36  *
  37  * For better accuracy, 1-x*x is computed as follows
  38  *      1-x*x                     if x <  0.5,
  39  *      2*(1-|x|)-(1-|x|)*(1-|x|) if x >= 0.5.
  40  *
  41  * Special cases:
  42  *      if x is NaN, return x itself;
  43  *      if |x|>1, return NaN with invalid signal.
  44  */
  45 
  46 #include "libm.h"
  47 
  48 static const long double zero = 0.0L, small = 1.0e-20L, half = 0.5L, one = 1.0L;
  49 #ifndef lint
  50 static const long double big = 1.0e+20L;
  51 #endif
  52 
  53 long double
  54 asinl(long double x) {
  55         long double t, w;

  56 
  57         w = fabsl(x);
  58         if (isnanl(x))
  59                 return (x + x);
  60         else if (w <= half) {
  61                 if (w < small) {
  62 #ifndef lint
  63                         volatile long double dummy = w + big;
  64                                                         /* inexact if w != 0 */
  65 #endif
  66                         return (x);
  67                 } else
  68                         return (atanl(x / sqrtl(one - x * x)));
  69         } else if (w < one) {
  70                 t = one - w;
  71                 w = t + t;
  72                 return (atanl(x / sqrtl(w - t * t)));
  73         } else if (w == one)
  74                 return (atan2l(x, zero));       /* asin(+-1) =  +- PI/2 */
  75         else
  76                 return (zero / zero);           /* |x| > 1: invalid */
  77 }

  36  *
  37  * For better accuracy, 1-x*x is computed as follows
  38  *      1-x*x                     if x <  0.5,
  39  *      2*(1-|x|)-(1-|x|)*(1-|x|) if x >= 0.5.
  40  *
  41  * Special cases:
  42  *      if x is NaN, return x itself;
  43  *      if |x|>1, return NaN with invalid signal.
  44  */
  45 
  46 #include "libm.h"
  47 
  48 static const long double zero = 0.0L, small = 1.0e-20L, half = 0.5L, one = 1.0L;
  49 #ifndef lint
  50 static const long double big = 1.0e+20L;
  51 #endif
  52 
  53 long double
  54 asinl(long double x) {
  55         long double t, w;
  56         volatile long double dummy;
  57 
  58         w = fabsl(x);
  59         if (isnanl(x))
  60                 return (x + x);
  61         else if (w <= half) {
  62                 if (w < small) {
  63 #ifndef lint
  64                         dummy = w + big;
  65                                                         /* inexact if w != 0 */
  66 #endif
  67                         return (x);
  68                 } else
  69                         return (atanl(x / sqrtl(one - x * x)));
  70         } else if (w < one) {
  71                 t = one - w;
  72                 w = t + t;
  73                 return (atanl(x / sqrtl(w - t * t)));
  74         } else if (w == one)
  75                 return (atan2l(x, zero));       /* asin(+-1) =  +- PI/2 */
  76         else
  77                 return (zero / zero);           /* |x| > 1: invalid */
  78 }