Yet more portability hacking for degree-based trig functions.

The true explanation for Peter Eisentraut's report of inexact asind results
seems to be that (a) he's compiling into x87 instruction set, which uses
wider-than-double float registers, plus (b) the library function asin() on
his platform returns a result that is wider than double and is not rounded
to double width.  To fix, we have to force the function's result to be
rounded comparably to what happened to the scaling constant asin_0_5.
Experimentation suggests that storing it into a volatile local variable is
the least ugly way of making that happen.  Although only asin() is known to
exhibit an observable inexact result, we'd better do this in all the places
where we're hoping to get an exact result by scaling.

Author: tglsfdc

src/backend/utils/adt/float.c

@@ -1830,6 +1830,19 @@ dtan(PG_FUNCTION_ARGS)
  * Other hazards we are trying to forestall with this kluge include the
  * possibility that compilers will rearrange the expressions, or compute
  * some intermediate results in registers wider than a standard double.
+ *
+ * In the places where we use these constants, the typical pattern is like
+ *		volatile float8 sin_x = sin(x * RADIANS_PER_DEGREE);
+ *		return (sin_x / sin_30);
+ * where we hope to get a value of exactly 1.0 from the division when x = 30.
+ * The volatile temporary variable is needed on machines with wide float
+ * registers, to ensure that the result of sin(x) is rounded to double width
+ * the same as the value of sin_30 has been.  Experimentation with gcc shows
+ * that marking the temp variable volatile is necessary to make the store and
+ * reload actually happen; hopefully the same trick works for other compilers.
+ * (gcc's documentation suggests using the -ffloat-store compiler switch to
+ * ensure this, but that is compiler-specific and it also pessimizes code in
+ * many places where we don't care about this.)
  */
 static void
 init_degree_constants(void)
@@ -1870,9 +1883,17 @@ asind_q1(double x)
 	 * over the full range.
 	 */
 	if (x <= 0.5)
-		return (asin(x) / asin_0_5) * 30.0;
+	{
+		volatile float8 asin_x = asin(x);
+
+		return (asin_x / asin_0_5) * 30.0;
+	}
 	else
-		return 90.0 - (acos(x) / acos_0_5) * 60.0;
+	{
+		volatile float8 acos_x = acos(x);
+
+		return 90.0 - (acos_x / acos_0_5) * 60.0;
+	}
 }
 
 
@@ -1895,9 +1916,17 @@ acosd_q1(double x)
 	 * over the full range.
 	 */
 	if (x <= 0.5)
-		return 90.0 - (asin(x) / asin_0_5) * 30.0;
+	{
+		volatile float8 asin_x = asin(x);
+
+		return 90.0 - (asin_x / asin_0_5) * 30.0;
+	}
 	else
-		return (acos(x) / acos_0_5) * 60.0;
+	{
+		volatile float8 acos_x = acos(x);
+
+		return (acos_x / acos_0_5) * 60.0;
+	}
 }
 
 
@@ -1979,6 +2008,7 @@ datand(PG_FUNCTION_ARGS)
 {
 	float8		arg1 = PG_GETARG_FLOAT8(0);
 	float8		result;
+	volatile float8 atan_arg1;
 
 	/* Per the POSIX spec, return NaN if the input is NaN */
 	if (isnan(arg1))
@@ -1992,7 +2022,8 @@ datand(PG_FUNCTION_ARGS)
 	 * even if the input is infinite.  Additionally, we take care to ensure
 	 * than when arg1 is 1, the result is exactly 45.
 	 */
-	result = (atan(arg1) / atan_1_0) * 45.0;
+	atan_arg1 = atan(arg1);
+	result = (atan_arg1 / atan_1_0) * 45.0;
 
 	CHECKFLOATVAL(result, false, true);
 	PG_RETURN_FLOAT8(result);
@@ -2008,6 +2039,7 @@ datan2d(PG_FUNCTION_ARGS)
 	float8		arg1 = PG_GETARG_FLOAT8(0);
 	float8		arg2 = PG_GETARG_FLOAT8(1);
 	float8		result;
+	volatile float8 atan2_arg1_arg2;
 
 	/* Per the POSIX spec, return NaN if either input is NaN */
 	if (isnan(arg1) || isnan(arg2))
@@ -2018,8 +2050,14 @@ datan2d(PG_FUNCTION_ARGS)
 	/*
 	 * atan2d maps all inputs to values in the range [-180, 180], so the
 	 * result should always be finite, even if the inputs are infinite.
+	 *
+	 * Note: this coding assumes that atan(1.0) is a suitable scaling constant
+	 * to get an exact result from atan2().  This might well fail on us at
+	 * some point, requiring us to decide exactly what inputs we think we're
+	 * going to guarantee an exact result for.
 	 */
-	result = (atan2(arg1, arg2) / atan_1_0) * 45.0;
+	atan2_arg1_arg2 = atan2(arg1, arg2);
+	result = (atan2_arg1_arg2 / atan_1_0) * 45.0;
 
 	CHECKFLOATVAL(result, false, true);
 	PG_RETURN_FLOAT8(result);
@@ -2034,7 +2072,9 @@ datan2d(PG_FUNCTION_ARGS)
 static double
 sind_0_to_30(double x)
 {
-	return (sin(x * RADIANS_PER_DEGREE) / sin_30) / 2.0;
+	volatile float8 sin_x = sin(x * RADIANS_PER_DEGREE);
+
+	return (sin_x / sin_30) / 2.0;
 }
 
 
@@ -2046,7 +2086,7 @@ sind_0_to_30(double x)
 static double
 cosd_0_to_60(double x)
 {
-	float8		one_minus_cos_x = 1.0 - cos(x * RADIANS_PER_DEGREE);
+	volatile float8 one_minus_cos_x = 1.0 - cos(x * RADIANS_PER_DEGREE);
 
 	return 1.0 - (one_minus_cos_x / one_minus_cos_60) / 2.0;
 }
@@ -2153,6 +2193,7 @@ dcotd(PG_FUNCTION_ARGS)
 {
 	float8		arg1 = PG_GETARG_FLOAT8(0);
 	float8		result;
+	volatile float8 cot_arg1;
 	int			sign = 1;
 
 	/*
@@ -2193,7 +2234,8 @@ dcotd(PG_FUNCTION_ARGS)
 		sign = -sign;
 	}
 
-	result = sign * ((cosd_q1(arg1) / sind_q1(arg1)) / cot_45);
+	cot_arg1 = cosd_q1(arg1) / sind_q1(arg1);
+	result = sign * (cot_arg1 / cot_45);
 
 	/*
 	 * On some machines we get cotd(270) = minus zero, but this isn't always
@@ -2270,6 +2312,7 @@ dtand(PG_FUNCTION_ARGS)
 {
 	float8		arg1 = PG_GETARG_FLOAT8(0);
 	float8		result;
+	volatile float8 tan_arg1;
 	int			sign = 1;
 
 	/*
@@ -2310,7 +2353,8 @@ dtand(PG_FUNCTION_ARGS)
 		sign = -sign;
 	}
 
-	result = sign * ((sind_q1(arg1) / cosd_q1(arg1)) / tan_45);
+	tan_arg1 = sind_q1(arg1) / cosd_q1(arg1);
+	result = sign * (tan_arg1 / tan_45);
 
 	/*
 	 * On some machines we get tand(180) = minus zero, but this isn't always