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
__lfsr_next(struct fio_lfsr * fl,unsigned int spin)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 */
lfsr_next(struct fio_lfsr * fl,uint64_t * off)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
lfsr_create_xormask(uint8_t * taps)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
find_lfsr(uint64_t size)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 */
prepare_spin(struct fio_lfsr * fl,unsigned int spin)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
lfsr_reset(struct fio_lfsr * fl,unsigned long seed)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
lfsr_init(struct fio_lfsr * fl,uint64_t nums,unsigned long seed,unsigned int spin)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