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Math::BigInt::Lib(3pm) Perl Programmers Reference Guide Math::BigInt::Lib(3pm)




NAME

       Math::BigInt::Lib - virtual parent class for Math::BigInt libraries


SYNOPSIS

       This module provides support for big integer calculations. It is not
       intended to be used directly, but rather as a parent class for backend
       libraries used by Math::BigInt, Math::BigFloat, Math::BigRat, and
       related modules. Backend libraries include Math::BigInt::Calc,
       Math::BigInt::FastCalc, Math::BigInt::GMP, Math::BigInt::Pari and
       others.


DESCRIPTION

       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.

       Some libraries use methods that don't modify their argument, and some
       libraries don't even use objects. Because of this, liberary methods are
       always called as class methods, not instance methods:

           $x = Class -> method($x, $y);     # like this
           $x = $x -> method($y);            # not like this ...
           $x -> method($y);                 # ... or like this

       And with boolean methods

           $bool = Class -> method($x, $y);  # like this
           $bool = $x -> method($y);         # not like this ...

       Return values are always objects, strings, Perl scalars, or true/false
       for comparison routines.

       API version

       api_version()
           Return API version as a Perl scalar, 1 for Math::BigInt v1.70, 2
           for Math::BigInt v1.83.

           This method is no longer used. Methods that are not implemented by
           a subclass will be inherited from this class.

       Constructors

       The following methods are mandatory: _new(), _str(), _add(), and
       _sub().  However, computations will be very slow without _mul() and
       _div().

       _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]*)$".

       _from_bytes(STR)
           Returns an object given a byte string representing the number. The
           byte string is in big endian byte order, so the two-byte input
           string "\x01\x00" should give an output value representing the
           number 256.

       Mathematical functions

       _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.

       _lcm(OBJ1, OBJ2)
           Return the least common multiple 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.

       _as_bytes(OBJ)
           Return a byte string representation of the number. The byte string
           is in big endian byte order, so if the object represents the number
           256, the output should be the two-byte string "\x01\x00".

       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 $obj-_digit(0)> is 3 and
           _digit(123, -1) is 1.

       _check(OBJ)
           Return true if the object is invalid and false otherwise.
           Preferably, the true value is a string describing the problem with
           the object. 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 a Perl scalar.

   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.

       _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 library 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
       Math::BigInt and Math::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(1) Math::BigInt::Calc(3)

       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.


AUTHOR

       Peter John Acklam, <pjacklam@online.no>

       Code and documentation based on the Math::BigInt::Calc module by Tels
       <nospam-abuse@bloodgate.com>


SEE ALSO

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



perl v5.26.1                      2017-07-18            Math::BigInt::Lib(3pm)

perl 5.26.1 - Generated Tue Nov 7 18:03:53 CST 2017
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