libc-top-half/musl/src/math/atanh.c

   1 #include "libm.h"
   2
   3 /* atanh(x) = log((1+x)/(1-x))/2 = log1p(2x/(1-x))/2 ~= x + x^3/3 + o(x^5) */
   4 double atanh(double x)
   5 {
   6         union {double f; uint64_t i;} u = {.f = x};
   7         unsigned e = u.i >> 52 & 0x7ff;
   8         unsigned s = u.i >> 63;
   9         double_t y;
  10
  11         /* |x| */
  12         u.i &= (uint64_t)-1/2;
  13         y = u.f;
  14
  15         if (e < 0x3ff - 1) {
  16                 if (e < 0x3ff - 32) {
  17                         /* handle underflow */
  18                         if (e == 0)
  19                                 FORCE_EVAL((float)y);
  20                 } else {
  21                         /* |x| < 0.5, up to 1.7ulp error */
  22                         y = 0.5*log1p(2*y + 2*y*y/(1-y));
  23                 }
  24         } else {
  25                 /* avoid overflow */
  26                 y = 0.5*log1p(2*(y/(1-y)));
  27         }
  28         return s ? -y : y;
  29 }