Replace the naive HYPOT() macro with a standards-conformant hypotenuse

function.  This avoids unnecessary overflows and probably gives a more
accurate result as well.

Paul Matthews, reviewed by Andrew Geery

src/backend/utils/adt/geo_ops.c

@@ -8,7 +8,7 @@
  *
  *
  * IDENTIFICATION
- *	  $PostgreSQL: pgsql/src/backend/utils/adt/geo_ops.c,v 1.108 2010/02/26 02:01:08 momjian Exp $
+ *	  $PostgreSQL: pgsql/src/backend/utils/adt/geo_ops.c,v 1.109 2010/08/03 21:21:03 tgl Exp $
  *
  *-------------------------------------------------------------------------
  */
@@ -5410,3 +5410,63 @@ plist_same(int npts, Point *p1, Point *p2)
 
 	return FALSE;
 }
+
+
+/*-------------------------------------------------------------------------
+ * Determine the hypotenuse.
+ *
+ * If required, x and y are swapped to make x the larger number. The
+ * traditional formula of x^2+y^2 is rearranged to factor x outside the
+ * sqrt. This allows computation of the hypotenuse for significantly
+ * larger values, and with a higher precision than when using the naive
+ * formula.  In particular, this cannot overflow unless the final result
+ * would be out-of-range.
+ *
+ * sqrt( x^2 + y^2 ) = sqrt( x^2( 1 + y^2/x^2) )
+ *					 = x * sqrt( 1 + y^2/x^2 )
+ *					 = x * sqrt( 1 + y/x * y/x )
+ *
+ * It is expected that this routine will eventually be replaced with the
+ * C99 hypot() function.
+ *
+ * This implementation conforms to IEEE Std 1003.1 and GLIBC, in that the
+ * case of hypot(inf,nan) results in INF, and not NAN.
+ *-----------------------------------------------------------------------
+ */
+double
+pg_hypot(double x, double y)
+{
+	double		yx;
+
+	/* Handle INF and NaN properly */
+	if (isinf(x) || isinf(y))
+		return get_float8_infinity();
+
+	if (isnan(x) || isnan(y))
+		return get_float8_nan();
+
+	/* Else, drop any minus signs */
+	x = fabs(x);
+	y = fabs(y);
+
+	/* Swap x and y if needed to make x the larger one */
+	if (x < y)
+	{
+		double		temp = x;
+
+		x = y;
+		y = temp;
+	}
+
+	/*
+	 * If y is zero, the hypotenuse is x.  This test saves a few cycles in
+	 * such cases, but more importantly it also protects against
+	 * divide-by-zero errors, since now x >= y.
+	 */
+	if (y == 0.0)
+		return x;
+
+	/* Determine the hypotenuse */
+	yx = y / x;
+	return x * sqrt(1.0 + (yx * yx));
+}

src/include/utils/geo_decls.h

@@ -6,7 +6,7 @@
  * Portions Copyright (c) 1996-2010, PostgreSQL Global Development Group
  * Portions Copyright (c) 1994, Regents of the University of California
  *
- * $PostgreSQL: pgsql/src/include/utils/geo_decls.h,v 1.57 2010/01/14 16:31:09 teodor Exp $
+ * $PostgreSQL: pgsql/src/include/utils/geo_decls.h,v 1.58 2010/08/03 21:21:03 tgl Exp $
  *
  * NOTE
  *	  These routines do *not* use the float types from adt/.
@@ -50,7 +50,7 @@
 #define FPge(A,B)				((A) >= (B))
 #endif
 
-#define HYPOT(A, B)				sqrt((A) * (A) + (B) * (B))
+#define HYPOT(A, B)				pg_hypot(A, B)
 
 /*---------------------------------------------------------------------
  * Point - (x,y)
@@ -211,6 +211,7 @@ extern Datum point_div(PG_FUNCTION_ARGS);
 /* private routines */
 extern double point_dt(Point *pt1, Point *pt2);
 extern double point_sl(Point *pt1, Point *pt2);
+extern double pg_hypot(double x, double y);
 
 /* public lseg routines */
 extern Datum lseg_in(PG_FUNCTION_ARGS);