1#include "libm.h"
2
3/* cosh(x) = (exp(x) + 1/exp(x))/2
4 *         = 1 + 0.5*(exp(x)-1)*(exp(x)-1)/exp(x)
5 *         = 1 + x*x/2 + o(x^4)
6 */
7double cosh(double x)
8{
9	union {double f; uint64_t i;} u = {.f = x};
10	uint32_t w;
11	double t;
12
13	/* |x| */
14	u.i &= (uint64_t)-1/2;
15	x = u.f;
16	w = u.i >> 32;
17
18	/* |x| < log(2) */
19	if (w < 0x3fe62e42) {
20		if (w < 0x3ff00000 - (26<<20)) {
21			/* raise inexact if x!=0 */
22			FORCE_EVAL(x + 0x1p120f);
23			return 1;
24		}
25		t = expm1(x);
26		return 1 + t*t/(2*(1+t));
27	}
28
29	/* |x| < log(DBL_MAX) */
30	if (w < 0x40862e42) {
31		t = exp(x);
32		/* note: if x>log(0x1p26) then the 1/t is not needed */
33		return 0.5*(t + 1/t);
34	}
35
36	/* |x| > log(DBL_MAX) or nan */
37	/* note: the result is stored to handle overflow */
38	t = __expo2(x);
39	return t;
40}
41