Pratik BhadaneandClaude Sonnet 4.6
5015716692
Co-Authored-By: Claude Sonnet 4.6 <noreply@anthropic.com>
589 lines
20 KiB
Rust
589 lines
20 KiB
Rust
//! Overlap studies — moving averages and trend indicators.
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//!
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//! All functions return a `Vec<f64>` of the same length as the input.
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//! Leading values are `f64::NAN` for the warm-up period.
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/// Compute the Simple Moving Average (SMA) over a rolling window.
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///
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/// Returns a `Vec<f64>` of the same length as `close`. The first
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/// `timeperiod - 1` values are `NaN` (warmup period).
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///
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/// # Arguments
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/// * `close` - Price series.
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/// * `timeperiod` - Rolling window size (must be >= 1).
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///
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/// # Edge Cases
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/// Returns all-NaN when `timeperiod < 1` or `close.len() < timeperiod`.
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pub fn sma(close: &[f64], timeperiod: usize) -> Vec<f64> {
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let n = close.len();
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let mut result = vec![f64::NAN; n];
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sma_into(close, timeperiod, &mut result, 0);
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result
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}
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/// Write a Simple Moving Average directly into a pre-allocated buffer.
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///
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/// Values before `dest_offset + timeperiod - 1` are left untouched.
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/// This avoids an intermediate allocation when composing indicators
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/// (e.g., Stochastic slow %K and slow %D).
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///
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/// # Arguments
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/// * `src` - Input price series.
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/// * `timeperiod` - Rolling window size (must be >= 1).
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/// * `dest` - Output buffer (must be at least `dest_offset + src.len()` long).
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/// * `dest_offset` - Starting index in `dest` to write results.
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pub fn sma_into(src: &[f64], timeperiod: usize, dest: &mut [f64], dest_offset: usize) {
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let n = src.len();
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if timeperiod < 1 || n < timeperiod {
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return;
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}
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#[cfg(feature = "simd")]
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let window_sum_init = {
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use wide::f64x4;
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let p_data = &src[..timeperiod];
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let mut sum = f64x4::splat(0.0);
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let mut chunks = p_data.chunks_exact(4);
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for chunk in &mut chunks {
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sum += f64x4::new([chunk[0], chunk[1], chunk[2], chunk[3]]);
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}
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let arr = sum.to_array();
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let mut total = arr[0] + arr[1] + arr[2] + arr[3];
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for &v in chunks.remainder() {
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total += v;
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}
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total
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};
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#[cfg(not(feature = "simd"))]
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let window_sum_init: f64 = src[..timeperiod].iter().sum();
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let mut window_sum = window_sum_init;
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let tp_f64 = timeperiod as f64;
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dest[dest_offset + timeperiod - 1] = window_sum / tp_f64;
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let mut i = timeperiod;
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while i + 1 < n {
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let old0 = src[i - timeperiod];
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let new0 = src[i];
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window_sum += new0 - old0;
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dest[dest_offset + i] = window_sum / tp_f64;
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let old1 = src[i + 1 - timeperiod];
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let new1 = src[i + 1];
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window_sum += new1 - old1;
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dest[dest_offset + i + 1] = window_sum / tp_f64;
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i += 2;
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}
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if i < n {
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window_sum += src[i] - src[i - timeperiod];
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dest[dest_offset + i] = window_sum / tp_f64;
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}
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}
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/// Compute the Exponential Moving Average (EMA).
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///
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/// The EMA is seeded with the SMA of the first `timeperiod` bars and uses
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/// a smoothing factor of `k = 2 / (timeperiod + 1)`. Returns a `Vec<f64>`
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/// of the same length as `close`; the first `timeperiod - 1` values are `NaN`.
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///
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/// # Arguments
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/// * `close` - Price series.
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/// * `timeperiod` - Lookback period (must be >= 1).
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pub fn ema(close: &[f64], timeperiod: usize) -> Vec<f64> {
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let n = close.len();
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let mut result = vec![f64::NAN; n];
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if timeperiod < 1 || n < timeperiod {
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return result;
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}
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let k = 2.0 / (timeperiod as f64 + 1.0);
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let seed: f64 = close[..timeperiod].iter().sum::<f64>() / timeperiod as f64;
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result[timeperiod - 1] = seed;
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for i in timeperiod..n {
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result[i] = (result[i - 1] * (1.0 - k)).mul_add(1.0, close[i] * k);
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}
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result
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}
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/// Compute the Weighted Moving Average (WMA).
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///
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/// Assigns linearly increasing weights (1, 2, ..., timeperiod) to the window.
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/// Uses an O(n) incremental recurrence to avoid recomputing weights each bar.
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/// Returns a `Vec<f64>` of length `n`; the first `timeperiod - 1` values are `NaN`.
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///
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/// # Arguments
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/// * `close` - Price series.
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/// * `timeperiod` - Rolling window size (must be >= 1).
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pub fn wma(close: &[f64], timeperiod: usize) -> Vec<f64> {
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let n = close.len();
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let mut result = vec![f64::NAN; n];
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if timeperiod < 1 || n < timeperiod {
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return result;
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}
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let denom: f64 = (timeperiod * (timeperiod + 1) / 2) as f64;
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let p = timeperiod as f64;
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// Seed: compute T and S for the first window.
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#[cfg(feature = "simd")]
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let (mut t, mut s) = {
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use wide::f64x4;
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let p_data = &close[..timeperiod];
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let mut t_simd = f64x4::splat(0.0);
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let mut s_simd = f64x4::splat(0.0);
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let mut chunks = p_data.chunks_exact(4);
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let mut idx = 1.0;
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let step = f64x4::new([0.0, 1.0, 2.0, 3.0]);
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for chunk in &mut chunks {
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let vals = f64x4::new([chunk[0], chunk[1], chunk[2], chunk[3]]);
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let mults = f64x4::splat(idx) + step;
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t_simd += vals * mults;
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s_simd += vals;
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idx += 4.0;
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}
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let t_arr = t_simd.to_array();
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let s_arr = s_simd.to_array();
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let mut t = t_arr[0] + t_arr[1] + t_arr[2] + t_arr[3];
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let mut s = s_arr[0] + s_arr[1] + s_arr[2] + s_arr[3];
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for &v in chunks.remainder() {
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t += v * idx;
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s += v;
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idx += 1.0;
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}
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(t, s)
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};
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#[cfg(not(feature = "simd"))]
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let (mut t, mut s) = {
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let t_val: f64 = close[..timeperiod]
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.iter()
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.enumerate()
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.map(|(k, &v)| v * (k + 1) as f64)
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.sum();
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let s_val: f64 = close[..timeperiod].iter().sum();
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(t_val, s_val)
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};
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result[timeperiod - 1] = t / denom;
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let mut i = timeperiod;
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while i + 1 < n {
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t += p * close[i] - s;
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s += close[i] - close[i - timeperiod];
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result[i] = t / denom;
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t += p * close[i + 1] - s;
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s += close[i + 1] - close[i + 1 - timeperiod];
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result[i + 1] = t / denom;
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i += 2;
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}
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if i < n {
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t += p * close[i] - s;
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result[i] = t / denom;
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}
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result
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}
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/// Compute Bollinger Bands, returning `(upper, middle, lower)`.
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///
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/// The middle band is the SMA; upper and lower bands are offset by
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/// `nbdevup` and `nbdevdn` standard deviations respectively. Uses
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/// Welford's rolling algorithm for numerically stable variance in O(n).
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///
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/// # Arguments
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/// * `close` - Price series.
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/// * `timeperiod` - SMA / standard deviation window (must be >= 1).
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/// * `nbdevup` - Number of standard deviations above the mean for the upper band.
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/// * `nbdevdn` - Number of standard deviations below the mean for the lower band.
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///
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/// # Returns
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/// `(upper, middle, lower)` -- each `Vec<f64>` of length `n`. The first
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/// `timeperiod - 1` values in each vector are `NaN`.
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///
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/// ## Welford's rolling algorithm
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///
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/// We maintain `mean` and `m2` (sum of squared deviations from the current
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/// mean) across a sliding window of size `N`. When a new value `x_new`
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/// replaces an old value `x_old` (window size stays constant):
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///
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/// ```text
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/// delta = x_new - x_old
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/// old_mean = mean
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/// mean += delta / N
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/// m2 += delta * ((x_new - mean) + (x_old - old_mean))
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///
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/// variance = m2 / N // population variance
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/// stddev = sqrt(variance)
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/// ```
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///
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/// The initial window is seeded using the standard (non-rolling) Welford
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/// incremental algorithm.
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///
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/// This avoids the catastrophic cancellation inherent in the naïve
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/// `Σx²/N − mean²` formula when values are large but close together.
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pub fn bbands(
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close: &[f64],
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timeperiod: usize,
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nbdevup: f64,
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nbdevdn: f64,
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) -> (Vec<f64>, Vec<f64>, Vec<f64>) {
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let n = close.len();
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let nan = vec![f64::NAN; n];
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if timeperiod < 1 || n < timeperiod {
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return (nan.clone(), nan.clone(), nan);
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}
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let mut upper = vec![f64::NAN; n];
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let mut middle = vec![f64::NAN; n];
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let mut lower = vec![f64::NAN; n];
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let p = timeperiod as f64;
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// --- Seed: build initial mean and m2 for the first window using
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// Welford's incremental (non-rolling) algorithm. ---
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let mut mean = 0.0_f64;
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let mut m2 = 0.0_f64;
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for (k, &x) in close[..timeperiod].iter().enumerate() {
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let count = (k + 1) as f64;
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let delta = x - mean;
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mean += delta / count;
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let delta2 = x - mean;
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m2 += delta * delta2;
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}
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let var = (m2 / p).max(0.0);
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let std = var.sqrt();
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middle[timeperiod - 1] = mean;
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upper[timeperiod - 1] = mean + nbdevup * std;
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lower[timeperiod - 1] = mean - nbdevdn * std;
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// --- Rolling phase: slide the window one element at a time,
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// removing the oldest value and adding the newest. ---
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/// Inline helper: replace `x_old` with `x_new` in the Welford accumulator
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/// (constant window size `p`), then write band values into the output slots.
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///
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/// Combined rolling Welford update (window size stays constant at N):
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///
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/// ```text
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/// delta = x_new - x_old
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/// old_mean = mean
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/// mean += delta / N
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/// m2 += delta * ((x_new - mean) + (x_old - old_mean))
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/// ```
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///
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/// This is algebraically equivalent to removing `x_old` and adding `x_new`
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/// in two separate Welford steps, but avoids the intermediate N-1 state.
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#[inline(always)]
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#[allow(clippy::too_many_arguments)]
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fn welford_step(
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x_old: f64,
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x_new: f64,
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mean: &mut f64,
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m2: &mut f64,
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p: f64,
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nbdevup: f64,
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nbdevdn: f64,
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upper: &mut f64,
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middle: &mut f64,
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lower: &mut f64,
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) {
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let delta = x_new - x_old;
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let old_mean = *mean;
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*mean += delta / p;
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// Update m2 using both old and new deviations.
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*m2 += delta * ((x_new - *mean) + (x_old - old_mean));
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// Clamp m2 to zero to guard against floating-point drift.
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if *m2 < 0.0 {
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*m2 = 0.0;
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}
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let var = *m2 / p;
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let std = var.sqrt();
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*middle = *mean;
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*upper = *mean + nbdevup * std;
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*lower = *mean - nbdevdn * std;
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}
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// Process two iterations at a time (loop unrolling) for throughput.
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let mut i = timeperiod;
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while i + 1 < n {
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welford_step(
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close[i - timeperiod],
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close[i],
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&mut mean,
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&mut m2,
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p,
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nbdevup,
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nbdevdn,
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&mut upper[i],
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&mut middle[i],
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&mut lower[i],
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);
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welford_step(
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close[i + 1 - timeperiod],
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close[i + 1],
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&mut mean,
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&mut m2,
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p,
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nbdevup,
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nbdevdn,
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&mut upper[i + 1],
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&mut middle[i + 1],
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&mut lower[i + 1],
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);
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i += 2;
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}
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if i < n {
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welford_step(
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close[i - timeperiod],
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close[i],
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&mut mean,
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&mut m2,
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p,
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nbdevup,
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nbdevdn,
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&mut upper[i],
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&mut middle[i],
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&mut lower[i],
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);
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}
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(upper, middle, lower)
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}
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/// Compute the Moving Average Convergence/Divergence (MACD).
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///
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/// `MACD = EMA(close, fastperiod) - EMA(close, slowperiod)`.
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/// The signal line is `EMA(macd, signalperiod)` and the histogram is
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/// `macd - signal`. TA-Lib compatible: leading values are `NaN` up to
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/// the point where all three outputs are valid.
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///
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/// # Arguments
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/// * `close` - Price series.
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/// * `fastperiod` - Fast EMA period (must be < `slowperiod`).
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/// * `slowperiod` - Slow EMA period.
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/// * `signalperiod` - Signal line EMA period.
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///
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/// # Returns
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/// `(macd_line, signal_line, histogram)` -- each `Vec<f64>` of length `n`.
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pub fn macd(
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close: &[f64],
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fastperiod: usize,
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slowperiod: usize,
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signalperiod: usize,
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) -> (Vec<f64>, Vec<f64>, Vec<f64>) {
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let n = close.len();
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let nan_vec = || vec![f64::NAN; n];
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if fastperiod < 1 || slowperiod < 1 || signalperiod < 1 || fastperiod >= slowperiod {
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return (nan_vec(), nan_vec(), nan_vec());
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}
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if n < slowperiod {
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return (nan_vec(), nan_vec(), nan_vec());
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}
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let kf = 2.0 / (fastperiod as f64 + 1.0);
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let ks = 2.0 / (slowperiod as f64 + 1.0);
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// Seed fast EMA from SMA of first fastperiod bars.
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let mut fast_val: f64 = close[..fastperiod].iter().sum::<f64>() / fastperiod as f64;
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// Seed slow EMA from SMA of first slowperiod bars.
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let mut slow_val: f64 = close[..slowperiod].iter().sum::<f64>() / slowperiod as f64;
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let mut macd_line = nan_vec();
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// From fastperiod-1 to slowperiod-2: advance fast EMA only.
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for &price in close.iter().take(slowperiod - 1).skip(fastperiod) {
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fast_val = price * kf + fast_val * (1.0 - kf);
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}
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// From fastperiod to slowperiod-1: advance fastEMA and compute initial MACD at slowperiod-1
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// Actually, fast_val currently holds the value for `slowperiod - 2` after `take(slowperiod - 1)`
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// So we apply it for `slowperiod - 1`.
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fast_val = close[slowperiod - 1] * kf + fast_val * (1.0 - kf);
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macd_line[slowperiod - 1] = fast_val - slow_val;
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for i in slowperiod..n {
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fast_val = close[i] * kf + fast_val * (1.0 - kf);
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slow_val = close[i] * ks + slow_val * (1.0 - ks);
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macd_line[i] = fast_val - slow_val;
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}
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// Signal line: EMA of macd_line, seeded from the first valid macd value.
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// The signal line starts producing values after slowperiod - 1 + signalperiod - 1 bars.
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let sig_start = slowperiod - 1 + signalperiod - 1;
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let mut signal_line = nan_vec();
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let mut histogram = nan_vec();
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if sig_start >= n {
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// If we can't compute signal, TA-Lib clears MACD!
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for v in macd_line.iter_mut().take(n) {
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*v = f64::NAN;
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}
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return (macd_line, signal_line, histogram);
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}
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let ksig = 2.0 / (signalperiod as f64 + 1.0);
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// Seed signal EMA with SMA of the first signalperiod macd values.
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let sig_seed: f64 = macd_line[(slowperiod - 1)..(slowperiod - 1 + signalperiod)]
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.iter()
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.sum::<f64>()
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/ signalperiod as f64;
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signal_line[sig_start] = sig_seed;
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histogram[sig_start] = macd_line[sig_start] - signal_line[sig_start];
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for i in (sig_start + 1)..n {
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signal_line[i] = macd_line[i] * ksig + signal_line[i - 1] * (1.0 - ksig);
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}
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for i in (sig_start + 1)..n {
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histogram[i] = macd_line[i] - signal_line[i];
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}
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// TA-Lib pads the MACD line itself with NaNs up to `sig_start`!
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for v in macd_line.iter_mut().take(sig_start) {
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*v = f64::NAN;
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}
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(macd_line, signal_line, histogram)
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}
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#[cfg(test)]
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mod tests {
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use super::*;
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#[test]
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fn sma_basic() {
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let prices = vec![1.0, 2.0, 3.0, 4.0, 5.0];
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let result = sma(&prices, 3);
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assert!(result[0].is_nan());
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assert!(result[1].is_nan());
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assert!((result[2] - 2.0).abs() < 1e-10);
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assert!((result[3] - 3.0).abs() < 1e-10);
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assert!((result[4] - 4.0).abs() < 1e-10);
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}
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#[test]
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fn ema_basic() {
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let prices = vec![1.0, 2.0, 3.0, 4.0, 5.0];
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let result = ema(&prices, 3);
|
||
assert!(result[0].is_nan());
|
||
assert!(result[1].is_nan());
|
||
assert!((result[2] - 2.0).abs() < 1e-10); // seed = SMA(3)
|
||
}
|
||
|
||
#[test]
|
||
fn wma_basic() {
|
||
let prices = vec![1.0, 2.0, 3.0];
|
||
let result = wma(&prices, 3);
|
||
assert!(result[0].is_nan());
|
||
assert!(result[1].is_nan());
|
||
// weights: 1, 2, 3; denom 6 => (1*1 + 2*2 + 3*3)/6 = 14/6
|
||
assert!((result[2] - 14.0 / 6.0).abs() < 1e-10);
|
||
}
|
||
|
||
#[test]
|
||
fn bbands_basic() {
|
||
let prices = vec![2.0, 2.0, 2.0, 2.0, 2.0];
|
||
let (upper, middle, lower) = bbands(&prices, 3, 2.0, 2.0);
|
||
assert!((middle[2] - 2.0).abs() < 1e-10);
|
||
assert!((upper[2] - 2.0).abs() < 1e-10); // std = 0
|
||
assert!((lower[2] - 2.0).abs() < 1e-10);
|
||
}
|
||
|
||
#[test]
|
||
fn bbands_varying_prices() {
|
||
// Verify against hand-computed values for a small window.
|
||
let prices = vec![1.0, 2.0, 3.0, 4.0, 5.0];
|
||
let (upper, middle, lower) = bbands(&prices, 3, 2.0, 2.0);
|
||
|
||
// First two values should be NaN (warmup).
|
||
assert!(middle[0].is_nan());
|
||
assert!(middle[1].is_nan());
|
||
|
||
// Window [1,2,3]: mean = 2.0, pop_var = 2/3, std = sqrt(2/3)
|
||
let expected_mean = 2.0;
|
||
let expected_std = (2.0_f64 / 3.0).sqrt();
|
||
assert!((middle[2] - expected_mean).abs() < 1e-10);
|
||
assert!((upper[2] - (expected_mean + 2.0 * expected_std)).abs() < 1e-10);
|
||
assert!((lower[2] - (expected_mean - 2.0 * expected_std)).abs() < 1e-10);
|
||
|
||
// Window [2,3,4]: mean = 3.0, pop_var = 2/3, std = sqrt(2/3)
|
||
assert!((middle[3] - 3.0).abs() < 1e-10);
|
||
assert!((upper[3] - (3.0 + 2.0 * expected_std)).abs() < 1e-10);
|
||
|
||
// Window [3,4,5]: mean = 4.0, pop_var = 2/3, std = sqrt(2/3)
|
||
assert!((middle[4] - 4.0).abs() < 1e-10);
|
||
assert!((upper[4] - (4.0 + 2.0 * expected_std)).abs() < 1e-10);
|
||
}
|
||
|
||
#[test]
|
||
fn bbands_numerical_stability() {
|
||
// Large offset with tiny variation — this is where the naïve sum_sq
|
||
// formula suffers from catastrophic cancellation.
|
||
let base = 1e12;
|
||
let prices: Vec<f64> = (0..100).map(|i| base + (i as f64) * 0.01).collect();
|
||
let (upper, middle, lower) = bbands(&prices, 20, 2.0, 2.0);
|
||
|
||
// Check that middle band matches SMA.
|
||
for i in 19..100 {
|
||
let window = &prices[i - 19..=i];
|
||
let expected_mean: f64 = window.iter().sum::<f64>() / 20.0;
|
||
// At scale 1e12, f64 absolute precision is ~2.2e-4; use 1e-3 headroom.
|
||
assert!(
|
||
(middle[i] - expected_mean).abs() < 1e-3,
|
||
"mean mismatch at {i}: got {} expected {}",
|
||
middle[i],
|
||
expected_mean,
|
||
);
|
||
// Bands should be above/below middle.
|
||
assert!(upper[i] >= middle[i]);
|
||
assert!(lower[i] <= middle[i]);
|
||
}
|
||
}
|
||
|
||
#[test]
|
||
fn bbands_edge_cases() {
|
||
// timeperiod == 1: every bar should have std = 0, bands == price.
|
||
let prices = vec![10.0, 20.0, 30.0];
|
||
let (upper, middle, lower) = bbands(&prices, 1, 2.0, 2.0);
|
||
for i in 0..3 {
|
||
assert!((middle[i] - prices[i]).abs() < 1e-10);
|
||
assert!((upper[i] - prices[i]).abs() < 1e-10);
|
||
assert!((lower[i] - prices[i]).abs() < 1e-10);
|
||
}
|
||
|
||
// Input shorter than timeperiod: all NaN.
|
||
let (u, m, l) = bbands(&[1.0, 2.0], 5, 2.0, 2.0);
|
||
assert!(u.iter().all(|v| v.is_nan()));
|
||
assert!(m.iter().all(|v| v.is_nan()));
|
||
assert!(l.iter().all(|v| v.is_nan()));
|
||
}
|
||
|
||
#[test]
|
||
fn macd_basic() {
|
||
// 40 bars of linearly increasing prices — MACD line should converge
|
||
let prices: Vec<f64> = (1..=40).map(|i| i as f64).collect();
|
||
let (macd_line, signal_line, histogram) = macd(&prices, 3, 5, 2);
|
||
// TA-Lib pads MACD line with NaN up to sig_start = slowperiod-1 + signalperiod-1 = 5
|
||
for i in 0..5 {
|
||
assert!(macd_line[i].is_nan(), "expected NaN at {i}");
|
||
}
|
||
// First valid macd bar is at index 5 (sig_start)
|
||
assert!(!macd_line[5].is_nan());
|
||
// First valid signal bar is at index 5
|
||
assert!(!signal_line[5].is_nan());
|
||
// histogram = macd - signal
|
||
assert!((histogram[5] - (macd_line[5] - signal_line[5])).abs() < 1e-10);
|
||
}
|
||
|
||
#[test]
|
||
fn macd_invalid_params() {
|
||
let prices = vec![1.0; 50];
|
||
// fastperiod >= slowperiod should return all-NaN
|
||
let (m, s, h) = macd(&prices, 5, 3, 9);
|
||
assert!(m.iter().all(|v| v.is_nan()));
|
||
assert!(s.iter().all(|v| v.is_nan()));
|
||
assert!(h.iter().all(|v| v.is_nan()));
|
||
}
|
||
}
|