interpretor/preprocessor/faust-0.9.47mr3/compiler/headers/sigtype.hh

   1 /************************************************************************
   2  ************************************************************************
   3     FAUST compiler
   4         Copyright (C) 2003-2004 GRAME, Centre National de Creation Musicale
   5     ---------------------------------------------------------------------
   6     This program is free software; you can redistribute it and/or modify
   7     it under the terms of the GNU General Public License as published by
   8     the Free Software Foundation; either version 2 of the License, or
   9     (at your option) any later version.
  10
  11     This program is distributed in the hope that it will be useful,
  12     but WITHOUT ANY WARRANTY; without even the implied warranty of
  13     MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
  14     GNU General Public License for more details.
  15
  16     You should have received a copy of the GNU General Public License
  17     along with this program; if not, write to the Free Software
  18     Foundation, Inc., 675 Mass Ave, Cambridge, MA 02139, USA.
  19  ************************************************************************
  20  ************************************************************************/
  21
  22
  23
  24 #ifndef _SigType_
  25 #define _SigType_
  26
  27 #include <vector>
  28 #include <string>
  29 #include <iostream>
  30 #include "tree.hh"
  31 #include "smartpointer.hh"
  32 #include "interval.hh"
  33
  34
  35 /*********************************************************************
  36 *
  37 *                                               Type System for FAUST
  38 *
  39 *       <type>                  ::= <simpletype> ||  table(<type>)
  40 *                                               ||  <type>|<type>  || <type>*<type>
  41 *       <simpletype>    ::= <nature><variability><computability><vectorability>||<boolean>
  42 *       <nature>                ::= TINT || TREAL
  43 *       <variability>   ::= TKONST || TBLOCK || TSAMP
  44 *       <computability> ::= TCOMP  || TINIT  || TEXEC
  45 *       <vectorability> ::= KVECT  || KSCAL  || KTRUESCAL
  46 *       <boolean>       ::= KNUM   || KBOOL
  47 *
  48 **********************************************************************/
  49
  50
  51 //--------------------------------------------------
  52 // qualite des types simples
  53
  54 enum { kInt = 0, kReal = 1 };                           ///< nature : integer or floating point values
  55 enum { kNum = 0 , kBool = 1};                           ///< boolean : when a signal stands for a boolean value ( while being of c-type int or float )
  56 enum { kKonst = 0, kBlock = 1, kSamp = 3 };             ///< variability : how fast values change
  57 enum { kComp = 0, kInit = 1, kExec = 3 };               ///< computability : when values are available
  58 enum { kVect = 0, kScal = 1, kTrueScal = 3/*, kIndex = 4*/};///< vectorability: when a signal can be vectorized ( actually, only kVect and kScal matter; kTrueScal and kIndex don't denote types but are here to simplify code generation )
  59
  60 /*---------------------------------------------------------------------
  61
  62         AbstractType :
  63         The root class for SimpleType, TableType and TupletType
  64
  65         Type :
  66         A smartPointer to type
  67
  68 ----------------------------------------------------------------------*/
  69
  70 using namespace std;
  71
  72 class AudioType;
  73
  74 typedef P<AudioType> Type;
  75
  76 /**
  77  * The Root class for all audio data types.
  78  * All audio types have a "variability" (how fast the values change) and
  79  * a "computability" (when the values are available). Simple types have
  80  * also a "nature" (integer or floating point).
  81  */
  82 class AudioType
  83 {
  84   public:
  85     static int  gAllocationCount;
  86   protected:
  87         int             fNature;                        ///< the kind of data represented
  88         int             fVariability;           ///< how fast values change
  89         int             fComputability;         ///< when are values available
  90     int                 fVectorability;     ///< when a signal can be vectorized
  91     int                 fBoolean;           ///< when a signal stands for a boolean value
  92
  93     interval    fInterval;                      ///< Minimal and maximal values the signal can take
  94     Tree        fCode;              ///< Tree representation (for memoization purposes)
  95
  96
  97   public :
  98     AudioType(int n, int v, int c, int vec = kVect, int b = kNum, interval i=interval())
  99                   : fNature(n), fVariability(v), fComputability(c),
 100                     fVectorability(vec), fBoolean(b),
 101             fInterval(i), fCode(0) {}                           ///< constructs an abstract audio type
 102
 103         virtual ~AudioType()                                                                    {}      ///< not really useful here, but make compiler happier
 104
 105         int     nature()                const   { return fNature;               }       ///< returns the kind of values (integre or floating point)
 106         int     variability()   const   { return fVariability; }        ///< returns how fast values change (constant, by blocks, by samples)
 107         int     computability() const   { return fComputability;}       ///< returns when values are available (compilation, initialisation, execution)
 108         int     vectorability() const   { return fVectorability;}       ///< returns when a signal can be vectorized
 109         int     boolean()               const   { return fBoolean; }            ///< returns when a signal stands for a boolean value
 110
 111     interval getInterval()      const   { return fInterval; }           ///< returns the interval (min dn max values) of a signal
 112
 113     void    setCode(Tree code)      { fCode = code; }           ///< returns the interval (min dn max values) of a signal
 114     Tree    getCode()               { return fCode; }           ///< returns the interval (min dn max values) of a signal
 115
 116
 117
 118         virtual AudioType* promoteNature(int n)         = 0;                    ///< promote the nature of a type
 119     virtual AudioType* promoteVariability(int n)        = 0;            ///< promote the variability of a type
 120     virtual AudioType* promoteComputability(int n)      = 0;            ///< promote the computability of a type
 121     virtual AudioType* promoteVectorability(int n)      = 0;            ///< promote the vectorability of a type
 122         virtual AudioType* promoteBoolean(int n)        = 0;                    ///< promote the booleanity of a type
 123         //virtual AudioType* promoteInterval(const interval& i) = 0;            ///< promote the interval of a type
 124
 125
 126     virtual ostream& print(ostream& dst) const          = 0;            ///< print nicely a type
 127     virtual bool    isMaximal() const               = 0;        ///< true when type is maximal (and therefore can't change depending of hypothesis)
 128
 129     virtual AudioType* dimensions(vector<int>& D)   = 0;        /// Fill D with the dimensions of the type and returns its base type
 130
 131   protected:
 132         void            setInterval(const interval& r)  { fInterval = r;}
 133
 134 };
 135
 136 //printing
 137 inline ostream& operator << (ostream& s, const AudioType& n) { return n.print(s); }
 138
 139
 140 /**
 141  * Return the nature of a vector of types.
 142  */
 143 inline int mergenature(const vector<Type>& v)
 144 {
 145         int r = 0;
 146         for (unsigned int i = 0; i < v.size(); i++) r |= v[i]->nature();
 147         return r;
 148 }
 149
 150
 151
 152 /**
 153  * Return the variability of a vector of types.
 154  */
 155 inline int mergevariability(const vector<Type>& v)
 156 {
 157         int r = 0;
 158         for (unsigned int i = 0; i < v.size(); i++) r |= v[i]->variability();
 159         return r;
 160 }
 161
 162
 163
 164 /**
 165  * Return the computability of a vector of types.
 166  */
 167 inline int mergecomputability(const vector<Type>& v)
 168 {
 169         int r = 0;
 170         for (unsigned int i = 0; i < v.size(); i++) r |= v[i]->computability();
 171         return r;
 172 }
 173
 174
 175
 176 /**
 177  * Return the vectorability of a vector of types.
 178  */
 179 inline int mergevectorability(const vector<Type>& v)
 180 {
 181         int r = 0;
 182         for (unsigned int i = 0; i < v.size(); i++) r |= v[i]->vectorability();
 183         return r;
 184 }
 185
 186
 187
 188 /**
 189  * Return the booleanity of a vector of types.
 190  */
 191 inline int mergeboolean(const vector<Type>& v)
 192 {
 193     int r = 0;
 194     for (unsigned int i = 0; i < v.size(); i++) r |= v[i]->boolean();
 195     return r;
 196 }
 197
 198
 199
 200 /**
 201  * Return the interval of a vector of types.
 202  */
 203 inline interval mergeinterval(const vector<Type>& v)
 204 {
 205         if (v.size()==0) {
 206                 return interval();
 207         } else {
 208                 double lo=0, hi=0;
 209                 for (unsigned int i = 0; i < v.size(); i++) {
 210                         interval r = v[i]->getInterval();
 211                         if (!r.valid) return r;
 212                         if (i==0) {
 213                                 lo = r.lo;
 214                                 hi = r.hi;
 215                         } else {
 216                                 lo = min(lo,r.lo);
 217                                 hi = max(hi,r.hi);
 218                         }
 219                 }
 220                 return interval(lo, hi);
 221         }
 222 }
 223
 224
 225 AudioType* makeSimpleType(int n, int v, int c, int vec, int b, const interval& i);
 226
 227 AudioType* makeTableType(const Type& ct);
 228 AudioType* makeTableType(const Type& ct, int n, int v, int c, int vec);
 229 AudioType* makeTableType(const Type& ct, int n, int v, int c, int vec, int b, const interval& i);
 230
 231
 232 AudioType* makeTupletType(const vector<Type>& vt);
 233 AudioType* makeTupletType(const vector<Type>& vt, int n, int v, int c, int vec, int b, const interval& i);
 234
 235 /**
 236  * The type of a simple numeric audio signal.
 237  * Beside a computability and a variability, SimpleTypes have
 238  * a "nature" indicating if they represent an integer or floating
 239  * point audio signals.
 240  */
 241 class SimpleType : public AudioType
 242 {
 243   public :
 244
 245         SimpleType(int n, int v, int c, int vec, int b, const interval& i) : AudioType(n,v,c,vec,b,i) {
 246                 //cerr << "new simple type " << i << " -> " << *this << endl;
 247         }                       ///< constructs a SimpleType from a nature a variability and a computability
 248
 249         virtual ostream& print(ostream& dst) const;                                             ///< print a SimpleType
 250
 251
 252
 253     virtual AudioType* promoteNature(int n)                             { return makeSimpleType(n|fNature, fVariability, fComputability, fVectorability, fBoolean, fInterval); }                ///< promote the nature of a type
 254     virtual AudioType* promoteVariability(int v)                        { return makeSimpleType(fNature, v|fVariability, fComputability, fVectorability, fBoolean, fInterval); }                ///< promote the variability of a type
 255     virtual AudioType* promoteComputability(int c)                      { return makeSimpleType(fNature, fVariability, c|fComputability, fVectorability, fBoolean, fInterval); }                ///< promote the computability of a type
 256     virtual AudioType* promoteVectorability(int vec)            { return makeSimpleType(fNature, fVariability, fComputability, vec|fVectorability, fBoolean, fInterval); }      ///< promote the vectorability of a type
 257     virtual AudioType* promoteBoolean(int b)                    { return makeSimpleType(fNature, fVariability, fComputability, fVectorability, b|fBoolean, fInterval); }                ///< promote the booleanity of a type
 258 //      virtual AudioType* promoteInterval(const interval& i)   {
 259 //              cerr << "promote to Interval " << i  << endl;
 260 //              cerr << "for type : " << *this << endl;
 261 //              Type t = makeSimpleType(fNature, fVariability, fComputability, fVectorability, fBoolean, i);                            ///< promote the interval of a type
 262 //              cerr << "gives type " << *t << endl;
 263 //              return t;
 264 //      }
 265     virtual AudioType* dimensions(vector<int>& D)       { D.clear(); return this; } // scalar have no dimensions
 266
 267     virtual bool    isMaximal() const;                              ///< true when type is maximal (and therefore can't change depending of hypothesis)
 268
 269
 270
 271 };
 272
 273 inline Type intCast (Type t)    { return makeSimpleType(kInt, t->variability(), t->computability(), t->vectorability(), t->boolean(), t->getInterval()); }
 274 inline Type floatCast (Type t)  { return makeSimpleType(kReal, t->variability(), t->computability(), t->vectorability(), t->boolean(), t->getInterval()); }
 275 inline Type sampCast (Type t)   { return makeSimpleType(t->nature(), kSamp, t->computability(), t->vectorability(), t->boolean(), t->getInterval()); }
 276 inline Type boolCast (Type t)   { return makeSimpleType(t->nature(), t->variability(), t->computability(), t->vectorability(), kBool, t->getInterval()); }
 277 inline Type numCast (Type t)    { return makeSimpleType(t->nature(), t->variability(), t->computability(), t->vectorability(), kNum, t->getInterval()); }
 278 inline Type vecCast (Type t)    { return makeSimpleType(t->nature(), t->variability(), t->computability(), kVect, t->boolean(), t->getInterval()); }
 279 inline Type scalCast (Type t)   { return makeSimpleType(t->nature(), t->variability(), t->computability(), kScal, t->boolean(), t->getInterval()); }
 280 inline Type truescalCast (Type t){ return makeSimpleType(t->nature(), t->variability(), t->computability(), kTrueScal, t->boolean(), t->getInterval()); }
 281
 282 inline Type castInterval (Type t, const interval& i)
 283 {
 284     return makeSimpleType(t->nature(), t->variability(), t->computability(), t->vectorability(), t->boolean(), i);
 285 }
 286
 287 /**
 288  * The type of a table of audio data.
 289  * Beside a computability and a variability, TableTypes have
 290  * a "content" indicating the type of the data stored in the table.
 291  */
 292 class TableType : public AudioType
 293 {
 294   protected :
 295         const Type fContent;                                                                                    ///< type of that data stored in the table
 296
 297   public :
 298         TableType(const Type& t) :
 299                   AudioType(t->nature(), t->variability(), t->computability(), t->vectorability(), t->boolean()),
 300                   fContent(t) {}                ///< construct a TableType with a content of a type t
 301 #if 0
 302         TableType(const Type& t, int v, int c) :
 303                   AudioType(t->nature(), t->variability()|v, t->computability()|c, t->vectorability(), t->boolean()),
 304                   fContent(t) {}                ///< construct a TableType with a content of a type t, promoting variability and computability
 305
 306         TableType(const Type& t, int n, int v, int c) :
 307                   AudioType(t->nature()|n, t->variability()|v, t->computability()|c, t->vectorability(), t->boolean()),
 308                   fContent(t) {}                ///< construct a TableType with a content of a type t, promoting nature, variability and computability
 309
 310         TableType(const Type& t, int n, int v, int c, int vec, int b) :
 311                   AudioType(t->nature()|n, t->variability()|v, t->computability()|c, t->vectorability()|vec, t->boolean()|b),
 312                   fContent(t) {}                ///< construct a TableType with a content of a type t, promoting nature, variability, computability, vectorability and booleanity
 313 #endif
 314
 315     TableType(const Type& t, int n, int v, int c, int vec, int b, const interval& i) :
 316           AudioType(t->nature()|n, t->variability()|v, t->computability()|c, t->vectorability()|vec, t->boolean()|b, i),
 317           fContent(t) {}                ///< construct a TableType with a content of a type t, promoting nature, variability, computability, vectorability and booleanity
 318
 319     TableType(const Type& t, int n, int v, int c, int vec) :
 320           AudioType(t->nature()|n, t->variability()|v, t->computability()|c, t->vectorability()|vec, t->boolean()),
 321           fContent(t) {}                ///< construct a TableType with a content of a type t, promoting nature, variability, computability and vectorability
 322
 323
 324         Type content() const                            { return fContent;      }               ///< return the type of data store in the table
 325         virtual ostream& print(ostream& dst) const;                                             ///< print a TableType
 326
 327     virtual AudioType* promoteNature(int n)                 { return makeTableType(fContent, n|fNature, fVariability, fComputability, fVectorability, fBoolean, fInterval); }   ///< promote the nature of a type
 328     virtual AudioType* promoteVariability(int v)                        { return makeTableType(fContent, fNature, v|fVariability, fComputability, fVectorability, fBoolean, fInterval); }       ///< promote the variability of a type
 329     virtual AudioType* promoteComputability(int c)                      { return makeTableType(fContent, fNature, fVariability, c|fComputability, fVectorability, fBoolean, fInterval); }       ///< promote the computability of a type
 330     virtual AudioType* promoteVectorability(int vec)            { return makeTableType(fContent, fNature, fVariability, fComputability, vec|fVectorability, fBoolean, fInterval);}///< promote the vectorability of a type
 331     virtual AudioType* promoteBoolean(int b)                    { return makeTableType(fContent, fNature, fVariability, fComputability, fVectorability, b|fBoolean, fInterval); }       ///< promote the booleanity of a type
 332     //virtual AudioType* promoteInterval(const interval& i)     { return makeTableType(fContent, fNature, fVariability, fComputability, fVectorability, fBoolean, i); }                 ///< promote the interval of a type
 333
 334     virtual bool    isMaximal() const;                              ///< true when type is maximal (and therefore can't change depending of hypothesis)
 335
 336     virtual AudioType* dimensions(vector<int>& D)       { D.clear(); return this; } // tables have no dimensions
 337
 338 };
 339
 340
 341
 342 /**
 343  * The type of a tuplet of data.
 344  * Beside a computability and a variability, TupletTypes have
 345  * a set of components.
 346  */
 347 class TupletType : public AudioType
 348 {
 349   protected:
 350         vector<Type> fComponents;
 351
 352   public:
 353     TupletType() :
 354           AudioType(0,0,0)
 355           {}
 356
 357     TupletType(const vector<Type>& vt) :
 358           AudioType(mergenature(vt),mergevariability(vt),mergecomputability(vt),mergevectorability(vt),mergeboolean(vt), mergeinterval(vt)),
 359           fComponents(vt) {}
 360
 361         TupletType(const vector<Type>& vt, int n, int v, int c, int vec, int b, const interval& i) :
 362                   AudioType(n|mergenature(vt), v|mergevariability(vt), c|mergecomputability(vt), vec|mergevectorability(vt), b|mergeboolean(vt), i),
 363                   fComponents(vt) {}
 364
 365         int arity()     const                                           { return fComponents.size(); }
 366         Type operator[](unsigned int i) const   { return fComponents[i]; }
 367         virtual ostream& print(ostream& dst) const;
 368
 369         virtual AudioType* promoteNature(int n)                         { return new TupletType(fComponents, n|fNature, fVariability, fComputability, fVectorability, fBoolean, fInterval); }   ///< promote the nature of a type
 370         virtual AudioType* promoteVariability(int v)                    { return new TupletType(fComponents, fNature, v|fVariability, fComputability, fVectorability, fBoolean, fInterval); }   ///< promote the variability of a type
 371         virtual AudioType* promoteComputability(int c)                  { return new TupletType(fComponents, fNature, fVariability, c|fComputability, fVectorability, fBoolean, fInterval); }   ///< promote the computability of a type
 372         virtual AudioType* promoteVectorability(int vec)                { return new TupletType(fComponents, fNature, fVariability, fComputability, vec|fVectorability, fBoolean, fInterval);}  ///< promote the vectorability of a type
 373         virtual AudioType* promoteBoolean(int b)                        { return new TupletType(fComponents, fNature, fVariability, fComputability, fVectorability, b|fBoolean, fInterval);  }  ///< promote the booleanity of a type
 374         //virtual AudioType* promoteInterval(const interval& i) { return new TupletType(fComponents, fNature, fVariability, fComputability, fVectorability, fBoolean, i);  }                    ///< promote the interval of a type
 375
 376     virtual bool    isMaximal() const;                              ///< true when type is maximal (and therefore can't change depending of hypothesis)
 377     virtual AudioType* dimensions(vector<int>& D)       { D.clear(); return this; } // tuples have no dimensions
 378
 379 };
 380
 381
 382
 383 /**
 384  * The type T = vector(n, T') of a signal of vectors of fixed size n and elements of type T'
 385  * The following properties hold :
 386  *     nature(vector(n,T')) = nature(T')
 387  *     variability(vector(n,T')) = variability(T')
 388  *     computability(vector(n,T')) = computability(T')
 389  *     vectorability(vector(n,T')) = ???                    (so probably no)
 390  *     boolean(vector(n,T')) = false                        (a vector is not a boolean)
 391  *     getInterval(vector(n,T')) = getInterval(T')          (is it meanuful ?)
 392  */
 393 class VectorType : public AudioType
 394 {
 395   protected:
 396     int         fSize;          ///< size of the vector
 397     Type        fContent;       ///< type of the elements
 398
 399   public:
 400     VectorType(int n, const Type& t) : AudioType(t->nature(), t->variability(), t->computability(), t->vectorability(),
 401                                                  t->boolean(), t->getInterval()),
 402                                        fSize(n),
 403                                        fContent(t)
 404           {}
 405
 406
 407     int size() const                { return fSize; }
 408     Type content() const            { return fContent; }
 409
 410     virtual ostream& print(ostream& dst) const;
 411
 412     virtual AudioType* promoteNature(int n)             { return new VectorType(fSize, fContent->promoteNature(n)); }               ///< promote the nature of a type
 413     virtual AudioType* promoteVariability(int v)                { return new VectorType(fSize, fContent->promoteVariability(v)); }          ///< promote the variability of a type
 414     virtual AudioType* promoteComputability(int c)              { return new VectorType(fSize, fContent->promoteComputability(c)); }        ///< promote the computability of a type
 415     virtual AudioType* promoteVectorability(int vec)    { return new VectorType(fSize, fContent->promoteVectorability(vec)); }      ///< promote the vectorability of a type
 416     virtual AudioType* promoteBoolean(int b)            { return new VectorType(fSize, fContent->promoteBoolean(b)); }              ///< promote the booleanity of a type
 417     virtual bool    isMaximal() const                   { return false; }           ///< true when type is maximal (and therefore can't change depending of hypothesis)
 418     virtual AudioType* dimensions(vector<int>& D)       { AudioType* t = fContent->dimensions(D); D.push_back(fSize); return t;}    ///< vectors have a dimension
 419
 420
 421 };
 422
 423 Type   makeVectorType(const Type& b, const vector<int>& dim);
 424 bool   maxdimensions(const vector<int>& D1, const vector<int>& D2, vector<int>& D3);
 425
 426
 427
 428
 429 //-------------------------------------------------
 430 //-------------------------------------------------
 431 //                              operations sur les types
 432 //-------------------------------------------------
 433 //-------------------------------------------------
 434
 435
 436
 437 //--------------------------------------------------
 438 // liste de types predefinis
 439
 440 extern Type TINT;
 441 extern Type TREAL;
 442
 443 extern Type TKONST;
 444 extern Type TBLOCK;
 445 extern Type TSAMP;
 446
 447 extern Type TCOMP;
 448 extern Type TINIT;
 449 extern Type TEXEC;
 450
 451 extern Type TINPUT;
 452 extern Type TGUI;
 453 extern Type TGUI01;
 454 extern Type INT_TGUI;
 455 extern Type TREC;
 456
 457
 458 //--------------------------------------------------
 459 // creation de types
 460
 461 Type table      (const Type& t);
 462 Type operator|  (const Type& t1, const Type& t2);
 463 Type operator*  (const Type& t1, const Type& t2);
 464
 465
 466 //--------------------------------------------------
 467 // comparaison de types
 468
 469 bool operator==(const Type& t1, const Type& t2);
 470 bool operator<=(const Type& t1, const Type& t2);
 471
 472 inline bool operator!=(const Type& t1, const Type& t2) { return !(t1==t2); }
 473 inline bool operator< (const Type& t1, const Type& t2) { return t1<=t2 && t1!=t2; }
 474 inline bool operator> (const Type& t1, const Type& t2) { return t2<t1;  }
 475 inline bool operator>=(const Type& t1, const Type& t2) { return t2<=t1; }
 476
 477
 478 //--------------------------------------------------
 479 // predicats-conversion de types
 480
 481 SimpleType*     isSimpleType (AudioType* t);
 482 TableType*              isTableType  (AudioType* t);
 483 TupletType*     isTupletType (AudioType* t);
 484 VectorType*     isVectorType (AudioType* t);
 485
 486
 487 //--------------------------------------------------
 488 // impressions de types
 489
 490 ostream& operator<<(ostream& dst, const SimpleType& t);
 491 ostream& operator<<(ostream& dst, const Type& t);
 492 ostream& operator<<(ostream& dst, const TableType& t);
 493 ostream& operator<<(ostream& dst, const TupletType& t);
 494 ostream& operator<<(ostream& dst, const VectorType& t);
 495
 496
 497 //--------------------------------------------------
 498 // verification de type
 499
 500 Type checkInt(Type t);                          ///< verifie que t est entier
 501 Type checkKonst(Type t);                        ///< verifie que t est constant
 502 Type checkInit(Type t);                         ///< verifie que t est connu a l'initialisation
 503
 504 Type checkIntParam(Type t);                     ///< verifie que t est connu a l'initialisation, constant et entier
 505
 506 Type checkWRTbl(Type tbl, Type wr);     ///< verifie que wr est compatible avec le contenu de tbl
 507
 508 int checkDelayInterval(Type t);         ///< Check if the interval of t is appropriate for a delay
 509
 510
 511 //--------------------------------------------------
 512 // conversion de type
 513
 514 string cType (Type t);
 515
 516 Tree codeAudioType(AudioType* t);   ///< Code an audio type as a tree (memoization)
 517
 518
 519 #endif