MirOS Manual: bignum(3p)


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

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 over-
     loaded. 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 operations, the following line will still work:

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             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:

             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 expres-
     sion 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 BigInt (or vice versa) and the upgrade/downgrad
     path was missing. This is a bug, please report it so that we
     can fix it.

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     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:

             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 argu-
       ment 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 argu-
       ment 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

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       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.

     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.

             $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 both the original and the copy beeing des-
     troyed:

             $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->is_zero();                # works fine

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     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" prop-
         erly.

       NaN()
         A shortcut to return Math::BigInt->bnan(). Usefull
         because Perl does not always handle bareword "NaN" prop-
         erly.

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

       MATH LIBRARY

       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::BigInt::Calc:

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

       Please see respective module documentation for further
       details.

       INTERNAL FORMAT

       The numbers are stored as objects, and their internals
       might change at anytime, especially between math opera-
       tions. 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.

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       SIGN

       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.

MODULES USED

     "bignum" is just a thin wrapper around various modules of
     the Math::BigInt family. Think of it as the head of the fam-
     ily, 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

EXAMPLES

     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->is_odd()'
             perl -Mbignum -le 'print log(2)'
             perl -Mbignum -le 'print 2 ** 0.5'
             perl -Mbignum=a,65 -le 'print 2 ** 0.2'

LICENSE

     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'".

     Math::BigFloat, Math::BigInt, Math::BigRat and Math::Big as
     well as Math::BigInt::BitVect, Math::BigInt::Pari and
     Math::BigInt::GMP.

AUTHORS

     (C) by Tels <http://bloodgate.com/> in early 2002, 2003.

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