stillwater-sc / universal / 29830039050
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feat(tools): accuracy-vs-compute-time characterization for elreal and ereal (#1174)

* feat(tools): accuracy-vs-compute-time characterization for elreal and ereal

New benchmark/accuracy/adaptive/characterize.cpp maps, for the two adaptive-
precision real oracles, the relationship between accuracy, the precision knob,
and wall-clock time -- so library default depths can be chosen from evidence.

For each function it sweeps the knob (elreal `depth` at runtime; ereal limb count
`N` over a fixed compile-time list {2,4,8,12,16}) and reports:
  * median wall-clock time per evaluation, and
  * accuracy as decimal digits of agreement with an independent ~320-digit
    reference (math/constants/reference_constants.hpp), via the exact dyadic
    oracle -- verification/elreal_reference_digits.hpp's zbcl_to_dyadic +
    agreed_decimal_digits for elreal, and a limb-sum dyadic for ereal -- plus
    correct bits and an implied relative error.

Output is a CSV (type, FpType, function, depth, time_ns, correct_digits,
correct_bits, rel_error) followed by a per-function saturation-depth + accuracy/
time-knee summary and an elreal-vs-ereal comparison (cheapest config reaching a
target accuracy). Functions: sqrt/exp/log/sin/cos/tan/sinh/cosh/tanh against
their reference values, plus add/mul/div timing (accuracy exact, so time-only).
A gnuplot script renders the accuracy-vs-time Pareto curves.

Usage: characterize [maxDepth=3] [reps=3]; raise maxDepth for a full run (the
elreal transcendentals cost 100s of ms at depth >= 4). Registered with
compile_all("false") -- it builds in CI but is a measurement utility, not a
pass/fail ctest. Host FpType fixed to double; the float/bfloat16/fp16 host matrix
is a follow-up.

Validated on gcc and clang. This is a measurement tool only; it does not touch
the implementations.

Resolves #1040

Co-Authored-By: Claude Opus 4.8 (1M context) <noreply@anthropic.com>

* fix(tools): add optimizer barrier to ereal timing + fix usage comment (Code... (continued)

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