Replace number-of-distinct-values estimator equation, per recent

pghackers discussion.

diff --git a/src/backend/commands/analyze.c b/src/backend/commands/analyze.c
index e6d9a574e2b8a29fc5f91aea17dca4b69b40b97e..0dc75cb4d4b91d2218eb90a7d0b00584d6ecf47d 100644 (file)
--- a/src/backend/commands/analyze.c
+++ b/src/backend/commands/analyze.c
@@ -8,7 +8,7 @@
  *
  *
  * IDENTIFICATION
- *   $Header: /cvsroot/pgsql/src/backend/commands/analyze.c,v 1.25 2002/01/06 00:37:44 tgl Exp $
+ *   $Header: /cvsroot/pgsql/src/backend/commands/analyze.c,v 1.26 2002/02/18 16:04:14 tgl Exp $
  *
  *-------------------------------------------------------------------------
  */
@@ -1009,10 +1009,15 @@ compute_minimal_stats(VacAttrStats *stats,
        {
            /*----------
             * Estimate the number of distinct values using the estimator
-            * proposed by Chaudhuri et al (see citation above).  This is
-            *      sqrt(n/r) * max(f1,1) + f2 + f3 + ...
-            * where fk is the number of distinct values that occurred
-            * exactly k times in our sample of r rows (from a total of n).
+            * proposed by Haas and Stokes in IBM Research Report RJ 10025:
+            *      n*d / (n - f1 + f1*n/N)
+            * where f1 is the number of distinct values that occurred
+            * exactly once in our sample of n rows (from a total of N),
+            * and d is the total number of distinct values in the sample.
+            * This is their Duj1 estimator; the other estimators they
+            * recommend are considerably more complex, and are numerically
+            * very unstable when n is much smaller than N.
+            *
             * We assume (not very reliably!) that all the multiply-occurring
             * values are reflected in the final track[] list, and the other
             * nonnull values all appeared but once.  (XXX this usually
@@ -1021,12 +1026,19 @@ compute_minimal_stats(VacAttrStats *stats,
             *----------
             */
            int         f1 = nonnull_cnt - summultiple;
-           double      term1;
-
-           if (f1 < 1)
-               f1 = 1;
-           term1 = sqrt(totalrows / (double) numrows) * f1;
-           stats->stadistinct = floor(term1 + nmultiple + 0.5);
+           int         d = f1 + nmultiple;
+           double      numer, denom, stadistinct;
+
+           numer = (double) numrows * (double) d;
+           denom = (double) (numrows - f1) +
+               (double) f1 * (double) numrows / totalrows;
+           stadistinct = numer / denom;
+           /* Clamp to sane range in case of roundoff error */
+           if (stadistinct < (double) d)
+               stadistinct = (double) d;
+           if (stadistinct > totalrows)
+               stadistinct = totalrows;
+           stats->stadistinct = floor(stadistinct + 0.5);
        }
 
        /*
@@ -1313,20 +1325,32 @@ compute_scalar_stats(VacAttrStats *stats,
        {
            /*----------
             * Estimate the number of distinct values using the estimator
-            * proposed by Chaudhuri et al (see citation above).  This is
-            *      sqrt(n/r) * max(f1,1) + f2 + f3 + ...
-            * where fk is the number of distinct values that occurred
-            * exactly k times in our sample of r rows (from a total of n).
+            * proposed by Haas and Stokes in IBM Research Report RJ 10025:
+            *      n*d / (n - f1 + f1*n/N)
+            * where f1 is the number of distinct values that occurred
+            * exactly once in our sample of n rows (from a total of N),
+            * and d is the total number of distinct values in the sample.
+            * This is their Duj1 estimator; the other estimators they
+            * recommend are considerably more complex, and are numerically
+            * very unstable when n is much smaller than N.
+            *
             * Overwidth values are assumed to have been distinct.
             *----------
             */
            int         f1 = ndistinct - nmultiple + toowide_cnt;
-           double      term1;
-
-           if (f1 < 1)
-               f1 = 1;
-           term1 = sqrt(totalrows / (double) numrows) * f1;
-           stats->stadistinct = floor(term1 + nmultiple + 0.5);
+           int         d = f1 + nmultiple;
+           double      numer, denom, stadistinct;
+
+           numer = (double) numrows * (double) d;
+           denom = (double) (numrows - f1) +
+               (double) f1 * (double) numrows / totalrows;
+           stadistinct = numer / denom;
+           /* Clamp to sane range in case of roundoff error */
+           if (stadistinct < (double) d)
+               stadistinct = (double) d;
+           if (stadistinct > totalrows)
+               stadistinct = totalrows;
+           stats->stadistinct = floor(stadistinct + 0.5);
        }
 
        /*