feat(eri): Elder Ray Index, Bull and Bear Power against one EMA (#361)

[kevinlincg]

Implements #361: TA_ERI — Bull Power = High − EMA(Close, n), Bear Power = Low − EMA(Close, n), both lines against one shared EMA (Elder, Trading for a Living, 1993). Default 13, two line outputs, lookback = ema_lookback(n) with the EMA unstable period consumed in the warm-up; UNSTABLE_MAP gains {"ERI", TA_FUNC_UNST_EMA} per the issue's item 3. One fused loop per the issue's Notes — a composed ema() + combine form cannot stream (the ACCBANDS rationale), and no compatibility branch (EFI/SMI precedent). No division anywhere: no NaN path (#112 by construction).

Two generator inventories, each caught by its own gate

ERI is the first function since those gates landed to be simultaneously fma-fusing (the inlined EMA recurrence lowers through explicit fma() via the #183 pass) and transitively unstable (through the hard-coded inner EMA). Both static inventories gained their row after their gate flagged the drift — FUSING_INVENTORY in backends/fma.rs and INHERITED in stability_suite.rs — which is exactly the drift those gates exist to catch (the efi incident in FUSING_INVENTORY's own docstring).

Tests (test_eri.c, registered in CMakeLists + Makefile.am + DO_TEST; note --function=ERI substring-matches HT_DCPERIOD, so the tag is exact)

• Differential, bit-exact and non-tautological: shipped TA_EMA + two subtractions, memcmp'd over 5 periods × 6 startIdx × 4 EMA-unstable-periods (≥10000-value floor), with the bull ≥ bear invariant free on every cell. The fused loop reproduces ema.c's DEFAULT arm op for op — seed-sum order and warm-up both covered by the unstable axis.
• Golden pins at the defaults, ABSOLUTE tolerance 1e-12 per the issue's decision 1: ERI is a cancelling difference and relative error is unbounded at the zero crossings that carry the signal (the issue measured 1.9e-10 rel at an out-value of −1.5e-4). Rows pinned away from zero crossings (|value| ≥ 0.5). Provenance: from-scratch transcription of ema.c's DEFAULT arm on the committed TA_SREF corpus — the NVI/PVI pattern; the issue measured pandas-ta-classic 0.6.52 against the same transcription at max abs 7.1e-14, so the rows hold against either.
• Edges: all-flat ⇒ both lines exactly 0.0; high == low ⇒ the two lines bitwise identical; n=1 ⇒ bull == high − close bit for bit (the EMA identity survives the fma lowering with no special case — verified, not assumed).
• In-place aliasing, each of the 2 outputs onto each of the 3 inputs — the widest aliasing surface of any recent addition; the bar's extremes are loaded into temps before either output is written.

Verification

Full --codegen (all four languages) rc 0, stream_verify green (tier T2 scalar recurrence), --xlang-hash zero non-baseline mismatches, full generator suite + clippy + regen-check + check-source-lists clean. The pandas oracle arm already exists in the oracle infrastructure outside this repo; the trading-signals arm is left to it. CHANGELOG entry added.

[mario4tier]

Reviewed. One blocker, one vacuous gate, and two doc items.

Blocker — the inlined EMA drops ema.c's period-1 identity arm

ema.c:61 carries an explicit if( optInTimePeriod == 1 ) short-circuit that returns a bit-exact copy of the input. eri.c's transcription has none, and eri.yaml declares range: [1, 100000], so period 1 is legal and reachable.

At n == 1, k is exactly 1.0 and the recursion degenerates to fma(x - prev, 1.0, prev) = fl(fl(x - prev) + prev), which equals x only while consecutive closes stay within a factor of two (Sterbenz). So TA_ERI(…, 1) is not high - TA_EMA(close, 1).

That breaks three things at once: the bit-exact contract issue #361 decision 2 ruled on, the assertion in your own comment at eri.c:44-47 ("the differential against shipped TA_EMA holds bitwise"), and the premise of the tests below.

The n=1 legs cannot catch it — test_eri.c:246 memcmps outBull against high - close, and n=1 is in eriPeriodGrid at :89 — because the TA_SREF corpus is Sterbenz-benign, so the recursion happens to return x on every bar of it. A series with a consecutive close ratio outside [0.5, 2] would turn both red.

The aliasing sweep detects nothing it exists for

test_eri.c:285 runs section 4 at optInTimePeriod = 13 only. There outBegIdx = 12, so every store sits 12 slots behind the load and none of the six aliasing combinations can bite. Running it at the minimum period is what would exercise it.

Documentation

• eri.md:5 — the Summary hard-codes the default as though the period were fixed: "distance … from a 13-period EMA of the close". optInTimePeriod is a parameter with range 1..100000, so the definition is false for every other value. This sentence is the only definition carried into rustdoc, javadoc and the C# XML docs, so it ships to three backends.
• eri.md:9 — "TradingView additionally plots the sum of the two as a third line" is not right. TradingView's built-in Bull Bear Power — which its own support page calls "otherwise known as the Elder-Ray Index" — plots only the sum, not three lines.