1=head1 Introduction 2 3C<isl> is a thread-safe C library for manipulating 4sets and relations of integer points bounded by affine constraints. 5The descriptions of the sets and relations may involve 6both parameters and existentially quantified variables. 7All computations are performed in exact integer arithmetic 8using C<GMP> or C<imath>. 9The C<isl> library offers functionality that is similar 10to that offered by the C<Omega> and C<Omega+> libraries, 11but the underlying algorithms are in most cases completely different. 12 13The library is by no means complete and some fairly basic 14functionality is still missing. 15Still, even in its current form, the library has been successfully 16used as a backend polyhedral library for the polyhedral 17scanner C<CLooG> and as part of an equivalence checker of 18static affine programs. 19For bug reports, feature requests and questions, 20visit the discussion group at 21L<http://groups.google.com/group/isl-development>. 22 23=head2 Backward Incompatible Changes 24 25=head3 Changes since isl-0.02 26 27=over 28 29=item * The old printing functions have been deprecated 30and replaced by C<isl_printer> functions, see L<Input and Output>. 31 32=item * Most functions related to dependence analysis have acquired 33an extra C<must> argument. To obtain the old behavior, this argument 34should be given the value 1. See L<Dependence Analysis>. 35 36=back 37 38=head3 Changes since isl-0.03 39 40=over 41 42=item * The function C<isl_pw_qpolynomial_fold_add> has been 43renamed to C<isl_pw_qpolynomial_fold_fold>. 44Similarly, C<isl_union_pw_qpolynomial_fold_add> has been 45renamed to C<isl_union_pw_qpolynomial_fold_fold>. 46 47=back 48 49=head3 Changes since isl-0.04 50 51=over 52 53=item * All header files have been renamed from C<isl_header.h> 54to C<isl/header.h>. 55 56=back 57 58=head3 Changes since isl-0.05 59 60=over 61 62=item * The functions C<isl_printer_print_basic_set> and 63C<isl_printer_print_basic_map> no longer print a newline. 64 65=item * The functions C<isl_flow_get_no_source> 66and C<isl_union_map_compute_flow> now return 67the accesses for which no source could be found instead of 68the iterations where those accesses occur. 69 70=item * The functions C<isl_basic_map_identity> and 71C<isl_map_identity> now take a B<map> space as input. An old call 72C<isl_map_identity(space)> can be rewritten to 73C<isl_map_identity(isl_space_map_from_set(space))>. 74 75=item * The function C<isl_map_power> no longer takes 76a parameter position as input. Instead, the exponent 77is now expressed as the domain of the resulting relation. 78 79=back 80 81=head3 Changes since isl-0.06 82 83=over 84 85=item * The format of C<isl_printer_print_qpolynomial>'s 86C<ISL_FORMAT_ISL> output has changed. 87Use C<ISL_FORMAT_C> to obtain the old output. 88 89=item * The C<*_fast_*> functions have been renamed to C<*_plain_*>. 90Some of the old names have been kept for backward compatibility, 91but they will be removed in the future. 92 93=back 94 95=head3 Changes since isl-0.07 96 97=over 98 99=item * The function C<isl_pw_aff_max> has been renamed to 100C<isl_pw_aff_union_max>. 101Similarly, the function C<isl_pw_aff_add> has been renamed to 102C<isl_pw_aff_union_add>. 103 104=item * The C<isl_dim> type has been renamed to C<isl_space> 105along with the associated functions. 106Some of the old names have been kept for backward compatibility, 107but they will be removed in the future. 108 109=item * Spaces of maps, sets and parameter domains are now 110treated differently. The distinction between map spaces and set spaces 111has always been made on a conceptual level, but proper use of such spaces 112was never checked. Furthermore, up until isl-0.07 there was no way 113of explicitly creating a parameter space. These can now be created 114directly using C<isl_space_params_alloc> or from other spaces using 115C<isl_space_params>. 116 117=item * The space in which C<isl_aff>, C<isl_pw_aff>, C<isl_qpolynomial>, 118C<isl_pw_qpolynomial>, C<isl_qpolynomial_fold> and C<isl_pw_qpolynomial_fold> 119objects live is now a map space 120instead of a set space. This means, for example, that the dimensions 121of the domain of an C<isl_aff> are now considered to be of type 122C<isl_dim_in> instead of C<isl_dim_set>. Extra functions have been 123added to obtain the domain space. Some of the constructors still 124take a domain space and have therefore been renamed. 125 126=item * The functions C<isl_equality_alloc> and C<isl_inequality_alloc> 127now take an C<isl_local_space> instead of an C<isl_space>. 128An C<isl_local_space> can be created from an C<isl_space> 129using C<isl_local_space_from_space>. 130 131=item * The C<isl_div> type has been removed. Functions that used 132to return an C<isl_div> now return an C<isl_aff>. 133Note that the space of an C<isl_aff> is that of relation. 134When replacing a call to C<isl_div_get_coefficient> by a call to 135C<isl_aff_get_coefficient> any C<isl_dim_set> argument needs 136to be replaced by C<isl_dim_in>. 137A call to C<isl_aff_from_div> can be replaced by a call 138to C<isl_aff_floor>. 139A call to C<isl_qpolynomial_div(div)> call be replaced by 140the nested call 141 142 isl_qpolynomial_from_aff(isl_aff_floor(div)) 143 144The function C<isl_constraint_div> has also been renamed 145to C<isl_constraint_get_div>. 146 147=item * The C<nparam> argument has been removed from 148C<isl_map_read_from_str> and similar functions. 149When reading input in the original PolyLib format, 150the result will have no parameters. 151If parameters are expected, the caller may want to perform 152dimension manipulation on the result. 153 154=back 155 156=head3 Changes since isl-0.09 157 158=over 159 160=item * The C<schedule_split_parallel> option has been replaced 161by the C<schedule_split_scaled> option. 162 163=item * The first argument of C<isl_pw_aff_cond> is now 164an C<isl_pw_aff> instead of an C<isl_set>. 165A call C<isl_pw_aff_cond(a, b, c)> can be replaced by 166 167 isl_pw_aff_cond(isl_set_indicator_function(a), b, c) 168 169=back 170 171=head3 Changes since isl-0.10 172 173=over 174 175=item * The functions C<isl_set_dim_has_lower_bound> and 176C<isl_set_dim_has_upper_bound> have been renamed to 177C<isl_set_dim_has_any_lower_bound> and 178C<isl_set_dim_has_any_upper_bound>. 179The new C<isl_set_dim_has_lower_bound> and 180C<isl_set_dim_has_upper_bound> have slightly different meanings. 181 182=back 183 184=head3 Changes since isl-0.12 185 186=over 187 188=item * C<isl_int> has been replaced by C<isl_val>. 189Some of the old functions are still available in C<isl/deprecated/*.h> 190but they will be removed in the future. 191 192=item * The functions C<isl_pw_qpolynomial_eval>, 193C<isl_union_pw_qpolynomial_eval>, C<isl_pw_qpolynomial_fold_eval> 194and C<isl_union_pw_qpolynomial_fold_eval> have been changed to return 195an C<isl_val> instead of an C<isl_qpolynomial>. 196 197=item * The function C<isl_band_member_is_zero_distance> 198has been removed. Essentially the same functionality is available 199through C<isl_band_member_is_coincident>, except that it requires 200setting up coincidence constraints. 201The option C<schedule_outer_zero_distance> has accordingly been 202replaced by the option C<schedule_outer_coincidence>. 203 204=item * The function C<isl_vertex_get_expr> has been changed 205to return an C<isl_multi_aff> instead of a rational C<isl_basic_set>. 206The function C<isl_vertex_get_domain> has been changed to return 207a regular basic set, rather than a rational basic set. 208 209=back 210 211=head3 Changes since isl-0.14 212 213=over 214 215=item * The function C<isl_union_pw_multi_aff_add> now consistently 216computes the sum on the shared definition domain. 217The function C<isl_union_pw_multi_aff_union_add> has been added 218to compute the sum on the union of definition domains. 219The original behavior of C<isl_union_pw_multi_aff_add> was 220confused and is no longer available. 221 222=item * Band forests have been replaced by schedule trees. 223 224=item * The function C<isl_union_map_compute_flow> has been 225replaced by the function C<isl_union_access_info_compute_flow>. 226Note that the may dependence relation returned by 227C<isl_union_flow_get_may_dependence> is the union of 228the two dependence relations returned by 229C<isl_union_map_compute_flow>. Similarly for the no source relations. 230The function C<isl_union_map_compute_flow> is still available 231for backward compatibility, but it will be removed in the future. 232 233=item * The function C<isl_basic_set_drop_constraint> has been 234deprecated. 235 236=item * The function C<isl_ast_build_ast_from_schedule> has been 237renamed to C<isl_ast_build_node_from_schedule_map>. 238The original name is still available 239for backward compatibility, but it will be removed in the future. 240 241=item * The C<separation_class> AST generation option has been 242deprecated. 243 244=item * The functions C<isl_equality_alloc> and C<isl_inequality_alloc> 245have been renamed to C<isl_constraint_alloc_equality> and 246C<isl_constraint_alloc_inequality>. The original names have been 247kept for backward compatibility, but they will be removed in the future. 248 249=item * The C<schedule_fuse> option has been replaced 250by the C<schedule_serialize_sccs> option. The effect 251of setting the C<schedule_fuse> option to C<ISL_SCHEDULE_FUSE_MIN> 252is now obtained by turning on the C<schedule_serialize_sccs> option. 253 254=back 255 256=head3 Changes since isl-0.17 257 258=over 259 260=item * The function C<isl_printer_print_ast_expr> no longer prints 261in C format by default. To print in C format, the output format 262of the printer needs to have been explicitly set to C<ISL_FORMAT_C>. 263As a result, the function C<isl_ast_expr_to_str> no longer prints 264the expression in C format. Use C<isl_ast_expr_to_C_str> instead. 265 266=item * The functions C<isl_set_align_divs> and C<isl_map_align_divs> 267have been deprecated. The function C<isl_set_lift> has an effect 268that is similar to C<isl_set_align_divs> and could in some cases 269be used as an alternative. 270 271=back 272 273=head3 Changes since isl-0.19 274 275=over 276 277=item * Zero-dimensional objects of type C<isl_multi_pw_aff> or 278C<isl_multi_union_pw_aff> can now keep track of an explicit domain. 279This explicit domain, if present, is taken into account 280by various operations that take such objects as input. 281 282=back 283 284=head3 Changes since isl-0.20 285 286=over 287 288=item * Several functions that used to return C<unsigned> 289now return C<isl_size>. This means that these functions may 290now return a negative value in case an error occurred. 291The same holds for functions that used to return C<int>, 292although some of those were already returning 293a negative value in case of error. 294 295=item * The C<isl_ast_op_type> enumeration type has been 296renamed to C<isl_ast_expr_op_type>. The corresponding 297enumeration constants have been similarly renamed. 298The old names are defined to the new names for backward 299compatibility. 300 301=item * Several functions returning an extra boolean value 302through an C<int *> argument now do so through an C<isl_bool *> 303argument. The returned values are the same, only the type 304of the pointer has been changed. 305 306=back 307 308=head1 License 309 310C<isl> is released under the MIT license. 311 312=over 313 314Permission is hereby granted, free of charge, to any person obtaining a copy of 315this software and associated documentation files (the "Software"), to deal in 316the Software without restriction, including without limitation the rights to 317use, copy, modify, merge, publish, distribute, sublicense, and/or sell copies 318of the Software, and to permit persons to whom the Software is furnished to do 319so, subject to the following conditions: 320 321The above copyright notice and this permission notice shall be included in all 322copies or substantial portions of the Software. 323 324THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR 325IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, 326FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE 327AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER 328LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, 329OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE 330SOFTWARE. 331 332=back 333 334Note that by default C<isl> requires C<GMP>, which is released 335under the GNU Lesser General Public License (LGPL). This means 336that code linked against C<isl> is also linked against LGPL code. 337 338When configuring with C<--with-int=imath> or C<--with-int=imath-32>, C<isl> 339will link against C<imath>, a library for exact integer arithmetic released 340under the MIT license. 341 342=head1 Installation 343 344The source of C<isl> can be obtained either as a tarball 345or from the git repository. Both are available from 346L<http://isl.gforge.inria.fr/>. 347The installation process depends on how you obtained 348the source. 349 350=head2 Installation from the git repository 351 352=over 353 354=item 1 Clone or update the repository 355 356The first time the source is obtained, you need to clone 357the repository. 358 359 git clone git://repo.or.cz/isl.git 360 361To obtain updates, you need to pull in the latest changes 362 363 git pull 364 365=item 2 Optionally get C<imath> submodule 366 367To build C<isl> with C<imath>, you need to obtain the C<imath> 368submodule by running in the git source tree of C<isl> 369 370 git submodule init 371 git submodule update 372 373This will fetch the required version of C<imath> in a subdirectory of C<isl>. 374 375=item 2 Generate C<configure> 376 377 ./autogen.sh 378 379=back 380 381After performing the above steps, continue 382with the L<Common installation instructions>. 383 384=head2 Common installation instructions 385 386=over 387 388=item 1 Obtain C<GMP> 389 390By default, building C<isl> requires C<GMP>, including its headers files. 391Your distribution may not provide these header files by default 392and you may need to install a package called C<gmp-devel> or something 393similar. Alternatively, C<GMP> can be built from 394source, available from L<http://gmplib.org/>. 395C<GMP> is not needed if you build C<isl> with C<imath>. 396 397=item 2 Configure 398 399C<isl> uses the standard C<autoconf> C<configure> script. 400To run it, just type 401 402 ./configure 403 404optionally followed by some configure options. 405A complete list of options can be obtained by running 406 407 ./configure --help 408 409Below we discuss some of the more common options. 410 411=over 412 413=item C<--prefix> 414 415Installation prefix for C<isl> 416 417=item C<--with-int=[gmp|imath|imath-32]> 418 419Select the integer library to be used by C<isl>, the default is C<gmp>. 420With C<imath-32>, C<isl> will use 32 bit integers, but fall back to C<imath> 421for values out of the 32 bit range. In most applications, C<isl> will run 422fastest with the C<imath-32> option, followed by C<gmp> and C<imath>, the 423slowest. 424 425=item C<--with-gmp-prefix> 426 427Installation prefix for C<GMP> (architecture-independent files). 428 429=item C<--with-gmp-exec-prefix> 430 431Installation prefix for C<GMP> (architecture-dependent files). 432 433=back 434 435=item 3 Compile 436 437 make 438 439=item 4 Install (optional) 440 441 make install 442 443=back 444 445=head1 Integer Set Library 446 447=head2 Memory Management 448 449Since a high-level operation on isl objects usually involves 450several substeps and since the user is usually not interested in 451the intermediate results, most functions that return a new object 452will also release all the objects passed as arguments. 453If the user still wants to use one or more of these arguments 454after the function call, she should pass along a copy of the 455object rather than the object itself. 456The user is then responsible for making sure that the original 457object gets used somewhere else or is explicitly freed. 458 459The arguments and return values of all documented functions are 460annotated to make clear which arguments are released and which 461arguments are preserved. In particular, the following annotations 462are used 463 464=over 465 466=item C<__isl_give> 467 468C<__isl_give> means that a new object is returned. 469The user should make sure that the returned pointer is 470used exactly once as a value for an C<__isl_take> argument. 471In between, it can be used as a value for as many 472C<__isl_keep> arguments as the user likes. 473There is one exception, and that is the case where the 474pointer returned is C<NULL>. In this case, the user 475is free to use it as an C<__isl_take> argument or not. 476When applied to a C<char *>, the returned pointer needs to be 477freed using C<free>. 478 479=item C<__isl_null> 480 481C<__isl_null> means that a C<NULL> value is returned. 482 483=item C<__isl_take> 484 485C<__isl_take> means that the object the argument points to 486is taken over by the function and may no longer be used 487by the user as an argument to any other function. 488The pointer value must be one returned by a function 489returning an C<__isl_give> pointer. 490If the user passes in a C<NULL> value, then this will 491be treated as an error in the sense that the function will 492not perform its usual operation. However, it will still 493make sure that all the other C<__isl_take> arguments 494are released. 495 496=item C<__isl_keep> 497 498C<__isl_keep> means that the function will only use the object 499temporarily. After the function has finished, the user 500can still use it as an argument to other functions. 501A C<NULL> value will be treated in the same way as 502a C<NULL> value for an C<__isl_take> argument. 503This annotation may also be used on return values of 504type C<const char *>, in which case the returned pointer should 505not be freed by the user and is only valid until the object 506from which it was derived is updated or freed. 507 508=back 509 510=head2 Initialization 511 512All manipulations of integer sets and relations occur within 513the context of an C<isl_ctx>. 514A given C<isl_ctx> can only be used within a single thread. 515All arguments of a function are required to have been allocated 516within the same context. 517There are currently no functions available for moving an object 518from one C<isl_ctx> to another C<isl_ctx>. This means that 519there is currently no way of safely moving an object from one 520thread to another, unless the whole C<isl_ctx> is moved. 521 522An C<isl_ctx> can be allocated using C<isl_ctx_alloc> and 523freed using C<isl_ctx_free>. 524All objects allocated within an C<isl_ctx> should be freed 525before the C<isl_ctx> itself is freed. 526 527 isl_ctx *isl_ctx_alloc(); 528 void isl_ctx_free(isl_ctx *ctx); 529 530The user can impose a bound on the number of low-level I<operations> 531that can be performed by an C<isl_ctx>. This bound can be set and 532retrieved using the following functions. A bound of zero means that 533no bound is imposed. The number of operations performed can be 534reset using C<isl_ctx_reset_operations>. Note that the number 535of low-level operations needed to perform a high-level computation 536may differ significantly across different versions 537of C<isl>, but it should be the same across different platforms 538for the same version of C<isl>. 539 540Warning: This feature is experimental. C<isl> has good support to abort and 541bail out during the computation, but this feature may exercise error code paths 542that are normally not used that much. Consequently, it is not unlikely that 543hidden bugs will be exposed. 544 545 void isl_ctx_set_max_operations(isl_ctx *ctx, 546 unsigned long max_operations); 547 unsigned long isl_ctx_get_max_operations(isl_ctx *ctx); 548 void isl_ctx_reset_operations(isl_ctx *ctx); 549 550In order to be able to create an object in the same context 551as another object, most object types (described later in 552this document) provide a function to obtain the context 553in which the object was created. 554 555 #include <isl/val.h> 556 isl_ctx *isl_val_get_ctx(__isl_keep isl_val *val); 557 isl_ctx *isl_multi_val_get_ctx( 558 __isl_keep isl_multi_val *mv); 559 560 #include <isl/id.h> 561 isl_ctx *isl_id_get_ctx(__isl_keep isl_id *id); 562 isl_ctx *isl_multi_id_get_ctx( 563 __isl_keep isl_multi_id *mi); 564 565 #include <isl/local_space.h> 566 isl_ctx *isl_local_space_get_ctx( 567 __isl_keep isl_local_space *ls); 568 569 #include <isl/set.h> 570 isl_ctx *isl_set_list_get_ctx( 571 __isl_keep isl_set_list *list); 572 573 #include <isl/aff.h> 574 isl_ctx *isl_aff_get_ctx(__isl_keep isl_aff *aff); 575 isl_ctx *isl_multi_aff_get_ctx( 576 __isl_keep isl_multi_aff *maff); 577 isl_ctx *isl_pw_aff_get_ctx(__isl_keep isl_pw_aff *pa); 578 isl_ctx *isl_pw_multi_aff_get_ctx( 579 __isl_keep isl_pw_multi_aff *pma); 580 isl_ctx *isl_multi_pw_aff_get_ctx( 581 __isl_keep isl_multi_pw_aff *mpa); 582 isl_ctx *isl_union_pw_aff_get_ctx( 583 __isl_keep isl_union_pw_aff *upa); 584 isl_ctx *isl_union_pw_multi_aff_get_ctx( 585 __isl_keep isl_union_pw_multi_aff *upma); 586 isl_ctx *isl_multi_union_pw_aff_get_ctx( 587 __isl_keep isl_multi_union_pw_aff *mupa); 588 589 #include <isl/id_to_ast_expr.h> 590 isl_ctx *isl_id_to_ast_expr_get_ctx( 591 __isl_keep isl_id_to_ast_expr *id2expr); 592 593 #include <isl/point.h> 594 isl_ctx *isl_point_get_ctx(__isl_keep isl_point *pnt); 595 596 #include <isl/vec.h> 597 isl_ctx *isl_vec_get_ctx(__isl_keep isl_vec *vec); 598 599 #include <isl/mat.h> 600 isl_ctx *isl_mat_get_ctx(__isl_keep isl_mat *mat); 601 602 #include <isl/vertices.h> 603 isl_ctx *isl_vertices_get_ctx( 604 __isl_keep isl_vertices *vertices); 605 isl_ctx *isl_vertex_get_ctx(__isl_keep isl_vertex *vertex); 606 isl_ctx *isl_cell_get_ctx(__isl_keep isl_cell *cell); 607 608 #include <isl/flow.h> 609 isl_ctx *isl_restriction_get_ctx( 610 __isl_keep isl_restriction *restr); 611 isl_ctx *isl_union_access_info_get_ctx( 612 __isl_keep isl_union_access_info *access); 613 isl_ctx *isl_union_flow_get_ctx( 614 __isl_keep isl_union_flow *flow); 615 616 #include <isl/schedule.h> 617 isl_ctx *isl_schedule_get_ctx( 618 __isl_keep isl_schedule *sched); 619 isl_ctx *isl_schedule_constraints_get_ctx( 620 __isl_keep isl_schedule_constraints *sc); 621 622 #include <isl/schedule_node.h> 623 isl_ctx *isl_schedule_node_get_ctx( 624 __isl_keep isl_schedule_node *node); 625 626 #include <isl/ast_build.h> 627 isl_ctx *isl_ast_build_get_ctx( 628 __isl_keep isl_ast_build *build); 629 630 #include <isl/ast.h> 631 isl_ctx *isl_ast_expr_get_ctx( 632 __isl_keep isl_ast_expr *expr); 633 isl_ctx *isl_ast_node_get_ctx( 634 __isl_keep isl_ast_node *node); 635 636 #include <isl/stride_info.h> 637 isl_ctx *isl_stride_info_get_ctx( 638 __isl_keep isl_stride_info *si); 639 640 #include <isl/fixed_box.h> 641 isl_ctx *isl_fixed_box_get_ctx( 642 __isl_keep isl_fixed_box *box); 643 644=head2 Return Types 645 646C<isl> uses the special return type C<isl_size> for functions 647that return a non-negative value, typically a number or a position. 648Besides the regular non-negative return values, a special (negative) 649value C<isl_size_error> may be returned, indicating that something 650went wrong. 651 652C<isl> also uses two special return types for functions that either return 653a boolean or that in principle do not return anything. 654In particular, the C<isl_bool> type has three possible values: 655C<isl_bool_true> (a positive integer value), indicating I<true> or I<yes>; 656C<isl_bool_false> (the integer value zero), indicating I<false> or I<no>; and 657C<isl_bool_error> (a negative integer value), indicating that something 658went wrong. The following operations are defined on C<isl_bool>. The function 659C<isl_bool_not> can be used to negate an C<isl_bool>, where the negation of 660C<isl_bool_error> is C<isl_bool_error> again. The function C<isl_bool_ok> 661converts an integer to an C<isl_bool>. Any non-zero values yields 662C<isl_bool_true> and zero yields C<isl_bool_false>. 663 664 #include <isl/ctx.h> 665 isl_bool isl_bool_not(isl_bool b); 666 isl_bool isl_bool_ok(int b); 667 668The C<isl_stat> type has two possible values: 669C<isl_stat_ok> (the integer value zero), indicating a successful 670operation; and 671C<isl_stat_error> (a negative integer value), indicating that something 672went wrong. 673The function C<isl_stat_non_null> converts an isl object pointer 674to an C<isl_stat>, returning C<isl_stat_ok> if the object pointer is valid and 675C<isl_stat_error> if it is C<NULL>. 676 677 #include <isl/ctx.h> 678 isl_stat isl_stat_non_null(void *obj); 679 680See L</"Error Handling"> for more information on 681C<isl_size_error>, C<isl_bool_error> and C<isl_stat_error>. 682 683=head2 Values 684 685An C<isl_val> represents an integer value, a rational value 686or one of three special values, infinity, negative infinity and NaN. 687Some predefined values can be created using the following functions. 688 689 #include <isl/val.h> 690 __isl_give isl_val *isl_val_zero(isl_ctx *ctx); 691 __isl_give isl_val *isl_val_one(isl_ctx *ctx); 692 __isl_give isl_val *isl_val_negone(isl_ctx *ctx); 693 __isl_give isl_val *isl_val_nan(isl_ctx *ctx); 694 __isl_give isl_val *isl_val_infty(isl_ctx *ctx); 695 __isl_give isl_val *isl_val_neginfty(isl_ctx *ctx); 696 697Specific integer values can be created using the following functions. 698 699 #include <isl/val.h> 700 __isl_give isl_val *isl_val_int_from_si(isl_ctx *ctx, 701 long i); 702 __isl_give isl_val *isl_val_int_from_ui(isl_ctx *ctx, 703 unsigned long u); 704 __isl_give isl_val *isl_val_int_from_chunks(isl_ctx *ctx, 705 size_t n, size_t size, const void *chunks); 706 707The function C<isl_val_int_from_chunks> constructs an C<isl_val> 708from the C<n> I<digits>, each consisting of C<size> bytes, stored at C<chunks>. 709The least significant digit is assumed to be stored first. 710 711Value objects can be copied and freed using the following functions. 712 713 #include <isl/val.h> 714 __isl_give isl_val *isl_val_copy(__isl_keep isl_val *v); 715 __isl_null isl_val *isl_val_free(__isl_take isl_val *v); 716 717They can be inspected using the following functions. 718 719 #include <isl/val.h> 720 long isl_val_get_num_si(__isl_keep isl_val *v); 721 long isl_val_get_den_si(__isl_keep isl_val *v); 722 __isl_give isl_val *isl_val_get_den_val( 723 __isl_keep isl_val *v); 724 double isl_val_get_d(__isl_keep isl_val *v); 725 isl_size isl_val_n_abs_num_chunks(__isl_keep isl_val *v, 726 size_t size); 727 isl_stat isl_val_get_abs_num_chunks(__isl_keep isl_val *v, 728 size_t size, void *chunks); 729 730C<isl_val_n_abs_num_chunks> returns the number of I<digits> 731of C<size> bytes needed to store the absolute value of the 732numerator of C<v>. 733C<isl_val_get_abs_num_chunks> stores these digits at C<chunks>, 734which is assumed to have been preallocated by the caller. 735The least significant digit is stored first. 736Note that C<isl_val_get_num_si>, C<isl_val_get_den_si>, 737C<isl_val_get_d>, C<isl_val_n_abs_num_chunks> 738and C<isl_val_get_abs_num_chunks> can only be applied to rational values. 739 740An C<isl_val> can be modified using the following function. 741 742 #include <isl/val.h> 743 __isl_give isl_val *isl_val_set_si(__isl_take isl_val *v, 744 long i); 745 746The following unary properties are defined on C<isl_val>s. 747 748 #include <isl/val.h> 749 int isl_val_sgn(__isl_keep isl_val *v); 750 isl_bool isl_val_is_zero(__isl_keep isl_val *v); 751 isl_bool isl_val_is_one(__isl_keep isl_val *v); 752 isl_bool isl_val_is_negone(__isl_keep isl_val *v); 753 isl_bool isl_val_is_nonneg(__isl_keep isl_val *v); 754 isl_bool isl_val_is_nonpos(__isl_keep isl_val *v); 755 isl_bool isl_val_is_pos(__isl_keep isl_val *v); 756 isl_bool isl_val_is_neg(__isl_keep isl_val *v); 757 isl_bool isl_val_is_int(__isl_keep isl_val *v); 758 isl_bool isl_val_is_rat(__isl_keep isl_val *v); 759 isl_bool isl_val_is_nan(__isl_keep isl_val *v); 760 isl_bool isl_val_is_infty(__isl_keep isl_val *v); 761 isl_bool isl_val_is_neginfty(__isl_keep isl_val *v); 762 763Note that the sign of NaN is undefined. 764 765The following binary properties are defined on pairs of C<isl_val>s. 766 767 #include <isl/val.h> 768 isl_bool isl_val_lt(__isl_keep isl_val *v1, 769 __isl_keep isl_val *v2); 770 isl_bool isl_val_le(__isl_keep isl_val *v1, 771 __isl_keep isl_val *v2); 772 isl_bool isl_val_gt(__isl_keep isl_val *v1, 773 __isl_keep isl_val *v2); 774 isl_bool isl_val_ge(__isl_keep isl_val *v1, 775 __isl_keep isl_val *v2); 776 isl_bool isl_val_eq(__isl_keep isl_val *v1, 777 __isl_keep isl_val *v2); 778 isl_bool isl_val_ne(__isl_keep isl_val *v1, 779 __isl_keep isl_val *v2); 780 isl_bool isl_val_abs_eq(__isl_keep isl_val *v1, 781 __isl_keep isl_val *v2); 782 783Comparisons to NaN always return false. 784That is, a NaN is not considered to hold any relative position 785with respect to any value. In particular, a NaN 786is neither considered to be equal to nor to be different from 787any value (including another NaN). 788The function C<isl_val_abs_eq> checks whether its two arguments 789are equal in absolute value. 790 791For integer C<isl_val>s we additionally have the following binary property. 792 793 #include <isl/val.h> 794 isl_bool isl_val_is_divisible_by(__isl_keep isl_val *v1, 795 __isl_keep isl_val *v2); 796 797An C<isl_val> can also be compared to an integer using the following 798functions. The result of C<isl_val_cmp_si> is undefined for NaN. 799 800 #include <isl/val.h> 801 isl_bool isl_val_gt_si(__isl_keep isl_val *v, long i); 802 isl_bool isl_val_eq_si(__isl_keep isl_val *v, long i); 803 int isl_val_cmp_si(__isl_keep isl_val *v, long i); 804 805The following unary operations are available on C<isl_val>s. 806 807 #include <isl/val.h> 808 __isl_give isl_val *isl_val_abs(__isl_take isl_val *v); 809 __isl_give isl_val *isl_val_neg(__isl_take isl_val *v); 810 __isl_give isl_val *isl_val_floor(__isl_take isl_val *v); 811 __isl_give isl_val *isl_val_ceil(__isl_take isl_val *v); 812 __isl_give isl_val *isl_val_trunc(__isl_take isl_val *v); 813 __isl_give isl_val *isl_val_inv(__isl_take isl_val *v); 814 815The following binary operations are available on C<isl_val>s. 816 817 #include <isl/val.h> 818 __isl_give isl_val *isl_val_min(__isl_take isl_val *v1, 819 __isl_take isl_val *v2); 820 __isl_give isl_val *isl_val_max(__isl_take isl_val *v1, 821 __isl_take isl_val *v2); 822 __isl_give isl_val *isl_val_add(__isl_take isl_val *v1, 823 __isl_take isl_val *v2); 824 __isl_give isl_val *isl_val_add_ui(__isl_take isl_val *v1, 825 unsigned long v2); 826 __isl_give isl_val *isl_val_sub(__isl_take isl_val *v1, 827 __isl_take isl_val *v2); 828 __isl_give isl_val *isl_val_sub_ui(__isl_take isl_val *v1, 829 unsigned long v2); 830 __isl_give isl_val *isl_val_mul(__isl_take isl_val *v1, 831 __isl_take isl_val *v2); 832 __isl_give isl_val *isl_val_mul_ui(__isl_take isl_val *v1, 833 unsigned long v2); 834 __isl_give isl_val *isl_val_div(__isl_take isl_val *v1, 835 __isl_take isl_val *v2); 836 __isl_give isl_val *isl_val_div_ui(__isl_take isl_val *v1, 837 unsigned long v2); 838 839On integer values, we additionally have the following operations. 840 841 #include <isl/val.h> 842 __isl_give isl_val *isl_val_pow2(__isl_take isl_val *v); 843 __isl_give isl_val *isl_val_2exp(__isl_take isl_val *v); 844 __isl_give isl_val *isl_val_mod(__isl_take isl_val *v1, 845 __isl_take isl_val *v2); 846 __isl_give isl_val *isl_val_gcd(__isl_take isl_val *v1, 847 __isl_take isl_val *v2); 848 __isl_give isl_val *isl_val_gcdext(__isl_take isl_val *v1, 849 __isl_take isl_val *v2, __isl_give isl_val **x, 850 __isl_give isl_val **y); 851 852C<isl_val_2exp> is an alternative name for C<isl_val_pow2>. 853The function C<isl_val_gcdext> returns the greatest common divisor g 854of C<v1> and C<v2> as well as two integers C<*x> and C<*y> such 855that C<*x> * C<v1> + C<*y> * C<v2> = g. 856 857=head3 GMP specific functions 858 859These functions are only available if C<isl> has been compiled with C<GMP> 860support. 861 862Specific integer and rational values can be created from C<GMP> values using 863the following functions. 864 865 #include <isl/val_gmp.h> 866 __isl_give isl_val *isl_val_int_from_gmp(isl_ctx *ctx, 867 mpz_t z); 868 __isl_give isl_val *isl_val_from_gmp(isl_ctx *ctx, 869 const mpz_t n, const mpz_t d); 870 871The numerator and denominator of a rational value can be extracted as 872C<GMP> values using the following functions. 873 874 #include <isl/val_gmp.h> 875 int isl_val_get_num_gmp(__isl_keep isl_val *v, mpz_t z); 876 int isl_val_get_den_gmp(__isl_keep isl_val *v, mpz_t z); 877 878=head2 Sets and Relations 879 880C<isl> uses six types of objects for representing sets and relations, 881C<isl_basic_set>, C<isl_basic_map>, C<isl_set>, C<isl_map>, 882C<isl_union_set> and C<isl_union_map>. 883C<isl_basic_set> and C<isl_basic_map> represent sets and relations that 884can be described as a conjunction of affine constraints, while 885C<isl_set> and C<isl_map> represent unions of 886C<isl_basic_set>s and C<isl_basic_map>s, respectively. 887However, all C<isl_basic_set>s or C<isl_basic_map>s in the union need 888to live in the same space. C<isl_union_set>s and C<isl_union_map>s 889represent unions of C<isl_set>s or C<isl_map>s in I<different> spaces, 890where spaces are considered different if they have a different number 891of dimensions and/or different names (see L<"Spaces">). 892The difference between sets and relations (maps) is that sets have 893one set of variables, while relations have two sets of variables, 894input variables and output variables. 895 896=head2 Error Handling 897 898C<isl> supports different ways to react in case a runtime error is triggered. 899Runtime errors arise, e.g., if a function such as C<isl_map_intersect> is called 900with two maps that have incompatible spaces. There are three possible ways 901to react on error: to warn, to continue or to abort. 902 903The default behavior is to warn. In this mode, C<isl> prints a warning, stores 904the last error in the corresponding C<isl_ctx> and the function in which the 905error was triggered returns a value indicating that some error has 906occurred. In case of functions returning a pointer, this value is 907C<NULL>. In case of functions returning an C<isl_size>, C<isl_bool> or an 908C<isl_stat>, this value is C<isl_size_error>, 909C<isl_bool_error> or C<isl_stat_error>. 910An error does not corrupt internal state, 911such that isl can continue to be used. C<isl> also provides functions to 912read the last error, including the specific error message, 913the isl source file where the error occurred and the line number, 914and to reset all information about the last error. The 915last error is only stored for information purposes. Its presence does not 916change the behavior of C<isl>. Hence, resetting an error is not required to 917continue to use isl, but only to observe new errors. 918 919 #include <isl/ctx.h> 920 enum isl_error isl_ctx_last_error(isl_ctx *ctx); 921 const char *isl_ctx_last_error_msg(isl_ctx *ctx); 922 const char *isl_ctx_last_error_file(isl_ctx *ctx); 923 int isl_ctx_last_error_line(isl_ctx *ctx); 924 void isl_ctx_reset_error(isl_ctx *ctx); 925 926If no error has occurred since the last call to C<isl_ctx_reset_error>, 927then the functions C<isl_ctx_last_error_msg> and 928C<isl_ctx_last_error_file> return C<NULL>. 929 930Another option is to continue on error. This is similar to warn on error mode, 931except that C<isl> does not print any warning. This allows a program to 932implement its own error reporting. 933 934The last option is to directly abort the execution of the program from within 935the isl library. This makes it obviously impossible to recover from an error, 936but it allows to directly spot the error location. By aborting on error, 937debuggers break at the location the error occurred and can provide a stack 938trace. Other tools that automatically provide stack traces on abort or that do 939not want to continue execution after an error was triggered may also prefer to 940abort on error. 941 942The on error behavior of isl can be specified by calling 943C<isl_options_set_on_error> or by setting the command line option 944C<--isl-on-error>. Valid arguments for the function call are 945C<ISL_ON_ERROR_WARN>, C<ISL_ON_ERROR_CONTINUE> and C<ISL_ON_ERROR_ABORT>. The 946choices for the command line option are C<warn>, C<continue> and C<abort>. 947It is also possible to query the current error mode. 948 949 #include <isl/options.h> 950 isl_stat isl_options_set_on_error(isl_ctx *ctx, int val); 951 int isl_options_get_on_error(isl_ctx *ctx); 952 953=head2 Identifiers 954 955Identifiers are used to identify both individual dimensions 956and tuples of dimensions. They consist of an optional name and an optional 957user pointer. The name and the user pointer cannot both be C<NULL>, however. 958Identifiers with the same name but different pointer values 959are considered to be distinct. 960Similarly, identifiers with different names but the same pointer value 961are also considered to be distinct. 962Equal identifiers are represented using the same object. 963Pairs of identifiers can therefore be tested for equality using the 964C<==> operator. 965Identifiers can be constructed, copied, freed, inspected and printed 966using the following functions. 967 968 #include <isl/id.h> 969 __isl_give isl_id *isl_id_alloc(isl_ctx *ctx, 970 __isl_keep const char *name, void *user); 971 __isl_give isl_id *isl_id_set_free_user( 972 __isl_take isl_id *id, 973 void (*free_user)(void *user)); 974 __isl_give isl_id *isl_id_copy(isl_id *id); 975 __isl_null isl_id *isl_id_free(__isl_take isl_id *id); 976 977 void *isl_id_get_user(__isl_keep isl_id *id); 978 __isl_keep const char *isl_id_get_name(__isl_keep isl_id *id); 979 980 __isl_give isl_printer *isl_printer_print_id( 981 __isl_take isl_printer *p, __isl_keep isl_id *id); 982 983The callback set by C<isl_id_set_free_user> is called on the user 984pointer when the last reference to the C<isl_id> is freed. 985Note that C<isl_id_get_name> returns a pointer to some internal 986data structure, so the result can only be used while the 987corresponding C<isl_id> is alive. 988 989=head2 Spaces 990 991Whenever a new set, relation or similar object is created from scratch, 992the space in which it lives needs to be specified using an C<isl_space>. 993Each space involves zero or more parameters and zero, one or two 994tuples of set or input/output dimensions. The parameters and dimensions 995are identified by an C<isl_dim_type> and a position. 996The type C<isl_dim_param> refers to parameters, 997the type C<isl_dim_set> refers to set dimensions (for spaces 998with a single tuple of dimensions) and the types C<isl_dim_in> 999and C<isl_dim_out> refer to input and output dimensions 1000(for spaces with two tuples of dimensions). 1001Local spaces (see L</"Local Spaces">) also contain dimensions 1002of type C<isl_dim_div>. 1003Note that parameters are only identified by their position within 1004a given object. Across different objects, parameters are (usually) 1005identified by their names or identifiers. Only unnamed parameters 1006are identified by their positions across objects. The use of unnamed 1007parameters is discouraged. 1008 1009 #include <isl/space.h> 1010 __isl_give isl_space *isl_space_unit(isl_ctx *ctx); 1011 __isl_give isl_space *isl_space_alloc(isl_ctx *ctx, 1012 unsigned nparam, unsigned n_in, unsigned n_out); 1013 __isl_give isl_space *isl_space_params_alloc(isl_ctx *ctx, 1014 unsigned nparam); 1015 __isl_give isl_space *isl_space_set_alloc(isl_ctx *ctx, 1016 unsigned nparam, unsigned dim); 1017 __isl_give isl_space *isl_space_copy(__isl_keep isl_space *space); 1018 __isl_null isl_space *isl_space_free(__isl_take isl_space *space); 1019 1020The space used for creating a parameter domain 1021needs to be created using C<isl_space_unit> or C<isl_space_params_alloc>. 1022For other sets, the space 1023needs to be created using C<isl_space_set_alloc>, while 1024for a relation, the space 1025needs to be created using C<isl_space_alloc>. 1026The use of C<isl_space_params_alloc>, 1027C<isl_space_set_alloc> and C<isl_space_alloc> is discouraged as they allow 1028for the introduction of unnamed parameters. 1029 1030To check whether a given space is that of a set or a map 1031or whether it is a parameter space, use these functions: 1032 1033 #include <isl/space.h> 1034 isl_bool isl_space_is_params(__isl_keep isl_space *space); 1035 isl_bool isl_space_is_set(__isl_keep isl_space *space); 1036 isl_bool isl_space_is_map(__isl_keep isl_space *space); 1037 1038Spaces can be compared using the following functions: 1039 1040 #include <isl/space.h> 1041 isl_bool isl_space_is_equal(__isl_keep isl_space *space1, 1042 __isl_keep isl_space *space2); 1043 isl_bool isl_space_has_equal_params( 1044 __isl_keep isl_space *space1, 1045 __isl_keep isl_space *space2); 1046 isl_bool isl_space_has_equal_tuples( 1047 __isl_keep isl_space *space1, 1048 __isl_keep isl_space *space2); 1049 isl_bool isl_space_is_domain(__isl_keep isl_space *space1, 1050 __isl_keep isl_space *space2); 1051 isl_bool isl_space_is_range(__isl_keep isl_space *space1, 1052 __isl_keep isl_space *space2); 1053 isl_bool isl_space_tuple_is_equal( 1054 __isl_keep isl_space *space1, 1055 enum isl_dim_type type1, 1056 __isl_keep isl_space *space2, 1057 enum isl_dim_type type2); 1058 1059C<isl_space_is_domain> checks whether the first argument is equal 1060to the domain of the second argument. This requires in particular that 1061the first argument is a set space and that the second argument 1062is a map space. C<isl_space_tuple_is_equal> checks whether the given 1063tuples (C<isl_dim_in>, C<isl_dim_out> or C<isl_dim_set>) of the given 1064spaces are the same. That is, it checks if they have the same 1065identifier (if any), the same dimension and the same internal structure 1066(if any). 1067The function 1068C<isl_space_has_equal_params> checks whether two spaces 1069have the same parameters in the same order. 1070C<isl_space_has_equal_tuples> check whether two spaces have 1071the same tuples. In contrast to C<isl_space_is_equal> below, 1072it does not check the 1073parameters. This is useful because many C<isl> functions align the 1074parameters before they perform their operations, such that equivalence 1075is not necessary. 1076C<isl_space_is_equal> checks whether two spaces are identical, 1077meaning that they have the same parameters and the same tuples. 1078That is, it checks whether both C<isl_space_has_equal_params> and 1079C<isl_space_has_equal_tuples> hold. 1080 1081It is often useful to create objects that live in the 1082same space as some other object. This can be accomplished 1083by creating the new objects 1084(see L</"Creating New Sets and Relations"> or 1085L</"Functions">) based on the space 1086of the original object. 1087 1088 #include <isl/set.h> 1089 __isl_give isl_space *isl_basic_set_get_space( 1090 __isl_keep isl_basic_set *bset); 1091 __isl_give isl_space *isl_set_get_space(__isl_keep isl_set *set); 1092 1093 #include <isl/union_set.h> 1094 __isl_give isl_space *isl_union_set_get_space( 1095 __isl_keep isl_union_set *uset); 1096 1097 #include <isl/map.h> 1098 __isl_give isl_space *isl_basic_map_get_space( 1099 __isl_keep isl_basic_map *bmap); 1100 __isl_give isl_space *isl_map_get_space(__isl_keep isl_map *map); 1101 1102 #include <isl/union_map.h> 1103 __isl_give isl_space *isl_union_map_get_space( 1104 __isl_keep isl_union_map *umap); 1105 1106 #include <isl/constraint.h> 1107 __isl_give isl_space *isl_constraint_get_space( 1108 __isl_keep isl_constraint *constraint); 1109 1110 #include <isl/polynomial.h> 1111 __isl_give isl_space *isl_qpolynomial_get_domain_space( 1112 __isl_keep isl_qpolynomial *qp); 1113 __isl_give isl_space *isl_qpolynomial_get_space( 1114 __isl_keep isl_qpolynomial *qp); 1115 __isl_give isl_space * 1116 isl_qpolynomial_fold_get_domain_space( 1117 __isl_keep isl_qpolynomial_fold *fold); 1118 __isl_give isl_space *isl_qpolynomial_fold_get_space( 1119 __isl_keep isl_qpolynomial_fold *fold); 1120 __isl_give isl_space *isl_pw_qpolynomial_get_domain_space( 1121 __isl_keep isl_pw_qpolynomial *pwqp); 1122 __isl_give isl_space *isl_pw_qpolynomial_get_space( 1123 __isl_keep isl_pw_qpolynomial *pwqp); 1124 __isl_give isl_space *isl_pw_qpolynomial_fold_get_domain_space( 1125 __isl_keep isl_pw_qpolynomial_fold *pwf); 1126 __isl_give isl_space *isl_pw_qpolynomial_fold_get_space( 1127 __isl_keep isl_pw_qpolynomial_fold *pwf); 1128 __isl_give isl_space *isl_union_pw_qpolynomial_get_space( 1129 __isl_keep isl_union_pw_qpolynomial *upwqp); 1130 __isl_give isl_space *isl_union_pw_qpolynomial_fold_get_space( 1131 __isl_keep isl_union_pw_qpolynomial_fold *upwf); 1132 1133 #include <isl/id.h> 1134 __isl_give isl_space *isl_multi_id_get_space( 1135 __isl_keep isl_multi_id *mi); 1136 1137 #include <isl/val.h> 1138 __isl_give isl_space *isl_multi_val_get_space( 1139 __isl_keep isl_multi_val *mv); 1140 1141 #include <isl/aff.h> 1142 __isl_give isl_space *isl_aff_get_domain_space( 1143 __isl_keep isl_aff *aff); 1144 __isl_give isl_space *isl_aff_get_space( 1145 __isl_keep isl_aff *aff); 1146 __isl_give isl_space *isl_pw_aff_get_domain_space( 1147 __isl_keep isl_pw_aff *pwaff); 1148 __isl_give isl_space *isl_pw_aff_get_space( 1149 __isl_keep isl_pw_aff *pwaff); 1150 __isl_give isl_space *isl_multi_aff_get_domain_space( 1151 __isl_keep isl_multi_aff *maff); 1152 __isl_give isl_space *isl_multi_aff_get_space( 1153 __isl_keep isl_multi_aff *maff); 1154 __isl_give isl_space *isl_pw_multi_aff_get_domain_space( 1155 __isl_keep isl_pw_multi_aff *pma); 1156 __isl_give isl_space *isl_pw_multi_aff_get_space( 1157 __isl_keep isl_pw_multi_aff *pma); 1158 __isl_give isl_space *isl_union_pw_aff_get_space( 1159 __isl_keep isl_union_pw_aff *upa); 1160 __isl_give isl_space *isl_union_pw_multi_aff_get_space( 1161 __isl_keep isl_union_pw_multi_aff *upma); 1162 __isl_give isl_space *isl_multi_pw_aff_get_domain_space( 1163 __isl_keep isl_multi_pw_aff *mpa); 1164 __isl_give isl_space *isl_multi_pw_aff_get_space( 1165 __isl_keep isl_multi_pw_aff *mpa); 1166 __isl_give isl_space * 1167 isl_multi_union_pw_aff_get_domain_space( 1168 __isl_keep isl_multi_union_pw_aff *mupa); 1169 __isl_give isl_space * 1170 isl_multi_union_pw_aff_get_space( 1171 __isl_keep isl_multi_union_pw_aff *mupa); 1172 1173 #include <isl/point.h> 1174 __isl_give isl_space *isl_point_get_space( 1175 __isl_keep isl_point *pnt); 1176 1177 #include <isl/fixed_box.h> 1178 __isl_give isl_space *isl_fixed_box_get_space( 1179 __isl_keep isl_fixed_box *box); 1180 1181The number of dimensions of a given type of space 1182may be read off from a space or an object that lives 1183in a space using the following functions. 1184In case of C<isl_space_dim>, type may be 1185C<isl_dim_param>, C<isl_dim_in> (only for relations), 1186C<isl_dim_out> (only for relations), C<isl_dim_set> 1187(only for sets) or C<isl_dim_all>. 1188 1189 #include <isl/space.h> 1190 isl_size isl_space_dim(__isl_keep isl_space *space, 1191 enum isl_dim_type type); 1192 1193 #include <isl/local_space.h> 1194 isl_size isl_local_space_dim(__isl_keep isl_local_space *ls, 1195 enum isl_dim_type type); 1196 1197 #include <isl/set.h> 1198 isl_size isl_basic_set_dim(__isl_keep isl_basic_set *bset, 1199 enum isl_dim_type type); 1200 isl_size isl_set_tuple_dim(__isl_keep isl_set *set); 1201 isl_size isl_set_dim(__isl_keep isl_set *set, 1202 enum isl_dim_type type); 1203 1204 #include <isl/union_set.h> 1205 isl_size isl_union_set_dim(__isl_keep isl_union_set *uset, 1206 enum isl_dim_type type); 1207 1208 #include <isl/map.h> 1209 isl_size isl_basic_map_dim(__isl_keep isl_basic_map *bmap, 1210 enum isl_dim_type type); 1211 isl_size isl_map_domain_tuple_dim( 1212 __isl_keep isl_map *map); 1213 isl_size isl_map_range_tuple_dim( 1214 __isl_keep isl_map *map); 1215 isl_size isl_map_dim(__isl_keep isl_map *map, 1216 enum isl_dim_type type); 1217 1218 #include <isl/union_map.h> 1219 isl_size isl_union_map_dim(__isl_keep isl_union_map *umap, 1220 enum isl_dim_type type); 1221 1222 #include <isl/val.h> 1223 isl_size isl_multi_val_dim(__isl_keep isl_multi_val *mv, 1224 enum isl_dim_type type); 1225 1226 #include <isl/aff.h> 1227 isl_size isl_aff_dim(__isl_keep isl_aff *aff, 1228 enum isl_dim_type type); 1229 isl_size isl_multi_aff_dim(__isl_keep isl_multi_aff *maff, 1230 enum isl_dim_type type); 1231 isl_size isl_pw_aff_dim(__isl_keep isl_pw_aff *pwaff, 1232 enum isl_dim_type type); 1233 isl_size isl_pw_multi_aff_dim( 1234 __isl_keep isl_pw_multi_aff *pma, 1235 enum isl_dim_type type); 1236 isl_size isl_multi_pw_aff_dim( 1237 __isl_keep isl_multi_pw_aff *mpa, 1238 enum isl_dim_type type); 1239 isl_size isl_union_pw_aff_dim( 1240 __isl_keep isl_union_pw_aff *upa, 1241 enum isl_dim_type type); 1242 isl_size isl_union_pw_multi_aff_dim( 1243 __isl_keep isl_union_pw_multi_aff *upma, 1244 enum isl_dim_type type); 1245 isl_size isl_multi_union_pw_aff_dim( 1246 __isl_keep isl_multi_union_pw_aff *mupa, 1247 enum isl_dim_type type); 1248 1249 #include <isl/polynomial.h> 1250 isl_size isl_union_pw_qpolynomial_dim( 1251 __isl_keep isl_union_pw_qpolynomial *upwqp, 1252 enum isl_dim_type type); 1253 isl_size isl_union_pw_qpolynomial_fold_dim( 1254 __isl_keep isl_union_pw_qpolynomial_fold *upwf, 1255 enum isl_dim_type type); 1256 1257Note that an C<isl_union_set>, an C<isl_union_map>, 1258an C<isl_union_pw_multi_aff>, 1259an C<isl_union_pw_qpolynomial> and 1260an C<isl_union_pw_qpolynomial_fold> 1261only have parameters. 1262 1263Additional parameters can be added to a space using the following function. 1264 1265 #include <isl/space.h> 1266 __isl_give isl_space *isl_space_add_param_id( 1267 __isl_take isl_space *space, 1268 __isl_take isl_id *id); 1269 1270If a parameter with the given identifier already appears in the space, 1271then it is not added again. 1272 1273Conversely, all parameters can be removed from a space 1274using the following function. 1275 1276 #include <isl/space.h> 1277 __isl_give isl_space *isl_space_drop_all_params( 1278 __isl_take isl_space *space); 1279 1280The identifiers or names of the individual dimensions of spaces 1281may be set or read off using the following functions on spaces 1282or objects that live in spaces. 1283These functions are mostly useful to obtain the identifiers, positions 1284or names of the parameters. Identifiers of individual dimensions are 1285essentially only useful for printing. They are ignored by all other 1286operations and may not be preserved across those operations. 1287To keep track of a space along with names/identifiers of 1288the set dimensions, use an C<isl_multi_id> as described in 1289L</"Functions">. 1290 1291 #include <isl/space.h> 1292 __isl_give isl_space *isl_space_set_dim_id( 1293 __isl_take isl_space *space, 1294 enum isl_dim_type type, unsigned pos, 1295 __isl_take isl_id *id); 1296 isl_bool isl_space_has_dim_id(__isl_keep isl_space *space, 1297 enum isl_dim_type type, unsigned pos); 1298 __isl_give isl_id *isl_space_get_dim_id( 1299 __isl_keep isl_space *space, 1300 enum isl_dim_type type, unsigned pos); 1301 __isl_give isl_space *isl_space_set_dim_name( 1302 __isl_take isl_space *space, 1303 enum isl_dim_type type, unsigned pos, 1304 __isl_keep const char *name); 1305 isl_bool isl_space_has_dim_name(__isl_keep isl_space *space, 1306 enum isl_dim_type type, unsigned pos); 1307 __isl_keep const char *isl_space_get_dim_name( 1308 __isl_keep isl_space *space, 1309 enum isl_dim_type type, unsigned pos); 1310 1311 #include <isl/local_space.h> 1312 __isl_give isl_local_space *isl_local_space_set_dim_id( 1313 __isl_take isl_local_space *ls, 1314 enum isl_dim_type type, unsigned pos, 1315 __isl_take isl_id *id); 1316 isl_bool isl_local_space_has_dim_id( 1317 __isl_keep isl_local_space *ls, 1318 enum isl_dim_type type, unsigned pos); 1319 __isl_give isl_id *isl_local_space_get_dim_id( 1320 __isl_keep isl_local_space *ls, 1321 enum isl_dim_type type, unsigned pos); 1322 __isl_give isl_local_space *isl_local_space_set_dim_name( 1323 __isl_take isl_local_space *ls, 1324 enum isl_dim_type type, unsigned pos, const char *s); 1325 isl_bool isl_local_space_has_dim_name( 1326 __isl_keep isl_local_space *ls, 1327 enum isl_dim_type type, unsigned pos) 1328 const char *isl_local_space_get_dim_name( 1329 __isl_keep isl_local_space *ls, 1330 enum isl_dim_type type, unsigned pos); 1331 1332 #include <isl/constraint.h> 1333 const char *isl_constraint_get_dim_name( 1334 __isl_keep isl_constraint *constraint, 1335 enum isl_dim_type type, unsigned pos); 1336 1337 #include <isl/set.h> 1338 __isl_give isl_id *isl_basic_set_get_dim_id( 1339 __isl_keep isl_basic_set *bset, 1340 enum isl_dim_type type, unsigned pos); 1341 __isl_give isl_set *isl_set_set_dim_id( 1342 __isl_take isl_set *set, enum isl_dim_type type, 1343 unsigned pos, __isl_take isl_id *id); 1344 isl_bool isl_set_has_dim_id(__isl_keep isl_set *set, 1345 enum isl_dim_type type, unsigned pos); 1346 __isl_give isl_id *isl_set_get_dim_id( 1347 __isl_keep isl_set *set, enum isl_dim_type type, 1348 unsigned pos); 1349 const char *isl_basic_set_get_dim_name( 1350 __isl_keep isl_basic_set *bset, 1351 enum isl_dim_type type, unsigned pos); 1352 isl_bool isl_set_has_dim_name(__isl_keep isl_set *set, 1353 enum isl_dim_type type, unsigned pos); 1354 const char *isl_set_get_dim_name( 1355 __isl_keep isl_set *set, 1356 enum isl_dim_type type, unsigned pos); 1357 1358 #include <isl/map.h> 1359 __isl_give isl_map *isl_map_set_dim_id( 1360 __isl_take isl_map *map, enum isl_dim_type type, 1361 unsigned pos, __isl_take isl_id *id); 1362 isl_bool isl_basic_map_has_dim_id( 1363 __isl_keep isl_basic_map *bmap, 1364 enum isl_dim_type type, unsigned pos); 1365 isl_bool isl_map_has_dim_id(__isl_keep isl_map *map, 1366 enum isl_dim_type type, unsigned pos); 1367 __isl_give isl_id *isl_map_get_dim_id( 1368 __isl_keep isl_map *map, enum isl_dim_type type, 1369 unsigned pos); 1370 __isl_give isl_id *isl_union_map_get_dim_id( 1371 __isl_keep isl_union_map *umap, 1372 enum isl_dim_type type, unsigned pos); 1373 const char *isl_basic_map_get_dim_name( 1374 __isl_keep isl_basic_map *bmap, 1375 enum isl_dim_type type, unsigned pos); 1376 isl_bool isl_map_has_dim_name(__isl_keep isl_map *map, 1377 enum isl_dim_type type, unsigned pos); 1378 const char *isl_map_get_dim_name( 1379 __isl_keep isl_map *map, 1380 enum isl_dim_type type, unsigned pos); 1381 1382 #include <isl/val.h> 1383 __isl_give isl_multi_val *isl_multi_val_set_dim_id( 1384 __isl_take isl_multi_val *mv, 1385 enum isl_dim_type type, unsigned pos, 1386 __isl_take isl_id *id); 1387 __isl_give isl_id *isl_multi_val_get_dim_id( 1388 __isl_keep isl_multi_val *mv, 1389 enum isl_dim_type type, unsigned pos); 1390 __isl_give isl_multi_val *isl_multi_val_set_dim_name( 1391 __isl_take isl_multi_val *mv, 1392 enum isl_dim_type type, unsigned pos, const char *s); 1393 1394 #include <isl/aff.h> 1395 __isl_give isl_aff *isl_aff_set_dim_id( 1396 __isl_take isl_aff *aff, enum isl_dim_type type, 1397 unsigned pos, __isl_take isl_id *id); 1398 __isl_give isl_multi_aff *isl_multi_aff_set_dim_id( 1399 __isl_take isl_multi_aff *maff, 1400 enum isl_dim_type type, unsigned pos, 1401 __isl_take isl_id *id); 1402 __isl_give isl_pw_aff *isl_pw_aff_set_dim_id( 1403 __isl_take isl_pw_aff *pma, 1404 enum isl_dim_type type, unsigned pos, 1405 __isl_take isl_id *id); 1406 __isl_give isl_multi_pw_aff * 1407 isl_multi_pw_aff_set_dim_id( 1408 __isl_take isl_multi_pw_aff *mpa, 1409 enum isl_dim_type type, unsigned pos, 1410 __isl_take isl_id *id); 1411 __isl_give isl_multi_union_pw_aff * 1412 isl_multi_union_pw_aff_set_dim_id( 1413 __isl_take isl_multi_union_pw_aff *mupa, 1414 enum isl_dim_type type, unsigned pos, 1415 __isl_take isl_id *id); 1416 __isl_give isl_id *isl_multi_aff_get_dim_id( 1417 __isl_keep isl_multi_aff *ma, 1418 enum isl_dim_type type, unsigned pos); 1419 isl_bool isl_pw_aff_has_dim_id(__isl_keep isl_pw_aff *pa, 1420 enum isl_dim_type type, unsigned pos); 1421 __isl_give isl_id *isl_pw_aff_get_dim_id( 1422 __isl_keep isl_pw_aff *pa, 1423 enum isl_dim_type type, unsigned pos); 1424 __isl_give isl_id *isl_pw_multi_aff_get_dim_id( 1425 __isl_keep isl_pw_multi_aff *pma, 1426 enum isl_dim_type type, unsigned pos); 1427 __isl_give isl_id *isl_multi_pw_aff_get_dim_id( 1428 __isl_keep isl_multi_pw_aff *mpa, 1429 enum isl_dim_type type, unsigned pos); 1430 __isl_give isl_id *isl_multi_union_pw_aff_get_dim_id( 1431 __isl_keep isl_multi_union_pw_aff *mupa, 1432 enum isl_dim_type type, unsigned pos); 1433 __isl_give isl_aff *isl_aff_set_dim_name( 1434 __isl_take isl_aff *aff, enum isl_dim_type type, 1435 unsigned pos, const char *s); 1436 __isl_give isl_multi_aff *isl_multi_aff_set_dim_name( 1437 __isl_take isl_multi_aff *maff, 1438 enum isl_dim_type type, unsigned pos, const char *s); 1439 __isl_give isl_multi_pw_aff * 1440 isl_multi_pw_aff_set_dim_name( 1441 __isl_take isl_multi_pw_aff *mpa, 1442 enum isl_dim_type type, unsigned pos, const char *s); 1443 __isl_give isl_union_pw_aff * 1444 isl_union_pw_aff_set_dim_name( 1445 __isl_take isl_union_pw_aff *upa, 1446 enum isl_dim_type type, unsigned pos, 1447 const char *s); 1448 __isl_give isl_union_pw_multi_aff * 1449 isl_union_pw_multi_aff_set_dim_name( 1450 __isl_take isl_union_pw_multi_aff *upma, 1451 enum isl_dim_type type, unsigned pos, 1452 const char *s); 1453 __isl_give isl_multi_union_pw_aff * 1454 isl_multi_union_pw_aff_set_dim_name( 1455 __isl_take isl_multi_union_pw_aff *mupa, 1456 enum isl_dim_type type, unsigned pos, 1457 const char *s); 1458 const char *isl_aff_get_dim_name(__isl_keep isl_aff *aff, 1459 enum isl_dim_type type, unsigned pos); 1460 const char *isl_pw_aff_get_dim_name( 1461 __isl_keep isl_pw_aff *pa, 1462 enum isl_dim_type type, unsigned pos); 1463 const char *isl_pw_multi_aff_get_dim_name( 1464 __isl_keep isl_pw_multi_aff *pma, 1465 enum isl_dim_type type, unsigned pos); 1466 1467 #include <isl/polynomial.h> 1468 __isl_give isl_qpolynomial *isl_qpolynomial_set_dim_name( 1469 __isl_take isl_qpolynomial *qp, 1470 enum isl_dim_type type, unsigned pos, 1471 const char *s); 1472 __isl_give isl_pw_qpolynomial * 1473 isl_pw_qpolynomial_set_dim_name( 1474 __isl_take isl_pw_qpolynomial *pwqp, 1475 enum isl_dim_type type, unsigned pos, 1476 const char *s); 1477 __isl_give isl_pw_qpolynomial_fold * 1478 isl_pw_qpolynomial_fold_set_dim_name( 1479 __isl_take isl_pw_qpolynomial_fold *pwf, 1480 enum isl_dim_type type, unsigned pos, 1481 const char *s); 1482 __isl_give isl_union_pw_qpolynomial * 1483 isl_union_pw_qpolynomial_set_dim_name( 1484 __isl_take isl_union_pw_qpolynomial *upwqp, 1485 enum isl_dim_type type, unsigned pos, 1486 const char *s); 1487 __isl_give isl_union_pw_qpolynomial_fold * 1488 isl_union_pw_qpolynomial_fold_set_dim_name( 1489 __isl_take isl_union_pw_qpolynomial_fold *upwf, 1490 enum isl_dim_type type, unsigned pos, 1491 const char *s); 1492 1493Note that C<isl_space_get_name> returns a pointer to some internal 1494data structure, so the result can only be used while the 1495corresponding C<isl_space> is alive. 1496Also note that every function that operates on two sets or relations 1497requires that both arguments have the same parameters. This also 1498means that if one of the arguments has named parameters, then the 1499other needs to have named parameters too and the names need to match. 1500Pairs of C<isl_set>, C<isl_map>, C<isl_union_set> and/or C<isl_union_map> 1501arguments may have different parameters (as long as they are named), 1502in which case the result will have as parameters the union of the parameters of 1503the arguments. 1504 1505Given the identifier or name of a dimension (typically a parameter), 1506its position can be obtained from the following functions. 1507 1508 #include <isl/space.h> 1509 int isl_space_find_dim_by_id(__isl_keep isl_space *space, 1510 enum isl_dim_type type, __isl_keep isl_id *id); 1511 int isl_space_find_dim_by_name(__isl_keep isl_space *space, 1512 enum isl_dim_type type, const char *name); 1513 1514 #include <isl/local_space.h> 1515 int isl_local_space_find_dim_by_name( 1516 __isl_keep isl_local_space *ls, 1517 enum isl_dim_type type, const char *name); 1518 1519 #include <isl/val.h> 1520 int isl_multi_val_find_dim_by_id( 1521 __isl_keep isl_multi_val *mv, 1522 enum isl_dim_type type, __isl_keep isl_id *id); 1523 int isl_multi_val_find_dim_by_name( 1524 __isl_keep isl_multi_val *mv, 1525 enum isl_dim_type type, const char *name); 1526 1527 #include <isl/set.h> 1528 int isl_set_find_dim_by_id(__isl_keep isl_set *set, 1529 enum isl_dim_type type, __isl_keep isl_id *id); 1530 int isl_set_find_dim_by_name(__isl_keep isl_set *set, 1531 enum isl_dim_type type, const char *name); 1532 1533 #include <isl/map.h> 1534 int isl_map_find_dim_by_id(__isl_keep isl_map *map, 1535 enum isl_dim_type type, __isl_keep isl_id *id); 1536 int isl_basic_map_find_dim_by_name( 1537 __isl_keep isl_basic_map *bmap, 1538 enum isl_dim_type type, const char *name); 1539 int isl_map_find_dim_by_name(__isl_keep isl_map *map, 1540 enum isl_dim_type type, const char *name); 1541 int isl_union_map_find_dim_by_name( 1542 __isl_keep isl_union_map *umap, 1543 enum isl_dim_type type, const char *name); 1544 1545 #include <isl/aff.h> 1546 int isl_multi_aff_find_dim_by_id( 1547 __isl_keep isl_multi_aff *ma, 1548 enum isl_dim_type type, __isl_keep isl_id *id); 1549 int isl_multi_pw_aff_find_dim_by_id( 1550 __isl_keep isl_multi_pw_aff *mpa, 1551 enum isl_dim_type type, __isl_keep isl_id *id); 1552 int isl_multi_union_pw_aff_find_dim_by_id( 1553 __isl_keep isl_multi_union_pw_aff *mupa, 1554 enum isl_dim_type type, __isl_keep isl_id *id); 1555 int isl_aff_find_dim_by_name(__isl_keep isl_aff *aff, 1556 enum isl_dim_type type, const char *name); 1557 int isl_multi_aff_find_dim_by_name( 1558 __isl_keep isl_multi_aff *ma, 1559 enum isl_dim_type type, const char *name); 1560 int isl_pw_aff_find_dim_by_name(__isl_keep isl_pw_aff *pa, 1561 enum isl_dim_type type, const char *name); 1562 int isl_multi_pw_aff_find_dim_by_name( 1563 __isl_keep isl_multi_pw_aff *mpa, 1564 enum isl_dim_type type, const char *name); 1565 int isl_pw_multi_aff_find_dim_by_name( 1566 __isl_keep isl_pw_multi_aff *pma, 1567 enum isl_dim_type type, const char *name); 1568 int isl_union_pw_aff_find_dim_by_name( 1569 __isl_keep isl_union_pw_aff *upa, 1570 enum isl_dim_type type, const char *name); 1571 int isl_union_pw_multi_aff_find_dim_by_name( 1572 __isl_keep isl_union_pw_multi_aff *upma, 1573 enum isl_dim_type type, const char *name); 1574 int isl_multi_union_pw_aff_find_dim_by_name( 1575 __isl_keep isl_multi_union_pw_aff *mupa, 1576 enum isl_dim_type type, const char *name); 1577 1578 #include <isl/polynomial.h> 1579 int isl_pw_qpolynomial_find_dim_by_name( 1580 __isl_keep isl_pw_qpolynomial *pwqp, 1581 enum isl_dim_type type, const char *name); 1582 int isl_pw_qpolynomial_fold_find_dim_by_name( 1583 __isl_keep isl_pw_qpolynomial_fold *pwf, 1584 enum isl_dim_type type, const char *name); 1585 int isl_union_pw_qpolynomial_find_dim_by_name( 1586 __isl_keep isl_union_pw_qpolynomial *upwqp, 1587 enum isl_dim_type type, const char *name); 1588 int isl_union_pw_qpolynomial_fold_find_dim_by_name( 1589 __isl_keep isl_union_pw_qpolynomial_fold *upwf, 1590 enum isl_dim_type type, const char *name); 1591 1592The identifiers or names of entire spaces may be set or read off 1593using the following functions. 1594 1595 #include <isl/space.h> 1596 __isl_give isl_space *isl_space_set_domain_tuple_id( 1597 __isl_take isl_space *space, 1598 __isl_take isl_id *id); 1599 __isl_give isl_space *isl_space_set_range_tuple_id( 1600 __isl_take isl_space *space, 1601 __isl_take isl_id *id); 1602 __isl_give isl_space *isl_space_set_tuple_id( 1603 __isl_take isl_space *space, 1604 enum isl_dim_type type, __isl_take isl_id *id); 1605 __isl_give isl_space *isl_space_reset_tuple_id( 1606 __isl_take isl_space *space, enum isl_dim_type type); 1607 isl_bool isl_space_has_domain_tuple_id( 1608 __isl_keep isl_space *space); 1609 isl_bool isl_space_has_range_tuple_id( 1610 __isl_keep isl_space *space); 1611 isl_bool isl_space_has_tuple_id( 1612 __isl_keep isl_space *space, 1613 enum isl_dim_type type); 1614 __isl_give isl_id *isl_space_get_domain_tuple_id( 1615 __isl_keep isl_space *space); 1616 __isl_give isl_id *isl_space_get_range_tuple_id( 1617 __isl_keep isl_space *space); 1618 __isl_give isl_id *isl_space_get_tuple_id( 1619 __isl_keep isl_space *space, enum isl_dim_type type); 1620 __isl_give isl_space *isl_space_set_tuple_name( 1621 __isl_take isl_space *space, 1622 enum isl_dim_type type, const char *s); 1623 isl_bool isl_space_has_tuple_name( 1624 __isl_keep isl_space *space, 1625 enum isl_dim_type type); 1626 __isl_keep const char *isl_space_get_tuple_name( 1627 __isl_keep isl_space *space, 1628 enum isl_dim_type type); 1629 1630 #include <isl/local_space.h> 1631 __isl_give isl_local_space *isl_local_space_set_tuple_id( 1632 __isl_take isl_local_space *ls, 1633 enum isl_dim_type type, __isl_take isl_id *id); 1634 1635 #include <isl/set.h> 1636 __isl_give isl_basic_set *isl_basic_set_set_tuple_id( 1637 __isl_take isl_basic_set *bset, 1638 __isl_take isl_id *id); 1639 __isl_give isl_set *isl_set_set_tuple_id( 1640 __isl_take isl_set *set, __isl_take isl_id *id); 1641 __isl_give isl_set *isl_set_reset_tuple_id( 1642 __isl_take isl_set *set); 1643 isl_bool isl_set_has_tuple_id(__isl_keep isl_set *set); 1644 __isl_give isl_id *isl_set_get_tuple_id( 1645 __isl_keep isl_set *set); 1646 __isl_give isl_basic_set *isl_basic_set_set_tuple_name( 1647 __isl_take isl_basic_set *set, const char *s); 1648 __isl_give isl_set *isl_set_set_tuple_name( 1649 __isl_take isl_set *set, const char *s); 1650 const char *isl_basic_set_get_tuple_name( 1651 __isl_keep isl_basic_set *bset); 1652 isl_bool isl_set_has_tuple_name(__isl_keep isl_set *set); 1653 const char *isl_set_get_tuple_name( 1654 __isl_keep isl_set *set); 1655 1656 #include <isl/map.h> 1657 __isl_give isl_basic_map *isl_basic_map_set_tuple_id( 1658 __isl_take isl_basic_map *bmap, 1659 enum isl_dim_type type, __isl_take isl_id *id); 1660 __isl_give isl_map *isl_map_set_domain_tuple_id( 1661 __isl_take isl_map *map, __isl_take isl_id *id); 1662 __isl_give isl_map *isl_map_set_range_tuple_id( 1663 __isl_take isl_map *map, __isl_take isl_id *id); 1664 __isl_give isl_map *isl_map_set_tuple_id( 1665 __isl_take isl_map *map, enum isl_dim_type type, 1666 __isl_take isl_id *id); 1667 __isl_give isl_map *isl_map_reset_tuple_id( 1668 __isl_take isl_map *map, enum isl_dim_type type); 1669 isl_bool isl_map_has_domain_tuple_id( 1670 __isl_keep isl_map *map); 1671 isl_bool isl_map_has_range_tuple_id( 1672 __isl_keep isl_map *map); 1673 isl_bool isl_map_has_tuple_id(__isl_keep isl_map *map, 1674 enum isl_dim_type type); 1675 __isl_give isl_id *isl_map_get_domain_tuple_id( 1676 __isl_keep isl_map *map); 1677 __isl_give isl_id *isl_map_get_range_tuple_id( 1678 __isl_keep isl_map *map); 1679 __isl_give isl_id *isl_map_get_tuple_id( 1680 __isl_keep isl_map *map, enum isl_dim_type type); 1681 __isl_give isl_map *isl_map_set_tuple_name( 1682 __isl_take isl_map *map, 1683 enum isl_dim_type type, const char *s); 1684 const char *isl_basic_map_get_tuple_name( 1685 __isl_keep isl_basic_map *bmap, 1686 enum isl_dim_type type); 1687 __isl_give isl_basic_map *isl_basic_map_set_tuple_name( 1688 __isl_take isl_basic_map *bmap, 1689 enum isl_dim_type type, const char *s); 1690 isl_bool isl_map_has_tuple_name(__isl_keep isl_map *map, 1691 enum isl_dim_type type); 1692 const char *isl_map_get_tuple_name( 1693 __isl_keep isl_map *map, 1694 enum isl_dim_type type); 1695 1696 #include <isl/val.h> 1697 __isl_give isl_multi_val *isl_multi_val_set_range_tuple_id( 1698 __isl_take isl_multi_val *mv, 1699 __isl_take isl_id *id); 1700 __isl_give isl_multi_val *isl_multi_val_set_tuple_id( 1701 __isl_take isl_multi_val *mv, 1702 enum isl_dim_type type, __isl_take isl_id *id); 1703 __isl_give isl_multi_val * 1704 isl_multi_val_reset_range_tuple_id( 1705 __isl_take isl_multi_val *mv); 1706 __isl_give isl_multi_val *isl_multi_val_reset_tuple_id( 1707 __isl_take isl_multi_val *mv, 1708 enum isl_dim_type type); 1709 isl_bool isl_multi_val_has_range_tuple_id( 1710 __isl_keep isl_multi_val *mv); 1711 __isl_give isl_id *isl_multi_val_get_range_tuple_id( 1712 __isl_keep isl_multi_val *mv); 1713 isl_bool isl_multi_val_has_tuple_id( 1714 __isl_keep isl_multi_val *mv, 1715 enum isl_dim_type type); 1716 __isl_give isl_id *isl_multi_val_get_tuple_id( 1717 __isl_keep isl_multi_val *mv, 1718 enum isl_dim_type type); 1719 __isl_give isl_multi_val *isl_multi_val_set_tuple_name( 1720 __isl_take isl_multi_val *mv, 1721 enum isl_dim_type type, const char *s); 1722 const char *isl_multi_val_get_tuple_name( 1723 __isl_keep isl_multi_val *mv, 1724 enum isl_dim_type type); 1725 1726 #include <isl/aff.h> 1727 __isl_give isl_aff *isl_aff_set_tuple_id( 1728 __isl_take isl_aff *aff, 1729 enum isl_dim_type type, __isl_take isl_id *id); 1730 __isl_give isl_multi_aff *isl_multi_aff_set_range_tuple_id( 1731 __isl_take isl_multi_aff *ma, 1732 __isl_take isl_id *id); 1733 __isl_give isl_multi_aff *isl_multi_aff_set_tuple_id( 1734 __isl_take isl_multi_aff *maff, 1735 enum isl_dim_type type, __isl_take isl_id *id); 1736 __isl_give isl_pw_aff *isl_pw_aff_set_tuple_id( 1737 __isl_take isl_pw_aff *pwaff, 1738 enum isl_dim_type type, __isl_take isl_id *id); 1739 __isl_give isl_pw_multi_aff * 1740 isl_pw_multi_aff_set_range_tuple_id( 1741 __isl_take isl_pw_multi_aff *pma, 1742 __isl_take isl_id *id); 1743 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_set_tuple_id( 1744 __isl_take isl_pw_multi_aff *pma, 1745 enum isl_dim_type type, __isl_take isl_id *id); 1746 __isl_give isl_multi_pw_aff * 1747 isl_multi_pw_aff_set_range_tuple_id( 1748 __isl_take isl_multi_pw_aff *mpa, 1749 __isl_take isl_id *id); 1750 __isl_give isl_multi_union_pw_aff * 1751 isl_multi_union_pw_aff_set_range_tuple_id( 1752 __isl_take isl_multi_union_pw_aff *mupa, 1753 __isl_take isl_id *id); 1754 __isl_give isl_multi_union_pw_aff * 1755 isl_multi_union_pw_aff_set_tuple_id( 1756 __isl_take isl_multi_union_pw_aff *mupa, 1757 enum isl_dim_type type, __isl_take isl_id *id); 1758 __isl_give isl_multi_aff * 1759 isl_multi_aff_reset_range_tuple_id( 1760 __isl_take isl_multi_aff *ma); 1761 __isl_give isl_multi_pw_aff * 1762 isl_multi_pw_aff_reset_range_tuple_id( 1763 __isl_take isl_multi_pw_aff *mpa); 1764 __isl_give isl_multi_union_pw_aff * 1765 isl_multi_union_pw_aff_reset_range_tuple_id( 1766 __isl_take isl_multi_union_pw_aff *mupa); 1767 __isl_give isl_multi_aff *isl_multi_aff_reset_tuple_id( 1768 __isl_take isl_multi_aff *ma, 1769 enum isl_dim_type type); 1770 __isl_give isl_pw_aff *isl_pw_aff_reset_tuple_id( 1771 __isl_take isl_pw_aff *pa, 1772 enum isl_dim_type type); 1773 __isl_give isl_multi_pw_aff * 1774 isl_multi_pw_aff_reset_tuple_id( 1775 __isl_take isl_multi_pw_aff *mpa, 1776 enum isl_dim_type type); 1777 __isl_give isl_pw_multi_aff * 1778 isl_pw_multi_aff_reset_tuple_id( 1779 __isl_take isl_pw_multi_aff *pma, 1780 enum isl_dim_type type); 1781 __isl_give isl_multi_union_pw_aff * 1782 isl_multi_union_pw_aff_reset_tuple_id( 1783 __isl_take isl_multi_union_pw_aff *mupa, 1784 enum isl_dim_type type); 1785 isl_bool isl_multi_aff_has_range_tuple_id( 1786 __isl_keep isl_multi_aff *ma); 1787 __isl_give isl_id *isl_multi_aff_get_range_tuple_id( 1788 __isl_keep isl_multi_aff *ma); 1789 isl_bool isl_multi_aff_has_tuple_id( 1790 __isl_keep isl_multi_aff *ma, 1791 enum isl_dim_type type); 1792 __isl_give isl_id *isl_multi_aff_get_tuple_id( 1793 __isl_keep isl_multi_aff *ma, 1794 enum isl_dim_type type); 1795 isl_bool isl_pw_aff_has_tuple_id(__isl_keep isl_pw_aff *pa, 1796 enum isl_dim_type type); 1797 __isl_give isl_id *isl_pw_aff_get_tuple_id( 1798 __isl_keep isl_pw_aff *pa, 1799 enum isl_dim_type type); 1800 isl_bool isl_pw_multi_aff_has_range_tuple_id( 1801 __isl_keep isl_pw_multi_aff *pma); 1802 isl_bool isl_pw_multi_aff_has_tuple_id( 1803 __isl_keep isl_pw_multi_aff *pma, 1804 enum isl_dim_type type); 1805 __isl_give isl_id *isl_pw_multi_aff_get_range_tuple_id( 1806 __isl_keep isl_pw_multi_aff *pma); 1807 __isl_give isl_id *isl_pw_multi_aff_get_tuple_id( 1808 __isl_keep isl_pw_multi_aff *pma, 1809 enum isl_dim_type type); 1810 isl_bool isl_multi_pw_aff_has_range_tuple_id( 1811 __isl_keep isl_multi_pw_aff *mpa); 1812 __isl_give isl_id *isl_multi_pw_aff_get_range_tuple_id( 1813 __isl_keep isl_multi_pw_aff *mpa); 1814 isl_bool isl_multi_pw_aff_has_tuple_id( 1815 __isl_keep isl_multi_pw_aff *mpa, 1816 enum isl_dim_type type); 1817 __isl_give isl_id *isl_multi_pw_aff_get_tuple_id( 1818 __isl_keep isl_multi_pw_aff *mpa, 1819 enum isl_dim_type type); 1820 isl_bool isl_multi_union_pw_aff_has_range_tuple_id( 1821 __isl_keep isl_multi_union_pw_aff *mupa); 1822 __isl_give isl_id * 1823 isl_multi_union_pw_aff_get_range_tuple_id( 1824 __isl_keep isl_multi_union_pw_aff *mupa); 1825 isl_bool isl_multi_union_pw_aff_has_tuple_id( 1826 __isl_keep isl_multi_union_pw_aff *mupa, 1827 enum isl_dim_type type); 1828 __isl_give isl_id *isl_multi_union_pw_aff_get_tuple_id( 1829 __isl_keep isl_multi_union_pw_aff *mupa, 1830 enum isl_dim_type type); 1831 __isl_give isl_multi_aff *isl_multi_aff_set_tuple_name( 1832 __isl_take isl_multi_aff *maff, 1833 enum isl_dim_type type, const char *s); 1834 __isl_give isl_multi_pw_aff * 1835 isl_multi_pw_aff_set_tuple_name( 1836 __isl_take isl_multi_pw_aff *mpa, 1837 enum isl_dim_type type, const char *s); 1838 __isl_give isl_multi_union_pw_aff * 1839 isl_multi_union_pw_aff_set_tuple_name( 1840 __isl_take isl_multi_union_pw_aff *mupa, 1841 enum isl_dim_type type, const char *s); 1842 const char *isl_multi_aff_get_tuple_name( 1843 __isl_keep isl_multi_aff *multi, 1844 enum isl_dim_type type); 1845 isl_bool isl_pw_multi_aff_has_tuple_name( 1846 __isl_keep isl_pw_multi_aff *pma, 1847 enum isl_dim_type type); 1848 const char *isl_pw_multi_aff_get_tuple_name( 1849 __isl_keep isl_pw_multi_aff *pma, 1850 enum isl_dim_type type); 1851 const char *isl_multi_union_pw_aff_get_tuple_name( 1852 __isl_keep isl_multi_union_pw_aff *mupa, 1853 enum isl_dim_type type); 1854 1855The C<type> argument needs to be one of C<isl_dim_in>, C<isl_dim_out> 1856or C<isl_dim_set>. As with C<isl_space_get_name>, 1857the C<isl_space_get_tuple_name> function returns a pointer to some internal 1858data structure. 1859Binary operations require the corresponding spaces of their arguments 1860to have the same name. 1861 1862To keep the names of all parameters and tuples, but reset the user pointers 1863of all the corresponding identifiers, use the following function. 1864 1865 #include <isl/space.h> 1866 __isl_give isl_space *isl_space_reset_user( 1867 __isl_take isl_space *space); 1868 1869 #include <isl/set.h> 1870 __isl_give isl_set *isl_set_reset_user( 1871 __isl_take isl_set *set); 1872 1873 #include <isl/map.h> 1874 __isl_give isl_map *isl_map_reset_user( 1875 __isl_take isl_map *map); 1876 1877 #include <isl/union_set.h> 1878 __isl_give isl_union_set *isl_union_set_reset_user( 1879 __isl_take isl_union_set *uset); 1880 1881 #include <isl/union_map.h> 1882 __isl_give isl_union_map *isl_union_map_reset_user( 1883 __isl_take isl_union_map *umap); 1884 1885 #include <isl/id.h> 1886 __isl_give isl_multi_id *isl_multi_id_reset_user( 1887 __isl_take isl_multi_id *mi); 1888 1889 #include <isl/val.h> 1890 __isl_give isl_multi_val *isl_multi_val_reset_user( 1891 __isl_take isl_multi_val *mv); 1892 1893 #include <isl/aff.h> 1894 __isl_give isl_multi_aff *isl_multi_aff_reset_user( 1895 __isl_take isl_multi_aff *ma); 1896 __isl_give isl_pw_aff *isl_pw_aff_reset_user( 1897 __isl_take isl_pw_aff *pa); 1898 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_reset_user( 1899 __isl_take isl_multi_pw_aff *mpa); 1900 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_reset_user( 1901 __isl_take isl_pw_multi_aff *pma); 1902 __isl_give isl_union_pw_aff *isl_union_pw_aff_reset_user( 1903 __isl_take isl_union_pw_aff *upa); 1904 __isl_give isl_multi_union_pw_aff * 1905 isl_multi_union_pw_aff_reset_user( 1906 __isl_take isl_multi_union_pw_aff *mupa); 1907 __isl_give isl_union_pw_multi_aff * 1908 isl_union_pw_multi_aff_reset_user( 1909 __isl_take isl_union_pw_multi_aff *upma); 1910 1911 #include <isl/polynomial.h> 1912 __isl_give isl_pw_qpolynomial * 1913 isl_pw_qpolynomial_reset_user( 1914 __isl_take isl_pw_qpolynomial *pwqp); 1915 __isl_give isl_union_pw_qpolynomial * 1916 isl_union_pw_qpolynomial_reset_user( 1917 __isl_take isl_union_pw_qpolynomial *upwqp); 1918 __isl_give isl_pw_qpolynomial_fold * 1919 isl_pw_qpolynomial_fold_reset_user( 1920 __isl_take isl_pw_qpolynomial_fold *pwf); 1921 __isl_give isl_union_pw_qpolynomial_fold * 1922 isl_union_pw_qpolynomial_fold_reset_user( 1923 __isl_take isl_union_pw_qpolynomial_fold *upwf); 1924 1925Spaces can be nested. In particular, the domain of a set or 1926the domain or range of a relation can be a nested relation. 1927This process is also called I<wrapping>. 1928The functions for detecting, constructing and deconstructing 1929such nested spaces can be found in the wrapping properties 1930of L</"Unary Properties">, the wrapping operations 1931of L</"Unary Operations"> and the Cartesian product operations 1932of L</"Basic Operations">. 1933 1934Spaces can be created from other spaces 1935using the functions described in L</"Unary Operations"> 1936and L</"Binary Operations">. 1937 1938=head2 Local Spaces 1939 1940A local space is essentially a space with 1941zero or more existentially quantified variables. 1942The local space of various objects can be obtained 1943using the following functions. 1944 1945 #include <isl/constraint.h> 1946 __isl_give isl_local_space *isl_constraint_get_local_space( 1947 __isl_keep isl_constraint *constraint); 1948 1949 #include <isl/set.h> 1950 __isl_give isl_local_space *isl_basic_set_get_local_space( 1951 __isl_keep isl_basic_set *bset); 1952 1953 #include <isl/map.h> 1954 __isl_give isl_local_space *isl_basic_map_get_local_space( 1955 __isl_keep isl_basic_map *bmap); 1956 1957 #include <isl/aff.h> 1958 __isl_give isl_local_space *isl_aff_get_domain_local_space( 1959 __isl_keep isl_aff *aff); 1960 __isl_give isl_local_space *isl_aff_get_local_space( 1961 __isl_keep isl_aff *aff); 1962 1963A new local space can be created from a space using 1964 1965 #include <isl/local_space.h> 1966 __isl_give isl_local_space *isl_local_space_from_space( 1967 __isl_take isl_space *space); 1968 1969They can be inspected, modified, copied and freed using the following functions. 1970 1971 #include <isl/local_space.h> 1972 isl_bool isl_local_space_is_params( 1973 __isl_keep isl_local_space *ls); 1974 isl_bool isl_local_space_is_set( 1975 __isl_keep isl_local_space *ls); 1976 __isl_give isl_space *isl_local_space_get_space( 1977 __isl_keep isl_local_space *ls); 1978 __isl_give isl_aff *isl_local_space_get_div( 1979 __isl_keep isl_local_space *ls, int pos); 1980 __isl_give isl_local_space *isl_local_space_copy( 1981 __isl_keep isl_local_space *ls); 1982 __isl_null isl_local_space *isl_local_space_free( 1983 __isl_take isl_local_space *ls); 1984 1985Note that C<isl_local_space_get_div> can only be used on local spaces 1986of sets. 1987 1988Two local spaces can be compared using 1989 1990 isl_bool isl_local_space_is_equal( 1991 __isl_keep isl_local_space *ls1, 1992 __isl_keep isl_local_space *ls2); 1993 1994Local spaces can be created from other local spaces 1995using the functions described in L</"Unary Operations"> 1996and L</"Binary Operations">. 1997 1998=head2 Creating New Sets and Relations 1999 2000C<isl> has functions for creating some standard sets and relations. 2001 2002=over 2003 2004=item * Empty sets and relations 2005 2006 __isl_give isl_basic_set *isl_basic_set_empty( 2007 __isl_take isl_space *space); 2008 __isl_give isl_basic_map *isl_basic_map_empty( 2009 __isl_take isl_space *space); 2010 __isl_give isl_set *isl_set_empty( 2011 __isl_take isl_space *space); 2012 __isl_give isl_map *isl_map_empty( 2013 __isl_take isl_space *space); 2014 __isl_give isl_union_set *isl_union_set_empty_ctx( 2015 isl_ctx *ctx); 2016 __isl_give isl_union_set *isl_union_set_empty_space( 2017 __isl_take isl_space *space); 2018 __isl_give isl_union_set *isl_union_set_empty( 2019 __isl_take isl_space *space); 2020 __isl_give isl_union_map *isl_union_map_empty_ctx( 2021 isl_ctx *ctx); 2022 __isl_give isl_union_map *isl_union_map_empty_space( 2023 __isl_take isl_space *space); 2024 __isl_give isl_union_map *isl_union_map_empty( 2025 __isl_take isl_space *space); 2026 2027For C<isl_union_set>s and C<isl_union_map>s, the space 2028is only used to specify the parameters. 2029C<isl_union_set_empty> is an alternative name for 2030C<isl_union_set_empty_space>. 2031Similarly for the other pair of functions. 2032 2033=item * Universe sets and relations 2034 2035 #include <isl/set.h> 2036 __isl_give isl_basic_set *isl_basic_set_universe( 2037 __isl_take isl_space *space); 2038 __isl_give isl_set *isl_set_universe( 2039 __isl_take isl_space *space); 2040 __isl_give isl_set *isl_space_universe_set( 2041 __isl_take isl_space *space); 2042 2043 #include <isl/map.h> 2044 __isl_give isl_basic_map *isl_basic_map_universe( 2045 __isl_take isl_space *space); 2046 __isl_give isl_map *isl_map_universe( 2047 __isl_take isl_space *space); 2048 __isl_give isl_map *isl_space_universe_map( 2049 __isl_take isl_space *space); 2050 2051 #include <isl/union_set.h> 2052 __isl_give isl_union_set *isl_union_set_universe( 2053 __isl_take isl_union_set *uset); 2054 2055 #include <isl/union_map.h> 2056 __isl_give isl_union_map *isl_union_map_universe( 2057 __isl_take isl_union_map *umap); 2058 2059C<isl_set_universe> and C<isl_space_universe_set> 2060perform the same operation. 2061Similarly 2062for the pair C<isl_map_universe> and C<isl_space_universe_map>. 2063 2064The sets and relations constructed by the functions above 2065contain all integer values, while those constructed by the 2066functions below only contain non-negative values. 2067 2068 __isl_give isl_basic_set *isl_basic_set_nat_universe( 2069 __isl_take isl_space *space); 2070 __isl_give isl_basic_map *isl_basic_map_nat_universe( 2071 __isl_take isl_space *space); 2072 __isl_give isl_set *isl_set_nat_universe( 2073 __isl_take isl_space *space); 2074 __isl_give isl_map *isl_map_nat_universe( 2075 __isl_take isl_space *space); 2076 2077=item * Identity relations 2078 2079 __isl_give isl_basic_map *isl_basic_map_identity( 2080 __isl_take isl_space *space); 2081 __isl_give isl_map *isl_map_identity( 2082 __isl_take isl_space *space); 2083 2084The number of input and output dimensions in C<space> needs 2085to be the same. 2086 2087=item * Lexicographic order 2088 2089 __isl_give isl_map *isl_map_lex_lt( 2090 __isl_take isl_space *set_space); 2091 __isl_give isl_map *isl_map_lex_le( 2092 __isl_take isl_space *set_space); 2093 __isl_give isl_map *isl_map_lex_gt( 2094 __isl_take isl_space *set_space); 2095 __isl_give isl_map *isl_map_lex_ge( 2096 __isl_take isl_space *set_space); 2097 __isl_give isl_map *isl_map_lex_lt_first( 2098 __isl_take isl_space *space, unsigned n); 2099 __isl_give isl_map *isl_map_lex_le_first( 2100 __isl_take isl_space *space, unsigned n); 2101 __isl_give isl_map *isl_map_lex_gt_first( 2102 __isl_take isl_space *space, unsigned n); 2103 __isl_give isl_map *isl_map_lex_ge_first( 2104 __isl_take isl_space *space, unsigned n); 2105 2106The first four functions take a space for a B<set> 2107and return relations that express that the elements in the domain 2108are lexicographically less 2109(C<isl_map_lex_lt>), less or equal (C<isl_map_lex_le>), 2110greater (C<isl_map_lex_gt>) or greater or equal (C<isl_map_lex_ge>) 2111than the elements in the range. 2112The last four functions take a space for a map 2113and return relations that express that the first C<n> dimensions 2114in the domain are lexicographically less 2115(C<isl_map_lex_lt_first>), less or equal (C<isl_map_lex_le_first>), 2116greater (C<isl_map_lex_gt_first>) or greater or equal (C<isl_map_lex_ge_first>) 2117than the first C<n> dimensions in the range. 2118 2119=back 2120 2121A basic set or relation can be converted to a set or relation 2122using the following functions. 2123 2124 __isl_give isl_set *isl_basic_set_to_set( 2125 __isl_take isl_basic_set *bset); 2126 __isl_give isl_set *isl_set_from_basic_set( 2127 __isl_take isl_basic_set *bset); 2128 __isl_give isl_map *isl_map_from_basic_map( 2129 __isl_take isl_basic_map *bmap); 2130 2131C<isl_basic_set_to_set> and C<isl_set_from_basic_set> perform 2132the same operation. 2133 2134Sets and relations can be converted to union sets and relations 2135using the following functions. 2136 2137 __isl_give isl_union_set *isl_union_set_from_basic_set( 2138 __isl_take isl_basic_set *bset); 2139 __isl_give isl_union_map *isl_union_map_from_basic_map( 2140 __isl_take isl_basic_map *bmap); 2141 __isl_give isl_union_set *isl_set_to_union_set( 2142 __isl_take isl_set *set); 2143 __isl_give isl_union_set *isl_union_set_from_set( 2144 __isl_take isl_set *set); 2145 __isl_give isl_union_map *isl_map_to_union_map( 2146 __isl_take isl_map *map); 2147 __isl_give isl_union_map *isl_union_map_from_map( 2148 __isl_take isl_map *map); 2149 2150C<isl_map_to_union_map> and C<isl_union_map_from_map> perform 2151the same operation. 2152Similarly for C<isl_set_to_union_set> and C<isl_union_set_from_set>. 2153 2154The inverse conversions below can only be used if the input 2155union set or relation is known to contain elements in exactly one 2156space. 2157 2158 #include <isl/union_set.h> 2159 isl_bool isl_union_set_isa_set( 2160 __isl_keep isl_union_set *uset); 2161 __isl_give isl_set *isl_union_set_as_set( 2162 __isl_take isl_union_set *uset); 2163 __isl_give isl_set *isl_set_from_union_set( 2164 __isl_take isl_union_set *uset); 2165 2166 #include <isl/union_map.h> 2167 isl_bool isl_union_map_isa_map( 2168 __isl_keep isl_union_map *umap); 2169 __isl_give isl_map *isl_union_map_as_map( 2170 __isl_take isl_union_map *umap); 2171 __isl_give isl_map *isl_map_from_union_map( 2172 __isl_take isl_union_map *umap); 2173 2174C<isl_union_map_as_map> and C<isl_map_from_union_map> perform 2175the same operation. 2176Similarly for C<isl_union_set_as_set> and C<isl_set_from_union_set>. 2177 2178Sets and relations can be copied and freed again using the following 2179functions. 2180 2181 __isl_give isl_basic_set *isl_basic_set_copy( 2182 __isl_keep isl_basic_set *bset); 2183 __isl_give isl_set *isl_set_copy(__isl_keep isl_set *set); 2184 __isl_give isl_union_set *isl_union_set_copy( 2185 __isl_keep isl_union_set *uset); 2186 __isl_give isl_basic_map *isl_basic_map_copy( 2187 __isl_keep isl_basic_map *bmap); 2188 __isl_give isl_map *isl_map_copy(__isl_keep isl_map *map); 2189 __isl_give isl_union_map *isl_union_map_copy( 2190 __isl_keep isl_union_map *umap); 2191 __isl_null isl_basic_set *isl_basic_set_free( 2192 __isl_take isl_basic_set *bset); 2193 __isl_null isl_set *isl_set_free(__isl_take isl_set *set); 2194 __isl_null isl_union_set *isl_union_set_free( 2195 __isl_take isl_union_set *uset); 2196 __isl_null isl_basic_map *isl_basic_map_free( 2197 __isl_take isl_basic_map *bmap); 2198 __isl_null isl_map *isl_map_free(__isl_take isl_map *map); 2199 __isl_null isl_union_map *isl_union_map_free( 2200 __isl_take isl_union_map *umap); 2201 2202Other sets and relations can be constructed by starting 2203from a universe set or relation, adding equality and/or 2204inequality constraints and then projecting out the 2205existentially quantified variables, if any. 2206Constraints can be constructed, manipulated and 2207added to (or removed from) (basic) sets and relations 2208using the following functions. 2209 2210 #include <isl/constraint.h> 2211 __isl_give isl_constraint *isl_constraint_alloc_equality( 2212 __isl_take isl_local_space *ls); 2213 __isl_give isl_constraint *isl_constraint_alloc_inequality( 2214 __isl_take isl_local_space *ls); 2215 __isl_give isl_constraint *isl_constraint_set_constant_si( 2216 __isl_take isl_constraint *constraint, int v); 2217 __isl_give isl_constraint *isl_constraint_set_constant_val( 2218 __isl_take isl_constraint *constraint, 2219 __isl_take isl_val *v); 2220 __isl_give isl_constraint *isl_constraint_set_coefficient_si( 2221 __isl_take isl_constraint *constraint, 2222 enum isl_dim_type type, int pos, int v); 2223 __isl_give isl_constraint * 2224 isl_constraint_set_coefficient_val( 2225 __isl_take isl_constraint *constraint, 2226 enum isl_dim_type type, int pos, 2227 __isl_take isl_val *v); 2228 __isl_give isl_basic_map *isl_basic_map_add_constraint( 2229 __isl_take isl_basic_map *bmap, 2230 __isl_take isl_constraint *constraint); 2231 __isl_give isl_basic_set *isl_basic_set_add_constraint( 2232 __isl_take isl_basic_set *bset, 2233 __isl_take isl_constraint *constraint); 2234 __isl_give isl_map *isl_map_add_constraint( 2235 __isl_take isl_map *map, 2236 __isl_take isl_constraint *constraint); 2237 __isl_give isl_set *isl_set_add_constraint( 2238 __isl_take isl_set *set, 2239 __isl_take isl_constraint *constraint); 2240 2241For example, to create a set containing the even integers 2242between 10 and 42, you could use the following code. 2243 2244 isl_space *space; 2245 isl_local_space *ls; 2246 isl_constraint *c; 2247 isl_basic_set *bset; 2248 2249 space = isl_space_set_alloc(ctx, 0, 2); 2250 bset = isl_basic_set_universe(isl_space_copy(space)); 2251 ls = isl_local_space_from_space(space); 2252 2253 c = isl_constraint_alloc_equality(isl_local_space_copy(ls)); 2254 c = isl_constraint_set_coefficient_si(c, isl_dim_set, 0, -1); 2255 c = isl_constraint_set_coefficient_si(c, isl_dim_set, 1, 2); 2256 bset = isl_basic_set_add_constraint(bset, c); 2257 2258 c = isl_constraint_alloc_inequality(isl_local_space_copy(ls)); 2259 c = isl_constraint_set_constant_si(c, -10); 2260 c = isl_constraint_set_coefficient_si(c, isl_dim_set, 0, 1); 2261 bset = isl_basic_set_add_constraint(bset, c); 2262 2263 c = isl_constraint_alloc_inequality(ls); 2264 c = isl_constraint_set_constant_si(c, 42); 2265 c = isl_constraint_set_coefficient_si(c, isl_dim_set, 0, -1); 2266 bset = isl_basic_set_add_constraint(bset, c); 2267 2268 bset = isl_basic_set_project_out(bset, isl_dim_set, 1, 1); 2269 2270However, this is considered to be a fairly low-level approach. 2271It is more appropriate to construct a (basic) set by means 2272of affine expressions (defined below in L</"Functions">). 2273For example, the same set could be constructed as follows. 2274 2275 isl_val *v, *two; 2276 isl_space *space; 2277 isl_multi_aff *ma; 2278 isl_aff *var, *cst; 2279 isl_basic_set *bset; 2280 2281 space = isl_space_unit(ctx); 2282 space = isl_space_add_unnamed_tuple_ui(space, 1); 2283 ma = isl_multi_aff_identity_on_domain_space( 2284 isl_space_copy(space)); 2285 var = isl_multi_aff_get_at(ma, 0); 2286 v = isl_val_int_from_si(ctx, 10); 2287 cst = isl_aff_val_on_domain_space(isl_space_copy(space), v); 2288 bset = isl_aff_ge_basic_set(isl_aff_copy(var), cst); 2289 2290 v = isl_val_int_from_si(ctx, 42); 2291 cst = isl_aff_val_on_domain_space(space, v); 2292 bset = isl_basic_set_intersect(bset, 2293 isl_aff_le_basic_set(var, cst)); 2294 2295 two = isl_val_int_from_si(ctx, 2); 2296 ma = isl_multi_aff_scale_val(ma, isl_val_copy(two)); 2297 bset = isl_basic_set_preimage_multi_aff(bset, 2298 isl_multi_aff_copy(ma)); 2299 ma = isl_multi_aff_scale_down_val(ma, isl_val_copy(two)); 2300 ma = isl_multi_aff_scale_down_val(ma, two); 2301 bset = isl_basic_set_preimage_multi_aff(bset, ma); 2302 2303Alternatively, the set can be parsed from a string representation. 2304 2305 isl_basic_set *bset; 2306 bset = isl_basic_set_read_from_str(ctx, 2307 "{[i] : exists (a : i = 2a and i >= 10 and i <= 42)}"); 2308 2309A basic set or relation can also be constructed from two matrices 2310describing the equalities and the inequalities. 2311 2312 __isl_give isl_basic_set *isl_basic_set_from_constraint_matrices( 2313 __isl_take isl_space *space, 2314 __isl_take isl_mat *eq, __isl_take isl_mat *ineq, 2315 enum isl_dim_type c1, 2316 enum isl_dim_type c2, enum isl_dim_type c3, 2317 enum isl_dim_type c4); 2318 __isl_give isl_basic_map *isl_basic_map_from_constraint_matrices( 2319 __isl_take isl_space *space, 2320 __isl_take isl_mat *eq, __isl_take isl_mat *ineq, 2321 enum isl_dim_type c1, 2322 enum isl_dim_type c2, enum isl_dim_type c3, 2323 enum isl_dim_type c4, enum isl_dim_type c5); 2324 2325The C<isl_dim_type> arguments indicate the order in which 2326different kinds of variables appear in the input matrices 2327and should be a permutation of C<isl_dim_cst> (the constant term), 2328C<isl_dim_param>, C<isl_dim_set> and C<isl_dim_div> for sets and 2329of C<isl_dim_cst>, C<isl_dim_param>, 2330C<isl_dim_in>, C<isl_dim_out> and C<isl_dim_div> for relations. 2331 2332A (basic or union) set or relation can also be constructed from a 2333(union) (piecewise) (multiple) affine expression 2334or a list of affine expressions 2335(See L</"Functions">), provided these affine expressions do not 2336involve any NaN. 2337 2338 #include <isl/set.h> 2339 __isl_give isl_basic_set *isl_basic_set_from_multi_aff( 2340 __isl_take isl_multi_aff *ma); 2341 __isl_give isl_set *isl_multi_aff_as_set( 2342 __isl_take isl_multi_aff *ma); 2343 __isl_give isl_set *isl_set_from_multi_aff( 2344 __isl_take isl_multi_aff *ma); 2345 2346 #include <isl/map.h> 2347 __isl_give isl_basic_map *isl_basic_map_from_aff( 2348 __isl_take isl_aff *aff); 2349 __isl_give isl_map *isl_map_from_aff( 2350 __isl_take isl_aff *aff); 2351 __isl_give isl_basic_map *isl_basic_map_from_aff_list( 2352 __isl_take isl_space *domain_space, 2353 __isl_take isl_aff_list *list); 2354 __isl_give isl_basic_map *isl_basic_map_from_multi_aff( 2355 __isl_take isl_multi_aff *maff) 2356 __isl_give isl_map *isl_multi_aff_as_map( 2357 __isl_take isl_multi_aff *ma); 2358 __isl_give isl_map *isl_map_from_multi_aff( 2359 __isl_take isl_multi_aff *maff) 2360 2361 #include <isl/aff.h> 2362 __isl_give isl_set *isl_set_from_pw_aff( 2363 __isl_take isl_pw_aff *pwaff); 2364 __isl_give isl_map *isl_pw_aff_as_map( 2365 __isl_take isl_pw_aff *pa); 2366 __isl_give isl_map *isl_map_from_pw_aff( 2367 __isl_take isl_pw_aff *pwaff); 2368 __isl_give isl_set *isl_pw_multi_aff_as_set( 2369 __isl_take isl_pw_multi_aff *pma); 2370 __isl_give isl_set *isl_set_from_pw_multi_aff( 2371 __isl_take isl_pw_multi_aff *pma); 2372 __isl_give isl_map *isl_pw_multi_aff_as_map( 2373 __isl_take isl_pw_multi_aff *pma); 2374 __isl_give isl_map *isl_map_from_pw_multi_aff( 2375 __isl_take isl_pw_multi_aff *pma); 2376 __isl_give isl_set *isl_multi_pw_aff_as_set( 2377 __isl_take isl_multi_pw_aff *mpa); 2378 __isl_give isl_set *isl_set_from_multi_pw_aff( 2379 __isl_take isl_multi_pw_aff *mpa); 2380 __isl_give isl_map *isl_multi_pw_aff_as_map( 2381 __isl_take isl_multi_pw_aff *mpa); 2382 __isl_give isl_map *isl_map_from_multi_pw_aff( 2383 __isl_take isl_multi_pw_aff *mpa); 2384 __isl_give isl_union_map *isl_union_map_from_union_pw_aff( 2385 __isl_take isl_union_pw_aff *upa); 2386 __isl_give isl_union_map * 2387 isl_union_pw_multi_aff_as_union_map( 2388 __isl_take isl_union_pw_multi_aff *upma); 2389 __isl_give isl_union_map * 2390 isl_union_map_from_union_pw_multi_aff( 2391 __isl_take isl_union_pw_multi_aff *upma); 2392 __isl_give isl_union_map * 2393 isl_union_map_from_multi_union_pw_aff( 2394 __isl_take isl_multi_union_pw_aff *mupa); 2395 2396The C<domain_space> argument describes the domain of the resulting 2397basic relation. It is required because the C<list> may consist 2398of zero affine expressions. 2399The C<mupa> passed to C<isl_union_map_from_multi_union_pw_aff> 2400is not allowed to be zero-dimensional. The domain of the result 2401is the shared domain of the union piecewise affine elements. 2402C<isl_multi_aff_as_set> and C<isl_set_from_multi_aff> perform 2403the same operation. 2404Similarly for the pair C<isl_multi_aff_as_map> and C<isl_map_from_multi_aff>, 2405for the pair C<isl_pw_aff_as_map> and C<isl_map_from_pw_aff>, 2406for the pair C<isl_pw_multi_aff_as_set> and C<isl_set_from_pw_multi_aff>, 2407for the pair C<isl_pw_multi_aff_as_map> and C<isl_map_from_pw_multi_aff>, 2408the pair C<isl_multi_pw_aff_as_set> and C<isl_set_from_multi_pw_aff>, 2409the pair C<isl_multi_pw_aff_as_map> and C<isl_map_from_multi_pw_aff>, 2410and 2411C<isl_union_pw_multi_aff_as_union_map> and 2412C<isl_union_map_from_union_pw_multi_aff>. 2413 2414=head2 Inspecting Sets and Relations 2415 2416Usually, the user should not have to care about the actual constraints 2417of the sets and maps, but should instead apply the abstract operations 2418explained in the following sections. 2419Occasionally, however, it may be required to inspect the individual 2420coefficients of the constraints. This section explains how to do so. 2421In these cases, it may also be useful to have C<isl> compute 2422an explicit representation of the existentially quantified variables. 2423 2424 __isl_give isl_set *isl_set_compute_divs( 2425 __isl_take isl_set *set); 2426 __isl_give isl_map *isl_map_compute_divs( 2427 __isl_take isl_map *map); 2428 __isl_give isl_union_set *isl_union_set_compute_divs( 2429 __isl_take isl_union_set *uset); 2430 __isl_give isl_union_map *isl_union_map_compute_divs( 2431 __isl_take isl_union_map *umap); 2432 2433This explicit representation defines the existentially quantified 2434variables as integer divisions of the other variables, possibly 2435including earlier existentially quantified variables. 2436An explicitly represented existentially quantified variable therefore 2437has a unique value when the values of the other variables are known. 2438 2439Alternatively, the existentially quantified variables can be removed 2440using the following functions, which compute an overapproximation. 2441 2442 #include <isl/set.h> 2443 __isl_give isl_basic_set *isl_basic_set_remove_divs( 2444 __isl_take isl_basic_set *bset); 2445 __isl_give isl_set *isl_set_remove_divs( 2446 __isl_take isl_set *set); 2447 2448 #include <isl/map.h> 2449 __isl_give isl_basic_map *isl_basic_map_remove_divs( 2450 __isl_take isl_basic_map *bmap); 2451 __isl_give isl_map *isl_map_remove_divs( 2452 __isl_take isl_map *map); 2453 2454 #include <isl/union_set.h> 2455 __isl_give isl_union_set *isl_union_set_remove_divs( 2456 __isl_take isl_union_set *bset); 2457 2458 #include <isl/union_map.h> 2459 __isl_give isl_union_map *isl_union_map_remove_divs( 2460 __isl_take isl_union_map *bmap); 2461 2462It is also possible to only remove those divs that are defined 2463in terms of a given range of dimensions or only those for which 2464no explicit representation is known. 2465 2466 __isl_give isl_basic_set * 2467 isl_basic_set_remove_divs_involving_dims( 2468 __isl_take isl_basic_set *bset, 2469 enum isl_dim_type type, 2470 unsigned first, unsigned n); 2471 __isl_give isl_basic_map * 2472 isl_basic_map_remove_divs_involving_dims( 2473 __isl_take isl_basic_map *bmap, 2474 enum isl_dim_type type, 2475 unsigned first, unsigned n); 2476 __isl_give isl_set *isl_set_remove_divs_involving_dims( 2477 __isl_take isl_set *set, enum isl_dim_type type, 2478 unsigned first, unsigned n); 2479 __isl_give isl_map *isl_map_remove_divs_involving_dims( 2480 __isl_take isl_map *map, enum isl_dim_type type, 2481 unsigned first, unsigned n); 2482 2483 __isl_give isl_basic_set * 2484 isl_basic_set_remove_unknown_divs( 2485 __isl_take isl_basic_set *bset); 2486 __isl_give isl_set *isl_set_remove_unknown_divs( 2487 __isl_take isl_set *set); 2488 __isl_give isl_map *isl_map_remove_unknown_divs( 2489 __isl_take isl_map *map); 2490 2491To iterate over all the sets or maps in a union set or map, use 2492 2493 #include <isl/union_set.h> 2494 isl_stat isl_union_set_foreach_set( 2495 __isl_keep isl_union_set *uset, 2496 isl_stat (*fn)(__isl_take isl_set *set, void *user), 2497 void *user); 2498 isl_bool isl_union_set_every_set( 2499 __isl_keep isl_union_set *uset, 2500 isl_bool (*test)(__isl_keep isl_set *set, 2501 void *user), 2502 void *user); 2503 2504 #include <isl/union_map.h> 2505 isl_stat isl_union_map_foreach_map( 2506 __isl_keep isl_union_map *umap, 2507 isl_stat (*fn)(__isl_take isl_map *map, void *user), 2508 void *user); 2509 isl_bool isl_union_map_every_map( 2510 __isl_keep isl_union_map *umap, 2511 isl_bool (*test)(__isl_keep isl_map *map, 2512 void *user), 2513 void *user); 2514 2515These functions call the callback function once for each 2516(pair of) space(s) for which there are elements in the input. 2517The argument to the callback contains all elements in the input 2518with that (pair of) space(s). 2519The C<isl_union_set_every_set> and 2520C<isl_union_map_every_map> variants check whether each 2521call to the callback returns true and stops checking as soon as one 2522of these calls returns false. 2523 2524The number of sets or maps in a union set or map can be obtained 2525from 2526 2527 isl_size isl_union_set_n_set(__isl_keep isl_union_set *uset); 2528 isl_size isl_union_map_n_map(__isl_keep isl_union_map *umap); 2529 2530To extract the set or map in a given space from a union, use 2531 2532 __isl_give isl_set *isl_union_set_extract_set( 2533 __isl_keep isl_union_set *uset, 2534 __isl_take isl_space *space); 2535 __isl_give isl_map *isl_union_map_extract_map( 2536 __isl_keep isl_union_map *umap, 2537 __isl_take isl_space *space); 2538 2539To iterate over all the basic sets or maps in a set or map, use 2540 2541 isl_stat isl_set_foreach_basic_set(__isl_keep isl_set *set, 2542 isl_stat (*fn)(__isl_take isl_basic_set *bset, 2543 void *user), 2544 void *user); 2545 isl_stat isl_map_foreach_basic_map(__isl_keep isl_map *map, 2546 isl_stat (*fn)(__isl_take isl_basic_map *bmap, 2547 void *user), 2548 void *user); 2549 2550The callback function C<fn> should return C<isl_stat_ok> if successful and 2551C<isl_stat_error> if an error occurs. In the latter case, or if any other error 2552occurs, the above functions will return C<isl_stat_error>. 2553 2554It should be noted that C<isl> does not guarantee that 2555the basic sets or maps passed to C<fn> are disjoint. 2556If this is required, then the user should call one of 2557the following functions first. 2558 2559 __isl_give isl_set *isl_set_make_disjoint( 2560 __isl_take isl_set *set); 2561 __isl_give isl_map *isl_map_make_disjoint( 2562 __isl_take isl_map *map); 2563 2564The number of basic sets in a set can be obtained 2565or the number of basic maps in a map can be obtained 2566from 2567 2568 #include <isl/set.h> 2569 isl_size isl_set_n_basic_set(__isl_keep isl_set *set); 2570 2571 #include <isl/map.h> 2572 isl_size isl_map_n_basic_map(__isl_keep isl_map *map); 2573 2574It is also possible to obtain a list of (basic) sets from a set 2575or union set, a list of basic maps from a map and a list of maps from a union 2576map. 2577 2578 #include <isl/set.h> 2579 __isl_give isl_basic_set_list *isl_set_get_basic_set_list( 2580 __isl_keep isl_set *set); 2581 2582 #include <isl/union_set.h> 2583 __isl_give isl_basic_set_list * 2584 isl_union_set_get_basic_set_list( 2585 __isl_keep isl_union_set *uset); 2586 __isl_give isl_set_list *isl_union_set_get_set_list( 2587 __isl_keep isl_union_set *uset); 2588 2589 #include <isl/map.h> 2590 __isl_give isl_basic_map_list *isl_map_get_basic_map_list( 2591 __isl_keep isl_map *map); 2592 2593 #include <isl/union_map.h> 2594 __isl_give isl_map_list *isl_union_map_get_map_list( 2595 __isl_keep isl_union_map *umap); 2596 2597The returned list can be manipulated using the functions in L<"Lists">. 2598 2599To iterate over the constraints of a basic set or map, use 2600 2601 #include <isl/constraint.h> 2602 2603 isl_size isl_basic_set_n_constraint( 2604 __isl_keep isl_basic_set *bset); 2605 isl_stat isl_basic_set_foreach_constraint( 2606 __isl_keep isl_basic_set *bset, 2607 isl_stat (*fn)(__isl_take isl_constraint *c, 2608 void *user), 2609 void *user); 2610 isl_size isl_basic_map_n_constraint( 2611 __isl_keep isl_basic_map *bmap); 2612 isl_stat isl_basic_map_foreach_constraint( 2613 __isl_keep isl_basic_map *bmap, 2614 isl_stat (*fn)(__isl_take isl_constraint *c, 2615 void *user), 2616 void *user); 2617 __isl_null isl_constraint *isl_constraint_free( 2618 __isl_take isl_constraint *c); 2619 2620Again, the callback function C<fn> should return C<isl_stat_ok> 2621if successful and 2622C<isl_stat_error> if an error occurs. In the latter case, or if any other error 2623occurs, the above functions will return C<isl_stat_error>. 2624The constraint C<c> represents either an equality or an inequality. 2625Use the following function to find out whether a constraint 2626represents an equality. If not, it represents an inequality. 2627 2628 isl_bool isl_constraint_is_equality( 2629 __isl_keep isl_constraint *constraint); 2630 2631It is also possible to obtain a list of constraints from a basic 2632map or set 2633 2634 #include <isl/constraint.h> 2635 __isl_give isl_constraint_list * 2636 isl_basic_map_get_constraint_list( 2637 __isl_keep isl_basic_map *bmap); 2638 __isl_give isl_constraint_list * 2639 isl_basic_set_get_constraint_list( 2640 __isl_keep isl_basic_set *bset); 2641 2642These functions require that all existentially quantified variables 2643have an explicit representation. 2644The returned list can be manipulated using the functions in L<"Lists">. 2645 2646The coefficients of the constraints can be inspected using 2647the following functions. 2648 2649 isl_bool isl_constraint_is_lower_bound( 2650 __isl_keep isl_constraint *constraint, 2651 enum isl_dim_type type, unsigned pos); 2652 isl_bool isl_constraint_is_upper_bound( 2653 __isl_keep isl_constraint *constraint, 2654 enum isl_dim_type type, unsigned pos); 2655 __isl_give isl_val *isl_constraint_get_constant_val( 2656 __isl_keep isl_constraint *constraint); 2657 __isl_give isl_val *isl_constraint_get_coefficient_val( 2658 __isl_keep isl_constraint *constraint, 2659 enum isl_dim_type type, int pos); 2660 2661The explicit representations of the existentially quantified 2662variables can be inspected using the following function. 2663Note that the user is only allowed to use this function 2664if the inspected set or map is the result of a call 2665to C<isl_set_compute_divs> or C<isl_map_compute_divs>. 2666The existentially quantified variable is equal to the floor 2667of the returned affine expression. The affine expression 2668itself can be inspected using the functions in 2669L</"Functions">. 2670 2671 __isl_give isl_aff *isl_constraint_get_div( 2672 __isl_keep isl_constraint *constraint, int pos); 2673 2674To obtain the constraints of a basic set or map in matrix 2675form, use the following functions. 2676 2677 __isl_give isl_mat *isl_basic_set_equalities_matrix( 2678 __isl_keep isl_basic_set *bset, 2679 enum isl_dim_type c1, enum isl_dim_type c2, 2680 enum isl_dim_type c3, enum isl_dim_type c4); 2681 __isl_give isl_mat *isl_basic_set_inequalities_matrix( 2682 __isl_keep isl_basic_set *bset, 2683 enum isl_dim_type c1, enum isl_dim_type c2, 2684 enum isl_dim_type c3, enum isl_dim_type c4); 2685 __isl_give isl_mat *isl_basic_map_equalities_matrix( 2686 __isl_keep isl_basic_map *bmap, 2687 enum isl_dim_type c1, 2688 enum isl_dim_type c2, enum isl_dim_type c3, 2689 enum isl_dim_type c4, enum isl_dim_type c5); 2690 __isl_give isl_mat *isl_basic_map_inequalities_matrix( 2691 __isl_keep isl_basic_map *bmap, 2692 enum isl_dim_type c1, 2693 enum isl_dim_type c2, enum isl_dim_type c3, 2694 enum isl_dim_type c4, enum isl_dim_type c5); 2695 2696The C<isl_dim_type> arguments dictate the order in which 2697different kinds of variables appear in the resulting matrix. 2698For set inputs, they should be a permutation of 2699C<isl_dim_cst> (the constant term), C<isl_dim_param>, C<isl_dim_set> and 2700C<isl_dim_div>. 2701For map inputs, they should be a permutation of 2702C<isl_dim_cst>, C<isl_dim_param>, 2703C<isl_dim_in>, C<isl_dim_out> and C<isl_dim_div>. 2704 2705=head2 Points 2706 2707Points are elements of a set. They can be used to construct 2708simple sets (boxes) or they can be used to represent the 2709individual elements of a set. 2710The zero point (the origin) can be created using 2711 2712 __isl_give isl_point *isl_point_zero(__isl_take isl_space *space); 2713 2714The coordinates of a point can be inspected, set and changed 2715using 2716 2717 #include <isl/point.h> 2718 __isl_give isl_multi_val *isl_point_get_multi_val( 2719 __isl_keep isl_point *pnt); 2720 __isl_give isl_val *isl_point_get_coordinate_val( 2721 __isl_keep isl_point *pnt, 2722 enum isl_dim_type type, int pos); 2723 __isl_give isl_point *isl_point_set_coordinate_val( 2724 __isl_take isl_point *pnt, 2725 enum isl_dim_type type, int pos, 2726 __isl_take isl_val *v); 2727 2728 __isl_give isl_point *isl_point_add_ui( 2729 __isl_take isl_point *pnt, 2730 enum isl_dim_type type, int pos, unsigned val); 2731 __isl_give isl_point *isl_point_sub_ui( 2732 __isl_take isl_point *pnt, 2733 enum isl_dim_type type, int pos, unsigned val); 2734 2735Points can be copied or freed using 2736 2737 __isl_give isl_point *isl_point_copy( 2738 __isl_keep isl_point *pnt); 2739 __isl_null isl_point *isl_point_free( 2740 __isl_take isl_point *pnt); 2741 2742A singleton set can be created from a point using the following functions. 2743 2744 __isl_give isl_basic_set *isl_basic_set_from_point( 2745 __isl_take isl_point *pnt); 2746 __isl_give isl_set *isl_point_to_set( 2747 __isl_take isl_point *pnt); 2748 __isl_give isl_set *isl_set_from_point( 2749 __isl_take isl_point *pnt); 2750 __isl_give isl_union_set *isl_union_set_from_point( 2751 __isl_take isl_point *pnt); 2752 2753C<isl_point_to_set> and C<isl_set_from_point> perform 2754the same operation. 2755 2756A box can be created from two opposite extremal points using 2757 2758 __isl_give isl_basic_set *isl_basic_set_box_from_points( 2759 __isl_take isl_point *pnt1, 2760 __isl_take isl_point *pnt2); 2761 __isl_give isl_set *isl_set_box_from_points( 2762 __isl_take isl_point *pnt1, 2763 __isl_take isl_point *pnt2); 2764 2765All elements of a B<bounded> (union) set can be enumerated using 2766the following functions. 2767 2768 isl_stat isl_set_foreach_point(__isl_keep isl_set *set, 2769 isl_stat (*fn)(__isl_take isl_point *pnt, 2770 void *user), 2771 void *user); 2772 isl_stat isl_union_set_foreach_point( 2773 __isl_keep isl_union_set *uset, 2774 isl_stat (*fn)(__isl_take isl_point *pnt, 2775 void *user), 2776 void *user); 2777 2778The function C<fn> is called for each integer point in 2779C<set> with as second argument the last argument of 2780the C<isl_set_foreach_point> call. The function C<fn> 2781should return C<isl_stat_ok> on success and C<isl_stat_error> on failure. 2782In the latter case, C<isl_set_foreach_point> will stop 2783enumerating and return C<isl_stat_error> as well. 2784If the enumeration is performed successfully and to completion, 2785then C<isl_set_foreach_point> returns C<isl_stat_ok>. 2786 2787To obtain a single point of a (basic or union) set, use 2788 2789 __isl_give isl_point *isl_basic_set_sample_point( 2790 __isl_take isl_basic_set *bset); 2791 __isl_give isl_point *isl_set_sample_point( 2792 __isl_take isl_set *set); 2793 __isl_give isl_point *isl_union_set_sample_point( 2794 __isl_take isl_union_set *uset); 2795 2796If C<set> does not contain any (integer) points, then the 2797resulting point will be ``void'', a property that can be 2798tested using 2799 2800 isl_bool isl_point_is_void(__isl_keep isl_point *pnt); 2801 2802=head2 Functions 2803 2804Besides sets and relation, C<isl> also supports various types of functions. 2805Each of these types is derived from the value type (see L</"Values">) 2806or from one of two primitive function types 2807through the application of zero or more type constructors. 2808As a special case, a multiple expression can also be derived 2809from an identifier (see L</"Identifiers">) although the result 2810is not really a function. 2811We first describe the primitive type and then we describe 2812the types derived from these primitive types. 2813 2814=head3 Primitive Functions 2815 2816C<isl> support two primitive function types, quasi-affine 2817expressions and quasipolynomials. 2818A quasi-affine expression is defined either over a parameter 2819space or over a set and is composed of integer constants, 2820parameters and set variables, addition, subtraction and 2821integer division by an integer constant. 2822For example, the quasi-affine expression 2823 2824 [n] -> { [x] -> [2*floor((4 n + x)/9)] } 2825 2826maps C<x> to C<2*floor((4 n + x)/9>. 2827A quasipolynomial is a polynomial expression in quasi-affine 2828expression. That is, it additionally allows for multiplication. 2829Note, though, that it is not allowed to construct an integer 2830division of an expression involving multiplications. 2831Here is an example of a quasipolynomial that is not 2832quasi-affine expression 2833 2834 [n] -> { [x] -> (n*floor((4 n + x)/9)) } 2835 2836Note that the external representations of quasi-affine expressions 2837and quasipolynomials are different. Quasi-affine expressions 2838use a notation with square brackets just like binary relations, 2839while quasipolynomials do not. This might change at some point. 2840 2841If a primitive function is defined over a parameter space, 2842then the space of the function itself is that of a set. 2843If it is defined over a set, then the space of the function 2844is that of a relation. In both cases, the set space (or 2845the output space) is single-dimensional, anonymous and unstructured. 2846To create functions with multiple dimensions or with other kinds 2847of set or output spaces, use multiple expressions 2848(see L</"Multiple Expressions">). 2849 2850=over 2851 2852=item * Quasi-affine Expressions 2853 2854Besides the expressions described above, a quasi-affine 2855expression can also be set to NaN. Such expressions 2856typically represent a failure to represent a result 2857as a quasi-affine expression. 2858 2859The zero quasi affine expression or the quasi affine expression 2860that is equal to a given value, parameter or 2861a specified dimension on a given domain can be created using 2862 2863 #include <isl/aff.h> 2864 __isl_give isl_aff *isl_aff_zero_on_domain_space( 2865 __isl_take isl_space *space); 2866 __isl_give isl_aff *isl_space_zero_aff_on_domain( 2867 __isl_take isl_space *space); 2868 __isl_give isl_aff *isl_aff_zero_on_domain( 2869 __isl_take isl_local_space *ls); 2870 __isl_give isl_aff *isl_aff_val_on_domain_space( 2871 __isl_take isl_space *space, 2872 __isl_take isl_val *val); 2873 __isl_give isl_aff *isl_aff_val_on_domain( 2874 __isl_take isl_local_space *ls, 2875 __isl_take isl_val *val); 2876 __isl_give isl_aff *isl_aff_param_on_domain_space_id( 2877 __isl_take isl_space *space, 2878 __isl_take isl_id *id); 2879 __isl_give isl_aff *isl_space_param_aff_on_domain_id( 2880 __isl_take isl_space *space, 2881 __isl_take isl_id *id); 2882 __isl_give isl_aff *isl_aff_var_on_domain( 2883 __isl_take isl_local_space *ls, 2884 enum isl_dim_type type, unsigned pos); 2885 __isl_give isl_aff *isl_aff_nan_on_domain_space( 2886 __isl_take isl_space *space); 2887 __isl_give isl_aff *isl_aff_nan_on_domain( 2888 __isl_take isl_local_space *ls); 2889 2890The space passed to C<isl_aff_param_on_domain_space_id> 2891is required to have a parameter with the given identifier. 2892C<isl_aff_param_on_domain_space_id> and 2893C<isl_space_param_aff_on_domain_id> perform the same operation. 2894 2895C<isl_aff_zero_on_domain_space> and C<isl_space_zero_aff_on_domain> 2896perform the same operation. 2897 2898Quasi affine expressions can be copied and freed using 2899 2900 #include <isl/aff.h> 2901 __isl_give isl_aff *isl_aff_copy( 2902 __isl_keep isl_aff *aff); 2903 __isl_null isl_aff *isl_aff_free( 2904 __isl_take isl_aff *aff); 2905 2906A (rational) bound on a dimension can be extracted from an C<isl_constraint> 2907using the following function. The constraint is required to have 2908a non-zero coefficient for the specified dimension. 2909 2910 #include <isl/constraint.h> 2911 __isl_give isl_aff *isl_constraint_get_bound( 2912 __isl_keep isl_constraint *constraint, 2913 enum isl_dim_type type, int pos); 2914 2915The entire affine expression of the constraint can also be extracted 2916using the following function. 2917 2918 #include <isl/constraint.h> 2919 __isl_give isl_aff *isl_constraint_get_aff( 2920 __isl_keep isl_constraint *constraint); 2921 2922Conversely, an equality constraint equating 2923the affine expression to zero or an inequality constraint enforcing 2924the affine expression to be non-negative, can be constructed using 2925 2926 __isl_give isl_constraint *isl_equality_from_aff( 2927 __isl_take isl_aff *aff); 2928 __isl_give isl_constraint *isl_inequality_from_aff( 2929 __isl_take isl_aff *aff); 2930 2931The coefficients and the integer divisions of an affine expression 2932can be inspected using the following functions. 2933 2934 #include <isl/aff.h> 2935 __isl_give isl_val *isl_aff_get_constant_val( 2936 __isl_keep isl_aff *aff); 2937 __isl_give isl_val *isl_aff_get_coefficient_val( 2938 __isl_keep isl_aff *aff, 2939 enum isl_dim_type type, int pos); 2940 int isl_aff_coefficient_sgn(__isl_keep isl_aff *aff, 2941 enum isl_dim_type type, int pos); 2942 __isl_give isl_val *isl_aff_get_denominator_val( 2943 __isl_keep isl_aff *aff); 2944 __isl_give isl_aff *isl_aff_get_div( 2945 __isl_keep isl_aff *aff, int pos); 2946 2947They can be modified using the following functions. 2948 2949 #include <isl/aff.h> 2950 __isl_give isl_aff *isl_aff_set_constant_si( 2951 __isl_take isl_aff *aff, int v); 2952 __isl_give isl_aff *isl_aff_set_constant_val( 2953 __isl_take isl_aff *aff, __isl_take isl_val *v); 2954 __isl_give isl_aff *isl_aff_set_coefficient_si( 2955 __isl_take isl_aff *aff, 2956 enum isl_dim_type type, int pos, int v); 2957 __isl_give isl_aff *isl_aff_set_coefficient_val( 2958 __isl_take isl_aff *aff, 2959 enum isl_dim_type type, int pos, 2960 __isl_take isl_val *v); 2961 2962 __isl_give isl_aff *isl_aff_add_constant_si( 2963 __isl_take isl_aff *aff, int v); 2964 __isl_give isl_aff *isl_aff_add_constant_val( 2965 __isl_take isl_aff *aff, __isl_take isl_val *v); 2966 __isl_give isl_aff *isl_aff_add_constant_num_si( 2967 __isl_take isl_aff *aff, int v); 2968 __isl_give isl_aff *isl_aff_add_coefficient_si( 2969 __isl_take isl_aff *aff, 2970 enum isl_dim_type type, int pos, int v); 2971 __isl_give isl_aff *isl_aff_add_coefficient_val( 2972 __isl_take isl_aff *aff, 2973 enum isl_dim_type type, int pos, 2974 __isl_take isl_val *v); 2975 2976Note that C<isl_aff_set_constant_si> and C<isl_aff_set_coefficient_si> 2977set the I<numerator> of the constant or coefficient, while 2978C<isl_aff_set_constant_val> and C<isl_aff_set_coefficient_val> set 2979the constant or coefficient as a whole. 2980The C<add_constant> and C<add_coefficient> functions add an integer 2981or rational value to 2982the possibly rational constant or coefficient. 2983The C<add_constant_num> functions add an integer value to 2984the numerator. 2985 2986=item * Quasipolynomials 2987 2988Some simple quasipolynomials can be created using the following functions. 2989 2990 #include <isl/polynomial.h> 2991 __isl_give isl_qpolynomial *isl_qpolynomial_zero_on_domain( 2992 __isl_take isl_space *domain); 2993 __isl_give isl_qpolynomial *isl_qpolynomial_one_on_domain( 2994 __isl_take isl_space *domain); 2995 __isl_give isl_qpolynomial *isl_qpolynomial_infty_on_domain( 2996 __isl_take isl_space *domain); 2997 __isl_give isl_qpolynomial *isl_qpolynomial_neginfty_on_domain( 2998 __isl_take isl_space *domain); 2999 __isl_give isl_qpolynomial *isl_qpolynomial_nan_on_domain( 3000 __isl_take isl_space *domain); 3001 __isl_give isl_qpolynomial *isl_qpolynomial_val_on_domain( 3002 __isl_take isl_space *domain, 3003 __isl_take isl_val *val); 3004 __isl_give isl_qpolynomial *isl_qpolynomial_var_on_domain( 3005 __isl_take isl_space *domain, 3006 enum isl_dim_type type, unsigned pos); 3007 __isl_give isl_qpolynomial *isl_qpolynomial_from_aff( 3008 __isl_take isl_aff *aff); 3009 3010Recall that the space in which a quasipolynomial lives is a map space 3011with a one-dimensional range. The C<domain> argument in some of 3012the functions above corresponds to the domain of this map space. 3013 3014Quasipolynomials can be copied and freed again using the following 3015functions. 3016 3017 #include <isl/polynomial.h> 3018 __isl_give isl_qpolynomial *isl_qpolynomial_copy( 3019 __isl_keep isl_qpolynomial *qp); 3020 __isl_null isl_qpolynomial *isl_qpolynomial_free( 3021 __isl_take isl_qpolynomial *qp); 3022 3023The constant term of a quasipolynomial can be extracted using 3024 3025 __isl_give isl_val *isl_qpolynomial_get_constant_val( 3026 __isl_keep isl_qpolynomial *qp); 3027 3028To iterate over all terms in a quasipolynomial, 3029use 3030 3031 isl_stat isl_qpolynomial_foreach_term( 3032 __isl_keep isl_qpolynomial *qp, 3033 isl_stat (*fn)(__isl_take isl_term *term, 3034 void *user), void *user); 3035 3036The terms themselves can be inspected and freed using 3037these functions 3038 3039 isl_size isl_term_dim(__isl_keep isl_term *term, 3040 enum isl_dim_type type); 3041 __isl_give isl_val *isl_term_get_coefficient_val( 3042 __isl_keep isl_term *term); 3043 isl_size isl_term_get_exp(__isl_keep isl_term *term, 3044 enum isl_dim_type type, unsigned pos); 3045 __isl_give isl_aff *isl_term_get_div( 3046 __isl_keep isl_term *term, unsigned pos); 3047 __isl_null isl_term *isl_term_free( 3048 __isl_take isl_term *term); 3049 3050Each term is a product of parameters, set variables and 3051integer divisions. The function C<isl_term_get_exp> 3052returns the exponent of a given dimensions in the given term. 3053 3054=back 3055 3056=head3 Reductions 3057 3058A reduction represents a maximum or a minimum of its 3059base expressions. 3060The only reduction type defined by C<isl> is 3061C<isl_qpolynomial_fold>. 3062 3063There are currently no functions to directly create such 3064objects, but they do appear in the piecewise quasipolynomial 3065reductions returned by the C<isl_pw_qpolynomial_bound> function. 3066See 3067L</"Bounds on Piecewise Quasipolynomials and Piecewise Quasipolynomial Reductions">. 3068 3069Reductions can be copied and freed using 3070the following functions. 3071 3072 #include <isl/polynomial.h> 3073 __isl_give isl_qpolynomial_fold * 3074 isl_qpolynomial_fold_copy( 3075 __isl_keep isl_qpolynomial_fold *fold); 3076 __isl_null isl_qpolynomial_fold * 3077 isl_qpolynomial_fold_free( 3078 __isl_take isl_qpolynomial_fold *fold); 3079 3080The type of a (union piecewise) reduction 3081can be obtained using the following functions. 3082 3083 #include <isl/polynomial.h> 3084 enum isl_fold isl_qpolynomial_fold_get_type( 3085 __isl_keep isl_qpolynomial_fold *fold); 3086 enum isl_fold isl_pw_qpolynomial_fold_get_type( 3087 __isl_keep isl_pw_qpolynomial_fold *pwf); 3088 enum isl_fold isl_union_pw_qpolynomial_fold_get_type( 3089 __isl_keep isl_union_pw_qpolynomial_fold *upwf); 3090 3091The type may be either C<isl_fold_min> or C<isl_fold_max> 3092(or C<isl_fold_error> in case of error). 3093 3094To iterate over all quasipolynomials in a reduction, use 3095 3096 isl_stat isl_qpolynomial_fold_foreach_qpolynomial( 3097 __isl_keep isl_qpolynomial_fold *fold, 3098 isl_stat (*fn)(__isl_take isl_qpolynomial *qp, 3099 void *user), void *user); 3100 3101=head3 Multiple Expressions 3102 3103A multiple expression represents a sequence of zero or 3104more base expressions, all defined on the same domain space. 3105The domain space of the multiple expression is the same 3106as that of the base expressions, but the range space 3107can be any space. In case the base expressions have 3108a set space, the corresponding multiple expression 3109also has a set space. 3110Objects of the value or identifier type do not have an associated space. 3111The space of a multiple value or 3112multiple identifier is therefore always a set space. 3113Similarly, the space of a multiple union piecewise 3114affine expression is always a set space. 3115If the base expressions are not total, then 3116a corresponding zero-dimensional multiple expression may 3117have an explicit domain that keeps track of the domain 3118outside of any base expressions. 3119 3120The multiple expression types defined by C<isl> 3121are C<isl_multi_val>, C<isl_multi_id>, C<isl_multi_aff>, C<isl_multi_pw_aff>, 3122C<isl_multi_union_pw_aff>. 3123 3124A multiple expression with the value zero for 3125each output (or set) dimension can be created 3126using the following functions. 3127 3128 #include <isl/val.h> 3129 __isl_give isl_multi_val *isl_multi_val_zero( 3130 __isl_take isl_space *space); 3131 __isl_give isl_multi_val *isl_space_zero_multi_val( 3132 __isl_take isl_space *space); 3133 3134 #include <isl/aff.h> 3135 __isl_give isl_multi_aff *isl_multi_aff_zero( 3136 __isl_take isl_space *space); 3137 __isl_give isl_multi_aff *isl_space_zero_multi_aff( 3138 __isl_take isl_space *space); 3139 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_zero( 3140 __isl_take isl_space *space); 3141 __isl_give isl_multi_pw_aff *isl_space_zero_multi_pw_aff( 3142 __isl_take isl_space *space); 3143 __isl_give isl_multi_union_pw_aff * 3144 isl_multi_union_pw_aff_zero( 3145 __isl_take isl_space *space); 3146 __isl_give isl_multi_union_pw_aff * 3147 isl_space_zero_multi_union_pw_aff( 3148 __isl_take isl_space *space); 3149 3150Since there is no canonical way of representing a zero 3151value of type C<isl_union_pw_aff>, the space passed 3152to C<isl_multi_union_pw_aff_zero> needs to be zero-dimensional. 3153C<isl_multi_val_zero> and C<isl_space_zero_multi_val> 3154perform the same operation. 3155Similarly 3156for the pair C<isl_multi_aff_zero> and C<isl_space_zero_multi_aff>, 3157for the pair C<isl_multi_pw_aff_zero> and C<isl_space_zero_multi_pw_aff> and 3158for the pair C<isl_multi_union_pw_aff_zero> and 3159C<isl_space_zero_multi_union_pw_aff>. 3160 3161 3162An identity function can be created using the following 3163functions. 3164For the first group of functions, the space needs to be that of a set. 3165For the second group, 3166the space needs to be that of a relation 3167with the same number of input and output dimensions. 3168For the third group, the input function needs to live in a space 3169with the same number of input and output dimensions and 3170the identity function is created in that space. 3171 3172 #include <isl/aff.h> 3173 __isl_give isl_multi_aff * 3174 isl_multi_aff_identity_on_domain_space( 3175 __isl_take isl_space *space); 3176 __isl_give isl_multi_aff * 3177 isl_space_identity_multi_aff_on_domain( 3178 __isl_take isl_space *space); 3179 __isl_give isl_multi_pw_aff * 3180 isl_multi_pw_aff_identity_on_domain_space( 3181 __isl_take isl_space *space); 3182 __isl_give isl_multi_pw_aff * 3183 isl_space_identity_multi_pw_aff_on_domain( 3184 __isl_take isl_space *space); 3185 __isl_give isl_multi_aff *isl_multi_aff_identity( 3186 __isl_take isl_space *space); 3187 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_identity( 3188 __isl_take isl_space *space); 3189 __isl_give isl_multi_aff * 3190 isl_multi_aff_identity_multi_aff( 3191 __isl_take isl_multi_aff *ma); 3192 __isl_give isl_multi_pw_aff * 3193 isl_multi_pw_aff_identity_multi_pw_aff( 3194 __isl_take isl_multi_pw_aff *mpa); 3195 3196C<isl_multi_aff_identity_on_domain_space> and 3197C<isl_space_identity_multi_aff_on_domain> 3198perform the same operation. 3199Similarly 3200for the pair C<isl_multi_pw_aff_identity_on_domain_space> and 3201C<isl_space_identity_multi_pw_aff_on_domain>. 3202 3203A function that performs a projection on a universe 3204relation or set can be created using the following functions. 3205See also the corresponding 3206projection operations in L</"Unary Operations">. 3207 3208 #include <isl/aff.h> 3209 __isl_give isl_multi_aff *isl_multi_aff_domain_map( 3210 __isl_take isl_space *space); 3211 __isl_give isl_multi_aff *isl_space_domain_map_multi_aff( 3212 __isl_take isl_space *space); 3213 __isl_give isl_multi_aff *isl_multi_aff_range_map( 3214 __isl_take isl_space *space); 3215 __isl_give isl_multi_aff *isl_space_range_map_multi_aff( 3216 __isl_take isl_space *space); 3217 __isl_give isl_multi_aff *isl_multi_aff_project_out_map( 3218 __isl_take isl_space *space, 3219 enum isl_dim_type type, 3220 unsigned first, unsigned n); 3221 3222C<isl_multi_aff_domain_map> and C<isl_space_domain_map_multi_aff> perform 3223the same operation. 3224Similarly 3225for the pair C<isl_multi_aff_range_map> and C<isl_space_range_map_multi_aff>. 3226 3227A multiple expression can be created from a single 3228base expression using the following functions. 3229The space of the created multiple expression is the same 3230as that of the base expression, except for 3231C<isl_multi_union_pw_aff_from_union_pw_aff> where the input 3232lives in a parameter space and the output lives 3233in a single-dimensional set space. 3234 3235 #include <isl/aff.h> 3236 __isl_give isl_multi_aff *isl_multi_aff_from_aff( 3237 __isl_take isl_aff *aff); 3238 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_from_pw_aff( 3239 __isl_take isl_pw_aff *pa); 3240 __isl_give isl_multi_union_pw_aff * 3241 isl_multi_union_pw_aff_from_union_pw_aff( 3242 __isl_take isl_union_pw_aff *upa); 3243 3244A multiple expression can be created from a list 3245of base expression in a specified space. 3246The domain of this space needs to be the same 3247as the domains of the base expressions in the list. 3248If the base expressions have a set space (or no associated space), 3249then this space also needs to be a set space. 3250 3251 #include <isl/id.h> 3252 __isl_give isl_multi_id *isl_multi_id_from_id_list( 3253 __isl_take isl_space *space, 3254 __isl_take isl_id_list *list); 3255 __isl_give isl_multi_id *isl_space_multi_id( 3256 __isl_take isl_space *space, 3257 __isl_take isl_id_list *list); 3258 3259 #include <isl/val.h> 3260 __isl_give isl_multi_val *isl_multi_val_from_val_list( 3261 __isl_take isl_space *space, 3262 __isl_take isl_val_list *list); 3263 __isl_give isl_multi_val *isl_space_multi_val( 3264 __isl_take isl_space *space, 3265 __isl_take isl_val_list *list); 3266 3267 #include <isl/aff.h> 3268 __isl_give isl_multi_aff *isl_multi_aff_from_aff_list( 3269 __isl_take isl_space *space, 3270 __isl_take isl_aff_list *list); 3271 __isl_give isl_multi_aff *isl_space_multi_aff( 3272 __isl_take isl_space *space, 3273 __isl_take isl_aff_list *list); 3274 __isl_give isl_multi_pw_aff * 3275 isl_multi_pw_aff_from_pw_aff_list( 3276 __isl_take isl_space *space, 3277 __isl_take isl_pw_aff_list *list); 3278 __isl_give isl_multi_pw_aff * 3279 isl_space_multi_pw_aff( 3280 __isl_take isl_space *space, 3281 __isl_take isl_pw_aff_list *list); 3282 __isl_give isl_multi_union_pw_aff * 3283 isl_multi_union_pw_aff_from_union_pw_aff_list( 3284 __isl_take isl_space *space, 3285 __isl_take isl_union_pw_aff_list *list); 3286 __isl_give isl_multi_union_pw_aff * 3287 isl_space_multi_union_pw_aff( 3288 __isl_take isl_space *space, 3289 __isl_take isl_union_pw_aff_list *list); 3290 3291C<isl_multi_id_from_id_list> and C<isl_space_multi_id> perform 3292the same operation. 3293Similarly for the pair C<isl_multi_val_from_val_list> and 3294C<isl_space_multi_val>, 3295for the pair C<isl_multi_aff_from_aff_list> and 3296C<isl_space_multi_aff>, 3297for the pair C<isl_multi_pw_aff_from_pw_aff_list> and 3298C<isl_space_multi_pw_aff> and 3299for the pair C<isl_multi_union_pw_aff_from_union_pw_aff_list> and 3300C<isl_space_multi_union_pw_aff>. 3301 3302As a convenience, a multiple piecewise expression can 3303also be created from a multiple expression, 3304or even directly from a single base expression. 3305Each piecewise expression in the result has a single 3306universe cell. 3307 3308 #include <isl/aff.h> 3309 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_from_aff( 3310 __isl_take isl_aff *aff); 3311 __isl_give isl_multi_pw_aff * 3312 isl_multi_aff_to_multi_pw_aff( 3313 __isl_take isl_multi_aff *ma); 3314 __isl_give isl_multi_pw_aff * 3315 isl_multi_pw_aff_from_multi_aff( 3316 __isl_take isl_multi_aff *ma); 3317 3318C<isl_multi_aff_to_multi_pw_aff> and 3319C<isl_multi_pw_aff_from_multi_aff> perform the same operation. 3320 3321Similarly, a multiple union expression can be 3322created from a multiple expression. 3323 3324 #include <isl/aff.h> 3325 __isl_give isl_multi_union_pw_aff * 3326 isl_multi_union_pw_aff_from_multi_aff( 3327 __isl_take isl_multi_aff *ma); 3328 __isl_give isl_multi_union_pw_aff * 3329 isl_multi_aff_to_multi_union_pw_aff( 3330 __isl_take isl_multi_aff *ma); 3331 __isl_give isl_multi_union_pw_aff * 3332 isl_multi_union_pw_aff_from_multi_pw_aff( 3333 __isl_take isl_multi_pw_aff *mpa); 3334 3335C<isl_multi_aff_to_multi_union_pw_aff> and 3336C<isl_multi_union_pw_aff_from_multi_aff> perform the same operation. 3337 3338A multiple quasi-affine expression can be created from 3339a multiple value with a given domain space using the following 3340function. 3341 3342 #include <isl/aff.h> 3343 __isl_give isl_multi_aff * 3344 isl_multi_aff_multi_val_on_domain_space( 3345 __isl_take isl_space *space, 3346 __isl_take isl_multi_val *mv); 3347 __isl_give isl_multi_aff * 3348 isl_space_multi_aff_on_domain_multi_val( 3349 __isl_take isl_space *space, 3350 __isl_take isl_multi_val *mv); 3351 __isl_give isl_multi_aff * 3352 isl_multi_aff_multi_val_on_space( 3353 __isl_take isl_space *space, 3354 __isl_take isl_multi_val *mv); 3355 3356C<isl_space_multi_aff_on_domain_multi_val> and 3357C<isl_multi_aff_multi_val_on_space> are alternative names 3358for C<isl_multi_aff_multi_val_on_domain_space>. 3359 3360Similarly, 3361a multiple union piecewise affine expression can be created from 3362a multiple value with a given domain or 3363a (piecewise) multiple affine expression with a given domain 3364using the following functions. 3365 3366 #include <isl/aff.h> 3367 __isl_give isl_multi_union_pw_aff * 3368 isl_multi_union_pw_aff_multi_val_on_domain( 3369 __isl_take isl_union_set *domain, 3370 __isl_take isl_multi_val *mv); 3371 __isl_give isl_multi_union_pw_aff * 3372 isl_multi_union_pw_aff_multi_aff_on_domain( 3373 __isl_take isl_union_set *domain, 3374 __isl_take isl_multi_aff *ma); 3375 __isl_give isl_multi_union_pw_aff * 3376 isl_multi_union_pw_aff_pw_multi_aff_on_domain( 3377 __isl_take isl_union_set *domain, 3378 __isl_take isl_pw_multi_aff *pma); 3379 3380Multiple expressions can be copied and freed using 3381the following functions. 3382 3383 #include <isl/id.h> 3384 __isl_give isl_multi_id *isl_multi_id_copy( 3385 __isl_keep isl_multi_id *mi); 3386 __isl_null isl_multi_id *isl_multi_id_free( 3387 __isl_take isl_multi_id *mi); 3388 3389 #include <isl/val.h> 3390 __isl_give isl_multi_val *isl_multi_val_copy( 3391 __isl_keep isl_multi_val *mv); 3392 __isl_null isl_multi_val *isl_multi_val_free( 3393 __isl_take isl_multi_val *mv); 3394 3395 #include <isl/aff.h> 3396 __isl_give isl_multi_aff *isl_multi_aff_copy( 3397 __isl_keep isl_multi_aff *maff); 3398 __isl_null isl_multi_aff *isl_multi_aff_free( 3399 __isl_take isl_multi_aff *maff); 3400 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_copy( 3401 __isl_keep isl_multi_pw_aff *mpa); 3402 __isl_null isl_multi_pw_aff *isl_multi_pw_aff_free( 3403 __isl_take isl_multi_pw_aff *mpa); 3404 __isl_give isl_multi_union_pw_aff * 3405 isl_multi_union_pw_aff_copy( 3406 __isl_keep isl_multi_union_pw_aff *mupa); 3407 __isl_null isl_multi_union_pw_aff * 3408 isl_multi_union_pw_aff_free( 3409 __isl_take isl_multi_union_pw_aff *mupa); 3410 3411The number of base expressions in a multiple 3412expression can be obtained using the following functions. 3413 3414 #include <isl/id.h> 3415 int isl_multi_id_size(__isl_keep isl_multi_id *mi); 3416 3417 #include <isl/val.h> 3418 isl_size isl_multi_val_size(__isl_keep isl_multi_val *mv); 3419 3420 #include <isl/aff.h> 3421 isl_size isl_multi_aff_size( 3422 __isl_keep isl_multi_aff *multi); 3423 isl_size isl_multi_pw_aff_size( 3424 __isl_keep isl_multi_pw_aff *mpa); 3425 isl_size isl_multi_union_pw_aff_size( 3426 __isl_keep isl_multi_union_pw_aff *mupa); 3427 3428The base expression at a given position of a multiple 3429expression can be extracted using the following functions. 3430 3431 #include <isl/id.h> 3432 __isl_give isl_id *isl_multi_id_get_at( 3433 __isl_keep isl_multi_id *mi, int pos); 3434 __isl_give isl_id *isl_multi_id_get_id( 3435 __isl_keep isl_multi_id *mi, int pos); 3436 3437 #include <isl/val.h> 3438 __isl_give isl_val *isl_multi_val_get_at( 3439 __isl_keep isl_multi_val *mv, int pos); 3440 __isl_give isl_val *isl_multi_val_get_val( 3441 __isl_keep isl_multi_val *mv, int pos); 3442 3443 #include <isl/aff.h> 3444 __isl_give isl_aff *isl_multi_aff_get_at( 3445 __isl_keep isl_multi_aff *ma, int pos); 3446 __isl_give isl_aff *isl_multi_aff_get_aff( 3447 __isl_keep isl_multi_aff *multi, int pos); 3448 __isl_give isl_pw_aff *isl_multi_pw_aff_get_at( 3449 __isl_keep isl_multi_pw_aff *mpa, int pos); 3450 __isl_give isl_pw_aff *isl_multi_pw_aff_get_pw_aff( 3451 __isl_keep isl_multi_pw_aff *mpa, int pos); 3452 __isl_give isl_union_pw_aff * 3453 isl_multi_union_pw_aff_get_at( 3454 __isl_keep isl_multi_union_pw_aff *mupa, int pos); 3455 __isl_give isl_union_pw_aff * 3456 isl_multi_union_pw_aff_get_union_pw_aff( 3457 __isl_keep isl_multi_union_pw_aff *mupa, int pos); 3458 3459C<isl_multi_id_get_id> is an alternative name for C<isl_multi_id_get_at>. 3460Similarly for the other pairs of functions. 3461 3462The base expression can be replaced using the following functions. 3463 3464 #include <isl/id.h> 3465 __isl_give isl_multi_id *isl_multi_id_set_at( 3466 __isl_take isl_multi_id *mi, int pos, 3467 __isl_take isl_id *id); 3468 __isl_give isl_multi_id *isl_multi_id_set_id( 3469 __isl_take isl_multi_id *mi, int pos, 3470 __isl_take isl_id *id); 3471 3472 #include <isl/val.h> 3473 __isl_give isl_multi_val *isl_multi_val_set_at( 3474 __isl_take isl_multi_val *mv, int pos, 3475 __isl_take isl_val *val); 3476 __isl_give isl_multi_val *isl_multi_val_set_val( 3477 __isl_take isl_multi_val *mv, int pos, 3478 __isl_take isl_val *val); 3479 3480 #include <isl/aff.h> 3481 __isl_give isl_multi_aff *isl_multi_aff_set_at( 3482 __isl_take isl_multi_aff *ma, int pos, 3483 __isl_take isl_aff *aff); 3484 __isl_give isl_multi_aff *isl_multi_aff_set_aff( 3485 __isl_take isl_multi_aff *multi, int pos, 3486 __isl_take isl_aff *aff); 3487 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_set_at( 3488 __isl_take isl_multi_pw_aff *mpa, int pos, 3489 __isl_take isl_pw_aff *pa); 3490 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_set_pw_aff( 3491 __isl_take isl_multi_pw_aff *mpa, int pos, 3492 __isl_take isl_pw_aff *pa); 3493 __isl_give isl_multi_union_pw_aff * 3494 isl_multi_union_pw_aff_set_at( 3495 __isl_take isl_multi_union_pw_aff *mupa, int pos, 3496 __isl_take isl_union_pw_aff *upa); 3497 __isl_give isl_multi_union_pw_aff * 3498 isl_multi_union_pw_aff_set_union_pw_aff( 3499 __isl_take isl_multi_union_pw_aff *mupa, int pos, 3500 __isl_take isl_union_pw_aff *upa); 3501 3502C<isl_multi_id_set_id> is an alternative name for C<isl_multi_id_set_at>. 3503Similarly for the other pairs of functions. 3504 3505A list of all base expressions of a multiple 3506expression can be extracted using the following functions. 3507 3508 #include <isl/id.h> 3509 __isl_give isl_id_list *isl_multi_id_get_list( 3510 __isl_keep isl_multi_id *mi); 3511 3512 #include <isl/val.h> 3513 __isl_give isl_val_list *isl_multi_val_get_list( 3514 __isl_keep isl_multi_val *mv); 3515 3516 #include <isl/aff.h> 3517 __isl_give isl_aff_list *isl_multi_aff_get_list( 3518 __isl_keep isl_multi_aff *multi); 3519 __isl_give isl_pw_aff_list *isl_multi_pw_aff_get_list( 3520 __isl_keep isl_multi_pw_aff *mpa); 3521 __isl_give isl_union_pw_aff_list * 3522 isl_multi_union_pw_aff_list( 3523 __isl_keep isl_multi_union_pw_aff *mupa); 3524 3525The constant terms of the base expressions can be obtained using 3526the following function. 3527 3528 #include <isl/aff.h> 3529 __isl_give isl_multi_val * 3530 isl_multi_aff_get_constant_multi_val( 3531 __isl_keep isl_multi_aff *ma); 3532 3533As a convenience, a sequence of base expressions that have 3534their domains in a given space can be extracted from a sequence 3535of union expressions using the following function. 3536 3537 #include <isl/aff.h> 3538 __isl_give isl_multi_pw_aff * 3539 isl_multi_union_pw_aff_extract_multi_pw_aff( 3540 __isl_keep isl_multi_union_pw_aff *mupa, 3541 __isl_take isl_space *space); 3542 3543Note that there is a difference between C<isl_multi_union_pw_aff> 3544and C<isl_union_pw_multi_aff> objects. The first is a sequence 3545of unions of piecewise expressions, while the second is a union 3546of piecewise sequences. In particular, multiple affine expressions 3547in an C<isl_union_pw_multi_aff> may live in different spaces, 3548while there is only a single multiple expression in 3549an C<isl_multi_union_pw_aff>, which can therefore only live 3550in a single space. This means that not every 3551C<isl_union_pw_multi_aff> can be converted to 3552an C<isl_multi_union_pw_aff>. Conversely, the elements 3553of an C<isl_multi_union_pw_aff> may be defined over different domains, 3554while each multiple expression inside an C<isl_union_pw_multi_aff> 3555has a single domain. The conversion of an C<isl_union_pw_multi_aff> 3556of dimension greater than one may therefore not be exact. 3557The following functions can 3558be used to perform these conversions when they are possible. 3559 3560 #include <isl/aff.h> 3561 __isl_give isl_multi_union_pw_aff * 3562 isl_union_pw_multi_aff_as_multi_union_pw_aff( 3563 __isl_take isl_union_pw_multi_aff *upma); 3564 __isl_give isl_multi_union_pw_aff * 3565 isl_multi_union_pw_aff_from_union_pw_multi_aff( 3566 __isl_take isl_union_pw_multi_aff *upma); 3567 __isl_give isl_union_pw_multi_aff * 3568 isl_union_pw_multi_aff_from_multi_union_pw_aff( 3569 __isl_take isl_multi_union_pw_aff *mupa); 3570 3571C<isl_union_pw_multi_aff_as_multi_union_pw_aff> and 3572C<isl_multi_union_pw_aff_from_union_pw_multi_aff> 3573perform the same operation. 3574 3575=head3 Piecewise Expressions 3576 3577A piecewise expression is an expression that is described 3578using zero or more base expression defined over the same 3579number of cells in the domain space of the base expressions. 3580All base expressions are defined over the same 3581domain space and the cells are disjoint. 3582The space of a piecewise expression is the same as 3583that of the base expressions. 3584If the union of the cells is a strict subset of the domain 3585space, then the value of the piecewise expression outside 3586this union is different for types derived from quasi-affine 3587expressions and those derived from quasipolynomials. 3588Piecewise expressions derived from quasi-affine expressions 3589are considered to be undefined outside the union of their cells. 3590Piecewise expressions derived from quasipolynomials 3591are considered to be zero outside the union of their cells. 3592 3593Piecewise quasipolynomials are mainly used by the C<barvinok> 3594library for representing the number of elements in a parametric set or map. 3595For example, the piecewise quasipolynomial 3596 3597 [n] -> { [x] -> ((1 + n) - x) : x <= n and x >= 0 } 3598 3599represents the number of points in the map 3600 3601 [n] -> { [x] -> [y] : x,y >= 0 and 0 <= x + y <= n } 3602 3603The piecewise expression types defined by C<isl> 3604are C<isl_pw_aff>, C<isl_pw_multi_aff>, 3605C<isl_pw_qpolynomial> and C<isl_pw_qpolynomial_fold>. 3606 3607A piecewise expression with no cells can be created using 3608the following functions. 3609 3610 #include <isl/aff.h> 3611 __isl_give isl_pw_aff *isl_pw_aff_empty( 3612 __isl_take isl_space *space); 3613 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_empty( 3614 __isl_take isl_space *space); 3615 3616A piecewise expression with a single universe cell can be 3617created using the following functions. 3618 3619 #include <isl/aff.h> 3620 __isl_give isl_pw_aff *isl_pw_aff_from_aff( 3621 __isl_take isl_aff *aff); 3622 __isl_give isl_pw_multi_aff * 3623 isl_multi_aff_to_pw_multi_aff( 3624 __isl_take isl_multi_aff *ma); 3625 __isl_give isl_pw_multi_aff * 3626 isl_pw_multi_aff_from_multi_aff( 3627 __isl_take isl_multi_aff *ma); 3628 3629 #include <isl/polynomial.h> 3630 __isl_give isl_pw_qpolynomial * 3631 isl_pw_qpolynomial_from_qpolynomial( 3632 __isl_take isl_qpolynomial *qp); 3633 __isl_give isl_pw_qpolynomial_fold * 3634 isl_pw_qpolynomial_fold_from_qpolynomial_fold( 3635 __isl_take isl_qpolynomial_fold *fold); 3636 3637C<isl_multi_aff_to_pw_multi_aff> and C<isl_pw_multi_aff_from_multi_aff> perform 3638the same operation. 3639 3640The inverse conversions below can only be used if the input 3641expression is known to be defined over a single universe domain. 3642 3643 #include <isl/aff.h> 3644 isl_bool isl_pw_aff_isa_aff(__isl_keep isl_pw_aff *pa); 3645 __isl_give isl_aff *isl_pw_aff_as_aff( 3646 __isl_take isl_pw_aff *pa); 3647 isl_bool isl_multi_pw_aff_isa_multi_aff( 3648 __isl_keep isl_multi_pw_aff *mpa); 3649 __isl_give isl_multi_aff *isl_multi_pw_aff_as_multi_aff( 3650 __isl_take isl_multi_pw_aff *mpa); 3651 isl_bool isl_pw_multi_aff_isa_multi_aff( 3652 __isl_keep isl_pw_multi_aff *pma); 3653 __isl_give isl_multi_aff *isl_pw_multi_aff_as_multi_aff( 3654 __isl_take isl_pw_multi_aff *pma); 3655 3656 #include <isl/polynomial.h> 3657 isl_bool isl_pw_qpolynomial_isa_qpolynomial( 3658 __isl_keep isl_pw_qpolynomial *pwqp); 3659 __isl_give isl_qpolynomial * 3660 isl_pw_qpolynomial_as_qpolynomial( 3661 __isl_take isl_pw_qpolynomial *pwqp); 3662 isl_bool isl_pw_qpolynomial_fold_isa_qpolynomial_fold( 3663 __isl_keep isl_pw_qpolynomial_fold *pwf); 3664 __isl_give isl_qpolynomial_fold * 3665 isl_pw_qpolynomial_fold_as_qpolynomial_fold( 3666 __isl_take isl_pw_qpolynomial_fold *pwf); 3667 3668A piecewise expression with a single specified cell can be 3669created using the following functions. 3670 3671 #include <isl/aff.h> 3672 __isl_give isl_pw_aff *isl_pw_aff_alloc( 3673 __isl_take isl_set *set, __isl_take isl_aff *aff); 3674 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_alloc( 3675 __isl_take isl_set *set, 3676 __isl_take isl_multi_aff *maff); 3677 3678 #include <isl/polynomial.h> 3679 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_alloc( 3680 __isl_take isl_set *set, 3681 __isl_take isl_qpolynomial *qp); 3682 3683The following convenience functions first create a base expression and 3684then create a piecewise expression over a universe domain. 3685 3686 #include <isl/aff.h> 3687 __isl_give isl_pw_aff *isl_pw_aff_zero_on_domain( 3688 __isl_take isl_local_space *ls); 3689 __isl_give isl_pw_aff *isl_pw_aff_var_on_domain( 3690 __isl_take isl_local_space *ls, 3691 enum isl_dim_type type, unsigned pos); 3692 __isl_give isl_pw_aff *isl_pw_aff_nan_on_domain_space( 3693 __isl_take isl_space *space); 3694 __isl_give isl_pw_aff *isl_pw_aff_nan_on_domain( 3695 __isl_take isl_local_space *ls); 3696 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_zero( 3697 __isl_take isl_space *space); 3698 __isl_give isl_pw_multi_aff * 3699 isl_pw_multi_aff_identity_on_domain_space( 3700 __isl_take isl_space *space) 3701 __isl_give isl_pw_multi_aff * 3702 isl_space_identity_pw_multi_aff_on_domain( 3703 __isl_take isl_space *space) 3704 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_identity( 3705 __isl_take isl_space *space); 3706 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_domain_map( 3707 __isl_take isl_space *space); 3708 __isl_give isl_pw_multi_aff * 3709 isl_space_domain_map_pw_multi_aff( 3710 __isl_take isl_space *space); 3711 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_range_map( 3712 __isl_take isl_space *space); 3713 __isl_give isl_pw_multi_aff * 3714 isl_space_range_map_pw_multi_aff( 3715 __isl_take isl_space *space); 3716 __isl_give isl_pw_multi_aff * 3717 isl_pw_multi_aff_project_out_map( 3718 __isl_take isl_space *space, 3719 enum isl_dim_type type, 3720 unsigned first, unsigned n); 3721 3722 #include <isl/polynomial.h> 3723 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_zero( 3724 __isl_take isl_space *space); 3725 3726C<isl_pw_multi_aff_identity_on_domain_space> and 3727C<isl_space_identity_pw_multi_aff_on_domain> 3728perform the same operation. 3729Similarly 3730for the pair C<isl_pw_multi_aff_domain_map> and 3731C<isl_space_domain_map_pw_multi_aff> and 3732for the pair C<isl_pw_multi_aff_range_map> and 3733C<isl_space_range_map_pw_multi_aff>. 3734 3735The following convenience functions first create a base expression and 3736then create a piecewise expression over a given domain. 3737 3738 #include <isl/aff.h> 3739 __isl_give isl_pw_aff *isl_pw_aff_val_on_domain( 3740 __isl_take isl_set *domain, 3741 __isl_take isl_val *v); 3742 __isl_give isl_pw_multi_aff * 3743 isl_pw_multi_aff_multi_val_on_domain( 3744 __isl_take isl_set *domain, 3745 __isl_take isl_multi_val *mv); 3746 __isl_give isl_pw_multi_aff * 3747 isl_set_pw_multi_aff_on_domain_multi_val( 3748 __isl_take isl_set *domain, 3749 __isl_take isl_multi_val *mv); 3750 __isl_give isl_pw_aff *isl_pw_aff_param_on_domain_id( 3751 __isl_take isl_set *domain, 3752 __isl_take isl_id *id); 3753 3754C<isl_set_pw_multi_aff_on_domain_multi_val> is an alternative name 3755for C<isl_pw_multi_aff_multi_val_on_domain>. 3756 3757As a convenience, a piecewise multiple expression can 3758also be created from a piecewise expression. 3759Each multiple expression in the result is derived 3760from the corresponding base expression. 3761 3762 #include <isl/aff.h> 3763 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_from_pw_aff( 3764 __isl_take isl_pw_aff *pa); 3765 3766Similarly, a piecewise quasipolynomial can be 3767created from a piecewise quasi-affine expression using 3768the following function. 3769 3770 #include <isl/polynomial.h> 3771 __isl_give isl_pw_qpolynomial * 3772 isl_pw_qpolynomial_from_pw_aff( 3773 __isl_take isl_pw_aff *pwaff); 3774 3775Piecewise expressions can be copied and freed using the following functions. 3776 3777 #include <isl/aff.h> 3778 __isl_give isl_pw_aff *isl_pw_aff_copy( 3779 __isl_keep isl_pw_aff *pwaff); 3780 __isl_null isl_pw_aff *isl_pw_aff_free( 3781 __isl_take isl_pw_aff *pwaff); 3782 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_copy( 3783 __isl_keep isl_pw_multi_aff *pma); 3784 __isl_null isl_pw_multi_aff *isl_pw_multi_aff_free( 3785 __isl_take isl_pw_multi_aff *pma); 3786 3787 #include <isl/polynomial.h> 3788 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_copy( 3789 __isl_keep isl_pw_qpolynomial *pwqp); 3790 __isl_null isl_pw_qpolynomial *isl_pw_qpolynomial_free( 3791 __isl_take isl_pw_qpolynomial *pwqp); 3792 __isl_give isl_pw_qpolynomial_fold * 3793 isl_pw_qpolynomial_fold_copy( 3794 __isl_keep isl_pw_qpolynomial_fold *pwf); 3795 __isl_null isl_pw_qpolynomial_fold * 3796 isl_pw_qpolynomial_fold_free( 3797 __isl_take isl_pw_qpolynomial_fold *pwf); 3798 3799To iterate over the different cells of a piecewise expression, 3800use the following functions. 3801 3802 #include <isl/aff.h> 3803 isl_bool isl_pw_aff_is_empty(__isl_keep isl_pw_aff *pwaff); 3804 isl_size isl_pw_aff_n_piece(__isl_keep isl_pw_aff *pwaff); 3805 isl_stat isl_pw_aff_foreach_piece( 3806 __isl_keep isl_pw_aff *pwaff, 3807 isl_stat (*fn)(__isl_take isl_set *set, 3808 __isl_take isl_aff *aff, 3809 void *user), void *user); 3810 isl_bool isl_pw_aff_every_piece(__isl_keep isl_pw_aff *pa, 3811 isl_bool (*test)(__isl_keep isl_set *set, 3812 __isl_keep isl_aff *aff, void *user), 3813 void *user); 3814 isl_size isl_pw_multi_aff_n_piece( 3815 __isl_keep isl_pw_multi_aff *pma); 3816 isl_stat isl_pw_multi_aff_foreach_piece( 3817 __isl_keep isl_pw_multi_aff *pma, 3818 isl_stat (*fn)(__isl_take isl_set *set, 3819 __isl_take isl_multi_aff *maff, 3820 void *user), void *user); 3821 isl_bool isl_pw_multi_aff_every_piece( 3822 __isl_keep isl_pw_multi_aff *pma, 3823 isl_bool (*test)(__isl_keep isl_set *set, 3824 __isl_keep isl_multi_aff *ma, void *user), 3825 void *user); 3826 3827 #include <isl/polynomial.h> 3828 isl_size isl_pw_qpolynomial_n_piece( 3829 __isl_keep isl_pw_qpolynomial *pwqp); 3830 isl_stat isl_pw_qpolynomial_foreach_piece( 3831 __isl_keep isl_pw_qpolynomial *pwqp, 3832 isl_stat (*fn)(__isl_take isl_set *set, 3833 __isl_take isl_qpolynomial *qp, 3834 void *user), void *user); 3835 isl_bool isl_pw_qpolynomial_every_piece( 3836 __isl_keep isl_pw_qpolynomial *pwqp, 3837 isl_bool (*test)(__isl_keep isl_set *set, 3838 __isl_keep isl_qpolynomial *qp, 3839 void *user), void *user); 3840 isl_stat isl_pw_qpolynomial_foreach_lifted_piece( 3841 __isl_keep isl_pw_qpolynomial *pwqp, 3842 isl_stat (*fn)(__isl_take isl_set *set, 3843 __isl_take isl_qpolynomial *qp, 3844 void *user), void *user); 3845 isl_size isl_pw_qpolynomial_fold_n_piece( 3846 __isl_keep isl_pw_qpolynomial_fold *pwf); 3847 isl_stat isl_pw_qpolynomial_fold_foreach_piece( 3848 __isl_keep isl_pw_qpolynomial_fold *pwf, 3849 isl_stat (*fn)(__isl_take isl_set *set, 3850 __isl_take isl_qpolynomial_fold *fold, 3851 void *user), void *user); 3852 isl_bool isl_pw_qpolynomial_fold_every_piece( 3853 __isl_keep isl_pw_qpolynomial_fold *pwf, 3854 isl_bool (*test)(__isl_keep isl_set *set, 3855 __isl_keep isl_qpolynomial_fold *fold, 3856 void *user), void *user); 3857 isl_stat isl_pw_qpolynomial_fold_foreach_lifted_piece( 3858 __isl_keep isl_pw_qpolynomial_fold *pwf, 3859 isl_stat (*fn)(__isl_take isl_set *set, 3860 __isl_take isl_qpolynomial_fold *fold, 3861 void *user), void *user); 3862 3863As usual, the function C<fn> should return C<isl_stat_ok> on success 3864and C<isl_stat_error> on failure. The difference between 3865C<isl_pw_qpolynomial_foreach_piece> and 3866C<isl_pw_qpolynomial_foreach_lifted_piece> is that 3867C<isl_pw_qpolynomial_foreach_lifted_piece> will first 3868compute unique representations for all existentially quantified 3869variables and then turn these existentially quantified variables 3870into extra set variables, adapting the associated quasipolynomial 3871accordingly. This means that the C<set> passed to C<fn> 3872will not have any existentially quantified variables, but that 3873the dimensions of the sets may be different for different 3874invocations of C<fn>. 3875Similarly for C<isl_pw_qpolynomial_fold_foreach_piece> 3876and C<isl_pw_qpolynomial_fold_foreach_lifted_piece>. 3877The function C<isl_pw_aff_every_piece> and its variants 3878check whether each call to the callback returns true and 3879stop checking as soon as one of these calls returns false (or error). 3880 3881A piecewise expression consisting of the expressions at a given 3882position of a piecewise multiple expression can be extracted 3883using the following function. 3884 3885 #include <isl/aff.h> 3886 __isl_give isl_pw_aff *isl_pw_multi_aff_get_at( 3887 __isl_keep isl_pw_multi_aff *pma, int pos); 3888 __isl_give isl_pw_aff *isl_pw_multi_aff_get_pw_aff( 3889 __isl_keep isl_pw_multi_aff *pma, int pos); 3890 3891C<isl_pw_multi_aff_get_pw_aff> is an alternative name for 3892C<isl_pw_multi_aff_get_at>. 3893 3894These expressions can be replaced using the following function. 3895 3896 #include <isl/aff.h> 3897 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_set_pw_aff( 3898 __isl_take isl_pw_multi_aff *pma, unsigned pos, 3899 __isl_take isl_pw_aff *pa); 3900 3901Note that there is a difference between C<isl_multi_pw_aff> and 3902C<isl_pw_multi_aff> objects. The first is a sequence of piecewise 3903affine expressions, while the second is a piecewise sequence 3904of affine expressions. In particular, each of the piecewise 3905affine expressions in an C<isl_multi_pw_aff> may have a different 3906domain, while all multiple expressions associated to a cell 3907in an C<isl_pw_multi_aff> have the same domain. 3908It is possible to convert between the two, but when converting 3909an C<isl_multi_pw_aff> to an C<isl_pw_multi_aff>, the domain 3910of the result is the intersection of the domains of the input. 3911The reverse conversion is exact. 3912 3913 #include <isl/aff.h> 3914 __isl_give isl_pw_multi_aff * 3915 isl_pw_multi_aff_from_multi_pw_aff( 3916 __isl_take isl_multi_pw_aff *mpa); 3917 __isl_give isl_multi_pw_aff * 3918 isl_pw_multi_aff_to_multi_pw_aff( 3919 __isl_take isl_pw_multi_aff *pma); 3920 __isl_give isl_multi_pw_aff * 3921 isl_multi_pw_aff_from_pw_multi_aff( 3922 __isl_take isl_pw_multi_aff *pma); 3923 3924C<isl_pw_multi_aff_to_multi_pw_aff> and 3925C<isl_multi_pw_aff_from_pw_multi_aff> perform the same operation. 3926 3927=head3 Union Expressions 3928 3929A union expression collects base expressions defined 3930over different domains. The space of a union expression 3931is that of the shared parameter space. 3932 3933The union expression types defined by C<isl> 3934are C<isl_union_pw_aff>, C<isl_union_pw_multi_aff>, 3935C<isl_union_pw_qpolynomial> and C<isl_union_pw_qpolynomial_fold>. 3936In case of 3937C<isl_union_pw_aff>, 3938C<isl_union_pw_qpolynomial> and C<isl_union_pw_qpolynomial_fold>, 3939there can be at most one base expression for a given domain space. 3940In case of 3941C<isl_union_pw_multi_aff>, 3942there can be multiple such expressions for a given domain space, 3943but the domains of these expressions need to be disjoint. 3944 3945An empty union expression can be created using the following functions. 3946 3947 #include <isl/aff.h> 3948 __isl_give isl_union_pw_aff * 3949 isl_union_pw_aff_empty_ctx( 3950 isl_ctx *ctx); 3951 __isl_give isl_union_pw_aff * 3952 isl_union_pw_aff_empty_space( 3953 __isl_take isl_space *space); 3954 __isl_give isl_union_pw_aff *isl_union_pw_aff_empty( 3955 __isl_take isl_space *space); 3956 __isl_give isl_union_pw_multi_aff * 3957 isl_union_pw_multi_aff_empty_ctx( 3958 isl_ctx *ctx); 3959 __isl_give isl_union_pw_multi_aff * 3960 isl_union_pw_multi_aff_empty_space( 3961 __isl_take isl_space *space); 3962 __isl_give isl_union_pw_multi_aff * 3963 isl_union_pw_multi_aff_empty( 3964 __isl_take isl_space *space); 3965 3966 #include <isl/polynomial.h> 3967 __isl_give isl_union_pw_qpolynomial * 3968 isl_union_pw_qpolynomial_zero_ctx( 3969 isl_ctx *ctx); 3970 __isl_give isl_union_pw_qpolynomial * 3971 isl_union_pw_qpolynomial_zero_space( 3972 __isl_take isl_space *space); 3973 __isl_give isl_union_pw_qpolynomial * 3974 isl_union_pw_qpolynomial_zero( 3975 __isl_take isl_space *space); 3976 3977C<isl_union_pw_aff_empty> is an alternative name for 3978C<isl_union_pw_aff_empty_space>. 3979Similarly for the other pairs of functions. 3980 3981A union expression containing a single base expression 3982can be created using the following functions. 3983 3984 #include <isl/aff.h> 3985 __isl_give isl_union_pw_aff * 3986 isl_pw_aff_to_union_pw_aff( 3987 __isl_take isl_pw_aff *pa); 3988 __isl_give isl_union_pw_aff * 3989 isl_union_pw_aff_from_pw_aff( 3990 __isl_take isl_pw_aff *pa); 3991 __isl_give isl_union_pw_multi_aff * 3992 isl_union_pw_multi_aff_from_aff( 3993 __isl_take isl_aff *aff); 3994 __isl_give isl_union_pw_multi_aff * 3995 isl_pw_multi_aff_to_union_pw_multi_aff( 3996 __isl_take isl_pw_multi_aff *pma); 3997 __isl_give isl_union_pw_multi_aff * 3998 isl_union_pw_multi_aff_from_pw_multi_aff( 3999 __isl_take isl_pw_multi_aff *pma); 4000 4001 #include <isl/polynomial.h> 4002 __isl_give isl_union_pw_qpolynomial * 4003 isl_pw_qpolynomial_to_union_pw_qpolynomial( 4004 __isl_take isl_pw_qpolynomial *pwqp); 4005 __isl_give isl_union_pw_qpolynomial * 4006 isl_union_pw_qpolynomial_from_pw_qpolynomial( 4007 __isl_take isl_pw_qpolynomial *pwqp); 4008 __isl_give isl_union_pw_qpolynomial_fold * 4009 isl_pw_qpolynomial_fold_to_union_pw_qpolynomial_fold( 4010 __isl_take isl_pw_qpolynomial_fold *pwf); 4011 __isl_give isl_union_pw_qpolynomial_fold * 4012 isl_union_pw_qpolynomial_fold_from_pw_qpolynomial_fold( 4013 __isl_take isl_pw_qpolynomial_fold *pwf); 4014 4015C<isl_pw_aff_to_union_pw_aff> and C<isl_union_pw_aff_from_pw_aff> perform 4016the same operation. 4017Similarly for C<isl_pw_multi_aff_to_union_pw_multi_aff> and 4018C<isl_union_pw_multi_aff_from_pw_multi_aff>, 4019for 4020C<isl_pw_qpolynomial_to_union_pw_qpolynomial> and 4021C<isl_union_pw_qpolynomial_from_pw_qpolynomial>, and 4022for 4023C<isl_pw_qpolynomial_fold_to_union_pw_qpolynomial_fold> and 4024C<isl_union_pw_qpolynomial_fold_from_pw_qpolynomial_fold>. 4025 4026The inverse conversions below can only be used if the input 4027expression is known to live in exactly one space. 4028 4029 #include <isl/aff.h> 4030 isl_bool isl_union_pw_multi_aff_isa_pw_multi_aff( 4031 __isl_keep isl_union_pw_multi_aff *upma); 4032 __isl_give isl_pw_multi_aff * 4033 isl_union_pw_multi_aff_as_pw_multi_aff( 4034 __isl_take isl_union_pw_multi_aff *upma); 4035 4036A union piecewise expression containing a single base expression 4037on a universe domain can also be created directly from 4038a base expression using the following functions. 4039 4040 #include <isl/aff.h> 4041 __isl_give isl_union_pw_aff *isl_union_pw_aff_from_aff( 4042 __isl_take isl_aff *aff); 4043 __isl_give isl_union_pw_multi_aff * 4044 isl_union_pw_multi_aff_from_multi_aff( 4045 __isl_take isl_multi_aff *ma); 4046 4047The following functions create a base expression on each 4048of the sets in the union set and collect the results. 4049 4050 #include <isl/aff.h> 4051 __isl_give isl_union_pw_multi_aff * 4052 isl_union_pw_multi_aff_from_union_pw_aff( 4053 __isl_take isl_union_pw_aff *upa); 4054 __isl_give isl_union_pw_aff * 4055 isl_union_pw_multi_aff_get_union_pw_aff( 4056 __isl_keep isl_union_pw_multi_aff *upma, int pos); 4057 __isl_give isl_union_pw_aff * 4058 isl_union_pw_aff_val_on_domain( 4059 __isl_take isl_union_set *domain, 4060 __isl_take isl_val *v); 4061 __isl_give isl_union_pw_multi_aff * 4062 isl_union_pw_multi_aff_multi_val_on_domain( 4063 __isl_take isl_union_set *domain, 4064 __isl_take isl_multi_val *mv); 4065 __isl_give isl_union_pw_aff * 4066 isl_union_pw_aff_param_on_domain_id( 4067 __isl_take isl_union_set *domain, 4068 __isl_take isl_id *id); 4069 4070The C<id> argument of C<isl_union_pw_aff_param_on_domain_id> 4071is the identifier of a parameter that may or may not already 4072be present in C<domain>. 4073 4074An C<isl_union_pw_aff> that is equal to a (parametric) affine 4075or piecewise affine 4076expression on a given domain can be created using the following 4077functions. 4078 4079 #include <isl/aff.h> 4080 __isl_give isl_union_pw_aff * 4081 isl_union_pw_aff_aff_on_domain( 4082 __isl_take isl_union_set *domain, 4083 __isl_take isl_aff *aff); 4084 __isl_give isl_union_pw_aff * 4085 isl_union_pw_aff_pw_aff_on_domain( 4086 __isl_take isl_union_set *domain, 4087 __isl_take isl_pw_aff *pa); 4088 4089A base expression can be added to a union expression using 4090the following functions. 4091 4092 #include <isl/aff.h> 4093 __isl_give isl_union_pw_aff * 4094 isl_union_pw_aff_add_pw_aff( 4095 __isl_take isl_union_pw_aff *upa, 4096 __isl_take isl_pw_aff *pa); 4097 __isl_give isl_union_pw_multi_aff * 4098 isl_union_pw_multi_aff_add_pw_multi_aff( 4099 __isl_take isl_union_pw_multi_aff *upma, 4100 __isl_take isl_pw_multi_aff *pma); 4101 4102 #include <isl/polynomial.h> 4103 __isl_give isl_union_pw_qpolynomial * 4104 isl_union_pw_qpolynomial_add_pw_qpolynomial( 4105 __isl_take isl_union_pw_qpolynomial *upwqp, 4106 __isl_take isl_pw_qpolynomial *pwqp); 4107 4108Union expressions can be copied and freed using 4109the following functions. 4110 4111 #include <isl/aff.h> 4112 __isl_give isl_union_pw_aff *isl_union_pw_aff_copy( 4113 __isl_keep isl_union_pw_aff *upa); 4114 __isl_null isl_union_pw_aff *isl_union_pw_aff_free( 4115 __isl_take isl_union_pw_aff *upa); 4116 __isl_give isl_union_pw_multi_aff * 4117 isl_union_pw_multi_aff_copy( 4118 __isl_keep isl_union_pw_multi_aff *upma); 4119 __isl_null isl_union_pw_multi_aff * 4120 isl_union_pw_multi_aff_free( 4121 __isl_take isl_union_pw_multi_aff *upma); 4122 4123 #include <isl/polynomial.h> 4124 __isl_give isl_union_pw_qpolynomial * 4125 isl_union_pw_qpolynomial_copy( 4126 __isl_keep isl_union_pw_qpolynomial *upwqp); 4127 __isl_null isl_union_pw_qpolynomial * 4128 isl_union_pw_qpolynomial_free( 4129 __isl_take isl_union_pw_qpolynomial *upwqp); 4130 __isl_give isl_union_pw_qpolynomial_fold * 4131 isl_union_pw_qpolynomial_fold_copy( 4132 __isl_keep isl_union_pw_qpolynomial_fold *upwf); 4133 __isl_null isl_union_pw_qpolynomial_fold * 4134 isl_union_pw_qpolynomial_fold_free( 4135 __isl_take isl_union_pw_qpolynomial_fold *upwf); 4136 4137To iterate over the base expressions in a union expression, 4138use the following functions. 4139 4140 #include <isl/aff.h> 4141 isl_size isl_union_pw_aff_n_pw_aff( 4142 __isl_keep isl_union_pw_aff *upa); 4143 isl_stat isl_union_pw_aff_foreach_pw_aff( 4144 __isl_keep isl_union_pw_aff *upa, 4145 isl_stat (*fn)(__isl_take isl_pw_aff *pa, 4146 void *user), void *user); 4147 isl_bool isl_union_pw_aff_every_pw_aff( 4148 __isl_keep isl_union_pw_aff *upa, 4149 isl_bool (*test)(__isl_keep isl_pw_aff *pa, 4150 void *user), void *user); 4151 isl_size isl_union_pw_multi_aff_n_pw_multi_aff( 4152 __isl_keep isl_union_pw_multi_aff *upma); 4153 isl_stat isl_union_pw_multi_aff_foreach_pw_multi_aff( 4154 __isl_keep isl_union_pw_multi_aff *upma, 4155 isl_stat (*fn)(__isl_take isl_pw_multi_aff *pma, 4156 void *user), void *user); 4157 isl_bool isl_union_pw_multi_aff_every_pw_multi_aff( 4158 __isl_keep isl_union_pw_multi_aff *upma, 4159 isl_bool (*test)( 4160 __isl_keep isl_pw_multi_aff *pma, 4161 void *user), void *user); 4162 4163 #include <isl/polynomial.h> 4164 isl_size isl_union_pw_qpolynomial_n_pw_qpolynomial( 4165 __isl_keep isl_union_pw_qpolynomial *upwqp); 4166 isl_stat isl_union_pw_qpolynomial_foreach_pw_qpolynomial( 4167 __isl_keep isl_union_pw_qpolynomial *upwqp, 4168 isl_stat (*fn)(__isl_take isl_pw_qpolynomial *pwqp, 4169 void *user), void *user); 4170 isl_bool isl_union_pw_qpolynomial_every_pw_qpolynomial( 4171 __isl_keep isl_union_pw_qpolynomial *upwqp, 4172 isl_bool (*test)( 4173 __isl_keep isl_pw_qpolynomial *pwqp, 4174 void *user), void *user); 4175 isl_size isl_union_pw_qpolynomial_fold_n_pw_qpolynomial_fold( 4176 __isl_keep isl_union_pw_qpolynomial_fold *upwf); 4177 isl_stat isl_union_pw_qpolynomial_fold_foreach_pw_qpolynomial_fold( 4178 __isl_keep isl_union_pw_qpolynomial_fold *upwf, 4179 isl_stat (*fn)(__isl_take isl_pw_qpolynomial_fold *pwf, 4180 void *user), void *user); 4181 isl_bool 4182 isl_union_pw_qpolynomial_fold_every_pw_qpolynomial_fold( 4183 __isl_keep isl_union_pw_qpolynomial_fold *upwf, 4184 isl_bool (*test)( 4185 __isl_keep isl_pw_qpolynomial_fold *pwf, 4186 void *user), void *user); 4187 4188To extract the base expression in a given space from a union, use 4189the following functions. 4190 4191 #include <isl/aff.h> 4192 __isl_give isl_pw_aff *isl_union_pw_aff_extract_pw_aff( 4193 __isl_keep isl_union_pw_aff *upa, 4194 __isl_take isl_space *space); 4195 __isl_give isl_pw_multi_aff * 4196 isl_union_pw_multi_aff_extract_pw_multi_aff( 4197 __isl_keep isl_union_pw_multi_aff *upma, 4198 __isl_take isl_space *space); 4199 4200 #include <isl/polynomial.h> 4201 __isl_give isl_pw_qpolynomial * 4202 isl_union_pw_qpolynomial_extract_pw_qpolynomial( 4203 __isl_keep isl_union_pw_qpolynomial *upwqp, 4204 __isl_take isl_space *space); 4205 4206It is also possible to obtain a list of the base expressions using 4207the following functions. 4208 4209 #include <isl/aff.h> 4210 __isl_give isl_pw_aff_list * 4211 isl_union_pw_aff_get_pw_aff_list( 4212 __isl_keep isl_union_pw_aff *upa); 4213 __isl_give isl_pw_multi_aff_list * 4214 isl_union_pw_multi_aff_get_pw_multi_aff_list( 4215 __isl_keep isl_union_pw_multi_aff *upma); 4216 4217 #include <isl/polynomial.h> 4218 __isl_give isl_pw_qpolynomial_list * 4219 isl_union_pw_qpolynomial_get_pw_qpolynomial_list( 4220 __isl_keep isl_union_pw_qpolynomial *upwqp); 4221 __isl_give isl_pw_qpolynomial_fold_list * 4222 isl_union_pw_qpolynomial_fold_get_pw_qpolynomial_fold_list( 4223 __isl_keep isl_union_pw_qpolynomial_fold *upwf); 4224 4225The returned list can be manipulated using the functions in L<"Lists">. 4226 4227=head2 Input and Output 4228 4229For set and relation, 4230C<isl> supports its own input/output format, which is similar 4231to the C<Omega> format, but also supports the C<PolyLib> format 4232in some cases. 4233For other object types, typically only an C<isl> format is supported. 4234 4235=head3 C<isl> format 4236 4237The C<isl> format is similar to that of C<Omega>, but has a different 4238syntax for describing the parameters and allows for the definition 4239of an existentially quantified variable as the integer division 4240of an affine expression. 4241For example, the set of integers C<i> between C<0> and C<n> 4242such that C<i % 10 <= 6> can be described as 4243 4244 [n] -> { [i] : exists (a = [i/10] : 0 <= i and i <= n and 4245 i - 10 a <= 6) } 4246 4247A set or relation can have several disjuncts, separated 4248by the keyword C<or>. Each disjunct is either a conjunction 4249of constraints or a projection (C<exists>) of a conjunction 4250of constraints. The constraints are separated by the keyword 4251C<and>. 4252 4253=head3 C<PolyLib> format 4254 4255If the represented set is a union, then the first line 4256contains a single number representing the number of disjuncts. 4257Otherwise, a line containing the number C<1> is optional. 4258 4259Each disjunct is represented by a matrix of constraints. 4260The first line contains two numbers representing 4261the number of rows and columns, 4262where the number of rows is equal to the number of constraints 4263and the number of columns is equal to two plus the number of variables. 4264The following lines contain the actual rows of the constraint matrix. 4265In each row, the first column indicates whether the constraint 4266is an equality (C<0>) or inequality (C<1>). The final column 4267corresponds to the constant term. 4268 4269If the set is parametric, then the coefficients of the parameters 4270appear in the last columns before the constant column. 4271The coefficients of any existentially quantified variables appear 4272between those of the set variables and those of the parameters. 4273 4274=head3 Extended C<PolyLib> format 4275 4276The extended C<PolyLib> format is nearly identical to the 4277C<PolyLib> format. The only difference is that the line 4278containing the number of rows and columns of a constraint matrix 4279also contains four additional numbers: 4280the number of output dimensions, the number of input dimensions, 4281the number of local dimensions (i.e., the number of existentially 4282quantified variables) and the number of parameters. 4283For sets, the number of ``output'' dimensions is equal 4284to the number of set dimensions, while the number of ``input'' 4285dimensions is zero. 4286 4287=head3 Input 4288 4289Objects can be read from input using the following functions. 4290 4291 #include <isl/id.h> 4292 __isl_give isl_id *isl_id_read_from_str(isl_ctx *ctx, 4293 const char *str); 4294 __isl_give isl_multi_id *isl_multi_id_read_from_str( 4295 isl_ctx *ctx, const char *str); 4296 4297 #include <isl/val.h> 4298 __isl_give isl_val *isl_val_read_from_str(isl_ctx *ctx, 4299 const char *str); 4300 __isl_give isl_multi_val *isl_multi_val_read_from_str( 4301 isl_ctx *ctx, const char *str); 4302 4303 #include <isl/set.h> 4304 __isl_give isl_basic_set *isl_basic_set_read_from_file( 4305 isl_ctx *ctx, FILE *input); 4306 __isl_give isl_basic_set *isl_basic_set_read_from_str( 4307 isl_ctx *ctx, const char *str); 4308 __isl_give isl_set *isl_set_read_from_file(isl_ctx *ctx, 4309 FILE *input); 4310 __isl_give isl_set *isl_set_read_from_str(isl_ctx *ctx, 4311 const char *str); 4312 4313 #include <isl/map.h> 4314 __isl_give isl_basic_map *isl_basic_map_read_from_file( 4315 isl_ctx *ctx, FILE *input); 4316 __isl_give isl_basic_map *isl_basic_map_read_from_str( 4317 isl_ctx *ctx, const char *str); 4318 __isl_give isl_map *isl_map_read_from_file( 4319 isl_ctx *ctx, FILE *input); 4320 __isl_give isl_map *isl_map_read_from_str(isl_ctx *ctx, 4321 const char *str); 4322 4323 #include <isl/union_set.h> 4324 __isl_give isl_union_set *isl_union_set_read_from_file( 4325 isl_ctx *ctx, FILE *input); 4326 __isl_give isl_union_set *isl_union_set_read_from_str( 4327 isl_ctx *ctx, const char *str); 4328 4329 #include <isl/union_map.h> 4330 __isl_give isl_union_map *isl_union_map_read_from_file( 4331 isl_ctx *ctx, FILE *input); 4332 __isl_give isl_union_map *isl_union_map_read_from_str( 4333 isl_ctx *ctx, const char *str); 4334 4335 #include <isl/aff.h> 4336 __isl_give isl_aff *isl_aff_read_from_str( 4337 isl_ctx *ctx, const char *str); 4338 __isl_give isl_multi_aff *isl_multi_aff_read_from_str( 4339 isl_ctx *ctx, const char *str); 4340 __isl_give isl_pw_aff *isl_pw_aff_read_from_str( 4341 isl_ctx *ctx, const char *str); 4342 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_read_from_str( 4343 isl_ctx *ctx, const char *str); 4344 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_read_from_str( 4345 isl_ctx *ctx, const char *str); 4346 __isl_give isl_union_pw_aff * 4347 isl_union_pw_aff_read_from_str( 4348 isl_ctx *ctx, const char *str); 4349 __isl_give isl_union_pw_multi_aff * 4350 isl_union_pw_multi_aff_read_from_str( 4351 isl_ctx *ctx, const char *str); 4352 __isl_give isl_multi_union_pw_aff * 4353 isl_multi_union_pw_aff_read_from_str( 4354 isl_ctx *ctx, const char *str); 4355 4356 #include <isl/polynomial.h> 4357 __isl_give isl_union_pw_qpolynomial * 4358 isl_union_pw_qpolynomial_read_from_str( 4359 isl_ctx *ctx, const char *str); 4360 4361 __isl_give isl_pw_qpolynomial_fold * 4362 isl_pw_qpolynomial_fold_read_from_str( 4363 isl_ctx *ctx, const char *str); 4364 4365For sets and relations, 4366the input format is autodetected and may be either the C<PolyLib> format 4367or the C<isl> format. 4368 4369=head3 Output 4370 4371Before anything can be printed, an C<isl_printer> needs to 4372be created. 4373 4374 __isl_give isl_printer *isl_printer_to_file(isl_ctx *ctx, 4375 FILE *file); 4376 __isl_give isl_printer *isl_printer_to_str(isl_ctx *ctx); 4377 __isl_null isl_printer *isl_printer_free( 4378 __isl_take isl_printer *printer); 4379 4380C<isl_printer_to_file> prints to the given file, while 4381C<isl_printer_to_str> prints to a string that can be extracted 4382using the following function. 4383 4384 #include <isl/printer.h> 4385 __isl_give char *isl_printer_get_str( 4386 __isl_keep isl_printer *printer); 4387 4388The printer can be inspected using the following functions. 4389 4390 FILE *isl_printer_get_file( 4391 __isl_keep isl_printer *printer); 4392 int isl_printer_get_output_format( 4393 __isl_keep isl_printer *p); 4394 int isl_printer_get_yaml_style(__isl_keep isl_printer *p); 4395 4396The behavior of the printer can be modified in various ways 4397 4398 __isl_give isl_printer *isl_printer_set_output_format( 4399 __isl_take isl_printer *p, int output_format); 4400 __isl_give isl_printer *isl_printer_set_indent( 4401 __isl_take isl_printer *p, int indent); 4402 __isl_give isl_printer *isl_printer_set_indent_prefix( 4403 __isl_take isl_printer *p, const char *prefix); 4404 __isl_give isl_printer *isl_printer_indent( 4405 __isl_take isl_printer *p, int indent); 4406 __isl_give isl_printer *isl_printer_set_prefix( 4407 __isl_take isl_printer *p, const char *prefix); 4408 __isl_give isl_printer *isl_printer_set_suffix( 4409 __isl_take isl_printer *p, const char *suffix); 4410 __isl_give isl_printer *isl_printer_set_yaml_style( 4411 __isl_take isl_printer *p, int yaml_style); 4412 4413The C<output_format> may be either C<ISL_FORMAT_ISL>, C<ISL_FORMAT_OMEGA>, 4414C<ISL_FORMAT_POLYLIB>, C<ISL_FORMAT_EXT_POLYLIB> or C<ISL_FORMAT_LATEX> 4415and defaults to C<ISL_FORMAT_ISL>. 4416Each line in the output is prefixed by C<indent_prefix>, 4417indented by C<indent> (set by C<isl_printer_set_indent>) spaces 4418(default: 0), prefixed by C<prefix> and suffixed by C<suffix>. 4419In the C<PolyLib> format output, 4420the coefficients of the existentially quantified variables 4421appear between those of the set variables and those 4422of the parameters. 4423The function C<isl_printer_indent> increases the indentation 4424by the specified amount (which may be negative). 4425The YAML style may be either C<ISL_YAML_STYLE_BLOCK> or 4426C<ISL_YAML_STYLE_FLOW> and when we are printing something 4427in YAML format. 4428 4429To actually print something, use 4430 4431 #include <isl/printer.h> 4432 __isl_give isl_printer *isl_printer_print_double( 4433 __isl_take isl_printer *p, double d); 4434 4435 #include <isl/val.h> 4436 __isl_give isl_printer *isl_printer_print_val( 4437 __isl_take isl_printer *p, __isl_keep isl_val *v); 4438 4439 #include <isl/set.h> 4440 __isl_give isl_printer *isl_printer_print_basic_set( 4441 __isl_take isl_printer *printer, 4442 __isl_keep isl_basic_set *bset); 4443 __isl_give isl_printer *isl_printer_print_set( 4444 __isl_take isl_printer *printer, 4445 __isl_keep isl_set *set); 4446 4447 #include <isl/map.h> 4448 __isl_give isl_printer *isl_printer_print_basic_map( 4449 __isl_take isl_printer *printer, 4450 __isl_keep isl_basic_map *bmap); 4451 __isl_give isl_printer *isl_printer_print_map( 4452 __isl_take isl_printer *printer, 4453 __isl_keep isl_map *map); 4454 4455 #include <isl/union_set.h> 4456 __isl_give isl_printer *isl_printer_print_union_set( 4457 __isl_take isl_printer *p, 4458 __isl_keep isl_union_set *uset); 4459 4460 #include <isl/union_map.h> 4461 __isl_give isl_printer *isl_printer_print_union_map( 4462 __isl_take isl_printer *p, 4463 __isl_keep isl_union_map *umap); 4464 4465 #include <isl/val.h> 4466 __isl_give isl_printer *isl_printer_print_multi_val( 4467 __isl_take isl_printer *p, 4468 __isl_keep isl_multi_val *mv); 4469 4470 #include <isl/id.h> 4471 __isl_give isl_printer *isl_printer_print_multi_id( 4472 __isl_take isl_printer *p, 4473 __isl_keep isl_multi_id *mi); 4474 4475 #include <isl/aff.h> 4476 __isl_give isl_printer *isl_printer_print_aff( 4477 __isl_take isl_printer *p, __isl_keep isl_aff *aff); 4478 __isl_give isl_printer *isl_printer_print_multi_aff( 4479 __isl_take isl_printer *p, 4480 __isl_keep isl_multi_aff *maff); 4481 __isl_give isl_printer *isl_printer_print_pw_aff( 4482 __isl_take isl_printer *p, 4483 __isl_keep isl_pw_aff *pwaff); 4484 __isl_give isl_printer *isl_printer_print_pw_multi_aff( 4485 __isl_take isl_printer *p, 4486 __isl_keep isl_pw_multi_aff *pma); 4487 __isl_give isl_printer *isl_printer_print_multi_pw_aff( 4488 __isl_take isl_printer *p, 4489 __isl_keep isl_multi_pw_aff *mpa); 4490 __isl_give isl_printer *isl_printer_print_union_pw_aff( 4491 __isl_take isl_printer *p, 4492 __isl_keep isl_union_pw_aff *upa); 4493 __isl_give isl_printer *isl_printer_print_union_pw_multi_aff( 4494 __isl_take isl_printer *p, 4495 __isl_keep isl_union_pw_multi_aff *upma); 4496 __isl_give isl_printer * 4497 isl_printer_print_multi_union_pw_aff( 4498 __isl_take isl_printer *p, 4499 __isl_keep isl_multi_union_pw_aff *mupa); 4500 4501 #include <isl/polynomial.h> 4502 __isl_give isl_printer *isl_printer_print_qpolynomial( 4503 __isl_take isl_printer *p, 4504 __isl_keep isl_qpolynomial *qp); 4505 __isl_give isl_printer *isl_printer_print_pw_qpolynomial( 4506 __isl_take isl_printer *p, 4507 __isl_keep isl_pw_qpolynomial *pwqp); 4508 __isl_give isl_printer *isl_printer_print_union_pw_qpolynomial( 4509 __isl_take isl_printer *p, 4510 __isl_keep isl_union_pw_qpolynomial *upwqp); 4511 4512 __isl_give isl_printer * 4513 isl_printer_print_pw_qpolynomial_fold( 4514 __isl_take isl_printer *p, 4515 __isl_keep isl_pw_qpolynomial_fold *pwf); 4516 __isl_give isl_printer * 4517 isl_printer_print_union_pw_qpolynomial_fold( 4518 __isl_take isl_printer *p, 4519 __isl_keep isl_union_pw_qpolynomial_fold *upwf); 4520 4521For C<isl_printer_print_qpolynomial>, 4522C<isl_printer_print_pw_qpolynomial> and 4523C<isl_printer_print_pw_qpolynomial_fold>, 4524the output format of the printer 4525needs to be set to either C<ISL_FORMAT_ISL> or C<ISL_FORMAT_C>. 4526For C<isl_printer_print_union_pw_qpolynomial> and 4527C<isl_printer_print_union_pw_qpolynomial_fold>, only C<ISL_FORMAT_ISL> 4528is supported. 4529In case of printing in C<ISL_FORMAT_C>, the user may want 4530to set the names of all dimensions first. 4531 4532C<isl> also provides limited support for printing YAML documents, 4533just enough for the internal use for printing such documents. 4534 4535 #include <isl/printer.h> 4536 __isl_give isl_printer *isl_printer_yaml_start_mapping( 4537 __isl_take isl_printer *p); 4538 __isl_give isl_printer *isl_printer_yaml_end_mapping( 4539 __isl_take isl_printer *p); 4540 __isl_give isl_printer *isl_printer_yaml_start_sequence( 4541 __isl_take isl_printer *p); 4542 __isl_give isl_printer *isl_printer_yaml_end_sequence( 4543 __isl_take isl_printer *p); 4544 __isl_give isl_printer *isl_printer_yaml_next( 4545 __isl_take isl_printer *p); 4546 4547A document is started by a call to either 4548C<isl_printer_yaml_start_mapping> or C<isl_printer_yaml_start_sequence>. 4549Anything printed to the printer after such a call belong to the 4550first key of the mapping or the first element in the sequence. 4551The function C<isl_printer_yaml_next> moves to the value if 4552we are currently printing a mapping key, the next key if we 4553are printing a value or the next element if we are printing 4554an element in a sequence. 4555Nested mappings and sequences are initiated by the same 4556C<isl_printer_yaml_start_mapping> or C<isl_printer_yaml_start_sequence>. 4557Each call to these functions needs to have a corresponding call to 4558C<isl_printer_yaml_end_mapping> or C<isl_printer_yaml_end_sequence>. 4559 4560When called on a file printer, the following function flushes 4561the file. When called on a string printer, the buffer is cleared. 4562 4563 __isl_give isl_printer *isl_printer_flush( 4564 __isl_take isl_printer *p); 4565 4566The following functions allow the user to attach 4567notes to a printer in order to keep track of additional state. 4568 4569 #include <isl/printer.h> 4570 isl_bool isl_printer_has_note(__isl_keep isl_printer *p, 4571 __isl_keep isl_id *id); 4572 __isl_give isl_id *isl_printer_get_note( 4573 __isl_keep isl_printer *p, __isl_take isl_id *id); 4574 __isl_give isl_printer *isl_printer_set_note( 4575 __isl_take isl_printer *p, 4576 __isl_take isl_id *id, __isl_take isl_id *note); 4577 4578C<isl_printer_set_note> associates the given note to the given 4579identifier in the printer. 4580C<isl_printer_get_note> retrieves a note associated to an 4581identifier, while 4582C<isl_printer_has_note> checks if there is such a note. 4583C<isl_printer_get_note> fails if the requested note does not exist. 4584 4585Alternatively, a string representation can be obtained 4586directly using the following functions, which always print 4587in isl format. 4588 4589 #include <isl/id.h> 4590 __isl_give char *isl_id_to_str( 4591 __isl_keep isl_id *id); 4592 __isl_give char *isl_multi_id_to_str( 4593 __isl_keep isl_multi_id *mi); 4594 4595 #include <isl/space.h> 4596 __isl_give char *isl_space_to_str( 4597 __isl_keep isl_space *space); 4598 4599 #include <isl/val.h> 4600 __isl_give char *isl_val_to_str(__isl_keep isl_val *v); 4601 __isl_give char *isl_multi_val_to_str( 4602 __isl_keep isl_multi_val *mv); 4603 4604 #include <isl/set.h> 4605 __isl_give char *isl_basic_set_to_str( 4606 __isl_keep isl_basic_set *bset); 4607 __isl_give char *isl_set_to_str( 4608 __isl_keep isl_set *set); 4609 4610 #include <isl/union_set.h> 4611 __isl_give char *isl_union_set_to_str( 4612 __isl_keep isl_union_set *uset); 4613 4614 #include <isl/map.h> 4615 __isl_give char *isl_basic_map_to_str( 4616 __isl_keep isl_basic_map *bmap); 4617 __isl_give char *isl_map_to_str( 4618 __isl_keep isl_map *map); 4619 4620 #include <isl/union_map.h> 4621 __isl_give char *isl_union_map_to_str( 4622 __isl_keep isl_union_map *umap); 4623 4624 #include <isl/aff.h> 4625 __isl_give char *isl_aff_to_str(__isl_keep isl_aff *aff); 4626 __isl_give char *isl_pw_aff_to_str( 4627 __isl_keep isl_pw_aff *pa); 4628 __isl_give char *isl_multi_aff_to_str( 4629 __isl_keep isl_multi_aff *ma); 4630 __isl_give char *isl_pw_multi_aff_to_str( 4631 __isl_keep isl_pw_multi_aff *pma); 4632 __isl_give char *isl_multi_pw_aff_to_str( 4633 __isl_keep isl_multi_pw_aff *mpa); 4634 __isl_give char *isl_union_pw_aff_to_str( 4635 __isl_keep isl_union_pw_aff *upa); 4636 __isl_give char *isl_union_pw_multi_aff_to_str( 4637 __isl_keep isl_union_pw_multi_aff *upma); 4638 __isl_give char *isl_multi_union_pw_aff_to_str( 4639 __isl_keep isl_multi_union_pw_aff *mupa); 4640 4641 #include <isl/point.h> 4642 __isl_give char *isl_point_to_str( 4643 __isl_keep isl_point *pnt); 4644 4645 #include <isl/polynomial.h> 4646 __isl_give char *isl_pw_qpolynomial_to_str( 4647 __isl_keep isl_pw_qpolynomial *pwqp); 4648 __isl_give char *isl_union_pw_qpolynomial_to_str( 4649 __isl_keep isl_union_pw_qpolynomial *upwqp); 4650 4651=head2 Properties 4652 4653=head3 Unary Properties 4654 4655=over 4656 4657=item * Emptiness 4658 4659The following functions test whether the given set or relation 4660contains any integer points. The ``plain'' variants do not perform 4661any computations, but simply check if the given set or relation 4662is already known to be empty. 4663 4664 #include <isl/set.h> 4665 isl_bool isl_basic_set_plain_is_empty( 4666 __isl_keep isl_basic_set *bset); 4667 isl_bool isl_basic_set_is_empty( 4668 __isl_keep isl_basic_set *bset); 4669 isl_bool isl_set_plain_is_empty( 4670 __isl_keep isl_set *set); 4671 isl_bool isl_set_is_empty(__isl_keep isl_set *set); 4672 4673 #include <isl/union_set.h> 4674 isl_bool isl_union_set_is_empty( 4675 __isl_keep isl_union_set *uset); 4676 4677 #include <isl/map.h> 4678 isl_bool isl_basic_map_plain_is_empty( 4679 __isl_keep isl_basic_map *bmap); 4680 isl_bool isl_basic_map_is_empty( 4681 __isl_keep isl_basic_map *bmap); 4682 isl_bool isl_map_plain_is_empty( 4683 __isl_keep isl_map *map); 4684 isl_bool isl_map_is_empty(__isl_keep isl_map *map); 4685 4686 #include <isl/union_map.h> 4687 isl_bool isl_union_map_plain_is_empty( 4688 __isl_keep isl_union_map *umap); 4689 isl_bool isl_union_map_is_empty( 4690 __isl_keep isl_union_map *umap); 4691 4692 #include <isl/aff.h> 4693 isl_bool isl_union_pw_multi_aff_plain_is_empty( 4694 __isl_keep isl_union_pw_multi_aff *upma); 4695 4696=item * Universality 4697 4698 isl_bool isl_basic_set_plain_is_universe( 4699 __isl_keep isl_basic_set *bset); 4700 isl_bool isl_basic_set_is_universe( 4701 __isl_keep isl_basic_set *bset); 4702 isl_bool isl_basic_map_plain_is_universe( 4703 __isl_keep isl_basic_map *bmap); 4704 isl_bool isl_basic_map_is_universe( 4705 __isl_keep isl_basic_map *bmap); 4706 isl_bool isl_set_plain_is_universe( 4707 __isl_keep isl_set *set); 4708 isl_bool isl_map_plain_is_universe( 4709 __isl_keep isl_map *map); 4710 4711=item * Single-valuedness 4712 4713 #include <isl/set.h> 4714 isl_bool isl_set_is_singleton(__isl_keep isl_set *set); 4715 4716 #include <isl/map.h> 4717 isl_bool isl_basic_map_is_single_valued( 4718 __isl_keep isl_basic_map *bmap); 4719 isl_bool isl_map_plain_is_single_valued( 4720 __isl_keep isl_map *map); 4721 isl_bool isl_map_is_single_valued(__isl_keep isl_map *map); 4722 4723 #include <isl/union_map.h> 4724 isl_bool isl_union_map_is_single_valued( 4725 __isl_keep isl_union_map *umap); 4726 4727=item * Injectivity 4728 4729 isl_bool isl_map_plain_is_injective( 4730 __isl_keep isl_map *map); 4731 isl_bool isl_map_is_injective( 4732 __isl_keep isl_map *map); 4733 isl_bool isl_union_map_plain_is_injective( 4734 __isl_keep isl_union_map *umap); 4735 isl_bool isl_union_map_is_injective( 4736 __isl_keep isl_union_map *umap); 4737 4738=item * Bijectivity 4739 4740 isl_bool isl_map_is_bijective( 4741 __isl_keep isl_map *map); 4742 isl_bool isl_union_map_is_bijective( 4743 __isl_keep isl_union_map *umap); 4744 4745=item * Identity 4746 4747The following functions test whether the given relation 4748only maps elements to themselves. 4749 4750 #include <isl/map.h> 4751 isl_bool isl_map_is_identity( 4752 __isl_keep isl_map *map); 4753 4754 #include <isl/union_map.h> 4755 isl_bool isl_union_map_is_identity( 4756 __isl_keep isl_union_map *umap); 4757 4758=item * Position 4759 4760 __isl_give isl_val * 4761 isl_basic_map_plain_get_val_if_fixed( 4762 __isl_keep isl_basic_map *bmap, 4763 enum isl_dim_type type, unsigned pos); 4764 __isl_give isl_val *isl_set_plain_get_val_if_fixed( 4765 __isl_keep isl_set *set, 4766 enum isl_dim_type type, unsigned pos); 4767 __isl_give isl_multi_val * 4768 isl_set_get_plain_multi_val_if_fixed( 4769 __isl_keep isl_set *set); 4770 __isl_give isl_val *isl_map_plain_get_val_if_fixed( 4771 __isl_keep isl_map *map, 4772 enum isl_dim_type type, unsigned pos); 4773 4774If the set or relation obviously lies on a hyperplane where the given dimension 4775has a fixed value, then return that value. 4776Otherwise return NaN. 4777C<isl_set_get_plain_multi_val_if_fixed> collects the results over 4778all set dimensions. 4779 4780=item * Stride 4781 4782Stride detection is based on heuristics. 4783The strides returned by the functions below are always valid, 4784but there may be larger valid strides that are not detected. 4785 4786 isl_stat isl_set_dim_residue_class_val( 4787 __isl_keep isl_set *set, 4788 int pos, __isl_give isl_val **modulo, 4789 __isl_give isl_val **residue); 4790 4791Check if the values of the given set dimension are equal to a fixed 4792value modulo some integer value. If so, assign the modulo to C<*modulo> 4793and the fixed value to C<*residue>. If the given dimension attains only 4794a single value, then assign C<0> to C<*modulo> and the fixed value to 4795C<*residue>. 4796If the dimension does not attain only a single value and if no modulo 4797can be found then assign C<1> to C<*modulo> and C<1> to C<*residue>. 4798 4799 #include <isl/set.h> 4800 __isl_give isl_stride_info *isl_set_get_stride_info( 4801 __isl_keep isl_set *set, int pos); 4802 __isl_give isl_val *isl_set_get_stride( 4803 __isl_keep isl_set *set, int pos); 4804 4805 #include <isl/map.h> 4806 __isl_give isl_stride_info * 4807 isl_map_get_range_stride_info( 4808 __isl_keep isl_map *map, int pos); 4809 __isl_give isl_fixed_box * 4810 isl_map_get_range_lattice_tile( 4811 __isl_keep isl_map *map); 4812 4813Check if the values of the given set dimension are equal to 4814some affine expression of the other dimensions (the offset) 4815modulo some integer stride or 4816check if the values of the given output dimensions are equal to 4817some affine expression of the input dimensions (the offset) 4818modulo some integer stride. 4819If no more specific information can be found, then the stride 4820is taken to be one and the offset is taken to be the zero expression. 4821The function C<isl_set_get_stride> performs the same 4822computation as C<isl_set_get_stride_info> but only returns the stride. 4823The function C<isl_map_get_range_lattice_tile> collects the stride 4824information over all output dimensions. 4825In particular, it returns a tile of a rectangular lattice 4826(possibly of size 1 in all directions) 4827containing the output in terms of the parameters and the input dimensions. 4828The size and the offset of this tile correspond to 4829the strides and the offsets of the stride information and 4830can be extracted from the returned 4831C<isl_fixed_box> using the functions described under "Box hull" in 4832L</"Unary Operations">. Note that the C<isl_fixed_box> object returned by 4833C<isl_map_get_range_lattice_tile> is always valid. 4834For the other functions, 4835the stride and offset can be extracted from the returned object 4836using the following functions. 4837 4838 #include <isl/stride_info.h> 4839 __isl_give isl_val *isl_stride_info_get_stride( 4840 __isl_keep isl_stride_info *si); 4841 __isl_give isl_aff *isl_stride_info_get_offset( 4842 __isl_keep isl_stride_info *si); 4843 4844The stride info object can be copied and released using the following 4845functions. 4846 4847 #include <isl/stride_info.h> 4848 __isl_give isl_stride_info *isl_stride_info_copy( 4849 __isl_keep isl_stride_info *si); 4850 __isl_null isl_stride_info *isl_stride_info_free( 4851 __isl_take isl_stride_info *si); 4852 4853=item * Dependence 4854 4855To check whether a function involves any local variables, 4856i.e., integer divisions, 4857the following functions can be used. 4858 4859 #include <isl/set.h> 4860 isl_bool isl_set_involves_locals( 4861 __isl_keep isl_set *set); 4862 4863 #include <isl/aff.h> 4864 isl_bool isl_aff_involves_locals( 4865 __isl_keep isl_aff *aff); 4866 isl_bool isl_multi_aff_involves_locals( 4867 __isl_keep isl_multi_aff *ma); 4868 isl_bool isl_pw_multi_aff_involves_locals( 4869 __isl_keep isl_pw_multi_aff *pma); 4870 isl_bool isl_union_pw_multi_aff_involves_locals( 4871 __isl_keep isl_union_pw_multi_aff *upma); 4872 4873To check whether the description of a set, relation or function depends 4874on a parameter or one or more given dimensions, 4875the following functions can be used. 4876 4877 #include <isl/constraint.h> 4878 isl_bool isl_constraint_involves_dims( 4879 __isl_keep isl_constraint *constraint, 4880 enum isl_dim_type type, unsigned first, unsigned n); 4881 4882 #include <isl/set.h> 4883 isl_bool isl_basic_set_involves_dims( 4884 __isl_keep isl_basic_set *bset, 4885 enum isl_dim_type type, unsigned first, unsigned n); 4886 isl_bool isl_set_involves_dims(__isl_keep isl_set *set, 4887 enum isl_dim_type type, unsigned first, unsigned n); 4888 4889 #include <isl/map.h> 4890 isl_bool isl_basic_map_involves_dims( 4891 __isl_keep isl_basic_map *bmap, 4892 enum isl_dim_type type, unsigned first, unsigned n); 4893 isl_bool isl_map_involves_dims(__isl_keep isl_map *map, 4894 enum isl_dim_type type, unsigned first, unsigned n); 4895 4896 #include <isl/union_map.h> 4897 isl_bool isl_union_map_involves_dims( 4898 __isl_keep isl_union_map *umap, 4899 enum isl_dim_type type, unsigned first, unsigned n); 4900 4901 #include <isl/aff.h> 4902 isl_bool isl_aff_involves_dims(__isl_keep isl_aff *aff, 4903 enum isl_dim_type type, unsigned first, unsigned n); 4904 isl_bool isl_pw_aff_involves_param_id( 4905 __isl_keep isl_pw_aff *pa, 4906 __isl_keep isl_id *id); 4907 isl_bool isl_pw_aff_involves_dims( 4908 __isl_keep isl_pw_aff *pwaff, 4909 enum isl_dim_type type, unsigned first, unsigned n); 4910 isl_bool isl_multi_aff_involves_dims( 4911 __isl_keep isl_multi_aff *ma, 4912 enum isl_dim_type type, unsigned first, unsigned n); 4913 isl_bool isl_pw_multi_aff_involves_param_id( 4914 __isl_keep isl_pw_multi_aff *pma, 4915 __isl_keep isl_id *id); 4916 isl_bool isl_pw_multi_aff_involves_dims( 4917 __isl_keep isl_pw_multi_aff *pma, 4918 enum isl_dim_type type, unsigned first, unsigned n); 4919 isl_bool isl_multi_pw_aff_involves_dims( 4920 __isl_keep isl_multi_pw_aff *mpa, 4921 enum isl_dim_type type, unsigned first, unsigned n); 4922 isl_bool isl_multi_pw_aff_involves_param_id( 4923 __isl_keep isl_multi_pw_aff *mpa, 4924 __isl_keep isl_id *id); 4925 isl_bool isl_multi_pw_aff_involves_param_id_list( 4926 __isl_keep isl_multi_pw_aff *mpa, 4927 __isl_keep isl_id_list *list); 4928 4929 #include <isl/polynomial.h> 4930 isl_bool isl_qpolynomial_involves_dims( 4931 __isl_keep isl_qpolynomial *qp, 4932 enum isl_dim_type type, unsigned first, unsigned n); 4933 isl_bool isl_pw_qpolynomial_involves_param_id( 4934 __isl_keep isl_pw_qpolynomial *pwqp, 4935 __isl_keep isl_id *id); 4936 isl_bool isl_pw_qpolynomial_fold_involves_param_id( 4937 __isl_keep isl_pw_qpolynomial_fold *pwf, 4938 __isl_keep isl_id *id); 4939 4940Similarly, the following functions can be used to check whether 4941a given dimension is involved in any lower or upper bound. 4942 4943 #include <isl/set.h> 4944 isl_bool isl_set_dim_has_any_lower_bound( 4945 __isl_keep isl_set *set, 4946 enum isl_dim_type type, unsigned pos); 4947 isl_bool isl_set_dim_has_any_upper_bound( 4948 __isl_keep isl_set *set, 4949 enum isl_dim_type type, unsigned pos); 4950 4951Note that these functions return true even if there is a bound on 4952the dimension on only some of the basic sets of C<set>. 4953To check if they have a bound for all of the basic sets in C<set>, 4954use the following functions instead. 4955 4956 #include <isl/set.h> 4957 isl_bool isl_set_dim_has_lower_bound( 4958 __isl_keep isl_set *set, 4959 enum isl_dim_type type, unsigned pos); 4960 isl_bool isl_set_dim_has_upper_bound( 4961 __isl_keep isl_set *set, 4962 enum isl_dim_type type, unsigned pos); 4963 4964=item * Space 4965 4966To check whether a set is a parameter domain, use this function: 4967 4968 isl_bool isl_set_is_params(__isl_keep isl_set *set); 4969 isl_bool isl_union_set_is_params( 4970 __isl_keep isl_union_set *uset); 4971 4972=item * Wrapping 4973 4974The following functions check whether the space of the given 4975(basic) set or relation domain and/or range is a wrapped relation. 4976 4977 #include <isl/space.h> 4978 isl_bool isl_space_is_wrapping( 4979 __isl_keep isl_space *space); 4980 isl_bool isl_space_domain_is_wrapping( 4981 __isl_keep isl_space *space); 4982 isl_bool isl_space_range_is_wrapping( 4983 __isl_keep isl_space *space); 4984 isl_bool isl_space_is_product( 4985 __isl_keep isl_space *space); 4986 4987 #include <isl/set.h> 4988 isl_bool isl_basic_set_is_wrapping( 4989 __isl_keep isl_basic_set *bset); 4990 isl_bool isl_set_is_wrapping(__isl_keep isl_set *set); 4991 4992 #include <isl/map.h> 4993 isl_bool isl_map_domain_is_wrapping( 4994 __isl_keep isl_map *map); 4995 isl_bool isl_map_range_is_wrapping( 4996 __isl_keep isl_map *map); 4997 isl_bool isl_map_is_product(__isl_keep isl_map *map); 4998 4999 #include <isl/id.h> 5000 isl_bool isl_multi_id_range_is_wrapping( 5001 __isl_keep isl_multi_id *mi); 5002 5003 #include <isl/val.h> 5004 isl_bool isl_multi_val_range_is_wrapping( 5005 __isl_keep isl_multi_val *mv); 5006 5007 #include <isl/aff.h> 5008 isl_bool isl_multi_aff_range_is_wrapping( 5009 __isl_keep isl_multi_aff *ma); 5010 isl_bool isl_multi_pw_aff_range_is_wrapping( 5011 __isl_keep isl_multi_pw_aff *mpa); 5012 isl_bool isl_multi_union_pw_aff_range_is_wrapping( 5013 __isl_keep isl_multi_union_pw_aff *mupa); 5014 5015The input to C<isl_space_is_wrapping> should 5016be the space of a set, while that of 5017C<isl_space_domain_is_wrapping> and 5018C<isl_space_range_is_wrapping> should be the space of a relation. 5019The input to C<isl_space_is_product> can be either the space 5020of a set or that of a binary relation. 5021In case the input is the space of a binary relation, it checks 5022whether both domain and range are wrapping. 5023 5024=item * Internal Product 5025 5026 isl_bool isl_basic_map_can_zip( 5027 __isl_keep isl_basic_map *bmap); 5028 isl_bool isl_map_can_zip(__isl_keep isl_map *map); 5029 5030Check whether the product of domain and range of the given relation 5031can be computed, 5032i.e., whether both domain and range are nested relations. 5033 5034=item * Currying 5035 5036 #include <isl/space.h> 5037 isl_bool isl_space_can_curry( 5038 __isl_keep isl_space *space); 5039 5040 #include <isl/map.h> 5041 isl_bool isl_basic_map_can_curry( 5042 __isl_keep isl_basic_map *bmap); 5043 isl_bool isl_map_can_curry(__isl_keep isl_map *map); 5044 5045Check whether the domain of the (basic) relation is a wrapped relation. 5046 5047 #include <isl/space.h> 5048 isl_bool isl_space_can_uncurry( 5049 __isl_keep isl_space *space); 5050 5051 #include <isl/map.h> 5052 isl_bool isl_basic_map_can_uncurry( 5053 __isl_keep isl_basic_map *bmap); 5054 isl_bool isl_map_can_uncurry(__isl_keep isl_map *map); 5055 5056Check whether the range of the (basic) relation is a wrapped relation. 5057 5058 #include <isl/space.h> 5059 isl_bool isl_space_can_range_curry( 5060 __isl_keep isl_space *space); 5061 5062 #include <isl/map.h> 5063 isl_bool isl_map_can_range_curry( 5064 __isl_keep isl_map *map); 5065 5066Check whether the domain of the relation wrapped in the range of 5067the input is itself a wrapped relation. 5068 5069=item * Special Values 5070 5071 #include <isl/aff.h> 5072 isl_bool isl_aff_is_cst(__isl_keep isl_aff *aff); 5073 isl_bool isl_pw_aff_is_cst(__isl_keep isl_pw_aff *pwaff); 5074 isl_bool isl_multi_pw_aff_is_cst( 5075 __isl_keep isl_multi_pw_aff *mpa); 5076 5077Check whether the given expression is a constant. 5078 5079 #include <isl/val.h> 5080 isl_bool isl_multi_val_involves_nan( 5081 __isl_keep isl_multi_val *mv); 5082 5083 #include <isl/aff.h> 5084 isl_bool isl_aff_is_nan(__isl_keep isl_aff *aff); 5085 isl_bool isl_multi_aff_involves_nan( 5086 __isl_keep isl_multi_aff *ma); 5087 isl_bool isl_pw_aff_involves_nan( 5088 __isl_keep isl_pw_aff *pa); 5089 isl_bool isl_pw_multi_aff_involves_nan( 5090 __isl_keep isl_pw_multi_aff *pma); 5091 isl_bool isl_multi_pw_aff_involves_nan( 5092 __isl_keep isl_multi_pw_aff *mpa); 5093 isl_bool isl_union_pw_aff_involves_nan( 5094 __isl_keep isl_union_pw_aff *upa); 5095 isl_bool isl_union_pw_multi_aff_involves_nan( 5096 __isl_keep isl_union_pw_multi_aff *upma); 5097 isl_bool isl_multi_union_pw_aff_involves_nan( 5098 __isl_keep isl_multi_union_pw_aff *mupa); 5099 5100 #include <isl/polynomial.h> 5101 isl_bool isl_qpolynomial_is_nan( 5102 __isl_keep isl_qpolynomial *qp); 5103 isl_bool isl_qpolynomial_fold_is_nan( 5104 __isl_keep isl_qpolynomial_fold *fold); 5105 isl_bool isl_pw_qpolynomial_involves_nan( 5106 __isl_keep isl_pw_qpolynomial *pwqp); 5107 isl_bool isl_pw_qpolynomial_fold_involves_nan( 5108 __isl_keep isl_pw_qpolynomial_fold *pwf); 5109 isl_bool isl_union_pw_qpolynomial_involves_nan( 5110 __isl_keep isl_union_pw_qpolynomial *upwqp); 5111 isl_bool isl_union_pw_qpolynomial_fold_involves_nan( 5112 __isl_keep isl_union_pw_qpolynomial_fold *upwf); 5113 5114Check whether the given expression is equal to or involves NaN. 5115 5116 #include <isl/val.h> 5117 isl_bool isl_multi_val_is_zero( 5118 __isl_keep isl_multi_val *mv); 5119 5120Check whether the multiple value is zero. 5121 5122 #include <isl/aff.h> 5123 isl_bool isl_aff_plain_is_zero( 5124 __isl_keep isl_aff *aff); 5125 5126Check whether the affine expression is obviously zero. 5127 5128=back 5129 5130=head3 Binary Properties 5131 5132=over 5133 5134=item * Equality 5135 5136The following functions check whether two objects 5137represent the same set, relation or function. 5138The C<plain> variants only return true if the objects 5139are obviously the same. That is, they may return false 5140even if the objects are the same, but they will never 5141return true if the objects are not the same. 5142 5143 #include <isl/set.h> 5144 isl_bool isl_basic_set_plain_is_equal( 5145 __isl_keep isl_basic_set *bset1, 5146 __isl_keep isl_basic_set *bset2); 5147 isl_bool isl_basic_set_is_equal( 5148 __isl_keep isl_basic_set *bset1, 5149 __isl_keep isl_basic_set *bset2); 5150 isl_bool isl_set_plain_is_equal( 5151 __isl_keep isl_set *set1, 5152 __isl_keep isl_set *set2); 5153 isl_bool isl_set_is_equal(__isl_keep isl_set *set1, 5154 __isl_keep isl_set *set2); 5155 5156 #include <isl/map.h> 5157 isl_bool isl_basic_map_is_equal( 5158 __isl_keep isl_basic_map *bmap1, 5159 __isl_keep isl_basic_map *bmap2); 5160 isl_bool isl_map_is_equal(__isl_keep isl_map *map1, 5161 __isl_keep isl_map *map2); 5162 isl_bool isl_map_plain_is_equal( 5163 __isl_keep isl_map *map1, 5164 __isl_keep isl_map *map2); 5165 5166 #include <isl/union_set.h> 5167 isl_bool isl_union_set_is_equal( 5168 __isl_keep isl_union_set *uset1, 5169 __isl_keep isl_union_set *uset2); 5170 5171 #include <isl/union_map.h> 5172 isl_bool isl_union_map_is_equal( 5173 __isl_keep isl_union_map *umap1, 5174 __isl_keep isl_union_map *umap2); 5175 5176 #include <isl/id.h> 5177 isl_bool isl_multi_id_plain_is_equal( 5178 __isl_keep isl_multi_id *mi1, 5179 __isl_keep isl_multi_id *mi2); 5180 5181 #include <isl/val.h> 5182 isl_bool isl_multi_val_plain_is_equal( 5183 __isl_keep isl_multi_val *mv1, 5184 __isl_keep isl_multi_val *mv2); 5185 5186 #include <isl/aff.h> 5187 isl_bool isl_aff_plain_is_equal( 5188 __isl_keep isl_aff *aff1, 5189 __isl_keep isl_aff *aff2); 5190 isl_bool isl_multi_aff_plain_is_equal( 5191 __isl_keep isl_multi_aff *maff1, 5192 __isl_keep isl_multi_aff *maff2); 5193 isl_bool isl_pw_aff_plain_is_equal( 5194 __isl_keep isl_pw_aff *pwaff1, 5195 __isl_keep isl_pw_aff *pwaff2); 5196 isl_bool isl_pw_aff_is_equal( 5197 __isl_keep isl_pw_aff *pa1, 5198 __isl_keep isl_pw_aff *pa2); 5199 isl_bool isl_pw_multi_aff_plain_is_equal( 5200 __isl_keep isl_pw_multi_aff *pma1, 5201 __isl_keep isl_pw_multi_aff *pma2); 5202 isl_bool isl_pw_multi_aff_is_equal( 5203 __isl_keep isl_pw_multi_aff *pma1, 5204 __isl_keep isl_pw_multi_aff *pma2); 5205 isl_bool isl_multi_pw_aff_plain_is_equal( 5206 __isl_keep isl_multi_pw_aff *mpa1, 5207 __isl_keep isl_multi_pw_aff *mpa2); 5208 isl_bool isl_multi_pw_aff_is_equal( 5209 __isl_keep isl_multi_pw_aff *mpa1, 5210 __isl_keep isl_multi_pw_aff *mpa2); 5211 isl_bool isl_union_pw_aff_plain_is_equal( 5212 __isl_keep isl_union_pw_aff *upa1, 5213 __isl_keep isl_union_pw_aff *upa2); 5214 isl_bool isl_union_pw_multi_aff_plain_is_equal( 5215 __isl_keep isl_union_pw_multi_aff *upma1, 5216 __isl_keep isl_union_pw_multi_aff *upma2); 5217 isl_bool isl_multi_union_pw_aff_plain_is_equal( 5218 __isl_keep isl_multi_union_pw_aff *mupa1, 5219 __isl_keep isl_multi_union_pw_aff *mupa2); 5220 5221 #include <isl/polynomial.h> 5222 isl_bool isl_union_pw_qpolynomial_plain_is_equal( 5223 __isl_keep isl_union_pw_qpolynomial *upwqp1, 5224 __isl_keep isl_union_pw_qpolynomial *upwqp2); 5225 isl_bool isl_union_pw_qpolynomial_fold_plain_is_equal( 5226 __isl_keep isl_union_pw_qpolynomial_fold *upwf1, 5227 __isl_keep isl_union_pw_qpolynomial_fold *upwf2); 5228 5229=item * Disjointness 5230 5231 #include <isl/set.h> 5232 isl_bool isl_basic_set_is_disjoint( 5233 __isl_keep isl_basic_set *bset1, 5234 __isl_keep isl_basic_set *bset2); 5235 isl_bool isl_set_plain_is_disjoint( 5236 __isl_keep isl_set *set1, 5237 __isl_keep isl_set *set2); 5238 isl_bool isl_set_is_disjoint(__isl_keep isl_set *set1, 5239 __isl_keep isl_set *set2); 5240 5241 #include <isl/map.h> 5242 isl_bool isl_basic_map_is_disjoint( 5243 __isl_keep isl_basic_map *bmap1, 5244 __isl_keep isl_basic_map *bmap2); 5245 isl_bool isl_map_is_disjoint(__isl_keep isl_map *map1, 5246 __isl_keep isl_map *map2); 5247 5248 #include <isl/union_set.h> 5249 isl_bool isl_union_set_is_disjoint( 5250 __isl_keep isl_union_set *uset1, 5251 __isl_keep isl_union_set *uset2); 5252 5253 #include <isl/union_map.h> 5254 isl_bool isl_union_map_is_disjoint( 5255 __isl_keep isl_union_map *umap1, 5256 __isl_keep isl_union_map *umap2); 5257 5258=item * Subset 5259 5260 isl_bool isl_basic_set_is_subset( 5261 __isl_keep isl_basic_set *bset1, 5262 __isl_keep isl_basic_set *bset2); 5263 isl_bool isl_set_is_subset(__isl_keep isl_set *set1, 5264 __isl_keep isl_set *set2); 5265 isl_bool isl_set_is_strict_subset( 5266 __isl_keep isl_set *set1, 5267 __isl_keep isl_set *set2); 5268 isl_bool isl_union_set_is_subset( 5269 __isl_keep isl_union_set *uset1, 5270 __isl_keep isl_union_set *uset2); 5271 isl_bool isl_union_set_is_strict_subset( 5272 __isl_keep isl_union_set *uset1, 5273 __isl_keep isl_union_set *uset2); 5274 isl_bool isl_basic_map_is_subset( 5275 __isl_keep isl_basic_map *bmap1, 5276 __isl_keep isl_basic_map *bmap2); 5277 isl_bool isl_basic_map_is_strict_subset( 5278 __isl_keep isl_basic_map *bmap1, 5279 __isl_keep isl_basic_map *bmap2); 5280 isl_bool isl_map_is_subset( 5281 __isl_keep isl_map *map1, 5282 __isl_keep isl_map *map2); 5283 isl_bool isl_map_is_strict_subset( 5284 __isl_keep isl_map *map1, 5285 __isl_keep isl_map *map2); 5286 isl_bool isl_union_map_is_subset( 5287 __isl_keep isl_union_map *umap1, 5288 __isl_keep isl_union_map *umap2); 5289 isl_bool isl_union_map_is_strict_subset( 5290 __isl_keep isl_union_map *umap1, 5291 __isl_keep isl_union_map *umap2); 5292 5293Check whether the first argument is a (strict) subset of the 5294second argument. 5295 5296=item * Order 5297 5298Every comparison function returns a negative value if the first 5299argument is considered smaller than the second, a positive value 5300if the first argument is considered greater and zero if the two 5301constraints are considered the same by the comparison criterion. 5302 5303 #include <isl/constraint.h> 5304 int isl_constraint_plain_cmp( 5305 __isl_keep isl_constraint *c1, 5306 __isl_keep isl_constraint *c2); 5307 5308This function is useful for sorting C<isl_constraint>s. 5309The order depends on the internal representation of the inputs. 5310The order is fixed over different calls to the function (assuming 5311the internal representation of the inputs has not changed), but may 5312change over different versions of C<isl>. 5313 5314 #include <isl/constraint.h> 5315 int isl_constraint_cmp_last_non_zero( 5316 __isl_keep isl_constraint *c1, 5317 __isl_keep isl_constraint *c2); 5318 5319This function can be used to sort constraints that live in the same 5320local space. Constraints that involve ``earlier'' dimensions or 5321that have a smaller coefficient for the shared latest dimension 5322are considered smaller than other constraints. 5323This function only defines a B<partial> order. 5324 5325 #include <isl/set.h> 5326 int isl_set_plain_cmp(__isl_keep isl_set *set1, 5327 __isl_keep isl_set *set2); 5328 5329This function is useful for sorting C<isl_set>s. 5330The order depends on the internal representation of the inputs. 5331The order is fixed over different calls to the function (assuming 5332the internal representation of the inputs has not changed), but may 5333change over different versions of C<isl>. 5334 5335 #include <isl/aff.h> 5336 int isl_multi_aff_plain_cmp( 5337 __isl_keep isl_multi_aff *ma1, 5338 __isl_keep isl_multi_aff *ma2); 5339 int isl_pw_aff_plain_cmp(__isl_keep isl_pw_aff *pa1, 5340 __isl_keep isl_pw_aff *pa2); 5341 5342The functions C<isl_multi_aff_plain_cmp> and 5343C<isl_pw_aff_plain_cmp> can be used to sort C<isl_multi_aff>s and 5344C<isl_pw_aff>s. The order is not strictly defined. 5345The current order sorts expressions that only involve 5346earlier dimensions before those that involve later dimensions. 5347 5348=back 5349 5350=head2 Unary Operations 5351 5352=over 5353 5354=item * Complement 5355 5356 __isl_give isl_set *isl_set_complement( 5357 __isl_take isl_set *set); 5358 __isl_give isl_map *isl_map_complement( 5359 __isl_take isl_map *map); 5360 5361=item * Inverse map 5362 5363 #include <isl/space.h> 5364 __isl_give isl_space *isl_space_reverse( 5365 __isl_take isl_space *space); 5366 __isl_give isl_space *isl_space_range_reverse( 5367 __isl_take isl_space *space); 5368 5369 #include <isl/map.h> 5370 __isl_give isl_basic_map *isl_basic_map_reverse( 5371 __isl_take isl_basic_map *bmap); 5372 __isl_give isl_map *isl_map_reverse( 5373 __isl_take isl_map *map); 5374 __isl_give isl_map *isl_map_range_reverse( 5375 __isl_take isl_map *map); 5376 5377 #include <isl/union_map.h> 5378 __isl_give isl_union_map *isl_union_map_reverse( 5379 __isl_take isl_union_map *umap); 5380 __isl_give isl_union_map *isl_union_map_range_reverse( 5381 __isl_take isl_union_map *umap); 5382 5383The function C<isl_space_range_reverse> reverses the relation 5384that is embedded in the range of the input map space. 5385The identifier of the range, if any, is only preserved 5386if this embedded relation has identical input and output tuples. 5387 5388=item * Tuple binding 5389 5390The following function binds 5391a tuple to a sequence of parameter identifiers, equating 5392the tuple dimensions to the parameters with those identifiers and 5393subsequently projecting out the tuple. 5394If the original object did not reference any such parameters, 5395then this means that the tuple dimensions are reinterpreted 5396as parameters. 5397The space of C<tuple> needs to match that of the bound tuple. 5398 5399 #include <isl/set.h> 5400 __isl_give isl_set *isl_set_bind( 5401 __isl_take isl_set *set, 5402 __isl_take isl_multi_id *tuple); 5403 5404 #include <isl/map.h> 5405 __isl_give isl_set *isl_map_bind_domain( 5406 __isl_take isl_map *map, 5407 __isl_take isl_multi_id *tuple); 5408 __isl_give isl_set *isl_map_bind_range( 5409 __isl_take isl_map *map, 5410 __isl_take isl_multi_id *tuple); 5411 5412 #include <isl/union_map.h> 5413 __isl_give isl_union_set *isl_union_map_bind_range( 5414 __isl_take isl_union_map *umap, 5415 __isl_take isl_multi_id *tuple); 5416 5417 #include <isl/aff.h> 5418 __isl_give isl_pw_aff *isl_pw_aff_bind_domain( 5419 __isl_take isl_pw_aff *pa, 5420 __isl_take isl_multi_id *tuple); 5421 __isl_give isl_multi_aff *isl_multi_aff_bind_domain( 5422 __isl_take isl_multi_aff *ma, 5423 __isl_take isl_multi_id *tuple); 5424 __isl_give isl_pw_multi_aff * 5425 isl_pw_multi_aff_bind_domain( 5426 __isl_take isl_pw_multi_aff *pma, 5427 __isl_take isl_multi_id *tuple); 5428 __isl_give isl_multi_pw_aff * 5429 isl_multi_pw_aff_bind_domain( 5430 __isl_take isl_multi_pw_aff *mpa, 5431 __isl_take isl_multi_id *tuple); 5432 __isl_give isl_pw_aff * 5433 isl_pw_aff_bind_domain_wrapped_domain( 5434 __isl_take isl_pw_aff *pa, 5435 __isl_take isl_multi_id *tuple); 5436 __isl_give isl_multi_aff * 5437 isl_multi_aff_bind_domain_wrapped_domain( 5438 __isl_take isl_multi_aff *ma, 5439 __isl_take isl_multi_id *tuple); 5440 __isl_give isl_pw_multi_aff * 5441 isl_pw_multi_aff_bind_domain_wrapped_domain( 5442 __isl_take isl_pw_multi_aff *pma, 5443 __isl_take isl_multi_id *tuple); 5444 __isl_give isl_multi_pw_aff * 5445 isl_multi_pw_aff_bind_domain_wrapped_domain( 5446 __isl_take isl_multi_pw_aff *mpa, 5447 __isl_take isl_multi_id *tuple); 5448 __isl_give isl_basic_set *isl_aff_bind_id( 5449 __isl_take isl_aff *aff, 5450 __isl_take isl_id *id); 5451 __isl_give isl_set *isl_pw_aff_bind_id( 5452 __isl_take isl_pw_aff *pa, 5453 __isl_take isl_id *id); 5454 __isl_give isl_basic_set *isl_multi_aff_bind( 5455 __isl_take isl_multi_aff *ma, 5456 __isl_take isl_multi_id *tuple); 5457 __isl_give isl_set *isl_multi_pw_aff_bind( 5458 __isl_take isl_multi_pw_aff *mpa, 5459 __isl_take isl_multi_id *tuple); 5460 __isl_give isl_union_set *isl_union_pw_aff_bind_id( 5461 __isl_take isl_union_pw_aff *upa, 5462 __isl_take isl_id *id); 5463 __isl_give isl_union_set * 5464 isl_multi_union_pw_aff_bind( 5465 __isl_take isl_multi_union_pw_aff *mupa, 5466 __isl_take isl_multi_id *tuple); 5467 5468Projecting out the domain of the wrapped relation in the domain 5469of a function leaves the range of that wrapped relation 5470in the domain of the resulting function. 5471In the case of C<isl_aff_bind_id>, C<isl_pw_aff_bind_id>, 5472C<isl_multi_aff_bind>, C<isl_multi_pw_aff_bind>, 5473C<isl_union_pw_aff_bind_id> and 5474C<isl_multi_union_pw_aff_bind>, the parameters 5475are bound to the function values and the result lives 5476in the domain of the input function. 5477 5478=item * Projection 5479 5480 #include <isl/space.h> 5481 __isl_give isl_space *isl_space_domain( 5482 __isl_take isl_space *space); 5483 __isl_give isl_space *isl_space_range( 5484 __isl_take isl_space *space); 5485 __isl_give isl_space *isl_space_params( 5486 __isl_take isl_space *space); 5487 5488 #include <isl/local_space.h> 5489 __isl_give isl_local_space *isl_local_space_domain( 5490 __isl_take isl_local_space *ls); 5491 __isl_give isl_local_space *isl_local_space_range( 5492 __isl_take isl_local_space *ls); 5493 5494 #include <isl/set.h> 5495 __isl_give isl_basic_set *isl_basic_set_project_out( 5496 __isl_take isl_basic_set *bset, 5497 enum isl_dim_type type, unsigned first, unsigned n); 5498 __isl_give isl_set *isl_set_project_out_param_id( 5499 __isl_take isl_set *set, 5500 __isl_take isl_id *id); 5501 __isl_give isl_set * 5502 isl_set_project_out_param_id_list( 5503 __isl_take isl_set *set, 5504 __isl_take isl_id_list *list); 5505 __isl_give isl_set *isl_set_project_out(__isl_take isl_set *set, 5506 enum isl_dim_type type, unsigned first, unsigned n); 5507 __isl_give isl_set *isl_set_project_out_all_params( 5508 __isl_take isl_set *set); 5509 __isl_give isl_map *isl_set_project_onto_map( 5510 __isl_take isl_set *set, 5511 enum isl_dim_type type, unsigned first, 5512 unsigned n); 5513 __isl_give isl_basic_set *isl_basic_set_params( 5514 __isl_take isl_basic_set *bset); 5515 __isl_give isl_set *isl_set_params(__isl_take isl_set *set); 5516 5517The function C<isl_set_project_onto_map> returns a relation 5518that projects the input set onto the given set dimensions. 5519 5520 #include <isl/map.h> 5521 __isl_give isl_basic_map *isl_basic_map_project_out( 5522 __isl_take isl_basic_map *bmap, 5523 enum isl_dim_type type, unsigned first, unsigned n); 5524 __isl_give isl_map *isl_map_project_out(__isl_take isl_map *map, 5525 enum isl_dim_type type, unsigned first, unsigned n); 5526 __isl_give isl_map *isl_map_project_out_all_params( 5527 __isl_take isl_map *map); 5528 __isl_give isl_basic_set *isl_basic_map_domain( 5529 __isl_take isl_basic_map *bmap); 5530 __isl_give isl_basic_set *isl_basic_map_range( 5531 __isl_take isl_basic_map *bmap); 5532 __isl_give isl_set *isl_map_params(__isl_take isl_map *map); 5533 __isl_give isl_set *isl_map_domain( 5534 __isl_take isl_map *bmap); 5535 __isl_give isl_set *isl_map_range( 5536 __isl_take isl_map *map); 5537 5538 #include <isl/union_set.h> 5539 __isl_give isl_union_set *isl_union_set_project_out( 5540 __isl_take isl_union_set *uset, 5541 enum isl_dim_type type, 5542 unsigned first, unsigned n); 5543 __isl_give isl_union_set * 5544 isl_union_set_project_out_all_params( 5545 __isl_take isl_union_set *uset); 5546 __isl_give isl_set *isl_union_set_params( 5547 __isl_take isl_union_set *uset); 5548 5549The function C<isl_union_set_project_out> can only project out 5550parameters. 5551 5552 #include <isl/union_map.h> 5553 __isl_give isl_union_map *isl_union_map_project_out( 5554 __isl_take isl_union_map *umap, 5555 enum isl_dim_type type, unsigned first, unsigned n); 5556 __isl_give isl_union_map * 5557 isl_union_map_project_out_all_params( 5558 __isl_take isl_union_map *umap); 5559 __isl_give isl_set *isl_union_map_params( 5560 __isl_take isl_union_map *umap); 5561 __isl_give isl_union_set *isl_union_map_domain( 5562 __isl_take isl_union_map *umap); 5563 __isl_give isl_union_set *isl_union_map_range( 5564 __isl_take isl_union_map *umap); 5565 5566The function C<isl_union_map_project_out> can only project out 5567parameters. 5568 5569 #include <isl/aff.h> 5570 __isl_give isl_aff *isl_aff_project_domain_on_params( 5571 __isl_take isl_aff *aff); 5572 __isl_give isl_multi_aff * 5573 isl_multi_aff_project_domain_on_params( 5574 __isl_take isl_multi_aff *ma); 5575 __isl_give isl_pw_aff * 5576 isl_pw_aff_project_domain_on_params( 5577 __isl_take isl_pw_aff *pa); 5578 __isl_give isl_multi_pw_aff * 5579 isl_multi_pw_aff_project_domain_on_params( 5580 __isl_take isl_multi_pw_aff *mpa); 5581 __isl_give isl_pw_multi_aff * 5582 isl_pw_multi_aff_project_domain_on_params( 5583 __isl_take isl_pw_multi_aff *pma); 5584 __isl_give isl_set *isl_pw_aff_domain( 5585 __isl_take isl_pw_aff *pwaff); 5586 __isl_give isl_set *isl_pw_multi_aff_domain( 5587 __isl_take isl_pw_multi_aff *pma); 5588 __isl_give isl_set *isl_multi_pw_aff_domain( 5589 __isl_take isl_multi_pw_aff *mpa); 5590 __isl_give isl_union_set *isl_union_pw_aff_domain( 5591 __isl_take isl_union_pw_aff *upa); 5592 __isl_give isl_union_set *isl_union_pw_multi_aff_domain( 5593 __isl_take isl_union_pw_multi_aff *upma); 5594 __isl_give isl_union_set * 5595 isl_multi_union_pw_aff_domain( 5596 __isl_take isl_multi_union_pw_aff *mupa); 5597 __isl_give isl_set *isl_pw_aff_params( 5598 __isl_take isl_pw_aff *pwa); 5599 5600If no explicit domain was set on a zero-dimensional input to 5601C<isl_multi_union_pw_aff_domain>, then this function will 5602return a parameter set. 5603 5604 #include <isl/polynomial.h> 5605 __isl_give isl_qpolynomial * 5606 isl_qpolynomial_project_domain_on_params( 5607 __isl_take isl_qpolynomial *qp); 5608 __isl_give isl_pw_qpolynomial * 5609 isl_pw_qpolynomial_project_domain_on_params( 5610 __isl_take isl_pw_qpolynomial *pwqp); 5611 __isl_give isl_pw_qpolynomial_fold * 5612 isl_pw_qpolynomial_fold_project_domain_on_params( 5613 __isl_take isl_pw_qpolynomial_fold *pwf); 5614 __isl_give isl_set *isl_pw_qpolynomial_domain( 5615 __isl_take isl_pw_qpolynomial *pwqp); 5616 __isl_give isl_union_set *isl_union_pw_qpolynomial_fold_domain( 5617 __isl_take isl_union_pw_qpolynomial_fold *upwf); 5618 __isl_give isl_union_set *isl_union_pw_qpolynomial_domain( 5619 __isl_take isl_union_pw_qpolynomial *upwqp); 5620 5621 #include <isl/space.h> 5622 __isl_give isl_space *isl_space_domain_map( 5623 __isl_take isl_space *space); 5624 __isl_give isl_space *isl_space_range_map( 5625 __isl_take isl_space *space); 5626 5627 #include <isl/map.h> 5628 __isl_give isl_map *isl_set_wrapped_domain_map( 5629 __isl_take isl_set *set); 5630 __isl_give isl_basic_map *isl_basic_map_domain_map( 5631 __isl_take isl_basic_map *bmap); 5632 __isl_give isl_basic_map *isl_basic_map_range_map( 5633 __isl_take isl_basic_map *bmap); 5634 __isl_give isl_map *isl_map_domain_map(__isl_take isl_map *map); 5635 __isl_give isl_map *isl_map_range_map(__isl_take isl_map *map); 5636 5637 #include <isl/union_map.h> 5638 __isl_give isl_union_map *isl_union_map_domain_map( 5639 __isl_take isl_union_map *umap); 5640 __isl_give isl_union_pw_multi_aff * 5641 isl_union_map_domain_map_union_pw_multi_aff( 5642 __isl_take isl_union_map *umap); 5643 __isl_give isl_union_map *isl_union_map_range_map( 5644 __isl_take isl_union_map *umap); 5645 __isl_give isl_union_map * 5646 isl_union_set_wrapped_domain_map( 5647 __isl_take isl_union_set *uset); 5648 5649The functions above construct a (basic, regular or union) relation 5650that maps (a wrapped version of) the input relation to its domain or range. 5651C<isl_set_wrapped_domain_map> maps the input set to the domain 5652of its wrapped relation. 5653 5654=item * Elimination 5655 5656 __isl_give isl_basic_set *isl_basic_set_eliminate( 5657 __isl_take isl_basic_set *bset, 5658 enum isl_dim_type type, 5659 unsigned first, unsigned n); 5660 __isl_give isl_set *isl_set_eliminate( 5661 __isl_take isl_set *set, enum isl_dim_type type, 5662 unsigned first, unsigned n); 5663 __isl_give isl_basic_map *isl_basic_map_eliminate( 5664 __isl_take isl_basic_map *bmap, 5665 enum isl_dim_type type, 5666 unsigned first, unsigned n); 5667 __isl_give isl_map *isl_map_eliminate( 5668 __isl_take isl_map *map, enum isl_dim_type type, 5669 unsigned first, unsigned n); 5670 5671Eliminate the coefficients for the given dimensions from the constraints, 5672without removing the dimensions. 5673 5674=item * Constructing a set from a parameter domain 5675 5676A set space of a given dimension and with an optional name 5677can be created from a parameter space using the following functions. 5678 5679 #include <isl/space.h> 5680 __isl_give isl_space *isl_space_add_unnamed_tuple_ui( 5681 __isl_take isl_space *space, unsigned dim); 5682 __isl_give isl_space * 5683 isl_space_add_named_tuple_id_ui( 5684 __isl_take isl_space *space, 5685 __isl_take isl_id *tuple_id, unsigned dim); 5686 5687A set with a given tuple can be created from a parameter domain 5688using the following function. 5689 5690 #include <isl/set.h> 5691 __isl_give isl_set *isl_set_unbind_params( 5692 __isl_take isl_set *set, 5693 __isl_take isl_multi_id *tuple); 5694 5695Any parameters with identifiers in C<tuple> are reinterpreted 5696as the corresponding set dimensions. 5697 5698A zero-dimensional (local) space or (basic) set can be constructed 5699on a given parameter domain using the following functions. 5700 5701 #include <isl/space.h> 5702 __isl_give isl_space *isl_space_set_from_params( 5703 __isl_take isl_space *space); 5704 5705 #include <isl/local_space.h> 5706 __isl_give isl_local_space * 5707 isl_local_space_set_from_params( 5708 __isl_take isl_local_space *ls); 5709 5710 #include <isl/set.h> 5711 __isl_give isl_basic_set *isl_basic_set_from_params( 5712 __isl_take isl_basic_set *bset); 5713 __isl_give isl_set *isl_set_from_params( 5714 __isl_take isl_set *set); 5715 5716=item * Constructing a relation from one or two sets 5717 5718A map space with a range of a given dimension and with an optional name 5719can be created from a domain space using the functions 5720C<isl_space_add_unnamed_tuple_ui> and C<isl_space_add_named_tuple_id_ui> 5721described above. 5722 5723A relation with a given domain tuple can be created from a set 5724that will become the range of the relation 5725using the following function. 5726 5727 #include <isl/set.h> 5728 __isl_give isl_map * 5729 isl_set_unbind_params_insert_domain( 5730 __isl_take isl_set *set, 5731 __isl_take isl_multi_id *domain); 5732 5733Any parameters with identifiers in C<domain> are reinterpreted 5734as the corresponding input dimensions. 5735 5736Similarly, a function defined over a parameter domain can 5737be converted into one defined over a set domain 5738using the following functions. 5739 5740 #include <isl/aff.h> 5741 __isl_give isl_aff * 5742 isl_aff_unbind_params_insert_domain( 5743 __isl_take isl_aff *aff, 5744 __isl_take isl_multi_id *domain); 5745 __isl_give isl_multi_aff * 5746 isl_multi_aff_unbind_params_insert_domain( 5747 __isl_take isl_multi_aff *ma, 5748 __isl_take isl_multi_id *domain); 5749 __isl_give isl_multi_pw_aff * 5750 isl_multi_pw_aff_unbind_params_insert_domain( 5751 __isl_take isl_multi_pw_aff *mpa, 5752 __isl_take isl_multi_id *domain); 5753 5754Again, 5755any parameters with identifiers in C<domain> are reinterpreted 5756as the corresponding input dimensions. 5757 5758Create a relation with the given set(s) as domain and/or range. 5759If only the domain or the range is specified, then 5760the range or domain of the created relation is a zero-dimensional 5761flat anonymous space. 5762If the case of C<isl_space_map_from_set>, the input space 5763specifies both the domain and the range of the result. 5764 5765 #include <isl/space.h> 5766 __isl_give isl_space *isl_space_from_domain( 5767 __isl_take isl_space *space); 5768 __isl_give isl_space *isl_space_from_range( 5769 __isl_take isl_space *space); 5770 __isl_give isl_space *isl_space_map_from_set( 5771 __isl_take isl_space *space); 5772 __isl_give isl_space *isl_space_map_from_domain_and_range( 5773 __isl_take isl_space *domain, 5774 __isl_take isl_space *range); 5775 5776 #include <isl/local_space.h> 5777 __isl_give isl_local_space *isl_local_space_from_domain( 5778 __isl_take isl_local_space *ls); 5779 5780 #include <isl/map.h> 5781 __isl_give isl_map *isl_set_insert_domain( 5782 __isl_take isl_set *set, 5783 __isl_take isl_space *domain); 5784 __isl_give isl_map *isl_map_from_domain( 5785 __isl_take isl_set *set); 5786 __isl_give isl_map *isl_map_from_range( 5787 __isl_take isl_set *set); 5788 5789 #include <isl/union_map.h> 5790 __isl_give isl_union_map *isl_union_map_from_domain( 5791 __isl_take isl_union_set *uset); 5792 __isl_give isl_union_map *isl_union_map_from_range( 5793 __isl_take isl_union_set *uset); 5794 __isl_give isl_union_map * 5795 isl_union_map_from_domain_and_range( 5796 __isl_take isl_union_set *domain, 5797 __isl_take isl_union_set *range); 5798 5799 #include <isl/id.h> 5800 __isl_give isl_multi_id *isl_multi_id_from_range( 5801 __isl_take isl_multi_id *mi); 5802 5803 #include <isl/val.h> 5804 __isl_give isl_multi_val *isl_multi_val_from_range( 5805 __isl_take isl_multi_val *mv); 5806 5807 #include <isl/aff.h> 5808 __isl_give isl_multi_aff * 5809 isl_multi_aff_insert_domain( 5810 __isl_take isl_multi_aff *ma, 5811 __isl_take isl_space *domain); 5812 __isl_give isl_pw_aff *isl_pw_aff_insert_domain( 5813 __isl_take isl_pw_aff *pa, 5814 __isl_take isl_space *domain); 5815 __isl_give isl_pw_multi_aff * 5816 isl_pw_multi_aff_insert_domain( 5817 __isl_take isl_pw_multi_aff *pma, 5818 __isl_take isl_space *domain); 5819 __isl_give isl_multi_pw_aff * 5820 isl_multi_pw_aff_insert_domain( 5821 __isl_take isl_multi_pw_aff *mpa, 5822 __isl_take isl_space *domain); 5823 __isl_give isl_aff *isl_aff_from_range( 5824 __isl_take isl_aff *aff); 5825 __isl_give isl_multi_aff *isl_multi_aff_from_range( 5826 __isl_take isl_multi_aff *ma); 5827 __isl_give isl_pw_aff *isl_pw_aff_from_range( 5828 __isl_take isl_pw_aff *pwa); 5829 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_from_range( 5830 __isl_take isl_multi_pw_aff *mpa); 5831 __isl_give isl_multi_union_pw_aff * 5832 isl_multi_union_pw_aff_from_range( 5833 __isl_take isl_multi_union_pw_aff *mupa); 5834 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_from_domain( 5835 __isl_take isl_set *set); 5836 __isl_give isl_union_pw_multi_aff * 5837 isl_union_pw_multi_aff_from_domain( 5838 __isl_take isl_union_set *uset); 5839 5840 #include <isl/polynomial.h> 5841 __isl_give isl_pw_qpolynomial * 5842 isl_pw_qpolynomial_from_range( 5843 __isl_take isl_pw_qpolynomial *pwqp); 5844 __isl_give isl_pw_qpolynomial_fold * 5845 isl_pw_qpolynomial_fold_from_range( 5846 __isl_take isl_pw_qpolynomial_fold *pwf); 5847 5848=item * Slicing 5849 5850 #include <isl/set.h> 5851 __isl_give isl_basic_set *isl_basic_set_fix_si( 5852 __isl_take isl_basic_set *bset, 5853 enum isl_dim_type type, unsigned pos, int value); 5854 __isl_give isl_basic_set *isl_basic_set_fix_val( 5855 __isl_take isl_basic_set *bset, 5856 enum isl_dim_type type, unsigned pos, 5857 __isl_take isl_val *v); 5858 __isl_give isl_set *isl_set_fix_si(__isl_take isl_set *set, 5859 enum isl_dim_type type, unsigned pos, int value); 5860 __isl_give isl_set *isl_set_fix_val( 5861 __isl_take isl_set *set, 5862 enum isl_dim_type type, unsigned pos, 5863 __isl_take isl_val *v); 5864 5865 #include <isl/map.h> 5866 __isl_give isl_basic_map *isl_basic_map_fix_si( 5867 __isl_take isl_basic_map *bmap, 5868 enum isl_dim_type type, unsigned pos, int value); 5869 __isl_give isl_basic_map *isl_basic_map_fix_val( 5870 __isl_take isl_basic_map *bmap, 5871 enum isl_dim_type type, unsigned pos, 5872 __isl_take isl_val *v); 5873 __isl_give isl_map *isl_map_fix_si(__isl_take isl_map *map, 5874 enum isl_dim_type type, unsigned pos, int value); 5875 __isl_give isl_map *isl_map_fix_val( 5876 __isl_take isl_map *map, 5877 enum isl_dim_type type, unsigned pos, 5878 __isl_take isl_val *v); 5879 5880 #include <isl/aff.h> 5881 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_fix_si( 5882 __isl_take isl_pw_multi_aff *pma, 5883 enum isl_dim_type type, unsigned pos, int value); 5884 5885 #include <isl/polynomial.h> 5886 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_fix_val( 5887 __isl_take isl_pw_qpolynomial *pwqp, 5888 enum isl_dim_type type, unsigned n, 5889 __isl_take isl_val *v); 5890 __isl_give isl_pw_qpolynomial_fold * 5891 isl_pw_qpolynomial_fold_fix_val( 5892 __isl_take isl_pw_qpolynomial_fold *pwf, 5893 enum isl_dim_type type, unsigned n, 5894 __isl_take isl_val *v); 5895 5896Intersect the set, relation or function domain 5897with the hyperplane where the given 5898dimension has the fixed given value. 5899 5900 #include <isl/set.h> 5901 __isl_give isl_basic_set * 5902 isl_basic_set_lower_bound_val( 5903 __isl_take isl_basic_set *bset, 5904 enum isl_dim_type type, unsigned pos, 5905 __isl_take isl_val *value); 5906 __isl_give isl_basic_set * 5907 isl_basic_set_upper_bound_val( 5908 __isl_take isl_basic_set *bset, 5909 enum isl_dim_type type, unsigned pos, 5910 __isl_take isl_val *value); 5911 __isl_give isl_set *isl_set_lower_bound_si( 5912 __isl_take isl_set *set, 5913 enum isl_dim_type type, unsigned pos, int value); 5914 __isl_give isl_set *isl_set_lower_bound_val( 5915 __isl_take isl_set *set, 5916 enum isl_dim_type type, unsigned pos, 5917 __isl_take isl_val *value); 5918 __isl_give isl_set *isl_set_upper_bound_si( 5919 __isl_take isl_set *set, 5920 enum isl_dim_type type, unsigned pos, int value); 5921 __isl_give isl_set *isl_set_upper_bound_val( 5922 __isl_take isl_set *set, 5923 enum isl_dim_type type, unsigned pos, 5924 __isl_take isl_val *value); 5925 __isl_give isl_set *isl_set_lower_bound_multi_val( 5926 __isl_take isl_set *set, 5927 __isl_take isl_multi_val *lower); 5928 __isl_give isl_set *isl_set_upper_bound_multi_val( 5929 __isl_take isl_set *set, 5930 __isl_take isl_multi_val *upper); 5931 __isl_give isl_set *isl_set_lower_bound_multi_pw_aff( 5932 __isl_take isl_set *set, 5933 __isl_take isl_multi_pw_aff *lower); 5934 __isl_give isl_set *isl_set_upper_bound_multi_pw_aff( 5935 __isl_take isl_set *set, 5936 __isl_take isl_multi_pw_aff *upper); 5937 5938 #include <isl/map.h> 5939 __isl_give isl_basic_map *isl_basic_map_lower_bound_si( 5940 __isl_take isl_basic_map *bmap, 5941 enum isl_dim_type type, unsigned pos, int value); 5942 __isl_give isl_basic_map *isl_basic_map_upper_bound_si( 5943 __isl_take isl_basic_map *bmap, 5944 enum isl_dim_type type, unsigned pos, int value); 5945 __isl_give isl_map *isl_map_lower_bound_si( 5946 __isl_take isl_map *map, 5947 enum isl_dim_type type, unsigned pos, int value); 5948 __isl_give isl_map *isl_map_upper_bound_si( 5949 __isl_take isl_map *map, 5950 enum isl_dim_type type, unsigned pos, int value); 5951 __isl_give isl_map *isl_map_lower_bound_val( 5952 __isl_take isl_map *map, 5953 enum isl_dim_type type, unsigned pos, 5954 __isl_take isl_val *value); 5955 __isl_give isl_map *isl_map_upper_bound_val( 5956 __isl_take isl_map *map, 5957 enum isl_dim_type type, unsigned pos, 5958 __isl_take isl_val *value); 5959 __isl_give isl_map *isl_map_lower_bound_multi_pw_aff( 5960 __isl_take isl_map *map, 5961 __isl_take isl_multi_pw_aff *lower); 5962 __isl_give isl_map *isl_map_upper_bound_multi_pw_aff( 5963 __isl_take isl_map *map, 5964 __isl_take isl_multi_pw_aff *upper); 5965 5966Intersect the set or relation with the half-space where the given 5967dimension has a value bounded by the given fixed integer value or 5968symbolic constant expression. 5969For functions taking a multi expression, 5970this applies to all set dimensions. 5971Those that bound a map, bound the range of that map. 5972If the multi expression is zero-dimensional but has an explicit domain, 5973then the (parameter) domain of the set or map is intersected 5974with this explicit domain. 5975 5976 __isl_give isl_set *isl_set_equate(__isl_take isl_set *set, 5977 enum isl_dim_type type1, int pos1, 5978 enum isl_dim_type type2, int pos2); 5979 __isl_give isl_basic_map *isl_basic_map_equate( 5980 __isl_take isl_basic_map *bmap, 5981 enum isl_dim_type type1, int pos1, 5982 enum isl_dim_type type2, int pos2); 5983 __isl_give isl_map *isl_map_equate(__isl_take isl_map *map, 5984 enum isl_dim_type type1, int pos1, 5985 enum isl_dim_type type2, int pos2); 5986 5987Intersect the set or relation with the hyperplane where the given 5988dimensions are equal to each other. 5989 5990 __isl_give isl_map *isl_map_oppose(__isl_take isl_map *map, 5991 enum isl_dim_type type1, int pos1, 5992 enum isl_dim_type type2, int pos2); 5993 5994Intersect the relation with the hyperplane where the given 5995dimensions have opposite values. 5996 5997 __isl_give isl_map *isl_map_order_le( 5998 __isl_take isl_map *map, 5999 enum isl_dim_type type1, int pos1, 6000 enum isl_dim_type type2, int pos2); 6001 __isl_give isl_basic_map *isl_basic_map_order_ge( 6002 __isl_take isl_basic_map *bmap, 6003 enum isl_dim_type type1, int pos1, 6004 enum isl_dim_type type2, int pos2); 6005 __isl_give isl_map *isl_map_order_ge( 6006 __isl_take isl_map *map, 6007 enum isl_dim_type type1, int pos1, 6008 enum isl_dim_type type2, int pos2); 6009 __isl_give isl_map *isl_map_order_lt(__isl_take isl_map *map, 6010 enum isl_dim_type type1, int pos1, 6011 enum isl_dim_type type2, int pos2); 6012 __isl_give isl_basic_map *isl_basic_map_order_gt( 6013 __isl_take isl_basic_map *bmap, 6014 enum isl_dim_type type1, int pos1, 6015 enum isl_dim_type type2, int pos2); 6016 __isl_give isl_map *isl_map_order_gt(__isl_take isl_map *map, 6017 enum isl_dim_type type1, int pos1, 6018 enum isl_dim_type type2, int pos2); 6019 6020Intersect the relation with the half-space where the given 6021dimensions satisfy the given ordering. 6022 6023 #include <isl/union_set.h> 6024 __isl_give isl_union_map *isl_union_map_remove_map_if( 6025 __isl_take isl_union_map *umap, 6026 isl_bool (*fn)(__isl_keep isl_map *map, 6027 void *user), void *user); 6028 6029This function calls the callback function once for each 6030pair of spaces for which there are elements in the input. 6031If the callback returns C<isl_bool_true>, then all those elements 6032are removed from the result. The only remaining elements in the output 6033are then those for which the callback returns C<isl_bool_false>. 6034 6035=item * Locus 6036 6037 #include <isl/aff.h> 6038 __isl_give isl_basic_set *isl_aff_zero_basic_set( 6039 __isl_take isl_aff *aff); 6040 __isl_give isl_basic_set *isl_aff_neg_basic_set( 6041 __isl_take isl_aff *aff); 6042 __isl_give isl_set *isl_pw_aff_pos_set( 6043 __isl_take isl_pw_aff *pa); 6044 __isl_give isl_set *isl_pw_aff_nonneg_set( 6045 __isl_take isl_pw_aff *pwaff); 6046 __isl_give isl_set *isl_pw_aff_zero_set( 6047 __isl_take isl_pw_aff *pwaff); 6048 __isl_give isl_set *isl_pw_aff_non_zero_set( 6049 __isl_take isl_pw_aff *pwaff); 6050 __isl_give isl_union_set * 6051 isl_union_pw_aff_zero_union_set( 6052 __isl_take isl_union_pw_aff *upa); 6053 __isl_give isl_union_set * 6054 isl_multi_union_pw_aff_zero_union_set( 6055 __isl_take isl_multi_union_pw_aff *mupa); 6056 6057The function C<isl_aff_neg_basic_set> returns a basic set 6058containing those elements in the domain space 6059of C<aff> where C<aff> is negative. 6060The function C<isl_pw_aff_nonneg_set> returns a set 6061containing those elements in the domain 6062of C<pwaff> where C<pwaff> is non-negative. 6063The function C<isl_multi_union_pw_aff_zero_union_set> 6064returns a union set containing those elements 6065in the domains of its elements where they are all zero. 6066 6067=item * Identity 6068 6069 __isl_give isl_map *isl_set_identity( 6070 __isl_take isl_set *set); 6071 __isl_give isl_union_map *isl_union_set_identity( 6072 __isl_take isl_union_set *uset); 6073 __isl_give isl_union_pw_multi_aff * 6074 isl_union_set_identity_union_pw_multi_aff( 6075 __isl_take isl_union_set *uset); 6076 6077Construct an identity relation on the given (union) set. 6078 6079=item * Function Extraction 6080 6081A piecewise quasi affine expression that is equal to 1 on a set 6082and 0 outside the set can be created using the following function. 6083 6084 #include <isl/aff.h> 6085 __isl_give isl_pw_aff *isl_set_indicator_function( 6086 __isl_take isl_set *set); 6087 6088A piecewise multiple quasi affine expression can be extracted 6089from an C<isl_set> or C<isl_map>, provided the C<isl_set> is a singleton 6090and the C<isl_map> is single-valued. 6091In case of a conversion from an C<isl_union_map> 6092to an C<isl_union_pw_multi_aff>, these properties need to hold 6093in each domain space. 6094A conversion to a C<isl_multi_union_pw_aff> additionally 6095requires that the input is non-empty and involves only a single 6096range space. 6097 6098 #include <isl/aff.h> 6099 __isl_give isl_pw_multi_aff *isl_set_as_pw_multi_aff( 6100 __isl_take isl_set *set); 6101 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_from_set( 6102 __isl_take isl_set *set); 6103 __isl_give isl_pw_multi_aff *isl_map_as_pw_multi_aff( 6104 __isl_take isl_map *map); 6105 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_from_map( 6106 __isl_take isl_map *map); 6107 6108 __isl_give isl_union_pw_multi_aff * 6109 isl_union_pw_multi_aff_from_union_set( 6110 __isl_take isl_union_set *uset); 6111 __isl_give isl_union_pw_multi_aff * 6112 isl_union_map_as_union_pw_multi_aff( 6113 __isl_take isl_union_map *umap); 6114 __isl_give isl_union_pw_multi_aff * 6115 isl_union_pw_multi_aff_from_union_map( 6116 __isl_take isl_union_map *umap); 6117 6118 __isl_give isl_multi_union_pw_aff * 6119 isl_union_map_as_multi_union_pw_aff( 6120 __isl_take isl_union_map *umap); 6121 __isl_give isl_multi_union_pw_aff * 6122 isl_multi_union_pw_aff_from_union_map( 6123 __isl_take isl_union_map *umap); 6124 6125C<isl_map_as_pw_multi_aff> and C<isl_pw_multi_aff_from_map> perform 6126the same operation. 6127Similarly for C<isl_set_as_pw_multi_aff> and 6128C<isl_pw_multi_aff_from_set>, 6129for C<isl_union_map_as_union_pw_multi_aff> and 6130C<isl_union_pw_multi_aff_from_union_map> and 6131for C<isl_union_map_as_multi_union_pw_aff> and 6132C<isl_multi_union_pw_aff_from_union_map>. 6133 6134=item * Deltas 6135 6136 __isl_give isl_basic_set *isl_basic_map_deltas( 6137 __isl_take isl_basic_map *bmap); 6138 __isl_give isl_set *isl_map_deltas(__isl_take isl_map *map); 6139 __isl_give isl_union_set *isl_union_map_deltas( 6140 __isl_take isl_union_map *umap); 6141 6142These functions return a (basic) set containing the differences 6143between image elements and corresponding domain elements in the input. 6144 6145 __isl_give isl_basic_map *isl_basic_map_deltas_map( 6146 __isl_take isl_basic_map *bmap); 6147 __isl_give isl_map *isl_map_deltas_map( 6148 __isl_take isl_map *map); 6149 __isl_give isl_union_map *isl_union_map_deltas_map( 6150 __isl_take isl_union_map *umap); 6151 6152The functions above construct a (basic, regular or union) relation 6153that maps (a wrapped version of) the input relation to its delta set. 6154 6155=item * Translation 6156 6157 #include <isl/map.h> 6158 __isl_give isl_map *isl_set_translation( 6159 __isl_take isl_set *deltas); 6160 6161This function performs essentially the opposite operation 6162of C<isl_map_deltas>. In particular, it returns pairs 6163of elements in the same space that have a difference in C<deltas>. 6164 6165=item * Coalescing 6166 6167Simplify the representation of a set, relation or functions by trying 6168to combine pairs of basic sets or relations into a single 6169basic set or relation. 6170 6171 #include <isl/set.h> 6172 __isl_give isl_set *isl_set_coalesce(__isl_take isl_set *set); 6173 6174 #include <isl/map.h> 6175 __isl_give isl_map *isl_map_coalesce(__isl_take isl_map *map); 6176 6177 #include <isl/union_set.h> 6178 __isl_give isl_union_set *isl_union_set_coalesce( 6179 __isl_take isl_union_set *uset); 6180 6181 #include <isl/union_map.h> 6182 __isl_give isl_union_map *isl_union_map_coalesce( 6183 __isl_take isl_union_map *umap); 6184 6185 #include <isl/aff.h> 6186 __isl_give isl_pw_aff *isl_pw_aff_coalesce( 6187 __isl_take isl_pw_aff *pa); 6188 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_coalesce( 6189 __isl_take isl_pw_multi_aff *pma); 6190 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_coalesce( 6191 __isl_take isl_multi_pw_aff *mpa); 6192 __isl_give isl_union_pw_aff *isl_union_pw_aff_coalesce( 6193 __isl_take isl_union_pw_aff *upa); 6194 __isl_give isl_union_pw_multi_aff * 6195 isl_union_pw_multi_aff_coalesce( 6196 __isl_take isl_union_pw_multi_aff *upma); 6197 __isl_give isl_multi_union_pw_aff * 6198 isl_multi_union_pw_aff_coalesce( 6199 __isl_take isl_multi_union_pw_aff *mupa); 6200 6201 #include <isl/polynomial.h> 6202 __isl_give isl_pw_qpolynomial_fold * 6203 isl_pw_qpolynomial_fold_coalesce( 6204 __isl_take isl_pw_qpolynomial_fold *pwf); 6205 __isl_give isl_union_pw_qpolynomial * 6206 isl_union_pw_qpolynomial_coalesce( 6207 __isl_take isl_union_pw_qpolynomial *upwqp); 6208 __isl_give isl_union_pw_qpolynomial_fold * 6209 isl_union_pw_qpolynomial_fold_coalesce( 6210 __isl_take isl_union_pw_qpolynomial_fold *upwf); 6211 6212One of the methods for combining pairs of basic sets or relations 6213can result in coefficients that are much larger than those that appear 6214in the constraints of the input. By default, the coefficients are 6215not allowed to grow larger, but this can be changed by unsetting 6216the following option. 6217 6218 isl_stat isl_options_set_coalesce_bounded_wrapping( 6219 isl_ctx *ctx, int val); 6220 int isl_options_get_coalesce_bounded_wrapping( 6221 isl_ctx *ctx); 6222 6223One of the other methods tries to combine pairs of basic sets 6224with different local variables, treating them as existentially 6225quantified variables even if they have known (but different) 6226integer division expressions. The result may then also have 6227existentially quantified variables. Turning on the following 6228option prevents this from happening. 6229 6230 isl_stat isl_options_set_coalesce_preserve_locals( 6231 isl_ctx *ctx, int val); 6232 int isl_options_get_coalesce_preserve_locals(isl_ctx *ctx); 6233 6234=item * Detecting equalities 6235 6236 __isl_give isl_basic_set *isl_basic_set_detect_equalities( 6237 __isl_take isl_basic_set *bset); 6238 __isl_give isl_basic_map *isl_basic_map_detect_equalities( 6239 __isl_take isl_basic_map *bmap); 6240 __isl_give isl_set *isl_set_detect_equalities( 6241 __isl_take isl_set *set); 6242 __isl_give isl_map *isl_map_detect_equalities( 6243 __isl_take isl_map *map); 6244 __isl_give isl_union_set *isl_union_set_detect_equalities( 6245 __isl_take isl_union_set *uset); 6246 __isl_give isl_union_map *isl_union_map_detect_equalities( 6247 __isl_take isl_union_map *umap); 6248 6249Simplify the representation of a set or relation by detecting implicit 6250equalities. 6251 6252=item * Removing redundant constraints 6253 6254 #include <isl/set.h> 6255 __isl_give isl_basic_set *isl_basic_set_remove_redundancies( 6256 __isl_take isl_basic_set *bset); 6257 __isl_give isl_set *isl_set_remove_redundancies( 6258 __isl_take isl_set *set); 6259 6260 #include <isl/union_set.h> 6261 __isl_give isl_union_set * 6262 isl_union_set_remove_redundancies( 6263 __isl_take isl_union_set *uset); 6264 6265 #include <isl/map.h> 6266 __isl_give isl_basic_map *isl_basic_map_remove_redundancies( 6267 __isl_take isl_basic_map *bmap); 6268 __isl_give isl_map *isl_map_remove_redundancies( 6269 __isl_take isl_map *map); 6270 6271 #include <isl/union_map.h> 6272 __isl_give isl_union_map * 6273 isl_union_map_remove_redundancies( 6274 __isl_take isl_union_map *umap); 6275 6276=item * Convex hull 6277 6278 __isl_give isl_basic_set *isl_set_convex_hull( 6279 __isl_take isl_set *set); 6280 __isl_give isl_basic_map *isl_map_convex_hull( 6281 __isl_take isl_map *map); 6282 6283If the input set or relation has any existentially quantified 6284variables, then the result of these operations is currently undefined. 6285 6286=item * Simple hull 6287 6288 #include <isl/set.h> 6289 __isl_give isl_basic_set * 6290 isl_set_unshifted_simple_hull( 6291 __isl_take isl_set *set); 6292 __isl_give isl_basic_set *isl_set_simple_hull( 6293 __isl_take isl_set *set); 6294 __isl_give isl_basic_set * 6295 isl_set_plain_unshifted_simple_hull( 6296 __isl_take isl_set *set); 6297 __isl_give isl_basic_set * 6298 isl_set_unshifted_simple_hull_from_set_list( 6299 __isl_take isl_set *set, 6300 __isl_take isl_set_list *list); 6301 6302 #include <isl/map.h> 6303 __isl_give isl_basic_map * 6304 isl_map_unshifted_simple_hull( 6305 __isl_take isl_map *map); 6306 __isl_give isl_basic_map *isl_map_simple_hull( 6307 __isl_take isl_map *map); 6308 __isl_give isl_basic_map * 6309 isl_map_plain_unshifted_simple_hull( 6310 __isl_take isl_map *map); 6311 __isl_give isl_basic_map * 6312 isl_map_unshifted_simple_hull_from_map_list( 6313 __isl_take isl_map *map, 6314 __isl_take isl_map_list *list); 6315 6316 #include <isl/union_map.h> 6317 __isl_give isl_union_map *isl_union_map_simple_hull( 6318 __isl_take isl_union_map *umap); 6319 6320These functions compute a single basic set or relation 6321that contains the whole input set or relation. 6322In particular, the output is described by translates 6323of the constraints describing the basic sets or relations in the input. 6324In case of C<isl_set_unshifted_simple_hull>, only the original 6325constraints are used, without any translation. 6326In case of C<isl_set_plain_unshifted_simple_hull> and 6327C<isl_map_plain_unshifted_simple_hull>, the result is described 6328by original constraints that are obviously satisfied 6329by the entire input set or relation. 6330In case of C<isl_set_unshifted_simple_hull_from_set_list> and 6331C<isl_map_unshifted_simple_hull_from_map_list>, the 6332constraints are taken from the elements of the second argument. 6333 6334=begin latex 6335 6336(See \autoref{s:simple hull}.) 6337 6338=end latex 6339 6340=item * Affine hull 6341 6342 __isl_give isl_basic_set *isl_basic_set_affine_hull( 6343 __isl_take isl_basic_set *bset); 6344 __isl_give isl_basic_set *isl_set_affine_hull( 6345 __isl_take isl_set *set); 6346 __isl_give isl_union_set *isl_union_set_affine_hull( 6347 __isl_take isl_union_set *uset); 6348 __isl_give isl_basic_map *isl_basic_map_affine_hull( 6349 __isl_take isl_basic_map *bmap); 6350 __isl_give isl_basic_map *isl_map_affine_hull( 6351 __isl_take isl_map *map); 6352 __isl_give isl_union_map *isl_union_map_affine_hull( 6353 __isl_take isl_union_map *umap); 6354 6355In case of union sets and relations, the affine hull is computed 6356per space. 6357 6358=item * Polyhedral hull 6359 6360 __isl_give isl_basic_set *isl_set_polyhedral_hull( 6361 __isl_take isl_set *set); 6362 __isl_give isl_basic_map *isl_map_polyhedral_hull( 6363 __isl_take isl_map *map); 6364 __isl_give isl_union_set *isl_union_set_polyhedral_hull( 6365 __isl_take isl_union_set *uset); 6366 __isl_give isl_union_map *isl_union_map_polyhedral_hull( 6367 __isl_take isl_union_map *umap); 6368 6369These functions compute a single basic set or relation 6370not involving any existentially quantified variables 6371that contains the whole input set or relation. 6372In case of union sets and relations, the polyhedral hull is computed 6373per space. 6374 6375=item * Box hull 6376 6377 #include <isl/set.h> 6378 __isl_give isl_fixed_box * 6379 isl_set_get_simple_fixed_box_hull( 6380 __isl_keep isl_set *set) 6381 6382 #include <isl/map.h> 6383 __isl_give isl_fixed_box * 6384 isl_map_get_range_simple_fixed_box_hull( 6385 __isl_keep isl_map *map); 6386 6387These functions try to approximate the set or 6388the range of the map by a box of fixed size. 6389The box is described in terms of an offset living in the same space as 6390the input and a size living in the set or range space. For any element 6391in the input map, the range value is greater than or equal to 6392the offset applied to the domain value and the difference with 6393this offset is strictly smaller than the size. 6394The same holds for the elements of the input set, where 6395the offset is a parametric constant value. 6396If no fixed-size approximation can be found, 6397an I<invalid> box is returned, i.e., one for which 6398C<isl_fixed_box_is_valid> below returns false. 6399 6400The validity, the offset and the size of the box can be obtained using 6401the following functions. 6402 6403 #include <isl/fixed_box.h> 6404 isl_bool isl_fixed_box_is_valid( 6405 __isl_keep isl_fixed_box *box); 6406 __isl_give isl_multi_aff *isl_fixed_box_get_offset( 6407 __isl_keep isl_fixed_box *box); 6408 __isl_give isl_multi_val *isl_fixed_box_get_size( 6409 __isl_keep isl_fixed_box *box); 6410 6411The box can be copied and freed using the following functions. 6412 6413 #include <isl/fixed_box.h> 6414 __isl_give isl_fixed_box *isl_fixed_box_copy( 6415 __isl_keep isl_fixed_box *box); 6416 __isl_null isl_fixed_box *isl_fixed_box_free( 6417 __isl_take isl_fixed_box *box); 6418 6419A representation of the information contained in an object 6420of type C<isl_fixed_box> can be obtained using 6421 6422 #include <isl/fixed_box.h> 6423 __isl_give isl_printer *isl_printer_print_fixed_box( 6424 __isl_take isl_printer *p, 6425 __isl_keep isl_fixed_box *box); 6426 __isl_give char *isl_fixed_box_to_str( 6427 __isl_keep isl_fixed_box *box); 6428 6429C<isl_fixed_box_to_str> prints the information in flow format. 6430 6431=item * Other approximations 6432 6433 #include <isl/set.h> 6434 __isl_give isl_basic_set * 6435 isl_basic_set_drop_constraints_involving_dims( 6436 __isl_take isl_basic_set *bset, 6437 enum isl_dim_type type, 6438 unsigned first, unsigned n); 6439 __isl_give isl_basic_set * 6440 isl_basic_set_drop_constraints_not_involving_dims( 6441 __isl_take isl_basic_set *bset, 6442 enum isl_dim_type type, 6443 unsigned first, unsigned n); 6444 __isl_give isl_set * 6445 isl_set_drop_constraints_involving_dims( 6446 __isl_take isl_set *set, 6447 enum isl_dim_type type, 6448 unsigned first, unsigned n); 6449 __isl_give isl_set * 6450 isl_set_drop_constraints_not_involving_dims( 6451 __isl_take isl_set *set, 6452 enum isl_dim_type type, 6453 unsigned first, unsigned n); 6454 6455 #include <isl/map.h> 6456 __isl_give isl_basic_map * 6457 isl_basic_map_drop_constraints_involving_dims( 6458 __isl_take isl_basic_map *bmap, 6459 enum isl_dim_type type, 6460 unsigned first, unsigned n); 6461 __isl_give isl_basic_map * 6462 isl_basic_map_drop_constraints_not_involving_dims( 6463 __isl_take isl_basic_map *bmap, 6464 enum isl_dim_type type, 6465 unsigned first, unsigned n); 6466 __isl_give isl_map * 6467 isl_map_drop_constraints_involving_dims( 6468 __isl_take isl_map *map, 6469 enum isl_dim_type type, 6470 unsigned first, unsigned n); 6471 __isl_give isl_map * 6472 isl_map_drop_constraints_not_involving_dims( 6473 __isl_take isl_map *map, 6474 enum isl_dim_type type, 6475 unsigned first, unsigned n); 6476 6477These functions drop any constraints (not) involving the specified dimensions. 6478Note that the result depends on the representation of the input. 6479 6480 #include <isl/polynomial.h> 6481 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_to_polynomial( 6482 __isl_take isl_pw_qpolynomial *pwqp, int sign); 6483 __isl_give isl_union_pw_qpolynomial * 6484 isl_union_pw_qpolynomial_to_polynomial( 6485 __isl_take isl_union_pw_qpolynomial *upwqp, int sign); 6486 6487Approximate each quasipolynomial by a polynomial. If C<sign> is positive, 6488the polynomial will be an overapproximation. If C<sign> is negative, 6489it will be an underapproximation. If C<sign> is zero, the approximation 6490will lie somewhere in between. 6491 6492=item * Feasibility 6493 6494 __isl_give isl_basic_set *isl_basic_set_sample( 6495 __isl_take isl_basic_set *bset); 6496 __isl_give isl_basic_set *isl_set_sample( 6497 __isl_take isl_set *set); 6498 __isl_give isl_basic_map *isl_basic_map_sample( 6499 __isl_take isl_basic_map *bmap); 6500 __isl_give isl_basic_map *isl_map_sample( 6501 __isl_take isl_map *map); 6502 6503If the input (basic) set or relation is non-empty, then return 6504a singleton subset of the input. Otherwise, return an empty set. 6505 6506=item * Optimization 6507 6508 #include <isl/ilp.h> 6509 __isl_give isl_val *isl_basic_set_max_val( 6510 __isl_keep isl_basic_set *bset, 6511 __isl_keep isl_aff *obj); 6512 __isl_give isl_val *isl_set_min_val( 6513 __isl_keep isl_set *set, 6514 __isl_keep isl_aff *obj); 6515 __isl_give isl_val *isl_set_max_val( 6516 __isl_keep isl_set *set, 6517 __isl_keep isl_aff *obj); 6518 __isl_give isl_multi_val * 6519 isl_union_set_min_multi_union_pw_aff( 6520 __isl_keep isl_union_set *uset, 6521 __isl_keep isl_multi_union_pw_aff *obj); 6522 6523Compute the minimum or maximum of the integer affine expression C<obj> 6524over the points in C<set>. 6525The result is C<NULL> in case of an error, the optimal value in case 6526there is one, negative infinity or infinity if the problem is unbounded and 6527NaN if the problem is empty. 6528 6529 #include <isl/ilp.h> 6530 __isl_give isl_multi_val * 6531 isl_pw_multi_aff_min_multi_val( 6532 __isl_take isl_pw_multi_aff *pma); 6533 __isl_give isl_multi_val * 6534 isl_pw_multi_aff_max_multi_val( 6535 __isl_take isl_pw_multi_aff *pma); 6536 __isl_give isl_multi_val * 6537 isl_multi_pw_aff_min_multi_val( 6538 __isl_take isl_multi_pw_aff *mpa); 6539 __isl_give isl_multi_val * 6540 isl_multi_pw_aff_max_multi_val( 6541 __isl_take isl_multi_pw_aff *mpa); 6542 __isl_give isl_val *isl_union_pw_aff_min_val( 6543 __isl_take isl_union_pw_aff *upa); 6544 __isl_give isl_val *isl_union_pw_aff_max_val( 6545 __isl_take isl_union_pw_aff *upa); 6546 __isl_give isl_multi_val * 6547 isl_multi_union_pw_aff_min_multi_val( 6548 __isl_take isl_multi_union_pw_aff *mupa); 6549 __isl_give isl_multi_val * 6550 isl_multi_union_pw_aff_max_multi_val( 6551 __isl_take isl_multi_union_pw_aff *mupa); 6552 6553Compute the minimum or maximum of the integer affine expression 6554over its definition domain. 6555The result is C<NULL> in case of an error, the optimal value in case 6556there is one, negative infinity or infinity if the problem is unbounded and 6557NaN if the problem is empty. 6558 6559 #include <isl/ilp.h> 6560 __isl_give isl_val *isl_basic_set_dim_max_val( 6561 __isl_take isl_basic_set *bset, int pos); 6562 __isl_give isl_val *isl_set_dim_min_val( 6563 __isl_take isl_set *set, int pos); 6564 __isl_give isl_val *isl_set_dim_max_val( 6565 __isl_take isl_set *set, int pos); 6566 6567Return the minimal or maximal value attained by the given set dimension, 6568independently of the parameter values and of any other dimensions. 6569The result is C<NULL> in case of an error, the optimal value in case 6570there is one, (negative) infinity if the problem is unbounded and 6571NaN if the input is empty. 6572 6573=item * Parametric optimization 6574 6575 __isl_give isl_pw_aff *isl_set_dim_min( 6576 __isl_take isl_set *set, int pos); 6577 __isl_give isl_pw_aff *isl_set_dim_max( 6578 __isl_take isl_set *set, int pos); 6579 __isl_give isl_pw_aff *isl_map_dim_min( 6580 __isl_take isl_map *map, int pos); 6581 __isl_give isl_pw_aff *isl_map_dim_max( 6582 __isl_take isl_map *map, int pos); 6583 __isl_give isl_multi_pw_aff * 6584 isl_set_min_multi_pw_aff( 6585 __isl_take isl_set *set); 6586 __isl_give isl_multi_pw_aff * 6587 isl_set_max_multi_pw_aff( 6588 __isl_take isl_set *set); 6589 __isl_give isl_multi_pw_aff * 6590 isl_map_min_multi_pw_aff( 6591 __isl_take isl_map *map); 6592 __isl_give isl_multi_pw_aff * 6593 isl_map_max_multi_pw_aff( 6594 __isl_take isl_map *map); 6595 6596Compute the minimum or maximum of the (given) set or output dimension(s) 6597as a function of the parameters (and input dimensions), but independently 6598of the other set or output dimensions. 6599For lexicographic optimization, see L<"Lexicographic Optimization">. 6600 6601=item * Dual 6602 6603The following functions compute either the set of (rational) coefficient 6604values of valid constraints for the given set or the set of (rational) 6605values satisfying the constraints with coefficients from the given set. 6606Internally, these two sets of functions perform essentially the 6607same operations, except that the set of coefficients is assumed to 6608be a cone, while the set of values may be any polyhedron. 6609The current implementation is based on the Farkas lemma and 6610Fourier-Motzkin elimination, but this may change or be made optional 6611in future. In particular, future implementations may use different 6612dualization algorithms or skip the elimination step. 6613 6614 #include <isl/set.h> 6615 __isl_give isl_basic_set *isl_basic_set_coefficients( 6616 __isl_take isl_basic_set *bset); 6617 __isl_give isl_basic_set_list * 6618 isl_basic_set_list_coefficients( 6619 __isl_take isl_basic_set_list *list); 6620 __isl_give isl_basic_set *isl_set_coefficients( 6621 __isl_take isl_set *set); 6622 __isl_give isl_union_set *isl_union_set_coefficients( 6623 __isl_take isl_union_set *bset); 6624 __isl_give isl_basic_set *isl_basic_set_solutions( 6625 __isl_take isl_basic_set *bset); 6626 __isl_give isl_basic_set *isl_set_solutions( 6627 __isl_take isl_set *set); 6628 __isl_give isl_union_set *isl_union_set_solutions( 6629 __isl_take isl_union_set *bset); 6630 6631=item * Power 6632 6633 __isl_give isl_map *isl_map_fixed_power_val( 6634 __isl_take isl_map *map, 6635 __isl_take isl_val *exp); 6636 __isl_give isl_union_map * 6637 isl_union_map_fixed_power_val( 6638 __isl_take isl_union_map *umap, 6639 __isl_take isl_val *exp); 6640 6641Compute the given power of C<map>, where C<exp> is assumed to be non-zero. 6642If the exponent C<exp> is negative, then the -C<exp> th power of the inverse 6643of C<map> is computed. 6644 6645 __isl_give isl_map *isl_map_power(__isl_take isl_map *map, 6646 isl_bool *exact); 6647 __isl_give isl_union_map *isl_union_map_power( 6648 __isl_take isl_union_map *umap, isl_bool *exact); 6649 6650Compute a parametric representation for all positive powers I<k> of C<map>. 6651The result maps I<k> to a nested relation corresponding to the 6652I<k>th power of C<map>. 6653The result may be an overapproximation. If the result is known to be exact, 6654then C<*exact> is set to C<1>. 6655 6656=item * Transitive closure 6657 6658 __isl_give isl_map *isl_map_transitive_closure( 6659 __isl_take isl_map *map, isl_bool *exact); 6660 __isl_give isl_union_map *isl_union_map_transitive_closure( 6661 __isl_take isl_union_map *umap, isl_bool *exact); 6662 6663Compute the transitive closure of C<map>. 6664The result may be an overapproximation. If the result is known to be exact, 6665then C<*exact> is set to C<1>. 6666 6667=item * Reaching path lengths 6668 6669 __isl_give isl_map *isl_map_reaching_path_lengths( 6670 __isl_take isl_map *map, isl_bool *exact); 6671 6672Compute a relation that maps each element in the range of C<map> 6673to the lengths of all paths composed of edges in C<map> that 6674end up in the given element. 6675The result may be an overapproximation. If the result is known to be exact, 6676then C<*exact> is set to C<1>. 6677To compute the I<maximal> path length, the resulting relation 6678should be postprocessed by C<isl_map_lexmax>. 6679In particular, if the input relation is a dependence relation 6680(mapping sources to sinks), then the maximal path length corresponds 6681to the free schedule. 6682Note, however, that C<isl_map_lexmax> expects the maximum to be 6683finite, so if the path lengths are unbounded (possibly due to 6684the overapproximation), then you will get an error message. 6685 6686=item * Wrapping 6687 6688 #include <isl/space.h> 6689 __isl_give isl_space *isl_space_wrap( 6690 __isl_take isl_space *space); 6691 __isl_give isl_space *isl_space_unwrap( 6692 __isl_take isl_space *space); 6693 6694 #include <isl/local_space.h> 6695 __isl_give isl_local_space *isl_local_space_wrap( 6696 __isl_take isl_local_space *ls); 6697 6698 #include <isl/set.h> 6699 __isl_give isl_basic_map *isl_basic_set_unwrap( 6700 __isl_take isl_basic_set *bset); 6701 __isl_give isl_map *isl_set_unwrap( 6702 __isl_take isl_set *set); 6703 6704 #include <isl/map.h> 6705 __isl_give isl_basic_set *isl_basic_map_wrap( 6706 __isl_take isl_basic_map *bmap); 6707 __isl_give isl_set *isl_map_wrap( 6708 __isl_take isl_map *map); 6709 6710 #include <isl/union_set.h> 6711 __isl_give isl_union_map *isl_union_set_unwrap( 6712 __isl_take isl_union_set *uset); 6713 6714 #include <isl/union_map.h> 6715 __isl_give isl_union_set *isl_union_map_wrap( 6716 __isl_take isl_union_map *umap); 6717 6718The input to C<isl_space_unwrap> should 6719be the space of a set, while that of 6720C<isl_space_wrap> should be the space of a relation. 6721Conversely, the output of C<isl_space_unwrap> is the space 6722of a relation, while that of C<isl_space_wrap> is the space of a set. 6723 6724=item * Flattening 6725 6726Remove any internal structure of domain (and range) of the given 6727set or relation. If there is any such internal structure in the input, 6728then the name of the space is also removed. 6729 6730 #include <isl/space.h> 6731 __isl_give isl_space *isl_space_flatten_domain( 6732 __isl_take isl_space *space); 6733 __isl_give isl_space *isl_space_flatten_range( 6734 __isl_take isl_space *space); 6735 6736 #include <isl/local_space.h> 6737 __isl_give isl_local_space * 6738 isl_local_space_flatten_domain( 6739 __isl_take isl_local_space *ls); 6740 __isl_give isl_local_space * 6741 isl_local_space_flatten_range( 6742 __isl_take isl_local_space *ls); 6743 6744 #include <isl/set.h> 6745 __isl_give isl_basic_set *isl_basic_set_flatten( 6746 __isl_take isl_basic_set *bset); 6747 __isl_give isl_set *isl_set_flatten( 6748 __isl_take isl_set *set); 6749 6750 #include <isl/map.h> 6751 __isl_give isl_basic_map *isl_basic_map_flatten_domain( 6752 __isl_take isl_basic_map *bmap); 6753 __isl_give isl_basic_map *isl_basic_map_flatten_range( 6754 __isl_take isl_basic_map *bmap); 6755 __isl_give isl_map *isl_map_flatten_range( 6756 __isl_take isl_map *map); 6757 __isl_give isl_map *isl_map_flatten_domain( 6758 __isl_take isl_map *map); 6759 __isl_give isl_basic_map *isl_basic_map_flatten( 6760 __isl_take isl_basic_map *bmap); 6761 __isl_give isl_map *isl_map_flatten( 6762 __isl_take isl_map *map); 6763 6764 #include <isl/id.h> 6765 __isl_give isl_multi_id *isl_multi_id_flatten_range( 6766 __isl_take isl_multi_id *mi); 6767 6768 #include <isl/val.h> 6769 __isl_give isl_multi_val *isl_multi_val_flatten_range( 6770 __isl_take isl_multi_val *mv); 6771 6772 #include <isl/aff.h> 6773 __isl_give isl_multi_aff *isl_multi_aff_flatten_domain( 6774 __isl_take isl_multi_aff *ma); 6775 __isl_give isl_multi_aff *isl_multi_aff_flatten_range( 6776 __isl_take isl_multi_aff *ma); 6777 __isl_give isl_multi_pw_aff * 6778 isl_multi_pw_aff_flatten_range( 6779 __isl_take isl_multi_pw_aff *mpa); 6780 __isl_give isl_multi_union_pw_aff * 6781 isl_multi_union_pw_aff_flatten_range( 6782 __isl_take isl_multi_union_pw_aff *mupa); 6783 6784 #include <isl/map.h> 6785 __isl_give isl_map *isl_set_flatten_map( 6786 __isl_take isl_set *set); 6787 6788The function above constructs a relation 6789that maps the input set to a flattened version of the set. 6790 6791=item * Lifting 6792 6793Lift the input set to a space with extra dimensions corresponding 6794to the existentially quantified variables in the input. 6795In particular, the result lives in a wrapped map where the domain 6796is the original space and the range corresponds to the original 6797existentially quantified variables. 6798 6799 #include <isl/set.h> 6800 __isl_give isl_basic_set *isl_basic_set_lift( 6801 __isl_take isl_basic_set *bset); 6802 __isl_give isl_set *isl_set_lift( 6803 __isl_take isl_set *set); 6804 __isl_give isl_union_set *isl_union_set_lift( 6805 __isl_take isl_union_set *uset); 6806 6807Given a local space that contains the existentially quantified 6808variables of a set, a basic relation that, when applied to 6809a basic set, has essentially the same effect as C<isl_basic_set_lift>, 6810can be constructed using the following function. 6811 6812 #include <isl/local_space.h> 6813 __isl_give isl_basic_map *isl_local_space_lifting( 6814 __isl_take isl_local_space *ls); 6815 6816 #include <isl/aff.h> 6817 __isl_give isl_multi_aff *isl_multi_aff_lift( 6818 __isl_take isl_multi_aff *maff, 6819 __isl_give isl_local_space **ls); 6820 6821If the C<ls> argument of C<isl_multi_aff_lift> is not C<NULL>, 6822then it is assigned the local space that lies at the basis of 6823the lifting applied. 6824 6825=item * Internal Product 6826 6827 #include <isl/space.h> 6828 __isl_give isl_space *isl_space_zip( 6829 __isl_take isl_space *space); 6830 6831 #include <isl/map.h> 6832 __isl_give isl_basic_map *isl_basic_map_zip( 6833 __isl_take isl_basic_map *bmap); 6834 __isl_give isl_map *isl_map_zip( 6835 __isl_take isl_map *map); 6836 6837 #include <isl/union_map.h> 6838 __isl_give isl_union_map *isl_union_map_zip( 6839 __isl_take isl_union_map *umap); 6840 6841Given a relation with nested relations for domain and range, 6842interchange the range of the domain with the domain of the range. 6843 6844=item * Currying 6845 6846 #include <isl/space.h> 6847 __isl_give isl_space *isl_space_curry( 6848 __isl_take isl_space *space); 6849 __isl_give isl_space *isl_space_uncurry( 6850 __isl_take isl_space *space); 6851 6852 #include <isl/map.h> 6853 __isl_give isl_basic_map *isl_basic_map_curry( 6854 __isl_take isl_basic_map *bmap); 6855 __isl_give isl_basic_map *isl_basic_map_uncurry( 6856 __isl_take isl_basic_map *bmap); 6857 __isl_give isl_map *isl_map_curry( 6858 __isl_take isl_map *map); 6859 __isl_give isl_map *isl_map_uncurry( 6860 __isl_take isl_map *map); 6861 6862 #include <isl/union_map.h> 6863 __isl_give isl_union_map *isl_union_map_curry( 6864 __isl_take isl_union_map *umap); 6865 __isl_give isl_union_map *isl_union_map_uncurry( 6866 __isl_take isl_union_map *umap); 6867 6868Given a relation with a nested relation for domain, 6869the C<curry> functions 6870move the range of the nested relation out of the domain 6871and use it as the domain of a nested relation in the range, 6872with the original range as range of this nested relation. 6873The C<uncurry> functions perform the inverse operation. 6874 6875 #include <isl/space.h> 6876 __isl_give isl_space *isl_space_range_curry( 6877 __isl_take isl_space *space); 6878 6879 #include <isl/map.h> 6880 __isl_give isl_map *isl_map_range_curry( 6881 __isl_take isl_map *map); 6882 6883 #include <isl/union_map.h> 6884 __isl_give isl_union_map *isl_union_map_range_curry( 6885 __isl_take isl_union_map *umap); 6886 6887These functions apply the currying to the relation that 6888is nested inside the range of the input. 6889 6890=item * Aligning parameters 6891 6892Change the order of the parameters of the given set, relation 6893or function 6894such that the first parameters match those of C<model>. 6895This may involve the introduction of extra parameters. 6896All parameters need to be named. 6897 6898 #include <isl/space.h> 6899 __isl_give isl_space *isl_space_align_params( 6900 __isl_take isl_space *space1, 6901 __isl_take isl_space *space2) 6902 6903 #include <isl/set.h> 6904 __isl_give isl_basic_set *isl_basic_set_align_params( 6905 __isl_take isl_basic_set *bset, 6906 __isl_take isl_space *model); 6907 __isl_give isl_set *isl_set_align_params( 6908 __isl_take isl_set *set, 6909 __isl_take isl_space *model); 6910 6911 #include <isl/map.h> 6912 __isl_give isl_basic_map *isl_basic_map_align_params( 6913 __isl_take isl_basic_map *bmap, 6914 __isl_take isl_space *model); 6915 __isl_give isl_map *isl_map_align_params( 6916 __isl_take isl_map *map, 6917 __isl_take isl_space *model); 6918 6919 #include <isl/id.h> 6920 __isl_give isl_multi_id *isl_multi_id_align_params( 6921 __isl_take isl_multi_id *mi, 6922 __isl_take isl_space *model); 6923 6924 #include <isl/val.h> 6925 __isl_give isl_multi_val *isl_multi_val_align_params( 6926 __isl_take isl_multi_val *mv, 6927 __isl_take isl_space *model); 6928 6929 #include <isl/aff.h> 6930 __isl_give isl_aff *isl_aff_align_params( 6931 __isl_take isl_aff *aff, 6932 __isl_take isl_space *model); 6933 __isl_give isl_multi_aff *isl_multi_aff_align_params( 6934 __isl_take isl_multi_aff *multi, 6935 __isl_take isl_space *model); 6936 __isl_give isl_pw_aff *isl_pw_aff_align_params( 6937 __isl_take isl_pw_aff *pwaff, 6938 __isl_take isl_space *model); 6939 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_align_params( 6940 __isl_take isl_pw_multi_aff *pma, 6941 __isl_take isl_space *model); 6942 __isl_give isl_union_pw_aff * 6943 isl_union_pw_aff_align_params( 6944 __isl_take isl_union_pw_aff *upa, 6945 __isl_take isl_space *model); 6946 __isl_give isl_union_pw_multi_aff * 6947 isl_union_pw_multi_aff_align_params( 6948 __isl_take isl_union_pw_multi_aff *upma, 6949 __isl_take isl_space *model); 6950 __isl_give isl_multi_union_pw_aff * 6951 isl_multi_union_pw_aff_align_params( 6952 __isl_take isl_multi_union_pw_aff *mupa, 6953 __isl_take isl_space *model); 6954 6955 #include <isl/polynomial.h> 6956 __isl_give isl_qpolynomial *isl_qpolynomial_align_params( 6957 __isl_take isl_qpolynomial *qp, 6958 __isl_take isl_space *model); 6959 6960=item * Drop unused parameters 6961 6962Drop parameters that are not referenced by the isl object. 6963All parameters need to be named. 6964 6965 #include <isl/set.h> 6966 __isl_give isl_basic_set * 6967 isl_basic_set_drop_unused_params( 6968 __isl_take isl_basic_set *bset); 6969 __isl_give isl_set *isl_set_drop_unused_params( 6970 __isl_take isl_set *set); 6971 6972 #include <isl/map.h> 6973 __isl_give isl_basic_map * 6974 isl_basic_map_drop_unused_params( 6975 __isl_take isl_basic_map *bmap); 6976 __isl_give isl_map *isl_map_drop_unused_params( 6977 __isl_take isl_map *map); 6978 6979 #include <isl/aff.h> 6980 __isl_give isl_pw_aff *isl_pw_aff_drop_unused_params( 6981 __isl_take isl_pw_aff *pa); 6982 __isl_give isl_pw_multi_aff * 6983 isl_pw_multi_aff_drop_unused_params( 6984 __isl_take isl_pw_multi_aff *pma); 6985 6986 #include <isl/polynomial.h> 6987 __isl_give isl_pw_qpolynomial * 6988 isl_pw_qpolynomial_drop_unused_params( 6989 __isl_take isl_pw_qpolynomial *pwqp); 6990 __isl_give isl_pw_qpolynomial_fold * 6991 isl_pw_qpolynomial_fold_drop_unused_params( 6992 __isl_take isl_pw_qpolynomial_fold *pwf); 6993 6994=item * Unary Arithmetic Operations 6995 6996 #include <isl/set.h> 6997 __isl_give isl_set *isl_set_neg( 6998 __isl_take isl_set *set); 6999 #include <isl/map.h> 7000 __isl_give isl_map *isl_map_neg( 7001 __isl_take isl_map *map); 7002 7003C<isl_set_neg> constructs a set containing the opposites of 7004the elements in its argument. 7005The domain of the result of C<isl_map_neg> is the same 7006as the domain of its argument. The corresponding range 7007elements are the opposites of the corresponding range 7008elements in the argument. 7009 7010 #include <isl/val.h> 7011 __isl_give isl_multi_val *isl_multi_val_neg( 7012 __isl_take isl_multi_val *mv); 7013 7014 #include <isl/aff.h> 7015 __isl_give isl_aff *isl_aff_neg( 7016 __isl_take isl_aff *aff); 7017 __isl_give isl_multi_aff *isl_multi_aff_neg( 7018 __isl_take isl_multi_aff *ma); 7019 __isl_give isl_pw_aff *isl_pw_aff_neg( 7020 __isl_take isl_pw_aff *pwaff); 7021 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_neg( 7022 __isl_take isl_pw_multi_aff *pma); 7023 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_neg( 7024 __isl_take isl_multi_pw_aff *mpa); 7025 __isl_give isl_union_pw_aff *isl_union_pw_aff_neg( 7026 __isl_take isl_union_pw_aff *upa); 7027 __isl_give isl_union_pw_multi_aff * 7028 isl_union_pw_multi_aff_neg( 7029 __isl_take isl_union_pw_multi_aff *upma); 7030 __isl_give isl_multi_union_pw_aff * 7031 isl_multi_union_pw_aff_neg( 7032 __isl_take isl_multi_union_pw_aff *mupa); 7033 __isl_give isl_aff *isl_aff_ceil( 7034 __isl_take isl_aff *aff); 7035 __isl_give isl_pw_aff *isl_pw_aff_ceil( 7036 __isl_take isl_pw_aff *pwaff); 7037 __isl_give isl_aff *isl_aff_floor( 7038 __isl_take isl_aff *aff); 7039 __isl_give isl_multi_aff *isl_multi_aff_floor( 7040 __isl_take isl_multi_aff *ma); 7041 __isl_give isl_pw_aff *isl_pw_aff_floor( 7042 __isl_take isl_pw_aff *pwaff); 7043 __isl_give isl_union_pw_aff *isl_union_pw_aff_floor( 7044 __isl_take isl_union_pw_aff *upa); 7045 __isl_give isl_multi_union_pw_aff * 7046 isl_multi_union_pw_aff_floor( 7047 __isl_take isl_multi_union_pw_aff *mupa); 7048 7049 #include <isl/aff.h> 7050 __isl_give isl_pw_aff *isl_pw_aff_list_min( 7051 __isl_take isl_pw_aff_list *list); 7052 __isl_give isl_pw_aff *isl_pw_aff_list_max( 7053 __isl_take isl_pw_aff_list *list); 7054 7055 #include <isl/polynomial.h> 7056 __isl_give isl_qpolynomial *isl_qpolynomial_neg( 7057 __isl_take isl_qpolynomial *qp); 7058 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_neg( 7059 __isl_take isl_pw_qpolynomial *pwqp); 7060 __isl_give isl_union_pw_qpolynomial * 7061 isl_union_pw_qpolynomial_neg( 7062 __isl_take isl_union_pw_qpolynomial *upwqp); 7063 __isl_give isl_qpolynomial *isl_qpolynomial_pow( 7064 __isl_take isl_qpolynomial *qp, 7065 unsigned exponent); 7066 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_pow( 7067 __isl_take isl_pw_qpolynomial *pwqp, 7068 unsigned exponent); 7069 7070=item * Evaluation 7071 7072The following functions evaluate a function in a point. 7073 7074 #include <isl/aff.h> 7075 __isl_give isl_val *isl_aff_eval( 7076 __isl_take isl_aff *aff, 7077 __isl_take isl_point *pnt); 7078 __isl_give isl_val *isl_pw_aff_eval( 7079 __isl_take isl_pw_aff *pa, 7080 __isl_take isl_point *pnt); 7081 7082 #include <isl/polynomial.h> 7083 __isl_give isl_val *isl_pw_qpolynomial_eval( 7084 __isl_take isl_pw_qpolynomial *pwqp, 7085 __isl_take isl_point *pnt); 7086 __isl_give isl_val *isl_pw_qpolynomial_fold_eval( 7087 __isl_take isl_pw_qpolynomial_fold *pwf, 7088 __isl_take isl_point *pnt); 7089 __isl_give isl_val *isl_union_pw_qpolynomial_eval( 7090 __isl_take isl_union_pw_qpolynomial *upwqp, 7091 __isl_take isl_point *pnt); 7092 __isl_give isl_val *isl_union_pw_qpolynomial_fold_eval( 7093 __isl_take isl_union_pw_qpolynomial_fold *upwf, 7094 __isl_take isl_point *pnt); 7095 7096These functions return NaN when evaluated at a void point. 7097Note that C<isl_pw_aff_eval> returns NaN when the function is evaluated outside 7098its definition domain, while C<isl_pw_qpolynomial_eval> returns zero 7099when the function is evaluated outside its explicit domain. 7100 7101=item * Dimension manipulation 7102 7103It is usually not advisable to directly change the (input or output) 7104space of a set or a relation as this removes the name and the internal 7105structure of the space. However, the functions below can be useful 7106to add new parameters, assuming 7107C<isl_set_align_params> and C<isl_map_align_params> 7108are not sufficient. 7109 7110 #include <isl/space.h> 7111 __isl_give isl_space *isl_space_add_dims( 7112 __isl_take isl_space *space, 7113 enum isl_dim_type type, unsigned n); 7114 __isl_give isl_space *isl_space_insert_dims( 7115 __isl_take isl_space *space, 7116 enum isl_dim_type type, unsigned pos, unsigned n); 7117 __isl_give isl_space *isl_space_drop_dims( 7118 __isl_take isl_space *space, 7119 enum isl_dim_type type, unsigned first, unsigned n); 7120 __isl_give isl_space *isl_space_move_dims( 7121 __isl_take isl_space *space, 7122 enum isl_dim_type dst_type, unsigned dst_pos, 7123 enum isl_dim_type src_type, unsigned src_pos, 7124 unsigned n); 7125 7126 #include <isl/local_space.h> 7127 __isl_give isl_local_space *isl_local_space_add_dims( 7128 __isl_take isl_local_space *ls, 7129 enum isl_dim_type type, unsigned n); 7130 __isl_give isl_local_space *isl_local_space_insert_dims( 7131 __isl_take isl_local_space *ls, 7132 enum isl_dim_type type, unsigned first, unsigned n); 7133 __isl_give isl_local_space *isl_local_space_drop_dims( 7134 __isl_take isl_local_space *ls, 7135 enum isl_dim_type type, unsigned first, unsigned n); 7136 7137 #include <isl/set.h> 7138 __isl_give isl_basic_set *isl_basic_set_add_dims( 7139 __isl_take isl_basic_set *bset, 7140 enum isl_dim_type type, unsigned n); 7141 __isl_give isl_set *isl_set_add_dims( 7142 __isl_take isl_set *set, 7143 enum isl_dim_type type, unsigned n); 7144 __isl_give isl_basic_set *isl_basic_set_insert_dims( 7145 __isl_take isl_basic_set *bset, 7146 enum isl_dim_type type, unsigned pos, 7147 unsigned n); 7148 __isl_give isl_set *isl_set_insert_dims( 7149 __isl_take isl_set *set, 7150 enum isl_dim_type type, unsigned pos, unsigned n); 7151 __isl_give isl_basic_set *isl_basic_set_move_dims( 7152 __isl_take isl_basic_set *bset, 7153 enum isl_dim_type dst_type, unsigned dst_pos, 7154 enum isl_dim_type src_type, unsigned src_pos, 7155 unsigned n); 7156 __isl_give isl_set *isl_set_move_dims( 7157 __isl_take isl_set *set, 7158 enum isl_dim_type dst_type, unsigned dst_pos, 7159 enum isl_dim_type src_type, unsigned src_pos, 7160 unsigned n); 7161 7162 #include <isl/map.h> 7163 __isl_give isl_basic_map *isl_basic_map_add_dims( 7164 __isl_take isl_basic_map *bmap, 7165 enum isl_dim_type type, unsigned n); 7166 __isl_give isl_map *isl_map_add_dims( 7167 __isl_take isl_map *map, 7168 enum isl_dim_type type, unsigned n); 7169 __isl_give isl_basic_map *isl_basic_map_insert_dims( 7170 __isl_take isl_basic_map *bmap, 7171 enum isl_dim_type type, unsigned pos, 7172 unsigned n); 7173 __isl_give isl_map *isl_map_insert_dims( 7174 __isl_take isl_map *map, 7175 enum isl_dim_type type, unsigned pos, unsigned n); 7176 __isl_give isl_basic_map *isl_basic_map_move_dims( 7177 __isl_take isl_basic_map *bmap, 7178 enum isl_dim_type dst_type, unsigned dst_pos, 7179 enum isl_dim_type src_type, unsigned src_pos, 7180 unsigned n); 7181 __isl_give isl_map *isl_map_move_dims( 7182 __isl_take isl_map *map, 7183 enum isl_dim_type dst_type, unsigned dst_pos, 7184 enum isl_dim_type src_type, unsigned src_pos, 7185 unsigned n); 7186 7187 #include <isl/val.h> 7188 __isl_give isl_multi_val *isl_multi_val_insert_dims( 7189 __isl_take isl_multi_val *mv, 7190 enum isl_dim_type type, unsigned first, unsigned n); 7191 __isl_give isl_multi_val *isl_multi_val_add_dims( 7192 __isl_take isl_multi_val *mv, 7193 enum isl_dim_type type, unsigned n); 7194 __isl_give isl_multi_val *isl_multi_val_drop_dims( 7195 __isl_take isl_multi_val *mv, 7196 enum isl_dim_type type, unsigned first, unsigned n); 7197 7198 #include <isl/aff.h> 7199 __isl_give isl_aff *isl_aff_insert_dims( 7200 __isl_take isl_aff *aff, 7201 enum isl_dim_type type, unsigned first, unsigned n); 7202 __isl_give isl_multi_aff *isl_multi_aff_insert_dims( 7203 __isl_take isl_multi_aff *ma, 7204 enum isl_dim_type type, unsigned first, unsigned n); 7205 __isl_give isl_pw_aff *isl_pw_aff_insert_dims( 7206 __isl_take isl_pw_aff *pwaff, 7207 enum isl_dim_type type, unsigned first, unsigned n); 7208 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_insert_dims( 7209 __isl_take isl_multi_pw_aff *mpa, 7210 enum isl_dim_type type, unsigned first, unsigned n); 7211 __isl_give isl_aff *isl_aff_add_dims( 7212 __isl_take isl_aff *aff, 7213 enum isl_dim_type type, unsigned n); 7214 __isl_give isl_multi_aff *isl_multi_aff_add_dims( 7215 __isl_take isl_multi_aff *ma, 7216 enum isl_dim_type type, unsigned n); 7217 __isl_give isl_pw_aff *isl_pw_aff_add_dims( 7218 __isl_take isl_pw_aff *pwaff, 7219 enum isl_dim_type type, unsigned n); 7220 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_add_dims( 7221 __isl_take isl_multi_pw_aff *mpa, 7222 enum isl_dim_type type, unsigned n); 7223 __isl_give isl_aff *isl_aff_drop_dims( 7224 __isl_take isl_aff *aff, 7225 enum isl_dim_type type, unsigned first, unsigned n); 7226 __isl_give isl_multi_aff *isl_multi_aff_drop_dims( 7227 __isl_take isl_multi_aff *maff, 7228 enum isl_dim_type type, unsigned first, unsigned n); 7229 __isl_give isl_pw_aff *isl_pw_aff_drop_dims( 7230 __isl_take isl_pw_aff *pwaff, 7231 enum isl_dim_type type, unsigned first, unsigned n); 7232 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_drop_dims( 7233 __isl_take isl_pw_multi_aff *pma, 7234 enum isl_dim_type type, unsigned first, unsigned n); 7235 __isl_give isl_union_pw_aff *isl_union_pw_aff_drop_dims( 7236 __isl_take isl_union_pw_aff *upa, 7237 enum isl_dim_type type, unsigned first, unsigned n); 7238 __isl_give isl_union_pw_multi_aff * 7239 isl_union_pw_multi_aff_drop_dims( 7240 __isl_take isl_union_pw_multi_aff *upma, 7241 enum isl_dim_type type, 7242 unsigned first, unsigned n); 7243 __isl_give isl_multi_union_pw_aff * 7244 isl_multi_union_pw_aff_drop_dims( 7245 __isl_take isl_multi_union_pw_aff *mupa, 7246 enum isl_dim_type type, unsigned first, 7247 unsigned n); 7248 __isl_give isl_aff *isl_aff_move_dims( 7249 __isl_take isl_aff *aff, 7250 enum isl_dim_type dst_type, unsigned dst_pos, 7251 enum isl_dim_type src_type, unsigned src_pos, 7252 unsigned n); 7253 __isl_give isl_multi_aff *isl_multi_aff_move_dims( 7254 __isl_take isl_multi_aff *ma, 7255 enum isl_dim_type dst_type, unsigned dst_pos, 7256 enum isl_dim_type src_type, unsigned src_pos, 7257 unsigned n); 7258 __isl_give isl_pw_aff *isl_pw_aff_move_dims( 7259 __isl_take isl_pw_aff *pa, 7260 enum isl_dim_type dst_type, unsigned dst_pos, 7261 enum isl_dim_type src_type, unsigned src_pos, 7262 unsigned n); 7263 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_move_dims( 7264 __isl_take isl_multi_pw_aff *pma, 7265 enum isl_dim_type dst_type, unsigned dst_pos, 7266 enum isl_dim_type src_type, unsigned src_pos, 7267 unsigned n); 7268 7269 #include <isl/polynomial.h> 7270 __isl_give isl_union_pw_qpolynomial * 7271 isl_union_pw_qpolynomial_drop_dims( 7272 __isl_take isl_union_pw_qpolynomial *upwqp, 7273 enum isl_dim_type type, 7274 unsigned first, unsigned n); 7275 __isl_give isl_union_pw_qpolynomial_fold * 7276 isl_union_pw_qpolynomial_fold_drop_dims( 7277 __isl_take isl_union_pw_qpolynomial_fold *upwf, 7278 enum isl_dim_type type, 7279 unsigned first, unsigned n); 7280 7281The operations on union expressions can only manipulate parameters. 7282 7283=back 7284 7285=head2 Binary Operations 7286 7287The two arguments of a binary operation not only need to live 7288in the same C<isl_ctx>, they currently also need to have 7289the same (number of) parameters. 7290 7291=head3 Basic Operations 7292 7293=over 7294 7295=item * Intersection 7296 7297 #include <isl/local_space.h> 7298 __isl_give isl_local_space *isl_local_space_intersect( 7299 __isl_take isl_local_space *ls1, 7300 __isl_take isl_local_space *ls2); 7301 7302 #include <isl/set.h> 7303 __isl_give isl_basic_set *isl_basic_set_intersect_params( 7304 __isl_take isl_basic_set *bset1, 7305 __isl_take isl_basic_set *bset2); 7306 __isl_give isl_basic_set *isl_basic_set_intersect( 7307 __isl_take isl_basic_set *bset1, 7308 __isl_take isl_basic_set *bset2); 7309 __isl_give isl_basic_set *isl_basic_set_list_intersect( 7310 __isl_take struct isl_basic_set_list *list); 7311 __isl_give isl_set *isl_set_intersect_params( 7312 __isl_take isl_set *set, 7313 __isl_take isl_set *params); 7314 __isl_give isl_set *isl_set_intersect( 7315 __isl_take isl_set *set1, 7316 __isl_take isl_set *set2); 7317 __isl_give isl_set *isl_set_intersect_factor_domain( 7318 __isl_take isl_set *set, 7319 __isl_take isl_set *domain); 7320 __isl_give isl_set *isl_set_intersect_factor_range( 7321 __isl_take isl_set *set, 7322 __isl_take isl_set *range); 7323 7324 #include <isl/map.h> 7325 __isl_give isl_basic_map *isl_basic_map_intersect_domain( 7326 __isl_take isl_basic_map *bmap, 7327 __isl_take isl_basic_set *bset); 7328 __isl_give isl_basic_map *isl_basic_map_intersect_range( 7329 __isl_take isl_basic_map *bmap, 7330 __isl_take isl_basic_set *bset); 7331 __isl_give isl_basic_map *isl_basic_map_intersect( 7332 __isl_take isl_basic_map *bmap1, 7333 __isl_take isl_basic_map *bmap2); 7334 __isl_give isl_basic_map *isl_basic_map_list_intersect( 7335 __isl_take isl_basic_map_list *list); 7336 __isl_give isl_map *isl_map_intersect_params( 7337 __isl_take isl_map *map, 7338 __isl_take isl_set *params); 7339 __isl_give isl_map *isl_map_intersect_domain( 7340 __isl_take isl_map *map, 7341 __isl_take isl_set *set); 7342 __isl_give isl_map *isl_map_intersect_range( 7343 __isl_take isl_map *map, 7344 __isl_take isl_set *set); 7345 __isl_give isl_map *isl_map_intersect( 7346 __isl_take isl_map *map1, 7347 __isl_take isl_map *map2); 7348 __isl_give isl_map * 7349 isl_map_intersect_domain_factor_domain( 7350 __isl_take isl_map *map, 7351 __isl_take isl_map *factor); 7352 __isl_give isl_map * 7353 isl_map_intersect_domain_factor_range( 7354 __isl_take isl_map *map, 7355 __isl_take isl_map *factor); 7356 __isl_give isl_map * 7357 isl_map_intersect_range_factor_domain( 7358 __isl_take isl_map *map, 7359 __isl_take isl_map *factor); 7360 __isl_give isl_map * 7361 isl_map_intersect_range_factor_range( 7362 __isl_take isl_map *map, 7363 __isl_take isl_map *factor); 7364 7365 #include <isl/union_set.h> 7366 __isl_give isl_union_set *isl_union_set_intersect_params( 7367 __isl_take isl_union_set *uset, 7368 __isl_take isl_set *set); 7369 __isl_give isl_union_set *isl_union_set_intersect( 7370 __isl_take isl_union_set *uset1, 7371 __isl_take isl_union_set *uset2); 7372 7373 #include <isl/union_map.h> 7374 __isl_give isl_union_map *isl_union_map_intersect_params( 7375 __isl_take isl_union_map *umap, 7376 __isl_take isl_set *set); 7377 __isl_give isl_union_map * 7378 isl_union_map_intersect_domain_union_set( 7379 __isl_take isl_union_map *umap, 7380 __isl_take isl_union_set *uset); 7381 __isl_give isl_union_map * 7382 isl_union_map_intersect_domain_space( 7383 __isl_take isl_union_map *umap, 7384 __isl_take isl_space *space); 7385 __isl_give isl_union_map *isl_union_map_intersect_domain( 7386 __isl_take isl_union_map *umap, 7387 __isl_take isl_union_set *uset); 7388 __isl_give isl_union_map * 7389 isl_union_map_intersect_range_union_set( 7390 __isl_take isl_union_map *umap, 7391 __isl_take isl_union_set *uset); 7392 __isl_give isl_union_map * 7393 isl_union_map_intersect_range_space( 7394 __isl_take isl_union_map *umap, 7395 __isl_take isl_space *space); 7396 __isl_give isl_union_map *isl_union_map_intersect_range( 7397 __isl_take isl_union_map *umap, 7398 __isl_take isl_union_set *uset); 7399 __isl_give isl_union_map *isl_union_map_intersect( 7400 __isl_take isl_union_map *umap1, 7401 __isl_take isl_union_map *umap2); 7402 __isl_give isl_union_map * 7403 isl_union_map_intersect_domain_factor_domain( 7404 __isl_take isl_union_map *umap, 7405 __isl_take isl_union_map *factor); 7406 __isl_give isl_union_map * 7407 isl_union_map_intersect_domain_factor_range( 7408 __isl_take isl_union_map *umap, 7409 __isl_take isl_union_map *factor); 7410 __isl_give isl_union_map * 7411 isl_union_map_intersect_range_factor_domain( 7412 __isl_take isl_union_map *umap, 7413 __isl_take isl_union_map *factor); 7414 __isl_give isl_union_map * 7415 isl_union_map_intersect_range_factor_range( 7416 __isl_take isl_union_map *umap, 7417 __isl_take isl_union_map *factor); 7418 7419 #include <isl/aff.h> 7420 __isl_give isl_pw_aff *isl_pw_aff_intersect_domain( 7421 __isl_take isl_pw_aff *pa, 7422 __isl_take isl_set *set); 7423 __isl_give isl_multi_pw_aff * 7424 isl_multi_pw_aff_intersect_domain( 7425 __isl_take isl_multi_pw_aff *mpa, 7426 __isl_take isl_set *domain); 7427 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_intersect_domain( 7428 __isl_take isl_pw_multi_aff *pma, 7429 __isl_take isl_set *set); 7430 __isl_give isl_union_pw_aff * 7431 isl_union_pw_aff_intersect_domain_space( 7432 __isl_take isl_union_pw_aff *upa, 7433 __isl_take isl_space *space); 7434 __isl_give isl_union_pw_aff * 7435 isl_union_pw_aff_intersect_domain_union_set( 7436 __isl_take isl_union_pw_aff *upa, 7437 __isl_take isl_union_set *uset); 7438 __isl_give isl_union_pw_aff *isl_union_pw_aff_intersect_domain( 7439 __isl_take isl_union_pw_aff *upa, 7440 __isl_take isl_union_set *uset); 7441 __isl_give isl_union_pw_multi_aff * 7442 isl_union_pw_multi_aff_intersect_domain_space( 7443 __isl_take isl_union_pw_multi_aff *upma, 7444 __isl_take isl_space *space); 7445 __isl_give isl_union_pw_multi_aff * 7446 isl_union_pw_multi_aff_intersect_domain_union_set( 7447 __isl_take isl_union_pw_multi_aff *upma, 7448 __isl_take isl_union_set *uset); 7449 __isl_give isl_union_pw_multi_aff * 7450 isl_union_pw_multi_aff_intersect_domain( 7451 __isl_take isl_union_pw_multi_aff *upma, 7452 __isl_take isl_union_set *uset); 7453 __isl_give isl_multi_union_pw_aff * 7454 isl_multi_union_pw_aff_intersect_domain( 7455 __isl_take isl_multi_union_pw_aff *mupa, 7456 __isl_take isl_union_set *uset); 7457 __isl_give isl_pw_aff * 7458 isl_pw_aff_intersect_domain_wrapped_domain( 7459 __isl_take isl_pw_aff *pa, 7460 __isl_take isl_set *set); 7461 __isl_give isl_pw_multi_aff * 7462 isl_pw_multi_aff_intersect_domain_wrapped_domain( 7463 __isl_take isl_pw_multi_aff *pma, 7464 __isl_take isl_set *set); 7465 __isl_give isl_union_pw_aff * 7466 isl_union_pw_aff_intersect_domain_wrapped_domain( 7467 __isl_take isl_union_pw_aff *upa, 7468 __isl_take isl_union_set *uset); 7469 __isl_give isl_union_pw_multi_aff * 7470 isl_union_pw_multi_aff_intersect_domain_wrapped_domain( 7471 __isl_take isl_union_pw_multi_aff *upma, 7472 __isl_take isl_union_set *uset); 7473 __isl_give isl_pw_aff * 7474 isl_pw_aff_intersect_domain_wrapped_range( 7475 __isl_take isl_pw_aff *pa, 7476 __isl_take isl_set *set); 7477 __isl_give isl_pw_multi_aff * 7478 isl_pw_multi_aff_intersect_domain_wrapped_range( 7479 __isl_take isl_pw_multi_aff *pma, 7480 __isl_take isl_set *set); 7481 __isl_give isl_union_pw_multi_aff * 7482 isl_union_pw_multi_aff_intersect_domain_wrapped_range( 7483 __isl_take isl_union_pw_multi_aff *upma, 7484 __isl_take isl_union_set *uset); 7485 __isl_give isl_union_pw_aff * 7486 isl_union_pw_aff_intersect_domain_wrapped_range( 7487 __isl_take isl_union_pw_aff *upa, 7488 __isl_take isl_union_set *uset); 7489 __isl_give isl_pw_aff *isl_pw_aff_intersect_params( 7490 __isl_take isl_pw_aff *pa, 7491 __isl_take isl_set *set); 7492 __isl_give isl_multi_pw_aff * 7493 isl_multi_pw_aff_intersect_params( 7494 __isl_take isl_multi_pw_aff *mpa, 7495 __isl_take isl_set *set); 7496 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_intersect_params( 7497 __isl_take isl_pw_multi_aff *pma, 7498 __isl_take isl_set *set); 7499 __isl_give isl_union_pw_aff * 7500 isl_union_pw_aff_intersect_params( 7501 __isl_take isl_union_pw_aff *upa, 7502 __isl_take isl_set *set); 7503 __isl_give isl_union_pw_multi_aff * 7504 isl_union_pw_multi_aff_intersect_params( 7505 __isl_take isl_union_pw_multi_aff *upma, 7506 __isl_take isl_set *set); 7507 __isl_give isl_multi_union_pw_aff * 7508 isl_multi_union_pw_aff_intersect_params( 7509 __isl_take isl_multi_union_pw_aff *mupa, 7510 __isl_take isl_set *params); 7511 __isl_give isl_multi_union_pw_aff * 7512 isl_multi_union_pw_aff_intersect_range( 7513 __isl_take isl_multi_union_pw_aff *mupa, 7514 __isl_take isl_set *set); 7515 7516 #include <isl/polynomial.h> 7517 __isl_give isl_pw_qpolynomial * 7518 isl_pw_qpolynomial_intersect_domain( 7519 __isl_take isl_pw_qpolynomial *pwpq, 7520 __isl_take isl_set *set); 7521 __isl_give isl_union_pw_qpolynomial * 7522 isl_union_pw_qpolynomial_intersect_domain_space( 7523 __isl_take isl_union_pw_qpolynomial *upwpq, 7524 __isl_take isl_space *space); 7525 __isl_give isl_union_pw_qpolynomial * 7526 isl_union_pw_qpolynomial_intersect_domain_union_set( 7527 __isl_take isl_union_pw_qpolynomial *upwpq, 7528 __isl_take isl_union_set *uset); 7529 __isl_give isl_union_pw_qpolynomial * 7530 isl_union_pw_qpolynomial_intersect_domain( 7531 __isl_take isl_union_pw_qpolynomial *upwpq, 7532 __isl_take isl_union_set *uset); 7533 __isl_give isl_union_pw_qpolynomial_fold * 7534 isl_union_pw_qpolynomial_fold_intersect_domain_space( 7535 __isl_take isl_union_pw_qpolynomial_fold *upwf, 7536 __isl_take isl_space *space); 7537 __isl_give isl_union_pw_qpolynomial_fold * 7538 isl_union_pw_qpolynomial_fold_intersect_domain_union_set( 7539 __isl_take isl_union_pw_qpolynomial_fold *upwf, 7540 __isl_take isl_union_set *uset); 7541 __isl_give isl_union_pw_qpolynomial_fold * 7542 isl_union_pw_qpolynomial_fold_intersect_domain( 7543 __isl_take isl_union_pw_qpolynomial_fold *upwf, 7544 __isl_take isl_union_set *uset); 7545 __isl_give isl_pw_qpolynomial * 7546 isl_pw_qpolynomial_intersect_domain_wrapped_domain( 7547 __isl_take isl_pw_qpolynomial *pwpq, 7548 __isl_take isl_set *set); 7549 __isl_give isl_pw_qpolynomial_fold * 7550 isl_pw_qpolynomial_fold_intersect_domain_wrapped_domain( 7551 __isl_take isl_pw_qpolynomial_fold *pwf, 7552 __isl_take isl_set *set); 7553 __isl_give isl_union_pw_qpolynomial * 7554 isl_union_pw_qpolynomial_intersect_domain_wrapped_domain( 7555 __isl_take isl_union_pw_qpolynomial *upwpq, 7556 __isl_take isl_union_set *uset); 7557 __isl_give isl_union_pw_qpolynomial_fold * 7558 isl_union_pw_qpolynomial_fold_intersect_domain_wrapped_domain( 7559 __isl_take isl_union_pw_qpolynomial_fold *upwf, 7560 __isl_take isl_union_set *uset); 7561 __isl_give isl_pw_qpolynomial * 7562 isl_pw_qpolynomial_intersect_domain_wrapped_range( 7563 __isl_take isl_pw_qpolynomial *pwpq, 7564 __isl_take isl_set *set); 7565 __isl_give isl_pw_qpolynomial_fold * 7566 isl_pw_qpolynomial_fold_intersect_domain_wrapped_range( 7567 __isl_take isl_pw_qpolynomial_fold *pwf, 7568 __isl_take isl_set *set); 7569 __isl_give isl_union_pw_qpolynomial * 7570 isl_union_pw_qpolynomial_intersect_domain_wrapped_range( 7571 __isl_take isl_union_pw_qpolynomial *upwpq, 7572 __isl_take isl_union_set *uset); 7573 __isl_give isl_union_pw_qpolynomial_fold * 7574 isl_union_pw_qpolynomial_fold_intersect_domain_wrapped_range( 7575 __isl_take isl_union_pw_qpolynomial_fold *upwf, 7576 __isl_take isl_union_set *uset); 7577 __isl_give isl_pw_qpolynomial * 7578 isl_pw_qpolynomial_intersect_params( 7579 __isl_take isl_pw_qpolynomial *pwpq, 7580 __isl_take isl_set *set); 7581 __isl_give isl_pw_qpolynomial_fold * 7582 isl_pw_qpolynomial_fold_intersect_params( 7583 __isl_take isl_pw_qpolynomial_fold *pwf, 7584 __isl_take isl_set *set); 7585 __isl_give isl_union_pw_qpolynomial * 7586 isl_union_pw_qpolynomial_intersect_params( 7587 __isl_take isl_union_pw_qpolynomial *upwpq, 7588 __isl_take isl_set *set); 7589 __isl_give isl_union_pw_qpolynomial_fold * 7590 isl_union_pw_qpolynomial_fold_intersect_params( 7591 __isl_take isl_union_pw_qpolynomial_fold *upwf, 7592 __isl_take isl_set *set); 7593 7594The second argument to the C<_params> functions needs to be 7595a parametric (basic) set. For the other functions, a parametric set 7596for either argument is only allowed if the other argument is 7597a parametric set as well. 7598The list passed to C<isl_basic_set_list_intersect> needs to have 7599at least one element and all elements need to live in the same space. 7600The function C<isl_multi_union_pw_aff_intersect_range> 7601restricts the input function to those shared domain elements 7602that map to the specified range. 7603C<isl_union_map_intersect_domain> is an alternative name for 7604C<isl_union_map_intersect_domain_union_set>. 7605Similarly for the other pairs of functions. 7606 7607=item * Union 7608 7609 #include <isl/set.h> 7610 __isl_give isl_set *isl_basic_set_union( 7611 __isl_take isl_basic_set *bset1, 7612 __isl_take isl_basic_set *bset2); 7613 __isl_give isl_set *isl_set_union( 7614 __isl_take isl_set *set1, 7615 __isl_take isl_set *set2); 7616 __isl_give isl_set *isl_set_list_union( 7617 __isl_take isl_set_list *list); 7618 7619 #include <isl/map.h> 7620 __isl_give isl_map *isl_basic_map_union( 7621 __isl_take isl_basic_map *bmap1, 7622 __isl_take isl_basic_map *bmap2); 7623 __isl_give isl_map *isl_map_union( 7624 __isl_take isl_map *map1, 7625 __isl_take isl_map *map2); 7626 7627 #include <isl/union_set.h> 7628 __isl_give isl_union_set *isl_union_set_union( 7629 __isl_take isl_union_set *uset1, 7630 __isl_take isl_union_set *uset2); 7631 __isl_give isl_union_set *isl_union_set_list_union( 7632 __isl_take isl_union_set_list *list); 7633 7634 #include <isl/union_map.h> 7635 __isl_give isl_union_map *isl_union_map_union( 7636 __isl_take isl_union_map *umap1, 7637 __isl_take isl_union_map *umap2); 7638 7639The list passed to C<isl_set_list_union> needs to have 7640at least one element and all elements need to live in the same space. 7641 7642=item * Set difference 7643 7644 #include <isl/set.h> 7645 __isl_give isl_set *isl_set_subtract( 7646 __isl_take isl_set *set1, 7647 __isl_take isl_set *set2); 7648 7649 #include <isl/map.h> 7650 __isl_give isl_map *isl_map_subtract( 7651 __isl_take isl_map *map1, 7652 __isl_take isl_map *map2); 7653 __isl_give isl_map *isl_map_subtract_domain( 7654 __isl_take isl_map *map, 7655 __isl_take isl_set *dom); 7656 __isl_give isl_map *isl_map_subtract_range( 7657 __isl_take isl_map *map, 7658 __isl_take isl_set *dom); 7659 7660 #include <isl/union_set.h> 7661 __isl_give isl_union_set *isl_union_set_subtract( 7662 __isl_take isl_union_set *uset1, 7663 __isl_take isl_union_set *uset2); 7664 7665 #include <isl/union_map.h> 7666 __isl_give isl_union_map *isl_union_map_subtract( 7667 __isl_take isl_union_map *umap1, 7668 __isl_take isl_union_map *umap2); 7669 __isl_give isl_union_map *isl_union_map_subtract_domain( 7670 __isl_take isl_union_map *umap, 7671 __isl_take isl_union_set *dom); 7672 __isl_give isl_union_map *isl_union_map_subtract_range( 7673 __isl_take isl_union_map *umap, 7674 __isl_take isl_union_set *dom); 7675 7676 #include <isl/aff.h> 7677 __isl_give isl_pw_aff *isl_pw_aff_subtract_domain( 7678 __isl_take isl_pw_aff *pa, 7679 __isl_take isl_set *set); 7680 __isl_give isl_pw_multi_aff * 7681 isl_pw_multi_aff_subtract_domain( 7682 __isl_take isl_pw_multi_aff *pma, 7683 __isl_take isl_set *set); 7684 __isl_give isl_union_pw_aff * 7685 isl_union_pw_aff_subtract_domain_union_set( 7686 __isl_take isl_union_pw_aff *upa, 7687 __isl_take isl_union_set *uset); 7688 __isl_give isl_union_pw_aff * 7689 isl_union_pw_aff_subtract_domain_space( 7690 __isl_take isl_union_pw_aff *upa, 7691 __isl_take isl_space *space); 7692 __isl_give isl_union_pw_aff * 7693 isl_union_pw_aff_subtract_domain( 7694 __isl_take isl_union_pw_aff *upa, 7695 __isl_take isl_union_set *uset); 7696 __isl_give isl_union_pw_multi_aff * 7697 isl_union_pw_multi_aff_subtract_domain_union_set( 7698 __isl_take isl_union_pw_multi_aff *upma, 7699 __isl_take isl_set *set); 7700 __isl_give isl_union_pw_multi_aff * 7701 isl_union_pw_multi_aff_subtract_domain_space( 7702 __isl_take isl_union_pw_multi_aff *upma, 7703 __isl_take isl_space *space); 7704 __isl_give isl_union_pw_multi_aff * 7705 isl_union_pw_multi_aff_subtract_domain( 7706 __isl_take isl_union_pw_multi_aff *upma, 7707 __isl_take isl_union_set *uset); 7708 7709 #include <isl/polynomial.h> 7710 __isl_give isl_pw_qpolynomial * 7711 isl_pw_qpolynomial_subtract_domain( 7712 __isl_take isl_pw_qpolynomial *pwpq, 7713 __isl_take isl_set *set); 7714 __isl_give isl_pw_qpolynomial_fold * 7715 isl_pw_qpolynomial_fold_subtract_domain( 7716 __isl_take isl_pw_qpolynomial_fold *pwf, 7717 __isl_take isl_set *set); 7718 __isl_give isl_union_pw_qpolynomial * 7719 isl_union_pw_qpolynomial_subtract_domain_union_set( 7720 __isl_take isl_union_pw_qpolynomial *upwpq, 7721 __isl_take isl_union_set *uset); 7722 __isl_give isl_union_pw_qpolynomial * 7723 isl_union_pw_qpolynomial_subtract_domain_space( 7724 __isl_take isl_union_pw_qpolynomial *upwpq, 7725 __isl_take isl_space *space); 7726 __isl_give isl_union_pw_qpolynomial * 7727 isl_union_pw_qpolynomial_subtract_domain( 7728 __isl_take isl_union_pw_qpolynomial *upwpq, 7729 __isl_take isl_union_set *uset); 7730 __isl_give isl_union_pw_qpolynomial_fold * 7731 isl_union_pw_qpolynomial_fold_subtract_domain_union_set( 7732 __isl_take isl_union_pw_qpolynomial_fold *upwf, 7733 __isl_take isl_union_set *uset); 7734 __isl_give isl_union_pw_qpolynomial_fold * 7735 isl_union_pw_qpolynomial_fold_subtract_domain_space( 7736 __isl_take isl_union_pw_qpolynomial_fold *upwf, 7737 __isl_take isl_space *space); 7738 __isl_give isl_union_pw_qpolynomial_fold * 7739 isl_union_pw_qpolynomial_fold_subtract_domain( 7740 __isl_take isl_union_pw_qpolynomial_fold *upwf, 7741 __isl_take isl_union_set *uset); 7742 7743C<isl_union_pw_aff_subtract_domain> is an alternative name for 7744C<isl_union_pw_aff_subtract_domain_union_set>. 7745Similarly for the other pairs of functions. 7746 7747=item * Application 7748 7749 #include <isl/space.h> 7750 __isl_give isl_space *isl_space_join( 7751 __isl_take isl_space *left, 7752 __isl_take isl_space *right); 7753 7754 #include <isl/set.h> 7755 __isl_give isl_basic_set *isl_basic_set_apply( 7756 __isl_take isl_basic_set *bset, 7757 __isl_take isl_basic_map *bmap); 7758 __isl_give isl_set *isl_set_apply( 7759 __isl_take isl_set *set, 7760 __isl_take isl_map *map); 7761 7762 #include <isl/union_set.h> 7763 __isl_give isl_union_set *isl_union_set_apply( 7764 __isl_take isl_union_set *uset, 7765 __isl_take isl_union_map *umap); 7766 7767 #include <isl/map.h> 7768 __isl_give isl_basic_map *isl_basic_map_apply_domain( 7769 __isl_take isl_basic_map *bmap1, 7770 __isl_take isl_basic_map *bmap2); 7771 __isl_give isl_basic_map *isl_basic_map_apply_range( 7772 __isl_take isl_basic_map *bmap1, 7773 __isl_take isl_basic_map *bmap2); 7774 __isl_give isl_map *isl_map_apply_domain( 7775 __isl_take isl_map *map1, 7776 __isl_take isl_map *map2); 7777 __isl_give isl_map *isl_map_apply_range( 7778 __isl_take isl_map *map1, 7779 __isl_take isl_map *map2); 7780 7781 #include <isl/union_map.h> 7782 __isl_give isl_union_map *isl_union_map_apply_domain( 7783 __isl_take isl_union_map *umap1, 7784 __isl_take isl_union_map *umap2); 7785 __isl_give isl_union_map *isl_union_map_apply_range( 7786 __isl_take isl_union_map *umap1, 7787 __isl_take isl_union_map *umap2); 7788 7789 #include <isl/aff.h> 7790 __isl_give isl_union_pw_multi_aff * 7791 isl_union_pw_multi_aff_apply_union_pw_multi_aff( 7792 __isl_take isl_union_pw_multi_aff *upma1, 7793 __isl_take isl_union_pw_multi_aff *upma2); 7794 __isl_give isl_union_pw_aff * 7795 isl_multi_union_pw_aff_apply_aff( 7796 __isl_take isl_multi_union_pw_aff *mupa, 7797 __isl_take isl_aff *aff); 7798 __isl_give isl_union_pw_aff * 7799 isl_multi_union_pw_aff_apply_pw_aff( 7800 __isl_take isl_multi_union_pw_aff *mupa, 7801 __isl_take isl_pw_aff *pa); 7802 __isl_give isl_multi_union_pw_aff * 7803 isl_multi_union_pw_aff_apply_multi_aff( 7804 __isl_take isl_multi_union_pw_aff *mupa, 7805 __isl_take isl_multi_aff *ma); 7806 __isl_give isl_multi_union_pw_aff * 7807 isl_multi_union_pw_aff_apply_pw_multi_aff( 7808 __isl_take isl_multi_union_pw_aff *mupa, 7809 __isl_take isl_pw_multi_aff *pma); 7810 7811The result of C<isl_multi_union_pw_aff_apply_aff> is defined 7812over the shared domain of the elements of the input. The dimension is 7813required to be greater than zero. 7814The C<isl_multi_union_pw_aff> argument of 7815C<isl_multi_union_pw_aff_apply_multi_aff> is allowed to be zero-dimensional, 7816but only if the range of the C<isl_multi_aff> argument 7817is also zero-dimensional. 7818Similarly for C<isl_multi_union_pw_aff_apply_pw_multi_aff>. 7819 7820 #include <isl/polynomial.h> 7821 __isl_give isl_pw_qpolynomial_fold * 7822 isl_set_apply_pw_qpolynomial_fold( 7823 __isl_take isl_set *set, 7824 __isl_take isl_pw_qpolynomial_fold *pwf, 7825 isl_bool *tight); 7826 __isl_give isl_pw_qpolynomial_fold * 7827 isl_map_apply_pw_qpolynomial_fold( 7828 __isl_take isl_map *map, 7829 __isl_take isl_pw_qpolynomial_fold *pwf, 7830 isl_bool *tight); 7831 __isl_give isl_union_pw_qpolynomial_fold * 7832 isl_union_set_apply_union_pw_qpolynomial_fold( 7833 __isl_take isl_union_set *uset, 7834 __isl_take isl_union_pw_qpolynomial_fold *upwf, 7835 isl_bool *tight); 7836 __isl_give isl_union_pw_qpolynomial_fold * 7837 isl_union_map_apply_union_pw_qpolynomial_fold( 7838 __isl_take isl_union_map *umap, 7839 __isl_take isl_union_pw_qpolynomial_fold *upwf, 7840 isl_bool *tight); 7841 7842The functions taking a map 7843compose the given map with the given piecewise quasipolynomial reduction. 7844That is, compute a bound (of the same type as C<pwf> or C<upwf> itself) 7845over all elements in the intersection of the range of the map 7846and the domain of the piecewise quasipolynomial reduction 7847as a function of an element in the domain of the map. 7848The functions taking a set compute a bound over all elements in the 7849intersection of the set and the domain of the 7850piecewise quasipolynomial reduction. 7851 7852=item * Preimage 7853 7854 #include <isl/set.h> 7855 __isl_give isl_basic_set * 7856 isl_basic_set_preimage_multi_aff( 7857 __isl_take isl_basic_set *bset, 7858 __isl_take isl_multi_aff *ma); 7859 __isl_give isl_set *isl_set_preimage_multi_aff( 7860 __isl_take isl_set *set, 7861 __isl_take isl_multi_aff *ma); 7862 __isl_give isl_set *isl_set_preimage_pw_multi_aff( 7863 __isl_take isl_set *set, 7864 __isl_take isl_pw_multi_aff *pma); 7865 __isl_give isl_set *isl_set_preimage_multi_pw_aff( 7866 __isl_take isl_set *set, 7867 __isl_take isl_multi_pw_aff *mpa); 7868 7869 #include <isl/union_set.h> 7870 __isl_give isl_union_set * 7871 isl_union_set_preimage_multi_aff( 7872 __isl_take isl_union_set *uset, 7873 __isl_take isl_multi_aff *ma); 7874 __isl_give isl_union_set * 7875 isl_union_set_preimage_pw_multi_aff( 7876 __isl_take isl_union_set *uset, 7877 __isl_take isl_pw_multi_aff *pma); 7878 __isl_give isl_union_set * 7879 isl_union_set_preimage_union_pw_multi_aff( 7880 __isl_take isl_union_set *uset, 7881 __isl_take isl_union_pw_multi_aff *upma); 7882 7883 #include <isl/map.h> 7884 __isl_give isl_basic_map * 7885 isl_basic_map_preimage_domain_multi_aff( 7886 __isl_take isl_basic_map *bmap, 7887 __isl_take isl_multi_aff *ma); 7888 __isl_give isl_map *isl_map_preimage_domain_multi_aff( 7889 __isl_take isl_map *map, 7890 __isl_take isl_multi_aff *ma); 7891 __isl_give isl_map *isl_map_preimage_range_multi_aff( 7892 __isl_take isl_map *map, 7893 __isl_take isl_multi_aff *ma); 7894 __isl_give isl_map * 7895 isl_map_preimage_domain_pw_multi_aff( 7896 __isl_take isl_map *map, 7897 __isl_take isl_pw_multi_aff *pma); 7898 __isl_give isl_map * 7899 isl_map_preimage_range_pw_multi_aff( 7900 __isl_take isl_map *map, 7901 __isl_take isl_pw_multi_aff *pma); 7902 __isl_give isl_map * 7903 isl_map_preimage_domain_multi_pw_aff( 7904 __isl_take isl_map *map, 7905 __isl_take isl_multi_pw_aff *mpa); 7906 __isl_give isl_basic_map * 7907 isl_basic_map_preimage_range_multi_aff( 7908 __isl_take isl_basic_map *bmap, 7909 __isl_take isl_multi_aff *ma); 7910 7911 #include <isl/union_map.h> 7912 __isl_give isl_union_map * 7913 isl_union_map_preimage_domain_multi_aff( 7914 __isl_take isl_union_map *umap, 7915 __isl_take isl_multi_aff *ma); 7916 __isl_give isl_union_map * 7917 isl_union_map_preimage_range_multi_aff( 7918 __isl_take isl_union_map *umap, 7919 __isl_take isl_multi_aff *ma); 7920 __isl_give isl_union_map * 7921 isl_union_map_preimage_domain_pw_multi_aff( 7922 __isl_take isl_union_map *umap, 7923 __isl_take isl_pw_multi_aff *pma); 7924 __isl_give isl_union_map * 7925 isl_union_map_preimage_range_pw_multi_aff( 7926 __isl_take isl_union_map *umap, 7927 __isl_take isl_pw_multi_aff *pma); 7928 __isl_give isl_union_map * 7929 isl_union_map_preimage_domain_union_pw_multi_aff( 7930 __isl_take isl_union_map *umap, 7931 __isl_take isl_union_pw_multi_aff *upma); 7932 __isl_give isl_union_map * 7933 isl_union_map_preimage_range_union_pw_multi_aff( 7934 __isl_take isl_union_map *umap, 7935 __isl_take isl_union_pw_multi_aff *upma); 7936 7937 #include <isl/aff.h> 7938 __isl_give isl_pw_multi_aff * 7939 isl_pw_multi_aff_preimage_domain_wrapped_domain_pw_multi_aff( 7940 __isl_take isl_pw_multi_aff *pma1, 7941 __isl_take isl_pw_multi_aff *pma2); 7942 __isl_give isl_union_pw_multi_aff * 7943 isl_union_pw_multi_aff_preimage_domain_wrapped_domain_union_pw_multi_aff( 7944 __isl_take isl_union_pw_multi_aff *upma1, 7945 __isl_take isl_union_pw_multi_aff *upma2); 7946 7947These functions compute the preimage of the given set or map domain/range under 7948the given function. In other words, the expression is plugged 7949into the set description or into the domain/range of the map or function. 7950 7951=item * Pullback 7952 7953 #include <isl/aff.h> 7954 __isl_give isl_aff *isl_aff_pullback_aff( 7955 __isl_take isl_aff *aff1, 7956 __isl_take isl_aff *aff2); 7957 __isl_give isl_aff *isl_aff_pullback_multi_aff( 7958 __isl_take isl_aff *aff, 7959 __isl_take isl_multi_aff *ma); 7960 __isl_give isl_pw_aff *isl_pw_aff_pullback_multi_aff( 7961 __isl_take isl_pw_aff *pa, 7962 __isl_take isl_multi_aff *ma); 7963 __isl_give isl_pw_aff *isl_pw_aff_pullback_pw_multi_aff( 7964 __isl_take isl_pw_aff *pa, 7965 __isl_take isl_pw_multi_aff *pma); 7966 __isl_give isl_pw_aff *isl_pw_aff_pullback_multi_pw_aff( 7967 __isl_take isl_pw_aff *pa, 7968 __isl_take isl_multi_pw_aff *mpa); 7969 __isl_give isl_multi_aff *isl_multi_aff_pullback_multi_aff( 7970 __isl_take isl_multi_aff *ma1, 7971 __isl_take isl_multi_aff *ma2); 7972 __isl_give isl_pw_multi_aff * 7973 isl_pw_multi_aff_pullback_multi_aff( 7974 __isl_take isl_pw_multi_aff *pma, 7975 __isl_take isl_multi_aff *ma); 7976 __isl_give isl_multi_pw_aff * 7977 isl_multi_pw_aff_pullback_multi_aff( 7978 __isl_take isl_multi_pw_aff *mpa, 7979 __isl_take isl_multi_aff *ma); 7980 __isl_give isl_pw_multi_aff * 7981 isl_pw_multi_aff_pullback_pw_multi_aff( 7982 __isl_take isl_pw_multi_aff *pma1, 7983 __isl_take isl_pw_multi_aff *pma2); 7984 __isl_give isl_multi_pw_aff * 7985 isl_multi_pw_aff_pullback_pw_multi_aff( 7986 __isl_take isl_multi_pw_aff *mpa, 7987 __isl_take isl_pw_multi_aff *pma); 7988 __isl_give isl_multi_pw_aff * 7989 isl_multi_pw_aff_pullback_multi_pw_aff( 7990 __isl_take isl_multi_pw_aff *mpa1, 7991 __isl_take isl_multi_pw_aff *mpa2); 7992 __isl_give isl_union_pw_aff * 7993 isl_union_pw_aff_pullback_union_pw_multi_aff( 7994 __isl_take isl_union_pw_aff *upa, 7995 __isl_take isl_union_pw_multi_aff *upma); 7996 __isl_give isl_union_pw_multi_aff * 7997 isl_union_pw_multi_aff_pullback_union_pw_multi_aff( 7998 __isl_take isl_union_pw_multi_aff *upma1, 7999 __isl_take isl_union_pw_multi_aff *upma2); 8000 __isl_give isl_multi_union_pw_aff * 8001 isl_multi_union_pw_aff_pullback_union_pw_multi_aff( 8002 __isl_take isl_multi_union_pw_aff *mupa, 8003 __isl_take isl_union_pw_multi_aff *upma); 8004 8005These functions precompose the first expression by the second function. 8006In other words, the second function is plugged 8007into the first expression. 8008 8009=item * Locus 8010 8011 #include <isl/aff.h> 8012 __isl_give isl_basic_set *isl_aff_eq_basic_set( 8013 __isl_take isl_aff *aff1, 8014 __isl_take isl_aff *aff2); 8015 __isl_give isl_set *isl_aff_eq_set( 8016 __isl_take isl_aff *aff1, 8017 __isl_take isl_aff *aff2); 8018 __isl_give isl_set *isl_aff_ne_set( 8019 __isl_take isl_aff *aff1, 8020 __isl_take isl_aff *aff2); 8021 __isl_give isl_basic_set *isl_aff_le_basic_set( 8022 __isl_take isl_aff *aff1, 8023 __isl_take isl_aff *aff2); 8024 __isl_give isl_set *isl_aff_le_set( 8025 __isl_take isl_aff *aff1, 8026 __isl_take isl_aff *aff2); 8027 __isl_give isl_basic_set *isl_aff_lt_basic_set( 8028 __isl_take isl_aff *aff1, 8029 __isl_take isl_aff *aff2); 8030 __isl_give isl_set *isl_aff_lt_set( 8031 __isl_take isl_aff *aff1, 8032 __isl_take isl_aff *aff2); 8033 __isl_give isl_basic_set *isl_aff_ge_basic_set( 8034 __isl_take isl_aff *aff1, 8035 __isl_take isl_aff *aff2); 8036 __isl_give isl_set *isl_aff_ge_set( 8037 __isl_take isl_aff *aff1, 8038 __isl_take isl_aff *aff2); 8039 __isl_give isl_basic_set *isl_aff_gt_basic_set( 8040 __isl_take isl_aff *aff1, 8041 __isl_take isl_aff *aff2); 8042 __isl_give isl_set *isl_aff_gt_set( 8043 __isl_take isl_aff *aff1, 8044 __isl_take isl_aff *aff2); 8045 __isl_give isl_set *isl_pw_aff_eq_set( 8046 __isl_take isl_pw_aff *pwaff1, 8047 __isl_take isl_pw_aff *pwaff2); 8048 __isl_give isl_set *isl_pw_aff_ne_set( 8049 __isl_take isl_pw_aff *pwaff1, 8050 __isl_take isl_pw_aff *pwaff2); 8051 __isl_give isl_set *isl_pw_aff_le_set( 8052 __isl_take isl_pw_aff *pwaff1, 8053 __isl_take isl_pw_aff *pwaff2); 8054 __isl_give isl_set *isl_pw_aff_lt_set( 8055 __isl_take isl_pw_aff *pwaff1, 8056 __isl_take isl_pw_aff *pwaff2); 8057 __isl_give isl_set *isl_pw_aff_ge_set( 8058 __isl_take isl_pw_aff *pwaff1, 8059 __isl_take isl_pw_aff *pwaff2); 8060 __isl_give isl_set *isl_pw_aff_gt_set( 8061 __isl_take isl_pw_aff *pwaff1, 8062 __isl_take isl_pw_aff *pwaff2); 8063 8064 __isl_give isl_set *isl_multi_aff_lex_le_set( 8065 __isl_take isl_multi_aff *ma1, 8066 __isl_take isl_multi_aff *ma2); 8067 __isl_give isl_set *isl_multi_aff_lex_lt_set( 8068 __isl_take isl_multi_aff *ma1, 8069 __isl_take isl_multi_aff *ma2); 8070 __isl_give isl_set *isl_multi_aff_lex_ge_set( 8071 __isl_take isl_multi_aff *ma1, 8072 __isl_take isl_multi_aff *ma2); 8073 __isl_give isl_set *isl_multi_aff_lex_gt_set( 8074 __isl_take isl_multi_aff *ma1, 8075 __isl_take isl_multi_aff *ma2); 8076 8077 __isl_give isl_set *isl_pw_aff_list_eq_set( 8078 __isl_take isl_pw_aff_list *list1, 8079 __isl_take isl_pw_aff_list *list2); 8080 __isl_give isl_set *isl_pw_aff_list_ne_set( 8081 __isl_take isl_pw_aff_list *list1, 8082 __isl_take isl_pw_aff_list *list2); 8083 __isl_give isl_set *isl_pw_aff_list_le_set( 8084 __isl_take isl_pw_aff_list *list1, 8085 __isl_take isl_pw_aff_list *list2); 8086 __isl_give isl_set *isl_pw_aff_list_lt_set( 8087 __isl_take isl_pw_aff_list *list1, 8088 __isl_take isl_pw_aff_list *list2); 8089 __isl_give isl_set *isl_pw_aff_list_ge_set( 8090 __isl_take isl_pw_aff_list *list1, 8091 __isl_take isl_pw_aff_list *list2); 8092 __isl_give isl_set *isl_pw_aff_list_gt_set( 8093 __isl_take isl_pw_aff_list *list1, 8094 __isl_take isl_pw_aff_list *list2); 8095 8096The function C<isl_aff_ge_basic_set> returns a basic set 8097containing those elements in the shared space 8098of C<aff1> and C<aff2> where C<aff1> is greater than or equal to C<aff2>. 8099The function C<isl_pw_aff_ge_set> returns a set 8100containing those elements in the shared domain 8101of C<pwaff1> and C<pwaff2> where C<pwaff1> is 8102greater than or equal to C<pwaff2>. 8103The function C<isl_multi_aff_lex_le_set> returns a set 8104containing those elements in the shared domain space 8105where C<ma1> is lexicographically smaller than or 8106equal to C<ma2>. 8107The functions operating on C<isl_pw_aff_list> apply the corresponding 8108C<isl_pw_aff> function to each pair of elements in the two lists. 8109 8110 #include <isl/aff.h> 8111 __isl_give isl_map *isl_pw_aff_eq_map( 8112 __isl_take isl_pw_aff *pa1, 8113 __isl_take isl_pw_aff *pa2); 8114 __isl_give isl_map *isl_pw_aff_le_map( 8115 __isl_take isl_pw_aff *pa1, 8116 __isl_take isl_pw_aff *pa2); 8117 __isl_give isl_map *isl_pw_aff_lt_map( 8118 __isl_take isl_pw_aff *pa1, 8119 __isl_take isl_pw_aff *pa2); 8120 __isl_give isl_map *isl_pw_aff_ge_map( 8121 __isl_take isl_pw_aff *pa1, 8122 __isl_take isl_pw_aff *pa2); 8123 __isl_give isl_map *isl_pw_aff_gt_map( 8124 __isl_take isl_pw_aff *pa1, 8125 __isl_take isl_pw_aff *pa2); 8126 8127 __isl_give isl_map *isl_multi_pw_aff_eq_map( 8128 __isl_take isl_multi_pw_aff *mpa1, 8129 __isl_take isl_multi_pw_aff *mpa2); 8130 __isl_give isl_map *isl_multi_pw_aff_lex_le_map( 8131 __isl_take isl_multi_pw_aff *mpa1, 8132 __isl_take isl_multi_pw_aff *mpa2); 8133 __isl_give isl_map *isl_multi_pw_aff_lex_lt_map( 8134 __isl_take isl_multi_pw_aff *mpa1, 8135 __isl_take isl_multi_pw_aff *mpa2); 8136 __isl_give isl_map *isl_multi_pw_aff_lex_ge_map( 8137 __isl_take isl_multi_pw_aff *mpa1, 8138 __isl_take isl_multi_pw_aff *mpa2); 8139 __isl_give isl_map *isl_multi_pw_aff_lex_gt_map( 8140 __isl_take isl_multi_pw_aff *mpa1, 8141 __isl_take isl_multi_pw_aff *mpa2); 8142 8143These functions return a map between domain elements of the arguments 8144where the function values satisfy the given relation. 8145 8146 #include <isl/map.h> 8147 __isl_give isl_map *isl_map_eq_at_multi_pw_aff( 8148 __isl_take isl_map *map, 8149 __isl_take isl_multi_pw_aff *mpa); 8150 __isl_give isl_map *isl_map_lex_lt_at_multi_pw_aff( 8151 __isl_take isl_map *map, 8152 __isl_take isl_multi_pw_aff *mpa); 8153 __isl_give isl_map *isl_map_lex_le_at_multi_pw_aff( 8154 __isl_take isl_map *map, 8155 __isl_take isl_multi_pw_aff *mpa); 8156 __isl_give isl_map *isl_map_lex_gt_at_multi_pw_aff( 8157 __isl_take isl_map *map, 8158 __isl_take isl_multi_pw_aff *mpa); 8159 __isl_give isl_map *isl_map_lex_ge_at_multi_pw_aff( 8160 __isl_take isl_map *map, 8161 __isl_take isl_multi_pw_aff *mpa); 8162 8163 #include <isl/union_map.h> 8164 __isl_give isl_union_map * 8165 isl_union_map_eq_at_multi_union_pw_aff( 8166 __isl_take isl_union_map *umap, 8167 __isl_take isl_multi_union_pw_aff *mupa); 8168 __isl_give isl_union_map * 8169 isl_union_map_lex_lt_at_multi_union_pw_aff( 8170 __isl_take isl_union_map *umap, 8171 __isl_take isl_multi_union_pw_aff *mupa); 8172 __isl_give isl_union_map * 8173 isl_union_map_lex_le_at_multi_union_pw_aff( 8174 __isl_take isl_union_map *umap, 8175 __isl_take isl_multi_union_pw_aff *mupa); 8176 __isl_give isl_union_map * 8177 isl_union_map_lex_gt_at_multi_union_pw_aff( 8178 __isl_take isl_union_map *umap, 8179 __isl_take isl_multi_union_pw_aff *mupa); 8180 __isl_give isl_union_map * 8181 isl_union_map_lex_ge_at_multi_union_pw_aff( 8182 __isl_take isl_union_map *umap, 8183 __isl_take isl_multi_union_pw_aff *mupa); 8184 8185These functions select the subset of elements in the union map 8186that have an equal or lexicographically smaller or greater function value. 8187 8188=item * Cartesian Product 8189 8190 #include <isl/space.h> 8191 __isl_give isl_space *isl_space_product( 8192 __isl_take isl_space *space1, 8193 __isl_take isl_space *space2); 8194 __isl_give isl_space *isl_space_domain_product( 8195 __isl_take isl_space *space1, 8196 __isl_take isl_space *space2); 8197 __isl_give isl_space *isl_space_range_product( 8198 __isl_take isl_space *space1, 8199 __isl_take isl_space *space2); 8200 8201The functions 8202C<isl_space_product>, C<isl_space_domain_product> 8203and C<isl_space_range_product> take pairs or relation spaces and 8204produce a single relations space, where either the domain, the range 8205or both domain and range are wrapped spaces of relations between 8206the domains and/or ranges of the input spaces. 8207If the product is only constructed over the domain or the range 8208then the ranges or the domains of the inputs should be the same. 8209The function C<isl_space_product> also accepts a pair of set spaces, 8210in which case it returns a wrapped space of a relation between the 8211two input spaces. 8212 8213 #include <isl/set.h> 8214 __isl_give isl_set *isl_set_product( 8215 __isl_take isl_set *set1, 8216 __isl_take isl_set *set2); 8217 8218 #include <isl/map.h> 8219 __isl_give isl_basic_map *isl_basic_map_domain_product( 8220 __isl_take isl_basic_map *bmap1, 8221 __isl_take isl_basic_map *bmap2); 8222 __isl_give isl_basic_map *isl_basic_map_range_product( 8223 __isl_take isl_basic_map *bmap1, 8224 __isl_take isl_basic_map *bmap2); 8225 __isl_give isl_basic_map *isl_basic_map_product( 8226 __isl_take isl_basic_map *bmap1, 8227 __isl_take isl_basic_map *bmap2); 8228 __isl_give isl_map *isl_map_domain_product( 8229 __isl_take isl_map *map1, 8230 __isl_take isl_map *map2); 8231 __isl_give isl_map *isl_map_range_product( 8232 __isl_take isl_map *map1, 8233 __isl_take isl_map *map2); 8234 __isl_give isl_map *isl_map_product( 8235 __isl_take isl_map *map1, 8236 __isl_take isl_map *map2); 8237 8238 #include <isl/union_set.h> 8239 __isl_give isl_union_set *isl_union_set_product( 8240 __isl_take isl_union_set *uset1, 8241 __isl_take isl_union_set *uset2); 8242 8243 #include <isl/union_map.h> 8244 __isl_give isl_union_map *isl_union_map_domain_product( 8245 __isl_take isl_union_map *umap1, 8246 __isl_take isl_union_map *umap2); 8247 __isl_give isl_union_map *isl_union_map_range_product( 8248 __isl_take isl_union_map *umap1, 8249 __isl_take isl_union_map *umap2); 8250 __isl_give isl_union_map *isl_union_map_product( 8251 __isl_take isl_union_map *umap1, 8252 __isl_take isl_union_map *umap2); 8253 8254 #include <isl/id.h> 8255 __isl_give isl_multi_id *isl_multi_id_range_product( 8256 __isl_take isl_multi_id *mi1, 8257 __isl_take isl_multi_id *mi2); 8258 8259 #include <isl/val.h> 8260 __isl_give isl_multi_val *isl_multi_val_range_product( 8261 __isl_take isl_multi_val *mv1, 8262 __isl_take isl_multi_val *mv2); 8263 __isl_give isl_multi_val *isl_multi_val_product( 8264 __isl_take isl_multi_val *mv1, 8265 __isl_take isl_multi_val *mv2); 8266 8267 #include <isl/aff.h> 8268 __isl_give isl_multi_aff *isl_multi_aff_range_product( 8269 __isl_take isl_multi_aff *ma1, 8270 __isl_take isl_multi_aff *ma2); 8271 __isl_give isl_multi_aff *isl_multi_aff_product( 8272 __isl_take isl_multi_aff *ma1, 8273 __isl_take isl_multi_aff *ma2); 8274 __isl_give isl_multi_pw_aff * 8275 isl_multi_pw_aff_range_product( 8276 __isl_take isl_multi_pw_aff *mpa1, 8277 __isl_take isl_multi_pw_aff *mpa2); 8278 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_product( 8279 __isl_take isl_multi_pw_aff *mpa1, 8280 __isl_take isl_multi_pw_aff *mpa2); 8281 __isl_give isl_pw_multi_aff * 8282 isl_pw_multi_aff_range_product( 8283 __isl_take isl_pw_multi_aff *pma1, 8284 __isl_take isl_pw_multi_aff *pma2); 8285 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_product( 8286 __isl_take isl_pw_multi_aff *pma1, 8287 __isl_take isl_pw_multi_aff *pma2); 8288 __isl_give isl_union_pw_multi_aff * 8289 isl_union_pw_multi_aff_range_product( 8290 __isl_take isl_union_pw_multi_aff *upma1, 8291 __isl_take isl_union_pw_multi_aff *upma2); 8292 __isl_give isl_multi_union_pw_aff * 8293 isl_multi_union_pw_aff_range_product( 8294 __isl_take isl_multi_union_pw_aff *mupa1, 8295 __isl_take isl_multi_union_pw_aff *mupa2); 8296 8297The above functions compute the cross product of the given 8298sets, relations or functions. The domains and ranges of the results 8299are wrapped maps between domains and ranges of the inputs. 8300To obtain a ``flat'' product, use the following functions 8301instead. 8302 8303 #include <isl/set.h> 8304 __isl_give isl_basic_set *isl_basic_set_flat_product( 8305 __isl_take isl_basic_set *bset1, 8306 __isl_take isl_basic_set *bset2); 8307 __isl_give isl_set *isl_set_flat_product( 8308 __isl_take isl_set *set1, 8309 __isl_take isl_set *set2); 8310 8311 #include <isl/map.h> 8312 __isl_give isl_basic_map *isl_basic_map_flat_range_product( 8313 __isl_take isl_basic_map *bmap1, 8314 __isl_take isl_basic_map *bmap2); 8315 __isl_give isl_map *isl_map_flat_domain_product( 8316 __isl_take isl_map *map1, 8317 __isl_take isl_map *map2); 8318 __isl_give isl_map *isl_map_flat_range_product( 8319 __isl_take isl_map *map1, 8320 __isl_take isl_map *map2); 8321 __isl_give isl_basic_map *isl_basic_map_flat_product( 8322 __isl_take isl_basic_map *bmap1, 8323 __isl_take isl_basic_map *bmap2); 8324 __isl_give isl_map *isl_map_flat_product( 8325 __isl_take isl_map *map1, 8326 __isl_take isl_map *map2); 8327 8328 #include <isl/union_map.h> 8329 __isl_give isl_union_map * 8330 isl_union_map_flat_domain_product( 8331 __isl_take isl_union_map *umap1, 8332 __isl_take isl_union_map *umap2); 8333 __isl_give isl_union_map * 8334 isl_union_map_flat_range_product( 8335 __isl_take isl_union_map *umap1, 8336 __isl_take isl_union_map *umap2); 8337 8338 #include <isl/id.h> 8339 __isl_give isl_multi_id * 8340 isl_multi_id_flat_range_product( 8341 __isl_take isl_multi_id *mi1, 8342 __isl_take isl_multi_id *mi2); 8343 8344 #include <isl/val.h> 8345 __isl_give isl_multi_val *isl_multi_val_flat_range_product( 8346 __isl_take isl_multi_val *mv1, 8347 __isl_take isl_multi_val *mv2); 8348 8349 #include <isl/aff.h> 8350 __isl_give isl_multi_aff *isl_multi_aff_flat_range_product( 8351 __isl_take isl_multi_aff *ma1, 8352 __isl_take isl_multi_aff *ma2); 8353 __isl_give isl_pw_multi_aff * 8354 isl_pw_multi_aff_flat_range_product( 8355 __isl_take isl_pw_multi_aff *pma1, 8356 __isl_take isl_pw_multi_aff *pma2); 8357 __isl_give isl_multi_pw_aff * 8358 isl_multi_pw_aff_flat_range_product( 8359 __isl_take isl_multi_pw_aff *mpa1, 8360 __isl_take isl_multi_pw_aff *mpa2); 8361 __isl_give isl_union_pw_multi_aff * 8362 isl_union_pw_multi_aff_flat_range_product( 8363 __isl_take isl_union_pw_multi_aff *upma1, 8364 __isl_take isl_union_pw_multi_aff *upma2); 8365 __isl_give isl_multi_union_pw_aff * 8366 isl_multi_union_pw_aff_flat_range_product( 8367 __isl_take isl_multi_union_pw_aff *mupa1, 8368 __isl_take isl_multi_union_pw_aff *mupa2); 8369 8370 #include <isl/space.h> 8371 __isl_give isl_space *isl_space_factor_domain( 8372 __isl_take isl_space *space); 8373 __isl_give isl_space *isl_space_factor_range( 8374 __isl_take isl_space *space); 8375 __isl_give isl_space *isl_space_domain_factor_domain( 8376 __isl_take isl_space *space); 8377 __isl_give isl_space *isl_space_domain_factor_range( 8378 __isl_take isl_space *space); 8379 __isl_give isl_space *isl_space_range_factor_domain( 8380 __isl_take isl_space *space); 8381 __isl_give isl_space *isl_space_range_factor_range( 8382 __isl_take isl_space *space); 8383 8384The functions C<isl_space_range_factor_domain> and 8385C<isl_space_range_factor_range> extract the two arguments from 8386the result of a call to C<isl_space_range_product>. 8387 8388The arguments of a call to a product can be extracted 8389from the result using the following functions. 8390 8391 #include <isl/map.h> 8392 __isl_give isl_map *isl_map_factor_domain( 8393 __isl_take isl_map *map); 8394 __isl_give isl_map *isl_map_factor_range( 8395 __isl_take isl_map *map); 8396 __isl_give isl_map *isl_map_domain_factor_domain( 8397 __isl_take isl_map *map); 8398 __isl_give isl_map *isl_map_domain_factor_range( 8399 __isl_take isl_map *map); 8400 __isl_give isl_map *isl_map_range_factor_domain( 8401 __isl_take isl_map *map); 8402 __isl_give isl_map *isl_map_range_factor_range( 8403 __isl_take isl_map *map); 8404 8405 #include <isl/union_map.h> 8406 __isl_give isl_union_map *isl_union_map_factor_domain( 8407 __isl_take isl_union_map *umap); 8408 __isl_give isl_union_map *isl_union_map_factor_range( 8409 __isl_take isl_union_map *umap); 8410 __isl_give isl_union_map * 8411 isl_union_map_domain_factor_domain( 8412 __isl_take isl_union_map *umap); 8413 __isl_give isl_union_map * 8414 isl_union_map_domain_factor_range( 8415 __isl_take isl_union_map *umap); 8416 __isl_give isl_union_map * 8417 isl_union_map_range_factor_domain( 8418 __isl_take isl_union_map *umap); 8419 __isl_give isl_union_map * 8420 isl_union_map_range_factor_range( 8421 __isl_take isl_union_map *umap); 8422 8423 #include <isl/id.h> 8424 __isl_give isl_multi_id *isl_multi_id_factor_range( 8425 __isl_take isl_multi_id *mi); 8426 __isl_give isl_multi_id * 8427 isl_multi_id_range_factor_domain( 8428 __isl_take isl_multi_id *mi); 8429 __isl_give isl_multi_id * 8430 isl_multi_id_range_factor_range( 8431 __isl_take isl_multi_id *mi); 8432 8433 #include <isl/val.h> 8434 __isl_give isl_multi_val *isl_multi_val_factor_range( 8435 __isl_take isl_multi_val *mv); 8436 __isl_give isl_multi_val * 8437 isl_multi_val_range_factor_domain( 8438 __isl_take isl_multi_val *mv); 8439 __isl_give isl_multi_val * 8440 isl_multi_val_range_factor_range( 8441 __isl_take isl_multi_val *mv); 8442 8443 #include <isl/aff.h> 8444 __isl_give isl_multi_aff *isl_multi_aff_factor_range( 8445 __isl_take isl_multi_aff *ma); 8446 __isl_give isl_multi_aff * 8447 isl_multi_aff_range_factor_domain( 8448 __isl_take isl_multi_aff *ma); 8449 __isl_give isl_multi_aff * 8450 isl_multi_aff_range_factor_range( 8451 __isl_take isl_multi_aff *ma); 8452 __isl_give isl_multi_pw_aff * 8453 isl_multi_pw_aff_factor_range( 8454 __isl_take isl_multi_pw_aff *mpa); 8455 __isl_give isl_multi_pw_aff * 8456 isl_multi_pw_aff_range_factor_domain( 8457 __isl_take isl_multi_pw_aff *mpa); 8458 __isl_give isl_multi_pw_aff * 8459 isl_multi_pw_aff_range_factor_range( 8460 __isl_take isl_multi_pw_aff *mpa); 8461 __isl_give isl_pw_multi_aff * 8462 isl_pw_multi_aff_range_factor_domain( 8463 __isl_take isl_pw_multi_aff *pma); 8464 __isl_give isl_pw_multi_aff * 8465 isl_pw_multi_aff_range_factor_range( 8466 __isl_take isl_pw_multi_aff *pma); 8467 __isl_give isl_union_pw_multi_aff * 8468 isl_union_pw_multi_aff_range_factor_domain( 8469 __isl_take isl_union_pw_multi_aff *upma); 8470 __isl_give isl_union_pw_multi_aff * 8471 isl_union_pw_multi_aff_range_factor_range( 8472 __isl_take isl_union_pw_multi_aff *upma); 8473 __isl_give isl_multi_union_pw_aff * 8474 isl_multi_union_pw_aff_factor_range( 8475 __isl_take isl_multi_union_pw_aff *mupa); 8476 __isl_give isl_multi_union_pw_aff * 8477 isl_multi_union_pw_aff_range_factor_domain( 8478 __isl_take isl_multi_union_pw_aff *mupa); 8479 __isl_give isl_multi_union_pw_aff * 8480 isl_multi_union_pw_aff_range_factor_range( 8481 __isl_take isl_multi_union_pw_aff *mupa); 8482 8483The splice functions are a generalization of the flat product functions, 8484where the second argument may be inserted at any position inside 8485the first argument rather than being placed at the end. 8486The functions C<isl_multi_val_factor_range>, 8487C<isl_multi_aff_factor_range>, 8488C<isl_multi_pw_aff_factor_range> and 8489C<isl_multi_union_pw_aff_factor_range> 8490take functions that live in a set space. 8491 8492 #include <isl/id.h> 8493 __isl_give isl_multi_id *isl_multi_id_range_splice( 8494 __isl_take isl_multi_id *mi1, unsigned pos, 8495 __isl_take isl_multi_id *mi2); 8496 8497 #include <isl/val.h> 8498 __isl_give isl_multi_val *isl_multi_val_range_splice( 8499 __isl_take isl_multi_val *mv1, unsigned pos, 8500 __isl_take isl_multi_val *mv2); 8501 8502 #include <isl/aff.h> 8503 __isl_give isl_multi_aff *isl_multi_aff_range_splice( 8504 __isl_take isl_multi_aff *ma1, unsigned pos, 8505 __isl_take isl_multi_aff *ma2); 8506 __isl_give isl_multi_aff *isl_multi_aff_splice( 8507 __isl_take isl_multi_aff *ma1, 8508 unsigned in_pos, unsigned out_pos, 8509 __isl_take isl_multi_aff *ma2); 8510 __isl_give isl_multi_pw_aff * 8511 isl_multi_pw_aff_range_splice( 8512 __isl_take isl_multi_pw_aff *mpa1, unsigned pos, 8513 __isl_take isl_multi_pw_aff *mpa2); 8514 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_splice( 8515 __isl_take isl_multi_pw_aff *mpa1, 8516 unsigned in_pos, unsigned out_pos, 8517 __isl_take isl_multi_pw_aff *mpa2); 8518 __isl_give isl_multi_union_pw_aff * 8519 isl_multi_union_pw_aff_range_splice( 8520 __isl_take isl_multi_union_pw_aff *mupa1, 8521 unsigned pos, 8522 __isl_take isl_multi_union_pw_aff *mupa2); 8523 8524=item * Simplification 8525 8526When applied to a set or relation, 8527the gist operation returns a set or relation that has the 8528same intersection with the context as the input set or relation. 8529Any implicit equality in the intersection is made explicit in the result, 8530while all inequalities that are redundant with respect to the intersection 8531are removed. 8532In case of union sets and relations, the gist operation is performed 8533per space. 8534 8535When applied to a function, 8536the gist operation applies the set gist operation to each of 8537the cells in the domain of the input piecewise expression. 8538The context is also exploited 8539to simplify the expression associated to each cell. 8540 8541 #include <isl/set.h> 8542 __isl_give isl_basic_set *isl_basic_set_gist( 8543 __isl_take isl_basic_set *bset, 8544 __isl_take isl_basic_set *context); 8545 __isl_give isl_set *isl_set_gist(__isl_take isl_set *set, 8546 __isl_take isl_set *context); 8547 __isl_give isl_set *isl_set_gist_params( 8548 __isl_take isl_set *set, 8549 __isl_take isl_set *context); 8550 8551 #include <isl/map.h> 8552 __isl_give isl_basic_map *isl_basic_map_gist( 8553 __isl_take isl_basic_map *bmap, 8554 __isl_take isl_basic_map *context); 8555 __isl_give isl_basic_map *isl_basic_map_gist_domain( 8556 __isl_take isl_basic_map *bmap, 8557 __isl_take isl_basic_set *context); 8558 __isl_give isl_map *isl_map_gist(__isl_take isl_map *map, 8559 __isl_take isl_map *context); 8560 __isl_give isl_map *isl_map_gist_params( 8561 __isl_take isl_map *map, 8562 __isl_take isl_set *context); 8563 __isl_give isl_map *isl_map_gist_domain( 8564 __isl_take isl_map *map, 8565 __isl_take isl_set *context); 8566 __isl_give isl_map *isl_map_gist_range( 8567 __isl_take isl_map *map, 8568 __isl_take isl_set *context); 8569 8570 #include <isl/union_set.h> 8571 __isl_give isl_union_set *isl_union_set_gist( 8572 __isl_take isl_union_set *uset, 8573 __isl_take isl_union_set *context); 8574 __isl_give isl_union_set *isl_union_set_gist_params( 8575 __isl_take isl_union_set *uset, 8576 __isl_take isl_set *set); 8577 8578 #include <isl/union_map.h> 8579 __isl_give isl_union_map *isl_union_map_gist( 8580 __isl_take isl_union_map *umap, 8581 __isl_take isl_union_map *context); 8582 __isl_give isl_union_map *isl_union_map_gist_params( 8583 __isl_take isl_union_map *umap, 8584 __isl_take isl_set *set); 8585 __isl_give isl_union_map *isl_union_map_gist_domain( 8586 __isl_take isl_union_map *umap, 8587 __isl_take isl_union_set *uset); 8588 __isl_give isl_union_map *isl_union_map_gist_range( 8589 __isl_take isl_union_map *umap, 8590 __isl_take isl_union_set *uset); 8591 8592 #include <isl/aff.h> 8593 __isl_give isl_aff *isl_aff_gist_params( 8594 __isl_take isl_aff *aff, 8595 __isl_take isl_set *context); 8596 __isl_give isl_aff *isl_aff_gist(__isl_take isl_aff *aff, 8597 __isl_take isl_set *context); 8598 __isl_give isl_multi_aff *isl_multi_aff_gist_params( 8599 __isl_take isl_multi_aff *maff, 8600 __isl_take isl_set *context); 8601 __isl_give isl_multi_aff *isl_multi_aff_gist( 8602 __isl_take isl_multi_aff *maff, 8603 __isl_take isl_set *context); 8604 __isl_give isl_pw_aff *isl_pw_aff_gist_params( 8605 __isl_take isl_pw_aff *pwaff, 8606 __isl_take isl_set *context); 8607 __isl_give isl_pw_aff *isl_pw_aff_gist( 8608 __isl_take isl_pw_aff *pwaff, 8609 __isl_take isl_set *context); 8610 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_gist_params( 8611 __isl_take isl_pw_multi_aff *pma, 8612 __isl_take isl_set *set); 8613 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_gist( 8614 __isl_take isl_pw_multi_aff *pma, 8615 __isl_take isl_set *set); 8616 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_gist_params( 8617 __isl_take isl_multi_pw_aff *mpa, 8618 __isl_take isl_set *set); 8619 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_gist( 8620 __isl_take isl_multi_pw_aff *mpa, 8621 __isl_take isl_set *set); 8622 __isl_give isl_union_pw_aff *isl_union_pw_aff_gist( 8623 __isl_take isl_union_pw_aff *upa, 8624 __isl_take isl_union_set *context); 8625 __isl_give isl_union_pw_aff *isl_union_pw_aff_gist_params( 8626 __isl_take isl_union_pw_aff *upa, 8627 __isl_take isl_set *context); 8628 __isl_give isl_union_pw_multi_aff * 8629 isl_union_pw_multi_aff_gist_params( 8630 __isl_take isl_union_pw_multi_aff *upma, 8631 __isl_take isl_set *context); 8632 __isl_give isl_union_pw_multi_aff * 8633 isl_union_pw_multi_aff_gist( 8634 __isl_take isl_union_pw_multi_aff *upma, 8635 __isl_take isl_union_set *context); 8636 __isl_give isl_multi_union_pw_aff * 8637 isl_multi_union_pw_aff_gist_params( 8638 __isl_take isl_multi_union_pw_aff *mupa, 8639 __isl_take isl_set *context); 8640 __isl_give isl_multi_union_pw_aff * 8641 isl_multi_union_pw_aff_gist( 8642 __isl_take isl_multi_union_pw_aff *mupa, 8643 __isl_take isl_union_set *context); 8644 8645 #include <isl/polynomial.h> 8646 __isl_give isl_qpolynomial *isl_qpolynomial_gist_params( 8647 __isl_take isl_qpolynomial *qp, 8648 __isl_take isl_set *context); 8649 __isl_give isl_qpolynomial *isl_qpolynomial_gist( 8650 __isl_take isl_qpolynomial *qp, 8651 __isl_take isl_set *context); 8652 __isl_give isl_qpolynomial_fold * 8653 isl_qpolynomial_fold_gist_params( 8654 __isl_take isl_qpolynomial_fold *fold, 8655 __isl_take isl_set *context); 8656 __isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_gist( 8657 __isl_take isl_qpolynomial_fold *fold, 8658 __isl_take isl_set *context); 8659 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_gist_params( 8660 __isl_take isl_pw_qpolynomial *pwqp, 8661 __isl_take isl_set *context); 8662 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_gist( 8663 __isl_take isl_pw_qpolynomial *pwqp, 8664 __isl_take isl_set *context); 8665 __isl_give isl_pw_qpolynomial_fold * 8666 isl_pw_qpolynomial_fold_gist( 8667 __isl_take isl_pw_qpolynomial_fold *pwf, 8668 __isl_take isl_set *context); 8669 __isl_give isl_pw_qpolynomial_fold * 8670 isl_pw_qpolynomial_fold_gist_params( 8671 __isl_take isl_pw_qpolynomial_fold *pwf, 8672 __isl_take isl_set *context); 8673 __isl_give isl_union_pw_qpolynomial * 8674 isl_union_pw_qpolynomial_gist_params( 8675 __isl_take isl_union_pw_qpolynomial *upwqp, 8676 __isl_take isl_set *context); 8677 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_gist( 8678 __isl_take isl_union_pw_qpolynomial *upwqp, 8679 __isl_take isl_union_set *context); 8680 __isl_give isl_union_pw_qpolynomial_fold * 8681 isl_union_pw_qpolynomial_fold_gist( 8682 __isl_take isl_union_pw_qpolynomial_fold *upwf, 8683 __isl_take isl_union_set *context); 8684 __isl_give isl_union_pw_qpolynomial_fold * 8685 isl_union_pw_qpolynomial_fold_gist_params( 8686 __isl_take isl_union_pw_qpolynomial_fold *upwf, 8687 __isl_take isl_set *context); 8688 8689=item * Binary Arithmetic Operations 8690 8691 #include <isl/set.h> 8692 __isl_give isl_set *isl_set_sum( 8693 __isl_take isl_set *set1, 8694 __isl_take isl_set *set2); 8695 #include <isl/map.h> 8696 __isl_give isl_map *isl_map_sum( 8697 __isl_take isl_map *map1, 8698 __isl_take isl_map *map2); 8699 8700C<isl_set_sum> computes the Minkowski sum of its two arguments, 8701i.e., the set containing the sums of pairs of elements from 8702C<set1> and C<set2>. 8703The domain of the result of C<isl_map_sum> is the intersection 8704of the domains of its two arguments. The corresponding range 8705elements are the sums of the corresponding range elements 8706in the two arguments. 8707 8708 #include <isl/val.h> 8709 __isl_give isl_multi_val *isl_multi_val_add( 8710 __isl_take isl_multi_val *mv1, 8711 __isl_take isl_multi_val *mv2); 8712 __isl_give isl_multi_val *isl_multi_val_sub( 8713 __isl_take isl_multi_val *mv1, 8714 __isl_take isl_multi_val *mv2); 8715 __isl_give isl_multi_val *isl_multi_val_min( 8716 __isl_take isl_multi_val *mv1, 8717 __isl_take isl_multi_val *mv2); 8718 __isl_give isl_multi_val *isl_multi_val_max( 8719 __isl_take isl_multi_val *mv1, 8720 __isl_take isl_multi_val *mv2); 8721 8722 #include <isl/aff.h> 8723 __isl_give isl_aff *isl_aff_add( 8724 __isl_take isl_aff *aff1, 8725 __isl_take isl_aff *aff2); 8726 __isl_give isl_multi_aff *isl_multi_aff_add( 8727 __isl_take isl_multi_aff *maff1, 8728 __isl_take isl_multi_aff *maff2); 8729 __isl_give isl_pw_aff *isl_pw_aff_add( 8730 __isl_take isl_pw_aff *pwaff1, 8731 __isl_take isl_pw_aff *pwaff2); 8732 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_add( 8733 __isl_take isl_multi_pw_aff *mpa1, 8734 __isl_take isl_multi_pw_aff *mpa2); 8735 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_add( 8736 __isl_take isl_pw_multi_aff *pma1, 8737 __isl_take isl_pw_multi_aff *pma2); 8738 __isl_give isl_union_pw_aff *isl_union_pw_aff_add( 8739 __isl_take isl_union_pw_aff *upa1, 8740 __isl_take isl_union_pw_aff *upa2); 8741 __isl_give isl_union_pw_multi_aff *isl_union_pw_multi_aff_add( 8742 __isl_take isl_union_pw_multi_aff *upma1, 8743 __isl_take isl_union_pw_multi_aff *upma2); 8744 __isl_give isl_multi_union_pw_aff * 8745 isl_multi_union_pw_aff_add( 8746 __isl_take isl_multi_union_pw_aff *mupa1, 8747 __isl_take isl_multi_union_pw_aff *mupa2); 8748 __isl_give isl_pw_aff *isl_pw_aff_add_constant_val( 8749 __isl_take isl_pw_aff *pa, 8750 __isl_take isl_val *v); 8751 __isl_give isl_multi_aff * 8752 isl_multi_aff_add_constant_val( 8753 __isl_take isl_multi_aff *pa, 8754 __isl_take isl_val *v); 8755 __isl_give isl_pw_multi_aff * 8756 isl_pw_multi_aff_add_constant_val( 8757 __isl_take isl_pw_multi_aff *pma, 8758 __isl_take isl_val *v); 8759 __isl_give isl_pw_multi_aff * 8760 isl_pw_multi_aff_add_constant_multi_val( 8761 __isl_take isl_pw_multi_aff *pma, 8762 __isl_take isl_multi_val *mv); 8763 __isl_give isl_multi_pw_aff * 8764 isl_multi_pw_aff_add_constant_val( 8765 __isl_take isl_multi_pw_aff *mpa, 8766 __isl_take isl_val *v); 8767 __isl_give isl_multi_aff * 8768 isl_multi_aff_add_constant_multi_val( 8769 __isl_take isl_multi_aff *pa, 8770 __isl_take isl_multi_val *mv); 8771 __isl_give isl_multi_pw_aff * 8772 isl_multi_pw_aff_add_constant_multi_val( 8773 __isl_take isl_multi_pw_aff *mpa, 8774 __isl_take isl_multi_val *mv); 8775 __isl_give isl_pw_aff *isl_pw_aff_min( 8776 __isl_take isl_pw_aff *pwaff1, 8777 __isl_take isl_pw_aff *pwaff2); 8778 __isl_give isl_pw_aff *isl_pw_aff_max( 8779 __isl_take isl_pw_aff *pwaff1, 8780 __isl_take isl_pw_aff *pwaff2); 8781 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_min( 8782 __isl_take isl_multi_pw_aff *mpa1, 8783 __isl_take isl_multi_pw_aff *mpa2); 8784 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_max( 8785 __isl_take isl_multi_pw_aff *mpa1, 8786 __isl_take isl_multi_pw_aff *mpa2); 8787 __isl_give isl_aff *isl_aff_sub( 8788 __isl_take isl_aff *aff1, 8789 __isl_take isl_aff *aff2); 8790 __isl_give isl_multi_aff *isl_multi_aff_sub( 8791 __isl_take isl_multi_aff *ma1, 8792 __isl_take isl_multi_aff *ma2); 8793 __isl_give isl_pw_aff *isl_pw_aff_sub( 8794 __isl_take isl_pw_aff *pwaff1, 8795 __isl_take isl_pw_aff *pwaff2); 8796 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_sub( 8797 __isl_take isl_multi_pw_aff *mpa1, 8798 __isl_take isl_multi_pw_aff *mpa2); 8799 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_sub( 8800 __isl_take isl_pw_multi_aff *pma1, 8801 __isl_take isl_pw_multi_aff *pma2); 8802 __isl_give isl_union_pw_aff *isl_union_pw_aff_sub( 8803 __isl_take isl_union_pw_aff *upa1, 8804 __isl_take isl_union_pw_aff *upa2); 8805 __isl_give isl_union_pw_multi_aff *isl_union_pw_multi_aff_sub( 8806 __isl_take isl_union_pw_multi_aff *upma1, 8807 __isl_take isl_union_pw_multi_aff *upma2); 8808 __isl_give isl_multi_union_pw_aff * 8809 isl_multi_union_pw_aff_sub( 8810 __isl_take isl_multi_union_pw_aff *mupa1, 8811 __isl_take isl_multi_union_pw_aff *mupa2); 8812 8813C<isl_aff_sub> subtracts the second argument from the first. 8814 8815 #include <isl/polynomial.h> 8816 __isl_give isl_qpolynomial *isl_qpolynomial_add( 8817 __isl_take isl_qpolynomial *qp1, 8818 __isl_take isl_qpolynomial *qp2); 8819 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_add( 8820 __isl_take isl_pw_qpolynomial *pwqp1, 8821 __isl_take isl_pw_qpolynomial *pwqp2); 8822 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_add_disjoint( 8823 __isl_take isl_pw_qpolynomial *pwqp1, 8824 __isl_take isl_pw_qpolynomial *pwqp2); 8825 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_add( 8826 __isl_take isl_pw_qpolynomial_fold *pwf1, 8827 __isl_take isl_pw_qpolynomial_fold *pwf2); 8828 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_add( 8829 __isl_take isl_union_pw_qpolynomial *upwqp1, 8830 __isl_take isl_union_pw_qpolynomial *upwqp2); 8831 __isl_give isl_qpolynomial *isl_qpolynomial_sub( 8832 __isl_take isl_qpolynomial *qp1, 8833 __isl_take isl_qpolynomial *qp2); 8834 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_sub( 8835 __isl_take isl_pw_qpolynomial *pwqp1, 8836 __isl_take isl_pw_qpolynomial *pwqp2); 8837 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_sub( 8838 __isl_take isl_union_pw_qpolynomial *upwqp1, 8839 __isl_take isl_union_pw_qpolynomial *upwqp2); 8840 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_fold( 8841 __isl_take isl_pw_qpolynomial_fold *pwf1, 8842 __isl_take isl_pw_qpolynomial_fold *pwf2); 8843 __isl_give isl_union_pw_qpolynomial_fold * 8844 isl_union_pw_qpolynomial_fold_fold( 8845 __isl_take isl_union_pw_qpolynomial_fold *upwf1, 8846 __isl_take isl_union_pw_qpolynomial_fold *upwf2); 8847 8848 #include <isl/aff.h> 8849 __isl_give isl_pw_aff *isl_pw_aff_union_add( 8850 __isl_take isl_pw_aff *pwaff1, 8851 __isl_take isl_pw_aff *pwaff2); 8852 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_union_add( 8853 __isl_take isl_multi_pw_aff *mpa1, 8854 __isl_take isl_multi_pw_aff *mpa2); 8855 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_union_add( 8856 __isl_take isl_pw_multi_aff *pma1, 8857 __isl_take isl_pw_multi_aff *pma2); 8858 __isl_give isl_union_pw_aff *isl_union_pw_aff_union_add( 8859 __isl_take isl_union_pw_aff *upa1, 8860 __isl_take isl_union_pw_aff *upa2); 8861 __isl_give isl_union_pw_multi_aff * 8862 isl_union_pw_multi_aff_union_add( 8863 __isl_take isl_union_pw_multi_aff *upma1, 8864 __isl_take isl_union_pw_multi_aff *upma2); 8865 __isl_give isl_multi_union_pw_aff * 8866 isl_multi_union_pw_aff_union_add( 8867 __isl_take isl_multi_union_pw_aff *mupa1, 8868 __isl_take isl_multi_union_pw_aff *mupa2); 8869 __isl_give isl_pw_aff *isl_pw_aff_union_min( 8870 __isl_take isl_pw_aff *pwaff1, 8871 __isl_take isl_pw_aff *pwaff2); 8872 __isl_give isl_pw_aff *isl_pw_aff_union_max( 8873 __isl_take isl_pw_aff *pwaff1, 8874 __isl_take isl_pw_aff *pwaff2); 8875 8876The function C<isl_pw_aff_union_max> computes a piecewise quasi-affine 8877expression with a domain that is the union of those of C<pwaff1> and 8878C<pwaff2> and such that on each cell, the quasi-affine expression is 8879the maximum of those of C<pwaff1> and C<pwaff2>. If only one of 8880C<pwaff1> or C<pwaff2> is defined on a given cell, then the 8881associated expression is the defined one. 8882This in contrast to the C<isl_pw_aff_max> function, which is 8883only defined on the shared definition domain of the arguments. 8884 8885 #include <isl/val.h> 8886 __isl_give isl_multi_val *isl_multi_val_add_val( 8887 __isl_take isl_multi_val *mv, 8888 __isl_take isl_val *v); 8889 __isl_give isl_multi_val *isl_multi_val_mod_val( 8890 __isl_take isl_multi_val *mv, 8891 __isl_take isl_val *v); 8892 __isl_give isl_multi_val *isl_multi_val_scale_val( 8893 __isl_take isl_multi_val *mv, 8894 __isl_take isl_val *v); 8895 __isl_give isl_multi_val *isl_multi_val_scale_down_val( 8896 __isl_take isl_multi_val *mv, 8897 __isl_take isl_val *v); 8898 8899 #include <isl/aff.h> 8900 __isl_give isl_aff *isl_aff_mod_val(__isl_take isl_aff *aff, 8901 __isl_take isl_val *mod); 8902 __isl_give isl_pw_aff *isl_pw_aff_mod_val( 8903 __isl_take isl_pw_aff *pa, 8904 __isl_take isl_val *mod); 8905 __isl_give isl_union_pw_aff *isl_union_pw_aff_mod_val( 8906 __isl_take isl_union_pw_aff *upa, 8907 __isl_take isl_val *f); 8908 __isl_give isl_aff *isl_aff_scale_val(__isl_take isl_aff *aff, 8909 __isl_take isl_val *v); 8910 __isl_give isl_multi_aff *isl_multi_aff_scale_val( 8911 __isl_take isl_multi_aff *ma, 8912 __isl_take isl_val *v); 8913 __isl_give isl_pw_aff *isl_pw_aff_scale_val( 8914 __isl_take isl_pw_aff *pa, __isl_take isl_val *v); 8915 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_scale_val( 8916 __isl_take isl_multi_pw_aff *mpa, 8917 __isl_take isl_val *v); 8918 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_scale_val( 8919 __isl_take isl_pw_multi_aff *pma, 8920 __isl_take isl_val *v); 8921 __isl_give isl_union_pw_aff *isl_union_pw_aff_scale_val( 8922 __isl_take isl_union_pw_aff *upa, 8923 __isl_take isl_val *f); 8924 __isl_give isl_union_pw_multi_aff * 8925 isl_union_pw_multi_aff_scale_val( 8926 __isl_take isl_union_pw_multi_aff *upma, 8927 __isl_take isl_val *val); 8928 __isl_give isl_multi_union_pw_aff * 8929 isl_multi_union_pw_aff_scale_val( 8930 __isl_take isl_multi_union_pw_aff *mupa, 8931 __isl_take isl_val *v); 8932 __isl_give isl_aff *isl_aff_scale_down_ui( 8933 __isl_take isl_aff *aff, unsigned f); 8934 __isl_give isl_aff *isl_aff_scale_down_val( 8935 __isl_take isl_aff *aff, __isl_take isl_val *v); 8936 __isl_give isl_multi_aff *isl_multi_aff_scale_down_val( 8937 __isl_take isl_multi_aff *ma, 8938 __isl_take isl_val *v); 8939 __isl_give isl_pw_aff *isl_pw_aff_scale_down_val( 8940 __isl_take isl_pw_aff *pa, 8941 __isl_take isl_val *f); 8942 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_scale_down_val( 8943 __isl_take isl_multi_pw_aff *mpa, 8944 __isl_take isl_val *v); 8945 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_scale_down_val( 8946 __isl_take isl_pw_multi_aff *pma, 8947 __isl_take isl_val *v); 8948 __isl_give isl_union_pw_aff *isl_union_pw_aff_scale_down_val( 8949 __isl_take isl_union_pw_aff *upa, 8950 __isl_take isl_val *v); 8951 __isl_give isl_union_pw_multi_aff * 8952 isl_union_pw_multi_aff_scale_down_val( 8953 __isl_take isl_union_pw_multi_aff *upma, 8954 __isl_take isl_val *val); 8955 __isl_give isl_multi_union_pw_aff * 8956 isl_multi_union_pw_aff_scale_down_val( 8957 __isl_take isl_multi_union_pw_aff *mupa, 8958 __isl_take isl_val *v); 8959 8960 #include <isl/polynomial.h> 8961 __isl_give isl_qpolynomial *isl_qpolynomial_scale_val( 8962 __isl_take isl_qpolynomial *qp, 8963 __isl_take isl_val *v); 8964 __isl_give isl_qpolynomial_fold * 8965 isl_qpolynomial_fold_scale_val( 8966 __isl_take isl_qpolynomial_fold *fold, 8967 __isl_take isl_val *v); 8968 __isl_give isl_pw_qpolynomial * 8969 isl_pw_qpolynomial_scale_val( 8970 __isl_take isl_pw_qpolynomial *pwqp, 8971 __isl_take isl_val *v); 8972 __isl_give isl_pw_qpolynomial_fold * 8973 isl_pw_qpolynomial_fold_scale_val( 8974 __isl_take isl_pw_qpolynomial_fold *pwf, 8975 __isl_take isl_val *v); 8976 __isl_give isl_union_pw_qpolynomial * 8977 isl_union_pw_qpolynomial_scale_val( 8978 __isl_take isl_union_pw_qpolynomial *upwqp, 8979 __isl_take isl_val *v); 8980 __isl_give isl_union_pw_qpolynomial_fold * 8981 isl_union_pw_qpolynomial_fold_scale_val( 8982 __isl_take isl_union_pw_qpolynomial_fold *upwf, 8983 __isl_take isl_val *v); 8984 __isl_give isl_qpolynomial * 8985 isl_qpolynomial_scale_down_val( 8986 __isl_take isl_qpolynomial *qp, 8987 __isl_take isl_val *v); 8988 __isl_give isl_qpolynomial_fold * 8989 isl_qpolynomial_fold_scale_down_val( 8990 __isl_take isl_qpolynomial_fold *fold, 8991 __isl_take isl_val *v); 8992 __isl_give isl_pw_qpolynomial * 8993 isl_pw_qpolynomial_scale_down_val( 8994 __isl_take isl_pw_qpolynomial *pwqp, 8995 __isl_take isl_val *v); 8996 __isl_give isl_pw_qpolynomial_fold * 8997 isl_pw_qpolynomial_fold_scale_down_val( 8998 __isl_take isl_pw_qpolynomial_fold *pwf, 8999 __isl_take isl_val *v); 9000 __isl_give isl_union_pw_qpolynomial * 9001 isl_union_pw_qpolynomial_scale_down_val( 9002 __isl_take isl_union_pw_qpolynomial *upwqp, 9003 __isl_take isl_val *v); 9004 __isl_give isl_union_pw_qpolynomial_fold * 9005 isl_union_pw_qpolynomial_fold_scale_down_val( 9006 __isl_take isl_union_pw_qpolynomial_fold *upwf, 9007 __isl_take isl_val *v); 9008 9009 #include <isl/val.h> 9010 __isl_give isl_multi_val *isl_multi_val_mod_multi_val( 9011 __isl_take isl_multi_val *mv1, 9012 __isl_take isl_multi_val *mv2); 9013 __isl_give isl_multi_val *isl_multi_val_scale_multi_val( 9014 __isl_take isl_multi_val *mv1, 9015 __isl_take isl_multi_val *mv2); 9016 __isl_give isl_multi_val * 9017 isl_multi_val_scale_down_multi_val( 9018 __isl_take isl_multi_val *mv1, 9019 __isl_take isl_multi_val *mv2); 9020 9021 #include <isl/aff.h> 9022 __isl_give isl_multi_aff *isl_multi_aff_mod_multi_val( 9023 __isl_take isl_multi_aff *ma, 9024 __isl_take isl_multi_val *mv); 9025 __isl_give isl_multi_union_pw_aff * 9026 isl_multi_union_pw_aff_mod_multi_val( 9027 __isl_take isl_multi_union_pw_aff *upma, 9028 __isl_take isl_multi_val *mv); 9029 __isl_give isl_multi_pw_aff * 9030 isl_multi_pw_aff_mod_multi_val( 9031 __isl_take isl_multi_pw_aff *mpa, 9032 __isl_take isl_multi_val *mv); 9033 __isl_give isl_multi_aff *isl_multi_aff_scale_multi_val( 9034 __isl_take isl_multi_aff *ma, 9035 __isl_take isl_multi_val *mv); 9036 __isl_give isl_pw_multi_aff * 9037 isl_pw_multi_aff_scale_multi_val( 9038 __isl_take isl_pw_multi_aff *pma, 9039 __isl_take isl_multi_val *mv); 9040 __isl_give isl_multi_pw_aff * 9041 isl_multi_pw_aff_scale_multi_val( 9042 __isl_take isl_multi_pw_aff *mpa, 9043 __isl_take isl_multi_val *mv); 9044 __isl_give isl_multi_union_pw_aff * 9045 isl_multi_union_pw_aff_scale_multi_val( 9046 __isl_take isl_multi_union_pw_aff *mupa, 9047 __isl_take isl_multi_val *mv); 9048 __isl_give isl_union_pw_multi_aff * 9049 isl_union_pw_multi_aff_scale_multi_val( 9050 __isl_take isl_union_pw_multi_aff *upma, 9051 __isl_take isl_multi_val *mv); 9052 __isl_give isl_multi_aff * 9053 isl_multi_aff_scale_down_multi_val( 9054 __isl_take isl_multi_aff *ma, 9055 __isl_take isl_multi_val *mv); 9056 __isl_give isl_multi_pw_aff * 9057 isl_multi_pw_aff_scale_down_multi_val( 9058 __isl_take isl_multi_pw_aff *mpa, 9059 __isl_take isl_multi_val *mv); 9060 __isl_give isl_multi_union_pw_aff * 9061 isl_multi_union_pw_aff_scale_down_multi_val( 9062 __isl_take isl_multi_union_pw_aff *mupa, 9063 __isl_take isl_multi_val *mv); 9064 9065C<isl_multi_aff_scale_multi_val> scales the elements of C<ma> 9066by the corresponding elements of C<mv>. 9067 9068 #include <isl/aff.h> 9069 __isl_give isl_aff *isl_aff_mul( 9070 __isl_take isl_aff *aff1, 9071 __isl_take isl_aff *aff2); 9072 __isl_give isl_aff *isl_aff_div( 9073 __isl_take isl_aff *aff1, 9074 __isl_take isl_aff *aff2); 9075 __isl_give isl_pw_aff *isl_pw_aff_mul( 9076 __isl_take isl_pw_aff *pwaff1, 9077 __isl_take isl_pw_aff *pwaff2); 9078 __isl_give isl_pw_aff *isl_pw_aff_div( 9079 __isl_take isl_pw_aff *pa1, 9080 __isl_take isl_pw_aff *pa2); 9081 __isl_give isl_pw_aff *isl_pw_aff_tdiv_q( 9082 __isl_take isl_pw_aff *pa1, 9083 __isl_take isl_pw_aff *pa2); 9084 __isl_give isl_pw_aff *isl_pw_aff_tdiv_r( 9085 __isl_take isl_pw_aff *pa1, 9086 __isl_take isl_pw_aff *pa2); 9087 9088When multiplying two affine expressions, at least one of the two needs 9089to be a constant. Similarly, when dividing an affine expression by another, 9090the second expression needs to be a constant. 9091C<isl_pw_aff_tdiv_q> computes the quotient of an integer division with 9092rounding towards zero. C<isl_pw_aff_tdiv_r> computes the corresponding 9093remainder. 9094 9095 #include <isl/polynomial.h> 9096 __isl_give isl_qpolynomial *isl_qpolynomial_mul( 9097 __isl_take isl_qpolynomial *qp1, 9098 __isl_take isl_qpolynomial *qp2); 9099 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_mul( 9100 __isl_take isl_pw_qpolynomial *pwqp1, 9101 __isl_take isl_pw_qpolynomial *pwqp2); 9102 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_mul( 9103 __isl_take isl_union_pw_qpolynomial *upwqp1, 9104 __isl_take isl_union_pw_qpolynomial *upwqp2); 9105 9106=back 9107 9108=head3 Lexicographic Optimization 9109 9110Given a (basic) set C<set> (or C<bset>) and a zero-dimensional domain C<dom>, 9111the following functions 9112compute a set that contains the lexicographic minimum or maximum 9113of the elements in C<set> (or C<bset>) for those values of the parameters 9114that satisfy C<dom>. 9115If C<empty> is not C<NULL>, then C<*empty> is assigned a set 9116that contains the parameter values in C<dom> for which C<set> (or C<bset>) 9117has no elements. 9118In other words, the union of the parameter values 9119for which the result is non-empty and of C<*empty> 9120is equal to C<dom>. 9121 9122 #include <isl/set.h> 9123 __isl_give isl_set *isl_basic_set_partial_lexmin( 9124 __isl_take isl_basic_set *bset, 9125 __isl_take isl_basic_set *dom, 9126 __isl_give isl_set **empty); 9127 __isl_give isl_set *isl_basic_set_partial_lexmax( 9128 __isl_take isl_basic_set *bset, 9129 __isl_take isl_basic_set *dom, 9130 __isl_give isl_set **empty); 9131 __isl_give isl_set *isl_set_partial_lexmin( 9132 __isl_take isl_set *set, __isl_take isl_set *dom, 9133 __isl_give isl_set **empty); 9134 __isl_give isl_set *isl_set_partial_lexmax( 9135 __isl_take isl_set *set, __isl_take isl_set *dom, 9136 __isl_give isl_set **empty); 9137 9138Given a (basic) set C<set> (or C<bset>), the following functions simply 9139return a set containing the lexicographic minimum or maximum 9140of the elements in C<set> (or C<bset>). 9141In case of union sets, the optimum is computed per space. 9142 9143 #include <isl/set.h> 9144 __isl_give isl_set *isl_basic_set_lexmin( 9145 __isl_take isl_basic_set *bset); 9146 __isl_give isl_set *isl_basic_set_lexmax( 9147 __isl_take isl_basic_set *bset); 9148 __isl_give isl_set *isl_set_lexmin( 9149 __isl_take isl_set *set); 9150 __isl_give isl_set *isl_set_lexmax( 9151 __isl_take isl_set *set); 9152 __isl_give isl_union_set *isl_union_set_lexmin( 9153 __isl_take isl_union_set *uset); 9154 __isl_give isl_union_set *isl_union_set_lexmax( 9155 __isl_take isl_union_set *uset); 9156 9157Given a (basic) relation C<map> (or C<bmap>) and a domain C<dom>, 9158the following functions 9159compute a relation that maps each element of C<dom> 9160to the single lexicographic minimum or maximum 9161of the elements that are associated to that same 9162element in C<map> (or C<bmap>). 9163If C<empty> is not C<NULL>, then C<*empty> is assigned a set 9164that contains the elements in C<dom> that do not map 9165to any elements in C<map> (or C<bmap>). 9166In other words, the union of the domain of the result and of C<*empty> 9167is equal to C<dom>. 9168 9169 #include <isl/map.h> 9170 __isl_give isl_map *isl_basic_map_partial_lexmax( 9171 __isl_take isl_basic_map *bmap, 9172 __isl_take isl_basic_set *dom, 9173 __isl_give isl_set **empty); 9174 __isl_give isl_map *isl_basic_map_partial_lexmin( 9175 __isl_take isl_basic_map *bmap, 9176 __isl_take isl_basic_set *dom, 9177 __isl_give isl_set **empty); 9178 __isl_give isl_map *isl_map_partial_lexmax( 9179 __isl_take isl_map *map, __isl_take isl_set *dom, 9180 __isl_give isl_set **empty); 9181 __isl_give isl_map *isl_map_partial_lexmin( 9182 __isl_take isl_map *map, __isl_take isl_set *dom, 9183 __isl_give isl_set **empty); 9184 9185Given a (basic) map C<map> (or C<bmap>), the following functions simply 9186return a map mapping each element in the domain of 9187C<map> (or C<bmap>) to the lexicographic minimum or maximum 9188of all elements associated to that element. 9189In case of union relations, the optimum is computed per space. 9190 9191 #include <isl/map.h> 9192 __isl_give isl_map *isl_basic_map_lexmin( 9193 __isl_take isl_basic_map *bmap); 9194 __isl_give isl_map *isl_basic_map_lexmax( 9195 __isl_take isl_basic_map *bmap); 9196 __isl_give isl_map *isl_map_lexmin( 9197 __isl_take isl_map *map); 9198 __isl_give isl_map *isl_map_lexmax( 9199 __isl_take isl_map *map); 9200 __isl_give isl_union_map *isl_union_map_lexmin( 9201 __isl_take isl_union_map *umap); 9202 __isl_give isl_union_map *isl_union_map_lexmax( 9203 __isl_take isl_union_map *umap); 9204 9205The following functions return their result in the form of 9206a piecewise multi-affine expression, 9207but are otherwise equivalent to the corresponding functions 9208returning a basic set or relation. 9209 9210 #include <isl/set.h> 9211 __isl_give isl_pw_multi_aff * 9212 isl_basic_set_partial_lexmin_pw_multi_aff( 9213 __isl_take isl_basic_set *bset, 9214 __isl_take isl_basic_set *dom, 9215 __isl_give isl_set **empty); 9216 __isl_give isl_pw_multi_aff * 9217 isl_basic_set_partial_lexmax_pw_multi_aff( 9218 __isl_take isl_basic_set *bset, 9219 __isl_take isl_basic_set *dom, 9220 __isl_give isl_set **empty); 9221 __isl_give isl_pw_multi_aff *isl_set_lexmin_pw_multi_aff( 9222 __isl_take isl_set *set); 9223 __isl_give isl_pw_multi_aff *isl_set_lexmax_pw_multi_aff( 9224 __isl_take isl_set *set); 9225 9226 #include <isl/map.h> 9227 __isl_give isl_pw_multi_aff * 9228 isl_basic_map_lexmin_pw_multi_aff( 9229 __isl_take isl_basic_map *bmap); 9230 __isl_give isl_pw_multi_aff * 9231 isl_basic_map_partial_lexmin_pw_multi_aff( 9232 __isl_take isl_basic_map *bmap, 9233 __isl_take isl_basic_set *dom, 9234 __isl_give isl_set **empty); 9235 __isl_give isl_pw_multi_aff * 9236 isl_basic_map_partial_lexmax_pw_multi_aff( 9237 __isl_take isl_basic_map *bmap, 9238 __isl_take isl_basic_set *dom, 9239 __isl_give isl_set **empty); 9240 __isl_give isl_pw_multi_aff *isl_map_lexmin_pw_multi_aff( 9241 __isl_take isl_map *map); 9242 __isl_give isl_pw_multi_aff *isl_map_lexmax_pw_multi_aff( 9243 __isl_take isl_map *map); 9244 9245The following functions return the lexicographic minimum or maximum 9246on the shared domain of the inputs and the single defined function 9247on those parts of the domain where only a single function is defined. 9248 9249 #include <isl/aff.h> 9250 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_union_lexmin( 9251 __isl_take isl_pw_multi_aff *pma1, 9252 __isl_take isl_pw_multi_aff *pma2); 9253 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_union_lexmax( 9254 __isl_take isl_pw_multi_aff *pma1, 9255 __isl_take isl_pw_multi_aff *pma2); 9256 9257If the input to a lexicographic optimization problem has 9258multiple constraints with the same coefficients for the optimized 9259variables, then, by default, this symmetry is exploited by 9260replacing those constraints by a single constraint with 9261an abstract bound, which is in turn bounded by the corresponding terms 9262in the original constraints. 9263Without this optimization, the solver would typically consider 9264all possible orderings of those original bounds, resulting in a needless 9265decomposition of the domain. 9266However, the optimization can also result in slowdowns since 9267an extra parameter is introduced that may get used in additional 9268integer divisions. 9269The following option determines whether symmetry detection is applied 9270during lexicographic optimization. 9271 9272 #include <isl/options.h> 9273 isl_stat isl_options_set_pip_symmetry(isl_ctx *ctx, 9274 int val); 9275 int isl_options_get_pip_symmetry(isl_ctx *ctx); 9276 9277=begin latex 9278 9279See also \autoref{s:offline}. 9280 9281=end latex 9282 9283=head2 Ternary Operations 9284 9285 #include <isl/aff.h> 9286 __isl_give isl_pw_aff *isl_pw_aff_cond( 9287 __isl_take isl_pw_aff *cond, 9288 __isl_take isl_pw_aff *pwaff_true, 9289 __isl_take isl_pw_aff *pwaff_false); 9290 9291The function C<isl_pw_aff_cond> performs a conditional operator 9292and returns an expression that is equal to C<pwaff_true> 9293for elements where C<cond> is non-zero and equal to C<pwaff_false> for elements 9294where C<cond> is zero. 9295 9296=head2 Lists 9297 9298Lists are defined over several element types, including 9299C<isl_val>, C<isl_id>, C<isl_aff>, C<isl_pw_aff>, C<isl_pw_multi_aff>, 9300C<isl_union_pw_aff>, 9301C<isl_union_pw_multi_aff>, 9302C<isl_qpolynomial>, C<isl_pw_qpolynomial>, C<isl_pw_qpolynomial_fold>, 9303C<isl_constraint>, 9304C<isl_basic_set>, C<isl_set>, C<isl_basic_map>, C<isl_map>, C<isl_union_set>, 9305C<isl_union_map>, C<isl_ast_expr> and C<isl_ast_node>. 9306Here we take lists of C<isl_set>s as an example. 9307Lists can be created, copied, modified and freed using the following functions. 9308 9309 #include <isl/set.h> 9310 __isl_give isl_set_list *isl_set_to_list( 9311 __isl_take isl_set *el); 9312 __isl_give isl_set_list *isl_set_list_from_set( 9313 __isl_take isl_set *el); 9314 __isl_give isl_set_list *isl_set_list_alloc( 9315 isl_ctx *ctx, int n); 9316 __isl_give isl_set_list *isl_set_list_copy( 9317 __isl_keep isl_set_list *list); 9318 __isl_give isl_set_list *isl_set_list_insert( 9319 __isl_take isl_set_list *list, unsigned pos, 9320 __isl_take isl_set *el); 9321 __isl_give isl_set_list *isl_set_list_add( 9322 __isl_take isl_set_list *list, 9323 __isl_take isl_set *el); 9324 __isl_give isl_set_list *isl_set_list_drop( 9325 __isl_take isl_set_list *list, 9326 unsigned first, unsigned n); 9327 __isl_give isl_set_list *isl_set_list_clear( 9328 __isl_take isl_set_list *list); 9329 __isl_give isl_set_list *isl_set_list_swap( 9330 __isl_take isl_set_list *list, 9331 unsigned pos1, unsigned pos2); 9332 __isl_give isl_set_list *isl_set_list_reverse( 9333 __isl_take isl_set_list *list); 9334 __isl_give isl_set_list *isl_set_list_set_set( 9335 __isl_take isl_set_list *list, int index, 9336 __isl_take isl_set *set); 9337 __isl_give isl_set_list *isl_set_list_concat( 9338 __isl_take isl_set_list *list1, 9339 __isl_take isl_set_list *list2); 9340 __isl_give isl_set_list *isl_set_list_map( 9341 __isl_take isl_set_list *list, 9342 __isl_give isl_set *(*fn)(__isl_take isl_set *el, 9343 void *user), 9344 void *user); 9345 __isl_give isl_set_list *isl_set_list_sort( 9346 __isl_take isl_set_list *list, 9347 int (*cmp)(__isl_keep isl_set *a, 9348 __isl_keep isl_set *b, void *user), 9349 void *user); 9350 __isl_null isl_set_list *isl_set_list_free( 9351 __isl_take isl_set_list *list); 9352 9353C<isl_set_list_alloc> creates an empty list with an initial capacity 9354for C<n> elements. C<isl_set_list_insert> and C<isl_set_list_add> 9355add elements to a list, increasing its capacity as needed. 9356C<isl_set_to_list> creates a list with a single element. 9357C<isl_set_list_from_set> performs the same operation. 9358C<isl_set_list_clear> removes all elements from a list. 9359C<isl_set_list_swap> swaps the elements at the specified locations. 9360C<isl_set_list_reverse> reverses the elements in the list. 9361 9362Lists can be inspected using the following functions. 9363 9364 #include <isl/set.h> 9365 isl_size isl_set_list_size(__isl_keep isl_set_list *list); 9366 isl_size isl_set_list_n_set(__isl_keep isl_set_list *list); 9367 __isl_give isl_set *isl_set_list_get_at( 9368 __isl_keep isl_set_list *list, int index); 9369 __isl_give isl_set *isl_set_list_get_set( 9370 __isl_keep isl_set_list *list, int index); 9371 isl_stat isl_set_list_foreach(__isl_keep isl_set_list *list, 9372 isl_stat (*fn)(__isl_take isl_set *el, void *user), 9373 void *user); 9374 isl_bool isl_set_list_every(__isl_keep isl_set_list *list, 9375 isl_bool (*test)(__isl_take isl_set *el, 9376 void *user), 9377 void *user); 9378 isl_stat isl_set_list_foreach_scc( 9379 __isl_keep isl_set_list *list, 9380 isl_bool (*follows)(__isl_keep isl_set *a, 9381 __isl_keep isl_set *b, void *user), 9382 void *follows_user, 9383 isl_stat (*fn)(__isl_take isl_set_list *scc, 9384 void *user), 9385 void *fn_user); 9386 9387C<isl_set_list_n_set> is an alternative name for C<isl_set_list_size>. 9388Similarly, 9389C<isl_set_list_get_set> is an alternative name for C<isl_set_list_get_at>. 9390The function C<isl_set_list_foreach_scc> calls C<fn> on each of the 9391strongly connected components of the graph with as vertices the elements 9392of C<list> and a directed edge from vertex C<b> to vertex C<a> 9393iff C<follows(a, b)> returns C<isl_bool_true>. The callbacks C<follows> and 9394C<fn> should return C<isl_bool_error> or C<isl_stat_error> on error. 9395 9396Lists can be printed using 9397 9398 #include <isl/set.h> 9399 __isl_give isl_printer *isl_printer_print_set_list( 9400 __isl_take isl_printer *p, 9401 __isl_keep isl_set_list *list); 9402 9403Alternatively, a string representation can be obtained 9404directly using the following function, which always prints 9405in isl format. 9406 9407 #include <isl/set.h> 9408 __isl_give char *isl_set_list_to_str( 9409 __isl_keep isl_set_list *list); 9410 9411An C<isl_val_list>, C<isl_id_list>, 9412C<isl_aff_list>, C<isl_pw_aff_list>, C<isl_pw_multi_aff_list>, 9413C<isl_union_pw_aff_list>, 9414C<isl_set_list>, C<isl_map_list> or C<isl_union_set_list> object 9415can also be read from input using the following functions. 9416 9417 #include <isl/val.h> 9418 __isl_give isl_val_list *isl_val_list_read_from_str( 9419 isl_ctx *ctx, const char *str); 9420 9421 #include <isl/id.h> 9422 __isl_give isl_id_list *isl_id_list_read_from_str( 9423 isl_ctx *ctx, const char *str); 9424 9425 #include <isl/aff.h> 9426 __isl_give isl_aff_list * 9427 isl_aff_list_read_from_str(isl_ctx *ctx, 9428 const char *str); 9429 __isl_give isl_pw_aff_list * 9430 isl_pw_aff_list_read_from_str(isl_ctx *ctx, 9431 const char *str); 9432 __isl_give isl_pw_multi_aff_list * 9433 isl_pw_multi_aff_list_read_from_str(isl_ctx *ctx, 9434 const char *str); 9435 __isl_give isl_union_pw_aff_list * 9436 isl_union_pw_aff_list_read_from_str(isl_ctx *ctx, 9437 const char *str); 9438 9439 #include <isl/set.h> 9440 __isl_give isl_set_list *isl_set_list_read_from_str( 9441 isl_ctx *ctx, const char *str); 9442 9443 #include <isl/map.h> 9444 __isl_give isl_map_list *isl_map_list_read_from_str( 9445 isl_ctx *ctx, const char *str); 9446 9447 #include <isl/union_set.h> 9448 __isl_give isl_union_set_list * 9449 isl_union_set_list_read_from_str(isl_ctx *ctx, 9450 const char *str); 9451 9452=head2 Associative arrays 9453 9454Associative arrays map isl objects of a specific type to isl objects 9455of some (other) specific type. They are defined for several pairs 9456of types, including (C<isl_map>, C<isl_basic_set>), 9457(C<isl_id>, C<isl_ast_expr>), 9458(C<isl_id>, C<isl_id>) and 9459(C<isl_id>, C<isl_pw_aff>). 9460Here, we take associative arrays that map C<isl_id>s to C<isl_ast_expr>s 9461as an example. 9462 9463Associative arrays can be created, copied and freed using 9464the following functions. 9465 9466 #include <isl/id_to_ast_expr.h> 9467 __isl_give isl_id_to_ast_expr *isl_id_to_ast_expr_alloc( 9468 isl_ctx *ctx, int min_size); 9469 __isl_give isl_id_to_ast_expr *isl_id_to_ast_expr_copy( 9470 __isl_keep isl_id_to_ast_expr *id2expr); 9471 __isl_null isl_id_to_ast_expr *isl_id_to_ast_expr_free( 9472 __isl_take isl_id_to_ast_expr *id2expr); 9473 9474The C<min_size> argument to C<isl_id_to_ast_expr_alloc> can be used 9475to specify the expected size of the associative array. 9476The associative array will be grown automatically as needed. 9477 9478Associative arrays can be inspected using the following functions. 9479 9480 #include <isl/id_to_ast_expr.h> 9481 __isl_give isl_maybe_isl_ast_expr 9482 isl_id_to_ast_expr_try_get( 9483 __isl_keep isl_id_to_ast_expr *id2expr, 9484 __isl_keep isl_id *key); 9485 isl_bool isl_id_to_ast_expr_has( 9486 __isl_keep isl_id_to_ast_expr *id2expr, 9487 __isl_keep isl_id *key); 9488 __isl_give isl_ast_expr *isl_id_to_ast_expr_get( 9489 __isl_keep isl_id_to_ast_expr *id2expr, 9490 __isl_take isl_id *key); 9491 isl_stat isl_id_to_ast_expr_foreach( 9492 __isl_keep isl_id_to_ast_expr *id2expr, 9493 isl_stat (*fn)(__isl_take isl_id *key, 9494 __isl_take isl_ast_expr *val, void *user), 9495 void *user); 9496 9497The function C<isl_id_to_ast_expr_try_get> returns a structure 9498containing two elements, C<valid> and C<value>. 9499If there is a value associated to the key, then C<valid> 9500is set to C<isl_bool_true> and C<value> contains a copy of 9501the associated value. Otherwise C<value> is C<NULL> and 9502C<valid> may be C<isl_bool_error> or C<isl_bool_false> depending 9503on whether some error has occurred or there simply is no associated value. 9504The function C<isl_id_to_ast_expr_has> returns the C<valid> field 9505in the structure and 9506the function C<isl_id_to_ast_expr_get> returns the C<value> field. 9507 9508Associative arrays can be modified using the following functions. 9509 9510 #include <isl/id_to_ast_expr.h> 9511 __isl_give isl_id_to_ast_expr *isl_id_to_ast_expr_set( 9512 __isl_take isl_id_to_ast_expr *id2expr, 9513 __isl_take isl_id *key, 9514 __isl_take isl_ast_expr *val); 9515 __isl_give isl_id_to_ast_expr *isl_id_to_ast_expr_drop( 9516 __isl_take isl_id_to_ast_expr *id2expr, 9517 __isl_take isl_id *key); 9518 9519Associative arrays can be printed using the following function. 9520 9521 #include <isl/id_to_ast_expr.h> 9522 __isl_give isl_printer *isl_printer_print_id_to_ast_expr( 9523 __isl_take isl_printer *p, 9524 __isl_keep isl_id_to_ast_expr *id2expr); 9525 9526=head2 Vectors 9527 9528Vectors can be created, copied and freed using the following functions. 9529 9530 #include <isl/vec.h> 9531 __isl_give isl_vec *isl_vec_alloc(isl_ctx *ctx, 9532 unsigned size); 9533 __isl_give isl_vec *isl_vec_zero(isl_ctx *ctx, 9534 unsigned size); 9535 __isl_give isl_vec *isl_vec_copy(__isl_keep isl_vec *vec); 9536 __isl_null isl_vec *isl_vec_free(__isl_take isl_vec *vec); 9537 9538Note that the elements of a vector created by C<isl_vec_alloc> 9539may have arbitrary values. 9540A vector created by C<isl_vec_zero> has elements with value zero. 9541The elements can be changed and inspected using the following functions. 9542 9543 isl_size isl_vec_size(__isl_keep isl_vec *vec); 9544 __isl_give isl_val *isl_vec_get_element_val( 9545 __isl_keep isl_vec *vec, int pos); 9546 __isl_give isl_vec *isl_vec_set_element_si( 9547 __isl_take isl_vec *vec, int pos, int v); 9548 __isl_give isl_vec *isl_vec_set_element_val( 9549 __isl_take isl_vec *vec, int pos, 9550 __isl_take isl_val *v); 9551 __isl_give isl_vec *isl_vec_set_si(__isl_take isl_vec *vec, 9552 int v); 9553 __isl_give isl_vec *isl_vec_set_val( 9554 __isl_take isl_vec *vec, __isl_take isl_val *v); 9555 int isl_vec_cmp_element(__isl_keep isl_vec *vec1, 9556 __isl_keep isl_vec *vec2, int pos); 9557 9558C<isl_vec_get_element> will return a negative value if anything went wrong. 9559In that case, the value of C<*v> is undefined. 9560 9561The following function can be used to concatenate two vectors. 9562 9563 __isl_give isl_vec *isl_vec_concat(__isl_take isl_vec *vec1, 9564 __isl_take isl_vec *vec2); 9565 9566=head2 Matrices 9567 9568Matrices can be created, copied and freed using the following functions. 9569 9570 #include <isl/mat.h> 9571 __isl_give isl_mat *isl_mat_alloc(isl_ctx *ctx, 9572 unsigned n_row, unsigned n_col); 9573 __isl_give isl_mat *isl_mat_copy(__isl_keep isl_mat *mat); 9574 __isl_null isl_mat *isl_mat_free(__isl_take isl_mat *mat); 9575 9576Note that the elements of a newly created matrix may have arbitrary values. 9577The elements can be changed and inspected using the following functions. 9578 9579 isl_size isl_mat_rows(__isl_keep isl_mat *mat); 9580 isl_size isl_mat_cols(__isl_keep isl_mat *mat); 9581 __isl_give isl_val *isl_mat_get_element_val( 9582 __isl_keep isl_mat *mat, int row, int col); 9583 __isl_give isl_mat *isl_mat_set_element_si(__isl_take isl_mat *mat, 9584 int row, int col, int v); 9585 __isl_give isl_mat *isl_mat_set_element_val( 9586 __isl_take isl_mat *mat, int row, int col, 9587 __isl_take isl_val *v); 9588 9589The following function computes the rank of a matrix. 9590The return value may be -1 if some error occurred. 9591 9592 #include <isl/mat.h> 9593 isl_size isl_mat_rank(__isl_keep isl_mat *mat); 9594 9595The following function can be used to compute the (right) inverse 9596of a matrix, i.e., a matrix such that the product of the original 9597and the inverse (in that order) is a multiple of the identity matrix. 9598The input matrix is assumed to be of full row-rank. 9599 9600 __isl_give isl_mat *isl_mat_right_inverse(__isl_take isl_mat *mat); 9601 9602The following function can be used to compute the (right) kernel 9603(or null space) of a matrix, i.e., a matrix such that the product of 9604the original and the kernel (in that order) is the zero matrix. 9605 9606 __isl_give isl_mat *isl_mat_right_kernel(__isl_take isl_mat *mat); 9607 9608The following function computes a basis for the space spanned 9609by the rows of a matrix. 9610 9611 __isl_give isl_mat *isl_mat_row_basis( 9612 __isl_take isl_mat *mat); 9613 9614The following function computes rows that extend a basis of C<mat1> 9615to a basis that also covers C<mat2>. 9616 9617 __isl_give isl_mat *isl_mat_row_basis_extension( 9618 __isl_take isl_mat *mat1, 9619 __isl_take isl_mat *mat2); 9620 9621The following function checks whether there is no linear dependence 9622among the combined rows of "mat1" and "mat2" that is not already present 9623in "mat1" or "mat2" individually. 9624If "mat1" and "mat2" have linearly independent rows by themselves, 9625then this means that there is no linear dependence among all rows together. 9626 9627 isl_bool isl_mat_has_linearly_independent_rows( 9628 __isl_keep isl_mat *mat1, 9629 __isl_keep isl_mat *mat2); 9630 9631=head2 Bounds on Piecewise Quasipolynomials and Piecewise Quasipolynomial Reductions 9632 9633The following functions determine 9634an upper or lower bound on a quasipolynomial over its domain. 9635 9636 __isl_give isl_pw_qpolynomial_fold * 9637 isl_pw_qpolynomial_bound( 9638 __isl_take isl_pw_qpolynomial *pwqp, 9639 enum isl_fold type, isl_bool *tight); 9640 9641 __isl_give isl_union_pw_qpolynomial_fold * 9642 isl_union_pw_qpolynomial_bound( 9643 __isl_take isl_union_pw_qpolynomial *upwqp, 9644 enum isl_fold type, isl_bool *tight); 9645 9646The C<type> argument may be either C<isl_fold_min> or C<isl_fold_max>. 9647If C<tight> is not C<NULL>, then C<*tight> is set to C<1> 9648is the returned bound is known be tight, i.e., for each value 9649of the parameters there is at least 9650one element in the domain that reaches the bound. 9651If the domain of C<pwqp> is not wrapping, then the bound is computed 9652over all elements in that domain and the result has a purely parametric 9653domain. If the domain of C<pwqp> is wrapping, then the bound is 9654computed over the range of the wrapped relation. The domain of the 9655wrapped relation becomes the domain of the result. 9656 9657=head2 Parametric Vertex Enumeration 9658 9659The parametric vertex enumeration described in this section 9660is mainly intended to be used internally and by the C<barvinok> 9661library. 9662 9663 #include <isl/vertices.h> 9664 __isl_give isl_vertices *isl_basic_set_compute_vertices( 9665 __isl_keep isl_basic_set *bset); 9666 9667The function C<isl_basic_set_compute_vertices> performs the 9668actual computation of the parametric vertices and the chamber 9669decomposition and stores the result in an C<isl_vertices> object. 9670This information can be queried by either iterating over all 9671the vertices or iterating over all the chambers or cells 9672and then iterating over all vertices that are active on the chamber. 9673 9674 isl_stat isl_vertices_foreach_vertex( 9675 __isl_keep isl_vertices *vertices, 9676 isl_stat (*fn)(__isl_take isl_vertex *vertex, 9677 void *user), void *user); 9678 9679 isl_stat isl_vertices_foreach_cell( 9680 __isl_keep isl_vertices *vertices, 9681 isl_stat (*fn)(__isl_take isl_cell *cell, 9682 void *user), void *user); 9683 isl_stat isl_cell_foreach_vertex(__isl_keep isl_cell *cell, 9684 isl_stat (*fn)(__isl_take isl_vertex *vertex, 9685 void *user), void *user); 9686 9687Other operations that can be performed on an C<isl_vertices> object are 9688the following. 9689 9690 isl_size isl_vertices_get_n_vertices( 9691 __isl_keep isl_vertices *vertices); 9692 __isl_null isl_vertices *isl_vertices_free( 9693 __isl_take isl_vertices *vertices); 9694 9695Vertices can be inspected and destroyed using the following functions. 9696 9697 isl_size isl_vertex_get_id(__isl_keep isl_vertex *vertex); 9698 __isl_give isl_basic_set *isl_vertex_get_domain( 9699 __isl_keep isl_vertex *vertex); 9700 __isl_give isl_multi_aff *isl_vertex_get_expr( 9701 __isl_keep isl_vertex *vertex); 9702 __isl_null isl_vertex *isl_vertex_free( 9703 __isl_take isl_vertex *vertex); 9704 9705C<isl_vertex_get_expr> returns a multiple quasi-affine expression 9706describing the vertex in terms of the parameters, 9707while C<isl_vertex_get_domain> returns the activity domain 9708of the vertex. 9709 9710Chambers can be inspected and destroyed using the following functions. 9711 9712 __isl_give isl_basic_set *isl_cell_get_domain( 9713 __isl_keep isl_cell *cell); 9714 __isl_null isl_cell *isl_cell_free( 9715 __isl_take isl_cell *cell); 9716 9717=head1 Polyhedral Compilation Library 9718 9719This section collects functionality in C<isl> that has been specifically 9720designed for use during polyhedral compilation. 9721 9722=head2 Schedule Trees 9723 9724A schedule tree is a structured representation of a schedule, 9725assigning a relative order to a set of domain elements. 9726The relative order expressed by the schedule tree is 9727defined recursively. In particular, the order between 9728two domain elements is determined by the node that is closest 9729to the root that refers to both elements and that orders them apart. 9730Each node in the tree is of one of several types. 9731The root node is always of type C<isl_schedule_node_domain> 9732(or C<isl_schedule_node_extension>) 9733and it describes the (extra) domain elements to which the schedule applies. 9734The other types of nodes are as follows. 9735 9736=over 9737 9738=item C<isl_schedule_node_band> 9739 9740A band of schedule dimensions. Each schedule dimension is represented 9741by a union piecewise quasi-affine expression. If this expression 9742assigns a different value to two domain elements, while all previous 9743schedule dimensions in the same band assign them the same value, 9744then the two domain elements are ordered according to these two 9745different values. 9746Each expression is required to be total in the domain elements 9747that reach the band node. 9748 9749=item C<isl_schedule_node_expansion> 9750 9751An expansion node maps each of the domain elements that reach the node 9752to one or more domain elements. The image of this mapping forms 9753the set of domain elements that reach the child of the expansion node. 9754The function that maps each of the expanded domain elements 9755to the original domain element from which it was expanded 9756is called the contraction. 9757 9758=item C<isl_schedule_node_filter> 9759 9760A filter node does not impose any ordering, but rather intersects 9761the set of domain elements that the current subtree refers to 9762with a given union set. The subtree of the filter node only 9763refers to domain elements in the intersection. 9764A filter node is typically only used as a child of a sequence or 9765set node. 9766 9767=item C<isl_schedule_node_leaf> 9768 9769A leaf of the schedule tree. Leaf nodes do not impose any ordering. 9770 9771=item C<isl_schedule_node_mark> 9772 9773A mark node can be used to attach any kind of information to a subtree 9774of the schedule tree. 9775 9776=item C<isl_schedule_node_sequence> 9777 9778A sequence node has one or more children, each of which is a filter node. 9779The filters on these filter nodes form a partition of 9780the domain elements that the current subtree refers to. 9781If two domain elements appear in distinct filters then the sequence 9782node orders them according to the child positions of the corresponding 9783filter nodes. 9784 9785=item C<isl_schedule_node_set> 9786 9787A set node is similar to a sequence node, except that 9788it expresses that domain elements appearing in distinct filters 9789may have any order. The order of the children of a set node 9790is therefore also immaterial. 9791 9792=back 9793 9794The following node types are only supported by the AST generator. 9795 9796=over 9797 9798=item C<isl_schedule_node_context> 9799 9800The context describes constraints on the parameters and 9801the schedule dimensions of outer 9802bands that the AST generator may assume to hold. It is also the only 9803kind of node that may introduce additional parameters. 9804The space of the context is that of the flat product of the outer 9805band nodes. In particular, if there are no outer band nodes, then 9806this space is the unnamed zero-dimensional space. 9807Since a context node references the outer band nodes, any tree 9808containing a context node is considered to be anchored. 9809 9810=item C<isl_schedule_node_extension> 9811 9812An extension node instructs the AST generator to add additional 9813domain elements that need to be scheduled. 9814The additional domain elements are described by the range of 9815the extension map in terms of the outer schedule dimensions, 9816i.e., the flat product of the outer band nodes. 9817Note that domain elements are added whenever the AST generator 9818reaches the extension node, meaning that there are still some 9819active domain elements for which an AST needs to be generated. 9820The conditions under which some domain elements are still active 9821may however not be completely described by the outer AST nodes 9822generated at that point. 9823Since an extension node references the outer band nodes, any tree 9824containing an extension node is considered to be anchored. 9825 9826An extension node may also appear as the root of a schedule tree, 9827when it is intended to be inserted into another tree 9828using C<isl_schedule_node_graft_before> or C<isl_schedule_node_graft_after>. 9829In this case, the domain of the extension node should 9830correspond to the flat product of the outer band nodes 9831in this other schedule tree at the point where the extension tree 9832will be inserted. 9833 9834=item C<isl_schedule_node_guard> 9835 9836The guard describes constraints on the parameters and 9837the schedule dimensions of outer 9838bands that need to be enforced by the outer nodes 9839in the generated AST. 9840That is, the part of the AST that is generated from descendants 9841of the guard node can assume that these constraints are satisfied. 9842The space of the guard is that of the flat product of the outer 9843band nodes. In particular, if there are no outer band nodes, then 9844this space is the unnamed zero-dimensional space. 9845Since a guard node references the outer band nodes, any tree 9846containing a guard node is considered to be anchored. 9847 9848=back 9849 9850Except for the C<isl_schedule_node_context> nodes, 9851none of the nodes may introduce any parameters that were not 9852already present in the root domain node. 9853 9854A schedule tree is encapsulated in an C<isl_schedule> object. 9855The simplest such objects, those with a tree consisting of single domain node, 9856can be created using the following functions with either an empty 9857domain or a given domain. 9858 9859 #include <isl/schedule.h> 9860 __isl_give isl_schedule *isl_schedule_empty( 9861 __isl_take isl_space *space); 9862 __isl_give isl_schedule *isl_schedule_from_domain( 9863 __isl_take isl_union_set *domain); 9864 9865The function C<isl_schedule_constraints_compute_schedule> described 9866in L</"Scheduling"> can also be used to construct schedules. 9867 9868C<isl_schedule> objects may be copied and freed using the following functions. 9869 9870 #include <isl/schedule.h> 9871 __isl_give isl_schedule *isl_schedule_copy( 9872 __isl_keep isl_schedule *sched); 9873 __isl_null isl_schedule *isl_schedule_free( 9874 __isl_take isl_schedule *sched); 9875 9876The following functions checks whether two C<isl_schedule> objects 9877are obviously the same. 9878 9879 #include <isl/schedule.h> 9880 isl_bool isl_schedule_plain_is_equal( 9881 __isl_keep isl_schedule *schedule1, 9882 __isl_keep isl_schedule *schedule2); 9883 9884The domain of the schedule, i.e., the domain described by the root node, 9885can be obtained using the following function. 9886 9887 #include <isl/schedule.h> 9888 __isl_give isl_union_set *isl_schedule_get_domain( 9889 __isl_keep isl_schedule *schedule); 9890 9891An extra top-level band node (right underneath the domain node) can 9892be introduced into the schedule using the following function. 9893The schedule tree is assumed not to have any anchored nodes. 9894 9895 #include <isl/schedule.h> 9896 __isl_give isl_schedule * 9897 isl_schedule_insert_partial_schedule( 9898 __isl_take isl_schedule *schedule, 9899 __isl_take isl_multi_union_pw_aff *partial); 9900 9901A top-level context node (right underneath the domain node) can 9902be introduced into the schedule using the following function. 9903 9904 #include <isl/schedule.h> 9905 __isl_give isl_schedule *isl_schedule_insert_context( 9906 __isl_take isl_schedule *schedule, 9907 __isl_take isl_set *context) 9908 9909A top-level guard node (right underneath the domain node) can 9910be introduced into the schedule using the following function. 9911 9912 #include <isl/schedule.h> 9913 __isl_give isl_schedule *isl_schedule_insert_guard( 9914 __isl_take isl_schedule *schedule, 9915 __isl_take isl_set *guard) 9916 9917A schedule that combines two schedules either in the given 9918order or in an arbitrary order, i.e., with an C<isl_schedule_node_sequence> 9919or an C<isl_schedule_node_set> node, 9920can be created using the following functions. 9921 9922 #include <isl/schedule.h> 9923 __isl_give isl_schedule *isl_schedule_sequence( 9924 __isl_take isl_schedule *schedule1, 9925 __isl_take isl_schedule *schedule2); 9926 __isl_give isl_schedule *isl_schedule_set( 9927 __isl_take isl_schedule *schedule1, 9928 __isl_take isl_schedule *schedule2); 9929 9930The domains of the two input schedules need to be disjoint. 9931 9932The following function can be used to restrict the domain 9933of a schedule with a domain node as root to be a subset of the given union set. 9934This operation may remove nodes in the tree that have become 9935redundant. 9936 9937 #include <isl/schedule.h> 9938 __isl_give isl_schedule *isl_schedule_intersect_domain( 9939 __isl_take isl_schedule *schedule, 9940 __isl_take isl_union_set *domain); 9941 9942The following function can be used to simplify the domain 9943of a schedule with a domain node as root with respect to the given 9944parameter domain. 9945 9946 #include <isl/schedule.h> 9947 __isl_give isl_schedule *isl_schedule_gist_domain_params( 9948 __isl_take isl_schedule *schedule, 9949 __isl_take isl_set *context); 9950 9951The following function resets the user pointers on all parameter 9952and tuple identifiers referenced by the nodes of the given schedule. 9953 9954 #include <isl/schedule.h> 9955 __isl_give isl_schedule *isl_schedule_reset_user( 9956 __isl_take isl_schedule *schedule); 9957 9958The following function aligns the parameters of all nodes 9959in the given schedule to the given space. 9960 9961 #include <isl/schedule.h> 9962 __isl_give isl_schedule *isl_schedule_align_params( 9963 __isl_take isl_schedule *schedule, 9964 __isl_take isl_space *space); 9965 9966The following function allows the user to plug in a given function 9967in the iteration domains. The input schedule is not allowed to contain 9968any expansion nodes. 9969 9970 #include <isl/schedule.h> 9971 __isl_give isl_schedule * 9972 isl_schedule_pullback_union_pw_multi_aff( 9973 __isl_take isl_schedule *schedule, 9974 __isl_take isl_union_pw_multi_aff *upma); 9975 9976The following function can be used to plug in the schedule C<expansion> 9977in the leaves of C<schedule>, where C<contraction> describes how 9978the domain elements of C<expansion> map to the domain elements 9979at the original leaves of C<schedule>. 9980The resulting schedule will contain expansion nodes, unless 9981C<contraction> is an identity function. 9982 9983 #include <isl/schedule.h> 9984 __isl_give isl_schedule *isl_schedule_expand( 9985 __isl_take isl_schedule *schedule, 9986 __isl_take isl_union_pw_multi_aff *contraction, 9987 __isl_take isl_schedule *expansion); 9988 9989An C<isl_union_map> representation of the schedule can be obtained 9990from an C<isl_schedule> using the following function. 9991 9992 #include <isl/schedule.h> 9993 __isl_give isl_union_map *isl_schedule_get_map( 9994 __isl_keep isl_schedule *sched); 9995 9996The resulting relation encodes the same relative ordering as 9997the schedule by mapping the domain elements to a common schedule space. 9998If the schedule_separate_components option is set, then the order 9999of the children of a set node is explicitly encoded in the result. 10000If the tree contains any expansion nodes, then the relation 10001is formulated in terms of the expanded domain elements. 10002 10003Schedules can be read from input using the following functions. 10004 10005 #include <isl/schedule.h> 10006 __isl_give isl_schedule *isl_schedule_read_from_file( 10007 isl_ctx *ctx, FILE *input); 10008 __isl_give isl_schedule *isl_schedule_read_from_str( 10009 isl_ctx *ctx, const char *str); 10010 10011A representation of the schedule can be printed using 10012 10013 #include <isl/schedule.h> 10014 __isl_give isl_printer *isl_printer_print_schedule( 10015 __isl_take isl_printer *p, 10016 __isl_keep isl_schedule *schedule); 10017 __isl_give char *isl_schedule_to_str( 10018 __isl_keep isl_schedule *schedule); 10019 10020C<isl_schedule_to_str> prints the schedule in flow format. 10021 10022The schedule tree can be traversed through the use of 10023C<isl_schedule_node> objects that point to a particular 10024position in the schedule tree. Whenever a C<isl_schedule_node> 10025is used to modify a node in the schedule tree, the original schedule 10026tree is left untouched and the modifications are performed to a copy 10027of the tree. The returned C<isl_schedule_node> then points to 10028this modified copy of the tree. 10029 10030The root of the schedule tree can be obtained using the following function. 10031 10032 #include <isl/schedule.h> 10033 __isl_give isl_schedule_node *isl_schedule_get_root( 10034 __isl_keep isl_schedule *schedule); 10035 10036A pointer to a newly created schedule tree with a single domain 10037node can be created using the following functions. 10038 10039 #include <isl/schedule_node.h> 10040 __isl_give isl_schedule_node * 10041 isl_schedule_node_from_domain( 10042 __isl_take isl_union_set *domain); 10043 __isl_give isl_schedule_node * 10044 isl_schedule_node_from_extension( 10045 __isl_take isl_union_map *extension); 10046 10047C<isl_schedule_node_from_extension> creates a tree with an extension 10048node as root. 10049 10050Schedule nodes can be copied and freed using the following functions. 10051 10052 #include <isl/schedule_node.h> 10053 __isl_give isl_schedule_node *isl_schedule_node_copy( 10054 __isl_keep isl_schedule_node *node); 10055 __isl_null isl_schedule_node *isl_schedule_node_free( 10056 __isl_take isl_schedule_node *node); 10057 10058The following functions can be used to check if two schedule 10059nodes point to the same position in the same schedule. 10060 10061 #include <isl/schedule_node.h> 10062 isl_bool isl_schedule_node_is_equal( 10063 __isl_keep isl_schedule_node *node1, 10064 __isl_keep isl_schedule_node *node2); 10065 10066The following properties can be obtained from a schedule node. 10067 10068 #include <isl/schedule_node.h> 10069 enum isl_schedule_node_type isl_schedule_node_get_type( 10070 __isl_keep isl_schedule_node *node); 10071 enum isl_schedule_node_type 10072 isl_schedule_node_get_parent_type( 10073 __isl_keep isl_schedule_node *node); 10074 __isl_give isl_schedule *isl_schedule_node_get_schedule( 10075 __isl_keep isl_schedule_node *node); 10076 10077The function C<isl_schedule_node_get_type> returns the type of 10078the node, while C<isl_schedule_node_get_parent_type> returns 10079type of the parent of the node, which is required to exist. 10080The function C<isl_schedule_node_get_schedule> returns a copy 10081to the schedule to which the node belongs. 10082 10083The following functions can be used to move the schedule node 10084to a different position in the tree or to check if such a position 10085exists. 10086 10087 #include <isl/schedule_node.h> 10088 isl_bool isl_schedule_node_has_parent( 10089 __isl_keep isl_schedule_node *node); 10090 __isl_give isl_schedule_node *isl_schedule_node_parent( 10091 __isl_take isl_schedule_node *node); 10092 __isl_give isl_schedule_node *isl_schedule_node_root( 10093 __isl_take isl_schedule_node *node); 10094 __isl_give isl_schedule_node *isl_schedule_node_ancestor( 10095 __isl_take isl_schedule_node *node, 10096 int generation); 10097 isl_size isl_schedule_node_n_children( 10098 __isl_keep isl_schedule_node *node); 10099 __isl_give isl_schedule_node *isl_schedule_node_child( 10100 __isl_take isl_schedule_node *node, int pos); 10101 isl_bool isl_schedule_node_has_children( 10102 __isl_keep isl_schedule_node *node); 10103 __isl_give isl_schedule_node *isl_schedule_node_first_child( 10104 __isl_take isl_schedule_node *node); 10105 isl_bool isl_schedule_node_has_previous_sibling( 10106 __isl_keep isl_schedule_node *node); 10107 __isl_give isl_schedule_node * 10108 isl_schedule_node_previous_sibling( 10109 __isl_take isl_schedule_node *node); 10110 isl_bool isl_schedule_node_has_next_sibling( 10111 __isl_keep isl_schedule_node *node); 10112 __isl_give isl_schedule_node * 10113 isl_schedule_node_next_sibling( 10114 __isl_take isl_schedule_node *node); 10115 10116For C<isl_schedule_node_ancestor>, the ancestor of generation 0 10117is the node itself, the ancestor of generation 1 is its parent and so on. 10118 10119It is also possible to query the number of ancestors of a node, 10120the position of the current node 10121within the children of its parent, the position of the subtree 10122containing a node within the children of an ancestor 10123or to obtain a copy of a given 10124child without destroying the current node. 10125Given two nodes that point to the same schedule, their closest 10126shared ancestor can be obtained using 10127C<isl_schedule_node_get_shared_ancestor>. 10128 10129 #include <isl/schedule_node.h> 10130 isl_size isl_schedule_node_get_tree_depth( 10131 __isl_keep isl_schedule_node *node); 10132 isl_size isl_schedule_node_get_child_position( 10133 __isl_keep isl_schedule_node *node); 10134 isl_size isl_schedule_node_get_ancestor_child_position( 10135 __isl_keep isl_schedule_node *node, 10136 __isl_keep isl_schedule_node *ancestor); 10137 __isl_give isl_schedule_node *isl_schedule_node_get_child( 10138 __isl_keep isl_schedule_node *node, int pos); 10139 __isl_give isl_schedule_node * 10140 isl_schedule_node_get_shared_ancestor( 10141 __isl_keep isl_schedule_node *node1, 10142 __isl_keep isl_schedule_node *node2); 10143 10144All nodes in a schedule tree or 10145all descendants of a specific node (including the node) can be visited 10146in depth-first pre-order using the following functions. 10147 10148 #include <isl/schedule.h> 10149 isl_stat isl_schedule_foreach_schedule_node_top_down( 10150 __isl_keep isl_schedule *sched, 10151 isl_bool (*fn)(__isl_keep isl_schedule_node *node, 10152 void *user), void *user); 10153 10154 #include <isl/schedule_node.h> 10155 isl_stat isl_schedule_node_foreach_descendant_top_down( 10156 __isl_keep isl_schedule_node *node, 10157 isl_bool (*fn)(__isl_keep isl_schedule_node *node, 10158 void *user), void *user); 10159 10160The callback function is slightly different from the usual 10161callbacks in that it not only indicates success (non-negative result) 10162or failure (negative result), but also indicates whether the children 10163of the given node should be visited. In particular, if the callback 10164returns a positive value, then the children are visited, but if 10165the callback returns zero, then the children are not visited. 10166 10167The following functions checks whether 10168all descendants of a specific node (including the node itself) 10169satisfy a user-specified test. 10170 10171 #include <isl/schedule_node.h> 10172 isl_bool isl_schedule_node_every_descendant( 10173 __isl_keep isl_schedule_node *node, 10174 isl_bool (*test)(__isl_keep isl_schedule_node *node, 10175 void *user), void *user) 10176 10177The ancestors of a node in a schedule tree can be visited from 10178the root down to and including the parent of the node using 10179the following function. 10180 10181 #include <isl/schedule_node.h> 10182 isl_stat isl_schedule_node_foreach_ancestor_top_down( 10183 __isl_keep isl_schedule_node *node, 10184 isl_stat (*fn)(__isl_keep isl_schedule_node *node, 10185 void *user), void *user); 10186 10187The following functions allows for a depth-first post-order 10188traversal of the nodes in a schedule tree or 10189of the descendants of a specific node (including the node 10190itself), where the user callback is allowed to modify the 10191visited node. 10192 10193 #include <isl/schedule.h> 10194 __isl_give isl_schedule * 10195 isl_schedule_map_schedule_node_bottom_up( 10196 __isl_take isl_schedule *schedule, 10197 __isl_give isl_schedule_node *(*fn)( 10198 __isl_take isl_schedule_node *node, 10199 void *user), void *user); 10200 10201 #include <isl/schedule_node.h> 10202 __isl_give isl_schedule_node * 10203 isl_schedule_node_map_descendant_bottom_up( 10204 __isl_take isl_schedule_node *node, 10205 __isl_give isl_schedule_node *(*fn)( 10206 __isl_take isl_schedule_node *node, 10207 void *user), void *user); 10208 10209The traversal continues from the node returned by the callback function. 10210It is the responsibility of the user to ensure that this does not 10211lead to an infinite loop. It is safest to always return a pointer 10212to the same position (same ancestors and child positions) as the input node. 10213 10214The following function removes a node (along with its descendants) 10215from a schedule tree and returns a pointer to the leaf at the 10216same position in the updated tree. 10217It is not allowed to remove the root of a schedule tree or 10218a child of a set or sequence node. 10219 10220 #include <isl/schedule_node.h> 10221 __isl_give isl_schedule_node *isl_schedule_node_cut( 10222 __isl_take isl_schedule_node *node); 10223 10224The following function removes a single node 10225from a schedule tree and returns a pointer to the child 10226of the node, now located at the position of the original node 10227or to a leaf node at that position if there was no child. 10228It is not allowed to remove the root of a schedule tree, 10229a set or sequence node, a child of a set or sequence node or 10230a band node with an anchored subtree. 10231 10232 #include <isl/schedule_node.h> 10233 __isl_give isl_schedule_node *isl_schedule_node_delete( 10234 __isl_take isl_schedule_node *node); 10235 10236Most nodes in a schedule tree only contain local information. 10237In some cases, however, a node may also refer to the schedule dimensions 10238of its outer band nodes. 10239This means that the position of the node within the tree should 10240not be changed, or at least that no changes are performed to the 10241outer band nodes. The following function can be used to test 10242whether the subtree rooted at a given node contains any such nodes. 10243 10244 #include <isl/schedule_node.h> 10245 isl_bool isl_schedule_node_is_subtree_anchored( 10246 __isl_keep isl_schedule_node *node); 10247 10248The following function resets the user pointers on all parameter 10249and tuple identifiers referenced by the given schedule node. 10250 10251 #include <isl/schedule_node.h> 10252 __isl_give isl_schedule_node *isl_schedule_node_reset_user( 10253 __isl_take isl_schedule_node *node); 10254 10255The following function aligns the parameters of the given schedule 10256node to the given space. 10257 10258 #include <isl/schedule_node.h> 10259 __isl_give isl_schedule_node * 10260 isl_schedule_node_align_params( 10261 __isl_take isl_schedule_node *node, 10262 __isl_take isl_space *space); 10263 10264Several node types have their own functions for querying 10265(and in some cases setting) some node type specific properties. 10266 10267 #include <isl/schedule_node.h> 10268 __isl_give isl_space *isl_schedule_node_band_get_space( 10269 __isl_keep isl_schedule_node *node); 10270 __isl_give isl_multi_union_pw_aff * 10271 isl_schedule_node_band_get_partial_schedule( 10272 __isl_keep isl_schedule_node *node); 10273 __isl_give isl_union_map * 10274 isl_schedule_node_band_get_partial_schedule_union_map( 10275 __isl_keep isl_schedule_node *node); 10276 isl_size isl_schedule_node_band_n_member( 10277 __isl_keep isl_schedule_node *node); 10278 isl_bool isl_schedule_node_band_member_get_coincident( 10279 __isl_keep isl_schedule_node *node, int pos); 10280 __isl_give isl_schedule_node * 10281 isl_schedule_node_band_member_set_coincident( 10282 __isl_take isl_schedule_node *node, int pos, 10283 int coincident); 10284 isl_bool isl_schedule_node_band_get_permutable( 10285 __isl_keep isl_schedule_node *node); 10286 __isl_give isl_schedule_node * 10287 isl_schedule_node_band_set_permutable( 10288 __isl_take isl_schedule_node *node, int permutable); 10289 enum isl_ast_loop_type 10290 isl_schedule_node_band_member_get_ast_loop_type( 10291 __isl_keep isl_schedule_node *node, int pos); 10292 __isl_give isl_schedule_node * 10293 isl_schedule_node_band_member_set_ast_loop_type( 10294 __isl_take isl_schedule_node *node, int pos, 10295 enum isl_ast_loop_type type); 10296 enum isl_ast_loop_type 10297 isl_schedule_node_band_member_get_isolate_ast_loop_type( 10298 __isl_keep isl_schedule_node *node, int pos); 10299 __isl_give isl_schedule_node * 10300 isl_schedule_node_band_member_set_isolate_ast_loop_type( 10301 __isl_take isl_schedule_node *node, int pos, 10302 enum isl_ast_loop_type type); 10303 __isl_give isl_union_set * 10304 isl_schedule_node_band_get_ast_build_options( 10305 __isl_keep isl_schedule_node *node); 10306 __isl_give isl_schedule_node * 10307 isl_schedule_node_band_set_ast_build_options( 10308 __isl_take isl_schedule_node *node, 10309 __isl_take isl_union_set *options); 10310 __isl_give isl_set * 10311 isl_schedule_node_band_get_ast_isolate_option( 10312 __isl_keep isl_schedule_node *node); 10313 10314The function C<isl_schedule_node_band_get_space> returns the space 10315of the partial schedule of the band. 10316The function C<isl_schedule_node_band_get_partial_schedule_union_map> 10317returns a representation of the partial schedule of the band node 10318in the form of an C<isl_union_map>. 10319The coincident and permutable properties are set by 10320C<isl_schedule_constraints_compute_schedule> on the schedule tree 10321it produces. 10322A scheduling dimension is considered to be ``coincident'' 10323if it satisfies the coincidence constraints within its band. 10324That is, if the dependence distances of the coincidence 10325constraints are all zero in that direction (for fixed 10326iterations of outer bands). 10327A band is marked permutable if it was produced using the Pluto-like scheduler. 10328Note that the scheduler may have to resort to a Feautrier style scheduling 10329step even if the default scheduler is used. 10330An C<isl_ast_loop_type> is one of C<isl_ast_loop_default>, 10331C<isl_ast_loop_atomic>, C<isl_ast_loop_unroll> or C<isl_ast_loop_separate>. 10332For the meaning of these loop AST generation types and the difference 10333between the regular loop AST generation type and the isolate 10334loop AST generation type, see L</"AST Generation Options (Schedule Tree)">. 10335The functions C<isl_schedule_node_band_member_get_ast_loop_type> 10336and C<isl_schedule_node_band_member_get_isolate_ast_loop_type> 10337may return C<isl_ast_loop_error> if an error occurs. 10338The AST build options govern how an AST is generated for 10339the individual schedule dimensions during AST generation. 10340See L</"AST Generation Options (Schedule Tree)">. 10341The isolate option for the given node can be extracted from these 10342AST build options using the function 10343C<isl_schedule_node_band_get_ast_isolate_option>. 10344 10345 #include <isl/schedule_node.h> 10346 __isl_give isl_set * 10347 isl_schedule_node_context_get_context( 10348 __isl_keep isl_schedule_node *node); 10349 10350 #include <isl/schedule_node.h> 10351 __isl_give isl_union_set * 10352 isl_schedule_node_domain_get_domain( 10353 __isl_keep isl_schedule_node *node); 10354 10355 #include <isl/schedule_node.h> 10356 __isl_give isl_union_map * 10357 isl_schedule_node_expansion_get_expansion( 10358 __isl_keep isl_schedule_node *node); 10359 __isl_give isl_union_pw_multi_aff * 10360 isl_schedule_node_expansion_get_contraction( 10361 __isl_keep isl_schedule_node *node); 10362 10363 #include <isl/schedule_node.h> 10364 __isl_give isl_union_map * 10365 isl_schedule_node_extension_get_extension( 10366 __isl_keep isl_schedule_node *node); 10367 10368 #include <isl/schedule_node.h> 10369 __isl_give isl_union_set * 10370 isl_schedule_node_filter_get_filter( 10371 __isl_keep isl_schedule_node *node); 10372 10373 #include <isl/schedule_node.h> 10374 __isl_give isl_set *isl_schedule_node_guard_get_guard( 10375 __isl_keep isl_schedule_node *node); 10376 10377 #include <isl/schedule_node.h> 10378 __isl_give isl_id *isl_schedule_node_mark_get_id( 10379 __isl_keep isl_schedule_node *node); 10380 10381The following functions can be used to obtain an C<isl_multi_union_pw_aff>, 10382an C<isl_union_pw_multi_aff> or C<isl_union_map> representation of 10383partial schedules related to the node. 10384 10385 #include <isl/schedule_node.h> 10386 __isl_give isl_multi_union_pw_aff * 10387 isl_schedule_node_get_prefix_schedule_multi_union_pw_aff( 10388 __isl_keep isl_schedule_node *node); 10389 __isl_give isl_union_pw_multi_aff * 10390 isl_schedule_node_get_prefix_schedule_union_pw_multi_aff( 10391 __isl_keep isl_schedule_node *node); 10392 __isl_give isl_union_map * 10393 isl_schedule_node_get_prefix_schedule_union_map( 10394 __isl_keep isl_schedule_node *node); 10395 __isl_give isl_union_map * 10396 isl_schedule_node_get_prefix_schedule_relation( 10397 __isl_keep isl_schedule_node *node); 10398 __isl_give isl_union_map * 10399 isl_schedule_node_get_subtree_schedule_union_map( 10400 __isl_keep isl_schedule_node *node); 10401 10402In particular, the functions 10403C<isl_schedule_node_get_prefix_schedule_multi_union_pw_aff>, 10404C<isl_schedule_node_get_prefix_schedule_union_pw_multi_aff> 10405and C<isl_schedule_node_get_prefix_schedule_union_map> 10406return a relative ordering on the domain elements that reach the given 10407node determined by its ancestors. 10408The function C<isl_schedule_node_get_prefix_schedule_relation> 10409additionally includes the domain constraints in the result. 10410The function C<isl_schedule_node_get_subtree_schedule_union_map> 10411returns a representation of the partial schedule defined by the 10412subtree rooted at the given node. 10413If the tree contains any expansion nodes, then the subtree schedule 10414is formulated in terms of the expanded domain elements. 10415The tree passed to functions returning a prefix schedule 10416may only contain extension nodes if these would not affect 10417the result of these functions. That is, if one of the ancestors 10418is an extension node, then all of the domain elements that were 10419added by the extension node need to have been filtered out 10420by filter nodes between the extension node and the input node. 10421The tree passed to C<isl_schedule_node_get_subtree_schedule_union_map> 10422may not contain in extension nodes in the selected subtree. 10423 10424The expansion/contraction defined by an entire subtree, combining 10425the expansions/contractions 10426on the expansion nodes in the subtree, can be obtained using 10427the following functions. 10428 10429 #include <isl/schedule_node.h> 10430 __isl_give isl_union_map * 10431 isl_schedule_node_get_subtree_expansion( 10432 __isl_keep isl_schedule_node *node); 10433 __isl_give isl_union_pw_multi_aff * 10434 isl_schedule_node_get_subtree_contraction( 10435 __isl_keep isl_schedule_node *node); 10436 10437The total number of outer band members of given node, i.e., 10438the shared output dimension of the maps in the result 10439of C<isl_schedule_node_get_prefix_schedule_union_map> can be obtained 10440using the following function. 10441 10442 #include <isl/schedule_node.h> 10443 isl_size isl_schedule_node_get_schedule_depth( 10444 __isl_keep isl_schedule_node *node); 10445 10446The following functions return the elements that reach the given node 10447or the union of universes in the spaces that contain these elements. 10448 10449 #include <isl/schedule_node.h> 10450 __isl_give isl_union_set * 10451 isl_schedule_node_get_domain( 10452 __isl_keep isl_schedule_node *node); 10453 __isl_give isl_union_set * 10454 isl_schedule_node_get_universe_domain( 10455 __isl_keep isl_schedule_node *node); 10456 10457The input tree of C<isl_schedule_node_get_domain> 10458may only contain extension nodes if these would not affect 10459the result of this function. That is, if one of the ancestors 10460is an extension node, then all of the domain elements that were 10461added by the extension node need to have been filtered out 10462by filter nodes between the extension node and the input node. 10463 10464The following functions can be used to introduce additional nodes 10465in the schedule tree. The new node is introduced at the point 10466in the tree where the C<isl_schedule_node> points to and 10467the results points to the new node. 10468 10469 #include <isl/schedule_node.h> 10470 __isl_give isl_schedule_node * 10471 isl_schedule_node_insert_partial_schedule( 10472 __isl_take isl_schedule_node *node, 10473 __isl_take isl_multi_union_pw_aff *schedule); 10474 10475This function inserts a new band node with (the greatest integer 10476part of) the given partial schedule. 10477The subtree rooted at the given node is assumed not to have 10478any anchored nodes. 10479 10480 #include <isl/schedule_node.h> 10481 __isl_give isl_schedule_node * 10482 isl_schedule_node_insert_context( 10483 __isl_take isl_schedule_node *node, 10484 __isl_take isl_set *context); 10485 10486This function inserts a new context node with the given context constraints. 10487 10488 #include <isl/schedule_node.h> 10489 __isl_give isl_schedule_node * 10490 isl_schedule_node_insert_filter( 10491 __isl_take isl_schedule_node *node, 10492 __isl_take isl_union_set *filter); 10493 10494This function inserts a new filter node with the given filter. 10495If the original node already pointed to a filter node, then the 10496two filter nodes are merged into one. 10497 10498 #include <isl/schedule_node.h> 10499 __isl_give isl_schedule_node * 10500 isl_schedule_node_insert_guard( 10501 __isl_take isl_schedule_node *node, 10502 __isl_take isl_set *guard); 10503 10504This function inserts a new guard node with the given guard constraints. 10505 10506 #include <isl/schedule_node.h> 10507 __isl_give isl_schedule_node * 10508 isl_schedule_node_insert_mark( 10509 __isl_take isl_schedule_node *node, 10510 __isl_take isl_id *mark); 10511 10512This function inserts a new mark node with the give mark identifier. 10513 10514 #include <isl/schedule_node.h> 10515 __isl_give isl_schedule_node * 10516 isl_schedule_node_insert_sequence( 10517 __isl_take isl_schedule_node *node, 10518 __isl_take isl_union_set_list *filters); 10519 __isl_give isl_schedule_node * 10520 isl_schedule_node_insert_set( 10521 __isl_take isl_schedule_node *node, 10522 __isl_take isl_union_set_list *filters); 10523 10524These functions insert a new sequence or set node with the given 10525filters as children. 10526 10527 #include <isl/schedule_node.h> 10528 __isl_give isl_schedule_node *isl_schedule_node_group( 10529 __isl_take isl_schedule_node *node, 10530 __isl_take isl_id *group_id); 10531 10532This function introduces an expansion node in between the current 10533node and its parent that expands instances of a space with tuple 10534identifier C<group_id> to the original domain elements that reach 10535the node. The group instances are identified by the prefix schedule 10536of those domain elements. The ancestors of the node are adjusted 10537to refer to the group instances instead of the original domain 10538elements. The return value points to the same node in the updated 10539schedule tree as the input node, i.e., to the child of the newly 10540introduced expansion node. Grouping instances of different statements 10541ensures that they will be treated as a single statement by the 10542AST generator up to the point of the expansion node. 10543 10544The following function can be used to flatten a nested 10545sequence. 10546 10547 #include <isl/schedule_node.h> 10548 __isl_give isl_schedule_node * 10549 isl_schedule_node_sequence_splice_child( 10550 __isl_take isl_schedule_node *node, int pos); 10551 10552That is, given a sequence node C<node> that has another sequence node 10553in its child at position C<pos> (in particular, the child of that filter 10554node is a sequence node), attach the children of that other sequence 10555node as children of C<node>, replacing the original child at position 10556C<pos>. 10557 10558The partial schedule of a band node can be scaled (down) or reduced using 10559the following functions. 10560 10561 #include <isl/schedule_node.h> 10562 __isl_give isl_schedule_node * 10563 isl_schedule_node_band_scale( 10564 __isl_take isl_schedule_node *node, 10565 __isl_take isl_multi_val *mv); 10566 __isl_give isl_schedule_node * 10567 isl_schedule_node_band_scale_down( 10568 __isl_take isl_schedule_node *node, 10569 __isl_take isl_multi_val *mv); 10570 __isl_give isl_schedule_node * 10571 isl_schedule_node_band_mod( 10572 __isl_take isl_schedule_node *node, 10573 __isl_take isl_multi_val *mv); 10574 10575The spaces of the two arguments need to match. 10576After scaling, the partial schedule is replaced by its greatest 10577integer part to ensure that the schedule remains integral. 10578 10579The partial schedule of a band node can be shifted by an 10580C<isl_multi_union_pw_aff> with a domain that is a superset 10581of the domain of the partial schedule using 10582the following function. 10583 10584 #include <isl/schedule_node.h> 10585 __isl_give isl_schedule_node * 10586 isl_schedule_node_band_shift( 10587 __isl_take isl_schedule_node *node, 10588 __isl_take isl_multi_union_pw_aff *shift); 10589 10590A band node can be tiled using the following function. 10591 10592 #include <isl/schedule_node.h> 10593 __isl_give isl_schedule_node *isl_schedule_node_band_tile( 10594 __isl_take isl_schedule_node *node, 10595 __isl_take isl_multi_val *sizes); 10596 10597 isl_stat isl_options_set_tile_scale_tile_loops(isl_ctx *ctx, 10598 int val); 10599 int isl_options_get_tile_scale_tile_loops(isl_ctx *ctx); 10600 isl_stat isl_options_set_tile_shift_point_loops(isl_ctx *ctx, 10601 int val); 10602 int isl_options_get_tile_shift_point_loops(isl_ctx *ctx); 10603 10604The C<isl_schedule_node_band_tile> function tiles 10605the band using the given tile sizes inside its schedule. 10606A new child band node is created to represent the point loops and it is 10607inserted between the modified band and its children. 10608The subtree rooted at the given node is assumed not to have 10609any anchored nodes. 10610The C<tile_scale_tile_loops> option specifies whether the tile 10611loops iterators should be scaled by the tile sizes. 10612If the C<tile_shift_point_loops> option is set, then the point loops 10613are shifted to start at zero. 10614 10615A band node can be split into two nested band nodes 10616using the following function. 10617 10618 #include <isl/schedule_node.h> 10619 __isl_give isl_schedule_node *isl_schedule_node_band_split( 10620 __isl_take isl_schedule_node *node, int pos); 10621 10622The resulting outer band node contains the first C<pos> dimensions of 10623the schedule of C<node> while the inner band contains the remaining dimensions. 10624The schedules of the two band nodes live in anonymous spaces. 10625The loop AST generation type options and the isolate option 10626are split over the two band nodes. 10627 10628A band node can be moved down to the leaves of the subtree rooted 10629at the band node using the following function. 10630 10631 #include <isl/schedule_node.h> 10632 __isl_give isl_schedule_node *isl_schedule_node_band_sink( 10633 __isl_take isl_schedule_node *node); 10634 10635The subtree rooted at the given node is assumed not to have 10636any anchored nodes. 10637The result points to the node in the resulting tree that is in the same 10638position as the node pointed to by C<node> in the original tree. 10639 10640 #include <isl/schedule_node.h> 10641 __isl_give isl_schedule_node * 10642 isl_schedule_node_order_before( 10643 __isl_take isl_schedule_node *node, 10644 __isl_take isl_union_set *filter); 10645 __isl_give isl_schedule_node * 10646 isl_schedule_node_order_after( 10647 __isl_take isl_schedule_node *node, 10648 __isl_take isl_union_set *filter); 10649 10650These functions split the domain elements that reach C<node> 10651into those that satisfy C<filter> and those that do not and 10652arranges for the elements that do satisfy the filter to be 10653executed before (in case of C<isl_schedule_node_order_before>) 10654or after (in case of C<isl_schedule_node_order_after>) 10655those that do not. The order is imposed by 10656a sequence node, possibly reusing the grandparent of C<node> 10657on two copies of the subtree attached to the original C<node>. 10658Both copies are simplified with respect to their filter. 10659 10660Return a pointer to the copy of the subtree that does not 10661satisfy C<filter>. If there is no such copy (because all 10662reaching domain elements satisfy the filter), then return 10663the original pointer. 10664 10665 #include <isl/schedule_node.h> 10666 __isl_give isl_schedule_node * 10667 isl_schedule_node_graft_before( 10668 __isl_take isl_schedule_node *node, 10669 __isl_take isl_schedule_node *graft); 10670 __isl_give isl_schedule_node * 10671 isl_schedule_node_graft_after( 10672 __isl_take isl_schedule_node *node, 10673 __isl_take isl_schedule_node *graft); 10674 10675This function inserts the C<graft> tree into the tree containing C<node> 10676such that it is executed before (in case of C<isl_schedule_node_graft_before>) 10677or after (in case of C<isl_schedule_node_graft_after>) C<node>. 10678The root node of C<graft> 10679should be an extension node where the domain of the extension 10680is the flat product of all outer band nodes of C<node>. 10681The root node may also be a domain node. 10682The elements of the domain or the range of the extension may not 10683intersect with the domain elements that reach "node". 10684The schedule tree of C<graft> may not be anchored. 10685 10686The schedule tree of C<node> is modified to include an extension node 10687corresponding to the root node of C<graft> as a child of the original 10688parent of C<node>. The original node that C<node> points to and the 10689child of the root node of C<graft> are attached to this extension node 10690through a sequence, with appropriate filters and with the child 10691of C<graft> appearing before or after the original C<node>. 10692 10693If C<node> already appears inside a sequence that is the child of 10694an extension node and if the spaces of the new domain elements 10695do not overlap with those of the original domain elements, 10696then that extension node is extended with the new extension 10697rather than introducing a new segment of extension and sequence nodes. 10698 10699Return a pointer to the same node in the modified tree that 10700C<node> pointed to in the original tree. 10701 10702A representation of the schedule node can be printed using 10703 10704 #include <isl/schedule_node.h> 10705 __isl_give isl_printer *isl_printer_print_schedule_node( 10706 __isl_take isl_printer *p, 10707 __isl_keep isl_schedule_node *node); 10708 __isl_give char *isl_schedule_node_to_str( 10709 __isl_keep isl_schedule_node *node); 10710 10711C<isl_schedule_node_to_str> prints the schedule node in block format. 10712 10713=head2 Dependence Analysis 10714 10715C<isl> contains specialized functionality for performing 10716array dataflow analysis. That is, given a I<sink> access relation, 10717a collection of possible I<source> accesses and 10718a collection of I<kill> accesses, 10719C<isl> can compute relations that describe 10720for each iteration of the sink access, which iterations 10721of which of the source access relations may have 10722accessed the same data element before the given iteration 10723of the sink access without any intermediate kill of that data element. 10724The resulting dependence relations map source iterations 10725to either the corresponding sink iterations or 10726pairs of corresponding sink iterations and accessed data elements. 10727To compute standard flow dependences, the sink should be 10728a read, while the sources should be writes. 10729If no kills are specified, 10730then memory based dependence analysis is performed. 10731If, on the other hand, all sources are also kills, 10732then value based dependence analysis is performed. 10733If any of the source accesses are marked as being I<must> 10734accesses, then they are also treated as kills. 10735Furthermore, the specification of must-sources results 10736in the computation of must-dependences. 10737Only dependences originating in a must access not coscheduled 10738with any other access to the same element and without 10739any may accesses between the must access and the sink access 10740are considered to be must dependences. 10741 10742=head3 High-level Interface 10743 10744A high-level interface to dependence analysis is provided 10745by the following function. 10746 10747 #include <isl/flow.h> 10748 __isl_give isl_union_flow * 10749 isl_union_access_info_compute_flow( 10750 __isl_take isl_union_access_info *access); 10751 10752The input C<isl_union_access_info> object describes the sink 10753access relations, the source access relations and a schedule, 10754while the output C<isl_union_flow> object describes 10755the resulting dependence relations and the subsets of the 10756sink relations for which no source was found. 10757 10758An C<isl_union_access_info> is created, modified, copied and freed using 10759the following functions. 10760 10761 #include <isl/flow.h> 10762 __isl_give isl_union_access_info * 10763 isl_union_access_info_from_sink( 10764 __isl_take isl_union_map *sink); 10765 __isl_give isl_union_access_info * 10766 isl_union_access_info_set_kill( 10767 __isl_take isl_union_access_info *access, 10768 __isl_take isl_union_map *kill); 10769 __isl_give isl_union_access_info * 10770 isl_union_access_info_set_may_source( 10771 __isl_take isl_union_access_info *access, 10772 __isl_take isl_union_map *may_source); 10773 __isl_give isl_union_access_info * 10774 isl_union_access_info_set_must_source( 10775 __isl_take isl_union_access_info *access, 10776 __isl_take isl_union_map *must_source); 10777 __isl_give isl_union_access_info * 10778 isl_union_access_info_set_schedule( 10779 __isl_take isl_union_access_info *access, 10780 __isl_take isl_schedule *schedule); 10781 __isl_give isl_union_access_info * 10782 isl_union_access_info_set_schedule_map( 10783 __isl_take isl_union_access_info *access, 10784 __isl_take isl_union_map *schedule_map); 10785 __isl_give isl_union_access_info * 10786 isl_union_access_info_copy( 10787 __isl_keep isl_union_access_info *access); 10788 __isl_null isl_union_access_info * 10789 isl_union_access_info_free( 10790 __isl_take isl_union_access_info *access); 10791 10792The may sources set by C<isl_union_access_info_set_may_source> 10793do not need to include the must sources set by 10794C<isl_union_access_info_set_must_source> as a subset. 10795The kills set by C<isl_union_access_info_set_kill> may overlap 10796with the may-sources and/or must-sources. 10797The user is free not to call one (or more) of these functions, 10798in which case the corresponding set is kept to its empty default. 10799Similarly, the default schedule initialized by 10800C<isl_union_access_info_from_sink> is empty. 10801The current schedule is determined by the last call to either 10802C<isl_union_access_info_set_schedule> or 10803C<isl_union_access_info_set_schedule_map>. 10804The domain of the schedule corresponds to the domains of 10805the access relations. In particular, the domains of the access 10806relations are effectively intersected with the domain of the schedule 10807and only the resulting accesses are considered by the dependence analysis. 10808 10809An C<isl_union_access_info> object can be read from input 10810using the following function. 10811 10812 #include <isl/flow.h> 10813 __isl_give isl_union_access_info * 10814 isl_union_access_info_read_from_file(isl_ctx *ctx, 10815 FILE *input); 10816 10817A representation of the information contained in an object 10818of type C<isl_union_access_info> can be obtained using 10819 10820 #include <isl/flow.h> 10821 __isl_give isl_printer * 10822 isl_printer_print_union_access_info( 10823 __isl_take isl_printer *p, 10824 __isl_keep isl_union_access_info *access); 10825 __isl_give char *isl_union_access_info_to_str( 10826 __isl_keep isl_union_access_info *access); 10827 10828C<isl_union_access_info_to_str> prints the information in flow format. 10829 10830The output of C<isl_union_access_info_compute_flow> can be examined, 10831copied, and freed using the following functions. 10832 10833 #include <isl/flow.h> 10834 __isl_give isl_union_map *isl_union_flow_get_must_dependence( 10835 __isl_keep isl_union_flow *flow); 10836 __isl_give isl_union_map *isl_union_flow_get_may_dependence( 10837 __isl_keep isl_union_flow *flow); 10838 __isl_give isl_union_map * 10839 isl_union_flow_get_full_must_dependence( 10840 __isl_keep isl_union_flow *flow); 10841 __isl_give isl_union_map * 10842 isl_union_flow_get_full_may_dependence( 10843 __isl_keep isl_union_flow *flow); 10844 __isl_give isl_union_map *isl_union_flow_get_must_no_source( 10845 __isl_keep isl_union_flow *flow); 10846 __isl_give isl_union_map *isl_union_flow_get_may_no_source( 10847 __isl_keep isl_union_flow *flow); 10848 __isl_give isl_union_flow *isl_union_flow_copy( 10849 __isl_keep isl_union_flow *flow); 10850 __isl_null isl_union_flow *isl_union_flow_free( 10851 __isl_take isl_union_flow *flow); 10852 10853The relation returned by C<isl_union_flow_get_must_dependence> 10854relates domain elements of must sources to domain elements of the sink. 10855The relation returned by C<isl_union_flow_get_may_dependence> 10856relates domain elements of must or may sources to domain elements of the sink 10857and includes the previous relation as a subset. 10858The relation returned by C<isl_union_flow_get_full_must_dependence> 10859relates domain elements of must sources to pairs of domain elements of the sink 10860and accessed data elements. 10861The relation returned by C<isl_union_flow_get_full_may_dependence> 10862relates domain elements of must or may sources to pairs of 10863domain elements of the sink and accessed data elements. 10864This relation includes the previous relation as a subset. 10865The relation returned by C<isl_union_flow_get_must_no_source> is the subset 10866of the sink relation for which no dependences have been found. 10867The relation returned by C<isl_union_flow_get_may_no_source> is the subset 10868of the sink relation for which no definite dependences have been found. 10869That is, it contains those sink access that do not contribute to any 10870of the elements in the relation returned 10871by C<isl_union_flow_get_must_dependence>. 10872 10873A representation of the information contained in an object 10874of type C<isl_union_flow> can be obtained using 10875 10876 #include <isl/flow.h> 10877 __isl_give isl_printer *isl_printer_print_union_flow( 10878 __isl_take isl_printer *p, 10879 __isl_keep isl_union_flow *flow); 10880 __isl_give char *isl_union_flow_to_str( 10881 __isl_keep isl_union_flow *flow); 10882 10883C<isl_union_flow_to_str> prints the information in flow format. 10884 10885=head3 Low-level Interface 10886 10887A lower-level interface is provided by the following functions. 10888 10889 #include <isl/flow.h> 10890 10891 typedef int (*isl_access_level_before)(void *first, void *second); 10892 10893 __isl_give isl_access_info *isl_access_info_alloc( 10894 __isl_take isl_map *sink, 10895 void *sink_user, isl_access_level_before fn, 10896 int max_source); 10897 __isl_give isl_access_info *isl_access_info_add_source( 10898 __isl_take isl_access_info *acc, 10899 __isl_take isl_map *source, int must, 10900 void *source_user); 10901 __isl_null isl_access_info *isl_access_info_free( 10902 __isl_take isl_access_info *acc); 10903 10904 __isl_give isl_flow *isl_access_info_compute_flow( 10905 __isl_take isl_access_info *acc); 10906 10907 isl_stat isl_flow_foreach(__isl_keep isl_flow *deps, 10908 isl_stat (*fn)(__isl_take isl_map *dep, int must, 10909 void *dep_user, void *user), 10910 void *user); 10911 __isl_give isl_map *isl_flow_get_no_source( 10912 __isl_keep isl_flow *deps, int must); 10913 __isl_null isl_flow *isl_flow_free( 10914 __isl_take isl_flow *deps); 10915 10916The function C<isl_access_info_compute_flow> performs the actual 10917dependence analysis. The other functions are used to construct 10918the input for this function or to read off the output. 10919 10920The input is collected in an C<isl_access_info>, which can 10921be created through a call to C<isl_access_info_alloc>. 10922The arguments to this functions are the sink access relation 10923C<sink>, a token C<sink_user> used to identify the sink 10924access to the user, a callback function for specifying the 10925relative order of source and sink accesses, and the number 10926of source access relations that will be added. 10927 10928The callback function has type C<int (*)(void *first, void *second)>. 10929The function is called with two user supplied tokens identifying 10930either a source or the sink and it should return the shared nesting 10931level and the relative order of the two accesses. 10932In particular, let I<n> be the number of loops shared by 10933the two accesses. If C<first> precedes C<second> textually, 10934then the function should return I<2 * n + 1>; otherwise, 10935it should return I<2 * n>. 10936The low-level interface assumes that no sources are coscheduled. 10937If the information returned by the callback does not allow 10938the relative order to be determined, then one of the sources 10939is arbitrarily taken to be executed after the other(s). 10940 10941The sources can be added to the C<isl_access_info> object by performing 10942(at most) C<max_source> calls to C<isl_access_info_add_source>. 10943C<must> indicates whether the source is a I<must> access 10944or a I<may> access. Note that a multi-valued access relation 10945should only be marked I<must> if every iteration in the domain 10946of the relation accesses I<all> elements in its image. 10947The C<source_user> token is again used to identify 10948the source access. The range of the source access relation 10949C<source> should have the same dimension as the range 10950of the sink access relation. 10951The C<isl_access_info_free> function should usually not be 10952called explicitly, because it is already called implicitly by 10953C<isl_access_info_compute_flow>. 10954 10955The result of the dependence analysis is collected in an 10956C<isl_flow>. There may be elements of 10957the sink access for which no preceding source access could be 10958found or for which all preceding sources are I<may> accesses. 10959The relations containing these elements can be obtained through 10960calls to C<isl_flow_get_no_source>, the first with C<must> set 10961and the second with C<must> unset. 10962In the case of standard flow dependence analysis, 10963with the sink a read and the sources I<must> writes, 10964the first relation corresponds to the reads from uninitialized 10965array elements and the second relation is empty. 10966The actual flow dependences can be extracted using 10967C<isl_flow_foreach>. This function will call the user-specified 10968callback function C<fn> for each B<non-empty> dependence between 10969a source and the sink. The callback function is called 10970with four arguments, the actual flow dependence relation 10971mapping source iterations to sink iterations, a boolean that 10972indicates whether it is a I<must> or I<may> dependence, a token 10973identifying the source and an additional C<void *> with value 10974equal to the third argument of the C<isl_flow_foreach> call. 10975A dependence is marked I<must> if it originates from a I<must> 10976source and if it is not followed by any I<may> sources. 10977 10978After finishing with an C<isl_flow>, the user should call 10979C<isl_flow_free> to free all associated memory. 10980 10981=head3 Interaction with the Low-level Interface 10982 10983During the dependence analysis, we frequently need to perform 10984the following operation. Given a relation between sink iterations 10985and potential source iterations from a particular source domain, 10986what is the last potential source iteration corresponding to each 10987sink iteration. It can sometimes be convenient to adjust 10988the set of potential source iterations before or after each such operation. 10989The prototypical example is fuzzy array dataflow analysis, 10990where we need to analyze if, based on data-dependent constraints, 10991the sink iteration can ever be executed without one or more of 10992the corresponding potential source iterations being executed. 10993If so, we can introduce extra parameters and select an unknown 10994but fixed source iteration from the potential source iterations. 10995To be able to perform such manipulations, C<isl> provides the following 10996function. 10997 10998 #include <isl/flow.h> 10999 11000 typedef __isl_give isl_restriction *(*isl_access_restrict)( 11001 __isl_keep isl_map *source_map, 11002 __isl_keep isl_set *sink, void *source_user, 11003 void *user); 11004 __isl_give isl_access_info *isl_access_info_set_restrict( 11005 __isl_take isl_access_info *acc, 11006 isl_access_restrict fn, void *user); 11007 11008The function C<isl_access_info_set_restrict> should be called 11009before calling C<isl_access_info_compute_flow> and registers a callback function 11010that will be called any time C<isl> is about to compute the last 11011potential source. The first argument is the (reverse) proto-dependence, 11012mapping sink iterations to potential source iterations. 11013The second argument represents the sink iterations for which 11014we want to compute the last source iteration. 11015The third argument is the token corresponding to the source 11016and the final argument is the token passed to C<isl_access_info_set_restrict>. 11017The callback is expected to return a restriction on either the input or 11018the output of the operation computing the last potential source. 11019If the input needs to be restricted then restrictions are needed 11020for both the source and the sink iterations. The sink iterations 11021and the potential source iterations will be intersected with these sets. 11022If the output needs to be restricted then only a restriction on the source 11023iterations is required. 11024If any error occurs, the callback should return C<NULL>. 11025An C<isl_restriction> object can be created, freed and inspected 11026using the following functions. 11027 11028 #include <isl/flow.h> 11029 11030 __isl_give isl_restriction *isl_restriction_input( 11031 __isl_take isl_set *source_restr, 11032 __isl_take isl_set *sink_restr); 11033 __isl_give isl_restriction *isl_restriction_output( 11034 __isl_take isl_set *source_restr); 11035 __isl_give isl_restriction *isl_restriction_none( 11036 __isl_take isl_map *source_map); 11037 __isl_give isl_restriction *isl_restriction_empty( 11038 __isl_take isl_map *source_map); 11039 __isl_null isl_restriction *isl_restriction_free( 11040 __isl_take isl_restriction *restr); 11041 11042C<isl_restriction_none> and C<isl_restriction_empty> are special 11043cases of C<isl_restriction_input>. C<isl_restriction_none> 11044is essentially equivalent to 11045 11046 isl_restriction_input(isl_set_universe( 11047 isl_space_range(isl_map_get_space(source_map))), 11048 isl_set_universe( 11049 isl_space_domain(isl_map_get_space(source_map)))); 11050 11051whereas C<isl_restriction_empty> is essentially equivalent to 11052 11053 isl_restriction_input(isl_set_empty( 11054 isl_space_range(isl_map_get_space(source_map))), 11055 isl_set_universe( 11056 isl_space_domain(isl_map_get_space(source_map)))); 11057 11058=head2 Scheduling 11059 11060 #include <isl/schedule.h> 11061 __isl_give isl_schedule * 11062 isl_schedule_constraints_compute_schedule( 11063 __isl_take isl_schedule_constraints *sc); 11064 11065The function C<isl_schedule_constraints_compute_schedule> can be 11066used to compute a schedule that satisfies the given schedule constraints. 11067These schedule constraints include the iteration domain for which 11068a schedule should be computed and dependences between pairs of 11069iterations. In particular, these dependences include 11070I<validity> dependences and I<proximity> dependences. 11071By default, the algorithm used to construct the schedule is similar 11072to that of C<Pluto>. 11073Alternatively, Feautrier's multi-dimensional scheduling algorithm can 11074be selected. 11075The generated schedule respects all validity dependences. 11076That is, all dependence distances over these dependences in the 11077scheduled space are lexicographically positive. 11078 11079The default algorithm tries to ensure that the dependence distances 11080over coincidence constraints are zero and to minimize the 11081dependence distances over proximity dependences. 11082Moreover, it tries to obtain sequences (bands) of schedule dimensions 11083for groups of domains where the dependence distances over validity 11084dependences have only non-negative values. 11085Note that when minimizing the maximal dependence distance 11086over proximity dependences, a single affine expression in the parameters 11087is constructed that bounds all dependence distances. If no such expression 11088exists, then the algorithm will fail and resort to an alternative 11089scheduling algorithm. In particular, this means that adding proximity 11090dependences may eliminate valid solutions. A typical example where this 11091phenomenon may occur is when some subset of the proximity dependences 11092has no restriction on some parameter, forcing the coefficient of that 11093parameter to be zero, while some other subset forces the dependence 11094distance to depend on that parameter, requiring the same coefficient 11095to be non-zero. 11096When using Feautrier's algorithm, the coincidence and proximity constraints 11097are only taken into account during the extension to a 11098full-dimensional schedule. 11099 11100An C<isl_schedule_constraints> object can be constructed 11101and manipulated using the following functions. 11102 11103 #include <isl/schedule.h> 11104 __isl_give isl_schedule_constraints * 11105 isl_schedule_constraints_copy( 11106 __isl_keep isl_schedule_constraints *sc); 11107 __isl_give isl_schedule_constraints * 11108 isl_schedule_constraints_on_domain( 11109 __isl_take isl_union_set *domain); 11110 __isl_give isl_schedule_constraints * 11111 isl_schedule_constraints_set_context( 11112 __isl_take isl_schedule_constraints *sc, 11113 __isl_take isl_set *context); 11114 __isl_give isl_schedule_constraints * 11115 isl_schedule_constraints_set_validity( 11116 __isl_take isl_schedule_constraints *sc, 11117 __isl_take isl_union_map *validity); 11118 __isl_give isl_schedule_constraints * 11119 isl_schedule_constraints_set_coincidence( 11120 __isl_take isl_schedule_constraints *sc, 11121 __isl_take isl_union_map *coincidence); 11122 __isl_give isl_schedule_constraints * 11123 isl_schedule_constraints_set_proximity( 11124 __isl_take isl_schedule_constraints *sc, 11125 __isl_take isl_union_map *proximity); 11126 __isl_give isl_schedule_constraints * 11127 isl_schedule_constraints_set_conditional_validity( 11128 __isl_take isl_schedule_constraints *sc, 11129 __isl_take isl_union_map *condition, 11130 __isl_take isl_union_map *validity); 11131 __isl_give isl_schedule_constraints * 11132 isl_schedule_constraints_apply( 11133 __isl_take isl_schedule_constraints *sc, 11134 __isl_take isl_union_map *umap); 11135 __isl_null isl_schedule_constraints * 11136 isl_schedule_constraints_free( 11137 __isl_take isl_schedule_constraints *sc); 11138 11139The initial C<isl_schedule_constraints> object created by 11140C<isl_schedule_constraints_on_domain> does not impose any constraints. 11141That is, it has an empty set of dependences. 11142The function C<isl_schedule_constraints_set_context> allows the user 11143to specify additional constraints on the parameters that may 11144be assumed to hold during the construction of the schedule. 11145The function C<isl_schedule_constraints_set_validity> replaces the 11146validity dependences, mapping domain elements I<i> to domain 11147elements that should be scheduled after I<i>. 11148The function C<isl_schedule_constraints_set_coincidence> replaces the 11149coincidence dependences, mapping domain elements I<i> to domain 11150elements that should be scheduled together with I<I>, if possible. 11151The function C<isl_schedule_constraints_set_proximity> replaces the 11152proximity dependences, mapping domain elements I<i> to domain 11153elements that should be scheduled either before I<I> 11154or as early as possible after I<i>. 11155 11156The function C<isl_schedule_constraints_set_conditional_validity> 11157replaces the conditional validity constraints. 11158A conditional validity constraint is only imposed when any of the corresponding 11159conditions is satisfied, i.e., when any of them is non-zero. 11160That is, the scheduler ensures that within each band if the dependence 11161distances over the condition constraints are not all zero 11162then all corresponding conditional validity constraints are respected. 11163A conditional validity constraint corresponds to a condition 11164if the two are adjacent, i.e., if the domain of one relation intersect 11165the range of the other relation. 11166The typical use case of conditional validity constraints is 11167to allow order constraints between live ranges to be violated 11168as long as the live ranges themselves are local to the band. 11169To allow more fine-grained control over which conditions correspond 11170to which conditional validity constraints, the domains and ranges 11171of these relations may include I<tags>. That is, the domains and 11172ranges of those relation may themselves be wrapped relations 11173where the iteration domain appears in the domain of those wrapped relations 11174and the range of the wrapped relations can be arbitrarily chosen 11175by the user. Conditions and conditional validity constraints are only 11176considered adjacent to each other if the entire wrapped relation matches. 11177In particular, a relation with a tag will never be considered adjacent 11178to a relation without a tag. 11179 11180The function C<isl_schedule_constraints_apply> takes 11181schedule constraints that are defined on some set of domain elements 11182and transforms them to schedule constraints on the elements 11183to which these domain elements are mapped by the given transformation. 11184 11185An C<isl_schedule_constraints> object can be inspected 11186using the following functions. 11187 11188 #include <isl/schedule.h> 11189 __isl_give isl_union_set * 11190 isl_schedule_constraints_get_domain( 11191 __isl_keep isl_schedule_constraints *sc); 11192 __isl_give isl_set *isl_schedule_constraints_get_context( 11193 __isl_keep isl_schedule_constraints *sc); 11194 __isl_give isl_union_map * 11195 isl_schedule_constraints_get_validity( 11196 __isl_keep isl_schedule_constraints *sc); 11197 __isl_give isl_union_map * 11198 isl_schedule_constraints_get_coincidence( 11199 __isl_keep isl_schedule_constraints *sc); 11200 __isl_give isl_union_map * 11201 isl_schedule_constraints_get_proximity( 11202 __isl_keep isl_schedule_constraints *sc); 11203 __isl_give isl_union_map * 11204 isl_schedule_constraints_get_conditional_validity( 11205 __isl_keep isl_schedule_constraints *sc); 11206 __isl_give isl_union_map * 11207 isl_schedule_constraints_get_conditional_validity_condition( 11208 __isl_keep isl_schedule_constraints *sc); 11209 11210An C<isl_schedule_constraints> object can be read from input 11211using the following functions. 11212 11213 #include <isl/schedule.h> 11214 __isl_give isl_schedule_constraints * 11215 isl_schedule_constraints_read_from_str(isl_ctx *ctx, 11216 const char *str); 11217 __isl_give isl_schedule_constraints * 11218 isl_schedule_constraints_read_from_file(isl_ctx *ctx, 11219 FILE *input); 11220 11221The contents of an C<isl_schedule_constraints> object can be printed 11222using the following functions. 11223 11224 #include <isl/schedule.h> 11225 __isl_give isl_printer * 11226 isl_printer_print_schedule_constraints( 11227 __isl_take isl_printer *p, 11228 __isl_keep isl_schedule_constraints *sc); 11229 __isl_give char *isl_schedule_constraints_to_str( 11230 __isl_keep isl_schedule_constraints *sc); 11231 11232The following function computes a schedule directly from 11233an iteration domain and validity and proximity dependences 11234and is implemented in terms of the functions described above. 11235The use of C<isl_union_set_compute_schedule> is discouraged. 11236 11237 #include <isl/schedule.h> 11238 __isl_give isl_schedule *isl_union_set_compute_schedule( 11239 __isl_take isl_union_set *domain, 11240 __isl_take isl_union_map *validity, 11241 __isl_take isl_union_map *proximity); 11242 11243The generated schedule represents a schedule tree. 11244For more information on schedule trees, see 11245L</"Schedule Trees">. 11246 11247=head3 Options 11248 11249 #include <isl/schedule.h> 11250 isl_stat isl_options_set_schedule_max_coefficient( 11251 isl_ctx *ctx, int val); 11252 int isl_options_get_schedule_max_coefficient( 11253 isl_ctx *ctx); 11254 isl_stat isl_options_set_schedule_max_constant_term( 11255 isl_ctx *ctx, int val); 11256 int isl_options_get_schedule_max_constant_term( 11257 isl_ctx *ctx); 11258 isl_stat isl_options_set_schedule_serialize_sccs( 11259 isl_ctx *ctx, int val); 11260 int isl_options_get_schedule_serialize_sccs(isl_ctx *ctx); 11261 isl_stat isl_options_set_schedule_whole_component( 11262 isl_ctx *ctx, int val); 11263 int isl_options_get_schedule_whole_component( 11264 isl_ctx *ctx); 11265 isl_stat isl_options_set_schedule_maximize_band_depth( 11266 isl_ctx *ctx, int val); 11267 int isl_options_get_schedule_maximize_band_depth( 11268 isl_ctx *ctx); 11269 isl_stat isl_options_set_schedule_maximize_coincidence( 11270 isl_ctx *ctx, int val); 11271 int isl_options_get_schedule_maximize_coincidence( 11272 isl_ctx *ctx); 11273 isl_stat isl_options_set_schedule_outer_coincidence( 11274 isl_ctx *ctx, int val); 11275 int isl_options_get_schedule_outer_coincidence( 11276 isl_ctx *ctx); 11277 isl_stat isl_options_set_schedule_split_scaled( 11278 isl_ctx *ctx, int val); 11279 int isl_options_get_schedule_split_scaled( 11280 isl_ctx *ctx); 11281 isl_stat isl_options_set_schedule_treat_coalescing( 11282 isl_ctx *ctx, int val); 11283 int isl_options_get_schedule_treat_coalescing( 11284 isl_ctx *ctx); 11285 isl_stat isl_options_set_schedule_algorithm( 11286 isl_ctx *ctx, int val); 11287 int isl_options_get_schedule_algorithm( 11288 isl_ctx *ctx); 11289 isl_stat isl_options_set_schedule_carry_self_first( 11290 isl_ctx *ctx, int val); 11291 int isl_options_get_schedule_carry_self_first( 11292 isl_ctx *ctx); 11293 isl_stat isl_options_set_schedule_separate_components( 11294 isl_ctx *ctx, int val); 11295 int isl_options_get_schedule_separate_components( 11296 isl_ctx *ctx); 11297 11298=over 11299 11300=item * schedule_max_coefficient 11301 11302This option enforces that the coefficients for variable and parameter 11303dimensions in the calculated schedule are not larger than the specified value. 11304This option can significantly increase the speed of the scheduling calculation 11305and may also prevent fusing of unrelated dimensions. A value of -1 means that 11306this option does not introduce bounds on the variable or parameter 11307coefficients. 11308This option has no effect on the Feautrier style scheduler. 11309 11310=item * schedule_max_constant_term 11311 11312This option enforces that the constant coefficients in the calculated schedule 11313are not larger than the maximal constant term. This option can significantly 11314increase the speed of the scheduling calculation and may also prevent fusing of 11315unrelated dimensions. A value of -1 means that this option does not introduce 11316bounds on the constant coefficients. 11317 11318=item * schedule_serialize_sccs 11319 11320If this option is set, then all strongly connected components 11321in the dependence graph are serialized as soon as they are detected. 11322This means in particular that instances of statements will only 11323appear in the same band node if these statements belong 11324to the same strongly connected component at the point where 11325the band node is constructed. 11326 11327=item * schedule_whole_component 11328 11329If this option is set, then entire (weakly) connected 11330components in the dependence graph are scheduled together 11331as a whole. 11332Otherwise, each strongly connected component within 11333such a weakly connected component is first scheduled separately 11334and then combined with other strongly connected components. 11335This option has no effect if C<schedule_serialize_sccs> is set. 11336 11337=item * schedule_maximize_band_depth 11338 11339If this option is set, then the scheduler tries to maximize 11340the width of the bands. Wider bands give more possibilities for tiling. 11341In particular, if the C<schedule_whole_component> option is set, 11342then bands are split if this might result in wider bands. 11343Otherwise, the effect of this option is to only allow 11344strongly connected components to be combined if this does 11345not reduce the width of the bands. 11346Note that if the C<schedule_serialize_sccs> options is set, then 11347the C<schedule_maximize_band_depth> option therefore has no effect. 11348 11349=item * schedule_maximize_coincidence 11350 11351This option is only effective if the C<schedule_whole_component> 11352option is turned off. 11353If the C<schedule_maximize_coincidence> option is set, then (clusters of) 11354strongly connected components are only combined with each other 11355if this does not reduce the number of coincident band members. 11356 11357=item * schedule_outer_coincidence 11358 11359If this option is set, then we try to construct schedules 11360where the outermost scheduling dimension in each band 11361satisfies the coincidence constraints. 11362 11363=item * schedule_algorithm 11364 11365Selects the scheduling algorithm to be used. 11366Available scheduling algorithms are C<ISL_SCHEDULE_ALGORITHM_ISL> 11367and C<ISL_SCHEDULE_ALGORITHM_FEAUTRIER>. 11368 11369=item * schedule_split_scaled 11370 11371If this option is set, then we try to construct schedules in which the 11372constant term is split off from the linear part if the linear parts of 11373the scheduling rows for all nodes in the graph have a common non-trivial 11374divisor. 11375The constant term is then dropped and the linear 11376part is reduced. 11377This option is only effective when the Feautrier style scheduler is 11378being used, either as the main scheduler or as a fallback for the 11379Pluto-like scheduler. 11380 11381=item * schedule_treat_coalescing 11382 11383If this option is set, then the scheduler will try and avoid 11384producing schedules that perform loop coalescing. 11385In particular, for the Pluto-like scheduler, this option places 11386bounds on the schedule coefficients based on the sizes of the instance sets. 11387For the Feautrier style scheduler, this option detects potentially 11388coalescing schedules and then tries to adjust the schedule to avoid 11389the coalescing. 11390 11391=item * schedule_carry_self_first 11392 11393If this option is set, then the Feautrier style scheduler 11394(when used as a fallback for the Pluto-like scheduler) will 11395first try to only carry self-dependences. 11396 11397=item * schedule_separate_components 11398 11399If this option is set then the function C<isl_schedule_get_map> 11400will treat set nodes in the same way as sequence nodes. 11401 11402=back 11403 11404=head2 AST Generation 11405 11406This section describes the C<isl> functionality for generating 11407ASTs that visit all the elements 11408in a domain in an order specified by a schedule tree or 11409a schedule map. 11410In case the schedule given as a C<isl_union_map>, an AST is generated 11411that visits all the elements in the domain of the C<isl_union_map> 11412according to the lexicographic order of the corresponding image 11413element(s). If the range of the C<isl_union_map> consists of 11414elements in more than one space, then each of these spaces is handled 11415separately in an arbitrary order. 11416It should be noted that the schedule tree or the image elements 11417in a schedule map only specify the I<order> 11418in which the corresponding domain elements should be visited. 11419No direct relation between the partial schedule values 11420or the image elements on the one hand and the loop iterators 11421in the generated AST on the other hand should be assumed. 11422 11423Each AST is generated within a build. The initial build 11424simply specifies the constraints on the parameters (if any) 11425and can be created, inspected, copied and freed using the following functions. 11426 11427 #include <isl/ast_build.h> 11428 __isl_give isl_ast_build *isl_ast_build_alloc( 11429 isl_ctx *ctx); 11430 __isl_give isl_ast_build *isl_ast_build_from_context( 11431 __isl_take isl_set *set); 11432 __isl_give isl_ast_build *isl_ast_build_copy( 11433 __isl_keep isl_ast_build *build); 11434 __isl_null isl_ast_build *isl_ast_build_free( 11435 __isl_take isl_ast_build *build); 11436 11437The C<set> argument is usually a parameter set with zero or more parameters. 11438In fact, when creating an AST using C<isl_ast_build_node_from_schedule>, 11439this set is required to be a parameter set. 11440An C<isl_ast_build> created using C<isl_ast_build_alloc> does not 11441specify any parameter constraints. 11442More C<isl_ast_build> functions are described in L</"Nested AST Generation"> 11443and L</"Fine-grained Control over AST Generation">. 11444Finally, the AST itself can be constructed using one of the following 11445functions. 11446 11447 #include <isl/ast_build.h> 11448 __isl_give isl_ast_node *isl_ast_build_node_from_schedule( 11449 __isl_keep isl_ast_build *build, 11450 __isl_take isl_schedule *schedule); 11451 __isl_give isl_ast_node * 11452 isl_ast_build_node_from_schedule_map( 11453 __isl_keep isl_ast_build *build, 11454 __isl_take isl_union_map *schedule); 11455 11456=head3 Inspecting the AST 11457 11458The basic properties of an AST node can be obtained as follows. 11459 11460 #include <isl/ast.h> 11461 enum isl_ast_node_type isl_ast_node_get_type( 11462 __isl_keep isl_ast_node *node); 11463 11464The type of an AST node is one of 11465C<isl_ast_node_for>, 11466C<isl_ast_node_if>, 11467C<isl_ast_node_block>, 11468C<isl_ast_node_mark> or 11469C<isl_ast_node_user>. 11470An C<isl_ast_node_for> represents a for node. 11471An C<isl_ast_node_if> represents an if node. 11472An C<isl_ast_node_block> represents a compound node. 11473An C<isl_ast_node_mark> introduces a mark in the AST. 11474An C<isl_ast_node_user> represents an expression statement. 11475An expression statement typically corresponds to a domain element, i.e., 11476one of the elements that is visited by the AST. 11477 11478Each type of node has its own additional properties. 11479 11480 #include <isl/ast.h> 11481 __isl_give isl_ast_expr *isl_ast_node_for_get_iterator( 11482 __isl_keep isl_ast_node *node); 11483 __isl_give isl_ast_expr *isl_ast_node_for_get_init( 11484 __isl_keep isl_ast_node *node); 11485 __isl_give isl_ast_expr *isl_ast_node_for_get_cond( 11486 __isl_keep isl_ast_node *node); 11487 __isl_give isl_ast_expr *isl_ast_node_for_get_inc( 11488 __isl_keep isl_ast_node *node); 11489 __isl_give isl_ast_node *isl_ast_node_for_get_body( 11490 __isl_keep isl_ast_node *node); 11491 isl_bool isl_ast_node_for_is_degenerate( 11492 __isl_keep isl_ast_node *node); 11493 11494An C<isl_ast_for> is considered degenerate if it is known to execute 11495exactly once. 11496 11497 #include <isl/ast.h> 11498 __isl_give isl_ast_expr *isl_ast_node_if_get_cond( 11499 __isl_keep isl_ast_node *node); 11500 __isl_give isl_ast_node *isl_ast_node_if_get_then_node( 11501 __isl_keep isl_ast_node *node); 11502 __isl_give isl_ast_node *isl_ast_node_if_get_then( 11503 __isl_keep isl_ast_node *node); 11504 isl_bool isl_ast_node_if_has_else_node( 11505 __isl_keep isl_ast_node *node); 11506 isl_bool isl_ast_node_if_has_else( 11507 __isl_keep isl_ast_node *node); 11508 __isl_give isl_ast_node *isl_ast_node_if_get_else_node( 11509 __isl_keep isl_ast_node *node); 11510 __isl_give isl_ast_node *isl_ast_node_if_get_else( 11511 __isl_keep isl_ast_node *node); 11512 11513C<isl_ast_node_if_get_then>, 11514C<isl_ast_node_if_has_else> and 11515C<isl_ast_node_if_get_else> 11516are alternative names for 11517C<isl_ast_node_if_get_then_node>, 11518C<isl_ast_node_if_has_else_node> and 11519C<isl_ast_node_if_get_else_node>, respectively. 11520 11521 __isl_give isl_ast_node_list * 11522 isl_ast_node_block_get_children( 11523 __isl_keep isl_ast_node *node); 11524 11525 __isl_give isl_id *isl_ast_node_mark_get_id( 11526 __isl_keep isl_ast_node *node); 11527 __isl_give isl_ast_node *isl_ast_node_mark_get_node( 11528 __isl_keep isl_ast_node *node); 11529 11530C<isl_ast_node_mark_get_id> returns the identifier of the mark. 11531C<isl_ast_node_mark_get_node> returns the child node that is being marked. 11532 11533 #include <isl/ast.h> 11534 __isl_give isl_ast_expr *isl_ast_node_user_get_expr( 11535 __isl_keep isl_ast_node *node); 11536 11537All descendants of a specific node in the AST (including the node itself) 11538can be visited 11539in depth-first pre-order using the following function. 11540 11541 #include <isl/ast.h> 11542 isl_stat isl_ast_node_foreach_descendant_top_down( 11543 __isl_keep isl_ast_node *node, 11544 isl_bool (*fn)(__isl_keep isl_ast_node *node, 11545 void *user), void *user); 11546 11547The callback function should return C<isl_bool_true> if the children 11548of the given node should be visited and C<isl_bool_false> if they should not. 11549It should return C<isl_bool_error> in case of failure, in which case 11550the entire traversal is aborted. 11551 11552Each of the returned C<isl_ast_expr>s can in turn be inspected using 11553the following functions. 11554 11555 #include <isl/ast.h> 11556 enum isl_ast_expr_type isl_ast_expr_get_type( 11557 __isl_keep isl_ast_expr *expr); 11558 11559The type of an AST expression is one of 11560C<isl_ast_expr_op>, 11561C<isl_ast_expr_id> or 11562C<isl_ast_expr_int>. 11563An C<isl_ast_expr_op> represents the result of an operation. 11564An C<isl_ast_expr_id> represents an identifier. 11565An C<isl_ast_expr_int> represents an integer value. 11566 11567Each type of expression has its own additional properties. 11568 11569 #include <isl/ast.h> 11570 enum isl_ast_expr_op_type isl_ast_expr_op_get_type( 11571 __isl_keep isl_ast_expr *expr); 11572 enum isl_ast_expr_op_type isl_ast_expr_get_op_type( 11573 __isl_keep isl_ast_expr *expr); 11574 isl_size isl_ast_expr_op_get_n_arg(__isl_keep isl_ast_expr *expr); 11575 isl_size isl_ast_expr_get_op_n_arg(__isl_keep isl_ast_expr *expr); 11576 __isl_give isl_ast_expr *isl_ast_expr_op_get_arg( 11577 __isl_keep isl_ast_expr *expr, int pos); 11578 __isl_give isl_ast_expr *isl_ast_expr_get_op_arg( 11579 __isl_keep isl_ast_expr *expr, int pos); 11580 isl_stat isl_ast_expr_foreach_ast_expr_op_type( 11581 __isl_keep isl_ast_expr *expr, 11582 isl_stat (*fn)(enum isl_ast_expr_op_type type, 11583 void *user), void *user); 11584 isl_stat isl_ast_expr_foreach_ast_op_type( 11585 __isl_keep isl_ast_expr *expr, 11586 isl_stat (*fn)(enum isl_ast_expr_op_type type, 11587 void *user), void *user); 11588 isl_stat isl_ast_node_foreach_ast_expr_op_type( 11589 __isl_keep isl_ast_node *node, 11590 isl_stat (*fn)(enum isl_ast_expr_op_type type, 11591 void *user), void *user); 11592 isl_stat isl_ast_node_foreach_ast_op_type( 11593 __isl_keep isl_ast_node *node, 11594 isl_stat (*fn)(enum isl_ast_expr_op_type type, 11595 void *user), void *user); 11596 11597C<isl_ast_expr_op_get_type> returns the type of the operation 11598performed. C<isl_ast_expr_op_get_n_arg> returns the number of 11599arguments. C<isl_ast_expr_get_op_arg> returns the specified 11600argument. 11601C<isl_ast_expr_get_op_type> is an alternative name for 11602C<isl_ast_expr_op_get_type>. 11603Similarly, 11604C<isl_ast_expr_get_op_n_arg> is an alternative name for 11605C<isl_ast_expr_op_get_n_arg> and 11606C<isl_ast_expr_get_op_arg> is an alternative name for 11607C<isl_ast_expr_op_get_arg>. 11608 11609C<isl_ast_expr_foreach_ast_expr_op_type> calls C<fn> for each distinct 11610C<isl_ast_expr_op_type> that appears in C<expr>. 11611C<isl_ast_expr_foreach_ast_op_type> is an alternative name for 11612C<isl_ast_expr_foreach_ast_expr_op_type>. 11613C<isl_ast_node_foreach_ast_expr_op_type> does the same for each distinct 11614C<isl_ast_expr_op_type> that appears in C<node>. 11615C<isl_ast_node_foreach_ast_op_type> is an alternative name for 11616C<isl_ast_node_foreach_ast_expr_op_type>. 11617The operation type is one of the following. 11618 11619=over 11620 11621=item C<isl_ast_expr_op_and> 11622 11623Logical I<and> of two arguments. 11624Both arguments can be evaluated. 11625 11626=item C<isl_ast_expr_op_and_then> 11627 11628Logical I<and> of two arguments. 11629The second argument can only be evaluated if the first evaluates to true. 11630 11631=item C<isl_ast_expr_op_or> 11632 11633Logical I<or> of two arguments. 11634Both arguments can be evaluated. 11635 11636=item C<isl_ast_expr_op_or_else> 11637 11638Logical I<or> of two arguments. 11639The second argument can only be evaluated if the first evaluates to false. 11640 11641=item C<isl_ast_expr_op_max> 11642 11643Maximum of two or more arguments. 11644 11645=item C<isl_ast_expr_op_min> 11646 11647Minimum of two or more arguments. 11648 11649=item C<isl_ast_expr_op_minus> 11650 11651Change sign. 11652 11653=item C<isl_ast_expr_op_add> 11654 11655Sum of two arguments. 11656 11657=item C<isl_ast_expr_op_sub> 11658 11659Difference of two arguments. 11660 11661=item C<isl_ast_expr_op_mul> 11662 11663Product of two arguments. 11664 11665=item C<isl_ast_expr_op_div> 11666 11667Exact division. That is, the result is known to be an integer. 11668 11669=item C<isl_ast_expr_op_fdiv_q> 11670 11671Result of integer division, rounded towards negative 11672infinity. 11673The divisor is known to be positive. 11674 11675=item C<isl_ast_expr_op_pdiv_q> 11676 11677Result of integer division, where dividend is known to be non-negative. 11678The divisor is known to be positive. 11679 11680=item C<isl_ast_expr_op_pdiv_r> 11681 11682Remainder of integer division, where dividend is known to be non-negative. 11683The divisor is known to be positive. 11684 11685=item C<isl_ast_expr_op_zdiv_r> 11686 11687Equal to zero iff the remainder on integer division is zero. 11688The divisor is known to be positive. 11689 11690=item C<isl_ast_expr_op_cond> 11691 11692Conditional operator defined on three arguments. 11693If the first argument evaluates to true, then the result 11694is equal to the second argument. Otherwise, the result 11695is equal to the third argument. 11696The second and third argument may only be evaluated if 11697the first argument evaluates to true and false, respectively. 11698Corresponds to C<a ? b : c> in C. 11699 11700=item C<isl_ast_expr_op_select> 11701 11702Conditional operator defined on three arguments. 11703If the first argument evaluates to true, then the result 11704is equal to the second argument. Otherwise, the result 11705is equal to the third argument. 11706The second and third argument may be evaluated independently 11707of the value of the first argument. 11708Corresponds to C<a * b + (1 - a) * c> in C. 11709 11710=item C<isl_ast_expr_op_eq> 11711 11712Equality relation. 11713 11714=item C<isl_ast_expr_op_le> 11715 11716Less than or equal relation. 11717 11718=item C<isl_ast_expr_op_lt> 11719 11720Less than relation. 11721 11722=item C<isl_ast_expr_op_ge> 11723 11724Greater than or equal relation. 11725 11726=item C<isl_ast_expr_op_gt> 11727 11728Greater than relation. 11729 11730=item C<isl_ast_expr_op_call> 11731 11732A function call. 11733The number of arguments of the C<isl_ast_expr> is one more than 11734the number of arguments in the function call, the first argument 11735representing the function being called. 11736 11737=item C<isl_ast_expr_op_access> 11738 11739An array access. 11740The number of arguments of the C<isl_ast_expr> is one more than 11741the number of index expressions in the array access, the first argument 11742representing the array being accessed. 11743 11744=item C<isl_ast_expr_op_member> 11745 11746A member access. 11747This operation has two arguments, a structure and the name of 11748the member of the structure being accessed. 11749 11750=back 11751 11752 #include <isl/ast.h> 11753 __isl_give isl_id *isl_ast_expr_id_get_id( 11754 __isl_keep isl_ast_expr *expr); 11755 __isl_give isl_id *isl_ast_expr_get_id( 11756 __isl_keep isl_ast_expr *expr); 11757 11758Return the identifier represented by the AST expression. 11759C<isl_ast_expr_get_id> is an alternative name for 11760C<isl_ast_expr_id_get_id>. 11761 11762 #include <isl/ast.h> 11763 __isl_give isl_val *isl_ast_expr_int_get_val( 11764 __isl_keep isl_ast_expr *expr); 11765 __isl_give isl_val *isl_ast_expr_get_val( 11766 __isl_keep isl_ast_expr *expr); 11767 11768Return the integer represented by the AST expression. 11769C<isl_ast_expr_get_val> is an alternative name for 11770C<isl_ast_expr_int_get_val>. 11771 11772=head3 Properties of ASTs 11773 11774 #include <isl/ast.h> 11775 isl_bool isl_ast_expr_is_equal( 11776 __isl_keep isl_ast_expr *expr1, 11777 __isl_keep isl_ast_expr *expr2); 11778 11779Check if two C<isl_ast_expr>s are equal to each other. 11780 11781=head3 Manipulating and printing the AST 11782 11783AST nodes can be copied and freed using the following functions. 11784 11785 #include <isl/ast.h> 11786 __isl_give isl_ast_node *isl_ast_node_copy( 11787 __isl_keep isl_ast_node *node); 11788 __isl_null isl_ast_node *isl_ast_node_free( 11789 __isl_take isl_ast_node *node); 11790 11791AST expressions can be copied and freed using the following functions. 11792 11793 #include <isl/ast.h> 11794 __isl_give isl_ast_expr *isl_ast_expr_copy( 11795 __isl_keep isl_ast_expr *expr); 11796 __isl_null isl_ast_expr *isl_ast_expr_free( 11797 __isl_take isl_ast_expr *expr); 11798 11799New AST expressions can be created either directly or within 11800the context of an C<isl_ast_build>. 11801 11802 #include <isl/ast.h> 11803 __isl_give isl_ast_expr *isl_ast_expr_from_val( 11804 __isl_take isl_val *v); 11805 __isl_give isl_ast_expr *isl_ast_expr_from_id( 11806 __isl_take isl_id *id); 11807 __isl_give isl_ast_expr *isl_ast_expr_neg( 11808 __isl_take isl_ast_expr *expr); 11809 __isl_give isl_ast_expr *isl_ast_expr_address_of( 11810 __isl_take isl_ast_expr *expr); 11811 __isl_give isl_ast_expr *isl_ast_expr_add( 11812 __isl_take isl_ast_expr *expr1, 11813 __isl_take isl_ast_expr *expr2); 11814 __isl_give isl_ast_expr *isl_ast_expr_sub( 11815 __isl_take isl_ast_expr *expr1, 11816 __isl_take isl_ast_expr *expr2); 11817 __isl_give isl_ast_expr *isl_ast_expr_mul( 11818 __isl_take isl_ast_expr *expr1, 11819 __isl_take isl_ast_expr *expr2); 11820 __isl_give isl_ast_expr *isl_ast_expr_div( 11821 __isl_take isl_ast_expr *expr1, 11822 __isl_take isl_ast_expr *expr2); 11823 __isl_give isl_ast_expr *isl_ast_expr_pdiv_q( 11824 __isl_take isl_ast_expr *expr1, 11825 __isl_take isl_ast_expr *expr2); 11826 __isl_give isl_ast_expr *isl_ast_expr_pdiv_r( 11827 __isl_take isl_ast_expr *expr1, 11828 __isl_take isl_ast_expr *expr2); 11829 __isl_give isl_ast_expr *isl_ast_expr_and( 11830 __isl_take isl_ast_expr *expr1, 11831 __isl_take isl_ast_expr *expr2) 11832 __isl_give isl_ast_expr *isl_ast_expr_and_then( 11833 __isl_take isl_ast_expr *expr1, 11834 __isl_take isl_ast_expr *expr2) 11835 __isl_give isl_ast_expr *isl_ast_expr_or( 11836 __isl_take isl_ast_expr *expr1, 11837 __isl_take isl_ast_expr *expr2) 11838 __isl_give isl_ast_expr *isl_ast_expr_or_else( 11839 __isl_take isl_ast_expr *expr1, 11840 __isl_take isl_ast_expr *expr2) 11841 __isl_give isl_ast_expr *isl_ast_expr_eq( 11842 __isl_take isl_ast_expr *expr1, 11843 __isl_take isl_ast_expr *expr2); 11844 __isl_give isl_ast_expr *isl_ast_expr_le( 11845 __isl_take isl_ast_expr *expr1, 11846 __isl_take isl_ast_expr *expr2); 11847 __isl_give isl_ast_expr *isl_ast_expr_lt( 11848 __isl_take isl_ast_expr *expr1, 11849 __isl_take isl_ast_expr *expr2); 11850 __isl_give isl_ast_expr *isl_ast_expr_ge( 11851 __isl_take isl_ast_expr *expr1, 11852 __isl_take isl_ast_expr *expr2); 11853 __isl_give isl_ast_expr *isl_ast_expr_gt( 11854 __isl_take isl_ast_expr *expr1, 11855 __isl_take isl_ast_expr *expr2); 11856 __isl_give isl_ast_expr *isl_ast_expr_access( 11857 __isl_take isl_ast_expr *array, 11858 __isl_take isl_ast_expr_list *indices); 11859 __isl_give isl_ast_expr *isl_ast_expr_call( 11860 __isl_take isl_ast_expr *function, 11861 __isl_take isl_ast_expr_list *arguments); 11862 11863The function C<isl_ast_expr_address_of> can be applied to an 11864C<isl_ast_expr> of type C<isl_ast_expr_op_access> only. It is meant 11865to represent the address of the C<isl_ast_expr_access>. 11866The second argument of the functions C<isl_ast_expr_pdiv_q> and 11867C<isl_ast_expr_pdiv_r> should always evaluate to a positive number. 11868The function 11869C<isl_ast_expr_and_then> as well as C<isl_ast_expr_or_else> are short-circuit 11870versions of C<isl_ast_expr_and> and C<isl_ast_expr_or>, respectively. 11871 11872 #include <isl/ast_build.h> 11873 __isl_give isl_ast_expr *isl_ast_build_expr_from_set( 11874 __isl_keep isl_ast_build *build, 11875 __isl_take isl_set *set); 11876 __isl_give isl_ast_expr *isl_ast_build_expr_from_pw_aff( 11877 __isl_keep isl_ast_build *build, 11878 __isl_take isl_pw_aff *pa); 11879 __isl_give isl_ast_expr * 11880 isl_ast_build_access_from_pw_multi_aff( 11881 __isl_keep isl_ast_build *build, 11882 __isl_take isl_pw_multi_aff *pma); 11883 __isl_give isl_ast_expr * 11884 isl_ast_build_access_from_multi_pw_aff( 11885 __isl_keep isl_ast_build *build, 11886 __isl_take isl_multi_pw_aff *mpa); 11887 __isl_give isl_ast_expr * 11888 isl_ast_build_call_from_pw_multi_aff( 11889 __isl_keep isl_ast_build *build, 11890 __isl_take isl_pw_multi_aff *pma); 11891 __isl_give isl_ast_expr * 11892 isl_ast_build_call_from_multi_pw_aff( 11893 __isl_keep isl_ast_build *build, 11894 __isl_take isl_multi_pw_aff *mpa); 11895 11896The set C<set> and 11897the domains of C<pa>, C<mpa> and C<pma> should correspond 11898to the schedule space of C<build>. 11899The tuple id of C<mpa> or C<pma> is used as the array being accessed or 11900the function being called. 11901If the accessed space is a nested relation, then it is taken 11902to represent an access of the member specified by the range 11903of this nested relation of the structure specified by the domain 11904of the nested relation. 11905 11906The following functions can be used to modify an C<isl_ast_expr>. 11907 11908 #include <isl/ast.h> 11909 __isl_give isl_ast_expr *isl_ast_expr_set_op_arg( 11910 __isl_take isl_ast_expr *expr, int pos, 11911 __isl_take isl_ast_expr *arg); 11912 11913Replace the argument of C<expr> at position C<pos> by C<arg>. 11914 11915 #include <isl/ast.h> 11916 __isl_give isl_ast_expr *isl_ast_expr_substitute_ids( 11917 __isl_take isl_ast_expr *expr, 11918 __isl_take isl_id_to_ast_expr *id2expr); 11919 11920The function C<isl_ast_expr_substitute_ids> replaces the 11921subexpressions of C<expr> of type C<isl_ast_expr_id> 11922by the corresponding expression in C<id2expr>, if there is any. 11923 11924 11925User specified data can be attached to an C<isl_ast_node> and obtained 11926from the same C<isl_ast_node> using the following functions. 11927 11928 #include <isl/ast.h> 11929 __isl_give isl_ast_node *isl_ast_node_set_annotation( 11930 __isl_take isl_ast_node *node, 11931 __isl_take isl_id *annotation); 11932 __isl_give isl_id *isl_ast_node_get_annotation( 11933 __isl_keep isl_ast_node *node); 11934 11935Basic printing can be performed using the following functions. 11936 11937 #include <isl/ast.h> 11938 __isl_give isl_printer *isl_printer_print_ast_expr( 11939 __isl_take isl_printer *p, 11940 __isl_keep isl_ast_expr *expr); 11941 __isl_give isl_printer *isl_printer_print_ast_node( 11942 __isl_take isl_printer *p, 11943 __isl_keep isl_ast_node *node); 11944 __isl_give char *isl_ast_expr_to_str( 11945 __isl_keep isl_ast_expr *expr); 11946 __isl_give char *isl_ast_node_to_str( 11947 __isl_keep isl_ast_node *node); 11948 __isl_give char *isl_ast_expr_to_C_str( 11949 __isl_keep isl_ast_expr *expr); 11950 __isl_give char *isl_ast_node_to_C_str( 11951 __isl_keep isl_ast_node *node); 11952 11953The functions C<isl_ast_expr_to_C_str> and 11954C<isl_ast_node_to_C_str> are convenience functions 11955that return a string representation of the input in C format. 11956 11957More advanced printing can be performed using the following functions. 11958 11959 #include <isl/ast.h> 11960 __isl_give isl_printer * 11961 isl_ast_expr_op_type_set_print_name( 11962 __isl_take isl_printer *p, 11963 enum isl_ast_expr_op_type type, 11964 __isl_keep const char *name); 11965 __isl_give isl_printer *isl_ast_op_type_set_print_name( 11966 __isl_take isl_printer *p, 11967 enum isl_ast_expr_op_type type, 11968 __isl_keep const char *name); 11969 isl_stat isl_options_set_ast_print_macro_once( 11970 isl_ctx *ctx, int val); 11971 int isl_options_get_ast_print_macro_once(isl_ctx *ctx); 11972 __isl_give isl_printer *isl_ast_expr_op_type_print_macro( 11973 enum isl_ast_expr_op_type type, 11974 __isl_take isl_printer *p); 11975 __isl_give isl_printer *isl_ast_op_type_print_macro( 11976 enum isl_ast_expr_op_type type, 11977 __isl_take isl_printer *p); 11978 __isl_give isl_printer *isl_ast_expr_print_macros( 11979 __isl_keep isl_ast_expr *expr, 11980 __isl_take isl_printer *p); 11981 __isl_give isl_printer *isl_ast_node_print_macros( 11982 __isl_keep isl_ast_node *node, 11983 __isl_take isl_printer *p); 11984 __isl_give isl_printer *isl_ast_node_print( 11985 __isl_keep isl_ast_node *node, 11986 __isl_take isl_printer *p, 11987 __isl_take isl_ast_print_options *options); 11988 __isl_give isl_printer *isl_ast_node_for_print( 11989 __isl_keep isl_ast_node *node, 11990 __isl_take isl_printer *p, 11991 __isl_take isl_ast_print_options *options); 11992 __isl_give isl_printer *isl_ast_node_if_print( 11993 __isl_keep isl_ast_node *node, 11994 __isl_take isl_printer *p, 11995 __isl_take isl_ast_print_options *options); 11996 11997While printing an C<isl_ast_node> in C<ISL_FORMAT_C>, 11998C<isl> may print out an AST that makes use of macros such 11999as C<floord>, C<min> and C<max>. 12000The names of these macros may be modified by a call 12001to C<isl_ast_expr_op_type_set_print_name>. The user-specified 12002names are associated to the printer object. 12003C<isl_ast_op_type_set_print_name> is an alternative name for 12004C<isl_ast_expr_op_type_set_print_name>. 12005C<isl_ast_expr_op_type_print_macro> prints out the macro 12006corresponding to a specific C<isl_ast_expr_op_type>. 12007If the print-macro-once option is set, then a given macro definition 12008is only printed once to any given printer object. 12009C<isl_ast_op_type_print_macro> is an alternative name for 12010C<isl_ast_expr_op_type_print_macro>. 12011C<isl_ast_expr_print_macros> scans the C<isl_ast_expr> 12012for subexpressions where these macros would be used and prints 12013out the required macro definitions. 12014Essentially, C<isl_ast_expr_print_macros> calls 12015C<isl_ast_expr_foreach_ast_expr_op_type> with 12016C<isl_ast_expr_op_type_print_macro> 12017as function argument. 12018C<isl_ast_node_print_macros> does the same 12019for expressions in its C<isl_ast_node> argument. 12020C<isl_ast_node_print>, C<isl_ast_node_for_print> and 12021C<isl_ast_node_if_print> print an C<isl_ast_node> 12022in C<ISL_FORMAT_C>, but allow for some extra control 12023through an C<isl_ast_print_options> object. 12024This object can be created using the following functions. 12025 12026 #include <isl/ast.h> 12027 __isl_give isl_ast_print_options * 12028 isl_ast_print_options_alloc(isl_ctx *ctx); 12029 __isl_give isl_ast_print_options * 12030 isl_ast_print_options_copy( 12031 __isl_keep isl_ast_print_options *options); 12032 __isl_null isl_ast_print_options * 12033 isl_ast_print_options_free( 12034 __isl_take isl_ast_print_options *options); 12035 12036 __isl_give isl_ast_print_options * 12037 isl_ast_print_options_set_print_user( 12038 __isl_take isl_ast_print_options *options, 12039 __isl_give isl_printer *(*print_user)( 12040 __isl_take isl_printer *p, 12041 __isl_take isl_ast_print_options *options, 12042 __isl_keep isl_ast_node *node, void *user), 12043 void *user); 12044 __isl_give isl_ast_print_options * 12045 isl_ast_print_options_set_print_for( 12046 __isl_take isl_ast_print_options *options, 12047 __isl_give isl_printer *(*print_for)( 12048 __isl_take isl_printer *p, 12049 __isl_take isl_ast_print_options *options, 12050 __isl_keep isl_ast_node *node, void *user), 12051 void *user); 12052 12053The callback set by C<isl_ast_print_options_set_print_user> 12054is called whenever a node of type C<isl_ast_node_user> needs to 12055be printed. 12056The callback set by C<isl_ast_print_options_set_print_for> 12057is called whenever a node of type C<isl_ast_node_for> needs to 12058be printed. 12059Note that C<isl_ast_node_for_print> will I<not> call the 12060callback set by C<isl_ast_print_options_set_print_for> on the node 12061on which C<isl_ast_node_for_print> is called, but only on nested 12062nodes of type C<isl_ast_node_for>. It is therefore safe to 12063call C<isl_ast_node_for_print> from within the callback set by 12064C<isl_ast_print_options_set_print_for>. 12065 12066The following option determines the type to be used for iterators 12067while printing the AST. 12068 12069 isl_stat isl_options_set_ast_iterator_type( 12070 isl_ctx *ctx, const char *val); 12071 const char *isl_options_get_ast_iterator_type( 12072 isl_ctx *ctx); 12073 12074The AST printer only prints body nodes of C<if> and C<for> nodes 12075as blocks if these 12076blocks cannot be safely omitted. 12077For example, a C<for> node with one body node will not be 12078surrounded with braces in C<ISL_FORMAT_C>. 12079A block will always be printed by setting the following option. 12080 12081 isl_stat isl_options_set_ast_always_print_block(isl_ctx *ctx, 12082 int val); 12083 int isl_options_get_ast_always_print_block(isl_ctx *ctx); 12084 12085Explicit block nodes that appear inside the AST are always printed as blocks. 12086If the block node appears as the outermost node, 12087then it is only printed if the following option is set. 12088 12089 isl_stat isl_options_set_ast_print_outermost_block( 12090 isl_ctx *ctx, int val); 12091 int isl_options_get_ast_print_outermost_block( 12092 isl_ctx *ctx); 12093 12094=head3 Options 12095 12096 #include <isl/ast_build.h> 12097 isl_stat isl_options_set_ast_build_atomic_upper_bound( 12098 isl_ctx *ctx, int val); 12099 int isl_options_get_ast_build_atomic_upper_bound( 12100 isl_ctx *ctx); 12101 isl_stat isl_options_set_ast_build_prefer_pdiv(isl_ctx *ctx, 12102 int val); 12103 int isl_options_get_ast_build_prefer_pdiv(isl_ctx *ctx); 12104 isl_stat isl_options_set_ast_build_detect_min_max( 12105 isl_ctx *ctx, int val); 12106 int isl_options_get_ast_build_detect_min_max( 12107 isl_ctx *ctx); 12108 isl_stat isl_options_set_ast_build_exploit_nested_bounds( 12109 isl_ctx *ctx, int val); 12110 int isl_options_get_ast_build_exploit_nested_bounds( 12111 isl_ctx *ctx); 12112 isl_stat isl_options_set_ast_build_group_coscheduled( 12113 isl_ctx *ctx, int val); 12114 int isl_options_get_ast_build_group_coscheduled( 12115 isl_ctx *ctx); 12116 isl_stat isl_options_set_ast_build_separation_bounds( 12117 isl_ctx *ctx, int val); 12118 int isl_options_get_ast_build_separation_bounds( 12119 isl_ctx *ctx); 12120 isl_stat isl_options_set_ast_build_scale_strides( 12121 isl_ctx *ctx, int val); 12122 int isl_options_get_ast_build_scale_strides( 12123 isl_ctx *ctx); 12124 isl_stat isl_options_set_ast_build_allow_else(isl_ctx *ctx, 12125 int val); 12126 int isl_options_get_ast_build_allow_else(isl_ctx *ctx); 12127 isl_stat isl_options_set_ast_build_allow_or(isl_ctx *ctx, 12128 int val); 12129 int isl_options_get_ast_build_allow_or(isl_ctx *ctx); 12130 12131=over 12132 12133=item * ast_build_atomic_upper_bound 12134 12135Generate loop upper bounds that consist of the current loop iterator, 12136an operator and an expression not involving the iterator. 12137If this option is not set, then the current loop iterator may appear 12138several times in the upper bound. 12139For example, when this option is turned off, AST generation 12140for the schedule 12141 12142 [n] -> { A[i] -> [i] : 0 <= i <= 100, n } 12143 12144produces 12145 12146 for (int c0 = 0; c0 <= 100 && n >= c0; c0 += 1) 12147 A(c0); 12148 12149When the option is turned on, the following AST is generated 12150 12151 for (int c0 = 0; c0 <= min(100, n); c0 += 1) 12152 A(c0); 12153 12154=item * ast_build_prefer_pdiv 12155 12156If this option is turned off, then the AST generation will 12157produce ASTs that may only contain C<isl_ast_expr_op_fdiv_q> 12158operators, but no C<isl_ast_expr_op_pdiv_q> or 12159C<isl_ast_expr_op_pdiv_r> operators. 12160If this option is turned on, then C<isl> will try to convert 12161some of the C<isl_ast_expr_op_fdiv_q> operators to (expressions containing) 12162C<isl_ast_expr_op_pdiv_q> or C<isl_ast_expr_op_pdiv_r> operators. 12163 12164=item * ast_build_detect_min_max 12165 12166If this option is turned on, then C<isl> will try and detect 12167min or max-expressions when building AST expressions from 12168piecewise affine expressions. 12169 12170=item * ast_build_exploit_nested_bounds 12171 12172Simplify conditions based on bounds of nested for loops. 12173In particular, remove conditions that are implied by the fact 12174that one or more nested loops have at least one iteration, 12175meaning that the upper bound is at least as large as the lower bound. 12176For example, when this option is turned off, AST generation 12177for the schedule 12178 12179 [N,M] -> { A[i,j] -> [i,j] : 0 <= i <= N and 12180 0 <= j <= M } 12181 12182produces 12183 12184 if (M >= 0) 12185 for (int c0 = 0; c0 <= N; c0 += 1) 12186 for (int c1 = 0; c1 <= M; c1 += 1) 12187 A(c0, c1); 12188 12189When the option is turned on, the following AST is generated 12190 12191 for (int c0 = 0; c0 <= N; c0 += 1) 12192 for (int c1 = 0; c1 <= M; c1 += 1) 12193 A(c0, c1); 12194 12195=item * ast_build_group_coscheduled 12196 12197If two domain elements are assigned the same schedule point, then 12198they may be executed in any order and they may even appear in different 12199loops. If this options is set, then the AST generator will make 12200sure that coscheduled domain elements do not appear in separate parts 12201of the AST. This is useful in case of nested AST generation 12202if the outer AST generation is given only part of a schedule 12203and the inner AST generation should handle the domains that are 12204coscheduled by this initial part of the schedule together. 12205For example if an AST is generated for a schedule 12206 12207 { A[i] -> [0]; B[i] -> [0] } 12208 12209then the C<isl_ast_build_set_create_leaf> callback described 12210below may get called twice, once for each domain. 12211Setting this option ensures that the callback is only called once 12212on both domains together. 12213 12214=item * ast_build_separation_bounds 12215 12216This option specifies which bounds to use during separation. 12217If this option is set to C<ISL_AST_BUILD_SEPARATION_BOUNDS_IMPLICIT> 12218then all (possibly implicit) bounds on the current dimension will 12219be used during separation. 12220If this option is set to C<ISL_AST_BUILD_SEPARATION_BOUNDS_EXPLICIT> 12221then only those bounds that are explicitly available will 12222be used during separation. 12223 12224=item * ast_build_scale_strides 12225 12226This option specifies whether the AST generator is allowed 12227to scale down iterators of strided loops. 12228 12229=item * ast_build_allow_else 12230 12231This option specifies whether the AST generator is allowed 12232to construct if statements with else branches. 12233 12234=item * ast_build_allow_or 12235 12236This option specifies whether the AST generator is allowed 12237to construct if conditions with disjunctions. 12238 12239=back 12240 12241=head3 AST Generation Options (Schedule Tree) 12242 12243In case of AST construction from a schedule tree, the options 12244that control how an AST is created from the individual schedule 12245dimensions are stored in the band nodes of the tree 12246(see L</"Schedule Trees">). 12247 12248In particular, a schedule dimension can be handled in four 12249different ways, atomic, separate, unroll or the default. 12250This loop AST generation type can be set using 12251C<isl_schedule_node_band_member_set_ast_loop_type>. 12252Alternatively, 12253the first three can be selected by including a one-dimensional 12254element with as value the position of the schedule dimension 12255within the band and as name one of C<atomic>, C<separate> 12256or C<unroll> in the options 12257set by C<isl_schedule_node_band_set_ast_build_options>. 12258Only one of these three may be specified for 12259any given schedule dimension within a band node. 12260If none of these is specified, then the default 12261is used. The meaning of the options is as follows. 12262 12263=over 12264 12265=item C<atomic> 12266 12267When this option is specified, the AST generator will make 12268sure that a given domain space only appears in a single 12269loop at the specified level. 12270 12271For example, for the schedule tree 12272 12273 domain: "{ a[i] : 0 <= i < 10; b[i] : 0 <= i < 10 }" 12274 child: 12275 schedule: "[{ a[i] -> [i]; b[i] -> [i+1] }]" 12276 options: "{ atomic[x] }" 12277 12278the following AST will be generated 12279 12280 for (int c0 = 0; c0 <= 10; c0 += 1) { 12281 if (c0 >= 1) 12282 b(c0 - 1); 12283 if (c0 <= 9) 12284 a(c0); 12285 } 12286 12287On the other hand, for the schedule tree 12288 12289 domain: "{ a[i] : 0 <= i < 10; b[i] : 0 <= i < 10 }" 12290 child: 12291 schedule: "[{ a[i] -> [i]; b[i] -> [i+1] }]" 12292 options: "{ separate[x] }" 12293 12294the following AST will be generated 12295 12296 { 12297 a(0); 12298 for (int c0 = 1; c0 <= 9; c0 += 1) { 12299 b(c0 - 1); 12300 a(c0); 12301 } 12302 b(9); 12303 } 12304 12305If neither C<atomic> nor C<separate> is specified, then the AST generator 12306may produce either of these two results or some intermediate form. 12307 12308=item C<separate> 12309 12310When this option is specified, the AST generator will 12311split the domain of the specified schedule dimension 12312into pieces with a fixed set of statements for which 12313instances need to be executed by the iterations in 12314the schedule domain part. This option tends to avoid 12315the generation of guards inside the corresponding loops. 12316See also the C<atomic> option. 12317 12318=item C<unroll> 12319 12320When this option is specified, the AST generator will 12321I<completely> unroll the corresponding schedule dimension. 12322It is the responsibility of the user to ensure that such 12323unrolling is possible. 12324To obtain a partial unrolling, the user should apply an additional 12325strip-mining to the schedule and fully unroll the inner schedule 12326dimension. 12327 12328=back 12329 12330The C<isolate> option is a bit more involved. It allows the user 12331to isolate a range of schedule dimension values from smaller and 12332greater values. Additionally, the user may specify a different 12333atomic/separate/unroll choice for the isolated part and the remaining 12334parts. The typical use case of the C<isolate> option is to isolate 12335full tiles from partial tiles. 12336The part that needs to be isolated may depend on outer schedule dimensions. 12337The option therefore needs to be able to reference those outer schedule 12338dimensions. In particular, the space of the C<isolate> option is that 12339of a wrapped map with as domain the flat product of all outer band nodes 12340and as range the space of the current band node. 12341The atomic/separate/unroll choice for the isolated part is determined 12342by an option that lives in an unnamed wrapped space with as domain 12343a zero-dimensional C<isolate> space and as range the regular 12344C<atomic>, C<separate> or C<unroll> space. 12345This option may also be set directly using 12346C<isl_schedule_node_band_member_set_isolate_ast_loop_type>. 12347The atomic/separate/unroll choice for the remaining part is determined 12348by the regular C<atomic>, C<separate> or C<unroll> option. 12349Since the C<isolate> option references outer schedule dimensions, 12350its use in a band node causes any tree containing the node 12351to be considered anchored. 12352 12353As an example, consider the isolation of full tiles from partial tiles 12354in a tiling of a triangular domain. The original schedule is as follows. 12355 12356 domain: "{ A[i,j] : 0 <= i,j and i + j <= 100 }" 12357 child: 12358 schedule: "[{ A[i,j] -> [floor(i/10)] }, \ 12359 { A[i,j] -> [floor(j/10)] }, \ 12360 { A[i,j] -> [i] }, { A[i,j] -> [j] }]" 12361 12362The output is 12363 12364 for (int c0 = 0; c0 <= 10; c0 += 1) 12365 for (int c1 = 0; c1 <= -c0 + 10; c1 += 1) 12366 for (int c2 = 10 * c0; 12367 c2 <= min(10 * c0 + 9, -10 * c1 + 100); c2 += 1) 12368 for (int c3 = 10 * c1; 12369 c3 <= min(10 * c1 + 9, -c2 + 100); c3 += 1) 12370 A(c2, c3); 12371 12372Isolating the full tiles, we have the following input 12373 12374 domain: "{ A[i,j] : 0 <= i,j and i + j <= 100 }" 12375 child: 12376 schedule: "[{ A[i,j] -> [floor(i/10)] }, \ 12377 { A[i,j] -> [floor(j/10)] }, \ 12378 { A[i,j] -> [i] }, { A[i,j] -> [j] }]" 12379 options: "{ isolate[[] -> [a,b,c,d]] : 0 <= 10a,10b and \ 12380 10a+9+10b+9 <= 100 }" 12381 12382and output 12383 12384 { 12385 for (int c0 = 0; c0 <= 8; c0 += 1) { 12386 for (int c1 = 0; c1 <= -c0 + 8; c1 += 1) 12387 for (int c2 = 10 * c0; 12388 c2 <= 10 * c0 + 9; c2 += 1) 12389 for (int c3 = 10 * c1; 12390 c3 <= 10 * c1 + 9; c3 += 1) 12391 A(c2, c3); 12392 for (int c1 = -c0 + 9; c1 <= -c0 + 10; c1 += 1) 12393 for (int c2 = 10 * c0; 12394 c2 <= min(10 * c0 + 9, -10 * c1 + 100); c2 += 1) 12395 for (int c3 = 10 * c1; 12396 c3 <= min(10 * c1 + 9, -c2 + 100); c3 += 1) 12397 A(c2, c3); 12398 } 12399 for (int c0 = 9; c0 <= 10; c0 += 1) 12400 for (int c1 = 0; c1 <= -c0 + 10; c1 += 1) 12401 for (int c2 = 10 * c0; 12402 c2 <= min(10 * c0 + 9, -10 * c1 + 100); c2 += 1) 12403 for (int c3 = 10 * c1; 12404 c3 <= min(10 * c1 + 9, -c2 + 100); c3 += 1) 12405 A(c2, c3); 12406 } 12407 12408We may then additionally unroll the innermost loop of the isolated part 12409 12410 domain: "{ A[i,j] : 0 <= i,j and i + j <= 100 }" 12411 child: 12412 schedule: "[{ A[i,j] -> [floor(i/10)] }, \ 12413 { A[i,j] -> [floor(j/10)] }, \ 12414 { A[i,j] -> [i] }, { A[i,j] -> [j] }]" 12415 options: "{ isolate[[] -> [a,b,c,d]] : 0 <= 10a,10b and \ 12416 10a+9+10b+9 <= 100; [isolate[] -> unroll[3]] }" 12417 12418to obtain 12419 12420 { 12421 for (int c0 = 0; c0 <= 8; c0 += 1) { 12422 for (int c1 = 0; c1 <= -c0 + 8; c1 += 1) 12423 for (int c2 = 10 * c0; c2 <= 10 * c0 + 9; c2 += 1) { 12424 A(c2, 10 * c1); 12425 A(c2, 10 * c1 + 1); 12426 A(c2, 10 * c1 + 2); 12427 A(c2, 10 * c1 + 3); 12428 A(c2, 10 * c1 + 4); 12429 A(c2, 10 * c1 + 5); 12430 A(c2, 10 * c1 + 6); 12431 A(c2, 10 * c1 + 7); 12432 A(c2, 10 * c1 + 8); 12433 A(c2, 10 * c1 + 9); 12434 } 12435 for (int c1 = -c0 + 9; c1 <= -c0 + 10; c1 += 1) 12436 for (int c2 = 10 * c0; 12437 c2 <= min(10 * c0 + 9, -10 * c1 + 100); c2 += 1) 12438 for (int c3 = 10 * c1; 12439 c3 <= min(10 * c1 + 9, -c2 + 100); c3 += 1) 12440 A(c2, c3); 12441 } 12442 for (int c0 = 9; c0 <= 10; c0 += 1) 12443 for (int c1 = 0; c1 <= -c0 + 10; c1 += 1) 12444 for (int c2 = 10 * c0; 12445 c2 <= min(10 * c0 + 9, -10 * c1 + 100); c2 += 1) 12446 for (int c3 = 10 * c1; 12447 c3 <= min(10 * c1 + 9, -c2 + 100); c3 += 1) 12448 A(c2, c3); 12449 } 12450 12451 12452=head3 AST Generation Options (Schedule Map) 12453 12454In case of AST construction using 12455C<isl_ast_build_node_from_schedule_map>, the options 12456that control how an AST is created from the individual schedule 12457dimensions are stored in the C<isl_ast_build>. 12458They can be set using the following function. 12459 12460 #include <isl/ast_build.h> 12461 __isl_give isl_ast_build * 12462 isl_ast_build_set_options( 12463 __isl_take isl_ast_build *build, 12464 __isl_take isl_union_map *options); 12465 12466The options are encoded in an C<isl_union_map>. 12467The domain of this union relation refers to the schedule domain, 12468i.e., the range of the schedule passed 12469to C<isl_ast_build_node_from_schedule_map>. 12470In the case of nested AST generation (see L</"Nested AST Generation">), 12471the domain of C<options> should refer to the extra piece of the schedule. 12472That is, it should be equal to the range of the wrapped relation in the 12473range of the schedule. 12474The range of the options can consist of elements in one or more spaces, 12475the names of which determine the effect of the option. 12476The values of the range typically also refer to the schedule dimension 12477to which the option applies, with value C<0> representing 12478the outermost schedule dimension. In case of nested AST generation 12479(see L</"Nested AST Generation">), these values refer to the position 12480of the schedule dimension within the innermost AST generation. 12481The constraints on the domain elements of 12482the option should only refer to this dimension and earlier dimensions. 12483We consider the following spaces. 12484 12485=over 12486 12487=item C<separation_class> 12488 12489B<This option has been deprecated. Use the isolate option on 12490schedule trees instead.> 12491 12492This space is a wrapped relation between two one dimensional spaces. 12493The input space represents the schedule dimension to which the option 12494applies and the output space represents the separation class. 12495While constructing a loop corresponding to the specified schedule 12496dimension(s), the AST generator will try to generate separate loops 12497for domain elements that are assigned different classes. 12498If only some of the elements are assigned a class, then those elements 12499that are not assigned any class will be treated as belonging to a class 12500that is separate from the explicitly assigned classes. 12501The typical use case for this option is to separate full tiles from 12502partial tiles. 12503The other options, described below, are applied after the separation 12504into classes. 12505 12506As an example, consider the separation into full and partial tiles 12507of a tiling of a triangular domain. 12508Take, for example, the domain 12509 12510 { A[i,j] : 0 <= i,j and i + j <= 100 } 12511 12512and a tiling into tiles of 10 by 10. The input to the AST generator 12513is then the schedule 12514 12515 { A[i,j] -> [([i/10]),[j/10],i,j] : 0 <= i,j and 12516 i + j <= 100 } 12517 12518Without any options, the following AST is generated 12519 12520 for (int c0 = 0; c0 <= 10; c0 += 1) 12521 for (int c1 = 0; c1 <= -c0 + 10; c1 += 1) 12522 for (int c2 = 10 * c0; 12523 c2 <= min(-10 * c1 + 100, 10 * c0 + 9); 12524 c2 += 1) 12525 for (int c3 = 10 * c1; 12526 c3 <= min(10 * c1 + 9, -c2 + 100); 12527 c3 += 1) 12528 A(c2, c3); 12529 12530Separation into full and partial tiles can be obtained by assigning 12531a class, say C<0>, to the full tiles. The full tiles are represented by those 12532values of the first and second schedule dimensions for which there are 12533values of the third and fourth dimensions to cover an entire tile. 12534That is, we need to specify the following option 12535 12536 { [a,b,c,d] -> separation_class[[0]->[0]] : 12537 exists b': 0 <= 10a,10b' and 12538 10a+9+10b'+9 <= 100; 12539 [a,b,c,d] -> separation_class[[1]->[0]] : 12540 0 <= 10a,10b and 10a+9+10b+9 <= 100 } 12541 12542which simplifies to 12543 12544 { [a, b, c, d] -> separation_class[[1] -> [0]] : 12545 a >= 0 and b >= 0 and b <= 8 - a; 12546 [a, b, c, d] -> separation_class[[0] -> [0]] : 12547 a >= 0 and a <= 8 } 12548 12549With this option, the generated AST is as follows 12550 12551 { 12552 for (int c0 = 0; c0 <= 8; c0 += 1) { 12553 for (int c1 = 0; c1 <= -c0 + 8; c1 += 1) 12554 for (int c2 = 10 * c0; 12555 c2 <= 10 * c0 + 9; c2 += 1) 12556 for (int c3 = 10 * c1; 12557 c3 <= 10 * c1 + 9; c3 += 1) 12558 A(c2, c3); 12559 for (int c1 = -c0 + 9; c1 <= -c0 + 10; c1 += 1) 12560 for (int c2 = 10 * c0; 12561 c2 <= min(-10 * c1 + 100, 10 * c0 + 9); 12562 c2 += 1) 12563 for (int c3 = 10 * c1; 12564 c3 <= min(-c2 + 100, 10 * c1 + 9); 12565 c3 += 1) 12566 A(c2, c3); 12567 } 12568 for (int c0 = 9; c0 <= 10; c0 += 1) 12569 for (int c1 = 0; c1 <= -c0 + 10; c1 += 1) 12570 for (int c2 = 10 * c0; 12571 c2 <= min(-10 * c1 + 100, 10 * c0 + 9); 12572 c2 += 1) 12573 for (int c3 = 10 * c1; 12574 c3 <= min(10 * c1 + 9, -c2 + 100); 12575 c3 += 1) 12576 A(c2, c3); 12577 } 12578 12579=item C<separate> 12580 12581This is a single-dimensional space representing the schedule dimension(s) 12582to which ``separation'' should be applied. Separation tries to split 12583a loop into several pieces if this can avoid the generation of guards 12584inside the loop. 12585See also the C<atomic> option. 12586 12587=item C<atomic> 12588 12589This is a single-dimensional space representing the schedule dimension(s) 12590for which the domains should be considered ``atomic''. That is, the 12591AST generator will make sure that any given domain space will only appear 12592in a single loop at the specified level. 12593 12594Consider the following schedule 12595 12596 { a[i] -> [i] : 0 <= i < 10; 12597 b[i] -> [i+1] : 0 <= i < 10 } 12598 12599If the following option is specified 12600 12601 { [i] -> separate[x] } 12602 12603then the following AST will be generated 12604 12605 { 12606 a(0); 12607 for (int c0 = 1; c0 <= 9; c0 += 1) { 12608 a(c0); 12609 b(c0 - 1); 12610 } 12611 b(9); 12612 } 12613 12614If, on the other hand, the following option is specified 12615 12616 { [i] -> atomic[x] } 12617 12618then the following AST will be generated 12619 12620 for (int c0 = 0; c0 <= 10; c0 += 1) { 12621 if (c0 <= 9) 12622 a(c0); 12623 if (c0 >= 1) 12624 b(c0 - 1); 12625 } 12626 12627If neither C<atomic> nor C<separate> is specified, then the AST generator 12628may produce either of these two results or some intermediate form. 12629 12630=item C<unroll> 12631 12632This is a single-dimensional space representing the schedule dimension(s) 12633that should be I<completely> unrolled. 12634To obtain a partial unrolling, the user should apply an additional 12635strip-mining to the schedule and fully unroll the inner loop. 12636 12637=back 12638 12639=head3 Fine-grained Control over AST Generation 12640 12641Besides specifying the constraints on the parameters, 12642an C<isl_ast_build> object can be used to control 12643various aspects of the AST generation process. 12644In case of AST construction using 12645C<isl_ast_build_node_from_schedule_map>, 12646the most prominent way of control is through ``options'', 12647as explained above. 12648 12649Additional control is available through the following functions. 12650 12651 #include <isl/ast_build.h> 12652 __isl_give isl_ast_build * 12653 isl_ast_build_set_iterators( 12654 __isl_take isl_ast_build *build, 12655 __isl_take isl_id_list *iterators); 12656 12657The function C<isl_ast_build_set_iterators> allows the user to 12658specify a list of iterator C<isl_id>s to be used as iterators. 12659If the input schedule is injective, then 12660the number of elements in this list should be as large as the dimension 12661of the schedule space, but no direct correspondence should be assumed 12662between dimensions and elements. 12663If the input schedule is not injective, then an additional number 12664of C<isl_id>s equal to the largest dimension of the input domains 12665may be required. 12666If the number of provided C<isl_id>s is insufficient, then additional 12667names are automatically generated. 12668 12669 #include <isl/ast_build.h> 12670 __isl_give isl_ast_build * 12671 isl_ast_build_set_create_leaf( 12672 __isl_take isl_ast_build *build, 12673 __isl_give isl_ast_node *(*fn)( 12674 __isl_take isl_ast_build *build, 12675 void *user), void *user); 12676 12677The 12678C<isl_ast_build_set_create_leaf> function allows for the 12679specification of a callback that should be called whenever the AST 12680generator arrives at an element of the schedule domain. 12681The callback should return an AST node that should be inserted 12682at the corresponding position of the AST. The default action (when 12683the callback is not set) is to continue generating parts of the AST to scan 12684all the domain elements associated to the schedule domain element 12685and to insert user nodes, ``calling'' the domain element, for each of them. 12686The C<build> argument contains the current state of the C<isl_ast_build>. 12687To ease nested AST generation (see L</"Nested AST Generation">), 12688all control information that is 12689specific to the current AST generation such as the options and 12690the callbacks has been removed from this C<isl_ast_build>. 12691The callback would typically return the result of a nested 12692AST generation or a 12693user defined node created using the following function. 12694 12695 #include <isl/ast.h> 12696 __isl_give isl_ast_node *isl_ast_node_alloc_user( 12697 __isl_take isl_ast_expr *expr); 12698 12699 #include <isl/ast_build.h> 12700 __isl_give isl_ast_build * 12701 isl_ast_build_set_at_each_domain( 12702 __isl_take isl_ast_build *build, 12703 __isl_give isl_ast_node *(*fn)( 12704 __isl_take isl_ast_node *node, 12705 __isl_keep isl_ast_build *build, 12706 void *user), void *user); 12707 __isl_give isl_ast_build * 12708 isl_ast_build_set_before_each_for( 12709 __isl_take isl_ast_build *build, 12710 __isl_give isl_id *(*fn)( 12711 __isl_keep isl_ast_build *build, 12712 void *user), void *user); 12713 __isl_give isl_ast_build * 12714 isl_ast_build_set_after_each_for( 12715 __isl_take isl_ast_build *build, 12716 __isl_give isl_ast_node *(*fn)( 12717 __isl_take isl_ast_node *node, 12718 __isl_keep isl_ast_build *build, 12719 void *user), void *user); 12720 __isl_give isl_ast_build * 12721 isl_ast_build_set_before_each_mark( 12722 __isl_take isl_ast_build *build, 12723 isl_stat (*fn)(__isl_keep isl_id *mark, 12724 __isl_keep isl_ast_build *build, 12725 void *user), void *user); 12726 __isl_give isl_ast_build * 12727 isl_ast_build_set_after_each_mark( 12728 __isl_take isl_ast_build *build, 12729 __isl_give isl_ast_node *(*fn)( 12730 __isl_take isl_ast_node *node, 12731 __isl_keep isl_ast_build *build, 12732 void *user), void *user); 12733 12734The callback set by C<isl_ast_build_set_at_each_domain> will 12735be called for each domain AST node. 12736The callbacks set by C<isl_ast_build_set_before_each_for> 12737and C<isl_ast_build_set_after_each_for> will be called 12738for each for AST node. The first will be called in depth-first 12739pre-order, while the second will be called in depth-first post-order. 12740Since C<isl_ast_build_set_before_each_for> is called before the for 12741node is actually constructed, it is only passed an C<isl_ast_build>. 12742The returned C<isl_id> will be added as an annotation (using 12743C<isl_ast_node_set_annotation>) to the constructed for node. 12744In particular, if the user has also specified an C<after_each_for> 12745callback, then the annotation can be retrieved from the node passed to 12746that callback using C<isl_ast_node_get_annotation>. 12747The callbacks set by C<isl_ast_build_set_before_each_mark> 12748and C<isl_ast_build_set_after_each_mark> will be called for each 12749mark AST node that is created, i.e., for each mark schedule node 12750in the input schedule tree. The first will be called in depth-first 12751pre-order, while the second will be called in depth-first post-order. 12752Since the callback set by C<isl_ast_build_set_before_each_mark> 12753is called before the mark AST node is actually constructed, it is passed 12754the identifier of the mark node. 12755All callbacks should C<NULL> (or C<isl_stat_error>) on failure. 12756The given C<isl_ast_build> can be used to create new 12757C<isl_ast_expr> objects using C<isl_ast_build_expr_from_pw_aff> 12758or C<isl_ast_build_call_from_pw_multi_aff>. 12759 12760=head3 Nested AST Generation 12761 12762C<isl> allows the user to create an AST within the context 12763of another AST. These nested ASTs are created using the 12764same C<isl_ast_build_node_from_schedule_map> function that is used to create 12765the outer AST. The C<build> argument should be an C<isl_ast_build> 12766passed to a callback set by 12767C<isl_ast_build_set_create_leaf>. 12768The space of the range of the C<schedule> argument should refer 12769to this build. In particular, the space should be a wrapped 12770relation and the domain of this wrapped relation should be the 12771same as that of the range of the schedule returned by 12772C<isl_ast_build_get_schedule> below. 12773In practice, the new schedule is typically 12774created by calling C<isl_union_map_range_product> on the old schedule 12775and some extra piece of the schedule. 12776The space of the schedule domain is also available from 12777the C<isl_ast_build>. 12778 12779 #include <isl/ast_build.h> 12780 __isl_give isl_union_map *isl_ast_build_get_schedule( 12781 __isl_keep isl_ast_build *build); 12782 __isl_give isl_space *isl_ast_build_get_schedule_space( 12783 __isl_keep isl_ast_build *build); 12784 __isl_give isl_ast_build *isl_ast_build_restrict( 12785 __isl_take isl_ast_build *build, 12786 __isl_take isl_set *set); 12787 12788The C<isl_ast_build_get_schedule> function returns a (partial) 12789schedule for the domains elements for which part of the AST still needs to 12790be generated in the current build. 12791In particular, the domain elements are mapped to those iterations of the loops 12792enclosing the current point of the AST generation inside which 12793the domain elements are executed. 12794No direct correspondence between 12795the input schedule and this schedule should be assumed. 12796The space obtained from C<isl_ast_build_get_schedule_space> can be used 12797to create a set for C<isl_ast_build_restrict> to intersect 12798with the current build. In particular, the set passed to 12799C<isl_ast_build_restrict> can have additional parameters. 12800The ids of the set dimensions in the space returned by 12801C<isl_ast_build_get_schedule_space> correspond to the 12802iterators of the already generated loops. 12803The user should not rely on the ids of the output dimensions 12804of the relations in the union relation returned by 12805C<isl_ast_build_get_schedule> having any particular value. 12806 12807=head1 Applications 12808 12809Although C<isl> is mainly meant to be used as a library, 12810it also contains some basic applications that use some 12811of the functionality of C<isl>. 12812For applications that take one or more polytopes or polyhedra 12813as input, this input may be specified in either the L<isl format> 12814or the L<PolyLib format>. 12815 12816=head2 C<isl_polyhedron_sample> 12817 12818C<isl_polyhedron_sample> takes a polyhedron as input and prints 12819an integer element of the polyhedron, if there is any. 12820The first column in the output is the denominator and is always 12821equal to 1. If the polyhedron contains no integer points, 12822then a vector of length zero is printed. 12823 12824=head2 C<isl_pip> 12825 12826C<isl_pip> takes the same input as the C<example> program 12827from the C<piplib> distribution, i.e., a set of constraints 12828on the parameters, a line containing only -1 and finally a set 12829of constraints on a parametric polyhedron. 12830The coefficients of the parameters appear in the last columns 12831(but before the final constant column). 12832The output is the lexicographic minimum of the parametric polyhedron. 12833As C<isl> currently does not have its own output format, the output 12834is just a dump of the internal state. 12835 12836=head2 C<isl_polyhedron_minimize> 12837 12838C<isl_polyhedron_minimize> computes the minimum of some linear 12839or affine objective function over the integer points in a polyhedron. 12840If an affine objective function 12841is given, then the constant should appear in the last column. 12842 12843=head2 C<isl_polytope_scan> 12844 12845Given a polytope, C<isl_polytope_scan> prints 12846all integer points in the polytope. 12847 12848=head2 C<isl_flow> 12849 12850Given an C<isl_union_access_info> object as input, 12851C<isl_flow> prints out the corresponding dependences, 12852as computed by C<isl_union_access_info_compute_flow>. 12853 12854=head2 C<isl_codegen> 12855 12856Given either a schedule tree or a sequence consisting of 12857a schedule map, a context set and an options relation, 12858C<isl_codegen> prints out an AST that scans the domain elements 12859of the schedule in the order of their image(s) taking into account 12860the constraints in the context set. 12861 12862=head2 C<isl_schedule> 12863 12864Given an C<isl_schedule_constraints> object as input, 12865C<isl_schedule> prints out a schedule that satisfies the given 12866constraints. 12867