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

package bignum;
use 5.006002;

$VERSION = '0.20';
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 $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, 'try' => $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 => '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 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
bce28014	4	$VERSION = '0.20';
126f3c5f	5	use Exporter;
b4bc5691	6	@EXPORT_OK = qw( );
	7	@EXPORT = qw( inf NaN );
	8	@ISA = qw( Exporter );
126f3c5f	9
126f3c5f	10	use strict;
95a2d02c	11	use overload;
126f3c5f	12
	13	##############################################################################
	14
	15	# These are all alike, and thus faked by AUTOLOAD
	16
	17	my @faked = qw/round_mode accuracy precision div_scale/;
	18	use vars qw/$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
233f7bc0	80	my $lib = '';
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; $i++;
	103	}
	104	elsif ($_[$i] =~ /^(l\|lib)$/)
	105	{
	106	# this causes a different low lib to take care...
	107	$lib = $_[$i+1] \|\| '';
	108	my $s = 2; $s = 1 if @a-$j < 2; # avoid "can not modify non-existant..."
	109	splice @a, $j, $s; $j -= $s; $i++;
	110	}
	111	elsif ($_[$i] =~ /^(a\|accuracy)$/)
	112	{
	113	$a = $_[$i+1];
	114	my $s = 2; $s = 1 if @a-$j < 2; # avoid "can not modify non-existant..."
	115	splice @a, $j, $s; $j -= $s; $i++;
	116	}
	117	elsif ($_[$i] =~ /^(p\|precision)$/)
	118	{
	119	$p = $_[$i+1];
	120	my $s = 2; $s = 1 if @a-$j < 2; # avoid "can not modify non-existant..."
	121	splice @a, $j, $s; $j -= $s; $i++;
	122	}
	123	elsif ($_[$i] =~ /^(v\|version)$/)
	124	{
	125	$ver = 1;
	126	splice @a, $j, 1; $j --;
	127	}
	128	elsif ($_[$i] =~ /^(t\|trace)$/)
	129	{
	130	$trace = 1;
	131	splice @a, $j, 1; $j --;
	132	}
	133	else { die "unknown option $_[$i]"; }
	134	}
	135	my $class;
	136	$_lite = 0; # using M::BI::L ?
	137	if ($trace)
	138	{
	139	require Math::BigInt::Trace; $class = 'Math::BigInt::Trace';
	140	$upgrade = 'Math::BigFloat::Trace';
126f3c5f	141	}
	142	else
	143	{
	144	# see if we can find Math::BigInt::Lite
	145	if (!defined $a && !defined $p) # rounding won't work to well
	146	{
	147	eval 'require Math::BigInt::Lite;';
	148	if ($@ eq '')
	149	{
	150	@import = ( ); # :constant in Lite, not MBI
	151	Math::BigInt::Lite->import( ':constant' );
	152	$_lite= 1; # signal okay
	153	}
	154	}
	155	require Math::BigInt if $_lite == 0; # not already loaded?
	156	$class = 'Math::BigInt'; # regardless of MBIL or not
233f7bc0	157	}
95a2d02c	158	push @import, 'try' => $lib if $lib ne '';
126f3c5f	159	# Math::BigInt::Trace or plain Math::BigInt
233f7bc0	160	$class->import(@import, upgrade => $upgrade);
126f3c5f	161
	162	if ($trace)
	163	{
	164	require Math::BigFloat::Trace; $class = 'Math::BigFloat::Trace';
	165	$downgrade = 'Math::BigInt::Trace';
126f3c5f	166	}
	167	else
	168	{
	169	require Math::BigFloat; $class = 'Math::BigFloat';
	170	}
	171	$class->import(':constant','downgrade',$downgrade);
	172
	173	bignum->accuracy($a) if defined $a;
	174	bignum->precision($p) if defined $p;
	175	if ($ver)
	176	{
	177	print "bignum\t\t\t v$VERSION\n";
	178	print "Math::BigInt::Lite\t v$Math::BigInt::Lite::VERSION\n" if $_lite;
	179	print "Math::BigInt\t\t v$Math::BigInt::VERSION";
	180	my $config = Math::BigInt->config();
	181	print " lib => $config->{lib} v$config->{lib_version}\n";
	182	print "Math::BigFloat\t\t v$Math::BigFloat::VERSION\n";
	183	exit;
	184	}
95a2d02c	185
	186	# Take care of octal/hexadecimal constants
	187	overload::constant 'binary' => sub { _binary_constant(shift) };
	188
b4bc5691	189	$self->export_to_level(1,$self,@a); # export inf and NaN
126f3c5f	190	}
126f3c5f	191
b4bc5691	192	sub inf () { Math::BigInt->binf(); }
	193	sub NaN () { Math::BigInt->bnan(); }
	194
126f3c5f	195	1;
	196
	197	__END__
	198
	199	=head1 NAME
	200
	201	bignum - Transparent BigNumber support for Perl
	202
	203	=head1 SYNOPSIS
	204
	205	use bignum;
	206
	207	$x = 2 + 4.5,"\n"; # BigFloat 6.5
b4bc5691	208	print 2 ** 512 * 0.1,"\n"; # really is what you think it is
	209	print inf * inf,"\n"; # prints inf
	210	print NaN * 3,"\n"; # prints NaN
126f3c5f	211
	212	=head1 DESCRIPTION
	213
	214	All operators (including basic math operations) are overloaded. Integer and
	215	floating-point constants are created as proper BigInts or BigFloats,
	216	respectively.
	217
24716a00	218	If you do
	219
	220	use bignum;
	221
	222	at the top of your script, Math::BigFloat and Math::BigInt will be loaded
	223	and any constant number will be converted to an object (Math::BigFloat for
	224	floats like 3.1415 and Math::BigInt for integers like 1234).
	225
	226	So, the following line:
	227
	228	$x = 1234;
	229
	230	creates actually a Math::BigInt and stores a reference to in $x.
	231	This happens transparently and behind your back, so to speak.
	232
	233	You can see this with the following:
	234
	235	perl -Mbignum -le 'print ref(1234)'
	236
	237	Don't worry if it says Math::BigInt::Lite, bignum and friends will use Lite
	238	if it is installed since it is faster for some operations. It will be
3c4b39be	239	automatically upgraded to BigInt whenever necessary:
24716a00	240
	241	perl -Mbignum -le 'print ref(2**255)'
	242
	243	This also means it is a bad idea to check for some specific package, since
	244	the actual contents of $x might be something unexpected. Due to the
3c4b39be	245	transparent way of bignum C<ref()> should not be necessary, anyway.
24716a00	246
	247	Since Math::BigInt and BigFloat also overload the normal math operations,
	248	the following line will still work:
	249
	250	perl -Mbignum -le 'print ref(1234+1234)'
	251
	252	Since numbers are actually objects, you can call all the usual methods from
	253	BigInt/BigFloat on them. This even works to some extent on expressions:
	254
	255	perl -Mbignum -le '$x = 1234; print $x->bdec()'
	256	perl -Mbignum -le 'print 1234->binc();'
	257	perl -Mbignum -le 'print 1234->binc->badd(6);'
	258	perl -Mbignum -le 'print +(1234)->binc()'
	259
	260	(Note that print doesn't do what you expect if the expression starts with
	261	'(' hence the C<+>)
	262
	263	You can even chain the operations together as usual:
	264
	265	perl -Mbignum -le 'print 1234->binc->badd(6);'
	266	1241
	267
	268	Under bignum (or bigint or bigrat), Perl will "upgrade" the numbers
	269	appropriately. This means that:
	270
	271	perl -Mbignum -le 'print 1234+4.5'
	272	1238.5
	273
	274	will work correctly. These mixed cases don't do always work when using
	275	Math::BigInt or Math::BigFloat alone, or at least not in the way normal Perl
	276	scalars work.
	277
	278	If you do want to work with large integers like under C<use integer;>, try
	279	C<use bigint;>:
	280
	281	perl -Mbigint -le 'print 1234.5+4.5'
	282	1238
	283
	284	There is also C<use bigrat;> which gives you big rationals:
	285
	286	perl -Mbigrat -le 'print 1234+4.1'
	287	12381/10
	288
	289	The entire upgrading/downgrading is still experimental and might not work
	290	as you expect or may even have bugs.
	291
	292	You might get errors like this:
	293
	294	Can't use an undefined value as an ARRAY reference at
	295	/usr/local/lib/perl5/5.8.0/Math/BigInt/Calc.pm line 864
	296
	297	This means somewhere a routine got a BigFloat/Lite but expected a BigInt (or
	298	vice versa) and the upgrade/downgrad path was missing. This is a bug, please
	299	report it so that we can fix it.
	300
	301	You might consider using just Math::BigInt or Math::BigFloat, since they
	302	allow you finer control over what get's done in which module/space. For
	303	instance, simple loop counters will be Math::BigInts under C<use bignum;> and
	304	this is slower than keeping them as Perl scalars:
	305
	306	perl -Mbignum -le 'for ($i = 0; $i < 10; $i++) { print ref($i); }'
	307
	308	Please note the following does not work as expected (prints nothing), since
	309	overloading of '..' is not yet possible in Perl (as of v5.8.0):
310
311	perl -Mbignum -le 'for (1..2) { print ref($_); }'
312
b68b7ab1	313	=head2 Options
126f3c5f	314
	315	bignum recognizes some options that can be passed while loading it via use.
	316	The options can (currently) be either a single letter form, or the long form.
	317	The following options exist:
	318
	319	=over 2
	320
	321	=item a or accuracy
	322
	323	This sets the accuracy for all math operations. The argument must be greater
	324	than or equal to zero. See Math::BigInt's bround() function for details.
	325
	326	perl -Mbignum=a,50 -le 'print sqrt(20)'
	327
95a2d02c	328	Note that setting precision and accurary at the same time is not possible.
95a2d02c	329
126f3c5f	330	=item p or precision
	331
	332	This sets the precision for all math operations. The argument can be any
	333	integer. Negative values mean a fixed number of digits after the dot, while
	334	a positive value rounds to this digit left from the dot. 0 or 1 mean round to
	335	integer. See Math::BigInt's bfround() function for details.
	336
	337	perl -Mbignum=p,-50 -le 'print sqrt(20)'
	338
95a2d02c	339	Note that setting precision and accurary at the same time is not possible.
95a2d02c	340
126f3c5f	341	=item t or trace
	342
	343	This enables a trace mode and is primarily for debugging bignum or
	344	Math::BigInt/Math::BigFloat.
	345
	346	=item l or lib
	347
	348	Load a different math lib, see L<MATH LIBRARY>.
	349
	350	perl -Mbignum=l,GMP -e 'print 2 ** 512'
	351
	352	Currently there is no way to specify more than one library on the command
95a2d02c	353	line. This means the following does not work:
	354
	355	perl -Mbignum=l,GMP,Pari -e 'print 2 ** 512'
	356
	357	This will be hopefully fixed soon ;)
126f3c5f	358
	359	=item v or version
	360
	361	This prints out the name and version of all modules used and then exits.
	362
b68b7ab1	363	perl -Mbignum=v
126f3c5f	364
95a2d02c	365	=back
95a2d02c	366
b68b7ab1	367	=head2 Methods
b4bc5691	368
	369	Beside import() and AUTOLOAD() there are only a few other methods.
	370
24716a00	371	Since all numbers are now objects, you can use all functions that are part of
	372	the BigInt or BigFloat API. It is wise to use only the bxxx() notation, and not
	373	the fxxx() notation, though. This makes it possible that the underlying object
	374	might morph into a different class than BigFloat.
	375
b68b7ab1	376	=head2 Caveat
990fb837	377
	378	But a warning is in order. When using the following to make a copy of a number,
	379	only a shallow copy will be made.
	380
	381	$x = 9; $y = $x;
	382	$x = $y = 7;
	383
b68b7ab1	384	If you want to make a real copy, use the following:
	385
	386	$y = $x->copy();
	387
990fb837	388	Using the copy or the original with overloaded math is okay, e.g. the
	389	following work:
	390
	391	$x = 9; $y = $x;
	392	print $x + 1, " ", $y,"\n"; # prints 10 9
	393
	394	but calling any method that modifies the number directly will result in
3c4b39be	395	B<both> the original and the copy being destroyed:
990fb837	396
	397	$x = 9; $y = $x;
	398	print $x->badd(1), " ", $y,"\n"; # prints 10 10
	399
	400	$x = 9; $y = $x;
	401	print $x->binc(1), " ", $y,"\n"; # prints 10 10
	402
	403	$x = 9; $y = $x;
	404	print $x->bmul(2), " ", $y,"\n"; # prints 18 18
	405
	406	Using methods that do not modify, but testthe contents works:
	407
	408	$x = 9; $y = $x;
	409	$z = 9 if $x->is_zero(); # works fine
	410
	411	See the documentation about the copy constructor and C<=> in overload, as
	412	well as the documentation in BigInt for further details.
	413
b4bc5691	414	=over 2
	415
	416	=item inf()
	417
3c4b39be	418	A shortcut to return Math::BigInt->binf(). Useful because Perl does not always
b4bc5691	419	handle bareword C<inf> properly.
	420
	421	=item NaN()
	422
3c4b39be	423	A shortcut to return Math::BigInt->bnan(). Useful because Perl does not always
b4bc5691	424	handle bareword C<NaN> properly.
	425
	426	=item upgrade()
	427
	428	Return the class that numbers are upgraded to, is in fact returning
	429	C<$Math::BigInt::upgrade>.
	430
	431	=back
	432
126f3c5f	433	=head2 MATH LIBRARY
	434
	435	Math with the numbers is done (by default) by a module called
	436	Math::BigInt::Calc. This is equivalent to saying:
	437
	438	use bignum lib => 'Calc';
	439
	440	You can change this by using:
	441
	442	use bignum lib => 'BitVect';
	443
	444	The following would first try to find Math::BigInt::Foo, then
	445	Math::BigInt::Bar, and when this also fails, revert to Math::BigInt::Calc:
	446
	447	use bignum lib => 'Foo,Math::BigInt::Bar';
	448
	449	Please see respective module documentation for further details.
	450
	451	=head2 INTERNAL FORMAT
	452
	453	The numbers are stored as objects, and their internals might change at anytime,
	454	especially between math operations. The objects also might belong to different
	455	classes, like Math::BigInt, or Math::BigFLoat. Mixing them together, even
	456	with normal scalars is not extraordinary, but normal and expected.
	457
	458	You should not depend on the internal format, all accesses must go through
	459	accessor methods. E.g. looking at $x->{sign} is not a bright idea since there
	460	is no guaranty that the object in question has such a hashkey, nor is a hash
	461	underneath at all.
	462
	463	=head2 SIGN
	464
	465	The sign is either '+', '-', 'NaN', '+inf' or '-inf' and stored seperately.
	466	You can access it with the sign() method.
	467
	468	A sign of 'NaN' is used to represent the result when input arguments are not
	469	numbers or as a result of 0/0. '+inf' and '-inf' represent plus respectively
	470	minus infinity. You will get '+inf' when dividing a positive number by 0, and
	471	'-inf' when dividing any negative number by 0.
	472
126f3c5f	473	=head1 MODULES USED
	474
	475	C<bignum> is just a thin wrapper around various modules of the Math::BigInt
	476	family. Think of it as the head of the family, who runs the shop, and orders
	477	the others to do the work.
	478
	479	The following modules are currently used by bignum:
	480
	481	Math::BigInt::Lite (for speed, and only if it is loadable)
	482	Math::BigInt
	483	Math::BigFloat
	484
	485	=head1 EXAMPLES
	486
	487	Some cool command line examples to impress the Python crowd ;)
	488
	489	perl -Mbignum -le 'print sqrt(33)'
	490	perl -Mbignum -le 'print 2*255'
	491	perl -Mbignum -le 'print 4.5+2*255'
	492	perl -Mbignum -le 'print 3/7 + 5/7 + 8/3'
	493	perl -Mbignum -le 'print 123->is_odd()'
	494	perl -Mbignum -le 'print log(2)'
bce28014	495	perl -Mbignum -le 'print exp(1)'
126f3c5f	496	perl -Mbignum -le 'print 2 ** 0.5'
126f3c5f	497	perl -Mbignum=a,65 -le 'print 2 ** 0.2'
95a2d02c	498	perl -Mbignum=a,65,l,GMP -le 'print 7 ** 7777'
126f3c5f	499
	500	=head1 LICENSE
	501
	502	This program is free software; you may redistribute it and/or modify it under
	503	the same terms as Perl itself.
	504
	505	=head1 SEE ALSO
	506
	507	Especially L<bigrat> as in C<perl -Mbigrat -le 'print 1/3+1/4'>.
	508
	509	L<Math::BigFloat>, L<Math::BigInt>, L<Math::BigRat> and L<Math::Big> as well
	510	as L<Math::BigInt::BitVect>, L<Math::BigInt::Pari> and L<Math::BigInt::GMP>.
	511
	512	=head1 AUTHORS
	513
95a2d02c	514	(C) by Tels L<http://bloodgate.com/> in early 2002 - 2007.
126f3c5f	515
126f3c5f	516	=cut