# GMP perl module # Copyright 2001 Free Software Foundation, Inc. # # This file is part of the GNU MP Library. # # The GNU MP Library is free software; you can redistribute it and/or modify # it under the terms of the GNU Lesser General Public License as published # by the Free Software Foundation; either version 2.1 of the License, or (at # your option) any later version. # # The GNU MP Library is distributed in the hope that it will be useful, but # WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY # or FITNESS FOR A PARTICULAR PURPOSE. See the GNU Lesser General Public # License for more details. # # You should have received a copy of the GNU Lesser General Public License # along with the GNU MP Library; see the file COPYING.LIB. If not, write to # the Free Software Foundation, Inc., 59 Temple Place - Suite 330, Boston, # MA 02111-1307, USA. # This code is designed to work with perl 5.005, so it and the sub-packages # aren't as modern as they could be. package GMP; require Symbol; require Exporter; require DynaLoader; @ISA = qw(Exporter DynaLoader); @EXPORT = qw(); @EXPORT_OK = qw(version); %EXPORT_TAGS = ('all' => [qw(get_d get_si get_str integer_p printf sgn sprintf)], 'constants' => [()]); Exporter::export_ok_tags('all'); $VERSION = '1'; bootstrap GMP $VERSION; # The format string is cut up into "%" specifiers so GMP types can be # passed to GMP::sprintf_internal. Any "*"s are interpolated before # calling sprintf_internal, which saves worrying about variable # argument lists there. # # Because sprintf_internal is only called after the conversion and # operand have been checked there won't be any crashes from a bad # format string. # sub sprintf { my $fmt = shift; my $out = ''; my ($pre, $dummy, $pat, $rest); while (($pre, $dummy, $pat, $rest) = ($fmt =~ /^((%%|[^%])*)(%[- +#.*hlLqv\d]*[bcdfeEgGinopsuxX])(.*)$/s)) { $out .= $pre; my $pat2 = $pat; # $pat with "*"s expanded my @params = (); # arguments per "*"s while ($pat2 =~ /[*]/) { my $arg = shift; $pat2 =~ s/[*]/$arg/; push @params, $arg; } if (UNIVERSAL::isa($_[0],"GMP::Mpz")) { if ($pat2 !~ /[dioxX]$/) { die "GMP::sprintf: unsupported output format for mpz: $pat2\n"; } $pat2 =~ s/(.)$/Z$1/; $out .= sprintf_internal ($pat2, shift); } elsif (UNIVERSAL::isa($_[0],"GMP::Mpq")) { if ($pat2 !~ /[dioxX]$/) { die "GMP::sprintf: unsupported output format for mpq: $pat2\n"; } $pat2 =~ s/(.)$/Q$1/; $out .= sprintf_internal ($pat2, shift); } elsif (UNIVERSAL::isa($_[0],"GMP::Mpf")) { if ($pat2 !~ /[eEfgG]$/) { die "GMP::sprintf: unsupported output format for mpf: $pat2\n"; } $pat2 =~ s/(.)$/F$1/; $out .= sprintf_internal ($pat2, shift); } elsif ($pat =~ /n$/) { # do it this way so h, l or V type modifiers are respected, and use a # dummy variable to avoid a warning about discarding the value my $dummy = sprintf "%s$pat", $out, $_[0]; shift; } else { $out .= sprintf $pat, @params, shift; } $fmt = $rest; } $out .= $fmt; return $out; } sub printf { if (ref($_[0]) eq 'GLOB') { my $h = Symbol::qualify_to_ref(shift, caller); print $h GMP::sprintf(@_); } else { print STDOUT GMP::sprintf(@_); } } 1; __END__ =head1 NAME GMP - Perl interface to the GNU Multiple Precision Arithmetic Library =head1 SYNOPSIS use GMP; use GMP::Mpz; use GMP::Mpq; use GMP::Mpf; use GMP::Rand; =head1 DESCRIPTION B This module provides access to GNU MP arbitrary precision integers, rationals and floating point. No functions are exported from these packages by default, but can be selected in the usual way, or the tag :all for everything. use GMP::Mpz qw(gcd, lcm); # just these functions use GMP::Mpq qw(:all); # everything in mpq =head2 GMP::Mpz This class provides arbitrary precision integers. A new mpz can be constructed with C. The initial value can be an integer, float, string, mpz, mpq or mpf. Floats, mpq and mpf will be automatically truncated to an integer. use GMP::Mpz qw(:all); my $a = mpz(123); my $b = mpz("0xFFFF"); my $c = mpz(1.5); # truncated The following overloaded operators are available, and corresponding assignment forms like C<+=>, =over 4 =item + - * / % EE EE ** & | ^ ! E E= == != E E= E=E abs not sqrt =back C and C<%> round towards zero (as per the C functions in GMP). The following functions are available, behaving the same as the corresponding GMP mpz functions, =over 4 =item bin, cdiv, cdiv_2exp, clrbit, congruent_p, congruent_2exp_p, divexact, divisible_p, divisible_2exp_p, even_p, fac, fdiv, fdiv_2exp, fib, fib2, gcd, gcdext, hamdist, invert, jacobi, kronecker, lcm, lucnum, lucnum2, mod, nextprime, odd_p, perfect_power_p, perfect_square_p, popcount, powm, probab_prime_p, realloc, remove, root, roote, scan0, scan1, setbit, sizeinbase, sqrtrem, tdiv, tdiv_2exp, tstbit =back C, C and C and their C<2exp> variants return a quotient/remainder pair. C returns a pair F[n] and F[n-1], similarly C. C and C accept a variable number of arguments (one or more). C returns a triplet of gcd and two cofactors, for example use GMP::Mpz qw(:all); $a = 7257; $b = 10701; ($g, $x, $y) = gcdext ($a, $b); print "gcd($a,$b) is $g, and $g == $a*$x + $b*$y\n"; C returns the inverse, or undef if it doesn't exist. C returns a remainder/multiplicty pair. C returns the nth root, and C returns a root/bool pair, the bool indicating whether the root is exact. C returns a root/remainder pair. C and C expect a variable which they can modify, it doesn't make sense to pass a literal constant. Only the given variable is modified, if other variables are referencing the same mpz object then a new copy is made of it. If the variable isn't an mpz it will be coerced to one. For instance, use GMP::Mpz qw(setbit); setbit (123, 0); # wrong, don't pass a constant $a = mpz(6); $b = $a; setbit ($a, 0); # $a becomes 7, $b stays at 6 C and C return ULONG_MAX if no 0 or 1 bit is found, as per the C functions. That value can be obtained in perl with C<~0>. =head2 GMP::Mpq This class provides rationals with arbitrary precision numerators and denominators. A new mpq can be constructed with C. The initial value can be an integer, float, string, mpz, mpq or mpf, or a pair of integers or mpz's. No precision is lost when converting a float or mpf, the exact value is retained. use GMP::Mpq qw(:all); $a = mpq(); # zero $b = mpq(0.5); # gives 1/2 $b = mpq(14); # integer 14 $b = mpq(3,4); # fraction 3/4 $b = mpq("7/12"); # fraction 7/12 $b = mpq("0xFF/0x100"); # fraction 255/256 When a fraction is given, it should be in the canonical form specified in the GMP manual, which is denominator positive, no common factors, and zero always represented as 0/1. If not then C can be called to put it in that form. For example, use GMP::Mpq qw(:all); $q = mpq(21,15); # eek! common factor 5 canonicalize($q); # get rid of it The following overloaded operators are available, and corresponding assignment forms like C<+=>, =over 4 =item + - * / EE EE ** ! E E= == != E E= E=E abs not =back The following functions are available, =over 4 =item den, inv, num =back C calculates 1/q, as per the corresponding GMP function. C and C return an mpz copy of the numerator or denominator respectively. In the future C and C might give lvalues so the original mpq can be modified through them, but this is not done currently. =head2 GMP::Mpf This class provides arbitrary precision floating point numbers. The mantissa is an arbitrary user-selected precision and the exponent is a fixed size (one machine word). A new mpf can be constructed with C. The initial value can be an integer, float, string, mpz, mpq or mpf. The second argument specifies the desired precision in bits, or if omitted then the default precision is used. use GMP::Mpf qw(:all); $a = mpf(); # zero $b = mpf(-7.5); # default precision $c = mpf(1.5, 500); # 500 bits precision $d = mpf("1.0000000000000001"); The following overloaded operators are available, with the corresponding assignment forms like C<+=>, =over 4 =item + - * / EE EE ** ! E E= == != E E= E=E abs not sqrt =back The following functions are available, behaving the same as the corresponding GMP mpf functions, =over 4 =item ceil, floor, get_default_prec, get_prec, mpf_eq, set_default_prec, set_prec, trunc =back C is so named to avoid clashing with the perl C operator. C expects a variable which it can modify, it doesn't make sense to pass a literal constant. Only the given variable is modified, if other variables are referencing the same mpf object then a new copy is made of it. If the variable isn't an mpf it will be coerced to one. Results are the same precision as inputs, or if two mpf's are given to a binary operator then the precision of the first is used. For example, use GMP::Mpf qw(mpf); $a = mpf(2.0, 100); $b = mpf(2.0, 500); $c = $a + $b; # gives 100 bits precision Mpf to string conversion via "" or the usual string contexts uses C<$#> the same as normal float to string conversions, or defaults to C<%.g> if C<$#> is not defined. C<%.g> means all significant digits in the selected precision. =head2 GMP class The following functions are available in the GMP class, =over 4 =item fits_slong_p, get_d, get_si, get_str, integer_p, printf, sgn, sprintf, version =back C accepts an integer, string, float, mpz, mpq or mpf. The base is specified by an optional second parameter, or defaults to decimal. A negative base means upper case, as per the C functions. For integer, integer string, mpz or mpq operands a string is returned. For example, use GMP qw(:all); use GMP::Mpq qw(:all); print get_str(mpq(-5,8)),"\n"; # -5/8 print get_str(255,16),"\n"; # ff For float, float strings or mpf operands C accepts an optional third parameter being how many digits to produce, which defaults to 0 meaning all digits. No more digits than can be accurately represented by the float precision are ever produced though. A string/exponent pair is returned, as per the C mpf_get_str function. For example, use GMP qw(:all); use GMP::Mpf qw(:all); ($s, $e) = get_str(111.111111111, 10, 4); printf ".$se$e\n"; # .1111e3 ($s, $e) = get_str(1.625, 10); print "0.$s*10^$e\n"; # 0.1625*10^1 ($s, $e) = get_str(mpf(2)**20, 16); printf ".%s@%x\n", $s, $e; # .1@14 C and C allow formatted output of GMP types. mpz and mpq values can be used with integer conversions (d, o, x, X) and mpf with float conversions (f, e, E, g, G). All the standard perl printf features are available too. For example, use GMP::Mpz qw(mpz); use GMP::Mpf qw(mpf); GMP::printf ("%d %d %s", 123, mpz(2)**128, 'foo'); GMP::printf STDERR "%.40f", mpf(1.234); In perl 5.6.1 it doesn't seem to work to export C, the plain builtin C is reached unless calls are C<&printf()> style. Explicit use of C is suggested. C doesn't suffer this problem. use GMP qw(sprintf); use GMP::Mpq qw(mpq); $s = sprintf "%x", mpq(15,16); C is not exported by default or by tag :all, calling it as C is recommended. It returns the GMP library version string, which is not to be confused with the module version number. The other GMP module functions behave as per the corresponding GMP routines, and accept any integer, string, float, mpz, mpq or mpf. For example, use GMP qw(:all); use GMP::Mpz qw(mpz); $z = mpz(123); print sgn($z); # gives 1 Because each of GMP::Mpz, GMP::Mpq and GMP::Mpf is a sub-class of GMP, C<-E> style calls work too. use GMP qw(:all); use GMP::Mpq qw(mpf); $q = mpq(-5,7); if ($q->integer_p()) # false ... =head2 GMP::Rand This class provides objects holding an algorithm and state for random number generation. C creates a new object, for example, use GMP::Rand qw(randstate); $r = randstate(); $r = randstate('lc_2exp_size', 64); $r = randstate('lc_2exp', 43840821, 1, 32); With no parameters this corresponds to the C function C, and is a compromise between speed and randomness. 'lc_2exp_size' corresponds to C, and 'lc_2exp' corresponds to C. 'lc_2exp_size' can fail if the requested size is bigger than the internal table provides for, in which case undef is returned. The maximum size currently supported is 128. The other forms always succeed. A randstate can be seeded with an integer or mpz, using the C method. /dev/random might be a good source of randomness, or time() or Time::HiRes::time() might be adequate, depending on the application. $r->seed(time())); Random numbers can be generated with the following functions, =over 4 =item mpf_urandomb, mpz_rrandomb, mpz_urandomb, mpz_urandomm =back Each constructs a new mpz or mpf and with a distribution per the corresponding GMP function. For example, use GMP::Rand (:all); $r = randstate(); $a = mpz_urandomb($r,256); # uniform, 256 bits $b = mpz_urandomm($r,mpz(3)**100); # uniform, 0 to 3**100-1 $c = mpz_rrandomb($r,1024); # special, 1024 bits $f = mpf_urandomb($r,128); # uniform, 128 bits, 0<=$f<1 =head2 Coercion Arguments to operators and functions are converted as necessary to the appropriate type. For instance C<**> requires an unsigned integer exponent, and an mpq argument will be converted, so long as it's an integer in the apropriate range. use GMP::Mpz (mpz); use GMP::Mpq (mpq); $p = mpz(3) ** mpq(45); # allowed, 45 is an integer It's an error if a conversion to an integer or mpz would cause any truncation. For example, use GMP::Mpz (mpz); $p = mpz(3) + 1.25; # not allowed $p = mpz(3) + mpz(1.25); # allowed, explicit truncation Comparisons, however, accept any combination of operands and are always done exactly. For example, use GMP::Mpz (mpz); print mpz(3) < 3.1; # true Variables used on the left of an assignment operator like C<+=> are subject to coercion too. An integer, float or string will change type when an mpz, mpq or mpf is applied to it. For example, use GMP::Mpz (mpz); $a = 1; $a += mpz(1234); # $a becomes an mpz =head2 Overloading The rule for binary operators in the C mechanism is that if both operands are class objects then the method from the first is used. This determines the result type when mixing GMP classes. For example, use GMP::Mpz (mpz); use GMP::Mpq (mpq); use GMP::Mpf (mpf); $z = mpz(123); $q = mpq(3,2); $f = mpf(1.375) print $q+$f; # gives an mpq print $f+$z; # gives an mpf print $z+$f; # not allowed, would lose precision =head2 Constants A special tag C<:constants> is recognised in the module exports list. It doesn't select any functions, but indicates that perl constants should be GMP objects. This can only be used on one of GMP::Mpz, GMP::Mpq or GMP::Mpf at any one time, since they apply different rules. GMP::Mpz will treat constants as mpz's if they're integers, or ordinary floats if not. For example, use GMP::Mpz qw(:constants); print 764861287634126387126378128,"\n"; # an mpz print 1.25,"\n"; # a float GMP::Mpq is similar, treating integers as mpq's and leaving floats to the normal perl handling. Something like 3/4 is read as two integer mpq's and a division, but that's fine since it gives the intended fraction. use GMP::Mpq qw(:constants); print 3/4,"\n"; # an mpq print 1.25,"\n"; # a float GMP::Mpf will treat all constants as mpf's using the default precision. BEGIN blocks can be used to set that precision while the code is parsed. For example, use GMP::Mpf qw(:constants); BEGIN { GMP::Mpf::set_default_prec(256); } print 1/3; BEGIN { GMP::Mpf::set_default_prec(64); } print 5/7; A similar special tag :noconstants is recognised to turn off the constants feature. For example, use GMP::Mpz qw(:constants); print 438249738748174928193,"\n"; # an mpz use GMP::Mpz qw(:noconstants); print 438249738748174928193,"\n"; # now a float All three 'integer', 'binary' and 'float' constant methods are captured. 'float' is captured even for GMP::Mpz and GMP::Mpq since perl by default treats integer strings as floats if they don't fit a plain integer. =head1 SEE ALSO GMP manual, L, L. =head1 BUGS The overloaded constants sometimes provoke seg faults from perl 5.005_03 on i386 FreeBSD. Don't know if that's a perl bug or a GMP module bug, though it does seem to go bad before reaching anything in GMP.xs. There's no way to specify an arbitrary base when converting a string to an mpz (or mpq or mpf), only hex or octal with 0x or 0 (for mpz and mpq, but not for mpf). These modules are not reentrant or thread safe, due to the implementation of the XSUBs. Returning a new object from the various functions is convenient, but assignment versions could avoid creating new objects. Perhaps they could be named after the C language functions, eg. mpq_inv($q,$q); It'd be good if C and C gave lvalues so the underlying mpq could be manipulated. C could usefully accept %b for mpz, mpq and mpf, and perhaps %x for mpf too. There's no interface to mpfr. =head1 INTERNALS In usual perl object style, an mpz is a reference to an object blessed into class C. The object holds a pointer to the C language C structure. Similarly for mpq, mpf and randstate. A free list of mpz and mpq values is kept to avoid repeated initializing and clearing when objects are created and destroyed. This aims to help speed, but it's not clear whether it's really needed. mpf doesn't use a free list because the precision of new objects can be different each time. No interface to C is provided. It wouldn't be very useful since there's no way to make an operation store its result in a particular object. The plain C is useful though, for truncating to a lower precision, or as a sort of directive that subsequent calculations involving that variable should use a higher precision. The overheads of perl dynamic typing (operator dispatch, operand type checking or coercion) will mean this interface is slower than using C directly. Some assertion checking is available as a compile-time option. =cut # Local variables: # perl-indent-level: 2 # fill-column: 76 # End: