perl/lib/bigint.pm

package bigint;
require 5.005;

$VERSION = '0.07';
use Exporter;
@ISA            = qw( Exporter );
@EXPORT_OK      = qw( ); 
@EXPORT         = qw( inf NaN ); 

use strict;
use overload;

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

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

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

sub _constant
  {
  # this takes a floating point constant string and returns it truncated to
  # integer. For instance, '4.5' => '4', '1.234e2' => '123' etc
  my $float = shift;

  # some simple cases first
  return $float if ($float =~ /^[+-]?[0-9]+$/);         # '+123','-1','0' etc
  return $float 
    if ($float =~ /^[+-]?[0-9]+\.?[eE]\+?[0-9]+$/);     # 123e2, 123.e+2
  return '0' if ($float =~ /^[+-]?[0]*\.[0-9]+$/);      # .2, 0.2, -.1
  if ($float =~ /^[+-]?[0-9]+\.[0-9]*$/)                # 1., 1.23, -1.2 etc
    {
    $float =~ s/\..*//;
    return $float;
    }
  my ($mis,$miv,$mfv,$es,$ev) = Math::BigInt::_split($float);
  return $float if !defined $mis;       # doesn't look like a number to me
  my $ec = int($$ev);
  my $sign = $$mis; $sign = '' if $sign eq '+';
  if ($$es eq '-')
    {
    # ignore fraction part entirely
    if ($ec >= length($$miv))                   # 123.23E-4
      {
      return '0';
      }
    return $sign . substr ($$miv,0,length($$miv)-$ec);  # 1234.45E-2 = 12
    }
  # xE+y
  if ($ec >= length($$mfv))
    {
    $ec -= length($$mfv);                       
    return $sign.$$miv.$$mfv if $ec == 0;       # 123.45E+2 => 12345
    return $sign.$$miv.$$mfv.'E'.$ec;           # 123.45e+3 => 12345e1
    }
  $mfv = substr($$mfv,0,$ec);
  return $sign.$$miv.$mfv;                      # 123.45e+1 => 1234
  }

sub import 
  {
  my $self = shift;

  # some defaults
  my $lib = '';

  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] =~ /^(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';
    }
  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);

  bigint->accuracy($a) if defined $a;
  bigint->precision($p) if defined $p;
  if ($ver)
    {
    print "bigint\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";
    exit;
    }
  # we take care of floating point constants, since BigFloat isn't available
  # and BigInt doesn't like them:
  overload::constant float => sub { Math::BigInt->new( _constant(shift) ); };

  $self->export_to_level(1,$self,@a);           # export inf and NaN
  }

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

1;

__END__

=head1 NAME

bigint - Transparent BigInteger support for Perl

=head1 SYNOPSIS

  use bigint;

  $x = 2 + 4.5,"\n";                    # BigInt 6
  print 2 ** 512,"\n";                  # really is what you think it is
  print inf + 42,"\n";                  # inf
  print NaN * 7,"\n";                   # NaN

=head1 DESCRIPTION

All operators (including basic math operations) are overloaded. Integer
constants are created as proper BigInts.

Floating point constants are truncated to integer. All results are also
truncated.

=head2 Options

bigint 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 -Mbigint=a,2 -le 'print 12345+1'

=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, and
are <B>ignored</B> since all operations happen in integer space.
A positive value rounds to this digit left from the dot. 0 or 1 mean round to
integer and are ignore like negative values.

See Math::BigInt's bfround() function for details.

        perl -Mbignum=p,5 -le 'print 123456789+123'

=item t or trace

This enables a trace mode and is primarily for debugging bigint or
Math::BigInt.

=item l or lib

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

        perl -Mbigint=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 -Mbigint=v

=head2 Math Library

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

        use bigint lib => 'Calc';

You can change this by using:

        use bigint 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 bigint 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::BigInt::Lite. 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 good idea since there
is no guaranty that the object in question has such a hash key, nor is a hash
underneath at all.

=head2 Sign

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

=head2 Methods

Since all numbers are now objects, you can use all functions that are part of
the BigInt API. You can only use the bxxx() notation, and not the fxxx()
notation, though. 

=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;

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 beeing 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.

=head1 MODULES USED

C<bigint> 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 bigint:

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

=head1 EXAMPLES

Some cool command line examples to impress the Python crowd ;) You might want
to compare them to the results under -Mbignum or -Mbigrat:
 
        perl -Mbigint -le 'print sqrt(33)'
        perl -Mbigint -le 'print 2*255'
        perl -Mbigint -le 'print 4.5+2*255'
        perl -Mbigint -le 'print 3/7 + 5/7 + 8/3'
        perl -Mbigint -le 'print 123->is_odd()'
        perl -Mbigint -le 'print log(2)'
        perl -Mbigint -le 'print 2 ** 0.5'
        perl -Mbigint=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'> and
L<bignum> as in C<perl -Mbignum -le 'print sqrt(2)'>.

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 - 2005.

=cut
Revision:	1.1
Committed:	Thu Jun 30 14:27:08 2005 UTC (21 years, 4 months ago) by root
Branch:	MAIN
CVS Tags:	PERL-5-8-7, HEAD
Branch point for:	PERL
Log Message:	* empty log message *
#	User	Rev	Content
1	root	1.1	package bigint;
2			require 5.005;
3
4			$VERSION = '0.07';
5			use Exporter;
6			@ISA = qw( Exporter );
7			@EXPORT_OK = qw( );
8			@EXPORT = qw( inf NaN );
9
10			use strict;
11			use overload;
12
13			##############################################################################
14
15			# These are all alike, and thus faked by AUTOLOAD
16
17			my @faked = qw/round_mode accuracy precision div_scale/;
18			use vars qw/$VERSION $AUTOLOAD $_lite/; # _lite for testsuite
19
20			sub AUTOLOAD
21			{
22			my $name = $AUTOLOAD;
23
24			$name =~ s/.*:://; # split package
25			no strict 'refs';
26			foreach my $n (@faked)
27			{
28			if ($n eq $name)
29			{
30			*{"bigint::$name"} = sub
31			{
32			my $self = shift;
33			no strict 'refs';
34			if (defined $_[0])
35			{
36			return Math::BigInt->$name($_[0]);
37			}
38			return Math::BigInt->$name();
39			};
40			return &$name;
41			}
42			}
43
44			# delayed load of Carp and avoid recursion
45			require Carp;
46			Carp::croak ("Can't call bigint\-\>$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			# }
57			return $Math::BigInt::upgrade;
58			}
59
60			sub _constant
61			{
62			# this takes a floating point constant string and returns it truncated to
63			# integer. For instance, '4.5' => '4', '1.234e2' => '123' etc
64			my $float = shift;
65
66			# some simple cases first
67			return $float if ($float =~ /^[+-]?[0-9]+$/); # '+123','-1','0' etc
68			return $float
69			if ($float =~ /^[+-]?[0-9]+\.?[eE]\+?[0-9]+$/); # 123e2, 123.e+2
70			return '0' if ($float =~ /^[+-]?[0]*\.[0-9]+$/); # .2, 0.2, -.1
71			if ($float =~ /^[+-]?[0-9]+\.[0-9]*$/) # 1., 1.23, -1.2 etc
72			{
73			$float =~ s/\..*//;
74			return $float;
75			}
76			my ($mis,$miv,$mfv,$es,$ev) = Math::BigInt::_split($float);
77			return $float if !defined $mis; # doesn't look like a number to me
78			my $ec = int($$ev);
79			my $sign = $$mis; $sign = '' if $sign eq '+';
80			if ($$es eq '-')
81			{
82			# ignore fraction part entirely
83			if ($ec >= length($$miv)) # 123.23E-4
84			{
85			return '0';
86			}
87			return $sign . substr ($$miv,0,length($$miv)-$ec); # 1234.45E-2 = 12
88			}
89			# xE+y
90			if ($ec >= length($$mfv))
91			{
92			$ec -= length($$mfv);
93			return $sign.$$miv.$$mfv if $ec == 0; # 123.45E+2 => 12345
94			return $sign.$$miv.$$mfv.'E'.$ec; # 123.45e+3 => 12345e1
95			}
96			$mfv = substr($$mfv,0,$ec);
97			return $sign.$$miv.$mfv; # 123.45e+1 => 1234
98			}
99
100			sub import
101			{
102			my $self = shift;
103
104			# some defaults
105			my $lib = '';
106
107			my @import = ( ':constant' ); # drive it w/ constant
108			my @a = @_; my $l = scalar @_; my $j = 0;
109			my ($ver,$trace); # version? trace?
110			my ($a,$p); # accuracy, precision
111			for ( my $i = 0; $i < $l ; $i++,$j++ )
112			{
113			if ($_[$i] =~ /^(l\|lib)$/)
114			{
115			# this causes a different low lib to take care...
116			$lib = $_[$i+1] \|\| '';
117			my $s = 2; $s = 1 if @a-$j < 2; # avoid "can not modify non-existant..."
118			splice @a, $j, $s; $j -= $s; $i++;
119			}
120			elsif ($_[$i] =~ /^(a\|accuracy)$/)
121			{
122			$a = $_[$i+1];
123			my $s = 2; $s = 1 if @a-$j < 2; # avoid "can not modify non-existant..."
124			splice @a, $j, $s; $j -= $s; $i++;
125			}
126			elsif ($_[$i] =~ /^(p\|precision)$/)
127			{
128			$p = $_[$i+1];
129			my $s = 2; $s = 1 if @a-$j < 2; # avoid "can not modify non-existant..."
130			splice @a, $j, $s; $j -= $s; $i++;
131			}
132			elsif ($_[$i] =~ /^(v\|version)$/)
133			{
134			$ver = 1;
135			splice @a, $j, 1; $j --;
136			}
137			elsif ($_[$i] =~ /^(t\|trace)$/)
138			{
139			$trace = 1;
140			splice @a, $j, 1; $j --;
141			}
142			else { die "unknown option $_[$i]"; }
143			}
144			my $class;
145			$_lite = 0; # using M::BI::L ?
146			if ($trace)
147			{
148			require Math::BigInt::Trace; $class = 'Math::BigInt::Trace';
149			}
150			else
151			{
152			# see if we can find Math::BigInt::Lite
153			if (!defined $a && !defined $p) # rounding won't work to well
154			{
155			eval 'require Math::BigInt::Lite;';
156			if ($@ eq '')
157			{
158			@import = ( ); # :constant in Lite, not MBI
159			Math::BigInt::Lite->import( ':constant' );
160			$_lite= 1; # signal okay
161			}
162			}
163			require Math::BigInt if $_lite == 0; # not already loaded?
164			$class = 'Math::BigInt'; # regardless of MBIL or not
165			}
166			push @import, 'lib' => $lib if $lib ne '';
167			# Math::BigInt::Trace or plain Math::BigInt
168			$class->import(@import);
169
170			bigint->accuracy($a) if defined $a;
171			bigint->precision($p) if defined $p;
172			if ($ver)
173			{
174			print "bigint\t\t\t v$VERSION\n";
175			print "Math::BigInt::Lite\t v$Math::BigInt::Lite::VERSION\n" if $_lite;
176			print "Math::BigInt\t\t v$Math::BigInt::VERSION";
177			my $config = Math::BigInt->config();
178			print " lib => $config->{lib} v$config->{lib_version}\n";
179			exit;
180			}
181			# we take care of floating point constants, since BigFloat isn't available
182			# and BigInt doesn't like them:
183			overload::constant float => sub { Math::BigInt->new( _constant(shift) ); };
184
185			$self->export_to_level(1,$self,@a); # export inf and NaN
186			}
187
188			sub inf () { Math::BigInt->binf(); }
189			sub NaN () { Math::BigInt->bnan(); }
190
191			1;
192
193			__END__
194
195			=head1 NAME
196
197			bigint - Transparent BigInteger support for Perl
198
199			=head1 SYNOPSIS
200
201			use bigint;
202
203			$x = 2 + 4.5,"\n"; # BigInt 6
204			print 2 ** 512,"\n"; # really is what you think it is
205			print inf + 42,"\n"; # inf
206			print NaN * 7,"\n"; # NaN
207
208			=head1 DESCRIPTION
209
210			All operators (including basic math operations) are overloaded. Integer
211			constants are created as proper BigInts.
212
213			Floating point constants are truncated to integer. All results are also
214			truncated.
215
216			=head2 Options
217
218			bigint recognizes some options that can be passed while loading it via use.
219			The options can (currently) be either a single letter form, or the long form.
220			The following options exist:
221
222			=over 2
223
224			=item a or accuracy
225
226			This sets the accuracy for all math operations. The argument must be greater
227			than or equal to zero. See Math::BigInt's bround() function for details.
228
229			perl -Mbigint=a,2 -le 'print 12345+1'
230
231			=item p or precision
232
233			This sets the precision for all math operations. The argument can be any
234			integer. Negative values mean a fixed number of digits after the dot, and
235			are <B>ignored</B> since all operations happen in integer space.
236			A positive value rounds to this digit left from the dot. 0 or 1 mean round to
237			integer and are ignore like negative values.
238
239			See Math::BigInt's bfround() function for details.
240
241			perl -Mbignum=p,5 -le 'print 123456789+123'
242
243			=item t or trace
244
245			This enables a trace mode and is primarily for debugging bigint or
246			Math::BigInt.
247
248			=item l or lib
249
250			Load a different math lib, see L<MATH LIBRARY>.
251
252			perl -Mbigint=l,GMP -e 'print 2 ** 512'
253
254			Currently there is no way to specify more than one library on the command
255			line. This will be hopefully fixed soon ;)
256
257			=item v or version
258
259			This prints out the name and version of all modules used and then exits.
260
261			perl -Mbigint=v
262
263			=head2 Math Library
264
265			Math with the numbers is done (by default) by a module called
266			Math::BigInt::Calc. This is equivalent to saying:
267
268			use bigint lib => 'Calc';
269
270			You can change this by using:
271
272			use bigint lib => 'BitVect';
273
274			The following would first try to find Math::BigInt::Foo, then
275			Math::BigInt::Bar, and when this also fails, revert to Math::BigInt::Calc:
276
277			use bigint lib => 'Foo,Math::BigInt::Bar';
278
279			Please see respective module documentation for further details.
280
281			=head2 Internal Format
282
283			The numbers are stored as objects, and their internals might change at anytime,
284			especially between math operations. The objects also might belong to different
285			classes, like Math::BigInt, or Math::BigInt::Lite. Mixing them together, even
286			with normal scalars is not extraordinary, but normal and expected.
287
288			You should not depend on the internal format, all accesses must go through
289			accessor methods. E.g. looking at $x->{sign} is not a good idea since there
290			is no guaranty that the object in question has such a hash key, nor is a hash
291			underneath at all.
292
293			=head2 Sign
294
295			The sign is either '+', '-', 'NaN', '+inf' or '-inf'.
296			You can access it with the sign() method.
297
298			A sign of 'NaN' is used to represent the result when input arguments are not
299			numbers or as a result of 0/0. '+inf' and '-inf' represent plus respectively
300			minus infinity. You will get '+inf' when dividing a positive number by 0, and
301			'-inf' when dividing any negative number by 0.
302
303			=head2 Methods
304
305			Since all numbers are now objects, you can use all functions that are part of
306			the BigInt API. You can only use the bxxx() notation, and not the fxxx()
307			notation, though.
308
309			=head2 Caveat
310
311			But a warning is in order. When using the following to make a copy of a number,
312			only a shallow copy will be made.
313
314			$x = 9; $y = $x;
315			$x = $y = 7;
316
317			Using the copy or the original with overloaded math is okay, e.g. the
318			following work:
319
320			$x = 9; $y = $x;
321			print $x + 1, " ", $y,"\n"; # prints 10 9
322
323			but calling any method that modifies the number directly will result in
324			B<both> the original and the copy beeing destroyed:
325
326			$x = 9; $y = $x;
327			print $x->badd(1), " ", $y,"\n"; # prints 10 10
328
329			$x = 9; $y = $x;
330			print $x->binc(1), " ", $y,"\n"; # prints 10 10
331
332			$x = 9; $y = $x;
333			print $x->bmul(2), " ", $y,"\n"; # prints 18 18
334
335			Using methods that do not modify, but testthe contents works:
336
337			$x = 9; $y = $x;
338			$z = 9 if $x->is_zero(); # works fine
339
340			See the documentation about the copy constructor and C<=> in overload, as
341			well as the documentation in BigInt for further details.
342
343			=head1 MODULES USED
344
345			C<bigint> is just a thin wrapper around various modules of the Math::BigInt
346			family. Think of it as the head of the family, who runs the shop, and orders
347			the others to do the work.
348
349			The following modules are currently used by bigint:
350
351			Math::BigInt::Lite (for speed, and only if it is loadable)
352			Math::BigInt
353
354			=head1 EXAMPLES
355
356			Some cool command line examples to impress the Python crowd ;) You might want
357			to compare them to the results under -Mbignum or -Mbigrat:
358
359			perl -Mbigint -le 'print sqrt(33)'
360			perl -Mbigint -le 'print 2*255'
361			perl -Mbigint -le 'print 4.5+2*255'
362			perl -Mbigint -le 'print 3/7 + 5/7 + 8/3'
363			perl -Mbigint -le 'print 123->is_odd()'
364			perl -Mbigint -le 'print log(2)'
365			perl -Mbigint -le 'print 2 ** 0.5'
366			perl -Mbigint=a,65 -le 'print 2 ** 0.2'
367
368			=head1 LICENSE
369
370			This program is free software; you may redistribute it and/or modify it under
371			the same terms as Perl itself.
372
373			=head1 SEE ALSO
374
375			Especially L<bigrat> as in C<perl -Mbigrat -le 'print 1/3+1/4'> and
376			L<bignum> as in C<perl -Mbignum -le 'print sqrt(2)'>.
377
378			L<Math::BigInt>, L<Math::BigRat> and L<Math::Big> as well
379			as L<Math::BigInt::BitVect>, L<Math::BigInt::Pari> and L<Math::BigInt::GMP>.
380
381			=head1 AUTHORS
382
383			(C) by Tels L<http://bloodgate.com/> in early 2002 - 2005.
384
385			=cut