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>.
197 =item * The function C<isl_band_member_is_zero_distance>
198 has been removed. Essentially the same functionality is available
199 through C<isl_band_member_is_coincident>, except that is requires
200 setting up coincidence constraints.
201 The option C<schedule_outer_zero_distance> has accordingly been
202 replaced by the option C<schedule_outer_coincidence>.
208 C<isl> is released under the MIT license.
212 Permission is hereby granted, free of charge, to any person obtaining a copy of
213 this software and associated documentation files (the "Software"), to deal in
214 the Software without restriction, including without limitation the rights to
215 use, copy, modify, merge, publish, distribute, sublicense, and/or sell copies
216 of the Software, and to permit persons to whom the Software is furnished to do
217 so, subject to the following conditions:
219 The above copyright notice and this permission notice shall be included in all
220 copies or substantial portions of the Software.
222 THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
223 IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
224 FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
225 AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
226 LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
227 OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
232 Note that C<isl> currently requires C<GMP>, which is released
233 under the GNU Lesser General Public License (LGPL). This means
234 that code linked against C<isl> is also linked against LGPL code.
238 The source of C<isl> can be obtained either as a tarball
239 or from the git repository. Both are available from
240 L<http://freshmeat.net/projects/isl/>.
241 The installation process depends on how you obtained
244 =head2 Installation from the git repository
248 =item 1 Clone or update the repository
250 The first time the source is obtained, you need to clone
253 git clone git://repo.or.cz/isl.git
255 To obtain updates, you need to pull in the latest changes
259 =item 2 Generate C<configure>
265 After performing the above steps, continue
266 with the L<Common installation instructions>.
268 =head2 Common installation instructions
272 =item 1 Obtain C<GMP>
274 Building C<isl> requires C<GMP>, including its headers files.
275 Your distribution may not provide these header files by default
276 and you may need to install a package called C<gmp-devel> or something
277 similar. Alternatively, C<GMP> can be built from
278 source, available from L<http://gmplib.org/>.
282 C<isl> uses the standard C<autoconf> C<configure> script.
287 optionally followed by some configure options.
288 A complete list of options can be obtained by running
292 Below we discuss some of the more common options.
298 Installation prefix for C<isl>
300 =item C<--with-gmp-prefix>
302 Installation prefix for C<GMP> (architecture-independent files).
304 =item C<--with-gmp-exec-prefix>
306 Installation prefix for C<GMP> (architecture-dependent files).
314 =item 4 Install (optional)
320 =head1 Integer Set Library
322 =head2 Initialization
324 All manipulations of integer sets and relations occur within
325 the context of an C<isl_ctx>.
326 A given C<isl_ctx> can only be used within a single thread.
327 All arguments of a function are required to have been allocated
328 within the same context.
329 There are currently no functions available for moving an object
330 from one C<isl_ctx> to another C<isl_ctx>. This means that
331 there is currently no way of safely moving an object from one
332 thread to another, unless the whole C<isl_ctx> is moved.
334 An C<isl_ctx> can be allocated using C<isl_ctx_alloc> and
335 freed using C<isl_ctx_free>.
336 All objects allocated within an C<isl_ctx> should be freed
337 before the C<isl_ctx> itself is freed.
339 isl_ctx *isl_ctx_alloc();
340 void isl_ctx_free(isl_ctx *ctx);
342 The user can impose a bound on the number of low-level I<operations>
343 that can be performed by an C<isl_ctx>. This bound can be set and
344 retrieved using the following functions. A bound of zero means that
345 no bound is imposed. The number of operations performed can be
346 reset using C<isl_ctx_reset_operations>. Note that the number
347 of low-level operations needed to perform a high-level computation
348 may differ significantly across different versions
349 of C<isl>, but it should be the same across different platforms
350 for the same version of C<isl>.
352 void isl_ctx_set_max_operations(isl_ctx *ctx,
353 unsigned long max_operations);
354 unsigned long isl_ctx_get_max_operations(isl_ctx *ctx);
355 void isl_ctx_reset_operations(isl_ctx *ctx);
359 An C<isl_val> represents an integer value, a rational value
360 or one of three special values, infinity, negative infinity and NaN.
361 Some predefined values can be created using the following functions.
364 __isl_give isl_val *isl_val_zero(isl_ctx *ctx);
365 __isl_give isl_val *isl_val_one(isl_ctx *ctx);
366 __isl_give isl_val *isl_val_negone(isl_ctx *ctx);
367 __isl_give isl_val *isl_val_nan(isl_ctx *ctx);
368 __isl_give isl_val *isl_val_infty(isl_ctx *ctx);
369 __isl_give isl_val *isl_val_neginfty(isl_ctx *ctx);
371 Specific integer values can be created using the following functions.
374 __isl_give isl_val *isl_val_int_from_si(isl_ctx *ctx,
376 __isl_give isl_val *isl_val_int_from_ui(isl_ctx *ctx,
378 __isl_give isl_val *isl_val_int_from_chunks(isl_ctx *ctx,
379 size_t n, size_t size, const void *chunks);
381 The function C<isl_val_int_from_chunks> constructs an C<isl_val>
382 from the C<n> I<digits>, each consisting of C<size> bytes, stored at C<chunks>.
383 The least significant digit is assumed to be stored first.
385 Value objects can be copied and freed using the following functions.
388 __isl_give isl_val *isl_val_copy(__isl_keep isl_val *v);
389 void *isl_val_free(__isl_take isl_val *v);
391 They can be inspected using the following functions.
394 isl_ctx *isl_val_get_ctx(__isl_keep isl_val *val);
395 long isl_val_get_num_si(__isl_keep isl_val *v);
396 long isl_val_get_den_si(__isl_keep isl_val *v);
397 double isl_val_get_d(__isl_keep isl_val *v);
398 size_t isl_val_n_abs_num_chunks(__isl_keep isl_val *v,
400 int isl_val_get_abs_num_chunks(__isl_keep isl_val *v,
401 size_t size, void *chunks);
403 C<isl_val_n_abs_num_chunks> returns the number of I<digits>
404 of C<size> bytes needed to store the absolute value of the
406 C<isl_val_get_abs_num_chunks> stores these digits at C<chunks>,
407 which is assumed to have been preallocated by the caller.
408 The least significant digit is stored first.
409 Note that C<isl_val_get_num_si>, C<isl_val_get_den_si>,
410 C<isl_val_get_d>, C<isl_val_n_abs_num_chunks>
411 and C<isl_val_get_abs_num_chunks> can only be applied to rational values.
413 An C<isl_val> can be modified using the following function.
416 __isl_give isl_val *isl_val_set_si(__isl_take isl_val *v,
419 The following unary properties are defined on C<isl_val>s.
422 int isl_val_sgn(__isl_keep isl_val *v);
423 int isl_val_is_zero(__isl_keep isl_val *v);
424 int isl_val_is_one(__isl_keep isl_val *v);
425 int isl_val_is_negone(__isl_keep isl_val *v);
426 int isl_val_is_nonneg(__isl_keep isl_val *v);
427 int isl_val_is_nonpos(__isl_keep isl_val *v);
428 int isl_val_is_pos(__isl_keep isl_val *v);
429 int isl_val_is_neg(__isl_keep isl_val *v);
430 int isl_val_is_int(__isl_keep isl_val *v);
431 int isl_val_is_rat(__isl_keep isl_val *v);
432 int isl_val_is_nan(__isl_keep isl_val *v);
433 int isl_val_is_infty(__isl_keep isl_val *v);
434 int isl_val_is_neginfty(__isl_keep isl_val *v);
436 Note that the sign of NaN is undefined.
438 The following binary properties are defined on pairs of C<isl_val>s.
441 int isl_val_lt(__isl_keep isl_val *v1,
442 __isl_keep isl_val *v2);
443 int isl_val_le(__isl_keep isl_val *v1,
444 __isl_keep isl_val *v2);
445 int isl_val_gt(__isl_keep isl_val *v1,
446 __isl_keep isl_val *v2);
447 int isl_val_ge(__isl_keep isl_val *v1,
448 __isl_keep isl_val *v2);
449 int isl_val_eq(__isl_keep isl_val *v1,
450 __isl_keep isl_val *v2);
451 int isl_val_ne(__isl_keep isl_val *v1,
452 __isl_keep isl_val *v2);
454 For integer C<isl_val>s we additionally have the following binary property.
457 int isl_val_is_divisible_by(__isl_keep isl_val *v1,
458 __isl_keep isl_val *v2);
460 An C<isl_val> can also be compared to an integer using the following
461 function. The result is undefined for NaN.
464 int isl_val_cmp_si(__isl_keep isl_val *v, long i);
466 The following unary operations are available on C<isl_val>s.
469 __isl_give isl_val *isl_val_abs(__isl_take isl_val *v);
470 __isl_give isl_val *isl_val_neg(__isl_take isl_val *v);
471 __isl_give isl_val *isl_val_floor(__isl_take isl_val *v);
472 __isl_give isl_val *isl_val_ceil(__isl_take isl_val *v);
473 __isl_give isl_val *isl_val_trunc(__isl_take isl_val *v);
475 The following binary operations are available on C<isl_val>s.
478 __isl_give isl_val *isl_val_abs(__isl_take isl_val *v);
479 __isl_give isl_val *isl_val_neg(__isl_take isl_val *v);
480 __isl_give isl_val *isl_val_floor(__isl_take isl_val *v);
481 __isl_give isl_val *isl_val_ceil(__isl_take isl_val *v);
482 __isl_give isl_val *isl_val_trunc(__isl_take isl_val *v);
483 __isl_give isl_val *isl_val_2exp(__isl_take isl_val *v);
484 __isl_give isl_val *isl_val_min(__isl_take isl_val *v1,
485 __isl_take isl_val *v2);
486 __isl_give isl_val *isl_val_max(__isl_take isl_val *v1,
487 __isl_take isl_val *v2);
488 __isl_give isl_val *isl_val_add(__isl_take isl_val *v1,
489 __isl_take isl_val *v2);
490 __isl_give isl_val *isl_val_add_ui(__isl_take isl_val *v1,
492 __isl_give isl_val *isl_val_sub(__isl_take isl_val *v1,
493 __isl_take isl_val *v2);
494 __isl_give isl_val *isl_val_sub_ui(__isl_take isl_val *v1,
496 __isl_give isl_val *isl_val_mul(__isl_take isl_val *v1,
497 __isl_take isl_val *v2);
498 __isl_give isl_val *isl_val_mul_ui(__isl_take isl_val *v1,
500 __isl_give isl_val *isl_val_div(__isl_take isl_val *v1,
501 __isl_take isl_val *v2);
503 On integer values, we additionally have the following operations.
506 __isl_give isl_val *isl_val_2exp(__isl_take isl_val *v);
507 __isl_give isl_val *isl_val_mod(__isl_take isl_val *v1,
508 __isl_take isl_val *v2);
509 __isl_give isl_val *isl_val_gcd(__isl_take isl_val *v1,
510 __isl_take isl_val *v2);
511 __isl_give isl_val *isl_val_gcdext(__isl_take isl_val *v1,
512 __isl_take isl_val *v2, __isl_give isl_val **x,
513 __isl_give isl_val **y);
515 The function C<isl_val_gcdext> returns the greatest common divisor g
516 of C<v1> and C<v2> as well as two integers C<*x> and C<*y> such
517 that C<*x> * C<v1> + C<*y> * C<v2> = g.
519 A value can be read from input using
522 __isl_give isl_val *isl_val_read_from_str(isl_ctx *ctx,
525 A value can be printed using
528 __isl_give isl_printer *isl_printer_print_val(
529 __isl_take isl_printer *p, __isl_keep isl_val *v);
531 =head3 GMP specific functions
533 These functions are only available if C<isl> has been compiled with C<GMP>
536 Specific integer and rational values can be created from C<GMP> values using
537 the following functions.
539 #include <isl/val_gmp.h>
540 __isl_give isl_val *isl_val_int_from_gmp(isl_ctx *ctx,
542 __isl_give isl_val *isl_val_from_gmp(isl_ctx *ctx,
543 const mpz_t n, const mpz_t d);
545 The numerator and denominator of a rational value can be extracted as
546 C<GMP> values using the following functions.
548 #include <isl/val_gmp.h>
549 int isl_val_get_num_gmp(__isl_keep isl_val *v, mpz_t z);
550 int isl_val_get_den_gmp(__isl_keep isl_val *v, mpz_t z);
552 =head2 Sets and Relations
554 C<isl> uses six types of objects for representing sets and relations,
555 C<isl_basic_set>, C<isl_basic_map>, C<isl_set>, C<isl_map>,
556 C<isl_union_set> and C<isl_union_map>.
557 C<isl_basic_set> and C<isl_basic_map> represent sets and relations that
558 can be described as a conjunction of affine constraints, while
559 C<isl_set> and C<isl_map> represent unions of
560 C<isl_basic_set>s and C<isl_basic_map>s, respectively.
561 However, all C<isl_basic_set>s or C<isl_basic_map>s in the union need
562 to live in the same space. C<isl_union_set>s and C<isl_union_map>s
563 represent unions of C<isl_set>s or C<isl_map>s in I<different> spaces,
564 where spaces are considered different if they have a different number
565 of dimensions and/or different names (see L<"Spaces">).
566 The difference between sets and relations (maps) is that sets have
567 one set of variables, while relations have two sets of variables,
568 input variables and output variables.
570 =head2 Memory Management
572 Since a high-level operation on sets and/or relations usually involves
573 several substeps and since the user is usually not interested in
574 the intermediate results, most functions that return a new object
575 will also release all the objects passed as arguments.
576 If the user still wants to use one or more of these arguments
577 after the function call, she should pass along a copy of the
578 object rather than the object itself.
579 The user is then responsible for making sure that the original
580 object gets used somewhere else or is explicitly freed.
582 The arguments and return values of all documented functions are
583 annotated to make clear which arguments are released and which
584 arguments are preserved. In particular, the following annotations
591 C<__isl_give> means that a new object is returned.
592 The user should make sure that the returned pointer is
593 used exactly once as a value for an C<__isl_take> argument.
594 In between, it can be used as a value for as many
595 C<__isl_keep> arguments as the user likes.
596 There is one exception, and that is the case where the
597 pointer returned is C<NULL>. Is this case, the user
598 is free to use it as an C<__isl_take> argument or not.
602 C<__isl_take> means that the object the argument points to
603 is taken over by the function and may no longer be used
604 by the user as an argument to any other function.
605 The pointer value must be one returned by a function
606 returning an C<__isl_give> pointer.
607 If the user passes in a C<NULL> value, then this will
608 be treated as an error in the sense that the function will
609 not perform its usual operation. However, it will still
610 make sure that all the other C<__isl_take> arguments
615 C<__isl_keep> means that the function will only use the object
616 temporarily. After the function has finished, the user
617 can still use it as an argument to other functions.
618 A C<NULL> value will be treated in the same way as
619 a C<NULL> value for an C<__isl_take> argument.
623 =head2 Error Handling
625 C<isl> supports different ways to react in case a runtime error is triggered.
626 Runtime errors arise, e.g., if a function such as C<isl_map_intersect> is called
627 with two maps that have incompatible spaces. There are three possible ways
628 to react on error: to warn, to continue or to abort.
630 The default behavior is to warn. In this mode, C<isl> prints a warning, stores
631 the last error in the corresponding C<isl_ctx> and the function in which the
632 error was triggered returns C<NULL>. An error does not corrupt internal state,
633 such that isl can continue to be used. C<isl> also provides functions to
634 read the last error and to reset the memory that stores the last error. The
635 last error is only stored for information purposes. Its presence does not
636 change the behavior of C<isl>. Hence, resetting an error is not required to
637 continue to use isl, but only to observe new errors.
640 enum isl_error isl_ctx_last_error(isl_ctx *ctx);
641 void isl_ctx_reset_error(isl_ctx *ctx);
643 Another option is to continue on error. This is similar to warn on error mode,
644 except that C<isl> does not print any warning. This allows a program to
645 implement its own error reporting.
647 The last option is to directly abort the execution of the program from within
648 the isl library. This makes it obviously impossible to recover from an error,
649 but it allows to directly spot the error location. By aborting on error,
650 debuggers break at the location the error occurred and can provide a stack
651 trace. Other tools that automatically provide stack traces on abort or that do
652 not want to continue execution after an error was triggered may also prefer to
655 The on error behavior of isl can be specified by calling
656 C<isl_options_set_on_error> or by setting the command line option
657 C<--isl-on-error>. Valid arguments for the function call are
658 C<ISL_ON_ERROR_WARN>, C<ISL_ON_ERROR_CONTINUE> and C<ISL_ON_ERROR_ABORT>. The
659 choices for the command line option are C<warn>, C<continue> and C<abort>.
660 It is also possible to query the current error mode.
662 #include <isl/options.h>
663 int isl_options_set_on_error(isl_ctx *ctx, int val);
664 int isl_options_get_on_error(isl_ctx *ctx);
668 Identifiers are used to identify both individual dimensions
669 and tuples of dimensions. They consist of an optional name and an optional
670 user pointer. The name and the user pointer cannot both be C<NULL>, however.
671 Identifiers with the same name but different pointer values
672 are considered to be distinct.
673 Similarly, identifiers with different names but the same pointer value
674 are also considered to be distinct.
675 Equal identifiers are represented using the same object.
676 Pairs of identifiers can therefore be tested for equality using the
678 Identifiers can be constructed, copied, freed, inspected and printed
679 using the following functions.
682 __isl_give isl_id *isl_id_alloc(isl_ctx *ctx,
683 __isl_keep const char *name, void *user);
684 __isl_give isl_id *isl_id_set_free_user(
685 __isl_take isl_id *id,
686 __isl_give void (*free_user)(void *user));
687 __isl_give isl_id *isl_id_copy(isl_id *id);
688 void *isl_id_free(__isl_take isl_id *id);
690 isl_ctx *isl_id_get_ctx(__isl_keep isl_id *id);
691 void *isl_id_get_user(__isl_keep isl_id *id);
692 __isl_keep const char *isl_id_get_name(__isl_keep isl_id *id);
694 __isl_give isl_printer *isl_printer_print_id(
695 __isl_take isl_printer *p, __isl_keep isl_id *id);
697 The callback set by C<isl_id_set_free_user> is called on the user
698 pointer when the last reference to the C<isl_id> is freed.
699 Note that C<isl_id_get_name> returns a pointer to some internal
700 data structure, so the result can only be used while the
701 corresponding C<isl_id> is alive.
705 Whenever a new set, relation or similiar object is created from scratch,
706 the space in which it lives needs to be specified using an C<isl_space>.
707 Each space involves zero or more parameters and zero, one or two
708 tuples of set or input/output dimensions. The parameters and dimensions
709 are identified by an C<isl_dim_type> and a position.
710 The type C<isl_dim_param> refers to parameters,
711 the type C<isl_dim_set> refers to set dimensions (for spaces
712 with a single tuple of dimensions) and the types C<isl_dim_in>
713 and C<isl_dim_out> refer to input and output dimensions
714 (for spaces with two tuples of dimensions).
715 Local spaces (see L</"Local Spaces">) also contain dimensions
716 of type C<isl_dim_div>.
717 Note that parameters are only identified by their position within
718 a given object. Across different objects, parameters are (usually)
719 identified by their names or identifiers. Only unnamed parameters
720 are identified by their positions across objects. The use of unnamed
721 parameters is discouraged.
723 #include <isl/space.h>
724 __isl_give isl_space *isl_space_alloc(isl_ctx *ctx,
725 unsigned nparam, unsigned n_in, unsigned n_out);
726 __isl_give isl_space *isl_space_params_alloc(isl_ctx *ctx,
728 __isl_give isl_space *isl_space_set_alloc(isl_ctx *ctx,
729 unsigned nparam, unsigned dim);
730 __isl_give isl_space *isl_space_copy(__isl_keep isl_space *space);
731 void *isl_space_free(__isl_take isl_space *space);
732 unsigned isl_space_dim(__isl_keep isl_space *space,
733 enum isl_dim_type type);
735 The space used for creating a parameter domain
736 needs to be created using C<isl_space_params_alloc>.
737 For other sets, the space
738 needs to be created using C<isl_space_set_alloc>, while
739 for a relation, the space
740 needs to be created using C<isl_space_alloc>.
741 C<isl_space_dim> can be used
742 to find out the number of dimensions of each type in
743 a space, where type may be
744 C<isl_dim_param>, C<isl_dim_in> (only for relations),
745 C<isl_dim_out> (only for relations), C<isl_dim_set>
746 (only for sets) or C<isl_dim_all>.
748 To check whether a given space is that of a set or a map
749 or whether it is a parameter space, use these functions:
751 #include <isl/space.h>
752 int isl_space_is_params(__isl_keep isl_space *space);
753 int isl_space_is_set(__isl_keep isl_space *space);
754 int isl_space_is_map(__isl_keep isl_space *space);
756 Spaces can be compared using the following functions:
758 #include <isl/space.h>
759 int isl_space_is_equal(__isl_keep isl_space *space1,
760 __isl_keep isl_space *space2);
761 int isl_space_is_domain(__isl_keep isl_space *space1,
762 __isl_keep isl_space *space2);
763 int isl_space_is_range(__isl_keep isl_space *space1,
764 __isl_keep isl_space *space2);
766 C<isl_space_is_domain> checks whether the first argument is equal
767 to the domain of the second argument. This requires in particular that
768 the first argument is a set space and that the second argument
771 It is often useful to create objects that live in the
772 same space as some other object. This can be accomplished
773 by creating the new objects
774 (see L</"Creating New Sets and Relations"> or
775 L</"Creating New (Piecewise) Quasipolynomials">) based on the space
776 of the original object.
779 __isl_give isl_space *isl_basic_set_get_space(
780 __isl_keep isl_basic_set *bset);
781 __isl_give isl_space *isl_set_get_space(__isl_keep isl_set *set);
783 #include <isl/union_set.h>
784 __isl_give isl_space *isl_union_set_get_space(
785 __isl_keep isl_union_set *uset);
788 __isl_give isl_space *isl_basic_map_get_space(
789 __isl_keep isl_basic_map *bmap);
790 __isl_give isl_space *isl_map_get_space(__isl_keep isl_map *map);
792 #include <isl/union_map.h>
793 __isl_give isl_space *isl_union_map_get_space(
794 __isl_keep isl_union_map *umap);
796 #include <isl/constraint.h>
797 __isl_give isl_space *isl_constraint_get_space(
798 __isl_keep isl_constraint *constraint);
800 #include <isl/polynomial.h>
801 __isl_give isl_space *isl_qpolynomial_get_domain_space(
802 __isl_keep isl_qpolynomial *qp);
803 __isl_give isl_space *isl_qpolynomial_get_space(
804 __isl_keep isl_qpolynomial *qp);
805 __isl_give isl_space *isl_qpolynomial_fold_get_space(
806 __isl_keep isl_qpolynomial_fold *fold);
807 __isl_give isl_space *isl_pw_qpolynomial_get_domain_space(
808 __isl_keep isl_pw_qpolynomial *pwqp);
809 __isl_give isl_space *isl_pw_qpolynomial_get_space(
810 __isl_keep isl_pw_qpolynomial *pwqp);
811 __isl_give isl_space *isl_pw_qpolynomial_fold_get_domain_space(
812 __isl_keep isl_pw_qpolynomial_fold *pwf);
813 __isl_give isl_space *isl_pw_qpolynomial_fold_get_space(
814 __isl_keep isl_pw_qpolynomial_fold *pwf);
815 __isl_give isl_space *isl_union_pw_qpolynomial_get_space(
816 __isl_keep isl_union_pw_qpolynomial *upwqp);
817 __isl_give isl_space *isl_union_pw_qpolynomial_fold_get_space(
818 __isl_keep isl_union_pw_qpolynomial_fold *upwf);
821 __isl_give isl_space *isl_multi_val_get_space(
822 __isl_keep isl_multi_val *mv);
825 __isl_give isl_space *isl_aff_get_domain_space(
826 __isl_keep isl_aff *aff);
827 __isl_give isl_space *isl_aff_get_space(
828 __isl_keep isl_aff *aff);
829 __isl_give isl_space *isl_pw_aff_get_domain_space(
830 __isl_keep isl_pw_aff *pwaff);
831 __isl_give isl_space *isl_pw_aff_get_space(
832 __isl_keep isl_pw_aff *pwaff);
833 __isl_give isl_space *isl_multi_aff_get_domain_space(
834 __isl_keep isl_multi_aff *maff);
835 __isl_give isl_space *isl_multi_aff_get_space(
836 __isl_keep isl_multi_aff *maff);
837 __isl_give isl_space *isl_pw_multi_aff_get_domain_space(
838 __isl_keep isl_pw_multi_aff *pma);
839 __isl_give isl_space *isl_pw_multi_aff_get_space(
840 __isl_keep isl_pw_multi_aff *pma);
841 __isl_give isl_space *isl_union_pw_multi_aff_get_space(
842 __isl_keep isl_union_pw_multi_aff *upma);
843 __isl_give isl_space *isl_multi_pw_aff_get_domain_space(
844 __isl_keep isl_multi_pw_aff *mpa);
845 __isl_give isl_space *isl_multi_pw_aff_get_space(
846 __isl_keep isl_multi_pw_aff *mpa);
848 #include <isl/point.h>
849 __isl_give isl_space *isl_point_get_space(
850 __isl_keep isl_point *pnt);
852 The identifiers or names of the individual dimensions may be set or read off
853 using the following functions.
855 #include <isl/space.h>
856 __isl_give isl_space *isl_space_set_dim_id(
857 __isl_take isl_space *space,
858 enum isl_dim_type type, unsigned pos,
859 __isl_take isl_id *id);
860 int isl_space_has_dim_id(__isl_keep isl_space *space,
861 enum isl_dim_type type, unsigned pos);
862 __isl_give isl_id *isl_space_get_dim_id(
863 __isl_keep isl_space *space,
864 enum isl_dim_type type, unsigned pos);
865 __isl_give isl_space *isl_space_set_dim_name(
866 __isl_take isl_space *space,
867 enum isl_dim_type type, unsigned pos,
868 __isl_keep const char *name);
869 int isl_space_has_dim_name(__isl_keep isl_space *space,
870 enum isl_dim_type type, unsigned pos);
871 __isl_keep const char *isl_space_get_dim_name(
872 __isl_keep isl_space *space,
873 enum isl_dim_type type, unsigned pos);
875 Note that C<isl_space_get_name> returns a pointer to some internal
876 data structure, so the result can only be used while the
877 corresponding C<isl_space> is alive.
878 Also note that every function that operates on two sets or relations
879 requires that both arguments have the same parameters. This also
880 means that if one of the arguments has named parameters, then the
881 other needs to have named parameters too and the names need to match.
882 Pairs of C<isl_set>, C<isl_map>, C<isl_union_set> and/or C<isl_union_map>
883 arguments may have different parameters (as long as they are named),
884 in which case the result will have as parameters the union of the parameters of
887 Given the identifier or name of a dimension (typically a parameter),
888 its position can be obtained from the following function.
890 #include <isl/space.h>
891 int isl_space_find_dim_by_id(__isl_keep isl_space *space,
892 enum isl_dim_type type, __isl_keep isl_id *id);
893 int isl_space_find_dim_by_name(__isl_keep isl_space *space,
894 enum isl_dim_type type, const char *name);
896 The identifiers or names of entire spaces may be set or read off
897 using the following functions.
899 #include <isl/space.h>
900 __isl_give isl_space *isl_space_set_tuple_id(
901 __isl_take isl_space *space,
902 enum isl_dim_type type, __isl_take isl_id *id);
903 __isl_give isl_space *isl_space_reset_tuple_id(
904 __isl_take isl_space *space, enum isl_dim_type type);
905 int isl_space_has_tuple_id(__isl_keep isl_space *space,
906 enum isl_dim_type type);
907 __isl_give isl_id *isl_space_get_tuple_id(
908 __isl_keep isl_space *space, enum isl_dim_type type);
909 __isl_give isl_space *isl_space_set_tuple_name(
910 __isl_take isl_space *space,
911 enum isl_dim_type type, const char *s);
912 int isl_space_has_tuple_name(__isl_keep isl_space *space,
913 enum isl_dim_type type);
914 const char *isl_space_get_tuple_name(__isl_keep isl_space *space,
915 enum isl_dim_type type);
917 The C<type> argument needs to be one of C<isl_dim_in>, C<isl_dim_out>
918 or C<isl_dim_set>. As with C<isl_space_get_name>,
919 the C<isl_space_get_tuple_name> function returns a pointer to some internal
921 Binary operations require the corresponding spaces of their arguments
922 to have the same name.
924 To keep the names of all parameters and tuples, but reset the user pointers
925 of all the corresponding identifiers, use the following function.
927 __isl_give isl_space *isl_space_reset_user(
928 __isl_take isl_space *space);
930 Spaces can be nested. In particular, the domain of a set or
931 the domain or range of a relation can be a nested relation.
932 This process is also called I<wrapping>.
933 The functions for detecting, constructing and deconstructing
934 such nested spaces can be found in the wrapping properties
935 of L</"Unary Properties">, the wrapping operations
936 of L</"Unary Operations"> and the Cartesian product operations
937 of L</"Basic Operations">.
939 Spaces can be created from other spaces
940 using the following functions.
942 __isl_give isl_space *isl_space_domain(__isl_take isl_space *space);
943 __isl_give isl_space *isl_space_from_domain(__isl_take isl_space *space);
944 __isl_give isl_space *isl_space_range(__isl_take isl_space *space);
945 __isl_give isl_space *isl_space_from_range(__isl_take isl_space *space);
946 __isl_give isl_space *isl_space_domain_map(
947 __isl_take isl_space *space);
948 __isl_give isl_space *isl_space_range_map(
949 __isl_take isl_space *space);
950 __isl_give isl_space *isl_space_params(
951 __isl_take isl_space *space);
952 __isl_give isl_space *isl_space_set_from_params(
953 __isl_take isl_space *space);
954 __isl_give isl_space *isl_space_reverse(__isl_take isl_space *space);
955 __isl_give isl_space *isl_space_join(__isl_take isl_space *left,
956 __isl_take isl_space *right);
957 __isl_give isl_space *isl_space_align_params(
958 __isl_take isl_space *space1, __isl_take isl_space *space2)
959 __isl_give isl_space *isl_space_insert_dims(__isl_take isl_space *space,
960 enum isl_dim_type type, unsigned pos, unsigned n);
961 __isl_give isl_space *isl_space_add_dims(__isl_take isl_space *space,
962 enum isl_dim_type type, unsigned n);
963 __isl_give isl_space *isl_space_drop_dims(__isl_take isl_space *space,
964 enum isl_dim_type type, unsigned first, unsigned n);
965 __isl_give isl_space *isl_space_move_dims(__isl_take isl_space *space,
966 enum isl_dim_type dst_type, unsigned dst_pos,
967 enum isl_dim_type src_type, unsigned src_pos,
969 __isl_give isl_space *isl_space_map_from_set(
970 __isl_take isl_space *space);
971 __isl_give isl_space *isl_space_map_from_domain_and_range(
972 __isl_take isl_space *domain,
973 __isl_take isl_space *range);
974 __isl_give isl_space *isl_space_zip(__isl_take isl_space *space);
975 __isl_give isl_space *isl_space_curry(
976 __isl_take isl_space *space);
977 __isl_give isl_space *isl_space_uncurry(
978 __isl_take isl_space *space);
980 Note that if dimensions are added or removed from a space, then
981 the name and the internal structure are lost.
985 A local space is essentially a space with
986 zero or more existentially quantified variables.
987 The local space of a (constraint of a) basic set or relation can be obtained
988 using the following functions.
990 #include <isl/constraint.h>
991 __isl_give isl_local_space *isl_constraint_get_local_space(
992 __isl_keep isl_constraint *constraint);
995 __isl_give isl_local_space *isl_basic_set_get_local_space(
996 __isl_keep isl_basic_set *bset);
999 __isl_give isl_local_space *isl_basic_map_get_local_space(
1000 __isl_keep isl_basic_map *bmap);
1002 A new local space can be created from a space using
1004 #include <isl/local_space.h>
1005 __isl_give isl_local_space *isl_local_space_from_space(
1006 __isl_take isl_space *space);
1008 They can be inspected, modified, copied and freed using the following functions.
1010 #include <isl/local_space.h>
1011 isl_ctx *isl_local_space_get_ctx(
1012 __isl_keep isl_local_space *ls);
1013 int isl_local_space_is_set(__isl_keep isl_local_space *ls);
1014 int isl_local_space_dim(__isl_keep isl_local_space *ls,
1015 enum isl_dim_type type);
1016 __isl_give isl_local_space *isl_local_space_set_tuple_id(
1017 __isl_take isl_local_space *ls,
1018 enum isl_dim_type type, __isl_take isl_id *id);
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 functions described in L</"Unary Operations">
1056 and L</"Binary Operations">.
1058 =head2 Input and Output
1060 C<isl> supports its own input/output format, which is similar
1061 to the C<Omega> format, but also supports the C<PolyLib> format
1064 =head3 C<isl> format
1066 The C<isl> format is similar to that of C<Omega>, but has a different
1067 syntax for describing the parameters and allows for the definition
1068 of an existentially quantified variable as the integer division
1069 of an affine expression.
1070 For example, the set of integers C<i> between C<0> and C<n>
1071 such that C<i % 10 <= 6> can be described as
1073 [n] -> { [i] : exists (a = [i/10] : 0 <= i and i <= n and
1076 A set or relation can have several disjuncts, separated
1077 by the keyword C<or>. Each disjunct is either a conjunction
1078 of constraints or a projection (C<exists>) of a conjunction
1079 of constraints. The constraints are separated by the keyword
1082 =head3 C<PolyLib> format
1084 If the represented set is a union, then the first line
1085 contains a single number representing the number of disjuncts.
1086 Otherwise, a line containing the number C<1> is optional.
1088 Each disjunct is represented by a matrix of constraints.
1089 The first line contains two numbers representing
1090 the number of rows and columns,
1091 where the number of rows is equal to the number of constraints
1092 and the number of columns is equal to two plus the number of variables.
1093 The following lines contain the actual rows of the constraint matrix.
1094 In each row, the first column indicates whether the constraint
1095 is an equality (C<0>) or inequality (C<1>). The final column
1096 corresponds to the constant term.
1098 If the set is parametric, then the coefficients of the parameters
1099 appear in the last columns before the constant column.
1100 The coefficients of any existentially quantified variables appear
1101 between those of the set variables and those of the parameters.
1103 =head3 Extended C<PolyLib> format
1105 The extended C<PolyLib> format is nearly identical to the
1106 C<PolyLib> format. The only difference is that the line
1107 containing the number of rows and columns of a constraint matrix
1108 also contains four additional numbers:
1109 the number of output dimensions, the number of input dimensions,
1110 the number of local dimensions (i.e., the number of existentially
1111 quantified variables) and the number of parameters.
1112 For sets, the number of ``output'' dimensions is equal
1113 to the number of set dimensions, while the number of ``input''
1118 #include <isl/set.h>
1119 __isl_give isl_basic_set *isl_basic_set_read_from_file(
1120 isl_ctx *ctx, FILE *input);
1121 __isl_give isl_basic_set *isl_basic_set_read_from_str(
1122 isl_ctx *ctx, const char *str);
1123 __isl_give isl_set *isl_set_read_from_file(isl_ctx *ctx,
1125 __isl_give isl_set *isl_set_read_from_str(isl_ctx *ctx,
1128 #include <isl/map.h>
1129 __isl_give isl_basic_map *isl_basic_map_read_from_file(
1130 isl_ctx *ctx, FILE *input);
1131 __isl_give isl_basic_map *isl_basic_map_read_from_str(
1132 isl_ctx *ctx, const char *str);
1133 __isl_give isl_map *isl_map_read_from_file(
1134 isl_ctx *ctx, FILE *input);
1135 __isl_give isl_map *isl_map_read_from_str(isl_ctx *ctx,
1138 #include <isl/union_set.h>
1139 __isl_give isl_union_set *isl_union_set_read_from_file(
1140 isl_ctx *ctx, FILE *input);
1141 __isl_give isl_union_set *isl_union_set_read_from_str(
1142 isl_ctx *ctx, const char *str);
1144 #include <isl/union_map.h>
1145 __isl_give isl_union_map *isl_union_map_read_from_file(
1146 isl_ctx *ctx, FILE *input);
1147 __isl_give isl_union_map *isl_union_map_read_from_str(
1148 isl_ctx *ctx, const char *str);
1150 The input format is autodetected and may be either the C<PolyLib> format
1151 or the C<isl> format.
1155 Before anything can be printed, an C<isl_printer> needs to
1158 __isl_give isl_printer *isl_printer_to_file(isl_ctx *ctx,
1160 __isl_give isl_printer *isl_printer_to_str(isl_ctx *ctx);
1161 void *isl_printer_free(__isl_take isl_printer *printer);
1162 __isl_give char *isl_printer_get_str(
1163 __isl_keep isl_printer *printer);
1165 The printer can be inspected using the following functions.
1167 FILE *isl_printer_get_file(
1168 __isl_keep isl_printer *printer);
1169 int isl_printer_get_output_format(
1170 __isl_keep isl_printer *p);
1172 The behavior of the printer can be modified in various ways
1174 __isl_give isl_printer *isl_printer_set_output_format(
1175 __isl_take isl_printer *p, int output_format);
1176 __isl_give isl_printer *isl_printer_set_indent(
1177 __isl_take isl_printer *p, int indent);
1178 __isl_give isl_printer *isl_printer_indent(
1179 __isl_take isl_printer *p, int indent);
1180 __isl_give isl_printer *isl_printer_set_prefix(
1181 __isl_take isl_printer *p, const char *prefix);
1182 __isl_give isl_printer *isl_printer_set_suffix(
1183 __isl_take isl_printer *p, const char *suffix);
1185 The C<output_format> may be either C<ISL_FORMAT_ISL>, C<ISL_FORMAT_OMEGA>,
1186 C<ISL_FORMAT_POLYLIB>, C<ISL_FORMAT_EXT_POLYLIB> or C<ISL_FORMAT_LATEX>
1187 and defaults to C<ISL_FORMAT_ISL>.
1188 Each line in the output is indented by C<indent> (set by
1189 C<isl_printer_set_indent>) spaces
1190 (default: 0), prefixed by C<prefix> and suffixed by C<suffix>.
1191 In the C<PolyLib> format output,
1192 the coefficients of the existentially quantified variables
1193 appear between those of the set variables and those
1195 The function C<isl_printer_indent> increases the indentation
1196 by the specified amount (which may be negative).
1198 To actually print something, use
1200 #include <isl/printer.h>
1201 __isl_give isl_printer *isl_printer_print_double(
1202 __isl_take isl_printer *p, double d);
1204 #include <isl/set.h>
1205 __isl_give isl_printer *isl_printer_print_basic_set(
1206 __isl_take isl_printer *printer,
1207 __isl_keep isl_basic_set *bset);
1208 __isl_give isl_printer *isl_printer_print_set(
1209 __isl_take isl_printer *printer,
1210 __isl_keep isl_set *set);
1212 #include <isl/map.h>
1213 __isl_give isl_printer *isl_printer_print_basic_map(
1214 __isl_take isl_printer *printer,
1215 __isl_keep isl_basic_map *bmap);
1216 __isl_give isl_printer *isl_printer_print_map(
1217 __isl_take isl_printer *printer,
1218 __isl_keep isl_map *map);
1220 #include <isl/union_set.h>
1221 __isl_give isl_printer *isl_printer_print_union_set(
1222 __isl_take isl_printer *p,
1223 __isl_keep isl_union_set *uset);
1225 #include <isl/union_map.h>
1226 __isl_give isl_printer *isl_printer_print_union_map(
1227 __isl_take isl_printer *p,
1228 __isl_keep isl_union_map *umap);
1230 When called on a file printer, the following function flushes
1231 the file. When called on a string printer, the buffer is cleared.
1233 __isl_give isl_printer *isl_printer_flush(
1234 __isl_take isl_printer *p);
1236 =head2 Creating New Sets and Relations
1238 C<isl> has functions for creating some standard sets and relations.
1242 =item * Empty sets and relations
1244 __isl_give isl_basic_set *isl_basic_set_empty(
1245 __isl_take isl_space *space);
1246 __isl_give isl_basic_map *isl_basic_map_empty(
1247 __isl_take isl_space *space);
1248 __isl_give isl_set *isl_set_empty(
1249 __isl_take isl_space *space);
1250 __isl_give isl_map *isl_map_empty(
1251 __isl_take isl_space *space);
1252 __isl_give isl_union_set *isl_union_set_empty(
1253 __isl_take isl_space *space);
1254 __isl_give isl_union_map *isl_union_map_empty(
1255 __isl_take isl_space *space);
1257 For C<isl_union_set>s and C<isl_union_map>s, the space
1258 is only used to specify the parameters.
1260 =item * Universe sets and relations
1262 __isl_give isl_basic_set *isl_basic_set_universe(
1263 __isl_take isl_space *space);
1264 __isl_give isl_basic_map *isl_basic_map_universe(
1265 __isl_take isl_space *space);
1266 __isl_give isl_set *isl_set_universe(
1267 __isl_take isl_space *space);
1268 __isl_give isl_map *isl_map_universe(
1269 __isl_take isl_space *space);
1270 __isl_give isl_union_set *isl_union_set_universe(
1271 __isl_take isl_union_set *uset);
1272 __isl_give isl_union_map *isl_union_map_universe(
1273 __isl_take isl_union_map *umap);
1275 The sets and relations constructed by the functions above
1276 contain all integer values, while those constructed by the
1277 functions below only contain non-negative values.
1279 __isl_give isl_basic_set *isl_basic_set_nat_universe(
1280 __isl_take isl_space *space);
1281 __isl_give isl_basic_map *isl_basic_map_nat_universe(
1282 __isl_take isl_space *space);
1283 __isl_give isl_set *isl_set_nat_universe(
1284 __isl_take isl_space *space);
1285 __isl_give isl_map *isl_map_nat_universe(
1286 __isl_take isl_space *space);
1288 =item * Identity relations
1290 __isl_give isl_basic_map *isl_basic_map_identity(
1291 __isl_take isl_space *space);
1292 __isl_give isl_map *isl_map_identity(
1293 __isl_take isl_space *space);
1295 The number of input and output dimensions in C<space> needs
1298 =item * Lexicographic order
1300 __isl_give isl_map *isl_map_lex_lt(
1301 __isl_take isl_space *set_space);
1302 __isl_give isl_map *isl_map_lex_le(
1303 __isl_take isl_space *set_space);
1304 __isl_give isl_map *isl_map_lex_gt(
1305 __isl_take isl_space *set_space);
1306 __isl_give isl_map *isl_map_lex_ge(
1307 __isl_take isl_space *set_space);
1308 __isl_give isl_map *isl_map_lex_lt_first(
1309 __isl_take isl_space *space, unsigned n);
1310 __isl_give isl_map *isl_map_lex_le_first(
1311 __isl_take isl_space *space, unsigned n);
1312 __isl_give isl_map *isl_map_lex_gt_first(
1313 __isl_take isl_space *space, unsigned n);
1314 __isl_give isl_map *isl_map_lex_ge_first(
1315 __isl_take isl_space *space, unsigned n);
1317 The first four functions take a space for a B<set>
1318 and return relations that express that the elements in the domain
1319 are lexicographically less
1320 (C<isl_map_lex_lt>), less or equal (C<isl_map_lex_le>),
1321 greater (C<isl_map_lex_gt>) or greater or equal (C<isl_map_lex_ge>)
1322 than the elements in the range.
1323 The last four functions take a space for a map
1324 and return relations that express that the first C<n> dimensions
1325 in the domain are lexicographically less
1326 (C<isl_map_lex_lt_first>), less or equal (C<isl_map_lex_le_first>),
1327 greater (C<isl_map_lex_gt_first>) or greater or equal (C<isl_map_lex_ge_first>)
1328 than the first C<n> dimensions in the range.
1332 A basic set or relation can be converted to a set or relation
1333 using the following functions.
1335 __isl_give isl_set *isl_set_from_basic_set(
1336 __isl_take isl_basic_set *bset);
1337 __isl_give isl_map *isl_map_from_basic_map(
1338 __isl_take isl_basic_map *bmap);
1340 Sets and relations can be converted to union sets and relations
1341 using the following functions.
1343 __isl_give isl_union_set *isl_union_set_from_basic_set(
1344 __isl_take isl_basic_set *bset);
1345 __isl_give isl_union_map *isl_union_map_from_basic_map(
1346 __isl_take isl_basic_map *bmap);
1347 __isl_give isl_union_set *isl_union_set_from_set(
1348 __isl_take isl_set *set);
1349 __isl_give isl_union_map *isl_union_map_from_map(
1350 __isl_take isl_map *map);
1352 The inverse conversions below can only be used if the input
1353 union set or relation is known to contain elements in exactly one
1356 __isl_give isl_set *isl_set_from_union_set(
1357 __isl_take isl_union_set *uset);
1358 __isl_give isl_map *isl_map_from_union_map(
1359 __isl_take isl_union_map *umap);
1361 A zero-dimensional (basic) set can be constructed on a given parameter domain
1362 using the following function.
1364 __isl_give isl_basic_set *isl_basic_set_from_params(
1365 __isl_take isl_basic_set *bset);
1366 __isl_give isl_set *isl_set_from_params(
1367 __isl_take isl_set *set);
1369 Sets and relations can be copied and freed again using the following
1372 __isl_give isl_basic_set *isl_basic_set_copy(
1373 __isl_keep isl_basic_set *bset);
1374 __isl_give isl_set *isl_set_copy(__isl_keep isl_set *set);
1375 __isl_give isl_union_set *isl_union_set_copy(
1376 __isl_keep isl_union_set *uset);
1377 __isl_give isl_basic_map *isl_basic_map_copy(
1378 __isl_keep isl_basic_map *bmap);
1379 __isl_give isl_map *isl_map_copy(__isl_keep isl_map *map);
1380 __isl_give isl_union_map *isl_union_map_copy(
1381 __isl_keep isl_union_map *umap);
1382 void *isl_basic_set_free(__isl_take isl_basic_set *bset);
1383 void *isl_set_free(__isl_take isl_set *set);
1384 void *isl_union_set_free(__isl_take isl_union_set *uset);
1385 void *isl_basic_map_free(__isl_take isl_basic_map *bmap);
1386 void *isl_map_free(__isl_take isl_map *map);
1387 void *isl_union_map_free(__isl_take isl_union_map *umap);
1389 Other sets and relations can be constructed by starting
1390 from a universe set or relation, adding equality and/or
1391 inequality constraints and then projecting out the
1392 existentially quantified variables, if any.
1393 Constraints can be constructed, manipulated and
1394 added to (or removed from) (basic) sets and relations
1395 using the following functions.
1397 #include <isl/constraint.h>
1398 __isl_give isl_constraint *isl_equality_alloc(
1399 __isl_take isl_local_space *ls);
1400 __isl_give isl_constraint *isl_inequality_alloc(
1401 __isl_take isl_local_space *ls);
1402 __isl_give isl_constraint *isl_constraint_set_constant_si(
1403 __isl_take isl_constraint *constraint, int v);
1404 __isl_give isl_constraint *isl_constraint_set_constant_val(
1405 __isl_take isl_constraint *constraint,
1406 __isl_take isl_val *v);
1407 __isl_give isl_constraint *isl_constraint_set_coefficient_si(
1408 __isl_take isl_constraint *constraint,
1409 enum isl_dim_type type, int pos, int v);
1410 __isl_give isl_constraint *
1411 isl_constraint_set_coefficient_val(
1412 __isl_take isl_constraint *constraint,
1413 enum isl_dim_type type, int pos,
1414 __isl_take isl_val *v);
1415 __isl_give isl_basic_map *isl_basic_map_add_constraint(
1416 __isl_take isl_basic_map *bmap,
1417 __isl_take isl_constraint *constraint);
1418 __isl_give isl_basic_set *isl_basic_set_add_constraint(
1419 __isl_take isl_basic_set *bset,
1420 __isl_take isl_constraint *constraint);
1421 __isl_give isl_map *isl_map_add_constraint(
1422 __isl_take isl_map *map,
1423 __isl_take isl_constraint *constraint);
1424 __isl_give isl_set *isl_set_add_constraint(
1425 __isl_take isl_set *set,
1426 __isl_take isl_constraint *constraint);
1427 __isl_give isl_basic_set *isl_basic_set_drop_constraint(
1428 __isl_take isl_basic_set *bset,
1429 __isl_take isl_constraint *constraint);
1431 For example, to create a set containing the even integers
1432 between 10 and 42, you would use the following code.
1435 isl_local_space *ls;
1437 isl_basic_set *bset;
1439 space = isl_space_set_alloc(ctx, 0, 2);
1440 bset = isl_basic_set_universe(isl_space_copy(space));
1441 ls = isl_local_space_from_space(space);
1443 c = isl_equality_alloc(isl_local_space_copy(ls));
1444 c = isl_constraint_set_coefficient_si(c, isl_dim_set, 0, -1);
1445 c = isl_constraint_set_coefficient_si(c, isl_dim_set, 1, 2);
1446 bset = isl_basic_set_add_constraint(bset, c);
1448 c = isl_inequality_alloc(isl_local_space_copy(ls));
1449 c = isl_constraint_set_constant_si(c, -10);
1450 c = isl_constraint_set_coefficient_si(c, isl_dim_set, 0, 1);
1451 bset = isl_basic_set_add_constraint(bset, c);
1453 c = isl_inequality_alloc(ls);
1454 c = isl_constraint_set_constant_si(c, 42);
1455 c = isl_constraint_set_coefficient_si(c, isl_dim_set, 0, -1);
1456 bset = isl_basic_set_add_constraint(bset, c);
1458 bset = isl_basic_set_project_out(bset, isl_dim_set, 1, 1);
1462 isl_basic_set *bset;
1463 bset = isl_basic_set_read_from_str(ctx,
1464 "{[i] : exists (a : i = 2a and i >= 10 and i <= 42)}");
1466 A basic set or relation can also be constructed from two matrices
1467 describing the equalities and the inequalities.
1469 __isl_give isl_basic_set *isl_basic_set_from_constraint_matrices(
1470 __isl_take isl_space *space,
1471 __isl_take isl_mat *eq, __isl_take isl_mat *ineq,
1472 enum isl_dim_type c1,
1473 enum isl_dim_type c2, enum isl_dim_type c3,
1474 enum isl_dim_type c4);
1475 __isl_give isl_basic_map *isl_basic_map_from_constraint_matrices(
1476 __isl_take isl_space *space,
1477 __isl_take isl_mat *eq, __isl_take isl_mat *ineq,
1478 enum isl_dim_type c1,
1479 enum isl_dim_type c2, enum isl_dim_type c3,
1480 enum isl_dim_type c4, enum isl_dim_type c5);
1482 The C<isl_dim_type> arguments indicate the order in which
1483 different kinds of variables appear in the input matrices
1484 and should be a permutation of C<isl_dim_cst>, C<isl_dim_param>,
1485 C<isl_dim_set> and C<isl_dim_div> for sets and
1486 of C<isl_dim_cst>, C<isl_dim_param>,
1487 C<isl_dim_in>, C<isl_dim_out> and C<isl_dim_div> for relations.
1489 A (basic or union) set or relation can also be constructed from a
1490 (union) (piecewise) (multiple) affine expression
1491 or a list of affine expressions
1492 (See L<"Piecewise Quasi Affine Expressions"> and
1493 L<"Piecewise Multiple Quasi Affine Expressions">).
1495 __isl_give isl_basic_map *isl_basic_map_from_aff(
1496 __isl_take isl_aff *aff);
1497 __isl_give isl_map *isl_map_from_aff(
1498 __isl_take isl_aff *aff);
1499 __isl_give isl_set *isl_set_from_pw_aff(
1500 __isl_take isl_pw_aff *pwaff);
1501 __isl_give isl_map *isl_map_from_pw_aff(
1502 __isl_take isl_pw_aff *pwaff);
1503 __isl_give isl_basic_map *isl_basic_map_from_aff_list(
1504 __isl_take isl_space *domain_space,
1505 __isl_take isl_aff_list *list);
1506 __isl_give isl_basic_map *isl_basic_map_from_multi_aff(
1507 __isl_take isl_multi_aff *maff)
1508 __isl_give isl_map *isl_map_from_multi_aff(
1509 __isl_take isl_multi_aff *maff)
1510 __isl_give isl_set *isl_set_from_pw_multi_aff(
1511 __isl_take isl_pw_multi_aff *pma);
1512 __isl_give isl_map *isl_map_from_pw_multi_aff(
1513 __isl_take isl_pw_multi_aff *pma);
1514 __isl_give isl_set *isl_set_from_multi_pw_aff(
1515 __isl_take isl_multi_pw_aff *mpa);
1516 __isl_give isl_map *isl_map_from_multi_pw_aff(
1517 __isl_take isl_multi_pw_aff *mpa);
1518 __isl_give isl_union_map *
1519 isl_union_map_from_union_pw_multi_aff(
1520 __isl_take isl_union_pw_multi_aff *upma);
1522 The C<domain_space> argument describes the domain of the resulting
1523 basic relation. It is required because the C<list> may consist
1524 of zero affine expressions.
1526 =head2 Inspecting Sets and Relations
1528 Usually, the user should not have to care about the actual constraints
1529 of the sets and maps, but should instead apply the abstract operations
1530 explained in the following sections.
1531 Occasionally, however, it may be required to inspect the individual
1532 coefficients of the constraints. This section explains how to do so.
1533 In these cases, it may also be useful to have C<isl> compute
1534 an explicit representation of the existentially quantified variables.
1536 __isl_give isl_set *isl_set_compute_divs(
1537 __isl_take isl_set *set);
1538 __isl_give isl_map *isl_map_compute_divs(
1539 __isl_take isl_map *map);
1540 __isl_give isl_union_set *isl_union_set_compute_divs(
1541 __isl_take isl_union_set *uset);
1542 __isl_give isl_union_map *isl_union_map_compute_divs(
1543 __isl_take isl_union_map *umap);
1545 This explicit representation defines the existentially quantified
1546 variables as integer divisions of the other variables, possibly
1547 including earlier existentially quantified variables.
1548 An explicitly represented existentially quantified variable therefore
1549 has a unique value when the values of the other variables are known.
1550 If, furthermore, the same existentials, i.e., existentials
1551 with the same explicit representations, should appear in the
1552 same order in each of the disjuncts of a set or map, then the user should call
1553 either of the following functions.
1555 __isl_give isl_set *isl_set_align_divs(
1556 __isl_take isl_set *set);
1557 __isl_give isl_map *isl_map_align_divs(
1558 __isl_take isl_map *map);
1560 Alternatively, the existentially quantified variables can be removed
1561 using the following functions, which compute an overapproximation.
1563 __isl_give isl_basic_set *isl_basic_set_remove_divs(
1564 __isl_take isl_basic_set *bset);
1565 __isl_give isl_basic_map *isl_basic_map_remove_divs(
1566 __isl_take isl_basic_map *bmap);
1567 __isl_give isl_set *isl_set_remove_divs(
1568 __isl_take isl_set *set);
1569 __isl_give isl_map *isl_map_remove_divs(
1570 __isl_take isl_map *map);
1572 It is also possible to only remove those divs that are defined
1573 in terms of a given range of dimensions or only those for which
1574 no explicit representation is known.
1576 __isl_give isl_basic_set *
1577 isl_basic_set_remove_divs_involving_dims(
1578 __isl_take isl_basic_set *bset,
1579 enum isl_dim_type type,
1580 unsigned first, unsigned n);
1581 __isl_give isl_basic_map *
1582 isl_basic_map_remove_divs_involving_dims(
1583 __isl_take isl_basic_map *bmap,
1584 enum isl_dim_type type,
1585 unsigned first, unsigned n);
1586 __isl_give isl_set *isl_set_remove_divs_involving_dims(
1587 __isl_take isl_set *set, enum isl_dim_type type,
1588 unsigned first, unsigned n);
1589 __isl_give isl_map *isl_map_remove_divs_involving_dims(
1590 __isl_take isl_map *map, enum isl_dim_type type,
1591 unsigned first, unsigned n);
1593 __isl_give isl_basic_set *
1594 isl_basic_set_remove_unknown_divs(
1595 __isl_take isl_basic_set *bset);
1596 __isl_give isl_set *isl_set_remove_unknown_divs(
1597 __isl_take isl_set *set);
1598 __isl_give isl_map *isl_map_remove_unknown_divs(
1599 __isl_take isl_map *map);
1601 To iterate over all the sets or maps in a union set or map, use
1603 int isl_union_set_foreach_set(__isl_keep isl_union_set *uset,
1604 int (*fn)(__isl_take isl_set *set, void *user),
1606 int isl_union_map_foreach_map(__isl_keep isl_union_map *umap,
1607 int (*fn)(__isl_take isl_map *map, void *user),
1610 The number of sets or maps in a union set or map can be obtained
1613 int isl_union_set_n_set(__isl_keep isl_union_set *uset);
1614 int isl_union_map_n_map(__isl_keep isl_union_map *umap);
1616 To extract the set or map in a given space from a union, use
1618 __isl_give isl_set *isl_union_set_extract_set(
1619 __isl_keep isl_union_set *uset,
1620 __isl_take isl_space *space);
1621 __isl_give isl_map *isl_union_map_extract_map(
1622 __isl_keep isl_union_map *umap,
1623 __isl_take isl_space *space);
1625 To iterate over all the basic sets or maps in a set or map, use
1627 int isl_set_foreach_basic_set(__isl_keep isl_set *set,
1628 int (*fn)(__isl_take isl_basic_set *bset, void *user),
1630 int isl_map_foreach_basic_map(__isl_keep isl_map *map,
1631 int (*fn)(__isl_take isl_basic_map *bmap, void *user),
1634 The callback function C<fn> should return 0 if successful and
1635 -1 if an error occurs. In the latter case, or if any other error
1636 occurs, the above functions will return -1.
1638 It should be noted that C<isl> does not guarantee that
1639 the basic sets or maps passed to C<fn> are disjoint.
1640 If this is required, then the user should call one of
1641 the following functions first.
1643 __isl_give isl_set *isl_set_make_disjoint(
1644 __isl_take isl_set *set);
1645 __isl_give isl_map *isl_map_make_disjoint(
1646 __isl_take isl_map *map);
1648 The number of basic sets in a set can be obtained
1651 int isl_set_n_basic_set(__isl_keep isl_set *set);
1653 To iterate over the constraints of a basic set or map, use
1655 #include <isl/constraint.h>
1657 int isl_basic_set_n_constraint(
1658 __isl_keep isl_basic_set *bset);
1659 int isl_basic_set_foreach_constraint(
1660 __isl_keep isl_basic_set *bset,
1661 int (*fn)(__isl_take isl_constraint *c, void *user),
1663 int isl_basic_map_foreach_constraint(
1664 __isl_keep isl_basic_map *bmap,
1665 int (*fn)(__isl_take isl_constraint *c, void *user),
1667 void *isl_constraint_free(__isl_take isl_constraint *c);
1669 Again, the callback function C<fn> should return 0 if successful and
1670 -1 if an error occurs. In the latter case, or if any other error
1671 occurs, the above functions will return -1.
1672 The constraint C<c> represents either an equality or an inequality.
1673 Use the following function to find out whether a constraint
1674 represents an equality. If not, it represents an inequality.
1676 int isl_constraint_is_equality(
1677 __isl_keep isl_constraint *constraint);
1679 The coefficients of the constraints can be inspected using
1680 the following functions.
1682 int isl_constraint_is_lower_bound(
1683 __isl_keep isl_constraint *constraint,
1684 enum isl_dim_type type, unsigned pos);
1685 int isl_constraint_is_upper_bound(
1686 __isl_keep isl_constraint *constraint,
1687 enum isl_dim_type type, unsigned pos);
1688 __isl_give isl_val *isl_constraint_get_constant_val(
1689 __isl_keep isl_constraint *constraint);
1690 __isl_give isl_val *isl_constraint_get_coefficient_val(
1691 __isl_keep isl_constraint *constraint,
1692 enum isl_dim_type type, int pos);
1693 int isl_constraint_involves_dims(
1694 __isl_keep isl_constraint *constraint,
1695 enum isl_dim_type type, unsigned first, unsigned n);
1697 The explicit representations of the existentially quantified
1698 variables can be inspected using the following function.
1699 Note that the user is only allowed to use this function
1700 if the inspected set or map is the result of a call
1701 to C<isl_set_compute_divs> or C<isl_map_compute_divs>.
1702 The existentially quantified variable is equal to the floor
1703 of the returned affine expression. The affine expression
1704 itself can be inspected using the functions in
1705 L<"Piecewise Quasi Affine Expressions">.
1707 __isl_give isl_aff *isl_constraint_get_div(
1708 __isl_keep isl_constraint *constraint, int pos);
1710 To obtain the constraints of a basic set or map in matrix
1711 form, use the following functions.
1713 __isl_give isl_mat *isl_basic_set_equalities_matrix(
1714 __isl_keep isl_basic_set *bset,
1715 enum isl_dim_type c1, enum isl_dim_type c2,
1716 enum isl_dim_type c3, enum isl_dim_type c4);
1717 __isl_give isl_mat *isl_basic_set_inequalities_matrix(
1718 __isl_keep isl_basic_set *bset,
1719 enum isl_dim_type c1, enum isl_dim_type c2,
1720 enum isl_dim_type c3, enum isl_dim_type c4);
1721 __isl_give isl_mat *isl_basic_map_equalities_matrix(
1722 __isl_keep isl_basic_map *bmap,
1723 enum isl_dim_type c1,
1724 enum isl_dim_type c2, enum isl_dim_type c3,
1725 enum isl_dim_type c4, enum isl_dim_type c5);
1726 __isl_give isl_mat *isl_basic_map_inequalities_matrix(
1727 __isl_keep isl_basic_map *bmap,
1728 enum isl_dim_type c1,
1729 enum isl_dim_type c2, enum isl_dim_type c3,
1730 enum isl_dim_type c4, enum isl_dim_type c5);
1732 The C<isl_dim_type> arguments dictate the order in which
1733 different kinds of variables appear in the resulting matrix
1734 and should be a permutation of C<isl_dim_cst>, C<isl_dim_param>,
1735 C<isl_dim_in>, C<isl_dim_out> and C<isl_dim_div>.
1737 The number of parameters, input, output or set dimensions can
1738 be obtained using the following functions.
1740 unsigned isl_basic_set_dim(__isl_keep isl_basic_set *bset,
1741 enum isl_dim_type type);
1742 unsigned isl_basic_map_dim(__isl_keep isl_basic_map *bmap,
1743 enum isl_dim_type type);
1744 unsigned isl_set_dim(__isl_keep isl_set *set,
1745 enum isl_dim_type type);
1746 unsigned isl_map_dim(__isl_keep isl_map *map,
1747 enum isl_dim_type type);
1749 To check whether the description of a set or relation depends
1750 on one or more given dimensions, it is not necessary to iterate over all
1751 constraints. Instead the following functions can be used.
1753 int isl_basic_set_involves_dims(
1754 __isl_keep isl_basic_set *bset,
1755 enum isl_dim_type type, unsigned first, unsigned n);
1756 int isl_set_involves_dims(__isl_keep isl_set *set,
1757 enum isl_dim_type type, unsigned first, unsigned n);
1758 int isl_basic_map_involves_dims(
1759 __isl_keep isl_basic_map *bmap,
1760 enum isl_dim_type type, unsigned first, unsigned n);
1761 int isl_map_involves_dims(__isl_keep isl_map *map,
1762 enum isl_dim_type type, unsigned first, unsigned n);
1764 Similarly, the following functions can be used to check whether
1765 a given dimension is involved in any lower or upper bound.
1767 int isl_set_dim_has_any_lower_bound(__isl_keep isl_set *set,
1768 enum isl_dim_type type, unsigned pos);
1769 int isl_set_dim_has_any_upper_bound(__isl_keep isl_set *set,
1770 enum isl_dim_type type, unsigned pos);
1772 Note that these functions return true even if there is a bound on
1773 the dimension on only some of the basic sets of C<set>.
1774 To check if they have a bound for all of the basic sets in C<set>,
1775 use the following functions instead.
1777 int isl_set_dim_has_lower_bound(__isl_keep isl_set *set,
1778 enum isl_dim_type type, unsigned pos);
1779 int isl_set_dim_has_upper_bound(__isl_keep isl_set *set,
1780 enum isl_dim_type type, unsigned pos);
1782 The identifiers or names of the domain and range spaces of a set
1783 or relation can be read off or set using the following functions.
1785 __isl_give isl_basic_set *isl_basic_set_set_tuple_id(
1786 __isl_take isl_basic_set *bset,
1787 __isl_take isl_id *id);
1788 __isl_give isl_set *isl_set_set_tuple_id(
1789 __isl_take isl_set *set, __isl_take isl_id *id);
1790 __isl_give isl_set *isl_set_reset_tuple_id(
1791 __isl_take isl_set *set);
1792 int isl_set_has_tuple_id(__isl_keep isl_set *set);
1793 __isl_give isl_id *isl_set_get_tuple_id(
1794 __isl_keep isl_set *set);
1795 __isl_give isl_basic_map *isl_basic_map_set_tuple_id(
1796 __isl_take isl_basic_map *bmap,
1797 enum isl_dim_type type, __isl_take isl_id *id);
1798 __isl_give isl_map *isl_map_set_tuple_id(
1799 __isl_take isl_map *map, enum isl_dim_type type,
1800 __isl_take isl_id *id);
1801 __isl_give isl_map *isl_map_reset_tuple_id(
1802 __isl_take isl_map *map, enum isl_dim_type type);
1803 int isl_map_has_tuple_id(__isl_keep isl_map *map,
1804 enum isl_dim_type type);
1805 __isl_give isl_id *isl_map_get_tuple_id(
1806 __isl_keep isl_map *map, enum isl_dim_type type);
1808 const char *isl_basic_set_get_tuple_name(
1809 __isl_keep isl_basic_set *bset);
1810 __isl_give isl_basic_set *isl_basic_set_set_tuple_name(
1811 __isl_take isl_basic_set *set, const char *s);
1812 int isl_set_has_tuple_name(__isl_keep isl_set *set);
1813 const char *isl_set_get_tuple_name(
1814 __isl_keep isl_set *set);
1815 const char *isl_basic_map_get_tuple_name(
1816 __isl_keep isl_basic_map *bmap,
1817 enum isl_dim_type type);
1818 __isl_give isl_basic_map *isl_basic_map_set_tuple_name(
1819 __isl_take isl_basic_map *bmap,
1820 enum isl_dim_type type, const char *s);
1821 int isl_map_has_tuple_name(__isl_keep isl_map *map,
1822 enum isl_dim_type type);
1823 const char *isl_map_get_tuple_name(
1824 __isl_keep isl_map *map,
1825 enum isl_dim_type type);
1827 As with C<isl_space_get_tuple_name>, the value returned points to
1828 an internal data structure.
1829 The identifiers, positions or names of individual dimensions can be
1830 read off using the following functions.
1832 __isl_give isl_id *isl_basic_set_get_dim_id(
1833 __isl_keep isl_basic_set *bset,
1834 enum isl_dim_type type, unsigned pos);
1835 __isl_give isl_set *isl_set_set_dim_id(
1836 __isl_take isl_set *set, enum isl_dim_type type,
1837 unsigned pos, __isl_take isl_id *id);
1838 int isl_set_has_dim_id(__isl_keep isl_set *set,
1839 enum isl_dim_type type, unsigned pos);
1840 __isl_give isl_id *isl_set_get_dim_id(
1841 __isl_keep isl_set *set, enum isl_dim_type type,
1843 int isl_basic_map_has_dim_id(
1844 __isl_keep isl_basic_map *bmap,
1845 enum isl_dim_type type, unsigned pos);
1846 __isl_give isl_map *isl_map_set_dim_id(
1847 __isl_take isl_map *map, enum isl_dim_type type,
1848 unsigned pos, __isl_take isl_id *id);
1849 int isl_map_has_dim_id(__isl_keep isl_map *map,
1850 enum isl_dim_type type, unsigned pos);
1851 __isl_give isl_id *isl_map_get_dim_id(
1852 __isl_keep isl_map *map, enum isl_dim_type type,
1855 int isl_set_find_dim_by_id(__isl_keep isl_set *set,
1856 enum isl_dim_type type, __isl_keep isl_id *id);
1857 int isl_map_find_dim_by_id(__isl_keep isl_map *map,
1858 enum isl_dim_type type, __isl_keep isl_id *id);
1859 int isl_set_find_dim_by_name(__isl_keep isl_set *set,
1860 enum isl_dim_type type, const char *name);
1861 int isl_map_find_dim_by_name(__isl_keep isl_map *map,
1862 enum isl_dim_type type, const char *name);
1864 const char *isl_constraint_get_dim_name(
1865 __isl_keep isl_constraint *constraint,
1866 enum isl_dim_type type, unsigned pos);
1867 const char *isl_basic_set_get_dim_name(
1868 __isl_keep isl_basic_set *bset,
1869 enum isl_dim_type type, unsigned pos);
1870 int isl_set_has_dim_name(__isl_keep isl_set *set,
1871 enum isl_dim_type type, unsigned pos);
1872 const char *isl_set_get_dim_name(
1873 __isl_keep isl_set *set,
1874 enum isl_dim_type type, unsigned pos);
1875 const char *isl_basic_map_get_dim_name(
1876 __isl_keep isl_basic_map *bmap,
1877 enum isl_dim_type type, unsigned pos);
1878 int isl_map_has_dim_name(__isl_keep isl_map *map,
1879 enum isl_dim_type type, unsigned pos);
1880 const char *isl_map_get_dim_name(
1881 __isl_keep isl_map *map,
1882 enum isl_dim_type type, unsigned pos);
1884 These functions are mostly useful to obtain the identifiers, positions
1885 or names of the parameters. Identifiers of individual dimensions are
1886 essentially only useful for printing. They are ignored by all other
1887 operations and may not be preserved across those operations.
1889 The user pointers on all parameters and tuples can be reset
1890 using the following functions.
1892 __isl_give isl_set *isl_set_reset_user(
1893 __isl_take isl_set *set);
1894 __isl_give isl_map *isl_map_reset_user(
1895 __isl_take isl_map *map);
1899 =head3 Unary Properties
1905 The following functions test whether the given set or relation
1906 contains any integer points. The ``plain'' variants do not perform
1907 any computations, but simply check if the given set or relation
1908 is already known to be empty.
1910 int isl_basic_set_plain_is_empty(__isl_keep isl_basic_set *bset);
1911 int isl_basic_set_is_empty(__isl_keep isl_basic_set *bset);
1912 int isl_set_plain_is_empty(__isl_keep isl_set *set);
1913 int isl_set_is_empty(__isl_keep isl_set *set);
1914 int isl_union_set_is_empty(__isl_keep isl_union_set *uset);
1915 int isl_basic_map_plain_is_empty(__isl_keep isl_basic_map *bmap);
1916 int isl_basic_map_is_empty(__isl_keep isl_basic_map *bmap);
1917 int isl_map_plain_is_empty(__isl_keep isl_map *map);
1918 int isl_map_is_empty(__isl_keep isl_map *map);
1919 int isl_union_map_is_empty(__isl_keep isl_union_map *umap);
1921 =item * Universality
1923 int isl_basic_set_is_universe(__isl_keep isl_basic_set *bset);
1924 int isl_basic_map_is_universe(__isl_keep isl_basic_map *bmap);
1925 int isl_set_plain_is_universe(__isl_keep isl_set *set);
1927 =item * Single-valuedness
1929 int isl_basic_map_is_single_valued(
1930 __isl_keep isl_basic_map *bmap);
1931 int isl_map_plain_is_single_valued(
1932 __isl_keep isl_map *map);
1933 int isl_map_is_single_valued(__isl_keep isl_map *map);
1934 int isl_union_map_is_single_valued(__isl_keep isl_union_map *umap);
1938 int isl_map_plain_is_injective(__isl_keep isl_map *map);
1939 int isl_map_is_injective(__isl_keep isl_map *map);
1940 int isl_union_map_plain_is_injective(
1941 __isl_keep isl_union_map *umap);
1942 int isl_union_map_is_injective(
1943 __isl_keep isl_union_map *umap);
1947 int isl_map_is_bijective(__isl_keep isl_map *map);
1948 int isl_union_map_is_bijective(__isl_keep isl_union_map *umap);
1952 __isl_give isl_val *
1953 isl_basic_map_plain_get_val_if_fixed(
1954 __isl_keep isl_basic_map *bmap,
1955 enum isl_dim_type type, unsigned pos);
1956 __isl_give isl_val *isl_set_plain_get_val_if_fixed(
1957 __isl_keep isl_set *set,
1958 enum isl_dim_type type, unsigned pos);
1959 __isl_give isl_val *isl_map_plain_get_val_if_fixed(
1960 __isl_keep isl_map *map,
1961 enum isl_dim_type type, unsigned pos);
1963 If the set or relation obviously lies on a hyperplane where the given dimension
1964 has a fixed value, then return that value.
1965 Otherwise return NaN.
1969 int isl_set_dim_residue_class_val(
1970 __isl_keep isl_set *set,
1971 int pos, __isl_give isl_val **modulo,
1972 __isl_give isl_val **residue);
1974 Check if the values of the given set dimension are equal to a fixed
1975 value modulo some integer value. If so, assign the modulo to C<*modulo>
1976 and the fixed value to C<*residue>. If the given dimension attains only
1977 a single value, then assign C<0> to C<*modulo> and the fixed value to
1979 If the dimension does not attain only a single value and if no modulo
1980 can be found then assign C<1> to C<*modulo> and C<1> to C<*residue>.
1984 To check whether a set is a parameter domain, use this function:
1986 int isl_set_is_params(__isl_keep isl_set *set);
1987 int isl_union_set_is_params(
1988 __isl_keep isl_union_set *uset);
1992 The following functions check whether the space of the given
1993 (basic) set or relation range is a wrapped relation.
1995 #include <isl/space.h>
1996 int isl_space_is_wrapping(
1997 __isl_keep isl_space *space);
1998 int isl_space_domain_is_wrapping(
1999 __isl_keep isl_space *space);
2000 int isl_space_range_is_wrapping(
2001 __isl_keep isl_space *space);
2003 #include <isl/set.h>
2004 int isl_basic_set_is_wrapping(
2005 __isl_keep isl_basic_set *bset);
2006 int isl_set_is_wrapping(__isl_keep isl_set *set);
2008 #include <isl/map.h>
2009 int isl_map_domain_is_wrapping(
2010 __isl_keep isl_map *map);
2011 int isl_map_range_is_wrapping(
2012 __isl_keep isl_map *map);
2014 The input to C<isl_space_is_wrapping> should
2015 be the space of a set, while that of
2016 C<isl_space_domain_is_wrapping> and
2017 C<isl_space_range_is_wrapping> should be the space of a relation.
2019 =item * Internal Product
2021 int isl_basic_map_can_zip(
2022 __isl_keep isl_basic_map *bmap);
2023 int isl_map_can_zip(__isl_keep isl_map *map);
2025 Check whether the product of domain and range of the given relation
2027 i.e., whether both domain and range are nested relations.
2031 int isl_basic_map_can_curry(
2032 __isl_keep isl_basic_map *bmap);
2033 int isl_map_can_curry(__isl_keep isl_map *map);
2035 Check whether the domain of the (basic) relation is a wrapped relation.
2037 int isl_basic_map_can_uncurry(
2038 __isl_keep isl_basic_map *bmap);
2039 int isl_map_can_uncurry(__isl_keep isl_map *map);
2041 Check whether the range of the (basic) relation is a wrapped relation.
2045 =head3 Binary Properties
2051 int isl_basic_set_plain_is_equal(
2052 __isl_keep isl_basic_set *bset1,
2053 __isl_keep isl_basic_set *bset2);
2054 int isl_set_plain_is_equal(__isl_keep isl_set *set1,
2055 __isl_keep isl_set *set2);
2056 int isl_set_is_equal(__isl_keep isl_set *set1,
2057 __isl_keep isl_set *set2);
2058 int isl_union_set_is_equal(
2059 __isl_keep isl_union_set *uset1,
2060 __isl_keep isl_union_set *uset2);
2061 int isl_basic_map_is_equal(
2062 __isl_keep isl_basic_map *bmap1,
2063 __isl_keep isl_basic_map *bmap2);
2064 int isl_map_is_equal(__isl_keep isl_map *map1,
2065 __isl_keep isl_map *map2);
2066 int isl_map_plain_is_equal(__isl_keep isl_map *map1,
2067 __isl_keep isl_map *map2);
2068 int isl_union_map_is_equal(
2069 __isl_keep isl_union_map *umap1,
2070 __isl_keep isl_union_map *umap2);
2072 =item * Disjointness
2074 int isl_basic_set_is_disjoint(
2075 __isl_keep isl_basic_set *bset1,
2076 __isl_keep isl_basic_set *bset2);
2077 int isl_set_plain_is_disjoint(__isl_keep isl_set *set1,
2078 __isl_keep isl_set *set2);
2079 int isl_set_is_disjoint(__isl_keep isl_set *set1,
2080 __isl_keep isl_set *set2);
2081 int isl_basic_map_is_disjoint(
2082 __isl_keep isl_basic_map *bmap1,
2083 __isl_keep isl_basic_map *bmap2);
2084 int isl_map_is_disjoint(__isl_keep isl_map *map1,
2085 __isl_keep isl_map *map2);
2089 int isl_basic_set_is_subset(
2090 __isl_keep isl_basic_set *bset1,
2091 __isl_keep isl_basic_set *bset2);
2092 int isl_set_is_subset(__isl_keep isl_set *set1,
2093 __isl_keep isl_set *set2);
2094 int isl_set_is_strict_subset(
2095 __isl_keep isl_set *set1,
2096 __isl_keep isl_set *set2);
2097 int isl_union_set_is_subset(
2098 __isl_keep isl_union_set *uset1,
2099 __isl_keep isl_union_set *uset2);
2100 int isl_union_set_is_strict_subset(
2101 __isl_keep isl_union_set *uset1,
2102 __isl_keep isl_union_set *uset2);
2103 int isl_basic_map_is_subset(
2104 __isl_keep isl_basic_map *bmap1,
2105 __isl_keep isl_basic_map *bmap2);
2106 int isl_basic_map_is_strict_subset(
2107 __isl_keep isl_basic_map *bmap1,
2108 __isl_keep isl_basic_map *bmap2);
2109 int isl_map_is_subset(
2110 __isl_keep isl_map *map1,
2111 __isl_keep isl_map *map2);
2112 int isl_map_is_strict_subset(
2113 __isl_keep isl_map *map1,
2114 __isl_keep isl_map *map2);
2115 int isl_union_map_is_subset(
2116 __isl_keep isl_union_map *umap1,
2117 __isl_keep isl_union_map *umap2);
2118 int isl_union_map_is_strict_subset(
2119 __isl_keep isl_union_map *umap1,
2120 __isl_keep isl_union_map *umap2);
2122 Check whether the first argument is a (strict) subset of the
2127 int isl_set_plain_cmp(__isl_keep isl_set *set1,
2128 __isl_keep isl_set *set2);
2130 This function is useful for sorting C<isl_set>s.
2131 The order depends on the internal representation of the inputs.
2132 The order is fixed over different calls to the function (assuming
2133 the internal representation of the inputs has not changed), but may
2134 change over different versions of C<isl>.
2138 =head2 Unary Operations
2144 __isl_give isl_set *isl_set_complement(
2145 __isl_take isl_set *set);
2146 __isl_give isl_map *isl_map_complement(
2147 __isl_take isl_map *map);
2151 __isl_give isl_basic_map *isl_basic_map_reverse(
2152 __isl_take isl_basic_map *bmap);
2153 __isl_give isl_map *isl_map_reverse(
2154 __isl_take isl_map *map);
2155 __isl_give isl_union_map *isl_union_map_reverse(
2156 __isl_take isl_union_map *umap);
2160 #include <isl/local_space.h>
2161 __isl_give isl_local_space *isl_local_space_domain(
2162 __isl_take isl_local_space *ls);
2163 __isl_give isl_local_space *isl_local_space_range(
2164 __isl_take isl_local_space *ls);
2166 #include <isl/set.h>
2167 __isl_give isl_basic_set *isl_basic_set_project_out(
2168 __isl_take isl_basic_set *bset,
2169 enum isl_dim_type type, unsigned first, unsigned n);
2170 __isl_give isl_set *isl_set_project_out(__isl_take isl_set *set,
2171 enum isl_dim_type type, unsigned first, unsigned n);
2172 __isl_give isl_basic_set *isl_basic_set_params(
2173 __isl_take isl_basic_set *bset);
2174 __isl_give isl_set *isl_set_params(__isl_take isl_set *set);
2176 #include <isl/map.h>
2177 __isl_give isl_basic_map *isl_basic_map_project_out(
2178 __isl_take isl_basic_map *bmap,
2179 enum isl_dim_type type, unsigned first, unsigned n);
2180 __isl_give isl_map *isl_map_project_out(__isl_take isl_map *map,
2181 enum isl_dim_type type, unsigned first, unsigned n);
2182 __isl_give isl_basic_set *isl_basic_map_domain(
2183 __isl_take isl_basic_map *bmap);
2184 __isl_give isl_basic_set *isl_basic_map_range(
2185 __isl_take isl_basic_map *bmap);
2186 __isl_give isl_set *isl_map_params(__isl_take isl_map *map);
2187 __isl_give isl_set *isl_map_domain(
2188 __isl_take isl_map *bmap);
2189 __isl_give isl_set *isl_map_range(
2190 __isl_take isl_map *map);
2192 #include <isl/union_set.h>
2193 __isl_give isl_set *isl_union_set_params(
2194 __isl_take isl_union_set *uset);
2196 #include <isl/union_map.h>
2197 __isl_give isl_set *isl_union_map_params(
2198 __isl_take isl_union_map *umap);
2199 __isl_give isl_union_set *isl_union_map_domain(
2200 __isl_take isl_union_map *umap);
2201 __isl_give isl_union_set *isl_union_map_range(
2202 __isl_take isl_union_map *umap);
2204 #include <isl/map.h>
2205 __isl_give isl_basic_map *isl_basic_map_domain_map(
2206 __isl_take isl_basic_map *bmap);
2207 __isl_give isl_basic_map *isl_basic_map_range_map(
2208 __isl_take isl_basic_map *bmap);
2209 __isl_give isl_map *isl_map_domain_map(__isl_take isl_map *map);
2210 __isl_give isl_map *isl_map_range_map(__isl_take isl_map *map);
2212 #include <isl/union_map.h>
2213 __isl_give isl_union_map *isl_union_map_domain_map(
2214 __isl_take isl_union_map *umap);
2215 __isl_give isl_union_map *isl_union_map_range_map(
2216 __isl_take isl_union_map *umap);
2218 The functions above construct a (basic, regular or union) relation
2219 that maps (a wrapped version of) the input relation to its domain or range.
2223 __isl_give isl_basic_set *isl_basic_set_eliminate(
2224 __isl_take isl_basic_set *bset,
2225 enum isl_dim_type type,
2226 unsigned first, unsigned n);
2227 __isl_give isl_set *isl_set_eliminate(
2228 __isl_take isl_set *set, enum isl_dim_type type,
2229 unsigned first, unsigned n);
2230 __isl_give isl_basic_map *isl_basic_map_eliminate(
2231 __isl_take isl_basic_map *bmap,
2232 enum isl_dim_type type,
2233 unsigned first, unsigned n);
2234 __isl_give isl_map *isl_map_eliminate(
2235 __isl_take isl_map *map, enum isl_dim_type type,
2236 unsigned first, unsigned n);
2238 Eliminate the coefficients for the given dimensions from the constraints,
2239 without removing the dimensions.
2241 =item * Constructing a relation from a set
2243 #include <isl/local_space.h>
2244 __isl_give isl_local_space *isl_local_space_from_domain(
2245 __isl_take isl_local_space *ls);
2247 #include <isl/map.h>
2248 __isl_give isl_map *isl_map_from_domain(
2249 __isl_take isl_set *set);
2250 __isl_give isl_map *isl_map_from_range(
2251 __isl_take isl_set *set);
2253 Create a relation with the given set as domain or range.
2254 The range or domain of the created relation is a zero-dimensional
2255 flat anonymous space.
2259 __isl_give isl_basic_set *isl_basic_set_fix_si(
2260 __isl_take isl_basic_set *bset,
2261 enum isl_dim_type type, unsigned pos, int value);
2262 __isl_give isl_basic_set *isl_basic_set_fix_val(
2263 __isl_take isl_basic_set *bset,
2264 enum isl_dim_type type, unsigned pos,
2265 __isl_take isl_val *v);
2266 __isl_give isl_set *isl_set_fix_si(__isl_take isl_set *set,
2267 enum isl_dim_type type, unsigned pos, int value);
2268 __isl_give isl_set *isl_set_fix_val(
2269 __isl_take isl_set *set,
2270 enum isl_dim_type type, unsigned pos,
2271 __isl_take isl_val *v);
2272 __isl_give isl_basic_map *isl_basic_map_fix_si(
2273 __isl_take isl_basic_map *bmap,
2274 enum isl_dim_type type, unsigned pos, int value);
2275 __isl_give isl_basic_map *isl_basic_map_fix_val(
2276 __isl_take isl_basic_map *bmap,
2277 enum isl_dim_type type, unsigned pos,
2278 __isl_take isl_val *v);
2279 __isl_give isl_map *isl_map_fix_si(__isl_take isl_map *map,
2280 enum isl_dim_type type, unsigned pos, int value);
2281 __isl_give isl_map *isl_map_fix_val(
2282 __isl_take isl_map *map,
2283 enum isl_dim_type type, unsigned pos,
2284 __isl_take isl_val *v);
2286 Intersect the set or relation with the hyperplane where the given
2287 dimension has the fixed given value.
2289 __isl_give isl_basic_map *isl_basic_map_lower_bound_si(
2290 __isl_take isl_basic_map *bmap,
2291 enum isl_dim_type type, unsigned pos, int value);
2292 __isl_give isl_basic_map *isl_basic_map_upper_bound_si(
2293 __isl_take isl_basic_map *bmap,
2294 enum isl_dim_type type, unsigned pos, int value);
2295 __isl_give isl_set *isl_set_lower_bound_si(
2296 __isl_take isl_set *set,
2297 enum isl_dim_type type, unsigned pos, int value);
2298 __isl_give isl_set *isl_set_lower_bound_val(
2299 __isl_take isl_set *set,
2300 enum isl_dim_type type, unsigned pos,
2301 __isl_take isl_val *value);
2302 __isl_give isl_map *isl_map_lower_bound_si(
2303 __isl_take isl_map *map,
2304 enum isl_dim_type type, unsigned pos, int value);
2305 __isl_give isl_set *isl_set_upper_bound_si(
2306 __isl_take isl_set *set,
2307 enum isl_dim_type type, unsigned pos, int value);
2308 __isl_give isl_set *isl_set_upper_bound_val(
2309 __isl_take isl_set *set,
2310 enum isl_dim_type type, unsigned pos,
2311 __isl_take isl_val *value);
2312 __isl_give isl_map *isl_map_upper_bound_si(
2313 __isl_take isl_map *map,
2314 enum isl_dim_type type, unsigned pos, int value);
2316 Intersect the set or relation with the half-space where the given
2317 dimension has a value bounded by the fixed given integer value.
2319 __isl_give isl_set *isl_set_equate(__isl_take isl_set *set,
2320 enum isl_dim_type type1, int pos1,
2321 enum isl_dim_type type2, int pos2);
2322 __isl_give isl_basic_map *isl_basic_map_equate(
2323 __isl_take isl_basic_map *bmap,
2324 enum isl_dim_type type1, int pos1,
2325 enum isl_dim_type type2, int pos2);
2326 __isl_give isl_map *isl_map_equate(__isl_take isl_map *map,
2327 enum isl_dim_type type1, int pos1,
2328 enum isl_dim_type type2, int pos2);
2330 Intersect the set or relation with the hyperplane where the given
2331 dimensions are equal to each other.
2333 __isl_give isl_map *isl_map_oppose(__isl_take isl_map *map,
2334 enum isl_dim_type type1, int pos1,
2335 enum isl_dim_type type2, int pos2);
2337 Intersect the relation with the hyperplane where the given
2338 dimensions have opposite values.
2340 __isl_give isl_map *isl_map_order_le(
2341 __isl_take isl_map *map,
2342 enum isl_dim_type type1, int pos1,
2343 enum isl_dim_type type2, int pos2);
2344 __isl_give isl_basic_map *isl_basic_map_order_ge(
2345 __isl_take isl_basic_map *bmap,
2346 enum isl_dim_type type1, int pos1,
2347 enum isl_dim_type type2, int pos2);
2348 __isl_give isl_map *isl_map_order_ge(
2349 __isl_take isl_map *map,
2350 enum isl_dim_type type1, int pos1,
2351 enum isl_dim_type type2, int pos2);
2352 __isl_give isl_map *isl_map_order_lt(__isl_take isl_map *map,
2353 enum isl_dim_type type1, int pos1,
2354 enum isl_dim_type type2, int pos2);
2355 __isl_give isl_basic_map *isl_basic_map_order_gt(
2356 __isl_take isl_basic_map *bmap,
2357 enum isl_dim_type type1, int pos1,
2358 enum isl_dim_type type2, int pos2);
2359 __isl_give isl_map *isl_map_order_gt(__isl_take isl_map *map,
2360 enum isl_dim_type type1, int pos1,
2361 enum isl_dim_type type2, int pos2);
2363 Intersect the relation with the half-space where the given
2364 dimensions satisfy the given ordering.
2368 __isl_give isl_map *isl_set_identity(
2369 __isl_take isl_set *set);
2370 __isl_give isl_union_map *isl_union_set_identity(
2371 __isl_take isl_union_set *uset);
2373 Construct an identity relation on the given (union) set.
2377 __isl_give isl_basic_set *isl_basic_map_deltas(
2378 __isl_take isl_basic_map *bmap);
2379 __isl_give isl_set *isl_map_deltas(__isl_take isl_map *map);
2380 __isl_give isl_union_set *isl_union_map_deltas(
2381 __isl_take isl_union_map *umap);
2383 These functions return a (basic) set containing the differences
2384 between image elements and corresponding domain elements in the input.
2386 __isl_give isl_basic_map *isl_basic_map_deltas_map(
2387 __isl_take isl_basic_map *bmap);
2388 __isl_give isl_map *isl_map_deltas_map(
2389 __isl_take isl_map *map);
2390 __isl_give isl_union_map *isl_union_map_deltas_map(
2391 __isl_take isl_union_map *umap);
2393 The functions above construct a (basic, regular or union) relation
2394 that maps (a wrapped version of) the input relation to its delta set.
2398 Simplify the representation of a set or relation by trying
2399 to combine pairs of basic sets or relations into a single
2400 basic set or relation.
2402 __isl_give isl_set *isl_set_coalesce(__isl_take isl_set *set);
2403 __isl_give isl_map *isl_map_coalesce(__isl_take isl_map *map);
2404 __isl_give isl_union_set *isl_union_set_coalesce(
2405 __isl_take isl_union_set *uset);
2406 __isl_give isl_union_map *isl_union_map_coalesce(
2407 __isl_take isl_union_map *umap);
2409 One of the methods for combining pairs of basic sets or relations
2410 can result in coefficients that are much larger than those that appear
2411 in the constraints of the input. By default, the coefficients are
2412 not allowed to grow larger, but this can be changed by unsetting
2413 the following option.
2415 int isl_options_set_coalesce_bounded_wrapping(
2416 isl_ctx *ctx, int val);
2417 int isl_options_get_coalesce_bounded_wrapping(
2420 =item * Detecting equalities
2422 __isl_give isl_basic_set *isl_basic_set_detect_equalities(
2423 __isl_take isl_basic_set *bset);
2424 __isl_give isl_basic_map *isl_basic_map_detect_equalities(
2425 __isl_take isl_basic_map *bmap);
2426 __isl_give isl_set *isl_set_detect_equalities(
2427 __isl_take isl_set *set);
2428 __isl_give isl_map *isl_map_detect_equalities(
2429 __isl_take isl_map *map);
2430 __isl_give isl_union_set *isl_union_set_detect_equalities(
2431 __isl_take isl_union_set *uset);
2432 __isl_give isl_union_map *isl_union_map_detect_equalities(
2433 __isl_take isl_union_map *umap);
2435 Simplify the representation of a set or relation by detecting implicit
2438 =item * Removing redundant constraints
2440 __isl_give isl_basic_set *isl_basic_set_remove_redundancies(
2441 __isl_take isl_basic_set *bset);
2442 __isl_give isl_set *isl_set_remove_redundancies(
2443 __isl_take isl_set *set);
2444 __isl_give isl_basic_map *isl_basic_map_remove_redundancies(
2445 __isl_take isl_basic_map *bmap);
2446 __isl_give isl_map *isl_map_remove_redundancies(
2447 __isl_take isl_map *map);
2451 __isl_give isl_basic_set *isl_set_convex_hull(
2452 __isl_take isl_set *set);
2453 __isl_give isl_basic_map *isl_map_convex_hull(
2454 __isl_take isl_map *map);
2456 If the input set or relation has any existentially quantified
2457 variables, then the result of these operations is currently undefined.
2461 __isl_give isl_basic_set *
2462 isl_set_unshifted_simple_hull(
2463 __isl_take isl_set *set);
2464 __isl_give isl_basic_map *
2465 isl_map_unshifted_simple_hull(
2466 __isl_take isl_map *map);
2467 __isl_give isl_basic_set *isl_set_simple_hull(
2468 __isl_take isl_set *set);
2469 __isl_give isl_basic_map *isl_map_simple_hull(
2470 __isl_take isl_map *map);
2471 __isl_give isl_union_map *isl_union_map_simple_hull(
2472 __isl_take isl_union_map *umap);
2474 These functions compute a single basic set or relation
2475 that contains the whole input set or relation.
2476 In particular, the output is described by translates
2477 of the constraints describing the basic sets or relations in the input.
2478 In case of C<isl_set_unshifted_simple_hull>, only the original
2479 constraints are used, without any translation.
2483 (See \autoref{s:simple hull}.)
2489 __isl_give isl_basic_set *isl_basic_set_affine_hull(
2490 __isl_take isl_basic_set *bset);
2491 __isl_give isl_basic_set *isl_set_affine_hull(
2492 __isl_take isl_set *set);
2493 __isl_give isl_union_set *isl_union_set_affine_hull(
2494 __isl_take isl_union_set *uset);
2495 __isl_give isl_basic_map *isl_basic_map_affine_hull(
2496 __isl_take isl_basic_map *bmap);
2497 __isl_give isl_basic_map *isl_map_affine_hull(
2498 __isl_take isl_map *map);
2499 __isl_give isl_union_map *isl_union_map_affine_hull(
2500 __isl_take isl_union_map *umap);
2502 In case of union sets and relations, the affine hull is computed
2505 =item * Polyhedral hull
2507 __isl_give isl_basic_set *isl_set_polyhedral_hull(
2508 __isl_take isl_set *set);
2509 __isl_give isl_basic_map *isl_map_polyhedral_hull(
2510 __isl_take isl_map *map);
2511 __isl_give isl_union_set *isl_union_set_polyhedral_hull(
2512 __isl_take isl_union_set *uset);
2513 __isl_give isl_union_map *isl_union_map_polyhedral_hull(
2514 __isl_take isl_union_map *umap);
2516 These functions compute a single basic set or relation
2517 not involving any existentially quantified variables
2518 that contains the whole input set or relation.
2519 In case of union sets and relations, the polyhedral hull is computed
2522 =item * Other approximations
2524 __isl_give isl_basic_set *
2525 isl_basic_set_drop_constraints_involving_dims(
2526 __isl_take isl_basic_set *bset,
2527 enum isl_dim_type type,
2528 unsigned first, unsigned n);
2529 __isl_give isl_basic_map *
2530 isl_basic_map_drop_constraints_involving_dims(
2531 __isl_take isl_basic_map *bmap,
2532 enum isl_dim_type type,
2533 unsigned first, unsigned n);
2534 __isl_give isl_basic_set *
2535 isl_basic_set_drop_constraints_not_involving_dims(
2536 __isl_take isl_basic_set *bset,
2537 enum isl_dim_type type,
2538 unsigned first, unsigned n);
2539 __isl_give isl_set *
2540 isl_set_drop_constraints_involving_dims(
2541 __isl_take isl_set *set,
2542 enum isl_dim_type type,
2543 unsigned first, unsigned n);
2544 __isl_give isl_map *
2545 isl_map_drop_constraints_involving_dims(
2546 __isl_take isl_map *map,
2547 enum isl_dim_type type,
2548 unsigned first, unsigned n);
2550 These functions drop any constraints (not) involving the specified dimensions.
2551 Note that the result depends on the representation of the input.
2555 __isl_give isl_basic_set *isl_basic_set_sample(
2556 __isl_take isl_basic_set *bset);
2557 __isl_give isl_basic_set *isl_set_sample(
2558 __isl_take isl_set *set);
2559 __isl_give isl_basic_map *isl_basic_map_sample(
2560 __isl_take isl_basic_map *bmap);
2561 __isl_give isl_basic_map *isl_map_sample(
2562 __isl_take isl_map *map);
2564 If the input (basic) set or relation is non-empty, then return
2565 a singleton subset of the input. Otherwise, return an empty set.
2567 =item * Optimization
2569 #include <isl/ilp.h>
2570 __isl_give isl_val *isl_basic_set_max_val(
2571 __isl_keep isl_basic_set *bset,
2572 __isl_keep isl_aff *obj);
2573 __isl_give isl_val *isl_set_min_val(
2574 __isl_keep isl_set *set,
2575 __isl_keep isl_aff *obj);
2576 __isl_give isl_val *isl_set_max_val(
2577 __isl_keep isl_set *set,
2578 __isl_keep isl_aff *obj);
2580 Compute the minimum or maximum of the integer affine expression C<obj>
2581 over the points in C<set>, returning the result in C<opt>.
2582 The result is C<NULL> in case of an error, the optimal value in case
2583 there is one, negative infinity or infinity if the problem is unbounded and
2584 NaN if the problem is empty.
2586 =item * Parametric optimization
2588 __isl_give isl_pw_aff *isl_set_dim_min(
2589 __isl_take isl_set *set, int pos);
2590 __isl_give isl_pw_aff *isl_set_dim_max(
2591 __isl_take isl_set *set, int pos);
2592 __isl_give isl_pw_aff *isl_map_dim_max(
2593 __isl_take isl_map *map, int pos);
2595 Compute the minimum or maximum of the given set or output dimension
2596 as a function of the parameters (and input dimensions), but independently
2597 of the other set or output dimensions.
2598 For lexicographic optimization, see L<"Lexicographic Optimization">.
2602 The following functions compute either the set of (rational) coefficient
2603 values of valid constraints for the given set or the set of (rational)
2604 values satisfying the constraints with coefficients from the given set.
2605 Internally, these two sets of functions perform essentially the
2606 same operations, except that the set of coefficients is assumed to
2607 be a cone, while the set of values may be any polyhedron.
2608 The current implementation is based on the Farkas lemma and
2609 Fourier-Motzkin elimination, but this may change or be made optional
2610 in future. In particular, future implementations may use different
2611 dualization algorithms or skip the elimination step.
2613 __isl_give isl_basic_set *isl_basic_set_coefficients(
2614 __isl_take isl_basic_set *bset);
2615 __isl_give isl_basic_set *isl_set_coefficients(
2616 __isl_take isl_set *set);
2617 __isl_give isl_union_set *isl_union_set_coefficients(
2618 __isl_take isl_union_set *bset);
2619 __isl_give isl_basic_set *isl_basic_set_solutions(
2620 __isl_take isl_basic_set *bset);
2621 __isl_give isl_basic_set *isl_set_solutions(
2622 __isl_take isl_set *set);
2623 __isl_give isl_union_set *isl_union_set_solutions(
2624 __isl_take isl_union_set *bset);
2628 __isl_give isl_map *isl_map_fixed_power_val(
2629 __isl_take isl_map *map,
2630 __isl_take isl_val *exp);
2631 __isl_give isl_union_map *
2632 isl_union_map_fixed_power_val(
2633 __isl_take isl_union_map *umap,
2634 __isl_take isl_val *exp);
2636 Compute the given power of C<map>, where C<exp> is assumed to be non-zero.
2637 If the exponent C<exp> is negative, then the -C<exp> th power of the inverse
2638 of C<map> is computed.
2640 __isl_give isl_map *isl_map_power(__isl_take isl_map *map,
2642 __isl_give isl_union_map *isl_union_map_power(
2643 __isl_take isl_union_map *umap, int *exact);
2645 Compute a parametric representation for all positive powers I<k> of C<map>.
2646 The result maps I<k> to a nested relation corresponding to the
2647 I<k>th power of C<map>.
2648 The result may be an overapproximation. If the result is known to be exact,
2649 then C<*exact> is set to C<1>.
2651 =item * Transitive closure
2653 __isl_give isl_map *isl_map_transitive_closure(
2654 __isl_take isl_map *map, int *exact);
2655 __isl_give isl_union_map *isl_union_map_transitive_closure(
2656 __isl_take isl_union_map *umap, int *exact);
2658 Compute the transitive closure of C<map>.
2659 The result may be an overapproximation. If the result is known to be exact,
2660 then C<*exact> is set to C<1>.
2662 =item * Reaching path lengths
2664 __isl_give isl_map *isl_map_reaching_path_lengths(
2665 __isl_take isl_map *map, int *exact);
2667 Compute a relation that maps each element in the range of C<map>
2668 to the lengths of all paths composed of edges in C<map> that
2669 end up in the given element.
2670 The result may be an overapproximation. If the result is known to be exact,
2671 then C<*exact> is set to C<1>.
2672 To compute the I<maximal> path length, the resulting relation
2673 should be postprocessed by C<isl_map_lexmax>.
2674 In particular, if the input relation is a dependence relation
2675 (mapping sources to sinks), then the maximal path length corresponds
2676 to the free schedule.
2677 Note, however, that C<isl_map_lexmax> expects the maximum to be
2678 finite, so if the path lengths are unbounded (possibly due to
2679 the overapproximation), then you will get an error message.
2683 #include <isl/space.h>
2684 __isl_give isl_space *isl_space_wrap(
2685 __isl_take isl_space *space);
2686 __isl_give isl_space *isl_space_unwrap(
2687 __isl_take isl_space *space);
2689 #include <isl/set.h>
2690 __isl_give isl_basic_map *isl_basic_set_unwrap(
2691 __isl_take isl_basic_set *bset);
2692 __isl_give isl_map *isl_set_unwrap(
2693 __isl_take isl_set *set);
2695 #include <isl/map.h>
2696 __isl_give isl_basic_set *isl_basic_map_wrap(
2697 __isl_take isl_basic_map *bmap);
2698 __isl_give isl_set *isl_map_wrap(
2699 __isl_take isl_map *map);
2701 #include <isl/union_set.h>
2702 __isl_give isl_union_map *isl_union_set_unwrap(
2703 __isl_take isl_union_set *uset);
2705 #include <isl/union_map.h>
2706 __isl_give isl_union_set *isl_union_map_wrap(
2707 __isl_take isl_union_map *umap);
2709 The input to C<isl_space_unwrap> should
2710 be the space of a set, while that of
2711 C<isl_space_wrap> should be the space of a relation.
2712 Conversely, the output of C<isl_space_unwrap> is the space
2713 of a relation, while that of C<isl_space_wrap> is the space of a set.
2717 Remove any internal structure of domain (and range) of the given
2718 set or relation. If there is any such internal structure in the input,
2719 then the name of the space is also removed.
2721 __isl_give isl_basic_set *isl_basic_set_flatten(
2722 __isl_take isl_basic_set *bset);
2723 __isl_give isl_set *isl_set_flatten(
2724 __isl_take isl_set *set);
2725 __isl_give isl_basic_map *isl_basic_map_flatten_domain(
2726 __isl_take isl_basic_map *bmap);
2727 __isl_give isl_basic_map *isl_basic_map_flatten_range(
2728 __isl_take isl_basic_map *bmap);
2729 __isl_give isl_map *isl_map_flatten_range(
2730 __isl_take isl_map *map);
2731 __isl_give isl_map *isl_map_flatten_domain(
2732 __isl_take isl_map *map);
2733 __isl_give isl_basic_map *isl_basic_map_flatten(
2734 __isl_take isl_basic_map *bmap);
2735 __isl_give isl_map *isl_map_flatten(
2736 __isl_take isl_map *map);
2738 __isl_give isl_map *isl_set_flatten_map(
2739 __isl_take isl_set *set);
2741 The function above constructs a relation
2742 that maps the input set to a flattened version of the set.
2746 Lift the input set to a space with extra dimensions corresponding
2747 to the existentially quantified variables in the input.
2748 In particular, the result lives in a wrapped map where the domain
2749 is the original space and the range corresponds to the original
2750 existentially quantified variables.
2752 __isl_give isl_basic_set *isl_basic_set_lift(
2753 __isl_take isl_basic_set *bset);
2754 __isl_give isl_set *isl_set_lift(
2755 __isl_take isl_set *set);
2756 __isl_give isl_union_set *isl_union_set_lift(
2757 __isl_take isl_union_set *uset);
2759 Given a local space that contains the existentially quantified
2760 variables of a set, a basic relation that, when applied to
2761 a basic set, has essentially the same effect as C<isl_basic_set_lift>,
2762 can be constructed using the following function.
2764 #include <isl/local_space.h>
2765 __isl_give isl_basic_map *isl_local_space_lifting(
2766 __isl_take isl_local_space *ls);
2768 =item * Internal Product
2770 __isl_give isl_basic_map *isl_basic_map_zip(
2771 __isl_take isl_basic_map *bmap);
2772 __isl_give isl_map *isl_map_zip(
2773 __isl_take isl_map *map);
2774 __isl_give isl_union_map *isl_union_map_zip(
2775 __isl_take isl_union_map *umap);
2777 Given a relation with nested relations for domain and range,
2778 interchange the range of the domain with the domain of the range.
2782 __isl_give isl_basic_map *isl_basic_map_curry(
2783 __isl_take isl_basic_map *bmap);
2784 __isl_give isl_basic_map *isl_basic_map_uncurry(
2785 __isl_take isl_basic_map *bmap);
2786 __isl_give isl_map *isl_map_curry(
2787 __isl_take isl_map *map);
2788 __isl_give isl_map *isl_map_uncurry(
2789 __isl_take isl_map *map);
2790 __isl_give isl_union_map *isl_union_map_curry(
2791 __isl_take isl_union_map *umap);
2792 __isl_give isl_union_map *isl_union_map_uncurry(
2793 __isl_take isl_union_map *umap);
2795 Given a relation with a nested relation for domain,
2796 the C<curry> functions
2797 move the range of the nested relation out of the domain
2798 and use it as the domain of a nested relation in the range,
2799 with the original range as range of this nested relation.
2800 The C<uncurry> functions perform the inverse operation.
2802 =item * Aligning parameters
2804 __isl_give isl_basic_set *isl_basic_set_align_params(
2805 __isl_take isl_basic_set *bset,
2806 __isl_take isl_space *model);
2807 __isl_give isl_set *isl_set_align_params(
2808 __isl_take isl_set *set,
2809 __isl_take isl_space *model);
2810 __isl_give isl_basic_map *isl_basic_map_align_params(
2811 __isl_take isl_basic_map *bmap,
2812 __isl_take isl_space *model);
2813 __isl_give isl_map *isl_map_align_params(
2814 __isl_take isl_map *map,
2815 __isl_take isl_space *model);
2817 Change the order of the parameters of the given set or relation
2818 such that the first parameters match those of C<model>.
2819 This may involve the introduction of extra parameters.
2820 All parameters need to be named.
2822 =item * Dimension manipulation
2824 #include <isl/local_space.h>
2825 __isl_give isl_local_space *isl_local_space_add_dims(
2826 __isl_take isl_local_space *ls,
2827 enum isl_dim_type type, unsigned n);
2828 __isl_give isl_local_space *isl_local_space_insert_dims(
2829 __isl_take isl_local_space *ls,
2830 enum isl_dim_type type, unsigned first, unsigned n);
2831 __isl_give isl_local_space *isl_local_space_drop_dims(
2832 __isl_take isl_local_space *ls,
2833 enum isl_dim_type type, unsigned first, unsigned n);
2835 #include <isl/set.h>
2836 __isl_give isl_basic_set *isl_basic_set_add_dims(
2837 __isl_take isl_basic_set *bset,
2838 enum isl_dim_type type, unsigned n);
2839 __isl_give isl_set *isl_set_add_dims(
2840 __isl_take isl_set *set,
2841 enum isl_dim_type type, unsigned n);
2842 __isl_give isl_basic_set *isl_basic_set_insert_dims(
2843 __isl_take isl_basic_set *bset,
2844 enum isl_dim_type type, unsigned pos,
2846 __isl_give isl_set *isl_set_insert_dims(
2847 __isl_take isl_set *set,
2848 enum isl_dim_type type, unsigned pos, unsigned n);
2849 __isl_give isl_basic_set *isl_basic_set_move_dims(
2850 __isl_take isl_basic_set *bset,
2851 enum isl_dim_type dst_type, unsigned dst_pos,
2852 enum isl_dim_type src_type, unsigned src_pos,
2854 __isl_give isl_set *isl_set_move_dims(
2855 __isl_take isl_set *set,
2856 enum isl_dim_type dst_type, unsigned dst_pos,
2857 enum isl_dim_type src_type, unsigned src_pos,
2860 #include <isl/map.h>
2861 __isl_give isl_map *isl_map_add_dims(
2862 __isl_take isl_map *map,
2863 enum isl_dim_type type, unsigned n);
2864 __isl_give isl_basic_map *isl_basic_map_insert_dims(
2865 __isl_take isl_basic_map *bmap,
2866 enum isl_dim_type type, unsigned pos,
2868 __isl_give isl_map *isl_map_insert_dims(
2869 __isl_take isl_map *map,
2870 enum isl_dim_type type, unsigned pos, unsigned n);
2871 __isl_give isl_basic_map *isl_basic_map_move_dims(
2872 __isl_take isl_basic_map *bmap,
2873 enum isl_dim_type dst_type, unsigned dst_pos,
2874 enum isl_dim_type src_type, unsigned src_pos,
2876 __isl_give isl_map *isl_map_move_dims(
2877 __isl_take isl_map *map,
2878 enum isl_dim_type dst_type, unsigned dst_pos,
2879 enum isl_dim_type src_type, unsigned src_pos,
2882 It is usually not advisable to directly change the (input or output)
2883 space of a set or a relation as this removes the name and the internal
2884 structure of the space. However, the above functions can be useful
2885 to add new parameters, assuming
2886 C<isl_set_align_params> and C<isl_map_align_params>
2891 =head2 Binary Operations
2893 The two arguments of a binary operation not only need to live
2894 in the same C<isl_ctx>, they currently also need to have
2895 the same (number of) parameters.
2897 =head3 Basic Operations
2901 =item * Intersection
2903 #include <isl/local_space.h>
2904 __isl_give isl_local_space *isl_local_space_intersect(
2905 __isl_take isl_local_space *ls1,
2906 __isl_take isl_local_space *ls2);
2908 #include <isl/set.h>
2909 __isl_give isl_basic_set *isl_basic_set_intersect_params(
2910 __isl_take isl_basic_set *bset1,
2911 __isl_take isl_basic_set *bset2);
2912 __isl_give isl_basic_set *isl_basic_set_intersect(
2913 __isl_take isl_basic_set *bset1,
2914 __isl_take isl_basic_set *bset2);
2915 __isl_give isl_set *isl_set_intersect_params(
2916 __isl_take isl_set *set,
2917 __isl_take isl_set *params);
2918 __isl_give isl_set *isl_set_intersect(
2919 __isl_take isl_set *set1,
2920 __isl_take isl_set *set2);
2922 #include <isl/map.h>
2923 __isl_give isl_basic_map *isl_basic_map_intersect_domain(
2924 __isl_take isl_basic_map *bmap,
2925 __isl_take isl_basic_set *bset);
2926 __isl_give isl_basic_map *isl_basic_map_intersect_range(
2927 __isl_take isl_basic_map *bmap,
2928 __isl_take isl_basic_set *bset);
2929 __isl_give isl_basic_map *isl_basic_map_intersect(
2930 __isl_take isl_basic_map *bmap1,
2931 __isl_take isl_basic_map *bmap2);
2932 __isl_give isl_map *isl_map_intersect_params(
2933 __isl_take isl_map *map,
2934 __isl_take isl_set *params);
2935 __isl_give isl_map *isl_map_intersect_domain(
2936 __isl_take isl_map *map,
2937 __isl_take isl_set *set);
2938 __isl_give isl_map *isl_map_intersect_range(
2939 __isl_take isl_map *map,
2940 __isl_take isl_set *set);
2941 __isl_give isl_map *isl_map_intersect(
2942 __isl_take isl_map *map1,
2943 __isl_take isl_map *map2);
2945 #include <isl/union_set.h>
2946 __isl_give isl_union_set *isl_union_set_intersect_params(
2947 __isl_take isl_union_set *uset,
2948 __isl_take isl_set *set);
2949 __isl_give isl_union_set *isl_union_set_intersect(
2950 __isl_take isl_union_set *uset1,
2951 __isl_take isl_union_set *uset2);
2953 #include <isl/union_map.h>
2954 __isl_give isl_union_map *isl_union_map_intersect_params(
2955 __isl_take isl_union_map *umap,
2956 __isl_take isl_set *set);
2957 __isl_give isl_union_map *isl_union_map_intersect_domain(
2958 __isl_take isl_union_map *umap,
2959 __isl_take isl_union_set *uset);
2960 __isl_give isl_union_map *isl_union_map_intersect_range(
2961 __isl_take isl_union_map *umap,
2962 __isl_take isl_union_set *uset);
2963 __isl_give isl_union_map *isl_union_map_intersect(
2964 __isl_take isl_union_map *umap1,
2965 __isl_take isl_union_map *umap2);
2967 The second argument to the C<_params> functions needs to be
2968 a parametric (basic) set. For the other functions, a parametric set
2969 for either argument is only allowed if the other argument is
2970 a parametric set as well.
2974 __isl_give isl_set *isl_basic_set_union(
2975 __isl_take isl_basic_set *bset1,
2976 __isl_take isl_basic_set *bset2);
2977 __isl_give isl_map *isl_basic_map_union(
2978 __isl_take isl_basic_map *bmap1,
2979 __isl_take isl_basic_map *bmap2);
2980 __isl_give isl_set *isl_set_union(
2981 __isl_take isl_set *set1,
2982 __isl_take isl_set *set2);
2983 __isl_give isl_map *isl_map_union(
2984 __isl_take isl_map *map1,
2985 __isl_take isl_map *map2);
2986 __isl_give isl_union_set *isl_union_set_union(
2987 __isl_take isl_union_set *uset1,
2988 __isl_take isl_union_set *uset2);
2989 __isl_give isl_union_map *isl_union_map_union(
2990 __isl_take isl_union_map *umap1,
2991 __isl_take isl_union_map *umap2);
2993 =item * Set difference
2995 __isl_give isl_set *isl_set_subtract(
2996 __isl_take isl_set *set1,
2997 __isl_take isl_set *set2);
2998 __isl_give isl_map *isl_map_subtract(
2999 __isl_take isl_map *map1,
3000 __isl_take isl_map *map2);
3001 __isl_give isl_map *isl_map_subtract_domain(
3002 __isl_take isl_map *map,
3003 __isl_take isl_set *dom);
3004 __isl_give isl_map *isl_map_subtract_range(
3005 __isl_take isl_map *map,
3006 __isl_take isl_set *dom);
3007 __isl_give isl_union_set *isl_union_set_subtract(
3008 __isl_take isl_union_set *uset1,
3009 __isl_take isl_union_set *uset2);
3010 __isl_give isl_union_map *isl_union_map_subtract(
3011 __isl_take isl_union_map *umap1,
3012 __isl_take isl_union_map *umap2);
3013 __isl_give isl_union_map *isl_union_map_subtract_domain(
3014 __isl_take isl_union_map *umap,
3015 __isl_take isl_union_set *dom);
3016 __isl_give isl_union_map *isl_union_map_subtract_range(
3017 __isl_take isl_union_map *umap,
3018 __isl_take isl_union_set *dom);
3022 __isl_give isl_basic_set *isl_basic_set_apply(
3023 __isl_take isl_basic_set *bset,
3024 __isl_take isl_basic_map *bmap);
3025 __isl_give isl_set *isl_set_apply(
3026 __isl_take isl_set *set,
3027 __isl_take isl_map *map);
3028 __isl_give isl_union_set *isl_union_set_apply(
3029 __isl_take isl_union_set *uset,
3030 __isl_take isl_union_map *umap);
3031 __isl_give isl_basic_map *isl_basic_map_apply_domain(
3032 __isl_take isl_basic_map *bmap1,
3033 __isl_take isl_basic_map *bmap2);
3034 __isl_give isl_basic_map *isl_basic_map_apply_range(
3035 __isl_take isl_basic_map *bmap1,
3036 __isl_take isl_basic_map *bmap2);
3037 __isl_give isl_map *isl_map_apply_domain(
3038 __isl_take isl_map *map1,
3039 __isl_take isl_map *map2);
3040 __isl_give isl_union_map *isl_union_map_apply_domain(
3041 __isl_take isl_union_map *umap1,
3042 __isl_take isl_union_map *umap2);
3043 __isl_give isl_map *isl_map_apply_range(
3044 __isl_take isl_map *map1,
3045 __isl_take isl_map *map2);
3046 __isl_give isl_union_map *isl_union_map_apply_range(
3047 __isl_take isl_union_map *umap1,
3048 __isl_take isl_union_map *umap2);
3052 __isl_give isl_basic_set *
3053 isl_basic_set_preimage_multi_aff(
3054 __isl_take isl_basic_set *bset,
3055 __isl_take isl_multi_aff *ma);
3056 __isl_give isl_set *isl_set_preimage_multi_aff(
3057 __isl_take isl_set *set,
3058 __isl_take isl_multi_aff *ma);
3059 __isl_give isl_set *isl_set_preimage_pw_multi_aff(
3060 __isl_take isl_set *set,
3061 __isl_take isl_pw_multi_aff *pma);
3062 __isl_give isl_set *isl_set_preimage_multi_pw_aff(
3063 __isl_take isl_set *set,
3064 __isl_take isl_multi_pw_aff *mpa);
3065 __isl_give isl_basic_map *
3066 isl_basic_map_preimage_domain_multi_aff(
3067 __isl_take isl_basic_map *bmap,
3068 __isl_take isl_multi_aff *ma);
3069 __isl_give isl_map *isl_map_preimage_domain_multi_aff(
3070 __isl_take isl_map *map,
3071 __isl_take isl_multi_aff *ma);
3072 __isl_give isl_map *
3073 isl_map_preimage_domain_pw_multi_aff(
3074 __isl_take isl_map *map,
3075 __isl_take isl_pw_multi_aff *pma);
3076 __isl_give isl_map *
3077 isl_map_preimage_domain_multi_pw_aff(
3078 __isl_take isl_map *map,
3079 __isl_take isl_multi_pw_aff *mpa);
3080 __isl_give isl_union_map *
3081 isl_union_map_preimage_domain_multi_aff(
3082 __isl_take isl_union_map *umap,
3083 __isl_take isl_multi_aff *ma);
3084 __isl_give isl_basic_map *
3085 isl_basic_map_preimage_range_multi_aff(
3086 __isl_take isl_basic_map *bmap,
3087 __isl_take isl_multi_aff *ma);
3089 These functions compute the preimage of the given set or map domain/range under
3090 the given function. In other words, the expression is plugged
3091 into the set description or into the domain/range of the map.
3092 Objects of types C<isl_multi_aff> and C<isl_pw_multi_aff> are described in
3093 L</"Piecewise Multiple Quasi Affine Expressions">.
3095 =item * Cartesian Product
3097 #include <isl/space.h>
3098 __isl_give isl_space *isl_space_product(
3099 __isl_take isl_space *space1,
3100 __isl_take isl_space *space2);
3101 __isl_give isl_space *isl_space_domain_product(
3102 __isl_take isl_space *space1,
3103 __isl_take isl_space *space2);
3104 __isl_give isl_space *isl_space_range_product(
3105 __isl_take isl_space *space1,
3106 __isl_take isl_space *space2);
3109 C<isl_space_product>, C<isl_space_domain_product>
3110 and C<isl_space_range_product> take pairs or relation spaces and
3111 produce a single relations space, where either the domain, the range
3112 or both domain and range are wrapped spaces of relations between
3113 the domains and/or ranges of the input spaces.
3114 If the product is only constructed over the domain or the range
3115 then the ranges or the domains of the inputs should be the same.
3117 #include <isl/set.h>
3118 __isl_give isl_set *isl_set_product(
3119 __isl_take isl_set *set1,
3120 __isl_take isl_set *set2);
3122 #include <isl/map.h>
3123 __isl_give isl_basic_map *isl_basic_map_domain_product(
3124 __isl_take isl_basic_map *bmap1,
3125 __isl_take isl_basic_map *bmap2);
3126 __isl_give isl_basic_map *isl_basic_map_range_product(
3127 __isl_take isl_basic_map *bmap1,
3128 __isl_take isl_basic_map *bmap2);
3129 __isl_give isl_basic_map *isl_basic_map_product(
3130 __isl_take isl_basic_map *bmap1,
3131 __isl_take isl_basic_map *bmap2);
3132 __isl_give isl_map *isl_map_domain_product(
3133 __isl_take isl_map *map1,
3134 __isl_take isl_map *map2);
3135 __isl_give isl_map *isl_map_range_product(
3136 __isl_take isl_map *map1,
3137 __isl_take isl_map *map2);
3138 __isl_give isl_map *isl_map_product(
3139 __isl_take isl_map *map1,
3140 __isl_take isl_map *map2);
3142 #include <isl/union_set.h>
3143 __isl_give isl_union_set *isl_union_set_product(
3144 __isl_take isl_union_set *uset1,
3145 __isl_take isl_union_set *uset2);
3147 #include <isl/union_map.h>
3148 __isl_give isl_union_map *isl_union_map_domain_product(
3149 __isl_take isl_union_map *umap1,
3150 __isl_take isl_union_map *umap2);
3151 __isl_give isl_union_map *isl_union_map_range_product(
3152 __isl_take isl_union_map *umap1,
3153 __isl_take isl_union_map *umap2);
3154 __isl_give isl_union_map *isl_union_map_product(
3155 __isl_take isl_union_map *umap1,
3156 __isl_take isl_union_map *umap2);
3158 The above functions compute the cross product of the given
3159 sets or relations. The domains and ranges of the results
3160 are wrapped maps between domains and ranges of the inputs.
3161 To obtain a ``flat'' product, use the following functions
3164 __isl_give isl_basic_set *isl_basic_set_flat_product(
3165 __isl_take isl_basic_set *bset1,
3166 __isl_take isl_basic_set *bset2);
3167 __isl_give isl_set *isl_set_flat_product(
3168 __isl_take isl_set *set1,
3169 __isl_take isl_set *set2);
3170 __isl_give isl_basic_map *isl_basic_map_flat_range_product(
3171 __isl_take isl_basic_map *bmap1,
3172 __isl_take isl_basic_map *bmap2);
3173 __isl_give isl_map *isl_map_flat_domain_product(
3174 __isl_take isl_map *map1,
3175 __isl_take isl_map *map2);
3176 __isl_give isl_map *isl_map_flat_range_product(
3177 __isl_take isl_map *map1,
3178 __isl_take isl_map *map2);
3179 __isl_give isl_union_map *isl_union_map_flat_range_product(
3180 __isl_take isl_union_map *umap1,
3181 __isl_take isl_union_map *umap2);
3182 __isl_give isl_basic_map *isl_basic_map_flat_product(
3183 __isl_take isl_basic_map *bmap1,
3184 __isl_take isl_basic_map *bmap2);
3185 __isl_give isl_map *isl_map_flat_product(
3186 __isl_take isl_map *map1,
3187 __isl_take isl_map *map2);
3189 #include <isl/space.h>
3190 __isl_give isl_space *isl_space_domain_factor_domain(
3191 __isl_take isl_space *space);
3192 __isl_give isl_space *isl_space_range_factor_domain(
3193 __isl_take isl_space *space);
3194 __isl_give isl_space *isl_space_range_factor_range(
3195 __isl_take isl_space *space);
3197 The functions C<isl_space_range_factor_domain> and
3198 C<isl_space_range_factor_range> extract the two arguments from
3199 the result of a call to C<isl_space_range_product>.
3201 The arguments of a call to C<isl_map_range_product> can be extracted
3202 from the result using the following two functions.
3204 #include <isl/map.h>
3205 __isl_give isl_map *isl_map_range_factor_domain(
3206 __isl_take isl_map *map);
3207 __isl_give isl_map *isl_map_range_factor_range(
3208 __isl_take isl_map *map);
3210 =item * Simplification
3212 __isl_give isl_basic_set *isl_basic_set_gist(
3213 __isl_take isl_basic_set *bset,
3214 __isl_take isl_basic_set *context);
3215 __isl_give isl_set *isl_set_gist(__isl_take isl_set *set,
3216 __isl_take isl_set *context);
3217 __isl_give isl_set *isl_set_gist_params(
3218 __isl_take isl_set *set,
3219 __isl_take isl_set *context);
3220 __isl_give isl_union_set *isl_union_set_gist(
3221 __isl_take isl_union_set *uset,
3222 __isl_take isl_union_set *context);
3223 __isl_give isl_union_set *isl_union_set_gist_params(
3224 __isl_take isl_union_set *uset,
3225 __isl_take isl_set *set);
3226 __isl_give isl_basic_map *isl_basic_map_gist(
3227 __isl_take isl_basic_map *bmap,
3228 __isl_take isl_basic_map *context);
3229 __isl_give isl_map *isl_map_gist(__isl_take isl_map *map,
3230 __isl_take isl_map *context);
3231 __isl_give isl_map *isl_map_gist_params(
3232 __isl_take isl_map *map,
3233 __isl_take isl_set *context);
3234 __isl_give isl_map *isl_map_gist_domain(
3235 __isl_take isl_map *map,
3236 __isl_take isl_set *context);
3237 __isl_give isl_map *isl_map_gist_range(
3238 __isl_take isl_map *map,
3239 __isl_take isl_set *context);
3240 __isl_give isl_union_map *isl_union_map_gist(
3241 __isl_take isl_union_map *umap,
3242 __isl_take isl_union_map *context);
3243 __isl_give isl_union_map *isl_union_map_gist_params(
3244 __isl_take isl_union_map *umap,
3245 __isl_take isl_set *set);
3246 __isl_give isl_union_map *isl_union_map_gist_domain(
3247 __isl_take isl_union_map *umap,
3248 __isl_take isl_union_set *uset);
3249 __isl_give isl_union_map *isl_union_map_gist_range(
3250 __isl_take isl_union_map *umap,
3251 __isl_take isl_union_set *uset);
3253 The gist operation returns a set or relation that has the
3254 same intersection with the context as the input set or relation.
3255 Any implicit equality in the intersection is made explicit in the result,
3256 while all inequalities that are redundant with respect to the intersection
3258 In case of union sets and relations, the gist operation is performed
3263 =head3 Lexicographic Optimization
3265 Given a (basic) set C<set> (or C<bset>) and a zero-dimensional domain C<dom>,
3266 the following functions
3267 compute a set that contains the lexicographic minimum or maximum
3268 of the elements in C<set> (or C<bset>) for those values of the parameters
3269 that satisfy C<dom>.
3270 If C<empty> is not C<NULL>, then C<*empty> is assigned a set
3271 that contains the parameter values in C<dom> for which C<set> (or C<bset>)
3273 In other words, the union of the parameter values
3274 for which the result is non-empty and of C<*empty>
3277 __isl_give isl_set *isl_basic_set_partial_lexmin(
3278 __isl_take isl_basic_set *bset,
3279 __isl_take isl_basic_set *dom,
3280 __isl_give isl_set **empty);
3281 __isl_give isl_set *isl_basic_set_partial_lexmax(
3282 __isl_take isl_basic_set *bset,
3283 __isl_take isl_basic_set *dom,
3284 __isl_give isl_set **empty);
3285 __isl_give isl_set *isl_set_partial_lexmin(
3286 __isl_take isl_set *set, __isl_take isl_set *dom,
3287 __isl_give isl_set **empty);
3288 __isl_give isl_set *isl_set_partial_lexmax(
3289 __isl_take isl_set *set, __isl_take isl_set *dom,
3290 __isl_give isl_set **empty);
3292 Given a (basic) set C<set> (or C<bset>), the following functions simply
3293 return a set containing the lexicographic minimum or maximum
3294 of the elements in C<set> (or C<bset>).
3295 In case of union sets, the optimum is computed per space.
3297 __isl_give isl_set *isl_basic_set_lexmin(
3298 __isl_take isl_basic_set *bset);
3299 __isl_give isl_set *isl_basic_set_lexmax(
3300 __isl_take isl_basic_set *bset);
3301 __isl_give isl_set *isl_set_lexmin(
3302 __isl_take isl_set *set);
3303 __isl_give isl_set *isl_set_lexmax(
3304 __isl_take isl_set *set);
3305 __isl_give isl_union_set *isl_union_set_lexmin(
3306 __isl_take isl_union_set *uset);
3307 __isl_give isl_union_set *isl_union_set_lexmax(
3308 __isl_take isl_union_set *uset);
3310 Given a (basic) relation C<map> (or C<bmap>) and a domain C<dom>,
3311 the following functions
3312 compute a relation that maps each element of C<dom>
3313 to the single lexicographic minimum or maximum
3314 of the elements that are associated to that same
3315 element in C<map> (or C<bmap>).
3316 If C<empty> is not C<NULL>, then C<*empty> is assigned a set
3317 that contains the elements in C<dom> that do not map
3318 to any elements in C<map> (or C<bmap>).
3319 In other words, the union of the domain of the result and of C<*empty>
3322 __isl_give isl_map *isl_basic_map_partial_lexmax(
3323 __isl_take isl_basic_map *bmap,
3324 __isl_take isl_basic_set *dom,
3325 __isl_give isl_set **empty);
3326 __isl_give isl_map *isl_basic_map_partial_lexmin(
3327 __isl_take isl_basic_map *bmap,
3328 __isl_take isl_basic_set *dom,
3329 __isl_give isl_set **empty);
3330 __isl_give isl_map *isl_map_partial_lexmax(
3331 __isl_take isl_map *map, __isl_take isl_set *dom,
3332 __isl_give isl_set **empty);
3333 __isl_give isl_map *isl_map_partial_lexmin(
3334 __isl_take isl_map *map, __isl_take isl_set *dom,
3335 __isl_give isl_set **empty);
3337 Given a (basic) map C<map> (or C<bmap>), the following functions simply
3338 return a map mapping each element in the domain of
3339 C<map> (or C<bmap>) to the lexicographic minimum or maximum
3340 of all elements associated to that element.
3341 In case of union relations, the optimum is computed per space.
3343 __isl_give isl_map *isl_basic_map_lexmin(
3344 __isl_take isl_basic_map *bmap);
3345 __isl_give isl_map *isl_basic_map_lexmax(
3346 __isl_take isl_basic_map *bmap);
3347 __isl_give isl_map *isl_map_lexmin(
3348 __isl_take isl_map *map);
3349 __isl_give isl_map *isl_map_lexmax(
3350 __isl_take isl_map *map);
3351 __isl_give isl_union_map *isl_union_map_lexmin(
3352 __isl_take isl_union_map *umap);
3353 __isl_give isl_union_map *isl_union_map_lexmax(
3354 __isl_take isl_union_map *umap);
3356 The following functions return their result in the form of
3357 a piecewise multi-affine expression
3358 (See L<"Piecewise Multiple Quasi Affine Expressions">),
3359 but are otherwise equivalent to the corresponding functions
3360 returning a basic set or relation.
3362 __isl_give isl_pw_multi_aff *
3363 isl_basic_map_lexmin_pw_multi_aff(
3364 __isl_take isl_basic_map *bmap);
3365 __isl_give isl_pw_multi_aff *
3366 isl_basic_set_partial_lexmin_pw_multi_aff(
3367 __isl_take isl_basic_set *bset,
3368 __isl_take isl_basic_set *dom,
3369 __isl_give isl_set **empty);
3370 __isl_give isl_pw_multi_aff *
3371 isl_basic_set_partial_lexmax_pw_multi_aff(
3372 __isl_take isl_basic_set *bset,
3373 __isl_take isl_basic_set *dom,
3374 __isl_give isl_set **empty);
3375 __isl_give isl_pw_multi_aff *
3376 isl_basic_map_partial_lexmin_pw_multi_aff(
3377 __isl_take isl_basic_map *bmap,
3378 __isl_take isl_basic_set *dom,
3379 __isl_give isl_set **empty);
3380 __isl_give isl_pw_multi_aff *
3381 isl_basic_map_partial_lexmax_pw_multi_aff(
3382 __isl_take isl_basic_map *bmap,
3383 __isl_take isl_basic_set *dom,
3384 __isl_give isl_set **empty);
3385 __isl_give isl_pw_multi_aff *isl_set_lexmin_pw_multi_aff(
3386 __isl_take isl_set *set);
3387 __isl_give isl_pw_multi_aff *isl_set_lexmax_pw_multi_aff(
3388 __isl_take isl_set *set);
3389 __isl_give isl_pw_multi_aff *isl_map_lexmin_pw_multi_aff(
3390 __isl_take isl_map *map);
3391 __isl_give isl_pw_multi_aff *isl_map_lexmax_pw_multi_aff(
3392 __isl_take isl_map *map);
3396 Lists are defined over several element types, including
3397 C<isl_val>, C<isl_id>, C<isl_aff>, C<isl_pw_aff>, C<isl_constraint>,
3398 C<isl_basic_set>, C<isl_set>, C<isl_ast_expr> and C<isl_ast_node>.
3399 Here we take lists of C<isl_set>s as an example.
3400 Lists can be created, copied, modified and freed using the following functions.
3402 #include <isl/list.h>
3403 __isl_give isl_set_list *isl_set_list_from_set(
3404 __isl_take isl_set *el);
3405 __isl_give isl_set_list *isl_set_list_alloc(
3406 isl_ctx *ctx, int n);
3407 __isl_give isl_set_list *isl_set_list_copy(
3408 __isl_keep isl_set_list *list);
3409 __isl_give isl_set_list *isl_set_list_insert(
3410 __isl_take isl_set_list *list, unsigned pos,
3411 __isl_take isl_set *el);
3412 __isl_give isl_set_list *isl_set_list_add(
3413 __isl_take isl_set_list *list,
3414 __isl_take isl_set *el);
3415 __isl_give isl_set_list *isl_set_list_drop(
3416 __isl_take isl_set_list *list,
3417 unsigned first, unsigned n);
3418 __isl_give isl_set_list *isl_set_list_set_set(
3419 __isl_take isl_set_list *list, int index,
3420 __isl_take isl_set *set);
3421 __isl_give isl_set_list *isl_set_list_concat(
3422 __isl_take isl_set_list *list1,
3423 __isl_take isl_set_list *list2);
3424 __isl_give isl_set_list *isl_set_list_sort(
3425 __isl_take isl_set_list *list,
3426 int (*cmp)(__isl_keep isl_set *a,
3427 __isl_keep isl_set *b, void *user),
3429 void *isl_set_list_free(__isl_take isl_set_list *list);
3431 C<isl_set_list_alloc> creates an empty list with a capacity for
3432 C<n> elements. C<isl_set_list_from_set> creates a list with a single
3435 Lists can be inspected using the following functions.
3437 #include <isl/list.h>
3438 isl_ctx *isl_set_list_get_ctx(__isl_keep isl_set_list *list);
3439 int isl_set_list_n_set(__isl_keep isl_set_list *list);
3440 __isl_give isl_set *isl_set_list_get_set(
3441 __isl_keep isl_set_list *list, int index);
3442 int isl_set_list_foreach(__isl_keep isl_set_list *list,
3443 int (*fn)(__isl_take isl_set *el, void *user),
3445 int isl_set_list_foreach_scc(__isl_keep isl_set_list *list,
3446 int (*follows)(__isl_keep isl_set *a,
3447 __isl_keep isl_set *b, void *user),
3449 int (*fn)(__isl_take isl_set *el, void *user),
3452 The function C<isl_set_list_foreach_scc> calls C<fn> on each of the
3453 strongly connected components of the graph with as vertices the elements
3454 of C<list> and a directed edge from vertex C<b> to vertex C<a>
3455 iff C<follows(a, b)> returns C<1>. The callbacks C<follows> and C<fn>
3456 should return C<-1> on error.
3458 Lists can be printed using
3460 #include <isl/list.h>
3461 __isl_give isl_printer *isl_printer_print_set_list(
3462 __isl_take isl_printer *p,
3463 __isl_keep isl_set_list *list);
3465 =head2 Associative arrays
3467 Associative arrays map isl objects of a specific type to isl objects
3468 of some (other) specific type. They are defined for several pairs
3469 of types, including (C<isl_map>, C<isl_basic_set>),
3470 (C<isl_id>, C<isl_ast_expr>) and.
3471 (C<isl_id>, C<isl_pw_aff>).
3472 Here, we take associative arrays that map C<isl_id>s to C<isl_ast_expr>s
3475 Associative arrays can be created, copied and freed using
3476 the following functions.
3478 #include <isl/id_to_ast_expr.h>
3479 __isl_give id_to_ast_expr *isl_id_to_ast_expr_alloc(
3480 isl_ctx *ctx, int min_size);
3481 __isl_give id_to_ast_expr *isl_id_to_ast_expr_copy(
3482 __isl_keep id_to_ast_expr *id2expr);
3483 void *isl_id_to_ast_expr_free(
3484 __isl_take id_to_ast_expr *id2expr);
3486 The C<min_size> argument to C<isl_id_to_ast_expr_alloc> can be used
3487 to specify the expected size of the associative array.
3488 The associative array will be grown automatically as needed.
3490 Associative arrays can be inspected using the following functions.
3492 #include <isl/id_to_ast_expr.h>
3493 isl_ctx *isl_id_to_ast_expr_get_ctx(
3494 __isl_keep id_to_ast_expr *id2expr);
3495 int isl_id_to_ast_expr_has(
3496 __isl_keep id_to_ast_expr *id2expr,
3497 __isl_keep isl_id *key);
3498 __isl_give isl_ast_expr *isl_id_to_ast_expr_get(
3499 __isl_keep id_to_ast_expr *id2expr,
3500 __isl_take isl_id *key);
3501 int isl_id_to_ast_expr_foreach(
3502 __isl_keep id_to_ast_expr *id2expr,
3503 int (*fn)(__isl_take isl_id *key,
3504 __isl_take isl_ast_expr *val, void *user),
3507 They can be modified using the following function.
3509 #include <isl/id_to_ast_expr.h>
3510 __isl_give id_to_ast_expr *isl_id_to_ast_expr_set(
3511 __isl_take id_to_ast_expr *id2expr,
3512 __isl_take isl_id *key,
3513 __isl_take isl_ast_expr *val);
3514 __isl_give id_to_ast_expr *isl_id_to_ast_expr_drop(
3515 __isl_take id_to_ast_expr *id2expr,
3516 __isl_take isl_id *key);
3518 Associative arrays can be printed using the following function.
3520 #include <isl/id_to_ast_expr.h>
3521 __isl_give isl_printer *isl_printer_print_id_to_ast_expr(
3522 __isl_take isl_printer *p,
3523 __isl_keep id_to_ast_expr *id2expr);
3525 =head2 Multiple Values
3527 An C<isl_multi_val> object represents a sequence of zero or more values,
3528 living in a set space.
3530 An C<isl_multi_val> can be constructed from an C<isl_val_list>
3531 using the following function
3533 #include <isl/val.h>
3534 __isl_give isl_multi_val *isl_multi_val_from_val_list(
3535 __isl_take isl_space *space,
3536 __isl_take isl_val_list *list);
3538 The zero multiple value (with value zero for each set dimension)
3539 can be created using the following function.
3541 #include <isl/val.h>
3542 __isl_give isl_multi_val *isl_multi_val_zero(
3543 __isl_take isl_space *space);
3545 Multiple values can be copied and freed using
3547 #include <isl/val.h>
3548 __isl_give isl_multi_val *isl_multi_val_copy(
3549 __isl_keep isl_multi_val *mv);
3550 void *isl_multi_val_free(__isl_take isl_multi_val *mv);
3552 They can be inspected using
3554 #include <isl/val.h>
3555 isl_ctx *isl_multi_val_get_ctx(
3556 __isl_keep isl_multi_val *mv);
3557 unsigned isl_multi_val_dim(__isl_keep isl_multi_val *mv,
3558 enum isl_dim_type type);
3559 __isl_give isl_val *isl_multi_val_get_val(
3560 __isl_keep isl_multi_val *mv, int pos);
3561 int isl_multi_val_find_dim_by_id(
3562 __isl_keep isl_multi_val *mv,
3563 enum isl_dim_type type, __isl_keep isl_id *id);
3564 __isl_give isl_id *isl_multi_val_get_dim_id(
3565 __isl_keep isl_multi_val *mv,
3566 enum isl_dim_type type, unsigned pos);
3567 const char *isl_multi_val_get_tuple_name(
3568 __isl_keep isl_multi_val *mv,
3569 enum isl_dim_type type);
3570 int isl_multi_val_has_tuple_id(__isl_keep isl_multi_val *mv,
3571 enum isl_dim_type type);
3572 __isl_give isl_id *isl_multi_val_get_tuple_id(
3573 __isl_keep isl_multi_val *mv,
3574 enum isl_dim_type type);
3575 int isl_multi_val_range_is_wrapping(
3576 __isl_keep isl_multi_val *mv);
3578 They can be modified using
3580 #include <isl/val.h>
3581 __isl_give isl_multi_val *isl_multi_val_set_val(
3582 __isl_take isl_multi_val *mv, int pos,
3583 __isl_take isl_val *val);
3584 __isl_give isl_multi_val *isl_multi_val_set_dim_name(
3585 __isl_take isl_multi_val *mv,
3586 enum isl_dim_type type, unsigned pos, const char *s);
3587 __isl_give isl_multi_val *isl_multi_val_set_dim_id(
3588 __isl_take isl_multi_val *mv,
3589 enum isl_dim_type type, unsigned pos,
3590 __isl_take isl_id *id);
3591 __isl_give isl_multi_val *isl_multi_val_set_tuple_name(
3592 __isl_take isl_multi_val *mv,
3593 enum isl_dim_type type, const char *s);
3594 __isl_give isl_multi_val *isl_multi_val_set_tuple_id(
3595 __isl_take isl_multi_val *mv,
3596 enum isl_dim_type type, __isl_take isl_id *id);
3597 __isl_give isl_multi_val *isl_multi_val_reset_tuple_id(
3598 __isl_take isl_multi_val *mv,
3599 enum isl_dim_type type);
3600 __isl_give isl_multi_val *isl_multi_val_reset_user(
3601 __isl_take isl_multi_val *mv);
3603 __isl_give isl_multi_val *isl_multi_val_insert_dims(
3604 __isl_take isl_multi_val *mv,
3605 enum isl_dim_type type, unsigned first, unsigned n);
3606 __isl_give isl_multi_val *isl_multi_val_add_dims(
3607 __isl_take isl_multi_val *mv,
3608 enum isl_dim_type type, unsigned n);
3609 __isl_give isl_multi_val *isl_multi_val_drop_dims(
3610 __isl_take isl_multi_val *mv,
3611 enum isl_dim_type type, unsigned first, unsigned n);
3615 #include <isl/val.h>
3616 __isl_give isl_multi_val *isl_multi_val_align_params(
3617 __isl_take isl_multi_val *mv,
3618 __isl_take isl_space *model);
3619 __isl_give isl_multi_val *isl_multi_val_from_range(
3620 __isl_take isl_multi_val *mv);
3621 __isl_give isl_multi_val *isl_multi_val_range_splice(
3622 __isl_take isl_multi_val *mv1, unsigned pos,
3623 __isl_take isl_multi_val *mv2);
3624 __isl_give isl_multi_val *isl_multi_val_range_product(
3625 __isl_take isl_multi_val *mv1,
3626 __isl_take isl_multi_val *mv2);
3627 __isl_give isl_multi_val *
3628 isl_multi_val_range_factor_domain(
3629 __isl_take isl_multi_val *mv);
3630 __isl_give isl_multi_val *
3631 isl_multi_val_range_factor_range(
3632 __isl_take isl_multi_val *mv);
3633 __isl_give isl_multi_val *isl_multi_val_flat_range_product(
3634 __isl_take isl_multi_val *mv1,
3635 __isl_take isl_multi_aff *mv2);
3636 __isl_give isl_multi_val *isl_multi_val_product(
3637 __isl_take isl_multi_val *mv1,
3638 __isl_take isl_multi_val *mv2);
3639 __isl_give isl_multi_val *isl_multi_val_add_val(
3640 __isl_take isl_multi_val *mv,
3641 __isl_take isl_val *v);
3642 __isl_give isl_multi_val *isl_multi_val_mod_val(
3643 __isl_take isl_multi_val *mv,
3644 __isl_take isl_val *v);
3645 __isl_give isl_multi_val *isl_multi_val_scale_val(
3646 __isl_take isl_multi_val *mv,
3647 __isl_take isl_val *v);
3648 __isl_give isl_multi_val *isl_multi_val_scale_multi_val(
3649 __isl_take isl_multi_val *mv1,
3650 __isl_take isl_multi_val *mv2);
3651 __isl_give isl_multi_val *
3652 isl_multi_val_scale_down_multi_val(
3653 __isl_take isl_multi_val *mv1,
3654 __isl_take isl_multi_val *mv2);
3656 A multiple value can be printed using
3658 __isl_give isl_printer *isl_printer_print_multi_val(
3659 __isl_take isl_printer *p,
3660 __isl_keep isl_multi_val *mv);
3664 Vectors can be created, copied and freed using the following functions.
3666 #include <isl/vec.h>
3667 __isl_give isl_vec *isl_vec_alloc(isl_ctx *ctx,
3669 __isl_give isl_vec *isl_vec_copy(__isl_keep isl_vec *vec);
3670 void *isl_vec_free(__isl_take isl_vec *vec);
3672 Note that the elements of a newly created vector may have arbitrary values.
3673 The elements can be changed and inspected using the following functions.
3675 isl_ctx *isl_vec_get_ctx(__isl_keep isl_vec *vec);
3676 int isl_vec_size(__isl_keep isl_vec *vec);
3677 __isl_give isl_val *isl_vec_get_element_val(
3678 __isl_keep isl_vec *vec, int pos);
3679 __isl_give isl_vec *isl_vec_set_element_si(
3680 __isl_take isl_vec *vec, int pos, int v);
3681 __isl_give isl_vec *isl_vec_set_element_val(
3682 __isl_take isl_vec *vec, int pos,
3683 __isl_take isl_val *v);
3684 __isl_give isl_vec *isl_vec_set_si(__isl_take isl_vec *vec,
3686 __isl_give isl_vec *isl_vec_set_val(
3687 __isl_take isl_vec *vec, __isl_take isl_val *v);
3688 int isl_vec_cmp_element(__isl_keep isl_vec *vec1,
3689 __isl_keep isl_vec *vec2, int pos);
3691 C<isl_vec_get_element> will return a negative value if anything went wrong.
3692 In that case, the value of C<*v> is undefined.
3694 The following function can be used to concatenate two vectors.
3696 __isl_give isl_vec *isl_vec_concat(__isl_take isl_vec *vec1,
3697 __isl_take isl_vec *vec2);
3701 Matrices can be created, copied and freed using the following functions.
3703 #include <isl/mat.h>
3704 __isl_give isl_mat *isl_mat_alloc(isl_ctx *ctx,
3705 unsigned n_row, unsigned n_col);
3706 __isl_give isl_mat *isl_mat_copy(__isl_keep isl_mat *mat);
3707 void *isl_mat_free(__isl_take isl_mat *mat);
3709 Note that the elements of a newly created matrix may have arbitrary values.
3710 The elements can be changed and inspected using the following functions.
3712 isl_ctx *isl_mat_get_ctx(__isl_keep isl_mat *mat);
3713 int isl_mat_rows(__isl_keep isl_mat *mat);
3714 int isl_mat_cols(__isl_keep isl_mat *mat);
3715 __isl_give isl_val *isl_mat_get_element_val(
3716 __isl_keep isl_mat *mat, int row, int col);
3717 __isl_give isl_mat *isl_mat_set_element_si(__isl_take isl_mat *mat,
3718 int row, int col, int v);
3719 __isl_give isl_mat *isl_mat_set_element_val(
3720 __isl_take isl_mat *mat, int row, int col,
3721 __isl_take isl_val *v);
3723 C<isl_mat_get_element> will return a negative value if anything went wrong.
3724 In that case, the value of C<*v> is undefined.
3726 The following function can be used to compute the (right) inverse
3727 of a matrix, i.e., a matrix such that the product of the original
3728 and the inverse (in that order) is a multiple of the identity matrix.
3729 The input matrix is assumed to be of full row-rank.
3731 __isl_give isl_mat *isl_mat_right_inverse(__isl_take isl_mat *mat);
3733 The following function can be used to compute the (right) kernel
3734 (or null space) of a matrix, i.e., a matrix such that the product of
3735 the original and the kernel (in that order) is the zero matrix.
3737 __isl_give isl_mat *isl_mat_right_kernel(__isl_take isl_mat *mat);
3739 =head2 Piecewise Quasi Affine Expressions
3741 The zero quasi affine expression or the quasi affine expression
3742 that is equal to a given value or
3743 a specified dimension on a given domain can be created using
3745 __isl_give isl_aff *isl_aff_zero_on_domain(
3746 __isl_take isl_local_space *ls);
3747 __isl_give isl_pw_aff *isl_pw_aff_zero_on_domain(
3748 __isl_take isl_local_space *ls);
3749 __isl_give isl_aff *isl_aff_val_on_domain(
3750 __isl_take isl_local_space *ls,
3751 __isl_take isl_val *val);
3752 __isl_give isl_aff *isl_aff_var_on_domain(
3753 __isl_take isl_local_space *ls,
3754 enum isl_dim_type type, unsigned pos);
3755 __isl_give isl_pw_aff *isl_pw_aff_var_on_domain(
3756 __isl_take isl_local_space *ls,
3757 enum isl_dim_type type, unsigned pos);
3759 Note that the space in which the resulting objects live is a map space
3760 with the given space as domain and a one-dimensional range.
3762 An empty piecewise quasi affine expression (one with no cells)
3763 or a piecewise quasi affine expression with a single cell can
3764 be created using the following functions.
3766 #include <isl/aff.h>
3767 __isl_give isl_pw_aff *isl_pw_aff_empty(
3768 __isl_take isl_space *space);
3769 __isl_give isl_pw_aff *isl_pw_aff_alloc(
3770 __isl_take isl_set *set, __isl_take isl_aff *aff);
3771 __isl_give isl_pw_aff *isl_pw_aff_from_aff(
3772 __isl_take isl_aff *aff);
3774 A piecewise quasi affine expression that is equal to 1 on a set
3775 and 0 outside the set can be created using the following function.
3777 #include <isl/aff.h>
3778 __isl_give isl_pw_aff *isl_set_indicator_function(
3779 __isl_take isl_set *set);
3781 Quasi affine expressions can be copied and freed using
3783 #include <isl/aff.h>
3784 __isl_give isl_aff *isl_aff_copy(__isl_keep isl_aff *aff);
3785 void *isl_aff_free(__isl_take isl_aff *aff);
3787 __isl_give isl_pw_aff *isl_pw_aff_copy(
3788 __isl_keep isl_pw_aff *pwaff);
3789 void *isl_pw_aff_free(__isl_take isl_pw_aff *pwaff);
3791 A (rational) bound on a dimension can be extracted from an C<isl_constraint>
3792 using the following function. The constraint is required to have
3793 a non-zero coefficient for the specified dimension.
3795 #include <isl/constraint.h>
3796 __isl_give isl_aff *isl_constraint_get_bound(
3797 __isl_keep isl_constraint *constraint,
3798 enum isl_dim_type type, int pos);
3800 The entire affine expression of the constraint can also be extracted
3801 using the following function.
3803 #include <isl/constraint.h>
3804 __isl_give isl_aff *isl_constraint_get_aff(
3805 __isl_keep isl_constraint *constraint);
3807 Conversely, an equality constraint equating
3808 the affine expression to zero or an inequality constraint enforcing
3809 the affine expression to be non-negative, can be constructed using
3811 __isl_give isl_constraint *isl_equality_from_aff(
3812 __isl_take isl_aff *aff);
3813 __isl_give isl_constraint *isl_inequality_from_aff(
3814 __isl_take isl_aff *aff);
3816 The expression can be inspected using
3818 #include <isl/aff.h>
3819 isl_ctx *isl_aff_get_ctx(__isl_keep isl_aff *aff);
3820 int isl_aff_dim(__isl_keep isl_aff *aff,
3821 enum isl_dim_type type);
3822 __isl_give isl_local_space *isl_aff_get_domain_local_space(
3823 __isl_keep isl_aff *aff);
3824 __isl_give isl_local_space *isl_aff_get_local_space(
3825 __isl_keep isl_aff *aff);
3826 const char *isl_aff_get_dim_name(__isl_keep isl_aff *aff,
3827 enum isl_dim_type type, unsigned pos);
3828 const char *isl_pw_aff_get_dim_name(
3829 __isl_keep isl_pw_aff *pa,
3830 enum isl_dim_type type, unsigned pos);
3831 int isl_pw_aff_has_dim_id(__isl_keep isl_pw_aff *pa,
3832 enum isl_dim_type type, unsigned pos);
3833 __isl_give isl_id *isl_pw_aff_get_dim_id(
3834 __isl_keep isl_pw_aff *pa,
3835 enum isl_dim_type type, unsigned pos);
3836 int isl_pw_aff_has_tuple_id(__isl_keep isl_pw_aff *pa,
3837 enum isl_dim_type type);
3838 __isl_give isl_id *isl_pw_aff_get_tuple_id(
3839 __isl_keep isl_pw_aff *pa,
3840 enum isl_dim_type type);
3841 __isl_give isl_val *isl_aff_get_constant_val(
3842 __isl_keep isl_aff *aff);
3843 __isl_give isl_val *isl_aff_get_coefficient_val(
3844 __isl_keep isl_aff *aff,
3845 enum isl_dim_type type, int pos);
3846 __isl_give isl_val *isl_aff_get_denominator_val(
3847 __isl_keep isl_aff *aff);
3848 __isl_give isl_aff *isl_aff_get_div(
3849 __isl_keep isl_aff *aff, int pos);
3851 int isl_pw_aff_n_piece(__isl_keep isl_pw_aff *pwaff);
3852 int isl_pw_aff_foreach_piece(__isl_keep isl_pw_aff *pwaff,
3853 int (*fn)(__isl_take isl_set *set,
3854 __isl_take isl_aff *aff,
3855 void *user), void *user);
3857 int isl_aff_is_cst(__isl_keep isl_aff *aff);
3858 int isl_pw_aff_is_cst(__isl_keep isl_pw_aff *pwaff);
3860 int isl_aff_involves_dims(__isl_keep isl_aff *aff,
3861 enum isl_dim_type type, unsigned first, unsigned n);
3862 int isl_pw_aff_involves_dims(__isl_keep isl_pw_aff *pwaff,
3863 enum isl_dim_type type, unsigned first, unsigned n);
3865 isl_ctx *isl_pw_aff_get_ctx(__isl_keep isl_pw_aff *pwaff);
3866 unsigned isl_pw_aff_dim(__isl_keep isl_pw_aff *pwaff,
3867 enum isl_dim_type type);
3868 int isl_pw_aff_is_empty(__isl_keep isl_pw_aff *pwaff);
3870 It can be modified using
3872 #include <isl/aff.h>
3873 __isl_give isl_aff *isl_aff_set_tuple_id(
3874 __isl_take isl_aff *aff,
3875 enum isl_dim_type type, __isl_take isl_id *id);
3876 __isl_give isl_pw_aff *isl_pw_aff_set_tuple_id(
3877 __isl_take isl_pw_aff *pwaff,
3878 enum isl_dim_type type, __isl_take isl_id *id);
3879 __isl_give isl_aff *isl_aff_set_dim_name(
3880 __isl_take isl_aff *aff, enum isl_dim_type type,
3881 unsigned pos, const char *s);
3882 __isl_give isl_aff *isl_aff_set_dim_id(
3883 __isl_take isl_aff *aff, enum isl_dim_type type,
3884 unsigned pos, __isl_take isl_id *id);
3885 __isl_give isl_pw_aff *isl_pw_aff_set_dim_id(
3886 __isl_take isl_pw_aff *pma,
3887 enum isl_dim_type type, unsigned pos,
3888 __isl_take isl_id *id);
3889 __isl_give isl_aff *isl_aff_set_constant_si(
3890 __isl_take isl_aff *aff, int v);
3891 __isl_give isl_aff *isl_aff_set_constant_val(
3892 __isl_take isl_aff *aff, __isl_take isl_val *v);
3893 __isl_give isl_aff *isl_aff_set_coefficient_si(
3894 __isl_take isl_aff *aff,
3895 enum isl_dim_type type, int pos, int v);
3896 __isl_give isl_aff *isl_aff_set_coefficient_val(
3897 __isl_take isl_aff *aff,
3898 enum isl_dim_type type, int pos,
3899 __isl_take isl_val *v);
3901 __isl_give isl_aff *isl_aff_add_constant_si(
3902 __isl_take isl_aff *aff, int v);
3903 __isl_give isl_aff *isl_aff_add_constant_val(
3904 __isl_take isl_aff *aff, __isl_take isl_val *v);
3905 __isl_give isl_aff *isl_aff_add_constant_num_si(
3906 __isl_take isl_aff *aff, int v);
3907 __isl_give isl_aff *isl_aff_add_coefficient_si(
3908 __isl_take isl_aff *aff,
3909 enum isl_dim_type type, int pos, int v);
3910 __isl_give isl_aff *isl_aff_add_coefficient_val(
3911 __isl_take isl_aff *aff,
3912 enum isl_dim_type type, int pos,
3913 __isl_take isl_val *v);
3915 __isl_give isl_aff *isl_aff_insert_dims(
3916 __isl_take isl_aff *aff,
3917 enum isl_dim_type type, unsigned first, unsigned n);
3918 __isl_give isl_pw_aff *isl_pw_aff_insert_dims(
3919 __isl_take isl_pw_aff *pwaff,
3920 enum isl_dim_type type, unsigned first, unsigned n);
3921 __isl_give isl_aff *isl_aff_add_dims(
3922 __isl_take isl_aff *aff,
3923 enum isl_dim_type type, unsigned n);
3924 __isl_give isl_pw_aff *isl_pw_aff_add_dims(
3925 __isl_take isl_pw_aff *pwaff,
3926 enum isl_dim_type type, unsigned n);
3927 __isl_give isl_aff *isl_aff_drop_dims(
3928 __isl_take isl_aff *aff,
3929 enum isl_dim_type type, unsigned first, unsigned n);
3930 __isl_give isl_pw_aff *isl_pw_aff_drop_dims(
3931 __isl_take isl_pw_aff *pwaff,
3932 enum isl_dim_type type, unsigned first, unsigned n);
3933 __isl_give isl_aff *isl_aff_move_dims(
3934 __isl_take isl_aff *aff,
3935 enum isl_dim_type dst_type, unsigned dst_pos,
3936 enum isl_dim_type src_type, unsigned src_pos,
3938 __isl_give isl_pw_aff *isl_pw_aff_move_dims(
3939 __isl_take isl_pw_aff *pa,
3940 enum isl_dim_type dst_type, unsigned dst_pos,
3941 enum isl_dim_type src_type, unsigned src_pos,
3944 Note that C<isl_aff_set_constant_si> and C<isl_aff_set_coefficient_si>
3945 set the I<numerator> of the constant or coefficient, while
3946 C<isl_aff_set_constant_val> and C<isl_aff_set_coefficient_val> set
3947 the constant or coefficient as a whole.
3948 The C<add_constant> and C<add_coefficient> functions add an integer
3949 or rational value to
3950 the possibly rational constant or coefficient.
3951 The C<add_constant_num> functions add an integer value to
3954 To check whether an affine expressions is obviously zero
3955 or (obviously) equal to some other affine expression, use
3957 #include <isl/aff.h>
3958 int isl_aff_plain_is_zero(__isl_keep isl_aff *aff);
3959 int isl_aff_plain_is_equal(__isl_keep isl_aff *aff1,
3960 __isl_keep isl_aff *aff2);
3961 int isl_pw_aff_plain_is_equal(
3962 __isl_keep isl_pw_aff *pwaff1,
3963 __isl_keep isl_pw_aff *pwaff2);
3964 int isl_pw_aff_is_equal(__isl_keep isl_pw_aff *pa1,
3965 __isl_keep isl_pw_aff *pa2);
3969 #include <isl/aff.h>
3970 __isl_give isl_aff *isl_aff_add(__isl_take isl_aff *aff1,
3971 __isl_take isl_aff *aff2);
3972 __isl_give isl_pw_aff *isl_pw_aff_add(
3973 __isl_take isl_pw_aff *pwaff1,
3974 __isl_take isl_pw_aff *pwaff2);
3975 __isl_give isl_pw_aff *isl_pw_aff_min(
3976 __isl_take isl_pw_aff *pwaff1,
3977 __isl_take isl_pw_aff *pwaff2);
3978 __isl_give isl_pw_aff *isl_pw_aff_max(
3979 __isl_take isl_pw_aff *pwaff1,
3980 __isl_take isl_pw_aff *pwaff2);
3981 __isl_give isl_aff *isl_aff_sub(__isl_take isl_aff *aff1,
3982 __isl_take isl_aff *aff2);
3983 __isl_give isl_pw_aff *isl_pw_aff_sub(
3984 __isl_take isl_pw_aff *pwaff1,
3985 __isl_take isl_pw_aff *pwaff2);
3986 __isl_give isl_aff *isl_aff_neg(__isl_take isl_aff *aff);
3987 __isl_give isl_pw_aff *isl_pw_aff_neg(
3988 __isl_take isl_pw_aff *pwaff);
3989 __isl_give isl_aff *isl_aff_ceil(__isl_take isl_aff *aff);
3990 __isl_give isl_pw_aff *isl_pw_aff_ceil(
3991 __isl_take isl_pw_aff *pwaff);
3992 __isl_give isl_aff *isl_aff_floor(__isl_take isl_aff *aff);
3993 __isl_give isl_pw_aff *isl_pw_aff_floor(
3994 __isl_take isl_pw_aff *pwaff);
3995 __isl_give isl_aff *isl_aff_mod_val(__isl_take isl_aff *aff,
3996 __isl_take isl_val *mod);
3997 __isl_give isl_pw_aff *isl_pw_aff_mod_val(
3998 __isl_take isl_pw_aff *pa,
3999 __isl_take isl_val *mod);
4000 __isl_give isl_aff *isl_aff_scale_val(__isl_take isl_aff *aff,
4001 __isl_take isl_val *v);
4002 __isl_give isl_pw_aff *isl_pw_aff_scale_val(
4003 __isl_take isl_pw_aff *pa, __isl_take isl_val *v);
4004 __isl_give isl_aff *isl_aff_scale_down_ui(
4005 __isl_take isl_aff *aff, unsigned f);
4006 __isl_give isl_aff *isl_aff_scale_down_val(
4007 __isl_take isl_aff *aff, __isl_take isl_val *v);
4008 __isl_give isl_pw_aff *isl_pw_aff_scale_down_val(
4009 __isl_take isl_pw_aff *pa,
4010 __isl_take isl_val *f);
4012 __isl_give isl_pw_aff *isl_pw_aff_list_min(
4013 __isl_take isl_pw_aff_list *list);
4014 __isl_give isl_pw_aff *isl_pw_aff_list_max(
4015 __isl_take isl_pw_aff_list *list);
4017 __isl_give isl_pw_aff *isl_pw_aff_coalesce(
4018 __isl_take isl_pw_aff *pwqp);
4020 __isl_give isl_aff *isl_aff_align_params(
4021 __isl_take isl_aff *aff,
4022 __isl_take isl_space *model);
4023 __isl_give isl_pw_aff *isl_pw_aff_align_params(
4024 __isl_take isl_pw_aff *pwaff,
4025 __isl_take isl_space *model);
4027 __isl_give isl_aff *isl_aff_project_domain_on_params(
4028 __isl_take isl_aff *aff);
4029 __isl_give isl_pw_aff *isl_pw_aff_from_range(
4030 __isl_take isl_pw_aff *pwa);
4032 __isl_give isl_aff *isl_aff_gist_params(
4033 __isl_take isl_aff *aff,
4034 __isl_take isl_set *context);
4035 __isl_give isl_aff *isl_aff_gist(__isl_take isl_aff *aff,
4036 __isl_take isl_set *context);
4037 __isl_give isl_pw_aff *isl_pw_aff_gist_params(
4038 __isl_take isl_pw_aff *pwaff,
4039 __isl_take isl_set *context);
4040 __isl_give isl_pw_aff *isl_pw_aff_gist(
4041 __isl_take isl_pw_aff *pwaff,
4042 __isl_take isl_set *context);
4044 __isl_give isl_set *isl_pw_aff_domain(
4045 __isl_take isl_pw_aff *pwaff);
4046 __isl_give isl_set *isl_pw_aff_params(
4047 __isl_take isl_pw_aff *pwa);
4048 __isl_give isl_pw_aff *isl_pw_aff_intersect_domain(
4049 __isl_take isl_pw_aff *pa,
4050 __isl_take isl_set *set);
4051 __isl_give isl_pw_aff *isl_pw_aff_intersect_params(
4052 __isl_take isl_pw_aff *pa,
4053 __isl_take isl_set *set);
4055 __isl_give isl_aff *isl_aff_mul(__isl_take isl_aff *aff1,
4056 __isl_take isl_aff *aff2);
4057 __isl_give isl_aff *isl_aff_div(__isl_take isl_aff *aff1,
4058 __isl_take isl_aff *aff2);
4059 __isl_give isl_pw_aff *isl_pw_aff_mul(
4060 __isl_take isl_pw_aff *pwaff1,
4061 __isl_take isl_pw_aff *pwaff2);
4062 __isl_give isl_pw_aff *isl_pw_aff_div(
4063 __isl_take isl_pw_aff *pa1,
4064 __isl_take isl_pw_aff *pa2);
4065 __isl_give isl_pw_aff *isl_pw_aff_tdiv_q(
4066 __isl_take isl_pw_aff *pa1,
4067 __isl_take isl_pw_aff *pa2);
4068 __isl_give isl_pw_aff *isl_pw_aff_tdiv_r(
4069 __isl_take isl_pw_aff *pa1,
4070 __isl_take isl_pw_aff *pa2);
4072 When multiplying two affine expressions, at least one of the two needs
4073 to be a constant. Similarly, when dividing an affine expression by another,
4074 the second expression needs to be a constant.
4075 C<isl_pw_aff_tdiv_q> computes the quotient of an integer division with
4076 rounding towards zero. C<isl_pw_aff_tdiv_r> computes the corresponding
4079 #include <isl/aff.h>
4080 __isl_give isl_aff *isl_aff_pullback_aff(
4081 __isl_take isl_aff *aff1,
4082 __isl_take isl_aff *aff2);
4083 __isl_give isl_aff *isl_aff_pullback_multi_aff(
4084 __isl_take isl_aff *aff,
4085 __isl_take isl_multi_aff *ma);
4086 __isl_give isl_pw_aff *isl_pw_aff_pullback_multi_aff(
4087 __isl_take isl_pw_aff *pa,
4088 __isl_take isl_multi_aff *ma);
4089 __isl_give isl_pw_aff *isl_pw_aff_pullback_pw_multi_aff(
4090 __isl_take isl_pw_aff *pa,
4091 __isl_take isl_pw_multi_aff *pma);
4093 These functions precompose the input expression by the given
4094 C<isl_aff>, C<isl_multi_aff> or C<isl_pw_multi_aff>. In other words,
4095 the C<isl_aff>, C<isl_multi_aff> or C<isl_pw_multi_aff> is plugged
4096 into the (piecewise) affine expression.
4097 Objects of type C<isl_multi_aff> are described in
4098 L</"Piecewise Multiple Quasi Affine Expressions">.
4100 #include <isl/aff.h>
4101 __isl_give isl_basic_set *isl_aff_zero_basic_set(
4102 __isl_take isl_aff *aff);
4103 __isl_give isl_basic_set *isl_aff_neg_basic_set(
4104 __isl_take isl_aff *aff);
4105 __isl_give isl_basic_set *isl_aff_le_basic_set(
4106 __isl_take isl_aff *aff1, __isl_take isl_aff *aff2);
4107 __isl_give isl_basic_set *isl_aff_ge_basic_set(
4108 __isl_take isl_aff *aff1, __isl_take isl_aff *aff2);
4109 __isl_give isl_set *isl_pw_aff_eq_set(
4110 __isl_take isl_pw_aff *pwaff1,
4111 __isl_take isl_pw_aff *pwaff2);
4112 __isl_give isl_set *isl_pw_aff_ne_set(
4113 __isl_take isl_pw_aff *pwaff1,
4114 __isl_take isl_pw_aff *pwaff2);
4115 __isl_give isl_set *isl_pw_aff_le_set(
4116 __isl_take isl_pw_aff *pwaff1,
4117 __isl_take isl_pw_aff *pwaff2);
4118 __isl_give isl_set *isl_pw_aff_lt_set(
4119 __isl_take isl_pw_aff *pwaff1,
4120 __isl_take isl_pw_aff *pwaff2);
4121 __isl_give isl_set *isl_pw_aff_ge_set(
4122 __isl_take isl_pw_aff *pwaff1,
4123 __isl_take isl_pw_aff *pwaff2);
4124 __isl_give isl_set *isl_pw_aff_gt_set(
4125 __isl_take isl_pw_aff *pwaff1,
4126 __isl_take isl_pw_aff *pwaff2);
4128 __isl_give isl_set *isl_pw_aff_list_eq_set(
4129 __isl_take isl_pw_aff_list *list1,
4130 __isl_take isl_pw_aff_list *list2);
4131 __isl_give isl_set *isl_pw_aff_list_ne_set(
4132 __isl_take isl_pw_aff_list *list1,
4133 __isl_take isl_pw_aff_list *list2);
4134 __isl_give isl_set *isl_pw_aff_list_le_set(
4135 __isl_take isl_pw_aff_list *list1,
4136 __isl_take isl_pw_aff_list *list2);
4137 __isl_give isl_set *isl_pw_aff_list_lt_set(
4138 __isl_take isl_pw_aff_list *list1,
4139 __isl_take isl_pw_aff_list *list2);
4140 __isl_give isl_set *isl_pw_aff_list_ge_set(
4141 __isl_take isl_pw_aff_list *list1,
4142 __isl_take isl_pw_aff_list *list2);
4143 __isl_give isl_set *isl_pw_aff_list_gt_set(
4144 __isl_take isl_pw_aff_list *list1,
4145 __isl_take isl_pw_aff_list *list2);
4147 The function C<isl_aff_neg_basic_set> returns a basic set
4148 containing those elements in the domain space
4149 of C<aff> where C<aff> is negative.
4150 The function C<isl_aff_ge_basic_set> returns a basic set
4151 containing those elements in the shared space
4152 of C<aff1> and C<aff2> where C<aff1> is greater than or equal to C<aff2>.
4153 The function C<isl_pw_aff_ge_set> returns a set
4154 containing those elements in the shared domain
4155 of C<pwaff1> and C<pwaff2> where C<pwaff1> is greater than or equal to C<pwaff2>.
4156 The functions operating on C<isl_pw_aff_list> apply the corresponding
4157 C<isl_pw_aff> function to each pair of elements in the two lists.
4159 #include <isl/aff.h>
4160 __isl_give isl_set *isl_pw_aff_nonneg_set(
4161 __isl_take isl_pw_aff *pwaff);
4162 __isl_give isl_set *isl_pw_aff_zero_set(
4163 __isl_take isl_pw_aff *pwaff);
4164 __isl_give isl_set *isl_pw_aff_non_zero_set(
4165 __isl_take isl_pw_aff *pwaff);
4167 The function C<isl_pw_aff_nonneg_set> returns a set
4168 containing those elements in the domain
4169 of C<pwaff> where C<pwaff> is non-negative.
4171 #include <isl/aff.h>
4172 __isl_give isl_pw_aff *isl_pw_aff_cond(
4173 __isl_take isl_pw_aff *cond,
4174 __isl_take isl_pw_aff *pwaff_true,
4175 __isl_take isl_pw_aff *pwaff_false);
4177 The function C<isl_pw_aff_cond> performs a conditional operator
4178 and returns an expression that is equal to C<pwaff_true>
4179 for elements where C<cond> is non-zero and equal to C<pwaff_false> for elements
4180 where C<cond> is zero.
4182 #include <isl/aff.h>
4183 __isl_give isl_pw_aff *isl_pw_aff_union_min(
4184 __isl_take isl_pw_aff *pwaff1,
4185 __isl_take isl_pw_aff *pwaff2);
4186 __isl_give isl_pw_aff *isl_pw_aff_union_max(
4187 __isl_take isl_pw_aff *pwaff1,
4188 __isl_take isl_pw_aff *pwaff2);
4189 __isl_give isl_pw_aff *isl_pw_aff_union_add(
4190 __isl_take isl_pw_aff *pwaff1,
4191 __isl_take isl_pw_aff *pwaff2);
4193 The function C<isl_pw_aff_union_max> computes a piecewise quasi-affine
4194 expression with a domain that is the union of those of C<pwaff1> and
4195 C<pwaff2> and such that on each cell, the quasi-affine expression is
4196 the maximum of those of C<pwaff1> and C<pwaff2>. If only one of
4197 C<pwaff1> or C<pwaff2> is defined on a given cell, then the
4198 associated expression is the defined one.
4200 An expression can be read from input using
4202 #include <isl/aff.h>
4203 __isl_give isl_aff *isl_aff_read_from_str(
4204 isl_ctx *ctx, const char *str);
4205 __isl_give isl_pw_aff *isl_pw_aff_read_from_str(
4206 isl_ctx *ctx, const char *str);
4208 An expression can be printed using
4210 #include <isl/aff.h>
4211 __isl_give isl_printer *isl_printer_print_aff(
4212 __isl_take isl_printer *p, __isl_keep isl_aff *aff);
4214 __isl_give isl_printer *isl_printer_print_pw_aff(
4215 __isl_take isl_printer *p,
4216 __isl_keep isl_pw_aff *pwaff);
4218 =head2 Piecewise Multiple Quasi Affine Expressions
4220 An C<isl_multi_aff> object represents a sequence of
4221 zero or more affine expressions, all defined on the same domain space.
4222 Similarly, an C<isl_multi_pw_aff> object represents a sequence of
4223 zero or more piecewise affine expressions.
4225 An C<isl_multi_aff> can be constructed from a single
4226 C<isl_aff> or an C<isl_aff_list> using the
4227 following functions. Similarly for C<isl_multi_pw_aff>
4228 and C<isl_pw_multi_aff>.
4230 #include <isl/aff.h>
4231 __isl_give isl_multi_aff *isl_multi_aff_from_aff(
4232 __isl_take isl_aff *aff);
4233 __isl_give isl_multi_pw_aff *
4234 isl_multi_pw_aff_from_multi_aff(
4235 __isl_take isl_multi_aff *ma);
4236 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_from_pw_aff(
4237 __isl_take isl_pw_aff *pa);
4238 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_from_pw_aff(
4239 __isl_take isl_pw_aff *pa);
4240 __isl_give isl_multi_aff *isl_multi_aff_from_aff_list(
4241 __isl_take isl_space *space,
4242 __isl_take isl_aff_list *list);
4244 An C<isl_multi_pw_aff> can be converted to an C<isl_pw_multi_aff>
4245 using the function C<isl_pw_multi_aff_from_multi_pw_aff> below.
4246 Note however that the domain
4247 of the result is the intersection of the domains of the input.
4248 The reverse conversion is exact.
4250 #include <isl/aff.h>
4251 __isl_give isl_pw_multi_aff *
4252 isl_pw_multi_aff_from_multi_pw_aff(
4253 __isl_take isl_multi_pw_aff *mpa);
4254 __isl_give isl_multi_pw_aff *
4255 isl_multi_pw_aff_from_pw_multi_aff(
4256 __isl_take isl_pw_multi_aff *pma);
4258 An empty piecewise multiple quasi affine expression (one with no cells),
4259 the zero piecewise multiple quasi affine expression (with value zero
4260 for each output dimension),
4261 a piecewise multiple quasi affine expression with a single cell (with
4262 either a universe or a specified domain) or
4263 a zero-dimensional piecewise multiple quasi affine expression
4265 can be created using the following functions.
4267 #include <isl/aff.h>
4268 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_empty(
4269 __isl_take isl_space *space);
4270 __isl_give isl_multi_aff *isl_multi_aff_zero(
4271 __isl_take isl_space *space);
4272 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_zero(
4273 __isl_take isl_space *space);
4274 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_zero(
4275 __isl_take isl_space *space);
4276 __isl_give isl_multi_aff *isl_multi_aff_identity(
4277 __isl_take isl_space *space);
4278 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_identity(
4279 __isl_take isl_space *space);
4280 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_identity(
4281 __isl_take isl_space *space);
4282 __isl_give isl_multi_aff *isl_multi_aff_domain_map(
4283 __isl_take isl_space *space);
4284 __isl_give isl_multi_aff *isl_multi_aff_range_map(
4285 __isl_take isl_space *space);
4286 __isl_give isl_multi_aff *isl_multi_aff_project_out_map(
4287 __isl_take isl_space *space,
4288 enum isl_dim_type type,
4289 unsigned first, unsigned n);
4290 __isl_give isl_pw_multi_aff *
4291 isl_pw_multi_aff_project_out_map(
4292 __isl_take isl_space *space,
4293 enum isl_dim_type type,
4294 unsigned first, unsigned n);
4295 __isl_give isl_pw_multi_aff *
4296 isl_pw_multi_aff_from_multi_aff(
4297 __isl_take isl_multi_aff *ma);
4298 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_alloc(
4299 __isl_take isl_set *set,
4300 __isl_take isl_multi_aff *maff);
4301 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_from_domain(
4302 __isl_take isl_set *set);
4304 __isl_give isl_union_pw_multi_aff *
4305 isl_union_pw_multi_aff_empty(
4306 __isl_take isl_space *space);
4307 __isl_give isl_union_pw_multi_aff *
4308 isl_union_pw_multi_aff_add_pw_multi_aff(
4309 __isl_take isl_union_pw_multi_aff *upma,
4310 __isl_take isl_pw_multi_aff *pma);
4311 __isl_give isl_union_pw_multi_aff *
4312 isl_union_pw_multi_aff_from_domain(
4313 __isl_take isl_union_set *uset);
4315 A piecewise multiple quasi affine expression can also be initialized
4316 from an C<isl_set> or C<isl_map>, provided the C<isl_set> is a singleton
4317 and the C<isl_map> is single-valued.
4318 In case of a conversion from an C<isl_union_set> or an C<isl_union_map>
4319 to an C<isl_union_pw_multi_aff>, these properties need to hold in each space.
4321 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_from_set(
4322 __isl_take isl_set *set);
4323 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_from_map(
4324 __isl_take isl_map *map);
4326 __isl_give isl_union_pw_multi_aff *
4327 isl_union_pw_multi_aff_from_union_set(
4328 __isl_take isl_union_set *uset);
4329 __isl_give isl_union_pw_multi_aff *
4330 isl_union_pw_multi_aff_from_union_map(
4331 __isl_take isl_union_map *umap);
4333 Multiple quasi affine expressions can be copied and freed using
4335 #include <isl/aff.h>
4336 __isl_give isl_multi_aff *isl_multi_aff_copy(
4337 __isl_keep isl_multi_aff *maff);
4338 void *isl_multi_aff_free(__isl_take isl_multi_aff *maff);
4340 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_copy(
4341 __isl_keep isl_pw_multi_aff *pma);
4342 void *isl_pw_multi_aff_free(
4343 __isl_take isl_pw_multi_aff *pma);
4345 __isl_give isl_union_pw_multi_aff *
4346 isl_union_pw_multi_aff_copy(
4347 __isl_keep isl_union_pw_multi_aff *upma);
4348 void *isl_union_pw_multi_aff_free(
4349 __isl_take isl_union_pw_multi_aff *upma);
4351 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_copy(
4352 __isl_keep isl_multi_pw_aff *mpa);
4353 void *isl_multi_pw_aff_free(
4354 __isl_take isl_multi_pw_aff *mpa);
4356 The expression can be inspected using
4358 #include <isl/aff.h>
4359 isl_ctx *isl_multi_aff_get_ctx(
4360 __isl_keep isl_multi_aff *maff);
4361 isl_ctx *isl_pw_multi_aff_get_ctx(
4362 __isl_keep isl_pw_multi_aff *pma);
4363 isl_ctx *isl_union_pw_multi_aff_get_ctx(
4364 __isl_keep isl_union_pw_multi_aff *upma);
4365 isl_ctx *isl_multi_pw_aff_get_ctx(
4366 __isl_keep isl_multi_pw_aff *mpa);
4367 unsigned isl_multi_aff_dim(__isl_keep isl_multi_aff *maff,
4368 enum isl_dim_type type);
4369 unsigned isl_pw_multi_aff_dim(
4370 __isl_keep isl_pw_multi_aff *pma,
4371 enum isl_dim_type type);
4372 unsigned isl_multi_pw_aff_dim(
4373 __isl_keep isl_multi_pw_aff *mpa,
4374 enum isl_dim_type type);
4375 __isl_give isl_aff *isl_multi_aff_get_aff(
4376 __isl_keep isl_multi_aff *multi, int pos);
4377 __isl_give isl_pw_aff *isl_pw_multi_aff_get_pw_aff(
4378 __isl_keep isl_pw_multi_aff *pma, int pos);
4379 __isl_give isl_pw_aff *isl_multi_pw_aff_get_pw_aff(
4380 __isl_keep isl_multi_pw_aff *mpa, int pos);
4381 int isl_multi_aff_find_dim_by_id(
4382 __isl_keep isl_multi_aff *ma,
4383 enum isl_dim_type type, __isl_keep isl_id *id);
4384 int isl_multi_pw_aff_find_dim_by_id(
4385 __isl_keep isl_multi_pw_aff *mpa,
4386 enum isl_dim_type type, __isl_keep isl_id *id);
4387 const char *isl_pw_multi_aff_get_dim_name(
4388 __isl_keep isl_pw_multi_aff *pma,
4389 enum isl_dim_type type, unsigned pos);
4390 __isl_give isl_id *isl_multi_aff_get_dim_id(
4391 __isl_keep isl_multi_aff *ma,
4392 enum isl_dim_type type, unsigned pos);
4393 __isl_give isl_id *isl_pw_multi_aff_get_dim_id(
4394 __isl_keep isl_pw_multi_aff *pma,
4395 enum isl_dim_type type, unsigned pos);
4396 __isl_give isl_id *isl_multi_pw_aff_get_dim_id(
4397 __isl_keep isl_multi_pw_aff *mpa,
4398 enum isl_dim_type type, unsigned pos);
4399 const char *isl_multi_aff_get_tuple_name(
4400 __isl_keep isl_multi_aff *multi,
4401 enum isl_dim_type type);
4402 int isl_pw_multi_aff_has_tuple_name(
4403 __isl_keep isl_pw_multi_aff *pma,
4404 enum isl_dim_type type);
4405 const char *isl_pw_multi_aff_get_tuple_name(
4406 __isl_keep isl_pw_multi_aff *pma,
4407 enum isl_dim_type type);
4408 int isl_multi_aff_has_tuple_id(__isl_keep isl_multi_aff *ma,
4409 enum isl_dim_type type);
4410 int isl_pw_multi_aff_has_tuple_id(
4411 __isl_keep isl_pw_multi_aff *pma,
4412 enum isl_dim_type type);
4413 int isl_multi_pw_aff_has_tuple_id(
4414 __isl_keep isl_multi_pw_aff *mpa,
4415 enum isl_dim_type type);
4416 __isl_give isl_id *isl_multi_aff_get_tuple_id(
4417 __isl_keep isl_multi_aff *ma,
4418 enum isl_dim_type type);
4419 __isl_give isl_id *isl_pw_multi_aff_get_tuple_id(
4420 __isl_keep isl_pw_multi_aff *pma,
4421 enum isl_dim_type type);
4422 __isl_give isl_id *isl_multi_pw_aff_get_tuple_id(
4423 __isl_keep isl_multi_pw_aff *mpa,
4424 enum isl_dim_type type);
4425 int isl_multi_aff_range_is_wrapping(
4426 __isl_keep isl_multi_aff *ma);
4427 int isl_multi_pw_aff_range_is_wrapping(
4428 __isl_keep isl_multi_pw_aff *mpa);
4430 int isl_pw_multi_aff_foreach_piece(
4431 __isl_keep isl_pw_multi_aff *pma,
4432 int (*fn)(__isl_take isl_set *set,
4433 __isl_take isl_multi_aff *maff,
4434 void *user), void *user);
4436 int isl_union_pw_multi_aff_foreach_pw_multi_aff(
4437 __isl_keep isl_union_pw_multi_aff *upma,
4438 int (*fn)(__isl_take isl_pw_multi_aff *pma,
4439 void *user), void *user);
4441 It can be modified using
4443 #include <isl/aff.h>
4444 __isl_give isl_multi_aff *isl_multi_aff_set_aff(
4445 __isl_take isl_multi_aff *multi, int pos,
4446 __isl_take isl_aff *aff);
4447 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_set_pw_aff(
4448 __isl_take isl_pw_multi_aff *pma, unsigned pos,
4449 __isl_take isl_pw_aff *pa);
4450 __isl_give isl_multi_aff *isl_multi_aff_set_dim_name(
4451 __isl_take isl_multi_aff *maff,
4452 enum isl_dim_type type, unsigned pos, const char *s);
4453 __isl_give isl_multi_aff *isl_multi_aff_set_dim_id(
4454 __isl_take isl_multi_aff *maff,
4455 enum isl_dim_type type, unsigned pos,
4456 __isl_take isl_id *id);
4457 __isl_give isl_multi_aff *isl_multi_aff_set_tuple_name(
4458 __isl_take isl_multi_aff *maff,
4459 enum isl_dim_type type, const char *s);
4460 __isl_give isl_multi_aff *isl_multi_aff_set_tuple_id(
4461 __isl_take isl_multi_aff *maff,
4462 enum isl_dim_type type, __isl_take isl_id *id);
4463 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_set_tuple_id(
4464 __isl_take isl_pw_multi_aff *pma,
4465 enum isl_dim_type type, __isl_take isl_id *id);
4466 __isl_give isl_multi_aff *isl_multi_aff_reset_tuple_id(
4467 __isl_take isl_multi_aff *ma,
4468 enum isl_dim_type type);
4469 __isl_give isl_multi_pw_aff *
4470 isl_multi_pw_aff_reset_tuple_id(
4471 __isl_take isl_multi_pw_aff *mpa,
4472 enum isl_dim_type type);
4473 __isl_give isl_multi_aff *isl_multi_aff_reset_user(
4474 __isl_take isl_multi_aff *ma);
4475 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_reset_user(
4476 __isl_take isl_multi_pw_aff *mpa);
4478 __isl_give isl_multi_pw_aff *
4479 isl_multi_pw_aff_set_dim_name(
4480 __isl_take isl_multi_pw_aff *mpa,
4481 enum isl_dim_type type, unsigned pos, const char *s);
4482 __isl_give isl_multi_pw_aff *
4483 isl_multi_pw_aff_set_dim_id(
4484 __isl_take isl_multi_pw_aff *mpa,
4485 enum isl_dim_type type, unsigned pos,
4486 __isl_take isl_id *id);
4487 __isl_give isl_multi_pw_aff *
4488 isl_multi_pw_aff_set_tuple_name(
4489 __isl_take isl_multi_pw_aff *mpa,
4490 enum isl_dim_type type, const char *s);
4492 __isl_give isl_multi_aff *isl_multi_aff_insert_dims(
4493 __isl_take isl_multi_aff *ma,
4494 enum isl_dim_type type, unsigned first, unsigned n);
4495 __isl_give isl_multi_aff *isl_multi_aff_add_dims(
4496 __isl_take isl_multi_aff *ma,
4497 enum isl_dim_type type, unsigned n);
4498 __isl_give isl_multi_aff *isl_multi_aff_drop_dims(
4499 __isl_take isl_multi_aff *maff,
4500 enum isl_dim_type type, unsigned first, unsigned n);
4501 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_drop_dims(
4502 __isl_take isl_pw_multi_aff *pma,
4503 enum isl_dim_type type, unsigned first, unsigned n);
4505 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_insert_dims(
4506 __isl_take isl_multi_pw_aff *mpa,
4507 enum isl_dim_type type, unsigned first, unsigned n);
4508 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_add_dims(
4509 __isl_take isl_multi_pw_aff *mpa,
4510 enum isl_dim_type type, unsigned n);
4511 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_move_dims(
4512 __isl_take isl_multi_pw_aff *pma,
4513 enum isl_dim_type dst_type, unsigned dst_pos,
4514 enum isl_dim_type src_type, unsigned src_pos,
4517 To check whether two multiple affine expressions are
4518 (obviously) equal to each other, use
4520 int isl_multi_aff_plain_is_equal(__isl_keep isl_multi_aff *maff1,
4521 __isl_keep isl_multi_aff *maff2);
4522 int isl_pw_multi_aff_plain_is_equal(
4523 __isl_keep isl_pw_multi_aff *pma1,
4524 __isl_keep isl_pw_multi_aff *pma2);
4525 int isl_multi_pw_aff_plain_is_equal(
4526 __isl_keep isl_multi_pw_aff *mpa1,
4527 __isl_keep isl_multi_pw_aff *mpa2);
4528 int isl_multi_pw_aff_is_equal(
4529 __isl_keep isl_multi_pw_aff *mpa1,
4530 __isl_keep isl_multi_pw_aff *mpa2);
4534 #include <isl/aff.h>
4535 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_union_lexmin(
4536 __isl_take isl_pw_multi_aff *pma1,
4537 __isl_take isl_pw_multi_aff *pma2);
4538 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_union_lexmax(
4539 __isl_take isl_pw_multi_aff *pma1,
4540 __isl_take isl_pw_multi_aff *pma2);
4541 __isl_give isl_multi_aff *isl_multi_aff_add(
4542 __isl_take isl_multi_aff *maff1,
4543 __isl_take isl_multi_aff *maff2);
4544 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_add(
4545 __isl_take isl_pw_multi_aff *pma1,
4546 __isl_take isl_pw_multi_aff *pma2);
4547 __isl_give isl_union_pw_multi_aff *isl_union_pw_multi_aff_add(
4548 __isl_take isl_union_pw_multi_aff *upma1,
4549 __isl_take isl_union_pw_multi_aff *upma2);
4550 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_union_add(
4551 __isl_take isl_pw_multi_aff *pma1,
4552 __isl_take isl_pw_multi_aff *pma2);
4553 __isl_give isl_multi_aff *isl_multi_aff_sub(
4554 __isl_take isl_multi_aff *ma1,
4555 __isl_take isl_multi_aff *ma2);
4556 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_sub(
4557 __isl_take isl_pw_multi_aff *pma1,
4558 __isl_take isl_pw_multi_aff *pma2);
4559 __isl_give isl_union_pw_multi_aff *isl_union_pw_multi_aff_sub(
4560 __isl_take isl_union_pw_multi_aff *upma1,
4561 __isl_take isl_union_pw_multi_aff *upma2);
4563 C<isl_multi_aff_sub> subtracts the second argument from the first.
4565 __isl_give isl_multi_aff *isl_multi_aff_scale_val(
4566 __isl_take isl_multi_aff *ma,
4567 __isl_take isl_val *v);
4568 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_scale_val(
4569 __isl_take isl_pw_multi_aff *pma,
4570 __isl_take isl_val *v);
4571 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_scale_val(
4572 __isl_take isl_multi_pw_aff *mpa,
4573 __isl_take isl_val *v);
4574 __isl_give isl_multi_aff *isl_multi_aff_scale_multi_val(
4575 __isl_take isl_multi_aff *ma,
4576 __isl_take isl_multi_val *mv);
4577 __isl_give isl_pw_multi_aff *
4578 isl_pw_multi_aff_scale_multi_val(
4579 __isl_take isl_pw_multi_aff *pma,
4580 __isl_take isl_multi_val *mv);
4581 __isl_give isl_multi_pw_aff *
4582 isl_multi_pw_aff_scale_multi_val(
4583 __isl_take isl_multi_pw_aff *mpa,
4584 __isl_take isl_multi_val *mv);
4585 __isl_give isl_union_pw_multi_aff *
4586 isl_union_pw_multi_aff_scale_multi_val(
4587 __isl_take isl_union_pw_multi_aff *upma,
4588 __isl_take isl_multi_val *mv);
4589 __isl_give isl_multi_aff *
4590 isl_multi_aff_scale_down_multi_val(
4591 __isl_take isl_multi_aff *ma,
4592 __isl_take isl_multi_val *mv);
4593 __isl_give isl_multi_pw_aff *
4594 isl_multi_pw_aff_scale_down_multi_val(
4595 __isl_take isl_multi_pw_aff *mpa,
4596 __isl_take isl_multi_val *mv);
4598 C<isl_multi_aff_scale_multi_val> scales the elements of C<ma>
4599 by the corresponding elements of C<mv>.
4601 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_fix_si(
4602 __isl_take isl_pw_multi_aff *pma,
4603 enum isl_dim_type type, unsigned pos, int value);
4604 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_intersect_params(
4605 __isl_take isl_pw_multi_aff *pma,
4606 __isl_take isl_set *set);
4607 __isl_give isl_set *isl_multi_pw_aff_domain(
4608 __isl_take isl_multi_pw_aff *mpa);
4609 __isl_give isl_multi_pw_aff *
4610 isl_multi_pw_aff_intersect_params(
4611 __isl_take isl_multi_pw_aff *mpa,
4612 __isl_take isl_set *set);
4613 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_intersect_domain(
4614 __isl_take isl_pw_multi_aff *pma,
4615 __isl_take isl_set *set);
4616 __isl_give isl_multi_pw_aff *
4617 isl_multi_pw_aff_intersect_domain(
4618 __isl_take isl_multi_pw_aff *mpa,
4619 __isl_take isl_set *domain);
4620 __isl_give isl_union_pw_multi_aff *
4621 isl_union_pw_multi_aff_intersect_domain(
4622 __isl_take isl_union_pw_multi_aff *upma,
4623 __isl_take isl_union_set *uset);
4624 __isl_give isl_multi_aff *isl_multi_aff_lift(
4625 __isl_take isl_multi_aff *maff,
4626 __isl_give isl_local_space **ls);
4627 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_coalesce(
4628 __isl_take isl_pw_multi_aff *pma);
4629 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_coalesce(
4630 __isl_take isl_multi_pw_aff *mpa);
4631 __isl_give isl_multi_aff *isl_multi_aff_align_params(
4632 __isl_take isl_multi_aff *multi,
4633 __isl_take isl_space *model);
4634 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_align_params(
4635 __isl_take isl_pw_multi_aff *pma,
4636 __isl_take isl_space *model);
4637 __isl_give isl_pw_multi_aff *
4638 isl_pw_multi_aff_project_domain_on_params(
4639 __isl_take isl_pw_multi_aff *pma);
4640 __isl_give isl_multi_aff *isl_multi_aff_gist_params(
4641 __isl_take isl_multi_aff *maff,
4642 __isl_take isl_set *context);
4643 __isl_give isl_multi_aff *isl_multi_aff_gist(
4644 __isl_take isl_multi_aff *maff,
4645 __isl_take isl_set *context);
4646 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_gist_params(
4647 __isl_take isl_pw_multi_aff *pma,
4648 __isl_take isl_set *set);
4649 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_gist(
4650 __isl_take isl_pw_multi_aff *pma,
4651 __isl_take isl_set *set);
4652 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_gist_params(
4653 __isl_take isl_multi_pw_aff *mpa,
4654 __isl_take isl_set *set);
4655 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_gist(
4656 __isl_take isl_multi_pw_aff *mpa,
4657 __isl_take isl_set *set);
4658 __isl_give isl_multi_aff *isl_multi_aff_from_range(
4659 __isl_take isl_multi_aff *ma);
4660 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_from_range(
4661 __isl_take isl_multi_pw_aff *mpa);
4662 __isl_give isl_set *isl_pw_multi_aff_domain(
4663 __isl_take isl_pw_multi_aff *pma);
4664 __isl_give isl_union_set *isl_union_pw_multi_aff_domain(
4665 __isl_take isl_union_pw_multi_aff *upma);
4666 __isl_give isl_multi_aff *isl_multi_aff_range_splice(
4667 __isl_take isl_multi_aff *ma1, unsigned pos,
4668 __isl_take isl_multi_aff *ma2);
4669 __isl_give isl_multi_aff *isl_multi_aff_splice(
4670 __isl_take isl_multi_aff *ma1,
4671 unsigned in_pos, unsigned out_pos,
4672 __isl_take isl_multi_aff *ma2);
4673 __isl_give isl_multi_aff *isl_multi_aff_range_product(
4674 __isl_take isl_multi_aff *ma1,
4675 __isl_take isl_multi_aff *ma2);
4676 __isl_give isl_multi_aff *
4677 isl_multi_aff_range_factor_domain(
4678 __isl_take isl_multi_aff *ma);
4679 __isl_give isl_multi_aff *
4680 isl_multi_aff_range_factor_range(
4681 __isl_take isl_multi_aff *ma);
4682 __isl_give isl_multi_aff *isl_multi_aff_flat_range_product(
4683 __isl_take isl_multi_aff *ma1,
4684 __isl_take isl_multi_aff *ma2);
4685 __isl_give isl_multi_aff *isl_multi_aff_product(
4686 __isl_take isl_multi_aff *ma1,
4687 __isl_take isl_multi_aff *ma2);
4688 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_product(
4689 __isl_take isl_multi_pw_aff *mpa1,
4690 __isl_take isl_multi_pw_aff *mpa2);
4691 __isl_give isl_pw_multi_aff *
4692 isl_pw_multi_aff_range_product(
4693 __isl_take isl_pw_multi_aff *pma1,
4694 __isl_take isl_pw_multi_aff *pma2);
4695 __isl_give isl_multi_pw_aff *
4696 isl_multi_pw_aff_range_factor_domain(
4697 __isl_take isl_multi_pw_aff *mpa);
4698 __isl_give isl_multi_pw_aff *
4699 isl_multi_pw_aff_range_factor_range(
4700 __isl_take isl_multi_pw_aff *mpa);
4701 __isl_give isl_pw_multi_aff *
4702 isl_pw_multi_aff_flat_range_product(
4703 __isl_take isl_pw_multi_aff *pma1,
4704 __isl_take isl_pw_multi_aff *pma2);
4705 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_product(
4706 __isl_take isl_pw_multi_aff *pma1,
4707 __isl_take isl_pw_multi_aff *pma2);
4708 __isl_give isl_union_pw_multi_aff *
4709 isl_union_pw_multi_aff_flat_range_product(
4710 __isl_take isl_union_pw_multi_aff *upma1,
4711 __isl_take isl_union_pw_multi_aff *upma2);
4712 __isl_give isl_multi_pw_aff *
4713 isl_multi_pw_aff_range_splice(
4714 __isl_take isl_multi_pw_aff *mpa1, unsigned pos,
4715 __isl_take isl_multi_pw_aff *mpa2);
4716 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_splice(
4717 __isl_take isl_multi_pw_aff *mpa1,
4718 unsigned in_pos, unsigned out_pos,
4719 __isl_take isl_multi_pw_aff *mpa2);
4720 __isl_give isl_multi_pw_aff *
4721 isl_multi_pw_aff_range_product(
4722 __isl_take isl_multi_pw_aff *mpa1,
4723 __isl_take isl_multi_pw_aff *mpa2);
4724 __isl_give isl_multi_pw_aff *
4725 isl_multi_pw_aff_flat_range_product(
4726 __isl_take isl_multi_pw_aff *mpa1,
4727 __isl_take isl_multi_pw_aff *mpa2);
4729 If the C<ls> argument of C<isl_multi_aff_lift> is not C<NULL>,
4730 then it is assigned the local space that lies at the basis of
4731 the lifting applied.
4733 #include <isl/aff.h>
4734 __isl_give isl_multi_aff *isl_multi_aff_pullback_multi_aff(
4735 __isl_take isl_multi_aff *ma1,
4736 __isl_take isl_multi_aff *ma2);
4737 __isl_give isl_pw_multi_aff *
4738 isl_pw_multi_aff_pullback_multi_aff(
4739 __isl_take isl_pw_multi_aff *pma,
4740 __isl_take isl_multi_aff *ma);
4741 __isl_give isl_multi_pw_aff *
4742 isl_multi_pw_aff_pullback_multi_aff(
4743 __isl_take isl_multi_pw_aff *mpa,
4744 __isl_take isl_multi_aff *ma);
4745 __isl_give isl_pw_multi_aff *
4746 isl_pw_multi_aff_pullback_pw_multi_aff(
4747 __isl_take isl_pw_multi_aff *pma1,
4748 __isl_take isl_pw_multi_aff *pma2);
4749 __isl_give isl_multi_pw_aff *
4750 isl_multi_pw_aff_pullback_pw_multi_aff(
4751 __isl_take isl_multi_pw_aff *mpa,
4752 __isl_take isl_pw_multi_aff *pma);
4753 __isl_give isl_multi_pw_aff *
4754 isl_multi_pw_aff_pullback_multi_pw_aff(
4755 __isl_take isl_multi_pw_aff *mpa1,
4756 __isl_take isl_multi_pw_aff *mpa2);
4758 The function C<isl_multi_aff_pullback_multi_aff> precomposes C<ma1> by C<ma2>.
4759 In other words, C<ma2> is plugged
4762 __isl_give isl_set *isl_multi_aff_lex_le_set(
4763 __isl_take isl_multi_aff *ma1,
4764 __isl_take isl_multi_aff *ma2);
4765 __isl_give isl_set *isl_multi_aff_lex_ge_set(
4766 __isl_take isl_multi_aff *ma1,
4767 __isl_take isl_multi_aff *ma2);
4769 The function C<isl_multi_aff_lex_le_set> returns a set
4770 containing those elements in the shared domain space
4771 where C<ma1> is lexicographically smaller than or
4774 An expression can be read from input using
4776 #include <isl/aff.h>
4777 __isl_give isl_multi_aff *isl_multi_aff_read_from_str(
4778 isl_ctx *ctx, const char *str);
4779 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_read_from_str(
4780 isl_ctx *ctx, const char *str);
4781 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_read_from_str(
4782 isl_ctx *ctx, const char *str);
4783 __isl_give isl_union_pw_multi_aff *
4784 isl_union_pw_multi_aff_read_from_str(
4785 isl_ctx *ctx, const char *str);
4787 An expression can be printed using
4789 #include <isl/aff.h>
4790 __isl_give isl_printer *isl_printer_print_multi_aff(
4791 __isl_take isl_printer *p,
4792 __isl_keep isl_multi_aff *maff);
4793 __isl_give isl_printer *isl_printer_print_pw_multi_aff(
4794 __isl_take isl_printer *p,
4795 __isl_keep isl_pw_multi_aff *pma);
4796 __isl_give isl_printer *isl_printer_print_union_pw_multi_aff(
4797 __isl_take isl_printer *p,
4798 __isl_keep isl_union_pw_multi_aff *upma);
4799 __isl_give isl_printer *isl_printer_print_multi_pw_aff(
4800 __isl_take isl_printer *p,
4801 __isl_keep isl_multi_pw_aff *mpa);
4805 Points are elements of a set. They can be used to construct
4806 simple sets (boxes) or they can be used to represent the
4807 individual elements of a set.
4808 The zero point (the origin) can be created using
4810 __isl_give isl_point *isl_point_zero(__isl_take isl_space *space);
4812 The coordinates of a point can be inspected, set and changed
4815 __isl_give isl_val *isl_point_get_coordinate_val(
4816 __isl_keep isl_point *pnt,
4817 enum isl_dim_type type, int pos);
4818 __isl_give isl_point *isl_point_set_coordinate_val(
4819 __isl_take isl_point *pnt,
4820 enum isl_dim_type type, int pos,
4821 __isl_take isl_val *v);
4823 __isl_give isl_point *isl_point_add_ui(
4824 __isl_take isl_point *pnt,
4825 enum isl_dim_type type, int pos, unsigned val);
4826 __isl_give isl_point *isl_point_sub_ui(
4827 __isl_take isl_point *pnt,
4828 enum isl_dim_type type, int pos, unsigned val);
4830 Other properties can be obtained using
4832 isl_ctx *isl_point_get_ctx(__isl_keep isl_point *pnt);
4834 Points can be copied or freed using
4836 __isl_give isl_point *isl_point_copy(
4837 __isl_keep isl_point *pnt);
4838 void isl_point_free(__isl_take isl_point *pnt);
4840 A singleton set can be created from a point using
4842 __isl_give isl_basic_set *isl_basic_set_from_point(
4843 __isl_take isl_point *pnt);
4844 __isl_give isl_set *isl_set_from_point(
4845 __isl_take isl_point *pnt);
4847 and a box can be created from two opposite extremal points using
4849 __isl_give isl_basic_set *isl_basic_set_box_from_points(
4850 __isl_take isl_point *pnt1,
4851 __isl_take isl_point *pnt2);
4852 __isl_give isl_set *isl_set_box_from_points(
4853 __isl_take isl_point *pnt1,
4854 __isl_take isl_point *pnt2);
4856 All elements of a B<bounded> (union) set can be enumerated using
4857 the following functions.
4859 int isl_set_foreach_point(__isl_keep isl_set *set,
4860 int (*fn)(__isl_take isl_point *pnt, void *user),
4862 int isl_union_set_foreach_point(__isl_keep isl_union_set *uset,
4863 int (*fn)(__isl_take isl_point *pnt, void *user),
4866 The function C<fn> is called for each integer point in
4867 C<set> with as second argument the last argument of
4868 the C<isl_set_foreach_point> call. The function C<fn>
4869 should return C<0> on success and C<-1> on failure.
4870 In the latter case, C<isl_set_foreach_point> will stop
4871 enumerating and return C<-1> as well.
4872 If the enumeration is performed successfully and to completion,
4873 then C<isl_set_foreach_point> returns C<0>.
4875 To obtain a single point of a (basic) set, use
4877 __isl_give isl_point *isl_basic_set_sample_point(
4878 __isl_take isl_basic_set *bset);
4879 __isl_give isl_point *isl_set_sample_point(
4880 __isl_take isl_set *set);
4882 If C<set> does not contain any (integer) points, then the
4883 resulting point will be ``void'', a property that can be
4886 int isl_point_is_void(__isl_keep isl_point *pnt);
4888 =head2 Piecewise Quasipolynomials
4890 A piecewise quasipolynomial is a particular kind of function that maps
4891 a parametric point to a rational value.
4892 More specifically, a quasipolynomial is a polynomial expression in greatest
4893 integer parts of affine expressions of parameters and variables.
4894 A piecewise quasipolynomial is a subdivision of a given parametric
4895 domain into disjoint cells with a quasipolynomial associated to
4896 each cell. The value of the piecewise quasipolynomial at a given
4897 point is the value of the quasipolynomial associated to the cell
4898 that contains the point. Outside of the union of cells,
4899 the value is assumed to be zero.
4900 For example, the piecewise quasipolynomial
4902 [n] -> { [x] -> ((1 + n) - x) : x <= n and x >= 0 }
4904 maps C<x> to C<1 + n - x> for values of C<x> between C<0> and C<n>.
4905 A given piecewise quasipolynomial has a fixed domain dimension.
4906 Union piecewise quasipolynomials are used to contain piecewise quasipolynomials
4907 defined over different domains.
4908 Piecewise quasipolynomials are mainly used by the C<barvinok>
4909 library for representing the number of elements in a parametric set or map.
4910 For example, the piecewise quasipolynomial above represents
4911 the number of points in the map
4913 [n] -> { [x] -> [y] : x,y >= 0 and 0 <= x + y <= n }
4915 =head3 Input and Output
4917 Piecewise quasipolynomials can be read from input using
4919 __isl_give isl_union_pw_qpolynomial *
4920 isl_union_pw_qpolynomial_read_from_str(
4921 isl_ctx *ctx, const char *str);
4923 Quasipolynomials and piecewise quasipolynomials can be printed
4924 using the following functions.
4926 __isl_give isl_printer *isl_printer_print_qpolynomial(
4927 __isl_take isl_printer *p,
4928 __isl_keep isl_qpolynomial *qp);
4930 __isl_give isl_printer *isl_printer_print_pw_qpolynomial(
4931 __isl_take isl_printer *p,
4932 __isl_keep isl_pw_qpolynomial *pwqp);
4934 __isl_give isl_printer *isl_printer_print_union_pw_qpolynomial(
4935 __isl_take isl_printer *p,
4936 __isl_keep isl_union_pw_qpolynomial *upwqp);
4938 The output format of the printer
4939 needs to be set to either C<ISL_FORMAT_ISL> or C<ISL_FORMAT_C>.
4940 For C<isl_printer_print_union_pw_qpolynomial>, only C<ISL_FORMAT_ISL>
4942 In case of printing in C<ISL_FORMAT_C>, the user may want
4943 to set the names of all dimensions
4945 __isl_give isl_qpolynomial *isl_qpolynomial_set_dim_name(
4946 __isl_take isl_qpolynomial *qp,
4947 enum isl_dim_type type, unsigned pos,
4949 __isl_give isl_pw_qpolynomial *
4950 isl_pw_qpolynomial_set_dim_name(
4951 __isl_take isl_pw_qpolynomial *pwqp,
4952 enum isl_dim_type type, unsigned pos,
4955 =head3 Creating New (Piecewise) Quasipolynomials
4957 Some simple quasipolynomials can be created using the following functions.
4958 More complicated quasipolynomials can be created by applying
4959 operations such as addition and multiplication
4960 on the resulting quasipolynomials
4962 __isl_give isl_qpolynomial *isl_qpolynomial_zero_on_domain(
4963 __isl_take isl_space *domain);
4964 __isl_give isl_qpolynomial *isl_qpolynomial_one_on_domain(
4965 __isl_take isl_space *domain);
4966 __isl_give isl_qpolynomial *isl_qpolynomial_infty_on_domain(
4967 __isl_take isl_space *domain);
4968 __isl_give isl_qpolynomial *isl_qpolynomial_neginfty_on_domain(
4969 __isl_take isl_space *domain);
4970 __isl_give isl_qpolynomial *isl_qpolynomial_nan_on_domain(
4971 __isl_take isl_space *domain);
4972 __isl_give isl_qpolynomial *isl_qpolynomial_val_on_domain(
4973 __isl_take isl_space *domain,
4974 __isl_take isl_val *val);
4975 __isl_give isl_qpolynomial *isl_qpolynomial_var_on_domain(
4976 __isl_take isl_space *domain,
4977 enum isl_dim_type type, unsigned pos);
4978 __isl_give isl_qpolynomial *isl_qpolynomial_from_aff(
4979 __isl_take isl_aff *aff);
4981 Note that the space in which a quasipolynomial lives is a map space
4982 with a one-dimensional range. The C<domain> argument in some of
4983 the functions above corresponds to the domain of this map space.
4985 The zero piecewise quasipolynomial or a piecewise quasipolynomial
4986 with a single cell can be created using the following functions.
4987 Multiple of these single cell piecewise quasipolynomials can
4988 be combined to create more complicated piecewise quasipolynomials.
4990 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_zero(
4991 __isl_take isl_space *space);
4992 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_alloc(
4993 __isl_take isl_set *set,
4994 __isl_take isl_qpolynomial *qp);
4995 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_from_qpolynomial(
4996 __isl_take isl_qpolynomial *qp);
4997 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_from_pw_aff(
4998 __isl_take isl_pw_aff *pwaff);
5000 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_zero(
5001 __isl_take isl_space *space);
5002 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_from_pw_qpolynomial(
5003 __isl_take isl_pw_qpolynomial *pwqp);
5004 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_add_pw_qpolynomial(
5005 __isl_take isl_union_pw_qpolynomial *upwqp,
5006 __isl_take isl_pw_qpolynomial *pwqp);
5008 Quasipolynomials can be copied and freed again using the following
5011 __isl_give isl_qpolynomial *isl_qpolynomial_copy(
5012 __isl_keep isl_qpolynomial *qp);
5013 void *isl_qpolynomial_free(__isl_take isl_qpolynomial *qp);
5015 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_copy(
5016 __isl_keep isl_pw_qpolynomial *pwqp);
5017 void *isl_pw_qpolynomial_free(
5018 __isl_take isl_pw_qpolynomial *pwqp);
5020 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_copy(
5021 __isl_keep isl_union_pw_qpolynomial *upwqp);
5022 void *isl_union_pw_qpolynomial_free(
5023 __isl_take isl_union_pw_qpolynomial *upwqp);
5025 =head3 Inspecting (Piecewise) Quasipolynomials
5027 To iterate over all piecewise quasipolynomials in a union
5028 piecewise quasipolynomial, use the following function
5030 int isl_union_pw_qpolynomial_foreach_pw_qpolynomial(
5031 __isl_keep isl_union_pw_qpolynomial *upwqp,
5032 int (*fn)(__isl_take isl_pw_qpolynomial *pwqp, void *user),
5035 To extract the piecewise quasipolynomial in a given space from a union, use
5037 __isl_give isl_pw_qpolynomial *
5038 isl_union_pw_qpolynomial_extract_pw_qpolynomial(
5039 __isl_keep isl_union_pw_qpolynomial *upwqp,
5040 __isl_take isl_space *space);
5042 To iterate over the cells in a piecewise quasipolynomial,
5043 use either of the following two functions
5045 int isl_pw_qpolynomial_foreach_piece(
5046 __isl_keep isl_pw_qpolynomial *pwqp,
5047 int (*fn)(__isl_take isl_set *set,
5048 __isl_take isl_qpolynomial *qp,
5049 void *user), void *user);
5050 int isl_pw_qpolynomial_foreach_lifted_piece(
5051 __isl_keep isl_pw_qpolynomial *pwqp,
5052 int (*fn)(__isl_take isl_set *set,
5053 __isl_take isl_qpolynomial *qp,
5054 void *user), void *user);
5056 As usual, the function C<fn> should return C<0> on success
5057 and C<-1> on failure. The difference between
5058 C<isl_pw_qpolynomial_foreach_piece> and
5059 C<isl_pw_qpolynomial_foreach_lifted_piece> is that
5060 C<isl_pw_qpolynomial_foreach_lifted_piece> will first
5061 compute unique representations for all existentially quantified
5062 variables and then turn these existentially quantified variables
5063 into extra set variables, adapting the associated quasipolynomial
5064 accordingly. This means that the C<set> passed to C<fn>
5065 will not have any existentially quantified variables, but that
5066 the dimensions of the sets may be different for different
5067 invocations of C<fn>.
5069 The constant term of a quasipolynomial can be extracted using
5071 __isl_give isl_val *isl_qpolynomial_get_constant_val(
5072 __isl_keep isl_qpolynomial *qp);
5074 To iterate over all terms in a quasipolynomial,
5077 int isl_qpolynomial_foreach_term(
5078 __isl_keep isl_qpolynomial *qp,
5079 int (*fn)(__isl_take isl_term *term,
5080 void *user), void *user);
5082 The terms themselves can be inspected and freed using
5085 unsigned isl_term_dim(__isl_keep isl_term *term,
5086 enum isl_dim_type type);
5087 __isl_give isl_val *isl_term_get_coefficient_val(
5088 __isl_keep isl_term *term);
5089 int isl_term_get_exp(__isl_keep isl_term *term,
5090 enum isl_dim_type type, unsigned pos);
5091 __isl_give isl_aff *isl_term_get_div(
5092 __isl_keep isl_term *term, unsigned pos);
5093 void isl_term_free(__isl_take isl_term *term);
5095 Each term is a product of parameters, set variables and
5096 integer divisions. The function C<isl_term_get_exp>
5097 returns the exponent of a given dimensions in the given term.
5099 =head3 Properties of (Piecewise) Quasipolynomials
5101 To check whether two union piecewise quasipolynomials are
5102 obviously equal, use
5104 int isl_union_pw_qpolynomial_plain_is_equal(
5105 __isl_keep isl_union_pw_qpolynomial *upwqp1,
5106 __isl_keep isl_union_pw_qpolynomial *upwqp2);
5108 =head3 Operations on (Piecewise) Quasipolynomials
5110 __isl_give isl_qpolynomial *isl_qpolynomial_scale_val(
5111 __isl_take isl_qpolynomial *qp,
5112 __isl_take isl_val *v);
5113 __isl_give isl_qpolynomial *isl_qpolynomial_neg(
5114 __isl_take isl_qpolynomial *qp);
5115 __isl_give isl_qpolynomial *isl_qpolynomial_add(
5116 __isl_take isl_qpolynomial *qp1,
5117 __isl_take isl_qpolynomial *qp2);
5118 __isl_give isl_qpolynomial *isl_qpolynomial_sub(
5119 __isl_take isl_qpolynomial *qp1,
5120 __isl_take isl_qpolynomial *qp2);
5121 __isl_give isl_qpolynomial *isl_qpolynomial_mul(
5122 __isl_take isl_qpolynomial *qp1,
5123 __isl_take isl_qpolynomial *qp2);
5124 __isl_give isl_qpolynomial *isl_qpolynomial_pow(
5125 __isl_take isl_qpolynomial *qp, unsigned exponent);
5127 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_fix_val(
5128 __isl_take isl_pw_qpolynomial *pwqp,
5129 enum isl_dim_type type, unsigned n,
5130 __isl_take isl_val *v);
5131 __isl_give isl_pw_qpolynomial *
5132 isl_pw_qpolynomial_scale_val(
5133 __isl_take isl_pw_qpolynomial *pwqp,
5134 __isl_take isl_val *v);
5135 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_add(
5136 __isl_take isl_pw_qpolynomial *pwqp1,
5137 __isl_take isl_pw_qpolynomial *pwqp2);
5138 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_sub(
5139 __isl_take isl_pw_qpolynomial *pwqp1,
5140 __isl_take isl_pw_qpolynomial *pwqp2);
5141 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_add_disjoint(
5142 __isl_take isl_pw_qpolynomial *pwqp1,
5143 __isl_take isl_pw_qpolynomial *pwqp2);
5144 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_neg(
5145 __isl_take isl_pw_qpolynomial *pwqp);
5146 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_mul(
5147 __isl_take isl_pw_qpolynomial *pwqp1,
5148 __isl_take isl_pw_qpolynomial *pwqp2);
5149 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_pow(
5150 __isl_take isl_pw_qpolynomial *pwqp, unsigned exponent);
5152 __isl_give isl_union_pw_qpolynomial *
5153 isl_union_pw_qpolynomial_scale_val(
5154 __isl_take isl_union_pw_qpolynomial *upwqp,
5155 __isl_take isl_val *v);
5156 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_add(
5157 __isl_take isl_union_pw_qpolynomial *upwqp1,
5158 __isl_take isl_union_pw_qpolynomial *upwqp2);
5159 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_sub(
5160 __isl_take isl_union_pw_qpolynomial *upwqp1,
5161 __isl_take isl_union_pw_qpolynomial *upwqp2);
5162 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_mul(
5163 __isl_take isl_union_pw_qpolynomial *upwqp1,
5164 __isl_take isl_union_pw_qpolynomial *upwqp2);
5166 __isl_give isl_val *isl_pw_qpolynomial_eval(
5167 __isl_take isl_pw_qpolynomial *pwqp,
5168 __isl_take isl_point *pnt);
5170 __isl_give isl_val *isl_union_pw_qpolynomial_eval(
5171 __isl_take isl_union_pw_qpolynomial *upwqp,
5172 __isl_take isl_point *pnt);
5174 __isl_give isl_set *isl_pw_qpolynomial_domain(
5175 __isl_take isl_pw_qpolynomial *pwqp);
5176 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_intersect_domain(
5177 __isl_take isl_pw_qpolynomial *pwpq,
5178 __isl_take isl_set *set);
5179 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_intersect_params(
5180 __isl_take isl_pw_qpolynomial *pwpq,
5181 __isl_take isl_set *set);
5183 __isl_give isl_union_set *isl_union_pw_qpolynomial_domain(
5184 __isl_take isl_union_pw_qpolynomial *upwqp);
5185 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_intersect_domain(
5186 __isl_take isl_union_pw_qpolynomial *upwpq,
5187 __isl_take isl_union_set *uset);
5188 __isl_give isl_union_pw_qpolynomial *
5189 isl_union_pw_qpolynomial_intersect_params(
5190 __isl_take isl_union_pw_qpolynomial *upwpq,
5191 __isl_take isl_set *set);
5193 __isl_give isl_qpolynomial *isl_qpolynomial_align_params(
5194 __isl_take isl_qpolynomial *qp,
5195 __isl_take isl_space *model);
5197 __isl_give isl_qpolynomial *isl_qpolynomial_project_domain_on_params(
5198 __isl_take isl_qpolynomial *qp);
5199 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_project_domain_on_params(
5200 __isl_take isl_pw_qpolynomial *pwqp);
5202 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_coalesce(
5203 __isl_take isl_union_pw_qpolynomial *upwqp);
5205 __isl_give isl_qpolynomial *isl_qpolynomial_gist_params(
5206 __isl_take isl_qpolynomial *qp,
5207 __isl_take isl_set *context);
5208 __isl_give isl_qpolynomial *isl_qpolynomial_gist(
5209 __isl_take isl_qpolynomial *qp,
5210 __isl_take isl_set *context);
5212 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_gist_params(
5213 __isl_take isl_pw_qpolynomial *pwqp,
5214 __isl_take isl_set *context);
5215 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_gist(
5216 __isl_take isl_pw_qpolynomial *pwqp,
5217 __isl_take isl_set *context);
5219 __isl_give isl_union_pw_qpolynomial *
5220 isl_union_pw_qpolynomial_gist_params(
5221 __isl_take isl_union_pw_qpolynomial *upwqp,
5222 __isl_take isl_set *context);
5223 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_gist(
5224 __isl_take isl_union_pw_qpolynomial *upwqp,
5225 __isl_take isl_union_set *context);
5227 The gist operation applies the gist operation to each of
5228 the cells in the domain of the input piecewise quasipolynomial.
5229 The context is also exploited
5230 to simplify the quasipolynomials associated to each cell.
5232 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_to_polynomial(
5233 __isl_take isl_pw_qpolynomial *pwqp, int sign);
5234 __isl_give isl_union_pw_qpolynomial *
5235 isl_union_pw_qpolynomial_to_polynomial(
5236 __isl_take isl_union_pw_qpolynomial *upwqp, int sign);
5238 Approximate each quasipolynomial by a polynomial. If C<sign> is positive,
5239 the polynomial will be an overapproximation. If C<sign> is negative,
5240 it will be an underapproximation. If C<sign> is zero, the approximation
5241 will lie somewhere in between.
5243 =head2 Bounds on Piecewise Quasipolynomials and Piecewise Quasipolynomial Reductions
5245 A piecewise quasipolynomial reduction is a piecewise
5246 reduction (or fold) of quasipolynomials.
5247 In particular, the reduction can be maximum or a minimum.
5248 The objects are mainly used to represent the result of
5249 an upper or lower bound on a quasipolynomial over its domain,
5250 i.e., as the result of the following function.
5252 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_bound(
5253 __isl_take isl_pw_qpolynomial *pwqp,
5254 enum isl_fold type, int *tight);
5256 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_bound(
5257 __isl_take isl_union_pw_qpolynomial *upwqp,
5258 enum isl_fold type, int *tight);
5260 The C<type> argument may be either C<isl_fold_min> or C<isl_fold_max>.
5261 If C<tight> is not C<NULL>, then C<*tight> is set to C<1>
5262 is the returned bound is known be tight, i.e., for each value
5263 of the parameters there is at least
5264 one element in the domain that reaches the bound.
5265 If the domain of C<pwqp> is not wrapping, then the bound is computed
5266 over all elements in that domain and the result has a purely parametric
5267 domain. If the domain of C<pwqp> is wrapping, then the bound is
5268 computed over the range of the wrapped relation. The domain of the
5269 wrapped relation becomes the domain of the result.
5271 A (piecewise) quasipolynomial reduction can be copied or freed using the
5272 following functions.
5274 __isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_copy(
5275 __isl_keep isl_qpolynomial_fold *fold);
5276 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_copy(
5277 __isl_keep isl_pw_qpolynomial_fold *pwf);
5278 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_copy(
5279 __isl_keep isl_union_pw_qpolynomial_fold *upwf);
5280 void isl_qpolynomial_fold_free(
5281 __isl_take isl_qpolynomial_fold *fold);
5282 void *isl_pw_qpolynomial_fold_free(
5283 __isl_take isl_pw_qpolynomial_fold *pwf);
5284 void *isl_union_pw_qpolynomial_fold_free(
5285 __isl_take isl_union_pw_qpolynomial_fold *upwf);
5287 =head3 Printing Piecewise Quasipolynomial Reductions
5289 Piecewise quasipolynomial reductions can be printed
5290 using the following function.
5292 __isl_give isl_printer *isl_printer_print_pw_qpolynomial_fold(
5293 __isl_take isl_printer *p,
5294 __isl_keep isl_pw_qpolynomial_fold *pwf);
5295 __isl_give isl_printer *isl_printer_print_union_pw_qpolynomial_fold(
5296 __isl_take isl_printer *p,
5297 __isl_keep isl_union_pw_qpolynomial_fold *upwf);
5299 For C<isl_printer_print_pw_qpolynomial_fold>,
5300 output format of the printer
5301 needs to be set to either C<ISL_FORMAT_ISL> or C<ISL_FORMAT_C>.
5302 For C<isl_printer_print_union_pw_qpolynomial_fold>,
5303 output format of the printer
5304 needs to be set to C<ISL_FORMAT_ISL>.
5305 In case of printing in C<ISL_FORMAT_C>, the user may want
5306 to set the names of all dimensions
5308 __isl_give isl_pw_qpolynomial_fold *
5309 isl_pw_qpolynomial_fold_set_dim_name(
5310 __isl_take isl_pw_qpolynomial_fold *pwf,
5311 enum isl_dim_type type, unsigned pos,
5314 =head3 Inspecting (Piecewise) Quasipolynomial Reductions
5316 To iterate over all piecewise quasipolynomial reductions in a union
5317 piecewise quasipolynomial reduction, use the following function
5319 int isl_union_pw_qpolynomial_fold_foreach_pw_qpolynomial_fold(
5320 __isl_keep isl_union_pw_qpolynomial_fold *upwf,
5321 int (*fn)(__isl_take isl_pw_qpolynomial_fold *pwf,
5322 void *user), void *user);
5324 To iterate over the cells in a piecewise quasipolynomial reduction,
5325 use either of the following two functions
5327 int isl_pw_qpolynomial_fold_foreach_piece(
5328 __isl_keep isl_pw_qpolynomial_fold *pwf,
5329 int (*fn)(__isl_take isl_set *set,
5330 __isl_take isl_qpolynomial_fold *fold,
5331 void *user), void *user);
5332 int isl_pw_qpolynomial_fold_foreach_lifted_piece(
5333 __isl_keep isl_pw_qpolynomial_fold *pwf,
5334 int (*fn)(__isl_take isl_set *set,
5335 __isl_take isl_qpolynomial_fold *fold,
5336 void *user), void *user);
5338 See L<Inspecting (Piecewise) Quasipolynomials> for an explanation
5339 of the difference between these two functions.
5341 To iterate over all quasipolynomials in a reduction, use
5343 int isl_qpolynomial_fold_foreach_qpolynomial(
5344 __isl_keep isl_qpolynomial_fold *fold,
5345 int (*fn)(__isl_take isl_qpolynomial *qp,
5346 void *user), void *user);
5348 =head3 Properties of Piecewise Quasipolynomial Reductions
5350 To check whether two union piecewise quasipolynomial reductions are
5351 obviously equal, use
5353 int isl_union_pw_qpolynomial_fold_plain_is_equal(
5354 __isl_keep isl_union_pw_qpolynomial_fold *upwf1,
5355 __isl_keep isl_union_pw_qpolynomial_fold *upwf2);
5357 =head3 Operations on Piecewise Quasipolynomial Reductions
5359 __isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_scale_val(
5360 __isl_take isl_qpolynomial_fold *fold,
5361 __isl_take isl_val *v);
5362 __isl_give isl_pw_qpolynomial_fold *
5363 isl_pw_qpolynomial_fold_scale_val(
5364 __isl_take isl_pw_qpolynomial_fold *pwf,
5365 __isl_take isl_val *v);
5366 __isl_give isl_union_pw_qpolynomial_fold *
5367 isl_union_pw_qpolynomial_fold_scale_val(
5368 __isl_take isl_union_pw_qpolynomial_fold *upwf,
5369 __isl_take isl_val *v);
5371 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_add(
5372 __isl_take isl_pw_qpolynomial_fold *pwf1,
5373 __isl_take isl_pw_qpolynomial_fold *pwf2);
5375 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_fold(
5376 __isl_take isl_pw_qpolynomial_fold *pwf1,
5377 __isl_take isl_pw_qpolynomial_fold *pwf2);
5379 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_fold(
5380 __isl_take isl_union_pw_qpolynomial_fold *upwf1,
5381 __isl_take isl_union_pw_qpolynomial_fold *upwf2);
5383 __isl_give isl_val *isl_pw_qpolynomial_fold_eval(
5384 __isl_take isl_pw_qpolynomial_fold *pwf,
5385 __isl_take isl_point *pnt);
5387 __isl_give isl_val *isl_union_pw_qpolynomial_fold_eval(
5388 __isl_take isl_union_pw_qpolynomial_fold *upwf,
5389 __isl_take isl_point *pnt);
5391 __isl_give isl_pw_qpolynomial_fold *
5392 isl_pw_qpolynomial_fold_intersect_params(
5393 __isl_take isl_pw_qpolynomial_fold *pwf,
5394 __isl_take isl_set *set);
5396 __isl_give isl_union_set *isl_union_pw_qpolynomial_fold_domain(
5397 __isl_take isl_union_pw_qpolynomial_fold *upwf);
5398 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_intersect_domain(
5399 __isl_take isl_union_pw_qpolynomial_fold *upwf,
5400 __isl_take isl_union_set *uset);
5401 __isl_give isl_union_pw_qpolynomial_fold *
5402 isl_union_pw_qpolynomial_fold_intersect_params(
5403 __isl_take isl_union_pw_qpolynomial_fold *upwf,
5404 __isl_take isl_set *set);
5406 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_project_domain_on_params(
5407 __isl_take isl_pw_qpolynomial_fold *pwf);
5409 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_coalesce(
5410 __isl_take isl_pw_qpolynomial_fold *pwf);
5412 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_coalesce(
5413 __isl_take isl_union_pw_qpolynomial_fold *upwf);
5415 __isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_gist_params(
5416 __isl_take isl_qpolynomial_fold *fold,
5417 __isl_take isl_set *context);
5418 __isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_gist(
5419 __isl_take isl_qpolynomial_fold *fold,
5420 __isl_take isl_set *context);
5422 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_gist(
5423 __isl_take isl_pw_qpolynomial_fold *pwf,
5424 __isl_take isl_set *context);
5425 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_gist_params(
5426 __isl_take isl_pw_qpolynomial_fold *pwf,
5427 __isl_take isl_set *context);
5429 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_gist(
5430 __isl_take isl_union_pw_qpolynomial_fold *upwf,
5431 __isl_take isl_union_set *context);
5432 __isl_give isl_union_pw_qpolynomial_fold *
5433 isl_union_pw_qpolynomial_fold_gist_params(
5434 __isl_take isl_union_pw_qpolynomial_fold *upwf,
5435 __isl_take isl_set *context);
5437 The gist operation applies the gist operation to each of
5438 the cells in the domain of the input piecewise quasipolynomial reduction.
5439 In future, the operation will also exploit the context
5440 to simplify the quasipolynomial reductions associated to each cell.
5442 __isl_give isl_pw_qpolynomial_fold *
5443 isl_set_apply_pw_qpolynomial_fold(
5444 __isl_take isl_set *set,
5445 __isl_take isl_pw_qpolynomial_fold *pwf,
5447 __isl_give isl_pw_qpolynomial_fold *
5448 isl_map_apply_pw_qpolynomial_fold(
5449 __isl_take isl_map *map,
5450 __isl_take isl_pw_qpolynomial_fold *pwf,
5452 __isl_give isl_union_pw_qpolynomial_fold *
5453 isl_union_set_apply_union_pw_qpolynomial_fold(
5454 __isl_take isl_union_set *uset,
5455 __isl_take isl_union_pw_qpolynomial_fold *upwf,
5457 __isl_give isl_union_pw_qpolynomial_fold *
5458 isl_union_map_apply_union_pw_qpolynomial_fold(
5459 __isl_take isl_union_map *umap,
5460 __isl_take isl_union_pw_qpolynomial_fold *upwf,
5463 The functions taking a map
5464 compose the given map with the given piecewise quasipolynomial reduction.
5465 That is, compute a bound (of the same type as C<pwf> or C<upwf> itself)
5466 over all elements in the intersection of the range of the map
5467 and the domain of the piecewise quasipolynomial reduction
5468 as a function of an element in the domain of the map.
5469 The functions taking a set compute a bound over all elements in the
5470 intersection of the set and the domain of the
5471 piecewise quasipolynomial reduction.
5473 =head2 Parametric Vertex Enumeration
5475 The parametric vertex enumeration described in this section
5476 is mainly intended to be used internally and by the C<barvinok>
5479 #include <isl/vertices.h>
5480 __isl_give isl_vertices *isl_basic_set_compute_vertices(
5481 __isl_keep isl_basic_set *bset);
5483 The function C<isl_basic_set_compute_vertices> performs the
5484 actual computation of the parametric vertices and the chamber
5485 decomposition and store the result in an C<isl_vertices> object.
5486 This information can be queried by either iterating over all
5487 the vertices or iterating over all the chambers or cells
5488 and then iterating over all vertices that are active on the chamber.
5490 int isl_vertices_foreach_vertex(
5491 __isl_keep isl_vertices *vertices,
5492 int (*fn)(__isl_take isl_vertex *vertex, void *user),
5495 int isl_vertices_foreach_cell(
5496 __isl_keep isl_vertices *vertices,
5497 int (*fn)(__isl_take isl_cell *cell, void *user),
5499 int isl_cell_foreach_vertex(__isl_keep isl_cell *cell,
5500 int (*fn)(__isl_take isl_vertex *vertex, void *user),
5503 Other operations that can be performed on an C<isl_vertices> object are
5506 isl_ctx *isl_vertices_get_ctx(
5507 __isl_keep isl_vertices *vertices);
5508 int isl_vertices_get_n_vertices(
5509 __isl_keep isl_vertices *vertices);
5510 void isl_vertices_free(__isl_take isl_vertices *vertices);
5512 Vertices can be inspected and destroyed using the following functions.
5514 isl_ctx *isl_vertex_get_ctx(__isl_keep isl_vertex *vertex);
5515 int isl_vertex_get_id(__isl_keep isl_vertex *vertex);
5516 __isl_give isl_basic_set *isl_vertex_get_domain(
5517 __isl_keep isl_vertex *vertex);
5518 __isl_give isl_basic_set *isl_vertex_get_expr(
5519 __isl_keep isl_vertex *vertex);
5520 void isl_vertex_free(__isl_take isl_vertex *vertex);
5522 C<isl_vertex_get_expr> returns a singleton parametric set describing
5523 the vertex, while C<isl_vertex_get_domain> returns the activity domain
5525 Note that C<isl_vertex_get_domain> and C<isl_vertex_get_expr> return
5526 B<rational> basic sets, so they should mainly be used for inspection
5527 and should not be mixed with integer sets.
5529 Chambers can be inspected and destroyed using the following functions.
5531 isl_ctx *isl_cell_get_ctx(__isl_keep isl_cell *cell);
5532 __isl_give isl_basic_set *isl_cell_get_domain(
5533 __isl_keep isl_cell *cell);
5534 void isl_cell_free(__isl_take isl_cell *cell);
5536 =head1 Polyhedral Compilation Library
5538 This section collects functionality in C<isl> that has been specifically
5539 designed for use during polyhedral compilation.
5541 =head2 Dependence Analysis
5543 C<isl> contains specialized functionality for performing
5544 array dataflow analysis. That is, given a I<sink> access relation
5545 and a collection of possible I<source> access relations,
5546 C<isl> can compute relations that describe
5547 for each iteration of the sink access, which iteration
5548 of which of the source access relations was the last
5549 to access the same data element before the given iteration
5551 The resulting dependence relations map source iterations
5552 to the corresponding sink iterations.
5553 To compute standard flow dependences, the sink should be
5554 a read, while the sources should be writes.
5555 If any of the source accesses are marked as being I<may>
5556 accesses, then there will be a dependence from the last
5557 I<must> access B<and> from any I<may> access that follows
5558 this last I<must> access.
5559 In particular, if I<all> sources are I<may> accesses,
5560 then memory based dependence analysis is performed.
5561 If, on the other hand, all sources are I<must> accesses,
5562 then value based dependence analysis is performed.
5564 #include <isl/flow.h>
5566 typedef int (*isl_access_level_before)(void *first, void *second);
5568 __isl_give isl_access_info *isl_access_info_alloc(
5569 __isl_take isl_map *sink,
5570 void *sink_user, isl_access_level_before fn,
5572 __isl_give isl_access_info *isl_access_info_add_source(
5573 __isl_take isl_access_info *acc,
5574 __isl_take isl_map *source, int must,
5576 void *isl_access_info_free(__isl_take isl_access_info *acc);
5578 __isl_give isl_flow *isl_access_info_compute_flow(
5579 __isl_take isl_access_info *acc);
5581 int isl_flow_foreach(__isl_keep isl_flow *deps,
5582 int (*fn)(__isl_take isl_map *dep, int must,
5583 void *dep_user, void *user),
5585 __isl_give isl_map *isl_flow_get_no_source(
5586 __isl_keep isl_flow *deps, int must);
5587 void isl_flow_free(__isl_take isl_flow *deps);
5589 The function C<isl_access_info_compute_flow> performs the actual
5590 dependence analysis. The other functions are used to construct
5591 the input for this function or to read off the output.
5593 The input is collected in an C<isl_access_info>, which can
5594 be created through a call to C<isl_access_info_alloc>.
5595 The arguments to this functions are the sink access relation
5596 C<sink>, a token C<sink_user> used to identify the sink
5597 access to the user, a callback function for specifying the
5598 relative order of source and sink accesses, and the number
5599 of source access relations that will be added.
5600 The callback function has type C<int (*)(void *first, void *second)>.
5601 The function is called with two user supplied tokens identifying
5602 either a source or the sink and it should return the shared nesting
5603 level and the relative order of the two accesses.
5604 In particular, let I<n> be the number of loops shared by
5605 the two accesses. If C<first> precedes C<second> textually,
5606 then the function should return I<2 * n + 1>; otherwise,
5607 it should return I<2 * n>.
5608 The sources can be added to the C<isl_access_info> by performing
5609 (at most) C<max_source> calls to C<isl_access_info_add_source>.
5610 C<must> indicates whether the source is a I<must> access
5611 or a I<may> access. Note that a multi-valued access relation
5612 should only be marked I<must> if every iteration in the domain
5613 of the relation accesses I<all> elements in its image.
5614 The C<source_user> token is again used to identify
5615 the source access. The range of the source access relation
5616 C<source> should have the same dimension as the range
5617 of the sink access relation.
5618 The C<isl_access_info_free> function should usually not be
5619 called explicitly, because it is called implicitly by
5620 C<isl_access_info_compute_flow>.
5622 The result of the dependence analysis is collected in an
5623 C<isl_flow>. There may be elements of
5624 the sink access for which no preceding source access could be
5625 found or for which all preceding sources are I<may> accesses.
5626 The relations containing these elements can be obtained through
5627 calls to C<isl_flow_get_no_source>, the first with C<must> set
5628 and the second with C<must> unset.
5629 In the case of standard flow dependence analysis,
5630 with the sink a read and the sources I<must> writes,
5631 the first relation corresponds to the reads from uninitialized
5632 array elements and the second relation is empty.
5633 The actual flow dependences can be extracted using
5634 C<isl_flow_foreach>. This function will call the user-specified
5635 callback function C<fn> for each B<non-empty> dependence between
5636 a source and the sink. The callback function is called
5637 with four arguments, the actual flow dependence relation
5638 mapping source iterations to sink iterations, a boolean that
5639 indicates whether it is a I<must> or I<may> dependence, a token
5640 identifying the source and an additional C<void *> with value
5641 equal to the third argument of the C<isl_flow_foreach> call.
5642 A dependence is marked I<must> if it originates from a I<must>
5643 source and if it is not followed by any I<may> sources.
5645 After finishing with an C<isl_flow>, the user should call
5646 C<isl_flow_free> to free all associated memory.
5648 A higher-level interface to dependence analysis is provided
5649 by the following function.
5651 #include <isl/flow.h>
5653 int isl_union_map_compute_flow(__isl_take isl_union_map *sink,
5654 __isl_take isl_union_map *must_source,
5655 __isl_take isl_union_map *may_source,
5656 __isl_take isl_union_map *schedule,
5657 __isl_give isl_union_map **must_dep,
5658 __isl_give isl_union_map **may_dep,
5659 __isl_give isl_union_map **must_no_source,
5660 __isl_give isl_union_map **may_no_source);
5662 The arrays are identified by the tuple names of the ranges
5663 of the accesses. The iteration domains by the tuple names
5664 of the domains of the accesses and of the schedule.
5665 The relative order of the iteration domains is given by the
5666 schedule. The relations returned through C<must_no_source>
5667 and C<may_no_source> are subsets of C<sink>.
5668 Any of C<must_dep>, C<may_dep>, C<must_no_source>
5669 or C<may_no_source> may be C<NULL>, but a C<NULL> value for
5670 any of the other arguments is treated as an error.
5672 =head3 Interaction with Dependence Analysis
5674 During the dependence analysis, we frequently need to perform
5675 the following operation. Given a relation between sink iterations
5676 and potential source iterations from a particular source domain,
5677 what is the last potential source iteration corresponding to each
5678 sink iteration. It can sometimes be convenient to adjust
5679 the set of potential source iterations before or after each such operation.
5680 The prototypical example is fuzzy array dataflow analysis,
5681 where we need to analyze if, based on data-dependent constraints,
5682 the sink iteration can ever be executed without one or more of
5683 the corresponding potential source iterations being executed.
5684 If so, we can introduce extra parameters and select an unknown
5685 but fixed source iteration from the potential source iterations.
5686 To be able to perform such manipulations, C<isl> provides the following
5689 #include <isl/flow.h>
5691 typedef __isl_give isl_restriction *(*isl_access_restrict)(
5692 __isl_keep isl_map *source_map,
5693 __isl_keep isl_set *sink, void *source_user,
5695 __isl_give isl_access_info *isl_access_info_set_restrict(
5696 __isl_take isl_access_info *acc,
5697 isl_access_restrict fn, void *user);
5699 The function C<isl_access_info_set_restrict> should be called
5700 before calling C<isl_access_info_compute_flow> and registers a callback function
5701 that will be called any time C<isl> is about to compute the last
5702 potential source. The first argument is the (reverse) proto-dependence,
5703 mapping sink iterations to potential source iterations.
5704 The second argument represents the sink iterations for which
5705 we want to compute the last source iteration.
5706 The third argument is the token corresponding to the source
5707 and the final argument is the token passed to C<isl_access_info_set_restrict>.
5708 The callback is expected to return a restriction on either the input or
5709 the output of the operation computing the last potential source.
5710 If the input needs to be restricted then restrictions are needed
5711 for both the source and the sink iterations. The sink iterations
5712 and the potential source iterations will be intersected with these sets.
5713 If the output needs to be restricted then only a restriction on the source
5714 iterations is required.
5715 If any error occurs, the callback should return C<NULL>.
5716 An C<isl_restriction> object can be created, freed and inspected
5717 using the following functions.
5719 #include <isl/flow.h>
5721 __isl_give isl_restriction *isl_restriction_input(
5722 __isl_take isl_set *source_restr,
5723 __isl_take isl_set *sink_restr);
5724 __isl_give isl_restriction *isl_restriction_output(
5725 __isl_take isl_set *source_restr);
5726 __isl_give isl_restriction *isl_restriction_none(
5727 __isl_take isl_map *source_map);
5728 __isl_give isl_restriction *isl_restriction_empty(
5729 __isl_take isl_map *source_map);
5730 void *isl_restriction_free(
5731 __isl_take isl_restriction *restr);
5732 isl_ctx *isl_restriction_get_ctx(
5733 __isl_keep isl_restriction *restr);
5735 C<isl_restriction_none> and C<isl_restriction_empty> are special
5736 cases of C<isl_restriction_input>. C<isl_restriction_none>
5737 is essentially equivalent to
5739 isl_restriction_input(isl_set_universe(
5740 isl_space_range(isl_map_get_space(source_map))),
5742 isl_space_domain(isl_map_get_space(source_map))));
5744 whereas C<isl_restriction_empty> is essentially equivalent to
5746 isl_restriction_input(isl_set_empty(
5747 isl_space_range(isl_map_get_space(source_map))),
5749 isl_space_domain(isl_map_get_space(source_map))));
5753 B<The functionality described in this section is fairly new
5754 and may be subject to change.>
5756 #include <isl/schedule.h>
5757 __isl_give isl_schedule *
5758 isl_schedule_constraints_compute_schedule(
5759 __isl_take isl_schedule_constraints *sc);
5760 void *isl_schedule_free(__isl_take isl_schedule *sched);
5762 The function C<isl_schedule_constraints_compute_schedule> can be
5763 used to compute a schedule that satisfy the given schedule constraints.
5764 These schedule constraints include the iteration domain for which
5765 a schedule should be computed and dependences between pairs of
5766 iterations. In particular, these dependences include
5767 I<validity> dependences and I<proximity> dependences.
5768 By default, the algorithm used to construct the schedule is similar
5769 to that of C<Pluto>.
5770 Alternatively, Feautrier's multi-dimensional scheduling algorithm can
5772 The generated schedule respects all validity dependences.
5773 That is, all dependence distances over these dependences in the
5774 scheduled space are lexicographically positive.
5775 The default algorithm tries to ensure that the dependence distances
5776 over coincidence constraints are zero and to minimize the
5777 dependence distances over proximity dependences.
5778 Moreover, it tries to obtain sequences (bands) of schedule dimensions
5779 for groups of domains where the dependence distances over validity
5780 dependences have only non-negative values.
5781 When using Feautrier's algorithm, the coincidence and proximity constraints
5782 are only taken into account during the extension to a
5783 full-dimensional schedule.
5785 An C<isl_schedule_constraints> object can be constructed
5786 and manipulated using the following functions.
5788 #include <isl/schedule.h>
5789 __isl_give isl_schedule_constraints *
5790 isl_schedule_constraints_copy(
5791 __isl_keep isl_schedule_constraints *sc);
5792 __isl_give isl_schedule_constraints *
5793 isl_schedule_constraints_on_domain(
5794 __isl_take isl_union_set *domain);
5795 isl_ctx *isl_schedule_constraints_get_ctx(
5796 __isl_keep isl_schedule_constraints *sc);
5797 __isl_give isl_schedule_constraints *
5798 isl_schedule_constraints_set_validity(
5799 __isl_take isl_schedule_constraints *sc,
5800 __isl_take isl_union_map *validity);
5801 __isl_give isl_schedule_constraints *
5802 isl_schedule_constraints_set_coincidence(
5803 __isl_take isl_schedule_constraints *sc,
5804 __isl_take isl_union_map *coincidence);
5805 __isl_give isl_schedule_constraints *
5806 isl_schedule_constraints_set_proximity(
5807 __isl_take isl_schedule_constraints *sc,
5808 __isl_take isl_union_map *proximity);
5809 __isl_give isl_schedule_constraints *
5810 isl_schedule_constraints_set_conditional_validity(
5811 __isl_take isl_schedule_constraints *sc,
5812 __isl_take isl_union_map *condition,
5813 __isl_take isl_union_map *validity);
5814 void *isl_schedule_constraints_free(
5815 __isl_take isl_schedule_constraints *sc);
5817 The initial C<isl_schedule_constraints> object created by
5818 C<isl_schedule_constraints_on_domain> does not impose any constraints.
5819 That is, it has an empty set of dependences.
5820 The function C<isl_schedule_constraints_set_validity> replaces the
5821 validity dependences, mapping domain elements I<i> to domain
5822 elements that should be scheduled after I<i>.
5823 The function C<isl_schedule_constraints_set_coincidence> replaces the
5824 coincidence dependences, mapping domain elements I<i> to domain
5825 elements that should be scheduled together with I<I>, if possible.
5826 The function C<isl_schedule_constraints_set_proximity> replaces the
5827 proximity dependences, mapping domain elements I<i> to domain
5828 elements that should be scheduled either before I<I>
5829 or as early as possible after I<i>.
5831 The function C<isl_schedule_constraints_set_conditional_validity>
5832 replaces the conditional validity constraints.
5833 A conditional validity constraint is only imposed when any of the corresponding
5834 conditions is satisfied, i.e., when any of them is non-zero.
5835 That is, the scheduler ensures that within each band if the dependence
5836 distances over the condition constraints are not all zero
5837 then all corresponding conditional validity constraints are respected.
5838 A conditional validity constraint corresponds to a condition
5839 if the two are adjacent, i.e., if the domain of one relation intersect
5840 the range of the other relation.
5841 The typical use case of conditional validity constraints is
5842 to allow order constraints between live ranges to be violated
5843 as long as the live ranges themselves are local to the band.
5844 To allow more fine-grained control over which conditions correspond
5845 to which conditional validity constraints, the domains and ranges
5846 of these relations may include I<tags>. That is, the domains and
5847 ranges of those relation may themselves be wrapped relations
5848 where the iteration domain appears in the domain of those wrapped relations
5849 and the range of the wrapped relations can be arbitrarily chosen
5850 by the user. Conditions and conditional validity constraints are only
5851 considere adjacent to each other if the entire wrapped relation matches.
5852 In particular, a relation with a tag will never be considered adjacent
5853 to a relation without a tag.
5855 The following function computes a schedule directly from
5856 an iteration domain and validity and proximity dependences
5857 and is implemented in terms of the functions described above.
5858 The use of C<isl_union_set_compute_schedule> is discouraged.
5860 #include <isl/schedule.h>
5861 __isl_give isl_schedule *isl_union_set_compute_schedule(
5862 __isl_take isl_union_set *domain,
5863 __isl_take isl_union_map *validity,
5864 __isl_take isl_union_map *proximity);
5866 A mapping from the domains to the scheduled space can be obtained
5867 from an C<isl_schedule> using the following function.
5869 __isl_give isl_union_map *isl_schedule_get_map(
5870 __isl_keep isl_schedule *sched);
5872 A representation of the schedule can be printed using
5874 __isl_give isl_printer *isl_printer_print_schedule(
5875 __isl_take isl_printer *p,
5876 __isl_keep isl_schedule *schedule);
5878 A representation of the schedule as a forest of bands can be obtained
5879 using the following function.
5881 __isl_give isl_band_list *isl_schedule_get_band_forest(
5882 __isl_keep isl_schedule *schedule);
5884 The individual bands can be visited in depth-first post-order
5885 using the following function.
5887 #include <isl/schedule.h>
5888 int isl_schedule_foreach_band(
5889 __isl_keep isl_schedule *sched,
5890 int (*fn)(__isl_keep isl_band *band, void *user),
5893 The list can be manipulated as explained in L<"Lists">.
5894 The bands inside the list can be copied and freed using the following
5897 #include <isl/band.h>
5898 __isl_give isl_band *isl_band_copy(
5899 __isl_keep isl_band *band);
5900 void *isl_band_free(__isl_take isl_band *band);
5902 Each band contains zero or more scheduling dimensions.
5903 These are referred to as the members of the band.
5904 The section of the schedule that corresponds to the band is
5905 referred to as the partial schedule of the band.
5906 For those nodes that participate in a band, the outer scheduling
5907 dimensions form the prefix schedule, while the inner scheduling
5908 dimensions form the suffix schedule.
5909 That is, if we take a cut of the band forest, then the union of
5910 the concatenations of the prefix, partial and suffix schedules of
5911 each band in the cut is equal to the entire schedule (modulo
5912 some possible padding at the end with zero scheduling dimensions).
5913 The properties of a band can be inspected using the following functions.
5915 #include <isl/band.h>
5916 isl_ctx *isl_band_get_ctx(__isl_keep isl_band *band);
5918 int isl_band_has_children(__isl_keep isl_band *band);
5919 __isl_give isl_band_list *isl_band_get_children(
5920 __isl_keep isl_band *band);
5922 __isl_give isl_union_map *isl_band_get_prefix_schedule(
5923 __isl_keep isl_band *band);
5924 __isl_give isl_union_map *isl_band_get_partial_schedule(
5925 __isl_keep isl_band *band);
5926 __isl_give isl_union_map *isl_band_get_suffix_schedule(
5927 __isl_keep isl_band *band);
5929 int isl_band_n_member(__isl_keep isl_band *band);
5930 int isl_band_member_is_coincident(
5931 __isl_keep isl_band *band, int pos);
5933 int isl_band_list_foreach_band(
5934 __isl_keep isl_band_list *list,
5935 int (*fn)(__isl_keep isl_band *band, void *user),
5938 Note that a scheduling dimension is considered to be ``coincident''
5939 if it satisfies the coincidence constraints within its band.
5940 That is, if the dependence distances of the coincidence
5941 constraints are all zero in that direction (for fixed
5942 iterations of outer bands).
5943 Like C<isl_schedule_foreach_band>,
5944 the function C<isl_band_list_foreach_band> calls C<fn> on the bands
5945 in depth-first post-order.
5947 A band can be tiled using the following function.
5949 #include <isl/band.h>
5950 int isl_band_tile(__isl_keep isl_band *band,
5951 __isl_take isl_vec *sizes);
5953 int isl_options_set_tile_scale_tile_loops(isl_ctx *ctx,
5955 int isl_options_get_tile_scale_tile_loops(isl_ctx *ctx);
5956 int isl_options_set_tile_shift_point_loops(isl_ctx *ctx,
5958 int isl_options_get_tile_shift_point_loops(isl_ctx *ctx);
5960 The C<isl_band_tile> function tiles the band using the given tile sizes
5961 inside its schedule.
5962 A new child band is created to represent the point loops and it is
5963 inserted between the modified band and its children.
5964 The C<tile_scale_tile_loops> option specifies whether the tile
5965 loops iterators should be scaled by the tile sizes.
5966 If the C<tile_shift_point_loops> option is set, then the point loops
5967 are shifted to start at zero.
5969 A band can be split into two nested bands using the following function.
5971 int isl_band_split(__isl_keep isl_band *band, int pos);
5973 The resulting outer band contains the first C<pos> dimensions of C<band>
5974 while the inner band contains the remaining dimensions.
5976 A representation of the band can be printed using
5978 #include <isl/band.h>
5979 __isl_give isl_printer *isl_printer_print_band(
5980 __isl_take isl_printer *p,
5981 __isl_keep isl_band *band);
5985 #include <isl/schedule.h>
5986 int isl_options_set_schedule_max_coefficient(
5987 isl_ctx *ctx, int val);
5988 int isl_options_get_schedule_max_coefficient(
5990 int isl_options_set_schedule_max_constant_term(
5991 isl_ctx *ctx, int val);
5992 int isl_options_get_schedule_max_constant_term(
5994 int isl_options_set_schedule_fuse(isl_ctx *ctx, int val);
5995 int isl_options_get_schedule_fuse(isl_ctx *ctx);
5996 int isl_options_set_schedule_maximize_band_depth(
5997 isl_ctx *ctx, int val);
5998 int isl_options_get_schedule_maximize_band_depth(
6000 int isl_options_set_schedule_outer_coincidence(
6001 isl_ctx *ctx, int val);
6002 int isl_options_get_schedule_outer_coincidence(
6004 int isl_options_set_schedule_split_scaled(
6005 isl_ctx *ctx, int val);
6006 int isl_options_get_schedule_split_scaled(
6008 int isl_options_set_schedule_algorithm(
6009 isl_ctx *ctx, int val);
6010 int isl_options_get_schedule_algorithm(
6012 int isl_options_set_schedule_separate_components(
6013 isl_ctx *ctx, int val);
6014 int isl_options_get_schedule_separate_components(
6019 =item * schedule_max_coefficient
6021 This option enforces that the coefficients for variable and parameter
6022 dimensions in the calculated schedule are not larger than the specified value.
6023 This option can significantly increase the speed of the scheduling calculation
6024 and may also prevent fusing of unrelated dimensions. A value of -1 means that
6025 this option does not introduce bounds on the variable or parameter
6028 =item * schedule_max_constant_term
6030 This option enforces that the constant coefficients in the calculated schedule
6031 are not larger than the maximal constant term. This option can significantly
6032 increase the speed of the scheduling calculation and may also prevent fusing of
6033 unrelated dimensions. A value of -1 means that this option does not introduce
6034 bounds on the constant coefficients.
6036 =item * schedule_fuse
6038 This option controls the level of fusion.
6039 If this option is set to C<ISL_SCHEDULE_FUSE_MIN>, then loops in the
6040 resulting schedule will be distributed as much as possible.
6041 If this option is set to C<ISL_SCHEDULE_FUSE_MAX>, then C<isl> will
6042 try to fuse loops in the resulting schedule.
6044 =item * schedule_maximize_band_depth
6046 If this option is set, we do not split bands at the point
6047 where we detect splitting is necessary. Instead, we
6048 backtrack and split bands as early as possible. This
6049 reduces the number of splits and maximizes the width of
6050 the bands. Wider bands give more possibilities for tiling.
6051 Note that if the C<schedule_fuse> option is set to C<ISL_SCHEDULE_FUSE_MIN>,
6052 then bands will be split as early as possible, even if there is no need.
6053 The C<schedule_maximize_band_depth> option therefore has no effect in this case.
6055 =item * schedule_outer_coincidence
6057 If this option is set, then we try to construct schedules
6058 where the outermost scheduling dimension in each band
6059 satisfies the coincidence constraints.
6061 =item * schedule_split_scaled
6063 If this option is set, then we try to construct schedules in which the
6064 constant term is split off from the linear part if the linear parts of
6065 the scheduling rows for all nodes in the graphs have a common non-trivial
6067 The constant term is then placed in a separate band and the linear
6070 =item * schedule_algorithm
6072 Selects the scheduling algorithm to be used.
6073 Available scheduling algorithms are C<ISL_SCHEDULE_ALGORITHM_ISL>
6074 and C<ISL_SCHEDULE_ALGORITHM_FEAUTRIER>.
6076 =item * schedule_separate_components
6078 If at any point the dependence graph contains any (weakly connected) components,
6079 then these components are scheduled separately.
6080 If this option is not set, then some iterations of the domains
6081 in these components may be scheduled together.
6082 If this option is set, then the components are given consecutive
6087 =head2 AST Generation
6089 This section describes the C<isl> functionality for generating
6090 ASTs that visit all the elements
6091 in a domain in an order specified by a schedule.
6092 In particular, given a C<isl_union_map>, an AST is generated
6093 that visits all the elements in the domain of the C<isl_union_map>
6094 according to the lexicographic order of the corresponding image
6095 element(s). If the range of the C<isl_union_map> consists of
6096 elements in more than one space, then each of these spaces is handled
6097 separately in an arbitrary order.
6098 It should be noted that the image elements only specify the I<order>
6099 in which the corresponding domain elements should be visited.
6100 No direct relation between the image elements and the loop iterators
6101 in the generated AST should be assumed.
6103 Each AST is generated within a build. The initial build
6104 simply specifies the constraints on the parameters (if any)
6105 and can be created, inspected, copied and freed using the following functions.
6107 #include <isl/ast_build.h>
6108 __isl_give isl_ast_build *isl_ast_build_from_context(
6109 __isl_take isl_set *set);
6110 isl_ctx *isl_ast_build_get_ctx(
6111 __isl_keep isl_ast_build *build);
6112 __isl_give isl_ast_build *isl_ast_build_copy(
6113 __isl_keep isl_ast_build *build);
6114 void *isl_ast_build_free(
6115 __isl_take isl_ast_build *build);
6117 The C<set> argument is usually a parameter set with zero or more parameters.
6118 More C<isl_ast_build> functions are described in L</"Nested AST Generation">
6119 and L</"Fine-grained Control over AST Generation">.
6120 Finally, the AST itself can be constructed using the following
6123 #include <isl/ast_build.h>
6124 __isl_give isl_ast_node *isl_ast_build_ast_from_schedule(
6125 __isl_keep isl_ast_build *build,
6126 __isl_take isl_union_map *schedule);
6128 =head3 Inspecting the AST
6130 The basic properties of an AST node can be obtained as follows.
6132 #include <isl/ast.h>
6133 isl_ctx *isl_ast_node_get_ctx(
6134 __isl_keep isl_ast_node *node);
6135 enum isl_ast_node_type isl_ast_node_get_type(
6136 __isl_keep isl_ast_node *node);
6138 The type of an AST node is one of
6139 C<isl_ast_node_for>,
6141 C<isl_ast_node_block> or
6142 C<isl_ast_node_user>.
6143 An C<isl_ast_node_for> represents a for node.
6144 An C<isl_ast_node_if> represents an if node.
6145 An C<isl_ast_node_block> represents a compound node.
6146 An C<isl_ast_node_user> represents an expression statement.
6147 An expression statement typically corresponds to a domain element, i.e.,
6148 one of the elements that is visited by the AST.
6150 Each type of node has its own additional properties.
6152 #include <isl/ast.h>
6153 __isl_give isl_ast_expr *isl_ast_node_for_get_iterator(
6154 __isl_keep isl_ast_node *node);
6155 __isl_give isl_ast_expr *isl_ast_node_for_get_init(
6156 __isl_keep isl_ast_node *node);
6157 __isl_give isl_ast_expr *isl_ast_node_for_get_cond(
6158 __isl_keep isl_ast_node *node);
6159 __isl_give isl_ast_expr *isl_ast_node_for_get_inc(
6160 __isl_keep isl_ast_node *node);
6161 __isl_give isl_ast_node *isl_ast_node_for_get_body(
6162 __isl_keep isl_ast_node *node);
6163 int isl_ast_node_for_is_degenerate(
6164 __isl_keep isl_ast_node *node);
6166 An C<isl_ast_for> is considered degenerate if it is known to execute
6169 #include <isl/ast.h>
6170 __isl_give isl_ast_expr *isl_ast_node_if_get_cond(
6171 __isl_keep isl_ast_node *node);
6172 __isl_give isl_ast_node *isl_ast_node_if_get_then(
6173 __isl_keep isl_ast_node *node);
6174 int isl_ast_node_if_has_else(
6175 __isl_keep isl_ast_node *node);
6176 __isl_give isl_ast_node *isl_ast_node_if_get_else(
6177 __isl_keep isl_ast_node *node);
6179 __isl_give isl_ast_node_list *
6180 isl_ast_node_block_get_children(
6181 __isl_keep isl_ast_node *node);
6183 __isl_give isl_ast_expr *isl_ast_node_user_get_expr(
6184 __isl_keep isl_ast_node *node);
6186 Each of the returned C<isl_ast_expr>s can in turn be inspected using
6187 the following functions.
6189 #include <isl/ast.h>
6190 isl_ctx *isl_ast_expr_get_ctx(
6191 __isl_keep isl_ast_expr *expr);
6192 enum isl_ast_expr_type isl_ast_expr_get_type(
6193 __isl_keep isl_ast_expr *expr);
6195 The type of an AST expression is one of
6197 C<isl_ast_expr_id> or
6198 C<isl_ast_expr_int>.
6199 An C<isl_ast_expr_op> represents the result of an operation.
6200 An C<isl_ast_expr_id> represents an identifier.
6201 An C<isl_ast_expr_int> represents an integer value.
6203 Each type of expression has its own additional properties.
6205 #include <isl/ast.h>
6206 enum isl_ast_op_type isl_ast_expr_get_op_type(
6207 __isl_keep isl_ast_expr *expr);
6208 int isl_ast_expr_get_op_n_arg(__isl_keep isl_ast_expr *expr);
6209 __isl_give isl_ast_expr *isl_ast_expr_get_op_arg(
6210 __isl_keep isl_ast_expr *expr, int pos);
6211 int isl_ast_node_foreach_ast_op_type(
6212 __isl_keep isl_ast_node *node,
6213 int (*fn)(enum isl_ast_op_type type, void *user),
6216 C<isl_ast_expr_get_op_type> returns the type of the operation
6217 performed. C<isl_ast_expr_get_op_n_arg> returns the number of
6218 arguments. C<isl_ast_expr_get_op_arg> returns the specified
6220 C<isl_ast_node_foreach_ast_op_type> calls C<fn> for each distinct
6221 C<isl_ast_op_type> that appears in C<node>.
6222 The operation type is one of the following.
6226 =item C<isl_ast_op_and>
6228 Logical I<and> of two arguments.
6229 Both arguments can be evaluated.
6231 =item C<isl_ast_op_and_then>
6233 Logical I<and> of two arguments.
6234 The second argument can only be evaluated if the first evaluates to true.
6236 =item C<isl_ast_op_or>
6238 Logical I<or> of two arguments.
6239 Both arguments can be evaluated.
6241 =item C<isl_ast_op_or_else>
6243 Logical I<or> of two arguments.
6244 The second argument can only be evaluated if the first evaluates to false.
6246 =item C<isl_ast_op_max>
6248 Maximum of two or more arguments.
6250 =item C<isl_ast_op_min>
6252 Minimum of two or more arguments.
6254 =item C<isl_ast_op_minus>
6258 =item C<isl_ast_op_add>
6260 Sum of two arguments.
6262 =item C<isl_ast_op_sub>
6264 Difference of two arguments.
6266 =item C<isl_ast_op_mul>
6268 Product of two arguments.
6270 =item C<isl_ast_op_div>
6272 Exact division. That is, the result is known to be an integer.
6274 =item C<isl_ast_op_fdiv_q>
6276 Result of integer division, rounded towards negative
6279 =item C<isl_ast_op_pdiv_q>
6281 Result of integer division, where dividend is known to be non-negative.
6283 =item C<isl_ast_op_pdiv_r>
6285 Remainder of integer division, where dividend is known to be non-negative.
6287 =item C<isl_ast_op_cond>
6289 Conditional operator defined on three arguments.
6290 If the first argument evaluates to true, then the result
6291 is equal to the second argument. Otherwise, the result
6292 is equal to the third argument.
6293 The second and third argument may only be evaluated if
6294 the first argument evaluates to true and false, respectively.
6295 Corresponds to C<a ? b : c> in C.
6297 =item C<isl_ast_op_select>
6299 Conditional operator defined on three arguments.
6300 If the first argument evaluates to true, then the result
6301 is equal to the second argument. Otherwise, the result
6302 is equal to the third argument.
6303 The second and third argument may be evaluated independently
6304 of the value of the first argument.
6305 Corresponds to C<a * b + (1 - a) * c> in C.
6307 =item C<isl_ast_op_eq>
6311 =item C<isl_ast_op_le>
6313 Less than or equal relation.
6315 =item C<isl_ast_op_lt>
6319 =item C<isl_ast_op_ge>
6321 Greater than or equal relation.
6323 =item C<isl_ast_op_gt>
6325 Greater than relation.
6327 =item C<isl_ast_op_call>
6330 The number of arguments of the C<isl_ast_expr> is one more than
6331 the number of arguments in the function call, the first argument
6332 representing the function being called.
6334 =item C<isl_ast_op_access>
6337 The number of arguments of the C<isl_ast_expr> is one more than
6338 the number of index expressions in the array access, the first argument
6339 representing the array being accessed.
6341 =item C<isl_ast_op_member>
6344 This operation has two arguments, a structure and the name of
6345 the member of the structure being accessed.
6349 #include <isl/ast.h>
6350 __isl_give isl_id *isl_ast_expr_get_id(
6351 __isl_keep isl_ast_expr *expr);
6353 Return the identifier represented by the AST expression.
6355 #include <isl/ast.h>
6356 __isl_give isl_val *isl_ast_expr_get_val(
6357 __isl_keep isl_ast_expr *expr);
6359 Return the integer represented by the AST expression.
6361 =head3 Properties of ASTs
6363 #include <isl/ast.h>
6364 int isl_ast_expr_is_equal(__isl_keep isl_ast_expr *expr1,
6365 __isl_keep isl_ast_expr *expr2);
6367 Check if two C<isl_ast_expr>s are equal to each other.
6369 =head3 Manipulating and printing the AST
6371 AST nodes can be copied and freed using the following functions.
6373 #include <isl/ast.h>
6374 __isl_give isl_ast_node *isl_ast_node_copy(
6375 __isl_keep isl_ast_node *node);
6376 void *isl_ast_node_free(__isl_take isl_ast_node *node);
6378 AST expressions can be copied and freed using the following functions.
6380 #include <isl/ast.h>
6381 __isl_give isl_ast_expr *isl_ast_expr_copy(
6382 __isl_keep isl_ast_expr *expr);
6383 void *isl_ast_expr_free(__isl_take isl_ast_expr *expr);
6385 New AST expressions can be created either directly or within
6386 the context of an C<isl_ast_build>.
6388 #include <isl/ast.h>
6389 __isl_give isl_ast_expr *isl_ast_expr_from_val(
6390 __isl_take isl_val *v);
6391 __isl_give isl_ast_expr *isl_ast_expr_from_id(
6392 __isl_take isl_id *id);
6393 __isl_give isl_ast_expr *isl_ast_expr_neg(
6394 __isl_take isl_ast_expr *expr);
6395 __isl_give isl_ast_expr *isl_ast_expr_add(
6396 __isl_take isl_ast_expr *expr1,
6397 __isl_take isl_ast_expr *expr2);
6398 __isl_give isl_ast_expr *isl_ast_expr_sub(
6399 __isl_take isl_ast_expr *expr1,
6400 __isl_take isl_ast_expr *expr2);
6401 __isl_give isl_ast_expr *isl_ast_expr_mul(
6402 __isl_take isl_ast_expr *expr1,
6403 __isl_take isl_ast_expr *expr2);
6404 __isl_give isl_ast_expr *isl_ast_expr_div(
6405 __isl_take isl_ast_expr *expr1,
6406 __isl_take isl_ast_expr *expr2);
6407 __isl_give isl_ast_expr *isl_ast_expr_and(
6408 __isl_take isl_ast_expr *expr1,
6409 __isl_take isl_ast_expr *expr2)
6410 __isl_give isl_ast_expr *isl_ast_expr_or(
6411 __isl_take isl_ast_expr *expr1,
6412 __isl_take isl_ast_expr *expr2)
6413 __isl_give isl_ast_expr *isl_ast_expr_access(
6414 __isl_take isl_ast_expr *array,
6415 __isl_take isl_ast_expr_list *indices);
6417 #include <isl/ast_build.h>
6418 __isl_give isl_ast_expr *isl_ast_build_expr_from_pw_aff(
6419 __isl_keep isl_ast_build *build,
6420 __isl_take isl_pw_aff *pa);
6421 __isl_give isl_ast_expr *
6422 isl_ast_build_access_from_pw_multi_aff(
6423 __isl_keep isl_ast_build *build,
6424 __isl_take isl_pw_multi_aff *pma);
6425 __isl_give isl_ast_expr *
6426 isl_ast_build_access_from_multi_pw_aff(
6427 __isl_keep isl_ast_build *build,
6428 __isl_take isl_multi_pw_aff *mpa);
6429 __isl_give isl_ast_expr *
6430 isl_ast_build_call_from_pw_multi_aff(
6431 __isl_keep isl_ast_build *build,
6432 __isl_take isl_pw_multi_aff *pma);
6433 __isl_give isl_ast_expr *
6434 isl_ast_build_call_from_multi_pw_aff(
6435 __isl_keep isl_ast_build *build,
6436 __isl_take isl_multi_pw_aff *mpa);
6438 The domains of C<pa>, C<mpa> and C<pma> should correspond
6439 to the schedule space of C<build>.
6440 The tuple id of C<mpa> or C<pma> is used as the array being accessed or
6441 the function being called.
6442 If the accessed space is a nested relation, then it is taken
6443 to represent an access of the member specified by the range
6444 of this nested relation of the structure specified by the domain
6445 of the nested relation.
6447 The following functions can be used to modify an C<isl_ast_expr>.
6449 #include <isl/ast.h>
6450 __isl_give isl_ast_expr *isl_ast_expr_set_op_arg(
6451 __isl_take isl_ast_expr *expr, int pos,
6452 __isl_take isl_ast_expr *arg);
6454 Replace the argument of C<expr> at position C<pos> by C<arg>.
6456 #include <isl/ast.h>
6457 __isl_give isl_ast_expr *isl_ast_expr_substitute_ids(
6458 __isl_take isl_ast_expr *expr,
6459 __isl_take isl_id_to_ast_expr *id2expr);
6461 The function C<isl_ast_expr_substitute_ids> replaces the
6462 subexpressions of C<expr> of type C<isl_ast_expr_id>
6463 by the corresponding expression in C<id2expr>, if there is any.
6466 User specified data can be attached to an C<isl_ast_node> and obtained
6467 from the same C<isl_ast_node> using the following functions.
6469 #include <isl/ast.h>
6470 __isl_give isl_ast_node *isl_ast_node_set_annotation(
6471 __isl_take isl_ast_node *node,
6472 __isl_take isl_id *annotation);
6473 __isl_give isl_id *isl_ast_node_get_annotation(
6474 __isl_keep isl_ast_node *node);
6476 Basic printing can be performed using the following functions.
6478 #include <isl/ast.h>
6479 __isl_give isl_printer *isl_printer_print_ast_expr(
6480 __isl_take isl_printer *p,
6481 __isl_keep isl_ast_expr *expr);
6482 __isl_give isl_printer *isl_printer_print_ast_node(
6483 __isl_take isl_printer *p,
6484 __isl_keep isl_ast_node *node);
6486 More advanced printing can be performed using the following functions.
6488 #include <isl/ast.h>
6489 __isl_give isl_printer *isl_ast_op_type_print_macro(
6490 enum isl_ast_op_type type,
6491 __isl_take isl_printer *p);
6492 __isl_give isl_printer *isl_ast_node_print_macros(
6493 __isl_keep isl_ast_node *node,
6494 __isl_take isl_printer *p);
6495 __isl_give isl_printer *isl_ast_node_print(
6496 __isl_keep isl_ast_node *node,
6497 __isl_take isl_printer *p,
6498 __isl_take isl_ast_print_options *options);
6499 __isl_give isl_printer *isl_ast_node_for_print(
6500 __isl_keep isl_ast_node *node,
6501 __isl_take isl_printer *p,
6502 __isl_take isl_ast_print_options *options);
6503 __isl_give isl_printer *isl_ast_node_if_print(
6504 __isl_keep isl_ast_node *node,
6505 __isl_take isl_printer *p,
6506 __isl_take isl_ast_print_options *options);
6508 While printing an C<isl_ast_node> in C<ISL_FORMAT_C>,
6509 C<isl> may print out an AST that makes use of macros such
6510 as C<floord>, C<min> and C<max>.
6511 C<isl_ast_op_type_print_macro> prints out the macro
6512 corresponding to a specific C<isl_ast_op_type>.
6513 C<isl_ast_node_print_macros> scans the C<isl_ast_node>
6514 for expressions where these macros would be used and prints
6515 out the required macro definitions.
6516 Essentially, C<isl_ast_node_print_macros> calls
6517 C<isl_ast_node_foreach_ast_op_type> with C<isl_ast_op_type_print_macro>
6518 as function argument.
6519 C<isl_ast_node_print>, C<isl_ast_node_for_print> and
6520 C<isl_ast_node_if_print> print an C<isl_ast_node>
6521 in C<ISL_FORMAT_C>, but allow for some extra control
6522 through an C<isl_ast_print_options> object.
6523 This object can be created using the following functions.
6525 #include <isl/ast.h>
6526 __isl_give isl_ast_print_options *
6527 isl_ast_print_options_alloc(isl_ctx *ctx);
6528 __isl_give isl_ast_print_options *
6529 isl_ast_print_options_copy(
6530 __isl_keep isl_ast_print_options *options);
6531 void *isl_ast_print_options_free(
6532 __isl_take isl_ast_print_options *options);
6534 __isl_give isl_ast_print_options *
6535 isl_ast_print_options_set_print_user(
6536 __isl_take isl_ast_print_options *options,
6537 __isl_give isl_printer *(*print_user)(
6538 __isl_take isl_printer *p,
6539 __isl_take isl_ast_print_options *options,
6540 __isl_keep isl_ast_node *node, void *user),
6542 __isl_give isl_ast_print_options *
6543 isl_ast_print_options_set_print_for(
6544 __isl_take isl_ast_print_options *options,
6545 __isl_give isl_printer *(*print_for)(
6546 __isl_take isl_printer *p,
6547 __isl_take isl_ast_print_options *options,
6548 __isl_keep isl_ast_node *node, void *user),
6551 The callback set by C<isl_ast_print_options_set_print_user>
6552 is called whenever a node of type C<isl_ast_node_user> needs to
6554 The callback set by C<isl_ast_print_options_set_print_for>
6555 is called whenever a node of type C<isl_ast_node_for> needs to
6557 Note that C<isl_ast_node_for_print> will I<not> call the
6558 callback set by C<isl_ast_print_options_set_print_for> on the node
6559 on which C<isl_ast_node_for_print> is called, but only on nested
6560 nodes of type C<isl_ast_node_for>. It is therefore safe to
6561 call C<isl_ast_node_for_print> from within the callback set by
6562 C<isl_ast_print_options_set_print_for>.
6564 The following option determines the type to be used for iterators
6565 while printing the AST.
6567 int isl_options_set_ast_iterator_type(
6568 isl_ctx *ctx, const char *val);
6569 const char *isl_options_get_ast_iterator_type(
6574 #include <isl/ast_build.h>
6575 int isl_options_set_ast_build_atomic_upper_bound(
6576 isl_ctx *ctx, int val);
6577 int isl_options_get_ast_build_atomic_upper_bound(
6579 int isl_options_set_ast_build_prefer_pdiv(isl_ctx *ctx,
6581 int isl_options_get_ast_build_prefer_pdiv(isl_ctx *ctx);
6582 int isl_options_set_ast_build_exploit_nested_bounds(
6583 isl_ctx *ctx, int val);
6584 int isl_options_get_ast_build_exploit_nested_bounds(
6586 int isl_options_set_ast_build_group_coscheduled(
6587 isl_ctx *ctx, int val);
6588 int isl_options_get_ast_build_group_coscheduled(
6590 int isl_options_set_ast_build_scale_strides(
6591 isl_ctx *ctx, int val);
6592 int isl_options_get_ast_build_scale_strides(
6594 int isl_options_set_ast_build_allow_else(isl_ctx *ctx,
6596 int isl_options_get_ast_build_allow_else(isl_ctx *ctx);
6597 int isl_options_set_ast_build_allow_or(isl_ctx *ctx,
6599 int isl_options_get_ast_build_allow_or(isl_ctx *ctx);
6603 =item * ast_build_atomic_upper_bound
6605 Generate loop upper bounds that consist of the current loop iterator,
6606 an operator and an expression not involving the iterator.
6607 If this option is not set, then the current loop iterator may appear
6608 several times in the upper bound.
6609 For example, when this option is turned off, AST generation
6612 [n] -> { A[i] -> [i] : 0 <= i <= 100, n }
6616 for (int c0 = 0; c0 <= 100 && n >= c0; c0 += 1)
6619 When the option is turned on, the following AST is generated
6621 for (int c0 = 0; c0 <= min(100, n); c0 += 1)
6624 =item * ast_build_prefer_pdiv
6626 If this option is turned off, then the AST generation will
6627 produce ASTs that may only contain C<isl_ast_op_fdiv_q>
6628 operators, but no C<isl_ast_op_pdiv_q> or
6629 C<isl_ast_op_pdiv_r> operators.
6630 If this options is turned on, then C<isl> will try to convert
6631 some of the C<isl_ast_op_fdiv_q> operators to (expressions containing)
6632 C<isl_ast_op_pdiv_q> or C<isl_ast_op_pdiv_r> operators.
6634 =item * ast_build_exploit_nested_bounds
6636 Simplify conditions based on bounds of nested for loops.
6637 In particular, remove conditions that are implied by the fact
6638 that one or more nested loops have at least one iteration,
6639 meaning that the upper bound is at least as large as the lower bound.
6640 For example, when this option is turned off, AST generation
6643 [N,M] -> { A[i,j] -> [i,j] : 0 <= i <= N and
6649 for (int c0 = 0; c0 <= N; c0 += 1)
6650 for (int c1 = 0; c1 <= M; c1 += 1)
6653 When the option is turned on, the following AST is generated
6655 for (int c0 = 0; c0 <= N; c0 += 1)
6656 for (int c1 = 0; c1 <= M; c1 += 1)
6659 =item * ast_build_group_coscheduled
6661 If two domain elements are assigned the same schedule point, then
6662 they may be executed in any order and they may even appear in different
6663 loops. If this options is set, then the AST generator will make
6664 sure that coscheduled domain elements do not appear in separate parts
6665 of the AST. This is useful in case of nested AST generation
6666 if the outer AST generation is given only part of a schedule
6667 and the inner AST generation should handle the domains that are
6668 coscheduled by this initial part of the schedule together.
6669 For example if an AST is generated for a schedule
6671 { A[i] -> [0]; B[i] -> [0] }
6673 then the C<isl_ast_build_set_create_leaf> callback described
6674 below may get called twice, once for each domain.
6675 Setting this option ensures that the callback is only called once
6676 on both domains together.
6678 =item * ast_build_separation_bounds
6680 This option specifies which bounds to use during separation.
6681 If this option is set to C<ISL_AST_BUILD_SEPARATION_BOUNDS_IMPLICIT>
6682 then all (possibly implicit) bounds on the current dimension will
6683 be used during separation.
6684 If this option is set to C<ISL_AST_BUILD_SEPARATION_BOUNDS_EXPLICIT>
6685 then only those bounds that are explicitly available will
6686 be used during separation.
6688 =item * ast_build_scale_strides
6690 This option specifies whether the AST generator is allowed
6691 to scale down iterators of strided loops.
6693 =item * ast_build_allow_else
6695 This option specifies whether the AST generator is allowed
6696 to construct if statements with else branches.
6698 =item * ast_build_allow_or
6700 This option specifies whether the AST generator is allowed
6701 to construct if conditions with disjunctions.
6705 =head3 Fine-grained Control over AST Generation
6707 Besides specifying the constraints on the parameters,
6708 an C<isl_ast_build> object can be used to control
6709 various aspects of the AST generation process.
6710 The most prominent way of control is through ``options'',
6711 which can be set using the following function.
6713 #include <isl/ast_build.h>
6714 __isl_give isl_ast_build *
6715 isl_ast_build_set_options(
6716 __isl_take isl_ast_build *control,
6717 __isl_take isl_union_map *options);
6719 The options are encoded in an <isl_union_map>.
6720 The domain of this union relation refers to the schedule domain,
6721 i.e., the range of the schedule passed to C<isl_ast_build_ast_from_schedule>.
6722 In the case of nested AST generation (see L</"Nested AST Generation">),
6723 the domain of C<options> should refer to the extra piece of the schedule.
6724 That is, it should be equal to the range of the wrapped relation in the
6725 range of the schedule.
6726 The range of the options can consist of elements in one or more spaces,
6727 the names of which determine the effect of the option.
6728 The values of the range typically also refer to the schedule dimension
6729 to which the option applies. In case of nested AST generation
6730 (see L</"Nested AST Generation">), these values refer to the position
6731 of the schedule dimension within the innermost AST generation.
6732 The constraints on the domain elements of
6733 the option should only refer to this dimension and earlier dimensions.
6734 We consider the following spaces.
6738 =item C<separation_class>
6740 This space is a wrapped relation between two one dimensional spaces.
6741 The input space represents the schedule dimension to which the option
6742 applies and the output space represents the separation class.
6743 While constructing a loop corresponding to the specified schedule
6744 dimension(s), the AST generator will try to generate separate loops
6745 for domain elements that are assigned different classes.
6746 If only some of the elements are assigned a class, then those elements
6747 that are not assigned any class will be treated as belonging to a class
6748 that is separate from the explicitly assigned classes.
6749 The typical use case for this option is to separate full tiles from
6751 The other options, described below, are applied after the separation
6754 As an example, consider the separation into full and partial tiles
6755 of a tiling of a triangular domain.
6756 Take, for example, the domain
6758 { A[i,j] : 0 <= i,j and i + j <= 100 }
6760 and a tiling into tiles of 10 by 10. The input to the AST generator
6761 is then the schedule
6763 { A[i,j] -> [([i/10]),[j/10],i,j] : 0 <= i,j and
6766 Without any options, the following AST is generated
6768 for (int c0 = 0; c0 <= 10; c0 += 1)
6769 for (int c1 = 0; c1 <= -c0 + 10; c1 += 1)
6770 for (int c2 = 10 * c0;
6771 c2 <= min(-10 * c1 + 100, 10 * c0 + 9);
6773 for (int c3 = 10 * c1;
6774 c3 <= min(10 * c1 + 9, -c2 + 100);
6778 Separation into full and partial tiles can be obtained by assigning
6779 a class, say C<0>, to the full tiles. The full tiles are represented by those
6780 values of the first and second schedule dimensions for which there are
6781 values of the third and fourth dimensions to cover an entire tile.
6782 That is, we need to specify the following option
6784 { [a,b,c,d] -> separation_class[[0]->[0]] :
6785 exists b': 0 <= 10a,10b' and
6786 10a+9+10b'+9 <= 100;
6787 [a,b,c,d] -> separation_class[[1]->[0]] :
6788 0 <= 10a,10b and 10a+9+10b+9 <= 100 }
6792 { [a, b, c, d] -> separation_class[[1] -> [0]] :
6793 a >= 0 and b >= 0 and b <= 8 - a;
6794 [a, b, c, d] -> separation_class[[0] -> [0]] :
6797 With this option, the generated AST is as follows
6800 for (int c0 = 0; c0 <= 8; c0 += 1) {
6801 for (int c1 = 0; c1 <= -c0 + 8; c1 += 1)
6802 for (int c2 = 10 * c0;
6803 c2 <= 10 * c0 + 9; c2 += 1)
6804 for (int c3 = 10 * c1;
6805 c3 <= 10 * c1 + 9; c3 += 1)
6807 for (int c1 = -c0 + 9; c1 <= -c0 + 10; c1 += 1)
6808 for (int c2 = 10 * c0;
6809 c2 <= min(-10 * c1 + 100, 10 * c0 + 9);
6811 for (int c3 = 10 * c1;
6812 c3 <= min(-c2 + 100, 10 * c1 + 9);
6816 for (int c0 = 9; c0 <= 10; c0 += 1)
6817 for (int c1 = 0; c1 <= -c0 + 10; c1 += 1)
6818 for (int c2 = 10 * c0;
6819 c2 <= min(-10 * c1 + 100, 10 * c0 + 9);
6821 for (int c3 = 10 * c1;
6822 c3 <= min(10 * c1 + 9, -c2 + 100);
6829 This is a single-dimensional space representing the schedule dimension(s)
6830 to which ``separation'' should be applied. Separation tries to split
6831 a loop into several pieces if this can avoid the generation of guards
6833 See also the C<atomic> option.
6837 This is a single-dimensional space representing the schedule dimension(s)
6838 for which the domains should be considered ``atomic''. That is, the
6839 AST generator will make sure that any given domain space will only appear
6840 in a single loop at the specified level.
6842 Consider the following schedule
6844 { a[i] -> [i] : 0 <= i < 10;
6845 b[i] -> [i+1] : 0 <= i < 10 }
6847 If the following option is specified
6849 { [i] -> separate[x] }
6851 then the following AST will be generated
6855 for (int c0 = 1; c0 <= 9; c0 += 1) {
6862 If, on the other hand, the following option is specified
6864 { [i] -> atomic[x] }
6866 then the following AST will be generated
6868 for (int c0 = 0; c0 <= 10; c0 += 1) {
6875 If neither C<atomic> nor C<separate> is specified, then the AST generator
6876 may produce either of these two results or some intermediate form.
6880 This is a single-dimensional space representing the schedule dimension(s)
6881 that should be I<completely> unrolled.
6882 To obtain a partial unrolling, the user should apply an additional
6883 strip-mining to the schedule and fully unroll the inner loop.
6887 Additional control is available through the following functions.
6889 #include <isl/ast_build.h>
6890 __isl_give isl_ast_build *
6891 isl_ast_build_set_iterators(
6892 __isl_take isl_ast_build *control,
6893 __isl_take isl_id_list *iterators);
6895 The function C<isl_ast_build_set_iterators> allows the user to
6896 specify a list of iterator C<isl_id>s to be used as iterators.
6897 If the input schedule is injective, then
6898 the number of elements in this list should be as large as the dimension
6899 of the schedule space, but no direct correspondence should be assumed
6900 between dimensions and elements.
6901 If the input schedule is not injective, then an additional number
6902 of C<isl_id>s equal to the largest dimension of the input domains
6904 If the number of provided C<isl_id>s is insufficient, then additional
6905 names are automatically generated.
6907 #include <isl/ast_build.h>
6908 __isl_give isl_ast_build *
6909 isl_ast_build_set_create_leaf(
6910 __isl_take isl_ast_build *control,
6911 __isl_give isl_ast_node *(*fn)(
6912 __isl_take isl_ast_build *build,
6913 void *user), void *user);
6916 C<isl_ast_build_set_create_leaf> function allows for the
6917 specification of a callback that should be called whenever the AST
6918 generator arrives at an element of the schedule domain.
6919 The callback should return an AST node that should be inserted
6920 at the corresponding position of the AST. The default action (when
6921 the callback is not set) is to continue generating parts of the AST to scan
6922 all the domain elements associated to the schedule domain element
6923 and to insert user nodes, ``calling'' the domain element, for each of them.
6924 The C<build> argument contains the current state of the C<isl_ast_build>.
6925 To ease nested AST generation (see L</"Nested AST Generation">),
6926 all control information that is
6927 specific to the current AST generation such as the options and
6928 the callbacks has been removed from this C<isl_ast_build>.
6929 The callback would typically return the result of a nested
6931 user defined node created using the following function.
6933 #include <isl/ast.h>
6934 __isl_give isl_ast_node *isl_ast_node_alloc_user(
6935 __isl_take isl_ast_expr *expr);
6937 #include <isl/ast_build.h>
6938 __isl_give isl_ast_build *
6939 isl_ast_build_set_at_each_domain(
6940 __isl_take isl_ast_build *build,
6941 __isl_give isl_ast_node *(*fn)(
6942 __isl_take isl_ast_node *node,
6943 __isl_keep isl_ast_build *build,
6944 void *user), void *user);
6945 __isl_give isl_ast_build *
6946 isl_ast_build_set_before_each_for(
6947 __isl_take isl_ast_build *build,
6948 __isl_give isl_id *(*fn)(
6949 __isl_keep isl_ast_build *build,
6950 void *user), void *user);
6951 __isl_give isl_ast_build *
6952 isl_ast_build_set_after_each_for(
6953 __isl_take isl_ast_build *build,
6954 __isl_give isl_ast_node *(*fn)(
6955 __isl_take isl_ast_node *node,
6956 __isl_keep isl_ast_build *build,
6957 void *user), void *user);
6959 The callback set by C<isl_ast_build_set_at_each_domain> will
6960 be called for each domain AST node.
6961 The callbacks set by C<isl_ast_build_set_before_each_for>
6962 and C<isl_ast_build_set_after_each_for> will be called
6963 for each for AST node. The first will be called in depth-first
6964 pre-order, while the second will be called in depth-first post-order.
6965 Since C<isl_ast_build_set_before_each_for> is called before the for
6966 node is actually constructed, it is only passed an C<isl_ast_build>.
6967 The returned C<isl_id> will be added as an annotation (using
6968 C<isl_ast_node_set_annotation>) to the constructed for node.
6969 In particular, if the user has also specified an C<after_each_for>
6970 callback, then the annotation can be retrieved from the node passed to
6971 that callback using C<isl_ast_node_get_annotation>.
6972 All callbacks should C<NULL> on failure.
6973 The given C<isl_ast_build> can be used to create new
6974 C<isl_ast_expr> objects using C<isl_ast_build_expr_from_pw_aff>
6975 or C<isl_ast_build_call_from_pw_multi_aff>.
6977 =head3 Nested AST Generation
6979 C<isl> allows the user to create an AST within the context
6980 of another AST. These nested ASTs are created using the
6981 same C<isl_ast_build_ast_from_schedule> function that is used to create the
6982 outer AST. The C<build> argument should be an C<isl_ast_build>
6983 passed to a callback set by
6984 C<isl_ast_build_set_create_leaf>.
6985 The space of the range of the C<schedule> argument should refer
6986 to this build. In particular, the space should be a wrapped
6987 relation and the domain of this wrapped relation should be the
6988 same as that of the range of the schedule returned by
6989 C<isl_ast_build_get_schedule> below.
6990 In practice, the new schedule is typically
6991 created by calling C<isl_union_map_range_product> on the old schedule
6992 and some extra piece of the schedule.
6993 The space of the schedule domain is also available from
6994 the C<isl_ast_build>.
6996 #include <isl/ast_build.h>
6997 __isl_give isl_union_map *isl_ast_build_get_schedule(
6998 __isl_keep isl_ast_build *build);
6999 __isl_give isl_space *isl_ast_build_get_schedule_space(
7000 __isl_keep isl_ast_build *build);
7001 __isl_give isl_ast_build *isl_ast_build_restrict(
7002 __isl_take isl_ast_build *build,
7003 __isl_take isl_set *set);
7005 The C<isl_ast_build_get_schedule> function returns a (partial)
7006 schedule for the domains elements for which part of the AST still needs to
7007 be generated in the current build.
7008 In particular, the domain elements are mapped to those iterations of the loops
7009 enclosing the current point of the AST generation inside which
7010 the domain elements are executed.
7011 No direct correspondence between
7012 the input schedule and this schedule should be assumed.
7013 The space obtained from C<isl_ast_build_get_schedule_space> can be used
7014 to create a set for C<isl_ast_build_restrict> to intersect
7015 with the current build. In particular, the set passed to
7016 C<isl_ast_build_restrict> can have additional parameters.
7017 The ids of the set dimensions in the space returned by
7018 C<isl_ast_build_get_schedule_space> correspond to the
7019 iterators of the already generated loops.
7020 The user should not rely on the ids of the output dimensions
7021 of the relations in the union relation returned by
7022 C<isl_ast_build_get_schedule> having any particular value.
7026 Although C<isl> is mainly meant to be used as a library,
7027 it also contains some basic applications that use some
7028 of the functionality of C<isl>.
7029 The input may be specified in either the L<isl format>
7030 or the L<PolyLib format>.
7032 =head2 C<isl_polyhedron_sample>
7034 C<isl_polyhedron_sample> takes a polyhedron as input and prints
7035 an integer element of the polyhedron, if there is any.
7036 The first column in the output is the denominator and is always
7037 equal to 1. If the polyhedron contains no integer points,
7038 then a vector of length zero is printed.
7042 C<isl_pip> takes the same input as the C<example> program
7043 from the C<piplib> distribution, i.e., a set of constraints
7044 on the parameters, a line containing only -1 and finally a set
7045 of constraints on a parametric polyhedron.
7046 The coefficients of the parameters appear in the last columns
7047 (but before the final constant column).
7048 The output is the lexicographic minimum of the parametric polyhedron.
7049 As C<isl> currently does not have its own output format, the output
7050 is just a dump of the internal state.
7052 =head2 C<isl_polyhedron_minimize>
7054 C<isl_polyhedron_minimize> computes the minimum of some linear
7055 or affine objective function over the integer points in a polyhedron.
7056 If an affine objective function
7057 is given, then the constant should appear in the last column.
7059 =head2 C<isl_polytope_scan>
7061 Given a polytope, C<isl_polytope_scan> prints
7062 all integer points in the polytope.
7064 =head2 C<isl_codegen>
7066 Given a schedule, a context set and an options relation,
7067 C<isl_codegen> prints out an AST that scans the domain elements
7068 of the schedule in the order of their image(s) taking into account
7069 the constraints in the context set.