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