Add two HyperLogLog functions

New functions initHyperLogLogError() and freeHyperLogLog() simplify
using this module from elsewhere.

Author: Tomáš Vondra
Review: Peter Geoghegan

src/backend/lib/hyperloglog.c

@@ -56,7 +56,7 @@
 static inline uint8 rho(uint32 x, uint8 b);
 
 /*
- * Initialize HyperLogLog track state
+ * Initialize HyperLogLog track state, by bit width
  *
  * bwidth is bit width (so register size will be 2 to the power of bwidth).
  * Must be between 4 and 16 inclusive.
@@ -107,6 +107,52 @@ initHyperLogLog(hyperLogLogState *cState, uint8 bwidth)
 	cState->alphaMM = alpha * cState->nRegisters * cState->nRegisters;
 }
 
+/*
+ * Initialize HyperLogLog track state, by error rate
+ *
+ * Instead of specifying bwidth (number of bits used for addressing the
+ * register), this method allows sizing the counter for particular error
+ * rate using a simple formula from the paper:
+ *
+ *	 e = 1.04 / sqrt(m)
+ *
+ * where 'm' is the number of registers, i.e. (2^bwidth). The method
+ * finds the lowest bwidth with 'e' below the requested error rate, and
+ * then uses it to initialize the counter.
+ *
+ * As bwidth has to be between 4 and 16, the worst possible error rate
+ * is between ~25% (bwidth=4) and 0.4% (bwidth=16).
+ */
+void
+initHyperLogLogError(hyperLogLogState *cState, double error)
+{
+	uint8		bwidth = 4;
+
+	while (bwidth < 16)
+	{
+		double		m = (Size) 1 << bwidth;
+
+		if (1.04 / sqrt(m) < error)
+			break;
+		bwidth++;
+	}
+
+	initHyperLogLog(cState, bwidth);
+}
+
+/*
+ * Free HyperLogLog track state
+ *
+ * Releases allocated resources, but not the state itself (in case it's not
+ * allocated by palloc).
+ */
+void
+freeHyperLogLog(hyperLogLogState *cState)
+{
+	Assert(cState->hashesArr != NULL);
+	pfree(cState->hashesArr);
+}
+
 /*
  * Adds element to the estimator, from caller-supplied hash.
  *

src/include/lib/hyperloglog.h

@@ -60,8 +60,10 @@ typedef struct hyperLogLogState
 } hyperLogLogState;
 
 extern void initHyperLogLog(hyperLogLogState *cState, uint8 bwidth);
+extern void initHyperLogLogError(hyperLogLogState *cState, double error);
 extern void addHyperLogLog(hyperLogLogState *cState, uint32 hash);
 extern double estimateHyperLogLog(hyperLogLogState *cState);
 extern void mergeHyperLogLog(hyperLogLogState *cState, const hyperLogLogState *oState);
+extern void freeHyperLogLog(hyperLogLogState *cState);
 
 #endif   /* HYPERLOGLOG_H */