Function moneyFlowIndex

Money Flow Index — rsi computed on money flow instead of price:

typicalPrice = (high + low + close) / 3
rawMoneyFlow = typicalPrice · volume
positive     = Σ rawMoneyFlow where typicalPrice rose        over `period`
negative     = Σ rawMoneyFlow where typicalPrice fell
MFI          = 100 · positive / (positive + negative)
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A bounded 0…100 oscillator, read for the same overbought / oversold / divergence signals as RSI, but with each bar's move weighted by the money that changed hands on it — which is why it is sometimes called "volume-weighted RSI". Appends one column.

Two differences from RSI, both real

• The window is a plain sum, not Wilder's smoothing. RSI averages its gains and losses with (prev·(n−1) + x)/n, which never forgets; MFI sums the last period flows and drops the rest. So MFI's answer depends only on the window, and a gap leaves it once the window passes — the asymmetry atr/rsi document from the other side.
• Direction comes from the typical price, not the close. A bar whose close rose but whose range fell can be a down-flow bar.

The sums are two rollingMeanValues passes over the up-flow and down-flow arrays. Means rather than sums because the kernel exists and the shared 1/period cancels in the ratio — the same trick rollingWeightedMeanValues uses — so nothing is lost and no second window loop is written.

Definition, verified

TA-Lib's MFI, exactly on gap-free bars: cross-checked bar-for-bar in the oracle fixture at period 14 and 5 (agreement to 2.8e-14, identical warm-up masks). An unchanged typical price contributes to neither sum, which is TA-Lib's rule too (its C code adds to posSumMF on > and to negSumMF on <, and to neither on equality).

Edges

• Warm-up is period rows, not period − 1 — the first bar has no previous typical price, so the first window of period changes closes on bar period. Same off-by-one rsi and atr have, and TA-Lib's own lookback.
• A window with no money flow at all → undefined. Reachable two ways: every typical price in the window unchanged (nothing rose or fell), or no volume at all. 0 / 0 has no relative strength, which is exactly the call rsi makes on a flat window. TA-Lib reports 0 for this case — measured (0.7.1): a 20-bar flat series at period 5 gives 0, and so does a rising series with zero volume. 0 is MFI's most bearish possible reading, for a window that showed no direction at all.
• TA-Lib also reports 0 whenever the window's total flow is below 1.0, which is a magnitude guard rather than a definition: measured on a strictly rising 20-bar series with volume 1e-9 per bar, TA-Lib returns 0 where the answer is 100. This study has no such threshold — a market denominated in small units is still a market — so the two disagree there by the whole range of the indicator. (Real money flow is a price times a share count; the case does not arise on equity data, which is presumably why it has survived in TA-Lib.)
• All up → 100, all down → 0, both agreeing with TA-Lib.
• A gap in any input costs two windows' worth: the bar itself and the bar after it (whose direction reads the missing typical price), and every window containing either. It recovers once they leave.
• Invariant under scaling price and under scaling volume — a ratio of flows, so both cancel. Pinned by property tests, with the 0…100 bound.