gistfile1.txt

    (*Original implementation*)
    MakeInPeriodicCellOrig = 
      Compile[{x, cellwidth}, 
       First@Sort[{x, x - cellwidth, x + cellwidth}, 
         Abs[#1] < Abs[#2] &], {{Sort[_], _Real}}, 
       CompilationOptions -> {"ExpressionOptimization" -> True, 
         "InlineCompiledFunctions" -> True, 
         "InlineExternalDefinitions" -> True},
           RuntimeAttributes -> {Listable},
           "RuntimeOptions" -> "Speed"
       ];
    (*my revritten*)
    MakeInPeriodicCellImp = Compile[{x, cellwidth},
       With[{  l = {x, x - cellwidth, x + cellwidth}},
        Sort[Transpose[{Abs[l], l}]][[1, 2]]
        ], CompilationOptions -> {"ExpressionOptimization" -> True, 
         "InlineCompiledFunctions" -> True, 
         "InlineExternalDefinitions" -> True},
           RuntimeAttributes -> {Listable},
           "RuntimeOptions" -> "Speed"
       ];
    
    (*F'x answer*)
    MakeInPeriodicCellFx = 
      Compile[{{x, _Real}, {cellwidth, _Real}}, 
       If[x < -(cellwidth/2.), x + cellwidth, 
        If[x > cellwidth/2., x - cellwidth, x]],
       CompilationOptions -> {"ExpressionOptimization" -> True, 
         "InlineCompiledFunctions" -> True, 
         "InlineExternalDefinitions" -> True},
           RuntimeAttributes -> {Listable},
           "RuntimeOptions" -> "Speed"];

        
    
    data = RandomReal[{-100, 100}, 100000];
    (*Original implementation*)
    m0 = MakeInPeriodicCellOrig[data, 30]; // AbsoluteTiming (*0.8370473*)
    (*my revritten*)
    m1 = MakeInPeriodicCellImp[data, 30]; // AbsoluteTiming  (*0.0360021*)
    (*F'x answer*)
    m2 = MakeInPeriodicCellFx[data, 30]; // AbsoluteTiming   (*0.0140008*)
    
    m0 == m1 == m2 (*True*)