Lean 4 fork for HoTT-compatible kernel extensions (Path types, transport, HITs). Maintained against upstream leanprover/lean4.
3e11f27ff4
This PR implements the fast circuit for overflow detection in unsigned multiplication used by Bitwuzla and proposed in: https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=987767 The theorem is based on three definitions: * `uppcRec`: the unsigned parallel prefix circuit for the bits until a certain `i` * `aandRec`: the conjunction between the parallel prefix circuit at of the first operand until a certain `i` and the `i`-th bit in the second operand * `resRec`: the preliminary overflow flag computed with these two definitions To establish the correspondence between these definitiions and their meaning in `Nat`, we rely on `clz` and `clzAuxRec` definitions. Therefore, this PR contains the `clz`- and `clzAuxRec`-related infrastructure that was necessary to get the proofs through. An additional change this PR contains is the moving of `### Count leading zeros` section in `BitVec.Lemmas` downwards. In fact, some of the proofs I wrote required introducing `Bitvec.toNat_lt_iff` and `BitVec.le_toNat_iff` which I believe should live in the `Inequalities` section. Therefore, to put these in the appropriate section, I decided to move the whole `clz` section downwards (while it's small and relatively self contained. Specifically, the theorems I moved are: `clzAuxRec_zero`, `clzAuxRec_succ`, `clzAuxRec_eq_clzAuxRec_of_le`, `clzAuxRec_eq_clzAuxRec_of_getLsbD_false`. The fast circuit is not yet the default one in the bitblaster, as it's performance is not yet competitive due to some missing rewrites that bitwuzla supports but are not in Lean yet. co-authored-by: @bollu --------- Co-authored-by: Tobias Grosser <tobias@grosser.es> |
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