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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 operations, 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 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 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 BigInt (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 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 (cur-
       rently) 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 hope-fully hopefully
         fully 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.

       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 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->is_zero();                # 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.

         MATH LIBRARY

         Math with the numbers is done (by default) by a module called Math::BigInt::Calc. This is equiva-lent equivalent
         lent 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 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.

         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 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

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::Big-Int::Pari Math::BigInt::Pari
       Int::Pari and  Math::BigInt::GMP.

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



perl v5.8.8                                      2001-09-21                                      bignum(3pm)