gf_t* galois_init_field(int w, int mult_type, int region_type, int divide_type, uint64_t prim_poly, int arg1, int arg2) { int scratch_size; void *scratch_memory; gf_t *gfp; if (w <= 0 || w > 32) { fprintf(stderr, "ERROR -- cannot init default Galois field for w=%d\n", w); abort(); } gfp = (gf_t *) malloc(sizeof(gf_t)); if (!gfp) { fprintf(stderr, "ERROR -- cannot allocate memory for Galois field w=%d\n", w); abort(); } scratch_size = gf_scratch_size(w, mult_type, region_type, divide_type, arg1, arg2); if (!scratch_size) { fprintf(stderr, "ERROR -- cannot get scratch size for base field w=%d\n", w); abort(); } scratch_memory = malloc(scratch_size); if (!scratch_memory) { fprintf(stderr, "ERROR -- cannot get scratch memory for base field w=%d\n", w); abort(); } if(!gf_init_hard(gfp, w, mult_type, region_type, divide_type, prim_poly, arg1, arg2, NULL, scratch_memory)) { fprintf(stderr, "ERROR -- cannot init default Galois field for w=%d\n", w); abort(); } gfp_is_composite[w] = 0; return gfp; }
int main(int argc, char **argv) { uint16_t *a, *b; int i, j; gf_t gf; if (gf_init_hard(&gf, 16, GF_MULT_SPLIT_TABLE, GF_REGION_ALTMAP, GF_DIVIDE_DEFAULT, 0, 16, 4, NULL, NULL) == 0) { fprintf(stderr, "gf_init_hard failed\n"); exit(1); } a = (uint16_t *) malloc(200); b = (uint16_t *) malloc(200); a += 6; b += 6; MOA_Seed(0); for (i = 0; i < 30; i++) a[i] = MOA_Random_W(16, 1); gf.multiply_region.w32(&gf, a, b, 0x1234, 30*2, 0); printf("a: 0x%lx b: 0x%lx\n", (unsigned long) a, (unsigned long) b); for (i = 0; i < 30; i += 10) { printf("\n"); printf(" "); for (j = 0; j < 10; j++) printf(" %4d", i+j); printf("\n"); printf("a:"); for (j = 0; j < 10; j++) printf(" %04x", a[i+j]); printf("\n"); printf("b:"); for (j = 0; j < 10; j++) printf(" %04x", b[i+j]); printf("\n"); printf("\n"); } for (i = 0; i < 15; i ++) { printf("Word %2d: 0x%04x * 0x1234 = 0x%04x ", i, gf.extract_word.w32(&gf, a, 30*2, i), gf.extract_word.w32(&gf, b, 30*2, i)); printf("Word %2d: 0x%04x * 0x1234 = 0x%04x\n", i+15, gf.extract_word.w32(&gf, a, 30*2, i+15), gf.extract_word.w32(&gf, b, 30*2, i+15)); } return 0; }
gf_t* galois_init_composite_field(int w, int region_type, int divide_type, int degree, gf_t* base_gf) { int scratch_size; void *scratch_memory; gf_t *gfp; if (w <= 0 || w > 32) { fprintf(stderr, "ERROR -- cannot init composite field for w=%d\n", w); abort(); } gfp = (gf_t *) malloc(sizeof(gf_t)); if (!gfp) { fprintf(stderr, "ERROR -- cannot allocate memory for Galois field w=%d\n", w); abort(); } scratch_size = gf_scratch_size(w, GF_MULT_COMPOSITE, region_type, divide_type, degree, 0); if (!scratch_size) { fprintf(stderr, "ERROR -- cannot get scratch size for composite field w=%d\n", w); abort(); } scratch_memory = malloc(scratch_size); if (!scratch_memory) { fprintf(stderr, "ERROR -- cannot get scratch memory for composite field w=%d\n", w); abort(); } if(!gf_init_hard(gfp, w, GF_MULT_COMPOSITE, region_type, divide_type, 0, degree, 0, base_gf, scratch_memory)) { fprintf(stderr, "ERROR -- cannot init default composite field for w=%d\n", w); abort(); } gfp_is_composite[w] = 1; return gfp; }
int main(int argc, char **argv) { signal(SIGSEGV, SigHandler); int w, i, verbose, single, region, tested, top; int s_start, d_start, bytes, xor, alignment_test; gf_t gf, gf_def; time_t t0; gf_internal_t *h; gf_general_t *a, *b, *c, *d, *ai, *bi; uint8_t a8, b8, c8, *mult4, *div4, *mult8, *div8; uint16_t a16, b16, c16, d16, *log16, *alog16; char as[50], bs[50], cs[50], ds[50], ais[50], bis[50]; uint32_t mask; char *ra, *rb, *rc, *rd, *target; int align; if (argc < 4) usage(NULL); if (sscanf(argv[1], "%d", &w) == 0){ usage("Bad w\n"); } if (sscanf(argv[3], "%ld", &t0) == 0) usage("Bad seed\n"); if (t0 == -1) t0 = time(0); MOA_Seed(t0); if (w > 32 && w != 64 && w != 128) usage("Bad w"); if (create_gf_from_argv(&gf, w, argc, argv, 4) == 0) usage(BM); printf("Size (bytes): %d\n", gf_size(&gf)); for (i = 0; i < strlen(argv[2]); i++) { if (strchr("ASRV", argv[2][i]) == NULL) usage("Bad test\n"); } h = (gf_internal_t *) gf.scratch; a = (gf_general_t *) malloc(sizeof(gf_general_t)); b = (gf_general_t *) malloc(sizeof(gf_general_t)); c = (gf_general_t *) malloc(sizeof(gf_general_t)); d = (gf_general_t *) malloc(sizeof(gf_general_t)); ai = (gf_general_t *) malloc(sizeof(gf_general_t)); bi = (gf_general_t *) malloc(sizeof(gf_general_t)); //15 bytes extra to make sure it's 16byte aligned ra = (char *) malloc(sizeof(char)*REGION_SIZE+15); rb = (char *) malloc(sizeof(char)*REGION_SIZE+15); rc = (char *) malloc(sizeof(char)*REGION_SIZE+15); rd = (char *) malloc(sizeof(char)*REGION_SIZE+15); //this still assumes 8 byte aligned pointer from malloc //(which is usual on 32-bit machines) ra += (uint64_t)ra & 0xf; rb += (uint64_t)rb & 0xf; rc += (uint64_t)rc & 0xf; rd += (uint64_t)rd & 0xf; if (w <= 32) { mask = 0; for (i = 0; i < w; i++) mask |= (1 << i); } verbose = (strchr(argv[2], 'V') != NULL); single = (strchr(argv[2], 'S') != NULL || strchr(argv[2], 'A') != NULL); region = (strchr(argv[2], 'R') != NULL || strchr(argv[2], 'A') != NULL); if (!gf_init_hard(&gf_def, w, GF_MULT_DEFAULT, GF_REGION_DEFAULT, GF_DIVIDE_DEFAULT, (h->mult_type != GF_MULT_COMPOSITE) ? h->prim_poly : 0, 0, 0, NULL, NULL)) problem("No default for this value of w"); if (w == 4) { mult4 = gf_w4_get_mult_table(&gf); div4 = gf_w4_get_div_table(&gf); } if (w == 8) { mult8 = gf_w8_get_mult_table(&gf); div8 = gf_w8_get_div_table(&gf); } if (w == 16) { log16 = gf_w16_get_log_table(&gf); alog16 = gf_w16_get_mult_alog_table(&gf); } if (verbose) printf("Seed: %ld\n", t0); if (single) { if (gf.multiply.w32 == NULL) problem("No multiplication operation defined."); if (verbose) { printf("Testing single multiplications/divisions.\n"); fflush(stdout); } if (w <= 10) { top = (1 << w)*(1 << w); } else { top = 1024*1024; } for (i = 0; i < top; i++) { if (w <= 10) { a->w32 = i % (1 << w); b->w32 = (i >> w); //Allen: the following conditions were being run 10 times each. That didn't seem like nearly enough to //me for these special cases, so I converted to doing this mod stuff to easily make the number of times //run both larger and proportional to the total size of the run. } else { switch (i % 32) { case 0: gf_general_set_zero(a, w); gf_general_set_random(b, w, 1); break; case 1: gf_general_set_random(a, w, 1); gf_general_set_zero(b, w); break; case 2: gf_general_set_one(a, w); gf_general_set_random(b, w, 1); break; case 3: gf_general_set_random(a, w, 1); gf_general_set_one(b, w); break; default: gf_general_set_random(a, w, 1); gf_general_set_random(b, w, 1); } } //Allen: the following special cases for w=64 are based on the code below for w=128. //These w=64 cases are based on Dr. Plank's suggestion because some of the methods for w=64 //involve splitting it in two. I think they're less likely to give errors than the 128-bit case //though, because the 128 bit case is always split in two. //As with w=128, I'm arbitrarily deciding to do this sort of thing with a quarter of the cases if (w == 64) { switch (i % 32) { case 0: if (!gf_general_is_one(a, w)) a->w64 &= RMASK; break; case 1: if (!gf_general_is_one(a, w)) a->w64 &= LMASK; break; case 2: if (!gf_general_is_one(a, w)) a->w64 &= RMASK; if (!gf_general_is_one(b, w)) b->w64 &= RMASK; break; case 3: if (!gf_general_is_one(a, w)) a->w64 &= RMASK; if (!gf_general_is_one(b, w)) b->w64 &= LMASK; break; case 4: if (!gf_general_is_one(a, w)) a->w64 &= LMASK; if (!gf_general_is_one(b, w)) b->w64 &= RMASK; break; case 5: if (!gf_general_is_one(a, w)) a->w64 &= LMASK; if (!gf_general_is_one(b, w)) b->w64 &= LMASK; break; case 6: if (!gf_general_is_one(b, w)) b->w64 &= RMASK; break; case 7: if (!gf_general_is_one(b, w)) b->w64 &= LMASK; break; } } //Allen: for w=128, we have important special cases where one half or the other of the number is all //zeros. The probability of hitting such a number randomly is 1^-64, so if we don't force these cases //we'll probably never hit them. This could be implemented more efficiently by changing the set-random //function for w=128, but I think this is easier to follow. //I'm arbitrarily deciding to do this sort of thing with a quarter of the cases if (w == 128) { switch (i % 32) { case 0: if (!gf_general_is_one(a, w)) a->w128[0] = 0; break; case 1: if (!gf_general_is_one(a, w)) a->w128[1] = 0; break; case 2: if (!gf_general_is_one(a, w)) a->w128[0] = 0; if (!gf_general_is_one(b, w)) b->w128[0] = 0; break; case 3: if (!gf_general_is_one(a, w)) a->w128[0] = 0; if (!gf_general_is_one(b, w)) b->w128[1] = 0; break; case 4: if (!gf_general_is_one(a, w)) a->w128[1] = 0; if (!gf_general_is_one(b, w)) b->w128[0] = 0; break; case 5: if (!gf_general_is_one(a, w)) a->w128[1] = 0; if (!gf_general_is_one(b, w)) b->w128[1] = 0; break; case 6: if (!gf_general_is_one(b, w)) b->w128[0] = 0; break; case 7: if (!gf_general_is_one(b, w)) b->w128[1] = 0; break; } } tested = 0; gf_general_multiply(&gf, a, b, c); /* If w is 4, 8 or 16, then there are inline multiplication/division methods. Test them here. */ if (w == 4 && mult4 != NULL) { a8 = a->w32; b8 = b->w32; c8 = GF_W4_INLINE_MULTDIV(mult4, a8, b8); if (c8 != c->w32) { printf("Error in inline multiplication. %d * %d. Inline = %d. Default = %d.\n", a8, b8, c8, c->w32); exit(1); } } if (w == 8 && mult8 != NULL) { a8 = a->w32; b8 = b->w32; c8 = GF_W8_INLINE_MULTDIV(mult8, a8, b8); if (c8 != c->w32) { printf("Error in inline multiplication. %d * %d. Inline = %d. Default = %d.\n", a8, b8, c8, c->w32); exit(1); } } if (w == 16 && log16 != NULL) { a16 = a->w32; b16 = b->w32; c16 = GF_W16_INLINE_MULT(log16, alog16, a16, b16); if (c16 != c->w32) { printf("Error in inline multiplication. %d * %d. Inline = %d. Default = %d.\n", a16, b16, c16, c->w32); printf("%d %d\n", log16[a16], log16[b16]); top = log16[a16] + log16[b16]; printf("%d %d\n", top, alog16[top]); exit(1); } } /* If this is not composite, then first test against the default: */ if (h->mult_type != GF_MULT_COMPOSITE) { tested = 1; gf_general_multiply(&gf_def, a, b, d); if (!gf_general_are_equal(c, d, w)) { gf_general_val_to_s(a, w, as, 1); gf_general_val_to_s(b, w, bs, 1); gf_general_val_to_s(c, w, cs, 1); gf_general_val_to_s(d, w, ds, 1); printf("Error in single multiplication (all numbers in hex):\n\n"); printf(" gf.multiply(gf, %s, %s) = %s\n", as, bs, cs); printf(" The default gf multiplier returned %s\n", ds); exit(1); } } /* Now, we also need to double-check by other means, in case the default is wanky, and when we're performing composite operations. Start with 0 and 1, where we know what the result should be. */ if (gf_general_is_zero(a, w) || gf_general_is_zero(b, w) || gf_general_is_one(a, w) || gf_general_is_one(b, w)) { tested = 1; if (((gf_general_is_zero(a, w) || gf_general_is_zero(b, w)) && !gf_general_is_zero(c, w)) || (gf_general_is_one(a, w) && !gf_general_are_equal(b, c, w)) || (gf_general_is_one(b, w) && !gf_general_are_equal(a, c, w))) { gf_general_val_to_s(a, w, as, 1); gf_general_val_to_s(b, w, bs, 1); gf_general_val_to_s(c, w, cs, 1); printf("Error in single multiplication (all numbers in hex):\n\n"); printf(" gf.multiply(gf, %s, %s) = %s, which is clearly wrong.\n", as, bs, cs); ; exit(1); } } /* Dumb check to make sure that it's not returning numbers that are too big: */ if (w < 32 && (c->w32 & mask) != c->w32) { gf_general_val_to_s(a, w, as, 1); gf_general_val_to_s(b, w, bs, 1); gf_general_val_to_s(c, w, cs, 1); printf("Error in single multiplication (all numbers in hex):\n\n"); printf(" gf.multiply.w32(gf, %s, %s) = %s, which is too big.\n", as, bs, cs); exit(1); } /* Finally, let's check to see that multiplication and division work together */ if (!gf_general_is_zero(a, w)) { gf_general_divide(&gf, c, a, d); if (!gf_general_are_equal(b, d, w)) { gf_general_val_to_s(a, w, as, 1); gf_general_val_to_s(b, w, bs, 1); gf_general_val_to_s(c, w, cs, 1); gf_general_val_to_s(d, w, ds, 1); printf("Error in single multiplication/division (all numbers in hex):\n\n"); printf(" gf.multiply(gf, %s, %s) = %s, but gf.divide(gf, %s, %s) = %s\n", as, bs, cs, cs, as, ds); exit(1); } } }