| import Mathlib |
| import OAI.Computability.QuantumFactoring.ArithmeticPredicates |
| import OAI.Computability.QuantumFactoring.AIGNetworkEmission |
| import OAI.Computability.QuantumFactoring.AIGNetworkProcedure |
| import OAI.Computability.QuantumFactoring.NativeAIGBinaryInputs |
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|
| namespace OAI |
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| section |
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| namespace ExactQuantumFactoring.AIGNetworkEmission |
| open Std.Sat Std.Tactic.BVDecide.BVExpr.bitblast |
| open BitStackProgram BitStackProgram.Procedure NetworkEmission |
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| def binaryPack (op : NativeAIG.Graph→List NativeAIG.Ref→List NativeAIG.Ref→NativeAIG.Graph×List NativeAIG.Ref) |
| (w : ℕ) : Pack:= |
| let r:=op (NativeAIG.rawInputs (w+w)) (NativeAIG.rawWord 0 w) (NativeAIG.rawWord w w) |
| compilePack (w+w) r.1.decls r.2 |
| lemma binaryPack_value (op : NativeAIG.Graph→List NativeAIG.Ref→List NativeAIG.Ref→NativeAIG.Graph×List NativeAIG.Ref) |
| (w : ℕ) (res : AIG.RefVecEntry (Fin (w+w)) w) |
| (hr : NativeAIG.VecRel (op (NativeAIG.rawInputs (w+w)) (NativeAIG.rawWord 0 w) (NativeAIG.rawWord w w)) res) : |
| (binaryPack op w).val.value=erase (AIGCompiler.compileVec res.aig res.vec):=by |
| dsimp only [binaryPack] |
| rw [hr.2] |
| exact compilePack_value hr.1 _ |
| lemma addPack_value (w : ℕ) : (binaryPack NativeAIG.add w).val.value=erase (BitArithmetic.add w):=by |
| apply binaryPack_value |
| have hh:=NativeAIG.add_rel (NativeAIG.inputs_rel (w+w)) (BitArithmetic.binaryInputs w) |
| simpa only [NativeAIG.eraseVec_binaryInputs_lhs,NativeAIG.eraseVec_binaryInputs_rhs] using hh |
| lemma mulPack_value (w : ℕ) : (binaryPack NativeAIG.mul w).val.value=erase (BitArithmetic.mul w):=by |
| apply binaryPack_value |
| have hh:=NativeAIG.mul_rel (NativeAIG.inputs_rel (w+w)) (BitArithmetic.binaryInputs w) |
| simpa only [NativeAIG.eraseVec_binaryInputs_lhs,NativeAIG.eraseVec_binaryInputs_rhs] using hh |
| lemma subPack_value (w : ℕ) : (binaryPack NativeAIG.sub w).val.value=erase (BitArithmetic.sub w):=by |
| apply binaryPack_value |
| have hh:=NativeAIG.sub_rel (NativeAIG.inputs_rel (w+w)) (BitArithmetic.binaryInputs w) |
| simpa only [NativeAIG.eraseVec_binaryInputs_lhs,NativeAIG.eraseVec_binaryInputs_rhs] using hh |
| lemma divPack_value (w : ℕ) : (binaryPack NativeAIG.divide w).val.value=erase (BitArithmetic.div w):=by |
| apply binaryPack_value |
| have hh:=NativeAIG.divide_rel (NativeAIG.inputs_rel (w+w)) (BitArithmetic.binaryInputs w) |
| simpa only [NativeAIG.eraseVec_binaryInputs_lhs,NativeAIG.eraseVec_binaryInputs_rhs] using hh |
| lemma modPack_value (w : ℕ) : (binaryPack NativeAIG.remainder w).val.value=erase (BitArithmetic.mod w):=by |
| apply binaryPack_value |
| have hh:=NativeAIG.remainder_rel (NativeAIG.inputs_rel (w+w)) (BitArithmetic.binaryInputs w) |
| simpa only [NativeAIG.eraseVec_binaryInputs_lhs,NativeAIG.eraseVec_binaryInputs_rhs] using hh |
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| def ultPack (w : ℕ) : Pack:= |
| let r:=NativeAIG.ult (NativeAIG.rawInputs (w+w)) (NativeAIG.rawWord 0 w) (NativeAIG.rawWord w w) |
| compilePack (w+w) r.1.decls [r.2] |
| lemma ultPack_value (w : ℕ) : (ultPack w).val.value=erase (BitArithmetic.ult w):=by |
| have hr:=NativeAIG.ult_rel (NativeAIG.inputs_rel (w+w)) (BitArithmetic.binaryInputs w) |
| simp only [NativeAIG.eraseVec_binaryInputs_lhs,NativeAIG.eraseVec_binaryInputs_rhs] at hr |
| unfold ultPack BitArithmetic.ult |
| have hh:=compilePack_value hr.1 (fun _ : Fin 1=>(Std.Tactic.BVDecide.BVPred.mkUlt |
| (AIGCompiler.inputs (w+w)).1 (BitArithmetic.binaryInputs w)).ref) |
| simpa only [List.ofFn_succ,List.ofFn_zero,hr.2] using hh |
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| namespace Emission |
| noncomputable def binaryPackP |
| {op : NativeAIG.Graph→List NativeAIG.Ref→List NativeAIG.Ref→NativeAIG.Graph×List NativeAIG.Ref} |
| (p : Procedure unaryCode (prodCode NativeAIG.graphCode (listCode NativeAIG.refCode)) |
| (fun w=>op (NativeAIG.rawInputs (w+w)) (NativeAIG.rawWord 0 w) (NativeAIG.rawWord w w))) : |
| Procedure unaryCode packCode (binaryPack op):=by |
| let width:=unaryAdd.comp ((identity unaryCode).pair (identity unaryCode)) |
| let graph:=(first NativeAIG.graphCode (listCode NativeAIG.refCode)).comp p |
| let ds:=NativeAIG.Emission.decls.comp graph |
| let refs:=(second NativeAIG.graphCode (listCode NativeAIG.refCode)).comp p |
| exact compilePackP.comp ((width.pair ds).pair refs) |
| noncomputable def addPackP : Procedure unaryCode packCode (binaryPack NativeAIG.add):=binaryPackP NativeAIG.Emission.inputAddP |
| noncomputable def mulPackP : Procedure unaryCode packCode (binaryPack NativeAIG.mul):=binaryPackP NativeAIG.Emission.inputMulP |
| noncomputable def subPackP : Procedure unaryCode packCode (binaryPack NativeAIG.sub):=binaryPackP NativeAIG.Emission.inputSubP |
| noncomputable def divPackP : Procedure unaryCode packCode (binaryPack NativeAIG.divide):=binaryPackP NativeAIG.Emission.inputDivP |
| noncomputable def modPackP : Procedure unaryCode packCode (binaryPack NativeAIG.remainder):=binaryPackP NativeAIG.Emission.inputModP |
| noncomputable def inputUltP : Procedure unaryCode (prodCode NativeAIG.graphCode NativeAIG.refCode) |
| (fun w=>NativeAIG.ult (NativeAIG.rawInputs (w+w)) (NativeAIG.rawWord 0 w) (NativeAIG.rawWord w w)):=by |
| refine (NativeAIG.Emission.ultP.comp (((identity NativeAIG.addStateCode).precompose |
| (fun s:NativeAIG.BinaryState=>s.val)).comp NativeAIG.Emission.binaryInputP)).congrFun ?_ |
| intro w |
| change NativeAIG.ult (NativeAIG.binaryInput w).val.val.graph (NativeAIG.binaryInput w).val.val.lhs |
| (NativeAIG.binaryInput w).val.val.rhs=_ |
| congr 1 |
| noncomputable def ultPackP : Procedure unaryCode packCode ultPack:=by |
| let width:=unaryAdd.comp ((identity unaryCode).pair (identity unaryCode)) |
| let ds:=NativeAIG.Emission.decls.comp ((first NativeAIG.graphCode NativeAIG.refCode).comp inputUltP) |
| let ref:=(second NativeAIG.graphCode NativeAIG.refCode).comp inputUltP |
| let refs:=(listCons NativeAIG.refCode).comp (ref.pair (Procedure.constant _ (listCode NativeAIG.refCode) [])) |
| exact compilePackP.comp ((width.pair ds).pair refs) |
| end Emission |
| end ExactQuantumFactoring.AIGNetworkEmission |
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| end |
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| end OAI |
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