1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
| | #include "libm.h"
/* tanh(x) = (exp(x) - exp(-x))/(exp(x) + exp(-x))
* = (exp(2*x) - 1)/(exp(2*x) - 1 + 2)
* = (1 - exp(-2*x))/(exp(-2*x) - 1 + 2)
*/
double tanh(double x)
{
union {double f; uint64_t i;} u = {.f = x};
uint32_t w;
int sign;
double t;
/* x = |x| */
sign = u.i >> 63;
u.i &= (uint64_t)-1/2;
x = u.f;
w = u.i >> 32;
if (w > 0x3fe193ea) {
/* |x| > log(3)/2 ~= 0.5493 or nan */
if (w > 0x40340000) {
/* |x| > 20 or nan */
/* note: this branch avoids raising overflow */
/* raise inexact if x!=+-inf and handle nan */
t = 1 + 0/(x + 0x1p-120f);
} else {
t = expm1(2*x);
t = 1 - 2/(t+2);
}
} else if (w > 0x3fd058ae) {
/* |x| > log(5/3)/2 ~= 0.2554 */
t = expm1(2*x);
t = t/(t+2);
} else {
/* |x| is small, up to 2ulp error in [0.1,0.2554] */
t = expm1(-2*x);
t = -t/(t+2);
}
return sign ? -t : t;
}
|