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e5a97c6 | 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 | import OAI.Combinatorics.LowSpaceSubsetSum.Word.WordSeedPowerExecution
import OAI.Combinatorics.LowSpaceSubsetSum.Storage.PrimeTestCells
namespace OAI
/-! # Prime testing with executed scalar initialization
Both powers used by the test are produced by the doubling cursor. The
divisor scan consumes the computed limit directly and retains scalar state.
-/
namespace LowSpaceSubsetSum.WordSeedPrimeTestExecution
def run (ell : ℕ) (p : Fin (2^ell)) : (Bool × ℕ) × ℕ :=
let modulus := WordSeedPowerExecution.run ell
let limit := WordSeedPowerExecution.run ((ell+1)/2)
let r := PrimeTestCells.scan p.val (limit.1-1) 2 0
((decide (modulus.1 ≤ 4*ell*p.val) && (decide (2 ≤ p.val) && r.1.1.isNone),
12*r.1.2+modulus.2+limit.2+7), max 16 (r.2+16))
theorem run_value (ell : ℕ) (p : Fin (2^ell)) :
(run ell p).1.1 = (SamplerAttempts.primeTest ell p).1 := by
rw [← PrimeTestCells.test_value]
simp only [run, WordSeedPowerExecution.run_value, PrimeTestCells.test,
PrimeTestCells.divisors]
theorem run_work (ell : ℕ) (p : Fin (2^ell)) :
(run ell p).1.2 ≤ 12*2^((ell+1)/2)+12*(ell+1) := by
have h := SamplerAttempts.divisorsBits_tests ell p
rw [← PrimeTestCells.divisors_value] at h
dsimp only [PrimeTestCells.divisors] at h
simp only [run, WordSeedPowerExecution.run_value, WordSeedPowerExecution.run_work]
omega
theorem run_cells (ell : ℕ) (p : Fin (2^ell)) : (run ell p).2 = 28 := by
simp only [run, PrimeTestCells.scan_cells]
rfl
end LowSpaceSubsetSum.WordSeedPrimeTestExecution
end OAI
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