(**
Module: Faustexp
- Description: dimension estimation and delay estimation of faust expressions.
+ Description: Faust expression evaluation
@author WANG Haisheng
- Created: 03/06/2013 Modified: 04/06/2013
+ Created: 03/06/2013 Modified: 04/08/2013
*)
open Types;;
+open Basic;;
+open Symbol;;
open Value;;
+open Signal;;
+open Beam;;
-(* EXCEPTIONS *)
-
-(** Exception raised in beam matching of faust expressions.*)
-exception Beam_Matching_Error of string;;
-
-(** Exception raised in case that the branch under call hasn't yet been programed.*)
exception NotYetDone;;
-
-
-(* PROCESS DELAY ESTIMATION *)
-
-(** val delay : faust_exp -> int, returns the number of delays estimated staticly.
-Attention: delays of "@" is estimated as 10 constant,
-delays of "vectorize" and "serialize" haven't been implemented,
-delays of "rdtable" hasn't been implemented.*)
-let rec delay exp_faust = match exp_faust with
- |Const v -> 0
- |Ident s ->
- (
- match s with
- |Add -> 0
- |Sup -> 0
- |Mul -> 0
- |Div -> 0
- |Pass -> 0
- |Stop -> 0
- |Mem -> 1
- |Delay -> 100000 (* danger! *)
- |Floor -> 0
- |Int -> 0
- |Sin -> 0
- |Cos -> 0
- |Atan -> 0
- |Atantwo -> 0
- |Sqrt -> 0
- |Rdtable -> 100000 (* danger! *)
- |Mod -> 0
- |Larger -> 0
- |Smaller -> 0
- |Vectorize -> 100 (* danger! *)
- |Concat -> 0
- |Nth -> 0
- |Serialize -> 0
- |Prefix -> 1
- |Selecttwo -> 0
- |Selectthree -> 0
- )
- |Par (e1, e2) -> max (delay e1) (delay e2)
- |Seq (e1, e2) -> (delay e1) + (delay e2)
- |Split (e1, e2) -> (delay e1) + (delay e2)
- |Merge (e1, e2) -> (delay e1) + (delay e2)
- |Rec (e1, e2) -> delay e1;;
+exception Dimension_error of string;;
+exception Process_error of string;;
(* PARSER *)
-(** val exp_of_string : string -> faust_exp, faust expression parser. *)
let exp_of_string s = (Parser.main Lexer.token (Lexing.from_string s));;
-
-(* PROCESS DIMENSION ESTIMATION *)
-(* process dimension := (size of input beam, size of output beam).*)
-
-
-(** val get_root : dimension -> int * int, returns the root of dimension tree. *)
-let get_root = fun d_tree -> match d_tree with
- | End d -> d
- | Tree (d, branches) -> d;;
-
-
-(** val subtree : dimention -> int -> dimension, returns a subtree of dimension tree.*)
-let subtree = fun d_tree -> fun i ->
- match d_tree with
- | End d -> raise (Beam_Matching_Error "Subtree left absent.")
- | Tree (d, branches) -> (
- match branches with
- (left, right) -> if i = 0 then left else right);;
-
-(** val subtree_left : dimension -> dimension, returns the left subtree of dimension tree.*)
-let subtree_left = fun d_tree -> subtree d_tree 0;;
-
-
-(** val subtree_right : dimension -> dimension, returns the right subtree of dimension tree.*)
-let subtree_right = fun d_tree -> subtree d_tree 1;;
-
-
-(** val d_par : int * int -> int * int -> int * int, process dimension for constructor "par(,)",
-which is the addition of two dimensions.*)
-let d_par a b = (((fst a) + (fst b)), ((snd a) + (snd b)));;
-
-
-(** val d_seq : int * int -> int * int -> int * int, process dimension for constructor "seq(:)",
-which is (size of input beam of first exp, size of output beam of second exp)
-along with beam matching.*)
-let d_seq a b = if (snd a) = (fst b) then (fst a, snd b) else raise (Beam_Matching_Error "seq");;
-
-
-(** val d_split : int * int -> int * int -> int * int, process dimension for constructor "split(<:)",
-which is (size of input beam of first exp, size of output beam of second exp)
-along with beam matching.*)
-let d_split a b =
- if ((fst b) mod (snd a)) = 0 then
- (fst a, snd b)
- else raise (Beam_Matching_Error "split");;
-
-
-(** val d_merge : int * int -> int * int -> int * int, process dimension for constructor "merge(:>)",
-which is (size of input beam of first exp, size of output beam of second exp)
-along with beam matching. *)
-let d_merge a b =
- if ((snd a) mod (fst b)) = 0 then
- (fst a, snd b)
- else raise (Beam_Matching_Error "merge");;
-
-
-(** val d_rec : int * int -> int * int -> int * int, process dimension for constructor "rec(~)",
-which is (size of input beam of first exp - size of output beam of second exp,
-size of output beam of first exp)
-along with beam matching.*)
-let d_rec a b =
- if (fst a) >= (snd b) && (snd a) >= (fst b) then
- ((fst a) - (snd b), snd a)
- else raise (Beam_Matching_Error "rec");;
-
-
-(** val dim : faust_exp -> int * int, returns dimension for faust expression,
-along with beam matching.*)
-let rec dim exp_faust =
-
-(** val dimension_constructor : ((int * int) -> (int * int) -> (int * int)) -> faust_exp
--> faust_exp -> dimension,
-returns the dimension tree of constructor(e1, e2).*)
- let dimension_constructor = fun constructor -> fun e1 -> fun e2 ->
- let subtree1 = dim e1 in
- let subtree2 = dim e2 in
- let root = constructor (get_root subtree1) (get_root subtree2) in
- Tree (root, (subtree1, subtree2)) in
-
- match exp_faust with
- |Const v -> End (0, 1)
- |Ident s ->
- (
- match s with
- |Add -> End (2, 1)
- |Sup -> End (2, 1)
- |Mul -> End (2, 1)
- |Div -> End (2, 1)
- |Pass -> End (1, 1)
- |Stop -> End (1, 0)
- |Mem -> End (1, 1)
- |Delay -> End (2, 1)
- |Floor -> End (1, 1)
- |Int -> End (1, 1)
- |Sin -> End (1, 1)
- |Cos -> End (1, 1)
- |Atan -> End (1, 1)
- |Atantwo -> End (2, 1)
- |Sqrt -> End (1, 1)
- |Rdtable -> End (3, 1)
- |Mod -> End (2, 1)
- |Vectorize -> End (2, 1)
- |Concat -> End (2, 1)
- |Nth -> End (2, 1)
- |Serialize -> End (1, 1)
- |Larger -> End (2, 1)
- |Smaller -> End (2, 1)
- |Prefix -> End (2, 1)
- |Selecttwo -> End (3, 1)
- |Selectthree -> End (4, 1)
- )
-
- |Par (e1, e2) -> dimension_constructor d_par e1 e2
- |Seq (e1, e2) -> dimension_constructor d_seq e1 e2
- |Split (e1, e2) -> dimension_constructor d_split e1 e2
- |Merge (e1, e2) -> dimension_constructor d_merge e1 e2
- |Rec (e1, e2) -> dimension_constructor d_rec e1 e2;;
-
-
-
-(* AUXILIARY 'CONVERT_TO_STRING' FUNCTIONS *)
-
-(** val print_exp : faust_exp -> unit, print to console the input faust expression.*)
-let print_exp exp =
- let rec string_of_exp exp = match exp with
- |Const v -> "Const" ^ " (" ^ (string_of_value v) ^ ")"
- |Ident s -> "Ident" ^ " \"" ^ "s" ^ "\""
- |Par (e1, e2) -> "Par" ^ " (" ^ (string_of_exp e1) ^ ", " ^ (string_of_exp e2) ^ ")"
- |Seq (e1, e2) -> "Seq" ^ " (" ^ (string_of_exp e1) ^ ", " ^ (string_of_exp e2) ^ ")"
- |Split (e1, e2) -> "Split" ^ " (" ^ (string_of_exp e1) ^ ", " ^ (string_of_exp e2) ^ ")"
- |Merge (e1, e2) -> "Merge" ^ " (" ^ (string_of_exp e1) ^ ", " ^ (string_of_exp e2) ^ ")"
- |Rec (e1, e2) -> "Rec" ^ " (" ^ (string_of_exp e1) ^ ", " ^ (string_of_exp e2) ^ ")"
- in
- print_string("Parer : Types.faust_exp = "^ (string_of_exp exp));;
+class dimension : int * int -> dimension_type =
+ fun (init : int * int) ->
+ object (self)
+ val _input = fst init
+ val _output = snd init
+
+ method input = _input
+ method output = _output
+
+ method par : dimension_type -> dimension_type =
+ fun dim ->
+ new dimension
+ ((self#input + dim#input), (self#output + dim#output))
+
+ method seq : dimension_type -> dimension_type =
+ fun dim ->
+ if self#output = dim#input then
+ new dimension (self#input, dim#output)
+ else raise (Dimension_error "seq dimension not matched.")
+
+ method split : dimension_type -> dimension_type =
+ fun dim ->
+ if dim#input mod self#output = 0 then
+ new dimension (self#input, dim#output)
+ else raise (Dimension_error "split dimension not matched.")
+
+ method merge : dimension_type -> dimension_type =
+ fun dim ->
+ if self#output mod dim#input = 0 then
+ new dimension (self#input, dim#output)
+ else raise (Dimension_error "merge dimension not matched.")
+
+ method _rec : dimension_type -> dimension_type =
+ fun dim ->
+ if self#output >= dim#input && self#input >= dim#output then
+ new dimension (self#input - dim#output, self#output)
+ else raise (Dimension_error "rec dimension not matched.")
+ end;;
+
+class virtual process =
+ fun (exp_init : faust_exp) ->
+ object
+ val _exp = exp_init
+ val virtual _dim : dimension_type
+ val virtual _delay : int
+ method exp = _exp
+ method dim = _dim
+ method delay = _delay
+ method virtual eval : beam_type -> beam_type
+ end
+
+class proc_const : faust_exp -> process_type =
+ fun (exp_init : faust_exp) ->
+ let _const =
+ match exp_init with
+ | Const b -> b
+ | _ -> raise (Process_error "const process constructor.") in
+
+ object (self)
+ inherit process exp_init
+ val _dim = new dimension (0,1)
+ val _delay = 0
+ method private const = _const
+ method eval : beam_type -> beam_type =
+ fun (input : beam_type) ->
+ if input#get = [||] then
+ new beam [| new signal 0 (fun t -> new value self#const)|]
+ else
+ raise (Process_error "proc_const accepts no input.")
+ end;;
+
+
+class proc_ident : faust_exp -> process_type =
+ fun (exp_init : faust_exp) ->
+ let _symbol =
+ match exp_init with
+ | Ident s -> s
+ | _ -> raise (Process_error "ident process constructor.") in
+
+ object (self)
+ inherit process exp_init
+ val _dim = new dimension (dimension_of_symbol _symbol)
+ val _delay = delay_of_symbol _symbol
+ method private symb = _symbol
+
+ method private beam_of_ident : int -> signal_type -> beam_type =
+ fun (n : int) ->
+ fun (s : signal_type) ->
+ if n = (self#dim)#input then
+ new beam [|s|]
+ else raise (Process_error ("Ident " ^ string_of_symbol self#symb))
+
+ method eval : beam_type -> beam_type =
+ fun (input : beam_type) ->
+ let n = Array.length input#get in
+ match self#symb with
+ | Pass -> self#beam_of_ident n input#get.(0)
+ | Stop -> if n = 1 then new beam [||]
+ else raise (Process_error "Ident !")
+ | Add -> self#beam_of_ident n
+ ((input#get.(0))#add input#get.(1))
+ | Sub -> self#beam_of_ident n
+ ((input#get.(0))#sub input#get.(1))
+ | Mul -> self#beam_of_ident n
+ ((input#get.(0))#mul input#get.(1))
+ | Div -> self#beam_of_ident n
+ ((input#get.(0))#div input#get.(1))
+ | Mem -> self#beam_of_ident n
+ ((input#get.(0))#mem)
+ | Delay -> self#beam_of_ident n
+ ((input#get.(0))#delay input#get.(1))
+ | Floor -> self#beam_of_ident n
+ ((input#get.(0))#floor)
+ | Int -> self#beam_of_ident n
+ ((input#get.(0))#int)
+ | Sin -> self#beam_of_ident n
+ ((input#get.(0))#sin)
+ | Cos -> self#beam_of_ident n
+ ((input#get.(0))#cos)
+ | Atan -> self#beam_of_ident n
+ ((input#get.(0))#atan)
+ | Atan2 -> self#beam_of_ident n
+ ((input#get.(0))#atan2 input#get.(1))
+ | Sqrt -> self#beam_of_ident n
+ ((input#get.(0))#sqrt)
+ | Rdtable -> self#beam_of_ident n
+ ((input#get.(1))#rdtable input#get.(0) input#get.(2))
+ | Mod -> self#beam_of_ident n
+ ((input#get.(0))#_mod input#get.(1))
+ | Vectorize -> self#beam_of_ident n
+ ((input#get.(0))#vectorize input#get.(1))
+ | Vconcat -> self#beam_of_ident n
+ ((input#get.(0))#vconcat input#get.(1))
+ | Vpick -> self#beam_of_ident n
+ ((input#get.(0))#vpick input#get.(1))
+ | Serialize -> self#beam_of_ident n
+ (input#get.(0))#serialize
+ | Larger -> self#beam_of_ident n
+ ((input#get.(0))#larger input#get.(1))
+ | Smaller -> self#beam_of_ident n
+ ((input#get.(0))#smaller input#get.(1))
+ | Prefix -> self#beam_of_ident n
+ ((input#get.(1))#prefix input#get.(0))
+ | Select2 -> self#beam_of_ident n
+ ((input#get.(0))#select2 input#get.(1) input#get.(2))
+ | Select3 -> self#beam_of_ident n
+ ((input#get.(0))#select3 input#get.(1)
+ input#get.(2) input#get.(3))
+ end;;
+
+class virtual process_binary =
+ fun (exp_init : faust_exp) ->
+ let (exp_left, exp_right) =
+ match exp_init with
+ | Par (e1, e2) -> (e1, e2)
+ | Seq (e1, e2) -> (e1, e2)
+ | Split (e1, e2) -> (e1, e2)
+ | Merge (e1, e2) -> (e1, e2)
+ | Rec (e1, e2) -> (e1, e2)
+ | _ -> raise (Process_error "binary process constructor.") in
+ let proc_left = (new proc_factory)#make exp_left in
+ let proc_right = (new proc_factory)#make exp_right in
+
+ object
+ inherit process exp_init
+ method private proc_left = proc_left
+ method private proc_right = proc_right
+
+ val _dim =
+ match exp_init with
+ | Par (e1, e2) -> (proc_left#dim)#par proc_right#dim
+ | Seq (e1, e2) -> (proc_left#dim)#seq proc_right#dim
+ | Split (e1, e2) -> (proc_left#dim)#split proc_right#dim
+ | Merge (e1, e2) -> (proc_left#dim)#merge proc_right#dim
+ | Rec (e1, e2) -> (proc_left#dim)#_rec proc_right#dim
+ | _ -> raise (Process_error "binary process constructor.")
+
+ val _delay =
+ match exp_init with
+ | Par (e1, e2) -> max proc_left#delay proc_right#delay
+ | Seq (e1, e2) -> proc_left#delay + proc_right#delay
+ | Split (e1, e2) -> proc_left#delay + proc_right#delay
+ | Merge (e1, e2) -> proc_left#delay + proc_right#delay
+ | Rec (e1, e2) -> 1 + proc_left#delay + proc_right#delay
+ | _ -> raise (Process_error "binary process constructor.")
+ end
+
+and proc_par : faust_exp -> process_type =
+ fun (exp_init : faust_exp) ->
+ object (self)
+ inherit process_binary exp_init
+ method eval : beam_type -> beam_type =
+ fun (input : beam_type) ->
+ let (sub_input1, sub_input2) = input#cut self#proc_left#dim#input in
+ let sub_output1 = self#proc_left#eval sub_input1 in
+ let sub_output2 = self#proc_right#eval sub_input2 in
+ sub_output1#append sub_output2
+ end
+
+and proc_split : faust_exp -> process_type =
+ fun (exp_init : faust_exp) ->
+ object (self)
+ inherit process_binary exp_init
+ method eval : beam_type -> beam_type =
+ fun (input : beam_type) ->
+ let mid_output = self#proc_left#eval input in
+ let mid_input = mid_output#matching self#proc_right#dim#input in
+ self#proc_right#eval mid_input
+ end
+
+and proc_merge : faust_exp -> process_type =
+ fun (exp_init : faust_exp) ->
+ object (self)
+ inherit process_binary exp_init
+ method eval : beam_type -> beam_type =
+ fun (input : beam_type) ->
+ let mid_output = self#proc_left#eval input in
+ let mid_input = mid_output#matching self#proc_right#dim#input in
+ self#proc_right#eval mid_input
+ end
+
+and proc_seq : faust_exp -> process_type =
+ fun (exp_init : faust_exp) ->
+ object (self)
+ inherit process_binary exp_init
+ method eval : beam_type -> beam_type =
+ fun (input : beam_type) ->
+ let mid_output = self#proc_left#eval input in
+ self#proc_right#eval mid_output
+ end
+
+and proc_rec : faust_exp -> process_type =
+ fun (exp_init : faust_exp) ->
+ object (self)
+ inherit process_binary exp_init
+ method eval : beam_type -> beam_type =
+ fun (input : beam_type) ->
+ let memory = Hashtbl.create self#delay in
+ let rates = ref (Array.make self#dim#output 0) in
+
+ let split : (time -> value_type array) -> (time -> value_type) array =
+ fun beam_at ->
+ let get_signal =
+ fun beam_func -> fun i -> fun t ->
+ (beam_func t).(i) in
+ Array.init self#dim#output (get_signal beam_at) in
+
+ let array_map2 = fun f -> fun a -> fun b ->
+ let n1 = Array.length a in
+ let n2 = Array.length b in
+ if n1 = n2 then Array.init n1 (fun i -> f a.(i) b.(i))
+ else raise (Process_error "Array.map2 size not matched.") in
+
+ let feedback : (time -> value_type array) -> beam =
+ fun beam_at ->
+ let signals_at = split beam_at in
+ let delay_by_one = fun s -> fun t -> s (t - 1) in
+ let delay_signal_funcs = Array.map delay_by_one
+ (Array.sub signals_at 0 self#proc_right#dim#input) in
+ new beam (array_map2 (new signal)
+ (Array.sub !rates 0 self#proc_right#dim#input)
+ delay_signal_funcs) in
+
+ let rec beam_at : time -> value_type array =
+ fun (t : time) ->
+ if t < 0 then
+ Array.make self#dim#output (new value Zero)
+ else if Hashtbl.mem memory t then
+ Hashtbl.find memory t
+ else
+ let beam_fb_in = feedback beam_at in
+ let beam_fb_out = self#proc_right#eval beam_fb_in in
+ let beam_in = beam_fb_out#append input in
+ let beam_out = self#proc_left#eval beam_in in
+ let values = beam_out#at t in
+ let () = (rates := beam_out#frequency) in
+ let () = Hashtbl.add memory t values in
+ let () = if t - self#delay >= 0 then
+ Hashtbl.remove memory (t - self#delay) else () in
+ values in
+ new beam (array_map2 (new signal) !rates (split beam_at))
+ end
+
+and proc_factory =
+ object
+ method make : faust_exp -> process_type =
+ fun (exp : faust_exp) ->
+ match exp with
+ | Const b -> new proc_const exp
+ | Ident s -> new proc_ident exp
+ | Par (e1, e2) -> new proc_par exp
+ | Seq (e1, e2) -> new proc_seq exp
+ | Split (e1, e2) -> new proc_split exp
+ | Merge (e1, e2) -> new proc_merge exp
+ | Rec (e1, e2) -> new proc_rec exp
+ end;;
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