[JS] Calculating imaginary and quaternionic numbers

imq.js

function imul(x, y) {
  return [x[0] * y[0] - x[1] * y[1], x[0] * y[1] + x[1] * y[0]];
}

function cross(x, y) {
  return [x[1] * y[2] - x[2] * y[1], x[2] * y[0] - x[0] * y[2], x[1] * y[2] - x[2] * y[1]];
}

function vdot(x, y) {
  return x.reduce((acc, xi, i) => acc + xi * y[i], 0);
}

function vadd(x, y) {
  return x.map((a, i) => a + y[i]);
}

function scale(a, v) {
  return v.map(x => a * x);
}

function qmul(x, y) {
  // (a+x)(b+y)=ab+ay+bx+xy
  const imx = x.slice(1, 4);
  const imy = y.slice(1, 4);
  const imr = vadd(vadd(scale(x[0], imy), scale(y[0], imx)), cross(imx, imy));
  return [x[0] * y[0] - vdot(imx, imy)].concat(imr);
}

function qconj(x) {
  return [x[0]].concat(scale(-1, x.slice(1, 4)));
}

function qnorm2(x) {
  return vdot(x, x);
}

function qinv(x) {
  return scale(qnorm2(x), qconj(x));
}

function normv(x) {
  return scale(1 / Math.sqrt(vdot(x, x)), x);
}

function qrot(x, th, n) {
  const r = [Math.cos(th / 2)].concat(scale(Math.sin(th / 2), normv(n)));
  return qmul(qmul(r, x), qconj(r));
}

// qrot([1, 2, 3, 4], Math.PI / 2, [1, 1, 1]);