[agourakis82]

Complex log1p(-2 - 0i) returns +pi instead of -pi in its imaginary component. The complex addition in u = 1 + z adds a positive imaginary zero to the input, losing the negative-zero side of the branch cut before log(u) is evaluated.

Translate only the real component and copy the imaginary component unchanged. Preserve the existing small-input correction. Add mixed-lane float/double coverage on both sides of the cut, immediately below -1, at the origin, and for nonzero-imaginary controls. The reference explicitly constructs (1 + real(z), imag(z)) before scalar std::log so it also preserves the zero sign.

Validation (C++23):

• ARM64: identical regression fails before the fix (36 assertions); after the fix, all 4 complex-exponential test cases and 264 assertions pass.
• ASan/UBSan: the same test unit passes.
• Combined exponential/trigonometric/hyperbolic test units pass.
• x86_64 SSE2 under Rosetta, Apple Clang: baseline failure and candidate pass confirmed.
• Physical x86_64 AVX2/FMA, GCC13.3 C++23 on Intel Xeon 6730P: identical baseline tests fail (72 assertions); candidate passes 4 cases / 528 assertions. CPU-only Slurm job 20284 completed with exit 0:0.
• Native AVX2 composition with Handle zero and infinite argument pairs in atan2 #1439 at 94a8f71 passes 12 cases / 2112 assertions (CPU-only Slurm20310), including infinite argument pairs and both zero signs at the endpoint z = -1. That endpoint remains outside this PR alone.
• The unchanged original Complex asin, acos, asinh, acosh, sqrt, log1p, tan, tanh return very different results from std:: #1432 reproducer now matches its scalar reference for log1p(-2 - 0i).
• Formatting and whitespace checks pass.

Addresses the reported log1p branch-cut example in #1432. The exact endpoint z = -1 remains outside this fix: a separate reproducer confirms that existing log(0 +/- 0i) inherits a NaN angle from atan2(0, 0) on the baseline and candidate. New signed-zero assertions are excluded under fast-math. No claim of complete #1432 resolution, nonfinite coverage, exception freedom, full-suite or all-architecture validation.