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, 10 insertions, 3 deletions

diff --git a/src/math/__rem_pio2f.c b/src/math/__rem_pio2f.c
index 838e1fca..f5163856 100644
--- a/src/math/__rem_pio2f.c
+++ b/src/math/__rem_pio2f.c
@@ -22,12 +22,19 @@
 
 #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
+
 /*
  * invpio2:  53 bits of 2/pi
  * pio2_1:   first 25 bits of pi/2
  * pio2_1t:  pi/2 - pio2_1
  */
 static const double
+toint   = 1.5/EPS,
 invpio2 = 6.36619772367581382433e-01, /* 0x3FE45F30, 0x6DC9C883 */
 pio2_1  = 1.57079631090164184570e+00, /* 0x3FF921FB, 0x50000000 */
 pio2_1t = 1.58932547735281966916e-08; /* 0x3E5110b4, 0x611A6263 */
@@ -35,7 +42,8 @@ pio2_1t = 1.58932547735281966916e-08; /* 0x3E5110b4, 0x611A6263 */
 int __rem_pio2f(float x, double *y)
 {
 	union {float f; uint32_t i;} u = {x};
-	double tx[1],ty[1],fn;
+	double tx[1],ty[1];
+	double_t fn;
 	uint32_t ix;
 	int n, sign, e0;
 
@@ -43,8 +51,7 @@ int __rem_pio2f(float x, double *y)
 	/* 25+53 bit pi is good enough for medium size */
 	if (ix < 0x4dc90fdb) {  /* |x| ~< 2^28*(pi/2), medium size */
 		/* Use a specialized rint() to get fn.  Assume round-to-nearest. */
-		fn = x*invpio2 + 0x1.8p52;
-		fn = fn - 0x1.8p52;
+		fn = x*invpio2 + toint - toint;
 		n  = (int32_t)fn;
 		*y = x - fn*pio2_1 - fn*pio2_1t;
 		return n;