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5d5048e | 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 | import OAI.Combinatorics.LowSpaceSubsetSum.Compression.CompressionInitialization
import OAI.Combinatorics.LowSpaceSubsetSum.Storage.MeasuredRowCells
namespace OAI
/-! # Constant live scratch for a compression row's three binary searches -/
namespace LowSpaceSubsetSum.CompressionRowCells
def low (x : ℤ) : (ℤ × ℕ) × ℕ := ((x%1,3),8)
def high (P x : ℤ) : (ℤ × ℕ) × ℕ := ((x%P,3),8)
def run (right : Array ℤ) (P : ℤ) (hs : FilteredRow.PrimarySorted right id 1)
(mode : FilteredStream.Mode) (x : ℤ) : (PairCursor.State ℤ right.size × ℕ) × ℕ :=
let k := FilteredStream.steps right.size
let rr := MeasuredRowCells.range right low ((0-x)%1) k hs
(FilteredStream.steps_sufficient right.size)
let q := match mode with
| .direct => MeasuredRowCells.start right rr.1.1 (high P) P (x%P) k false
| .complementary t => MeasuredRowCells.start right rr.1.1 (high P) P ((t-x)%P) k true
((⟨x,q.1.1⟩,1+rr.1.2+q.1.2+4),rr.2+q.2+32)
theorem value (right : Array ℤ) (P : ℤ) (hs : FilteredRow.PrimarySorted right id 1)
(mode : FilteredStream.Mode) (x : ℤ) :
(run right P hs mode x).1 = CompressionInitialization.row right P hs mode x := by
have h := MeasuredRowCells.range_value right low ((0-x)%1)
(FilteredStream.steps right.size) hs (FilteredStream.steps_sufficient right.size)
have hv := congrArg Prod.fst h
have hw := congrArg Prod.snd h
cases mode <;>
simp only [run, MeasuredRowCells.start_value, hv, hw, Bool.false_eq_true, ↓reduceIte] <;> rfl
theorem cells (right : Array ℤ) (P : ℤ) (hs : FilteredRow.PrimarySorted right id 1)
(mode : FilteredStream.Mode) (x : ℤ) : (run right P hs mode x).2 ≤ 200 := by
let rr := MeasuredRowCells.range right low ((0-x)%1) (FilteredStream.steps right.size) hs
(FilteredStream.steps_sufficient right.size)
have hr := MeasuredRowCells.range_cells right low ((0-x)%1)
(FilteredStream.steps right.size) 8 hs (FilteredStream.steps_sufficient right.size)
(fun _ => le_rfl)
change rr.2 ≤ 80 at hr
cases mode with
| direct =>
have hq := MeasuredRowCells.start_cells right rr.1.1 (high P) P (x%P)
(FilteredStream.steps right.size) 8 false (fun _ => le_rfl)
change rr.2+(MeasuredRowCells.start right rr.1.1 (high P) P (x%P)
(FilteredStream.steps right.size) false).2+32 ≤ _
omega
| complementary t =>
have hq := MeasuredRowCells.start_cells right rr.1.1 (high P) P ((t-x)%P)
(FilteredStream.steps right.size) 8 true (fun _ => le_rfl)
change rr.2+(MeasuredRowCells.start right rr.1.1 (high P) P ((t-x)%P)
(FilteredStream.steps right.size) true).2+32 ≤ _
omega
end LowSpaceSubsetSum.CompressionRowCells
end OAI
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