interpretor/basic.ml

   1 (**
   2         Module: Basic
   3         Description: basic data type in the vectorial faust interpreter.
   4         @author WANG Haisheng
   5         Created: 31/05/2013     Modified: 17/07/2013
   6 *)
   7
   8 open Types;;
   9 open Aux;;
  10
  11 exception Convert_Error of string;;
  12 exception Basic_operation of string;;
  13
  14
  15 (* MACRO *)
  16
  17 let faust_max = 2147483647;;
  18 let faust_min = -2147483648;;
  19 let faust_bits = 32;;
  20
  21 (* Functional operations *)
  22
  23 let fun_unary oper f = fun x -> oper (f x);;
  24 let fun_binary oper f g = fun x -> oper (f x) (g x);;
  25 let fun_ternary oper f g h = fun x -> oper (f x) (g x) (h x);;
  26
  27 (* basic operations *)
  28
  29 let memorize : int -> (index -> basic) -> (index -> basic) =
  30   fun size ->
  31     fun vec ->
  32       let memory = Array.create size Error in
  33       let filled = Array.create size false in
  34       let vec_mem : index -> basic =
  35         fun i ->
  36           if i >= 0 && i < size then (
  37             if filled.(i) then
  38               memory.(i)
  39             else
  40               let result = vec i in
  41               let () = memory.(i) <- result in
  42               let () = filled.(i) <- true in
  43               result)
  44           else raise (Invalid_argument "vector overflow.") in
  45       vec_mem;;
  46
  47 class vector : int -> (index -> basic) -> vector_type =
  48   fun (size_init : int) ->
  49     fun (vec_init : index -> basic) ->
  50   object
  51     val s = size_init
  52     val vec = memorize size_init vec_init
  53     method size = s
  54     method nth = vec
  55   end;;
  56
  57 let rec basic_to_int : basic -> int =
  58   fun v ->
  59         match v with
  60         |N i -> i
  61         |R f -> int_of_float f
  62         |Vec vec ->
  63             raise (Convert_Error "basic_to_int : vector.")
  64         |Zero -> 0
  65         |Error -> raise (Convert_Error "basic_to_int : Error");;
  66
  67
  68 let basic_to_float : basic -> float =
  69   fun v ->
  70         match v with
  71         |N i -> float_of_int i
  72         |R f -> f
  73         |Vec vec ->
  74             raise (Convert_Error "basic_to_float : vector.")
  75         |Zero -> 0.
  76         |Error -> 0.;;
  77
  78
  79 let basic_to_float_array : basic -> float array =
  80   fun v ->
  81         match v with
  82         |Vec vec ->
  83                 let basics : basic array =
  84                   Array.init vec#size vec#nth in
  85                 Array.map basic_to_float basics
  86         |_ -> [| (basic_to_float v)|];;
  87
  88
  89 let rec basic_to_string : basic -> string =
  90   fun (v : basic) ->
  91         match v with
  92         |N i1 -> string_of_int i1
  93         |R f1 -> string_of_float f1
  94         |Vec vec ->
  95             let basics : basic array =
  96               Array.init vec#size vec#nth in
  97             let strings = Array.to_list
  98                 (Array.map basic_to_string basics) in
  99             String.concat "," strings
 100         |Zero -> "0"
 101         |Error -> "0";;
 102
 103 let basic_of_float : float -> basic = fun f -> R f;;
 104
 105 let rec basic_of_float_array : float array -> basic =
 106   fun (data : float array) ->
 107     let n = Array.length data in
 108     if n = 0 then
 109       raise (Convert_Error "basic_of_float_array : empty.")
 110     else if n = 1 then basic_of_float data.(0)
 111     else
 112       let vec = Array.get (Array.map basic_of_float data) in
 113       Vec (new vector n vec);;
 114
 115 let basic_to_bool : basic -> bool =
 116   fun b ->
 117     match b with
 118     | N i ->
 119         if i = 1 then true
 120         else if i = 0 then false
 121         else raise (Convert_Error "basic_to_bool : only for 0 or 1.")
 122     | Zero -> false
 123     | _ -> raise (Convert_Error "basic_to_bool : only for 0 or 1.");;
 124
 125 (* VALUE OPERATIONS *)
 126
 127 let rec basic_normalize : basic -> basic =
 128   fun b ->
 129     let n = 2. ** float_of_int (faust_bits) in
 130     match b with
 131     |N i ->
 132         if i > faust_max then
 133           N (i - int_of_float
 134                (n *. floor (((float_of_int i) +. n/.2.)/.n)))
 135         else if i < faust_min then
 136           N (i + int_of_float
 137                (n *. floor ((n/.2. -. (float_of_int i) -. 1.)/.n)))
 138         else N i
 139     |R f ->
 140         if f > float_of_int (faust_max) then
 141           R (f -. (n *. floor ((f +. n/.2.)/.n)))
 142         else if f < float_of_int (faust_min) then
 143           R (f +. (n *. floor ((n/.2. -. f -. 1.)/.n)))
 144         else R f
 145     |Vec vec ->
 146         Vec (new vector vec#size
 147                (fun_unary basic_normalize vec#nth))
 148     |Zero -> Zero
 149     |Error -> Error;;
 150
 151
 152 let rec basic_add : basic -> basic -> basic =
 153   fun b1 -> fun b2 ->
 154   match (b1, b2) with
 155   | (Zero, _) -> b2
 156   | (_, Zero) -> b1
 157
 158   | (Vec vec1, Vec vec2) ->
 159       if vec1#size = vec2#size then
 160         Vec (new vector vec1#size
 161                (fun_binary basic_add vec1#nth vec2#nth))
 162       else raise (Basic_operation "vector size not matched.")
 163   | (Vec vec1, _) -> raise (Basic_operation "vec1 +~ sca2")
 164
 165   | (N i1, N i2) -> basic_normalize (N (i1 + i2))
 166   | (N i1, R f2) -> basic_normalize (R ((float_of_int i1) +. f2))
 167   | (N i1, Vec vec2) -> raise (Basic_operation "i1 +~ vec2")
 168   | (N i1, Error) -> Error
 169
 170   | (R f1, N i2) -> basic_normalize (R (f1 +. (float_of_int i2)))
 171   | (R f1, R f2) -> basic_normalize (R (f1 +. f2))
 172   | (R f1, Vec vec2) -> raise (Basic_operation "f1 +~ vec2")
 173   | (R f1, Error) -> Error
 174
 175   | (Error, Vec vec2) -> raise (Basic_operation "Error +~ vec2")
 176   | (Error, _) -> Error;;
 177
 178
 179 let (+~) b1 b2 = basic_add b1 b2;;
 180
 181
 182 let rec basic_neg : basic -> basic =
 183   fun b ->
 184     match b with
 185     |N i -> N (-i)
 186     |R f -> R (-.f)
 187     |Vec vec -> Vec (new vector vec#size (fun_unary basic_neg vec#nth))
 188     |Zero -> Zero
 189     |Error -> Error;;
 190
 191
 192 let basic_sub : basic -> basic -> basic =
 193   fun b1 ->
 194     fun b2 ->
 195       basic_add b1 (basic_neg b2);;
 196
 197
 198 let (-~) b1 b2 = basic_sub b1 b2;;
 199
 200
 201 let rec basic_mul : basic -> basic -> basic =
 202   fun b1 ->
 203     fun b2 ->
 204       match (b1, b2) with
 205       | (Vec vec1, Vec vec2) ->
 206           if vec1#size = vec2#size then
 207             Vec (new vector vec1#size
 208                    (fun_binary basic_mul vec1#nth vec2#nth))
 209           else raise (Basic_operation "vector size not matched.")
 210       | (Vec vec1, Zero) ->
 211           Vec (new vector vec1#size
 212                  (fun_unary (basic_mul Zero) vec1#nth))
 213       | (Vec vec1, _) -> raise (Basic_operation "vec1 *~ sca2")
 214
 215       | (N i1, N i2) -> basic_normalize (N (i1 * i2))
 216       | (N i1, R f2) -> basic_normalize (R ((float_of_int i1) *. f2))
 217       | (N i1, Vec vec2) -> raise (Basic_operation "i1 *~ vec2")
 218       | (N i1, Zero) -> N 0
 219       | (N i1, Error) -> Error
 220
 221       | (R f1, N i2) -> basic_normalize (R (f1 *. (float_of_int i2)))
 222       | (R f1, R f2) -> basic_normalize (R (f1 *. f2))
 223       | (R f1, Vec vec2) -> raise (Basic_operation "f1 *~ vec2")
 224       | (R f1, Zero) -> R 0.
 225       | (R f1, Error) -> Error
 226
 227       | (Zero, N i2) -> N 0
 228       | (Zero, R f2) -> R 0.
 229       | (Zero, Vec vec2) ->
 230           Vec (new vector vec2#size
 231                  (fun i -> basic_mul Zero (vec2#nth i)))
 232       | (Zero, Zero) -> Zero
 233       | (Zero, Error) -> Error
 234
 235       | (Error, Vec vec2) -> raise (Basic_operation "Error +~ vec2")
 236       | (Error, _) -> Error;;
 237
 238
 239 let ( *~ ) b1 b2 = basic_mul b1 b2;;
 240
 241
 242 let rec basic_recip : basic -> basic =
 243   fun v ->
 244     match v with
 245         |N i -> basic_recip (R (float_of_int i))
 246         |R f -> if f = 0. then Error else R (1./.f)
 247         |Vec vec -> Vec (new vector vec#size
 248               (fun_unary basic_recip vec#nth))
 249         |Zero -> Error
 250         |Error -> R 0.;;
 251
 252
 253 let basic_div : basic -> basic -> basic =
 254   fun b1 ->
 255     fun b2 ->
 256       basic_mul b1 (basic_recip b2);;
 257
 258
 259 let (/~) b1 b2 = basic_div b1 b2;;
 260
 261
 262 let rec basic_zero : basic -> basic =
 263   fun v ->
 264     match v with
 265     |N i -> N 0
 266     |R f -> R 0.
 267     |Vec vec -> Vec (new vector vec#size
 268                        (fun_unary basic_zero vec#nth))
 269     |Zero -> Zero
 270     |Error -> R 0.;;
 271
 272
 273 let rec basic_power : basic -> basic -> basic =
 274   fun b1 ->
 275     fun b2 ->
 276       match (b1, b2) with
 277       | (Vec vec1, Vec vec2) ->
 278           if vec1#size = vec2#size then
 279             Vec (new vector vec1#size
 280                    (fun_binary basic_power vec1#nth vec2#nth))
 281           else raise (Basic_operation "vector size not matched.")
 282       | (Vec vec1, Zero) ->
 283           let vec_zeros = Vec (new vector vec1#size (fun i -> Zero)) in
 284           basic_power b1 vec_zeros
 285       | (Vec vec1, _) -> raise (Basic_operation "vec1 *~ sca2")
 286
 287       | (N i1, _) -> basic_power (R (float_of_int i1)) b2
 288
 289       | (R f1, N i2) -> basic_power b1 (R (float_of_int i2))
 290       | (R f1, R f2) -> basic_normalize (R (f1 ** f2))
 291       | (R f1, Vec vec2) -> raise (Basic_operation "f1 *~ vec2")
 292       | (R f1, Zero) -> R 1.
 293       | (R f1, Error) -> Error
 294
 295       | (Zero, N i2) -> basic_power b1 (R (float_of_int i2))
 296       | (Zero, R f2) -> R 0.
 297       | (Zero, Vec vec2) ->
 298           let vec_zeros = Vec (new vector vec2#size (fun i -> Zero)) in
 299           basic_power vec_zeros b2
 300       | (Zero, Zero) -> basic_power (R 0.) (R 0.)
 301       | (Zero, Error) -> Error
 302
 303       | (Error, Vec vec2) -> raise (Basic_operation "Error +~ vec2")
 304       | (Error, _) -> Error;;
 305
 306
 307 let rec basic_logic :
 308     (bool -> bool -> bool) -> basic -> basic -> basic =
 309       fun oper -> fun b1 -> fun b2 ->
 310         match (b1, b2) with
 311         | (Vec vec1, Vec vec2) ->
 312             if vec1#size = vec2#size then
 313               Vec (new vector vec1#size
 314                      (fun_binary (basic_logic oper) vec1#nth vec2#nth))
 315             else raise (Basic_operation "vector size not matched.")
 316         | (Vec vec1, Zero) ->
 317             let vec_zeros = Vec (new vector vec1#size (fun i -> Zero)) in
 318             basic_and b1 vec_zeros
 319         | (Vec vec1, _) -> raise (Basic_operation "vec1 logic sca2")
 320
 321       | (N i1, N i2) -> oper (basic_to_bool b1) (basic_to_bool b2)
 322       | (N i1, R f2) ->
 323           raise (Basic_operation "Float shouldn't be in logical oper.")
 324       | (N i1, Vec vec2) -> raise (Basic_operation "f1 logic vec2")
 325       | (N i1, Zero) -> basic_logic oper b1 (N 0)
 326       | (N i1, Error) -> Error
 327
 328       | (R f1, _) ->
 329           raise (Basic_operation "Float shouldn't be in logical oper.")
 330
 331       | (Zero, N i2) -> basic_logic oper (N 0) b2
 332       | (Zero, R f2) ->
 333           raise (Basic_operation "Float shouldn't be in logical oper.")
 334       | (Zero, Vec vec2) ->
 335           let vec_zeros = Vec (new vector vec2#size (fun i -> Zero)) in
 336           basic_logic oper vec_zeros b2
 337       | (Zero, Zero) -> basic_logic oper (N 0) (N 0)
 338       | (Zero, Error) -> Error
 339
 340       | (Error, Vec vec2) -> raise (Basic_operation "Error logic vec2")
 341       | (Error, _) -> Error;;
 342
 343 let basic_and = basic_logic (&&);;
 344 let basic_or = basic_logic (||);;
 345 let basic_xor = basic_logic xor;;
 346
 347 let rec basic_adjust : (float -> float) -> basic -> basic =
 348   fun oper -> fun b ->
 349     match b with
 350     |N i -> R (float_of_int i)
 351     |R f -> R (floor f)
 352     |Vec vec -> Vec (new vector vec#size
 353                        (fun_unary basic_floor vec#nth))
 354     |Zero -> R 0.
 355     |Error -> Error;;
 356
 357 let basic_floor = basic_adjust floor;;
 358 let basic_ceil = basic_adjust ceil;;
 359 let basic_rint = basic_adjust rint;;
 360
 361 let rec basic_int : basic -> basic =
 362   fun b ->
 363     match b with
 364     |N i -> b
 365     |R f -> N (int_of_float f)
 366     |Vec vec -> Vec (new vector vec#size
 367                        (fun_unary basic_int vec#nth))
 368     |Zero -> N 0
 369     |Error -> Error;;
 370
 371 let rec basic_float : basic -> basic =
 372   fun b ->
 373     match b with
 374     | N i -> R (float_of_int i)
 375     | R f -> b
 376     | Vec vec -> Vec (new vector vec#size
 377                         (fun_unary basic_float vec#nth))
 378     | Zero -> R 0.
 379     | Error -> Error;;
 380
 381
 382 let rec basic_unary : (float -> float) -> basic -> basic =
 383   fun oper ->
 384     fun b ->
 385       match b with
 386       |N i -> R (oper (float_of_int i))
 387       |R f -> R (oper f)
 388       |Vec vec -> Vec (new vector vec#size
 389                          (fun_unary (basic_unary oper) vec#nth))
 390       |Zero -> R (oper 0.)
 391       |Error -> Error;;
 392
 393
 394 let basic_sin : basic -> basic = basic_unary sin;;
 395 let basic_cos : basic -> basic = basic_unary cos;;
 396 let basic_atan : basic -> basic = basic_unary atan;;
 397
 398
 399 let rec basic_atan2 : basic -> basic -> basic =
 400   fun v1 ->
 401     fun v2 ->
 402       match (v1, v2) with
 403       | (N i1, N i2) -> basic_atan2
 404             (R (float_of_int i1)) (R (float_of_int i2))
 405       | (N i1, R f2) -> basic_atan2 (R (float_of_int i1)) v2
 406       | (N i1, Zero) -> basic_atan2 (R (float_of_int i1)) (R 0.)
 407       | (N i1, Vec vec2) -> raise (Basic_operation "atan2 sca vec.")
 408       | (N i1, Error) -> Error
 409
 410       | (R f1, N i2) -> basic_atan2 v1 (R (float_of_int i2))
 411       | (R f1, R f2) -> R (atan2 f1 f2)
 412       | (R f1, Zero) -> basic_atan2 v1 (R 0.)
 413       | (R f1, Vec vec2) -> raise (Basic_operation "atan2 sca vec.")
 414       | (R f1, Error) -> Error
 415
 416       | (Vec vec1, Vec vec2) -> Vec (new vector vec1#size
 417                           (fun_binary basic_atan2 vec1#nth vec2#nth))
 418       | (Vec vec1, Zero) -> Vec (new vector vec1#size
 419                                    (fun i -> basic_atan2 (vec1#nth i) Zero))
 420       | (Vec vec1, _) -> raise (Basic_operation "atan2 vec sca.")
 421
 422       | (Zero, N i2) -> basic_atan2 (R 0.) (R (float_of_int i2))
 423       | (Zero, R f2) -> basic_atan2 (R 0.) v2
 424       | (Zero, Vec vec2) -> Vec (new vector vec2#size
 425                                    (fun_unary (basic_atan2 Zero) vec2#nth))
 426       | (Zero, Zero) -> basic_atan2 (R 0.) (R 0.)
 427       | (Zero, Error) -> Error
 428
 429       | (Error, Vec vec2) -> raise (Basic_operation "atan2 sca vec.")
 430       | (Error, _) -> Error;;
 431
 432
 433 let rec basic_sqrt v = match v with
 434         |N i ->
 435             if i >= 0 then R (sqrt (float_of_int i))
 436             else raise (Basic_operation "sqrt parameter < 0.")
 437         |R f ->
 438             if f >= 0. then R (sqrt f)
 439             else raise (Basic_operation "sqrt parameter < 0.")
 440         |Vec vec -> Vec (new vector vec#size (fun_unary basic_sqrt vec#nth))
 441         |Zero -> R (sqrt 0.)
 442         |Error -> Error;;
 443
 444
 445 let rec basic_mod : basic -> basic -> basic =
 446   fun b1 ->
 447     fun b2 ->
 448       match (b1, b2) with
 449       | (N i1, N i2) -> N (i1 mod i2)
 450       | (_, R f2) ->
 451           raise (Basic_operation "b1 mod b2: b2 cannot be float.")
 452       | (R f1, _) ->
 453           raise (Basic_operation "b1 mod b2: b1 cannot be float.")
 454       | (N i1, Vec vec2) ->
 455           raise (Basic_operation "Scalar_Vector: sca mod vec.")
 456       | (_, Zero) ->
 457           raise (Basic_operation "b1 mod b2: b2 cannot be zero.")
 458       | (N i1, Error) -> Error
 459       | (Vec vec1, Vec vec2) ->
 460           if vec1#size = vec2#size then
 461             Vec (new vector vec1#size
 462                    (fun_binary basic_mod vec1#nth vec2#nth))
 463           else raise (Basic_operation "vector size not matched.")
 464       | (Vec vec1, _) ->
 465           raise (Basic_operation "Vector_Scalar: vec mod sca.")
 466       | (Zero, Vec vec2) ->
 467           basic_mod (Vec (new vector vec2#size (fun i -> Zero))) b2
 468       | (Zero, _) -> basic_mod (N 0) b2
 469       | (Error, Vec vec2) ->
 470           raise (Basic_operation "Scalar_Vector: sca mod vec.")
 471       | (Error, _) -> Error;;
 472
 473 let rec basic_fmod : basic -> basic -> basic =
 474   fun b1 ->
 475     fun b2 ->
 476       match (b1, b2) with
 477       | (R f1, R f2) -> R (mod_float f1 f2)
 478       | (_, N i2) ->
 479           raise (Basic_operation "b1 fmod b2: b2 cannot be int.")
 480       | (N i1, _) ->
 481           raise (Basic_operation "b1 fmod b2: b1 cannot be int.")
 482       | (R f1, Vec vec2) ->
 483           raise (Basic_operation "Scalar_Vector: sca fmod vec.")
 484       | (_, Zero) ->
 485           raise (Basic_operation "b1 fmod b2: b2 cannot be zero.")
 486       | (R f1, Error) -> Error
 487       | (Vec vec1, Vec vec2) ->
 488           if vec1#size = vec2#size then
 489             Vec (new vector vec1#size
 490                    (fun_binary basic_fmod vec1#nth vec2#nth))
 491           else raise (Basic_operation "vector size not matched.")
 492       | (Vec vec1, _) ->
 493           raise (Basic_operation "Vector_Scalaire: vec fmod sca.")
 494       | (Zero, Vec vec2) ->
 495           basic_fmod (Vec (new vector vec2#size (fun i -> Zero))) b2
 496       | (Zero, _) -> basic_mod (N 0) b2
 497       | (Error, Vec vec2) ->
 498           raise (Basic_operation "Scalaire_Vector: int mod vec.")
 499       | (Error, _) -> Error;;
 500
 501
 502 let rec basic_larger_than_zero : basic -> basic =
 503   fun v ->
 504     match v with
 505     |N i -> if i > 0 then N 1 else N 0
 506     |R f -> if f > 0. then N 1 else N 0
 507     |Vec vec ->
 508         Vec (new vector vec#size
 509                (fun_unary basic_larger_than_zero vec#nth ))
 510     |Zero -> N 0
 511     |Error -> Error;;
 512
 513
 514 let basic_larger : basic -> basic -> basic =
 515   fun b1 ->
 516     fun b2 ->
 517       basic_larger_than_zero (b1 -~ b2);;
 518
 519
 520 let basic_smaller : basic -> basic -> basic =
 521   fun b1 ->
 522     fun b2 ->
 523       basic_larger_than_zero (b2 -~ b1);;
 524
 525
 526 let basic_max : basic -> basic -> basic =
 527   fun b1 ->
 528     fun b2 ->
 529       let compare = basic_larger_than_zero (b1 -~ b2) in
 530       match compare with
 531       | N i ->
 532           if i = 1 then b1
 533           else if i = 0 then b2
 534           else raise (Basic_operation "compare result not bool.")
 535       | Vec vec ->
 536           let basics = Array.init vec#size vec#nth in
 537           let sum = basic_to_int (Array.fold_left basic_add Zero basics) in
 538           if sum = vec#size then b1
 539           else if sum = 0 then b2
 540           else Error
 541       | Error -> Error
 542       | _ -> raise (Basic_operation "compare result not bool.");;
 543
 544
 545 let basic_min : basic -> basic -> basic =
 546   fun b1 ->
 547     fun b2 ->
 548       let compare = basic_larger_than_zero (b1 -~ b2) in
 549       match compare with
 550       | N i ->
 551           if i = 1 then b2
 552           else if i = 0 then b1
 553           else raise (Basic_operation "compare result not bool.")
 554       | Vec vec ->
 555           let basics = Array.init vec#size vec#nth in
 556           let sum = basic_to_int (Array.fold_left basic_add Zero basics) in
 557           if sum = vec#size then b2
 558           else if sum = 0 then b1
 559           else Error
 560       | Error -> Error
 561       | _ -> raise (Basic_operation "compare result not bool.");;