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|
type uop = Neg
type bop = Add | Sub | CLe | CEq
type bref = int (* Block references. *)
type 'op seqi = [ `Con of int | `Uop of uop * 'op | `Bop of 'op * bop * 'op ]
type 'op jmpi = [ `Brz of 'op * bref * bref | `Jmp of bref ]
type ('ins, 'phi, 'jmp) bb =
{ mutable bb_name: string
; mutable bb_phis: 'phi array
; mutable bb_inss: 'ins array
; mutable bb_jmp: 'jmp
}
(* ** Liveness analysis. ** *)
type iref = IRPhi of (bref * int) | IRIns of (bref * int)
let blk = function IRPhi (b, _) | IRIns (b, _) -> b
type iprog = (iref seqi, [`Phi of iref list], iref jmpi) bb array
module IRSet = Set.Make(
struct type t = iref let compare = compare end
)
let liveout lh ir =
try Hashtbl.find lh ir with Not_found ->
let e = IRSet.empty in Hashtbl.add lh ir e; e
let livein lh p ir =
let gen (b, i) = IRSet.of_list begin
let {bb_inss; bb_jmp; _} = p.(b) in
if i = -1 then [] else
if i = Array.length bb_inss
then match bb_jmp with
| `Brz (i1, _, _) -> [i1]
| `Jmp _ -> []
else match bb_inss.(i) with
| `Uop (_, i1) -> [i1]
| `Bop (i1, _, i2) -> [i1; i2]
| `Con _ -> []
end in
let kill ((b, i) as ir) =
if i >= 0 then IRSet.singleton (IRIns ir) else
fst (Array.fold_left
(fun (k, i) _ -> (IRSet.add (IRPhi (b, i)) k, i+1))
(IRSet.empty, 0) p.(b).bb_phis
) in
let s = liveout lh ir in
let s = IRSet.union s (gen ir) in
IRSet.diff s (kill ir)
let liveness (p: iprog) =
let module H = Hashtbl in
let changed = ref true in (* Witness for fixpoint. *)
let nbb = Array.length p in
let lh = H.create 1001 in
let setlive ir ir' = (* Mark ir live at ir'. *)
let lir' = liveout lh ir' in
if not (IRSet.mem ir lir') then begin
changed := true;
H.replace lh ir' (IRSet.add ir lir');
end in
let succs (b, i) = (* Successor nodes of an instruction. *)
let {bb_inss; bb_jmp; _} = p.(b) in
if i = Array.length bb_inss then
if b+1 = nbb then [] else
match bb_jmp with
| `Brz (_, b1, b2) -> [(b1, -1); (b2, -1)]
| `Jmp b1 -> [(b1, -1)]
else [(b, i+1)] in
while !changed do
changed := false;
for b = nbb - 1 downto 0 do
let bb = p.(b) in
for i = Array.length bb.bb_inss downto -1 do
let ir = (b, i) in
let live = List.fold_left (fun live ir' ->
IRSet.union live (livein lh p ir')
) IRSet.empty (succs ir) in
IRSet.iter (fun ir' -> setlive ir' ir) live
done;
Array.iter (fun (`Phi il) ->
List.iter (fun ir ->
let br = blk ir in
setlive ir (br, Array.length p.(br).bb_inss)
) il
) bb.bb_phis;
done
done;
lh (* Return the final hash table. *)
(* ** Register allocation. ** *)
type loc = LVoid | LReg of int | LSpill of int | LCon of int
type 'op rins = { ri_res: 'op; ri_ins: [ 'op seqi | `Mov of 'op ] }
type 'op rphi = { rp_res: 'op; rp_list: (bref * loc) list }
type rprog = (loc rins, loc rphi, loc jmpi) bb array
let regalloc (p: iprog): rprog =
let module H = struct
include Hashtbl
let find h ir = try find h ir with Not_found -> LVoid
end in
let lh = liveness p in
let nbb = Array.length p in
let rp = Array.init nbb (fun i ->
{ bb_name = p.(i).bb_name
; bb_phis = [| |]
; bb_inss = [| |]
; bb_jmp = `Jmp (-1)
}
) in
let outmaps = Array.make nbb [] in
let inmaps = Array.make nbb [] in
let bb = ref [] in (* Basic block in construction. *)
let emiti l i = bb := {ri_res=l; ri_ins=i} :: !bb in
let act = H.create 101 in (* The active list. *)
let free = ref [0;1;2;3] in (* Free registers. *)
let nspill = ref 0 in
let newspill () = incr nspill; !nspill - 1 in
let getspill ir =
match H.find act ir with
| LSpill s -> s
| _ -> -1 in
let kill ir =
match H.find act ir with
| LReg r -> H.remove act ir; free := r :: !free
| _ -> H.remove act ir in
let loc ir =
match H.find act ir with
| LVoid ->
let l =
match !free with
| r :: f -> free := f; LReg r
| [] -> LSpill (newspill ())
in
H.add act ir l; l
| l -> l in
let rec getreg frz = (* Aggressively obtain one register. *)
match !free with
| r :: f when List.mem r frz -> (* Frozen, can't use it. *)
free := f;
let r' = getreg frz in
free := r :: !free; r'
| r :: f -> free := f; r
| [] -> (* Spill needed! *)
match
H.fold (fun ir loc l -> (* Find candidates. *)
match loc with
| LReg r when not (List.mem r frz) ->
(ir, r) :: l
| _ -> l
) act [] (* |> sort by spill cost *)
with [] -> failwith "god damn it, not enough registers"
| (ir, r) :: _ ->
H.remove act ir;
let s = getspill ir in
let s =
if s >= 0 then s else
let s' = newspill () in
H.add act ir (LSpill s'); s' in
emiti (LReg r) (`Mov (LSpill s));
r in
let regloc frz ir =
match H.find act ir with
| LReg r -> r
| _ ->
let r = getreg frz in
H.add act ir (LReg r); r in
for b = nbb - 1 downto 0 do
let bi = p.(b).bb_inss in
let bl = Array.length bi in
(* Fill outmaps with the allocation state at
* the end of the block (after the final branch).
*)
let lvout = liveout lh (b, bl) in
outmaps.(b) <- begin
IRSet.fold (fun ir m -> (ir, loc ir) :: m) lvout []
end;
let jmp =
match p.(b).bb_jmp with
| `Jmp br -> `Jmp br
| `Brz (ir, br1, br2) ->
`Brz (loc ir, br1, br2) in
rp.(b).bb_jmp <- jmp;
for i = bl - 1 downto 0 do
let ir = IRIns (b, i) in
begin match H.find act ir with
| LVoid -> () (* Dead code. *)
| lir ->
let r, frz =
match lir with
| LSpill s ->
let r = getreg [] in
emiti (LSpill s) (`Mov (LReg r));
if not (List.mem r !free) then
free := r :: !free; (* Add it straight back to free, but freeze it. *)
(r, [r])
| LReg r -> (r, [])
| _ -> assert false
in
kill ir;
let s = getspill ir in
begin match bi.(i) with
| `Con k ->
if s >= 0 then emiti (LSpill s) (`Mov (LReg r));
emiti (LReg r) (`Mov (LCon k))
| `Uop (op, ir') ->
let r' = regloc frz ir' in
if s >= 0 then emiti (LSpill s) (`Mov (LReg r));
emiti (LReg r) (`Uop (op, LReg r'))
| `Bop (ir1, op, ir2) ->
let r1 = regloc frz ir1 in
let frz = r :: r1 :: frz in
let r2 = regloc frz ir2 in
if s >= 0 then emiti (LSpill s) (`Mov (LReg r));
emiti (LReg r) (`Bop (LReg r1, op, LReg r2))
end;
end
done;
let lvin = liveout lh (b, -1) in
inmaps.(b) <- begin
IRSet.fold (fun ir l ->
let loc = H.find act ir in
if blk ir = b then
kill ir; (* Kill current block's phis *)
(ir, loc) :: l
) lvin []
end;
rp.(b).bb_inss <- Array.of_list !bb;
bb := [];
done;
(* Compute phis. *)
for b = 0 to nbb - 1 do
rp.(b).bb_phis <- Array.of_list begin
IRSet.fold (fun ir l ->
match ir with
| IRPhi (b', pr) when b' = b ->
let `Phi pl = p.(b).bb_phis.(pr) in
let pl =
let f ir =
let b = blk ir in
(b, List.assoc ir outmaps.(b)) in
List.map f pl |>
List.sort (fun (a,_) (b,_) -> compare a b) in
{ rp_res = List.assoc ir inmaps.(b)
; rp_list = pl
} :: l
| _ -> assert (blk ir <> b);
(* Forgive me, I sin!! *)
let rl = ref [] in
for b = 0 to nbb - 1 do
let bl = Array.length p.(b).bb_inss in
if IRSet.mem ir (liveout lh (b, bl)) then
rl := (b, List.assoc ir outmaps.(b)) :: !rl
done;
{ rp_res = List.assoc ir inmaps.(b)
; rp_list = List.rev !rl
} :: l
) (liveout lh (b, -1)) []
end
done;
rp
(* ** Phi resolution. ** *)
(* Machine program, ready for code generation. *)
type mprog = (loc rins, unit, loc jmpi) bb array
let movgen (p: rprog): mprog =
let parmov b b' =
let tmp = LReg (-1) in
let src, dst =
let phis = p.(b').bb_phis in
Array.map (fun x -> List.assoc b x.rp_list) phis,
Array.map (fun x -> x.rp_res) phis in
let n = Array.length dst in
let status = Array.make n `Mv in
let ms = ref [] in
let emov dst src =
ms := {ri_res = dst; ri_ins = `Mov src} :: !ms in
let rec mv i =
if src.(i) <> dst.(i) then begin
status.(i) <- `Mvg;
for j = 0 to n - 1 do
if src.(j) = dst.(i) then
match status.(j) with
| `Mv -> mv j
| `Mvg -> emov tmp src.(j); src.(j) <- tmp
| `Mvd -> ()
done;
emov dst.(i) src.(i);
status.(i) <- `Mvd;
end in
for i = 0 to n - 1 do
if status.(i) = `Mv then mv i
done;
List.rev !ms |> Array.of_list in
let nbb = Array.length p in
let bmap = Array.init nbb (fun i -> -i - 1) in
let bn = ref 0 in
let mp = ref [] in
let addb b = mp := b :: !mp; incr bn; !bn - 1 in
for b = 0 to nbb - 1 do
let b' =
{ bb_name = p.(b).bb_name
; bb_phis = [| |]
; bb_inss = p.(b).bb_inss
; bb_jmp = `Jmp (-1)
} in
bmap.(b) <- addb b';
let movbb suff jb =
if jb = -1 then -1 else
let c = parmov b jb in
if c = [| |] then bmap.(jb) else
addb
{ bb_name = p.(b).bb_name ^ suff
; bb_phis = [| |]
; bb_inss = c
; bb_jmp = `Jmp bmap.(jb)
} in
b'.bb_jmp <- begin
match p.(b).bb_jmp with
| `Jmp b1 -> `Jmp (movbb "_mov" b1)
| `Brz (l, b1, b2) ->
let b1', b2' =
if b1 = b + 1 then
let b2' = movbb "_mov2" b2 in
let b1' = movbb "_mov1" b1 in
(b1', b2')
else
let b1' = movbb "_mov1" b1 in
let b2' = movbb "_mov2" b2 in
(b1', b2') in
`Brz (l, b1', b2')
end;
done;
List.rev !mp
|> Array.of_list
|> Array.map (fun b ->
let f n =
if n >= -1 then n else bmap.(-n - 1) in
{ b with bb_jmp =
match b.bb_jmp with
| `Jmp b1 -> `Jmp (f b1)
| `Brz (l, b1, b2) -> `Brz (l, f b1, f b2)
}
)
(* Little test programs. *)
let pbasic: iprog =
[| { bb_name = "start"
; bb_phis = [| |]
; bb_inss =
[| `Con 2
; `Con 3
; `Bop (IRIns (0, 0), Add, IRIns (0, 1))
; `Bop (IRIns (0, 0), Add, IRIns (0, 2))
|]
; bb_jmp = `Brz (IRIns (0, 3), -1, -1)
}
|]
let pcount: iprog =
[| { bb_name = "init"
; bb_phis = [||]
; bb_inss = [| `Con 100; `Con 1 |]
; bb_jmp = `Jmp 1
}
; { bb_name = "loop"
; bb_phis = [| `Phi [IRIns (0, 0); IRIns (1, 0)] |]
; bb_inss = [| `Bop (IRPhi (1, 0), Sub, IRIns (0, 1)) |]
; bb_jmp = `Brz (IRIns (1, 0), 2, 1)
}
; { bb_name = "end"
; bb_phis = [||]
; bb_inss = [| `Con 42 |]
; bb_jmp = `Jmp (-1)
}
|]
let psum: iprog =
[| { bb_name = "init"
; bb_phis = [||]
; bb_inss = [| `Con 100; `Con 1 |]
; bb_jmp = `Jmp 1
}
; { bb_name = "loop"
; bb_phis =
[| `Phi [IRIns (0, 0); IRIns (1, 0)] (* n = phi(100, n1) *)
; `Phi [IRIns (0, 1); IRIns (1, 1)] (* s = phi(1, s1) *)
|]
; bb_inss =
[| `Bop (IRPhi (1, 0), Sub, IRIns (0, 1)) (* n1 = n - 1 *)
; `Bop (IRPhi (1, 1), Add, IRPhi (1, 0)) (* s1 = s + n *)
|]
; bb_jmp = `Brz (IRIns (1, 0), 2, 1)
}
; { bb_name = "end"
; bb_phis = [||]
; bb_inss = [| `Con 42 |]
; bb_jmp = `Jmp (-1)
}
|]
let pspill: iprog =
[| { bb_name = "init"
; bb_phis = [||]
; bb_inss =
(* 00 *) [| `Con 42
(* 01 *) ; `Bop (IRIns (0, 0), Add, IRIns (0, 0))
(* 02 *) ; `Bop (IRIns (0, 0), Add, IRIns (0, 1))
(* 03 *) ; `Bop (IRIns (0, 0), Add, IRIns (0, 2))
(* 04 *) ; `Bop (IRIns (0, 0), Add, IRIns (0, 3))
(* 05 *) ; `Bop (IRIns (0, 0), Add, IRIns (0, 4))
(* 06 *) ; `Bop (IRIns (0, 0), Add, IRIns (0, 5))
(* 07 *) ; `Bop (IRIns (0, 6), Add, IRIns (0, 6))
(* 08 *) ; `Bop (IRIns (0, 5), Add, IRIns (0, 7))
(* 09 *) ; `Bop (IRIns (0, 4), Add, IRIns (0, 8))
(* 10 *) ; `Bop (IRIns (0, 3), Add, IRIns (0, 9))
(* 11 *) ; `Bop (IRIns (0, 2), Add, IRIns (0, 10))
(* 12 *) ; `Bop (IRIns (0, 1), Add, IRIns (0, 11))
(* 13 *) ; `Bop (IRIns (0, 0), Add, IRIns (0, 12))
|]
; bb_jmp = `Brz (IRIns (0, 13), -1, -1)
}
|]
|