math: clean up inverse trigonometric functions

[musl] / src / math / asinl.c

diff --git a/src/math/asinl.c b/src/math/asinl.c
index 7572767..0ef9853 100644 (file)
--- a/src/math/asinl.c
+++ b/src/math/asinl.c
@@ -23,60 +23,49 @@ long double asinl(long double x)
 }
 #elif (LDBL_MANT_DIG == 64 || LDBL_MANT_DIG == 113) && LDBL_MAX_EXP == 16384
 #include "__invtrigl.h"
-static const long double huge = 1.000e+300;
-static const long double pio4_hi = 7.85398163397448309628e-01L;
-#define ASIN_LINEAR     (BIAS - 32)     /* 2**-32 */
 /* 0.95 */
-#define THRESH  ((0xe666666666666666ULL>>(64-(MANH_SIZE-1)))|LDBL_NBIT)
+#define THRESH  ((0xe666666666666666ULL>>(64-(LDBL_MANH_SIZE-1)))|LDBL_NBIT)
 
 long double asinl(long double x)
 {
        union IEEEl2bits u;
-       long double t=0.0,w,p,q,c,r,s;
-       int16_t expsign, expt;
+       long double z,r,s;
+       uint16_t expsign, expt;
 
        u.e = x;
        expsign = u.xbits.expsign;
        expt = expsign & 0x7fff;
-       if (expt >= BIAS) {          /* |x|>= 1 */
-               if (expt == BIAS &&
+       if (expt >= 0x3fff) {   /* |x| >= 1 or nan */
+               if (expt == 0x3fff &&
                    ((u.bits.manh&~LDBL_NBIT)|u.bits.manl) == 0)
-                       /* asin(1)=+-pi/2 with inexact */
-                       return x*pio2_hi + x*pio2_lo;
-               return (x-x)/(x-x);  /* asin(|x|>1) is NaN */
-       } else if (expt < BIAS-1) {  /* |x|<0.5 */
-               if (expt < ASIN_LINEAR) {  /* if |x| is small, asinl(x)=x */
+                       /* asin(+-1)=+-pi/2 with inexact */
+                       return x*pio2_hi + 0x1p-1000;
+               return 0/(x-x);
+       }
+       if (expt < 0x3fff - 1) {  /* |x| < 0.5 */
+               if (expt < 0x3fff - 32) {  /* |x|<0x1p-32, asinl(x)=x */
                        /* return x with inexact if x!=0 */
-                       if (huge+x > 1.0)
-                               return x;
+                       FORCE_EVAL(x + 0x1p1000);
+                       return x;
                }
-               t = x*x;
-               p = P(t);
-               q = Q(t);
-               w = p/q;
-               return x + x*w;
+               return x + x*__invtrigl_R(x*x);
        }
        /* 1 > |x| >= 0.5 */
-       w = 1.0 - fabsl(x);
-       t = w*0.5;
-       p = P(t);
-       q = Q(t);
-       s = sqrtl(t);
+       z = (1.0 - fabsl(x))*0.5;
+       s = sqrtl(z);
+       r = __invtrigl_R(z);
        if (u.bits.manh >= THRESH) { /* if |x| is close to 1 */
-               w = p/q;
-               t = pio2_hi-(2.0*(s+s*w)-pio2_lo);
+               x = pio2_hi - (2*(s+s*r)-pio2_lo);
        } else {
+               long double f, c;
                u.e = s;
                u.bits.manl = 0;
-               w = u.e;
-               c = (t-w*w)/(s+w);
-               r = p/q;
-               p = 2.0*s*r-(pio2_lo-2.0*c);
-               q = pio4_hi-2.0*w;
-               t = pio4_hi-(p-q);
+               f = u.e;
+               c = (z-f*f)/(s+f);
+               x = 0.5*pio2_hi-(2*s*r - (pio2_lo-2*c) - (0.5*pio2_hi-2*f));
        }
-       if (expsign > 0)
-               return t;
-       return -t;
+       if (expsign>>15)
+               return -x;
+       return x;
 }
 #endif