c++ - C++:求解三次方程式

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这个site解三次方程，并且有它使用的方程
我写这个函数是为了得到相同的结果，但它不起作用

void cubicFormula(float a, float b, float c, float d, float *results)
{
    float a2 = a*a;
    float b2 = b*b;
    float b3 = b2*b;

    float q = (3*c- b2)/9;
    float q2 = q*q;
    float q3 = q2*q;
    float r = -27*d + b*(9*c-2*b2);
    float r2 = r*r;

    float discriminant = q3 + r2;

    float s = r + sqrtf(discriminant);
    float t = r - sqrtf(discriminant);

    float term1 = powf((-t + s)/2, 1/3.);

    float r13= 2 * sqrtf(q);

    results[0] = (- term1 + r13 * cosf(q3/3));
    results[1] = (- term1 + r13 * cosf(q3 + (2*M_PI)/3));
    results[2] = (- term1 + r13 * cosf(q3 + (4*M_PI)/3));
}

有什么问题，我有什么遗漏吗？
更新：
例如，使用这些值

a = -1.000000;
b = 36.719475;
c = -334.239960;
d = 629.877808;

鉴别器小于零，所以r13为NaN
但是上面提到的网站和我测试过的一些在线解决方案找到了三个根源

23.775687816485593
2.548516232734247
10.395270950780164

都是实数

最佳答案

您链接以提供Cubic Equation Calculator的站点。你可以从你的代码和他们的代码之间的差异开始：

function cubicsolve(dataForm)
{
    var a = parseFloat(dataForm.aIn.value);
    var b = parseFloat(dataForm.bIn.value);
    var c = parseFloat(dataForm.cIn.value);
    var d = parseFloat(dataForm.dIn.value);
    if (a == 0)
    {
        alert("The coefficient of the cube of x is 0. Please use the utility for a SECOND degree quadratic. No further action taken.");
        return;
    } //End if a == 0

    if (d == 0)
    {
        alert("One root is 0. Now divide through by x and use the utility for a SECOND degree quadratic to solve the resulting equation for the other two roots. No further action taken.");
        return;
    } //End if d == 0
    b /= a;
    c /= a;
    d /= a;
    var disc, q, r, dum1, s, t, term1, r13;
    q = (3.0*c - (b*b))/9.0;
    r = -(27.0*d) + b*(9.0*c - 2.0*(b*b));
    r /= 54.0;
    disc = q*q*q + r*r;
    dataForm.x1Im.value = 0; //The first root is always real.
    term1 = (b/3.0);
    if (disc > 0) { // one root real, two are complex
        s = r + Math.sqrt(disc);
        s = ((s < 0) ? -Math.pow(-s, (1.0/3.0)) : Math.pow(s, (1.0/3.0)));
        t = r - Math.sqrt(disc);
        t = ((t < 0) ? -Math.pow(-t, (1.0/3.0)) : Math.pow(t, (1.0/3.0)));
        dataForm.x1Re.value = -term1 + s + t;
        term1 += (s + t)/2.0;
        dataForm.x3Re.value = dataForm.x2Re.value = -term1;
        term1 = Math.sqrt(3.0)*(-t + s)/2;
        dataForm.x2Im.value = term1;
        dataForm.x3Im.value = -term1;
        return;
    }
    // End if (disc > 0)
    // The remaining options are all real
    dataForm.x3Im.value = dataForm.x2Im.value = 0;
    if (disc == 0){ // All roots real, at least two are equal.
        r13 = ((r < 0) ? -Math.pow(-r,(1.0/3.0)) : Math.pow(r,(1.0/3.0)));
        dataForm.x1Re.value = -term1 + 2.0*r13;
        dataForm.x3Re.value = dataForm.x2Re.value = -(r13 + term1);
        return;
    } // End if (disc == 0)
    // Only option left is that all roots are real and unequal (to get here, q < 0)
    q = -q;
    dum1 = q*q*q;
    dum1 = Math.acos(r/Math.sqrt(dum1));
    r13 = 2.0*Math.sqrt(q);
    dataForm.x1Re.value = -term1 + r13*Math.cos(dum1/3.0);
    dataForm.x2Re.value = -term1 + r13*Math.cos((dum1 + 2.0*Math.PI)/3.0);
    dataForm.x3Re.value = -term1 + r13*Math.cos((dum1 + 4.0*Math.PI)/3.0);
    return;
}  //End of cubicSolve

关于c++ - C++:求解三次方程式，我们在Stack Overflow上找到一个类似的问题：https://stackoverflow.com/questions/13328676/