math: use the rounding idiom consistently

the idiomatic rounding of x is

  n = x + toint - toint;

where toint is either 1/EPSILON (x is non-negative) or 1.5/EPSILON
(x may be negative and nearest rounding mode is assumed) and EPSILON is
according to the evaluation precision (the type of toint is not very
important, because single precision float can represent the 1/EPSILON of
ieee binary128).

in case of FLT_EVAL_METHOD!=0 this avoids a useless store to double or
float precision, and the long double code became cleaner with
1/LDBL_EPSILON instead of ifdefs for toint.

__rem_pio2f and __rem_pio2 functions slightly changed semantics:
on i386 a double-rounding is avoided so close to half-way cases may
get evaluated differently eg. as sin(pi/4-eps) instead of cos(pi/4+eps)

1 files changed, 9 insertions, 2 deletions

diff --git a/src/math/floor.c b/src/math/floor.c
index ebc9fabe..14a31cd8 100644
--- a/src/math/floor.c
+++ b/src/math/floor.c
@@ -1,5 +1,12 @@
 #include "libm.h"
 
+#if FLT_EVAL_METHOD==0 || FLT_EVAL_METHOD==1
+#define EPS DBL_EPSILON
+#elif FLT_EVAL_METHOD==2
+#define EPS LDBL_EPSILON
+#endif
+static const double_t toint = 1/EPS;
+
 double floor(double x)
 {
 	union {double f; uint64_t i;} u = {x};
@@ -10,9 +17,9 @@ double floor(double x)
 		return x;
 	/* y = int(x) - x, where int(x) is an integer neighbor of x */
 	if (u.i >> 63)
-		y = (double)(x - 0x1p52) + 0x1p52 - x;
+		y = x - toint + toint - x;
 	else
-		y = (double)(x + 0x1p52) - 0x1p52 - x;
+		y = x + toint - toint - x;
 	/* special case because of non-nearest rounding modes */
 	if (e <= 0x3ff-1) {
 		FORCE_EVAL(y);