From c30be3b694dbc95c38df9212d1f01b68c8ecdd26 Mon Sep 17 00:00:00 2001 From: Vladimir 'phcoder' Serbinenko Date: Sun, 13 Nov 2011 14:48:19 +0100 Subject: [PATCH] Make Reed-Solomon faster by using power of generator representation of GF(256)*. * grub-core/lib/reed_solomon.c (grub_uint16_t) [TEST]: Removed. (gf_double_t): Likewise. (gf_invert): Removed. (gf_powx): New array. (gf_powx_inv): Likewise. (scratch): Move higher. (gf_reduce): Removed. (gf_mul): Use powx. (gf_invert): Likewise. (init_inverts): Replaced with ... (init_powx): ...this. All users updated. (pol_evaluate): Replace multiplications with additions. (rs_encode): Likewise. (gauss_eliminate): Call gf_invert. (grub_reed_solomon_add_redundancy): Call init_powx. (grub_reed_solomon_recover): Call init_powx unconditionally. --- ChangeLog | 22 ++++++++ grub-core/lib/reed_solomon.c | 105 +++++++++++++++++++---------------- 2 files changed, 78 insertions(+), 49 deletions(-) diff --git a/ChangeLog b/ChangeLog index 623313b3c..229567014 100644 --- a/ChangeLog +++ b/ChangeLog @@ -1,3 +1,25 @@ +2011-11-13 Vladimir Serbinenko + + Make Reed-Solomon faster by using power of generator representation of + GF(256)*. + + * grub-core/lib/reed_solomon.c (grub_uint16_t) [TEST]: Removed. + (gf_double_t): Likewise. + (gf_invert): Removed. + (gf_powx): New array. + (gf_powx_inv): Likewise. + (scratch): Move higher. + (gf_reduce): Removed. + (gf_mul): Use powx. + (gf_invert): Likewise. + (init_inverts): Replaced with ... + (init_powx): ...this. All users updated. + (pol_evaluate): Replace multiplications with additions. + (rs_encode): Likewise. + (gauss_eliminate): Call gf_invert. + (grub_reed_solomon_add_redundancy): Call init_powx. + (grub_reed_solomon_recover): Call init_powx unconditionally. + 2011-11-12 Vladimir Serbinenko * grub-core/partmap/gpt.c (gpt_partition_map_embed): Fix spelling. diff --git a/grub-core/lib/reed_solomon.c b/grub-core/lib/reed_solomon.c index 78d249c2f..7da5f204c 100644 --- a/grub-core/lib/reed_solomon.c +++ b/grub-core/lib/reed_solomon.c @@ -29,7 +29,6 @@ #ifdef TEST typedef unsigned int grub_size_t; typedef unsigned char grub_uint8_t; -typedef unsigned short grub_uint16_t; #else #include #include @@ -42,7 +41,6 @@ typedef unsigned short grub_uint16_t; #ifdef TEST typedef unsigned int grub_size_t; typedef unsigned char grub_uint8_t; -typedef unsigned short grub_uint16_t; #else #include #include @@ -53,65 +51,72 @@ grub_reed_solomon_recover (void *ptr_, grub_size_t s, grub_size_t rs); #define GF_SIZE 8 typedef grub_uint8_t gf_single_t; -typedef grub_uint16_t gf_double_t; #define GF_POLYNOMIAL 0x1d #define GF_INVERT2 0x8e #if defined (STANDALONE) && !defined (TEST) -static gf_single_t * const gf_invert __attribute__ ((section(".text"))) = (void *) 0x100000; -static char *scratch __attribute__ ((section(".text"))) = (void *) 0x100100; +static gf_single_t * const gf_powx __attribute__ ((section(".text"))) = (void *) 0x100000; +static gf_single_t * const gf_powx_inv __attribute__ ((section(".text"))) = (void *) 0x100200; + +static char *scratch __attribute__ ((section(".text"))) = (void *) 0x100300; #else #if defined (STANDALONE) static char *scratch; #endif -static gf_single_t gf_invert[256]; +static gf_single_t gf_powx[255 * 2]; +static gf_single_t gf_powx_inv[256]; #endif #define SECTOR_SIZE 512 #define MAX_BLOCK_SIZE (200 * SECTOR_SIZE) -static gf_single_t -gf_reduce (gf_double_t a) -{ - int i; - for (i = GF_SIZE - 1; i >= 0; i--) - if (a & (1ULL << (i + GF_SIZE))) - a ^= (((gf_double_t) GF_POLYNOMIAL) << i); - return a & ((1ULL << GF_SIZE) - 1); -} - static gf_single_t gf_mul (gf_single_t a, gf_single_t b) { - gf_double_t res = 0; - int i; - for (i = 0; i < GF_SIZE; i++) - if (b & (1 << i)) - res ^= ((gf_double_t) a) << i; - return gf_reduce (res); + if (a == 0 || b == 0) + return 0; + return gf_powx[(int) gf_powx_inv[a] + (int) gf_powx_inv[b]]; +} + +static inline gf_single_t +gf_invert (gf_single_t a) +{ + return gf_powx[255 - (int) gf_powx_inv[a]]; } static void -init_inverts (void) +init_powx (void) { - gf_single_t a = 1, ai = 1; - do + int i; + grub_uint8_t cur = 1; + + for (i = 0; i < 255; i++) { - a = gf_mul (a, 2); - ai = gf_mul (ai, GF_INVERT2); - gf_invert[a] = ai; + gf_powx[i] = cur; + gf_powx[i + 255] = cur; + gf_powx_inv[cur] = i; + if (cur & (1ULL << (GF_SIZE - 1))) + cur = (cur << 1) ^ GF_POLYNOMIAL; + else + cur <<= 1; } - while (a != 1); } static gf_single_t pol_evaluate (gf_single_t *pol, grub_size_t degree, gf_single_t x) { int i; - gf_single_t xn = 1, s = 0; + gf_single_t s = 0; + int log_xn = 0, log_x; + if (x == 0) + return pol[0]; + log_x = gf_powx_inv[x]; for (i = degree; i >= 0; i--) { - s ^= gf_mul (pol[i], xn); - xn = gf_mul (x, xn); + if (pol[i]) + s ^= gf_powx[(int) gf_powx_inv[pol[i]] + log_xn]; + log_xn += log_x; + if (log_xn >= ((1 << GF_SIZE) - 1)) + log_xn -= ((1 << GF_SIZE) - 1); } return s; } @@ -120,7 +125,7 @@ pol_evaluate (gf_single_t *pol, grub_size_t degree, gf_single_t x) static void rs_encode (gf_single_t *data, grub_size_t s, grub_size_t rs) { - gf_single_t *rs_polynomial, a = 1; + gf_single_t *rs_polynomial; int i, j; gf_single_t *m; m = xmalloc ((s + rs) * sizeof (gf_single_t)); @@ -132,16 +137,14 @@ rs_encode (gf_single_t *data, grub_size_t s, grub_size_t rs) /* Multiply with X - a^r */ for (j = 0; j < rs; j++) { - if (a & (1 << (GF_SIZE - 1))) - { - a <<= 1; - a ^= GF_POLYNOMIAL; - } - else - a <<= 1; for (i = 0; i < rs; i++) - rs_polynomial[i] = rs_polynomial[i + 1] ^ gf_mul (a, rs_polynomial[i]); - rs_polynomial[rs] = gf_mul (a, rs_polynomial[rs]); + if (rs_polynomial[i]) + rs_polynomial[i] = (rs_polynomial[i + 1] + ^ gf_powx[j + (int) gf_powx_inv[rs_polynomial[i]]]); + else + rs_polynomial[i] = rs_polynomial[i + 1]; + if (rs_polynomial[rs]) + rs_polynomial[rs] = gf_powx[j + (int) gf_powx_inv[rs_polynomial[rs]]]; } for (j = 0; j < s; j++) if (m[j]) @@ -190,7 +193,7 @@ gauss_eliminate (gf_single_t *eq, int n, int m, int *chosen) if (nzidx == m) continue; chosen[i] = nzidx; - r = gf_invert [eq[i * (m + 1) + nzidx]]; + r = gf_invert (eq[i * (m + 1) + nzidx]); for (j = 0; j < m + 1; j++) eq[i * (m + 1) + j] = gf_mul (eq[i * (m + 1) + j], r); for (j = i + 1; j < n; j++) @@ -437,6 +440,8 @@ grub_reed_solomon_add_redundancy (void *buffer, grub_size_t data_size, if (!rs) return; + init_powx (); + while (s > 0) { grub_size_t tt; @@ -468,9 +473,7 @@ grub_reed_solomon_recover (void *ptr_, grub_size_t s, grub_size_t rs) if (!rs) return; -#if defined (STANDALONE) - init_inverts (); -#endif + init_powx (); while (s > 0) { @@ -500,12 +503,15 @@ main (int argc, char **argv) grub_size_t s, rs; char *buf; + grub_memset (gf_powx, 0xee, sizeof (gf_powx)); + grub_memset (gf_powx_inv, 0xdd, sizeof (gf_powx_inv)); + #ifdef STANDALONE scratch = xmalloc (1048576); #endif #ifndef STANDALONE - init_inverts (); + init_powx (); #endif in = fopen ("tst.bin", "rb"); @@ -514,7 +520,7 @@ main (int argc, char **argv) fseek (in, 0, SEEK_END); s = ftell (in); fseek (in, 0, SEEK_SET); - rs = s / 3; + rs = 0x7007; buf = xmalloc (s + rs + SECTOR_SIZE); fread (buf, 1, s, in); fclose (in); @@ -524,8 +530,9 @@ main (int argc, char **argv) out = fopen ("tst_rs.bin", "wb"); fwrite (buf, 1, s + rs, out); fclose (out); - +#if 0 grub_memset (buf + 512 * 15, 0, 512); +#endif out = fopen ("tst_dam.bin", "wb"); fwrite (buf, 1, s + rs, out);