#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;
}