1#include "libm.h"
 2
 3/* sinh(x) = (exp(x) - 1/exp(x))/2
 4 *         = (exp(x)-1 + (exp(x)-1)/exp(x))/2
 5 *         = x + x^3/6 + o(x^5)
 6 */
 7double sinh(double x)
 8{
 9	union {double f; uint64_t i;} u = {.f = x};
10	uint32_t w;
11	double t, h, absx;
12
13	h = 0.5;
14	if (u.i >> 63)
15		h = -h;
16	/* |x| */
17	u.i &= (uint64_t)-1/2;
18	absx = u.f;
19	w = u.i >> 32;
20
21	/* |x| < log(DBL_MAX) */
22	if (w < 0x40862e42) {
23		t = expm1(absx);
24		if (w < 0x3ff00000) {
25			if (w < 0x3ff00000 - (26<<20))
26				/* note: inexact and underflow are raised by expm1 */
27				/* note: this branch avoids spurious underflow */
28				return x;
29			return h*(2*t - t*t/(t+1));
30		}
31		/* note: |x|>log(0x1p26)+eps could be just h*exp(x) */
32		return h*(t + t/(t+1));
33	}
34
35	/* |x| > log(DBL_MAX) or nan */
36	/* note: the result is stored to handle overflow */
37	t = __expo2(absx, 2*h);
38	return t;
39}