Cubic Roots Solver Function in JS

gistfile1.js

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;
} 

Great work. One problem is that this does not work when a===0. This can be avoided by using quadratic and linear solver when a===0 or b===0, I think.

good point!

Line 27 should be

roots[2].real = roots[1].real = -term1;

Good catch

Math.cbrt(x) will work more efficiently and correctly than Math.pow(x, 1/3) in some cases so this code would be better with that change.

Math.cbrt(-8) returns -2 but Math.pow(-8, 1/3) returns NaN for example. The -2 is a more desirable result.

The browser support for Math.cbrt is very good now. All major browsers support Math.cbrt including Chrome, Firefox, Edge, Safari. Internet Explorer 11 doesn't but that browser isn't at all popular now.

Yes that's right Math.pow doesn't work well for 1/3 for negative numbers.