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  1. #include <math.h>
  2. #include <errno.h>
  3. #include "fastmath.h"
  4.  
  5. /* acosh(x) = log (x + sqrt(x * x - 1)) */
  6. float acoshf (float x)
  7. {
  8.   if (isnan (x))
  9.     return x;
  10.   if (x < 1.0f)
  11.     {
  12.       errno = EDOM;
  13.       return nan("");
  14.     }
  15.  
  16.  if (x > 0x1p32f)
  17.     /*  Avoid overflow (and unnecessary calculation when
  18.         sqrt (x * x - 1) == x). GCC optimizes by replacing
  19.         the long double M_LN2 const with a fldln2 insn.  */
  20.     return __fast_log (x) + 6.9314718055994530941723E-1L;
  21.  
  22.   /* Since  x >= 1, the arg to log will always be greater than
  23.      the fyl2xp1 limit (approx 0.29) so just use logl. */
  24.   return __fast_log (x + __fast_sqrt((x + 1.0) * (x - 1.0)));
  25. }
  26.