[gcc] GCC 4.5.0=>4.5.1

gcc/gmp/demos/perl/GMP.pm

Index: gcc/gmp/demos/perl/GMP.pm
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-# GMP perl module
-
-# Copyright 2001, 2002, 2003, 2004 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 3 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.  If not, see http://www.gnu.org/licenses/.
-
-# [Note: The above copyright notice is repeated in the documentation section
-# below, in order to get it into man pages etc generated by the various pod
-# conversions.  When changing, be sure to update below too.]
-
-
-# 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_d_2exp get_si get_str integer_p
-                             printf sgn sprintf)],
-		'constants' => [()]);
-Exporter::export_ok_tags('all');
-
-$VERSION = '2.00';
-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
-
-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<mpz>.  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
-
-+ - * / % E<lt>E<lt> E<gt>E<gt> ** & | ^ ! E<lt> E<lt>= == != E<gt> E<gt>=
-E<lt>=E<gt> abs not sqrt
-
-=back
-
-C</> and C<%> round towards zero (as per the C<tdiv> 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, combit, 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, mpz_export, mpz_import, 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<cdiv>, C<fdiv> and C<tdiv> and their C<2exp> variants return a
-quotient/remainder pair.  C<fib2> returns a pair F[n] and F[n-1], similarly
-C<lucnum2>.  C<gcd> and C<lcm> accept a variable number of arguments (one or
-more).  C<gcdext> 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<mpz_import> and C<mpz_export> are so named to avoid the C<import> keyword.
-Their parameters are as follows,
-
-    $z = mpz_import ($order, $size, $endian, $nails, $string);
-    $string = mpz_export ($order, $size, $endian, $nails, $z);
-
-The order, size, endian and nails parameters are as per the corresponding C
-functions.  The string input for C<mpz_import> is interpreted as byte data
-and must be a multiple of $size bytes.  C<mpz_export> conversely returns a
-string of byte data, which will be a multiple of $size bytes.
-
-C<invert> returns the inverse, or undef if it doesn't exist.  C<remove>
-returns a remainder/multiplicty pair.  C<root> returns the nth root, and
-C<roote> returns a root/bool pair, the bool indicating whether the root is
-exact.  C<sqrtrem> and C<rootrem> return a root/remainder pair.
-
-C<clrbit>, C<combit> and C<setbit> 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<scan0> and C<scan1> return ~0 if no 0 or 1 bit respectively is found.
-
-=head2 GMP::Mpq
-
-This class provides rationals with arbitrary precision numerators and
-denominators.  A new mpq can be constructed with C<mpq>.  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<canonicalize> can be called to put
-it in that form.  For example,
-
-    use GMP::Mpq qw(:all);
-    $q = mpq(21,15);   # eek! common factor 3
-    canonicalize($q);  # get rid of it
-
-The following overloaded operators are available, and corresponding
-assignment forms like C<+=>,
-
-=over 4
-
-=item
-
-+ - * / E<lt>E<lt> E<gt>E<gt> ** ! E<lt> E<lt>= == != E<gt> E<gt>=
-E<lt>=E<gt> abs not
-
-=back
-
-The following functions are available,
-
-=over 4
-
-=item
-
-den, inv, num
-
-=back
-
-C<inv> calculates 1/q, as per the corresponding GMP function.  C<num> and
-C<den> return an mpz copy of the numerator or denominator respectively.  In
-the future C<num> and C<den> 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<mpf>.  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
-
-+ - * / E<lt>E<lt> E<gt>E<gt> ** ! E<lt> E<lt>= == != E<gt> E<gt>=
-E<lt>=E<gt> 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<mpf_eq> is so named to avoid clashing with the perl C<eq> operator.
-
-C<set_prec> 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<$#>
-is not defined.  C<%.g> means all significant digits in the selected
-precision.
-
-=head2 GMP class
-
-The following functions are available in the GMP class,
-
-=over 4
-
-=item
-
-fits_slong_p, get_d, get_d_2exp, get_si, get_str, integer_p, printf, sgn,
-sprintf, version
-
-=back
-
-C<get_d_2exp> accepts any integer, string, float, mpz, mpq or mpf operands
-and returns a float and an integer exponent,
-
-    ($dbl, $exp) = get_d_2exp (mpf ("3.0"));
-    # dbl is 0.75, exp is 2
-
-C<get_str> takes an optional second argument which is the base, defaulting
-to decimal.  A negative base means upper case, as per the C functions.  For
-integer, integer string, mpz or mpq operands a string is returned.
-
-    use GMP qw(:all);
-    use GMP::Mpq qw(:all);
-    print get_str(mpq(-5,8)),"\n";      # -5/8
-    print get_str(255,16),"\n";         # ff
-
-For float, float strings or mpf operands, C<get_str> accepts an optional
-third parameter being how many digits to produce, defaulting to 0 which
-means all digits.  (Only as many digits as can be accurately represented by
-the float precision are ever produced though.)  A string/exponent pair is
-returned, as per the C mpf_get_str function.  For example,
-
-    use GMP qw(:all);
-    use GMP::Mpf qw(:all);
-    ($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<printf> and C<sprintf> 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<printf>, the plain builtin
-C<printf> is reached unless calls are C<&printf()> style.  Explicit use of
-C<GMP::printf> is suggested.  C<sprintf> doesn't suffer this problem.
-
-    use GMP qw(sprintf);
-    use GMP::Mpq qw(mpq);
-    $s = sprintf "%x", mpq(15,16);
-
-C<version> is not exported by default or by tag :all, calling it as
-C<GMP::version()> 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<gt>> 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<randstate> 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);
-    $r = randstate('mt');
-    $r = randstate($another_r);
-
-With no parameters this corresponds to the C function
-C<gmp_randinit_default>, and is a compromise between speed and randomness.
-'lc_2exp_size' corresponds to C<gmp_randinit_lc_2exp_size>, 'lc_2exp'
-corresponds to C<gmp_randinit_lc_2exp>, and 'mt' corresponds to
-C<gmp_randinit_mt>.  Or when passed another randstate object, a copy of that
-object is made.
-
-'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<seed> 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,
-gmp_urandomb_ui, gmp_urandomm_ui
-
-=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 mpz, 256 bits
-    $b = mpz_urandomm($r,mpz(3)**100); # uniform mpz, 0 to 3**100-1
-    $c = mpz_rrandomb($r,1024);        # special mpz, 1024 bits
-    $f = mpf_urandomb($r,128);         # uniform mpf, 128 bits, 0<=$f<1
-    $f = gmp_urandomm_ui($r,56);       # uniform int, 0 to 55
-
-=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<overload> 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<perl>, L<overload>.
-
-=head1 BUGS
-
-In perl 5.005_03 on i386 FreeBSD, the overloaded constants sometimes provoke
-seg faults.  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<num> and C<den> gave lvalues so the underlying mpq could
-be manipulated.
-
-C<printf> could usefully accept %b for mpz, mpq and mpf, and perhaps %x for
-mpf too.
-
-C<get_str> returning different style values for integer versus float is a
-bit unfortunate.  With mpz, mpq and mpf objects there's no doubt what it
-will do, but on a plain scalar its action depends on whether the scalar was
-promoted to a float at any stage, and then on the GMP module rules about
-using the integer or float part.
-
-=head1 INTERNALS
-
-In usual perl object style, an mpz is a reference to an object blessed into
-class C<GMP::Mpz>.  The object holds a pointer to the C language C<mpz_t>
-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<mpf_set_prec_raw> 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<set_prec> 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.
-
-=head1 COPYRIGHT
-
-Copyright 2001, 2002, 2003, 2004 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 3 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.  If not, see http://www.gnu.org/licenses/.
-
-=cut
-
-# Local variables:
-# perl-indent-level: 2
-# fill-column: 76
-# End: