src/math/atanhf.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 float atanhf(float x)
   5 {
   6         union {float f; uint32_t i;} u = {.f = x};
   7         unsigned s = u.i >> 31;
   8         float_t y;
   9
  10         /* |x| */
  11         u.i &= 0x7fffffff;
  12         y = u.f;
  13
  14         if (u.i < 0x3f800000 - (1<<23)) {
  15                 if (u.i < 0x3f800000 - (32<<23)) {
  16                         /* handle underflow */
  17                         if (u.i < (1<<23))
  18                                 FORCE_EVAL((float)(y*y));
  19                 } else {
  20                         /* |x| < 0.5, up to 1.7ulp error */
  21                         y = 0.5f*log1pf(2*y + 2*y*y/(1-y));
  22                 }
  23         } else {
  24                 /* avoid overflow */
  25                 y = 0.5f*log1pf(2*(y/(1-y)));
  26         }
  27         return s ? -y : y;
  28 }