File size: 3,506 Bytes
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 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 | import OAI.Combinatorics.LowSpaceSubsetSum.Word.WordSeedPreparedBind
import OAI.Combinatorics.LowSpaceSubsetSum.Storage.LayoutPreparationCells
namespace OAI
/-! # Computing layout-dependent sampling parameters from a stored seed
The mixer counts, order and prime widths are obtained by the counted stored
preparation. They are not evaluated implicitly while selecting a sampler.
-/
noncomputable section
namespace LowSpaceSubsetSum.WordLayoutPreparation
variable {n : ℕ}
abbrev Layout (I : Instance n) :=
WordSeedMeasured.Accepted (canonicalRepresentationData I).zeroSetup.layoutCoupling
abbrev Prepared (I : Instance n) (a : Layout I) :=
{d : RepresentationLayoutPreparation.Data n //
(LayoutPreparationCells.run I a.seed.val).1.1 = some d}
theorem source (I : Instance n) (a : Layout I) :
(canonicalRepresentationData I).zeroSetup.layoutCoupling.bounded a.seed.val = some a.value :=
(WordSeedRealization.successful_agrees a.seed).trans (congrArg some a.correct.symm)
theorem exists_data (I : Instance n) (a : Layout I) : Nonempty (Prepared I a) := by
obtain ⟨d,hd,_⟩ := RepresentationLayoutPreparation.complete
(canonicalRepresentationData I) a.seed.val a.value.1 a.value.2 (source I a)
exact ⟨⟨d,(congrArg Prod.fst (LayoutPreparationCells.value I a.seed.val)).trans hd⟩⟩
def compute (I : Instance n) (a : Layout I) : (Prepared I a × ℕ) × ℕ :=
let out := LayoutPreparationCells.run I a.seed.val
match h : out.1.1 with
| none => False.elim (by
obtain ⟨d⟩ := exists_data I a
cases h.symm.trans d.property)
| some d => ((⟨d,h⟩,out.1.2+1),out.2+8)
theorem fields (I : Instance n) (a : Layout I) (d : Prepared I a) :
(∀ i : Fin n, d.val.permutation[i.val] = a.value.1 i) ∧
(∀ i : Fin 4, d.val.parameters.widths[i.val] =
(canonicalRepresentationData I).zeroSetup.samplerPrimeWidths a.value i) := by
have hd := (congrArg Prod.fst (LayoutPreparationCells.value I a.seed.val)).symm.trans d.property
obtain ⟨e,he,hv,_,hw⟩ := RepresentationLayoutPreparation.value
(canonicalRepresentationData I) a.seed.val d.val hd
have heq : (e,d.val.signs.semantic) = a.value := Option.some.inj (he.symm.trans (source I a))
constructor
· intro i
have hi := congrArg (fun z => z.1 i) heq
exact (hv i).trans hi
· intro i
exact (hw i).trans (congrArg
(fun z => (canonicalRepresentationData I).zeroSetup.samplerPrimeWidths z i) heq)
theorem work (I : Instance n) (hn : 10000 ≤ n) (a : Layout I) :
(compute I a).1.2 ≤ n*n^3+10*(n+1)^2+4*n+7+
inputScale I^6*2^mixerSize n := by
have hw := RepresentationLayoutPreparation.work (canonicalRepresentationData I) hn a.seed.val
change (RepresentationLayoutPreparation.run (canonicalRepresentationData I) a.seed.val).2 ≤
n*n^3+10*(n+1)^2+4*n+6+inputScale I^6*2^mixerSize n at hw
have hv := congrArg Prod.snd (LayoutPreparationCells.value I a.seed.val)
rw [←hv] at hw
obtain ⟨d⟩ := exists_data I a
unfold compute
dsimp only
split
next h => cases h.symm.trans d.property
· dsimp only
omega
theorem cells (I : Instance n) (hn : 10000 ≤ n) (a : Layout I) :
(compute I a).2 ≤ inputScale I^10*(compressionDictionaryCapacity n+1)+8 := by
have hc := LayoutPreparationCells.cells I hn a.seed.val
obtain ⟨d⟩ := exists_data I a
unfold compute
dsimp only
split
next h => cases h.symm.trans d.property
· dsimp only
omega
end LowSpaceSubsetSum.WordLayoutPreparation
end
end OAI
|