#include "libm.h"

/* cosh(x) = (exp(x) + 1/exp(x))/2
 *         = 1 + 0.5*(exp(x)-1)*(exp(x)-1)/exp(x)
 *         = 1 + x*x/2 + o(x^4)
 */
double cosh(double x)
{
        union {double f; uint64_t i;} u = {.f = x};
        uint32_t w;
        double t;

        /* |x| */
        u.i &= (uint64_t)-1/2;
        x = u.f;
        w = u.i >> 32;

        /* |x| < log(2) */
        if (w < 0x3fe62e42) {
                if (w < 0x3ff00000 - (26<<20)) {
                        /* raise inexact if x!=0 */
                        FORCE_EVAL(x + 0x1p120f);
                        return 1;
                }
                t = expm1(x);
                return 1 + t*t/(2*(1+t));
        }

        /* |x| < log(DBL_MAX) */
        if (w < 0x40862e42) {
                t = exp(x);
                /* note: if x>log(0x1p26) then the 1/t is not needed */
                return 0.5*(t + 1/t);
        }

        /* |x| > log(DBL_MAX) or nan */
        /* note: the result is stored to handle overflow */
        t = __expo2(x);
        return t;
}