5 #define CODE_BITS (DATA_BITS + PARITY_BITS)
6 #define NUM_DATA_WORDS (1 << DATA_BITS)
8 unsigned char hamming_lookup[NUM_DATA_WORDS];
11 * Needed since we store all the parity at the end of the word, not at the expected
12 * power-of-two bit positions. This is the inverse of the mapping
13 * (0..15) -> (0, 8, 4, 2, 1, the rest in ascending order)
15 unsigned char permutation_table[CODE_BITS] = {
16 0, 4, 3, 5, 2, 6, 7, 8, 1, 9, 10, 11, 12, 13, 14, 15
19 unsigned generate_parity(unsigned data)
21 unsigned bits[DATA_BITS];
22 unsigned parity[PARITY_BITS];
27 for (i = 0; i < DATA_BITS; ++i) {
28 bits[i] = (data & (1 << i)) ? 1 : 0;
32 parity[0] = bits[0] ^ bits[1] ^ bits[3] ^ bits[4] ^ bits[6] ^ bits[8] ^ bits[10];
33 parity[1] = bits[0] ^ bits[2] ^ bits[3] ^ bits[5] ^ bits[6] ^ bits[9] ^ bits[10];
34 parity[2] = bits[1] ^ bits[2] ^ bits[3] ^ bits[7] ^ bits[8] ^ bits[9] ^ bits[10];
35 parity[3] = bits[4] ^ bits[5] ^ bits[6] ^ bits[7] ^ bits[8] ^ bits[9] ^ bits[10];
36 parity[4] ^= parity[0] ^ parity[1] ^ parity[2] ^ parity[3];
38 return parity[4] | (parity[3] << 1) | (parity[2] << 2) | (parity[1] << 3) | (parity[0] << 4);
41 unsigned make_codeword(unsigned data)
43 return (data << PARITY_BITS) | hamming_lookup[data];
46 void generate_lookup()
50 printf("Generating lookup table.\n");
52 for (i = 0; i < NUM_DATA_WORDS; ++i) {
53 hamming_lookup[i] = generate_parity(i);
57 /* can detect all single or double bit errors */
58 int has_error(unsigned code)
60 unsigned data = code >> PARITY_BITS;
61 unsigned parity = code & ((1 << PARITY_BITS) - 1);
63 return (hamming_lookup[data] != parity);
66 int has_double_error(unsigned code)
69 unsigned data = code >> PARITY_BITS;
70 unsigned parity = code & ((1 << PARITY_BITS) - 1);
71 unsigned gen_parity = hamming_lookup[data];
73 unsigned hamming_parity = parity >> 1;
74 unsigned gen_hamming_parity = gen_parity >> 1;
75 unsigned extra_parity = 0;
77 /* check the lowest parity bit */
78 for (i = 0; i < CODE_BITS; ++i) {
79 extra_parity ^= (code & 1);
83 /* no errors at all (user should have used has_error() first; boo, hiss) */
84 if (hamming_parity == gen_hamming_parity && extra_parity == 0)
87 /* both hamming and simple parity errors; this is a single-bit error */
88 if (hamming_parity != gen_hamming_parity && extra_parity == 1)
91 /* hamming says OK, but simple parity indicates an error => simple parity error is wrong */
92 if (hamming_parity == gen_hamming_parity && extra_parity == 1)
95 /* hamming says error, simple parity says OK => DOUBLE ERROR */
99 /* Correct any single-bit error -- assumes there are no double-bit errors */
100 unsigned correct_single_bit_error(unsigned code)
102 unsigned bits[CODE_BITS];
103 unsigned parity[PARITY_BITS];
108 for (i = 0; i < CODE_BITS; ++i) {
109 bits[i] = (code & (1 << i)) ? 1 : 0;
111 for (i = 1; i < CODE_BITS; ++i) {
112 parity[4] ^= bits[i];
115 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];
116 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];
117 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];
118 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];
120 for (i = 0; i < PARITY_BITS - 1; ++i) {
121 if (parity[i] != bits[PARITY_BITS - 1 - i]) {
127 /* flip the wrong bit */
128 code ^= (1 << permutation_table[bp]);
132 /* recompute the lower parity */
133 return (code & ~1) | parity[4];
136 void check_zero_bit_detection()
139 printf("Checking zero bit detection.\n");
141 for (i = 0; i < NUM_DATA_WORDS; ++i) {
142 unsigned code = make_codeword(i);
143 if (has_error(code)) {
144 printf("ERROR: Failed zero-bit test 1 for %x\n", i);
146 if (has_double_error(code)) {
147 printf("ERROR: Failed zero-bit test 2 for %x\n", i);
152 void check_single_bit_detection()
155 printf("Checking single bit detection and correction.\n");
157 for (i = 0; i < NUM_DATA_WORDS; ++i) {
158 unsigned code = make_codeword(i);
159 for (j = 0; j < CODE_BITS; ++j) {
160 unsigned corrupted_code = code ^ (1 << j);
162 if (!has_error(corrupted_code)) {
163 printf("ERROR: Failed single-bit test 1 for %x with bit %u flipped\n", i, j);
165 if (has_double_error(corrupted_code)) {
166 printf("ERROR: Failed single-bit test 2 for %x with bit %u flipped\n", i, j);
168 if (correct_single_bit_error(corrupted_code) != code) {
169 printf("ERROR: Failed single-bit correction test for %x with bit %u flipped\n", i, j);
175 void check_double_bit_detection()
178 printf("Checking double bit detection.\n");
180 for (i = 0; i < NUM_DATA_WORDS; ++i) {
181 unsigned code = make_codeword(i);
182 for (j = 0; j < CODE_BITS; ++j) {
183 for (k = 0; k < CODE_BITS; ++k) {
184 unsigned corrupted_code = code ^ (1 << j) ^ (1 << k);
188 if (!has_error(corrupted_code)) {
189 printf("ERROR: Failed double-bit test 1 for %x with bit %u and %u flipped\n", i, j, k);
191 if (!has_double_error(corrupted_code)) {
192 printf("ERROR: Failed double-bit test 2 for %x with bit %u and %u flipped\n", i, j, k);
202 check_zero_bit_detection();
203 check_single_bit_detection();
204 check_double_bit_detection();