5 #define EXTRA_BIT_POSITION (PARITY_BITS - 1)
6 #define CODE_BITS (DATA_BITS + PARITY_BITS)
7 #define NUM_DATA_WORDS (1 << DATA_BITS)
9 unsigned char hamming_lookup[NUM_DATA_WORDS];
12 * Needed since we store all the parity at the end of the word, not at the expected
13 * power-of-two bit positions. This is the inverse of the mapping
14 * (0..15) -> (0, 8, 4, 2, 1, the rest in ascending order)
16 unsigned char permutation_table[CODE_BITS] = {
17 0, 4, 3, 5, 2, 6, 7, 8, 1, 9, 10, 11, 12, 13, 14, 15
20 unsigned generate_parity(unsigned data)
22 unsigned bits[DATA_BITS];
23 unsigned parity[PARITY_BITS];
26 parity[EXTRA_BIT_POSITION] = 0;
28 for (i = 0; i < DATA_BITS; ++i) {
29 bits[i] = (data & (1 << i)) ? 1 : 0;
30 parity[EXTRA_BIT_POSITION] ^= bits[i];
33 parity[0] = bits[0] ^ bits[1] ^ bits[3] ^ bits[4] ^ bits[6] ^ bits[8] ^ bits[10];
34 parity[1] = bits[0] ^ bits[2] ^ bits[3] ^ bits[5] ^ bits[6] ^ bits[9] ^ bits[10];
35 parity[2] = bits[1] ^ bits[2] ^ bits[3] ^ bits[7] ^ bits[8] ^ bits[9] ^ bits[10];
36 parity[3] = bits[4] ^ bits[5] ^ bits[6] ^ bits[7] ^ bits[8] ^ bits[9] ^ bits[10];
37 parity[EXTRA_BIT_POSITION] ^= parity[0] ^ parity[1] ^ parity[2] ^ parity[3];
39 return parity[EXTRA_BIT_POSITION] | (parity[3] << 1) | (parity[2] << 2) | (parity[1] << 3) | (parity[0] << 4);
42 unsigned make_codeword(unsigned data)
44 return (data << PARITY_BITS) | hamming_lookup[data];
47 void generate_lookup()
51 printf("Generating lookup table.\n");
53 for (i = 0; i < NUM_DATA_WORDS; ++i) {
54 hamming_lookup[i] = generate_parity(i);
58 /* can detect all single or double bit errors */
59 int has_error(unsigned code)
61 unsigned data = code >> PARITY_BITS;
62 unsigned parity = code & ((1 << PARITY_BITS) - 1);
64 return (hamming_lookup[data] != parity);
67 int has_double_error(unsigned code)
70 unsigned data = code >> PARITY_BITS;
71 unsigned parity = code & ((1 << PARITY_BITS) - 1);
72 unsigned gen_parity = hamming_lookup[data];
74 unsigned hamming_parity = parity >> 1;
75 unsigned gen_hamming_parity = gen_parity >> 1;
76 unsigned extra_parity = 0;
78 /* check the lowest parity bit */
79 for (i = 0; i < CODE_BITS; ++i) {
80 extra_parity ^= (code & 1);
84 /* no errors at all (user should have used has_error() first; boo, hiss) */
85 if (hamming_parity == gen_hamming_parity && extra_parity == 0)
88 /* both hamming and simple parity errors; this is a single-bit error */
89 if (hamming_parity != gen_hamming_parity && extra_parity == 1)
92 /* hamming says OK, but simple parity indicates an error => simple parity error is wrong */
93 if (hamming_parity == gen_hamming_parity && extra_parity == 1)
96 /* hamming says error, simple parity says OK => DOUBLE ERROR */
100 /* Correct any single-bit error -- assumes there are no double-bit errors */
101 unsigned correct_single_bit_error(unsigned code)
103 unsigned bits[CODE_BITS];
104 unsigned parity[PARITY_BITS];
107 parity[EXTRA_BIT_POSITION] = 0;
109 for (i = 0; i < CODE_BITS; ++i) {
110 bits[i] = (code & (1 << i)) ? 1 : 0;
112 for (i = 1; i < CODE_BITS; ++i) {
113 parity[EXTRA_BIT_POSITION] ^= bits[i];
116 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];
117 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];
118 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];
119 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];
121 for (i = 0; i < PARITY_BITS - 1; ++i) {
122 if (parity[i] != bits[PARITY_BITS - 1 - i]) {
128 /* flip the wrong bit */
129 code ^= (1 << permutation_table[bp]);
130 parity[EXTRA_BIT_POSITION] ^= 1;
133 /* recompute the lower parity */
134 return (code & ~1) | parity[EXTRA_BIT_POSITION];
137 void check_zero_bit_detection()
140 printf("Checking zero bit detection.\n");
142 for (i = 0; i < NUM_DATA_WORDS; ++i) {
143 unsigned code = make_codeword(i);
144 if (has_error(code)) {
145 printf("ERROR: Failed zero-bit test 1 for %x\n", i);
147 if (has_double_error(code)) {
148 printf("ERROR: Failed zero-bit test 2 for %x\n", i);
153 void check_single_bit_detection()
156 printf("Checking single bit detection and correction.\n");
158 for (i = 0; i < NUM_DATA_WORDS; ++i) {
159 unsigned code = make_codeword(i);
160 for (j = 0; j < CODE_BITS; ++j) {
161 unsigned corrupted_code = code ^ (1 << j);
163 if (!has_error(corrupted_code)) {
164 printf("ERROR: Failed single-bit test 1 for %x with bit %u flipped\n", i, j);
166 if (has_double_error(corrupted_code)) {
167 printf("ERROR: Failed single-bit test 2 for %x with bit %u flipped\n", i, j);
169 if (correct_single_bit_error(corrupted_code) != code) {
170 printf("ERROR: Failed single-bit correction test for %x with bit %u flipped\n", i, j);
176 void check_double_bit_detection()
179 printf("Checking double bit detection.\n");
181 for (i = 0; i < NUM_DATA_WORDS; ++i) {
182 unsigned code = make_codeword(i);
183 for (j = 0; j < CODE_BITS; ++j) {
184 for (k = 0; k < CODE_BITS; ++k) {
185 unsigned corrupted_code = code ^ (1 << j) ^ (1 << k);
189 if (!has_error(corrupted_code)) {
190 printf("ERROR: Failed double-bit test 1 for %x with bit %u and %u flipped\n", i, j, k);
192 if (!has_double_error(corrupted_code)) {
193 printf("ERROR: Failed double-bit test 2 for %x with bit %u and %u flipped\n", i, j, k);
203 check_zero_bit_detection();
204 check_single_bit_detection();
205 check_double_bit_detection();