3 C<isl> is a thread-safe C library for manipulating
4 sets and relations of integer points bounded by affine constraints.
5 The descriptions of the sets and relations may involve
6 both parameters and existentially quantified variables.
7 All computations are performed in exact integer arithmetic
9 The C<isl> library offers functionality that is similar
10 to that offered by the C<Omega> and C<Omega+> libraries,
11 but the underlying algorithms are in most cases completely different.
13 The library is by no means complete and some fairly basic
14 functionality is still missing.
15 Still, even in its current form, the library has been successfully
16 used as a backend polyhedral library for the polyhedral
17 scanner C<CLooG> and as part of an equivalence checker of
18 static affine programs.
19 For bug reports, feature requests and questions,
20 visit the the discussion group at
21 L<http://groups.google.com/group/isl-development>.
23 =head2 Backward Incompatible Changes
25 =head3 Changes since isl-0.02
29 =item * The old printing functions have been deprecated
30 and replaced by C<isl_printer> functions, see L<Input and Output>.
32 =item * Most functions related to dependence analysis have acquired
33 an extra C<must> argument. To obtain the old behavior, this argument
34 should be given the value 1. See L<Dependence Analysis>.
38 =head3 Changes since isl-0.03
42 =item * The function C<isl_pw_qpolynomial_fold_add> has been
43 renamed to C<isl_pw_qpolynomial_fold_fold>.
44 Similarly, C<isl_union_pw_qpolynomial_fold_add> has been
45 renamed to C<isl_union_pw_qpolynomial_fold_fold>.
49 =head3 Changes since isl-0.04
53 =item * All header files have been renamed from C<isl_header.h>
58 =head3 Changes since isl-0.05
62 =item * The functions C<isl_printer_print_basic_set> and
63 C<isl_printer_print_basic_map> no longer print a newline.
65 =item * The functions C<isl_flow_get_no_source>
66 and C<isl_union_map_compute_flow> now return
67 the accesses for which no source could be found instead of
68 the iterations where those accesses occur.
70 =item * The functions C<isl_basic_map_identity> and
71 C<isl_map_identity> now take a B<map> space as input. An old call
72 C<isl_map_identity(space)> can be rewritten to
73 C<isl_map_identity(isl_space_map_from_set(space))>.
75 =item * The function C<isl_map_power> no longer takes
76 a parameter position as input. Instead, the exponent
77 is now expressed as the domain of the resulting relation.
81 =head3 Changes since isl-0.06
85 =item * The format of C<isl_printer_print_qpolynomial>'s
86 C<ISL_FORMAT_ISL> output has changed.
87 Use C<ISL_FORMAT_C> to obtain the old output.
89 =item * The C<*_fast_*> functions have been renamed to C<*_plain_*>.
90 Some of the old names have been kept for backward compatibility,
91 but they will be removed in the future.
95 =head3 Changes since isl-0.07
99 =item * The function C<isl_pw_aff_max> has been renamed to
100 C<isl_pw_aff_union_max>.
101 Similarly, the function C<isl_pw_aff_add> has been renamed to
102 C<isl_pw_aff_union_add>.
104 =item * The C<isl_dim> type has been renamed to C<isl_space>
105 along with the associated functions.
106 Some of the old names have been kept for backward compatibility,
107 but they will be removed in the future.
109 =item * Spaces of maps, sets and parameter domains are now
110 treated differently. The distinction between map spaces and set spaces
111 has always been made on a conceptual level, but proper use of such spaces
112 was never checked. Furthermore, up until isl-0.07 there was no way
113 of explicitly creating a parameter space. These can now be created
114 directly using C<isl_space_params_alloc> or from other spaces using
117 =item * The space in which C<isl_aff>, C<isl_pw_aff>, C<isl_qpolynomial>,
118 C<isl_pw_qpolynomial>, C<isl_qpolynomial_fold> and C<isl_pw_qpolynomial_fold>
119 objects live is now a map space
120 instead of a set space. This means, for example, that the dimensions
121 of the domain of an C<isl_aff> are now considered to be of type
122 C<isl_dim_in> instead of C<isl_dim_set>. Extra functions have been
123 added to obtain the domain space. Some of the constructors still
124 take a domain space and have therefore been renamed.
126 =item * The functions C<isl_equality_alloc> and C<isl_inequality_alloc>
127 now take an C<isl_local_space> instead of an C<isl_space>.
128 An C<isl_local_space> can be created from an C<isl_space>
129 using C<isl_local_space_from_space>.
131 =item * The C<isl_div> type has been removed. Functions that used
132 to return an C<isl_div> now return an C<isl_aff>.
133 Note that the space of an C<isl_aff> is that of relation.
134 When replacing a call to C<isl_div_get_coefficient> by a call to
135 C<isl_aff_get_coefficient> any C<isl_dim_set> argument needs
136 to be replaced by C<isl_dim_in>.
137 A call to C<isl_aff_from_div> can be replaced by a call
139 A call to C<isl_qpolynomial_div(div)> call be replaced by
142 isl_qpolynomial_from_aff(isl_aff_floor(div))
144 The function C<isl_constraint_div> has also been renamed
145 to C<isl_constraint_get_div>.
147 =item * The C<nparam> argument has been removed from
148 C<isl_map_read_from_str> and similar functions.
149 When reading input in the original PolyLib format,
150 the result will have no parameters.
151 If parameters are expected, the caller may want to perform
152 dimension manipulation on the result.
156 =head3 Changes since isl-0.09
160 =item * The C<schedule_split_parallel> option has been replaced
161 by the C<schedule_split_scaled> option.
163 =item * The first argument of C<isl_pw_aff_cond> is now
164 an C<isl_pw_aff> instead of an C<isl_set>.
165 A call C<isl_pw_aff_cond(a, b, c)> can be replaced by
167 isl_pw_aff_cond(isl_set_indicator_function(a), b, c)
171 =head3 Changes since isl-0.10
175 =item * The functions C<isl_set_dim_has_lower_bound> and
176 C<isl_set_dim_has_upper_bound> have been renamed to
177 C<isl_set_dim_has_any_lower_bound> and
178 C<isl_set_dim_has_any_upper_bound>.
179 The new C<isl_set_dim_has_lower_bound> and
180 C<isl_set_dim_has_upper_bound> have slightly different meanings.
184 =head3 Changes since isl-0.12
188 =item * C<isl_int> has been replaced by C<isl_val>.
189 Some of the old functions are still available in C<isl/deprecated/*.h>
190 but they will be removed in the future.
192 =item * The functions C<isl_pw_qpolynomial_eval>,
193 C<isl_union_pw_qpolynomial_eval>, C<isl_pw_qpolynomial_fold_eval>
194 and C<isl_union_pw_qpolynomial_fold_eval> have been changed to return
195 an C<isl_val> instead of an C<isl_qpolynomial>.
201 C<isl> is released under the MIT license.
205 Permission is hereby granted, free of charge, to any person obtaining a copy of
206 this software and associated documentation files (the "Software"), to deal in
207 the Software without restriction, including without limitation the rights to
208 use, copy, modify, merge, publish, distribute, sublicense, and/or sell copies
209 of the Software, and to permit persons to whom the Software is furnished to do
210 so, subject to the following conditions:
212 The above copyright notice and this permission notice shall be included in all
213 copies or substantial portions of the Software.
215 THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
216 IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
217 FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
218 AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
219 LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
220 OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
225 Note that C<isl> currently requires C<GMP>, which is released
226 under the GNU Lesser General Public License (LGPL). This means
227 that code linked against C<isl> is also linked against LGPL code.
231 The source of C<isl> can be obtained either as a tarball
232 or from the git repository. Both are available from
233 L<http://freshmeat.net/projects/isl/>.
234 The installation process depends on how you obtained
237 =head2 Installation from the git repository
241 =item 1 Clone or update the repository
243 The first time the source is obtained, you need to clone
246 git clone git://repo.or.cz/isl.git
248 To obtain updates, you need to pull in the latest changes
252 =item 2 Generate C<configure>
258 After performing the above steps, continue
259 with the L<Common installation instructions>.
261 =head2 Common installation instructions
265 =item 1 Obtain C<GMP>
267 Building C<isl> requires C<GMP>, including its headers files.
268 Your distribution may not provide these header files by default
269 and you may need to install a package called C<gmp-devel> or something
270 similar. Alternatively, C<GMP> can be built from
271 source, available from L<http://gmplib.org/>.
275 C<isl> uses the standard C<autoconf> C<configure> script.
280 optionally followed by some configure options.
281 A complete list of options can be obtained by running
285 Below we discuss some of the more common options.
291 Installation prefix for C<isl>
293 =item C<--with-gmp-prefix>
295 Installation prefix for C<GMP> (architecture-independent files).
297 =item C<--with-gmp-exec-prefix>
299 Installation prefix for C<GMP> (architecture-dependent files).
307 =item 4 Install (optional)
313 =head1 Integer Set Library
315 =head2 Initialization
317 All manipulations of integer sets and relations occur within
318 the context of an C<isl_ctx>.
319 A given C<isl_ctx> can only be used within a single thread.
320 All arguments of a function are required to have been allocated
321 within the same context.
322 There are currently no functions available for moving an object
323 from one C<isl_ctx> to another C<isl_ctx>. This means that
324 there is currently no way of safely moving an object from one
325 thread to another, unless the whole C<isl_ctx> is moved.
327 An C<isl_ctx> can be allocated using C<isl_ctx_alloc> and
328 freed using C<isl_ctx_free>.
329 All objects allocated within an C<isl_ctx> should be freed
330 before the C<isl_ctx> itself is freed.
332 isl_ctx *isl_ctx_alloc();
333 void isl_ctx_free(isl_ctx *ctx);
337 An C<isl_val> represents an integer value, a rational value
338 or one of three special values, infinity, negative infinity and NaN.
339 Some predefined values can be created using the following functions.
342 __isl_give isl_val *isl_val_zero(isl_ctx *ctx);
343 __isl_give isl_val *isl_val_one(isl_ctx *ctx);
344 __isl_give isl_val *isl_val_nan(isl_ctx *ctx);
345 __isl_give isl_val *isl_val_infty(isl_ctx *ctx);
346 __isl_give isl_val *isl_val_neginfty(isl_ctx *ctx);
348 Specific integer values can be created using the following functions.
351 __isl_give isl_val *isl_val_int_from_si(isl_ctx *ctx,
353 __isl_give isl_val *isl_val_int_from_ui(isl_ctx *ctx,
355 __isl_give isl_val *isl_val_int_from_chunks(isl_ctx *ctx,
356 size_t n, size_t size, const void *chunks);
358 The function C<isl_val_int_from_chunks> constructs an C<isl_val>
359 from the C<n> I<digits>, each consisting of C<size> bytes, stored at C<chunks>.
360 The least significant digit is assumed to be stored first.
362 Value objects can be copied and freed using the following functions.
365 __isl_give isl_val *isl_val_copy(__isl_keep isl_val *v);
366 void *isl_val_free(__isl_take isl_val *v);
368 They can be inspected using the following functions.
371 isl_ctx *isl_val_get_ctx(__isl_keep isl_val *val);
372 long isl_val_get_num_si(__isl_keep isl_val *v);
373 long isl_val_get_den_si(__isl_keep isl_val *v);
374 double isl_val_get_d(__isl_keep isl_val *v);
375 size_t isl_val_n_abs_num_chunks(__isl_keep isl_val *v,
377 int isl_val_get_abs_num_chunks(__isl_keep isl_val *v,
378 size_t size, void *chunks);
380 C<isl_val_n_abs_num_chunks> returns the number of I<digits>
381 of C<size> bytes needed to store the absolute value of the
383 C<isl_val_get_abs_num_chunks> stores these digits at C<chunks>,
384 which is assumed to have been preallocated by the caller.
385 The least significant digit is stored first.
386 Note that C<isl_val_get_num_si>, C<isl_val_get_den_si>,
387 C<isl_val_get_d>, C<isl_val_n_abs_num_chunks>
388 and C<isl_val_get_abs_num_chunks> can only be applied to rational values.
390 An C<isl_val> can be modified using the following function.
393 __isl_give isl_val *isl_val_set_si(__isl_take isl_val *v,
396 The following unary properties are defined on C<isl_val>s.
399 int isl_val_sgn(__isl_keep isl_val *v);
400 int isl_val_is_zero(__isl_keep isl_val *v);
401 int isl_val_is_one(__isl_keep isl_val *v);
402 int isl_val_is_negone(__isl_keep isl_val *v);
403 int isl_val_is_nonneg(__isl_keep isl_val *v);
404 int isl_val_is_nonpos(__isl_keep isl_val *v);
405 int isl_val_is_pos(__isl_keep isl_val *v);
406 int isl_val_is_neg(__isl_keep isl_val *v);
407 int isl_val_is_int(__isl_keep isl_val *v);
408 int isl_val_is_rat(__isl_keep isl_val *v);
409 int isl_val_is_nan(__isl_keep isl_val *v);
410 int isl_val_is_infty(__isl_keep isl_val *v);
411 int isl_val_is_neginfty(__isl_keep isl_val *v);
413 Note that the sign of NaN is undefined.
415 The following binary properties are defined on pairs of C<isl_val>s.
418 int isl_val_lt(__isl_keep isl_val *v1,
419 __isl_keep isl_val *v2);
420 int isl_val_le(__isl_keep isl_val *v1,
421 __isl_keep isl_val *v2);
422 int isl_val_gt(__isl_keep isl_val *v1,
423 __isl_keep isl_val *v2);
424 int isl_val_ge(__isl_keep isl_val *v1,
425 __isl_keep isl_val *v2);
426 int isl_val_eq(__isl_keep isl_val *v1,
427 __isl_keep isl_val *v2);
428 int isl_val_ne(__isl_keep isl_val *v1,
429 __isl_keep isl_val *v2);
431 For integer C<isl_val>s we additionally have the following binary property.
434 int isl_val_is_divisible_by(__isl_keep isl_val *v1,
435 __isl_keep isl_val *v2);
437 An C<isl_val> can also be compared to an integer using the following
438 function. The result is undefined for NaN.
441 int isl_val_cmp_si(__isl_keep isl_val *v, long i);
443 The following unary operations are available on C<isl_val>s.
446 __isl_give isl_val *isl_val_abs(__isl_take isl_val *v);
447 __isl_give isl_val *isl_val_neg(__isl_take isl_val *v);
448 __isl_give isl_val *isl_val_floor(__isl_take isl_val *v);
449 __isl_give isl_val *isl_val_ceil(__isl_take isl_val *v);
450 __isl_give isl_val *isl_val_trunc(__isl_take isl_val *v);
452 The following binary operations are available on C<isl_val>s.
455 __isl_give isl_val *isl_val_abs(__isl_take isl_val *v);
456 __isl_give isl_val *isl_val_neg(__isl_take isl_val *v);
457 __isl_give isl_val *isl_val_floor(__isl_take isl_val *v);
458 __isl_give isl_val *isl_val_ceil(__isl_take isl_val *v);
459 __isl_give isl_val *isl_val_trunc(__isl_take isl_val *v);
460 __isl_give isl_val *isl_val_2exp(__isl_take isl_val *v);
461 __isl_give isl_val *isl_val_min(__isl_take isl_val *v1,
462 __isl_take isl_val *v2);
463 __isl_give isl_val *isl_val_max(__isl_take isl_val *v1,
464 __isl_take isl_val *v2);
465 __isl_give isl_val *isl_val_add(__isl_take isl_val *v1,
466 __isl_take isl_val *v2);
467 __isl_give isl_val *isl_val_add_ui(__isl_take isl_val *v1,
469 __isl_give isl_val *isl_val_sub(__isl_take isl_val *v1,
470 __isl_take isl_val *v2);
471 __isl_give isl_val *isl_val_sub_ui(__isl_take isl_val *v1,
473 __isl_give isl_val *isl_val_mul(__isl_take isl_val *v1,
474 __isl_take isl_val *v2);
475 __isl_give isl_val *isl_val_mul_ui(__isl_take isl_val *v1,
477 __isl_give isl_val *isl_val_div(__isl_take isl_val *v1,
478 __isl_take isl_val *v2);
480 On integer values, we additionally have the following operations.
483 __isl_give isl_val *isl_val_2exp(__isl_take isl_val *v);
484 __isl_give isl_val *isl_val_mod(__isl_take isl_val *v1,
485 __isl_take isl_val *v2);
486 __isl_give isl_val *isl_val_gcd(__isl_take isl_val *v1,
487 __isl_take isl_val *v2);
488 __isl_give isl_val *isl_val_gcdext(__isl_take isl_val *v1,
489 __isl_take isl_val *v2, __isl_give isl_val **x,
490 __isl_give isl_val **y);
492 The function C<isl_val_gcdext> returns the greatest common divisor g
493 of C<v1> and C<v2> as well as two integers C<*x> and C<*y> such
494 that C<*x> * C<v1> + C<*y> * C<v2> = g.
496 A value can be read from input using
499 __isl_give isl_val *isl_val_read_from_str(isl_ctx *ctx,
502 A value can be printed using
505 __isl_give isl_printer *isl_printer_print_val(
506 __isl_take isl_printer *p, __isl_keep isl_val *v);
508 =head3 GMP specific functions
510 These functions are only available if C<isl> has been compiled with C<GMP>
513 Specific integer and rational values can be created from C<GMP> values using
514 the following functions.
516 #include <isl/val_gmp.h>
517 __isl_give isl_val *isl_val_int_from_gmp(isl_ctx *ctx,
519 __isl_give isl_val *isl_val_from_gmp(isl_ctx *ctx,
520 const mpz_t n, const mpz_t d);
522 The numerator and denominator of a rational value can be extracted as
523 C<GMP> values using the following functions.
525 #include <isl/val_gmp.h>
526 int isl_val_get_num_gmp(__isl_keep isl_val *v, mpz_t z);
527 int isl_val_get_den_gmp(__isl_keep isl_val *v, mpz_t z);
529 =head2 Sets and Relations
531 C<isl> uses six types of objects for representing sets and relations,
532 C<isl_basic_set>, C<isl_basic_map>, C<isl_set>, C<isl_map>,
533 C<isl_union_set> and C<isl_union_map>.
534 C<isl_basic_set> and C<isl_basic_map> represent sets and relations that
535 can be described as a conjunction of affine constraints, while
536 C<isl_set> and C<isl_map> represent unions of
537 C<isl_basic_set>s and C<isl_basic_map>s, respectively.
538 However, all C<isl_basic_set>s or C<isl_basic_map>s in the union need
539 to live in the same space. C<isl_union_set>s and C<isl_union_map>s
540 represent unions of C<isl_set>s or C<isl_map>s in I<different> spaces,
541 where spaces are considered different if they have a different number
542 of dimensions and/or different names (see L<"Spaces">).
543 The difference between sets and relations (maps) is that sets have
544 one set of variables, while relations have two sets of variables,
545 input variables and output variables.
547 =head2 Memory Management
549 Since a high-level operation on sets and/or relations usually involves
550 several substeps and since the user is usually not interested in
551 the intermediate results, most functions that return a new object
552 will also release all the objects passed as arguments.
553 If the user still wants to use one or more of these arguments
554 after the function call, she should pass along a copy of the
555 object rather than the object itself.
556 The user is then responsible for making sure that the original
557 object gets used somewhere else or is explicitly freed.
559 The arguments and return values of all documented functions are
560 annotated to make clear which arguments are released and which
561 arguments are preserved. In particular, the following annotations
568 C<__isl_give> means that a new object is returned.
569 The user should make sure that the returned pointer is
570 used exactly once as a value for an C<__isl_take> argument.
571 In between, it can be used as a value for as many
572 C<__isl_keep> arguments as the user likes.
573 There is one exception, and that is the case where the
574 pointer returned is C<NULL>. Is this case, the user
575 is free to use it as an C<__isl_take> argument or not.
579 C<__isl_take> means that the object the argument points to
580 is taken over by the function and may no longer be used
581 by the user as an argument to any other function.
582 The pointer value must be one returned by a function
583 returning an C<__isl_give> pointer.
584 If the user passes in a C<NULL> value, then this will
585 be treated as an error in the sense that the function will
586 not perform its usual operation. However, it will still
587 make sure that all the other C<__isl_take> arguments
592 C<__isl_keep> means that the function will only use the object
593 temporarily. After the function has finished, the user
594 can still use it as an argument to other functions.
595 A C<NULL> value will be treated in the same way as
596 a C<NULL> value for an C<__isl_take> argument.
600 =head2 Error Handling
602 C<isl> supports different ways to react in case a runtime error is triggered.
603 Runtime errors arise, e.g., if a function such as C<isl_map_intersect> is called
604 with two maps that have incompatible spaces. There are three possible ways
605 to react on error: to warn, to continue or to abort.
607 The default behavior is to warn. In this mode, C<isl> prints a warning, stores
608 the last error in the corresponding C<isl_ctx> and the function in which the
609 error was triggered returns C<NULL>. An error does not corrupt internal state,
610 such that isl can continue to be used. C<isl> also provides functions to
611 read the last error and to reset the memory that stores the last error. The
612 last error is only stored for information purposes. Its presence does not
613 change the behavior of C<isl>. Hence, resetting an error is not required to
614 continue to use isl, but only to observe new errors.
617 enum isl_error isl_ctx_last_error(isl_ctx *ctx);
618 void isl_ctx_reset_error(isl_ctx *ctx);
620 Another option is to continue on error. This is similar to warn on error mode,
621 except that C<isl> does not print any warning. This allows a program to
622 implement its own error reporting.
624 The last option is to directly abort the execution of the program from within
625 the isl library. This makes it obviously impossible to recover from an error,
626 but it allows to directly spot the error location. By aborting on error,
627 debuggers break at the location the error occurred and can provide a stack
628 trace. Other tools that automatically provide stack traces on abort or that do
629 not want to continue execution after an error was triggered may also prefer to
632 The on error behavior of isl can be specified by calling
633 C<isl_options_set_on_error> or by setting the command line option
634 C<--isl-on-error>. Valid arguments for the function call are
635 C<ISL_ON_ERROR_WARN>, C<ISL_ON_ERROR_CONTINUE> and C<ISL_ON_ERROR_ABORT>. The
636 choices for the command line option are C<warn>, C<continue> and C<abort>.
637 It is also possible to query the current error mode.
639 #include <isl/options.h>
640 int isl_options_set_on_error(isl_ctx *ctx, int val);
641 int isl_options_get_on_error(isl_ctx *ctx);
645 Identifiers are used to identify both individual dimensions
646 and tuples of dimensions. They consist of an optional name and an optional
647 user pointer. The name and the user pointer cannot both be C<NULL>, however.
648 Identifiers with the same name but different pointer values
649 are considered to be distinct.
650 Similarly, identifiers with different names but the same pointer value
651 are also considered to be distinct.
652 Equal identifiers are represented using the same object.
653 Pairs of identifiers can therefore be tested for equality using the
655 Identifiers can be constructed, copied, freed, inspected and printed
656 using the following functions.
659 __isl_give isl_id *isl_id_alloc(isl_ctx *ctx,
660 __isl_keep const char *name, void *user);
661 __isl_give isl_id *isl_id_set_free_user(
662 __isl_take isl_id *id,
663 __isl_give void (*free_user)(void *user));
664 __isl_give isl_id *isl_id_copy(isl_id *id);
665 void *isl_id_free(__isl_take isl_id *id);
667 isl_ctx *isl_id_get_ctx(__isl_keep isl_id *id);
668 void *isl_id_get_user(__isl_keep isl_id *id);
669 __isl_keep const char *isl_id_get_name(__isl_keep isl_id *id);
671 __isl_give isl_printer *isl_printer_print_id(
672 __isl_take isl_printer *p, __isl_keep isl_id *id);
674 The callback set by C<isl_id_set_free_user> is called on the user
675 pointer when the last reference to the C<isl_id> is freed.
676 Note that C<isl_id_get_name> returns a pointer to some internal
677 data structure, so the result can only be used while the
678 corresponding C<isl_id> is alive.
682 Whenever a new set, relation or similiar object is created from scratch,
683 the space in which it lives needs to be specified using an C<isl_space>.
684 Each space involves zero or more parameters and zero, one or two
685 tuples of set or input/output dimensions. The parameters and dimensions
686 are identified by an C<isl_dim_type> and a position.
687 The type C<isl_dim_param> refers to parameters,
688 the type C<isl_dim_set> refers to set dimensions (for spaces
689 with a single tuple of dimensions) and the types C<isl_dim_in>
690 and C<isl_dim_out> refer to input and output dimensions
691 (for spaces with two tuples of dimensions).
692 Local spaces (see L</"Local Spaces">) also contain dimensions
693 of type C<isl_dim_div>.
694 Note that parameters are only identified by their position within
695 a given object. Across different objects, parameters are (usually)
696 identified by their names or identifiers. Only unnamed parameters
697 are identified by their positions across objects. The use of unnamed
698 parameters is discouraged.
700 #include <isl/space.h>
701 __isl_give isl_space *isl_space_alloc(isl_ctx *ctx,
702 unsigned nparam, unsigned n_in, unsigned n_out);
703 __isl_give isl_space *isl_space_params_alloc(isl_ctx *ctx,
705 __isl_give isl_space *isl_space_set_alloc(isl_ctx *ctx,
706 unsigned nparam, unsigned dim);
707 __isl_give isl_space *isl_space_copy(__isl_keep isl_space *space);
708 void *isl_space_free(__isl_take isl_space *space);
709 unsigned isl_space_dim(__isl_keep isl_space *space,
710 enum isl_dim_type type);
712 The space used for creating a parameter domain
713 needs to be created using C<isl_space_params_alloc>.
714 For other sets, the space
715 needs to be created using C<isl_space_set_alloc>, while
716 for a relation, the space
717 needs to be created using C<isl_space_alloc>.
718 C<isl_space_dim> can be used
719 to find out the number of dimensions of each type in
720 a space, where type may be
721 C<isl_dim_param>, C<isl_dim_in> (only for relations),
722 C<isl_dim_out> (only for relations), C<isl_dim_set>
723 (only for sets) or C<isl_dim_all>.
725 To check whether a given space is that of a set or a map
726 or whether it is a parameter space, use these functions:
728 #include <isl/space.h>
729 int isl_space_is_params(__isl_keep isl_space *space);
730 int isl_space_is_set(__isl_keep isl_space *space);
731 int isl_space_is_map(__isl_keep isl_space *space);
733 Spaces can be compared using the following functions:
735 #include <isl/space.h>
736 int isl_space_is_equal(__isl_keep isl_space *space1,
737 __isl_keep isl_space *space2);
738 int isl_space_is_domain(__isl_keep isl_space *space1,
739 __isl_keep isl_space *space2);
740 int isl_space_is_range(__isl_keep isl_space *space1,
741 __isl_keep isl_space *space2);
743 C<isl_space_is_domain> checks whether the first argument is equal
744 to the domain of the second argument. This requires in particular that
745 the first argument is a set space and that the second argument
748 It is often useful to create objects that live in the
749 same space as some other object. This can be accomplished
750 by creating the new objects
751 (see L<Creating New Sets and Relations> or
752 L<Creating New (Piecewise) Quasipolynomials>) based on the space
753 of the original object.
756 __isl_give isl_space *isl_basic_set_get_space(
757 __isl_keep isl_basic_set *bset);
758 __isl_give isl_space *isl_set_get_space(__isl_keep isl_set *set);
760 #include <isl/union_set.h>
761 __isl_give isl_space *isl_union_set_get_space(
762 __isl_keep isl_union_set *uset);
765 __isl_give isl_space *isl_basic_map_get_space(
766 __isl_keep isl_basic_map *bmap);
767 __isl_give isl_space *isl_map_get_space(__isl_keep isl_map *map);
769 #include <isl/union_map.h>
770 __isl_give isl_space *isl_union_map_get_space(
771 __isl_keep isl_union_map *umap);
773 #include <isl/constraint.h>
774 __isl_give isl_space *isl_constraint_get_space(
775 __isl_keep isl_constraint *constraint);
777 #include <isl/polynomial.h>
778 __isl_give isl_space *isl_qpolynomial_get_domain_space(
779 __isl_keep isl_qpolynomial *qp);
780 __isl_give isl_space *isl_qpolynomial_get_space(
781 __isl_keep isl_qpolynomial *qp);
782 __isl_give isl_space *isl_qpolynomial_fold_get_space(
783 __isl_keep isl_qpolynomial_fold *fold);
784 __isl_give isl_space *isl_pw_qpolynomial_get_domain_space(
785 __isl_keep isl_pw_qpolynomial *pwqp);
786 __isl_give isl_space *isl_pw_qpolynomial_get_space(
787 __isl_keep isl_pw_qpolynomial *pwqp);
788 __isl_give isl_space *isl_pw_qpolynomial_fold_get_domain_space(
789 __isl_keep isl_pw_qpolynomial_fold *pwf);
790 __isl_give isl_space *isl_pw_qpolynomial_fold_get_space(
791 __isl_keep isl_pw_qpolynomial_fold *pwf);
792 __isl_give isl_space *isl_union_pw_qpolynomial_get_space(
793 __isl_keep isl_union_pw_qpolynomial *upwqp);
794 __isl_give isl_space *isl_union_pw_qpolynomial_fold_get_space(
795 __isl_keep isl_union_pw_qpolynomial_fold *upwf);
798 __isl_give isl_space *isl_multi_val_get_space(
799 __isl_keep isl_multi_val *mv);
802 __isl_give isl_space *isl_aff_get_domain_space(
803 __isl_keep isl_aff *aff);
804 __isl_give isl_space *isl_aff_get_space(
805 __isl_keep isl_aff *aff);
806 __isl_give isl_space *isl_pw_aff_get_domain_space(
807 __isl_keep isl_pw_aff *pwaff);
808 __isl_give isl_space *isl_pw_aff_get_space(
809 __isl_keep isl_pw_aff *pwaff);
810 __isl_give isl_space *isl_multi_aff_get_domain_space(
811 __isl_keep isl_multi_aff *maff);
812 __isl_give isl_space *isl_multi_aff_get_space(
813 __isl_keep isl_multi_aff *maff);
814 __isl_give isl_space *isl_pw_multi_aff_get_domain_space(
815 __isl_keep isl_pw_multi_aff *pma);
816 __isl_give isl_space *isl_pw_multi_aff_get_space(
817 __isl_keep isl_pw_multi_aff *pma);
818 __isl_give isl_space *isl_union_pw_multi_aff_get_space(
819 __isl_keep isl_union_pw_multi_aff *upma);
820 __isl_give isl_space *isl_multi_pw_aff_get_domain_space(
821 __isl_keep isl_multi_pw_aff *mpa);
822 __isl_give isl_space *isl_multi_pw_aff_get_space(
823 __isl_keep isl_multi_pw_aff *mpa);
825 #include <isl/point.h>
826 __isl_give isl_space *isl_point_get_space(
827 __isl_keep isl_point *pnt);
829 The identifiers or names of the individual dimensions may be set or read off
830 using the following functions.
832 #include <isl/space.h>
833 __isl_give isl_space *isl_space_set_dim_id(
834 __isl_take isl_space *space,
835 enum isl_dim_type type, unsigned pos,
836 __isl_take isl_id *id);
837 int isl_space_has_dim_id(__isl_keep isl_space *space,
838 enum isl_dim_type type, unsigned pos);
839 __isl_give isl_id *isl_space_get_dim_id(
840 __isl_keep isl_space *space,
841 enum isl_dim_type type, unsigned pos);
842 __isl_give isl_space *isl_space_set_dim_name(
843 __isl_take isl_space *space,
844 enum isl_dim_type type, unsigned pos,
845 __isl_keep const char *name);
846 int isl_space_has_dim_name(__isl_keep isl_space *space,
847 enum isl_dim_type type, unsigned pos);
848 __isl_keep const char *isl_space_get_dim_name(
849 __isl_keep isl_space *space,
850 enum isl_dim_type type, unsigned pos);
852 Note that C<isl_space_get_name> returns a pointer to some internal
853 data structure, so the result can only be used while the
854 corresponding C<isl_space> is alive.
855 Also note that every function that operates on two sets or relations
856 requires that both arguments have the same parameters. This also
857 means that if one of the arguments has named parameters, then the
858 other needs to have named parameters too and the names need to match.
859 Pairs of C<isl_set>, C<isl_map>, C<isl_union_set> and/or C<isl_union_map>
860 arguments may have different parameters (as long as they are named),
861 in which case the result will have as parameters the union of the parameters of
864 Given the identifier or name of a dimension (typically a parameter),
865 its position can be obtained from the following function.
867 #include <isl/space.h>
868 int isl_space_find_dim_by_id(__isl_keep isl_space *space,
869 enum isl_dim_type type, __isl_keep isl_id *id);
870 int isl_space_find_dim_by_name(__isl_keep isl_space *space,
871 enum isl_dim_type type, const char *name);
873 The identifiers or names of entire spaces may be set or read off
874 using the following functions.
876 #include <isl/space.h>
877 __isl_give isl_space *isl_space_set_tuple_id(
878 __isl_take isl_space *space,
879 enum isl_dim_type type, __isl_take isl_id *id);
880 __isl_give isl_space *isl_space_reset_tuple_id(
881 __isl_take isl_space *space, enum isl_dim_type type);
882 int isl_space_has_tuple_id(__isl_keep isl_space *space,
883 enum isl_dim_type type);
884 __isl_give isl_id *isl_space_get_tuple_id(
885 __isl_keep isl_space *space, enum isl_dim_type type);
886 __isl_give isl_space *isl_space_set_tuple_name(
887 __isl_take isl_space *space,
888 enum isl_dim_type type, const char *s);
889 int isl_space_has_tuple_name(__isl_keep isl_space *space,
890 enum isl_dim_type type);
891 const char *isl_space_get_tuple_name(__isl_keep isl_space *space,
892 enum isl_dim_type type);
894 The C<type> argument needs to be one of C<isl_dim_in>, C<isl_dim_out>
895 or C<isl_dim_set>. As with C<isl_space_get_name>,
896 the C<isl_space_get_tuple_name> function returns a pointer to some internal
898 Binary operations require the corresponding spaces of their arguments
899 to have the same name.
901 Spaces can be nested. In particular, the domain of a set or
902 the domain or range of a relation can be a nested relation.
903 The following functions can be used to construct and deconstruct
906 #include <isl/space.h>
907 int isl_space_is_wrapping(__isl_keep isl_space *space);
908 __isl_give isl_space *isl_space_wrap(__isl_take isl_space *space);
909 __isl_give isl_space *isl_space_unwrap(__isl_take isl_space *space);
911 The input to C<isl_space_is_wrapping> and C<isl_space_unwrap> should
912 be the space of a set, while that of
913 C<isl_space_wrap> should be the space of a relation.
914 Conversely, the output of C<isl_space_unwrap> is the space
915 of a relation, while that of C<isl_space_wrap> is the space of a set.
917 Spaces can be created from other spaces
918 using the following functions.
920 __isl_give isl_space *isl_space_domain(__isl_take isl_space *space);
921 __isl_give isl_space *isl_space_from_domain(__isl_take isl_space *space);
922 __isl_give isl_space *isl_space_range(__isl_take isl_space *space);
923 __isl_give isl_space *isl_space_from_range(__isl_take isl_space *space);
924 __isl_give isl_space *isl_space_domain_map(
925 __isl_take isl_space *space);
926 __isl_give isl_space *isl_space_range_map(
927 __isl_take isl_space *space);
928 __isl_give isl_space *isl_space_params(
929 __isl_take isl_space *space);
930 __isl_give isl_space *isl_space_set_from_params(
931 __isl_take isl_space *space);
932 __isl_give isl_space *isl_space_reverse(__isl_take isl_space *space);
933 __isl_give isl_space *isl_space_join(__isl_take isl_space *left,
934 __isl_take isl_space *right);
935 __isl_give isl_space *isl_space_align_params(
936 __isl_take isl_space *space1, __isl_take isl_space *space2)
937 __isl_give isl_space *isl_space_insert_dims(__isl_take isl_space *space,
938 enum isl_dim_type type, unsigned pos, unsigned n);
939 __isl_give isl_space *isl_space_add_dims(__isl_take isl_space *space,
940 enum isl_dim_type type, unsigned n);
941 __isl_give isl_space *isl_space_drop_dims(__isl_take isl_space *space,
942 enum isl_dim_type type, unsigned first, unsigned n);
943 __isl_give isl_space *isl_space_move_dims(__isl_take isl_space *space,
944 enum isl_dim_type dst_type, unsigned dst_pos,
945 enum isl_dim_type src_type, unsigned src_pos,
947 __isl_give isl_space *isl_space_map_from_set(
948 __isl_take isl_space *space);
949 __isl_give isl_space *isl_space_map_from_domain_and_range(
950 __isl_take isl_space *domain,
951 __isl_take isl_space *range);
952 __isl_give isl_space *isl_space_zip(__isl_take isl_space *space);
953 __isl_give isl_space *isl_space_curry(
954 __isl_take isl_space *space);
955 __isl_give isl_space *isl_space_uncurry(
956 __isl_take isl_space *space);
958 Note that if dimensions are added or removed from a space, then
959 the name and the internal structure are lost.
963 A local space is essentially a space with
964 zero or more existentially quantified variables.
965 The local space of a (constraint of a) basic set or relation can be obtained
966 using the following functions.
968 #include <isl/constraint.h>
969 __isl_give isl_local_space *isl_constraint_get_local_space(
970 __isl_keep isl_constraint *constraint);
973 __isl_give isl_local_space *isl_basic_set_get_local_space(
974 __isl_keep isl_basic_set *bset);
977 __isl_give isl_local_space *isl_basic_map_get_local_space(
978 __isl_keep isl_basic_map *bmap);
980 A new local space can be created from a space using
982 #include <isl/local_space.h>
983 __isl_give isl_local_space *isl_local_space_from_space(
984 __isl_take isl_space *space);
986 They can be inspected, modified, copied and freed using the following functions.
988 #include <isl/local_space.h>
989 isl_ctx *isl_local_space_get_ctx(
990 __isl_keep isl_local_space *ls);
991 int isl_local_space_is_set(__isl_keep isl_local_space *ls);
992 int isl_local_space_dim(__isl_keep isl_local_space *ls,
993 enum isl_dim_type type);
994 int isl_local_space_has_dim_id(
995 __isl_keep isl_local_space *ls,
996 enum isl_dim_type type, unsigned pos);
997 __isl_give isl_id *isl_local_space_get_dim_id(
998 __isl_keep isl_local_space *ls,
999 enum isl_dim_type type, unsigned pos);
1000 int isl_local_space_has_dim_name(
1001 __isl_keep isl_local_space *ls,
1002 enum isl_dim_type type, unsigned pos)
1003 const char *isl_local_space_get_dim_name(
1004 __isl_keep isl_local_space *ls,
1005 enum isl_dim_type type, unsigned pos);
1006 __isl_give isl_local_space *isl_local_space_set_dim_name(
1007 __isl_take isl_local_space *ls,
1008 enum isl_dim_type type, unsigned pos, const char *s);
1009 __isl_give isl_local_space *isl_local_space_set_dim_id(
1010 __isl_take isl_local_space *ls,
1011 enum isl_dim_type type, unsigned pos,
1012 __isl_take isl_id *id);
1013 __isl_give isl_space *isl_local_space_get_space(
1014 __isl_keep isl_local_space *ls);
1015 __isl_give isl_aff *isl_local_space_get_div(
1016 __isl_keep isl_local_space *ls, int pos);
1017 __isl_give isl_local_space *isl_local_space_copy(
1018 __isl_keep isl_local_space *ls);
1019 void *isl_local_space_free(__isl_take isl_local_space *ls);
1021 Note that C<isl_local_space_get_div> can only be used on local spaces
1024 Two local spaces can be compared using
1026 int isl_local_space_is_equal(__isl_keep isl_local_space *ls1,
1027 __isl_keep isl_local_space *ls2);
1029 Local spaces can be created from other local spaces
1030 using the following functions.
1032 __isl_give isl_local_space *isl_local_space_domain(
1033 __isl_take isl_local_space *ls);
1034 __isl_give isl_local_space *isl_local_space_range(
1035 __isl_take isl_local_space *ls);
1036 __isl_give isl_local_space *isl_local_space_from_domain(
1037 __isl_take isl_local_space *ls);
1038 __isl_give isl_local_space *isl_local_space_intersect(
1039 __isl_take isl_local_space *ls1,
1040 __isl_take isl_local_space *ls2);
1041 __isl_give isl_local_space *isl_local_space_add_dims(
1042 __isl_take isl_local_space *ls,
1043 enum isl_dim_type type, unsigned n);
1044 __isl_give isl_local_space *isl_local_space_insert_dims(
1045 __isl_take isl_local_space *ls,
1046 enum isl_dim_type type, unsigned first, unsigned n);
1047 __isl_give isl_local_space *isl_local_space_drop_dims(
1048 __isl_take isl_local_space *ls,
1049 enum isl_dim_type type, unsigned first, unsigned n);
1051 =head2 Input and Output
1053 C<isl> supports its own input/output format, which is similar
1054 to the C<Omega> format, but also supports the C<PolyLib> format
1057 =head3 C<isl> format
1059 The C<isl> format is similar to that of C<Omega>, but has a different
1060 syntax for describing the parameters and allows for the definition
1061 of an existentially quantified variable as the integer division
1062 of an affine expression.
1063 For example, the set of integers C<i> between C<0> and C<n>
1064 such that C<i % 10 <= 6> can be described as
1066 [n] -> { [i] : exists (a = [i/10] : 0 <= i and i <= n and
1069 A set or relation can have several disjuncts, separated
1070 by the keyword C<or>. Each disjunct is either a conjunction
1071 of constraints or a projection (C<exists>) of a conjunction
1072 of constraints. The constraints are separated by the keyword
1075 =head3 C<PolyLib> format
1077 If the represented set is a union, then the first line
1078 contains a single number representing the number of disjuncts.
1079 Otherwise, a line containing the number C<1> is optional.
1081 Each disjunct is represented by a matrix of constraints.
1082 The first line contains two numbers representing
1083 the number of rows and columns,
1084 where the number of rows is equal to the number of constraints
1085 and the number of columns is equal to two plus the number of variables.
1086 The following lines contain the actual rows of the constraint matrix.
1087 In each row, the first column indicates whether the constraint
1088 is an equality (C<0>) or inequality (C<1>). The final column
1089 corresponds to the constant term.
1091 If the set is parametric, then the coefficients of the parameters
1092 appear in the last columns before the constant column.
1093 The coefficients of any existentially quantified variables appear
1094 between those of the set variables and those of the parameters.
1096 =head3 Extended C<PolyLib> format
1098 The extended C<PolyLib> format is nearly identical to the
1099 C<PolyLib> format. The only difference is that the line
1100 containing the number of rows and columns of a constraint matrix
1101 also contains four additional numbers:
1102 the number of output dimensions, the number of input dimensions,
1103 the number of local dimensions (i.e., the number of existentially
1104 quantified variables) and the number of parameters.
1105 For sets, the number of ``output'' dimensions is equal
1106 to the number of set dimensions, while the number of ``input''
1111 #include <isl/set.h>
1112 __isl_give isl_basic_set *isl_basic_set_read_from_file(
1113 isl_ctx *ctx, FILE *input);
1114 __isl_give isl_basic_set *isl_basic_set_read_from_str(
1115 isl_ctx *ctx, const char *str);
1116 __isl_give isl_set *isl_set_read_from_file(isl_ctx *ctx,
1118 __isl_give isl_set *isl_set_read_from_str(isl_ctx *ctx,
1121 #include <isl/map.h>
1122 __isl_give isl_basic_map *isl_basic_map_read_from_file(
1123 isl_ctx *ctx, FILE *input);
1124 __isl_give isl_basic_map *isl_basic_map_read_from_str(
1125 isl_ctx *ctx, const char *str);
1126 __isl_give isl_map *isl_map_read_from_file(
1127 isl_ctx *ctx, FILE *input);
1128 __isl_give isl_map *isl_map_read_from_str(isl_ctx *ctx,
1131 #include <isl/union_set.h>
1132 __isl_give isl_union_set *isl_union_set_read_from_file(
1133 isl_ctx *ctx, FILE *input);
1134 __isl_give isl_union_set *isl_union_set_read_from_str(
1135 isl_ctx *ctx, const char *str);
1137 #include <isl/union_map.h>
1138 __isl_give isl_union_map *isl_union_map_read_from_file(
1139 isl_ctx *ctx, FILE *input);
1140 __isl_give isl_union_map *isl_union_map_read_from_str(
1141 isl_ctx *ctx, const char *str);
1143 The input format is autodetected and may be either the C<PolyLib> format
1144 or the C<isl> format.
1148 Before anything can be printed, an C<isl_printer> needs to
1151 __isl_give isl_printer *isl_printer_to_file(isl_ctx *ctx,
1153 __isl_give isl_printer *isl_printer_to_str(isl_ctx *ctx);
1154 void *isl_printer_free(__isl_take isl_printer *printer);
1155 __isl_give char *isl_printer_get_str(
1156 __isl_keep isl_printer *printer);
1158 The printer can be inspected using the following functions.
1160 FILE *isl_printer_get_file(
1161 __isl_keep isl_printer *printer);
1162 int isl_printer_get_output_format(
1163 __isl_keep isl_printer *p);
1165 The behavior of the printer can be modified in various ways
1167 __isl_give isl_printer *isl_printer_set_output_format(
1168 __isl_take isl_printer *p, int output_format);
1169 __isl_give isl_printer *isl_printer_set_indent(
1170 __isl_take isl_printer *p, int indent);
1171 __isl_give isl_printer *isl_printer_indent(
1172 __isl_take isl_printer *p, int indent);
1173 __isl_give isl_printer *isl_printer_set_prefix(
1174 __isl_take isl_printer *p, const char *prefix);
1175 __isl_give isl_printer *isl_printer_set_suffix(
1176 __isl_take isl_printer *p, const char *suffix);
1178 The C<output_format> may be either C<ISL_FORMAT_ISL>, C<ISL_FORMAT_OMEGA>,
1179 C<ISL_FORMAT_POLYLIB>, C<ISL_FORMAT_EXT_POLYLIB> or C<ISL_FORMAT_LATEX>
1180 and defaults to C<ISL_FORMAT_ISL>.
1181 Each line in the output is indented by C<indent> (set by
1182 C<isl_printer_set_indent>) spaces
1183 (default: 0), prefixed by C<prefix> and suffixed by C<suffix>.
1184 In the C<PolyLib> format output,
1185 the coefficients of the existentially quantified variables
1186 appear between those of the set variables and those
1188 The function C<isl_printer_indent> increases the indentation
1189 by the specified amount (which may be negative).
1191 To actually print something, use
1193 #include <isl/printer.h>
1194 __isl_give isl_printer *isl_printer_print_double(
1195 __isl_take isl_printer *p, double d);
1197 #include <isl/set.h>
1198 __isl_give isl_printer *isl_printer_print_basic_set(
1199 __isl_take isl_printer *printer,
1200 __isl_keep isl_basic_set *bset);
1201 __isl_give isl_printer *isl_printer_print_set(
1202 __isl_take isl_printer *printer,
1203 __isl_keep isl_set *set);
1205 #include <isl/map.h>
1206 __isl_give isl_printer *isl_printer_print_basic_map(
1207 __isl_take isl_printer *printer,
1208 __isl_keep isl_basic_map *bmap);
1209 __isl_give isl_printer *isl_printer_print_map(
1210 __isl_take isl_printer *printer,
1211 __isl_keep isl_map *map);
1213 #include <isl/union_set.h>
1214 __isl_give isl_printer *isl_printer_print_union_set(
1215 __isl_take isl_printer *p,
1216 __isl_keep isl_union_set *uset);
1218 #include <isl/union_map.h>
1219 __isl_give isl_printer *isl_printer_print_union_map(
1220 __isl_take isl_printer *p,
1221 __isl_keep isl_union_map *umap);
1223 When called on a file printer, the following function flushes
1224 the file. When called on a string printer, the buffer is cleared.
1226 __isl_give isl_printer *isl_printer_flush(
1227 __isl_take isl_printer *p);
1229 =head2 Creating New Sets and Relations
1231 C<isl> has functions for creating some standard sets and relations.
1235 =item * Empty sets and relations
1237 __isl_give isl_basic_set *isl_basic_set_empty(
1238 __isl_take isl_space *space);
1239 __isl_give isl_basic_map *isl_basic_map_empty(
1240 __isl_take isl_space *space);
1241 __isl_give isl_set *isl_set_empty(
1242 __isl_take isl_space *space);
1243 __isl_give isl_map *isl_map_empty(
1244 __isl_take isl_space *space);
1245 __isl_give isl_union_set *isl_union_set_empty(
1246 __isl_take isl_space *space);
1247 __isl_give isl_union_map *isl_union_map_empty(
1248 __isl_take isl_space *space);
1250 For C<isl_union_set>s and C<isl_union_map>s, the space
1251 is only used to specify the parameters.
1253 =item * Universe sets and relations
1255 __isl_give isl_basic_set *isl_basic_set_universe(
1256 __isl_take isl_space *space);
1257 __isl_give isl_basic_map *isl_basic_map_universe(
1258 __isl_take isl_space *space);
1259 __isl_give isl_set *isl_set_universe(
1260 __isl_take isl_space *space);
1261 __isl_give isl_map *isl_map_universe(
1262 __isl_take isl_space *space);
1263 __isl_give isl_union_set *isl_union_set_universe(
1264 __isl_take isl_union_set *uset);
1265 __isl_give isl_union_map *isl_union_map_universe(
1266 __isl_take isl_union_map *umap);
1268 The sets and relations constructed by the functions above
1269 contain all integer values, while those constructed by the
1270 functions below only contain non-negative values.
1272 __isl_give isl_basic_set *isl_basic_set_nat_universe(
1273 __isl_take isl_space *space);
1274 __isl_give isl_basic_map *isl_basic_map_nat_universe(
1275 __isl_take isl_space *space);
1276 __isl_give isl_set *isl_set_nat_universe(
1277 __isl_take isl_space *space);
1278 __isl_give isl_map *isl_map_nat_universe(
1279 __isl_take isl_space *space);
1281 =item * Identity relations
1283 __isl_give isl_basic_map *isl_basic_map_identity(
1284 __isl_take isl_space *space);
1285 __isl_give isl_map *isl_map_identity(
1286 __isl_take isl_space *space);
1288 The number of input and output dimensions in C<space> needs
1291 =item * Lexicographic order
1293 __isl_give isl_map *isl_map_lex_lt(
1294 __isl_take isl_space *set_space);
1295 __isl_give isl_map *isl_map_lex_le(
1296 __isl_take isl_space *set_space);
1297 __isl_give isl_map *isl_map_lex_gt(
1298 __isl_take isl_space *set_space);
1299 __isl_give isl_map *isl_map_lex_ge(
1300 __isl_take isl_space *set_space);
1301 __isl_give isl_map *isl_map_lex_lt_first(
1302 __isl_take isl_space *space, unsigned n);
1303 __isl_give isl_map *isl_map_lex_le_first(
1304 __isl_take isl_space *space, unsigned n);
1305 __isl_give isl_map *isl_map_lex_gt_first(
1306 __isl_take isl_space *space, unsigned n);
1307 __isl_give isl_map *isl_map_lex_ge_first(
1308 __isl_take isl_space *space, unsigned n);
1310 The first four functions take a space for a B<set>
1311 and return relations that express that the elements in the domain
1312 are lexicographically less
1313 (C<isl_map_lex_lt>), less or equal (C<isl_map_lex_le>),
1314 greater (C<isl_map_lex_gt>) or greater or equal (C<isl_map_lex_ge>)
1315 than the elements in the range.
1316 The last four functions take a space for a map
1317 and return relations that express that the first C<n> dimensions
1318 in the domain are lexicographically less
1319 (C<isl_map_lex_lt_first>), less or equal (C<isl_map_lex_le_first>),
1320 greater (C<isl_map_lex_gt_first>) or greater or equal (C<isl_map_lex_ge_first>)
1321 than the first C<n> dimensions in the range.
1325 A basic set or relation can be converted to a set or relation
1326 using the following functions.
1328 __isl_give isl_set *isl_set_from_basic_set(
1329 __isl_take isl_basic_set *bset);
1330 __isl_give isl_map *isl_map_from_basic_map(
1331 __isl_take isl_basic_map *bmap);
1333 Sets and relations can be converted to union sets and relations
1334 using the following functions.
1336 __isl_give isl_union_set *isl_union_set_from_basic_set(
1337 __isl_take isl_basic_set *bset);
1338 __isl_give isl_union_map *isl_union_map_from_basic_map(
1339 __isl_take isl_basic_map *bmap);
1340 __isl_give isl_union_set *isl_union_set_from_set(
1341 __isl_take isl_set *set);
1342 __isl_give isl_union_map *isl_union_map_from_map(
1343 __isl_take isl_map *map);
1345 The inverse conversions below can only be used if the input
1346 union set or relation is known to contain elements in exactly one
1349 __isl_give isl_set *isl_set_from_union_set(
1350 __isl_take isl_union_set *uset);
1351 __isl_give isl_map *isl_map_from_union_map(
1352 __isl_take isl_union_map *umap);
1354 A zero-dimensional (basic) set can be constructed on a given parameter domain
1355 using the following function.
1357 __isl_give isl_basic_set *isl_basic_set_from_params(
1358 __isl_take isl_basic_set *bset);
1359 __isl_give isl_set *isl_set_from_params(
1360 __isl_take isl_set *set);
1362 Sets and relations can be copied and freed again using the following
1365 __isl_give isl_basic_set *isl_basic_set_copy(
1366 __isl_keep isl_basic_set *bset);
1367 __isl_give isl_set *isl_set_copy(__isl_keep isl_set *set);
1368 __isl_give isl_union_set *isl_union_set_copy(
1369 __isl_keep isl_union_set *uset);
1370 __isl_give isl_basic_map *isl_basic_map_copy(
1371 __isl_keep isl_basic_map *bmap);
1372 __isl_give isl_map *isl_map_copy(__isl_keep isl_map *map);
1373 __isl_give isl_union_map *isl_union_map_copy(
1374 __isl_keep isl_union_map *umap);
1375 void *isl_basic_set_free(__isl_take isl_basic_set *bset);
1376 void *isl_set_free(__isl_take isl_set *set);
1377 void *isl_union_set_free(__isl_take isl_union_set *uset);
1378 void *isl_basic_map_free(__isl_take isl_basic_map *bmap);
1379 void *isl_map_free(__isl_take isl_map *map);
1380 void *isl_union_map_free(__isl_take isl_union_map *umap);
1382 Other sets and relations can be constructed by starting
1383 from a universe set or relation, adding equality and/or
1384 inequality constraints and then projecting out the
1385 existentially quantified variables, if any.
1386 Constraints can be constructed, manipulated and
1387 added to (or removed from) (basic) sets and relations
1388 using the following functions.
1390 #include <isl/constraint.h>
1391 __isl_give isl_constraint *isl_equality_alloc(
1392 __isl_take isl_local_space *ls);
1393 __isl_give isl_constraint *isl_inequality_alloc(
1394 __isl_take isl_local_space *ls);
1395 __isl_give isl_constraint *isl_constraint_set_constant_si(
1396 __isl_take isl_constraint *constraint, int v);
1397 __isl_give isl_constraint *isl_constraint_set_constant_val(
1398 __isl_take isl_constraint *constraint,
1399 __isl_take isl_val *v);
1400 __isl_give isl_constraint *isl_constraint_set_coefficient_si(
1401 __isl_take isl_constraint *constraint,
1402 enum isl_dim_type type, int pos, int v);
1403 __isl_give isl_constraint *
1404 isl_constraint_set_coefficient_val(
1405 __isl_take isl_constraint *constraint,
1406 enum isl_dim_type type, int pos, isl_val *v);
1407 __isl_give isl_basic_map *isl_basic_map_add_constraint(
1408 __isl_take isl_basic_map *bmap,
1409 __isl_take isl_constraint *constraint);
1410 __isl_give isl_basic_set *isl_basic_set_add_constraint(
1411 __isl_take isl_basic_set *bset,
1412 __isl_take isl_constraint *constraint);
1413 __isl_give isl_map *isl_map_add_constraint(
1414 __isl_take isl_map *map,
1415 __isl_take isl_constraint *constraint);
1416 __isl_give isl_set *isl_set_add_constraint(
1417 __isl_take isl_set *set,
1418 __isl_take isl_constraint *constraint);
1419 __isl_give isl_basic_set *isl_basic_set_drop_constraint(
1420 __isl_take isl_basic_set *bset,
1421 __isl_take isl_constraint *constraint);
1423 For example, to create a set containing the even integers
1424 between 10 and 42, you would use the following code.
1427 isl_local_space *ls;
1429 isl_basic_set *bset;
1431 space = isl_space_set_alloc(ctx, 0, 2);
1432 bset = isl_basic_set_universe(isl_space_copy(space));
1433 ls = isl_local_space_from_space(space);
1435 c = isl_equality_alloc(isl_local_space_copy(ls));
1436 c = isl_constraint_set_coefficient_si(c, isl_dim_set, 0, -1);
1437 c = isl_constraint_set_coefficient_si(c, isl_dim_set, 1, 2);
1438 bset = isl_basic_set_add_constraint(bset, c);
1440 c = isl_inequality_alloc(isl_local_space_copy(ls));
1441 c = isl_constraint_set_constant_si(c, -10);
1442 c = isl_constraint_set_coefficient_si(c, isl_dim_set, 0, 1);
1443 bset = isl_basic_set_add_constraint(bset, c);
1445 c = isl_inequality_alloc(ls);
1446 c = isl_constraint_set_constant_si(c, 42);
1447 c = isl_constraint_set_coefficient_si(c, isl_dim_set, 0, -1);
1448 bset = isl_basic_set_add_constraint(bset, c);
1450 bset = isl_basic_set_project_out(bset, isl_dim_set, 1, 1);
1454 isl_basic_set *bset;
1455 bset = isl_basic_set_read_from_str(ctx,
1456 "{[i] : exists (a : i = 2a and i >= 10 and i <= 42)}");
1458 A basic set or relation can also be constructed from two matrices
1459 describing the equalities and the inequalities.
1461 __isl_give isl_basic_set *isl_basic_set_from_constraint_matrices(
1462 __isl_take isl_space *space,
1463 __isl_take isl_mat *eq, __isl_take isl_mat *ineq,
1464 enum isl_dim_type c1,
1465 enum isl_dim_type c2, enum isl_dim_type c3,
1466 enum isl_dim_type c4);
1467 __isl_give isl_basic_map *isl_basic_map_from_constraint_matrices(
1468 __isl_take isl_space *space,
1469 __isl_take isl_mat *eq, __isl_take isl_mat *ineq,
1470 enum isl_dim_type c1,
1471 enum isl_dim_type c2, enum isl_dim_type c3,
1472 enum isl_dim_type c4, enum isl_dim_type c5);
1474 The C<isl_dim_type> arguments indicate the order in which
1475 different kinds of variables appear in the input matrices
1476 and should be a permutation of C<isl_dim_cst>, C<isl_dim_param>,
1477 C<isl_dim_set> and C<isl_dim_div> for sets and
1478 of C<isl_dim_cst>, C<isl_dim_param>,
1479 C<isl_dim_in>, C<isl_dim_out> and C<isl_dim_div> for relations.
1481 A (basic or union) set or relation can also be constructed from a
1482 (union) (piecewise) (multiple) affine expression
1483 or a list of affine expressions
1484 (See L<"Piecewise Quasi Affine Expressions"> and
1485 L<"Piecewise Multiple Quasi Affine Expressions">).
1487 __isl_give isl_basic_map *isl_basic_map_from_aff(
1488 __isl_take isl_aff *aff);
1489 __isl_give isl_map *isl_map_from_aff(
1490 __isl_take isl_aff *aff);
1491 __isl_give isl_set *isl_set_from_pw_aff(
1492 __isl_take isl_pw_aff *pwaff);
1493 __isl_give isl_map *isl_map_from_pw_aff(
1494 __isl_take isl_pw_aff *pwaff);
1495 __isl_give isl_basic_map *isl_basic_map_from_aff_list(
1496 __isl_take isl_space *domain_space,
1497 __isl_take isl_aff_list *list);
1498 __isl_give isl_basic_map *isl_basic_map_from_multi_aff(
1499 __isl_take isl_multi_aff *maff)
1500 __isl_give isl_map *isl_map_from_multi_aff(
1501 __isl_take isl_multi_aff *maff)
1502 __isl_give isl_set *isl_set_from_pw_multi_aff(
1503 __isl_take isl_pw_multi_aff *pma);
1504 __isl_give isl_map *isl_map_from_pw_multi_aff(
1505 __isl_take isl_pw_multi_aff *pma);
1506 __isl_give isl_set *isl_set_from_multi_pw_aff(
1507 __isl_take isl_multi_pw_aff *mpa);
1508 __isl_give isl_map *isl_map_from_multi_pw_aff(
1509 __isl_take isl_multi_pw_aff *mpa);
1510 __isl_give isl_union_map *
1511 isl_union_map_from_union_pw_multi_aff(
1512 __isl_take isl_union_pw_multi_aff *upma);
1514 The C<domain_dim> argument describes the domain of the resulting
1515 basic relation. It is required because the C<list> may consist
1516 of zero affine expressions.
1518 =head2 Inspecting Sets and Relations
1520 Usually, the user should not have to care about the actual constraints
1521 of the sets and maps, but should instead apply the abstract operations
1522 explained in the following sections.
1523 Occasionally, however, it may be required to inspect the individual
1524 coefficients of the constraints. This section explains how to do so.
1525 In these cases, it may also be useful to have C<isl> compute
1526 an explicit representation of the existentially quantified variables.
1528 __isl_give isl_set *isl_set_compute_divs(
1529 __isl_take isl_set *set);
1530 __isl_give isl_map *isl_map_compute_divs(
1531 __isl_take isl_map *map);
1532 __isl_give isl_union_set *isl_union_set_compute_divs(
1533 __isl_take isl_union_set *uset);
1534 __isl_give isl_union_map *isl_union_map_compute_divs(
1535 __isl_take isl_union_map *umap);
1537 This explicit representation defines the existentially quantified
1538 variables as integer divisions of the other variables, possibly
1539 including earlier existentially quantified variables.
1540 An explicitly represented existentially quantified variable therefore
1541 has a unique value when the values of the other variables are known.
1542 If, furthermore, the same existentials, i.e., existentials
1543 with the same explicit representations, should appear in the
1544 same order in each of the disjuncts of a set or map, then the user should call
1545 either of the following functions.
1547 __isl_give isl_set *isl_set_align_divs(
1548 __isl_take isl_set *set);
1549 __isl_give isl_map *isl_map_align_divs(
1550 __isl_take isl_map *map);
1552 Alternatively, the existentially quantified variables can be removed
1553 using the following functions, which compute an overapproximation.
1555 __isl_give isl_basic_set *isl_basic_set_remove_divs(
1556 __isl_take isl_basic_set *bset);
1557 __isl_give isl_basic_map *isl_basic_map_remove_divs(
1558 __isl_take isl_basic_map *bmap);
1559 __isl_give isl_set *isl_set_remove_divs(
1560 __isl_take isl_set *set);
1561 __isl_give isl_map *isl_map_remove_divs(
1562 __isl_take isl_map *map);
1564 It is also possible to only remove those divs that are defined
1565 in terms of a given range of dimensions or only those for which
1566 no explicit representation is known.
1568 __isl_give isl_basic_set *
1569 isl_basic_set_remove_divs_involving_dims(
1570 __isl_take isl_basic_set *bset,
1571 enum isl_dim_type type,
1572 unsigned first, unsigned n);
1573 __isl_give isl_basic_map *
1574 isl_basic_map_remove_divs_involving_dims(
1575 __isl_take isl_basic_map *bmap,
1576 enum isl_dim_type type,
1577 unsigned first, unsigned n);
1578 __isl_give isl_set *isl_set_remove_divs_involving_dims(
1579 __isl_take isl_set *set, enum isl_dim_type type,
1580 unsigned first, unsigned n);
1581 __isl_give isl_map *isl_map_remove_divs_involving_dims(
1582 __isl_take isl_map *map, enum isl_dim_type type,
1583 unsigned first, unsigned n);
1585 __isl_give isl_basic_set *
1586 isl_basic_set_remove_unknown_divs(
1587 __isl_take isl_basic_set *bset);
1588 __isl_give isl_set *isl_set_remove_unknown_divs(
1589 __isl_take isl_set *set);
1590 __isl_give isl_map *isl_map_remove_unknown_divs(
1591 __isl_take isl_map *map);
1593 To iterate over all the sets or maps in a union set or map, use
1595 int isl_union_set_foreach_set(__isl_keep isl_union_set *uset,
1596 int (*fn)(__isl_take isl_set *set, void *user),
1598 int isl_union_map_foreach_map(__isl_keep isl_union_map *umap,
1599 int (*fn)(__isl_take isl_map *map, void *user),
1602 The number of sets or maps in a union set or map can be obtained
1605 int isl_union_set_n_set(__isl_keep isl_union_set *uset);
1606 int isl_union_map_n_map(__isl_keep isl_union_map *umap);
1608 To extract the set or map in a given space from a union, use
1610 __isl_give isl_set *isl_union_set_extract_set(
1611 __isl_keep isl_union_set *uset,
1612 __isl_take isl_space *space);
1613 __isl_give isl_map *isl_union_map_extract_map(
1614 __isl_keep isl_union_map *umap,
1615 __isl_take isl_space *space);
1617 To iterate over all the basic sets or maps in a set or map, use
1619 int isl_set_foreach_basic_set(__isl_keep isl_set *set,
1620 int (*fn)(__isl_take isl_basic_set *bset, void *user),
1622 int isl_map_foreach_basic_map(__isl_keep isl_map *map,
1623 int (*fn)(__isl_take isl_basic_map *bmap, void *user),
1626 The callback function C<fn> should return 0 if successful and
1627 -1 if an error occurs. In the latter case, or if any other error
1628 occurs, the above functions will return -1.
1630 It should be noted that C<isl> does not guarantee that
1631 the basic sets or maps passed to C<fn> are disjoint.
1632 If this is required, then the user should call one of
1633 the following functions first.
1635 __isl_give isl_set *isl_set_make_disjoint(
1636 __isl_take isl_set *set);
1637 __isl_give isl_map *isl_map_make_disjoint(
1638 __isl_take isl_map *map);
1640 The number of basic sets in a set can be obtained
1643 int isl_set_n_basic_set(__isl_keep isl_set *set);
1645 To iterate over the constraints of a basic set or map, use
1647 #include <isl/constraint.h>
1649 int isl_basic_set_n_constraint(
1650 __isl_keep isl_basic_set *bset);
1651 int isl_basic_set_foreach_constraint(
1652 __isl_keep isl_basic_set *bset,
1653 int (*fn)(__isl_take isl_constraint *c, void *user),
1655 int isl_basic_map_foreach_constraint(
1656 __isl_keep isl_basic_map *bmap,
1657 int (*fn)(__isl_take isl_constraint *c, void *user),
1659 void *isl_constraint_free(__isl_take isl_constraint *c);
1661 Again, the callback function C<fn> should return 0 if successful and
1662 -1 if an error occurs. In the latter case, or if any other error
1663 occurs, the above functions will return -1.
1664 The constraint C<c> represents either an equality or an inequality.
1665 Use the following function to find out whether a constraint
1666 represents an equality. If not, it represents an inequality.
1668 int isl_constraint_is_equality(
1669 __isl_keep isl_constraint *constraint);
1671 The coefficients of the constraints can be inspected using
1672 the following functions.
1674 int isl_constraint_is_lower_bound(
1675 __isl_keep isl_constraint *constraint,
1676 enum isl_dim_type type, unsigned pos);
1677 int isl_constraint_is_upper_bound(
1678 __isl_keep isl_constraint *constraint,
1679 enum isl_dim_type type, unsigned pos);
1680 __isl_give isl_val *isl_constraint_get_constant_val(
1681 __isl_keep isl_constraint *constraint);
1682 __isl_give isl_val *isl_constraint_get_coefficient_val(
1683 __isl_keep isl_constraint *constraint,
1684 enum isl_dim_type type, int pos);
1685 int isl_constraint_involves_dims(
1686 __isl_keep isl_constraint *constraint,
1687 enum isl_dim_type type, unsigned first, unsigned n);
1689 The explicit representations of the existentially quantified
1690 variables can be inspected using the following function.
1691 Note that the user is only allowed to use this function
1692 if the inspected set or map is the result of a call
1693 to C<isl_set_compute_divs> or C<isl_map_compute_divs>.
1694 The existentially quantified variable is equal to the floor
1695 of the returned affine expression. The affine expression
1696 itself can be inspected using the functions in
1697 L<"Piecewise Quasi Affine Expressions">.
1699 __isl_give isl_aff *isl_constraint_get_div(
1700 __isl_keep isl_constraint *constraint, int pos);
1702 To obtain the constraints of a basic set or map in matrix
1703 form, use the following functions.
1705 __isl_give isl_mat *isl_basic_set_equalities_matrix(
1706 __isl_keep isl_basic_set *bset,
1707 enum isl_dim_type c1, enum isl_dim_type c2,
1708 enum isl_dim_type c3, enum isl_dim_type c4);
1709 __isl_give isl_mat *isl_basic_set_inequalities_matrix(
1710 __isl_keep isl_basic_set *bset,
1711 enum isl_dim_type c1, enum isl_dim_type c2,
1712 enum isl_dim_type c3, enum isl_dim_type c4);
1713 __isl_give isl_mat *isl_basic_map_equalities_matrix(
1714 __isl_keep isl_basic_map *bmap,
1715 enum isl_dim_type c1,
1716 enum isl_dim_type c2, enum isl_dim_type c3,
1717 enum isl_dim_type c4, enum isl_dim_type c5);
1718 __isl_give isl_mat *isl_basic_map_inequalities_matrix(
1719 __isl_keep isl_basic_map *bmap,
1720 enum isl_dim_type c1,
1721 enum isl_dim_type c2, enum isl_dim_type c3,
1722 enum isl_dim_type c4, enum isl_dim_type c5);
1724 The C<isl_dim_type> arguments dictate the order in which
1725 different kinds of variables appear in the resulting matrix
1726 and should be a permutation of C<isl_dim_cst>, C<isl_dim_param>,
1727 C<isl_dim_in>, C<isl_dim_out> and C<isl_dim_div>.
1729 The number of parameters, input, output or set dimensions can
1730 be obtained using the following functions.
1732 unsigned isl_basic_set_dim(__isl_keep isl_basic_set *bset,
1733 enum isl_dim_type type);
1734 unsigned isl_basic_map_dim(__isl_keep isl_basic_map *bmap,
1735 enum isl_dim_type type);
1736 unsigned isl_set_dim(__isl_keep isl_set *set,
1737 enum isl_dim_type type);
1738 unsigned isl_map_dim(__isl_keep isl_map *map,
1739 enum isl_dim_type type);
1741 To check whether the description of a set or relation depends
1742 on one or more given dimensions, it is not necessary to iterate over all
1743 constraints. Instead the following functions can be used.
1745 int isl_basic_set_involves_dims(
1746 __isl_keep isl_basic_set *bset,
1747 enum isl_dim_type type, unsigned first, unsigned n);
1748 int isl_set_involves_dims(__isl_keep isl_set *set,
1749 enum isl_dim_type type, unsigned first, unsigned n);
1750 int isl_basic_map_involves_dims(
1751 __isl_keep isl_basic_map *bmap,
1752 enum isl_dim_type type, unsigned first, unsigned n);
1753 int isl_map_involves_dims(__isl_keep isl_map *map,
1754 enum isl_dim_type type, unsigned first, unsigned n);
1756 Similarly, the following functions can be used to check whether
1757 a given dimension is involved in any lower or upper bound.
1759 int isl_set_dim_has_any_lower_bound(__isl_keep isl_set *set,
1760 enum isl_dim_type type, unsigned pos);
1761 int isl_set_dim_has_any_upper_bound(__isl_keep isl_set *set,
1762 enum isl_dim_type type, unsigned pos);
1764 Note that these functions return true even if there is a bound on
1765 the dimension on only some of the basic sets of C<set>.
1766 To check if they have a bound for all of the basic sets in C<set>,
1767 use the following functions instead.
1769 int isl_set_dim_has_lower_bound(__isl_keep isl_set *set,
1770 enum isl_dim_type type, unsigned pos);
1771 int isl_set_dim_has_upper_bound(__isl_keep isl_set *set,
1772 enum isl_dim_type type, unsigned pos);
1774 The identifiers or names of the domain and range spaces of a set
1775 or relation can be read off or set using the following functions.
1777 __isl_give isl_set *isl_set_set_tuple_id(
1778 __isl_take isl_set *set, __isl_take isl_id *id);
1779 __isl_give isl_set *isl_set_reset_tuple_id(
1780 __isl_take isl_set *set);
1781 int isl_set_has_tuple_id(__isl_keep isl_set *set);
1782 __isl_give isl_id *isl_set_get_tuple_id(
1783 __isl_keep isl_set *set);
1784 __isl_give isl_map *isl_map_set_tuple_id(
1785 __isl_take isl_map *map, enum isl_dim_type type,
1786 __isl_take isl_id *id);
1787 __isl_give isl_map *isl_map_reset_tuple_id(
1788 __isl_take isl_map *map, enum isl_dim_type type);
1789 int isl_map_has_tuple_id(__isl_keep isl_map *map,
1790 enum isl_dim_type type);
1791 __isl_give isl_id *isl_map_get_tuple_id(
1792 __isl_keep isl_map *map, enum isl_dim_type type);
1794 const char *isl_basic_set_get_tuple_name(
1795 __isl_keep isl_basic_set *bset);
1796 __isl_give isl_basic_set *isl_basic_set_set_tuple_name(
1797 __isl_take isl_basic_set *set, const char *s);
1798 int isl_set_has_tuple_name(__isl_keep isl_set *set);
1799 const char *isl_set_get_tuple_name(
1800 __isl_keep isl_set *set);
1801 const char *isl_basic_map_get_tuple_name(
1802 __isl_keep isl_basic_map *bmap,
1803 enum isl_dim_type type);
1804 __isl_give isl_basic_map *isl_basic_map_set_tuple_name(
1805 __isl_take isl_basic_map *bmap,
1806 enum isl_dim_type type, const char *s);
1807 int isl_map_has_tuple_name(__isl_keep isl_map *map,
1808 enum isl_dim_type type);
1809 const char *isl_map_get_tuple_name(
1810 __isl_keep isl_map *map,
1811 enum isl_dim_type type);
1813 As with C<isl_space_get_tuple_name>, the value returned points to
1814 an internal data structure.
1815 The identifiers, positions or names of individual dimensions can be
1816 read off using the following functions.
1818 __isl_give isl_id *isl_basic_set_get_dim_id(
1819 __isl_keep isl_basic_set *bset,
1820 enum isl_dim_type type, unsigned pos);
1821 __isl_give isl_set *isl_set_set_dim_id(
1822 __isl_take isl_set *set, enum isl_dim_type type,
1823 unsigned pos, __isl_take isl_id *id);
1824 int isl_set_has_dim_id(__isl_keep isl_set *set,
1825 enum isl_dim_type type, unsigned pos);
1826 __isl_give isl_id *isl_set_get_dim_id(
1827 __isl_keep isl_set *set, enum isl_dim_type type,
1829 int isl_basic_map_has_dim_id(
1830 __isl_keep isl_basic_map *bmap,
1831 enum isl_dim_type type, unsigned pos);
1832 __isl_give isl_map *isl_map_set_dim_id(
1833 __isl_take isl_map *map, enum isl_dim_type type,
1834 unsigned pos, __isl_take isl_id *id);
1835 int isl_map_has_dim_id(__isl_keep isl_map *map,
1836 enum isl_dim_type type, unsigned pos);
1837 __isl_give isl_id *isl_map_get_dim_id(
1838 __isl_keep isl_map *map, enum isl_dim_type type,
1841 int isl_set_find_dim_by_id(__isl_keep isl_set *set,
1842 enum isl_dim_type type, __isl_keep isl_id *id);
1843 int isl_map_find_dim_by_id(__isl_keep isl_map *map,
1844 enum isl_dim_type type, __isl_keep isl_id *id);
1845 int isl_set_find_dim_by_name(__isl_keep isl_set *set,
1846 enum isl_dim_type type, const char *name);
1847 int isl_map_find_dim_by_name(__isl_keep isl_map *map,
1848 enum isl_dim_type type, const char *name);
1850 const char *isl_constraint_get_dim_name(
1851 __isl_keep isl_constraint *constraint,
1852 enum isl_dim_type type, unsigned pos);
1853 const char *isl_basic_set_get_dim_name(
1854 __isl_keep isl_basic_set *bset,
1855 enum isl_dim_type type, unsigned pos);
1856 int isl_set_has_dim_name(__isl_keep isl_set *set,
1857 enum isl_dim_type type, unsigned pos);
1858 const char *isl_set_get_dim_name(
1859 __isl_keep isl_set *set,
1860 enum isl_dim_type type, unsigned pos);
1861 const char *isl_basic_map_get_dim_name(
1862 __isl_keep isl_basic_map *bmap,
1863 enum isl_dim_type type, unsigned pos);
1864 int isl_map_has_dim_name(__isl_keep isl_map *map,
1865 enum isl_dim_type type, unsigned pos);
1866 const char *isl_map_get_dim_name(
1867 __isl_keep isl_map *map,
1868 enum isl_dim_type type, unsigned pos);
1870 These functions are mostly useful to obtain the identifiers, positions
1871 or names of the parameters. Identifiers of individual dimensions are
1872 essentially only useful for printing. They are ignored by all other
1873 operations and may not be preserved across those operations.
1877 =head3 Unary Properties
1883 The following functions test whether the given set or relation
1884 contains any integer points. The ``plain'' variants do not perform
1885 any computations, but simply check if the given set or relation
1886 is already known to be empty.
1888 int isl_basic_set_plain_is_empty(__isl_keep isl_basic_set *bset);
1889 int isl_basic_set_is_empty(__isl_keep isl_basic_set *bset);
1890 int isl_set_plain_is_empty(__isl_keep isl_set *set);
1891 int isl_set_is_empty(__isl_keep isl_set *set);
1892 int isl_union_set_is_empty(__isl_keep isl_union_set *uset);
1893 int isl_basic_map_plain_is_empty(__isl_keep isl_basic_map *bmap);
1894 int isl_basic_map_is_empty(__isl_keep isl_basic_map *bmap);
1895 int isl_map_plain_is_empty(__isl_keep isl_map *map);
1896 int isl_map_is_empty(__isl_keep isl_map *map);
1897 int isl_union_map_is_empty(__isl_keep isl_union_map *umap);
1899 =item * Universality
1901 int isl_basic_set_is_universe(__isl_keep isl_basic_set *bset);
1902 int isl_basic_map_is_universe(__isl_keep isl_basic_map *bmap);
1903 int isl_set_plain_is_universe(__isl_keep isl_set *set);
1905 =item * Single-valuedness
1907 int isl_basic_map_is_single_valued(
1908 __isl_keep isl_basic_map *bmap);
1909 int isl_map_plain_is_single_valued(
1910 __isl_keep isl_map *map);
1911 int isl_map_is_single_valued(__isl_keep isl_map *map);
1912 int isl_union_map_is_single_valued(__isl_keep isl_union_map *umap);
1916 int isl_map_plain_is_injective(__isl_keep isl_map *map);
1917 int isl_map_is_injective(__isl_keep isl_map *map);
1918 int isl_union_map_plain_is_injective(
1919 __isl_keep isl_union_map *umap);
1920 int isl_union_map_is_injective(
1921 __isl_keep isl_union_map *umap);
1925 int isl_map_is_bijective(__isl_keep isl_map *map);
1926 int isl_union_map_is_bijective(__isl_keep isl_union_map *umap);
1930 __isl_give isl_val *
1931 isl_basic_map_plain_get_val_if_fixed(
1932 __isl_keep isl_basic_map *bmap,
1933 enum isl_dim_type type, unsigned pos);
1934 __isl_give isl_val *isl_set_plain_get_val_if_fixed(
1935 __isl_keep isl_set *set,
1936 enum isl_dim_type type, unsigned pos);
1937 __isl_give isl_val *isl_map_plain_get_val_if_fixed(
1938 __isl_keep isl_map *map,
1939 enum isl_dim_type type, unsigned pos);
1941 If the set or relation obviously lies on a hyperplane where the given dimension
1942 has a fixed value, then return that value.
1943 Otherwise return NaN.
1947 int isl_set_dim_residue_class_val(
1948 __isl_keep isl_set *set,
1949 int pos, __isl_give isl_val **modulo,
1950 __isl_give isl_val **residue);
1952 Check if the values of the given set dimension are equal to a fixed
1953 value modulo some integer value. If so, assign the modulo to C<*modulo>
1954 and the fixed value to C<*residue>. If the given dimension attains only
1955 a single value, then assign C<0> to C<*modulo> and the fixed value to
1957 If the dimension does not attain only a single value and if no modulo
1958 can be found then assign C<1> to C<*modulo> and C<1> to C<*residue>.
1962 To check whether a set is a parameter domain, use this function:
1964 int isl_set_is_params(__isl_keep isl_set *set);
1965 int isl_union_set_is_params(
1966 __isl_keep isl_union_set *uset);
1970 The following functions check whether the domain of the given
1971 (basic) set is a wrapped relation.
1973 int isl_basic_set_is_wrapping(
1974 __isl_keep isl_basic_set *bset);
1975 int isl_set_is_wrapping(__isl_keep isl_set *set);
1977 =item * Internal Product
1979 int isl_basic_map_can_zip(
1980 __isl_keep isl_basic_map *bmap);
1981 int isl_map_can_zip(__isl_keep isl_map *map);
1983 Check whether the product of domain and range of the given relation
1985 i.e., whether both domain and range are nested relations.
1989 int isl_basic_map_can_curry(
1990 __isl_keep isl_basic_map *bmap);
1991 int isl_map_can_curry(__isl_keep isl_map *map);
1993 Check whether the domain of the (basic) relation is a wrapped relation.
1995 int isl_basic_map_can_uncurry(
1996 __isl_keep isl_basic_map *bmap);
1997 int isl_map_can_uncurry(__isl_keep isl_map *map);
1999 Check whether the range of the (basic) relation is a wrapped relation.
2003 =head3 Binary Properties
2009 int isl_basic_set_plain_is_equal(
2010 __isl_keep isl_basic_set *bset1,
2011 __isl_keep isl_basic_set *bset2);
2012 int isl_set_plain_is_equal(__isl_keep isl_set *set1,
2013 __isl_keep isl_set *set2);
2014 int isl_set_is_equal(__isl_keep isl_set *set1,
2015 __isl_keep isl_set *set2);
2016 int isl_union_set_is_equal(
2017 __isl_keep isl_union_set *uset1,
2018 __isl_keep isl_union_set *uset2);
2019 int isl_basic_map_is_equal(
2020 __isl_keep isl_basic_map *bmap1,
2021 __isl_keep isl_basic_map *bmap2);
2022 int isl_map_is_equal(__isl_keep isl_map *map1,
2023 __isl_keep isl_map *map2);
2024 int isl_map_plain_is_equal(__isl_keep isl_map *map1,
2025 __isl_keep isl_map *map2);
2026 int isl_union_map_is_equal(
2027 __isl_keep isl_union_map *umap1,
2028 __isl_keep isl_union_map *umap2);
2030 =item * Disjointness
2032 int isl_basic_set_is_disjoint(
2033 __isl_keep isl_basic_set *bset1,
2034 __isl_keep isl_basic_set *bset2);
2035 int isl_set_plain_is_disjoint(__isl_keep isl_set *set1,
2036 __isl_keep isl_set *set2);
2037 int isl_set_is_disjoint(__isl_keep isl_set *set1,
2038 __isl_keep isl_set *set2);
2039 int isl_basic_map_is_disjoint(
2040 __isl_keep isl_basic_map *bmap1,
2041 __isl_keep isl_basic_map *bmap2);
2042 int isl_map_is_disjoint(__isl_keep isl_map *map1,
2043 __isl_keep isl_map *map2);
2047 int isl_basic_set_is_subset(
2048 __isl_keep isl_basic_set *bset1,
2049 __isl_keep isl_basic_set *bset2);
2050 int isl_set_is_subset(__isl_keep isl_set *set1,
2051 __isl_keep isl_set *set2);
2052 int isl_set_is_strict_subset(
2053 __isl_keep isl_set *set1,
2054 __isl_keep isl_set *set2);
2055 int isl_union_set_is_subset(
2056 __isl_keep isl_union_set *uset1,
2057 __isl_keep isl_union_set *uset2);
2058 int isl_union_set_is_strict_subset(
2059 __isl_keep isl_union_set *uset1,
2060 __isl_keep isl_union_set *uset2);
2061 int isl_basic_map_is_subset(
2062 __isl_keep isl_basic_map *bmap1,
2063 __isl_keep isl_basic_map *bmap2);
2064 int isl_basic_map_is_strict_subset(
2065 __isl_keep isl_basic_map *bmap1,
2066 __isl_keep isl_basic_map *bmap2);
2067 int isl_map_is_subset(
2068 __isl_keep isl_map *map1,
2069 __isl_keep isl_map *map2);
2070 int isl_map_is_strict_subset(
2071 __isl_keep isl_map *map1,
2072 __isl_keep isl_map *map2);
2073 int isl_union_map_is_subset(
2074 __isl_keep isl_union_map *umap1,
2075 __isl_keep isl_union_map *umap2);
2076 int isl_union_map_is_strict_subset(
2077 __isl_keep isl_union_map *umap1,
2078 __isl_keep isl_union_map *umap2);
2080 Check whether the first argument is a (strict) subset of the
2085 int isl_set_plain_cmp(__isl_keep isl_set *set1,
2086 __isl_keep isl_set *set2);
2088 This function is useful for sorting C<isl_set>s.
2089 The order depends on the internal representation of the inputs.
2090 The order is fixed over different calls to the function (assuming
2091 the internal representation of the inputs has not changed), but may
2092 change over different versions of C<isl>.
2096 =head2 Unary Operations
2102 __isl_give isl_set *isl_set_complement(
2103 __isl_take isl_set *set);
2104 __isl_give isl_map *isl_map_complement(
2105 __isl_take isl_map *map);
2109 __isl_give isl_basic_map *isl_basic_map_reverse(
2110 __isl_take isl_basic_map *bmap);
2111 __isl_give isl_map *isl_map_reverse(
2112 __isl_take isl_map *map);
2113 __isl_give isl_union_map *isl_union_map_reverse(
2114 __isl_take isl_union_map *umap);
2118 __isl_give isl_basic_set *isl_basic_set_project_out(
2119 __isl_take isl_basic_set *bset,
2120 enum isl_dim_type type, unsigned first, unsigned n);
2121 __isl_give isl_basic_map *isl_basic_map_project_out(
2122 __isl_take isl_basic_map *bmap,
2123 enum isl_dim_type type, unsigned first, unsigned n);
2124 __isl_give isl_set *isl_set_project_out(__isl_take isl_set *set,
2125 enum isl_dim_type type, unsigned first, unsigned n);
2126 __isl_give isl_map *isl_map_project_out(__isl_take isl_map *map,
2127 enum isl_dim_type type, unsigned first, unsigned n);
2128 __isl_give isl_basic_set *isl_basic_set_params(
2129 __isl_take isl_basic_set *bset);
2130 __isl_give isl_basic_set *isl_basic_map_domain(
2131 __isl_take isl_basic_map *bmap);
2132 __isl_give isl_basic_set *isl_basic_map_range(
2133 __isl_take isl_basic_map *bmap);
2134 __isl_give isl_set *isl_set_params(__isl_take isl_set *set);
2135 __isl_give isl_set *isl_map_params(__isl_take isl_map *map);
2136 __isl_give isl_set *isl_map_domain(
2137 __isl_take isl_map *bmap);
2138 __isl_give isl_set *isl_map_range(
2139 __isl_take isl_map *map);
2140 __isl_give isl_set *isl_union_set_params(
2141 __isl_take isl_union_set *uset);
2142 __isl_give isl_set *isl_union_map_params(
2143 __isl_take isl_union_map *umap);
2144 __isl_give isl_union_set *isl_union_map_domain(
2145 __isl_take isl_union_map *umap);
2146 __isl_give isl_union_set *isl_union_map_range(
2147 __isl_take isl_union_map *umap);
2149 __isl_give isl_basic_map *isl_basic_map_domain_map(
2150 __isl_take isl_basic_map *bmap);
2151 __isl_give isl_basic_map *isl_basic_map_range_map(
2152 __isl_take isl_basic_map *bmap);
2153 __isl_give isl_map *isl_map_domain_map(__isl_take isl_map *map);
2154 __isl_give isl_map *isl_map_range_map(__isl_take isl_map *map);
2155 __isl_give isl_union_map *isl_union_map_domain_map(
2156 __isl_take isl_union_map *umap);
2157 __isl_give isl_union_map *isl_union_map_range_map(
2158 __isl_take isl_union_map *umap);
2160 The functions above construct a (basic, regular or union) relation
2161 that maps (a wrapped version of) the input relation to its domain or range.
2165 __isl_give isl_basic_set *isl_basic_set_eliminate(
2166 __isl_take isl_basic_set *bset,
2167 enum isl_dim_type type,
2168 unsigned first, unsigned n);
2169 __isl_give isl_set *isl_set_eliminate(
2170 __isl_take isl_set *set, enum isl_dim_type type,
2171 unsigned first, unsigned n);
2172 __isl_give isl_basic_map *isl_basic_map_eliminate(
2173 __isl_take isl_basic_map *bmap,
2174 enum isl_dim_type type,
2175 unsigned first, unsigned n);
2176 __isl_give isl_map *isl_map_eliminate(
2177 __isl_take isl_map *map, enum isl_dim_type type,
2178 unsigned first, unsigned n);
2180 Eliminate the coefficients for the given dimensions from the constraints,
2181 without removing the dimensions.
2185 __isl_give isl_basic_set *isl_basic_set_fix_si(
2186 __isl_take isl_basic_set *bset,
2187 enum isl_dim_type type, unsigned pos, int value);
2188 __isl_give isl_basic_set *isl_basic_set_fix_val(
2189 __isl_take isl_basic_set *bset,
2190 enum isl_dim_type type, unsigned pos,
2191 __isl_take isl_val *v);
2192 __isl_give isl_set *isl_set_fix_si(__isl_take isl_set *set,
2193 enum isl_dim_type type, unsigned pos, int value);
2194 __isl_give isl_set *isl_set_fix_val(
2195 __isl_take isl_set *set,
2196 enum isl_dim_type type, unsigned pos,
2197 __isl_take isl_val *v);
2198 __isl_give isl_basic_map *isl_basic_map_fix_si(
2199 __isl_take isl_basic_map *bmap,
2200 enum isl_dim_type type, unsigned pos, int value);
2201 __isl_give isl_basic_map *isl_basic_map_fix_val(
2202 __isl_take isl_basic_map *bmap,
2203 enum isl_dim_type type, unsigned pos,
2204 __isl_take isl_val *v);
2205 __isl_give isl_map *isl_map_fix_si(__isl_take isl_map *map,
2206 enum isl_dim_type type, unsigned pos, int value);
2207 __isl_give isl_map *isl_map_fix_val(
2208 __isl_take isl_map *map,
2209 enum isl_dim_type type, unsigned pos,
2210 __isl_take isl_val *v);
2212 Intersect the set or relation with the hyperplane where the given
2213 dimension has the fixed given value.
2215 __isl_give isl_basic_map *isl_basic_map_lower_bound_si(
2216 __isl_take isl_basic_map *bmap,
2217 enum isl_dim_type type, unsigned pos, int value);
2218 __isl_give isl_basic_map *isl_basic_map_upper_bound_si(
2219 __isl_take isl_basic_map *bmap,
2220 enum isl_dim_type type, unsigned pos, int value);
2221 __isl_give isl_set *isl_set_lower_bound_si(
2222 __isl_take isl_set *set,
2223 enum isl_dim_type type, unsigned pos, int value);
2224 __isl_give isl_set *isl_set_lower_bound_val(
2225 __isl_take isl_set *set,
2226 enum isl_dim_type type, unsigned pos,
2227 __isl_take isl_val *value);
2228 __isl_give isl_map *isl_map_lower_bound_si(
2229 __isl_take isl_map *map,
2230 enum isl_dim_type type, unsigned pos, int value);
2231 __isl_give isl_set *isl_set_upper_bound_si(
2232 __isl_take isl_set *set,
2233 enum isl_dim_type type, unsigned pos, int value);
2234 __isl_give isl_set *isl_set_upper_bound_val(
2235 __isl_take isl_set *set,
2236 enum isl_dim_type type, unsigned pos,
2237 __isl_take isl_val *value);
2238 __isl_give isl_map *isl_map_upper_bound_si(
2239 __isl_take isl_map *map,
2240 enum isl_dim_type type, unsigned pos, int value);
2242 Intersect the set or relation with the half-space where the given
2243 dimension has a value bounded by the fixed given integer value.
2245 __isl_give isl_set *isl_set_equate(__isl_take isl_set *set,
2246 enum isl_dim_type type1, int pos1,
2247 enum isl_dim_type type2, int pos2);
2248 __isl_give isl_basic_map *isl_basic_map_equate(
2249 __isl_take isl_basic_map *bmap,
2250 enum isl_dim_type type1, int pos1,
2251 enum isl_dim_type type2, int pos2);
2252 __isl_give isl_map *isl_map_equate(__isl_take isl_map *map,
2253 enum isl_dim_type type1, int pos1,
2254 enum isl_dim_type type2, int pos2);
2256 Intersect the set or relation with the hyperplane where the given
2257 dimensions are equal to each other.
2259 __isl_give isl_map *isl_map_oppose(__isl_take isl_map *map,
2260 enum isl_dim_type type1, int pos1,
2261 enum isl_dim_type type2, int pos2);
2263 Intersect the relation with the hyperplane where the given
2264 dimensions have opposite values.
2266 __isl_give isl_basic_map *isl_basic_map_order_ge(
2267 __isl_take isl_basic_map *bmap,
2268 enum isl_dim_type type1, int pos1,
2269 enum isl_dim_type type2, int pos2);
2270 __isl_give isl_map *isl_map_order_lt(__isl_take isl_map *map,
2271 enum isl_dim_type type1, int pos1,
2272 enum isl_dim_type type2, int pos2);
2273 __isl_give isl_basic_map *isl_basic_map_order_gt(
2274 __isl_take isl_basic_map *bmap,
2275 enum isl_dim_type type1, int pos1,
2276 enum isl_dim_type type2, int pos2);
2277 __isl_give isl_map *isl_map_order_gt(__isl_take isl_map *map,
2278 enum isl_dim_type type1, int pos1,
2279 enum isl_dim_type type2, int pos2);
2281 Intersect the relation with the half-space where the given
2282 dimensions satisfy the given ordering.
2286 __isl_give isl_map *isl_set_identity(
2287 __isl_take isl_set *set);
2288 __isl_give isl_union_map *isl_union_set_identity(
2289 __isl_take isl_union_set *uset);
2291 Construct an identity relation on the given (union) set.
2295 __isl_give isl_basic_set *isl_basic_map_deltas(
2296 __isl_take isl_basic_map *bmap);
2297 __isl_give isl_set *isl_map_deltas(__isl_take isl_map *map);
2298 __isl_give isl_union_set *isl_union_map_deltas(
2299 __isl_take isl_union_map *umap);
2301 These functions return a (basic) set containing the differences
2302 between image elements and corresponding domain elements in the input.
2304 __isl_give isl_basic_map *isl_basic_map_deltas_map(
2305 __isl_take isl_basic_map *bmap);
2306 __isl_give isl_map *isl_map_deltas_map(
2307 __isl_take isl_map *map);
2308 __isl_give isl_union_map *isl_union_map_deltas_map(
2309 __isl_take isl_union_map *umap);
2311 The functions above construct a (basic, regular or union) relation
2312 that maps (a wrapped version of) the input relation to its delta set.
2316 Simplify the representation of a set or relation by trying
2317 to combine pairs of basic sets or relations into a single
2318 basic set or relation.
2320 __isl_give isl_set *isl_set_coalesce(__isl_take isl_set *set);
2321 __isl_give isl_map *isl_map_coalesce(__isl_take isl_map *map);
2322 __isl_give isl_union_set *isl_union_set_coalesce(
2323 __isl_take isl_union_set *uset);
2324 __isl_give isl_union_map *isl_union_map_coalesce(
2325 __isl_take isl_union_map *umap);
2327 One of the methods for combining pairs of basic sets or relations
2328 can result in coefficients that are much larger than those that appear
2329 in the constraints of the input. By default, the coefficients are
2330 not allowed to grow larger, but this can be changed by unsetting
2331 the following option.
2333 int isl_options_set_coalesce_bounded_wrapping(
2334 isl_ctx *ctx, int val);
2335 int isl_options_get_coalesce_bounded_wrapping(
2338 =item * Detecting equalities
2340 __isl_give isl_basic_set *isl_basic_set_detect_equalities(
2341 __isl_take isl_basic_set *bset);
2342 __isl_give isl_basic_map *isl_basic_map_detect_equalities(
2343 __isl_take isl_basic_map *bmap);
2344 __isl_give isl_set *isl_set_detect_equalities(
2345 __isl_take isl_set *set);
2346 __isl_give isl_map *isl_map_detect_equalities(
2347 __isl_take isl_map *map);
2348 __isl_give isl_union_set *isl_union_set_detect_equalities(
2349 __isl_take isl_union_set *uset);
2350 __isl_give isl_union_map *isl_union_map_detect_equalities(
2351 __isl_take isl_union_map *umap);
2353 Simplify the representation of a set or relation by detecting implicit
2356 =item * Removing redundant constraints
2358 __isl_give isl_basic_set *isl_basic_set_remove_redundancies(
2359 __isl_take isl_basic_set *bset);
2360 __isl_give isl_set *isl_set_remove_redundancies(
2361 __isl_take isl_set *set);
2362 __isl_give isl_basic_map *isl_basic_map_remove_redundancies(
2363 __isl_take isl_basic_map *bmap);
2364 __isl_give isl_map *isl_map_remove_redundancies(
2365 __isl_take isl_map *map);
2369 __isl_give isl_basic_set *isl_set_convex_hull(
2370 __isl_take isl_set *set);
2371 __isl_give isl_basic_map *isl_map_convex_hull(
2372 __isl_take isl_map *map);
2374 If the input set or relation has any existentially quantified
2375 variables, then the result of these operations is currently undefined.
2379 __isl_give isl_basic_set *
2380 isl_set_unshifted_simple_hull(
2381 __isl_take isl_set *set);
2382 __isl_give isl_basic_map *
2383 isl_map_unshifted_simple_hull(
2384 __isl_take isl_map *map);
2385 __isl_give isl_basic_set *isl_set_simple_hull(
2386 __isl_take isl_set *set);
2387 __isl_give isl_basic_map *isl_map_simple_hull(
2388 __isl_take isl_map *map);
2389 __isl_give isl_union_map *isl_union_map_simple_hull(
2390 __isl_take isl_union_map *umap);
2392 These functions compute a single basic set or relation
2393 that contains the whole input set or relation.
2394 In particular, the output is described by translates
2395 of the constraints describing the basic sets or relations in the input.
2396 In case of C<isl_set_unshifted_simple_hull>, only the original
2397 constraints are used, without any translation.
2401 (See \autoref{s:simple hull}.)
2407 __isl_give isl_basic_set *isl_basic_set_affine_hull(
2408 __isl_take isl_basic_set *bset);
2409 __isl_give isl_basic_set *isl_set_affine_hull(
2410 __isl_take isl_set *set);
2411 __isl_give isl_union_set *isl_union_set_affine_hull(
2412 __isl_take isl_union_set *uset);
2413 __isl_give isl_basic_map *isl_basic_map_affine_hull(
2414 __isl_take isl_basic_map *bmap);
2415 __isl_give isl_basic_map *isl_map_affine_hull(
2416 __isl_take isl_map *map);
2417 __isl_give isl_union_map *isl_union_map_affine_hull(
2418 __isl_take isl_union_map *umap);
2420 In case of union sets and relations, the affine hull is computed
2423 =item * Polyhedral hull
2425 __isl_give isl_basic_set *isl_set_polyhedral_hull(
2426 __isl_take isl_set *set);
2427 __isl_give isl_basic_map *isl_map_polyhedral_hull(
2428 __isl_take isl_map *map);
2429 __isl_give isl_union_set *isl_union_set_polyhedral_hull(
2430 __isl_take isl_union_set *uset);
2431 __isl_give isl_union_map *isl_union_map_polyhedral_hull(
2432 __isl_take isl_union_map *umap);
2434 These functions compute a single basic set or relation
2435 not involving any existentially quantified variables
2436 that contains the whole input set or relation.
2437 In case of union sets and relations, the polyhedral hull is computed
2440 =item * Other approximations
2442 __isl_give isl_basic_set *
2443 isl_basic_set_drop_constraints_involving_dims(
2444 __isl_take isl_basic_set *bset,
2445 enum isl_dim_type type,
2446 unsigned first, unsigned n);
2447 __isl_give isl_basic_map *
2448 isl_basic_map_drop_constraints_involving_dims(
2449 __isl_take isl_basic_map *bmap,
2450 enum isl_dim_type type,
2451 unsigned first, unsigned n);
2452 __isl_give isl_basic_set *
2453 isl_basic_set_drop_constraints_not_involving_dims(
2454 __isl_take isl_basic_set *bset,
2455 enum isl_dim_type type,
2456 unsigned first, unsigned n);
2457 __isl_give isl_set *
2458 isl_set_drop_constraints_involving_dims(
2459 __isl_take isl_set *set,
2460 enum isl_dim_type type,
2461 unsigned first, unsigned n);
2462 __isl_give isl_map *
2463 isl_map_drop_constraints_involving_dims(
2464 __isl_take isl_map *map,
2465 enum isl_dim_type type,
2466 unsigned first, unsigned n);
2468 These functions drop any constraints (not) involving the specified dimensions.
2469 Note that the result depends on the representation of the input.
2473 __isl_give isl_basic_set *isl_basic_set_sample(
2474 __isl_take isl_basic_set *bset);
2475 __isl_give isl_basic_set *isl_set_sample(
2476 __isl_take isl_set *set);
2477 __isl_give isl_basic_map *isl_basic_map_sample(
2478 __isl_take isl_basic_map *bmap);
2479 __isl_give isl_basic_map *isl_map_sample(
2480 __isl_take isl_map *map);
2482 If the input (basic) set or relation is non-empty, then return
2483 a singleton subset of the input. Otherwise, return an empty set.
2485 =item * Optimization
2487 #include <isl/ilp.h>
2488 __isl_give isl_val *isl_basic_set_max_val(
2489 __isl_keep isl_basic_set *bset,
2490 __isl_keep isl_aff *obj);
2491 __isl_give isl_val *isl_set_min_val(
2492 __isl_keep isl_set *set,
2493 __isl_keep isl_aff *obj);
2494 __isl_give isl_val *isl_set_max_val(
2495 __isl_keep isl_set *set,
2496 __isl_keep isl_aff *obj);
2498 Compute the minimum or maximum of the integer affine expression C<obj>
2499 over the points in C<set>, returning the result in C<opt>.
2500 The result is C<NULL> in case of an error, the optimal value in case
2501 there is one, negative infinity or infinity if the problem is unbounded and
2502 NaN if the problem is empty.
2504 =item * Parametric optimization
2506 __isl_give isl_pw_aff *isl_set_dim_min(
2507 __isl_take isl_set *set, int pos);
2508 __isl_give isl_pw_aff *isl_set_dim_max(
2509 __isl_take isl_set *set, int pos);
2510 __isl_give isl_pw_aff *isl_map_dim_max(
2511 __isl_take isl_map *map, int pos);
2513 Compute the minimum or maximum of the given set or output dimension
2514 as a function of the parameters (and input dimensions), but independently
2515 of the other set or output dimensions.
2516 For lexicographic optimization, see L<"Lexicographic Optimization">.
2520 The following functions compute either the set of (rational) coefficient
2521 values of valid constraints for the given set or the set of (rational)
2522 values satisfying the constraints with coefficients from the given set.
2523 Internally, these two sets of functions perform essentially the
2524 same operations, except that the set of coefficients is assumed to
2525 be a cone, while the set of values may be any polyhedron.
2526 The current implementation is based on the Farkas lemma and
2527 Fourier-Motzkin elimination, but this may change or be made optional
2528 in future. In particular, future implementations may use different
2529 dualization algorithms or skip the elimination step.
2531 __isl_give isl_basic_set *isl_basic_set_coefficients(
2532 __isl_take isl_basic_set *bset);
2533 __isl_give isl_basic_set *isl_set_coefficients(
2534 __isl_take isl_set *set);
2535 __isl_give isl_union_set *isl_union_set_coefficients(
2536 __isl_take isl_union_set *bset);
2537 __isl_give isl_basic_set *isl_basic_set_solutions(
2538 __isl_take isl_basic_set *bset);
2539 __isl_give isl_basic_set *isl_set_solutions(
2540 __isl_take isl_set *set);
2541 __isl_give isl_union_set *isl_union_set_solutions(
2542 __isl_take isl_union_set *bset);
2546 __isl_give isl_map *isl_map_fixed_power_val(
2547 __isl_take isl_map *map,
2548 __isl_take isl_val *exp);
2549 __isl_give isl_union_map *
2550 isl_union_map_fixed_power_val(
2551 __isl_take isl_union_map *umap,
2552 __isl_take isl_val *exp);
2554 Compute the given power of C<map>, where C<exp> is assumed to be non-zero.
2555 If the exponent C<exp> is negative, then the -C<exp> th power of the inverse
2556 of C<map> is computed.
2558 __isl_give isl_map *isl_map_power(__isl_take isl_map *map,
2560 __isl_give isl_union_map *isl_union_map_power(
2561 __isl_take isl_union_map *umap, int *exact);
2563 Compute a parametric representation for all positive powers I<k> of C<map>.
2564 The result maps I<k> to a nested relation corresponding to the
2565 I<k>th power of C<map>.
2566 The result may be an overapproximation. If the result is known to be exact,
2567 then C<*exact> is set to C<1>.
2569 =item * Transitive closure
2571 __isl_give isl_map *isl_map_transitive_closure(
2572 __isl_take isl_map *map, int *exact);
2573 __isl_give isl_union_map *isl_union_map_transitive_closure(
2574 __isl_take isl_union_map *umap, int *exact);
2576 Compute the transitive closure of C<map>.
2577 The result may be an overapproximation. If the result is known to be exact,
2578 then C<*exact> is set to C<1>.
2580 =item * Reaching path lengths
2582 __isl_give isl_map *isl_map_reaching_path_lengths(
2583 __isl_take isl_map *map, int *exact);
2585 Compute a relation that maps each element in the range of C<map>
2586 to the lengths of all paths composed of edges in C<map> that
2587 end up in the given element.
2588 The result may be an overapproximation. If the result is known to be exact,
2589 then C<*exact> is set to C<1>.
2590 To compute the I<maximal> path length, the resulting relation
2591 should be postprocessed by C<isl_map_lexmax>.
2592 In particular, if the input relation is a dependence relation
2593 (mapping sources to sinks), then the maximal path length corresponds
2594 to the free schedule.
2595 Note, however, that C<isl_map_lexmax> expects the maximum to be
2596 finite, so if the path lengths are unbounded (possibly due to
2597 the overapproximation), then you will get an error message.
2601 __isl_give isl_basic_set *isl_basic_map_wrap(
2602 __isl_take isl_basic_map *bmap);
2603 __isl_give isl_set *isl_map_wrap(
2604 __isl_take isl_map *map);
2605 __isl_give isl_union_set *isl_union_map_wrap(
2606 __isl_take isl_union_map *umap);
2607 __isl_give isl_basic_map *isl_basic_set_unwrap(
2608 __isl_take isl_basic_set *bset);
2609 __isl_give isl_map *isl_set_unwrap(
2610 __isl_take isl_set *set);
2611 __isl_give isl_union_map *isl_union_set_unwrap(
2612 __isl_take isl_union_set *uset);
2616 Remove any internal structure of domain (and range) of the given
2617 set or relation. If there is any such internal structure in the input,
2618 then the name of the space is also removed.
2620 __isl_give isl_basic_set *isl_basic_set_flatten(
2621 __isl_take isl_basic_set *bset);
2622 __isl_give isl_set *isl_set_flatten(
2623 __isl_take isl_set *set);
2624 __isl_give isl_basic_map *isl_basic_map_flatten_domain(
2625 __isl_take isl_basic_map *bmap);
2626 __isl_give isl_basic_map *isl_basic_map_flatten_range(
2627 __isl_take isl_basic_map *bmap);
2628 __isl_give isl_map *isl_map_flatten_range(
2629 __isl_take isl_map *map);
2630 __isl_give isl_map *isl_map_flatten_domain(
2631 __isl_take isl_map *map);
2632 __isl_give isl_basic_map *isl_basic_map_flatten(
2633 __isl_take isl_basic_map *bmap);
2634 __isl_give isl_map *isl_map_flatten(
2635 __isl_take isl_map *map);
2637 __isl_give isl_map *isl_set_flatten_map(
2638 __isl_take isl_set *set);
2640 The function above constructs a relation
2641 that maps the input set to a flattened version of the set.
2645 Lift the input set to a space with extra dimensions corresponding
2646 to the existentially quantified variables in the input.
2647 In particular, the result lives in a wrapped map where the domain
2648 is the original space and the range corresponds to the original
2649 existentially quantified variables.
2651 __isl_give isl_basic_set *isl_basic_set_lift(
2652 __isl_take isl_basic_set *bset);
2653 __isl_give isl_set *isl_set_lift(
2654 __isl_take isl_set *set);
2655 __isl_give isl_union_set *isl_union_set_lift(
2656 __isl_take isl_union_set *uset);
2658 Given a local space that contains the existentially quantified
2659 variables of a set, a basic relation that, when applied to
2660 a basic set, has essentially the same effect as C<isl_basic_set_lift>,
2661 can be constructed using the following function.
2663 #include <isl/local_space.h>
2664 __isl_give isl_basic_map *isl_local_space_lifting(
2665 __isl_take isl_local_space *ls);
2667 =item * Internal Product
2669 __isl_give isl_basic_map *isl_basic_map_zip(
2670 __isl_take isl_basic_map *bmap);
2671 __isl_give isl_map *isl_map_zip(
2672 __isl_take isl_map *map);
2673 __isl_give isl_union_map *isl_union_map_zip(
2674 __isl_take isl_union_map *umap);
2676 Given a relation with nested relations for domain and range,
2677 interchange the range of the domain with the domain of the range.
2681 __isl_give isl_basic_map *isl_basic_map_curry(
2682 __isl_take isl_basic_map *bmap);
2683 __isl_give isl_basic_map *isl_basic_map_uncurry(
2684 __isl_take isl_basic_map *bmap);
2685 __isl_give isl_map *isl_map_curry(
2686 __isl_take isl_map *map);
2687 __isl_give isl_map *isl_map_uncurry(
2688 __isl_take isl_map *map);
2689 __isl_give isl_union_map *isl_union_map_curry(
2690 __isl_take isl_union_map *umap);
2691 __isl_give isl_union_map *isl_union_map_uncurry(
2692 __isl_take isl_union_map *umap);
2694 Given a relation with a nested relation for domain,
2695 the C<curry> functions
2696 move the range of the nested relation out of the domain
2697 and use it as the domain of a nested relation in the range,
2698 with the original range as range of this nested relation.
2699 The C<uncurry> functions perform the inverse operation.
2701 =item * Aligning parameters
2703 __isl_give isl_basic_set *isl_basic_set_align_params(
2704 __isl_take isl_basic_set *bset,
2705 __isl_take isl_space *model);
2706 __isl_give isl_set *isl_set_align_params(
2707 __isl_take isl_set *set,
2708 __isl_take isl_space *model);
2709 __isl_give isl_basic_map *isl_basic_map_align_params(
2710 __isl_take isl_basic_map *bmap,
2711 __isl_take isl_space *model);
2712 __isl_give isl_map *isl_map_align_params(
2713 __isl_take isl_map *map,
2714 __isl_take isl_space *model);
2716 Change the order of the parameters of the given set or relation
2717 such that the first parameters match those of C<model>.
2718 This may involve the introduction of extra parameters.
2719 All parameters need to be named.
2721 =item * Dimension manipulation
2723 __isl_give isl_basic_set *isl_basic_set_add_dims(
2724 __isl_take isl_basic_set *bset,
2725 enum isl_dim_type type, unsigned n);
2726 __isl_give isl_set *isl_set_add_dims(
2727 __isl_take isl_set *set,
2728 enum isl_dim_type type, unsigned n);
2729 __isl_give isl_map *isl_map_add_dims(
2730 __isl_take isl_map *map,
2731 enum isl_dim_type type, unsigned n);
2732 __isl_give isl_basic_set *isl_basic_set_insert_dims(
2733 __isl_take isl_basic_set *bset,
2734 enum isl_dim_type type, unsigned pos,
2736 __isl_give isl_basic_map *isl_basic_map_insert_dims(
2737 __isl_take isl_basic_map *bmap,
2738 enum isl_dim_type type, unsigned pos,
2740 __isl_give isl_set *isl_set_insert_dims(
2741 __isl_take isl_set *set,
2742 enum isl_dim_type type, unsigned pos, unsigned n);
2743 __isl_give isl_map *isl_map_insert_dims(
2744 __isl_take isl_map *map,
2745 enum isl_dim_type type, unsigned pos, unsigned n);
2746 __isl_give isl_basic_set *isl_basic_set_move_dims(
2747 __isl_take isl_basic_set *bset,
2748 enum isl_dim_type dst_type, unsigned dst_pos,
2749 enum isl_dim_type src_type, unsigned src_pos,
2751 __isl_give isl_basic_map *isl_basic_map_move_dims(
2752 __isl_take isl_basic_map *bmap,
2753 enum isl_dim_type dst_type, unsigned dst_pos,
2754 enum isl_dim_type src_type, unsigned src_pos,
2756 __isl_give isl_set *isl_set_move_dims(
2757 __isl_take isl_set *set,
2758 enum isl_dim_type dst_type, unsigned dst_pos,
2759 enum isl_dim_type src_type, unsigned src_pos,
2761 __isl_give isl_map *isl_map_move_dims(
2762 __isl_take isl_map *map,
2763 enum isl_dim_type dst_type, unsigned dst_pos,
2764 enum isl_dim_type src_type, unsigned src_pos,
2767 It is usually not advisable to directly change the (input or output)
2768 space of a set or a relation as this removes the name and the internal
2769 structure of the space. However, the above functions can be useful
2770 to add new parameters, assuming
2771 C<isl_set_align_params> and C<isl_map_align_params>
2776 =head2 Binary Operations
2778 The two arguments of a binary operation not only need to live
2779 in the same C<isl_ctx>, they currently also need to have
2780 the same (number of) parameters.
2782 =head3 Basic Operations
2786 =item * Intersection
2788 __isl_give isl_basic_set *isl_basic_set_intersect_params(
2789 __isl_take isl_basic_set *bset1,
2790 __isl_take isl_basic_set *bset2);
2791 __isl_give isl_basic_set *isl_basic_set_intersect(
2792 __isl_take isl_basic_set *bset1,
2793 __isl_take isl_basic_set *bset2);
2794 __isl_give isl_set *isl_set_intersect_params(
2795 __isl_take isl_set *set,
2796 __isl_take isl_set *params);
2797 __isl_give isl_set *isl_set_intersect(
2798 __isl_take isl_set *set1,
2799 __isl_take isl_set *set2);
2800 __isl_give isl_union_set *isl_union_set_intersect_params(
2801 __isl_take isl_union_set *uset,
2802 __isl_take isl_set *set);
2803 __isl_give isl_union_map *isl_union_map_intersect_params(
2804 __isl_take isl_union_map *umap,
2805 __isl_take isl_set *set);
2806 __isl_give isl_union_set *isl_union_set_intersect(
2807 __isl_take isl_union_set *uset1,
2808 __isl_take isl_union_set *uset2);
2809 __isl_give isl_basic_map *isl_basic_map_intersect_domain(
2810 __isl_take isl_basic_map *bmap,
2811 __isl_take isl_basic_set *bset);
2812 __isl_give isl_basic_map *isl_basic_map_intersect_range(
2813 __isl_take isl_basic_map *bmap,
2814 __isl_take isl_basic_set *bset);
2815 __isl_give isl_basic_map *isl_basic_map_intersect(
2816 __isl_take isl_basic_map *bmap1,
2817 __isl_take isl_basic_map *bmap2);
2818 __isl_give isl_map *isl_map_intersect_params(
2819 __isl_take isl_map *map,
2820 __isl_take isl_set *params);
2821 __isl_give isl_map *isl_map_intersect_domain(
2822 __isl_take isl_map *map,
2823 __isl_take isl_set *set);
2824 __isl_give isl_map *isl_map_intersect_range(
2825 __isl_take isl_map *map,
2826 __isl_take isl_set *set);
2827 __isl_give isl_map *isl_map_intersect(
2828 __isl_take isl_map *map1,
2829 __isl_take isl_map *map2);
2830 __isl_give isl_union_map *isl_union_map_intersect_domain(
2831 __isl_take isl_union_map *umap,
2832 __isl_take isl_union_set *uset);
2833 __isl_give isl_union_map *isl_union_map_intersect_range(
2834 __isl_take isl_union_map *umap,
2835 __isl_take isl_union_set *uset);
2836 __isl_give isl_union_map *isl_union_map_intersect(
2837 __isl_take isl_union_map *umap1,
2838 __isl_take isl_union_map *umap2);
2840 The second argument to the C<_params> functions needs to be
2841 a parametric (basic) set. For the other functions, a parametric set
2842 for either argument is only allowed if the other argument is
2843 a parametric set as well.
2847 __isl_give isl_set *isl_basic_set_union(
2848 __isl_take isl_basic_set *bset1,
2849 __isl_take isl_basic_set *bset2);
2850 __isl_give isl_map *isl_basic_map_union(
2851 __isl_take isl_basic_map *bmap1,
2852 __isl_take isl_basic_map *bmap2);
2853 __isl_give isl_set *isl_set_union(
2854 __isl_take isl_set *set1,
2855 __isl_take isl_set *set2);
2856 __isl_give isl_map *isl_map_union(
2857 __isl_take isl_map *map1,
2858 __isl_take isl_map *map2);
2859 __isl_give isl_union_set *isl_union_set_union(
2860 __isl_take isl_union_set *uset1,
2861 __isl_take isl_union_set *uset2);
2862 __isl_give isl_union_map *isl_union_map_union(
2863 __isl_take isl_union_map *umap1,
2864 __isl_take isl_union_map *umap2);
2866 =item * Set difference
2868 __isl_give isl_set *isl_set_subtract(
2869 __isl_take isl_set *set1,
2870 __isl_take isl_set *set2);
2871 __isl_give isl_map *isl_map_subtract(
2872 __isl_take isl_map *map1,
2873 __isl_take isl_map *map2);
2874 __isl_give isl_map *isl_map_subtract_domain(
2875 __isl_take isl_map *map,
2876 __isl_take isl_set *dom);
2877 __isl_give isl_map *isl_map_subtract_range(
2878 __isl_take isl_map *map,
2879 __isl_take isl_set *dom);
2880 __isl_give isl_union_set *isl_union_set_subtract(
2881 __isl_take isl_union_set *uset1,
2882 __isl_take isl_union_set *uset2);
2883 __isl_give isl_union_map *isl_union_map_subtract(
2884 __isl_take isl_union_map *umap1,
2885 __isl_take isl_union_map *umap2);
2886 __isl_give isl_union_map *isl_union_map_subtract_domain(
2887 __isl_take isl_union_map *umap,
2888 __isl_take isl_union_set *dom);
2889 __isl_give isl_union_map *isl_union_map_subtract_range(
2890 __isl_take isl_union_map *umap,
2891 __isl_take isl_union_set *dom);
2895 __isl_give isl_basic_set *isl_basic_set_apply(
2896 __isl_take isl_basic_set *bset,
2897 __isl_take isl_basic_map *bmap);
2898 __isl_give isl_set *isl_set_apply(
2899 __isl_take isl_set *set,
2900 __isl_take isl_map *map);
2901 __isl_give isl_union_set *isl_union_set_apply(
2902 __isl_take isl_union_set *uset,
2903 __isl_take isl_union_map *umap);
2904 __isl_give isl_basic_map *isl_basic_map_apply_domain(
2905 __isl_take isl_basic_map *bmap1,
2906 __isl_take isl_basic_map *bmap2);
2907 __isl_give isl_basic_map *isl_basic_map_apply_range(
2908 __isl_take isl_basic_map *bmap1,
2909 __isl_take isl_basic_map *bmap2);
2910 __isl_give isl_map *isl_map_apply_domain(
2911 __isl_take isl_map *map1,
2912 __isl_take isl_map *map2);
2913 __isl_give isl_union_map *isl_union_map_apply_domain(
2914 __isl_take isl_union_map *umap1,
2915 __isl_take isl_union_map *umap2);
2916 __isl_give isl_map *isl_map_apply_range(
2917 __isl_take isl_map *map1,
2918 __isl_take isl_map *map2);
2919 __isl_give isl_union_map *isl_union_map_apply_range(
2920 __isl_take isl_union_map *umap1,
2921 __isl_take isl_union_map *umap2);
2925 __isl_give isl_basic_set *
2926 isl_basic_set_preimage_multi_aff(
2927 __isl_take isl_basic_set *bset,
2928 __isl_take isl_multi_aff *ma);
2929 __isl_give isl_set *isl_set_preimage_multi_aff(
2930 __isl_take isl_set *set,
2931 __isl_take isl_multi_aff *ma);
2932 __isl_give isl_set *isl_set_preimage_pw_multi_aff(
2933 __isl_take isl_set *set,
2934 __isl_take isl_pw_multi_aff *pma);
2935 __isl_give isl_set *isl_set_preimage_multi_pw_aff(
2936 __isl_take isl_set *set,
2937 __isl_take isl_multi_pw_aff *mpa);
2938 __isl_give isl_basic_map *
2939 isl_basic_map_preimage_domain_multi_aff(
2940 __isl_take isl_basic_map *bmap,
2941 __isl_take isl_multi_aff *ma);
2942 __isl_give isl_map *isl_map_preimage_domain_multi_aff(
2943 __isl_take isl_map *map,
2944 __isl_take isl_multi_aff *ma);
2945 __isl_give isl_map *
2946 isl_map_preimage_domain_pw_multi_aff(
2947 __isl_take isl_map *map,
2948 __isl_take isl_pw_multi_aff *pma);
2949 __isl_give isl_map *
2950 isl_map_preimage_domain_multi_pw_aff(
2951 __isl_take isl_map *map,
2952 __isl_take isl_multi_pw_aff *mpa);
2953 __isl_give isl_union_map *
2954 isl_union_map_preimage_domain_multi_aff(
2955 __isl_take isl_union_map *umap,
2956 __isl_take isl_multi_aff *ma);
2957 __isl_give isl_basic_map *
2958 isl_basic_map_preimage_range_multi_aff(
2959 __isl_take isl_basic_map *bmap,
2960 __isl_take isl_multi_aff *ma);
2962 These functions compute the preimage of the given set or map domain/range under
2963 the given function. In other words, the expression is plugged
2964 into the set description or into the domain/range of the map.
2965 Objects of types C<isl_multi_aff> and C<isl_pw_multi_aff> are described in
2966 L</"Piecewise Multiple Quasi Affine Expressions">.
2968 =item * Cartesian Product
2970 __isl_give isl_set *isl_set_product(
2971 __isl_take isl_set *set1,
2972 __isl_take isl_set *set2);
2973 __isl_give isl_union_set *isl_union_set_product(
2974 __isl_take isl_union_set *uset1,
2975 __isl_take isl_union_set *uset2);
2976 __isl_give isl_basic_map *isl_basic_map_domain_product(
2977 __isl_take isl_basic_map *bmap1,
2978 __isl_take isl_basic_map *bmap2);
2979 __isl_give isl_basic_map *isl_basic_map_range_product(
2980 __isl_take isl_basic_map *bmap1,
2981 __isl_take isl_basic_map *bmap2);
2982 __isl_give isl_basic_map *isl_basic_map_product(
2983 __isl_take isl_basic_map *bmap1,
2984 __isl_take isl_basic_map *bmap2);
2985 __isl_give isl_map *isl_map_domain_product(
2986 __isl_take isl_map *map1,
2987 __isl_take isl_map *map2);
2988 __isl_give isl_map *isl_map_range_product(
2989 __isl_take isl_map *map1,
2990 __isl_take isl_map *map2);
2991 __isl_give isl_union_map *isl_union_map_domain_product(
2992 __isl_take isl_union_map *umap1,
2993 __isl_take isl_union_map *umap2);
2994 __isl_give isl_union_map *isl_union_map_range_product(
2995 __isl_take isl_union_map *umap1,
2996 __isl_take isl_union_map *umap2);
2997 __isl_give isl_map *isl_map_product(
2998 __isl_take isl_map *map1,
2999 __isl_take isl_map *map2);
3000 __isl_give isl_union_map *isl_union_map_product(
3001 __isl_take isl_union_map *umap1,
3002 __isl_take isl_union_map *umap2);
3004 The above functions compute the cross product of the given
3005 sets or relations. The domains and ranges of the results
3006 are wrapped maps between domains and ranges of the inputs.
3007 To obtain a ``flat'' product, use the following functions
3010 __isl_give isl_basic_set *isl_basic_set_flat_product(
3011 __isl_take isl_basic_set *bset1,
3012 __isl_take isl_basic_set *bset2);
3013 __isl_give isl_set *isl_set_flat_product(
3014 __isl_take isl_set *set1,
3015 __isl_take isl_set *set2);
3016 __isl_give isl_basic_map *isl_basic_map_flat_range_product(
3017 __isl_take isl_basic_map *bmap1,
3018 __isl_take isl_basic_map *bmap2);
3019 __isl_give isl_map *isl_map_flat_domain_product(
3020 __isl_take isl_map *map1,
3021 __isl_take isl_map *map2);
3022 __isl_give isl_map *isl_map_flat_range_product(
3023 __isl_take isl_map *map1,
3024 __isl_take isl_map *map2);
3025 __isl_give isl_union_map *isl_union_map_flat_range_product(
3026 __isl_take isl_union_map *umap1,
3027 __isl_take isl_union_map *umap2);
3028 __isl_give isl_basic_map *isl_basic_map_flat_product(
3029 __isl_take isl_basic_map *bmap1,
3030 __isl_take isl_basic_map *bmap2);
3031 __isl_give isl_map *isl_map_flat_product(
3032 __isl_take isl_map *map1,
3033 __isl_take isl_map *map2);
3035 =item * Simplification
3037 __isl_give isl_basic_set *isl_basic_set_gist(
3038 __isl_take isl_basic_set *bset,
3039 __isl_take isl_basic_set *context);
3040 __isl_give isl_set *isl_set_gist(__isl_take isl_set *set,
3041 __isl_take isl_set *context);
3042 __isl_give isl_set *isl_set_gist_params(
3043 __isl_take isl_set *set,
3044 __isl_take isl_set *context);
3045 __isl_give isl_union_set *isl_union_set_gist(
3046 __isl_take isl_union_set *uset,
3047 __isl_take isl_union_set *context);
3048 __isl_give isl_union_set *isl_union_set_gist_params(
3049 __isl_take isl_union_set *uset,
3050 __isl_take isl_set *set);
3051 __isl_give isl_basic_map *isl_basic_map_gist(
3052 __isl_take isl_basic_map *bmap,
3053 __isl_take isl_basic_map *context);
3054 __isl_give isl_map *isl_map_gist(__isl_take isl_map *map,
3055 __isl_take isl_map *context);
3056 __isl_give isl_map *isl_map_gist_params(
3057 __isl_take isl_map *map,
3058 __isl_take isl_set *context);
3059 __isl_give isl_map *isl_map_gist_domain(
3060 __isl_take isl_map *map,
3061 __isl_take isl_set *context);
3062 __isl_give isl_map *isl_map_gist_range(
3063 __isl_take isl_map *map,
3064 __isl_take isl_set *context);
3065 __isl_give isl_union_map *isl_union_map_gist(
3066 __isl_take isl_union_map *umap,
3067 __isl_take isl_union_map *context);
3068 __isl_give isl_union_map *isl_union_map_gist_params(
3069 __isl_take isl_union_map *umap,
3070 __isl_take isl_set *set);
3071 __isl_give isl_union_map *isl_union_map_gist_domain(
3072 __isl_take isl_union_map *umap,
3073 __isl_take isl_union_set *uset);
3074 __isl_give isl_union_map *isl_union_map_gist_range(
3075 __isl_take isl_union_map *umap,
3076 __isl_take isl_union_set *uset);
3078 The gist operation returns a set or relation that has the
3079 same intersection with the context as the input set or relation.
3080 Any implicit equality in the intersection is made explicit in the result,
3081 while all inequalities that are redundant with respect to the intersection
3083 In case of union sets and relations, the gist operation is performed
3088 =head3 Lexicographic Optimization
3090 Given a (basic) set C<set> (or C<bset>) and a zero-dimensional domain C<dom>,
3091 the following functions
3092 compute a set that contains the lexicographic minimum or maximum
3093 of the elements in C<set> (or C<bset>) for those values of the parameters
3094 that satisfy C<dom>.
3095 If C<empty> is not C<NULL>, then C<*empty> is assigned a set
3096 that contains the parameter values in C<dom> for which C<set> (or C<bset>)
3098 In other words, the union of the parameter values
3099 for which the result is non-empty and of C<*empty>
3102 __isl_give isl_set *isl_basic_set_partial_lexmin(
3103 __isl_take isl_basic_set *bset,
3104 __isl_take isl_basic_set *dom,
3105 __isl_give isl_set **empty);
3106 __isl_give isl_set *isl_basic_set_partial_lexmax(
3107 __isl_take isl_basic_set *bset,
3108 __isl_take isl_basic_set *dom,
3109 __isl_give isl_set **empty);
3110 __isl_give isl_set *isl_set_partial_lexmin(
3111 __isl_take isl_set *set, __isl_take isl_set *dom,
3112 __isl_give isl_set **empty);
3113 __isl_give isl_set *isl_set_partial_lexmax(
3114 __isl_take isl_set *set, __isl_take isl_set *dom,
3115 __isl_give isl_set **empty);
3117 Given a (basic) set C<set> (or C<bset>), the following functions simply
3118 return a set containing the lexicographic minimum or maximum
3119 of the elements in C<set> (or C<bset>).
3120 In case of union sets, the optimum is computed per space.
3122 __isl_give isl_set *isl_basic_set_lexmin(
3123 __isl_take isl_basic_set *bset);
3124 __isl_give isl_set *isl_basic_set_lexmax(
3125 __isl_take isl_basic_set *bset);
3126 __isl_give isl_set *isl_set_lexmin(
3127 __isl_take isl_set *set);
3128 __isl_give isl_set *isl_set_lexmax(
3129 __isl_take isl_set *set);
3130 __isl_give isl_union_set *isl_union_set_lexmin(
3131 __isl_take isl_union_set *uset);
3132 __isl_give isl_union_set *isl_union_set_lexmax(
3133 __isl_take isl_union_set *uset);
3135 Given a (basic) relation C<map> (or C<bmap>) and a domain C<dom>,
3136 the following functions
3137 compute a relation that maps each element of C<dom>
3138 to the single lexicographic minimum or maximum
3139 of the elements that are associated to that same
3140 element in C<map> (or C<bmap>).
3141 If C<empty> is not C<NULL>, then C<*empty> is assigned a set
3142 that contains the elements in C<dom> that do not map
3143 to any elements in C<map> (or C<bmap>).
3144 In other words, the union of the domain of the result and of C<*empty>
3147 __isl_give isl_map *isl_basic_map_partial_lexmax(
3148 __isl_take isl_basic_map *bmap,
3149 __isl_take isl_basic_set *dom,
3150 __isl_give isl_set **empty);
3151 __isl_give isl_map *isl_basic_map_partial_lexmin(
3152 __isl_take isl_basic_map *bmap,
3153 __isl_take isl_basic_set *dom,
3154 __isl_give isl_set **empty);
3155 __isl_give isl_map *isl_map_partial_lexmax(
3156 __isl_take isl_map *map, __isl_take isl_set *dom,
3157 __isl_give isl_set **empty);
3158 __isl_give isl_map *isl_map_partial_lexmin(
3159 __isl_take isl_map *map, __isl_take isl_set *dom,
3160 __isl_give isl_set **empty);
3162 Given a (basic) map C<map> (or C<bmap>), the following functions simply
3163 return a map mapping each element in the domain of
3164 C<map> (or C<bmap>) to the lexicographic minimum or maximum
3165 of all elements associated to that element.
3166 In case of union relations, the optimum is computed per space.
3168 __isl_give isl_map *isl_basic_map_lexmin(
3169 __isl_take isl_basic_map *bmap);
3170 __isl_give isl_map *isl_basic_map_lexmax(
3171 __isl_take isl_basic_map *bmap);
3172 __isl_give isl_map *isl_map_lexmin(
3173 __isl_take isl_map *map);
3174 __isl_give isl_map *isl_map_lexmax(
3175 __isl_take isl_map *map);
3176 __isl_give isl_union_map *isl_union_map_lexmin(
3177 __isl_take isl_union_map *umap);
3178 __isl_give isl_union_map *isl_union_map_lexmax(
3179 __isl_take isl_union_map *umap);
3181 The following functions return their result in the form of
3182 a piecewise multi-affine expression
3183 (See L<"Piecewise Multiple Quasi Affine Expressions">),
3184 but are otherwise equivalent to the corresponding functions
3185 returning a basic set or relation.
3187 __isl_give isl_pw_multi_aff *
3188 isl_basic_map_lexmin_pw_multi_aff(
3189 __isl_take isl_basic_map *bmap);
3190 __isl_give isl_pw_multi_aff *
3191 isl_basic_set_partial_lexmin_pw_multi_aff(
3192 __isl_take isl_basic_set *bset,
3193 __isl_take isl_basic_set *dom,
3194 __isl_give isl_set **empty);
3195 __isl_give isl_pw_multi_aff *
3196 isl_basic_set_partial_lexmax_pw_multi_aff(
3197 __isl_take isl_basic_set *bset,
3198 __isl_take isl_basic_set *dom,
3199 __isl_give isl_set **empty);
3200 __isl_give isl_pw_multi_aff *
3201 isl_basic_map_partial_lexmin_pw_multi_aff(
3202 __isl_take isl_basic_map *bmap,
3203 __isl_take isl_basic_set *dom,
3204 __isl_give isl_set **empty);
3205 __isl_give isl_pw_multi_aff *
3206 isl_basic_map_partial_lexmax_pw_multi_aff(
3207 __isl_take isl_basic_map *bmap,
3208 __isl_take isl_basic_set *dom,
3209 __isl_give isl_set **empty);
3210 __isl_give isl_pw_multi_aff *isl_set_lexmin_pw_multi_aff(
3211 __isl_take isl_set *set);
3212 __isl_give isl_pw_multi_aff *isl_set_lexmax_pw_multi_aff(
3213 __isl_take isl_set *set);
3214 __isl_give isl_pw_multi_aff *isl_map_lexmin_pw_multi_aff(
3215 __isl_take isl_map *map);
3216 __isl_give isl_pw_multi_aff *isl_map_lexmax_pw_multi_aff(
3217 __isl_take isl_map *map);
3221 Lists are defined over several element types, including
3222 C<isl_val>, C<isl_id>, C<isl_aff>, C<isl_pw_aff>, C<isl_constraint>,
3223 C<isl_basic_set>, C<isl_set>, C<isl_ast_expr> and C<isl_ast_node>.
3224 Here we take lists of C<isl_set>s as an example.
3225 Lists can be created, copied, modified and freed using the following functions.
3227 #include <isl/list.h>
3228 __isl_give isl_set_list *isl_set_list_from_set(
3229 __isl_take isl_set *el);
3230 __isl_give isl_set_list *isl_set_list_alloc(
3231 isl_ctx *ctx, int n);
3232 __isl_give isl_set_list *isl_set_list_copy(
3233 __isl_keep isl_set_list *list);
3234 __isl_give isl_set_list *isl_set_list_insert(
3235 __isl_take isl_set_list *list, unsigned pos,
3236 __isl_take isl_set *el);
3237 __isl_give isl_set_list *isl_set_list_add(
3238 __isl_take isl_set_list *list,
3239 __isl_take isl_set *el);
3240 __isl_give isl_set_list *isl_set_list_drop(
3241 __isl_take isl_set_list *list,
3242 unsigned first, unsigned n);
3243 __isl_give isl_set_list *isl_set_list_set_set(
3244 __isl_take isl_set_list *list, int index,
3245 __isl_take isl_set *set);
3246 __isl_give isl_set_list *isl_set_list_concat(
3247 __isl_take isl_set_list *list1,
3248 __isl_take isl_set_list *list2);
3249 __isl_give isl_set_list *isl_set_list_sort(
3250 __isl_take isl_set_list *list,
3251 int (*cmp)(__isl_keep isl_set *a,
3252 __isl_keep isl_set *b, void *user),
3254 void *isl_set_list_free(__isl_take isl_set_list *list);
3256 C<isl_set_list_alloc> creates an empty list with a capacity for
3257 C<n> elements. C<isl_set_list_from_set> creates a list with a single
3260 Lists can be inspected using the following functions.
3262 #include <isl/list.h>
3263 isl_ctx *isl_set_list_get_ctx(__isl_keep isl_set_list *list);
3264 int isl_set_list_n_set(__isl_keep isl_set_list *list);
3265 __isl_give isl_set *isl_set_list_get_set(
3266 __isl_keep isl_set_list *list, int index);
3267 int isl_set_list_foreach(__isl_keep isl_set_list *list,
3268 int (*fn)(__isl_take isl_set *el, void *user),
3270 int isl_set_list_foreach_scc(__isl_keep isl_set_list *list,
3271 int (*follows)(__isl_keep isl_set *a,
3272 __isl_keep isl_set *b, void *user),
3274 int (*fn)(__isl_take isl_set *el, void *user),
3277 The function C<isl_set_list_foreach_scc> calls C<fn> on each of the
3278 strongly connected components of the graph with as vertices the elements
3279 of C<list> and a directed edge from vertex C<b> to vertex C<a>
3280 iff C<follows(a, b)> returns C<1>. The callbacks C<follows> and C<fn>
3281 should return C<-1> on error.
3283 Lists can be printed using
3285 #include <isl/list.h>
3286 __isl_give isl_printer *isl_printer_print_set_list(
3287 __isl_take isl_printer *p,
3288 __isl_keep isl_set_list *list);
3290 =head2 Associative arrays
3292 Associative arrays map isl objects of a specific type to isl objects
3293 of some (other) specific type. They are defined for several pairs
3294 of types, including (C<isl_map>, C<isl_basic_set>),
3295 (C<isl_id>, C<isl_ast_expr>) and.
3296 (C<isl_id>, C<isl_pw_aff>).
3297 Here, we take associative arrays that map C<isl_id>s to C<isl_ast_expr>s
3300 Associative arrays can be created, copied and freed using
3301 the following functions.
3303 #include <isl/id_to_ast_expr.h>
3304 __isl_give id_to_ast_expr *isl_id_to_ast_expr_alloc(
3305 isl_ctx *ctx, int min_size);
3306 __isl_give id_to_ast_expr *isl_id_to_ast_expr_copy(
3307 __isl_keep id_to_ast_expr *id2expr);
3308 void *isl_id_to_ast_expr_free(
3309 __isl_take id_to_ast_expr *id2expr);
3311 The C<min_size> argument to C<isl_id_to_ast_expr_alloc> can be used
3312 to specify the expected size of the associative array.
3313 The associative array will be grown automatically as needed.
3315 Associative arrays can be inspected using the following functions.
3317 #include <isl/id_to_ast_expr.h>
3318 isl_ctx *isl_id_to_ast_expr_get_ctx(
3319 __isl_keep id_to_ast_expr *id2expr);
3320 int isl_id_to_ast_expr_has(
3321 __isl_keep id_to_ast_expr *id2expr,
3322 __isl_keep isl_id *key);
3323 __isl_give isl_ast_expr *isl_id_to_ast_expr_get(
3324 __isl_keep id_to_ast_expr *id2expr,
3325 __isl_take isl_id *key);
3326 int isl_id_to_ast_expr_foreach(
3327 __isl_keep id_to_ast_expr *id2expr,
3328 int (*fn)(__isl_take isl_id *key,
3329 __isl_take isl_ast_expr *val, void *user),
3332 They can be modified using the following function.
3334 #include <isl/id_to_ast_expr.h>
3335 __isl_give id_to_ast_expr *isl_id_to_ast_expr_set(
3336 __isl_take id_to_ast_expr *id2expr,
3337 __isl_take isl_id *key,
3338 __isl_take isl_ast_expr *val);
3340 Associative arrays can be printed using the following function.
3342 #include <isl/id_to_ast_expr.h>
3343 __isl_give isl_printer *isl_printer_print_id_to_ast_expr(
3344 __isl_take isl_printer *p,
3345 __isl_keep id_to_ast_expr *id2expr);
3347 =head2 Multiple Values
3349 An C<isl_multi_val> object represents a sequence of zero or more values,
3350 living in a set space.
3352 An C<isl_multi_val> can be constructed from an C<isl_val_list>
3353 using the following function
3355 #include <isl/val.h>
3356 __isl_give isl_multi_val *isl_multi_val_from_val_list(
3357 __isl_take isl_space *space,
3358 __isl_take isl_val_list *list);
3360 The zero multiple value (with value zero for each set dimension)
3361 can be created using the following function.
3363 #include <isl/val.h>
3364 __isl_give isl_multi_val *isl_multi_val_zero(
3365 __isl_take isl_space *space);
3367 Multiple values can be copied and freed using
3369 #include <isl/val.h>
3370 __isl_give isl_multi_val *isl_multi_val_copy(
3371 __isl_keep isl_multi_val *mv);
3372 void *isl_multi_val_free(__isl_take isl_multi_val *mv);
3374 They can be inspected using
3376 #include <isl/val.h>
3377 isl_ctx *isl_multi_val_get_ctx(
3378 __isl_keep isl_multi_val *mv);
3379 unsigned isl_multi_val_dim(__isl_keep isl_multi_val *mv,
3380 enum isl_dim_type type);
3381 __isl_give isl_val *isl_multi_val_get_val(
3382 __isl_keep isl_multi_val *mv, int pos);
3383 int isl_multi_val_find_dim_by_id(
3384 __isl_keep isl_multi_val *mv,
3385 enum isl_dim_type type, __isl_keep isl_id *id);
3386 __isl_give isl_id *isl_multi_val_get_dim_id(
3387 __isl_keep isl_multi_val *mv,
3388 enum isl_dim_type type, unsigned pos);
3389 const char *isl_multi_val_get_tuple_name(
3390 __isl_keep isl_multi_val *mv,
3391 enum isl_dim_type type);
3392 int isl_multi_val_has_tuple_id(__isl_keep isl_multi_val *mv,
3393 enum isl_dim_type type);
3394 __isl_give isl_id *isl_multi_val_get_tuple_id(
3395 __isl_keep isl_multi_val *mv,
3396 enum isl_dim_type type);
3397 __isl_give isl_multi_val *isl_multi_val_reset_tuple_id(
3398 __isl_take isl_multi_val *mv,
3399 enum isl_dim_type type);
3401 They can be modified using
3403 #include <isl/val.h>
3404 __isl_give isl_multi_val *isl_multi_val_set_val(
3405 __isl_take isl_multi_val *mv, int pos,
3406 __isl_take isl_val *val);
3407 __isl_give isl_multi_val *isl_multi_val_set_dim_name(
3408 __isl_take isl_multi_val *mv,
3409 enum isl_dim_type type, unsigned pos, const char *s);
3410 __isl_give isl_multi_val *isl_multi_val_set_dim_id(
3411 __isl_take isl_multi_val *mv,
3412 enum isl_dim_type type, unsigned pos,
3413 __isl_take isl_id *id);
3414 __isl_give isl_multi_val *isl_multi_val_set_tuple_name(
3415 __isl_take isl_multi_val *mv,
3416 enum isl_dim_type type, const char *s);
3417 __isl_give isl_multi_val *isl_multi_val_set_tuple_id(
3418 __isl_take isl_multi_val *mv,
3419 enum isl_dim_type type, __isl_take isl_id *id);
3421 __isl_give isl_multi_val *isl_multi_val_insert_dims(
3422 __isl_take isl_multi_val *mv,
3423 enum isl_dim_type type, unsigned first, unsigned n);
3424 __isl_give isl_multi_val *isl_multi_val_add_dims(
3425 __isl_take isl_multi_val *mv,
3426 enum isl_dim_type type, unsigned n);
3427 __isl_give isl_multi_val *isl_multi_val_drop_dims(
3428 __isl_take isl_multi_val *mv,
3429 enum isl_dim_type type, unsigned first, unsigned n);
3433 #include <isl/val.h>
3434 __isl_give isl_multi_val *isl_multi_val_align_params(
3435 __isl_take isl_multi_val *mv,
3436 __isl_take isl_space *model);
3437 __isl_give isl_multi_val *isl_multi_val_from_range(
3438 __isl_take isl_multi_val *mv);
3439 __isl_give isl_multi_val *isl_multi_val_range_splice(
3440 __isl_take isl_multi_val *mv1, unsigned pos,
3441 __isl_take isl_multi_val *mv2);
3442 __isl_give isl_multi_val *isl_multi_val_range_product(
3443 __isl_take isl_multi_val *mv1,
3444 __isl_take isl_multi_val *mv2);
3445 __isl_give isl_multi_val *isl_multi_val_flat_range_product(
3446 __isl_take isl_multi_val *mv1,
3447 __isl_take isl_multi_aff *mv2);
3448 __isl_give isl_multi_val *isl_multi_val_product(
3449 __isl_take isl_multi_val *mv1,
3450 __isl_take isl_multi_val *mv2);
3451 __isl_give isl_multi_val *isl_multi_val_add_val(
3452 __isl_take isl_multi_val *mv,
3453 __isl_take isl_val *v);
3454 __isl_give isl_multi_val *isl_multi_val_mod_val(
3455 __isl_take isl_multi_val *mv,
3456 __isl_take isl_val *v);
3457 __isl_give isl_multi_val *isl_multi_val_scale_val(
3458 __isl_take isl_multi_val *mv,
3459 __isl_take isl_val *v);
3460 __isl_give isl_multi_val *isl_multi_val_scale_multi_val(
3461 __isl_take isl_multi_val *mv1,
3462 __isl_take isl_multi_val *mv2);
3463 __isl_give isl_multi_val *
3464 isl_multi_val_scale_down_multi_val(
3465 __isl_take isl_multi_val *mv1,
3466 __isl_take isl_multi_val *mv2);
3468 A multiple value can be printed using
3470 __isl_give isl_printer *isl_printer_print_multi_val(
3471 __isl_take isl_printer *p,
3472 __isl_keep isl_multi_val *mv);
3476 Vectors can be created, copied and freed using the following functions.
3478 #include <isl/vec.h>
3479 __isl_give isl_vec *isl_vec_alloc(isl_ctx *ctx,
3481 __isl_give isl_vec *isl_vec_copy(__isl_keep isl_vec *vec);
3482 void *isl_vec_free(__isl_take isl_vec *vec);
3484 Note that the elements of a newly created vector may have arbitrary values.
3485 The elements can be changed and inspected using the following functions.
3487 isl_ctx *isl_vec_get_ctx(__isl_keep isl_vec *vec);
3488 int isl_vec_size(__isl_keep isl_vec *vec);
3489 __isl_give isl_val *isl_vec_get_element_val(
3490 __isl_keep isl_vec *vec, int pos);
3491 __isl_give isl_vec *isl_vec_set_element_si(
3492 __isl_take isl_vec *vec, int pos, int v);
3493 __isl_give isl_vec *isl_vec_set_element_val(
3494 __isl_take isl_vec *vec, int pos,
3495 __isl_take isl_val *v);
3496 __isl_give isl_vec *isl_vec_set_si(__isl_take isl_vec *vec,
3498 __isl_give isl_vec *isl_vec_set_val(
3499 __isl_take isl_vec *vec, __isl_take isl_val *v);
3500 int isl_vec_cmp_element(__isl_keep isl_vec *vec1,
3501 __isl_keep isl_vec *vec2, int pos);
3503 C<isl_vec_get_element> will return a negative value if anything went wrong.
3504 In that case, the value of C<*v> is undefined.
3506 The following function can be used to concatenate two vectors.
3508 __isl_give isl_vec *isl_vec_concat(__isl_take isl_vec *vec1,
3509 __isl_take isl_vec *vec2);
3513 Matrices can be created, copied and freed using the following functions.
3515 #include <isl/mat.h>
3516 __isl_give isl_mat *isl_mat_alloc(isl_ctx *ctx,
3517 unsigned n_row, unsigned n_col);
3518 __isl_give isl_mat *isl_mat_copy(__isl_keep isl_mat *mat);
3519 void *isl_mat_free(__isl_take isl_mat *mat);
3521 Note that the elements of a newly created matrix may have arbitrary values.
3522 The elements can be changed and inspected using the following functions.
3524 isl_ctx *isl_mat_get_ctx(__isl_keep isl_mat *mat);
3525 int isl_mat_rows(__isl_keep isl_mat *mat);
3526 int isl_mat_cols(__isl_keep isl_mat *mat);
3527 __isl_give isl_val *isl_mat_get_element_val(
3528 __isl_keep isl_mat *mat, int row, int col);
3529 __isl_give isl_mat *isl_mat_set_element_si(__isl_take isl_mat *mat,
3530 int row, int col, int v);
3531 __isl_give isl_mat *isl_mat_set_element_val(
3532 __isl_take isl_mat *mat, int row, int col,
3533 __isl_take isl_val *v);
3535 C<isl_mat_get_element> will return a negative value if anything went wrong.
3536 In that case, the value of C<*v> is undefined.
3538 The following function can be used to compute the (right) inverse
3539 of a matrix, i.e., a matrix such that the product of the original
3540 and the inverse (in that order) is a multiple of the identity matrix.
3541 The input matrix is assumed to be of full row-rank.
3543 __isl_give isl_mat *isl_mat_right_inverse(__isl_take isl_mat *mat);
3545 The following function can be used to compute the (right) kernel
3546 (or null space) of a matrix, i.e., a matrix such that the product of
3547 the original and the kernel (in that order) is the zero matrix.
3549 __isl_give isl_mat *isl_mat_right_kernel(__isl_take isl_mat *mat);
3551 =head2 Piecewise Quasi Affine Expressions
3553 The zero quasi affine expression or the quasi affine expression
3554 that is equal to a given value or
3555 a specified dimension on a given domain can be created using
3557 __isl_give isl_aff *isl_aff_zero_on_domain(
3558 __isl_take isl_local_space *ls);
3559 __isl_give isl_pw_aff *isl_pw_aff_zero_on_domain(
3560 __isl_take isl_local_space *ls);
3561 __isl_give isl_aff *isl_aff_val_on_domain(
3562 __isl_take isl_local_space *ls,
3563 __isl_take isl_val *val);
3564 __isl_give isl_aff *isl_aff_var_on_domain(
3565 __isl_take isl_local_space *ls,
3566 enum isl_dim_type type, unsigned pos);
3567 __isl_give isl_pw_aff *isl_pw_aff_var_on_domain(
3568 __isl_take isl_local_space *ls,
3569 enum isl_dim_type type, unsigned pos);
3571 Note that the space in which the resulting objects live is a map space
3572 with the given space as domain and a one-dimensional range.
3574 An empty piecewise quasi affine expression (one with no cells)
3575 or a piecewise quasi affine expression with a single cell can
3576 be created using the following functions.
3578 #include <isl/aff.h>
3579 __isl_give isl_pw_aff *isl_pw_aff_empty(
3580 __isl_take isl_space *space);
3581 __isl_give isl_pw_aff *isl_pw_aff_alloc(
3582 __isl_take isl_set *set, __isl_take isl_aff *aff);
3583 __isl_give isl_pw_aff *isl_pw_aff_from_aff(
3584 __isl_take isl_aff *aff);
3586 A piecewise quasi affine expression that is equal to 1 on a set
3587 and 0 outside the set can be created using the following function.
3589 #include <isl/aff.h>
3590 __isl_give isl_pw_aff *isl_set_indicator_function(
3591 __isl_take isl_set *set);
3593 Quasi affine expressions can be copied and freed using
3595 #include <isl/aff.h>
3596 __isl_give isl_aff *isl_aff_copy(__isl_keep isl_aff *aff);
3597 void *isl_aff_free(__isl_take isl_aff *aff);
3599 __isl_give isl_pw_aff *isl_pw_aff_copy(
3600 __isl_keep isl_pw_aff *pwaff);
3601 void *isl_pw_aff_free(__isl_take isl_pw_aff *pwaff);
3603 A (rational) bound on a dimension can be extracted from an C<isl_constraint>
3604 using the following function. The constraint is required to have
3605 a non-zero coefficient for the specified dimension.
3607 #include <isl/constraint.h>
3608 __isl_give isl_aff *isl_constraint_get_bound(
3609 __isl_keep isl_constraint *constraint,
3610 enum isl_dim_type type, int pos);
3612 The entire affine expression of the constraint can also be extracted
3613 using the following function.
3615 #include <isl/constraint.h>
3616 __isl_give isl_aff *isl_constraint_get_aff(
3617 __isl_keep isl_constraint *constraint);
3619 Conversely, an equality constraint equating
3620 the affine expression to zero or an inequality constraint enforcing
3621 the affine expression to be non-negative, can be constructed using
3623 __isl_give isl_constraint *isl_equality_from_aff(
3624 __isl_take isl_aff *aff);
3625 __isl_give isl_constraint *isl_inequality_from_aff(
3626 __isl_take isl_aff *aff);
3628 The expression can be inspected using
3630 #include <isl/aff.h>
3631 isl_ctx *isl_aff_get_ctx(__isl_keep isl_aff *aff);
3632 int isl_aff_dim(__isl_keep isl_aff *aff,
3633 enum isl_dim_type type);
3634 __isl_give isl_local_space *isl_aff_get_domain_local_space(
3635 __isl_keep isl_aff *aff);
3636 __isl_give isl_local_space *isl_aff_get_local_space(
3637 __isl_keep isl_aff *aff);
3638 const char *isl_aff_get_dim_name(__isl_keep isl_aff *aff,
3639 enum isl_dim_type type, unsigned pos);
3640 const char *isl_pw_aff_get_dim_name(
3641 __isl_keep isl_pw_aff *pa,
3642 enum isl_dim_type type, unsigned pos);
3643 int isl_pw_aff_has_dim_id(__isl_keep isl_pw_aff *pa,
3644 enum isl_dim_type type, unsigned pos);
3645 __isl_give isl_id *isl_pw_aff_get_dim_id(
3646 __isl_keep isl_pw_aff *pa,
3647 enum isl_dim_type type, unsigned pos);
3648 int isl_pw_aff_has_tuple_id(__isl_keep isl_pw_aff *pa,
3649 enum isl_dim_type type);
3650 __isl_give isl_id *isl_pw_aff_get_tuple_id(
3651 __isl_keep isl_pw_aff *pa,
3652 enum isl_dim_type type);
3653 __isl_give isl_val *isl_aff_get_constant_val(
3654 __isl_keep isl_aff *aff);
3655 __isl_give isl_val *isl_aff_get_coefficient_val(
3656 __isl_keep isl_aff *aff,
3657 enum isl_dim_type type, int pos);
3658 __isl_give isl_val *isl_aff_get_denominator_val(
3659 __isl_keep isl_aff *aff);
3660 __isl_give isl_aff *isl_aff_get_div(
3661 __isl_keep isl_aff *aff, int pos);
3663 int isl_pw_aff_n_piece(__isl_keep isl_pw_aff *pwaff);
3664 int isl_pw_aff_foreach_piece(__isl_keep isl_pw_aff *pwaff,
3665 int (*fn)(__isl_take isl_set *set,
3666 __isl_take isl_aff *aff,
3667 void *user), void *user);
3669 int isl_aff_is_cst(__isl_keep isl_aff *aff);
3670 int isl_pw_aff_is_cst(__isl_keep isl_pw_aff *pwaff);
3672 int isl_aff_involves_dims(__isl_keep isl_aff *aff,
3673 enum isl_dim_type type, unsigned first, unsigned n);
3674 int isl_pw_aff_involves_dims(__isl_keep isl_pw_aff *pwaff,
3675 enum isl_dim_type type, unsigned first, unsigned n);
3677 isl_ctx *isl_pw_aff_get_ctx(__isl_keep isl_pw_aff *pwaff);
3678 unsigned isl_pw_aff_dim(__isl_keep isl_pw_aff *pwaff,
3679 enum isl_dim_type type);
3680 int isl_pw_aff_is_empty(__isl_keep isl_pw_aff *pwaff);
3682 It can be modified using
3684 #include <isl/aff.h>
3685 __isl_give isl_pw_aff *isl_pw_aff_set_tuple_id(
3686 __isl_take isl_pw_aff *pwaff,
3687 enum isl_dim_type type, __isl_take isl_id *id);
3688 __isl_give isl_aff *isl_aff_set_dim_name(
3689 __isl_take isl_aff *aff, enum isl_dim_type type,
3690 unsigned pos, const char *s);
3691 __isl_give isl_aff *isl_aff_set_dim_id(
3692 __isl_take isl_aff *aff, enum isl_dim_type type,
3693 unsigned pos, __isl_take isl_id *id);
3694 __isl_give isl_pw_aff *isl_pw_aff_set_dim_id(
3695 __isl_take isl_pw_aff *pma,
3696 enum isl_dim_type type, unsigned pos,
3697 __isl_take isl_id *id);
3698 __isl_give isl_aff *isl_aff_set_constant_si(
3699 __isl_take isl_aff *aff, int v);
3700 __isl_give isl_aff *isl_aff_set_constant_val(
3701 __isl_take isl_aff *aff, __isl_take isl_val *v);
3702 __isl_give isl_aff *isl_aff_set_coefficient_si(
3703 __isl_take isl_aff *aff,
3704 enum isl_dim_type type, int pos, int v);
3705 __isl_give isl_aff *isl_aff_set_coefficient_val(
3706 __isl_take isl_aff *aff,
3707 enum isl_dim_type type, int pos,
3708 __isl_take isl_val *v);
3710 __isl_give isl_aff *isl_aff_add_constant_si(
3711 __isl_take isl_aff *aff, int v);
3712 __isl_give isl_aff *isl_aff_add_constant_val(
3713 __isl_take isl_aff *aff, __isl_take isl_val *v);
3714 __isl_give isl_aff *isl_aff_add_constant_num_si(
3715 __isl_take isl_aff *aff, int v);
3716 __isl_give isl_aff *isl_aff_add_coefficient_si(
3717 __isl_take isl_aff *aff,
3718 enum isl_dim_type type, int pos, int v);
3719 __isl_give isl_aff *isl_aff_add_coefficient_val(
3720 __isl_take isl_aff *aff,
3721 enum isl_dim_type type, int pos,
3722 __isl_take isl_val *v);
3724 __isl_give isl_aff *isl_aff_insert_dims(
3725 __isl_take isl_aff *aff,
3726 enum isl_dim_type type, unsigned first, unsigned n);
3727 __isl_give isl_pw_aff *isl_pw_aff_insert_dims(
3728 __isl_take isl_pw_aff *pwaff,
3729 enum isl_dim_type type, unsigned first, unsigned n);
3730 __isl_give isl_aff *isl_aff_add_dims(
3731 __isl_take isl_aff *aff,
3732 enum isl_dim_type type, unsigned n);
3733 __isl_give isl_pw_aff *isl_pw_aff_add_dims(
3734 __isl_take isl_pw_aff *pwaff,
3735 enum isl_dim_type type, unsigned n);
3736 __isl_give isl_aff *isl_aff_drop_dims(
3737 __isl_take isl_aff *aff,
3738 enum isl_dim_type type, unsigned first, unsigned n);
3739 __isl_give isl_pw_aff *isl_pw_aff_drop_dims(
3740 __isl_take isl_pw_aff *pwaff,
3741 enum isl_dim_type type, unsigned first, unsigned n);
3742 __isl_give isl_aff *isl_aff_move_dims(
3743 __isl_take isl_aff *aff,
3744 enum isl_dim_type dst_type, unsigned dst_pos,
3745 enum isl_dim_type src_type, unsigned src_pos,
3747 __isl_give isl_pw_aff *isl_pw_aff_move_dims(
3748 __isl_take isl_pw_aff *pa,
3749 enum isl_dim_type dst_type, unsigned dst_pos,
3750 enum isl_dim_type src_type, unsigned src_pos,
3753 Note that C<isl_aff_set_constant_si> and C<isl_aff_set_coefficient_si>
3754 set the I<numerator> of the constant or coefficient, while
3755 C<isl_aff_set_constant_val> and C<isl_aff_set_coefficient_val> set
3756 the constant or coefficient as a whole.
3757 The C<add_constant> and C<add_coefficient> functions add an integer
3758 or rational value to
3759 the possibly rational constant or coefficient.
3760 The C<add_constant_num> functions add an integer value to
3763 To check whether an affine expressions is obviously zero
3764 or (obviously) equal to some other affine expression, use
3766 #include <isl/aff.h>
3767 int isl_aff_plain_is_zero(__isl_keep isl_aff *aff);
3768 int isl_aff_plain_is_equal(__isl_keep isl_aff *aff1,
3769 __isl_keep isl_aff *aff2);
3770 int isl_pw_aff_plain_is_equal(
3771 __isl_keep isl_pw_aff *pwaff1,
3772 __isl_keep isl_pw_aff *pwaff2);
3773 int isl_pw_aff_is_equal(__isl_keep isl_pw_aff *pa1,
3774 __isl_keep isl_pw_aff *pa2);
3778 #include <isl/aff.h>
3779 __isl_give isl_aff *isl_aff_add(__isl_take isl_aff *aff1,
3780 __isl_take isl_aff *aff2);
3781 __isl_give isl_pw_aff *isl_pw_aff_add(
3782 __isl_take isl_pw_aff *pwaff1,
3783 __isl_take isl_pw_aff *pwaff2);
3784 __isl_give isl_pw_aff *isl_pw_aff_min(
3785 __isl_take isl_pw_aff *pwaff1,
3786 __isl_take isl_pw_aff *pwaff2);
3787 __isl_give isl_pw_aff *isl_pw_aff_max(
3788 __isl_take isl_pw_aff *pwaff1,
3789 __isl_take isl_pw_aff *pwaff2);
3790 __isl_give isl_aff *isl_aff_sub(__isl_take isl_aff *aff1,
3791 __isl_take isl_aff *aff2);
3792 __isl_give isl_pw_aff *isl_pw_aff_sub(
3793 __isl_take isl_pw_aff *pwaff1,
3794 __isl_take isl_pw_aff *pwaff2);
3795 __isl_give isl_aff *isl_aff_neg(__isl_take isl_aff *aff);
3796 __isl_give isl_pw_aff *isl_pw_aff_neg(
3797 __isl_take isl_pw_aff *pwaff);
3798 __isl_give isl_aff *isl_aff_ceil(__isl_take isl_aff *aff);
3799 __isl_give isl_pw_aff *isl_pw_aff_ceil(
3800 __isl_take isl_pw_aff *pwaff);
3801 __isl_give isl_aff *isl_aff_floor(__isl_take isl_aff *aff);
3802 __isl_give isl_pw_aff *isl_pw_aff_floor(
3803 __isl_take isl_pw_aff *pwaff);
3804 __isl_give isl_aff *isl_aff_mod_val(__isl_take isl_aff *aff,
3805 __isl_take isl_val *mod);
3806 __isl_give isl_pw_aff *isl_pw_aff_mod_val(
3807 __isl_take isl_pw_aff *pa,
3808 __isl_take isl_val *mod);
3809 __isl_give isl_aff *isl_aff_scale_val(__isl_take isl_aff *aff,
3810 __isl_take isl_val *v);
3811 __isl_give isl_pw_aff *isl_pw_aff_scale_val(
3812 __isl_take isl_pw_aff *pa, __isl_take isl_val *v);
3813 __isl_give isl_aff *isl_aff_scale_down_ui(
3814 __isl_take isl_aff *aff, unsigned f);
3815 __isl_give isl_aff *isl_aff_scale_down_val(
3816 __isl_take isl_aff *aff, __isl_take isl_val *v);
3817 __isl_give isl_pw_aff *isl_pw_aff_scale_down_val(
3818 __isl_take isl_pw_aff *pa,
3819 __isl_take isl_val *f);
3821 __isl_give isl_pw_aff *isl_pw_aff_list_min(
3822 __isl_take isl_pw_aff_list *list);
3823 __isl_give isl_pw_aff *isl_pw_aff_list_max(
3824 __isl_take isl_pw_aff_list *list);
3826 __isl_give isl_pw_aff *isl_pw_aff_coalesce(
3827 __isl_take isl_pw_aff *pwqp);
3829 __isl_give isl_aff *isl_aff_align_params(
3830 __isl_take isl_aff *aff,
3831 __isl_take isl_space *model);
3832 __isl_give isl_pw_aff *isl_pw_aff_align_params(
3833 __isl_take isl_pw_aff *pwaff,
3834 __isl_take isl_space *model);
3836 __isl_give isl_aff *isl_aff_project_domain_on_params(
3837 __isl_take isl_aff *aff);
3838 __isl_give isl_pw_aff *isl_pw_aff_from_range(
3839 __isl_take isl_pw_aff *pwa);
3841 __isl_give isl_aff *isl_aff_gist_params(
3842 __isl_take isl_aff *aff,
3843 __isl_take isl_set *context);
3844 __isl_give isl_aff *isl_aff_gist(__isl_take isl_aff *aff,
3845 __isl_take isl_set *context);
3846 __isl_give isl_pw_aff *isl_pw_aff_gist_params(
3847 __isl_take isl_pw_aff *pwaff,
3848 __isl_take isl_set *context);
3849 __isl_give isl_pw_aff *isl_pw_aff_gist(
3850 __isl_take isl_pw_aff *pwaff,
3851 __isl_take isl_set *context);
3853 __isl_give isl_set *isl_pw_aff_domain(
3854 __isl_take isl_pw_aff *pwaff);
3855 __isl_give isl_set *isl_pw_aff_params(
3856 __isl_take isl_pw_aff *pwa);
3857 __isl_give isl_pw_aff *isl_pw_aff_intersect_domain(
3858 __isl_take isl_pw_aff *pa,
3859 __isl_take isl_set *set);
3860 __isl_give isl_pw_aff *isl_pw_aff_intersect_params(
3861 __isl_take isl_pw_aff *pa,
3862 __isl_take isl_set *set);
3864 __isl_give isl_aff *isl_aff_mul(__isl_take isl_aff *aff1,
3865 __isl_take isl_aff *aff2);
3866 __isl_give isl_aff *isl_aff_div(__isl_take isl_aff *aff1,
3867 __isl_take isl_aff *aff2);
3868 __isl_give isl_pw_aff *isl_pw_aff_mul(
3869 __isl_take isl_pw_aff *pwaff1,
3870 __isl_take isl_pw_aff *pwaff2);
3871 __isl_give isl_pw_aff *isl_pw_aff_div(
3872 __isl_take isl_pw_aff *pa1,
3873 __isl_take isl_pw_aff *pa2);
3874 __isl_give isl_pw_aff *isl_pw_aff_tdiv_q(
3875 __isl_take isl_pw_aff *pa1,
3876 __isl_take isl_pw_aff *pa2);
3877 __isl_give isl_pw_aff *isl_pw_aff_tdiv_r(
3878 __isl_take isl_pw_aff *pa1,
3879 __isl_take isl_pw_aff *pa2);
3881 When multiplying two affine expressions, at least one of the two needs
3882 to be a constant. Similarly, when dividing an affine expression by another,
3883 the second expression needs to be a constant.
3884 C<isl_pw_aff_tdiv_q> computes the quotient of an integer division with
3885 rounding towards zero. C<isl_pw_aff_tdiv_r> computes the corresponding
3888 #include <isl/aff.h>
3889 __isl_give isl_aff *isl_aff_pullback_aff(
3890 __isl_take isl_aff *aff1,
3891 __isl_take isl_aff *aff2);
3892 __isl_give isl_aff *isl_aff_pullback_multi_aff(
3893 __isl_take isl_aff *aff,
3894 __isl_take isl_multi_aff *ma);
3895 __isl_give isl_pw_aff *isl_pw_aff_pullback_multi_aff(
3896 __isl_take isl_pw_aff *pa,
3897 __isl_take isl_multi_aff *ma);
3898 __isl_give isl_pw_aff *isl_pw_aff_pullback_pw_multi_aff(
3899 __isl_take isl_pw_aff *pa,
3900 __isl_take isl_pw_multi_aff *pma);
3902 These functions precompose the input expression by the given
3903 C<isl_aff>, C<isl_multi_aff> or C<isl_pw_multi_aff>. In other words,
3904 the C<isl_aff>, C<isl_multi_aff> or C<isl_pw_multi_aff> is plugged
3905 into the (piecewise) affine expression.
3906 Objects of type C<isl_multi_aff> are described in
3907 L</"Piecewise Multiple Quasi Affine Expressions">.
3909 #include <isl/aff.h>
3910 __isl_give isl_basic_set *isl_aff_zero_basic_set(
3911 __isl_take isl_aff *aff);
3912 __isl_give isl_basic_set *isl_aff_neg_basic_set(
3913 __isl_take isl_aff *aff);
3914 __isl_give isl_basic_set *isl_aff_le_basic_set(
3915 __isl_take isl_aff *aff1, __isl_take isl_aff *aff2);
3916 __isl_give isl_basic_set *isl_aff_ge_basic_set(
3917 __isl_take isl_aff *aff1, __isl_take isl_aff *aff2);
3918 __isl_give isl_set *isl_pw_aff_eq_set(
3919 __isl_take isl_pw_aff *pwaff1,
3920 __isl_take isl_pw_aff *pwaff2);
3921 __isl_give isl_set *isl_pw_aff_ne_set(
3922 __isl_take isl_pw_aff *pwaff1,
3923 __isl_take isl_pw_aff *pwaff2);
3924 __isl_give isl_set *isl_pw_aff_le_set(
3925 __isl_take isl_pw_aff *pwaff1,
3926 __isl_take isl_pw_aff *pwaff2);
3927 __isl_give isl_set *isl_pw_aff_lt_set(
3928 __isl_take isl_pw_aff *pwaff1,
3929 __isl_take isl_pw_aff *pwaff2);
3930 __isl_give isl_set *isl_pw_aff_ge_set(
3931 __isl_take isl_pw_aff *pwaff1,
3932 __isl_take isl_pw_aff *pwaff2);
3933 __isl_give isl_set *isl_pw_aff_gt_set(
3934 __isl_take isl_pw_aff *pwaff1,
3935 __isl_take isl_pw_aff *pwaff2);
3937 __isl_give isl_set *isl_pw_aff_list_eq_set(
3938 __isl_take isl_pw_aff_list *list1,
3939 __isl_take isl_pw_aff_list *list2);
3940 __isl_give isl_set *isl_pw_aff_list_ne_set(
3941 __isl_take isl_pw_aff_list *list1,
3942 __isl_take isl_pw_aff_list *list2);
3943 __isl_give isl_set *isl_pw_aff_list_le_set(
3944 __isl_take isl_pw_aff_list *list1,
3945 __isl_take isl_pw_aff_list *list2);
3946 __isl_give isl_set *isl_pw_aff_list_lt_set(
3947 __isl_take isl_pw_aff_list *list1,
3948 __isl_take isl_pw_aff_list *list2);
3949 __isl_give isl_set *isl_pw_aff_list_ge_set(
3950 __isl_take isl_pw_aff_list *list1,
3951 __isl_take isl_pw_aff_list *list2);
3952 __isl_give isl_set *isl_pw_aff_list_gt_set(
3953 __isl_take isl_pw_aff_list *list1,
3954 __isl_take isl_pw_aff_list *list2);
3956 The function C<isl_aff_neg_basic_set> returns a basic set
3957 containing those elements in the domain space
3958 of C<aff> where C<aff> is negative.
3959 The function C<isl_aff_ge_basic_set> returns a basic set
3960 containing those elements in the shared space
3961 of C<aff1> and C<aff2> where C<aff1> is greater than or equal to C<aff2>.
3962 The function C<isl_pw_aff_ge_set> returns a set
3963 containing those elements in the shared domain
3964 of C<pwaff1> and C<pwaff2> where C<pwaff1> is greater than or equal to C<pwaff2>.
3965 The functions operating on C<isl_pw_aff_list> apply the corresponding
3966 C<isl_pw_aff> function to each pair of elements in the two lists.
3968 #include <isl/aff.h>
3969 __isl_give isl_set *isl_pw_aff_nonneg_set(
3970 __isl_take isl_pw_aff *pwaff);
3971 __isl_give isl_set *isl_pw_aff_zero_set(
3972 __isl_take isl_pw_aff *pwaff);
3973 __isl_give isl_set *isl_pw_aff_non_zero_set(
3974 __isl_take isl_pw_aff *pwaff);
3976 The function C<isl_pw_aff_nonneg_set> returns a set
3977 containing those elements in the domain
3978 of C<pwaff> where C<pwaff> is non-negative.
3980 #include <isl/aff.h>
3981 __isl_give isl_pw_aff *isl_pw_aff_cond(
3982 __isl_take isl_pw_aff *cond,
3983 __isl_take isl_pw_aff *pwaff_true,
3984 __isl_take isl_pw_aff *pwaff_false);
3986 The function C<isl_pw_aff_cond> performs a conditional operator
3987 and returns an expression that is equal to C<pwaff_true>
3988 for elements where C<cond> is non-zero and equal to C<pwaff_false> for elements
3989 where C<cond> is zero.
3991 #include <isl/aff.h>
3992 __isl_give isl_pw_aff *isl_pw_aff_union_min(
3993 __isl_take isl_pw_aff *pwaff1,
3994 __isl_take isl_pw_aff *pwaff2);
3995 __isl_give isl_pw_aff *isl_pw_aff_union_max(
3996 __isl_take isl_pw_aff *pwaff1,
3997 __isl_take isl_pw_aff *pwaff2);
3998 __isl_give isl_pw_aff *isl_pw_aff_union_add(
3999 __isl_take isl_pw_aff *pwaff1,
4000 __isl_take isl_pw_aff *pwaff2);
4002 The function C<isl_pw_aff_union_max> computes a piecewise quasi-affine
4003 expression with a domain that is the union of those of C<pwaff1> and
4004 C<pwaff2> and such that on each cell, the quasi-affine expression is
4005 the maximum of those of C<pwaff1> and C<pwaff2>. If only one of
4006 C<pwaff1> or C<pwaff2> is defined on a given cell, then the
4007 associated expression is the defined one.
4009 An expression can be read from input using
4011 #include <isl/aff.h>
4012 __isl_give isl_aff *isl_aff_read_from_str(
4013 isl_ctx *ctx, const char *str);
4014 __isl_give isl_pw_aff *isl_pw_aff_read_from_str(
4015 isl_ctx *ctx, const char *str);
4017 An expression can be printed using
4019 #include <isl/aff.h>
4020 __isl_give isl_printer *isl_printer_print_aff(
4021 __isl_take isl_printer *p, __isl_keep isl_aff *aff);
4023 __isl_give isl_printer *isl_printer_print_pw_aff(
4024 __isl_take isl_printer *p,
4025 __isl_keep isl_pw_aff *pwaff);
4027 =head2 Piecewise Multiple Quasi Affine Expressions
4029 An C<isl_multi_aff> object represents a sequence of
4030 zero or more affine expressions, all defined on the same domain space.
4031 Similarly, an C<isl_multi_pw_aff> object represents a sequence of
4032 zero or more piecewise affine expressions.
4034 An C<isl_multi_aff> can be constructed from a single
4035 C<isl_aff> or an C<isl_aff_list> using the
4036 following functions. Similarly for C<isl_multi_pw_aff>
4037 and C<isl_pw_multi_aff>.
4039 #include <isl/aff.h>
4040 __isl_give isl_multi_aff *isl_multi_aff_from_aff(
4041 __isl_take isl_aff *aff);
4042 __isl_give isl_multi_pw_aff *
4043 isl_multi_pw_aff_from_multi_aff(
4044 __isl_take isl_multi_aff *ma);
4045 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_from_pw_aff(
4046 __isl_take isl_pw_aff *pa);
4047 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_from_pw_aff(
4048 __isl_take isl_pw_aff *pa);
4049 __isl_give isl_multi_aff *isl_multi_aff_from_aff_list(
4050 __isl_take isl_space *space,
4051 __isl_take isl_aff_list *list);
4053 An C<isl_multi_pw_aff> can be converted to an C<isl_pw_multi_aff>
4054 using the function C<isl_pw_multi_aff_from_multi_pw_aff> below.
4055 Note however that the domain
4056 of the result is the intersection of the domains of the input.
4057 The reverse conversion is exact.
4059 #include <isl/aff.h>
4060 __isl_give isl_pw_multi_aff *
4061 isl_pw_multi_aff_from_multi_pw_aff(
4062 __isl_take isl_multi_pw_aff *mpa);
4063 __isl_give isl_multi_pw_aff *
4064 isl_multi_pw_aff_from_pw_multi_aff(
4065 __isl_take isl_pw_multi_aff *pma);
4067 An empty piecewise multiple quasi affine expression (one with no cells),
4068 the zero piecewise multiple quasi affine expression (with value zero
4069 for each output dimension),
4070 a piecewise multiple quasi affine expression with a single cell (with
4071 either a universe or a specified domain) or
4072 a zero-dimensional piecewise multiple quasi affine expression
4074 can be created using the following functions.
4076 #include <isl/aff.h>
4077 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_empty(
4078 __isl_take isl_space *space);
4079 __isl_give isl_multi_aff *isl_multi_aff_zero(
4080 __isl_take isl_space *space);
4081 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_zero(
4082 __isl_take isl_space *space);
4083 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_zero(
4084 __isl_take isl_space *space);
4085 __isl_give isl_multi_aff *isl_multi_aff_identity(
4086 __isl_take isl_space *space);
4087 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_identity(
4088 __isl_take isl_space *space);
4089 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_identity(
4090 __isl_take isl_space *space);
4091 __isl_give isl_multi_aff *isl_multi_aff_domain_map(
4092 __isl_take isl_space *space);
4093 __isl_give isl_multi_aff *isl_multi_aff_range_map(
4094 __isl_take isl_space *space);
4095 __isl_give isl_multi_aff *isl_multi_aff_project_out_map(
4096 __isl_take isl_space *space,
4097 enum isl_dim_type type,
4098 unsigned first, unsigned n);
4099 __isl_give isl_pw_multi_aff *
4100 isl_pw_multi_aff_project_out_map(
4101 __isl_take isl_space *space,
4102 enum isl_dim_type type,
4103 unsigned first, unsigned n);
4104 __isl_give isl_pw_multi_aff *
4105 isl_pw_multi_aff_from_multi_aff(
4106 __isl_take isl_multi_aff *ma);
4107 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_alloc(
4108 __isl_take isl_set *set,
4109 __isl_take isl_multi_aff *maff);
4110 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_from_domain(
4111 __isl_take isl_set *set);
4113 __isl_give isl_union_pw_multi_aff *
4114 isl_union_pw_multi_aff_empty(
4115 __isl_take isl_space *space);
4116 __isl_give isl_union_pw_multi_aff *
4117 isl_union_pw_multi_aff_add_pw_multi_aff(
4118 __isl_take isl_union_pw_multi_aff *upma,
4119 __isl_take isl_pw_multi_aff *pma);
4120 __isl_give isl_union_pw_multi_aff *
4121 isl_union_pw_multi_aff_from_domain(
4122 __isl_take isl_union_set *uset);
4124 A piecewise multiple quasi affine expression can also be initialized
4125 from an C<isl_set> or C<isl_map>, provided the C<isl_set> is a singleton
4126 and the C<isl_map> is single-valued.
4127 In case of a conversion from an C<isl_union_set> or an C<isl_union_map>
4128 to an C<isl_union_pw_multi_aff>, these properties need to hold in each space.
4130 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_from_set(
4131 __isl_take isl_set *set);
4132 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_from_map(
4133 __isl_take isl_map *map);
4135 __isl_give isl_union_pw_multi_aff *
4136 isl_union_pw_multi_aff_from_union_set(
4137 __isl_take isl_union_set *uset);
4138 __isl_give isl_union_pw_multi_aff *
4139 isl_union_pw_multi_aff_from_union_map(
4140 __isl_take isl_union_map *umap);
4142 Multiple quasi affine expressions can be copied and freed using
4144 #include <isl/aff.h>
4145 __isl_give isl_multi_aff *isl_multi_aff_copy(
4146 __isl_keep isl_multi_aff *maff);
4147 void *isl_multi_aff_free(__isl_take isl_multi_aff *maff);
4149 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_copy(
4150 __isl_keep isl_pw_multi_aff *pma);
4151 void *isl_pw_multi_aff_free(
4152 __isl_take isl_pw_multi_aff *pma);
4154 __isl_give isl_union_pw_multi_aff *
4155 isl_union_pw_multi_aff_copy(
4156 __isl_keep isl_union_pw_multi_aff *upma);
4157 void *isl_union_pw_multi_aff_free(
4158 __isl_take isl_union_pw_multi_aff *upma);
4160 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_copy(
4161 __isl_keep isl_multi_pw_aff *mpa);
4162 void *isl_multi_pw_aff_free(
4163 __isl_take isl_multi_pw_aff *mpa);
4165 The expression can be inspected using
4167 #include <isl/aff.h>
4168 isl_ctx *isl_multi_aff_get_ctx(
4169 __isl_keep isl_multi_aff *maff);
4170 isl_ctx *isl_pw_multi_aff_get_ctx(
4171 __isl_keep isl_pw_multi_aff *pma);
4172 isl_ctx *isl_union_pw_multi_aff_get_ctx(
4173 __isl_keep isl_union_pw_multi_aff *upma);
4174 isl_ctx *isl_multi_pw_aff_get_ctx(
4175 __isl_keep isl_multi_pw_aff *mpa);
4176 unsigned isl_multi_aff_dim(__isl_keep isl_multi_aff *maff,
4177 enum isl_dim_type type);
4178 unsigned isl_pw_multi_aff_dim(
4179 __isl_keep isl_pw_multi_aff *pma,
4180 enum isl_dim_type type);
4181 unsigned isl_multi_pw_aff_dim(
4182 __isl_keep isl_multi_pw_aff *mpa,
4183 enum isl_dim_type type);
4184 __isl_give isl_aff *isl_multi_aff_get_aff(
4185 __isl_keep isl_multi_aff *multi, int pos);
4186 __isl_give isl_pw_aff *isl_pw_multi_aff_get_pw_aff(
4187 __isl_keep isl_pw_multi_aff *pma, int pos);
4188 __isl_give isl_pw_aff *isl_multi_pw_aff_get_pw_aff(
4189 __isl_keep isl_multi_pw_aff *mpa, int pos);
4190 int isl_multi_aff_find_dim_by_id(
4191 __isl_keep isl_multi_aff *ma,
4192 enum isl_dim_type type, __isl_keep isl_id *id);
4193 int isl_multi_pw_aff_find_dim_by_id(
4194 __isl_keep isl_multi_pw_aff *mpa,
4195 enum isl_dim_type type, __isl_keep isl_id *id);
4196 const char *isl_pw_multi_aff_get_dim_name(
4197 __isl_keep isl_pw_multi_aff *pma,
4198 enum isl_dim_type type, unsigned pos);
4199 __isl_give isl_id *isl_multi_aff_get_dim_id(
4200 __isl_keep isl_multi_aff *ma,
4201 enum isl_dim_type type, unsigned pos);
4202 __isl_give isl_id *isl_pw_multi_aff_get_dim_id(
4203 __isl_keep isl_pw_multi_aff *pma,
4204 enum isl_dim_type type, unsigned pos);
4205 __isl_give isl_id *isl_multi_pw_aff_get_dim_id(
4206 __isl_keep isl_multi_pw_aff *mpa,
4207 enum isl_dim_type type, unsigned pos);
4208 const char *isl_multi_aff_get_tuple_name(
4209 __isl_keep isl_multi_aff *multi,
4210 enum isl_dim_type type);
4211 int isl_pw_multi_aff_has_tuple_name(
4212 __isl_keep isl_pw_multi_aff *pma,
4213 enum isl_dim_type type);
4214 const char *isl_pw_multi_aff_get_tuple_name(
4215 __isl_keep isl_pw_multi_aff *pma,
4216 enum isl_dim_type type);
4217 int isl_multi_aff_has_tuple_id(__isl_keep isl_multi_aff *ma,
4218 enum isl_dim_type type);
4219 int isl_pw_multi_aff_has_tuple_id(
4220 __isl_keep isl_pw_multi_aff *pma,
4221 enum isl_dim_type type);
4222 int isl_multi_pw_aff_has_tuple_id(
4223 __isl_keep isl_multi_pw_aff *mpa,
4224 enum isl_dim_type type);
4225 __isl_give isl_id *isl_multi_aff_get_tuple_id(
4226 __isl_keep isl_multi_aff *ma,
4227 enum isl_dim_type type);
4228 __isl_give isl_id *isl_pw_multi_aff_get_tuple_id(
4229 __isl_keep isl_pw_multi_aff *pma,
4230 enum isl_dim_type type);
4231 __isl_give isl_id *isl_multi_pw_aff_get_tuple_id(
4232 __isl_keep isl_multi_pw_aff *mpa,
4233 enum isl_dim_type type);
4234 __isl_give isl_multi_aff *isl_multi_aff_reset_tuple_id(
4235 __isl_take isl_multi_aff *ma,
4236 enum isl_dim_type type);
4237 __isl_give isl_multi_pw_aff *
4238 isl_multi_pw_aff_reset_tuple_id(
4239 __isl_take isl_multi_pw_aff *mpa,
4240 enum isl_dim_type type);
4242 int isl_pw_multi_aff_foreach_piece(
4243 __isl_keep isl_pw_multi_aff *pma,
4244 int (*fn)(__isl_take isl_set *set,
4245 __isl_take isl_multi_aff *maff,
4246 void *user), void *user);
4248 int isl_union_pw_multi_aff_foreach_pw_multi_aff(
4249 __isl_keep isl_union_pw_multi_aff *upma,
4250 int (*fn)(__isl_take isl_pw_multi_aff *pma,
4251 void *user), void *user);
4253 It can be modified using
4255 #include <isl/aff.h>
4256 __isl_give isl_multi_aff *isl_multi_aff_set_aff(
4257 __isl_take isl_multi_aff *multi, int pos,
4258 __isl_take isl_aff *aff);
4259 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_set_pw_aff(
4260 __isl_take isl_pw_multi_aff *pma, unsigned pos,
4261 __isl_take isl_pw_aff *pa);
4262 __isl_give isl_multi_aff *isl_multi_aff_set_dim_name(
4263 __isl_take isl_multi_aff *maff,
4264 enum isl_dim_type type, unsigned pos, const char *s);
4265 __isl_give isl_multi_aff *isl_multi_aff_set_dim_id(
4266 __isl_take isl_multi_aff *maff,
4267 enum isl_dim_type type, unsigned pos,
4268 __isl_take isl_id *id);
4269 __isl_give isl_multi_aff *isl_multi_aff_set_tuple_name(
4270 __isl_take isl_multi_aff *maff,
4271 enum isl_dim_type type, const char *s);
4272 __isl_give isl_multi_aff *isl_multi_aff_set_tuple_id(
4273 __isl_take isl_multi_aff *maff,
4274 enum isl_dim_type type, __isl_take isl_id *id);
4275 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_set_tuple_id(
4276 __isl_take isl_pw_multi_aff *pma,
4277 enum isl_dim_type type, __isl_take isl_id *id);
4279 __isl_give isl_multi_pw_aff *
4280 isl_multi_pw_aff_set_dim_name(
4281 __isl_take isl_multi_pw_aff *mpa,
4282 enum isl_dim_type type, unsigned pos, const char *s);
4283 __isl_give isl_multi_pw_aff *
4284 isl_multi_pw_aff_set_dim_id(
4285 __isl_take isl_multi_pw_aff *mpa,
4286 enum isl_dim_type type, unsigned pos,
4287 __isl_take isl_id *id);
4288 __isl_give isl_multi_pw_aff *
4289 isl_multi_pw_aff_set_tuple_name(
4290 __isl_take isl_multi_pw_aff *mpa,
4291 enum isl_dim_type type, const char *s);
4293 __isl_give isl_multi_aff *isl_multi_aff_insert_dims(
4294 __isl_take isl_multi_aff *ma,
4295 enum isl_dim_type type, unsigned first, unsigned n);
4296 __isl_give isl_multi_aff *isl_multi_aff_add_dims(
4297 __isl_take isl_multi_aff *ma,
4298 enum isl_dim_type type, unsigned n);
4299 __isl_give isl_multi_aff *isl_multi_aff_drop_dims(
4300 __isl_take isl_multi_aff *maff,
4301 enum isl_dim_type type, unsigned first, unsigned n);
4302 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_drop_dims(
4303 __isl_take isl_pw_multi_aff *pma,
4304 enum isl_dim_type type, unsigned first, unsigned n);
4306 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_insert_dims(
4307 __isl_take isl_multi_pw_aff *mpa,
4308 enum isl_dim_type type, unsigned first, unsigned n);
4309 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_add_dims(
4310 __isl_take isl_multi_pw_aff *mpa,
4311 enum isl_dim_type type, unsigned n);
4312 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_move_dims(
4313 __isl_take isl_multi_pw_aff *pma,
4314 enum isl_dim_type dst_type, unsigned dst_pos,
4315 enum isl_dim_type src_type, unsigned src_pos,
4318 To check whether two multiple affine expressions are
4319 (obviously) equal to each other, use
4321 int isl_multi_aff_plain_is_equal(__isl_keep isl_multi_aff *maff1,
4322 __isl_keep isl_multi_aff *maff2);
4323 int isl_pw_multi_aff_plain_is_equal(
4324 __isl_keep isl_pw_multi_aff *pma1,
4325 __isl_keep isl_pw_multi_aff *pma2);
4326 int isl_multi_pw_aff_plain_is_equal(
4327 __isl_keep isl_multi_pw_aff *mpa1,
4328 __isl_keep isl_multi_pw_aff *mpa2);
4329 int isl_multi_pw_aff_is_equal(
4330 __isl_keep isl_multi_pw_aff *mpa1,
4331 __isl_keep isl_multi_pw_aff *mpa2);
4335 #include <isl/aff.h>
4336 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_union_lexmin(
4337 __isl_take isl_pw_multi_aff *pma1,
4338 __isl_take isl_pw_multi_aff *pma2);
4339 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_union_lexmax(
4340 __isl_take isl_pw_multi_aff *pma1,
4341 __isl_take isl_pw_multi_aff *pma2);
4342 __isl_give isl_multi_aff *isl_multi_aff_add(
4343 __isl_take isl_multi_aff *maff1,
4344 __isl_take isl_multi_aff *maff2);
4345 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_add(
4346 __isl_take isl_pw_multi_aff *pma1,
4347 __isl_take isl_pw_multi_aff *pma2);
4348 __isl_give isl_union_pw_multi_aff *isl_union_pw_multi_aff_add(
4349 __isl_take isl_union_pw_multi_aff *upma1,
4350 __isl_take isl_union_pw_multi_aff *upma2);
4351 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_union_add(
4352 __isl_take isl_pw_multi_aff *pma1,
4353 __isl_take isl_pw_multi_aff *pma2);
4354 __isl_give isl_multi_aff *isl_multi_aff_sub(
4355 __isl_take isl_multi_aff *ma1,
4356 __isl_take isl_multi_aff *ma2);
4357 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_sub(
4358 __isl_take isl_pw_multi_aff *pma1,
4359 __isl_take isl_pw_multi_aff *pma2);
4360 __isl_give isl_union_pw_multi_aff *isl_union_pw_multi_aff_sub(
4361 __isl_take isl_union_pw_multi_aff *upma1,
4362 __isl_take isl_union_pw_multi_aff *upma2);
4364 C<isl_multi_aff_sub> subtracts the second argument from the first.
4366 __isl_give isl_multi_aff *isl_multi_aff_scale_val(
4367 __isl_take isl_multi_aff *ma,
4368 __isl_take isl_val *v);
4369 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_scale_val(
4370 __isl_take isl_pw_multi_aff *pma,
4371 __isl_take isl_val *v);
4372 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_scale_val(
4373 __isl_take isl_multi_pw_aff *mpa,
4374 __isl_take isl_val *v);
4375 __isl_give isl_multi_aff *isl_multi_aff_scale_multi_val(
4376 __isl_take isl_multi_aff *ma,
4377 __isl_take isl_multi_val *mv);
4378 __isl_give isl_pw_multi_aff *
4379 isl_pw_multi_aff_scale_multi_val(
4380 __isl_take isl_pw_multi_aff *pma,
4381 __isl_take isl_multi_val *mv);
4382 __isl_give isl_multi_pw_aff *
4383 isl_multi_pw_aff_scale_multi_val(
4384 __isl_take isl_multi_pw_aff *mpa,
4385 __isl_take isl_multi_val *mv);
4386 __isl_give isl_union_pw_multi_aff *
4387 isl_union_pw_multi_aff_scale_multi_val(
4388 __isl_take isl_union_pw_multi_aff *upma,
4389 __isl_take isl_multi_val *mv);
4390 __isl_give isl_multi_aff *
4391 isl_multi_aff_scale_down_multi_val(
4392 __isl_take isl_multi_aff *ma,
4393 __isl_take isl_multi_val *mv);
4394 __isl_give isl_multi_pw_aff *
4395 isl_multi_pw_aff_scale_down_multi_val(
4396 __isl_take isl_multi_pw_aff *mpa,
4397 __isl_take isl_multi_val *mv);
4399 C<isl_multi_aff_scale_multi_val> scales the elements of C<ma>
4400 by the corresponding elements of C<mv>.
4402 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_fix_si(
4403 __isl_take isl_pw_multi_aff *pma,
4404 enum isl_dim_type type, unsigned pos, int value);
4405 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_intersect_params(
4406 __isl_take isl_pw_multi_aff *pma,
4407 __isl_take isl_set *set);
4408 __isl_give isl_set *isl_multi_pw_aff_domain(
4409 __isl_take isl_multi_pw_aff *mpa);
4410 __isl_give isl_multi_pw_aff *
4411 isl_multi_pw_aff_intersect_params(
4412 __isl_take isl_multi_pw_aff *mpa,
4413 __isl_take isl_set *set);
4414 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_intersect_domain(
4415 __isl_take isl_pw_multi_aff *pma,
4416 __isl_take isl_set *set);
4417 __isl_give isl_multi_pw_aff *
4418 isl_multi_pw_aff_intersect_domain(
4419 __isl_take isl_multi_pw_aff *mpa,
4420 __isl_take isl_set *domain);
4421 __isl_give isl_union_pw_multi_aff *
4422 isl_union_pw_multi_aff_intersect_domain(
4423 __isl_take isl_union_pw_multi_aff *upma,
4424 __isl_take isl_union_set *uset);
4425 __isl_give isl_multi_aff *isl_multi_aff_lift(
4426 __isl_take isl_multi_aff *maff,
4427 __isl_give isl_local_space **ls);
4428 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_coalesce(
4429 __isl_take isl_pw_multi_aff *pma);
4430 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_coalesce(
4431 __isl_take isl_multi_pw_aff *mpa);
4432 __isl_give isl_multi_aff *isl_multi_aff_align_params(
4433 __isl_take isl_multi_aff *multi,
4434 __isl_take isl_space *model);
4435 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_align_params(
4436 __isl_take isl_pw_multi_aff *pma,
4437 __isl_take isl_space *model);
4438 __isl_give isl_pw_multi_aff *
4439 isl_pw_multi_aff_project_domain_on_params(
4440 __isl_take isl_pw_multi_aff *pma);
4441 __isl_give isl_multi_aff *isl_multi_aff_gist_params(
4442 __isl_take isl_multi_aff *maff,
4443 __isl_take isl_set *context);
4444 __isl_give isl_multi_aff *isl_multi_aff_gist(
4445 __isl_take isl_multi_aff *maff,
4446 __isl_take isl_set *context);
4447 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_gist_params(
4448 __isl_take isl_pw_multi_aff *pma,
4449 __isl_take isl_set *set);
4450 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_gist(
4451 __isl_take isl_pw_multi_aff *pma,
4452 __isl_take isl_set *set);
4453 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_gist_params(
4454 __isl_take isl_multi_pw_aff *mpa,
4455 __isl_take isl_set *set);
4456 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_gist(
4457 __isl_take isl_multi_pw_aff *mpa,
4458 __isl_take isl_set *set);
4459 __isl_give isl_multi_aff *isl_multi_aff_from_range(
4460 __isl_take isl_multi_aff *ma);
4461 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_from_range(
4462 __isl_take isl_multi_pw_aff *mpa);
4463 __isl_give isl_set *isl_pw_multi_aff_domain(
4464 __isl_take isl_pw_multi_aff *pma);
4465 __isl_give isl_union_set *isl_union_pw_multi_aff_domain(
4466 __isl_take isl_union_pw_multi_aff *upma);
4467 __isl_give isl_multi_aff *isl_multi_aff_range_splice(
4468 __isl_take isl_multi_aff *ma1, unsigned pos,
4469 __isl_take isl_multi_aff *ma2);
4470 __isl_give isl_multi_aff *isl_multi_aff_splice(
4471 __isl_take isl_multi_aff *ma1,
4472 unsigned in_pos, unsigned out_pos,
4473 __isl_take isl_multi_aff *ma2);
4474 __isl_give isl_multi_aff *isl_multi_aff_range_product(
4475 __isl_take isl_multi_aff *ma1,
4476 __isl_take isl_multi_aff *ma2);
4477 __isl_give isl_multi_aff *isl_multi_aff_flat_range_product(
4478 __isl_take isl_multi_aff *ma1,
4479 __isl_take isl_multi_aff *ma2);
4480 __isl_give isl_multi_aff *isl_multi_aff_product(
4481 __isl_take isl_multi_aff *ma1,
4482 __isl_take isl_multi_aff *ma2);
4483 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_product(
4484 __isl_take isl_multi_pw_aff *mpa1,
4485 __isl_take isl_multi_pw_aff *mpa2);
4486 __isl_give isl_pw_multi_aff *
4487 isl_pw_multi_aff_range_product(
4488 __isl_take isl_pw_multi_aff *pma1,
4489 __isl_take isl_pw_multi_aff *pma2);
4490 __isl_give isl_pw_multi_aff *
4491 isl_pw_multi_aff_flat_range_product(
4492 __isl_take isl_pw_multi_aff *pma1,
4493 __isl_take isl_pw_multi_aff *pma2);
4494 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_product(
4495 __isl_take isl_pw_multi_aff *pma1,
4496 __isl_take isl_pw_multi_aff *pma2);
4497 __isl_give isl_union_pw_multi_aff *
4498 isl_union_pw_multi_aff_flat_range_product(
4499 __isl_take isl_union_pw_multi_aff *upma1,
4500 __isl_take isl_union_pw_multi_aff *upma2);
4501 __isl_give isl_multi_pw_aff *
4502 isl_multi_pw_aff_range_splice(
4503 __isl_take isl_multi_pw_aff *mpa1, unsigned pos,
4504 __isl_take isl_multi_pw_aff *mpa2);
4505 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_splice(
4506 __isl_take isl_multi_pw_aff *mpa1,
4507 unsigned in_pos, unsigned out_pos,
4508 __isl_take isl_multi_pw_aff *mpa2);
4509 __isl_give isl_multi_pw_aff *
4510 isl_multi_pw_aff_range_product(
4511 __isl_take isl_multi_pw_aff *mpa1,
4512 __isl_take isl_multi_pw_aff *mpa2);
4513 __isl_give isl_multi_pw_aff *
4514 isl_multi_pw_aff_flat_range_product(
4515 __isl_take isl_multi_pw_aff *mpa1,
4516 __isl_take isl_multi_pw_aff *mpa2);
4518 If the C<ls> argument of C<isl_multi_aff_lift> is not C<NULL>,
4519 then it is assigned the local space that lies at the basis of
4520 the lifting applied.
4522 #include <isl/aff.h>
4523 __isl_give isl_multi_aff *isl_multi_aff_pullback_multi_aff(
4524 __isl_take isl_multi_aff *ma1,
4525 __isl_take isl_multi_aff *ma2);
4526 __isl_give isl_pw_multi_aff *
4527 isl_pw_multi_aff_pullback_multi_aff(
4528 __isl_take isl_pw_multi_aff *pma,
4529 __isl_take isl_multi_aff *ma);
4530 __isl_give isl_multi_pw_aff *
4531 isl_multi_pw_aff_pullback_multi_aff(
4532 __isl_take isl_multi_pw_aff *mpa,
4533 __isl_take isl_multi_aff *ma);
4534 __isl_give isl_pw_multi_aff *
4535 isl_pw_multi_aff_pullback_pw_multi_aff(
4536 __isl_take isl_pw_multi_aff *pma1,
4537 __isl_take isl_pw_multi_aff *pma2);
4538 __isl_give isl_multi_pw_aff *
4539 isl_multi_pw_aff_pullback_pw_multi_aff(
4540 __isl_take isl_multi_pw_aff *mpa,
4541 __isl_take isl_pw_multi_aff *pma);
4542 __isl_give isl_multi_pw_aff *
4543 isl_multi_pw_aff_pullback_multi_pw_aff(
4544 __isl_take isl_multi_pw_aff *mpa1,
4545 __isl_take isl_multi_pw_aff *mpa2);
4547 The function C<isl_multi_aff_pullback_multi_aff> precomposes C<ma1> by C<ma2>.
4548 In other words, C<ma2> is plugged
4551 __isl_give isl_set *isl_multi_aff_lex_le_set(
4552 __isl_take isl_multi_aff *ma1,
4553 __isl_take isl_multi_aff *ma2);
4554 __isl_give isl_set *isl_multi_aff_lex_ge_set(
4555 __isl_take isl_multi_aff *ma1,
4556 __isl_take isl_multi_aff *ma2);
4558 The function C<isl_multi_aff_lex_le_set> returns a set
4559 containing those elements in the shared domain space
4560 where C<ma1> is lexicographically smaller than or
4563 An expression can be read from input using
4565 #include <isl/aff.h>
4566 __isl_give isl_multi_aff *isl_multi_aff_read_from_str(
4567 isl_ctx *ctx, const char *str);
4568 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_read_from_str(
4569 isl_ctx *ctx, const char *str);
4570 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_read_from_str(
4571 isl_ctx *ctx, const char *str);
4572 __isl_give isl_union_pw_multi_aff *
4573 isl_union_pw_multi_aff_read_from_str(
4574 isl_ctx *ctx, const char *str);
4576 An expression can be printed using
4578 #include <isl/aff.h>
4579 __isl_give isl_printer *isl_printer_print_multi_aff(
4580 __isl_take isl_printer *p,
4581 __isl_keep isl_multi_aff *maff);
4582 __isl_give isl_printer *isl_printer_print_pw_multi_aff(
4583 __isl_take isl_printer *p,
4584 __isl_keep isl_pw_multi_aff *pma);
4585 __isl_give isl_printer *isl_printer_print_union_pw_multi_aff(
4586 __isl_take isl_printer *p,
4587 __isl_keep isl_union_pw_multi_aff *upma);
4588 __isl_give isl_printer *isl_printer_print_multi_pw_aff(
4589 __isl_take isl_printer *p,
4590 __isl_keep isl_multi_pw_aff *mpa);
4594 Points are elements of a set. They can be used to construct
4595 simple sets (boxes) or they can be used to represent the
4596 individual elements of a set.
4597 The zero point (the origin) can be created using
4599 __isl_give isl_point *isl_point_zero(__isl_take isl_space *space);
4601 The coordinates of a point can be inspected, set and changed
4604 __isl_give isl_val *isl_point_get_coordinate_val(
4605 __isl_keep isl_point *pnt,
4606 enum isl_dim_type type, int pos);
4607 __isl_give isl_point *isl_point_set_coordinate_val(
4608 __isl_take isl_point *pnt,
4609 enum isl_dim_type type, int pos,
4610 __isl_take isl_val *v);
4612 __isl_give isl_point *isl_point_add_ui(
4613 __isl_take isl_point *pnt,
4614 enum isl_dim_type type, int pos, unsigned val);
4615 __isl_give isl_point *isl_point_sub_ui(
4616 __isl_take isl_point *pnt,
4617 enum isl_dim_type type, int pos, unsigned val);
4619 Other properties can be obtained using
4621 isl_ctx *isl_point_get_ctx(__isl_keep isl_point *pnt);
4623 Points can be copied or freed using
4625 __isl_give isl_point *isl_point_copy(
4626 __isl_keep isl_point *pnt);
4627 void isl_point_free(__isl_take isl_point *pnt);
4629 A singleton set can be created from a point using
4631 __isl_give isl_basic_set *isl_basic_set_from_point(
4632 __isl_take isl_point *pnt);
4633 __isl_give isl_set *isl_set_from_point(
4634 __isl_take isl_point *pnt);
4636 and a box can be created from two opposite extremal points using
4638 __isl_give isl_basic_set *isl_basic_set_box_from_points(
4639 __isl_take isl_point *pnt1,
4640 __isl_take isl_point *pnt2);
4641 __isl_give isl_set *isl_set_box_from_points(
4642 __isl_take isl_point *pnt1,
4643 __isl_take isl_point *pnt2);
4645 All elements of a B<bounded> (union) set can be enumerated using
4646 the following functions.
4648 int isl_set_foreach_point(__isl_keep isl_set *set,
4649 int (*fn)(__isl_take isl_point *pnt, void *user),
4651 int isl_union_set_foreach_point(__isl_keep isl_union_set *uset,
4652 int (*fn)(__isl_take isl_point *pnt, void *user),
4655 The function C<fn> is called for each integer point in
4656 C<set> with as second argument the last argument of
4657 the C<isl_set_foreach_point> call. The function C<fn>
4658 should return C<0> on success and C<-1> on failure.
4659 In the latter case, C<isl_set_foreach_point> will stop
4660 enumerating and return C<-1> as well.
4661 If the enumeration is performed successfully and to completion,
4662 then C<isl_set_foreach_point> returns C<0>.
4664 To obtain a single point of a (basic) set, use
4666 __isl_give isl_point *isl_basic_set_sample_point(
4667 __isl_take isl_basic_set *bset);
4668 __isl_give isl_point *isl_set_sample_point(
4669 __isl_take isl_set *set);
4671 If C<set> does not contain any (integer) points, then the
4672 resulting point will be ``void'', a property that can be
4675 int isl_point_is_void(__isl_keep isl_point *pnt);
4677 =head2 Piecewise Quasipolynomials
4679 A piecewise quasipolynomial is a particular kind of function that maps
4680 a parametric point to a rational value.
4681 More specifically, a quasipolynomial is a polynomial expression in greatest
4682 integer parts of affine expressions of parameters and variables.
4683 A piecewise quasipolynomial is a subdivision of a given parametric
4684 domain into disjoint cells with a quasipolynomial associated to
4685 each cell. The value of the piecewise quasipolynomial at a given
4686 point is the value of the quasipolynomial associated to the cell
4687 that contains the point. Outside of the union of cells,
4688 the value is assumed to be zero.
4689 For example, the piecewise quasipolynomial
4691 [n] -> { [x] -> ((1 + n) - x) : x <= n and x >= 0 }
4693 maps C<x> to C<1 + n - x> for values of C<x> between C<0> and C<n>.
4694 A given piecewise quasipolynomial has a fixed domain dimension.
4695 Union piecewise quasipolynomials are used to contain piecewise quasipolynomials
4696 defined over different domains.
4697 Piecewise quasipolynomials are mainly used by the C<barvinok>
4698 library for representing the number of elements in a parametric set or map.
4699 For example, the piecewise quasipolynomial above represents
4700 the number of points in the map
4702 [n] -> { [x] -> [y] : x,y >= 0 and 0 <= x + y <= n }
4704 =head3 Input and Output
4706 Piecewise quasipolynomials can be read from input using
4708 __isl_give isl_union_pw_qpolynomial *
4709 isl_union_pw_qpolynomial_read_from_str(
4710 isl_ctx *ctx, const char *str);
4712 Quasipolynomials and piecewise quasipolynomials can be printed
4713 using the following functions.
4715 __isl_give isl_printer *isl_printer_print_qpolynomial(
4716 __isl_take isl_printer *p,
4717 __isl_keep isl_qpolynomial *qp);
4719 __isl_give isl_printer *isl_printer_print_pw_qpolynomial(
4720 __isl_take isl_printer *p,
4721 __isl_keep isl_pw_qpolynomial *pwqp);
4723 __isl_give isl_printer *isl_printer_print_union_pw_qpolynomial(
4724 __isl_take isl_printer *p,
4725 __isl_keep isl_union_pw_qpolynomial *upwqp);
4727 The output format of the printer
4728 needs to be set to either C<ISL_FORMAT_ISL> or C<ISL_FORMAT_C>.
4729 For C<isl_printer_print_union_pw_qpolynomial>, only C<ISL_FORMAT_ISL>
4731 In case of printing in C<ISL_FORMAT_C>, the user may want
4732 to set the names of all dimensions
4734 __isl_give isl_qpolynomial *isl_qpolynomial_set_dim_name(
4735 __isl_take isl_qpolynomial *qp,
4736 enum isl_dim_type type, unsigned pos,
4738 __isl_give isl_pw_qpolynomial *
4739 isl_pw_qpolynomial_set_dim_name(
4740 __isl_take isl_pw_qpolynomial *pwqp,
4741 enum isl_dim_type type, unsigned pos,
4744 =head3 Creating New (Piecewise) Quasipolynomials
4746 Some simple quasipolynomials can be created using the following functions.
4747 More complicated quasipolynomials can be created by applying
4748 operations such as addition and multiplication
4749 on the resulting quasipolynomials
4751 __isl_give isl_qpolynomial *isl_qpolynomial_zero_on_domain(
4752 __isl_take isl_space *domain);
4753 __isl_give isl_qpolynomial *isl_qpolynomial_one_on_domain(
4754 __isl_take isl_space *domain);
4755 __isl_give isl_qpolynomial *isl_qpolynomial_infty_on_domain(
4756 __isl_take isl_space *domain);
4757 __isl_give isl_qpolynomial *isl_qpolynomial_neginfty_on_domain(
4758 __isl_take isl_space *domain);
4759 __isl_give isl_qpolynomial *isl_qpolynomial_nan_on_domain(
4760 __isl_take isl_space *domain);
4761 __isl_give isl_qpolynomial *isl_qpolynomial_val_on_domain(
4762 __isl_take isl_space *domain,
4763 __isl_take isl_val *val);
4764 __isl_give isl_qpolynomial *isl_qpolynomial_var_on_domain(
4765 __isl_take isl_space *domain,
4766 enum isl_dim_type type, unsigned pos);
4767 __isl_give isl_qpolynomial *isl_qpolynomial_from_aff(
4768 __isl_take isl_aff *aff);
4770 Note that the space in which a quasipolynomial lives is a map space
4771 with a one-dimensional range. The C<domain> argument in some of
4772 the functions above corresponds to the domain of this map space.
4774 The zero piecewise quasipolynomial or a piecewise quasipolynomial
4775 with a single cell can be created using the following functions.
4776 Multiple of these single cell piecewise quasipolynomials can
4777 be combined to create more complicated piecewise quasipolynomials.
4779 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_zero(
4780 __isl_take isl_space *space);
4781 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_alloc(
4782 __isl_take isl_set *set,
4783 __isl_take isl_qpolynomial *qp);
4784 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_from_qpolynomial(
4785 __isl_take isl_qpolynomial *qp);
4786 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_from_pw_aff(
4787 __isl_take isl_pw_aff *pwaff);
4789 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_zero(
4790 __isl_take isl_space *space);
4791 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_from_pw_qpolynomial(
4792 __isl_take isl_pw_qpolynomial *pwqp);
4793 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_add_pw_qpolynomial(
4794 __isl_take isl_union_pw_qpolynomial *upwqp,
4795 __isl_take isl_pw_qpolynomial *pwqp);
4797 Quasipolynomials can be copied and freed again using the following
4800 __isl_give isl_qpolynomial *isl_qpolynomial_copy(
4801 __isl_keep isl_qpolynomial *qp);
4802 void *isl_qpolynomial_free(__isl_take isl_qpolynomial *qp);
4804 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_copy(
4805 __isl_keep isl_pw_qpolynomial *pwqp);
4806 void *isl_pw_qpolynomial_free(
4807 __isl_take isl_pw_qpolynomial *pwqp);
4809 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_copy(
4810 __isl_keep isl_union_pw_qpolynomial *upwqp);
4811 void *isl_union_pw_qpolynomial_free(
4812 __isl_take isl_union_pw_qpolynomial *upwqp);
4814 =head3 Inspecting (Piecewise) Quasipolynomials
4816 To iterate over all piecewise quasipolynomials in a union
4817 piecewise quasipolynomial, use the following function
4819 int isl_union_pw_qpolynomial_foreach_pw_qpolynomial(
4820 __isl_keep isl_union_pw_qpolynomial *upwqp,
4821 int (*fn)(__isl_take isl_pw_qpolynomial *pwqp, void *user),
4824 To extract the piecewise quasipolynomial in a given space from a union, use
4826 __isl_give isl_pw_qpolynomial *
4827 isl_union_pw_qpolynomial_extract_pw_qpolynomial(
4828 __isl_keep isl_union_pw_qpolynomial *upwqp,
4829 __isl_take isl_space *space);
4831 To iterate over the cells in a piecewise quasipolynomial,
4832 use either of the following two functions
4834 int isl_pw_qpolynomial_foreach_piece(
4835 __isl_keep isl_pw_qpolynomial *pwqp,
4836 int (*fn)(__isl_take isl_set *set,
4837 __isl_take isl_qpolynomial *qp,
4838 void *user), void *user);
4839 int isl_pw_qpolynomial_foreach_lifted_piece(
4840 __isl_keep isl_pw_qpolynomial *pwqp,
4841 int (*fn)(__isl_take isl_set *set,
4842 __isl_take isl_qpolynomial *qp,
4843 void *user), void *user);
4845 As usual, the function C<fn> should return C<0> on success
4846 and C<-1> on failure. The difference between
4847 C<isl_pw_qpolynomial_foreach_piece> and
4848 C<isl_pw_qpolynomial_foreach_lifted_piece> is that
4849 C<isl_pw_qpolynomial_foreach_lifted_piece> will first
4850 compute unique representations for all existentially quantified
4851 variables and then turn these existentially quantified variables
4852 into extra set variables, adapting the associated quasipolynomial
4853 accordingly. This means that the C<set> passed to C<fn>
4854 will not have any existentially quantified variables, but that
4855 the dimensions of the sets may be different for different
4856 invocations of C<fn>.
4858 The constant term of a quasipolynomial can be extracted using
4860 __isl_give isl_val *isl_qpolynomial_get_constant_val(
4861 __isl_keep isl_qpolynomial *qp);
4863 To iterate over all terms in a quasipolynomial,
4866 int isl_qpolynomial_foreach_term(
4867 __isl_keep isl_qpolynomial *qp,
4868 int (*fn)(__isl_take isl_term *term,
4869 void *user), void *user);
4871 The terms themselves can be inspected and freed using
4874 unsigned isl_term_dim(__isl_keep isl_term *term,
4875 enum isl_dim_type type);
4876 __isl_give isl_val *isl_term_get_coefficient_val(
4877 __isl_keep isl_term *term);
4878 int isl_term_get_exp(__isl_keep isl_term *term,
4879 enum isl_dim_type type, unsigned pos);
4880 __isl_give isl_aff *isl_term_get_div(
4881 __isl_keep isl_term *term, unsigned pos);
4882 void isl_term_free(__isl_take isl_term *term);
4884 Each term is a product of parameters, set variables and
4885 integer divisions. The function C<isl_term_get_exp>
4886 returns the exponent of a given dimensions in the given term.
4888 =head3 Properties of (Piecewise) Quasipolynomials
4890 To check whether two union piecewise quasipolynomials are
4891 obviously equal, use
4893 int isl_union_pw_qpolynomial_plain_is_equal(
4894 __isl_keep isl_union_pw_qpolynomial *upwqp1,
4895 __isl_keep isl_union_pw_qpolynomial *upwqp2);
4897 =head3 Operations on (Piecewise) Quasipolynomials
4899 __isl_give isl_qpolynomial *isl_qpolynomial_scale_val(
4900 __isl_take isl_qpolynomial *qp,
4901 __isl_take isl_val *v);
4902 __isl_give isl_qpolynomial *isl_qpolynomial_neg(
4903 __isl_take isl_qpolynomial *qp);
4904 __isl_give isl_qpolynomial *isl_qpolynomial_add(
4905 __isl_take isl_qpolynomial *qp1,
4906 __isl_take isl_qpolynomial *qp2);
4907 __isl_give isl_qpolynomial *isl_qpolynomial_sub(
4908 __isl_take isl_qpolynomial *qp1,
4909 __isl_take isl_qpolynomial *qp2);
4910 __isl_give isl_qpolynomial *isl_qpolynomial_mul(
4911 __isl_take isl_qpolynomial *qp1,
4912 __isl_take isl_qpolynomial *qp2);
4913 __isl_give isl_qpolynomial *isl_qpolynomial_pow(
4914 __isl_take isl_qpolynomial *qp, unsigned exponent);
4916 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_fix_val(
4917 __isl_take isl_pw_qpolynomial *pwqp,
4918 enum isl_dim_type type, unsigned n,
4919 __isl_take isl_val *v);
4920 __isl_give isl_pw_qpolynomial *
4921 isl_pw_qpolynomial_scale_val(
4922 __isl_take isl_pw_qpolynomial *pwqp,
4923 __isl_take isl_val *v);
4924 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_add(
4925 __isl_take isl_pw_qpolynomial *pwqp1,
4926 __isl_take isl_pw_qpolynomial *pwqp2);
4927 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_sub(
4928 __isl_take isl_pw_qpolynomial *pwqp1,
4929 __isl_take isl_pw_qpolynomial *pwqp2);
4930 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_add_disjoint(
4931 __isl_take isl_pw_qpolynomial *pwqp1,
4932 __isl_take isl_pw_qpolynomial *pwqp2);
4933 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_neg(
4934 __isl_take isl_pw_qpolynomial *pwqp);
4935 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_mul(
4936 __isl_take isl_pw_qpolynomial *pwqp1,
4937 __isl_take isl_pw_qpolynomial *pwqp2);
4938 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_pow(
4939 __isl_take isl_pw_qpolynomial *pwqp, unsigned exponent);
4941 __isl_give isl_union_pw_qpolynomial *
4942 isl_union_pw_qpolynomial_scale_val(
4943 __isl_take isl_union_pw_qpolynomial *upwqp,
4944 __isl_take isl_val *v);
4945 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_add(
4946 __isl_take isl_union_pw_qpolynomial *upwqp1,
4947 __isl_take isl_union_pw_qpolynomial *upwqp2);
4948 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_sub(
4949 __isl_take isl_union_pw_qpolynomial *upwqp1,
4950 __isl_take isl_union_pw_qpolynomial *upwqp2);
4951 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_mul(
4952 __isl_take isl_union_pw_qpolynomial *upwqp1,
4953 __isl_take isl_union_pw_qpolynomial *upwqp2);
4955 __isl_give isl_val *isl_pw_qpolynomial_eval(
4956 __isl_take isl_pw_qpolynomial *pwqp,
4957 __isl_take isl_point *pnt);
4959 __isl_give isl_val *isl_union_pw_qpolynomial_eval(
4960 __isl_take isl_union_pw_qpolynomial *upwqp,
4961 __isl_take isl_point *pnt);
4963 __isl_give isl_set *isl_pw_qpolynomial_domain(
4964 __isl_take isl_pw_qpolynomial *pwqp);
4965 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_intersect_domain(
4966 __isl_take isl_pw_qpolynomial *pwpq,
4967 __isl_take isl_set *set);
4968 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_intersect_params(
4969 __isl_take isl_pw_qpolynomial *pwpq,
4970 __isl_take isl_set *set);
4972 __isl_give isl_union_set *isl_union_pw_qpolynomial_domain(
4973 __isl_take isl_union_pw_qpolynomial *upwqp);
4974 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_intersect_domain(
4975 __isl_take isl_union_pw_qpolynomial *upwpq,
4976 __isl_take isl_union_set *uset);
4977 __isl_give isl_union_pw_qpolynomial *
4978 isl_union_pw_qpolynomial_intersect_params(
4979 __isl_take isl_union_pw_qpolynomial *upwpq,
4980 __isl_take isl_set *set);
4982 __isl_give isl_qpolynomial *isl_qpolynomial_align_params(
4983 __isl_take isl_qpolynomial *qp,
4984 __isl_take isl_space *model);
4986 __isl_give isl_qpolynomial *isl_qpolynomial_project_domain_on_params(
4987 __isl_take isl_qpolynomial *qp);
4988 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_project_domain_on_params(
4989 __isl_take isl_pw_qpolynomial *pwqp);
4991 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_coalesce(
4992 __isl_take isl_union_pw_qpolynomial *upwqp);
4994 __isl_give isl_qpolynomial *isl_qpolynomial_gist_params(
4995 __isl_take isl_qpolynomial *qp,
4996 __isl_take isl_set *context);
4997 __isl_give isl_qpolynomial *isl_qpolynomial_gist(
4998 __isl_take isl_qpolynomial *qp,
4999 __isl_take isl_set *context);
5001 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_gist_params(
5002 __isl_take isl_pw_qpolynomial *pwqp,
5003 __isl_take isl_set *context);
5004 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_gist(
5005 __isl_take isl_pw_qpolynomial *pwqp,
5006 __isl_take isl_set *context);
5008 __isl_give isl_union_pw_qpolynomial *
5009 isl_union_pw_qpolynomial_gist_params(
5010 __isl_take isl_union_pw_qpolynomial *upwqp,
5011 __isl_take isl_set *context);
5012 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_gist(
5013 __isl_take isl_union_pw_qpolynomial *upwqp,
5014 __isl_take isl_union_set *context);
5016 The gist operation applies the gist operation to each of
5017 the cells in the domain of the input piecewise quasipolynomial.
5018 The context is also exploited
5019 to simplify the quasipolynomials associated to each cell.
5021 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_to_polynomial(
5022 __isl_take isl_pw_qpolynomial *pwqp, int sign);
5023 __isl_give isl_union_pw_qpolynomial *
5024 isl_union_pw_qpolynomial_to_polynomial(
5025 __isl_take isl_union_pw_qpolynomial *upwqp, int sign);
5027 Approximate each quasipolynomial by a polynomial. If C<sign> is positive,
5028 the polynomial will be an overapproximation. If C<sign> is negative,
5029 it will be an underapproximation. If C<sign> is zero, the approximation
5030 will lie somewhere in between.
5032 =head2 Bounds on Piecewise Quasipolynomials and Piecewise Quasipolynomial Reductions
5034 A piecewise quasipolynomial reduction is a piecewise
5035 reduction (or fold) of quasipolynomials.
5036 In particular, the reduction can be maximum or a minimum.
5037 The objects are mainly used to represent the result of
5038 an upper or lower bound on a quasipolynomial over its domain,
5039 i.e., as the result of the following function.
5041 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_bound(
5042 __isl_take isl_pw_qpolynomial *pwqp,
5043 enum isl_fold type, int *tight);
5045 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_bound(
5046 __isl_take isl_union_pw_qpolynomial *upwqp,
5047 enum isl_fold type, int *tight);
5049 The C<type> argument may be either C<isl_fold_min> or C<isl_fold_max>.
5050 If C<tight> is not C<NULL>, then C<*tight> is set to C<1>
5051 is the returned bound is known be tight, i.e., for each value
5052 of the parameters there is at least
5053 one element in the domain that reaches the bound.
5054 If the domain of C<pwqp> is not wrapping, then the bound is computed
5055 over all elements in that domain and the result has a purely parametric
5056 domain. If the domain of C<pwqp> is wrapping, then the bound is
5057 computed over the range of the wrapped relation. The domain of the
5058 wrapped relation becomes the domain of the result.
5060 A (piecewise) quasipolynomial reduction can be copied or freed using the
5061 following functions.
5063 __isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_copy(
5064 __isl_keep isl_qpolynomial_fold *fold);
5065 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_copy(
5066 __isl_keep isl_pw_qpolynomial_fold *pwf);
5067 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_copy(
5068 __isl_keep isl_union_pw_qpolynomial_fold *upwf);
5069 void isl_qpolynomial_fold_free(
5070 __isl_take isl_qpolynomial_fold *fold);
5071 void *isl_pw_qpolynomial_fold_free(
5072 __isl_take isl_pw_qpolynomial_fold *pwf);
5073 void *isl_union_pw_qpolynomial_fold_free(
5074 __isl_take isl_union_pw_qpolynomial_fold *upwf);
5076 =head3 Printing Piecewise Quasipolynomial Reductions
5078 Piecewise quasipolynomial reductions can be printed
5079 using the following function.
5081 __isl_give isl_printer *isl_printer_print_pw_qpolynomial_fold(
5082 __isl_take isl_printer *p,
5083 __isl_keep isl_pw_qpolynomial_fold *pwf);
5084 __isl_give isl_printer *isl_printer_print_union_pw_qpolynomial_fold(
5085 __isl_take isl_printer *p,
5086 __isl_keep isl_union_pw_qpolynomial_fold *upwf);
5088 For C<isl_printer_print_pw_qpolynomial_fold>,
5089 output format of the printer
5090 needs to be set to either C<ISL_FORMAT_ISL> or C<ISL_FORMAT_C>.
5091 For C<isl_printer_print_union_pw_qpolynomial_fold>,
5092 output format of the printer
5093 needs to be set to C<ISL_FORMAT_ISL>.
5094 In case of printing in C<ISL_FORMAT_C>, the user may want
5095 to set the names of all dimensions
5097 __isl_give isl_pw_qpolynomial_fold *
5098 isl_pw_qpolynomial_fold_set_dim_name(
5099 __isl_take isl_pw_qpolynomial_fold *pwf,
5100 enum isl_dim_type type, unsigned pos,
5103 =head3 Inspecting (Piecewise) Quasipolynomial Reductions
5105 To iterate over all piecewise quasipolynomial reductions in a union
5106 piecewise quasipolynomial reduction, use the following function
5108 int isl_union_pw_qpolynomial_fold_foreach_pw_qpolynomial_fold(
5109 __isl_keep isl_union_pw_qpolynomial_fold *upwf,
5110 int (*fn)(__isl_take isl_pw_qpolynomial_fold *pwf,
5111 void *user), void *user);
5113 To iterate over the cells in a piecewise quasipolynomial reduction,
5114 use either of the following two functions
5116 int isl_pw_qpolynomial_fold_foreach_piece(
5117 __isl_keep isl_pw_qpolynomial_fold *pwf,
5118 int (*fn)(__isl_take isl_set *set,
5119 __isl_take isl_qpolynomial_fold *fold,
5120 void *user), void *user);
5121 int isl_pw_qpolynomial_fold_foreach_lifted_piece(
5122 __isl_keep isl_pw_qpolynomial_fold *pwf,
5123 int (*fn)(__isl_take isl_set *set,
5124 __isl_take isl_qpolynomial_fold *fold,
5125 void *user), void *user);
5127 See L<Inspecting (Piecewise) Quasipolynomials> for an explanation
5128 of the difference between these two functions.
5130 To iterate over all quasipolynomials in a reduction, use
5132 int isl_qpolynomial_fold_foreach_qpolynomial(
5133 __isl_keep isl_qpolynomial_fold *fold,
5134 int (*fn)(__isl_take isl_qpolynomial *qp,
5135 void *user), void *user);
5137 =head3 Properties of Piecewise Quasipolynomial Reductions
5139 To check whether two union piecewise quasipolynomial reductions are
5140 obviously equal, use
5142 int isl_union_pw_qpolynomial_fold_plain_is_equal(
5143 __isl_keep isl_union_pw_qpolynomial_fold *upwf1,
5144 __isl_keep isl_union_pw_qpolynomial_fold *upwf2);
5146 =head3 Operations on Piecewise Quasipolynomial Reductions
5148 __isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_scale_val(
5149 __isl_take isl_qpolynomial_fold *fold,
5150 __isl_take isl_val *v);
5151 __isl_give isl_pw_qpolynomial_fold *
5152 isl_pw_qpolynomial_fold_scale_val(
5153 __isl_take isl_pw_qpolynomial_fold *pwf,
5154 __isl_take isl_val *v);
5155 __isl_give isl_union_pw_qpolynomial_fold *
5156 isl_union_pw_qpolynomial_fold_scale_val(
5157 __isl_take isl_union_pw_qpolynomial_fold *upwf,
5158 __isl_take isl_val *v);
5160 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_add(
5161 __isl_take isl_pw_qpolynomial_fold *pwf1,
5162 __isl_take isl_pw_qpolynomial_fold *pwf2);
5164 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_fold(
5165 __isl_take isl_pw_qpolynomial_fold *pwf1,
5166 __isl_take isl_pw_qpolynomial_fold *pwf2);
5168 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_fold(
5169 __isl_take isl_union_pw_qpolynomial_fold *upwf1,
5170 __isl_take isl_union_pw_qpolynomial_fold *upwf2);
5172 __isl_give isl_val *isl_pw_qpolynomial_fold_eval(
5173 __isl_take isl_pw_qpolynomial_fold *pwf,
5174 __isl_take isl_point *pnt);
5176 __isl_give isl_val *isl_union_pw_qpolynomial_fold_eval(
5177 __isl_take isl_union_pw_qpolynomial_fold *upwf,
5178 __isl_take isl_point *pnt);
5180 __isl_give isl_pw_qpolynomial_fold *
5181 isl_pw_qpolynomial_fold_intersect_params(
5182 __isl_take isl_pw_qpolynomial_fold *pwf,
5183 __isl_take isl_set *set);
5185 __isl_give isl_union_set *isl_union_pw_qpolynomial_fold_domain(
5186 __isl_take isl_union_pw_qpolynomial_fold *upwf);
5187 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_intersect_domain(
5188 __isl_take isl_union_pw_qpolynomial_fold *upwf,
5189 __isl_take isl_union_set *uset);
5190 __isl_give isl_union_pw_qpolynomial_fold *
5191 isl_union_pw_qpolynomial_fold_intersect_params(
5192 __isl_take isl_union_pw_qpolynomial_fold *upwf,
5193 __isl_take isl_set *set);
5195 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_project_domain_on_params(
5196 __isl_take isl_pw_qpolynomial_fold *pwf);
5198 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_coalesce(
5199 __isl_take isl_pw_qpolynomial_fold *pwf);
5201 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_coalesce(
5202 __isl_take isl_union_pw_qpolynomial_fold *upwf);
5204 __isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_gist_params(
5205 __isl_take isl_qpolynomial_fold *fold,
5206 __isl_take isl_set *context);
5207 __isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_gist(
5208 __isl_take isl_qpolynomial_fold *fold,
5209 __isl_take isl_set *context);
5211 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_gist(
5212 __isl_take isl_pw_qpolynomial_fold *pwf,
5213 __isl_take isl_set *context);
5214 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_gist_params(
5215 __isl_take isl_pw_qpolynomial_fold *pwf,
5216 __isl_take isl_set *context);
5218 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_gist(
5219 __isl_take isl_union_pw_qpolynomial_fold *upwf,
5220 __isl_take isl_union_set *context);
5221 __isl_give isl_union_pw_qpolynomial_fold *
5222 isl_union_pw_qpolynomial_fold_gist_params(
5223 __isl_take isl_union_pw_qpolynomial_fold *upwf,
5224 __isl_take isl_set *context);
5226 The gist operation applies the gist operation to each of
5227 the cells in the domain of the input piecewise quasipolynomial reduction.
5228 In future, the operation will also exploit the context
5229 to simplify the quasipolynomial reductions associated to each cell.
5231 __isl_give isl_pw_qpolynomial_fold *
5232 isl_set_apply_pw_qpolynomial_fold(
5233 __isl_take isl_set *set,
5234 __isl_take isl_pw_qpolynomial_fold *pwf,
5236 __isl_give isl_pw_qpolynomial_fold *
5237 isl_map_apply_pw_qpolynomial_fold(
5238 __isl_take isl_map *map,
5239 __isl_take isl_pw_qpolynomial_fold *pwf,
5241 __isl_give isl_union_pw_qpolynomial_fold *
5242 isl_union_set_apply_union_pw_qpolynomial_fold(
5243 __isl_take isl_union_set *uset,
5244 __isl_take isl_union_pw_qpolynomial_fold *upwf,
5246 __isl_give isl_union_pw_qpolynomial_fold *
5247 isl_union_map_apply_union_pw_qpolynomial_fold(
5248 __isl_take isl_union_map *umap,
5249 __isl_take isl_union_pw_qpolynomial_fold *upwf,
5252 The functions taking a map
5253 compose the given map with the given piecewise quasipolynomial reduction.
5254 That is, compute a bound (of the same type as C<pwf> or C<upwf> itself)
5255 over all elements in the intersection of the range of the map
5256 and the domain of the piecewise quasipolynomial reduction
5257 as a function of an element in the domain of the map.
5258 The functions taking a set compute a bound over all elements in the
5259 intersection of the set and the domain of the
5260 piecewise quasipolynomial reduction.
5262 =head2 Parametric Vertex Enumeration
5264 The parametric vertex enumeration described in this section
5265 is mainly intended to be used internally and by the C<barvinok>
5268 #include <isl/vertices.h>
5269 __isl_give isl_vertices *isl_basic_set_compute_vertices(
5270 __isl_keep isl_basic_set *bset);
5272 The function C<isl_basic_set_compute_vertices> performs the
5273 actual computation of the parametric vertices and the chamber
5274 decomposition and store the result in an C<isl_vertices> object.
5275 This information can be queried by either iterating over all
5276 the vertices or iterating over all the chambers or cells
5277 and then iterating over all vertices that are active on the chamber.
5279 int isl_vertices_foreach_vertex(
5280 __isl_keep isl_vertices *vertices,
5281 int (*fn)(__isl_take isl_vertex *vertex, void *user),
5284 int isl_vertices_foreach_cell(
5285 __isl_keep isl_vertices *vertices,
5286 int (*fn)(__isl_take isl_cell *cell, void *user),
5288 int isl_cell_foreach_vertex(__isl_keep isl_cell *cell,
5289 int (*fn)(__isl_take isl_vertex *vertex, void *user),
5292 Other operations that can be performed on an C<isl_vertices> object are
5295 isl_ctx *isl_vertices_get_ctx(
5296 __isl_keep isl_vertices *vertices);
5297 int isl_vertices_get_n_vertices(
5298 __isl_keep isl_vertices *vertices);
5299 void isl_vertices_free(__isl_take isl_vertices *vertices);
5301 Vertices can be inspected and destroyed using the following functions.
5303 isl_ctx *isl_vertex_get_ctx(__isl_keep isl_vertex *vertex);
5304 int isl_vertex_get_id(__isl_keep isl_vertex *vertex);
5305 __isl_give isl_basic_set *isl_vertex_get_domain(
5306 __isl_keep isl_vertex *vertex);
5307 __isl_give isl_basic_set *isl_vertex_get_expr(
5308 __isl_keep isl_vertex *vertex);
5309 void isl_vertex_free(__isl_take isl_vertex *vertex);
5311 C<isl_vertex_get_expr> returns a singleton parametric set describing
5312 the vertex, while C<isl_vertex_get_domain> returns the activity domain
5314 Note that C<isl_vertex_get_domain> and C<isl_vertex_get_expr> return
5315 B<rational> basic sets, so they should mainly be used for inspection
5316 and should not be mixed with integer sets.
5318 Chambers can be inspected and destroyed using the following functions.
5320 isl_ctx *isl_cell_get_ctx(__isl_keep isl_cell *cell);
5321 __isl_give isl_basic_set *isl_cell_get_domain(
5322 __isl_keep isl_cell *cell);
5323 void isl_cell_free(__isl_take isl_cell *cell);
5325 =head1 Polyhedral Compilation Library
5327 This section collects functionality in C<isl> that has been specifically
5328 designed for use during polyhedral compilation.
5330 =head2 Dependence Analysis
5332 C<isl> contains specialized functionality for performing
5333 array dataflow analysis. That is, given a I<sink> access relation
5334 and a collection of possible I<source> access relations,
5335 C<isl> can compute relations that describe
5336 for each iteration of the sink access, which iteration
5337 of which of the source access relations was the last
5338 to access the same data element before the given iteration
5340 The resulting dependence relations map source iterations
5341 to the corresponding sink iterations.
5342 To compute standard flow dependences, the sink should be
5343 a read, while the sources should be writes.
5344 If any of the source accesses are marked as being I<may>
5345 accesses, then there will be a dependence from the last
5346 I<must> access B<and> from any I<may> access that follows
5347 this last I<must> access.
5348 In particular, if I<all> sources are I<may> accesses,
5349 then memory based dependence analysis is performed.
5350 If, on the other hand, all sources are I<must> accesses,
5351 then value based dependence analysis is performed.
5353 #include <isl/flow.h>
5355 typedef int (*isl_access_level_before)(void *first, void *second);
5357 __isl_give isl_access_info *isl_access_info_alloc(
5358 __isl_take isl_map *sink,
5359 void *sink_user, isl_access_level_before fn,
5361 __isl_give isl_access_info *isl_access_info_add_source(
5362 __isl_take isl_access_info *acc,
5363 __isl_take isl_map *source, int must,
5365 void *isl_access_info_free(__isl_take isl_access_info *acc);
5367 __isl_give isl_flow *isl_access_info_compute_flow(
5368 __isl_take isl_access_info *acc);
5370 int isl_flow_foreach(__isl_keep isl_flow *deps,
5371 int (*fn)(__isl_take isl_map *dep, int must,
5372 void *dep_user, void *user),
5374 __isl_give isl_map *isl_flow_get_no_source(
5375 __isl_keep isl_flow *deps, int must);
5376 void isl_flow_free(__isl_take isl_flow *deps);
5378 The function C<isl_access_info_compute_flow> performs the actual
5379 dependence analysis. The other functions are used to construct
5380 the input for this function or to read off the output.
5382 The input is collected in an C<isl_access_info>, which can
5383 be created through a call to C<isl_access_info_alloc>.
5384 The arguments to this functions are the sink access relation
5385 C<sink>, a token C<sink_user> used to identify the sink
5386 access to the user, a callback function for specifying the
5387 relative order of source and sink accesses, and the number
5388 of source access relations that will be added.
5389 The callback function has type C<int (*)(void *first, void *second)>.
5390 The function is called with two user supplied tokens identifying
5391 either a source or the sink and it should return the shared nesting
5392 level and the relative order of the two accesses.
5393 In particular, let I<n> be the number of loops shared by
5394 the two accesses. If C<first> precedes C<second> textually,
5395 then the function should return I<2 * n + 1>; otherwise,
5396 it should return I<2 * n>.
5397 The sources can be added to the C<isl_access_info> by performing
5398 (at most) C<max_source> calls to C<isl_access_info_add_source>.
5399 C<must> indicates whether the source is a I<must> access
5400 or a I<may> access. Note that a multi-valued access relation
5401 should only be marked I<must> if every iteration in the domain
5402 of the relation accesses I<all> elements in its image.
5403 The C<source_user> token is again used to identify
5404 the source access. The range of the source access relation
5405 C<source> should have the same dimension as the range
5406 of the sink access relation.
5407 The C<isl_access_info_free> function should usually not be
5408 called explicitly, because it is called implicitly by
5409 C<isl_access_info_compute_flow>.
5411 The result of the dependence analysis is collected in an
5412 C<isl_flow>. There may be elements of
5413 the sink access for which no preceding source access could be
5414 found or for which all preceding sources are I<may> accesses.
5415 The relations containing these elements can be obtained through
5416 calls to C<isl_flow_get_no_source>, the first with C<must> set
5417 and the second with C<must> unset.
5418 In the case of standard flow dependence analysis,
5419 with the sink a read and the sources I<must> writes,
5420 the first relation corresponds to the reads from uninitialized
5421 array elements and the second relation is empty.
5422 The actual flow dependences can be extracted using
5423 C<isl_flow_foreach>. This function will call the user-specified
5424 callback function C<fn> for each B<non-empty> dependence between
5425 a source and the sink. The callback function is called
5426 with four arguments, the actual flow dependence relation
5427 mapping source iterations to sink iterations, a boolean that
5428 indicates whether it is a I<must> or I<may> dependence, a token
5429 identifying the source and an additional C<void *> with value
5430 equal to the third argument of the C<isl_flow_foreach> call.
5431 A dependence is marked I<must> if it originates from a I<must>
5432 source and if it is not followed by any I<may> sources.
5434 After finishing with an C<isl_flow>, the user should call
5435 C<isl_flow_free> to free all associated memory.
5437 A higher-level interface to dependence analysis is provided
5438 by the following function.
5440 #include <isl/flow.h>
5442 int isl_union_map_compute_flow(__isl_take isl_union_map *sink,
5443 __isl_take isl_union_map *must_source,
5444 __isl_take isl_union_map *may_source,
5445 __isl_take isl_union_map *schedule,
5446 __isl_give isl_union_map **must_dep,
5447 __isl_give isl_union_map **may_dep,
5448 __isl_give isl_union_map **must_no_source,
5449 __isl_give isl_union_map **may_no_source);
5451 The arrays are identified by the tuple names of the ranges
5452 of the accesses. The iteration domains by the tuple names
5453 of the domains of the accesses and of the schedule.
5454 The relative order of the iteration domains is given by the
5455 schedule. The relations returned through C<must_no_source>
5456 and C<may_no_source> are subsets of C<sink>.
5457 Any of C<must_dep>, C<may_dep>, C<must_no_source>
5458 or C<may_no_source> may be C<NULL>, but a C<NULL> value for
5459 any of the other arguments is treated as an error.
5461 =head3 Interaction with Dependence Analysis
5463 During the dependence analysis, we frequently need to perform
5464 the following operation. Given a relation between sink iterations
5465 and potential source iterations from a particular source domain,
5466 what is the last potential source iteration corresponding to each
5467 sink iteration. It can sometimes be convenient to adjust
5468 the set of potential source iterations before or after each such operation.
5469 The prototypical example is fuzzy array dataflow analysis,
5470 where we need to analyze if, based on data-dependent constraints,
5471 the sink iteration can ever be executed without one or more of
5472 the corresponding potential source iterations being executed.
5473 If so, we can introduce extra parameters and select an unknown
5474 but fixed source iteration from the potential source iterations.
5475 To be able to perform such manipulations, C<isl> provides the following
5478 #include <isl/flow.h>
5480 typedef __isl_give isl_restriction *(*isl_access_restrict)(
5481 __isl_keep isl_map *source_map,
5482 __isl_keep isl_set *sink, void *source_user,
5484 __isl_give isl_access_info *isl_access_info_set_restrict(
5485 __isl_take isl_access_info *acc,
5486 isl_access_restrict fn, void *user);
5488 The function C<isl_access_info_set_restrict> should be called
5489 before calling C<isl_access_info_compute_flow> and registers a callback function
5490 that will be called any time C<isl> is about to compute the last
5491 potential source. The first argument is the (reverse) proto-dependence,
5492 mapping sink iterations to potential source iterations.
5493 The second argument represents the sink iterations for which
5494 we want to compute the last source iteration.
5495 The third argument is the token corresponding to the source
5496 and the final argument is the token passed to C<isl_access_info_set_restrict>.
5497 The callback is expected to return a restriction on either the input or
5498 the output of the operation computing the last potential source.
5499 If the input needs to be restricted then restrictions are needed
5500 for both the source and the sink iterations. The sink iterations
5501 and the potential source iterations will be intersected with these sets.
5502 If the output needs to be restricted then only a restriction on the source
5503 iterations is required.
5504 If any error occurs, the callback should return C<NULL>.
5505 An C<isl_restriction> object can be created, freed and inspected
5506 using the following functions.
5508 #include <isl/flow.h>
5510 __isl_give isl_restriction *isl_restriction_input(
5511 __isl_take isl_set *source_restr,
5512 __isl_take isl_set *sink_restr);
5513 __isl_give isl_restriction *isl_restriction_output(
5514 __isl_take isl_set *source_restr);
5515 __isl_give isl_restriction *isl_restriction_none(
5516 __isl_take isl_map *source_map);
5517 __isl_give isl_restriction *isl_restriction_empty(
5518 __isl_take isl_map *source_map);
5519 void *isl_restriction_free(
5520 __isl_take isl_restriction *restr);
5521 isl_ctx *isl_restriction_get_ctx(
5522 __isl_keep isl_restriction *restr);
5524 C<isl_restriction_none> and C<isl_restriction_empty> are special
5525 cases of C<isl_restriction_input>. C<isl_restriction_none>
5526 is essentially equivalent to
5528 isl_restriction_input(isl_set_universe(
5529 isl_space_range(isl_map_get_space(source_map))),
5531 isl_space_domain(isl_map_get_space(source_map))));
5533 whereas C<isl_restriction_empty> is essentially equivalent to
5535 isl_restriction_input(isl_set_empty(
5536 isl_space_range(isl_map_get_space(source_map))),
5538 isl_space_domain(isl_map_get_space(source_map))));
5542 B<The functionality described in this section is fairly new
5543 and may be subject to change.>
5545 The following function can be used to compute a schedule
5546 for a union of domains.
5547 By default, the algorithm used to construct the schedule is similar
5548 to that of C<Pluto>.
5549 Alternatively, Feautrier's multi-dimensional scheduling algorithm can
5551 The generated schedule respects all C<validity> dependences.
5552 That is, all dependence distances over these dependences in the
5553 scheduled space are lexicographically positive.
5554 The default algorithm tries to minimize the dependence distances over
5555 C<proximity> dependences.
5556 Moreover, it tries to obtain sequences (bands) of schedule dimensions
5557 for groups of domains where the dependence distances have only
5558 non-negative values.
5559 When using Feautrier's algorithm, the C<proximity> dependence
5560 distances are only minimized during the extension to a
5561 full-dimensional schedule.
5563 #include <isl/schedule.h>
5564 __isl_give isl_schedule *isl_union_set_compute_schedule(
5565 __isl_take isl_union_set *domain,
5566 __isl_take isl_union_map *validity,
5567 __isl_take isl_union_map *proximity);
5568 void *isl_schedule_free(__isl_take isl_schedule *sched);
5570 A mapping from the domains to the scheduled space can be obtained
5571 from an C<isl_schedule> using the following function.
5573 __isl_give isl_union_map *isl_schedule_get_map(
5574 __isl_keep isl_schedule *sched);
5576 A representation of the schedule can be printed using
5578 __isl_give isl_printer *isl_printer_print_schedule(
5579 __isl_take isl_printer *p,
5580 __isl_keep isl_schedule *schedule);
5582 A representation of the schedule as a forest of bands can be obtained
5583 using the following function.
5585 __isl_give isl_band_list *isl_schedule_get_band_forest(
5586 __isl_keep isl_schedule *schedule);
5588 The individual bands can be visited in depth-first post-order
5589 using the following function.
5591 #include <isl/schedule.h>
5592 int isl_schedule_foreach_band(
5593 __isl_keep isl_schedule *sched,
5594 int (*fn)(__isl_keep isl_band *band, void *user),
5597 The list can be manipulated as explained in L<"Lists">.
5598 The bands inside the list can be copied and freed using the following
5601 #include <isl/band.h>
5602 __isl_give isl_band *isl_band_copy(
5603 __isl_keep isl_band *band);
5604 void *isl_band_free(__isl_take isl_band *band);
5606 Each band contains zero or more scheduling dimensions.
5607 These are referred to as the members of the band.
5608 The section of the schedule that corresponds to the band is
5609 referred to as the partial schedule of the band.
5610 For those nodes that participate in a band, the outer scheduling
5611 dimensions form the prefix schedule, while the inner scheduling
5612 dimensions form the suffix schedule.
5613 That is, if we take a cut of the band forest, then the union of
5614 the concatenations of the prefix, partial and suffix schedules of
5615 each band in the cut is equal to the entire schedule (modulo
5616 some possible padding at the end with zero scheduling dimensions).
5617 The properties of a band can be inspected using the following functions.
5619 #include <isl/band.h>
5620 isl_ctx *isl_band_get_ctx(__isl_keep isl_band *band);
5622 int isl_band_has_children(__isl_keep isl_band *band);
5623 __isl_give isl_band_list *isl_band_get_children(
5624 __isl_keep isl_band *band);
5626 __isl_give isl_union_map *isl_band_get_prefix_schedule(
5627 __isl_keep isl_band *band);
5628 __isl_give isl_union_map *isl_band_get_partial_schedule(
5629 __isl_keep isl_band *band);
5630 __isl_give isl_union_map *isl_band_get_suffix_schedule(
5631 __isl_keep isl_band *band);
5633 int isl_band_n_member(__isl_keep isl_band *band);
5634 int isl_band_member_is_zero_distance(
5635 __isl_keep isl_band *band, int pos);
5637 int isl_band_list_foreach_band(
5638 __isl_keep isl_band_list *list,
5639 int (*fn)(__isl_keep isl_band *band, void *user),
5642 Note that a scheduling dimension is considered to be ``zero
5643 distance'' if it does not carry any proximity dependences
5645 That is, if the dependence distances of the proximity
5646 dependences are all zero in that direction (for fixed
5647 iterations of outer bands).
5648 Like C<isl_schedule_foreach_band>,
5649 the function C<isl_band_list_foreach_band> calls C<fn> on the bands
5650 in depth-first post-order.
5652 A band can be tiled using the following function.
5654 #include <isl/band.h>
5655 int isl_band_tile(__isl_keep isl_band *band,
5656 __isl_take isl_vec *sizes);
5658 int isl_options_set_tile_scale_tile_loops(isl_ctx *ctx,
5660 int isl_options_get_tile_scale_tile_loops(isl_ctx *ctx);
5661 int isl_options_set_tile_shift_point_loops(isl_ctx *ctx,
5663 int isl_options_get_tile_shift_point_loops(isl_ctx *ctx);
5665 The C<isl_band_tile> function tiles the band using the given tile sizes
5666 inside its schedule.
5667 A new child band is created to represent the point loops and it is
5668 inserted between the modified band and its children.
5669 The C<tile_scale_tile_loops> option specifies whether the tile
5670 loops iterators should be scaled by the tile sizes.
5671 If the C<tile_shift_point_loops> option is set, then the point loops
5672 are shifted to start at zero.
5674 A band can be split into two nested bands using the following function.
5676 int isl_band_split(__isl_keep isl_band *band, int pos);
5678 The resulting outer band contains the first C<pos> dimensions of C<band>
5679 while the inner band contains the remaining dimensions.
5681 A representation of the band can be printed using
5683 #include <isl/band.h>
5684 __isl_give isl_printer *isl_printer_print_band(
5685 __isl_take isl_printer *p,
5686 __isl_keep isl_band *band);
5690 #include <isl/schedule.h>
5691 int isl_options_set_schedule_max_coefficient(
5692 isl_ctx *ctx, int val);
5693 int isl_options_get_schedule_max_coefficient(
5695 int isl_options_set_schedule_max_constant_term(
5696 isl_ctx *ctx, int val);
5697 int isl_options_get_schedule_max_constant_term(
5699 int isl_options_set_schedule_fuse(isl_ctx *ctx, int val);
5700 int isl_options_get_schedule_fuse(isl_ctx *ctx);
5701 int isl_options_set_schedule_maximize_band_depth(
5702 isl_ctx *ctx, int val);
5703 int isl_options_get_schedule_maximize_band_depth(
5705 int isl_options_set_schedule_outer_zero_distance(
5706 isl_ctx *ctx, int val);
5707 int isl_options_get_schedule_outer_zero_distance(
5709 int isl_options_set_schedule_split_scaled(
5710 isl_ctx *ctx, int val);
5711 int isl_options_get_schedule_split_scaled(
5713 int isl_options_set_schedule_algorithm(
5714 isl_ctx *ctx, int val);
5715 int isl_options_get_schedule_algorithm(
5717 int isl_options_set_schedule_separate_components(
5718 isl_ctx *ctx, int val);
5719 int isl_options_get_schedule_separate_components(
5724 =item * schedule_max_coefficient
5726 This option enforces that the coefficients for variable and parameter
5727 dimensions in the calculated schedule are not larger than the specified value.
5728 This option can significantly increase the speed of the scheduling calculation
5729 and may also prevent fusing of unrelated dimensions. A value of -1 means that
5730 this option does not introduce bounds on the variable or parameter
5733 =item * schedule_max_constant_term
5735 This option enforces that the constant coefficients in the calculated schedule
5736 are not larger than the maximal constant term. This option can significantly
5737 increase the speed of the scheduling calculation and may also prevent fusing of
5738 unrelated dimensions. A value of -1 means that this option does not introduce
5739 bounds on the constant coefficients.
5741 =item * schedule_fuse
5743 This option controls the level of fusion.
5744 If this option is set to C<ISL_SCHEDULE_FUSE_MIN>, then loops in the
5745 resulting schedule will be distributed as much as possible.
5746 If this option is set to C<ISL_SCHEDULE_FUSE_MAX>, then C<isl> will
5747 try to fuse loops in the resulting schedule.
5749 =item * schedule_maximize_band_depth
5751 If this option is set, we do not split bands at the point
5752 where we detect splitting is necessary. Instead, we
5753 backtrack and split bands as early as possible. This
5754 reduces the number of splits and maximizes the width of
5755 the bands. Wider bands give more possibilities for tiling.
5756 Note that if the C<schedule_fuse> option is set to C<ISL_SCHEDULE_FUSE_MIN>,
5757 then bands will be split as early as possible, even if there is no need.
5758 The C<schedule_maximize_band_depth> option therefore has no effect in this case.
5760 =item * schedule_outer_zero_distance
5762 If this option is set, then we try to construct schedules
5763 where the outermost scheduling dimension in each band
5764 results in a zero dependence distance over the proximity
5767 =item * schedule_split_scaled
5769 If this option is set, then we try to construct schedules in which the
5770 constant term is split off from the linear part if the linear parts of
5771 the scheduling rows for all nodes in the graphs have a common non-trivial
5773 The constant term is then placed in a separate band and the linear
5776 =item * schedule_algorithm
5778 Selects the scheduling algorithm to be used.
5779 Available scheduling algorithms are C<ISL_SCHEDULE_ALGORITHM_ISL>
5780 and C<ISL_SCHEDULE_ALGORITHM_FEAUTRIER>.
5782 =item * schedule_separate_components
5784 If at any point the dependence graph contains any (weakly connected) components,
5785 then these components are scheduled separately.
5786 If this option is not set, then some iterations of the domains
5787 in these components may be scheduled together.
5788 If this option is set, then the components are given consecutive
5793 =head2 AST Generation
5795 This section describes the C<isl> functionality for generating
5796 ASTs that visit all the elements
5797 in a domain in an order specified by a schedule.
5798 In particular, given a C<isl_union_map>, an AST is generated
5799 that visits all the elements in the domain of the C<isl_union_map>
5800 according to the lexicographic order of the corresponding image
5801 element(s). If the range of the C<isl_union_map> consists of
5802 elements in more than one space, then each of these spaces is handled
5803 separately in an arbitrary order.
5804 It should be noted that the image elements only specify the I<order>
5805 in which the corresponding domain elements should be visited.
5806 No direct relation between the image elements and the loop iterators
5807 in the generated AST should be assumed.
5809 Each AST is generated within a build. The initial build
5810 simply specifies the constraints on the parameters (if any)
5811 and can be created, inspected, copied and freed using the following functions.
5813 #include <isl/ast_build.h>
5814 __isl_give isl_ast_build *isl_ast_build_from_context(
5815 __isl_take isl_set *set);
5816 isl_ctx *isl_ast_build_get_ctx(
5817 __isl_keep isl_ast_build *build);
5818 __isl_give isl_ast_build *isl_ast_build_copy(
5819 __isl_keep isl_ast_build *build);
5820 void *isl_ast_build_free(
5821 __isl_take isl_ast_build *build);
5823 The C<set> argument is usually a parameter set with zero or more parameters.
5824 More C<isl_ast_build> functions are described in L</"Nested AST Generation">
5825 and L</"Fine-grained Control over AST Generation">.
5826 Finally, the AST itself can be constructed using the following
5829 #include <isl/ast_build.h>
5830 __isl_give isl_ast_node *isl_ast_build_ast_from_schedule(
5831 __isl_keep isl_ast_build *build,
5832 __isl_take isl_union_map *schedule);
5834 =head3 Inspecting the AST
5836 The basic properties of an AST node can be obtained as follows.
5838 #include <isl/ast.h>
5839 isl_ctx *isl_ast_node_get_ctx(
5840 __isl_keep isl_ast_node *node);
5841 enum isl_ast_node_type isl_ast_node_get_type(
5842 __isl_keep isl_ast_node *node);
5844 The type of an AST node is one of
5845 C<isl_ast_node_for>,
5847 C<isl_ast_node_block> or
5848 C<isl_ast_node_user>.
5849 An C<isl_ast_node_for> represents a for node.
5850 An C<isl_ast_node_if> represents an if node.
5851 An C<isl_ast_node_block> represents a compound node.
5852 An C<isl_ast_node_user> represents an expression statement.
5853 An expression statement typically corresponds to a domain element, i.e.,
5854 one of the elements that is visited by the AST.
5856 Each type of node has its own additional properties.
5858 #include <isl/ast.h>
5859 __isl_give isl_ast_expr *isl_ast_node_for_get_iterator(
5860 __isl_keep isl_ast_node *node);
5861 __isl_give isl_ast_expr *isl_ast_node_for_get_init(
5862 __isl_keep isl_ast_node *node);
5863 __isl_give isl_ast_expr *isl_ast_node_for_get_cond(
5864 __isl_keep isl_ast_node *node);
5865 __isl_give isl_ast_expr *isl_ast_node_for_get_inc(
5866 __isl_keep isl_ast_node *node);
5867 __isl_give isl_ast_node *isl_ast_node_for_get_body(
5868 __isl_keep isl_ast_node *node);
5869 int isl_ast_node_for_is_degenerate(
5870 __isl_keep isl_ast_node *node);
5872 An C<isl_ast_for> is considered degenerate if it is known to execute
5875 #include <isl/ast.h>
5876 __isl_give isl_ast_expr *isl_ast_node_if_get_cond(
5877 __isl_keep isl_ast_node *node);
5878 __isl_give isl_ast_node *isl_ast_node_if_get_then(
5879 __isl_keep isl_ast_node *node);
5880 int isl_ast_node_if_has_else(
5881 __isl_keep isl_ast_node *node);
5882 __isl_give isl_ast_node *isl_ast_node_if_get_else(
5883 __isl_keep isl_ast_node *node);
5885 __isl_give isl_ast_node_list *
5886 isl_ast_node_block_get_children(
5887 __isl_keep isl_ast_node *node);
5889 __isl_give isl_ast_expr *isl_ast_node_user_get_expr(
5890 __isl_keep isl_ast_node *node);
5892 Each of the returned C<isl_ast_expr>s can in turn be inspected using
5893 the following functions.
5895 #include <isl/ast.h>
5896 isl_ctx *isl_ast_expr_get_ctx(
5897 __isl_keep isl_ast_expr *expr);
5898 enum isl_ast_expr_type isl_ast_expr_get_type(
5899 __isl_keep isl_ast_expr *expr);
5901 The type of an AST expression is one of
5903 C<isl_ast_expr_id> or
5904 C<isl_ast_expr_int>.
5905 An C<isl_ast_expr_op> represents the result of an operation.
5906 An C<isl_ast_expr_id> represents an identifier.
5907 An C<isl_ast_expr_int> represents an integer value.
5909 Each type of expression has its own additional properties.
5911 #include <isl/ast.h>
5912 enum isl_ast_op_type isl_ast_expr_get_op_type(
5913 __isl_keep isl_ast_expr *expr);
5914 int isl_ast_expr_get_op_n_arg(__isl_keep isl_ast_expr *expr);
5915 __isl_give isl_ast_expr *isl_ast_expr_get_op_arg(
5916 __isl_keep isl_ast_expr *expr, int pos);
5917 int isl_ast_node_foreach_ast_op_type(
5918 __isl_keep isl_ast_node *node,
5919 int (*fn)(enum isl_ast_op_type type, void *user),
5922 C<isl_ast_expr_get_op_type> returns the type of the operation
5923 performed. C<isl_ast_expr_get_op_n_arg> returns the number of
5924 arguments. C<isl_ast_expr_get_op_arg> returns the specified
5926 C<isl_ast_node_foreach_ast_op_type> calls C<fn> for each distinct
5927 C<isl_ast_op_type> that appears in C<node>.
5928 The operation type is one of the following.
5932 =item C<isl_ast_op_and>
5934 Logical I<and> of two arguments.
5935 Both arguments can be evaluated.
5937 =item C<isl_ast_op_and_then>
5939 Logical I<and> of two arguments.
5940 The second argument can only be evaluated if the first evaluates to true.
5942 =item C<isl_ast_op_or>
5944 Logical I<or> of two arguments.
5945 Both arguments can be evaluated.
5947 =item C<isl_ast_op_or_else>
5949 Logical I<or> of two arguments.
5950 The second argument can only be evaluated if the first evaluates to false.
5952 =item C<isl_ast_op_max>
5954 Maximum of two or more arguments.
5956 =item C<isl_ast_op_min>
5958 Minimum of two or more arguments.
5960 =item C<isl_ast_op_minus>
5964 =item C<isl_ast_op_add>
5966 Sum of two arguments.
5968 =item C<isl_ast_op_sub>
5970 Difference of two arguments.
5972 =item C<isl_ast_op_mul>
5974 Product of two arguments.
5976 =item C<isl_ast_op_div>
5978 Exact division. That is, the result is known to be an integer.
5980 =item C<isl_ast_op_fdiv_q>
5982 Result of integer division, rounded towards negative
5985 =item C<isl_ast_op_pdiv_q>
5987 Result of integer division, where dividend is known to be non-negative.
5989 =item C<isl_ast_op_pdiv_r>
5991 Remainder of integer division, where dividend is known to be non-negative.
5993 =item C<isl_ast_op_cond>
5995 Conditional operator defined on three arguments.
5996 If the first argument evaluates to true, then the result
5997 is equal to the second argument. Otherwise, the result
5998 is equal to the third argument.
5999 The second and third argument may only be evaluated if
6000 the first argument evaluates to true and false, respectively.
6001 Corresponds to C<a ? b : c> in C.
6003 =item C<isl_ast_op_select>
6005 Conditional operator defined on three arguments.
6006 If the first argument evaluates to true, then the result
6007 is equal to the second argument. Otherwise, the result
6008 is equal to the third argument.
6009 The second and third argument may be evaluated independently
6010 of the value of the first argument.
6011 Corresponds to C<a * b + (1 - a) * c> in C.
6013 =item C<isl_ast_op_eq>
6017 =item C<isl_ast_op_le>
6019 Less than or equal relation.
6021 =item C<isl_ast_op_lt>
6025 =item C<isl_ast_op_ge>
6027 Greater than or equal relation.
6029 =item C<isl_ast_op_gt>
6031 Greater than relation.
6033 =item C<isl_ast_op_call>
6036 The number of arguments of the C<isl_ast_expr> is one more than
6037 the number of arguments in the function call, the first argument
6038 representing the function being called.
6040 =item C<isl_ast_op_access>
6043 The number of arguments of the C<isl_ast_expr> is one more than
6044 the number of index expressions in the array access, the first argument
6045 representing the array being accessed.
6049 #include <isl/ast.h>
6050 __isl_give isl_id *isl_ast_expr_get_id(
6051 __isl_keep isl_ast_expr *expr);
6053 Return the identifier represented by the AST expression.
6055 #include <isl/ast.h>
6056 __isl_give isl_val *isl_ast_expr_get_val(
6057 __isl_keep isl_ast_expr *expr);
6059 Return the integer represented by the AST expression.
6061 =head3 Properties of ASTs
6063 #include <isl/ast.h>
6064 int isl_ast_expr_is_equal(__isl_keep isl_ast_expr *expr1,
6065 __isl_keep isl_ast_expr *expr2);
6067 Check if two C<isl_ast_expr>s are equal to each other.
6069 =head3 Manipulating and printing the AST
6071 AST nodes can be copied and freed using the following functions.
6073 #include <isl/ast.h>
6074 __isl_give isl_ast_node *isl_ast_node_copy(
6075 __isl_keep isl_ast_node *node);
6076 void *isl_ast_node_free(__isl_take isl_ast_node *node);
6078 AST expressions can be copied and freed using the following functions.
6080 #include <isl/ast.h>
6081 __isl_give isl_ast_expr *isl_ast_expr_copy(
6082 __isl_keep isl_ast_expr *expr);
6083 void *isl_ast_expr_free(__isl_take isl_ast_expr *expr);
6085 New AST expressions can be created either directly or within
6086 the context of an C<isl_ast_build>.
6088 #include <isl/ast.h>
6089 __isl_give isl_ast_expr *isl_ast_expr_from_val(
6090 __isl_take isl_val *v);
6091 __isl_give isl_ast_expr *isl_ast_expr_from_id(
6092 __isl_take isl_id *id);
6093 __isl_give isl_ast_expr *isl_ast_expr_neg(
6094 __isl_take isl_ast_expr *expr);
6095 __isl_give isl_ast_expr *isl_ast_expr_add(
6096 __isl_take isl_ast_expr *expr1,
6097 __isl_take isl_ast_expr *expr2);
6098 __isl_give isl_ast_expr *isl_ast_expr_sub(
6099 __isl_take isl_ast_expr *expr1,
6100 __isl_take isl_ast_expr *expr2);
6101 __isl_give isl_ast_expr *isl_ast_expr_mul(
6102 __isl_take isl_ast_expr *expr1,
6103 __isl_take isl_ast_expr *expr2);
6104 __isl_give isl_ast_expr *isl_ast_expr_div(
6105 __isl_take isl_ast_expr *expr1,
6106 __isl_take isl_ast_expr *expr2);
6107 __isl_give isl_ast_expr *isl_ast_expr_and(
6108 __isl_take isl_ast_expr *expr1,
6109 __isl_take isl_ast_expr *expr2)
6110 __isl_give isl_ast_expr *isl_ast_expr_or(
6111 __isl_take isl_ast_expr *expr1,
6112 __isl_take isl_ast_expr *expr2)
6113 __isl_give isl_ast_expr *isl_ast_expr_access(
6114 __isl_take isl_ast_expr *array,
6115 __isl_take isl_ast_expr_list *indices);
6116 __isl_give isl_ast_expr *isl_ast_expr_substitute_ids(
6117 __isl_take isl_ast_expr *expr,
6118 __isl_take isl_id_to_ast_expr *id2expr);
6120 The function C<isl_ast_expr_substitute_ids> replaces the
6121 subexpressions of C<expr> of type C<isl_ast_expr_id>
6122 by the corresponding expression in C<id2expr>, if there is any.
6124 #include <isl/ast_build.h>
6125 __isl_give isl_ast_expr *isl_ast_build_expr_from_pw_aff(
6126 __isl_keep isl_ast_build *build,
6127 __isl_take isl_pw_aff *pa);
6128 __isl_give isl_ast_expr *
6129 isl_ast_build_access_from_pw_multi_aff(
6130 __isl_keep isl_ast_build *build,
6131 __isl_take isl_pw_multi_aff *pma);
6132 __isl_give isl_ast_expr *
6133 isl_ast_build_access_from_multi_pw_aff(
6134 __isl_keep isl_ast_build *build,
6135 __isl_take isl_multi_pw_aff *mpa);
6136 __isl_give isl_ast_expr *
6137 isl_ast_build_call_from_pw_multi_aff(
6138 __isl_keep isl_ast_build *build,
6139 __isl_take isl_pw_multi_aff *pma);
6140 __isl_give isl_ast_expr *
6141 isl_ast_build_call_from_multi_pw_aff(
6142 __isl_keep isl_ast_build *build,
6143 __isl_take isl_multi_pw_aff *mpa);
6145 The domains of C<pa>, C<mpa> and C<pma> should correspond
6146 to the schedule space of C<build>.
6147 The tuple id of C<mpa> or C<pma> is used as the array being accessed or
6148 the function being called.
6150 User specified data can be attached to an C<isl_ast_node> and obtained
6151 from the same C<isl_ast_node> using the following functions.
6153 #include <isl/ast.h>
6154 __isl_give isl_ast_node *isl_ast_node_set_annotation(
6155 __isl_take isl_ast_node *node,
6156 __isl_take isl_id *annotation);
6157 __isl_give isl_id *isl_ast_node_get_annotation(
6158 __isl_keep isl_ast_node *node);
6160 Basic printing can be performed using the following functions.
6162 #include <isl/ast.h>
6163 __isl_give isl_printer *isl_printer_print_ast_expr(
6164 __isl_take isl_printer *p,
6165 __isl_keep isl_ast_expr *expr);
6166 __isl_give isl_printer *isl_printer_print_ast_node(
6167 __isl_take isl_printer *p,
6168 __isl_keep isl_ast_node *node);
6170 More advanced printing can be performed using the following functions.
6172 #include <isl/ast.h>
6173 __isl_give isl_printer *isl_ast_op_type_print_macro(
6174 enum isl_ast_op_type type,
6175 __isl_take isl_printer *p);
6176 __isl_give isl_printer *isl_ast_node_print_macros(
6177 __isl_keep isl_ast_node *node,
6178 __isl_take isl_printer *p);
6179 __isl_give isl_printer *isl_ast_node_print(
6180 __isl_keep isl_ast_node *node,
6181 __isl_take isl_printer *p,
6182 __isl_take isl_ast_print_options *options);
6183 __isl_give isl_printer *isl_ast_node_for_print(
6184 __isl_keep isl_ast_node *node,
6185 __isl_take isl_printer *p,
6186 __isl_take isl_ast_print_options *options);
6187 __isl_give isl_printer *isl_ast_node_if_print(
6188 __isl_keep isl_ast_node *node,
6189 __isl_take isl_printer *p,
6190 __isl_take isl_ast_print_options *options);
6192 While printing an C<isl_ast_node> in C<ISL_FORMAT_C>,
6193 C<isl> may print out an AST that makes use of macros such
6194 as C<floord>, C<min> and C<max>.
6195 C<isl_ast_op_type_print_macro> prints out the macro
6196 corresponding to a specific C<isl_ast_op_type>.
6197 C<isl_ast_node_print_macros> scans the C<isl_ast_node>
6198 for expressions where these macros would be used and prints
6199 out the required macro definitions.
6200 Essentially, C<isl_ast_node_print_macros> calls
6201 C<isl_ast_node_foreach_ast_op_type> with C<isl_ast_op_type_print_macro>
6202 as function argument.
6203 C<isl_ast_node_print>, C<isl_ast_node_for_print> and
6204 C<isl_ast_node_if_print> print an C<isl_ast_node>
6205 in C<ISL_FORMAT_C>, but allow for some extra control
6206 through an C<isl_ast_print_options> object.
6207 This object can be created using the following functions.
6209 #include <isl/ast.h>
6210 __isl_give isl_ast_print_options *
6211 isl_ast_print_options_alloc(isl_ctx *ctx);
6212 __isl_give isl_ast_print_options *
6213 isl_ast_print_options_copy(
6214 __isl_keep isl_ast_print_options *options);
6215 void *isl_ast_print_options_free(
6216 __isl_take isl_ast_print_options *options);
6218 __isl_give isl_ast_print_options *
6219 isl_ast_print_options_set_print_user(
6220 __isl_take isl_ast_print_options *options,
6221 __isl_give isl_printer *(*print_user)(
6222 __isl_take isl_printer *p,
6223 __isl_take isl_ast_print_options *options,
6224 __isl_keep isl_ast_node *node, void *user),
6226 __isl_give isl_ast_print_options *
6227 isl_ast_print_options_set_print_for(
6228 __isl_take isl_ast_print_options *options,
6229 __isl_give isl_printer *(*print_for)(
6230 __isl_take isl_printer *p,
6231 __isl_take isl_ast_print_options *options,
6232 __isl_keep isl_ast_node *node, void *user),
6235 The callback set by C<isl_ast_print_options_set_print_user>
6236 is called whenever a node of type C<isl_ast_node_user> needs to
6238 The callback set by C<isl_ast_print_options_set_print_for>
6239 is called whenever a node of type C<isl_ast_node_for> needs to
6241 Note that C<isl_ast_node_for_print> will I<not> call the
6242 callback set by C<isl_ast_print_options_set_print_for> on the node
6243 on which C<isl_ast_node_for_print> is called, but only on nested
6244 nodes of type C<isl_ast_node_for>. It is therefore safe to
6245 call C<isl_ast_node_for_print> from within the callback set by
6246 C<isl_ast_print_options_set_print_for>.
6248 The following option determines the type to be used for iterators
6249 while printing the AST.
6251 int isl_options_set_ast_iterator_type(
6252 isl_ctx *ctx, const char *val);
6253 const char *isl_options_get_ast_iterator_type(
6258 #include <isl/ast_build.h>
6259 int isl_options_set_ast_build_atomic_upper_bound(
6260 isl_ctx *ctx, int val);
6261 int isl_options_get_ast_build_atomic_upper_bound(
6263 int isl_options_set_ast_build_prefer_pdiv(isl_ctx *ctx,
6265 int isl_options_get_ast_build_prefer_pdiv(isl_ctx *ctx);
6266 int isl_options_set_ast_build_exploit_nested_bounds(
6267 isl_ctx *ctx, int val);
6268 int isl_options_get_ast_build_exploit_nested_bounds(
6270 int isl_options_set_ast_build_group_coscheduled(
6271 isl_ctx *ctx, int val);
6272 int isl_options_get_ast_build_group_coscheduled(
6274 int isl_options_set_ast_build_scale_strides(
6275 isl_ctx *ctx, int val);
6276 int isl_options_get_ast_build_scale_strides(
6278 int isl_options_set_ast_build_allow_else(isl_ctx *ctx,
6280 int isl_options_get_ast_build_allow_else(isl_ctx *ctx);
6281 int isl_options_set_ast_build_allow_or(isl_ctx *ctx,
6283 int isl_options_get_ast_build_allow_or(isl_ctx *ctx);
6287 =item * ast_build_atomic_upper_bound
6289 Generate loop upper bounds that consist of the current loop iterator,
6290 an operator and an expression not involving the iterator.
6291 If this option is not set, then the current loop iterator may appear
6292 several times in the upper bound.
6293 For example, when this option is turned off, AST generation
6296 [n] -> { A[i] -> [i] : 0 <= i <= 100, n }
6300 for (int c0 = 0; c0 <= 100 && n >= c0; c0 += 1)
6303 When the option is turned on, the following AST is generated
6305 for (int c0 = 0; c0 <= min(100, n); c0 += 1)
6308 =item * ast_build_prefer_pdiv
6310 If this option is turned off, then the AST generation will
6311 produce ASTs that may only contain C<isl_ast_op_fdiv_q>
6312 operators, but no C<isl_ast_op_pdiv_q> or
6313 C<isl_ast_op_pdiv_r> operators.
6314 If this options is turned on, then C<isl> will try to convert
6315 some of the C<isl_ast_op_fdiv_q> operators to (expressions containing)
6316 C<isl_ast_op_pdiv_q> or C<isl_ast_op_pdiv_r> operators.
6318 =item * ast_build_exploit_nested_bounds
6320 Simplify conditions based on bounds of nested for loops.
6321 In particular, remove conditions that are implied by the fact
6322 that one or more nested loops have at least one iteration,
6323 meaning that the upper bound is at least as large as the lower bound.
6324 For example, when this option is turned off, AST generation
6327 [N,M] -> { A[i,j] -> [i,j] : 0 <= i <= N and
6333 for (int c0 = 0; c0 <= N; c0 += 1)
6334 for (int c1 = 0; c1 <= M; c1 += 1)
6337 When the option is turned on, the following AST is generated
6339 for (int c0 = 0; c0 <= N; c0 += 1)
6340 for (int c1 = 0; c1 <= M; c1 += 1)
6343 =item * ast_build_group_coscheduled
6345 If two domain elements are assigned the same schedule point, then
6346 they may be executed in any order and they may even appear in different
6347 loops. If this options is set, then the AST generator will make
6348 sure that coscheduled domain elements do not appear in separate parts
6349 of the AST. This is useful in case of nested AST generation
6350 if the outer AST generation is given only part of a schedule
6351 and the inner AST generation should handle the domains that are
6352 coscheduled by this initial part of the schedule together.
6353 For example if an AST is generated for a schedule
6355 { A[i] -> [0]; B[i] -> [0] }
6357 then the C<isl_ast_build_set_create_leaf> callback described
6358 below may get called twice, once for each domain.
6359 Setting this option ensures that the callback is only called once
6360 on both domains together.
6362 =item * ast_build_separation_bounds
6364 This option specifies which bounds to use during separation.
6365 If this option is set to C<ISL_AST_BUILD_SEPARATION_BOUNDS_IMPLICIT>
6366 then all (possibly implicit) bounds on the current dimension will
6367 be used during separation.
6368 If this option is set to C<ISL_AST_BUILD_SEPARATION_BOUNDS_EXPLICIT>
6369 then only those bounds that are explicitly available will
6370 be used during separation.
6372 =item * ast_build_scale_strides
6374 This option specifies whether the AST generator is allowed
6375 to scale down iterators of strided loops.
6377 =item * ast_build_allow_else
6379 This option specifies whether the AST generator is allowed
6380 to construct if statements with else branches.
6382 =item * ast_build_allow_or
6384 This option specifies whether the AST generator is allowed
6385 to construct if conditions with disjunctions.
6389 =head3 Fine-grained Control over AST Generation
6391 Besides specifying the constraints on the parameters,
6392 an C<isl_ast_build> object can be used to control
6393 various aspects of the AST generation process.
6394 The most prominent way of control is through ``options'',
6395 which can be set using the following function.
6397 #include <isl/ast_build.h>
6398 __isl_give isl_ast_build *
6399 isl_ast_build_set_options(
6400 __isl_take isl_ast_build *control,
6401 __isl_take isl_union_map *options);
6403 The options are encoded in an <isl_union_map>.
6404 The domain of this union relation refers to the schedule domain,
6405 i.e., the range of the schedule passed to C<isl_ast_build_ast_from_schedule>.
6406 In the case of nested AST generation (see L</"Nested AST Generation">),
6407 the domain of C<options> should refer to the extra piece of the schedule.
6408 That is, it should be equal to the range of the wrapped relation in the
6409 range of the schedule.
6410 The range of the options can consist of elements in one or more spaces,
6411 the names of which determine the effect of the option.
6412 The values of the range typically also refer to the schedule dimension
6413 to which the option applies. In case of nested AST generation
6414 (see L</"Nested AST Generation">), these values refer to the position
6415 of the schedule dimension within the innermost AST generation.
6416 The constraints on the domain elements of
6417 the option should only refer to this dimension and earlier dimensions.
6418 We consider the following spaces.
6422 =item C<separation_class>
6424 This space is a wrapped relation between two one dimensional spaces.
6425 The input space represents the schedule dimension to which the option
6426 applies and the output space represents the separation class.
6427 While constructing a loop corresponding to the specified schedule
6428 dimension(s), the AST generator will try to generate separate loops
6429 for domain elements that are assigned different classes.
6430 If only some of the elements are assigned a class, then those elements
6431 that are not assigned any class will be treated as belonging to a class
6432 that is separate from the explicitly assigned classes.
6433 The typical use case for this option is to separate full tiles from
6435 The other options, described below, are applied after the separation
6438 As an example, consider the separation into full and partial tiles
6439 of a tiling of a triangular domain.
6440 Take, for example, the domain
6442 { A[i,j] : 0 <= i,j and i + j <= 100 }
6444 and a tiling into tiles of 10 by 10. The input to the AST generator
6445 is then the schedule
6447 { A[i,j] -> [([i/10]),[j/10],i,j] : 0 <= i,j and
6450 Without any options, the following AST is generated
6452 for (int c0 = 0; c0 <= 10; c0 += 1)
6453 for (int c1 = 0; c1 <= -c0 + 10; c1 += 1)
6454 for (int c2 = 10 * c0;
6455 c2 <= min(-10 * c1 + 100, 10 * c0 + 9);
6457 for (int c3 = 10 * c1;
6458 c3 <= min(10 * c1 + 9, -c2 + 100);
6462 Separation into full and partial tiles can be obtained by assigning
6463 a class, say C<0>, to the full tiles. The full tiles are represented by those
6464 values of the first and second schedule dimensions for which there are
6465 values of the third and fourth dimensions to cover an entire tile.
6466 That is, we need to specify the following option
6468 { [a,b,c,d] -> separation_class[[0]->[0]] :
6469 exists b': 0 <= 10a,10b' and
6470 10a+9+10b'+9 <= 100;
6471 [a,b,c,d] -> separation_class[[1]->[0]] :
6472 0 <= 10a,10b and 10a+9+10b+9 <= 100 }
6476 { [a, b, c, d] -> separation_class[[1] -> [0]] :
6477 a >= 0 and b >= 0 and b <= 8 - a;
6478 [a, b, c, d] -> separation_class[[0] -> [0]] :
6481 With this option, the generated AST is as follows
6484 for (int c0 = 0; c0 <= 8; c0 += 1) {
6485 for (int c1 = 0; c1 <= -c0 + 8; c1 += 1)
6486 for (int c2 = 10 * c0;
6487 c2 <= 10 * c0 + 9; c2 += 1)
6488 for (int c3 = 10 * c1;
6489 c3 <= 10 * c1 + 9; c3 += 1)
6491 for (int c1 = -c0 + 9; c1 <= -c0 + 10; c1 += 1)
6492 for (int c2 = 10 * c0;
6493 c2 <= min(-10 * c1 + 100, 10 * c0 + 9);
6495 for (int c3 = 10 * c1;
6496 c3 <= min(-c2 + 100, 10 * c1 + 9);
6500 for (int c0 = 9; c0 <= 10; c0 += 1)
6501 for (int c1 = 0; c1 <= -c0 + 10; c1 += 1)
6502 for (int c2 = 10 * c0;
6503 c2 <= min(-10 * c1 + 100, 10 * c0 + 9);
6505 for (int c3 = 10 * c1;
6506 c3 <= min(10 * c1 + 9, -c2 + 100);
6513 This is a single-dimensional space representing the schedule dimension(s)
6514 to which ``separation'' should be applied. Separation tries to split
6515 a loop into several pieces if this can avoid the generation of guards
6517 See also the C<atomic> option.
6521 This is a single-dimensional space representing the schedule dimension(s)
6522 for which the domains should be considered ``atomic''. That is, the
6523 AST generator will make sure that any given domain space will only appear
6524 in a single loop at the specified level.
6526 Consider the following schedule
6528 { a[i] -> [i] : 0 <= i < 10;
6529 b[i] -> [i+1] : 0 <= i < 10 }
6531 If the following option is specified
6533 { [i] -> separate[x] }
6535 then the following AST will be generated
6539 for (int c0 = 1; c0 <= 9; c0 += 1) {
6546 If, on the other hand, the following option is specified
6548 { [i] -> atomic[x] }
6550 then the following AST will be generated
6552 for (int c0 = 0; c0 <= 10; c0 += 1) {
6559 If neither C<atomic> nor C<separate> is specified, then the AST generator
6560 may produce either of these two results or some intermediate form.
6564 This is a single-dimensional space representing the schedule dimension(s)
6565 that should be I<completely> unrolled.
6566 To obtain a partial unrolling, the user should apply an additional
6567 strip-mining to the schedule and fully unroll the inner loop.
6571 Additional control is available through the following functions.
6573 #include <isl/ast_build.h>
6574 __isl_give isl_ast_build *
6575 isl_ast_build_set_iterators(
6576 __isl_take isl_ast_build *control,
6577 __isl_take isl_id_list *iterators);
6579 The function C<isl_ast_build_set_iterators> allows the user to
6580 specify a list of iterator C<isl_id>s to be used as iterators.
6581 If the input schedule is injective, then
6582 the number of elements in this list should be as large as the dimension
6583 of the schedule space, but no direct correspondence should be assumed
6584 between dimensions and elements.
6585 If the input schedule is not injective, then an additional number
6586 of C<isl_id>s equal to the largest dimension of the input domains
6588 If the number of provided C<isl_id>s is insufficient, then additional
6589 names are automatically generated.
6591 #include <isl/ast_build.h>
6592 __isl_give isl_ast_build *
6593 isl_ast_build_set_create_leaf(
6594 __isl_take isl_ast_build *control,
6595 __isl_give isl_ast_node *(*fn)(
6596 __isl_take isl_ast_build *build,
6597 void *user), void *user);
6600 C<isl_ast_build_set_create_leaf> function allows for the
6601 specification of a callback that should be called whenever the AST
6602 generator arrives at an element of the schedule domain.
6603 The callback should return an AST node that should be inserted
6604 at the corresponding position of the AST. The default action (when
6605 the callback is not set) is to continue generating parts of the AST to scan
6606 all the domain elements associated to the schedule domain element
6607 and to insert user nodes, ``calling'' the domain element, for each of them.
6608 The C<build> argument contains the current state of the C<isl_ast_build>.
6609 To ease nested AST generation (see L</"Nested AST Generation">),
6610 all control information that is
6611 specific to the current AST generation such as the options and
6612 the callbacks has been removed from this C<isl_ast_build>.
6613 The callback would typically return the result of a nested
6615 user defined node created using the following function.
6617 #include <isl/ast.h>
6618 __isl_give isl_ast_node *isl_ast_node_alloc_user(
6619 __isl_take isl_ast_expr *expr);
6621 #include <isl/ast_build.h>
6622 __isl_give isl_ast_build *
6623 isl_ast_build_set_at_each_domain(
6624 __isl_take isl_ast_build *build,
6625 __isl_give isl_ast_node *(*fn)(
6626 __isl_take isl_ast_node *node,
6627 __isl_keep isl_ast_build *build,
6628 void *user), void *user);
6629 __isl_give isl_ast_build *
6630 isl_ast_build_set_before_each_for(
6631 __isl_take isl_ast_build *build,
6632 __isl_give isl_id *(*fn)(
6633 __isl_keep isl_ast_build *build,
6634 void *user), void *user);
6635 __isl_give isl_ast_build *
6636 isl_ast_build_set_after_each_for(
6637 __isl_take isl_ast_build *build,
6638 __isl_give isl_ast_node *(*fn)(
6639 __isl_take isl_ast_node *node,
6640 __isl_keep isl_ast_build *build,
6641 void *user), void *user);
6643 The callback set by C<isl_ast_build_set_at_each_domain> will
6644 be called for each domain AST node.
6645 The callbacks set by C<isl_ast_build_set_before_each_for>
6646 and C<isl_ast_build_set_after_each_for> will be called
6647 for each for AST node. The first will be called in depth-first
6648 pre-order, while the second will be called in depth-first post-order.
6649 Since C<isl_ast_build_set_before_each_for> is called before the for
6650 node is actually constructed, it is only passed an C<isl_ast_build>.
6651 The returned C<isl_id> will be added as an annotation (using
6652 C<isl_ast_node_set_annotation>) to the constructed for node.
6653 In particular, if the user has also specified an C<after_each_for>
6654 callback, then the annotation can be retrieved from the node passed to
6655 that callback using C<isl_ast_node_get_annotation>.
6656 All callbacks should C<NULL> on failure.
6657 The given C<isl_ast_build> can be used to create new
6658 C<isl_ast_expr> objects using C<isl_ast_build_expr_from_pw_aff>
6659 or C<isl_ast_build_call_from_pw_multi_aff>.
6661 =head3 Nested AST Generation
6663 C<isl> allows the user to create an AST within the context
6664 of another AST. These nested ASTs are created using the
6665 same C<isl_ast_build_ast_from_schedule> function that is used to create the
6666 outer AST. The C<build> argument should be an C<isl_ast_build>
6667 passed to a callback set by
6668 C<isl_ast_build_set_create_leaf>.
6669 The space of the range of the C<schedule> argument should refer
6670 to this build. In particular, the space should be a wrapped
6671 relation and the domain of this wrapped relation should be the
6672 same as that of the range of the schedule returned by
6673 C<isl_ast_build_get_schedule> below.
6674 In practice, the new schedule is typically
6675 created by calling C<isl_union_map_range_product> on the old schedule
6676 and some extra piece of the schedule.
6677 The space of the schedule domain is also available from
6678 the C<isl_ast_build>.
6680 #include <isl/ast_build.h>
6681 __isl_give isl_union_map *isl_ast_build_get_schedule(
6682 __isl_keep isl_ast_build *build);
6683 __isl_give isl_space *isl_ast_build_get_schedule_space(
6684 __isl_keep isl_ast_build *build);
6685 __isl_give isl_ast_build *isl_ast_build_restrict(
6686 __isl_take isl_ast_build *build,
6687 __isl_take isl_set *set);
6689 The C<isl_ast_build_get_schedule> function returns a (partial)
6690 schedule for the domains elements for which part of the AST still needs to
6691 be generated in the current build.
6692 In particular, the domain elements are mapped to those iterations of the loops
6693 enclosing the current point of the AST generation inside which
6694 the domain elements are executed.
6695 No direct correspondence between
6696 the input schedule and this schedule should be assumed.
6697 The space obtained from C<isl_ast_build_get_schedule_space> can be used
6698 to create a set for C<isl_ast_build_restrict> to intersect
6699 with the current build. In particular, the set passed to
6700 C<isl_ast_build_restrict> can have additional parameters.
6701 The ids of the set dimensions in the space returned by
6702 C<isl_ast_build_get_schedule_space> correspond to the
6703 iterators of the already generated loops.
6704 The user should not rely on the ids of the output dimensions
6705 of the relations in the union relation returned by
6706 C<isl_ast_build_get_schedule> having any particular value.
6710 Although C<isl> is mainly meant to be used as a library,
6711 it also contains some basic applications that use some
6712 of the functionality of C<isl>.
6713 The input may be specified in either the L<isl format>
6714 or the L<PolyLib format>.
6716 =head2 C<isl_polyhedron_sample>
6718 C<isl_polyhedron_sample> takes a polyhedron as input and prints
6719 an integer element of the polyhedron, if there is any.
6720 The first column in the output is the denominator and is always
6721 equal to 1. If the polyhedron contains no integer points,
6722 then a vector of length zero is printed.
6726 C<isl_pip> takes the same input as the C<example> program
6727 from the C<piplib> distribution, i.e., a set of constraints
6728 on the parameters, a line containing only -1 and finally a set
6729 of constraints on a parametric polyhedron.
6730 The coefficients of the parameters appear in the last columns
6731 (but before the final constant column).
6732 The output is the lexicographic minimum of the parametric polyhedron.
6733 As C<isl> currently does not have its own output format, the output
6734 is just a dump of the internal state.
6736 =head2 C<isl_polyhedron_minimize>
6738 C<isl_polyhedron_minimize> computes the minimum of some linear
6739 or affine objective function over the integer points in a polyhedron.
6740 If an affine objective function
6741 is given, then the constant should appear in the last column.
6743 =head2 C<isl_polytope_scan>
6745 Given a polytope, C<isl_polytope_scan> prints
6746 all integer points in the polytope.
6748 =head2 C<isl_codegen>
6750 Given a schedule, a context set and an options relation,
6751 C<isl_codegen> prints out an AST that scans the domain elements
6752 of the schedule in the order of their image(s) taking into account
6753 the constraints in the context set.