[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( PI e ); 
@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  $^H{bignum} = undef;					# no longer in effect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 --;
      $oct = \&bigint::_oct_global;
      }
    elsif ($_[$i] !~ /^(PI|e)\z/)
      {
      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;
  }
  }

sub PI { Math::BigFloat::bpi(@_); }
sub e  { Math::BigFloat->bone->bexp(@_); }

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 e()

Returns Euler's number C<e>, aka exp(1), to the given number of digits.

=item PI()

Returns PI to the given number of digits.

=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	$VERSION = '0.22';
126f3c5f	5	use Exporter;
d1a15766	6	@ISA = qw( bigint );
fade31f0	7	@EXPORT_OK = qw( PI e );
b4bc5691	8	@EXPORT = qw( inf NaN );
126f3c5f	9
126f3c5f	10	use strict;
95a2d02c	11	use overload;
d1a15766	12	require bigint; # no "use" to avoid import being called
126f3c5f	13
	14	##############################################################################
	15
d1a15766	16	BEGIN
	17	{
	18	*inf = \&bigint::inf;
	19	*NaN = \&bigint::NaN;
	20	}
	21
126f3c5f	22	# These are all alike, and thus faked by AUTOLOAD
	23
	24	my @faked = qw/round_mode accuracy precision div_scale/;
	25	use vars qw/$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	$oct = \&bigint::_oct_global;
d1a15766	168	}
fade31f0	169	elsif ($_[$i] !~ /^(PI\|e)\z/)
	170	{
	171	die ("unknown option $_[$i]");
	172	}
126f3c5f	173	}
	174	my $class;
	175	$_lite = 0; # using M::BI::L ?
	176	if ($trace)
	177	{
	178	require Math::BigInt::Trace; $class = 'Math::BigInt::Trace';
	179	$upgrade = 'Math::BigFloat::Trace';
126f3c5f	180	}
	181	else
	182	{
	183	# see if we can find Math::BigInt::Lite
	184	if (!defined $a && !defined $p) # rounding won't work to well
	185	{
	186	eval 'require Math::BigInt::Lite;';
	187	if ($@ eq '')
	188	{
	189	@import = ( ); # :constant in Lite, not MBI
	190	Math::BigInt::Lite->import( ':constant' );
	191	$_lite= 1; # signal okay
	192	}
	193	}
	194	require Math::BigInt if $_lite == 0; # not already loaded?
	195	$class = 'Math::BigInt'; # regardless of MBIL or not
233f7bc0	196	}
48441d71	197	push @import, $lib_kind => $lib if $lib ne '';
126f3c5f	198	# Math::BigInt::Trace or plain Math::BigInt
233f7bc0	199	$class->import(@import, upgrade => $upgrade);
126f3c5f	200
	201	if ($trace)
	202	{
	203	require Math::BigFloat::Trace; $class = 'Math::BigFloat::Trace';
	204	$downgrade = 'Math::BigInt::Trace';
126f3c5f	205	}
	206	else
	207	{
	208	require Math::BigFloat; $class = 'Math::BigFloat';
	209	}
	210	$class->import(':constant','downgrade',$downgrade);
	211
	212	bignum->accuracy($a) if defined $a;
	213	bignum->precision($p) if defined $p;
	214	if ($ver)
	215	{
	216	print "bignum\t\t\t v$VERSION\n";
	217	print "Math::BigInt::Lite\t v$Math::BigInt::Lite::VERSION\n" if $_lite;
	218	print "Math::BigInt\t\t v$Math::BigInt::VERSION";
	219	my $config = Math::BigInt->config();
	220	print " lib => $config->{lib} v$config->{lib_version}\n";
	221	print "Math::BigFloat\t\t v$Math::BigFloat::VERSION\n";
	222	exit;
	223	}
95a2d02c	224
95a2d02c	225	# Take care of octal/hexadecimal constants
d1a15766	226	overload::constant binary => sub { bigint::_binary_constant(shift) };
95a2d02c	227
4440d13a	228	# if another big* was already loaded:
	229	my ($package) = caller();
	230
	231	no strict 'refs';
	232	if (!defined *{"${package}::inf"})
	233	{
	234	$self->export_to_level(1,$self,@a); # export inf and NaN
	235	}
075d4edd	236	{
	237	no warnings 'redefine';
	238	*CORE::GLOBAL::oct = $oct if $oct;
	239	*CORE::GLOBAL::hex = $hex if $hex;
	240	}
126f3c5f	241	}
126f3c5f	242
13201e38	243	sub PI { Math::BigFloat::bpi(@_); }
13201e38	244	sub e { Math::BigFloat->bone->bexp(@_); }
fade31f0	245
126f3c5f	246	1;
	247
	248	__END__
	249
	250	=head1 NAME
	251
	252	bignum - Transparent BigNumber support for Perl
	253
	254	=head1 SYNOPSIS
	255
	256	use bignum;
	257
	258	$x = 2 + 4.5,"\n"; # BigFloat 6.5
b4bc5691	259	print 2 ** 512 * 0.1,"\n"; # really is what you think it is
	260	print inf * inf,"\n"; # prints inf
	261	print NaN * 3,"\n"; # prints NaN
126f3c5f	262
4440d13a	263	{
	264	no bignum;
	265	print 2 ** 256,"\n"; # a normal Perl scalar now
	266	}
	267
d1a15766	268	# for older Perls, note that this will be global:
	269	use bignum qw/hex oct/;
	270	print hex("0x1234567890123490"),"\n";
	271	print oct("01234567890123490"),"\n";
	272
126f3c5f	273	=head1 DESCRIPTION
	274
	275	All operators (including basic math operations) are overloaded. Integer and
	276	floating-point constants are created as proper BigInts or BigFloats,
	277	respectively.
	278
24716a00	279	If you do
	280
	281	use bignum;
	282
	283	at the top of your script, Math::BigFloat and Math::BigInt will be loaded
	284	and any constant number will be converted to an object (Math::BigFloat for
	285	floats like 3.1415 and Math::BigInt for integers like 1234).
	286
	287	So, the following line:
	288
	289	$x = 1234;
	290
	291	creates actually a Math::BigInt and stores a reference to in $x.
	292	This happens transparently and behind your back, so to speak.
	293
	294	You can see this with the following:
	295
	296	perl -Mbignum -le 'print ref(1234)'
	297
	298	Don't worry if it says Math::BigInt::Lite, bignum and friends will use Lite
	299	if it is installed since it is faster for some operations. It will be
3c4b39be	300	automatically upgraded to BigInt whenever necessary:
24716a00	301
	302	perl -Mbignum -le 'print ref(2**255)'
	303
	304	This also means it is a bad idea to check for some specific package, since
	305	the actual contents of $x might be something unexpected. Due to the
3c4b39be	306	transparent way of bignum C<ref()> should not be necessary, anyway.
24716a00	307
	308	Since Math::BigInt and BigFloat also overload the normal math operations,
	309	the following line will still work:
	310
	311	perl -Mbignum -le 'print ref(1234+1234)'
	312
	313	Since numbers are actually objects, you can call all the usual methods from
	314	BigInt/BigFloat on them. This even works to some extent on expressions:
	315
	316	perl -Mbignum -le '$x = 1234; print $x->bdec()'
d1a15766	317	perl -Mbignum -le 'print 1234->copy()->binc();'
	318	perl -Mbignum -le 'print 1234->copy()->binc->badd(6);'
	319	perl -Mbignum -le 'print +(1234)->copy()->binc()'
24716a00	320
	321	(Note that print doesn't do what you expect if the expression starts with
	322	'(' hence the C<+>)
	323
	324	You can even chain the operations together as usual:
	325
d1a15766	326	perl -Mbignum -le 'print 1234->copy()->binc->badd(6);'
24716a00	327	1241
	328
	329	Under bignum (or bigint or bigrat), Perl will "upgrade" the numbers
	330	appropriately. This means that:
	331
	332	perl -Mbignum -le 'print 1234+4.5'
	333	1238.5
	334
	335	will work correctly. These mixed cases don't do always work when using
	336	Math::BigInt or Math::BigFloat alone, or at least not in the way normal Perl
	337	scalars work.
	338
	339	If you do want to work with large integers like under C<use integer;>, try
	340	C<use bigint;>:
	341
	342	perl -Mbigint -le 'print 1234.5+4.5'
	343	1238
	344
	345	There is also C<use bigrat;> which gives you big rationals:
	346
	347	perl -Mbigrat -le 'print 1234+4.1'
	348	12381/10
	349
	350	The entire upgrading/downgrading is still experimental and might not work
d1a15766	351	as you expect or may even have bugs. You might get errors like this:
24716a00	352
	353	Can't use an undefined value as an ARRAY reference at
	354	/usr/local/lib/perl5/5.8.0/Math/BigInt/Calc.pm line 864
	355
	356	This means somewhere a routine got a BigFloat/Lite but expected a BigInt (or
	357	vice versa) and the upgrade/downgrad path was missing. This is a bug, please
	358	report it so that we can fix it.
	359
	360	You might consider using just Math::BigInt or Math::BigFloat, since they
	361	allow you finer control over what get's done in which module/space. For
	362	instance, simple loop counters will be Math::BigInts under C<use bignum;> and
	363	this is slower than keeping them as Perl scalars:
	364
	365	perl -Mbignum -le 'for ($i = 0; $i < 10; $i++) { print ref($i); }'
	366
	367	Please note the following does not work as expected (prints nothing), since
	368	overloading of '..' is not yet possible in Perl (as of v5.8.0):
	369
	370	perl -Mbignum -le 'for (1..2) { print ref($_); }'
	371
b68b7ab1	372	=head2 Options
126f3c5f	373
	374	bignum recognizes some options that can be passed while loading it via use.
	375	The options can (currently) be either a single letter form, or the long form.
	376	The following options exist:
	377
	378	=over 2
	379
	380	=item a or accuracy
	381
	382	This sets the accuracy for all math operations. The argument must be greater
	383	than or equal to zero. See Math::BigInt's bround() function for details.
	384
	385	perl -Mbignum=a,50 -le 'print sqrt(20)'
	386
95a2d02c	387	Note that setting precision and accurary at the same time is not possible.
95a2d02c	388
126f3c5f	389	=item p or precision
	390
	391	This sets the precision for all math operations. The argument can be any
	392	integer. Negative values mean a fixed number of digits after the dot, while
	393	a positive value rounds to this digit left from the dot. 0 or 1 mean round to
	394	integer. See Math::BigInt's bfround() function for details.
	395
	396	perl -Mbignum=p,-50 -le 'print sqrt(20)'
	397
95a2d02c	398	Note that setting precision and accurary at the same time is not possible.
95a2d02c	399
126f3c5f	400	=item t or trace
	401
	402	This enables a trace mode and is primarily for debugging bignum or
	403	Math::BigInt/Math::BigFloat.
	404
	405	=item l or lib
	406
	407	Load a different math lib, see L<MATH LIBRARY>.
	408
	409	perl -Mbignum=l,GMP -e 'print 2 ** 512'
	410
	411	Currently there is no way to specify more than one library on the command
95a2d02c	412	line. This means the following does not work:
	413
	414	perl -Mbignum=l,GMP,Pari -e 'print 2 ** 512'
	415
	416	This will be hopefully fixed soon ;)
126f3c5f	417
d1a15766	418	=item hex
	419
	420	Override the build-in hex() 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
	424	=item oct
	425
	426	Override the build-in oct() method with a version that can handle big
	427	integers. Note that under Perl older than v5.9.4, this will be global
	428	and cannot be disabled with "no bigint;".
	429
126f3c5f	430	=item v or version
	431
	432	This prints out the name and version of all modules used and then exits.
	433
b68b7ab1	434	perl -Mbignum=v
126f3c5f	435
95a2d02c	436	=back
95a2d02c	437
b68b7ab1	438	=head2 Methods
b4bc5691	439
	440	Beside import() and AUTOLOAD() there are only a few other methods.
	441
24716a00	442	Since all numbers are now objects, you can use all functions that are part of
	443	the BigInt or BigFloat API. It is wise to use only the bxxx() notation, and not
	444	the fxxx() notation, though. This makes it possible that the underlying object
	445	might morph into a different class than BigFloat.
	446
4440d13a	447	=head2 Caveats
990fb837	448
	449	But a warning is in order. When using the following to make a copy of a number,
	450	only a shallow copy will be made.
	451
	452	$x = 9; $y = $x;
	453	$x = $y = 7;
	454
b68b7ab1	455	If you want to make a real copy, use the following:
	456
	457	$y = $x->copy();
	458
990fb837	459	Using the copy or the original with overloaded math is okay, e.g. the
	460	following work:
	461
	462	$x = 9; $y = $x;
	463	print $x + 1, " ", $y,"\n"; # prints 10 9
	464
	465	but calling any method that modifies the number directly will result in
3c4b39be	466	B<both> the original and the copy being destroyed:
990fb837	467
	468	$x = 9; $y = $x;
	469	print $x->badd(1), " ", $y,"\n"; # prints 10 10
	470
	471	$x = 9; $y = $x;
	472	print $x->binc(1), " ", $y,"\n"; # prints 10 10
	473
	474	$x = 9; $y = $x;
	475	print $x->bmul(2), " ", $y,"\n"; # prints 18 18
	476
d1a15766	477	Using methods that do not modify, but test the contents works:
990fb837	478
	479	$x = 9; $y = $x;
	480	$z = 9 if $x->is_zero(); # works fine
	481
	482	See the documentation about the copy constructor and C<=> in overload, as
	483	well as the documentation in BigInt for further details.
	484
b4bc5691	485	=over 2
	486
	487	=item inf()
	488
3c4b39be	489	A shortcut to return Math::BigInt->binf(). Useful because Perl does not always
b4bc5691	490	handle bareword C<inf> properly.
	491
	492	=item NaN()
	493
3c4b39be	494	A shortcut to return Math::BigInt->bnan(). Useful because Perl does not always
b4bc5691	495	handle bareword C<NaN> properly.
b4bc5691	496
fade31f0	497	=item e()
	498
	499	Returns Euler's number C<e>, aka exp(1), to the given number of digits.
	500
	501	=item PI()
	502
	503	Returns PI to the given number of digits.
	504
b4bc5691	505	=item upgrade()
	506
	507	Return the class that numbers are upgraded to, is in fact returning
	508	C<$Math::BigInt::upgrade>.
	509
4440d13a	510	=item in_effect()
	511
	512	use bignum;
	513
	514	print "in effect\n" if bignum::in_effect; # true
	515	{
	516	no bignum;
	517	print "in effect\n" if bignum::in_effect; # false
	518	}
	519
	520	Returns true or false if C<bignum> is in effect in the current scope.
	521
	522	This method only works on Perl v5.9.4 or later.
	523
b4bc5691	524	=back
b4bc5691	525
bd49aa09	526	=head2 Math Library
126f3c5f	527
	528	Math with the numbers is done (by default) by a module called
	529	Math::BigInt::Calc. This is equivalent to saying:
	530
	531	use bignum lib => 'Calc';
	532
	533	You can change this by using:
	534
bd49aa09	535	use bignum lib => 'GMP';
126f3c5f	536
	537	The following would first try to find Math::BigInt::Foo, then
	538	Math::BigInt::Bar, and when this also fails, revert to Math::BigInt::Calc:
	539
	540	use bignum lib => 'Foo,Math::BigInt::Bar';
	541
	542	Please see respective module documentation for further details.
	543
bd49aa09	544	Using C<lib> warns if none of the specified libraries can be found and
	545	L<Math::BigInt> did fall back to one of the default libraries.
	546	To supress this warning, use C<try> instead:
	547
	548	use bignum try => 'GMP';
	549
	550	If you want the code to die instead of falling back, use C<only> instead:
	551
	552	use bignum only => 'GMP';
	553
126f3c5f	554	=head2 INTERNAL FORMAT
	555
	556	The numbers are stored as objects, and their internals might change at anytime,
	557	especially between math operations. The objects also might belong to different
	558	classes, like Math::BigInt, or Math::BigFLoat. Mixing them together, even
	559	with normal scalars is not extraordinary, but normal and expected.
	560
	561	You should not depend on the internal format, all accesses must go through
	562	accessor methods. E.g. looking at $x->{sign} is not a bright idea since there
	563	is no guaranty that the object in question has such a hashkey, nor is a hash
	564	underneath at all.
	565
	566	=head2 SIGN
	567
	568	The sign is either '+', '-', 'NaN', '+inf' or '-inf' and stored seperately.
	569	You can access it with the sign() method.
	570
	571	A sign of 'NaN' is used to represent the result when input arguments are not
	572	numbers or as a result of 0/0. '+inf' and '-inf' represent plus respectively
	573	minus infinity. You will get '+inf' when dividing a positive number by 0, and
	574	'-inf' when dividing any negative number by 0.
	575
d1a15766	576	=head1 CAVAETS
	577
	578	=over 2
	579
	580	=item in_effect()
	581
	582	This method only works on Perl v5.9.4 or later.
	583
	584	=item hex()/oct()
	585
	586	C<bigint> overrides these routines with versions that can also handle
	587	big integer values. Under Perl prior to version v5.9.4, however, this
	588	will not happen unless you specifically ask for it with the two
	589	import tags "hex" and "oct" - and then it will be global and cannot be
	590	disabled inside a scope with "no bigint":
	591
	592	use bigint qw/hex oct/;
	593
	594	print hex("0x1234567890123456");
	595	{
	596	no bigint;
	597	print hex("0x1234567890123456");
	598	}
	599
	600	The second call to hex() will warn about a non-portable constant.
	601
	602	Compare this to:
	603
	604	use bigint;
	605
	606	# will warn only under older than v5.9.4
	607	print hex("0x1234567890123456");
	608
	609	=back
	610
126f3c5f	611	=head1 MODULES USED
	612
	613	C<bignum> is just a thin wrapper around various modules of the Math::BigInt
	614	family. Think of it as the head of the family, who runs the shop, and orders
	615	the others to do the work.
	616
	617	The following modules are currently used by bignum:
	618
	619	Math::BigInt::Lite (for speed, and only if it is loadable)
	620	Math::BigInt
	621	Math::BigFloat
	622
	623	=head1 EXAMPLES
	624
	625	Some cool command line examples to impress the Python crowd ;)
	626
	627	perl -Mbignum -le 'print sqrt(33)'
	628	perl -Mbignum -le 'print 2*255'
	629	perl -Mbignum -le 'print 4.5+2*255'
	630	perl -Mbignum -le 'print 3/7 + 5/7 + 8/3'
	631	perl -Mbignum -le 'print 123->is_odd()'
	632	perl -Mbignum -le 'print log(2)'
bce28014	633	perl -Mbignum -le 'print exp(1)'
126f3c5f	634	perl -Mbignum -le 'print 2 ** 0.5'
126f3c5f	635	perl -Mbignum=a,65 -le 'print 2 ** 0.2'
95a2d02c	636	perl -Mbignum=a,65,l,GMP -le 'print 7 ** 7777'
126f3c5f	637
	638	=head1 LICENSE
	639
	640	This program is free software; you may redistribute it and/or modify it under
	641	the same terms as Perl itself.
	642
	643	=head1 SEE ALSO
	644
	645	Especially L<bigrat> as in C<perl -Mbigrat -le 'print 1/3+1/4'>.
	646
	647	L<Math::BigFloat>, L<Math::BigInt>, L<Math::BigRat> and L<Math::Big> as well
	648	as L<Math::BigInt::BitVect>, L<Math::BigInt::Pari> and L<Math::BigInt::GMP>.
	649
	650	=head1 AUTHORS
	651
95a2d02c	652	(C) by Tels L<http://bloodgate.com/> in early 2002 - 2007.
126f3c5f	653
126f3c5f	654	=cut