export function gcd(a: number, b: number): number {
  a = Math.abs(a);
  b = Math.abs(b);
  while (b) {
    [a, b] = [b, a % b];
  }
  return a;
}

export function lcm(a: number, b: number): number {
  return Math.abs(a * b) / gcd(a, b);
}

export function simplify(num: number, den: number): [number, number] {
  if (den === 0) return [num, den];
  const g = gcd(Math.abs(num), Math.abs(den));
  const sign = den < 0 ? -1 : 1;
  return [(num / g) * sign, (den / g) * sign];
}

export function add(
  n1: number, d1: number,
  n2: number, d2: number,
): [number, number] {
  const num = n1 * d2 + n2 * d1;
  const den = d1 * d2;
  return simplify(num, den);
}

export function subtract(
  n1: number, d1: number,
  n2: number, d2: number,
): [number, number] {
  const num = n1 * d2 - n2 * d1;
  const den = d1 * d2;
  return simplify(num, den);
}

export function multiply(
  n1: number, d1: number,
  n2: number, d2: number,
): [number, number] {
  return simplify(n1 * n2, d1 * d2);
}

export function divide(
  n1: number, d1: number,
  n2: number, d2: number,
): [number, number] {
  return simplify(n1 * d2, d1 * n2);
}

export function toDecimal(num: number, den: number): number {
  return num / den;
}

export function fromDecimal(decimal: number, precision: number = 6): [number, number] {
  const str = decimal.toFixed(precision);
  const parts = str.split(".");
  if (!parts[1]) return [parseInt(parts[0]), 1];
  const den = Math.pow(10, parts[1].length);
  const num = Math.round(decimal * den);
  return simplify(num, den);
}

export function compare(
  n1: number, d1: number,
  n2: number, d2: number,
): -1 | 0 | 1 {
  const diff = n1 * d2 - n2 * d1;
  if (diff > 0) return 1;
  if (diff < 0) return -1;
  return 0;
}

export function fractionOfQuantity(num: number, den: number, quantity: number): number {
  return (num / den) * quantity;
}

export function wholeFromFraction(num: number, den: number, part: number): number {
  return (part * den) / num;
}

export function isProper(num: number, den: number): boolean {
  return Math.abs(num) < Math.abs(den);
}

export function toMixed(num: number, den: number): [number, number, number] {
  const whole = Math.floor(Math.abs(num) / Math.abs(den));
  const remainder = Math.abs(num) % Math.abs(den);
  const sign = (num < 0) !== (den < 0) ? -1 : 1;
  return [whole * sign, remainder, Math.abs(den)];
}

export function fromMixed(whole: number, num: number, den: number): [number, number] {
  const sign = whole < 0 ? -1 : 1;
  return [sign * (Math.abs(whole) * den + num), den];
}

export function isSimplified(num: number, den: number): boolean {
  return gcd(Math.abs(num), Math.abs(den)) === 1;
}

export function toKatex(num: number, den: number): string {
  if (den === 1) return `${num}`;
  return `\\frac{${num}}{${den}}`;
}