musl/src/math/cosh.c

#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;
}