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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 | import OAI.Combinatorics.LowSpaceSubsetSum.Word.WordSeedScalarExecution
namespace OAI
/-! # Executed prime-modulus initialization from its known width -/
noncomputable section
namespace LowSpaceSubsetSum.WordSeedMeasured
def primeInitialized (w n ell : ℕ) (hell : 4 ≤ ell) (hw : ell ≤ w) :
Execution (WordSeedRealization.prime w n ell hell hw) where
run stream cursor :=
let modulus := WordSeedPowerExecution.run ell
let r := (prime w n ell hell hw modulus.1
(WordSeedPowerExecution.run_value ell)).run stream cursor
⟨r.accepted,r.cursor,modulus.2+r.work+1,max 16 (r.cells+8),r.retained⟩
value stream cursor :=
(prime w n ell hell hw (WordSeedPowerExecution.run ell).1
(WordSeedPowerExecution.run_value ell)).value stream cursor
theorem primeInitialized_bounded (w n ell : ℕ) (hell : 4 ≤ ell) (hw : ell ≤ w) :
(primeInitialized w n ell hell hw).Bounded
(n^3*(12*2^((ell+1)/2)+12*(ell+1)+11)+3*ell+17)
(2*n^3+124) (n^3+18) := by
intro stream cursor
have h := prime_bounded w n ell hell hw (WordSeedPowerExecution.run ell).1
(WordSeedPowerExecution.run_value ell) stream cursor
dsimp only [primeInitialized]
rw [WordSeedPowerExecution.run_work]
exact ⟨by omega,max_le (by omega) (by omega),h.2.2⟩
end LowSpaceSubsetSum.WordSeedMeasured
end
end OAI
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