Math::BigInt::Calc (3)
Leading comments
Automatically generated by Pod::Man 4.09 (Pod::Simple 3.35) Standard preamble: ========================================================================
NAME
Math::BigInt::Calc  Pure Perl module to support Math::BigIntSYNOPSIS
This library provides support for big integer calculations. It is not intended to be used by other modules. Other modules which support the sameDESCRIPTION
In this library, the numbers are represented in base B = 10**N, where N is the largest possible value that does not cause overflow in the intermediate computations. The base B elements are stored in an array, with the least significant element stored in array element zero. There are no leading zero elements, except a single zero element when the number is zero.For instance, if B = 10000, the number 1234567890 is represented internally as [3456, 7890, 12].
THE Math::BigInt API
In order to allow for multiple big integer libraries, Math::BigInt was rewritten to use a plugin library for core math routines. Any module which conforms to the
use Math::BigInt lib => 'libname';
'libname' is either the long name, like 'Math::BigInt::Pari', or only the short version, like 'Pari'.
General Notes
A library only needs to deal with unsigned big integers. Testing of input parameter validity is done by the caller, so there is no need to worry about underflow (e.g., in "_sub()" and "_dec()") nor about division by zero (e.g., in "_div()") or similar cases.For some methods, 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 objects, strings, Perl scalars, or true/false for comparison routines.
API version 1
The following methods must be defined in order to support the use by
Math::BigInt v1.70 or later.
 api_version()

Return APIversion as a Perl scalar, 1 for Math::BigInt v1.70, 2 for Math::BigInt v1.83.
Constructors
 _new(STR)
 Convert a string representing an unsigned decimal number to an object representing the same number. The input is normalize, i.e., it matches "^(0[19]\d*)$".
 _zero()
 Return an object representing the number zero.
 _one()
 Return an object representing the number one.
 _two()
 Return an object representing the number two.
 _ten()
 Return an object representing the number ten.
 _from_bin(STR)
 Return an object given a string representing a binary number. The input has a '0b' prefix and matches the regular expression "^0[bB](01[01]*)$".
 _from_oct(STR)
 Return an object given a string representing an octal number. The input has a '0' prefix and matches the regular expression "^0[17]*$".
 _from_hex(STR)
 Return an object given a string representing a hexadecimal number. The input has a '0x' prefix and matches the regular expression "^0x(0[19afAF][\dafAF]*)$".
Mathematical functions
Each of these methods may modify the first input argument, except _bgcd(), which shall not modify any input argument, and _sub() which may modify the second input argument.
 _add(OBJ1, OBJ2)

Returns the result of adding OBJ2toOBJ1.
 _mul(OBJ1, OBJ2)

Returns the result of multiplying OBJ2andOBJ1.
 _div(OBJ1, OBJ2)

Returns the result of dividing OBJ1byOBJ2and truncating the result to an integer.
 _sub(OBJ1, OBJ2, FLAG)
 _sub(OBJ1, OBJ2)

Returns the result of subtracting OBJ2byOBJ1.If "flag" is false or omitted,OBJ1might be modified. If "flag" is true,OBJ2might be modified.
 _dec(OBJ)

Decrement OBJby one.
 _inc(OBJ)

Increment OBJby one.
 _mod(OBJ1, OBJ2)

Return OBJ1moduloOBJ2,i.e., the remainder after dividingOBJ1byOBJ2.
 _sqrt(OBJ)
 Return the square root of the object, truncated to integer.
 _root(OBJ, N)
 Return Nth root of the object, truncated to int. N is >= 3.
 _fac(OBJ)
 Return factorial of object (1*2*3*4*...).
 _pow(OBJ1, OBJ2)

Return OBJ1to the power ofOBJ2.By convention, 0**0 = 1.
 _modinv(OBJ1, OBJ2)

Return modular multiplicative inverse, i.e., return OBJ3so that
(OBJ3 * OBJ1) % OBJ2 = 1 % OBJ2
The result is returned as two arguments. If the modular multiplicative inverse does not exist, both arguments are undefined. Otherwise, the arguments are a number (object) and its sign (``+'' or ``'').
The output value, with its sign, must either be a positive value in the range 1,2,...,OBJ21 or the same value subtracted
OBJ2.For instance, if the input arguments are objects representing the numbers 7 and 5, the method must either return an object representing the number 3 and a ``+'' sign, since (3*7) % 5 = 1 % 5, or an object representing the number 2 and ``'' sign, since (2*7) % 5 = 1 % 5.  _modpow(OBJ1, OBJ2, OBJ3)

Return modular exponentiation, (OBJ1**OBJ2) %OBJ3.
 _rsft(OBJ, N, B)

Shift object N digits right in base B and return the resulting object. This is
equivalent to performing integer division by B**N and discarding the remainder,
except that it might be much faster, depending on how the number is represented
internally.
For instance, if the object $obj represents the hexadecimal number 0xabcde, then "_rsft($obj, 2, 16)" returns an object representing the number 0xabc. The ``remainer'', 0xde, is discarded and not returned.
 _lsft(OBJ, N, B)
 Shift the object N digits left in base B. This is equivalent to multiplying by B**N, except that it might be much faster, depending on how the number is represented internally.
 _log_int(OBJ, B)

Return integer log of OBJto baseBASE.This method has two output arguments, theOBJECTand aSTATUS.TheSTATUSis Perl scalar; it is 1 ifOBJis the exact result, 0 if the result was truncted to giveOBJ,and undef if it is unknown whetherOBJis the exact result.
 _gcd(OBJ1, OBJ2)

Return the greatest common divisor of OBJ1andOBJ2.
Bitwise operators
Each of these methods may modify the first input argument.
 _and(OBJ1, OBJ2)
 Return bitwise and. If necessary, the smallest number is padded with leading zeros.
 _or(OBJ1, OBJ2)
 Return bitwise or. If necessary, the smallest number is padded with leading zeros.
 _xor(OBJ1, OBJ2)
 Return bitwise exclusive or. If necessary, the smallest number is padded with leading zeros.
Boolean operators
 _is_zero(OBJ)

Returns a true value if OBJis zero, and false value otherwise.
 _is_one(OBJ)

Returns a true value if OBJis one, and false value otherwise.
 _is_two(OBJ)

Returns a true value if OBJis two, and false value otherwise.
 _is_ten(OBJ)

Returns a true value if OBJis ten, and false value otherwise.
 _is_even(OBJ)

Return a true value if OBJis an even integer, and a false value otherwise.
 _is_odd(OBJ)

Return a true value if OBJis an even integer, and a false value otherwise.
 _acmp(OBJ1, OBJ2)

Compare OBJ1andOBJ2and return 1, 0, or 1, ifOBJ1is less than, equal to, or larger thanOBJ2,respectively.
String conversion
 _str(OBJ)
 Return a string representing the object. The returned string should have no leading zeros, i.e., it should match "^(0[19]\d*)$".
 _as_bin(OBJ)
 Return the binary string representation of the number. The string must have a '0b' prefix.
 _as_oct(OBJ)

Return the octal string representation of the number. The string must have
a '0x' prefix.
Note: This method was required from Math::BigInt version 1.78, but the required
APIversion number was not incremented, so there are older libraries that supportAPIversion 1, but do not support "_as_oct()".  _as_hex(OBJ)
 Return the hexadecimal string representation of the number. The string must have a '0x' prefix.
Numeric conversion
 _num(OBJ)
 Given an object, return a Perl scalar number (int/float) representing this number.
Miscellaneous
 _copy(OBJ)
 Return a true copy of the object.
 _len(OBJ)
 Returns the number of the decimal digits in the number. The output is a Perl scalar.
 _zeros(OBJ)
 Return the number of trailing decimal zeros. The output is a Perl scalar.
 _digit(OBJ, N)
 Return the Nth digit as a Perl scalar. N is a Perl scalar, where zero refers to the rightmost (least significant) digit, and negative values count from the left (most significant digit). If $obj represents the number 123, then _digit($obj, 0) is 3 and _digit(123, 1) is 1.
 _check(OBJ)

Return a true value if the object is OK,and a false value otherwise. This is a check routine to test the internal state of the object for corruption.
API version 2
The following methods are required for an Constructors
 _1ex(N)
 Return an object representing the number 10**N where N >= 0 is a Perl scalar.
Mathematical functions
 _nok(OBJ1, OBJ2)

Return the binomial coefficient OBJ1overOBJ1.
Miscellaneous
 _alen(OBJ)
 Return the approximate number of decimal digits of the object. The output is one Perl scalar. This estimate must be greater than or equal to what "_len()" returns.
API optional methods
The following methods 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 bitwise operators.
Each of these methods may modify the first input argument.
 _signed_or(OBJ1, OBJ2, SIGN1, SIGN2)
 Return the signed bitwise or.
 _signed_and(OBJ1, OBJ2, SIGN1, SIGN2)
 Return the signed bitwise and.
 _signed_xor(OBJ1, OBJ2, SIGN1, SIGN2)
 Return the signed bitwise exclusive or.
WRAP YOUR OWN
If you want to port your own favourite clib 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.
BUGS
Please report any bugs or feature requests to "bugmathbigint at rt.cpan.org", or through the web interface at <rt.cpan.org/Ticket/Create.html?Queue=MathBigInt> (requires login). We will be notified, and then you'll automatically be notified of progress on your bug as I make changes.SUPPORT
You can find documentation for this module with the perldoc command.
perldoc Math::BigInt::Calc
You can also look for information at:
 *

RT: CPAN's request tracker
 *

AnnoCPAN: Annotated CPANdocumentation
 *

CPANRatings
 *

Search CPAN
 *

CPANTesters Matrix
 *

The Bignum mailing list

 *

Post to mailing list
"bignum at lists.scsys.co.uk"
 *
 View mailing list
 *
 Subscribe/Unsubscribe

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 <bloodgate.com> in late 2000.
 *

Separated from BigInt and shaped APIwith the help of John Peacock.
 *
 Fixed, speedup, streamlined and enhanced by Tels 2001  2007.
 *

APIdocumentation corrected and extended by Peter John Acklam, <pjacklam@online.no>