function mean(values: number[]): number {
  if (values.length === 0) return 0;
  return values.reduce((a, b) => a + b, 0) / values.length;
}

function stddev(values: number[]): number {
  if (values.length === 0) return 0;
  const m = mean(values);
  const v = values.reduce((acc, x) => acc + (x - m) * (x - m), 0) / values.length;
  return Math.sqrt(v);
}

export function sma(values: number[], period: number): Array<number | null> {
  if (period <= 0) throw new Error('period must be > 0');
  const out: Array<number | null> = new Array(values.length).fill(null);
  let sum = 0;
  for (let i = 0; i < values.length; i++) {
    sum += values[i];
    if (i >= period) sum -= values[i - period];
    if (i >= period - 1) out[i] = sum / period;
  }
  return out;
}

export function ema(values: number[], period: number): Array<number | null> {
  if (period <= 0) throw new Error('period must be > 0');
  const out: Array<number | null> = new Array(values.length).fill(null);
  const k = 2 / (period + 1);
  if (values.length < period) return out;

  const first = mean(values.slice(0, period));
  out[period - 1] = first;
  let prev = first;
  for (let i = period; i < values.length; i++) {
    const next = values[i] * k + prev * (1 - k);
    out[i] = next;
    prev = next;
  }
  return out;
}

export function rsi(values: number[], period: number): Array<number | null> {
  if (period <= 0) throw new Error('period must be > 0');
  const out: Array<number | null> = new Array(values.length).fill(null);
  if (values.length <= period) return out;

  let gains = 0;
  let losses = 0;
  for (let i = 1; i <= period; i++) {
    const change = values[i] - values[i - 1];
    if (change >= 0) gains += change;
    else losses -= change;
  }
  let avgGain = gains / period;
  let avgLoss = losses / period;

  const rs = avgLoss === 0 ? Number.POSITIVE_INFINITY : avgGain / avgLoss;
  out[period] = 100 - 100 / (1 + rs);

  for (let i = period + 1; i < values.length; i++) {
    const change = values[i] - values[i - 1];
    const gain = Math.max(change, 0);
    const loss = Math.max(-change, 0);
    avgGain = (avgGain * (period - 1) + gain) / period;
    avgLoss = (avgLoss * (period - 1) + loss) / period;
    const rs2 = avgLoss === 0 ? Number.POSITIVE_INFINITY : avgGain / avgLoss;
    out[i] = 100 - 100 / (1 + rs2);
  }
  return out;
}

export function bollingerBands(values: number[], period: number, stdDevMult: number) {
  if (period <= 0) throw new Error('period must be > 0');
  const upper: Array<number | null> = new Array(values.length).fill(null);
  const lower: Array<number | null> = new Array(values.length).fill(null);
  const mid = sma(values, period);

  for (let i = period - 1; i < values.length; i++) {
    const window = values.slice(i - period + 1, i + 1);
    const sd = stddev(window);
    const m = mid[i];
    if (m == null) continue;
    upper[i] = m + stdDevMult * sd;
    lower[i] = m - stdDevMult * sd;
  }

  return { upper, lower, mid };
}

export function macd(values: number[], fastPeriod = 12, slowPeriod = 26, signalPeriod = 9) {
  const fast = ema(values, fastPeriod);
  const slow = ema(values, slowPeriod);
  const macdLine: Array<number | null> = values.map((_, i) => {
    const f = fast[i];
    const s = slow[i];
    return f == null || s == null ? null : f - s;
  });

  // EMA over a nullable series, aligned by index.
  const signal: Array<number | null> = new Array(values.length).fill(null);
  const k = 2 / (signalPeriod + 1);
  let seeded = false;
  let prev = 0;
  const buf: number[] = [];

  for (let i = 0; i < macdLine.length; i++) {
    const v = macdLine[i];
    if (v == null) continue;

    if (!seeded) {
      buf.push(v);
      if (buf.length === signalPeriod) {
        const first = mean(buf);
        signal[i] = first;
        prev = first;
        seeded = true;
      }
      continue;
    }

    const next = v * k + prev * (1 - k);
    signal[i] = next;
    prev = next;
  }

  return { macd: macdLine, signal };
}

export function lastNonNull(values: Array<number | null>): number | null {
  for (let i = values.length - 1; i >= 0; i--) {
    const v = values[i];
    if (v != null && Number.isFinite(v)) return v;
  }
  return null;
}