Improve the gin index scan performance in pg_trgm.

Previous coding assumes too pessimistic upper bound of similarity
in consistent method of GIN.

Author: Fornaroli Christophe with comments by me.

Author: feodor

contrib/pg_trgm/trgm_gin.c

@@ -190,11 +190,23 @@ gin_trgm_consistent(PG_FUNCTION_ARGS)
 				if (check[i])
 					ntrue++;
 			}
-#ifdef DIVUNION
-			res = (nkeys == ntrue) ? true : ((((((float4) ntrue) / ((float4) (nkeys - ntrue)))) >= trgm_limit) ? true : false);
-#else
+
+			/*--------------------
+			 * If DIVUNION is defined then similarity formula is:
+			 * c / (len1 + len2 - c)
+			 * where c is number of common trigrams and it stands as ntrue in
+			 * this code.  Here we don't know value of len2 but we can assume
+			 * that c (ntrue) is a lower bound of len2, so upper bound of
+			 * similarity is:
+			 * c / (len1 + c - c)  => c / len1
+			 * If DIVUNION is not defined then similarity formula is:
+			 * c / max(len1, len2)
+			 * And again, c (ntrue) is a lower bound of len2, but c <= len1
+			 * just by definition and, consequently, upper bound of
+			 * similarity is just c / len1.
+			 * So, independly on DIVUNION the upper bound formula is the same.
+			 */
 			res = (nkeys == 0) ? false : ((((((float4) ntrue) / ((float4) nkeys))) >= trgm_limit) ? true : false);
-#endif
 			break;
 		case ILikeStrategyNumber:
 #ifndef IGNORECASE
@@ -267,11 +279,11 @@ gin_trgm_triconsistent(PG_FUNCTION_ARGS)
 				if (check[i] != GIN_FALSE)
 					ntrue++;
 			}
-#ifdef DIVUNION
-			res = (nkeys == ntrue) ? GIN_MAYBE : (((((float4) ntrue) / ((float4) (nkeys - ntrue))) >= trgm_limit) ? GIN_MAYBE : GIN_FALSE);
-#else
+
+			/*
+			 * See comment in gin_trgm_consistent() about * upper bound formula
+			 */
 			res = (nkeys == 0) ? GIN_FALSE : (((((float4) ntrue) / ((float4) nkeys)) >= trgm_limit) ? GIN_MAYBE : GIN_FALSE);
-#endif
 			break;
 		case ILikeStrategyNumber:
 #ifndef IGNORECASE