


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


______________________________________________________________________________

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                           3.1                              1





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


       ::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") 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.





math                           3.1                              2





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


           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 speci-
              fied 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



math                           3.1                              3





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


              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  implementa-
              tion  uses Karatsuba multiplication if both the numbers are big-
              ger 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 quo-
              tient 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                           3.1                              4





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


       ::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  num-
              ber 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 representa-
              tion of bits positions on the left.  This is equivalent to  mul-
              tiplying by 2^bits but much faster.

       ::math::bignum::rshift bignum bits
              Return  the result of right shifting bignum's binary representa-
              tion 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,



math                           3.1                              5





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


              otherwise  false is returned. If bit is out of range, it is con-
              sidered 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                              6


