math: clean up inverse trigonometric functions

[musl] / src / math / acosl.c

diff --git a/src/math/acosl.c b/src/math/acosl.c
index 83857d4..9e9b01e 100644 (file)
--- a/src/math/acosl.c
+++ b/src/math/acosl.c
@@ -23,55 +23,46 @@ long double acosl(long double x)
 }
 #elif (LDBL_MANT_DIG == 64 || LDBL_MANT_DIG == 113) && LDBL_MAX_EXP == 16384
 #include "__invtrigl.h"
-#define ACOS_CONST      (BIAS - 65)     /* 2**-65 */
 
 long double acosl(long double x)
 {
        union IEEEl2bits u;
-       long double z, p, q, r, w, s, c, df;
+       long double z, w, s, c, df;
        int16_t expsign, expt;
        u.e = x;
        expsign = u.xbits.expsign;
        expt = expsign & 0x7fff;
-       if (expt >= BIAS) {        /* |x| >= 1 */
-               if (expt == BIAS &&
+       /* |x| >= 1 or nan */
+       if (expt >= 0x3fff) {
+               if (expt == 0x3fff &&
                        ((u.bits.manh & ~LDBL_NBIT) | u.bits.manl) == 0) {
                        if (expsign > 0)
-                               return 0.0;  /* acos(1) = 0 */
-                       else
-                               // FIXME
-                               return pi_hi + 2.0 * pio2_lo;  /* acos(-1)= pi */
+                               return 0;  /* acos(1) = 0 */
+                       return 2*pio2_hi + 0x1p-1000;  /* acos(-1)= pi */
                }
-               return (x - x) / (x - x);  /* acos(|x|>1) is NaN */
+               return 0/(x-x);  /* acos(|x|>1) is NaN */
        }
-       if (expt < BIAS - 1) {     /* |x| < 0.5 */
-               if (expt < ACOS_CONST)
-                       return pio2_hi + pio2_lo;  /* x tiny: acosl=pi/2 */
-               z = x * x;
-               p = P(z);
-               q = Q(z);
-               r = p / q;
-               return pio2_hi - (x - (pio2_lo - x * r));
-       } else if (expsign < 0) {  /* x < -0.5 */
+       /* |x| < 0.5 */
+       if (expt < 0x3fff - 1) {
+               if (expt < 0x3fff - 65)
+                       return pio2_hi + 0x1p-1000;  /* x < 0x1p-65: acosl(x)=pi/2 */
+               return pio2_hi - (x - (pio2_lo - x * __invtrigl_R(x*x)));
+       }
+       /* x < -0.5 */
+       if (expsign < 0) {
                z = (1.0 + x) * 0.5;
-               p = P(z);
-               q = Q(z);
-               s = sqrtl(z);
-               r = p / q;
-               w = r * s - pio2_lo;
-               return pi_hi - 2.0 * (s + w);
-       } else {                   /* x > 0.5 */
-               z = (1.0 - x) * 0.5;
                s = sqrtl(z);
-               u.e = s;
-               u.bits.manl = 0;
-               df = u.e;
-               c = (z - df * df) / (s + df);
-               p = P(z);
-               q = Q(z);
-               r = p / q;
-               w = r * s + c;
-               return 2.0 * (df + w);
+               w = __invtrigl_R(z) * s - pio2_lo;
+               return 2*(pio2_hi - (s + w));
        }
+       /* x > 0.5 */
+       z = (1.0 - x) * 0.5;
+       s = sqrtl(z);
+       u.e = s;
+       u.bits.manl = 0;
+       df = u.e;
+       c = (z - df * df) / (s + df);
+       w = __invtrigl_R(z) * s + c;
+       return 2*(df + w);
 }
 #endif