#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 33 bit of pi/2
* pio2_3t: pi/2 - (pio2_1+pio2_2+pio2_3)
*/
static const double
+toint = 1.5/EPS,
+pio4 = 0x1.921fb54442d18p-1,
invpio2 = 6.36619772367581382433e-01, /* 0x3FE45F30, 0x6DC9C883 */
pio2_1 = 1.57079632673412561417e+00, /* 0x3FF921FB, 0x54400000 */
pio2_1t = 6.07710050650619224932e-11, /* 0x3DD0B461, 0x1A626331 */
int __rem_pio2(double x, double *y)
{
union {double f; uint64_t i;} u = {x};
- double_t z,w,t,r;
- double tx[3],ty[2],fn;
+ double_t z,w,t,r,fn;
+ double tx[3],ty[2];
uint32_t ix;
int sign, n, ex, ey, i;
}
if (ix < 0x413921fb) { /* |x| ~< 2^20*(pi/2), medium size */
medium:
- /* rint(x/(pi/2)), Assume round-to-nearest. */
- fn = x*invpio2 + 0x1.8p52;
- fn = fn - 0x1.8p52;
+ /* rint(x/(pi/2)) */
+ fn = (double_t)x*invpio2 + toint - toint;
n = (int32_t)fn;
r = x - fn*pio2_1;
w = fn*pio2_1t; /* 1st round, good to 85 bits */
+ /* Matters with directed rounding. */
+ if (predict_false(r - w < -pio4)) {
+ n--;
+ fn--;
+ r = x - fn*pio2_1;
+ w = fn*pio2_1t;
+ } else if (predict_false(r - w > pio4)) {
+ n++;
+ fn++;
+ r = x - fn*pio2_1;
+ w = fn*pio2_1t;
+ }
y[0] = r - w;
u.f = y[0];
ey = u.i>>52 & 0x7ff;