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

package bignum;
use 5.006002;

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

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

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

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

# These are all alike, and thus faked by AUTOLOAD

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

sub AUTOLOAD
  {
  my $name = $AUTOLOAD;

  $name =~ s/.*:://;    # split package
  no strict 'refs';
  foreach my $n (@faked)
    {
    if ($n eq $name)
      {
      *{"bignum::$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 unimport
  {
  $^H{bignum} = undef;					# no longer in effect
  overload::remove_constant('binary','','float','','integer');
  }

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

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

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

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

sub import 
  {
  my $self = shift;

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

  my ($hex,$oct);

  # for newer Perls override hex() and oct() with a lexical version:
  if ($] > 5.009003)
    {
    $hex = \&_hex;
    $oct = \&_oct;
    }

  # 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; $j --;
      }
    elsif ($_[$i] eq 'hex')
      {
      splice @a, $j, 1; $j --;
      $hex = \&bigint::_hex_global;
      }
    elsif ($_[$i] eq 'oct')
      {
      splice @a, $j, 1; $j --;
      $oct = \&bigint::_oct_global;
      }
    else { die "unknown option $_[$i]"; }
    }
  my $class;
  $_lite = 0;					# using M::BI::L ?
  if ($trace)
    {
    require Math::BigInt::Trace; $class = 'Math::BigInt::Trace';
    $upgrade = 'Math::BigFloat::Trace';	
    }
  else
    {
    # see if we can find Math::BigInt::Lite
    if (!defined $a && !defined $p)		# rounding won't work to well
      {
      eval 'require Math::BigInt::Lite;';
      if ($@ eq '')
        {
        @import = ( );				# :constant in Lite, not MBI
        Math::BigInt::Lite->import( ':constant' );
        $_lite= 1;				# signal okay
        }
      }
    require Math::BigInt if $_lite == 0;	# not already loaded?
    $class = 'Math::BigInt';			# regardless of MBIL or not
    }
  push @import, $lib_kind => $lib if $lib ne ''; 
  # Math::BigInt::Trace or plain Math::BigInt
  $class->import(@import, upgrade => $upgrade);

  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 { bigint::_binary_constant(shift) };

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

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

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

  {
    no bignum;
    print 2 ** 256,"\n";		# a normal Perl scalar now
  }

  # for older Perls, note that this will be global:
  use bignum qw/hex oct/;
  print hex("0x1234567890123490"),"\n";
  print oct("01234567890123490"),"\n";

=head1 DESCRIPTION

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

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->copy()->binc();'
        perl -Mbignum -le 'print 1234->copy()->binc->badd(6);'
        perl -Mbignum -le 'print +(1234)->copy()->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->copy()->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 hex

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

=item oct

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

=item v or version

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

	perl -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 Caveats

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 test the 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>.

=item in_effect()

	use bignum;

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

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

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

=back

=head2 Math Library

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

=over 2

=item in_effect()

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

=item hex()/oct()

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

	use bigint qw/hex oct/;

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

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

Compare this to:

	use bigint;

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

=back

=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
4440d13a	4	$VERSION = '0.22';
126f3c5f	5	use Exporter;
d1a15766	6	@ISA = qw( bigint );
b4bc5691	7	@EXPORT_OK = qw( );
b4bc5691	8	@EXPORT = qw( inf NaN );
126f3c5f	9
126f3c5f	10	use strict;
95a2d02c	11	use overload;
d1a15766	12	require bigint; # no "use" to avoid import being called
126f3c5f	13
	14	##############################################################################
	15
d1a15766	16	BEGIN
	17	{
	18	*inf = \&bigint::inf;
	19	*NaN = \&bigint::NaN;
	20	}
	21
126f3c5f	22	# These are all alike, and thus faked by AUTOLOAD
	23
	24	my @faked = qw/round_mode accuracy precision div_scale/;
	25	use vars qw/$VERSION $AUTOLOAD $_lite/; # _lite for testsuite
	26
	27	sub AUTOLOAD
	28	{
	29	my $name = $AUTOLOAD;
	30
	31	$name =~ s/.*:://; # split package
	32	no strict 'refs';
	33	foreach my $n (@faked)
	34	{
	35	if ($n eq $name)
	36	{
	37	*{"bignum::$name"} = sub
	38	{
	39	my $self = shift;
	40	no strict 'refs';
	41	if (defined $_[0])
	42	{
	43	Math::BigInt->$name($_[0]);
990fb837	44	return Math::BigFloat->$name($_[0]);
126f3c5f	45	}
	46	return Math::BigInt->$name();
	47	};
	48	return &$name;
	49	}
	50	}
	51
	52	# delayed load of Carp and avoid recursion
	53	require Carp;
	54	Carp::croak ("Can't call bignum\-\>$name, not a valid method");
	55	}
	56
4440d13a	57	sub unimport
	58	{
	59	$^H{bignum} = undef; # no longer in effect
	60	overload::remove_constant('binary','','float','','integer');
	61	}
	62
	63	sub in_effect
	64	{
	65	my $level = shift \|\| 0;
	66	my $hinthash = (caller($level))[10];
	67	$hinthash->{bignum};
	68	}
	69
d1a15766	70	#############################################################################
	71	# the following two routines are for Perl 5.9.4 or later and are lexical
	72
	73	sub _hex
	74	{
	75	return CORE::hex($_[0]) unless in_effect(1);
	76	my $i = $_[0];
	77	$i = '0x'.$i unless $i =~ /^0x/;
	78	Math::BigInt->new($i);
	79	}
	80
	81	sub _oct
	82	{
	83	return CORE::oct($_[0]) unless in_effect(1);
	84	my $i = $_[0];
	85	return Math::BigInt->from_oct($i) if $i =~ /^0[0-7]/;
	86	Math::BigInt->new($i);
	87	}
	88
126f3c5f	89	sub import
	90	{
	91	my $self = shift;
	92
4440d13a	93	$^H{bignum} = 1; # we are in effect
4440d13a	94
075d4edd	95	my ($hex,$oct);
075d4edd	96
d1a15766	97	# for newer Perls override hex() and oct() with a lexical version:
	98	if ($] > 5.009003)
	99	{
075d4edd	100	$hex = \&_hex;
075d4edd	101	$oct = \&_oct;
d1a15766	102	}
d1a15766	103
126f3c5f	104	# some defaults
bd49aa09	105	my $lib = ''; my $lib_kind = 'try';
126f3c5f	106	my $upgrade = 'Math::BigFloat';
	107	my $downgrade = 'Math::BigInt';
	108
	109	my @import = ( ':constant' ); # drive it w/ constant
	110	my @a = @_; my $l = scalar @_; my $j = 0;
	111	my ($ver,$trace); # version? trace?
	112	my ($a,$p); # accuracy, precision
	113	for ( my $i = 0; $i < $l ; $i++,$j++ )
	114	{
	115	if ($_[$i] eq 'upgrade')
	116	{
	117	# this causes upgrading
	118	$upgrade = $_[$i+1]; # or undef to disable
	119	my $s = 2; $s = 1 if @a-$j < 2; # avoid "can not modify non-existant..."
	120	splice @a, $j, $s; $j -= $s; $i++;
	121	}
	122	elsif ($_[$i] eq 'downgrade')
	123	{
	124	# this causes downgrading
	125	$downgrade = $_[$i+1]; # or undef to disable
	126	my $s = 2; $s = 1 if @a-$j < 2; # avoid "can not modify non-existant..."
	127	splice @a, $j, $s; $j -= $s; $i++;
	128	}
bd49aa09	129	elsif ($_[$i] =~ /^(l\|lib\|try\|only)$/)
126f3c5f	130	{
126f3c5f	131	# this causes a different low lib to take care...
bd49aa09	132	$lib_kind = $1; $lib_kind = 'lib' if $lib_kind eq 'l';
126f3c5f	133	$lib = $_[$i+1] \|\| '';
	134	my $s = 2; $s = 1 if @a-$j < 2; # avoid "can not modify non-existant..."
	135	splice @a, $j, $s; $j -= $s; $i++;
	136	}
	137	elsif ($_[$i] =~ /^(a\|accuracy)$/)
	138	{
	139	$a = $_[$i+1];
	140	my $s = 2; $s = 1 if @a-$j < 2; # avoid "can not modify non-existant..."
	141	splice @a, $j, $s; $j -= $s; $i++;
	142	}
	143	elsif ($_[$i] =~ /^(p\|precision)$/)
	144	{
	145	$p = $_[$i+1];
	146	my $s = 2; $s = 1 if @a-$j < 2; # avoid "can not modify non-existant..."
	147	splice @a, $j, $s; $j -= $s; $i++;
	148	}
	149	elsif ($_[$i] =~ /^(v\|version)$/)
	150	{
	151	$ver = 1;
	152	splice @a, $j, 1; $j --;
	153	}
	154	elsif ($_[$i] =~ /^(t\|trace)$/)
	155	{
	156	$trace = 1;
	157	splice @a, $j, 1; $j --;
	158	}
d1a15766	159	elsif ($_[$i] eq 'hex')
	160	{
	161	splice @a, $j, 1; $j --;
075d4edd	162	$hex = \&bigint::_hex_global;
d1a15766	163	}
	164	elsif ($_[$i] eq 'oct')
	165	{
	166	splice @a, $j, 1; $j --;
075d4edd	167	$oct = \&bigint::_oct_global;
d1a15766	168	}
126f3c5f	169	else { die "unknown option $_[$i]"; }
	170	}
	171	my $class;
	172	$_lite = 0; # using M::BI::L ?
	173	if ($trace)
	174	{
	175	require Math::BigInt::Trace; $class = 'Math::BigInt::Trace';
	176	$upgrade = 'Math::BigFloat::Trace';
126f3c5f	177	}
	178	else
	179	{
	180	# see if we can find Math::BigInt::Lite
	181	if (!defined $a && !defined $p) # rounding won't work to well
	182	{
	183	eval 'require Math::BigInt::Lite;';
	184	if ($@ eq '')
	185	{
	186	@import = ( ); # :constant in Lite, not MBI
	187	Math::BigInt::Lite->import( ':constant' );
	188	$_lite= 1; # signal okay
	189	}
	190	}
	191	require Math::BigInt if $_lite == 0; # not already loaded?
	192	$class = 'Math::BigInt'; # regardless of MBIL or not
233f7bc0	193	}
48441d71	194	push @import, $lib_kind => $lib if $lib ne '';
126f3c5f	195	# Math::BigInt::Trace or plain Math::BigInt
233f7bc0	196	$class->import(@import, upgrade => $upgrade);
126f3c5f	197
	198	if ($trace)
	199	{
	200	require Math::BigFloat::Trace; $class = 'Math::BigFloat::Trace';
	201	$downgrade = 'Math::BigInt::Trace';
126f3c5f	202	}
	203	else
	204	{
	205	require Math::BigFloat; $class = 'Math::BigFloat';
	206	}
	207	$class->import(':constant','downgrade',$downgrade);
	208
	209	bignum->accuracy($a) if defined $a;
	210	bignum->precision($p) if defined $p;
	211	if ($ver)
	212	{
	213	print "bignum\t\t\t v$VERSION\n";
	214	print "Math::BigInt::Lite\t v$Math::BigInt::Lite::VERSION\n" if $_lite;
	215	print "Math::BigInt\t\t v$Math::BigInt::VERSION";
	216	my $config = Math::BigInt->config();
	217	print " lib => $config->{lib} v$config->{lib_version}\n";
	218	print "Math::BigFloat\t\t v$Math::BigFloat::VERSION\n";
	219	exit;
	220	}
95a2d02c	221
95a2d02c	222	# Take care of octal/hexadecimal constants
d1a15766	223	overload::constant binary => sub { bigint::_binary_constant(shift) };
95a2d02c	224
4440d13a	225	# if another big* was already loaded:
	226	my ($package) = caller();
	227
	228	no strict 'refs';
	229	if (!defined *{"${package}::inf"})
	230	{
	231	$self->export_to_level(1,$self,@a); # export inf and NaN
	232	}
075d4edd	233	{
	234	no warnings 'redefine';
	235	*CORE::GLOBAL::oct = $oct if $oct;
	236	*CORE::GLOBAL::hex = $hex if $hex;
	237	}
126f3c5f	238	}
	239
	240	1;
	241
	242	__END__
	243
	244	=head1 NAME
	245
	246	bignum - Transparent BigNumber support for Perl
	247
	248	=head1 SYNOPSIS
	249
	250	use bignum;
	251
	252	$x = 2 + 4.5,"\n"; # BigFloat 6.5
b4bc5691	253	print 2 ** 512 * 0.1,"\n"; # really is what you think it is
	254	print inf * inf,"\n"; # prints inf
	255	print NaN * 3,"\n"; # prints NaN
126f3c5f	256
4440d13a	257	{
	258	no bignum;
	259	print 2 ** 256,"\n"; # a normal Perl scalar now
	260	}
	261
d1a15766	262	# for older Perls, note that this will be global:
	263	use bignum qw/hex oct/;
	264	print hex("0x1234567890123490"),"\n";
	265	print oct("01234567890123490"),"\n";
	266
126f3c5f	267	=head1 DESCRIPTION
	268
	269	All operators (including basic math operations) are overloaded. Integer and
	270	floating-point constants are created as proper BigInts or BigFloats,
	271	respectively.
	272
24716a00	273	If you do
	274
	275	use bignum;
	276
	277	at the top of your script, Math::BigFloat and Math::BigInt will be loaded
	278	and any constant number will be converted to an object (Math::BigFloat for
	279	floats like 3.1415 and Math::BigInt for integers like 1234).
	280
	281	So, the following line:
	282
	283	$x = 1234;
	284
	285	creates actually a Math::BigInt and stores a reference to in $x.
	286	This happens transparently and behind your back, so to speak.
	287
	288	You can see this with the following:
	289
	290	perl -Mbignum -le 'print ref(1234)'
	291
	292	Don't worry if it says Math::BigInt::Lite, bignum and friends will use Lite
	293	if it is installed since it is faster for some operations. It will be
3c4b39be	294	automatically upgraded to BigInt whenever necessary:
24716a00	295
	296	perl -Mbignum -le 'print ref(2**255)'
	297
	298	This also means it is a bad idea to check for some specific package, since
	299	the actual contents of $x might be something unexpected. Due to the
3c4b39be	300	transparent way of bignum C<ref()> should not be necessary, anyway.
24716a00	301
	302	Since Math::BigInt and BigFloat also overload the normal math operations,
	303	the following line will still work:
	304
	305	perl -Mbignum -le 'print ref(1234+1234)'
	306
	307	Since numbers are actually objects, you can call all the usual methods from
	308	BigInt/BigFloat on them. This even works to some extent on expressions:
	309
	310	perl -Mbignum -le '$x = 1234; print $x->bdec()'
d1a15766	311	perl -Mbignum -le 'print 1234->copy()->binc();'
	312	perl -Mbignum -le 'print 1234->copy()->binc->badd(6);'
	313	perl -Mbignum -le 'print +(1234)->copy()->binc()'
24716a00	314
	315	(Note that print doesn't do what you expect if the expression starts with
	316	'(' hence the C<+>)
	317
	318	You can even chain the operations together as usual:
	319
d1a15766	320	perl -Mbignum -le 'print 1234->copy()->binc->badd(6);'
24716a00	321	1241
	322
	323	Under bignum (or bigint or bigrat), Perl will "upgrade" the numbers
	324	appropriately. This means that:
	325
	326	perl -Mbignum -le 'print 1234+4.5'
	327	1238.5
	328
	329	will work correctly. These mixed cases don't do always work when using
	330	Math::BigInt or Math::BigFloat alone, or at least not in the way normal Perl
	331	scalars work.
	332
	333	If you do want to work with large integers like under C<use integer;>, try
	334	C<use bigint;>:
	335
	336	perl -Mbigint -le 'print 1234.5+4.5'
	337	1238
	338
	339	There is also C<use bigrat;> which gives you big rationals:
	340
	341	perl -Mbigrat -le 'print 1234+4.1'
	342	12381/10
	343
	344	The entire upgrading/downgrading is still experimental and might not work
d1a15766	345	as you expect or may even have bugs. You might get errors like this:
24716a00	346
	347	Can't use an undefined value as an ARRAY reference at
	348	/usr/local/lib/perl5/5.8.0/Math/BigInt/Calc.pm line 864
	349
	350	This means somewhere a routine got a BigFloat/Lite but expected a BigInt (or
	351	vice versa) and the upgrade/downgrad path was missing. This is a bug, please
	352	report it so that we can fix it.
	353
	354	You might consider using just Math::BigInt or Math::BigFloat, since they
	355	allow you finer control over what get's done in which module/space. For
	356	instance, simple loop counters will be Math::BigInts under C<use bignum;> and
	357	this is slower than keeping them as Perl scalars:
	358
	359	perl -Mbignum -le 'for ($i = 0; $i < 10; $i++) { print ref($i); }'
	360
	361	Please note the following does not work as expected (prints nothing), since
	362	overloading of '..' is not yet possible in Perl (as of v5.8.0):
	363
	364	perl -Mbignum -le 'for (1..2) { print ref($_); }'
	365
b68b7ab1	366	=head2 Options
126f3c5f	367
	368	bignum recognizes some options that can be passed while loading it via use.
	369	The options can (currently) be either a single letter form, or the long form.
	370	The following options exist:
	371
	372	=over 2
	373
	374	=item a or accuracy
	375
	376	This sets the accuracy for all math operations. The argument must be greater
	377	than or equal to zero. See Math::BigInt's bround() function for details.
	378
	379	perl -Mbignum=a,50 -le 'print sqrt(20)'
	380
95a2d02c	381	Note that setting precision and accurary at the same time is not possible.
95a2d02c	382
126f3c5f	383	=item p or precision
	384
	385	This sets the precision for all math operations. The argument can be any
	386	integer. Negative values mean a fixed number of digits after the dot, while
	387	a positive value rounds to this digit left from the dot. 0 or 1 mean round to
	388	integer. See Math::BigInt's bfround() function for details.
	389
	390	perl -Mbignum=p,-50 -le 'print sqrt(20)'
	391
95a2d02c	392	Note that setting precision and accurary at the same time is not possible.
95a2d02c	393
126f3c5f	394	=item t or trace
	395
	396	This enables a trace mode and is primarily for debugging bignum or
	397	Math::BigInt/Math::BigFloat.
	398
	399	=item l or lib
	400
	401	Load a different math lib, see L<MATH LIBRARY>.
	402
	403	perl -Mbignum=l,GMP -e 'print 2 ** 512'
	404
	405	Currently there is no way to specify more than one library on the command
95a2d02c	406	line. This means the following does not work:
	407
	408	perl -Mbignum=l,GMP,Pari -e 'print 2 ** 512'
	409
	410	This will be hopefully fixed soon ;)
126f3c5f	411
d1a15766	412	=item hex
	413
	414	Override the build-in hex() method with a version that can handle big
	415	integers. Note that under Perl older than v5.9.4, this will be global
	416	and cannot be disabled with "no bigint;".
	417
	418	=item oct
	419
	420	Override the build-in oct() method with a version that can handle big
	421	integers. Note that under Perl older than v5.9.4, this will be global
	422	and cannot be disabled with "no bigint;".
	423
126f3c5f	424	=item v or version
	425
	426	This prints out the name and version of all modules used and then exits.
	427
b68b7ab1	428	perl -Mbignum=v
126f3c5f	429
95a2d02c	430	=back
95a2d02c	431
b68b7ab1	432	=head2 Methods
b4bc5691	433
	434	Beside import() and AUTOLOAD() there are only a few other methods.
	435
24716a00	436	Since all numbers are now objects, you can use all functions that are part of
	437	the BigInt or BigFloat API. It is wise to use only the bxxx() notation, and not
	438	the fxxx() notation, though. This makes it possible that the underlying object
	439	might morph into a different class than BigFloat.
	440
4440d13a	441	=head2 Caveats
990fb837	442
	443	But a warning is in order. When using the following to make a copy of a number,
	444	only a shallow copy will be made.
	445
	446	$x = 9; $y = $x;
	447	$x = $y = 7;
	448
b68b7ab1	449	If you want to make a real copy, use the following:
	450
	451	$y = $x->copy();
	452
990fb837	453	Using the copy or the original with overloaded math is okay, e.g. the
	454	following work:
	455
	456	$x = 9; $y = $x;
	457	print $x + 1, " ", $y,"\n"; # prints 10 9
	458
	459	but calling any method that modifies the number directly will result in
3c4b39be	460	B<both> the original and the copy being destroyed:
990fb837	461
	462	$x = 9; $y = $x;
	463	print $x->badd(1), " ", $y,"\n"; # prints 10 10
	464
	465	$x = 9; $y = $x;
	466	print $x->binc(1), " ", $y,"\n"; # prints 10 10
	467
	468	$x = 9; $y = $x;
	469	print $x->bmul(2), " ", $y,"\n"; # prints 18 18
	470
d1a15766	471	Using methods that do not modify, but test the contents works:
990fb837	472
	473	$x = 9; $y = $x;
	474	$z = 9 if $x->is_zero(); # works fine
	475
	476	See the documentation about the copy constructor and C<=> in overload, as
	477	well as the documentation in BigInt for further details.
	478
b4bc5691	479	=over 2
	480
	481	=item inf()
	482
3c4b39be	483	A shortcut to return Math::BigInt->binf(). Useful because Perl does not always
b4bc5691	484	handle bareword C<inf> properly.
	485
	486	=item NaN()
	487
3c4b39be	488	A shortcut to return Math::BigInt->bnan(). Useful because Perl does not always
b4bc5691	489	handle bareword C<NaN> properly.
	490
	491	=item upgrade()
	492
	493	Return the class that numbers are upgraded to, is in fact returning
	494	C<$Math::BigInt::upgrade>.
	495
4440d13a	496	=item in_effect()
	497
	498	use bignum;
	499
	500	print "in effect\n" if bignum::in_effect; # true
	501	{
	502	no bignum;
	503	print "in effect\n" if bignum::in_effect; # false
	504	}
	505
	506	Returns true or false if C<bignum> is in effect in the current scope.
	507
	508	This method only works on Perl v5.9.4 or later.
	509
b4bc5691	510	=back
b4bc5691	511
bd49aa09	512	=head2 Math Library
126f3c5f	513
	514	Math with the numbers is done (by default) by a module called
	515	Math::BigInt::Calc. This is equivalent to saying:
	516
	517	use bignum lib => 'Calc';
	518
	519	You can change this by using:
	520
bd49aa09	521	use bignum lib => 'GMP';
126f3c5f	522
	523	The following would first try to find Math::BigInt::Foo, then
	524	Math::BigInt::Bar, and when this also fails, revert to Math::BigInt::Calc:
	525
	526	use bignum lib => 'Foo,Math::BigInt::Bar';
	527
	528	Please see respective module documentation for further details.
	529
bd49aa09	530	Using C<lib> warns if none of the specified libraries can be found and
	531	L<Math::BigInt> did fall back to one of the default libraries.
	532	To supress this warning, use C<try> instead:
	533
	534	use bignum try => 'GMP';
	535
	536	If you want the code to die instead of falling back, use C<only> instead:
	537
	538	use bignum only => 'GMP';
	539
126f3c5f	540	=head2 INTERNAL FORMAT
	541
	542	The numbers are stored as objects, and their internals might change at anytime,
	543	especially between math operations. The objects also might belong to different
	544	classes, like Math::BigInt, or Math::BigFLoat. Mixing them together, even
	545	with normal scalars is not extraordinary, but normal and expected.
	546
	547	You should not depend on the internal format, all accesses must go through
	548	accessor methods. E.g. looking at $x->{sign} is not a bright idea since there
	549	is no guaranty that the object in question has such a hashkey, nor is a hash
	550	underneath at all.
	551
	552	=head2 SIGN
	553
	554	The sign is either '+', '-', 'NaN', '+inf' or '-inf' and stored seperately.
	555	You can access it with the sign() method.
	556
	557	A sign of 'NaN' is used to represent the result when input arguments are not
	558	numbers or as a result of 0/0. '+inf' and '-inf' represent plus respectively
	559	minus infinity. You will get '+inf' when dividing a positive number by 0, and
	560	'-inf' when dividing any negative number by 0.
	561
d1a15766	562	=head1 CAVAETS
	563
	564	=over 2
	565
	566	=item in_effect()
	567
	568	This method only works on Perl v5.9.4 or later.
	569
	570	=item hex()/oct()
	571
	572	C<bigint> overrides these routines with versions that can also handle
	573	big integer values. Under Perl prior to version v5.9.4, however, this
	574	will not happen unless you specifically ask for it with the two
	575	import tags "hex" and "oct" - and then it will be global and cannot be
	576	disabled inside a scope with "no bigint":
	577
	578	use bigint qw/hex oct/;
	579
	580	print hex("0x1234567890123456");
	581	{
	582	no bigint;
	583	print hex("0x1234567890123456");
	584	}
	585
	586	The second call to hex() will warn about a non-portable constant.
	587
	588	Compare this to:
	589
	590	use bigint;
	591
	592	# will warn only under older than v5.9.4
	593	print hex("0x1234567890123456");
	594
	595	=back
	596
126f3c5f	597	=head1 MODULES USED
	598
	599	C<bignum> is just a thin wrapper around various modules of the Math::BigInt
	600	family. Think of it as the head of the family, who runs the shop, and orders
	601	the others to do the work.
	602
	603	The following modules are currently used by bignum:
	604
	605	Math::BigInt::Lite (for speed, and only if it is loadable)
	606	Math::BigInt
	607	Math::BigFloat
	608
	609	=head1 EXAMPLES
	610
	611	Some cool command line examples to impress the Python crowd ;)
	612
	613	perl -Mbignum -le 'print sqrt(33)'
	614	perl -Mbignum -le 'print 2*255'
	615	perl -Mbignum -le 'print 4.5+2*255'
	616	perl -Mbignum -le 'print 3/7 + 5/7 + 8/3'
	617	perl -Mbignum -le 'print 123->is_odd()'
	618	perl -Mbignum -le 'print log(2)'
bce28014	619	perl -Mbignum -le 'print exp(1)'
126f3c5f	620	perl -Mbignum -le 'print 2 ** 0.5'
126f3c5f	621	perl -Mbignum=a,65 -le 'print 2 ** 0.2'
95a2d02c	622	perl -Mbignum=a,65,l,GMP -le 'print 7 ** 7777'
126f3c5f	623
	624	=head1 LICENSE
	625
	626	This program is free software; you may redistribute it and/or modify it under
	627	the same terms as Perl itself.
	628
	629	=head1 SEE ALSO
	630
	631	Especially L<bigrat> as in C<perl -Mbigrat -le 'print 1/3+1/4'>.
	632
	633	L<Math::BigFloat>, L<Math::BigInt>, L<Math::BigRat> and L<Math::Big> as well
	634	as L<Math::BigInt::BitVect>, L<Math::BigInt::Pari> and L<Math::BigInt::GMP>.
	635
	636	=head1 AUTHORS
	637
95a2d02c	638	(C) by Tels L<http://bloodgate.com/> in early 2002 - 2007.
126f3c5f	639
126f3c5f	640	=cut