=encoding euc-jp

=head1 NAME

=begin original

bigint - Transparent BigInteger support for Perl

=end original

bigint - Perl 用の透過的な BigInteger 対応

=head1 SYNOPSIS

  use bigint;

  $x = 2 + 4.5,"\n";			# BigInt 6
  print 2 ** 512,"\n";			# really is what you think it is
  print inf + 42,"\n";			# inf
  print NaN * 7,"\n";			# NaN
  print hex("0x1234567890123490"),"\n";	# Perl v5.9.4 or later

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

  # Note that this will be global:
  use bigint qw/hex oct/;
  print hex("0x1234567890123490"),"\n";
  print oct("01234567890123490"),"\n";

=head1 DESCRIPTION

=begin original

All operators (including basic math operations) are overloaded. Integer
constants are created as proper BigInts.

=end original

(基本算術演算子を含む)全ての演算子がオーバーロードされます。
整数定数は適切な BigInt として作成されます。

=begin original

Floating point constants are truncated to integer. All parts and results of
expressions are also truncated.

=end original

浮動小数点数定数は整数に切り詰められます。
式の全ての部分と結果も切り詰められます。

=begin original

Unlike L<integer>, this pragma creates integer constants that are only
limited in their size by the available memory and CPU time.

=end original

L<integer> と違って、このプラグマは利用可能なメモリと CPU 時間によってのみ
制限されるサイズの整数定数を作成します。

=head2 use integer vs. use bigint

(use integer 対 use bigint)

=begin original

There is one small difference between C<use integer> and C<use bigint>: the
former will not affect assignments to variables and the return value of
some functions. C<bigint> truncates these results to integer too:

=end original

C<use integer> と C<use bigint> には一つの小さな違いがあります: 前者は
変数への代入と一部の関数の返り値には影響を与えません。
C<bigint> もこれらの結果を整数に切り詰めます:

	# perl -Minteger -wle 'print 3.2'
	3.2
	# perl -Minteger -wle 'print 3.2 + 0'
	3
	# perl -Mbigint -wle 'print 3.2'
	3
	# perl -Mbigint -wle 'print 3.2 + 0'
	3

	# perl -Mbigint -wle 'print exp(1) + 0'
	2
	# perl -Mbigint -wle 'print exp(1)'
	2
	# perl -Minteger -wle 'print exp(1)'
	2.71828182845905
	# perl -Minteger -wle 'print exp(1) + 0'
	2

=begin original

In practice this makes seldom a difference as B<parts and results> of
expressions will be truncated anyway, but this can, for instance, affect the
return value of subroutines:

=end original

In practice this makes seldom a difference as B<parts and results> of
expressions will be truncated anyway, but this can, for instance, affect the
return value of subroutines:
(TBT)

	sub three_integer { use integer; return 3.2; } 
	sub three_bigint { use bigint; return 3.2; }
 
	print three_integer(), " ", three_bigint(),"\n";	# prints "3.2 3"

=head2 Options

(オプション)

=begin original

bigint 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:

=end original

bigint は use で読み込むときに渡せるオプションがいくつかあります。
オプションは(現在のところ)一文字形式と長い形式のどちらかです。
以下のオプションがあります:

=over 2

=item a or accuracy

(a または accuracy)

=begin original

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.

=end original

これは全ての算術演算の有効桁数を設定します。
この引数は 0 以上でなければなりません。
詳しくは Math::BigInt の bround() 関数を参照してください。

	perl -Mbigint=a,2 -le 'print 12345+1'

=begin original

Note that setting precision and accurary at the same time is not possible.

=end original

精度と有効桁数を同時に設定することはできないことに注意してください。

=item p or precision

(p または precision)

=begin original

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, and
are <B>ignored</B> since all operations happen in integer space.
A positive value rounds to this digit left from the dot. 0 or 1 mean round to
integer and are ignore like negative values.

=end original

これは全ての算術演算の精度を設定します。
引数は任意の整数です。
負の値は小数点の後の固定桁数を意味し、全ての演算は整数の範囲で行われるので
これは B<無視されます> 。
正数は小数点からこの値だけ左側の数字で丸めます。
0 または 1 は整数に丸めることを意味し、負数と同様に無視されます。

=begin original

See Math::BigInt's bfround() function for details.

=end original

詳しくは Math::BigInt の bfround() 関数を参照してください。

	perl -Mbignum=p,5 -le 'print 123456789+123'

=begin original

Note that setting precision and accurary at the same time is not possible.

=end original

精度と有効桁数を同時に設定することはできないことに注意してください。

=item t or trace

=begin original

This enables a trace mode and is primarily for debugging bigint or
Math::BigInt.

=end original

This enables a trace mode and is primarily for debugging bigint or
Math::BigInt.
(TBT)

=item hex

=begin original

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

=end original

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

=item oct

=begin original

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

=end original

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

=item l, lib, try or only

=begin original

Load a different math lib, see L<Math Library>.

=end original

Load a different math lib, see L<Math Library>.
(TBT)

	perl -Mbigint=lib,GMP -e 'print 2 ** 512'
	perl -Mbigint=try,GMP -e 'print 2 ** 512'
	perl -Mbigint=only,GMP -e 'print 2 ** 512'

=begin original

Currently there is no way to specify more than one library on the command
line. This means the following does not work:

=end original

Currently there is no way to specify more than one library on the command
line. This means the following does not work:
(TBT)

	perl -Mbignum=l,GMP,Pari -e 'print 2 ** 512'

=begin original

This will be hopefully fixed soon ;)

=end original

This will be hopefully fixed soon ;)
(TBT)

=item v or version

=begin original

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

=end original

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

	perl -Mbigint=v

=back

=head2 Math Library

(算術ライブラリ)

=begin original

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

=end original

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

	use bigint lib => 'Calc';

=begin original

You can change this by using:

=end original

You can change this by using:
(TBT)

	use bignum lib => 'GMP';

=begin original

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

=end original

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

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

=begin original

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:

=end original

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:
(TBT)

        use bignum try => 'GMP';

=begin original

If you want the code to die instead of falling back, use C<only> instead:

=end original

If you want the code to die instead of falling back, use C<only> instead:
(TBT)

        use bignum only => 'GMP';

=begin original

Please see respective module documentation for further details.

=end original

Please see respective module documentation for further details.
(TBT)

=head2 Internal Format

(内部形式)

=begin original

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::BigInt::Lite. Mixing them together, even
with normal scalars is not extraordinary, but normal and expected.

=end original

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::BigInt::Lite. Mixing them together, even
with normal scalars is not extraordinary, but normal and expected.
(TBT)

=begin original

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

=end original

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

=head2 Sign

(符号)

=begin original

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

=end original

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

=begin original

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.

=end original

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.
(TBT)

=head2 Methods

(メソッド)

=begin original

Since all numbers are now objects, you can use all functions that are part of
the BigInt API. You can only use the bxxx() notation, and not the fxxx()
notation, though. 

=end original

Since all numbers are now objects, you can use all functions that are part of
the BigInt API. You can only use the bxxx() notation, and not the fxxx()
notation, though. 
(TBT)

=over 2

=item inf()

=begin original

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

=end original

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

=item NaN()

=begin original

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

=end original

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

=item e

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

=begin original

Returns Euler's number C<e>, aka exp(1). Note that under bigint, this is
truncated to an integer, and hence simple '2'.

=end original

Returns Euler's number C<e>, aka exp(1). Note that under bigint, this is
truncated to an integer, and hence simple '2'.
(TBT)

=item PI

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

=begin original

Returns PI. Note that under bigint, this is truncated to an integer, and hence
simple '3'.

=end original

Returns PI. Note that under bigint, this is truncated to an integer, and hence
simple '3'.
(TBT)

=item bexp()

	bexp($power,$accuracy);

=begin original

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

=end original

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

=begin original

Note that under bigint, the result is truncated to an integer.

=end original

Note that under bigint, the result is truncated to an integer.
(TBT)

=begin original

Example:

=end original

Example:
(TBT)

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

=item bpi()

	bpi($accuracy);

=begin original

Returns PI to the wanted accuracy. Note that under bigint, this is truncated
to an integer, and hence simple '3'.

=end original

Returns PI to the wanted accuracy. Note that under bigint, this is truncated
to an integer, and hence simple '3'.
(TBT)

=begin original

Example:

=end original

Example:
(TBT)

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

=item upgrade()

=begin original

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

=end original

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

=item in_effect()

	use bigint;

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

=begin original

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

=end original

Returns true or false if C<bigint> is in effect in the current scope.
(TBT)

=begin original

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

=end original

This method only works on Perl v5.9.4 or later.
(TBT)

=back

=head2 MATH LIBRARY

(算術ライブラリ)

=begin original

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

=end original

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

=head2 Caveat

=begin original

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

=end original

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

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

=begin original

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

=end original

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

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

=begin original

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

=end original

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

	$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

=begin original

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

=end original

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

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

=begin original

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

=end original

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

=head1 CAVAETS

=over 2

=item in_effect()

=begin original

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

=end original

This method only works on Perl v5.9.4 or later.
(TBT)

=item hex()/oct()

=begin original

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":

=end original

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":
(TBT)

	use bigint qw/hex oct/;

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

=begin original

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

=end original

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

=begin original

Compare this to:

=end original

Compare this to:
(TBT)

	use bigint;

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

=back

=head1 MODULES USED

(使用するモジュール)

=begin original

C<bigint> 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.

=end original

C<bigint> 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.
(TBT)

=begin original

The following modules are currently used by bigint:

=end original

The following modules are currently used by bigint:
(TBT)

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

=head1 EXAMPLES

(例)

=begin original

Some cool command line examples to impress the Python crowd ;) You might want
to compare them to the results under -Mbignum or -Mbigrat:

=end original

Some cool command line examples to impress the Python crowd ;) You might want
to compare them to the results under -Mbignum or -Mbigrat:
(TBT)

	perl -Mbigint -le 'print sqrt(33)'
	perl -Mbigint -le 'print 2*255'
	perl -Mbigint -le 'print 4.5+2*255'
	perl -Mbigint -le 'print 3/7 + 5/7 + 8/3'
	perl -Mbigint -le 'print 123->is_odd()'
	perl -Mbigint -le 'print log(2)'
	perl -Mbigint -le 'print 2 ** 0.5'
	perl -Mbigint=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

=begin original

Especially L<bigrat> as in C<perl -Mbigrat -le 'print 1/3+1/4'> and
L<bignum> as in C<perl -Mbignum -le 'print sqrt(2)'>.

=end original

特に C<perl -Mbigrat -le 'print 1/3+1/4'> のような L<bigrat> と
C<perl -Mbignum -le 'print sqrt(2)'> のような L<bignum>。

=begin original

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>.

=end original

L<Math::BigInt>, L<Math::BigRat>, L<Math::Big> および
L<Math::BigInt::BitVect>, L<Math::BigInt::Pari>, L<Math::BigInt::GMP>。

=head1 AUTHORS

(C) by Tels L<http://bloodgate.com/> in early 2002 - 2007.

=begin meta

Translate: SHIRAKATA Kentaro <argrath@ub32.org> (0.23)
Status: in progress

=end meta

=cut