From db04f2b3225aa7e6d496a087c4c0e46161744573 Mon Sep 17 00:00:00 2001
From: Tom Lane <tgl@sss.pgh.pa.us>
Date: Tue, 3 Aug 2010 21:21:03 +0000
Subject: [PATCH] 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 | 62 ++++++++++++++++++++++++++++++++-
src/include/utils/geo_decls.h | 5 +--
2 files changed, 64 insertions(+), 3 deletions(-)
diff --git a/src/backend/utils/adt/geo_ops.c b/src/backend/utils/adt/geo_ops.c
index cd1d6c2cc6..3eef2f47da 100644
--- a/src/backend/utils/adt/geo_ops.c
+++ b/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));
+}
diff --git a/src/include/utils/geo_decls.h b/src/include/utils/geo_decls.h
index f43d2d5fdc..904d9f7948 100644
--- a/src/include/utils/geo_decls.h
+++ b/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);
--
2.49.0