名前¶
bignum  Transparent BigNumber support for Perl
bignum  Perl 用の透過的な BigNumber 対応
概要¶
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";
説明¶
All operators (including basic math operations) are overloaded. Integer and floatingpoint constants are created as proper BigInts or BigFloats, respectively.
(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。
If you do
このように
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).
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)。
So, the following line:
それで、以下の行は:
$x = 1234;
creates actually a Math::BigInt and stores a reference to in $x. This happens transparently and behind your back, so to speak.
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。
You can see this with the following:
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)'
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:
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)'
This also means it is a bad idea to check for some specific package, since the actual contents of $x might be something unexpected. Due to the transparent way of bignum ref()
should not be necessary, anyway.
これは、$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 ref()
の透過的な方法は不要のはずです。
Since Math::BigInt and BigFloat also overload the normal math operations, the following line will still work:
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)'
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:
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()'
(Note that print doesn't do what you expect if the expression starts with '(' hence the +
)
(Note that print doesn't do what you expect if the expression starts with '(' hence the +
) (TBT)
You can even chain the operations together as usual:
You can even chain the operations together as usual: (TBT)
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:
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
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.
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)
If you do want to work with large integers like under use integer;
, try use bigint;
:
If you do want to work with large integers like under use integer;
, try use bigint;
: (TBT)
perl Mbigint le 'print 1234.5+4.5'
1238
There is also use bigrat;
which gives you big rationals:
There is also use bigrat;
which gives you big rationals: (TBT)
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:
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
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.
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)
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 use bignum;
and this is slower than keeping them as Perl scalars:
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 use bignum;
and this is slower than keeping them as Perl scalars: (TBT)
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):
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($_); }'
オプション¶
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:
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)
 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.
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)'
Note that setting precision and accurary at the same time is not possible.
Note that setting precision and accurary at the same time is not possible. (TBT)
 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.
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)'
Note that setting precision and accurary at the same time is not possible.
Note that setting precision and accurary at the same time is not possible. (TBT)
 t or trace

This enables a trace mode and is primarily for debugging bignum or Math::BigInt/Math::BigFloat.
This enables a trace mode and is primarily for debugging bignum or Math::BigInt/Math::BigFloat. (TBT)
 l or lib

Load a different math lib, see "MATH LIBRARY".
Load a different math lib, see "MATH LIBRARY". (TBT)
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:
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)
 hex

Override the builtin 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;".
Override the builtin 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)
 oct

Override the builtin 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;".
Override the builtin 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)
 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 Mbignum=v
メソッド¶
Beside import() and AUTOLOAD() there are only a few other methods.
Beside import() and AUTOLOAD() there are only a few other methods. (TBT)
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.
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)
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.
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;
If you want to make a real copy, use the following:
If you want to make a real copy, use the following: (TBT)
$y = $x>copy();
Using the copy or the original with overloaded math is okay, e.g. the following work:
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:
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 test the contents works:
Using methods that do not modify, but test the 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.
See the documentation about the copy constructor and =
in overload, as well as the documentation in BigInt for further details. (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 Mbignum=e wle 'print e'
Returns Euler's number
e
, aka exp(1).Returns Euler's number
e
, aka exp(1). (TBT)  PI()

# perl Mbignum=PI wle 'print PI'
Returns PI.
Returns PI. (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)Example:
Example: (TBT)
# perl Mbignum=bexp wle 'print bexp(1,80)'
 bpi()

bpi($accuracy);
Returns PI to the wanted accuracy.
Returns PI to the wanted accuracy. (TBT)
Example:
Example: (TBT)
# perl Mbignum=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 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
bignum
is in effect in the current scope.Returns true or false if
bignum
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 Math::BigInt::Calc. This is equivalent to saying:
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';
You can change this by using:
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:
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';
Please see respective module documentation for further details.
Please see respective module documentation for further details. (TBT)
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:
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:
If you want the code to die instead of falling back, use only
instead: (TBT)
use bignum only => 'GMP';
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::BigFLoat. Mixing them together, even with normal scalars is not extraordinary, but normal and expected.
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)
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.
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)
符号¶
The sign is either '+', '', 'NaN', '+inf' or 'inf' and stored seperately. You can access it with the sign() method.
The sign is either '+', '', 'NaN', '+inf' or 'inf' and stored seperately. 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.
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)
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 nonportable constant.
The second call to hex() will warn about a nonportable constant. (TBT)
Compare this to:
Compare this to: (TBT)
use bigint; # will warn only under older than v5.9.4 print hex("0x1234567890123456");
使用するモジュール¶
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.
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. (TBT)
The following modules are currently used by bignum:
The following modules are currently used by bignum: (TBT)
Math::BigInt::Lite (for speed, and only if it is loadable)
Math::BigInt
Math::BigFloat
例¶
Some cool command line examples to impress the Python crowd ;)
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'
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¶
Especially bigrat as in perl Mbigrat le 'print 1/3+1/4'
.
特に perl Mbigrat le 'print 1/3+1/4'
のような bigrat。
Math::BigFloat, Math::BigInt, Math::BigRat and Math::Big as well as Math::BigInt::BitVect, Math::BigInt::Pari and Math::BigInt::GMP.
Math::BigFloat, 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.