switch.ml

(***********************************************************************)
(*                                                                     *)
(*                                OCaml                                *)
(*                                                                     *)
(*            Luc Maranget, projet Moscova, INRIA Rocquencourt         *)
(*                                                                     *)
(*  Copyright 2000 Institut National de Recherche en Informatique et   *)
(*  en Automatique.  All rights reserved.  This file is distributed    *)
(*  under the terms of the Q Public License version 1.0.               *)
(*                                                                     *)
(***********************************************************************)

(* Store for actions in object style *)
exception Found of int

type 'a t_store =
    {act_get : unit -> 'a array ; act_store : 'a -> int}

let mk_store same =
  let r_acts = ref [] in
  let store act =
    let rec store_rec i = function
      | [] -> i,[act]
      | act0::rem ->
          if same act0 act then raise (Found i)
          else
            let i,rem = store_rec (i+1) rem in
            i,act0::rem in
    try
      let i,acts = store_rec 0 !r_acts in
      r_acts := acts ;
      i
    with
    | Found i -> i

  and get () = Array.of_list !r_acts in
  {act_store=store ; act_get=get}



module type S =
 sig
   type primitive
   val eqint : primitive
   val neint : primitive
   val leint : primitive
   val ltint : primitive
   val geint : primitive
   val gtint : primitive
   type act

   val bind : act -> (act -> act) -> act
   val make_offset : act -> int -> act
   val make_prim : primitive -> act list -> act
   val make_isout : act -> act -> act
   val make_isin : act -> act -> act
   val make_if : act -> act -> act -> act
   val make_switch :
      act -> int array -> act array -> act
 end

(* The module will ``produce good code for the case statement'' *)
(*
  Adaptation of
   R.L. Berstein
   ``Producing good code for the case statement''
   Sofware Practice and Experience, 15(10) (1985)
 and
   D.L. Spuler
    ``Two-Way Comparison Search Trees, a Generalisation of Binary Search Trees
      and Split Trees''
    ``Compiler Code Generation for Multiway Branch Statement as
      a Static Search Problem''
   Technical Reports, James Cook University
*)
(*
  Main adaptation is considering interval tests
 (implemented as one addition + one unsigned test and branch)
  which leads to exhaustive search for finding the optimal
  test sequence in small cases and heuristics otherwise.
*)
module Make (Arg : S) =
  struct

    type 'a inter =
        {cases : (int * int * int) array ;
          actions : 'a array}

type 'a t_ctx =  {off : int ; arg : 'a}

let cut = ref 8
and more_cut = ref 16

let pint chan i =
  if i = min_int then Printf.fprintf chan "-oo"
  else if i=max_int then Printf.fprintf chan "oo"
  else Printf.fprintf chan "%d" i

let pcases chan cases =
  for i =0 to Array.length cases-1 do
    let l,h,act = cases.(i) in
    if l=h then
      Printf.fprintf chan "%d:%d " l act
    else
      Printf.fprintf chan "%a..%a:%d " pint l pint h act
  done

    let prerr_inter i = Printf.fprintf stderr
        "cases=%a" pcases i.cases

let get_act cases i =
  let _,_,r = cases.(i) in
  r
and get_low cases i =
  let r,_,_ = cases.(i) in
  r

type ctests = {
    mutable n : int ;
    mutable ni : int ;
  }

let too_much = {n=max_int ; ni=max_int}

let ptests chan {n=n ; ni=ni} =
  Printf.fprintf chan "{n=%d ; ni=%d}" n ni

let pta chan t =
  for i =0 to Array.length t-1 do
    Printf.fprintf chan "%d: %a\n" i ptests t.(i)
  done

let count_tests s =
  let r =
    Array.init
      (Array.length s.actions)
      (fun _ -> {n=0 ; ni=0 }) in
  let c = s.cases in
  let imax = Array.length c-1 in
  for i=0 to imax do
    let l,h,act = c.(i) in
    let x = r.(act) in
    x.n <- x.n+1 ;
    if l < h && i<> 0 && i<>imax then
      x.ni <- x.ni+1 ;
  done ;
  r


let less_tests c1 c2 =
  if c1.n < c2.n then
    true
  else if c1.n = c2.n then begin
    if c1.ni < c2.ni then
      true
    else
      false
  end else
    false

and eq_tests c1 c2 = c1.n = c2.n && c1.ni=c2.ni

let min_tests c1 c2 = if less_tests c1 c2 then c1 else c2

let less2tests (c1,d1) (c2,d2) =
  if eq_tests c1 c2 then
    less_tests d1 d2
  else
    less_tests c1 c2

let add_test t1 t2 =
  t1.n <- t1.n + t2.n ;
  t1.ni <- t1.ni + t2.ni ;

type t_ret = Inter of int * int  | Sep of int | No

let pret chan = function
  | Inter (i,j)-> Printf.fprintf chan "Inter %d %d" i j
  | Sep i -> Printf.fprintf chan "Sep %d" i
  | No -> Printf.fprintf chan "No"

let coupe cases i =
  let l,_,_ = cases.(i) in
  l,
  Array.sub cases 0 i,
  Array.sub cases i (Array.length cases-i)


let case_append c1 c2 =
  let len1 = Array.length c1
  and len2 = Array.length c2 in
  match len1,len2 with
  | 0,_ -> c2
  | _,0 -> c1
  | _,_ ->
      let l1,h1,act1 = c1.(Array.length c1-1)
      and l2,h2,act2 = c2.(0) in
      if act1 = act2 then
        let r = Array.create (len1+len2-1) c1.(0) in
        for i = 0 to len1-2 do
          r.(i) <- c1.(i)
        done ;

        let l =
          if len1-2 >= 0 then begin
            let _,h,_ = r.(len1-2) in
            if h+1 < l1 then
              h+1
            else
              l1
          end else
            l1
        and h =
          if 1 < len2-1 then begin
            let l,_,_ = c2.(1) in
            if h2+1 < l then
              l-1
            else
              h2
          end else
            h2 in
        r.(len1-1) <- (l,h,act1) ;
        for i=1 to len2-1  do
          r.(len1-1+i) <- c2.(i)
        done ;
        r
      else if h1 > l1 then
        let r = Array.create (len1+len2) c1.(0) in
        for i = 0 to len1-2 do
          r.(i) <- c1.(i)
        done ;
        r.(len1-1) <- (l1,l2-1,act1) ;
        for i=0 to len2-1  do
          r.(len1+i) <- c2.(i)
        done ;
        r
      else if h2 > l2 then
        let r = Array.create (len1+len2) c1.(0) in
        for i = 0 to len1-1 do
          r.(i) <- c1.(i)
        done ;
        r.(len1) <- (h1+1,h2,act2) ;
        for i=1 to len2-1  do
          r.(len1+i) <- c2.(i)
        done ;
        r
      else
        Array.append c1 c2


let coupe_inter i j cases =
  let lcases = Array.length cases in
  let low,_,_ = cases.(i)
  and _,high,_ = cases.(j) in
  low,high,
  Array.sub cases i (j-i+1),
  case_append (Array.sub cases 0 i) (Array.sub cases (j+1) (lcases-(j+1)))

type kind = Kvalue of int | Kinter of int | Kempty

let pkind chan = function
  | Kvalue i ->Printf.fprintf chan "V%d" i
  | Kinter i -> Printf.fprintf chan "I%d" i
  | Kempty -> Printf.fprintf chan "E"

let rec pkey chan  = function
  | [] -> ()
  | [k] -> pkind chan k
  | k::rem ->
      Printf.fprintf chan "%a %a" pkey rem pkind k

let t = Hashtbl.create 17

let make_key  cases =
  let seen = ref []
  and count = ref 0 in
  let rec got_it act = function
    | [] ->
        seen := (act,!count):: !seen ;
        let r = !count in
        incr count ;
        r
    | (act0,index) :: rem ->
        if act0 = act then
          index
        else
          got_it act rem in

  let make_one l h act =
    if l=h then
      Kvalue (got_it act !seen)
    else
      Kinter (got_it act !seen) in

  let rec make_rec i pl =
    if i < 0 then
      []
    else
      let l,h,act = cases.(i) in
      if pl = h+1 then
        make_one l h act::make_rec (i-1) l
      else
        Kempty::make_one l h act::make_rec (i-1) l in

  let l,h,act = cases.(Array.length cases-1) in
  make_one l h act::make_rec (Array.length cases-2) l


    let same_act t =
      let len = Array.length t in
      let a = get_act t (len-1) in
      let rec do_rec i =
        if i < 0 then true
        else
          let b = get_act t i in
          b=a && do_rec (i-1) in
      do_rec (len-2)


(*
  Intervall test x in [l,h] works by checking x-l in [0,h-l]
   * This may be false for arithmetic modulo 2^31
   * Subtracting l may change the relative ordering of values
     and invalid the invariant that matched values are given in
     increasing order

   To avoid this, interval check is allowed only when the
   integers indeed present in the whole case interval are
   in [-2^16 ; 2^16]

   This condition is checked by zyva
*)

let inter_limit = 1 lsl 16

let ok_inter = ref false

let rec opt_count top cases =
  let key = make_key cases in
  try
    let r = Hashtbl.find t key in
    r
  with
  | Not_found ->
      let r =
        let lcases = Array.length cases in
        match lcases with
        | 0 -> assert false
        | _ when same_act cases -> No, ({n=0; ni=0},{n=0; ni=0})
        | _ ->
            if lcases < !cut then
              enum top cases
            else if lcases < !more_cut then
              heuristic top cases
            else
              divide top cases in
      Hashtbl.add t key r ;
      r

and divide top cases =
  let lcases = Array.length cases in
  let m = lcases/2 in
  let _,left,right = coupe cases m in
  let ci = {n=1 ; ni=0}
  and cm = {n=1 ; ni=0}
  and _,(cml,cleft) = opt_count false left
  and _,(cmr,cright) = opt_count false right in
  add_test ci cleft ;
  add_test ci cright ;
  if less_tests cml cmr then
    add_test cm cmr
  else
    add_test cm cml ;
  Sep m,(cm, ci)

and heuristic top cases =
  let lcases = Array.length cases in

  let sep,csep = divide false cases

  and inter,cinter =
    if !ok_inter then begin
      let _,_,act0 = cases.(0)
      and _,_,act1 = cases.(lcases-1) in
      if act0 = act1 then begin
        let low, high, inside, outside = coupe_inter 1 (lcases-2) cases in
        let _,(cmi,cinside) = opt_count false inside
        and _,(cmo,coutside) = opt_count false outside
        and cmij = {n=1 ; ni=(if low=high then 0 else 1)}
        and cij = {n=1 ; ni=(if low=high then 0 else 1)} in
        add_test cij cinside ;
        add_test cij coutside ;
        if less_tests cmi cmo then
          add_test cmij cmo
        else
          add_test cmij cmi ;
        Inter (1,lcases-2),(cmij,cij)
      end else
        Inter (-1,-1),(too_much, too_much)
    end else
      Inter (-1,-1),(too_much, too_much) in
  if less2tests csep cinter then
    sep,csep
  else
    inter,cinter


and enum top cases =
  let lcases = Array.length cases in
  let lim, with_sep =
    let best = ref (-1) and best_cost = ref (too_much,too_much) in

    for i = 1 to lcases-(1) do
      let _,left,right = coupe cases i in
      let ci = {n=1 ; ni=0}
      and cm = {n=1 ; ni=0}
      and _,(cml,cleft) = opt_count false left
      and _,(cmr,cright) = opt_count false right in
      add_test ci cleft ;
      add_test ci cright ;
      if less_tests cml cmr then
        add_test cm cmr
      else
        add_test cm cml ;

      if
        less2tests (cm,ci) !best_cost
      then begin
        if top then
          Printf.fprintf stderr "Get it: %d\n" i ;
        best := i ;
        best_cost := (cm,ci)
      end
    done ;
    !best, !best_cost in

  let ilow, ihigh, with_inter =
    if not !ok_inter then
      let rlow = ref (-1) and rhigh = ref (-1)
      and best_cost= ref (too_much,too_much) in
      for i=1 to lcases-2 do
        let low, high, inside, outside = coupe_inter i i cases in
         if low=high then begin
           let _,(cmi,cinside) = opt_count false inside
           and _,(cmo,coutside) = opt_count false outside
           and cmij = {n=1 ; ni=0}
           and cij = {n=1 ; ni=0} in
           add_test cij cinside ;
           add_test cij coutside ;
           if less_tests cmi cmo then
             add_test cmij cmo
           else
             add_test cmij cmi ;
           if less2tests (cmij,cij) !best_cost then begin
             rlow := i ;
             rhigh := i ;
             best_cost := (cmij,cij)
           end
         end
      done ;
      !rlow, !rhigh, !best_cost
    else
      let rlow = ref (-1) and rhigh = ref (-1)
      and best_cost= ref (too_much,too_much) in
      for i=1 to lcases-2 do
        for j=i to lcases-2 do
          let low, high, inside, outside = coupe_inter i j cases in
          let _,(cmi,cinside) = opt_count false inside
          and _,(cmo,coutside) = opt_count false outside
          and cmij = {n=1 ; ni=(if low=high then 0 else 1)}
          and cij = {n=1 ; ni=(if low=high then 0 else 1)} in
          add_test cij cinside ;
          add_test cij coutside ;
          if less_tests cmi cmo then
            add_test cmij cmo
          else
            add_test cmij cmi ;
          if less2tests (cmij,cij) !best_cost then begin
            rlow := i ;
            rhigh := j ;
            best_cost := (cmij,cij)
          end
        done
      done ;
      !rlow, !rhigh, !best_cost in
  let r = ref (Inter (ilow,ihigh)) and rc = ref with_inter in
  if less2tests with_sep !rc then begin
    r := Sep lim ; rc := with_sep
  end ;
  !r, !rc

    let make_if_test konst test arg i ifso ifnot =
      Arg.make_if
        (Arg.make_prim test [arg ; konst i])
        ifso ifnot

    let make_if_lt konst arg i  ifso ifnot = match i with
    | 1 ->
        make_if_test konst Arg.leint arg 0 ifso ifnot
    | _ ->
        make_if_test konst Arg.ltint arg i ifso ifnot

    and make_if_le konst arg i ifso ifnot = match i with
    | -1 ->
        make_if_test konst Arg.ltint arg 0 ifso ifnot
    | _ ->
        make_if_test konst Arg.leint arg i ifso ifnot

    and make_if_gt konst arg i  ifso ifnot = match i with
    | -1 ->
        make_if_test konst Arg.geint arg 0 ifso ifnot
    | _ ->
        make_if_test konst Arg.gtint arg i ifso ifnot

    and make_if_ge konst arg i  ifso ifnot = match i with
    | 1 ->
        make_if_test konst Arg.gtint arg 0 ifso ifnot
    | _ ->
        make_if_test konst Arg.geint arg i ifso ifnot

    and make_if_eq  konst arg i ifso ifnot =
      make_if_test konst Arg.eqint arg i ifso ifnot

    and make_if_ne  konst arg i ifso ifnot =
      make_if_test konst Arg.neint arg i ifso ifnot

    let do_make_if_out h arg ifso ifno =
      Arg.make_if (Arg.make_isout h arg) ifso ifno

    let make_if_out konst ctx l d mk_ifso mk_ifno = match l with
    | 0 ->
        do_make_if_out
          (konst d) ctx.arg (mk_ifso ctx) (mk_ifno ctx)
    | _ ->
        Arg.bind
          (Arg.make_offset ctx.arg (-l))
          (fun arg ->
            let ctx = {off= (-l+ctx.off) ; arg=arg} in
            do_make_if_out
              (konst d) arg (mk_ifso ctx) (mk_ifno ctx))

    let do_make_if_in h arg ifso ifno =
      Arg.make_if (Arg.make_isin h arg) ifso ifno

    let make_if_in konst ctx l d mk_ifso mk_ifno = match l with
    | 0 ->
        do_make_if_in
          (konst d) ctx.arg (mk_ifso ctx) (mk_ifno ctx)
    | _ ->
        Arg.bind
          (Arg.make_offset ctx.arg (-l))
          (fun arg ->
            let ctx = {off= (-l+ctx.off) ; arg=arg} in
            do_make_if_in
              (konst d) arg (mk_ifso ctx) (mk_ifno ctx))


    let rec c_test konst ctx ({cases=cases ; actions=actions} as s) =
      let lcases = Array.length cases in
      assert(lcases > 0) ;
      if lcases = 1 then
        actions.(get_act cases 0) ctx
      else begin

        let w,c = opt_count false cases in
(*
  Printf.fprintf stderr
  "off=%d tactic=%a for %a\n"
  ctx.off pret w pcases cases ;
  *)
    match w with
    | No -> actions.(get_act cases 0) ctx
    | Inter (i,j) ->
        let low,high,inside, outside = coupe_inter i j cases in
        let _,(cinside,_) = opt_count false inside
        and _,(coutside,_) = opt_count false outside in
(* Costs are retrieved to put the code with more remaining tests
   in the privileged (positive) branch of ``if'' *)
        if low=high then begin
          if less_tests coutside cinside then
            make_if_eq
              konst ctx.arg
              (low+ctx.off)
              (c_test konst ctx {s with cases=inside})
              (c_test konst ctx {s with cases=outside})
          else
            make_if_ne
              konst ctx.arg
              (low+ctx.off)
              (c_test konst ctx {s with cases=outside})
              (c_test konst ctx {s with cases=inside})
        end else begin
          if less_tests coutside cinside then
            make_if_in
              konst ctx
              (low+ctx.off)
              (high-low)
              (fun ctx -> c_test konst ctx {s with cases=inside})
              (fun ctx -> c_test konst ctx {s with cases=outside})
          else
            make_if_out
              konst ctx
              (low+ctx.off)
              (high-low)
              (fun ctx -> c_test konst ctx {s with cases=outside})
              (fun ctx -> c_test konst ctx {s with cases=inside})
        end
    | Sep i ->
        let lim,left,right = coupe cases i in
        let _,(cleft,_) = opt_count false left
        and _,(cright,_) = opt_count false right in
        let left = {s with cases=left}
        and right = {s with cases=right} in

        if i=1 && (lim+ctx.off)=1 && get_low cases 0+ctx.off=0 then
          make_if_ne konst
            ctx.arg 0
            (c_test konst ctx right) (c_test konst ctx left)
        else if less_tests cright cleft then
          make_if_lt konst
            ctx.arg (lim+ctx.off)
            (c_test konst ctx left) (c_test konst ctx right)
        else
          make_if_ge konst
             ctx.arg (lim+ctx.off)
            (c_test konst ctx right) (c_test konst ctx left)

  end


(* Minimal density of switches *)
let theta = ref 0.33333

(* Minmal number of tests to make a switch *)
let switch_min = ref 3

(* Particular case 0, 1, 2 *)
let particular_case cases i j =
  j-i = 2 &&
  (let l1,h1,act1 = cases.(i)
  and  l2,h2,act2 = cases.(i+1)
  and  l3,h3,act3 = cases.(i+2) in
  l1+1=l2 && l2+1=l3 && l3=h3 &&
  act1 <> act3)

let approx_count cases i j n_actions =
  let l = j-i+1 in
  if l < !cut then
     let _,(_,{n=ntests}) = opt_count false (Array.sub cases i l) in
     ntests
  else
    l-1

(* Sends back a boolean that says whether is switch is worth or not *)

let dense {cases=cases ; actions=actions} i j =
  if i=j then true
  else
    let l,_,_ = cases.(i)
    and _,h,_ = cases.(j) in
    let ntests =  approx_count cases i j (Array.length actions) in
(*
  (ntests+1) >= theta * (h-l+1)
*)
    particular_case cases i j ||
    (ntests >= !switch_min &&
    float_of_int ntests +. 1.0 >=
    !theta *. (float_of_int h -. float_of_int l +. 1.0))

(* Compute clusters by dynamic programming
   Adaptation of the correction to Bernstein
   ``Correction to `Producing Good Code for the Case Statement' ''
   S.K. Kannan and T.A. Proebsting
   Software Practice and Exprience Vol. 24(2) 233 (Feb 1994)
*)

let comp_clusters ({cases=cases ; actions=actions} as s) =
  let len = Array.length cases in
  let min_clusters = Array.create len max_int
  and k = Array.create len 0 in
  let get_min i = if i < 0 then 0 else min_clusters.(i) in

  for i = 0 to len-1 do
    for j = 0 to i do
      if
        dense s j i &&
        get_min (j-1) + 1 < min_clusters.(i)
      then begin
        k.(i) <- j ;
        min_clusters.(i) <- get_min (j-1) + 1
      end
    done ;
  done ;
  min_clusters.(len-1),k

(* Assume j > i *)
let make_switch  {cases=cases ; actions=actions} i j =
  let ll,_,_ = cases.(i)
  and _,hh,_ = cases.(j) in
  let tbl = Array.create (hh-ll+1) 0
  and t = Hashtbl.create 17
  and index = ref 0 in
  let get_index act =
    try
      Hashtbl.find t act
    with
    | Not_found ->
        let i = !index in
        incr index ;
        Hashtbl.add t act i ;
        i in

  for k=i to j do
    let l,h,act = cases.(k) in
    let index = get_index act in
    for kk=l-ll to h-ll do
      tbl.(kk) <- index
    done
  done ;
  let acts = Array.create !index actions.(0) in
  Hashtbl.iter
    (fun act i -> acts.(i) <- actions.(act))
    t ;
  (fun ctx ->
    match -ll-ctx.off with
    | 0 -> Arg.make_switch ctx.arg tbl acts
    | _ ->
        Arg.bind
          (Arg.make_offset ctx.arg (-ll-ctx.off))
          (fun arg -> Arg.make_switch arg tbl acts))


let make_clusters ({cases=cases ; actions=actions} as s) n_clusters k =
  let len = Array.length cases in
  let r = Array.create n_clusters (0,0,0)
  and t = Hashtbl.create 17
  and index = ref 0
  and bidon = ref (Array.length actions) in
  let get_index act =
    try
      let i,_ = Hashtbl.find t act in
      i
    with
    | Not_found ->
        let i = !index in
        incr index ;
        Hashtbl.add
          t act
          (i,(fun _ -> actions.(act))) ;
        i
  and add_index act =
    let i = !index in
    incr index ;
    incr bidon ;
    Hashtbl.add t !bidon (i,act) ;
    i in

  let rec zyva j ir =
    let i = k.(j) in
    begin if i=j then
      let l,h,act = cases.(i) in
      r.(ir) <- (l,h,get_index act)
    else (* assert i < j *)
      let l,_,_ = cases.(i)
      and _,h,_ = cases.(j) in
      r.(ir) <- (l,h,add_index (make_switch s i j))
    end ;
    if i > 0 then zyva (i-1) (ir-1) in

  zyva (len-1) (n_clusters-1) ;
  let acts = Array.create !index (fun _ -> assert false) in
  Hashtbl.iter (fun _ (i,act) -> acts.(i) <- act) t ;
  {cases = r ; actions = acts}
;;


let zyva (low,high) konst arg cases actions =
  let old_ok = !ok_inter in
  ok_inter := (abs low <= inter_limit && abs high <= inter_limit) ;
  if !ok_inter <> old_ok then Hashtbl.clear t ;

  let s = {cases=cases ; actions=actions} in
(*
  Printf.eprintf "ZYVA: %b\n" !ok_inter ;
  pcases stderr cases ;
  prerr_endline "" ;
*)
  let n_clusters,k = comp_clusters s in
  let clusters = make_clusters s n_clusters k in
  let r = c_test konst {arg=arg ; off=0} clusters in
  r



and test_sequence konst arg cases actions =
  let old_ok = !ok_inter in
  ok_inter := false ;
  if !ok_inter <> old_ok then Hashtbl.clear t ;
  let s =
    {cases=cases ;
    actions=Array.map (fun act -> (fun _ -> act)) actions} in
(*
  Printf.eprintf "SEQUENCE: %b\n" !ok_inter ;
  pcases stderr cases ;
  prerr_endline "" ;
*)
  let r = c_test konst {arg=arg ; off=0} s in
  r
;;

end