蒙特卡洛自动求函数积分的Javascript(Nodejs)算法实现与测试

用Javascript实现了函数积分的算法。

从计算结果可以看出，算法精度受随机数发生器的影响较大。

[javascript]
//Monte carro求给定函数的定积分
//给定一个函数
function f1(x, xmin, xmax)
{
    if (x >= xmin && x <= xmax)
        return x * x * Math.sqrt(1 + x * x * x) - 1;
}

function f2(x, xmin, xmax)
{
    if (x >= xmin && x <= xmax)
        return x * Math.log(1 + x);
}

function f3(x, xmin, xmax)
{
    if (x >= xmin && x <= xmax)
        return Math.sqrt(1 - x * x);
}

function f4(x, xmin, xmax)
{
    if (x >= xmin && x <= xmax)
        return Math.cos(x) - 0.9;
}

//取得函数的上下极限——其精确度影响很大---由于用于积分，故若y>0，底限0；若y<0，则高限0；若y穿越x轴，则不修改默认极限
function getLimit(func, xmin, xmax)
{
    //边界极限
    var t1 = func(xmin, xmin, xmax), t2 = func(xmax, xmin, xmax);
    var limit = {y0: Math.min(t1, t2), y1: Math.max(t1, t2)};
    var delta = 1e-3, lastX, lastY;
    for(var x = xmin, i = 0; x <= xmax; x += delta, i++)
    {
        y = func(x, xmin, xmax);
        if (y < limit.y0)
            limit.y0 = y;
        if (y > limit.y1)
            limit.y1 = y;
        if (i == 0)
        {
            lastX = x;
            lastY = y;
        }
        else
        {
            var tx = (lastX + x) / 2;
            var ty = func(tx, xmin, xmax);
            if (Math.abs(lastY) > Math.abs(y))
            {
                if (Math.abs(lastY) < Math.abs(ty))
                {
                    lastX = tx;
                    lastY = ty;
                    if (ty < 0 && limit.y0 > ty)
                        limit.y0 = ty;
                    else if (ty >= 0 && limit.y1 <= ty)
                        limit.y1 = ty;
                }
            }
            if (Math.abs(lastY) < Math.abs(y))
            {
                if (Math.abs(y) < Math.abs(ty))
                {
                    lastX = tx;
                    lastY = ty;
                    if (ty < 0 && limit.y0 > ty)
                        limit.y0 = ty;
                    else if (ty >= 0 && limit.y1 <= ty)
                        limit.y1 = ty;
                }
            }
        }
    }
    if (limit.y0 > 0)
        limit.y0 = 0;
    if (limit.y1 < 0)
        limit.y1 = 0;
    return limit;
}

//积分
function cumulate(func, N, xmin, xmax)
{
    var limit = getLimit(func, xmin, xmax);
    //console.log('Limit=', limit.y0, limit.y1);
    var x, yr, y;
    var cntA = 0, cntB = 0;
    for(var i = 0; i < N; i++)
    {
        x = xmin + (xmax - xmin) * Math.random();
        yr = limit.y0 + (l

补充：web前端 , JavaScript ,