src/math/atanhl.c

   1 #include "libm.h"
   2
   3 #if LDBL_MANT_DIG == 53 && LDBL_MAX_EXP == 1024
   4 long double atanhl(long double x)
   5 {
   6         return atanh(x);
   7 }
   8 #elif (LDBL_MANT_DIG == 64 || LDBL_MANT_DIG == 113) && LDBL_MAX_EXP == 16384
   9 /* atanh(x) = log((1+x)/(1-x))/2 = log1p(2x/(1-x))/2 ~= x + x^3/3 + o(x^5) */
  10 long double atanhl(long double x)
  11 {
  12         union ldshape u = {x};
  13         unsigned e = u.i.se & 0x7fff;
  14         unsigned s = u.i.se >> 15;
  15
  16         /* |x| */
  17         u.i.se = e;
  18         x = u.f;
  19
  20         if (e < 0x3ff - 1) {
  21                 if (e < 0x3ff - LDBL_MANT_DIG/2) {
  22                         /* handle underflow */
  23                         if (e == 0)
  24                                 FORCE_EVAL((float)x);
  25                 } else {
  26                         /* |x| < 0.5, up to 1.7ulp error */
  27                         x = 0.5*log1pl(2*x + 2*x*x/(1-x));
  28                 }
  29         } else {
  30                 /* avoid overflow */
  31                 x = 0.5*log1pl(2*(x/(1-x)));
  32         }
  33         return s ? -x : x;
  34 }
  35 #endif