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 */
cosh(double x)7 double 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