1 #include <stdio.h>
2
3 #include "lfsr.h"
4 #include "../compiler/compiler.h"
5
6 /*
7 * LFSR taps retrieved from:
8 * http://home1.gte.net/res0658s/electronics/LFSRtaps.html
9 *
10 * The memory overhead of the following tap table should be relatively small,
11 * no more than 400 bytes.
12 */
13 static uint8_t lfsr_taps[64][FIO_MAX_TAPS] =
14 {
15 {0}, {0}, {0}, //LFSRs with less that 3-bits cannot exist
16 {3, 2}, //Tap position for 3-bit LFSR
17 {4, 3}, //Tap position for 4-bit LFSR
18 {5, 3}, //Tap position for 5-bit LFSR
19 {6, 5}, //Tap position for 6-bit LFSR
20 {7, 6}, //Tap position for 7-bit LFSR
21 {8, 6, 5 ,4}, //Tap position for 8-bit LFSR
22 {9, 5}, //Tap position for 9-bit LFSR
23 {10, 7}, //Tap position for 10-bit LFSR
24 {11, 9}, //Tap position for 11-bit LFSR
25 {12, 6, 4, 1}, //Tap position for 12-bit LFSR
26 {13, 4, 3, 1}, //Tap position for 13-bit LFSR
27 {14, 5, 3, 1}, //Tap position for 14-bit LFSR
28 {15, 14}, //Tap position for 15-bit LFSR
29 {16, 15, 13, 4}, //Tap position for 16-bit LFSR
30 {17, 14}, //Tap position for 17-bit LFSR
31 {18, 11}, //Tap position for 18-bit LFSR
32 {19, 6, 2, 1}, //Tap position for 19-bit LFSR
33 {20, 17}, //Tap position for 20-bit LFSR
34 {21, 19}, //Tap position for 21-bit LFSR
35 {22, 21}, //Tap position for 22-bit LFSR
36 {23, 18}, //Tap position for 23-bit LFSR
37 {24, 23, 22, 17}, //Tap position for 24-bit LFSR
38 {25, 22}, //Tap position for 25-bit LFSR
39 {26, 6, 2, 1}, //Tap position for 26-bit LFSR
40 {27, 5, 2, 1}, //Tap position for 27-bit LFSR
41 {28, 25}, //Tap position for 28-bit LFSR
42 {29, 27}, //Tap position for 29-bit LFSR
43 {30, 6, 4, 1}, //Tap position for 30-bit LFSR
44 {31, 28}, //Tap position for 31-bit LFSR
45 {32, 31, 29, 1}, //Tap position for 32-bit LFSR
46 {33, 20}, //Tap position for 33-bit LFSR
47 {34, 27, 2, 1}, //Tap position for 34-bit LFSR
48 {35, 33}, //Tap position for 35-bit LFSR
49 {36, 25}, //Tap position for 36-bit LFSR
50 {37, 5, 4, 3, 2, 1}, //Tap position for 37-bit LFSR
51 {38, 6, 5, 1}, //Tap position for 38-bit LFSR
52 {39, 35}, //Tap position for 39-bit LFSR
53 {40, 38, 21, 19}, //Tap position for 40-bit LFSR
54 {41, 38}, //Tap position for 41-bit LFSR
55 {42, 41, 20, 19}, //Tap position for 42-bit LFSR
56 {43, 42, 38, 37}, //Tap position for 43-bit LFSR
57 {44, 43, 18, 17}, //Tap position for 44-bit LFSR
58 {45, 44, 42, 41}, //Tap position for 45-bit LFSR
59 {46, 45, 26, 25}, //Tap position for 46-bit LFSR
60 {47, 42}, //Tap position for 47-bit LFSR
61 {48, 47, 21, 20}, //Tap position for 48-bit LFSR
62 {49, 40}, //Tap position for 49-bit LFSR
63 {50, 49, 24, 23}, //Tap position for 50-bit LFSR
64 {51, 50, 36, 35}, //Tap position for 51-bit LFSR
65 {52, 49}, //Tap position for 52-bit LFSR
66 {53, 52, 38, 37}, //Tap position for 53-bit LFSR
67 {54, 53, 18, 17}, //Tap position for 54-bit LFSR
68 {55, 31}, //Tap position for 55-bit LFSR
69 {56, 55, 35, 34}, //Tap position for 56-bit LFSR
70 {57, 50}, //Tap position for 57-bit LFSR
71 {58, 39}, //Tap position for 58-bit LFSR
72 {59, 58, 38, 37}, //Tap position for 59-bit LFSR
73 {60, 59}, //Tap position for 60-bit LFSR
74 {61, 60, 46, 45}, //Tap position for 61-bit LFSR
75 {62, 61, 6, 5}, //Tap position for 62-bit LFSR
76 {63, 62}, //Tap position for 63-bit LFSR
77 };
78
79 #define __LFSR_NEXT(__fl, __v) \
80 __v = ((__v >> 1) | __fl->cached_bit) ^ \
81 (((__v & 1ULL) - 1ULL) & __fl->xormask);
82
__lfsr_next(struct fio_lfsr * fl,unsigned int spin)83 static inline void __lfsr_next(struct fio_lfsr *fl, unsigned int spin)
84 {
85 /*
86 * This should be O(1) since most compilers will create a jump table for
87 * this switch.
88 */
89 switch (spin) {
90 case 15: __LFSR_NEXT(fl, fl->last_val);
91 fallthrough;
92 case 14: __LFSR_NEXT(fl, fl->last_val);
93 fallthrough;
94 case 13: __LFSR_NEXT(fl, fl->last_val);
95 fallthrough;
96 case 12: __LFSR_NEXT(fl, fl->last_val);
97 fallthrough;
98 case 11: __LFSR_NEXT(fl, fl->last_val);
99 fallthrough;
100 case 10: __LFSR_NEXT(fl, fl->last_val);
101 fallthrough;
102 case 9: __LFSR_NEXT(fl, fl->last_val);
103 fallthrough;
104 case 8: __LFSR_NEXT(fl, fl->last_val);
105 fallthrough;
106 case 7: __LFSR_NEXT(fl, fl->last_val);
107 fallthrough;
108 case 6: __LFSR_NEXT(fl, fl->last_val);
109 fallthrough;
110 case 5: __LFSR_NEXT(fl, fl->last_val);
111 fallthrough;
112 case 4: __LFSR_NEXT(fl, fl->last_val);
113 fallthrough;
114 case 3: __LFSR_NEXT(fl, fl->last_val);
115 fallthrough;
116 case 2: __LFSR_NEXT(fl, fl->last_val);
117 fallthrough;
118 case 1: __LFSR_NEXT(fl, fl->last_val);
119 fallthrough;
120 case 0: __LFSR_NEXT(fl, fl->last_val);
121 fallthrough;
122 default: break;
123 }
124 }
125
126 /*
127 * lfsr_next does the following:
128 *
129 * a. Return if the number of max values has been exceeded.
130 * b. Check if we have a spin value that produces a repeating subsequence.
131 * This is previously calculated in `prepare_spin` and cycle_length should
132 * be > 0. If we do have such a spin:
133 *
134 * i. Decrement the calculated cycle.
135 * ii. If it reaches zero, add "+1" to the spin and reset the cycle_length
136 * (we have it cached in the struct fio_lfsr)
137 *
138 * In either case, continue with the calculation of the next value.
139 * c. Check if the calculated value exceeds the desirable range. In this case,
140 * go back to b, else return.
141 */
lfsr_next(struct fio_lfsr * fl,uint64_t * off)142 int lfsr_next(struct fio_lfsr *fl, uint64_t *off)
143 {
144 if (fl->num_vals++ > fl->max_val)
145 return 1;
146
147 do {
148 if (fl->cycle_length && !--fl->cycle_length) {
149 __lfsr_next(fl, fl->spin + 1);
150 fl->cycle_length = fl->cached_cycle_length;
151 } else
152 __lfsr_next(fl, fl->spin);
153 } while (fio_unlikely(fl->last_val > fl->max_val));
154
155 *off = fl->last_val;
156 return 0;
157 }
158
lfsr_create_xormask(uint8_t * taps)159 static uint64_t lfsr_create_xormask(uint8_t *taps)
160 {
161 int i;
162 uint64_t xormask = 0;
163
164 for(i = 0; i < FIO_MAX_TAPS && taps[i] != 0; i++)
165 xormask |= 1ULL << (taps[i] - 1);
166
167 return xormask;
168 }
169
find_lfsr(uint64_t size)170 static uint8_t *find_lfsr(uint64_t size)
171 {
172 int i;
173
174 /*
175 * For an LFSR, there is always a prohibited state (all ones).
176 * Thus, if we need to find the proper LFSR for our size, we must
177 * take that into account.
178 */
179 for (i = 3; i < 64; i++)
180 if ((1ULL << i) > size)
181 return lfsr_taps[i];
182
183 return NULL;
184 }
185
186 /*
187 * It is well-known that all maximal n-bit LFSRs will start repeating
188 * themselves after their 2^n iteration. The introduction of spins however, is
189 * possible to create a repetition of a sub-sequence before we hit that mark.
190 * This happens if:
191 *
192 * [1]: ((2^n - 1) * i) % (spin + 1) == 0,
193 * where "n" is LFSR's bits and "i" any number within the range [1,spin]
194 *
195 * It is important to know beforehand if a spin can cause a repetition of a
196 * sub-sequence (cycle) and its length. However, calculating (2^n - 1) * i may
197 * produce a buffer overflow for "n" close to 64, so we expand the above to:
198 *
199 * [2]: (2^n - 1) -> (x * (spin + 1) + y), where x >= 0 and 0 <= y <= spin
200 *
201 * Thus, [1] is equivalent to (y * i) % (spin + 1) == 0;
202 * Also, the cycle's length will be (x * i) + (y * i) / (spin + 1)
203 */
prepare_spin(struct fio_lfsr * fl,unsigned int spin)204 static int prepare_spin(struct fio_lfsr *fl, unsigned int spin)
205 {
206 uint64_t max = (fl->cached_bit << 1) - 1;
207 uint64_t x, y;
208 int i;
209
210 if (spin > 15)
211 return 1;
212
213 x = max / (spin + 1);
214 y = max % (spin + 1);
215 fl->cycle_length = 0; /* No cycle occurs, other than the expected */
216 fl->spin = spin;
217
218 for (i = 1; i <= spin; i++) {
219 if ((y * i) % (spin + 1) == 0) {
220 fl->cycle_length = (x * i) + (y * i) / (spin + 1);
221 break;
222 }
223 }
224 fl->cached_cycle_length = fl->cycle_length;
225
226 /*
227 * Increment cycle length for the first time only since the stored value
228 * will not be printed otherwise.
229 */
230 fl->cycle_length++;
231
232 return 0;
233 }
234
lfsr_reset(struct fio_lfsr * fl,uint64_t seed)235 int lfsr_reset(struct fio_lfsr *fl, uint64_t seed)
236 {
237 uint64_t bitmask = (fl->cached_bit << 1) - 1;
238
239 fl->num_vals = 0;
240 fl->last_val = seed & bitmask;
241
242 /* All-ones state is illegal for XNOR LFSRs */
243 if (fl->last_val == bitmask)
244 return 1;
245
246 return 0;
247 }
248
lfsr_init(struct fio_lfsr * fl,uint64_t nums,uint64_t seed,unsigned int spin)249 int lfsr_init(struct fio_lfsr *fl, uint64_t nums, uint64_t seed,
250 unsigned int spin)
251 {
252 uint8_t *taps;
253
254 taps = find_lfsr(nums);
255 if (!taps)
256 return 1;
257
258 fl->max_val = nums - 1;
259 fl->xormask = lfsr_create_xormask(taps);
260 fl->cached_bit = 1ULL << (taps[0] - 1);
261
262 if (prepare_spin(fl, spin))
263 return 1;
264
265 if (lfsr_reset(fl, seed))
266 return 1;
267
268 return 0;
269 }
270