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:

        _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

        _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_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

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:

        _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 ref to scalar 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
                        For unsupported bases B, return undef to signal failure
        _lsft(obj,N,B)  shift object in base B by N 'digits' left
                        For unsupported bases B, return undef to signal failure
        
        _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

        _signed_or
        _signed_and
        _signed_xor

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

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.

Exceptions are _lsft() and _rsft(), which return undef if they can not shift the argument. This is used to delegate shifting of bases different than the one you can support back to Math::BigInt, which will use some generic code to calculate the result.

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, sped-up and enhanced by Tels http://bloodgate.com 2001-2003.

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

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