docs(wiki): document O(1) regression update and long-stream sum reseed (R2, R7)

Three indicator pages get a short follow-up paragraph that surfaces an
internal implementation detail the audit findings made user-visible:

- `Indicator-LinearRegression.md` gains a "Complexity" section explaining
  the O(1) update (precomputed `Σx`, `Σxx`; incrementally slid `Σy`,
  `Σxy` via the closed-form sliding identity), and the existing
  "Reset" bullet mentions the additional running accumulators. The same
  story applies to `LinRegSlope` and `LinRegAngle` (the page now links
  to both rather than repeating the derivation three times).

- `Indicator-Sma.md` and `Indicator-BollingerBands.md` mention the
  periodic reseed (`16 · period` updates) that caps floating-point
  drift on long-running streams. Amortised cost is still O(1) and the
  user-facing behaviour on benign inputs is unchanged.

No behavioural claim, no API claim, no example changes — just narrative
catching up with the implementation.
This commit is contained in:
kingchenc
2026-05-23 11:03:18 +02:00
parent 896b71fc62
commit 6fd110b4ce
3 changed files with 23 additions and 3 deletions
@@ -23,7 +23,12 @@ SMA_t = (1 / n) * Σ_{i=0}^{n-1} price_{t-i}
where `n = period`. Maintained incrementally as `sum -= window.pop_front();
sum += new_price; out = sum / n`, so `update` is O(1) regardless of
`period`.
`period`. To keep f64 rounding error bounded on long-running streams (where
catastrophic cancellation between add/subtract pairs could otherwise
accumulate), the running `sum` is reseeded from the live window every
`16 · period` updates — still amortised O(1) (`O(period)` work amortised
over `O(period)` updates), zero observable change on inputs that did not
drift to begin with.
## Parameters
@@ -57,6 +57,16 @@ step. Because `Input = f64` it can sit inside a [`Chain`](../../Indicator-Chaini
`LinearRegression::new(14).warmup_period() == 14`. The first value lands once
the window holds a full `period` prices — on input index `period 1`.
## Complexity
Each `update` is **O(1)**: the `Σx` and `Σxx` terms depend only on `period`
and are precomputed once at construction, and `Σy` / `Σxy` are maintained
incrementally as the window slides via the closed-form identity
`new_Σxy = old_Σxy old_Σy + popped_y₀` (then `Σxy += (n 1) · new_value`
and `Σy += new_value`). The same applies to
[`LinRegSlope`](Indicator-LinRegSlope.md) and
[`LinRegAngle`](Indicator-LinRegAngle.md).
## Edge cases
- **`period < 2`.** Rejected at construction — a regression line is undefined
@@ -65,7 +75,8 @@ the window holds a full `period` prices — on input index `period 1`.
the endpoint equals the current value (`perfect_line_returns_current_value`
pins this).
- **Constant series.** A flat input returns that constant.
- **Reset.** `lr.reset()` clears the rolling window.
- **Reset.** `lr.reset()` clears the rolling window and the running `Σy` /
`Σxy` accumulators.
## Examples
@@ -31,7 +31,11 @@ lower = mean - multiplier * stddev
Wickra computes `var` from the streaming sums `Σ x` and `Σ x²` as
`Σx²/n - (Σx/n)²` and clamps to `0.0` to absorb catastrophic cancellation on
near-constant inputs (`crates/wickra-core/src/indicators/bollinger.rs:82`).
near-constant inputs (`crates/wickra-core/src/indicators/bollinger.rs`). On
long-running streams the running `Σ x` and `Σ x²` are reseeded from the live
window every `16 · period` updates — amortised O(1), bounds the cancellation
drift to roughly `16 · period · ULP · max(|x|²)` (sub-picodollar on
real-world price scales).
## Parameters