1 /*****************************************************************************/
2 /*****************************************************************************/
3 // asinhf from musl-0.9.15
4 /*****************************************************************************/
5 /*****************************************************************************/
6 
7 #include "libm.h"
8 
9 /* asinh(x) = sign(x)*log(|x|+sqrt(x*x+1)) ~= x - x^3/6 + o(x^5) */
asinhf(float x)10 float asinhf(float x)
11 {
12 	union {float f; uint32_t i;} u = {.f = x};
13 	uint32_t i = u.i & 0x7fffffff;
14 	unsigned s = u.i >> 31;
15 
16 	/* |x| */
17 	u.i = i;
18 	x = u.f;
19 
20 	if (i >= 0x3f800000 + (12<<23)) {
21 		/* |x| >= 0x1p12 or inf or nan */
22 		x = logf(x) + 0.693147180559945309417232121458176568f;
23 	} else if (i >= 0x3f800000 + (1<<23)) {
24 		/* |x| >= 2 */
25 		x = logf(2*x + 1/(sqrtf(x*x+1)+x));
26 	} else if (i >= 0x3f800000 - (12<<23)) {
27 		/* |x| >= 0x1p-12, up to 1.6ulp error in [0.125,0.5] */
28 		x = log1pf(x + x*x/(sqrtf(x*x+1)+1));
29 	} else {
30 		/* |x| < 0x1p-12, raise inexact if x!=0 */
31 		FORCE_EVAL(x + 0x1p120f);
32 	}
33 	return s ? -x : x;
34 }
35