File size: 3,422 Bytes
e63eb7f | 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 | import OAI.Combinatorics.EditApproximation.Queries.QueryFamilySpace
import OAI.Combinatorics.EditApproximation.Queries.QueryChargedWarmupSpace
import OAI.Combinatorics.EditApproximation.Queries.QueryChargedFamily
namespace OAI
namespace EditApproximation
open BitQuery
section Family
variable {M J R passes copies T S : ℕ} [NeZero M] [NeZero R]
(source target : List ℕ) (N P F exponent H Q eM eF : ℕ)
(hP : 0 < P) (hM : M = 2 ^ eM) (hF : F = 2 ^ eF)
(A a : ℕ → BinaryFraction) (tau eta kappa delta : BinaryFraction) (multiplier : ℕ → ℕ)
(occurrence : BinaryMemo PositionCounts) (symbolBits positionBits : ℕ)
def queryChargedFamilyTableHeap
(parent : {r : PhysicalTableRequest M J target.length // r.Bounded (passes + 1) copies T S}) :
Heap (queryChargedFamilyTable (R := R) source target N P F exponent H Q eM eF hP hM hF
A a tau eta kappa delta multiplier occurrence symbolBits positionBits parent) := by
have hinit := queryPhysicalInitialHeap source target N P F (A parent.val.pass) (a parent.val.pass)
multiplier parent occurrence symbolBits positionBits parent.val.state
unfold queryChargedFamilyTable
refine Heap.chargeOf (naturalWordLEAllocation parent.val.index.bits T.bits)
((naturalWordLEAllocation_le_work _ _).trans (Nat.le_succ _)) ?_
split
· exact (queryChargedWarmupHeap source target N P F (A parent.val.pass) (a parent.val.pass)
multiplier parent occurrence symbolBits positionBits).mapKeysWithWork _ (fun _ => 1) (fun _ => le_rfl)
· refine Heap.chargeOf (parent.val.node.1.val.bits.length + J.bits.length)
((bitCompareWithWork_input_cells _ _).trans (Nat.le_succ _)) ?_
split
· let interval := physicalSourceInterval source.length parent.val.node
have hl := saturatingSubtractAllocation_le_work interval.hi interval.lo
have ht := naturalWordLEAllocation_le_work (saturatingSubtractWithWork interval.hi interval.lo).1 [true]
refine Heap.chargeOf (saturatingSubtractAllocation interval.hi interval.lo +
naturalWordLEAllocation (saturatingSubtractWithWork interval.hi interval.lo).1 [true]) (by
dsimp only [interval] at hl ht ⊢
omega) ?_
split
· exact hinit.mapKeysWithWork _ (fun _ => 1) (fun _ => le_rfl)
· exact (queryFamilyBoundedActiveHeap (R := R) source target N P F exponent H Q eM eF hP hM hF
tau (a parent.val.pass) eta kappa delta T S passes copies parent _ _).mapKeysWithWork _
(fun _ => 1) (fun _ => le_rfl)
· exact hinit.mapKeysWithWork _ (fun _ => 1) (fun _ => le_rfl)
def queryChargedFamilyGlobalHeap
(coarse : PhysicalEntry M J target.length → BinaryFraction × ℕ)
(allocation : PhysicalEntry M J target.length → ℕ)
(hc : ∀ entry, allocation entry ≤ 3 * (coarse entry).2)
(request : ChargedPhysicalRequest M J target.length (passes + 1) copies T S) :
Heap (queryChargedFamilyGlobal (R := R) source target N P F exponent H Q eM eF hP hM hF
A a tau eta kappa delta multiplier occurrence symbolBits positionBits coarse request) := by
cases request with
| inl entry => exact Heap.compute (coarse entry) (allocation entry) (hc entry)
| inr parent =>
exact queryChargedFamilyTableHeap (R := R) source target N P F exponent H Q eM eF hP hM hF
A a tau eta kappa delta multiplier occurrence symbolBits positionBits parent
end Family
end EditApproximation
end OAI
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