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  1. #include <math.h>
  2. #include <errno.h>
  3. #include "fastmath.h"
  4.  
  5.  /* asinh(x) = copysign(log(fabs(x) + sqrt(x * x + 1.0)), x) */
  6. double asinh(double x)
  7. {
  8.   double z;
  9.   if (!isfinite (x))
  10.     return x;
  11.   z = fabs (x);
  12.  
  13.   /* Avoid setting FPU underflow exception flag in x * x. */
  14. #if 0
  15.   if ( z < 0x1p-32)
  16.     return x;
  17. #endif
  18.  
  19.   /* Use log1p to avoid cancellation with small x. Put
  20.      x * x in denom, so overflow is harmless.
  21.      asinh(x) = log1p (x + sqrt (x * x + 1.0) - 1.0)
  22.               = log1p (x + x * x / (sqrt (x * x + 1.0) + 1.0))  */
  23.  
  24.   z = __fast_log1p (z + z * z / (__fast_sqrt (z * z + 1.0) + 1.0));
  25.  
  26.   return ( x > 0.0 ? z : -z);
  27. }
  28.  
  29.