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


       bignum - Transparent BigNumber support for Perl


         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, import into current package:
         use bignum qw/hex oct/;
         print hex("0x1234567890123490"),"\n";
         print oct("01234567890123490"),"\n";


       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 necessary:

               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.

       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

               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 "+")

       You can even chain the operations together as usual:

               perl -Mbignum -le 'print 1234->copy()->binc->badd(6);'

       Under bignum (or bigint or bigrat), Perl will "upgrade" the numbers
       appropriately. This means that:

               perl -Mbignum -le 'print 1234+4.5'

       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'

       There is also "use bigrat;" which gives you big rationals:

               perl -Mbigrat -le 'print 1234+4.1'

       The entire upgrading/downgrading is still experimental and might not
       work as you expect or may even have bugs. You might get errors like

               Can't use an undefined value as an ARRAY reference at
               /usr/local/lib/perl5/5.8.0/Math/BigInt/ 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

           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($_); }'

       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)'

         Note that setting precision and accuracy at the same time is not

       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

                 perl -Mbignum=p,-50 -le 'print sqrt(20)'

         Note that setting precision and accuracy at the same time is not

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

       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 means the following does not work:

                 perl -Mbignum=l,GMP,Pari -e 'print 2 ** 512'

         This will be hopefully fixed soon ;)

         Override the built-in hex() method with a version that can handle big
         numbers. This overrides it by exporting it to the current package.
         Under Perl v5.10.0 and higher, this is not so necessary, as hex() is
         lexically overridden in the current scope whenever the bignum pragma
         is active.

         Override the built-in oct() method with a version that can handle big
         numbers. This overrides it by exporting it to the current package.
         Under Perl v5.10.0 and higher, this is not so necessary, as oct() is
         lexically overridden in the current scope whenever the bigint pragma
         is active.

       v or version
         This prints out the name and version of all modules used and then

                 perl -Mbignum=v

       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

       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 being 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 test the 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.

         A shortcut to return Math::BigInt->binf(). Useful because Perl does
         not always handle bareword "inf" properly.

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

                 # perl -Mbignum=e -wle 'print e'

         Returns Euler's number "e", aka exp(1).

                 # perl -Mbignum=PI -wle 'print PI'

         Returns PI.


         Returns Euler's number "e" raised to the appropriate power, to the
         wanted accuracy.


                 # perl -Mbignum=bexp -wle 'print bexp(1,80)'


         Returns PI to the wanted accuracy.


                 # perl -Mbignum=bpi -wle 'print bpi(80)'

         Return the class that numbers are upgraded to, is in fact returning

                 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.

         This method only works on Perl v5.9.4 or later.

   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 => 'GMP';

       The following would first try to find Math::BigInt::Foo, then
       Math::BigInt::Bar, and when this also fails, revert to

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

       Please see respective module documentation for further details.

       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
       suppress this warning, use "try" instead:

               use bignum try => 'GMP';

       If you want the code to die instead of falling back, use "only"

               use bignum only => 'GMP';

       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.

       The sign is either '+', '-', 'NaN', '+inf' or '-inf' and stored
       separately.  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


       Operator vs literal overloading
         "bignum" works by overloading handling of integer and floating point
         literals, converting them to Math::BigInt or Math::BigFloat objects.

         This means that arithmetic involving only string values or string
         literals will be performed using Perl's built-in operators.

         For example:

             use bignum;
             my $x = "900000000000000009";
             my $y = "900000000000000007";
             print $x - $y;

         will output 0 on default 32-bit builds, since "bigrat" never sees the
         string literals.  To ensure the expression is all treated as
         "Math::BigInt" or "BigFloat" objects, use a literal number in the

             print +(0+$x) - $y;

         This method only works on Perl v5.9.4 or later.

         "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":

                 use bigint qw/hex oct/;

                 print hex("0x1234567890123456");
                         no bigint;
                         print hex("0x1234567890123456");

         The second call to hex() will warn about a non-portable constant.

         Compare this to:

                 use bigint;

                 # will warn only under older than v5.9.4
                 print hex("0x1234567890123456");


       "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)


       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 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'


       Please report any bugs or feature requests to "bug-math-bigint at", or through the web interface at
       <> (requires login).
       We will be notified, and then you'll automatically be notified of
       progress on your bug as I make changes.


       You can find documentation for this module with the perldoc command.

           perldoc bignum

       You can also look for information at:

       o   RT: CPAN's request tracker


       o   AnnoCPAN: Annotated CPAN documentation


       o   CPAN Ratings


       o   Search CPAN


       o   CPAN Testers Matrix



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


       bigint(3) and bigrat(3).

       Math::BigFloat(3), Math::BigInt(3), Math::BigRat(3) and Math::Big(3) as
       well as Math::BigInt::Pari(3) and  Math::BigInt::GMP(3).


       o   (C) by Tels <> in early 2002 - 2007.

       o   Maintained by Peter John Acklam <<gt>, 2014-.

perl v5.26.1                      2017-07-18                       bignum(3pm)

perl 5.26.1 - Generated Tue Nov 7 07:11:09 CST 2017
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