thomas.forbriger committed Dec 06, 2002 1 /*! \file README thomas.forbriger committed Dec 06, 2002 2 * \brief C++ containers for numbers (libaff) thomas.forbriger committed Dec 06, 2002 3 4 5 * * ---------------------------------------------------------------------------- * thomas.forbriger committed Dec 06, 2002 6 * $Id: README,v 1.2 2002-12-06 19:21:01 forbrig Exp$ thomas.forbriger committed Dec 06, 2002 7 8 9 * * Copyright (c) 2002 by Thomas Forbriger (IMG Frankfurt) * thomas.forbriger committed Dec 06, 2002 10 * C++ containers for numbers (libaff) thomas.forbriger committed Dec 06, 2002 11 12 * * This file contains: thomas.forbriger committed Dec 06, 2002 13 * - documentation of namespace aff thomas.forbriger committed Dec 06, 2002 14 15 16 17 18 19 20 21 * - mainpage text * - documentation for pages: * - \ref page_naming * - \ref page_general * - \ref page_using * - \ref page_notes * * REVISIONS and CHANGES thomas.forbriger committed Dec 06, 2002 22 * - 06/12/2002 V1.0 Thomas Forbriger (copied from libcontxx) thomas.forbriger committed Dec 06, 2002 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 * * ============================================================================ */ /*! \brief Root namespace of library This namespace contains all modules of the library (see \ref sec_main_modules). While contxx::Array is the only compound in this namespace, all others are placed in sub namespaces. When working with the binary version of the library, you have to use contxx::prebuilt in place of contxx (see \ref sec_main_binary). */ namespace contxx { } // namespace contxx /*======================================================================*/ /*! \mainpage \author Thomas Forbriger thomas.forbriger committed Dec 06, 2002 44 45 46 \author Wolfgang Friederich \since December 2002 \date December 2002 thomas.forbriger committed Dec 06, 2002 47 \version V1.0 thomas.forbriger committed Dec 06, 2002 48 $Id: README,v 1.2 2002-12-06 19:21:01 forbrig Exp$ thomas.forbriger committed Dec 06, 2002 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196 197 198 199 200 201 202 203 204 205 206 207 208 209 210 211 212 213 214 215 216 217 218 219 220 221 222 223 224 225 226 227 228 229 230 231 232 233 234 235 236 237 238 239 240 241 242 243 244 245 246 247 248 249 250 251 252 253 254 255 256 257 258 259 260 261 262 263 264 265 266 267 268 269 270 271 272 273 274 275 276 277 278 279 280 281 282 283 284 285 286 287 288 289 290 291 292 293 294 295 296 297 298 299 300 301 302 303 304 305 306 307 308 309 310 311 312 313 314 315 316 317 318 319 320 321 322 323 324 325 326 327 328 329 330 331 332 333 334 335 336 337 338 339 340 341 342 343 344 345 346 347 348 349 350 351 352 353 354 355 356 357 358 359 360 361 362 363 364 365 366 367 368 369 370 371 372 373 374 375 376 377 378 379 380 381 382 383 384 385 386 387 388 389 390 391 392 393 394 395 396 397 398 399 400 401 402 403 404 405 406 407 408 409 410 411 412 413 414 415 416 417 418 419 420 421 422 423 424 425 426 427 428 429 430 431 432 433 434 435 436 437 438 439 440 441 442 443 444 445 446 447 448 449 450 451 452 453 454 455 456 457 458 459 460 461 462 463 464 465 466 467 468 469 470 471 472 473 474 475 476 477 478 479 480 481 482 483 484 485 486 487 488 489 490 491 492 493 494 495 496 497 498 499 500 501 502 503 504 505 506 507 508 509 510 511 512 513 514 515 516 517 518 519 520 521 522 523 524 525 526 527 528 529 530 531 532 533 534 535 536 537 538 539 540 541 542 543 544 545 546 547 548 549 550 551 552 553 554 555 556 557 558 559 560 561 562 563 564 565 566 567 568 569 570 571 572 573 574 575 576 577 578 579 580 581 582 583 584 585 586 587 588 589 590 591 592 593 594 595 596 597 598 599 600 601 602 603 604 605 606 607 608 609 610 611 612 613 614 615 616 617 618 619 620 621 622 623 624 625 626 627 628 629 630 631 632 633 634 635 636 637 638 639 640 641 642 643 644 645 646 647 648 649 650 651 652 653 654 655 656 657 658 659 660 661 662 663 664 665 666 667 668 669 670 671 672 673 674 675 \section main_aims Aims of the library One major reason for replacing Fortran77 by C++ in numerical code is the convenience in expressing logistics. Data of different type and size may be packed into classes and encapsulated from the outside world. Most numerical results are to be stored in arrays, multi-dimensional arrays in particular. This library provides the basic functionality for storing many data of the same type in memory, passing them around between subroutines in an efficient way and accessing them through convenient interfaces. The main purpose of this library is not calculation but managing (passing between program modules, selection of subsets of the data) large amounts of numbers. In the future it might provide interfaces to libraries like blitz++ for finite difference calculations, MTL for linear algebra calculations, and POOMA for parallel computations. Contents of this page: - \ref sec_main_modules - \ref sec_main_modules_array - \ref sec_main_modules_subscriptor - \ref sec_main_modules_shape - \ref sec_main_modules_representation - \ref sec_main_modules_shaper - \ref sec_main_modules_iterator - \ref sec_main_helpers - \ref sec_main_helpers_tuple - \ref sec_main_helpers_types - \ref sec_main_helpers_range - \ref sec_main_helpers_other - \ref sec_main_namespaces - \ref sec_main_constness - \ref sec_main_binary Additional information: - \ref page_using - \ref sec_using_constructor - \ref sec_using_include - \ref page_representation - \ref sec_representation_types - \ref sec_representation_const - \ref page_shapes_and_subscriptors - \ref page_naming - \ref sec_nameing_identifiers - \ref sec_nameing_files - \ref page_general - \ref sec_arrays_decisions - \ref sec_arrays_represented - \ref sec_arrays_interfaced - \ref sec_arrays_const - \ref sec_arrays_questions \section sec_main_modules Modules of the library The main container class provided by the library is contxx::Array. It inherits from a Subscriptor class, which again inherits from a Shape and a Representation class (see inheritance diagram for contxx::Array). The roles of these classes are: - contxx::Array: The user interface (see \ref sec_main_modules_array). - Subscriptor: Provides bracket-operator, i.e. multidimensional index operator (see \ref sec_main_modules_subscriptor). - Shape: Defines the storage layout and index ranges (see \ref sec_main_modules_shape). - Representation: Provides the actual storage in memory (see \ref sec_main_modules_representation). \sa \ref page_shapes_and_subscriptors \sa \ref page_representation \todo In the near future the library has to provide projection operator classes to select subsets of the data. \todo A future version of the library has to provide iterators for sequential access. \subsection sec_main_modules_array Module Array The array class inherits from a subscriptor. There is only one array class template (contxx::Array presented in array.h). Its functionality is selected through the template arguments Subscriptor and Representation. The array class template is declared in the main namspace contxx. \subsection sec_main_modules_subscriptor Module Subscriptor Subscriptors are also called "shaped representations". They combine the functionality of representations and shapes on a raw level. They just add multi-dimensional access operators, with multi-index argument lists. They are collected in the namespace contxx::subscriptor. You have to pass a Subscriptor template parameter to contxx::Array. This template parameters selects a Subscriptor and a Shape (since both are closely related) Provided subscriptors are: -# contxx::subscriptor::StridedRepresentation (for contxx::shape::Strided shaped arrays) is presented in shape/strided_repr.h -# contxx::subscriptor::DenseStridedRepresentation (for contxx::shape::DenseStrided shaped arrays) is presented in shape/densestrided_repr.h \sa \ref page_shapes_and_subscriptors \subsection sec_main_modules_shape Shapes Shapes define the index mapping from a multi-dimensional domain to the linear domain of memory storage (as provided through %representations). It also defines index ranges applicable to the array. A Shape class for the array is selected indirectly through the Subscriptor template parameter (see \ref sec_main_modules_subscriptor) contxx::shape::Strided provides the common rectangular array layout. A variant contxx::shape::DenseStrided will provide the %shape of a dense memory layout (with stride(0)=1). All shape classes are collected in the namespace contxx::shape. Provided shapes are: -# contxx::shape::Strided (rectangular layout) presented in shape/strided.h -# contxx::shape::DenseStrided (rectangular but addressing the memory continuously) presented in shape/densestrided.h Additional shapes may be defined for packed array layouts (e.g. for band-matrices, upper triangular matrices, etc.) in future versions of the library. \sa \ref page_shapes_and_subscriptors \subsection sec_main_modules_representation Memory Representations Memory Representations are means to access a block of memory. The %representation classes provide automatic memory allocation control. The Representation is selected through a template parameter passed to contxx::Arrays. The standard %representation is contxx::representation::SharedHeap, which provides reference semantics, i.e. it performs shallow copies. The classes implementing different concepts of memory representations are collected in namespace contxx::representation. Provided representations are: -# contxx::representation::SharedHeap (heap allocation, reference counting and shallow copy) presented in repr/sharedheap.h -# contxx::representation::NormalHeap (heap allocation and deep copy) presented in repr/normalheap.h -# contxx::representation::Global (access to external global data, shallow copies) presented in repr/global.h -# contxx::representation::Rigid (fixed size, stack data, deep copy) presented in repr/rigid.h \sa \ref page_representation \sa \ref sec_representation_types \subsection sec_main_modules_shaper Shapers When constructing an array you have to define its layout. Normally you will not like to deal with index range arrays and internals of the Shape base class. Shapers offer a compact means to define an array's shape. If you want e.g. define an array \c A of ints with Fortran layout, three dimensions and the index ranges [-2:2], [1:4], and [6:10] you have to code \code contxx::Array A(contxx::shaper::Fortran<3>(-2,2)(4)(6,10)); \endcode Shapers are presented in namespace contxx::shaper. Provided shapers are: -# contxx::shaper::Fortran (presented in contxx/shaper/fortran.h \sa \ref Shaper \subsection sec_main_modules_iterator Iterators Iterators provide sequential access to the elements of an array. This is most convenient for copying, input/output operations and scalar operations. Iterators in that way hide the dimensionality of the corresponding array and thus are most useful together with multi-dimensional arrays. /*----------------------------------------------------------------------*/ \section sec_main_helpers Library utilities There exists some code that is not directly part of the main modules, but supports their use. \subsection sec_main_helpers_tuple contxx::shape::tuple You have to pass arguments of type contxx::util::SimpleRigidArray to the constructors of contxx::Array. Use contxx::shape::tuple (collected in contxx::shape and presented in shape/shaper.h) to create them conveniently. \sa \ref sec_general_dimension \sa \ref anchor_simplerigigarray "discussion at SimpleRigidArray" \sa tests/arraytest.cc \subsection sec_main_helpers_types Types Explicit types used within the library base on typedefs presented in util/types.h This allows us to change the type of a subscript index (e.g.) if needed on future architecture. The following typedefs are collected in namespace contxx::util: -# contxx::util::Tdim -# contxx::util::Tsize -# contxx::util::Tsubscript Use the using directive if you want to access them conveniently (see \ref sec_main_namespaces). \subsection sec_main_helpers_range contxx::shape::range The index ranges are handled within the Shape category module by menas of a range class. This class is presented in shape/range.h and may be found in namespace contxx::shape. The range class is in particular usefull to find the smallest index range matching several ranges given or the total index range spanned by some subranges. \subsection sec_main_helpers_other Others -# contxx::util::SimpleRigidArray is a convenient means to pass a small set of values. It is presented in util/simplearray.h and namespace contxx::util -# contxx::util::Inline and its associated functions is a means to conveniently inline operations on raw arrays. It is presented in util/rawarfun.h and namespace contxx::util -# contxx::util::Qualified is a traits-like class needed to provide conversion operators to arrays of const elements. It is presented in util/qualified.h and namespace contxx::util /*----------------------------------------------------------------------*/ \section sec_main_namespaces Namespaces We make excessive use of namespaces. This my seem inconvenient at a first glance. Use statements like \code using namespace contxx::representations; \endcode or \code using contxx::util::SimpleRigidArray; \endcode for convenient access. /*----------------------------------------------------------------------*/ \section sec_main_constness Const correctness Since the standard %representation contxx::representation::SharedHeap has reference semantics, we have to distinguish between the const-ness of the container (its shape, the memory it refers to, etc.) and the contained elements. - const-ness of the container: is achived by declaring the container instance with the qualifier \c const. - const-ness of the elements: is achieved by using a container for an element type with qualifier \c const. Convenient operators for conversion from containers of elements with type \c T to containers of elements with type \c const \c T are provided. \sa \ref sec_representation_const /*----------------------------------------------------------------------*/ \section sec_main_binary Binary library We provide a binary version of the library. It contains a set of prebuilt class objects. Using this version and linking against the binary library libcontxx.a should reducde compilation times in comparison to complete template evaluation. This will become more significant the more code is factored out to separate definition headers. This approach offers no improvement with inlined code (which we use extensively in array access functions). To use the binary version you should include binarry.h in place of array.h You will find all modules in contxx::prebuilt that are in contxx in the full-template version. \sa tests/binarraytest.cc \sa binarray.h */ /*======================================================================*/ /*! \page page_naming Naming conventions \section sec_nameing_identifiers Classes, Typedefs, etc. During coding it is sometimes helpfull to recognize the meaning of an identifier due to some signals in irs name. Therefor the following guidelines are used. The nameing of template parameters is left free for convenience. \par Classes Class names always start with a capital letter. \par Typedefs Typedefs always start with a capital \c T. \par Member data Member data identifiers always start with a capital \c M. \section sec_nameing_files Filenames Files with the extension \c .cc contain only non-template definitions. Files with the extension \c .h may contain prototypes, class declarations or template code. Files ending on \c def.h contain template code definitions that is factored out to be compilable into a binary library for explicit instantiation. */ /*======================================================================*/ /*! \page page_general General notes This page contains some brainstorming collected during the design and construction phase. \section sec_arrays_decisions Design Desicions \subsection sec_general_dimension Template defined dimensionality We make excessive use of template code. This includes that we define the dimensionality of arrays by a template parameter. In most cases this works just fine. However for some of the jobs we have to define different functions for arrays of different dimensionality. Examples are the construction of the arrays, where we want to pass explicit index ranges for each dimension and the index (bracket) operators where we need one index per dimension. The quick-and-dirty approach is to provide constructors and index operators for every dimensionality supported by the library. However this doesn't work for precompiled template code (see \ref sec_main_binary). In the case of explicit instantiation every part of the class definition must be compilable for the given set of template parameters. But the index operator with five arguments will not compile for arrays with three dimensions. I tackle this problem in three different ways: \par 1. The constructors used with classes from the Shaper category A Shaper class offers a very compact notation to create an arrays shape and pass it to the constructor of contxx:Array. \sa \ref Shaper \sa \ref sec_main_modules_shaper \sa contxx::shaper \sa contxx::shaper::Fortran \sa tests/arraytest.cc \par 2. The constructors used with tuple-functions The array constructors take a contxx::util::SimpleRigidArray of appropriate size. For an array with three dimensions we must pass a SimpleRigidArray with three elements. Since the size of SimpleRigidArray is defined by a template parameter it just fits well in the template code. However this just migrates the problem from the contxx::Array constructors to the contxx::util::SimpleRigidArray constructors. The problem is solved finally through a set of helper functions with an overloaded version for each dimensionality. The are called contxx::shape::tuple and are just used to create objects of type contxx::util::SimpleRigidArray. They are a kind of external constructors with an appropriate number of arguments. If you need a SimpleRidigArray initialized with {3,8,2}, just code the construct \code contxx::shape::tuple(int(3),8,2) \endcode This function returns exactly the SimpleRigidArray object you need. See the \ref anchor_simplerigigarray "discussion" in the documentation of contxx::util::SimpleRigidArray \deprecated The approach to construct arrays by means of passing index ranges directly is deprecated. It highly depends on the internal structure of the used Shape. Since there may be future Shape classes to which rectangular index ranges make no sense, we prefer to construct arrays be means of Shaper classes. The contxx::Array constructors that take index-array arguments will be removed in the future! \par 3. Index operators The first approach with SimpleRigidArray is not appropriate for index operators. Index operators are typically used in the innermost loop of code. A bad performance of index operators is a severe penalty for the whole program. The approach with SimpleRigidArray involves the creation of temporary objects. This cannot be tolerated in index access to array elements. \par The approach we use for index operators involves a Subscriptor base class category. Subscriptors are just used to factor out the multidimensional index operators from the other modules. Thus we may provide a specialization for each dimensionality with not too much code overhead. See the discussion \ref page_shapes_and_subscriptors \subsection sec_arrays_represented Represented memory The arrays are implemented as interfaces to represented memory. They are interfaces to a set of different memory representations. This allows us to use the same array class templates for totally different purposes with different needs of memory access and execution efficiency. All arrays guarantee to -# allocate memory only through their specific representation -# perform a shallow (full array) copy (be copy constructor or copy operator) only by copying the representation -# access their elements through their representation Elementwise (deep) copy must be requested if you want to ensure this type of copy. However, there are representations that do a deep copy in any case. Although the element access has always to be done through the representation, this may be implemented fairly efficient by inlined member functions. \subsection sec_arrays_interfaced Concrete and interfaced arrays All standard array interfaces are templates. The element type, the type of memory representation and the subscription type are selected through template parameters. Thus dense onedimensional arrays are of a different type than any other onedimensional memory subscription. Shared heap for integers are of a different type then a stack array of integers, although the same interface and functionality is used for element access. No virtual function are involved in that concept. In some rare cases it may be usefull to have a standard interface class to (say) 1D-arrays. This may be achieved by an abstract base class defining the interface and a set of different implementations that inherit from this base and fill the user-must-define functions. For this the pure templates may be used to implement the functionality. However, this concept involves virtual functions. And since the main job of an array class is element acces, the virtual function call overhead will be present for each element access. This might be not desireable. \subsection sec_arrays_const Constness of arrays \deprecated This discussion of a solution of const correctness is out-dated! Please refer to \ref sec_main_constness and \ref sec_representation_const for a recent approach. The solution discussed below is based on the usual textbook approach which is to define a second class which allows no change of elements. \b The \b library \b chooses \b a \b different \b solution: We simply use the same class definition as for non-const value and define them for a const element type. The classes provide conversion operators from arrays of element type \c T to arrays of element type \c const \c T. This approach is so direct, elegant and easy to implement, that it remains a mystery, why it doesn't appear in textbooks. The array classes and classes derived from them (e.g. series classes) are desingned to implement handle semantics through using tf_generic::TSharedHeap. Their use follows reference semantics. Passing an instance together with a \c const qualifier just means that the array instance itself may not be changed in a function. I.e. it may not be filled with another heap reference or another projection. However a local copy of the heap reference may be created. Thus the array values may be changed by a function that promises const-ness to its arguments. For this reason we provide also \c const versions of the array classes. They provide no mechanism to manipulate array contents or to creat non-const local copies. A declaration \code const ArrayType array; \endcode means: The array instance (the container) is const. I.e. its reference to the heap may not be changed, its projection may not be changed. However, its elements (the contained data) \b may \b be \b changed! A declaration \code ConstArrayType array; \endcode means: The instance is designed to forbid any changes of the array elements (the contained data). Local copies are only allowed to types that forbid array element manipulation too. However, without \c const qualifier an instance (container) of type \c ConstArrayT may be changed. I.e. a new reference to heap or a new projection may be assigned to it. The element access functions declared \c const normally do not allow array element manipulation. Thus also a \c const \c ArrayT follows the typical meaning of const-ness in this regard. However, it may not promise full const-ness, since a local, non-const copy may be created. The latter might be prohobited by the full access array classes, if they do not promise const-ness of the argument of the copy constructor or the copy operator. However, in that case it would not be possible to pass arrays as return values. Why? The return value of a function is an R-value (in case you do not return a reference). It must be used in the sense of a variable declared \c const. Returning from a function involves creating copies. When the compiler allows only for const-ness of the copy argument, it automatically performs a type conversion to the \c ConstArrayType base class. Thus we would always receiver \c ConstArrayType arrays from functions --- which we do not want. \sa tf_array::TDenseShiftedArray1D \subsection sec_arrays_questions Questions and Answers \par Why do we define all these array types ourselves? Standard array packages and libraries also contain various array representations with array projections. But, what we want to implement mainly is a set of arrays and projections with handle semnatics. There is only one heap location where the actual array values are stored. We may have a lot of array projections using this heap area. They do memory control through a handle mechanism. Thus the heap is allocted as long as any of the projections exists. The last projection frees the heap in its destructor. This mechanism \b must be done inside the arrays and projections. It cannot be done with outside handle classes. \par Why don't we use a standard matrix package? There is no real "standard" matrix package up to now. There are several different matrix packages all with different design ideas. Common to all of them is, that they allow array handles only in the sense of array handles. That means, that you allways have a handle that contains an array. This makes the use of them more obscure and complicated. Since the possibility to allow structured access to the same data with shallow copy and projections to subsets of the data, was a main reason to use C++, I decided to start my own array module. Cooperation with existing code (like LAPACK) is always possible, if we also provide appropriate interfaces to the memory that holds the array contents. \par Why don't we use the STL vector valarray classes? The Standard Template Library (STL) offers a rich, powerful and well tested set of containers. However, they are all one-dimensional. So this would have saved us only the work for the 1D-classes. The \c valarray containers offer also multi-dimensional access through slices. But the application of slices is rather complicated. They may not be representated by one object alone. It always needs the arrays together with a slice object. This may be ultimately efficient. But with our applications in mind, efficiency has to take place in the Fortran kernel of the code. Our array design is efficient enough and we emphasize easy-of-use instead. \par Why don't we use the STL allocator concept? The STL allocator concept is similar to our \ref sec_arrays_represented "representation" concept. It is designed to hide the actual task of memory allocation from the implementation of the containers. This may allow implementers to make memory allocation more efficients by providing system dependent allocators. However, the interaction between containers and allocators is rather complicated and was in a state of transition. It is not obvious to me that it could be possible to implement the concept of shared heap through the definition of an appropriate allocator allone. This would afford the containers to copy their content only by using the copy constructor and copy operator of the allocator and to access elements only through member functions of the allocator. \par On the other hand, if there is a very powerful STL allocator available, it is still possible to implement a \ref sec_arrays_represented "memory representation" that uses an STL type allocator to retreive memory an thus may benefit from any high-performance memory management (like pooled memory). However, this is not the main aim of our module. */ /*======================================================================*/ /*! \page page_using HOWTO use this library \section sec_using_constructor Constructing arrays Arrays are most easy constructed by means of a Shaper. If you want e.g. define an array \c A of ints with Fortran layout, three dimensions and the index ranges [-2:2], [1:4], and [6:10] you have to code \code contxx::Array A(contxx::shaper::Fortran<3>(-2,2)(4)(6,10)); \endcode Shapers are presented in namespace contxx::shaper. \sa \ref Shaper \sa \ref sec_main_modules_shaper \sa contxx::shaper \sa contxx::shaper::Fortran \sa tests/arraytest.cc \sa \ref sec_general_dimension \section sec_using_include Including header files The main set of \ref sec_main_modules "array modules" is included by contxx/array.h. This include the full templatized version of the library. We you want to take advantage of the \ref sec_main_binary "precompiled binary library" you have to include contxx/binarray.h. This will set CONTXX_PREBUILT which places all definitions in contxx::prebuilt rather than just namespace contxx. Files like contxx/shaper/fortran.h or contxx/iterator.h are not included automatically by array.h or binarray.h. You have to include them separately. If you are using the precompiled library, you must include them \b after binarray.h so that they will place their declarations in contxx::prebuilt and take the declarations for other parts of the library from that namespace too. \par Mixing the pure template library and the binary version Mixing the pure template library and the binary version might not work with this version of the library. Once you included either array.h or binarray.h the include guards will prevent the precompiler from reading the files again. This problem may be solved in a future version with a more elaborate include guard mechanism that takes account for CONTXX_PREBUILT. */ /*======================================================================*/ /* \page page_notes Programming notes */ // ----- END OF README -----