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authorFlorian Ragwitz <rafl@debian.org>2010-09-02 23:11:26 +0200
committerFlorian Ragwitz <rafl@debian.org>2010-09-02 23:51:30 +0200
commitc510e33d30368bc5440f1651f6b31f73d2354eba (patch)
tree9286faae98a201e6c1a3da345e868f082d142879 /cpan/Math-BigInt
parent69f857902b1b105d96448597da9c4bc9cd4e90a3 (diff)
downloadperl-c510e33d30368bc5440f1651f6b31f73d2354eba.tar.gz
blead is upstream for Math-BigInt
Diffstat (limited to 'cpan/Math-BigInt')
-rw-r--r--cpan/Math-BigInt/lib/Math/BigFloat.pm4402
-rw-r--r--cpan/Math-BigInt/lib/Math/BigInt.pm5115
-rw-r--r--cpan/Math-BigInt/lib/Math/BigInt/Calc.pm2612
-rw-r--r--cpan/Math-BigInt/lib/Math/BigInt/CalcEmu.pm329
-rw-r--r--cpan/Math-BigInt/t/Math/BigFloat/Subclass.pm49
-rw-r--r--cpan/Math-BigInt/t/Math/BigInt/BareCalc.pm44
-rw-r--r--cpan/Math-BigInt/t/Math/BigInt/Scalar.pm355
-rw-r--r--cpan/Math-BigInt/t/Math/BigInt/Subclass.pm90
-rw-r--r--cpan/Math-BigInt/t/_e_math.t111
-rw-r--r--cpan/Math-BigInt/t/alias.inc12
-rw-r--r--cpan/Math-BigInt/t/bare_mbf.t39
-rw-r--r--cpan/Math-BigInt/t/bare_mbi.t43
-rw-r--r--cpan/Math-BigInt/t/bare_mif.t48
-rw-r--r--cpan/Math-BigInt/t/big_pi_e.t59
-rw-r--r--cpan/Math-BigInt/t/bigfltpm.inc1823
-rw-r--r--cpan/Math-BigInt/t/bigfltpm.t54
-rw-r--r--cpan/Math-BigInt/t/bigintc.t464
-rw-r--r--cpan/Math-BigInt/t/bigintpm.inc2511
-rw-r--r--cpan/Math-BigInt/t/bigintpm.t46
-rw-r--r--cpan/Math-BigInt/t/bigints.t123
-rw-r--r--cpan/Math-BigInt/t/biglog.t213
-rw-r--r--cpan/Math-BigInt/t/bigroot.t69
-rw-r--r--cpan/Math-BigInt/t/calling.t176
-rw-r--r--cpan/Math-BigInt/t/config.t136
-rw-r--r--cpan/Math-BigInt/t/const_mbf.t40
-rw-r--r--cpan/Math-BigInt/t/constant.t62
-rw-r--r--cpan/Math-BigInt/t/downgrade.t55
-rw-r--r--cpan/Math-BigInt/t/inf_nan.t355
-rw-r--r--cpan/Math-BigInt/t/isa.t59
-rw-r--r--cpan/Math-BigInt/t/lib_load.t53
-rw-r--r--cpan/Math-BigInt/t/mbf_ali.t42
-rw-r--r--cpan/Math-BigInt/t/mbi_ali.t42
-rw-r--r--cpan/Math-BigInt/t/mbi_rand.t93
-rw-r--r--cpan/Math-BigInt/t/mbimbf.inc967
-rw-r--r--cpan/Math-BigInt/t/mbimbf.t110
-rw-r--r--cpan/Math-BigInt/t/nan_cmp.t44
-rw-r--r--cpan/Math-BigInt/t/new_overloaded.t32
-rw-r--r--cpan/Math-BigInt/t/req_mbf0.t39
-rw-r--r--cpan/Math-BigInt/t/req_mbf1.t37
-rw-r--r--cpan/Math-BigInt/t/req_mbfa.t37
-rw-r--r--cpan/Math-BigInt/t/req_mbfi.t37
-rw-r--r--cpan/Math-BigInt/t/req_mbfn.t37
-rw-r--r--cpan/Math-BigInt/t/req_mbfw.t48
-rw-r--r--cpan/Math-BigInt/t/require.t41
-rw-r--r--cpan/Math-BigInt/t/round.t120
-rw-r--r--cpan/Math-BigInt/t/sub_ali.t40
-rw-r--r--cpan/Math-BigInt/t/sub_mbf.t56
-rw-r--r--cpan/Math-BigInt/t/sub_mbi.t58
-rw-r--r--cpan/Math-BigInt/t/sub_mif.t43
-rw-r--r--cpan/Math-BigInt/t/trap.t92
-rw-r--r--cpan/Math-BigInt/t/upgrade.inc1500
-rw-r--r--cpan/Math-BigInt/t/upgrade.t45
-rw-r--r--cpan/Math-BigInt/t/upgradef.t84
-rw-r--r--cpan/Math-BigInt/t/use.t46
-rw-r--r--cpan/Math-BigInt/t/use_lib1.t40
-rw-r--r--cpan/Math-BigInt/t/use_lib2.t41
-rw-r--r--cpan/Math-BigInt/t/use_lib3.t41
-rw-r--r--cpan/Math-BigInt/t/use_lib4.t42
-rw-r--r--cpan/Math-BigInt/t/use_mbfw.t52
-rw-r--r--cpan/Math-BigInt/t/with_sub.t44
60 files changed, 0 insertions, 23497 deletions
diff --git a/cpan/Math-BigInt/lib/Math/BigFloat.pm b/cpan/Math-BigInt/lib/Math/BigFloat.pm
deleted file mode 100644
index 27d60b3143..0000000000
--- a/cpan/Math-BigInt/lib/Math/BigFloat.pm
+++ /dev/null
@@ -1,4402 +0,0 @@
-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/cpan/Math-BigInt/lib/Math/BigInt.pm b/cpan/Math-BigInt/lib/Math/BigInt.pm
deleted file mode 100644
index f97e438079..0000000000
--- a/cpan/Math-BigInt/lib/Math/BigInt.pm
+++ /dev/null
@@ -1,5115 +0,0 @@
-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/cpan/Math-BigInt/lib/Math/BigInt/Calc.pm b/cpan/Math-BigInt/lib/Math/BigInt/Calc.pm
deleted file mode 100644
index 52e33d232a..0000000000
--- a/cpan/Math-BigInt/lib/Math/BigInt/Calc.pm
+++ /dev/null
@@ -1,2612 +0,0 @@
-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/cpan/Math-BigInt/lib/Math/BigInt/CalcEmu.pm b/cpan/Math-BigInt/lib/Math/BigInt/CalcEmu.pm
deleted file mode 100644
index 5810f5db9f..0000000000
--- a/cpan/Math-BigInt/lib/Math/BigInt/CalcEmu.pm
+++ /dev/null
@@ -1,329 +0,0 @@
-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/cpan/Math-BigInt/t/Math/BigFloat/Subclass.pm b/cpan/Math-BigInt/t/Math/BigFloat/Subclass.pm
deleted file mode 100644
index 94d3f2a624..0000000000
--- a/cpan/Math-BigInt/t/Math/BigFloat/Subclass.pm
+++ /dev/null
@@ -1,49 +0,0 @@
-#!/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/cpan/Math-BigInt/t/Math/BigInt/BareCalc.pm b/cpan/Math-BigInt/t/Math/BigInt/BareCalc.pm
deleted file mode 100644
index 0bbe861cf8..0000000000
--- a/cpan/Math-BigInt/t/Math/BigInt/BareCalc.pm
+++ /dev/null
@@ -1,44 +0,0 @@
-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/cpan/Math-BigInt/t/Math/BigInt/Scalar.pm b/cpan/Math-BigInt/t/Math/BigInt/Scalar.pm
deleted file mode 100644
index c20a3e377e..0000000000
--- a/cpan/Math-BigInt/t/Math/BigInt/Scalar.pm
+++ /dev/null
@@ -1,355 +0,0 @@
-###############################################################################
-# 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/cpan/Math-BigInt/t/Math/BigInt/Subclass.pm b/cpan/Math-BigInt/t/Math/BigInt/Subclass.pm
deleted file mode 100644
index d45e9e53ad..0000000000
--- a/cpan/Math-BigInt/t/Math/BigInt/Subclass.pm
+++ /dev/null
@@ -1,90 +0,0 @@
-#!/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/cpan/Math-BigInt/t/_e_math.t b/cpan/Math-BigInt/t/_e_math.t
deleted file mode 100644
index b3eb644437..0000000000
--- a/cpan/Math-BigInt/t/_e_math.t
+++ /dev/null
@@ -1,111 +0,0 @@
-#!/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; $location =~ s/_e_math.t//i;
- if ($ENV{PERL_CORE})
- {
- # testing with the core distribution
- @INC = qw(../lib);
- }
- 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/cpan/Math-BigInt/t/alias.inc b/cpan/Math-BigInt/t/alias.inc
deleted file mode 100644
index 746a20c99e..0000000000
--- a/cpan/Math-BigInt/t/alias.inc
+++ /dev/null
@@ -1,12 +0,0 @@
-
-# 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/cpan/Math-BigInt/t/bare_mbf.t b/cpan/Math-BigInt/t/bare_mbf.t
deleted file mode 100644
index 9bb4bcea5f..0000000000
--- a/cpan/Math-BigInt/t/bare_mbf.t
+++ /dev/null
@@ -1,39 +0,0 @@
-#!/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 "# $0\n";
- if ($ENV{PERL_CORE})
- {
- # testing with the core distribution
- @INC = qw(../t/lib);
- }
- 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/cpan/Math-BigInt/t/bare_mbi.t b/cpan/Math-BigInt/t/bare_mbi.t
deleted file mode 100644
index 637e695b69..0000000000
--- a/cpan/Math-BigInt/t/bare_mbi.t
+++ /dev/null
@@ -1,43 +0,0 @@
-#!/usr/bin/perl -w
-
-use Test;
-use strict;
-
-BEGIN
- {
- $| = 1;
- # to locate the testing files
- my $location = $0; $location =~ s/bare_mbi.t//i;
- if ($ENV{PERL_CORE})
- {
- # testing with the core distribution
- @INC = qw(../t/lib);
- }
- 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/cpan/Math-BigInt/t/bare_mif.t b/cpan/Math-BigInt/t/bare_mif.t
deleted file mode 100644
index 0cc1de9365..0000000000
--- a/cpan/Math-BigInt/t/bare_mif.t
+++ /dev/null
@@ -1,48 +0,0 @@
-#!/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; $location =~ s/bare_mif.t//i;
- if ($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, $location;
- }
- print "# INC = @INC\n";
-
- plan tests => 684
- + 1; # our own tests
- }
-
-print "# ",Math::BigInt->config()->{lib},"\n";
-
-use Math::BigInt lib => 'BareCalc';
-use Math::BigFloat lib => 'BareCalc';
-
-use vars qw/$mbi $mbf/;
-
-$mbi = 'Math::BigInt';
-$mbf = 'Math::BigFloat';
-
-ok (Math::BigInt->config()->{lib},'Math::BigInt::BareCalc');
-
-require 'mbimbf.inc';
-
diff --git a/cpan/Math-BigInt/t/big_pi_e.t b/cpan/Math-BigInt/t/big_pi_e.t
deleted file mode 100644
index 9ecae00dcc..0000000000
--- a/cpan/Math-BigInt/t/big_pi_e.t
+++ /dev/null
@@ -1,59 +0,0 @@
-#!/usr/bin/perl -w
-
-# Test bpi() and bexp()
-
-use Test::More;
-use strict;
-
-BEGIN
- {
- $| = 1;
- # to locate the testing files
- my $location = $0; $location =~ s/big_pi_e.t//i;
- if ($ENV{PERL_CORE})
- {
- # testing with the core distribution
- @INC = qw(../lib);
- }
- 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 $e->{_p}, 'P not set');
-
-
diff --git a/cpan/Math-BigInt/t/bigfltpm.inc b/cpan/Math-BigInt/t/bigfltpm.inc
deleted file mode 100644
index 7d650e5cba..0000000000
--- a/cpan/Math-BigInt/t/bigfltpm.inc
+++ /dev/null
@@ -1,1823 +0,0 @@
-#include this file into another test for subclass testing...
-
-ok ($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/cpan/Math-BigInt/t/bigfltpm.t b/cpan/Math-BigInt/t/bigfltpm.t
deleted file mode 100644
index a41996e8ed..0000000000
--- a/cpan/Math-BigInt/t/bigfltpm.t
+++ /dev/null
@@ -1,54 +0,0 @@
-#!/usr/bin/perl -w
-
-use Test;
-use strict;
-
-BEGIN
- {
- $| = 1;
- # to locate the testing files
- my $location = $0; $location =~ s/bigfltpm.t//i;
- if ($ENV{PERL_CORE})
- {
- # testing with the core distribution
- @INC = qw(../lib);
- }
- 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/cpan/Math-BigInt/t/bigintc.t b/cpan/Math-BigInt/t/bigintc.t
deleted file mode 100644
index 5dbace06a3..0000000000
--- a/cpan/Math-BigInt/t/bigintc.t
+++ /dev/null
@@ -1,464 +0,0 @@
-#!/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/cpan/Math-BigInt/t/bigintpm.inc b/cpan/Math-BigInt/t/bigintpm.inc
deleted file mode 100644
index 87140ba44d..0000000000
--- a/cpan/Math-BigInt/t/bigintpm.inc
+++ /dev/null
@@ -1,2511 +0,0 @@
-#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/cpan/Math-BigInt/t/bigintpm.t b/cpan/Math-BigInt/t/bigintpm.t
deleted file mode 100644
index b4f5bf2fb1..0000000000
--- a/cpan/Math-BigInt/t/bigintpm.t
+++ /dev/null
@@ -1,46 +0,0 @@
-#!/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/cpan/Math-BigInt/t/bigints.t b/cpan/Math-BigInt/t/bigints.t
deleted file mode 100644
index de073e21e5..0000000000
--- a/cpan/Math-BigInt/t/bigints.t
+++ /dev/null
@@ -1,123 +0,0 @@
-#!/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/cpan/Math-BigInt/t/biglog.t b/cpan/Math-BigInt/t/biglog.t
deleted file mode 100644
index 9478f7634e..0000000000
--- a/cpan/Math-BigInt/t/biglog.t
+++ /dev/null
@@ -1,213 +0,0 @@
-#!/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; $location =~ s/biglog.t//i;
- if ($ENV{PERL_CORE})
- {
- # testing with the core distribution
- @INC = qw(../lib);
- }
- 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/cpan/Math-BigInt/t/bigroot.t b/cpan/Math-BigInt/t/bigroot.t
deleted file mode 100644
index 41fee89970..0000000000
--- a/cpan/Math-BigInt/t/bigroot.t
+++ /dev/null
@@ -1,69 +0,0 @@
-#!/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; $location =~ s/bigroot.t//i;
- if ($ENV{PERL_CORE})
- {
- # testing with the core distribution
- @INC = qw(../lib);
- }
- 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/cpan/Math-BigInt/t/calling.t b/cpan/Math-BigInt/t/calling.t
deleted file mode 100644
index 4789cc7357..0000000000
--- a/cpan/Math-BigInt/t/calling.t
+++ /dev/null
@@ -1,176 +0,0 @@
-#!/usr/bin/perl -w
-
-# test calling conventions, and :constant overloading
-
-use strict;
-use Test;
-
-BEGIN
- {
- $| = 1;
- # to locate the testing files
- my $location = $0; $location =~ s/calling.t//i;
- if ($ENV{PERL_CORE})
- {
- # testing with the core distribution
- @INC = qw(../lib lib);
- }
- else
- {
- 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/cpan/Math-BigInt/t/config.t b/cpan/Math-BigInt/t/config.t
deleted file mode 100644
index 3bc9d2efee..0000000000
--- a/cpan/Math-BigInt/t/config.t
+++ /dev/null
@@ -1,136 +0,0 @@
-#!/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/cpan/Math-BigInt/t/const_mbf.t b/cpan/Math-BigInt/t/const_mbf.t
deleted file mode 100644
index a73177edb6..0000000000
--- a/cpan/Math-BigInt/t/const_mbf.t
+++ /dev/null
@@ -1,40 +0,0 @@
-#!/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; $location =~ s/const_mbf.t//i;
- if ($ENV{PERL_CORE})
- {
- # testing with the core distribution
- @INC = qw(../t/lib);
- }
- 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/cpan/Math-BigInt/t/constant.t b/cpan/Math-BigInt/t/constant.t
deleted file mode 100644
index 3e69bae0f7..0000000000
--- a/cpan/Math-BigInt/t/constant.t
+++ /dev/null
@@ -1,62 +0,0 @@
-#!/usr/bin/perl -w
-
-use strict;
-use Test;
-
-BEGIN
- {
- $| = 1;
- # to locate the testing files
- my $location = $0; $location =~ s/constant.t//i;
- if ($ENV{PERL_CORE})
- {
- # testing with the core distribution
- @INC = qw(../t/lib);
- }
- 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/cpan/Math-BigInt/t/downgrade.t b/cpan/Math-BigInt/t/downgrade.t
deleted file mode 100644
index 25d672c50f..0000000000
--- a/cpan/Math-BigInt/t/downgrade.t
+++ /dev/null
@@ -1,55 +0,0 @@
-#!/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/cpan/Math-BigInt/t/inf_nan.t b/cpan/Math-BigInt/t/inf_nan.t
deleted file mode 100644
index 0e5294fe44..0000000000
--- a/cpan/Math-BigInt/t/inf_nan.t
+++ /dev/null
@@ -1,355 +0,0 @@
-#!/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; $location =~ s/inf_nan.t//i;
- if ($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, $location;
- }
- print "# INC = @INC\n";
-
- # values groups operators classes tests
- plan tests => 7 * 6 * 5 * 4 * 2 +
- 7 * 6 * 2 * 4 * 1 # bmod
-;
-# see bottom: + 4 * 10; # 4 classes * 10 NaN == NaN tests
- }
-
-use Math::BigInt;
-use Math::BigFloat;
-use Math::BigInt::Subclass;
-use Math::BigFloat::Subclass;
-
-my @classes =
- qw/Math::BigInt Math::BigFloat
- Math::BigInt::Subclass Math::BigFloat::Subclass
- /;
-
-my (@args,$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/cpan/Math-BigInt/t/isa.t b/cpan/Math-BigInt/t/isa.t
deleted file mode 100644
index adb80f9331..0000000000
--- a/cpan/Math-BigInt/t/isa.t
+++ /dev/null
@@ -1,59 +0,0 @@
-#!/usr/bin/perl -w
-
-use Test;
-use strict;
-
-BEGIN
- {
- $| = 1;
- # to locate the testing files
- my $location = $0; $location =~ s/isa.t//i;
- if ($ENV{PERL_CORE})
- {
- # testing with the core distribution
- @INC = qw(../t/lib);
- }
- 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/cpan/Math-BigInt/t/lib_load.t b/cpan/Math-BigInt/t/lib_load.t
deleted file mode 100644
index ff3972effa..0000000000
--- a/cpan/Math-BigInt/t/lib_load.t
+++ /dev/null
@@ -1,53 +0,0 @@
-#!/usr/bin/perl -w
-
-use Test::More;
-use strict;
-
-BEGIN
- {
- $| = 1;
- # to locate the testing files
- my $location = $0; $location =~ s/sub_mbf.t//i;
- if ($ENV{PERL_CORE})
- {
- # testing with the core distribution
- @INC = qw(../t/lib);
- }
- 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/cpan/Math-BigInt/t/mbf_ali.t b/cpan/Math-BigInt/t/mbf_ali.t
deleted file mode 100644
index 1ca43157e3..0000000000
--- a/cpan/Math-BigInt/t/mbf_ali.t
+++ /dev/null
@@ -1,42 +0,0 @@
-#!/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; $location =~ s/mbf_ali.t//i;
- if ($ENV{PERL_CORE})
- {
- # testing with the core distribution
- @INC = qw(../t/lib);
- }
- 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/cpan/Math-BigInt/t/mbi_ali.t b/cpan/Math-BigInt/t/mbi_ali.t
deleted file mode 100644
index 402801733b..0000000000
--- a/cpan/Math-BigInt/t/mbi_ali.t
+++ /dev/null
@@ -1,42 +0,0 @@
-#!/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; $location =~ s/mbi_ali.t//i;
- if ($ENV{PERL_CORE})
- {
- # testing with the core distribution
- @INC = qw(../t/lib);
- }
- 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/cpan/Math-BigInt/t/mbi_rand.t b/cpan/Math-BigInt/t/mbi_rand.t
deleted file mode 100644
index e2bf6637de..0000000000
--- a/cpan/Math-BigInt/t/mbi_rand.t
+++ /dev/null
@@ -1,93 +0,0 @@
-#!/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/cpan/Math-BigInt/t/mbimbf.inc b/cpan/Math-BigInt/t/mbimbf.inc
deleted file mode 100644
index b057eee3ec..0000000000
--- a/cpan/Math-BigInt/t/mbimbf.inc
+++ /dev/null
@@ -1,967 +0,0 @@
-# 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/cpan/Math-BigInt/t/mbimbf.t b/cpan/Math-BigInt/t/mbimbf.t
deleted file mode 100644
index 1ac9adadbd..0000000000
--- a/cpan/Math-BigInt/t/mbimbf.t
+++ /dev/null
@@ -1,110 +0,0 @@
-#!/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; $location =~ s/mbimbf.t//i;
- if ($ENV{PERL_CORE})
- {
- @INC = qw(../lib); # testing with the core distribution
- }
- else
- {
- 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/cpan/Math-BigInt/t/nan_cmp.t b/cpan/Math-BigInt/t/nan_cmp.t
deleted file mode 100644
index ffe7b14b23..0000000000
--- a/cpan/Math-BigInt/t/nan_cmp.t
+++ /dev/null
@@ -1,44 +0,0 @@
-#!/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/cpan/Math-BigInt/t/new_overloaded.t b/cpan/Math-BigInt/t/new_overloaded.t
deleted file mode 100644
index 08708dc557..0000000000
--- a/cpan/Math-BigInt/t/new_overloaded.t
+++ /dev/null
@@ -1,32 +0,0 @@
-#!/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/cpan/Math-BigInt/t/req_mbf0.t b/cpan/Math-BigInt/t/req_mbf0.t
deleted file mode 100644
index 90cd57cc9a..0000000000
--- a/cpan/Math-BigInt/t/req_mbf0.t
+++ /dev/null
@@ -1,39 +0,0 @@
-#!/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; $location =~ s/req_mbf0.t//i;
- if ($ENV{PERL_CORE})
- {
- # testing with the core distribution
- @INC = qw(../t/lib);
- }
- 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/cpan/Math-BigInt/t/req_mbf1.t b/cpan/Math-BigInt/t/req_mbf1.t
deleted file mode 100644
index b0b4aea810..0000000000
--- a/cpan/Math-BigInt/t/req_mbf1.t
+++ /dev/null
@@ -1,37 +0,0 @@
-#!/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; $location =~ s/req_mbf1.t//i;
- if ($ENV{PERL_CORE})
- {
- # testing with the core distribution
- @INC = qw(../t/lib);
- }
- 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/cpan/Math-BigInt/t/req_mbfa.t b/cpan/Math-BigInt/t/req_mbfa.t
deleted file mode 100644
index b2d2a07099..0000000000
--- a/cpan/Math-BigInt/t/req_mbfa.t
+++ /dev/null
@@ -1,37 +0,0 @@
-#!/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; $location =~ s/req_mbfa.t//i;
- if ($ENV{PERL_CORE})
- {
- # testing with the core distribution
- @INC = qw(../t/lib);
- }
- 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/cpan/Math-BigInt/t/req_mbfi.t b/cpan/Math-BigInt/t/req_mbfi.t
deleted file mode 100644
index 2c0ec67b02..0000000000
--- a/cpan/Math-BigInt/t/req_mbfi.t
+++ /dev/null
@@ -1,37 +0,0 @@
-#!/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; $location =~ s/req_mbfi.t//i;
- if ($ENV{PERL_CORE})
- {
- # testing with the core distribution
- @INC = qw(../t/lib);
- }
- 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/cpan/Math-BigInt/t/req_mbfn.t b/cpan/Math-BigInt/t/req_mbfn.t
deleted file mode 100644
index e3887d41de..0000000000
--- a/cpan/Math-BigInt/t/req_mbfn.t
+++ /dev/null
@@ -1,37 +0,0 @@
-#!/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; $location =~ s/req_mbfn.t//i;
- if ($ENV{PERL_CORE})
- {
- # testing with the core distribution
- @INC = qw(../t/lib);
- }
- 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/cpan/Math-BigInt/t/req_mbfw.t b/cpan/Math-BigInt/t/req_mbfw.t
deleted file mode 100644
index 10afc7a272..0000000000
--- a/cpan/Math-BigInt/t/req_mbfw.t
+++ /dev/null
@@ -1,48 +0,0 @@
-#!/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; $location =~ s/req_mbfw.t//i;
- if ($ENV{PERL_CORE})
- {
- # testing with the core distribution
- @INC = qw(../t/lib);
- }
- 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/cpan/Math-BigInt/t/require.t b/cpan/Math-BigInt/t/require.t
deleted file mode 100644
index 50831e611d..0000000000
--- a/cpan/Math-BigInt/t/require.t
+++ /dev/null
@@ -1,41 +0,0 @@
-#!/usr/bin/perl -w
-
-# check that simple requiring BigInt works
-
-use strict;
-use Test;
-
-BEGIN
- {
- $| = 1;
- # to locate the testing files
- my $location = $0; $location =~ s/require.t//i;
- if ($ENV{PERL_CORE})
- {
- # testing with the core distribution
- @INC = qw(../t/lib);
- }
- 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/cpan/Math-BigInt/t/round.t b/cpan/Math-BigInt/t/round.t
deleted file mode 100644
index 90c46758a7..0000000000
--- a/cpan/Math-BigInt/t/round.t
+++ /dev/null
@@ -1,120 +0,0 @@
-#!/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; $location =~ s/round.t//i;
- if ($ENV{PERL_CORE})
- {
- # testing with the core distribution
- @INC = qw(../t/lib);
- }
- 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/cpan/Math-BigInt/t/sub_ali.t b/cpan/Math-BigInt/t/sub_ali.t
deleted file mode 100644
index 93620a9d82..0000000000
--- a/cpan/Math-BigInt/t/sub_ali.t
+++ /dev/null
@@ -1,40 +0,0 @@
-#!/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; $location =~ s/sub_ali.t//i;
- if ($ENV{PERL_CORE})
- {
- # testing with the core distribution
- @INC = qw(../t/lib);
- }
- 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/cpan/Math-BigInt/t/sub_mbf.t b/cpan/Math-BigInt/t/sub_mbf.t
deleted file mode 100644
index 11f63ddc4a..0000000000
--- a/cpan/Math-BigInt/t/sub_mbf.t
+++ /dev/null
@@ -1,56 +0,0 @@
-#!/usr/bin/perl -w
-
-use Test;
-use strict;
-
-BEGIN
- {
- $| = 1;
- # to locate the testing files
- my $location = $0; $location =~ s/sub_mbf.t//i;
- if ($ENV{PERL_CORE})
- {
- # testing with the core distribution
- @INC = qw(../t/lib);
- }
- 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/cpan/Math-BigInt/t/sub_mbi.t b/cpan/Math-BigInt/t/sub_mbi.t
deleted file mode 100644
index 7a6b1e2b26..0000000000
--- a/cpan/Math-BigInt/t/sub_mbi.t
+++ /dev/null
@@ -1,58 +0,0 @@
-#!/usr/bin/perl -w
-
-use Test;
-use strict;
-
-BEGIN
- {
- $| = 1;
- # to locate the testing files
- my $location = $0; $location =~ s/sub_mbi.t//i;
- if ($ENV{PERL_CORE})
- {
- # testing with the core distribution
- @INC = qw(../t/lib);
- }
- 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/cpan/Math-BigInt/t/sub_mif.t b/cpan/Math-BigInt/t/sub_mif.t
deleted file mode 100644
index cd0c863075..0000000000
--- a/cpan/Math-BigInt/t/sub_mif.t
+++ /dev/null
@@ -1,43 +0,0 @@
-#!/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; $location =~ s/sub_mif.t//i;
- if ($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, $location;
- }
- print "# INC = @INC\n";
-
- plan tests => 684;
- }
-
-use Math::BigInt::Subclass;
-use Math::BigFloat::Subclass;
-
-use vars qw/$mbi $mbf/;
-
-$mbi = 'Math::BigInt::Subclass';
-$mbf = 'Math::BigFloat::Subclass';
-
-require 'mbimbf.inc';
-
diff --git a/cpan/Math-BigInt/t/trap.t b/cpan/Math-BigInt/t/trap.t
deleted file mode 100644
index 94a7da4acb..0000000000
--- a/cpan/Math-BigInt/t/trap.t
+++ /dev/null
@@ -1,92 +0,0 @@
-#!/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/cpan/Math-BigInt/t/upgrade.inc b/cpan/Math-BigInt/t/upgrade.inc
deleted file mode 100644
index 1160a21c6b..0000000000
--- a/cpan/Math-BigInt/t/upgrade.inc
+++ /dev/null
@@ -1,1500 +0,0 @@
-# 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/cpan/Math-BigInt/t/upgrade.t b/cpan/Math-BigInt/t/upgrade.t
deleted file mode 100644
index 20d8990c55..0000000000
--- a/cpan/Math-BigInt/t/upgrade.t
+++ /dev/null
@@ -1,45 +0,0 @@
-#!/usr/bin/perl -w
-
-use Test;
-use strict;
-
-BEGIN
- {
- $| = 1;
- # to locate the testing files
- my $location = $0; $location =~ s/upgrade.t//i;
- if ($ENV{PERL_CORE})
- {
- # testing with the core distribution
- @INC = qw(../t/lib);
- }
- 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/cpan/Math-BigInt/t/upgradef.t b/cpan/Math-BigInt/t/upgradef.t
deleted file mode 100644
index 437268db65..0000000000
--- a/cpan/Math-BigInt/t/upgradef.t
+++ /dev/null
@@ -1,84 +0,0 @@
-#!/usr/bin/perl -w
-
-use Test;
-use strict;
-
-BEGIN
- {
- $| = 1;
- # to locate the testing files
- my $location = $0; $location =~ s/upgradef.t//i;
- if ($ENV{PERL_CORE})
- {
- # testing with the core distribution
- @INC = qw(../t/lib);
- }
- 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/cpan/Math-BigInt/t/use.t b/cpan/Math-BigInt/t/use.t
deleted file mode 100644
index 1f09f5e43c..0000000000
--- a/cpan/Math-BigInt/t/use.t
+++ /dev/null
@@ -1,46 +0,0 @@
-#!/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; $location =~ s/use.t//i;
- if ($ENV{PERL_CORE})
- {
- # testing with the core distribution
- @INC = qw(../t/lib);
- }
- 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/cpan/Math-BigInt/t/use_lib1.t b/cpan/Math-BigInt/t/use_lib1.t
deleted file mode 100644
index a6eda82b37..0000000000
--- a/cpan/Math-BigInt/t/use_lib1.t
+++ /dev/null
@@ -1,40 +0,0 @@
-#!/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; $location =~ s/use_lib1.t//i;
- if ($ENV{PERL_CORE})
- {
- # testing with the core distribution
- @INC = qw(../t/lib);
- }
- 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/cpan/Math-BigInt/t/use_lib2.t b/cpan/Math-BigInt/t/use_lib2.t
deleted file mode 100644
index aa4ba5fbe2..0000000000
--- a/cpan/Math-BigInt/t/use_lib2.t
+++ /dev/null
@@ -1,41 +0,0 @@
-#!/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; $location =~ s/use_lib2.t//i;
- if ($ENV{PERL_CORE})
- {
- # testing with the core distribution
- @INC = qw(../t/lib);
- }
- 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/cpan/Math-BigInt/t/use_lib3.t b/cpan/Math-BigInt/t/use_lib3.t
deleted file mode 100644
index b46b939551..0000000000
--- a/cpan/Math-BigInt/t/use_lib3.t
+++ /dev/null
@@ -1,41 +0,0 @@
-#!/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; $location =~ s/use_lib3.t//i;
- if ($ENV{PERL_CORE})
- {
- # testing with the core distribution
- @INC = qw(../t/lib);
- }
- 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/cpan/Math-BigInt/t/use_lib4.t b/cpan/Math-BigInt/t/use_lib4.t
deleted file mode 100644
index bfd85d5f70..0000000000
--- a/cpan/Math-BigInt/t/use_lib4.t
+++ /dev/null
@@ -1,42 +0,0 @@
-#!/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; $location =~ s/use_lib4.t//i;
- if ($ENV{PERL_CORE})
- {
- # testing with the core distribution
- @INC = qw(../t/lib);
- }
- 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/cpan/Math-BigInt/t/use_mbfw.t b/cpan/Math-BigInt/t/use_mbfw.t
deleted file mode 100644
index c6a047143e..0000000000
--- a/cpan/Math-BigInt/t/use_mbfw.t
+++ /dev/null
@@ -1,52 +0,0 @@
-#!/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; $location =~ s/use_mbfw.t//i;
- if ($ENV{PERL_CORE})
- {
- # testing with the core distribution
- @INC = qw(../t/lib);
- }
- 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/cpan/Math-BigInt/t/with_sub.t b/cpan/Math-BigInt/t/with_sub.t
deleted file mode 100644
index 878fe07f1f..0000000000
--- a/cpan/Math-BigInt/t/with_sub.t
+++ /dev/null
@@ -1,44 +0,0 @@
-#!/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; $location =~ s/with_sub.t//i;
- if ($ENV{PERL_CORE})
- {
- # testing with the core distribution
- @INC = qw(../t/lib);
- }
- 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