math: fix __rem_pio2 in non-nearest rounding modes

[musl] / src / math / __rem_pio2.c

diff --git a/src/math/__rem_pio2.c b/src/math/__rem_pio2.c
index 5fafc4a..dcf672f 100644 (file)
--- a/src/math/__rem_pio2.c
+++ b/src/math/__rem_pio2.c
@@ -19,6 +19,12 @@
 
 #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
+
 /*
  * invpio2:  53 bits of 2/pi
  * pio2_1:   first  33 bit of pi/2
@@ -29,6 +35,8 @@
  * 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 */
@@ -41,8 +49,8 @@ pio2_3t = 8.47842766036889956997e-32; /* 0x397B839A, 0x252049C1 */
 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;
 
@@ -110,12 +118,23 @@ int __rem_pio2(double x, double *y)
        }
        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;