[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 bexp bpi ); 
@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  $^H{bignum} = undef;					# no longer in effect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|bexp|bpi)\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->new('3.141592653589793238462643383279502884197'); }
sub e () { Math::BigFloat->new('2.718281828459045235360287471352662497757'); }
sub bpi ($) { Math::BigFloat::bpi(@_); }
sub bexp ($$) { my $x = Math::BigFloat->new($_[0]); $x->bexp($_[1]); }

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 built-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 built-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

	# perl -Mbignum=e -wle 'print e'

Returns Euler's number C<e>, aka exp(1).

=item PI()

	# perl -Mbignum=PI -wle 'print PI'

Returns PI.

=item bexp()

	bexp($power,$accuracy);

Returns Euler's number C<e> raised to the appropriate power, to
the wanted accuracy.

Example:

	# perl -Mbignum=bexp -wle 'print bexp(1,80)'

=item bpi()

	bpi($accuracy);

Returns PI to the wanted accuracy.

Example:

	# perl -Mbignum=bpi -wle 'print bpi(80)'

=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	$VERSION = '0.22';
126f3c5f	5	use Exporter;
d1a15766	6	@ISA = qw( bigint );
d98d5fa0	7	@EXPORT_OK = qw( PI e bexp bpi );
b4bc5691	8	@EXPORT = qw( inf NaN );
126f3c5f	9
126f3c5f	10	use strict;
95a2d02c	11	use overload;
d1a15766	12	require bigint; # no "use" to avoid import being called
126f3c5f	13
	14	##############################################################################
	15
d1a15766	16	BEGIN
	17	{
	18	*inf = \&bigint::inf;
	19	*NaN = \&bigint::NaN;
	20	}
	21
126f3c5f	22	# These are all alike, and thus faked by AUTOLOAD
	23
	24	my @faked = qw/round_mode accuracy precision div_scale/;
	25	use vars qw/$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	$oct = \&bigint::_oct_global;
d1a15766	168	}
d98d5fa0	169	elsif ($_[$i] !~ /^(PI\|e\|bexp\|bpi)\z/)
fade31f0	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 $hex;
	240	}
126f3c5f	241	}
126f3c5f	242
d98d5fa0	243	sub PI () { Math::BigFloat->new('3.141592653589793238462643383279502884197'); }
	244	sub e () { Math::BigFloat->new('2.718281828459045235360287471352662497757'); }
	245	sub bpi ($) { Math::BigFloat::bpi(@_); }
	246	sub bexp ($$) { my $x = Math::BigFloat->new($_[0]); $x->bexp($_[1]); }
fade31f0	247
126f3c5f	248	1;
	249
	250	__END__
	251
	252	=head1 NAME
	253
	254	bignum - Transparent BigNumber support for Perl
	255
	256	=head1 SYNOPSIS
	257
	258	use bignum;
	259
	260	$x = 2 + 4.5,"\n"; # BigFloat 6.5
b4bc5691	261	print 2 ** 512 * 0.1,"\n"; # really is what you think it is
	262	print inf * inf,"\n"; # prints inf
	263	print NaN * 3,"\n"; # prints NaN
126f3c5f	264
4440d13a	265	{
	266	no bignum;
	267	print 2 ** 256,"\n"; # a normal Perl scalar now
	268	}
	269
d1a15766	270	# for older Perls, note that this will be global:
	271	use bignum qw/hex oct/;
	272	print hex("0x1234567890123490"),"\n";
	273	print oct("01234567890123490"),"\n";
	274
126f3c5f	275	=head1 DESCRIPTION
	276
	277	All operators (including basic math operations) are overloaded. Integer and
	278	floating-point constants are created as proper BigInts or BigFloats,
	279	respectively.
	280
24716a00	281	If you do
	282
	283	use bignum;
	284
	285	at the top of your script, Math::BigFloat and Math::BigInt will be loaded
	286	and any constant number will be converted to an object (Math::BigFloat for
	287	floats like 3.1415 and Math::BigInt for integers like 1234).
	288
	289	So, the following line:
	290
	291	$x = 1234;
	292
	293	creates actually a Math::BigInt and stores a reference to in $x.
	294	This happens transparently and behind your back, so to speak.
	295
	296	You can see this with the following:
	297
	298	perl -Mbignum -le 'print ref(1234)'
	299
	300	Don't worry if it says Math::BigInt::Lite, bignum and friends will use Lite
	301	if it is installed since it is faster for some operations. It will be
3c4b39be	302	automatically upgraded to BigInt whenever necessary:
24716a00	303
	304	perl -Mbignum -le 'print ref(2**255)'
	305
	306	This also means it is a bad idea to check for some specific package, since
	307	the actual contents of $x might be something unexpected. Due to the
3c4b39be	308	transparent way of bignum C<ref()> should not be necessary, anyway.
24716a00	309
	310	Since Math::BigInt and BigFloat also overload the normal math operations,
	311	the following line will still work:
	312
	313	perl -Mbignum -le 'print ref(1234+1234)'
	314
	315	Since numbers are actually objects, you can call all the usual methods from
	316	BigInt/BigFloat on them. This even works to some extent on expressions:
	317
	318	perl -Mbignum -le '$x = 1234; print $x->bdec()'
d1a15766	319	perl -Mbignum -le 'print 1234->copy()->binc();'
	320	perl -Mbignum -le 'print 1234->copy()->binc->badd(6);'
	321	perl -Mbignum -le 'print +(1234)->copy()->binc()'
24716a00	322
	323	(Note that print doesn't do what you expect if the expression starts with
	324	'(' hence the C<+>)
	325
	326	You can even chain the operations together as usual:
	327
d1a15766	328	perl -Mbignum -le 'print 1234->copy()->binc->badd(6);'
24716a00	329	1241
	330
	331	Under bignum (or bigint or bigrat), Perl will "upgrade" the numbers
	332	appropriately. This means that:
	333
	334	perl -Mbignum -le 'print 1234+4.5'
	335	1238.5
	336
	337	will work correctly. These mixed cases don't do always work when using
	338	Math::BigInt or Math::BigFloat alone, or at least not in the way normal Perl
	339	scalars work.
	340
	341	If you do want to work with large integers like under C<use integer;>, try
	342	C<use bigint;>:
	343
	344	perl -Mbigint -le 'print 1234.5+4.5'
	345	1238
	346
	347	There is also C<use bigrat;> which gives you big rationals:
	348
	349	perl -Mbigrat -le 'print 1234+4.1'
	350	12381/10
	351
	352	The entire upgrading/downgrading is still experimental and might not work
d1a15766	353	as you expect or may even have bugs. You might get errors like this:
24716a00	354
	355	Can't use an undefined value as an ARRAY reference at
	356	/usr/local/lib/perl5/5.8.0/Math/BigInt/Calc.pm line 864
	357
	358	This means somewhere a routine got a BigFloat/Lite but expected a BigInt (or
	359	vice versa) and the upgrade/downgrad path was missing. This is a bug, please
	360	report it so that we can fix it.
	361
	362	You might consider using just Math::BigInt or Math::BigFloat, since they
	363	allow you finer control over what get's done in which module/space. For
	364	instance, simple loop counters will be Math::BigInts under C<use bignum;> and
	365	this is slower than keeping them as Perl scalars:
	366
	367	perl -Mbignum -le 'for ($i = 0; $i < 10; $i++) { print ref($i); }'
	368
	369	Please note the following does not work as expected (prints nothing), since
	370	overloading of '..' is not yet possible in Perl (as of v5.8.0):
	371
	372	perl -Mbignum -le 'for (1..2) { print ref($_); }'
	373
b68b7ab1	374	=head2 Options
126f3c5f	375
	376	bignum recognizes some options that can be passed while loading it via use.
	377	The options can (currently) be either a single letter form, or the long form.
	378	The following options exist:
	379
	380	=over 2
	381
	382	=item a or accuracy
	383
	384	This sets the accuracy for all math operations. The argument must be greater
	385	than or equal to zero. See Math::BigInt's bround() function for details.
	386
	387	perl -Mbignum=a,50 -le 'print sqrt(20)'
	388
95a2d02c	389	Note that setting precision and accurary at the same time is not possible.
95a2d02c	390
126f3c5f	391	=item p or precision
	392
	393	This sets the precision for all math operations. The argument can be any
	394	integer. Negative values mean a fixed number of digits after the dot, while
	395	a positive value rounds to this digit left from the dot. 0 or 1 mean round to
	396	integer. See Math::BigInt's bfround() function for details.
	397
	398	perl -Mbignum=p,-50 -le 'print sqrt(20)'
	399
95a2d02c	400	Note that setting precision and accurary at the same time is not possible.
95a2d02c	401
126f3c5f	402	=item t or trace
	403
	404	This enables a trace mode and is primarily for debugging bignum or
	405	Math::BigInt/Math::BigFloat.
	406
	407	=item l or lib
	408
	409	Load a different math lib, see L<MATH LIBRARY>.
	410
	411	perl -Mbignum=l,GMP -e 'print 2 ** 512'
	412
	413	Currently there is no way to specify more than one library on the command
95a2d02c	414	line. This means the following does not work:
	415
	416	perl -Mbignum=l,GMP,Pari -e 'print 2 ** 512'
	417
	418	This will be hopefully fixed soon ;)
126f3c5f	419
d1a15766	420	=item hex
d1a15766	421
43cde5e1	422	Override the built-in hex() method with a version that can handle big
d1a15766	423	integers. Note that under Perl older than v5.9.4, this will be global
	424	and cannot be disabled with "no bigint;".
	425
	426	=item oct
	427
43cde5e1	428	Override the built-in oct() method with a version that can handle big
d1a15766	429	integers. Note that under Perl older than v5.9.4, this will be global
	430	and cannot be disabled with "no bigint;".
	431
126f3c5f	432	=item v or version
	433
	434	This prints out the name and version of all modules used and then exits.
	435
b68b7ab1	436	perl -Mbignum=v
126f3c5f	437
95a2d02c	438	=back
95a2d02c	439
b68b7ab1	440	=head2 Methods
b4bc5691	441
	442	Beside import() and AUTOLOAD() there are only a few other methods.
	443
24716a00	444	Since all numbers are now objects, you can use all functions that are part of
	445	the BigInt or BigFloat API. It is wise to use only the bxxx() notation, and not
	446	the fxxx() notation, though. This makes it possible that the underlying object
	447	might morph into a different class than BigFloat.
	448
4440d13a	449	=head2 Caveats
990fb837	450
	451	But a warning is in order. When using the following to make a copy of a number,
	452	only a shallow copy will be made.
	453
	454	$x = 9; $y = $x;
	455	$x = $y = 7;
	456
b68b7ab1	457	If you want to make a real copy, use the following:
	458
	459	$y = $x->copy();
	460
990fb837	461	Using the copy or the original with overloaded math is okay, e.g. the
	462	following work:
	463
	464	$x = 9; $y = $x;
	465	print $x + 1, " ", $y,"\n"; # prints 10 9
	466
	467	but calling any method that modifies the number directly will result in
3c4b39be	468	B<both> the original and the copy being destroyed:
990fb837	469
	470	$x = 9; $y = $x;
	471	print $x->badd(1), " ", $y,"\n"; # prints 10 10
	472
	473	$x = 9; $y = $x;
	474	print $x->binc(1), " ", $y,"\n"; # prints 10 10
	475
	476	$x = 9; $y = $x;
	477	print $x->bmul(2), " ", $y,"\n"; # prints 18 18
	478
d1a15766	479	Using methods that do not modify, but test the contents works:
990fb837	480
	481	$x = 9; $y = $x;
	482	$z = 9 if $x->is_zero(); # works fine
	483
	484	See the documentation about the copy constructor and C<=> in overload, as
	485	well as the documentation in BigInt for further details.
	486
b4bc5691	487	=over 2
	488
	489	=item inf()
	490
3c4b39be	491	A shortcut to return Math::BigInt->binf(). Useful because Perl does not always
b4bc5691	492	handle bareword C<inf> properly.
	493
	494	=item NaN()
	495
3c4b39be	496	A shortcut to return Math::BigInt->bnan(). Useful because Perl does not always
b4bc5691	497	handle bareword C<NaN> properly.
b4bc5691	498
d98d5fa0	499	=item e
fade31f0	500
d98d5fa0	501	# perl -Mbignum=e -wle 'print e'
	502
	503	Returns Euler's number C<e>, aka exp(1).
fade31f0	504
	505	=item PI()
	506
d98d5fa0	507	# perl -Mbignum=PI -wle 'print PI'
	508
	509	Returns PI.
	510
	511	=item bexp()
	512
	513	bexp($power,$accuracy);
	514
	515	Returns Euler's number C<e> raised to the appropriate power, to
	516	the wanted accuracy.
	517
	518	Example:
	519
	520	# perl -Mbignum=bexp -wle 'print bexp(1,80)'
	521
	522	=item bpi()
	523
	524	bpi($accuracy);
	525
	526	Returns PI to the wanted accuracy.
	527
	528	Example:
	529
	530	# perl -Mbignum=bpi -wle 'print bpi(80)'
fade31f0	531
b4bc5691	532	=item upgrade()
	533
	534	Return the class that numbers are upgraded to, is in fact returning
	535	C<$Math::BigInt::upgrade>.
	536
4440d13a	537	=item in_effect()
	538
	539	use bignum;
	540
	541	print "in effect\n" if bignum::in_effect; # true
	542	{
	543	no bignum;
	544	print "in effect\n" if bignum::in_effect; # false
	545	}
	546
	547	Returns true or false if C<bignum> is in effect in the current scope.
	548
	549	This method only works on Perl v5.9.4 or later.
	550
b4bc5691	551	=back
b4bc5691	552
bd49aa09	553	=head2 Math Library
126f3c5f	554
	555	Math with the numbers is done (by default) by a module called
	556	Math::BigInt::Calc. This is equivalent to saying:
	557
	558	use bignum lib => 'Calc';
	559
	560	You can change this by using:
	561
bd49aa09	562	use bignum lib => 'GMP';
126f3c5f	563
	564	The following would first try to find Math::BigInt::Foo, then
	565	Math::BigInt::Bar, and when this also fails, revert to Math::BigInt::Calc:
	566
	567	use bignum lib => 'Foo,Math::BigInt::Bar';
	568
	569	Please see respective module documentation for further details.
	570
bd49aa09	571	Using C<lib> warns if none of the specified libraries can be found and
	572	L<Math::BigInt> did fall back to one of the default libraries.
	573	To supress this warning, use C<try> instead:
	574
	575	use bignum try => 'GMP';
	576
	577	If you want the code to die instead of falling back, use C<only> instead:
	578
	579	use bignum only => 'GMP';
	580
126f3c5f	581	=head2 INTERNAL FORMAT
	582
	583	The numbers are stored as objects, and their internals might change at anytime,
	584	especially between math operations. The objects also might belong to different
	585	classes, like Math::BigInt, or Math::BigFLoat. Mixing them together, even
	586	with normal scalars is not extraordinary, but normal and expected.
	587
	588	You should not depend on the internal format, all accesses must go through
	589	accessor methods. E.g. looking at $x->{sign} is not a bright idea since there
	590	is no guaranty that the object in question has such a hashkey, nor is a hash
	591	underneath at all.
	592
	593	=head2 SIGN
	594
	595	The sign is either '+', '-', 'NaN', '+inf' or '-inf' and stored seperately.
	596	You can access it with the sign() method.
	597
	598	A sign of 'NaN' is used to represent the result when input arguments are not
	599	numbers or as a result of 0/0. '+inf' and '-inf' represent plus respectively
	600	minus infinity. You will get '+inf' when dividing a positive number by 0, and
	601	'-inf' when dividing any negative number by 0.
	602
d1a15766	603	=head1 CAVAETS
	604
	605	=over 2
	606
	607	=item in_effect()
	608
	609	This method only works on Perl v5.9.4 or later.
	610
	611	=item hex()/oct()
	612
	613	C<bigint> overrides these routines with versions that can also handle
	614	big integer values. Under Perl prior to version v5.9.4, however, this
	615	will not happen unless you specifically ask for it with the two
	616	import tags "hex" and "oct" - and then it will be global and cannot be
	617	disabled inside a scope with "no bigint":
	618
	619	use bigint qw/hex oct/;
	620
	621	print hex("0x1234567890123456");
	622	{
	623	no bigint;
	624	print hex("0x1234567890123456");
	625	}
	626
	627	The second call to hex() will warn about a non-portable constant.
	628
	629	Compare this to:
	630
	631	use bigint;
	632
	633	# will warn only under older than v5.9.4
	634	print hex("0x1234567890123456");
	635
	636	=back
	637
126f3c5f	638	=head1 MODULES USED
	639
	640	C<bignum> is just a thin wrapper around various modules of the Math::BigInt
	641	family. Think of it as the head of the family, who runs the shop, and orders
	642	the others to do the work.
	643
	644	The following modules are currently used by bignum:
	645
	646	Math::BigInt::Lite (for speed, and only if it is loadable)
	647	Math::BigInt
	648	Math::BigFloat
	649
	650	=head1 EXAMPLES
	651
	652	Some cool command line examples to impress the Python crowd ;)
	653
	654	perl -Mbignum -le 'print sqrt(33)'
	655	perl -Mbignum -le 'print 2*255'
	656	perl -Mbignum -le 'print 4.5+2*255'
	657	perl -Mbignum -le 'print 3/7 + 5/7 + 8/3'
	658	perl -Mbignum -le 'print 123->is_odd()'
	659	perl -Mbignum -le 'print log(2)'
bce28014	660	perl -Mbignum -le 'print exp(1)'
126f3c5f	661	perl -Mbignum -le 'print 2 ** 0.5'
126f3c5f	662	perl -Mbignum=a,65 -le 'print 2 ** 0.2'
95a2d02c	663	perl -Mbignum=a,65,l,GMP -le 'print 7 ** 7777'
126f3c5f	664
	665	=head1 LICENSE
	666
	667	This program is free software; you may redistribute it and/or modify it under
	668	the same terms as Perl itself.
	669
	670	=head1 SEE ALSO
	671
	672	Especially L<bigrat> as in C<perl -Mbigrat -le 'print 1/3+1/4'>.
	673
	674	L<Math::BigFloat>, L<Math::BigInt>, L<Math::BigRat> and L<Math::Big> as well
	675	as L<Math::BigInt::BitVect>, L<Math::BigInt::Pari> and L<Math::BigInt::GMP>.
	676
	677	=head1 AUTHORS
	678
95a2d02c	679	(C) by Tels L<http://bloodgate.com/> in early 2002 - 2007.
126f3c5f	680
126f3c5f	681	=cut