stillwater-sc / universal / 29875024018
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test(elreal): diagnostic + characterization for the asin/sqrt round-trip cap (#1076) (#1179)

Preserves the #1076 investigation in the test suite (the MANUAL_TESTING-guarded
diagnostic-code habit): why sin(asin(x))==x / cos(acos(x))==x caps at ~234 digits,
the sole remaining Phase-7 (#931) acceptance gate.

New elastic/elreal/math/asin_sqrt_precision.cpp carries:
- ASSESSMENT (file header): the full root-cause chain --
  1. premature termination of the sin Maclaurin series (asin arg drives the term
     stream EMPTY at term 60 vs a clean pi/6's 76; the dropped terms 60-76,
     mag 10^-234..10^-306, ARE the cap);
  2. terms progressively lose deep blocks via value cancellation (a deeper series
     floor has no effect);
  3. upstream root: sqrt(0.75) (Newton) plateaus at 19 blocks regardless of depth
     (D=20..40), starving the asin argument; pi_zbcl (no sqrt) reaches 20+;
  4. it is the decomposition, not accuracy/count: a clean pi/6 TRUNCATED to 19
     blocks still gives sin=306, but asin's 19-block form gives 234.
  Plus the fix directions ruled out and two candidate fixes for a follow-up.
- MANUAL_TESTING diagnostic: the instrumented term-stream trace, the chain
  block-count-vs-depth trace, and the decomposition-vs-count experiment, with the
  measured results, hand-run by flipping MANUAL_TESTING to 1.
- REGRESSION_LEVEL_4 characterization that LOCKS the diagnosis facts: sqrt's
  19-block plateau is depth-independent, a clean pi/6@19-blocks still reaches
  >=300, and the round-trip is at its ~234 floor. It fails loudly (with the exact
  next step) if the round-trip reaches >=300 -- i.e. when #1076 is fixed, prompting
  the ELREAL_SINCOS_ROUNDTRIP_HIGH_PRECISION gate flip in
  transcendentals_highprecision.cpp.

Fast tiers (LEVEL_1) run a near no-op (instant); the depth-20 characterization is
~6s at LEVEL_4. gcc + clang, warning/cppcheck clean.

Relates to #1076, #931

49913 of 58859 relevant lines covered (84.8%)

7019595.87 hits per line

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