stillwater-sc / universal / 29876384483
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test(elreal): disprove the sqrt-Newton hypothesis for #1076 (sqrt is 308-digit accurate) (#1180)

Attempted candidate fix (1) -- "make sqrt resolve past the 19-block plateau" --
and DISPROVED it with hard data, updating the #1076 diagnostic accordingly.

Findings:
- sqrt(0.75) is NOT under-resolving: its Newton iteration converges quadratically
  (33 -> 65 -> 129 -> 260 -> 309 digits) and is 308-digit ACCURATE at its 19-block
  floor, unchanged at depth 20..40. The plateau is the ~2^-1022 double-host
  precision floor, not a bug -- sqrt physically cannot go deeper on a double host.
  (div_online inside the Newton step is strictly worse: 224 digits. My earlier
  "125 digits" reading was a truncated reference string.)
- Argument-truncation sweep: pi/6's deep blocks each add ~16 digits to sin (usable),
  but asin's blocks 15..19 add NOTHING (sin stuck at 234). asin's value is
  306-accurate and sin is well-conditioned at pi/6, so sin(asin) OUGHT to reach
  ~306; it reaches 234 because the sin Maclaurin recurrence cannot extract
  precision from asin's deep-block decomposition. The bug is in the series
  machinery, not sqrt/asin accuracy.

Updated asin_sqrt_precision.cpp:
- ASSESSMENT point 3 rewritten: sqrt is accurate/floored, not the bottleneck
  (sqrt-Newton fix disproven). Candidate fixes narrowed to (a) a series recurrence
  robust to a non-prefix deep tail, or (b) a wider intermediate host.
- MANUAL diagnostic gains [3] the sqrt Newton convergence trace and [5] the
  argument-truncation sweep, with measured results.
- LEVEL_4 characterization (a) now locks sqrt's >=300-digit ACCURACY and its
  depth-independence (was locking only block count), so the disproven hypothesis
  cannot silently return.

gcc + clang: MANUAL / LEVEL_1 / LEVEL_4 all pass; warning/cppcheck/ASCII clean.

Relates to #1076, #931

49910 of 58917 relevant lines covered (84.71%)

7012080.1 hits per line

Coverage Regressions

Lines Coverage ∆ File
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 0.0% include/sw/universal/number/posit1/specialized/posit_16_1.hpp
Jobs
ID Job ID Ran Files Coverage
1 29876384483.1 702
84.71
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Source Files on build 29876384483