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Math-Logic-Ternary-0.004
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/ Math::Logic::Ternary::TAPI_9

NAME

Math::Logic::Ternary::TAPI_9 - ternary arbitrary precision integer format

VERSION

This documentation refers to version 0.004 of Math::Logic::Ternary::TAPI_9.

SYNOPSIS

  use Math::Logic::Ternary::TAPI_9;

  $i1 = Math::Logic::Ternary::TAPI_9->new(@trits);

  $i2 = $i1->Ineg;
  $i3 = $i1->Iadd($i2);
  $i3 = $i1->Isub($i2);
  $i3 = $i1->Imul($i2);
  $i3 = $i1->Idiv($i2);
  $i3 = $i1->Imod($i2);
  ($q, $r) = $i1->Idivmod($i2);
  $i3 = $i1->Ipow($i2);
  $i2 = $i1->Iabs;

  $trit = $i1->Icmp($i2);
  $trit = $i1->Iasc($i2);

  @nonets = $i1->Words(9);
  $bigint = $i1->as_int;

DESCRIPTION

This module defines an arbitrary precision ternary integer format and emulates some basic operations on numbers of this format.

Number Format

TAPI_9 numbers are coded as sequences of 9-trit words (nonets) of variable length. The first nonet is interpreted as a balanced ternary integer number. If not negative, it denotes the size of the actual number in nonets (not including itself). Thus zero has the smallest possible representation of a single 9-trit zero. If negative, its absolute value denotes the size of the following size value in nonets. In practice, only two negative values are common unless huge numbers are involved: Minus two means the size is given as another 18-trit balanced ternary integer, and minus one means another single size nonet is following. If that integer is also negative, the actual size follows in yet another group of nonets, and so on. Thus leading minus one nonets can be used for padding.

Examples (trits written in least to most significant order):

              0 = nnnnnnnnn
              1 = tnnnnnnnn, tnnnnnnnn
              2 = tnnnnnnnn, ftnnnnnnn
              3 = tnnnnnnnn, ntnnnnnnn
           9841 = tnnnnnnnn, ttttttttt
           9842 = ftnnnnnnn, fffffffff tnnnnnnnn
           9843 = ftnnnnnnn, nffffffff tnnnnnnnn
      193710244 = ftnnnnnnn, ttttttttt ttttttttt
      193710245 = ntnnnnnnn, fffffffff fffffffff tnnnnnnnn
      193710246 = ntnnnnnnn, nffffffff fffffffff tnnnnnnnn
  3812798742493 = ntnnnnnnn, ttttttttt ttttttttt ttttttttt
  3812798742494 = ttnnnnnnn, fffffffff fffffffff fffffffff tnnnnnnnn
  3812798742495 = ttnnnnnnn, nffffffff fffffffff fffffffff tnnnnnnnn

The largest number representable with a single size nonet takes 88578 trits, all true, and is equal to (3 ** 88569 - 1) / 2, which is a 42258-digit number. The largest number representable with a minus 2 prefix followed by two size nonets takes 1743392223 trits and is equal to (3 ** 1743392196 - 1) / 2, which is an 831809472-digit number. The largest number with a minus 3 prefix followed by three size nonets takes 34315188682473 trits (34 Teratrits) and is about 10 ** 16372505880106.

Exports

Nothing is exported into the caller's namespace.

DEPENDENCIES

This module depends on Math::BigInt and Math::Logic::Ternary::Word. Installing Math::BigInt::GMP or Math::BigInt::Pari should make it faster.

BUGS AND LIMITATIONS

As of version 0.004, this module is not fully implemented. The documentation is intended as a preview of its eventual content.

However, the definition of the TAPI_9 number format, as given here, should be taken as authoritative, and can be used as a reference.

SEE ALSO

AUTHOR

Martin Becker <becker-cpan-mp@cozap.com>

COPYRIGHT AND LICENSE

Copyright (c) 2012-2017 by Martin Becker. All rights reserved.

This library is free software; you can redistribute it and/or modify it under the same terms as Perl itself, either Perl version 5.8.0 or, at your option, any later version of Perl 5 you may have available.