You are viewing the version of this documentation from Perl 5.12.3. View the latest version



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


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.


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'.



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

 api_version()   return API version, 1 for v1.70, 2 for v1.83
 _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-dependent 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 guaranteed 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 new object from a hexadecimal string
 _from_bin(str)  return new object from a binary string
 _from_oct(str)  return new object from an octal 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(obj1,obj2) 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(obj1,obj2) 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 REQUIRED for an api_version of 2 or greater:

_1ex($x)        create the number 1Ex where x >= 0
_alen(obj)      returns approximate count of the decimal digits of the
                object. This estimate MUST always be greater or equal
                to what _len() returns.
_nok(n,k)       calculate n over k (binomial coefficient)

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:


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 its contents is preferred over creating and returning a different reference.

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


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.


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


Original math code by Mark Biggar, rewritten by Tels in late 2000. Seperated from BigInt and shaped API with the help of John Peacock.

Fixed, speed-up, streamlined and enhanced by Tels 2001 - 2007.


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