/** finds the zeros of a function, given two starting points (which must
 * have opposite signs */
export function bisect(f, a, b, parameters?: any) {
  parameters = parameters || {};
  const maxIterations = parameters.maxIterations || 100;
  const tolerance = parameters.tolerance || 1e-10;
  const fA = f(a);
  const fB = f(b);
  let delta = b - a;

  if (fA * fB > 0) {
    throw 'Initial bisect points must have opposite signs';
  }

  if (fA === 0) return a;
  if (fB === 0) return b;

  for (let i = 0; i < maxIterations; ++i) {
    delta /= 2;
    const mid = a + delta;
    const fMid = f(mid);

    if (fMid * fA >= 0) {
      a = mid;
    }

    if (Math.abs(delta) < tolerance || fMid === 0) {
      return mid;
    }
  }
  return a + delta;
}