416 lines
11 KiB
Perl
416 lines
11 KiB
Perl
package Math::BigInt;
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use overload
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'+' => sub {new Math::BigInt &badd},
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'-' => sub {new Math::BigInt
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$_[2]? bsub($_[1],${$_[0]}) : bsub(${$_[0]},$_[1])},
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'<=>' => sub {new Math::BigInt
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$_[2]? bcmp($_[1],${$_[0]}) : bcmp(${$_[0]},$_[1])},
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'cmp' => sub {new Math::BigInt
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$_[2]? ($_[1] cmp ${$_[0]}) : (${$_[0]} cmp $_[1])},
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'*' => sub {new Math::BigInt &bmul},
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'/' => sub {new Math::BigInt
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$_[2]? scalar bdiv($_[1],${$_[0]}) :
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scalar bdiv(${$_[0]},$_[1])},
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'%' => sub {new Math::BigInt
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$_[2]? bmod($_[1],${$_[0]}) : bmod(${$_[0]},$_[1])},
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'**' => sub {new Math::BigInt
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$_[2]? bpow($_[1],${$_[0]}) : bpow(${$_[0]},$_[1])},
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'neg' => sub {new Math::BigInt &bneg},
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'abs' => sub {new Math::BigInt &babs},
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qw(
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"" stringify
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0+ numify) # Order of arguments unsignificant
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;
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$NaNOK=1;
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sub new {
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my($class) = shift;
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my($foo) = bnorm(shift);
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die "Not a number initialized to Math::BigInt" if !$NaNOK && $foo eq "NaN";
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bless \$foo, $class;
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}
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sub stringify { "${$_[0]}" }
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sub numify { 0 + "${$_[0]}" } # Not needed, additional overhead
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# comparing to direct compilation based on
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# stringify
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sub import {
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shift;
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return unless @_;
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die "unknown import: @_" unless @_ == 1 and $_[0] eq ':constant';
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overload::constant integer => sub {Math::BigInt->new(shift)};
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}
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$zero = 0;
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# normalize string form of number. Strip leading zeros. Strip any
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# white space and add a sign, if missing.
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# Strings that are not numbers result the value 'NaN'.
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sub bnorm { #(num_str) return num_str
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local($_) = @_;
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s/\s+//g; # strip white space
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if (s/^([+-]?)0*(\d+)$/$1$2/) { # test if number
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substr($_,$[,0) = '+' unless $1; # Add missing sign
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s/^-0/+0/;
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$_;
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} else {
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'NaN';
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}
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}
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# Convert a number from string format to internal base 100000 format.
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# Assumes normalized value as input.
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sub internal { #(num_str) return int_num_array
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local($d) = @_;
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($is,$il) = (substr($d,$[,1),length($d)-2);
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substr($d,$[,1) = '';
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($is, reverse(unpack("a" . ($il%5+1) . ("a5" x ($il/5)), $d)));
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}
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# Convert a number from internal base 100000 format to string format.
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# This routine scribbles all over input array.
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sub external { #(int_num_array) return num_str
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$es = shift;
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grep($_ > 9999 || ($_ = substr('0000'.$_,-5)), @_); # zero pad
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&bnorm(join('', $es, reverse(@_))); # reverse concat and normalize
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}
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# Negate input value.
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sub bneg { #(num_str) return num_str
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local($_) = &bnorm(@_);
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return $_ if $_ eq '+0' or $_ eq 'NaN';
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vec($_,0,8) ^= ord('+') ^ ord('-');
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$_;
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}
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# Returns the absolute value of the input.
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sub babs { #(num_str) return num_str
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&abs(&bnorm(@_));
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}
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sub abs { # post-normalized abs for internal use
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local($_) = @_;
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s/^-/+/;
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$_;
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}
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# Compares 2 values. Returns one of undef, <0, =0, >0. (suitable for sort)
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sub bcmp { #(num_str, num_str) return cond_code
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local($x,$y) = (&bnorm($_[$[]),&bnorm($_[$[+1]));
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if ($x eq 'NaN') {
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undef;
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} elsif ($y eq 'NaN') {
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undef;
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} else {
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&cmp($x,$y) <=> 0;
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}
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}
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sub cmp { # post-normalized compare for internal use
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local($cx, $cy) = @_;
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return 0 if ($cx eq $cy);
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local($sx, $sy) = (substr($cx, 0, 1), substr($cy, 0, 1));
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local($ld);
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if ($sx eq '+') {
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return 1 if ($sy eq '-' || $cy eq '+0');
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$ld = length($cx) - length($cy);
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return $ld if ($ld);
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return $cx cmp $cy;
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} else { # $sx eq '-'
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return -1 if ($sy eq '+');
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$ld = length($cy) - length($cx);
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return $ld if ($ld);
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return $cy cmp $cx;
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}
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}
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sub badd { #(num_str, num_str) return num_str
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local(*x, *y); ($x, $y) = (&bnorm($_[$[]),&bnorm($_[$[+1]));
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if ($x eq 'NaN') {
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'NaN';
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} elsif ($y eq 'NaN') {
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'NaN';
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} else {
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@x = &internal($x); # convert to internal form
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@y = &internal($y);
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local($sx, $sy) = (shift @x, shift @y); # get signs
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if ($sx eq $sy) {
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&external($sx, &add(*x, *y)); # if same sign add
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} else {
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($x, $y) = (&abs($x),&abs($y)); # make abs
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if (&cmp($y,$x) > 0) {
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&external($sy, &sub(*y, *x));
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} else {
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&external($sx, &sub(*x, *y));
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}
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}
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}
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}
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sub bsub { #(num_str, num_str) return num_str
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&badd($_[$[],&bneg($_[$[+1]));
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}
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# GCD -- Euclids algorithm Knuth Vol 2 pg 296
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sub bgcd { #(num_str, num_str) return num_str
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local($x,$y) = (&bnorm($_[$[]),&bnorm($_[$[+1]));
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if ($x eq 'NaN' || $y eq 'NaN') {
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'NaN';
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} else {
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($x, $y) = ($y,&bmod($x,$y)) while $y ne '+0';
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$x;
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}
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}
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# routine to add two base 1e5 numbers
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# stolen from Knuth Vol 2 Algorithm A pg 231
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# there are separate routines to add and sub as per Kunth pg 233
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sub add { #(int_num_array, int_num_array) return int_num_array
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local(*x, *y) = @_;
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$car = 0;
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for $x (@x) {
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last unless @y || $car;
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$x -= 1e5 if $car = (($x += (@y ? shift(@y) : 0) + $car) >= 1e5) ? 1 : 0;
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}
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for $y (@y) {
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last unless $car;
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$y -= 1e5 if $car = (($y += $car) >= 1e5) ? 1 : 0;
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}
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(@x, @y, $car);
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}
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# subtract base 1e5 numbers -- stolen from Knuth Vol 2 pg 232, $x > $y
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sub sub { #(int_num_array, int_num_array) return int_num_array
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local(*sx, *sy) = @_;
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$bar = 0;
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for $sx (@sx) {
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last unless @sy || $bar;
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$sx += 1e5 if $bar = (($sx -= (@sy ? shift(@sy) : 0) + $bar) < 0);
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}
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@sx;
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}
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# multiply two numbers -- stolen from Knuth Vol 2 pg 233
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sub bmul { #(num_str, num_str) return num_str
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local(*x, *y); ($x, $y) = (&bnorm($_[$[]), &bnorm($_[$[+1]));
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if ($x eq 'NaN') {
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'NaN';
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} elsif ($y eq 'NaN') {
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'NaN';
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} else {
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@x = &internal($x);
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@y = &internal($y);
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&external(&mul(*x,*y));
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}
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}
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# multiply two numbers in internal representation
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# destroys the arguments, supposes that two arguments are different
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sub mul { #(*int_num_array, *int_num_array) return int_num_array
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local(*x, *y) = (shift, shift);
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local($signr) = (shift @x ne shift @y) ? '-' : '+';
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@prod = ();
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for $x (@x) {
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($car, $cty) = (0, $[);
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for $y (@y) {
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$prod = $x * $y + ($prod[$cty] || 0) + $car;
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$prod[$cty++] =
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$prod - ($car = int($prod * 1e-5)) * 1e5;
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}
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$prod[$cty] += $car if $car;
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$x = shift @prod;
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}
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($signr, @x, @prod);
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}
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# modulus
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sub bmod { #(num_str, num_str) return num_str
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(&bdiv(@_))[$[+1];
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}
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sub bdiv { #(dividend: num_str, divisor: num_str) return num_str
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local (*x, *y); ($x, $y) = (&bnorm($_[$[]), &bnorm($_[$[+1]));
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return wantarray ? ('NaN','NaN') : 'NaN'
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if ($x eq 'NaN' || $y eq 'NaN' || $y eq '+0');
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return wantarray ? ('+0',$x) : '+0' if (&cmp(&abs($x),&abs($y)) < 0);
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@x = &internal($x); @y = &internal($y);
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$srem = $y[$[];
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$sr = (shift @x ne shift @y) ? '-' : '+';
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$car = $bar = $prd = 0;
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if (($dd = int(1e5/($y[$#y]+1))) != 1) {
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for $x (@x) {
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$x = $x * $dd + $car;
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$x -= ($car = int($x * 1e-5)) * 1e5;
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}
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push(@x, $car); $car = 0;
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for $y (@y) {
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$y = $y * $dd + $car;
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$y -= ($car = int($y * 1e-5)) * 1e5;
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}
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}
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else {
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push(@x, 0);
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}
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@q = (); ($v2,$v1) = @y[-2,-1];
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while ($#x > $#y) {
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($u2,$u1,$u0) = @x[-3..-1];
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$q = (($u0 == $v1) ? 99999 : int(($u0*1e5+$u1)/$v1));
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--$q while ($v2*$q > ($u0*1e5+$u1-$q*$v1)*1e5+$u2);
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if ($q) {
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($car, $bar) = (0,0);
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for ($y = $[, $x = $#x-$#y+$[-1; $y <= $#y; ++$y,++$x) {
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$prd = $q * $y[$y] + $car;
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$prd -= ($car = int($prd * 1e-5)) * 1e5;
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$x[$x] += 1e5 if ($bar = (($x[$x] -= $prd + $bar) < 0));
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}
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if ($x[$#x] < $car + $bar) {
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$car = 0; --$q;
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for ($y = $[, $x = $#x-$#y+$[-1; $y <= $#y; ++$y,++$x) {
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$x[$x] -= 1e5
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if ($car = (($x[$x] += $y[$y] + $car) > 1e5));
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}
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}
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}
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pop(@x); unshift(@q, $q);
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}
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if (wantarray) {
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@d = ();
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if ($dd != 1) {
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$car = 0;
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for $x (reverse @x) {
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$prd = $car * 1e5 + $x;
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$car = $prd - ($tmp = int($prd / $dd)) * $dd;
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unshift(@d, $tmp);
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}
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}
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else {
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@d = @x;
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}
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(&external($sr, @q), &external($srem, @d, $zero));
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} else {
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&external($sr, @q);
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}
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}
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# compute power of two numbers -- stolen from Knuth Vol 2 pg 233
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sub bpow { #(num_str, num_str) return num_str
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local(*x, *y); ($x, $y) = (&bnorm($_[$[]), &bnorm($_[$[+1]));
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if ($x eq 'NaN') {
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'NaN';
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} elsif ($y eq 'NaN') {
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'NaN';
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} elsif ($x eq '+1') {
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'+1';
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} elsif ($x eq '-1') {
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&bmod($x,2) ? '-1': '+1';
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} elsif ($y =~ /^-/) {
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'NaN';
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} elsif ($x eq '+0' && $y eq '+0') {
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'NaN';
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} else {
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@x = &internal($x);
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local(@pow2)=@x;
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local(@pow)=&internal("+1");
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local($y1,$res,@tmp1,@tmp2)=(1); # need tmp to send to mul
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while ($y ne '+0') {
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($y,$res)=&bdiv($y,2);
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if ($res ne '+0') {@tmp=@pow2; @pow=&mul(*pow,*tmp);}
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if ($y ne '+0') {@tmp=@pow2;@pow2=&mul(*pow2,*tmp);}
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}
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&external(@pow);
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}
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}
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1;
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__END__
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=head1 NAME
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Math::BigInt - Arbitrary size integer math package
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=head1 SYNOPSIS
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use Math::BigInt;
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$i = Math::BigInt->new($string);
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$i->bneg return BINT negation
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$i->babs return BINT absolute value
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$i->bcmp(BINT) return CODE compare numbers (undef,<0,=0,>0)
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$i->badd(BINT) return BINT addition
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$i->bsub(BINT) return BINT subtraction
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$i->bmul(BINT) return BINT multiplication
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$i->bdiv(BINT) return (BINT,BINT) division (quo,rem) just quo if scalar
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$i->bmod(BINT) return BINT modulus
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$i->bgcd(BINT) return BINT greatest common divisor
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$i->bnorm return BINT normalization
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=head1 DESCRIPTION
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All basic math operations are overloaded if you declare your big
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integers as
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$i = new Math::BigInt '123 456 789 123 456 789';
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=over 2
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=item Canonical notation
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Big integer value are strings of the form C</^[+-]\d+$/> with leading
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zeros suppressed.
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=item Input
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Input values to these routines may be strings of the form
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C</^\s*[+-]?[\d\s]+$/>.
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=item Output
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Output values always always in canonical form
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=back
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Actual math is done in an internal format consisting of an array
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whose first element is the sign (/^[+-]$/) and whose remaining
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elements are base 100000 digits with the least significant digit first.
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The string 'NaN' is used to represent the result when input arguments
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are not numbers, as well as the result of dividing by zero.
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=head1 EXAMPLES
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'+0' canonical zero value
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' -123 123 123' canonical value '-123123123'
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'1 23 456 7890' canonical value '+1234567890'
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=head1 Autocreating constants
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After C<use Math::BigInt ':constant'> all the integer decimal constants
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in the given scope are converted to C<Math::BigInt>. This conversion
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happens at compile time.
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In particular
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perl -MMath::BigInt=:constant -e 'print 2**100'
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print the integer value of C<2**100>. Note that without convertion of
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constants the expression 2**100 will be calculatted as floating point number.
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=head1 BUGS
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The current version of this module is a preliminary version of the
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real thing that is currently (as of perl5.002) under development.
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=head1 AUTHOR
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Mark Biggar, overloaded interface by Ilya Zakharevich.
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=cut
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