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Cubic Roots Solver Function in JS
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function CubicSolve(a, b, c, d){ | |
b /= a; | |
c /= a; | |
d /= a; | |
var discrim, 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; | |
discrim = q*q*q + r*r; | |
var roots = [ {real: 0, i: 0}, {real: 0, i: 0}, {real: 0, i: 0} ] | |
term1 = (b/3.0); | |
if (discrim > 0) { // one root real, two are complex | |
s = r + Math.sqrt(discrim); | |
s = ((s < 0) ? -Math.pow(-s, (1.0/3.0)) : Math.pow(s, (1.0/3.0))); | |
t = r - Math.sqrt(discrim); | |
t = ((t < 0) ? -Math.pow(-t, (1.0/3.0)) : Math.pow(t, (1.0/3.0))); | |
roots[0].real = -term1 + s + t; | |
term1 += (s + t)/2.0; | |
roots[1].real = roots[2].real = -term1; | |
term1 = Math.sqrt(3.0)*(-t + s)/2; | |
roots[1].i = term1; | |
roots[2].i = -term1; | |
return roots; | |
} // End if (discrim > 0) | |
// The remaining options are all real | |
if (discrim == 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))); | |
roots[0].real = -term1 + 2.0*r13; | |
roots[2].real = roots[1].real = -(r13 + term1); | |
return roots; | |
} // End if (discrim == 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); | |
roots[0].real = -term1 + r13*Math.cos(dum1/3.0); | |
roots[1].real = -term1 + r13*Math.cos((dum1 + 2.0*Math.PI)/3.0); | |
roots[2].real = -term1 + r13*Math.cos((dum1 + 4.0*Math.PI)/3.0); | |
return roots; | |
} | |
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Yes that's right Math.pow doesn't work well for 1/3 for negative numbers.