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:
- _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 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 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 - 2007.
Math::BigInt, Math::BigFloat, Math::BigInt::GMP, Math::BigInt::FastCalc and Math::BigInt::Pari.