| 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 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, uint64_t last) |
| 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 take that |
| 162 | * into account. |
| 163 | */ |
| 164 | for (i = 3; i < 64; i++) |
| 165 | if ((1UL << i) > size) |
| 166 | return 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 *lfsr_taps; |
| 238 | |
| 239 | lfsr_taps = find_lfsr(nums); |
| 240 | if (!lfsr_taps) |
| 241 | return 1; |
| 242 | |
| 243 | fl->max_val = nums - 1; |
| 244 | fl->xormask = lfsr_create_xormask(lfsr_taps); |
| 245 | fl->cached_bit = 1UL << (lfsr_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 | } |