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package Math::BigInt::Pari; use 5.006002; use strict; use warnings; use Math::BigInt::Lib 1.999801; our @ISA = qw< Math::BigInt::Lib >; our $VERSION = '1.3016'; use Math::Pari qw(PARI pari2pv gdivent bittest gcmp gcmp0 gcmp1 gcd ifact gpui gmul binomial lcm ); # MBI will call this, so catch it and throw it away sub import { } sub api_version() { 2; } # we are compatible with MBI v1.83 and up my $zero = PARI(0); # for _copy my $one = PARI(1); # for _inc and _dec my $two = PARI(2); # for _is_two my $ten = PARI(10); # for _digit sub _new { # the . '' is because new($2) will give a magical scalar to us, and PARI # does not like this at all :/ # use Devel::Peek; print Dump($_[1]); PARI($_[1] . '') } sub _from_hex { my $hex = $_[1]; $hex = '0x' . $hex unless substr($hex, 0, 2) eq '0x'; Math::Pari::_hex_cvt($hex); } sub _from_oct { Math::Pari::_hex_cvt('0' . $_[1]); } sub _from_bin { my $bin = $_[1]; $bin = '0b' . $bin unless substr($bin, 0, 2) eq '0b'; Math::Pari::_hex_cvt($bin); } sub _as_bin { my $v = unpack('B', _mp2os($_[1])); return "0b0" if $v eq ''; $v =~ s/^0/0b/; $v; } sub _as_oct { my $v = _mp2oct($_[1]); return "00" if $v eq ''; $v =~ s/^0/0/; $v; } sub _as_hex { my $v = unpack('H', _mp2os($_[1])); return "0x0" if $v eq ''; $v =~ s/^0/0x/; $v; } sub _to_bin { my $v = unpack('B', _mp2os($_[1])); $v =~ s/^0+//; return "0" if $v eq ''; $v; } sub _to_oct { my $v = _mp2oct($_[1]); $v =~ s/^0+//; return "0" if $v eq ''; $v; } sub _to_hex { my $v = unpack('H', _mp2os($_[1])); $v =~ s/^0+//; return "0" if $v eq ''; $v; } sub _to_bytes { my $bytes = _mp2os($_[1]); return $bytes eq '' ? "\x00" : $bytes; } sub _mp2os { my($p) = @_; $p = PARI($p); my $base = PARI(1) << PARI(48); my $res = ''; while ($p != 0) { my $r = $p % $base; $p = ($p - $r) / $base; my $buf = pack 'V', $r; if ($p == 0) { $buf = $r >= 16777216 ? $buf : $r >= 65536 ? substr($buf, 0, 3) : $r >= 256 ? substr($buf, 0, 2) : substr($buf, 0, 1); } $res .= $buf; } scalar reverse $res; } sub _mp2oct { my($p) = @_; $p = PARI($p); my $base = PARI(8); my $res = ''; while ($p != 0) { my $r = $p % $base; $p = ($p - $r) / $base; $res .= $r; } scalar reverse $res; } sub _zero { PARI(0) } sub _one { PARI(1) } sub _two { PARI(2) } sub _ten { PARI(10) } sub _1ex { gpui(PARI(10), $_[1]) } sub _copy { $_[1] + $zero; } sub _str { pari2pv($_[1]) } sub _num { 0 + pari2pv($_[1]) } sub _add { $_[1] += $_[2] } sub _sub { if ($_[3]) { $_[2] = $_[1] - $_[2]; return $_[2]; } $_[1] -= $_[2]; } sub _mul { $_[1] = gmul($_[1], $_[2]) } sub _div { if (wantarray) { my $r = $_[1] % $_[2]; $_[1] = gdivent($_[1], $_[2]); return ($_[1], $r); } $_[1] = gdivent($_[1], $_[2]); } sub _mod { $_[1] %= $_[2]; } sub _nok { my ($class, $n, $k) = @_; # Math::Pari::binomial() doesn't seem to be able to handle input larger # than 9223372036854775807, i.e., 2*63-1. For instance, the following # returns zero, not one (at least for certain versions and configurations): # # $n = PARI("9223372036854775808"); # $k = PARI("9223372036854775808"); # print Math::Pari::binomial($n, $k); # If k > n/2, or, equivalently, 2k > n, compute nok(n, k) as nok(n, n-k). #my $imax = $class -> _new("9223372036854775807"); #if ($class -> _acmp($n, $imax) > 0 \|\| # $class -> _acmp($k, $imax) > 0) #{ # return $class -> SUPER::_nok($n, $k); #} my $twok = $class -> _mul($class -> _two(), $class -> _copy($k)); if ($class -> _acmp($twok, $n) > 0) { $k = $class -> _sub($class -> _copy($n), $k); } binomial($n, $k); } sub _inc { ++$_[1]; } sub _dec { --$_[1]; } sub _and { $_[1] &= $_[2] } sub _xor { $_[1] ^= $_[2] } sub _or { $_[1] \|= $_[2] } sub _pow { gpui($_[1], $_[2]) } sub _gcd { gcd($_[1], $_[2]) } sub _lcm { lcm($_[1], $_[2]) } sub _len { length(pari2pv($_[1])) } # costly! # XXX TODO: calc len in base 2 then appr. in base 10 sub _alen { length(pari2pv($_[1])) } sub _zeros { my ($class, $x) = @_; return 0 if gcmp0($x); # 0 has no trailing zeros my $u = $class -> _str($x); $u =~ /(0)\z/; return length($1); #my $s = pari2pv($_[1]); #my $i = length($s); #my $zeros = 0; #while (--$i >= 0) { # substr($s, $i, 1) eq '0' ? $zeros ++ : last; #} #$zeros; } sub _digit { # if $n < 0, we need to count from left and thus can't use the other method: if ($_[2] < 0) { return substr(pari2pv($_[1]), -1 - $_[2], 1); } # else this is faster (except for very short numbers) # shift the number right by $n digits, then extract last digit via % 10 pari2pv(gdivent($_[1], $ten * $_[2]) % $ten); } sub _is_zero { gcmp0($_[1]) } sub _is_one { gcmp1($_[1]) } sub _is_two { gcmp($_[1], $two) ? 0 : 1 } sub _is_ten { gcmp($_[1], $ten) ? 0 : 1 } sub _is_even { bittest($_[1], 0) ? 0 : 1 } sub _is_odd { bittest($_[1], 0) ? 1 : 0 } sub _acmp { my $i = gcmp($_[1], $_[2]) \|\| 0; # work around bug in Pari (on 64bit systems?) $i = -1 if $i == 4294967295; $i; } sub _check { my ($class, $x) = @_; return "Undefined" unless defined $x; return "$x is not a reference to Math::Pari" unless ref($x) eq 'Math::Pari'; return 0; } sub _sqrt { # square root of $x my ($class, $x) = @_; my $y = Math::Pari::sqrtint($x); return $y * $y > $x ? $y - $one : $y; # bug in sqrtint()? } sub _root { # n'th root # Native version: return $_[1] = int(Math::Pari::sqrtn($_[1] + 0.5, $_[2])); } sub _modpow { # modulus of power ($x $y) % $z my ($c, $num, $exp, $mod) = @_; # in the trivial case, if (gcmp1($mod)) { $num = PARI(0); return $num; } if (gcmp1($num)) { $num = PARI(1); return $num; } if (gcmp0($num)) { if (gcmp0($exp)) { return PARI(1); } else { return PARI(0); } } my $acc = $c -> _copy($num); my $t = $c -> _one(); my $expbin = $c -> _to_bin($exp); my $len = length($expbin); while (--$len >= 0) { if (substr($expbin, $len, 1) eq '1') { # is_odd $c -> _mul($t, $acc); $t = $c -> _mod($t, $mod); } $c -> _mul($acc, $acc); $acc = $c -> _mod($acc, $mod); } $num = $t; $num; } sub _rsft { # (X, Y, N) = @_; means X >> Y in base N if ($_[3] != 2) { return $_[1] = gdivent($_[1], PARI($_[3]) $_[2]); } $_[1] >>= $_[2]; } sub _lsft { # (X, Y, N) = @_; means X >> Y in base N if ($_[3] != 2) { return $_[1] = PARI($_[3]) * $_[2]; } $_[1] <<= $_[2]; } sub _fac { # factorial of argument $_[1] = ifact($_[1]); } # _set() - set an already existing object to the given scalar value sub _set { my ($c, $x, $y) = @_; x = \PARI($y . ''); } 1; __END__ =pod =head1 NAME Math::BigInt::Pari - a math backend library based on Math::Pari =head1 SYNOPSIS # to use it with Math::BigInt use Math::BigInt lib => 'Pari'; # to use it with Math::BigFloat use Math::BigFloat lib => 'Pari'; # to use it with Math::BigRat use Math::BigRat lib => 'Pari'; =head1 DESCRIPTION Math::BigInt::Pari inherits from Math::BigInt::Lib. Provides support for big integer in Math::BigInt et al. calculations via means of Math::Pari, an XS layer on top of the very fast PARI library. =head1 BUGS Please report any bugs or feature requests to C<bug-math-bigint-pari at rt.cpan.org>, or through the web interface at L<https://rt.cpan.org/Ticket/Create.html?Queue=Math-BigInt-Pari> (requires login). We will be notified, and then you'll automatically be notified of progress on your bug as I make changes. =head1 SUPPORT After installing, you can find documentation for this module with the perldoc command. perldoc Math::BigInt::Pari You can also look for information at: =over 4 =item GitHub Source Repository L<https://github.com/pjacklam/p5-Math-BigInt-Pari> =item * RT: CPAN's request tracker L<https://rt.cpan.org/Public/Dist/Display.html?Name=Math-BigInt-Pari> =item * MetaCPAN L<https://metacpan.org/release/Math-BigInt-Pari> =item * CPAN Testers Matrix L<http://matrix.cpantesters.org/?dist=Math-BigInt-Pari> =back =head1 LICENSE This program is free software; you may redistribute it and/or modify it under the same terms as Perl itself. =head1 AUTHOR Original Math::BigInt::Pari written by Benjamin Trott 2001, E<lt>ben@rhumba.pair.comE<gt>. Extended and maintained by Tels 2001-2007 L<http://bloodgate.com> Maintained by Peter John Acklam E<lt>pjacklam@gmail.comE<gt> 2010-2021. L<Math::Pari> was written by Ilya Zakharevich. =head1 SEE ALSO L<Math::BigInt>, L<Math::BigFloat>, L<Math::Pari>, and the other backends L<Math::BigInt::Calc>, L<Math::BigInt::GMP>, and L<Math::BigInt::Pari>. =cut

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