%PDF-
%PDF-
Mini Shell
Mini Shell
package Math::BigInt::LTM;
use strict;
use warnings;
our $VERSION = '0.076';
use CryptX;
use Carp;
sub CLONE_SKIP { 1 } # prevent cloning
sub api_version() { 2 } # compatible with Math::BigInt v1.83+
sub import { }
### the following functions are implemented in XS
# _1ex()
# _acmp()
# _add()
# _alen()
# _alen()
# _and()
# _as_bytes()
# _copy()
# _dec()
# _div()
# _from_base()
# _from_bin()
# _from_bytes()
# _from_hex()
# _from_oct()
# _gcd()
# _inc()
# _is_even()
# _is_odd()
# _is_one()
# _is_ten()
# _is_two()
# _is_zero()
# _lcm()
# _len()
# _lsft()
# _mod()
# _modinv()
# _modpow()
# _mul()
# _new()
# _one()
# _or()
# _pow()
# _root()
# _rsft()
# _set()
# _sqrt()
# _str()
# _sub()
# _ten()
# _to_base()
# _to_bin()
# _to_bytes()
# _to_hex()
# _to_oct()
# _two()
# _xor()
# _zero()
# _zeros()
### same as overloading in Math::BigInt::Lib
use overload
# overload key: with_assign
'+' => sub {
my $class = ref $_[0];
my $x = $class -> _copy($_[0]);
my $y = ref($_[1]) ? $_[1] : $class -> _new($_[1]);
return $class -> _add($x, $y);
},
'-' => sub {
my $class = ref $_[0];
my ($x, $y);
if ($_[2]) { # if swapped
$y = $_[0];
$x = ref($_[1]) ? $_[1] : $class -> _new($_[1]);
} else {
$x = $class -> _copy($_[0]);
$y = ref($_[1]) ? $_[1] : $class -> _new($_[1]);
}
return $class -> _sub($x, $y);
},
'*' => sub {
my $class = ref $_[0];
my $x = $class -> _copy($_[0]);
my $y = ref($_[1]) ? $_[1] : $class -> _new($_[1]);
return $class -> _mul($x, $y);
},
'/' => sub {
my $class = ref $_[0];
my ($x, $y);
if ($_[2]) { # if swapped
$y = $_[0];
$x = ref($_[1]) ? $_[1] : $class -> _new($_[1]);
} else {
$x = $class -> _copy($_[0]);
$y = ref($_[1]) ? $_[1] : $class -> _new($_[1]);
}
return $class -> _div($x, $y);
},
'%' => sub {
my $class = ref $_[0];
my ($x, $y);
if ($_[2]) { # if swapped
$y = $_[0];
$x = ref($_[1]) ? $_[1] : $class -> _new($_[1]);
} else {
$x = $class -> _copy($_[0]);
$y = ref($_[1]) ? $_[1] : $class -> _new($_[1]);
}
return $class -> _mod($x, $y);
},
'**' => sub {
my $class = ref $_[0];
my ($x, $y);
if ($_[2]) { # if swapped
$y = $_[0];
$x = ref($_[1]) ? $_[1] : $class -> _new($_[1]);
} else {
$x = $class -> _copy($_[0]);
$y = ref($_[1]) ? $_[1] : $class -> _new($_[1]);
}
return $class -> _pow($x, $y);
},
'<<' => sub {
my $class = ref $_[0];
my ($x, $y);
if ($_[2]) { # if swapped
$y = $class -> _num($_[0]);
$x = ref($_[1]) ? $_[1] : $class -> _new($_[1]);
} else {
$x = $_[0];
$y = ref($_[1]) ? $class -> _num($_[1]) : $_[1];
}
return $class -> _blsft($x, $y);
},
'>>' => sub {
my $class = ref $_[0];
my ($x, $y);
if ($_[2]) { # if swapped
$y = $_[0];
$x = ref($_[1]) ? $_[1] : $class -> _new($_[1]);
} else {
$x = $class -> _copy($_[0]);
$y = ref($_[1]) ? $_[1] : $class -> _new($_[1]);
}
return $class -> _brsft($x, $y);
},
# overload key: num_comparison
'<' => sub {
my $class = ref $_[0];
my ($x, $y);
if ($_[2]) { # if swapped
$y = $_[0];
$x = ref($_[1]) ? $_[1] : $class -> _new($_[1]);
} else {
$x = $class -> _copy($_[0]);
$y = ref($_[1]) ? $_[1] : $class -> _new($_[1]);
}
return $class -> _acmp($x, $y) < 0;
},
'<=' => sub {
my $class = ref $_[0];
my ($x, $y);
if ($_[2]) { # if swapped
$y = $_[0];
$x = ref($_[1]) ? $_[1] : $class -> _new($_[1]);
} else {
$x = $class -> _copy($_[0]);
$y = ref($_[1]) ? $_[1] : $class -> _new($_[1]);
}
return $class -> _acmp($x, $y) <= 0;
},
'>' => sub {
my $class = ref $_[0];
my ($x, $y);
if ($_[2]) { # if swapped
$y = $_[0];
$x = ref($_[1]) ? $_[1] : $class -> _new($_[1]);
} else {
$x = $class -> _copy($_[0]);
$y = ref($_[1]) ? $_[1] : $class -> _new($_[1]);
}
return $class -> _acmp($x, $y) > 0;
},
'>=' => sub {
my $class = ref $_[0];
my ($x, $y);
if ($_[2]) { # if swapped
$y = $_[0];
$x = ref($_[1]) ? $_[1] : $class -> _new($_[1]);
} else {
$x = $class -> _copy($_[0]);
$y = ref($_[1]) ? $_[1] : $class -> _new($_[1]);
}
return $class -> _acmp($x, $y) >= 0;
},
'==' => sub {
my $class = ref $_[0];
my $x = $class -> _copy($_[0]);
my $y = ref($_[1]) ? $_[1] : $class -> _new($_[1]);
return $class -> _acmp($x, $y) == 0;
},
'!=' => sub {
my $class = ref $_[0];
my $x = $class -> _copy($_[0]);
my $y = ref($_[1]) ? $_[1] : $class -> _new($_[1]);
return $class -> _acmp($x, $y) != 0;
},
# overload key: 3way_comparison
'<=>' => sub {
my $class = ref $_[0];
my ($x, $y);
if ($_[2]) { # if swapped
$y = $_[0];
$x = ref($_[1]) ? $_[1] : $class -> _new($_[1]);
} else {
$x = $class -> _copy($_[0]);
$y = ref($_[1]) ? $_[1] : $class -> _new($_[1]);
}
return $class -> _acmp($x, $y);
},
# overload key: binary
'&' => sub {
my $class = ref $_[0];
my ($x, $y);
if ($_[2]) { # if swapped
$y = $_[0];
$x = ref($_[1]) ? $_[1] : $class -> _new($_[1]);
} else {
$x = $class -> _copy($_[0]);
$y = ref($_[1]) ? $_[1] : $class -> _new($_[1]);
}
return $class -> _and($x, $y);
},
'|' => sub {
my $class = ref $_[0];
my ($x, $y);
if ($_[2]) { # if swapped
$y = $_[0];
$x = ref($_[1]) ? $_[1] : $class -> _new($_[1]);
} else {
$x = $class -> _copy($_[0]);
$y = ref($_[1]) ? $_[1] : $class -> _new($_[1]);
}
return $class -> _or($x, $y);
},
'^' => sub {
my $class = ref $_[0];
my ($x, $y);
if ($_[2]) { # if swapped
$y = $_[0];
$x = ref($_[1]) ? $_[1] : $class -> _new($_[1]);
} else {
$x = $class -> _copy($_[0]);
$y = ref($_[1]) ? $_[1] : $class -> _new($_[1]);
}
return $class -> _xor($x, $y);
},
# overload key: func
'abs' => sub { $_[0] },
'sqrt' => sub {
my $class = ref $_[0];
return $class -> _sqrt($class -> _copy($_[0]));
},
'int' => sub { $_[0] },
# overload key: conversion
'bool' => sub { ref($_[0]) -> _is_zero($_[0]) ? '' : 1; },
'""' => sub { ref($_[0]) -> _str($_[0]); },
'0+' => sub { ref($_[0]) -> _num($_[0]); },
'=' => sub { ref($_[0]) -> _copy($_[0]); },
;
### same as _check() in Math::BigInt::Lib
sub _check {
# used by the test suite
my ($class, $x) = @_;
return "Input is undefined" unless defined $x;
return "$x is not a reference" unless ref($x);
return 0;
}
### same as _digit() in Math::BigInt::Lib
sub _digit {
my ($class, $x, $n) = @_;
substr($class ->_str($x), -($n+1), 1);
}
### same as _num() in Math::BigInt::Lib
sub _num {
my ($class, $x) = @_;
0 + $class -> _str($x);
}
### PATCHED _fac() from Math::BigInt::Lib
sub _fac {
# factorial
my ($class, $x) = @_;
my $two = $class -> _two();
if ($class -> _acmp($x, $two) < 0) {
###HACK: needed for MBI 1.999715 compatibility
###return $class -> _one();
$class->_set($x, 1); return $x
}
my $i = $class -> _copy($x);
while ($class -> _acmp($i, $two) > 0) {
$i = $class -> _dec($i);
$x = $class -> _mul($x, $i);
}
return $x;
}
### PATCHED _dfac() from Math::BigInt::Lib
sub _dfac {
# double factorial
my ($class, $x) = @_;
my $two = $class -> _two();
if ($class -> _acmp($x, $two) < 0) {
###HACK: needed for MBI 1.999715 compatibility
###return $class -> _one();
$class->_set($x, 1); return $x
}
my $i = $class -> _copy($x);
while ($class -> _acmp($i, $two) > 0) {
$i = $class -> _sub($i, $two);
$x = $class -> _mul($x, $i);
}
return $x;
}
### same as _nok() in Math::BigInt::Lib
sub _nok {
# Return binomial coefficient (n over k).
my ($class, $n, $k) = @_;
# If k > n/2, or, equivalently, 2*k > n, compute nok(n, k) as
# nok(n, n-k), to minimize the number if iterations in the loop.
{
my $twok = $class -> _mul($class -> _two(), $class -> _copy($k));
if ($class -> _acmp($twok, $n) > 0) {
$k = $class -> _sub($class -> _copy($n), $k);
}
}
# Example:
#
# / 7 \ 7! 1*2*3*4 * 5*6*7 5 * 6 * 7
# | | = --------- = --------------- = --------- = ((5 * 6) / 2 * 7) / 3
# \ 3 / (7-3)! 3! 1*2*3*4 * 1*2*3 1 * 2 * 3
#
# Equivalently, _nok(11, 5) is computed as
#
# (((((((7 * 8) / 2) * 9) / 3) * 10) / 4) * 11) / 5
if ($class -> _is_zero($k)) {
return $class -> _one();
}
# Make a copy of the original n, in case the subclass modifies n in-place.
my $n_orig = $class -> _copy($n);
# n = 5, f = 6, d = 2 (cf. example above)
$n = $class -> _sub($n, $k);
$n = $class -> _inc($n);
my $f = $class -> _copy($n);
$f = $class -> _inc($f);
my $d = $class -> _two();
# while f <= n (the original n, that is) ...
while ($class -> _acmp($f, $n_orig) <= 0) {
$n = $class -> _mul($n, $f);
$n = $class -> _div($n, $d);
$f = $class -> _inc($f);
$d = $class -> _inc($d);
}
return $n;
}
### same as _sadd() in Math::BigInt::Lib
# Signed addition. If the flag is false, $xa might be modified, but not $ya. If
# the false is true, $ya might be modified, but not $xa.
sub _sadd {
my $class = shift;
my ($xa, $xs, $ya, $ys, $flag) = @_;
my ($za, $zs);
# If the signs are equal we can add them (-5 + -3 => -(5 + 3) => -8)
if ($xs eq $ys) {
if ($flag) {
$za = $class -> _add($ya, $xa);
} else {
$za = $class -> _add($xa, $ya);
}
$zs = $class -> _is_zero($za) ? '+' : $xs;
return $za, $zs;
}
my $acmp = $class -> _acmp($xa, $ya); # abs(x) = abs(y)
if ($acmp == 0) { # x = -y or -x = y
$za = $class -> _zero();
$zs = '+';
return $za, $zs;
}
if ($acmp > 0) { # abs(x) > abs(y)
$za = $class -> _sub($xa, $ya, $flag);
$zs = $xs;
} else { # abs(x) < abs(y)
$za = $class -> _sub($ya, $xa, !$flag);
$zs = $ys;
}
return $za, $zs;
}
### same as _ssub() in Math::BigInt::Lib
# Signed subtraction. If the flag is false, $xa might be modified, but not $ya.
# If the false is true, $ya might be modified, but not $xa.
sub _ssub {
my $class = shift;
my ($xa, $xs, $ya, $ys, $flag) = @_;
# Swap sign of second operand and let _sadd() do the job.
$ys = $ys eq '+' ? '-' : '+';
$class -> _sadd($xa, $xs, $ya, $ys, $flag);
}
### same as _log_int() in Math::BigInt::Lib
sub _log_int {
# calculate integer log of $x to base $base
# ref to array, ref to array - return ref to array
my ($class, $x, $base) = @_;
# X == 0 => NaN
return if $class -> _is_zero($x);
$base = $class -> _new(2) unless defined($base);
$base = $class -> _new($base) unless ref($base);
# BASE 0 or 1 => NaN
return if $class -> _is_zero($base) || $class -> _is_one($base);
# X == 1 => 0 (is exact)
if ($class -> _is_one($x)) {
return $class -> _zero(), 1;
}
my $cmp = $class -> _acmp($x, $base);
# X == BASE => 1 (is exact)
if ($cmp == 0) {
return $class -> _one(), 1;
}
# 1 < X < BASE => 0 (is truncated)
if ($cmp < 0) {
return $class -> _zero(), 0;
}
my $y;
# log(x) / log(b) = log(xm * 10^xe) / log(bm * 10^be)
# = (log(xm) + xe*(log(10))) / (log(bm) + be*log(10))
{
my $x_str = $class -> _str($x);
my $b_str = $class -> _str($base);
my $xm = "." . $x_str;
my $bm = "." . $b_str;
my $xe = length($x_str);
my $be = length($b_str);
my $log10 = log(10);
my $guess = int((log($xm) + $xe * $log10) / (log($bm) + $be * $log10));
$y = $class -> _new($guess);
}
my $trial = $class -> _pow($class -> _copy($base), $y);
my $acmp = $class -> _acmp($trial, $x);
# Did we get the exact result?
return $y, 1 if $acmp == 0;
# Too small?
while ($acmp < 0) {
$trial = $class -> _mul($trial, $base);
$y = $class -> _inc($y);
$acmp = $class -> _acmp($trial, $x);
}
# Too big?
while ($acmp > 0) {
$trial = $class -> _div($trial, $base);
$y = $class -> _dec($y);
$acmp = $class -> _acmp($trial, $x);
}
return $y, 1 if $acmp == 0; # result is exact
return $y, 0; # result is too small
}
### same as _lucas() in Math::BigInt::Lib
sub _lucas {
my ($class, $n) = @_;
$n = $class -> _num($n) if ref $n;
# In list context, use lucas(n) = lucas(n-1) + lucas(n-2)
if (wantarray) {
my @y;
push @y, $class -> _two();
return @y if $n == 0;
push @y, $class -> _one();
return @y if $n == 1;
for (my $i = 2 ; $i <= $n ; ++ $i) {
$y[$i] = $class -> _add($class -> _copy($y[$i - 1]), $y[$i - 2]);
}
return @y;
}
require Scalar::Util;
# In scalar context use that lucas(n) = fib(n-1) + fib(n+1).
#
# Remember that _fib() behaves differently in scalar context and list
# context, so we must add scalar() to get the desired behaviour.
return $class -> _two() if $n == 0;
return $class -> _add(scalar $class -> _fib($n - 1),
scalar $class -> _fib($n + 1));
}
### same as _fib() in Math::BigInt::Lib
sub _fib {
my ($class, $n) = @_;
$n = $class -> _num($n) if ref $n;
# In list context, use fib(n) = fib(n-1) + fib(n-2)
if (wantarray) {
my @y;
push @y, $class -> _zero();
return @y if $n == 0;
push @y, $class -> _one();
return @y if $n == 1;
for (my $i = 2 ; $i <= $n ; ++ $i) {
$y[$i] = $class -> _add($class -> _copy($y[$i - 1]), $y[$i - 2]);
}
return @y;
}
# In scalar context use a fast algorithm that is much faster than the
# recursive algorith used in list context.
my $cache = {};
my $two = $class -> _two();
my $fib;
$fib = sub {
my $n = shift;
return $class -> _zero() if $n <= 0;
return $class -> _one() if $n <= 2;
return $cache -> {$n} if exists $cache -> {$n};
my $k = int($n / 2);
my $a = $fib -> ($k + 1);
my $b = $fib -> ($k);
my $y;
if ($n % 2 == 1) {
# a*a + b*b
$y = $class -> _add($class -> _mul($class -> _copy($a), $a),
$class -> _mul($class -> _copy($b), $b));
} else {
# (2*a - b)*b
$y = $class -> _mul($class -> _sub($class -> _mul(
$class -> _copy($two), $a), $b), $b);
}
$cache -> {$n} = $y;
return $y;
};
return $fib -> ($n);
}
### same as _sand() in Math::BigInt::Lib
sub _sand {
my ($class, $x, $sx, $y, $sy) = @_;
return ($class -> _zero(), '+')
if $class -> _is_zero($x) || $class -> _is_zero($y);
my $sign = $sx eq '-' && $sy eq '-' ? '-' : '+';
my ($bx, $by);
if ($sx eq '-') { # if x is negative
# two's complement: inc (dec unsigned value) and flip all "bits" in $bx
$bx = $class -> _copy($x);
$bx = $class -> _dec($bx);
$bx = $class -> _as_hex($bx);
$bx =~ s/^-?0x//;
$bx =~ tr<0123456789abcdef>
<\x0f\x0e\x0d\x0c\x0b\x0a\x09\x08\x07\x06\x05\x04\x03\x02\x01\x00>;
} else { # if x is positive
$bx = $class -> _as_hex($x); # 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 eq '-') { # if y is negative
# two's complement: inc (dec unsigned value) and flip all "bits" in $by
$by = $class -> _copy($y);
$by = $class -> _dec($by);
$by = $class -> _as_hex($by);
$by =~ s/^-?0x//;
$by =~ tr<0123456789abcdef>
<\x0f\x0e\x0d\x0c\x0b\x0a\x09\x08\x07\x06\x05\x04\x03\x02\x01\x00>;
} else {
$by = $class -> _as_hex($y); # 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 eq '-';
my $yy = "\x00"; $yy = "\x0f" if $sy eq '-';
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 $bx or $by was negative, so need to flip bits in the result. In both
# cases (one or two of them negative, or both positive) we need to get the
# characters back.
if ($sign eq '-') {
$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;
$bx = $class -> _from_hex($bx);
$bx = $class -> _inc($bx) if $sign eq '-';
# avoid negative zero
$sign = '+' if $class -> _is_zero($bx);
return $bx, $sign;
}
### same as _sxor() in Math::BigInt::Lib
sub _sxor {
my ($class, $x, $sx, $y, $sy) = @_;
return ($class -> _zero(), '+')
if $class -> _is_zero($x) && $class -> _is_zero($y);
my $sign = $sx ne $sy ? '-' : '+';
my ($bx, $by);
if ($sx eq '-') { # if x is negative
# two's complement: inc (dec unsigned value) and flip all "bits" in $bx
$bx = $class -> _copy($x);
$bx = $class -> _dec($bx);
$bx = $class -> _as_hex($bx);
$bx =~ s/^-?0x//;
$bx =~ tr<0123456789abcdef>
<\x0f\x0e\x0d\x0c\x0b\x0a\x09\x08\x07\x06\x05\x04\x03\x02\x01\x00>;
} else { # if x is positive
$bx = $class -> _as_hex($x); # 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 eq '-') { # if y is negative
# two's complement: inc (dec unsigned value) and flip all "bits" in $by
$by = $class -> _copy($y);
$by = $class -> _dec($by);
$by = $class -> _as_hex($by);
$by =~ s/^-?0x//;
$by =~ tr<0123456789abcdef>
<\x0f\x0e\x0d\x0c\x0b\x0a\x09\x08\x07\x06\x05\x04\x03\x02\x01\x00>;
} else {
$by = $class -> _as_hex($y); # 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 eq '-';
my $yy = "\x00"; $yy = "\x0f" if $sy eq '-';
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);
}
# xor the strings together
my $r = $bx ^ $by;
# and reverse the result again
$bx = reverse $r;
# One of $bx or $by was negative, so need to flip bits in the result. In both
# cases (one or two of them negative, or both positive) we need to get the
# characters back.
if ($sign eq '-') {
$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;
$bx = $class -> _from_hex($bx);
$bx = $class -> _inc($bx) if $sign eq '-';
# avoid negative zero
$sign = '+' if $class -> _is_zero($bx);
return $bx, $sign;
}
### same as _sor() in Math::BigInt::Lib
sub _sor {
my ($class, $x, $sx, $y, $sy) = @_;
return ($class -> _zero(), '+')
if $class -> _is_zero($x) && $class -> _is_zero($y);
my $sign = $sx eq '-' || $sy eq '-' ? '-' : '+';
my ($bx, $by);
if ($sx eq '-') { # if x is negative
# two's complement: inc (dec unsigned value) and flip all "bits" in $bx
$bx = $class -> _copy($x);
$bx = $class -> _dec($bx);
$bx = $class -> _as_hex($bx);
$bx =~ s/^-?0x//;
$bx =~ tr<0123456789abcdef>
<\x0f\x0e\x0d\x0c\x0b\x0a\x09\x08\x07\x06\x05\x04\x03\x02\x01\x00>;
} else { # if x is positive
$bx = $class -> _as_hex($x); # 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 eq '-') { # if y is negative
# two's complement: inc (dec unsigned value) and flip all "bits" in $by
$by = $class -> _copy($y);
$by = $class -> _dec($by);
$by = $class -> _as_hex($by);
$by =~ s/^-?0x//;
$by =~ tr<0123456789abcdef>
<\x0f\x0e\x0d\x0c\x0b\x0a\x09\x08\x07\x06\x05\x04\x03\x02\x01\x00>;
} else {
$by = $class -> _as_hex($y); # 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 eq '-';
my $yy = "\x00"; $yy = "\x0f" if $sy eq '-';
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);
}
# or the strings together
my $r = $bx | $by;
# and reverse the result again
$bx = reverse $r;
# One of $bx or $by was negative, so need to flip bits in the result. In both
# cases (one or two of them negative, or both positive) we need to get the
# characters back.
if ($sign eq '-') {
$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;
$bx = $class -> _from_hex($bx);
$bx = $class -> _inc($bx) if $sign eq '-';
# avoid negative zero
$sign = '+' if $class -> _is_zero($bx);
return $bx, $sign;
}
### same as _as_bin() in Math::BigInt::Lib
sub _as_bin {
# convert the number to a string of binary digits with prefix
my ($class, $x) = @_;
return '0b' . $class -> _to_bin($x);
}
### same as _as_oct() in Math::BigInt::Lib
sub _as_oct {
# convert the number to a string of octal digits with prefix
my ($class, $x) = @_;
return '0' . $class -> _to_oct($x); # yes, 0 becomes "00"
}
### same as _as_hex() in Math::BigInt::Lib
sub _as_hex {
# convert the number to a string of hexadecimal digits with prefix
my ($class, $x) = @_;
return '0x' . $class -> _to_hex($x);
}
1;
=pod
=head1 NAME
Math::BigInt::LTM - Use the libtommath library for Math::BigInt routines
=head1 SYNOPSIS
use Math::BigInt lib => 'LTM';
## See Math::BigInt docs for usage.
=head1 DESCRIPTION
Provides support for big integer calculations by means of the libtommath c-library.
I<Since: CryptX-0.029>
=head1 SEE ALSO
L<Math::BigInt>, L<https://github.com/libtom/libtommath>
=cut
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