third_party/ulib/musl/src/math/sinh.c

#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;
}