PostgreSQL Source Code git master
sampling.c
Go to the documentation of this file.
1/*-------------------------------------------------------------------------
2 *
3 * sampling.c
4 * Relation block sampling routines.
5 *
6 * Portions Copyright (c) 1996-2025, PostgreSQL Global Development Group
7 * Portions Copyright (c) 1994, Regents of the University of California
8 *
9 *
10 * IDENTIFICATION
11 * src/backend/utils/misc/sampling.c
12 *
13 *-------------------------------------------------------------------------
14 */
15
16#include "postgres.h"
17
18#include <math.h>
19
20#include "utils/sampling.h"
21
22
23/*
24 * BlockSampler_Init -- prepare for random sampling of blocknumbers
25 *
26 * BlockSampler provides algorithm for block level sampling of a relation
27 * as discussed on pgsql-hackers 2004-04-02 (subject "Large DB")
28 * It selects a random sample of samplesize blocks out of
29 * the nblocks blocks in the table. If the table has less than
30 * samplesize blocks, all blocks are selected.
31 *
32 * Since we know the total number of blocks in advance, we can use the
33 * straightforward Algorithm S from Knuth 3.4.2, rather than Vitter's
34 * algorithm.
35 *
36 * Returns the number of blocks that BlockSampler_Next will return.
37 */
39BlockSampler_Init(BlockSampler bs, BlockNumber nblocks, int samplesize,
40 uint32 randseed)
41{
42 bs->N = nblocks; /* measured table size */
43
44 /*
45 * If we decide to reduce samplesize for tables that have less or not much
46 * more than samplesize blocks, here is the place to do it.
47 */
48 bs->n = samplesize;
49 bs->t = 0; /* blocks scanned so far */
50 bs->m = 0; /* blocks selected so far */
51
53
54 return Min(bs->n, bs->N);
55}
56
57bool
59{
60 return (bs->t < bs->N) && (bs->m < bs->n);
61}
62
65{
66 BlockNumber K = bs->N - bs->t; /* remaining blocks */
67 int k = bs->n - bs->m; /* blocks still to sample */
68 double p; /* probability to skip block */
69 double V; /* random */
70
71 Assert(BlockSampler_HasMore(bs)); /* hence K > 0 and k > 0 */
72
73 if ((BlockNumber) k >= K)
74 {
75 /* need all the rest */
76 bs->m++;
77 return bs->t++;
78 }
79
80 /*----------
81 * It is not obvious that this code matches Knuth's Algorithm S.
82 * Knuth says to skip the current block with probability 1 - k/K.
83 * If we are to skip, we should advance t (hence decrease K), and
84 * repeat the same probabilistic test for the next block. The naive
85 * implementation thus requires a sampler_random_fract() call for each
86 * block number. But we can reduce this to one sampler_random_fract()
87 * call per selected block, by noting that each time the while-test
88 * succeeds, we can reinterpret V as a uniform random number in the range
89 * 0 to p. Therefore, instead of choosing a new V, we just adjust p to be
90 * the appropriate fraction of its former value, and our next loop
91 * makes the appropriate probabilistic test.
92 *
93 * We have initially K > k > 0. If the loop reduces K to equal k,
94 * the next while-test must fail since p will become exactly zero
95 * (we assume there will not be roundoff error in the division).
96 * (Note: Knuth suggests a "<=" loop condition, but we use "<" just
97 * to be doubly sure about roundoff error.) Therefore K cannot become
98 * less than k, which means that we cannot fail to select enough blocks.
99 *----------
100 */
102 p = 1.0 - (double) k / (double) K;
103 while (V < p)
104 {
105 /* skip */
106 bs->t++;
107 K--; /* keep K == N - t */
108
109 /* adjust p to be new cutoff point in reduced range */
110 p *= 1.0 - (double) k / (double) K;
111 }
112
113 /* select */
114 bs->m++;
115 return bs->t++;
116}
117
118/*
119 * These two routines embody Algorithm Z from "Random sampling with a
120 * reservoir" by Jeffrey S. Vitter, in ACM Trans. Math. Softw. 11, 1
121 * (Mar. 1985), Pages 37-57. Vitter describes his algorithm in terms
122 * of the count S of records to skip before processing another record.
123 * It is computed primarily based on t, the number of records already read.
124 * The only extra state needed between calls is W, a random state variable.
125 *
126 * reservoir_init_selection_state computes the initial W value.
127 *
128 * Given that we've already read t records (t >= n), reservoir_get_next_S
129 * determines the number of records to skip before the next record is
130 * processed.
131 */
132void
134{
135 /*
136 * Reservoir sampling is not used anywhere where it would need to return
137 * repeatable results so we can initialize it randomly.
138 */
140 &rs->randstate);
141
142 /* Initial value of W (for use when Algorithm Z is first applied) */
143 rs->W = exp(-log(sampler_random_fract(&rs->randstate)) / n);
144}
145
146double
148{
149 double S;
150
151 /* The magic constant here is T from Vitter's paper */
152 if (t <= (22.0 * n))
153 {
154 /* Process records using Algorithm X until t is large enough */
155 double V,
156 quot;
157
158 V = sampler_random_fract(&rs->randstate); /* Generate V */
159 S = 0;
160 t += 1;
161 /* Note: "num" in Vitter's code is always equal to t - n */
162 quot = (t - (double) n) / t;
163 /* Find min S satisfying (4.1) */
164 while (quot > V)
165 {
166 S += 1;
167 t += 1;
168 quot *= (t - (double) n) / t;
169 }
170 }
171 else
172 {
173 /* Now apply Algorithm Z */
174 double W = rs->W;
175 double term = t - (double) n + 1;
176
177 for (;;)
178 {
179 double numer,
180 numer_lim,
181 denom;
182 double U,
183 X,
184 lhs,
185 rhs,
186 y,
187 tmp;
188
189 /* Generate U and X */
191 X = t * (W - 1.0);
192 S = floor(X); /* S is tentatively set to floor(X) */
193 /* Test if U <= h(S)/cg(X) in the manner of (6.3) */
194 tmp = (t + 1) / term;
195 lhs = exp(log(((U * tmp * tmp) * (term + S)) / (t + X)) / n);
196 rhs = (((t + X) / (term + S)) * term) / t;
197 if (lhs <= rhs)
198 {
199 W = rhs / lhs;
200 break;
201 }
202 /* Test if U <= f(S)/cg(X) */
203 y = (((U * (t + 1)) / term) * (t + S + 1)) / (t + X);
204 if ((double) n < S)
205 {
206 denom = t;
207 numer_lim = term + S;
208 }
209 else
210 {
211 denom = t - (double) n + S;
212 numer_lim = t + 1;
213 }
214 for (numer = t + S; numer >= numer_lim; numer -= 1)
215 {
216 y *= numer / denom;
217 denom -= 1;
218 }
219 W = exp(-log(sampler_random_fract(&rs->randstate)) / n); /* Generate W in advance */
220 if (exp(log(y) / n) <= (t + X) / t)
221 break;
222 }
223 rs->W = W;
224 }
225 return S;
226}
227
228
229/*----------
230 * Random number generator used by sampling
231 *----------
232 */
233void
235{
236 pg_prng_seed(randstate, (uint64) seed);
237}
238
239/* Select a random value R uniformly distributed in (0 - 1) */
240double
242{
243 double res;
244
245 /* pg_prng_double returns a value in [0.0 - 1.0), so we must reject 0.0 */
246 do
247 {
248 res = pg_prng_double(randstate);
249 } while (unlikely(res == 0.0));
250 return res;
251}
252
253
254/*
255 * Backwards-compatible API for block sampling
256 *
257 * This code is now deprecated, but since it's still in use by many FDWs,
258 * we should keep it for awhile at least. The functionality is the same as
259 * sampler_random_fract/reservoir_init_selection_state/reservoir_get_next_S,
260 * except that a common random state is used across all callers.
261 */
263static bool oldrs_initialized = false;
264
265double
267{
268 /* initialize if first time through */
270 {
273 oldrs_initialized = true;
274 }
275
276 /* and compute a random fraction */
278}
279
280double
282{
283 /* initialize if first time through */
285 {
288 oldrs_initialized = true;
289 }
290
291 /* Initial value of W (for use when Algorithm Z is first applied) */
292 return exp(-log(sampler_random_fract(&oldrs.randstate)) / n);
293}
294
295double
296anl_get_next_S(double t, int n, double *stateptr)
297{
298 double result;
299
300 oldrs.W = *stateptr;
301 result = reservoir_get_next_S(&oldrs, t, n);
302 *stateptr = oldrs.W;
303 return result;
304}
uint32 BlockNumber
Definition: block.h:31
#define Min(x, y)
Definition: c.h:961
#define Assert(condition)
Definition: c.h:815
uint64_t uint64
Definition: c.h:489
#define unlikely(x)
Definition: c.h:333
uint32_t uint32
Definition: c.h:488
int y
Definition: isn.c:71
double pg_prng_double(pg_prng_state *state)
Definition: pg_prng.c:268
uint32 pg_prng_uint32(pg_prng_state *state)
Definition: pg_prng.c:227
void pg_prng_seed(pg_prng_state *state, uint64 seed)
Definition: pg_prng.c:89
pg_prng_state pg_global_prng_state
Definition: pg_prng.c:34
static ReservoirStateData oldrs
Definition: sampling.c:262
static bool oldrs_initialized
Definition: sampling.c:263
BlockNumber BlockSampler_Init(BlockSampler bs, BlockNumber nblocks, int samplesize, uint32 randseed)
Definition: sampling.c:39
void reservoir_init_selection_state(ReservoirState rs, int n)
Definition: sampling.c:133
double anl_get_next_S(double t, int n, double *stateptr)
Definition: sampling.c:296
double sampler_random_fract(pg_prng_state *randstate)
Definition: sampling.c:241
bool BlockSampler_HasMore(BlockSampler bs)
Definition: sampling.c:58
BlockNumber BlockSampler_Next(BlockSampler bs)
Definition: sampling.c:64
double anl_init_selection_state(int n)
Definition: sampling.c:281
void sampler_random_init_state(uint32 seed, pg_prng_state *randstate)
Definition: sampling.c:234
double anl_random_fract(void)
Definition: sampling.c:266
double reservoir_get_next_S(ReservoirState rs, double t, int n)
Definition: sampling.c:147
#define K(t)
Definition: sha1.c:66
#define W(n)
Definition: sha1.c:78
#define S(n, x)
Definition: sha1.c:73
BlockNumber N
Definition: sampling.h:30
pg_prng_state randstate
Definition: sampling.h:34
BlockNumber t
Definition: sampling.h:32
pg_prng_state randstate
Definition: sampling.h:49