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NAME

       Math::GMP - High speed arbitrary size integer math

SYNOPSIS

         use Math::GMP;
         my $n = new Math::GMP 2;

         $n = $n ** (256*1024);
         $n = $n - 1;
         print "n is now $n
";

DESCRIPTION

       Math::GMP was designed to be a drop-in replacement both for
       Math::BigInt and for regular integer arithmetic.  Unlike BigInt,
       though, Math::GMP uses the GNU gmp library for all of its calculations,
       as opposed to straight Perl functions.  This can result in speed
       improvements.

       The downside is that this module requires a C compiler to install -- a
       small tradeoff in most cases. Also, this module is not 100% compatible
       with Math::BigInt.

       A Math::GMP object can be used just as a normal numeric scalar would be
       -- the module overloads most of the normal arithmetic operators to
       provide as seamless an interface as possible. However, if you need a
       perfect interface, you can do the following:

         use Math::GMP qw(:constant);

         $n = 2 ** (256 * 1024);
         print "n is $n
";

       This would fail without the ':constant' since Perl would use normal
       doubles to compute the 250,000 bit number, and thereby overflow it into
       meaninglessness (smaller exponents yield less accurate data due to
       floating point rounding).

METHODS

       Although the non-overload interface is not complete, the following
       functions do exist:

   new
         $x = Math::GMP->new(123);

       Creates a new Math::GMP object from the passed string or scalar.

         $x = Math::GMP->new('abcd', 36);

       Creates a new Math::GMP object from the first parameter which should be
       represented in the base specified by the second parameter.

   bfac
         $x = Math::GMP->new(5);
         $x->bfac();      # 1*2*3*4*5 = 120

       Calculates the factorial of $x and modifies $x to contain the result.

   band
         $x = Math::GMP->new(6);
         $x->band(3);      # 0b110 & 0b11 = 1

       Calculates the bit-wise AND of its two arguments and modifies the first
       argument.

   bxor
         $x = Math::GMP->new(6);
         $x->bxor(3);      # 0b110 & 0b11 = 0b101

       Calculates the bit-wise XOR of its two arguments and modifies the first
       argument.

   bior
         $x = Math::GMP->new(6);
         $x->bior(3);      # 0b110 & 0b11 = 0b111

       Calculates the bit-wise OR of its two arguments and modifies the first
       argument.

   bgcd
         $x = Math::GMP->new(6);
         $x->bgcd(4);      # 6 / 2 = 2, 4 / 2 = 2 => 2

       Returns the Greatest Common Divisor of the two arguments.

   blcm
         $x = Math::GMP->new(6);
         $x->blcm(4);      # 6 * 2 = 12, 4 * 3 = 12 => 12

       Returns the Least Common Multiple of the two arguments.

   bmodinv
         $x = Math::GMP->new(5);
         $x->bmodinv(7);   # 5 * 3 == 1 (mod 7) => 3

       Returns the modular inverse of $x (mod $y), if defined. This currently
       returns 0 if there is no inverse (but that may change in the future).
       Behaviour is undefined when $y is 0.

   bsqrt
         $x = Math::GMP->new(6);
         $x->bsqrt();      # int(sqrt(6)) => 2

       Returns the integer square root of its argument.

   legendre
         $x = Math::GMP->new(6);
         $x->legendre(3);

       Returns the value of the Legendre symbol ($x/$y). The value is defined
       only when $y is an odd prime; when the value is not defined, this
       currently returns 0 (but that may change in the future).

   jacobi
         $x = Math::GMP->new(6);
         $x->jacobi(3);

       Returns the value of the Jacobi symbol ($x/$y). The value is defined
       only when $y is odd; when the value is not defined, this currently
       returns 0 (but that may change in the future).

   fibonacci
         $x = Math::GMP->fibonacci(16);

       Calculates the n'th number in the Fibonacci sequence.

   probab_prime
         $x = Math::GMP->new(7);
         $x->probab_prime(10);

       Probabilistically determines if the number is a prime. Argument is the
       number of checks to perform. Returns 0 if the number is definitely not
       a prime, 1 if it may be, and 2 if it definitely is a prime.

BUGS

       As of version 1.0, Math::GMP is mostly compatible with the old
       Math::BigInt version. It is not a full replacement for the rewritten
       Math::BigInt versions, though. See the SEE ALSO section on how to
       achieve to use Math::GMP and retain full compatibility to Math::BigInt.

       There are some slight incompatibilities, such as output of positive
       numbers not being prefixed by a '+' sign.  This is intentional.

       There are also some things missing, and not everything might work as
       expected.

SEE ALSO

       Math::BigInt has a new interface to use a different library than the
       default pure Perl implementation. You can use, for instance, Math::GMP
       with it:

         use Math::BigInt lib => 'GMP';

       If Math::GMP is not installed, it will fall back to its own Perl
       implementation.

       See Math::BigInt and Math::BigInt::GMP or Math::BigInt::Pari or
       Math::BigInt::BitVect.

AUTHOR

       Chip Turner <chip@redhat.com>, based on the old Math::BigInt by Mark
       Biggar and Ilya Zakharevich.  Further extensive work provided by Tels
       <tels@bloodgate.com>.



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