帮你精通JavaScript：求sqrt平方根的三种方法

总结求平方根sqrt的三种方法，首先是牛顿迭代法：

function abs(x) {
    return x >= 0 ? x : -x;
}

function square(x) {
    return x * x;
}

function good_enough(guess, x) {
    return abs(square(guess) - x) < 0.001;
}

function average(x, y) {
    return (x + y) / 2;
}

function improve(guess, x) {
    return average(guess, x / guess);
}

function sqrt_iter(guess, x) {
    return good_enough(guess, x)
           ? guess
           : sqrt_iter(improve(guess, x), x);
}

function sqrt(x) {
    return sqrt_iter(1, x);
}

sqrt(5);
> 2.2360688956433634

其次是二分法：

function average(x, y) {
    return (x + y) / 2;
}

function positive(x) { return x > 0; }
function negative(x) { return x < 0; }

function abs(x) {
    return x >= 0 ? x : -x;
}

function close_enough(x, y) {
    return abs(x - y) < 0.001;
}

function search(f, neg_point, pos_point) {
    let midpoint = average(neg_point, pos_point);
    if (close_enough(neg_point, pos_point)) {
        return midpoint;
    } else {
        let test_value = f(midpoint);
        if (positive(test_value)) {
            return search(f, neg_point, midpoint);
        } else if (negative(test_value)) {
            return search(f, midpoint, pos_point);
        } else {
            return midpoint;
        }
    }
}

function binary_search_method(f, a, b) {
    let a_value = f(a);
    let b_value = f(b);
    return negative(a_value) && positive(b_value) ? search(f, a, b)
           : negative(b_value) && positive(a_value) ? search(f, b, a)
           : error("values are not of opposite sign");
}

console.log(binary_search_method(x => x ** 2  - 5, 0, 5));

>  2.23602294921875

最后是“不动点方程”：

function abs(x) {
    return x >= 0 ? x : -x;
}

const tolerance = 0.00001;
function fixed_point(f, first_guess) {
    function close_enough(x, y) {
        return abs(x - y) < tolerance;
    }
    function try_with(guess) {
        const next = f(guess);
        return close_enough(guess, next)
               ? next
               : try_with(next);
    }
    return try_with(first_guess);
}

function average(x, y) {
    return (x + y) / 2;
}

function sqrt(x) {
    return fixed_point(y => average(y, x / y), 1);
}

sqrt(5);

以上为三种求“平方根”的方法。