[p5sagit/p5-mst-13.2.git] / lib / bigrat.pm

package bigrat;
use 5.006002;

$VERSION = '0.22';
require Exporter;
@ISA		= qw( bigint );
@EXPORT_OK	= qw( ); 
@EXPORT		= qw( inf NaN ); 

use strict;
use overload;
require bigint;		# no "use" to avoid callind import

############################################################################## 

BEGIN 
  {
  *inf = \&bigint::inf;
  *NaN = \&bigint::NaN;
  }

# These are all alike, and thus faked by AUTOLOAD

my @faked = qw/round_mode accuracy precision div_scale/;
use vars qw/$VERSION $AUTOLOAD $_lite/;		# _lite for testsuite

sub AUTOLOAD
  {
  my $name = $AUTOLOAD;

  $name =~ s/.*:://;    # split package
  no strict 'refs';
  foreach my $n (@faked)
    {
    if ($n eq $name)
      {
      *{"bigrat::$name"} = sub 
        {
        my $self = shift;
        no strict 'refs';
        if (defined $_[0])
          {
          Math::BigInt->$name($_[0]);
          Math::BigFloat->$name($_[0]);
          return Math::BigRat->$name($_[0]);
          }
        return Math::BigInt->$name();
        };
      return &$name;
      }
    }
 
  # delayed load of Carp and avoid recursion
  require Carp;
  Carp::croak ("Can't call bigrat\-\>$name, not a valid method");
  }

sub unimport
  {
  $^H{bigrat} = undef;					# no longer in effect
  overload::remove_constant('binary','','float','','integer');
  }

sub in_effect
  {
  my $level = shift || 0;
  my $hinthash = (caller($level))[10];
  $hinthash->{bigrat};
  }

#############################################################################
# the following two routines are for Perl 5.9.4 or later and are lexical

sub _hex
  {
  return CORE::hex($_[0]) unless in_effect(1);
  my $i = $_[0];
  $i = '0x'.$i unless $i =~ /^0x/;
  Math::BigInt->new($i);
  }

sub _oct
  {
  return CORE::oct($_[0]) unless in_effect(1);
  my $i = $_[0];
  return Math::BigInt->from_oct($i) if $i =~ /^0[0-7]/;
  Math::BigInt->new($i);
  }

sub import 
  {
  my $self = shift;

  # see also bignum->import() for additional comments

  $^H{bigrat} = 1;					# we are in effect

  # for newer Perls always override hex() and oct() with a lexical version:
  if ($] > 5.009004)
    {
    no warnings 'redefine';
    *CORE::GLOBAL::oct = \&_oct;
    *CORE::GLOBAL::hex = \&_hex;
    }
  # some defaults
  my $lib = ''; my $lib_kind = 'try'; my $upgrade = 'Math::BigFloat';

  my @import = ( ':constant' );				# drive it w/ constant
  my @a = @_; my $l = scalar @_; my $j = 0;
  my ($a,$p);
  my ($ver,$trace);					# version? trace?
  for ( my $i = 0; $i < $l ; $i++,$j++ )
    {
    if ($_[$i] eq 'upgrade')
      {
      # this causes upgrading
      $upgrade = $_[$i+1];		# or undef to disable
      my $s = 2; $s = 1 if @a-$j < 2;	# avoid "can not modify non-existant..."
      splice @a, $j, $s; $j -= $s;
      }
    elsif ($_[$i] =~ /^(l|lib|try|only)$/)
      {
      # this causes a different low lib to take care...
      $lib_kind = $1; $lib_kind = 'lib' if $lib_kind eq 'l';
      $lib = $_[$i+1] || '';
      my $s = 2; $s = 1 if @a-$j < 2;	# avoid "can not modify non-existant..."
      splice @a, $j, $s; $j -= $s; $i++;
      }
    elsif ($_[$i] =~ /^(a|accuracy)$/)
      {
      $a = $_[$i+1];
      my $s = 2; $s = 1 if @a-$j < 2;   # avoid "can not modify non-existant..."
      splice @a, $j, $s; $j -= $s; $i++;
      }
    elsif ($_[$i] =~ /^(p|precision)$/)
      {
      $p = $_[$i+1];
      my $s = 2; $s = 1 if @a-$j < 2;   # avoid "can not modify non-existant..."
      splice @a, $j, $s; $j -= $s; $i++;
      }
    elsif ($_[$i] =~ /^(v|version)$/)
      {
      $ver = 1;
      splice @a, $j, 1; $j --;
      }
    elsif ($_[$i] =~ /^(t|trace)$/)
      {
      $trace = 1;
      splice @a, $j, 1; $j --;
      }
    elsif ($_[$i] eq 'hex')
      {
      splice @a, $j, 1; $j --;
      no warnings 'redefine';
      *CORE::GLOBAL::hex = \&bigint::_hex_global;
      }
    elsif ($_[$i] eq 'oct')
      {
      splice @a, $j, 1; $j --;
      no warnings 'redefine';
      *CORE::GLOBAL::oct = \&bigint::_oct_global;
      }
    else
      {
      die ("unknown option $_[$i]");
      }
    }
  my $class;
  $_lite = 0;                                   # using M::BI::L ?
  if ($trace)
    {
    require Math::BigInt::Trace; $class = 'Math::BigInt::Trace';
    $upgrade = 'Math::BigFloat::Trace';
    }
  else
    {
    # see if we can find Math::BigInt::Lite
    if (!defined $a && !defined $p)             # rounding won't work to well
      {
      eval 'require Math::BigInt::Lite;';
      if ($@ eq '')
        {
        @import = ( );                          # :constant in Lite, not MBI
        Math::BigInt::Lite->import( ':constant' );
        $_lite= 1;                              # signal okay
        }
      }
    require Math::BigInt if $_lite == 0;        # not already loaded?
    $class = 'Math::BigInt';                    # regardless of MBIL or not
    }
  push @import, $lib_kind => $lib if $lib ne ''; 
  # Math::BigInt::Trace or plain Math::BigInt
  $class->import(@import, upgrade => $upgrade);

  require Math::BigFloat;
  Math::BigFloat->import( upgrade => 'Math::BigRat', ':constant' );
  require Math::BigRat;

  bigrat->accuracy($a) if defined $a;
  bigrat->precision($p) if defined $p;
  if ($ver)
    {
    print "bigrat\t\t\t v$VERSION\n";
    print "Math::BigInt::Lite\t v$Math::BigInt::Lite::VERSION\n" if $_lite;  
    print "Math::BigInt\t\t v$Math::BigInt::VERSION";
    my $config = Math::BigInt->config();
    print " lib => $config->{lib} v$config->{lib_version}\n";
    print "Math::BigFloat\t\t v$Math::BigFloat::VERSION\n";
    print "Math::BigRat\t\t v$Math::BigRat::VERSION\n";
    exit;
    }

  # Take care of octal/hexadecimal constants
  overload::constant binary => sub { bigint::_binary_constant(shift) };

  # if another big* was already loaded:
  my ($package) = caller();

  no strict 'refs';
  if (!defined *{"${package}::inf"})
    {
    $self->export_to_level(1,$self,@a);           # export inf and NaN
    }
  }

1;

__END__

=head1 NAME

bigrat - Transparent BigNumber/BigRational support for Perl

=head1 SYNOPSIS

  use bigrat;

  print 2 + 4.5,"\n";			# BigFloat 6.5
  print 1/3 + 1/4,"\n";			# produces 7/12

  {
    no bigrat;
    print 1/3,"\n";			# 0.33333...
  }

  # Note that this will make hex() and oct() be globally overriden:
  use bigrat qw/hex oct/;
  print hex("0x1234567890123490"),"\n";
  print oct("01234567890123490"),"\n";

=head1 DESCRIPTION

All operators (including basic math operations) are overloaded. Integer and
floating-point constants are created as proper BigInts or BigFloats,
respectively.

Other than L<bignum>, this module upgrades to Math::BigRat, meaning that
instead of 2.5 you will get 2+1/2 as output.

=head2 Modules Used

C<bigrat> is just a thin wrapper around various modules of the Math::BigInt
family. Think of it as the head of the family, who runs the shop, and orders
the others to do the work.

The following modules are currently used by bignum:

        Math::BigInt::Lite      (for speed, and only if it is loadable)
        Math::BigInt
        Math::BigFloat
        Math::BigRat

=head2 Math Library

Math with the numbers is done (by default) by a module called
Math::BigInt::Calc. This is equivalent to saying:

	use bigrat lib => 'Calc';

You can change this by using:

        use bignum lib => 'GMP';

The following would first try to find Math::BigInt::Foo, then
Math::BigInt::Bar, and when this also fails, revert to Math::BigInt::Calc:

	use bigrat lib => 'Foo,Math::BigInt::Bar';

Using C<lib> warns if none of the specified libraries can be found and
L<Math::BigInt> did fall back to one of the default libraries.
To supress this warning, use C<try> instead:

        use bignum try => 'GMP';

If you want the code to die instead of falling back, use C<only> instead:

        use bignum only => 'GMP';

Please see respective module documentation for further details.

=head2 Sign

The sign is either '+', '-', 'NaN', '+inf' or '-inf'.

A sign of 'NaN' is used to represent the result when input arguments are not
numbers or as a result of 0/0. '+inf' and '-inf' represent plus respectively
minus infinity. You will get '+inf' when dividing a positive number by 0, and
'-inf' when dividing any negative number by 0.

=head2 Methods

Since all numbers are not objects, you can use all functions that are part of
the BigInt or BigFloat API. It is wise to use only the bxxx() notation, and not
the fxxx() notation, though. This makes you independed on the fact that the
underlying object might morph into a different class than BigFloat.

=over 2

=item inf()

A shortcut to return Math::BigInt->binf(). Useful because Perl does not always
handle bareword C<inf> properly.

=item NaN()

A shortcut to return Math::BigInt->bnan(). Useful because Perl does not always
handle bareword C<NaN> properly.

=item upgrade()

Return the class that numbers are upgraded to, is in fact returning
C<$Math::BigInt::upgrade>.

=item in_effect()

	use bigrat;

	print "in effect\n" if bigrat::in_effect;	# true
	{
	  no bigrat;
	  print "in effect\n" if bigrat::in_effect;	# false
	}

Returns true or false if C<bigrat> is in effect in the current scope.

This method only works on Perl v5.9.4 or later.

=back

=head2 MATH LIBRARY

Math with the numbers is done (by default) by a module called

=head2 Cavaet

But a warning is in order. When using the following to make a copy of a number,
only a shallow copy will be made.

        $x = 9; $y = $x;
        $x = $y = 7;

If you want to make a real copy, use the following:

	$y = $x->copy();

Using the copy or the original with overloaded math is okay, e.g. the
following work:

        $x = 9; $y = $x;
        print $x + 1, " ", $y,"\n";     # prints 10 9

but calling any method that modifies the number directly will result in
B<both> the original and the copy being destroyed:

        $x = 9; $y = $x;
        print $x->badd(1), " ", $y,"\n";        # prints 10 10

        $x = 9; $y = $x;
        print $x->binc(1), " ", $y,"\n";        # prints 10 10

        $x = 9; $y = $x;
        print $x->bmul(2), " ", $y,"\n";        # prints 18 18

Using methods that do not modify, but testthe contents works:

        $x = 9; $y = $x;
        $z = 9 if $x->is_zero();                # works fine

See the documentation about the copy constructor and C<=> in overload, as
well as the documentation in BigInt for further details.

=head2 Options

bignum recognizes some options that can be passed while loading it via use.
The options can (currently) be either a single letter form, or the long form.
The following options exist:

=over 2

=item a or accuracy

This sets the accuracy for all math operations. The argument must be greater
than or equal to zero. See Math::BigInt's bround() function for details.

	perl -Mbigrat=a,50 -le 'print sqrt(20)'

Note that setting precision and accurary at the same time is not possible.

=item p or precision

This sets the precision for all math operations. The argument can be any
integer. Negative values mean a fixed number of digits after the dot, while
a positive value rounds to this digit left from the dot. 0 or 1 mean round to
integer. See Math::BigInt's bfround() function for details.

	perl -Mbigrat=p,-50 -le 'print sqrt(20)'

Note that setting precision and accurary at the same time is not possible.

=item t or trace

This enables a trace mode and is primarily for debugging bignum or
Math::BigInt/Math::BigFloat.

=item l or lib

Load a different math lib, see L<MATH LIBRARY>.

	perl -Mbigrat=l,GMP -e 'print 2 ** 512'

Currently there is no way to specify more than one library on the command
line. This means the following does not work:

	perl -Mbignum=l,GMP,Pari -e 'print 2 ** 512'

This will be hopefully fixed soon ;)

=item hex

Override the build-in hex() method with a version that can handle big
integers. Note that under Perl v5.9.4 or ealier, this will be global
and cannot be disabled with "no bigint;".

=item oct

Override the build-in oct() method with a version that can handle big
integers. Note that under Perl v5.9.4 or ealier, this will be global
and cannot be disabled with "no bigint;".

=item v or version

This prints out the name and version of all modules used and then exits.

	perl -Mbigrat=v

=back

=head1 CAVAETS

=over 2

=item in_effect()

This method only works on Perl v5.9.4 or later.

=item hex()/oct()

C<bigint> overrides these routines with versions that can also handle
big integer values. Under Perl prior to version v5.9.4, however, this
will not happen unless you specifically ask for it with the two
import tags "hex" and "oct" - and then it will be global and cannot be
disabled inside a scope with "no bigint":

	use bigint qw/hex oct/;

	print hex("0x1234567890123456");
	{
		no bigint;
		print hex("0x1234567890123456");
	}

The second call to hex() will warn about a non-portable constant.

Compare this to:

	use bigint;

	# will warn only under Perl older than v5.9.4
	print hex("0x1234567890123456");

=back

=head1 EXAMPLES
 
	perl -Mbigrat -le 'print sqrt(33)'
	perl -Mbigrat -le 'print 2*255'
	perl -Mbigrat -le 'print 4.5+2*255'
	perl -Mbigrat -le 'print 3/7 + 5/7 + 8/3'	
	perl -Mbigrat -le 'print 12->is_odd()';
	perl -Mbignum=l,GMP -le 'print 7 ** 7777'

=head1 LICENSE

This program is free software; you may redistribute it and/or modify it under
the same terms as Perl itself.

=head1 SEE ALSO

Especially L<bignum>.

L<Math::BigFloat>, L<Math::BigInt>, L<Math::BigRat> and L<Math::Big> as well
as L<Math::BigInt::BitVect>, L<Math::BigInt::Pari> and  L<Math::BigInt::GMP>.

=head1 AUTHORS

(C) by Tels L<http://bloodgate.com/> in early 2002 - 2007.

=cut
Commit	Line	Data
126f3c5f	1	package bigrat;
95a2d02c	2	use 5.006002;
126f3c5f	3
4440d13a	4	$VERSION = '0.22';
b68b7ab1	5	require Exporter;
d1a15766	6	@ISA = qw( bigint );
b4bc5691	7	@EXPORT_OK = qw( );
b4bc5691	8	@EXPORT = qw( inf NaN );
126f3c5f	9
126f3c5f	10	use strict;
95a2d02c	11	use overload;
d1a15766	12	require bigint; # no "use" to avoid callind import
126f3c5f	13
	14	##############################################################################
	15
d1a15766	16	BEGIN
	17	{
	18	*inf = \&bigint::inf;
	19	*NaN = \&bigint::NaN;
	20	}
	21
126f3c5f	22	# These are all alike, and thus faked by AUTOLOAD
	23
	24	my @faked = qw/round_mode accuracy precision div_scale/;
	25	use vars qw/$VERSION $AUTOLOAD $_lite/; # _lite for testsuite
	26
	27	sub AUTOLOAD
	28	{
	29	my $name = $AUTOLOAD;
	30
	31	$name =~ s/.*:://; # split package
	32	no strict 'refs';
	33	foreach my $n (@faked)
	34	{
	35	if ($n eq $name)
	36	{
	37	*{"bigrat::$name"} = sub
	38	{
	39	my $self = shift;
	40	no strict 'refs';
	41	if (defined $_[0])
	42	{
	43	Math::BigInt->$name($_[0]);
	44	Math::BigFloat->$name($_[0]);
990fb837	45	return Math::BigRat->$name($_[0]);
126f3c5f	46	}
	47	return Math::BigInt->$name();
	48	};
	49	return &$name;
	50	}
	51	}
	52
	53	# delayed load of Carp and avoid recursion
	54	require Carp;
	55	Carp::croak ("Can't call bigrat\-\>$name, not a valid method");
	56	}
	57
4440d13a	58	sub unimport
	59	{
	60	$^H{bigrat} = undef; # no longer in effect
	61	overload::remove_constant('binary','','float','','integer');
	62	}
	63
	64	sub in_effect
	65	{
	66	my $level = shift \|\| 0;
	67	my $hinthash = (caller($level))[10];
	68	$hinthash->{bigrat};
	69	}
	70
d1a15766	71	#############################################################################
	72	# the following two routines are for Perl 5.9.4 or later and are lexical
	73
	74	sub _hex
	75	{
	76	return CORE::hex($_[0]) unless in_effect(1);
	77	my $i = $_[0];
	78	$i = '0x'.$i unless $i =~ /^0x/;
	79	Math::BigInt->new($i);
	80	}
	81
	82	sub _oct
	83	{
	84	return CORE::oct($_[0]) unless in_effect(1);
	85	my $i = $_[0];
	86	return Math::BigInt->from_oct($i) if $i =~ /^0[0-7]/;
	87	Math::BigInt->new($i);
	88	}
	89
126f3c5f	90	sub import
	91	{
	92	my $self = shift;
	93
	94	# see also bignum->import() for additional comments
	95
4440d13a	96	$^H{bigrat} = 1; # we are in effect
4440d13a	97
d1a15766	98	# for newer Perls always override hex() and oct() with a lexical version:
	99	if ($] > 5.009004)
	100	{
	101	no warnings 'redefine';
	102	*CORE::GLOBAL::oct = \&_oct;
	103	*CORE::GLOBAL::hex = \&_hex;
	104	}
126f3c5f	105	# some defaults
bd49aa09	106	my $lib = ''; my $lib_kind = 'try'; my $upgrade = 'Math::BigFloat';
126f3c5f	107
	108	my @import = ( ':constant' ); # drive it w/ constant
	109	my @a = @_; my $l = scalar @_; my $j = 0;
	110	my ($a,$p);
	111	my ($ver,$trace); # version? trace?
	112	for ( my $i = 0; $i < $l ; $i++,$j++ )
	113	{
	114	if ($_[$i] eq 'upgrade')
	115	{
	116	# this causes upgrading
	117	$upgrade = $_[$i+1]; # or undef to disable
	118	my $s = 2; $s = 1 if @a-$j < 2; # avoid "can not modify non-existant..."
	119	splice @a, $j, $s; $j -= $s;
	120	}
bd49aa09	121	elsif ($_[$i] =~ /^(l\|lib\|try\|only)$/)
126f3c5f	122	{
126f3c5f	123	# this causes a different low lib to take care...
bd49aa09	124	$lib_kind = $1; $lib_kind = 'lib' if $lib_kind eq 'l';
126f3c5f	125	$lib = $_[$i+1] \|\| '';
126f3c5f	126	my $s = 2; $s = 1 if @a-$j < 2; # avoid "can not modify non-existant..."
b68b7ab1	127	splice @a, $j, $s; $j -= $s; $i++;
	128	}
	129	elsif ($_[$i] =~ /^(a\|accuracy)$/)
	130	{
	131	$a = $_[$i+1];
	132	my $s = 2; $s = 1 if @a-$j < 2; # avoid "can not modify non-existant..."
	133	splice @a, $j, $s; $j -= $s; $i++;
	134	}
	135	elsif ($_[$i] =~ /^(p\|precision)$/)
	136	{
	137	$p = $_[$i+1];
	138	my $s = 2; $s = 1 if @a-$j < 2; # avoid "can not modify non-existant..."
	139	splice @a, $j, $s; $j -= $s; $i++;
126f3c5f	140	}
	141	elsif ($_[$i] =~ /^(v\|version)$/)
	142	{
	143	$ver = 1;
	144	splice @a, $j, 1; $j --;
	145	}
	146	elsif ($_[$i] =~ /^(t\|trace)$/)
	147	{
	148	$trace = 1;
	149	splice @a, $j, 1; $j --;
	150	}
d1a15766	151	elsif ($_[$i] eq 'hex')
	152	{
	153	splice @a, $j, 1; $j --;
	154	no warnings 'redefine';
	155	*CORE::GLOBAL::hex = \&bigint::_hex_global;
	156	}
	157	elsif ($_[$i] eq 'oct')
	158	{
	159	splice @a, $j, 1; $j --;
	160	no warnings 'redefine';
	161	*CORE::GLOBAL::oct = \&bigint::_oct_global;
	162	}
126f3c5f	163	else
	164	{
	165	die ("unknown option $_[$i]");
	166	}
	167	}
	168	my $class;
	169	$_lite = 0; # using M::BI::L ?
	170	if ($trace)
	171	{
	172	require Math::BigInt::Trace; $class = 'Math::BigInt::Trace';
	173	$upgrade = 'Math::BigFloat::Trace';
126f3c5f	174	}
	175	else
	176	{
	177	# see if we can find Math::BigInt::Lite
	178	if (!defined $a && !defined $p) # rounding won't work to well
	179	{
	180	eval 'require Math::BigInt::Lite;';
	181	if ($@ eq '')
	182	{
	183	@import = ( ); # :constant in Lite, not MBI
	184	Math::BigInt::Lite->import( ':constant' );
	185	$_lite= 1; # signal okay
	186	}
	187	}
	188	require Math::BigInt if $_lite == 0; # not already loaded?
	189	$class = 'Math::BigInt'; # regardless of MBIL or not
	190	}
bd49aa09	191	push @import, $lib_kind => $lib if $lib ne '';
126f3c5f	192	# Math::BigInt::Trace or plain Math::BigInt
233f7bc0	193	$class->import(@import, upgrade => $upgrade);
126f3c5f	194
	195	require Math::BigFloat;
	196	Math::BigFloat->import( upgrade => 'Math::BigRat', ':constant' );
	197	require Math::BigRat;
b68b7ab1	198
	199	bigrat->accuracy($a) if defined $a;
	200	bigrat->precision($p) if defined $p;
126f3c5f	201	if ($ver)
	202	{
	203	print "bigrat\t\t\t v$VERSION\n";
	204	print "Math::BigInt::Lite\t v$Math::BigInt::Lite::VERSION\n" if $_lite;
	205	print "Math::BigInt\t\t v$Math::BigInt::VERSION";
	206	my $config = Math::BigInt->config();
	207	print " lib => $config->{lib} v$config->{lib_version}\n";
	208	print "Math::BigFloat\t\t v$Math::BigFloat::VERSION\n";
	209	print "Math::BigRat\t\t v$Math::BigRat::VERSION\n";
	210	exit;
	211	}
95a2d02c	212
95a2d02c	213	# Take care of octal/hexadecimal constants
d1a15766	214	overload::constant binary => sub { bigint::_binary_constant(shift) };
95a2d02c	215
4440d13a	216	# if another big* was already loaded:
	217	my ($package) = caller();
	218
	219	no strict 'refs';
	220	if (!defined *{"${package}::inf"})
	221	{
	222	$self->export_to_level(1,$self,@a); # export inf and NaN
	223	}
126f3c5f	224	}
	225
	226	1;
	227
	228	__END__
	229
	230	=head1 NAME
	231
b1f79218	232	bigrat - Transparent BigNumber/BigRational support for Perl
126f3c5f	233
	234	=head1 SYNOPSIS
	235
	236	use bigrat;
	237
4440d13a	238	print 2 + 4.5,"\n"; # BigFloat 6.5
126f3c5f	239	print 1/3 + 1/4,"\n"; # produces 7/12
126f3c5f	240
4440d13a	241	{
	242	no bigrat;
	243	print 1/3,"\n"; # 0.33333...
	244	}
	245
d1a15766	246	# Note that this will make hex() and oct() be globally overriden:
	247	use bigrat qw/hex oct/;
	248	print hex("0x1234567890123490"),"\n";
	249	print oct("01234567890123490"),"\n";
	250
126f3c5f	251	=head1 DESCRIPTION
126f3c5f	252
3c4b39be	253	All operators (including basic math operations) are overloaded. Integer and
126f3c5f	254	floating-point constants are created as proper BigInts or BigFloats,
	255	respectively.
	256
	257	Other than L<bignum>, this module upgrades to Math::BigRat, meaning that
	258	instead of 2.5 you will get 2+1/2 as output.
	259
b68b7ab1	260	=head2 Modules Used
126f3c5f	261
	262	C<bigrat> is just a thin wrapper around various modules of the Math::BigInt
	263	family. Think of it as the head of the family, who runs the shop, and orders
	264	the others to do the work.
	265
	266	The following modules are currently used by bignum:
	267
	268	Math::BigInt::Lite (for speed, and only if it is loadable)
	269	Math::BigInt
	270	Math::BigFloat
	271	Math::BigRat
	272
b68b7ab1	273	=head2 Math Library
126f3c5f	274
	275	Math with the numbers is done (by default) by a module called
	276	Math::BigInt::Calc. This is equivalent to saying:
	277
	278	use bigrat lib => 'Calc';
	279
	280	You can change this by using:
	281
bd49aa09	282	use bignum lib => 'GMP';
126f3c5f	283
	284	The following would first try to find Math::BigInt::Foo, then
	285	Math::BigInt::Bar, and when this also fails, revert to Math::BigInt::Calc:
	286
	287	use bigrat lib => 'Foo,Math::BigInt::Bar';
	288
bd49aa09	289	Using C<lib> warns if none of the specified libraries can be found and
	290	L<Math::BigInt> did fall back to one of the default libraries.
	291	To supress this warning, use C<try> instead:
	292
	293	use bignum try => 'GMP';
	294
	295	If you want the code to die instead of falling back, use C<only> instead:
	296
	297	use bignum only => 'GMP';
	298
126f3c5f	299	Please see respective module documentation for further details.
126f3c5f	300
b68b7ab1	301	=head2 Sign
126f3c5f	302
b68b7ab1	303	The sign is either '+', '-', 'NaN', '+inf' or '-inf'.
126f3c5f	304
	305	A sign of 'NaN' is used to represent the result when input arguments are not
	306	numbers or as a result of 0/0. '+inf' and '-inf' represent plus respectively
	307	minus infinity. You will get '+inf' when dividing a positive number by 0, and
	308	'-inf' when dividing any negative number by 0.
	309
b68b7ab1	310	=head2 Methods
126f3c5f	311
	312	Since all numbers are not objects, you can use all functions that are part of
	313	the BigInt or BigFloat API. It is wise to use only the bxxx() notation, and not
	314	the fxxx() notation, though. This makes you independed on the fact that the
	315	underlying object might morph into a different class than BigFloat.
	316
95a2d02c	317	=over 2
	318
	319	=item inf()
	320
	321	A shortcut to return Math::BigInt->binf(). Useful because Perl does not always
	322	handle bareword C<inf> properly.
	323
	324	=item NaN()
	325
	326	A shortcut to return Math::BigInt->bnan(). Useful because Perl does not always
	327	handle bareword C<NaN> properly.
	328
	329	=item upgrade()
	330
	331	Return the class that numbers are upgraded to, is in fact returning
	332	C<$Math::BigInt::upgrade>.
	333
4440d13a	334	=item in_effect()
	335
	336	use bigrat;
	337
	338	print "in effect\n" if bigrat::in_effect; # true
	339	{
	340	no bigrat;
	341	print "in effect\n" if bigrat::in_effect; # false
	342	}
	343
	344	Returns true or false if C<bigrat> is in effect in the current scope.
	345
	346	This method only works on Perl v5.9.4 or later.
	347
95a2d02c	348	=back
	349
	350	=head2 MATH LIBRARY
	351
	352	Math with the numbers is done (by default) by a module called
	353
	354	=head2 Cavaet
990fb837	355
	356	But a warning is in order. When using the following to make a copy of a number,
	357	only a shallow copy will be made.
	358
	359	$x = 9; $y = $x;
	360	$x = $y = 7;
	361
b68b7ab1	362	If you want to make a real copy, use the following:
	363
	364	$y = $x->copy();
	365
990fb837	366	Using the copy or the original with overloaded math is okay, e.g. the
	367	following work:
	368
	369	$x = 9; $y = $x;
	370	print $x + 1, " ", $y,"\n"; # prints 10 9
	371
	372	but calling any method that modifies the number directly will result in
3c4b39be	373	B<both> the original and the copy being destroyed:
990fb837	374
	375	$x = 9; $y = $x;
	376	print $x->badd(1), " ", $y,"\n"; # prints 10 10
	377
	378	$x = 9; $y = $x;
	379	print $x->binc(1), " ", $y,"\n"; # prints 10 10
	380
	381	$x = 9; $y = $x;
	382	print $x->bmul(2), " ", $y,"\n"; # prints 18 18
	383
	384	Using methods that do not modify, but testthe contents works:
	385
	386	$x = 9; $y = $x;
	387	$z = 9 if $x->is_zero(); # works fine
	388
	389	See the documentation about the copy constructor and C<=> in overload, as
	390	well as the documentation in BigInt for further details.
	391
b68b7ab1	392	=head2 Options
	393
	394	bignum recognizes some options that can be passed while loading it via use.
	395	The options can (currently) be either a single letter form, or the long form.
	396	The following options exist:
	397
	398	=over 2
	399
	400	=item a or accuracy
	401
	402	This sets the accuracy for all math operations. The argument must be greater
	403	than or equal to zero. See Math::BigInt's bround() function for details.
	404
	405	perl -Mbigrat=a,50 -le 'print sqrt(20)'
	406
95a2d02c	407	Note that setting precision and accurary at the same time is not possible.
95a2d02c	408
b68b7ab1	409	=item p or precision
	410
	411	This sets the precision for all math operations. The argument can be any
	412	integer. Negative values mean a fixed number of digits after the dot, while
	413	a positive value rounds to this digit left from the dot. 0 or 1 mean round to
	414	integer. See Math::BigInt's bfround() function for details.
	415
	416	perl -Mbigrat=p,-50 -le 'print sqrt(20)'
	417
95a2d02c	418	Note that setting precision and accurary at the same time is not possible.
95a2d02c	419
b68b7ab1	420	=item t or trace
	421
	422	This enables a trace mode and is primarily for debugging bignum or
	423	Math::BigInt/Math::BigFloat.
	424
	425	=item l or lib
	426
	427	Load a different math lib, see L<MATH LIBRARY>.
	428
	429	perl -Mbigrat=l,GMP -e 'print 2 ** 512'
	430
	431	Currently there is no way to specify more than one library on the command
95a2d02c	432	line. This means the following does not work:
	433
	434	perl -Mbignum=l,GMP,Pari -e 'print 2 ** 512'
	435
	436	This will be hopefully fixed soon ;)
b68b7ab1	437
d1a15766	438	=item hex
	439
	440	Override the build-in hex() method with a version that can handle big
	441	integers. Note that under Perl v5.9.4 or ealier, this will be global
	442	and cannot be disabled with "no bigint;".
	443
	444	=item oct
	445
	446	Override the build-in oct() method with a version that can handle big
	447	integers. Note that under Perl v5.9.4 or ealier, this will be global
	448	and cannot be disabled with "no bigint;".
	449
b68b7ab1	450	=item v or version
	451
	452	This prints out the name and version of all modules used and then exits.
	453
	454	perl -Mbigrat=v
	455
95a2d02c	456	=back
95a2d02c	457
d1a15766	458	=head1 CAVAETS
	459
	460	=over 2
	461
	462	=item in_effect()
	463
	464	This method only works on Perl v5.9.4 or later.
	465
	466	=item hex()/oct()
	467
	468	C<bigint> overrides these routines with versions that can also handle
	469	big integer values. Under Perl prior to version v5.9.4, however, this
	470	will not happen unless you specifically ask for it with the two
	471	import tags "hex" and "oct" - and then it will be global and cannot be
	472	disabled inside a scope with "no bigint":
	473
	474	use bigint qw/hex oct/;
	475
	476	print hex("0x1234567890123456");
	477	{
	478	no bigint;
	479	print hex("0x1234567890123456");
	480	}
	481
	482	The second call to hex() will warn about a non-portable constant.
	483
	484	Compare this to:
	485
	486	use bigint;
	487
	488	# will warn only under Perl older than v5.9.4
	489	print hex("0x1234567890123456");
	490
	491	=back
	492
126f3c5f	493	=head1 EXAMPLES
	494
	495	perl -Mbigrat -le 'print sqrt(33)'
	496	perl -Mbigrat -le 'print 2*255'
	497	perl -Mbigrat -le 'print 4.5+2*255'
	498	perl -Mbigrat -le 'print 3/7 + 5/7 + 8/3'
	499	perl -Mbigrat -le 'print 12->is_odd()';
95a2d02c	500	perl -Mbignum=l,GMP -le 'print 7 ** 7777'
126f3c5f	501
	502	=head1 LICENSE
	503
	504	This program is free software; you may redistribute it and/or modify it under
	505	the same terms as Perl itself.
	506
	507	=head1 SEE ALSO
	508
	509	Especially L<bignum>.
	510
	511	L<Math::BigFloat>, L<Math::BigInt>, L<Math::BigRat> and L<Math::Big> as well
	512	as L<Math::BigInt::BitVect>, L<Math::BigInt::Pari> and L<Math::BigInt::GMP>.
	513
	514	=head1 AUTHORS
	515
95a2d02c	516	(C) by Tels L<http://bloodgate.com/> in early 2002 - 2007.
126f3c5f	517
126f3c5f	518	=cut