456789123456789');
+
+Without the quotes Perl would convert the large number to a floating point
+constant at compile time and then hand the result to BigInt, which results in
+an truncated result or a NaN.
+
+This also applies to integers that look like floating point constants:
+
+	use Math::BigInt ':constant';
+
+	print ref(123e2),"\n";
+	print ref(123.2e2),"\n";
+
+will print nothing but newlines. Use either L<bignum> or L<Math::BigFloat>
+to get this to work.
+
+=head1 PERFORMANCE
+
+Using the form $x += $y; etc over $x = $x + $y is faster, since a copy of $x
+must be made in the second case. For long numbers, the copy can eat up to 20%
+of the work (in the case of addition/subtraction, less for
+multiplication/division). If $y is very small compared to $x, the form
+$x += $y is MUCH faster than $x = $x + $y since making the copy of $x takes
+more time then the actual addition.
+
+With a technique called copy-on-write, the cost of copying with overload could
+be minimized or even completely avoided. A test implementation of COW did show
+performance gains for overloaded math, but introduced a performance loss due
+to a constant overhead for all other operations. So Math::BigInt does currently
+not COW.
+
+The rewritten version of this module (vs. v0.01) is slower on certain
+operations, like C<new()>, C<bstr()> and C<numify()>. The reason are that it
+does now more work and handles much more cases. The time spent in these
+operations is usually gained in the other math operations so that code on
+the average should get (much) faster. If they don't, please contact the author.
+
+Some operations may be slower for small numbers, but are significantly faster
+for big numbers. Other operations are now constant (O(1), like C<bneg()>,
+C<babs()> etc), instead of O(N) and thus nearly always take much less time.
+These optimizations were done on purpose.
+
+If you find the Calc module to slow, try to install any of the replacement
+modules and see if they help you. 
+
+=head2 Alternative math libraries
+
+You can use an alternative library to drive Math::BigInt. See the section
+L<MATH LIBRARY> for more information.
+
+For more benchmark results see L<http://bloodgate.com/perl/benchmarks.html>.
+
+=head2 SUBCLASSING
+
+=head1 Subclassing Math::BigInt
+
+The basic design of Math::BigInt allows simple subclasses with very little
+work, as long as a few simple rules are followed:
+
+=over 2
+
+=item *
+
+The public API must remain consistent, i.e. if a sub-class is overloading
+addition, the sub-class must use the same name, in this case badd(). The
+reason for this is that Math::BigInt is optimized to call the object methods
+directly.
+
+=item *
+
+The private object hash keys like C<$x->{sign}> may not be changed, but
+additional keys can be added, like C<$x->{_custom}>.
+
+=item *
+
+Accessor functions are available for all existing object hash keys and should
+be used instead of directly accessing the internal hash keys. The reason for
+this is that Math::BigInt itself has a pluggable interface which permits it
+to support different storage methods.
+
+=back
+
+More complex sub-classes may have to replicate more of the logic internal of
+Math::BigInt if they need to change more basic behaviors. A subclass that
+needs to merely change the output only needs to overload C<bstr()>. 
+
+All other object methods and overloaded functions can be directly inherited
+from the parent class.
+
+At the very minimum, any subclass will need to provide its own C<new()> and can
+store additional hash keys in the object. There are also some package globals
+that must be defined, e.g.:
+
+  # Globals
+  $accuracy = undef;
+  $precision = -2;       # round to 2 decimal places
+  $round_mode = 'even';
+  $div_scale = 40;
+
+Additionally, you might want to provide the following two globals to allow
+auto-upgrading and auto-downgrading to work correctly:
+
+  $upgrade = undef;
+  $downgrade = undef;
+
+This allows Math::BigInt to correctly retrieve package globals from the 
+subclass, like C<$SubClass::precision>.  See t/Math/BigInt/Subclass.pm or
+t/Math/BigFloat/SubClass.pm completely functional subclass examples.
+
+Don't forget to 
+
+	use overload;
+
+in your subclass to automatically inherit the overloading from the parent. If
+you like, you can change part of the overloading, look at Math::String for an
+example.
+
+=head1 UPGRADING
+
+When used like this:
+
+	use Math::BigInt upgrade => 'Foo::Bar';
+
+certain operations will 'upgrade' their calculation and thus the result to
+the class Foo::Bar. Usually this is used in conjunction with Math::BigFloat:
+
+	use Math::BigInt upgrade => 'Math::BigFloat';
+
+As a shortcut, you can use the module C<bignum>:
+
+	use bignum;
+
+Also good for oneliners:
+
+	perl -Mbignum -le 'print 2 ** 255'
+
+This makes it possible to mix arguments of different classes (as in 2.5 + 2)
+as well es preserve accuracy (as in sqrt(3)).
+
+Beware: This feature is not fully implemented yet.
+
+=head2 Auto-upgrade
+
+The following methods upgrade themselves unconditionally; that is if upgrade
+is in effect, they will always hand up their work:
+
+=over 2
+
+=item bsqrt()
+
+=item div()
+
+=item blog()
+
+=item bexp()
+
+=back
+
+Beware: This list is not complete.
+
+All other methods upgrade themselves only when one (or all) of their
+arguments are of the class mentioned in $upgrade (This might change in later
+versions to a more sophisticated scheme):
+
+=head1 EXPORTS
+
+C<Math::BigInt> exports nothing by default, but can export the following methods:
+
+	bgcd
+	blcm
+
+=head1 CAVEATS
+
+Some things might not work as you expect them. Below is documented what is
+known to be troublesome:
+
+=over 1
+
+=item bstr(), bsstr() and 'cmp'
+
+Both C<bstr()> and C<bsstr()> as well as automated stringify via overload now
+drop the leading '+'. The old code would return '+3', the new returns '3'.
+This is to be consistent with Perl and to make C<cmp> (especially with
+overloading) to work as you expect. It also solves problems with C<Test.pm>,
+because its C<ok()> uses 'eq' internally. 
+
+Mark Biggar said, when asked about to drop the '+' altogether, or make only
+C<cmp> work:
+
+	I agree (with the first alternative), don't add the '+' on positive
+	numbers.  It's not as important anymore with the new internal 
+	form for numbers.  It made doing things like abs and neg easier,
+	but those have to be done differently now anyway.
+
+So, the following examples will now work all as expected:
+
+	use Test;
+        BEGIN { plan tests => 1 }
+	use Math::BigInt;
+
+	my $x = new Math::BigInt 3*3;
+	my $y = new Math::BigInt 3*3;
+
+	ok ($x,3*3);
+	print "$x eq 9" if $x eq $y;
+	print "$x eq 9" if $x eq '9';
+	print "$x eq 9" if $x eq 3*3;
+
+Additionally, the following still works:
+	
+	print "$x == 9" if $x == $y;
+	print "$x == 9" if $x == 9;
+	print "$x == 9" if $x == 3*3;
+
+There is now a C<bsstr()> method to get the string in scientific notation aka
+C<1e+2> instead of C<100>. Be advised that overloaded 'eq' always uses bstr()
+for comparison, but Perl will represent some numbers as 100 and others
+as 1e+308. If in doubt, convert both arguments to Math::BigInt before 
+comparing them as strings:
+
+	use Test;
+        BEGIN { plan tests => 3 }
+	use Math::BigInt;
+
+	$x = Math::BigInt->new('1e56'); $y = 1e56;
+	ok ($x,$y);			# will fail
+	ok ($x->bsstr(),$y);		# okay
+	$y = Math::BigInt->new($y);
+	ok ($x,$y);			# okay
+
+Alternatively, simple use C<< <=> >> for comparisons, this will get it
+always right. There is not yet a way to get a number automatically represented
+as a string that matches exactly the way Perl represents it.
+
+See also the section about L<Infinity and Not a Number> for problems in
+comparing NaNs.
+
+=item int()
+
+C<int()> will return (at least for Perl v5.7.1 and up) another BigInt, not a 
+Perl scalar:
+
+	$x = Math::BigInt->new(123);
+	$y = int($x);				# BigInt 123
+	$x = Math::BigFloat->new(123.45);
+	$y = int($x);				# BigInt 123
+
+In all Perl versions you can use C<as_number()> or C<as_int> for the same
+effect:
+
+	$x = Math::BigFloat->new(123.45);
+	$y = $x->as_number();			# BigInt 123
+	$y = $x->as_int();			# ditto
+
+This also works for other subclasses, like Math::String.
+
+If you want a real Perl scalar, use C<numify()>:
+
+	$y = $x->numify();			# 123 as scalar
+
+This is seldom necessary, though, because this is done automatically, like
+when you access an array:
+
+	$z = $array[$x];			# does work automatically
+
+=item length
+
+The following will probably not do what you expect:
+
+	$c = Math::BigInt->new(123);
+	print $c->length(),"\n";		# prints 30
+
+It prints both the number of digits in the number and in the fraction part
+since print calls C<length()> in list context. Use something like: 
+	
+	print scalar $c->length(),"\n";		# prints 3 
+
+=item bdiv
+
+The following will probably not do what you expect:
+
+	print $c->bdiv(10000),"\n";
+
+It prints both quotient and remainder since print calls C<bdiv()> in list
+context. Also, C<bdiv()> will modify $c, so be careful. You probably want
+to use
+	
+	print $c / 10000,"\n";
+	print scalar $c->bdiv(10000),"\n";  # or if you want to modify $c
+
+instead.
+
+The quotient is always the greatest integer less than or equal to the
+real-valued quotient of the two operands, and the remainder (when it is
+nonzero) always has the same sign as the second operand; so, for
+example,
+
+	  1 / 4  => ( 0, 1)
+	  1 / -4 => (-1,-3)
+	 -3 / 4  => (-1, 1)
+	 -3 / -4 => ( 0,-3)
+	-11 / 2  => (-5,1)
+	 11 /-2  => (-5,-1)
+
+As a consequence, the behavior of the operator % agrees with the
+behavior of Perl's built-in % operator (as documented in the perlop
+manpage), and the equation
+
+	$x == ($x / $y) * $y + ($x % $y)
+
+holds true for any $x and $y, which justifies calling the two return
+values of bdiv() the quotient and remainder. The only exception to this rule
+are when $y == 0 and $x is negative, then the remainder will also be
+negative. See below under "infinity handling" for the reasoning behind this.
+
+Perl's 'use integer;' changes the behaviour of % and / for scalars, but will
+not change BigInt's way to do things. This is because under 'use integer' Perl
+will do what the underlying C thinks is right and this is different for each
+system. If you need BigInt's behaving exactly like Perl's 'use integer', bug
+the author to implement it ;)
+
+=item infinity handling
+
+Here are some examples that explain the reasons why certain results occur while
+handling infinity:
+
+The following table shows the result of the division and the remainder, so that
+the equation above holds true. Some "ordinary" cases are strewn in to show more
+clearly the reasoning:
+
+	A /  B  =   C,     R so that C *    B +    R =    A
+     =========================================================
+	5 /   8 =   0,     5 	     0 *    8 +    5 =    5
+	0 /   8 =   0,     0	     0 *    8 +    0 =    0
+	0 / inf =   0,     0	     0 *  inf +    0 =    0
+	0 /-inf =   0,     0	     0 * -inf +    0 =    0
+	5 / inf =   0,     5	     0 *  inf +    5 =    5
+	5 /-inf =   0,     5	     0 * -inf +    5 =    5
+	-5/ inf =   0,    -5	     0 *  inf +   -5 =   -5
+	-5/-inf =   0,    -5	     0 * -inf +   -5 =   -5
+       inf/   5 =  inf,    0	   inf *    5 +    0 =  inf
+      -inf/   5 = -inf,    0      -inf *    5 +    0 = -inf
+       inf/  -5 = -inf,    0	  -inf *   -5 +    0 =  inf
+      -inf/  -5 =  inf,    0       inf *   -5 +    0 = -inf
+	 5/   5 =    1,    0         1 *    5 +    0 =    5
+	-5/  -5 =    1,    0         1 *   -5 +    0 =   -5
+       inf/ inf =    1,    0         1 *  inf +    0 =  inf
+      -inf/-inf =    1,    0         1 * -inf +    0 = -inf
+       inf/-inf =   -1,    0        -1 * -inf +    0 =  inf
+      -inf/ inf =   -1,    0         1 * -inf +    0 = -inf
+	 8/   0 =  inf,    8       inf *    0 +    8 =    8 
+       inf/   0 =  inf,  inf       inf *    0 +  inf =  inf 
+         0/   0 =  NaN
+
+These cases below violate the "remainder has the sign of the second of the two
+arguments", since they wouldn't match up otherwise.
+
+	A /  B  =   C,     R so that C *    B +    R =    A
+     ========================================================
+      -inf/   0 = -inf, -inf      -inf *    0 +  inf = -inf 
+	-8/   0 = -inf,   -8      -inf *    0 +    8 = -8 
+
+=item Modifying and =
+
+Beware of:
+
+        $x = Math::BigFloat->new(5);
+        $y = $x;
+
+It will not do what you think, e.g. making a copy of $x. Instead it just makes
+a second reference to the B<same> object and stores it in $y. Thus anything
+that modifies $x (except overloaded operators) will modify $y, and vice versa.
+Or in other words, C<=> is only safe if you modify your BigInts only via
+overloaded math. As soon as you use a method call it breaks:
+
+        $x->bmul(2);
+        print "$x, $y\n";       # prints '10, 10'
+
+If you want a true copy of $x, use:
+
+        $y = $x->copy();
+
+You can also chain the calls like this, this will make first a copy and then
+multiply it by 2:
+
+        $y = $x->copy()->bmul(2);
+
+See also the documentation for overload.pm regarding C<=>.
+
+=item bpow
+
+C<bpow()> (and the rounding functions) now modifies the first argument and
+returns it, unlike the old code which left it alone and only returned the
+result. This is to be consistent with C<badd()> etc. The first three will
+modify $x, the last one won't:
+
+	print bpow($x,$i),"\n"; 	# modify $x
+	print $x->bpow($i),"\n"; 	# ditto
+	print $x **= $i,"\n";		# the same
+	print $x ** $i,"\n";		# leave $x alone 
+
+The form C<$x **= $y> is faster than C<$x = $x ** $y;>, though.
+
+=item Overloading -$x
+
+The following:
+
+	$x = -$x;
+
+is slower than
+
+	$x->bneg();
+
+since overload calls C<sub($x,0,1);> instead of C<neg($x)>. The first variant
+needs to preserve $x since it does not know that it later will get overwritten.
+This makes a copy of $x and takes O(N), but $x->bneg() is O(1).
+
+=item Mixing different object types
+
+In Perl you will get a floating point value if you do one of the following:
+
+	$float = 5.0 + 2;
+	$float = 2 + 5.0;
+	$float = 5 / 2;
+
+With overloaded math, only the first two variants will result in a BigFloat:
+
+	use Math::BigInt;
+	use Math::BigFloat;
+	
+	$mbf = Math::BigFloat->new(5);
+	$mbi2 = Math::BigInteger->new(5);
+	$mbi = Math::BigInteger->new(2);
+
+					# what actually gets called:
+	$float = $mbf + $mbi;		# $mbf->badd()
+	$float = $mbf / $mbi;		# $mbf->bdiv()
+	$integer = $mbi + $mbf;		# $mbi->badd()
+	$integer = $mbi2 / $mbi;	# $mbi2->bdiv()
+	$integer = $mbi2 / $mbf;	# $mbi2->bdiv()
+
+This is because math with overloaded operators follows the first (dominating)
+operand, and the operation of that is called and returns thus the result. So,
+Math::BigInt::bdiv() will always return a Math::BigInt, regardless whether
+the result should be a Math::BigFloat or the second operant is one.
+
+To get a Math::BigFloat you either need to call the operation manually,
+make sure the operands are already of the proper type or casted to that type
+via Math::BigFloat->new():
+	
+	$float = Math::BigFloat->new($mbi2) / $mbi;	# = 2.5
+
+Beware of simple "casting" the entire expression, this would only convert
+the already computed result:
+
+	$float = Math::BigFloat->new($mbi2 / $mbi);	# = 2.0 thus wrong!
+
+Beware also of the order of more complicated expressions like:
+
+	$integer = ($mbi2 + $mbi) / $mbf;		# int / float => int
+	$integer = $mbi2 / Math::BigFloat->new($mbi);	# ditto
+
+If in doubt, break the expression into simpler terms, or cast all operands
+to the desired resulting type.
+
+Scalar values are a bit different, since:
+	
+	$float = 2 + $mbf;
+	$float = $mbf + 2;
+
+will both result in the proper type due to the way the overloaded math works.
+
+This section also applies to other overloaded math packages, like Math::String.
+
+One solution to you problem might be autoupgrading|upgrading. See the
+pragmas L<bignum>, L<bigint> and L<bigrat> for an easy way to do this.
+
+=item bsqrt()
+
+C<bsqrt()> works only good if the result is a big integer, e.g. the square
+root of 144 is 12, but from 12 the square root is 3, regardless of rounding
+mode. The reason is that the result is always truncated to an integer.
+
+If you want a better approximation of the square root, then use:
+
+	$x = Math::BigFloat->new(12);
+	Math::BigFloat->precision(0);
+	Math::BigFloat->round_mode('even');
+	print $x->copy->bsqrt(),"\n";		# 4
+
+	Math::BigFloat->precision(2);
+	print $x->bsqrt(),"\n";			# 3.46
+	print $x->bsqrt(3),"\n";		# 3.464
+
+=item brsft()
+
+For negative numbers in base see also L<brsft|brsft>.
+
+=back
+
+=head1 LICENSE
+
+This program is free software; you may redistribute it and/or modify it under
+the same terms as Perl itself.
+
+=head1 SEE ALSO
+
+L<Math::BigFloat>, L<Math::BigRat> and L<Math::Big> as well as
+L<Math::BigInt::BitVect>, L<Math::BigInt::Pari> and  L<Math::BigInt::GMP>.
+
+The pragmas L<bignum>, L<bigint> and L<bigrat> also might be of interest
+because they solve the autoupgrading/downgrading issue, at least partly.
+
+The package at
+L<http://search.cpan.org/search?mode=module&query=Math%3A%3ABigInt> contains
+more documentation including a full version history, testcases, empty
+subclass files and benchmarks.
+
+=head1 AUTHORS
+
+Original code by Mark Biggar, overloaded interface by Ilya Zakharevich.
+Completely rewritten by Tels http://bloodgate.com in late 2000, 2001 - 2006
+and still at it in 2007.
+
+Many people contributed in one or more ways to the final beast, see the file
+CREDITS for an (incomplete) list. If you miss your name, please drop me a
+mail. Thank you!
+
+=cut
diff --git a/dist/Math-BigInt/lib/Math/BigInt/Calc.pm b/dist/Math-BigInt/lib/Math/BigInt/Calc.pm
new file mode 100644
index 0000000000..52e33d232a
--- /dev/null
+++ b/dist/Math-BigInt/lib/Math/BigInt/Calc.pm
@@ -0,0 +1,2612 @@
+package Math::BigInt::Calc;
+
+use 5.006;
+use strict;
+# use warnings;	# dont use warnings for older Perls
+
+our $VERSION = '0.52';
+
+# Package to store unsigned big integers in decimal and do math with them
+
+# Internally the numbers are stored in an array with at least 1 element, no
+# leading zero parts (except the first) and in base 1eX where X is determined
+# automatically at loading time to be the maximum possible value
+
+# todo:
+# - fully remove funky $# stuff in div() (maybe - that code scares me...)
+
+# USE_MUL: due to problems on certain os (os390, posix-bc) "* 1e-5" is used
+# instead of "/ 1e5" at some places, (marked with USE_MUL). Other platforms
+# BS2000, some Crays need USE_DIV instead.
+# The BEGIN block is used to determine which of the two variants gives the
+# correct result.
+
+# Beware of things like:
+# $i = $i * $y + $car; $car = int($i / $BASE); $i = $i % $BASE;
+# This works on x86, but fails on ARM (SA1100, iPAQ) due to whoknows what
+# reasons. So, use this instead (slower, but correct):
+# $i = $i * $y + $car; $car = int($i / $BASE); $i -= $BASE * $car;
+
+##############################################################################
+# global constants, flags and accessory
+
+# announce that we are compatible with MBI v1.83 and up
+sub api_version () { 2; }
+ 
+# constants for easier life
+my ($BASE,$BASE_LEN,$RBASE,$MAX_VAL);
+my ($AND_BITS,$XOR_BITS,$OR_BITS);
+my ($AND_MASK,$XOR_MASK,$OR_MASK);
+
+sub _base_len 
+  {
+  # Set/get the BASE_LEN and assorted other, connected values.
+  # Used only by the testsuite, the set variant is used only by the BEGIN
+  # block below:
+  shift;
+
+  my ($b, $int) = @_;
+  if (defined $b)
+    {
+    # avoid redefinitions
+    undef &_mul;
+    undef &_div;
+
+    if ($] >= 5.008 && $int && $b > 7)
+      {
+      $BASE_LEN = $b;
+      *_mul = \&_mul_use_div_64;
+      *_div = \&_div_use_div_64;
+      $BASE = int("1e".$BASE_LEN);
+      $MAX_VAL = $BASE-1;
+      return $BASE_LEN unless wantarray;
+      return ($BASE_LEN, $AND_BITS, $XOR_BITS, $OR_BITS, $BASE_LEN, $MAX_VAL, $BASE);
+      }
+
+    # find whether we can use mul or div in mul()/div()
+    $BASE_LEN = $b+1;
+    my $caught = 0;
+    while (--$BASE_LEN > 5)
+      {
+      $BASE = int("1e".$BASE_LEN);
+      $RBASE = abs('1e-'.$BASE_LEN);			# see USE_MUL
+      $caught = 0;
+      $caught += 1 if (int($BASE * $RBASE) != 1);	# should be 1
+      $caught += 2 if (int($BASE / $BASE) != 1);	# should be 1
+      last if $caught != 3;
+      }
+    $BASE = int("1e".$BASE_LEN);
+    $RBASE = abs('1e-'.$BASE_LEN);			# see USE_MUL
+    $MAX_VAL = $BASE-1;
+   
+    # ($caught & 1) != 0 => cannot use MUL
+    # ($caught & 2) != 0 => cannot use DIV
+    if ($caught == 2)				# 2
+      {
+      # must USE_MUL since we cannot use DIV
+      *_mul = \&_mul_use_mul;
+      *_div = \&_div_use_mul;
+      }
+    else					# 0 or 1
+      {
+      # can USE_DIV instead
+      *_mul = \&_mul_use_div;
+      *_div = \&_div_use_div;
+      }
+    }
+  return $BASE_LEN unless wantarray;
+  return ($BASE_LEN, $AND_BITS, $XOR_BITS, $OR_BITS, $BASE_LEN, $MAX_VAL, $BASE);
+  }
+
+sub _new
+  {
+  # (ref to string) return ref to num_array
+  # Convert a number from string format (without sign) to internal base
+  # 1ex format. Assumes normalized value as input.
+  my $il = length($_[1])-1;
+
+  # < BASE_LEN due len-1 above
+  return [ int($_[1]) ] if $il < $BASE_LEN;	# shortcut for short numbers
+
+  # this leaves '00000' instead of int 0 and will be corrected after any op
+  [ reverse(unpack("a" . ($il % $BASE_LEN+1) 
+    . ("a$BASE_LEN" x ($il / $BASE_LEN)), $_[1])) ];
+  }                                                                             
+
+BEGIN
+  {
+  # from Daniel Pfeiffer: determine largest group of digits that is precisely
+  # multipliable with itself plus carry
+  # Test now changed to expect the proper pattern, not a result off by 1 or 2
+  my ($e, $num) = 3;	# lowest value we will use is 3+1-1 = 3
+  do 
+    {
+    $num = ('9' x ++$e) + 0;
+    $num *= $num + 1.0;
+    } while ("$num" =~ /9{$e}0{$e}/);	# must be a certain pattern
+  $e--; 				# last test failed, so retract one step
+  # the limits below brush the problems with the test above under the rug:
+  # the test should be able to find the proper $e automatically
+  $e = 5 if $^O =~ /^uts/;	# UTS get's some special treatment
+  $e = 5 if $^O =~ /^unicos/;	# unicos is also problematic (6 seems to work
+				# there, but we play safe)
+
+  my $int = 0;
+  if ($e > 7)
+    {
+    use integer;
+    my $e1 = 7;
+    $num = 7;
+    do 
+      {
+      $num = ('9' x ++$e1) + 0;
+      $num *= $num + 1;
+      } while ("$num" =~ /9{$e1}0{$e1}/);	# must be a certain pattern
+    $e1--; 					# last test failed, so retract one step
+    if ($e1 > 7)
+      { 
+      $int = 1; $e = $e1; 
+      }
+    }
+ 
+  __PACKAGE__->_base_len($e,$int);	# set and store
+
+  use integer;
+  # find out how many bits _and, _or and _xor can take (old default = 16)
+  # I don't think anybody has yet 128 bit scalars, so let's play safe.
+  local $^W = 0;	# don't warn about 'nonportable number'
+  $AND_BITS = 15; $XOR_BITS = 15; $OR_BITS = 15;
+
+  # find max bits, we will not go higher than numberofbits that fit into $BASE
+  # to make _and etc simpler (and faster for smaller, slower for large numbers)
+  my $max = 16;
+  while (2 ** $max < $BASE) { $max++; }
+  {
+    no integer;
+    $max = 16 if $] < 5.006;	# older Perls might not take >16 too well
+  }
+  my ($x,$y,$z);
+  do {
+    $AND_BITS++;
+    $x = CORE::oct('0b' . '1' x $AND_BITS); $y = $x & $x;
+    $z = (2 ** $AND_BITS) - 1;
+    } while ($AND_BITS < $max && $x == $z && $y == $x);
+  $AND_BITS --;						# retreat one step
+  do {
+    $XOR_BITS++;
+    $x = CORE::oct('0b' . '1' x $XOR_BITS); $y = $x ^ 0;
+    $z = (2 ** $XOR_BITS) - 1;
+    } while ($XOR_BITS < $max && $x == $z && $y == $x);
+  $XOR_BITS --;						# retreat one step
+  do {
+    $OR_BITS++;
+    $x = CORE::oct('0b' . '1' x $OR_BITS); $y = $x | $x;
+    $z = (2 ** $OR_BITS) - 1;
+    } while ($OR_BITS < $max && $x == $z && $y == $x);
+  $OR_BITS --;						# retreat one step
+  
+  $AND_MASK = __PACKAGE__->_new( ( 2 ** $AND_BITS ));
+  $XOR_MASK = __PACKAGE__->_new( ( 2 ** $XOR_BITS ));
+  $OR_MASK = __PACKAGE__->_new( ( 2 ** $OR_BITS ));
+
+  # We can compute the approximate lenght no faster than the real length:
+  *_alen = \&_len;
+  }
+
+###############################################################################
+
+sub _zero
+  {
+  # create a zero
+  [ 0 ];
+  }
+
+sub _one
+  {
+  # create a one
+  [ 1 ];
+  }
+
+sub _two
+  {
+  # create a two (used internally for shifting)
+  [ 2 ];
+  }
+
+sub _ten
+  {
+  # create a 10 (used internally for shifting)
+  [ 10 ];
+  }
+
+sub _1ex
+  {
+  # create a 1Ex
+  my $rem = $_[1] % $BASE_LEN;		# remainder
+  my $parts = $_[1] / $BASE_LEN;	# parts
+
+  # 000000, 000000, 100 
+  [ (0) x $parts, '1' . ('0' x $rem) ];
+  }
+
+sub _copy
+  {
+  # make a true copy
+  [ @{$_[1]} ];
+  }
+
+# catch and throw away
+sub import { }
+
+##############################################################################
+# convert back to string and number
+
+sub _str
+  {
+  # (ref to BINT) return num_str
+  # Convert number from internal base 100000 format to string format.
+  # internal format is always normalized (no leading zeros, "-0" => "+0")
+  my $ar = $_[1];
+
+  my $l = scalar @$ar;				# number of parts
+  if ($l < 1)					# should not happen
+    {
+    require Carp;
+    Carp::croak("$_[1] has no elements");
+    }
+
+  my $ret = "";
+  # handle first one different to strip leading zeros from it (there are no
+  # leading zero parts in internal representation)
+  $l --; $ret .= int($ar->[$l]); $l--;
+  # Interestingly, the pre-padd method uses more time
+  # the old grep variant takes longer (14 vs. 10 sec)
+  my $z = '0' x ($BASE_LEN-1);                            
+  while ($l >= 0)
+    {
+    $ret .= substr($z.$ar->[$l],-$BASE_LEN); # fastest way I could think of
+    $l--;
+    }
+  $ret;
+  }                                                                             
+
+sub _num
+  {
+  # Make a number (scalar int/float) from a BigInt object 
+  my $x = $_[1];
+
+  return 0+$x->[0] if scalar @$x == 1;  # below $BASE
+  my $fac = 1;
+  my $num = 0;
+  foreach (@$x)
+    {
+    $num += $fac*$_; $fac *= $BASE;
+    }
+  $num; 
+  }
+
+##############################################################################
+# actual math code
+
+sub _add
+  {
+  # (ref to int_num_array, ref to int_num_array)
+  # routine to add two base 1eX numbers
+  # stolen from Knuth Vol 2 Algorithm A pg 231
+  # there are separate routines to add and sub as per Knuth pg 233
+  # This routine clobbers up array x, but not y.
+ 
+  my ($c,$x,$y) = @_;
+
+  return $x if (@$y == 1) && $y->[0] == 0;		# $x + 0 => $x
+  if ((@$x == 1) && $x->[0] == 0)			# 0 + $y => $y->copy
+    {
+    # twice as slow as $x = [ @$y ], but nec. to retain $x as ref :(
+    @$x = @$y; return $x;		
+    }
+ 
+  # for each in Y, add Y to X and carry. If after that, something is left in
+  # X, foreach in X add carry to X and then return X, carry
+  # Trades one "$j++" for having to shift arrays
+  my $i; my $car = 0; my $j = 0;
+  for $i (@$y)
+    {
+    $x->[$j] -= $BASE if $car = (($x->[$j] += $i + $car) >= $BASE) ? 1 : 0;
+    $j++;
+    }
+  while ($car != 0)
+    {
+    $x->[$j] -= $BASE if $car = (($x->[$j] += $car) >= $BASE) ? 1 : 0; $j++;
+    }
+  $x;
+  }                                                                             
+
+sub _inc
+  {
+  # (ref to int_num_array, ref to int_num_array)
+  # Add 1 to $x, modify $x in place
+  my ($c,$x) = @_;
+
+  for my $i (@$x)
+    {
+    return $x if (($i += 1) < $BASE);		# early out
+    $i = 0;					# overflow, next
+    }
+  push @$x,1 if (($x->[-1] || 0) == 0);		# last overflowed, so extend
+  $x;
+  }                                                                             
+
+sub _dec
+  {
+  # (ref to int_num_array, ref to int_num_array)
+  # Sub 1 from $x, modify $x in place
+  my ($c,$x) = @_;
+
+  my $MAX = $BASE-1;				# since MAX_VAL based on BASE
+  for my $i (@$x)
+    {
+    last if (($i -= 1) >= 0);			# early out
+    $i = $MAX;					# underflow, next
+    }
+  pop @$x if $x->[-1] == 0 && @$x > 1;		# last underflowed (but leave 0)
+  $x;
+  }                                                                             
+
+sub _sub
+  {
+  # (ref to int_num_array, ref to int_num_array, swap)
+  # subtract base 1eX numbers -- stolen from Knuth Vol 2 pg 232, $x > $y
+  # subtract Y from X by modifying x in place
+  my ($c,$sx,$sy,$s) = @_;
+ 
+  my $car = 0; my $i; my $j = 0;
+  if (!$s)
+    {
+    for $i (@$sx)
+      {
+      last unless defined $sy->[$j] || $car;
+      $i += $BASE if $car = (($i -= ($sy->[$j] || 0) + $car) < 0); $j++;
+      }
+    # might leave leading zeros, so fix that
+    return __strip_zeros($sx);
+    }
+  for $i (@$sx)
+    {
+    # we can't do an early out if $x is < than $y, since we
+    # need to copy the high chunks from $y. Found by Bob Mathews.
+    #last unless defined $sy->[$j] || $car;
+    $sy->[$j] += $BASE
+     if $car = (($sy->[$j] = $i-($sy->[$j]||0) - $car) < 0);
+    $j++;
+    }
+  # might leave leading zeros, so fix that
+  __strip_zeros($sy);
+  }                                                                             
+
+sub _mul_use_mul
+  {
+  # (ref to int_num_array, ref to int_num_array)
+  # multiply two numbers in internal representation
+  # modifies first arg, second need not be different from first
+  my ($c,$xv,$yv) = @_;
+
+  if (@$yv == 1)
+    {
+    # shortcut for two very short numbers (improved by Nathan Zook)
+    # works also if xv and yv are the same reference, and handles also $x == 0
+    if (@$xv == 1)
+      {
+      if (($xv->[0] *= $yv->[0]) >= $BASE)
+         {
+         $xv->[0] = $xv->[0] - ($xv->[1] = int($xv->[0] * $RBASE)) * $BASE;
+         };
+      return $xv;
+      }
+    # $x * 0 => 0
+    if ($yv->[0] == 0)
+      {
+      @$xv = (0);
+      return $xv;
+      }
+    # multiply a large number a by a single element one, so speed up
+    my $y = $yv->[0]; my $car = 0;
+    foreach my $i (@$xv)
+      {
+      $i = $i * $y + $car; $car = int($i * $RBASE); $i -= $car * $BASE;
+      }
+    push @$xv, $car if $car != 0;
+    return $xv;
+    }
+  # shortcut for result $x == 0 => result = 0
+  return $xv if ( ((@$xv == 1) && ($xv->[0] == 0)) ); 
+
+  # since multiplying $x with $x fails, make copy in this case
+  $yv = [@$xv] if $xv == $yv;	# same references?
+
+  my @prod = (); my ($prod,$car,$cty,$xi,$yi);
+
+  for $xi (@$xv)
+    {
+    $car = 0; $cty = 0;
+
+    # slow variant
+#    for $yi (@$yv)
+#      {
+#      $prod = $xi * $yi + ($prod[$cty] || 0) + $car;
+#      $prod[$cty++] =
+#       $prod - ($car = int($prod * RBASE)) * $BASE;  # see USE_MUL
+#      }
+#    $prod[$cty] += $car if $car; # need really to check for 0?
+#    $xi = shift @prod;
+
+    # faster variant
+    # looping through this if $xi == 0 is silly - so optimize it away!
+    $xi = (shift @prod || 0), next if $xi == 0;
+    for $yi (@$yv)
+      {
+      $prod = $xi * $yi + ($prod[$cty] || 0) + $car;
+##     this is actually a tad slower
+##        $prod = $prod[$cty]; $prod += ($car + $xi * $yi);	# no ||0 here
+      $prod[$cty++] =
+       $prod - ($car = int($prod * $RBASE)) * $BASE;  # see USE_MUL
+      }
+    $prod[$cty] += $car if $car; # need really to check for 0?
+    $xi = shift @prod || 0;	# || 0 makes v5.005_3 happy
+    }
+  push @$xv, @prod;
+  # can't have leading zeros
+#  __strip_zeros($xv);
+  $xv;
+  }                                                                             
+
+sub _mul_use_div_64
+  {
+  # (ref to int_num_array, ref to int_num_array)
+  # multiply two numbers in internal representation
+  # modifies first arg, second need not be different from first
+  # works for 64 bit integer with "use integer"
+  my ($c,$xv,$yv) = @_;
+
+  use integer;
+  if (@$yv == 1)
+    {
+    # shortcut for two small numbers, also handles $x == 0
+    if (@$xv == 1)
+      {
+      # shortcut for two very short numbers (improved by Nathan Zook)
+      # works also if xv and yv are the same reference, and handles also $x == 0
+      if (($xv->[0] *= $yv->[0]) >= $BASE)
+          {
+          $xv->[0] =
+              $xv->[0] - ($xv->[1] = $xv->[0] / $BASE) * $BASE;
+          };
+      return $xv;
+      }
+    # $x * 0 => 0
+    if ($yv->[0] == 0)
+      {
+      @$xv = (0);
+      return $xv;
+      }
+    # multiply a large number a by a single element one, so speed up
+    my $y = $yv->[0]; my $car = 0;
+    foreach my $i (@$xv)
+      {
+      #$i = $i * $y + $car; $car = $i / $BASE; $i -= $car * $BASE;
+      $i = $i * $y + $car; $i -= ($car = $i / $BASE) * $BASE;
+      }
+    push @$xv, $car if $car != 0;
+    return $xv;
+    }
+  # shortcut for result $x == 0 => result = 0
+  return $xv if ( ((@$xv == 1) && ($xv->[0] == 0)) ); 
+
+  # since multiplying $x with $x fails, make copy in this case
+  $yv = [@$xv] if $xv == $yv;	# same references?
+
+  my @prod = (); my ($prod,$car,$cty,$xi,$yi);
+  for $xi (@$xv)
+    {
+    $car = 0; $cty = 0;
+    # looping through this if $xi == 0 is silly - so optimize it away!
+    $xi = (shift @prod || 0), next if $xi == 0;
+    for $yi (@$yv)
+      {
+      $prod = $xi * $yi + ($prod[$cty] || 0) + $car;
+      $prod[$cty++] = $prod - ($car = $prod / $BASE) * $BASE;
+      }
+    $prod[$cty] += $car if $car; # need really to check for 0?
+    $xi = shift @prod || 0;	# || 0 makes v5.005_3 happy
+    }
+  push @$xv, @prod;
+  $xv;
+  }                                                                             
+
+sub _mul_use_div
+  {
+  # (ref to int_num_array, ref to int_num_array)
+  # multiply two numbers in internal representation
+  # modifies first arg, second need not be different from first
+  my ($c,$xv,$yv) = @_;
+
+  if (@$yv == 1)
+    {
+    # shortcut for two small numbers, also handles $x == 0
+    if (@$xv == 1)
+      {
+      # shortcut for two very short numbers (improved by Nathan Zook)
+      # works also if xv and yv are the same reference, and handles also $x == 0
+      if (($xv->[0] *= $yv->[0]) >= $BASE)
+          {
+          $xv->[0] =
+              $xv->[0] - ($xv->[1] = int($xv->[0] / $BASE)) * $BASE;
+          };
+      return $xv;
+      }
+    # $x * 0 => 0
+    if ($yv->[0] == 0)
+      {
+      @$xv = (0);
+      return $xv;
+      }
+    # multiply a large number a by a single element one, so speed up
+    my $y = $yv->[0]; my $car = 0;
+    foreach my $i (@$xv)
+      {
+      $i = $i * $y + $car; $car = int($i / $BASE); $i -= $car * $BASE;
+      # This (together with use integer;) does not work on 32-bit Perls
+      #$i = $i * $y + $car; $i -= ($car = $i / $BASE) * $BASE;
+      }
+    push @$xv, $car if $car != 0;
+    return $xv;
+    }
+  # shortcut for result $x == 0 => result = 0
+  return $xv if ( ((@$xv == 1) && ($xv->[0] == 0)) ); 
+
+  # since multiplying $x with $x fails, make copy in this case
+  $yv = [@$xv] if $xv == $yv;	# same references?
+
+  my @prod = (); my ($prod,$car,$cty,$xi,$yi);
+  for $xi (@$xv)
+    {
+    $car = 0; $cty = 0;
+    # looping through this if $xi == 0 is silly - so optimize it away!
+    $xi = (shift @prod || 0), next if $xi == 0;
+    for $yi (@$yv)
+      {
+      $prod = $xi * $yi + ($prod[$cty] || 0) + $car;
+      $prod[$cty++] = $prod - ($car = int($prod / $BASE)) * $BASE;
+      }
+    $prod[$cty] += $car if $car; # need really to check for 0?
+    $xi = shift @prod || 0;	# || 0 makes v5.005_3 happy
+    }
+  push @$xv, @prod;
+  # can't have leading zeros
+#  __strip_zeros($xv);
+  $xv;
+  }                                                                             
+
+sub _div_use_mul
+  {
+  # ref to array, ref to array, modify first array and return remainder if 
+  # in list context
+
+  # see comments in _div_use_div() for more explanations
+
+  my ($c,$x,$yorg) = @_;
+  
+  # the general div algorithmn here is about O(N*N) and thus quite slow, so
+  # we first check for some special cases and use shortcuts to handle them.
+
+  # This works, because we store the numbers in a chunked format where each
+  # element contains 5..7 digits (depending on system).
+
+  # if both numbers have only one element:
+  if (@$x == 1 && @$yorg == 1)
+    {
+    # shortcut, $yorg and $x are two small numbers
+    if (wantarray)
+      {
+      my $r = [ $x->[0] % $yorg->[0] ];
+      $x->[0] = int($x->[0] / $yorg->[0]);
+      return ($x,$r); 
+      }
+    else
+      {
+      $x->[0] = int($x->[0] / $yorg->[0]);
+      return $x; 
+      }
+    }
+
+  # if x has more than one, but y has only one element:
+  if (@$yorg == 1)
+    {
+    my $rem;
+    $rem = _mod($c,[ @$x ],$yorg) if wantarray;
+
+    # shortcut, $y is < $BASE
+    my $j = scalar @$x; my $r = 0; 
+    my $y = $yorg->[0]; my $b;
+    while ($j-- > 0)
+      {
+      $b = $r * $BASE + $x->[$j];
+      $x->[$j] = int($b/$y);
+      $r = $b % $y;
+      }
+    pop @$x if @$x > 1 && $x->[-1] == 0;	# splice up a leading zero 
+    return ($x,$rem) if wantarray;
+    return $x;
+    }
+
+  # now x and y have more than one element
+
+  # check whether y has more elements than x, if yet, the result will be 0
+  if (@$yorg > @$x)
+    {
+    my $rem;
+    $rem = [@$x] if wantarray;                  # make copy
+    splice (@$x,1);                             # keep ref to original array
+    $x->[0] = 0;                                # set to 0
+    return ($x,$rem) if wantarray;              # including remainder?
+    return $x;					# only x, which is [0] now
+    }
+  # check whether the numbers have the same number of elements, in that case
+  # the result will fit into one element and can be computed efficiently
+  if (@$yorg == @$x)
+    {
+    my $rem;
+    # if $yorg has more digits than $x (it's leading element is longer than
+    # the one from $x), the result will also be 0:
+    if (length(int($yorg->[-1])) > length(int($x->[-1])))
+      {
+      $rem = [@$x] if wantarray;		# make copy
+      splice (@$x,1);				# keep ref to org array
+      $x->[0] = 0;				# set to 0
+      return ($x,$rem) if wantarray;		# including remainder?
+      return $x;
+      }
+    # now calculate $x / $yorg
+    if (length(int($yorg->[-1])) == length(int($x->[-1])))
+      {
+      # same length, so make full compare
+
+      my $a = 0; my $j = scalar @$x - 1;
+      # manual way (abort if unequal, good for early ne)
+      while ($j >= 0)
+        {
+        last if ($a = $x->[$j] - $yorg->[$j]); $j--;
+        }
+      # $a contains the result of the compare between X and Y
+      # a < 0: x < y, a == 0: x == y, a > 0: x > y
+      if ($a <= 0)
+        {
+        $rem = [ 0 ];                   # a = 0 => x == y => rem 0
+        $rem = [@$x] if $a != 0;        # a < 0 => x < y => rem = x
+        splice(@$x,1);                  # keep single element
+        $x->[0] = 0;                    # if $a < 0
+        $x->[0] = 1 if $a == 0;         # $x == $y
+        return ($x,$rem) if wantarray;
+        return $x;
+        }
+      # $x >= $y, so proceed normally
+      }
+    }
+
+  # all other cases:
+
+  my $y = [ @$yorg ];				# always make copy to preserve
+
+  my ($car,$bar,$prd,$dd,$xi,$yi,@q,$v2,$v1,@d,$tmp,$q,$u2,$u1,$u0);
+
+  $car = $bar = $prd = 0;
+  if (($dd = int($BASE/($y->[-1]+1))) != 1) 
+    {
+    for $xi (@$x) 
+      {
+      $xi = $xi * $dd + $car;
+      $xi -= ($car = int($xi * $RBASE)) * $BASE;	# see USE_MUL
+      }
+    push(@$x, $car); $car = 0;
+    for $yi (@$y) 
+      {
+      $yi = $yi * $dd + $car;
+      $yi -= ($car = int($yi * $RBASE)) * $BASE;	# see USE_MUL
+      }
+    }
+  else 
+    {
+    push(@$x, 0);
+    }
+  @q = (); ($v2,$v1) = @$y[-2,-1];
+  $v2 = 0 unless $v2;
+  while ($#$x > $#$y) 
+    {
+    ($u2,$u1,$u0) = @$x[-3..-1];
+    $u2 = 0 unless $u2;
+    #warn "oups v1 is 0, u0: $u0 $y->[-2] $y->[-1] l ",scalar @$y,"\n"
+    # if $v1 == 0;
+    $q = (($u0 == $v1) ? $MAX_VAL : int(($u0*$BASE+$u1)/$v1));
+    --$q while ($v2*$q > ($u0*$BASE+$u1-$q*$v1)*$BASE+$u2);
+    if ($q)
+      {
+      ($car, $bar) = (0,0);
+      for ($yi = 0, $xi = $#$x-$#$y-1; $yi <= $#$y; ++$yi,++$xi) 
+        {
+        $prd = $q * $y->[$yi] + $car;
+        $prd -= ($car = int($prd * $RBASE)) * $BASE;	# see USE_MUL
+	$x->[$xi] += $BASE if ($bar = (($x->[$xi] -= $prd + $bar) < 0));
+	}
+      if ($x->[-1] < $car + $bar) 
+        {
+        $car = 0; --$q;
+	for ($yi = 0, $xi = $#$x-$#$y-1; $yi <= $#$y; ++$yi,++$xi) 
+          {
+	  $x->[$xi] -= $BASE
+	   if ($car = (($x->[$xi] += $y->[$yi] + $car) >= $BASE));
+	  }
+	}   
+      }
+    pop(@$x);
+    unshift(@q, $q);
+    }
+  if (wantarray) 
+    {
+    @d = ();
+    if ($dd != 1)  
+      {
+      $car = 0; 
+      for $xi (reverse @$x) 
+        {
+        $prd = $car * $BASE + $xi;
+        $car = $prd - ($tmp = int($prd / $dd)) * $dd; # see USE_MUL
+        unshift(@d, $tmp);
+        }
+      }
+    else 
+      {
+      @d = @$x;
+      }
+    @$x = @q;
+    my $d = \@d; 
+    __strip_zeros($x);
+    __strip_zeros($d);
+    return ($x,$d);
+    }
+  @$x = @q;
+  __strip_zeros($x);
+  $x;
+  }
+
+sub _div_use_div_64
+  {
+  # ref to array, ref to array, modify first array and return remainder if 
+  # in list context
+  # This version works on 64 bit integers
+  my ($c,$x,$yorg) = @_;
+
+  use integer;
+  # the general div algorithmn here is about O(N*N) and thus quite slow, so
+  # we first check for some special cases and use shortcuts to handle them.
+
+  # This works, because we store the numbers in a chunked format where each
+  # element contains 5..7 digits (depending on system).
+
+  # if both numbers have only one element:
+  if (@$x == 1 && @$yorg == 1)
+    {
+    # shortcut, $yorg and $x are two small numbers
+    if (wantarray)
+      {
+      my $r = [ $x->[0] % $yorg->[0] ];
+      $x->[0] = int($x->[0] / $yorg->[0]);
+      return ($x,$r); 
+      }
+    else
+      {
+      $x->[0] = int($x->[0] / $yorg->[0]);
+      return $x; 
+      }
+    }
+  # if x has more than one, but y has only one element:
+  if (@$yorg == 1)
+    {
+    my $rem;
+    $rem = _mod($c,[ @$x ],$yorg) if wantarray;
+
+    # shortcut, $y is < $BASE
+    my $j = scalar @$x; my $r = 0; 
+    my $y = $yorg->[0]; my $b;
+    while ($j-- > 0)
+      {
+      $b = $r * $BASE + $x->[$j];
+      $x->[$j] = int($b/$y);
+      $r = $b % $y;
+      }
+    pop @$x if @$x > 1 && $x->[-1] == 0;	# splice up a leading zero 
+    return ($x,$rem) if wantarray;
+    return $x;
+    }
+  # now x and y have more than one element
+
+  # check whether y has more elements than x, if yet, the result will be 0
+  if (@$yorg > @$x)
+    {
+    my $rem;
+    $rem = [@$x] if wantarray;			# make copy
+    splice (@$x,1);				# keep ref to original array
+    $x->[0] = 0;				# set to 0
+    return ($x,$rem) if wantarray;		# including remainder?
+    return $x;					# only x, which is [0] now
+    }
+  # check whether the numbers have the same number of elements, in that case
+  # the result will fit into one element and can be computed efficiently
+  if (@$yorg == @$x)
+    {
+    my $rem;
+    # if $yorg has more digits than $x (it's leading element is longer than
+    # the one from $x), the result will also be 0:
+    if (length(int($yorg->[-1])) > length(int($x->[-1])))
+      {
+      $rem = [@$x] if wantarray;		# make copy
+      splice (@$x,1);				# keep ref to org array
+      $x->[0] = 0;				# set to 0
+      return ($x,$rem) if wantarray;		# including remainder?
+      return $x;
+      }
+    # now calculate $x / $yorg
+
+    if (length(int($yorg->[-1])) == length(int($x->[-1])))
+      {
+      # same length, so make full compare
+
+      my $a = 0; my $j = scalar @$x - 1;
+      # manual way (abort if unequal, good for early ne)
+      while ($j >= 0)
+        {
+        last if ($a = $x->[$j] - $yorg->[$j]); $j--;
+        }
+      # $a contains the result of the compare between X and Y
+      # a < 0: x < y, a == 0: x == y, a > 0: x > y
+      if ($a <= 0)
+        {
+        $rem = [ 0 ];			# a = 0 => x == y => rem 0
+        $rem = [@$x] if $a != 0;	# a < 0 => x < y => rem = x
+        splice(@$x,1);			# keep single element
+        $x->[0] = 0;			# if $a < 0
+        $x->[0] = 1 if $a == 0; 	# $x == $y
+        return ($x,$rem) if wantarray;	# including remainder?
+        return $x;
+        }
+      # $x >= $y, so proceed normally
+
+      }
+    }
+
+  # all other cases:
+
+  my $y = [ @$yorg ];				# always make copy to preserve
+ 
+  my ($car,$bar,$prd,$dd,$xi,$yi,@q,$v2,$v1,@d,$tmp,$q,$u2,$u1,$u0);
+
+  $car = $bar = $prd = 0;
+  if (($dd = int($BASE/($y->[-1]+1))) != 1) 
+    {
+    for $xi (@$x) 
+      {
+      $xi = $xi * $dd + $car;
+      $xi -= ($car = int($xi / $BASE)) * $BASE;
+      }
+    push(@$x, $car); $car = 0;
+    for $yi (@$y) 
+      {
+      $yi = $yi * $dd + $car;
+      $yi -= ($car = int($yi / $BASE)) * $BASE;
+      }
+    }
+  else 
+    {
+    push(@$x, 0);
+    }
+
+  # @q will accumulate the final result, $q contains the current computed
+  # part of the final result
+
+  @q = (); ($v2,$v1) = @$y[-2,-1];
+  $v2 = 0 unless $v2;
+  while ($#$x > $#$y) 
+    {
+    ($u2,$u1,$u0) = @$x[-3..-1];
+    $u2 = 0 unless $u2;
+    #warn "oups v1 is 0, u0: $u0 $y->[-2] $y->[-1] l ",scalar @$y,"\n"
+    # if $v1 == 0;
+    $q = (($u0 == $v1) ? $MAX_VAL : int(($u0*$BASE+$u1)/$v1));
+    --$q while ($v2*$q > ($u0*$BASE+$u1-$q*$v1)*$BASE+$u2);
+    if ($q)
+      {
+      ($car, $bar) = (0,0);
+      for ($yi = 0, $xi = $#$x-$#$y-1; $yi <= $#$y; ++$yi,++$xi) 
+        {
+        $prd = $q * $y->[$yi] + $car;
+        $prd -= ($car = int($prd / $BASE)) * $BASE;
+	$x->[$xi] += $BASE if ($bar = (($x->[$xi] -= $prd + $bar) < 0));
+	}
+      if ($x->[-1] < $car + $bar) 
+        {
+        $car = 0; --$q;
+	for ($yi = 0, $xi = $#$x-$#$y-1; $yi <= $#$y; ++$yi,++$xi) 
+          {
+	  $x->[$xi] -= $BASE
+	   if ($car = (($x->[$xi] += $y->[$yi] + $car) >= $BASE));
+	  }
+	}   
+      }
+    pop(@$x); unshift(@q, $q);
+    }
+  if (wantarray) 
+    {
+    @d = ();
+    if ($dd != 1)  
+      {
+      $car = 0; 
+      for $xi (reverse @$x) 
+        {
+        $prd = $car * $BASE + $xi;
+        $car = $prd - ($tmp = int($prd / $dd)) * $dd;
+        unshift(@d, $tmp);
+        }
+      }
+    else 
+      {
+      @d = @$x;
+      }
+    @$x = @q;
+    my $d = \@d; 
+    __strip_zeros($x);
+    __strip_zeros($d);
+    return ($x,$d);
+    }
+  @$x = @q;
+  __strip_zeros($x);
+  $x;
+  }
+
+sub _div_use_div
+  {
+  # ref to array, ref to array, modify first array and return remainder if 
+  # in list context
+  my ($c,$x,$yorg) = @_;
+
+  # the general div algorithmn here is about O(N*N) and thus quite slow, so
+  # we first check for some special cases and use shortcuts to handle them.
+
+  # This works, because we store the numbers in a chunked format where each
+  # element contains 5..7 digits (depending on system).
+
+  # if both numbers have only one element:
+  if (@$x == 1 && @$yorg == 1)
+    {
+    # shortcut, $yorg and $x are two small numbers
+    if (wantarray)
+      {
+      my $r = [ $x->[0] % $yorg->[0] ];
+      $x->[0] = int($x->[0] / $yorg->[0]);
+      return ($x,$r); 
+      }
+    else
+      {
+      $x->[0] = int($x->[0] / $yorg->[0]);
+      return $x; 
+      }
+    }
+  # if x has more than one, but y has only one element:
+  if (@$yorg == 1)
+    {
+    my $rem;
+    $rem = _mod($c,[ @$x ],$yorg) if wantarray;
+
+    # shortcut, $y is < $BASE
+    my $j = scalar @$x; my $r = 0; 
+    my $y = $yorg->[0]; my $b;
+    while ($j-- > 0)
+      {
+      $b = $r * $BASE + $x->[$j];
+      $x->[$j] = int($b/$y);
+      $r = $b % $y;
+      }
+    pop @$x if @$x > 1 && $x->[-1] == 0;	# splice up a leading zero 
+    return ($x,$rem) if wantarray;
+    return $x;
+    }
+  # now x and y have more than one element
+
+  # check whether y has more elements than x, if yet, the result will be 0
+  if (@$yorg > @$x)
+    {
+    my $rem;
+    $rem = [@$x] if wantarray;			# make copy
+    splice (@$x,1);				# keep ref to original array
+    $x->[0] = 0;				# set to 0
+    return ($x,$rem) if wantarray;		# including remainder?
+    return $x;					# only x, which is [0] now
+    }
+  # check whether the numbers have the same number of elements, in that case
+  # the result will fit into one element and can be computed efficiently
+  if (@$yorg == @$x)
+    {
+    my $rem;
+    # if $yorg has more digits than $x (it's leading element is longer than
+    # the one from $x), the result will also be 0:
+    if (length(int($yorg->[-1])) > length(int($x->[-1])))
+      {
+      $rem = [@$x] if wantarray;		# make copy
+      splice (@$x,1);				# keep ref to org array
+      $x->[0] = 0;				# set to 0
+      return ($x,$rem) if wantarray;		# including remainder?
+      return $x;
+      }
+    # now calculate $x / $yorg
+
+    if (length(int($yorg->[-1])) == length(int($x->[-1])))
+      {
+      # same length, so make full compare
+
+      my $a = 0; my $j = scalar @$x - 1;
+      # manual way (abort if unequal, good for early ne)
+      while ($j >= 0)
+        {
+        last if ($a = $x->[$j] - $yorg->[$j]); $j--;
+        }
+      # $a contains the result of the compare between X and Y
+      # a < 0: x < y, a == 0: x == y, a > 0: x > y
+      if ($a <= 0)
+        {
+        $rem = [ 0 ];			# a = 0 => x == y => rem 0
+        $rem = [@$x] if $a != 0;	# a < 0 => x < y => rem = x
+        splice(@$x,1);			# keep single element
+        $x->[0] = 0;			# if $a < 0
+        $x->[0] = 1 if $a == 0; 	# $x == $y
+        return ($x,$rem) if wantarray;	# including remainder?
+        return $x;
+        }
+      # $x >= $y, so proceed normally
+
+      }
+    }
+
+  # all other cases:
+
+  my $y = [ @$yorg ];				# always make copy to preserve
+ 
+  my ($car,$bar,$prd,$dd,$xi,$yi,@q,$v2,$v1,@d,$tmp,$q,$u2,$u1,$u0);
+
+  $car = $bar = $prd = 0;
+  if (($dd = int($BASE/($y->[-1]+1))) != 1) 
+    {
+    for $xi (@$x) 
+      {
+      $xi = $xi * $dd + $car;
+      $xi -= ($car = int($xi / $BASE)) * $BASE;
+      }
+    push(@$x, $car); $car = 0;
+    for $yi (@$y) 
+      {
+      $yi = $yi * $dd + $car;
+      $yi -= ($car = int($yi / $BASE)) * $BASE;
+      }
+    }
+  else 
+    {
+    push(@$x, 0);
+    }
+
+  # @q will accumulate the final result, $q contains the current computed
+  # part of the final result
+
+  @q = (); ($v2,$v1) = @$y[-2,-1];
+  $v2 = 0 unless $v2;
+  while ($#$x > $#$y) 
+    {
+    ($u2,$u1,$u0) = @$x[-3..-1];
+    $u2 = 0 unless $u2;
+    #warn "oups v1 is 0, u0: $u0 $y->[-2] $y->[-1] l ",scalar @$y,"\n"
+    # if $v1 == 0;
+    $q = (($u0 == $v1) ? $MAX_VAL : int(($u0*$BASE+$u1)/$v1));
+    --$q while ($v2*$q > ($u0*$BASE+$u1-$q*$v1)*$BASE+$u2);
+    if ($q)
+      {
+      ($car, $bar) = (0,0);
+      for ($yi = 0, $xi = $#$x-$#$y-1; $yi <= $#$y; ++$yi,++$xi) 
+        {
+        $prd = $q * $y->[$yi] + $car;
+        $prd -= ($car = int($prd / $BASE)) * $BASE;
+	$x->[$xi] += $BASE if ($bar = (($x->[$xi] -= $prd + $bar) < 0));
+	}
+      if ($x->[-1] < $car + $bar) 
+        {
+        $car = 0; --$q;
+	for ($yi = 0, $xi = $#$x-$#$y-1; $yi <= $#$y; ++$yi,++$xi) 
+          {
+	  $x->[$xi] -= $BASE
+	   if ($car = (($x->[$xi] += $y->[$yi] + $car) >= $BASE));
+	  }
+	}   
+      }
+    pop(@$x); unshift(@q, $q);
+    }
+  if (wantarray) 
+    {
+    @d = ();
+    if ($dd != 1)  
+      {
+      $car = 0; 
+      for $xi (reverse @$x) 
+        {
+        $prd = $car * $BASE + $xi;
+        $car = $prd - ($tmp = int($prd / $dd)) * $dd;
+        unshift(@d, $tmp);
+        }
+      }
+    else 
+      {
+      @d = @$x;
+      }
+    @$x = @q;
+    my $d = \@d; 
+    __strip_zeros($x);
+    __strip_zeros($d);
+    return ($x,$d);
+    }
+  @$x = @q;
+  __strip_zeros($x);
+  $x;
+  }
+
+##############################################################################
+# testing
+
+sub _acmp
+  {
+  # internal absolute post-normalized compare (ignore signs)
+  # ref to array, ref to array, return <0, 0, >0
+  # arrays must have at least one entry; this is not checked for
+  my ($c,$cx,$cy) = @_;
+ 
+  # shortcut for short numbers 
+  return (($cx->[0] <=> $cy->[0]) <=> 0) 
+   if scalar @$cx == scalar @$cy && scalar @$cx == 1;
+
+  # fast comp based on number of array elements (aka pseudo-length)
+  my $lxy = (scalar @$cx - scalar @$cy)
+  # or length of first element if same number of elements (aka difference 0)
+    ||
+  # need int() here because sometimes the last element is '00018' vs '18'
+   (length(int($cx->[-1])) - length(int($cy->[-1])));
+  return -1 if $lxy < 0;				# already differs, ret
+  return 1 if $lxy > 0;					# ditto
+
+  # manual way (abort if unequal, good for early ne)
+  my $a; my $j = scalar @$cx;
+  while (--$j >= 0)
+    {
+    last if ($a = $cx->[$j] - $cy->[$j]);
+    }
+  $a <=> 0;
+  }
+
+sub _len
+  {
+  # compute number of digits in base 10
+
+  # int() because add/sub sometimes leaves strings (like '00005') instead of
+  # '5' in this place, thus causing length() to report wrong length
+  my $cx = $_[1];
+
+  (@$cx-1)*$BASE_LEN+length(int($cx->[-1]));
+  }
+
+sub _digit
+  {
+  # return the nth digit, negative values count backward
+  # zero is rightmost, so _digit(123,0) will give 3
+  my ($c,$x,$n) = @_;
+
+  my $len = _len('',$x);
+
+  $n = $len+$n if $n < 0;		# -1 last, -2 second-to-last
+  $n = abs($n);				# if negative was too big
+  $len--; $n = $len if $n > $len;	# n to big?
+  
+  my $elem = int($n / $BASE_LEN);	# which array element
+  my $digit = $n % $BASE_LEN;		# which digit in this element
+  $elem = '0' x $BASE_LEN . @$x[$elem];	# get element padded with 0's
+  substr($elem,-$digit-1,1);
+  }
+
+sub _zeros
+  {
+  # return amount of trailing zeros in decimal
+  # check each array elem in _m for having 0 at end as long as elem == 0
+  # Upon finding a elem != 0, stop
+  my $x = $_[1];
+
+  return 0 if scalar @$x == 1 && $x->[0] == 0;
+
+  my $zeros = 0; my $elem;
+  foreach my $e (@$x)
+    {
+    if ($e != 0)
+      {
+      $elem = "$e";				# preserve x
+      $elem =~ s/.*?(0*$)/$1/;			# strip anything not zero
+      $zeros *= $BASE_LEN;			# elems * 5
+      $zeros += length($elem);			# count trailing zeros
+      last;					# early out
+      }
+    $zeros ++;					# real else branch: 50% slower!
+    }
+  $zeros;
+  }
+
+##############################################################################
+# _is_* routines
+
+sub _is_zero
+  {
+  # return true if arg is zero 
+  (((scalar @{$_[1]} == 1) && ($_[1]->[0] == 0))) <=> 0;
+  }
+
+sub _is_even
+  {
+  # return true if arg is even
+  (!($_[1]->[0] & 1)) <=> 0; 
+  }
+
+sub _is_odd
+  {
+  # return true if arg is even
+  (($_[1]->[0] & 1)) <=> 0; 
+  }
+
+sub _is_one
+  {
+  # return true if arg is one
+  (scalar @{$_[1]} == 1) && ($_[1]->[0] == 1) <=> 0; 
+  }
+
+sub _is_two
+  {
+  # return true if arg is two 
+  (scalar @{$_[1]} == 1) && ($_[1]->[0] == 2) <=> 0; 
+  }
+
+sub _is_ten
+  {
+  # return true if arg is ten 
+  (scalar @{$_[1]} == 1) && ($_[1]->[0] == 10) <=> 0; 
+  }
+
+sub __strip_zeros
+  {
+  # internal normalization function that strips leading zeros from the array
+  # args: ref to array
+  my $s = shift;
+ 
+  my $cnt = scalar @$s; # get count of parts
+  my $i = $cnt-1;
+  push @$s,0 if $i < 0;		# div might return empty results, so fix it
+
+  return $s if @$s == 1;		# early out
+
+  #print "strip: cnt $cnt i $i\n";
+  # '0', '3', '4', '0', '0',
+  #  0    1    2    3    4
+  # cnt = 5, i = 4
+  # i = 4
+  # i = 3
+  # => fcnt = cnt - i (5-2 => 3, cnt => 5-1 = 4, throw away from 4th pos)
+  # >= 1: skip first part (this can be zero)
+  while ($i > 0) { last if $s->[$i] != 0; $i--; }
+  $i++; splice @$s,$i if ($i < $cnt); # $i cant be 0
+  $s;                                                                    
+  }                                                                             
+
+###############################################################################
+# check routine to test internal state for corruptions
+
+sub _check
+  {
+  # used by the test suite
+  my $x = $_[1];
+
+  return "$x is not a reference" if !ref($x);
+
+  # are all parts are valid?
+  my $i = 0; my $j = scalar @$x; my ($e,$try);
+  while ($i < $j)
+    {
+    $e = $x->[$i]; $e = 'undef' unless defined $e;
+    $try = '=~ /^[\+]?[0-9]+\$/; '."($x, $e)";
+    last if $e !~ /^[+]?[0-9]+$/;
+    $try = '=~ /^[\+]?[0-9]+\$/; '."($x, $e) (stringify)";
+    last if "$e" !~ /^[+]?[0-9]+$/;
+    $try = '=~ /^[\+]?[0-9]+\$/; '."($x, $e) (cat-stringify)";
+    last if '' . "$e" !~ /^[+]?[0-9]+$/;
+    $try = ' < 0 || >= $BASE; '."($x, $e)";
+    last if $e <0 || $e >= $BASE;
+    # this test is disabled, since new/bnorm and certain ops (like early out
+    # in add/sub) are allowed/expected to leave '00000' in some elements
+    #$try = '=~ /^00+/; '."($x, $e)";
+    #last if $e =~ /^00+/;
+    $i++;
+    }
+  return "Illegal part '$e' at pos $i (tested: $try)" if $i < $j;
+  0;
+  }
+
+
+###############################################################################
+
+sub _mod
+  {
+  # if possible, use mod shortcut
+  my ($c,$x,$yo) = @_;
+
+  # slow way since $y to big
+  if (scalar @$yo > 1)
+    {
+    my ($xo,$rem) = _div($c,$x,$yo);
+    return $rem;
+    }
+
+  my $y = $yo->[0];
+  # both are single element arrays
+  if (scalar @$x == 1)
+    {
+    $x->[0] %= $y;
+    return $x;
+    }
+
+  # @y is a single element, but @x has more than one element
+  my $b = $BASE % $y;
+  if ($b == 0)
+    {
+    # when BASE % Y == 0 then (B * BASE) % Y == 0
+    # (B * BASE) % $y + A % Y => A % Y
+    # so need to consider only last element: O(1)
+    $x->[0] %= $y;
+    }
+  elsif ($b == 1)
+    {
+    # else need to go through all elements: O(N), but loop is a bit simplified
+    my $r = 0;
+    foreach (@$x)
+      {
+      $r = ($r + $_) % $y;		# not much faster, but heh...
+      #$r += $_ % $y; $r %= $y;
+      }
+    $r = 0 if $r == $y;
+    $x->[0] = $r;
+    }
+  else
+    {
+    # else need to go through all elements: O(N)
+    my $r = 0; my $bm = 1;
+    foreach (@$x)
+      {
+      $r = ($_ * $bm + $r) % $y;
+      $bm = ($bm * $b) % $y;
+
+      #$r += ($_ % $y) * $bm;
+      #$bm *= $b;
+      #$bm %= $y;
+      #$r %= $y;
+      }
+    $r = 0 if $r == $y;
+    $x->[0] = $r;
+    }
+  splice (@$x,1);		# keep one element of $x
+  $x;
+  }
+
+##############################################################################
+# shifts
+
+sub _rsft
+  {
+  my ($c,$x,$y,$n) = @_;
+
+  if ($n != 10)
+    {
+    $n = _new($c,$n); return _div($c,$x, _pow($c,$n,$y));
+    }
+
+  # shortcut (faster) for shifting by 10)
+  # multiples of $BASE_LEN
+  my $dst = 0;				# destination
+  my $src = _num($c,$y);		# as normal int
+  my $xlen = (@$x-1)*$BASE_LEN+length(int($x->[-1]));  # len of x in digits
+  if ($src >= $xlen or ($src == $xlen and ! defined $x->[1]))
+    {
+    # 12345 67890 shifted right by more than 10 digits => 0
+    splice (@$x,1);                    # leave only one element
+    $x->[0] = 0;                       # set to zero
+    return $x;
+    }
+  my $rem = $src % $BASE_LEN;		# remainder to shift
+  $src = int($src / $BASE_LEN);		# source
+  if ($rem == 0)
+    {
+    splice (@$x,0,$src);		# even faster, 38.4 => 39.3
+    }
+  else
+    {
+    my $len = scalar @$x - $src;	# elems to go
+    my $vd; my $z = '0'x $BASE_LEN;
+    $x->[scalar @$x] = 0;		# avoid || 0 test inside loop
+    while ($dst < $len)
+      {
+      $vd = $z.$x->[$src];
+      $vd = substr($vd,-$BASE_LEN,$BASE_LEN-$rem);
+      $src++;
+      $vd = substr($z.$x->[$src],-$rem,$rem) . $vd;
+      $vd = substr($vd,-$BASE_LEN,$BASE_LEN) if length($vd) > $BASE_LEN;
+      $x->[$dst] = int($vd);
+      $dst++;
+      }
+    splice (@$x,$dst) if $dst > 0;		# kill left-over array elems
+    pop @$x if $x->[-1] == 0 && @$x > 1;	# kill last element if 0
+    } # else rem == 0
+  $x;
+  }
+
+sub _lsft
+  {
+  my ($c,$x,$y,$n) = @_;
+
+  if ($n != 10)
+    {
+    $n = _new($c,$n); return _mul($c,$x, _pow($c,$n,$y));
+    }
+
+  # shortcut (faster) for shifting by 10) since we are in base 10eX
+  # multiples of $BASE_LEN:
+  my $src = scalar @$x;			# source
+  my $len = _num($c,$y);		# shift-len as normal int
+  my $rem = $len % $BASE_LEN;		# remainder to shift
+  my $dst = $src + int($len/$BASE_LEN);	# destination
+  my $vd;				# further speedup
+  $x->[$src] = 0;			# avoid first ||0 for speed
+  my $z = '0' x $BASE_LEN;
+  while ($src >= 0)
+    {
+    $vd = $x->[$src]; $vd = $z.$vd;
+    $vd = substr($vd,-$BASE_LEN+$rem,$BASE_LEN-$rem);
+    $vd .= $src > 0 ? substr($z.$x->[$src-1],-$BASE_LEN,$rem) : '0' x $rem;
+    $vd = substr($vd,-$BASE_LEN,$BASE_LEN) if length($vd) > $BASE_LEN;
+    $x->[$dst] = int($vd);
+    $dst--; $src--;
+    }
+  # set lowest parts to 0
+  while ($dst >= 0) { $x->[$dst--] = 0; }
+  # fix spurios last zero element
+  splice @$x,-1 if $x->[-1] == 0;
+  $x;
+  }
+
+sub _pow
+  {
+  # power of $x to $y
+  # ref to array, ref to array, return ref to array
+  my ($c,$cx,$cy) = @_;
+
+  if (scalar @$cy == 1 && $cy->[0] == 0)
+    {
+    splice (@$cx,1); $cx->[0] = 1;		# y == 0 => x => 1
+    return $cx;
+    }
+  if ((scalar @$cx == 1 && $cx->[0] == 1) ||	#    x == 1
+      (scalar @$cy == 1 && $cy->[0] == 1))	# or y == 1
+    {
+    return $cx;
+    }
+  if (scalar @$cx == 1 && $cx->[0] == 0)
+    {
+    splice (@$cx,1); $cx->[0] = 0;		# 0 ** y => 0 (if not y <= 0)
+    return $cx;
+    }
+
+  my $pow2 = _one();
+
+  my $y_bin = _as_bin($c,$cy); $y_bin =~ s/^0b//;
+  my $len = length($y_bin);
+  while (--$len > 0)
+    {
+    _mul($c,$pow2,$cx) if substr($y_bin,$len,1) eq '1';		# is odd?
+    _mul($c,$cx,$cx);
+    }
+
+  _mul($c,$cx,$pow2);
+  $cx;
+  }
+
+sub _nok
+  {
+  # n over k
+  # ref to array, return ref to array
+  my ($c,$n,$k) = @_;
+
+  # ( 7 )    7!          7*6*5 * 4*3*2*1   7 * 6 * 5
+  # ( - ) = --------- =  --------------- = ---------
+  # ( 3 )   3! (7-3)!    3*2*1 * 4*3*2*1   3 * 2 * 1 
+
+  # compute n - k + 2 (so we start with 5 in the example above)
+  my $x = _copy($c,$n);
+
+  _sub($c,$n,$k);
+  if (!_is_one($c,$n))
+    {
+    _inc($c,$n);
+    my $f = _copy($c,$n); _inc($c,$f);		# n = 5, f = 6, d = 2
+    my $d = _two($c);
+    while (_acmp($c,$f,$x) <= 0)		# f < n ?
+      {
+      # n = (n * f / d) == 5 * 6 / 2 => n == 3
+      $n = _mul($c,$n,$f); $n = _div($c,$n,$d);
+      # f = 7, d = 3
+      _inc($c,$f); _inc($c,$d);
+      }
+    }
+  else 
+    {
+    # keep ref to $n and set it to 1
+    splice (@$n,1); $n->[0] = 1;
+    }
+  $n;
+  }
+
+my @factorials = (
+  1,
+  1,
+  2,
+  2*3,
+  2*3*4,
+  2*3*4*5,
+  2*3*4*5*6,
+  2*3*4*5*6*7,
+);
+
+sub _fac
+  {
+  # factorial of $x
+  # ref to array, return ref to array
+  my ($c,$cx) = @_;
+
+  if ((@$cx == 1) && ($cx->[0] <= 7))
+    {
+    $cx->[0] = $factorials[$cx->[0]];		# 0 => 1, 1 => 1, 2 => 2 etc.
+    return $cx;
+    }
+
+  if ((@$cx == 1) && 		# we do this only if $x >= 12 and $x <= 7000
+      ($cx->[0] >= 12 && $cx->[0] < 7000))
+    {
+
+  # Calculate (k-j) * (k-j+1) ... k .. (k+j-1) * (k + j)
+  # See http://blogten.blogspot.com/2007/01/calculating-n.html
+  # The above series can be expressed as factors:
+  #   k * k - (j - i) * 2
+  # We cache k*k, and calculate (j * j) as the sum of the first j odd integers
+
+  # This will not work when N exceeds the storage of a Perl scalar, however,
+  # in this case the algorithm would be way to slow to terminate, anyway.
+
+  # As soon as the last element of $cx is 0, we split it up and remember
+  # how many zeors we got so far. The reason is that n! will accumulate
+  # zeros at the end rather fast.
+  my $zero_elements = 0;
+
+  # If n is even, set n = n -1
+  my $k = _num($c,$cx); my $even = 1;
+  if (($k & 1) == 0)
+    {
+    $even = $k; $k --;
+    }
+  # set k to the center point
+  $k = ($k + 1) / 2;
+#  print "k $k even: $even\n";
+  # now calculate k * k
+  my $k2 = $k * $k;
+  my $odd = 1; my $sum = 1;
+  my $i = $k - 1;
+  # keep reference to x
+  my $new_x = _new($c, $k * $even);
+  @$cx = @$new_x;
+  if ($cx->[0] == 0)
+    {
+    $zero_elements ++; shift @$cx;
+    }
+#  print STDERR "x = ", _str($c,$cx),"\n";
+  my $BASE2 = int(sqrt($BASE))-1;
+  my $j = 1; 
+  while ($j <= $i)
+    {
+    my $m = ($k2 - $sum); $odd += 2; $sum += $odd; $j++;
+    while ($j <= $i && ($m < $BASE2) && (($k2 - $sum) < $BASE2))
+      {
+      $m *= ($k2 - $sum);
+      $odd += 2; $sum += $odd; $j++;
+#      print STDERR "\n k2 $k2 m $m sum $sum odd $odd\n"; sleep(1);
+      }
+    if ($m < $BASE)
+      {
+      _mul($c,$cx,[$m]);
+      }
+    else
+      {
+      _mul($c,$cx,$c->_new($m));
+      }
+    if ($cx->[0] == 0)
+      {
+      $zero_elements ++; shift @$cx;
+      }
+#    print STDERR "Calculate $k2 - $sum = $m (x = ", _str($c,$cx),")\n";
+    }
+  # multiply in the zeros again
+  unshift @$cx, (0) x $zero_elements; 
+  return $cx;
+  }
+
+  # go forward until $base is exceeded
+  # limit is either $x steps (steps == 100 means a result always too high) or
+  # $base.
+  my $steps = 100; $steps = $cx->[0] if @$cx == 1;
+  my $r = 2; my $cf = 3; my $step = 2; my $last = $r;
+  while ($r*$cf < $BASE && $step < $steps)
+    {
+    $last = $r; $r *= $cf++; $step++;
+    }
+  if ((@$cx == 1) && $step == $cx->[0])
+    {
+    # completely done, so keep reference to $x and return
+    $cx->[0] = $r;
+    return $cx;
+    }
+  
+  # now we must do the left over steps
+  my $n;					# steps still to do
+  if (scalar @$cx == 1)
+    {
+    $n = $cx->[0];
+    }
+  else
+    {
+    $n = _copy($c,$cx);
+    }
+
+  # Set $cx to the last result below $BASE (but keep ref to $x)
+  $cx->[0] = $last; splice (@$cx,1);
+  # As soon as the last element of $cx is 0, we split it up and remember
+  # how many zeors we got so far. The reason is that n! will accumulate
+  # zeros at the end rather fast.
+  my $zero_elements = 0;
+
+  # do left-over steps fit into a scalar?
+  if (ref $n eq 'ARRAY')
+    {
+    # No, so use slower inc() & cmp()
+    # ($n is at least $BASE here)
+    my $base_2 = int(sqrt($BASE)) - 1;
+    #print STDERR "base_2: $base_2\n"; 
+    while ($step < $base_2)
+      {
+      if ($cx->[0] == 0)
+        {
+        $zero_elements ++; shift @$cx;
+        }
+      my $b = $step * ($step + 1); $step += 2;
+      _mul($c,$cx,[$b]);
+      }
+    $step = [$step];
+    while (_acmp($c,$step,$n) <= 0)
+      {
+      if ($cx->[0] == 0)
+        {
+        $zero_elements ++; shift @$cx;
+        }
+      _mul($c,$cx,$step); _inc($c,$step);
+      }
+    }
+  else
+    {
+    # Yes, so we can speed it up slightly
+  
+#    print "# left over steps $n\n";
+
+    my $base_4 = int(sqrt(sqrt($BASE))) - 2;
+    #print STDERR "base_4: $base_4\n";
+    my $n4 = $n - 4; 
+    while ($step < $n4 && $step < $base_4)
+      {
+      if ($cx->[0] == 0)
+        {
+        $zero_elements ++; shift @$cx;
+        }
+      my $b = $step * ($step + 1); $step += 2; $b *= $step * ($step + 1); $step += 2;
+      _mul($c,$cx,[$b]);
+      }
+    my $base_2 = int(sqrt($BASE)) - 1;
+    my $n2 = $n - 2; 
+    #print STDERR "base_2: $base_2\n"; 
+    while ($step < $n2 && $step < $base_2)
+      {
+      if ($cx->[0] == 0)
+        {
+        $zero_elements ++; shift @$cx;
+        }
+      my $b = $step * ($step + 1); $step += 2;
+      _mul($c,$cx,[$b]);
+      }
+    # do what's left over
+    while ($step <= $n)
+      {
+      _mul($c,$cx,[$step]); $step++;
+      if ($cx->[0] == 0)
+        {
+        $zero_elements ++; shift @$cx;
+        }
+      }
+    }
+  # multiply in the zeros again
+  unshift @$cx, (0) x $zero_elements;
+  $cx;			# return result
+  }
+
+#############################################################################
+
+sub _log_int
+  {
+  # calculate integer log of $x to base $base
+  # ref to array, ref to array - return ref to array
+  my ($c,$x,$base) = @_;
+
+  # X == 0 => NaN
+  return if (scalar @$x == 1 && $x->[0] == 0);
+  # BASE 0 or 1 => NaN
+  return if (scalar @$base == 1 && $base->[0] < 2);
+  my $cmp = _acmp($c,$x,$base); # X == BASE => 1
+  if ($cmp == 0)
+    {
+    splice (@$x,1); $x->[0] = 1;
+    return ($x,1)
+    }
+  # X < BASE
+  if ($cmp < 0)
+    {
+    splice (@$x,1); $x->[0] = 0;
+    return ($x,undef);
+    }
+
+  my $x_org = _copy($c,$x);		# preserve x
+  splice(@$x,1); $x->[0] = 1;		# keep ref to $x
+
+  # Compute a guess for the result based on:
+  # $guess = int ( length_in_base_10(X) / ( log(base) / log(10) ) )
+  my $len = _len($c,$x_org);
+  my $log = log($base->[-1]) / log(10);
+
+  # for each additional element in $base, we add $BASE_LEN to the result,
+  # based on the observation that log($BASE,10) is BASE_LEN and
+  # log(x*y) == log(x) + log(y):
+  $log += ((scalar @$base)-1) * $BASE_LEN;
+
+  # calculate now a guess based on the values obtained above:
+  my $res = int($len / $log);
+
+  $x->[0] = $res;
+  my $trial = _pow ($c, _copy($c, $base), $x);
+  my $a = _acmp($c,$trial,$x_org);
+
+#  print STDERR "# trial ", _str($c,$x)," was: $a (0 = exact, -1 too small, +1 too big)\n";
+
+  # found an exact result?
+  return ($x,1) if $a == 0;
+
+  if ($a > 0)
+    {
+    # or too big
+    _div($c,$trial,$base); _dec($c, $x);
+    while (($a = _acmp($c,$trial,$x_org)) > 0)
+      {
+#      print STDERR "# big _log_int at ", _str($c,$x), "\n"; 
+      _div($c,$trial,$base); _dec($c, $x);
+      }
+    # result is now exact (a == 0), or too small (a < 0)
+    return ($x, $a == 0 ? 1 : 0);
+    }
+
+  # else: result was to small
+  _mul($c,$trial,$base);
+
+  # did we now get the right result?
+  $a = _acmp($c,$trial,$x_org);
+
+  if ($a == 0)				# yes, exactly
+    {
+    _inc($c, $x);
+    return ($x,1); 
+    }
+  return ($x,0) if $a > 0;  
+
+  # Result still too small (we should come here only if the estimate above
+  # was very off base):
+ 
+  # Now let the normal trial run obtain the real result
+  # Simple loop that increments $x by 2 in each step, possible overstepping
+  # the real result
+
+  my $base_mul = _mul($c, _copy($c,$base), $base);	# $base * $base
+
+  while (($a = _acmp($c,$trial,$x_org)) < 0)
+    {
+#    print STDERR "# small _log_int at ", _str($c,$x), "\n"; 
+    _mul($c,$trial,$base_mul); _add($c, $x, [2]);
+    }
+
+  my $exact = 1;
+  if ($a > 0)
+    {
+    # overstepped the result
+    _dec($c, $x);
+    _div($c,$trial,$base);
+    $a = _acmp($c,$trial,$x_org);
+    if ($a > 0)
+      {
+      _dec($c, $x);
+      }
+    $exact = 0 if $a != 0;		# a = -1 => not exact result, a = 0 => exact
+    }
+  
+  ($x,$exact);				# return result
+  }
+
+# for debugging:
+  use constant DEBUG => 0;
+  my $steps = 0;
+  sub steps { $steps };
+
+sub _sqrt
+  {
+  # square-root of $x in place
+  # Compute a guess of the result (by rule of thumb), then improve it via
+  # Newton's method.
+  my ($c,$x) = @_;
+
+  if (scalar @$x == 1)
+    {
+    # fits into one Perl scalar, so result can be computed directly
+    $x->[0] = int(sqrt($x->[0]));
+    return $x;
+    } 
+  my $y = _copy($c,$x);
+  # hopefully _len/2 is < $BASE, the -1 is to always undershot the guess
+  # since our guess will "grow"
+  my $l = int((_len($c,$x)-1) / 2);	
+
+  my $lastelem = $x->[-1];					# for guess
+  my $elems = scalar @$x - 1;
+  # not enough digits, but could have more?
+  if ((length($lastelem) <= 3) && ($elems > 1))
+    {
+    # right-align with zero pad
+    my $len = length($lastelem) & 1;
+    print "$lastelem => " if DEBUG;
+    $lastelem .= substr($x->[-2] . '0' x $BASE_LEN,0,$BASE_LEN);
+    # former odd => make odd again, or former even to even again
+    $lastelem = $lastelem / 10 if (length($lastelem) & 1) != $len;
+    print "$lastelem\n" if DEBUG;
+    }
+
+  # construct $x (instead of _lsft($c,$x,$l,10)
+  my $r = $l % $BASE_LEN;	# 10000 00000 00000 00000 ($BASE_LEN=5)
+  $l = int($l / $BASE_LEN);
+  print "l =  $l " if DEBUG;
+
+  splice @$x,$l;		# keep ref($x), but modify it
+
+  # we make the first part of the guess not '1000...0' but int(sqrt($lastelem))
+  # that gives us:
+  # 14400 00000 => sqrt(14400) => guess first digits to be 120
+  # 144000 000000 => sqrt(144000) => guess 379
+
+  print "$lastelem (elems $elems) => " if DEBUG;
+  $lastelem = $lastelem / 10 if ($elems & 1 == 1);		# odd or even?
+  my $g = sqrt($lastelem); $g =~ s/\.//;			# 2.345 => 2345
+  $r -= 1 if $elems & 1 == 0;					# 70 => 7
+
+  # padd with zeros if result is too short
+  $x->[$l--] = int(substr($g . '0' x $r,0,$r+1));
+  print "now ",$x->[-1] if DEBUG;
+  print " would have been ", int('1' . '0' x $r),"\n" if DEBUG;
+
+  # If @$x > 1, we could compute the second elem of the guess, too, to create
+  # an even better guess. Not implemented yet. Does it improve performance?
+  $x->[$l--] = 0 while ($l >= 0);	# all other digits of guess are zero
+
+  print "start x= ",_str($c,$x),"\n" if DEBUG;
+  my $two = _two();
+  my $last = _zero();
+  my $lastlast = _zero();
+  $steps = 0 if DEBUG;
+  while (_acmp($c,$last,$x) != 0 && _acmp($c,$lastlast,$x) != 0)
+    {
+    $steps++ if DEBUG;
+    $lastlast = _copy($c,$last);
+    $last = _copy($c,$x);
+    _add($c,$x, _div($c,_copy($c,$y),$x));
+    _div($c,$x, $two );
+    print " x= ",_str($c,$x),"\n" if DEBUG;
+    }
+  print "\nsteps in sqrt: $steps, " if DEBUG;
+  _dec($c,$x) if _acmp($c,$y,_mul($c,_copy($c,$x),$x)) < 0;	# overshot? 
+  print " final ",$x->[-1],"\n" if DEBUG;
+  $x;
+  }
+
+sub _root
+  {
+  # take n'th root of $x in place (n >= 3)
+  my ($c,$x,$n) = @_;
+ 
+  if (scalar @$x == 1)
+    {
+    if (scalar @$n > 1)
+      {
+      # result will always be smaller than 2 so trunc to 1 at once
+      $x->[0] = 1;
+      }
+    else
+      {
+      # fits into one Perl scalar, so result can be computed directly
+      # cannot use int() here, because it rounds wrongly (try 
+      # (81 ** 3) ** (1/3) to see what I mean)
+      #$x->[0] = int( $x->[0] ** (1 / $n->[0]) );
+      # round to 8 digits, then truncate result to integer
+      $x->[0] = int ( sprintf ("%.8f", $x->[0] ** (1 / $n->[0]) ) );
+      }
+    return $x;
+    } 
+
+  # we know now that X is more than one element long
+
+  # if $n is a power of two, we can repeatedly take sqrt($X) and find the
+  # proper result, because sqrt(sqrt($x)) == root($x,4)
+  my $b = _as_bin($c,$n);
+  if ($b =~ /0b1(0+)$/)
+    {
+    my $count = CORE::length($1);	# 0b100 => len('00') => 2
+    my $cnt = $count;			# counter for loop
+    unshift (@$x, 0);			# add one element, together with one
+					# more below in the loop this makes 2
+    while ($cnt-- > 0)
+      {
+      # 'inflate' $X by adding one element, basically computing
+      # $x * $BASE * $BASE. This gives us more $BASE_LEN digits for result
+      # since len(sqrt($X)) approx == len($x) / 2.
+      unshift (@$x, 0);
+      # calculate sqrt($x), $x is now one element to big, again. In the next
+      # round we make that two, again.
+      _sqrt($c,$x);
+      }
+    # $x is now one element to big, so truncate result by removing it
+    splice (@$x,0,1);
+    } 
+  else
+    {
+    # trial computation by starting with 2,4,8,16 etc until we overstep
+    my $step;
+    my $trial = _two();
+
+    # while still to do more than X steps
+    do
+      {
+      $step = _two();
+      while (_acmp($c, _pow($c, _copy($c, $trial), $n), $x) < 0)
+        {
+        _mul ($c, $step, [2]);
+        _add ($c, $trial, $step);
+        }
+
+      # hit exactly?
+      if (_acmp($c, _pow($c, _copy($c, $trial), $n), $x) == 0)
+        {
+        @$x = @$trial;			# make copy while preserving ref to $x
+        return $x;
+        }
+      # overstepped, so go back on step
+      _sub($c, $trial, $step);
+      } while (scalar @$step > 1 || $step->[0] > 128);
+
+    # reset step to 2
+    $step = _two();
+    # add two, because $trial cannot be exactly the result (otherwise we would
+    # alrady have found it)
+    _add($c, $trial, $step);
+ 
+    # and now add more and more (2,4,6,8,10 etc)
+    while (_acmp($c, _pow($c, _copy($c, $trial), $n), $x) < 0)
+      {
+      _add ($c, $trial, $step);
+      }
+
+    # hit not exactly? (overstepped)
+    if (_acmp($c, _pow($c, _copy($c, $trial), $n), $x) > 0)
+      {
+      _dec($c,$trial);
+      }
+
+    # hit not exactly? (overstepped)
+    # 80 too small, 81 slightly too big, 82 too big
+    if (_acmp($c, _pow($c, _copy($c, $trial), $n), $x) > 0)
+      {
+      _dec ($c, $trial); 
+      }
+
+    @$x = @$trial;			# make copy while preserving ref to $x
+    return $x;
+    }
+  $x; 
+  }
+
+##############################################################################
+# binary stuff
+
+sub _and
+  {
+  my ($c,$x,$y) = @_;
+
+  # the shortcut makes equal, large numbers _really_ fast, and makes only a
+  # very small performance drop for small numbers (e.g. something with less
+  # than 32 bit) Since we optimize for large numbers, this is enabled.
+  return $x if _acmp($c,$x,$y) == 0;		# shortcut
+  
+  my $m = _one(); my ($xr,$yr);
+  my $mask = $AND_MASK;
+
+  my $x1 = $x;
+  my $y1 = _copy($c,$y);			# make copy
+  $x = _zero();
+  my ($b,$xrr,$yrr);
+  use integer;
+  while (!_is_zero($c,$x1) && !_is_zero($c,$y1))
+    {
+    ($x1, $xr) = _div($c,$x1,$mask);
+    ($y1, $yr) = _div($c,$y1,$mask);
+
+    # make ints() from $xr, $yr
+    # this is when the AND_BITS are greater than $BASE and is slower for
+    # small (<256 bits) numbers, but faster for large numbers. Disabled
+    # due to KISS principle
+
+#    $b = 1; $xrr = 0; foreach (@$xr) { $xrr += $_ * $b; $b *= $BASE; }
+#    $b = 1; $yrr = 0; foreach (@$yr) { $yrr += $_ * $b; $b *= $BASE; }
+#    _add($c,$x, _mul($c, _new( $c, ($xrr & $yrr) ), $m) );
+    
+    # 0+ due to '&' doesn't work in strings
+    _add($c,$x, _mul($c, [ 0+$xr->[0] & 0+$yr->[0] ], $m) );
+    _mul($c,$m,$mask);
+    }
+  $x;
+  }
+
+sub _xor
+  {
+  my ($c,$x,$y) = @_;
+
+  return _zero() if _acmp($c,$x,$y) == 0;	# shortcut (see -and)
+
+  my $m = _one(); my ($xr,$yr);
+  my $mask = $XOR_MASK;
+
+  my $x1 = $x;
+  my $y1 = _copy($c,$y);			# make copy
+  $x = _zero();
+  my ($b,$xrr,$yrr);
+  use integer;
+  while (!_is_zero($c,$x1) && !_is_zero($c,$y1))
+    {
+    ($x1, $xr) = _div($c,$x1,$mask);
+    ($y1, $yr) = _div($c,$y1,$mask);
+    # make ints() from $xr, $yr (see _and())
+    #$b = 1; $xrr = 0; foreach (@$xr) { $xrr += $_ * $b; $b *= $BASE; }
+    #$b = 1; $yrr = 0; foreach (@$yr) { $yrr += $_ * $b; $b *= $BASE; }
+    #_add($c,$x, _mul($c, _new( $c, ($xrr ^ $yrr) ), $m) );
+
+    # 0+ due to '^' doesn't work in strings
+    _add($c,$x, _mul($c, [ 0+$xr->[0] ^ 0+$yr->[0] ], $m) );
+    _mul($c,$m,$mask);
+    }
+  # the loop stops when the shorter of the two numbers is exhausted
+  # the remainder of the longer one will survive bit-by-bit, so we simple
+  # multiply-add it in
+  _add($c,$x, _mul($c, $x1, $m) ) if !_is_zero($c,$x1);
+  _add($c,$x, _mul($c, $y1, $m) ) if !_is_zero($c,$y1);
+  
+  $x;
+  }
+
+sub _or
+  {
+  my ($c,$x,$y) = @_;
+
+  return $x if _acmp($c,$x,$y) == 0;		# shortcut (see _and)
+
+  my $m = _one(); my ($xr,$yr);
+  my $mask = $OR_MASK;
+
+  my $x1 = $x;
+  my $y1 = _copy($c,$y);			# make copy
+  $x = _zero();
+  my ($b,$xrr,$yrr);
+  use integer;
+  while (!_is_zero($c,$x1) && !_is_zero($c,$y1))
+    {
+    ($x1, $xr) = _div($c,$x1,$mask);
+    ($y1, $yr) = _div($c,$y1,$mask);
+    # make ints() from $xr, $yr (see _and())
+#    $b = 1; $xrr = 0; foreach (@$xr) { $xrr += $_ * $b; $b *= $BASE; }
+#    $b = 1; $yrr = 0; foreach (@$yr) { $yrr += $_ * $b; $b *= $BASE; }
+#    _add($c,$x, _mul($c, _new( $c, ($xrr | $yrr) ), $m) );
+    
+    # 0+ due to '|' doesn't work in strings
+    _add($c,$x, _mul($c, [ 0+$xr->[0] | 0+$yr->[0] ], $m) );
+    _mul($c,$m,$mask);
+    }
+  # the loop stops when the shorter of the two numbers is exhausted
+  # the remainder of the longer one will survive bit-by-bit, so we simple
+  # multiply-add it in
+  _add($c,$x, _mul($c, $x1, $m) ) if !_is_zero($c,$x1);
+  _add($c,$x, _mul($c, $y1, $m) ) if !_is_zero($c,$y1);
+  
+  $x;
+  }
+
+sub _as_hex
+  {
+  # convert a decimal number to hex (ref to array, return ref to string)
+  my ($c,$x) = @_;
+
+  # fits into one element (handle also 0x0 case)
+  return sprintf("0x%x",$x->[0]) if @$x == 1;
+
+  my $x1 = _copy($c,$x);
+
+  my $es = '';
+  my ($xr, $h, $x10000);
+  if ($] >= 5.006)
+    {
+    $x10000 = [ 0x10000 ]; $h = 'h4';
+    }
+  else
+    {
+    $x10000 = [ 0x1000 ]; $h = 'h3';
+    }
+  while (@$x1 != 1 || $x1->[0] != 0)		# _is_zero()
+    {
+    ($x1, $xr) = _div($c,$x1,$x10000);
+    $es .= unpack($h,pack('V',$xr->[0]));
+    }
+  $es = reverse $es;
+  $es =~ s/^[0]+//;   # strip leading zeros
+  '0x' . $es;					# return result prepended with 0x
+  }
+
+sub _as_bin
+  {
+  # convert a decimal number to bin (ref to array, return ref to string)
+  my ($c,$x) = @_;
+
+  # fits into one element (and Perl recent enough), handle also 0b0 case
+  # handle zero case for older Perls
+  if ($] <= 5.005 && @$x == 1 && $x->[0] == 0)
+    {
+    my $t = '0b0'; return $t;
+    }
+  if (@$x == 1 && $] >= 5.006)
+    {
+    my $t = sprintf("0b%b",$x->[0]);
+    return $t;
+    }
+  my $x1 = _copy($c,$x);
+
+  my $es = '';
+  my ($xr, $b, $x10000);
+  if ($] >= 5.006)
+    {
+    $x10000 = [ 0x10000 ]; $b = 'b16';
+    }
+  else
+    {
+    $x10000 = [ 0x1000 ]; $b = 'b12';
+    }
+  while (!(@$x1 == 1 && $x1->[0] == 0))		# _is_zero()
+    {
+    ($x1, $xr) = _div($c,$x1,$x10000);
+    $es .= unpack($b,pack('v',$xr->[0]));
+    }
+  $es = reverse $es;
+  $es =~ s/^[0]+//;   # strip leading zeros
+  '0b' . $es;					# return result prepended with 0b
+  }
+
+sub _as_oct
+  {
+  # convert a decimal number to octal (ref to array, return ref to string)
+  my ($c,$x) = @_;
+
+  # fits into one element (handle also 0 case)
+  return sprintf("0%o",$x->[0]) if @$x == 1;
+
+  my $x1 = _copy($c,$x);
+
+  my $es = '';
+  my $xr;
+  my $x1000 = [ 0100000 ];
+  while (@$x1 != 1 || $x1->[0] != 0)		# _is_zero()
+    {
+    ($x1, $xr) = _div($c,$x1,$x1000);
+    $es .= reverse sprintf("%05o", $xr->[0]);
+    }
+  $es = reverse $es;
+  $es =~ s/^[0]+//;   # strip leading zeros
+  '0' . $es;					# return result prepended with 0
+  }
+
+sub _from_oct
+  {
+  # convert a octal number to decimal (string, return ref to array)
+  my ($c,$os) = @_;
+
+  # for older Perls, play safe
+  my $m = [ 0100000 ];
+  my $d = 5;					# 5 digits at a time
+
+  my $mul = _one();
+  my $x = _zero();
+
+  my $len = int( (length($os)-1)/$d );		# $d digit parts, w/o the '0'
+  my $val; my $i = -$d;
+  while ($len >= 0)
+    {
+    $val = substr($os,$i,$d);			# get oct digits
+    $val = CORE::oct($val);
+    $i -= $d; $len --;
+    my $adder = [ $val ];
+    _add ($c, $x, _mul ($c, $adder, $mul ) ) if $val != 0;
+    _mul ($c, $mul, $m ) if $len >= 0; 		# skip last mul
+    }
+  $x;
+  }
+
+sub _from_hex
+  {
+  # convert a hex number to decimal (string, return ref to array)
+  my ($c,$hs) = @_;
+
+  my $m = _new($c, 0x10000000);			# 28 bit at a time (<32 bit!)
+  my $d = 7;					# 7 digits at a time
+  if ($] <= 5.006)
+    {
+    # for older Perls, play safe
+    $m = [ 0x10000 ];				# 16 bit at a time (<32 bit!)
+    $d = 4;					# 4 digits at a time
+    }
+
+  my $mul = _one();
+  my $x = _zero();
+
+  my $len = int( (length($hs)-2)/$d );		# $d digit parts, w/o the '0x'
+  my $val; my $i = -$d;
+  while ($len >= 0)
+    {
+    $val = substr($hs,$i,$d);			# get hex digits
+    $val =~ s/^0x// if $len == 0;		# for last part only because
+    $val = CORE::hex($val);			# hex does not like wrong chars
+    $i -= $d; $len --;
+    my $adder = [ $val ];
+    # if the resulting number was to big to fit into one element, create a
+    # two-element version (bug found by Mark Lakata - Thanx!)
+    if (CORE::length($val) > $BASE_LEN)
+      {
+      $adder = _new($c,$val);
+      }
+    _add ($c, $x, _mul ($c, $adder, $mul ) ) if $val != 0;
+    _mul ($c, $mul, $m ) if $len >= 0; 		# skip last mul
+    }
+  $x;
+  }
+
+sub _from_bin
+  {
+  # convert a hex number to decimal (string, return ref to array)
+  my ($c,$bs) = @_;
+
+  # instead of converting X (8) bit at a time, it is faster to "convert" the
+  # number to hex, and then call _from_hex.
+
+  my $hs = $bs;
+  $hs =~ s/^[+-]?0b//;					# remove sign and 0b
+  my $l = length($hs);					# bits
+  $hs = '0' x (8-($l % 8)) . $hs if ($l % 8) != 0;	# padd left side w/ 0
+  my $h = '0x' . unpack('H*', pack ('B*', $hs));	# repack as hex
+  
+  $c->_from_hex($h);
+  }
+
+##############################################################################
+# special modulus functions
+
+sub _modinv
+  {
+  # modular inverse
+  my ($c,$x,$y) = @_;
+
+  my $u = _zero($c); my $u1 = _one($c);
+  my $a = _copy($c,$y); my $b = _copy($c,$x);
+
+  # Euclid's Algorithm for bgcd(), only that we calc bgcd() ($a) and the
+  # result ($u) at the same time. See comments in BigInt for why this works.
+  my $q;
+  ($a, $q, $b) = ($b, _div($c,$a,$b));		# step 1
+  my $sign = 1;
+  while (!_is_zero($c,$b))
+    {
+    my $t = _add($c, 				# step 2:
+       _mul($c,_copy($c,$u1), $q) ,		#  t =  u1 * q
+       $u );					#     + u
+    $u = $u1;					#  u = u1, u1 = t
+    $u1 = $t;
+    $sign = -$sign;
+    ($a, $q, $b) = ($b, _div($c,$a,$b));	# step 1
+    }
+
+  # if the gcd is not 1, then return NaN
+  return (undef,undef) unless _is_one($c,$a);
+ 
+  ($u1, $sign == 1 ? '+' : '-');
+  }
+
+sub _modpow
+  {
+  # modulus of power ($x ** $y) % $z
+  my ($c,$num,$exp,$mod) = @_;
+
+  # in the trivial case,
+  if (_is_one($c,$mod))
+    {
+    splice @$num,0,1; $num->[0] = 0;
+    return $num;
+    }
+  if ((scalar @$num == 1) && (($num->[0] == 0) || ($num->[0] == 1)))
+    {
+    $num->[0] = 1;
+    return $num;
+    }
+
+#  $num = _mod($c,$num,$mod);	# this does not make it faster
+
+  my $acc = _copy($c,$num); my $t = _one();
+
+  my $expbin = _as_bin($c,$exp); $expbin =~ s/^0b//;
+  my $len = length($expbin);
+  while (--$len >= 0)
+    {
+    if ( substr($expbin,$len,1) eq '1')			# is_odd
+      {
+      _mul($c,$t,$acc);
+      $t = _mod($c,$t,$mod);
+      }
+    _mul($c,$acc,$acc);
+    $acc = _mod($c,$acc,$mod);
+    }
+  @$num = @$t;
+  $num;
+  }
+
+sub _gcd
+  {
+  # greatest common divisor
+  my ($c,$x,$y) = @_;
+
+  while ( (scalar @$y != 1) || ($y->[0] != 0) )		# while ($y != 0)
+    {
+    my $t = _copy($c,$y);
+    $y = _mod($c, $x, $y);
+    $x = $t;
+    }
+  $x;
+  }
+
+##############################################################################
+##############################################################################
+
+1;
+__END__
+
+=head1 NAME
+
+Math::BigInt::Calc - Pure Perl module to support Math::BigInt
+
+=head1 SYNOPSIS
+
+Provides support for big integer calculations. Not intended to be used by other
+modules. Other modules which sport the same functions can also be used to support
+Math::BigInt, like Math::BigInt::GMP or Math::BigInt::Pari.
+
+=head1 DESCRIPTION
+
+In order to allow for multiple big integer libraries, Math::BigInt was
+rewritten to use library modules for core math routines. Any module which
+follows the same API as this can be used instead by using the following:
+
+	use Math::BigInt lib => 'libname';
+
+'libname' is either the long name ('Math::BigInt::Pari'), or only the short
+version like 'Pari'.
+
+=head1 STORAGE
+
+=head1 METHODS
+
+The following functions MUST be defined in order to support the use by
+Math::BigInt v1.70 or later:
+
+	api_version()	return API version, 1 for v1.70, 2 for v1.83
+	_new(string)	return ref to new object from ref to decimal string
+	_zero()		return a new object with value 0
+	_one()		return a new object with value 1
+	_two()		return a new object with value 2
+	_ten()		return a new object with value 10
+
+	_str(obj)	return ref to a string representing the object
+	_num(obj)	returns a Perl integer/floating point number
+			NOTE: because of Perl numeric notation defaults,
+			the _num'ified obj may lose accuracy due to 
+			machine-dependent floating point size limitations
+                    
+	_add(obj,obj)	Simple addition of two objects
+	_mul(obj,obj)	Multiplication of two objects
+	_div(obj,obj)	Division of the 1st object by the 2nd
+			In list context, returns (result,remainder).
+			NOTE: this is integer math, so no
+			fractional part will be returned.
+			The second operand will be not be 0, so no need to
+			check for that.
+	_sub(obj,obj)	Simple subtraction of 1 object from another
+			a third, optional parameter indicates that the params
+			are swapped. In this case, the first param needs to
+			be preserved, while you can destroy the second.
+			sub (x,y,1) => return x - y and keep x intact!
+	_dec(obj)	decrement object by one (input is guaranteed to be > 0)
+	_inc(obj)	increment object by one
+
+
+	_acmp(obj,obj)	<=> operator for objects (return -1, 0 or 1)
+
+	_len(obj)	returns count of the decimal digits of the object
+	_digit(obj,n)	returns the n'th decimal digit of object
+
+	_is_one(obj)	return true if argument is 1
+	_is_two(obj)	return true if argument is 2
+	_is_ten(obj)	return true if argument is 10
+	_is_zero(obj)	return true if argument is 0
+	_is_even(obj)	return true if argument is even (0,2,4,6..)
+	_is_odd(obj)	return true if argument is odd (1,3,5,7..)
+
+	_copy		return a ref to a true copy of the object
+
+	_check(obj)	check whether internal representation is still intact
+			return 0 for ok, otherwise error message as string
+
+	_from_hex(str)	return new object from a hexadecimal string
+	_from_bin(str)	return new object from a binary string
+	_from_oct(str)	return new object from an octal string
+	
+	_as_hex(str)	return string containing the value as
+			unsigned hex string, with the '0x' prepended.
+			Leading zeros must be stripped.
+	_as_bin(str)	Like as_hex, only as binary string containing only
+			zeros and ones. Leading zeros must be stripped and a
+			'0b' must be prepended.
+	
+	_rsft(obj,N,B)	shift object in base B by N 'digits' right
+	_lsft(obj,N,B)	shift object in base B by N 'digits' left
+	
+	_xor(obj1,obj2)	XOR (bit-wise) object 1 with object 2
+			Note: XOR, AND and OR pad with zeros if size mismatches
+	_and(obj1,obj2)	AND (bit-wise) object 1 with object 2
+	_or(obj1,obj2)	OR (bit-wise) object 1 with object 2
+
+	_mod(obj1,obj2)	Return remainder of div of the 1st by the 2nd object
+	_sqrt(obj)	return the square root of object (truncated to int)
+	_root(obj)	return the n'th (n >= 3) root of obj (truncated to int)
+	_fac(obj)	return factorial of object 1 (1*2*3*4..)
+	_pow(obj1,obj2)	return object 1 to the power of object 2
+			return undef for NaN
+	_zeros(obj)	return number of trailing decimal zeros
+	_modinv		return inverse modulus
+	_modpow		return modulus of power ($x ** $y) % $z
+	_log_int(X,N)	calculate integer log() of X in base N
+			X >= 0, N >= 0 (return undef for NaN)
+			returns (RESULT, EXACT) where EXACT is:
+			 1     : result is exactly RESULT
+			 0     : result was truncated to RESULT
+			 undef : unknown whether result is exactly RESULT
+        _gcd(obj,obj)	return Greatest Common Divisor of two objects
+
+The following functions are REQUIRED for an api_version of 2 or greater:
+
+	_1ex($x)	create the number 1Ex where x >= 0
+	_alen(obj)	returns approximate count of the decimal digits of the
+			object. This estimate MUST always be greater or equal
+			to what _len() returns.
+        _nok(n,k)	calculate n over k (binomial coefficient)
+
+The following functions are optional, and can be defined if the underlying lib
+has a fast way to do them. If undefined, Math::BigInt will use pure Perl (hence
+slow) fallback routines to emulate these:
+	
+	_signed_or
+	_signed_and
+	_signed_xor
+
+Input strings come in as unsigned but with prefix (i.e. as '123', '0xabc'
+or '0b1101').
+
+So the library needs only to deal with unsigned big integers. Testing of input
+parameter validity is done by the caller, so you need not worry about
+underflow (f.i. in C<_sub()>, C<_dec()>) nor about division by zero or similar
+cases.
+
+The first parameter can be modified, that includes the possibility that you
+return a reference to a completely different object instead. Although keeping
+the reference and just changing its contents is preferred over creating and
+returning a different reference.
+
+Return values are always references to objects, strings, or true/false for
+comparison routines.
+
+=head1 WRAP YOUR OWN
+
+If you want to port your own favourite c-lib for big numbers to the
+Math::BigInt interface, you can take any of the already existing modules as
+a rough guideline. You should really wrap up the latest BigInt and BigFloat
+testsuites with your module, and replace in them any of the following:
+
+	use Math::BigInt;
+
+by this:
+
+	use Math::BigInt lib => 'yourlib';
+
+This way you ensure that your library really works 100% within Math::BigInt.
+
+=head1 LICENSE
+ 
+This program is free software; you may redistribute it and/or modify it under
+the same terms as Perl itself. 
+
+=head1 AUTHORS
+
+Original math code by Mark Biggar, rewritten by Tels L<http://bloodgate.com/>
+in late 2000.
+Seperated from BigInt and shaped API with the help of John Peacock.
+
+Fixed, speed-up, streamlined and enhanced by Tels 2001 - 2007.
+
+=head1 SEE ALSO
+
+L<Math::BigInt>, L<Math::BigFloat>,
+L<Math::BigInt::GMP>, L<Math::BigInt::FastCalc> and L<Math::BigInt::Pari>.
+
+=cut
diff --git a/dist/Math-BigInt/lib/Math/BigInt/CalcEmu.pm b/dist/Math-BigInt/lib/Math/BigInt/CalcEmu.pm
new file mode 100644
index 0000000000..5810f5db9f
--- /dev/null
+++ b/dist/Math-BigInt/lib/Math/BigInt/CalcEmu.pm
@@ -0,0 +1,329 @@
+package Math::BigInt::CalcEmu;
+
+use 5.006002;
+use strict;
+# use warnings;	# dont use warnings for older Perls
+use vars qw/$VERSION/;
+
+$VERSION = '0.05';
+
+package Math::BigInt;
+
+# See SYNOPSIS below.
+
+my $CALC_EMU;
+
+BEGIN
+  {
+  $CALC_EMU = Math::BigInt->config()->{'lib'};
+  # register us with MBI to get notified of future lib changes
+  Math::BigInt::_register_callback( __PACKAGE__, sub { $CALC_EMU = $_[0]; } );
+  }
+
+sub __emu_band
+  {
+  my ($self,$x,$y,$sx,$sy,@r) = @_;
+
+  return $x->bzero(@r) if $y->is_zero() || $x->is_zero();
+  
+  my $sign = 0;					# sign of result
+  $sign = 1 if $sx == -1 && $sy == -1;
+
+  my ($bx,$by);
+
+  if ($sx == -1)				# if x is negative
+    {
+    # two's complement: inc and flip all "bits" in $bx
+    $bx = $x->binc()->as_hex();			# -1 => 0, -2 => 1, -3 => 2 etc
+    $bx =~ s/-?0x//;
+    $bx =~ tr/0123456789abcdef/\x0f\x0e\x0d\x0c\x0b\x0a\x09\x08\x07\x06\x05\x04\x03\x02\x01\x00/;
+    }
+  else
+    {
+    $bx = $x->as_hex();				# get binary representation
+    $bx =~ s/-?0x//;
+    $bx =~ tr/fedcba9876543210/\x0f\x0e\x0d\x0c\x0b\x0a\x09\x08\x07\x06\x05\x04\x03\x02\x01\x00/;
+    }
+  if ($sy == -1)				# if y is negative
+    {
+    # two's complement: inc and flip all "bits" in $by
+    $by = $y->copy()->binc()->as_hex();		# -1 => 0, -2 => 1, -3 => 2 etc
+    $by =~ s/-?0x//;
+    $by =~ tr/0123456789abcdef/\x0f\x0e\x0d\x0c\x0b\x0a\x09\x08\x07\x06\x05\x04\x03\x02\x01\x00/;
+    }
+  else
+    {
+    $by = $y->as_hex();				# get binary representation
+    $by =~ s/-?0x//;
+    $by =~ tr/fedcba9876543210/\x0f\x0e\x0d\x0c\x0b\x0a\x09\x08\x07\x06\x05\x04\x03\x02\x01\x00/;
+    }
+  # now we have bit-strings from X and Y, reverse them for padding
+  $bx = reverse $bx;
+  $by = reverse $by;
+
+  # padd the shorter string
+  my $xx = "\x00"; $xx = "\x0f" if $sx == -1;
+  my $yy = "\x00"; $yy = "\x0f" if $sy == -1;
+  my $diff = CORE::length($bx) - CORE::length($by);
+  if ($diff > 0)
+    {
+    # if $yy eq "\x00", we can cut $bx, otherwise we need to padd $by
+    $by .= $yy x $diff;
+    }
+  elsif ($diff < 0)
+    {
+    # if $xx eq "\x00", we can cut $by, otherwise we need to padd $bx
+    $bx .= $xx x abs($diff);
+    }
+  
+  # and the strings together
+  my $r = $bx & $by;
+
+  # and reverse the result again
+  $bx = reverse $r;
+
+  # One of $x or $y was negative, so need to flip bits in the result.
+  # In both cases (one or two of them negative, or both positive) we need
+  # to get the characters back.
+  if ($sign == 1)
+    {
+    $bx =~ tr/\x0f\x0e\x0d\x0c\x0b\x0a\x09\x08\x07\x06\x05\x04\x03\x02\x01\x00/0123456789abcdef/;
+    }
+  else
+    {
+    $bx =~ tr/\x0f\x0e\x0d\x0c\x0b\x0a\x09\x08\x07\x06\x05\x04\x03\x02\x01\x00/fedcba9876543210/;
+    }
+
+  # leading zeros will be stripped by _from_hex()
+  $bx = '0x' . $bx;
+  $x->{value} = $CALC_EMU->_from_hex( $bx );
+
+  # calculate sign of result
+  $x->{sign} = '+';
+  $x->{sign} = '-' if $sign == 1 && !$x->is_zero();
+
+  $x->bdec() if $sign == 1;
+
+  $x->round(@r);
+  }
+
+sub __emu_bior
+  {
+  my ($self,$x,$y,$sx,$sy,@r) = @_;
+
+  return $x->round(@r) if $y->is_zero();
+
+  my $sign = 0;					# sign of result
+  $sign = 1 if ($sx == -1) || ($sy == -1);
+
+  my ($bx,$by);
+
+  if ($sx == -1)				# if x is negative
+    {
+    # two's complement: inc and flip all "bits" in $bx
+    $bx = $x->binc()->as_hex();			# -1 => 0, -2 => 1, -3 => 2 etc
+    $bx =~ s/-?0x//;
+    $bx =~ tr/0123456789abcdef/\x0f\x0e\x0d\x0c\x0b\x0a\x09\x08\x07\x06\x05\x04\x03\x02\x01\x00/;
+    }
+  else
+    {
+    $bx = $x->as_hex();				# get binary representation
+    $bx =~ s/-?0x//;
+    $bx =~ tr/fedcba9876543210/\x0f\x0e\x0d\x0c\x0b\x0a\x09\x08\x07\x06\x05\x04\x03\x02\x01\x00/;
+    }
+  if ($sy == -1)				# if y is negative
+    {
+    # two's complement: inc and flip all "bits" in $by
+    $by = $y->copy()->binc()->as_hex();		# -1 => 0, -2 => 1, -3 => 2 etc
+    $by =~ s/-?0x//;
+    $by =~ tr/0123456789abcdef/\x0f\x0e\x0d\x0c\x0b\x0a\x09\x08\x07\x06\x05\x04\x03\x02\x01\x00/;
+    }
+  else
+    {
+    $by = $y->as_hex();				# get binary representation
+    $by =~ s/-?0x//;
+    $by =~ tr/fedcba9876543210/\x0f\x0e\x0d\x0c\x0b\x0a\x09\x08\x07\x06\x05\x04\x03\x02\x01\x00/;
+    }
+  # now we have bit-strings from X and Y, reverse them for padding
+  $bx = reverse $bx;
+  $by = reverse $by;
+
+  # padd the shorter string
+  my $xx = "\x00"; $xx = "\x0f" if $sx == -1;
+  my $yy = "\x00"; $yy = "\x0f" if $sy == -1;
+  my $diff = CORE::length($bx) - CORE::length($by);
+  if ($diff > 0)
+    {
+    $by .= $yy x $diff;
+    }
+  elsif ($diff < 0)
+    {
+    $bx .= $xx x abs($diff);
+    }
+
+  # or the strings together
+  my $r = $bx | $by;
+
+  # and reverse the result again
+  $bx = reverse $r;
+
+  # one of $x or $y was negative, so need to flip bits in the result
+  # in both cases (one or two of them negative, or both positive) we need
+  # to get the characters back.
+  if ($sign == 1)
+    {
+    $bx =~ tr/\x0f\x0e\x0d\x0c\x0b\x0a\x09\x08\x07\x06\x05\x04\x03\x02\x01\x00/0123456789abcdef/;
+    }
+  else
+    {
+    $bx =~ tr/\x0f\x0e\x0d\x0c\x0b\x0a\x09\x08\x07\x06\x05\x04\x03\x02\x01\x00/fedcba9876543210/;
+    }
+
+  # leading zeros will be stripped by _from_hex()
+  $bx = '0x' . $bx;
+  $x->{value} = $CALC_EMU->_from_hex( $bx );
+
+  # calculate sign of result
+  $x->{sign} = '+';
+  $x->{sign} = '-' if $sign == 1 && !$x->is_zero();
+
+  # if one of X or Y was negative, we need to decrement result
+  $x->bdec() if $sign == 1;
+
+  $x->round(@r);
+  }
+
+sub __emu_bxor
+  {
+  my ($self,$x,$y,$sx,$sy,@r) = @_;
+
+  return $x->round(@r) if $y->is_zero();
+
+  my $sign = 0;					# sign of result
+  $sign = 1 if $x->{sign} ne $y->{sign};
+
+  my ($bx,$by);
+
+  if ($sx == -1)				# if x is negative
+    {
+    # two's complement: inc and flip all "bits" in $bx
+    $bx = $x->binc()->as_hex();			# -1 => 0, -2 => 1, -3 => 2 etc
+    $bx =~ s/-?0x//;
+    $bx =~ tr/0123456789abcdef/\x0f\x0e\x0d\x0c\x0b\x0a\x09\x08\x07\x06\x05\x04\x03\x02\x01\x00/;
+    }
+  else
+    {
+    $bx = $x->as_hex();				# get binary representation
+    $bx =~ s/-?0x//;
+    $bx =~ tr/fedcba9876543210/\x0f\x0e\x0d\x0c\x0b\x0a\x09\x08\x07\x06\x05\x04\x03\x02\x01\x00/;
+    }
+  if ($sy == -1)				# if y is negative
+    {
+    # two's complement: inc and flip all "bits" in $by
+    $by = $y->copy()->binc()->as_hex();		# -1 => 0, -2 => 1, -3 => 2 etc
+    $by =~ s/-?0x//;
+    $by =~ tr/0123456789abcdef/\x0f\x0e\x0d\x0c\x0b\x0a\x09\x08\x07\x06\x05\x04\x03\x02\x01\x00/;
+    }
+  else
+    {
+    $by = $y->as_hex();				# get binary representation
+    $by =~ s/-?0x//;
+    $by =~ tr/fedcba9876543210/\x0f\x0e\x0d\x0c\x0b\x0a\x09\x08\x07\x06\x05\x04\x03\x02\x01\x00/;
+    }
+  # now we have bit-strings from X and Y, reverse them for padding
+  $bx = reverse $bx;
+  $by = reverse $by;
+
+  # padd the shorter string
+  my $xx = "\x00"; $xx = "\x0f" if $sx == -1;
+  my $yy = "\x00"; $yy = "\x0f" if $sy == -1;
+  my $diff = CORE::length($bx) - CORE::length($by);
+  if ($diff > 0)
+    {
+    $by .= $yy x $diff;
+    }
+  elsif ($diff < 0)
+    {
+    $bx .= $xx x abs($diff);
+    }
+
+  # xor the strings together
+  my $r = $bx ^ $by;
+
+  # and reverse the result again
+  $bx = reverse $r;
+
+  # one of $x or $y was negative, so need to flip bits in the result
+  # in both cases (one or two of them negative, or both positive) we need
+  # to get the characters back.
+  if ($sign == 1)
+    {
+    $bx =~ tr/\x0f\x0e\x0d\x0c\x0b\x0a\x09\x08\x07\x06\x05\x04\x03\x02\x01\x00/0123456789abcdef/;
+    }
+  else
+    {
+    $bx =~ tr/\x0f\x0e\x0d\x0c\x0b\x0a\x09\x08\x07\x06\x05\x04\x03\x02\x01\x00/fedcba9876543210/;
+    }
+
+  # leading zeros will be stripped by _from_hex()
+  $bx = '0x' . $bx;
+  $x->{value} = $CALC_EMU->_from_hex( $bx );
+
+  # calculate sign of result
+  $x->{sign} = '+';
+  $x->{sign} = '-' if $sx != $sy && !$x->is_zero();
+
+  $x->bdec() if $sign == 1;
+
+  $x->round(@r);
+  }
+
+##############################################################################
+##############################################################################
+
+1;
+__END__
+
+=head1 NAME
+
+Math::BigInt::CalcEmu - Emulate low-level math with BigInt code
+
+=head1 SYNOPSIS
+
+	use Math::BigInt::CalcEmu;
+
+=head1 DESCRIPTION
+
+Contains routines that emulate low-level math functions in BigInt, e.g.
+optional routines the low-level math package does not provide on its own.
+
+Will be loaded on demand and called automatically by BigInt.
+
+Stuff here is really low-priority to optimize, since it is far better to
+implement the operation in the low-level math libary directly, possible even
+using a call to the native lib.
+
+=head1 METHODS
+
+=head2 __emu_bxor
+
+=head2 __emu_band
+
+=head2 __emu_bior
+
+=head1 LICENSE
+ 
+This program is free software; you may redistribute it and/or modify it under
+the same terms as Perl itself. 
+
+=head1 AUTHORS
+
+(c) Tels http://bloodgate.com 2003, 2004 - based on BigInt code by
+Tels from 2001-2003.
+
+=head1 SEE ALSO
+
+L<Math::BigInt>, L<Math::BigFloat>, L<Math::BigInt::BitVect>,
+L<Math::BigInt::GMP> and L<Math::BigInt::Pari>.
+
+=cut
diff --git a/dist/Math-BigInt/t/Math/BigFloat/Subclass.pm b/dist/Math-BigInt/t/Math/BigFloat/Subclass.pm
new file mode 100644
index 0000000000..94d3f2a624
--- /dev/null
+++ b/dist/Math-BigInt/t/Math/BigFloat/Subclass.pm
@@ -0,0 +1,49 @@
+#!/usr/bin/perl -w
+
+# for testing subclassing Math::BigFloat
+
+package Math::BigFloat::Subclass;
+
+require 5.005_02;
+use strict;
+
+use Exporter;
+use Math::BigFloat(1.38);
+use vars qw($VERSION @ISA $PACKAGE
+            $accuracy $precision $round_mode $div_scale);
+
+@ISA = qw(Exporter Math::BigFloat);
+
+$VERSION = 0.05;
+
+use overload; 		# inherit overload from BigInt
+
+# Globals
+$accuracy = $precision = undef;
+$round_mode = 'even';
+$div_scale = 40;
+
+sub new
+{
+        my $proto  = shift;
+        my $class  = ref($proto) || $proto;
+
+        my $value       = shift;
+	my $a = $accuracy; $a = $_[0] if defined $_[0];
+	my $p = $precision; $p = $_[1] if defined $_[1];
+        # Store the floating point value
+        my $self = Math::BigFloat->new($value,$a,$p,$round_mode);
+        bless $self, $class;
+        $self->{'_custom'} = 1; # make sure this never goes away
+        return $self;
+}
+
+BEGIN
+  {
+  *objectify = \&Math::BigInt::objectify;
+  # to allow Math::BigFloat::Subclass::bgcd( ... ) style calls
+  *bgcd = \&Math::BigFloat::bgcd;
+  *blcm = \&Math::BigFloat::blcm;
+  }
+
+1;
diff --git a/dist/Math-BigInt/t/Math/BigInt/BareCalc.pm b/dist/Math-BigInt/t/Math/BigInt/BareCalc.pm
new file mode 100644
index 0000000000..0bbe861cf8
--- /dev/null
+++ b/dist/Math-BigInt/t/Math/BigInt/BareCalc.pm
@@ -0,0 +1,44 @@
+package Math::BigInt::BareCalc;
+
+use 5.005;
+use strict;
+# use warnings;	# dont use warnings for older Perls
+
+require Exporter;
+use vars qw/@ISA $VERSION/;
+@ISA = qw(Exporter);
+
+$VERSION = '0.05';
+
+sub api_version () { 1; }
+
+# Package to to test Bigint's simulation of Calc
+
+# uses Calc, but only features the strictly necc. methods.
+
+use Math::BigInt::Calc '0.51';
+
+BEGIN
+  {
+  no strict 'refs';
+  foreach (qw/	
+	base_len new zero one two ten copy str num add sub mul div mod inc dec
+	acmp alen len digit zeros
+	rsft lsft
+	fac pow gcd log_int sqrt root
+	is_zero is_one is_odd is_even is_one is_two is_ten check
+	as_hex as_bin as_oct from_hex from_bin from_oct
+	modpow modinv
+	and xor or
+	/)
+    {
+    my $name  = "Math::BigInt::Calc::_$_";
+    *{"Math::BigInt::BareCalc::_$_"} = \&$name;
+    }
+  print "# BareCalc using Calc v$Math::BigInt::Calc::VERSION\n";
+  }
+
+# catch and throw away
+sub import { }
+
+1;
diff --git a/dist/Math-BigInt/t/Math/BigInt/Scalar.pm b/dist/Math-BigInt/t/Math/BigInt/Scalar.pm
new file mode 100644
index 0000000000..c20a3e377e
--- /dev/null
+++ b/dist/Math-BigInt/t/Math/BigInt/Scalar.pm
@@ -0,0 +1,355 @@
+###############################################################################
+# core math lib for BigInt, representing big numbers by normal int/float's
+# for testing only, will fail any bignum test if range is exceeded
+
+package Math::BigInt::Scalar;
+
+use 5.005;
+use strict;
+# use warnings; # dont use warnings for older Perls
+
+require Exporter;
+
+use vars qw/@ISA $VERSION/;
+@ISA = qw(Exporter);
+
+$VERSION = '0.13';
+
+sub api_version() { 1; }
+
+##############################################################################
+# global constants, flags and accessory
+ 
+# constants for easier life
+my $nan = 'NaN';
+
+##############################################################################
+# create objects from various representations
+
+sub _new
+  {
+  # create scalar ref from string
+  my $d = $_[1];
+  my $x = $d;	# make copy
+  \$x;
+  }                                                                             
+
+sub _from_hex
+  {
+  # not used
+  }
+
+sub _from_oct
+  {
+  # not used
+  }
+
+sub _from_bin
+  {
+  # not used
+  }
+
+sub _zero
+  {
+  my $x = 0; \$x;
+  }
+
+sub _one
+  {
+  my $x = 1; \$x;
+  }
+
+sub _two
+  {
+  my $x = 2; \$x;
+  } 
+
+sub _ten
+  {
+  my $x = 10; \$x;
+  }
+
+sub _copy
+  {
+  my $x = $_[1];
+  my $z = $$x;
+  \$z;
+  }
+
+# catch and throw away
+sub import { }
+
+##############################################################################
+# convert back to string and number
+
+sub _str
+  {
+  # make string
+  "${$_[1]}";
+  }                                                                             
+
+sub _num
+  {
+  # make a number
+  0+${$_[1]};
+  }
+
+sub _zeros
+  {
+  my $x = $_[1];
+
+  $x =~ /\d(0*)$/;
+  length($1 || '');  
+  }
+
+sub _rsft
+  {
+  # not used
+  }
+
+sub _lsft
+  {
+  # not used
+  }
+
+sub _mod
+  {
+  # not used
+  }
+
+sub _gcd
+  {
+  # not used
+  }
+
+sub _sqrt
+  {
+  # not used
+  }
+
+sub _root
+  {
+  # not used
+  }
+
+sub _fac
+  {
+  # not used
+  }
+
+sub _modinv
+  {
+  # not used
+  }
+
+sub _modpow
+  {
+  # not used
+  }
+
+sub _log_int
+  {
+  # not used
+  }
+
+sub _as_hex
+  {
+  sprintf("0x%x",${$_[1]});
+  }
+
+sub _as_bin
+  {
+  sprintf("0b%b",${$_[1]});
+  }
+
+sub _as_oct
+  {
+  sprintf("0%o",${$_[1]});
+  }
+
+##############################################################################
+# actual math code
+
+sub _add
+  {
+  my ($c,$x,$y) = @_;
+  $$x += $$y;
+  return $x;
+  }                                                                             
+
+sub _sub
+  {
+  my ($c,$x,$y) = @_;
+  $$x -= $$y;
+  return $x;
+  }                                                                             
+
+sub _mul
+  {
+  my ($c,$x,$y) = @_;
+  $$x *= $$y;
+  return $x;
+  }                                                                             
+
+sub _div
+  {
+  my ($c,$x,$y) = @_;
+
+  my $u = int($$x / $$y); my $r = $$x % $$y; $$x = $u;
+  return ($x,\$r) if wantarray;
+  return $x;
+  }                                                                             
+
+sub _pow
+  {
+  my ($c,$x,$y) = @_;
+  my $u = $$x ** $$y; $$x = $u;
+  return $x;
+  }
+
+sub _and
+  {
+  my ($c,$x,$y) = @_;
+  my $u = int($$x) & int($$y); $$x = $u;
+  return $x;
+  }
+
+sub _xor
+  {
+  my ($c,$x,$y) = @_;
+  my $u = int($$x) ^ int($$y); $$x = $u;
+  return $x;
+  }
+
+sub _or
+  {
+  my ($c,$x,$y) = @_;
+  my $u = int($$x) | int($$y); $$x = $u;
+  return $x;
+  }
+
+sub _inc
+  {
+  my ($c,$x) = @_;
+  my $u = int($$x)+1; $$x = $u;
+  return $x;
+  }
+
+sub _dec
+  {
+  my ($c,$x) = @_;
+  my $u = int($$x)-1; $$x = $u;
+  return $x;
+  }
+
+##############################################################################
+# testing
+
+sub _acmp
+  {
+  my ($c,$x, $y) = @_;
+  return ($$x <=> $$y);
+  }
+
+sub _len
+  {
+  return length("${$_[1]}");
+  }
+
+sub _digit
+  {
+  # return the nth digit, negative values count backward
+  # 0 is the rightmost digit
+  my ($c,$x,$n) = @_;
+  
+  $n ++;			# 0 => 1, 1 => 2
+  return substr($$x,-$n,1);	# 1 => -1, -2 => 2 etc
+  }
+
+##############################################################################
+# _is_* routines
+
+sub _is_zero
+  {
+  # return true if arg is zero
+  my ($c,$x) = @_;
+  ($$x == 0) <=> 0;
+  }
+
+sub _is_even
+  {
+  # return true if arg is even
+  my ($c,$x) = @_;
+  (!($$x & 1)) <=> 0; 
+  }
+
+sub _is_odd
+  {
+  # return true if arg is odd
+  my ($c,$x) = @_;
+  ($$x & 1) <=> 0;
+  }
+
+sub _is_one
+  {
+  # return true if arg is one
+  my ($c,$x) = @_;
+  ($$x == 1) <=> 0;
+  }
+
+sub _is_two
+  {
+  # return true if arg is one
+  my ($c,$x) = @_;
+  ($$x == 2) <=> 0;
+  }
+
+sub _is_ten
+  {
+  # return true if arg is one
+  my ($c,$x) = @_;
+  ($$x == 10) <=> 0;
+  }
+
+###############################################################################
+# check routine to test internal state of corruptions
+
+sub _check
+  {
+  # no checks yet, pull it out from the test suite
+  my ($c,$x) = @_;
+  return "$x is not a reference" if !ref($x);
+  return 0;
+  }
+
+1;
+__END__
+
+=head1 NAME
+
+Math::BigInt::Scalar - Pure Perl module to test Math::BigInt with scalars
+
+=head1 SYNOPSIS
+
+Provides support for big integer calculations via means of 'small' int/floats.
+Only for testing purposes, since it will fail at large values. But it is simple
+enough not to introduce bugs on it's own and to serve as a testbed.
+
+=head1 DESCRIPTION
+
+Please see Math::BigInt::Calc.
+
+=head1 LICENSE
+ 
+This program is free software; you may redistribute it and/or modify it under
+the same terms as Perl itself. 
+
+=head1 AUTHOR
+
+Tels http://bloodgate.com in 2001 - 2007.
+
+=head1 SEE ALSO
+
+L<Math::BigInt>, L<Math::BigInt::Calc>.
+
+=cut
diff --git a/dist/Math-BigInt/t/Math/BigInt/Subclass.pm b/dist/Math-BigInt/t/Math/BigInt/Subclass.pm
new file mode 100644
index 0000000000..d45e9e53ad
--- /dev/null
+++ b/dist/Math-BigInt/t/Math/BigInt/Subclass.pm
@@ -0,0 +1,90 @@
+#!/usr/bin/perl -w
+
+package Math::BigInt::Subclass;
+
+require 5.005_02;
+use strict;
+
+use Exporter;
+use Math::BigInt (1.64);
+# $lib is for the "lib => " test
+use vars qw($VERSION @ISA $PACKAGE @EXPORT_OK
+	    $lib						
+            $accuracy $precision $round_mode $div_scale);
+
+@ISA = qw(Exporter Math::BigInt);
+@EXPORT_OK = qw(bgcd objectify);
+
+$VERSION = 0.04;
+
+use overload;	# inherit overload from BigInt
+
+# Globals
+$accuracy = $precision = undef;
+$round_mode = 'even';
+$div_scale = 40;
+$lib = '';
+
+sub new
+{
+        my $proto  = shift;
+        my $class  = ref($proto) || $proto;
+
+        my $value       = shift;
+	my $a = $accuracy; $a = $_[0] if defined $_[0];
+	my $p = $precision; $p = $_[1] if defined $_[1];
+        my $self = Math::BigInt->new($value,$a,$p,$round_mode);
+	bless $self,$class;
+        $self->{'_custom'} = 1; # make sure this never goes away
+        return $self;
+}
+
+sub bgcd
+  {
+  Math::BigInt::bgcd(@_);
+  }
+
+sub blcm
+  {
+  Math::BigInt::blcm(@_);
+  }
+
+sub as_int
+  {
+  Math::BigInt->new($_[0]);
+  }
+
+BEGIN
+  {
+  *objectify = \&Math::BigInt::objectify;
+
+  # these are called by AUTOLOAD from BigFloat, so we need at least these.
+  # We cheat, of course..
+  *bneg = \&Math::BigInt::bneg;
+  *babs = \&Math::BigInt::babs;
+  *bnan = \&Math::BigInt::bnan;
+  *binf = \&Math::BigInt::binf;
+  *bzero = \&Math::BigInt::bzero;
+  *bone = \&Math::BigInt::bone;
+  }
+
+sub import
+  {
+  my $self = shift;
+
+  my @a; my $t = 0;
+  foreach (@_)
+    {
+    # remove the "lib => foo" parameters and store it
+    $lib = $_, $t = 0, next if $t == 1;
+    if ($_ eq 'lib')
+      {
+      $t = 1; next;
+      }
+    push @a,$_;
+    }
+  $self->SUPER::import(@a);			# need it for subclasses
+  $self->export_to_level(1,$self,@a);		# need this ?
+  }
+
+1;
diff --git a/dist/Math-BigInt/t/_e_math.t b/dist/Math-BigInt/t/_e_math.t
new file mode 100644
index 0000000000..013985b064
--- /dev/null
+++ b/dist/Math-BigInt/t/_e_math.t
@@ -0,0 +1,106 @@
+#!/usr/bin/perl -w
+
+# test the helper math routines in Math::BigFloat
+
+use Test::More;
+use strict;
+
+BEGIN
+  {
+  $| = 1;
+  # to locate the testing files
+  my $location = $0; $location =~ s/_e_math.t//i;
+  unshift @INC, '../lib';
+  if (-d 't')
+    {
+    chdir 't';
+    require File::Spec;
+    unshift @INC, File::Spec->catdir(File::Spec->updir, $location);
+    }
+  else
+    {
+    unshift @INC, $location;
+    }
+  print "# INC = @INC\n";
+
+  plan tests => 26;
+  }
+
+use Math::BigFloat lib => 'Calc';
+
+#############################################################################
+# add
+
+my $a = Math::BigInt::Calc->_new("123");
+my $b = Math::BigInt::Calc->_new("321");
+
+my ($x, $xs) = Math::BigFloat::_e_add($a,$b,'+','+');
+is (_str($x,$xs), '+444', 'add two positive numbers');
+is (_str($a,''), '444', 'a modified');
+
+($x,$xs) = _add (123,321,'+','+');
+is (_str($x,$xs), '+444', 'add two positive numbers');
+
+($x,$xs) = _add (123,321,'+','-');
+is (_str($x,$xs), '-198', 'add +x + -y');
+($x,$xs) = _add (123,321,'-','+');
+is (_str($x,$xs), '+198', 'add -x + +y');
+
+($x,$xs) = _add (321,123,'-','+');
+is (_str($x,$xs), '-198', 'add -x + +y');
+($x,$xs) = _add (321,123,'+','-');
+is (_str($x,$xs), '+198', 'add +x + -y');
+
+($x,$xs) = _add (10,1,'+','-');
+is (_str($x,$xs), '+9', 'add 10 + -1');
+($x,$xs) = _add (10,1,'-','+');
+is (_str($x,$xs), '-9', 'add -10 + +1');
+($x,$xs) = _add (1,10,'-','+');
+is (_str($x,$xs), '+9', 'add -1 + 10');
+($x,$xs) = _add (1,10,'+','-');
+is (_str($x,$xs), '-9', 'add 1 + -10');
+
+#############################################################################
+# sub
+
+$a = Math::BigInt::Calc->_new("123");
+$b = Math::BigInt::Calc->_new("321");
+($x, $xs) = Math::BigFloat::_e_sub($b,$a,'+','+');
+is (_str($x,$xs), '+198', 'sub two positive numbers');
+is (_str($b,''), '198', 'a modified');
+
+($x,$xs) = _sub (123,321,'+','-');
+is (_str($x,$xs), '+444', 'sub +x + -y');
+($x,$xs) = _sub (123,321,'-','+');
+is (_str($x,$xs), '-444', 'sub -x + +y');
+
+sub _add
+  {
+  my ($a,$b,$as,$bs) = @_;
+
+  my $aa = Math::BigInt::Calc->_new($a);
+  my $bb = Math::BigInt::Calc->_new($b);
+  my ($x, $xs) = Math::BigFloat::_e_add($aa,$bb,$as,$bs);
+  is (Math::BigInt::Calc->_str($x), Math::BigInt::Calc->_str($aa),
+    'param0 modified');
+  ($x,$xs);
+  }
+
+sub _sub
+  {
+  my ($a,$b,$as,$bs) = @_;
+
+  my $aa = Math::BigInt::Calc->_new($a);
+  my $bb = Math::BigInt::Calc->_new($b);
+  my ($x, $xs) = Math::BigFloat::_e_sub($aa,$bb,$as,$bs);
+  is (Math::BigInt::Calc->_str($x), Math::BigInt::Calc->_str($aa),
+    'param0 modified');
+  ($x,$xs);
+  }
+
+sub _str
+  {
+  my ($x,$s) = @_;
+
+  $s . Math::BigInt::Calc->_str($x);
+  }
diff --git a/dist/Math-BigInt/t/alias.inc b/dist/Math-BigInt/t/alias.inc
new file mode 100644
index 0000000000..746a20c99e
--- /dev/null
+++ b/dist/Math-BigInt/t/alias.inc
@@ -0,0 +1,12 @@
+
+# alias subroutine testing, included by sub_ali.t and mbi_ali.t
+
+my $x = $CL->new(123);
+
+is ($x->is_pos(), 1, '123 is positive');
+is ($x->is_neg(), 0, '123 is not negative');
+is ($x->as_int(), 123, '123 is 123 as int');
+is (ref($x->as_int()), 'Math::BigInt', "as_int(123) is of class Math::BigInt");
+$x->bneg();
+is ($x->is_pos(), 0, '-123 is not positive');
+is ($x->is_neg(), 1, '-123 is negative');
diff --git a/dist/Math-BigInt/t/bare_mbf.t b/dist/Math-BigInt/t/bare_mbf.t
new file mode 100644
index 0000000000..44792064ac
--- /dev/null
+++ b/dist/Math-BigInt/t/bare_mbf.t
@@ -0,0 +1,34 @@
+#!/usr/bin/perl -w
+
+use Test;
+use strict;
+
+BEGIN
+  {
+  $| = 1;
+  # to locate the testing files
+  my $location = $0; $location =~ s/bare_mbf.t//i;
+  print "# $0\n";
+  unshift @INC, '../lib';
+  if (-d 't')
+    {
+    chdir 't';
+    require File::Spec;
+    unshift @INC, File::Spec->catdir(File::Spec->updir, $location);
+    }
+  else
+    {
+    unshift @INC, $location;
+    }
+  print "# INC = @INC\n";
+
+  plan tests => 2308;
+  }
+
+use Math::BigFloat lib => 'BareCalc';
+
+use vars qw ($class $try $x $y $f @args $ans $ans1 $ans1_str $setup $CL);
+$class = "Math::BigFloat";
+$CL = "Math::BigInt::BareCalc";
+   
+require 'bigfltpm.inc';	# all tests here for sharing
diff --git a/dist/Math-BigInt/t/bare_mbi.t b/dist/Math-BigInt/t/bare_mbi.t
new file mode 100644
index 0000000000..f005edeccd
--- /dev/null
+++ b/dist/Math-BigInt/t/bare_mbi.t
@@ -0,0 +1,38 @@
+#!/usr/bin/perl -w
+
+use Test;
+use strict;
+
+BEGIN
+  {
+  $| = 1;
+  # to locate the testing files
+  my $location = $0; $location =~ s/bare_mbi.t//i;
+  unshift @INC, qw(../lib);	# to locate the modules
+  if (-d 't')
+    {
+    chdir 't';
+    require File::Spec;
+    unshift @INC, File::Spec->catdir(File::Spec->updir, $location);
+    }
+  else
+    {
+    unshift @INC, $location;
+    }
+  print "# INC = @INC\n";
+
+  plan tests => 3273;
+  }
+
+use Math::BigInt lib => 'BareCalc';
+
+print "# ",Math::BigInt->config()->{lib},"\n";
+
+use vars qw ($class $try $x $y $f @args $ans $ans1 $ans1_str $setup $CL);
+$class = "Math::BigInt";
+$CL = "Math::BigInt::BareCalc";
+
+my $version = '1.84';	# for $VERSION tests, match current release (by hand!)
+
+require 'bigintpm.inc';	# perform same tests as bigintpm
+
diff --git a/dist/Math-BigInt/t/bare_mif.t b/dist/Math-BigInt/t/bare_mif.t
new file mode 100644
index 0000000000..c508e10450
--- /dev/null
+++ b/dist/Math-BigInt/t/bare_mif.t
@@ -0,0 +1,44 @@
+#!/usr/bin/perl -w
+
+# test rounding, accuracy, precicion and fallback, round_mode and mixing
+# of classes under BareCalc
+
+use strict;
+use Test;
+
+BEGIN
+  {
+  $| = 1;
+  # to locate the testing files
+  my $location = $0; $location =~ s/bare_mif.t//i;
+  unshift @INC, '../lib';	# for testing manually
+  if (-d 't')
+    {
+    chdir 't';
+    require File::Spec;
+    unshift @INC, File::Spec->catdir(File::Spec->updir, $location);
+    }
+  else
+    {
+    unshift @INC, $location;
+    }
+  print "# INC = @INC\n";
+
+  plan tests => 684
+    + 1;		# our own tests
+  }
+
+print "# ",Math::BigInt->config()->{lib},"\n";
+
+use Math::BigInt lib => 'BareCalc';
+use Math::BigFloat lib => 'BareCalc';
+
+use vars qw/$mbi $mbf/;
+
+$mbi = 'Math::BigInt';
+$mbf = 'Math::BigFloat';
+
+ok (Math::BigInt->config()->{lib},'Math::BigInt::BareCalc');
+
+require 'mbimbf.inc';
+
diff --git a/dist/Math-BigInt/t/big_pi_e.t b/dist/Math-BigInt/t/big_pi_e.t
new file mode 100644
index 0000000000..1e3d08f6c1
--- /dev/null
+++ b/dist/Math-BigInt/t/big_pi_e.t
@@ -0,0 +1,54 @@
+#!/usr/bin/perl -w
+
+# Test bpi() and bexp()
+
+use Test::More;
+use strict;
+
+BEGIN
+  {
+  $| = 1;
+  # to locate the testing files
+  my $location = $0; $location =~ s/big_pi_e.t//i;
+  unshift @INC, '../lib';
+  if (-d 't')
+    {
+    chdir 't';
+    require File::Spec;
+    unshift @INC, File::Spec->catdir(File::Spec->updir, $location);
+    }
+  else
+    {
+    unshift @INC, $location;
+    }
+  print "# INC = @INC\n";
+
+  plan tests => 8;
+  }
+
+use Math::BigFloat;
+
+#############################################################################
+
+my $pi = Math::BigFloat::bpi();
+
+ok (!exists $pi->{_a}, 'A not set');
+ok (!exists $pi->{_p}, 'P not set');
+
+$pi = Math::BigFloat->bpi();
+
+ok (!exists $pi->{_a}, 'A not set');
+ok (!exists $pi->{_p}, 'P not set');
+
+$pi = Math::BigFloat->bpi(10);
+
+is ($pi->{_a}, 10, 'A set');
+is ($pi->{_p}, undef, 'P not set');
+
+#############################################################################
+my $e = Math::BigFloat->new(1)->bexp();
+
+ok (!exists $e->{_a}, 'A not set');
+ok (!exists $e->{_p}, 'P not set');
+
+
diff --git a/dist/Math-BigInt/t/bigfltpm.inc b/dist/Math-BigInt/t/bigfltpm.inc
new file mode 100644
index 0000000000..7d650e5cba
--- /dev/null
+++ b/dist/Math-BigInt/t/bigfltpm.inc
@@ -0,0 +1,1823 @@
+#include this file into another test for subclass testing...
+
+ok ($class->config()->{lib},$CL);
+
+use strict;
+
+my $z;
+
+while (<DATA>)
+  {
+  $_ =~ s/[\n\r]//g;	# remove newlines
+  $_ =~ s/#.*$//;	# remove comments
+  $_ =~ s/\s+$//;	# trailing spaces
+  next if /^$/;		# skip empty lines & comments
+  if (s/^&//)
+    {
+    $f = $_;
+    }
+  elsif (/^\$/)
+    {
+    $setup = $_; $setup =~ s/\$/\$${class}::/g;	# round_mode, div_scale
+    #print "\$setup== $setup\n";
+    }
+  else
+    {
+    if (m|^(.*?):(/.+)$|)
+      {
+      $ans = $2;
+      @args = split(/:/,$1,99);
+      }
+    else
+      {
+      @args = split(/:/,$_,99); $ans = pop(@args);
+      }
+    $try = "\$x = $class->new(\"$args[0]\");";
+    if ($f eq "fnorm")
+      {
+        $try .= "\$x;";
+      } elsif ($f eq "finf") {
+        $try .= "\$x->finf('$args[1]');";
+      } elsif ($f eq "is_inf") {
+        $try .= "\$x->is_inf('$args[1]');"; 
+      } elsif ($f eq "fone") {
+        $try .= "\$x->bone('$args[1]');";
+      } elsif ($f eq "fstr") {
+        $try .= "\$x->accuracy($args[1]); \$x->precision($args[2]);";
+        $try .= '$x->fstr();';
+      } elsif ($f eq "parts") {
+        # ->bstr() to see if an object is returned
+        $try .= '($a,$b) = $x->parts(); $a = $a->bstr(); $b = $b->bstr();';
+        $try .= '"$a $b";';
+      } elsif ($f eq "exponent") {
+        # ->bstr() to see if an object is returned
+        $try .= '$x->exponent()->bstr();';
+      } elsif ($f eq "mantissa") {
+        # ->bstr() to see if an object is returned
+        $try .= '$x->mantissa()->bstr();';
+      } elsif ($f =~ /^(numify|length|as_number|as_hex|as_bin)$/) {
+        $try .= "\$x->$f();";
+      # some unary ops (test the fxxx form, since that is done by AUTOLOAD)
+      } elsif ($f =~ /^f(nan|sstr|neg|floor|ceil|abs)$/) {
+        $try .= "\$x->f$1();";
+      # some is_xxx test function	
+      } elsif ($f =~ /^is_(zero|one|negative|positive|odd|even|nan|int)$/) {
+        $try .= "\$x->$f();";
+      } elsif ($f eq "bpi") {
+        $try .= '$class->bpi($x);';
+      } elsif ($f eq "finc") {
+        $try .= '++$x;';
+      } elsif ($f eq "fdec") {
+        $try .= '--$x;';
+      }elsif ($f eq "fround") {
+        $try .= "$setup; \$x->fround($args[1]);";
+      } elsif ($f eq "ffround") {
+        $try .= "$setup; \$x->ffround($args[1]);";
+      } elsif ($f eq "fsqrt") {
+        $try .= "$setup; \$x->fsqrt();";
+      } elsif ($f eq "ffac") {
+        $try .= "$setup; \$x->ffac();";
+      } elsif ($f eq "flog") {
+        if (defined $args[1] && $args[1] ne '')
+          {
+          $try .= "\$y = $class->new($args[1]);";
+          $try .= "$setup; \$x->flog(\$y);";
+          }
+        else
+          {
+          $try .= "$setup; \$x->flog();";
+          }
+      }
+    else
+      {
+      $try .= "\$y = $class->new(\"$args[1]\");";
+      
+      if ($f eq "bgcd")
+        {
+        if (defined $args[2])
+          {
+          $try .= " \$z = $class->new(\"$args[2]\"); ";
+          }
+        $try .= "$class\::bgcd(\$x, \$y";
+        $try .= ", \$z" if (defined $args[2]);
+        $try .= " );";
+        }
+      elsif ($f eq "blcm")
+        {
+        if (defined $args[2])
+          {
+          $try .= " \$z = $class->new(\"$args[2]\"); ";
+          }
+        $try .= "$class\::blcm(\$x, \$y";
+        $try .= ", \$z" if (defined $args[2]);
+        $try .= " );";
+      } elsif ($f eq "fcmp") {
+        $try .= '$x->fcmp($y);';
+      } elsif ($f eq "facmp") {
+        $try .= '$x->facmp($y);';
+      } elsif ($f eq "fpow") {
+        $try .= '$x ** $y;';
+      } elsif ($f eq "bnok") {
+        $try .= '$x->bnok($y);';
+      } elsif ($f eq "bcos") {
+        $try .= '$x->bcos($y);';
+      } elsif ($f eq "bsin") {
+        $try .= '$x->bsin($y);';
+      } elsif ($f eq "batan") {
+        $try .= '$x->batan($y);';
+      } elsif ($f eq "froot") {
+        $try .= "$setup; \$x->froot(\$y);";
+      } elsif ($f eq "fadd") {
+        $try .= '$x + $y;';
+      } elsif ($f eq "fsub") {
+        $try .= '$x - $y;';
+      } elsif ($f eq "fmul") {
+        $try .= '$x * $y;';
+      } elsif ($f eq "fdiv") {
+        $try .= "$setup; \$x / \$y;";
+      } elsif ($f eq "fdiv-list") {
+        $try .= "$setup; join(',',\$x->fdiv(\$y));";
+      } elsif ($f eq "frsft") {
+        $try .= '$x >> $y;';
+      } elsif ($f eq "flsft") {
+        $try .= '$x << $y;';
+      } elsif ($f eq "fmod") {
+        $try .= '$x % $y;';
+       } else {
+       # Functions with three arguments
+       $try .= "\$z = $class->new(\"$args[2]\");";
+
+       if( $f eq "bmodpow") {
+          $try .= '$x->bmodpow($y,$z);';
+         } elsif ($f eq "bmuladd"){
+          $try .= '$x->bmuladd($y,$z);';
+         } elsif ($f eq "batan2"){
+          $try .= '$x->batan2($y,$z);';
+         } else { warn "Unknown op '$f'"; }
+       }
+    }
+    # print "# Trying: '$try'\n";
+    $ans1 = eval $try;
+    print "# Error: $@\n" if $@;
+    if ($ans =~ m|^/(.*)$|)
+      {
+      my $pat = $1;
+      if ($ans1 =~ /$pat/)
+        {
+        ok (1,1);
+        }
+      else
+        {
+        print "# '$try' expected: /$pat/ got: '$ans1'\n" if !ok(1,0);
+        }
+      }
+    else
+      {
+      if ($ans eq "")
+        {
+        ok_undef ($ans1);
+        }
+      else
+        {
+        print "# Tried: '$try'\n" if !ok ($ans1, $ans);
+        if (ref($ans1) eq "$class")
+	  {
+	  # float numbers are normalized (for now), so mantissa shouldn't have
+	  # trailing zeros
+	  #print $ans1->_trailing_zeros(),"\n";
+          print "# Has trailing zeros after '$try'\n"
+	   if !ok ($CL->_zeros( $ans1->{_m}), 0);
+	  }
+        }
+      } # end pattern or string
+    }
+  } # end while
+
+# check whether $class->new( Math::BigInt->new()) destroys it 
+# ($y == 12 in this case)
+$x = Math::BigInt->new(1200); $y = $class->new($x);
+ok ($y,1200); ok ($x,1200);
+
+###############################################################################
+# Really huge, big, ultra-mega-biggy-monster exponents
+# Technically, the exponents should not be limited (they are BigInts), but
+# practically there are a few places were they are limited to a Perl scalar.
+# This is sometimes for speed, sometimes because otherwise the number wouldn't
+# fit into your memory (just think of 1e123456789012345678901234567890 + 1!)
+# anyway. We don't test everything here, but let's make sure it just basically
+# works.
+
+my $monster = '1e1234567890123456789012345678901234567890';
+
+# new and exponent
+ok ($class->new($monster)->bsstr(), 
+		'1e+1234567890123456789012345678901234567890');
+ok ($class->new($monster)->exponent(), 
+		'1234567890123456789012345678901234567890');
+# cmp
+ok ($class->new($monster) > 0,1);
+
+# sub/mul 
+ok ($class->new($monster)->bsub( $monster),0);
+ok ($class->new($monster)->bmul(2)->bsstr(),
+                '2e+1234567890123456789012345678901234567890');
+
+# mantissa
+$monster = '1234567890123456789012345678901234567890e2';
+ok ($class->new($monster)->mantissa(), 
+		'123456789012345678901234567890123456789');
+
+###############################################################################
+# zero,inf,one,nan
+
+$x = $class->new(2); $x->fzero(); ok_undef ($x->{_a}); ok_undef ($x->{_p});
+$x = $class->new(2); $x->finf();  ok_undef ($x->{_a}); ok_undef ($x->{_p});
+$x = $class->new(2); $x->fone();  ok_undef ($x->{_a}); ok_undef ($x->{_p});
+$x = $class->new(2); $x->fnan();  ok_undef ($x->{_a}); ok_undef ($x->{_p});
+
+###############################################################################
+# bone/binf etc as plain calls (Lite failed them)
+
+ok ($class->fzero(),0);
+ok ($class->fone(),1);
+ok ($class->fone('+'),1);
+ok ($class->fone('-'),-1);
+ok ($class->fnan(),'NaN');
+ok ($class->finf(),'inf');
+ok ($class->finf('+'),'inf');
+ok ($class->finf('-'),'-inf');
+ok ($class->finf('-inf'),'-inf');
+        
+$class->accuracy(undef); $class->precision(undef);	# reset
+
+###############################################################################
+# bug in bsstr()/numify() showed up in after-rounding in bdiv()
+
+$x = $class->new('0.008'); $y = $class->new(2);
+$x->bdiv(3,$y);
+ok ($x,'0.0027');
+
+###############################################################################
+# fsqrt() with set global A/P or A/P enabled on $x, also a test whether fsqrt()
+# correctly modifies $x
+
+
+$x = $class->new(12); $class->precision(-2); $x->fsqrt(); ok ($x,'3.46');
+
+$class->precision(undef);
+$x = $class->new(12); $class->precision(0); $x->fsqrt(); ok ($x,'3');
+
+$class->precision(-3); $x = $class->new(12); $x->fsqrt(); ok ($x,'3.464');
+
+{
+  no strict 'refs';
+  # A and P set => NaN
+  ${${class}.'::accuracy'} = 4; $x = $class->new(12);
+  $x->fsqrt(3); ok ($x,'NaN');
+  # supplied arg overrides set global
+  $class->precision(undef); $x = $class->new(12); $x->fsqrt(3); ok ($x,'3.46');
+  $class->accuracy(undef); $class->precision(undef); # reset for further tests
+}
+
+#############################################################################
+# can we call objectify (broken until v1.52)
+
+{
+  no strict;
+  $try = 
+    '@args' . " = $class" . "::objectify(2,$class,4,5);".'join(" ",@args);';
+  $ans = eval $try;
+  ok ($ans,"$class 4 5");
+}
+
+#############################################################################
+# is_one('-') (broken until v1.64)
+
+ok ($class->new(-1)->is_one(),0);
+ok ($class->new(-1)->is_one('-'),1);
+
+#############################################################################
+# bug 1/0.5 leaving 2e-0 instead of 2e0
+
+ok ($class->new(1)->fdiv('0.5')->bsstr(),'2e+0');
+
+###############################################################################
+# [perl #30609] bug with $x -= $x not being 0, but 2*$x
+
+$x = $class->new(3);  $x -= $x; ok ($x, 0);
+$x = $class->new(-3); $x -= $x; ok ($x, 0);
+$x = $class->new(3);  $x += $x; ok ($x, 6);
+$x = $class->new(-3); $x += $x; ok ($x, -6);
+
+$x = $class->new('NaN'); $x -= $x; ok ($x->is_nan(), 1);
+$x = $class->new('inf'); $x -= $x; ok ($x->is_nan(), 1);
+$x = $class->new('-inf'); $x -= $x; ok ($x->is_nan(), 1);
+
+$x = $class->new('NaN'); $x += $x; ok ($x->is_nan(), 1);
+$x = $class->new('inf'); $x += $x; ok ($x->is_inf(), 1);
+$x = $class->new('-inf'); $x += $x; ok ($x->is_inf('-'), 1);
+
+$x = $class->new('3.14');  $x -= $x; ok ($x, 0);
+$x = $class->new('-3.14'); $x -= $x; ok ($x, 0);
+$x = $class->new('3.14');  $x += $x; ok ($x, '6.28');
+$x = $class->new('-3.14'); $x += $x; ok ($x, '-6.28');
+
+$x = $class->new('3.14');  $x *= $x; ok ($x, '9.8596');
+$x = $class->new('-3.14'); $x *= $x; ok ($x, '9.8596');
+$x = $class->new('3.14');  $x /= $x; ok ($x, '1');
+$x = $class->new('-3.14'); $x /= $x; ok ($x, '1');
+$x = $class->new('3.14');  $x %= $x; ok ($x, '0');
+$x = $class->new('-3.14'); $x %= $x; ok ($x, '0');
+
+###############################################################################
+# the following two were reported by "kenny" via hotmail.com:
+
+#perl -MMath::BigFloat -wle 'print Math::BigFloat->new(0)->bpow(".1")'
+#Use of uninitialized value in numeric le (<=) at BigFloat.pm line 1851.
+
+$x = $class->new(0); $y = $class->new('0.1');
+ok ($x ** $y, 0, 'no warnings and zero result');
+
+#perl -MMath::BigFloat -lwe 'print Math::BigFloat->new(".222222222222222222222222222222222222222222")->bceil()'
+#Use of uninitialized value in numeric le (<=) at BigFloat.pm line 1851.
+
+$x = $class->new(".222222222222222222222222222222222222222222"); 
+ok ($x->bceil(), 1, 'no warnings and one as result');
+
+###############################################################################
+# test **=, <<=, >>=
+
+# ((2^148)-1)/17
+$x = $class->new(2); $x **= 148; $x++; $x->bdiv(17, 60)->bfloor(); $x->accuracy(undef);
+ok ($x,"20988936657440586486151264256610222593863921");
+ok ($x->length(),length "20988936657440586486151264256610222593863921");
+
+$x = $class->new('2');
+my $y = $class->new('18');
+ok ($x <<= $y, 2 << 18);
+ok ($x, 2 << 18);
+ok ($x >>= $y, 2);
+ok ($x, 2);
+
+$x = $class->new('2');
+$y = $class->new('18.2');
+$x <<= $y;		# 2 * (2 ** 18.2);
+
+ok ($x->copy()->bfround(-9), '602248.763144685');
+ok ($x >>= $y, 2);	# 2 * (2 ** 18.2) / (2 ** 18.2) => 2
+ok ($x, 2);
+
+1; # all done
+
+###############################################################################
+# Perl 5.005 does not like ok ($x,undef)
+
+sub ok_undef
+  {
+  my $x = shift;
+
+  ok (1,1) and return if !defined $x;
+  ok ($x,'undef');
+  }
+
+__DATA__
+&bgcd
+inf:12:NaN
+-inf:12:NaN
+12:inf:NaN
+12:-inf:NaN
+inf:inf:NaN
+inf:-inf:NaN
+-inf:-inf:NaN
+abc:abc:NaN
+abc:+0:NaN
++0:abc:NaN
++0:+0:0
++0:+1:1
++1:+0:1
++1:+1:1
++2:+3:1
++3:+2:1
+-3:+2:1
+-3:-2:1
+-144:-60:12
+144:-60:12
+144:60:12
+100:625:25
+4096:81:1
+1034:804:2
+27:90:56:1
+27:90:54:9
+&blcm
+abc:abc:NaN
+abc:+0:NaN
++0:abc:NaN
++0:+0:NaN
++1:+0:0
++0:+1:0
++27:+90:270
++1034:+804:415668
+$div_scale = 40;
+&bcos
+1.2:10:0.3623577545
+2.4:12:-0.737393715541
+0:10:1
+0:20:1
+1:10:0.5403023059
+1:12:0.540302305868
+&bsin
+1:10:0.8414709848
+0:10:0
+0:20:0
+2.1:12:0.863209366649
+1.2:13:0.9320390859672
+0.2:13:0.1986693307951
+3.2:12:-0.0583741434276
+&batan
+NaN:10:NaN
+inf:14:1.5707963267949
+-inf:14:-1.5707963267949
+0.2:13:0.1973955598499
+0.2:14:0.19739555984988
+0:10:0
+1:14:0.78539816339744
+-1:14:-0.78539816339744
+# test an argument X > 1
+2:14:1.1071487177941
+&batan2
+NaN:1:10:NaN
+NaN:NaN:10:NaN
+1:NaN:10:NaN
+inf:1:14:1.5707963267949
+-inf:1:14:-1.5707963267949
+0:-inf:14:3.1415926535898
+-1:-inf:14:-3.1415926535898
+1:-inf:14:3.1415926535898
+0:inf:14:0
+inf:-inf:14:2.3561944901923
+-inf:-inf:14:-2.3561944901923
+inf:+inf:14:0.7853981633974
+-inf:+inf:14:-0.7853981633974
+1:5:13:0.1973955598499
+1:5:14:0.19739555984988
+0:0:10:0
+0:1:14:0
+0:2:14:0
+1:0:14:1.5707963267949
+5:0:14:1.5707963267949
+-1:0:11:-1.5707963268
+-2:0:77:-1.5707963267948966192313216916397514420985846996875529104874722961539082031431
+2:0:77:1.5707963267948966192313216916397514420985846996875529104874722961539082031431
+-1:5:14:-0.19739555984988
+1:5:14:0.19739555984988
+-1:8:14:-0.12435499454676
+1:8:14:0.12435499454676
+-1:1:14:-0.78539816339744
+# test an argument X > 1 and one X < 1
+1:2:24:0.463647609000806116214256
+2:1:14:1.1071487177941
+-2:1:14:-1.1071487177941
+&bpi
+150:3.14159265358979323846264338327950288419716939937510582097494459230781640628620899862803482534211706798214808651328230664709384460955058223172535940813
+77:3.1415926535897932384626433832795028841971693993751058209749445923078164062862
++0:3.141592653589793238462643383279502884197
+11:3.1415926536
+&bnok
++inf:10:inf
+NaN:NaN:NaN
+NaN:1:NaN
+1:NaN:NaN
+1:1:1
+# k > n
+1:2:0
+2:3:0
+# k < 0
+1:-2:0
+# 7 over 3 = 35
+7:3:35
+7:6:1
+100:90:17310309456440
+&flog
+0::NaN
+-1::NaN
+-2::NaN
+# base > 0, base != 1
+2:-1:NaN
+2:0:NaN
+2:1:NaN
+# log(1) is always 1, regardless of $base
+1::0
+1:1:0
+1:2:0
+2::0.6931471805599453094172321214581765680755
+2.718281828::0.9999999998311266953289851340574956564911
+$div_scale = 20;
+2.718281828::0.99999999983112669533
+$div_scale = 15;
+123::4.81218435537242
+10::2.30258509299405
+1000::6.90775527898214
+100::4.60517018598809
+2::0.693147180559945
+3.1415::1.14470039286086
+12345::9.42100640177928
+0.001::-6.90775527898214
+# bug until v1.71:
+10:10:1
+100:100:1
+# reset for further tests
+$div_scale = 40;
+1::0
+&frsft
+NaNfrsft:2:NaN
+0:2:0
+1:1:0.5
+2:1:1
+4:1:2
+123:1:61.5
+32:3:4
+&flsft
+NaNflsft:0:NaN
+2:1:4
+4:3:32
+5:3:40
+1:2:4
+0:5:0
+&fnorm
+1:1
+-0:0
+fnormNaN:NaN
++inf:inf
+-inf:-inf
+123:123
+-123.4567:-123.4567
+# invalid inputs
+1__2:NaN
+1E1__2:NaN
+11__2E2:NaN
+.2E-3.:NaN
+1e3e4:NaN
+# strange, but valid
+.2E2:20
+1.E3:1000
+# some inputs that result in zero
+0e0:0
++0e0:0
++0e+0:0
+-0e+0:0
+0e-0:0
+-0e-0:0
++0e-0:0
+000:0
+00e2:0
+00e02:0
+000e002:0
+000e1230:0
+00e-3:0
+00e+3:0
+00e-03:0
+00e+03:0
+-000:0
+-00e2:0
+-00e02:0
+-000e002:0
+-000e1230:0
+-00e-3:0
+-00e+3:0
+-00e-03:0
+-00e+03:0
+&as_number
+0:0
+1:1
+1.2:1
+2.345:2
+-2:-2
+-123.456:-123
+-200:-200
+# test for bug in brsft() not handling cases that return 0
+0.000641:0
+0.0006412:0
+0.00064123:0
+0.000641234:0
+0.0006412345:0
+0.00064123456:0
+0.000641234567:0
+0.0006412345678:0
+0.00064123456789:0
+0.1:0
+0.01:0
+0.001:0
+0.0001:0
+0.00001:0
+0.000001:0
+0.0000001:0
+0.00000001:0
+0.000000001:0
+0.0000000001:0
+0.00000000001:0
+0.12345:0
+0.123456:0
+0.1234567:0
+0.12345678:0
+0.123456789:0
+&finf
+1:+:inf
+2:-:-inf
+3:abc:inf
+&as_hex
++inf:inf
+-inf:-inf
+hexNaN:NaN
+0:0x0
+5:0x5
+-5:-0x5
+&as_bin
++inf:inf
+-inf:-inf
+hexNaN:NaN
+0:0b0
+5:0b101
+-5:-0b101
+&numify
+# uses bsstr() so 5 => 5e+0 to be compatible w/ Perls output
+0:0e+1
++1:1e+0
+1234:1234e+0
+NaN:NaN
++inf:inf
+-inf:-inf
+-5:-5e+0
+100:1e+2
+-100:-1e+2
+&fnan
+abc:NaN
+2:NaN
+-2:NaN
+0:NaN
+&fone
+2:+:1
+-2:-:-1
+-2:+:1
+2:-:-1
+0::1
+-2::1
+abc::1
+2:abc:1
+&fsstr
++inf:inf
+-inf:-inf
+abcfsstr:NaN
+-abcfsstr:NaN
+1234.567:1234567e-3
+123:123e+0
+-5:-5e+0
+-100:-1e+2
+&fstr
++inf:::inf
+-inf:::-inf
+abcfstr:::NaN
+1234.567:9::1234.56700
+1234.567::-6:1234.567000
+12345:5::12345
+0.001234:6::0.00123400
+0.001234::-8:0.00123400
+0:4::0
+0::-4:0.0000
+&fnorm
+inf:inf
++inf:inf
+-inf:-inf
++infinity:NaN
++-inf:NaN
+abc:NaN
+   1 a:NaN
+1bcd2:NaN
+11111b:NaN
++1z:NaN
+-1z:NaN
+0e999:0
+0e-999:0
+-0e999:0
+-0e-999:0
+0:0
++0:0
++00:0
++0_0_0:0
+000000_0000000_00000:0
+-0:0
+-0000:0
++1:1
++01:1
++001:1
++00000100000:100000
+123456789:123456789
+-1:-1
+-01:-1
+-001:-1
+-123456789:-123456789
+-00000100000:-100000
+123.456a:NaN
+123.456:123.456
+0.01:0.01
+.002:0.002
++.2:0.2
+-0.0003:-0.0003
+-.0000000004:-0.0000000004
+123456E2:12345600
+123456E-2:1234.56
+-123456E2:-12345600
+-123456E-2:-1234.56
+1e1:10
+2e-11:0.00000000002
+# excercise _split
+  .02e-1:0.002
+   000001:1
+   -00001:-1
+   -1:-1
+  000.01:0.01
+   -000.0023:-0.0023
+  1.1e1:11
+-3e111:-3000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
+-4e-1111:-0.0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000004
+&fpow
+NaN:1:NaN
+1:NaN:NaN
+NaN:-1:NaN
+-1:NaN:NaN
+NaN:-21:NaN
+-21:NaN:NaN
+NaN:21:NaN
+21:NaN:NaN
+0:0:1
+0:1:0
+0:9:0
+0:-2:inf
+2:2:4
+1:2:1
+1:3:1
+-1:2:1
+-1:3:-1
+123.456:2:15241.383936
+2:-2:0.25
+2:-3:0.125
+128:-2:0.00006103515625
+abc:123.456:NaN
+123.456:abc:NaN
++inf:123.45:inf
+-inf:123.45:-inf
++inf:-123.45:inf
+-inf:-123.45:-inf
+-2:2:4
+-2:3:-8
+-2:4:16
+-2:5:-32
+-3:2:9
+-3:3:-27
+-3:4:81
+-3:5:-243
+# 2 ** 0.5 == sqrt(2)
+#     1.41..7 and not 1.4170 since fallback (bsqrt(9) is '3', not 3.0...0)
+2:0.5:1.41421356237309504880168872420969807857
+#2:0.2:1.148698354997035006798626946777927589444
+#6:1.5:14.6969384566990685891837044482353483518
+$div_scale = 20;
+#62.5:12.5:26447206647554886213592.3959144
+$div_scale = 40;
+&fneg
+fnegNaN:NaN
++inf:-inf
+-inf:inf
++0:0
++1:-1
+-1:1
++123456789:-123456789
+-123456789:123456789
++123.456789:-123.456789
+-123456.789:123456.789
+&fabs
+fabsNaN:NaN
++inf:inf
+-inf:inf
++0:0
++1:1
+-1:1
++123456789:123456789
+-123456789:123456789
++123.456789:123.456789
+-123456.789:123456.789
+&fround
+$round_mode = "trunc"
++inf:5:inf
+-inf:5:-inf
+0:5:0
+NaNfround:5:NaN
++10123456789:5:10123000000
+-10123456789:5:-10123000000
++10123456789.123:5:10123000000
+-10123456789.123:5:-10123000000
++10123456789:9:10123456700
+-10123456789:9:-10123456700
++101234500:6:101234000
+-101234500:6:-101234000
+$round_mode = "zero"
++20123456789:5:20123000000
+-20123456789:5:-20123000000
++20123456789.123:5:20123000000
+-20123456789.123:5:-20123000000
++20123456789:9:20123456800
+-20123456789:9:-20123456800
++201234500:6:201234000
+-201234500:6:-201234000
+$round_mode = "+inf"
++30123456789:5:30123000000
+-30123456789:5:-30123000000
++30123456789.123:5:30123000000
+-30123456789.123:5:-30123000000
++30123456789:9:30123456800
+-30123456789:9:-30123456800
++301234500:6:301235000
+-301234500:6:-301234000
+$round_mode = "-inf"
++40123456789:5:40123000000
+-40123456789:5:-40123000000
++40123456789.123:5:40123000000
+-40123456789.123:5:-40123000000
++40123456789:9:40123456800
+-40123456789:9:-40123456800
++401234500:6:401234000
+-401234500:6:-401235000
+$round_mode = "odd"
++50123456789:5:50123000000
+-50123456789:5:-50123000000
++50123456789.123:5:50123000000
+-50123456789.123:5:-50123000000
++50123456789:9:50123456800
+-50123456789:9:-50123456800
++501234500:6:501235000
+-501234500:6:-501235000
+$round_mode = "even"
++60123456789:5:60123000000
+-60123456789:5:-60123000000
++60123456789:9:60123456800
+-60123456789:9:-60123456800
++601234500:6:601234000
+-601234500:6:-601234000
++60123456789.0123:5:60123000000
+-60123456789.0123:5:-60123000000
+$round_mode = "common"
++60123456789:5:60123000000
+-60123456789:5:-60123000000
++60123456789:6:60123500000
+-60123456789:6:-60123500000
++60123456789:9:60123456800
+-60123456789:9:-60123456800
++601234500:6:601235000
+-601234500:6:-601235000
++601234400:6:601234000
+-601234400:6:-601234000
++601234600:6:601235000
+-601234600:6:-601235000
++601234300:6:601234000
++60123456789.0123:5:60123000000
+-60123456789.0123:5:-60123000000
+&ffround
+$round_mode = "trunc"
++inf:5:inf
+-inf:5:-inf
+0:5:0
+NaNffround:5:NaN
++1.23:-1:1.2
++1.234:-1:1.2
++1.2345:-1:1.2
++1.23:-2:1.23
++1.234:-2:1.23
++1.2345:-2:1.23
++1.23:-3:1.230
++1.234:-3:1.234
++1.2345:-3:1.234
+-1.23:-1:-1.2
++1.27:-1:1.2
+-1.27:-1:-1.2
++1.25:-1:1.2
+-1.25:-1:-1.2
++1.35:-1:1.3
+-1.35:-1:-1.3
+-0.0061234567890:-1:0.0
+-0.0061:-1:0.0
+-0.00612:-1:0.0
+-0.00612:-2:0.00
+-0.006:-1:0.0
+-0.006:-2:0.00
+-0.0006:-2:0.00
+-0.0006:-3:0.000
+-0.0065:-3:/-0\.006|-6e-03
+-0.0065:-4:/-0\.006(?:5|49{5}\d+)|-6\.5e-03
+-0.0065:-5:/-0\.006(?:5|49{5}\d+)|-6\.5e-03
+0.05:0:0
+0.5:0:0
+0.51:0:0
+0.41:0:0
+$round_mode = "zero"
++2.23:-1:/2.2(?:0{5}\d+)?
+-2.23:-1:/-2.2(?:0{5}\d+)?
++2.27:-1:/2.(?:3|29{5}\d+)
+-2.27:-1:/-2.(?:3|29{5}\d+)
++2.25:-1:/2.2(?:0{5}\d+)?
+-2.25:-1:/-2.2(?:0{5}\d+)?
++2.35:-1:/2.(?:3|29{5}\d+)
+-2.35:-1:/-2.(?:3|29{5}\d+)
+-0.0065:-1:0.0
+-0.0065:-2:/-0\.01|-1e-02
+-0.0065:-3:/-0\.006|-6e-03
+-0.0065:-4:/-0\.006(?:5|49{5}\d+)|-6\.5e-03
+-0.0065:-5:/-0\.006(?:5|49{5}\d+)|-6\.5e-03
+0.05:0:0
+0.5:0:0
+0.51:0:1
+0.41:0:0
+$round_mode = "+inf"
++3.23:-1:/3.2(?:0{5}\d+)?
+-3.23:-1:/-3.2(?:0{5}\d+)?
++3.27:-1:/3.(?:3|29{5}\d+)
+-3.27:-1:/-3.(?:3|29{5}\d+)
++3.25:-1:/3.(?:3|29{5}\d+)
+-3.25:-1:/-3.2(?:0{5}\d+)?
++3.35:-1:/3.(?:4|39{5}\d+)
+-3.35:-1:/-3.(?:3|29{5}\d+)
+-0.0065:-1:0.0
+-0.0065:-2:/-0\.01|-1e-02
+-0.0065:-3:/-0\.006|-6e-03
+-0.0065:-4:/-0\.006(?:5|49{5}\d+)|-6\.5e-03
+-0.0065:-5:/-0\.006(?:5|49{5}\d+)|-6\.5e-03
+0.05:0:0
+0.5:0:1
+0.51:0:1
+0.41:0:0
+$round_mode = "-inf"
++4.23:-1:/4.2(?:0{5}\d+)?
+-4.23:-1:/-4.2(?:0{5}\d+)?
++4.27:-1:/4.(?:3|29{5}\d+)
+-4.27:-1:/-4.(?:3|29{5}\d+)
++4.25:-1:/4.2(?:0{5}\d+)?
+-4.25:-1:/-4.(?:3|29{5}\d+)
++4.35:-1:/4.(?:3|29{5}\d+)
+-4.35:-1:/-4.(?:4|39{5}\d+)
+-0.0065:-1:0.0
+-0.0065:-2:/-0\.01|-1e-02
+-0.0065:-3:/-0\.007|-7e-03
+-0.0065:-4:/-0\.006(?:5|49{5}\d+)|-6\.5e-03
+-0.0065:-5:/-0\.006(?:5|49{5}\d+)|-6\.5e-03
+0.05:0:0
+0.5:0:0
+0.51:0:1
+0.41:0:0
+$round_mode = "odd"
++5.23:-1:/5.2(?:0{5}\d+)?
+-5.23:-1:/-5.2(?:0{5}\d+)?
++5.27:-1:/5.(?:3|29{5}\d+)
+-5.27:-1:/-5.(?:3|29{5}\d+)
++5.25:-1:/5.(?:3|29{5}\d+)
+-5.25:-1:/-5.(?:3|29{5}\d+)
++5.35:-1:/5.(?:3|29{5}\d+)
+-5.35:-1:/-5.(?:3|29{5}\d+)
+-0.0065:-1:0.0
+-0.0065:-2:/-0\.01|-1e-02
+-0.0065:-3:/-0\.007|-7e-03
+-0.0065:-4:/-0\.006(?:5|49{5}\d+)|-6\.5e-03
+-0.0065:-5:/-0\.006(?:5|49{5}\d+)|-6\.5e-03
+0.05:0:0
+0.5:0:1
+0.51:0:1
+0.41:0:0
+$round_mode = "even"
++6.23:-1:/6.2(?:0{5}\d+)?
+-6.23:-1:/-6.2(?:0{5}\d+)?
++6.27:-1:/6.(?:3|29{5}\d+)
+-6.27:-1:/-6.(?:3|29{5}\d+)
++6.25:-1:/6.(?:2(?:0{5}\d+)?|29{5}\d+)
+-6.25:-1:/-6.(?:2(?:0{5}\d+)?|29{5}\d+)
++6.35:-1:/6.(?:4|39{5}\d+|29{8}\d+)
+-6.35:-1:/-6.(?:4|39{5}\d+|29{8}\d+)
+-0.0065:-1:0.0
+-0.0065:-2:/-0\.01|-1e-02
+-0.0065:-3:/-0\.006|-7e-03
+-0.0065:-4:/-0\.006(?:5|49{5}\d+)|-6\.5e-03
+-0.0065:-5:/-0\.006(?:5|49{5}\d+)|-6\.5e-03
+0.05:0:0
+0.5:0:0
+0.51:0:1
+0.41:0:0
+0.01234567:-3:0.012
+0.01234567:-4:0.0123
+0.01234567:-5:0.01235
+0.01234567:-6:0.012346
+0.01234567:-7:0.0123457
+0.01234567:-8:0.01234567
+0.01234567:-9:0.012345670
+0.01234567:-12:0.012345670000
+&fcmp
+fcmpNaN:fcmpNaN:
+fcmpNaN:+0:
++0:fcmpNaN:
++0:+0:0
+-1:+0:-1
++0:-1:1
++1:+0:1
++0:+1:-1
+-1:+1:-1
++1:-1:1
+-1:-1:0
++1:+1:0
+-1.1:0:-1
++0:-1.1:1
++1.1:+0:1
++0:+1.1:-1
++123:+123:0
++123:+12:1
++12:+123:-1
+-123:-123:0
+-123:-12:-1
+-12:-123:1
++123:+124:-1
++124:+123:1
+-123:-124:1
+-124:-123:-1
+0:0.01:-1
+0:0.0001:-1
+0:-0.0001:1
+0:-0.1:1
+0.1:0:1
+0.00001:0:1
+-0.0001:0:-1
+-0.1:0:-1
+0:0.0001234:-1
+0:-0.0001234:1
+0.0001234:0:1
+-0.0001234:0:-1
+0.0001:0.0005:-1
+0.0005:0.0001:1
+0.005:0.0001:1
+0.001:0.0005:1
+0.000001:0.0005:-1
+0.00000123:0.0005:-1
+0.00512:0.0001:1
+0.005:0.000112:1
+0.00123:0.0005:1
+1.5:2:-1
+2:1.5:1
+1.54321:234:-1
+234:1.54321:1
+# infinity
+-inf:5432112345:-1
++inf:5432112345:1
+-inf:-5432112345:-1
++inf:-5432112345:1
+-inf:54321.12345:-1
++inf:54321.12345:1
+-inf:-54321.12345:-1
++inf:-54321.12345:1
++inf:+inf:0
+-inf:-inf:0
++inf:-inf:1
+-inf:+inf:-1
+# return undef
++inf:NaN:
+NaN:inf:
+-inf:NaN:
+NaN:-inf:
+&facmp
+fcmpNaN:fcmpNaN:
+fcmpNaN:+0:
++0:fcmpNaN:
++0:+0:0
+-1:+0:1
++0:-1:-1
++1:+0:1
++0:+1:-1
+-1:+1:0
++1:-1:0
+-1:-1:0
++1:+1:0
+-1.1:0:1
++0:-1.1:-1
++1.1:+0:1
++0:+1.1:-1
++123:+123:0
++123:+12:1
++12:+123:-1
+-123:-123:0
+-123:-12:1
+-12:-123:-1
++123:+124:-1
++124:+123:1
+-123:-124:-1
+-124:-123:1
+0:0.01:-1
+0:0.0001:-1
+0:-0.0001:-1
+0:-0.1:-1
+0.1:0:1
+0.00001:0:1
+-0.0001:0:1
+-0.1:0:1
+0:0.0001234:-1
+0:-0.0001234:-1
+0.0001234:0:1
+-0.0001234:0:1
+0.0001:0.0005:-1
+0.0005:0.0001:1
+0.005:0.0001:1
+0.001:0.0005:1
+0.000001:0.0005:-1
+0.00000123:0.0005:-1
+0.00512:0.0001:1
+0.005:0.000112:1
+0.00123:0.0005:1
+1.5:2:-1
+2:1.5:1
+1.54321:234:-1
+234:1.54321:1
+# infinity
+-inf:5432112345:1
++inf:5432112345:1
+-inf:-5432112345:1
++inf:-5432112345:1
+-inf:54321.12345:1
++inf:54321.12345:1
+-inf:-54321.12345:1
++inf:-54321.12345:1
++inf:+inf:0
+-inf:-inf:0
++inf:-inf:0
+-inf:+inf:0
+5:inf:-1
+-1:inf:-1
+5:-inf:-1
+-1:-inf:-1
+# return undef
++inf:facmpNaN:
+facmpNaN:inf:
+-inf:facmpNaN:
+facmpNaN:-inf:
+&fdec
+fdecNaN:NaN
++inf:inf
+-inf:-inf
++0:-1
++1:0
+-1:-2
+1.23:0.23
+-1.23:-2.23
+100:99
+101:100
+-100:-101
+-99:-100
+-98:-99
+99:98
+&finc
+fincNaN:NaN
++inf:inf
+-inf:-inf
++0:1
++1:2
+-1:0
+1.23:2.23
+-1.23:-0.23
+100:101
+-100:-99
+-99:-98
+-101:-100
+99:100
+&fadd
+abc:abc:NaN
+abc:+0:NaN
++0:abc:NaN
++inf:-inf:NaN
+-inf:+inf:NaN
++inf:+inf:inf
+-inf:-inf:-inf
+baddNaN:+inf:NaN
+baddNaN:+inf:NaN
++inf:baddNaN:NaN
+-inf:baddNaN:NaN
++0:+0:0
++1:+0:1
++0:+1:1
++1:+1:2
+-1:+0:-1
++0:-1:-1
+-1:-1:-2
+-1:+1:0
++1:-1:0
++9:+1:10
++99:+1:100
++999:+1:1000
++9999:+1:10000
++99999:+1:100000
++999999:+1:1000000
++9999999:+1:10000000
++99999999:+1:100000000
++999999999:+1:1000000000
++9999999999:+1:10000000000
++99999999999:+1:100000000000
++10:-1:9
++100:-1:99
++1000:-1:999
++10000:-1:9999
++100000:-1:99999
++1000000:-1:999999
++10000000:-1:9999999
++100000000:-1:99999999
++1000000000:-1:999999999
++10000000000:-1:9999999999
++123456789:+987654321:1111111110
+-123456789:+987654321:864197532
+-123456789:-987654321:-1111111110
++123456789:-987654321:-864197532
+0.001234:0.0001234:0.0013574
+&fsub
+abc:abc:NaN
+abc:+0:NaN
++0:abc:NaN
++inf:-inf:inf
+-inf:+inf:-inf
++inf:+inf:NaN
+-inf:-inf:NaN
+baddNaN:+inf:NaN
+baddNaN:+inf:NaN
++inf:baddNaN:NaN
+-inf:baddNaN:NaN
++0:+0:0
++1:+0:1
++0:+1:-1
++1:+1:0
+-1:+0:-1
++0:-1:1
+-1:-1:0
+-1:+1:-2
++1:-1:2
++9:+1:8
++99:+1:98
++999:+1:998
++9999:+1:9998
++99999:+1:99998
++999999:+1:999998
++9999999:+1:9999998
++99999999:+1:99999998
++999999999:+1:999999998
++9999999999:+1:9999999998
++99999999999:+1:99999999998
++10:-1:11
++100:-1:101
++1000:-1:1001
++10000:-1:10001
++100000:-1:100001
++1000000:-1:1000001
++10000000:-1:10000001
++100000000:-1:100000001
++1000000000:-1:1000000001
++10000000000:-1:10000000001
++123456789:+987654321:-864197532
+-123456789:+987654321:-1111111110
+-123456789:-987654321:864197532
++123456789:-987654321:1111111110
+&bmuladd
+abc:abc:0:NaN
+abc:+0:0:NaN
++0:abc:0:NaN
++0:0:abc:NaN
+NaNmul:+inf:0:NaN
+NaNmul:-inf:0:NaN
+-inf:NaNmul:0:NaN
++inf:NaNmul:0:NaN
++inf:+inf:0:inf
++inf:-inf:0:-inf
+-inf:+inf:0:-inf
+-inf:-inf:0:inf
++0:+0:0:0
++0:+1:0:0
++1:+0:0:0
++0:-1:0:0
+-1:+0:0:0
+123456789123456789:0:0:0
+0:123456789123456789:0:0
+-1:-1:0:1
+-1:-1:0:1
+-1:+1:0:-1
++1:-1:0:-1
++1:+1:0:1
++2:+3:0:6
+-2:+3:0:-6
++2:-3:0:-6
+-2:-3:0:6
+111:111:0:12321
+10101:10101:0:102030201
+1001001:1001001:0:1002003002001
+100010001:100010001:0:10002000300020001
+10000100001:10000100001:0:100002000030000200001
+11111111111:9:0:99999999999
+22222222222:9:0:199999999998
+33333333333:9:0:299999999997
+44444444444:9:0:399999999996
+55555555555:9:0:499999999995
+66666666666:9:0:599999999994
+77777777777:9:0:699999999993
+88888888888:9:0:799999999992
+99999999999:9:0:899999999991
+11111111111:9:1:100000000000
+22222222222:9:1:199999999999
+33333333333:9:1:299999999998
+44444444444:9:1:399999999997
+55555555555:9:1:499999999996
+66666666666:9:1:599999999995
+77777777777:9:1:699999999994
+88888888888:9:1:799999999993
+99999999999:9:1:899999999992
+-3:-4:-5:7
+3:-4:-5:-17
+-3:4:-5:-17
+3:4:-5:7
+-3:4:5:-7
+3:-4:5:-7
+9999999999999999999:10000000000000000000:1234567890:99999999999999999990000000001234567890
+3.2:5.7:8.9:27.14
+-3.2:5.197:6.05:-10.5804
+&bmodpow
+3:4:8:1
+3:4:7:4
+3:4:7:4
+77777:777:123456789:99995084
+3.2:6.2:5.2:2.970579856718063040273642739529400818
+&fmul
+abc:abc:NaN
+abc:+0:NaN
++0:abc:NaN
++inf:NaNmul:NaN
++inf:NaNmul:NaN
+NaNmul:+inf:NaN
+NaNmul:-inf:NaN
++inf:+inf:inf
++inf:-inf:-inf
++inf:-inf:-inf
++inf:+inf:inf
++inf:123.34:inf
++inf:-123.34:-inf
+-inf:123.34:-inf
+-inf:-123.34:inf
+123.34:+inf:inf
+-123.34:+inf:-inf
+123.34:-inf:-inf
+-123.34:-inf:inf
++0:+0:0
++0:+1:0
++1:+0:0
++0:-1:0
+-1:+0:0
++123456789123456789:+0:0
++0:+123456789123456789:0
+-1:-1:1
+-1:+1:-1
++1:-1:-1
++1:+1:1
++2:+3:6
+-2:+3:-6
++2:-3:-6
+-2:-3:6
++111:+111:12321
++10101:+10101:102030201
++1001001:+1001001:1002003002001
++100010001:+100010001:10002000300020001
++10000100001:+10000100001:100002000030000200001
++11111111111:+9:99999999999
++22222222222:+9:199999999998
++33333333333:+9:299999999997
++44444444444:+9:399999999996
++55555555555:+9:499999999995
++66666666666:+9:599999999994
++77777777777:+9:699999999993
++88888888888:+9:799999999992
++99999999999:+9:899999999991
+6:120:720
+10:10000:100000
+&fdiv-list
+0:0:NaN,NaN
+0:1:0,0
+9:4:2.25,1
+9:5:1.8,4
+# bug in v1.74 with bdiv in list context, when $y is 1 or -1
+2.1:-1:-2.1,0
+2.1:1:2.1,0
+-2.1:-1:2.1,0
+-2.1:1:-2.1,0
+&fdiv
+$div_scale = 40; $round_mode = 'even'
+abc:abc:NaN
+abc:+1:abc:NaN
++1:abc:NaN
+-1:abc:NaN
+0:abc:NaN
++0:+0:NaN
++0:+1:0
++1:+0:inf
++3214:+0:inf
++0:-1:0
+-1:+0:-inf
+-3214:+0:-inf
++1:+1:1
+-1:-1:1
++1:-1:-1
+-1:+1:-1
++1:+2:0.5
++2:+1:2
+123:+inf:0
+123:-inf:0
++10:+5:2
++100:+4:25
++1000:+8:125
++10000:+16:625
++10000:-16:-625
++999999999999:+9:111111111111
++999999999999:+99:10101010101
++999999999999:+999:1001001001
++999999999999:+9999:100010001
++999999999999999:+99999:10000100001
++1000000000:+9:111111111.1111111111111111111111111111111
++2000000000:+9:222222222.2222222222222222222222222222222
++3000000000:+9:333333333.3333333333333333333333333333333
++4000000000:+9:444444444.4444444444444444444444444444444
++5000000000:+9:555555555.5555555555555555555555555555556
++6000000000:+9:666666666.6666666666666666666666666666667
++7000000000:+9:777777777.7777777777777777777777777777778
++8000000000:+9:888888888.8888888888888888888888888888889
++9000000000:+9:1000000000
++35500000:+113:314159.2920353982300884955752212389380531
++71000000:+226:314159.2920353982300884955752212389380531
++106500000:+339:314159.2920353982300884955752212389380531
++1000000000:+3:333333333.3333333333333333333333333333333
+2:25.024996000799840031993601279744051189762:0.07992009269196593320152084692285869265447
+123456:1:123456
+$div_scale = 20
++1000000000:+9:111111111.11111111111
++2000000000:+9:222222222.22222222222
++3000000000:+9:333333333.33333333333
++4000000000:+9:444444444.44444444444
++5000000000:+9:555555555.55555555556
++6000000000:+9:666666666.66666666667
++7000000000:+9:777777777.77777777778
++8000000000:+9:888888888.88888888889
++9000000000:+9:1000000000
+1:10:0.1
+1:100:0.01
+1:1000:0.001
+1:10000:0.0001
+1:504:0.001984126984126984127
+2:1.987654321:1.0062111801179738436
+123456789.123456789123456789123456789:1:123456789.12345678912
+# the next two cases are the "old" behaviour, but are now (>v0.01) different
+#+35500000:+113:314159.292035398230088
+#+71000000:+226:314159.292035398230088
++35500000:+113:314159.29203539823009
++71000000:+226:314159.29203539823009
++106500000:+339:314159.29203539823009
++1000000000:+3:333333333.33333333333
+$div_scale = 1
+# round to accuracy 1 after bdiv
++124:+3:40
+123456789.1234:1:100000000
+# reset scale for further tests
+$div_scale = 40
+&fmod
++9:4:1
++9:5:4
++9000:56:40
++56:9000:56
+# inf handling, see table in doc
+0:inf:0
+0:-inf:0
+5:inf:5
+5:-inf:5
+-5:inf:-5
+-5:-inf:-5
+inf:5:0
+-inf:5:0
+inf:-5:0
+-inf:-5:0
+5:5:0
+-5:-5:0
+inf:inf:NaN
+-inf:-inf:NaN
+-inf:inf:NaN
+inf:-inf:NaN
+8:0:8
+inf:0:inf
+# exceptions to reminder rule
+-inf:0:-inf
+-8:0:-8
+0:0:NaN
+abc:abc:NaN
+abc:1:abc:NaN
+1:abc:NaN
+0:0:NaN
+0:1:0
+1:0:1
+0:-1:0
+-1:0:-1
+1:1:0
+-1:-1:0
+1:-1:0
+-1:1:0
+1:2:1
+2:1:0
+1000000000:9:1
+2000000000:9:2
+3000000000:9:3
+4000000000:9:4
+5000000000:9:5
+6000000000:9:6
+7000000000:9:7
+8000000000:9:8
+9000000000:9:0
+35500000:113:33
+71000000:226:66
+106500000:339:99
+1000000000:3:1
+10:5:0
+100:4:0
+1000:8:0
+10000:16:0
+999999999999:9:0
+999999999999:99:0
+999999999999:999:0
+999999999999:9999:0
+999999999999999:99999:0
+-9:+5:1
++9:-5:-1
+-9:-5:-4
+-5:3:1
+-2:3:1
+4:3:1
+1:3:1
+-5:-3:-2
+-2:-3:-2
+4:-3:-2
+1:-3:-2
+4095:4095:0
+100041000510123:3:0
+152403346:12345:4321
+87654321:87654321:0
+# now some floating point tests
+123:2.5:0.5
+1230:2.5:0
+123.4:2.5:0.9
+123e1:25:5
+-2.1:1:0.9
+2.1:1:0.1
+-2.1:-1:-0.1
+2.1:-1:-0.9
+-3:1:0
+3:1:0
+-3:-1:0
+3:-1:0
+&ffac
+Nanfac:NaN
+-1:NaN
++inf:inf
+-inf:NaN
+0:1
+1:1
+2:2
+3:6
+4:24
+5:120
+6:720
+10:3628800
+11:39916800
+12:479001600
+&froot
+# sqrt()
++0:2:0
++1:2:1
+-1:2:NaN
+# -$x ** (1/2) => -$y, but not in froot()
+-123.456:2:NaN
++inf:2:inf
+-inf:2:NaN
+2:2:1.41421356237309504880168872420969807857
+-2:2:NaN
+4:2:2
+9:2:3
+16:2:4
+100:2:10
+123.456:2:11.11107555549866648462149404118219234119
+15241.38393:2:123.4559999756998444766131352122991626468
+1.44:2:1.2
+12:2:3.464101615137754587054892683011744733886
+0.49:2:0.7
+0.0049:2:0.07
+# invalid ones
+1:NaN:NaN
+-1:NaN:NaN
+0:NaN:NaN
+-inf:NaN:NaN
++inf:NaN:NaN
+NaN:0:NaN
+NaN:2:NaN
+NaN:inf:NaN
+NaN:inf:NaN
+12:-inf:NaN
+12:inf:NaN
++0:0:NaN
++1:0:NaN
+-1:0:NaN
+-2:0:NaN
+-123.45:0:NaN
++inf:0:NaN
+12:1:12
+-12:1:NaN
+8:-1:NaN
+-8:-1:NaN
+# cubic root
+8:3:2
+-8:3:NaN
+# fourths root
+16:4:2
+81:4:3
+# see t/bigroot() for more tests
+&fsqrt
++0:0
+-1:NaN
+-2:NaN
+-16:NaN
+-123.45:NaN
+nanfsqrt:NaN
++inf:inf
+-inf:NaN
+1:1
+2:1.41421356237309504880168872420969807857
+4:2
+9:3
+16:4
+100:10
+123.456:11.11107555549866648462149404118219234119
+15241.38393:123.4559999756998444766131352122991626468
+1.44:1.2
+# sqrt(1.44) = 1.2, sqrt(e10) = e5 => 12e4
+1.44E10:120000
+2e10:141421.356237309504880168872420969807857
+144e20:120000000000
+# proved to be an endless loop under 7-9
+12:3.464101615137754587054892683011744733886
+0.49:0.7
+0.0049:0.07
+&is_nan
+123:0
+abc:1
+NaN:1
+-123:0
+&is_inf
++inf::1
+-inf::1
+abc::0
+1::0
+NaN::0
+-1::0
++inf:-:0
++inf:+:1
+-inf:-:1
+-inf:+:0
+# it must be exactly /^[+-]inf$/
++infinity::0
+-infinity::0
+&is_odd
+abc:0
+0:0
+-1:1
+-3:1
+1:1
+3:1
+1000001:1
+1000002:0
++inf:0
+-inf:0
+123.45:0
+-123.45:0
+2:0
+&is_int
+NaNis_int:0
+0:1
+1:1
+2:1
+-2:1
+-1:1
+-inf:0
++inf:0
+123.4567:0
+-0.1:0
+-0.002:0
+&is_even
+abc:0
+0:1
+-1:0
+-3:0
+1:0
+3:0
+1000001:0
+1000002:1
+2:1
++inf:0
+-inf:0
+123.456:0
+-123.456:0
+0.01:0
+-0.01:0
+120:1
+1200:1
+-1200:1
+&is_positive
+0:0
+1:1
+-1:0
+-123:0
+NaN:0
+-inf:0
++inf:1
+&is_negative
+0:0
+1:0
+-1:1
+-123:1
+NaN:0
+-inf:1
++inf:0
+&parts
+0:0 1
+1:1 0
+123:123 0
+-123:-123 0
+-1200:-12 2
+NaNparts:NaN NaN
++inf:inf inf
+-inf:-inf inf
+&exponent
+0:1
+1:0
+123:0
+-123:0
+-1200:2
++inf:inf
+-inf:inf
+NaNexponent:NaN
+&mantissa
+0:0
+1:1
+123:123
+-123:-123
+-1200:-12
++inf:inf
+-inf:-inf
+NaNmantissa:NaN
+&length
+123:3
+-123:3
+0:1
+1:1
+12345678901234567890:20
+&is_zero
+NaNzero:0
++inf:0
+-inf:0
+0:1
+-1:0
+1:0
+&is_one
+NaNone:0
++inf:0
+-inf:0
+0:0
+2:0
+1:1
+-1:0
+-2:0
+&ffloor
+0:0
+abc:NaN
++inf:inf
+-inf:-inf
+1:1
+-51:-51
+-51.2:-52
+12.2:12
+0.12345:0
+0.123456:0
+0.1234567:0
+0.12345678:0
+0.123456789:0
+&fceil
+0:0
+abc:NaN
++inf:inf
+-inf:-inf
+1:1
+-51:-51
+-51.2:-51
+12.2:13
diff --git a/dist/Math-BigInt/t/bigfltpm.t b/dist/Math-BigInt/t/bigfltpm.t
new file mode 100644
index 0000000000..50b47afac4
--- /dev/null
+++ b/dist/Math-BigInt/t/bigfltpm.t
@@ -0,0 +1,49 @@
+#!/usr/bin/perl -w
+
+use Test;
+use strict;
+
+BEGIN
+  {
+  $| = 1;
+  # to locate the testing files
+  my $location = $0; $location =~ s/bigfltpm.t//i;
+  unshift @INC, '../lib';
+  if (-d 't')
+    {
+    chdir 't';
+    require File::Spec;
+    unshift @INC, File::Spec->catdir(File::Spec->updir, $location);
+    }
+  else
+    {
+    unshift @INC, $location;
+    }
+  print "# INC = @INC\n";
+
+  plan tests => 2308
+	+ 5;		# own tests
+  }
+
+use Math::BigInt lib => 'Calc';
+use Math::BigFloat;
+
+use vars qw ($class $try $x $y $f @args $ans $ans1 $ans1_str $setup $CL);
+$class = "Math::BigFloat";
+$CL = "Math::BigInt::Calc";
+
+ok ($class->config()->{class},$class);
+ok ($class->config()->{with}, $CL);
+
+# bug #17447: Can't call method Math::BigFloat->bsub, not a valid method
+my $c = Math::BigFloat->new( '123.3' );
+ok ($c->fsub(123) eq '0.3', 1); # calling fsub on a BigFloat works
+
+# Bug until BigInt v1.86, the scale wasn't treated as a scalar:
+$c = Math::BigFloat->new('0.008'); my $d = Math::BigFloat->new(3);
+my $e = $c->bdiv(Math::BigFloat->new(3),$d);
+
+ok ($e,'0.00267'); # '0.008 / 3 => 0.0027');
+ok (ref($e->{_e}->[0]), ''); # 'Not a BigInt');
+
+require 'bigfltpm.inc';	# all tests here for sharing
diff --git a/dist/Math-BigInt/t/bigintc.t b/dist/Math-BigInt/t/bigintc.t
new file mode 100644
index 0000000000..5dbace06a3
--- /dev/null
+++ b/dist/Math-BigInt/t/bigintc.t
@@ -0,0 +1,464 @@
+#!/usr/bin/perl -w
+
+use strict;
+use Test;
+
+BEGIN 
+  {
+  $| = 1;
+  chdir 't' if -d 't';
+  unshift @INC, '../lib';		# for running manually
+  if ($^O eq 'unicos')			# the tests hang under "unicos"
+    {
+    print "1..0\n";
+    exit(0);
+    }
+  plan tests => 375;
+  }
+
+use Math::BigInt::Calc;
+
+my ($BASE_LEN, $AND_BITS, $XOR_BITS, $OR_BITS, $BASE_LEN_SMALL, $MAX_VAL) =
+  Math::BigInt::Calc->_base_len();
+
+print "# BASE_LEN = $BASE_LEN\n";
+print "# MAX_VAL = $MAX_VAL\n";
+print "# AND_BITS = $AND_BITS\n";
+print "# XOR_BITS = $XOR_BITS\n";
+print "# IOR_BITS = $OR_BITS\n";
+
+# testing of Math::BigInt::Calc
+
+my $C = 'Math::BigInt::Calc';		# pass classname to sub's
+
+# _new and _str
+my $x = $C->_new("123"); my $y = $C->_new("321");
+ok (ref($x),'ARRAY'); ok ($C->_str($x),123); ok ($C->_str($y),321);
+
+###############################################################################
+# _add, _sub, _mul, _div
+ok ($C->_str($C->_add($x,$y)),444);
+ok ($C->_str($C->_sub($x,$y)),123);
+ok ($C->_str($C->_mul($x,$y)),39483);
+ok ($C->_str($C->_div($x,$y)),123);
+
+###############################################################################
+# check that mul/div doesn't change $y
+# and returns the same reference, not something new
+ok ($C->_str($C->_mul($x,$y)),39483);
+ok ($C->_str($x),39483); ok ($C->_str($y),321);
+
+ok ($C->_str($C->_div($x,$y)),123);
+ok ($C->_str($x),123); ok ($C->_str($y),321);
+
+$x = $C->_new("39483");
+my ($x1,$r1) = $C->_div($x,$y);
+ok ("$x1","$x");
+$C->_inc($x1);
+ok ("$x1","$x");
+ok ($C->_str($r1),'0');
+
+$x = $C->_new("39483");	# reset
+
+###############################################################################
+my $z = $C->_new("2");
+ok ($C->_str($C->_add($x,$z)),39485);
+my ($re,$rr) = $C->_div($x,$y);
+
+ok ($C->_str($re),123); ok ($C->_str($rr),2);
+
+# is_zero, _is_one, _one, _zero
+ok ($C->_is_zero($x)||0,0);
+ok ($C->_is_one($x)||0,0);
+
+ok ($C->_str($C->_zero()),"0");
+ok ($C->_str($C->_one()),"1");
+
+# _two() and _ten()
+ok ($C->_str($C->_two()),"2");
+ok ($C->_str($C->_ten()),"10");
+ok ($C->_is_ten($C->_two()),0);
+ok ($C->_is_two($C->_two()),1);
+ok ($C->_is_ten($C->_ten()),1);
+ok ($C->_is_two($C->_ten()),0);
+
+ok ($C->_is_one($C->_one()),1);
+ok ($C->_is_one($C->_two()),0);
+ok ($C->_is_one($C->_ten()),0);
+
+ok ($C->_is_one($C->_zero()) || 0,0);
+
+ok ($C->_is_zero($C->_zero()),1);
+
+ok ($C->_is_zero($C->_one()) || 0,0);
+
+# is_odd, is_even
+ok ($C->_is_odd($C->_one()),1); ok ($C->_is_odd($C->_zero())||0,0);
+ok ($C->_is_even($C->_one()) || 0,0); ok ($C->_is_even($C->_zero()),1);
+
+# _len
+for my $method (qw/_alen _len/)
+  {
+  $x = $C->_new("1"); ok ($C->$method($x),1);
+  $x = $C->_new("12"); ok ($C->$method($x),2);
+  $x = $C->_new("123"); ok ($C->$method($x),3);
+  $x = $C->_new("1234"); ok ($C->$method($x),4);
+  $x = $C->_new("12345"); ok ($C->$method($x),5);
+  $x = $C->_new("123456"); ok ($C->$method($x),6);
+  $x = $C->_new("1234567"); ok ($C->$method($x),7);
+  $x = $C->_new("12345678"); ok ($C->$method($x),8);
+  $x = $C->_new("123456789"); ok ($C->$method($x),9);
+
+  $x = $C->_new("8"); ok ($C->$method($x),1);
+  $x = $C->_new("21"); ok ($C->$method($x),2);
+  $x = $C->_new("321"); ok ($C->$method($x),3);
+  $x = $C->_new("4321"); ok ($C->$method($x),4);
+  $x = $C->_new("54321"); ok ($C->$method($x),5);
+  $x = $C->_new("654321"); ok ($C->$method($x),6);
+  $x = $C->_new("7654321"); ok ($C->$method($x),7);
+  $x = $C->_new("87654321"); ok ($C->$method($x),8);
+  $x = $C->_new("987654321"); ok ($C->$method($x),9);
+
+  $x = $C->_new("0"); ok ($C->$method($x),1);
+  $x = $C->_new("20"); ok ($C->$method($x),2);
+  $x = $C->_new("320"); ok ($C->$method($x),3);
+  $x = $C->_new("4320"); ok ($C->$method($x),4);
+  $x = $C->_new("54320"); ok ($C->$method($x),5);
+  $x = $C->_new("654320"); ok ($C->$method($x),6);
+  $x = $C->_new("7654320"); ok ($C->$method($x),7);
+  $x = $C->_new("87654320"); ok ($C->$method($x),8);
+  $x = $C->_new("987654320"); ok ($C->$method($x),9);
+
+  for (my $i = 1; $i < 9; $i++)
+    {
+    my $a = "$i" . '0' x ($i-1);
+    $x = $C->_new($a); 
+    print "# Tried len '$a'\n" unless ok ($C->_len($x),$i);
+    }
+  }
+
+# _digit
+$x = $C->_new("123456789");
+ok ($C->_digit($x,0),9);
+ok ($C->_digit($x,1),8);
+ok ($C->_digit($x,2),7);
+ok ($C->_digit($x,-1),1);
+ok ($C->_digit($x,-2),2);
+ok ($C->_digit($x,-3),3);
+
+# _copy
+foreach (qw/ 1 12 123 1234 12345 123456 1234567 12345678 123456789/)
+  {
+  $x = $C->_new("$_");
+  ok ($C->_str($C->_copy($x)),"$_");
+  ok ($C->_str($x),"$_");		# did _copy destroy original x?
+  }
+
+# _zeros
+$x = $C->_new("1256000000"); ok ($C->_zeros($x),6);
+$x = $C->_new("152"); ok ($C->_zeros($x),0);
+$x = $C->_new("123000"); ok ($C->_zeros($x),3); 
+$x = $C->_new("0"); ok ($C->_zeros($x),0); 
+
+# _lsft, _rsft
+$x = $C->_new("10"); $y = $C->_new("3"); 
+ok ($C->_str($C->_lsft($x,$y,10)),10000);
+$x = $C->_new("20"); $y = $C->_new("3"); 
+ok ($C->_str($C->_lsft($x,$y,10)),20000);
+
+$x = $C->_new("128"); $y = $C->_new("4");
+ok ($C->_str($C->_lsft($x,$y,2)), 128 << 4);
+
+$x = $C->_new("1000"); $y = $C->_new("3"); 
+ok ($C->_str($C->_rsft($x,$y,10)),1);
+$x = $C->_new("20000"); $y = $C->_new("3"); 
+ok ($C->_str($C->_rsft($x,$y,10)),20);
+$x = $C->_new("256"); $y = $C->_new("4");
+ok ($C->_str($C->_rsft($x,$y,2)),256 >> 4);
+
+$x = $C->_new("6411906467305339182857313397200584952398");
+$y = $C->_new("45");
+ok ($C->_str($C->_rsft($x,$y,10)),0);
+
+# _acmp
+$x = $C->_new("123456789");
+$y = $C->_new("987654321");
+ok ($C->_acmp($x,$y),-1);
+ok ($C->_acmp($y,$x),1);
+ok ($C->_acmp($x,$x),0);
+ok ($C->_acmp($y,$y),0);
+$x = $C->_new("12");
+$y = $C->_new("12");
+ok ($C->_acmp($x,$y),0);
+$x = $C->_new("21");
+ok ($C->_acmp($x,$y),1);
+ok ($C->_acmp($y,$x),-1);
+$x = $C->_new("123456789");
+$y = $C->_new("1987654321");
+ok ($C->_acmp($x,$y),-1);
+ok ($C->_acmp($y,$x),+1);
+
+$x = $C->_new("1234567890123456789");
+$y = $C->_new("987654321012345678");
+ok ($C->_acmp($x,$y),1);
+ok ($C->_acmp($y,$x),-1);
+ok ($C->_acmp($x,$x),0);
+ok ($C->_acmp($y,$y),0);
+
+$x = $C->_new("1234");
+$y = $C->_new("987654321012345678");
+ok ($C->_acmp($x,$y),-1);
+ok ($C->_acmp($y,$x),1);
+ok ($C->_acmp($x,$x),0);
+ok ($C->_acmp($y,$y),0);
+
+# _modinv
+$x = $C->_new("8");
+$y = $C->_new("5033");
+my ($xmod,$sign) = $C->_modinv($x,$y);
+ok ($C->_str($xmod),'629');		# -629 % 5033 == 4404
+ok ($sign, '-');
+
+# _div
+$x = $C->_new("3333"); $y = $C->_new("1111");
+ok ($C->_str(scalar $C->_div($x,$y)),3);
+$x = $C->_new("33333"); $y = $C->_new("1111"); ($x,$y) = $C->_div($x,$y);
+ok ($C->_str($x),30); ok ($C->_str($y),3);
+$x = $C->_new("123"); $y = $C->_new("1111"); 
+($x,$y) = $C->_div($x,$y); ok ($C->_str($x),0); ok ($C->_str($y),123);
+
+# _num
+foreach (qw/1 12 123 1234 12345 1234567 12345678 123456789 1234567890/)
+  {
+  $x = $C->_new("$_"); 
+  ok (ref($x)||'','ARRAY'); ok ($C->_str($x),"$_");
+  $x = $C->_num($x); ok (ref($x)||'',''); ok ($x,$_);
+  }
+
+# _sqrt
+$x = $C->_new("144"); ok ($C->_str($C->_sqrt($x)),'12');
+$x = $C->_new("144000000000000"); ok ($C->_str($C->_sqrt($x)),'12000000');
+
+# _root
+$x = $C->_new("81"); my $n = $C->_new("3"); 	# 4*4*4 = 64, 5*5*5 = 125
+ok ($C->_str($C->_root($x,$n)),'4');	# 4.xx => 4.0
+$x = $C->_new("81"); $n = $C->_new("4"); 	# 3*3*3*3 == 81
+ok ($C->_str($C->_root($x,$n)),'3');
+
+# _pow (and _root)
+$x = $C->_new("0"); $n = $C->_new("3"); 	# 0 ** y => 0
+ok ($C->_str($C->_pow($x,$n)), 0);
+$x = $C->_new("3"); $n = $C->_new("0"); 	# x ** 0 => 1
+ok ($C->_str($C->_pow($x,$n)), 1);
+$x = $C->_new("1"); $n = $C->_new("3"); 	# 1 ** y => 1
+ok ($C->_str($C->_pow($x,$n)), 1);
+$x = $C->_new("5"); $n = $C->_new("1"); 	# x ** 1 => x
+ok ($C->_str($C->_pow($x,$n)), 5);
+
+$x = $C->_new("81"); $n = $C->_new("3"); 	# 81 ** 3 == 531441 
+ok ($C->_str($C->_pow($x,$n)),81 ** 3);
+
+ok ($C->_str($C->_root($x,$n)),81);
+
+$x = $C->_new("81");
+ok ($C->_str($C->_pow($x,$n)),81 ** 3);
+ok ($C->_str($C->_pow($x,$n)),'150094635296999121'); # 531441 ** 3 ==
+
+ok ($C->_str($C->_root($x,$n)),'531441');
+ok ($C->_str($C->_root($x,$n)),'81');
+
+$x = $C->_new("81"); $n = $C->_new("14"); 	
+ok ($C->_str($C->_pow($x,$n)),'523347633027360537213511521');
+ok ($C->_str($C->_root($x,$n)),'81');
+
+$x = $C->_new("523347633027360537213511520");
+ok ($C->_str($C->_root($x,$n)),'80');
+
+$x = $C->_new("523347633027360537213511522");
+ok ($C->_str($C->_root($x,$n)),'81');
+
+my $res = [ qw/9 31 99 316 999 3162 9999 31622 99999/ ];
+
+# 99 ** 2 = 9801, 999 ** 2 = 998001 etc
+for my $i (2 .. 9)
+  {
+  $x = '9' x $i; $x = $C->_new($x);
+  $n = $C->_new("2");
+  my $rc = '9' x ($i-1). '8' . '0' x ($i-1) . '1';
+  print "# _pow( ", '9' x $i, ", 2) \n" unless
+   ok ($C->_str($C->_pow($x,$n)),$rc);
+ 
+  # if $i > $BASE_LEN, the test takes a really long time:
+  if ($i <= $BASE_LEN)
+    {
+    $x = '9' x $i; $x = $C->_new($x);
+    $n = '9' x $i; $n = $C->_new($n);
+    print "# _root( ", '9' x $i, ", ", 9 x $i, ") \n";
+    print "# _root( ", '9' x $i, ", ", 9 x $i, ") \n" unless
+     ok ($C->_str($C->_root($x,$n)),'1');
+
+    $x = '9' x $i; $x = $C->_new($x);
+    $n = $C->_new("2");
+    print "# BASE_LEN $BASE_LEN _root( ", '9' x $i, ", ", 9 x $i, ") \n" unless
+     ok ($C->_str($C->_root($x,$n)), $res->[$i-2]);
+    }
+  else
+    {
+    ok ("skipped $i", "skipped $i");
+    ok ("skipped $i", "skipped $i");
+    } 
+  }
+
+##############################################################################
+# _fac
+$x = $C->_new("0"); ok ($C->_str($C->_fac($x)),'1');
+$x = $C->_new("1"); ok ($C->_str($C->_fac($x)),'1');
+$x = $C->_new("2"); ok ($C->_str($C->_fac($x)),'2');
+$x = $C->_new("3"); ok ($C->_str($C->_fac($x)),'6');
+$x = $C->_new("4"); ok ($C->_str($C->_fac($x)),'24');
+$x = $C->_new("5"); ok ($C->_str($C->_fac($x)),'120');
+$x = $C->_new("10"); ok ($C->_str($C->_fac($x)),'3628800');
+$x = $C->_new("11"); ok ($C->_str($C->_fac($x)),'39916800');
+$x = $C->_new("12"); ok ($C->_str($C->_fac($x)),'479001600');
+$x = $C->_new("13"); ok ($C->_str($C->_fac($x)),'6227020800');
+
+# test that _fac modifes $x in place for small arguments
+$x = $C->_new("3"); $C->_fac($x); ok ($C->_str($x),'6');
+$x = $C->_new("13"); $C->_fac($x); ok ($C->_str($x),'6227020800');
+
+##############################################################################
+# _inc and _dec
+foreach (qw/1 11 121 1231 12341 1234561 12345671 123456781 1234567891/)
+  {
+  $x = $C->_new("$_"); $C->_inc($x);
+  print "# \$x = ",$C->_str($x),"\n"
+   unless ok ($C->_str($x),substr($_,0,length($_)-1) . '2');
+  $C->_dec($x); ok ($C->_str($x),$_);
+  }
+foreach (qw/19 119 1219 12319 1234519 12345619 123456719 1234567819/)
+  {
+  $x = $C->_new("$_"); $C->_inc($x);
+  print "# \$x = ",$C->_str($x),"\n"
+   unless ok ($C->_str($x),substr($_,0,length($_)-2) . '20');
+  $C->_dec($x); ok ($C->_str($x),$_);
+  }
+foreach (qw/999 9999 99999 9999999 99999999 999999999 9999999999 99999999999/)
+  {
+  $x = $C->_new("$_"); $C->_inc($x);
+  print "# \$x = ",$C->_str($x),"\n"
+   unless ok ($C->_str($x), '1' . '0' x (length($_)));
+  $C->_dec($x); ok ($C->_str($x),$_);
+  }
+
+$x = $C->_new("1000"); $C->_inc($x); ok ($C->_str($x),'1001');
+$C->_dec($x); ok ($C->_str($x),'1000');
+
+my $BL;
+{
+  no strict 'refs';
+  $BL = &{"$C"."::_base_len"}();
+}
+
+$x = '1' . '0' x $BL;
+$z = '1' . '0' x ($BL-1); $z .= '1';
+$x = $C->_new($x); $C->_inc($x); ok ($C->_str($x),$z);
+
+$x = '1' . '0' x $BL; $z = '9' x $BL;
+$x = $C->_new($x); $C->_dec($x); ok ($C->_str($x),$z);
+
+# should not happen:
+# $x = $C->_new("-2"); $y = $C->_new("4"); ok ($C->_acmp($x,$y),-1);
+
+###############################################################################
+# _mod
+$x = $C->_new("1000"); $y = $C->_new("3");
+ok ($C->_str(scalar $C->_mod($x,$y)),1);
+$x = $C->_new("1000"); $y = $C->_new("2");
+ok ($C->_str(scalar $C->_mod($x,$y)),0);
+
+# _and, _or, _xor
+$x = $C->_new("5"); $y = $C->_new("2");
+ok ($C->_str(scalar $C->_xor($x,$y)),7);
+$x = $C->_new("5"); $y = $C->_new("2");
+ok ($C->_str(scalar $C->_or($x,$y)),7);
+$x = $C->_new("5"); $y = $C->_new("3");
+ok ($C->_str(scalar $C->_and($x,$y)),1);
+
+# _from_hex, _from_bin, _from_oct
+ok ($C->_str( $C->_from_hex("0xFf")),255);
+ok ($C->_str( $C->_from_bin("0b10101011")),160+11);
+ok ($C->_str( $C->_from_oct("0100")), 8*8);
+ok ($C->_str( $C->_from_oct("01000")), 8*8*8);
+ok ($C->_str( $C->_from_oct("010001")), 8*8*8*8+1);
+ok ($C->_str( $C->_from_oct("010007")), 8*8*8*8+7);
+
+# _as_hex, _as_bin, as_oct
+ok ($C->_str( $C->_from_hex( $C->_as_hex( $C->_new("128")))), 128);
+ok ($C->_str( $C->_from_bin( $C->_as_bin( $C->_new("128")))), 128);
+ok ($C->_str( $C->_from_oct( $C->_as_oct( $C->_new("128")))), 128);
+
+ok ($C->_str( $C->_from_oct( $C->_as_oct( $C->_new("123456")))), 123456);
+ok ($C->_str( $C->_from_oct( $C->_as_oct( $C->_new("123456789")))), "123456789");
+ok ($C->_str( $C->_from_oct( $C->_as_oct( $C->_new("1234567890123")))), "1234567890123");
+
+my $long = '123456789012345678901234567890';
+ok ($C->_str( $C->_from_hex( $C->_as_hex( $C->_new($long)))), $long);
+ok ($C->_str( $C->_from_bin( $C->_as_bin( $C->_new($long)))), $long);
+ok ($C->_str( $C->_from_oct( $C->_as_oct( $C->_new($long)))), $long);
+ok ($C->_str( $C->_from_hex( $C->_as_hex( $C->_new("0")))), 0);
+ok ($C->_str( $C->_from_bin( $C->_as_bin( $C->_new("0")))), 0);
+ok ($C->_str( $C->_from_oct( $C->_as_oct( $C->_new("0")))), 0);
+ok ($C->_as_hex( $C->_new("0")), '0x0');
+ok ($C->_as_bin( $C->_new("0")), '0b0');
+ok ($C->_as_oct( $C->_new("0")), '00');
+ok ($C->_as_hex( $C->_new("12")), '0xc');
+ok ($C->_as_bin( $C->_new("12")), '0b1100');
+ok ($C->_as_oct( $C->_new("64")), '0100');
+
+# _1ex
+ok ($C->_str($C->_1ex(0)), "1");
+ok ($C->_str($C->_1ex(1)), "10");
+ok ($C->_str($C->_1ex(2)), "100");
+ok ($C->_str($C->_1ex(12)), "1000000000000");
+ok ($C->_str($C->_1ex(16)), "10000000000000000");
+
+# _check
+$x = $C->_new("123456789");
+ok ($C->_check($x),0);
+ok ($C->_check(123),'123 is not a reference');
+
+###############################################################################
+# __strip_zeros
+
+{
+  no strict 'refs';
+  # correct empty arrays
+  $x = &{$C."::__strip_zeros"}([]); ok (@$x,1); ok ($x->[0],0);
+  # don't strip single elements
+  $x = &{$C."::__strip_zeros"}([0]); ok (@$x,1); ok ($x->[0],0);
+  $x = &{$C."::__strip_zeros"}([1]); ok (@$x,1); ok ($x->[0],1);
+  # don't strip non-zero elements
+  $x = &{$C."::__strip_zeros"}([0,1]);
+  ok (@$x,2); ok ($x->[0],0); ok ($x->[1],1);
+  $x = &{$C."::__strip_zeros"}([0,1,2]);
+  ok (@$x,3); ok ($x->[0],0); ok ($x->[1],1); ok ($x->[2],2);
+
+  # but strip leading zeros
+  $x = &{$C."::__strip_zeros"}([0,1,2,0]);
+  ok (@$x,3); ok ($x->[0],0); ok ($x->[1],1); ok ($x->[2],2);
+
+  $x = &{$C."::__strip_zeros"}([0,1,2,0,0]);
+  ok (@$x,3); ok ($x->[0],0); ok ($x->[1],1); ok ($x->[2],2);
+
+  $x = &{$C."::__strip_zeros"}([0,1,2,0,0,0]);
+  ok (@$x,3); ok ($x->[0],0); ok ($x->[1],1); ok ($x->[2],2);
+
+  # collapse multiple zeros
+  $x = &{$C."::__strip_zeros"}([0,0,0,0]);
+  ok (@$x,1); ok ($x->[0],0);
+}
+
+# done
+
+1;
+
diff --git a/dist/Math-BigInt/t/bigintpm.inc b/dist/Math-BigInt/t/bigintpm.inc
new file mode 100644
index 0000000000..87140ba44d
--- /dev/null
+++ b/dist/Math-BigInt/t/bigintpm.inc
@@ -0,0 +1,2511 @@
+#include this file into another for subclass testing
+
+my $version = ${"$class\::VERSION"};
+
+use strict;
+
+##############################################################################
+# for testing inheritance of _swap
+
+package Math::Foo;
+
+use Math::BigInt lib => $main::CL;
+use vars qw/@ISA/;
+@ISA = (qw/Math::BigInt/);
+
+use overload
+# customized overload for sub, since original does not use swap there
+'-'     =>      sub { my @a = ref($_[0])->_swap(@_);
+                   $a[0]->bsub($a[1])};
+
+sub _swap
+  {
+  # a fake _swap, which reverses the params
+  my $self = shift;                     # for override in subclass
+  if ($_[2])
+    {
+    my $c = ref ($_[0] ) || 'Math::Foo';
+    return ( $_[0]->copy(), $_[1] );
+    }
+  else
+    {
+    return ( Math::Foo->new($_[1]), $_[0] );
+    }
+  }
+
+##############################################################################
+package main;
+
+my $CALC = $class->config()->{lib}; ok ($CALC,$CL);
+
+my ($f,$z,$a,$exp,@a,$m,$e,$round_mode,$expected_class);
+
+while (<DATA>) 
+  {
+  $_ =~ s/[\n\r]//g;	# remove newlines
+  next if /^#/;	# skip comments
+  if (s/^&//) 
+    {
+    $f = $_; next;
+    }
+  elsif (/^\$/) 
+    {
+    $round_mode = $_; $round_mode =~ s/^\$/$class\->/; next;
+    }
+
+  @args = split(/:/,$_,99); $ans = pop(@args);
+  $expected_class = $class;
+  if ($ans =~ /(.*?)=(.*)/)
+    {
+    $expected_class = $2; $ans = $1;
+    }
+  $try = "\$x = $class->new(\"$args[0]\");";
+  if ($f eq "bnorm")
+    {
+    $try = "\$x = $class->bnorm(\"$args[0]\");";
+  # some is_xxx tests
+   } elsif ($f =~ /^is_(zero|one|odd|even|negative|positive|nan|int)$/) {
+    $try .= "\$x->$f() || 0;";
+   } elsif ($f eq "is_inf") {
+    $try .= "\$x->is_inf('$args[1]');";
+   } elsif ($f eq "binf") {
+    $try .= "\$x->binf('$args[1]');";
+   } elsif ($f eq "bone") {
+    $try .= "\$x->bone('$args[1]');";
+  # some unary ops
+   } elsif ($f =~ /^b(nan|floor|ceil|sstr|neg|abs|inc|dec|not|sqrt|fac)$/) {
+    $try .= "\$x->$f();";
+   } elsif ($f =~ /^(numify|length|stringify|as_hex|as_bin)$/) {
+    $try .= "\$x->$f();";
+   } elsif ($f eq "exponent"){
+    # ->bstr() to see if an object is returned
+    $try .= '$x = $x->exponent()->bstr();';
+   } elsif ($f eq "mantissa"){
+    # ->bstr() to see if an object is returned
+    $try .= '$x = $x->mantissa()->bstr();';
+   } elsif ($f eq "parts"){
+    $try .= '($m,$e) = $x->parts();'; 
+    # ->bstr() to see if an object is returned
+    $try .= '$m = $m->bstr(); $m = "NaN" if !defined $m;';
+    $try .= '$e = $e->bstr(); $e = "NaN" if !defined $e;';
+    $try .= '"$m,$e";';
+   }elsif ($f eq "bexp"){
+    $try .= "\$x->bexp();";
+   } elsif ($f eq "bpi"){
+    $try .= "$class\->bpi(\$x);";
+   } else {
+    # binary ops
+    $try .= "\$y = $class->new('$args[1]');";
+    if ($f eq "bcmp")
+      {
+      $try .= '$x->bcmp($y);';
+      } elsif ($f eq "bround") {
+      $try .= "$round_mode; \$x->bround(\$y);";
+      } elsif ($f eq "bacmp"){
+      $try .= '$x->bacmp($y);';
+      } elsif ($f eq "badd"){
+      $try .= '$x + $y;';
+      } elsif ($f eq "bsub"){
+      $try .= '$x - $y;';
+      } elsif ($f eq "bmul"){
+      $try .= '$x * $y;';
+      } elsif ($f eq "bdiv"){
+      $try .= '$x / $y;';
+      } elsif ($f eq "bdiv-list"){
+      $try .= 'join (",",$x->bdiv($y));';
+      # overload via x=
+      } elsif ($f =~ /^.=$/){
+      $try .= "\$x $f \$y;";
+      # overload via x
+      } elsif ($f =~ /^.$/){
+      $try .= "\$x $f \$y;";
+      } elsif ($f eq "bmod"){
+      $try .= '$x % $y;';
+      } elsif ($f eq "bgcd")
+        {
+        if (defined $args[2])
+          {
+          $try .= " \$z = $class->new('$args[2]'); ";
+          }
+        $try .= "$class\::bgcd(\$x, \$y";
+        $try .= ", \$z" if (defined $args[2]);
+        $try .= " );";
+        }
+      elsif ($f eq "blcm")
+        {
+        if (defined $args[2])
+          {
+          $try .= " \$z = $class->new('$args[2]'); ";
+          }
+        $try .= "$class\::blcm(\$x, \$y";
+        $try .= ", \$z" if (defined $args[2]);
+        $try .= " );";
+      }elsif ($f eq "blsft"){
+        if (defined $args[2])
+          {
+          $try .= "\$x->blsft(\$y,$args[2]);";
+          }
+        else
+          {
+          $try .= "\$x << \$y;";
+          }
+      }elsif ($f eq "brsft"){
+        if (defined $args[2])
+          {
+          $try .= "\$x->brsft(\$y,$args[2]);";
+          }
+        else
+          {
+          $try .= "\$x >> \$y;";
+          }
+      }elsif ($f eq "bnok"){
+        $try .= "\$x->bnok(\$y);";
+      }elsif ($f eq "broot"){
+        $try .= "\$x->broot(\$y);";
+      }elsif ($f eq "blog"){
+        $try .= "\$x->blog(\$y);";
+      }elsif ($f eq "band"){
+        $try .= "\$x & \$y;";
+      }elsif ($f eq "bior"){
+        $try .= "\$x | \$y;";
+      }elsif ($f eq "bxor"){
+        $try .= "\$x ^ \$y;";
+      }elsif ($f eq "bpow"){
+        $try .= "\$x ** \$y;";
+      } elsif( $f eq "bmodinv") {
+       $try .= "\$x->bmodinv(\$y);";
+      }elsif ($f eq "digit"){
+        $try .= "\$x->digit(\$y);";
+      }elsif ($f eq "batan2"){
+        $try .= "\$x->batan2(\$y);";
+      } else {
+       # Functions with three arguments
+       $try .= "\$z = $class->new(\"$args[2]\");";
+
+       if( $f eq "bmodpow") {
+         $try .= "\$x->bmodpow(\$y,\$z);";
+      } elsif ($f eq "bmuladd"){
+         $try .= "\$x->bmuladd(\$y,\$z);";
+       } else { warn "Unknown op '$f'"; }
+      }
+    } # end else all other ops
+
+  $ans1 = eval $try;
+  # convert hex/binary targets to decimal	
+  if ($ans =~ /^(0x0x|0b0b)/)
+    {
+    $ans =~ s/^0[xb]//; $ans = Math::BigInt->new($ans)->bstr();
+    }
+  if ($ans eq "")
+    {
+    ok_undef ($ans1); 
+    }
+  else
+    {
+    # print "try: $try ans: $ans1 $ans\n";
+    print "# Tried: '$try'\n" if !ok ($ans1, $ans);
+    ok (ref($ans),$expected_class) if $expected_class ne $class;
+    }
+  # check internal state of number objects
+  is_valid($ans1,$f) if ref $ans1; 
+  } # endwhile data tests
+close DATA;
+
+# test some more
+@a = ();
+for (my $i = 1; $i < 10; $i++) 
+  {
+  push @a, $i;
+  }
+ok "@a", "1 2 3 4 5 6 7 8 9";
+
+# test whether self-multiplication works correctly (result is 2**64)
+$try = "\$x = $class->new('4294967296');";
+$try .= '$a = $x->bmul($x);';
+$ans1 = eval $try;
+print "# Tried: '$try'\n" if !ok ($ans1, $class->new(2) ** 64);
+# test self-pow
+$try = "\$x = $class->new(10);";
+$try .= '$a = $x->bpow($x);';
+$ans1 = eval $try;
+print "# Tried: '$try'\n" if !ok ($ans1, $class->new(10) ** 10);
+
+###############################################################################
+# test whether op destroys args or not (should better not)
+
+$x = $class->new(3);
+$y = $class->new(4);
+$z = $x & $y;
+ok ($x,3);
+ok ($y,4);
+ok ($z,0);
+$z = $x | $y;
+ok ($x,3);
+ok ($y,4);
+ok ($z,7);
+$x = $class->new(1);
+$y = $class->new(2);
+$z = $x | $y;
+ok ($x,1);
+ok ($y,2);
+ok ($z,3);
+
+$x = $class->new(5);
+$y = $class->new(4);
+$z = $x ^ $y;
+ok ($x,5);
+ok ($y,4);
+ok ($z,1);
+
+$x = $class->new(-5); $y = -$x;
+ok ($x, -5);
+
+$x = $class->new(-5); $y = abs($x);
+ok ($x, -5);
+
+$x = $class->new(8);
+$y = $class->new(-1);
+$z = $class->new(5033);
+my $u = $x->copy()->bmodpow($y,$z);
+ok ($u,4404);
+ok ($y,-1);
+ok ($z,5033);
+
+$x = $class->new(-5); $y = -$x; ok ($x,-5); ok ($y,5);
+$x = $class->new(-5); $y = $x->copy()->bneg(); ok ($x,-5); ok ($y,5);
+
+$x = $class->new(-5); $y = $class->new(3); $x->bmul($y); ok ($x,-15); ok ($y,3);
+$x = $class->new(-5); $y = $class->new(3); $x->badd($y); ok ($x,-2); ok ($y,3);
+$x = $class->new(-5); $y = $class->new(3); $x->bsub($y); ok ($x,-8); ok ($y,3);
+$x = $class->new(-15); $y = $class->new(3); $x->bdiv($y); ok ($x,-5); ok ($y,3);
+$x = $class->new(-5); $y = $class->new(3); $x->bmod($y); ok ($x,1); ok ($y,3);
+
+$x = $class->new(5); $y = $class->new(3); $x->bmul($y); ok ($x,15); ok ($y,3);
+$x = $class->new(5); $y = $class->new(3); $x->badd($y); ok ($x,8); ok ($y,3);
+$x = $class->new(5); $y = $class->new(3); $x->bsub($y); ok ($x,2); ok ($y,3);
+$x = $class->new(15); $y = $class->new(3); $x->bdiv($y); ok ($x,5); ok ($y,3);
+$x = $class->new(5); $y = $class->new(3); $x->bmod($y); ok ($x,2); ok ($y,3);
+
+$x = $class->new(5); $y = $class->new(-3); $x->bmul($y); ok ($x,-15); ok($y,-3);
+$x = $class->new(5); $y = $class->new(-3); $x->badd($y); ok ($x,2); ok($y,-3);
+$x = $class->new(5); $y = $class->new(-3); $x->bsub($y); ok ($x,8); ok($y,-3);
+$x = $class->new(15); $y = $class->new(-3); $x->bdiv($y); ok ($x,-5); ok($y,-3);
+$x = $class->new(5); $y = $class->new(-3); $x->bmod($y); ok ($x,-1); ok($y,-3);
+
+###############################################################################
+# check whether overloading cmp works
+$try = "\$x = $class->new(0);";
+$try .= "\$y = 10;";
+$try .= "'false' if \$x ne \$y;";
+$ans = eval $try;
+print "# For '$try'\n" if (!ok "$ans" , "false" ); 
+
+# we cant test for working cmpt with other objects here, we would need a dummy
+# object with stringify overload for this. see Math::String tests as example
+
+###############################################################################
+# check reversed order of arguments
+
+$try = "\$x = $class->new(10); \$x = 2 ** \$x;";
+$try .= "'ok' if \$x == 1024;"; $ans = eval $try;
+print "# For '$try'\n" if (!ok "$ans" , "ok" ); 
+
+$try = "\$x = $class->new(10); \$x = 2 * \$x;";
+$try .= "'ok' if \$x == 20;"; $ans = eval $try;
+print "# For '$try'\n" if (!ok "$ans" , "ok" ); 
+
+$try = "\$x = $class->new(10); \$x = 2 + \$x;";
+$try .= "'ok' if \$x == 12;"; $ans = eval $try;
+print "# For '$try'\n" if (!ok "$ans" , "ok" ); 
+
+$try = "\$x = $class\->new(10); \$x = 2 - \$x;";
+$try .= "'ok' if \$x == -8;"; $ans = eval $try;
+print "# For '$try'\n" if (!ok "$ans" , "ok" ); 
+
+$try = "\$x = $class\->new(10); \$x = 20 / \$x;";
+$try .= "'ok' if \$x == 2;"; $ans = eval $try;
+print "# For '$try'\n" if (!ok "$ans" , "ok" ); 
+
+$try = "\$x = $class\->new(3); \$x = 20 % \$x;";
+$try .= "'ok' if \$x == 2;"; $ans = eval $try;
+print "# For '$try'\n" if (!ok "$ans" , "ok" ); 
+
+$try = "\$x = $class\->new(7); \$x = 20 & \$x;";
+$try .= "'ok' if \$x == 4;"; $ans = eval $try;
+print "# For '$try'\n" if (!ok "$ans" , "ok" ); 
+
+$try = "\$x = $class\->new(7); \$x = 0x20 | \$x;";
+$try .= "'ok' if \$x == 0x27;"; $ans = eval $try;
+print "# For '$try'\n" if (!ok "$ans" , "ok" ); 
+
+$try = "\$x = $class\->new(7); \$x = 0x20 ^ \$x;";
+$try .= "'ok' if \$x == 0x27;"; $ans = eval $try;
+print "# For '$try'\n" if (!ok "$ans" , "ok" ); 
+
+###############################################################################
+# check badd(4,5) form
+
+$try = "\$x = $class\->badd(4,5);";
+$try .= "'ok' if \$x == 9;";
+$ans = eval $try;
+print "# For '$try'\n" if (!ok "$ans" , "ok" ); 
+
+###############################################################################
+# check undefs: NOT DONE YET
+
+###############################################################################
+# bool
+
+$x = $class->new(1); if ($x) { ok (1,1); } else { ok($x,'to be true') }
+$x = $class->new(0); if (!$x) { ok (1,1); } else { ok($x,'to be false') }
+
+###############################################################################
+# objectify()
+
+@args = Math::BigInt::objectify(2,4,5);
+ok (scalar @args,3);		# $class, 4, 5
+ok ($args[0] =~ /^Math::BigInt/);
+ok ($args[1],4);
+ok ($args[2],5);
+
+@args = Math::BigInt::objectify(0,4,5);
+ok (scalar @args,3);		# $class, 4, 5
+ok ($args[0] =~ /^Math::BigInt/);
+ok ($args[1],4);
+ok ($args[2],5);
+
+@args = Math::BigInt::objectify(2,4,5);
+ok (scalar @args,3);		# $class, 4, 5
+ok ($args[0] =~ /^Math::BigInt/);
+ok ($args[1],4);
+ok ($args[2],5);
+
+@args = Math::BigInt::objectify(2,4,5,6,7);
+ok (scalar @args,5);		# $class, 4, 5, 6, 7
+ok ($args[0] =~ /^Math::BigInt/);
+ok ($args[1],4); ok (ref($args[1]),$args[0]);
+ok ($args[2],5); ok (ref($args[2]),$args[0]);
+ok ($args[3],6); ok (ref($args[3]),'');
+ok ($args[4],7); ok (ref($args[4]),'');
+
+@args = Math::BigInt::objectify(2,$class,4,5,6,7);
+ok (scalar @args,5);		# $class, 4, 5, 6, 7
+ok ($args[0],$class);
+ok ($args[1],4); ok (ref($args[1]),$args[0]);
+ok ($args[2],5); ok (ref($args[2]),$args[0]);
+ok ($args[3],6); ok (ref($args[3]),'');
+ok ($args[4],7); ok (ref($args[4]),'');
+
+###############################################################################
+# test whether an opp calls objectify properly or not (or at least does what
+# it should do given non-objects, w/ or w/o objectify())
+
+ok ($class->new(123)->badd(123),246);
+ok ($class->badd(123,321),444);
+ok ($class->badd(123,$class->new(321)),444);
+
+ok ($class->new(123)->bsub(122),1);
+ok ($class->bsub(321,123),198);
+ok ($class->bsub(321,$class->new(123)),198);
+
+ok ($class->new(123)->bmul(123),15129);
+ok ($class->bmul(123,123),15129);
+ok ($class->bmul(123,$class->new(123)),15129);
+
+ok ($class->new(15129)->bdiv(123),123);
+ok ($class->bdiv(15129,123),123);
+ok ($class->bdiv(15129,$class->new(123)),123);
+
+ok ($class->new(15131)->bmod(123),2);
+ok ($class->bmod(15131,123),2);
+ok ($class->bmod(15131,$class->new(123)),2);
+
+ok ($class->new(2)->bpow(16),65536);
+ok ($class->bpow(2,16),65536);
+ok ($class->bpow(2,$class->new(16)),65536);
+
+ok ($class->new(2**15)->brsft(1),2**14);
+ok ($class->brsft(2**15,1),2**14);
+ok ($class->brsft(2**15,$class->new(1)),2**14);
+
+ok ($class->new(2**13)->blsft(1),2**14);
+ok ($class->blsft(2**13,1),2**14);
+ok ($class->blsft(2**13,$class->new(1)),2**14);
+
+###############################################################################
+# test for floating-point input (other tests in bnorm() below)
+
+$z = 1050000000000000;          # may be int on systems with 64bit?
+$x = $class->new($z); ok ($x->bsstr(),'105e+13');	# not 1.05e+15
+$z = 1e+129;			# definitely a float (may fail on UTS)
+# don't compare to $z, since some Perl versions stringify $z into something
+# like '1.e+129' or something equally ugly
+$x = $class->new($z); ok ($x->bsstr(),'1e+129');
+
+###############################################################################
+# test for whitespace inlcuding newlines to be handled correctly
+
+# ok ($Math::BigInt::strict,1);		# the default
+
+foreach my $c (
+  qw/1 12 123 1234 12345 123456 1234567 12345678 123456789 1234567890/)
+  {
+  my $m = $class->new($c);
+  ok ($class->new("$c"),$m);
+  ok ($class->new(" $c"),$m);
+  ok ($class->new("$c "),$m);
+  ok ($class->new(" $c "),$m);
+  ok ($class->new("\n$c"),$m);
+  ok ($class->new("$c\n"),$m);
+  ok ($class->new("\n$c\n"),$m);
+  ok ($class->new(" \n$c\n"),$m);
+  ok ($class->new(" \n$c \n"),$m);
+  ok ($class->new(" \n$c\n "),$m);
+  ok ($class->new(" \n$c\n1"),'NaN');
+  ok ($class->new("1 \n$c\n1"),'NaN');
+  }
+
+###############################################################################
+# prime number tests, also test for **= and length()
+# found on: http://www.utm.edu/research/primes/notes/by_year.html
+
+# ((2^148)-1)/17
+$x = $class->new(2); $x **= 148; $x++; $x = $x / 17;
+ok ($x,"20988936657440586486151264256610222593863921");
+ok ($x->length(),length "20988936657440586486151264256610222593863921");
+
+# MM7 = 2^127-1
+$x = $class->new(2); $x **= 127; $x--;
+ok ($x,"170141183460469231731687303715884105727");
+
+$x = $class->new('215960156869840440586892398248');
+($x,$y) = $x->length();
+ok ($x,30); ok ($y,0);
+
+$x = $class->new('1_000_000_000_000');
+($x,$y) = $x->length();
+ok ($x,13); ok ($y,0);
+
+# test <<=, >>=
+$x = $class->new('2');
+my $y = $class->new('18');
+ok ($x <<= $y, 2 << 18);
+ok ($x, 2 << 18);
+ok ($x >>= $y, 2);
+ok ($x, 2);
+
+# I am afraid the following is not yet possible due to slowness
+# Also, testing for 2 meg output is a bit hard ;)
+#$x = $class->new(2); $x **= 6972593; $x--;
+
+# 593573509*2^332162+1 has exactly 1,000,000 digits
+# takes about 24 mins on 300 Mhz, so cannot be done yet ;)
+#$x = $class->new(2); $x **= 332162; $x *= "593573509"; $x++;
+#ok ($x->length(),1_000_000);
+
+###############################################################################
+# inheritance and overriding of _swap
+
+$x = Math::Foo->new(5);
+$x = $x - 8;		# 8 - 5 instead of 5-8
+ok ($x,3);
+ok (ref($x),'Math::Foo');
+
+$x = Math::Foo->new(5);
+$x = 8 - $x;		# 5 - 8 instead of 8 - 5
+ok ($x,-3);
+ok (ref($x),'Math::Foo');
+
+###############################################################################
+# Test whether +inf eq inf
+# This tried to test whether BigInt inf equals Perl inf. Unfortunately, Perl
+# hasn't (before 5.7.3 at least) a consistent way to say inf, and some things
+# like 1e100000 crash on some platforms. So simple test for the string 'inf'
+$x = $class->new('+inf'); ok ($x,'inf');
+
+###############################################################################
+###############################################################################
+# the followin tests only make sense with Math::BigInt::Calc or BareCalc or
+# FastCalc
+
+exit if $CALC !~ /^Math::BigInt::(|Bare|Fast)Calc$/; # for Pari et al.
+
+###############################################################################
+# check proper length of internal arrays
+
+my $bl = $CL->_base_len();
+my $BASE = '9' x $bl;
+my $MAX = $BASE;
+$BASE++;
+
+$x = $class->new($MAX); is_valid($x);	# f.i. 9999
+$x += 1; ok ($x,$BASE); is_valid($x); 	# 10000
+$x -= 1; ok ($x,$MAX); is_valid($x);	# 9999 again
+
+###############################################################################
+# check numify
+
+$x = $class->new($BASE-1);     ok ($x->numify(),$BASE-1); 
+$x = $class->new(-($BASE-1));  ok ($x->numify(),-($BASE-1)); 
+
+# +0 is to protect from 1e15 vs 100000000 (stupid to_string aaaarglburblll...)
+$x = $class->new($BASE);       ok ($x->numify()+0,$BASE+0); 	
+$x = $class->new(-$BASE);      ok ($x->numify(),-$BASE);
+$x = $class->new( -($BASE*$BASE*1+$BASE*1+1) ); 
+ok($x->numify(),-($BASE*$BASE*1+$BASE*1+1)); 
+
+###############################################################################
+# test bug in _digits with length($c[-1]) where $c[-1] was "00001" instead of 1
+
+$x = $class->new($BASE-2); $x++; $x++; $x++; $x++;
+if ($x > $BASE) { ok (1,1) } else { ok ("$x < $BASE","$x > $BASE"); }
+
+$x = $class->new($BASE+3); $x++;
+if ($x > $BASE) { ok (1,1) } else { ok ("$x > $BASE","$x < $BASE"); }
+
+# test for +0 instead of int(): 
+$x = $class->new($MAX); ok ($x->length(), length($MAX));
+
+###############################################################################
+# test bug that $class->digit($string) did not work
+
+ok ($class->digit(123,2),1);
+
+###############################################################################
+# bug in sub where number with at least 6 trailing zeros after any op failed
+
+$x = $class->new(123456); $z = $class->new(10000); $z *= 10; $x -= $z;
+ok ($z, 100000);
+ok ($x, 23456);
+
+###############################################################################
+# bug in shortcut in mul()
+
+# construct a number with a zero-hole of BASE_LEN_SMALL
+{
+ my @bl = $CL->_base_len(); my $bl = $bl[4];
+
+ $x = '1' x $bl . '0' x $bl . '1' x $bl . '0' x $bl;
+ $y = '1' x (2*$bl);
+ $x = $class->new($x)->bmul($y);
+ # result is 123..$bl .  $bl x (3*bl-1) . $bl...321 . '0' x $bl
+ $y = ''; my $d = '';
+ for (my $i = 1; $i <= $bl; $i++)
+   {
+   $y .= $i; $d = $i.$d;
+   }
+ $y .= $bl x (3*$bl-1) . $d . '0' x $bl;
+ ok ($x,$y);
+
+
+  #############################################################################
+  # see if mul shortcut for small numbers works
+
+  $x = '9' x $bl;
+  $x = $class->new($x); 
+  # 999 * 999 => 998 . 001, 9999*9999 => 9998 . 0001
+  ok ($x*$x, '9' x ($bl-1) . '8' . '0' x ($bl-1) . '1');
+}
+
+###############################################################################
+# bug with rest "-0" in div, causing further div()s to fail
+
+$x = $class->new('-322056000'); ($x,$y) = $x->bdiv('-12882240');
+
+ok ($y,'0'); is_valid($y);	# $y not '-0'
+
+###############################################################################
+# bug in $x->bmod($y)
+
+# if $x < 0 and $y > 0
+$x = $class->new('-629'); ok ($x->bmod(5033),4404);
+
+###############################################################################
+# bone/binf etc as plain calls (Lite failed them)
+
+ok ($class->bzero(),0);
+ok ($class->bone(),1);
+ok ($class->bone('+'),1);
+ok ($class->bone('-'),-1);
+ok ($class->bnan(),'NaN');
+ok ($class->binf(),'inf');
+ok ($class->binf('+'),'inf');
+ok ($class->binf('-'),'-inf');
+ok ($class->binf('-inf'),'-inf');
+
+###############################################################################
+# is_one('-')
+
+ok ($class->new(1)->is_one('-'),0);
+ok ($class->new(-1)->is_one('-'),1);
+ok ($class->new(1)->is_one(),1);
+ok ($class->new(-1)->is_one(),0);
+
+###############################################################################
+# [perl #30609] bug with $x -= $x not being 0, but 2*$x
+
+$x = $class->new(3);  $x -= $x; ok ($x, 0);
+$x = $class->new(-3); $x -= $x; ok ($x, 0);
+$x = $class->new('NaN'); $x -= $x; ok ($x->is_nan(), 1);
+$x = $class->new('inf'); $x -= $x; ok ($x->is_nan(), 1);
+$x = $class->new('-inf'); $x -= $x; ok ($x->is_nan(), 1);
+
+$x = $class->new('NaN'); $x += $x; ok ($x->is_nan(), 1);
+$x = $class->new('inf'); $x += $x; ok ($x->is_inf(), 1);
+$x = $class->new('-inf'); $x += $x; ok ($x->is_inf('-'), 1);
+$x = $class->new(3);  $x += $x; ok ($x, 6);
+$x = $class->new(-3); $x += $x; ok ($x, -6);
+
+$x = $class->new(3);  $x *= $x; ok ($x, 9);
+$x = $class->new(-3); $x *= $x; ok ($x, 9);
+$x = $class->new(3);  $x /= $x; ok ($x, 1);
+$x = $class->new(-3); $x /= $x; ok ($x, 1);
+$x = $class->new(3);  $x %= $x; ok ($x, 0);
+$x = $class->new(-3); $x %= $x; ok ($x, 0);
+
+###############################################################################
+# all tests done
+
+1;
+
+###############################################################################
+###############################################################################
+# Perl 5.005 does not like ok ($x,undef)
+
+sub ok_undef
+  {
+  my $x = shift;
+
+  ok (1,1) and return if !defined $x;
+  ok ($x,'undef');
+  }
+
+###############################################################################
+# sub to check validity of a BigInt internally, to ensure that no op leaves a
+# number object in an invalid state (f.i. "-0")
+
+sub is_valid
+  {
+  my ($x,$f) = @_;
+
+  my $e = 0;			# error?
+
+  # allow the check to pass for all Lite, and all MBI and subclasses
+  # ok as reference? 
+  $e = 'Not a reference to Math::BigInt' if ref($x) !~ /^Math::BigInt/;
+
+  if (ref($x) ne 'Math::BigInt::Lite')
+    {
+    # has ok sign?
+    $e = "Illegal sign $x->{sign} (expected: '+', '-', '-inf', '+inf' or 'NaN'"
+     if $e eq '0' && $x->{sign} !~ /^(\+|-|\+inf|-inf|NaN)$/;
+  
+    $e = "-0 is invalid!" if $e ne '0' && $x->{sign} eq '-' && $x == 0;
+    $e = $CALC->_check($x->{value}) if $e eq '0';
+    }
+
+  # test done, see if error did crop up
+  ok (1,1), return if ($e eq '0');
+
+  ok (1,$e." after op '$f'");
+  }
+
+__DATA__
+&.=
+1234:-345:1234-345
+&+=
+1:2:3
+-1:-2:-3
+&-=
+1:2:-1
+-1:-2:1
+&*=
+2:3:6
+-1:5:-5
+&%=
+100:3:1
+8:9:8
+-629:5033:4404
+&/=
+100:3:33
+-8:2:-4
+&|=
+2:1:3
+&&=
+5:7:5
+&^=
+5:7:2
+&blog
+NaNlog:2:NaN
+122:NaNlog:NaN
+NaNlog1:NaNlog:NaN
+122:inf:NaN
+inf:122:NaN
+122:-inf:NaN
+-inf:122:NaN
+-inf:-inf:NaN
+inf:inf:NaN
+0:4:NaN
+-21:4:NaN
+21:-21:NaN
+# normal results
+1024:2:10
+81:3:4
+# 3.01.. truncate
+82:3:4
+# 3.9... truncate
+80:3:3
+15625:5:6
+15626:5:6
+15624:5:5
+1000:10:3
+10000:10:4
+100000:10:5
+1000000:10:6
+10000000:10:7
+100000000:10:8
+8916100448256:12:12
+8916100448257:12:12
+8916100448255:12:11
+2251799813685248:8:17
+72057594037927936:2:56
+144115188075855872:2:57
+288230376151711744:2:58
+576460752303423488:2:59
+4096:2:12
+1329227995784915872903807060280344576:2:120
+# $x == $base => result 1
+3:3:1
+# $x < $base => result 0 ($base ** 0 <= $x)
+3:4:0
+# $x == 1 => result 0
+1:5:0
+&is_negative
+0:0
+-1:1
+1:0
++inf:0
+-inf:1
+NaNneg:0
+&is_positive
+0:0
+-1:0
+1:1
++inf:1
+-inf:0
+NaNneg:0
+&is_int
+-inf:0
++inf:0
+NaNis_int:0
+1:1
+0:1
+123e12:1
+&is_odd
+abc:0
+0:0
+1:1
+3:1
+-1:1
+-3:1
+10000001:1
+10000002:0
+2:0
+120:0
+121:1
+&is_even
+abc:0
+0:1
+1:0
+3:0
+-1:0
+-3:0
+10000001:0
+10000002:1
+2:1
+120:1
+121:0
+&bacmp
++0:-0:0
++0:+1:-1
+-1:+1:0
++1:-1:0
+-1:+2:-1
++2:-1:1
+-123456789:+987654321:-1
++123456789:-987654321:-1
++987654321:+123456789:1
+-987654321:+123456789:1
+-123:+4567889:-1
+# NaNs
+acmpNaN:123:
+123:acmpNaN:
+acmpNaN:acmpNaN:
+# infinity
++inf:+inf:0
+-inf:-inf:0
++inf:-inf:0
+-inf:+inf:0
++inf:123:1
+-inf:123:1
++inf:-123:1
+-inf:-123:1
+123:-inf:-1
+-123:inf:-1
+-123:-inf:-1
+123:inf:-1
+# return undef
++inf:NaN:
+NaN:inf:
+-inf:NaN:
+NaN:-inf:
+&bnorm
+0e999:0
+0e-999:0
+-0e999:0
+-0e-999:0
+123:123
+# binary input
+0babc:NaN
+0b123:NaN
+0b0:0
+-0b0:0
+-0b1:-1
+0b0001:1
+0b001:1
+0b011:3
+0b101:5
+0b1001:9
+0b10001:17
+0b100001:33
+0b1000001:65
+0b10000001:129
+0b100000001:257
+0b1000000001:513
+0b10000000001:1025
+0b100000000001:2049
+0b1000000000001:4097
+0b10000000000001:8193
+0b100000000000001:16385
+0b1000000000000001:32769
+0b10000000000000001:65537
+0b100000000000000001:131073
+0b1000000000000000001:262145
+0b10000000000000000001:524289
+0b100000000000000000001:1048577
+0b1000000000000000000001:2097153
+0b10000000000000000000001:4194305
+0b100000000000000000000001:8388609
+0b1000000000000000000000001:16777217
+0b10000000000000000000000001:33554433
+0b100000000000000000000000001:67108865
+0b1000000000000000000000000001:134217729
+0b10000000000000000000000000001:268435457
+0b100000000000000000000000000001:536870913
+0b1000000000000000000000000000001:1073741825
+0b10000000000000000000000000000001:2147483649
+0b100000000000000000000000000000001:4294967297
+0b1000000000000000000000000000000001:8589934593
+0b10000000000000000000000000000000001:17179869185
+0b_101:NaN
+0b1_0_1:5
+0b0_0_0_1:1
+# hex input
+-0x0:0
+0xabcdefgh:NaN
+0x1234:4660
+0xabcdef:11259375
+-0xABCDEF:-11259375
+-0x1234:-4660
+0x12345678:305419896
+0x1_2_3_4_56_78:305419896
+0xa_b_c_d_e_f:11259375
+0x_123:NaN
+0x9:9
+0x11:17
+0x21:33
+0x41:65
+0x81:129
+0x101:257
+0x201:513
+0x401:1025
+0x801:2049
+0x1001:4097
+0x2001:8193
+0x4001:16385
+0x8001:32769
+0x10001:65537
+0x20001:131073
+0x40001:262145
+0x80001:524289
+0x100001:1048577
+0x200001:2097153
+0x400001:4194305
+0x800001:8388609
+0x1000001:16777217
+0x2000001:33554433
+0x4000001:67108865
+0x8000001:134217729
+0x10000001:268435457
+0x20000001:536870913
+0x40000001:1073741825
+0x80000001:2147483649
+0x100000001:4294967297
+0x200000001:8589934593
+0x400000001:17179869185
+0x800000001:34359738369
+# bug found by Mark Lakata in Calc.pm creating too big one-element numbers in _from_hex()
+0x2dd59e18a125dbed30a6ab1d93e9c855569f44f75806f0645dc9a2e98b808c3:1295719234436071846486578237372801883390756472611551858964079371952886122691
+# inf input
+inf:inf
++inf:inf
+-inf:-inf
+0inf:NaN
+# abnormal input
+:NaN
+abc:NaN
+   1 a:NaN
+1bcd2:NaN
+11111b:NaN
++1z:NaN
+-1z:NaN
+# only one underscore between two digits
+_123:NaN
+_123_:NaN
+123_:NaN
+1__23:NaN
+1E1__2:NaN
+1_E12:NaN
+1E_12:NaN
+1_E_12:NaN
++_1E12:NaN
++0_1E2:100
++0_0_1E2:100
+-0_0_1E2:-100
+-0_0_1E+0_0_2:-100
+E1:NaN
+E23:NaN
+1.23E1:NaN
+1.23E-1:NaN
+# bug with two E's in number being valid
+1e2e3:NaN
+1e2r:NaN
+1e2.0:NaN
+# bug with two '.' in number being valid
+1.2.2:NaN
+1.2.3e1:NaN
+-1.2.3:NaN
+-1.2.3e-4:NaN
+1.2e3.4:NaN
+1.2e-3.4:NaN
+1.2.3.4:NaN
+1.2.t:NaN
+1..2:NaN
+1..2e1:NaN
+1..2e1..1:NaN
+12e1..1:NaN
+..2:NaN
+.-2:NaN
+# leading zeros
+012:12
+0123:123
+01234:1234
+012345:12345
+0123456:123456
+01234567:1234567
+012345678:12345678
+0123456789:123456789
+01234567891:1234567891
+012345678912:12345678912
+0123456789123:123456789123
+01234567891234:1234567891234
+# some inputs that result in zero
+0e0:0
++0e0:0
++0e+0:0
+-0e+0:0
+0e-0:0
+-0e-0:0
++0e-0:0
+000:0
+00e2:0
+00e02:0
+000e002:0
+000e1230:0
+00e-3:0
+00e+3:0
+00e-03:0
+00e+03:0
+-000:0
+-00e2:0
+-00e02:0
+-000e002:0
+-000e1230:0
+-00e-3:0
+-00e+3:0
+-00e-03:0
+-00e+03:0
+# normal input
+0:0
++0:0
++00:0
++000:0
+000000000000000000:0
+-0:0
+-0000:0
++1:1
++01:1
++001:1
++00000100000:100000
+123456789:123456789
+-1:-1
+-01:-1
+-001:-1
+-123456789:-123456789
+-00000100000:-100000
+1_2_3:123
+10000000000E-1_0:1
+1E2:100
+1E1:10
+1E0:1
+1.23E2:123
+100E-1:10
+# floating point input
+# .2e2:20
+1.E3:1000
+1.01E2:101
+1010E-1:101
+-1010E0:-1010
+-1010E1:-10100
+1234.00:1234
+# non-integer numbers
+-1010E-2:NaN
+-1.01E+1:NaN
+-1.01E-1:NaN
+&bnan
+1:NaN
+2:NaN
+abc:NaN
+&bone
+2:+:1
+2:-:-1
+boneNaN:-:-1
+boneNaN:+:1
+2:abc:1
+3::1
+&binf
+1:+:inf
+2:-:-inf
+3:abc:inf
+&is_nan
+123:0
+abc:1
+NaN:1
+-123:0
+&is_inf
++inf::1
+-inf::1
+abc::0
+1::0
+NaN::0
+-1::0
++inf:-:0
++inf:+:1
+-inf:-:1
+-inf:+:0
+-inf:-inf:1
+-inf:+inf:0
++inf:-inf:0
++inf:+inf:1
+# it must be exactly /^[+-]inf$/
++infinity::0
+-infinity::0
+&blsft
+abc:abc:NaN
++2:+2:8
++1:+32:4294967296
++1:+48:281474976710656
++8:-2:NaN
+# excercise base 10
++12345:4:10:123450000
+-1234:0:10:-1234
++1234:0:10:1234
++2:2:10:200
++12:2:10:1200
++1234:-3:10:NaN
+1234567890123:12:10:1234567890123000000000000
+-3:1:2:-6
+-5:1:2:-10
+-2:1:2:-4
+-102533203:1:2:-205066406
+&brsft
+abc:abc:NaN
++8:+2:2
++4294967296:+32:1
++281474976710656:+48:1
++2:-2:NaN
+# excercise base 10
+-1234:0:10:-1234
++1234:0:10:1234
++200:2:10:2
++1234:3:10:1
++1234:2:10:12
++1234:-3:10:NaN
+310000:4:10:31
+12300000:5:10:123
+1230000000000:10:10:123
+09876123456789067890:12:10:9876123
+1234561234567890123:13:10:123456
+820265627:1:2:410132813
+# test shifting negative numbers in base 2
+-15:1:2:-8
+-14:1:2:-7
+-13:1:2:-7
+-12:1:2:-6
+-11:1:2:-6
+-10:1:2:-5
+-9:1:2:-5
+-8:1:2:-4
+-7:1:2:-4
+-6:1:2:-3
+-5:1:2:-3
+-4:1:2:-2
+-3:1:2:-2
+-2:1:2:-1
+-1:1:2:-1
+-1640531254:2:2:-410132814
+-1640531254:1:2:-820265627
+-820265627:1:2:-410132814
+-205066405:1:2:-102533203
+&bsstr
++inf:inf
+-inf:-inf
+1e+34:1e+34
+123.456E3:123456e+0
+100:1e+2
+bsstrabc:NaN
+-5:-5e+0
+-100:-1e+2
+&numify
+numifyabc:NaN
++inf:inf
+-inf:-inf
+5:5
+-5:-5
+100:100
+-100:-100
+&bneg
+bnegNaN:NaN
++inf:-inf
+-inf:inf
+abd:NaN
+0:0
+1:-1
+-1:1
++123456789:-123456789
+-123456789:123456789
+&babs
+babsNaN:NaN
++inf:inf
+-inf:inf
+0:0
+1:1
+-1:1
++123456789:123456789
+-123456789:123456789
+&bcmp
+bcmpNaN:bcmpNaN:
+bcmpNaN:0:
+0:bcmpNaN:
+0:0:0
+-1:0:-1
+0:-1:1
+1:0:1
+0:1:-1
+-1:1:-1
+1:-1:1
+-1:-1:0
+1:1:0
+123:123:0
+123:12:1
+12:123:-1
+-123:-123:0
+-123:-12:-1
+-12:-123:1
+123:124:-1
+124:123:1
+-123:-124:1
+-124:-123:-1
+100:5:1
+-123456789:987654321:-1
++123456789:-987654321:1
+-987654321:123456789:-1
+-inf:5432112345:-1
++inf:5432112345:1
+-inf:-5432112345:-1
++inf:-5432112345:1
++inf:+inf:0
+-inf:-inf:0
++inf:-inf:1
+-inf:+inf:-1
+5:inf:-1
+5:inf:-1
+-5:-inf:1
+-5:-inf:1
+# return undef
++inf:NaN:
+NaN:inf:
+-inf:NaN:
+NaN:-inf:
+&binc
+abc:NaN
++inf:inf
+-inf:-inf
++0:1
++1:2
+-1:0
+&bdec
+abc:NaN
++inf:inf
+-inf:-inf
++0:-1
++1:0
+-1:-2
+&badd
+abc:abc:NaN
+abc:0:NaN
++0:abc:NaN
++inf:-inf:NaN
+-inf:+inf:NaN
++inf:+inf:inf
+-inf:-inf:-inf
+baddNaN:+inf:NaN
+baddNaN:+inf:NaN
++inf:baddNaN:NaN
+-inf:baddNaN:NaN
+0:0:0
+1:0:1
+0:1:1
+1:1:2
+-1:0:-1
+0:-1:-1
+-1:-1:-2
+-1:+1:0
++1:-1:0
++9:+1:10
++99:+1:100
++999:+1:1000
++9999:+1:10000
++99999:+1:100000
++999999:+1:1000000
++9999999:+1:10000000
++99999999:+1:100000000
++999999999:+1:1000000000
++9999999999:+1:10000000000
++99999999999:+1:100000000000
++10:-1:9
++100:-1:99
++1000:-1:999
++10000:-1:9999
++100000:-1:99999
++1000000:-1:999999
++10000000:-1:9999999
++100000000:-1:99999999
++1000000000:-1:999999999
++10000000000:-1:9999999999
++123456789:987654321:1111111110
+-123456789:987654321:864197532
+-123456789:-987654321:-1111111110
++123456789:-987654321:-864197532
+-1:10001:10000
+-1:100001:100000
+-1:1000001:1000000
+-1:10000001:10000000
+-1:100000001:100000000
+-1:1000000001:1000000000
+-1:10000000001:10000000000
+-1:100000000001:100000000000
+-1:1000000000001:1000000000000
+-1:10000000000001:10000000000000
+-1:-10001:-10002
+-1:-100001:-100002
+-1:-1000001:-1000002
+-1:-10000001:-10000002
+-1:-100000001:-100000002
+-1:-1000000001:-1000000002
+-1:-10000000001:-10000000002
+-1:-100000000001:-100000000002
+-1:-1000000000001:-1000000000002
+-1:-10000000000001:-10000000000002
+&bsub
+abc:abc:NaN
+abc:+0:NaN
++0:abc:NaN
++inf:-inf:inf
+-inf:+inf:-inf
++inf:+inf:NaN
+-inf:-inf:NaN
++0:+0:0
++1:+0:1
++0:+1:-1
++1:+1:0
+-1:+0:-1
++0:-1:1
+-1:-1:0
+-1:+1:-2
++1:-1:2
++9:+1:8
++99:+1:98
++999:+1:998
++9999:+1:9998
++99999:+1:99998
++999999:+1:999998
++9999999:+1:9999998
++99999999:+1:99999998
++999999999:+1:999999998
++9999999999:+1:9999999998
++99999999999:+1:99999999998
++10:-1:11
++100:-1:101
++1000:-1:1001
++10000:-1:10001
++100000:-1:100001
++1000000:-1:1000001
++10000000:-1:10000001
++100000000:-1:100000001
++1000000000:-1:1000000001
++10000000000:-1:10000000001
++123456789:+987654321:-864197532
+-123456789:+987654321:-1111111110
+-123456789:-987654321:864197532
++123456789:-987654321:1111111110
+10001:1:10000
+100001:1:100000
+1000001:1:1000000
+10000001:1:10000000
+100000001:1:100000000
+1000000001:1:1000000000
+10000000001:1:10000000000
+100000000001:1:100000000000
+1000000000001:1:1000000000000
+10000000000001:1:10000000000000
+10001:-1:10002
+100001:-1:100002
+1000001:-1:1000002
+10000001:-1:10000002
+100000001:-1:100000002
+1000000001:-1:1000000002
+10000000001:-1:10000000002
+100000000001:-1:100000000002
+1000000000001:-1:1000000000002
+10000000000001:-1:10000000000002
+&bmuladd
+abc:abc:0:NaN
+abc:+0:0:NaN
++0:abc:0:NaN
++0:0:abc:NaN
+NaNmul:+inf:0:NaN
+NaNmul:-inf:0:NaN
+-inf:NaNmul:0:NaN
++inf:NaNmul:0:NaN
++inf:+inf:0:inf
++inf:-inf:0:-inf
+-inf:+inf:0:-inf
+-inf:-inf:0:inf
++0:+0:0:0
++0:+1:0:0
++1:+0:0:0
++0:-1:0:0
+-1:+0:0:0
+123456789123456789:0:0:0
+0:123456789123456789:0:0
+-1:-1:0:1
+-1:-1:0:1
+-1:+1:0:-1
++1:-1:0:-1
++1:+1:0:1
++2:+3:0:6
+-2:+3:0:-6
++2:-3:0:-6
+-2:-3:0:6
+111:111:0:12321
+10101:10101:0:102030201
+1001001:1001001:0:1002003002001
+100010001:100010001:0:10002000300020001
+10000100001:10000100001:0:100002000030000200001
+11111111111:9:0:99999999999
+22222222222:9:0:199999999998
+33333333333:9:0:299999999997
+44444444444:9:0:399999999996
+55555555555:9:0:499999999995
+66666666666:9:0:599999999994
+77777777777:9:0:699999999993
+88888888888:9:0:799999999992
+99999999999:9:0:899999999991
+11111111111:9:1:100000000000
+22222222222:9:1:199999999999
+33333333333:9:1:299999999998
+44444444444:9:1:399999999997
+55555555555:9:1:499999999996
+66666666666:9:1:599999999995
+77777777777:9:1:699999999994
+88888888888:9:1:799999999993
+99999999999:9:1:899999999992
+-3:-4:-5:7
+3:-4:-5:-17
+-3:4:-5:-17
+3:4:-5:7
+-3:4:5:-7
+3:-4:5:-7
+9999999999999999999:10000000000000000000:1234567890:99999999999999999990000000001234567890
+2:3:12345678901234567890:12345678901234567896
+&bmul
+abc:abc:NaN
+abc:+0:NaN
++0:abc:NaN
+NaNmul:+inf:NaN
+NaNmul:-inf:NaN
+-inf:NaNmul:NaN
++inf:NaNmul:NaN
++inf:+inf:inf
++inf:-inf:-inf
+-inf:+inf:-inf
+-inf:-inf:inf
++0:+0:0
++0:+1:0
++1:+0:0
++0:-1:0
+-1:+0:0
+123456789123456789:0:0
+0:123456789123456789:0
+-1:-1:1
+-1:+1:-1
++1:-1:-1
++1:+1:1
++2:+3:6
+-2:+3:-6
++2:-3:-6
+-2:-3:6
+111:111:12321
+10101:10101:102030201
+1001001:1001001:1002003002001
+100010001:100010001:10002000300020001
+10000100001:10000100001:100002000030000200001
+11111111111:9:99999999999
+22222222222:9:199999999998
+33333333333:9:299999999997
+44444444444:9:399999999996
+55555555555:9:499999999995
+66666666666:9:599999999994
+77777777777:9:699999999993
+88888888888:9:799999999992
+99999999999:9:899999999991
++25:+25:625
++12345:+12345:152399025
++99999:+11111:1111088889
+9999:10000:99990000
+99999:100000:9999900000
+999999:1000000:999999000000
+9999999:10000000:99999990000000
+99999999:100000000:9999999900000000
+999999999:1000000000:999999999000000000
+9999999999:10000000000:99999999990000000000
+99999999999:100000000000:9999999999900000000000
+999999999999:1000000000000:999999999999000000000000
+9999999999999:10000000000000:99999999999990000000000000
+99999999999999:100000000000000:9999999999999900000000000000
+999999999999999:1000000000000000:999999999999999000000000000000
+9999999999999999:10000000000000000:99999999999999990000000000000000
+99999999999999999:100000000000000000:9999999999999999900000000000000000
+999999999999999999:1000000000000000000:999999999999999999000000000000000000
+9999999999999999999:10000000000000000000:99999999999999999990000000000000000000
+&bdiv-list
+100:20:5,0
+4095:4095:1,0
+-4095:-4095:1,0
+4095:-4095:-1,0
+-4095:4095:-1,0
+123:2:61,1
+9:5:1,4
+9:4:2,1
+# inf handling and general remainder
+5:8:0,5
+0:8:0,0
+11:2:5,1
+11:-2:-5,-1
+-11:2:-5,1
+# see table in documentation in MBI
+0:inf:0,0
+0:-inf:0,0
+5:inf:0,5
+5:-inf:0,5
+-5:inf:0,-5
+-5:-inf:0,-5
+inf:5:inf,0
+-inf:5:-inf,0
+inf:-5:-inf,0
+-inf:-5:inf,0
+5:5:1,0
+-5:-5:1,0
+inf:inf:NaN,NaN
+-inf:-inf:NaN,NaN
+-inf:inf:NaN,NaN
+inf:-inf:NaN,NaN
+8:0:inf,8
+inf:0:inf,inf
+# exceptions to reminder rule
+-8:0:-inf,-8
+-inf:0:-inf,-inf
+0:0:NaN,NaN
+# test the shortcut in Calc if @$x == @$yorg
+1234567812345678:123456712345678:10,688888898
+12345671234567:1234561234567:10,58888897
+123456123456:12345123456:10,4888896
+1234512345:123412345:10,388895
+1234567890999999999:1234567890:1000000000,999999999
+1234567890000000000:1234567890:1000000000,0
+1234567890999999999:9876543210:124999998,9503086419
+1234567890000000000:9876543210:124999998,8503086420
+96969696969696969696969696969678787878626262626262626262626262:484848484848484848484848486666666666666689898989898989898989:199,484848484848484848484848123012121211954972727272727272727451
+# bug in v1.76
+1267650600228229401496703205375:1267650600228229401496703205376:0,1267650600228229401496703205375
+# excercise shortcut for numbers of the same length in div
+999999999999999999999999999999999:999999999999999999999999999999999:1,0
+999999999999999999999999999999999:888888888888888888888888888888888:1,111111111111111111111111111111111
+999999999999999999999999999999999:777777777777777777777777777777777:1,222222222222222222222222222222222
+999999999999999999999999999999999:666666666666666666666666666666666:1,333333333333333333333333333333333
+999999999999999999999999999999999:555555555555555555555555555555555:1,444444444444444444444444444444444
+999999999999999999999999999999999:444444444444444444444444444444444:2,111111111111111111111111111111111
+999999999999999999999999999999999:333333333333333333333333333333333:3,0
+999999999999999999999999999999999:222222222222222222222222222222222:4,111111111111111111111111111111111
+999999999999999999999999999999999:111111111111111111111111111111111:9,0
+9999999_9999999_9999999_9999999:3333333_3333333_3333333_3333333:3,0
+9999999_9999999_9999999_9999999:3333333_0000000_0000000_0000000:3,999999999999999999999
+9999999_9999999_9999999_9999999:3000000_0000000_0000000_0000000:3,999999999999999999999999999
+9999999_9999999_9999999_9999999:2000000_0000000_0000000_0000000:4,1999999999999999999999999999
+9999999_9999999_9999999_9999999:1000000_0000000_0000000_0000000:9,999999999999999999999999999
+9999999_9999999_9999999_9999999:100000_0000000_0000000_0000000:99,99999999999999999999999999
+9999999_9999999_9999999_9999999:10000_0000000_0000000_0000000:999,9999999999999999999999999
+9999999_9999999_9999999_9999999:1000_0000000_0000000_0000000:9999,999999999999999999999999
+9999999_9999999_9999999_9999999:100_0000000_0000000_0000000:99999,99999999999999999999999
+9999999_9999999_9999999_9999999:10_0000000_0000000_0000000:999999,9999999999999999999999
+9999999_9999999_9999999_9999999:1_0000000_0000000_0000000:9999999,999999999999999999999
+&bdiv
+abc:abc:NaN
+abc:1:NaN
+1:abc:NaN
+0:0:NaN
+# inf handling (see table in doc)
+0:inf:0
+0:-inf:0
+5:inf:0
+5:-inf:0
+-5:inf:0
+-5:-inf:0
+inf:5:inf
+-inf:5:-inf
+inf:-5:-inf
+-inf:-5:inf
+5:5:1
+-5:-5:1
+inf:inf:NaN
+-inf:-inf:NaN
+-inf:inf:NaN
+inf:-inf:NaN
+8:0:inf
+inf:0:inf
+-8:0:-inf
+-inf:0:-inf
+0:0:NaN
+11:2:5
+-11:-2:5
+-11:2:-5
+11:-2:-5
+0:1:0
+0:-1:0
+1:1:1
+-1:-1:1
+1:-1:-1
+-1:1:-1
+1:2:0
+2:1:2
+1:26:0
+1000000000:9:111111111
+2000000000:9:222222222
+3000000000:9:333333333
+4000000000:9:444444444
+5000000000:9:555555555
+6000000000:9:666666666
+7000000000:9:777777777
+8000000000:9:888888888
+9000000000:9:1000000000
+35500000:113:314159
+71000000:226:314159
+106500000:339:314159
+1000000000:3:333333333
++10:+5:2
++100:+4:25
++1000:+8:125
++10000:+16:625
+999999999999:9:111111111111
+999999999999:99:10101010101
+999999999999:999:1001001001
+999999999999:9999:100010001
+999999999999999:99999:10000100001
++1111088889:99999:11111
+-5:-3:1
+-5:3:-1
+4:3:1
+4:-3:-1
+1:3:0
+1:-3:0
+-2:-3:0
+-2:3:0
+8:3:2
+-8:3:-2
+14:-3:-4
+-14:3:-4
+-14:-3:4
+14:3:4
+# bug in Calc with '99999' vs $BASE-1
+10000000000000000000000000000000000000000000000000000000000000000000000000000000000:10000000375084540248994272022843165711074:999999962491547381984643365663244474111576
+# test the shortcut in Calc if @$x == @$yorg
+1234567812345678:123456712345678:10
+12345671234567:1234561234567:10
+123456123456:12345123456:10
+1234512345:123412345:10
+1234567890999999999:1234567890:1000000000
+1234567890000000000:1234567890:1000000000
+1234567890999999999:9876543210:124999998
+1234567890000000000:9876543210:124999998
+96969696969696969696969696969678787878626262626262626262626262:484848484848484848484848486666666666666689898989898989898989:199
+# bug up to v0.35 in Calc (--$q one too many)
+84696969696969696956565656566184292929292929292847474747436308080808080808086765396464646464646465:13131313131313131313131313131394949494949494949494949494943535353535353535353535:6449999999999999999
+84696969696969696943434343434871161616161616161452525252486813131313131313143230042929292929292930:13131313131313131313131313131394949494949494949494949494943535353535353535353535:6449999999999999998
+84696969696969696969696969697497424242424242424242424242385803030303030303030300750000000000000000:13131313131313131313131313131394949494949494949494949494943535353535353535353535:6450000000000000000
+84696969696969696930303030303558030303030303030057575757537318181818181818199694689393939393939395:13131313131313131313131313131394949494949494949494949494943535353535353535353535:6449999999999999997
+# excercise shortcut for numbers of the same length in div
+999999999999999999999999999999999:999999999999999999999999999999999:1
+999999999999999999999999999999999:888888888888888888888888888888888:1
+999999999999999999999999999999999:777777777777777777777777777777777:1
+999999999999999999999999999999999:666666666666666666666666666666666:1
+999999999999999999999999999999999:555555555555555555555555555555555:1
+999999999999999999999999999999999:444444444444444444444444444444444:2
+999999999999999999999999999999999:333333333333333333333333333333333:3
+999999999999999999999999999999999:222222222222222222222222222222222:4
+999999999999999999999999999999999:111111111111111111111111111111111:9
+9999999_9999999_9999999_9999999:3333333_3333333_3333333_3333333:3
+9999999_9999999_9999999_9999999:3333333_0000000_0000000_0000000:3
+9999999_9999999_9999999_9999999:3000000_0000000_0000000_0000000:3
+9999999_9999999_9999999_9999999:2000000_0000000_0000000_0000000:4
+9999999_9999999_9999999_9999999:1000000_0000000_0000000_0000000:9
+9999999_9999999_9999999_9999999:100000_0000000_0000000_0000000:99
+9999999_9999999_9999999_9999999:10000_0000000_0000000_0000000:999
+9999999_9999999_9999999_9999999:1000_0000000_0000000_0000000:9999
+9999999_9999999_9999999_9999999:100_0000000_0000000_0000000:99999
+9999999_9999999_9999999_9999999:10_0000000_0000000_0000000:999999
+9999999_9999999_9999999_9999999:1_0000000_0000000_0000000:9999999
+# bug with shortcut in Calc 0.44
+949418181818187070707070707070707070:181818181853535353535353535353535353:5
+&bmodinv
+# format: number:modulus:result
+# bmodinv Data errors
+abc:abc:NaN
+abc:5:NaN
+5:abc:NaN
+# bmodinv Expected Results from normal use
+1:5:1
+3:5:2
+-2:5:2
+8:5033:4404
+1234567891:13:6
+-1234567891:13:7
+324958749843759385732954874325984357439658735983745:2348249874968739:1741662881064902
+## bmodinv Error cases / useless use of function
+3:-5:NaN
+inf:5:NaN
+5:inf:NaN
+-inf:5:NaN
+5:-inf:NaN
+&bmodpow
+# format: number:exponent:modulus:result
+# bmodpow Data errors
+abc:abc:abc:NaN
+5:abc:abc:NaN
+abc:5:abc:NaN
+abc:abc:5:NaN
+5:5:abc:NaN
+5:abc:5:NaN
+abc:5:5:NaN
+# bmodpow Expected results
+0:0:2:1
+1:0:2:1
+0:0:1:0
+8:7:5032:3840
+8:-1:5033:4404
+98436739867439843769485798542749827593285729587325:43698764986460981048259837659386739857456983759328457:6943857329857295827698367:3104744730915914415259518
+# bmodpow Error cases
+8:8:-5:NaN
+8:-1:16:NaN
+inf:5:13:NaN
+5:inf:13:NaN
+&bmod
+# inf handling, see table in doc
+0:inf:0
+0:-inf:0
+5:inf:5
+5:-inf:5
+-5:inf:-5
+-5:-inf:-5
+inf:5:0
+-inf:5:0
+inf:-5:0
+-inf:-5:0
+5:5:0
+-5:-5:0
+inf:inf:NaN
+-inf:-inf:NaN
+-inf:inf:NaN
+inf:-inf:NaN
+8:0:8
+inf:0:inf
+# exceptions to reminder rule
+-inf:0:-inf
+-8:0:-8
+0:0:NaN
+abc:abc:NaN
+abc:1:abc:NaN
+1:abc:NaN
+0:0:NaN
+0:1:0
+1:0:1
+0:-1:0
+-1:0:-1
+1:1:0
+-1:-1:0
+1:-1:0
+-1:1:0
+1:2:1
+2:1:0
+1000000000:9:1
+2000000000:9:2
+3000000000:9:3
+4000000000:9:4
+5000000000:9:5
+6000000000:9:6
+7000000000:9:7
+8000000000:9:8
+9000000000:9:0
+35500000:113:33
+71000000:226:66
+106500000:339:99
+1000000000:3:1
+10:5:0
+100:4:0
+1000:8:0
+10000:16:0
+999999999999:9:0
+999999999999:99:0
+999999999999:999:0
+999999999999:9999:0
+999999999999999:99999:0
+-9:+5:1
++9:-5:-1
+-9:-5:-4
+-5:3:1
+-2:3:1
+4:3:1
+1:3:1
+-5:-3:-2
+-2:-3:-2
+4:-3:-2
+1:-3:-2
+4095:4095:0
+100041000510123:3:0
+152403346:12345:4321
+9:5:4
+# test shortcuts in Calc
+# 1ex % 9 is always == 1, 1ex % 113 is != 1 for x = (4..9), 1ex % 10 = 0
+1234:9:1
+123456:9:3
+12345678:9:0
+1234567891:9:1
+123456789123:9:6
+12345678912345:9:6
+1234567891234567:9:1
+123456789123456789:9:0
+1234:10:4
+123456:10:6
+12345678:10:8
+1234567891:10:1
+123456789123:10:3
+12345678912345:10:5
+1234567891234567:10:7
+123456789123456789:10:9
+1234:113:104
+123456:113:60
+12345678:113:89
+1234567891:113:64
+123456789123:113:95
+12345678912345:113:53
+1234567891234567:113:56
+123456789123456789:113:39
+# bug in bmod() not modifying the variable in place
+-629:5033:4404
+# bug in bmod() in Calc in the _div_use_div() shortcut code path,
+# when X == X and X was big 
+111111111111111111111111111111:111111111111111111111111111111:0
+12345678901234567890:12345678901234567890:0
+&bgcd
+inf:12:NaN
+-inf:12:NaN
+12:inf:NaN
+12:-inf:NaN
+inf:inf:NaN
+inf:-inf:NaN
+-inf:-inf:NaN
+abc:abc:NaN
+abc:+0:NaN
++0:abc:NaN
++0:+0:0
++0:+1:1
++1:+0:1
++1:+1:1
++2:+3:1
++3:+2:1
+-3:+2:1
+-3:-2:1
+-144:-60:12
+144:-60:12
+144:60:12
+100:625:25
+4096:81:1
+1034:804:2
+27:90:56:1
+27:90:54:9
+&blcm
+abc:abc:NaN
+abc:+0:NaN
++0:abc:NaN
++0:+0:NaN
++1:+0:0
++0:+1:0
++27:+90:270
++1034:+804:415668
+&band
+abc:abc:NaN
+abc:0:NaN
+0:abc:NaN
+1:2:0
+3:2:2
++8:+2:0
++281474976710656:0:0
++281474976710656:1:0
++281474976710656:+281474976710656:281474976710656
+281474976710656:-1:281474976710656
+-2:-3:-4
+-1:-1:-1
+-6:-6:-6
+-7:-4:-8
+-7:4:0
+-4:7:4
+# negative argument is bitwise shorter than positive [perl #26559]
+30:-3:28
+123:-1:123
+# equal arguments are treated special, so also do some test with unequal ones
+0xFFFF:0xFFFF:0x0xFFFF
+0xFFFFFF:0xFFFFFF:0x0xFFFFFF
+0xFFFFFFFF:0xFFFFFFFF:0x0xFFFFFFFF
+0xFFFFFFFFFF:0xFFFFFFFFFF:0x0xFFFFFFFFFF
+0xFFFFFFFFFFFF:0xFFFFFFFFFFFF:0x0xFFFFFFFFFFFF
+0xF0F0:0xF0F0:0x0xF0F0
+0x0F0F:0x0F0F:0x0x0F0F
+0xF0F0F0:0xF0F0F0:0x0xF0F0F0
+0x0F0F0F:0x0F0F0F:0x0x0F0F0F
+0xF0F0F0F0:0xF0F0F0F0:0x0xF0F0F0F0
+0x0F0F0F0F:0x0F0F0F0F:0x0x0F0F0F0F
+0xF0F0F0F0F0:0xF0F0F0F0F0:0x0xF0F0F0F0F0
+0x0F0F0F0F0F:0x0F0F0F0F0F:0x0x0F0F0F0F0F
+0xF0F0F0F0F0F0:0xF0F0F0F0F0F0:0x0xF0F0F0F0F0F0
+0x0F0F0F0F0F0F:0x0F0F0F0F0F0F:0x0x0F0F0F0F0F0F
+0x1F0F0F0F0F0F:0x3F0F0F0F0F0F:0x0x1F0F0F0F0F0F
+&bior
+abc:abc:NaN
+abc:0:NaN
+0:abc:NaN
+1:2:3
++8:+2:10
++281474976710656:0:281474976710656
++281474976710656:1:281474976710657
++281474976710656:281474976710656:281474976710656
+-2:-3:-1
+-1:-1:-1
+-6:-6:-6
+-7:4:-3
+-4:7:-1
++281474976710656:-1:-1
+30:-3:-1
+30:-4:-2
+300:-76:-68
+-76:300:-68
+# equal arguments are treated special, so also do some test with unequal ones
+0xFFFF:0xFFFF:0x0xFFFF
+0xFFFFFF:0xFFFFFF:0x0xFFFFFF
+0xFFFFFFFF:0xFFFFFFFF:0x0xFFFFFFFF
+0xFFFFFFFFFF:0xFFFFFFFFFF:0x0xFFFFFFFFFF
+0xFFFFFFFFFFFF:0xFFFFFFFFFFFF:0x0xFFFFFFFFFFFF
+0:0xFFFF:0x0xFFFF
+0:0xFFFFFF:0x0xFFFFFF
+0:0xFFFFFFFF:0x0xFFFFFFFF
+0:0xFFFFFFFFFF:0x0xFFFFFFFFFF
+0:0xFFFFFFFFFFFF:0x0xFFFFFFFFFFFF
+0xFFFF:0:0x0xFFFF
+0xFFFFFF:0:0x0xFFFFFF
+0xFFFFFFFF:0:0x0xFFFFFFFF
+0xFFFFFFFFFF:0:0x0xFFFFFFFFFF
+0xFFFFFFFFFFFF:0:0x0xFFFFFFFFFFFF
+0xF0F0:0xF0F0:0x0xF0F0
+0x0F0F:0x0F0F:0x0x0F0F
+0xF0F0:0x0F0F:0x0xFFFF
+0xF0F0F0:0xF0F0F0:0x0xF0F0F0
+0x0F0F0F:0x0F0F0F:0x0x0F0F0F
+0x0F0F0F:0xF0F0F0:0x0xFFFFFF
+0xF0F0F0F0:0xF0F0F0F0:0x0xF0F0F0F0
+0x0F0F0F0F:0x0F0F0F0F:0x0x0F0F0F0F
+0x0F0F0F0F:0xF0F0F0F0:0x0xFFFFFFFF
+0xF0F0F0F0F0:0xF0F0F0F0F0:0x0xF0F0F0F0F0
+0x0F0F0F0F0F:0x0F0F0F0F0F:0x0x0F0F0F0F0F
+0x0F0F0F0F0F:0xF0F0F0F0F0:0x0xFFFFFFFFFF
+0xF0F0F0F0F0F0:0xF0F0F0F0F0F0:0x0xF0F0F0F0F0F0
+0x0F0F0F0F0F0F:0x0F0F0F0F0F0F:0x0x0F0F0F0F0F0F
+0x0F0F0F0F0F0F:0xF0F0F0F0F0F0:0x0xFFFFFFFFFFFF
+0x1F0F0F0F0F0F:0xF0F0F0F0F0F0:0x0xFFFFFFFFFFFF
+&bxor
+abc:abc:NaN
+abc:0:NaN
+0:abc:NaN
+1:2:3
++8:+2:10
++281474976710656:0:281474976710656
++281474976710656:1:281474976710657
++281474976710656:281474976710656:0
+-2:-3:3
+-1:-1:0
+-6:-6:0
+-7:4:-3
+-4:7:-5
+4:-7:-3
+-4:-7:5
+30:-3:-29
+30:-4:-30
+300:-76:-360
+-76:300:-360
+# equal arguments are treated special, so also do some test with unequal ones
+0xFFFF:0xFFFF:0
+0xFFFFFF:0xFFFFFF:0
+0xFFFFFFFF:0xFFFFFFFF:0
+0xFFFFFFFFFF:0xFFFFFFFFFF:0
+0xFFFFFFFFFFFF:0xFFFFFFFFFFFF:0
+0:0xFFFF:0x0xFFFF
+0:0xFFFFFF:0x0xFFFFFF
+0:0xFFFFFFFF:0x0xFFFFFFFF
+0:0xFFFFFFFFFF:0x0xFFFFFFFFFF
+0:0xFFFFFFFFFFFF:0x0xFFFFFFFFFFFF
+0xFFFF:0:0x0xFFFF
+0xFFFFFF:0:0x0xFFFFFF
+0xFFFFFFFF:0:0x0xFFFFFFFF
+0xFFFFFFFFFF:0:0x0xFFFFFFFFFF
+0xFFFFFFFFFFFF:0:0x0xFFFFFFFFFFFF
+0xF0F0:0xF0F0:0
+0x0F0F:0x0F0F:0
+0xF0F0:0x0F0F:0x0xFFFF
+0xF0F0F0:0xF0F0F0:0
+0x0F0F0F:0x0F0F0F:0
+0x0F0F0F:0xF0F0F0:0x0xFFFFFF
+0xF0F0F0F0:0xF0F0F0F0:0
+0x0F0F0F0F:0x0F0F0F0F:0
+0x0F0F0F0F:0xF0F0F0F0:0x0xFFFFFFFF
+0xF0F0F0F0F0:0xF0F0F0F0F0:0
+0x0F0F0F0F0F:0x0F0F0F0F0F:0
+0x0F0F0F0F0F:0xF0F0F0F0F0:0x0xFFFFFFFFFF
+0xF0F0F0F0F0F0:0xF0F0F0F0F0F0:0
+0x0F0F0F0F0F0F:0x0F0F0F0F0F0F:0
+0x0F0F0F0F0F0F:0xF0F0F0F0F0F0:0x0xFFFFFFFFFFFF
+&bnot
+abc:NaN
++0:-1
++8:-9
++281474976710656:-281474976710657
+-1:0
+-2:1
+-12:11
+&digit
+0:0:0
+12:0:2
+12:1:1
+123:0:3
+123:1:2
+123:2:1
+123:-1:1
+123:-2:2
+123:-3:3
+123456:0:6
+123456:1:5
+123456:2:4
+123456:3:3
+123456:4:2
+123456:5:1
+123456:-1:1
+123456:-2:2
+123456:-3:3
+100000:-3:0
+100000:0:0
+100000:1:0
+&mantissa
+abc:NaN
+1e4:1
+2e0:2
+123:123
+-1:-1
+-2:-2
++inf:inf
+-inf:-inf
+&exponent
+abc:NaN
+1e4:4
+2e0:0
+123:0
+-1:0
+-2:0
+0:1
++inf:inf
+-inf:inf
+&parts
+abc:NaN,NaN
+1e4:1,4
+2e0:2,0
+123:123,0
+-1:-1,0
+-2:-2,0
+0:0,1
++inf:inf,inf
+-inf:-inf,inf
+&bfac
+-1:NaN
+NaNfac:NaN
++inf:inf
+-inf:NaN
+0:1
+1:1
+2:2
+3:6
+4:24
+5:120
+6:720
+7:5040
+8:40320
+9:362880
+10:3628800
+11:39916800
+12:479001600
+20:2432902008176640000
+22:1124000727777607680000
+69:171122452428141311372468338881272839092270544893520369393648040923257279754140647424000000000000000
+&bpow
+abc:12:NaN
+12:abc:NaN
+0:0:1
+0:1:0
+0:2:0
+0:-1:inf
+0:-2:inf
+1:0:1
+1:1:1
+1:2:1
+1:3:1
+1:-1:1
+1:-2:1
+1:-3:1
+2:0:1
+2:1:2
+2:2:4
+2:3:8
+3:3:27
+-2:2:4
+-2:3:-8
+-2:4:16
+-2:5:-32
+2:-1:NaN
+-2:-1:NaN
+2:-2:NaN
+-2:-2:NaN
+# inf tests
++inf:1234500012:inf
+-inf:1234500012:inf
+-inf:1234500013:-inf
++inf:-12345000123:inf
+-inf:-12345000123:-inf
+#  -inf * -inf = inf
+-inf:2:inf
+-inf:0:NaN
+-inf:-1:0
+-inf:inf:NaN
+2:inf:inf
+2:-inf:0
+0:inf:0
+0:-inf:inf
+-1:-inf:NaN
+-1:inf:NaN
+-2:inf:NaN
+-2:-inf:0
+NaN:inf:NaN
+NaN:-inf:NaN
+-inf:NaN:NaN
+inf:NaN:NaN
+inf:-inf:NaN
+1:inf:1
+1:-inf:1
+# 1 ** -x => 1 / (1 ** x)
+-1:0:1
+-2:0:1
+-1:1:-1
+-1:2:1
+-1:3:-1
+-1:4:1
+-1:5:-1
+-1:-1:-1
+-1:-2:1
+-1:-3:-1
+-1:-4:1
+10:2:100
+10:3:1000
+10:4:10000
+10:5:100000
+10:6:1000000
+10:7:10000000
+10:8:100000000
+10:9:1000000000
+10:20:100000000000000000000
+123456:2:15241383936
+-2:2:4
+-2:3:-8
+-2:4:16
+-2:5:-32
+-3:2:9
+-3:3:-27
+-3:4:81
+-3:5:-243
+&length
+100:3
+10:2
+1:1
+0:1
+12345:5
+10000000000000000:17
+-123:3
+215960156869840440586892398248:30
+&broot
+# sqrt()
++0:2:0
++1:2:1
+-1:2:NaN
+# -$x ** (1/2) => -$y, but not in froot()
+-123:2:NaN
++inf:2:inf
+-inf:2:NaN
+2:2:1
+-2:2:NaN
+4:2:2
+9:2:3
+16:2:4
+100:2:10
+123:2:11
+15241:2:123
+144:2:12
+12:2:3
+0.49:2:0
+0.0049:2:0
+# invalid ones
+1:NaN:NaN
+-1:NaN:NaN
+0:NaN:NaN
+-inf:NaN:NaN
++inf:NaN:NaN
+NaN:0:NaN
+NaN:2:NaN
+NaN:inf:NaN
+NaN:inf:NaN
+12:-inf:NaN
+12:inf:NaN
++0:0:NaN
++1:0:NaN
+-1:0:NaN
+-2:0:NaN
+-123.45:0:NaN
++inf:0:NaN
+12:1:12
+-12:1:NaN
+8:-1:NaN
+-8:-1:NaN
+# cubic root
+8:3:2
+-8:3:NaN
+# fourths root
+16:4:2
+81:4:3
+# 2 ** 64
+18446744073709551616:4:65536
+18446744073709551616:8:256
+18446744073709551616:16:16
+18446744073709551616:32:4
+18446744073709551616:64:2
+18446744073709551616:128:1
+# 213 ** 15
+84274086103068221283760416414557757:15:213
+# see t/bigroot.t for more tests
+&bsqrt
+145:12
+144:12
+143:11
+16:4
+170:13
+169:13
+168:12
+4:2
+3:1
+2:1
+9:3
+12:3
+256:16
+100000000:10000
+4000000000000:2000000
+152399026:12345
+152399025:12345
+152399024:12344
+# 2 ** 64 => 2 ** 32
+18446744073709551616:4294967296
+84274086103068221283760416414557757:290299993288095377
+1:1
+0:0
+-2:NaN
+-123:NaN
+Nan:NaN
++inf:inf
+-inf:NaN
+# see t/biglog.t for more tests
+&bexp
+NaN:NaN
+inf:inf
+1:2
+2:7
+&batan2
+NaN:1:10:NaN
+NaN:NaN:10:NaN
+1:NaN:10:NaN
+inf:1:14:1
+-inf:1:14:-1
+0:-inf:14:3
+-1:-inf:14:-3
+1:-inf:14:3
+0:inf:14:0
+inf:-inf:14:2
+-inf:-inf:14:-2
+# +- 0.78....
+inf:+inf:14:0
+-inf:+inf:14:0
+1:5:13:0
+1:5:14:0
+0:0:10:0
+0:1:14:0
+0:2:14:0
+1:0:14:1
+5:0:14:1
+-1:0:11:-1
+-2:0:77:-1
+2:0:77:1
+-1:5:14:0
+1:5:14:0
+-1:8:14:0
+1:8:14:0
+-1:1:14:0
+&bpi
+77:3
++0:3
+11:3
+# see t/bignok.t for more tests
+&bnok
++inf:10:inf
+NaN:NaN:NaN
+NaN:1:NaN
+1:NaN:NaN
+1:1:1
+# k > n
+1:2:0
+2:3:0
+# k < 0
+1:-2:0
+# 7 over 3 = 35
+7:3:35
+7:6:1
+100:90:17310309456440
+100:95:75287520
+&bround
+$round_mode('trunc')
+0:12:0
+NaNbround:12:NaN
++inf:12:inf
+-inf:12:-inf
+1234:0:1234
+1234:2:1200
+123456:4:123400
+123456:5:123450
+123456:6:123456
++10123456789:5:10123000000
+-10123456789:5:-10123000000
++10123456789:9:10123456700
+-10123456789:9:-10123456700
++101234500:6:101234000
+-101234500:6:-101234000
+#+101234500:-4:101234000
+#-101234500:-4:-101234000
+$round_mode('zero')
++20123456789:5:20123000000
+-20123456789:5:-20123000000
++20123456789:9:20123456800
+-20123456789:9:-20123456800
++201234500:6:201234000
+-201234500:6:-201234000
+#+201234500:-4:201234000
+#-201234500:-4:-201234000
++12345000:4:12340000
+-12345000:4:-12340000
+$round_mode('+inf')
++30123456789:5:30123000000
+-30123456789:5:-30123000000
++30123456789:9:30123456800
+-30123456789:9:-30123456800
++301234500:6:301235000
+-301234500:6:-301234000
+#+301234500:-4:301235000
+#-301234500:-4:-301234000
++12345000:4:12350000
+-12345000:4:-12340000
+$round_mode('-inf')
++40123456789:5:40123000000
+-40123456789:5:-40123000000
++40123456789:9:40123456800
+-40123456789:9:-40123456800
++401234500:6:401234000
++401234500:6:401234000
+#-401234500:-4:-401235000
+#-401234500:-4:-401235000
++12345000:4:12340000
+-12345000:4:-12350000
+$round_mode('odd')
++50123456789:5:50123000000
+-50123456789:5:-50123000000
++50123456789:9:50123456800
+-50123456789:9:-50123456800
++501234500:6:501235000
+-501234500:6:-501235000
+#+501234500:-4:501235000
+#-501234500:-4:-501235000
++12345000:4:12350000
+-12345000:4:-12350000
+$round_mode('even')
++60123456789:5:60123000000
+-60123456789:5:-60123000000
++60123456789:9:60123456800
+-60123456789:9:-60123456800
++601234500:6:601234000
+-601234500:6:-601234000
+#+601234500:-4:601234000
+#-601234500:-4:-601234000
+#-601234500:-9:0
+#-501234500:-9:0
+#-601234500:-8:0
+#-501234500:-8:0
++1234567:7:1234567
++1234567:6:1234570
++12345000:4:12340000
+-12345000:4:-12340000
+$round_mode('common')
++60123456789:5:60123000000
++60123199999:5:60123000000
++60123299999:5:60123000000
++60123399999:5:60123000000
++60123499999:5:60123000000
++60123500000:5:60124000000
++60123600000:5:60124000000
++60123700000:5:60124000000
++60123800000:5:60124000000
++60123900000:5:60124000000
+-60123456789:5:-60123000000
+-60123199999:5:-60123000000
+-60123299999:5:-60123000000
+-60123399999:5:-60123000000
+-60123499999:5:-60123000000
+-60123500000:5:-60124000000
+-60123600000:5:-60124000000
+-60123700000:5:-60124000000
+-60123800000:5:-60124000000
+-60123900000:5:-60124000000
+&is_zero
+0:1
+NaNzero:0
++inf:0
+-inf:0
+123:0
+-1:0
+1:0
+&is_one
+0:0
+NaNone:0
++inf:0
+-inf:0
+1:1
+2:0
+-1:0
+-2:0
+# floor and ceil tests are pretty pointless in integer space...but play safe
+&bfloor
+0:0
+NaNfloor:NaN
++inf:inf
+-inf:-inf
+-1:-1
+-2:-2
+2:2
+3:3
+abc:NaN
+&bceil
+NaNceil:NaN
++inf:inf
+-inf:-inf
+0:0
+-1:-1
+-2:-2
+2:2
+3:3
+abc:NaN
+&as_hex
+128:0x80
+-128:-0x80
+0:0x0
+-0:0x0
+1:0x1
+0x123456789123456789:0x123456789123456789
++inf:inf
+-inf:-inf
+NaNas_hex:NaN
+&as_bin
+128:0b10000000
+-128:-0b10000000
+0:0b0
+-0:0b0
+1:0b1
+0b1010111101010101010110110110110110101:0b1010111101010101010110110110110110101
+0x123456789123456789:0b100100011010001010110011110001001000100100011010001010110011110001001
++inf:inf
+-inf:-inf
+NaNas_bin:NaN
diff --git a/dist/Math-BigInt/t/bigintpm.t b/dist/Math-BigInt/t/bigintpm.t
new file mode 100644
index 0000000000..b4f5bf2fb1
--- /dev/null
+++ b/dist/Math-BigInt/t/bigintpm.t
@@ -0,0 +1,46 @@
+#!/usr/bin/perl -w
+
+use Test;
+use strict;
+
+BEGIN
+  {
+  $| = 1;
+  unshift @INC, '../lib'; # for running manually
+  my $location = $0; $location =~ s/bigintpm.t//;
+  unshift @INC, $location; # to locate the testing files
+  chdir 't' if -d 't';
+  plan tests => 3273 + 6;
+  }
+
+use Math::BigInt lib => 'Calc';
+
+use vars qw ($scale $class $try $x $y $f @args $ans $ans1 $ans1_str $setup $CL);
+$class = "Math::BigInt";
+$CL = "Math::BigInt::Calc";
+
+#############################################################################
+# from_hex(), from_bin() and from_oct() tests
+
+my $x = Math::BigInt->from_hex('0xcafe');
+ok ($x, "51966", 'from_hex() works');
+ 
+$x = Math::BigInt->from_hex('0xcafebabedead');
+ok ($x, "223195403574957", 'from_hex() works with long numbers');
+ 
+$x = Math::BigInt->from_bin('0b1001');
+ok ($x, "9", 'from_bin() works');
+ 
+$x = Math::BigInt->from_bin('0b1001100110011001100110011001');
+ok ($x, "161061273", 'from_bin() works with big numbers');
+
+$x = Math::BigInt->from_oct('0775');
+ok ($x, "509", 'from_oct() works');
+ 
+$x = Math::BigInt->from_oct('07777777777777711111111222222222');
+ok ($x, "9903520314281112085086151826", 'from_oct() works with big numbers');
+
+#############################################################################
+# all the other tests
+ 
+require 'bigintpm.inc';	# all tests here for sharing
diff --git a/dist/Math-BigInt/t/bigints.t b/dist/Math-BigInt/t/bigints.t
new file mode 100644
index 0000000000..de073e21e5
--- /dev/null
+++ b/dist/Math-BigInt/t/bigints.t
@@ -0,0 +1,123 @@
+#!/usr/bin/perl -w
+
+use strict;
+use Test;
+
+BEGIN 
+  {
+  $| = 1;
+  # to locate the testing files
+  my $location = $0; $location =~ s/bigints.t//i;
+  if ($ENV{PERL_CORE})
+    {
+    @INC = qw(../t/lib);                # testing with the core distribution
+    }
+  unshift @INC, '../lib';       # for testing manually
+  if (-d 't')
+    {
+    chdir 't';
+    require File::Spec;
+    unshift @INC, File::Spec->catdir(File::Spec->updir, $location);
+    }
+  else
+    {
+    unshift @INC, $location;
+    }
+  print "# INC = @INC\n";
+
+  plan tests => 51;
+  }
+
+# testing of Math::BigInt:Scalar (used by the testsuite),
+# primarily for interface/api and not for the math functionality
+
+use Math::BigInt::Scalar;
+
+my $C = 'Math::BigInt::Scalar';	# pass classname to sub's
+
+# _new and _str
+my $x = $C->_new("123"); my $y = $C->_new("321");
+ok (ref($x),'SCALAR'); ok ($C->_str($x),123); ok ($C->_str($y),321);
+
+# _add, _sub, _mul, _div
+
+ok ($C->_str($C->_add($x,$y)),444);
+ok ($C->_str($C->_sub($x,$y)),123);
+ok ($C->_str($C->_mul($x,$y)),39483);
+ok ($C->_str($C->_div($x,$y)),123);
+
+ok ($C->_str($C->_mul($x,$y)),39483);
+ok ($C->_str($x),39483);
+ok ($C->_str($y),321);
+my $z = $C->_new("2");
+ok ($C->_str($C->_add($x,$z)),39485);
+my ($re,$rr) = $C->_div($x,$y);
+
+ok ($C->_str($re),123); ok ($C->_str($rr),2);
+
+# is_zero, _is_one, _one, _zero
+ok ($C->_is_zero($x),0);
+ok ($C->_is_one($x),0);
+
+ok ($C->_is_one($C->_one()),1); ok ($C->_is_one($C->_zero()),0);
+ok ($C->_is_zero($C->_zero()),1); ok ($C->_is_zero($C->_one()),0);
+
+# is_odd, is_even
+ok ($C->_is_odd($C->_one()),1); ok ($C->_is_odd($C->_zero()),0);
+ok ($C->_is_even($C->_one()),0); ok ($C->_is_even($C->_zero()),1);
+
+# _digit
+$x = $C->_new("123456789");
+ok ($C->_digit($x,0),9);
+ok ($C->_digit($x,1),8);
+ok ($C->_digit($x,2),7);
+ok ($C->_digit($x,-1),1);
+ok ($C->_digit($x,-2),2);
+ok ($C->_digit($x,-3),3);
+
+# _copy
+$x = $C->_new("12356");
+ok ($C->_str($C->_copy($x)),12356);
+
+# _acmp
+$x = $C->_new("123456789");
+$y = $C->_new("987654321");
+ok ($C->_acmp($x,$y),-1);
+ok ($C->_acmp($y,$x),1);
+ok ($C->_acmp($x,$x),0);
+ok ($C->_acmp($y,$y),0);
+
+# _div
+$x = $C->_new("3333"); $y = $C->_new("1111");
+ok ($C->_str( scalar $C->_div($x,$y)),3);
+$x = $C->_new("33333"); $y = $C->_new("1111"); ($x,$y) = $C->_div($x,$y);
+ok ($C->_str($x),30); ok ($C->_str($y),3);
+$x = $C->_new("123"); $y = $C->_new("1111"); 
+($x,$y) = $C->_div($x,$y); ok ($C->_str($x),0); ok ($C->_str($y),123);
+
+# _num
+$x = $C->_new("12345"); $x = $C->_num($x); ok (ref($x)||'',''); ok ($x,12345);
+
+# _len
+$x = $C->_new("12345"); $x = $C->_len($x); ok (ref($x)||'',''); ok ($x,5);
+
+# _and, _or, _xor
+$x = $C->_new("3"); $y = $C->_new("4"); ok ($C->_str( $C->_or($x,$y)),7);
+$x = $C->_new("1"); $y = $C->_new("4"); ok ($C->_str( $C->_xor($x,$y)),5);
+$x = $C->_new("7"); $y = $C->_new("3"); ok ($C->_str( $C->_and($x,$y)),3);
+
+# _pow
+$x = $C->_new("2"); $y = $C->_new("4"); ok ($C->_str( $C->_pow($x,$y)),16);
+$x = $C->_new("2"); $y = $C->_new("5"); ok ($C->_str( $C->_pow($x,$y)),32);
+$x = $C->_new("3"); $y = $C->_new("3"); ok ($C->_str( $C->_pow($x,$y)),27);
+
+
+# _check
+$x = $C->_new("123456789");
+ok ($C->_check($x),0);
+ok ($C->_check(123),'123 is not a reference');
+
+# done
+
+1;
+
diff --git a/dist/Math-BigInt/t/biglog.t b/dist/Math-BigInt/t/biglog.t
new file mode 100644
index 0000000000..a2a04767f5
--- /dev/null
+++ b/dist/Math-BigInt/t/biglog.t
@@ -0,0 +1,208 @@
+#!/usr/bin/perl -w
+
+# Test blog function (and bpow, since it uses blog), as well as bexp().
+
+# It is too slow to be simple included in bigfltpm.inc, where it would get
+# executed 3 times. One time would be under BareCalc, which shouldn't make any
+# difference since there is no CALC->_log() function, and one time under a
+# subclass, which *should* work.
+
+# But it is better to test the numerical functionality, instead of not testing
+# it at all (which did lead to wrong answers for 0 < $x < 1 in blog() in
+# versions up to v1.63, and for bsqrt($x) when $x << 1 for instance).
+
+use Test::More;
+use strict;
+
+BEGIN
+  {
+  $| = 1;
+  # to locate the testing files
+  my $location = $0; $location =~ s/biglog.t//i;
+  unshift @INC, '../lib';
+  if (-d 't')
+    {
+    chdir 't';
+    require File::Spec;
+    unshift @INC, File::Spec->catdir(File::Spec->updir, $location);
+    }
+  else
+    {
+    unshift @INC, $location;
+    }
+  print "# INC = @INC\n";
+
+  plan tests => 70;
+  }
+
+use Math::BigFloat;
+use Math::BigInt;
+
+my $cl = "Math::BigInt";
+
+#############################################################################
+# test log($n) in BigInt (broken until 1.80)
+
+is ($cl->new(2)->blog(), '0', "blog(2)");
+is ($cl->new(288)->blog(), '5',"blog(288)");
+is ($cl->new(2000)->blog(), '7', "blog(2000)");
+
+#############################################################################
+# test exp($n) in BigInt
+
+is ($cl->new(1)->bexp(), '2', "bexp(1)");
+is ($cl->new(2)->bexp(), '7',"bexp(2)");
+is ($cl->new(3)->bexp(), '20', "bexp(3)");
+
+#############################################################################
+#############################################################################
+# BigFloat tests
+
+#############################################################################
+# test log(2, N) where N > 67 (broken until 1.82)
+
+$cl = "Math::BigFloat";
+
+# These tests can take quite a while, but are nec. Maybe protect them with
+# some alarm()?
+
+# this triggers the calculation and caching of ln(2):
+ok ($cl->new(5)->blog(undef,71), 
+'1.6094379124341003746007593332261876395256013542685177219126478914741790');
+
+# if the cache was correct, we should get this result, fast:
+ok ($cl->new(2)->blog(undef,71), 
+'0.69314718055994530941723212145817656807550013436025525412068000949339362');
+
+ok ($cl->new(10)->blog(undef,71), 
+'2.3025850929940456840179914546843642076011014886287729760333279009675726');
+
+ok ($cl->new(21)->blog(undef,71), 
+'3.0445224377234229965005979803657054342845752874046106401940844835750742');
+
+#############################################################################
+
+# These tests are now really fast, since they collapse to blog(10), basically
+# Don't attempt to run them with older versions. You are warned.
+
+# $x < 0 => NaN
+ok ($cl->new(-2)->blog(), 'NaN');
+ok ($cl->new(-1)->blog(), 'NaN');
+ok ($cl->new(-10)->blog(), 'NaN');
+ok ($cl->new(-2,2)->blog(), 'NaN');
+
+my $ten = $cl->new(10)->blog();
+
+# 10 is cached (up to 75 digits)
+ok ($cl->new(10)->blog(), '2.302585092994045684017991454684364207601');
+
+# 0.1 is using the cached value for log(10), too
+
+ok ($cl->new(0.1)->blog(), -$ten);
+ok ($cl->new(0.01)->blog(), -$ten * 2);
+ok ($cl->new(0.001)->blog(), -$ten * 3);
+ok ($cl->new(0.0001)->blog(), -$ten * 4);
+
+# also cached
+ok ($cl->new(2)->blog(), '0.6931471805599453094172321214581765680755');
+ok ($cl->new(4)->blog(), $cl->new(2)->blog * 2);
+
+# These are still slow, so do them only to 10 digits
+
+ok ($cl->new('0.2')->blog(undef,10), '-1.609437912');
+ok ($cl->new('0.3')->blog(undef,10), '-1.203972804');
+ok ($cl->new('0.4')->blog(undef,10), '-0.9162907319');
+ok ($cl->new('0.5')->blog(undef,10), '-0.6931471806');
+ok ($cl->new('0.6')->blog(undef,10), '-0.5108256238');
+ok ($cl->new('0.7')->blog(undef,10), '-0.3566749439');
+ok ($cl->new('0.8')->blog(undef,10), '-0.2231435513');
+ok ($cl->new('0.9')->blog(undef,10), '-0.1053605157');
+
+ok ($cl->new('9')->blog(undef,10), '2.197224577');
+
+ok ($cl->new('10')->blog(10,10),   '1.000000000');
+ok ($cl->new('20')->blog(20,10),   '1.000000000');
+ok ($cl->new('100')->blog(100,10), '1.000000000');
+
+ok ($cl->new('100')->blog(10,10),  '2.000000000');	# 10 ** 2 == 100
+ok ($cl->new('400')->blog(20,10),  '2.000000000');	# 20 ** 2 == 400
+
+ok ($cl->new('4')->blog(2,10),  '2.000000000');		# 2 ** 2 == 4
+ok ($cl->new('16')->blog(2,10), '4.000000000');		# 2 ** 4 == 16
+
+ok ($cl->new('1.2')->bpow('0.3',10),  '1.056219968');	
+ok ($cl->new('10')->bpow('0.6',10),   '3.981071706');
+
+# blog should handle bigint input
+is (Math::BigFloat::blog(Math::BigInt->new(100),10), 2, "blog(100)");
+
+#############################################################################
+# some integer results
+is ($cl->new(2)->bpow(32)->blog(2),  '32', "2 ** 32");
+is ($cl->new(3)->bpow(32)->blog(3),  '32', "3 ** 32");
+is ($cl->new(2)->bpow(65)->blog(2),  '65', "2 ** 65");
+
+my $x = Math::BigInt->new( '777' ) ** 256;
+my $base = Math::BigInt->new( '12345678901234' );
+is ($x->copy()->blog($base), 56, 'blog(777**256, 12345678901234)');
+
+$x = Math::BigInt->new( '777' ) ** 777;
+$base = Math::BigInt->new( '777' );
+is ($x->copy()->blog($base), 777, 'blog(777**777, 777)');
+
+#############################################################################
+# test for bug in bsqrt() not taking negative _e into account
+test_bpow ('200','0.5',10,      '14.14213562');
+test_bpow ('20','0.5',10,       '4.472135955');
+test_bpow ('2','0.5',10,        '1.414213562');
+test_bpow ('0.2','0.5',10,      '0.4472135955');
+test_bpow ('0.02','0.5',10,     '0.1414213562');
+test_bpow ('0.49','0.5',undef , '0.7');
+test_bpow ('0.49','0.5',10 ,    '0.7000000000');
+test_bpow ('0.002','0.5',10,    '0.04472135955');
+test_bpow ('0.0002','0.5',10,   '0.01414213562');
+test_bpow ('0.0049','0.5',undef,'0.07');
+test_bpow ('0.0049','0.5',10 ,  '0.07000000000');
+test_bpow ('0.000002','0.5',10, '0.001414213562');
+test_bpow ('0.021','0.5',10,    '0.1449137675');
+test_bpow ('1.2','0.5',10,      '1.095445115');
+test_bpow ('1.23','0.5',10,     '1.109053651');
+test_bpow ('12.3','0.5',10,     '3.507135583');
+
+test_bpow ('9.9','0.5',10,        '3.146426545');
+test_bpow ('9.86902225','0.5',10, '3.141500000');
+test_bpow ('9.86902225','0.5',undef, '3.1415');
+
+test_bpow ('0.2','0.41',10,   '0.5169187652');
+
+#############################################################################
+# test bexp() with cached results
+
+is ($cl->new(1)->bexp(), '2.718281828459045235360287471352662497757', 'bexp(1)');
+is ($cl->new(2)->bexp(40), $cl->new(1)->bexp(45)->bpow(2,40), 'bexp(2)'); 
+
+is ($cl->new("12.5")->bexp(61), $cl->new(1)->bexp(65)->bpow(12.5,61), 'bexp(12.5)'); 
+
+#############################################################################
+# test bexp() with big values (non-cached)
+
+is ($cl->new(1)->bexp(100), 
+  '2.718281828459045235360287471352662497757247093699959574966967627724076630353547594571382178525166427',
+ 'bexp(100)');
+
+is ($cl->new("12.5")->bexp(91), $cl->new(1)->bexp(95)->bpow(12.5,91), 
+  'bexp(12.5) to 91 digits'); 
+
+# all done
+1;
+
+#############################################################################
+sub test_bpow
+  {
+  my ($x,$y,$scale,$result) = @_;
+
+  print "# Tried: $x->bpow($y,$scale);\n"
+   unless ok ($cl->new($x)->bpow($y,$scale),$result);
+  }
+
+
diff --git a/dist/Math-BigInt/t/bigroot.t b/dist/Math-BigInt/t/bigroot.t
new file mode 100644
index 0000000000..11d99d2dca
--- /dev/null
+++ b/dist/Math-BigInt/t/bigroot.t
@@ -0,0 +1,64 @@
+#!/usr/bin/perl -w
+
+# Test broot function (and bsqrt() function, since it is used by broot()).
+
+# It is too slow to be simple included in bigfltpm.inc, where it would get
+# executed 3 times.
+
+# But it is better to test the numerical functionality, instead of not testing
+# it at all.
+
+use Test::More;
+use strict;
+
+BEGIN
+  {
+  $| = 1;
+  # to locate the testing files
+  my $location = $0; $location =~ s/bigroot.t//i;
+  unshift @INC, '../lib';
+  if (-d 't')
+    {
+    chdir 't';
+    require File::Spec;
+    unshift @INC, File::Spec->catdir(File::Spec->updir, $location);
+    }
+  else
+    {
+    unshift @INC, $location;
+    }
+  print "# INC = @INC\n";
+
+  plan tests => 4 * 2;
+  }
+
+use Math::BigFloat;
+use Math::BigInt;
+
+my $cl = "Math::BigFloat";
+my $c = "Math::BigInt";
+
+# 2 ** 240 = 
+# 1766847064778384329583297500742918515827483896875618958121606201292619776
+
+# takes way too long
+#test_broot ('2','240', 8, undef,   '1073741824');
+#test_broot ('2','240', 9, undef,   '106528681.3099908308759836475139583940127');
+#test_broot ('2','120', 9, undef,   '10321.27324073880096577298929482324664787');
+#test_broot ('2','120', 17, undef,   '133.3268493632747279600707813049418888729');
+
+test_broot ('2','120', 8, undef,   '32768');
+test_broot ('2','60', 8, undef,   '181.0193359837561662466161566988413540569');
+test_broot ('2','60', 9, undef,   '101.5936673259647663841091609134277286651');
+test_broot ('2','60', 17, undef,   '11.54672461623965153271017217302844672562');
+
+sub test_broot
+  {
+  my ($x,$n,$y,$scale,$result) = @_;
+
+  my $s = $scale || 'undef';
+  is ($cl->new($x)->bpow($n)->broot($y,$scale),$result, "Try: $cl $x->bpow($n)->broot($y,$s) == $result");
+  $result =~ s/\..*//;
+  is ($c->new($x)->bpow($n)->broot($y,$scale),$result, "Try: $c $x->bpow($n)->broot($y,$s) == $result");
+  }
+
diff --git a/dist/Math-BigInt/t/calling.t b/dist/Math-BigInt/t/calling.t
new file mode 100644
index 0000000000..30a9862a0e
--- /dev/null
+++ b/dist/Math-BigInt/t/calling.t
@@ -0,0 +1,168 @@
+#!/usr/bin/perl -w
+
+# test calling conventions, and :constant overloading
+
+use strict;
+use Test;
+
+BEGIN 
+  {
+  $| = 1;
+  # to locate the testing files
+  my $location = $0; $location =~ s/calling.t//i;
+  unshift @INC, '../lib';
+  if (-d 't')
+    {
+    chdir 't';
+    require File::Spec;
+    unshift @INC, File::Spec->catdir(File::Spec->updir, $location);
+    }
+  else
+    {
+    unshift @INC, $location;
+    }
+  print "# INC = @INC\n";
+  my $tests = 160;
+  plan tests => $tests;
+  }
+
+package Math::BigInt::Test;
+
+use Math::BigInt;
+use vars qw/@ISA/;
+@ISA = qw/Math::BigInt/;		# child of MBI
+use overload;
+
+package Math::BigFloat::Test;
+
+use Math::BigFloat;
+use vars qw/@ISA/;
+@ISA = qw/Math::BigFloat/;		# child of MBI
+use overload;
+
+package main;
+
+use Math::BigInt try => 'Calc';
+use Math::BigFloat;
+
+my ($x,$y,$z,$u);
+my $version = '1.76';	# adjust manually to match latest release
+
+###############################################################################
+# check whether op's accept normal strings, even when inherited by subclasses
+
+# do one positive and one negative test to avoid false positives by "accident"
+
+my ($func,@args,$ans,$rc,$class,$try);
+while (<DATA>)
+  {
+  $_ =~ s/[\n\r]//g;	# remove newlines
+  next if /^#/; # skip comments
+  if (s/^&//)
+    {
+    $func = $_;
+    }
+  else
+    {
+    @args = split(/:/,$_,99);
+    $ans = pop @args;
+    foreach $class (qw/
+      Math::BigInt Math::BigFloat Math::BigInt::Test Math::BigFloat::Test/)
+      {
+      $try = "'$args[0]'"; 			# quote it
+      $try = $args[0] if $args[0] =~ /'/;	# already quoted
+      $try = '' if $args[0] eq '';		# undef, no argument
+      $try = "$class\->$func($try);";
+      $rc = eval $try;
+      print "# Tried: '$try'\n" if !ok ($rc, $ans);
+      }
+    } 
+
+  }
+
+$class = 'Math::BigInt';
+
+# XXX TODO this test does not work/fail.
+# test whether use Math::BigInt qw/version/ works
+#$try = "use $class ($version.'1');";
+#$try .= ' $x = $class->new(123); $x = "$x";';
+#eval $try;
+#ok_undef ( $x );               # should result in error!
+
+# test whether fallback to calc works
+$try = "use $class ($version,'try','foo, bar , ');";
+$try .= "$class\->config()->{lib};";
+$ans = eval $try;
+ok ( $ans =~ /^Math::BigInt::(Fast)?Calc\z/, 1);
+
+# test whether constant works or not, also test for qw($version)
+# bgcd() is present in subclass, too
+$try = "use Math::BigInt ($version,'bgcd',':constant');";
+$try .= ' $x = 2**150; bgcd($x); $x = "$x";';
+$ans = eval $try;
+ok ( $ans, "1427247692705959881058285969449495136382746624");
+
+# test wether Math::BigInt::Scalar via use works (w/ dff. spellings of calc)
+$try = "use $class ($version,'lib','Scalar');";
+$try .= ' $x = 2**10; $x = "$x";';
+$ans = eval $try; ok ( $ans, "1024");
+$try = "use $class ($version,'lib','$class\::Scalar');";
+$try .= ' $x = 2**10; $x = "$x";';
+$ans = eval $try; ok ( $ans, "1024");
+
+# all done
+
+__END__
+&is_zero
+1:0
+0:1
+&is_one
+1:1
+0:0
+&is_positive
+1:1
+-1:0
+&is_negative
+1:0
+-1:1
+&is_nan
+abc:1
+1:0
+&is_inf
+inf:1
+0:0
+&bstr
+5:5
+10:10
+-10:-10
+abc:NaN
+'+inf':inf
+'-inf':-inf
+&bsstr
+1:1e+0
+0:0e+1
+2:2e+0
+200:2e+2
+-5:-5e+0
+-100:-1e+2
+abc:NaN
+'+inf':inf
+&babs
+-1:1
+1:1
+&bnot
+-2:1
+1:-2
+&bzero
+:0
+&bnan
+:NaN
+abc:NaN
+&bone
+:1
+'+':1
+'-':-1
+&binf
+:inf
+'+':inf
+'-':-inf
diff --git a/dist/Math-BigInt/t/config.t b/dist/Math-BigInt/t/config.t
new file mode 100644
index 0000000000..3bc9d2efee
--- /dev/null
+++ b/dist/Math-BigInt/t/config.t
@@ -0,0 +1,136 @@
+#!/usr/bin/perl -w
+
+use strict;
+use Test::More;
+
+BEGIN
+  {
+  $| = 1;
+  chdir 't' if -d 't';
+  unshift @INC, '../lib'; # for running manually
+  plan tests => 55;
+  } 
+
+# test whether Math::BigInt->config() and Math::BigFloat->config() works
+
+use Math::BigInt lib => 'Calc';
+use Math::BigFloat;
+
+my $mbi = 'Math::BigInt'; my $mbf = 'Math::BigFloat';
+
+##############################################################################
+# BigInt
+
+ok ($mbi->can('config'));
+
+my $cfg = $mbi->config();
+
+ok (ref($cfg),'HASH');
+
+is ($cfg->{lib},'Math::BigInt::Calc', 'lib');
+is ($cfg->{lib_version}, $Math::BigInt::Calc::VERSION, 'lib_version');
+is ($cfg->{class},$mbi,'class');
+is ($cfg->{upgrade}||'','', 'upgrade');
+is ($cfg->{div_scale},40, 'div_Scale');
+
+is ($cfg->{precision}||0,0, 'precision');	# should test for undef
+is ($cfg->{accuracy}||0,0,'accuracy');
+is ($cfg->{round_mode},'even','round_mode');
+
+is ($cfg->{trap_nan},0, 'trap_nan');
+is ($cfg->{trap_inf},0, 'trap_inf');
+
+is ($mbi->config('lib'), 'Math::BigInt::Calc', 'config("lib")');
+
+# can set via hash ref?
+$cfg = $mbi->config( { trap_nan => 1 } );
+is ($cfg->{trap_nan},1, 'can set via hash ref');
+
+# reset for later
+$mbi->config( trap_nan => 0 );
+
+##############################################################################
+# BigFloat
+
+ok ($mbf->can('config'));
+
+$cfg = $mbf->config();
+
+ok (ref($cfg),'HASH');
+
+is ($cfg->{lib},'Math::BigInt::Calc', 'lib');
+is ($cfg->{with},'Math::BigInt::Calc', 'with');
+is ($cfg->{lib_version}, $Math::BigInt::Calc::VERSION, 'lib_version');
+is ($cfg->{class},$mbf,'class');
+is ($cfg->{upgrade}||'','', 'upgrade');
+is ($cfg->{div_scale},40, 'div_Scale');
+
+is ($cfg->{precision}||0,0, 'precision');	# should test for undef
+is ($cfg->{accuracy}||0,0,'accuracy');
+is ($cfg->{round_mode},'even','round_mode');
+
+is ($cfg->{trap_nan},0, 'trap_nan');
+is ($cfg->{trap_inf},0, 'trap_inf');
+
+is ($mbf->config('lib'), 'Math::BigInt::Calc', 'config("lib")');
+
+# can set via hash ref?
+$cfg = $mbf->config( { trap_nan => 1 } );
+is ($cfg->{trap_nan},1, 'can set via hash ref');
+
+# reset for later
+$mbf->config( trap_nan => 0 );
+
+##############################################################################
+# test setting values
+
+my $test = {
+   trap_nan => 1, 
+   trap_inf => 1, 
+   accuracy => 2,
+   precision => 3,
+   round_mode => 'zero',
+   div_scale => '100',
+   upgrade => 'Math::BigInt::SomeClass',
+   downgrade => 'Math::BigInt::SomeClass',
+  };
+
+my $c;
+
+foreach my $key (keys %$test)
+  {
+  # see if setting in MBI works
+  eval ( "$mbi\->config( $key => '$test->{$key}' );" );
+  $c = $mbi->config(); ok ("$key = $c->{$key}", "$key = $test->{$key}");
+  $c = $mbf->config(); 
+  # see if setting it in MBI leaves MBF alone
+  if (($c->{$key}||0) ne $test->{$key})
+    {
+    is (1,1);
+    }
+  else
+    {
+    is ("$key eq $c->{$key}","$key ne $test->{$key}", "$key");
+    }
+
+  # see if setting in MBF works
+  eval ( "$mbf\->config( $key => '$test->{$key}' );" );
+  $c = $mbf->config(); ok ("$key = $c->{$key}", "$key = $test->{$key}");
+  }
+
+##############################################################################
+# test setting illegal keys (should croak)
+  
+$@ = ""; my $never_reached = 0;
+eval ("$mbi\->config( 'some_garbage' => 1 ); $never_reached = 1;");
+is ($never_reached,0);
+
+$@ = ""; $never_reached = 0;
+eval ("$mbf\->config( 'some_garbage' => 1 ); $never_reached = 1;");
+is ($never_reached,0);
+
+# this does not work. Why?
+#ok ($@ eq "Illegal keys 'some_garbage' passed to Math::BigInt->config() at ./config.t line 104", 1);
+
+# all tests done
+
diff --git a/dist/Math-BigInt/t/const_mbf.t b/dist/Math-BigInt/t/const_mbf.t
new file mode 100644
index 0000000000..aa6f9651c1
--- /dev/null
+++ b/dist/Math-BigInt/t/const_mbf.t
@@ -0,0 +1,35 @@
+#!/usr/bin/perl -w
+
+# test BigFloat constants alone (w/o BigInt loading)
+
+use strict;
+use Test;
+
+BEGIN
+  {
+  $| = 1;
+  # to locate the testing files
+  my $location = $0; $location =~ s/const_mbf.t//i;
+  unshift @INC, qw(../lib);
+  if (-d 't')
+    {
+    chdir 't';
+    require File::Spec;
+    unshift @INC, File::Spec->catdir(File::Spec->updir, $location);
+    }
+  else
+    {
+    unshift @INC, $location;
+    }
+  print "# INC = @INC\n";
+
+  plan tests => 2;
+  } 
+
+use Math::BigFloat ':constant';
+
+ok (1.0 / 3.0, '0.3333333333333333333333333333333333333333');
+
+# BigInt was not loadede with ':constant', so only floats are handled
+ok (ref(2 ** 2),'');
+
diff --git a/dist/Math-BigInt/t/constant.t b/dist/Math-BigInt/t/constant.t
new file mode 100644
index 0000000000..e39312e8dd
--- /dev/null
+++ b/dist/Math-BigInt/t/constant.t
@@ -0,0 +1,57 @@
+#!/usr/bin/perl -w
+
+use strict;
+use Test;
+
+BEGIN
+  {
+  $| = 1;
+  # to locate the testing files
+  my $location = $0; $location =~ s/constant.t//i;
+  unshift @INC, qw(../lib);
+  if (-d 't')
+    {
+    chdir 't';
+    require File::Spec;
+    unshift @INC, File::Spec->catdir(File::Spec->updir, $location);
+    }
+  else
+    {
+    unshift @INC, $location;
+    }
+  print "# INC = @INC\n";
+
+  plan tests => 7;
+  } 
+
+use Math::BigInt ':constant';
+
+ok (2 ** 255,'57896044618658097711785492504343953926634992332820282019728792003956564819968');
+
+{
+  no warnings 'portable';	# protect against "non-portable" warnings
+# hexadecimal constants
+ok (0x123456789012345678901234567890,
+    Math::BigInt->new('0x123456789012345678901234567890'));
+# binary constants
+ok (0b01010100011001010110110001110011010010010110000101101101,
+    Math::BigInt->new(
+     '0b01010100011001010110110001110011010010010110000101101101'));
+}
+
+use Math::BigFloat ':constant';
+ok (1.0 / 3.0, '0.3333333333333333333333333333333333333333');
+
+# stress-test Math::BigFloat->import()
+
+Math::BigFloat->import( qw/:constant/ );
+ok (1,1);
+
+Math::BigFloat->import( qw/:constant upgrade Math::BigRat/ );
+ok (1,1);
+
+Math::BigFloat->import( qw/upgrade Math::BigRat :constant/ );
+ok (1,1);
+
+# all tests done
+
diff --git a/dist/Math-BigInt/t/downgrade.t b/dist/Math-BigInt/t/downgrade.t
new file mode 100644
index 0000000000..25d672c50f
--- /dev/null
+++ b/dist/Math-BigInt/t/downgrade.t
@@ -0,0 +1,55 @@
+#!/usr/bin/perl -w
+
+use Test;
+use strict;
+
+BEGIN
+  {
+  $| = 1;
+  unshift @INC, '../lib'; # for running manually
+  my $location = $0; $location =~ s/downgrade.t//;
+  unshift @INC, $location; # to locate the testing files
+  chdir 't' if -d 't';
+  plan tests => 15;
+  }
+
+use Math::BigInt upgrade => 'Math::BigFloat';
+use Math::BigFloat downgrade => 'Math::BigInt', upgrade => 'Math::BigInt';
+
+use vars qw ($scale $class $try $x $y $f @args $ans $ans1 $ans1_str $setup
+             $ECL $CL);
+$class = "Math::BigInt";
+$CL = "Math::BigInt::Calc";
+$ECL = "Math::BigFloat";
+
+# simplistic test for now 
+ok (Math::BigFloat->downgrade(),'Math::BigInt');
+ok (Math::BigFloat->upgrade(),'Math::BigInt');
+
+# these downgrade
+ok (ref(Math::BigFloat->new('inf')),'Math::BigInt');
+ok (ref(Math::BigFloat->new('-inf')),'Math::BigInt');
+ok (ref(Math::BigFloat->new('NaN')),'Math::BigInt');
+ok (ref(Math::BigFloat->new('0')),'Math::BigInt');
+ok (ref(Math::BigFloat->new('1')),'Math::BigInt');
+ok (ref(Math::BigFloat->new('10')),'Math::BigInt');
+ok (ref(Math::BigFloat->new('-10')),'Math::BigInt');
+ok (ref(Math::BigFloat->new('-10.0E1')),'Math::BigInt');
+
+# bug until v1.67:
+ok (Math::BigFloat->new('0.2E0'), '0.2');
+ok (Math::BigFloat->new('0.2E1'), '2');
+# until v1.67 resulted in 200:
+ok (Math::BigFloat->new('0.2E2'), '20');
+
+# disable, otherwise it screws calculations
+Math::BigFloat->upgrade(undef);
+ok (Math::BigFloat->upgrade()||'','');
+
+Math::BigFloat->div_scale(20); 				# make it a bit faster
+my $x = Math::BigFloat->new(2);				# downgrades
+# the following test upgrade for bsqrt() and also makes new() NOT downgrade
+# for the bpow() side
+ok (Math::BigFloat->bpow('2','0.5'),$x->bsqrt());
+
+#require 'upgrade.inc';	# all tests here for sharing
diff --git a/dist/Math-BigInt/t/inf_nan.t b/dist/Math-BigInt/t/inf_nan.t
new file mode 100644
index 0000000000..9a4cd240ee
--- /dev/null
+++ b/dist/Math-BigInt/t/inf_nan.t
@@ -0,0 +1,351 @@
+#!/usr/bin/perl -w
+
+# test inf/NaN handling all in one place
+# Thanx to Jarkko for the excellent explanations and the tables
+
+use Test::More;
+use strict;
+
+BEGIN
+  {
+  $| = 1;	
+  # to locate the testing files
+  my $location = $0; $location =~ s/inf_nan.t//i;
+  unshift @INC, '../lib';       # for testing manually
+  if (-d 't')
+    {
+    chdir 't';
+    require File::Spec;
+    unshift @INC, File::Spec->catdir(File::Spec->updir, $location);
+    }
+  else
+    {
+    unshift @INC, $location;
+    }
+  print "# INC = @INC\n";
+
+	        # values    groups   operators   classes   tests 
+  plan tests =>   7       * 6      * 5         * 4       * 2 +
+                  7       * 6      * 2         * 4       * 1	  # bmod
+;
+# see bottom:		+ 4 * 10;					  # 4 classes * 10 NaN == NaN tests
+  }
+
+use Math::BigInt;
+use Math::BigFloat;
+use Math::BigInt::Subclass;
+use Math::BigFloat::Subclass;
+
+my @classes = 
+  qw/Math::BigInt Math::BigFloat
+     Math::BigInt::Subclass Math::BigFloat::Subclass
+    /;
+
+my (@args,$x,$y,$z);
+
+# +
+foreach (qw/
+  -inf:-inf:-inf
+  -1:-inf:-inf
+  -0:-inf:-inf
+  0:-inf:-inf
+  1:-inf:-inf
+  inf:-inf:NaN
+  NaN:-inf:NaN
+
+  -inf:-1:-inf
+  -1:-1:-2
+  -0:-1:-1
+  0:-1:-1
+  1:-1:0
+  inf:-1:inf
+  NaN:-1:NaN
+
+  -inf:0:-inf
+  -1:0:-1
+  -0:0:0
+  0:0:0
+  1:0:1
+  inf:0:inf
+  NaN:0:NaN
+
+  -inf:1:-inf
+  -1:1:0
+  -0:1:1
+  0:1:1
+  1:1:2
+  inf:1:inf
+  NaN:1:NaN
+
+  -inf:inf:NaN
+  -1:inf:inf
+  -0:inf:inf
+  0:inf:inf
+  1:inf:inf
+  inf:inf:inf
+  NaN:inf:NaN
+
+  -inf:NaN:NaN
+  -1:NaN:NaN
+  -0:NaN:NaN
+  0:NaN:NaN
+  1:NaN:NaN
+  inf:NaN:NaN
+  NaN:NaN:NaN
+  /)
+  {
+  @args = split /:/,$_;
+  for my $class (@classes)
+    {
+    $x = $class->new($args[0]);
+    $y = $class->new($args[1]);
+    $args[2] = '0' if $args[2] eq '-0';		# BigInt/Float hasn't got -0
+    my $r = $x->badd($y);
+
+    is($x->bstr(),$args[2],"x $class $args[0] + $args[1]");
+    is($x->bstr(),$args[2],"r $class $args[0] + $args[1]");
+    }
+  }
+
+# -
+foreach (qw/
+  -inf:-inf:NaN
+  -1:-inf:inf
+  -0:-inf:inf
+  0:-inf:inf
+  1:-inf:inf
+  inf:-inf:inf
+  NaN:-inf:NaN
+
+  -inf:-1:-inf
+  -1:-1:0
+  -0:-1:1
+  0:-1:1
+  1:-1:2
+  inf:-1:inf
+  NaN:-1:NaN
+
+  -inf:0:-inf
+  -1:0:-1
+  -0:0:-0
+  0:0:0
+  1:0:1
+  inf:0:inf
+  NaN:0:NaN
+
+  -inf:1:-inf
+  -1:1:-2
+  -0:1:-1
+  0:1:-1
+  1:1:0
+  inf:1:inf
+  NaN:1:NaN
+
+  -inf:inf:-inf
+  -1:inf:-inf
+  -0:inf:-inf
+  0:inf:-inf
+  1:inf:-inf
+  inf:inf:NaN
+  NaN:inf:NaN
+
+  -inf:NaN:NaN
+  -1:NaN:NaN
+  -0:NaN:NaN
+  0:NaN:NaN
+  1:NaN:NaN
+  inf:NaN:NaN
+  NaN:NaN:NaN
+  /)
+  {
+  @args = split /:/,$_;
+  for my $class (@classes)
+    {
+    $x = $class->new($args[0]);
+    $y = $class->new($args[1]);
+    $args[2] = '0' if $args[2] eq '-0';		# BigInt/Float hasn't got -0
+    my $r = $x->bsub($y);
+
+    is($x->bstr(),$args[2],"x $class $args[0] - $args[1]");
+    is($r->bstr(),$args[2],"r $class $args[0] - $args[1]");
+    }
+  }
+
+# *
+foreach (qw/
+  -inf:-inf:inf
+  -1:-inf:inf
+  -0:-inf:NaN
+  0:-inf:NaN
+  1:-inf:-inf
+  inf:-inf:-inf
+  NaN:-inf:NaN
+
+  -inf:-1:inf
+  -1:-1:1
+  -0:-1:0
+  0:-1:-0
+  1:-1:-1
+  inf:-1:-inf
+  NaN:-1:NaN
+
+  -inf:0:NaN
+  -1:0:-0
+  -0:0:-0
+  0:0:0
+  1:0:0
+  inf:0:NaN
+  NaN:0:NaN
+
+  -inf:1:-inf
+  -1:1:-1
+  -0:1:-0
+  0:1:0
+  1:1:1
+  inf:1:inf
+  NaN:1:NaN
+
+  -inf:inf:-inf
+  -1:inf:-inf
+  -0:inf:NaN
+  0:inf:NaN
+  1:inf:inf
+  inf:inf:inf
+  NaN:inf:NaN
+
+  -inf:NaN:NaN
+  -1:NaN:NaN
+  -0:NaN:NaN
+  0:NaN:NaN
+  1:NaN:NaN
+  inf:NaN:NaN
+  NaN:NaN:NaN
+  /)
+  {
+  @args = split /:/,$_;
+  for my $class (@classes)
+    {
+    $x = $class->new($args[0]);
+    $y = $class->new($args[1]);
+    $args[2] = '0' if $args[2] eq '-0';		# BigInt/Float hasn't got -0
+    $args[2] = '0' if $args[2] eq '-0';	# BigInt hasn't got -0
+    my $r = $x->bmul($y);
+
+    is($x->bstr(),$args[2],"x $class $args[0] * $args[1]");
+    is($r->bstr(),$args[2],"r $class $args[0] * $args[1]");
+    }
+  }
+
+# /
+foreach (qw/
+  -inf:-inf:NaN
+  -1:-inf:0
+  -0:-inf:0
+  0:-inf:-0
+  1:-inf:-0
+  inf:-inf:NaN
+  NaN:-inf:NaN
+
+  -inf:-1:inf
+  -1:-1:1
+  -0:-1:0
+  0:-1:-0
+  1:-1:-1
+  inf:-1:-inf
+  NaN:-1:NaN
+
+  -inf:0:-inf
+  -1:0:-inf
+  -0:0:NaN
+  0:0:NaN
+  1:0:inf
+  inf:0:inf
+  NaN:0:NaN
+
+  -inf:1:-inf
+  -1:1:-1
+  -0:1:-0
+  0:1:0
+  1:1:1
+  inf:1:inf
+  NaN:1:NaN
+
+  -inf:inf:NaN
+  -1:inf:-0
+  -0:inf:-0
+  0:inf:0
+  1:inf:0
+  inf:inf:NaN
+  NaN:inf:NaN
+
+  -inf:NaN:NaN
+  -1:NaN:NaN
+  -0:NaN:NaN
+  0:NaN:NaN
+  1:NaN:NaN
+  inf:NaN:NaN
+  NaN:NaN:NaN
+  /)
+  {
+  @args = split /:/,$_;
+  for my $class (@classes)
+    {
+    $x = $class->new($args[0]);
+    $y = $class->new($args[1]);
+    $args[2] = '0' if $args[2] eq '-0';		# BigInt/Float hasn't got -0
+
+    my $t = $x->copy();
+    my $tmod = $t->copy();
+
+    # bdiv in scalar context
+    my $r = $x->bdiv($y);
+    is($x->bstr(),$args[2],"x $class $args[0] / $args[1]");
+    is($r->bstr(),$args[2],"r $class $args[0] / $args[1]");
+
+    # bmod and bdiv in list context
+    my ($d,$rem) = $t->bdiv($y);
+
+    # bdiv in list context
+    is($t->bstr(),$args[2],"t $class $args[0] / $args[1]");
+    is($d->bstr(),$args[2],"d $class $args[0] / $args[1]");
+    
+    # bmod
+    my $m = $tmod->bmod($y);
+
+    # bmod() agrees with bdiv?
+    is($m->bstr(),$rem->bstr(),"m $class $args[0] % $args[1]");
+    # bmod() return agrees with set value?
+    is($tmod->bstr(),$m->bstr(),"o $class $args[0] % $args[1]");
+
+    }
+  }
+
+#############################################################################
+# overloaded comparisations
+
+# these are disabled for now, since Perl itself can't seem to make up it's
+# mind what NaN actually is, see [perl #33106].
+
+#
+#foreach my $c (@classes)
+#  {
+#  my $x = $c->bnan();
+#  my $y = $c->bnan();		# test with two different objects, too
+#  my $a = $c->bzero();
+#
+#  is ($x == $y, undef, 'NaN == NaN: undef');
+#  is ($x != $y, 1, 'NaN != NaN: 1');
+#  
+#  is ($x == $x, undef, 'NaN == NaN: undef');
+#  is ($x != $x, 1, 'NaN != NaN: 1');
+#  
+#  is ($a != $x, 1, '0 != NaN: 1');
+#  is ($a == $x, undef, '0 == NaN: undef');
+#
+#  is ($a < $x, undef, '0 < NaN: undef');
+#  is ($a <= $x, undef, '0 <= NaN: undef');
+#  is ($a >= $x, undef, '0 >= NaN: undef');
+#  is ($a > $x, undef, '0 > NaN: undef');
+#  }
+
+# All done.
diff --git a/dist/Math-BigInt/t/isa.t b/dist/Math-BigInt/t/isa.t
new file mode 100644
index 0000000000..3c8aed5e37
--- /dev/null
+++ b/dist/Math-BigInt/t/isa.t
@@ -0,0 +1,54 @@
+#!/usr/bin/perl -w
+
+use Test;
+use strict;
+
+BEGIN
+  {
+  $| = 1;
+  # to locate the testing files
+  my $location = $0; $location =~ s/isa.t//i;
+  unshift @INC, qw(../lib);
+  if (-d 't')
+    {
+    chdir 't';
+    require File::Spec;
+    unshift @INC, File::Spec->catdir(File::Spec->updir, $location);
+    }
+  else
+    {
+    unshift @INC, $location;
+    }
+  print "# INC = @INC\n";
+
+  plan tests => 7;
+  }
+
+use Math::BigInt::Subclass;
+use Math::BigFloat::Subclass;
+use Math::BigInt;
+use Math::BigFloat;
+
+use vars qw ($class $try $x $y $f @args $ans $ans1 $ans1_str $setup $CL);
+$class = "Math::BigInt::Subclass";
+$CL = "Math::BigInt::Calc";
+
+# Check that a subclass is still considered a BigInt
+ok ($class->new(123)->isa('Math::BigInt'),1);
+
+# ditto for plain Math::BigInt
+ok (Math::BigInt->new(123)->isa('Math::BigInt'),1);
+
+# But Math::BigFloats aren't
+ok (Math::BigFloat->new(123)->isa('Math::BigInt') || 0,0);
+
+# see what happens if we feed a Math::BigFloat into new()
+$x = Math::BigInt->new(Math::BigFloat->new(123));
+ok (ref($x),'Math::BigInt');
+ok ($x->isa('Math::BigInt'),1);
+
+# ditto for subclass
+$x = Math::BigInt->new(Math::BigFloat->new(123));
+ok (ref($x),'Math::BigInt');
+ok ($x->isa('Math::BigInt'),1);
+
diff --git a/dist/Math-BigInt/t/lib_load.t b/dist/Math-BigInt/t/lib_load.t
new file mode 100644
index 0000000000..ab3cf2a95e
--- /dev/null
+++ b/dist/Math-BigInt/t/lib_load.t
@@ -0,0 +1,48 @@
+#!/usr/bin/perl -w
+
+use Test::More;
+use strict;
+
+BEGIN
+  {
+  $| = 1;
+  # to locate the testing files
+  my $location = $0; $location =~ s/sub_mbf.t//i;
+  unshift @INC, '../lib';
+  if (-d 't')
+    {
+    chdir 't';
+    require File::Spec;
+    unshift @INC, File::Spec->catdir(File::Spec->updir, $location);
+    }
+  else
+    {
+    unshift @INC, $location;
+    }
+  print "# INC = @INC\n";
+
+  plan tests => 4;
+  }
+
+# first load BigInt with Calc
+use Math::BigInt lib => 'Calc';
+
+# BigFloat will remember that we loaded Calc
+require Math::BigFloat;
+is (Math::BigFloat::config()->{lib}, 'Math::BigInt::Calc', 'BigFloat got Calc');
+
+# now load BigInt again with a different lib
+Math::BigInt->import( lib => 'BareCalc' );
+
+# and finally test that BigFloat knows about BareCalc
+
+is (Math::BigFloat::config()->{lib}, 'Math::BigInt::BareCalc', 'BigFloat was notified');
+
+# See that Math::BigFloat supports "only"
+eval "Math::BigFloat->import('only' => 'Calc')";
+is (Math::BigFloat::config()->{lib}, 'Math::BigInt::Calc', '"only" worked');
+
+# See that Math::BigFloat supports "try"
+eval "Math::BigFloat->import('try' => 'BareCalc')";
+is (Math::BigFloat::config()->{lib}, 'Math::BigInt::BareCalc', '"try" worked');
+
diff --git a/dist/Math-BigInt/t/mbf_ali.t b/dist/Math-BigInt/t/mbf_ali.t
new file mode 100644
index 0000000000..71e4b1383a
--- /dev/null
+++ b/dist/Math-BigInt/t/mbf_ali.t
@@ -0,0 +1,37 @@
+#!/usr/bin/perl -w
+
+# test that the new alias names work
+
+use Test::More;
+use strict;
+
+BEGIN
+  {
+  $| = 1;
+  # to locate the testing files
+  my $location = $0; $location =~ s/mbf_ali.t//i;
+  unshift @INC, qw(../lib);
+  if (-d 't')
+    {
+    chdir 't';
+    require File::Spec;
+    unshift @INC, File::Spec->catdir(File::Spec->updir, $location);
+    }
+  else
+    {
+    unshift @INC, $location;
+    }
+  print "# INC = @INC\n";
+
+  plan tests => 6;
+  }
+
+use Math::BigFloat;
+
+use vars qw/$x $CL/;
+
+$CL = 'Math::BigFloat';
+
+require 'alias.inc';
+
+
diff --git a/dist/Math-BigInt/t/mbi_ali.t b/dist/Math-BigInt/t/mbi_ali.t
new file mode 100644
index 0000000000..921d16fc5f
--- /dev/null
+++ b/dist/Math-BigInt/t/mbi_ali.t
@@ -0,0 +1,37 @@
+#!/usr/bin/perl -w
+
+# test that the new alias names work
+
+use Test::More;
+use strict;
+
+BEGIN
+  {
+  $| = 1;
+  # to locate the testing files
+  my $location = $0; $location =~ s/mbi_ali.t//i;
+  unshift @INC, qw(../lib);
+  if (-d 't')
+    {
+    chdir 't';
+    require File::Spec;
+    unshift @INC, File::Spec->catdir(File::Spec->updir, $location);
+    }
+  else
+    {
+    unshift @INC, $location;
+    }
+  print "# INC = @INC\n";
+
+  plan tests => 6;
+  }
+
+use Math::BigInt;
+
+use vars qw/$x $CL/;
+
+$CL = 'Math::BigInt';
+
+require 'alias.inc';
+
+
diff --git a/dist/Math-BigInt/t/mbi_rand.t b/dist/Math-BigInt/t/mbi_rand.t
new file mode 100644
index 0000000000..e2bf6637de
--- /dev/null
+++ b/dist/Math-BigInt/t/mbi_rand.t
@@ -0,0 +1,93 @@
+#!/usr/bin/perl -w
+
+use Test::More;
+use strict;
+
+my $count;
+  
+BEGIN
+  {
+  $| = 1;
+  if ($^O eq 'os390') { print "1..0\n"; exit(0) } # test takes too long there
+  unshift @INC, '../lib'; # for running manually
+  my $location = $0; $location =~ s/mbi_rand.t//;
+  unshift @INC, $location; # to locate the testing files
+  chdir 't' if -d 't';
+  $count = 128;
+  plan tests => $count*4;
+  }
+
+use Math::BigInt;
+my $c = 'Math::BigInt';
+
+my $length = 128;
+
+# If you get a failure here, please re-run the test with the printed seed
+# value as input "perl t/mbi_rand.t seed" and send me the output
+
+my $seed = ($#ARGV == 0) ? $ARGV[0] : int(rand(1165537));
+print "# seed: $seed\n"; srand($seed);
+
+print "# lib: ", Math::BigInt->config()->{lib},"\n";
+if (Math::BigInt->config()->{lib} =~ /::Calc/)
+  {
+  print "# base len: ", scalar Math::BigInt::Calc->_base_len(),"\n";
+  }
+
+my ($A,$B,$As,$Bs,$ADB,$AMB,$la,$lb);
+my $two = Math::BigInt->new(2);
+for (my $i = 0; $i < $count; $i++)
+  {
+  # length of A and B
+  $la = int(rand($length)+1); $lb = int(rand($length)+1);
+  $As = ''; $Bs = '';
+
+  # we create the numbers from "patterns", e.g. get a random number and a
+  # random count and string them together. This means things like
+  # "100000999999999999911122222222" are much more likely. If we just strung
+  # together digits, we would end up with "1272398823211223" etc. It also means
+  # that we get more frequently equal numbers or other special cases.
+  while (length($As) < $la) { $As .= int(rand(100)) x int(rand(16)); }
+  while (length($Bs) < $lb) { $Bs .= int(rand(100)) x int(rand(16)); }
+
+  $As =~ s/^0+//; $Bs =~ s/^0+//; 
+  $As = $As || '0'; $Bs = $Bs || '0';
+#  print "# As $As\n# Bs $Bs\n";
+  $A = $c->new($As); $B = $c->new($Bs);
+  print "# A $A\n# B $B\n";
+  if ($A->is_zero() || $B->is_zero())
+    {
+    for (1..4) { is (1,1, 'skipped this test'); } next;
+    }
+
+  # check that int(A/B)*B + A % B == A holds for all inputs
+
+  # $X = ($A/$B)*$B + 2 * ($A % $B) - ($A % $B);
+
+  ($ADB,$AMB) = $A->copy()->bdiv($B);
+  print "# ($A / $B, $A % $B ) = $ADB $AMB\n";
+
+  print "# seed $seed, ". join(' ',Math::BigInt::Calc->_base_len()),"\n".
+        "# tried $ADB * $B + $two*$AMB - $AMB\n"
+   unless is ($ADB*$B+$two*$AMB-$AMB,$As, "ADB * B + 2 * AMB - AMB == A");
+  if (is ($ADB*$B/$B,$ADB, "ADB * B / B == ADB"))
+    {
+    print "# seed: $seed, \$ADB * \$B / \$B = ", $ADB * $B / $B, " != $ADB (\$B=$B)\n";
+    if (Math::BigInt->config()->{lib} =~ /::Calc/)
+      {
+      print "# ADB->[-1]: ", $ADB->{value}->[-1], " B->[-1]: ", $B->{value}->[-1],"\n";
+      }
+    }
+  # swap 'em and try this, too
+  # $X = ($B/$A)*$A + $B % $A;
+  ($ADB,$AMB) = $B->copy()->bdiv($A);
+  # print "check: $ADB $AMB";
+  print "# seed $seed, ". join(' ',Math::BigInt::Calc->_base_len()),"\n".
+        "# tried $ADB * $A + $two*$AMB - $AMB\n"
+   unless is ($ADB*$A+$two*$AMB-$AMB,$Bs, "ADB * A + 2 * AMB - AMB == B");
+  print "# +$two * $AMB = ",$ADB * $A + $two * $AMB,"\n";
+  print "# -$AMB = ",$ADB * $A + $two * $AMB - $AMB,"\n";
+  print "# seed $seed, \$ADB * \$A / \$A = ", $ADB * $A / $A, " != $ADB (\$A=$A)\n"
+   unless is ($ADB*$A/$A,$ADB, "ADB * A/A == ADB");
+  }
+
diff --git a/dist/Math-BigInt/t/mbimbf.inc b/dist/Math-BigInt/t/mbimbf.inc
new file mode 100644
index 0000000000..b057eee3ec
--- /dev/null
+++ b/dist/Math-BigInt/t/mbimbf.inc
@@ -0,0 +1,967 @@
+# test rounding, accuracy, precicion and fallback, round_mode and mixing
+# of classes
+
+# Make sure you always quote any bare floating-point values, lest 123.46 will
+# be stringified to 123.4599999999 due to limited float prevision.
+
+use strict;
+my ($x,$y,$z,$u,$rc);
+
+###############################################################################
+# test defaults and set/get
+
+{
+  no strict 'refs';
+  ok_undef (${"$mbi\::accuracy"});
+  ok_undef (${"$mbi\::precision"});
+  ok_undef ($mbi->accuracy());
+  ok_undef ($mbi->precision());
+  ok (${"$mbi\::div_scale"},40);
+  ok (${"$mbi\::round_mode"},'even');
+  ok ($mbi->round_mode(),'even');
+
+  ok_undef (${"$mbf\::accuracy"});
+  ok_undef (${"$mbf\::precision"});
+  ok_undef ($mbf->precision());
+  ok_undef ($mbf->precision());
+  ok (${"$mbf\::div_scale"},40);
+  ok (${"$mbf\::round_mode"},'even');
+  ok ($mbf->round_mode(),'even');
+}
+
+# accessors
+foreach my $class ($mbi,$mbf)
+  {
+  ok_undef ($class->accuracy());
+  ok_undef ($class->precision());
+  ok ($class->round_mode(),'even');
+  ok ($class->div_scale(),40);
+   
+  ok ($class->div_scale(20),20);
+  $class->div_scale(40); ok ($class->div_scale(),40);
+  
+  ok ($class->round_mode('odd'),'odd');
+  $class->round_mode('even'); ok ($class->round_mode(),'even');
+  
+  ok ($class->accuracy(2),2);
+  $class->accuracy(3); ok ($class->accuracy(),3);
+  ok_undef ($class->accuracy(undef));
+
+  ok ($class->precision(2),2);
+  ok ($class->precision(-2),-2);
+  $class->precision(3); ok ($class->precision(),3);
+  ok_undef ($class->precision(undef));
+  }
+
+{
+  no strict 'refs';
+  # accuracy
+  foreach (qw/5 42 -1 0/)
+    {
+    ok (${"$mbf\::accuracy"} = $_,$_);
+    ok (${"$mbi\::accuracy"} = $_,$_);
+    }
+  ok_undef (${"$mbf\::accuracy"} = undef);
+  ok_undef (${"$mbi\::accuracy"} = undef);
+
+  # precision
+  foreach (qw/5 42 -1 0/)
+    {
+    ok (${"$mbf\::precision"} = $_,$_);
+    ok (${"$mbi\::precision"} = $_,$_);
+    }
+  ok_undef (${"$mbf\::precision"} = undef);
+  ok_undef (${"$mbi\::precision"} = undef);
+
+  # fallback
+  foreach (qw/5 42 1/)
+    {
+    ok (${"$mbf\::div_scale"} = $_,$_);
+    ok (${"$mbi\::div_scale"} = $_,$_);
+    }
+  # illegal values are possible for fallback due to no accessor
+
+  # round_mode
+  foreach (qw/odd even zero trunc +inf -inf/)
+    {
+    ok (${"$mbf\::round_mode"} = $_,$_);
+    ok (${"$mbi\::round_mode"} = $_,$_);
+    }
+  ${"$mbf\::round_mode"} = 'zero';
+  ok (${"$mbf\::round_mode"},'zero');
+  ok (${"$mbi\::round_mode"},'-inf');	# from above
+
+  # reset for further tests
+  ${"$mbi\::accuracy"} = undef;
+  ${"$mbi\::precision"} = undef;
+  ${"$mbf\::div_scale"} = 40;
+}
+
+# local copies
+$x = $mbf->new('123.456');
+ok_undef ($x->accuracy());
+ok ($x->accuracy(5),5);
+ok_undef ($x->accuracy(undef),undef);
+ok_undef ($x->precision());
+ok ($x->precision(5),5);
+ok_undef ($x->precision(undef),undef);
+
+{
+  no strict 'refs';
+  # see if MBF changes MBIs values
+  ok (${"$mbi\::accuracy"} = 42,42);
+  ok (${"$mbf\::accuracy"} = 64,64);
+  ok (${"$mbi\::accuracy"},42);		# should be still 42
+  ok (${"$mbf\::accuracy"},64);		# should be now 64
+}
+
+###############################################################################
+# see if creating a number under set A or P will round it
+
+{
+  no strict 'refs';
+  ${"$mbi\::accuracy"} = 4;
+  ${"$mbi\::precision"} = undef;
+
+  ok ($mbi->new(123456),123500);		# with A
+  ${"$mbi\::accuracy"} = undef;
+  ${"$mbi\::precision"} = 3;
+  ok ($mbi->new(123456),123000);		# with P
+
+  ${"$mbf\::accuracy"} = 4;
+  ${"$mbf\::precision"} = undef;
+  ${"$mbi\::precision"} = undef;
+
+  ok ($mbf->new('123.456'),'123.5');	# with A
+  ${"$mbf\::accuracy"} = undef;
+  ${"$mbf\::precision"} = -1;
+  ok ($mbf->new('123.456'),'123.5');	# with P from MBF, not MBI!
+
+  ${"$mbf\::precision"} = undef;		# reset
+}
+
+###############################################################################
+# see if MBI leaves MBF's private parts alone
+
+{
+  no strict 'refs';
+  ${"$mbi\::precision"} = undef; ${"$mbf\::precision"} = undef;
+  ${"$mbi\::accuracy"} = 4; ${"$mbf\::accuracy"} = undef;
+  ok ($mbf->new('123.456'),'123.456');
+  ${"$mbi\::accuracy"} = undef; 		# reset
+}
+
+###############################################################################
+# see if setting accuracy/precision actually rounds the number
+
+$x = $mbf->new('123.456'); $x->accuracy(4);   ok ($x,'123.5');
+$x = $mbf->new('123.456'); $x->precision(-2); ok ($x,'123.46');
+
+$x = $mbi->new(123456);    $x->accuracy(4);   ok ($x,123500);
+$x = $mbi->new(123456);    $x->precision(2);  ok ($x,123500);
+
+###############################################################################
+# test actual rounding via round()
+
+$x = $mbf->new('123.456');
+ok ($x->copy()->round(5),'123.46');
+ok ($x->copy()->round(4),'123.5');
+ok ($x->copy()->round(5,2),'NaN');
+ok ($x->copy()->round(undef,-2),'123.46');
+ok ($x->copy()->round(undef,2),120);
+
+$x = $mbi->new('123');
+ok ($x->round(5,2),'NaN');
+
+$x = $mbf->new('123.45000');
+ok ($x->copy()->round(undef,-1,'odd'),'123.5');
+
+# see if rounding is 'sticky'
+$x = $mbf->new('123.4567');
+$y = $x->copy()->bround();		# no-op since nowhere A or P defined
+
+ok ($y,123.4567);			
+$y = $x->copy()->round(5);
+ok ($y->accuracy(),5);
+ok_undef ($y->precision());		# A has precedence, so P still unset
+$y = $x->copy()->round(undef,2);
+ok ($y->precision(),2);
+ok_undef ($y->accuracy());		# P has precedence, so A still unset
+
+# see if setting A clears P and vice versa
+$x = $mbf->new('123.4567');
+ok ($x,'123.4567');
+ok ($x->accuracy(4),4);
+ok ($x->precision(-2),-2);		# clear A
+ok_undef ($x->accuracy());
+
+$x = $mbf->new('123.4567');
+ok ($x,'123.4567');
+ok ($x->precision(-2),-2);
+ok ($x->accuracy(4),4);			# clear P
+ok_undef ($x->precision());
+
+# does copy work?
+$x = $mbf->new(123.456); $x->accuracy(4); $x->precision(2);
+$z = $x->copy(); ok_undef ($z->accuracy(),undef); ok ($z->precision(),2);
+
+# does $x->bdiv($y,d) work when $d > div_scale?
+$x = $mbf->new('0.008'); $x->accuracy(8);
+
+for my $e ( 4, 8, 16, 32 )
+  {
+  print "# Tried: $x->bdiv(3,$e)\n"
+    unless ok (scalar $x->copy()->bdiv(3,$e), '0.002' . ('6' x ($e-2)) . '7');
+  }
+
+# does accuracy()/precision work on zeros?
+foreach my $c ($mbi,$mbf)
+  {
+  $x = $c->bzero(); $x->accuracy(5); ok ($x->{_a},5);
+  $x = $c->bzero(); $x->precision(5); ok ($x->{_p},5);
+  $x = $c->new(0); $x->accuracy(5); ok ($x->{_a},5);
+  $x = $c->new(0); $x->precision(5); ok ($x->{_p},5);
+
+  $x = $c->bzero(); $x->round(5); ok ($x->{_a},5);
+  $x = $c->bzero(); $x->round(undef,5); ok ($x->{_p},5);
+  $x = $c->new(0); $x->round(5); ok ($x->{_a},5);
+  $x = $c->new(0); $x->round(undef,5); ok ($x->{_p},5);
+
+  # see if trying to increasing A in bzero() doesn't do something
+  $x = $c->bzero(); $x->{_a} = 3; $x->round(5); ok ($x->{_a},3);
+  }
+
+###############################################################################
+# test whether an opp calls objectify properly or not (or at least does what
+# it should do given non-objects, w/ or w/o objectify())
+
+foreach my $c ($mbi,$mbf)
+  {
+#  ${"$c\::precision"} = undef;		# reset
+#  ${"$c\::accuracy"} = undef;		# reset
+
+  ok ($c->new(123)->badd(123),246);
+  ok ($c->badd(123,321),444);
+  ok ($c->badd(123,$c->new(321)),444);
+
+  ok ($c->new(123)->bsub(122),1);
+  ok ($c->bsub(321,123),198);
+  ok ($c->bsub(321,$c->new(123)),198);
+
+  ok ($c->new(123)->bmul(123),15129);
+  ok ($c->bmul(123,123),15129);
+  ok ($c->bmul(123,$c->new(123)),15129);
+
+# ok ($c->new(15129)->bdiv(123),123);
+# ok ($c->bdiv(15129,123),123);
+# ok ($c->bdiv(15129,$c->new(123)),123);
+
+  ok ($c->new(15131)->bmod(123),2);
+  ok ($c->bmod(15131,123),2);
+  ok ($c->bmod(15131,$c->new(123)),2);
+
+  ok ($c->new(2)->bpow(16),65536);
+  ok ($c->bpow(2,16),65536);
+  ok ($c->bpow(2,$c->new(16)),65536);
+
+  ok ($c->new(2**15)->brsft(1),2**14);
+  ok ($c->brsft(2**15,1),2**14);
+  ok ($c->brsft(2**15,$c->new(1)),2**14);
+
+  ok ($c->new(2**13)->blsft(1),2**14);
+  ok ($c->blsft(2**13,1),2**14);
+  ok ($c->blsft(2**13,$c->new(1)),2**14);
+  }
+
+###############################################################################
+# test wether operations round properly afterwards
+# These tests are not complete, since they do not excercise every "return"
+# statement in the op's. But heh, it's better than nothing...
+
+$x = $mbf->new('123.456');
+$y = $mbf->new('654.321');
+$x->{_a} = 5;		# $x->accuracy(5) would round $x straightaway
+$y->{_a} = 4;		# $y->accuracy(4) would round $x straightaway
+
+$z = $x + $y;		ok ($z,'777.8');
+$z = $y - $x;		ok ($z,'530.9');
+$z = $y * $x;		ok ($z,'80780');
+$z = $x ** 2;		ok ($z,'15241');
+$z = $x * $x;		ok ($z,'15241');
+
+# not: $z = -$x;		ok ($z,'-123.46'); ok ($x,'123.456');
+$z = $x->copy(); $z->{_a} = 2; $z = $z / 2; ok ($z,62);
+$x = $mbf->new(123456); $x->{_a} = 4;
+$z = $x->copy; $z++;	ok ($z,123500);
+
+$x = $mbi->new(123456);
+$y = $mbi->new(654321);
+$x->{_a} = 5;		# $x->accuracy(5) would round $x straightaway
+$y->{_a} = 4;		# $y->accuracy(4) would round $x straightaway
+
+$z = $x + $y; 		ok ($z,777800);
+$z = $y - $x; 		ok ($z,530900);
+$z = $y * $x;		ok ($z,80780000000);
+$z = $x ** 2;		ok ($z,15241000000);
+# not yet: $z = -$x;		ok ($z,-123460); ok ($x,123456);
+$z = $x->copy; $z++;	ok ($z,123460);
+$z = $x->copy(); $z->{_a} = 2; $z = $z / 2; ok ($z,62000);
+
+$x = $mbi->new(123400); $x->{_a} = 4;
+ok ($x->bnot(),-123400);			# not -1234001
+
+# both babs() and bneg() don't need to round, since the input will already
+# be rounded (either as $x or via new($string)), and they don't change the
+# value. The two tests below peek at this by using _a (illegally) directly
+$x = $mbi->new(-123401); $x->{_a} = 4; ok ($x->babs(),123401);
+$x = $mbi->new(-123401); $x->{_a} = 4; ok ($x->bneg(),123401);
+
+# test fdiv rounding to A and R (bug in v1.48 and maybe earlier versions)
+$mbf->round_mode('even');
+$x = $mbf->new('740.7')->fdiv('6',4,undef,'zero'); ok ($x,'123.4');
+
+$x = $mbi->new('123456'); $y = $mbi->new('123456'); $y->{_a} = 6;
+ok ($x->bdiv($y),1); ok ($x->{_a},6);			# carried over
+
+$x = $mbi->new('123456'); $y = $mbi->new('123456'); $x->{_a} = 6;
+ok ($x->bdiv($y),1); ok ($x->{_a},6);			# carried over
+
+$x = $mbi->new('123456'); $y = $mbi->new('223456'); $y->{_a} = 6;
+ok ($x->bdiv($y),0); ok ($x->{_a},6);			# carried over
+
+$x = $mbi->new('123456'); $y = $mbi->new('223456'); $x->{_a} = 6;
+ok ($x->bdiv($y),0); ok ($x->{_a},6);			# carried over
+
+###############################################################################
+# test that bop(0) does the same than bop(undef)
+
+$x = $mbf->new('1234567890');
+ok ($x->copy()->bsqrt(0),$x->copy()->bsqrt(undef));
+ok ($x->copy->bsqrt(0),'35136.41828644462161665823116758077037159');
+
+ok_undef ($x->{_a});
+
+# test that bsqrt() modifies $x and does not just return something else
+# (especially under BareCalc)
+$z = $x->bsqrt();
+ok ($z,$x); ok ($x,'35136.41828644462161665823116758077037159');
+
+$x = $mbf->new('1.234567890123456789');
+ok ($x->copy()->bpow('0.5',0),$x->copy()->bpow('0.5',undef));
+ok ($x->copy()->bpow('0.5',0),$x->copy()->bsqrt(undef));
+ok ($x->copy()->bpow('2',0),'1.524157875323883675019051998750190521');
+
+###############################################################################
+# test (also under Bare) that bfac() rounds at last step
+
+ok ($mbi->new(12)->bfac(),'479001600');
+ok ($mbi->new(12)->bfac(2),'480000000');
+$x = $mbi->new(12); $x->accuracy(2); ok ($x->bfac(),'480000000');
+$x = $mbi->new(13); $x->accuracy(2); ok ($x->bfac(),'6200000000');
+$x = $mbi->new(13); $x->accuracy(3); ok ($x->bfac(),'6230000000');
+$x = $mbi->new(13); $x->accuracy(4); ok ($x->bfac(),'6227000000');
+# this does 1,2,3...9,10,11,12...20
+$x = $mbi->new(20); $x->accuracy(1); ok ($x->bfac(),'2000000000000000000');
+
+###############################################################################
+# test bsqrt) rounding to given A/P/R (bug prior to v1.60)
+$x = $mbi->new('123456')->bsqrt(2,undef); ok ($x,'350');	# not 351
+$x = $mbi->new('3')->bsqrt(2,undef); ok ($x->accuracy(),2);
+
+$mbi->round_mode('even'); $x = $mbi->new('126025')->bsqrt(2,undef,'+inf');
+ok ($x,'360');	# not 355 nor 350
+
+$x = $mbi->new('126025')->bsqrt(undef,2); ok ($x,'400');	 # not 355
+
+
+###############################################################################
+# test mixed arguments
+
+$x = $mbf->new(10);
+$u = $mbf->new(2.5);
+$y = $mbi->new(2);
+
+$z = $x + $y; ok ($z,12); ok (ref($z),$mbf);
+$z = $x / $y; ok ($z,5); ok (ref($z),$mbf);
+$z = $u * $y; ok ($z,5); ok (ref($z),$mbf);
+
+$y = $mbi->new(12345);
+$z = $u->copy()->bmul($y,2,undef,'odd'); ok ($z,31000);
+$z = $u->copy()->bmul($y,3,undef,'odd'); ok ($z,30900);
+$z = $u->copy()->bmul($y,undef,0,'odd'); ok ($z,30863);
+$z = $u->copy()->bmul($y,undef,1,'odd'); ok ($z,30863);
+$z = $u->copy()->bmul($y,undef,2,'odd'); ok ($z,30860);
+$z = $u->copy()->bmul($y,undef,3,'odd'); ok ($z,30900);
+$z = $u->copy()->bmul($y,undef,-1,'odd'); ok ($z,30862.5);
+
+my $warn = ''; $SIG{__WARN__} = sub { $warn = shift; };
+# these should no longer warn, even tho '3.17' is a NaN in BigInt (>= returns
+# now false, bug until v1.80)
+$warn = ''; eval "\$z = 3.17 <= \$y"; ok ($z, '');
+print "# Got: '$warn'\n" unless
+ok ($warn !~ /^Use of uninitialized value (\$y )?(in numeric le \(<=\) |)at/);	
+$warn = ''; eval "\$z = \$y >= 3.17"; ok ($z, '');
+print "# Got: '$warn'\n" unless
+ok ($warn !~ /^Use of uninitialized value (\$y )?(in numeric ge \(>=\) |)at/);	
+
+# XXX TODO breakage:
+# $z = $y->copy()->bmul($u,2,0,'odd'); ok ($z,31000);
+# $z = $y * $u; ok ($z,5); ok (ref($z),$mbi);
+# $z = $y + $x; ok ($z,12); ok (ref($z),$mbi);
+# $z = $y / $x; ok ($z,0); ok (ref($z),$mbi);
+
+###############################################################################
+# rounding in bdiv with fallback and already set A or P
+
+{
+  no strict 'refs';
+  ${"$mbf\::accuracy"} = undef;
+  ${"$mbf\::precision"} = undef;
+  ${"$mbf\::div_scale"} = 40;
+}
+
+  $x = $mbf->new(10); $x->{_a} = 4;
+  ok ($x->bdiv(3),'3.333');
+  ok ($x->{_a},4);			# set's it since no fallback
+
+$x = $mbf->new(10); $x->{_a} = 4; $y = $mbf->new(3);
+ok ($x->bdiv($y),'3.333');
+ok ($x->{_a},4);			# set's it since no fallback
+
+# rounding to P of x
+$x = $mbf->new(10); $x->{_p} = -2;
+ok ($x->bdiv(3),'3.33');
+
+# round in div with requested P
+$x = $mbf->new(10);
+ok ($x->bdiv(3,undef,-2),'3.33');
+
+# round in div with requested P greater than fallback
+{
+  no strict 'refs';
+  ${"$mbf\::div_scale"} = 5;
+  $x = $mbf->new(10);
+  ok ($x->bdiv(3,undef,-8),'3.33333333');
+  ${"$mbf\::div_scale"} = 40;
+}
+
+$x = $mbf->new(10); $y = $mbf->new(3); $y->{_a} = 4;
+ok ($x->bdiv($y),'3.333');
+ok ($x->{_a},4); ok ($y->{_a},4);	# set's it since no fallback
+ok_undef ($x->{_p}); ok_undef ($y->{_p});
+
+# rounding to P of y
+$x = $mbf->new(10); $y = $mbf->new(3); $y->{_p} = -2;
+ok ($x->bdiv($y),'3.33');
+ok ($x->{_p},-2);
+ ok ($y->{_p},-2);
+ok_undef ($x->{_a}); ok_undef ($y->{_a});
+
+###############################################################################
+# test whether bround(-n) fails in MBF (undocumented in MBI)
+eval { $x = $mbf->new(1); $x->bround(-2); };
+ok ($@ =~ /^bround\(\) needs positive accuracy/,1);
+
+# test whether rounding to higher accuracy is no-op
+$x = $mbf->new(1); $x->{_a} = 4;
+ok ($x,'1.000');
+$x->bround(6);                  # must be no-op
+ok ($x->{_a},4);
+ok ($x,'1.000');
+
+$x = $mbi->new(1230); $x->{_a} = 3;
+ok ($x,'1230');
+$x->bround(6);                  # must be no-op
+ok ($x->{_a},3);
+ok ($x,'1230');
+
+# bround(n) should set _a
+$x->bround(2);                  # smaller works
+ok ($x,'1200');
+ok ($x->{_a},2);
+ 
+# bround(-n) is undocumented and only used by MBF
+# bround(-n) should set _a
+$x = $mbi->new(12345);
+$x->bround(-1);
+ok ($x,'12300');
+ok ($x->{_a},4);
+ 
+# bround(-n) should set _a
+$x = $mbi->new(12345);
+$x->bround(-2);
+ok ($x,'12000');
+ok ($x->{_a},3);
+ 
+# bround(-n) should set _a
+$x = $mbi->new(12345); $x->{_a} = 5;
+$x->bround(-3);
+ok ($x,'10000');
+ok ($x->{_a},2);
+ 
+# bround(-n) should set _a
+$x = $mbi->new(12345); $x->{_a} = 5;
+$x->bround(-4);
+ok ($x,'0');
+ok ($x->{_a},1);
+
+# bround(-n) should be noop if n too big
+$x = $mbi->new(12345);
+$x->bround(-5);
+ok ($x,'0');			# scale to "big" => 0
+ok ($x->{_a},0);
+ 
+# bround(-n) should be noop if n too big
+$x = $mbi->new(54321);
+$x->bround(-5);
+ok ($x,'100000');		# used by MBF to round 0.0054321 at 0.0_6_00000
+ok ($x->{_a},0);
+ 
+# bround(-n) should be noop if n too big
+$x = $mbi->new(54321); $x->{_a} = 5;
+$x->bround(-6);
+ok ($x,'100000');		# no-op
+ok ($x->{_a},0);
+ 
+# bround(n) should set _a
+$x = $mbi->new(12345); $x->{_a} = 5;
+$x->bround(5);                  # must be no-op
+ok ($x,'12345');
+ok ($x->{_a},5);
+ 
+# bround(n) should set _a
+$x = $mbi->new(12345); $x->{_a} = 5;
+$x->bround(6);                  # must be no-op
+ok ($x,'12345');
+
+$x = $mbf->new('0.0061'); $x->bfround(-2); ok ($x,'0.01');
+$x = $mbf->new('0.004'); $x->bfround(-2);  ok ($x,'0.00');
+$x = $mbf->new('0.005'); $x->bfround(-2);  ok ($x,'0.00');
+
+$x = $mbf->new('12345'); $x->bfround(2); ok ($x,'12340');
+$x = $mbf->new('12340'); $x->bfround(2); ok ($x,'12340');
+
+# MBI::bfround should clear A for negative P
+$x = $mbi->new('1234'); $x->accuracy(3); $x->bfround(-2);
+ok_undef ($x->{_a});
+
+# test that bfround() and bround() work with large numbers
+
+$x = $mbf->new(1)->bdiv(5678,undef,-63);
+ok ($x, '0.000176118351532229658330398027474462839027826699542092286016203');
+
+$x = $mbf->new(1)->bdiv(5678,undef,-90);
+ok ($x, '0.000176118351532229658330398027474462839027826699542092286016202888340965128566396618527651');
+
+$x = $mbf->new(1)->bdiv(5678,80);
+ok ($x, '0.00017611835153222965833039802747446283902782669954209228601620288834096512856639662');
+
+###############################################################################
+# rounding with already set precision/accuracy
+
+$x = $mbf->new(1); $x->{_p} = -5;
+ok ($x,'1.00000');
+
+# further rounding donw
+ok ($x->bfround(-2),'1.00');
+ok ($x->{_p},-2);
+
+$x = $mbf->new(12345); $x->{_a} = 5;
+ok ($x->bround(2),'12000');
+ok ($x->{_a},2);
+
+$x = $mbf->new('1.2345'); $x->{_a} = 5;
+ok ($x->bround(2),'1.2');
+ok ($x->{_a},2);
+
+# mantissa/exponent format and A/P
+$x = $mbf->new('12345.678'); $x->accuracy(4);
+ok ($x,'12350'); ok ($x->{_a},4); ok_undef ($x->{_p});
+
+#ok_undef ($x->{_m}->{_a}); ok_undef ($x->{_e}->{_a});
+#ok_undef ($x->{_m}->{_p}); ok_undef ($x->{_e}->{_p});
+
+# check for no A/P in case of fallback
+# result
+$x = $mbf->new(100) / 3;
+ok_undef ($x->{_a}); ok_undef ($x->{_p});
+
+# result & reminder
+$x = $mbf->new(100) / 3; ($x,$y) = $x->bdiv(3);
+ok_undef ($x->{_a}); ok_undef ($x->{_p});
+ok_undef ($y->{_a}); ok_undef ($y->{_p});
+
+###############################################################################
+# math with two numbers with differen A and P
+
+$x = $mbf->new(12345); $x->accuracy(4);		# '12340'
+$y = $mbf->new(12345); $y->accuracy(2);		# '12000'
+ok ($x+$y,24000);				# 12340+12000=> 24340 => 24000
+
+$x = $mbf->new(54321); $x->accuracy(4);		# '12340'
+$y = $mbf->new(12345); $y->accuracy(3);		# '12000'
+ok ($x-$y,42000);				# 54320+12300=> 42020 => 42000
+
+$x = $mbf->new('1.2345'); $x->precision(-2);	# '1.23'
+$y = $mbf->new('1.2345'); $y->precision(-4);	# '1.2345'
+ok ($x+$y,'2.46');				# 1.2345+1.2300=> 2.4645 => 2.46
+
+###############################################################################
+# round should find and use proper class
+
+#$x = Foo->new();
+#ok ($x->round($Foo::accuracy),'a' x $Foo::accuracy);
+#ok ($x->round(undef,$Foo::precision),'p' x $Foo::precision);
+#ok ($x->bfround($Foo::precision),'p' x $Foo::precision);
+#ok ($x->bround($Foo::accuracy),'a' x $Foo::accuracy);
+
+###############################################################################
+# find out whether _find_round_parameters is doing what's it's supposed to do
+
+{
+  no strict 'refs'; 
+  ${"$mbi\::accuracy"} = undef;
+  ${"$mbi\::precision"} = undef;
+  ${"$mbi\::div_scale"} = 40;
+  ${"$mbi\::round_mode"} = 'odd';
+}
+
+$x = $mbi->new(123);
+my @params = $x->_find_round_parameters();
+ok (scalar @params,1);				# nothing to round
+
+@params = $x->_find_round_parameters(1);
+ok (scalar @params,4);				# a=1
+ok ($params[0],$x);				# self
+ok ($params[1],1);				# a
+ok_undef ($params[2]);				# p
+ok ($params[3],'odd');				# round_mode
+
+@params = $x->_find_round_parameters(undef,2);
+ok (scalar @params,4);				# p=2
+ok ($params[0],$x);				# self
+ok_undef ($params[1]);				# a
+ok ($params[2],2);				# p
+ok ($params[3],'odd');				# round_mode
+
+eval { @params = $x->_find_round_parameters(undef,2,'foo'); };
+ok ($@ =~ /^Unknown round mode 'foo'/,1);
+
+@params = $x->_find_round_parameters(undef,2,'+inf');
+ok (scalar @params,4);				# p=2
+ok ($params[0],$x);				# self
+ok_undef ($params[1]);				# a
+ok ($params[2],2);				# p
+ok ($params[3],'+inf');				# round_mode
+
+@params = $x->_find_round_parameters(2,-2,'+inf');
+ok (scalar @params,1);				# error, A and P defined
+ok ($params[0],$x);				# self
+
+{
+  no strict 'refs';
+  ${"$mbi\::accuracy"} = 1;
+  @params = $x->_find_round_parameters(undef,-2);
+  ok (scalar @params,1);			# error, A and P defined
+  ok ($params[0],$x);				# self
+  ok ($x->is_nan(),1);				# and must be NaN
+
+  ${"$mbi\::accuracy"} = undef;
+  ${"$mbi\::precision"} = 1;
+  @params = $x->_find_round_parameters(1,undef);
+  ok (scalar @params,1);			# error, A and P defined
+  ok ($params[0],$x);				# self
+  ok ($x->is_nan(),1);				# and must be NaN
+ 
+  ${"$mbi\::precision"} = undef;		# reset
+}
+
+###############################################################################
+# test whether bone/bzero take additional A & P, or reset it etc
+
+foreach my $c ($mbi,$mbf)
+  {
+  $x = $c->new(2)->bzero(); ok_undef ($x->{_a}); ok_undef ($x->{_p});
+  $x = $c->new(2)->bone();  ok_undef ($x->{_a}); ok_undef ($x->{_p});
+  $x = $c->new(2)->binf();  ok_undef ($x->{_a}); ok_undef ($x->{_p});
+  $x = $c->new(2)->bnan();  ok_undef ($x->{_a}); ok_undef ($x->{_p});
+
+  $x = $c->new(2); $x->{_a} = 1; $x->{_p} = 2; $x->bnan();
+  ok_undef ($x->{_a}); ok_undef ($x->{_p});
+  $x = $c->new(2); $x->{_a} = 1; $x->{_p} = 2; $x->binf();
+  ok_undef ($x->{_a}); ok_undef ($x->{_p});
+
+  $x = $c->new(2,1); ok ($x->{_a},1); ok_undef ($x->{_p});
+  $x = $c->new(2,undef,1); ok_undef ($x->{_a}); ok ($x->{_p},1);
+  
+  $x = $c->new(2,1)->bzero(); ok ($x->{_a},1); ok_undef ($x->{_p});
+  $x = $c->new(2,undef,1)->bzero(); ok_undef ($x->{_a}); ok ($x->{_p},1);
+
+  $x = $c->new(2,1)->bone(); ok ($x->{_a},1); ok_undef ($x->{_p});
+  $x = $c->new(2,undef,1)->bone(); ok_undef ($x->{_a}); ok ($x->{_p},1);
+
+  $x = $c->new(2); $x->bone('+',2,undef); ok ($x->{_a},2); ok_undef ($x->{_p});
+  $x = $c->new(2); $x->bone('+',undef,2); ok_undef ($x->{_a}); ok ($x->{_p},2);
+  $x = $c->new(2); $x->bone('-',2,undef); ok ($x->{_a},2); ok_undef ($x->{_p});
+  $x = $c->new(2); $x->bone('-',undef,2); ok_undef ($x->{_a}); ok ($x->{_p},2);
+  
+  $x = $c->new(2); $x->bzero(2,undef); ok ($x->{_a},2); ok_undef ($x->{_p});
+  $x = $c->new(2); $x->bzero(undef,2); ok_undef ($x->{_a}); ok ($x->{_p},2);
+  }
+
+###############################################################################
+# test whether bone/bzero honour globals
+
+for my $c ($mbi,$mbf)
+  {
+  $c->accuracy(2);
+  $x = $c->bone(); ok ($x->accuracy(),2);
+  $x = $c->bzero(); ok ($x->accuracy(),2);
+  $c->accuracy(undef);
+  
+  $c->precision(-2);
+  $x = $c->bone(); ok ($x->precision(),-2);
+  $x = $c->bzero(); ok ($x->precision(),-2);
+  $c->precision(undef);
+  }
+
+###############################################################################
+# check whether mixing A and P creates a NaN
+
+# new with set accuracy/precision and with parameters
+{
+  no strict 'refs'; 
+  foreach my $c ($mbi,$mbf)
+    {
+    ok ($c->new(123,4,-3),'NaN');			# with parameters
+    ${"$c\::accuracy"} = 42;
+    ${"$c\::precision"} = 2;
+    ok ($c->new(123),'NaN');			# with globals
+    ${"$c\::accuracy"} = undef;
+    ${"$c\::precision"} = undef;
+    }
+}
+
+# binary ops
+foreach my $class ($mbi,$mbf)
+  {
+  foreach (qw/add sub mul pow mod/)
+  #foreach (qw/add sub mul div pow mod/)
+    {
+    my $try = "my \$x = $class->new(1234); \$x->accuracy(5); ";
+      $try .= "my \$y = $class->new(12); \$y->precision(-3); ";
+      $try .= "\$x->b$_(\$y);";
+    $rc = eval $try;
+    print "# Tried: '$try'\n" if !ok ($rc, 'NaN');
+    }
+  }
+
+# unary ops
+foreach (qw/new bsqrt/)
+  {
+  my $try = 'my $x = $mbi->$_(1234,5,-3); ';
+  $rc = eval $try;
+  print "# Tried: '$try'\n" if !ok ($rc, 'NaN');
+  }
+
+# see if $x->bsub(0) and $x->badd(0) really round
+foreach my $class ($mbi,$mbf)
+  {
+  $x = $class->new(123); $class->accuracy(2); $x->bsub(0);
+  ok ($x,120);
+  $class->accuracy(undef);
+  $x = $class->new(123); $class->accuracy(2); $x->badd(0);
+  ok ($x,120);
+  $class->accuracy(undef);
+  }
+
+###############################################################################
+# test whether shortcuts returning zero/one preserve A and P
+
+my ($ans1,$f,$a,$p,$xp,$yp,$xa,$ya,$try,$ans,@args);
+my $CALC = Math::BigInt->config()->{lib};
+while (<DATA>)
+  {
+  $_ =~ s/[\n\r]//g;	# remove newlines
+  next if /^\s*(#|$)/;	# skip comments and empty lines
+  if (s/^&//)
+    {
+    $f = $_; next;	# function
+    }
+  @args = split(/:/,$_,99);
+  my $ans = pop(@args);
+
+  ($x,$xa,$xp) = split (/,/,$args[0]);
+  $xa = $xa || ''; $xp = $xp || '';
+  $try  = "\$x = $mbi->new('$x'); ";
+  $try .= "\$x->accuracy($xa); " if $xa ne '';
+  $try .= "\$x->precision($xp); " if $xp ne '';
+
+  ($y,$ya,$yp) = split (/,/,$args[1]);
+  $ya = $ya || ''; $yp = $yp || '';
+  $try .= "\$y = $mbi->new('$y'); ";
+  $try .= "\$y->accuracy($ya); " if $ya ne '';
+  $try .= "\$y->precision($yp); " if $yp ne '';
+  
+  $try .= "\$x->$f(\$y);";
+  
+  # print "trying $try\n";
+  $rc = eval $try;
+  # convert hex/binary targets to decimal
+  if ($ans =~ /^(0x0x|0b0b)/)
+    {
+    $ans =~ s/^0[xb]//;
+    $ans = $mbi->new($ans)->bstr();
+    }
+  print "# Tried: '$try'\n" if !ok ($rc, $ans);
+  # check internal state of number objects
+  is_valid($rc,$f) if ref $rc;
+
+  # now check whether A and P are set correctly
+  # only one of $a or $p will be set (no crossing here)
+  $a = $xa || $ya; $p = $xp || $yp;
+
+  # print "Check a=$a p=$p\n";
+  # print "# Tried: '$try'\n";
+  if ($a ne '')
+    {
+    if (!(ok ($x->{_a}, $a) && ok_undef ($x->{_p})))
+      {
+      print "# Check: A=$a and P=undef\n";
+      print "# Tried: '$try'\n";
+      } 
+    }
+  if ($p ne '')
+    {
+    if (!(ok ($x->{_p}, $p) && ok_undef ($x->{_a})))
+      {
+      print "# Check: A=undef and P=$p\n";
+      print "# Tried: '$try'\n";
+      }
+    }
+  }
+
+# all done
+1;
+
+###############################################################################
+###############################################################################
+# Perl 5.005 does not like ok ($x,undef)
+
+sub ok_undef
+  {
+  my $x = shift;
+
+  ok (1,1) and return 1 if !defined $x;
+  ok ($x,'undef');
+  print "# Called from ",join(' ',caller()),"\n";
+  return 0;
+  }
+
+###############################################################################
+# sub to check validity of a BigInt internally, to ensure that no op leaves a
+# number object in an invalid state (f.i. "-0")
+
+sub is_valid
+  {
+  my ($x,$f) = @_;
+
+  my $e = 0;                    # error?
+  # ok as reference?
+  $e = 'Not a reference' if !ref($x);
+
+  # has ok sign?
+  $e = "Illegal sign $x->{sign} (expected: '+', '-', '-inf', '+inf' or 'NaN'"
+   if $e eq '0' && $x->{sign} !~ /^(\+|-|\+inf|-inf|NaN)$/;
+
+  $e = "-0 is invalid!" if $e ne '0' && $x->{sign} eq '-' && $x == 0;
+  $e = $CALC->_check($x->{value}) if $e eq '0';
+
+  # test done, see if error did crop up
+  ok (1,1), return if ($e eq '0');
+
+  ok (1,$e." after op '$f'");
+  } 
+
+# format is:
+# x,A,P:x,A,P:result
+# 123,,3 means 123 with precision 3 (A is undef)
+# the A or P of the result is calculated automatically
+__DATA__
+&badd
+123,,:123,,:246
+123,3,:0,,:123
+123,,-3:0,,:123
+123,,:0,3,:123
+123,,:0,,-3:123
+&bmul
+123,,:1,,:123
+123,3,:0,,:0
+123,,-3:0,,:0
+123,,:0,3,:0
+123,,:0,,-3:0
+123,3,:1,,:123
+123,,-3:1,,:123
+123,,:1,3,:123
+123,,:1,,-3:123
+1,3,:123,,:123
+1,,-3:123,,:123
+1,,:123,3,:123
+1,,:123,,-3:123
+&bdiv
+123,,:1,,:123
+123,4,:1,,:123
+123,,:1,4,:123
+123,,:1,,-4:123
+123,,-4:1,,:123
+1,4,:123,,:0
+1,,:123,4,:0
+1,,:123,,-4:0
+1,,-4:123,,:0
+&band
+1,,:3,,:1
+1234,1,:0,,:0
+1234,,:0,1,:0
+1234,,-1:0,,:0
+1234,,:0,,-1:0
+0xFF,,:0x10,,:0x0x10
+0xFF,2,:0xFF,,:250
+0xFF,,:0xFF,2,:250
+0xFF,,1:0xFF,,:250
+0xFF,,:0xFF,,1:250
+&bxor
+1,,:3,,:2
+1234,1,:0,,:1000
+1234,,:0,1,:1000
+1234,,3:0,,:1000
+1234,,:0,,3:1000
+0xFF,,:0x10,,:239
+# 250 ^ 255 => 5
+0xFF,2,:0xFF,,:5
+0xFF,,:0xFF,2,:5
+0xFF,,1:0xFF,,:5
+0xFF,,:0xFF,,1:5
+# 250 ^ 4095 = 3845 => 3800
+0xFF,2,:0xFFF,,:3800
+# 255 ^ 4100 = 4347 => 4300
+0xFF,,:0xFFF,2,:4300
+0xFF,,2:0xFFF,,:3800
+# 255 ^ 4100 = 10fb => 4347 => 4300
+0xFF,,:0xFFF,,2:4300
+&bior
+1,,:3,,:3
+1234,1,:0,,:1000
+1234,,:0,1,:1000
+1234,,3:0,,:1000
+1234,,:0,,3:1000
+0xFF,,:0x10,,:0x0xFF
+# FF | FA = FF => 250
+250,2,:0xFF,,:250
+0xFF,,:250,2,:250
+0xFF,,1:0xFF,,:250
+0xFF,,:0xFF,,1:250
+&bpow
+2,,:3,,:8
+2,,:0,,:1
+2,2,:0,,:1
+2,,:0,2,:1
diff --git a/dist/Math-BigInt/t/mbimbf.t b/dist/Math-BigInt/t/mbimbf.t
new file mode 100644
index 0000000000..5bc8793478
--- /dev/null
+++ b/dist/Math-BigInt/t/mbimbf.t
@@ -0,0 +1,103 @@
+#!/usr/bin/perl -w
+
+# test rounding, accuracy, precicion and fallback, round_mode and mixing
+# of classes
+
+use strict;
+use Test;
+
+BEGIN
+  {
+  $| = 1;
+  # to locate the testing files
+  my $location = $0; $location =~ s/mbimbf.t//i;
+  unshift @INC, '../lib';	# for testing manually
+  if (-d 't')
+    {
+    chdir 't';
+    require File::Spec;
+    unshift @INC, File::Spec->catdir(File::Spec->updir, $location);
+    }
+  else
+    {
+    unshift @INC, $location;
+    }
+  print "# INC = @INC\n";
+
+  plan tests => 684 
+    + 26;		# own tests
+  }
+
+use Math::BigInt 1.70;
+use Math::BigFloat 1.43;
+
+use vars qw/$mbi $mbf/;
+
+$mbi = 'Math::BigInt';
+$mbf = 'Math::BigFloat';
+
+require 'mbimbf.inc';
+
+# some tests that won't work with subclasses, since the things are only
+# garantied in the Math::BigInt/BigFloat (unless subclass chooses to support
+# this)
+
+Math::BigInt->round_mode('even');	# reset for tests
+Math::BigFloat->round_mode('even');	# reset for tests
+
+ok ($Math::BigInt::rnd_mode,'even');
+ok ($Math::BigFloat::rnd_mode,'even');
+
+my $x = eval '$mbi->round_mode("huhmbi");';
+print "# Got '$@'\n" unless
+ ok ($@ =~ /^Unknown round mode 'huhmbi' at/);
+
+$x = eval '$mbf->round_mode("huhmbf");';
+print "# Got '$@'\n" unless
+ ok ($@ =~ /^Unknown round mode 'huhmbf' at/);
+
+# old way (now with test for validity)
+$x = eval '$Math::BigInt::rnd_mode = "huhmbi";';
+print "# Got '$@'\n" unless
+ ok ($@ =~ /^Unknown round mode 'huhmbi' at/);
+$x = eval '$Math::BigFloat::rnd_mode = "huhmbf";';
+print "# Got '$@'\n" unless
+ ok ($@ =~ /^Unknown round mode 'huhmbf' at/);
+# see if accessor also changes old variable
+$mbi->round_mode('odd'); ok ($Math::BigInt::rnd_mode,'odd');
+$mbf->round_mode('odd'); ok ($Math::BigInt::rnd_mode,'odd');
+
+foreach my $class (qw/Math::BigInt Math::BigFloat/)
+  {
+  ok ($class->accuracy(5),5);		# set A
+  ok_undef ($class->precision());	# and now P must be cleared
+  ok ($class->precision(5),5);		# set P
+  ok_undef ($class->accuracy());	# and now A must be cleared
+  }
+
+foreach my $class (qw/Math::BigInt Math::BigFloat/)
+  {
+  $class->accuracy(42);
+  my $x = $class->new(123);	# $x gets A of 42, too!
+  ok ($x->accuracy(),42);	# really?
+  ok ($x->accuracy(undef),42);	# $x has no A, but the
+				# global is still in effect for $x
+				# so the return value of that operation should
+				# be 42, not undef
+  ok ($x->accuracy(),42);	# so $x should still have A = 42
+  $class->accuracy(undef);	# reset for further tests
+  $class->precision(undef);
+  }
+# bug with flog(Math::BigFloat,Math::BigInt)
+$x = Math::BigFloat->new(100);
+$x = $x->blog(Math::BigInt->new(10));
+
+ok ($x,2);
+
+# bug until v1.88 for sqrt() with enough digits
+for my $i (80,88,100)
+  {
+  $x = Math::BigFloat->new("1." . ("0" x $i) . "1");
+  $x = $x->bsqrt;
+  ok ($x, 1);
+  }
diff --git a/dist/Math-BigInt/t/nan_cmp.t b/dist/Math-BigInt/t/nan_cmp.t
new file mode 100644
index 0000000000..ffe7b14b23
--- /dev/null
+++ b/dist/Math-BigInt/t/nan_cmp.t
@@ -0,0 +1,44 @@
+#!/usr/bin/perl -w
+
+# test that overloaded compare works when NaN are involved
+
+use strict;
+use Test::More;
+
+BEGIN
+  {
+  $| = 1;
+  chdir 't' if -d 't';
+  unshift @INC, '../lib';	# for running manually
+  plan tests => 26;
+  }
+
+use Math::BigInt;
+use Math::BigFloat;
+
+compare (Math::BigInt->bnan(),   Math::BigInt->bone() );
+compare (Math::BigFloat->bnan(), Math::BigFloat->bone() );
+
+sub compare
+  {
+  my ($nan, $one) = @_;
+
+  is ($one, $one, '1 == 1');
+
+  is ($one != $nan, 1, "1 != NaN");
+  is ($nan != $one, 1, "NaN != 1");
+  is ($nan != $nan, 1, "NaN != NaN");
+
+  is ($nan == $one, '', "NaN == 1");
+  is ($one == $nan, '', "1 == NaN");
+  is ($nan == $nan, '', "NaN == NaN");
+
+  is ($nan <= $one, '', "NaN <= 1");
+  is ($one <= $nan, '', "1 <= NaN");
+  is ($nan <= $nan, '', "NaN <= NaN");
+
+  is ($nan >= $one, '', "NaN >= 1");
+  is ($one >= $nan, '', "1 >= NaN");
+  is ($nan >= $nan, '', "NaN >= NaN");
+  }
+
diff --git a/dist/Math-BigInt/t/new_overloaded.t b/dist/Math-BigInt/t/new_overloaded.t
new file mode 100644
index 0000000000..08708dc557
--- /dev/null
+++ b/dist/Math-BigInt/t/new_overloaded.t
@@ -0,0 +1,32 @@
+#!/usr/bin/perl -w
+
+# Math::BigFloat->new had a bug where it would assume any object is a
+# BigInt which broke overloaded non-BigInts.
+
+use Test::More tests => 4;
+
+
+package Overloaded::Num;
+
+use overload '0+' => sub { ${$_[0]} },
+             fallback => 1;
+sub new {
+    my($class, $num) = @_;
+    return bless \$num, $class;
+}
+
+
+package main;
+
+use Math::BigFloat;
+
+my $overloaded_num = Overloaded::Num->new(2.23);
+is $overloaded_num, 2.23;
+
+my $bigfloat = Math::BigFloat->new($overloaded_num);
+is $bigfloat, 2.23, 'BigFloat->new accepts overloaded numbers';
+
+my $bigint = Math::BigInt->new(Overloaded::Num->new(3));
+is $bigint, 3, 'BigInt->new accepts overloaded numbers';
+
+is( Math::BigFloat->new($bigint), 3, 'BigFloat from BigInt' );
diff --git a/dist/Math-BigInt/t/req_mbf0.t b/dist/Math-BigInt/t/req_mbf0.t
new file mode 100644
index 0000000000..9c51a16ee5
--- /dev/null
+++ b/dist/Math-BigInt/t/req_mbf0.t
@@ -0,0 +1,34 @@
+#!/usr/bin/perl -w 
+
+# check that simple requiring BigFloat and then bzero() works
+
+use strict;
+use Test::More;
+
+BEGIN
+  {
+  $| = 1;
+  # to locate the testing files
+  my $location = $0; $location =~ s/req_mbf0.t//i;
+  unshift @INC, qw(../lib);     # to locate the modules
+  if (-d 't')
+    {
+    chdir 't';
+    require File::Spec;
+    unshift @INC, File::Spec->catdir(File::Spec->updir, $location);
+    }
+  else
+    {
+    unshift @INC, $location;
+    }
+  print "# INC = @INC\n";
+
+  plan tests => 1;
+  } 
+
+require Math::BigFloat;
+my $x = Math::BigFloat->bzero(); $x++;
+is ($x,1, '$x is 1');
+
+# all tests done
+
diff --git a/dist/Math-BigInt/t/req_mbf1.t b/dist/Math-BigInt/t/req_mbf1.t
new file mode 100644
index 0000000000..964980de28
--- /dev/null
+++ b/dist/Math-BigInt/t/req_mbf1.t
@@ -0,0 +1,32 @@
+#!/usr/bin/perl -w 
+
+# check that simple requiring BigFloat and then bone() works
+
+use strict;
+use Test;
+
+BEGIN
+  {
+  $| = 1;
+  # to locate the testing files
+  my $location = $0; $location =~ s/req_mbf1.t//i;
+  unshift @INC, qw(../lib);     # to locate the modules
+  if (-d 't')
+    {
+    chdir 't';
+    require File::Spec;
+    unshift @INC, File::Spec->catdir(File::Spec->updir, $location);
+    }
+  else
+    {
+    unshift @INC, $location;
+    }
+  print "# INC = @INC\n";
+
+  plan tests => 1;
+  } 
+
+require Math::BigFloat; my $x = Math::BigFloat->bone(); ok ($x,1);
+
+# all tests done
+
diff --git a/dist/Math-BigInt/t/req_mbfa.t b/dist/Math-BigInt/t/req_mbfa.t
new file mode 100644
index 0000000000..2c2f9f2257
--- /dev/null
+++ b/dist/Math-BigInt/t/req_mbfa.t
@@ -0,0 +1,32 @@
+#!/usr/bin/perl -w 
+
+# check that simple requiring BigFloat and then bnan() works
+
+use strict;
+use Test;
+
+BEGIN
+  {
+  $| = 1;
+  # to locate the testing files
+  my $location = $0; $location =~ s/req_mbfa.t//i;
+  unshift @INC, qw(../lib);     # to locate the modules
+  if (-d 't')
+    {
+    chdir 't';
+    require File::Spec;
+    unshift @INC, File::Spec->catdir(File::Spec->updir, $location);
+    }
+  else
+    {
+    unshift @INC, $location;
+    }
+  print "# INC = @INC\n";
+
+  plan tests => 1;
+  } 
+
+require Math::BigFloat; my $x = Math::BigFloat->bnan(1); ok ($x,'NaN');
+
+# all tests done
+
diff --git a/dist/Math-BigInt/t/req_mbfi.t b/dist/Math-BigInt/t/req_mbfi.t
new file mode 100644
index 0000000000..b2b655e657
--- /dev/null
+++ b/dist/Math-BigInt/t/req_mbfi.t
@@ -0,0 +1,32 @@
+#!/usr/bin/perl -w 
+
+# check that simple requiring BigFloat and then binf() works
+
+use strict;
+use Test;
+
+BEGIN
+  {
+  $| = 1;
+  # to locate the testing files
+  my $location = $0; $location =~ s/req_mbfi.t//i;
+  unshift @INC, qw(../lib);     # to locate the modules
+  if (-d 't')
+    {
+    chdir 't';
+    require File::Spec;
+    unshift @INC, File::Spec->catdir(File::Spec->updir, $location);
+    }
+  else
+    {
+    unshift @INC, $location;
+    }
+  print "# INC = @INC\n";
+
+  plan tests => 1;
+  } 
+
+require Math::BigFloat; my $x = Math::BigFloat->binf(); ok ($x,'inf');
+
+# all tests done
+
diff --git a/dist/Math-BigInt/t/req_mbfn.t b/dist/Math-BigInt/t/req_mbfn.t
new file mode 100644
index 0000000000..3aa6c3e1f6
--- /dev/null
+++ b/dist/Math-BigInt/t/req_mbfn.t
@@ -0,0 +1,32 @@
+#!/usr/bin/perl -w
+
+# check that simple requiring BigFloat and then new() works
+
+use strict;
+use Test;
+
+BEGIN
+  {
+  $| = 1;
+  # to locate the testing files
+  my $location = $0; $location =~ s/req_mbfn.t//i;
+  unshift @INC, qw(../lib);     # to locate the modules
+  if (-d 't')
+    {
+    chdir 't';
+    require File::Spec;
+    unshift @INC, File::Spec->catdir(File::Spec->updir, $location);
+    }
+  else
+    {
+    unshift @INC, $location;
+    }
+  print "# INC = @INC\n";
+
+  plan tests => 1;
+  } 
+
+require Math::BigFloat; my $x = Math::BigFloat->new(1);  ++$x; ok ($x,2);
+
+# all tests done
+
diff --git a/dist/Math-BigInt/t/req_mbfw.t b/dist/Math-BigInt/t/req_mbfw.t
new file mode 100644
index 0000000000..682b0cfb96
--- /dev/null
+++ b/dist/Math-BigInt/t/req_mbfw.t
@@ -0,0 +1,43 @@
+#!/usr/bin/perl -w
+
+# check that requiring BigFloat and then calling import() works
+
+use strict;
+use Test::More;
+
+BEGIN
+  {
+  $| = 1;
+  # to locate the testing files
+  my $location = $0; $location =~ s/req_mbfw.t//i;
+  unshift @INC, qw(../lib);     # to locate the modules
+  if (-d 't')
+    {
+    chdir 't';
+    require File::Spec;
+    unshift @INC, File::Spec->catdir(File::Spec->updir, $location);
+    }
+  else
+    {
+    unshift @INC, $location;
+    }
+  print "# INC = @INC\n";
+
+  plan tests => 3;
+  } 
+
+# normal require that calls import automatically (we thus have MBI afterwards)
+require Math::BigFloat;
+my $x = Math::BigFloat->new(1); ++$x;
+is ($x,2, '$x is 2');
+
+like (Math::BigFloat->config()->{with}, qr/^Math::BigInt::(Fast)?Calc\z/, 'with ignored' );
+
+# now override
+Math::BigFloat->import ( with => 'Math::BigInt::Subclass' );
+
+# the "with" argument is ignored
+like (Math::BigFloat->config()->{with}, qr/^Math::BigInt::(Fast)?Calc\z/, 'with ignored' );
+
+# all tests done
+
diff --git a/dist/Math-BigInt/t/require.t b/dist/Math-BigInt/t/require.t
new file mode 100644
index 0000000000..66bf6279e3
--- /dev/null
+++ b/dist/Math-BigInt/t/require.t
@@ -0,0 +1,36 @@
+#!/usr/bin/perl -w
+
+# check that simple requiring BigInt works
+
+use strict;
+use Test;
+
+BEGIN
+  {
+  $| = 1;
+  # to locate the testing files
+  my $location = $0; $location =~ s/require.t//i;
+  unshift @INC, qw(../lib);     # to locate the modules
+  if (-d 't')
+    {
+    chdir 't';
+    require File::Spec;
+    unshift @INC, File::Spec->catdir(File::Spec->updir, $location);
+    }
+  else
+    {
+    unshift @INC, $location;
+    }
+  print "# INC = @INC\n";
+
+  plan tests => 1;
+  } 
+
+my ($x);
+
+require Math::BigInt; $x = Math::BigInt->new(1); ++$x;
+
+ok ($x||'undef',2);
+
+# all tests done
+
diff --git a/dist/Math-BigInt/t/round.t b/dist/Math-BigInt/t/round.t
new file mode 100644
index 0000000000..6f4426b107
--- /dev/null
+++ b/dist/Math-BigInt/t/round.t
@@ -0,0 +1,115 @@
+#!/usr/bin/perl -w
+
+# test rounding with non-integer A and P parameters
+
+use strict;
+use Test::More;
+
+BEGIN
+  {
+  $| = 1;
+  # to locate the testing files
+  my $location = $0; $location =~ s/round.t//i;
+  unshift @INC, qw(../lib);
+  if (-d 't')
+    {
+    chdir 't';
+    require File::Spec;
+    unshift @INC, File::Spec->catdir(File::Spec->updir, $location);
+    }
+  else
+    {
+    unshift @INC, $location;
+    }
+  print "# INC = @INC\n";
+
+  plan tests => 95;
+  } 
+
+use Math::BigFloat;
+
+my $cf = 'Math::BigFloat';
+my $ci = 'Math::BigInt';
+
+my $x = $cf->new('123456.123456');
+
+# unary ops with A
+_do_a($x, 'round', 3, '123000');
+_do_a($x, 'bfround', 3, '123500');
+_do_a($x, 'bfround', 2, '123460');
+_do_a($x, 'bfround', -2, '123456.12');
+_do_a($x, 'bfround', -3, '123456.123');
+
+_do_a($x, 'bround', 4, '123500');
+_do_a($x, 'bround', 3, '123000');
+_do_a($x, 'bround', 2, '120000');
+
+_do_a($x, 'bsqrt', 4, '351.4');
+_do_a($x, 'bsqrt', 3, '351');
+_do_a($x, 'bsqrt', 2, '350');
+
+# setting P
+_do_p($x, 'bsqrt', 2,  '350');
+_do_p($x, 'bsqrt', -2, '351.36');
+
+# binary ops
+_do_2_a($x, 'bdiv', 2, 6, '61728.1');
+_do_2_a($x, 'bdiv', 2, 4, '61730');
+_do_2_a($x, 'bdiv', 2, 3, '61700');
+
+_do_2_p($x, 'bdiv', 2, -6, '61728.061728');
+_do_2_p($x, 'bdiv', 2, -4, '61728.0617');
+_do_2_p($x, 'bdiv', 2, -3, '61728.062');
+
+# all tests done
+
+#############################################################################
+
+sub _do_a
+  { 
+  my ($x, $method, $A, $result) = @_;
+
+  is ($x->copy->$method($A), $result, "$method($A)");
+  is ($x->copy->$method($A.'.1'), $result, "$method(${A}.1)");
+  is ($x->copy->$method($A.'.5'), $result, "$method(${A}.5)");
+  is ($x->copy->$method($A.'.6'), $result, "$method(${A}.6)");
+  is ($x->copy->$method($A.'.9'), $result, "$method(${A}.9)");
+  }
+
+sub _do_p
+  { 
+  my ($x, $method, $P, $result) = @_;
+
+  is ($x->copy->$method(undef,$P), $result, "$method(undef,$P)");
+  is ($x->copy->$method(undef,$P.'.1'), $result, "$method(undef,${P}.1)");
+  is ($x->copy->$method(undef,$P.'.5'), $result, "$method(undef.${P}.5)");
+  is ($x->copy->$method(undef,$P.'.6'), $result, "$method(undef,${P}.6)");
+  is ($x->copy->$method(undef,$P.'.9'), $result, "$method(undef,${P}.9)");
+  }
+
+sub _do_2_a
+  { 
+  my ($x, $method, $y, $A, $result) = @_;
+
+  my $cy = $cf->new($y);
+
+  is ($x->copy->$method($cy,$A), $result, "$method($cy,$A)");
+  is ($x->copy->$method($cy,$A.'.1'), $result, "$method($cy,${A}.1)");
+  is ($x->copy->$method($cy,$A.'.5'), $result, "$method($cy,${A}.5)");
+  is ($x->copy->$method($cy,$A.'.6'), $result, "$method($cy,${A}.6)");
+  is ($x->copy->$method($cy,$A.'.9'), $result, "$method($cy,${A}.9)");
+  }
+
+sub _do_2_p
+  { 
+  my ($x, $method, $y, $P, $result) = @_;
+
+  my $cy = $cf->new($y);
+
+  is ($x->copy->$method($cy,undef,$P), $result, "$method(undef,$P)");
+  is ($x->copy->$method($cy,undef,$P.'.1'), $result, "$method($cy,undef,${P}.1)");
+  is ($x->copy->$method($cy,undef,$P.'.5'), $result, "$method($cy,undef.${P}.5)");
+  is ($x->copy->$method($cy,undef,$P.'.6'), $result, "$method($cy,undef,${P}.6)");
+  is ($x->copy->$method($cy,undef,$P.'.9'), $result, "$method($cy,undef,${P}.9)");
+  }
+
diff --git a/dist/Math-BigInt/t/sub_ali.t b/dist/Math-BigInt/t/sub_ali.t
new file mode 100644
index 0000000000..d6c17530f8
--- /dev/null
+++ b/dist/Math-BigInt/t/sub_ali.t
@@ -0,0 +1,35 @@
+#!/usr/bin/perl -w
+
+# test that the new alias names work
+
+use Test::More;
+use strict;
+
+BEGIN
+  {
+  $| = 1;
+  # to locate the testing files
+  my $location = $0; $location =~ s/sub_ali.t//i;
+  unshift @INC, qw(../lib);
+  if (-d 't')
+    {
+    chdir 't';
+    require File::Spec;
+    unshift @INC, File::Spec->catdir(File::Spec->updir, $location);
+    }
+  else
+    {
+    unshift @INC, $location;
+    }
+  print "# INC = @INC\n";
+
+  plan tests => 6;
+  }
+
+use Math::BigInt::Subclass;
+
+use vars qw/$CL $x/;
+$CL = 'Math::BigInt::Subclass';
+
+require 'alias.inc';
+
diff --git a/dist/Math-BigInt/t/sub_mbf.t b/dist/Math-BigInt/t/sub_mbf.t
new file mode 100644
index 0000000000..94375b6998
--- /dev/null
+++ b/dist/Math-BigInt/t/sub_mbf.t
@@ -0,0 +1,51 @@
+#!/usr/bin/perl -w
+
+use Test;
+use strict;
+
+BEGIN
+  {
+  $| = 1;
+  # to locate the testing files
+  my $location = $0; $location =~ s/sub_mbf.t//i;
+  unshift @INC, '../lib';
+  if (-d 't')
+    {
+    chdir 't';
+    require File::Spec;
+    unshift @INC, File::Spec->catdir(File::Spec->updir, $location);
+    }
+  else
+    {
+    unshift @INC, $location;
+    }
+  print "# INC = @INC\n"; 
+  
+  plan tests => 2308
+    + 6;	# + our own tests
+  }
+
+use Math::BigFloat::Subclass;
+
+use vars qw ($class $try $x $y $f @args $ans $ans1 $ans1_str $setup $CL);
+$class = "Math::BigFloat::Subclass";
+$CL = Math::BigFloat->config()->{lib}; # "Math::BigInt::Calc"; or FastCalc
+
+require 'bigfltpm.inc';	# perform same tests as bigfltpm
+
+###############################################################################
+# Now do custom tests for Subclass itself
+my $ms = $class->new(23);
+print "# Missing custom attribute \$ms->{_custom}" if !ok (1, $ms->{_custom});
+
+# Check that subclass is a Math::BigFloat, but not a Math::Bigint
+ok ($ms->isa('Math::BigFloat'),1);
+ok ($ms->isa('Math::BigInt') || 0,0);
+
+use Math::BigFloat;
+
+my $bf = Math::BigFloat->new(23);		# same as other
+$ms += $bf;
+print "# Tried: \$ms += \$bf, got $ms" if !ok (46, $ms);
+print "# Missing custom attribute \$ms->{_custom}" if !ok (1, $ms->{_custom});
+print "# Wrong class: ref(\$ms) was ".ref($ms) if !ok ($class, ref($ms));
diff --git a/dist/Math-BigInt/t/sub_mbi.t b/dist/Math-BigInt/t/sub_mbi.t
new file mode 100644
index 0000000000..edb4daf058
--- /dev/null
+++ b/dist/Math-BigInt/t/sub_mbi.t
@@ -0,0 +1,53 @@
+#!/usr/bin/perl -w
+
+use Test;
+use strict;
+
+BEGIN
+  {
+  $| = 1;
+  # to locate the testing files
+  my $location = $0; $location =~ s/sub_mbi.t//i;
+  unshift @INC, qw(../lib);
+  if (-d 't')
+    {
+    chdir 't';
+    require File::Spec;
+    unshift @INC, File::Spec->catdir(File::Spec->updir, $location);
+    }
+  else
+    {
+    unshift @INC, $location;
+    }
+  print "# INC = @INC\n";
+
+  plan tests => 3273
+    + 5;	# +5 own tests
+  }
+
+use Math::BigInt::Subclass;
+
+use vars qw ($class $try $x $y $f @args $ans $ans1 $ans1_str $setup $CL);
+$class = "Math::BigInt::Subclass";
+$CL = "Math::BigInt::Calc";
+
+my $version = '0.02';   # for $VERSION tests, match current release (by hand!)
+
+require 'bigintpm.inc';	# perform same tests as bigintpm
+
+###############################################################################
+# Now do custom tests for Subclass itself
+ 
+my $ms = $class->new(23);
+print "# Missing custom attribute \$ms->{_custom}" if !ok (1, $ms->{_custom});
+
+# Check that a subclass is still considered a BigInt
+ok ($ms->isa('Math::BigInt'),1);
+
+use Math::BigInt;
+
+my $bi = Math::BigInt->new(23);		# same as other
+$ms += $bi;
+print "# Tried: \$ms += \$bi, got $ms" if !ok (46, $ms);
+print "# Missing custom attribute \$ms->{_custom}" if !ok (1, $ms->{_custom});
+print "# Wrong class: ref(\$ms) was ".ref($ms) if !ok ($class, ref($ms));
diff --git a/dist/Math-BigInt/t/sub_mif.t b/dist/Math-BigInt/t/sub_mif.t
new file mode 100644
index 0000000000..14d041b3da
--- /dev/null
+++ b/dist/Math-BigInt/t/sub_mif.t
@@ -0,0 +1,39 @@
+#!/usr/bin/perl -w
+
+# test rounding, accuracy, precicion and fallback, round_mode and mixing
+# of classes
+
+use strict;
+use Test;
+
+BEGIN
+  {
+  $| = 1;
+  # to locate the testing files
+  my $location = $0; $location =~ s/sub_mif.t//i;
+  unshift @INC, '../lib';	# for testing manually
+  if (-d 't')
+    {
+    chdir 't';
+    require File::Spec;
+    unshift @INC, File::Spec->catdir(File::Spec->updir, $location);
+    }
+  else
+    {
+    unshift @INC, $location;
+    }
+  print "# INC = @INC\n";
+
+  plan tests => 684;
+  }
+
+use Math::BigInt::Subclass;
+use Math::BigFloat::Subclass;
+
+use vars qw/$mbi $mbf/;
+
+$mbi = 'Math::BigInt::Subclass';
+$mbf = 'Math::BigFloat::Subclass';
+
+require 'mbimbf.inc';
+
diff --git a/dist/Math-BigInt/t/trap.t b/dist/Math-BigInt/t/trap.t
new file mode 100644
index 0000000000..94a7da4acb
--- /dev/null
+++ b/dist/Math-BigInt/t/trap.t
@@ -0,0 +1,92 @@
+#!/usr/bin/perl -w
+
+# test that config ( trap_nan => 1, trap_inf => 1) really works/dies
+
+use strict;
+use Test::More;
+
+BEGIN
+  {
+  $| = 1;
+  chdir 't' if -d 't';
+  unshift @INC, '../lib'; # for running manually
+  plan tests => 43;
+  } 
+
+use Math::BigInt;
+use Math::BigFloat;
+
+my $mbi = 'Math::BigInt'; my $mbf = 'Math::BigFloat';
+my ($cfg,$x);
+
+foreach my $class ($mbi, $mbf)
+  {
+  # can do and defaults are okay?
+  ok ($class->can('config'), 'can config()');
+  is ($class->config()->{trap_nan}, 0, 'trap_nan defaults to 0');
+  is ($class->config()->{trap_inf}, 0, 'trap_inf defaults to 0');
+
+  # can set?
+  $cfg = $class->config( trap_nan => 1 );
+  is ($cfg->{trap_nan},1, 'trap_nan now true');
+
+  # also test that new() still works normally
+  eval ("\$x = \$class->new('42'); \$x->bnan();");
+  like ($@, qr/^Tried to set/, 'died');
+  is ($x,42,'$x after new() never modified');
+
+  # can reset?
+  $cfg = $class->config( trap_nan => 0 );
+  is ($cfg->{trap_nan}, 0, 'trap_nan disabled');
+  
+  # can set?
+  $cfg = $class->config( trap_inf => 1 );
+  is ($cfg->{trap_inf}, 1, 'trap_inf enabled');
+
+  eval ("\$x = \$class->new('4711'); \$x->binf();");
+  like ($@, qr/^Tried to set/, 'died');
+  is ($x,4711,'$x after new() never modified');
+
+  eval ("\$x = \$class->new('inf');");
+  like ($@, qr/^Tried to set/, 'died');
+  is ($x,4711,'$x after new() never modified');
+  
+  eval ("\$x = \$class->new('-inf');");
+  like ($@, qr/^Tried to set/, 'died');
+  is ($x,4711,'$x after new() never modified');
+  
+  # +$x/0 => +inf
+  eval ("\$x = \$class->new('4711'); \$x->bdiv(0);");
+  like ($@, qr/^Tried to set/, 'died');
+  is ($x,4711,'$x after new() never modified');
+  
+  # -$x/0 => -inf
+  eval ("\$x = \$class->new('-0815'); \$x->bdiv(0);");
+  like ($@, qr/^Tried to set/, 'died');
+  is ($x,'-815', '$x after new not modified');
+  
+  $cfg = $class->config( trap_nan => 1 );
+  # 0/0 => NaN
+  eval ("\$x = \$class->new('0'); \$x->bdiv(0);");
+  like ($@, qr/^Tried to set/, 'died');
+  is ($x,'0', '$x after new not modified');
+  }
+
+##############################################################################
+# BigInt
+
+$x = Math::BigInt->new(2);
+eval ("\$x = \$mbi->new('0.1');");
+is ($x,2,'never modified since it dies');
+eval ("\$x = \$mbi->new('0a.1');");
+is ($x,2,'never modified since it dies');
+
+##############################################################################
+# BigFloat
+
+$x = Math::BigFloat->new(2);
+eval ("\$x = \$mbf->new('0.1a');");
+is ($x,2,'never modified since it dies');
+
+# all tests done
+
diff --git a/dist/Math-BigInt/t/upgrade.inc b/dist/Math-BigInt/t/upgrade.inc
new file mode 100644
index 0000000000..1160a21c6b
--- /dev/null
+++ b/dist/Math-BigInt/t/upgrade.inc
@@ -0,0 +1,1500 @@
+# include this file into another for subclass testing
+
+# This file is nearly identical to bigintpm.t, except that certain results
+# are _requird_ to be different due to "upgrading" or "promoting" to BigFloat.
+# The reverse is not true, any unmarked results can be either BigInt or
+# BigFloat, depending on how good the internal optimization is (e.g. it
+# is usually desirable to have 2 ** 2 return a BigInt, not a BigFloat).
+
+# Results that are required to be BigFloat are marked with C<^> at the end.
+
+# Please note that the testcount goes up by two for each extra result marked
+# with ^, since then we test whether it has the proper class and that it left
+# the upgrade variable alone.
+
+my $version = ${"$class\::VERSION"};
+
+##############################################################################
+# for testing inheritance of _swap
+
+package Math::Foo;
+
+use Math::BigInt lib => $main::CL;
+use vars qw/@ISA/;
+@ISA = (qw/Math::BigInt/);
+
+use overload
+# customized overload for sub, since original does not use swap there
+'-'     =>      sub { my @a = ref($_[0])->_swap(@_);
+                   $a[0]->bsub($a[1])};
+
+sub _swap
+  {
+  # a fake _swap, which reverses the params
+  my $self = shift;                     # for override in subclass
+  if ($_[2])
+    {
+    my $c = ref ($_[0] ) || 'Math::Foo';
+    return ( $_[0]->copy(), $_[1] );
+    }
+  else
+    {
+    return ( Math::Foo->new($_[1]), $_[0] );
+    }
+  }
+
+##############################################################################
+package main;
+
+my $CALC = $class->config()->{lib}; ok ($CALC,$CL);
+
+my ($f,$z,$a,$exp,@a,$m,$e,$round_mode,$expected_class);
+
+while (<DATA>) 
+  {
+  $_ =~ s/[\n\r]//g;	# remove newlines
+  next if /^#/;	# skip comments
+  if (s/^&//) 
+    {
+    $f = $_; next;
+    }
+  elsif (/^\$/) 
+    {
+    $round_mode = $_; $round_mode =~ s/^\$/$class\->/; next;
+    }
+
+  @args = split(/:/,$_,99); $ans = pop(@args);
+  $expected_class = $class;
+  if ($ans =~ /\^$/)
+    {
+    $expected_class = $ECL; $ans =~ s/\^$//;
+    }
+  $try = "\$x = $class->new(\"$args[0]\");";
+  if ($f eq "bnorm")
+    {
+    $try = "\$x = $class->bnorm(\"$args[0]\");";
+  # some is_xxx tests
+   } elsif ($f =~ /^is_(zero|one|odd|even|negative|positive|nan|int)$/) {
+    $try .= "\$x->$f();";
+   } elsif ($f eq "as_hex") {
+    $try .= '$x->as_hex();';
+   } elsif ($f eq "as_bin") {
+    $try .= '$x->as_bin();';
+   } elsif ($f eq "is_inf") {
+    $try .= "\$x->is_inf('$args[1]');";
+   } elsif ($f eq "binf") {
+    $try .= "\$x->binf('$args[1]');";
+   } elsif ($f eq "bone") {
+    $try .= "\$x->bone('$args[1]');";
+   # some unary ops
+   } elsif ($f =~ /^b(nan|floor|ceil|sstr|neg|abs|inc|dec|not|sqrt|fac)$/) {
+    $try .= "\$x->$f();";
+   } elsif ($f eq "length") {
+    $try .= '$x->length();';
+   } elsif ($f eq "exponent"){
+    # ->bstr() to see if an object is returned
+    $try .= '$x = $x->exponent()->bstr();';
+   } elsif ($f eq "mantissa"){
+    # ->bstr() to see if an object is returned
+    $try .= '$x = $x->mantissa()->bstr();';
+   } elsif ($f eq "parts"){
+    $try .= '($m,$e) = $x->parts();'; 
+    # ->bstr() to see if an object is returned
+    $try .= '$m = $m->bstr(); $m = "NaN" if !defined $m;';
+    $try .= '$e = $e->bstr(); $e = "NaN" if !defined $e;';
+    $try .= '"$m,$e";';
+   } else {
+    if ($args[1] !~ /\./)
+      {
+      $try .= "\$y = $class->new(\"$args[1]\");";	# BigInt
+      }
+    else
+      {
+      $try .= "\$y = $ECL->new(\"$args[1]\");";		# BigFloat
+      }
+    if ($f eq "bcmp")
+      {
+      $try .= '$x->bcmp($y);';
+      } elsif ($f eq "bround") {
+      $try .= "$round_mode; \$x->bround(\$y);";
+      } elsif ($f eq "broot") {
+      $try .= "\$x->broot(\$y);";
+      } elsif ($f eq "bacmp"){
+      $try .= '$x->bacmp($y);';
+      } elsif ($f eq "badd"){
+      $try .= '$x + $y;';
+      } elsif ($f eq "bsub"){
+      $try .= '$x - $y;';
+      } elsif ($f eq "bmul"){
+      $try .= '$x * $y;';
+      } elsif ($f eq "bdiv"){
+      $try .= '$x / $y;';
+      } elsif ($f eq "bdiv-list"){
+      $try .= 'join (",",$x->bdiv($y));';
+      # overload via x=
+      } elsif ($f =~ /^.=$/){
+      $try .= "\$x $f \$y;";
+      # overload via x
+      } elsif ($f =~ /^.$/){
+      $try .= "\$x $f \$y;";
+      } elsif ($f eq "bmod"){
+      $try .= '$x % $y;';
+      } elsif ($f eq "bgcd")
+        {
+        if (defined $args[2])
+          {
+          $try .= " \$z = $class->new('$args[2]'); ";
+          }
+        $try .= "$class\::bgcd(\$x, \$y";
+        $try .= ", \$z" if (defined $args[2]);
+        $try .= " );";
+        }
+      elsif ($f eq "blcm")
+        {
+        if (defined $args[2])
+          {
+          $try .= " \$z = $class->new('$args[2]'); ";
+          }
+        $try .= "$class\::blcm(\$x, \$y";
+        $try .= ", \$z" if (defined $args[2]);
+        $try .= " );";
+      }elsif ($f eq "blsft"){
+        if (defined $args[2])
+          {
+          $try .= "\$x->blsft(\$y,$args[2]);";
+          }
+        else
+          {
+          $try .= "\$x << \$y;";
+          }
+      }elsif ($f eq "brsft"){
+        if (defined $args[2])
+          {
+          $try .= "\$x->brsft(\$y,$args[2]);";
+          }
+        else
+          {
+          $try .= "\$x >> \$y;";
+          }
+      }elsif ($f eq "band"){
+        $try .= "\$x & \$y;";
+      }elsif ($f eq "bior"){
+        $try .= "\$x | \$y;";
+      }elsif ($f eq "bxor"){
+        $try .= "\$x ^ \$y;";
+      }elsif ($f eq "bpow"){
+        $try .= "\$x ** \$y;";
+      }elsif ($f eq "digit"){
+        $try = "\$x = $class->new('$args[0]'); \$x->digit($args[1]);";
+      } else { warn "Unknown op '$f'"; }
+    } # end else all other ops
+
+  $ans1 = eval $try;
+  # convert hex/binary targets to decimal	
+  if ($ans =~ /^(0x0x|0b0b)/)
+    {
+    $ans =~ s/^0[xb]//; $ans = Math::BigInt->new($ans)->bstr();
+    }
+  if ($ans eq "")
+    {
+    ok_undef ($ans1); 
+    }
+  else
+    {
+    # print "try: $try ans: $ans1 $ans\n";
+    print "# Tried: '$try'\n" if !ok ($ans1, $ans);
+    if ($expected_class ne $class)
+      {
+      ok (ref($ans1),$expected_class);	# also checks that it really is ref!
+      ok ($Math::BigInt::upgrade,'Math::BigFloat');	# still okay?
+      }
+    }
+  # check internal state of number objects
+  is_valid($ans1,$f) if ref $ans1; 
+  } # endwhile data tests
+close DATA;
+
+my $warn = ''; $SIG{__WARN__} = sub { $warn = shift; };
+
+# these should not warn
+$warn = ''; eval "\$z = 3.17 <= \$y"; ok ($z, 1); ok ($warn, '');
+$warn = ''; eval "\$z = \$y >= 3.17"; ok ($z, 1); ok ($warn, '');
+
+# all tests done
+
+1;
+
+###############################################################################
+###############################################################################
+# Perl 5.005 does not like ok ($x,undef)
+
+sub ok_undef
+  {
+  my $x = shift;
+
+  ok (1,1) and return if !defined $x;
+  ok ($x,'undef');
+  }
+
+###############################################################################
+# sub to check validity of a BigInt internally, to ensure that no op leaves a
+# number object in an invalid state (f.i. "-0")
+
+sub is_valid
+  {
+  my ($x,$f,$c) = @_;
+
+  # The checks here are loosened a bit to allow BigInt or BigFloats to pass
+
+  my $e = 0;			# error?
+  # ok as reference? 
+  # $e = "Not a reference to $c" if (ref($x) || '') ne $c;
+
+  # has ok sign?
+  $e = "Illegal sign $x->{sign} (expected: '+', '-', '-inf', '+inf' or 'NaN'"
+   if $e eq '0' && $x->{sign} !~ /^(\+|-|\+inf|-inf|NaN)$/;
+
+  $e = "-0 is invalid!" if $e ne '0' && $x->{sign} eq '-' && $x == 0;
+  #$e = $CALC->_check($x->{value}) if $e eq '0';
+
+  # test done, see if error did crop up
+  ok (1,1), return if ($e eq '0');
+
+  ok (1,$e." after op '$f'");
+  }
+
+__DATA__
+&.=
+1234:-345:1234-345
+&+=
+1:2:3
+-1:-2:-3
+&-=
+1:2:-1
+-1:-2:1
+&*=
+2:3:6
+-1:5:-5
+&%=
+100:3:1
+8:9:8
+&/=
+100:3:33.33333333333333333333333333333333333333
+-8:2:-4
+&|=
+2:1:3
+&&=
+5:7:5
+&^=
+5:7:2
+&is_negative
+0:0
+-1:1
+1:0
++inf:0
+-inf:1
+NaNneg:0
+&is_positive
+0:0
+-1:0
+1:1
++inf:1
+-inf:0
+NaNneg:0
+&is_odd
+abc:0
+0:0
+1:1
+3:1
+-1:1
+-3:1
+10000001:1
+10000002:0
+2:0
+120:0
+121:1
+&is_int
+NaN:0
+inf:0
+-inf:0
+1:1
+12:1
+123e12:1
+&is_even
+abc:0
+0:1
+1:0
+3:0
+-1:0
+-3:0
+10000001:0
+10000002:1
+2:1
+120:1
+121:0
+&bacmp
++0:-0:0
++0:+1:-1
+-1:+1:0
++1:-1:0
+-1:+2:-1
++2:-1:1
+-123456789:+987654321:-1
++123456789:-987654321:-1
++987654321:+123456789:1
+-987654321:+123456789:1
+-123:+4567889:-1
+# NaNs
+acmpNaN:123:
+123:acmpNaN:
+acmpNaN:acmpNaN:
+# infinity
++inf:+inf:0
+-inf:-inf:0
++inf:-inf:0
+-inf:+inf:0
++inf:123:1
+-inf:123:1
++inf:-123:1
+-inf:-123:1
+# return undef
++inf:NaN:
+NaN:inf:
+-inf:NaN:
+NaN:-inf:
+&bnorm
+123:123
+12.3:12.3^
+# binary input
+0babc:NaN
+0b123:NaN
+0b0:0
+-0b0:0
+-0b1:-1
+0b0001:1
+0b001:1
+0b011:3
+0b101:5
+0b1001:9
+0b10001:17
+0b100001:33
+0b1000001:65
+0b10000001:129
+0b100000001:257
+0b1000000001:513
+0b10000000001:1025
+0b100000000001:2049
+0b1000000000001:4097
+0b10000000000001:8193
+0b100000000000001:16385
+0b1000000000000001:32769
+0b10000000000000001:65537
+0b100000000000000001:131073
+0b1000000000000000001:262145
+0b10000000000000000001:524289
+0b100000000000000000001:1048577
+0b1000000000000000000001:2097153
+0b10000000000000000000001:4194305
+0b100000000000000000000001:8388609
+0b1000000000000000000000001:16777217
+0b10000000000000000000000001:33554433
+0b100000000000000000000000001:67108865
+0b1000000000000000000000000001:134217729
+0b10000000000000000000000000001:268435457
+0b100000000000000000000000000001:536870913
+0b1000000000000000000000000000001:1073741825
+0b10000000000000000000000000000001:2147483649
+0b100000000000000000000000000000001:4294967297
+0b1000000000000000000000000000000001:8589934593
+0b10000000000000000000000000000000001:17179869185
+0b_101:NaN
+0b1_0_1:5
+0b0_0_0_1:1
+# hex input
+-0x0:0
+0xabcdefgh:NaN
+0x1234:4660
+0xabcdef:11259375
+-0xABCDEF:-11259375
+-0x1234:-4660
+0x12345678:305419896
+0x1_2_3_4_56_78:305419896
+0xa_b_c_d_e_f:11259375
+0x_123:NaN
+0x9:9
+0x11:17
+0x21:33
+0x41:65
+0x81:129
+0x101:257
+0x201:513
+0x401:1025
+0x801:2049
+0x1001:4097
+0x2001:8193
+0x4001:16385
+0x8001:32769
+0x10001:65537
+0x20001:131073
+0x40001:262145
+0x80001:524289
+0x100001:1048577
+0x200001:2097153
+0x400001:4194305
+0x800001:8388609
+0x1000001:16777217
+0x2000001:33554433
+0x4000001:67108865
+0x8000001:134217729
+0x10000001:268435457
+0x20000001:536870913
+0x40000001:1073741825
+0x80000001:2147483649
+0x100000001:4294967297
+0x200000001:8589934593
+0x400000001:17179869185
+0x800000001:34359738369
+# inf input
+inf:inf
++inf:inf
+-inf:-inf
+0inf:NaN
+# abnormal input
+:NaN
+abc:NaN
+   1 a:NaN
+1bcd2:NaN
+11111b:NaN
++1z:NaN
+-1z:NaN
+# only one underscore between two digits
+_123:NaN
+_123_:NaN
+123_:NaN
+1__23:NaN
+1E1__2:NaN
+1_E12:NaN
+1E_12:NaN
+1_E_12:NaN
++_1E12:NaN
++0_1E2:100
++0_0_1E2:100
+-0_0_1E2:-100
+-0_0_1E+0_0_2:-100
+E1:NaN
+E23:NaN
+1.23E1:12.3^
+1.23E-1:0.123^
+# bug with two E's in number being valid
+1e2e3:NaN
+1e2r:NaN
+1e2.0:NaN
+# leading zeros
+012:12
+0123:123
+01234:1234
+012345:12345
+0123456:123456
+01234567:1234567
+012345678:12345678
+0123456789:123456789
+01234567891:1234567891
+012345678912:12345678912
+0123456789123:123456789123
+01234567891234:1234567891234
+# normal input
+0:0
++0:0
++00:0
++000:0
+000000000000000000:0
+-0:0
+-0000:0
++1:1
++01:1
++001:1
++00000100000:100000
+123456789:123456789
+-1:-1
+-01:-1
+-001:-1
+-123456789:-123456789
+-00000100000:-100000
+1_2_3:123
+10000000000E-1_0:1
+1E2:100
+1E1:10
+1E0:1
+1.23E2:123
+100E-1:10
+# floating point input
+# .2e2:20
+1.E3:1000
+1.01E2:101
+1010E-1:101
+-1010E0:-1010
+-1010E1:-10100
+1234.00:1234
+# non-integer numbers
+-1010E-2:-10.1^
+-1.01E+1:-10.1^
+-1.01E-1:-0.101^
+&bnan
+1:NaN
+2:NaN
+abc:NaN
+&bone
+2:+:1
+2:-:-1
+boneNaN:-:-1
+boneNaN:+:1
+2:abc:1
+3::1
+&binf
+1:+:inf
+2:-:-inf
+3:abc:inf
+&is_nan
+123:0
+abc:1
+NaN:1
+-123:0
+&is_inf
++inf::1
+-inf::1
+abc::0
+1::0
+NaN::0
+-1::0
++inf:-:0
++inf:+:1
+-inf:-:1
+-inf:+:0
+# it must be exactly /^[+-]inf$/
++infinity::0
+-infinity::0
+&blsft
+abc:abc:NaN
++2:+2:8
++1:+32:4294967296
++1:+48:281474976710656
++8:-2:NaN
+# excercise base 10
++12345:4:10:123450000
+-1234:0:10:-1234
++1234:0:10:1234
++2:2:10:200
++12:2:10:1200
++1234:-3:10:NaN
+1234567890123:12:10:1234567890123000000000000
+&brsft
+abc:abc:NaN
++8:+2:2
++4294967296:+32:1
++281474976710656:+48:1
++2:-2:NaN
+# excercise base 10
+-1234:0:10:-1234
++1234:0:10:1234
++200:2:10:2
++1234:3:10:1
++1234:2:10:12
++1234:-3:10:NaN
+310000:4:10:31
+12300000:5:10:123
+1230000000000:10:10:123
+09876123456789067890:12:10:9876123
+1234561234567890123:13:10:123456
+&bsstr
+1e+34:1e+34
+123.456E3:123456e+0
+100:1e+2
+abc:NaN
+&bneg
+bnegNaN:NaN
++inf:-inf
+-inf:inf
+abd:NaN
+0:0
+1:-1
+-1:1
++123456789:-123456789
+-123456789:123456789
+&babs
+babsNaN:NaN
++inf:inf
+-inf:inf
+0:0
+1:1
+-1:1
++123456789:123456789
+-123456789:123456789
+&bcmp
+bcmpNaN:bcmpNaN:
+bcmpNaN:0:
+0:bcmpNaN:
+0:0:0
+-1:0:-1
+0:-1:1
+1:0:1
+0:1:-1
+-1:1:-1
+1:-1:1
+-1:-1:0
+1:1:0
+123:123:0
+123:12:1
+12:123:-1
+-123:-123:0
+-123:-12:-1
+-12:-123:1
+123:124:-1
+124:123:1
+-123:-124:1
+-124:-123:-1
+100:5:1
+-123456789:987654321:-1
++123456789:-987654321:1
+-987654321:123456789:-1
+-inf:5432112345:-1
++inf:5432112345:1
+-inf:-5432112345:-1
++inf:-5432112345:1
++inf:+inf:0
+-inf:-inf:0
++inf:-inf:1
+-inf:+inf:-1
+5:inf:-1
+5:inf:-1
+-5:-inf:1
+-5:-inf:1
+# return undef
++inf:NaN:
+NaN:inf:
+-inf:NaN:
+NaN:-inf:
+&binc
+abc:NaN
++inf:inf
+-inf:-inf
++0:1
++1:2
+-1:0
+&bdec
+abc:NaN
++inf:inf
+-inf:-inf
++0:-1
++1:0
+-1:-2
+&badd
+abc:abc:NaN
+abc:0:NaN
++0:abc:NaN
++inf:-inf:NaN
+-inf:+inf:NaN
++inf:+inf:inf
+-inf:-inf:-inf
+baddNaN:+inf:NaN
+baddNaN:+inf:NaN
++inf:baddNaN:NaN
+-inf:baddNaN:NaN
+0:0:0
+1:0:1
+0:1:1
+1:1:2
+-1:0:-1
+0:-1:-1
+-1:-1:-2
+-1:+1:0
++1:-1:0
++9:+1:10
++99:+1:100
++999:+1:1000
++9999:+1:10000
++99999:+1:100000
++999999:+1:1000000
++9999999:+1:10000000
++99999999:+1:100000000
++999999999:+1:1000000000
++9999999999:+1:10000000000
++99999999999:+1:100000000000
++10:-1:9
++100:-1:99
++1000:-1:999
++10000:-1:9999
++100000:-1:99999
++1000000:-1:999999
++10000000:-1:9999999
++100000000:-1:99999999
++1000000000:-1:999999999
++10000000000:-1:9999999999
++123456789:987654321:1111111110
+-123456789:987654321:864197532
+-123456789:-987654321:-1111111110
++123456789:-987654321:-864197532
+2:2.5:4.5^
+-123:-1.5:-124.5^
+-1.2:1:-0.2^
+&bsub
+abc:abc:NaN
+abc:+0:NaN
++0:abc:NaN
++inf:-inf:inf
+-inf:+inf:-inf
++inf:+inf:NaN
+-inf:-inf:NaN
++0:+0:0
++1:+0:1
++0:+1:-1
++1:+1:0
+-1:+0:-1
++0:-1:1
+-1:-1:0
+-1:+1:-2
++1:-1:2
++9:+1:8
++99:+1:98
++999:+1:998
++9999:+1:9998
++99999:+1:99998
++999999:+1:999998
++9999999:+1:9999998
++99999999:+1:99999998
++999999999:+1:999999998
++9999999999:+1:9999999998
++99999999999:+1:99999999998
++10:-1:11
++100:-1:101
++1000:-1:1001
++10000:-1:10001
++100000:-1:100001
++1000000:-1:1000001
++10000000:-1:10000001
++100000000:-1:100000001
++1000000000:-1:1000000001
++10000000000:-1:10000000001
++123456789:+987654321:-864197532
+-123456789:+987654321:-1111111110
+-123456789:-987654321:864197532
++123456789:-987654321:1111111110
+&bmul
+abc:abc:NaN
+abc:+0:NaN
++0:abc:NaN
+NaNmul:+inf:NaN
+NaNmul:-inf:NaN
+-inf:NaNmul:NaN
++inf:NaNmul:NaN
++inf:+inf:inf
++inf:-inf:-inf
+-inf:+inf:-inf
+-inf:-inf:inf
++0:+0:0
++0:+1:0
++1:+0:0
++0:-1:0
+-1:+0:0
+123456789123456789:0:0
+0:123456789123456789:0
+-1:-1:1
+-1:+1:-1
++1:-1:-1
++1:+1:1
++2:+3:6
+-2:+3:-6
++2:-3:-6
+-2:-3:6
+111:111:12321
+10101:10101:102030201
+1001001:1001001:1002003002001
+100010001:100010001:10002000300020001
+10000100001:10000100001:100002000030000200001
+11111111111:9:99999999999
+22222222222:9:199999999998
+33333333333:9:299999999997
+44444444444:9:399999999996
+55555555555:9:499999999995
+66666666666:9:599999999994
+77777777777:9:699999999993
+88888888888:9:799999999992
+99999999999:9:899999999991
++25:+25:625
++12345:+12345:152399025
++99999:+11111:1111088889
+9999:10000:99990000
+99999:100000:9999900000
+999999:1000000:999999000000
+9999999:10000000:99999990000000
+99999999:100000000:9999999900000000
+999999999:1000000000:999999999000000000
+9999999999:10000000000:99999999990000000000
+99999999999:100000000000:9999999999900000000000
+999999999999:1000000000000:999999999999000000000000
+9999999999999:10000000000000:99999999999990000000000000
+99999999999999:100000000000000:9999999999999900000000000000
+999999999999999:1000000000000000:999999999999999000000000000000
+9999999999999999:10000000000000000:99999999999999990000000000000000
+99999999999999999:100000000000000000:9999999999999999900000000000000000
+999999999999999999:1000000000000000000:999999999999999999000000000000000000
+9999999999999999999:10000000000000000000:99999999999999999990000000000000000000
+3:3.5:10.5^
+3.5:3:10.5^
+&bdiv-list
+100:20:5,0
+4095:4095:1,0
+-4095:-4095:1,0
+4095:-4095:-1,0
+-4095:4095:-1,0
+123:2:61.5,1
+9:5:1.8,4
+9:4:2.25,1
+# inf handling and general remainder
+5:8:0.625,5
+0:8:0,0
+11:2:5.5,1
+11:-2:-5.5,-1
+-11:2:-5.5,1
+# see table in documentation in MBI
+0:inf:0,0
+0:-inf:0,0
+5:inf:0,5
+5:-inf:0,5
+-5:inf:0,-5
+-5:-inf:0,-5
+inf:5:inf,0
+-inf:5:-inf,0
+inf:-5:-inf,0
+-inf:-5:inf,0
+5:5:1,0
+-5:-5:1,0
+inf:inf:NaN,NaN
+-inf:-inf:NaN,NaN
+-inf:inf:NaN,NaN
+inf:-inf:NaN,NaN
+8:0:inf,8
+inf:0:inf,inf
+# exceptions to reminder rule
+-8:0:-inf,-8
+-inf:0:-inf,-inf
+0:0:NaN,NaN
+&bdiv
+abc:abc:NaN
+abc:1:NaN
+1:abc:NaN
+0:0:NaN
+# inf handling (see table in doc)
+0:inf:0
+0:-inf:0
+5:inf:0
+5:-inf:0
+-5:inf:0
+-5:-inf:0
+inf:5:inf
+-inf:5:-inf
+inf:-5:-inf
+-inf:-5:inf
+5:5:1
+-5:-5:1
+inf:inf:NaN
+-inf:-inf:NaN
+-inf:inf:NaN
+inf:-inf:NaN
+8:0:inf
+inf:0:inf
+-8:0:-inf
+-inf:0:-inf
+0:0:NaN
+11:2:5.5^
+-11:-2:5.5^
+-11:2:-5.5^
+11:-2:-5.5^
+0:1:0
+0:-1:0
+1:1:1
+-1:-1:1
+1:-1:-1
+-1:1:-1
+1:2:0.5^
+2:1:2
+1000000000:9:111111111.1111111111111111111111111111111^
+2000000000:9:222222222.2222222222222222222222222222222^
+3000000000:9:333333333.3333333333333333333333333333333^
+4000000000:9:444444444.4444444444444444444444444444444^
+5000000000:9:555555555.5555555555555555555555555555556^
+6000000000:9:666666666.6666666666666666666666666666667^
+7000000000:9:777777777.7777777777777777777777777777778^
+8000000000:9:888888888.8888888888888888888888888888889^
+9000000000:9:1000000000
+35500000:113:314159.2920353982300884955752212389380531^
+71000000:226:314159.2920353982300884955752212389380531^
+106500000:339:314159.2920353982300884955752212389380531^
+1000000000:3:333333333.3333333333333333333333333333333^
++10:+5:2
++100:+4:25
++1000:+8:125
++10000:+16:625
+999999999999:9:111111111111
+999999999999:99:10101010101
+999999999999:999:1001001001
+999999999999:9999:100010001
+999999999999999:99999:10000100001
++1111088889:99999:11111
+-5:-3:1.666666666666666666666666666666666666667^
+-5:3:-1.666666666666666666666666666666666666667^
+4:3:1.333333333333333333333333333333333333333^
+4:-3:-1.333333333333333333333333333333333333333^
+1:3:0.3333333333333333333333333333333333333333^
+1:-3:-0.3333333333333333333333333333333333333333^
+-2:-3:0.6666666666666666666666666666666666666667^
+-2:3:-0.6666666666666666666666666666666666666667^
+8:5:1.6^
+-8:5:-1.6^
+14:-3:-4.666666666666666666666666666666666666667^
+-14:3:-4.666666666666666666666666666666666666667^
+-14:-3:4.666666666666666666666666666666666666667^
+14:3:4.666666666666666666666666666666666666667^
+# bug in Calc with '99999' vs $BASE-1
+#10000000000000000000000000000000000000000000000000000000000000000000000000000000000:10000000375084540248994272022843165711074:999999962491547381984643365663244474111576
+12:24:0.5^
+&bmod
+# inf handling, see table in doc
+0:inf:0
+0:-inf:0
+5:inf:5
+5:-inf:5
+-5:inf:-5
+-5:-inf:-5
+inf:5:0
+-inf:5:0
+inf:-5:0
+-inf:-5:0
+5:5:0
+-5:-5:0
+inf:inf:NaN
+-inf:-inf:NaN
+-inf:inf:NaN
+inf:-inf:NaN
+8:0:8
+inf:0:inf
+# exceptions to reminder rule
+-inf:0:-inf
+-8:0:-8
+0:0:NaN
+abc:abc:NaN
+abc:1:abc:NaN
+1:abc:NaN
+0:0:NaN
+0:1:0
+1:0:1
+0:-1:0
+-1:0:-1
+1:1:0
+-1:-1:0
+1:-1:0
+-1:1:0
+1:2:1
+2:1:0
+1000000000:9:1
+2000000000:9:2
+3000000000:9:3
+4000000000:9:4
+5000000000:9:5
+6000000000:9:6
+7000000000:9:7
+8000000000:9:8
+9000000000:9:0
+35500000:113:33
+71000000:226:66
+106500000:339:99
+1000000000:3:1
+10:5:0
+100:4:0
+1000:8:0
+10000:16:0
+999999999999:9:0
+999999999999:99:0
+999999999999:999:0
+999999999999:9999:0
+999999999999999:99999:0
+-9:+5:1
++9:-5:-1
+-9:-5:-4
+-5:3:1
+-2:3:1
+4:3:1
+1:3:1
+-5:-3:-2
+-2:-3:-2
+4:-3:-2
+1:-3:-2
+4095:4095:0
+100041000510123:3:0
+152403346:12345:4321
+9:5:4
+&bgcd
+abc:abc:NaN
+abc:+0:NaN
++0:abc:NaN
++0:+0:0
++0:+1:1
++1:+0:1
++1:+1:1
++2:+3:1
++3:+2:1
+-3:+2:1
+100:625:25
+4096:81:1
+1034:804:2
+27:90:56:1
+27:90:54:9
+&blcm
+abc:abc:NaN
+abc:+0:NaN
++0:abc:NaN
++0:+0:NaN
++1:+0:0
++0:+1:0
++27:+90:270
++1034:+804:415668
+&band
+abc:abc:NaN
+abc:0:NaN
+0:abc:NaN
+1:2:0
+3:2:2
++8:+2:0
++281474976710656:0:0
++281474976710656:1:0
++281474976710656:+281474976710656:281474976710656
+-2:-3:-4
+-1:-1:-1
+-6:-6:-6
+-7:-4:-8
+-7:4:0
+-4:7:4
+# equal arguments are treated special, so also do some test with unequal ones
+0xFFFF:0xFFFF:0x0xFFFF
+0xFFFFFF:0xFFFFFF:0x0xFFFFFF
+0xFFFFFFFF:0xFFFFFFFF:0x0xFFFFFFFF
+0xFFFFFFFFFF:0xFFFFFFFFFF:0x0xFFFFFFFFFF
+0xFFFFFFFFFFFF:0xFFFFFFFFFFFF:0x0xFFFFFFFFFFFF
+0xF0F0:0xF0F0:0x0xF0F0
+0x0F0F:0x0F0F:0x0x0F0F
+0xF0F0F0:0xF0F0F0:0x0xF0F0F0
+0x0F0F0F:0x0F0F0F:0x0x0F0F0F
+0xF0F0F0F0:0xF0F0F0F0:0x0xF0F0F0F0
+0x0F0F0F0F:0x0F0F0F0F:0x0x0F0F0F0F
+0xF0F0F0F0F0:0xF0F0F0F0F0:0x0xF0F0F0F0F0
+0x0F0F0F0F0F:0x0F0F0F0F0F:0x0x0F0F0F0F0F
+0xF0F0F0F0F0F0:0xF0F0F0F0F0F0:0x0xF0F0F0F0F0F0
+0x0F0F0F0F0F0F:0x0F0F0F0F0F0F:0x0x0F0F0F0F0F0F
+0x1F0F0F0F0F0F:0x3F0F0F0F0F0F:0x0x1F0F0F0F0F0F
+&bior
+abc:abc:NaN
+abc:0:NaN
+0:abc:NaN
+1:2:3
++8:+2:10
++281474976710656:0:281474976710656
++281474976710656:1:281474976710657
++281474976710656:281474976710656:281474976710656
+-2:-3:-1
+-1:-1:-1
+-6:-6:-6
+-7:4:-3
+-4:7:-1
+# equal arguments are treated special, so also do some test with unequal ones
+0xFFFF:0xFFFF:0x0xFFFF
+0xFFFFFF:0xFFFFFF:0x0xFFFFFF
+0xFFFFFFFF:0xFFFFFFFF:0x0xFFFFFFFF
+0xFFFFFFFFFF:0xFFFFFFFFFF:0x0xFFFFFFFFFF
+0xFFFFFFFFFFFF:0xFFFFFFFFFFFF:0x0xFFFFFFFFFFFF
+0:0xFFFF:0x0xFFFF
+0:0xFFFFFF:0x0xFFFFFF
+0:0xFFFFFFFF:0x0xFFFFFFFF
+0:0xFFFFFFFFFF:0x0xFFFFFFFFFF
+0:0xFFFFFFFFFFFF:0x0xFFFFFFFFFFFF
+0xFFFF:0:0x0xFFFF
+0xFFFFFF:0:0x0xFFFFFF
+0xFFFFFFFF:0:0x0xFFFFFFFF
+0xFFFFFFFFFF:0:0x0xFFFFFFFFFF
+0xFFFFFFFFFFFF:0:0x0xFFFFFFFFFFFF
+0xF0F0:0xF0F0:0x0xF0F0
+0x0F0F:0x0F0F:0x0x0F0F
+0xF0F0:0x0F0F:0x0xFFFF
+0xF0F0F0:0xF0F0F0:0x0xF0F0F0
+0x0F0F0F:0x0F0F0F:0x0x0F0F0F
+0x0F0F0F:0xF0F0F0:0x0xFFFFFF
+0xF0F0F0F0:0xF0F0F0F0:0x0xF0F0F0F0
+0x0F0F0F0F:0x0F0F0F0F:0x0x0F0F0F0F
+0x0F0F0F0F:0xF0F0F0F0:0x0xFFFFFFFF
+0xF0F0F0F0F0:0xF0F0F0F0F0:0x0xF0F0F0F0F0
+0x0F0F0F0F0F:0x0F0F0F0F0F:0x0x0F0F0F0F0F
+0x0F0F0F0F0F:0xF0F0F0F0F0:0x0xFFFFFFFFFF
+0xF0F0F0F0F0F0:0xF0F0F0F0F0F0:0x0xF0F0F0F0F0F0
+0x0F0F0F0F0F0F:0x0F0F0F0F0F0F:0x0x0F0F0F0F0F0F
+0x0F0F0F0F0F0F:0xF0F0F0F0F0F0:0x0xFFFFFFFFFFFF
+0x1F0F0F0F0F0F:0xF0F0F0F0F0F0:0x0xFFFFFFFFFFFF
+&bxor
+abc:abc:NaN
+abc:0:NaN
+0:abc:NaN
+1:2:3
++8:+2:10
++281474976710656:0:281474976710656
++281474976710656:1:281474976710657
++281474976710656:281474976710656:0
+-2:-3:3
+-1:-1:0
+-6:-6:0
+-7:4:-3
+-4:7:-5
+4:-7:-3
+-4:-7:5
+# equal arguments are treated special, so also do some test with unequal ones
+0xFFFF:0xFFFF:0
+0xFFFFFF:0xFFFFFF:0
+0xFFFFFFFF:0xFFFFFFFF:0
+0xFFFFFFFFFF:0xFFFFFFFFFF:0
+0xFFFFFFFFFFFF:0xFFFFFFFFFFFF:0
+0:0xFFFF:0x0xFFFF
+0:0xFFFFFF:0x0xFFFFFF
+0:0xFFFFFFFF:0x0xFFFFFFFF
+0:0xFFFFFFFFFF:0x0xFFFFFFFFFF
+0:0xFFFFFFFFFFFF:0x0xFFFFFFFFFFFF
+0xFFFF:0:0x0xFFFF
+0xFFFFFF:0:0x0xFFFFFF
+0xFFFFFFFF:0:0x0xFFFFFFFF
+0xFFFFFFFFFF:0:0x0xFFFFFFFFFF
+0xFFFFFFFFFFFF:0:0x0xFFFFFFFFFFFF
+0xF0F0:0xF0F0:0
+0x0F0F:0x0F0F:0
+0xF0F0:0x0F0F:0x0xFFFF
+0xF0F0F0:0xF0F0F0:0
+0x0F0F0F:0x0F0F0F:0
+0x0F0F0F:0xF0F0F0:0x0xFFFFFF
+0xF0F0F0F0:0xF0F0F0F0:0
+0x0F0F0F0F:0x0F0F0F0F:0
+0x0F0F0F0F:0xF0F0F0F0:0x0xFFFFFFFF
+0xF0F0F0F0F0:0xF0F0F0F0F0:0
+0x0F0F0F0F0F:0x0F0F0F0F0F:0
+0x0F0F0F0F0F:0xF0F0F0F0F0:0x0xFFFFFFFFFF
+0xF0F0F0F0F0F0:0xF0F0F0F0F0F0:0
+0x0F0F0F0F0F0F:0x0F0F0F0F0F0F:0
+0x0F0F0F0F0F0F:0xF0F0F0F0F0F0:0x0xFFFFFFFFFFFF
+&bnot
+abc:NaN
++0:-1
++8:-9
++281474976710656:-281474976710657
+-1:0
+-2:1
+-12:11
+&digit
+0:0:0
+12:0:2
+12:1:1
+123:0:3
+123:1:2
+123:2:1
+123:-1:1
+123:-2:2
+123:-3:3
+123456:0:6
+123456:1:5
+123456:2:4
+123456:3:3
+123456:4:2
+123456:5:1
+123456:-1:1
+123456:-2:2
+123456:-3:3
+100000:-3:0
+100000:0:0
+100000:1:0
+&mantissa
+abc:NaN
+1e4:1
+2e0:2
+123:123
+-1:-1
+-2:-2
++inf:inf
+-inf:-inf
+&exponent
+abc:NaN
+1e4:4
+2e0:0
+123:0
+-1:0
+-2:0
+0:1
++inf:inf
+-inf:inf
+&parts
+abc:NaN,NaN
+1e4:1,4
+2e0:2,0
+123:123,0
+-1:-1,0
+-2:-2,0
+0:0,1
++inf:inf,inf
+-inf:-inf,inf
+&bfac
+-1:NaN
+NaNfac:NaN
++inf:inf
+-inf:NaN
+0:1
+1:1
+2:2
+3:6
+4:24
+5:120
+6:720
+10:3628800
+11:39916800
+12:479001600
+&bpow
+abc:12:NaN
+12:abc:NaN
+0:0:1
+0:1:0
+0:2:0
+0:-1:inf
+0:-2:inf
+1:0:1
+1:1:1
+1:2:1
+1:3:1
+1:-1:1
+1:-2:1
+1:-3:1
+2:0:1
+2:1:2
+2:2:4
+2:3:8
+3:3:27
+2:-1:0.5^
+-2:-1:-0.5^
+2:-2:0.25^
+# Y is even => result positive
+-2:-2:0.25^
+# Y is odd => result negative
+-2:-3:-0.125^
++inf:1234500012:inf
+-inf:1234500012:inf
+-inf:1234500013:-inf
++inf:-12345000123:inf
+-inf:-12345000123:-inf
+# 1 ** -x => 1 / (1 ** x)
+-1:0:1
+-2:0:1
+-1:1:-1
+-1:2:1
+-1:3:-1
+-1:4:1
+-1:5:-1
+-1:-1:-1
+-1:-2:1
+-1:-3:-1
+-1:-4:1
+-2:2:4
+-2:3:-8
+-2:4:16
+-2:5:-32
+-3:2:9
+-3:3:-27
+-3:4:81
+-3:5:-243
+10:2:100
+10:3:1000
+10:4:10000
+10:5:100000
+10:6:1000000
+10:7:10000000
+10:8:100000000
+10:9:1000000000
+10:20:100000000000000000000
+123456:2:15241383936
+#2:0.5:1.41^
+&length
+100:3
+10:2
+1:1
+0:1
+12345:5
+10000000000000000:17
+-123:3
+215960156869840440586892398248:30
+# broot always upgrades
+&broot
+144:2:12^
+123:2:11.09053650640941716205160010260993291846^
+# bsqrt always upgrades
+&bsqrt
+145:12.04159457879229548012824103037860805243^
+144:12^
+143:11.95826074310139802112984075619561661399^
+16:4
+170:13.03840481040529742916594311485836883306^
+169:13
+168:12.96148139681572046193193487217599331541^
+4:2
+3:1.732050807568877293527446341505872366943^
+2:1.41421356237309504880168872420969807857^
+9:3
+12:3.464101615137754587054892683011744733886^
+256:16
+100000000:10000
+4000000000000:2000000
+152399026:12345.00004050222755607815159966235881398^
+152399025:12345
+152399024:12344.99995949777231103967404745303741942^
+1:1
+0:0
+-2:NaN
+-123:NaN
+Nan:NaN
++inf:inf
+-inf:NaN
+&bround
+$round_mode('trunc')
+0:12:0
+NaNbround:12:NaN
++inf:12:inf
+-inf:12:-inf
+1234:0:1234
+1234:2:1200
+123456:4:123400
+123456:5:123450
+123456:6:123456
++10123456789:5:10123000000
+-10123456789:5:-10123000000
++10123456789:9:10123456700
+-10123456789:9:-10123456700
++101234500:6:101234000
+-101234500:6:-101234000
+#+101234500:-4:101234000
+#-101234500:-4:-101234000
+$round_mode('zero')
++20123456789:5:20123000000
+-20123456789:5:-20123000000
++20123456789:9:20123456800
+-20123456789:9:-20123456800
++201234500:6:201234000
+-201234500:6:-201234000
+#+201234500:-4:201234000
+#-201234500:-4:-201234000
++12345000:4:12340000
+-12345000:4:-12340000
+$round_mode('+inf')
++30123456789:5:30123000000
+-30123456789:5:-30123000000
++30123456789:9:30123456800
+-30123456789:9:-30123456800
++301234500:6:301235000
+-301234500:6:-301234000
+#+301234500:-4:301235000
+#-301234500:-4:-301234000
++12345000:4:12350000
+-12345000:4:-12340000
+$round_mode('-inf')
++40123456789:5:40123000000
+-40123456789:5:-40123000000
++40123456789:9:40123456800
+-40123456789:9:-40123456800
++401234500:6:401234000
++401234500:6:401234000
+#-401234500:-4:-401235000
+#-401234500:-4:-401235000
++12345000:4:12340000
+-12345000:4:-12350000
+$round_mode('odd')
++50123456789:5:50123000000
+-50123456789:5:-50123000000
++50123456789:9:50123456800
+-50123456789:9:-50123456800
++501234500:6:501235000
+-501234500:6:-501235000
+#+501234500:-4:501235000
+#-501234500:-4:-501235000
++12345000:4:12350000
+-12345000:4:-12350000
+$round_mode('even')
++60123456789:5:60123000000
+-60123456789:5:-60123000000
++60123456789:9:60123456800
+-60123456789:9:-60123456800
++601234500:6:601234000
+-601234500:6:-601234000
+#+601234500:-4:601234000
+#-601234500:-4:-601234000
+#-601234500:-9:0
+#-501234500:-9:0
+#-601234500:-8:0
+#-501234500:-8:0
++1234567:7:1234567
++1234567:6:1234570
++12345000:4:12340000
+-12345000:4:-12340000
+&is_zero
+0:1
+NaNzero:0
++inf:0
+-inf:0
+123:0
+-1:0
+1:0
+&is_one
+0:0
+NaNone:0
++inf:0
+-inf:0
+1:1
+2:0
+-1:0
+-2:0
+# floor and ceil tests are pretty pointless in integer space...but play safe
+&bfloor
+0:0
+NaNfloor:NaN
++inf:inf
+-inf:-inf
+-1:-1
+-2:-2
+2:2
+3:3
+abc:NaN
+&bceil
+NaNceil:NaN
++inf:inf
+-inf:-inf
+0:0
+-1:-1
+-2:-2
+2:2
+3:3
+abc:NaN
+&as_hex
+128:0x80
+-128:-0x80
+0:0x0
+-0:0x0
+1:0x1
+0x123456789123456789:0x123456789123456789
++inf:inf
+-inf:-inf
+NaNas_hex:NaN
+&as_bin
+128:0b10000000
+-128:-0b10000000
+0:0b0
+-0:0b0
+1:0b1
+0b1010111101010101010110110110110110101:0b1010111101010101010110110110110110101
++inf:inf
+-inf:-inf
+NaNas_bin:NaN
diff --git a/dist/Math-BigInt/t/upgrade.t b/dist/Math-BigInt/t/upgrade.t
new file mode 100644
index 0000000000..dff9c326b3
--- /dev/null
+++ b/dist/Math-BigInt/t/upgrade.t
@@ -0,0 +1,40 @@
+#!/usr/bin/perl -w
+
+use Test;
+use strict;
+
+BEGIN
+  {
+  $| = 1;
+  # to locate the testing files
+  my $location = $0; $location =~ s/upgrade.t//i;
+  unshift @INC, qw(../lib);     # to locate the modules
+  if (-d 't')
+    {
+    chdir 't';
+    require File::Spec;
+    unshift @INC, File::Spec->catdir(File::Spec->updir, $location);
+    }
+  else
+    {
+    unshift @INC, $location;
+    }
+  print "# INC = @INC\n";
+
+  plan tests => 2112
+   + 2;			# our own tests
+  }
+
+use Math::BigInt upgrade => 'Math::BigFloat';
+use Math::BigFloat;
+
+use vars qw ($scale $class $try $x $y $f @args $ans $ans1 $ans1_str $setup
+             $ECL $CL);
+$class = "Math::BigInt";
+$CL = "Math::BigInt::Calc";
+$ECL = "Math::BigFloat";
+
+ok (Math::BigInt->upgrade(),'Math::BigFloat');
+ok (Math::BigInt->downgrade()||'','');
+
+require 'upgrade.inc';	# all tests here for sharing
diff --git a/dist/Math-BigInt/t/upgradef.t b/dist/Math-BigInt/t/upgradef.t
new file mode 100644
index 0000000000..2bc4a482ed
--- /dev/null
+++ b/dist/Math-BigInt/t/upgradef.t
@@ -0,0 +1,79 @@
+#!/usr/bin/perl -w
+
+use Test;
+use strict;
+
+BEGIN
+  {
+  $| = 1;
+  # to locate the testing files
+  my $location = $0; $location =~ s/upgradef.t//i;
+  unshift @INC, qw(../lib);     # to locate the modules
+  if (-d 't')
+    {
+    chdir 't';
+    require File::Spec;
+    unshift @INC, File::Spec->catdir(File::Spec->updir, $location);
+    }
+  else
+    {
+    unshift @INC, $location;
+    }
+  print "# INC = @INC\n";
+
+  plan tests => 0
+   + 6;			# our own tests
+  }
+
+###############################################################################
+package Math::BigFloat::Test;
+
+use Math::BigFloat;
+require Exporter;
+use vars qw/@ISA/;
+@ISA = qw/Exporter Math::BigFloat/;
+
+use overload;
+
+sub isa
+  {
+  my ($self,$class) = @_;
+  return if $class =~ /^Math::Big(Int|Float)/;	# we aren't one of these
+  UNIVERSAL::isa($self,$class);
+  }
+
+sub bmul
+  {
+  return __PACKAGE__->new(123);
+  }
+
+sub badd
+  {
+  return __PACKAGE__->new(321);
+  }
+
+###############################################################################
+package main;
+
+# use Math::BigInt upgrade => 'Math::BigFloat';
+use Math::BigFloat upgrade => 'Math::BigFloat::Test';
+
+use vars qw ($scale $class $try $x $y $z $f @args $ans $ans1 $ans1_str $setup
+             $ECL $CL);
+$class = "Math::BigFloat";
+$CL = "Math::BigInt::Calc";
+$ECL = "Math::BigFloat::Test";
+
+ok (Math::BigFloat->upgrade(),$ECL);
+ok (Math::BigFloat->downgrade()||'','');
+
+$x = $class->new(123); $y = $ECL->new(123); $z = $x->bmul($y);
+ok (ref($z),$ECL); ok ($z,123);
+
+$x = $class->new(123); $y = $ECL->new(123); $z = $x->badd($y);
+ok (ref($z),$ECL); ok ($z,321);
+
+
+
+# not yet:
+# require 'upgrade.inc';	# all tests here for sharing
diff --git a/dist/Math-BigInt/t/use.t b/dist/Math-BigInt/t/use.t
new file mode 100644
index 0000000000..4865ba5399
--- /dev/null
+++ b/dist/Math-BigInt/t/use.t
@@ -0,0 +1,41 @@
+#!/usr/bin/perl -w
+
+# use Module(); doesn't call import() - thanx for cpan testers David. M. Town
+# and Andreas Marcel Riechert for spotting it. It is fixed by the same code
+# that fixes require Math::BigInt, but we make a test to be sure it really
+# works.
+
+use strict;
+use Test;
+
+BEGIN
+  {
+  $| = 1;
+  # to locate the testing files
+  my $location = $0; $location =~ s/use.t//i;
+  unshift @INC, qw(../lib);     # to locate the modules
+  if (-d 't')
+    {
+    chdir 't';
+    require File::Spec;
+    unshift @INC, File::Spec->catdir(File::Spec->updir, $location);
+    }
+  else
+    {
+    unshift @INC, $location;
+    }
+  print "# INC = @INC\n";
+
+  plan tests => 1;
+  } 
+
+my ($try,$ans,$x);
+
+use Math::BigInt(); $x = Math::BigInt->new(1); ++$x;
+
+ok ($x||'undef',2);
+
+# all tests done
+
+1;
+
diff --git a/dist/Math-BigInt/t/use_lib1.t b/dist/Math-BigInt/t/use_lib1.t
new file mode 100644
index 0000000000..ecb60eb0a4
--- /dev/null
+++ b/dist/Math-BigInt/t/use_lib1.t
@@ -0,0 +1,35 @@
+#!/usr/bin/perl -w
+
+# see if using Math::BigInt and Math::BigFloat works together nicely.
+# all use_lib*.t should be equivalent
+
+use strict;
+use Test;
+
+BEGIN
+  {
+  $| = 1;
+  # to locate the testing files
+  my $location = $0; $location =~ s/use_lib1.t//i;
+  unshift @INC, qw(../lib);     # to locate the modules
+  if (-d 't')
+    {
+    chdir 't';
+    require File::Spec;
+    unshift @INC, File::Spec->catdir(File::Spec->updir, $location);
+    }
+  else
+    {
+    unshift @INC, $location;
+    }
+  print "# INC = @INC\n";
+
+  plan tests => 2;
+  } 
+
+use Math::BigFloat lib => 'BareCalc';
+
+ok (Math::BigInt->config()->{lib},'Math::BigInt::BareCalc');
+
+ok (Math::BigFloat->new(123)->badd(123),246);
+
diff --git a/dist/Math-BigInt/t/use_lib2.t b/dist/Math-BigInt/t/use_lib2.t
new file mode 100644
index 0000000000..298ff7d0e8
--- /dev/null
+++ b/dist/Math-BigInt/t/use_lib2.t
@@ -0,0 +1,36 @@
+#!/usr/bin/perl -w
+
+# see if using Math::BigInt and Math::BigFloat works together nicely.
+# all use_lib*.t should be equivalent
+
+use strict;
+use Test;
+
+BEGIN
+  {
+  $| = 1;
+  # to locate the testing files
+  my $location = $0; $location =~ s/use_lib2.t//i;
+  unshift @INC, qw(../lib);     # to locate the modules
+  if (-d 't')
+    {
+    chdir 't';
+    require File::Spec;
+    unshift @INC, File::Spec->catdir(File::Spec->updir, $location);
+    }
+  else
+    {
+    unshift @INC, $location;
+    }
+  print "# INC = @INC\n";
+
+  plan tests => 2;
+  } 
+
+use Math::BigInt;
+use Math::BigFloat lib => 'BareCalc';
+
+ok (Math::BigInt->config()->{lib},'Math::BigInt::BareCalc');
+
+ok (Math::BigFloat->new(123)->badd(123),246);
+
diff --git a/dist/Math-BigInt/t/use_lib3.t b/dist/Math-BigInt/t/use_lib3.t
new file mode 100644
index 0000000000..06a1086554
--- /dev/null
+++ b/dist/Math-BigInt/t/use_lib3.t
@@ -0,0 +1,36 @@
+#!/usr/bin/perl -w
+
+# see if using Math::BigInt and Math::BigFloat works together nicely.
+# all use_lib*.t should be equivalent
+
+use strict;
+use Test;
+
+BEGIN
+  {
+  $| = 1;
+  # to locate the testing files
+  my $location = $0; $location =~ s/use_lib3.t//i;
+  unshift @INC, qw(../lib);     # to locate the modules
+  if (-d 't')
+    {
+    chdir 't';
+    require File::Spec;
+    unshift @INC, File::Spec->catdir(File::Spec->updir, $location);
+    }
+  else
+    {
+    unshift @INC, $location;
+    }
+  print "# INC = @INC\n";
+
+  plan tests => 2;
+  } 
+
+use Math::BigInt lib => 'BareCalc';
+use Math::BigFloat;
+
+ok (Math::BigInt->config()->{lib},'Math::BigInt::BareCalc');
+
+ok (Math::BigFloat->new(123)->badd(123),246);
+
diff --git a/dist/Math-BigInt/t/use_lib4.t b/dist/Math-BigInt/t/use_lib4.t
new file mode 100644
index 0000000000..070beb8755
--- /dev/null
+++ b/dist/Math-BigInt/t/use_lib4.t
@@ -0,0 +1,37 @@
+#!/usr/bin/perl -w
+
+# see if using Math::BigInt and Math::BigFloat works together nicely.
+# all use_lib*.t should be equivalent, except this, since the later overrides
+# the former lib statement
+
+use strict;
+use Test;
+
+BEGIN
+  {
+  $| = 1;
+  # to locate the testing files
+  my $location = $0; $location =~ s/use_lib4.t//i;
+  unshift @INC, qw(../lib);     # to locate the modules
+  if (-d 't')
+    {
+    chdir 't';
+    require File::Spec;
+    unshift @INC, File::Spec->catdir(File::Spec->updir, $location);
+    }
+  else
+    {
+    unshift @INC, $location;
+    }
+  print "# INC = @INC\n";
+
+  plan tests => 2;
+  } 
+
+use Math::BigInt lib => 'BareCalc';
+use Math::BigFloat lib => 'Calc';
+
+ok (Math::BigInt->config()->{lib},'Math::BigInt::Calc');
+
+ok (Math::BigFloat->new(123)->badd(123),246);
+
diff --git a/dist/Math-BigInt/t/use_mbfw.t b/dist/Math-BigInt/t/use_mbfw.t
new file mode 100644
index 0000000000..298cb800da
--- /dev/null
+++ b/dist/Math-BigInt/t/use_mbfw.t
@@ -0,0 +1,47 @@
+#!/usr/bin/perl -w
+
+# check that using BigFloat with "with" and "lib" at the same time works
+# broken in versions up to v1.63
+
+use strict;
+use Test;
+
+BEGIN
+  {
+  $| = 1;
+  # to locate the testing files
+  my $location = $0; $location =~ s/use_mbfw.t//i;
+  unshift @INC, qw(../lib);     # to locate the modules
+  if (-d 't')
+    {
+    chdir 't';
+    require File::Spec;
+    unshift @INC, File::Spec->catdir(File::Spec->updir, $location);
+    }
+  else
+    {
+    unshift @INC, $location;
+    }
+  print "# INC = @INC\n";
+
+  plan tests => 2;
+  } 
+
+
+# the replacement lib can handle the lib statement, but it could also ignore
+# it completely, for instance, when it is a 100% replacement for BigInt, but
+# doesn't know the concept of alternative libs. But it still needs to cope
+# with "lib => ". SubClass does record it, so we test here essential if
+# BigFloat hands the lib properly down, any more is outside out testing reach.
+
+use Math::BigFloat with => 'Math::BigInt::Subclass', lib => 'BareCalc';
+
+ok (Math::BigFloat->config()->{with}, 'Math::BigInt::BareCalc' );
+
+# ok ($Math::BigInt::Subclass::lib, 'BareCalc' );
+
+# it never arrives here, but that is a design decision in SubClass
+ok (Math::BigInt->config->{lib}, 'Math::BigInt::BareCalc' );
+
+# all tests done
+
diff --git a/dist/Math-BigInt/t/with_sub.t b/dist/Math-BigInt/t/with_sub.t
new file mode 100644
index 0000000000..d34d9fb885
--- /dev/null
+++ b/dist/Math-BigInt/t/with_sub.t
@@ -0,0 +1,39 @@
+#!/usr/bin/perl -w
+
+# Test use Math::BigFloat with => 'Math::BigInt::SomeSubclass';
+
+use Test;
+use strict;
+
+BEGIN
+  {
+  $| = 1;
+  # to locate the testing files
+  my $location = $0; $location =~ s/with_sub.t//i;
+  unshift @INC, '../lib';
+  if (-d 't')
+    {
+    chdir 't';
+    require File::Spec;
+    unshift @INC, File::Spec->catdir(File::Spec->updir, $location);
+    }
+  else
+    {
+    unshift @INC, $location;
+    }
+  print "# INC = @INC\n";
+
+  plan tests => 2308
+	+ 1;
+  }
+
+use Math::BigFloat with => 'Math::BigInt::Subclass', lib => 'Calc';
+
+use vars qw ($class $try $x $y $f @args $ans $ans1 $ans1_str $setup $CL);
+$class = "Math::BigFloat";
+$CL = "Math::BigInt::Calc";
+
+# the with argument is ignored
+ok (Math::BigFloat->config()->{with}, 'Math::BigInt::Calc');
+
+require 'bigfltpm.inc';	# all tests here for sharing