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::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.
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(n)
Mac OS X 10.8 - Generated Wed Sep 5 15:40:27 CDT 2012