git.sesse.net Git - hamming/blob - hamming.c

   1 #include <stdio.h>
   2
   3 #define DATA_BITS    11
   4 #define PARITY_BITS  5
   5 #define CODE_BITS    (DATA_BITS + PARITY_BITS)
   6 #define NUM_DATA_WORDS (1 << DATA_BITS)
   7
   8 unsigned char hamming_lookup[NUM_DATA_WORDS];
   9
  10 /*
  11  * Needed since we store all the parity at the end of the word, not at the expected
  12  * power-of-two bit positions.
  13  */
  14 unsigned char permutation_table[CODE_BITS] = {
  15         0, 4, 3, 5, 2, 6, 7, 8, 1, 9, 10, 11, 12, 13, 14, 15
  16 };
  17
  18 unsigned generate_parity(unsigned data)
  19 {
  20         unsigned bits[DATA_BITS];
  21         unsigned parity[PARITY_BITS];
  22         unsigned i;
  23
  24         parity[4] = 0;
  25
  26         for (i = 0; i < DATA_BITS; ++i) {
  27                 bits[i] = (data & (1 << i)) ? 1 : 0;
  28                 parity[4] ^= bits[i];
  29         }
  30
  31         parity[0] = bits[0] ^ bits[1] ^ bits[3] ^ bits[4] ^ bits[6] ^ bits[8] ^ bits[10];
  32         parity[1] = bits[0] ^ bits[2] ^ bits[3] ^ bits[5] ^ bits[6] ^ bits[9] ^ bits[10];
  33         parity[2] = bits[1] ^ bits[2] ^ bits[3] ^ bits[7] ^ bits[8] ^ bits[9] ^ bits[10];
  34         parity[3] = bits[4] ^ bits[5] ^ bits[6] ^ bits[7] ^ bits[8] ^ bits[9] ^ bits[10];
  35         parity[4] ^= parity[0] ^ parity[1] ^ parity[2] ^ parity[3];
  36
  37         return parity[4] | (parity[3] << 1) | (parity[2] << 2) | (parity[1] << 3) | (parity[0] << 4);
  38 }
  39
  40 unsigned make_codeword(unsigned data)
  41 {
  42         return (data << PARITY_BITS) | hamming_lookup[data];
  43 }
  44
  45 void generate_lookup()
  46 {
  47         unsigned i;
  48
  49         printf("Generating lookup table.\n");
  50
  51         for (i = 0; i < NUM_DATA_WORDS; ++i) {
  52                 hamming_lookup[i] = generate_parity(i);
  53         }
  54 }
  55
  56 /* can detect all single or double bit errors */
  57 int has_error(unsigned code)
  58 {
  59         unsigned data = code >> PARITY_BITS;
  60         unsigned parity = code & ((1 << PARITY_BITS) - 1);
  61
  62         return (hamming_lookup[data] != parity);
  63 }
  64
  65 int has_double_error(unsigned code)
  66 {
  67         unsigned i;
  68         unsigned data = code >> PARITY_BITS;
  69         unsigned parity = code & ((1 << PARITY_BITS) - 1);
  70         unsigned gen_parity = hamming_lookup[data];
  71
  72         unsigned hamming_parity = parity >> 1;
  73         unsigned gen_hamming_parity = gen_parity >> 1;
  74         unsigned extra_parity = 0;
  75
  76         /* check the lowest parity bit */
  77         for (i = 0; i < CODE_BITS; ++i) {
  78                 extra_parity ^= (code & 1);
  79                 code >>= 1;
  80         }
  81
  82         /* no errors at all (user should have used has_error() first; boo, hiss) */
  83         if (hamming_parity == gen_hamming_parity && extra_parity == 0)
  84                 return 0;
  85
  86         /* both hamming and simple parity errors; this is a single-bit error */
  87         if (hamming_parity != gen_hamming_parity && extra_parity == 1)
  88                 return 0;
  89
  90         /* hamming says OK, but simple parity indicates an error => simple parity error is wrong */
  91         if (hamming_parity == gen_hamming_parity && extra_parity == 1)
  92                 return 0;
  93
  94         /* hamming says error, simple parity says OK => DOUBLE ERROR */
  95         return 1;
  96 }
  97
  98 /* Correct any single-bit error -- assumes there are no double-bit errors */
  99 unsigned correct_single_bit_error(unsigned code)
 100 {
 101         unsigned bits[CODE_BITS];
 102         unsigned parity[PARITY_BITS];
 103         unsigned i, bp = 0;
 104
 105         parity[4] = 0;
 106
 107         for (i = 0; i < CODE_BITS; ++i) {
 108                 bits[i] = (code & (1 << i)) ? 1 : 0;
 109         }
 110         for (i = 1; i < CODE_BITS; ++i) {
 111                 parity[4] ^= bits[i];
 112         }
 113
 114         parity[0] = bits[PARITY_BITS+0] ^ bits[PARITY_BITS+1] ^ bits[PARITY_BITS+3] ^ bits[PARITY_BITS+4] ^ bits[PARITY_BITS+6] ^ bits[PARITY_BITS+8] ^ bits[PARITY_BITS+10];
 115         parity[1] = bits[PARITY_BITS+0] ^ bits[PARITY_BITS+2] ^ bits[PARITY_BITS+3] ^ bits[PARITY_BITS+5] ^ bits[PARITY_BITS+6] ^ bits[PARITY_BITS+9] ^ bits[PARITY_BITS+10];
 116         parity[2] = bits[PARITY_BITS+1] ^ bits[PARITY_BITS+2] ^ bits[PARITY_BITS+3] ^ bits[PARITY_BITS+7] ^ bits[PARITY_BITS+8] ^ bits[PARITY_BITS+9] ^ bits[PARITY_BITS+10];
 117         parity[3] = bits[PARITY_BITS+4] ^ bits[PARITY_BITS+5] ^ bits[PARITY_BITS+6] ^ bits[PARITY_BITS+7] ^ bits[PARITY_BITS+8] ^ bits[PARITY_BITS+9] ^ bits[PARITY_BITS+10];
 118
 119         for (i = 0; i < PARITY_BITS - 1; ++i) {
 120                 if (parity[i] != bits[PARITY_BITS - 1 - i]) {
 121                         bp |= (1 << i);
 122                 }
 123         }
 124
 125         if (bp != 0) {
 126                 /* flip the wrong bit */
 127                 code ^= (1 << permutation_table[bp]);
 128                 parity[4] ^= 1;
 129         }
 130
 131         /* recompute the lower parity */
 132         return (code & ~1) | parity[4];
 133 }
 134
 135 void check_zero_bit_detection()
 136 {
 137         unsigned i;
 138         printf("Checking zero bit detection.\n");
 139
 140         for (i = 0; i < NUM_DATA_WORDS; ++i) {
 141                 unsigned code = make_codeword(i);
 142                 if (has_error(code)) {
 143                         printf("ERROR: Failed zero-bit test 1 for %x\n", i);
 144                 }
 145                 if (has_double_error(code)) {
 146                         printf("ERROR: Failed zero-bit test 2 for %x\n", i);
 147                 }
 148         }
 149 }
 150
 151 void check_single_bit_detection()
 152 {
 153         unsigned i, j;
 154         printf("Checking single bit detection and correction.\n");
 155
 156         for (i = 0; i < NUM_DATA_WORDS; ++i) {
 157                 unsigned code = make_codeword(i);
 158                 for (j = 0; j < CODE_BITS; ++j) {
 159                         unsigned corrupted_code = code ^ (1 << j);
 160
 161                         if (!has_error(corrupted_code)) {
 162                                 printf("ERROR: Failed single-bit test 1 for %x with bit %u flipped\n", i, j);
 163                         }
 164                         if (has_double_error(corrupted_code)) {
 165                                 printf("ERROR: Failed single-bit test 2 for %x with bit %u flipped\n", i, j);
 166                         }
 167                         if (correct_single_bit_error(corrupted_code) != code) {
 168                                 printf("ERROR: Failed single-bit correction test for %x with bit %u flipped\n", i, j);
 169                         }
 170                 }
 171         }
 172 }
 173
 174 void check_double_bit_detection()
 175 {
 176         unsigned i, j, k;
 177         printf("Checking double bit detection.\n");
 178
 179         for (i = 0; i < NUM_DATA_WORDS; ++i) {
 180                 unsigned code = make_codeword(i);
 181                 for (j = 0; j < CODE_BITS; ++j) {
 182                         for (k = 0; k < CODE_BITS; ++k) {
 183                                 unsigned corrupted_code = code ^ (1 << j) ^ (1 << k);
 184                                 if (j == k)
 185                                         continue;
 186
 187                                 if (!has_error(corrupted_code)) {
 188                                         printf("ERROR: Failed double-bit test 1 for %x with bit %u and %u flipped\n", i, j, k);
 189                                 }
 190                                 if (!has_double_error(corrupted_code)) {
 191                                         printf("ERROR: Failed double-bit test 2 for %x with bit %u and %u flipped\n", i, j, k);
 192                                 }
 193                         }
 194                 }
 195         }
 196 }
 197
 198 int main()
 199 {
 200         generate_lookup();
 201         check_zero_bit_detection();
 202         check_single_bit_detection();
 203         check_double_bit_detection();
 204
 205         return 0;
 206 }