[agourakis82]

When cosh(2*real(z)) overflows, the real part of complex tanh was an inf/inf quotient and became NaN. The non-fast-math path now substitutes the sign of the real input once the denominator is infinite. An 8 by 8 grid compares the batch with std::tanh, covering huge real parts, signed zeros and ordinary controls. That grid is omitted under fast-math, which does not implement the recovery.

Part of #1432.

Written by me with AI assistance.

[agourakis82]

Published in 1b61a71.

I moved the overflow regression into the existing typed tanh subcase and added finite near-saturation inputs that execute with and without fast-math. The overflow and largest-value inputs retain a narrow strict-mode guard because the implementation's infinity correction is itself guarded in fast-math. The finite comparisons use explicit numerical assertions in both modes.

On macOS ARM64 with Apple Clang 21 and C++23, the scoped complex and real hyperbolic tests pass all four cases in each mode, with 128 assertions in strict mode and 28 in fast-math. Removing the overflow correction in an isolated header copy causes 40 assertions to fail in strict mode. A separate numerator mutation is rejected in both modes, confirming that the shared finite numerical checks execute.

Prepared with OpenAI Codex assistance.

[DiamonDinoia]

Superseded by #1456