Separate block sampling functions

Refactoring ahead of tablesample patch

Requested and reviewed by Michael Paquier

Petr Jelinek

src/backend/utils/misc/sampling.c

@@ -0,0 +1,226 @@
+/*-------------------------------------------------------------------------
+ *
+ * sampling.c
+ *	  Relation block sampling routines.
+ *
+ * Portions Copyright (c) 1996-2012, PostgreSQL Global Development Group
+ * Portions Copyright (c) 1994, Regents of the University of California
+ *
+ *
+ * IDENTIFICATION
+ *	  src/backend/utils/misc/sampling.c
+ *
+ *-------------------------------------------------------------------------
+ */
+
+#include "postgres.h"
+
+#include <math.h>
+
+#include "utils/sampling.h"
+
+
+/*
+ * BlockSampler_Init -- prepare for random sampling of blocknumbers
+ *
+ * BlockSampler provides algorithm for block level sampling of a relation
+ * as discussed on pgsql-hackers 2004-04-02 (subject "Large DB")
+ * It selects a random sample of samplesize blocks out of
+ * the nblocks blocks in the table. If the table has less than
+ * samplesize blocks, all blocks are selected.
+ *
+ * Since we know the total number of blocks in advance, we can use the
+ * straightforward Algorithm S from Knuth 3.4.2, rather than Vitter's
+ * algorithm.
+ */
+void
+BlockSampler_Init(BlockSampler bs, BlockNumber nblocks, int samplesize,
+				  long randseed)
+{
+	bs->N = nblocks;			/* measured table size */
+
+	/*
+	 * If we decide to reduce samplesize for tables that have less or not much
+	 * more than samplesize blocks, here is the place to do it.
+	 */
+	bs->n = samplesize;
+	bs->t = 0;					/* blocks scanned so far */
+	bs->m = 0;					/* blocks selected so far */
+}
+
+bool
+BlockSampler_HasMore(BlockSampler bs)
+{
+	return (bs->t < bs->N) && (bs->m < bs->n);
+}
+
+BlockNumber
+BlockSampler_Next(BlockSampler bs)
+{
+	BlockNumber K = bs->N - bs->t;		/* remaining blocks */
+	int			k = bs->n - bs->m;		/* blocks still to sample */
+	double		p;				/* probability to skip block */
+	double		V;				/* random */
+
+	Assert(BlockSampler_HasMore(bs));	/* hence K > 0 and k > 0 */
+
+	if ((BlockNumber) k >= K)
+	{
+		/* need all the rest */
+		bs->m++;
+		return bs->t++;
+	}
+
+	/*----------
+	 * It is not obvious that this code matches Knuth's Algorithm S.
+	 * Knuth says to skip the current block with probability 1 - k/K.
+	 * If we are to skip, we should advance t (hence decrease K), and
+	 * repeat the same probabilistic test for the next block.  The naive
+	 * implementation thus requires an sampler_random_fract() call for each
+	 * block number.  But we can reduce this to one sampler_random_fract()
+	 * call per selected block, by noting that each time the while-test
+	 * succeeds, we can reinterpret V as a uniform random number in the range
+	 * 0 to p. Therefore, instead of choosing a new V, we just adjust p to be
+	 * the appropriate fraction of its former value, and our next loop
+	 * makes the appropriate probabilistic test.
+	 *
+	 * We have initially K > k > 0.  If the loop reduces K to equal k,
+	 * the next while-test must fail since p will become exactly zero
+	 * (we assume there will not be roundoff error in the division).
+	 * (Note: Knuth suggests a "<=" loop condition, but we use "<" just
+	 * to be doubly sure about roundoff error.)  Therefore K cannot become
+	 * less than k, which means that we cannot fail to select enough blocks.
+	 *----------
+	 */
+	V = sampler_random_fract();
+	p = 1.0 - (double) k / (double) K;
+	while (V < p)
+	{
+		/* skip */
+		bs->t++;
+		K--;					/* keep K == N - t */
+
+		/* adjust p to be new cutoff point in reduced range */
+		p *= 1.0 - (double) k / (double) K;
+	}
+
+	/* select */
+	bs->m++;
+	return bs->t++;
+}
+
+/*
+ * These two routines embody Algorithm Z from "Random sampling with a
+ * reservoir" by Jeffrey S. Vitter, in ACM Trans. Math. Softw. 11, 1
+ * (Mar. 1985), Pages 37-57.  Vitter describes his algorithm in terms
+ * of the count S of records to skip before processing another record.
+ * It is computed primarily based on t, the number of records already read.
+ * The only extra state needed between calls is W, a random state variable.
+ *
+ * reservoir_init_selection_state computes the initial W value.
+ *
+ * Given that we've already read t records (t >= n), reservoir_get_next_S
+ * determines the number of records to skip before the next record is
+ * processed.
+ */
+void
+reservoir_init_selection_state(ReservoirState rs, int n)
+{
+	/* Initial value of W (for use when Algorithm Z is first applied) */
+	*rs = exp(-log(sampler_random_fract()) / n);
+}
+
+double
+reservoir_get_next_S(ReservoirState rs, double t, int n)
+{
+	double		S;
+
+	/* The magic constant here is T from Vitter's paper */
+	if (t <= (22.0 * n))
+	{
+		/* Process records using Algorithm X until t is large enough */
+		double		V,
+					quot;
+
+		V = sampler_random_fract(); /* Generate V */
+		S = 0;
+		t += 1;
+		/* Note: "num" in Vitter's code is always equal to t - n */
+		quot = (t - (double) n) / t;
+		/* Find min S satisfying (4.1) */
+		while (quot > V)
+		{
+			S += 1;
+			t += 1;
+			quot *= (t - (double) n) / t;
+		}
+	}
+	else
+	{
+		/* Now apply Algorithm Z */
+		double		W = *rs;
+		double		term = t - (double) n + 1;
+
+		for (;;)
+		{
+			double		numer,
+						numer_lim,
+						denom;
+			double		U,
+						X,
+						lhs,
+						rhs,
+						y,
+						tmp;
+
+			/* Generate U and X */
+			U = sampler_random_fract();
+			X = t * (W - 1.0);
+			S = floor(X);		/* S is tentatively set to floor(X) */
+			/* Test if U <= h(S)/cg(X) in the manner of (6.3) */
+			tmp = (t + 1) / term;
+			lhs = exp(log(((U * tmp * tmp) * (term + S)) / (t + X)) / n);
+			rhs = (((t + X) / (term + S)) * term) / t;
+			if (lhs <= rhs)
+			{
+				W = rhs / lhs;
+				break;
+			}
+			/* Test if U <= f(S)/cg(X) */
+			y = (((U * (t + 1)) / term) * (t + S + 1)) / (t + X);
+			if ((double) n < S)
+			{
+				denom = t;
+				numer_lim = term + S;
+			}
+			else
+			{
+				denom = t - (double) n + S;
+				numer_lim = t + 1;
+			}
+			for (numer = t + S; numer >= numer_lim; numer -= 1)
+			{
+				y *= numer / denom;
+				denom -= 1;
+			}
+			W = exp(-log(sampler_random_fract()) / n);		/* Generate W in advance */
+			if (exp(log(y) / n) <= (t + X) / t)
+				break;
+		}
+		*rs = W;
+	}
+	return S;
+}
+
+
+/*----------
+ * Random number generator used by sampling
+ *----------
+ */
+
+/* Select a random value R uniformly distributed in (0 - 1) */
+double
+sampler_random_fract()
+{
+	return ((double) random() + 1) / ((double) MAX_RANDOM_VALUE + 2);
+}