perl 3.0 patch #38 (combined patch)

Forget the description, it's too late at night...

1 files changed, 275 insertions, 0 deletions

diff --git a/lib/bigint.pl b/lib/bigint.pl
new file mode 100644
index 0000000000..503c7837c2
--- /dev/null
+++ b/lib/bigint.pl
@@ -0,0 +1,275 @@
+package bigint;
+
+# arbitrary size integer math package
+#
+# by Mark Biggar
+#
+# Canonical Big integer value are strings of the form
+#       /^[+-]\d+$/ with leading zeros suppressed
+# Input values to these routines may be strings of the form
+#       /^\s*[+-]?[\d\s]+$/.
+# Examples:
+#   '+0'                            canonical zero value
+#   '   -123 123 123'               canonical value '-123123123'
+#   '1 23 456 7890'                 canonical value '+1234567890'
+# Output values always always in canonical form
+#
+# Actual math is done in an internal format consisting of an array
+#   whose first element is the sign (/^[+-]$/) and whose remaining 
+#   elements are base 100000 digits with the least significant digit first.
+# The string 'NaN' is used to represent the result when input arguments 
+#   are not numbers, as well as the result of dividing by zero
+#
+# routines provided are:
+#
+#   bneg(BINT) return BINT              negation
+#   babs(BINT) return BINT              absolute value
+#   bcmp(BINT,BINT) return CODE         compare numbers (undef,<0,=0,>0)
+#   badd(BINT,BINT) return BINT         addition
+#   bsub(BINT,BINT) return BINT         subtraction
+#   bmul(BINT,BINT) return BINT         multiplication
+#   bdiv(BINT,BINT) return (BINT,BINT)  division (quo,rem) just quo if scalar
+#   bmod(BINT,BINT) return BINT         modulus
+#   bgcd(BINT,BINT) return BINT         greatest common divisor
+#   bnorm(BINT) return BINT             normalization
+#
+
+# normalize string form of number.   Strip leading zeros.  Strip any
+#   white space and add a sign, if missing.
+# Strings that are not numbers result the value 'NaN'.
+sub main'bnorm { #(num_str) return num_str
+    local($_) = @_;
+    s/\s+//g;                           # strip white space
+    if (s/^([+-]?)0*(\d+)$/$1$2/) {     # test if number
+	substr($_,0,0) = '+' unless $1; # Add missing sign
+	s/^-0/+0/;
+	$_;
+    } else {
+	'NaN';
+    }
+}
+
+# Convert a number from string format to internal base 100000 format.
+#   Assumes normalized value as input.
+sub internal { #(num_str) return int_num_array
+    local($d) = @_;
+    ($is,$il) = (substr($d,0,1),length($d)-2);
+    substr($d,0,1) = '';
+    ($is, reverse(unpack("a" . ($il%5+1) . ("a5" x ($il/5)), $d)));
+}
+
+# Convert a number from internal base 100000 format to string format.
+#   This routine scribbles all over input array.
+sub external { #(int_num_array) return num_str
+    $es = shift;
+    grep($_ > 9999 || ($_ = substr('0000'.$_,-5)), @_);   # zero pad
+    &'bnorm(join('', $es, reverse(@_)));    # reverse concat and normalize
+}
+
+# Negate input value.
+sub main'bneg { #(num_str) return num_str
+    local($_) = &'bnorm(@_);
+    vec($_,0,8) ^= ord('+') ^ ord('-') unless $_ eq '+0';
+    s/^H/N/;
+    $_;
+}
+
+# Returns the absolute value of the input.
+sub main'babs { #(num_str) return num_str
+    &abs(&'bnorm(@_));
+}
+
+sub abs { # post-normalized abs for internal use
+    local($_) = @_;
+    s/^-/+/;
+    $_;
+}
+
+# Compares 2 values.  Returns one of undef, <0, =0, >0. (suitable for sort)
+sub main'bcmp { #(num_str, num_str) return cond_code
+    local($x,$y) = (&'bnorm($_[0]),&'bnorm($_[1]));
+    if ($x eq 'NaN') {
+	undef;
+    } elsif ($y eq 'NaN') {
+	undef;
+    } else {
+	&cmp($x,$y);
+    }
+}
+
+sub cmp { # post-normalized compare for internal use
+    local($cx, $cy) = @_;
+    $cx cmp $cy
+    &&
+    (
+	ord($cy) <=> ord($cx)
+	||
+	($cx cmp ',') * (length($cy) <=> length($cx) || $cy cmp $cx)
+    );
+}
+
+sub main'badd { #(num_str, num_str) return num_str
+    local(*x, *y); ($x, $y) = (&'bnorm($_[0]),&'bnorm($_[1]));
+    if ($x eq 'NaN') {
+	'NaN';
+    } elsif ($y eq 'NaN') {
+	'NaN';
+    } else {
+	@x = &internal($x);             # convert to internal form
+	@y = &internal($y);
+	local($sx, $sy) = (shift @x, shift @y); # get signs
+	if ($sx eq $sy) {
+	    &external($sx, &add(*x, *y)); # if same sign add
+	} else {
+	    ($x, $y) = (&abs($x),&abs($y)); # make abs
+	    if (&cmp($y,$x) > 0) {
+		&external($sy, &sub(*y, *x));
+	    } else {
+		&external($sx, &sub(*x, *y));
+	    }
+	}
+    }
+}
+
+sub main'bsub { #(num_str, num_str) return num_str
+    &'badd($_[0],&'bneg($_[1]));    
+}
+
+# GCD -- Euclids algorithm Knuth Vol 2 pg 296
+sub main'bgcd { #(num_str, num_str) return num_str
+    local($x,$y) = (&'bnorm($_[0]),&'bnorm($_[1]));
+    if ($x eq 'NaN') {
+	'NaN';
+    }
+    elsif ($y eq 'NaN') {
+	'NaN';
+    }
+    else {
+	($x, $y) = ($y,&'bmod($x,$y)) while $y ne '+0';
+	$x;
+    }
+}
+
+# routine to add two base 100000 numbers
+#   stolen from Knuth Vol 2 Algorithm A pg 231
+#   there are separate routines to add and sub as per Kunth pg 233
+sub add { #(int_num_array, int_num_array) return int_num_array
+    local(*x, *y) = @_;
+    $car = 0;
+    for $x (@x) {
+	last unless @y || $car;
+	$x -= 100000 if $car = (($x += shift @y + $car) >= 100000);
+    }
+    for $y (@y) {
+	last unless $car;
+	$y -= 100000 if $car = (($y += $car) >= 100000);
+    }
+    (@x, @y, $car);
+}
+
+# subtract base 100000 numbers -- stolen from Knuth Vol 2 pg 232, $x > $y
+sub sub { #(int_num_array, int_num_array) return int_num_array
+    local(*sx, *sy) = @_;
+    $bar = 0;
+    for $sx (@sx) {
+	last unless @y || $bar;
+	$sx += 100000 if $bar = (($sx -= shift @sy + $bar) < 0);
+    }
+    @sx;
+}
+
+# multiply two numbers -- stolen from Knuth Vol 2 pg 233
+sub main'bmul { #(num_str, num_str) return num_str
+    local(*x, *y); ($x, $y) = (&'bnorm($_[0]), &'bnorm($_[1]));
+    if ($x eq 'NaN') {
+	'NaN';
+    } elsif ($y eq 'NaN') {
+	'NaN';
+    } else {
+	@x = &internal($x);
+	@y = &internal($y);
+	local($signr) = (shift @x ne shift @y) ? '-' : '+';
+	@prod = ();
+	for $x (@x) {
+	    ($car, $cty) = (0, 0);
+	    for $y (@y) {
+		$prod = $x * $y + $prod[$cty] + $car;
+		$prod[$cty++] =
+		    $prod - ($car = int($prod * (1/100000))) * 100000;
+	    }
+	    $prod[$cty] += $car if $car;
+	    $x = shift @prod;
+	}
+	&external($signr, @x, @prod);
+    }
+}
+
+# modulus
+sub main'bmod { #(num_str, num_str) return num_str
+    (&'bdiv(@_))[1];
+}
+
+sub main'bdiv { #(dividend: num_str, divisor: num_str) return num_str
+    local (*x, *y); ($x, $y) = (&'bnorm($_[0]), &'bnorm($_[1]));
+    return wantarray ? ('NaN','NaN') : 'NaN'
+	if ($x eq 'NaN' || $y eq 'NaN' || $y eq '+0');
+    return wantarray ? ('+0',$x) : '+0' if (&cmp(&abs($x),&abs($y)) < 0);
+    @x = &internal($x); @y = &internal($y);
+    $srem = $y[0];
+    $sr = (shift @x ne shift @y) ? '-' : '+';
+    $car = $bar = $prd = 0;
+    if (($dd = int(100000/($y[$#y]+1))) != 1) {
+	for $x (@x) {
+	    $x = $x * $dd + $car;
+	    $x -= ($car = int($x * (1/100000))) * 100000;
+	}
+	push(@x, $car); $car = 0;
+	for $y (@y) {
+	    $y = $y * $dd + $car;
+	    $y -= ($car = int($y * (1/100000))) * 100000;
+	}
+    }
+    else {
+	push(@x, 0);
+    }
+    @q = (); ($v2,$v1) = @y[$#y-1,$#y];
+    while ($#x > $#y) {
+	($u2,$u1,$u0) = @x[($#x-2)..$#x];
+	$q = (($u0 == $v1) ? 99999 : int(($u0*100000+$u1)/$v1));
+	--$q while ($v2*$q > ($u0*100000+$u1-$q*$v1)*100000+$u2);
+	if ($q) {
+	    ($car, $bar) = (0,0);
+	    for ($y = 0, $x = $#x-$#y-1; $y <= $#y; ++$y,++$x) {
+		$prd = $q * $y[$y] + $car;
+		$prd -= ($car = int($prd * (1/100000))) * 100000;
+		$x[$x] += 100000 if ($bar = (($x[$x] -= $prd + $bar) < 0));
+	    }
+	    if ($x[$#x] < $car + $bar) {
+		$car = 0; --$q;
+		for ($y = 0, $x = $#x-$#y-1; $y <= $#y; ++$y,++$x) {
+		    $x[$x] -= 100000
+			if ($car = (($x[$x] += $y[$y] + $car) > 100000));
+		}
+	    }   
+	}
+	pop(@x); unshift(@q, $q);
+    }
+    if (wantarray) {
+	@d = ();
+	if ($dd != 1) {
+	    $car = 0;
+	    for $x (reverse @x) {
+		$prd = $car * 100000 + $x;
+		$car = $prd - ($tmp = int($prd / $dd)) * $dd;
+		unshift(@d, $tmp);
+	    }
+	}
+	else {
+	    @d = @x;
+	}
+	(&external($sr, @q), &external($srem, @d, 0));
+    } else {
+	&external($sr, @q);
+    }
+}
+1;