javascript - Javascript 中的快速双曲正切近似

Question

我正在用 javascript 做一些数字信号处理计算，我发现计算双曲正切 (tanh) 有点太昂贵了。这就是我目前近似 tanh 的方式:

function tanh (arg) {
    // sinh(number)/cosh(number)
    return (Math.exp(arg) - Math.exp(-arg)) / (Math.exp(arg) + Math.exp(-arg));
}

有人知道更快的计算方法吗？

Answer 1

来自 here .

function rational_tanh(x)
{
    if( x < -3 )
        return -1;
    else if( x > 3 )
        return 1;
    else
        return x * ( 27 + x * x ) / ( 27 + 9 * x * x );
}

This is a rational function to approximate a tanh-like soft clipper. It is based on the pade-approximation of the tanh function with tweaked coefficients.

The function is in the range x=-3..3 and outputs the range y=-1..1. Beyond this range the output must be clamped to -1..1.

The first to derivatives of the function vanish at -3 and 3, so the transition to the hard clipped region is C2-continuous.

Padé 近似比泰勒展开好几个数量级。夹紧也可能是一个问题(取决于您的范围)。