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+package Math::BigInt;
+
+use overload
+'+' => sub {new Math::BigInt &badd},
+'-' => sub {new Math::BigInt
+ $_[2]? bsub($_[1],${$_[0]}) : bsub(${$_[0]},$_[1])},
+'<=>' => sub {new Math::BigInt
+ $_[2]? bcmp($_[1],${$_[0]}) : bcmp(${$_[0]},$_[1])},
+'cmp' => sub {new Math::BigInt
+ $_[2]? ($_[1] cmp ${$_[0]}) : (${$_[0]} cmp $_[1])},
+'*' => sub {new Math::BigInt &bmul},
+'/' => sub {new Math::BigInt
+ $_[2]? scalar bdiv($_[1],${$_[0]}) :
+ scalar bdiv(${$_[0]},$_[1])},
+'%' => sub {new Math::BigInt
+ $_[2]? bmod($_[1],${$_[0]}) : bmod(${$_[0]},$_[1])},
+'**' => sub {new Math::BigInt
+ $_[2]? bpow($_[1],${$_[0]}) : bpow(${$_[0]},$_[1])},
+'neg' => sub {new Math::BigInt &bneg},
+'abs' => sub {new Math::BigInt &babs},
+
+qw(
+"" stringify
+0+ numify) # Order of arguments unsignificant
+;
+
+$NaNOK=1;
+
+sub new {
+ my($class) = shift;
+ my($foo) = bnorm(shift);
+ die "Not a number initialized to Math::BigInt" if !$NaNOK && $foo eq "NaN";
+ bless \$foo, $class;
+}
+sub stringify { "${$_[0]}" }
+sub numify { 0 + "${$_[0]}" } # Not needed, additional overhead
+ # comparing to direct compilation based on
+ # stringify
+sub import {
+ shift;
+ return unless @_;
+ die "unknown import: @_" unless @_ == 1 and $_[0] eq ':constant';
+ overload::constant integer => sub {Math::BigInt->new(shift)};
+}
+
+$zero = 0;
+
+
+# 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 bnorm { #(num_str) return num_str
+ local($_) = @_;
+ s/\s+//g; # strip white space
+ if (s/^([+-]?)0*(\d+)$/$1$2/) { # test if number
+ substr($_,$[,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($d,$[,1),length($d)-2);
+ substr($d,$[,1) = '';
+ ($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('', $es, reverse(@_))); # reverse concat and normalize
+}
+
+# Negate input value.
+sub bneg { #(num_str) return num_str
+ local($_) = &bnorm(@_);
+ return $_ if $_ eq '+0' or $_ eq 'NaN';
+ vec($_,0,8) ^= ord('+') ^ ord('-');
+ $_;
+}
+
+# Returns the absolute value of the input.
+sub babs { #(num_str) return num_str
+ &abs(&bnorm(@_));
+}
+
+sub abs { # post-normalized abs for internal use
+ local($_) = @_;
+ s/^-/+/;
+ $_;
+}
+
+# Compares 2 values. Returns one of undef, <0, =0, >0. (suitable for sort)
+sub bcmp { #(num_str, num_str) return cond_code
+ local($x,$y) = (&bnorm($_[$[]),&bnorm($_[$[+1]));
+ if ($x eq 'NaN') {
+ undef;
+ } elsif ($y eq 'NaN') {
+ undef;
+ } else {
+ &cmp($x,$y) <=> 0;
+ }
+}
+
+sub cmp { # post-normalized compare for internal use
+ local($cx, $cy) = @_;
+
+ return 0 if ($cx eq $cy);
+
+ local($sx, $sy) = (substr($cx, 0, 1), substr($cy, 0, 1));
+ local($ld);
+
+ if ($sx eq '+') {
+ return 1 if ($sy eq '-' || $cy eq '+0');
+ $ld = length($cx) - length($cy);
+ return $ld if ($ld);
+ return $cx cmp $cy;
+ } else { # $sx eq '-'
+ return -1 if ($sy eq '+');
+ $ld = length($cy) - length($cx);
+ return $ld if ($ld);
+ return $cy cmp $cx;
+ }
+}
+
+sub badd { #(num_str, num_str) return num_str
+ local(*x, *y); ($x, $y) = (&bnorm($_[$[]),&bnorm($_[$[+1]));
+ if ($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($sx, &sub(*x, *y));
+ }
+ }
+ }
+}
+
+sub bsub { #(num_str, num_str) return num_str
+ &badd($_[$[],&bneg($_[$[+1]));
+}
+
+# GCD -- Euclids algorithm Knuth Vol 2 pg 296
+sub bgcd { #(num_str, num_str) return num_str
+ local($x,$y) = (&bnorm($_[$[]),&bnorm($_[$[+1]));
+ if ($x eq 'NaN' || $y eq 'NaN') {
+ 'NaN';
+ } else {
+ ($x, $y) = ($y,&bmod($x,$y)) while $y ne '+0';
+ $x;
+ }
+}
+
+# routine to add two base 1e5 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 -= 1e5 if $car = (($x += (@y ? shift(@y) : 0) + $car) >= 1e5) ? 1 : 0;
+ }
+ for $y (@y) {
+ last unless $car;
+ $y -= 1e5 if $car = (($y += $car) >= 1e5) ? 1 : 0;
+ }
+ (@x, @y, $car);
+}
+
+# subtract base 1e5 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 @sy || $bar;
+ $sx += 1e5 if $bar = (($sx -= (@sy ? shift(@sy) : 0) + $bar) < 0);
+ }
+ @sx;
+}
+
+# multiply two numbers -- stolen from Knuth Vol 2 pg 233
+sub bmul { #(num_str, num_str) return num_str
+ local(*x, *y); ($x, $y) = (&bnorm($_[$[]), &bnorm($_[$[+1]));
+ if ($x eq 'NaN') {
+ 'NaN';
+ } elsif ($y eq 'NaN') {
+ 'NaN';
+ } else {
+ @x = &internal($x);
+ @y = &internal($y);
+ &external(&mul(*x,*y));
+ }
+}
+
+# multiply two numbers in internal representation
+# destroys the arguments, supposes that two arguments are different
+sub mul { #(*int_num_array, *int_num_array) return int_num_array
+ local(*x, *y) = (shift, shift);
+ local($signr) = (shift @x ne shift @y) ? '-' : '+';
+ @prod = ();
+ for $x (@x) {
+ ($car, $cty) = (0, $[);
+ for $y (@y) {
+ $prod = $x * $y + ($prod[$cty] || 0) + $car;
+ $prod[$cty++] =
+ $prod - ($car = int($prod * 1e-5)) * 1e5;
+ }
+ $prod[$cty] += $car if $car;
+ $x = shift @prod;
+ }
+ ($signr, @x, @prod);
+}
+
+# modulus
+sub bmod { #(num_str, num_str) return num_str
+ (&bdiv(@_))[$[+1];
+}
+
+sub bdiv { #(dividend: num_str, divisor: num_str) return num_str
+ local (*x, *y); ($x, $y) = (&bnorm($_[$[]), &bnorm($_[$[+1]));
+ return wantarray ? ('NaN','NaN') : 'NaN'
+ if ($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 = $y[$[];
+ $sr = (shift @x ne shift @y) ? '-' : '+';
+ $car = $bar = $prd = 0;
+ if (($dd = int(1e5/($y[$#y]+1))) != 1) {
+ for $x (@x) {
+ $x = $x * $dd + $car;
+ $x -= ($car = int($x * 1e-5)) * 1e5;
+ }
+ push(@x, $car); $car = 0;
+ for $y (@y) {
+ $y = $y * $dd + $car;
+ $y -= ($car = int($y * 1e-5)) * 1e5;
+ }
+ }
+ else {
+ push(@x, 0);
+ }
+ @q = (); ($v2,$v1) = @y[-2,-1];
+ while ($#x > $#y) {
+ ($u2,$u1,$u0) = @x[-3..-1];
+ $q = (($u0 == $v1) ? 99999 : int(($u0*1e5+$u1)/$v1));
+ --$q while ($v2*$q > ($u0*1e5+$u1-$q*$v1)*1e5+$u2);
+ if ($q) {
+ ($car, $bar) = (0,0);
+ for ($y = $[, $x = $#x-$#y+$[-1; $y <= $#y; ++$y,++$x) {
+ $prd = $q * $y[$y] + $car;
+ $prd -= ($car = int($prd * 1e-5)) * 1e5;
+ $x[$x] += 1e5 if ($bar = (($x[$x] -= $prd + $bar) < 0));
+ }
+ if ($x[$#x] < $car + $bar) {
+ $car = 0; --$q;
+ for ($y = $[, $x = $#x-$#y+$[-1; $y <= $#y; ++$y,++$x) {
+ $x[$x] -= 1e5
+ if ($car = (($x[$x] += $y[$y] + $car) > 1e5));
+ }
+ }
+ }
+ pop(@x); unshift(@q, $q);
+ }
+ if (wantarray) {
+ @d = ();
+ if ($dd != 1) {
+ $car = 0;
+ for $x (reverse @x) {
+ $prd = $car * 1e5 + $x;
+ $car = $prd - ($tmp = int($prd / $dd)) * $dd;
+ unshift(@d, $tmp);
+ }
+ }
+ else {
+ @d = @x;
+ }
+ (&external($sr, @q), &external($srem, @d, $zero));
+ } else {
+ &external($sr, @q);
+ }
+}
+
+# compute power of two numbers -- stolen from Knuth Vol 2 pg 233
+sub bpow { #(num_str, num_str) return num_str
+ local(*x, *y); ($x, $y) = (&bnorm($_[$[]), &bnorm($_[$[+1]));
+ if ($x eq 'NaN') {
+ 'NaN';
+ } elsif ($y eq 'NaN') {
+ 'NaN';
+ } elsif ($x eq '+1') {
+ '+1';
+ } elsif ($x eq '-1') {
+ &bmod($x,2) ? '-1': '+1';
+ } elsif ($y =~ /^-/) {
+ 'NaN';
+ } elsif ($x eq '+0' && $y eq '+0') {
+ 'NaN';
+ } else {
+ @x = &internal($x);
+ local(@pow2)=@x;
+ local(@pow)=&internal("+1");
+ local($y1,$res,@tmp1,@tmp2)=(1); # need tmp to send to mul
+ while ($y ne '+0') {
+ ($y,$res)=&bdiv($y,2);
+ if ($res ne '+0') {@tmp=@pow2; @pow=&mul(*pow,*tmp);}
+ if ($y ne '+0') {@tmp=@pow2;@pow2=&mul(*pow2,*tmp);}
+ }
+ &external(@pow);
+ }
+}
+
+1;
+__END__
+
+=head1 NAME
+
+Math::BigInt - Arbitrary size integer math package
+
+=head1 SYNOPSIS
+
+ use Math::BigInt;
+ $i = Math::BigInt->new($string);
+
+ $i->bneg return BINT negation
+ $i->babs return BINT absolute value
+ $i->bcmp(BINT) return CODE compare numbers (undef,<0,=0,>0)
+ $i->badd(BINT) return BINT addition
+ $i->bsub(BINT) return BINT subtraction
+ $i->bmul(BINT) return BINT multiplication
+ $i->bdiv(BINT) return (BINT,BINT) division (quo,rem) just quo if scalar
+ $i->bmod(BINT) return BINT modulus
+ $i->bgcd(BINT) return BINT greatest common divisor
+ $i->bnorm return BINT normalization
+
+=head1 DESCRIPTION
+
+All basic math operations are overloaded if you declare your big
+integers as
+
+ $i = new Math::BigInt '123 456 789 123 456 789';
+
+
+=over 2
+
+=item Canonical notation
+
+Big integer value are strings of the form C</^[+-]\d+$/> with leading
+zeros suppressed.
+
+=item Input
+
+Input values to these routines may be strings of the form
+C</^\s*[+-]?[\d\s]+$/>.
+
+=item Output
+
+Output values always always in canonical form
+
+=back
+
+Actual math is done in an internal format consisting of an array
+whose first element is the sign (/^[+-]$/) 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.
+
+=head1 EXAMPLES
+
+ '+0' canonical zero value
+ ' -123 123 123' canonical value '-123123123'
+ '1 23 456 7890' canonical value '+1234567890'
+
+
+=head1 Autocreating constants
+
+After C<use Math::BigInt ':constant'> all the integer decimal 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'
+
+print the integer value of C<2**100>. Note that without convertion of
+constants the expression 2**100 will be calculatted as floating point number.
+
+=head1 BUGS
+
+The current version of this module is a preliminary version of the
+real thing that is currently (as of perl5.002) under development.
+
+=head1 AUTHOR
+
+Mark Biggar, overloaded interface by Ilya Zakharevich.
+
+=cut
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