(** Module: Interpreter Description: input beam -> process -> output beam @author WANG Haisheng Created: 15/05/2013 Modified: 04/06/2013 *) open Types;; open Value;; open Signal;; open Faustexp;; (* EXCEPTIONS *) (** Exception raised during interpretation of faust process.*) exception Evaluation_Error of string;; (* MACRO *) (** Macro constants of this file.*) type interpreter_macro = | Number_samples_int | Max_Eval_Time_int;; (** val interpreter_macro_to_value : returns the value associated with the macro.*) let interpreter_macro_to_value m = match m with | Number_samples_int -> 0xFF | Max_Eval_Time_int -> 0xFFFFFFFF;; (* OUTPUT WAVE COMPUTATION *) (** val func_of_func_array : (int -> value) array -> (int -> value array), applies the same int parameter to each element of function array, produces a value array.*) let fun_array_to_fun = fun fun_array -> let reverse = fun t -> fun f -> f t in let new_fun = fun t-> Array.map (reverse t) fun_array in new_fun;; (** val computing : (int -> value array) -> int -> int -> float array array array, applies time sequence "0,1,2,3,...,max" to signal beam, returns primitive output data.*) let computing = fun f -> fun width -> fun length -> let container_float_array_array_array = ref (Array.make length (Array.make width [||])) in let index = ref 0 in try while !index < length do (!container_float_array_array_array).(!index) <- (Array.map convert_back_R (f (!index))); incr index; done; let () = print_string ("Done.") in !container_float_array_array_array with x -> let error_message = match x with |Convert_Error s -> "Convert_Error: " ^ s |Value_operation s -> "Value_operation: " ^ s |Signal_operation s -> "Signal_operation: " ^ s |Beam_Matching_Error s -> "Beam_Matching_Error: " ^ s |Evaluation_Error s -> "Evaluation_Error: " ^ s |NotYetDone -> "NotYetDone" |_ -> "Done." in let () = print_string error_message in Array.sub (!container_float_array_array_array) 0 !index;; (** val matrix_transpose : 'a array array -> 'a array array, transposes the input matrix.*) let matrix_transpose = fun m_array_array -> fun width -> let get_element = fun i -> fun array -> Array.get array i in let get_line = fun array_array -> fun i -> Array.map (get_element i) array_array in let transpose array_array = Array.init width (get_line array_array) in transpose m_array_array;; (** val channels : 'a array array array -> int -> int array, returns an array of number of channels. *) let channels = fun f_array_array_array -> fun width -> let channel = fun faaa -> fun i -> let faa = faaa.(i) in let length = Array.length faa in let fa = faa.(length - 1) in Array.length fa in let channel_array = Array.init width (channel f_array_array_array) in channel_array;; (** val arrange : 'a array array array -> int -> 'a array list, arranges the output data in "array list" form. *) let arrange = fun float_array_array_array -> fun width -> let concat faaa = fun i -> let faa = faaa.(i) in Array.concat (Array.to_list faa) in let float_array_array = Array.init width (concat float_array_array_array) in let float_array_list = Array.to_list float_array_array in float_array_list;; (** val compute : (int -> value) list -> (int list) * (float array list). input: a list of signal functions output: channel number list, data list.*) let compute fun_list = let () = print_string(" Faustine -> Signals computing... ") in let tic = Sys.time () in (* arrange input information *) let length = interpreter_macro_to_value Number_samples_int in let width = List.length fun_list in let beam_fun = fun_array_to_fun (Array.of_list fun_list) in (* calculate output wave *) let tmp_float_array_array_array = computing beam_fun width length in (* arrange output data *) let output_float_array_array_array = matrix_transpose tmp_float_array_array_array width in let channel_array = channels output_float_array_array_array width in let channel_list = Array.to_list channel_array in let output_float_array_list = arrange output_float_array_array_array width in let toc = Sys.time () in let () = print_endline(" (duration: " ^ (string_of_float (toc -. tic)) ^ "s)") in (channel_list, output_float_array_list);; (* INTERPRETATION *) (** val sublist : 'a list -> int -> int -> 'a list, [sublist l start length], returns the sublist of list 'l', from index 'start', with length 'length'.*) let sublist l start length = try let arr = Array.of_list l in let sub_array = Array.sub arr start length in Array.to_list sub_array with (Invalid_argument "Array.sub") -> raise (Invalid_argument "List.sub");; (** val make_beam : (int list) * (float array list) -> (int * (int -> value)) list, input: (sample rate list, data list) output: beam = (sample rate, function) list *) let make_beam = fun input -> let rate_list = fst input in let float_array_list = snd input in let value_array_list = List.map (Array.map return_R) float_array_list in let fun_list = List.map Array.get value_array_list in let make_signal = fun rate -> fun f -> (rate, f) in let beam = List.map2 make_signal rate_list fun_list in beam;; (** val interpret_const : value -> beam -> beam, generates constant signal with frequency 0. *) let interpret_const = fun v -> fun input_beam -> let n = List.length input_beam in if n = 0 then [(0,(fun t -> v))] else raise (Evaluation_Error "Const");; (** val interpret_ident : string -> beam -> beam, generates signals according to identified symbols. *) let interpret_ident = fun s -> fun input_beam -> let n = List.length input_beam in match s with |Pass -> if n = 1 then input_beam else raise (Evaluation_Error "Ident _") |Stop -> if n = 1 then [] else raise (Evaluation_Error "Ident !") |Add -> if n = 2 then [signal_add (List.nth input_beam 0) (List.nth input_beam 1)] else raise (Evaluation_Error "Ident +") |Sup -> if n = 2 then [signal_sub (List.nth input_beam 0) (List.nth input_beam 1)] else raise (Evaluation_Error "Ident -") |Mul -> if n = 2 then [signal_mul (List.nth input_beam 0) (List.nth input_beam 1)] else raise (Evaluation_Error "Ident *") |Div -> if n = 2 then [signal_div (List.nth input_beam 0) (List.nth input_beam 1)] else raise (Evaluation_Error "Ident /") |Delay -> if n = 2 then [signal_delay (List.nth input_beam 0) (List.nth input_beam 1)] else raise (Evaluation_Error "Ident @") |Mem -> if n = 1 then [signal_mem (List.nth input_beam 0)] else raise (Evaluation_Error "Ident mem") |Vectorize -> if n = 2 then [signal_vectorize (List.nth input_beam 0) (List.nth input_beam 1)] else raise (Evaluation_Error "Ident vectorize") |Serialize -> if n = 1 then [signal_serialize (List.nth input_beam 0)] else raise (Evaluation_Error "Ident serialize") |Concat -> if n = 2 then [signal_append (List.nth input_beam 0) (List.nth input_beam 1)] else raise (Evaluation_Error "Ident #") |Nth -> if n = 2 then [signal_nth (List.nth input_beam 0) (List.nth input_beam 1)] else raise (Evaluation_Error "Ident []") |Floor -> if n = 1 then [signal_floor (List.nth input_beam 0)] else raise (Evaluation_Error "Ident floor") |Int -> if n = 1 then [signal_int (List.nth input_beam 0)] else raise (Evaluation_Error "Ident int") |Sin -> if n = 1 then [signal_sin (List.nth input_beam 0)] else raise (Evaluation_Error "Ident sin") |Cos -> if n = 1 then [signal_cos (List.nth input_beam 0)] else raise (Evaluation_Error "Ident cos") |Atan -> if n = 1 then [signal_atan (List.nth input_beam 0)] else raise (Evaluation_Error "Ident atan") |Atantwo -> if n = 2 then [signal_atantwo (List.nth input_beam 0) (List.nth input_beam 1)] else raise (Evaluation_Error "Ident atantwo") |Sqrt -> if n = 1 then [signal_sqrt (List.nth input_beam 0)] else raise (Evaluation_Error "Ident sqrt") |Rdtable -> if n = 3 then [signal_rdtable (List.nth input_beam 0) (List.nth input_beam 1) (List.nth input_beam 2)] else raise (Evaluation_Error "Ident rdtable") |Selecttwo -> if n = 3 then [signal_select2 (List.nth input_beam 0) (List.nth input_beam 1) (List.nth input_beam 2)] else raise (Evaluation_Error "Ident select2") |Selectthree -> if n = 4 then [signal_select3 (List.nth input_beam 0) (List.nth input_beam 1) (List.nth input_beam 2) (List.nth input_beam 3)] else raise (Evaluation_Error "Ident select3") |Prefix -> if n = 2 then [signal_prefix (List.nth input_beam 0) (List.nth input_beam 1)] else raise (Evaluation_Error "Ident prefix") |Mod -> if n = 2 then [signal_mod (List.nth input_beam 0) (List.nth input_beam 1)] else raise (Evaluation_Error "Ident %") |Larger -> if n = 2 then [signal_sup (List.nth input_beam 0) (List.nth input_beam 1)] else raise (Evaluation_Error "Ident >") |Smaller -> if n = 2 then [signal_inf (List.nth input_beam 0) (List.nth input_beam 1)] else raise (Evaluation_Error "Ident <");; (** val rec eval : faust_exp -> beam -> beam, main interpretation work is done here. *) let rec eval exp_faust dimension_tree input_beam = (** val interpret_par : faust_exp -> faust_exp -> beam -> beam, interprets par(e1, e2) with input beam, produces output beam.*) let interpret_par = fun e1 -> fun e2 -> fun dimension_tree -> fun input_beam -> (* dimension information *) let n = List.length input_beam in let subtree1 = subtree_left dimension_tree in let subtree2 = subtree_right dimension_tree in let d1 = get_root subtree1 in let d2 = get_root subtree2 in if n = (fst d1) + (fst d2) then ( (* segmentation of input beam *) let input_beam1 = sublist input_beam 0 (fst d1) in let input_beam2 = sublist input_beam (fst d1) (fst d2) in (* evaluate two expressions respectively *) let output_beam1 = eval e1 subtree1 input_beam1 in let output_beam2 = eval e2 subtree2 input_beam2 in (* concat two output beams *) if List.length output_beam1 = snd d1 && List.length output_beam2 = snd d2 then (output_beam1 @ output_beam2) else raise (Evaluation_Error "Par") ) else raise (Evaluation_Error "Par") in (** val interpret_seq : faust_exp -> faust_exp -> beam -> beam, interprets seq(e1, e2) with input beam, produces output beam.*) let interpret_seq = fun e1 -> fun e2 -> fun dimension_tree -> fun input_beam -> (* dimension information *) let n = List.length input_beam in let subtree1 = subtree_left dimension_tree in let subtree2 = subtree_right dimension_tree in let d1 = get_root subtree1 in let d2 = get_root subtree2 in if n = fst d1 then ( (* evaluate the first expression *) let output_beam1 = eval e1 subtree1 input_beam in (* evaluate the second expression *) if List.length output_beam1 = fst d2 then eval e2 subtree2 output_beam1 else raise (Evaluation_Error "Seq") ) else raise (Evaluation_Error "Seq") in (** val interpret_split : faust_exp -> faust_exp -> beam -> beam, interprets split(e1, e2) with input beam, produces output beam.*) let interpret_split = fun e1 -> fun e2 -> fun dimension_tree -> fun input_beam -> (* dimension information *) let n = List.length input_beam in let subtree1 = subtree_left dimension_tree in let subtree2 = subtree_right dimension_tree in let d1 = get_root subtree1 in let d2 = get_root subtree2 in if n = fst d1 then ( (* evaluate the first expression *) let output_beam1 = eval e1 subtree1 input_beam in (* beam matching *) let ref_output_beam1 = ref (beam_add_one_memory output_beam1) in let input_beam2 = List.concat (Array.to_list (Array.make ((fst d2)/(List.length output_beam1)) !ref_output_beam1)) in (* evaluate the second expression *) if List.length input_beam2 = fst d2 then eval e2 subtree2 input_beam2 else raise (Evaluation_Error "Split") ) else raise (Evaluation_Error "Split") in (** val interpret_merge : faust_exp -> faust_exp -> beam -> beam, interprets merge(e1, e2) with input beam, produces output beam.*) let interpret_merge = fun e1 -> fun e2 -> fun dimension_tree -> fun input_beam -> (* dimension information *) let n = List.length input_beam in let subtree1 = subtree_left dimension_tree in let subtree2 = subtree_right dimension_tree in let d1 = get_root subtree1 in let d2 = get_root subtree2 in if n = fst d1 then ( (* evaluate the first expression *) let output_beam1 = eval e1 subtree1 input_beam in (* beam matching *) let input_beam2 = ( let fois = (snd d1)/(fst d2) in let ref_beam = ref (sublist output_beam1 0 (fst d2)) in for i = 1 to fois - 1 do let temp_beam = sublist output_beam1 (i*(fst d2)) (fst d2) in ref_beam := List.map2 signal_add (!ref_beam) temp_beam; done; !ref_beam ) in (* evaluate the second expression *) if List.length input_beam2 = fst d2 then eval e2 subtree2 input_beam2 else raise (Evaluation_Error "Merge") ) else raise (Evaluation_Error "Merge") in (** val interpret_rec : faust_exp -> faust_exp -> beam -> beam, interprets rec(e1, e2) with input beam, produces output beam.*) let interpret_rec = fun e1 -> fun e2 -> fun dimension_tree -> fun input_beam -> (* dimension information *) let subtree1 = subtree_left dimension_tree in let subtree2 = subtree_right dimension_tree in let d1 = get_root subtree1 in let d2 = get_root subtree2 in (* estimate stockage size for delay *) let delay_int = 1 + delay e2 + delay e1 in (* prepare stockage *) let memory_hashtbl = Hashtbl.create delay_int in let rate_list = ref (Array.to_list (Array.make (snd d1) 0)) in (** val apply_to : 'a -> ('a -> 'b) -> 'b *) let apply_to = fun t -> fun f -> f t in (** val get_value_fun_list : (int -> (int list) * (value list)) -> (int -> value) list *) let get_value_fun_list = fun beam_fun -> let tmp = fun beam_fun -> fun i -> fun t -> List.nth (snd (beam_fun t)) i in List.map (tmp beam_fun) (Array.to_list (Array.init (snd d1) (fun n -> n))) in (** val make_signal : int -> (int -> value) -> signal, combines rate and function. *) let make_signal = fun rate -> fun f -> (rate, f) in (** val output_beam_fun : int -> (int list) * (value list), with input : time output: rate list * value list *) let rec output_beam_fun = fun t -> (* initial value in constrctor "rec '~'" *) if t < 0 then let init_rate_list = Array.to_list (Array.make (snd d1) 0) in let value_list = Array.to_list (Array.make (snd d1) Zero) in (init_rate_list, value_list) (* check stockage at time t *) else if Hashtbl.mem memory_hashtbl t then (!rate_list, Hashtbl.find memory_hashtbl t) (* blocks : "a ~ b", calculate rate list and value list at time t *) else (* mid_output_fun_list : (int -> value) list *) let mid_output_fun_list = get_value_fun_list output_beam_fun in (* b_input_fun_list : (int -> value) list *) let b_input_fun_list = List.map (fun s -> fun t -> s (t - 1)) (sublist mid_output_fun_list 0 (fst d2)) in (* b_input_beam : signal list *) let b_input_beam = List.map2 make_signal (sublist !rate_list 0 (fst d2)) b_input_fun_list in (* evaluation of block "b" *) let b_output_beam = (eval e2 subtree2 b_input_beam) in (* evaluation of block "a" *) let a_input_beam = b_output_beam @ input_beam in let mid_output_beam = eval e1 subtree1 a_input_beam in (* calculate rate list and value list at time t *) let mid_output_rate_list = List.map fst mid_output_beam in let mid_output_value_list = List.map (apply_to t) (List.map snd mid_output_beam) in (* update stockage *) let () = (rate_list := mid_output_rate_list) in let () = Hashtbl.add memory_hashtbl t mid_output_value_list in let () = Hashtbl.remove memory_hashtbl (t - delay_int) in (mid_output_rate_list, mid_output_value_list) in (* output_beam : signal list *) let output_beam = List.map2 make_signal !rate_list (get_value_fun_list output_beam_fun) in output_beam in (** Call for previous functions *) match exp_faust with |Const v -> interpret_const v input_beam |Ident s -> interpret_ident s input_beam |Par (e1, e2) -> interpret_par e1 e2 dimension_tree input_beam |Seq (e1, e2) -> interpret_seq e1 e2 dimension_tree input_beam |Split (e1, e2) -> interpret_split e1 e2 dimension_tree input_beam |Merge (e1, e2) -> interpret_merge e1 e2 dimension_tree input_beam |Rec (e1, e2) -> interpret_rec e1 e2 dimension_tree input_beam;; (** val extract_rate : (int * (int -> value)) list -> int list, gets the sample rate list from beam.*) let extract_rate = fun beam -> let rate_naive_list = List.map fst beam in let correct_rate r = if r = 0 then 44100 else if r > 0 then r else raise (Evaluation_Error "Rec2") in let rate_list = List.map correct_rate rate_naive_list in rate_list;; (** val interpreter : faust_exp -> (int list) * (float array list) -> (int list) * (int list) * (float array list) input: faust expression, sample rate list * input data list output: channel list * sample rate list * output data list.*) let interpreter exp_faust input = let () = print_string(" Faustine -> Interpretation...") in let tic = Sys.time () in (* make input beam *) let input_beam = make_beam input in (* estimate process dimension *) let dimension_tree = dim exp_faust in (* interprete output beam *) let output_beam = eval exp_faust dimension_tree input_beam in let toc = Sys.time () in let () = print_endline(" Done. (duration: " ^ (string_of_float (toc -. tic)) ^ "s)") in (* get rate list from output beam *) let rate_list = extract_rate output_beam in (* get channel list and data list from output beam *) let (channel_list, float_array_list) = compute (List.map snd output_beam) in (channel_list, rate_list, float_array_list);;