furnace/extern/fftw/genfft/to_alist.ml

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(*
* Copyright (c) 1997-1999 Massachusetts Institute of Technology
* Copyright (c) 2003, 2007-14 Matteo Frigo
* Copyright (c) 2003, 2007-14 Massachusetts Institute of Technology
*
* This program is free software; you can redistribute it and/or modify
* it under the terms of the GNU General Public License as published by
* the Free Software Foundation; either version 2 of the License, or
* (at your option) any later version.
*
* This program is distributed in the hope that it will be useful,
* but WITHOUT ANY WARRANTY; without even the implied warranty of
* MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
* GNU General Public License for more details.
*
* You should have received a copy of the GNU General Public License
* along with this program; if not, write to the Free Software
* Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA
*
*)
(*************************************************************
* Conversion of the dag to an assignment list
*************************************************************)
(*
* This function is messy. The main problem is that we want to
* inline dag nodes conditionally, depending on how many times they
* are used. The Right Thing to do would be to modify the
* state monad to propagate some of the state backwards, so that
* we know whether a given node will be used again in the future.
* This modification is trivial in a lazy language, but it is
* messy in a strict language like ML.
*
* In this implementation, we just do the obvious thing, i.e., visit
* the dag twice, the first to count the node usages, and the second to
* produce the output.
*)
open Monads.StateMonad
open Monads.MemoMonad
open Expr
let fresh = Variable.make_temporary
let node_insert x = Assoctable.insert Expr.hash x
let node_lookup x = Assoctable.lookup Expr.hash (==) x
let empty = Assoctable.empty
let fetchAl =
fetchState >>= (fun (al, _, _) -> returnM al)
let storeAl al =
fetchState >>= (fun (_, visited, visited') ->
storeState (al, visited, visited'))
let fetchVisited = fetchState >>= (fun (_, v, _) -> returnM v)
let storeVisited visited =
fetchState >>= (fun (al, _, visited') ->
storeState (al, visited, visited'))
let fetchVisited' = fetchState >>= (fun (_, _, v') -> returnM v')
let storeVisited' visited' =
fetchState >>= (fun (al, visited, _) ->
storeState (al, visited, visited'))
let lookupVisitedM' key =
fetchVisited' >>= fun table ->
returnM (node_lookup key table)
let insertVisitedM' key value =
fetchVisited' >>= fun table ->
storeVisited' (node_insert key value table)
let counting f x =
fetchVisited >>= (fun v ->
match node_lookup x v with
Some count ->
let incr_cnt =
fetchVisited >>= (fun v' ->
storeVisited (node_insert x (count + 1) v'))
in
begin
match x with
(* Uminus is always inlined. Visit child *)
Uminus y -> f y >> incr_cnt
| _ -> incr_cnt
end
| None ->
f x >> fetchVisited >>= (fun v' ->
storeVisited (node_insert x 1 v')))
let with_varM v x =
fetchAl >>= (fun al -> storeAl ((v, x) :: al)) >> returnM (Load v)
let inlineM = returnM
let with_tempM x = match x with
| Load v when Variable.is_temporary v -> inlineM x (* avoid trivial moves *)
| _ -> with_varM (fresh ()) x
(* declare a temporary only if node is used more than once *)
let with_temp_maybeM node x =
fetchVisited >>= (fun v ->
match node_lookup node v with
Some count ->
if (count = 1 && !Magic.inline_single) then
inlineM x
else
with_tempM x
| None ->
failwith "with_temp_maybeM")
type fma =
NO_FMA
| FMA of expr * expr * expr (* FMA (a, b, c) => a + b * c *)
| FMS of expr * expr * expr (* FMS (a, b, c) => -a + b * c *)
| FNMS of expr * expr * expr (* FNMS (a, b, c) => a - b * c *)
let good_for_fma (a, b) =
let good = function
| NaN I -> true
| NaN CONJ -> true
| NaN _ -> false
| Times(NaN _, _) -> false
| Times(_, NaN _) -> false
| _ -> true
in good a && good b
let build_fma l =
if (not !Magic.enable_fma) then NO_FMA
else match l with
| [a; Uminus (Times (b, c))] when good_for_fma (b, c) -> FNMS (a, b, c)
| [Uminus (Times (b, c)); a] when good_for_fma (b, c) -> FNMS (a, b, c)
| [Uminus a; Times (b, c)] when good_for_fma (b, c) -> FMS (a, b, c)
| [Times (b, c); Uminus a] when good_for_fma (b, c) -> FMS (a, b, c)
| [a; Times (b, c)] when good_for_fma (b, c) -> FMA (a, b, c)
| [Times (b, c); a] when good_for_fma (b, c) -> FMA (a, b, c)
| _ -> NO_FMA
let children_fma l = match build_fma l with
| FMA (a, b, c) -> Some (a, b, c)
| FMS (a, b, c) -> Some (a, b, c)
| FNMS (a, b, c) -> Some (a, b, c)
| NO_FMA -> None
let rec visitM x =
counting (function
| Load v -> returnM ()
| Num a -> returnM ()
| NaN a -> returnM ()
| Store (v, x) -> visitM x
| Plus a -> (match children_fma a with
None -> mapM visitM a >> returnM ()
| Some (a, b, c) ->
(* visit fma's arguments twice to make sure they are not inlined *)
visitM a >> visitM a >>
visitM b >> visitM b >>
visitM c >> visitM c)
| Times (a, b) -> visitM a >> visitM b
| CTimes (a, b) -> visitM a >> visitM b
| CTimesJ (a, b) -> visitM a >> visitM b
| Uminus a -> visitM a)
x
let visit_rootsM = mapM visitM
let rec expr_of_nodeM x =
memoizing lookupVisitedM' insertVisitedM'
(function x -> match x with
| Load v ->
if (Variable.is_temporary v) then
inlineM (Load v)
else if (Variable.is_locative v && !Magic.inline_loads) then
inlineM (Load v)
else if (Variable.is_constant v && !Magic.inline_loads_constants) then
inlineM (Load v)
else
with_tempM (Load v)
| Num a ->
if !Magic.inline_constants then
inlineM (Num a)
else
with_temp_maybeM x (Num a)
| NaN a -> inlineM (NaN a)
| Store (v, x) ->
expr_of_nodeM x >>=
(if !Magic.trivial_stores then with_tempM else inlineM) >>=
with_varM v
| Plus a ->
begin
match build_fma a with
FMA (a, b, c) ->
expr_of_nodeM a >>= fun a' ->
expr_of_nodeM b >>= fun b' ->
expr_of_nodeM c >>= fun c' ->
with_temp_maybeM x (Plus [a'; Times (b', c')])
| FMS (a, b, c) ->
expr_of_nodeM a >>= fun a' ->
expr_of_nodeM b >>= fun b' ->
expr_of_nodeM c >>= fun c' ->
with_temp_maybeM x
(Plus [Times (b', c'); Uminus a'])
| FNMS (a, b, c) ->
expr_of_nodeM a >>= fun a' ->
expr_of_nodeM b >>= fun b' ->
expr_of_nodeM c >>= fun c' ->
with_temp_maybeM x
(Plus [a'; Uminus (Times (b', c'))])
| NO_FMA ->
mapM expr_of_nodeM a >>= fun a' ->
with_temp_maybeM x (Plus a')
end
| CTimes (Load _ as a, b) when !Magic.generate_bytw ->
expr_of_nodeM b >>= fun b' ->
with_tempM (CTimes (a, b'))
| CTimes (a, b) ->
expr_of_nodeM a >>= fun a' ->
expr_of_nodeM b >>= fun b' ->
with_tempM (CTimes (a', b'))
| CTimesJ (Load _ as a, b) when !Magic.generate_bytw ->
expr_of_nodeM b >>= fun b' ->
with_tempM (CTimesJ (a, b'))
| CTimesJ (a, b) ->
expr_of_nodeM a >>= fun a' ->
expr_of_nodeM b >>= fun b' ->
with_tempM (CTimesJ (a', b'))
| Times (a, b) ->
expr_of_nodeM a >>= fun a' ->
expr_of_nodeM b >>= fun b' ->
begin
match a' with
Num a'' when !Magic.strength_reduce_mul && Number.is_two a'' ->
(inlineM b' >>= fun b'' ->
with_temp_maybeM x (Plus [b''; b'']))
| _ -> with_temp_maybeM x (Times (a', b'))
end
| Uminus a ->
expr_of_nodeM a >>= fun a' ->
inlineM (Uminus a'))
x
let expr_of_rootsM = mapM expr_of_nodeM
let peek_alistM roots =
visit_rootsM roots >> expr_of_rootsM roots >> fetchAl
let wrap_assign (a, b) = Expr.Assign (a, b)
let to_assignments dag =
let () = Util.info "begin to_alist" in
let al = List.rev (runM ([], empty, empty) peek_alistM dag) in
let res = List.map wrap_assign al in
let () = Util.info "end to_alist" in
res
(* dump alist in `dot' format *)
let dump print alist =
let vs v = "\"" ^ (Variable.unparse v) ^ "\"" in
begin
print "digraph G {\n";
print "\tsize=\"6,6\";\n";
(* all input nodes have the same rank *)
print "{ rank = same;\n";
List.iter (fun (Expr.Assign (v, x)) ->
List.iter (fun y ->
if (Variable.is_locative y) then print("\t" ^ (vs y) ^ ";\n"))
(Expr.find_vars x))
alist;
print "}\n";
(* all output nodes have the same rank *)
print "{ rank = same;\n";
List.iter (fun (Expr.Assign (v, x)) ->
if (Variable.is_locative v) then print("\t" ^ (vs v) ^ ";\n"))
alist;
print "}\n";
(* edges *)
List.iter (fun (Expr.Assign (v, x)) ->
List.iter (fun y -> print("\t" ^ (vs y) ^ " -> " ^ (vs v) ^ ";\n"))
(Expr.find_vars x))
alist;
print "}\n";
end