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

package bignum;
require 5.005;

$VERSION = '0.17';
use Exporter;
@EXPORT_OK 	= qw( ); 
@EXPORT 	= qw( inf NaN ); 
@ISA 		= qw( Exporter );

use strict;

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

# 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 $name)
      {
      *{"bignum::$name"} = sub 
        {
        my $self = shift;
        no strict 'refs';
        if (defined $_[0])
          {
          Math::BigInt->$name($_[0]);
          return Math::BigFloat->$name($_[0]);
          }
        return Math::BigInt->$name();
        };
      return &$name;
      }
    }
 
  # delayed load of Carp and avoid recursion
  require Carp;
  Carp::croak ("Can't call bignum\-\>$name, not a valid method");
  }

sub upgrade
  {
  my $self = shift;
  no strict 'refs';
#  if (defined $_[0])
#    {
#    $Math::BigInt::upgrade = $_[0];
#    $Math::BigFloat::upgrade = $_[0];
#    }
  return $Math::BigInt::upgrade;
  }

sub import 
  {
  my $self = shift;

  # some defaults
  my $lib = '';
  my $upgrade = 'Math::BigFloat';
  my $downgrade = 'Math::BigInt';

  my @import = ( ':constant' );				# drive it w/ constant
  my @a = @_; my $l = scalar @_; my $j = 0;
  my ($ver,$trace);					# version? trace?
  my ($a,$p);						# accuracy, precision
  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; $i++;
      }
    elsif ($_[$i] eq 'downgrade')
      {
      # this causes downgrading
      $downgrade = $_[$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; $i++;
      }
    elsif ($_[$i] =~ /^(l|lib)$/)
      {
      # this causes a different low lib to take care...
      $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 --;
      }
    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' => $lib if $lib ne ''; 
  # Math::BigInt::Trace or plain Math::BigInt
  $class->import(@import, upgrade => $upgrade);

  if ($trace)
    {
    require Math::BigFloat::Trace; $class = 'Math::BigFloat::Trace';
    $downgrade = 'Math::BigInt::Trace';	
    }
  else
    {
    require Math::BigFloat; $class = 'Math::BigFloat';
    }
  $class->import(':constant','downgrade',$downgrade);

  bignum->accuracy($a) if defined $a;
  bignum->precision($p) if defined $p;
  if ($ver)
    {
    print "bignum\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";
    exit;
    }
  $self->export_to_level(1,$self,@a);		# export inf and NaN
  }

sub inf () { Math::BigInt->binf(); }
sub NaN () { Math::BigInt->bnan(); }

1;

__END__

=head1 NAME

bignum - Transparent BigNumber support for Perl

=head1 SYNOPSIS

  use bignum;

  $x = 2 + 4.5,"\n";			# BigFloat 6.5
  print 2 ** 512 * 0.1,"\n";		# really is what you think it is
  print inf * inf,"\n";			# prints inf
  print NaN * 3,"\n";			# prints NaN

=head1 DESCRIPTION

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

If you do 

        use bignum;

at the top of your script, Math::BigFloat and Math::BigInt will be loaded
and any constant number will be converted to an object (Math::BigFloat for
floats like 3.1415 and Math::BigInt for integers like 1234).

So, the following line:

        $x = 1234;

creates actually a Math::BigInt and stores a reference to in $x.
This happens transparently and behind your back, so to speak.

You can see this with the following:

        perl -Mbignum -le 'print ref(1234)'

Don't worry if it says Math::BigInt::Lite, bignum and friends will use Lite
if it is installed since it is faster for some operations. It will be
automatically upgraded to BigInt whenever necessary:

        perl -Mbignum -le 'print ref(2**255)'

This also means it is a bad idea to check for some specific package, since
the actual contents of $x might be something unexpected. Due to the
transparent way of bignum C<ref()> should not be necessary, anyway.

Since Math::BigInt and BigFloat also overload the normal math operations,
the following line will still work:

        perl -Mbignum -le 'print ref(1234+1234)'

Since numbers are actually objects, you can call all the usual methods from
BigInt/BigFloat on them. This even works to some extent on expressions:

        perl -Mbignum -le '$x = 1234; print $x->bdec()'
        perl -Mbignum -le 'print 1234->binc();'
        perl -Mbignum -le 'print 1234->binc->badd(6);'
        perl -Mbignum -le 'print +(1234)->binc()'

(Note that print doesn't do what you expect if the expression starts with
'(' hence the C<+>)

You can even chain the operations together as usual:

        perl -Mbignum -le 'print 1234->binc->badd(6);'
        1241

Under bignum (or bigint or bigrat), Perl will "upgrade" the numbers
appropriately. This means that:

        perl -Mbignum -le 'print 1234+4.5'
        1238.5

will work correctly. These mixed cases don't do always work when using
Math::BigInt or Math::BigFloat alone, or at least not in the way normal Perl
scalars work. 

If you do want to work with large integers like under C<use integer;>, try
C<use bigint;>:

        perl -Mbigint -le 'print 1234.5+4.5'
        1238

There is also C<use bigrat;> which gives you big rationals:

        perl -Mbigrat -le 'print 1234+4.1'
        12381/10

The entire upgrading/downgrading is still experimental and might not work
as you expect or may even have bugs.

You might get errors like this:

        Can't use an undefined value as an ARRAY reference at
        /usr/local/lib/perl5/5.8.0/Math/BigInt/Calc.pm line 864

This means somewhere a routine got a BigFloat/Lite but expected a BigInt (or
vice versa) and the upgrade/downgrad path was missing. This is a bug, please
report it so that we can fix it.

You might consider using just Math::BigInt or Math::BigFloat, since they
allow you finer control over what get's done in which module/space. For
instance, simple loop counters will be Math::BigInts under C<use bignum;> and
this is slower than keeping them as Perl scalars:

        perl -Mbignum -le 'for ($i = 0; $i < 10; $i++) { print ref($i); }'

Please note the following does not work as expected (prints nothing), since
overloading of '..' is not yet possible in Perl (as of v5.8.0):

        perl -Mbignum -le 'for (1..2) { print ref($_); }'

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

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

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

Currently there is no way to specify more than one library on the command
line. This will be hopefully fixed soon ;)

=item v or version

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

	perl -Mbignum=v

=head2 Methods

Beside import() and AUTOLOAD() there are only a few other methods.

Since all numbers are now 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 it possible that the underlying object
might morph into a different class than BigFloat.

=head2 Caveat

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.

=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>.

=back

=head2 MATH LIBRARY

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

	use bignum lib => 'Calc';

You can change this by using:

	use bignum lib => 'BitVect';

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 bignum lib => 'Foo,Math::BigInt::Bar';

Please see respective module documentation for further details.

=head2 INTERNAL FORMAT

The numbers are stored as objects, and their internals might change at anytime,
especially between math operations. The objects also might belong to different
classes, like Math::BigInt, or Math::BigFLoat. Mixing them together, even
with normal scalars is not extraordinary, but normal and expected.

You should not depend on the internal format, all accesses must go through
accessor methods. E.g. looking at $x->{sign} is not a bright idea since there
is no guaranty that the object in question has such a hashkey, nor is a hash
underneath at all.

=head2 SIGN

The sign is either '+', '-', 'NaN', '+inf' or '-inf' and stored seperately.
You can access it with the sign() method.

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.

=head1 MODULES USED

C<bignum> 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

=head1 EXAMPLES

Some cool command line examples to impress the Python crowd ;)
 
	perl -Mbignum -le 'print sqrt(33)'
	perl -Mbignum -le 'print 2*255'
	perl -Mbignum -le 'print 4.5+2*255'
	perl -Mbignum -le 'print 3/7 + 5/7 + 8/3'
	perl -Mbignum -le 'print 123->is_odd()'
	perl -Mbignum -le 'print log(2)'
	perl -Mbignum -le 'print 2 ** 0.5'
	perl -Mbignum=a,65 -le 'print 2 ** 0.2'

=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<bigrat> as in C<perl -Mbigrat -le 'print 1/3+1/4'>.

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, 2003.

=cut
Commit	Line	Data
126f3c5f	1	package bignum;
	2	require 5.005;
	3
233f7bc0	4	$VERSION = '0.17';
126f3c5f	5	use Exporter;
b4bc5691	6	@EXPORT_OK = qw( );
	7	@EXPORT = qw( inf NaN );
	8	@ISA = qw( Exporter );
126f3c5f	9
	10	use strict;
	11
	12	##############################################################################
	13
	14	# These are all alike, and thus faked by AUTOLOAD
	15
	16	my @faked = qw/round_mode accuracy precision div_scale/;
	17	use vars qw/$VERSION $AUTOLOAD $_lite/; # _lite for testsuite
	18
	19	sub AUTOLOAD
	20	{
	21	my $name = $AUTOLOAD;
	22
	23	$name =~ s/.*:://; # split package
	24	no strict 'refs';
	25	foreach my $n (@faked)
	26	{
	27	if ($n eq $name)
	28	{
	29	*{"bignum::$name"} = sub
	30	{
	31	my $self = shift;
	32	no strict 'refs';
	33	if (defined $_[0])
	34	{
	35	Math::BigInt->$name($_[0]);
990fb837	36	return Math::BigFloat->$name($_[0]);
126f3c5f	37	}
	38	return Math::BigInt->$name();
	39	};
	40	return &$name;
	41	}
	42	}
	43
	44	# delayed load of Carp and avoid recursion
	45	require Carp;
	46	Carp::croak ("Can't call bignum\-\>$name, not a valid method");
	47	}
	48
	49	sub upgrade
	50	{
	51	my $self = shift;
	52	no strict 'refs';
	53	# if (defined $_[0])
	54	# {
	55	# $Math::BigInt::upgrade = $_[0];
	56	# $Math::BigFloat::upgrade = $_[0];
	57	# }
	58	return $Math::BigInt::upgrade;
	59	}
	60
	61	sub import
	62	{
	63	my $self = shift;
	64
	65	# some defaults
233f7bc0	66	my $lib = '';
126f3c5f	67	my $upgrade = 'Math::BigFloat';
	68	my $downgrade = 'Math::BigInt';
	69
	70	my @import = ( ':constant' ); # drive it w/ constant
	71	my @a = @_; my $l = scalar @_; my $j = 0;
	72	my ($ver,$trace); # version? trace?
	73	my ($a,$p); # accuracy, precision
	74	for ( my $i = 0; $i < $l ; $i++,$j++ )
	75	{
	76	if ($_[$i] eq 'upgrade')
	77	{
	78	# this causes upgrading
	79	$upgrade = $_[$i+1]; # or undef to disable
	80	my $s = 2; $s = 1 if @a-$j < 2; # avoid "can not modify non-existant..."
	81	splice @a, $j, $s; $j -= $s; $i++;
	82	}
	83	elsif ($_[$i] eq 'downgrade')
	84	{
	85	# this causes downgrading
	86	$downgrade = $_[$i+1]; # or undef to disable
	87	my $s = 2; $s = 1 if @a-$j < 2; # avoid "can not modify non-existant..."
	88	splice @a, $j, $s; $j -= $s; $i++;
	89	}
	90	elsif ($_[$i] =~ /^(l\|lib)$/)
	91	{
	92	# this causes a different low lib to take care...
	93	$lib = $_[$i+1] \|\| '';
	94	my $s = 2; $s = 1 if @a-$j < 2; # avoid "can not modify non-existant..."
	95	splice @a, $j, $s; $j -= $s; $i++;
	96	}
	97	elsif ($_[$i] =~ /^(a\|accuracy)$/)
	98	{
	99	$a = $_[$i+1];
	100	my $s = 2; $s = 1 if @a-$j < 2; # avoid "can not modify non-existant..."
	101	splice @a, $j, $s; $j -= $s; $i++;
	102	}
	103	elsif ($_[$i] =~ /^(p\|precision)$/)
	104	{
	105	$p = $_[$i+1];
	106	my $s = 2; $s = 1 if @a-$j < 2; # avoid "can not modify non-existant..."
	107	splice @a, $j, $s; $j -= $s; $i++;
	108	}
	109	elsif ($_[$i] =~ /^(v\|version)$/)
	110	{
	111	$ver = 1;
	112	splice @a, $j, 1; $j --;
	113	}
	114	elsif ($_[$i] =~ /^(t\|trace)$/)
	115	{
	116	$trace = 1;
	117	splice @a, $j, 1; $j --;
	118	}
	119	else { die "unknown option $_[$i]"; }
	120	}
	121	my $class;
	122	$_lite = 0; # using M::BI::L ?
	123	if ($trace)
	124	{
	125	require Math::BigInt::Trace; $class = 'Math::BigInt::Trace';
	126	$upgrade = 'Math::BigFloat::Trace';
126f3c5f	127	}
	128	else
	129	{
	130	# see if we can find Math::BigInt::Lite
	131	if (!defined $a && !defined $p) # rounding won't work to well
	132	{
	133	eval 'require Math::BigInt::Lite;';
	134	if ($@ eq '')
	135	{
	136	@import = ( ); # :constant in Lite, not MBI
	137	Math::BigInt::Lite->import( ':constant' );
	138	$_lite= 1; # signal okay
	139	}
	140	}
	141	require Math::BigInt if $_lite == 0; # not already loaded?
	142	$class = 'Math::BigInt'; # regardless of MBIL or not
233f7bc0	143	}
233f7bc0	144	push @import, 'lib' => $lib if $lib ne '';
126f3c5f	145	# Math::BigInt::Trace or plain Math::BigInt
233f7bc0	146	$class->import(@import, upgrade => $upgrade);
126f3c5f	147
	148	if ($trace)
	149	{
	150	require Math::BigFloat::Trace; $class = 'Math::BigFloat::Trace';
	151	$downgrade = 'Math::BigInt::Trace';
126f3c5f	152	}
	153	else
	154	{
	155	require Math::BigFloat; $class = 'Math::BigFloat';
	156	}
	157	$class->import(':constant','downgrade',$downgrade);
	158
	159	bignum->accuracy($a) if defined $a;
	160	bignum->precision($p) if defined $p;
	161	if ($ver)
	162	{
	163	print "bignum\t\t\t v$VERSION\n";
	164	print "Math::BigInt::Lite\t v$Math::BigInt::Lite::VERSION\n" if $_lite;
	165	print "Math::BigInt\t\t v$Math::BigInt::VERSION";
	166	my $config = Math::BigInt->config();
	167	print " lib => $config->{lib} v$config->{lib_version}\n";
	168	print "Math::BigFloat\t\t v$Math::BigFloat::VERSION\n";
	169	exit;
	170	}
b4bc5691	171	$self->export_to_level(1,$self,@a); # export inf and NaN
126f3c5f	172	}
126f3c5f	173
b4bc5691	174	sub inf () { Math::BigInt->binf(); }
	175	sub NaN () { Math::BigInt->bnan(); }
	176
126f3c5f	177	1;
	178
	179	__END__
	180
	181	=head1 NAME
	182
	183	bignum - Transparent BigNumber support for Perl
	184
	185	=head1 SYNOPSIS
	186
	187	use bignum;
	188
	189	$x = 2 + 4.5,"\n"; # BigFloat 6.5
b4bc5691	190	print 2 ** 512 * 0.1,"\n"; # really is what you think it is
	191	print inf * inf,"\n"; # prints inf
	192	print NaN * 3,"\n"; # prints NaN
126f3c5f	193
	194	=head1 DESCRIPTION
	195
	196	All operators (including basic math operations) are overloaded. Integer and
	197	floating-point constants are created as proper BigInts or BigFloats,
	198	respectively.
	199
24716a00	200	If you do
	201
	202	use bignum;
	203
	204	at the top of your script, Math::BigFloat and Math::BigInt will be loaded
	205	and any constant number will be converted to an object (Math::BigFloat for
	206	floats like 3.1415 and Math::BigInt for integers like 1234).
	207
	208	So, the following line:
	209
	210	$x = 1234;
	211
	212	creates actually a Math::BigInt and stores a reference to in $x.
	213	This happens transparently and behind your back, so to speak.
	214
	215	You can see this with the following:
	216
	217	perl -Mbignum -le 'print ref(1234)'
	218
	219	Don't worry if it says Math::BigInt::Lite, bignum and friends will use Lite
	220	if it is installed since it is faster for some operations. It will be
3c4b39be	221	automatically upgraded to BigInt whenever necessary:
24716a00	222
	223	perl -Mbignum -le 'print ref(2**255)'
	224
	225	This also means it is a bad idea to check for some specific package, since
	226	the actual contents of $x might be something unexpected. Due to the
3c4b39be	227	transparent way of bignum C<ref()> should not be necessary, anyway.
24716a00	228
	229	Since Math::BigInt and BigFloat also overload the normal math operations,
	230	the following line will still work:
	231
	232	perl -Mbignum -le 'print ref(1234+1234)'
	233
	234	Since numbers are actually objects, you can call all the usual methods from
	235	BigInt/BigFloat on them. This even works to some extent on expressions:
	236
	237	perl -Mbignum -le '$x = 1234; print $x->bdec()'
	238	perl -Mbignum -le 'print 1234->binc();'
	239	perl -Mbignum -le 'print 1234->binc->badd(6);'
	240	perl -Mbignum -le 'print +(1234)->binc()'
	241
	242	(Note that print doesn't do what you expect if the expression starts with
	243	'(' hence the C<+>)
	244
	245	You can even chain the operations together as usual:
	246
	247	perl -Mbignum -le 'print 1234->binc->badd(6);'
	248	1241
	249
	250	Under bignum (or bigint or bigrat), Perl will "upgrade" the numbers
	251	appropriately. This means that:
	252
	253	perl -Mbignum -le 'print 1234+4.5'
	254	1238.5
	255
	256	will work correctly. These mixed cases don't do always work when using
	257	Math::BigInt or Math::BigFloat alone, or at least not in the way normal Perl
	258	scalars work.
	259
	260	If you do want to work with large integers like under C<use integer;>, try
	261	C<use bigint;>:
	262
	263	perl -Mbigint -le 'print 1234.5+4.5'
	264	1238
	265
	266	There is also C<use bigrat;> which gives you big rationals:
	267
	268	perl -Mbigrat -le 'print 1234+4.1'
	269	12381/10
	270
	271	The entire upgrading/downgrading is still experimental and might not work
	272	as you expect or may even have bugs.
	273
	274	You might get errors like this:
	275
	276	Can't use an undefined value as an ARRAY reference at
	277	/usr/local/lib/perl5/5.8.0/Math/BigInt/Calc.pm line 864
	278
	279	This means somewhere a routine got a BigFloat/Lite but expected a BigInt (or
	280	vice versa) and the upgrade/downgrad path was missing. This is a bug, please
	281	report it so that we can fix it.
	282
	283	You might consider using just Math::BigInt or Math::BigFloat, since they
	284	allow you finer control over what get's done in which module/space. For
	285	instance, simple loop counters will be Math::BigInts under C<use bignum;> and
	286	this is slower than keeping them as Perl scalars:
	287
	288	perl -Mbignum -le 'for ($i = 0; $i < 10; $i++) { print ref($i); }'
	289
	290	Please note the following does not work as expected (prints nothing), since
	291	overloading of '..' is not yet possible in Perl (as of v5.8.0):
292
293	perl -Mbignum -le 'for (1..2) { print ref($_); }'
294
b68b7ab1	295	=head2 Options
126f3c5f	296
	297	bignum recognizes some options that can be passed while loading it via use.
	298	The options can (currently) be either a single letter form, or the long form.
	299	The following options exist:
	300
	301	=over 2
	302
	303	=item a or accuracy
	304
	305	This sets the accuracy for all math operations. The argument must be greater
	306	than or equal to zero. See Math::BigInt's bround() function for details.
	307
	308	perl -Mbignum=a,50 -le 'print sqrt(20)'
	309
	310	=item p or precision
	311
	312	This sets the precision for all math operations. The argument can be any
	313	integer. Negative values mean a fixed number of digits after the dot, while
	314	a positive value rounds to this digit left from the dot. 0 or 1 mean round to
	315	integer. See Math::BigInt's bfround() function for details.
	316
	317	perl -Mbignum=p,-50 -le 'print sqrt(20)'
	318
	319	=item t or trace
	320
	321	This enables a trace mode and is primarily for debugging bignum or
	322	Math::BigInt/Math::BigFloat.
	323
	324	=item l or lib
	325
	326	Load a different math lib, see L<MATH LIBRARY>.
	327
	328	perl -Mbignum=l,GMP -e 'print 2 ** 512'
	329
	330	Currently there is no way to specify more than one library on the command
	331	line. This will be hopefully fixed soon ;)
	332
	333	=item v or version
	334
	335	This prints out the name and version of all modules used and then exits.
	336
b68b7ab1	337	perl -Mbignum=v
126f3c5f	338
b68b7ab1	339	=head2 Methods
b4bc5691	340
	341	Beside import() and AUTOLOAD() there are only a few other methods.
	342
24716a00	343	Since all numbers are now objects, you can use all functions that are part of
	344	the BigInt or BigFloat API. It is wise to use only the bxxx() notation, and not
	345	the fxxx() notation, though. This makes it possible that the underlying object
	346	might morph into a different class than BigFloat.
	347
b68b7ab1	348	=head2 Caveat
990fb837	349
	350	But a warning is in order. When using the following to make a copy of a number,
	351	only a shallow copy will be made.
	352
	353	$x = 9; $y = $x;
	354	$x = $y = 7;
	355
b68b7ab1	356	If you want to make a real copy, use the following:
	357
	358	$y = $x->copy();
	359
990fb837	360	Using the copy or the original with overloaded math is okay, e.g. the
	361	following work:
	362
	363	$x = 9; $y = $x;
	364	print $x + 1, " ", $y,"\n"; # prints 10 9
	365
	366	but calling any method that modifies the number directly will result in
3c4b39be	367	B<both> the original and the copy being destroyed:
990fb837	368
	369	$x = 9; $y = $x;
	370	print $x->badd(1), " ", $y,"\n"; # prints 10 10
	371
	372	$x = 9; $y = $x;
	373	print $x->binc(1), " ", $y,"\n"; # prints 10 10
	374
	375	$x = 9; $y = $x;
	376	print $x->bmul(2), " ", $y,"\n"; # prints 18 18
	377
	378	Using methods that do not modify, but testthe contents works:
	379
	380	$x = 9; $y = $x;
	381	$z = 9 if $x->is_zero(); # works fine
	382
	383	See the documentation about the copy constructor and C<=> in overload, as
	384	well as the documentation in BigInt for further details.
	385
b4bc5691	386	=over 2
	387
	388	=item inf()
	389
3c4b39be	390	A shortcut to return Math::BigInt->binf(). Useful because Perl does not always
b4bc5691	391	handle bareword C<inf> properly.
	392
	393	=item NaN()
	394
3c4b39be	395	A shortcut to return Math::BigInt->bnan(). Useful because Perl does not always
b4bc5691	396	handle bareword C<NaN> properly.
	397
	398	=item upgrade()
	399
	400	Return the class that numbers are upgraded to, is in fact returning
	401	C<$Math::BigInt::upgrade>.
	402
	403	=back
	404
126f3c5f	405	=head2 MATH LIBRARY
	406
	407	Math with the numbers is done (by default) by a module called
	408	Math::BigInt::Calc. This is equivalent to saying:
	409
	410	use bignum lib => 'Calc';
	411
	412	You can change this by using:
	413
	414	use bignum lib => 'BitVect';
	415
	416	The following would first try to find Math::BigInt::Foo, then
	417	Math::BigInt::Bar, and when this also fails, revert to Math::BigInt::Calc:
	418
	419	use bignum lib => 'Foo,Math::BigInt::Bar';
	420
	421	Please see respective module documentation for further details.
	422
	423	=head2 INTERNAL FORMAT
	424
	425	The numbers are stored as objects, and their internals might change at anytime,
	426	especially between math operations. The objects also might belong to different
	427	classes, like Math::BigInt, or Math::BigFLoat. Mixing them together, even
	428	with normal scalars is not extraordinary, but normal and expected.
	429
	430	You should not depend on the internal format, all accesses must go through
	431	accessor methods. E.g. looking at $x->{sign} is not a bright idea since there
	432	is no guaranty that the object in question has such a hashkey, nor is a hash
	433	underneath at all.
	434
	435	=head2 SIGN
	436
	437	The sign is either '+', '-', 'NaN', '+inf' or '-inf' and stored seperately.
	438	You can access it with the sign() method.
	439
	440	A sign of 'NaN' is used to represent the result when input arguments are not
	441	numbers or as a result of 0/0. '+inf' and '-inf' represent plus respectively
	442	minus infinity. You will get '+inf' when dividing a positive number by 0, and
	443	'-inf' when dividing any negative number by 0.
	444
126f3c5f	445	=head1 MODULES USED
	446
	447	C<bignum> is just a thin wrapper around various modules of the Math::BigInt
	448	family. Think of it as the head of the family, who runs the shop, and orders
	449	the others to do the work.
	450
	451	The following modules are currently used by bignum:
	452
	453	Math::BigInt::Lite (for speed, and only if it is loadable)
	454	Math::BigInt
	455	Math::BigFloat
	456
	457	=head1 EXAMPLES
	458
	459	Some cool command line examples to impress the Python crowd ;)
	460
	461	perl -Mbignum -le 'print sqrt(33)'
	462	perl -Mbignum -le 'print 2*255'
	463	perl -Mbignum -le 'print 4.5+2*255'
	464	perl -Mbignum -le 'print 3/7 + 5/7 + 8/3'
	465	perl -Mbignum -le 'print 123->is_odd()'
	466	perl -Mbignum -le 'print log(2)'
	467	perl -Mbignum -le 'print 2 ** 0.5'
	468	perl -Mbignum=a,65 -le 'print 2 ** 0.2'
	469
	470	=head1 LICENSE
	471
	472	This program is free software; you may redistribute it and/or modify it under
	473	the same terms as Perl itself.
	474
	475	=head1 SEE ALSO
	476
	477	Especially L<bigrat> as in C<perl -Mbigrat -le 'print 1/3+1/4'>.
	478
	479	L<Math::BigFloat>, L<Math::BigInt>, L<Math::BigRat> and L<Math::Big> as well
	480	as L<Math::BigInt::BitVect>, L<Math::BigInt::Pari> and L<Math::BigInt::GMP>.
	481
	482	=head1 AUTHORS
	483
27e7b8bb	484	(C) by Tels L<http://bloodgate.com/> in early 2002, 2003.
126f3c5f	485
126f3c5f	486	=cut