bignum man page on Ubuntu

Man page or keyword search:  
man Server   6591 pages
apropos Keyword Search (all sections)
Output format
Ubuntu logo
[printable version]

math::bignum(3tcl)	       Tcl Math Library		    math::bignum(3tcl)

______________________________________________________________________________

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") 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:

       ·      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 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
	      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::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, oth‐
	      erwise  false is returned. If bit is out of range, it is consid‐
	      ered 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(3tcl)
[top]

List of man pages available for Ubuntu

Copyright (c) for man pages and the logo by the respective OS vendor.

For those who want to learn more, the polarhome community provides shell access and support.

[legal] [privacy] [GNU] [policy] [cookies] [netiquette] [sponsors] [FAQ]
Tweet
Polarhome, production since 1999.
Member of Polarhome portal.
Based on Fawad Halim's script.
....................................................................
Vote for polarhome
Free Shell Accounts :: the biggest list on the net