1 #include <stdio.h> 2 #include <math.h> 3 4 #include "lfsr.h" 5 #include "../compiler/compiler.h" 6 7 /* 8 * LFSR taps retrieved from: 9 * http://home1.gte.net/res0658s/electronics/LFSRtaps.html 10 * 11 * The memory overhead of the following tap table should be relatively small, 12 * no more than 400 bytes. 13 */ 14 static uint8_t lfsr_taps[64][FIO_MAX_TAPS] = 15 { 16 {0}, {0}, {0}, //LFSRs with less that 3-bits cannot exist 17 {3, 2}, //Tap position for 3-bit LFSR 18 {4, 3}, //Tap position for 4-bit LFSR 19 {5, 3}, //Tap position for 5-bit LFSR 20 {6, 5}, //Tap position for 6-bit LFSR 21 {7, 6}, //Tap position for 7-bit LFSR 22 {8, 6, 5 ,4}, //Tap position for 8-bit LFSR 23 {9, 5}, //Tap position for 9-bit LFSR 24 {10, 7}, //Tap position for 10-bit LFSR 25 {11, 9}, //Tap position for 11-bit LFSR 26 {12, 6, 4, 1}, //Tap position for 12-bit LFSR 27 {13, 4, 3, 1}, //Tap position for 13-bit LFSR 28 {14, 5, 3, 1}, //Tap position for 14-bit LFSR 29 {15, 14}, //Tap position for 15-bit LFSR 30 {16, 15, 13, 4}, //Tap position for 16-bit LFSR 31 {17, 14}, //Tap position for 17-bit LFSR 32 {18, 11}, //Tap position for 18-bit LFSR 33 {19, 6, 2, 1}, //Tap position for 19-bit LFSR 34 {20, 17}, //Tap position for 20-bit LFSR 35 {21, 19}, //Tap position for 21-bit LFSR 36 {22, 21}, //Tap position for 22-bit LFSR 37 {23, 18}, //Tap position for 23-bit LFSR 38 {24, 23, 22, 17}, //Tap position for 24-bit LFSR 39 {25, 22}, //Tap position for 25-bit LFSR 40 {26, 6, 2, 1}, //Tap position for 26-bit LFSR 41 {27, 5, 2, 1}, //Tap position for 27-bit LFSR 42 {28, 25}, //Tap position for 28-bit LFSR 43 {29, 27}, //Tap position for 29-bit LFSR 44 {30, 6, 4, 1}, //Tap position for 30-bit LFSR 45 {31, 28}, //Tap position for 31-bit LFSR 46 {32, 31, 29, 1}, //Tap position for 32-bit LFSR 47 {33, 20}, //Tap position for 33-bit LFSR 48 {34, 27, 2, 1}, //Tap position for 34-bit LFSR 49 {35, 33}, //Tap position for 35-bit LFSR 50 {36, 25}, //Tap position for 36-bit LFSR 51 {37, 5, 4, 3, 2, 1}, //Tap position for 37-bit LFSR 52 {38, 6, 5, 1}, //Tap position for 38-bit LFSR 53 {39, 35}, //Tap position for 39-bit LFSR 54 {40, 38, 21, 19}, //Tap position for 40-bit LFSR 55 {41, 38}, //Tap position for 41-bit LFSR 56 {42, 41, 20, 19}, //Tap position for 42-bit LFSR 57 {43, 42, 38, 37}, //Tap position for 43-bit LFSR 58 {44, 43, 18, 17}, //Tap position for 44-bit LFSR 59 {45, 44, 42, 41}, //Tap position for 45-bit LFSR 60 {46, 45, 26, 25}, //Tap position for 46-bit LFSR 61 {47, 42}, //Tap position for 47-bit LFSR 62 {48, 47, 21, 20}, //Tap position for 48-bit LFSR 63 {49, 40}, //Tap position for 49-bit LFSR 64 {50, 49, 24, 23}, //Tap position for 50-bit LFSR 65 {51, 50, 36, 35}, //Tap position for 51-bit LFSR 66 {52, 49}, //Tap position for 52-bit LFSR 67 {53, 52, 38, 37}, //Tap position for 53-bit LFSR 68 {54, 53, 18, 17}, //Tap position for 54-bit LFSR 69 {55, 31}, //Tap position for 55-bit LFSR 70 {56, 55, 35, 34}, //Tap position for 56-bit LFSR 71 {57, 50}, //Tap position for 57-bit LFSR 72 {58, 39}, //Tap position for 58-bit LFSR 73 {59, 58, 38, 37}, //Tap position for 59-bit LFSR 74 {60, 59}, //Tap position for 60-bit LFSR 75 {61, 60, 46, 45}, //Tap position for 61-bit LFSR 76 {62, 61, 6, 5}, //Tap position for 62-bit LFSR 77 {63, 62}, //Tap position for 63-bit LFSR 78 }; 79 80 #define __LFSR_NEXT(__fl, __v) \ 81 __v = ((__v >> 1) | __fl->cached_bit) ^ \ 82 (((__v & 1UL) - 1UL) & __fl->xormask); 83 84 static inline void __lfsr_next(struct fio_lfsr *fl, unsigned int spin) 85 { 86 /* 87 * This should be O(1) since most compilers will create a jump table for 88 * this switch. 89 */ 90 switch (spin) { 91 case 15: __LFSR_NEXT(fl, fl->last_val); 92 case 14: __LFSR_NEXT(fl, fl->last_val); 93 case 13: __LFSR_NEXT(fl, fl->last_val); 94 case 12: __LFSR_NEXT(fl, fl->last_val); 95 case 11: __LFSR_NEXT(fl, fl->last_val); 96 case 10: __LFSR_NEXT(fl, fl->last_val); 97 case 9: __LFSR_NEXT(fl, fl->last_val); 98 case 8: __LFSR_NEXT(fl, fl->last_val); 99 case 7: __LFSR_NEXT(fl, fl->last_val); 100 case 6: __LFSR_NEXT(fl, fl->last_val); 101 case 5: __LFSR_NEXT(fl, fl->last_val); 102 case 4: __LFSR_NEXT(fl, fl->last_val); 103 case 3: __LFSR_NEXT(fl, fl->last_val); 104 case 2: __LFSR_NEXT(fl, fl->last_val); 105 case 1: __LFSR_NEXT(fl, fl->last_val); 106 case 0: __LFSR_NEXT(fl, fl->last_val); 107 default: break; 108 } 109 } 110 111 /* 112 * lfsr_next does the following: 113 * 114 * a. Return if the number of max values has been exceeded. 115 * b. Check if we have a spin value that produces a repeating subsequence. 116 * This is previously calculated in `prepare_spin` and cycle_length should 117 * be > 0. If we do have such a spin: 118 * 119 * i. Decrement the calculated cycle. 120 * ii. If it reaches zero, add "+1" to the spin and reset the cycle_length 121 * (we have it cached in the struct fio_lfsr) 122 * 123 * In either case, continue with the calculation of the next value. 124 * c. Check if the calculated value exceeds the desirable range. In this case, 125 * go back to b, else return. 126 */ 127 int lfsr_next(struct fio_lfsr *fl, uint64_t *off) 128 { 129 if (fl->num_vals++ > fl->max_val) 130 return 1; 131 132 do { 133 if (fl->cycle_length && !--fl->cycle_length) { 134 __lfsr_next(fl, fl->spin + 1); 135 fl->cycle_length = fl->cached_cycle_length; 136 } else 137 __lfsr_next(fl, fl->spin); 138 } while (fio_unlikely(fl->last_val > fl->max_val)); 139 140 *off = fl->last_val; 141 return 0; 142 } 143 144 static uint64_t lfsr_create_xormask(uint8_t *taps) 145 { 146 int i; 147 uint64_t xormask = 0; 148 149 for(i = 0; i < FIO_MAX_TAPS && taps[i] != 0; i++) 150 xormask |= 1UL << (taps[i] - 1); 151 152 return xormask; 153 } 154 155 static uint8_t *find_lfsr(uint64_t size) 156 { 157 int i; 158 159 /* 160 * For an LFSR, there is always a prohibited state (all ones). 161 * Thus, if we need to find the proper LFSR for our size, we must 162 * take that into account. 163 */ 164 for (i = 3; i < 64; i++) 165 if ((1UL << i) > size) 166 return lfsr_taps[i]; 167 168 return NULL; 169 } 170 171 /* 172 * It is well-known that all maximal n-bit LFSRs will start repeating 173 * themselves after their 2^n iteration. The introduction of spins however, is 174 * possible to create a repetition of a sub-sequence before we hit that mark. 175 * This happens if: 176 * 177 * [1]: ((2^n - 1) * i) % (spin + 1) == 0, 178 * where "n" is LFSR's bits and "i" any number within the range [1,spin] 179 * 180 * It is important to know beforehand if a spin can cause a repetition of a 181 * sub-sequence (cycle) and its length. However, calculating (2^n - 1) * i may 182 * produce a buffer overflow for "n" close to 64, so we expand the above to: 183 * 184 * [2]: (2^n - 1) -> (x * (spin + 1) + y), where x >= 0 and 0 <= y <= spin 185 * 186 * Thus, [1] is equivalent to (y * i) % (spin + 1) == 0; 187 * Also, the cycle's length will be (x * i) + (y * i) / (spin + 1) 188 */ 189 static int prepare_spin(struct fio_lfsr *fl, unsigned int spin) 190 { 191 uint64_t max = (fl->cached_bit << 1) - 1; 192 uint64_t x, y; 193 int i; 194 195 if (spin > 15) 196 return 1; 197 198 x = max / (spin + 1); 199 y = max % (spin + 1); 200 fl->cycle_length = 0; /* No cycle occurs, other than the expected */ 201 fl->spin = spin; 202 203 for (i = 1; i <= spin; i++) { 204 if ((y * i) % (spin + 1) == 0) { 205 fl->cycle_length = (x * i) + (y * i) / (spin + 1); 206 break; 207 } 208 } 209 fl->cached_cycle_length = fl->cycle_length; 210 211 /* 212 * Increment cycle length for the first time only since the stored value 213 * will not be printed otherwise. 214 */ 215 fl->cycle_length++; 216 217 return 0; 218 } 219 220 int lfsr_reset(struct fio_lfsr *fl, unsigned long seed) 221 { 222 uint64_t bitmask = (fl->cached_bit << 1) - 1; 223 224 fl->num_vals = 0; 225 fl->last_val = seed & bitmask; 226 227 /* All-ones state is illegal for XNOR LFSRs */ 228 if (fl->last_val == bitmask) 229 return 1; 230 231 return 0; 232 } 233 234 int lfsr_init(struct fio_lfsr *fl, uint64_t nums, unsigned long seed, 235 unsigned int spin) 236 { 237 uint8_t *taps; 238 239 taps = find_lfsr(nums); 240 if (!taps) 241 return 1; 242 243 fl->max_val = nums - 1; 244 fl->xormask = lfsr_create_xormask(taps); 245 fl->cached_bit = 1UL << (taps[0] - 1); 246 247 if (prepare_spin(fl, spin)) 248 return 1; 249 250 if (lfsr_reset(fl, seed)) 251 return 1; 252 253 return 0; 254 } 255
