413 lines
14 KiB
Rust
413 lines
14 KiB
Rust
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//! 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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/// Simple Moving Average over `timeperiod` bars.
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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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/// Simple Moving Average written directly into `dest` starting at `dest_offset`.
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/// Leaves values before `dest_offset + timeperiod - 1` untouched (e.g. they can be NaN).
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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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/// Exponential Moving Average — seeded with SMA of first `timeperiod` bars.
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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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/// Weighted Moving Average — O(n) incremental algorithm using running weighted sum.
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///
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/// Recurrence: `T[i] = T[i-1] + n*close[i] - S[i-1]`
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/// where `S[i]` is the rolling sum over `timeperiod` bars.
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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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/// Bollinger Bands — returns `(upper, middle, lower)`.
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///
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/// Middle is SMA; bands are `± nbdev * stddev`.
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/// Uses O(n) sliding `sum` and `sum_sq` windows for mean and variance.
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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 sliding sums for the first window.
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#[cfg(feature = "simd")]
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let (mut sum, mut sum_sq) = {
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use wide::f64x4;
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let p_data = &close[..timeperiod];
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let mut sum_simd = f64x4::splat(0.0);
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let mut sq_simd = 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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let vals = f64x4::new([chunk[0], chunk[1], chunk[2], chunk[3]]);
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sum_simd += vals;
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sq_simd += vals * vals;
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}
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let s_arr = sum_simd.to_array();
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let sq_arr = sq_simd.to_array();
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let mut sum = s_arr[0] + s_arr[1] + s_arr[2] + s_arr[3];
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let mut sum_sq = sq_arr[0] + sq_arr[1] + sq_arr[2] + sq_arr[3];
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for &v in chunks.remainder() {
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sum += v;
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sum_sq += v * v;
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}
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(sum, sum_sq)
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};
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#[cfg(not(feature = "simd"))]
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let (mut sum, mut sum_sq) = {
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let s: f64 = close[..timeperiod].iter().sum();
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let sq: f64 = close[..timeperiod].iter().map(|&x| x * x).sum();
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(s, sq)
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};
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let mean = sum / p;
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let var = (sum_sq / p - mean * mean).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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let mut i = timeperiod;
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while i + 1 < n {
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let old0 = close[i - timeperiod];
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sum += close[i] - old0;
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sum_sq += close[i] * close[i] - old0 * old0;
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let mean = sum / p;
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let var = (sum_sq / p - mean * mean).max(0.0);
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let std = var.sqrt();
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middle[i] = mean;
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upper[i] = mean + nbdevup * std;
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lower[i] = mean - nbdevdn * std;
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let old1 = close[i + 1 - timeperiod];
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sum += close[i + 1] - old1;
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sum_sq += close[i + 1] * close[i + 1] - old1 * old1;
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let mean1 = sum / p;
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let var1 = (sum_sq / p - mean1 * mean1).max(0.0);
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let std1 = var1.sqrt();
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middle[i + 1] = mean1;
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upper[i + 1] = mean1 + nbdevup * std1;
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lower[i + 1] = mean1 - nbdevdn * std1;
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i += 2;
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}
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if i < n {
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let old = close[i - timeperiod];
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sum += close[i] - old;
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sum_sq += close[i] * close[i] - old * old;
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let mean = sum / p;
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let var = (sum_sq / p - mean * mean).max(0.0);
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let std = var.sqrt();
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middle[i] = mean;
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upper[i] = mean + nbdevup * std;
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lower[i] = mean - nbdevdn * std;
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}
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(upper, middle, lower)
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}
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/// MACD — EMA(fastperiod) minus EMA(slowperiod), signal = EMA(macd, signalperiod).
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///
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/// Returns `(macd_line, signal_line, histogram)`, each of length `n`.
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/// Leading values are `NaN` during warmup.
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/// `fastperiod` must be less than `slowperiod`.
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///
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/// Fast and slow EMAs are computed in a **single combined loop** to minimise
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/// memory round-trips, then the signal EMA is computed in a second pass.
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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`!
|
||
|
|
for v in macd_line.iter_mut().take(sig_start) {
|
||
|
|
*v = f64::NAN;
|
||
|
|
}
|
||
|
|
|
||
|
|
(macd_line, signal_line, histogram)
|
||
|
|
}
|
||
|
|
|
||
|
|
#[cfg(test)]
|
||
|
|
mod tests {
|
||
|
|
use super::*;
|
||
|
|
|
||
|
|
#[test]
|
||
|
|
fn sma_basic() {
|
||
|
|
let prices = vec![1.0, 2.0, 3.0, 4.0, 5.0];
|
||
|
|
let result = sma(&prices, 3);
|
||
|
|
assert!(result[0].is_nan());
|
||
|
|
assert!(result[1].is_nan());
|
||
|
|
assert!((result[2] - 2.0).abs() < 1e-10);
|
||
|
|
assert!((result[3] - 3.0).abs() < 1e-10);
|
||
|
|
assert!((result[4] - 4.0).abs() < 1e-10);
|
||
|
|
}
|
||
|
|
|
||
|
|
#[test]
|
||
|
|
fn ema_basic() {
|
||
|
|
let prices = vec![1.0, 2.0, 3.0, 4.0, 5.0];
|
||
|
|
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 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()));
|
||
|
|
}
|
||
|
|
}
|