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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. long double asinhl(long double x)
  7. {
  8.   long double z;
  9.   if (!isfinite (x))
  10.     return x;
  11.  
  12.   z = fabsl (x);
  13.  
  14.   /* Avoid setting FPU underflow exception flag in x * x. */
  15. #if 0
  16.   if ( z < 0x1p-32)
  17.     return x;
  18. #endif
  19.  
  20.   /* Use log1p to avoid cancellation with small x. Put
  21.      x * x in denom, so overflow is harmless.
  22.      asinh(x) = log1p (x + sqrt (x * x + 1.0) - 1.0)
  23.               = log1p (x + x * x / (sqrt (x * x + 1.0) + 1.0))  */
  24.  
  25.   z = __fast_log1pl (z + z * z / (__fast_sqrtl (z * z + 1.0L) + 1.0L));
  26.  
  27.   return ( x > 0.0 ? z : -z);
  28. }
  29.