(**************************************************************************)
(*                                                                        *)
(*                                 OCaml                                  *)
(*                                                                        *)
                , projet Cristal , INRIA Rocquencourt           
(*                                                                        *)
    Copyright 1996 Institut National de Recherche en Informatique et     
(*     en Automatique.                                                    *)
(*                                                                        *)
(*   All rights reserved.  This file is distributed under the terms of    *)
    the GNU Lesser General Public License version 2.1 , with the          
(*   special exception on linking described in the file LICENSE.          *)
(*                                                                        *)
(**************************************************************************)

(* Array operations *)

external length : 'a array -> int = "%array_length"
external get: 'a array -> int -> 'a = "%array_safe_get"
external set: 'a array -> int -> 'a -> unit = "%array_safe_set"
external unsafe_get: 'a array -> int -> 'a = "%array_unsafe_get"
external unsafe_set: 'a array -> int -> 'a -> unit = "%array_unsafe_set"
external make: int -> 'a -> 'a array = "caml_make_vect"
external create: int -> 'a -> 'a array = "caml_make_vect"
external unsafe_sub : 'a array -> int -> int -> 'a array = "caml_array_sub"
external append_prim : 'a array -> 'a array -> 'a array = "caml_array_append"
external concat : 'a array list -> 'a array = "caml_array_concat"
external unsafe_blit :
  'a array -> int -> 'a array -> int -> int -> unit = "caml_array_blit"
external create_float: int -> float array = "caml_make_float_vect"
let make_float = create_float

let init l f =
  if l = 0 then [||] else
  if l < 0 then invalid_arg "Array.init"
  See # 6575 . We could also check for maximum array size , but this depends 
      on whether we create a float array or a regular one ...
     on whether we create a float array or a regular one... *)
  else
   let res = create l (f 0) in
   for i = 1 to pred l do
     unsafe_set res i (f i)
   done;
   res

let make_matrix sx sy init =
  let res = create sx [||] in
  for x = 0 to pred sx do
    unsafe_set res x (create sy init)
  done;
  res

let create_matrix = make_matrix

let copy a =
  let l = length a in if l = 0 then [||] else unsafe_sub a 0 l

let append a1 a2 =
  let l1 = length a1 in
  if l1 = 0 then copy a2
  else if length a2 = 0 then unsafe_sub a1 0 l1
  else append_prim a1 a2

let sub a ofs len =
  if ofs < 0 || len < 0 || ofs > length a - len
  then invalid_arg "Array.sub"
  else unsafe_sub a ofs len

let fill a ofs len v =
  if ofs < 0 || len < 0 || ofs > length a - len
  then invalid_arg "Array.fill"
  else for i = ofs to ofs + len - 1 do unsafe_set a i v done

let blit a1 ofs1 a2 ofs2 len =
  if len < 0 || ofs1 < 0 || ofs1 > length a1 - len
             || ofs2 < 0 || ofs2 > length a2 - len
  then invalid_arg "Array.blit"
  else unsafe_blit a1 ofs1 a2 ofs2 len

let iter f a =
  for i = 0 to length a - 1 do f(unsafe_get a i) done

let iter2 f a b =
  if length a <> length b then
    invalid_arg "Array.iter2: arrays must have the same length"
  else
    for i = 0 to length a - 1 do f (unsafe_get a i) (unsafe_get b i) done

let map f a =
  let l = length a in
  if l = 0 then [||] else begin
    let r = create l (f(unsafe_get a 0)) in
    for i = 1 to l - 1 do
      unsafe_set r i (f(unsafe_get a i))
    done;
    r
  end

let map2 f a b =
  let la = length a in
  let lb = length b in
  if la <> lb then
    invalid_arg "Array.map2: arrays must have the same length"
  else begin
    if la = 0 then [||] else begin
      let r = create la (f (unsafe_get a 0) (unsafe_get b 0)) in
      for i = 1 to la - 1 do
        unsafe_set r i (f (unsafe_get a i) (unsafe_get b i))
      done;
      r
    end
  end

let iteri f a =
  for i = 0 to length a - 1 do f i (unsafe_get a i) done

let mapi f a =
  let l = length a in
  if l = 0 then [||] else begin
    let r = create l (f 0 (unsafe_get a 0)) in
    for i = 1 to l - 1 do
      unsafe_set r i (f i (unsafe_get a i))
    done;
    r
  end

let to_list a =
  let rec tolist i res =
    if i < 0 then res else tolist (i - 1) (unsafe_get a i :: res) in
  tolist (length a - 1) []

  Can not use  here because the List module depends on Array .
let rec list_length accu = function
  | [] -> accu
  | _::t -> list_length (succ accu) t

let of_list = function
    [] -> [||]
  | hd::tl as l ->
      let a = create (list_length 0 l) hd in
      let rec fill i = function
          [] -> a
        | hd::tl -> unsafe_set a i hd; fill (i+1) tl in
      fill 1 tl

let fold_left f x a =
  let r = ref x in
  for i = 0 to length a - 1 do
    r := f !r (unsafe_get a i)
  done;
  !r

let fold_right f a x =
  let r = ref x in
  for i = length a - 1 downto 0 do
    r := f (unsafe_get a i) !r
  done;
  !r

let exists p a =
  let n = length a in
  let rec loop i =
    if i = n then false
    else if p (unsafe_get a i) then true
    else loop (succ i) in
  loop 0

let for_all p a =
  let n = length a in
  let rec loop i =
    if i = n then true
    else if p (unsafe_get a i) then loop (succ i)
    else false in
  loop 0

let mem x a =
  let n = length a in
  let rec loop i =
    if i = n then false
    else if compare (unsafe_get a i) x = 0 then true
    else loop (succ i) in
  loop 0

let memq x a =
  let n = length a in
  let rec loop i =
    if i = n then false
    else if x == (unsafe_get a i) then true
    else loop (succ i) in
  loop 0

exception Bottom of int
let sort cmp a =
  let maxson l i =
    let i31 = i+i+i+1 in
    let x = ref i31 in
    if i31+2 < l then begin
      if cmp (get a i31) (get a (i31+1)) < 0 then x := i31+1;
      if cmp (get a !x) (get a (i31+2)) < 0 then x := i31+2;
      !x
    end else
      if i31+1 < l && cmp (get a i31) (get a (i31+1)) < 0
      then i31+1
      else if i31 < l then i31 else raise (Bottom i)
  in
  let rec trickledown l i e =
    let j = maxson l i in
    if cmp (get a j) e > 0 then begin
      set a i (get a j);
      trickledown l j e;
    end else begin
      set a i e;
    end;
  in
  let trickle l i e = try trickledown l i e with Bottom i -> set a i e in
  let rec bubbledown l i =
    let j = maxson l i in
    set a i (get a j);
    bubbledown l j
  in
  let bubble l i = try bubbledown l i with Bottom i -> i in
  let rec trickleup i e =
    let father = (i - 1) / 3 in
    assert (i <> father);
    if cmp (get a father) e < 0 then begin
      set a i (get a father);
      if father > 0 then trickleup father e else set a 0 e;
    end else begin
      set a i e;
    end;
  in
  let l = length a in
  for i = (l + 1) / 3 - 1 downto 0 do trickle l i (get a i); done;
  for i = l - 1 downto 2 do
    let e = (get a i) in
    set a i (get a 0);
    trickleup (bubble i 0) e;
  done;
  if l > 1 then (let e = (get a 1) in set a 1 (get a 0); set a 0 e)


let cutoff = 5
let stable_sort cmp a =
  let merge src1ofs src1len src2 src2ofs src2len dst dstofs =
    let src1r = src1ofs + src1len and src2r = src2ofs + src2len in
    let rec loop i1 s1 i2 s2 d =
      if cmp s1 s2 <= 0 then begin
        set dst d s1;
        let i1 = i1 + 1 in
        if i1 < src1r then
          loop i1 (get a i1) i2 s2 (d + 1)
        else
          blit src2 i2 dst (d + 1) (src2r - i2)
      end else begin
        set dst d s2;
        let i2 = i2 + 1 in
        if i2 < src2r then
          loop i1 s1 i2 (get src2 i2) (d + 1)
        else
          blit a i1 dst (d + 1) (src1r - i1)
      end
    in loop src1ofs (get a src1ofs) src2ofs (get src2 src2ofs) dstofs;
  in
  let isortto srcofs dst dstofs len =
    for i = 0 to len - 1 do
      let e = (get a (srcofs + i)) in
      let j = ref (dstofs + i - 1) in
      while (!j >= dstofs && cmp (get dst !j) e > 0) do
        set dst (!j + 1) (get dst !j);
        decr j;
      done;
      set dst (!j + 1) e;
    done;
  in
  let rec sortto srcofs dst dstofs len =
    if len <= cutoff then isortto srcofs dst dstofs len else begin
      let l1 = len / 2 in
      let l2 = len - l1 in
      sortto (srcofs + l1) dst (dstofs + l1) l2;
      sortto srcofs a (srcofs + l2) l1;
      merge (srcofs + l2) l1 dst (dstofs + l1) l2 dst dstofs;
    end;
  in
  let l = length a in
  if l <= cutoff then isortto 0 a 0 l else begin
    let l1 = l / 2 in
    let l2 = l - l1 in
    let t = make l2 (get a 0) in
    sortto l1 t 0 l2;
    sortto 0 a l2 l1;
    merge l2 l1 t 0 l2 a 0;
  end


let fast_sort = stable_sort

************************************************************************
                                                                        
                                 OCaml                                  
                                                                        
                                                                        
     en Automatique.                                                    
                                                                        
   All rights reserved.  This file is distributed under the terms of    
   special exception on linking described in the file LICENSE.          
                                                                        
************************************************************************
 Array operations 
                , projet Cristal , INRIA Rocquencourt           
    Copyright 1996 Institut National de Recherche en Informatique et     
    the GNU Lesser General Public License version 2.1 , with the          


external length : 'a array -> int = "%array_length"
external get: 'a array -> int -> 'a = "%array_safe_get"
external set: 'a array -> int -> 'a -> unit = "%array_safe_set"
external unsafe_get: 'a array -> int -> 'a = "%array_unsafe_get"
external unsafe_set: 'a array -> int -> 'a -> unit = "%array_unsafe_set"
external make: int -> 'a -> 'a array = "caml_make_vect"
external create: int -> 'a -> 'a array = "caml_make_vect"
external unsafe_sub : 'a array -> int -> int -> 'a array = "caml_array_sub"
external append_prim : 'a array -> 'a array -> 'a array = "caml_array_append"
external concat : 'a array list -> 'a array = "caml_array_concat"
external unsafe_blit :
  'a array -> int -> 'a array -> int -> int -> unit = "caml_array_blit"
external create_float: int -> float array = "caml_make_float_vect"
let make_float = create_float

let init l f =
  if l = 0 then [||] else
  if l < 0 then invalid_arg "Array.init"
  See # 6575 . We could also check for maximum array size , but this depends 
      on whether we create a float array or a regular one ...
     on whether we create a float array or a regular one... *)
  else
   let res = create l (f 0) in
   for i = 1 to pred l do
     unsafe_set res i (f i)
   done;
   res

let make_matrix sx sy init =
  let res = create sx [||] in
  for x = 0 to pred sx do
    unsafe_set res x (create sy init)
  done;
  res

let create_matrix = make_matrix

let copy a =
  let l = length a in if l = 0 then [||] else unsafe_sub a 0 l

let append a1 a2 =
  let l1 = length a1 in
  if l1 = 0 then copy a2
  else if length a2 = 0 then unsafe_sub a1 0 l1
  else append_prim a1 a2

let sub a ofs len =
  if ofs < 0 || len < 0 || ofs > length a - len
  then invalid_arg "Array.sub"
  else unsafe_sub a ofs len

let fill a ofs len v =
  if ofs < 0 || len < 0 || ofs > length a - len
  then invalid_arg "Array.fill"
  else for i = ofs to ofs + len - 1 do unsafe_set a i v done

let blit a1 ofs1 a2 ofs2 len =
  if len < 0 || ofs1 < 0 || ofs1 > length a1 - len
             || ofs2 < 0 || ofs2 > length a2 - len
  then invalid_arg "Array.blit"
  else unsafe_blit a1 ofs1 a2 ofs2 len

let iter f a =
  for i = 0 to length a - 1 do f(unsafe_get a i) done

let iter2 f a b =
  if length a <> length b then
    invalid_arg "Array.iter2: arrays must have the same length"
  else
    for i = 0 to length a - 1 do f (unsafe_get a i) (unsafe_get b i) done

let map f a =
  let l = length a in
  if l = 0 then [||] else begin
    let r = create l (f(unsafe_get a 0)) in
    for i = 1 to l - 1 do
      unsafe_set r i (f(unsafe_get a i))
    done;
    r
  end

let map2 f a b =
  let la = length a in
  let lb = length b in
  if la <> lb then
    invalid_arg "Array.map2: arrays must have the same length"
  else begin
    if la = 0 then [||] else begin
      let r = create la (f (unsafe_get a 0) (unsafe_get b 0)) in
      for i = 1 to la - 1 do
        unsafe_set r i (f (unsafe_get a i) (unsafe_get b i))
      done;
      r
    end
  end

let iteri f a =
  for i = 0 to length a - 1 do f i (unsafe_get a i) done

let mapi f a =
  let l = length a in
  if l = 0 then [||] else begin
    let r = create l (f 0 (unsafe_get a 0)) in
    for i = 1 to l - 1 do
      unsafe_set r i (f i (unsafe_get a i))
    done;
    r
  end

let to_list a =
  let rec tolist i res =
    if i < 0 then res else tolist (i - 1) (unsafe_get a i :: res) in
  tolist (length a - 1) []

  Can not use  here because the List module depends on Array .
let rec list_length accu = function
  | [] -> accu
  | _::t -> list_length (succ accu) t

let of_list = function
    [] -> [||]
  | hd::tl as l ->
      let a = create (list_length 0 l) hd in
      let rec fill i = function
          [] -> a
        | hd::tl -> unsafe_set a i hd; fill (i+1) tl in
      fill 1 tl

let fold_left f x a =
  let r = ref x in
  for i = 0 to length a - 1 do
    r := f !r (unsafe_get a i)
  done;
  !r

let fold_right f a x =
  let r = ref x in
  for i = length a - 1 downto 0 do
    r := f (unsafe_get a i) !r
  done;
  !r

let exists p a =
  let n = length a in
  let rec loop i =
    if i = n then false
    else if p (unsafe_get a i) then true
    else loop (succ i) in
  loop 0

let for_all p a =
  let n = length a in
  let rec loop i =
    if i = n then true
    else if p (unsafe_get a i) then loop (succ i)
    else false in
  loop 0

let mem x a =
  let n = length a in
  let rec loop i =
    if i = n then false
    else if compare (unsafe_get a i) x = 0 then true
    else loop (succ i) in
  loop 0

let memq x a =
  let n = length a in
  let rec loop i =
    if i = n then false
    else if x == (unsafe_get a i) then true
    else loop (succ i) in
  loop 0

exception Bottom of int
let sort cmp a =
  let maxson l i =
    let i31 = i+i+i+1 in
    let x = ref i31 in
    if i31+2 < l then begin
      if cmp (get a i31) (get a (i31+1)) < 0 then x := i31+1;
      if cmp (get a !x) (get a (i31+2)) < 0 then x := i31+2;
      !x
    end else
      if i31+1 < l && cmp (get a i31) (get a (i31+1)) < 0
      then i31+1
      else if i31 < l then i31 else raise (Bottom i)
  in
  let rec trickledown l i e =
    let j = maxson l i in
    if cmp (get a j) e > 0 then begin
      set a i (get a j);
      trickledown l j e;
    end else begin
      set a i e;
    end;
  in
  let trickle l i e = try trickledown l i e with Bottom i -> set a i e in
  let rec bubbledown l i =
    let j = maxson l i in
    set a i (get a j);
    bubbledown l j
  in
  let bubble l i = try bubbledown l i with Bottom i -> i in
  let rec trickleup i e =
    let father = (i - 1) / 3 in
    assert (i <> father);
    if cmp (get a father) e < 0 then begin
      set a i (get a father);
      if father > 0 then trickleup father e else set a 0 e;
    end else begin
      set a i e;
    end;
  in
  let l = length a in
  for i = (l + 1) / 3 - 1 downto 0 do trickle l i (get a i); done;
  for i = l - 1 downto 2 do
    let e = (get a i) in
    set a i (get a 0);
    trickleup (bubble i 0) e;
  done;
  if l > 1 then (let e = (get a 1) in set a 1 (get a 0); set a 0 e)


let cutoff = 5
let stable_sort cmp a =
  let merge src1ofs src1len src2 src2ofs src2len dst dstofs =
    let src1r = src1ofs + src1len and src2r = src2ofs + src2len in
    let rec loop i1 s1 i2 s2 d =
      if cmp s1 s2 <= 0 then begin
        set dst d s1;
        let i1 = i1 + 1 in
        if i1 < src1r then
          loop i1 (get a i1) i2 s2 (d + 1)
        else
          blit src2 i2 dst (d + 1) (src2r - i2)
      end else begin
        set dst d s2;
        let i2 = i2 + 1 in
        if i2 < src2r then
          loop i1 s1 i2 (get src2 i2) (d + 1)
        else
          blit a i1 dst (d + 1) (src1r - i1)
      end
    in loop src1ofs (get a src1ofs) src2ofs (get src2 src2ofs) dstofs;
  in
  let isortto srcofs dst dstofs len =
    for i = 0 to len - 1 do
      let e = (get a (srcofs + i)) in
      let j = ref (dstofs + i - 1) in
      while (!j >= dstofs && cmp (get dst !j) e > 0) do
        set dst (!j + 1) (get dst !j);
        decr j;
      done;
      set dst (!j + 1) e;
    done;
  in
  let rec sortto srcofs dst dstofs len =
    if len <= cutoff then isortto srcofs dst dstofs len else begin
      let l1 = len / 2 in
      let l2 = len - l1 in
      sortto (srcofs + l1) dst (dstofs + l1) l2;
      sortto srcofs a (srcofs + l2) l1;
      merge (srcofs + l2) l1 dst (dstofs + l1) l2 dst dstofs;
    end;
  in
  let l = length a in
  if l <= cutoff then isortto 0 a 0 l else begin
    let l1 = l / 2 in
    let l2 = l - l1 in
    let t = make l2 (get a 0) in
    sortto l1 t 0 l2;
    sortto 0 a l2 l1;
    merge l2 l1 t 0 l2 a 0;
  end


let fast_sort = stable_sort
