1 /**
2 * This file has no copyright assigned and is placed in the Public Domain.
3 * This file is part of the mingw-w64 runtime package.
4 * No warranty is given; refer to the file DISCLAIMER.PD within this package.
5 */
6 #include <math.h>
7 #include <errno.h>
8 #include "fastmath.h"
9
10 /* asinh(x) = copysign(log(fabs(x) + sqrt(x * x + 1.0)), x) */
asinh(double x)11 double asinh(double x)
12 {
13 double z;
14 if (!isfinite (x))
15 return x;
16 z = fabs (x);
17
18 /* Avoid setting FPU underflow exception flag in x * x. */
19 #if 0
20 if ( z < 0x1p-32)
21 return x;
22 #endif
23
24 /* Use log1p to avoid cancellation with small x. Put
25 x * x in denom, so overflow is harmless.
26 asinh(x) = log1p (x + sqrt (x * x + 1.0) - 1.0)
27 = log1p (x + x * x / (sqrt (x * x + 1.0) + 1.0)) */
28
29 z = __fast_log1p (z + z * z / (__fast_sqrt (z * z + 1.0) + 1.0));
30
31 return ( x > 0.0 ? z : -z);
32 }
33
34