stillwater-sc / universal / 26231867755
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feat(elreal): Phase E.4 -- hyperbolic family with depth-1 derivative refinement (#896)

Phase E.4 of epic #873 (resolves #890). Six hyperbolic functions
(sinh, cosh, tanh + inverses) following the same uniform pattern
established in Phase E.3: std library at depth 0, derivative-based
correction at depth 1.

Per-function derivatives:
  d/dx sinh(x)  = cosh(x)         -> cosh(a0) * a.at(1)
  d/dx cosh(x)  = sinh(x)         -> sinh(a0) * a.at(1)
  d/dx tanh(x)  = 1 - tanh^2(x)   -> (1 - c0*c0) * a.at(1)
  d/dx asinh(x) = 1 / sqrt(1+x^2) -> a.at(1) / sqrt(1+a0*a0)
  d/dx acosh(x) = 1 / sqrt(x^2-1) -> a.at(1) / sqrt(a0*a0-1)
  d/dx atanh(x) = 1 / (1 - x^2)   -> a.at(1) / (1 - a0*a0)

Edge cases handled by std lib propagation:
  acosh(x < 1)    -> NaN
  atanh(|x| > 1)  -> NaN
  atanh(+/-1)     -> +/-inf (derivative diverges; depth-1 skipped)

Tests under elastic/elreal/math/hyperbolic.cpp:
  - Anchor values at zero (sinh(0)=0, cosh(0)=1, tanh(0)=0,
    asinh(0)=0, acosh(1)=0, atanh(0)=0)
  - Hyperbolic Pythagorean identity cosh^2 - sinh^2 == 1
  - Cross-validation vs std::sinh/cosh/tanh/asinh/acosh/atanh
  - Round-trip identities asinh(sinh(x))=x, acosh(cosh(x))=|x|,
    atanh(tanh(x))=x
  - Edge cases acosh(0.5)=NaN, atanh(2)=NaN, atanh(1)=inf
  - NaN propagation through all six
  - Depth-1 propagation on rational input (1/3 and 4/3 for acosh)

20 elreal binaries (1 new + 19 prior) PASS on gcc 13 and clang.

Co-authored-by: Claude Opus 4.7 (1M context) <noreply@anthropic.com>

46942 of 55729 relevant lines covered (84.23%)

5278467.79 hits per line

Coverage Regressions

Lines Coverage ∆ File
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Jobs
ID Job ID Ran Files Coverage
1 26231867755.1 651
84.23
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