Adjust degree-based trig functions for more portability.

The buildfarm isn't very happy with the results of commit e1bd684a. To try to get the expected exact results everywhere: * Replace M_PI / 180 subexpressions with a precomputed constant, so that the compiler can't decide to rearrange that division with an adjacent operation. Hopefully this will fix failures to get exactly 0.5 from sind(30) and cosd(60). * Add scaling to ensure that tand(45) and cotd(45) give exactly 1; there was nothing particularly guaranteeing that before. * Replace minus zero by zero when tand() or cotd() would output that; many machines did so for tand(180) and cotd(270), but not all. We could alternatively deem both results valid, but that doesn't seem likely to be what users will want.

Adjust degree-based trig functions for more portability.
The buildfarm isn't very happy with the results of commit e1bd684a. To try to get the expected exact results everywhere: * Replace M_PI / 180 subexpressions with a precomputed constant, so that the compiler can't decide to rearrange that division with an adjacent operation. Hopefully this will fix failures to get exactly 0.5 from sind(30) and cosd(60). * Add scaling to ensure that tand(45) and cotd(45) give exactly 1; there was nothing particularly guaranteeing that before. * Replace minus zero by zero when tand() or cotd() would output that; many machines did so for tand(180) and cotd(270), but not all. We could alternatively deem both results valid, but that doesn't seem likely to be what users will want.
73193d82 · Tom Lane · 6ae4c8de · 73193d82 · 73193d82 · 73193d82
Commit 73193d82 authored Jan 23, 2016 by Tom Lane
5 changed files
--- a/src/backend/utils/adt/float.c
+++ b/src/backend/utils/adt/float.c
@@ -31,6 +31,9 @@
 #define M_PI 3.14159265358979323846
 #endif

+/* Radians per degree, a.k.a. PI / 180 */
+#define RADIANS_PER_DEGREE 0.0174532925199432957692
+
 /* Visual C++ etc lacks NAN, and won't accept 0.0/0.0.  NAN definition from
 * http://msdn.microsoft.com/library/default.asp?url=/library/en-us/vclang/html/vclrfNotNumberNANItems.asp
 */
@@ -1919,7 +1922,7 @@ datan2d(PG_FUNCTION_ARGS)
 static double
 sind_0_to_30(double x)
 {
-	return (sin(x * (M_PI / 180.0)) / sin(30.0 * (M_PI / 180.0))) / 2.0;
+	return (sin(x * RADIANS_PER_DEGREE) / sin(30.0 * RADIANS_PER_DEGREE)) / 2.0;
 }


@@ -1931,8 +1934,8 @@ sind_0_to_30(double x)
 static double
 cosd_0_to_60(double x)
 {
-	return 1.0 - ((1.0 - cos(x * (M_PI / 180.0))) /
-				  (1.0 - cos(60.0 * (M_PI / 180.0)))) / 2.0;
+	return 1.0 - ((1.0 - cos(x * RADIANS_PER_DEGREE)) /
+				  (1.0 - cos(60.0 * RADIANS_PER_DEGREE))) / 2.0;
 }


@@ -2030,8 +2033,9 @@ Datum
 dcotd(PG_FUNCTION_ARGS)
 {
 	float8		arg1 = PG_GETARG_FLOAT8(0);
-	int			sign = 1;
 	float8		result;
+	int			sign = 1;
+	static float8 cot45 = 0.0;

 	/*
 	 * Per the POSIX spec, return NaN if the input is NaN and throw an error
@@ -2071,6 +2075,26 @@ dcotd(PG_FUNCTION_ARGS)

 	result = sign * cosd_q1(arg1) / sind_q1(arg1);

+	/*
+	 * We want cotd(45) to be exactly 1, but the above computation might've
+	 * produced something different, so scale to get the right result.  To
+	 * avoid redoing cosd_q1(45) / sind_q1(45) many times, and to prevent the
+	 * compiler from maybe rearranging the calculation, cache that value in a
+	 * static variable.
+	 */
+	if (cot45 == 0.0)
+		cot45 = cosd_q1(45.0) / sind_q1(45.0);
+
+	result /= cot45;
+
+	/*
+	 * On some machines, we get cotd(270) = minus zero, but this isn't always
+	 * true.  For portability, and because the user constituency for this
+	 * function probably doesn't want minus zero, force it to plain zero.
+	 */
+	if (result == 0.0)
+		result = 0.0;
+
 	CHECKFLOATVAL(result, true /* cotd(0) == Inf */ , true);
 	PG_RETURN_FLOAT8(result);
 }
@@ -2133,8 +2157,9 @@ Datum
 dtand(PG_FUNCTION_ARGS)
 {
 	float8		arg1 = PG_GETARG_FLOAT8(0);
-	int			sign = 1;
 	float8		result;
+	int			sign = 1;
+	static float8 tan45 = 0.0;

 	/*
 	 * Per the POSIX spec, return NaN if the input is NaN and throw an error
@@ -2174,6 +2199,26 @@ dtand(PG_FUNCTION_ARGS)

 	result = sign * sind_q1(arg1) / cosd_q1(arg1);

+	/*
+	 * We want tand(45) to be exactly 1, but the above computation might've
+	 * produced something different, so scale to get the right result.  To
+	 * avoid redoing sind_q1(45) / cosd_q1(45) many times, and to prevent the
+	 * compiler from maybe rearranging the calculation, cache that value in a
+	 * static variable.
+	 */
+	if (tan45 == 0.0)
+		tan45 = sind_q1(45.0) / cosd_q1(45.0);
+
+	result /= tan45;
+
+	/*
+	 * On some machines, we get tand(180) = minus zero, but this isn't always
+	 * true.  For portability, and because the user constituency for this
+	 * function probably doesn't want minus zero, force it to plain zero.
+	 */
+	if (result == 0.0)
+		result = 0.0;
+
 	CHECKFLOATVAL(result, true /* tand(90) == Inf */ , true);
 	PG_RETURN_FLOAT8(result);
 }
@@ -2188,7 +2233,7 @@ degrees(PG_FUNCTION_ARGS)
 	float8		arg1 = PG_GETARG_FLOAT8(0);
 	float8		result;

-	result = arg1 * (180.0 / M_PI);
+	result = arg1 / RADIANS_PER_DEGREE;

 	CHECKFLOATVAL(result, isinf(arg1), arg1 == 0);
 	PG_RETURN_FLOAT8(result);
@@ -2214,7 +2259,7 @@ radians(PG_FUNCTION_ARGS)
 	float8		arg1 = PG_GETARG_FLOAT8(0);
 	float8		result;

-	result = arg1 * (M_PI / 180.0);
+	result = arg1 * RADIANS_PER_DEGREE;

 	CHECKFLOATVAL(result, isinf(arg1), arg1 == 0);
 	PG_RETURN_FLOAT8(result);

--- a/src/test/regress/expected/float8-exp-three-digits-win32.out
+++ b/src/test/regress/expected/float8-exp-three-digits-win32.out
@@ -467,13 +467,13 @@ FROM generate_series(0, 360, 15) AS t(x);
 135 |      |      |        -1 |        -1
 150 |  0.5 |      |           |          
 165 |      |      |           |          
- 180 |    0 |   -1 |        -0 | -Infinity
+ 180 |    0 |   -1 |         0 | -Infinity
 195 |      |      |           |          
 210 | -0.5 |      |           |          
 225 |      |      |         1 |         1
 240 |      | -0.5 |           |          
 255 |      |      |           |          
- 270 |   -1 |    0 | -Infinity |        -0
+ 270 |   -1 |    0 | -Infinity |         0
 285 |      |      |           |          
 300 |      |  0.5 |           |          
 315 |      |      |        -1 |        -1

--- a/src/test/regress/expected/float8-small-is-zero.out
+++ b/src/test/regress/expected/float8-small-is-zero.out
@@ -465,13 +465,13 @@ FROM generate_series(0, 360, 15) AS t(x);
 135 |      |      |        -1 |        -1
 150 |  0.5 |      |           |          
 165 |      |      |           |          
- 180 |    0 |   -1 |        -0 | -Infinity
+ 180 |    0 |   -1 |         0 | -Infinity
 195 |      |      |           |          
 210 | -0.5 |      |           |          
 225 |      |      |         1 |         1
 240 |      | -0.5 |           |          
 255 |      |      |           |          
- 270 |   -1 |    0 | -Infinity |        -0
+ 270 |   -1 |    0 | -Infinity |         0
 285 |      |      |           |          
 300 |      |  0.5 |           |          
 315 |      |      |        -1 |        -1

--- a/src/test/regress/expected/float8-small-is-zero_1.out
+++ b/src/test/regress/expected/float8-small-is-zero_1.out
@@ -465,13 +465,13 @@ FROM generate_series(0, 360, 15) AS t(x);
 135 |      |      |        -1 |        -1
 150 |  0.5 |      |           |          
 165 |      |      |           |          
- 180 |    0 |   -1 |        -0 | -Infinity
+ 180 |    0 |   -1 |         0 | -Infinity
 195 |      |      |           |          
 210 | -0.5 |      |           |          
 225 |      |      |         1 |         1
 240 |      | -0.5 |           |          
 255 |      |      |           |          
- 270 |   -1 |    0 | -Infinity |        -0
+ 270 |   -1 |    0 | -Infinity |         0
 285 |      |      |           |          
 300 |      |  0.5 |           |          
 315 |      |      |        -1 |        -1

--- a/src/test/regress/expected/float8.out
+++ b/src/test/regress/expected/float8.out
@@ -467,13 +467,13 @@ FROM generate_series(0, 360, 15) AS t(x);
 135 |      |      |        -1 |        -1
 150 |  0.5 |      |           |          
 165 |      |      |           |          
- 180 |    0 |   -1 |        -0 | -Infinity
+ 180 |    0 |   -1 |         0 | -Infinity
 195 |      |      |           |          
 210 | -0.5 |      |           |          
 225 |      |      |         1 |         1
 240 |      | -0.5 |           |          
 255 |      |      |           |          
- 270 |   -1 |    0 | -Infinity |        -0
+ 270 |   -1 |    0 | -Infinity |         0
 285 |      |      |           |          
 300 |      |  0.5 |           |          
 315 |      |      |        -1 |        -1