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Math::BigInt::Calc(3pm)Perl Programmers Reference GuideMath::BigInt::Calc(3pm)




NAME

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


SYNOPSIS

       This library provides support for big integer calculations. It is not
       intended to be used by other modules. Other modules which support the
       same API (see below) can also be used to support Math::BigInt, like
       Math::BigInt::GMP and Math::BigInt::Pari.


DESCRIPTION

       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 plug-in library for core math routines. Any module
       which conforms to the API can be used by Math::BigInt by using this in
       your program:

               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

       api_version()
           Return API version 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|[1-9]\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](0|1[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[1-7]*$".

       _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|[1-9a-fA-F][\da-fA-F]*)$".

       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 OBJ2 to OBJ1.

       _mul(OBJ1, OBJ2)
           Returns the result of multiplying OBJ2 and OBJ1.

       _div(OBJ1, OBJ2)
           Returns the result of dividing OBJ1 by OBJ2 and truncating the
           result to an integer.

       _sub(OBJ1, OBJ2, FLAG)
       _sub(OBJ1, OBJ2)
           Returns the result of subtracting OBJ2 by OBJ1. If "flag" is false
           or omitted, OBJ1 might be modified. If "flag" is true, OBJ2 might
           be modified.

       _dec(OBJ)
           Decrement OBJ by one.

       _inc(OBJ)
           Increment OBJ by one.

       _mod(OBJ1, OBJ2)
           Return OBJ1 modulo OBJ2, i.e., the remainder after dividing OBJ1 by
           OBJ2.

       _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 OBJ1 to the power of OBJ2. By convention, 0**0 = 1.

       _modinv(OBJ1, OBJ2)
           Return modular multiplicative inverse, i.e., return OBJ3 so 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,...,OBJ2-1 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 OBJ to base BASE. This method has two output
           arguments, the OBJECT and a STATUS. The STATUS is Perl scalar; it
           is 1 if OBJ is the exact result, 0 if the result was truncted to
           give OBJ, and undef if it is unknown whether OBJ is the exact
           result.

       _gcd(OBJ1, OBJ2)
           Return the greatest common divisor of OBJ1 and OBJ2.

       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 OBJ is zero, and false value otherwise.

       _is_one(OBJ)
           Returns a true value if OBJ is one, and false value otherwise.

       _is_two(OBJ)
           Returns a true value if OBJ is two, and false value otherwise.

       _is_ten(OBJ)
           Returns a true value if OBJ is ten, and false value otherwise.

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

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

       _acmp(OBJ1, OBJ2)
           Compare OBJ1 and OBJ2 and return -1, 0, or 1, if OBJ1 is less than,
           equal to, or larger than OBJ2, 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|[1-9]\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 API version number was not incremented, so there are
           older libraries that support API version 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 API version of 2 or greater.

       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 OBJ1 over OBJ1.

       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 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.


BUGS

       Please report any bugs or feature requests to "bug-math-bigint at
       rt.cpan.org", or through the web interface at
       <https://rt.cpan.org/Ticket/Create.html?Queue=Math-BigInt> (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:

       o   RT: CPAN's request tracker

           <https://rt.cpan.org/Public/Dist/Display.html?Name=Math-BigInt>

       o   AnnoCPAN: Annotated CPAN documentation

           <http://annocpan.org/dist/Math-BigInt>

       o   CPAN Ratings

           <http://cpanratings.perl.org/dist/Math-BigInt>

       o   Search CPAN

           <http://search.cpan.org/dist/Math-BigInt/>

       o   CPAN Testers Matrix

           <http://matrix.cpantesters.org/?dist=Math-BigInt>

       o   The Bignum mailing list

           o   Post to mailing list

               "bignum at lists.scsys.co.uk"

           o   View mailing list

               <http://lists.scsys.co.uk/pipermail/bignum/>

           o   Subscribe/Unsubscribe

               <http://lists.scsys.co.uk/cgi-bin/mailman/listinfo/bignum>


LICENSE

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


AUTHORS

       o   Original math code by Mark Biggar, rewritten by Tels
           <http://bloodgate.com/> in late 2000.

       o   Separated from BigInt and shaped API with the help of John Peacock.

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

       o   API documentation corrected and extended by Peter John Acklam,
           <pjacklam@online.no>


SEE ALSO

       Math::BigInt(3), Math::BigFloat(3), Math::BigInt::GMP(3),
       Math::BigInt::FastCalc(3) and Math::BigInt::Pari(3).



perl v5.24.0                      2016-03-01           Math::BigInt::Calc(3pm)

perl 5.24 - Generated Wed Nov 16 19:15:26 CST 2016
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