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

#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;
}