feat: use nat_pow in the kernel#2310
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leodemoura merged 1 commit intoleanprover:masterfrom Jul 10, 2023
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Alternative to leanprover/lean4#2310. The original implementation of the pow extension would force a `Nat.pow` application by defeq, but this should only be done for kernel-approved definitions and `Nat.pow` is not one of them. Rather than adding more things to the kernel, we can implement an efficient pow implementation by binary recursion, using the clauses: * `a ^ (2*b) = a^b * a^b` * `a ^ (2*b + 1) = a^b * a^b * a` Co-authored-by: Scott Morrison <scott.morrison@gmail.com>
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@leodemoura Just so you know, after this PR I posted a fix to norm_num (linked above) which solves the motivating issue for this change (it was not supposed to be as slow as it was). This modification is still a ~2x performance boost over building proof terms as in the linked issue, but it is no longer the 1000x improvement quoted in the PR description. I am okay with either keeping the new function or reverting it, but it is not essential to us. |
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Alternative to leanprover/lean4#2310. The original implementation of the pow extension would force a `Nat.pow` application by defeq, but this should only be done for kernel-approved definitions and `Nat.pow` is not one of them. Rather than adding more things to the kernel, we can implement an efficient pow implementation by binary recursion, using the clauses: * `a ^ (2*b) = a^b * a^b` * `a ^ (2*b + 1) = a^b * a^b * a` Co-authored-by: Scott Morrison <scott.morrison@gmail.com>
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Enable using the existing
lean_nat_powfunction in the kernel.This enables mathlib4's Mersenne prime checker to get beyond
2^23209 - 1(from 1979). It's now done2^216091 - 1(from 1985), and I suspect that the current implementation, plus this tweak, would be sufficient to get (slowly) to the modern era if someone wanted to spend the CPU time.