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.
This commit is contained in:
Vladimir 'phcoder' Serbinenko
parent
fa5aeffcc2
commit
c30be3b694
2 changed files with 78 additions and 49 deletions
22
ChangeLog
22
ChangeLog
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@ -1,3 +1,25 @@
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2011-11-13 Vladimir Serbinenko <phcoder@gmail.com>
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Make Reed-Solomon faster by using power of generator representation of
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GF(256)*.
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* grub-core/lib/reed_solomon.c (grub_uint16_t) [TEST]: Removed.
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(gf_double_t): Likewise.
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(gf_invert): Removed.
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(gf_powx): New array.
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(gf_powx_inv): Likewise.
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(scratch): Move higher.
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(gf_reduce): Removed.
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(gf_mul): Use powx.
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(gf_invert): Likewise.
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(init_inverts): Replaced with ...
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(init_powx): ...this. All users updated.
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(pol_evaluate): Replace multiplications with additions.
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(rs_encode): Likewise.
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(gauss_eliminate): Call gf_invert.
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(grub_reed_solomon_add_redundancy): Call init_powx.
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(grub_reed_solomon_recover): Call init_powx unconditionally.
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2011-11-12 Vladimir Serbinenko <phcoder@gmail.com>
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* grub-core/partmap/gpt.c (gpt_partition_map_embed): Fix spelling.
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@ -29,7 +29,6 @@
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#ifdef TEST
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typedef unsigned int grub_size_t;
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typedef unsigned char grub_uint8_t;
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typedef unsigned short grub_uint16_t;
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#else
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#include <grub/types.h>
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#include <grub/reed_solomon.h>
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@ -42,7 +41,6 @@ typedef unsigned short grub_uint16_t;
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#ifdef TEST
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typedef unsigned int grub_size_t;
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typedef unsigned char grub_uint8_t;
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typedef unsigned short grub_uint16_t;
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#else
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#include <grub/types.h>
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#include <grub/misc.h>
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@ -53,65 +51,72 @@ grub_reed_solomon_recover (void *ptr_, grub_size_t s, grub_size_t rs);
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#define GF_SIZE 8
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typedef grub_uint8_t gf_single_t;
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typedef grub_uint16_t gf_double_t;
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#define GF_POLYNOMIAL 0x1d
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#define GF_INVERT2 0x8e
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#if defined (STANDALONE) && !defined (TEST)
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static gf_single_t * const gf_invert __attribute__ ((section(".text"))) = (void *) 0x100000;
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static char *scratch __attribute__ ((section(".text"))) = (void *) 0x100100;
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static gf_single_t * const gf_powx __attribute__ ((section(".text"))) = (void *) 0x100000;
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static gf_single_t * const gf_powx_inv __attribute__ ((section(".text"))) = (void *) 0x100200;
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static char *scratch __attribute__ ((section(".text"))) = (void *) 0x100300;
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#else
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#if defined (STANDALONE)
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static char *scratch;
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#endif
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static gf_single_t gf_invert[256];
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static gf_single_t gf_powx[255 * 2];
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static gf_single_t gf_powx_inv[256];
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#endif
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#define SECTOR_SIZE 512
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#define MAX_BLOCK_SIZE (200 * SECTOR_SIZE)
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static gf_single_t
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gf_reduce (gf_double_t a)
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{
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int i;
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for (i = GF_SIZE - 1; i >= 0; i--)
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if (a & (1ULL << (i + GF_SIZE)))
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a ^= (((gf_double_t) GF_POLYNOMIAL) << i);
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return a & ((1ULL << GF_SIZE) - 1);
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}
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static gf_single_t
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gf_mul (gf_single_t a, gf_single_t b)
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{
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gf_double_t res = 0;
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int i;
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for (i = 0; i < GF_SIZE; i++)
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if (b & (1 << i))
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res ^= ((gf_double_t) a) << i;
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return gf_reduce (res);
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if (a == 0 || b == 0)
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return 0;
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return gf_powx[(int) gf_powx_inv[a] + (int) gf_powx_inv[b]];
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}
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static inline gf_single_t
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gf_invert (gf_single_t a)
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{
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return gf_powx[255 - (int) gf_powx_inv[a]];
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}
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static void
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init_inverts (void)
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init_powx (void)
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{
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gf_single_t a = 1, ai = 1;
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do
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int i;
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grub_uint8_t cur = 1;
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for (i = 0; i < 255; i++)
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{
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a = gf_mul (a, 2);
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ai = gf_mul (ai, GF_INVERT2);
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gf_invert[a] = ai;
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gf_powx[i] = cur;
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gf_powx[i + 255] = cur;
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gf_powx_inv[cur] = i;
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if (cur & (1ULL << (GF_SIZE - 1)))
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cur = (cur << 1) ^ GF_POLYNOMIAL;
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else
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cur <<= 1;
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}
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while (a != 1);
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}
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static gf_single_t
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pol_evaluate (gf_single_t *pol, grub_size_t degree, gf_single_t x)
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{
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int i;
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gf_single_t xn = 1, s = 0;
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gf_single_t s = 0;
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int log_xn = 0, log_x;
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if (x == 0)
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return pol[0];
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log_x = gf_powx_inv[x];
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for (i = degree; i >= 0; i--)
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{
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s ^= gf_mul (pol[i], xn);
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xn = gf_mul (x, xn);
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if (pol[i])
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s ^= gf_powx[(int) gf_powx_inv[pol[i]] + log_xn];
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log_xn += log_x;
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if (log_xn >= ((1 << GF_SIZE) - 1))
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log_xn -= ((1 << GF_SIZE) - 1);
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}
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return s;
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}
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@ -120,7 +125,7 @@ pol_evaluate (gf_single_t *pol, grub_size_t degree, gf_single_t x)
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static void
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rs_encode (gf_single_t *data, grub_size_t s, grub_size_t rs)
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{
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gf_single_t *rs_polynomial, a = 1;
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gf_single_t *rs_polynomial;
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int i, j;
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gf_single_t *m;
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m = xmalloc ((s + rs) * sizeof (gf_single_t));
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@ -132,16 +137,14 @@ rs_encode (gf_single_t *data, grub_size_t s, grub_size_t rs)
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/* Multiply with X - a^r */
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for (j = 0; j < rs; j++)
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{
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if (a & (1 << (GF_SIZE - 1)))
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{
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a <<= 1;
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a ^= GF_POLYNOMIAL;
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}
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else
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a <<= 1;
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for (i = 0; i < rs; i++)
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rs_polynomial[i] = rs_polynomial[i + 1] ^ gf_mul (a, rs_polynomial[i]);
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rs_polynomial[rs] = gf_mul (a, rs_polynomial[rs]);
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if (rs_polynomial[i])
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rs_polynomial[i] = (rs_polynomial[i + 1]
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^ gf_powx[j + (int) gf_powx_inv[rs_polynomial[i]]]);
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else
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rs_polynomial[i] = rs_polynomial[i + 1];
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if (rs_polynomial[rs])
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rs_polynomial[rs] = gf_powx[j + (int) gf_powx_inv[rs_polynomial[rs]]];
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}
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for (j = 0; j < s; j++)
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if (m[j])
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@ -190,7 +193,7 @@ gauss_eliminate (gf_single_t *eq, int n, int m, int *chosen)
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if (nzidx == m)
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continue;
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chosen[i] = nzidx;
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r = gf_invert [eq[i * (m + 1) + nzidx]];
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r = gf_invert (eq[i * (m + 1) + nzidx]);
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for (j = 0; j < m + 1; j++)
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eq[i * (m + 1) + j] = gf_mul (eq[i * (m + 1) + j], r);
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for (j = i + 1; j < n; j++)
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@ -437,6 +440,8 @@ grub_reed_solomon_add_redundancy (void *buffer, grub_size_t data_size,
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if (!rs)
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return;
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init_powx ();
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while (s > 0)
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{
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grub_size_t tt;
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@ -468,9 +473,7 @@ grub_reed_solomon_recover (void *ptr_, grub_size_t s, grub_size_t rs)
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if (!rs)
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return;
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#if defined (STANDALONE)
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init_inverts ();
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#endif
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init_powx ();
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while (s > 0)
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{
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@ -500,12 +503,15 @@ main (int argc, char **argv)
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grub_size_t s, rs;
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char *buf;
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grub_memset (gf_powx, 0xee, sizeof (gf_powx));
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grub_memset (gf_powx_inv, 0xdd, sizeof (gf_powx_inv));
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#ifdef STANDALONE
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scratch = xmalloc (1048576);
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#endif
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#ifndef STANDALONE
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init_inverts ();
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init_powx ();
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#endif
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in = fopen ("tst.bin", "rb");
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@ -514,7 +520,7 @@ main (int argc, char **argv)
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fseek (in, 0, SEEK_END);
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s = ftell (in);
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fseek (in, 0, SEEK_SET);
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rs = s / 3;
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rs = 0x7007;
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buf = xmalloc (s + rs + SECTOR_SIZE);
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fread (buf, 1, s, in);
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fclose (in);
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@ -524,8 +530,9 @@ main (int argc, char **argv)
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out = fopen ("tst_rs.bin", "wb");
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fwrite (buf, 1, s + rs, out);
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fclose (out);
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#if 0
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grub_memset (buf + 512 * 15, 0, 512);
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#endif
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out = fopen ("tst_dam.bin", "wb");
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fwrite (buf, 1, s + rs, out);
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