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bignum(3pm) Perl Programmers Reference Guide bignum(3pm)

NAME

bignum - Transparent BigNumber support for Perl

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

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 "ref()" should not be neccessary, anyway.

Since Math::BigInt and BigFloat also overload the normal math opera-

tions, 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 expres-

sions:

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 "+") 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 "use integer;", try "use bigint;":

perl -Mbigint -le 'print 1234.5+4.5'

1238 There is also "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 Big-

Int (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 mod-

ule/space. For instance, simple loop counters will be Math::BigInts

under "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($); }'

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: 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)'

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)'

t or trace

This enables a trace mode and is primarily for debugging bignum or

Math::BigInt/Math::BigFloat. l or lib Load a different math lib, see "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 ;) v or version This prints out the name and version of all modules used and then exits.

perl -Mbignum=v

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. CCaavveeaatt 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 bbootthh 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->iszero(); # works fine

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

A shortcut to return Math::BigInt->binf(). Usefull because Perl

does not always handle bareword "inf" properly. NaN()

A shortcut to return Math::BigInt->bnan(). Usefull because Perl

does not always handle bareword "NaN" properly. upgrade() Return the class that numbers are upgraded to, is in fact returning

$Math::BigInt::upgrade.

MMAATTHH LLIIBBRRAARRYY 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::Big-

Int::Calc:

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

Please see respective module documentation for further details. IINNTTEERRNNAALL FFOORRMMAATT 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. SSIIGGNN

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. MMOODDUULLEESS UUSSEEDD

"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 EEXXAAMMPPLLEESS 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->isodd()'

perl -Mbignum -le 'print log(2)'

perl -Mbignum -le 'print 2 ** 0.5'

perl -Mbignum=a,65 -le 'print 2 ** 0.2'

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