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Math::BigInt::Calc.3pm

NAME

Math::BigInt::Calc - Pure Perl module to support Math::BigInt

SYNOPSIS

Provides support for big integer calculations. Not intended to be used by other modules. Other modules which sport the same functions can also be used to support Math::BigInt, like Math::BigInt::GMP or Math::BigInt::Pari.

DESCRIPTION

In order to allow for multiple big integer libraries, Math::BigInt was rewritten to use library modules for core math routines. Any module which follows the same API as this can be used instead by using the following:

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

'libname' is either the long name ('Math::BigInt::Pari'), or only the short version like 'Pari'.

STORAGE

METHODS

The following functions MUST be defined in order to support the use by Math::BigInt v1.70 or later:

        api_version()   return API version, minimum 1 for v1.70

        _new(string)    return ref to new object from ref to decimal string

        _zero()         return a new object with value 0

        _one()          return a new object with value 1

        _two()          return a new object with value 2

        _ten()          return a new object with value 10

        _str(obj)       return ref to a string representing the object

        _num(obj)       returns a Perl integer/floating point number

                        NOTE: because of Perl numeric notation defaults,

                        the _num'ified obj may lose accuracy due to 

                        machine-dependend floating point size limitations

        _add(obj,obj)   Simple addition of two objects

        _mul(obj,obj)   Multiplication of two objects

        _div(obj,obj)   Division of the 1st object by the 2nd

                        In list context, returns (result,remainder).

                        NOTE: this is integer math, so no

                        fractional part will be returned.

                        The second operand will be not be 0, so no need to

                        check for that.

        _sub(obj,obj)   Simple subtraction of 1 object from another

                        a third, optional parameter indicates that the params

                        are swapped. In this case, the first param needs to

                        be preserved, while you can destroy the second.

                        sub (x,y,1) => return x - y and keep x intact!

        _dec(obj)       decrement object by one (input is garant. to be > 0)

        _inc(obj)       increment object by one

        _acmp(obj,obj)  <=> operator for objects (return -1, 0 or 1)

        _len(obj)       returns count of the decimal digits of the object

        _digit(obj,n)   returns the n'th decimal digit of object

        _is_one(obj)    return true if argument is 1

        _is_two(obj)    return true if argument is 2

        _is_ten(obj)    return true if argument is 10

        _is_zero(obj)   return true if argument is 0

        _is_even(obj)   return true if argument is even (0,2,4,6..)

        _is_odd(obj)    return true if argument is odd (1,3,5,7..)

        _copy           return a ref to a true copy of the object

        _check(obj)     check whether internal representation is still intact

                        return 0 for ok, otherwise error message as string

        _from_hex(str)  return ref to new object from ref to hexadecimal string

        _from_bin(str)  return ref to new object from ref to binary string

        _as_hex(str)    return string containing the value as

                        unsigned hex string, with the '0x' prepended.

                        Leading zeros must be stripped.

        _as_bin(str)    Like as_hex, only as binary string containing only

                        zeros and ones. Leading zeros must be stripped and a

                        '0b' must be prepended.

        _rsft(obj,N,B)  shift object in base B by N 'digits' right

        _lsft(obj,N,B)  shift object in base B by N 'digits' left

        _xor(obj1,obj2) XOR (bit-wise) object 1 with object 2

                        Note: XOR, AND and OR pad with zeros if size mismatches

        _and(obj1,obj2) AND (bit-wise) object 1 with object 2

        _or(obj1,obj2)  OR (bit-wise) object 1 with object 2

        _mod(obj,obj)   Return remainder of div of the 1st by the 2nd object

        _sqrt(obj)      return the square root of object (truncated to int)

        _root(obj)      return the n'th (n >= 3) root of obj (truncated to int)

        _fac(obj)       return factorial of object 1 (1*2*3*4..)

        _pow(obj,obj)   return object 1 to the power of object 2

                        return undef for NaN

        _zeros(obj)     return number of trailing decimal zeros

        _modinv         return inverse modulus

        _modpow         return modulus of power ($x ** $y) % $z

        _log_int(X,N)   calculate integer log() of X in base N

                        X >= 0, N >= 0 (return undef for NaN)

                        returns (RESULT, EXACT) where EXACT is:

                         1     : result is exactly RESULT

                         0     : result was truncated to RESULT

                         undef : unknown whether result is exactly RESULT

        _gcd(obj,obj)   return Greatest Common Divisor of two objects

The following functions are optional, and can be defined if the underlying lib has a fast way to do them. If undefined, Math::BigInt will use pure Perl (hence slow) fallback routines to emulate these:

        _signed_or

        _signed_and

        _signed_xor

Input strings come in as unsigned but with prefix (i.e. as '123', '0xabc' or '0b1101').

So the library needs only to deal with unsigned big integers. Testing of input parameter validity is done by the caller, so you need not worry about underflow (f.i. in "_sub()", "_dec()") nor about division by zero or similar cases.

The first parameter can be modified, that includes the possibility that you return a reference to a completely different object instead. Although keeping the reference and just changing it's contents is prefered over creating and returning a different reference.

Return values are always references to objects, strings, or true/false for comparisation routines.

WRAP YOUR OWN

If you want to port your own favourite c-lib for big numbers to the Math::BigInt interface, you can take any of the already existing modules as a rough guideline. You should really wrap up the latest BigInt and BigFloat testsuites with your module, and replace in them any of the following:

        use Math::BigInt;

by this:

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

This way you ensure that your library really works 100% within Math::BigInt.

LICENSE

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

AUTHORS

Original math code by Mark Biggar, rewritten by Tels <http://bloodgate.com/> in late 2000. Seperated from BigInt and shaped API with the help of John Peacock.

Fixed, speed-up, streamlined and enhanced by Tels 2001 - 2005.

SEE ALSO

Math::BigInt, Math::BigFloat, Math::BigInt::BitVect, Math::BigInt::GMP, Math::BigInt::FastCalc and Math::BigInt::Pari.