^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 1) // SPDX-License-Identifier: GPL-2.0
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 2) /*
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 3) * Generic Reed Solomon encoder / decoder library
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 4) *
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 5) * Copyright 2002, Phil Karn, KA9Q
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 6) * May be used under the terms of the GNU General Public License (GPL)
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 7) *
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 8) * Adaption to the kernel by Thomas Gleixner (tglx@linutronix.de)
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 9) *
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 10) * Generic data width independent code which is included by the wrappers.
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 11) */
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 12) {
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 13) struct rs_codec *rs = rsc->codec;
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 14) int deg_lambda, el, deg_omega;
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 15) int i, j, r, k, pad;
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 16) int nn = rs->nn;
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 17) int nroots = rs->nroots;
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 18) int fcr = rs->fcr;
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 19) int prim = rs->prim;
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 20) int iprim = rs->iprim;
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 21) uint16_t *alpha_to = rs->alpha_to;
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 22) uint16_t *index_of = rs->index_of;
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 23) uint16_t u, q, tmp, num1, num2, den, discr_r, syn_error;
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 24) int count = 0;
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 25) int num_corrected;
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 26) uint16_t msk = (uint16_t) rs->nn;
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 27)
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 28) /*
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 29) * The decoder buffers are in the rs control struct. They are
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 30) * arrays sized [nroots + 1]
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 31) */
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 32) uint16_t *lambda = rsc->buffers + RS_DECODE_LAMBDA * (nroots + 1);
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 33) uint16_t *syn = rsc->buffers + RS_DECODE_SYN * (nroots + 1);
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 34) uint16_t *b = rsc->buffers + RS_DECODE_B * (nroots + 1);
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 35) uint16_t *t = rsc->buffers + RS_DECODE_T * (nroots + 1);
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 36) uint16_t *omega = rsc->buffers + RS_DECODE_OMEGA * (nroots + 1);
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 37) uint16_t *root = rsc->buffers + RS_DECODE_ROOT * (nroots + 1);
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 38) uint16_t *reg = rsc->buffers + RS_DECODE_REG * (nroots + 1);
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 39) uint16_t *loc = rsc->buffers + RS_DECODE_LOC * (nroots + 1);
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 40)
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 41) /* Check length parameter for validity */
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 42) pad = nn - nroots - len;
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 43) BUG_ON(pad < 0 || pad >= nn - nroots);
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 44)
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 45) /* Does the caller provide the syndrome ? */
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 46) if (s != NULL) {
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 47) for (i = 0; i < nroots; i++) {
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 48) /* The syndrome is in index form,
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 49) * so nn represents zero
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 50) */
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 51) if (s[i] != nn)
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 52) goto decode;
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 53) }
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 54)
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 55) /* syndrome is zero, no errors to correct */
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 56) return 0;
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 57) }
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 58)
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 59) /* form the syndromes; i.e., evaluate data(x) at roots of
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 60) * g(x) */
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 61) for (i = 0; i < nroots; i++)
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 62) syn[i] = (((uint16_t) data[0]) ^ invmsk) & msk;
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 63)
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 64) for (j = 1; j < len; j++) {
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 65) for (i = 0; i < nroots; i++) {
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 66) if (syn[i] == 0) {
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 67) syn[i] = (((uint16_t) data[j]) ^
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 68) invmsk) & msk;
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 69) } else {
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 70) syn[i] = ((((uint16_t) data[j]) ^
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 71) invmsk) & msk) ^
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 72) alpha_to[rs_modnn(rs, index_of[syn[i]] +
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 73) (fcr + i) * prim)];
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 74) }
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 75) }
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 76) }
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 77)
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 78) for (j = 0; j < nroots; j++) {
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 79) for (i = 0; i < nroots; i++) {
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 80) if (syn[i] == 0) {
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 81) syn[i] = ((uint16_t) par[j]) & msk;
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 82) } else {
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 83) syn[i] = (((uint16_t) par[j]) & msk) ^
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 84) alpha_to[rs_modnn(rs, index_of[syn[i]] +
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 85) (fcr+i)*prim)];
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 86) }
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 87) }
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 88) }
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 89) s = syn;
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 90)
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 91) /* Convert syndromes to index form, checking for nonzero condition */
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 92) syn_error = 0;
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 93) for (i = 0; i < nroots; i++) {
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 94) syn_error |= s[i];
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 95) s[i] = index_of[s[i]];
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 96) }
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 97)
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 98) if (!syn_error) {
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 99) /* if syndrome is zero, data[] is a codeword and there are no
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 100) * errors to correct. So return data[] unmodified
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 101) */
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 102) return 0;
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 103) }
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 104)
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 105) decode:
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 106) memset(&lambda[1], 0, nroots * sizeof(lambda[0]));
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 107) lambda[0] = 1;
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 108)
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 109) if (no_eras > 0) {
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 110) /* Init lambda to be the erasure locator polynomial */
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 111) lambda[1] = alpha_to[rs_modnn(rs,
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 112) prim * (nn - 1 - (eras_pos[0] + pad)))];
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 113) for (i = 1; i < no_eras; i++) {
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 114) u = rs_modnn(rs, prim * (nn - 1 - (eras_pos[i] + pad)));
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 115) for (j = i + 1; j > 0; j--) {
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 116) tmp = index_of[lambda[j - 1]];
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 117) if (tmp != nn) {
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 118) lambda[j] ^=
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 119) alpha_to[rs_modnn(rs, u + tmp)];
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 120) }
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 121) }
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 122) }
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 123) }
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 124)
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 125) for (i = 0; i < nroots + 1; i++)
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 126) b[i] = index_of[lambda[i]];
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 127)
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 128) /*
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 129) * Begin Berlekamp-Massey algorithm to determine error+erasure
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 130) * locator polynomial
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 131) */
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 132) r = no_eras;
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 133) el = no_eras;
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 134) while (++r <= nroots) { /* r is the step number */
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 135) /* Compute discrepancy at the r-th step in poly-form */
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 136) discr_r = 0;
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 137) for (i = 0; i < r; i++) {
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 138) if ((lambda[i] != 0) && (s[r - i - 1] != nn)) {
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 139) discr_r ^=
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 140) alpha_to[rs_modnn(rs,
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 141) index_of[lambda[i]] +
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 142) s[r - i - 1])];
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 143) }
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 144) }
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 145) discr_r = index_of[discr_r]; /* Index form */
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 146) if (discr_r == nn) {
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 147) /* 2 lines below: B(x) <-- x*B(x) */
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 148) memmove (&b[1], b, nroots * sizeof (b[0]));
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 149) b[0] = nn;
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 150) } else {
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 151) /* 7 lines below: T(x) <-- lambda(x)-discr_r*x*b(x) */
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 152) t[0] = lambda[0];
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 153) for (i = 0; i < nroots; i++) {
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 154) if (b[i] != nn) {
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 155) t[i + 1] = lambda[i + 1] ^
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 156) alpha_to[rs_modnn(rs, discr_r +
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 157) b[i])];
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 158) } else
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 159) t[i + 1] = lambda[i + 1];
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 160) }
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 161) if (2 * el <= r + no_eras - 1) {
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 162) el = r + no_eras - el;
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 163) /*
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 164) * 2 lines below: B(x) <-- inv(discr_r) *
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 165) * lambda(x)
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 166) */
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 167) for (i = 0; i <= nroots; i++) {
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 168) b[i] = (lambda[i] == 0) ? nn :
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 169) rs_modnn(rs, index_of[lambda[i]]
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 170) - discr_r + nn);
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 171) }
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 172) } else {
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 173) /* 2 lines below: B(x) <-- x*B(x) */
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 174) memmove(&b[1], b, nroots * sizeof(b[0]));
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 175) b[0] = nn;
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 176) }
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 177) memcpy(lambda, t, (nroots + 1) * sizeof(t[0]));
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 178) }
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 179) }
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 180)
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 181) /* Convert lambda to index form and compute deg(lambda(x)) */
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 182) deg_lambda = 0;
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 183) for (i = 0; i < nroots + 1; i++) {
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 184) lambda[i] = index_of[lambda[i]];
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 185) if (lambda[i] != nn)
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 186) deg_lambda = i;
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 187) }
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 188)
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 189) if (deg_lambda == 0) {
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 190) /*
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 191) * deg(lambda) is zero even though the syndrome is non-zero
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 192) * => uncorrectable error detected
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 193) */
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 194) return -EBADMSG;
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 195) }
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 196)
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 197) /* Find roots of error+erasure locator polynomial by Chien search */
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 198) memcpy(®[1], &lambda[1], nroots * sizeof(reg[0]));
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 199) count = 0; /* Number of roots of lambda(x) */
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 200) for (i = 1, k = iprim - 1; i <= nn; i++, k = rs_modnn(rs, k + iprim)) {
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 201) q = 1; /* lambda[0] is always 0 */
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 202) for (j = deg_lambda; j > 0; j--) {
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 203) if (reg[j] != nn) {
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 204) reg[j] = rs_modnn(rs, reg[j] + j);
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 205) q ^= alpha_to[reg[j]];
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 206) }
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 207) }
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 208) if (q != 0)
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 209) continue; /* Not a root */
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 210)
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 211) if (k < pad) {
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 212) /* Impossible error location. Uncorrectable error. */
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 213) return -EBADMSG;
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 214) }
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 215)
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 216) /* store root (index-form) and error location number */
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 217) root[count] = i;
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 218) loc[count] = k;
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 219) /* If we've already found max possible roots,
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 220) * abort the search to save time
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 221) */
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 222) if (++count == deg_lambda)
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 223) break;
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 224) }
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 225) if (deg_lambda != count) {
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 226) /*
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 227) * deg(lambda) unequal to number of roots => uncorrectable
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 228) * error detected
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 229) */
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 230) return -EBADMSG;
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 231) }
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 232) /*
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 233) * Compute err+eras evaluator poly omega(x) = s(x)*lambda(x) (modulo
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 234) * x**nroots). in index form. Also find deg(omega).
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 235) */
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 236) deg_omega = deg_lambda - 1;
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 237) for (i = 0; i <= deg_omega; i++) {
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 238) tmp = 0;
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 239) for (j = i; j >= 0; j--) {
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 240) if ((s[i - j] != nn) && (lambda[j] != nn))
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 241) tmp ^=
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 242) alpha_to[rs_modnn(rs, s[i - j] + lambda[j])];
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 243) }
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 244) omega[i] = index_of[tmp];
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 245) }
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 246)
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 247) /*
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 248) * Compute error values in poly-form. num1 = omega(inv(X(l))), num2 =
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 249) * inv(X(l))**(fcr-1) and den = lambda_pr(inv(X(l))) all in poly-form
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 250) * Note: we reuse the buffer for b to store the correction pattern
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 251) */
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 252) num_corrected = 0;
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 253) for (j = count - 1; j >= 0; j--) {
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 254) num1 = 0;
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 255) for (i = deg_omega; i >= 0; i--) {
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 256) if (omega[i] != nn)
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 257) num1 ^= alpha_to[rs_modnn(rs, omega[i] +
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 258) i * root[j])];
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 259) }
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 260)
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 261) if (num1 == 0) {
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 262) /* Nothing to correct at this position */
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 263) b[j] = 0;
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 264) continue;
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 265) }
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 266)
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 267) num2 = alpha_to[rs_modnn(rs, root[j] * (fcr - 1) + nn)];
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 268) den = 0;
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 269)
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 270) /* lambda[i+1] for i even is the formal derivative
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 271) * lambda_pr of lambda[i] */
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 272) for (i = min(deg_lambda, nroots - 1) & ~1; i >= 0; i -= 2) {
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 273) if (lambda[i + 1] != nn) {
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 274) den ^= alpha_to[rs_modnn(rs, lambda[i + 1] +
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 275) i * root[j])];
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 276) }
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 277) }
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 278)
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 279) b[j] = alpha_to[rs_modnn(rs, index_of[num1] +
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 280) index_of[num2] +
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 281) nn - index_of[den])];
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 282) num_corrected++;
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 283) }
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 284)
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 285) /*
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 286) * We compute the syndrome of the 'error' and check that it matches
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 287) * the syndrome of the received word
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 288) */
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 289) for (i = 0; i < nroots; i++) {
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 290) tmp = 0;
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 291) for (j = 0; j < count; j++) {
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 292) if (b[j] == 0)
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 293) continue;
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 294)
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 295) k = (fcr + i) * prim * (nn-loc[j]-1);
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 296) tmp ^= alpha_to[rs_modnn(rs, index_of[b[j]] + k)];
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 297) }
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 298)
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 299) if (tmp != alpha_to[s[i]])
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 300) return -EBADMSG;
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 301) }
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 302)
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 303) /*
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 304) * Store the error correction pattern, if a
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 305) * correction buffer is available
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 306) */
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 307) if (corr && eras_pos) {
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 308) j = 0;
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 309) for (i = 0; i < count; i++) {
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 310) if (b[i]) {
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 311) corr[j] = b[i];
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 312) eras_pos[j++] = loc[i] - pad;
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 313) }
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 314) }
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 315) } else if (data && par) {
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 316) /* Apply error to data and parity */
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 317) for (i = 0; i < count; i++) {
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 318) if (loc[i] < (nn - nroots))
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 319) data[loc[i] - pad] ^= b[i];
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 320) else
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 321) par[loc[i] - pad - len] ^= b[i];
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 322) }
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 323) }
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 324)
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 325) return num_corrected;
^8f3ce5b39 (kx 2023-10-28 12:00:06 +0300 326) }
Orange Pi5 kernel
Deprecated Linux kernel 5.10.110 for OrangePi 5/5B/5+ boards
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