2 This is a maximally equidistributed combined Tausworthe generator
3 based on code from GNU Scientific Library 1.5 (30 Jun 2004)
5 x_n = (s1_n ^ s2_n ^ s3_n)
7 s1_{n+1} = (((s1_n & 4294967294) <<12) ^ (((s1_n <<13) ^ s1_n) >>19))
8 s2_{n+1} = (((s2_n & 4294967288) << 4) ^ (((s2_n << 2) ^ s2_n) >>25))
9 s3_{n+1} = (((s3_n & 4294967280) <<17) ^ (((s3_n << 3) ^ s3_n) >>11))
11 The period of this generator is about 2^88.
13 From: P. L'Ecuyer, "Maximally Equidistributed Combined Tausworthe
14 Generators", Mathematics of Computation, 65, 213 (1996), 203--213.
16 This is available on the net from L'Ecuyer's home page,
18 http://www.iro.umontreal.ca/~lecuyer/myftp/papers/tausme.ps
19 ftp://ftp.iro.umontreal.ca/pub/simulation/lecuyer/papers/tausme.ps
21 There is an erratum in the paper "Tables of Maximally
22 Equidistributed Combined LFSR Generators", Mathematics of
23 Computation, 68, 225 (1999), 261--269:
24 http://www.iro.umontreal.ca/~lecuyer/myftp/papers/tausme2.ps
26 ... the k_j most significant bits of z_j must be non-
27 zero, for each j. (Note: this restriction also applies to the
28 computer code given in [4], but was mistakenly not mentioned in
31 This affects the seeding procedure by imposing the requirement
32 s1 > 1, s2 > 7, s3 > 15.
43 static inline uint64_t __seed(uint64_t x, uint64_t m)
45 return (x < m) ? x + m : x;
48 static void __init_rand32(struct taus88_state *state, unsigned int seed)
52 #define LCG(x, seed) ((x) * 69069 ^ (seed))
54 state->s1 = __seed(LCG((2^31) + (2^17) + (2^7), seed), 1);
55 state->s2 = __seed(LCG(state->s1, seed), 7);
56 state->s3 = __seed(LCG(state->s2, seed), 15);
62 void __init_rand64(struct taus258_state *state, uint64_t seed)
66 #define LCG64(x, seed) ((x) * 6906969069ULL ^ (seed))
68 state->s1 = __seed(LCG64((2^31) + (2^17) + (2^7), seed), 1);
69 state->s2 = __seed(LCG64(state->s1, seed), 7);
70 state->s3 = __seed(LCG64(state->s2, seed), 15);
71 state->s4 = __seed(LCG64(state->s3, seed), 33);
72 state->s5 = __seed(LCG64(state->s4, seed), 49);
78 void init_rand(struct frand_state *state, bool use64)
83 __init_rand32(&state->state32, 1);
85 __init_rand64(&state->state64, 1);
88 void init_rand_seed(struct frand_state *state, uint64_t seed, bool use64)
93 __init_rand32(&state->state32, (unsigned int) seed);
95 __init_rand64(&state->state64, seed);
98 void __fill_random_buf_small(void *buf, unsigned int len, uint64_t seed)
101 uint64_t *e = b + len / sizeof(*b);
102 unsigned int rest = len % sizeof(*b);
104 for (; b != e; ++b) {
106 seed = __hash_u64(seed);
109 if (fio_unlikely(rest))
110 __builtin_memcpy(e, &seed, rest);
113 void __fill_random_buf(void *buf, unsigned int len, uint64_t seed)
115 #define MAX_SEED_BUCKETS 16
116 static uint64_t prime[MAX_SEED_BUCKETS] = {1, 2, 3, 5,
121 uint64_t *b, *e, s[CONFIG_SEED_BUCKETS];
126 * Calculate the max index which is multiples of the seed buckets.
128 rest = (len / sizeof(*b) / CONFIG_SEED_BUCKETS) * CONFIG_SEED_BUCKETS;
133 rest = len - (rest * sizeof(*b));
135 for (p = 0; p < CONFIG_SEED_BUCKETS; p++)
136 s[p] = seed * prime[p];
138 for (; b != e; b += CONFIG_SEED_BUCKETS) {
139 for (p = 0; p < CONFIG_SEED_BUCKETS; ++p) {
141 s[p] = __hash_u64(s[p]);
145 __fill_random_buf_small(b, rest, s[0]);
148 uint64_t fill_random_buf(struct frand_state *fs, void *buf,
151 uint64_t r = __get_next_seed(fs);
153 __fill_random_buf(buf, len, r);
157 void __fill_random_buf_percentage(uint64_t seed, void *buf,
158 unsigned int percentage,
159 unsigned int segment, unsigned int len,
160 char *pattern, unsigned int pbytes)
162 unsigned int this_len;
164 if (percentage == 100) {
166 (void)cpy_pattern(pattern, pbytes, buf, len);
179 this_len = ((unsigned long long)segment * (100 - percentage)) / 100;
183 __fill_random_buf(buf, this_len, seed);
189 this_len = segment - this_len;
193 else if (len - this_len <= sizeof(long))
197 (void)cpy_pattern(pattern, pbytes, buf, this_len);
199 memset(buf, 0, this_len);
206 uint64_t fill_random_buf_percentage(struct frand_state *fs, void *buf,
207 unsigned int percentage,
208 unsigned int segment, unsigned int len,
209 char *pattern, unsigned int pbytes)
211 uint64_t r = __get_next_seed(fs);
213 __fill_random_buf_percentage(r, buf, percentage, segment, len,