Documentation

Std.Tactic.BVDecide.Bitblast.BVExpr.Circuit.Impl.Operations.Mul

This module contains the implementation of a bitblaster for BitVec.mul. The implemented circuit mirrors the behavior of BitVec.mulRec.

Note that the implementation performs a symbolic branch over the bits of the right hand side. Thus if the right hand side is (partially) known through constant propagation etc. the symbolic branches will be (partially) constant folded away by the AIG optimizer. The preprocessing of blastMul ensures that the value with more known bits always end up on the right hand side for this reason.

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def Std.Tactic.BVDecide.BVExpr.bitblast.blastMul {w : Nat} (aig : Std.Sat.AIG Std.Tactic.BVDecide.BVBit) (input : aig.BinaryRefVec w) :
Std.Sat.AIG.RefVecEntry Std.Tactic.BVDecide.BVBit w
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    def Std.Tactic.BVDecide.BVExpr.bitblast.blastMul.blast {w : Nat} (aig : Std.Sat.AIG Std.Tactic.BVDecide.BVBit) (input : aig.BinaryRefVec w) :
    Std.Sat.AIG.RefVecEntry Std.Tactic.BVDecide.BVBit w
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      @[irreducible]
      def Std.Tactic.BVDecide.BVExpr.bitblast.blastMul.go {w : Nat} (aig : Std.Sat.AIG Std.Tactic.BVDecide.BVBit) (lhs rhs : aig.RefVec w) (curr : Nat) (acc : aig.RefVec w) :
      Std.Sat.AIG.RefVecEntry Std.Tactic.BVDecide.BVBit w
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        @[irreducible]
        theorem Std.Tactic.BVDecide.BVExpr.bitblast.blastMul.go_le_size {w : Nat} (aig : Std.Sat.AIG Std.Tactic.BVDecide.BVBit) (curr : Nat) (acc lhs rhs : aig.RefVec w) :
        aig.decls.size ≤ (Std.Tactic.BVDecide.BVExpr.bitblast.blastMul.go aig lhs rhs curr acc).aig.decls.size
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        @[irreducible]
        theorem Std.Tactic.BVDecide.BVExpr.bitblast.blastMul.go_decl_eq {w : Nat} (aig : Std.Sat.AIG Std.Tactic.BVDecide.BVBit) (curr : Nat) (acc lhs rhs : aig.RefVec w) (idx : Nat) (h1 : idx < aig.decls.size) (h2 : idx < (Std.Tactic.BVDecide.BVExpr.bitblast.blastMul.go aig lhs rhs curr acc).aig.decls.size) :
        (Std.Tactic.BVDecide.BVExpr.bitblast.blastMul.go aig lhs rhs curr acc).aig.decls[idx] = aig.decls[idx]
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        instance Std.Tactic.BVDecide.BVExpr.bitblast.blastMul.instLawfulVecOperatorBVBitBinaryRefVecBlast :
        Std.Sat.AIG.LawfulVecOperator Std.Tactic.BVDecide.BVBit Std.Sat.AIG.BinaryRefVec fun {len : Nat} => Std.Tactic.BVDecide.BVExpr.bitblast.blastMul.blast
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        instance Std.Tactic.BVDecide.BVExpr.bitblast.instLawfulVecOperatorBVBitBinaryRefVecBlastMul :
        Std.Sat.AIG.LawfulVecOperator Std.Tactic.BVDecide.BVBit Std.Sat.AIG.BinaryRefVec fun {len : Nat} => Std.Tactic.BVDecide.BVExpr.bitblast.blastMul