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View of /branches/charisee_dev/src/compiler/high-il/normalize-ein.sml

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Revision 2844 - (download) (annotate)
Tue Dec 9 18:05:29 2014 UTC (4 years, 10 months ago) by cchiw
Original Path: branches/charisee/src/compiler/high-il/normalize-ein.sml
File size: 12938 byte(s)
code cleanup
structure NormalizeEin = struct

    local

    structure E = Ein
    structure P=Printer
    structure F=Filter
    structure G=EpsHelpers

    in

fun err str=raise Fail (String.concat["Ill-formed EIN Operator",str])
val testing=1
fun flatProd e =F.rewriteProd e
fun mkProd e= F.mkProd e
fun filterSca e=F.filterSca e
fun filterField e=F.filterField e
fun mkAdd e=F.mkAdd e
fun filterGreek e=F.filterGreek e


fun testp n=(case testing
of 0=> 1
| _ =>(print(String.concat n);1)
(*end case*))

(*prodAppPartia:ein_exp list * mu list ->ein_exp
* chain rule 
*)
fun prodAppPartial(es,p1)=(case es
    of []      => err "Empty App Partial"
    | [e1]     => E.Apply(E.Partial p1,e1)
    | (e1::e2) => let
        val l= prodAppPartial(e2,p1)
        val (_,e2')= mkProd[e1,l]
        val (_,e1')=mkProd(e2@ [E.Apply(E.Partial p1, e1)])
        in
            E.Add[e1',e2']
        end
    (* end case *))
                
(*mkSum:sum_indexid list * ein_exp->int *ein_exp
*distribute summation expression 
*)
fun mkSum(c1,e1)=(case e1
    of E.Conv _   => (0,E.Sum(c1,e1))
    | E.Field _   => (0,E.Sum(c1,e1))
    | E.Probe _   => (0,E.Sum(c1,e1))
    | E.Apply _   => (0,E.Sum(c1,e1))
    | E.Delta _   => (0,E.Sum(c1,e1))
    | E.Epsilon _ => (0,E.Sum(c1,e1))
    | E.Eps2 _    => (0,E.Sum(c1,e1))
    | E.Tensor(_,[]) => (1,e1)
    | E.Tensor _  => (0,E.Sum(c1,e1))
    | E.Neg e2    => (1,E.Neg(E.Sum(c1,e2)))
    | E.Sub (a,b) => (1,E.Sub(E.Sum(c1,a),E.Sum(c1,b)))
    | E.Add e     => (1,E.Add (List.map (fn(a)=>E.Sum(c1,a)) e))
    | E.Div (a,b) => (1,E.Div(E.Sum(c1,a),E.Sum(c1,b)))
    | E.Lift e    => (1,E.Lift(E.Sum(c1,e)))
    | E.Sum(c2,e2)=> (1,E.Sum(c1@c2,e2))
    | E.Prod p    => filterSca(c1,p)
    | E.Const _   => err("Sum of Const")
    | E.Partial _ => err("Sum of Partial")
    | E.Krn _     => err("Krn used before expand")
    | E.Value _   => err("Value used before expand")
    | E.Img _     => err("Probe used before expand")
    (*end case*))
                
(* mkapply:mu list*ein_exp->int*ein_exp
* rewrite Apply
*)
fun mkapply(d1,e1)=(case e1
    of E.Lift e   => (1,E.Const 0)
    | E.Prod []   => err("Apply of empty product")
    | E.Add []    => err("Apply of empty Addition")
    | E.Conv(v, alpha, h, d2)    =>let
            val E.Partial d3=d1
            in
                (1,E.Conv(v,alpha,h,d2@d3))
            end
    | E.Field _   => (0,E.Apply(d1,e1))
    | E.Probe _   => (0,E.Apply(d1,e1))
    | E.Apply(E.Partial d2,e2)  => let
            val E.Partial d3=d1
            in
                (1,E.Apply(E.Partial(d3@d2),e2))
            end
    | E.Apply _   => err" Apply of non-Partial expression"
    | E.Sum(c2,e2)=> (1,E.Sum(c2,E.Apply(d1,e2)))
    | E.Neg e2    => (1,E.Neg(E.Apply(d1,e2)))
    | E.Add e     => (1,E.Add (List.map (fn(a)=>E.Apply(d1,a)) e))
    | E.Sub (a,b) => (1,E.Sub(E.Apply(d1,a),E.Apply(d1,b)))
    | E.Div (g,b) => (case filterField[b]
        of (_,[]) => (1,E.Div(E.Apply(d1,g),b)) (*Division by a real*)
        | (pre,h) => let
            (*quotient rule*)
            val g'=E.Apply(d1,g)
            val h'=E.Apply(d1,flatProd(h))
            val num=E.Sub(E.Prod([g']@h),E.Prod[g,h'])
            val denom=E.Prod(pre@h@h)
            in (1,E.Div(num,denom))
            end
        (*end case*))
    | E.Prod p =>let
        val (pre, post)= filterField p
        val E.Partial d3=d1
        in mkProd(pre@[prodAppPartial(post,d3)])
        end
    | E.Const _   => err("Const without Lift")
    | E.Tensor _  => err("Tensor without Lift")
    | E.Delta _   => err("Apply of Delta")
    | E.Epsilon _ => err("Apply of Eps")
    | E.Eps2 _ => err("Apply of Eps")
    | E.Partial _ => err("Apply of Partial")
    | E.Krn _     => err("Krn used before expand")
    | E.Value _   => err("Value used before expand")
    | E.Img _     => err("Probe used before expand")
    (*end case*))

                
(*mkprobe:ein_exp* ein_exp-> int ein_exp
*rewritten probe
*)
fun mkprobe(e1,x)=(case e1
    of E.Lift e   => (1,e)
    | E.Prod []   => err("Probe of empty product")
    | E.Prod p    => (1,E.Prod (List.map (fn(a)=>E.Probe(a,x)) p))
    | E.Apply _   => (0,E.Probe(e1,x))
    | E.Conv _    => (0,E.Probe(e1,x))
    | E.Field _   => (0,E.Probe(e1,x))
    | E.Sum(c,e') => (1,E.Sum(c,E.Probe(e',x)))
    | E.Add e     => (1,E.Add (List.map (fn(a)=>E.Probe(a,x)) e))
    | E.Sub (a,b) => (1,E.Sub(E.Probe(a,x),E.Probe(b,x)))
    | E.Neg e'    => (1,E.Neg(E.Probe(e',x)))
    | E.Div (a,b) => (1,E.Div(E.Probe(a,x),E.Probe(b,x)))
    | E.Const _   => err("Const without Lift")
    | E.Tensor _  => err("Tensor without Lift")
    | E.Delta _   => (0,e1)
    | E.Epsilon _ => (0,e1)
    | E.Eps2 _    => (0,e1)
    | E.Partial _ => err("Probe Partial")
    | E.Probe _   => err("Probe of a Probe")
    | E.Krn _     => err("Krn used before expand")
    | E.Value _   => err("Value used before expand")
    | E.Img _     => err("Probe used before expand")
(*end case*))
                

(*normalize: EIN->EIN
*rewrite body of EIN 
*)
fun normalize (ee as Ein.EIN{params, index, body}) = let
      val changed = ref false
        
      fun rewriteBody body =(case body
            of E.Const _    => body
            | E.Tensor _    => body
            | E.Field _     => body
            | E.Delta _     => body
            | E.Epsilon _   => body
            | E.Eps2 _      => body
            | E.Conv _      => body
            | E.Partial _   => body
            | E.Krn _       => raise Fail"Krn before Expand"
            | E.Img _       => raise Fail"Img before Expand"
            | E.Value _     => raise Fail"Value before Expand"

                (*************Algebraic Rewrites **************)
            | E.Neg(E.Neg e)    => rewriteBody e
            | E.Neg e           => E.Neg(rewriteBody e)
            | E.Lift e          => E.Lift(rewriteBody e)
            | E.Add es          => let val (change,body')= mkAdd(List.map rewriteBody es)
                   in if (change=1) then ( changed:=true;body') else body' end
            | E.Sub(a, E.Field f)=> (changed:=true;E.Add[a, E.Neg(E.Field(f))])
            | E.Sub(E.Sub(a,b),E.Sub(c,d))  => rewriteBody(E.Sub(E.Add[a,d],E.Add[b,c]))
            | E.Sub(E.Sub(a,b),e2)          => rewriteBody (E.Sub(a,E.Add[b,e2]))
            | E.Sub(e1,E.Sub(c,d))          => rewriteBody(E.Add([E.Sub(e1,c),d]))
            | E.Sub (a,b)                   => E.Sub(rewriteBody a, rewriteBody b)
            | E.Div(e1 as E.Tensor(_,[_]),e2 as E.Tensor(_,[]))=>
                    rewriteBody (E.Prod[E.Div(E.Const 1, e2),e1])
            | E.Div(E.Div(a,b),E.Div(c,d))  => rewriteBody(E.Div(E.Prod[a,d],E.Prod[b,c]))
            | E.Div(E.Div(a,b),c)           => rewriteBody (E.Div(a, E.Prod[b,c]))
            | E.Div(a,E.Div(b,c))           => rewriteBody (E.Div(E.Prod[a,c],b))
            | E.Div (a, b)                  => E.Div(rewriteBody a, rewriteBody b)
          
                (**************Apply, Sum, Probe**************)
            | E.Apply(E.Partial [],e)   => e
            | E.Apply(E.Partial d1, e1) =>
                let
                val e2 = rewriteBody e1
                val (c,e3)=mkapply(E.Partial d1,e2)
                in (case c of 1=>(changed:=true;e3)| _ =>e3 (*end case*))
                end
            | E.Apply _                 => raise Fail" Not well-formed Apply expression"
            | E.Sum([],e)               => (changed:=true;rewriteBody e)
            | E.Sum(c,e)                => let
                val (c,e')=mkSum(c,rewriteBody e)
                in (case c of 0 => e'|_ => (changed:=true;e'))
                end
            | E.Probe(u,v)              =>
                let
                val (c',b')=mkprobe(rewriteBody u,rewriteBody v)
                in (case c'
                    of 1=> (changed:=true;b')
                    |_=> b'
                    (*end case*))
                end
                (*************Product**************)
              | E.Prod [] => raise Fail"missing elements in product"
              | E.Prod [e1] => rewriteBody e1
              | E.Prod((E.Add(e2))::e3)=>
                   (changed := true; E.Add(List.map (fn e=> E.Prod([e]@e3)) e2))
              | E.Prod((E.Sub(e2,e3))::e4)=>
                (changed :=true; E.Sub(E.Prod([e2]@e4), E.Prod([e3]@e4 )))
              | E.Prod((E.Div(e2,e3))::e4)=> (changed :=true; E.Div(E.Prod([e2]@e4), e3 ))
              | E.Prod(e1::E.Add(e2)::e3)=>
                (changed := true; E.Add(List.map (fn e=> E.Prod([e1,e]@e3)) e2))
              | E.Prod(e1::E.Sub(e2,e3)::e4)=>
                (changed :=true; E.Sub(E.Prod([e1,e2]@e4), E.Prod([e1,e3]@e4 )))
          
                
                (*************Product EPS **************)
  
              | E.Prod(E.Epsilon(i,j,k)::E.Apply(E.Partial d,e)::es)=>let
                 val change= G.matchEps(0,d,[],[i,j,k])
                 in case (change,es)
                    of (1,_) =>(changed:=true; E.Const 0)
                    | (_,[]) =>E.Prod[E.Epsilon(i,j,k),rewriteBody (E.Apply(E.Partial d,e))]
                    |(_,_)=> let
                        val a=rewriteBody(E.Prod([E.Apply(E.Partial d,e)]@ es))
                        val (_,b)=mkProd [E.Epsilon(i,j,k),a]
                        in b end
                end
              | E.Prod(E.Epsilon(i,j,k)::E.Conv(V,alpha, h, d)::es)=>let
                    val change= G.matchEps(0,d,[],[i,j,k])
                    in case (change,es)
                        of (1,_) =>(changed:=true; E.Const 0)
                        | (_,[]) =>E.Prod[E.Epsilon(i,j,k),E.Conv(V,alpha, h, d)]
                        | (_,_) =>let
                            val a=rewriteBody(E.Prod([E.Conv(V,alpha, h, d)]@ es))
                            val (_,b) = mkProd [E.Epsilon(i,j,k),a]
                            in b end
                    end

              | E.Prod[(E.Epsilon(e1,e2,e3)), E.Tensor(_,[E.V i1,E.V i2])]=>
                    if(e2=i1 andalso e3=i2) then (changed :=true;E.Const(0))
                    else body

            | E.Prod(E.Epsilon eps1::ps)=> (case (G.epsToDels(E.Epsilon eps1::ps))
                of (1,e,[],_,_)      =>(changed:=true;e)(* Changed to Deltas *)
                | (1,e,sx,_,_)      =>(changed:=true;E.Sum(sx,e))(* Changed to Deltas *)
                | (_,_,_,_,[])   =>  body
                | (_,_,_,epsAll,rest) => let
                        val p'=rewriteBody(E.Prod rest)
                        val(_,b)= mkProd(epsAll@[p'])
                        in b end
                (*end case*))

            | E.Prod(E.Sum(c1,E.Prod(E.Epsilon e1::es1))::E.Sum(c2,E.Prod(E.Epsilon e2::es2))::es) =>
                (case G.epsToDels([E.Epsilon e1, E.Epsilon e2]@es1@es2@es)
                of (1,e,sx,_,_)=> (changed:=true; E.Sum(c1@c2@sx,e))
                | (_,_,_,_,_)=>let
                    val eA=rewriteBody(E.Sum(c1,E.Prod(E.Epsilon e1::es1)))
                    val eB=rewriteBody(E.Prod(E.Sum(c2,E.Prod(E.Epsilon e2::es2))::es))
                    val (_,e)=mkProd([eA,eB])
                    in e
                    end
                (*end case*))

            | E.Prod[E.Delta d, E.Neg e]=> (changed:=true;E.Neg(E.Prod[E.Delta d, e]))
            | E.Prod(E.Delta d::es)=>let
                val (pre',eps, dels,post)= filterGreek(E.Delta d::es)
                val (change,a)=G.reduceDelta(eps, dels, post)
                in (case (change,a)
                    of (0, _)=> E.Prod [E.Delta d,rewriteBody(E.Prod es)]
                    | (_, E.Prod p)=>let
                        val (_, p') = mkProd p
                        in (changed:=true;p') end
                    | _ => (changed:=true;a )
                    (*end case*))
                    end
                
              | E.Prod[e1,e2]=> let val (_,b)=mkProd[rewriteBody e1, rewriteBody e2] in b end
              | E.Prod(e::es)=>let
                    val e'=rewriteBody e
                    val e2=rewriteBody(E.Prod es)
                    val(_,b)=(case e2
                        of E.Prod p'=> mkProd([e']@p')
                        |_=>mkProd [e',e2])
                in b
                   end                

            (*end case*))
  
            fun loop(body ,count) = let
                val _= testp["\n\n N =>",Int.toString(count),"--",P.printbody(body)]
                val body' = rewriteBody body

                           in 
              if !changed
                then  (changed := false ;loop(body',count+1))
                else (body',count)
            end
            val _ =testp["\n ******************* \n Start Normalize \n\n "]
            val (b,count) = loop(body,0)
            val _ =testp["\n Out of normalize \n",P.printbody(b),
                "\n    Final CounterXX:",Int.toString(count),"\n\n"]
            in
                (Ein.EIN{params=params, index=index, body=b},count)
            end
end
                


end (* local *)

root@smlnj-gforge.cs.uchicago.edu
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