/* This is similar to hamming.c but the main program does an exhaustive test, for all 2**32 possible information words, corrupting 0, 1, or 2 bits of either the information bits or the check bits. The number of 39-bit words with 0, 1, or 2 bits set is 39*40/2 + 1 = 781. Hence the inner loop is done 781*2**32 = 3354*10**9 times). Took 24 hours on linux61. */ /* This program generates check bits for a Hamming SEC-DED code with 32 information bits, and simulates error creation, detection, and correction for 0-, 1-, and 2- bit errors. The errors may be in the data or the check bits (or both). Max line length is 57, to fit in hacker.book. */ #include #include // ----------------------------- parity -------------------------------- unsigned int parity(unsigned int x) { x = x ^ (x >> 1); x = x ^ (x >> 2); x = x ^ (x >> 4); x = x ^ (x >> 8); x = x ^ (x >> 16); return x & 1; } // --------------------------- checkbits ------------------------------- unsigned int checkbits(unsigned int u) { /* Computes the six parity check bits for the "information" bits given in the 32-bit word u. The check bits are p[5:0]. On sending, an overall parity bit will be prepended to p (by another process). Bit Checks these bits of u p[0] 0, 1, 3, 5, ..., 31 (0 and the odd positions). p[1] 0, 2-3, 6-7, ..., 30-31 (0 and positions xxx1x). p[2] 0, 4-7, 12-15, 20-23, 28-31 (0 and posns xx1xx). p[3] 0, 8-15, 24-31 (0 and positions x1xxx). p[4] 0, 16-31 (0 and positions 1xxxx). p[5] 1-31 */ unsigned int p0, p1, p2, p3, p4, p5, p6, p; unsigned int t1, t2, t3; // First calculate p[5:0] ignoring u[0]. p0 = u ^ (u >> 2); p0 = p0 ^ (p0 >> 4); p0 = p0 ^ (p0 >> 8); p0 = p0 ^ (p0 >> 16); // p0 is in posn 1. t1 = u ^ (u >> 1); p1 = t1 ^ (t1 >> 4); p1 = p1 ^ (p1 >> 8); p1 = p1 ^ (p1 >> 16); // p1 is in posn 2. t2 = t1 ^ (t1 >> 2); p2 = t2 ^ (t2 >> 8); p2 = p2 ^ (p2 >> 16); // p2 is in posn 4. t3 = t2 ^ (t2 >> 4); p3 = t3 ^ (t3 >> 16); // p3 is in posn 8. p4 = t3 ^ (t3 >> 8); // p4 is in posn 16. p5 = p4 ^ (p4 >> 16); // p5 is in posn 0. p = ((p0>>1) & 1) | ((p1>>1) & 2) | ((p2>>2) & 4) | ((p3>>5) & 8) | ((p4>>12) & 16) | ((p5 & 1) << 5); p = p ^ (-(u & 1) & 0x3F); // Now account for u[0]. return p; } // ---------------------------- perturb -------------------------------- int perturb(unsigned int *p, unsigned int *u) { /* This generates all the possible 39-bit quantities with 0, 1, or 2 bits set, and alters the corresponding 0, 1, or 2 bits of p and u, treating them as a concatenation of p and u (39 bits long). The error bit words are generated in the order (illustrated for a 5-bit quantitity): 00011, 00101, 01001, 10001, 00001, 00110, 01010, 10010, 00010, 01100, 10100, 00100, 11000, 01000, 10000, 00000. */ static unsigned long long mask = (1LL << 39) - 1; static unsigned long long x = 1, y = 2; unsigned long long errorBits; int num; errorBits = x | y; if (errorBits == 0) num = 0; // Set num = number else if (x == 0 || y == 0) num = 1; // of 1-bits in else num = 2; // errorBits. *u = *u ^ (unsigned)errorBits; // Apply the *p = *p ^ (errorBits >> 32); // error bits. if (y != 0) y = (y << 1) & mask; else if (x != 0) {x = (x << 1) & mask; y = (x << 1) & mask;} else {x = 1; y = 2;} // If both = 0, start over. return num; } // ---------------------------- correct -------------------------------- int correct(unsigned int pr, unsigned int *ur) { /* This function looks at the received seven check bits and 32 information bits (pr and ur), and determines how many errors occurred (under the presumption that it must be 0, 1, or 2). It returns with 0, 1, or 2, meaning that no errors, one error, or two errors occurred. It corrects the information word received (ur) if there was one error in it. */ unsigned int po, p, syn, b; po = parity(pr ^ *ur); // Compute overall parity // of the received data. p = checkbits(*ur); // Calculate check bits // for the received info. syn = p ^ (pr & 0x3F); // Syndrome (exclusive of // overall parity bit). if (po == 0) { if (syn == 0) return 0; // If no errors, return 0. else return 2; // Two errors, return 2. } // One error occurred. if (((syn - 1) & syn) == 0) // If syn has zero or one return 1; // bits set, then the // error is in the check // bits or the overall // parity bit (no // correction required). // One error, and syn bits 5:0 tell where it is in ur. b = syn - 31 - (syn >> 5); // Map syn to range 0 to 31. // if (syn == 0x1f) b = 0; // (These two lines equiv. // else b = syn & 0x1f; // to the one line above.) *ur = *ur ^ (1 << b); // Correct the bit. return 1; } // ------------------------------ main --------------------------------- int main(int argc, char *argv[]) { unsigned int us, ur, uc; // Information words, sent, received, // and corrected. unsigned int ps, pr; // Check bits sent and received. int e, c; // Number of errors made and detected. int i; clock_t cloc; time_t start_time; cloc = clock(); start_time = time(NULL); printf("----sent---- --received-- corrected\n"); printf("ps us pr ur e c uc\n"); us = 0xFFFFFFFF; // This loops through all do { // 2**32 values of us us = us + 1; // (information bits sent). ps = checkbits(us); // Compute their 6 check bits ps = ps | (parity(us ^ ps) << 6); // and prepend the overall // parity bit. for (i = 0; i < (39*40)/2 + 1; i++) {// For all 0, 1, or 2-bit errors: /* Corrupt us and/or ps by flipping 0, 1, or 2 bits, producing ur and pr (information and parity, resp., received). */ ur = us; // Set up the received data. pr = ps; e = perturb(&pr, &ur); // Alter 0, 1, or 2 bits of pr and ur, // and set e = number of bits altered. uc = ur; c = correct(pr, &uc); // Correct ur if 1 error occurred. if ((us & 0xFFFFFF) == 0) { printf("%02x %08x %02x %08x ", ps, us, pr, ur); // Program printf("%d %d %08x\n", e, c, uc); // trace. } if (e != c) { printf("Program error, e = %d, c = %d\n", e, c); return 1; } if (e <= 1 && uc != us) { printf("Program error, e = %d, us = %08x, uc = %08x\n", e, us, uc); return 1; } } } while (us < 0xFFFFFFFF); // End of us loop. printf("hamming_exhaustive_012 ended, no errors.\n"); printf("Process time = %4.2f secs\n", (float)(clock() - cloc)/CLOCKS_PER_SEC); printf("Wall clock time = %d secs\n", (int)difftime(time(NULL), start_time)); return 0; }