名前¶

bigint - Perl 用の透過的な BigInteger 対応

概要¶

  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";

説明¶

(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。

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。

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。

use integer 対 use bigint¶

use integer と 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。 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

In practice this makes seldom a difference as 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"

オプション¶

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:

a or accuracy

(a または 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.

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'

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

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。

p or precision

(p または 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, 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.

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 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。

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

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'

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

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。

t or trace

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

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

hex

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;".

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)

oct

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;".

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)

l, lib, try or only

Load a different math lib, see "Math Library".

Load a different math lib, see "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'

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

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'

This will be hopefully fixed soon ;)

This will be hopefully fixed soon ;) (TBT)

v or version

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

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

        perl -Mbigint=v

算術ライブラリ¶

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';

You can change this by using: (TBT)

        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: (TBT)

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

Using lib warns if none of the specified libraries can be found and Math::BigInt did fall back to one of the default libraries. To supress this warning, use try instead: (TBT)

        use bignum try => 'GMP';

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

        use bignum only => 'GMP';

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

内部形式¶

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)

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)

符号¶

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

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)

メソッド¶

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)

inf()

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

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

NaN()

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

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

e

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

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

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

PI

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

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

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

bexp()

        bexp($power,$accuracy);

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

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

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

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

Example:

Example: (TBT)

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

bpi()

        bpi($accuracy);

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

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

Example:

Example: (TBT)

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

upgrade()

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

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

in_effect()

        use bigint;

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

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

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

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

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

算術ライブラリ¶

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

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. (TBT)

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

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

but calling any method that modifies the number directly will result in 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

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

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

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

CAVAETS¶

in_effect()

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

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

hex()/oct()

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":

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");
        }

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

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

Compare this to:

Compare this to: (TBT)

        use bigint;

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

使用するモジュール¶

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)

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

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

例¶

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'

ライセンス¶

This program is free software; you may redistribute it and/or modify it under the same terms as Perl itself.

SEE ALSO¶

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

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

作者¶

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