github.com/afumu/libc@v0.0.6/musl/src/math/asinh.c (about)

     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  }