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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

           # In the backend library for Math::BigInt et al.

           package Math::BigInt::MyBackend;

           use Math::BigInt::lib;
           our @ISA = qw< Math::BigInt::lib >;

           sub _new { ... }
           sub _str { ... }
           sub _add { ... }
           str _sub { ... }
           ...

           # In your main program.

           use Math::BigInt lib => 'MyBackend';


DESCRIPTION

       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.

       Other backend libraries include Math::BigInt::Calc,
       Math::BigInt::FastCalc, Math::BigInt::GMP, and Math::BigInt::Pari.

       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()") or about
       division by zero (e.g., in "_div()" and "_mod()")) or similar cases.

       Some libraries use methods that don't modify their argument, and some
       libraries don't even use objects, but rather unblessed references.
       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

       CLASS->api_version()
           This method is no longer used and can be omitted. 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().

       CLASS->_new(STR)
           Convert a string representing an unsigned decimal number to an
           object representing the same number. The input is normalized, i.e.,
           it matches "^(0|[1-9]\d*)$".

       CLASS->_zero()
           Return an object representing the number zero.

       CLASS->_one()
           Return an object representing the number one.

       CLASS->_two()
           Return an object representing the number two.

       CLASS->_ten()
           Return an object representing the number ten.

       CLASS->_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]*)$".

       CLASS->_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]*$".

       CLASS->_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]*)$".

       CLASS->_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.

       CLASS->_from_base(STR, BASE, COLLSEQ)
           Returns an object given a string STR, a base BASE, and a collation
           sequence COLLSEQ. Each character in STR represents a numerical
           value identical to the character's position in COLLSEQ. All
           characters in STR must be present in COLLSEQ.

           If BASE is less than or equal to 94, and a collation sequence is
           not specified, the following default collation sequence is used. It
           contains of all the 94 printable ASCII characters except
           space/blank:

               0123456789                  # ASCII  48 to  57
               ABCDEFGHIJKLMNOPQRSTUVWXYZ  # ASCII  65 to  90
               abcdefghijklmnopqrstuvwxyz  # ASCII  97 to 122
               !"#$%&'()*+,-./             # ASCII  33 to  47
               :;<=>?@                     # ASCII  58 to  64
               [\]^_`                      # ASCII  91 to  96
               {|}~                        # ASCII 123 to 126

           If the default collation sequence is used, and the BASE is less
           than or equal to 36, the letter case in STR is ignored.

           For instance, with base 3 and collation sequence "-/|", the
           character "-" represents 0, "/" represents 1, and "|" represents 2.
           So if STR is "/|-", the output is 1 * 3**2 + 2 * 3**1 + 0 * 3**0 =
           15.

           The following examples show standard binary, octal, decimal, and
           hexadecimal conversion. All examples return 250.

               $x = $class -> _from_base("11111010", 2)
               $x = $class -> _from_base("372", 8)
               $x = $class -> _from_base("250", 10)
               $x = $class -> _from_base("FA", 16)

           Some more examples, all returning 250:

               $x = $class -> _from_base("100021", 3)
               $x = $class -> _from_base("3322", 4)
               $x = $class -> _from_base("2000", 5)
               $x = $class -> _from_base("caaa", 5, "abcde")
               $x = $class -> _from_base("42", 62)
               $x = $class -> _from_base("2!", 94)

       Mathematical functions

       CLASS->_add(OBJ1, OBJ2)
           Returns the result of adding OBJ2 to OBJ1.

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

       CLASS->_div(OBJ1, OBJ2)
           In scalar context, returns the quotient after dividing OBJ1 by OBJ2
           and truncating the result to an integer. In list context, return
           the quotient and the remainder.

       CLASS->_sub(OBJ1, OBJ2, FLAG)
       CLASS->_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.

       CLASS->_dec(OBJ)
           Returns the result after decrementing OBJ by one.

       CLASS->_inc(OBJ)
           Returns the result after incrementing OBJ by one.

       CLASS->_mod(OBJ1, OBJ2)
           Returns OBJ1 modulo OBJ2, i.e., the remainder after dividing OBJ1
           by OBJ2.

       CLASS->_sqrt(OBJ)
           Returns the square root of OBJ, truncated to an integer.

       CLASS->_root(OBJ, N)
           Returns the Nth root of OBJ, truncated to an integer.

       CLASS->_fac(OBJ)
           Returns the factorial of OBJ, i.e., the product of all positive
           integers up to and including OBJ.

       CLASS->_dfac(OBJ)
           Returns the double factorial of OBJ. If OBJ is an even integer,
           returns the product of all positive, even integers up to and
           including OBJ, i.e., 2*4*6*...*OBJ. If OBJ is an odd integer,
           returns the product of all positive, odd integers, i.e.,
           1*3*5*...*OBJ.

       CLASS->_pow(OBJ1, OBJ2)
           Returns OBJ1 raised to the power of OBJ2. By convention, 0**0 = 1.

       CLASS->_modinv(OBJ1, OBJ2)
           Returns the 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 a "-" sign, since (-2*7)
           % 5 = 1 % 5.

       CLASS->_modpow(OBJ1, OBJ2, OBJ3)
           Returns the modular exponentiation, i.e., (OBJ1 ** OBJ2) % OBJ3.

       CLASS->_rsft(OBJ, N, B)
           Returns the result after shifting OBJ N digits to thee right in
           base B. This is equivalent to performing integer division by B**N
           and discarding the remainder, except that it might be much faster.

           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.

       CLASS->_lsft(OBJ, N, B)
           Returns the result after shifting OBJ N digits to the left in base
           B. This is equivalent to multiplying by B**N, except that it might
           be much faster.

       CLASS->_log_int(OBJ, B)
           Returns the logarithm of OBJ to base BASE truncted to an integer.
           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.

       CLASS->_gcd(OBJ1, OBJ2)
           Returns the greatest common divisor of OBJ1 and OBJ2.

       CLASS->_lcm(OBJ1, OBJ2)
           Return the least common multiple of OBJ1 and OBJ2.

       CLASS->_fib(OBJ)
           In scalar context, returns the nth Fibonacci number: _fib(0)
           returns 0, _fib(1) returns 1, _fib(2) returns 1, _fib(3) returns 2
           etc. In list context, returns the Fibonacci numbers from F(0) to
           F(n): 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, ...

       CLASS->_lucas(OBJ)
           In scalar context, returns the nth Lucas number: _lucas(0) returns
           2, _lucas(1) returns 1, _lucas(2) returns 3, etc. In list context,
           returns the Lucas numbers from L(0) to L(n): 2, 1, 3, 4, 7, 11, 18,
           29,47, 76, ...

       Bitwise operators

       CLASS->_and(OBJ1, OBJ2)
           Returns bitwise and.

       CLASS->_or(OBJ1, OBJ2)
           Returns bitwise or.

       CLASS->_xor(OBJ1, OBJ2)
           Returns bitwise exclusive or.

       CLASS->_sand(OBJ1, OBJ2, SIGN1, SIGN2)
           Returns bitwise signed and.

       CLASS->_sor(OBJ1, OBJ2, SIGN1, SIGN2)
           Returns bitwise signed or.

       CLASS->_sxor(OBJ1, OBJ2, SIGN1, SIGN2)
           Returns bitwise signed exclusive or.

       Boolean operators

       CLASS->_is_zero(OBJ)
           Returns a true value if OBJ is zero, and false value otherwise.

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

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

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

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

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

       CLASS->_acmp(OBJ1, OBJ2)
           Compare OBJ1 and OBJ2 and return -1, 0, or 1, if OBJ1 is
           numerically less than, equal to, or larger than OBJ2, respectively.

       String conversion

       CLASS->_str(OBJ)
           Returns a string representing OBJ in decimal notation. The returned
           string should have no leading zeros, i.e., it should match
           "^(0|[1-9]\d*)$".

       CLASS->_to_bin(OBJ)
           Returns the binary string representation of OBJ.

       CLASS->_to_oct(OBJ)
           Returns the octal string representation of the number.

       CLASS->_to_hex(OBJ)
           Returns the hexadecimal string representation of the number.

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

       CLASS->_to_base(OBJ, BASE, COLLSEQ)
           Returns a string representation of OBJ in base BASE with collation
           sequence COLLSEQ.

               $val = $class -> _new("210");
               $str = $class -> _to_base($val, 10, "xyz")  # $str is "zyx"

               $val = $class -> _new("32");
               $str = $class -> _to_base($val, 2, "-|")  # $str is "|-----"

           See _from_base() for more information.

       CLASS->_as_bin(OBJ)
           Like "_to_bin()" but with a '0b' prefix.

       CLASS->_as_oct(OBJ)
           Like "_to_oct()" but with a '0' prefix.

       CLASS->_as_hex(OBJ)
           Like "_to_hex()" but with a '0x' prefix.

       CLASS->_as_bytes(OBJ)
           This is an alias to "_to_bytes()".

       Numeric conversion

       CLASS->_num(OBJ)
           Returns a Perl scalar number representing the number OBJ as close
           as possible. Since Perl scalars have limited precision, the
           returned value might not be exactly the same as OBJ.

       Miscellaneous

       CLASS->_copy(OBJ)
           Returns a true copy OBJ.

       CLASS->_len(OBJ)
           Returns the number of the decimal digits in OBJ. The output is a
           Perl scalar.

       CLASS->_zeros(OBJ)
           Returns the number of trailing decimal zeros. The output is a Perl
           scalar. The number zero has no trailing decimal zeros.

       CLASS->_digit(OBJ, N)
           Returns the Nth digit in OBJ 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

               CLASS->_digit($obj,  0)     # returns 3
               CLASS->_digit($obj,  1)     # returns 2
               CLASS->_digit($obj,  2)     # returns 1
               CLASS->_digit($obj, -1)     # returns 1

       CLASS->_digitsum(OBJ)
           Returns the sum of the base 10 digits.

       CLASS->_check(OBJ)
           Returns 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.

       CLASS->_set(OBJ)
           xxx

   API version 2
       The following methods are required for an API version of 2 or greater.

       Constructors

       CLASS->_1ex(N)
           Return an object representing the number 10**N where N >= 0 is a
           Perl scalar.

       Mathematical functions

       CLASS->_nok(OBJ1, OBJ2)
           Return the binomial coefficient OBJ1 over OBJ1.

       Miscellaneous

       CLASS->_alen(OBJ)
           Return the approximate number of decimal digits of the object. The
           output is a Perl scalar.


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 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

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

       o   MetaCPAN

           <https://metacpan.org/release/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 v5.34.0                      2020-06-14            Math::BigInt::Lib(3pm)

perl 5.34.0 - Generated Thu Mar 3 07:48:06 CST 2022
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