math: fix __rem_pio2 in non-nearest rounding modes

[oweals/musl.git] / src / math / __rem_pio2l.c

diff --git a/src/math/__rem_pio2l.c b/src/math/__rem_pio2l.c
index 8b15b7b2a3d802192772fa2ea34dd583cfa2995f..236b2def3d276e52152794d7fc91e2a1820a0b08 100644 (file)
--- a/src/math/__rem_pio2l.c
+++ b/src/math/__rem_pio2l.c
@@ -20,10 +20,11 @@
  * use __rem_pio2_large() for large x
  */
 
+static const long double toint = 1.5/LDBL_EPSILON;
+
 #if LDBL_MANT_DIG == 64
 /* u ~< 0x1p25*pi/2 */
 #define SMALL(u) (((u.i.se & 0x7fffU)<<16 | u.i.m>>48) < ((0x3fff + 25)<<16 | 0x921f>>1 | 0x8000))
-#define TOINT 0x1.8p63
 #define QUOBITS(x) ((uint32_t)(int32_t)x & 0x7fffffff)
 #define ROUND1 22
 #define ROUND2 61
@@ -43,6 +44,7 @@ pio2_1 =  1.57079632679597125389e+00, /* 0x3FF921FB, 0x54444000 */
 pio2_2 = -1.07463465549783099519e-12, /* -0x12e7b967674000.0p-92 */
 pio2_3 =  6.36831716351370313614e-25; /*  0x18a2e037074000.0p-133 */
 static const long double
+pio4    =  0x1.921fb54442d1846ap-1L,
 invpio2 =  6.36619772367581343076e-01L, /*  0xa2f9836e4e44152a.0p-64 */
 pio2_1t = -1.07463465549719416346e-12L, /* -0x973dcb3b399d747f.0p-103 */
 pio2_2t =  6.36831716351095013979e-25L, /*  0xc51701b839a25205.0p-144 */
@@ -50,13 +52,13 @@ pio2_3t = -2.75299651904407171810e-37L; /* -0xbb5bf6c7ddd660ce.0p-185 */
 #elif LDBL_MANT_DIG == 113
 /* u ~< 0x1p45*pi/2 */
 #define SMALL(u) (((u.i.se & 0x7fffU)<<16 | u.i.top) < ((0x3fff + 45)<<16 | 0x921f))
-#define TOINT 0x1.8p112
 #define QUOBITS(x) ((uint32_t)(int64_t)x & 0x7fffffff)
 #define ROUND1 51
 #define ROUND2 119
 #define NX 5
 #define NY 3
 static const long double
+pio4    =  0x1.921fb54442d18469898cc51701b8p-1L,
 invpio2 =  6.3661977236758134307553505349005747e-01L,  /*  0x145f306dc9c882a53f84eafa3ea6a.0p-113 */
 pio2_1  =  1.5707963267948966192292994253909555e+00L,  /*  0x1921fb54442d18469800000000000.0p-112 */
 pio2_1t =  2.0222662487959507323996846200947577e-21L,  /*  0x13198a2e03707344a4093822299f3.0p-181 */
@@ -76,11 +78,23 @@ int __rem_pio2l(long double x, long double *y)
        u.f = x;
        ex = u.i.se & 0x7fff;
        if (SMALL(u)) {
-               /* rint(x/(pi/2)), Assume round-to-nearest. */
-               fn = x*invpio2 + TOINT - TOINT;
+               /* rint(x/(pi/2)) */
+               fn = x*invpio2 + toint - toint;
                n = QUOBITS(fn);
                r = x-fn*pio2_1;
                w = fn*pio2_1t;  /* 1st round good to 102/180 bits (ld80/ld128) */
+               /* 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.se & 0x7fff;