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

package bignum;
use 5.006002;

$VERSION = '0.21';
use Exporter;
@EXPORT_OK 	= qw( ); 
@EXPORT 	= qw( inf NaN ); 
@ISA 		= qw( Exporter );

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 $name)
      {
      *{"bignum::$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];
#    }
  $Math::BigInt::upgrade;
  }

sub _binary_constant
  {
  # this takes a binary/hexadecimal/octal constant string and returns it
  # as string suitable for new. Basically it converts octal to decimal, and
  # passes every thing else unmodified back.
  my $string = shift;

  return Math::BigInt->new($string) if $string =~ /^0[bx]/;

  # so it must be an octal constant
  Math::BigInt->from_oct($string);
  }

sub import 
  {
  my $self = shift;

  # some defaults
  my $lib = ''; my $lib_kind = 'try';
  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; $i++;
      }
    elsif ($_[$i] =~ /^(l|lib|try|only)$/)
      {
      # 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 --;
      }
    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);

  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;
    }

  # Take care of octal/hexadecimal constants
  overload::constant 'binary' => sub { _binary_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

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)'

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 -Mbignum=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 -Mbignum=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 v or version

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

	perl -Mbignum=v

=back

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

Please see respective module documentation for further details.

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';

=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 exp(1)'
	perl -Mbignum -le 'print 2 ** 0.5'
	perl -Mbignum=a,65 -le 'print 2 ** 0.2'
	perl -Mbignum=a,65,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<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 - 2007.

=cut
Commit	Line	Data
126f3c5f	1	package bignum;
95a2d02c	2	use 5.006002;
126f3c5f	3
bd49aa09	4	$VERSION = '0.21';
126f3c5f	5	use Exporter;
b4bc5691	6	@EXPORT_OK = qw( );
	7	@EXPORT = qw( inf NaN );
	8	@ISA = qw( Exporter );
126f3c5f	9
126f3c5f	10	use strict;
95a2d02c	11	use overload;
126f3c5f	12
	13	##############################################################################
	14
	15	# These are all alike, and thus faked by AUTOLOAD
	16
	17	my @faked = qw/round_mode accuracy precision div_scale/;
	18	use vars qw/$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 $name)
	29	{
	30	*{"bignum::$name"} = sub
	31	{
	32	my $self = shift;
	33	no strict 'refs';
	34	if (defined $_[0])
	35	{
	36	Math::BigInt->$name($_[0]);
990fb837	37	return Math::BigFloat->$name($_[0]);
126f3c5f	38	}
	39	return Math::BigInt->$name();
	40	};
	41	return &$name;
	42	}
	43	}
	44
	45	# delayed load of Carp and avoid recursion
	46	require Carp;
	47	Carp::croak ("Can't call bignum\-\>$name, not a valid method");
	48	}
	49
	50	sub upgrade
	51	{
	52	my $self = shift;
	53	no strict 'refs';
	54	# if (defined $_[0])
	55	# {
	56	# $Math::BigInt::upgrade = $_[0];
	57	# $Math::BigFloat::upgrade = $_[0];
	58	# }
95a2d02c	59	$Math::BigInt::upgrade;
	60	}
	61
	62	sub _binary_constant
	63	{
	64	# this takes a binary/hexadecimal/octal constant string and returns it
	65	# as string suitable for new. Basically it converts octal to decimal, and
	66	# passes every thing else unmodified back.
	67	my $string = shift;
	68
	69	return Math::BigInt->new($string) if $string =~ /^0[bx]/;
	70
	71	# so it must be an octal constant
	72	Math::BigInt->from_oct($string);
126f3c5f	73	}
	74
	75	sub import
	76	{
	77	my $self = shift;
	78
	79	# some defaults
bd49aa09	80	my $lib = ''; my $lib_kind = 'try';
126f3c5f	81	my $upgrade = 'Math::BigFloat';
	82	my $downgrade = 'Math::BigInt';
	83
	84	my @import = ( ':constant' ); # drive it w/ constant
	85	my @a = @_; my $l = scalar @_; my $j = 0;
	86	my ($ver,$trace); # version? trace?
	87	my ($a,$p); # accuracy, precision
	88	for ( my $i = 0; $i < $l ; $i++,$j++ )
	89	{
	90	if ($_[$i] eq 'upgrade')
	91	{
	92	# this causes upgrading
	93	$upgrade = $_[$i+1]; # or undef to disable
	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] eq 'downgrade')
	98	{
	99	# this causes downgrading
	100	$downgrade = $_[$i+1]; # or undef to disable
	101	my $s = 2; $s = 1 if @a-$j < 2; # avoid "can not modify non-existant..."
	102	splice @a, $j, $s; $j -= $s; $i++;
	103	}
bd49aa09	104	elsif ($_[$i] =~ /^(l\|lib\|try\|only)$/)
126f3c5f	105	{
126f3c5f	106	# this causes a different low lib to take care...
bd49aa09	107	$lib_kind = $1; $lib_kind = 'lib' if $lib_kind eq 'l';
126f3c5f	108	$lib = $_[$i+1] \|\| '';
	109	my $s = 2; $s = 1 if @a-$j < 2; # avoid "can not modify non-existant..."
	110	splice @a, $j, $s; $j -= $s; $i++;
	111	}
	112	elsif ($_[$i] =~ /^(a\|accuracy)$/)
	113	{
	114	$a = $_[$i+1];
	115	my $s = 2; $s = 1 if @a-$j < 2; # avoid "can not modify non-existant..."
	116	splice @a, $j, $s; $j -= $s; $i++;
	117	}
	118	elsif ($_[$i] =~ /^(p\|precision)$/)
	119	{
	120	$p = $_[$i+1];
	121	my $s = 2; $s = 1 if @a-$j < 2; # avoid "can not modify non-existant..."
	122	splice @a, $j, $s; $j -= $s; $i++;
	123	}
	124	elsif ($_[$i] =~ /^(v\|version)$/)
	125	{
	126	$ver = 1;
	127	splice @a, $j, 1; $j --;
	128	}
	129	elsif ($_[$i] =~ /^(t\|trace)$/)
	130	{
	131	$trace = 1;
	132	splice @a, $j, 1; $j --;
	133	}
	134	else { die "unknown option $_[$i]"; }
	135	}
	136	my $class;
	137	$_lite = 0; # using M::BI::L ?
	138	if ($trace)
	139	{
	140	require Math::BigInt::Trace; $class = 'Math::BigInt::Trace';
	141	$upgrade = 'Math::BigFloat::Trace';
126f3c5f	142	}
	143	else
	144	{
	145	# see if we can find Math::BigInt::Lite
	146	if (!defined $a && !defined $p) # rounding won't work to well
	147	{
	148	eval 'require Math::BigInt::Lite;';
	149	if ($@ eq '')
	150	{
	151	@import = ( ); # :constant in Lite, not MBI
	152	Math::BigInt::Lite->import( ':constant' );
	153	$_lite= 1; # signal okay
	154	}
	155	}
	156	require Math::BigInt if $_lite == 0; # not already loaded?
	157	$class = 'Math::BigInt'; # regardless of MBIL or not
233f7bc0	158	}
bd49aa09	159	push @import, $lib_kind => $lib if $lib ne '';
126f3c5f	160	# Math::BigInt::Trace or plain Math::BigInt
233f7bc0	161	$class->import(@import, upgrade => $upgrade);
126f3c5f	162
	163	if ($trace)
	164	{
	165	require Math::BigFloat::Trace; $class = 'Math::BigFloat::Trace';
	166	$downgrade = 'Math::BigInt::Trace';
126f3c5f	167	}
	168	else
	169	{
	170	require Math::BigFloat; $class = 'Math::BigFloat';
	171	}
	172	$class->import(':constant','downgrade',$downgrade);
	173
	174	bignum->accuracy($a) if defined $a;
	175	bignum->precision($p) if defined $p;
	176	if ($ver)
	177	{
	178	print "bignum\t\t\t v$VERSION\n";
	179	print "Math::BigInt::Lite\t v$Math::BigInt::Lite::VERSION\n" if $_lite;
	180	print "Math::BigInt\t\t v$Math::BigInt::VERSION";
	181	my $config = Math::BigInt->config();
	182	print " lib => $config->{lib} v$config->{lib_version}\n";
	183	print "Math::BigFloat\t\t v$Math::BigFloat::VERSION\n";
	184	exit;
	185	}
95a2d02c	186
	187	# Take care of octal/hexadecimal constants
	188	overload::constant 'binary' => sub { _binary_constant(shift) };
	189
b4bc5691	190	$self->export_to_level(1,$self,@a); # export inf and NaN
126f3c5f	191	}
126f3c5f	192
b4bc5691	193	sub inf () { Math::BigInt->binf(); }
	194	sub NaN () { Math::BigInt->bnan(); }
	195
126f3c5f	196	1;
	197
	198	__END__
	199
	200	=head1 NAME
	201
	202	bignum - Transparent BigNumber support for Perl
	203
	204	=head1 SYNOPSIS
	205
	206	use bignum;
	207
	208	$x = 2 + 4.5,"\n"; # BigFloat 6.5
b4bc5691	209	print 2 ** 512 * 0.1,"\n"; # really is what you think it is
	210	print inf * inf,"\n"; # prints inf
	211	print NaN * 3,"\n"; # prints NaN
126f3c5f	212
	213	=head1 DESCRIPTION
	214
	215	All operators (including basic math operations) are overloaded. Integer and
	216	floating-point constants are created as proper BigInts or BigFloats,
	217	respectively.
	218
24716a00	219	If you do
	220
	221	use bignum;
	222
	223	at the top of your script, Math::BigFloat and Math::BigInt will be loaded
	224	and any constant number will be converted to an object (Math::BigFloat for
	225	floats like 3.1415 and Math::BigInt for integers like 1234).
	226
	227	So, the following line:
	228
	229	$x = 1234;
	230
	231	creates actually a Math::BigInt and stores a reference to in $x.
	232	This happens transparently and behind your back, so to speak.
	233
	234	You can see this with the following:
	235
	236	perl -Mbignum -le 'print ref(1234)'
	237
	238	Don't worry if it says Math::BigInt::Lite, bignum and friends will use Lite
	239	if it is installed since it is faster for some operations. It will be
3c4b39be	240	automatically upgraded to BigInt whenever necessary:
24716a00	241
	242	perl -Mbignum -le 'print ref(2**255)'
	243
	244	This also means it is a bad idea to check for some specific package, since
	245	the actual contents of $x might be something unexpected. Due to the
3c4b39be	246	transparent way of bignum C<ref()> should not be necessary, anyway.
24716a00	247
	248	Since Math::BigInt and BigFloat also overload the normal math operations,
	249	the following line will still work:
	250
	251	perl -Mbignum -le 'print ref(1234+1234)'
	252
	253	Since numbers are actually objects, you can call all the usual methods from
	254	BigInt/BigFloat on them. This even works to some extent on expressions:
	255
	256	perl -Mbignum -le '$x = 1234; print $x->bdec()'
	257	perl -Mbignum -le 'print 1234->binc();'
	258	perl -Mbignum -le 'print 1234->binc->badd(6);'
	259	perl -Mbignum -le 'print +(1234)->binc()'
	260
	261	(Note that print doesn't do what you expect if the expression starts with
	262	'(' hence the C<+>)
	263
	264	You can even chain the operations together as usual:
	265
	266	perl -Mbignum -le 'print 1234->binc->badd(6);'
	267	1241
	268
	269	Under bignum (or bigint or bigrat), Perl will "upgrade" the numbers
	270	appropriately. This means that:
	271
	272	perl -Mbignum -le 'print 1234+4.5'
	273	1238.5
	274
	275	will work correctly. These mixed cases don't do always work when using
	276	Math::BigInt or Math::BigFloat alone, or at least not in the way normal Perl
	277	scalars work.
	278
	279	If you do want to work with large integers like under C<use integer;>, try
	280	C<use bigint;>:
	281
	282	perl -Mbigint -le 'print 1234.5+4.5'
	283	1238
	284
	285	There is also C<use bigrat;> which gives you big rationals:
	286
	287	perl -Mbigrat -le 'print 1234+4.1'
	288	12381/10
	289
	290	The entire upgrading/downgrading is still experimental and might not work
	291	as you expect or may even have bugs.
	292
	293	You might get errors like this:
	294
	295	Can't use an undefined value as an ARRAY reference at
	296	/usr/local/lib/perl5/5.8.0/Math/BigInt/Calc.pm line 864
	297
	298	This means somewhere a routine got a BigFloat/Lite but expected a BigInt (or
	299	vice versa) and the upgrade/downgrad path was missing. This is a bug, please
	300	report it so that we can fix it.
	301
	302	You might consider using just Math::BigInt or Math::BigFloat, since they
	303	allow you finer control over what get's done in which module/space. For
	304	instance, simple loop counters will be Math::BigInts under C<use bignum;> and
	305	this is slower than keeping them as Perl scalars:
	306
	307	perl -Mbignum -le 'for ($i = 0; $i < 10; $i++) { print ref($i); }'
	308
	309	Please note the following does not work as expected (prints nothing), since
	310	overloading of '..' is not yet possible in Perl (as of v5.8.0):
311
312	perl -Mbignum -le 'for (1..2) { print ref($_); }'
313
b68b7ab1	314	=head2 Options
126f3c5f	315
	316	bignum recognizes some options that can be passed while loading it via use.
	317	The options can (currently) be either a single letter form, or the long form.
	318	The following options exist:
	319
	320	=over 2
	321
	322	=item a or accuracy
	323
	324	This sets the accuracy for all math operations. The argument must be greater
	325	than or equal to zero. See Math::BigInt's bround() function for details.
	326
	327	perl -Mbignum=a,50 -le 'print sqrt(20)'
	328
95a2d02c	329	Note that setting precision and accurary at the same time is not possible.
95a2d02c	330
126f3c5f	331	=item p or precision
	332
	333	This sets the precision for all math operations. The argument can be any
	334	integer. Negative values mean a fixed number of digits after the dot, while
	335	a positive value rounds to this digit left from the dot. 0 or 1 mean round to
	336	integer. See Math::BigInt's bfround() function for details.
	337
	338	perl -Mbignum=p,-50 -le 'print sqrt(20)'
	339
95a2d02c	340	Note that setting precision and accurary at the same time is not possible.
95a2d02c	341
126f3c5f	342	=item t or trace
	343
	344	This enables a trace mode and is primarily for debugging bignum or
	345	Math::BigInt/Math::BigFloat.
	346
	347	=item l or lib
	348
	349	Load a different math lib, see L<MATH LIBRARY>.
	350
	351	perl -Mbignum=l,GMP -e 'print 2 ** 512'
	352
	353	Currently there is no way to specify more than one library on the command
95a2d02c	354	line. This means the following does not work:
	355
	356	perl -Mbignum=l,GMP,Pari -e 'print 2 ** 512'
	357
	358	This will be hopefully fixed soon ;)
126f3c5f	359
	360	=item v or version
	361
	362	This prints out the name and version of all modules used and then exits.
	363
b68b7ab1	364	perl -Mbignum=v
126f3c5f	365
95a2d02c	366	=back
95a2d02c	367
b68b7ab1	368	=head2 Methods
b4bc5691	369
	370	Beside import() and AUTOLOAD() there are only a few other methods.
	371
24716a00	372	Since all numbers are now objects, you can use all functions that are part of
	373	the BigInt or BigFloat API. It is wise to use only the bxxx() notation, and not
	374	the fxxx() notation, though. This makes it possible that the underlying object
	375	might morph into a different class than BigFloat.
	376
b68b7ab1	377	=head2 Caveat
990fb837	378
	379	But a warning is in order. When using the following to make a copy of a number,
	380	only a shallow copy will be made.
	381
	382	$x = 9; $y = $x;
	383	$x = $y = 7;
	384
b68b7ab1	385	If you want to make a real copy, use the following:
	386
	387	$y = $x->copy();
	388
990fb837	389	Using the copy or the original with overloaded math is okay, e.g. the
	390	following work:
	391
	392	$x = 9; $y = $x;
	393	print $x + 1, " ", $y,"\n"; # prints 10 9
	394
	395	but calling any method that modifies the number directly will result in
3c4b39be	396	B<both> the original and the copy being destroyed:
990fb837	397
	398	$x = 9; $y = $x;
	399	print $x->badd(1), " ", $y,"\n"; # prints 10 10
	400
	401	$x = 9; $y = $x;
	402	print $x->binc(1), " ", $y,"\n"; # prints 10 10
	403
	404	$x = 9; $y = $x;
	405	print $x->bmul(2), " ", $y,"\n"; # prints 18 18
	406
	407	Using methods that do not modify, but testthe contents works:
	408
	409	$x = 9; $y = $x;
	410	$z = 9 if $x->is_zero(); # works fine
	411
	412	See the documentation about the copy constructor and C<=> in overload, as
	413	well as the documentation in BigInt for further details.
	414
b4bc5691	415	=over 2
	416
	417	=item inf()
	418
3c4b39be	419	A shortcut to return Math::BigInt->binf(). Useful because Perl does not always
b4bc5691	420	handle bareword C<inf> properly.
	421
	422	=item NaN()
	423
3c4b39be	424	A shortcut to return Math::BigInt->bnan(). Useful because Perl does not always
b4bc5691	425	handle bareword C<NaN> properly.
	426
	427	=item upgrade()
	428
	429	Return the class that numbers are upgraded to, is in fact returning
	430	C<$Math::BigInt::upgrade>.
	431
	432	=back
	433
bd49aa09	434	=head2 Math Library
126f3c5f	435
	436	Math with the numbers is done (by default) by a module called
	437	Math::BigInt::Calc. This is equivalent to saying:
	438
	439	use bignum lib => 'Calc';
	440
	441	You can change this by using:
	442
bd49aa09	443	use bignum lib => 'GMP';
126f3c5f	444
	445	The following would first try to find Math::BigInt::Foo, then
	446	Math::BigInt::Bar, and when this also fails, revert to Math::BigInt::Calc:
	447
	448	use bignum lib => 'Foo,Math::BigInt::Bar';
	449
	450	Please see respective module documentation for further details.
	451
bd49aa09	452	Using C<lib> warns if none of the specified libraries can be found and
	453	L<Math::BigInt> did fall back to one of the default libraries.
	454	To supress this warning, use C<try> instead:
	455
	456	use bignum try => 'GMP';
	457
	458	If you want the code to die instead of falling back, use C<only> instead:
	459
	460	use bignum only => 'GMP';
	461
126f3c5f	462	=head2 INTERNAL FORMAT
	463
	464	The numbers are stored as objects, and their internals might change at anytime,
	465	especially between math operations. The objects also might belong to different
	466	classes, like Math::BigInt, or Math::BigFLoat. Mixing them together, even
	467	with normal scalars is not extraordinary, but normal and expected.
	468
	469	You should not depend on the internal format, all accesses must go through
	470	accessor methods. E.g. looking at $x->{sign} is not a bright idea since there
	471	is no guaranty that the object in question has such a hashkey, nor is a hash
	472	underneath at all.
	473
	474	=head2 SIGN
	475
	476	The sign is either '+', '-', 'NaN', '+inf' or '-inf' and stored seperately.
	477	You can access it with the sign() method.
	478
	479	A sign of 'NaN' is used to represent the result when input arguments are not
	480	numbers or as a result of 0/0. '+inf' and '-inf' represent plus respectively
	481	minus infinity. You will get '+inf' when dividing a positive number by 0, and
	482	'-inf' when dividing any negative number by 0.
	483
126f3c5f	484	=head1 MODULES USED
	485
	486	C<bignum> is just a thin wrapper around various modules of the Math::BigInt
	487	family. Think of it as the head of the family, who runs the shop, and orders
	488	the others to do the work.
	489
	490	The following modules are currently used by bignum:
	491
	492	Math::BigInt::Lite (for speed, and only if it is loadable)
	493	Math::BigInt
	494	Math::BigFloat
	495
	496	=head1 EXAMPLES
	497
	498	Some cool command line examples to impress the Python crowd ;)
	499
	500	perl -Mbignum -le 'print sqrt(33)'
	501	perl -Mbignum -le 'print 2*255'
	502	perl -Mbignum -le 'print 4.5+2*255'
	503	perl -Mbignum -le 'print 3/7 + 5/7 + 8/3'
	504	perl -Mbignum -le 'print 123->is_odd()'
	505	perl -Mbignum -le 'print log(2)'
bce28014	506	perl -Mbignum -le 'print exp(1)'
126f3c5f	507	perl -Mbignum -le 'print 2 ** 0.5'
126f3c5f	508	perl -Mbignum=a,65 -le 'print 2 ** 0.2'
95a2d02c	509	perl -Mbignum=a,65,l,GMP -le 'print 7 ** 7777'
126f3c5f	510
	511	=head1 LICENSE
	512
	513	This program is free software; you may redistribute it and/or modify it under
	514	the same terms as Perl itself.
	515
	516	=head1 SEE ALSO
	517
	518	Especially L<bigrat> as in C<perl -Mbigrat -le 'print 1/3+1/4'>.
	519
	520	L<Math::BigFloat>, L<Math::BigInt>, L<Math::BigRat> and L<Math::Big> as well
	521	as L<Math::BigInt::BitVect>, L<Math::BigInt::Pari> and L<Math::BigInt::GMP>.
	522
	523	=head1 AUTHORS
	524
95a2d02c	525	(C) by Tels L<http://bloodgate.com/> in early 2002 - 2007.
126f3c5f	526
126f3c5f	527	=cut