=encoding euc-jp =head1 NAME =begin original bignum - Transparent BigNumber support for Perl =end original bignum - Perl 用の透過的な BigNumber 対応 =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 =begin original All operators (including basic math operations) are overloaded. Integer and floating-point constants are created as proper BigInts or BigFloats, respectively. =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。 整数定数と浮動小数点数定数はそれぞれ適切な BigInt または BigFloat として 作成されます。 =begin original If you do =end original このように use bignum; =begin original 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). =end original スクリプトの先頭に書くと、Math::BigFloat と Math::BigInt が読み込まれ、 全ての定数はオブジェクトに変換されます (3.1415 のようは浮動小数点数は Math::BigFloat に、1234 のような整数は Math::BigInt に)。 =begin original So, the following line: =end original それで、以下の行は: $x = 1234; =begin original creates actually a Math::BigInt and stores a reference to in $x. This happens transparently and behind your back, so to speak. =end original 実際には Math::BigInt を作成して、リファレンスを $x に保管します。 これは透過的に、いわば背後で行われます。 =begin original You can see this with the following: =end original 以下のようにすればこれを見ることができます: perl -Mbignum -le 'print ref(1234)' =begin original 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: =end original Math::BigInt::Lite と言われても気にしないで下さい; bignum および 親類は、Lite がインストールされている場合は使います; これはいくつかの 演算がより速いからです。 もし必要なら自動的に BigInt に昇格します: perl -Mbignum -le 'print ref(2**255)' =begin original This also means it is a bad idea to check for some specific package, since the actual contents of $x might be something unexpected. Due to the transparent way of bignum C should not be necessary, anyway. =end original これは、$x の実際の内容は不確定なので、特定のパッケージかどうかを チェックするというのは良くない考えであることも示しています。 とにかく、bignum での C の透過的な方法は不要のはずです。 =begin original Since Math::BigInt and BigFloat also overload the normal math operations, the following line will still work: =end original Math::BigInt と BigFloat は通常の算術演算もオーバーロードするので、 以下のような行も動作するままです: perl -Mbignum -le 'print ref(1234+1234)' =begin original 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: =end original 数値は実際にはオブジェクトなので、使われている BigInt/BigFloat の全ての 通常のメソッドを呼び出すことができます。 これは式のいくつかの拡張に対してさえ動作します: 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()' =begin original (Note that print doesn't do what you expect if the expression starts with '(' hence the C<+>) =end original (Note that print doesn't do what you expect if the expression starts with '(' hence the C<+>) (TBT) =begin original You can even chain the operations together as usual: =end original You can even chain the operations together as usual: (TBT) perl -Mbignum -le 'print 1234->copy()->binc->badd(6);' 1241 =begin original Under bignum (or bigint or bigrat), Perl will "upgrade" the numbers appropriately. This means that: =end original Under bignum (or bigint or bigrat), Perl will "upgrade" the numbers appropriately. This means that: (TBT) perl -Mbignum -le 'print 1234+4.5' 1238.5 =begin original 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. =end original 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. (TBT) =begin original If you do want to work with large integers like under C, try C: =end original If you do want to work with large integers like under C, try C: (TBT) perl -Mbigint -le 'print 1234.5+4.5' 1238 =begin original There is also C which gives you big rationals: =end original There is also C which gives you big rationals: (TBT) perl -Mbigrat -le 'print 1234+4.1' 12381/10 =begin original 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: =end original 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: (TBT) Can't use an undefined value as an ARRAY reference at /usr/local/lib/perl5/5.8.0/Math/BigInt/Calc.pm line 864 =begin original 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. =end original 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. (TBT) =begin original 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 and this is slower than keeping them as Perl scalars: =end original 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 and this is slower than keeping them as Perl scalars: (TBT) perl -Mbignum -le 'for ($i = 0; $i < 10; $i++) { print ref($i); }' =begin original 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): =end original 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): (TBT) perl -Mbignum -le 'for (1..2) { print ref($_); }' =head2 Options (オプション) =begin original 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: =end original 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: (TBT) =over 2 =item a or 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 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. (TBT) perl -Mbignum=a,50 -le 'print sqrt(20)' =begin original Note that setting precision and accurary at the same time is not possible. =end original Note that setting precision and accurary at the same time is not possible. (TBT) =item p or 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, 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. =end 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, 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. (TBT) perl -Mbignum=p,-50 -le 'print sqrt(20)' =begin original Note that setting precision and accurary at the same time is not possible. =end original Note that setting precision and accurary at the same time is not possible. (TBT) =item t or trace =begin original This enables a trace mode and is primarily for debugging bignum or Math::BigInt/Math::BigFloat. =end original This enables a trace mode and is primarily for debugging bignum or Math::BigInt/Math::BigFloat. (TBT) =item l or lib =begin original Load a different math lib, see L. =end original Load a different math lib, see L. (TBT) perl -Mbignum=l,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 hex =begin original 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;". =end original 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;". (TBT) =item oct =begin original 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;". =end original 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;". (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 -Mbignum=v =back =head2 Methods (メソッド) =begin original Beside import() and AUTOLOAD() there are only a few other methods. =end original Beside import() and AUTOLOAD() there are only a few other methods. (TBT) =begin original 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. =end original 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. (TBT) =head2 Caveats =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 If you want to make a real copy, use the following: =end original If you want to make a real copy, use the following: (TBT) $y = $x->copy(); =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 the original and the copy being destroyed: =end original but calling any method that modifies the number directly will result in B 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 test the contents works: =end original Using methods that do not modify, but test the contents works: (TBT) $x = 9; $y = $x; $z = 9 if $x->is_zero(); # works fine =begin original See the documentation about the copy constructor and C<=> in overload, as well as the documentation in BigInt for further details. =end original See the documentation about the copy constructor and C<=> in overload, as well as the documentation in BigInt for further details. (TBT) =over 2 =item inf() =begin original A shortcut to return Math::BigInt->binf(). Useful because Perl does not always handle bareword C properly. =end original A shortcut to return Math::BigInt->binf(). Useful because Perl does not always handle bareword C properly. (TBT) =item NaN() =begin original A shortcut to return Math::BigInt->bnan(). Useful because Perl does not always handle bareword C properly. =end original A shortcut to return Math::BigInt->bnan(). Useful because Perl does not always handle bareword C properly. (TBT) =item e # perl -Mbignum=e -wle 'print e' =begin original Returns Euler's number C, aka exp(1). =end original Returns Euler's number C, aka exp(1). (TBT) =item PI() # perl -Mbignum=PI -wle 'print PI' =begin original Returns PI. =end original Returns PI. (TBT) =item bexp() bexp($power,$accuracy); =begin original Returns Euler's number C raised to the appropriate power, to the wanted accuracy. =end original Returns Euler's number C raised to the appropriate power, to the wanted accuracy. (TBT) =begin original Example: =end original Example: (TBT) # perl -Mbignum=bexp -wle 'print bexp(1,80)' =item bpi() bpi($accuracy); =begin original Returns PI to the wanted accuracy. =end original Returns PI to the wanted accuracy. (TBT) =begin original Example: =end original Example: (TBT) # perl -Mbignum=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 bignum; print "in effect\n" if bignum::in_effect; # true { no bignum; print "in effect\n" if bignum::in_effect; # false } =begin original Returns true or false if C is in effect in the current scope. =end original Returns true or false if C 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 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 bignum 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 bignum lib => 'Foo,Math::BigInt::Bar'; =begin original Please see respective module documentation for further details. =end original Please see respective module documentation for further details. (TBT) =begin original Using C warns if none of the specified libraries can be found and L did fall back to one of the default libraries. To supress this warning, use C instead: =end original Using C warns if none of the specified libraries can be found and L did fall back to one of the default libraries. To supress this warning, use C instead: (TBT) use bignum try => 'GMP'; =begin original If you want the code to die instead of falling back, use C instead: =end original If you want the code to die instead of falling back, use C instead: (TBT) use bignum only => 'GMP'; =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::BigFLoat. 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::BigFLoat. 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 bright idea since there is no guaranty that the object in question has such a hashkey, 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 bright idea since there is no guaranty that the object in question has such a hashkey, nor is a hash underneath at all. (TBT) =head2 SIGN (符号) =begin original The sign is either '+', '-', 'NaN', '+inf' or '-inf' and stored seperately. You can access it with the sign() method. =end original The sign is either '+', '-', 'NaN', '+inf' or '-inf' and stored seperately. 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) =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 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 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 older than v5.9.4 print hex("0x1234567890123456"); =back =head1 MODULES USED (使用するモジュール) =begin original C 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 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 bignum: =end original The following modules are currently used by bignum: (TBT) Math::BigInt::Lite (for speed, and only if it is loadable) Math::BigInt Math::BigFloat =head1 EXAMPLES (例) =begin original Some cool command line examples to impress the Python crowd ;) =end original Some cool command line examples to impress the Python crowd ;) (TBT) 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 =begin original Especially L as in C. =end original 特に C のような L。 =begin original L, L, L and L as well as L, L and L. =end original L, L, L, L および L, L, L。. =head1 AUTHORS (C) by Tels L in early 2002 - 2007. =begin meta Translate: SHIRAKATA Kentaro (0.23) Status: in progress =end meta =cut