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

package bignum;
require 5.005;

$VERSION = '0.16';
use Exporter;
@EXPORT_OK 	= qw( ); 
@EXPORT 	= qw( inf NaN ); 
@ISA 		= qw( Exporter );

use strict;

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

# These are all alike, and thus faked by AUTOLOAD

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

sub AUTOLOAD
  {
  my $name = $AUTOLOAD;

  $name =~ s/.*:://;    # split package
  no strict 'refs';
  foreach my $n (@faked)
    {
    if ($n eq $name)
      {
      *{"bignum::$name"} = sub 
        {
        my $self = shift;
        no strict 'refs';
        if (defined $_[0])
          {
          Math::BigInt->$name($_[0]);
          return Math::BigFloat->$name($_[0]);
          }
        return Math::BigInt->$name();
        };
      return &$name;
      }
    }
 
  # delayed load of Carp and avoid recursion
  require Carp;
  Carp::croak ("Can't call bignum\-\>$name, not a valid method");
  }

sub upgrade
  {
  my $self = shift;
  no strict 'refs';
#  if (defined $_[0])
#    {
#    $Math::BigInt::upgrade = $_[0];
#    $Math::BigFloat::upgrade = $_[0];
#    }
  return $Math::BigInt::upgrade;
  }

sub import 
  {
  my $self = shift;

  # some defaults
  my $lib = 'Calc';
  my $upgrade = 'Math::BigFloat';
  my $downgrade = 'Math::BigInt';

  my @import = ( ':constant' );				# drive it w/ constant
  my @a = @_; my $l = scalar @_; my $j = 0;
  my ($ver,$trace);					# version? trace?
  my ($a,$p);						# accuracy, precision
  for ( my $i = 0; $i < $l ; $i++,$j++ )
    {
    if ($_[$i] eq 'upgrade')
      {
      # this causes upgrading
      $upgrade = $_[$i+1];		# or undef to disable
      my $s = 2; $s = 1 if @a-$j < 2;	# avoid "can not modify non-existant..."
      splice @a, $j, $s; $j -= $s; $i++;
      }
    elsif ($_[$i] eq 'downgrade')
      {
      # this causes downgrading
      $downgrade = $_[$i+1];		# or undef to disable
      my $s = 2; $s = 1 if @a-$j < 2;	# avoid "can not modify non-existant..."
      splice @a, $j, $s; $j -= $s; $i++;
      }
    elsif ($_[$i] =~ /^(l|lib)$/)
      {
      # this causes a different low lib to take care...
      $lib = $_[$i+1] || '';
      my $s = 2; $s = 1 if @a-$j < 2;	# avoid "can not modify non-existant..."
      splice @a, $j, $s; $j -= $s; $i++;
      }
    elsif ($_[$i] =~ /^(a|accuracy)$/)
      {
      $a = $_[$i+1];
      my $s = 2; $s = 1 if @a-$j < 2;	# avoid "can not modify non-existant..."
      splice @a, $j, $s; $j -= $s; $i++;
      }
    elsif ($_[$i] =~ /^(p|precision)$/)
      {
      $p = $_[$i+1];
      my $s = 2; $s = 1 if @a-$j < 2;	# avoid "can not modify non-existant..."
      splice @a, $j, $s; $j -= $s; $i++;
      }
    elsif ($_[$i] =~ /^(v|version)$/)
      {
      $ver = 1;
      splice @a, $j, 1; $j --;
      }
    elsif ($_[$i] =~ /^(t|trace)$/)
      {
      $trace = 1;
      splice @a, $j, 1; $j --;
      }
    else { die "unknown option $_[$i]"; }
    }
  my $class;
  $_lite = 0;					# using M::BI::L ?
  if ($trace)
    {
    require Math::BigInt::Trace; $class = 'Math::BigInt::Trace';
    $upgrade = 'Math::BigFloat::Trace';	
    }
  else
    {
    # see if we can find Math::BigInt::Lite
    if (!defined $a && !defined $p)		# rounding won't work to well
      {
      eval 'require Math::BigInt::Lite;';
      if ($@ eq '')
        {
        @import = ( );				# :constant in Lite, not MBI
        Math::BigInt::Lite->import( ':constant' );
        $_lite= 1;				# signal okay
        }
      }
    require Math::BigInt if $_lite == 0;	# not already loaded?
    $class = 'Math::BigInt';			# regardless of MBIL or not
    } 
  # Math::BigInt::Trace or plain Math::BigInt
  $class->import(@import, upgrade => $upgrade, lib => $lib);

  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;
    }
  $self->export_to_level(1,$self,@a);		# export inf and NaN
  }

sub inf () { Math::BigInt->binf(); }
sub NaN () { Math::BigInt->bnan(); }

1;

__END__

=head1 NAME

bignum - Transparent BigNumber support for Perl

=head1 SYNOPSIS

  use bignum;

  $x = 2 + 4.5,"\n";			# BigFloat 6.5
  print 2 ** 512 * 0.1,"\n";		# really is what you think it is
  print inf * inf,"\n";			# prints inf
  print NaN * 3,"\n";			# prints NaN

=head1 DESCRIPTION

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

If you do 

        use bignum;

at the top of your script, Math::BigFloat and Math::BigInt will be loaded
and any constant number will be converted to an object (Math::BigFloat for
floats like 3.1415 and Math::BigInt for integers like 1234).

So, the following line:

        $x = 1234;

creates actually a Math::BigInt and stores a reference to in $x.
This happens transparently and behind your back, so to speak.

You can see this with the following:

        perl -Mbignum -le 'print ref(1234)'

Don't worry if it says Math::BigInt::Lite, bignum and friends will use Lite
if it is installed since it is faster for some operations. It will be
automatically upgraded to BigInt whenever neccessary:

        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 neccessary, anyway.

Since Math::BigInt and BigFloat also overload the normal math operations,
the following line will still work:

        perl -Mbignum -le 'print ref(1234+1234)'

Since numbers are actually objects, you can call all the usual methods from
BigInt/BigFloat on them. This even works to some extent on expressions:

        perl -Mbignum -le '$x = 1234; print $x->bdec()'
        perl -Mbignum -le 'print 1234->binc();'
        perl -Mbignum -le 'print 1234->binc->badd(6);'
        perl -Mbignum -le 'print +(1234)->binc()'

(Note that print doesn't do what you expect if the expression starts with
'(' hence the C<+>)

You can even chain the operations together as usual:

        perl -Mbignum -le 'print 1234->binc->badd(6);'
        1241

Under bignum (or bigint or bigrat), Perl will "upgrade" the numbers
appropriately. This means that:

        perl -Mbignum -le 'print 1234+4.5'
        1238.5

will work correctly. These mixed cases don't do always work when using
Math::BigInt or Math::BigFloat alone, or at least not in the way normal Perl
scalars work. 

If you do want to work with large integers like under C<use integer;>, try
C<use bigint;>:

        perl -Mbigint -le 'print 1234.5+4.5'
        1238

There is also C<use bigrat;> which gives you big rationals:

        perl -Mbigrat -le 'print 1234+4.1'
        12381/10

The entire upgrading/downgrading is still experimental and might not work
as you expect or may even have bugs.

You might get errors like this:

        Can't use an undefined value as an ARRAY reference at
        /usr/local/lib/perl5/5.8.0/Math/BigInt/Calc.pm line 864

This means somewhere a routine got a BigFloat/Lite but expected a BigInt (or
vice versa) and the upgrade/downgrad path was missing. This is a bug, please
report it so that we can fix it.

You might consider using just Math::BigInt or Math::BigFloat, since they
allow you finer control over what get's done in which module/space. For
instance, simple loop counters will be Math::BigInts under C<use bignum;> and
this is slower than keeping them as Perl scalars:

        perl -Mbignum -le 'for ($i = 0; $i < 10; $i++) { print ref($i); }'

Please note the following does not work as expected (prints nothing), since
overloading of '..' is not yet possible in Perl (as of v5.8.0):

        perl -Mbignum -le 'for (1..2) { print ref($_); }'

=head2 Options

bignum recognizes some options that can be passed while loading it via use.
The options can (currently) be either a single letter form, or the long form.
The following options exist:

=over 2

=item a or accuracy

This sets the accuracy for all math operations. The argument must be greater
than or equal to zero. See Math::BigInt's bround() function for details.

	perl -Mbignum=a,50 -le 'print sqrt(20)'

=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)'

=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 will be hopefully fixed soon ;)

=item v or version

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

	perl -Mbignum=v

=head2 Methods

Beside import() and AUTOLOAD() there are only a few other methods.

Since all numbers are now objects, you can use all functions that are part of
the BigInt or BigFloat API. It is wise to use only the bxxx() notation, and not
the fxxx() notation, though. This makes it possible that the underlying object
might morph into a different class than BigFloat.

=head2 Caveat

But a warning is in order. When using the following to make a copy of a number,
only a shallow copy will be made.

        $x = 9; $y = $x;
        $x = $y = 7;

If you want to make a real copy, use the following:

        $y = $x->copy();

Using the copy or the original with overloaded math is okay, e.g. the
following work:

        $x = 9; $y = $x;
        print $x + 1, " ", $y,"\n";     # prints 10 9

but calling any method that modifies the number directly will result in
B<both> the original and the copy beeing destroyed:

        $x = 9; $y = $x;
        print $x->badd(1), " ", $y,"\n";        # prints 10 10

        $x = 9; $y = $x;
        print $x->binc(1), " ", $y,"\n";        # prints 10 10

        $x = 9; $y = $x;
        print $x->bmul(2), " ", $y,"\n";        # prints 18 18

Using methods that do not modify, but testthe contents works:

        $x = 9; $y = $x;
        $z = 9 if $x->is_zero();                # works fine

See the documentation about the copy constructor and C<=> in overload, as
well as the documentation in BigInt for further details.

=over 2

=item inf()

A shortcut to return Math::BigInt->binf(). Usefull because Perl does not always
handle bareword C<inf> properly.

=item NaN()

A shortcut to return Math::BigInt->bnan(). Usefull because Perl does not always
handle bareword C<NaN> properly.

=item upgrade()

Return the class that numbers are upgraded to, is in fact returning
C<$Math::BigInt::upgrade>.

=back

=head2 MATH LIBRARY

Math with the numbers is done (by default) by a module called
Math::BigInt::Calc. This is equivalent to saying:

	use bignum lib => 'Calc';

You can change this by using:

	use bignum lib => 'BitVect';

The following would first try to find Math::BigInt::Foo, then
Math::BigInt::Bar, and when this also fails, revert to Math::BigInt::Calc:

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

Please see respective module documentation for further details.

=head2 INTERNAL FORMAT

The numbers are stored as objects, and their internals might change at anytime,
especially between math operations. The objects also might belong to different
classes, like Math::BigInt, or Math::BigFLoat. Mixing them together, even
with normal scalars is not extraordinary, but normal and expected.

You should not depend on the internal format, all accesses must go through
accessor methods. E.g. looking at $x->{sign} is not a bright idea since there
is no guaranty that the object in question has such a hashkey, nor is a hash
underneath at all.

=head2 SIGN

The sign is either '+', '-', 'NaN', '+inf' or '-inf' and stored seperately.
You can access it with the sign() method.

A sign of 'NaN' is used to represent the result when input arguments are not
numbers or as a result of 0/0. '+inf' and '-inf' represent plus respectively
minus infinity. You will get '+inf' when dividing a positive number by 0, and
'-inf' when dividing any negative number by 0.

=head1 MODULES USED

C<bignum> is just a thin wrapper around various modules of the Math::BigInt
family. Think of it as the head of the family, who runs the shop, and orders
the others to do the work.

The following modules are currently used by bignum:

	Math::BigInt::Lite	(for speed, and only if it is loadable)
	Math::BigInt
	Math::BigFloat

=head1 EXAMPLES

Some cool command line examples to impress the Python crowd ;)
 
	perl -Mbignum -le 'print sqrt(33)'
	perl -Mbignum -le 'print 2*255'
	perl -Mbignum -le 'print 4.5+2*255'
	perl -Mbignum -le 'print 3/7 + 5/7 + 8/3'
	perl -Mbignum -le 'print 123->is_odd()'
	perl -Mbignum -le 'print log(2)'
	perl -Mbignum -le 'print 2 ** 0.5'
	perl -Mbignum=a,65 -le 'print 2 ** 0.2'

=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, 2003.

=cut
Commit	Line	Data
126f3c5f	1	package bignum;
	2	require 5.005;
	3
b68b7ab1	4	$VERSION = '0.16';
126f3c5f	5	use Exporter;
b4bc5691	6	@EXPORT_OK = qw( );
	7	@EXPORT = qw( inf NaN );
	8	@ISA = qw( Exporter );
126f3c5f	9
	10	use strict;
	11
	12	##############################################################################
	13
	14	# These are all alike, and thus faked by AUTOLOAD
	15
	16	my @faked = qw/round_mode accuracy precision div_scale/;
	17	use vars qw/$VERSION $AUTOLOAD $_lite/; # _lite for testsuite
	18
	19	sub AUTOLOAD
	20	{
	21	my $name = $AUTOLOAD;
	22
	23	$name =~ s/.*:://; # split package
	24	no strict 'refs';
	25	foreach my $n (@faked)
	26	{
	27	if ($n eq $name)
	28	{
	29	*{"bignum::$name"} = sub
	30	{
	31	my $self = shift;
	32	no strict 'refs';
	33	if (defined $_[0])
	34	{
	35	Math::BigInt->$name($_[0]);
990fb837	36	return Math::BigFloat->$name($_[0]);
126f3c5f	37	}
	38	return Math::BigInt->$name();
	39	};
	40	return &$name;
	41	}
	42	}
	43
	44	# delayed load of Carp and avoid recursion
	45	require Carp;
	46	Carp::croak ("Can't call bignum\-\>$name, not a valid method");
	47	}
	48
	49	sub upgrade
	50	{
	51	my $self = shift;
	52	no strict 'refs';
	53	# if (defined $_[0])
	54	# {
	55	# $Math::BigInt::upgrade = $_[0];
	56	# $Math::BigFloat::upgrade = $_[0];
	57	# }
	58	return $Math::BigInt::upgrade;
	59	}
	60
	61	sub import
	62	{
	63	my $self = shift;
	64
	65	# some defaults
	66	my $lib = 'Calc';
	67	my $upgrade = 'Math::BigFloat';
	68	my $downgrade = 'Math::BigInt';
	69
	70	my @import = ( ':constant' ); # drive it w/ constant
	71	my @a = @_; my $l = scalar @_; my $j = 0;
	72	my ($ver,$trace); # version? trace?
	73	my ($a,$p); # accuracy, precision
	74	for ( my $i = 0; $i < $l ; $i++,$j++ )
	75	{
	76	if ($_[$i] eq 'upgrade')
	77	{
	78	# this causes upgrading
	79	$upgrade = $_[$i+1]; # or undef to disable
	80	my $s = 2; $s = 1 if @a-$j < 2; # avoid "can not modify non-existant..."
	81	splice @a, $j, $s; $j -= $s; $i++;
	82	}
	83	elsif ($_[$i] eq 'downgrade')
	84	{
	85	# this causes downgrading
	86	$downgrade = $_[$i+1]; # or undef to disable
	87	my $s = 2; $s = 1 if @a-$j < 2; # avoid "can not modify non-existant..."
	88	splice @a, $j, $s; $j -= $s; $i++;
	89	}
	90	elsif ($_[$i] =~ /^(l\|lib)$/)
	91	{
	92	# this causes a different low lib to take care...
	93	$lib = $_[$i+1] \|\| '';
	94	my $s = 2; $s = 1 if @a-$j < 2; # avoid "can not modify non-existant..."
	95	splice @a, $j, $s; $j -= $s; $i++;
	96	}
	97	elsif ($_[$i] =~ /^(a\|accuracy)$/)
	98	{
	99	$a = $_[$i+1];
	100	my $s = 2; $s = 1 if @a-$j < 2; # avoid "can not modify non-existant..."
101	splice @a, $j, $s; $j -= $s; $i++;
102	}
103	elsif ($_[$i] =~ /^(p\|precision)$/)
104	{
105	$p = $_[$i+1];
106	my $s = 2; $s = 1 if @a-$j < 2; # avoid "can not modify non-existant..."
107	splice @a, $j, $s; $j -= $s; $i++;
108	}
109	elsif ($_[$i] =~ /^(v\|version)$/)
110	{
111	$ver = 1;
112	splice @a, $j, 1; $j --;
113	}
114	elsif ($_[$i] =~ /^(t\|trace)$/)
115	{
116	$trace = 1;
117	splice @a, $j, 1; $j --;
118	}
119	else { die "unknown option $_[$i]"; }
120	}
121	my $class;
122	$_lite = 0; # using M::BI::L ?
123	if ($trace)
124	{
125	require Math::BigInt::Trace; $class = 'Math::BigInt::Trace';
126	$upgrade = 'Math::BigFloat::Trace';
126f3c5f	127	}
	128	else
	129	{
	130	# see if we can find Math::BigInt::Lite
	131	if (!defined $a && !defined $p) # rounding won't work to well
	132	{
	133	eval 'require Math::BigInt::Lite;';
	134	if ($@ eq '')
	135	{
	136	@import = ( ); # :constant in Lite, not MBI
	137	Math::BigInt::Lite->import( ':constant' );
	138	$_lite= 1; # signal okay
	139	}
	140	}
	141	require Math::BigInt if $_lite == 0; # not already loaded?
	142	$class = 'Math::BigInt'; # regardless of MBIL or not
	143	}
	144	# Math::BigInt::Trace or plain Math::BigInt
	145	$class->import(@import, upgrade => $upgrade, lib => $lib);
	146
	147	if ($trace)
	148	{
	149	require Math::BigFloat::Trace; $class = 'Math::BigFloat::Trace';
	150	$downgrade = 'Math::BigInt::Trace';
126f3c5f	151	}
	152	else
	153	{
	154	require Math::BigFloat; $class = 'Math::BigFloat';
	155	}
	156	$class->import(':constant','downgrade',$downgrade);
	157
	158	bignum->accuracy($a) if defined $a;
	159	bignum->precision($p) if defined $p;
	160	if ($ver)
	161	{
	162	print "bignum\t\t\t v$VERSION\n";
	163	print "Math::BigInt::Lite\t v$Math::BigInt::Lite::VERSION\n" if $_lite;
	164	print "Math::BigInt\t\t v$Math::BigInt::VERSION";
	165	my $config = Math::BigInt->config();
	166	print " lib => $config->{lib} v$config->{lib_version}\n";
	167	print "Math::BigFloat\t\t v$Math::BigFloat::VERSION\n";
	168	exit;
	169	}
b4bc5691	170	$self->export_to_level(1,$self,@a); # export inf and NaN
126f3c5f	171	}
126f3c5f	172
b4bc5691	173	sub inf () { Math::BigInt->binf(); }
	174	sub NaN () { Math::BigInt->bnan(); }
	175
126f3c5f	176	1;
	177
	178	__END__
	179
	180	=head1 NAME
	181
	182	bignum - Transparent BigNumber support for Perl
	183
	184	=head1 SYNOPSIS
	185
	186	use bignum;
	187
	188	$x = 2 + 4.5,"\n"; # BigFloat 6.5
b4bc5691	189	print 2 ** 512 * 0.1,"\n"; # really is what you think it is
	190	print inf * inf,"\n"; # prints inf
	191	print NaN * 3,"\n"; # prints NaN
126f3c5f	192
	193	=head1 DESCRIPTION
	194
	195	All operators (including basic math operations) are overloaded. Integer and
	196	floating-point constants are created as proper BigInts or BigFloats,
	197	respectively.
	198
24716a00	199	If you do
	200
	201	use bignum;
	202
	203	at the top of your script, Math::BigFloat and Math::BigInt will be loaded
	204	and any constant number will be converted to an object (Math::BigFloat for
	205	floats like 3.1415 and Math::BigInt for integers like 1234).
	206
	207	So, the following line:
	208
	209	$x = 1234;
	210
	211	creates actually a Math::BigInt and stores a reference to in $x.
	212	This happens transparently and behind your back, so to speak.
	213
	214	You can see this with the following:
	215
	216	perl -Mbignum -le 'print ref(1234)'
	217
	218	Don't worry if it says Math::BigInt::Lite, bignum and friends will use Lite
	219	if it is installed since it is faster for some operations. It will be
	220	automatically upgraded to BigInt whenever neccessary:
	221
	222	perl -Mbignum -le 'print ref(2**255)'
	223
	224	This also means it is a bad idea to check for some specific package, since
	225	the actual contents of $x might be something unexpected. Due to the
	226	transparent way of bignum C<ref()> should not be neccessary, anyway.
	227
	228	Since Math::BigInt and BigFloat also overload the normal math operations,
	229	the following line will still work:
	230
	231	perl -Mbignum -le 'print ref(1234+1234)'
	232
	233	Since numbers are actually objects, you can call all the usual methods from
	234	BigInt/BigFloat on them. This even works to some extent on expressions:
	235
	236	perl -Mbignum -le '$x = 1234; print $x->bdec()'
	237	perl -Mbignum -le 'print 1234->binc();'
	238	perl -Mbignum -le 'print 1234->binc->badd(6);'
	239	perl -Mbignum -le 'print +(1234)->binc()'
	240
	241	(Note that print doesn't do what you expect if the expression starts with
	242	'(' hence the C<+>)
	243
	244	You can even chain the operations together as usual:
	245
	246	perl -Mbignum -le 'print 1234->binc->badd(6);'
	247	1241
	248
	249	Under bignum (or bigint or bigrat), Perl will "upgrade" the numbers
	250	appropriately. This means that:
	251
	252	perl -Mbignum -le 'print 1234+4.5'
	253	1238.5
	254
	255	will work correctly. These mixed cases don't do always work when using
	256	Math::BigInt or Math::BigFloat alone, or at least not in the way normal Perl
	257	scalars work.
	258
	259	If you do want to work with large integers like under C<use integer;>, try
	260	C<use bigint;>:
	261
	262	perl -Mbigint -le 'print 1234.5+4.5'
263	1238
264
265	There is also C<use bigrat;> which gives you big rationals:
266
267	perl -Mbigrat -le 'print 1234+4.1'
268	12381/10
269
270	The entire upgrading/downgrading is still experimental and might not work
271	as you expect or may even have bugs.
272
273	You might get errors like this:
274
275	Can't use an undefined value as an ARRAY reference at
276	/usr/local/lib/perl5/5.8.0/Math/BigInt/Calc.pm line 864
277
278	This means somewhere a routine got a BigFloat/Lite but expected a BigInt (or
279	vice versa) and the upgrade/downgrad path was missing. This is a bug, please
280	report it so that we can fix it.
281
282	You might consider using just Math::BigInt or Math::BigFloat, since they
283	allow you finer control over what get's done in which module/space. For
284	instance, simple loop counters will be Math::BigInts under C<use bignum;> and
285	this is slower than keeping them as Perl scalars:
286
287	perl -Mbignum -le 'for ($i = 0; $i < 10; $i++) { print ref($i); }'
288
289	Please note the following does not work as expected (prints nothing), since
290	overloading of '..' is not yet possible in Perl (as of v5.8.0):
291
292	perl -Mbignum -le 'for (1..2) { print ref($_); }'
293
b68b7ab1	294	=head2 Options
126f3c5f	295
	296	bignum recognizes some options that can be passed while loading it via use.
	297	The options can (currently) be either a single letter form, or the long form.
	298	The following options exist:
	299
	300	=over 2
	301
	302	=item a or accuracy
	303
	304	This sets the accuracy for all math operations. The argument must be greater
	305	than or equal to zero. See Math::BigInt's bround() function for details.
	306
	307	perl -Mbignum=a,50 -le 'print sqrt(20)'
	308
	309	=item p or precision
	310
	311	This sets the precision for all math operations. The argument can be any
	312	integer. Negative values mean a fixed number of digits after the dot, while
	313	a positive value rounds to this digit left from the dot. 0 or 1 mean round to
	314	integer. See Math::BigInt's bfround() function for details.
	315
	316	perl -Mbignum=p,-50 -le 'print sqrt(20)'
	317
	318	=item t or trace
	319
	320	This enables a trace mode and is primarily for debugging bignum or
	321	Math::BigInt/Math::BigFloat.
	322
	323	=item l or lib
	324
	325	Load a different math lib, see L<MATH LIBRARY>.
	326
	327	perl -Mbignum=l,GMP -e 'print 2 ** 512'
	328
	329	Currently there is no way to specify more than one library on the command
	330	line. This will be hopefully fixed soon ;)
	331
	332	=item v or version
	333
	334	This prints out the name and version of all modules used and then exits.
	335
b68b7ab1	336	perl -Mbignum=v
126f3c5f	337
b68b7ab1	338	=head2 Methods
b4bc5691	339
	340	Beside import() and AUTOLOAD() there are only a few other methods.
	341
24716a00	342	Since all numbers are now objects, you can use all functions that are part of
	343	the BigInt or BigFloat API. It is wise to use only the bxxx() notation, and not
	344	the fxxx() notation, though. This makes it possible that the underlying object
	345	might morph into a different class than BigFloat.
	346
b68b7ab1	347	=head2 Caveat
990fb837	348
	349	But a warning is in order. When using the following to make a copy of a number,
	350	only a shallow copy will be made.
	351
	352	$x = 9; $y = $x;
	353	$x = $y = 7;
	354
b68b7ab1	355	If you want to make a real copy, use the following:
	356
	357	$y = $x->copy();
	358
990fb837	359	Using the copy or the original with overloaded math is okay, e.g. the
	360	following work:
	361
	362	$x = 9; $y = $x;
	363	print $x + 1, " ", $y,"\n"; # prints 10 9
	364
	365	but calling any method that modifies the number directly will result in
	366	B<both> the original and the copy beeing destroyed:
	367
	368	$x = 9; $y = $x;
	369	print $x->badd(1), " ", $y,"\n"; # prints 10 10
	370
	371	$x = 9; $y = $x;
	372	print $x->binc(1), " ", $y,"\n"; # prints 10 10
	373
	374	$x = 9; $y = $x;
	375	print $x->bmul(2), " ", $y,"\n"; # prints 18 18
	376
	377	Using methods that do not modify, but testthe contents works:
	378
	379	$x = 9; $y = $x;
	380	$z = 9 if $x->is_zero(); # works fine
	381
	382	See the documentation about the copy constructor and C<=> in overload, as
	383	well as the documentation in BigInt for further details.
	384
b4bc5691	385	=over 2
	386
	387	=item inf()
	388
	389	A shortcut to return Math::BigInt->binf(). Usefull because Perl does not always
	390	handle bareword C<inf> properly.
	391
	392	=item NaN()
	393
	394	A shortcut to return Math::BigInt->bnan(). Usefull because Perl does not always
	395	handle bareword C<NaN> properly.
	396
	397	=item upgrade()
	398
	399	Return the class that numbers are upgraded to, is in fact returning
	400	C<$Math::BigInt::upgrade>.
	401
	402	=back
	403
126f3c5f	404	=head2 MATH LIBRARY
	405
	406	Math with the numbers is done (by default) by a module called
	407	Math::BigInt::Calc. This is equivalent to saying:
	408
	409	use bignum lib => 'Calc';
	410
	411	You can change this by using:
	412
	413	use bignum lib => 'BitVect';
	414
	415	The following would first try to find Math::BigInt::Foo, then
	416	Math::BigInt::Bar, and when this also fails, revert to Math::BigInt::Calc:
	417
	418	use bignum lib => 'Foo,Math::BigInt::Bar';
	419
	420	Please see respective module documentation for further details.
	421
	422	=head2 INTERNAL FORMAT
	423
	424	The numbers are stored as objects, and their internals might change at anytime,
	425	especially between math operations. The objects also might belong to different
	426	classes, like Math::BigInt, or Math::BigFLoat. Mixing them together, even
	427	with normal scalars is not extraordinary, but normal and expected.
	428
	429	You should not depend on the internal format, all accesses must go through
	430	accessor methods. E.g. looking at $x->{sign} is not a bright idea since there
	431	is no guaranty that the object in question has such a hashkey, nor is a hash
	432	underneath at all.
	433
	434	=head2 SIGN
	435
	436	The sign is either '+', '-', 'NaN', '+inf' or '-inf' and stored seperately.
	437	You can access it with the sign() method.
	438
	439	A sign of 'NaN' is used to represent the result when input arguments are not
	440	numbers or as a result of 0/0. '+inf' and '-inf' represent plus respectively
	441	minus infinity. You will get '+inf' when dividing a positive number by 0, and
	442	'-inf' when dividing any negative number by 0.
	443
126f3c5f	444	=head1 MODULES USED
	445
	446	C<bignum> is just a thin wrapper around various modules of the Math::BigInt
	447	family. Think of it as the head of the family, who runs the shop, and orders
	448	the others to do the work.
	449
	450	The following modules are currently used by bignum:
	451
	452	Math::BigInt::Lite (for speed, and only if it is loadable)
	453	Math::BigInt
	454	Math::BigFloat
	455
	456	=head1 EXAMPLES
	457
	458	Some cool command line examples to impress the Python crowd ;)
	459
	460	perl -Mbignum -le 'print sqrt(33)'
	461	perl -Mbignum -le 'print 2*255'
	462	perl -Mbignum -le 'print 4.5+2*255'
	463	perl -Mbignum -le 'print 3/7 + 5/7 + 8/3'
	464	perl -Mbignum -le 'print 123->is_odd()'
	465	perl -Mbignum -le 'print log(2)'
	466	perl -Mbignum -le 'print 2 ** 0.5'
	467	perl -Mbignum=a,65 -le 'print 2 ** 0.2'
	468
	469	=head1 LICENSE
	470
	471	This program is free software; you may redistribute it and/or modify it under
	472	the same terms as Perl itself.
	473
	474	=head1 SEE ALSO
	475
	476	Especially L<bigrat> as in C<perl -Mbigrat -le 'print 1/3+1/4'>.
	477
	478	L<Math::BigFloat>, L<Math::BigInt>, L<Math::BigRat> and L<Math::Big> as well
	479	as L<Math::BigInt::BitVect>, L<Math::BigInt::Pari> and L<Math::BigInt::GMP>.
	480
	481	=head1 AUTHORS
	482
27e7b8bb	483	(C) by Tels L<http://bloodgate.com/> in early 2002, 2003.
126f3c5f	484
126f3c5f	485	=cut