Every single sliding piece (ie: Rooks, Bishops, and Queens) use PEXT (or magic-bitboards if the PEXT code is unavailable) to determine where to go. Its a fundamental calculation to determine very, very quickly which moves are legal or not.
Both PEXT and Magic Bitboards are incredible techniques for solving the sliding-piece question. However, PEXT is much much much faster, but relies upon an obscure x86-only assembly instruction (that is slower on AMD Zen or Zen2 unfortunately. So you still need to know your hardware details, Intel machines should use the PEXT version).
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Still, even AMD users want the BMI2 version, which has a bunch of bit-operations that can be optimized that are used all the time. (And besides, AMD Zen3 is actually faster on PEXT now, so PEXT is looking good for the future)
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In either case, I have my doubts that the NNUE neural-net runs anywhere near as good on WASM than on the hand-optimized SIMD / AVX kernels that the Stockfish team wrote.
Even if there's some auto-vectorization that WASM can do, its really hard to beat handcrafted assembly / intrinsics (https://github.com/official-stockfish/Stockfish/blob/master/...)
Both Magic Bitboards and PEXT are run every single time Stockfish thinks of a Queen, Bishop, or Rook. Literally every, single, time.
Stockfish does something like 10-million positions per second or something. That's a lot of times the "where can the Queen move" analysis is run. Speeding that routine up by 50% or something (PEXT vs Magic Bitboards) really does make a difference in the great scheme of speed.
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Unless you're playing some fantasy-version of Chess (or maybe some extreme endgame where all pawns, queens, bishops, and rooks are dead... pawns because they might promote into a queen/bishop/rook), you'll be benefiting from selecting that PEXT version if you're on an Intel or Zen3 processor.
EDIT: Both PEXT and Magic Bitboards have a "Setup" phase that is run once. But there's also a separate phase that is run on every single position in the actual chess-board part.
I should probably know this, since I "discovered" PEXT bitboards, but I got out of computer chess before I got BMI-capable hardware, and so I never actually implemented them :)