464 lines
13 KiB
Perl
464 lines
13 KiB
Perl
package Math::BigInt::LTM;
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use strict;
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use warnings;
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our $VERSION = '0.048';
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use CryptX;
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sub api_version() { 2 }
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sub CLONE_SKIP { 1 } # prevent cloning
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### same as overloading in Math::BigInt::Lib
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use overload
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# overload key: with_assign
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'+' => sub {
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my $class = ref $_[0];
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my $x = $class -> _copy($_[0]);
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my $y = ref($_[1]) ? $_[1] : $class -> _new($_[1]);
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return $class -> _add($x, $y);
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},
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'-' => sub {
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my $class = ref $_[0];
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my ($x, $y);
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if ($_[2]) { # if swapped
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$y = $_[0];
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$x = ref($_[1]) ? $_[1] : $class -> _new($_[1]);
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} else {
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$x = $class -> _copy($_[0]);
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$y = ref($_[1]) ? $_[1] : $class -> _new($_[1]);
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}
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return $class -> _sub($x, $y);
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},
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'*' => sub {
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my $class = ref $_[0];
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my $x = $class -> _copy($_[0]);
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my $y = ref($_[1]) ? $_[1] : $class -> _new($_[1]);
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return $class -> _mul($x, $y);
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},
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'/' => sub {
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my $class = ref $_[0];
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my ($x, $y);
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if ($_[2]) { # if swapped
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$y = $_[0];
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$x = ref($_[1]) ? $_[1] : $class -> _new($_[1]);
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} else {
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$x = $class -> _copy($_[0]);
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$y = ref($_[1]) ? $_[1] : $class -> _new($_[1]);
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}
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return $class -> _div($x, $y);
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},
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'%' => sub {
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my $class = ref $_[0];
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my ($x, $y);
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if ($_[2]) { # if swapped
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$y = $_[0];
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$x = ref($_[1]) ? $_[1] : $class -> _new($_[1]);
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} else {
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$x = $class -> _copy($_[0]);
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$y = ref($_[1]) ? $_[1] : $class -> _new($_[1]);
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}
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return $class -> _mod($x, $y);
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},
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'**' => sub {
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my $class = ref $_[0];
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my ($x, $y);
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if ($_[2]) { # if swapped
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$y = $_[0];
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$x = ref($_[1]) ? $_[1] : $class -> _new($_[1]);
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} else {
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$x = $class -> _copy($_[0]);
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$y = ref($_[1]) ? $_[1] : $class -> _new($_[1]);
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}
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return $class -> _pow($x, $y);
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},
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'<<' => sub {
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my $class = ref $_[0];
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my ($x, $y);
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if ($_[2]) { # if swapped
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$y = $class -> _num($_[0]);
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$x = ref($_[1]) ? $_[1] : $class -> _new($_[1]);
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} else {
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$x = $_[0];
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$y = ref($_[1]) ? $class -> _num($_[1]) : $_[1];
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}
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return $class -> _blsft($x, $y);
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},
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'>>' => sub {
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my $class = ref $_[0];
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my ($x, $y);
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if ($_[2]) { # if swapped
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$y = $_[0];
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$x = ref($_[1]) ? $_[1] : $class -> _new($_[1]);
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} else {
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$x = $class -> _copy($_[0]);
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$y = ref($_[1]) ? $_[1] : $class -> _new($_[1]);
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}
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return $class -> _brsft($x, $y);
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},
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# overload key: num_comparison
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'<' => sub {
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my $class = ref $_[0];
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my ($x, $y);
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if ($_[2]) { # if swapped
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$y = $_[0];
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$x = ref($_[1]) ? $_[1] : $class -> _new($_[1]);
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} else {
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$x = $class -> _copy($_[0]);
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$y = ref($_[1]) ? $_[1] : $class -> _new($_[1]);
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}
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return $class -> _acmp($x, $y) < 0;
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},
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'<=' => sub {
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my $class = ref $_[0];
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my ($x, $y);
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if ($_[2]) { # if swapped
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$y = $_[0];
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$x = ref($_[1]) ? $_[1] : $class -> _new($_[1]);
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} else {
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$x = $class -> _copy($_[0]);
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$y = ref($_[1]) ? $_[1] : $class -> _new($_[1]);
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}
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return $class -> _acmp($x, $y) <= 0;
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},
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'>' => sub {
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my $class = ref $_[0];
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my ($x, $y);
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if ($_[2]) { # if swapped
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$y = $_[0];
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$x = ref($_[1]) ? $_[1] : $class -> _new($_[1]);
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} else {
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$x = $class -> _copy($_[0]);
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$y = ref($_[1]) ? $_[1] : $class -> _new($_[1]);
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}
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return $class -> _acmp($x, $y) > 0;
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},
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'>=' => sub {
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my $class = ref $_[0];
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my ($x, $y);
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if ($_[2]) { # if swapped
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$y = $_[0];
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$x = ref($_[1]) ? $_[1] : $class -> _new($_[1]);
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} else {
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$x = $class -> _copy($_[0]);
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$y = ref($_[1]) ? $_[1] : $class -> _new($_[1]);
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}
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return $class -> _acmp($x, $y) >= 0;
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},
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'==' => sub {
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my $class = ref $_[0];
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my $x = $class -> _copy($_[0]);
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my $y = ref($_[1]) ? $_[1] : $class -> _new($_[1]);
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return $class -> _acmp($x, $y) == 0;
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},
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'!=' => sub {
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my $class = ref $_[0];
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my $x = $class -> _copy($_[0]);
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my $y = ref($_[1]) ? $_[1] : $class -> _new($_[1]);
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return $class -> _acmp($x, $y) != 0;
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},
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# overload key: 3way_comparison
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'<=>' => sub {
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my $class = ref $_[0];
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my ($x, $y);
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if ($_[2]) { # if swapped
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$y = $_[0];
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$x = ref($_[1]) ? $_[1] : $class -> _new($_[1]);
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} else {
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$x = $class -> _copy($_[0]);
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$y = ref($_[1]) ? $_[1] : $class -> _new($_[1]);
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}
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return $class -> _acmp($x, $y);
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},
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# overload key: binary
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'&' => sub {
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my $class = ref $_[0];
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my ($x, $y);
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if ($_[2]) { # if swapped
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$y = $_[0];
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$x = ref($_[1]) ? $_[1] : $class -> _new($_[1]);
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} else {
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$x = $class -> _copy($_[0]);
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$y = ref($_[1]) ? $_[1] : $class -> _new($_[1]);
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}
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return $class -> _and($x, $y);
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},
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'|' => sub {
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my $class = ref $_[0];
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my ($x, $y);
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if ($_[2]) { # if swapped
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$y = $_[0];
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$x = ref($_[1]) ? $_[1] : $class -> _new($_[1]);
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} else {
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$x = $class -> _copy($_[0]);
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$y = ref($_[1]) ? $_[1] : $class -> _new($_[1]);
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}
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return $class -> _or($x, $y);
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},
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'^' => sub {
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my $class = ref $_[0];
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my ($x, $y);
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if ($_[2]) { # if swapped
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$y = $_[0];
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$x = ref($_[1]) ? $_[1] : $class -> _new($_[1]);
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} else {
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$x = $class -> _copy($_[0]);
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$y = ref($_[1]) ? $_[1] : $class -> _new($_[1]);
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}
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return $class -> _xor($x, $y);
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},
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# overload key: func
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'abs' => sub { $_[0] },
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'sqrt' => sub {
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my $class = ref $_[0];
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return $class -> _sqrt($class -> _copy($_[0]));
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},
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'int' => sub { $_[0] -> copy() -> bint(); },
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# overload key: conversion
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'bool' => sub { ref($_[0]) -> _is_zero($_[0]) ? '' : 1; },
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'""' => sub { ref($_[0]) -> _str($_[0]); },
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'0+' => sub { ref($_[0]) -> _num($_[0]); },
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'=' => sub { ref($_[0]) -> _copy($_[0]); },
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;
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### same as import() in Math::BigInt::Lib
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sub import { }
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### same as _check() in Math::BigInt::Lib
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sub _check {
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# used by the test suite
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my ($class, $x) = @_;
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return "Input is undefined" unless defined $x;
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return "$x is not a reference" unless ref($x);
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return 0;
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}
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### same as _digit() in Math::BigInt::Lib
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sub _digit {
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my ($class, $x, $n) = @_;
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substr($class ->_str($x), -($n+1), 1);
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}
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### same as _num() in Math::BigInt::Lib
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sub _num {
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my ($class, $x) = @_;
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0 + $class -> _str($x);
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}
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### BEWARE!!! NOT THE SAME as _fac() in Math::BigInt::Lib
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sub _fac {
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# factorial
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my ($class, $x) = @_;
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my $two = $class -> _two();
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if ($class -> _acmp($x, $two) < 0) {
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$class->_set($x, 1);
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return $x;
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}
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my $i = $class -> _copy($x);
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while ($class -> _acmp($i, $two) > 0) {
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$i = $class -> _dec($i);
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$x = $class -> _mul($x, $i);
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}
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return $x;
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}
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### same as _nok() in Math::BigInt::Lib
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sub _nok {
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# Return binomial coefficient (n over k).
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# Given refs to arrays, return ref to array.
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# First input argument is modified.
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my ($class, $n, $k) = @_;
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# If k > n/2, or, equivalently, 2*k > n, compute nok(n, k) as
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# nok(n, n-k), to minimize the number if iterations in the loop.
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{
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my $twok = $class -> _mul($class -> _two(), $class -> _copy($k));
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if ($class -> _acmp($twok, $n) > 0) {
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$k = $class -> _sub($class -> _copy($n), $k);
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}
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}
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# Example:
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#
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# / 7 \ 7! 1*2*3*4 * 5*6*7 5 * 6 * 7 6 7
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# | | = --------- = --------------- = --------- = 5 * - * -
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# \ 3 / (7-3)! 3! 1*2*3*4 * 1*2*3 1 * 2 * 3 2 3
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if ($class -> _is_zero($k)) {
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return $class -> _one();
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}
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# Make a copy of the original n, since we'll be modifying n in-place.
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my $n_orig = $class -> _copy($n);
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# n = 5, f = 6, d = 2 (cf. example above)
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$n = $class -> _sub($n, $k);
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$n = $class -> _inc($n);
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my $f = $class -> _copy($n);
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$class -> _inc($f);
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my $d = $class -> _two();
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# while f <= n (the original n, that is) ...
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while ($class -> _acmp($f, $n_orig) <= 0) {
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# n = (n * f / d) == 5 * 6 / 2 (cf. example above)
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$n = $class -> _mul($n, $f);
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$n = $class -> _div($n, $d);
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# f = 7, d = 3 (cf. example above)
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$f = $class -> _inc($f);
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$d = $class -> _inc($d);
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}
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return $n;
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}
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### same as _log_int() in Math::BigInt::Lib
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sub _log_int {
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# calculate integer log of $x to base $base
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# ref to array, ref to array - return ref to array
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my ($class, $x, $base) = @_;
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# X == 0 => NaN
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return if $class -> _is_zero($x);
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$base = $class -> _new(2) unless defined($base);
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$base = $class -> _new($base) unless ref($base);
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# BASE 0 or 1 => NaN
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return if $class -> _is_zero($base) || $class -> _is_one($base);
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# X == 1 => 0 (is exact)
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if ($class -> _is_one($x)) {
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return $class -> _zero(), 1;
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}
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my $cmp = $class -> _acmp($x, $base);
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# X == BASE => 1 (is exact)
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if ($cmp == 0) {
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return $class -> _one(), 1;
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}
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# 1 < X < BASE => 0 (is truncated)
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if ($cmp < 0) {
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return $class -> _zero(), 0;
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}
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my $y;
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# log(x) / log(b) = log(xm * 10^xe) / log(bm * 10^be)
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# = (log(xm) + xe*(log(10))) / (log(bm) + be*log(10))
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{
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my $x_str = $class -> _str($x);
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my $b_str = $class -> _str($base);
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my $xm = "." . $x_str;
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my $bm = "." . $b_str;
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my $xe = length($x_str);
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my $be = length($b_str);
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my $log10 = log(10);
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my $guess = int((log($xm) + $xe * $log10) / (log($bm) + $be * $log10));
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$y = $class -> _new($guess);
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}
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my $trial = $class -> _pow($class -> _copy($base), $y);
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my $acmp = $class -> _acmp($trial, $x);
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# Did we get the exact result?
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return $y, 1 if $acmp == 0;
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# Too small?
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while ($acmp < 0) {
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$trial = $class -> _mul($trial, $base);
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$y = $class -> _inc($y);
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$acmp = $class -> _acmp($trial, $x);
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}
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# Too big?
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while ($acmp > 0) {
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$trial = $class -> _div($trial, $base);
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$y = $class -> _dec($y);
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$acmp = $class -> _acmp($trial, $x);
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}
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return $y, 1 if $acmp == 0; # result is exact
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return $y, 0; # result is too small
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}
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1;
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__END__
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=pod
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=head1 NAME
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Math::BigInt::LTM - Use the libtommath library for Math::BigInt routines
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=head1 SYNOPSIS
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use Math::BigInt lib => 'LTM';
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## See Math::BigInt docs for usage.
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=head1 DESCRIPTION
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Provides support for big integer calculations by means of the libtommath c-library.
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I<Since: CryptX-0.029>
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=head1 SEE ALSO
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L<Math::BigInt>, L<https://github.com/libtom/libtommath>
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=cut
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