IxVM kernel: klimbs_pow via binary exponentiation#455
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Replace `klimbs_mul(base, klimbs_pow(base, klimbs_dec(exp)))`'s O(exp) per-step memo growth with a binary-exponentiation recursion of depth O(log exp). Both `exp / 2` and `exp % 2` route through the native `unconstrained_big_uint_div_mod` op, so each level pays O(1) for the division — `log2(exp)` memo entries for `klimbs_pow` itself + the `klimbs_mul(base, base)` doublings. `lake test -- --ignored ixvm` on `IxVMPrim.nat_pow_big` (`(2 ^ 16384 : Nat) - 2 ^ 16384 = 0`, measured against the current `ap/utf8-mod-witness` baseline): 3_941_276_885 → 71_856_587 FFT (-98.2%). Tests/Ix/IxVM.lean: * new `IxVMPrim.nat_pow_big` synthetic — exercises `klimbs_pow` at a non-trivial exponent (`2 ^ 16384`) so future regressions in the body shift its FFT pin. * small pin shifts in `nat_shl_lit`, `nat_shr_lit`, `nat_div_lit`, `nat_mod_lit`, `nat_gcd_lit`, `bv_to_nat_lit` — all reduce via `klimbs_pow` / `klimbs_div_mod` and absorb the new cost shape.
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Replace
klimbs_mul(base, klimbs_pow(base, klimbs_dec(exp)))'s O(exp) per-step memo growth with a binary-exponentiation recursion of depth O(log exp). Bothexp / 2andexp % 2route through the nativeunconstrained_big_uint_div_modop, so each level pays O(1) for the division —log2(exp)memo entries forklimbs_powitself + theklimbs_mul(base, base)doublings.lake test -- --ignored ixvmonIxVMPrim.nat_pow_big((2 ^ 16384 : Nat) - 2 ^ 16384 = 0, measured against the currentap/utf8-mod-witnessbaseline):3_941_276_885 → 71_856_587 FFT (-98.2%).
Tests/Ix/IxVM.lean:
IxVMPrim.nat_pow_bigsynthetic — exercisesklimbs_powat a non-trivial exponent (2 ^ 16384) so future regressions in the body shift its FFT pin.nat_shl_lit,nat_shr_lit,nat_div_lit,nat_mod_lit,nat_gcd_lit,bv_to_nat_lit— all reduce viaklimbs_pow/klimbs_div_modand absorb the new cost shape.