#include "libm.h"

/* tanh(x) = (exp(x) - exp(-x))/(exp(x) + exp(-x))
 *         = (exp(2*x) - 1)/(exp(2*x) - 1 + 2)
 *         = (1 - exp(-2*x))/(exp(-2*x) - 1 + 2)
 */
double tanh(double x)
{
        union {double f; uint64_t i;} u = {.f = x};
        uint32_t w;
        int sign;
        double_t t;

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

        if (w > 0x3fe193ea) {
                /* |x| > log(3)/2 ~= 0.5493 or nan */
                if (w > 0x40340000) {
                        /* |x| > 20 or nan */
                        /* note: this branch avoids raising overflow */
                        t = 1 - 0/x;
                } else {
                        t = expm1(2*x);
                        t = 1 - 2/(t+2);
                }
        } else if (w > 0x3fd058ae) {
                /* |x| > log(5/3)/2 ~= 0.2554 */
                t = expm1(2*x);
                t = t/(t+2);
        } else if (w >= 0x00100000) {
                /* |x| >= 0x1p-1022, up to 2ulp error in [0.1,0.2554] */
                t = expm1(-2*x);
                t = -t/(t+2);
        } else {
                /* |x| is subnormal */
                /* note: the branch above would not raise underflow in [0x1p-1023,0x1p-1022) */
                FORCE_EVAL((float)x);
                t = x;
        }
        return sign ? -t : t;
}