asinh.c raw

   1  #include "libm.h"
   2  
   3  /* asinh(x) = sign(x)*log(|x|+sqrt(x*x+1)) ~= x - x^3/6 + o(x^5) */
   4  double asinh(double x)
   5  {
   6  	union {double f; uint64_t i;} u = {.f = x};
   7  	unsigned e = u.i >> 52 & 0x7ff;
   8  	unsigned s = u.i >> 63;
   9  
  10  	/* |x| */
  11  	u.i &= (uint64_t)-1/2;
  12  	x = u.f;
  13  
  14  	if (e >= 0x3ff + 26) {
  15  		/* |x| >= 0x1p26 or inf or nan */
  16  		x = log(x) + 0.693147180559945309417232121458176568;
  17  	} else if (e >= 0x3ff + 1) {
  18  		/* |x| >= 2 */
  19  		x = log(2*x + 1/(sqrt(x*x+1)+x));
  20  	} else if (e >= 0x3ff - 26) {
  21  		/* |x| >= 0x1p-26, up to 1.6ulp error in [0.125,0.5] */
  22  		x = log1p(x + x*x/(sqrt(x*x+1)+1));
  23  	} else {
  24  		/* |x| < 0x1p-26, raise inexact if x != 0 */
  25  		FORCE_EVAL(x + 0x1p120f);
  26  	}
  27  	return s ? -x : x;
  28  }
  29