From 6fd110b4ce8f227b02d2a84aee2836b0f2ca0c81 Mon Sep 17 00:00:00 2001
From: kingchenc <kingchencp@gmail.com>
Date: Sat, 23 May 2026 11:03:18 +0200
Subject: [PATCH] docs(wiki): document O(1) regression update and long-stream
 sum reseed (R2, R7)
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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.
---
 .../indicators/moving-averages/Indicator-Sma.md     |  7 ++++++-
 .../price-statistics/Indicator-LinearRegression.md  | 13 ++++++++++++-
 .../volatility-bands/Indicator-BollingerBands.md    |  6 +++++-
 3 files changed, 23 insertions(+), 3 deletions(-)

diff --git a/docs/wiki/indicators/moving-averages/Indicator-Sma.md b/docs/wiki/indicators/moving-averages/Indicator-Sma.md
index 2e25ef1b..f828820a 100644
--- a/docs/wiki/indicators/moving-averages/Indicator-Sma.md
+++ b/docs/wiki/indicators/moving-averages/Indicator-Sma.md
@@ -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
 
diff --git a/docs/wiki/indicators/price-statistics/Indicator-LinearRegression.md b/docs/wiki/indicators/price-statistics/Indicator-LinearRegression.md
index c332a165..a5d18044 100644
--- a/docs/wiki/indicators/price-statistics/Indicator-LinearRegression.md
+++ b/docs/wiki/indicators/price-statistics/Indicator-LinearRegression.md
@@ -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
 
diff --git a/docs/wiki/indicators/volatility-bands/Indicator-BollingerBands.md b/docs/wiki/indicators/volatility-bands/Indicator-BollingerBands.md
index c8b4c9c5..bb163454 100644
--- a/docs/wiki/indicators/volatility-bands/Indicator-BollingerBands.md
+++ b/docs/wiki/indicators/volatility-bands/Indicator-BollingerBands.md
@@ -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