Ubuntu Manpage: math::bignum - Arbitrary precision integer numbers

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 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  Trackers
       [http://core.tcl.tk/tcllib/reportlist].  Please also report any ideas for enhancements you
       may have for either package and/or documentation.

       When proposing code changes, please provide unified diffs, i.e the output of diff -u.

       Note further that attachments are strongly preferred over inlined patches. Attachments can
       be  made  by going to the Edit form of the ticket immediately after its creation, and then
       using the left-most button in the secondary navigation bar.

KEYWORDS

       bignums, math, multiprecision, tcl

COPYRIGHT

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