acosh.c raw

   1  #include "libm.h"
   2  
   3  #if FLT_EVAL_METHOD==2
   4  #undef sqrt
   5  #define sqrt sqrtl
   6  #endif
   7  
   8  /* acosh(x) = log(x + sqrt(x*x-1)) */
   9  double acosh(double x)
  10  {
  11  	union {double f; uint64_t i;} u = {.f = x};
  12  	unsigned e = u.i >> 52 & 0x7ff;
  13  
  14  	/* x < 1 domain error is handled in the called functions */
  15  
  16  	if (e < 0x3ff + 1)
  17  		/* |x| < 2, up to 2ulp error in [1,1.125] */
  18  		return log1p(x-1 + sqrt((x-1)*(x-1)+2*(x-1)));
  19  	if (e < 0x3ff + 26)
  20  		/* |x| < 0x1p26 */
  21  		return log(2*x - 1/(x+sqrt(x*x-1)));
  22  	/* |x| >= 0x1p26 or nan */
  23  	return log(x) + 0.693147180559945309417232121458176568;
  24  }
  25