Package COM.INFORMATIMAGO.COMMON-LISP.ARITHMETIC.P127N2


This module implements routines to compute modulo-2 polynomials
in P127[N/2]. (Ensemble de polynômes de degré inférieur ou égal à 127
dans l'ensemble quotient N/2 (ensemble des classes d'équivalences
modulo 2 dans ℕ)).


License:

    AGPL3

    Copyright Pascal J. Bourguignon 1994 - 2012

    This program is free software: you can redistribute it and/or modify
    it under the terms of the GNU Affero General Public License as published by
    the Free Software Foundation, either version 3 of the License, or
    (at your option) any later version.

    This program is distributed in the hope that it will be useful,
    but WITHOUT ANY WARRANTY; without even the implied warranty of
    MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
    GNU Affero General Public License for more details.

    You should have received a copy of the GNU Affero General Public License
    along with this program.
    If not, see <http://www.gnu.org/licenses/>

(add32 poly gg)

function

POLY:    A polynom of degree 127 modulo N/2 (type POLY).
GG:      A polynom of degree 32 modulo N/2 (type (unsigned-byte 32)).
DO:      Adds the polynom GG to POLY.
RETURN:  The modified POLY.

(divide32 poly gg)

function

POLY:    A polynom of degree 127 modulo N/2 (type POLY).
GG:      A polynom of degree 32 modulo N/2 (type (unsigned-byte 32)).
DO:      Divides the polynom POLY by GG.
RETURN:  POLY; the remainder (unsigned-byte 32)..

(even-parity byte)

function

RETURN: The BYTE with the parity bit set to even parity.

(insert-bit7 poly)

function

POLY:    A polynom of degree 127 modulo N/2 (type POLY).
DO:      Inserts into the POLY a 7th bit that is the even parity of the lowest 7 bits.
RETURN:  POLY

(multiply32 poly gg)

function

POLY:    A polynom of degree 127 modulo N/2 (type POLY).
GG:      A polynom of degree 32 modulo N/2 (type (unsigned-byte 32)).
DO:      Multiplies the polynom POLY by GG.
RETURN:  The modified POLY.

(odd-parity byte)

function

RETURN: The BYTE with the parity bit set to odd parity.

poly

type

A polynom of order 127.  We represent them as vectors of four 32-bit words.

(poly-from-bytes bytes)

function

BYTES:   A vector of at least 16 octets, in big endian order.
         Only the 16 first octets are used.
RETURN:  The poly stored in the bytes.

(poly-prin1-to-string poly)

function

POLY:    A polynom of degree 127 modulo N/2 (type POLY).
RETURN:  A string containing a human readable representation of the polynom POLY.
         (it is of the form "x^M + … + x^m").

(poly-to-bytes poly)

function

POLY:    A polynom of degree 127 modulo N/2 (type POLY).
RETURN:  A vector of 16 octets in big endian order encoding the polynom.

(remainder32 poly gg)

function

POLY:    A polynom of degree 127 modulo N/2 (type POLY).
GG:      A polynom of degree 32 modulo N/2 (type (unsigned-byte 32)).
RETURN:  the remainder (unsigned-byte 32) of POLY divided by GG.
NOTE:    Doesn't modify POLY.

(remove-bit7 poly)

function

POLY:    A polynom of degree 127 modulo N/2 (type POLY).
DO:      Modifies POLY, removing the 7th bit.
RETURN:  POLY