Tristan Matthews | 0a329cc | 2013-07-17 13:20:14 -0400 | [diff] [blame] | 1 | /* |
| 2 | * lfsr.c |
| 3 | * |
| 4 | */ |
| 5 | |
| 6 | |
| 7 | #include <stdio.h> |
| 8 | #include "datatypes.h" |
| 9 | |
| 10 | uint32_t |
| 11 | parity(uint32_t x) { |
| 12 | |
| 13 | x ^= (x >> 16); |
| 14 | x ^= (x >> 8); |
| 15 | x ^= (x >> 4); |
| 16 | x ^= (x >> 2); |
| 17 | x ^= (x >> 1); |
| 18 | |
| 19 | return x & 1; |
| 20 | } |
| 21 | |
| 22 | |
| 23 | /* typedef struct { */ |
| 24 | /* uint32_t register[8]; */ |
| 25 | /* } lfsr_t; */ |
| 26 | |
| 27 | void |
| 28 | compute_period(uint32_t feedback_polynomial) { |
| 29 | int i; |
| 30 | v32_t lfsr; |
| 31 | v32_t mask; |
| 32 | |
| 33 | mask.value = feedback_polynomial; |
| 34 | lfsr.value = 1; |
| 35 | |
| 36 | printf("polynomial: %s\t", v32_bit_string(mask)); |
| 37 | |
| 38 | for (i=0; i < 256; i++) { |
| 39 | /* printf("%s\n", v32_bit_string(lfsr)); */ |
| 40 | if (parity(mask.value & lfsr.value)) |
| 41 | lfsr.value = ((lfsr.value << 1) | 1) & 0xff; |
| 42 | else |
| 43 | lfsr.value = (lfsr.value << 1) & 0xff; |
| 44 | |
| 45 | /* now halt if we're back at the initial state */ |
| 46 | if (lfsr.value == 1) { |
| 47 | printf("period: %d\n", i); |
| 48 | break; |
| 49 | } |
| 50 | } |
| 51 | } |
| 52 | |
| 53 | uint32_t poly0 = 223; |
| 54 | |
| 55 | |
| 56 | uint32_t polynomials[39] = { |
| 57 | 31, |
| 58 | 47, |
| 59 | 55, |
| 60 | 59, |
| 61 | 61, |
| 62 | 79, |
| 63 | 87, |
| 64 | 91, |
| 65 | 103, |
| 66 | 107, |
| 67 | 109, |
| 68 | 115, |
| 69 | 117, |
| 70 | 121, |
| 71 | 143, |
| 72 | 151, |
| 73 | 157, |
| 74 | 167, |
| 75 | 171, |
| 76 | 173, |
| 77 | 179, |
| 78 | 181, |
| 79 | 185, |
| 80 | 199, |
| 81 | 203, |
| 82 | 205, |
| 83 | 211, |
| 84 | 213, |
| 85 | 227, |
| 86 | 229, |
| 87 | 233, |
| 88 | 241, |
| 89 | 127, |
| 90 | 191, |
| 91 | 223, |
| 92 | 239, |
| 93 | 247, |
| 94 | 251, |
| 95 | 253 |
| 96 | }; |
| 97 | |
| 98 | char binary_string[32]; |
| 99 | |
| 100 | char * |
| 101 | u32_bit_string(uint32_t x, unsigned int length) { |
| 102 | unsigned int mask; |
| 103 | int index; |
| 104 | |
| 105 | mask = 1 << length; |
| 106 | index = 0; |
| 107 | for (; mask > 0; mask >>= 1) |
| 108 | if ((x & mask) == 0) |
| 109 | binary_string[index++] = '0'; |
| 110 | else |
| 111 | binary_string[index++] = '1'; |
| 112 | |
| 113 | binary_string[index++] = 0; /* NULL terminate string */ |
| 114 | return binary_string; |
| 115 | } |
| 116 | |
| 117 | extern int octet_weight[256]; |
| 118 | |
| 119 | unsigned int |
| 120 | weight(uint32_t poly) { |
| 121 | int wt = 0; |
| 122 | |
| 123 | /* note: endian-ness makes no difference */ |
| 124 | wt += octet_weight[poly & 0xff]; |
| 125 | wt += octet_weight[(poly >> 8) & 0xff]; |
| 126 | wt += octet_weight[(poly >> 16) & 0xff]; |
| 127 | wt += octet_weight[(poly >> 24)]; |
| 128 | |
| 129 | return wt; |
| 130 | } |
| 131 | |
| 132 | #define MAX_PERIOD 65535 |
| 133 | |
| 134 | #define debug_print 0 |
| 135 | |
| 136 | int |
| 137 | period(uint32_t poly) { |
| 138 | int i; |
| 139 | uint32_t x; |
| 140 | |
| 141 | |
| 142 | /* set lfsr to 1 */ |
| 143 | x = 1; |
| 144 | #if debug_print |
| 145 | printf("%d:\t%s\n", 0, u32_bit_string(x,8)); |
| 146 | #endif |
| 147 | for (i=1; i < MAX_PERIOD; i++) { |
| 148 | if (x & 1) |
| 149 | x = (x >> 1) ^ poly; |
| 150 | else |
| 151 | x = (x >> 1); |
| 152 | |
| 153 | #if debug_print |
| 154 | /* print for a sanity check */ |
| 155 | printf("%d:\t%s\n", i, u32_bit_string(x,8)); |
| 156 | #endif |
| 157 | |
| 158 | /* check for return to original value */ |
| 159 | if (x == 1) |
| 160 | return i; |
| 161 | } |
| 162 | return i; |
| 163 | } |
| 164 | |
| 165 | /* |
| 166 | * weight distribution computes the weight distribution of the |
| 167 | * code generated by the polynomial poly |
| 168 | */ |
| 169 | |
| 170 | #define MAX_LEN 8 |
| 171 | #define MAX_WEIGHT (1 << MAX_LEN) |
| 172 | |
| 173 | int A[MAX_WEIGHT+1]; |
| 174 | |
| 175 | void |
| 176 | weight_distribution2(uint32_t poly, int *A) { |
| 177 | int i; |
| 178 | uint32_t x; |
| 179 | |
| 180 | /* zeroize array */ |
| 181 | for (i=0; i < MAX_WEIGHT+1; i++) |
| 182 | A[i] = 0; |
| 183 | |
| 184 | /* loop over all input sequences */ |
| 185 | |
| 186 | |
| 187 | /* set lfsr to 1 */ |
| 188 | x = 1; |
| 189 | #if debug_print |
| 190 | printf("%d:\t%s\n", 0, u32_bit_string(x,8)); |
| 191 | #endif |
| 192 | for (i=1; i < MAX_PERIOD; i++) { |
| 193 | if (x & 1) |
| 194 | x = (x >> 1) ^ poly; |
| 195 | else |
| 196 | x = (x >> 1); |
| 197 | |
| 198 | #if debug_print |
| 199 | /* print for a sanity check */ |
| 200 | printf("%d:\t%s\n", i, u32_bit_string(x,8)); |
| 201 | #endif |
| 202 | |
| 203 | /* increment weight */ |
| 204 | wt += (x & 1); |
| 205 | |
| 206 | /* check for return to original value */ |
| 207 | if (x == 1) |
| 208 | break; |
| 209 | } |
| 210 | |
| 211 | /* set zero */ |
| 212 | A[0] = 0; |
| 213 | } |
| 214 | |
| 215 | |
| 216 | void |
| 217 | weight_distribution(uint32_t poly, int *A) { |
| 218 | int i; |
| 219 | uint32_t x; |
| 220 | |
| 221 | /* zeroize array */ |
| 222 | for (i=0; i < MAX_WEIGHT+1; i++) |
| 223 | A[i] = 0; |
| 224 | |
| 225 | /* set lfsr to 1 */ |
| 226 | x = 1; |
| 227 | #if debug_print |
| 228 | printf("%d:\t%s\n", 0, u32_bit_string(x,8)); |
| 229 | #endif |
| 230 | for (i=1; i < MAX_PERIOD; i++) { |
| 231 | if (x & 1) |
| 232 | x = (x >> 1) ^ poly; |
| 233 | else |
| 234 | x = (x >> 1); |
| 235 | |
| 236 | #if debug_print |
| 237 | /* print for a sanity check */ |
| 238 | printf("%d:\t%s\n", i, u32_bit_string(x,8)); |
| 239 | #endif |
| 240 | |
| 241 | /* compute weight, increment proper element */ |
| 242 | A[weight(x)]++; |
| 243 | |
| 244 | /* check for return to original value */ |
| 245 | if (x == 1) |
| 246 | break; |
| 247 | } |
| 248 | |
| 249 | /* set zero */ |
| 250 | A[0] = 0; |
| 251 | } |
| 252 | |
| 253 | |
| 254 | |
| 255 | |
| 256 | int |
| 257 | main () { |
| 258 | |
| 259 | int i,j; |
| 260 | v32_t x; |
| 261 | v32_t p; |
| 262 | |
| 263 | /* originally 0xaf */ |
| 264 | p.value = 0x9; |
| 265 | |
| 266 | printf("polynomial: %s\tperiod: %d\n", |
| 267 | u32_bit_string(p.value,8), period(p.value)); |
| 268 | |
| 269 | /* compute weight distribution */ |
| 270 | weight_distribution(p.value, A); |
| 271 | |
| 272 | /* print weight distribution */ |
| 273 | for (i=0; i <= 8; i++) { |
| 274 | printf("A[%d]: %d\n", i, A[i]); |
| 275 | } |
| 276 | |
| 277 | #if 0 |
| 278 | for (i=0; i < 39; i++) { |
| 279 | printf("polynomial: %s\tperiod: %d\n", |
| 280 | u32_bit_string(polynomials[i],8), period(polynomials[i])); |
| 281 | |
| 282 | /* compute weight distribution */ |
| 283 | weight_distribution(p.value, A); |
| 284 | |
| 285 | /* print weight distribution */ |
| 286 | for (j=0; j <= 8; j++) { |
| 287 | printf("A[%d]: %d\n", j, A[j]); |
| 288 | } |
| 289 | } |
| 290 | #endif |
| 291 | |
| 292 | { |
| 293 | int bits = 8; |
| 294 | uint32_t y; |
| 295 | for (y=0; y < (1 << bits); y++) { |
| 296 | printf("polynomial: %s\tweight: %d\tperiod: %d\n", |
| 297 | u32_bit_string(y,bits), weight(y), period(y)); |
| 298 | |
| 299 | /* compute weight distribution */ |
| 300 | weight_distribution(y, A); |
| 301 | |
| 302 | /* print weight distribution */ |
| 303 | for (j=0; j <= 8; j++) { |
| 304 | printf("A[%d]: %d\n", j, A[j]); |
| 305 | } |
| 306 | } |
| 307 | } |
| 308 | |
| 309 | return 0; |
| 310 | } |