mirror of https://github.com/postgres/postgres
Refactoring ahead of tablesample patch Requested and reviewed by Michael Paquier Petr Jelinekpull/14/head
Simon Riggs
10 years ago
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/*-------------------------------------------------------------------------
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* |
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* sampling.c |
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* Relation block sampling routines. |
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* |
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* Portions Copyright (c) 1996-2012, PostgreSQL Global Development Group |
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* Portions Copyright (c) 1994, Regents of the University of California |
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* |
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* |
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* IDENTIFICATION |
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* src/backend/utils/misc/sampling.c |
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* |
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*------------------------------------------------------------------------- |
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*/ |
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#include "postgres.h" |
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#include <math.h> |
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#include "utils/sampling.h" |
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/*
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* BlockSampler_Init -- prepare for random sampling of blocknumbers |
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* |
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* BlockSampler provides algorithm for block level sampling of a relation |
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* as discussed on pgsql-hackers 2004-04-02 (subject "Large DB") |
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* It selects a random sample of samplesize blocks out of |
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* the nblocks blocks in the table. If the table has less than |
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* samplesize blocks, all blocks are selected. |
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* |
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* Since we know the total number of blocks in advance, we can use the |
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* straightforward Algorithm S from Knuth 3.4.2, rather than Vitter's |
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* algorithm. |
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*/ |
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void |
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BlockSampler_Init(BlockSampler bs, BlockNumber nblocks, int samplesize, |
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long randseed) |
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{ |
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bs->N = nblocks; /* measured table size */ |
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/*
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* If we decide to reduce samplesize for tables that have less or not much |
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* more than samplesize blocks, here is the place to do it. |
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*/ |
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bs->n = samplesize; |
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bs->t = 0; /* blocks scanned so far */ |
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bs->m = 0; /* blocks selected so far */ |
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} |
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bool |
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BlockSampler_HasMore(BlockSampler bs) |
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{ |
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return (bs->t < bs->N) && (bs->m < bs->n); |
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} |
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BlockNumber |
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BlockSampler_Next(BlockSampler bs) |
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{ |
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BlockNumber K = bs->N - bs->t; /* remaining blocks */ |
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int k = bs->n - bs->m; /* blocks still to sample */ |
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double p; /* probability to skip block */ |
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double V; /* random */ |
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Assert(BlockSampler_HasMore(bs)); /* hence K > 0 and k > 0 */ |
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if ((BlockNumber) k >= K) |
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{ |
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/* need all the rest */ |
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bs->m++; |
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return bs->t++; |
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} |
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/*----------
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* It is not obvious that this code matches Knuth's Algorithm S. |
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* Knuth says to skip the current block with probability 1 - k/K. |
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* If we are to skip, we should advance t (hence decrease K), and |
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* repeat the same probabilistic test for the next block. The naive |
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* implementation thus requires an sampler_random_fract() call for each |
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* block number. But we can reduce this to one sampler_random_fract() |
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* call per selected block, by noting that each time the while-test |
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* succeeds, we can reinterpret V as a uniform random number in the range |
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* 0 to p. Therefore, instead of choosing a new V, we just adjust p to be |
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* the appropriate fraction of its former value, and our next loop |
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* makes the appropriate probabilistic test. |
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* |
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* We have initially K > k > 0. If the loop reduces K to equal k, |
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* the next while-test must fail since p will become exactly zero |
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* (we assume there will not be roundoff error in the division). |
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* (Note: Knuth suggests a "<=" loop condition, but we use "<" just |
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* to be doubly sure about roundoff error.) Therefore K cannot become |
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* less than k, which means that we cannot fail to select enough blocks. |
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*---------- |
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*/ |
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V = sampler_random_fract(); |
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p = 1.0 - (double) k / (double) K; |
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while (V < p) |
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{ |
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/* skip */ |
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bs->t++; |
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K--; /* keep K == N - t */ |
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/* adjust p to be new cutoff point in reduced range */ |
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p *= 1.0 - (double) k / (double) K; |
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} |
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/* select */ |
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bs->m++; |
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return bs->t++; |
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} |
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/*
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* These two routines embody Algorithm Z from "Random sampling with a |
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* reservoir" by Jeffrey S. Vitter, in ACM Trans. Math. Softw. 11, 1 |
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* (Mar. 1985), Pages 37-57. Vitter describes his algorithm in terms |
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* of the count S of records to skip before processing another record. |
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* It is computed primarily based on t, the number of records already read. |
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* The only extra state needed between calls is W, a random state variable. |
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* |
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* reservoir_init_selection_state computes the initial W value. |
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* |
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* Given that we've already read t records (t >= n), reservoir_get_next_S |
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* determines the number of records to skip before the next record is |
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* processed. |
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*/ |
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void |
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reservoir_init_selection_state(ReservoirState rs, int n) |
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{ |
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/* Initial value of W (for use when Algorithm Z is first applied) */ |
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*rs = exp(-log(sampler_random_fract()) / n); |
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} |
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double |
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reservoir_get_next_S(ReservoirState rs, double t, int n) |
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{ |
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double S; |
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/* The magic constant here is T from Vitter's paper */ |
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if (t <= (22.0 * n)) |
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{ |
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/* Process records using Algorithm X until t is large enough */ |
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double V, |
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quot; |
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V = sampler_random_fract(); /* Generate V */ |
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S = 0; |
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t += 1; |
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/* Note: "num" in Vitter's code is always equal to t - n */ |
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quot = (t - (double) n) / t; |
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/* Find min S satisfying (4.1) */ |
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while (quot > V) |
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{ |
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S += 1; |
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t += 1; |
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quot *= (t - (double) n) / t; |
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} |
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} |
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else |
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{ |
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/* Now apply Algorithm Z */ |
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double W = *rs; |
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double term = t - (double) n + 1; |
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for (;;) |
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{ |
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double numer, |
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numer_lim, |
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denom; |
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double U, |
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X, |
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lhs, |
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rhs, |
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y, |
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tmp; |
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/* Generate U and X */ |
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U = sampler_random_fract(); |
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X = t * (W - 1.0); |
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S = floor(X); /* S is tentatively set to floor(X) */ |
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/* Test if U <= h(S)/cg(X) in the manner of (6.3) */ |
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tmp = (t + 1) / term; |
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lhs = exp(log(((U * tmp * tmp) * (term + S)) / (t + X)) / n); |
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rhs = (((t + X) / (term + S)) * term) / t; |
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if (lhs <= rhs) |
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{ |
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W = rhs / lhs; |
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break; |
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} |
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/* Test if U <= f(S)/cg(X) */ |
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y = (((U * (t + 1)) / term) * (t + S + 1)) / (t + X); |
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if ((double) n < S) |
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{ |
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denom = t; |
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numer_lim = term + S; |
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} |
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else |
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{ |
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denom = t - (double) n + S; |
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numer_lim = t + 1; |
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} |
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for (numer = t + S; numer >= numer_lim; numer -= 1) |
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{ |
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y *= numer / denom; |
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denom -= 1; |
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} |
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W = exp(-log(sampler_random_fract()) / n); /* Generate W in advance */ |
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if (exp(log(y) / n) <= (t + X) / t) |
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break; |
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} |
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*rs = W; |
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} |
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return S; |
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} |
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/*----------
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* Random number generator used by sampling |
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*---------- |
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*/ |
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/* Select a random value R uniformly distributed in (0 - 1) */ |
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double |
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sampler_random_fract() |
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{ |
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return ((double) random() + 1) / ((double) MAX_RANDOM_VALUE + 2); |
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} |
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@ -0,0 +1,44 @@ |
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/*-------------------------------------------------------------------------
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* |
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* sampling.h |
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* definitions for sampling functions |
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* |
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* Portions Copyright (c) 1996-2014, PostgreSQL Global Development Group |
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* Portions Copyright (c) 1994, Regents of the University of California |
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* |
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* src/include/utils/sampling.h |
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* |
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*------------------------------------------------------------------------- |
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*/ |
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#ifndef SAMPLING_H |
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#define SAMPLING_H |
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#include "storage/bufmgr.h" |
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extern double sampler_random_fract(void); |
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/* Block sampling methods */ |
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/* Data structure for Algorithm S from Knuth 3.4.2 */ |
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typedef struct |
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{ |
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BlockNumber N; /* number of blocks, known in advance */ |
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int n; /* desired sample size */ |
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BlockNumber t; /* current block number */ |
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int m; /* blocks selected so far */ |
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} BlockSamplerData; |
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typedef BlockSamplerData *BlockSampler; |
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extern void BlockSampler_Init(BlockSampler bs, BlockNumber nblocks, |
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int samplesize, long randseed); |
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extern bool BlockSampler_HasMore(BlockSampler bs); |
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extern BlockNumber BlockSampler_Next(BlockSampler bs); |
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/* Reservoid sampling methods */ |
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typedef double ReservoirStateData; |
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typedef ReservoirStateData *ReservoirState; |
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extern void reservoir_init_selection_state(ReservoirState rs, int n); |
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extern double reservoir_get_next_S(ReservoirState rs, double t, int n); |
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#endif /* SAMPLING_H */ |
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