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 To keep the names of all parameters and tuples, but reset the user pointers
902 of all the corresponding identifiers, use the following function.
904 __isl_give isl_space *isl_space_reset_user(
905 __isl_take isl_space *space);
907 Spaces can be nested. In particular, the domain of a set or
908 the domain or range of a relation can be a nested relation.
909 The following functions can be used to construct and deconstruct
912 #include <isl/space.h>
913 int isl_space_is_wrapping(__isl_keep isl_space *space);
914 int isl_space_range_is_wrapping(
915 __isl_keep isl_space *space);
916 __isl_give isl_space *isl_space_wrap(__isl_take isl_space *space);
917 __isl_give isl_space *isl_space_unwrap(__isl_take isl_space *space);
918 __isl_give isl_space *isl_space_product(__isl_take isl_space *space1,
919 __isl_take isl_space *space2);
920 __isl_give isl_space *isl_space_domain_product(
921 __isl_take isl_space *space1,
922 __isl_take isl_space *space2);
923 __isl_give isl_space *isl_space_range_product(
924 __isl_take isl_space *space1,
925 __isl_take isl_space *space2);
927 The input to C<isl_space_is_wrapping> and C<isl_space_unwrap> should
928 be the space of a set, while that of
929 C<isl_space_range_is_wrapping> and
930 C<isl_space_wrap> should be the space of a relation.
931 Conversely, the output of C<isl_space_unwrap> is the space
932 of a relation, while that of C<isl_space_wrap> is the space of a set.
934 C<isl_space_product>, C<isl_space_domain_product>
935 and C<isl_space_range_product> take pairs or relation spaces and
936 produce a single relations space, where either the domain, the range
937 or both domain and range are wrapped spaces of relations between
938 the domains and/or ranges of the input spaces.
939 If the product is only constructed over the domain or the range
940 then the ranges or the domains of the inputs should be the same.
942 Spaces can be created from other spaces
943 using the following functions.
945 __isl_give isl_space *isl_space_domain(__isl_take isl_space *space);
946 __isl_give isl_space *isl_space_from_domain(__isl_take isl_space *space);
947 __isl_give isl_space *isl_space_range(__isl_take isl_space *space);
948 __isl_give isl_space *isl_space_from_range(__isl_take isl_space *space);
949 __isl_give isl_space *isl_space_domain_map(
950 __isl_take isl_space *space);
951 __isl_give isl_space *isl_space_range_map(
952 __isl_take isl_space *space);
953 __isl_give isl_space *isl_space_params(
954 __isl_take isl_space *space);
955 __isl_give isl_space *isl_space_set_from_params(
956 __isl_take isl_space *space);
957 __isl_give isl_space *isl_space_reverse(__isl_take isl_space *space);
958 __isl_give isl_space *isl_space_join(__isl_take isl_space *left,
959 __isl_take isl_space *right);
960 __isl_give isl_space *isl_space_align_params(
961 __isl_take isl_space *space1, __isl_take isl_space *space2)
962 __isl_give isl_space *isl_space_insert_dims(__isl_take isl_space *space,
963 enum isl_dim_type type, unsigned pos, unsigned n);
964 __isl_give isl_space *isl_space_add_dims(__isl_take isl_space *space,
965 enum isl_dim_type type, unsigned n);
966 __isl_give isl_space *isl_space_drop_dims(__isl_take isl_space *space,
967 enum isl_dim_type type, unsigned first, unsigned n);
968 __isl_give isl_space *isl_space_move_dims(__isl_take isl_space *space,
969 enum isl_dim_type dst_type, unsigned dst_pos,
970 enum isl_dim_type src_type, unsigned src_pos,
972 __isl_give isl_space *isl_space_map_from_set(
973 __isl_take isl_space *space);
974 __isl_give isl_space *isl_space_map_from_domain_and_range(
975 __isl_take isl_space *domain,
976 __isl_take isl_space *range);
977 __isl_give isl_space *isl_space_zip(__isl_take isl_space *space);
978 __isl_give isl_space *isl_space_curry(
979 __isl_take isl_space *space);
980 __isl_give isl_space *isl_space_uncurry(
981 __isl_take isl_space *space);
983 Note that if dimensions are added or removed from a space, then
984 the name and the internal structure are lost.
988 A local space is essentially a space with
989 zero or more existentially quantified variables.
990 The local space of a (constraint of a) basic set or relation can be obtained
991 using the following functions.
993 #include <isl/constraint.h>
994 __isl_give isl_local_space *isl_constraint_get_local_space(
995 __isl_keep isl_constraint *constraint);
998 __isl_give isl_local_space *isl_basic_set_get_local_space(
999 __isl_keep isl_basic_set *bset);
1001 #include <isl/map.h>
1002 __isl_give isl_local_space *isl_basic_map_get_local_space(
1003 __isl_keep isl_basic_map *bmap);
1005 A new local space can be created from a space using
1007 #include <isl/local_space.h>
1008 __isl_give isl_local_space *isl_local_space_from_space(
1009 __isl_take isl_space *space);
1011 They can be inspected, modified, copied and freed using the following functions.
1013 #include <isl/local_space.h>
1014 isl_ctx *isl_local_space_get_ctx(
1015 __isl_keep isl_local_space *ls);
1016 int isl_local_space_is_set(__isl_keep isl_local_space *ls);
1017 int isl_local_space_dim(__isl_keep isl_local_space *ls,
1018 enum isl_dim_type type);
1019 int isl_local_space_has_dim_id(
1020 __isl_keep isl_local_space *ls,
1021 enum isl_dim_type type, unsigned pos);
1022 __isl_give isl_id *isl_local_space_get_dim_id(
1023 __isl_keep isl_local_space *ls,
1024 enum isl_dim_type type, unsigned pos);
1025 int isl_local_space_has_dim_name(
1026 __isl_keep isl_local_space *ls,
1027 enum isl_dim_type type, unsigned pos)
1028 const char *isl_local_space_get_dim_name(
1029 __isl_keep isl_local_space *ls,
1030 enum isl_dim_type type, unsigned pos);
1031 __isl_give isl_local_space *isl_local_space_set_dim_name(
1032 __isl_take isl_local_space *ls,
1033 enum isl_dim_type type, unsigned pos, const char *s);
1034 __isl_give isl_local_space *isl_local_space_set_dim_id(
1035 __isl_take isl_local_space *ls,
1036 enum isl_dim_type type, unsigned pos,
1037 __isl_take isl_id *id);
1038 __isl_give isl_space *isl_local_space_get_space(
1039 __isl_keep isl_local_space *ls);
1040 __isl_give isl_aff *isl_local_space_get_div(
1041 __isl_keep isl_local_space *ls, int pos);
1042 __isl_give isl_local_space *isl_local_space_copy(
1043 __isl_keep isl_local_space *ls);
1044 void *isl_local_space_free(__isl_take isl_local_space *ls);
1046 Note that C<isl_local_space_get_div> can only be used on local spaces
1049 Two local spaces can be compared using
1051 int isl_local_space_is_equal(__isl_keep isl_local_space *ls1,
1052 __isl_keep isl_local_space *ls2);
1054 Local spaces can be created from other local spaces
1055 using the following functions.
1057 __isl_give isl_local_space *isl_local_space_domain(
1058 __isl_take isl_local_space *ls);
1059 __isl_give isl_local_space *isl_local_space_range(
1060 __isl_take isl_local_space *ls);
1061 __isl_give isl_local_space *isl_local_space_from_domain(
1062 __isl_take isl_local_space *ls);
1063 __isl_give isl_local_space *isl_local_space_intersect(
1064 __isl_take isl_local_space *ls1,
1065 __isl_take isl_local_space *ls2);
1066 __isl_give isl_local_space *isl_local_space_add_dims(
1067 __isl_take isl_local_space *ls,
1068 enum isl_dim_type type, unsigned n);
1069 __isl_give isl_local_space *isl_local_space_insert_dims(
1070 __isl_take isl_local_space *ls,
1071 enum isl_dim_type type, unsigned first, unsigned n);
1072 __isl_give isl_local_space *isl_local_space_drop_dims(
1073 __isl_take isl_local_space *ls,
1074 enum isl_dim_type type, unsigned first, unsigned n);
1076 =head2 Input and Output
1078 C<isl> supports its own input/output format, which is similar
1079 to the C<Omega> format, but also supports the C<PolyLib> format
1082 =head3 C<isl> format
1084 The C<isl> format is similar to that of C<Omega>, but has a different
1085 syntax for describing the parameters and allows for the definition
1086 of an existentially quantified variable as the integer division
1087 of an affine expression.
1088 For example, the set of integers C<i> between C<0> and C<n>
1089 such that C<i % 10 <= 6> can be described as
1091 [n] -> { [i] : exists (a = [i/10] : 0 <= i and i <= n and
1094 A set or relation can have several disjuncts, separated
1095 by the keyword C<or>. Each disjunct is either a conjunction
1096 of constraints or a projection (C<exists>) of a conjunction
1097 of constraints. The constraints are separated by the keyword
1100 =head3 C<PolyLib> format
1102 If the represented set is a union, then the first line
1103 contains a single number representing the number of disjuncts.
1104 Otherwise, a line containing the number C<1> is optional.
1106 Each disjunct is represented by a matrix of constraints.
1107 The first line contains two numbers representing
1108 the number of rows and columns,
1109 where the number of rows is equal to the number of constraints
1110 and the number of columns is equal to two plus the number of variables.
1111 The following lines contain the actual rows of the constraint matrix.
1112 In each row, the first column indicates whether the constraint
1113 is an equality (C<0>) or inequality (C<1>). The final column
1114 corresponds to the constant term.
1116 If the set is parametric, then the coefficients of the parameters
1117 appear in the last columns before the constant column.
1118 The coefficients of any existentially quantified variables appear
1119 between those of the set variables and those of the parameters.
1121 =head3 Extended C<PolyLib> format
1123 The extended C<PolyLib> format is nearly identical to the
1124 C<PolyLib> format. The only difference is that the line
1125 containing the number of rows and columns of a constraint matrix
1126 also contains four additional numbers:
1127 the number of output dimensions, the number of input dimensions,
1128 the number of local dimensions (i.e., the number of existentially
1129 quantified variables) and the number of parameters.
1130 For sets, the number of ``output'' dimensions is equal
1131 to the number of set dimensions, while the number of ``input''
1136 #include <isl/set.h>
1137 __isl_give isl_basic_set *isl_basic_set_read_from_file(
1138 isl_ctx *ctx, FILE *input);
1139 __isl_give isl_basic_set *isl_basic_set_read_from_str(
1140 isl_ctx *ctx, const char *str);
1141 __isl_give isl_set *isl_set_read_from_file(isl_ctx *ctx,
1143 __isl_give isl_set *isl_set_read_from_str(isl_ctx *ctx,
1146 #include <isl/map.h>
1147 __isl_give isl_basic_map *isl_basic_map_read_from_file(
1148 isl_ctx *ctx, FILE *input);
1149 __isl_give isl_basic_map *isl_basic_map_read_from_str(
1150 isl_ctx *ctx, const char *str);
1151 __isl_give isl_map *isl_map_read_from_file(
1152 isl_ctx *ctx, FILE *input);
1153 __isl_give isl_map *isl_map_read_from_str(isl_ctx *ctx,
1156 #include <isl/union_set.h>
1157 __isl_give isl_union_set *isl_union_set_read_from_file(
1158 isl_ctx *ctx, FILE *input);
1159 __isl_give isl_union_set *isl_union_set_read_from_str(
1160 isl_ctx *ctx, const char *str);
1162 #include <isl/union_map.h>
1163 __isl_give isl_union_map *isl_union_map_read_from_file(
1164 isl_ctx *ctx, FILE *input);
1165 __isl_give isl_union_map *isl_union_map_read_from_str(
1166 isl_ctx *ctx, const char *str);
1168 The input format is autodetected and may be either the C<PolyLib> format
1169 or the C<isl> format.
1173 Before anything can be printed, an C<isl_printer> needs to
1176 __isl_give isl_printer *isl_printer_to_file(isl_ctx *ctx,
1178 __isl_give isl_printer *isl_printer_to_str(isl_ctx *ctx);
1179 void *isl_printer_free(__isl_take isl_printer *printer);
1180 __isl_give char *isl_printer_get_str(
1181 __isl_keep isl_printer *printer);
1183 The printer can be inspected using the following functions.
1185 FILE *isl_printer_get_file(
1186 __isl_keep isl_printer *printer);
1187 int isl_printer_get_output_format(
1188 __isl_keep isl_printer *p);
1190 The behavior of the printer can be modified in various ways
1192 __isl_give isl_printer *isl_printer_set_output_format(
1193 __isl_take isl_printer *p, int output_format);
1194 __isl_give isl_printer *isl_printer_set_indent(
1195 __isl_take isl_printer *p, int indent);
1196 __isl_give isl_printer *isl_printer_indent(
1197 __isl_take isl_printer *p, int indent);
1198 __isl_give isl_printer *isl_printer_set_prefix(
1199 __isl_take isl_printer *p, const char *prefix);
1200 __isl_give isl_printer *isl_printer_set_suffix(
1201 __isl_take isl_printer *p, const char *suffix);
1203 The C<output_format> may be either C<ISL_FORMAT_ISL>, C<ISL_FORMAT_OMEGA>,
1204 C<ISL_FORMAT_POLYLIB>, C<ISL_FORMAT_EXT_POLYLIB> or C<ISL_FORMAT_LATEX>
1205 and defaults to C<ISL_FORMAT_ISL>.
1206 Each line in the output is indented by C<indent> (set by
1207 C<isl_printer_set_indent>) spaces
1208 (default: 0), prefixed by C<prefix> and suffixed by C<suffix>.
1209 In the C<PolyLib> format output,
1210 the coefficients of the existentially quantified variables
1211 appear between those of the set variables and those
1213 The function C<isl_printer_indent> increases the indentation
1214 by the specified amount (which may be negative).
1216 To actually print something, use
1218 #include <isl/printer.h>
1219 __isl_give isl_printer *isl_printer_print_double(
1220 __isl_take isl_printer *p, double d);
1222 #include <isl/set.h>
1223 __isl_give isl_printer *isl_printer_print_basic_set(
1224 __isl_take isl_printer *printer,
1225 __isl_keep isl_basic_set *bset);
1226 __isl_give isl_printer *isl_printer_print_set(
1227 __isl_take isl_printer *printer,
1228 __isl_keep isl_set *set);
1230 #include <isl/map.h>
1231 __isl_give isl_printer *isl_printer_print_basic_map(
1232 __isl_take isl_printer *printer,
1233 __isl_keep isl_basic_map *bmap);
1234 __isl_give isl_printer *isl_printer_print_map(
1235 __isl_take isl_printer *printer,
1236 __isl_keep isl_map *map);
1238 #include <isl/union_set.h>
1239 __isl_give isl_printer *isl_printer_print_union_set(
1240 __isl_take isl_printer *p,
1241 __isl_keep isl_union_set *uset);
1243 #include <isl/union_map.h>
1244 __isl_give isl_printer *isl_printer_print_union_map(
1245 __isl_take isl_printer *p,
1246 __isl_keep isl_union_map *umap);
1248 When called on a file printer, the following function flushes
1249 the file. When called on a string printer, the buffer is cleared.
1251 __isl_give isl_printer *isl_printer_flush(
1252 __isl_take isl_printer *p);
1254 =head2 Creating New Sets and Relations
1256 C<isl> has functions for creating some standard sets and relations.
1260 =item * Empty sets and relations
1262 __isl_give isl_basic_set *isl_basic_set_empty(
1263 __isl_take isl_space *space);
1264 __isl_give isl_basic_map *isl_basic_map_empty(
1265 __isl_take isl_space *space);
1266 __isl_give isl_set *isl_set_empty(
1267 __isl_take isl_space *space);
1268 __isl_give isl_map *isl_map_empty(
1269 __isl_take isl_space *space);
1270 __isl_give isl_union_set *isl_union_set_empty(
1271 __isl_take isl_space *space);
1272 __isl_give isl_union_map *isl_union_map_empty(
1273 __isl_take isl_space *space);
1275 For C<isl_union_set>s and C<isl_union_map>s, the space
1276 is only used to specify the parameters.
1278 =item * Universe sets and relations
1280 __isl_give isl_basic_set *isl_basic_set_universe(
1281 __isl_take isl_space *space);
1282 __isl_give isl_basic_map *isl_basic_map_universe(
1283 __isl_take isl_space *space);
1284 __isl_give isl_set *isl_set_universe(
1285 __isl_take isl_space *space);
1286 __isl_give isl_map *isl_map_universe(
1287 __isl_take isl_space *space);
1288 __isl_give isl_union_set *isl_union_set_universe(
1289 __isl_take isl_union_set *uset);
1290 __isl_give isl_union_map *isl_union_map_universe(
1291 __isl_take isl_union_map *umap);
1293 The sets and relations constructed by the functions above
1294 contain all integer values, while those constructed by the
1295 functions below only contain non-negative values.
1297 __isl_give isl_basic_set *isl_basic_set_nat_universe(
1298 __isl_take isl_space *space);
1299 __isl_give isl_basic_map *isl_basic_map_nat_universe(
1300 __isl_take isl_space *space);
1301 __isl_give isl_set *isl_set_nat_universe(
1302 __isl_take isl_space *space);
1303 __isl_give isl_map *isl_map_nat_universe(
1304 __isl_take isl_space *space);
1306 =item * Identity relations
1308 __isl_give isl_basic_map *isl_basic_map_identity(
1309 __isl_take isl_space *space);
1310 __isl_give isl_map *isl_map_identity(
1311 __isl_take isl_space *space);
1313 The number of input and output dimensions in C<space> needs
1316 =item * Lexicographic order
1318 __isl_give isl_map *isl_map_lex_lt(
1319 __isl_take isl_space *set_space);
1320 __isl_give isl_map *isl_map_lex_le(
1321 __isl_take isl_space *set_space);
1322 __isl_give isl_map *isl_map_lex_gt(
1323 __isl_take isl_space *set_space);
1324 __isl_give isl_map *isl_map_lex_ge(
1325 __isl_take isl_space *set_space);
1326 __isl_give isl_map *isl_map_lex_lt_first(
1327 __isl_take isl_space *space, unsigned n);
1328 __isl_give isl_map *isl_map_lex_le_first(
1329 __isl_take isl_space *space, unsigned n);
1330 __isl_give isl_map *isl_map_lex_gt_first(
1331 __isl_take isl_space *space, unsigned n);
1332 __isl_give isl_map *isl_map_lex_ge_first(
1333 __isl_take isl_space *space, unsigned n);
1335 The first four functions take a space for a B<set>
1336 and return relations that express that the elements in the domain
1337 are lexicographically less
1338 (C<isl_map_lex_lt>), less or equal (C<isl_map_lex_le>),
1339 greater (C<isl_map_lex_gt>) or greater or equal (C<isl_map_lex_ge>)
1340 than the elements in the range.
1341 The last four functions take a space for a map
1342 and return relations that express that the first C<n> dimensions
1343 in the domain are lexicographically less
1344 (C<isl_map_lex_lt_first>), less or equal (C<isl_map_lex_le_first>),
1345 greater (C<isl_map_lex_gt_first>) or greater or equal (C<isl_map_lex_ge_first>)
1346 than the first C<n> dimensions in the range.
1350 A basic set or relation can be converted to a set or relation
1351 using the following functions.
1353 __isl_give isl_set *isl_set_from_basic_set(
1354 __isl_take isl_basic_set *bset);
1355 __isl_give isl_map *isl_map_from_basic_map(
1356 __isl_take isl_basic_map *bmap);
1358 Sets and relations can be converted to union sets and relations
1359 using the following functions.
1361 __isl_give isl_union_set *isl_union_set_from_basic_set(
1362 __isl_take isl_basic_set *bset);
1363 __isl_give isl_union_map *isl_union_map_from_basic_map(
1364 __isl_take isl_basic_map *bmap);
1365 __isl_give isl_union_set *isl_union_set_from_set(
1366 __isl_take isl_set *set);
1367 __isl_give isl_union_map *isl_union_map_from_map(
1368 __isl_take isl_map *map);
1370 The inverse conversions below can only be used if the input
1371 union set or relation is known to contain elements in exactly one
1374 __isl_give isl_set *isl_set_from_union_set(
1375 __isl_take isl_union_set *uset);
1376 __isl_give isl_map *isl_map_from_union_map(
1377 __isl_take isl_union_map *umap);
1379 A zero-dimensional (basic) set can be constructed on a given parameter domain
1380 using the following function.
1382 __isl_give isl_basic_set *isl_basic_set_from_params(
1383 __isl_take isl_basic_set *bset);
1384 __isl_give isl_set *isl_set_from_params(
1385 __isl_take isl_set *set);
1387 Sets and relations can be copied and freed again using the following
1390 __isl_give isl_basic_set *isl_basic_set_copy(
1391 __isl_keep isl_basic_set *bset);
1392 __isl_give isl_set *isl_set_copy(__isl_keep isl_set *set);
1393 __isl_give isl_union_set *isl_union_set_copy(
1394 __isl_keep isl_union_set *uset);
1395 __isl_give isl_basic_map *isl_basic_map_copy(
1396 __isl_keep isl_basic_map *bmap);
1397 __isl_give isl_map *isl_map_copy(__isl_keep isl_map *map);
1398 __isl_give isl_union_map *isl_union_map_copy(
1399 __isl_keep isl_union_map *umap);
1400 void *isl_basic_set_free(__isl_take isl_basic_set *bset);
1401 void *isl_set_free(__isl_take isl_set *set);
1402 void *isl_union_set_free(__isl_take isl_union_set *uset);
1403 void *isl_basic_map_free(__isl_take isl_basic_map *bmap);
1404 void *isl_map_free(__isl_take isl_map *map);
1405 void *isl_union_map_free(__isl_take isl_union_map *umap);
1407 Other sets and relations can be constructed by starting
1408 from a universe set or relation, adding equality and/or
1409 inequality constraints and then projecting out the
1410 existentially quantified variables, if any.
1411 Constraints can be constructed, manipulated and
1412 added to (or removed from) (basic) sets and relations
1413 using the following functions.
1415 #include <isl/constraint.h>
1416 __isl_give isl_constraint *isl_equality_alloc(
1417 __isl_take isl_local_space *ls);
1418 __isl_give isl_constraint *isl_inequality_alloc(
1419 __isl_take isl_local_space *ls);
1420 __isl_give isl_constraint *isl_constraint_set_constant_si(
1421 __isl_take isl_constraint *constraint, int v);
1422 __isl_give isl_constraint *isl_constraint_set_constant_val(
1423 __isl_take isl_constraint *constraint,
1424 __isl_take isl_val *v);
1425 __isl_give isl_constraint *isl_constraint_set_coefficient_si(
1426 __isl_take isl_constraint *constraint,
1427 enum isl_dim_type type, int pos, int v);
1428 __isl_give isl_constraint *
1429 isl_constraint_set_coefficient_val(
1430 __isl_take isl_constraint *constraint,
1431 enum isl_dim_type type, int pos, isl_val *v);
1432 __isl_give isl_basic_map *isl_basic_map_add_constraint(
1433 __isl_take isl_basic_map *bmap,
1434 __isl_take isl_constraint *constraint);
1435 __isl_give isl_basic_set *isl_basic_set_add_constraint(
1436 __isl_take isl_basic_set *bset,
1437 __isl_take isl_constraint *constraint);
1438 __isl_give isl_map *isl_map_add_constraint(
1439 __isl_take isl_map *map,
1440 __isl_take isl_constraint *constraint);
1441 __isl_give isl_set *isl_set_add_constraint(
1442 __isl_take isl_set *set,
1443 __isl_take isl_constraint *constraint);
1444 __isl_give isl_basic_set *isl_basic_set_drop_constraint(
1445 __isl_take isl_basic_set *bset,
1446 __isl_take isl_constraint *constraint);
1448 For example, to create a set containing the even integers
1449 between 10 and 42, you would use the following code.
1452 isl_local_space *ls;
1454 isl_basic_set *bset;
1456 space = isl_space_set_alloc(ctx, 0, 2);
1457 bset = isl_basic_set_universe(isl_space_copy(space));
1458 ls = isl_local_space_from_space(space);
1460 c = isl_equality_alloc(isl_local_space_copy(ls));
1461 c = isl_constraint_set_coefficient_si(c, isl_dim_set, 0, -1);
1462 c = isl_constraint_set_coefficient_si(c, isl_dim_set, 1, 2);
1463 bset = isl_basic_set_add_constraint(bset, c);
1465 c = isl_inequality_alloc(isl_local_space_copy(ls));
1466 c = isl_constraint_set_constant_si(c, -10);
1467 c = isl_constraint_set_coefficient_si(c, isl_dim_set, 0, 1);
1468 bset = isl_basic_set_add_constraint(bset, c);
1470 c = isl_inequality_alloc(ls);
1471 c = isl_constraint_set_constant_si(c, 42);
1472 c = isl_constraint_set_coefficient_si(c, isl_dim_set, 0, -1);
1473 bset = isl_basic_set_add_constraint(bset, c);
1475 bset = isl_basic_set_project_out(bset, isl_dim_set, 1, 1);
1479 isl_basic_set *bset;
1480 bset = isl_basic_set_read_from_str(ctx,
1481 "{[i] : exists (a : i = 2a and i >= 10 and i <= 42)}");
1483 A basic set or relation can also be constructed from two matrices
1484 describing the equalities and the inequalities.
1486 __isl_give isl_basic_set *isl_basic_set_from_constraint_matrices(
1487 __isl_take isl_space *space,
1488 __isl_take isl_mat *eq, __isl_take isl_mat *ineq,
1489 enum isl_dim_type c1,
1490 enum isl_dim_type c2, enum isl_dim_type c3,
1491 enum isl_dim_type c4);
1492 __isl_give isl_basic_map *isl_basic_map_from_constraint_matrices(
1493 __isl_take isl_space *space,
1494 __isl_take isl_mat *eq, __isl_take isl_mat *ineq,
1495 enum isl_dim_type c1,
1496 enum isl_dim_type c2, enum isl_dim_type c3,
1497 enum isl_dim_type c4, enum isl_dim_type c5);
1499 The C<isl_dim_type> arguments indicate the order in which
1500 different kinds of variables appear in the input matrices
1501 and should be a permutation of C<isl_dim_cst>, C<isl_dim_param>,
1502 C<isl_dim_set> and C<isl_dim_div> for sets and
1503 of C<isl_dim_cst>, C<isl_dim_param>,
1504 C<isl_dim_in>, C<isl_dim_out> and C<isl_dim_div> for relations.
1506 A (basic or union) set or relation can also be constructed from a
1507 (union) (piecewise) (multiple) affine expression
1508 or a list of affine expressions
1509 (See L<"Piecewise Quasi Affine Expressions"> and
1510 L<"Piecewise Multiple Quasi Affine Expressions">).
1512 __isl_give isl_basic_map *isl_basic_map_from_aff(
1513 __isl_take isl_aff *aff);
1514 __isl_give isl_map *isl_map_from_aff(
1515 __isl_take isl_aff *aff);
1516 __isl_give isl_set *isl_set_from_pw_aff(
1517 __isl_take isl_pw_aff *pwaff);
1518 __isl_give isl_map *isl_map_from_pw_aff(
1519 __isl_take isl_pw_aff *pwaff);
1520 __isl_give isl_basic_map *isl_basic_map_from_aff_list(
1521 __isl_take isl_space *domain_space,
1522 __isl_take isl_aff_list *list);
1523 __isl_give isl_basic_map *isl_basic_map_from_multi_aff(
1524 __isl_take isl_multi_aff *maff)
1525 __isl_give isl_map *isl_map_from_multi_aff(
1526 __isl_take isl_multi_aff *maff)
1527 __isl_give isl_set *isl_set_from_pw_multi_aff(
1528 __isl_take isl_pw_multi_aff *pma);
1529 __isl_give isl_map *isl_map_from_pw_multi_aff(
1530 __isl_take isl_pw_multi_aff *pma);
1531 __isl_give isl_set *isl_set_from_multi_pw_aff(
1532 __isl_take isl_multi_pw_aff *mpa);
1533 __isl_give isl_map *isl_map_from_multi_pw_aff(
1534 __isl_take isl_multi_pw_aff *mpa);
1535 __isl_give isl_union_map *
1536 isl_union_map_from_union_pw_multi_aff(
1537 __isl_take isl_union_pw_multi_aff *upma);
1539 The C<domain_dim> argument describes the domain of the resulting
1540 basic relation. It is required because the C<list> may consist
1541 of zero affine expressions.
1543 =head2 Inspecting Sets and Relations
1545 Usually, the user should not have to care about the actual constraints
1546 of the sets and maps, but should instead apply the abstract operations
1547 explained in the following sections.
1548 Occasionally, however, it may be required to inspect the individual
1549 coefficients of the constraints. This section explains how to do so.
1550 In these cases, it may also be useful to have C<isl> compute
1551 an explicit representation of the existentially quantified variables.
1553 __isl_give isl_set *isl_set_compute_divs(
1554 __isl_take isl_set *set);
1555 __isl_give isl_map *isl_map_compute_divs(
1556 __isl_take isl_map *map);
1557 __isl_give isl_union_set *isl_union_set_compute_divs(
1558 __isl_take isl_union_set *uset);
1559 __isl_give isl_union_map *isl_union_map_compute_divs(
1560 __isl_take isl_union_map *umap);
1562 This explicit representation defines the existentially quantified
1563 variables as integer divisions of the other variables, possibly
1564 including earlier existentially quantified variables.
1565 An explicitly represented existentially quantified variable therefore
1566 has a unique value when the values of the other variables are known.
1567 If, furthermore, the same existentials, i.e., existentials
1568 with the same explicit representations, should appear in the
1569 same order in each of the disjuncts of a set or map, then the user should call
1570 either of the following functions.
1572 __isl_give isl_set *isl_set_align_divs(
1573 __isl_take isl_set *set);
1574 __isl_give isl_map *isl_map_align_divs(
1575 __isl_take isl_map *map);
1577 Alternatively, the existentially quantified variables can be removed
1578 using the following functions, which compute an overapproximation.
1580 __isl_give isl_basic_set *isl_basic_set_remove_divs(
1581 __isl_take isl_basic_set *bset);
1582 __isl_give isl_basic_map *isl_basic_map_remove_divs(
1583 __isl_take isl_basic_map *bmap);
1584 __isl_give isl_set *isl_set_remove_divs(
1585 __isl_take isl_set *set);
1586 __isl_give isl_map *isl_map_remove_divs(
1587 __isl_take isl_map *map);
1589 It is also possible to only remove those divs that are defined
1590 in terms of a given range of dimensions or only those for which
1591 no explicit representation is known.
1593 __isl_give isl_basic_set *
1594 isl_basic_set_remove_divs_involving_dims(
1595 __isl_take isl_basic_set *bset,
1596 enum isl_dim_type type,
1597 unsigned first, unsigned n);
1598 __isl_give isl_basic_map *
1599 isl_basic_map_remove_divs_involving_dims(
1600 __isl_take isl_basic_map *bmap,
1601 enum isl_dim_type type,
1602 unsigned first, unsigned n);
1603 __isl_give isl_set *isl_set_remove_divs_involving_dims(
1604 __isl_take isl_set *set, enum isl_dim_type type,
1605 unsigned first, unsigned n);
1606 __isl_give isl_map *isl_map_remove_divs_involving_dims(
1607 __isl_take isl_map *map, enum isl_dim_type type,
1608 unsigned first, unsigned n);
1610 __isl_give isl_basic_set *
1611 isl_basic_set_remove_unknown_divs(
1612 __isl_take isl_basic_set *bset);
1613 __isl_give isl_set *isl_set_remove_unknown_divs(
1614 __isl_take isl_set *set);
1615 __isl_give isl_map *isl_map_remove_unknown_divs(
1616 __isl_take isl_map *map);
1618 To iterate over all the sets or maps in a union set or map, use
1620 int isl_union_set_foreach_set(__isl_keep isl_union_set *uset,
1621 int (*fn)(__isl_take isl_set *set, void *user),
1623 int isl_union_map_foreach_map(__isl_keep isl_union_map *umap,
1624 int (*fn)(__isl_take isl_map *map, void *user),
1627 The number of sets or maps in a union set or map can be obtained
1630 int isl_union_set_n_set(__isl_keep isl_union_set *uset);
1631 int isl_union_map_n_map(__isl_keep isl_union_map *umap);
1633 To extract the set or map in a given space from a union, use
1635 __isl_give isl_set *isl_union_set_extract_set(
1636 __isl_keep isl_union_set *uset,
1637 __isl_take isl_space *space);
1638 __isl_give isl_map *isl_union_map_extract_map(
1639 __isl_keep isl_union_map *umap,
1640 __isl_take isl_space *space);
1642 To iterate over all the basic sets or maps in a set or map, use
1644 int isl_set_foreach_basic_set(__isl_keep isl_set *set,
1645 int (*fn)(__isl_take isl_basic_set *bset, void *user),
1647 int isl_map_foreach_basic_map(__isl_keep isl_map *map,
1648 int (*fn)(__isl_take isl_basic_map *bmap, void *user),
1651 The callback function C<fn> should return 0 if successful and
1652 -1 if an error occurs. In the latter case, or if any other error
1653 occurs, the above functions will return -1.
1655 It should be noted that C<isl> does not guarantee that
1656 the basic sets or maps passed to C<fn> are disjoint.
1657 If this is required, then the user should call one of
1658 the following functions first.
1660 __isl_give isl_set *isl_set_make_disjoint(
1661 __isl_take isl_set *set);
1662 __isl_give isl_map *isl_map_make_disjoint(
1663 __isl_take isl_map *map);
1665 The number of basic sets in a set can be obtained
1668 int isl_set_n_basic_set(__isl_keep isl_set *set);
1670 To iterate over the constraints of a basic set or map, use
1672 #include <isl/constraint.h>
1674 int isl_basic_set_n_constraint(
1675 __isl_keep isl_basic_set *bset);
1676 int isl_basic_set_foreach_constraint(
1677 __isl_keep isl_basic_set *bset,
1678 int (*fn)(__isl_take isl_constraint *c, void *user),
1680 int isl_basic_map_foreach_constraint(
1681 __isl_keep isl_basic_map *bmap,
1682 int (*fn)(__isl_take isl_constraint *c, void *user),
1684 void *isl_constraint_free(__isl_take isl_constraint *c);
1686 Again, the callback function C<fn> should return 0 if successful and
1687 -1 if an error occurs. In the latter case, or if any other error
1688 occurs, the above functions will return -1.
1689 The constraint C<c> represents either an equality or an inequality.
1690 Use the following function to find out whether a constraint
1691 represents an equality. If not, it represents an inequality.
1693 int isl_constraint_is_equality(
1694 __isl_keep isl_constraint *constraint);
1696 The coefficients of the constraints can be inspected using
1697 the following functions.
1699 int isl_constraint_is_lower_bound(
1700 __isl_keep isl_constraint *constraint,
1701 enum isl_dim_type type, unsigned pos);
1702 int isl_constraint_is_upper_bound(
1703 __isl_keep isl_constraint *constraint,
1704 enum isl_dim_type type, unsigned pos);
1705 __isl_give isl_val *isl_constraint_get_constant_val(
1706 __isl_keep isl_constraint *constraint);
1707 __isl_give isl_val *isl_constraint_get_coefficient_val(
1708 __isl_keep isl_constraint *constraint,
1709 enum isl_dim_type type, int pos);
1710 int isl_constraint_involves_dims(
1711 __isl_keep isl_constraint *constraint,
1712 enum isl_dim_type type, unsigned first, unsigned n);
1714 The explicit representations of the existentially quantified
1715 variables can be inspected using the following function.
1716 Note that the user is only allowed to use this function
1717 if the inspected set or map is the result of a call
1718 to C<isl_set_compute_divs> or C<isl_map_compute_divs>.
1719 The existentially quantified variable is equal to the floor
1720 of the returned affine expression. The affine expression
1721 itself can be inspected using the functions in
1722 L<"Piecewise Quasi Affine Expressions">.
1724 __isl_give isl_aff *isl_constraint_get_div(
1725 __isl_keep isl_constraint *constraint, int pos);
1727 To obtain the constraints of a basic set or map in matrix
1728 form, use the following functions.
1730 __isl_give isl_mat *isl_basic_set_equalities_matrix(
1731 __isl_keep isl_basic_set *bset,
1732 enum isl_dim_type c1, enum isl_dim_type c2,
1733 enum isl_dim_type c3, enum isl_dim_type c4);
1734 __isl_give isl_mat *isl_basic_set_inequalities_matrix(
1735 __isl_keep isl_basic_set *bset,
1736 enum isl_dim_type c1, enum isl_dim_type c2,
1737 enum isl_dim_type c3, enum isl_dim_type c4);
1738 __isl_give isl_mat *isl_basic_map_equalities_matrix(
1739 __isl_keep isl_basic_map *bmap,
1740 enum isl_dim_type c1,
1741 enum isl_dim_type c2, enum isl_dim_type c3,
1742 enum isl_dim_type c4, enum isl_dim_type c5);
1743 __isl_give isl_mat *isl_basic_map_inequalities_matrix(
1744 __isl_keep isl_basic_map *bmap,
1745 enum isl_dim_type c1,
1746 enum isl_dim_type c2, enum isl_dim_type c3,
1747 enum isl_dim_type c4, enum isl_dim_type c5);
1749 The C<isl_dim_type> arguments dictate the order in which
1750 different kinds of variables appear in the resulting matrix
1751 and should be a permutation of C<isl_dim_cst>, C<isl_dim_param>,
1752 C<isl_dim_in>, C<isl_dim_out> and C<isl_dim_div>.
1754 The number of parameters, input, output or set dimensions can
1755 be obtained using the following functions.
1757 unsigned isl_basic_set_dim(__isl_keep isl_basic_set *bset,
1758 enum isl_dim_type type);
1759 unsigned isl_basic_map_dim(__isl_keep isl_basic_map *bmap,
1760 enum isl_dim_type type);
1761 unsigned isl_set_dim(__isl_keep isl_set *set,
1762 enum isl_dim_type type);
1763 unsigned isl_map_dim(__isl_keep isl_map *map,
1764 enum isl_dim_type type);
1766 To check whether the description of a set or relation depends
1767 on one or more given dimensions, it is not necessary to iterate over all
1768 constraints. Instead the following functions can be used.
1770 int isl_basic_set_involves_dims(
1771 __isl_keep isl_basic_set *bset,
1772 enum isl_dim_type type, unsigned first, unsigned n);
1773 int isl_set_involves_dims(__isl_keep isl_set *set,
1774 enum isl_dim_type type, unsigned first, unsigned n);
1775 int isl_basic_map_involves_dims(
1776 __isl_keep isl_basic_map *bmap,
1777 enum isl_dim_type type, unsigned first, unsigned n);
1778 int isl_map_involves_dims(__isl_keep isl_map *map,
1779 enum isl_dim_type type, unsigned first, unsigned n);
1781 Similarly, the following functions can be used to check whether
1782 a given dimension is involved in any lower or upper bound.
1784 int isl_set_dim_has_any_lower_bound(__isl_keep isl_set *set,
1785 enum isl_dim_type type, unsigned pos);
1786 int isl_set_dim_has_any_upper_bound(__isl_keep isl_set *set,
1787 enum isl_dim_type type, unsigned pos);
1789 Note that these functions return true even if there is a bound on
1790 the dimension on only some of the basic sets of C<set>.
1791 To check if they have a bound for all of the basic sets in C<set>,
1792 use the following functions instead.
1794 int isl_set_dim_has_lower_bound(__isl_keep isl_set *set,
1795 enum isl_dim_type type, unsigned pos);
1796 int isl_set_dim_has_upper_bound(__isl_keep isl_set *set,
1797 enum isl_dim_type type, unsigned pos);
1799 The identifiers or names of the domain and range spaces of a set
1800 or relation can be read off or set using the following functions.
1802 __isl_give isl_set *isl_set_set_tuple_id(
1803 __isl_take isl_set *set, __isl_take isl_id *id);
1804 __isl_give isl_set *isl_set_reset_tuple_id(
1805 __isl_take isl_set *set);
1806 int isl_set_has_tuple_id(__isl_keep isl_set *set);
1807 __isl_give isl_id *isl_set_get_tuple_id(
1808 __isl_keep isl_set *set);
1809 __isl_give isl_map *isl_map_set_tuple_id(
1810 __isl_take isl_map *map, enum isl_dim_type type,
1811 __isl_take isl_id *id);
1812 __isl_give isl_map *isl_map_reset_tuple_id(
1813 __isl_take isl_map *map, enum isl_dim_type type);
1814 int isl_map_has_tuple_id(__isl_keep isl_map *map,
1815 enum isl_dim_type type);
1816 __isl_give isl_id *isl_map_get_tuple_id(
1817 __isl_keep isl_map *map, enum isl_dim_type type);
1819 const char *isl_basic_set_get_tuple_name(
1820 __isl_keep isl_basic_set *bset);
1821 __isl_give isl_basic_set *isl_basic_set_set_tuple_name(
1822 __isl_take isl_basic_set *set, const char *s);
1823 int isl_set_has_tuple_name(__isl_keep isl_set *set);
1824 const char *isl_set_get_tuple_name(
1825 __isl_keep isl_set *set);
1826 const char *isl_basic_map_get_tuple_name(
1827 __isl_keep isl_basic_map *bmap,
1828 enum isl_dim_type type);
1829 __isl_give isl_basic_map *isl_basic_map_set_tuple_name(
1830 __isl_take isl_basic_map *bmap,
1831 enum isl_dim_type type, const char *s);
1832 int isl_map_has_tuple_name(__isl_keep isl_map *map,
1833 enum isl_dim_type type);
1834 const char *isl_map_get_tuple_name(
1835 __isl_keep isl_map *map,
1836 enum isl_dim_type type);
1838 As with C<isl_space_get_tuple_name>, the value returned points to
1839 an internal data structure.
1840 The identifiers, positions or names of individual dimensions can be
1841 read off using the following functions.
1843 __isl_give isl_id *isl_basic_set_get_dim_id(
1844 __isl_keep isl_basic_set *bset,
1845 enum isl_dim_type type, unsigned pos);
1846 __isl_give isl_set *isl_set_set_dim_id(
1847 __isl_take isl_set *set, enum isl_dim_type type,
1848 unsigned pos, __isl_take isl_id *id);
1849 int isl_set_has_dim_id(__isl_keep isl_set *set,
1850 enum isl_dim_type type, unsigned pos);
1851 __isl_give isl_id *isl_set_get_dim_id(
1852 __isl_keep isl_set *set, enum isl_dim_type type,
1854 int isl_basic_map_has_dim_id(
1855 __isl_keep isl_basic_map *bmap,
1856 enum isl_dim_type type, unsigned pos);
1857 __isl_give isl_map *isl_map_set_dim_id(
1858 __isl_take isl_map *map, enum isl_dim_type type,
1859 unsigned pos, __isl_take isl_id *id);
1860 int isl_map_has_dim_id(__isl_keep isl_map *map,
1861 enum isl_dim_type type, unsigned pos);
1862 __isl_give isl_id *isl_map_get_dim_id(
1863 __isl_keep isl_map *map, enum isl_dim_type type,
1866 int isl_set_find_dim_by_id(__isl_keep isl_set *set,
1867 enum isl_dim_type type, __isl_keep isl_id *id);
1868 int isl_map_find_dim_by_id(__isl_keep isl_map *map,
1869 enum isl_dim_type type, __isl_keep isl_id *id);
1870 int isl_set_find_dim_by_name(__isl_keep isl_set *set,
1871 enum isl_dim_type type, const char *name);
1872 int isl_map_find_dim_by_name(__isl_keep isl_map *map,
1873 enum isl_dim_type type, const char *name);
1875 const char *isl_constraint_get_dim_name(
1876 __isl_keep isl_constraint *constraint,
1877 enum isl_dim_type type, unsigned pos);
1878 const char *isl_basic_set_get_dim_name(
1879 __isl_keep isl_basic_set *bset,
1880 enum isl_dim_type type, unsigned pos);
1881 int isl_set_has_dim_name(__isl_keep isl_set *set,
1882 enum isl_dim_type type, unsigned pos);
1883 const char *isl_set_get_dim_name(
1884 __isl_keep isl_set *set,
1885 enum isl_dim_type type, unsigned pos);
1886 const char *isl_basic_map_get_dim_name(
1887 __isl_keep isl_basic_map *bmap,
1888 enum isl_dim_type type, unsigned pos);
1889 int isl_map_has_dim_name(__isl_keep isl_map *map,
1890 enum isl_dim_type type, unsigned pos);
1891 const char *isl_map_get_dim_name(
1892 __isl_keep isl_map *map,
1893 enum isl_dim_type type, unsigned pos);
1895 These functions are mostly useful to obtain the identifiers, positions
1896 or names of the parameters. Identifiers of individual dimensions are
1897 essentially only useful for printing. They are ignored by all other
1898 operations and may not be preserved across those operations.
1900 The user pointers on all parameters and tuples can be reset
1901 using the following functions.
1903 __isl_give isl_set *isl_set_reset_user(
1904 __isl_take isl_set *set);
1905 __isl_give isl_map *isl_map_reset_user(
1906 __isl_take isl_map *map);
1910 =head3 Unary Properties
1916 The following functions test whether the given set or relation
1917 contains any integer points. The ``plain'' variants do not perform
1918 any computations, but simply check if the given set or relation
1919 is already known to be empty.
1921 int isl_basic_set_plain_is_empty(__isl_keep isl_basic_set *bset);
1922 int isl_basic_set_is_empty(__isl_keep isl_basic_set *bset);
1923 int isl_set_plain_is_empty(__isl_keep isl_set *set);
1924 int isl_set_is_empty(__isl_keep isl_set *set);
1925 int isl_union_set_is_empty(__isl_keep isl_union_set *uset);
1926 int isl_basic_map_plain_is_empty(__isl_keep isl_basic_map *bmap);
1927 int isl_basic_map_is_empty(__isl_keep isl_basic_map *bmap);
1928 int isl_map_plain_is_empty(__isl_keep isl_map *map);
1929 int isl_map_is_empty(__isl_keep isl_map *map);
1930 int isl_union_map_is_empty(__isl_keep isl_union_map *umap);
1932 =item * Universality
1934 int isl_basic_set_is_universe(__isl_keep isl_basic_set *bset);
1935 int isl_basic_map_is_universe(__isl_keep isl_basic_map *bmap);
1936 int isl_set_plain_is_universe(__isl_keep isl_set *set);
1938 =item * Single-valuedness
1940 int isl_basic_map_is_single_valued(
1941 __isl_keep isl_basic_map *bmap);
1942 int isl_map_plain_is_single_valued(
1943 __isl_keep isl_map *map);
1944 int isl_map_is_single_valued(__isl_keep isl_map *map);
1945 int isl_union_map_is_single_valued(__isl_keep isl_union_map *umap);
1949 int isl_map_plain_is_injective(__isl_keep isl_map *map);
1950 int isl_map_is_injective(__isl_keep isl_map *map);
1951 int isl_union_map_plain_is_injective(
1952 __isl_keep isl_union_map *umap);
1953 int isl_union_map_is_injective(
1954 __isl_keep isl_union_map *umap);
1958 int isl_map_is_bijective(__isl_keep isl_map *map);
1959 int isl_union_map_is_bijective(__isl_keep isl_union_map *umap);
1963 __isl_give isl_val *
1964 isl_basic_map_plain_get_val_if_fixed(
1965 __isl_keep isl_basic_map *bmap,
1966 enum isl_dim_type type, unsigned pos);
1967 __isl_give isl_val *isl_set_plain_get_val_if_fixed(
1968 __isl_keep isl_set *set,
1969 enum isl_dim_type type, unsigned pos);
1970 __isl_give isl_val *isl_map_plain_get_val_if_fixed(
1971 __isl_keep isl_map *map,
1972 enum isl_dim_type type, unsigned pos);
1974 If the set or relation obviously lies on a hyperplane where the given dimension
1975 has a fixed value, then return that value.
1976 Otherwise return NaN.
1980 int isl_set_dim_residue_class_val(
1981 __isl_keep isl_set *set,
1982 int pos, __isl_give isl_val **modulo,
1983 __isl_give isl_val **residue);
1985 Check if the values of the given set dimension are equal to a fixed
1986 value modulo some integer value. If so, assign the modulo to C<*modulo>
1987 and the fixed value to C<*residue>. If the given dimension attains only
1988 a single value, then assign C<0> to C<*modulo> and the fixed value to
1990 If the dimension does not attain only a single value and if no modulo
1991 can be found then assign C<1> to C<*modulo> and C<1> to C<*residue>.
1995 To check whether a set is a parameter domain, use this function:
1997 int isl_set_is_params(__isl_keep isl_set *set);
1998 int isl_union_set_is_params(
1999 __isl_keep isl_union_set *uset);
2003 The following functions check whether the domain of the given
2004 (basic) set is a wrapped relation.
2006 int isl_basic_set_is_wrapping(
2007 __isl_keep isl_basic_set *bset);
2008 int isl_set_is_wrapping(__isl_keep isl_set *set);
2010 =item * Internal Product
2012 int isl_basic_map_can_zip(
2013 __isl_keep isl_basic_map *bmap);
2014 int isl_map_can_zip(__isl_keep isl_map *map);
2016 Check whether the product of domain and range of the given relation
2018 i.e., whether both domain and range are nested relations.
2022 int isl_basic_map_can_curry(
2023 __isl_keep isl_basic_map *bmap);
2024 int isl_map_can_curry(__isl_keep isl_map *map);
2026 Check whether the domain of the (basic) relation is a wrapped relation.
2028 int isl_basic_map_can_uncurry(
2029 __isl_keep isl_basic_map *bmap);
2030 int isl_map_can_uncurry(__isl_keep isl_map *map);
2032 Check whether the range of the (basic) relation is a wrapped relation.
2036 =head3 Binary Properties
2042 int isl_basic_set_plain_is_equal(
2043 __isl_keep isl_basic_set *bset1,
2044 __isl_keep isl_basic_set *bset2);
2045 int isl_set_plain_is_equal(__isl_keep isl_set *set1,
2046 __isl_keep isl_set *set2);
2047 int isl_set_is_equal(__isl_keep isl_set *set1,
2048 __isl_keep isl_set *set2);
2049 int isl_union_set_is_equal(
2050 __isl_keep isl_union_set *uset1,
2051 __isl_keep isl_union_set *uset2);
2052 int isl_basic_map_is_equal(
2053 __isl_keep isl_basic_map *bmap1,
2054 __isl_keep isl_basic_map *bmap2);
2055 int isl_map_is_equal(__isl_keep isl_map *map1,
2056 __isl_keep isl_map *map2);
2057 int isl_map_plain_is_equal(__isl_keep isl_map *map1,
2058 __isl_keep isl_map *map2);
2059 int isl_union_map_is_equal(
2060 __isl_keep isl_union_map *umap1,
2061 __isl_keep isl_union_map *umap2);
2063 =item * Disjointness
2065 int isl_basic_set_is_disjoint(
2066 __isl_keep isl_basic_set *bset1,
2067 __isl_keep isl_basic_set *bset2);
2068 int isl_set_plain_is_disjoint(__isl_keep isl_set *set1,
2069 __isl_keep isl_set *set2);
2070 int isl_set_is_disjoint(__isl_keep isl_set *set1,
2071 __isl_keep isl_set *set2);
2072 int isl_basic_map_is_disjoint(
2073 __isl_keep isl_basic_map *bmap1,
2074 __isl_keep isl_basic_map *bmap2);
2075 int isl_map_is_disjoint(__isl_keep isl_map *map1,
2076 __isl_keep isl_map *map2);
2080 int isl_basic_set_is_subset(
2081 __isl_keep isl_basic_set *bset1,
2082 __isl_keep isl_basic_set *bset2);
2083 int isl_set_is_subset(__isl_keep isl_set *set1,
2084 __isl_keep isl_set *set2);
2085 int isl_set_is_strict_subset(
2086 __isl_keep isl_set *set1,
2087 __isl_keep isl_set *set2);
2088 int isl_union_set_is_subset(
2089 __isl_keep isl_union_set *uset1,
2090 __isl_keep isl_union_set *uset2);
2091 int isl_union_set_is_strict_subset(
2092 __isl_keep isl_union_set *uset1,
2093 __isl_keep isl_union_set *uset2);
2094 int isl_basic_map_is_subset(
2095 __isl_keep isl_basic_map *bmap1,
2096 __isl_keep isl_basic_map *bmap2);
2097 int isl_basic_map_is_strict_subset(
2098 __isl_keep isl_basic_map *bmap1,
2099 __isl_keep isl_basic_map *bmap2);
2100 int isl_map_is_subset(
2101 __isl_keep isl_map *map1,
2102 __isl_keep isl_map *map2);
2103 int isl_map_is_strict_subset(
2104 __isl_keep isl_map *map1,
2105 __isl_keep isl_map *map2);
2106 int isl_union_map_is_subset(
2107 __isl_keep isl_union_map *umap1,
2108 __isl_keep isl_union_map *umap2);
2109 int isl_union_map_is_strict_subset(
2110 __isl_keep isl_union_map *umap1,
2111 __isl_keep isl_union_map *umap2);
2113 Check whether the first argument is a (strict) subset of the
2118 int isl_set_plain_cmp(__isl_keep isl_set *set1,
2119 __isl_keep isl_set *set2);
2121 This function is useful for sorting C<isl_set>s.
2122 The order depends on the internal representation of the inputs.
2123 The order is fixed over different calls to the function (assuming
2124 the internal representation of the inputs has not changed), but may
2125 change over different versions of C<isl>.
2129 =head2 Unary Operations
2135 __isl_give isl_set *isl_set_complement(
2136 __isl_take isl_set *set);
2137 __isl_give isl_map *isl_map_complement(
2138 __isl_take isl_map *map);
2142 __isl_give isl_basic_map *isl_basic_map_reverse(
2143 __isl_take isl_basic_map *bmap);
2144 __isl_give isl_map *isl_map_reverse(
2145 __isl_take isl_map *map);
2146 __isl_give isl_union_map *isl_union_map_reverse(
2147 __isl_take isl_union_map *umap);
2151 __isl_give isl_basic_set *isl_basic_set_project_out(
2152 __isl_take isl_basic_set *bset,
2153 enum isl_dim_type type, unsigned first, unsigned n);
2154 __isl_give isl_basic_map *isl_basic_map_project_out(
2155 __isl_take isl_basic_map *bmap,
2156 enum isl_dim_type type, unsigned first, unsigned n);
2157 __isl_give isl_set *isl_set_project_out(__isl_take isl_set *set,
2158 enum isl_dim_type type, unsigned first, unsigned n);
2159 __isl_give isl_map *isl_map_project_out(__isl_take isl_map *map,
2160 enum isl_dim_type type, unsigned first, unsigned n);
2161 __isl_give isl_basic_set *isl_basic_set_params(
2162 __isl_take isl_basic_set *bset);
2163 __isl_give isl_basic_set *isl_basic_map_domain(
2164 __isl_take isl_basic_map *bmap);
2165 __isl_give isl_basic_set *isl_basic_map_range(
2166 __isl_take isl_basic_map *bmap);
2167 __isl_give isl_set *isl_set_params(__isl_take isl_set *set);
2168 __isl_give isl_set *isl_map_params(__isl_take isl_map *map);
2169 __isl_give isl_set *isl_map_domain(
2170 __isl_take isl_map *bmap);
2171 __isl_give isl_set *isl_map_range(
2172 __isl_take isl_map *map);
2173 __isl_give isl_set *isl_union_set_params(
2174 __isl_take isl_union_set *uset);
2175 __isl_give isl_set *isl_union_map_params(
2176 __isl_take isl_union_map *umap);
2177 __isl_give isl_union_set *isl_union_map_domain(
2178 __isl_take isl_union_map *umap);
2179 __isl_give isl_union_set *isl_union_map_range(
2180 __isl_take isl_union_map *umap);
2182 __isl_give isl_basic_map *isl_basic_map_domain_map(
2183 __isl_take isl_basic_map *bmap);
2184 __isl_give isl_basic_map *isl_basic_map_range_map(
2185 __isl_take isl_basic_map *bmap);
2186 __isl_give isl_map *isl_map_domain_map(__isl_take isl_map *map);
2187 __isl_give isl_map *isl_map_range_map(__isl_take isl_map *map);
2188 __isl_give isl_union_map *isl_union_map_domain_map(
2189 __isl_take isl_union_map *umap);
2190 __isl_give isl_union_map *isl_union_map_range_map(
2191 __isl_take isl_union_map *umap);
2193 The functions above construct a (basic, regular or union) relation
2194 that maps (a wrapped version of) the input relation to its domain or range.
2198 __isl_give isl_basic_set *isl_basic_set_eliminate(
2199 __isl_take isl_basic_set *bset,
2200 enum isl_dim_type type,
2201 unsigned first, unsigned n);
2202 __isl_give isl_set *isl_set_eliminate(
2203 __isl_take isl_set *set, enum isl_dim_type type,
2204 unsigned first, unsigned n);
2205 __isl_give isl_basic_map *isl_basic_map_eliminate(
2206 __isl_take isl_basic_map *bmap,
2207 enum isl_dim_type type,
2208 unsigned first, unsigned n);
2209 __isl_give isl_map *isl_map_eliminate(
2210 __isl_take isl_map *map, enum isl_dim_type type,
2211 unsigned first, unsigned n);
2213 Eliminate the coefficients for the given dimensions from the constraints,
2214 without removing the dimensions.
2218 __isl_give isl_basic_set *isl_basic_set_fix_si(
2219 __isl_take isl_basic_set *bset,
2220 enum isl_dim_type type, unsigned pos, int value);
2221 __isl_give isl_basic_set *isl_basic_set_fix_val(
2222 __isl_take isl_basic_set *bset,
2223 enum isl_dim_type type, unsigned pos,
2224 __isl_take isl_val *v);
2225 __isl_give isl_set *isl_set_fix_si(__isl_take isl_set *set,
2226 enum isl_dim_type type, unsigned pos, int value);
2227 __isl_give isl_set *isl_set_fix_val(
2228 __isl_take isl_set *set,
2229 enum isl_dim_type type, unsigned pos,
2230 __isl_take isl_val *v);
2231 __isl_give isl_basic_map *isl_basic_map_fix_si(
2232 __isl_take isl_basic_map *bmap,
2233 enum isl_dim_type type, unsigned pos, int value);
2234 __isl_give isl_basic_map *isl_basic_map_fix_val(
2235 __isl_take isl_basic_map *bmap,
2236 enum isl_dim_type type, unsigned pos,
2237 __isl_take isl_val *v);
2238 __isl_give isl_map *isl_map_fix_si(__isl_take isl_map *map,
2239 enum isl_dim_type type, unsigned pos, int value);
2240 __isl_give isl_map *isl_map_fix_val(
2241 __isl_take isl_map *map,
2242 enum isl_dim_type type, unsigned pos,
2243 __isl_take isl_val *v);
2245 Intersect the set or relation with the hyperplane where the given
2246 dimension has the fixed given value.
2248 __isl_give isl_basic_map *isl_basic_map_lower_bound_si(
2249 __isl_take isl_basic_map *bmap,
2250 enum isl_dim_type type, unsigned pos, int value);
2251 __isl_give isl_basic_map *isl_basic_map_upper_bound_si(
2252 __isl_take isl_basic_map *bmap,
2253 enum isl_dim_type type, unsigned pos, int value);
2254 __isl_give isl_set *isl_set_lower_bound_si(
2255 __isl_take isl_set *set,
2256 enum isl_dim_type type, unsigned pos, int value);
2257 __isl_give isl_set *isl_set_lower_bound_val(
2258 __isl_take isl_set *set,
2259 enum isl_dim_type type, unsigned pos,
2260 __isl_take isl_val *value);
2261 __isl_give isl_map *isl_map_lower_bound_si(
2262 __isl_take isl_map *map,
2263 enum isl_dim_type type, unsigned pos, int value);
2264 __isl_give isl_set *isl_set_upper_bound_si(
2265 __isl_take isl_set *set,
2266 enum isl_dim_type type, unsigned pos, int value);
2267 __isl_give isl_set *isl_set_upper_bound_val(
2268 __isl_take isl_set *set,
2269 enum isl_dim_type type, unsigned pos,
2270 __isl_take isl_val *value);
2271 __isl_give isl_map *isl_map_upper_bound_si(
2272 __isl_take isl_map *map,
2273 enum isl_dim_type type, unsigned pos, int value);
2275 Intersect the set or relation with the half-space where the given
2276 dimension has a value bounded by the fixed given integer value.
2278 __isl_give isl_set *isl_set_equate(__isl_take isl_set *set,
2279 enum isl_dim_type type1, int pos1,
2280 enum isl_dim_type type2, int pos2);
2281 __isl_give isl_basic_map *isl_basic_map_equate(
2282 __isl_take isl_basic_map *bmap,
2283 enum isl_dim_type type1, int pos1,
2284 enum isl_dim_type type2, int pos2);
2285 __isl_give isl_map *isl_map_equate(__isl_take isl_map *map,
2286 enum isl_dim_type type1, int pos1,
2287 enum isl_dim_type type2, int pos2);
2289 Intersect the set or relation with the hyperplane where the given
2290 dimensions are equal to each other.
2292 __isl_give isl_map *isl_map_oppose(__isl_take isl_map *map,
2293 enum isl_dim_type type1, int pos1,
2294 enum isl_dim_type type2, int pos2);
2296 Intersect the relation with the hyperplane where the given
2297 dimensions have opposite values.
2299 __isl_give isl_basic_map *isl_basic_map_order_ge(
2300 __isl_take isl_basic_map *bmap,
2301 enum isl_dim_type type1, int pos1,
2302 enum isl_dim_type type2, int pos2);
2303 __isl_give isl_map *isl_map_order_lt(__isl_take isl_map *map,
2304 enum isl_dim_type type1, int pos1,
2305 enum isl_dim_type type2, int pos2);
2306 __isl_give isl_basic_map *isl_basic_map_order_gt(
2307 __isl_take isl_basic_map *bmap,
2308 enum isl_dim_type type1, int pos1,
2309 enum isl_dim_type type2, int pos2);
2310 __isl_give isl_map *isl_map_order_gt(__isl_take isl_map *map,
2311 enum isl_dim_type type1, int pos1,
2312 enum isl_dim_type type2, int pos2);
2314 Intersect the relation with the half-space where the given
2315 dimensions satisfy the given ordering.
2319 __isl_give isl_map *isl_set_identity(
2320 __isl_take isl_set *set);
2321 __isl_give isl_union_map *isl_union_set_identity(
2322 __isl_take isl_union_set *uset);
2324 Construct an identity relation on the given (union) set.
2328 __isl_give isl_basic_set *isl_basic_map_deltas(
2329 __isl_take isl_basic_map *bmap);
2330 __isl_give isl_set *isl_map_deltas(__isl_take isl_map *map);
2331 __isl_give isl_union_set *isl_union_map_deltas(
2332 __isl_take isl_union_map *umap);
2334 These functions return a (basic) set containing the differences
2335 between image elements and corresponding domain elements in the input.
2337 __isl_give isl_basic_map *isl_basic_map_deltas_map(
2338 __isl_take isl_basic_map *bmap);
2339 __isl_give isl_map *isl_map_deltas_map(
2340 __isl_take isl_map *map);
2341 __isl_give isl_union_map *isl_union_map_deltas_map(
2342 __isl_take isl_union_map *umap);
2344 The functions above construct a (basic, regular or union) relation
2345 that maps (a wrapped version of) the input relation to its delta set.
2349 Simplify the representation of a set or relation by trying
2350 to combine pairs of basic sets or relations into a single
2351 basic set or relation.
2353 __isl_give isl_set *isl_set_coalesce(__isl_take isl_set *set);
2354 __isl_give isl_map *isl_map_coalesce(__isl_take isl_map *map);
2355 __isl_give isl_union_set *isl_union_set_coalesce(
2356 __isl_take isl_union_set *uset);
2357 __isl_give isl_union_map *isl_union_map_coalesce(
2358 __isl_take isl_union_map *umap);
2360 One of the methods for combining pairs of basic sets or relations
2361 can result in coefficients that are much larger than those that appear
2362 in the constraints of the input. By default, the coefficients are
2363 not allowed to grow larger, but this can be changed by unsetting
2364 the following option.
2366 int isl_options_set_coalesce_bounded_wrapping(
2367 isl_ctx *ctx, int val);
2368 int isl_options_get_coalesce_bounded_wrapping(
2371 =item * Detecting equalities
2373 __isl_give isl_basic_set *isl_basic_set_detect_equalities(
2374 __isl_take isl_basic_set *bset);
2375 __isl_give isl_basic_map *isl_basic_map_detect_equalities(
2376 __isl_take isl_basic_map *bmap);
2377 __isl_give isl_set *isl_set_detect_equalities(
2378 __isl_take isl_set *set);
2379 __isl_give isl_map *isl_map_detect_equalities(
2380 __isl_take isl_map *map);
2381 __isl_give isl_union_set *isl_union_set_detect_equalities(
2382 __isl_take isl_union_set *uset);
2383 __isl_give isl_union_map *isl_union_map_detect_equalities(
2384 __isl_take isl_union_map *umap);
2386 Simplify the representation of a set or relation by detecting implicit
2389 =item * Removing redundant constraints
2391 __isl_give isl_basic_set *isl_basic_set_remove_redundancies(
2392 __isl_take isl_basic_set *bset);
2393 __isl_give isl_set *isl_set_remove_redundancies(
2394 __isl_take isl_set *set);
2395 __isl_give isl_basic_map *isl_basic_map_remove_redundancies(
2396 __isl_take isl_basic_map *bmap);
2397 __isl_give isl_map *isl_map_remove_redundancies(
2398 __isl_take isl_map *map);
2402 __isl_give isl_basic_set *isl_set_convex_hull(
2403 __isl_take isl_set *set);
2404 __isl_give isl_basic_map *isl_map_convex_hull(
2405 __isl_take isl_map *map);
2407 If the input set or relation has any existentially quantified
2408 variables, then the result of these operations is currently undefined.
2412 __isl_give isl_basic_set *
2413 isl_set_unshifted_simple_hull(
2414 __isl_take isl_set *set);
2415 __isl_give isl_basic_map *
2416 isl_map_unshifted_simple_hull(
2417 __isl_take isl_map *map);
2418 __isl_give isl_basic_set *isl_set_simple_hull(
2419 __isl_take isl_set *set);
2420 __isl_give isl_basic_map *isl_map_simple_hull(
2421 __isl_take isl_map *map);
2422 __isl_give isl_union_map *isl_union_map_simple_hull(
2423 __isl_take isl_union_map *umap);
2425 These functions compute a single basic set or relation
2426 that contains the whole input set or relation.
2427 In particular, the output is described by translates
2428 of the constraints describing the basic sets or relations in the input.
2429 In case of C<isl_set_unshifted_simple_hull>, only the original
2430 constraints are used, without any translation.
2434 (See \autoref{s:simple hull}.)
2440 __isl_give isl_basic_set *isl_basic_set_affine_hull(
2441 __isl_take isl_basic_set *bset);
2442 __isl_give isl_basic_set *isl_set_affine_hull(
2443 __isl_take isl_set *set);
2444 __isl_give isl_union_set *isl_union_set_affine_hull(
2445 __isl_take isl_union_set *uset);
2446 __isl_give isl_basic_map *isl_basic_map_affine_hull(
2447 __isl_take isl_basic_map *bmap);
2448 __isl_give isl_basic_map *isl_map_affine_hull(
2449 __isl_take isl_map *map);
2450 __isl_give isl_union_map *isl_union_map_affine_hull(
2451 __isl_take isl_union_map *umap);
2453 In case of union sets and relations, the affine hull is computed
2456 =item * Polyhedral hull
2458 __isl_give isl_basic_set *isl_set_polyhedral_hull(
2459 __isl_take isl_set *set);
2460 __isl_give isl_basic_map *isl_map_polyhedral_hull(
2461 __isl_take isl_map *map);
2462 __isl_give isl_union_set *isl_union_set_polyhedral_hull(
2463 __isl_take isl_union_set *uset);
2464 __isl_give isl_union_map *isl_union_map_polyhedral_hull(
2465 __isl_take isl_union_map *umap);
2467 These functions compute a single basic set or relation
2468 not involving any existentially quantified variables
2469 that contains the whole input set or relation.
2470 In case of union sets and relations, the polyhedral hull is computed
2473 =item * Other approximations
2475 __isl_give isl_basic_set *
2476 isl_basic_set_drop_constraints_involving_dims(
2477 __isl_take isl_basic_set *bset,
2478 enum isl_dim_type type,
2479 unsigned first, unsigned n);
2480 __isl_give isl_basic_map *
2481 isl_basic_map_drop_constraints_involving_dims(
2482 __isl_take isl_basic_map *bmap,
2483 enum isl_dim_type type,
2484 unsigned first, unsigned n);
2485 __isl_give isl_basic_set *
2486 isl_basic_set_drop_constraints_not_involving_dims(
2487 __isl_take isl_basic_set *bset,
2488 enum isl_dim_type type,
2489 unsigned first, unsigned n);
2490 __isl_give isl_set *
2491 isl_set_drop_constraints_involving_dims(
2492 __isl_take isl_set *set,
2493 enum isl_dim_type type,
2494 unsigned first, unsigned n);
2495 __isl_give isl_map *
2496 isl_map_drop_constraints_involving_dims(
2497 __isl_take isl_map *map,
2498 enum isl_dim_type type,
2499 unsigned first, unsigned n);
2501 These functions drop any constraints (not) involving the specified dimensions.
2502 Note that the result depends on the representation of the input.
2506 __isl_give isl_basic_set *isl_basic_set_sample(
2507 __isl_take isl_basic_set *bset);
2508 __isl_give isl_basic_set *isl_set_sample(
2509 __isl_take isl_set *set);
2510 __isl_give isl_basic_map *isl_basic_map_sample(
2511 __isl_take isl_basic_map *bmap);
2512 __isl_give isl_basic_map *isl_map_sample(
2513 __isl_take isl_map *map);
2515 If the input (basic) set or relation is non-empty, then return
2516 a singleton subset of the input. Otherwise, return an empty set.
2518 =item * Optimization
2520 #include <isl/ilp.h>
2521 __isl_give isl_val *isl_basic_set_max_val(
2522 __isl_keep isl_basic_set *bset,
2523 __isl_keep isl_aff *obj);
2524 __isl_give isl_val *isl_set_min_val(
2525 __isl_keep isl_set *set,
2526 __isl_keep isl_aff *obj);
2527 __isl_give isl_val *isl_set_max_val(
2528 __isl_keep isl_set *set,
2529 __isl_keep isl_aff *obj);
2531 Compute the minimum or maximum of the integer affine expression C<obj>
2532 over the points in C<set>, returning the result in C<opt>.
2533 The result is C<NULL> in case of an error, the optimal value in case
2534 there is one, negative infinity or infinity if the problem is unbounded and
2535 NaN if the problem is empty.
2537 =item * Parametric optimization
2539 __isl_give isl_pw_aff *isl_set_dim_min(
2540 __isl_take isl_set *set, int pos);
2541 __isl_give isl_pw_aff *isl_set_dim_max(
2542 __isl_take isl_set *set, int pos);
2543 __isl_give isl_pw_aff *isl_map_dim_max(
2544 __isl_take isl_map *map, int pos);
2546 Compute the minimum or maximum of the given set or output dimension
2547 as a function of the parameters (and input dimensions), but independently
2548 of the other set or output dimensions.
2549 For lexicographic optimization, see L<"Lexicographic Optimization">.
2553 The following functions compute either the set of (rational) coefficient
2554 values of valid constraints for the given set or the set of (rational)
2555 values satisfying the constraints with coefficients from the given set.
2556 Internally, these two sets of functions perform essentially the
2557 same operations, except that the set of coefficients is assumed to
2558 be a cone, while the set of values may be any polyhedron.
2559 The current implementation is based on the Farkas lemma and
2560 Fourier-Motzkin elimination, but this may change or be made optional
2561 in future. In particular, future implementations may use different
2562 dualization algorithms or skip the elimination step.
2564 __isl_give isl_basic_set *isl_basic_set_coefficients(
2565 __isl_take isl_basic_set *bset);
2566 __isl_give isl_basic_set *isl_set_coefficients(
2567 __isl_take isl_set *set);
2568 __isl_give isl_union_set *isl_union_set_coefficients(
2569 __isl_take isl_union_set *bset);
2570 __isl_give isl_basic_set *isl_basic_set_solutions(
2571 __isl_take isl_basic_set *bset);
2572 __isl_give isl_basic_set *isl_set_solutions(
2573 __isl_take isl_set *set);
2574 __isl_give isl_union_set *isl_union_set_solutions(
2575 __isl_take isl_union_set *bset);
2579 __isl_give isl_map *isl_map_fixed_power_val(
2580 __isl_take isl_map *map,
2581 __isl_take isl_val *exp);
2582 __isl_give isl_union_map *
2583 isl_union_map_fixed_power_val(
2584 __isl_take isl_union_map *umap,
2585 __isl_take isl_val *exp);
2587 Compute the given power of C<map>, where C<exp> is assumed to be non-zero.
2588 If the exponent C<exp> is negative, then the -C<exp> th power of the inverse
2589 of C<map> is computed.
2591 __isl_give isl_map *isl_map_power(__isl_take isl_map *map,
2593 __isl_give isl_union_map *isl_union_map_power(
2594 __isl_take isl_union_map *umap, int *exact);
2596 Compute a parametric representation for all positive powers I<k> of C<map>.
2597 The result maps I<k> to a nested relation corresponding to the
2598 I<k>th power of C<map>.
2599 The result may be an overapproximation. If the result is known to be exact,
2600 then C<*exact> is set to C<1>.
2602 =item * Transitive closure
2604 __isl_give isl_map *isl_map_transitive_closure(
2605 __isl_take isl_map *map, int *exact);
2606 __isl_give isl_union_map *isl_union_map_transitive_closure(
2607 __isl_take isl_union_map *umap, int *exact);
2609 Compute the transitive closure of C<map>.
2610 The result may be an overapproximation. If the result is known to be exact,
2611 then C<*exact> is set to C<1>.
2613 =item * Reaching path lengths
2615 __isl_give isl_map *isl_map_reaching_path_lengths(
2616 __isl_take isl_map *map, int *exact);
2618 Compute a relation that maps each element in the range of C<map>
2619 to the lengths of all paths composed of edges in C<map> that
2620 end up in the given element.
2621 The result may be an overapproximation. If the result is known to be exact,
2622 then C<*exact> is set to C<1>.
2623 To compute the I<maximal> path length, the resulting relation
2624 should be postprocessed by C<isl_map_lexmax>.
2625 In particular, if the input relation is a dependence relation
2626 (mapping sources to sinks), then the maximal path length corresponds
2627 to the free schedule.
2628 Note, however, that C<isl_map_lexmax> expects the maximum to be
2629 finite, so if the path lengths are unbounded (possibly due to
2630 the overapproximation), then you will get an error message.
2634 __isl_give isl_basic_set *isl_basic_map_wrap(
2635 __isl_take isl_basic_map *bmap);
2636 __isl_give isl_set *isl_map_wrap(
2637 __isl_take isl_map *map);
2638 __isl_give isl_union_set *isl_union_map_wrap(
2639 __isl_take isl_union_map *umap);
2640 __isl_give isl_basic_map *isl_basic_set_unwrap(
2641 __isl_take isl_basic_set *bset);
2642 __isl_give isl_map *isl_set_unwrap(
2643 __isl_take isl_set *set);
2644 __isl_give isl_union_map *isl_union_set_unwrap(
2645 __isl_take isl_union_set *uset);
2649 Remove any internal structure of domain (and range) of the given
2650 set or relation. If there is any such internal structure in the input,
2651 then the name of the space is also removed.
2653 __isl_give isl_basic_set *isl_basic_set_flatten(
2654 __isl_take isl_basic_set *bset);
2655 __isl_give isl_set *isl_set_flatten(
2656 __isl_take isl_set *set);
2657 __isl_give isl_basic_map *isl_basic_map_flatten_domain(
2658 __isl_take isl_basic_map *bmap);
2659 __isl_give isl_basic_map *isl_basic_map_flatten_range(
2660 __isl_take isl_basic_map *bmap);
2661 __isl_give isl_map *isl_map_flatten_range(
2662 __isl_take isl_map *map);
2663 __isl_give isl_map *isl_map_flatten_domain(
2664 __isl_take isl_map *map);
2665 __isl_give isl_basic_map *isl_basic_map_flatten(
2666 __isl_take isl_basic_map *bmap);
2667 __isl_give isl_map *isl_map_flatten(
2668 __isl_take isl_map *map);
2670 __isl_give isl_map *isl_set_flatten_map(
2671 __isl_take isl_set *set);
2673 The function above constructs a relation
2674 that maps the input set to a flattened version of the set.
2678 Lift the input set to a space with extra dimensions corresponding
2679 to the existentially quantified variables in the input.
2680 In particular, the result lives in a wrapped map where the domain
2681 is the original space and the range corresponds to the original
2682 existentially quantified variables.
2684 __isl_give isl_basic_set *isl_basic_set_lift(
2685 __isl_take isl_basic_set *bset);
2686 __isl_give isl_set *isl_set_lift(
2687 __isl_take isl_set *set);
2688 __isl_give isl_union_set *isl_union_set_lift(
2689 __isl_take isl_union_set *uset);
2691 Given a local space that contains the existentially quantified
2692 variables of a set, a basic relation that, when applied to
2693 a basic set, has essentially the same effect as C<isl_basic_set_lift>,
2694 can be constructed using the following function.
2696 #include <isl/local_space.h>
2697 __isl_give isl_basic_map *isl_local_space_lifting(
2698 __isl_take isl_local_space *ls);
2700 =item * Internal Product
2702 __isl_give isl_basic_map *isl_basic_map_zip(
2703 __isl_take isl_basic_map *bmap);
2704 __isl_give isl_map *isl_map_zip(
2705 __isl_take isl_map *map);
2706 __isl_give isl_union_map *isl_union_map_zip(
2707 __isl_take isl_union_map *umap);
2709 Given a relation with nested relations for domain and range,
2710 interchange the range of the domain with the domain of the range.
2714 __isl_give isl_basic_map *isl_basic_map_curry(
2715 __isl_take isl_basic_map *bmap);
2716 __isl_give isl_basic_map *isl_basic_map_uncurry(
2717 __isl_take isl_basic_map *bmap);
2718 __isl_give isl_map *isl_map_curry(
2719 __isl_take isl_map *map);
2720 __isl_give isl_map *isl_map_uncurry(
2721 __isl_take isl_map *map);
2722 __isl_give isl_union_map *isl_union_map_curry(
2723 __isl_take isl_union_map *umap);
2724 __isl_give isl_union_map *isl_union_map_uncurry(
2725 __isl_take isl_union_map *umap);
2727 Given a relation with a nested relation for domain,
2728 the C<curry> functions
2729 move the range of the nested relation out of the domain
2730 and use it as the domain of a nested relation in the range,
2731 with the original range as range of this nested relation.
2732 The C<uncurry> functions perform the inverse operation.
2734 =item * Aligning parameters
2736 __isl_give isl_basic_set *isl_basic_set_align_params(
2737 __isl_take isl_basic_set *bset,
2738 __isl_take isl_space *model);
2739 __isl_give isl_set *isl_set_align_params(
2740 __isl_take isl_set *set,
2741 __isl_take isl_space *model);
2742 __isl_give isl_basic_map *isl_basic_map_align_params(
2743 __isl_take isl_basic_map *bmap,
2744 __isl_take isl_space *model);
2745 __isl_give isl_map *isl_map_align_params(
2746 __isl_take isl_map *map,
2747 __isl_take isl_space *model);
2749 Change the order of the parameters of the given set or relation
2750 such that the first parameters match those of C<model>.
2751 This may involve the introduction of extra parameters.
2752 All parameters need to be named.
2754 =item * Dimension manipulation
2756 __isl_give isl_basic_set *isl_basic_set_add_dims(
2757 __isl_take isl_basic_set *bset,
2758 enum isl_dim_type type, unsigned n);
2759 __isl_give isl_set *isl_set_add_dims(
2760 __isl_take isl_set *set,
2761 enum isl_dim_type type, unsigned n);
2762 __isl_give isl_map *isl_map_add_dims(
2763 __isl_take isl_map *map,
2764 enum isl_dim_type type, unsigned n);
2765 __isl_give isl_basic_set *isl_basic_set_insert_dims(
2766 __isl_take isl_basic_set *bset,
2767 enum isl_dim_type type, unsigned pos,
2769 __isl_give isl_basic_map *isl_basic_map_insert_dims(
2770 __isl_take isl_basic_map *bmap,
2771 enum isl_dim_type type, unsigned pos,
2773 __isl_give isl_set *isl_set_insert_dims(
2774 __isl_take isl_set *set,
2775 enum isl_dim_type type, unsigned pos, unsigned n);
2776 __isl_give isl_map *isl_map_insert_dims(
2777 __isl_take isl_map *map,
2778 enum isl_dim_type type, unsigned pos, unsigned n);
2779 __isl_give isl_basic_set *isl_basic_set_move_dims(
2780 __isl_take isl_basic_set *bset,
2781 enum isl_dim_type dst_type, unsigned dst_pos,
2782 enum isl_dim_type src_type, unsigned src_pos,
2784 __isl_give isl_basic_map *isl_basic_map_move_dims(
2785 __isl_take isl_basic_map *bmap,
2786 enum isl_dim_type dst_type, unsigned dst_pos,
2787 enum isl_dim_type src_type, unsigned src_pos,
2789 __isl_give isl_set *isl_set_move_dims(
2790 __isl_take isl_set *set,
2791 enum isl_dim_type dst_type, unsigned dst_pos,
2792 enum isl_dim_type src_type, unsigned src_pos,
2794 __isl_give isl_map *isl_map_move_dims(
2795 __isl_take isl_map *map,
2796 enum isl_dim_type dst_type, unsigned dst_pos,
2797 enum isl_dim_type src_type, unsigned src_pos,
2800 It is usually not advisable to directly change the (input or output)
2801 space of a set or a relation as this removes the name and the internal
2802 structure of the space. However, the above functions can be useful
2803 to add new parameters, assuming
2804 C<isl_set_align_params> and C<isl_map_align_params>
2809 =head2 Binary Operations
2811 The two arguments of a binary operation not only need to live
2812 in the same C<isl_ctx>, they currently also need to have
2813 the same (number of) parameters.
2815 =head3 Basic Operations
2819 =item * Intersection
2821 __isl_give isl_basic_set *isl_basic_set_intersect_params(
2822 __isl_take isl_basic_set *bset1,
2823 __isl_take isl_basic_set *bset2);
2824 __isl_give isl_basic_set *isl_basic_set_intersect(
2825 __isl_take isl_basic_set *bset1,
2826 __isl_take isl_basic_set *bset2);
2827 __isl_give isl_set *isl_set_intersect_params(
2828 __isl_take isl_set *set,
2829 __isl_take isl_set *params);
2830 __isl_give isl_set *isl_set_intersect(
2831 __isl_take isl_set *set1,
2832 __isl_take isl_set *set2);
2833 __isl_give isl_union_set *isl_union_set_intersect_params(
2834 __isl_take isl_union_set *uset,
2835 __isl_take isl_set *set);
2836 __isl_give isl_union_map *isl_union_map_intersect_params(
2837 __isl_take isl_union_map *umap,
2838 __isl_take isl_set *set);
2839 __isl_give isl_union_set *isl_union_set_intersect(
2840 __isl_take isl_union_set *uset1,
2841 __isl_take isl_union_set *uset2);
2842 __isl_give isl_basic_map *isl_basic_map_intersect_domain(
2843 __isl_take isl_basic_map *bmap,
2844 __isl_take isl_basic_set *bset);
2845 __isl_give isl_basic_map *isl_basic_map_intersect_range(
2846 __isl_take isl_basic_map *bmap,
2847 __isl_take isl_basic_set *bset);
2848 __isl_give isl_basic_map *isl_basic_map_intersect(
2849 __isl_take isl_basic_map *bmap1,
2850 __isl_take isl_basic_map *bmap2);
2851 __isl_give isl_map *isl_map_intersect_params(
2852 __isl_take isl_map *map,
2853 __isl_take isl_set *params);
2854 __isl_give isl_map *isl_map_intersect_domain(
2855 __isl_take isl_map *map,
2856 __isl_take isl_set *set);
2857 __isl_give isl_map *isl_map_intersect_range(
2858 __isl_take isl_map *map,
2859 __isl_take isl_set *set);
2860 __isl_give isl_map *isl_map_intersect(
2861 __isl_take isl_map *map1,
2862 __isl_take isl_map *map2);
2863 __isl_give isl_union_map *isl_union_map_intersect_domain(
2864 __isl_take isl_union_map *umap,
2865 __isl_take isl_union_set *uset);
2866 __isl_give isl_union_map *isl_union_map_intersect_range(
2867 __isl_take isl_union_map *umap,
2868 __isl_take isl_union_set *uset);
2869 __isl_give isl_union_map *isl_union_map_intersect(
2870 __isl_take isl_union_map *umap1,
2871 __isl_take isl_union_map *umap2);
2873 The second argument to the C<_params> functions needs to be
2874 a parametric (basic) set. For the other functions, a parametric set
2875 for either argument is only allowed if the other argument is
2876 a parametric set as well.
2880 __isl_give isl_set *isl_basic_set_union(
2881 __isl_take isl_basic_set *bset1,
2882 __isl_take isl_basic_set *bset2);
2883 __isl_give isl_map *isl_basic_map_union(
2884 __isl_take isl_basic_map *bmap1,
2885 __isl_take isl_basic_map *bmap2);
2886 __isl_give isl_set *isl_set_union(
2887 __isl_take isl_set *set1,
2888 __isl_take isl_set *set2);
2889 __isl_give isl_map *isl_map_union(
2890 __isl_take isl_map *map1,
2891 __isl_take isl_map *map2);
2892 __isl_give isl_union_set *isl_union_set_union(
2893 __isl_take isl_union_set *uset1,
2894 __isl_take isl_union_set *uset2);
2895 __isl_give isl_union_map *isl_union_map_union(
2896 __isl_take isl_union_map *umap1,
2897 __isl_take isl_union_map *umap2);
2899 =item * Set difference
2901 __isl_give isl_set *isl_set_subtract(
2902 __isl_take isl_set *set1,
2903 __isl_take isl_set *set2);
2904 __isl_give isl_map *isl_map_subtract(
2905 __isl_take isl_map *map1,
2906 __isl_take isl_map *map2);
2907 __isl_give isl_map *isl_map_subtract_domain(
2908 __isl_take isl_map *map,
2909 __isl_take isl_set *dom);
2910 __isl_give isl_map *isl_map_subtract_range(
2911 __isl_take isl_map *map,
2912 __isl_take isl_set *dom);
2913 __isl_give isl_union_set *isl_union_set_subtract(
2914 __isl_take isl_union_set *uset1,
2915 __isl_take isl_union_set *uset2);
2916 __isl_give isl_union_map *isl_union_map_subtract(
2917 __isl_take isl_union_map *umap1,
2918 __isl_take isl_union_map *umap2);
2919 __isl_give isl_union_map *isl_union_map_subtract_domain(
2920 __isl_take isl_union_map *umap,
2921 __isl_take isl_union_set *dom);
2922 __isl_give isl_union_map *isl_union_map_subtract_range(
2923 __isl_take isl_union_map *umap,
2924 __isl_take isl_union_set *dom);
2928 __isl_give isl_basic_set *isl_basic_set_apply(
2929 __isl_take isl_basic_set *bset,
2930 __isl_take isl_basic_map *bmap);
2931 __isl_give isl_set *isl_set_apply(
2932 __isl_take isl_set *set,
2933 __isl_take isl_map *map);
2934 __isl_give isl_union_set *isl_union_set_apply(
2935 __isl_take isl_union_set *uset,
2936 __isl_take isl_union_map *umap);
2937 __isl_give isl_basic_map *isl_basic_map_apply_domain(
2938 __isl_take isl_basic_map *bmap1,
2939 __isl_take isl_basic_map *bmap2);
2940 __isl_give isl_basic_map *isl_basic_map_apply_range(
2941 __isl_take isl_basic_map *bmap1,
2942 __isl_take isl_basic_map *bmap2);
2943 __isl_give isl_map *isl_map_apply_domain(
2944 __isl_take isl_map *map1,
2945 __isl_take isl_map *map2);
2946 __isl_give isl_union_map *isl_union_map_apply_domain(
2947 __isl_take isl_union_map *umap1,
2948 __isl_take isl_union_map *umap2);
2949 __isl_give isl_map *isl_map_apply_range(
2950 __isl_take isl_map *map1,
2951 __isl_take isl_map *map2);
2952 __isl_give isl_union_map *isl_union_map_apply_range(
2953 __isl_take isl_union_map *umap1,
2954 __isl_take isl_union_map *umap2);
2958 __isl_give isl_basic_set *
2959 isl_basic_set_preimage_multi_aff(
2960 __isl_take isl_basic_set *bset,
2961 __isl_take isl_multi_aff *ma);
2962 __isl_give isl_set *isl_set_preimage_multi_aff(
2963 __isl_take isl_set *set,
2964 __isl_take isl_multi_aff *ma);
2965 __isl_give isl_set *isl_set_preimage_pw_multi_aff(
2966 __isl_take isl_set *set,
2967 __isl_take isl_pw_multi_aff *pma);
2968 __isl_give isl_set *isl_set_preimage_multi_pw_aff(
2969 __isl_take isl_set *set,
2970 __isl_take isl_multi_pw_aff *mpa);
2971 __isl_give isl_basic_map *
2972 isl_basic_map_preimage_domain_multi_aff(
2973 __isl_take isl_basic_map *bmap,
2974 __isl_take isl_multi_aff *ma);
2975 __isl_give isl_map *isl_map_preimage_domain_multi_aff(
2976 __isl_take isl_map *map,
2977 __isl_take isl_multi_aff *ma);
2978 __isl_give isl_map *
2979 isl_map_preimage_domain_pw_multi_aff(
2980 __isl_take isl_map *map,
2981 __isl_take isl_pw_multi_aff *pma);
2982 __isl_give isl_map *
2983 isl_map_preimage_domain_multi_pw_aff(
2984 __isl_take isl_map *map,
2985 __isl_take isl_multi_pw_aff *mpa);
2986 __isl_give isl_union_map *
2987 isl_union_map_preimage_domain_multi_aff(
2988 __isl_take isl_union_map *umap,
2989 __isl_take isl_multi_aff *ma);
2990 __isl_give isl_basic_map *
2991 isl_basic_map_preimage_range_multi_aff(
2992 __isl_take isl_basic_map *bmap,
2993 __isl_take isl_multi_aff *ma);
2995 These functions compute the preimage of the given set or map domain/range under
2996 the given function. In other words, the expression is plugged
2997 into the set description or into the domain/range of the map.
2998 Objects of types C<isl_multi_aff> and C<isl_pw_multi_aff> are described in
2999 L</"Piecewise Multiple Quasi Affine Expressions">.
3001 =item * Cartesian Product
3003 __isl_give isl_set *isl_set_product(
3004 __isl_take isl_set *set1,
3005 __isl_take isl_set *set2);
3006 __isl_give isl_union_set *isl_union_set_product(
3007 __isl_take isl_union_set *uset1,
3008 __isl_take isl_union_set *uset2);
3009 __isl_give isl_basic_map *isl_basic_map_domain_product(
3010 __isl_take isl_basic_map *bmap1,
3011 __isl_take isl_basic_map *bmap2);
3012 __isl_give isl_basic_map *isl_basic_map_range_product(
3013 __isl_take isl_basic_map *bmap1,
3014 __isl_take isl_basic_map *bmap2);
3015 __isl_give isl_basic_map *isl_basic_map_product(
3016 __isl_take isl_basic_map *bmap1,
3017 __isl_take isl_basic_map *bmap2);
3018 __isl_give isl_map *isl_map_domain_product(
3019 __isl_take isl_map *map1,
3020 __isl_take isl_map *map2);
3021 __isl_give isl_map *isl_map_range_product(
3022 __isl_take isl_map *map1,
3023 __isl_take isl_map *map2);
3024 __isl_give isl_union_map *isl_union_map_domain_product(
3025 __isl_take isl_union_map *umap1,
3026 __isl_take isl_union_map *umap2);
3027 __isl_give isl_union_map *isl_union_map_range_product(
3028 __isl_take isl_union_map *umap1,
3029 __isl_take isl_union_map *umap2);
3030 __isl_give isl_map *isl_map_product(
3031 __isl_take isl_map *map1,
3032 __isl_take isl_map *map2);
3033 __isl_give isl_union_map *isl_union_map_product(
3034 __isl_take isl_union_map *umap1,
3035 __isl_take isl_union_map *umap2);
3037 The above functions compute the cross product of the given
3038 sets or relations. The domains and ranges of the results
3039 are wrapped maps between domains and ranges of the inputs.
3040 To obtain a ``flat'' product, use the following functions
3043 __isl_give isl_basic_set *isl_basic_set_flat_product(
3044 __isl_take isl_basic_set *bset1,
3045 __isl_take isl_basic_set *bset2);
3046 __isl_give isl_set *isl_set_flat_product(
3047 __isl_take isl_set *set1,
3048 __isl_take isl_set *set2);
3049 __isl_give isl_basic_map *isl_basic_map_flat_range_product(
3050 __isl_take isl_basic_map *bmap1,
3051 __isl_take isl_basic_map *bmap2);
3052 __isl_give isl_map *isl_map_flat_domain_product(
3053 __isl_take isl_map *map1,
3054 __isl_take isl_map *map2);
3055 __isl_give isl_map *isl_map_flat_range_product(
3056 __isl_take isl_map *map1,
3057 __isl_take isl_map *map2);
3058 __isl_give isl_union_map *isl_union_map_flat_range_product(
3059 __isl_take isl_union_map *umap1,
3060 __isl_take isl_union_map *umap2);
3061 __isl_give isl_basic_map *isl_basic_map_flat_product(
3062 __isl_take isl_basic_map *bmap1,
3063 __isl_take isl_basic_map *bmap2);
3064 __isl_give isl_map *isl_map_flat_product(
3065 __isl_take isl_map *map1,
3066 __isl_take isl_map *map2);
3068 =item * Simplification
3070 __isl_give isl_basic_set *isl_basic_set_gist(
3071 __isl_take isl_basic_set *bset,
3072 __isl_take isl_basic_set *context);
3073 __isl_give isl_set *isl_set_gist(__isl_take isl_set *set,
3074 __isl_take isl_set *context);
3075 __isl_give isl_set *isl_set_gist_params(
3076 __isl_take isl_set *set,
3077 __isl_take isl_set *context);
3078 __isl_give isl_union_set *isl_union_set_gist(
3079 __isl_take isl_union_set *uset,
3080 __isl_take isl_union_set *context);
3081 __isl_give isl_union_set *isl_union_set_gist_params(
3082 __isl_take isl_union_set *uset,
3083 __isl_take isl_set *set);
3084 __isl_give isl_basic_map *isl_basic_map_gist(
3085 __isl_take isl_basic_map *bmap,
3086 __isl_take isl_basic_map *context);
3087 __isl_give isl_map *isl_map_gist(__isl_take isl_map *map,
3088 __isl_take isl_map *context);
3089 __isl_give isl_map *isl_map_gist_params(
3090 __isl_take isl_map *map,
3091 __isl_take isl_set *context);
3092 __isl_give isl_map *isl_map_gist_domain(
3093 __isl_take isl_map *map,
3094 __isl_take isl_set *context);
3095 __isl_give isl_map *isl_map_gist_range(
3096 __isl_take isl_map *map,
3097 __isl_take isl_set *context);
3098 __isl_give isl_union_map *isl_union_map_gist(
3099 __isl_take isl_union_map *umap,
3100 __isl_take isl_union_map *context);
3101 __isl_give isl_union_map *isl_union_map_gist_params(
3102 __isl_take isl_union_map *umap,
3103 __isl_take isl_set *set);
3104 __isl_give isl_union_map *isl_union_map_gist_domain(
3105 __isl_take isl_union_map *umap,
3106 __isl_take isl_union_set *uset);
3107 __isl_give isl_union_map *isl_union_map_gist_range(
3108 __isl_take isl_union_map *umap,
3109 __isl_take isl_union_set *uset);
3111 The gist operation returns a set or relation that has the
3112 same intersection with the context as the input set or relation.
3113 Any implicit equality in the intersection is made explicit in the result,
3114 while all inequalities that are redundant with respect to the intersection
3116 In case of union sets and relations, the gist operation is performed
3121 =head3 Lexicographic Optimization
3123 Given a (basic) set C<set> (or C<bset>) and a zero-dimensional domain C<dom>,
3124 the following functions
3125 compute a set that contains the lexicographic minimum or maximum
3126 of the elements in C<set> (or C<bset>) for those values of the parameters
3127 that satisfy C<dom>.
3128 If C<empty> is not C<NULL>, then C<*empty> is assigned a set
3129 that contains the parameter values in C<dom> for which C<set> (or C<bset>)
3131 In other words, the union of the parameter values
3132 for which the result is non-empty and of C<*empty>
3135 __isl_give isl_set *isl_basic_set_partial_lexmin(
3136 __isl_take isl_basic_set *bset,
3137 __isl_take isl_basic_set *dom,
3138 __isl_give isl_set **empty);
3139 __isl_give isl_set *isl_basic_set_partial_lexmax(
3140 __isl_take isl_basic_set *bset,
3141 __isl_take isl_basic_set *dom,
3142 __isl_give isl_set **empty);
3143 __isl_give isl_set *isl_set_partial_lexmin(
3144 __isl_take isl_set *set, __isl_take isl_set *dom,
3145 __isl_give isl_set **empty);
3146 __isl_give isl_set *isl_set_partial_lexmax(
3147 __isl_take isl_set *set, __isl_take isl_set *dom,
3148 __isl_give isl_set **empty);
3150 Given a (basic) set C<set> (or C<bset>), the following functions simply
3151 return a set containing the lexicographic minimum or maximum
3152 of the elements in C<set> (or C<bset>).
3153 In case of union sets, the optimum is computed per space.
3155 __isl_give isl_set *isl_basic_set_lexmin(
3156 __isl_take isl_basic_set *bset);
3157 __isl_give isl_set *isl_basic_set_lexmax(
3158 __isl_take isl_basic_set *bset);
3159 __isl_give isl_set *isl_set_lexmin(
3160 __isl_take isl_set *set);
3161 __isl_give isl_set *isl_set_lexmax(
3162 __isl_take isl_set *set);
3163 __isl_give isl_union_set *isl_union_set_lexmin(
3164 __isl_take isl_union_set *uset);
3165 __isl_give isl_union_set *isl_union_set_lexmax(
3166 __isl_take isl_union_set *uset);
3168 Given a (basic) relation C<map> (or C<bmap>) and a domain C<dom>,
3169 the following functions
3170 compute a relation that maps each element of C<dom>
3171 to the single lexicographic minimum or maximum
3172 of the elements that are associated to that same
3173 element in C<map> (or C<bmap>).
3174 If C<empty> is not C<NULL>, then C<*empty> is assigned a set
3175 that contains the elements in C<dom> that do not map
3176 to any elements in C<map> (or C<bmap>).
3177 In other words, the union of the domain of the result and of C<*empty>
3180 __isl_give isl_map *isl_basic_map_partial_lexmax(
3181 __isl_take isl_basic_map *bmap,
3182 __isl_take isl_basic_set *dom,
3183 __isl_give isl_set **empty);
3184 __isl_give isl_map *isl_basic_map_partial_lexmin(
3185 __isl_take isl_basic_map *bmap,
3186 __isl_take isl_basic_set *dom,
3187 __isl_give isl_set **empty);
3188 __isl_give isl_map *isl_map_partial_lexmax(
3189 __isl_take isl_map *map, __isl_take isl_set *dom,
3190 __isl_give isl_set **empty);
3191 __isl_give isl_map *isl_map_partial_lexmin(
3192 __isl_take isl_map *map, __isl_take isl_set *dom,
3193 __isl_give isl_set **empty);
3195 Given a (basic) map C<map> (or C<bmap>), the following functions simply
3196 return a map mapping each element in the domain of
3197 C<map> (or C<bmap>) to the lexicographic minimum or maximum
3198 of all elements associated to that element.
3199 In case of union relations, the optimum is computed per space.
3201 __isl_give isl_map *isl_basic_map_lexmin(
3202 __isl_take isl_basic_map *bmap);
3203 __isl_give isl_map *isl_basic_map_lexmax(
3204 __isl_take isl_basic_map *bmap);
3205 __isl_give isl_map *isl_map_lexmin(
3206 __isl_take isl_map *map);
3207 __isl_give isl_map *isl_map_lexmax(
3208 __isl_take isl_map *map);
3209 __isl_give isl_union_map *isl_union_map_lexmin(
3210 __isl_take isl_union_map *umap);
3211 __isl_give isl_union_map *isl_union_map_lexmax(
3212 __isl_take isl_union_map *umap);
3214 The following functions return their result in the form of
3215 a piecewise multi-affine expression
3216 (See L<"Piecewise Multiple Quasi Affine Expressions">),
3217 but are otherwise equivalent to the corresponding functions
3218 returning a basic set or relation.
3220 __isl_give isl_pw_multi_aff *
3221 isl_basic_map_lexmin_pw_multi_aff(
3222 __isl_take isl_basic_map *bmap);
3223 __isl_give isl_pw_multi_aff *
3224 isl_basic_set_partial_lexmin_pw_multi_aff(
3225 __isl_take isl_basic_set *bset,
3226 __isl_take isl_basic_set *dom,
3227 __isl_give isl_set **empty);
3228 __isl_give isl_pw_multi_aff *
3229 isl_basic_set_partial_lexmax_pw_multi_aff(
3230 __isl_take isl_basic_set *bset,
3231 __isl_take isl_basic_set *dom,
3232 __isl_give isl_set **empty);
3233 __isl_give isl_pw_multi_aff *
3234 isl_basic_map_partial_lexmin_pw_multi_aff(
3235 __isl_take isl_basic_map *bmap,
3236 __isl_take isl_basic_set *dom,
3237 __isl_give isl_set **empty);
3238 __isl_give isl_pw_multi_aff *
3239 isl_basic_map_partial_lexmax_pw_multi_aff(
3240 __isl_take isl_basic_map *bmap,
3241 __isl_take isl_basic_set *dom,
3242 __isl_give isl_set **empty);
3243 __isl_give isl_pw_multi_aff *isl_set_lexmin_pw_multi_aff(
3244 __isl_take isl_set *set);
3245 __isl_give isl_pw_multi_aff *isl_set_lexmax_pw_multi_aff(
3246 __isl_take isl_set *set);
3247 __isl_give isl_pw_multi_aff *isl_map_lexmin_pw_multi_aff(
3248 __isl_take isl_map *map);
3249 __isl_give isl_pw_multi_aff *isl_map_lexmax_pw_multi_aff(
3250 __isl_take isl_map *map);
3254 Lists are defined over several element types, including
3255 C<isl_val>, C<isl_id>, C<isl_aff>, C<isl_pw_aff>, C<isl_constraint>,
3256 C<isl_basic_set>, C<isl_set>, C<isl_ast_expr> and C<isl_ast_node>.
3257 Here we take lists of C<isl_set>s as an example.
3258 Lists can be created, copied, modified and freed using the following functions.
3260 #include <isl/list.h>
3261 __isl_give isl_set_list *isl_set_list_from_set(
3262 __isl_take isl_set *el);
3263 __isl_give isl_set_list *isl_set_list_alloc(
3264 isl_ctx *ctx, int n);
3265 __isl_give isl_set_list *isl_set_list_copy(
3266 __isl_keep isl_set_list *list);
3267 __isl_give isl_set_list *isl_set_list_insert(
3268 __isl_take isl_set_list *list, unsigned pos,
3269 __isl_take isl_set *el);
3270 __isl_give isl_set_list *isl_set_list_add(
3271 __isl_take isl_set_list *list,
3272 __isl_take isl_set *el);
3273 __isl_give isl_set_list *isl_set_list_drop(
3274 __isl_take isl_set_list *list,
3275 unsigned first, unsigned n);
3276 __isl_give isl_set_list *isl_set_list_set_set(
3277 __isl_take isl_set_list *list, int index,
3278 __isl_take isl_set *set);
3279 __isl_give isl_set_list *isl_set_list_concat(
3280 __isl_take isl_set_list *list1,
3281 __isl_take isl_set_list *list2);
3282 __isl_give isl_set_list *isl_set_list_sort(
3283 __isl_take isl_set_list *list,
3284 int (*cmp)(__isl_keep isl_set *a,
3285 __isl_keep isl_set *b, void *user),
3287 void *isl_set_list_free(__isl_take isl_set_list *list);
3289 C<isl_set_list_alloc> creates an empty list with a capacity for
3290 C<n> elements. C<isl_set_list_from_set> creates a list with a single
3293 Lists can be inspected using the following functions.
3295 #include <isl/list.h>
3296 isl_ctx *isl_set_list_get_ctx(__isl_keep isl_set_list *list);
3297 int isl_set_list_n_set(__isl_keep isl_set_list *list);
3298 __isl_give isl_set *isl_set_list_get_set(
3299 __isl_keep isl_set_list *list, int index);
3300 int isl_set_list_foreach(__isl_keep isl_set_list *list,
3301 int (*fn)(__isl_take isl_set *el, void *user),
3303 int isl_set_list_foreach_scc(__isl_keep isl_set_list *list,
3304 int (*follows)(__isl_keep isl_set *a,
3305 __isl_keep isl_set *b, void *user),
3307 int (*fn)(__isl_take isl_set *el, void *user),
3310 The function C<isl_set_list_foreach_scc> calls C<fn> on each of the
3311 strongly connected components of the graph with as vertices the elements
3312 of C<list> and a directed edge from vertex C<b> to vertex C<a>
3313 iff C<follows(a, b)> returns C<1>. The callbacks C<follows> and C<fn>
3314 should return C<-1> on error.
3316 Lists can be printed using
3318 #include <isl/list.h>
3319 __isl_give isl_printer *isl_printer_print_set_list(
3320 __isl_take isl_printer *p,
3321 __isl_keep isl_set_list *list);
3323 =head2 Associative arrays
3325 Associative arrays map isl objects of a specific type to isl objects
3326 of some (other) specific type. They are defined for several pairs
3327 of types, including (C<isl_map>, C<isl_basic_set>),
3328 (C<isl_id>, C<isl_ast_expr>) and.
3329 (C<isl_id>, C<isl_pw_aff>).
3330 Here, we take associative arrays that map C<isl_id>s to C<isl_ast_expr>s
3333 Associative arrays can be created, copied and freed using
3334 the following functions.
3336 #include <isl/id_to_ast_expr.h>
3337 __isl_give id_to_ast_expr *isl_id_to_ast_expr_alloc(
3338 isl_ctx *ctx, int min_size);
3339 __isl_give id_to_ast_expr *isl_id_to_ast_expr_copy(
3340 __isl_keep id_to_ast_expr *id2expr);
3341 void *isl_id_to_ast_expr_free(
3342 __isl_take id_to_ast_expr *id2expr);
3344 The C<min_size> argument to C<isl_id_to_ast_expr_alloc> can be used
3345 to specify the expected size of the associative array.
3346 The associative array will be grown automatically as needed.
3348 Associative arrays can be inspected using the following functions.
3350 #include <isl/id_to_ast_expr.h>
3351 isl_ctx *isl_id_to_ast_expr_get_ctx(
3352 __isl_keep id_to_ast_expr *id2expr);
3353 int isl_id_to_ast_expr_has(
3354 __isl_keep id_to_ast_expr *id2expr,
3355 __isl_keep isl_id *key);
3356 __isl_give isl_ast_expr *isl_id_to_ast_expr_get(
3357 __isl_keep id_to_ast_expr *id2expr,
3358 __isl_take isl_id *key);
3359 int isl_id_to_ast_expr_foreach(
3360 __isl_keep id_to_ast_expr *id2expr,
3361 int (*fn)(__isl_take isl_id *key,
3362 __isl_take isl_ast_expr *val, void *user),
3365 They can be modified using the following function.
3367 #include <isl/id_to_ast_expr.h>
3368 __isl_give id_to_ast_expr *isl_id_to_ast_expr_set(
3369 __isl_take id_to_ast_expr *id2expr,
3370 __isl_take isl_id *key,
3371 __isl_take isl_ast_expr *val);
3373 Associative arrays can be printed using the following function.
3375 #include <isl/id_to_ast_expr.h>
3376 __isl_give isl_printer *isl_printer_print_id_to_ast_expr(
3377 __isl_take isl_printer *p,
3378 __isl_keep id_to_ast_expr *id2expr);
3380 =head2 Multiple Values
3382 An C<isl_multi_val> object represents a sequence of zero or more values,
3383 living in a set space.
3385 An C<isl_multi_val> can be constructed from an C<isl_val_list>
3386 using the following function
3388 #include <isl/val.h>
3389 __isl_give isl_multi_val *isl_multi_val_from_val_list(
3390 __isl_take isl_space *space,
3391 __isl_take isl_val_list *list);
3393 The zero multiple value (with value zero for each set dimension)
3394 can be created using the following function.
3396 #include <isl/val.h>
3397 __isl_give isl_multi_val *isl_multi_val_zero(
3398 __isl_take isl_space *space);
3400 Multiple values can be copied and freed using
3402 #include <isl/val.h>
3403 __isl_give isl_multi_val *isl_multi_val_copy(
3404 __isl_keep isl_multi_val *mv);
3405 void *isl_multi_val_free(__isl_take isl_multi_val *mv);
3407 They can be inspected using
3409 #include <isl/val.h>
3410 isl_ctx *isl_multi_val_get_ctx(
3411 __isl_keep isl_multi_val *mv);
3412 unsigned isl_multi_val_dim(__isl_keep isl_multi_val *mv,
3413 enum isl_dim_type type);
3414 __isl_give isl_val *isl_multi_val_get_val(
3415 __isl_keep isl_multi_val *mv, int pos);
3416 int isl_multi_val_find_dim_by_id(
3417 __isl_keep isl_multi_val *mv,
3418 enum isl_dim_type type, __isl_keep isl_id *id);
3419 __isl_give isl_id *isl_multi_val_get_dim_id(
3420 __isl_keep isl_multi_val *mv,
3421 enum isl_dim_type type, unsigned pos);
3422 const char *isl_multi_val_get_tuple_name(
3423 __isl_keep isl_multi_val *mv,
3424 enum isl_dim_type type);
3425 int isl_multi_val_has_tuple_id(__isl_keep isl_multi_val *mv,
3426 enum isl_dim_type type);
3427 __isl_give isl_id *isl_multi_val_get_tuple_id(
3428 __isl_keep isl_multi_val *mv,
3429 enum isl_dim_type type);
3431 They can be modified using
3433 #include <isl/val.h>
3434 __isl_give isl_multi_val *isl_multi_val_set_val(
3435 __isl_take isl_multi_val *mv, int pos,
3436 __isl_take isl_val *val);
3437 __isl_give isl_multi_val *isl_multi_val_set_dim_name(
3438 __isl_take isl_multi_val *mv,
3439 enum isl_dim_type type, unsigned pos, const char *s);
3440 __isl_give isl_multi_val *isl_multi_val_set_dim_id(
3441 __isl_take isl_multi_val *mv,
3442 enum isl_dim_type type, unsigned pos,
3443 __isl_take isl_id *id);
3444 __isl_give isl_multi_val *isl_multi_val_set_tuple_name(
3445 __isl_take isl_multi_val *mv,
3446 enum isl_dim_type type, const char *s);
3447 __isl_give isl_multi_val *isl_multi_val_set_tuple_id(
3448 __isl_take isl_multi_val *mv,
3449 enum isl_dim_type type, __isl_take isl_id *id);
3450 __isl_give isl_multi_val *isl_multi_val_reset_tuple_id(
3451 __isl_take isl_multi_val *mv,
3452 enum isl_dim_type type);
3453 __isl_give isl_multi_val *isl_multi_val_reset_user(
3454 __isl_take isl_multi_val *mv);
3456 __isl_give isl_multi_val *isl_multi_val_insert_dims(
3457 __isl_take isl_multi_val *mv,
3458 enum isl_dim_type type, unsigned first, unsigned n);
3459 __isl_give isl_multi_val *isl_multi_val_add_dims(
3460 __isl_take isl_multi_val *mv,
3461 enum isl_dim_type type, unsigned n);
3462 __isl_give isl_multi_val *isl_multi_val_drop_dims(
3463 __isl_take isl_multi_val *mv,
3464 enum isl_dim_type type, unsigned first, unsigned n);
3468 #include <isl/val.h>
3469 __isl_give isl_multi_val *isl_multi_val_align_params(
3470 __isl_take isl_multi_val *mv,
3471 __isl_take isl_space *model);
3472 __isl_give isl_multi_val *isl_multi_val_from_range(
3473 __isl_take isl_multi_val *mv);
3474 __isl_give isl_multi_val *isl_multi_val_range_splice(
3475 __isl_take isl_multi_val *mv1, unsigned pos,
3476 __isl_take isl_multi_val *mv2);
3477 __isl_give isl_multi_val *isl_multi_val_range_product(
3478 __isl_take isl_multi_val *mv1,
3479 __isl_take isl_multi_val *mv2);
3480 __isl_give isl_multi_val *isl_multi_val_flat_range_product(
3481 __isl_take isl_multi_val *mv1,
3482 __isl_take isl_multi_aff *mv2);
3483 __isl_give isl_multi_val *isl_multi_val_product(
3484 __isl_take isl_multi_val *mv1,
3485 __isl_take isl_multi_val *mv2);
3486 __isl_give isl_multi_val *isl_multi_val_add_val(
3487 __isl_take isl_multi_val *mv,
3488 __isl_take isl_val *v);
3489 __isl_give isl_multi_val *isl_multi_val_mod_val(
3490 __isl_take isl_multi_val *mv,
3491 __isl_take isl_val *v);
3492 __isl_give isl_multi_val *isl_multi_val_scale_val(
3493 __isl_take isl_multi_val *mv,
3494 __isl_take isl_val *v);
3495 __isl_give isl_multi_val *isl_multi_val_scale_multi_val(
3496 __isl_take isl_multi_val *mv1,
3497 __isl_take isl_multi_val *mv2);
3498 __isl_give isl_multi_val *
3499 isl_multi_val_scale_down_multi_val(
3500 __isl_take isl_multi_val *mv1,
3501 __isl_take isl_multi_val *mv2);
3503 A multiple value can be printed using
3505 __isl_give isl_printer *isl_printer_print_multi_val(
3506 __isl_take isl_printer *p,
3507 __isl_keep isl_multi_val *mv);
3511 Vectors can be created, copied and freed using the following functions.
3513 #include <isl/vec.h>
3514 __isl_give isl_vec *isl_vec_alloc(isl_ctx *ctx,
3516 __isl_give isl_vec *isl_vec_copy(__isl_keep isl_vec *vec);
3517 void *isl_vec_free(__isl_take isl_vec *vec);
3519 Note that the elements of a newly created vector may have arbitrary values.
3520 The elements can be changed and inspected using the following functions.
3522 isl_ctx *isl_vec_get_ctx(__isl_keep isl_vec *vec);
3523 int isl_vec_size(__isl_keep isl_vec *vec);
3524 __isl_give isl_val *isl_vec_get_element_val(
3525 __isl_keep isl_vec *vec, int pos);
3526 __isl_give isl_vec *isl_vec_set_element_si(
3527 __isl_take isl_vec *vec, int pos, int v);
3528 __isl_give isl_vec *isl_vec_set_element_val(
3529 __isl_take isl_vec *vec, int pos,
3530 __isl_take isl_val *v);
3531 __isl_give isl_vec *isl_vec_set_si(__isl_take isl_vec *vec,
3533 __isl_give isl_vec *isl_vec_set_val(
3534 __isl_take isl_vec *vec, __isl_take isl_val *v);
3535 int isl_vec_cmp_element(__isl_keep isl_vec *vec1,
3536 __isl_keep isl_vec *vec2, int pos);
3538 C<isl_vec_get_element> will return a negative value if anything went wrong.
3539 In that case, the value of C<*v> is undefined.
3541 The following function can be used to concatenate two vectors.
3543 __isl_give isl_vec *isl_vec_concat(__isl_take isl_vec *vec1,
3544 __isl_take isl_vec *vec2);
3548 Matrices can be created, copied and freed using the following functions.
3550 #include <isl/mat.h>
3551 __isl_give isl_mat *isl_mat_alloc(isl_ctx *ctx,
3552 unsigned n_row, unsigned n_col);
3553 __isl_give isl_mat *isl_mat_copy(__isl_keep isl_mat *mat);
3554 void *isl_mat_free(__isl_take isl_mat *mat);
3556 Note that the elements of a newly created matrix may have arbitrary values.
3557 The elements can be changed and inspected using the following functions.
3559 isl_ctx *isl_mat_get_ctx(__isl_keep isl_mat *mat);
3560 int isl_mat_rows(__isl_keep isl_mat *mat);
3561 int isl_mat_cols(__isl_keep isl_mat *mat);
3562 __isl_give isl_val *isl_mat_get_element_val(
3563 __isl_keep isl_mat *mat, int row, int col);
3564 __isl_give isl_mat *isl_mat_set_element_si(__isl_take isl_mat *mat,
3565 int row, int col, int v);
3566 __isl_give isl_mat *isl_mat_set_element_val(
3567 __isl_take isl_mat *mat, int row, int col,
3568 __isl_take isl_val *v);
3570 C<isl_mat_get_element> will return a negative value if anything went wrong.
3571 In that case, the value of C<*v> is undefined.
3573 The following function can be used to compute the (right) inverse
3574 of a matrix, i.e., a matrix such that the product of the original
3575 and the inverse (in that order) is a multiple of the identity matrix.
3576 The input matrix is assumed to be of full row-rank.
3578 __isl_give isl_mat *isl_mat_right_inverse(__isl_take isl_mat *mat);
3580 The following function can be used to compute the (right) kernel
3581 (or null space) of a matrix, i.e., a matrix such that the product of
3582 the original and the kernel (in that order) is the zero matrix.
3584 __isl_give isl_mat *isl_mat_right_kernel(__isl_take isl_mat *mat);
3586 =head2 Piecewise Quasi Affine Expressions
3588 The zero quasi affine expression or the quasi affine expression
3589 that is equal to a given value or
3590 a specified dimension on a given domain can be created using
3592 __isl_give isl_aff *isl_aff_zero_on_domain(
3593 __isl_take isl_local_space *ls);
3594 __isl_give isl_pw_aff *isl_pw_aff_zero_on_domain(
3595 __isl_take isl_local_space *ls);
3596 __isl_give isl_aff *isl_aff_val_on_domain(
3597 __isl_take isl_local_space *ls,
3598 __isl_take isl_val *val);
3599 __isl_give isl_aff *isl_aff_var_on_domain(
3600 __isl_take isl_local_space *ls,
3601 enum isl_dim_type type, unsigned pos);
3602 __isl_give isl_pw_aff *isl_pw_aff_var_on_domain(
3603 __isl_take isl_local_space *ls,
3604 enum isl_dim_type type, unsigned pos);
3606 Note that the space in which the resulting objects live is a map space
3607 with the given space as domain and a one-dimensional range.
3609 An empty piecewise quasi affine expression (one with no cells)
3610 or a piecewise quasi affine expression with a single cell can
3611 be created using the following functions.
3613 #include <isl/aff.h>
3614 __isl_give isl_pw_aff *isl_pw_aff_empty(
3615 __isl_take isl_space *space);
3616 __isl_give isl_pw_aff *isl_pw_aff_alloc(
3617 __isl_take isl_set *set, __isl_take isl_aff *aff);
3618 __isl_give isl_pw_aff *isl_pw_aff_from_aff(
3619 __isl_take isl_aff *aff);
3621 A piecewise quasi affine expression that is equal to 1 on a set
3622 and 0 outside the set can be created using the following function.
3624 #include <isl/aff.h>
3625 __isl_give isl_pw_aff *isl_set_indicator_function(
3626 __isl_take isl_set *set);
3628 Quasi affine expressions can be copied and freed using
3630 #include <isl/aff.h>
3631 __isl_give isl_aff *isl_aff_copy(__isl_keep isl_aff *aff);
3632 void *isl_aff_free(__isl_take isl_aff *aff);
3634 __isl_give isl_pw_aff *isl_pw_aff_copy(
3635 __isl_keep isl_pw_aff *pwaff);
3636 void *isl_pw_aff_free(__isl_take isl_pw_aff *pwaff);
3638 A (rational) bound on a dimension can be extracted from an C<isl_constraint>
3639 using the following function. The constraint is required to have
3640 a non-zero coefficient for the specified dimension.
3642 #include <isl/constraint.h>
3643 __isl_give isl_aff *isl_constraint_get_bound(
3644 __isl_keep isl_constraint *constraint,
3645 enum isl_dim_type type, int pos);
3647 The entire affine expression of the constraint can also be extracted
3648 using the following function.
3650 #include <isl/constraint.h>
3651 __isl_give isl_aff *isl_constraint_get_aff(
3652 __isl_keep isl_constraint *constraint);
3654 Conversely, an equality constraint equating
3655 the affine expression to zero or an inequality constraint enforcing
3656 the affine expression to be non-negative, can be constructed using
3658 __isl_give isl_constraint *isl_equality_from_aff(
3659 __isl_take isl_aff *aff);
3660 __isl_give isl_constraint *isl_inequality_from_aff(
3661 __isl_take isl_aff *aff);
3663 The expression can be inspected using
3665 #include <isl/aff.h>
3666 isl_ctx *isl_aff_get_ctx(__isl_keep isl_aff *aff);
3667 int isl_aff_dim(__isl_keep isl_aff *aff,
3668 enum isl_dim_type type);
3669 __isl_give isl_local_space *isl_aff_get_domain_local_space(
3670 __isl_keep isl_aff *aff);
3671 __isl_give isl_local_space *isl_aff_get_local_space(
3672 __isl_keep isl_aff *aff);
3673 const char *isl_aff_get_dim_name(__isl_keep isl_aff *aff,
3674 enum isl_dim_type type, unsigned pos);
3675 const char *isl_pw_aff_get_dim_name(
3676 __isl_keep isl_pw_aff *pa,
3677 enum isl_dim_type type, unsigned pos);
3678 int isl_pw_aff_has_dim_id(__isl_keep isl_pw_aff *pa,
3679 enum isl_dim_type type, unsigned pos);
3680 __isl_give isl_id *isl_pw_aff_get_dim_id(
3681 __isl_keep isl_pw_aff *pa,
3682 enum isl_dim_type type, unsigned pos);
3683 int isl_pw_aff_has_tuple_id(__isl_keep isl_pw_aff *pa,
3684 enum isl_dim_type type);
3685 __isl_give isl_id *isl_pw_aff_get_tuple_id(
3686 __isl_keep isl_pw_aff *pa,
3687 enum isl_dim_type type);
3688 __isl_give isl_val *isl_aff_get_constant_val(
3689 __isl_keep isl_aff *aff);
3690 __isl_give isl_val *isl_aff_get_coefficient_val(
3691 __isl_keep isl_aff *aff,
3692 enum isl_dim_type type, int pos);
3693 __isl_give isl_val *isl_aff_get_denominator_val(
3694 __isl_keep isl_aff *aff);
3695 __isl_give isl_aff *isl_aff_get_div(
3696 __isl_keep isl_aff *aff, int pos);
3698 int isl_pw_aff_n_piece(__isl_keep isl_pw_aff *pwaff);
3699 int isl_pw_aff_foreach_piece(__isl_keep isl_pw_aff *pwaff,
3700 int (*fn)(__isl_take isl_set *set,
3701 __isl_take isl_aff *aff,
3702 void *user), void *user);
3704 int isl_aff_is_cst(__isl_keep isl_aff *aff);
3705 int isl_pw_aff_is_cst(__isl_keep isl_pw_aff *pwaff);
3707 int isl_aff_involves_dims(__isl_keep isl_aff *aff,
3708 enum isl_dim_type type, unsigned first, unsigned n);
3709 int isl_pw_aff_involves_dims(__isl_keep isl_pw_aff *pwaff,
3710 enum isl_dim_type type, unsigned first, unsigned n);
3712 isl_ctx *isl_pw_aff_get_ctx(__isl_keep isl_pw_aff *pwaff);
3713 unsigned isl_pw_aff_dim(__isl_keep isl_pw_aff *pwaff,
3714 enum isl_dim_type type);
3715 int isl_pw_aff_is_empty(__isl_keep isl_pw_aff *pwaff);
3717 It can be modified using
3719 #include <isl/aff.h>
3720 __isl_give isl_pw_aff *isl_pw_aff_set_tuple_id(
3721 __isl_take isl_pw_aff *pwaff,
3722 enum isl_dim_type type, __isl_take isl_id *id);
3723 __isl_give isl_aff *isl_aff_set_dim_name(
3724 __isl_take isl_aff *aff, enum isl_dim_type type,
3725 unsigned pos, const char *s);
3726 __isl_give isl_aff *isl_aff_set_dim_id(
3727 __isl_take isl_aff *aff, enum isl_dim_type type,
3728 unsigned pos, __isl_take isl_id *id);
3729 __isl_give isl_pw_aff *isl_pw_aff_set_dim_id(
3730 __isl_take isl_pw_aff *pma,
3731 enum isl_dim_type type, unsigned pos,
3732 __isl_take isl_id *id);
3733 __isl_give isl_aff *isl_aff_set_constant_si(
3734 __isl_take isl_aff *aff, int v);
3735 __isl_give isl_aff *isl_aff_set_constant_val(
3736 __isl_take isl_aff *aff, __isl_take isl_val *v);
3737 __isl_give isl_aff *isl_aff_set_coefficient_si(
3738 __isl_take isl_aff *aff,
3739 enum isl_dim_type type, int pos, int v);
3740 __isl_give isl_aff *isl_aff_set_coefficient_val(
3741 __isl_take isl_aff *aff,
3742 enum isl_dim_type type, int pos,
3743 __isl_take isl_val *v);
3745 __isl_give isl_aff *isl_aff_add_constant_si(
3746 __isl_take isl_aff *aff, int v);
3747 __isl_give isl_aff *isl_aff_add_constant_val(
3748 __isl_take isl_aff *aff, __isl_take isl_val *v);
3749 __isl_give isl_aff *isl_aff_add_constant_num_si(
3750 __isl_take isl_aff *aff, int v);
3751 __isl_give isl_aff *isl_aff_add_coefficient_si(
3752 __isl_take isl_aff *aff,
3753 enum isl_dim_type type, int pos, int v);
3754 __isl_give isl_aff *isl_aff_add_coefficient_val(
3755 __isl_take isl_aff *aff,
3756 enum isl_dim_type type, int pos,
3757 __isl_take isl_val *v);
3759 __isl_give isl_aff *isl_aff_insert_dims(
3760 __isl_take isl_aff *aff,
3761 enum isl_dim_type type, unsigned first, unsigned n);
3762 __isl_give isl_pw_aff *isl_pw_aff_insert_dims(
3763 __isl_take isl_pw_aff *pwaff,
3764 enum isl_dim_type type, unsigned first, unsigned n);
3765 __isl_give isl_aff *isl_aff_add_dims(
3766 __isl_take isl_aff *aff,
3767 enum isl_dim_type type, unsigned n);
3768 __isl_give isl_pw_aff *isl_pw_aff_add_dims(
3769 __isl_take isl_pw_aff *pwaff,
3770 enum isl_dim_type type, unsigned n);
3771 __isl_give isl_aff *isl_aff_drop_dims(
3772 __isl_take isl_aff *aff,
3773 enum isl_dim_type type, unsigned first, unsigned n);
3774 __isl_give isl_pw_aff *isl_pw_aff_drop_dims(
3775 __isl_take isl_pw_aff *pwaff,
3776 enum isl_dim_type type, unsigned first, unsigned n);
3777 __isl_give isl_aff *isl_aff_move_dims(
3778 __isl_take isl_aff *aff,
3779 enum isl_dim_type dst_type, unsigned dst_pos,
3780 enum isl_dim_type src_type, unsigned src_pos,
3782 __isl_give isl_pw_aff *isl_pw_aff_move_dims(
3783 __isl_take isl_pw_aff *pa,
3784 enum isl_dim_type dst_type, unsigned dst_pos,
3785 enum isl_dim_type src_type, unsigned src_pos,
3788 Note that C<isl_aff_set_constant_si> and C<isl_aff_set_coefficient_si>
3789 set the I<numerator> of the constant or coefficient, while
3790 C<isl_aff_set_constant_val> and C<isl_aff_set_coefficient_val> set
3791 the constant or coefficient as a whole.
3792 The C<add_constant> and C<add_coefficient> functions add an integer
3793 or rational value to
3794 the possibly rational constant or coefficient.
3795 The C<add_constant_num> functions add an integer value to
3798 To check whether an affine expressions is obviously zero
3799 or (obviously) equal to some other affine expression, use
3801 #include <isl/aff.h>
3802 int isl_aff_plain_is_zero(__isl_keep isl_aff *aff);
3803 int isl_aff_plain_is_equal(__isl_keep isl_aff *aff1,
3804 __isl_keep isl_aff *aff2);
3805 int isl_pw_aff_plain_is_equal(
3806 __isl_keep isl_pw_aff *pwaff1,
3807 __isl_keep isl_pw_aff *pwaff2);
3808 int isl_pw_aff_is_equal(__isl_keep isl_pw_aff *pa1,
3809 __isl_keep isl_pw_aff *pa2);
3813 #include <isl/aff.h>
3814 __isl_give isl_aff *isl_aff_add(__isl_take isl_aff *aff1,
3815 __isl_take isl_aff *aff2);
3816 __isl_give isl_pw_aff *isl_pw_aff_add(
3817 __isl_take isl_pw_aff *pwaff1,
3818 __isl_take isl_pw_aff *pwaff2);
3819 __isl_give isl_pw_aff *isl_pw_aff_min(
3820 __isl_take isl_pw_aff *pwaff1,
3821 __isl_take isl_pw_aff *pwaff2);
3822 __isl_give isl_pw_aff *isl_pw_aff_max(
3823 __isl_take isl_pw_aff *pwaff1,
3824 __isl_take isl_pw_aff *pwaff2);
3825 __isl_give isl_aff *isl_aff_sub(__isl_take isl_aff *aff1,
3826 __isl_take isl_aff *aff2);
3827 __isl_give isl_pw_aff *isl_pw_aff_sub(
3828 __isl_take isl_pw_aff *pwaff1,
3829 __isl_take isl_pw_aff *pwaff2);
3830 __isl_give isl_aff *isl_aff_neg(__isl_take isl_aff *aff);
3831 __isl_give isl_pw_aff *isl_pw_aff_neg(
3832 __isl_take isl_pw_aff *pwaff);
3833 __isl_give isl_aff *isl_aff_ceil(__isl_take isl_aff *aff);
3834 __isl_give isl_pw_aff *isl_pw_aff_ceil(
3835 __isl_take isl_pw_aff *pwaff);
3836 __isl_give isl_aff *isl_aff_floor(__isl_take isl_aff *aff);
3837 __isl_give isl_pw_aff *isl_pw_aff_floor(
3838 __isl_take isl_pw_aff *pwaff);
3839 __isl_give isl_aff *isl_aff_mod_val(__isl_take isl_aff *aff,
3840 __isl_take isl_val *mod);
3841 __isl_give isl_pw_aff *isl_pw_aff_mod_val(
3842 __isl_take isl_pw_aff *pa,
3843 __isl_take isl_val *mod);
3844 __isl_give isl_aff *isl_aff_scale_val(__isl_take isl_aff *aff,
3845 __isl_take isl_val *v);
3846 __isl_give isl_pw_aff *isl_pw_aff_scale_val(
3847 __isl_take isl_pw_aff *pa, __isl_take isl_val *v);
3848 __isl_give isl_aff *isl_aff_scale_down_ui(
3849 __isl_take isl_aff *aff, unsigned f);
3850 __isl_give isl_aff *isl_aff_scale_down_val(
3851 __isl_take isl_aff *aff, __isl_take isl_val *v);
3852 __isl_give isl_pw_aff *isl_pw_aff_scale_down_val(
3853 __isl_take isl_pw_aff *pa,
3854 __isl_take isl_val *f);
3856 __isl_give isl_pw_aff *isl_pw_aff_list_min(
3857 __isl_take isl_pw_aff_list *list);
3858 __isl_give isl_pw_aff *isl_pw_aff_list_max(
3859 __isl_take isl_pw_aff_list *list);
3861 __isl_give isl_pw_aff *isl_pw_aff_coalesce(
3862 __isl_take isl_pw_aff *pwqp);
3864 __isl_give isl_aff *isl_aff_align_params(
3865 __isl_take isl_aff *aff,
3866 __isl_take isl_space *model);
3867 __isl_give isl_pw_aff *isl_pw_aff_align_params(
3868 __isl_take isl_pw_aff *pwaff,
3869 __isl_take isl_space *model);
3871 __isl_give isl_aff *isl_aff_project_domain_on_params(
3872 __isl_take isl_aff *aff);
3873 __isl_give isl_pw_aff *isl_pw_aff_from_range(
3874 __isl_take isl_pw_aff *pwa);
3876 __isl_give isl_aff *isl_aff_gist_params(
3877 __isl_take isl_aff *aff,
3878 __isl_take isl_set *context);
3879 __isl_give isl_aff *isl_aff_gist(__isl_take isl_aff *aff,
3880 __isl_take isl_set *context);
3881 __isl_give isl_pw_aff *isl_pw_aff_gist_params(
3882 __isl_take isl_pw_aff *pwaff,
3883 __isl_take isl_set *context);
3884 __isl_give isl_pw_aff *isl_pw_aff_gist(
3885 __isl_take isl_pw_aff *pwaff,
3886 __isl_take isl_set *context);
3888 __isl_give isl_set *isl_pw_aff_domain(
3889 __isl_take isl_pw_aff *pwaff);
3890 __isl_give isl_set *isl_pw_aff_params(
3891 __isl_take isl_pw_aff *pwa);
3892 __isl_give isl_pw_aff *isl_pw_aff_intersect_domain(
3893 __isl_take isl_pw_aff *pa,
3894 __isl_take isl_set *set);
3895 __isl_give isl_pw_aff *isl_pw_aff_intersect_params(
3896 __isl_take isl_pw_aff *pa,
3897 __isl_take isl_set *set);
3899 __isl_give isl_aff *isl_aff_mul(__isl_take isl_aff *aff1,
3900 __isl_take isl_aff *aff2);
3901 __isl_give isl_aff *isl_aff_div(__isl_take isl_aff *aff1,
3902 __isl_take isl_aff *aff2);
3903 __isl_give isl_pw_aff *isl_pw_aff_mul(
3904 __isl_take isl_pw_aff *pwaff1,
3905 __isl_take isl_pw_aff *pwaff2);
3906 __isl_give isl_pw_aff *isl_pw_aff_div(
3907 __isl_take isl_pw_aff *pa1,
3908 __isl_take isl_pw_aff *pa2);
3909 __isl_give isl_pw_aff *isl_pw_aff_tdiv_q(
3910 __isl_take isl_pw_aff *pa1,
3911 __isl_take isl_pw_aff *pa2);
3912 __isl_give isl_pw_aff *isl_pw_aff_tdiv_r(
3913 __isl_take isl_pw_aff *pa1,
3914 __isl_take isl_pw_aff *pa2);
3916 When multiplying two affine expressions, at least one of the two needs
3917 to be a constant. Similarly, when dividing an affine expression by another,
3918 the second expression needs to be a constant.
3919 C<isl_pw_aff_tdiv_q> computes the quotient of an integer division with
3920 rounding towards zero. C<isl_pw_aff_tdiv_r> computes the corresponding
3923 #include <isl/aff.h>
3924 __isl_give isl_aff *isl_aff_pullback_aff(
3925 __isl_take isl_aff *aff1,
3926 __isl_take isl_aff *aff2);
3927 __isl_give isl_aff *isl_aff_pullback_multi_aff(
3928 __isl_take isl_aff *aff,
3929 __isl_take isl_multi_aff *ma);
3930 __isl_give isl_pw_aff *isl_pw_aff_pullback_multi_aff(
3931 __isl_take isl_pw_aff *pa,
3932 __isl_take isl_multi_aff *ma);
3933 __isl_give isl_pw_aff *isl_pw_aff_pullback_pw_multi_aff(
3934 __isl_take isl_pw_aff *pa,
3935 __isl_take isl_pw_multi_aff *pma);
3937 These functions precompose the input expression by the given
3938 C<isl_aff>, C<isl_multi_aff> or C<isl_pw_multi_aff>. In other words,
3939 the C<isl_aff>, C<isl_multi_aff> or C<isl_pw_multi_aff> is plugged
3940 into the (piecewise) affine expression.
3941 Objects of type C<isl_multi_aff> are described in
3942 L</"Piecewise Multiple Quasi Affine Expressions">.
3944 #include <isl/aff.h>
3945 __isl_give isl_basic_set *isl_aff_zero_basic_set(
3946 __isl_take isl_aff *aff);
3947 __isl_give isl_basic_set *isl_aff_neg_basic_set(
3948 __isl_take isl_aff *aff);
3949 __isl_give isl_basic_set *isl_aff_le_basic_set(
3950 __isl_take isl_aff *aff1, __isl_take isl_aff *aff2);
3951 __isl_give isl_basic_set *isl_aff_ge_basic_set(
3952 __isl_take isl_aff *aff1, __isl_take isl_aff *aff2);
3953 __isl_give isl_set *isl_pw_aff_eq_set(
3954 __isl_take isl_pw_aff *pwaff1,
3955 __isl_take isl_pw_aff *pwaff2);
3956 __isl_give isl_set *isl_pw_aff_ne_set(
3957 __isl_take isl_pw_aff *pwaff1,
3958 __isl_take isl_pw_aff *pwaff2);
3959 __isl_give isl_set *isl_pw_aff_le_set(
3960 __isl_take isl_pw_aff *pwaff1,
3961 __isl_take isl_pw_aff *pwaff2);
3962 __isl_give isl_set *isl_pw_aff_lt_set(
3963 __isl_take isl_pw_aff *pwaff1,
3964 __isl_take isl_pw_aff *pwaff2);
3965 __isl_give isl_set *isl_pw_aff_ge_set(
3966 __isl_take isl_pw_aff *pwaff1,
3967 __isl_take isl_pw_aff *pwaff2);
3968 __isl_give isl_set *isl_pw_aff_gt_set(
3969 __isl_take isl_pw_aff *pwaff1,
3970 __isl_take isl_pw_aff *pwaff2);
3972 __isl_give isl_set *isl_pw_aff_list_eq_set(
3973 __isl_take isl_pw_aff_list *list1,
3974 __isl_take isl_pw_aff_list *list2);
3975 __isl_give isl_set *isl_pw_aff_list_ne_set(
3976 __isl_take isl_pw_aff_list *list1,
3977 __isl_take isl_pw_aff_list *list2);
3978 __isl_give isl_set *isl_pw_aff_list_le_set(
3979 __isl_take isl_pw_aff_list *list1,
3980 __isl_take isl_pw_aff_list *list2);
3981 __isl_give isl_set *isl_pw_aff_list_lt_set(
3982 __isl_take isl_pw_aff_list *list1,
3983 __isl_take isl_pw_aff_list *list2);
3984 __isl_give isl_set *isl_pw_aff_list_ge_set(
3985 __isl_take isl_pw_aff_list *list1,
3986 __isl_take isl_pw_aff_list *list2);
3987 __isl_give isl_set *isl_pw_aff_list_gt_set(
3988 __isl_take isl_pw_aff_list *list1,
3989 __isl_take isl_pw_aff_list *list2);
3991 The function C<isl_aff_neg_basic_set> returns a basic set
3992 containing those elements in the domain space
3993 of C<aff> where C<aff> is negative.
3994 The function C<isl_aff_ge_basic_set> returns a basic set
3995 containing those elements in the shared space
3996 of C<aff1> and C<aff2> where C<aff1> is greater than or equal to C<aff2>.
3997 The function C<isl_pw_aff_ge_set> returns a set
3998 containing those elements in the shared domain
3999 of C<pwaff1> and C<pwaff2> where C<pwaff1> is greater than or equal to C<pwaff2>.
4000 The functions operating on C<isl_pw_aff_list> apply the corresponding
4001 C<isl_pw_aff> function to each pair of elements in the two lists.
4003 #include <isl/aff.h>
4004 __isl_give isl_set *isl_pw_aff_nonneg_set(
4005 __isl_take isl_pw_aff *pwaff);
4006 __isl_give isl_set *isl_pw_aff_zero_set(
4007 __isl_take isl_pw_aff *pwaff);
4008 __isl_give isl_set *isl_pw_aff_non_zero_set(
4009 __isl_take isl_pw_aff *pwaff);
4011 The function C<isl_pw_aff_nonneg_set> returns a set
4012 containing those elements in the domain
4013 of C<pwaff> where C<pwaff> is non-negative.
4015 #include <isl/aff.h>
4016 __isl_give isl_pw_aff *isl_pw_aff_cond(
4017 __isl_take isl_pw_aff *cond,
4018 __isl_take isl_pw_aff *pwaff_true,
4019 __isl_take isl_pw_aff *pwaff_false);
4021 The function C<isl_pw_aff_cond> performs a conditional operator
4022 and returns an expression that is equal to C<pwaff_true>
4023 for elements where C<cond> is non-zero and equal to C<pwaff_false> for elements
4024 where C<cond> is zero.
4026 #include <isl/aff.h>
4027 __isl_give isl_pw_aff *isl_pw_aff_union_min(
4028 __isl_take isl_pw_aff *pwaff1,
4029 __isl_take isl_pw_aff *pwaff2);
4030 __isl_give isl_pw_aff *isl_pw_aff_union_max(
4031 __isl_take isl_pw_aff *pwaff1,
4032 __isl_take isl_pw_aff *pwaff2);
4033 __isl_give isl_pw_aff *isl_pw_aff_union_add(
4034 __isl_take isl_pw_aff *pwaff1,
4035 __isl_take isl_pw_aff *pwaff2);
4037 The function C<isl_pw_aff_union_max> computes a piecewise quasi-affine
4038 expression with a domain that is the union of those of C<pwaff1> and
4039 C<pwaff2> and such that on each cell, the quasi-affine expression is
4040 the maximum of those of C<pwaff1> and C<pwaff2>. If only one of
4041 C<pwaff1> or C<pwaff2> is defined on a given cell, then the
4042 associated expression is the defined one.
4044 An expression can be read from input using
4046 #include <isl/aff.h>
4047 __isl_give isl_aff *isl_aff_read_from_str(
4048 isl_ctx *ctx, const char *str);
4049 __isl_give isl_pw_aff *isl_pw_aff_read_from_str(
4050 isl_ctx *ctx, const char *str);
4052 An expression can be printed using
4054 #include <isl/aff.h>
4055 __isl_give isl_printer *isl_printer_print_aff(
4056 __isl_take isl_printer *p, __isl_keep isl_aff *aff);
4058 __isl_give isl_printer *isl_printer_print_pw_aff(
4059 __isl_take isl_printer *p,
4060 __isl_keep isl_pw_aff *pwaff);
4062 =head2 Piecewise Multiple Quasi Affine Expressions
4064 An C<isl_multi_aff> object represents a sequence of
4065 zero or more affine expressions, all defined on the same domain space.
4066 Similarly, an C<isl_multi_pw_aff> object represents a sequence of
4067 zero or more piecewise affine expressions.
4069 An C<isl_multi_aff> can be constructed from a single
4070 C<isl_aff> or an C<isl_aff_list> using the
4071 following functions. Similarly for C<isl_multi_pw_aff>
4072 and C<isl_pw_multi_aff>.
4074 #include <isl/aff.h>
4075 __isl_give isl_multi_aff *isl_multi_aff_from_aff(
4076 __isl_take isl_aff *aff);
4077 __isl_give isl_multi_pw_aff *
4078 isl_multi_pw_aff_from_multi_aff(
4079 __isl_take isl_multi_aff *ma);
4080 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_from_pw_aff(
4081 __isl_take isl_pw_aff *pa);
4082 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_from_pw_aff(
4083 __isl_take isl_pw_aff *pa);
4084 __isl_give isl_multi_aff *isl_multi_aff_from_aff_list(
4085 __isl_take isl_space *space,
4086 __isl_take isl_aff_list *list);
4088 An C<isl_multi_pw_aff> can be converted to an C<isl_pw_multi_aff>
4089 using the function C<isl_pw_multi_aff_from_multi_pw_aff> below.
4090 Note however that the domain
4091 of the result is the intersection of the domains of the input.
4092 The reverse conversion is exact.
4094 #include <isl/aff.h>
4095 __isl_give isl_pw_multi_aff *
4096 isl_pw_multi_aff_from_multi_pw_aff(
4097 __isl_take isl_multi_pw_aff *mpa);
4098 __isl_give isl_multi_pw_aff *
4099 isl_multi_pw_aff_from_pw_multi_aff(
4100 __isl_take isl_pw_multi_aff *pma);
4102 An empty piecewise multiple quasi affine expression (one with no cells),
4103 the zero piecewise multiple quasi affine expression (with value zero
4104 for each output dimension),
4105 a piecewise multiple quasi affine expression with a single cell (with
4106 either a universe or a specified domain) or
4107 a zero-dimensional piecewise multiple quasi affine expression
4109 can be created using the following functions.
4111 #include <isl/aff.h>
4112 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_empty(
4113 __isl_take isl_space *space);
4114 __isl_give isl_multi_aff *isl_multi_aff_zero(
4115 __isl_take isl_space *space);
4116 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_zero(
4117 __isl_take isl_space *space);
4118 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_zero(
4119 __isl_take isl_space *space);
4120 __isl_give isl_multi_aff *isl_multi_aff_identity(
4121 __isl_take isl_space *space);
4122 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_identity(
4123 __isl_take isl_space *space);
4124 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_identity(
4125 __isl_take isl_space *space);
4126 __isl_give isl_multi_aff *isl_multi_aff_domain_map(
4127 __isl_take isl_space *space);
4128 __isl_give isl_multi_aff *isl_multi_aff_range_map(
4129 __isl_take isl_space *space);
4130 __isl_give isl_multi_aff *isl_multi_aff_project_out_map(
4131 __isl_take isl_space *space,
4132 enum isl_dim_type type,
4133 unsigned first, unsigned n);
4134 __isl_give isl_pw_multi_aff *
4135 isl_pw_multi_aff_project_out_map(
4136 __isl_take isl_space *space,
4137 enum isl_dim_type type,
4138 unsigned first, unsigned n);
4139 __isl_give isl_pw_multi_aff *
4140 isl_pw_multi_aff_from_multi_aff(
4141 __isl_take isl_multi_aff *ma);
4142 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_alloc(
4143 __isl_take isl_set *set,
4144 __isl_take isl_multi_aff *maff);
4145 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_from_domain(
4146 __isl_take isl_set *set);
4148 __isl_give isl_union_pw_multi_aff *
4149 isl_union_pw_multi_aff_empty(
4150 __isl_take isl_space *space);
4151 __isl_give isl_union_pw_multi_aff *
4152 isl_union_pw_multi_aff_add_pw_multi_aff(
4153 __isl_take isl_union_pw_multi_aff *upma,
4154 __isl_take isl_pw_multi_aff *pma);
4155 __isl_give isl_union_pw_multi_aff *
4156 isl_union_pw_multi_aff_from_domain(
4157 __isl_take isl_union_set *uset);
4159 A piecewise multiple quasi affine expression can also be initialized
4160 from an C<isl_set> or C<isl_map>, provided the C<isl_set> is a singleton
4161 and the C<isl_map> is single-valued.
4162 In case of a conversion from an C<isl_union_set> or an C<isl_union_map>
4163 to an C<isl_union_pw_multi_aff>, these properties need to hold in each space.
4165 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_from_set(
4166 __isl_take isl_set *set);
4167 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_from_map(
4168 __isl_take isl_map *map);
4170 __isl_give isl_union_pw_multi_aff *
4171 isl_union_pw_multi_aff_from_union_set(
4172 __isl_take isl_union_set *uset);
4173 __isl_give isl_union_pw_multi_aff *
4174 isl_union_pw_multi_aff_from_union_map(
4175 __isl_take isl_union_map *umap);
4177 Multiple quasi affine expressions can be copied and freed using
4179 #include <isl/aff.h>
4180 __isl_give isl_multi_aff *isl_multi_aff_copy(
4181 __isl_keep isl_multi_aff *maff);
4182 void *isl_multi_aff_free(__isl_take isl_multi_aff *maff);
4184 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_copy(
4185 __isl_keep isl_pw_multi_aff *pma);
4186 void *isl_pw_multi_aff_free(
4187 __isl_take isl_pw_multi_aff *pma);
4189 __isl_give isl_union_pw_multi_aff *
4190 isl_union_pw_multi_aff_copy(
4191 __isl_keep isl_union_pw_multi_aff *upma);
4192 void *isl_union_pw_multi_aff_free(
4193 __isl_take isl_union_pw_multi_aff *upma);
4195 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_copy(
4196 __isl_keep isl_multi_pw_aff *mpa);
4197 void *isl_multi_pw_aff_free(
4198 __isl_take isl_multi_pw_aff *mpa);
4200 The expression can be inspected using
4202 #include <isl/aff.h>
4203 isl_ctx *isl_multi_aff_get_ctx(
4204 __isl_keep isl_multi_aff *maff);
4205 isl_ctx *isl_pw_multi_aff_get_ctx(
4206 __isl_keep isl_pw_multi_aff *pma);
4207 isl_ctx *isl_union_pw_multi_aff_get_ctx(
4208 __isl_keep isl_union_pw_multi_aff *upma);
4209 isl_ctx *isl_multi_pw_aff_get_ctx(
4210 __isl_keep isl_multi_pw_aff *mpa);
4211 unsigned isl_multi_aff_dim(__isl_keep isl_multi_aff *maff,
4212 enum isl_dim_type type);
4213 unsigned isl_pw_multi_aff_dim(
4214 __isl_keep isl_pw_multi_aff *pma,
4215 enum isl_dim_type type);
4216 unsigned isl_multi_pw_aff_dim(
4217 __isl_keep isl_multi_pw_aff *mpa,
4218 enum isl_dim_type type);
4219 __isl_give isl_aff *isl_multi_aff_get_aff(
4220 __isl_keep isl_multi_aff *multi, int pos);
4221 __isl_give isl_pw_aff *isl_pw_multi_aff_get_pw_aff(
4222 __isl_keep isl_pw_multi_aff *pma, int pos);
4223 __isl_give isl_pw_aff *isl_multi_pw_aff_get_pw_aff(
4224 __isl_keep isl_multi_pw_aff *mpa, int pos);
4225 int isl_multi_aff_find_dim_by_id(
4226 __isl_keep isl_multi_aff *ma,
4227 enum isl_dim_type type, __isl_keep isl_id *id);
4228 int isl_multi_pw_aff_find_dim_by_id(
4229 __isl_keep isl_multi_pw_aff *mpa,
4230 enum isl_dim_type type, __isl_keep isl_id *id);
4231 const char *isl_pw_multi_aff_get_dim_name(
4232 __isl_keep isl_pw_multi_aff *pma,
4233 enum isl_dim_type type, unsigned pos);
4234 __isl_give isl_id *isl_multi_aff_get_dim_id(
4235 __isl_keep isl_multi_aff *ma,
4236 enum isl_dim_type type, unsigned pos);
4237 __isl_give isl_id *isl_pw_multi_aff_get_dim_id(
4238 __isl_keep isl_pw_multi_aff *pma,
4239 enum isl_dim_type type, unsigned pos);
4240 __isl_give isl_id *isl_multi_pw_aff_get_dim_id(
4241 __isl_keep isl_multi_pw_aff *mpa,
4242 enum isl_dim_type type, unsigned pos);
4243 const char *isl_multi_aff_get_tuple_name(
4244 __isl_keep isl_multi_aff *multi,
4245 enum isl_dim_type type);
4246 int isl_pw_multi_aff_has_tuple_name(
4247 __isl_keep isl_pw_multi_aff *pma,
4248 enum isl_dim_type type);
4249 const char *isl_pw_multi_aff_get_tuple_name(
4250 __isl_keep isl_pw_multi_aff *pma,
4251 enum isl_dim_type type);
4252 int isl_multi_aff_has_tuple_id(__isl_keep isl_multi_aff *ma,
4253 enum isl_dim_type type);
4254 int isl_pw_multi_aff_has_tuple_id(
4255 __isl_keep isl_pw_multi_aff *pma,
4256 enum isl_dim_type type);
4257 int isl_multi_pw_aff_has_tuple_id(
4258 __isl_keep isl_multi_pw_aff *mpa,
4259 enum isl_dim_type type);
4260 __isl_give isl_id *isl_multi_aff_get_tuple_id(
4261 __isl_keep isl_multi_aff *ma,
4262 enum isl_dim_type type);
4263 __isl_give isl_id *isl_pw_multi_aff_get_tuple_id(
4264 __isl_keep isl_pw_multi_aff *pma,
4265 enum isl_dim_type type);
4266 __isl_give isl_id *isl_multi_pw_aff_get_tuple_id(
4267 __isl_keep isl_multi_pw_aff *mpa,
4268 enum isl_dim_type type);
4270 int isl_pw_multi_aff_foreach_piece(
4271 __isl_keep isl_pw_multi_aff *pma,
4272 int (*fn)(__isl_take isl_set *set,
4273 __isl_take isl_multi_aff *maff,
4274 void *user), void *user);
4276 int isl_union_pw_multi_aff_foreach_pw_multi_aff(
4277 __isl_keep isl_union_pw_multi_aff *upma,
4278 int (*fn)(__isl_take isl_pw_multi_aff *pma,
4279 void *user), void *user);
4281 It can be modified using
4283 #include <isl/aff.h>
4284 __isl_give isl_multi_aff *isl_multi_aff_set_aff(
4285 __isl_take isl_multi_aff *multi, int pos,
4286 __isl_take isl_aff *aff);
4287 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_set_pw_aff(
4288 __isl_take isl_pw_multi_aff *pma, unsigned pos,
4289 __isl_take isl_pw_aff *pa);
4290 __isl_give isl_multi_aff *isl_multi_aff_set_dim_name(
4291 __isl_take isl_multi_aff *maff,
4292 enum isl_dim_type type, unsigned pos, const char *s);
4293 __isl_give isl_multi_aff *isl_multi_aff_set_dim_id(
4294 __isl_take isl_multi_aff *maff,
4295 enum isl_dim_type type, unsigned pos,
4296 __isl_take isl_id *id);
4297 __isl_give isl_multi_aff *isl_multi_aff_set_tuple_name(
4298 __isl_take isl_multi_aff *maff,
4299 enum isl_dim_type type, const char *s);
4300 __isl_give isl_multi_aff *isl_multi_aff_set_tuple_id(
4301 __isl_take isl_multi_aff *maff,
4302 enum isl_dim_type type, __isl_take isl_id *id);
4303 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_set_tuple_id(
4304 __isl_take isl_pw_multi_aff *pma,
4305 enum isl_dim_type type, __isl_take isl_id *id);
4306 __isl_give isl_multi_aff *isl_multi_aff_reset_tuple_id(
4307 __isl_take isl_multi_aff *ma,
4308 enum isl_dim_type type);
4309 __isl_give isl_multi_pw_aff *
4310 isl_multi_pw_aff_reset_tuple_id(
4311 __isl_take isl_multi_pw_aff *mpa,
4312 enum isl_dim_type type);
4313 __isl_give isl_multi_aff *isl_multi_aff_reset_user(
4314 __isl_take isl_multi_aff *ma);
4315 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_reset_user(
4316 __isl_take isl_multi_pw_aff *mpa);
4318 __isl_give isl_multi_pw_aff *
4319 isl_multi_pw_aff_set_dim_name(
4320 __isl_take isl_multi_pw_aff *mpa,
4321 enum isl_dim_type type, unsigned pos, const char *s);
4322 __isl_give isl_multi_pw_aff *
4323 isl_multi_pw_aff_set_dim_id(
4324 __isl_take isl_multi_pw_aff *mpa,
4325 enum isl_dim_type type, unsigned pos,
4326 __isl_take isl_id *id);
4327 __isl_give isl_multi_pw_aff *
4328 isl_multi_pw_aff_set_tuple_name(
4329 __isl_take isl_multi_pw_aff *mpa,
4330 enum isl_dim_type type, const char *s);
4332 __isl_give isl_multi_aff *isl_multi_aff_insert_dims(
4333 __isl_take isl_multi_aff *ma,
4334 enum isl_dim_type type, unsigned first, unsigned n);
4335 __isl_give isl_multi_aff *isl_multi_aff_add_dims(
4336 __isl_take isl_multi_aff *ma,
4337 enum isl_dim_type type, unsigned n);
4338 __isl_give isl_multi_aff *isl_multi_aff_drop_dims(
4339 __isl_take isl_multi_aff *maff,
4340 enum isl_dim_type type, unsigned first, unsigned n);
4341 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_drop_dims(
4342 __isl_take isl_pw_multi_aff *pma,
4343 enum isl_dim_type type, unsigned first, unsigned n);
4345 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_insert_dims(
4346 __isl_take isl_multi_pw_aff *mpa,
4347 enum isl_dim_type type, unsigned first, unsigned n);
4348 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_add_dims(
4349 __isl_take isl_multi_pw_aff *mpa,
4350 enum isl_dim_type type, unsigned n);
4351 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_move_dims(
4352 __isl_take isl_multi_pw_aff *pma,
4353 enum isl_dim_type dst_type, unsigned dst_pos,
4354 enum isl_dim_type src_type, unsigned src_pos,
4357 To check whether two multiple affine expressions are
4358 (obviously) equal to each other, use
4360 int isl_multi_aff_plain_is_equal(__isl_keep isl_multi_aff *maff1,
4361 __isl_keep isl_multi_aff *maff2);
4362 int isl_pw_multi_aff_plain_is_equal(
4363 __isl_keep isl_pw_multi_aff *pma1,
4364 __isl_keep isl_pw_multi_aff *pma2);
4365 int isl_multi_pw_aff_plain_is_equal(
4366 __isl_keep isl_multi_pw_aff *mpa1,
4367 __isl_keep isl_multi_pw_aff *mpa2);
4368 int isl_multi_pw_aff_is_equal(
4369 __isl_keep isl_multi_pw_aff *mpa1,
4370 __isl_keep isl_multi_pw_aff *mpa2);
4374 #include <isl/aff.h>
4375 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_union_lexmin(
4376 __isl_take isl_pw_multi_aff *pma1,
4377 __isl_take isl_pw_multi_aff *pma2);
4378 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_union_lexmax(
4379 __isl_take isl_pw_multi_aff *pma1,
4380 __isl_take isl_pw_multi_aff *pma2);
4381 __isl_give isl_multi_aff *isl_multi_aff_add(
4382 __isl_take isl_multi_aff *maff1,
4383 __isl_take isl_multi_aff *maff2);
4384 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_add(
4385 __isl_take isl_pw_multi_aff *pma1,
4386 __isl_take isl_pw_multi_aff *pma2);
4387 __isl_give isl_union_pw_multi_aff *isl_union_pw_multi_aff_add(
4388 __isl_take isl_union_pw_multi_aff *upma1,
4389 __isl_take isl_union_pw_multi_aff *upma2);
4390 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_union_add(
4391 __isl_take isl_pw_multi_aff *pma1,
4392 __isl_take isl_pw_multi_aff *pma2);
4393 __isl_give isl_multi_aff *isl_multi_aff_sub(
4394 __isl_take isl_multi_aff *ma1,
4395 __isl_take isl_multi_aff *ma2);
4396 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_sub(
4397 __isl_take isl_pw_multi_aff *pma1,
4398 __isl_take isl_pw_multi_aff *pma2);
4399 __isl_give isl_union_pw_multi_aff *isl_union_pw_multi_aff_sub(
4400 __isl_take isl_union_pw_multi_aff *upma1,
4401 __isl_take isl_union_pw_multi_aff *upma2);
4403 C<isl_multi_aff_sub> subtracts the second argument from the first.
4405 __isl_give isl_multi_aff *isl_multi_aff_scale_val(
4406 __isl_take isl_multi_aff *ma,
4407 __isl_take isl_val *v);
4408 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_scale_val(
4409 __isl_take isl_pw_multi_aff *pma,
4410 __isl_take isl_val *v);
4411 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_scale_val(
4412 __isl_take isl_multi_pw_aff *mpa,
4413 __isl_take isl_val *v);
4414 __isl_give isl_multi_aff *isl_multi_aff_scale_multi_val(
4415 __isl_take isl_multi_aff *ma,
4416 __isl_take isl_multi_val *mv);
4417 __isl_give isl_pw_multi_aff *
4418 isl_pw_multi_aff_scale_multi_val(
4419 __isl_take isl_pw_multi_aff *pma,
4420 __isl_take isl_multi_val *mv);
4421 __isl_give isl_multi_pw_aff *
4422 isl_multi_pw_aff_scale_multi_val(
4423 __isl_take isl_multi_pw_aff *mpa,
4424 __isl_take isl_multi_val *mv);
4425 __isl_give isl_union_pw_multi_aff *
4426 isl_union_pw_multi_aff_scale_multi_val(
4427 __isl_take isl_union_pw_multi_aff *upma,
4428 __isl_take isl_multi_val *mv);
4429 __isl_give isl_multi_aff *
4430 isl_multi_aff_scale_down_multi_val(
4431 __isl_take isl_multi_aff *ma,
4432 __isl_take isl_multi_val *mv);
4433 __isl_give isl_multi_pw_aff *
4434 isl_multi_pw_aff_scale_down_multi_val(
4435 __isl_take isl_multi_pw_aff *mpa,
4436 __isl_take isl_multi_val *mv);
4438 C<isl_multi_aff_scale_multi_val> scales the elements of C<ma>
4439 by the corresponding elements of C<mv>.
4441 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_fix_si(
4442 __isl_take isl_pw_multi_aff *pma,
4443 enum isl_dim_type type, unsigned pos, int value);
4444 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_intersect_params(
4445 __isl_take isl_pw_multi_aff *pma,
4446 __isl_take isl_set *set);
4447 __isl_give isl_set *isl_multi_pw_aff_domain(
4448 __isl_take isl_multi_pw_aff *mpa);
4449 __isl_give isl_multi_pw_aff *
4450 isl_multi_pw_aff_intersect_params(
4451 __isl_take isl_multi_pw_aff *mpa,
4452 __isl_take isl_set *set);
4453 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_intersect_domain(
4454 __isl_take isl_pw_multi_aff *pma,
4455 __isl_take isl_set *set);
4456 __isl_give isl_multi_pw_aff *
4457 isl_multi_pw_aff_intersect_domain(
4458 __isl_take isl_multi_pw_aff *mpa,
4459 __isl_take isl_set *domain);
4460 __isl_give isl_union_pw_multi_aff *
4461 isl_union_pw_multi_aff_intersect_domain(
4462 __isl_take isl_union_pw_multi_aff *upma,
4463 __isl_take isl_union_set *uset);
4464 __isl_give isl_multi_aff *isl_multi_aff_lift(
4465 __isl_take isl_multi_aff *maff,
4466 __isl_give isl_local_space **ls);
4467 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_coalesce(
4468 __isl_take isl_pw_multi_aff *pma);
4469 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_coalesce(
4470 __isl_take isl_multi_pw_aff *mpa);
4471 __isl_give isl_multi_aff *isl_multi_aff_align_params(
4472 __isl_take isl_multi_aff *multi,
4473 __isl_take isl_space *model);
4474 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_align_params(
4475 __isl_take isl_pw_multi_aff *pma,
4476 __isl_take isl_space *model);
4477 __isl_give isl_pw_multi_aff *
4478 isl_pw_multi_aff_project_domain_on_params(
4479 __isl_take isl_pw_multi_aff *pma);
4480 __isl_give isl_multi_aff *isl_multi_aff_gist_params(
4481 __isl_take isl_multi_aff *maff,
4482 __isl_take isl_set *context);
4483 __isl_give isl_multi_aff *isl_multi_aff_gist(
4484 __isl_take isl_multi_aff *maff,
4485 __isl_take isl_set *context);
4486 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_gist_params(
4487 __isl_take isl_pw_multi_aff *pma,
4488 __isl_take isl_set *set);
4489 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_gist(
4490 __isl_take isl_pw_multi_aff *pma,
4491 __isl_take isl_set *set);
4492 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_gist_params(
4493 __isl_take isl_multi_pw_aff *mpa,
4494 __isl_take isl_set *set);
4495 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_gist(
4496 __isl_take isl_multi_pw_aff *mpa,
4497 __isl_take isl_set *set);
4498 __isl_give isl_multi_aff *isl_multi_aff_from_range(
4499 __isl_take isl_multi_aff *ma);
4500 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_from_range(
4501 __isl_take isl_multi_pw_aff *mpa);
4502 __isl_give isl_set *isl_pw_multi_aff_domain(
4503 __isl_take isl_pw_multi_aff *pma);
4504 __isl_give isl_union_set *isl_union_pw_multi_aff_domain(
4505 __isl_take isl_union_pw_multi_aff *upma);
4506 __isl_give isl_multi_aff *isl_multi_aff_range_splice(
4507 __isl_take isl_multi_aff *ma1, unsigned pos,
4508 __isl_take isl_multi_aff *ma2);
4509 __isl_give isl_multi_aff *isl_multi_aff_splice(
4510 __isl_take isl_multi_aff *ma1,
4511 unsigned in_pos, unsigned out_pos,
4512 __isl_take isl_multi_aff *ma2);
4513 __isl_give isl_multi_aff *isl_multi_aff_range_product(
4514 __isl_take isl_multi_aff *ma1,
4515 __isl_take isl_multi_aff *ma2);
4516 __isl_give isl_multi_aff *isl_multi_aff_flat_range_product(
4517 __isl_take isl_multi_aff *ma1,
4518 __isl_take isl_multi_aff *ma2);
4519 __isl_give isl_multi_aff *isl_multi_aff_product(
4520 __isl_take isl_multi_aff *ma1,
4521 __isl_take isl_multi_aff *ma2);
4522 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_product(
4523 __isl_take isl_multi_pw_aff *mpa1,
4524 __isl_take isl_multi_pw_aff *mpa2);
4525 __isl_give isl_pw_multi_aff *
4526 isl_pw_multi_aff_range_product(
4527 __isl_take isl_pw_multi_aff *pma1,
4528 __isl_take isl_pw_multi_aff *pma2);
4529 __isl_give isl_pw_multi_aff *
4530 isl_pw_multi_aff_flat_range_product(
4531 __isl_take isl_pw_multi_aff *pma1,
4532 __isl_take isl_pw_multi_aff *pma2);
4533 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_product(
4534 __isl_take isl_pw_multi_aff *pma1,
4535 __isl_take isl_pw_multi_aff *pma2);
4536 __isl_give isl_union_pw_multi_aff *
4537 isl_union_pw_multi_aff_flat_range_product(
4538 __isl_take isl_union_pw_multi_aff *upma1,
4539 __isl_take isl_union_pw_multi_aff *upma2);
4540 __isl_give isl_multi_pw_aff *
4541 isl_multi_pw_aff_range_splice(
4542 __isl_take isl_multi_pw_aff *mpa1, unsigned pos,
4543 __isl_take isl_multi_pw_aff *mpa2);
4544 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_splice(
4545 __isl_take isl_multi_pw_aff *mpa1,
4546 unsigned in_pos, unsigned out_pos,
4547 __isl_take isl_multi_pw_aff *mpa2);
4548 __isl_give isl_multi_pw_aff *
4549 isl_multi_pw_aff_range_product(
4550 __isl_take isl_multi_pw_aff *mpa1,
4551 __isl_take isl_multi_pw_aff *mpa2);
4552 __isl_give isl_multi_pw_aff *
4553 isl_multi_pw_aff_flat_range_product(
4554 __isl_take isl_multi_pw_aff *mpa1,
4555 __isl_take isl_multi_pw_aff *mpa2);
4557 If the C<ls> argument of C<isl_multi_aff_lift> is not C<NULL>,
4558 then it is assigned the local space that lies at the basis of
4559 the lifting applied.
4561 #include <isl/aff.h>
4562 __isl_give isl_multi_aff *isl_multi_aff_pullback_multi_aff(
4563 __isl_take isl_multi_aff *ma1,
4564 __isl_take isl_multi_aff *ma2);
4565 __isl_give isl_pw_multi_aff *
4566 isl_pw_multi_aff_pullback_multi_aff(
4567 __isl_take isl_pw_multi_aff *pma,
4568 __isl_take isl_multi_aff *ma);
4569 __isl_give isl_multi_pw_aff *
4570 isl_multi_pw_aff_pullback_multi_aff(
4571 __isl_take isl_multi_pw_aff *mpa,
4572 __isl_take isl_multi_aff *ma);
4573 __isl_give isl_pw_multi_aff *
4574 isl_pw_multi_aff_pullback_pw_multi_aff(
4575 __isl_take isl_pw_multi_aff *pma1,
4576 __isl_take isl_pw_multi_aff *pma2);
4577 __isl_give isl_multi_pw_aff *
4578 isl_multi_pw_aff_pullback_pw_multi_aff(
4579 __isl_take isl_multi_pw_aff *mpa,
4580 __isl_take isl_pw_multi_aff *pma);
4581 __isl_give isl_multi_pw_aff *
4582 isl_multi_pw_aff_pullback_multi_pw_aff(
4583 __isl_take isl_multi_pw_aff *mpa1,
4584 __isl_take isl_multi_pw_aff *mpa2);
4586 The function C<isl_multi_aff_pullback_multi_aff> precomposes C<ma1> by C<ma2>.
4587 In other words, C<ma2> is plugged
4590 __isl_give isl_set *isl_multi_aff_lex_le_set(
4591 __isl_take isl_multi_aff *ma1,
4592 __isl_take isl_multi_aff *ma2);
4593 __isl_give isl_set *isl_multi_aff_lex_ge_set(
4594 __isl_take isl_multi_aff *ma1,
4595 __isl_take isl_multi_aff *ma2);
4597 The function C<isl_multi_aff_lex_le_set> returns a set
4598 containing those elements in the shared domain space
4599 where C<ma1> is lexicographically smaller than or
4602 An expression can be read from input using
4604 #include <isl/aff.h>
4605 __isl_give isl_multi_aff *isl_multi_aff_read_from_str(
4606 isl_ctx *ctx, const char *str);
4607 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_read_from_str(
4608 isl_ctx *ctx, const char *str);
4609 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_read_from_str(
4610 isl_ctx *ctx, const char *str);
4611 __isl_give isl_union_pw_multi_aff *
4612 isl_union_pw_multi_aff_read_from_str(
4613 isl_ctx *ctx, const char *str);
4615 An expression can be printed using
4617 #include <isl/aff.h>
4618 __isl_give isl_printer *isl_printer_print_multi_aff(
4619 __isl_take isl_printer *p,
4620 __isl_keep isl_multi_aff *maff);
4621 __isl_give isl_printer *isl_printer_print_pw_multi_aff(
4622 __isl_take isl_printer *p,
4623 __isl_keep isl_pw_multi_aff *pma);
4624 __isl_give isl_printer *isl_printer_print_union_pw_multi_aff(
4625 __isl_take isl_printer *p,
4626 __isl_keep isl_union_pw_multi_aff *upma);
4627 __isl_give isl_printer *isl_printer_print_multi_pw_aff(
4628 __isl_take isl_printer *p,
4629 __isl_keep isl_multi_pw_aff *mpa);
4633 Points are elements of a set. They can be used to construct
4634 simple sets (boxes) or they can be used to represent the
4635 individual elements of a set.
4636 The zero point (the origin) can be created using
4638 __isl_give isl_point *isl_point_zero(__isl_take isl_space *space);
4640 The coordinates of a point can be inspected, set and changed
4643 __isl_give isl_val *isl_point_get_coordinate_val(
4644 __isl_keep isl_point *pnt,
4645 enum isl_dim_type type, int pos);
4646 __isl_give isl_point *isl_point_set_coordinate_val(
4647 __isl_take isl_point *pnt,
4648 enum isl_dim_type type, int pos,
4649 __isl_take isl_val *v);
4651 __isl_give isl_point *isl_point_add_ui(
4652 __isl_take isl_point *pnt,
4653 enum isl_dim_type type, int pos, unsigned val);
4654 __isl_give isl_point *isl_point_sub_ui(
4655 __isl_take isl_point *pnt,
4656 enum isl_dim_type type, int pos, unsigned val);
4658 Other properties can be obtained using
4660 isl_ctx *isl_point_get_ctx(__isl_keep isl_point *pnt);
4662 Points can be copied or freed using
4664 __isl_give isl_point *isl_point_copy(
4665 __isl_keep isl_point *pnt);
4666 void isl_point_free(__isl_take isl_point *pnt);
4668 A singleton set can be created from a point using
4670 __isl_give isl_basic_set *isl_basic_set_from_point(
4671 __isl_take isl_point *pnt);
4672 __isl_give isl_set *isl_set_from_point(
4673 __isl_take isl_point *pnt);
4675 and a box can be created from two opposite extremal points using
4677 __isl_give isl_basic_set *isl_basic_set_box_from_points(
4678 __isl_take isl_point *pnt1,
4679 __isl_take isl_point *pnt2);
4680 __isl_give isl_set *isl_set_box_from_points(
4681 __isl_take isl_point *pnt1,
4682 __isl_take isl_point *pnt2);
4684 All elements of a B<bounded> (union) set can be enumerated using
4685 the following functions.
4687 int isl_set_foreach_point(__isl_keep isl_set *set,
4688 int (*fn)(__isl_take isl_point *pnt, void *user),
4690 int isl_union_set_foreach_point(__isl_keep isl_union_set *uset,
4691 int (*fn)(__isl_take isl_point *pnt, void *user),
4694 The function C<fn> is called for each integer point in
4695 C<set> with as second argument the last argument of
4696 the C<isl_set_foreach_point> call. The function C<fn>
4697 should return C<0> on success and C<-1> on failure.
4698 In the latter case, C<isl_set_foreach_point> will stop
4699 enumerating and return C<-1> as well.
4700 If the enumeration is performed successfully and to completion,
4701 then C<isl_set_foreach_point> returns C<0>.
4703 To obtain a single point of a (basic) set, use
4705 __isl_give isl_point *isl_basic_set_sample_point(
4706 __isl_take isl_basic_set *bset);
4707 __isl_give isl_point *isl_set_sample_point(
4708 __isl_take isl_set *set);
4710 If C<set> does not contain any (integer) points, then the
4711 resulting point will be ``void'', a property that can be
4714 int isl_point_is_void(__isl_keep isl_point *pnt);
4716 =head2 Piecewise Quasipolynomials
4718 A piecewise quasipolynomial is a particular kind of function that maps
4719 a parametric point to a rational value.
4720 More specifically, a quasipolynomial is a polynomial expression in greatest
4721 integer parts of affine expressions of parameters and variables.
4722 A piecewise quasipolynomial is a subdivision of a given parametric
4723 domain into disjoint cells with a quasipolynomial associated to
4724 each cell. The value of the piecewise quasipolynomial at a given
4725 point is the value of the quasipolynomial associated to the cell
4726 that contains the point. Outside of the union of cells,
4727 the value is assumed to be zero.
4728 For example, the piecewise quasipolynomial
4730 [n] -> { [x] -> ((1 + n) - x) : x <= n and x >= 0 }
4732 maps C<x> to C<1 + n - x> for values of C<x> between C<0> and C<n>.
4733 A given piecewise quasipolynomial has a fixed domain dimension.
4734 Union piecewise quasipolynomials are used to contain piecewise quasipolynomials
4735 defined over different domains.
4736 Piecewise quasipolynomials are mainly used by the C<barvinok>
4737 library for representing the number of elements in a parametric set or map.
4738 For example, the piecewise quasipolynomial above represents
4739 the number of points in the map
4741 [n] -> { [x] -> [y] : x,y >= 0 and 0 <= x + y <= n }
4743 =head3 Input and Output
4745 Piecewise quasipolynomials can be read from input using
4747 __isl_give isl_union_pw_qpolynomial *
4748 isl_union_pw_qpolynomial_read_from_str(
4749 isl_ctx *ctx, const char *str);
4751 Quasipolynomials and piecewise quasipolynomials can be printed
4752 using the following functions.
4754 __isl_give isl_printer *isl_printer_print_qpolynomial(
4755 __isl_take isl_printer *p,
4756 __isl_keep isl_qpolynomial *qp);
4758 __isl_give isl_printer *isl_printer_print_pw_qpolynomial(
4759 __isl_take isl_printer *p,
4760 __isl_keep isl_pw_qpolynomial *pwqp);
4762 __isl_give isl_printer *isl_printer_print_union_pw_qpolynomial(
4763 __isl_take isl_printer *p,
4764 __isl_keep isl_union_pw_qpolynomial *upwqp);
4766 The output format of the printer
4767 needs to be set to either C<ISL_FORMAT_ISL> or C<ISL_FORMAT_C>.
4768 For C<isl_printer_print_union_pw_qpolynomial>, only C<ISL_FORMAT_ISL>
4770 In case of printing in C<ISL_FORMAT_C>, the user may want
4771 to set the names of all dimensions
4773 __isl_give isl_qpolynomial *isl_qpolynomial_set_dim_name(
4774 __isl_take isl_qpolynomial *qp,
4775 enum isl_dim_type type, unsigned pos,
4777 __isl_give isl_pw_qpolynomial *
4778 isl_pw_qpolynomial_set_dim_name(
4779 __isl_take isl_pw_qpolynomial *pwqp,
4780 enum isl_dim_type type, unsigned pos,
4783 =head3 Creating New (Piecewise) Quasipolynomials
4785 Some simple quasipolynomials can be created using the following functions.
4786 More complicated quasipolynomials can be created by applying
4787 operations such as addition and multiplication
4788 on the resulting quasipolynomials
4790 __isl_give isl_qpolynomial *isl_qpolynomial_zero_on_domain(
4791 __isl_take isl_space *domain);
4792 __isl_give isl_qpolynomial *isl_qpolynomial_one_on_domain(
4793 __isl_take isl_space *domain);
4794 __isl_give isl_qpolynomial *isl_qpolynomial_infty_on_domain(
4795 __isl_take isl_space *domain);
4796 __isl_give isl_qpolynomial *isl_qpolynomial_neginfty_on_domain(
4797 __isl_take isl_space *domain);
4798 __isl_give isl_qpolynomial *isl_qpolynomial_nan_on_domain(
4799 __isl_take isl_space *domain);
4800 __isl_give isl_qpolynomial *isl_qpolynomial_val_on_domain(
4801 __isl_take isl_space *domain,
4802 __isl_take isl_val *val);
4803 __isl_give isl_qpolynomial *isl_qpolynomial_var_on_domain(
4804 __isl_take isl_space *domain,
4805 enum isl_dim_type type, unsigned pos);
4806 __isl_give isl_qpolynomial *isl_qpolynomial_from_aff(
4807 __isl_take isl_aff *aff);
4809 Note that the space in which a quasipolynomial lives is a map space
4810 with a one-dimensional range. The C<domain> argument in some of
4811 the functions above corresponds to the domain of this map space.
4813 The zero piecewise quasipolynomial or a piecewise quasipolynomial
4814 with a single cell can be created using the following functions.
4815 Multiple of these single cell piecewise quasipolynomials can
4816 be combined to create more complicated piecewise quasipolynomials.
4818 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_zero(
4819 __isl_take isl_space *space);
4820 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_alloc(
4821 __isl_take isl_set *set,
4822 __isl_take isl_qpolynomial *qp);
4823 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_from_qpolynomial(
4824 __isl_take isl_qpolynomial *qp);
4825 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_from_pw_aff(
4826 __isl_take isl_pw_aff *pwaff);
4828 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_zero(
4829 __isl_take isl_space *space);
4830 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_from_pw_qpolynomial(
4831 __isl_take isl_pw_qpolynomial *pwqp);
4832 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_add_pw_qpolynomial(
4833 __isl_take isl_union_pw_qpolynomial *upwqp,
4834 __isl_take isl_pw_qpolynomial *pwqp);
4836 Quasipolynomials can be copied and freed again using the following
4839 __isl_give isl_qpolynomial *isl_qpolynomial_copy(
4840 __isl_keep isl_qpolynomial *qp);
4841 void *isl_qpolynomial_free(__isl_take isl_qpolynomial *qp);
4843 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_copy(
4844 __isl_keep isl_pw_qpolynomial *pwqp);
4845 void *isl_pw_qpolynomial_free(
4846 __isl_take isl_pw_qpolynomial *pwqp);
4848 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_copy(
4849 __isl_keep isl_union_pw_qpolynomial *upwqp);
4850 void *isl_union_pw_qpolynomial_free(
4851 __isl_take isl_union_pw_qpolynomial *upwqp);
4853 =head3 Inspecting (Piecewise) Quasipolynomials
4855 To iterate over all piecewise quasipolynomials in a union
4856 piecewise quasipolynomial, use the following function
4858 int isl_union_pw_qpolynomial_foreach_pw_qpolynomial(
4859 __isl_keep isl_union_pw_qpolynomial *upwqp,
4860 int (*fn)(__isl_take isl_pw_qpolynomial *pwqp, void *user),
4863 To extract the piecewise quasipolynomial in a given space from a union, use
4865 __isl_give isl_pw_qpolynomial *
4866 isl_union_pw_qpolynomial_extract_pw_qpolynomial(
4867 __isl_keep isl_union_pw_qpolynomial *upwqp,
4868 __isl_take isl_space *space);
4870 To iterate over the cells in a piecewise quasipolynomial,
4871 use either of the following two functions
4873 int isl_pw_qpolynomial_foreach_piece(
4874 __isl_keep isl_pw_qpolynomial *pwqp,
4875 int (*fn)(__isl_take isl_set *set,
4876 __isl_take isl_qpolynomial *qp,
4877 void *user), void *user);
4878 int isl_pw_qpolynomial_foreach_lifted_piece(
4879 __isl_keep isl_pw_qpolynomial *pwqp,
4880 int (*fn)(__isl_take isl_set *set,
4881 __isl_take isl_qpolynomial *qp,
4882 void *user), void *user);
4884 As usual, the function C<fn> should return C<0> on success
4885 and C<-1> on failure. The difference between
4886 C<isl_pw_qpolynomial_foreach_piece> and
4887 C<isl_pw_qpolynomial_foreach_lifted_piece> is that
4888 C<isl_pw_qpolynomial_foreach_lifted_piece> will first
4889 compute unique representations for all existentially quantified
4890 variables and then turn these existentially quantified variables
4891 into extra set variables, adapting the associated quasipolynomial
4892 accordingly. This means that the C<set> passed to C<fn>
4893 will not have any existentially quantified variables, but that
4894 the dimensions of the sets may be different for different
4895 invocations of C<fn>.
4897 The constant term of a quasipolynomial can be extracted using
4899 __isl_give isl_val *isl_qpolynomial_get_constant_val(
4900 __isl_keep isl_qpolynomial *qp);
4902 To iterate over all terms in a quasipolynomial,
4905 int isl_qpolynomial_foreach_term(
4906 __isl_keep isl_qpolynomial *qp,
4907 int (*fn)(__isl_take isl_term *term,
4908 void *user), void *user);
4910 The terms themselves can be inspected and freed using
4913 unsigned isl_term_dim(__isl_keep isl_term *term,
4914 enum isl_dim_type type);
4915 __isl_give isl_val *isl_term_get_coefficient_val(
4916 __isl_keep isl_term *term);
4917 int isl_term_get_exp(__isl_keep isl_term *term,
4918 enum isl_dim_type type, unsigned pos);
4919 __isl_give isl_aff *isl_term_get_div(
4920 __isl_keep isl_term *term, unsigned pos);
4921 void isl_term_free(__isl_take isl_term *term);
4923 Each term is a product of parameters, set variables and
4924 integer divisions. The function C<isl_term_get_exp>
4925 returns the exponent of a given dimensions in the given term.
4927 =head3 Properties of (Piecewise) Quasipolynomials
4929 To check whether two union piecewise quasipolynomials are
4930 obviously equal, use
4932 int isl_union_pw_qpolynomial_plain_is_equal(
4933 __isl_keep isl_union_pw_qpolynomial *upwqp1,
4934 __isl_keep isl_union_pw_qpolynomial *upwqp2);
4936 =head3 Operations on (Piecewise) Quasipolynomials
4938 __isl_give isl_qpolynomial *isl_qpolynomial_scale_val(
4939 __isl_take isl_qpolynomial *qp,
4940 __isl_take isl_val *v);
4941 __isl_give isl_qpolynomial *isl_qpolynomial_neg(
4942 __isl_take isl_qpolynomial *qp);
4943 __isl_give isl_qpolynomial *isl_qpolynomial_add(
4944 __isl_take isl_qpolynomial *qp1,
4945 __isl_take isl_qpolynomial *qp2);
4946 __isl_give isl_qpolynomial *isl_qpolynomial_sub(
4947 __isl_take isl_qpolynomial *qp1,
4948 __isl_take isl_qpolynomial *qp2);
4949 __isl_give isl_qpolynomial *isl_qpolynomial_mul(
4950 __isl_take isl_qpolynomial *qp1,
4951 __isl_take isl_qpolynomial *qp2);
4952 __isl_give isl_qpolynomial *isl_qpolynomial_pow(
4953 __isl_take isl_qpolynomial *qp, unsigned exponent);
4955 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_fix_val(
4956 __isl_take isl_pw_qpolynomial *pwqp,
4957 enum isl_dim_type type, unsigned n,
4958 __isl_take isl_val *v);
4959 __isl_give isl_pw_qpolynomial *
4960 isl_pw_qpolynomial_scale_val(
4961 __isl_take isl_pw_qpolynomial *pwqp,
4962 __isl_take isl_val *v);
4963 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_add(
4964 __isl_take isl_pw_qpolynomial *pwqp1,
4965 __isl_take isl_pw_qpolynomial *pwqp2);
4966 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_sub(
4967 __isl_take isl_pw_qpolynomial *pwqp1,
4968 __isl_take isl_pw_qpolynomial *pwqp2);
4969 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_add_disjoint(
4970 __isl_take isl_pw_qpolynomial *pwqp1,
4971 __isl_take isl_pw_qpolynomial *pwqp2);
4972 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_neg(
4973 __isl_take isl_pw_qpolynomial *pwqp);
4974 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_mul(
4975 __isl_take isl_pw_qpolynomial *pwqp1,
4976 __isl_take isl_pw_qpolynomial *pwqp2);
4977 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_pow(
4978 __isl_take isl_pw_qpolynomial *pwqp, unsigned exponent);
4980 __isl_give isl_union_pw_qpolynomial *
4981 isl_union_pw_qpolynomial_scale_val(
4982 __isl_take isl_union_pw_qpolynomial *upwqp,
4983 __isl_take isl_val *v);
4984 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_add(
4985 __isl_take isl_union_pw_qpolynomial *upwqp1,
4986 __isl_take isl_union_pw_qpolynomial *upwqp2);
4987 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_sub(
4988 __isl_take isl_union_pw_qpolynomial *upwqp1,
4989 __isl_take isl_union_pw_qpolynomial *upwqp2);
4990 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_mul(
4991 __isl_take isl_union_pw_qpolynomial *upwqp1,
4992 __isl_take isl_union_pw_qpolynomial *upwqp2);
4994 __isl_give isl_val *isl_pw_qpolynomial_eval(
4995 __isl_take isl_pw_qpolynomial *pwqp,
4996 __isl_take isl_point *pnt);
4998 __isl_give isl_val *isl_union_pw_qpolynomial_eval(
4999 __isl_take isl_union_pw_qpolynomial *upwqp,
5000 __isl_take isl_point *pnt);
5002 __isl_give isl_set *isl_pw_qpolynomial_domain(
5003 __isl_take isl_pw_qpolynomial *pwqp);
5004 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_intersect_domain(
5005 __isl_take isl_pw_qpolynomial *pwpq,
5006 __isl_take isl_set *set);
5007 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_intersect_params(
5008 __isl_take isl_pw_qpolynomial *pwpq,
5009 __isl_take isl_set *set);
5011 __isl_give isl_union_set *isl_union_pw_qpolynomial_domain(
5012 __isl_take isl_union_pw_qpolynomial *upwqp);
5013 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_intersect_domain(
5014 __isl_take isl_union_pw_qpolynomial *upwpq,
5015 __isl_take isl_union_set *uset);
5016 __isl_give isl_union_pw_qpolynomial *
5017 isl_union_pw_qpolynomial_intersect_params(
5018 __isl_take isl_union_pw_qpolynomial *upwpq,
5019 __isl_take isl_set *set);
5021 __isl_give isl_qpolynomial *isl_qpolynomial_align_params(
5022 __isl_take isl_qpolynomial *qp,
5023 __isl_take isl_space *model);
5025 __isl_give isl_qpolynomial *isl_qpolynomial_project_domain_on_params(
5026 __isl_take isl_qpolynomial *qp);
5027 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_project_domain_on_params(
5028 __isl_take isl_pw_qpolynomial *pwqp);
5030 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_coalesce(
5031 __isl_take isl_union_pw_qpolynomial *upwqp);
5033 __isl_give isl_qpolynomial *isl_qpolynomial_gist_params(
5034 __isl_take isl_qpolynomial *qp,
5035 __isl_take isl_set *context);
5036 __isl_give isl_qpolynomial *isl_qpolynomial_gist(
5037 __isl_take isl_qpolynomial *qp,
5038 __isl_take isl_set *context);
5040 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_gist_params(
5041 __isl_take isl_pw_qpolynomial *pwqp,
5042 __isl_take isl_set *context);
5043 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_gist(
5044 __isl_take isl_pw_qpolynomial *pwqp,
5045 __isl_take isl_set *context);
5047 __isl_give isl_union_pw_qpolynomial *
5048 isl_union_pw_qpolynomial_gist_params(
5049 __isl_take isl_union_pw_qpolynomial *upwqp,
5050 __isl_take isl_set *context);
5051 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_gist(
5052 __isl_take isl_union_pw_qpolynomial *upwqp,
5053 __isl_take isl_union_set *context);
5055 The gist operation applies the gist operation to each of
5056 the cells in the domain of the input piecewise quasipolynomial.
5057 The context is also exploited
5058 to simplify the quasipolynomials associated to each cell.
5060 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_to_polynomial(
5061 __isl_take isl_pw_qpolynomial *pwqp, int sign);
5062 __isl_give isl_union_pw_qpolynomial *
5063 isl_union_pw_qpolynomial_to_polynomial(
5064 __isl_take isl_union_pw_qpolynomial *upwqp, int sign);
5066 Approximate each quasipolynomial by a polynomial. If C<sign> is positive,
5067 the polynomial will be an overapproximation. If C<sign> is negative,
5068 it will be an underapproximation. If C<sign> is zero, the approximation
5069 will lie somewhere in between.
5071 =head2 Bounds on Piecewise Quasipolynomials and Piecewise Quasipolynomial Reductions
5073 A piecewise quasipolynomial reduction is a piecewise
5074 reduction (or fold) of quasipolynomials.
5075 In particular, the reduction can be maximum or a minimum.
5076 The objects are mainly used to represent the result of
5077 an upper or lower bound on a quasipolynomial over its domain,
5078 i.e., as the result of the following function.
5080 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_bound(
5081 __isl_take isl_pw_qpolynomial *pwqp,
5082 enum isl_fold type, int *tight);
5084 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_bound(
5085 __isl_take isl_union_pw_qpolynomial *upwqp,
5086 enum isl_fold type, int *tight);
5088 The C<type> argument may be either C<isl_fold_min> or C<isl_fold_max>.
5089 If C<tight> is not C<NULL>, then C<*tight> is set to C<1>
5090 is the returned bound is known be tight, i.e., for each value
5091 of the parameters there is at least
5092 one element in the domain that reaches the bound.
5093 If the domain of C<pwqp> is not wrapping, then the bound is computed
5094 over all elements in that domain and the result has a purely parametric
5095 domain. If the domain of C<pwqp> is wrapping, then the bound is
5096 computed over the range of the wrapped relation. The domain of the
5097 wrapped relation becomes the domain of the result.
5099 A (piecewise) quasipolynomial reduction can be copied or freed using the
5100 following functions.
5102 __isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_copy(
5103 __isl_keep isl_qpolynomial_fold *fold);
5104 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_copy(
5105 __isl_keep isl_pw_qpolynomial_fold *pwf);
5106 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_copy(
5107 __isl_keep isl_union_pw_qpolynomial_fold *upwf);
5108 void isl_qpolynomial_fold_free(
5109 __isl_take isl_qpolynomial_fold *fold);
5110 void *isl_pw_qpolynomial_fold_free(
5111 __isl_take isl_pw_qpolynomial_fold *pwf);
5112 void *isl_union_pw_qpolynomial_fold_free(
5113 __isl_take isl_union_pw_qpolynomial_fold *upwf);
5115 =head3 Printing Piecewise Quasipolynomial Reductions
5117 Piecewise quasipolynomial reductions can be printed
5118 using the following function.
5120 __isl_give isl_printer *isl_printer_print_pw_qpolynomial_fold(
5121 __isl_take isl_printer *p,
5122 __isl_keep isl_pw_qpolynomial_fold *pwf);
5123 __isl_give isl_printer *isl_printer_print_union_pw_qpolynomial_fold(
5124 __isl_take isl_printer *p,
5125 __isl_keep isl_union_pw_qpolynomial_fold *upwf);
5127 For C<isl_printer_print_pw_qpolynomial_fold>,
5128 output format of the printer
5129 needs to be set to either C<ISL_FORMAT_ISL> or C<ISL_FORMAT_C>.
5130 For C<isl_printer_print_union_pw_qpolynomial_fold>,
5131 output format of the printer
5132 needs to be set to C<ISL_FORMAT_ISL>.
5133 In case of printing in C<ISL_FORMAT_C>, the user may want
5134 to set the names of all dimensions
5136 __isl_give isl_pw_qpolynomial_fold *
5137 isl_pw_qpolynomial_fold_set_dim_name(
5138 __isl_take isl_pw_qpolynomial_fold *pwf,
5139 enum isl_dim_type type, unsigned pos,
5142 =head3 Inspecting (Piecewise) Quasipolynomial Reductions
5144 To iterate over all piecewise quasipolynomial reductions in a union
5145 piecewise quasipolynomial reduction, use the following function
5147 int isl_union_pw_qpolynomial_fold_foreach_pw_qpolynomial_fold(
5148 __isl_keep isl_union_pw_qpolynomial_fold *upwf,
5149 int (*fn)(__isl_take isl_pw_qpolynomial_fold *pwf,
5150 void *user), void *user);
5152 To iterate over the cells in a piecewise quasipolynomial reduction,
5153 use either of the following two functions
5155 int isl_pw_qpolynomial_fold_foreach_piece(
5156 __isl_keep isl_pw_qpolynomial_fold *pwf,
5157 int (*fn)(__isl_take isl_set *set,
5158 __isl_take isl_qpolynomial_fold *fold,
5159 void *user), void *user);
5160 int isl_pw_qpolynomial_fold_foreach_lifted_piece(
5161 __isl_keep isl_pw_qpolynomial_fold *pwf,
5162 int (*fn)(__isl_take isl_set *set,
5163 __isl_take isl_qpolynomial_fold *fold,
5164 void *user), void *user);
5166 See L<Inspecting (Piecewise) Quasipolynomials> for an explanation
5167 of the difference between these two functions.
5169 To iterate over all quasipolynomials in a reduction, use
5171 int isl_qpolynomial_fold_foreach_qpolynomial(
5172 __isl_keep isl_qpolynomial_fold *fold,
5173 int (*fn)(__isl_take isl_qpolynomial *qp,
5174 void *user), void *user);
5176 =head3 Properties of Piecewise Quasipolynomial Reductions
5178 To check whether two union piecewise quasipolynomial reductions are
5179 obviously equal, use
5181 int isl_union_pw_qpolynomial_fold_plain_is_equal(
5182 __isl_keep isl_union_pw_qpolynomial_fold *upwf1,
5183 __isl_keep isl_union_pw_qpolynomial_fold *upwf2);
5185 =head3 Operations on Piecewise Quasipolynomial Reductions
5187 __isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_scale_val(
5188 __isl_take isl_qpolynomial_fold *fold,
5189 __isl_take isl_val *v);
5190 __isl_give isl_pw_qpolynomial_fold *
5191 isl_pw_qpolynomial_fold_scale_val(
5192 __isl_take isl_pw_qpolynomial_fold *pwf,
5193 __isl_take isl_val *v);
5194 __isl_give isl_union_pw_qpolynomial_fold *
5195 isl_union_pw_qpolynomial_fold_scale_val(
5196 __isl_take isl_union_pw_qpolynomial_fold *upwf,
5197 __isl_take isl_val *v);
5199 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_add(
5200 __isl_take isl_pw_qpolynomial_fold *pwf1,
5201 __isl_take isl_pw_qpolynomial_fold *pwf2);
5203 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_fold(
5204 __isl_take isl_pw_qpolynomial_fold *pwf1,
5205 __isl_take isl_pw_qpolynomial_fold *pwf2);
5207 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_fold(
5208 __isl_take isl_union_pw_qpolynomial_fold *upwf1,
5209 __isl_take isl_union_pw_qpolynomial_fold *upwf2);
5211 __isl_give isl_val *isl_pw_qpolynomial_fold_eval(
5212 __isl_take isl_pw_qpolynomial_fold *pwf,
5213 __isl_take isl_point *pnt);
5215 __isl_give isl_val *isl_union_pw_qpolynomial_fold_eval(
5216 __isl_take isl_union_pw_qpolynomial_fold *upwf,
5217 __isl_take isl_point *pnt);
5219 __isl_give isl_pw_qpolynomial_fold *
5220 isl_pw_qpolynomial_fold_intersect_params(
5221 __isl_take isl_pw_qpolynomial_fold *pwf,
5222 __isl_take isl_set *set);
5224 __isl_give isl_union_set *isl_union_pw_qpolynomial_fold_domain(
5225 __isl_take isl_union_pw_qpolynomial_fold *upwf);
5226 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_intersect_domain(
5227 __isl_take isl_union_pw_qpolynomial_fold *upwf,
5228 __isl_take isl_union_set *uset);
5229 __isl_give isl_union_pw_qpolynomial_fold *
5230 isl_union_pw_qpolynomial_fold_intersect_params(
5231 __isl_take isl_union_pw_qpolynomial_fold *upwf,
5232 __isl_take isl_set *set);
5234 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_project_domain_on_params(
5235 __isl_take isl_pw_qpolynomial_fold *pwf);
5237 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_coalesce(
5238 __isl_take isl_pw_qpolynomial_fold *pwf);
5240 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_coalesce(
5241 __isl_take isl_union_pw_qpolynomial_fold *upwf);
5243 __isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_gist_params(
5244 __isl_take isl_qpolynomial_fold *fold,
5245 __isl_take isl_set *context);
5246 __isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_gist(
5247 __isl_take isl_qpolynomial_fold *fold,
5248 __isl_take isl_set *context);
5250 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_gist(
5251 __isl_take isl_pw_qpolynomial_fold *pwf,
5252 __isl_take isl_set *context);
5253 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_gist_params(
5254 __isl_take isl_pw_qpolynomial_fold *pwf,
5255 __isl_take isl_set *context);
5257 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_gist(
5258 __isl_take isl_union_pw_qpolynomial_fold *upwf,
5259 __isl_take isl_union_set *context);
5260 __isl_give isl_union_pw_qpolynomial_fold *
5261 isl_union_pw_qpolynomial_fold_gist_params(
5262 __isl_take isl_union_pw_qpolynomial_fold *upwf,
5263 __isl_take isl_set *context);
5265 The gist operation applies the gist operation to each of
5266 the cells in the domain of the input piecewise quasipolynomial reduction.
5267 In future, the operation will also exploit the context
5268 to simplify the quasipolynomial reductions associated to each cell.
5270 __isl_give isl_pw_qpolynomial_fold *
5271 isl_set_apply_pw_qpolynomial_fold(
5272 __isl_take isl_set *set,
5273 __isl_take isl_pw_qpolynomial_fold *pwf,
5275 __isl_give isl_pw_qpolynomial_fold *
5276 isl_map_apply_pw_qpolynomial_fold(
5277 __isl_take isl_map *map,
5278 __isl_take isl_pw_qpolynomial_fold *pwf,
5280 __isl_give isl_union_pw_qpolynomial_fold *
5281 isl_union_set_apply_union_pw_qpolynomial_fold(
5282 __isl_take isl_union_set *uset,
5283 __isl_take isl_union_pw_qpolynomial_fold *upwf,
5285 __isl_give isl_union_pw_qpolynomial_fold *
5286 isl_union_map_apply_union_pw_qpolynomial_fold(
5287 __isl_take isl_union_map *umap,
5288 __isl_take isl_union_pw_qpolynomial_fold *upwf,
5291 The functions taking a map
5292 compose the given map with the given piecewise quasipolynomial reduction.
5293 That is, compute a bound (of the same type as C<pwf> or C<upwf> itself)
5294 over all elements in the intersection of the range of the map
5295 and the domain of the piecewise quasipolynomial reduction
5296 as a function of an element in the domain of the map.
5297 The functions taking a set compute a bound over all elements in the
5298 intersection of the set and the domain of the
5299 piecewise quasipolynomial reduction.
5301 =head2 Parametric Vertex Enumeration
5303 The parametric vertex enumeration described in this section
5304 is mainly intended to be used internally and by the C<barvinok>
5307 #include <isl/vertices.h>
5308 __isl_give isl_vertices *isl_basic_set_compute_vertices(
5309 __isl_keep isl_basic_set *bset);
5311 The function C<isl_basic_set_compute_vertices> performs the
5312 actual computation of the parametric vertices and the chamber
5313 decomposition and store the result in an C<isl_vertices> object.
5314 This information can be queried by either iterating over all
5315 the vertices or iterating over all the chambers or cells
5316 and then iterating over all vertices that are active on the chamber.
5318 int isl_vertices_foreach_vertex(
5319 __isl_keep isl_vertices *vertices,
5320 int (*fn)(__isl_take isl_vertex *vertex, void *user),
5323 int isl_vertices_foreach_cell(
5324 __isl_keep isl_vertices *vertices,
5325 int (*fn)(__isl_take isl_cell *cell, void *user),
5327 int isl_cell_foreach_vertex(__isl_keep isl_cell *cell,
5328 int (*fn)(__isl_take isl_vertex *vertex, void *user),
5331 Other operations that can be performed on an C<isl_vertices> object are
5334 isl_ctx *isl_vertices_get_ctx(
5335 __isl_keep isl_vertices *vertices);
5336 int isl_vertices_get_n_vertices(
5337 __isl_keep isl_vertices *vertices);
5338 void isl_vertices_free(__isl_take isl_vertices *vertices);
5340 Vertices can be inspected and destroyed using the following functions.
5342 isl_ctx *isl_vertex_get_ctx(__isl_keep isl_vertex *vertex);
5343 int isl_vertex_get_id(__isl_keep isl_vertex *vertex);
5344 __isl_give isl_basic_set *isl_vertex_get_domain(
5345 __isl_keep isl_vertex *vertex);
5346 __isl_give isl_basic_set *isl_vertex_get_expr(
5347 __isl_keep isl_vertex *vertex);
5348 void isl_vertex_free(__isl_take isl_vertex *vertex);
5350 C<isl_vertex_get_expr> returns a singleton parametric set describing
5351 the vertex, while C<isl_vertex_get_domain> returns the activity domain
5353 Note that C<isl_vertex_get_domain> and C<isl_vertex_get_expr> return
5354 B<rational> basic sets, so they should mainly be used for inspection
5355 and should not be mixed with integer sets.
5357 Chambers can be inspected and destroyed using the following functions.
5359 isl_ctx *isl_cell_get_ctx(__isl_keep isl_cell *cell);
5360 __isl_give isl_basic_set *isl_cell_get_domain(
5361 __isl_keep isl_cell *cell);
5362 void isl_cell_free(__isl_take isl_cell *cell);
5364 =head1 Polyhedral Compilation Library
5366 This section collects functionality in C<isl> that has been specifically
5367 designed for use during polyhedral compilation.
5369 =head2 Dependence Analysis
5371 C<isl> contains specialized functionality for performing
5372 array dataflow analysis. That is, given a I<sink> access relation
5373 and a collection of possible I<source> access relations,
5374 C<isl> can compute relations that describe
5375 for each iteration of the sink access, which iteration
5376 of which of the source access relations was the last
5377 to access the same data element before the given iteration
5379 The resulting dependence relations map source iterations
5380 to the corresponding sink iterations.
5381 To compute standard flow dependences, the sink should be
5382 a read, while the sources should be writes.
5383 If any of the source accesses are marked as being I<may>
5384 accesses, then there will be a dependence from the last
5385 I<must> access B<and> from any I<may> access that follows
5386 this last I<must> access.
5387 In particular, if I<all> sources are I<may> accesses,
5388 then memory based dependence analysis is performed.
5389 If, on the other hand, all sources are I<must> accesses,
5390 then value based dependence analysis is performed.
5392 #include <isl/flow.h>
5394 typedef int (*isl_access_level_before)(void *first, void *second);
5396 __isl_give isl_access_info *isl_access_info_alloc(
5397 __isl_take isl_map *sink,
5398 void *sink_user, isl_access_level_before fn,
5400 __isl_give isl_access_info *isl_access_info_add_source(
5401 __isl_take isl_access_info *acc,
5402 __isl_take isl_map *source, int must,
5404 void *isl_access_info_free(__isl_take isl_access_info *acc);
5406 __isl_give isl_flow *isl_access_info_compute_flow(
5407 __isl_take isl_access_info *acc);
5409 int isl_flow_foreach(__isl_keep isl_flow *deps,
5410 int (*fn)(__isl_take isl_map *dep, int must,
5411 void *dep_user, void *user),
5413 __isl_give isl_map *isl_flow_get_no_source(
5414 __isl_keep isl_flow *deps, int must);
5415 void isl_flow_free(__isl_take isl_flow *deps);
5417 The function C<isl_access_info_compute_flow> performs the actual
5418 dependence analysis. The other functions are used to construct
5419 the input for this function or to read off the output.
5421 The input is collected in an C<isl_access_info>, which can
5422 be created through a call to C<isl_access_info_alloc>.
5423 The arguments to this functions are the sink access relation
5424 C<sink>, a token C<sink_user> used to identify the sink
5425 access to the user, a callback function for specifying the
5426 relative order of source and sink accesses, and the number
5427 of source access relations that will be added.
5428 The callback function has type C<int (*)(void *first, void *second)>.
5429 The function is called with two user supplied tokens identifying
5430 either a source or the sink and it should return the shared nesting
5431 level and the relative order of the two accesses.
5432 In particular, let I<n> be the number of loops shared by
5433 the two accesses. If C<first> precedes C<second> textually,
5434 then the function should return I<2 * n + 1>; otherwise,
5435 it should return I<2 * n>.
5436 The sources can be added to the C<isl_access_info> by performing
5437 (at most) C<max_source> calls to C<isl_access_info_add_source>.
5438 C<must> indicates whether the source is a I<must> access
5439 or a I<may> access. Note that a multi-valued access relation
5440 should only be marked I<must> if every iteration in the domain
5441 of the relation accesses I<all> elements in its image.
5442 The C<source_user> token is again used to identify
5443 the source access. The range of the source access relation
5444 C<source> should have the same dimension as the range
5445 of the sink access relation.
5446 The C<isl_access_info_free> function should usually not be
5447 called explicitly, because it is called implicitly by
5448 C<isl_access_info_compute_flow>.
5450 The result of the dependence analysis is collected in an
5451 C<isl_flow>. There may be elements of
5452 the sink access for which no preceding source access could be
5453 found or for which all preceding sources are I<may> accesses.
5454 The relations containing these elements can be obtained through
5455 calls to C<isl_flow_get_no_source>, the first with C<must> set
5456 and the second with C<must> unset.
5457 In the case of standard flow dependence analysis,
5458 with the sink a read and the sources I<must> writes,
5459 the first relation corresponds to the reads from uninitialized
5460 array elements and the second relation is empty.
5461 The actual flow dependences can be extracted using
5462 C<isl_flow_foreach>. This function will call the user-specified
5463 callback function C<fn> for each B<non-empty> dependence between
5464 a source and the sink. The callback function is called
5465 with four arguments, the actual flow dependence relation
5466 mapping source iterations to sink iterations, a boolean that
5467 indicates whether it is a I<must> or I<may> dependence, a token
5468 identifying the source and an additional C<void *> with value
5469 equal to the third argument of the C<isl_flow_foreach> call.
5470 A dependence is marked I<must> if it originates from a I<must>
5471 source and if it is not followed by any I<may> sources.
5473 After finishing with an C<isl_flow>, the user should call
5474 C<isl_flow_free> to free all associated memory.
5476 A higher-level interface to dependence analysis is provided
5477 by the following function.
5479 #include <isl/flow.h>
5481 int isl_union_map_compute_flow(__isl_take isl_union_map *sink,
5482 __isl_take isl_union_map *must_source,
5483 __isl_take isl_union_map *may_source,
5484 __isl_take isl_union_map *schedule,
5485 __isl_give isl_union_map **must_dep,
5486 __isl_give isl_union_map **may_dep,
5487 __isl_give isl_union_map **must_no_source,
5488 __isl_give isl_union_map **may_no_source);
5490 The arrays are identified by the tuple names of the ranges
5491 of the accesses. The iteration domains by the tuple names
5492 of the domains of the accesses and of the schedule.
5493 The relative order of the iteration domains is given by the
5494 schedule. The relations returned through C<must_no_source>
5495 and C<may_no_source> are subsets of C<sink>.
5496 Any of C<must_dep>, C<may_dep>, C<must_no_source>
5497 or C<may_no_source> may be C<NULL>, but a C<NULL> value for
5498 any of the other arguments is treated as an error.
5500 =head3 Interaction with Dependence Analysis
5502 During the dependence analysis, we frequently need to perform
5503 the following operation. Given a relation between sink iterations
5504 and potential source iterations from a particular source domain,
5505 what is the last potential source iteration corresponding to each
5506 sink iteration. It can sometimes be convenient to adjust
5507 the set of potential source iterations before or after each such operation.
5508 The prototypical example is fuzzy array dataflow analysis,
5509 where we need to analyze if, based on data-dependent constraints,
5510 the sink iteration can ever be executed without one or more of
5511 the corresponding potential source iterations being executed.
5512 If so, we can introduce extra parameters and select an unknown
5513 but fixed source iteration from the potential source iterations.
5514 To be able to perform such manipulations, C<isl> provides the following
5517 #include <isl/flow.h>
5519 typedef __isl_give isl_restriction *(*isl_access_restrict)(
5520 __isl_keep isl_map *source_map,
5521 __isl_keep isl_set *sink, void *source_user,
5523 __isl_give isl_access_info *isl_access_info_set_restrict(
5524 __isl_take isl_access_info *acc,
5525 isl_access_restrict fn, void *user);
5527 The function C<isl_access_info_set_restrict> should be called
5528 before calling C<isl_access_info_compute_flow> and registers a callback function
5529 that will be called any time C<isl> is about to compute the last
5530 potential source. The first argument is the (reverse) proto-dependence,
5531 mapping sink iterations to potential source iterations.
5532 The second argument represents the sink iterations for which
5533 we want to compute the last source iteration.
5534 The third argument is the token corresponding to the source
5535 and the final argument is the token passed to C<isl_access_info_set_restrict>.
5536 The callback is expected to return a restriction on either the input or
5537 the output of the operation computing the last potential source.
5538 If the input needs to be restricted then restrictions are needed
5539 for both the source and the sink iterations. The sink iterations
5540 and the potential source iterations will be intersected with these sets.
5541 If the output needs to be restricted then only a restriction on the source
5542 iterations is required.
5543 If any error occurs, the callback should return C<NULL>.
5544 An C<isl_restriction> object can be created, freed and inspected
5545 using the following functions.
5547 #include <isl/flow.h>
5549 __isl_give isl_restriction *isl_restriction_input(
5550 __isl_take isl_set *source_restr,
5551 __isl_take isl_set *sink_restr);
5552 __isl_give isl_restriction *isl_restriction_output(
5553 __isl_take isl_set *source_restr);
5554 __isl_give isl_restriction *isl_restriction_none(
5555 __isl_take isl_map *source_map);
5556 __isl_give isl_restriction *isl_restriction_empty(
5557 __isl_take isl_map *source_map);
5558 void *isl_restriction_free(
5559 __isl_take isl_restriction *restr);
5560 isl_ctx *isl_restriction_get_ctx(
5561 __isl_keep isl_restriction *restr);
5563 C<isl_restriction_none> and C<isl_restriction_empty> are special
5564 cases of C<isl_restriction_input>. C<isl_restriction_none>
5565 is essentially equivalent to
5567 isl_restriction_input(isl_set_universe(
5568 isl_space_range(isl_map_get_space(source_map))),
5570 isl_space_domain(isl_map_get_space(source_map))));
5572 whereas C<isl_restriction_empty> is essentially equivalent to
5574 isl_restriction_input(isl_set_empty(
5575 isl_space_range(isl_map_get_space(source_map))),
5577 isl_space_domain(isl_map_get_space(source_map))));
5581 B<The functionality described in this section is fairly new
5582 and may be subject to change.>
5584 The following function can be used to compute a schedule
5585 for a union of domains.
5586 By default, the algorithm used to construct the schedule is similar
5587 to that of C<Pluto>.
5588 Alternatively, Feautrier's multi-dimensional scheduling algorithm can
5590 The generated schedule respects all C<validity> dependences.
5591 That is, all dependence distances over these dependences in the
5592 scheduled space are lexicographically positive.
5593 The default algorithm tries to minimize the dependence distances over
5594 C<proximity> dependences.
5595 Moreover, it tries to obtain sequences (bands) of schedule dimensions
5596 for groups of domains where the dependence distances have only
5597 non-negative values.
5598 When using Feautrier's algorithm, the C<proximity> dependence
5599 distances are only minimized during the extension to a
5600 full-dimensional schedule.
5602 #include <isl/schedule.h>
5603 __isl_give isl_schedule *isl_union_set_compute_schedule(
5604 __isl_take isl_union_set *domain,
5605 __isl_take isl_union_map *validity,
5606 __isl_take isl_union_map *proximity);
5607 void *isl_schedule_free(__isl_take isl_schedule *sched);
5609 A mapping from the domains to the scheduled space can be obtained
5610 from an C<isl_schedule> using the following function.
5612 __isl_give isl_union_map *isl_schedule_get_map(
5613 __isl_keep isl_schedule *sched);
5615 A representation of the schedule can be printed using
5617 __isl_give isl_printer *isl_printer_print_schedule(
5618 __isl_take isl_printer *p,
5619 __isl_keep isl_schedule *schedule);
5621 A representation of the schedule as a forest of bands can be obtained
5622 using the following function.
5624 __isl_give isl_band_list *isl_schedule_get_band_forest(
5625 __isl_keep isl_schedule *schedule);
5627 The individual bands can be visited in depth-first post-order
5628 using the following function.
5630 #include <isl/schedule.h>
5631 int isl_schedule_foreach_band(
5632 __isl_keep isl_schedule *sched,
5633 int (*fn)(__isl_keep isl_band *band, void *user),
5636 The list can be manipulated as explained in L<"Lists">.
5637 The bands inside the list can be copied and freed using the following
5640 #include <isl/band.h>
5641 __isl_give isl_band *isl_band_copy(
5642 __isl_keep isl_band *band);
5643 void *isl_band_free(__isl_take isl_band *band);
5645 Each band contains zero or more scheduling dimensions.
5646 These are referred to as the members of the band.
5647 The section of the schedule that corresponds to the band is
5648 referred to as the partial schedule of the band.
5649 For those nodes that participate in a band, the outer scheduling
5650 dimensions form the prefix schedule, while the inner scheduling
5651 dimensions form the suffix schedule.
5652 That is, if we take a cut of the band forest, then the union of
5653 the concatenations of the prefix, partial and suffix schedules of
5654 each band in the cut is equal to the entire schedule (modulo
5655 some possible padding at the end with zero scheduling dimensions).
5656 The properties of a band can be inspected using the following functions.
5658 #include <isl/band.h>
5659 isl_ctx *isl_band_get_ctx(__isl_keep isl_band *band);
5661 int isl_band_has_children(__isl_keep isl_band *band);
5662 __isl_give isl_band_list *isl_band_get_children(
5663 __isl_keep isl_band *band);
5665 __isl_give isl_union_map *isl_band_get_prefix_schedule(
5666 __isl_keep isl_band *band);
5667 __isl_give isl_union_map *isl_band_get_partial_schedule(
5668 __isl_keep isl_band *band);
5669 __isl_give isl_union_map *isl_band_get_suffix_schedule(
5670 __isl_keep isl_band *band);
5672 int isl_band_n_member(__isl_keep isl_band *band);
5673 int isl_band_member_is_zero_distance(
5674 __isl_keep isl_band *band, int pos);
5676 int isl_band_list_foreach_band(
5677 __isl_keep isl_band_list *list,
5678 int (*fn)(__isl_keep isl_band *band, void *user),
5681 Note that a scheduling dimension is considered to be ``zero
5682 distance'' if it does not carry any proximity dependences
5684 That is, if the dependence distances of the proximity
5685 dependences are all zero in that direction (for fixed
5686 iterations of outer bands).
5687 Like C<isl_schedule_foreach_band>,
5688 the function C<isl_band_list_foreach_band> calls C<fn> on the bands
5689 in depth-first post-order.
5691 A band can be tiled using the following function.
5693 #include <isl/band.h>
5694 int isl_band_tile(__isl_keep isl_band *band,
5695 __isl_take isl_vec *sizes);
5697 int isl_options_set_tile_scale_tile_loops(isl_ctx *ctx,
5699 int isl_options_get_tile_scale_tile_loops(isl_ctx *ctx);
5700 int isl_options_set_tile_shift_point_loops(isl_ctx *ctx,
5702 int isl_options_get_tile_shift_point_loops(isl_ctx *ctx);
5704 The C<isl_band_tile> function tiles the band using the given tile sizes
5705 inside its schedule.
5706 A new child band is created to represent the point loops and it is
5707 inserted between the modified band and its children.
5708 The C<tile_scale_tile_loops> option specifies whether the tile
5709 loops iterators should be scaled by the tile sizes.
5710 If the C<tile_shift_point_loops> option is set, then the point loops
5711 are shifted to start at zero.
5713 A band can be split into two nested bands using the following function.
5715 int isl_band_split(__isl_keep isl_band *band, int pos);
5717 The resulting outer band contains the first C<pos> dimensions of C<band>
5718 while the inner band contains the remaining dimensions.
5720 A representation of the band can be printed using
5722 #include <isl/band.h>
5723 __isl_give isl_printer *isl_printer_print_band(
5724 __isl_take isl_printer *p,
5725 __isl_keep isl_band *band);
5729 #include <isl/schedule.h>
5730 int isl_options_set_schedule_max_coefficient(
5731 isl_ctx *ctx, int val);
5732 int isl_options_get_schedule_max_coefficient(
5734 int isl_options_set_schedule_max_constant_term(
5735 isl_ctx *ctx, int val);
5736 int isl_options_get_schedule_max_constant_term(
5738 int isl_options_set_schedule_fuse(isl_ctx *ctx, int val);
5739 int isl_options_get_schedule_fuse(isl_ctx *ctx);
5740 int isl_options_set_schedule_maximize_band_depth(
5741 isl_ctx *ctx, int val);
5742 int isl_options_get_schedule_maximize_band_depth(
5744 int isl_options_set_schedule_outer_zero_distance(
5745 isl_ctx *ctx, int val);
5746 int isl_options_get_schedule_outer_zero_distance(
5748 int isl_options_set_schedule_split_scaled(
5749 isl_ctx *ctx, int val);
5750 int isl_options_get_schedule_split_scaled(
5752 int isl_options_set_schedule_algorithm(
5753 isl_ctx *ctx, int val);
5754 int isl_options_get_schedule_algorithm(
5756 int isl_options_set_schedule_separate_components(
5757 isl_ctx *ctx, int val);
5758 int isl_options_get_schedule_separate_components(
5763 =item * schedule_max_coefficient
5765 This option enforces that the coefficients for variable and parameter
5766 dimensions in the calculated schedule are not larger than the specified value.
5767 This option can significantly increase the speed of the scheduling calculation
5768 and may also prevent fusing of unrelated dimensions. A value of -1 means that
5769 this option does not introduce bounds on the variable or parameter
5772 =item * schedule_max_constant_term
5774 This option enforces that the constant coefficients in the calculated schedule
5775 are not larger than the maximal constant term. This option can significantly
5776 increase the speed of the scheduling calculation and may also prevent fusing of
5777 unrelated dimensions. A value of -1 means that this option does not introduce
5778 bounds on the constant coefficients.
5780 =item * schedule_fuse
5782 This option controls the level of fusion.
5783 If this option is set to C<ISL_SCHEDULE_FUSE_MIN>, then loops in the
5784 resulting schedule will be distributed as much as possible.
5785 If this option is set to C<ISL_SCHEDULE_FUSE_MAX>, then C<isl> will
5786 try to fuse loops in the resulting schedule.
5788 =item * schedule_maximize_band_depth
5790 If this option is set, we do not split bands at the point
5791 where we detect splitting is necessary. Instead, we
5792 backtrack and split bands as early as possible. This
5793 reduces the number of splits and maximizes the width of
5794 the bands. Wider bands give more possibilities for tiling.
5795 Note that if the C<schedule_fuse> option is set to C<ISL_SCHEDULE_FUSE_MIN>,
5796 then bands will be split as early as possible, even if there is no need.
5797 The C<schedule_maximize_band_depth> option therefore has no effect in this case.
5799 =item * schedule_outer_zero_distance
5801 If this option is set, then we try to construct schedules
5802 where the outermost scheduling dimension in each band
5803 results in a zero dependence distance over the proximity
5806 =item * schedule_split_scaled
5808 If this option is set, then we try to construct schedules in which the
5809 constant term is split off from the linear part if the linear parts of
5810 the scheduling rows for all nodes in the graphs have a common non-trivial
5812 The constant term is then placed in a separate band and the linear
5815 =item * schedule_algorithm
5817 Selects the scheduling algorithm to be used.
5818 Available scheduling algorithms are C<ISL_SCHEDULE_ALGORITHM_ISL>
5819 and C<ISL_SCHEDULE_ALGORITHM_FEAUTRIER>.
5821 =item * schedule_separate_components
5823 If at any point the dependence graph contains any (weakly connected) components,
5824 then these components are scheduled separately.
5825 If this option is not set, then some iterations of the domains
5826 in these components may be scheduled together.
5827 If this option is set, then the components are given consecutive
5832 =head2 AST Generation
5834 This section describes the C<isl> functionality for generating
5835 ASTs that visit all the elements
5836 in a domain in an order specified by a schedule.
5837 In particular, given a C<isl_union_map>, an AST is generated
5838 that visits all the elements in the domain of the C<isl_union_map>
5839 according to the lexicographic order of the corresponding image
5840 element(s). If the range of the C<isl_union_map> consists of
5841 elements in more than one space, then each of these spaces is handled
5842 separately in an arbitrary order.
5843 It should be noted that the image elements only specify the I<order>
5844 in which the corresponding domain elements should be visited.
5845 No direct relation between the image elements and the loop iterators
5846 in the generated AST should be assumed.
5848 Each AST is generated within a build. The initial build
5849 simply specifies the constraints on the parameters (if any)
5850 and can be created, inspected, copied and freed using the following functions.
5852 #include <isl/ast_build.h>
5853 __isl_give isl_ast_build *isl_ast_build_from_context(
5854 __isl_take isl_set *set);
5855 isl_ctx *isl_ast_build_get_ctx(
5856 __isl_keep isl_ast_build *build);
5857 __isl_give isl_ast_build *isl_ast_build_copy(
5858 __isl_keep isl_ast_build *build);
5859 void *isl_ast_build_free(
5860 __isl_take isl_ast_build *build);
5862 The C<set> argument is usually a parameter set with zero or more parameters.
5863 More C<isl_ast_build> functions are described in L</"Nested AST Generation">
5864 and L</"Fine-grained Control over AST Generation">.
5865 Finally, the AST itself can be constructed using the following
5868 #include <isl/ast_build.h>
5869 __isl_give isl_ast_node *isl_ast_build_ast_from_schedule(
5870 __isl_keep isl_ast_build *build,
5871 __isl_take isl_union_map *schedule);
5873 =head3 Inspecting the AST
5875 The basic properties of an AST node can be obtained as follows.
5877 #include <isl/ast.h>
5878 isl_ctx *isl_ast_node_get_ctx(
5879 __isl_keep isl_ast_node *node);
5880 enum isl_ast_node_type isl_ast_node_get_type(
5881 __isl_keep isl_ast_node *node);
5883 The type of an AST node is one of
5884 C<isl_ast_node_for>,
5886 C<isl_ast_node_block> or
5887 C<isl_ast_node_user>.
5888 An C<isl_ast_node_for> represents a for node.
5889 An C<isl_ast_node_if> represents an if node.
5890 An C<isl_ast_node_block> represents a compound node.
5891 An C<isl_ast_node_user> represents an expression statement.
5892 An expression statement typically corresponds to a domain element, i.e.,
5893 one of the elements that is visited by the AST.
5895 Each type of node has its own additional properties.
5897 #include <isl/ast.h>
5898 __isl_give isl_ast_expr *isl_ast_node_for_get_iterator(
5899 __isl_keep isl_ast_node *node);
5900 __isl_give isl_ast_expr *isl_ast_node_for_get_init(
5901 __isl_keep isl_ast_node *node);
5902 __isl_give isl_ast_expr *isl_ast_node_for_get_cond(
5903 __isl_keep isl_ast_node *node);
5904 __isl_give isl_ast_expr *isl_ast_node_for_get_inc(
5905 __isl_keep isl_ast_node *node);
5906 __isl_give isl_ast_node *isl_ast_node_for_get_body(
5907 __isl_keep isl_ast_node *node);
5908 int isl_ast_node_for_is_degenerate(
5909 __isl_keep isl_ast_node *node);
5911 An C<isl_ast_for> is considered degenerate if it is known to execute
5914 #include <isl/ast.h>
5915 __isl_give isl_ast_expr *isl_ast_node_if_get_cond(
5916 __isl_keep isl_ast_node *node);
5917 __isl_give isl_ast_node *isl_ast_node_if_get_then(
5918 __isl_keep isl_ast_node *node);
5919 int isl_ast_node_if_has_else(
5920 __isl_keep isl_ast_node *node);
5921 __isl_give isl_ast_node *isl_ast_node_if_get_else(
5922 __isl_keep isl_ast_node *node);
5924 __isl_give isl_ast_node_list *
5925 isl_ast_node_block_get_children(
5926 __isl_keep isl_ast_node *node);
5928 __isl_give isl_ast_expr *isl_ast_node_user_get_expr(
5929 __isl_keep isl_ast_node *node);
5931 Each of the returned C<isl_ast_expr>s can in turn be inspected using
5932 the following functions.
5934 #include <isl/ast.h>
5935 isl_ctx *isl_ast_expr_get_ctx(
5936 __isl_keep isl_ast_expr *expr);
5937 enum isl_ast_expr_type isl_ast_expr_get_type(
5938 __isl_keep isl_ast_expr *expr);
5940 The type of an AST expression is one of
5942 C<isl_ast_expr_id> or
5943 C<isl_ast_expr_int>.
5944 An C<isl_ast_expr_op> represents the result of an operation.
5945 An C<isl_ast_expr_id> represents an identifier.
5946 An C<isl_ast_expr_int> represents an integer value.
5948 Each type of expression has its own additional properties.
5950 #include <isl/ast.h>
5951 enum isl_ast_op_type isl_ast_expr_get_op_type(
5952 __isl_keep isl_ast_expr *expr);
5953 int isl_ast_expr_get_op_n_arg(__isl_keep isl_ast_expr *expr);
5954 __isl_give isl_ast_expr *isl_ast_expr_get_op_arg(
5955 __isl_keep isl_ast_expr *expr, int pos);
5956 int isl_ast_node_foreach_ast_op_type(
5957 __isl_keep isl_ast_node *node,
5958 int (*fn)(enum isl_ast_op_type type, void *user),
5961 C<isl_ast_expr_get_op_type> returns the type of the operation
5962 performed. C<isl_ast_expr_get_op_n_arg> returns the number of
5963 arguments. C<isl_ast_expr_get_op_arg> returns the specified
5965 C<isl_ast_node_foreach_ast_op_type> calls C<fn> for each distinct
5966 C<isl_ast_op_type> that appears in C<node>.
5967 The operation type is one of the following.
5971 =item C<isl_ast_op_and>
5973 Logical I<and> of two arguments.
5974 Both arguments can be evaluated.
5976 =item C<isl_ast_op_and_then>
5978 Logical I<and> of two arguments.
5979 The second argument can only be evaluated if the first evaluates to true.
5981 =item C<isl_ast_op_or>
5983 Logical I<or> of two arguments.
5984 Both arguments can be evaluated.
5986 =item C<isl_ast_op_or_else>
5988 Logical I<or> of two arguments.
5989 The second argument can only be evaluated if the first evaluates to false.
5991 =item C<isl_ast_op_max>
5993 Maximum of two or more arguments.
5995 =item C<isl_ast_op_min>
5997 Minimum of two or more arguments.
5999 =item C<isl_ast_op_minus>
6003 =item C<isl_ast_op_add>
6005 Sum of two arguments.
6007 =item C<isl_ast_op_sub>
6009 Difference of two arguments.
6011 =item C<isl_ast_op_mul>
6013 Product of two arguments.
6015 =item C<isl_ast_op_div>
6017 Exact division. That is, the result is known to be an integer.
6019 =item C<isl_ast_op_fdiv_q>
6021 Result of integer division, rounded towards negative
6024 =item C<isl_ast_op_pdiv_q>
6026 Result of integer division, where dividend is known to be non-negative.
6028 =item C<isl_ast_op_pdiv_r>
6030 Remainder of integer division, where dividend is known to be non-negative.
6032 =item C<isl_ast_op_cond>
6034 Conditional operator defined on three arguments.
6035 If the first argument evaluates to true, then the result
6036 is equal to the second argument. Otherwise, the result
6037 is equal to the third argument.
6038 The second and third argument may only be evaluated if
6039 the first argument evaluates to true and false, respectively.
6040 Corresponds to C<a ? b : c> in C.
6042 =item C<isl_ast_op_select>
6044 Conditional operator defined on three arguments.
6045 If the first argument evaluates to true, then the result
6046 is equal to the second argument. Otherwise, the result
6047 is equal to the third argument.
6048 The second and third argument may be evaluated independently
6049 of the value of the first argument.
6050 Corresponds to C<a * b + (1 - a) * c> in C.
6052 =item C<isl_ast_op_eq>
6056 =item C<isl_ast_op_le>
6058 Less than or equal relation.
6060 =item C<isl_ast_op_lt>
6064 =item C<isl_ast_op_ge>
6066 Greater than or equal relation.
6068 =item C<isl_ast_op_gt>
6070 Greater than relation.
6072 =item C<isl_ast_op_call>
6075 The number of arguments of the C<isl_ast_expr> is one more than
6076 the number of arguments in the function call, the first argument
6077 representing the function being called.
6079 =item C<isl_ast_op_access>
6082 The number of arguments of the C<isl_ast_expr> is one more than
6083 the number of index expressions in the array access, the first argument
6084 representing the array being accessed.
6088 #include <isl/ast.h>
6089 __isl_give isl_id *isl_ast_expr_get_id(
6090 __isl_keep isl_ast_expr *expr);
6092 Return the identifier represented by the AST expression.
6094 #include <isl/ast.h>
6095 __isl_give isl_val *isl_ast_expr_get_val(
6096 __isl_keep isl_ast_expr *expr);
6098 Return the integer represented by the AST expression.
6100 =head3 Properties of ASTs
6102 #include <isl/ast.h>
6103 int isl_ast_expr_is_equal(__isl_keep isl_ast_expr *expr1,
6104 __isl_keep isl_ast_expr *expr2);
6106 Check if two C<isl_ast_expr>s are equal to each other.
6108 =head3 Manipulating and printing the AST
6110 AST nodes can be copied and freed using the following functions.
6112 #include <isl/ast.h>
6113 __isl_give isl_ast_node *isl_ast_node_copy(
6114 __isl_keep isl_ast_node *node);
6115 void *isl_ast_node_free(__isl_take isl_ast_node *node);
6117 AST expressions can be copied and freed using the following functions.
6119 #include <isl/ast.h>
6120 __isl_give isl_ast_expr *isl_ast_expr_copy(
6121 __isl_keep isl_ast_expr *expr);
6122 void *isl_ast_expr_free(__isl_take isl_ast_expr *expr);
6124 New AST expressions can be created either directly or within
6125 the context of an C<isl_ast_build>.
6127 #include <isl/ast.h>
6128 __isl_give isl_ast_expr *isl_ast_expr_from_val(
6129 __isl_take isl_val *v);
6130 __isl_give isl_ast_expr *isl_ast_expr_from_id(
6131 __isl_take isl_id *id);
6132 __isl_give isl_ast_expr *isl_ast_expr_neg(
6133 __isl_take isl_ast_expr *expr);
6134 __isl_give isl_ast_expr *isl_ast_expr_add(
6135 __isl_take isl_ast_expr *expr1,
6136 __isl_take isl_ast_expr *expr2);
6137 __isl_give isl_ast_expr *isl_ast_expr_sub(
6138 __isl_take isl_ast_expr *expr1,
6139 __isl_take isl_ast_expr *expr2);
6140 __isl_give isl_ast_expr *isl_ast_expr_mul(
6141 __isl_take isl_ast_expr *expr1,
6142 __isl_take isl_ast_expr *expr2);
6143 __isl_give isl_ast_expr *isl_ast_expr_div(
6144 __isl_take isl_ast_expr *expr1,
6145 __isl_take isl_ast_expr *expr2);
6146 __isl_give isl_ast_expr *isl_ast_expr_and(
6147 __isl_take isl_ast_expr *expr1,
6148 __isl_take isl_ast_expr *expr2)
6149 __isl_give isl_ast_expr *isl_ast_expr_or(
6150 __isl_take isl_ast_expr *expr1,
6151 __isl_take isl_ast_expr *expr2)
6152 __isl_give isl_ast_expr *isl_ast_expr_access(
6153 __isl_take isl_ast_expr *array,
6154 __isl_take isl_ast_expr_list *indices);
6155 __isl_give isl_ast_expr *isl_ast_expr_substitute_ids(
6156 __isl_take isl_ast_expr *expr,
6157 __isl_take isl_id_to_ast_expr *id2expr);
6159 The function C<isl_ast_expr_substitute_ids> replaces the
6160 subexpressions of C<expr> of type C<isl_ast_expr_id>
6161 by the corresponding expression in C<id2expr>, if there is any.
6163 #include <isl/ast_build.h>
6164 __isl_give isl_ast_expr *isl_ast_build_expr_from_pw_aff(
6165 __isl_keep isl_ast_build *build,
6166 __isl_take isl_pw_aff *pa);
6167 __isl_give isl_ast_expr *
6168 isl_ast_build_access_from_pw_multi_aff(
6169 __isl_keep isl_ast_build *build,
6170 __isl_take isl_pw_multi_aff *pma);
6171 __isl_give isl_ast_expr *
6172 isl_ast_build_access_from_multi_pw_aff(
6173 __isl_keep isl_ast_build *build,
6174 __isl_take isl_multi_pw_aff *mpa);
6175 __isl_give isl_ast_expr *
6176 isl_ast_build_call_from_pw_multi_aff(
6177 __isl_keep isl_ast_build *build,
6178 __isl_take isl_pw_multi_aff *pma);
6179 __isl_give isl_ast_expr *
6180 isl_ast_build_call_from_multi_pw_aff(
6181 __isl_keep isl_ast_build *build,
6182 __isl_take isl_multi_pw_aff *mpa);
6184 The domains of C<pa>, C<mpa> and C<pma> should correspond
6185 to the schedule space of C<build>.
6186 The tuple id of C<mpa> or C<pma> is used as the array being accessed or
6187 the function being called.
6189 User specified data can be attached to an C<isl_ast_node> and obtained
6190 from the same C<isl_ast_node> using the following functions.
6192 #include <isl/ast.h>
6193 __isl_give isl_ast_node *isl_ast_node_set_annotation(
6194 __isl_take isl_ast_node *node,
6195 __isl_take isl_id *annotation);
6196 __isl_give isl_id *isl_ast_node_get_annotation(
6197 __isl_keep isl_ast_node *node);
6199 Basic printing can be performed using the following functions.
6201 #include <isl/ast.h>
6202 __isl_give isl_printer *isl_printer_print_ast_expr(
6203 __isl_take isl_printer *p,
6204 __isl_keep isl_ast_expr *expr);
6205 __isl_give isl_printer *isl_printer_print_ast_node(
6206 __isl_take isl_printer *p,
6207 __isl_keep isl_ast_node *node);
6209 More advanced printing can be performed using the following functions.
6211 #include <isl/ast.h>
6212 __isl_give isl_printer *isl_ast_op_type_print_macro(
6213 enum isl_ast_op_type type,
6214 __isl_take isl_printer *p);
6215 __isl_give isl_printer *isl_ast_node_print_macros(
6216 __isl_keep isl_ast_node *node,
6217 __isl_take isl_printer *p);
6218 __isl_give isl_printer *isl_ast_node_print(
6219 __isl_keep isl_ast_node *node,
6220 __isl_take isl_printer *p,
6221 __isl_take isl_ast_print_options *options);
6222 __isl_give isl_printer *isl_ast_node_for_print(
6223 __isl_keep isl_ast_node *node,
6224 __isl_take isl_printer *p,
6225 __isl_take isl_ast_print_options *options);
6226 __isl_give isl_printer *isl_ast_node_if_print(
6227 __isl_keep isl_ast_node *node,
6228 __isl_take isl_printer *p,
6229 __isl_take isl_ast_print_options *options);
6231 While printing an C<isl_ast_node> in C<ISL_FORMAT_C>,
6232 C<isl> may print out an AST that makes use of macros such
6233 as C<floord>, C<min> and C<max>.
6234 C<isl_ast_op_type_print_macro> prints out the macro
6235 corresponding to a specific C<isl_ast_op_type>.
6236 C<isl_ast_node_print_macros> scans the C<isl_ast_node>
6237 for expressions where these macros would be used and prints
6238 out the required macro definitions.
6239 Essentially, C<isl_ast_node_print_macros> calls
6240 C<isl_ast_node_foreach_ast_op_type> with C<isl_ast_op_type_print_macro>
6241 as function argument.
6242 C<isl_ast_node_print>, C<isl_ast_node_for_print> and
6243 C<isl_ast_node_if_print> print an C<isl_ast_node>
6244 in C<ISL_FORMAT_C>, but allow for some extra control
6245 through an C<isl_ast_print_options> object.
6246 This object can be created using the following functions.
6248 #include <isl/ast.h>
6249 __isl_give isl_ast_print_options *
6250 isl_ast_print_options_alloc(isl_ctx *ctx);
6251 __isl_give isl_ast_print_options *
6252 isl_ast_print_options_copy(
6253 __isl_keep isl_ast_print_options *options);
6254 void *isl_ast_print_options_free(
6255 __isl_take isl_ast_print_options *options);
6257 __isl_give isl_ast_print_options *
6258 isl_ast_print_options_set_print_user(
6259 __isl_take isl_ast_print_options *options,
6260 __isl_give isl_printer *(*print_user)(
6261 __isl_take isl_printer *p,
6262 __isl_take isl_ast_print_options *options,
6263 __isl_keep isl_ast_node *node, void *user),
6265 __isl_give isl_ast_print_options *
6266 isl_ast_print_options_set_print_for(
6267 __isl_take isl_ast_print_options *options,
6268 __isl_give isl_printer *(*print_for)(
6269 __isl_take isl_printer *p,
6270 __isl_take isl_ast_print_options *options,
6271 __isl_keep isl_ast_node *node, void *user),
6274 The callback set by C<isl_ast_print_options_set_print_user>
6275 is called whenever a node of type C<isl_ast_node_user> needs to
6277 The callback set by C<isl_ast_print_options_set_print_for>
6278 is called whenever a node of type C<isl_ast_node_for> needs to
6280 Note that C<isl_ast_node_for_print> will I<not> call the
6281 callback set by C<isl_ast_print_options_set_print_for> on the node
6282 on which C<isl_ast_node_for_print> is called, but only on nested
6283 nodes of type C<isl_ast_node_for>. It is therefore safe to
6284 call C<isl_ast_node_for_print> from within the callback set by
6285 C<isl_ast_print_options_set_print_for>.
6287 The following option determines the type to be used for iterators
6288 while printing the AST.
6290 int isl_options_set_ast_iterator_type(
6291 isl_ctx *ctx, const char *val);
6292 const char *isl_options_get_ast_iterator_type(
6297 #include <isl/ast_build.h>
6298 int isl_options_set_ast_build_atomic_upper_bound(
6299 isl_ctx *ctx, int val);
6300 int isl_options_get_ast_build_atomic_upper_bound(
6302 int isl_options_set_ast_build_prefer_pdiv(isl_ctx *ctx,
6304 int isl_options_get_ast_build_prefer_pdiv(isl_ctx *ctx);
6305 int isl_options_set_ast_build_exploit_nested_bounds(
6306 isl_ctx *ctx, int val);
6307 int isl_options_get_ast_build_exploit_nested_bounds(
6309 int isl_options_set_ast_build_group_coscheduled(
6310 isl_ctx *ctx, int val);
6311 int isl_options_get_ast_build_group_coscheduled(
6313 int isl_options_set_ast_build_scale_strides(
6314 isl_ctx *ctx, int val);
6315 int isl_options_get_ast_build_scale_strides(
6317 int isl_options_set_ast_build_allow_else(isl_ctx *ctx,
6319 int isl_options_get_ast_build_allow_else(isl_ctx *ctx);
6320 int isl_options_set_ast_build_allow_or(isl_ctx *ctx,
6322 int isl_options_get_ast_build_allow_or(isl_ctx *ctx);
6326 =item * ast_build_atomic_upper_bound
6328 Generate loop upper bounds that consist of the current loop iterator,
6329 an operator and an expression not involving the iterator.
6330 If this option is not set, then the current loop iterator may appear
6331 several times in the upper bound.
6332 For example, when this option is turned off, AST generation
6335 [n] -> { A[i] -> [i] : 0 <= i <= 100, n }
6339 for (int c0 = 0; c0 <= 100 && n >= c0; c0 += 1)
6342 When the option is turned on, the following AST is generated
6344 for (int c0 = 0; c0 <= min(100, n); c0 += 1)
6347 =item * ast_build_prefer_pdiv
6349 If this option is turned off, then the AST generation will
6350 produce ASTs that may only contain C<isl_ast_op_fdiv_q>
6351 operators, but no C<isl_ast_op_pdiv_q> or
6352 C<isl_ast_op_pdiv_r> operators.
6353 If this options is turned on, then C<isl> will try to convert
6354 some of the C<isl_ast_op_fdiv_q> operators to (expressions containing)
6355 C<isl_ast_op_pdiv_q> or C<isl_ast_op_pdiv_r> operators.
6357 =item * ast_build_exploit_nested_bounds
6359 Simplify conditions based on bounds of nested for loops.
6360 In particular, remove conditions that are implied by the fact
6361 that one or more nested loops have at least one iteration,
6362 meaning that the upper bound is at least as large as the lower bound.
6363 For example, when this option is turned off, AST generation
6366 [N,M] -> { A[i,j] -> [i,j] : 0 <= i <= N and
6372 for (int c0 = 0; c0 <= N; c0 += 1)
6373 for (int c1 = 0; c1 <= M; c1 += 1)
6376 When the option is turned on, the following AST is generated
6378 for (int c0 = 0; c0 <= N; c0 += 1)
6379 for (int c1 = 0; c1 <= M; c1 += 1)
6382 =item * ast_build_group_coscheduled
6384 If two domain elements are assigned the same schedule point, then
6385 they may be executed in any order and they may even appear in different
6386 loops. If this options is set, then the AST generator will make
6387 sure that coscheduled domain elements do not appear in separate parts
6388 of the AST. This is useful in case of nested AST generation
6389 if the outer AST generation is given only part of a schedule
6390 and the inner AST generation should handle the domains that are
6391 coscheduled by this initial part of the schedule together.
6392 For example if an AST is generated for a schedule
6394 { A[i] -> [0]; B[i] -> [0] }
6396 then the C<isl_ast_build_set_create_leaf> callback described
6397 below may get called twice, once for each domain.
6398 Setting this option ensures that the callback is only called once
6399 on both domains together.
6401 =item * ast_build_separation_bounds
6403 This option specifies which bounds to use during separation.
6404 If this option is set to C<ISL_AST_BUILD_SEPARATION_BOUNDS_IMPLICIT>
6405 then all (possibly implicit) bounds on the current dimension will
6406 be used during separation.
6407 If this option is set to C<ISL_AST_BUILD_SEPARATION_BOUNDS_EXPLICIT>
6408 then only those bounds that are explicitly available will
6409 be used during separation.
6411 =item * ast_build_scale_strides
6413 This option specifies whether the AST generator is allowed
6414 to scale down iterators of strided loops.
6416 =item * ast_build_allow_else
6418 This option specifies whether the AST generator is allowed
6419 to construct if statements with else branches.
6421 =item * ast_build_allow_or
6423 This option specifies whether the AST generator is allowed
6424 to construct if conditions with disjunctions.
6428 =head3 Fine-grained Control over AST Generation
6430 Besides specifying the constraints on the parameters,
6431 an C<isl_ast_build> object can be used to control
6432 various aspects of the AST generation process.
6433 The most prominent way of control is through ``options'',
6434 which can be set using the following function.
6436 #include <isl/ast_build.h>
6437 __isl_give isl_ast_build *
6438 isl_ast_build_set_options(
6439 __isl_take isl_ast_build *control,
6440 __isl_take isl_union_map *options);
6442 The options are encoded in an <isl_union_map>.
6443 The domain of this union relation refers to the schedule domain,
6444 i.e., the range of the schedule passed to C<isl_ast_build_ast_from_schedule>.
6445 In the case of nested AST generation (see L</"Nested AST Generation">),
6446 the domain of C<options> should refer to the extra piece of the schedule.
6447 That is, it should be equal to the range of the wrapped relation in the
6448 range of the schedule.
6449 The range of the options can consist of elements in one or more spaces,
6450 the names of which determine the effect of the option.
6451 The values of the range typically also refer to the schedule dimension
6452 to which the option applies. In case of nested AST generation
6453 (see L</"Nested AST Generation">), these values refer to the position
6454 of the schedule dimension within the innermost AST generation.
6455 The constraints on the domain elements of
6456 the option should only refer to this dimension and earlier dimensions.
6457 We consider the following spaces.
6461 =item C<separation_class>
6463 This space is a wrapped relation between two one dimensional spaces.
6464 The input space represents the schedule dimension to which the option
6465 applies and the output space represents the separation class.
6466 While constructing a loop corresponding to the specified schedule
6467 dimension(s), the AST generator will try to generate separate loops
6468 for domain elements that are assigned different classes.
6469 If only some of the elements are assigned a class, then those elements
6470 that are not assigned any class will be treated as belonging to a class
6471 that is separate from the explicitly assigned classes.
6472 The typical use case for this option is to separate full tiles from
6474 The other options, described below, are applied after the separation
6477 As an example, consider the separation into full and partial tiles
6478 of a tiling of a triangular domain.
6479 Take, for example, the domain
6481 { A[i,j] : 0 <= i,j and i + j <= 100 }
6483 and a tiling into tiles of 10 by 10. The input to the AST generator
6484 is then the schedule
6486 { A[i,j] -> [([i/10]),[j/10],i,j] : 0 <= i,j and
6489 Without any options, the following AST is generated
6491 for (int c0 = 0; c0 <= 10; c0 += 1)
6492 for (int c1 = 0; c1 <= -c0 + 10; c1 += 1)
6493 for (int c2 = 10 * c0;
6494 c2 <= min(-10 * c1 + 100, 10 * c0 + 9);
6496 for (int c3 = 10 * c1;
6497 c3 <= min(10 * c1 + 9, -c2 + 100);
6501 Separation into full and partial tiles can be obtained by assigning
6502 a class, say C<0>, to the full tiles. The full tiles are represented by those
6503 values of the first and second schedule dimensions for which there are
6504 values of the third and fourth dimensions to cover an entire tile.
6505 That is, we need to specify the following option
6507 { [a,b,c,d] -> separation_class[[0]->[0]] :
6508 exists b': 0 <= 10a,10b' and
6509 10a+9+10b'+9 <= 100;
6510 [a,b,c,d] -> separation_class[[1]->[0]] :
6511 0 <= 10a,10b and 10a+9+10b+9 <= 100 }
6515 { [a, b, c, d] -> separation_class[[1] -> [0]] :
6516 a >= 0 and b >= 0 and b <= 8 - a;
6517 [a, b, c, d] -> separation_class[[0] -> [0]] :
6520 With this option, the generated AST is as follows
6523 for (int c0 = 0; c0 <= 8; c0 += 1) {
6524 for (int c1 = 0; c1 <= -c0 + 8; c1 += 1)
6525 for (int c2 = 10 * c0;
6526 c2 <= 10 * c0 + 9; c2 += 1)
6527 for (int c3 = 10 * c1;
6528 c3 <= 10 * c1 + 9; c3 += 1)
6530 for (int c1 = -c0 + 9; c1 <= -c0 + 10; c1 += 1)
6531 for (int c2 = 10 * c0;
6532 c2 <= min(-10 * c1 + 100, 10 * c0 + 9);
6534 for (int c3 = 10 * c1;
6535 c3 <= min(-c2 + 100, 10 * c1 + 9);
6539 for (int c0 = 9; c0 <= 10; c0 += 1)
6540 for (int c1 = 0; c1 <= -c0 + 10; c1 += 1)
6541 for (int c2 = 10 * c0;
6542 c2 <= min(-10 * c1 + 100, 10 * c0 + 9);
6544 for (int c3 = 10 * c1;
6545 c3 <= min(10 * c1 + 9, -c2 + 100);
6552 This is a single-dimensional space representing the schedule dimension(s)
6553 to which ``separation'' should be applied. Separation tries to split
6554 a loop into several pieces if this can avoid the generation of guards
6556 See also the C<atomic> option.
6560 This is a single-dimensional space representing the schedule dimension(s)
6561 for which the domains should be considered ``atomic''. That is, the
6562 AST generator will make sure that any given domain space will only appear
6563 in a single loop at the specified level.
6565 Consider the following schedule
6567 { a[i] -> [i] : 0 <= i < 10;
6568 b[i] -> [i+1] : 0 <= i < 10 }
6570 If the following option is specified
6572 { [i] -> separate[x] }
6574 then the following AST will be generated
6578 for (int c0 = 1; c0 <= 9; c0 += 1) {
6585 If, on the other hand, the following option is specified
6587 { [i] -> atomic[x] }
6589 then the following AST will be generated
6591 for (int c0 = 0; c0 <= 10; c0 += 1) {
6598 If neither C<atomic> nor C<separate> is specified, then the AST generator
6599 may produce either of these two results or some intermediate form.
6603 This is a single-dimensional space representing the schedule dimension(s)
6604 that should be I<completely> unrolled.
6605 To obtain a partial unrolling, the user should apply an additional
6606 strip-mining to the schedule and fully unroll the inner loop.
6610 Additional control is available through the following functions.
6612 #include <isl/ast_build.h>
6613 __isl_give isl_ast_build *
6614 isl_ast_build_set_iterators(
6615 __isl_take isl_ast_build *control,
6616 __isl_take isl_id_list *iterators);
6618 The function C<isl_ast_build_set_iterators> allows the user to
6619 specify a list of iterator C<isl_id>s to be used as iterators.
6620 If the input schedule is injective, then
6621 the number of elements in this list should be as large as the dimension
6622 of the schedule space, but no direct correspondence should be assumed
6623 between dimensions and elements.
6624 If the input schedule is not injective, then an additional number
6625 of C<isl_id>s equal to the largest dimension of the input domains
6627 If the number of provided C<isl_id>s is insufficient, then additional
6628 names are automatically generated.
6630 #include <isl/ast_build.h>
6631 __isl_give isl_ast_build *
6632 isl_ast_build_set_create_leaf(
6633 __isl_take isl_ast_build *control,
6634 __isl_give isl_ast_node *(*fn)(
6635 __isl_take isl_ast_build *build,
6636 void *user), void *user);
6639 C<isl_ast_build_set_create_leaf> function allows for the
6640 specification of a callback that should be called whenever the AST
6641 generator arrives at an element of the schedule domain.
6642 The callback should return an AST node that should be inserted
6643 at the corresponding position of the AST. The default action (when
6644 the callback is not set) is to continue generating parts of the AST to scan
6645 all the domain elements associated to the schedule domain element
6646 and to insert user nodes, ``calling'' the domain element, for each of them.
6647 The C<build> argument contains the current state of the C<isl_ast_build>.
6648 To ease nested AST generation (see L</"Nested AST Generation">),
6649 all control information that is
6650 specific to the current AST generation such as the options and
6651 the callbacks has been removed from this C<isl_ast_build>.
6652 The callback would typically return the result of a nested
6654 user defined node created using the following function.
6656 #include <isl/ast.h>
6657 __isl_give isl_ast_node *isl_ast_node_alloc_user(
6658 __isl_take isl_ast_expr *expr);
6660 #include <isl/ast_build.h>
6661 __isl_give isl_ast_build *
6662 isl_ast_build_set_at_each_domain(
6663 __isl_take isl_ast_build *build,
6664 __isl_give isl_ast_node *(*fn)(
6665 __isl_take isl_ast_node *node,
6666 __isl_keep isl_ast_build *build,
6667 void *user), void *user);
6668 __isl_give isl_ast_build *
6669 isl_ast_build_set_before_each_for(
6670 __isl_take isl_ast_build *build,
6671 __isl_give isl_id *(*fn)(
6672 __isl_keep isl_ast_build *build,
6673 void *user), void *user);
6674 __isl_give isl_ast_build *
6675 isl_ast_build_set_after_each_for(
6676 __isl_take isl_ast_build *build,
6677 __isl_give isl_ast_node *(*fn)(
6678 __isl_take isl_ast_node *node,
6679 __isl_keep isl_ast_build *build,
6680 void *user), void *user);
6682 The callback set by C<isl_ast_build_set_at_each_domain> will
6683 be called for each domain AST node.
6684 The callbacks set by C<isl_ast_build_set_before_each_for>
6685 and C<isl_ast_build_set_after_each_for> will be called
6686 for each for AST node. The first will be called in depth-first
6687 pre-order, while the second will be called in depth-first post-order.
6688 Since C<isl_ast_build_set_before_each_for> is called before the for
6689 node is actually constructed, it is only passed an C<isl_ast_build>.
6690 The returned C<isl_id> will be added as an annotation (using
6691 C<isl_ast_node_set_annotation>) to the constructed for node.
6692 In particular, if the user has also specified an C<after_each_for>
6693 callback, then the annotation can be retrieved from the node passed to
6694 that callback using C<isl_ast_node_get_annotation>.
6695 All callbacks should C<NULL> on failure.
6696 The given C<isl_ast_build> can be used to create new
6697 C<isl_ast_expr> objects using C<isl_ast_build_expr_from_pw_aff>
6698 or C<isl_ast_build_call_from_pw_multi_aff>.
6700 =head3 Nested AST Generation
6702 C<isl> allows the user to create an AST within the context
6703 of another AST. These nested ASTs are created using the
6704 same C<isl_ast_build_ast_from_schedule> function that is used to create the
6705 outer AST. The C<build> argument should be an C<isl_ast_build>
6706 passed to a callback set by
6707 C<isl_ast_build_set_create_leaf>.
6708 The space of the range of the C<schedule> argument should refer
6709 to this build. In particular, the space should be a wrapped
6710 relation and the domain of this wrapped relation should be the
6711 same as that of the range of the schedule returned by
6712 C<isl_ast_build_get_schedule> below.
6713 In practice, the new schedule is typically
6714 created by calling C<isl_union_map_range_product> on the old schedule
6715 and some extra piece of the schedule.
6716 The space of the schedule domain is also available from
6717 the C<isl_ast_build>.
6719 #include <isl/ast_build.h>
6720 __isl_give isl_union_map *isl_ast_build_get_schedule(
6721 __isl_keep isl_ast_build *build);
6722 __isl_give isl_space *isl_ast_build_get_schedule_space(
6723 __isl_keep isl_ast_build *build);
6724 __isl_give isl_ast_build *isl_ast_build_restrict(
6725 __isl_take isl_ast_build *build,
6726 __isl_take isl_set *set);
6728 The C<isl_ast_build_get_schedule> function returns a (partial)
6729 schedule for the domains elements for which part of the AST still needs to
6730 be generated in the current build.
6731 In particular, the domain elements are mapped to those iterations of the loops
6732 enclosing the current point of the AST generation inside which
6733 the domain elements are executed.
6734 No direct correspondence between
6735 the input schedule and this schedule should be assumed.
6736 The space obtained from C<isl_ast_build_get_schedule_space> can be used
6737 to create a set for C<isl_ast_build_restrict> to intersect
6738 with the current build. In particular, the set passed to
6739 C<isl_ast_build_restrict> can have additional parameters.
6740 The ids of the set dimensions in the space returned by
6741 C<isl_ast_build_get_schedule_space> correspond to the
6742 iterators of the already generated loops.
6743 The user should not rely on the ids of the output dimensions
6744 of the relations in the union relation returned by
6745 C<isl_ast_build_get_schedule> having any particular value.
6749 Although C<isl> is mainly meant to be used as a library,
6750 it also contains some basic applications that use some
6751 of the functionality of C<isl>.
6752 The input may be specified in either the L<isl format>
6753 or the L<PolyLib format>.
6755 =head2 C<isl_polyhedron_sample>
6757 C<isl_polyhedron_sample> takes a polyhedron as input and prints
6758 an integer element of the polyhedron, if there is any.
6759 The first column in the output is the denominator and is always
6760 equal to 1. If the polyhedron contains no integer points,
6761 then a vector of length zero is printed.
6765 C<isl_pip> takes the same input as the C<example> program
6766 from the C<piplib> distribution, i.e., a set of constraints
6767 on the parameters, a line containing only -1 and finally a set
6768 of constraints on a parametric polyhedron.
6769 The coefficients of the parameters appear in the last columns
6770 (but before the final constant column).
6771 The output is the lexicographic minimum of the parametric polyhedron.
6772 As C<isl> currently does not have its own output format, the output
6773 is just a dump of the internal state.
6775 =head2 C<isl_polyhedron_minimize>
6777 C<isl_polyhedron_minimize> computes the minimum of some linear
6778 or affine objective function over the integer points in a polyhedron.
6779 If an affine objective function
6780 is given, then the constant should appear in the last column.
6782 =head2 C<isl_polytope_scan>
6784 Given a polytope, C<isl_polytope_scan> prints
6785 all integer points in the polytope.
6787 =head2 C<isl_codegen>
6789 Given a schedule, a context set and an options relation,
6790 C<isl_codegen> prints out an AST that scans the domain elements
6791 of the schedule in the order of their image(s) taking into account
6792 the constraints in the context set.