| import Mathlib |
| import OAI.Computability.QuantumFactoring.BitArithmetic |
| import OAI.Computability.QuantumFactoring.AIGDivisionBounds |
|
|
| namespace OAI |
|
|
| section |
| open scoped BigOperators |
|
|
|
|
| namespace ExactQuantumFactoring.BitArithmetic |
| open Std.Sat Std.Tactic.BVDecide.BVExpr.bitblast |
| open AIGCompiler BooleanNetwork |
|
|
| def sub (w : ℕ) : BooleanNetwork (w+w) w := |
| let res := blastSub (inputs (w+w)).1 (binaryInputs w) |
| compileVec res.aig res.vec |
|
|
| lemma sub_correct (w : ℕ) (x : Fin (w+w) → Bool) (i : Fin w) : |
| (sub w).eval x i = (leftWord x - rightWord x).getLsbD i.val := by |
| rw [sub, compileVec_correct] |
| exact denote_blastSub _ _ _ _ _ (binaryInputs_left w x) (binaryInputs_right w x) _ _ |
|
|
| lemma sub_count (w : ℕ) : (sub w).net.count ≤ 158*w+6 := by |
| have h := compileVec_count (blastSub (inputs (w+w)).1 (binaryInputs w)).aig |
| (blastSub (inputs (w+w)).1 (binaryInputs w)).vec |
| have hs := AIGBounds.sub_size (inputs (w+w)).1 (binaryInputs w) |
| rw [inputs_size] at hs |
| dsimp only [sub] |
| nlinarith |
|
|
| def div (w : ℕ) : BooleanNetwork (w+w) w := |
| let res := blastUdiv (inputs (w+w)).1 (binaryInputs w) |
| compileVec res.aig res.vec |
|
|
| lemma div_correct (w : ℕ) (x : Fin (w+w) → Bool) (i : Fin w) : |
| (div w).eval x i = (leftWord x / rightWord x).getLsbD i.val := by |
| rw [div, compileVec_correct] |
| exact denote_blastUdiv _ _ _ _ _ (binaryInputs_left w x) (binaryInputs_right w x) _ _ |
|
|
| lemma div_count (w : ℕ) : (div w).net.count ≤ 216*w*w+56*w+6 := by |
| have h := compileVec_count (blastUdiv (inputs (w+w)).1 (binaryInputs w)).aig |
| (blastUdiv (inputs (w+w)).1 (binaryInputs w)).vec |
| have hs := AIGBounds.div_size (inputs (w+w)).1 (binaryInputs w) |
| rw [inputs_size] at hs |
| dsimp only [div] |
| nlinarith |
|
|
| def mod (w : ℕ) : BooleanNetwork (w+w) w := |
| let res := blastUmod (inputs (w+w)).1 (binaryInputs w) |
| compileVec res.aig res.vec |
|
|
| lemma mod_correct (w : ℕ) (x : Fin (w+w) → Bool) (i : Fin w) : |
| (mod w).eval x i = (leftWord x % rightWord x).getLsbD i.val := by |
| rw [mod, compileVec_correct] |
| exact denote_blastUmod _ _ _ _ _ (binaryInputs_left w x) (binaryInputs_right w x) _ _ |
|
|
| lemma mod_count (w : ℕ) : (mod w).net.count ≤ 216*w*w+56*w+6 := by |
| have h := compileVec_count (blastUmod (inputs (w+w)).1 (binaryInputs w)).aig |
| (blastUmod (inputs (w+w)).1 (binaryInputs w)).vec |
| have hs := AIGBounds.mod_size (inputs (w+w)).1 (binaryInputs w) |
| rw [inputs_size] at hs |
| dsimp only [mod] |
| nlinarith |
|
|
| end ExactQuantumFactoring.BitArithmetic |
|
|
|
|
| end |
|
|
| end OAI |
|
|
