#include "libm.h"

/* sinh(x) = (exp(x) - 1/exp(x))/2
 *         = (exp(x)-1 + (exp(x)-1)/exp(x))/2
 *         = x + x^3/6 + o(x^5)
 */
double sinh(double x)
{
        union {double f; uint64_t i;} u = {.f = x};
        uint32_t w;
        double t, h, absx;

        h = 0.5;
        if (u.i >> 63)
                h = -h;
        /* |x| */
        u.i &= (uint64_t)-1/2;
        absx = u.f;
        w = u.i >> 32;

        /* |x| < log(DBL_MAX) */
        if (w < 0x40862e42) {
                t = expm1(absx);
                if (w < 0x3ff00000) {
                        if (w < 0x3ff00000 - (26<<20))
                                /* note: inexact and underflow are raised by expm1 */
                                /* note: this branch avoids spurious underflow */
                                return x;
                        return h*(2*t - t*t/(t+1));
                }
                /* note: |x|>log(0x1p26)+eps could be just h*exp(x) */
                return h*(t + t/(t+1));
        }

        /* |x| > log(DBL_MAX) or nan */
        /* note: the result is stored to handle overflow */
        t = 2*h*__expo2(absx);
        return t;
}