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2f887db | 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 90 91 92 93 94 95 96 97 | import Mathlib
import OAI.Computability.QuantumFactoring.ArithmeticPredicates
import OAI.Computability.QuantumFactoring.AIGNetworkEmission
import OAI.Computability.QuantumFactoring.AIGNetworkProcedure
import OAI.Computability.QuantumFactoring.NativeAIGBinaryInputs
namespace OAI
section
namespace ExactQuantumFactoring.AIGNetworkEmission
open Std.Sat Std.Tactic.BVDecide.BVExpr.bitblast
open BitStackProgram BitStackProgram.Procedure NetworkEmission
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
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
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
end
end OAI
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