decode_rs.c

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/*
 * lib/reed_solomon/decode_rs.c
 *
 * Overview:
 *   Generic Reed Solomon encoder / decoder library
 *
 * Copyright 2002, Phil Karn, KA9Q
 * May be used under the terms of the GNU General Public License (GPL)
 *
 * Adaption to the kernel by Thomas Gleixner ([email protected])
 *
 * $Id: decode_rs.c,v 1.7 2005/11/07 11:14:59 gleixner Exp $
 *
 */

/* Generic data width independent code which is included by the
 * wrappers.
 */
{
    int deg_lambda, el, deg_omega;
    int i, j, r, k, pad;
    int nn = rs->nn;
    int nroots = rs->nroots;
    int fcr = rs->fcr;
    int prim = rs->prim;
    int iprim = rs->iprim;
    uint16_t *alpha_to = rs->alpha_to;
    uint16_t *index_of = rs->index_of;
    uint16_t u, q, tmp, num1, num2, den, discr_r, syn_error;
    /* Err+Eras Locator poly and syndrome poly The maximum value
     * of nroots is 8. So the necessary stack size will be about
     * 220 bytes max.
     */
    uint16_t lambda[nroots + 1], syn[nroots];
    uint16_t b[nroots + 1], t[nroots + 1], omega[nroots + 1];
    uint16_t root[nroots], reg[nroots + 1], loc[nroots];
    int count = 0;
    uint16_t msk = (uint16_t) rs->nn;

    /* Check length parameter for validity */
    pad = nn - nroots - len;
    BUG_ON(pad < 0 || pad >= nn);

    /* Does the caller provide the syndrome ? */
    if (s != NULL)
        goto decode;

    /* form the syndromes; i.e., evaluate data(x) at roots of
     * g(x) */
    for (i = 0; i < nroots; i++)
        syn[i] = (((uint16_t) data[0]) ^ invmsk) & msk;

    for (j = 1; j < len; j++) {
        for (i = 0; i < nroots; i++) {
            if (syn[i] == 0) {
                syn[i] = (((uint16_t) data[j]) ^
                      invmsk) & msk;
            } else {
                syn[i] = ((((uint16_t) data[j]) ^
                       invmsk) & msk) ^
                    alpha_to[rs_modnn(rs, index_of[syn[i]] +
                               (fcr + i) * prim)];
            }
        }
    }

    for (j = 0; j < nroots; j++) {
        for (i = 0; i < nroots; i++) {
            if (syn[i] == 0) {
                syn[i] = ((uint16_t) par[j]) & msk;
            } else {
                syn[i] = (((uint16_t) par[j]) & msk) ^
                    alpha_to[rs_modnn(rs, index_of[syn[i]] +
                               (fcr+i)*prim)];
            }
        }
    }
    s = syn;

    /* Convert syndromes to index form, checking for nonzero condition */
    syn_error = 0;
    for (i = 0; i < nroots; i++) {
        syn_error |= s[i];
        s[i] = index_of[s[i]];
    }

    if (!syn_error) {
        /* if syndrome is zero, data[] is a codeword and there are no
         * errors to correct. So return data[] unmodified
         */
        count = 0;
        goto finish;
    }

 decode:
    memset(&lambda[1], 0, nroots * sizeof(lambda[0]));
    lambda[0] = 1;

    if (no_eras > 0) {
        /* Init lambda to be the erasure locator polynomial */
        lambda[1] = alpha_to[rs_modnn(rs,
                          prim * (nn - 1 - eras_pos[0]))];
        for (i = 1; i < no_eras; i++) {
            u = rs_modnn(rs, prim * (nn - 1 - eras_pos[i]));
            for (j = i + 1; j > 0; j--) {
                tmp = index_of[lambda[j - 1]];
                if (tmp != nn) {
                    lambda[j] ^=
                        alpha_to[rs_modnn(rs, u + tmp)];
                }
            }
        }
    }

    for (i = 0; i < nroots + 1; i++)
        b[i] = index_of[lambda[i]];

    /*
     * Begin Berlekamp-Massey algorithm to determine error+erasure
     * locator polynomial
     */
    r = no_eras;
    el = no_eras;
    while (++r <= nroots) { /* r is the step number */
        /* Compute discrepancy at the r-th step in poly-form */
        discr_r = 0;
        for (i = 0; i < r; i++) {
            if ((lambda[i] != 0) && (s[r - i - 1] != nn)) {
                discr_r ^=
                    alpha_to[rs_modnn(rs,
                              index_of[lambda[i]] +
                              s[r - i - 1])];
            }
        }
        discr_r = index_of[discr_r];    /* Index form */
        if (discr_r == nn) {
            /* 2 lines below: B(x) <-- x*B(x) */
            memmove (&b[1], b, nroots * sizeof (b[0]));
            b[0] = nn;
        } else {
            /* 7 lines below: T(x) <-- lambda(x)-discr_r*x*b(x) */
            t[0] = lambda[0];
            for (i = 0; i < nroots; i++) {
                if (b[i] != nn) {
                    t[i + 1] = lambda[i + 1] ^
                        alpha_to[rs_modnn(rs, discr_r +
                                  b[i])];
                } else
                    t[i + 1] = lambda[i + 1];
            }
            if (2 * el <= r + no_eras - 1) {
                el = r + no_eras - el;
                /*
                 * 2 lines below: B(x) <-- inv(discr_r) *
                 * lambda(x)
                 */
                for (i = 0; i <= nroots; i++) {
                    b[i] = (lambda[i] == 0) ? nn :
                        rs_modnn(rs, index_of[lambda[i]]
                             - discr_r + nn);
                }
            } else {
                /* 2 lines below: B(x) <-- x*B(x) */
                memmove(&b[1], b, nroots * sizeof(b[0]));
                b[0] = nn;
            }
            memcpy(lambda, t, (nroots + 1) * sizeof(t[0]));
        }
    }

    /* Convert lambda to index form and compute deg(lambda(x)) */
    deg_lambda = 0;
    for (i = 0; i < nroots + 1; i++) {
        lambda[i] = index_of[lambda[i]];
        if (lambda[i] != nn)
            deg_lambda = i;
    }
    /* Find roots of error+erasure locator polynomial by Chien search */
    memcpy(&reg[1], &lambda[1], nroots * sizeof(reg[0]));
    count = 0;      /* Number of roots of lambda(x) */
    for (i = 1, k = iprim - 1; i <= nn; i++, k = rs_modnn(rs, k + iprim)) {
        q = 1;      /* lambda[0] is always 0 */
        for (j = deg_lambda; j > 0; j--) {
            if (reg[j] != nn) {
                reg[j] = rs_modnn(rs, reg[j] + j);
                q ^= alpha_to[reg[j]];
            }
        }
        if (q != 0)
            continue;   /* Not a root */
        /* store root (index-form) and error location number */
        root[count] = i;
        loc[count] = k;
        /* If we've already found max possible roots,
         * abort the search to save time
         */
        if (++count == deg_lambda)
            break;
    }
    if (deg_lambda != count) {
        /*
         * deg(lambda) unequal to number of roots => uncorrectable
         * error detected
         */
        count = -EBADMSG;
        goto finish;
    }
    /*
     * Compute err+eras evaluator poly omega(x) = s(x)*lambda(x) (modulo
     * x**nroots). in index form. Also find deg(omega).
     */
    deg_omega = deg_lambda - 1;
    for (i = 0; i <= deg_omega; i++) {
        tmp = 0;
        for (j = i; j >= 0; j--) {
            if ((s[i - j] != nn) && (lambda[j] != nn))
                tmp ^=
                    alpha_to[rs_modnn(rs, s[i - j] + lambda[j])];
        }
        omega[i] = index_of[tmp];
    }

    /*
     * Compute error values in poly-form. num1 = omega(inv(X(l))), num2 =
     * inv(X(l))**(fcr-1) and den = lambda_pr(inv(X(l))) all in poly-form
     */
    for (j = count - 1; j >= 0; j--) {
        num1 = 0;
        for (i = deg_omega; i >= 0; i--) {
            if (omega[i] != nn)
                num1 ^= alpha_to[rs_modnn(rs, omega[i] +
                            i * root[j])];
        }
        num2 = alpha_to[rs_modnn(rs, root[j] * (fcr - 1) + nn)];
        den = 0;

        /* lambda[i+1] for i even is the formal derivative
         * lambda_pr of lambda[i] */
        for (i = min(deg_lambda, nroots - 1) & ~1; i >= 0; i -= 2) {
            if (lambda[i + 1] != nn) {
                den ^= alpha_to[rs_modnn(rs, lambda[i + 1] +
                               i * root[j])];
            }
        }
        /* Apply error to data */
        if (num1 != 0 && loc[j] >= pad) {
            uint16_t cor = alpha_to[rs_modnn(rs,index_of[num1] +
                               index_of[num2] +
                               nn - index_of[den])];
            /* Store the error correction pattern, if a
             * correction buffer is available */
            if (corr) {
                corr[j] = cor;
            } else {
                /* If a data buffer is given and the
                 * error is inside the message,
                 * correct it */
                if (data && (loc[j] < (nn - nroots)))
                    data[loc[j] - pad] ^= cor;
            }
        }
    }

finish:
    if (eras_pos != NULL) {
        for (i = 0; i < count; i++)
            eras_pos[i] = loc[i] - pad;
    }
    return count;

}