KACTL ModMul. It says that it runs around 2x faster than naive
(__int128_t)a * b % M
When I ran my benchmarks with -O2, the results were similar. Am I mistaken?
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This is only one mod operation, try doing more operations and benchmarking.
I did that. I did 1e5 runs and their running time was basically the same.
1e5 operations is not very many. That should take around 1 millisecond. Try something like 1e10 of them to spot a consistent difference. Also make sure the compiler can't optimize it out.