'\"
'\" Generated from file 'bignum\&.man' by tcllib/doctools with format 'nroff'
'\" Copyright (c) 2004 Salvatore Sanfilippo <antirez at invece dot org>
'\" Copyright (c) 2004 Arjen Markus <arjenmarkus at users dot sourceforge dot net>
'\"
.TH "math::bignum" n 3\&.1 tcllib "Tcl Math Library"
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.BS
.SH NAME
math::bignum \- Arbitrary precision integer numbers
.SH SYNOPSIS
package require \fBTcl  ?8\&.4?\fR
.sp
package require \fBmath::bignum  ?3\&.1?\fR
.sp
\fB::math::bignum::fromstr\fR \fIstring\fR ?\fIradix\fR?
.sp
\fB::math::bignum::tostr\fR \fIbignum\fR ?\fIradix\fR?
.sp
\fB::math::bignum::sign\fR \fIbignum\fR
.sp
\fB::math::bignum::abs\fR \fIbignum\fR
.sp
\fB::math::bignum::cmp\fR \fIa\fR \fIb\fR
.sp
\fB::math::bignum::iszero\fR \fIbignum\fR
.sp
\fB::math::bignum::lt\fR \fIa\fR \fIb\fR
.sp
\fB::math::bignum::le\fR \fIa\fR \fIb\fR
.sp
\fB::math::bignum::gt\fR \fIa\fR \fIb\fR
.sp
\fB::math::bignum::ge\fR \fIa\fR \fIb\fR
.sp
\fB::math::bignum::eq\fR \fIa\fR \fIb\fR
.sp
\fB::math::bignum::ne\fR \fIa\fR \fIb\fR
.sp
\fB::math::bignum::isodd\fR \fIbignum\fR
.sp
\fB::math::bignum::iseven\fR \fIbignum\fR
.sp
\fB::math::bignum::add\fR \fIa\fR \fIb\fR
.sp
\fB::math::bignum::sub\fR \fIa\fR \fIb\fR
.sp
\fB::math::bignum::mul\fR \fIa\fR \fIb\fR
.sp
\fB::math::bignum::divqr\fR \fIa\fR \fIb\fR
.sp
\fB::math::bignum::div\fR \fIa\fR \fIb\fR
.sp
\fB::math::bignum::rem\fR \fIa\fR \fIb\fR
.sp
\fB::math::bignum::mod\fR \fIn\fR \fIm\fR
.sp
\fB::math::bignum::pow\fR \fIbase\fR \fIexp\fR
.sp
\fB::math::bignum::powm\fR \fIbase\fR \fIexp\fR \fIm\fR
.sp
\fB::math::bignum::sqrt\fR \fIbignum\fR
.sp
\fB::math::bignum::rand\fR \fIbits\fR
.sp
\fB::math::bignum::lshift\fR \fIbignum\fR \fIbits\fR
.sp
\fB::math::bignum::rshift\fR \fIbignum\fR \fIbits\fR
.sp
\fB::math::bignum::bitand\fR \fIa\fR \fIb\fR
.sp
\fB::math::bignum::bitor\fR \fIa\fR \fIb\fR
.sp
\fB::math::bignum::bitxor\fR \fIa\fR \fIb\fR
.sp
\fB::math::bignum::setbit\fR \fIbignumVar\fR \fIbit\fR
.sp
\fB::math::bignum::clearbit\fR \fIbignumVar\fR \fIbit\fR
.sp
\fB::math::bignum::testbit\fR \fIbignum\fR \fIbit\fR
.sp
\fB::math::bignum::bits\fR \fIbignum\fR
.sp
.BE
.SH DESCRIPTION
.PP
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:
.IP \(bu
perform math operations
.IP \(bu
convert bignums from the internal representation to a string in
the desired radix and vice versa\&.
.PP
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\&.
.PP
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\&.
.SH 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\&.
.PP
.CS


    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]]

.CE
.SH API
.TP
\fB::math::bignum::fromstr\fR \fIstring\fR ?\fIradix\fR?
Convert \fIstring\fR into a bignum\&. If \fIradix\fR is omitted or zero,
the string is interpreted in hex if prefixed with
\fI0x\fR, in octal if prefixed with \fIox\fR,
in binary if it's pefixed with \fIbx\fR, as a number in
radix 10 otherwise\&. If instead the \fIradix\fR argument
is specified in the range 2-36, the \fIstring\fR is interpreted
in the given radix\&. Please note that this conversion is
not needed for two constants : \fI0\fR and \fI1\fR\&. (see the example)
.TP
\fB::math::bignum::tostr\fR \fIbignum\fR ?\fIradix\fR?
Convert \fIbignum\fR into a string representing the number
in the specified radix\&. If \fIradix\fR is omitted, the
default is 10\&.
.TP
\fB::math::bignum::sign\fR \fIbignum\fR
Return the sign of the bignum\&.
The procedure returns 0 if the number is positive, 1 if it's negative\&.
.TP
\fB::math::bignum::abs\fR \fIbignum\fR
Return the absolute value of the bignum\&.
.TP
\fB::math::bignum::cmp\fR \fIa\fR \fIb\fR
Compare the two bignums a and b, returning \fI0\fR if \fIa == b\fR,
\fI1\fR if \fIa > b\fR, and \fI-1\fR if \fIa < b\fR\&.
.TP
\fB::math::bignum::iszero\fR \fIbignum\fR
Return true if \fIbignum\fR value is zero, otherwise false is returned\&.
.TP
\fB::math::bignum::lt\fR \fIa\fR \fIb\fR
Return true if \fIa < b\fR, otherwise false is returned\&.
.TP
\fB::math::bignum::le\fR \fIa\fR \fIb\fR
Return true if \fIa <= b\fR, otherwise false is returned\&.
.TP
\fB::math::bignum::gt\fR \fIa\fR \fIb\fR
Return true if \fIa > b\fR, otherwise false is returned\&.
.TP
\fB::math::bignum::ge\fR \fIa\fR \fIb\fR
Return true if \fIa >= b\fR, otherwise false is returned\&.
.TP
\fB::math::bignum::eq\fR \fIa\fR \fIb\fR
Return true if \fIa == b\fR, otherwise false is returned\&.
.TP
\fB::math::bignum::ne\fR \fIa\fR \fIb\fR
Return true if \fIa != b\fR, otherwise false is returned\&.
.TP
\fB::math::bignum::isodd\fR \fIbignum\fR
Return true if \fIbignum\fR is odd\&.
.TP
\fB::math::bignum::iseven\fR \fIbignum\fR
Return true if \fIbignum\fR is even\&.
.TP
\fB::math::bignum::add\fR \fIa\fR \fIb\fR
Return the sum of the two bignums \fIa\fR and \fIb\fR\&.
.TP
\fB::math::bignum::sub\fR \fIa\fR \fIb\fR
Return the difference of the two bignums \fIa\fR and \fIb\fR\&.
.TP
\fB::math::bignum::mul\fR \fIa\fR \fIb\fR
Return the product of the two bignums \fIa\fR and \fIb\fR\&.
The implementation uses Karatsuba multiplication if both
the numbers are bigger than a given threshold, otherwise
the direct algorith is used\&.
.TP
\fB::math::bignum::divqr\fR \fIa\fR \fIb\fR
Return a two-elements list containing as first element
the quotient of the division between the two bignums
\fIa\fR and \fIb\fR, and the remainder of the division as second element\&.
.TP
\fB::math::bignum::div\fR \fIa\fR \fIb\fR
Return the quotient of the division between the two
bignums \fIa\fR and \fIb\fR\&.
.TP
\fB::math::bignum::rem\fR \fIa\fR \fIb\fR
Return the remainder of the division between the two
bignums \fIa\fR and \fIb\fR\&.
.TP
\fB::math::bignum::mod\fR \fIn\fR \fIm\fR
Return \fIn\fR modulo \fIm\fR\&. This operation is
called modular reduction\&.
.TP
\fB::math::bignum::pow\fR \fIbase\fR \fIexp\fR
Return \fIbase\fR raised to the exponent \fIexp\fR\&.
.TP
\fB::math::bignum::powm\fR \fIbase\fR \fIexp\fR \fIm\fR
Return \fIbase\fR raised to the exponent \fIexp\fR,
modulo \fIm\fR\&. This function is often used in the field
of cryptography\&.
.TP
\fB::math::bignum::sqrt\fR \fIbignum\fR
Return the integer part of the square root of \fIbignum\fR
.TP
\fB::math::bignum::rand\fR \fIbits\fR
Return a random number of at most \fIbits\fR bits\&.
The returned number is internally generated using Tcl's \fIexpr rand()\fR
function and is not suitable where an unguessable and cryptographically
secure random number is needed\&.
.TP
\fB::math::bignum::lshift\fR \fIbignum\fR \fIbits\fR
Return the result of left shifting \fIbignum\fR's binary
representation of \fIbits\fR positions on the left\&.
This is equivalent to multiplying by 2^\fIbits\fR but much faster\&.
.TP
\fB::math::bignum::rshift\fR \fIbignum\fR \fIbits\fR
Return the result of right shifting \fIbignum\fR's binary
representation of \fIbits\fR positions on the right\&.
This is equivalent to dividing by \fI2^bits\fR but much faster\&.
.TP
\fB::math::bignum::bitand\fR \fIa\fR \fIb\fR
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\&.
.TP
\fB::math::bignum::bitor\fR \fIa\fR \fIb\fR
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\&.
.TP
\fB::math::bignum::bitxor\fR \fIa\fR \fIb\fR
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\&.
.TP
\fB::math::bignum::setbit\fR \fIbignumVar\fR \fIbit\fR
Set the bit at \fIbit\fR position to 1 in the bignum stored
in the variable \fIbignumVar\fR\&. Bit 0 is the least significant\&.
.TP
\fB::math::bignum::clearbit\fR \fIbignumVar\fR \fIbit\fR
Set the bit at \fIbit\fR position to 0 in the bignum stored
in the variable \fIbignumVar\fR\&. Bit 0 is the least significant\&.
.TP
\fB::math::bignum::testbit\fR \fIbignum\fR \fIbit\fR
Return true if the bit at the \fIbit\fR position of \fIbignum\fR
is on, otherwise false is returned\&. If \fIbit\fR is out of
range, it is considered as set to zero\&.
.TP
\fB::math::bignum::bits\fR \fIbignum\fR
Return the number of bits needed to represent bignum in radix 2\&.
.PP
.PP
.SH "BUGS, IDEAS, FEEDBACK"
This document, and the package it describes, will undoubtedly contain
bugs and other problems\&.
Please report such in the category \fImath :: bignum\fR of the
\fITcllib Trackers\fR [http://core\&.tcl\&.tk/tcllib/reportlist]\&.
Please also report any ideas for enhancements you may have for either
package and/or documentation\&.
.PP
When proposing code changes, please provide \fIunified diffs\fR,
i\&.e the output of \fBdiff -u\fR\&.
.PP
Note further that \fIattachments\fR are strongly preferred over
inlined patches\&. Attachments can be made by going to the \fBEdit\fR
form of the ticket immediately after its creation, and then using the
left-most button in the secondary navigation bar\&.
.SH KEYWORDS
bignums, math, multiprecision, tcl
.SH CATEGORY
Mathematics
.SH COPYRIGHT
.nf
Copyright (c) 2004 Salvatore Sanfilippo <antirez at invece dot org>
Copyright (c) 2004 Arjen Markus <arjenmarkus at users dot sourceforge dot net>

.fi