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root/lib/reed_solomon/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 (tglx@linutronix.de)
 *
 * $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;

}

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