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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

____________________________________________________________________________________________________________

DESCRIPTION
       The  bignum package provides arbitrary precision integer math (also known as "big numbers") capabili-ties capabilities
       ties 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:

       •      perform math operations

       •      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 _x, 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 : _ 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 omit-
              ted, 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 _ 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 multiplica-tion multiplication
              tion 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  cryptographi-cally cryptographically
              cally 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://source -
       forge.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)