Replace __sync builtins with C11 atomics in linear algebra

[wegank]

The parallel linear algebra in neogb publishes new pivot rows with __sync_bool_compare_and_swap. That GCC builtin isn't available with MSVC. Also, other threads read the same pivot arrays with plain loads, which is a data race under the C11 memory model. This PR switches to standard <stdatomic.h>.

Changes

• Atomic pivot arrays. The arrays that threads publish into concurrently become _Atomic(T *) arrays: pivs in the sparse echelon forms and nps in the dense ones. So do the sequential interreduction steps that pass them to the same reducers. This covers la_ff_8.c, la_ff_16.c, la_ff_32.c, la_qq.c and the io.c wrappers.
• Memory ordering.
  • New pivots are published by a compare and swap with release ordering, after the row is fully reduced and normalized.
  • The reducers load entries with acquire ordering, so a published row and its coefficients are fully visible to them. Each entry is now loaded once instead of twice.
  • Sequential code after the parallel regions uses relaxed accesses.
  • The rule is documented once, above the new allocate_atomic_pivots() helper in data.c.
• Plain arrays. Arrays that are only read during parallel regions stay plain (sparse_AB_CD_*, the known pivots in probabilistic_sparse_dense_echelon_form_*, SBA). The compare and swap in the sequential kernel computation of exact_sparse_reduced_echelon_form_sat_ff_32 becomes a plain check and store.
• Public headers. data.h is installed and reached from msolve.h, which has extern "C" guards for C++ users. GCC and MSVC reject _Atomic in C++ before C++23, so the four internal 32-bit reducer prototypes whose signatures changed now live only in data.c, which is compiled as part of gb.c. The installed headers don't use atomics.
• configure. It now checks for C11 atomics and fails with a clear message if they're missing.
• Small cleanup. The unrolled pivot-counting loops in the dense linear algebra become a plain loop, which avoids five atomic loads per iteration.

Testing

• neogb compiles without warnings with clang's -Watomic-implicit-seq-cst, so every access to the atomic arrays is explicit.
• make check passes (68/68).
• Stress test: 120 runs with -t 8 produced reduced Gröbner bases identical to single-threaded runs. That covers -l 1/2/42/44 over 8-, 16- and 31-bit primes (eco11 with characteristic 251, 65521 and 1073741827), plus -l 2/42/44 over QQ (kat7).
• Runtime on arm64 (Apple Silicon) is within ±2% of master for eco11 with 1 and 8 threads, -l 2 and -l 44.

Notes

• ./msolve -g 2 -l 1 -f input_files/kat7-qq.ms segfaults even single-threaded. It does so on master as well, so it's unrelated to this PR.
• flag and bad_prime in some echelon form functions are still plain ints written by several threads. This PR doesn't touch them.
• Full MSVC support needs more work beyond this PR (C11 atomics flags, OpenMP 2.0 loop variables, other GCC-isms).

This PR was prepared with the assistance of generative AI (Claude Code). I reviewed the changes and the testing.

🤖 Generated with Claude Code