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[diderot] View of /branches/ein16/src/compiler/high-il/normalize-ein.sml
 [diderot] / branches / ein16 / src / compiler / high-il / normalize-ein.sml

# View of /branches/ein16/src/compiler/high-il/normalize-ein.sml

Mon Nov 16 19:16:54 2015 UTC (3 years, 9 months ago) by cchiw
Original Path: branches/charisee_dev/src/compiler/high-il/normalize-ein.sml
File size: 12340 byte(s)
`added trig`
```structure NormalizeEin = struct

local

structure E = Ein
structure P=Printer
structure F=Filter
structure G=EpsHelpers
structure Eq=EqualEin
structure R=RationalEin

in

val testing=0
fun err str=raise Fail (String.concat["Ill-formed EIN Operator",str])
fun mkProd e= F.mkProd e
fun filterSca e=F.filterSca e
fun filterGreek e=F.filterGreek e
fun mkapply e= derivativeEin.mkapply e
fun testp n=(case testing
of 0=> 1
| _ =>(print(String.concat n);1)
(*end case*))

(*mkSum:sum_indexid list * ein_exp->int *ein_exp
*distribute summation expression
*)
fun mkSum(c1,b)=(case b
of E.Lift e         => (1,E.Lift(E.Sum(c1,e)))
| E.Tensor(_,[])    => (1,b)
| E.Const _         => (1,b)
| E.ConstR _        => (1,b)
| E.Prod p          => filterSca(c1,p)
| _                 => (0,E.Sum(c1,b))
(*end case*))

(*mkprobe:ein_exp* ein_exp-> int ein_exp
*rewritten probe
*)
fun mkprobe(b,x)=let
val (c,rtn)=(case b
of E.Lift e1            => (1,e1)
| E.Sqrt e1             => (1,E.Sqrt(E.Probe(e1,x)))
| E.Trig(t,e1)          => (1,E.Trig(t,E.Probe(e1,x)))
| E.PowInt(e1,n1)       => (1,E.PowInt(E.Probe(e1,x),n1))
| E.PowReal(e1,n1)      => (1,E.PowReal(E.Probe(e1,x),n1))
| E.PowEmb(a,b,c)       => (1,Ein.PowEmb(E.Probe(a,x),b,c))
| 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(b,x))
| E.Conv _              => (0,E.Probe(b,x))
| E.Field _             => (0,E.Probe(b,x))
| E.Sum(c,e1)           => (1,E.Sum(c,E.Probe(e1,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 e1              => (1,E.Neg(E.Probe(e1,x)))
| E.Div (a,b)           => (1,E.Div(E.Probe(a,x),E.Probe(b,x)))
| E.Exp e1              => (1,E.Exp(E.Probe(e1,x)))
| E.Const _             => (1,b)
| E.ConstR _            => (1,b)
| E.Tensor _            => err("Tensor without Lift")
| E.Delta _             => (0,b)
| E.Epsilon _           => (0,b)
| E.Eps2 _              => (0,b)
| 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*))
in
(c,rtn)
end

(* normalize: EIN->EIN
* rewrite body of EIN
* note "c" keeps track if ein_exp is changed
*)
fun normalize (ee as Ein.EIN{params, index, body},args) = let
val changed = ref false
fun rewriteBody body =(case body
of E.Const _                            => body
| E.ConstR _                            => 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"
| E.Lift e                              => E.Lift(rewriteBody e)
| E.Sqrt e                              => E.Sqrt(rewriteBody e)
| E.Trig(t1,e1)                         => E.Trig(t1,rewriteBody e1)
| E.PowInt(e,n1)                        => E.PowInt(rewriteBody e,n1)
| E.PowReal(e,n1)                       => E.PowReal(rewriteBody e,n1)
| E.PowEmb(e1,sx,n1)                    => E.PowEmb(rewriteBody e1,sx,n1)
| E.Exp e1                              => E.Exp(rewriteBody e1)
(*************Algebraic Rewrites **************)
| E.Neg(E.Neg e)                        => rewriteBody e
| E.Neg(E.Const 0)                      => (changed:=true;E.Const 0)
| E.Neg e                               => E.Neg(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 (E.Const 0,b)                   => (changed:=true;E.Neg(rewriteBody b))
| E.Sub (a,E.Const 0)                   => (changed:=true;rewriteBody a)
| E.Sub (a,b)                           => E.Sub(rewriteBody a, rewriteBody b)
| E.Div(E.Const 0,e)                    => (changed:=true;E.Const 0)
| 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[(e1 as E.Sqrt(s1)),(e2 as E.Sqrt(s2))]=>
if(Eq.isBodyEq(s1,s2)) then (changed :=true;s1)
else let
val a=rewriteBody e1
val b=rewriteBody e2
val  (_,d)=mkProd ([a,b])
in d
end

(*************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(V1,[a1], h1, d1)::E.Conv(V,alpha, h, d)::es)=>let
val change= G.matchEps(0,alpha@d,[],[i,j,k])
in case (change,es)
of (1,_) =>(changed:=true; E.Lift(E.Const 0))
| (_,[]) =>E.Prod[E.Epsilon(i,j,k),E.Conv(V1,[a1], h1, d1),E.Conv(V,alpha, h, d)]
| (_,_) =>let
val a=rewriteBody(E.Prod([E.Conv(V1,[a1], h1, d1),E.Conv(V,alpha, h, d)]@ 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.Lift(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 e1::E.Sum(c1,E.Prod(E.Sum(c2,E.Prod(E.Epsilon e2::es3))::es2))::es1) =>
(case G.epsToDels([E.Epsilon e1, E.Epsilon e2]@es3@es2@es1)
of (1,e,sx,_,_)=> (changed:=true; E.Sum(c1@c2@sx,e))
| (_,_,_,_,_)=>let
val eA=rewriteBody(E.Epsilon e1)
val eB=rewriteBody(E.Prod(E.Sum(c1,E.Prod(E.Sum(c2,E.Prod(E.Epsilon e2::es3))::es2))::es1))
val (_,e)=mkProd([eA,eB])
in
e
end
(*end case*))
*)
| 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 _= testp["\n\n Reduce delta--",P.printbody(body)]
val (change,a)=G.reduceDelta(eps, dels, post)
val _= testp["\n\n ---delta moved--",P.printbody(a)]
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*))
val _ =raise Fail"Dev branch do not use"

val _=testp["\n******** Start Normalize: \n",P.printerE ee,"\n*****\n"]
fun loop(body ,count) = let
(*val _=raise Fail"do not use dev branch"*)
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 (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 *)```

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