zint/backend/reedsol.c

/** 
 
  This is a simple Reed-Solomon encoder
  (C) Cliff Hones 2004
 
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       may be used to endorse or promote products derived from this software
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    THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS" AND
    ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
    IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
    ARE DISCLAIMED.  IN NO EVENT SHALL THE COPYRIGHT OWNER OR CONTRIBUTORS BE LIABLE
    FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL
    DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS
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 */

// It is not written with high efficiency in mind, so is probably
// not suitable for real-time encoding.  The aim was to keep it
// simple, general and clear.
//
// <Some notes on the theory and implementation need to be added here>

// Usage:
// First call rs_init_gf(poly) to set up the Galois Field parameters.
// Then  call rs_init_code(size, index) to set the encoding size
// Then  call rs_encode(datasize, data, out) to encode the data.
//
// These can be called repeatedly as required - but note that
// rs_init_code must be called following any rs_init_gf call.
//
// If the parameters are fixed, some of the statics below can be
// replaced with constants in the obvious way, and additionally
// malloc/free can be avoided by using static arrays of a suitable
// size.

#include <stdio.h>		// only needed for debug (main)
#include <stdlib.h>		// only needed for malloc/free
#include "reedsol.h"
static int logmod; // 2**symsize - 1
static int rlen;

static int *logt = NULL, *alog = NULL, *rspoly = NULL;

// rs_init_gf(poly) initialises the parameters for the Galois Field.
// The symbol size is determined from the highest bit set in poly
// This implementation will support sizes up to 30 bits (though that
// will result in very large log/antilog tables) - bit sizes of
// 8 or 4 are typical
//
// The poly is the bit pattern representing the GF characteristic
// polynomial.  e.g. for ECC200 (8-bit symbols) the polynomial is
// a**8 + a**5 + a**3 + a**2 + 1, which translates to 0x12d.

void rs_init_gf(const int poly) {
    int m, b, p, v;

    // Find the top bit, and hence the symbol size
    for (b = 1, m = 0; b <= poly; b <<= 1)
        m++;
    b >>= 1;
    m--;

    // Calculate the log/alog tables
    logmod = (1 << m) - 1;
    logt = (int *) malloc(sizeof (int) * (logmod + 1));
    alog = (int *) malloc(sizeof (int) * logmod);

    for (p = 1, v = 0; v < logmod; v++) {
        alog[v] = p;
        logt[p] = v;
        p <<= 1;
        if (p & b)
            p ^= poly;
    }
}

// rs_init_code(nsym, index) initialises the Reed-Solomon encoder
// nsym is the number of symbols to be generated (to be appended
// to the input data).  index is usually 1 - it is the index of
// the constant in the first term (i) of the RS generator polynomial:
// (x + 2**i)*(x + 2**(i+1))*...   [nsym terms]
// For ECC200, index is 1.

void rs_init_code(const int nsym, int index) {
    int i, k;

    rspoly = (int *) malloc(sizeof (int) * (nsym + 1));

    rlen = nsym;

    rspoly[0] = 1;
    for (i = 1; i <= nsym; i++) {
        rspoly[i] = 1;
        for (k = i - 1; k > 0; k--) {
            if (rspoly[k])
                rspoly[k] = alog[(logt[rspoly[k]] + index) % logmod];
            rspoly[k] ^= rspoly[k - 1];
        }
        rspoly[0] = alog[(logt[rspoly[0]] + index) % logmod];
        index++;
    }
}

void rs_encode(const int len, const unsigned char *data, unsigned char *res) {
    int i, k, m;
    for (i = 0; i < rlen; i++)
        res[i] = 0;
    for (i = 0; i < len; i++) {
        m = res[rlen - 1] ^ data[i];
        for (k = rlen - 1; k > 0; k--) {
            if (m && rspoly[k])
                res[k] = (unsigned char) (res[k - 1] ^ alog[(logt[m] + logt[rspoly[k]]) % logmod]);
            else
                res[k] = res[k - 1];
        }
        if (m && rspoly[0])
            res[0] = (unsigned char) (alog[(logt[m] + logt[rspoly[0]]) % logmod]);
        else
            res[0] = 0;
    }
}

/* The same as above but for larger bitlengths - Aztec code compatible */
void rs_encode_long(const int len, const unsigned int *data, unsigned int *res) {
    int i, k, m;
    for (i = 0; i < rlen; i++)
        res[i] = 0;
    for (i = 0; i < len; i++) {
        m = res[rlen - 1] ^ data[i];
        for (k = rlen - 1; k > 0; k--) {
            if (m && rspoly[k])
                res[k] = res[k - 1] ^ alog[(logt[m] + logt[rspoly[k]]) % logmod];
            else
                res[k] = res[k - 1];
        }
        if (m && rspoly[0])
            res[0] = alog[(logt[m] + logt[rspoly[0]]) % logmod];
        else
            res[0] = 0;
    }
}

/* Free memory */
void rs_free(void) {
    free(logt);
    free(alog);
    free(rspoly);
    rspoly = NULL;
}