math::bignum(n)                Tcl Math Library                math::bignum(n)



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NAME
       math::bignum - Arbitrary precision integer numbers

SYNOPSIS
       package require Tcl  ?8.4?

       package require math::bignum  ?3.1?

       ::math::bignum::fromstr string ?radix?

       ::math::bignum::tostr bignum ?radix?

       ::math::bignum::sign bignum

       ::math::bignum::abs bignum

       ::math::bignum::cmp a b

       ::math::bignum::iszero bignum

       ::math::bignum::lt a b

       ::math::bignum::le a b

       ::math::bignum::gt a b

       ::math::bignum::ge a b

       ::math::bignum::eq a b

       ::math::bignum::ne a b

       ::math::bignum::isodd bignum

       ::math::bignum::iseven bignum

       ::math::bignum::add a b

       ::math::bignum::sub a b

       ::math::bignum::mul a b

       ::math::bignum::divqr a b

       ::math::bignum::div a b

       ::math::bignum::rem a b

       ::math::bignum::mod n m

       ::math::bignum::pow base exp

       ::math::bignum::powm base exp m

       ::math::bignum::sqrt bignum

       ::math::bignum::rand bits

       ::math::bignum::lshift bignum bits

       ::math::bignum::rshift bignum bits

       ::math::bignum::bitand a b

       ::math::bignum::bitor a b

       ::math::bignum::bitxor a b

       ::math::bignum::setbit bignumVar bit

       ::math::bignum::clearbit bignumVar bit

       ::math::bignum::testbit bignum bit

       ::math::bignum::bits bignum

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DESCRIPTION
       The bignum package provides arbitrary precision integer math (also
       known as "big numbers") capabilities to the Tcl language.  Big numbers
       are internally represented at Tcl lists: this package provides a set of
       procedures operating against the internal representation in order to:

       o      perform math operations

       o      convert bignums from the internal representation to a string in
              the desired radix and vice versa.

       But the two constants "0" and "1" are automatically converted to the
       internal representation, in order to easily compare a number to zero,
       or increment a big number.

       The bignum interface is opaque, so operations on bignums that are not
       returned by procedures in this package (but created by hand) may lead
       to unspecified behaviours.  It's safe to treat bignums as pure values,
       so there is no need to free a bignum, or to duplicate it via a special
       operation.

EXAMPLES
       This section shows some simple example. This library being just a way
       to perform math operations, examples may be the simplest way to learn
       how to work with it. Consult the API section of this man page for
       information about individual procedures.

                  package require math::bignum

                  # Multiplication of two bignums
                  set a [::math::bignum::fromstr 88888881111111]
                  set b [::math::bignum::fromstr 22222220000000]
                  set c [::math::bignum::mul $a $b]
                  puts [::math::bignum::tostr $c] ; # => will output 1975308271604953086420000000
                  set c [::math::bignum::sqrt $c]
                  puts [::math::bignum::tostr $c] ; # => will output 44444440277777

                  # From/To string conversion in different radix
                  set a [::math::bignum::fromstr 1100010101010111001001111010111 2]
                  puts [::math::bignum::tostr $a 16] ; # => will output 62ab93d7

                  # Factorial example
                  proc fact n {
                      # fromstr is not needed for 0 and 1
                      set z 1
                      for {set i 2} {$i <= $n} {incr i} {
                          set z [::math::bignum::mul $z [::math::bignum::fromstr $i]]
                      }
                      return $z
                  }

                  puts [::math::bignum::tostr [fact 100]]


API
       ::math::bignum::fromstr string ?radix?
              Convert string into a bignum. If radix is omitted or zero, the
              string is interpreted in hex if prefixed with 0x, in octal if
              prefixed with ox, in binary if it's pefixed with bx, as a number
              in radix 10 otherwise. If instead the radix argument is
              specified in the range 2-36, the string is interpreted in the
              given radix. Please note that this conversion is not needed for
              two constants : 0 and 1. (see the example)

       ::math::bignum::tostr bignum ?radix?
              Convert bignum into a string representing the number in the
              specified radix. If radix is omitted, the default is 10.

       ::math::bignum::sign bignum
              Return the sign of the bignum.  The procedure returns 0 if the
              number is positive, 1 if it's negative.

       ::math::bignum::abs bignum
              Return the absolute value of the bignum.

       ::math::bignum::cmp a b
              Compare the two bignums a and b, returning 0 if a == b, 1 if a >
              b, and -1 if a < b.

       ::math::bignum::iszero bignum
              Return true if bignum value is zero, otherwise false is
              returned.

       ::math::bignum::lt a b
              Return true if a < b, otherwise false is returned.

       ::math::bignum::le a b
              Return true if a <= b, otherwise false is returned.

       ::math::bignum::gt a b
              Return true if a > b, otherwise false is returned.

       ::math::bignum::ge a b
              Return true if a >= b, otherwise false is returned.

       ::math::bignum::eq a b
              Return true if a == b, otherwise false is returned.

       ::math::bignum::ne a b
              Return true if a != b, otherwise false is returned.

       ::math::bignum::isodd bignum
              Return true if bignum is odd.

       ::math::bignum::iseven bignum
              Return true if bignum is even.

       ::math::bignum::add a b
              Return the sum of the two bignums a and b.

       ::math::bignum::sub a b
              Return the difference of the two bignums a and b.

       ::math::bignum::mul a b
              Return the product of the two bignums a and b.  The
              implementation uses Karatsuba multiplication if both the numbers
              are bigger than a given threshold, otherwise the direct algorith
              is used.

       ::math::bignum::divqr a b
              Return a two-elements list containing as first element the
              quotient of the division between the two bignums a and b, and
              the remainder of the division as second element.

       ::math::bignum::div a b
              Return the quotient of the division between the two bignums a
              and b.

       ::math::bignum::rem a b
              Return the remainder of the division between the two bignums a
              and b.

       ::math::bignum::mod n m
              Return n modulo m. This operation is called modular reduction.

       ::math::bignum::pow base exp
              Return base raised to the exponent exp.

       ::math::bignum::powm base exp m
              Return base raised to the exponent exp, modulo m. This function
              is often used in the field of cryptography.

       ::math::bignum::sqrt bignum
              Return the integer part of the square root of bignum

       ::math::bignum::rand bits
              Return a random number of at most bits bits.  The returned
              number is internally generated using Tcl's expr rand() function
              and is not suitable where an unguessable and cryptographically
              secure random number is needed.

       ::math::bignum::lshift bignum bits
              Return the result of left shifting bignum's binary
              representation of bits positions on the left.  This is
              equivalent to multiplying by 2^bits but much faster.

       ::math::bignum::rshift bignum bits
              Return the result of right shifting bignum's binary
              representation of bits positions on the right.  This is
              equivalent to dividing by 2^bits but much faster.

       ::math::bignum::bitand a b
              Return the result of doing a bitwise AND operation on a and b.
              The operation is restricted to positive numbers, including zero.
              When negative numbers are provided as arguments the result is
              undefined.

       ::math::bignum::bitor a b
              Return the result of doing a bitwise OR operation on a and b.
              The operation is restricted to positive numbers, including zero.
              When negative numbers are provided as arguments the result is
              undefined.

       ::math::bignum::bitxor a b
              Return the result of doing a bitwise XOR operation on a and b.
              The operation is restricted to positive numbers, including zero.
              When negative numbers are provided as arguments the result is
              undefined.

       ::math::bignum::setbit bignumVar bit
              Set the bit at bit position to 1 in the bignum stored in the
              variable bignumVar. Bit 0 is the least significant.

       ::math::bignum::clearbit bignumVar bit
              Set the bit at bit position to 0 in the bignum stored in the
              variable bignumVar. Bit 0 is the least significant.

       ::math::bignum::testbit bignum bit
              Return true if the bit at the bit position of bignum is on,
              otherwise false is returned. If bit is out of range, it is
              considered as set to zero.

       ::math::bignum::bits bignum
              Return the number of bits needed to represent bignum in radix 2.

BUGS, IDEAS, FEEDBACK
       This document, and the package it describes, will undoubtedly contain
       bugs and other problems.  Please report such in the category math ::
       bignum of the Tcllib SF Trackers
       [http://sourceforge.net/tracker/?group_id=12883].  Please also report
       any ideas for enhancements you may have for either package and/or
       documentation.

KEYWORDS
       bignums, math, multiprecision, tcl

CATEGORY
       Mathematics

COPYRIGHT
       Copyright (c) 2004 Salvatore Sanfilippo <antirez at invece dot org>
       Copyright (c) 2004 Arjen Markus <arjenmarkus at users dot sourceforge dot net>




math                                  3.1                      math::bignum(n)
