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 #include <isl/local_space.h>
2722 __isl_give isl_local_space *
2723 isl_local_space_flatten_domain(
2724 __isl_take isl_local_space *ls);
2725 __isl_give isl_local_space *
2726 isl_local_space_flatten_range(
2727 __isl_take isl_local_space *ls);
2729 #include <isl/set.h>
2730 __isl_give isl_basic_set *isl_basic_set_flatten(
2731 __isl_take isl_basic_set *bset);
2732 __isl_give isl_set *isl_set_flatten(
2733 __isl_take isl_set *set);
2735 #include <isl/map.h>
2736 __isl_give isl_basic_map *isl_basic_map_flatten_domain(
2737 __isl_take isl_basic_map *bmap);
2738 __isl_give isl_basic_map *isl_basic_map_flatten_range(
2739 __isl_take isl_basic_map *bmap);
2740 __isl_give isl_map *isl_map_flatten_range(
2741 __isl_take isl_map *map);
2742 __isl_give isl_map *isl_map_flatten_domain(
2743 __isl_take isl_map *map);
2744 __isl_give isl_basic_map *isl_basic_map_flatten(
2745 __isl_take isl_basic_map *bmap);
2746 __isl_give isl_map *isl_map_flatten(
2747 __isl_take isl_map *map);
2749 #include <isl/map.h>
2750 __isl_give isl_map *isl_set_flatten_map(
2751 __isl_take isl_set *set);
2753 The function above constructs a relation
2754 that maps the input set to a flattened version of the set.
2758 Lift the input set to a space with extra dimensions corresponding
2759 to the existentially quantified variables in the input.
2760 In particular, the result lives in a wrapped map where the domain
2761 is the original space and the range corresponds to the original
2762 existentially quantified variables.
2764 __isl_give isl_basic_set *isl_basic_set_lift(
2765 __isl_take isl_basic_set *bset);
2766 __isl_give isl_set *isl_set_lift(
2767 __isl_take isl_set *set);
2768 __isl_give isl_union_set *isl_union_set_lift(
2769 __isl_take isl_union_set *uset);
2771 Given a local space that contains the existentially quantified
2772 variables of a set, a basic relation that, when applied to
2773 a basic set, has essentially the same effect as C<isl_basic_set_lift>,
2774 can be constructed using the following function.
2776 #include <isl/local_space.h>
2777 __isl_give isl_basic_map *isl_local_space_lifting(
2778 __isl_take isl_local_space *ls);
2780 =item * Internal Product
2782 __isl_give isl_basic_map *isl_basic_map_zip(
2783 __isl_take isl_basic_map *bmap);
2784 __isl_give isl_map *isl_map_zip(
2785 __isl_take isl_map *map);
2786 __isl_give isl_union_map *isl_union_map_zip(
2787 __isl_take isl_union_map *umap);
2789 Given a relation with nested relations for domain and range,
2790 interchange the range of the domain with the domain of the range.
2794 __isl_give isl_basic_map *isl_basic_map_curry(
2795 __isl_take isl_basic_map *bmap);
2796 __isl_give isl_basic_map *isl_basic_map_uncurry(
2797 __isl_take isl_basic_map *bmap);
2798 __isl_give isl_map *isl_map_curry(
2799 __isl_take isl_map *map);
2800 __isl_give isl_map *isl_map_uncurry(
2801 __isl_take isl_map *map);
2802 __isl_give isl_union_map *isl_union_map_curry(
2803 __isl_take isl_union_map *umap);
2804 __isl_give isl_union_map *isl_union_map_uncurry(
2805 __isl_take isl_union_map *umap);
2807 Given a relation with a nested relation for domain,
2808 the C<curry> functions
2809 move the range of the nested relation out of the domain
2810 and use it as the domain of a nested relation in the range,
2811 with the original range as range of this nested relation.
2812 The C<uncurry> functions perform the inverse operation.
2814 =item * Aligning parameters
2816 __isl_give isl_basic_set *isl_basic_set_align_params(
2817 __isl_take isl_basic_set *bset,
2818 __isl_take isl_space *model);
2819 __isl_give isl_set *isl_set_align_params(
2820 __isl_take isl_set *set,
2821 __isl_take isl_space *model);
2822 __isl_give isl_basic_map *isl_basic_map_align_params(
2823 __isl_take isl_basic_map *bmap,
2824 __isl_take isl_space *model);
2825 __isl_give isl_map *isl_map_align_params(
2826 __isl_take isl_map *map,
2827 __isl_take isl_space *model);
2829 Change the order of the parameters of the given set or relation
2830 such that the first parameters match those of C<model>.
2831 This may involve the introduction of extra parameters.
2832 All parameters need to be named.
2834 =item * Dimension manipulation
2836 #include <isl/local_space.h>
2837 __isl_give isl_local_space *isl_local_space_add_dims(
2838 __isl_take isl_local_space *ls,
2839 enum isl_dim_type type, unsigned n);
2840 __isl_give isl_local_space *isl_local_space_insert_dims(
2841 __isl_take isl_local_space *ls,
2842 enum isl_dim_type type, unsigned first, unsigned n);
2843 __isl_give isl_local_space *isl_local_space_drop_dims(
2844 __isl_take isl_local_space *ls,
2845 enum isl_dim_type type, unsigned first, unsigned n);
2847 #include <isl/set.h>
2848 __isl_give isl_basic_set *isl_basic_set_add_dims(
2849 __isl_take isl_basic_set *bset,
2850 enum isl_dim_type type, unsigned n);
2851 __isl_give isl_set *isl_set_add_dims(
2852 __isl_take isl_set *set,
2853 enum isl_dim_type type, unsigned n);
2854 __isl_give isl_basic_set *isl_basic_set_insert_dims(
2855 __isl_take isl_basic_set *bset,
2856 enum isl_dim_type type, unsigned pos,
2858 __isl_give isl_set *isl_set_insert_dims(
2859 __isl_take isl_set *set,
2860 enum isl_dim_type type, unsigned pos, unsigned n);
2861 __isl_give isl_basic_set *isl_basic_set_move_dims(
2862 __isl_take isl_basic_set *bset,
2863 enum isl_dim_type dst_type, unsigned dst_pos,
2864 enum isl_dim_type src_type, unsigned src_pos,
2866 __isl_give isl_set *isl_set_move_dims(
2867 __isl_take isl_set *set,
2868 enum isl_dim_type dst_type, unsigned dst_pos,
2869 enum isl_dim_type src_type, unsigned src_pos,
2872 #include <isl/map.h>
2873 __isl_give isl_map *isl_map_add_dims(
2874 __isl_take isl_map *map,
2875 enum isl_dim_type type, unsigned n);
2876 __isl_give isl_basic_map *isl_basic_map_insert_dims(
2877 __isl_take isl_basic_map *bmap,
2878 enum isl_dim_type type, unsigned pos,
2880 __isl_give isl_map *isl_map_insert_dims(
2881 __isl_take isl_map *map,
2882 enum isl_dim_type type, unsigned pos, unsigned n);
2883 __isl_give isl_basic_map *isl_basic_map_move_dims(
2884 __isl_take isl_basic_map *bmap,
2885 enum isl_dim_type dst_type, unsigned dst_pos,
2886 enum isl_dim_type src_type, unsigned src_pos,
2888 __isl_give isl_map *isl_map_move_dims(
2889 __isl_take isl_map *map,
2890 enum isl_dim_type dst_type, unsigned dst_pos,
2891 enum isl_dim_type src_type, unsigned src_pos,
2894 It is usually not advisable to directly change the (input or output)
2895 space of a set or a relation as this removes the name and the internal
2896 structure of the space. However, the above functions can be useful
2897 to add new parameters, assuming
2898 C<isl_set_align_params> and C<isl_map_align_params>
2903 =head2 Binary Operations
2905 The two arguments of a binary operation not only need to live
2906 in the same C<isl_ctx>, they currently also need to have
2907 the same (number of) parameters.
2909 =head3 Basic Operations
2913 =item * Intersection
2915 #include <isl/local_space.h>
2916 __isl_give isl_local_space *isl_local_space_intersect(
2917 __isl_take isl_local_space *ls1,
2918 __isl_take isl_local_space *ls2);
2920 #include <isl/set.h>
2921 __isl_give isl_basic_set *isl_basic_set_intersect_params(
2922 __isl_take isl_basic_set *bset1,
2923 __isl_take isl_basic_set *bset2);
2924 __isl_give isl_basic_set *isl_basic_set_intersect(
2925 __isl_take isl_basic_set *bset1,
2926 __isl_take isl_basic_set *bset2);
2927 __isl_give isl_set *isl_set_intersect_params(
2928 __isl_take isl_set *set,
2929 __isl_take isl_set *params);
2930 __isl_give isl_set *isl_set_intersect(
2931 __isl_take isl_set *set1,
2932 __isl_take isl_set *set2);
2934 #include <isl/map.h>
2935 __isl_give isl_basic_map *isl_basic_map_intersect_domain(
2936 __isl_take isl_basic_map *bmap,
2937 __isl_take isl_basic_set *bset);
2938 __isl_give isl_basic_map *isl_basic_map_intersect_range(
2939 __isl_take isl_basic_map *bmap,
2940 __isl_take isl_basic_set *bset);
2941 __isl_give isl_basic_map *isl_basic_map_intersect(
2942 __isl_take isl_basic_map *bmap1,
2943 __isl_take isl_basic_map *bmap2);
2944 __isl_give isl_map *isl_map_intersect_params(
2945 __isl_take isl_map *map,
2946 __isl_take isl_set *params);
2947 __isl_give isl_map *isl_map_intersect_domain(
2948 __isl_take isl_map *map,
2949 __isl_take isl_set *set);
2950 __isl_give isl_map *isl_map_intersect_range(
2951 __isl_take isl_map *map,
2952 __isl_take isl_set *set);
2953 __isl_give isl_map *isl_map_intersect(
2954 __isl_take isl_map *map1,
2955 __isl_take isl_map *map2);
2957 #include <isl/union_set.h>
2958 __isl_give isl_union_set *isl_union_set_intersect_params(
2959 __isl_take isl_union_set *uset,
2960 __isl_take isl_set *set);
2961 __isl_give isl_union_set *isl_union_set_intersect(
2962 __isl_take isl_union_set *uset1,
2963 __isl_take isl_union_set *uset2);
2965 #include <isl/union_map.h>
2966 __isl_give isl_union_map *isl_union_map_intersect_params(
2967 __isl_take isl_union_map *umap,
2968 __isl_take isl_set *set);
2969 __isl_give isl_union_map *isl_union_map_intersect_domain(
2970 __isl_take isl_union_map *umap,
2971 __isl_take isl_union_set *uset);
2972 __isl_give isl_union_map *isl_union_map_intersect_range(
2973 __isl_take isl_union_map *umap,
2974 __isl_take isl_union_set *uset);
2975 __isl_give isl_union_map *isl_union_map_intersect(
2976 __isl_take isl_union_map *umap1,
2977 __isl_take isl_union_map *umap2);
2979 The second argument to the C<_params> functions needs to be
2980 a parametric (basic) set. For the other functions, a parametric set
2981 for either argument is only allowed if the other argument is
2982 a parametric set as well.
2986 __isl_give isl_set *isl_basic_set_union(
2987 __isl_take isl_basic_set *bset1,
2988 __isl_take isl_basic_set *bset2);
2989 __isl_give isl_map *isl_basic_map_union(
2990 __isl_take isl_basic_map *bmap1,
2991 __isl_take isl_basic_map *bmap2);
2992 __isl_give isl_set *isl_set_union(
2993 __isl_take isl_set *set1,
2994 __isl_take isl_set *set2);
2995 __isl_give isl_map *isl_map_union(
2996 __isl_take isl_map *map1,
2997 __isl_take isl_map *map2);
2998 __isl_give isl_union_set *isl_union_set_union(
2999 __isl_take isl_union_set *uset1,
3000 __isl_take isl_union_set *uset2);
3001 __isl_give isl_union_map *isl_union_map_union(
3002 __isl_take isl_union_map *umap1,
3003 __isl_take isl_union_map *umap2);
3005 =item * Set difference
3007 __isl_give isl_set *isl_set_subtract(
3008 __isl_take isl_set *set1,
3009 __isl_take isl_set *set2);
3010 __isl_give isl_map *isl_map_subtract(
3011 __isl_take isl_map *map1,
3012 __isl_take isl_map *map2);
3013 __isl_give isl_map *isl_map_subtract_domain(
3014 __isl_take isl_map *map,
3015 __isl_take isl_set *dom);
3016 __isl_give isl_map *isl_map_subtract_range(
3017 __isl_take isl_map *map,
3018 __isl_take isl_set *dom);
3019 __isl_give isl_union_set *isl_union_set_subtract(
3020 __isl_take isl_union_set *uset1,
3021 __isl_take isl_union_set *uset2);
3022 __isl_give isl_union_map *isl_union_map_subtract(
3023 __isl_take isl_union_map *umap1,
3024 __isl_take isl_union_map *umap2);
3025 __isl_give isl_union_map *isl_union_map_subtract_domain(
3026 __isl_take isl_union_map *umap,
3027 __isl_take isl_union_set *dom);
3028 __isl_give isl_union_map *isl_union_map_subtract_range(
3029 __isl_take isl_union_map *umap,
3030 __isl_take isl_union_set *dom);
3034 __isl_give isl_basic_set *isl_basic_set_apply(
3035 __isl_take isl_basic_set *bset,
3036 __isl_take isl_basic_map *bmap);
3037 __isl_give isl_set *isl_set_apply(
3038 __isl_take isl_set *set,
3039 __isl_take isl_map *map);
3040 __isl_give isl_union_set *isl_union_set_apply(
3041 __isl_take isl_union_set *uset,
3042 __isl_take isl_union_map *umap);
3043 __isl_give isl_basic_map *isl_basic_map_apply_domain(
3044 __isl_take isl_basic_map *bmap1,
3045 __isl_take isl_basic_map *bmap2);
3046 __isl_give isl_basic_map *isl_basic_map_apply_range(
3047 __isl_take isl_basic_map *bmap1,
3048 __isl_take isl_basic_map *bmap2);
3049 __isl_give isl_map *isl_map_apply_domain(
3050 __isl_take isl_map *map1,
3051 __isl_take isl_map *map2);
3052 __isl_give isl_union_map *isl_union_map_apply_domain(
3053 __isl_take isl_union_map *umap1,
3054 __isl_take isl_union_map *umap2);
3055 __isl_give isl_map *isl_map_apply_range(
3056 __isl_take isl_map *map1,
3057 __isl_take isl_map *map2);
3058 __isl_give isl_union_map *isl_union_map_apply_range(
3059 __isl_take isl_union_map *umap1,
3060 __isl_take isl_union_map *umap2);
3064 __isl_give isl_basic_set *
3065 isl_basic_set_preimage_multi_aff(
3066 __isl_take isl_basic_set *bset,
3067 __isl_take isl_multi_aff *ma);
3068 __isl_give isl_set *isl_set_preimage_multi_aff(
3069 __isl_take isl_set *set,
3070 __isl_take isl_multi_aff *ma);
3071 __isl_give isl_set *isl_set_preimage_pw_multi_aff(
3072 __isl_take isl_set *set,
3073 __isl_take isl_pw_multi_aff *pma);
3074 __isl_give isl_set *isl_set_preimage_multi_pw_aff(
3075 __isl_take isl_set *set,
3076 __isl_take isl_multi_pw_aff *mpa);
3077 __isl_give isl_basic_map *
3078 isl_basic_map_preimage_domain_multi_aff(
3079 __isl_take isl_basic_map *bmap,
3080 __isl_take isl_multi_aff *ma);
3081 __isl_give isl_map *isl_map_preimage_domain_multi_aff(
3082 __isl_take isl_map *map,
3083 __isl_take isl_multi_aff *ma);
3084 __isl_give isl_map *
3085 isl_map_preimage_domain_pw_multi_aff(
3086 __isl_take isl_map *map,
3087 __isl_take isl_pw_multi_aff *pma);
3088 __isl_give isl_map *
3089 isl_map_preimage_domain_multi_pw_aff(
3090 __isl_take isl_map *map,
3091 __isl_take isl_multi_pw_aff *mpa);
3092 __isl_give isl_union_map *
3093 isl_union_map_preimage_domain_multi_aff(
3094 __isl_take isl_union_map *umap,
3095 __isl_take isl_multi_aff *ma);
3096 __isl_give isl_basic_map *
3097 isl_basic_map_preimage_range_multi_aff(
3098 __isl_take isl_basic_map *bmap,
3099 __isl_take isl_multi_aff *ma);
3101 These functions compute the preimage of the given set or map domain/range under
3102 the given function. In other words, the expression is plugged
3103 into the set description or into the domain/range of the map.
3104 Objects of types C<isl_multi_aff> and C<isl_pw_multi_aff> are described in
3105 L</"Piecewise Multiple Quasi Affine Expressions">.
3107 =item * Cartesian Product
3109 #include <isl/space.h>
3110 __isl_give isl_space *isl_space_product(
3111 __isl_take isl_space *space1,
3112 __isl_take isl_space *space2);
3113 __isl_give isl_space *isl_space_domain_product(
3114 __isl_take isl_space *space1,
3115 __isl_take isl_space *space2);
3116 __isl_give isl_space *isl_space_range_product(
3117 __isl_take isl_space *space1,
3118 __isl_take isl_space *space2);
3121 C<isl_space_product>, C<isl_space_domain_product>
3122 and C<isl_space_range_product> take pairs or relation spaces and
3123 produce a single relations space, where either the domain, the range
3124 or both domain and range are wrapped spaces of relations between
3125 the domains and/or ranges of the input spaces.
3126 If the product is only constructed over the domain or the range
3127 then the ranges or the domains of the inputs should be the same.
3129 #include <isl/set.h>
3130 __isl_give isl_set *isl_set_product(
3131 __isl_take isl_set *set1,
3132 __isl_take isl_set *set2);
3134 #include <isl/map.h>
3135 __isl_give isl_basic_map *isl_basic_map_domain_product(
3136 __isl_take isl_basic_map *bmap1,
3137 __isl_take isl_basic_map *bmap2);
3138 __isl_give isl_basic_map *isl_basic_map_range_product(
3139 __isl_take isl_basic_map *bmap1,
3140 __isl_take isl_basic_map *bmap2);
3141 __isl_give isl_basic_map *isl_basic_map_product(
3142 __isl_take isl_basic_map *bmap1,
3143 __isl_take isl_basic_map *bmap2);
3144 __isl_give isl_map *isl_map_domain_product(
3145 __isl_take isl_map *map1,
3146 __isl_take isl_map *map2);
3147 __isl_give isl_map *isl_map_range_product(
3148 __isl_take isl_map *map1,
3149 __isl_take isl_map *map2);
3150 __isl_give isl_map *isl_map_product(
3151 __isl_take isl_map *map1,
3152 __isl_take isl_map *map2);
3154 #include <isl/union_set.h>
3155 __isl_give isl_union_set *isl_union_set_product(
3156 __isl_take isl_union_set *uset1,
3157 __isl_take isl_union_set *uset2);
3159 #include <isl/union_map.h>
3160 __isl_give isl_union_map *isl_union_map_domain_product(
3161 __isl_take isl_union_map *umap1,
3162 __isl_take isl_union_map *umap2);
3163 __isl_give isl_union_map *isl_union_map_range_product(
3164 __isl_take isl_union_map *umap1,
3165 __isl_take isl_union_map *umap2);
3166 __isl_give isl_union_map *isl_union_map_product(
3167 __isl_take isl_union_map *umap1,
3168 __isl_take isl_union_map *umap2);
3170 The above functions compute the cross product of the given
3171 sets or relations. The domains and ranges of the results
3172 are wrapped maps between domains and ranges of the inputs.
3173 To obtain a ``flat'' product, use the following functions
3176 __isl_give isl_basic_set *isl_basic_set_flat_product(
3177 __isl_take isl_basic_set *bset1,
3178 __isl_take isl_basic_set *bset2);
3179 __isl_give isl_set *isl_set_flat_product(
3180 __isl_take isl_set *set1,
3181 __isl_take isl_set *set2);
3182 __isl_give isl_basic_map *isl_basic_map_flat_range_product(
3183 __isl_take isl_basic_map *bmap1,
3184 __isl_take isl_basic_map *bmap2);
3185 __isl_give isl_map *isl_map_flat_domain_product(
3186 __isl_take isl_map *map1,
3187 __isl_take isl_map *map2);
3188 __isl_give isl_map *isl_map_flat_range_product(
3189 __isl_take isl_map *map1,
3190 __isl_take isl_map *map2);
3191 __isl_give isl_union_map *isl_union_map_flat_range_product(
3192 __isl_take isl_union_map *umap1,
3193 __isl_take isl_union_map *umap2);
3194 __isl_give isl_basic_map *isl_basic_map_flat_product(
3195 __isl_take isl_basic_map *bmap1,
3196 __isl_take isl_basic_map *bmap2);
3197 __isl_give isl_map *isl_map_flat_product(
3198 __isl_take isl_map *map1,
3199 __isl_take isl_map *map2);
3201 #include <isl/space.h>
3202 __isl_give isl_space *isl_space_domain_factor_domain(
3203 __isl_take isl_space *space);
3204 __isl_give isl_space *isl_space_range_factor_domain(
3205 __isl_take isl_space *space);
3206 __isl_give isl_space *isl_space_range_factor_range(
3207 __isl_take isl_space *space);
3209 The functions C<isl_space_range_factor_domain> and
3210 C<isl_space_range_factor_range> extract the two arguments from
3211 the result of a call to C<isl_space_range_product>.
3213 The arguments of a call to C<isl_map_range_product> can be extracted
3214 from the result using the following two functions.
3216 #include <isl/map.h>
3217 __isl_give isl_map *isl_map_range_factor_domain(
3218 __isl_take isl_map *map);
3219 __isl_give isl_map *isl_map_range_factor_range(
3220 __isl_take isl_map *map);
3222 =item * Simplification
3224 __isl_give isl_basic_set *isl_basic_set_gist(
3225 __isl_take isl_basic_set *bset,
3226 __isl_take isl_basic_set *context);
3227 __isl_give isl_set *isl_set_gist(__isl_take isl_set *set,
3228 __isl_take isl_set *context);
3229 __isl_give isl_set *isl_set_gist_params(
3230 __isl_take isl_set *set,
3231 __isl_take isl_set *context);
3232 __isl_give isl_union_set *isl_union_set_gist(
3233 __isl_take isl_union_set *uset,
3234 __isl_take isl_union_set *context);
3235 __isl_give isl_union_set *isl_union_set_gist_params(
3236 __isl_take isl_union_set *uset,
3237 __isl_take isl_set *set);
3238 __isl_give isl_basic_map *isl_basic_map_gist(
3239 __isl_take isl_basic_map *bmap,
3240 __isl_take isl_basic_map *context);
3241 __isl_give isl_map *isl_map_gist(__isl_take isl_map *map,
3242 __isl_take isl_map *context);
3243 __isl_give isl_map *isl_map_gist_params(
3244 __isl_take isl_map *map,
3245 __isl_take isl_set *context);
3246 __isl_give isl_map *isl_map_gist_domain(
3247 __isl_take isl_map *map,
3248 __isl_take isl_set *context);
3249 __isl_give isl_map *isl_map_gist_range(
3250 __isl_take isl_map *map,
3251 __isl_take isl_set *context);
3252 __isl_give isl_union_map *isl_union_map_gist(
3253 __isl_take isl_union_map *umap,
3254 __isl_take isl_union_map *context);
3255 __isl_give isl_union_map *isl_union_map_gist_params(
3256 __isl_take isl_union_map *umap,
3257 __isl_take isl_set *set);
3258 __isl_give isl_union_map *isl_union_map_gist_domain(
3259 __isl_take isl_union_map *umap,
3260 __isl_take isl_union_set *uset);
3261 __isl_give isl_union_map *isl_union_map_gist_range(
3262 __isl_take isl_union_map *umap,
3263 __isl_take isl_union_set *uset);
3265 The gist operation returns a set or relation that has the
3266 same intersection with the context as the input set or relation.
3267 Any implicit equality in the intersection is made explicit in the result,
3268 while all inequalities that are redundant with respect to the intersection
3270 In case of union sets and relations, the gist operation is performed
3275 =head3 Lexicographic Optimization
3277 Given a (basic) set C<set> (or C<bset>) and a zero-dimensional domain C<dom>,
3278 the following functions
3279 compute a set that contains the lexicographic minimum or maximum
3280 of the elements in C<set> (or C<bset>) for those values of the parameters
3281 that satisfy C<dom>.
3282 If C<empty> is not C<NULL>, then C<*empty> is assigned a set
3283 that contains the parameter values in C<dom> for which C<set> (or C<bset>)
3285 In other words, the union of the parameter values
3286 for which the result is non-empty and of C<*empty>
3289 __isl_give isl_set *isl_basic_set_partial_lexmin(
3290 __isl_take isl_basic_set *bset,
3291 __isl_take isl_basic_set *dom,
3292 __isl_give isl_set **empty);
3293 __isl_give isl_set *isl_basic_set_partial_lexmax(
3294 __isl_take isl_basic_set *bset,
3295 __isl_take isl_basic_set *dom,
3296 __isl_give isl_set **empty);
3297 __isl_give isl_set *isl_set_partial_lexmin(
3298 __isl_take isl_set *set, __isl_take isl_set *dom,
3299 __isl_give isl_set **empty);
3300 __isl_give isl_set *isl_set_partial_lexmax(
3301 __isl_take isl_set *set, __isl_take isl_set *dom,
3302 __isl_give isl_set **empty);
3304 Given a (basic) set C<set> (or C<bset>), the following functions simply
3305 return a set containing the lexicographic minimum or maximum
3306 of the elements in C<set> (or C<bset>).
3307 In case of union sets, the optimum is computed per space.
3309 __isl_give isl_set *isl_basic_set_lexmin(
3310 __isl_take isl_basic_set *bset);
3311 __isl_give isl_set *isl_basic_set_lexmax(
3312 __isl_take isl_basic_set *bset);
3313 __isl_give isl_set *isl_set_lexmin(
3314 __isl_take isl_set *set);
3315 __isl_give isl_set *isl_set_lexmax(
3316 __isl_take isl_set *set);
3317 __isl_give isl_union_set *isl_union_set_lexmin(
3318 __isl_take isl_union_set *uset);
3319 __isl_give isl_union_set *isl_union_set_lexmax(
3320 __isl_take isl_union_set *uset);
3322 Given a (basic) relation C<map> (or C<bmap>) and a domain C<dom>,
3323 the following functions
3324 compute a relation that maps each element of C<dom>
3325 to the single lexicographic minimum or maximum
3326 of the elements that are associated to that same
3327 element in C<map> (or C<bmap>).
3328 If C<empty> is not C<NULL>, then C<*empty> is assigned a set
3329 that contains the elements in C<dom> that do not map
3330 to any elements in C<map> (or C<bmap>).
3331 In other words, the union of the domain of the result and of C<*empty>
3334 __isl_give isl_map *isl_basic_map_partial_lexmax(
3335 __isl_take isl_basic_map *bmap,
3336 __isl_take isl_basic_set *dom,
3337 __isl_give isl_set **empty);
3338 __isl_give isl_map *isl_basic_map_partial_lexmin(
3339 __isl_take isl_basic_map *bmap,
3340 __isl_take isl_basic_set *dom,
3341 __isl_give isl_set **empty);
3342 __isl_give isl_map *isl_map_partial_lexmax(
3343 __isl_take isl_map *map, __isl_take isl_set *dom,
3344 __isl_give isl_set **empty);
3345 __isl_give isl_map *isl_map_partial_lexmin(
3346 __isl_take isl_map *map, __isl_take isl_set *dom,
3347 __isl_give isl_set **empty);
3349 Given a (basic) map C<map> (or C<bmap>), the following functions simply
3350 return a map mapping each element in the domain of
3351 C<map> (or C<bmap>) to the lexicographic minimum or maximum
3352 of all elements associated to that element.
3353 In case of union relations, the optimum is computed per space.
3355 __isl_give isl_map *isl_basic_map_lexmin(
3356 __isl_take isl_basic_map *bmap);
3357 __isl_give isl_map *isl_basic_map_lexmax(
3358 __isl_take isl_basic_map *bmap);
3359 __isl_give isl_map *isl_map_lexmin(
3360 __isl_take isl_map *map);
3361 __isl_give isl_map *isl_map_lexmax(
3362 __isl_take isl_map *map);
3363 __isl_give isl_union_map *isl_union_map_lexmin(
3364 __isl_take isl_union_map *umap);
3365 __isl_give isl_union_map *isl_union_map_lexmax(
3366 __isl_take isl_union_map *umap);
3368 The following functions return their result in the form of
3369 a piecewise multi-affine expression
3370 (See L<"Piecewise Multiple Quasi Affine Expressions">),
3371 but are otherwise equivalent to the corresponding functions
3372 returning a basic set or relation.
3374 __isl_give isl_pw_multi_aff *
3375 isl_basic_map_lexmin_pw_multi_aff(
3376 __isl_take isl_basic_map *bmap);
3377 __isl_give isl_pw_multi_aff *
3378 isl_basic_set_partial_lexmin_pw_multi_aff(
3379 __isl_take isl_basic_set *bset,
3380 __isl_take isl_basic_set *dom,
3381 __isl_give isl_set **empty);
3382 __isl_give isl_pw_multi_aff *
3383 isl_basic_set_partial_lexmax_pw_multi_aff(
3384 __isl_take isl_basic_set *bset,
3385 __isl_take isl_basic_set *dom,
3386 __isl_give isl_set **empty);
3387 __isl_give isl_pw_multi_aff *
3388 isl_basic_map_partial_lexmin_pw_multi_aff(
3389 __isl_take isl_basic_map *bmap,
3390 __isl_take isl_basic_set *dom,
3391 __isl_give isl_set **empty);
3392 __isl_give isl_pw_multi_aff *
3393 isl_basic_map_partial_lexmax_pw_multi_aff(
3394 __isl_take isl_basic_map *bmap,
3395 __isl_take isl_basic_set *dom,
3396 __isl_give isl_set **empty);
3397 __isl_give isl_pw_multi_aff *isl_set_lexmin_pw_multi_aff(
3398 __isl_take isl_set *set);
3399 __isl_give isl_pw_multi_aff *isl_set_lexmax_pw_multi_aff(
3400 __isl_take isl_set *set);
3401 __isl_give isl_pw_multi_aff *isl_map_lexmin_pw_multi_aff(
3402 __isl_take isl_map *map);
3403 __isl_give isl_pw_multi_aff *isl_map_lexmax_pw_multi_aff(
3404 __isl_take isl_map *map);
3408 Lists are defined over several element types, including
3409 C<isl_val>, C<isl_id>, C<isl_aff>, C<isl_pw_aff>, C<isl_constraint>,
3410 C<isl_basic_set>, C<isl_set>, C<isl_ast_expr> and C<isl_ast_node>.
3411 Here we take lists of C<isl_set>s as an example.
3412 Lists can be created, copied, modified and freed using the following functions.
3414 #include <isl/list.h>
3415 __isl_give isl_set_list *isl_set_list_from_set(
3416 __isl_take isl_set *el);
3417 __isl_give isl_set_list *isl_set_list_alloc(
3418 isl_ctx *ctx, int n);
3419 __isl_give isl_set_list *isl_set_list_copy(
3420 __isl_keep isl_set_list *list);
3421 __isl_give isl_set_list *isl_set_list_insert(
3422 __isl_take isl_set_list *list, unsigned pos,
3423 __isl_take isl_set *el);
3424 __isl_give isl_set_list *isl_set_list_add(
3425 __isl_take isl_set_list *list,
3426 __isl_take isl_set *el);
3427 __isl_give isl_set_list *isl_set_list_drop(
3428 __isl_take isl_set_list *list,
3429 unsigned first, unsigned n);
3430 __isl_give isl_set_list *isl_set_list_set_set(
3431 __isl_take isl_set_list *list, int index,
3432 __isl_take isl_set *set);
3433 __isl_give isl_set_list *isl_set_list_concat(
3434 __isl_take isl_set_list *list1,
3435 __isl_take isl_set_list *list2);
3436 __isl_give isl_set_list *isl_set_list_sort(
3437 __isl_take isl_set_list *list,
3438 int (*cmp)(__isl_keep isl_set *a,
3439 __isl_keep isl_set *b, void *user),
3441 void *isl_set_list_free(__isl_take isl_set_list *list);
3443 C<isl_set_list_alloc> creates an empty list with a capacity for
3444 C<n> elements. C<isl_set_list_from_set> creates a list with a single
3447 Lists can be inspected using the following functions.
3449 #include <isl/list.h>
3450 isl_ctx *isl_set_list_get_ctx(__isl_keep isl_set_list *list);
3451 int isl_set_list_n_set(__isl_keep isl_set_list *list);
3452 __isl_give isl_set *isl_set_list_get_set(
3453 __isl_keep isl_set_list *list, int index);
3454 int isl_set_list_foreach(__isl_keep isl_set_list *list,
3455 int (*fn)(__isl_take isl_set *el, void *user),
3457 int isl_set_list_foreach_scc(__isl_keep isl_set_list *list,
3458 int (*follows)(__isl_keep isl_set *a,
3459 __isl_keep isl_set *b, void *user),
3461 int (*fn)(__isl_take isl_set *el, void *user),
3464 The function C<isl_set_list_foreach_scc> calls C<fn> on each of the
3465 strongly connected components of the graph with as vertices the elements
3466 of C<list> and a directed edge from vertex C<b> to vertex C<a>
3467 iff C<follows(a, b)> returns C<1>. The callbacks C<follows> and C<fn>
3468 should return C<-1> on error.
3470 Lists can be printed using
3472 #include <isl/list.h>
3473 __isl_give isl_printer *isl_printer_print_set_list(
3474 __isl_take isl_printer *p,
3475 __isl_keep isl_set_list *list);
3477 =head2 Associative arrays
3479 Associative arrays map isl objects of a specific type to isl objects
3480 of some (other) specific type. They are defined for several pairs
3481 of types, including (C<isl_map>, C<isl_basic_set>),
3482 (C<isl_id>, C<isl_ast_expr>) and.
3483 (C<isl_id>, C<isl_pw_aff>).
3484 Here, we take associative arrays that map C<isl_id>s to C<isl_ast_expr>s
3487 Associative arrays can be created, copied and freed using
3488 the following functions.
3490 #include <isl/id_to_ast_expr.h>
3491 __isl_give id_to_ast_expr *isl_id_to_ast_expr_alloc(
3492 isl_ctx *ctx, int min_size);
3493 __isl_give id_to_ast_expr *isl_id_to_ast_expr_copy(
3494 __isl_keep id_to_ast_expr *id2expr);
3495 void *isl_id_to_ast_expr_free(
3496 __isl_take id_to_ast_expr *id2expr);
3498 The C<min_size> argument to C<isl_id_to_ast_expr_alloc> can be used
3499 to specify the expected size of the associative array.
3500 The associative array will be grown automatically as needed.
3502 Associative arrays can be inspected using the following functions.
3504 #include <isl/id_to_ast_expr.h>
3505 isl_ctx *isl_id_to_ast_expr_get_ctx(
3506 __isl_keep id_to_ast_expr *id2expr);
3507 int isl_id_to_ast_expr_has(
3508 __isl_keep id_to_ast_expr *id2expr,
3509 __isl_keep isl_id *key);
3510 __isl_give isl_ast_expr *isl_id_to_ast_expr_get(
3511 __isl_keep id_to_ast_expr *id2expr,
3512 __isl_take isl_id *key);
3513 int isl_id_to_ast_expr_foreach(
3514 __isl_keep id_to_ast_expr *id2expr,
3515 int (*fn)(__isl_take isl_id *key,
3516 __isl_take isl_ast_expr *val, void *user),
3519 They can be modified using the following function.
3521 #include <isl/id_to_ast_expr.h>
3522 __isl_give id_to_ast_expr *isl_id_to_ast_expr_set(
3523 __isl_take id_to_ast_expr *id2expr,
3524 __isl_take isl_id *key,
3525 __isl_take isl_ast_expr *val);
3526 __isl_give id_to_ast_expr *isl_id_to_ast_expr_drop(
3527 __isl_take id_to_ast_expr *id2expr,
3528 __isl_take isl_id *key);
3530 Associative arrays can be printed using the following function.
3532 #include <isl/id_to_ast_expr.h>
3533 __isl_give isl_printer *isl_printer_print_id_to_ast_expr(
3534 __isl_take isl_printer *p,
3535 __isl_keep id_to_ast_expr *id2expr);
3537 =head2 Multiple Values
3539 An C<isl_multi_val> object represents a sequence of zero or more values,
3540 living in a set space.
3542 An C<isl_multi_val> can be constructed from an C<isl_val_list>
3543 using the following function
3545 #include <isl/val.h>
3546 __isl_give isl_multi_val *isl_multi_val_from_val_list(
3547 __isl_take isl_space *space,
3548 __isl_take isl_val_list *list);
3550 The zero multiple value (with value zero for each set dimension)
3551 can be created using the following function.
3553 #include <isl/val.h>
3554 __isl_give isl_multi_val *isl_multi_val_zero(
3555 __isl_take isl_space *space);
3557 Multiple values can be copied and freed using
3559 #include <isl/val.h>
3560 __isl_give isl_multi_val *isl_multi_val_copy(
3561 __isl_keep isl_multi_val *mv);
3562 void *isl_multi_val_free(__isl_take isl_multi_val *mv);
3564 They can be inspected using
3566 #include <isl/val.h>
3567 isl_ctx *isl_multi_val_get_ctx(
3568 __isl_keep isl_multi_val *mv);
3569 unsigned isl_multi_val_dim(__isl_keep isl_multi_val *mv,
3570 enum isl_dim_type type);
3571 __isl_give isl_val *isl_multi_val_get_val(
3572 __isl_keep isl_multi_val *mv, int pos);
3573 int isl_multi_val_find_dim_by_id(
3574 __isl_keep isl_multi_val *mv,
3575 enum isl_dim_type type, __isl_keep isl_id *id);
3576 __isl_give isl_id *isl_multi_val_get_dim_id(
3577 __isl_keep isl_multi_val *mv,
3578 enum isl_dim_type type, unsigned pos);
3579 const char *isl_multi_val_get_tuple_name(
3580 __isl_keep isl_multi_val *mv,
3581 enum isl_dim_type type);
3582 int isl_multi_val_has_tuple_id(__isl_keep isl_multi_val *mv,
3583 enum isl_dim_type type);
3584 __isl_give isl_id *isl_multi_val_get_tuple_id(
3585 __isl_keep isl_multi_val *mv,
3586 enum isl_dim_type type);
3587 int isl_multi_val_range_is_wrapping(
3588 __isl_keep isl_multi_val *mv);
3590 They can be modified using
3592 #include <isl/val.h>
3593 __isl_give isl_multi_val *isl_multi_val_set_val(
3594 __isl_take isl_multi_val *mv, int pos,
3595 __isl_take isl_val *val);
3596 __isl_give isl_multi_val *isl_multi_val_set_dim_name(
3597 __isl_take isl_multi_val *mv,
3598 enum isl_dim_type type, unsigned pos, const char *s);
3599 __isl_give isl_multi_val *isl_multi_val_set_dim_id(
3600 __isl_take isl_multi_val *mv,
3601 enum isl_dim_type type, unsigned pos,
3602 __isl_take isl_id *id);
3603 __isl_give isl_multi_val *isl_multi_val_set_tuple_name(
3604 __isl_take isl_multi_val *mv,
3605 enum isl_dim_type type, const char *s);
3606 __isl_give isl_multi_val *isl_multi_val_set_tuple_id(
3607 __isl_take isl_multi_val *mv,
3608 enum isl_dim_type type, __isl_take isl_id *id);
3609 __isl_give isl_multi_val *isl_multi_val_reset_tuple_id(
3610 __isl_take isl_multi_val *mv,
3611 enum isl_dim_type type);
3612 __isl_give isl_multi_val *isl_multi_val_reset_user(
3613 __isl_take isl_multi_val *mv);
3615 __isl_give isl_multi_val *isl_multi_val_insert_dims(
3616 __isl_take isl_multi_val *mv,
3617 enum isl_dim_type type, unsigned first, unsigned n);
3618 __isl_give isl_multi_val *isl_multi_val_add_dims(
3619 __isl_take isl_multi_val *mv,
3620 enum isl_dim_type type, unsigned n);
3621 __isl_give isl_multi_val *isl_multi_val_drop_dims(
3622 __isl_take isl_multi_val *mv,
3623 enum isl_dim_type type, unsigned first, unsigned n);
3627 #include <isl/val.h>
3628 __isl_give isl_multi_val *isl_multi_val_align_params(
3629 __isl_take isl_multi_val *mv,
3630 __isl_take isl_space *model);
3631 __isl_give isl_multi_val *isl_multi_val_from_range(
3632 __isl_take isl_multi_val *mv);
3633 __isl_give isl_multi_val *isl_multi_val_range_splice(
3634 __isl_take isl_multi_val *mv1, unsigned pos,
3635 __isl_take isl_multi_val *mv2);
3636 __isl_give isl_multi_val *isl_multi_val_range_product(
3637 __isl_take isl_multi_val *mv1,
3638 __isl_take isl_multi_val *mv2);
3639 __isl_give isl_multi_val *
3640 isl_multi_val_range_factor_domain(
3641 __isl_take isl_multi_val *mv);
3642 __isl_give isl_multi_val *
3643 isl_multi_val_range_factor_range(
3644 __isl_take isl_multi_val *mv);
3645 __isl_give isl_multi_val *isl_multi_val_flat_range_product(
3646 __isl_take isl_multi_val *mv1,
3647 __isl_take isl_multi_aff *mv2);
3648 __isl_give isl_multi_val *isl_multi_val_product(
3649 __isl_take isl_multi_val *mv1,
3650 __isl_take isl_multi_val *mv2);
3651 __isl_give isl_multi_val *isl_multi_val_add_val(
3652 __isl_take isl_multi_val *mv,
3653 __isl_take isl_val *v);
3654 __isl_give isl_multi_val *isl_multi_val_mod_val(
3655 __isl_take isl_multi_val *mv,
3656 __isl_take isl_val *v);
3657 __isl_give isl_multi_val *isl_multi_val_scale_val(
3658 __isl_take isl_multi_val *mv,
3659 __isl_take isl_val *v);
3660 __isl_give isl_multi_val *isl_multi_val_scale_multi_val(
3661 __isl_take isl_multi_val *mv1,
3662 __isl_take isl_multi_val *mv2);
3663 __isl_give isl_multi_val *
3664 isl_multi_val_scale_down_multi_val(
3665 __isl_take isl_multi_val *mv1,
3666 __isl_take isl_multi_val *mv2);
3668 A multiple value can be printed using
3670 __isl_give isl_printer *isl_printer_print_multi_val(
3671 __isl_take isl_printer *p,
3672 __isl_keep isl_multi_val *mv);
3676 Vectors can be created, copied and freed using the following functions.
3678 #include <isl/vec.h>
3679 __isl_give isl_vec *isl_vec_alloc(isl_ctx *ctx,
3681 __isl_give isl_vec *isl_vec_copy(__isl_keep isl_vec *vec);
3682 void *isl_vec_free(__isl_take isl_vec *vec);
3684 Note that the elements of a newly created vector may have arbitrary values.
3685 The elements can be changed and inspected using the following functions.
3687 isl_ctx *isl_vec_get_ctx(__isl_keep isl_vec *vec);
3688 int isl_vec_size(__isl_keep isl_vec *vec);
3689 __isl_give isl_val *isl_vec_get_element_val(
3690 __isl_keep isl_vec *vec, int pos);
3691 __isl_give isl_vec *isl_vec_set_element_si(
3692 __isl_take isl_vec *vec, int pos, int v);
3693 __isl_give isl_vec *isl_vec_set_element_val(
3694 __isl_take isl_vec *vec, int pos,
3695 __isl_take isl_val *v);
3696 __isl_give isl_vec *isl_vec_set_si(__isl_take isl_vec *vec,
3698 __isl_give isl_vec *isl_vec_set_val(
3699 __isl_take isl_vec *vec, __isl_take isl_val *v);
3700 int isl_vec_cmp_element(__isl_keep isl_vec *vec1,
3701 __isl_keep isl_vec *vec2, int pos);
3703 C<isl_vec_get_element> will return a negative value if anything went wrong.
3704 In that case, the value of C<*v> is undefined.
3706 The following function can be used to concatenate two vectors.
3708 __isl_give isl_vec *isl_vec_concat(__isl_take isl_vec *vec1,
3709 __isl_take isl_vec *vec2);
3713 Matrices can be created, copied and freed using the following functions.
3715 #include <isl/mat.h>
3716 __isl_give isl_mat *isl_mat_alloc(isl_ctx *ctx,
3717 unsigned n_row, unsigned n_col);
3718 __isl_give isl_mat *isl_mat_copy(__isl_keep isl_mat *mat);
3719 void *isl_mat_free(__isl_take isl_mat *mat);
3721 Note that the elements of a newly created matrix may have arbitrary values.
3722 The elements can be changed and inspected using the following functions.
3724 isl_ctx *isl_mat_get_ctx(__isl_keep isl_mat *mat);
3725 int isl_mat_rows(__isl_keep isl_mat *mat);
3726 int isl_mat_cols(__isl_keep isl_mat *mat);
3727 __isl_give isl_val *isl_mat_get_element_val(
3728 __isl_keep isl_mat *mat, int row, int col);
3729 __isl_give isl_mat *isl_mat_set_element_si(__isl_take isl_mat *mat,
3730 int row, int col, int v);
3731 __isl_give isl_mat *isl_mat_set_element_val(
3732 __isl_take isl_mat *mat, int row, int col,
3733 __isl_take isl_val *v);
3735 C<isl_mat_get_element> will return a negative value if anything went wrong.
3736 In that case, the value of C<*v> is undefined.
3738 The following function can be used to compute the (right) inverse
3739 of a matrix, i.e., a matrix such that the product of the original
3740 and the inverse (in that order) is a multiple of the identity matrix.
3741 The input matrix is assumed to be of full row-rank.
3743 __isl_give isl_mat *isl_mat_right_inverse(__isl_take isl_mat *mat);
3745 The following function can be used to compute the (right) kernel
3746 (or null space) of a matrix, i.e., a matrix such that the product of
3747 the original and the kernel (in that order) is the zero matrix.
3749 __isl_give isl_mat *isl_mat_right_kernel(__isl_take isl_mat *mat);
3751 =head2 Piecewise Quasi Affine Expressions
3753 The zero quasi affine expression or the quasi affine expression
3754 that is equal to a given value or
3755 a specified dimension on a given domain can be created using
3757 __isl_give isl_aff *isl_aff_zero_on_domain(
3758 __isl_take isl_local_space *ls);
3759 __isl_give isl_pw_aff *isl_pw_aff_zero_on_domain(
3760 __isl_take isl_local_space *ls);
3761 __isl_give isl_aff *isl_aff_val_on_domain(
3762 __isl_take isl_local_space *ls,
3763 __isl_take isl_val *val);
3764 __isl_give isl_aff *isl_aff_var_on_domain(
3765 __isl_take isl_local_space *ls,
3766 enum isl_dim_type type, unsigned pos);
3767 __isl_give isl_pw_aff *isl_pw_aff_var_on_domain(
3768 __isl_take isl_local_space *ls,
3769 enum isl_dim_type type, unsigned pos);
3771 Note that the space in which the resulting objects live is a map space
3772 with the given space as domain and a one-dimensional range.
3774 An empty piecewise quasi affine expression (one with no cells)
3775 or a piecewise quasi affine expression with a single cell can
3776 be created using the following functions.
3778 #include <isl/aff.h>
3779 __isl_give isl_pw_aff *isl_pw_aff_empty(
3780 __isl_take isl_space *space);
3781 __isl_give isl_pw_aff *isl_pw_aff_alloc(
3782 __isl_take isl_set *set, __isl_take isl_aff *aff);
3783 __isl_give isl_pw_aff *isl_pw_aff_from_aff(
3784 __isl_take isl_aff *aff);
3786 A piecewise quasi affine expression that is equal to 1 on a set
3787 and 0 outside the set can be created using the following function.
3789 #include <isl/aff.h>
3790 __isl_give isl_pw_aff *isl_set_indicator_function(
3791 __isl_take isl_set *set);
3793 Quasi affine expressions can be copied and freed using
3795 #include <isl/aff.h>
3796 __isl_give isl_aff *isl_aff_copy(__isl_keep isl_aff *aff);
3797 void *isl_aff_free(__isl_take isl_aff *aff);
3799 __isl_give isl_pw_aff *isl_pw_aff_copy(
3800 __isl_keep isl_pw_aff *pwaff);
3801 void *isl_pw_aff_free(__isl_take isl_pw_aff *pwaff);
3803 A (rational) bound on a dimension can be extracted from an C<isl_constraint>
3804 using the following function. The constraint is required to have
3805 a non-zero coefficient for the specified dimension.
3807 #include <isl/constraint.h>
3808 __isl_give isl_aff *isl_constraint_get_bound(
3809 __isl_keep isl_constraint *constraint,
3810 enum isl_dim_type type, int pos);
3812 The entire affine expression of the constraint can also be extracted
3813 using the following function.
3815 #include <isl/constraint.h>
3816 __isl_give isl_aff *isl_constraint_get_aff(
3817 __isl_keep isl_constraint *constraint);
3819 Conversely, an equality constraint equating
3820 the affine expression to zero or an inequality constraint enforcing
3821 the affine expression to be non-negative, can be constructed using
3823 __isl_give isl_constraint *isl_equality_from_aff(
3824 __isl_take isl_aff *aff);
3825 __isl_give isl_constraint *isl_inequality_from_aff(
3826 __isl_take isl_aff *aff);
3828 The expression can be inspected using
3830 #include <isl/aff.h>
3831 isl_ctx *isl_aff_get_ctx(__isl_keep isl_aff *aff);
3832 int isl_aff_dim(__isl_keep isl_aff *aff,
3833 enum isl_dim_type type);
3834 __isl_give isl_local_space *isl_aff_get_domain_local_space(
3835 __isl_keep isl_aff *aff);
3836 __isl_give isl_local_space *isl_aff_get_local_space(
3837 __isl_keep isl_aff *aff);
3838 const char *isl_aff_get_dim_name(__isl_keep isl_aff *aff,
3839 enum isl_dim_type type, unsigned pos);
3840 const char *isl_pw_aff_get_dim_name(
3841 __isl_keep isl_pw_aff *pa,
3842 enum isl_dim_type type, unsigned pos);
3843 int isl_pw_aff_has_dim_id(__isl_keep isl_pw_aff *pa,
3844 enum isl_dim_type type, unsigned pos);
3845 __isl_give isl_id *isl_pw_aff_get_dim_id(
3846 __isl_keep isl_pw_aff *pa,
3847 enum isl_dim_type type, unsigned pos);
3848 int isl_pw_aff_has_tuple_id(__isl_keep isl_pw_aff *pa,
3849 enum isl_dim_type type);
3850 __isl_give isl_id *isl_pw_aff_get_tuple_id(
3851 __isl_keep isl_pw_aff *pa,
3852 enum isl_dim_type type);
3853 __isl_give isl_val *isl_aff_get_constant_val(
3854 __isl_keep isl_aff *aff);
3855 __isl_give isl_val *isl_aff_get_coefficient_val(
3856 __isl_keep isl_aff *aff,
3857 enum isl_dim_type type, int pos);
3858 __isl_give isl_val *isl_aff_get_denominator_val(
3859 __isl_keep isl_aff *aff);
3860 __isl_give isl_aff *isl_aff_get_div(
3861 __isl_keep isl_aff *aff, int pos);
3863 int isl_pw_aff_n_piece(__isl_keep isl_pw_aff *pwaff);
3864 int isl_pw_aff_foreach_piece(__isl_keep isl_pw_aff *pwaff,
3865 int (*fn)(__isl_take isl_set *set,
3866 __isl_take isl_aff *aff,
3867 void *user), void *user);
3869 int isl_aff_is_cst(__isl_keep isl_aff *aff);
3870 int isl_pw_aff_is_cst(__isl_keep isl_pw_aff *pwaff);
3872 int isl_aff_involves_dims(__isl_keep isl_aff *aff,
3873 enum isl_dim_type type, unsigned first, unsigned n);
3874 int isl_pw_aff_involves_dims(__isl_keep isl_pw_aff *pwaff,
3875 enum isl_dim_type type, unsigned first, unsigned n);
3877 isl_ctx *isl_pw_aff_get_ctx(__isl_keep isl_pw_aff *pwaff);
3878 unsigned isl_pw_aff_dim(__isl_keep isl_pw_aff *pwaff,
3879 enum isl_dim_type type);
3880 int isl_pw_aff_is_empty(__isl_keep isl_pw_aff *pwaff);
3882 It can be modified using
3884 #include <isl/aff.h>
3885 __isl_give isl_aff *isl_aff_set_tuple_id(
3886 __isl_take isl_aff *aff,
3887 enum isl_dim_type type, __isl_take isl_id *id);
3888 __isl_give isl_pw_aff *isl_pw_aff_set_tuple_id(
3889 __isl_take isl_pw_aff *pwaff,
3890 enum isl_dim_type type, __isl_take isl_id *id);
3891 __isl_give isl_aff *isl_aff_set_dim_name(
3892 __isl_take isl_aff *aff, enum isl_dim_type type,
3893 unsigned pos, const char *s);
3894 __isl_give isl_aff *isl_aff_set_dim_id(
3895 __isl_take isl_aff *aff, enum isl_dim_type type,
3896 unsigned pos, __isl_take isl_id *id);
3897 __isl_give isl_pw_aff *isl_pw_aff_set_dim_id(
3898 __isl_take isl_pw_aff *pma,
3899 enum isl_dim_type type, unsigned pos,
3900 __isl_take isl_id *id);
3901 __isl_give isl_aff *isl_aff_set_constant_si(
3902 __isl_take isl_aff *aff, int v);
3903 __isl_give isl_aff *isl_aff_set_constant_val(
3904 __isl_take isl_aff *aff, __isl_take isl_val *v);
3905 __isl_give isl_aff *isl_aff_set_coefficient_si(
3906 __isl_take isl_aff *aff,
3907 enum isl_dim_type type, int pos, int v);
3908 __isl_give isl_aff *isl_aff_set_coefficient_val(
3909 __isl_take isl_aff *aff,
3910 enum isl_dim_type type, int pos,
3911 __isl_take isl_val *v);
3913 __isl_give isl_aff *isl_aff_add_constant_si(
3914 __isl_take isl_aff *aff, int v);
3915 __isl_give isl_aff *isl_aff_add_constant_val(
3916 __isl_take isl_aff *aff, __isl_take isl_val *v);
3917 __isl_give isl_aff *isl_aff_add_constant_num_si(
3918 __isl_take isl_aff *aff, int v);
3919 __isl_give isl_aff *isl_aff_add_coefficient_si(
3920 __isl_take isl_aff *aff,
3921 enum isl_dim_type type, int pos, int v);
3922 __isl_give isl_aff *isl_aff_add_coefficient_val(
3923 __isl_take isl_aff *aff,
3924 enum isl_dim_type type, int pos,
3925 __isl_take isl_val *v);
3927 __isl_give isl_aff *isl_aff_insert_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_insert_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_add_dims(
3934 __isl_take isl_aff *aff,
3935 enum isl_dim_type type, unsigned n);
3936 __isl_give isl_pw_aff *isl_pw_aff_add_dims(
3937 __isl_take isl_pw_aff *pwaff,
3938 enum isl_dim_type type, unsigned n);
3939 __isl_give isl_aff *isl_aff_drop_dims(
3940 __isl_take isl_aff *aff,
3941 enum isl_dim_type type, unsigned first, unsigned n);
3942 __isl_give isl_pw_aff *isl_pw_aff_drop_dims(
3943 __isl_take isl_pw_aff *pwaff,
3944 enum isl_dim_type type, unsigned first, unsigned n);
3945 __isl_give isl_aff *isl_aff_move_dims(
3946 __isl_take isl_aff *aff,
3947 enum isl_dim_type dst_type, unsigned dst_pos,
3948 enum isl_dim_type src_type, unsigned src_pos,
3950 __isl_give isl_pw_aff *isl_pw_aff_move_dims(
3951 __isl_take isl_pw_aff *pa,
3952 enum isl_dim_type dst_type, unsigned dst_pos,
3953 enum isl_dim_type src_type, unsigned src_pos,
3956 Note that C<isl_aff_set_constant_si> and C<isl_aff_set_coefficient_si>
3957 set the I<numerator> of the constant or coefficient, while
3958 C<isl_aff_set_constant_val> and C<isl_aff_set_coefficient_val> set
3959 the constant or coefficient as a whole.
3960 The C<add_constant> and C<add_coefficient> functions add an integer
3961 or rational value to
3962 the possibly rational constant or coefficient.
3963 The C<add_constant_num> functions add an integer value to
3966 To check whether an affine expressions is obviously zero
3967 or (obviously) equal to some other affine expression, use
3969 #include <isl/aff.h>
3970 int isl_aff_plain_is_zero(__isl_keep isl_aff *aff);
3971 int isl_aff_plain_is_equal(__isl_keep isl_aff *aff1,
3972 __isl_keep isl_aff *aff2);
3973 int isl_pw_aff_plain_is_equal(
3974 __isl_keep isl_pw_aff *pwaff1,
3975 __isl_keep isl_pw_aff *pwaff2);
3976 int isl_pw_aff_is_equal(__isl_keep isl_pw_aff *pa1,
3977 __isl_keep isl_pw_aff *pa2);
3981 #include <isl/aff.h>
3982 __isl_give isl_aff *isl_aff_add(__isl_take isl_aff *aff1,
3983 __isl_take isl_aff *aff2);
3984 __isl_give isl_pw_aff *isl_pw_aff_add(
3985 __isl_take isl_pw_aff *pwaff1,
3986 __isl_take isl_pw_aff *pwaff2);
3987 __isl_give isl_pw_aff *isl_pw_aff_min(
3988 __isl_take isl_pw_aff *pwaff1,
3989 __isl_take isl_pw_aff *pwaff2);
3990 __isl_give isl_pw_aff *isl_pw_aff_max(
3991 __isl_take isl_pw_aff *pwaff1,
3992 __isl_take isl_pw_aff *pwaff2);
3993 __isl_give isl_aff *isl_aff_sub(__isl_take isl_aff *aff1,
3994 __isl_take isl_aff *aff2);
3995 __isl_give isl_pw_aff *isl_pw_aff_sub(
3996 __isl_take isl_pw_aff *pwaff1,
3997 __isl_take isl_pw_aff *pwaff2);
3998 __isl_give isl_aff *isl_aff_neg(__isl_take isl_aff *aff);
3999 __isl_give isl_pw_aff *isl_pw_aff_neg(
4000 __isl_take isl_pw_aff *pwaff);
4001 __isl_give isl_aff *isl_aff_ceil(__isl_take isl_aff *aff);
4002 __isl_give isl_pw_aff *isl_pw_aff_ceil(
4003 __isl_take isl_pw_aff *pwaff);
4004 __isl_give isl_aff *isl_aff_floor(__isl_take isl_aff *aff);
4005 __isl_give isl_pw_aff *isl_pw_aff_floor(
4006 __isl_take isl_pw_aff *pwaff);
4007 __isl_give isl_aff *isl_aff_mod_val(__isl_take isl_aff *aff,
4008 __isl_take isl_val *mod);
4009 __isl_give isl_pw_aff *isl_pw_aff_mod_val(
4010 __isl_take isl_pw_aff *pa,
4011 __isl_take isl_val *mod);
4012 __isl_give isl_aff *isl_aff_scale_val(__isl_take isl_aff *aff,
4013 __isl_take isl_val *v);
4014 __isl_give isl_pw_aff *isl_pw_aff_scale_val(
4015 __isl_take isl_pw_aff *pa, __isl_take isl_val *v);
4016 __isl_give isl_aff *isl_aff_scale_down_ui(
4017 __isl_take isl_aff *aff, unsigned f);
4018 __isl_give isl_aff *isl_aff_scale_down_val(
4019 __isl_take isl_aff *aff, __isl_take isl_val *v);
4020 __isl_give isl_pw_aff *isl_pw_aff_scale_down_val(
4021 __isl_take isl_pw_aff *pa,
4022 __isl_take isl_val *f);
4024 __isl_give isl_pw_aff *isl_pw_aff_list_min(
4025 __isl_take isl_pw_aff_list *list);
4026 __isl_give isl_pw_aff *isl_pw_aff_list_max(
4027 __isl_take isl_pw_aff_list *list);
4029 __isl_give isl_pw_aff *isl_pw_aff_coalesce(
4030 __isl_take isl_pw_aff *pwqp);
4032 __isl_give isl_aff *isl_aff_align_params(
4033 __isl_take isl_aff *aff,
4034 __isl_take isl_space *model);
4035 __isl_give isl_pw_aff *isl_pw_aff_align_params(
4036 __isl_take isl_pw_aff *pwaff,
4037 __isl_take isl_space *model);
4039 __isl_give isl_aff *isl_aff_project_domain_on_params(
4040 __isl_take isl_aff *aff);
4041 __isl_give isl_pw_aff *isl_pw_aff_from_range(
4042 __isl_take isl_pw_aff *pwa);
4044 __isl_give isl_aff *isl_aff_gist_params(
4045 __isl_take isl_aff *aff,
4046 __isl_take isl_set *context);
4047 __isl_give isl_aff *isl_aff_gist(__isl_take isl_aff *aff,
4048 __isl_take isl_set *context);
4049 __isl_give isl_pw_aff *isl_pw_aff_gist_params(
4050 __isl_take isl_pw_aff *pwaff,
4051 __isl_take isl_set *context);
4052 __isl_give isl_pw_aff *isl_pw_aff_gist(
4053 __isl_take isl_pw_aff *pwaff,
4054 __isl_take isl_set *context);
4056 __isl_give isl_set *isl_pw_aff_domain(
4057 __isl_take isl_pw_aff *pwaff);
4058 __isl_give isl_set *isl_pw_aff_params(
4059 __isl_take isl_pw_aff *pwa);
4060 __isl_give isl_pw_aff *isl_pw_aff_intersect_domain(
4061 __isl_take isl_pw_aff *pa,
4062 __isl_take isl_set *set);
4063 __isl_give isl_pw_aff *isl_pw_aff_intersect_params(
4064 __isl_take isl_pw_aff *pa,
4065 __isl_take isl_set *set);
4067 __isl_give isl_aff *isl_aff_mul(__isl_take isl_aff *aff1,
4068 __isl_take isl_aff *aff2);
4069 __isl_give isl_aff *isl_aff_div(__isl_take isl_aff *aff1,
4070 __isl_take isl_aff *aff2);
4071 __isl_give isl_pw_aff *isl_pw_aff_mul(
4072 __isl_take isl_pw_aff *pwaff1,
4073 __isl_take isl_pw_aff *pwaff2);
4074 __isl_give isl_pw_aff *isl_pw_aff_div(
4075 __isl_take isl_pw_aff *pa1,
4076 __isl_take isl_pw_aff *pa2);
4077 __isl_give isl_pw_aff *isl_pw_aff_tdiv_q(
4078 __isl_take isl_pw_aff *pa1,
4079 __isl_take isl_pw_aff *pa2);
4080 __isl_give isl_pw_aff *isl_pw_aff_tdiv_r(
4081 __isl_take isl_pw_aff *pa1,
4082 __isl_take isl_pw_aff *pa2);
4084 When multiplying two affine expressions, at least one of the two needs
4085 to be a constant. Similarly, when dividing an affine expression by another,
4086 the second expression needs to be a constant.
4087 C<isl_pw_aff_tdiv_q> computes the quotient of an integer division with
4088 rounding towards zero. C<isl_pw_aff_tdiv_r> computes the corresponding
4091 #include <isl/aff.h>
4092 __isl_give isl_aff *isl_aff_pullback_aff(
4093 __isl_take isl_aff *aff1,
4094 __isl_take isl_aff *aff2);
4095 __isl_give isl_aff *isl_aff_pullback_multi_aff(
4096 __isl_take isl_aff *aff,
4097 __isl_take isl_multi_aff *ma);
4098 __isl_give isl_pw_aff *isl_pw_aff_pullback_multi_aff(
4099 __isl_take isl_pw_aff *pa,
4100 __isl_take isl_multi_aff *ma);
4101 __isl_give isl_pw_aff *isl_pw_aff_pullback_pw_multi_aff(
4102 __isl_take isl_pw_aff *pa,
4103 __isl_take isl_pw_multi_aff *pma);
4105 These functions precompose the input expression by the given
4106 C<isl_aff>, C<isl_multi_aff> or C<isl_pw_multi_aff>. In other words,
4107 the C<isl_aff>, C<isl_multi_aff> or C<isl_pw_multi_aff> is plugged
4108 into the (piecewise) affine expression.
4109 Objects of type C<isl_multi_aff> are described in
4110 L</"Piecewise Multiple Quasi Affine Expressions">.
4112 #include <isl/aff.h>
4113 __isl_give isl_basic_set *isl_aff_zero_basic_set(
4114 __isl_take isl_aff *aff);
4115 __isl_give isl_basic_set *isl_aff_neg_basic_set(
4116 __isl_take isl_aff *aff);
4117 __isl_give isl_basic_set *isl_aff_le_basic_set(
4118 __isl_take isl_aff *aff1, __isl_take isl_aff *aff2);
4119 __isl_give isl_basic_set *isl_aff_ge_basic_set(
4120 __isl_take isl_aff *aff1, __isl_take isl_aff *aff2);
4121 __isl_give isl_set *isl_pw_aff_eq_set(
4122 __isl_take isl_pw_aff *pwaff1,
4123 __isl_take isl_pw_aff *pwaff2);
4124 __isl_give isl_set *isl_pw_aff_ne_set(
4125 __isl_take isl_pw_aff *pwaff1,
4126 __isl_take isl_pw_aff *pwaff2);
4127 __isl_give isl_set *isl_pw_aff_le_set(
4128 __isl_take isl_pw_aff *pwaff1,
4129 __isl_take isl_pw_aff *pwaff2);
4130 __isl_give isl_set *isl_pw_aff_lt_set(
4131 __isl_take isl_pw_aff *pwaff1,
4132 __isl_take isl_pw_aff *pwaff2);
4133 __isl_give isl_set *isl_pw_aff_ge_set(
4134 __isl_take isl_pw_aff *pwaff1,
4135 __isl_take isl_pw_aff *pwaff2);
4136 __isl_give isl_set *isl_pw_aff_gt_set(
4137 __isl_take isl_pw_aff *pwaff1,
4138 __isl_take isl_pw_aff *pwaff2);
4140 __isl_give isl_set *isl_pw_aff_list_eq_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_ne_set(
4144 __isl_take isl_pw_aff_list *list1,
4145 __isl_take isl_pw_aff_list *list2);
4146 __isl_give isl_set *isl_pw_aff_list_le_set(
4147 __isl_take isl_pw_aff_list *list1,
4148 __isl_take isl_pw_aff_list *list2);
4149 __isl_give isl_set *isl_pw_aff_list_lt_set(
4150 __isl_take isl_pw_aff_list *list1,
4151 __isl_take isl_pw_aff_list *list2);
4152 __isl_give isl_set *isl_pw_aff_list_ge_set(
4153 __isl_take isl_pw_aff_list *list1,
4154 __isl_take isl_pw_aff_list *list2);
4155 __isl_give isl_set *isl_pw_aff_list_gt_set(
4156 __isl_take isl_pw_aff_list *list1,
4157 __isl_take isl_pw_aff_list *list2);
4159 The function C<isl_aff_neg_basic_set> returns a basic set
4160 containing those elements in the domain space
4161 of C<aff> where C<aff> is negative.
4162 The function C<isl_aff_ge_basic_set> returns a basic set
4163 containing those elements in the shared space
4164 of C<aff1> and C<aff2> where C<aff1> is greater than or equal to C<aff2>.
4165 The function C<isl_pw_aff_ge_set> returns a set
4166 containing those elements in the shared domain
4167 of C<pwaff1> and C<pwaff2> where C<pwaff1> is greater than or equal to C<pwaff2>.
4168 The functions operating on C<isl_pw_aff_list> apply the corresponding
4169 C<isl_pw_aff> function to each pair of elements in the two lists.
4171 #include <isl/aff.h>
4172 __isl_give isl_set *isl_pw_aff_nonneg_set(
4173 __isl_take isl_pw_aff *pwaff);
4174 __isl_give isl_set *isl_pw_aff_zero_set(
4175 __isl_take isl_pw_aff *pwaff);
4176 __isl_give isl_set *isl_pw_aff_non_zero_set(
4177 __isl_take isl_pw_aff *pwaff);
4179 The function C<isl_pw_aff_nonneg_set> returns a set
4180 containing those elements in the domain
4181 of C<pwaff> where C<pwaff> is non-negative.
4183 #include <isl/aff.h>
4184 __isl_give isl_pw_aff *isl_pw_aff_cond(
4185 __isl_take isl_pw_aff *cond,
4186 __isl_take isl_pw_aff *pwaff_true,
4187 __isl_take isl_pw_aff *pwaff_false);
4189 The function C<isl_pw_aff_cond> performs a conditional operator
4190 and returns an expression that is equal to C<pwaff_true>
4191 for elements where C<cond> is non-zero and equal to C<pwaff_false> for elements
4192 where C<cond> is zero.
4194 #include <isl/aff.h>
4195 __isl_give isl_pw_aff *isl_pw_aff_union_min(
4196 __isl_take isl_pw_aff *pwaff1,
4197 __isl_take isl_pw_aff *pwaff2);
4198 __isl_give isl_pw_aff *isl_pw_aff_union_max(
4199 __isl_take isl_pw_aff *pwaff1,
4200 __isl_take isl_pw_aff *pwaff2);
4201 __isl_give isl_pw_aff *isl_pw_aff_union_add(
4202 __isl_take isl_pw_aff *pwaff1,
4203 __isl_take isl_pw_aff *pwaff2);
4205 The function C<isl_pw_aff_union_max> computes a piecewise quasi-affine
4206 expression with a domain that is the union of those of C<pwaff1> and
4207 C<pwaff2> and such that on each cell, the quasi-affine expression is
4208 the maximum of those of C<pwaff1> and C<pwaff2>. If only one of
4209 C<pwaff1> or C<pwaff2> is defined on a given cell, then the
4210 associated expression is the defined one.
4212 An expression can be read from input using
4214 #include <isl/aff.h>
4215 __isl_give isl_aff *isl_aff_read_from_str(
4216 isl_ctx *ctx, const char *str);
4217 __isl_give isl_pw_aff *isl_pw_aff_read_from_str(
4218 isl_ctx *ctx, const char *str);
4220 An expression can be printed using
4222 #include <isl/aff.h>
4223 __isl_give isl_printer *isl_printer_print_aff(
4224 __isl_take isl_printer *p, __isl_keep isl_aff *aff);
4226 __isl_give isl_printer *isl_printer_print_pw_aff(
4227 __isl_take isl_printer *p,
4228 __isl_keep isl_pw_aff *pwaff);
4230 =head2 Piecewise Multiple Quasi Affine Expressions
4232 An C<isl_multi_aff> object represents a sequence of
4233 zero or more affine expressions, all defined on the same domain space.
4234 Similarly, an C<isl_multi_pw_aff> object represents a sequence of
4235 zero or more piecewise affine expressions.
4237 An C<isl_multi_aff> can be constructed from a single
4238 C<isl_aff> or an C<isl_aff_list> using the
4239 following functions. Similarly for C<isl_multi_pw_aff>
4240 and C<isl_pw_multi_aff>.
4242 #include <isl/aff.h>
4243 __isl_give isl_multi_aff *isl_multi_aff_from_aff(
4244 __isl_take isl_aff *aff);
4245 __isl_give isl_multi_pw_aff *
4246 isl_multi_pw_aff_from_multi_aff(
4247 __isl_take isl_multi_aff *ma);
4248 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_from_pw_aff(
4249 __isl_take isl_pw_aff *pa);
4250 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_from_pw_aff(
4251 __isl_take isl_pw_aff *pa);
4252 __isl_give isl_multi_aff *isl_multi_aff_from_aff_list(
4253 __isl_take isl_space *space,
4254 __isl_take isl_aff_list *list);
4256 An C<isl_multi_pw_aff> can be converted to an C<isl_pw_multi_aff>
4257 using the function C<isl_pw_multi_aff_from_multi_pw_aff> below.
4258 Note however that the domain
4259 of the result is the intersection of the domains of the input.
4260 The reverse conversion is exact.
4262 #include <isl/aff.h>
4263 __isl_give isl_pw_multi_aff *
4264 isl_pw_multi_aff_from_multi_pw_aff(
4265 __isl_take isl_multi_pw_aff *mpa);
4266 __isl_give isl_multi_pw_aff *
4267 isl_multi_pw_aff_from_pw_multi_aff(
4268 __isl_take isl_pw_multi_aff *pma);
4270 An empty piecewise multiple quasi affine expression (one with no cells),
4271 the zero piecewise multiple quasi affine expression (with value zero
4272 for each output dimension),
4273 a piecewise multiple quasi affine expression with a single cell (with
4274 either a universe or a specified domain) or
4275 a zero-dimensional piecewise multiple quasi affine expression
4277 can be created using the following functions.
4279 #include <isl/aff.h>
4280 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_empty(
4281 __isl_take isl_space *space);
4282 __isl_give isl_multi_aff *isl_multi_aff_zero(
4283 __isl_take isl_space *space);
4284 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_zero(
4285 __isl_take isl_space *space);
4286 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_zero(
4287 __isl_take isl_space *space);
4288 __isl_give isl_multi_aff *isl_multi_aff_identity(
4289 __isl_take isl_space *space);
4290 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_identity(
4291 __isl_take isl_space *space);
4292 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_identity(
4293 __isl_take isl_space *space);
4294 __isl_give isl_multi_aff *isl_multi_aff_domain_map(
4295 __isl_take isl_space *space);
4296 __isl_give isl_multi_aff *isl_multi_aff_range_map(
4297 __isl_take isl_space *space);
4298 __isl_give isl_multi_aff *isl_multi_aff_project_out_map(
4299 __isl_take isl_space *space,
4300 enum isl_dim_type type,
4301 unsigned first, unsigned n);
4302 __isl_give isl_pw_multi_aff *
4303 isl_pw_multi_aff_project_out_map(
4304 __isl_take isl_space *space,
4305 enum isl_dim_type type,
4306 unsigned first, unsigned n);
4307 __isl_give isl_pw_multi_aff *
4308 isl_pw_multi_aff_from_multi_aff(
4309 __isl_take isl_multi_aff *ma);
4310 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_alloc(
4311 __isl_take isl_set *set,
4312 __isl_take isl_multi_aff *maff);
4313 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_from_domain(
4314 __isl_take isl_set *set);
4316 __isl_give isl_union_pw_multi_aff *
4317 isl_union_pw_multi_aff_empty(
4318 __isl_take isl_space *space);
4319 __isl_give isl_union_pw_multi_aff *
4320 isl_union_pw_multi_aff_add_pw_multi_aff(
4321 __isl_take isl_union_pw_multi_aff *upma,
4322 __isl_take isl_pw_multi_aff *pma);
4323 __isl_give isl_union_pw_multi_aff *
4324 isl_union_pw_multi_aff_from_domain(
4325 __isl_take isl_union_set *uset);
4327 A piecewise multiple quasi affine expression can also be initialized
4328 from an C<isl_set> or C<isl_map>, provided the C<isl_set> is a singleton
4329 and the C<isl_map> is single-valued.
4330 In case of a conversion from an C<isl_union_set> or an C<isl_union_map>
4331 to an C<isl_union_pw_multi_aff>, these properties need to hold in each space.
4333 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_from_set(
4334 __isl_take isl_set *set);
4335 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_from_map(
4336 __isl_take isl_map *map);
4338 __isl_give isl_union_pw_multi_aff *
4339 isl_union_pw_multi_aff_from_union_set(
4340 __isl_take isl_union_set *uset);
4341 __isl_give isl_union_pw_multi_aff *
4342 isl_union_pw_multi_aff_from_union_map(
4343 __isl_take isl_union_map *umap);
4345 Multiple quasi affine expressions can be copied and freed using
4347 #include <isl/aff.h>
4348 __isl_give isl_multi_aff *isl_multi_aff_copy(
4349 __isl_keep isl_multi_aff *maff);
4350 void *isl_multi_aff_free(__isl_take isl_multi_aff *maff);
4352 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_copy(
4353 __isl_keep isl_pw_multi_aff *pma);
4354 void *isl_pw_multi_aff_free(
4355 __isl_take isl_pw_multi_aff *pma);
4357 __isl_give isl_union_pw_multi_aff *
4358 isl_union_pw_multi_aff_copy(
4359 __isl_keep isl_union_pw_multi_aff *upma);
4360 void *isl_union_pw_multi_aff_free(
4361 __isl_take isl_union_pw_multi_aff *upma);
4363 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_copy(
4364 __isl_keep isl_multi_pw_aff *mpa);
4365 void *isl_multi_pw_aff_free(
4366 __isl_take isl_multi_pw_aff *mpa);
4368 The expression can be inspected using
4370 #include <isl/aff.h>
4371 isl_ctx *isl_multi_aff_get_ctx(
4372 __isl_keep isl_multi_aff *maff);
4373 isl_ctx *isl_pw_multi_aff_get_ctx(
4374 __isl_keep isl_pw_multi_aff *pma);
4375 isl_ctx *isl_union_pw_multi_aff_get_ctx(
4376 __isl_keep isl_union_pw_multi_aff *upma);
4377 isl_ctx *isl_multi_pw_aff_get_ctx(
4378 __isl_keep isl_multi_pw_aff *mpa);
4379 unsigned isl_multi_aff_dim(__isl_keep isl_multi_aff *maff,
4380 enum isl_dim_type type);
4381 unsigned isl_pw_multi_aff_dim(
4382 __isl_keep isl_pw_multi_aff *pma,
4383 enum isl_dim_type type);
4384 unsigned isl_multi_pw_aff_dim(
4385 __isl_keep isl_multi_pw_aff *mpa,
4386 enum isl_dim_type type);
4387 __isl_give isl_aff *isl_multi_aff_get_aff(
4388 __isl_keep isl_multi_aff *multi, int pos);
4389 __isl_give isl_pw_aff *isl_pw_multi_aff_get_pw_aff(
4390 __isl_keep isl_pw_multi_aff *pma, int pos);
4391 __isl_give isl_pw_aff *isl_multi_pw_aff_get_pw_aff(
4392 __isl_keep isl_multi_pw_aff *mpa, int pos);
4393 int isl_multi_aff_find_dim_by_id(
4394 __isl_keep isl_multi_aff *ma,
4395 enum isl_dim_type type, __isl_keep isl_id *id);
4396 int isl_multi_pw_aff_find_dim_by_id(
4397 __isl_keep isl_multi_pw_aff *mpa,
4398 enum isl_dim_type type, __isl_keep isl_id *id);
4399 const char *isl_pw_multi_aff_get_dim_name(
4400 __isl_keep isl_pw_multi_aff *pma,
4401 enum isl_dim_type type, unsigned pos);
4402 __isl_give isl_id *isl_multi_aff_get_dim_id(
4403 __isl_keep isl_multi_aff *ma,
4404 enum isl_dim_type type, unsigned pos);
4405 __isl_give isl_id *isl_pw_multi_aff_get_dim_id(
4406 __isl_keep isl_pw_multi_aff *pma,
4407 enum isl_dim_type type, unsigned pos);
4408 __isl_give isl_id *isl_multi_pw_aff_get_dim_id(
4409 __isl_keep isl_multi_pw_aff *mpa,
4410 enum isl_dim_type type, unsigned pos);
4411 const char *isl_multi_aff_get_tuple_name(
4412 __isl_keep isl_multi_aff *multi,
4413 enum isl_dim_type type);
4414 int isl_pw_multi_aff_has_tuple_name(
4415 __isl_keep isl_pw_multi_aff *pma,
4416 enum isl_dim_type type);
4417 const char *isl_pw_multi_aff_get_tuple_name(
4418 __isl_keep isl_pw_multi_aff *pma,
4419 enum isl_dim_type type);
4420 int isl_multi_aff_has_tuple_id(__isl_keep isl_multi_aff *ma,
4421 enum isl_dim_type type);
4422 int isl_pw_multi_aff_has_tuple_id(
4423 __isl_keep isl_pw_multi_aff *pma,
4424 enum isl_dim_type type);
4425 int isl_multi_pw_aff_has_tuple_id(
4426 __isl_keep isl_multi_pw_aff *mpa,
4427 enum isl_dim_type type);
4428 __isl_give isl_id *isl_multi_aff_get_tuple_id(
4429 __isl_keep isl_multi_aff *ma,
4430 enum isl_dim_type type);
4431 __isl_give isl_id *isl_pw_multi_aff_get_tuple_id(
4432 __isl_keep isl_pw_multi_aff *pma,
4433 enum isl_dim_type type);
4434 __isl_give isl_id *isl_multi_pw_aff_get_tuple_id(
4435 __isl_keep isl_multi_pw_aff *mpa,
4436 enum isl_dim_type type);
4437 int isl_multi_aff_range_is_wrapping(
4438 __isl_keep isl_multi_aff *ma);
4439 int isl_multi_pw_aff_range_is_wrapping(
4440 __isl_keep isl_multi_pw_aff *mpa);
4442 int isl_pw_multi_aff_foreach_piece(
4443 __isl_keep isl_pw_multi_aff *pma,
4444 int (*fn)(__isl_take isl_set *set,
4445 __isl_take isl_multi_aff *maff,
4446 void *user), void *user);
4448 int isl_union_pw_multi_aff_foreach_pw_multi_aff(
4449 __isl_keep isl_union_pw_multi_aff *upma,
4450 int (*fn)(__isl_take isl_pw_multi_aff *pma,
4451 void *user), void *user);
4453 It can be modified using
4455 #include <isl/aff.h>
4456 __isl_give isl_multi_aff *isl_multi_aff_set_aff(
4457 __isl_take isl_multi_aff *multi, int pos,
4458 __isl_take isl_aff *aff);
4459 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_set_pw_aff(
4460 __isl_take isl_pw_multi_aff *pma, unsigned pos,
4461 __isl_take isl_pw_aff *pa);
4462 __isl_give isl_multi_aff *isl_multi_aff_set_dim_name(
4463 __isl_take isl_multi_aff *maff,
4464 enum isl_dim_type type, unsigned pos, const char *s);
4465 __isl_give isl_multi_aff *isl_multi_aff_set_dim_id(
4466 __isl_take isl_multi_aff *maff,
4467 enum isl_dim_type type, unsigned pos,
4468 __isl_take isl_id *id);
4469 __isl_give isl_multi_aff *isl_multi_aff_set_tuple_name(
4470 __isl_take isl_multi_aff *maff,
4471 enum isl_dim_type type, const char *s);
4472 __isl_give isl_multi_aff *isl_multi_aff_set_tuple_id(
4473 __isl_take isl_multi_aff *maff,
4474 enum isl_dim_type type, __isl_take isl_id *id);
4475 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_set_tuple_id(
4476 __isl_take isl_pw_multi_aff *pma,
4477 enum isl_dim_type type, __isl_take isl_id *id);
4478 __isl_give isl_multi_aff *isl_multi_aff_reset_tuple_id(
4479 __isl_take isl_multi_aff *ma,
4480 enum isl_dim_type type);
4481 __isl_give isl_multi_pw_aff *
4482 isl_multi_pw_aff_reset_tuple_id(
4483 __isl_take isl_multi_pw_aff *mpa,
4484 enum isl_dim_type type);
4485 __isl_give isl_multi_aff *isl_multi_aff_reset_user(
4486 __isl_take isl_multi_aff *ma);
4487 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_reset_user(
4488 __isl_take isl_multi_pw_aff *mpa);
4490 __isl_give isl_multi_pw_aff *
4491 isl_multi_pw_aff_set_dim_name(
4492 __isl_take isl_multi_pw_aff *mpa,
4493 enum isl_dim_type type, unsigned pos, const char *s);
4494 __isl_give isl_multi_pw_aff *
4495 isl_multi_pw_aff_set_dim_id(
4496 __isl_take isl_multi_pw_aff *mpa,
4497 enum isl_dim_type type, unsigned pos,
4498 __isl_take isl_id *id);
4499 __isl_give isl_multi_pw_aff *
4500 isl_multi_pw_aff_set_tuple_name(
4501 __isl_take isl_multi_pw_aff *mpa,
4502 enum isl_dim_type type, const char *s);
4504 __isl_give isl_multi_aff *isl_multi_aff_flatten_domain(
4505 __isl_take isl_multi_aff *ma);
4507 __isl_give isl_multi_aff *isl_multi_aff_insert_dims(
4508 __isl_take isl_multi_aff *ma,
4509 enum isl_dim_type type, unsigned first, unsigned n);
4510 __isl_give isl_multi_aff *isl_multi_aff_add_dims(
4511 __isl_take isl_multi_aff *ma,
4512 enum isl_dim_type type, unsigned n);
4513 __isl_give isl_multi_aff *isl_multi_aff_drop_dims(
4514 __isl_take isl_multi_aff *maff,
4515 enum isl_dim_type type, unsigned first, unsigned n);
4516 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_drop_dims(
4517 __isl_take isl_pw_multi_aff *pma,
4518 enum isl_dim_type type, unsigned first, unsigned n);
4520 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_insert_dims(
4521 __isl_take isl_multi_pw_aff *mpa,
4522 enum isl_dim_type type, unsigned first, unsigned n);
4523 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_add_dims(
4524 __isl_take isl_multi_pw_aff *mpa,
4525 enum isl_dim_type type, unsigned n);
4526 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_move_dims(
4527 __isl_take isl_multi_pw_aff *pma,
4528 enum isl_dim_type dst_type, unsigned dst_pos,
4529 enum isl_dim_type src_type, unsigned src_pos,
4532 To check whether two multiple affine expressions are
4533 (obviously) equal to each other, use
4535 int isl_multi_aff_plain_is_equal(__isl_keep isl_multi_aff *maff1,
4536 __isl_keep isl_multi_aff *maff2);
4537 int isl_pw_multi_aff_plain_is_equal(
4538 __isl_keep isl_pw_multi_aff *pma1,
4539 __isl_keep isl_pw_multi_aff *pma2);
4540 int isl_multi_pw_aff_plain_is_equal(
4541 __isl_keep isl_multi_pw_aff *mpa1,
4542 __isl_keep isl_multi_pw_aff *mpa2);
4543 int isl_multi_pw_aff_is_equal(
4544 __isl_keep isl_multi_pw_aff *mpa1,
4545 __isl_keep isl_multi_pw_aff *mpa2);
4549 #include <isl/aff.h>
4550 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_union_lexmin(
4551 __isl_take isl_pw_multi_aff *pma1,
4552 __isl_take isl_pw_multi_aff *pma2);
4553 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_union_lexmax(
4554 __isl_take isl_pw_multi_aff *pma1,
4555 __isl_take isl_pw_multi_aff *pma2);
4556 __isl_give isl_multi_aff *isl_multi_aff_add(
4557 __isl_take isl_multi_aff *maff1,
4558 __isl_take isl_multi_aff *maff2);
4559 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_add(
4560 __isl_take isl_pw_multi_aff *pma1,
4561 __isl_take isl_pw_multi_aff *pma2);
4562 __isl_give isl_union_pw_multi_aff *isl_union_pw_multi_aff_add(
4563 __isl_take isl_union_pw_multi_aff *upma1,
4564 __isl_take isl_union_pw_multi_aff *upma2);
4565 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_union_add(
4566 __isl_take isl_pw_multi_aff *pma1,
4567 __isl_take isl_pw_multi_aff *pma2);
4568 __isl_give isl_multi_aff *isl_multi_aff_sub(
4569 __isl_take isl_multi_aff *ma1,
4570 __isl_take isl_multi_aff *ma2);
4571 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_sub(
4572 __isl_take isl_pw_multi_aff *pma1,
4573 __isl_take isl_pw_multi_aff *pma2);
4574 __isl_give isl_union_pw_multi_aff *isl_union_pw_multi_aff_sub(
4575 __isl_take isl_union_pw_multi_aff *upma1,
4576 __isl_take isl_union_pw_multi_aff *upma2);
4578 C<isl_multi_aff_sub> subtracts the second argument from the first.
4580 __isl_give isl_multi_aff *isl_multi_aff_scale_val(
4581 __isl_take isl_multi_aff *ma,
4582 __isl_take isl_val *v);
4583 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_scale_val(
4584 __isl_take isl_pw_multi_aff *pma,
4585 __isl_take isl_val *v);
4586 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_scale_val(
4587 __isl_take isl_multi_pw_aff *mpa,
4588 __isl_take isl_val *v);
4589 __isl_give isl_multi_aff *isl_multi_aff_scale_multi_val(
4590 __isl_take isl_multi_aff *ma,
4591 __isl_take isl_multi_val *mv);
4592 __isl_give isl_pw_multi_aff *
4593 isl_pw_multi_aff_scale_multi_val(
4594 __isl_take isl_pw_multi_aff *pma,
4595 __isl_take isl_multi_val *mv);
4596 __isl_give isl_multi_pw_aff *
4597 isl_multi_pw_aff_scale_multi_val(
4598 __isl_take isl_multi_pw_aff *mpa,
4599 __isl_take isl_multi_val *mv);
4600 __isl_give isl_union_pw_multi_aff *
4601 isl_union_pw_multi_aff_scale_multi_val(
4602 __isl_take isl_union_pw_multi_aff *upma,
4603 __isl_take isl_multi_val *mv);
4604 __isl_give isl_multi_aff *
4605 isl_multi_aff_scale_down_multi_val(
4606 __isl_take isl_multi_aff *ma,
4607 __isl_take isl_multi_val *mv);
4608 __isl_give isl_multi_pw_aff *
4609 isl_multi_pw_aff_scale_down_multi_val(
4610 __isl_take isl_multi_pw_aff *mpa,
4611 __isl_take isl_multi_val *mv);
4613 C<isl_multi_aff_scale_multi_val> scales the elements of C<ma>
4614 by the corresponding elements of C<mv>.
4616 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_fix_si(
4617 __isl_take isl_pw_multi_aff *pma,
4618 enum isl_dim_type type, unsigned pos, int value);
4619 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_intersect_params(
4620 __isl_take isl_pw_multi_aff *pma,
4621 __isl_take isl_set *set);
4622 __isl_give isl_set *isl_multi_pw_aff_domain(
4623 __isl_take isl_multi_pw_aff *mpa);
4624 __isl_give isl_multi_pw_aff *
4625 isl_multi_pw_aff_intersect_params(
4626 __isl_take isl_multi_pw_aff *mpa,
4627 __isl_take isl_set *set);
4628 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_intersect_domain(
4629 __isl_take isl_pw_multi_aff *pma,
4630 __isl_take isl_set *set);
4631 __isl_give isl_multi_pw_aff *
4632 isl_multi_pw_aff_intersect_domain(
4633 __isl_take isl_multi_pw_aff *mpa,
4634 __isl_take isl_set *domain);
4635 __isl_give isl_union_pw_multi_aff *
4636 isl_union_pw_multi_aff_intersect_domain(
4637 __isl_take isl_union_pw_multi_aff *upma,
4638 __isl_take isl_union_set *uset);
4639 __isl_give isl_multi_aff *isl_multi_aff_lift(
4640 __isl_take isl_multi_aff *maff,
4641 __isl_give isl_local_space **ls);
4642 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_coalesce(
4643 __isl_take isl_pw_multi_aff *pma);
4644 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_coalesce(
4645 __isl_take isl_multi_pw_aff *mpa);
4646 __isl_give isl_multi_aff *isl_multi_aff_align_params(
4647 __isl_take isl_multi_aff *multi,
4648 __isl_take isl_space *model);
4649 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_align_params(
4650 __isl_take isl_pw_multi_aff *pma,
4651 __isl_take isl_space *model);
4652 __isl_give isl_pw_multi_aff *
4653 isl_pw_multi_aff_project_domain_on_params(
4654 __isl_take isl_pw_multi_aff *pma);
4655 __isl_give isl_multi_aff *isl_multi_aff_gist_params(
4656 __isl_take isl_multi_aff *maff,
4657 __isl_take isl_set *context);
4658 __isl_give isl_multi_aff *isl_multi_aff_gist(
4659 __isl_take isl_multi_aff *maff,
4660 __isl_take isl_set *context);
4661 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_gist_params(
4662 __isl_take isl_pw_multi_aff *pma,
4663 __isl_take isl_set *set);
4664 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_gist(
4665 __isl_take isl_pw_multi_aff *pma,
4666 __isl_take isl_set *set);
4667 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_gist_params(
4668 __isl_take isl_multi_pw_aff *mpa,
4669 __isl_take isl_set *set);
4670 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_gist(
4671 __isl_take isl_multi_pw_aff *mpa,
4672 __isl_take isl_set *set);
4673 __isl_give isl_multi_aff *isl_multi_aff_from_range(
4674 __isl_take isl_multi_aff *ma);
4675 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_from_range(
4676 __isl_take isl_multi_pw_aff *mpa);
4677 __isl_give isl_set *isl_pw_multi_aff_domain(
4678 __isl_take isl_pw_multi_aff *pma);
4679 __isl_give isl_union_set *isl_union_pw_multi_aff_domain(
4680 __isl_take isl_union_pw_multi_aff *upma);
4681 __isl_give isl_multi_aff *isl_multi_aff_range_splice(
4682 __isl_take isl_multi_aff *ma1, unsigned pos,
4683 __isl_take isl_multi_aff *ma2);
4684 __isl_give isl_multi_aff *isl_multi_aff_splice(
4685 __isl_take isl_multi_aff *ma1,
4686 unsigned in_pos, unsigned out_pos,
4687 __isl_take isl_multi_aff *ma2);
4688 __isl_give isl_multi_aff *isl_multi_aff_range_product(
4689 __isl_take isl_multi_aff *ma1,
4690 __isl_take isl_multi_aff *ma2);
4691 __isl_give isl_multi_aff *
4692 isl_multi_aff_range_factor_domain(
4693 __isl_take isl_multi_aff *ma);
4694 __isl_give isl_multi_aff *
4695 isl_multi_aff_range_factor_range(
4696 __isl_take isl_multi_aff *ma);
4697 __isl_give isl_multi_aff *isl_multi_aff_flat_range_product(
4698 __isl_take isl_multi_aff *ma1,
4699 __isl_take isl_multi_aff *ma2);
4700 __isl_give isl_multi_aff *isl_multi_aff_product(
4701 __isl_take isl_multi_aff *ma1,
4702 __isl_take isl_multi_aff *ma2);
4703 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_product(
4704 __isl_take isl_multi_pw_aff *mpa1,
4705 __isl_take isl_multi_pw_aff *mpa2);
4706 __isl_give isl_pw_multi_aff *
4707 isl_pw_multi_aff_range_product(
4708 __isl_take isl_pw_multi_aff *pma1,
4709 __isl_take isl_pw_multi_aff *pma2);
4710 __isl_give isl_multi_pw_aff *
4711 isl_multi_pw_aff_range_factor_domain(
4712 __isl_take isl_multi_pw_aff *mpa);
4713 __isl_give isl_multi_pw_aff *
4714 isl_multi_pw_aff_range_factor_range(
4715 __isl_take isl_multi_pw_aff *mpa);
4716 __isl_give isl_pw_multi_aff *
4717 isl_pw_multi_aff_flat_range_product(
4718 __isl_take isl_pw_multi_aff *pma1,
4719 __isl_take isl_pw_multi_aff *pma2);
4720 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_product(
4721 __isl_take isl_pw_multi_aff *pma1,
4722 __isl_take isl_pw_multi_aff *pma2);
4723 __isl_give isl_union_pw_multi_aff *
4724 isl_union_pw_multi_aff_flat_range_product(
4725 __isl_take isl_union_pw_multi_aff *upma1,
4726 __isl_take isl_union_pw_multi_aff *upma2);
4727 __isl_give isl_multi_pw_aff *
4728 isl_multi_pw_aff_range_splice(
4729 __isl_take isl_multi_pw_aff *mpa1, unsigned pos,
4730 __isl_take isl_multi_pw_aff *mpa2);
4731 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_splice(
4732 __isl_take isl_multi_pw_aff *mpa1,
4733 unsigned in_pos, unsigned out_pos,
4734 __isl_take isl_multi_pw_aff *mpa2);
4735 __isl_give isl_multi_pw_aff *
4736 isl_multi_pw_aff_range_product(
4737 __isl_take isl_multi_pw_aff *mpa1,
4738 __isl_take isl_multi_pw_aff *mpa2);
4739 __isl_give isl_multi_pw_aff *
4740 isl_multi_pw_aff_flat_range_product(
4741 __isl_take isl_multi_pw_aff *mpa1,
4742 __isl_take isl_multi_pw_aff *mpa2);
4744 If the C<ls> argument of C<isl_multi_aff_lift> is not C<NULL>,
4745 then it is assigned the local space that lies at the basis of
4746 the lifting applied.
4748 #include <isl/aff.h>
4749 __isl_give isl_multi_aff *isl_multi_aff_pullback_multi_aff(
4750 __isl_take isl_multi_aff *ma1,
4751 __isl_take isl_multi_aff *ma2);
4752 __isl_give isl_pw_multi_aff *
4753 isl_pw_multi_aff_pullback_multi_aff(
4754 __isl_take isl_pw_multi_aff *pma,
4755 __isl_take isl_multi_aff *ma);
4756 __isl_give isl_multi_pw_aff *
4757 isl_multi_pw_aff_pullback_multi_aff(
4758 __isl_take isl_multi_pw_aff *mpa,
4759 __isl_take isl_multi_aff *ma);
4760 __isl_give isl_pw_multi_aff *
4761 isl_pw_multi_aff_pullback_pw_multi_aff(
4762 __isl_take isl_pw_multi_aff *pma1,
4763 __isl_take isl_pw_multi_aff *pma2);
4764 __isl_give isl_multi_pw_aff *
4765 isl_multi_pw_aff_pullback_pw_multi_aff(
4766 __isl_take isl_multi_pw_aff *mpa,
4767 __isl_take isl_pw_multi_aff *pma);
4768 __isl_give isl_multi_pw_aff *
4769 isl_multi_pw_aff_pullback_multi_pw_aff(
4770 __isl_take isl_multi_pw_aff *mpa1,
4771 __isl_take isl_multi_pw_aff *mpa2);
4773 The function C<isl_multi_aff_pullback_multi_aff> precomposes C<ma1> by C<ma2>.
4774 In other words, C<ma2> is plugged
4777 __isl_give isl_set *isl_multi_aff_lex_le_set(
4778 __isl_take isl_multi_aff *ma1,
4779 __isl_take isl_multi_aff *ma2);
4780 __isl_give isl_set *isl_multi_aff_lex_ge_set(
4781 __isl_take isl_multi_aff *ma1,
4782 __isl_take isl_multi_aff *ma2);
4784 The function C<isl_multi_aff_lex_le_set> returns a set
4785 containing those elements in the shared domain space
4786 where C<ma1> is lexicographically smaller than or
4789 An expression can be read from input using
4791 #include <isl/aff.h>
4792 __isl_give isl_multi_aff *isl_multi_aff_read_from_str(
4793 isl_ctx *ctx, const char *str);
4794 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_read_from_str(
4795 isl_ctx *ctx, const char *str);
4796 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_read_from_str(
4797 isl_ctx *ctx, const char *str);
4798 __isl_give isl_union_pw_multi_aff *
4799 isl_union_pw_multi_aff_read_from_str(
4800 isl_ctx *ctx, const char *str);
4802 An expression can be printed using
4804 #include <isl/aff.h>
4805 __isl_give isl_printer *isl_printer_print_multi_aff(
4806 __isl_take isl_printer *p,
4807 __isl_keep isl_multi_aff *maff);
4808 __isl_give isl_printer *isl_printer_print_pw_multi_aff(
4809 __isl_take isl_printer *p,
4810 __isl_keep isl_pw_multi_aff *pma);
4811 __isl_give isl_printer *isl_printer_print_union_pw_multi_aff(
4812 __isl_take isl_printer *p,
4813 __isl_keep isl_union_pw_multi_aff *upma);
4814 __isl_give isl_printer *isl_printer_print_multi_pw_aff(
4815 __isl_take isl_printer *p,
4816 __isl_keep isl_multi_pw_aff *mpa);
4820 Points are elements of a set. They can be used to construct
4821 simple sets (boxes) or they can be used to represent the
4822 individual elements of a set.
4823 The zero point (the origin) can be created using
4825 __isl_give isl_point *isl_point_zero(__isl_take isl_space *space);
4827 The coordinates of a point can be inspected, set and changed
4830 __isl_give isl_val *isl_point_get_coordinate_val(
4831 __isl_keep isl_point *pnt,
4832 enum isl_dim_type type, int pos);
4833 __isl_give isl_point *isl_point_set_coordinate_val(
4834 __isl_take isl_point *pnt,
4835 enum isl_dim_type type, int pos,
4836 __isl_take isl_val *v);
4838 __isl_give isl_point *isl_point_add_ui(
4839 __isl_take isl_point *pnt,
4840 enum isl_dim_type type, int pos, unsigned val);
4841 __isl_give isl_point *isl_point_sub_ui(
4842 __isl_take isl_point *pnt,
4843 enum isl_dim_type type, int pos, unsigned val);
4845 Other properties can be obtained using
4847 isl_ctx *isl_point_get_ctx(__isl_keep isl_point *pnt);
4849 Points can be copied or freed using
4851 __isl_give isl_point *isl_point_copy(
4852 __isl_keep isl_point *pnt);
4853 void isl_point_free(__isl_take isl_point *pnt);
4855 A singleton set can be created from a point using
4857 __isl_give isl_basic_set *isl_basic_set_from_point(
4858 __isl_take isl_point *pnt);
4859 __isl_give isl_set *isl_set_from_point(
4860 __isl_take isl_point *pnt);
4862 and a box can be created from two opposite extremal points using
4864 __isl_give isl_basic_set *isl_basic_set_box_from_points(
4865 __isl_take isl_point *pnt1,
4866 __isl_take isl_point *pnt2);
4867 __isl_give isl_set *isl_set_box_from_points(
4868 __isl_take isl_point *pnt1,
4869 __isl_take isl_point *pnt2);
4871 All elements of a B<bounded> (union) set can be enumerated using
4872 the following functions.
4874 int isl_set_foreach_point(__isl_keep isl_set *set,
4875 int (*fn)(__isl_take isl_point *pnt, void *user),
4877 int isl_union_set_foreach_point(__isl_keep isl_union_set *uset,
4878 int (*fn)(__isl_take isl_point *pnt, void *user),
4881 The function C<fn> is called for each integer point in
4882 C<set> with as second argument the last argument of
4883 the C<isl_set_foreach_point> call. The function C<fn>
4884 should return C<0> on success and C<-1> on failure.
4885 In the latter case, C<isl_set_foreach_point> will stop
4886 enumerating and return C<-1> as well.
4887 If the enumeration is performed successfully and to completion,
4888 then C<isl_set_foreach_point> returns C<0>.
4890 To obtain a single point of a (basic) set, use
4892 __isl_give isl_point *isl_basic_set_sample_point(
4893 __isl_take isl_basic_set *bset);
4894 __isl_give isl_point *isl_set_sample_point(
4895 __isl_take isl_set *set);
4897 If C<set> does not contain any (integer) points, then the
4898 resulting point will be ``void'', a property that can be
4901 int isl_point_is_void(__isl_keep isl_point *pnt);
4903 =head2 Piecewise Quasipolynomials
4905 A piecewise quasipolynomial is a particular kind of function that maps
4906 a parametric point to a rational value.
4907 More specifically, a quasipolynomial is a polynomial expression in greatest
4908 integer parts of affine expressions of parameters and variables.
4909 A piecewise quasipolynomial is a subdivision of a given parametric
4910 domain into disjoint cells with a quasipolynomial associated to
4911 each cell. The value of the piecewise quasipolynomial at a given
4912 point is the value of the quasipolynomial associated to the cell
4913 that contains the point. Outside of the union of cells,
4914 the value is assumed to be zero.
4915 For example, the piecewise quasipolynomial
4917 [n] -> { [x] -> ((1 + n) - x) : x <= n and x >= 0 }
4919 maps C<x> to C<1 + n - x> for values of C<x> between C<0> and C<n>.
4920 A given piecewise quasipolynomial has a fixed domain dimension.
4921 Union piecewise quasipolynomials are used to contain piecewise quasipolynomials
4922 defined over different domains.
4923 Piecewise quasipolynomials are mainly used by the C<barvinok>
4924 library for representing the number of elements in a parametric set or map.
4925 For example, the piecewise quasipolynomial above represents
4926 the number of points in the map
4928 [n] -> { [x] -> [y] : x,y >= 0 and 0 <= x + y <= n }
4930 =head3 Input and Output
4932 Piecewise quasipolynomials can be read from input using
4934 __isl_give isl_union_pw_qpolynomial *
4935 isl_union_pw_qpolynomial_read_from_str(
4936 isl_ctx *ctx, const char *str);
4938 Quasipolynomials and piecewise quasipolynomials can be printed
4939 using the following functions.
4941 __isl_give isl_printer *isl_printer_print_qpolynomial(
4942 __isl_take isl_printer *p,
4943 __isl_keep isl_qpolynomial *qp);
4945 __isl_give isl_printer *isl_printer_print_pw_qpolynomial(
4946 __isl_take isl_printer *p,
4947 __isl_keep isl_pw_qpolynomial *pwqp);
4949 __isl_give isl_printer *isl_printer_print_union_pw_qpolynomial(
4950 __isl_take isl_printer *p,
4951 __isl_keep isl_union_pw_qpolynomial *upwqp);
4953 The output format of the printer
4954 needs to be set to either C<ISL_FORMAT_ISL> or C<ISL_FORMAT_C>.
4955 For C<isl_printer_print_union_pw_qpolynomial>, only C<ISL_FORMAT_ISL>
4957 In case of printing in C<ISL_FORMAT_C>, the user may want
4958 to set the names of all dimensions
4960 __isl_give isl_qpolynomial *isl_qpolynomial_set_dim_name(
4961 __isl_take isl_qpolynomial *qp,
4962 enum isl_dim_type type, unsigned pos,
4964 __isl_give isl_pw_qpolynomial *
4965 isl_pw_qpolynomial_set_dim_name(
4966 __isl_take isl_pw_qpolynomial *pwqp,
4967 enum isl_dim_type type, unsigned pos,
4970 =head3 Creating New (Piecewise) Quasipolynomials
4972 Some simple quasipolynomials can be created using the following functions.
4973 More complicated quasipolynomials can be created by applying
4974 operations such as addition and multiplication
4975 on the resulting quasipolynomials
4977 __isl_give isl_qpolynomial *isl_qpolynomial_zero_on_domain(
4978 __isl_take isl_space *domain);
4979 __isl_give isl_qpolynomial *isl_qpolynomial_one_on_domain(
4980 __isl_take isl_space *domain);
4981 __isl_give isl_qpolynomial *isl_qpolynomial_infty_on_domain(
4982 __isl_take isl_space *domain);
4983 __isl_give isl_qpolynomial *isl_qpolynomial_neginfty_on_domain(
4984 __isl_take isl_space *domain);
4985 __isl_give isl_qpolynomial *isl_qpolynomial_nan_on_domain(
4986 __isl_take isl_space *domain);
4987 __isl_give isl_qpolynomial *isl_qpolynomial_val_on_domain(
4988 __isl_take isl_space *domain,
4989 __isl_take isl_val *val);
4990 __isl_give isl_qpolynomial *isl_qpolynomial_var_on_domain(
4991 __isl_take isl_space *domain,
4992 enum isl_dim_type type, unsigned pos);
4993 __isl_give isl_qpolynomial *isl_qpolynomial_from_aff(
4994 __isl_take isl_aff *aff);
4996 Note that the space in which a quasipolynomial lives is a map space
4997 with a one-dimensional range. The C<domain> argument in some of
4998 the functions above corresponds to the domain of this map space.
5000 The zero piecewise quasipolynomial or a piecewise quasipolynomial
5001 with a single cell can be created using the following functions.
5002 Multiple of these single cell piecewise quasipolynomials can
5003 be combined to create more complicated piecewise quasipolynomials.
5005 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_zero(
5006 __isl_take isl_space *space);
5007 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_alloc(
5008 __isl_take isl_set *set,
5009 __isl_take isl_qpolynomial *qp);
5010 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_from_qpolynomial(
5011 __isl_take isl_qpolynomial *qp);
5012 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_from_pw_aff(
5013 __isl_take isl_pw_aff *pwaff);
5015 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_zero(
5016 __isl_take isl_space *space);
5017 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_from_pw_qpolynomial(
5018 __isl_take isl_pw_qpolynomial *pwqp);
5019 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_add_pw_qpolynomial(
5020 __isl_take isl_union_pw_qpolynomial *upwqp,
5021 __isl_take isl_pw_qpolynomial *pwqp);
5023 Quasipolynomials can be copied and freed again using the following
5026 __isl_give isl_qpolynomial *isl_qpolynomial_copy(
5027 __isl_keep isl_qpolynomial *qp);
5028 void *isl_qpolynomial_free(__isl_take isl_qpolynomial *qp);
5030 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_copy(
5031 __isl_keep isl_pw_qpolynomial *pwqp);
5032 void *isl_pw_qpolynomial_free(
5033 __isl_take isl_pw_qpolynomial *pwqp);
5035 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_copy(
5036 __isl_keep isl_union_pw_qpolynomial *upwqp);
5037 void *isl_union_pw_qpolynomial_free(
5038 __isl_take isl_union_pw_qpolynomial *upwqp);
5040 =head3 Inspecting (Piecewise) Quasipolynomials
5042 To iterate over all piecewise quasipolynomials in a union
5043 piecewise quasipolynomial, use the following function
5045 int isl_union_pw_qpolynomial_foreach_pw_qpolynomial(
5046 __isl_keep isl_union_pw_qpolynomial *upwqp,
5047 int (*fn)(__isl_take isl_pw_qpolynomial *pwqp, void *user),
5050 To extract the piecewise quasipolynomial in a given space from a union, use
5052 __isl_give isl_pw_qpolynomial *
5053 isl_union_pw_qpolynomial_extract_pw_qpolynomial(
5054 __isl_keep isl_union_pw_qpolynomial *upwqp,
5055 __isl_take isl_space *space);
5057 To iterate over the cells in a piecewise quasipolynomial,
5058 use either of the following two functions
5060 int isl_pw_qpolynomial_foreach_piece(
5061 __isl_keep isl_pw_qpolynomial *pwqp,
5062 int (*fn)(__isl_take isl_set *set,
5063 __isl_take isl_qpolynomial *qp,
5064 void *user), void *user);
5065 int isl_pw_qpolynomial_foreach_lifted_piece(
5066 __isl_keep isl_pw_qpolynomial *pwqp,
5067 int (*fn)(__isl_take isl_set *set,
5068 __isl_take isl_qpolynomial *qp,
5069 void *user), void *user);
5071 As usual, the function C<fn> should return C<0> on success
5072 and C<-1> on failure. The difference between
5073 C<isl_pw_qpolynomial_foreach_piece> and
5074 C<isl_pw_qpolynomial_foreach_lifted_piece> is that
5075 C<isl_pw_qpolynomial_foreach_lifted_piece> will first
5076 compute unique representations for all existentially quantified
5077 variables and then turn these existentially quantified variables
5078 into extra set variables, adapting the associated quasipolynomial
5079 accordingly. This means that the C<set> passed to C<fn>
5080 will not have any existentially quantified variables, but that
5081 the dimensions of the sets may be different for different
5082 invocations of C<fn>.
5084 The constant term of a quasipolynomial can be extracted using
5086 __isl_give isl_val *isl_qpolynomial_get_constant_val(
5087 __isl_keep isl_qpolynomial *qp);
5089 To iterate over all terms in a quasipolynomial,
5092 int isl_qpolynomial_foreach_term(
5093 __isl_keep isl_qpolynomial *qp,
5094 int (*fn)(__isl_take isl_term *term,
5095 void *user), void *user);
5097 The terms themselves can be inspected and freed using
5100 unsigned isl_term_dim(__isl_keep isl_term *term,
5101 enum isl_dim_type type);
5102 __isl_give isl_val *isl_term_get_coefficient_val(
5103 __isl_keep isl_term *term);
5104 int isl_term_get_exp(__isl_keep isl_term *term,
5105 enum isl_dim_type type, unsigned pos);
5106 __isl_give isl_aff *isl_term_get_div(
5107 __isl_keep isl_term *term, unsigned pos);
5108 void isl_term_free(__isl_take isl_term *term);
5110 Each term is a product of parameters, set variables and
5111 integer divisions. The function C<isl_term_get_exp>
5112 returns the exponent of a given dimensions in the given term.
5114 =head3 Properties of (Piecewise) Quasipolynomials
5116 To check whether two union piecewise quasipolynomials are
5117 obviously equal, use
5119 int isl_union_pw_qpolynomial_plain_is_equal(
5120 __isl_keep isl_union_pw_qpolynomial *upwqp1,
5121 __isl_keep isl_union_pw_qpolynomial *upwqp2);
5123 =head3 Operations on (Piecewise) Quasipolynomials
5125 __isl_give isl_qpolynomial *isl_qpolynomial_scale_val(
5126 __isl_take isl_qpolynomial *qp,
5127 __isl_take isl_val *v);
5128 __isl_give isl_qpolynomial *isl_qpolynomial_neg(
5129 __isl_take isl_qpolynomial *qp);
5130 __isl_give isl_qpolynomial *isl_qpolynomial_add(
5131 __isl_take isl_qpolynomial *qp1,
5132 __isl_take isl_qpolynomial *qp2);
5133 __isl_give isl_qpolynomial *isl_qpolynomial_sub(
5134 __isl_take isl_qpolynomial *qp1,
5135 __isl_take isl_qpolynomial *qp2);
5136 __isl_give isl_qpolynomial *isl_qpolynomial_mul(
5137 __isl_take isl_qpolynomial *qp1,
5138 __isl_take isl_qpolynomial *qp2);
5139 __isl_give isl_qpolynomial *isl_qpolynomial_pow(
5140 __isl_take isl_qpolynomial *qp, unsigned exponent);
5142 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_fix_val(
5143 __isl_take isl_pw_qpolynomial *pwqp,
5144 enum isl_dim_type type, unsigned n,
5145 __isl_take isl_val *v);
5146 __isl_give isl_pw_qpolynomial *
5147 isl_pw_qpolynomial_scale_val(
5148 __isl_take isl_pw_qpolynomial *pwqp,
5149 __isl_take isl_val *v);
5150 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_add(
5151 __isl_take isl_pw_qpolynomial *pwqp1,
5152 __isl_take isl_pw_qpolynomial *pwqp2);
5153 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_sub(
5154 __isl_take isl_pw_qpolynomial *pwqp1,
5155 __isl_take isl_pw_qpolynomial *pwqp2);
5156 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_add_disjoint(
5157 __isl_take isl_pw_qpolynomial *pwqp1,
5158 __isl_take isl_pw_qpolynomial *pwqp2);
5159 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_neg(
5160 __isl_take isl_pw_qpolynomial *pwqp);
5161 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_mul(
5162 __isl_take isl_pw_qpolynomial *pwqp1,
5163 __isl_take isl_pw_qpolynomial *pwqp2);
5164 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_pow(
5165 __isl_take isl_pw_qpolynomial *pwqp, unsigned exponent);
5167 __isl_give isl_union_pw_qpolynomial *
5168 isl_union_pw_qpolynomial_scale_val(
5169 __isl_take isl_union_pw_qpolynomial *upwqp,
5170 __isl_take isl_val *v);
5171 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_add(
5172 __isl_take isl_union_pw_qpolynomial *upwqp1,
5173 __isl_take isl_union_pw_qpolynomial *upwqp2);
5174 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_sub(
5175 __isl_take isl_union_pw_qpolynomial *upwqp1,
5176 __isl_take isl_union_pw_qpolynomial *upwqp2);
5177 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_mul(
5178 __isl_take isl_union_pw_qpolynomial *upwqp1,
5179 __isl_take isl_union_pw_qpolynomial *upwqp2);
5181 __isl_give isl_val *isl_pw_qpolynomial_eval(
5182 __isl_take isl_pw_qpolynomial *pwqp,
5183 __isl_take isl_point *pnt);
5185 __isl_give isl_val *isl_union_pw_qpolynomial_eval(
5186 __isl_take isl_union_pw_qpolynomial *upwqp,
5187 __isl_take isl_point *pnt);
5189 __isl_give isl_set *isl_pw_qpolynomial_domain(
5190 __isl_take isl_pw_qpolynomial *pwqp);
5191 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_intersect_domain(
5192 __isl_take isl_pw_qpolynomial *pwpq,
5193 __isl_take isl_set *set);
5194 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_intersect_params(
5195 __isl_take isl_pw_qpolynomial *pwpq,
5196 __isl_take isl_set *set);
5198 __isl_give isl_union_set *isl_union_pw_qpolynomial_domain(
5199 __isl_take isl_union_pw_qpolynomial *upwqp);
5200 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_intersect_domain(
5201 __isl_take isl_union_pw_qpolynomial *upwpq,
5202 __isl_take isl_union_set *uset);
5203 __isl_give isl_union_pw_qpolynomial *
5204 isl_union_pw_qpolynomial_intersect_params(
5205 __isl_take isl_union_pw_qpolynomial *upwpq,
5206 __isl_take isl_set *set);
5208 __isl_give isl_qpolynomial *isl_qpolynomial_align_params(
5209 __isl_take isl_qpolynomial *qp,
5210 __isl_take isl_space *model);
5212 __isl_give isl_qpolynomial *isl_qpolynomial_project_domain_on_params(
5213 __isl_take isl_qpolynomial *qp);
5214 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_project_domain_on_params(
5215 __isl_take isl_pw_qpolynomial *pwqp);
5217 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_coalesce(
5218 __isl_take isl_union_pw_qpolynomial *upwqp);
5220 __isl_give isl_qpolynomial *isl_qpolynomial_gist_params(
5221 __isl_take isl_qpolynomial *qp,
5222 __isl_take isl_set *context);
5223 __isl_give isl_qpolynomial *isl_qpolynomial_gist(
5224 __isl_take isl_qpolynomial *qp,
5225 __isl_take isl_set *context);
5227 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_gist_params(
5228 __isl_take isl_pw_qpolynomial *pwqp,
5229 __isl_take isl_set *context);
5230 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_gist(
5231 __isl_take isl_pw_qpolynomial *pwqp,
5232 __isl_take isl_set *context);
5234 __isl_give isl_union_pw_qpolynomial *
5235 isl_union_pw_qpolynomial_gist_params(
5236 __isl_take isl_union_pw_qpolynomial *upwqp,
5237 __isl_take isl_set *context);
5238 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_gist(
5239 __isl_take isl_union_pw_qpolynomial *upwqp,
5240 __isl_take isl_union_set *context);
5242 The gist operation applies the gist operation to each of
5243 the cells in the domain of the input piecewise quasipolynomial.
5244 The context is also exploited
5245 to simplify the quasipolynomials associated to each cell.
5247 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_to_polynomial(
5248 __isl_take isl_pw_qpolynomial *pwqp, int sign);
5249 __isl_give isl_union_pw_qpolynomial *
5250 isl_union_pw_qpolynomial_to_polynomial(
5251 __isl_take isl_union_pw_qpolynomial *upwqp, int sign);
5253 Approximate each quasipolynomial by a polynomial. If C<sign> is positive,
5254 the polynomial will be an overapproximation. If C<sign> is negative,
5255 it will be an underapproximation. If C<sign> is zero, the approximation
5256 will lie somewhere in between.
5258 =head2 Bounds on Piecewise Quasipolynomials and Piecewise Quasipolynomial Reductions
5260 A piecewise quasipolynomial reduction is a piecewise
5261 reduction (or fold) of quasipolynomials.
5262 In particular, the reduction can be maximum or a minimum.
5263 The objects are mainly used to represent the result of
5264 an upper or lower bound on a quasipolynomial over its domain,
5265 i.e., as the result of the following function.
5267 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_bound(
5268 __isl_take isl_pw_qpolynomial *pwqp,
5269 enum isl_fold type, int *tight);
5271 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_bound(
5272 __isl_take isl_union_pw_qpolynomial *upwqp,
5273 enum isl_fold type, int *tight);
5275 The C<type> argument may be either C<isl_fold_min> or C<isl_fold_max>.
5276 If C<tight> is not C<NULL>, then C<*tight> is set to C<1>
5277 is the returned bound is known be tight, i.e., for each value
5278 of the parameters there is at least
5279 one element in the domain that reaches the bound.
5280 If the domain of C<pwqp> is not wrapping, then the bound is computed
5281 over all elements in that domain and the result has a purely parametric
5282 domain. If the domain of C<pwqp> is wrapping, then the bound is
5283 computed over the range of the wrapped relation. The domain of the
5284 wrapped relation becomes the domain of the result.
5286 A (piecewise) quasipolynomial reduction can be copied or freed using the
5287 following functions.
5289 __isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_copy(
5290 __isl_keep isl_qpolynomial_fold *fold);
5291 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_copy(
5292 __isl_keep isl_pw_qpolynomial_fold *pwf);
5293 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_copy(
5294 __isl_keep isl_union_pw_qpolynomial_fold *upwf);
5295 void isl_qpolynomial_fold_free(
5296 __isl_take isl_qpolynomial_fold *fold);
5297 void *isl_pw_qpolynomial_fold_free(
5298 __isl_take isl_pw_qpolynomial_fold *pwf);
5299 void *isl_union_pw_qpolynomial_fold_free(
5300 __isl_take isl_union_pw_qpolynomial_fold *upwf);
5302 =head3 Printing Piecewise Quasipolynomial Reductions
5304 Piecewise quasipolynomial reductions can be printed
5305 using the following function.
5307 __isl_give isl_printer *isl_printer_print_pw_qpolynomial_fold(
5308 __isl_take isl_printer *p,
5309 __isl_keep isl_pw_qpolynomial_fold *pwf);
5310 __isl_give isl_printer *isl_printer_print_union_pw_qpolynomial_fold(
5311 __isl_take isl_printer *p,
5312 __isl_keep isl_union_pw_qpolynomial_fold *upwf);
5314 For C<isl_printer_print_pw_qpolynomial_fold>,
5315 output format of the printer
5316 needs to be set to either C<ISL_FORMAT_ISL> or C<ISL_FORMAT_C>.
5317 For C<isl_printer_print_union_pw_qpolynomial_fold>,
5318 output format of the printer
5319 needs to be set to C<ISL_FORMAT_ISL>.
5320 In case of printing in C<ISL_FORMAT_C>, the user may want
5321 to set the names of all dimensions
5323 __isl_give isl_pw_qpolynomial_fold *
5324 isl_pw_qpolynomial_fold_set_dim_name(
5325 __isl_take isl_pw_qpolynomial_fold *pwf,
5326 enum isl_dim_type type, unsigned pos,
5329 =head3 Inspecting (Piecewise) Quasipolynomial Reductions
5331 To iterate over all piecewise quasipolynomial reductions in a union
5332 piecewise quasipolynomial reduction, use the following function
5334 int isl_union_pw_qpolynomial_fold_foreach_pw_qpolynomial_fold(
5335 __isl_keep isl_union_pw_qpolynomial_fold *upwf,
5336 int (*fn)(__isl_take isl_pw_qpolynomial_fold *pwf,
5337 void *user), void *user);
5339 To iterate over the cells in a piecewise quasipolynomial reduction,
5340 use either of the following two functions
5342 int isl_pw_qpolynomial_fold_foreach_piece(
5343 __isl_keep isl_pw_qpolynomial_fold *pwf,
5344 int (*fn)(__isl_take isl_set *set,
5345 __isl_take isl_qpolynomial_fold *fold,
5346 void *user), void *user);
5347 int isl_pw_qpolynomial_fold_foreach_lifted_piece(
5348 __isl_keep isl_pw_qpolynomial_fold *pwf,
5349 int (*fn)(__isl_take isl_set *set,
5350 __isl_take isl_qpolynomial_fold *fold,
5351 void *user), void *user);
5353 See L<Inspecting (Piecewise) Quasipolynomials> for an explanation
5354 of the difference between these two functions.
5356 To iterate over all quasipolynomials in a reduction, use
5358 int isl_qpolynomial_fold_foreach_qpolynomial(
5359 __isl_keep isl_qpolynomial_fold *fold,
5360 int (*fn)(__isl_take isl_qpolynomial *qp,
5361 void *user), void *user);
5363 =head3 Properties of Piecewise Quasipolynomial Reductions
5365 To check whether two union piecewise quasipolynomial reductions are
5366 obviously equal, use
5368 int isl_union_pw_qpolynomial_fold_plain_is_equal(
5369 __isl_keep isl_union_pw_qpolynomial_fold *upwf1,
5370 __isl_keep isl_union_pw_qpolynomial_fold *upwf2);
5372 =head3 Operations on Piecewise Quasipolynomial Reductions
5374 __isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_scale_val(
5375 __isl_take isl_qpolynomial_fold *fold,
5376 __isl_take isl_val *v);
5377 __isl_give isl_pw_qpolynomial_fold *
5378 isl_pw_qpolynomial_fold_scale_val(
5379 __isl_take isl_pw_qpolynomial_fold *pwf,
5380 __isl_take isl_val *v);
5381 __isl_give isl_union_pw_qpolynomial_fold *
5382 isl_union_pw_qpolynomial_fold_scale_val(
5383 __isl_take isl_union_pw_qpolynomial_fold *upwf,
5384 __isl_take isl_val *v);
5386 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_add(
5387 __isl_take isl_pw_qpolynomial_fold *pwf1,
5388 __isl_take isl_pw_qpolynomial_fold *pwf2);
5390 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_fold(
5391 __isl_take isl_pw_qpolynomial_fold *pwf1,
5392 __isl_take isl_pw_qpolynomial_fold *pwf2);
5394 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_fold(
5395 __isl_take isl_union_pw_qpolynomial_fold *upwf1,
5396 __isl_take isl_union_pw_qpolynomial_fold *upwf2);
5398 __isl_give isl_val *isl_pw_qpolynomial_fold_eval(
5399 __isl_take isl_pw_qpolynomial_fold *pwf,
5400 __isl_take isl_point *pnt);
5402 __isl_give isl_val *isl_union_pw_qpolynomial_fold_eval(
5403 __isl_take isl_union_pw_qpolynomial_fold *upwf,
5404 __isl_take isl_point *pnt);
5406 __isl_give isl_pw_qpolynomial_fold *
5407 isl_pw_qpolynomial_fold_intersect_params(
5408 __isl_take isl_pw_qpolynomial_fold *pwf,
5409 __isl_take isl_set *set);
5411 __isl_give isl_union_set *isl_union_pw_qpolynomial_fold_domain(
5412 __isl_take isl_union_pw_qpolynomial_fold *upwf);
5413 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_intersect_domain(
5414 __isl_take isl_union_pw_qpolynomial_fold *upwf,
5415 __isl_take isl_union_set *uset);
5416 __isl_give isl_union_pw_qpolynomial_fold *
5417 isl_union_pw_qpolynomial_fold_intersect_params(
5418 __isl_take isl_union_pw_qpolynomial_fold *upwf,
5419 __isl_take isl_set *set);
5421 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_project_domain_on_params(
5422 __isl_take isl_pw_qpolynomial_fold *pwf);
5424 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_coalesce(
5425 __isl_take isl_pw_qpolynomial_fold *pwf);
5427 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_coalesce(
5428 __isl_take isl_union_pw_qpolynomial_fold *upwf);
5430 __isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_gist_params(
5431 __isl_take isl_qpolynomial_fold *fold,
5432 __isl_take isl_set *context);
5433 __isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_gist(
5434 __isl_take isl_qpolynomial_fold *fold,
5435 __isl_take isl_set *context);
5437 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_gist(
5438 __isl_take isl_pw_qpolynomial_fold *pwf,
5439 __isl_take isl_set *context);
5440 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_gist_params(
5441 __isl_take isl_pw_qpolynomial_fold *pwf,
5442 __isl_take isl_set *context);
5444 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_gist(
5445 __isl_take isl_union_pw_qpolynomial_fold *upwf,
5446 __isl_take isl_union_set *context);
5447 __isl_give isl_union_pw_qpolynomial_fold *
5448 isl_union_pw_qpolynomial_fold_gist_params(
5449 __isl_take isl_union_pw_qpolynomial_fold *upwf,
5450 __isl_take isl_set *context);
5452 The gist operation applies the gist operation to each of
5453 the cells in the domain of the input piecewise quasipolynomial reduction.
5454 In future, the operation will also exploit the context
5455 to simplify the quasipolynomial reductions associated to each cell.
5457 __isl_give isl_pw_qpolynomial_fold *
5458 isl_set_apply_pw_qpolynomial_fold(
5459 __isl_take isl_set *set,
5460 __isl_take isl_pw_qpolynomial_fold *pwf,
5462 __isl_give isl_pw_qpolynomial_fold *
5463 isl_map_apply_pw_qpolynomial_fold(
5464 __isl_take isl_map *map,
5465 __isl_take isl_pw_qpolynomial_fold *pwf,
5467 __isl_give isl_union_pw_qpolynomial_fold *
5468 isl_union_set_apply_union_pw_qpolynomial_fold(
5469 __isl_take isl_union_set *uset,
5470 __isl_take isl_union_pw_qpolynomial_fold *upwf,
5472 __isl_give isl_union_pw_qpolynomial_fold *
5473 isl_union_map_apply_union_pw_qpolynomial_fold(
5474 __isl_take isl_union_map *umap,
5475 __isl_take isl_union_pw_qpolynomial_fold *upwf,
5478 The functions taking a map
5479 compose the given map with the given piecewise quasipolynomial reduction.
5480 That is, compute a bound (of the same type as C<pwf> or C<upwf> itself)
5481 over all elements in the intersection of the range of the map
5482 and the domain of the piecewise quasipolynomial reduction
5483 as a function of an element in the domain of the map.
5484 The functions taking a set compute a bound over all elements in the
5485 intersection of the set and the domain of the
5486 piecewise quasipolynomial reduction.
5488 =head2 Parametric Vertex Enumeration
5490 The parametric vertex enumeration described in this section
5491 is mainly intended to be used internally and by the C<barvinok>
5494 #include <isl/vertices.h>
5495 __isl_give isl_vertices *isl_basic_set_compute_vertices(
5496 __isl_keep isl_basic_set *bset);
5498 The function C<isl_basic_set_compute_vertices> performs the
5499 actual computation of the parametric vertices and the chamber
5500 decomposition and store the result in an C<isl_vertices> object.
5501 This information can be queried by either iterating over all
5502 the vertices or iterating over all the chambers or cells
5503 and then iterating over all vertices that are active on the chamber.
5505 int isl_vertices_foreach_vertex(
5506 __isl_keep isl_vertices *vertices,
5507 int (*fn)(__isl_take isl_vertex *vertex, void *user),
5510 int isl_vertices_foreach_cell(
5511 __isl_keep isl_vertices *vertices,
5512 int (*fn)(__isl_take isl_cell *cell, void *user),
5514 int isl_cell_foreach_vertex(__isl_keep isl_cell *cell,
5515 int (*fn)(__isl_take isl_vertex *vertex, void *user),
5518 Other operations that can be performed on an C<isl_vertices> object are
5521 isl_ctx *isl_vertices_get_ctx(
5522 __isl_keep isl_vertices *vertices);
5523 int isl_vertices_get_n_vertices(
5524 __isl_keep isl_vertices *vertices);
5525 void isl_vertices_free(__isl_take isl_vertices *vertices);
5527 Vertices can be inspected and destroyed using the following functions.
5529 isl_ctx *isl_vertex_get_ctx(__isl_keep isl_vertex *vertex);
5530 int isl_vertex_get_id(__isl_keep isl_vertex *vertex);
5531 __isl_give isl_basic_set *isl_vertex_get_domain(
5532 __isl_keep isl_vertex *vertex);
5533 __isl_give isl_basic_set *isl_vertex_get_expr(
5534 __isl_keep isl_vertex *vertex);
5535 void isl_vertex_free(__isl_take isl_vertex *vertex);
5537 C<isl_vertex_get_expr> returns a singleton parametric set describing
5538 the vertex, while C<isl_vertex_get_domain> returns the activity domain
5540 Note that C<isl_vertex_get_domain> and C<isl_vertex_get_expr> return
5541 B<rational> basic sets, so they should mainly be used for inspection
5542 and should not be mixed with integer sets.
5544 Chambers can be inspected and destroyed using the following functions.
5546 isl_ctx *isl_cell_get_ctx(__isl_keep isl_cell *cell);
5547 __isl_give isl_basic_set *isl_cell_get_domain(
5548 __isl_keep isl_cell *cell);
5549 void isl_cell_free(__isl_take isl_cell *cell);
5551 =head1 Polyhedral Compilation Library
5553 This section collects functionality in C<isl> that has been specifically
5554 designed for use during polyhedral compilation.
5556 =head2 Dependence Analysis
5558 C<isl> contains specialized functionality for performing
5559 array dataflow analysis. That is, given a I<sink> access relation
5560 and a collection of possible I<source> access relations,
5561 C<isl> can compute relations that describe
5562 for each iteration of the sink access, which iteration
5563 of which of the source access relations was the last
5564 to access the same data element before the given iteration
5566 The resulting dependence relations map source iterations
5567 to the corresponding sink iterations.
5568 To compute standard flow dependences, the sink should be
5569 a read, while the sources should be writes.
5570 If any of the source accesses are marked as being I<may>
5571 accesses, then there will be a dependence from the last
5572 I<must> access B<and> from any I<may> access that follows
5573 this last I<must> access.
5574 In particular, if I<all> sources are I<may> accesses,
5575 then memory based dependence analysis is performed.
5576 If, on the other hand, all sources are I<must> accesses,
5577 then value based dependence analysis is performed.
5579 #include <isl/flow.h>
5581 typedef int (*isl_access_level_before)(void *first, void *second);
5583 __isl_give isl_access_info *isl_access_info_alloc(
5584 __isl_take isl_map *sink,
5585 void *sink_user, isl_access_level_before fn,
5587 __isl_give isl_access_info *isl_access_info_add_source(
5588 __isl_take isl_access_info *acc,
5589 __isl_take isl_map *source, int must,
5591 void *isl_access_info_free(__isl_take isl_access_info *acc);
5593 __isl_give isl_flow *isl_access_info_compute_flow(
5594 __isl_take isl_access_info *acc);
5596 int isl_flow_foreach(__isl_keep isl_flow *deps,
5597 int (*fn)(__isl_take isl_map *dep, int must,
5598 void *dep_user, void *user),
5600 __isl_give isl_map *isl_flow_get_no_source(
5601 __isl_keep isl_flow *deps, int must);
5602 void isl_flow_free(__isl_take isl_flow *deps);
5604 The function C<isl_access_info_compute_flow> performs the actual
5605 dependence analysis. The other functions are used to construct
5606 the input for this function or to read off the output.
5608 The input is collected in an C<isl_access_info>, which can
5609 be created through a call to C<isl_access_info_alloc>.
5610 The arguments to this functions are the sink access relation
5611 C<sink>, a token C<sink_user> used to identify the sink
5612 access to the user, a callback function for specifying the
5613 relative order of source and sink accesses, and the number
5614 of source access relations that will be added.
5615 The callback function has type C<int (*)(void *first, void *second)>.
5616 The function is called with two user supplied tokens identifying
5617 either a source or the sink and it should return the shared nesting
5618 level and the relative order of the two accesses.
5619 In particular, let I<n> be the number of loops shared by
5620 the two accesses. If C<first> precedes C<second> textually,
5621 then the function should return I<2 * n + 1>; otherwise,
5622 it should return I<2 * n>.
5623 The sources can be added to the C<isl_access_info> by performing
5624 (at most) C<max_source> calls to C<isl_access_info_add_source>.
5625 C<must> indicates whether the source is a I<must> access
5626 or a I<may> access. Note that a multi-valued access relation
5627 should only be marked I<must> if every iteration in the domain
5628 of the relation accesses I<all> elements in its image.
5629 The C<source_user> token is again used to identify
5630 the source access. The range of the source access relation
5631 C<source> should have the same dimension as the range
5632 of the sink access relation.
5633 The C<isl_access_info_free> function should usually not be
5634 called explicitly, because it is called implicitly by
5635 C<isl_access_info_compute_flow>.
5637 The result of the dependence analysis is collected in an
5638 C<isl_flow>. There may be elements of
5639 the sink access for which no preceding source access could be
5640 found or for which all preceding sources are I<may> accesses.
5641 The relations containing these elements can be obtained through
5642 calls to C<isl_flow_get_no_source>, the first with C<must> set
5643 and the second with C<must> unset.
5644 In the case of standard flow dependence analysis,
5645 with the sink a read and the sources I<must> writes,
5646 the first relation corresponds to the reads from uninitialized
5647 array elements and the second relation is empty.
5648 The actual flow dependences can be extracted using
5649 C<isl_flow_foreach>. This function will call the user-specified
5650 callback function C<fn> for each B<non-empty> dependence between
5651 a source and the sink. The callback function is called
5652 with four arguments, the actual flow dependence relation
5653 mapping source iterations to sink iterations, a boolean that
5654 indicates whether it is a I<must> or I<may> dependence, a token
5655 identifying the source and an additional C<void *> with value
5656 equal to the third argument of the C<isl_flow_foreach> call.
5657 A dependence is marked I<must> if it originates from a I<must>
5658 source and if it is not followed by any I<may> sources.
5660 After finishing with an C<isl_flow>, the user should call
5661 C<isl_flow_free> to free all associated memory.
5663 A higher-level interface to dependence analysis is provided
5664 by the following function.
5666 #include <isl/flow.h>
5668 int isl_union_map_compute_flow(__isl_take isl_union_map *sink,
5669 __isl_take isl_union_map *must_source,
5670 __isl_take isl_union_map *may_source,
5671 __isl_take isl_union_map *schedule,
5672 __isl_give isl_union_map **must_dep,
5673 __isl_give isl_union_map **may_dep,
5674 __isl_give isl_union_map **must_no_source,
5675 __isl_give isl_union_map **may_no_source);
5677 The arrays are identified by the tuple names of the ranges
5678 of the accesses. The iteration domains by the tuple names
5679 of the domains of the accesses and of the schedule.
5680 The relative order of the iteration domains is given by the
5681 schedule. The relations returned through C<must_no_source>
5682 and C<may_no_source> are subsets of C<sink>.
5683 Any of C<must_dep>, C<may_dep>, C<must_no_source>
5684 or C<may_no_source> may be C<NULL>, but a C<NULL> value for
5685 any of the other arguments is treated as an error.
5687 =head3 Interaction with Dependence Analysis
5689 During the dependence analysis, we frequently need to perform
5690 the following operation. Given a relation between sink iterations
5691 and potential source iterations from a particular source domain,
5692 what is the last potential source iteration corresponding to each
5693 sink iteration. It can sometimes be convenient to adjust
5694 the set of potential source iterations before or after each such operation.
5695 The prototypical example is fuzzy array dataflow analysis,
5696 where we need to analyze if, based on data-dependent constraints,
5697 the sink iteration can ever be executed without one or more of
5698 the corresponding potential source iterations being executed.
5699 If so, we can introduce extra parameters and select an unknown
5700 but fixed source iteration from the potential source iterations.
5701 To be able to perform such manipulations, C<isl> provides the following
5704 #include <isl/flow.h>
5706 typedef __isl_give isl_restriction *(*isl_access_restrict)(
5707 __isl_keep isl_map *source_map,
5708 __isl_keep isl_set *sink, void *source_user,
5710 __isl_give isl_access_info *isl_access_info_set_restrict(
5711 __isl_take isl_access_info *acc,
5712 isl_access_restrict fn, void *user);
5714 The function C<isl_access_info_set_restrict> should be called
5715 before calling C<isl_access_info_compute_flow> and registers a callback function
5716 that will be called any time C<isl> is about to compute the last
5717 potential source. The first argument is the (reverse) proto-dependence,
5718 mapping sink iterations to potential source iterations.
5719 The second argument represents the sink iterations for which
5720 we want to compute the last source iteration.
5721 The third argument is the token corresponding to the source
5722 and the final argument is the token passed to C<isl_access_info_set_restrict>.
5723 The callback is expected to return a restriction on either the input or
5724 the output of the operation computing the last potential source.
5725 If the input needs to be restricted then restrictions are needed
5726 for both the source and the sink iterations. The sink iterations
5727 and the potential source iterations will be intersected with these sets.
5728 If the output needs to be restricted then only a restriction on the source
5729 iterations is required.
5730 If any error occurs, the callback should return C<NULL>.
5731 An C<isl_restriction> object can be created, freed and inspected
5732 using the following functions.
5734 #include <isl/flow.h>
5736 __isl_give isl_restriction *isl_restriction_input(
5737 __isl_take isl_set *source_restr,
5738 __isl_take isl_set *sink_restr);
5739 __isl_give isl_restriction *isl_restriction_output(
5740 __isl_take isl_set *source_restr);
5741 __isl_give isl_restriction *isl_restriction_none(
5742 __isl_take isl_map *source_map);
5743 __isl_give isl_restriction *isl_restriction_empty(
5744 __isl_take isl_map *source_map);
5745 void *isl_restriction_free(
5746 __isl_take isl_restriction *restr);
5747 isl_ctx *isl_restriction_get_ctx(
5748 __isl_keep isl_restriction *restr);
5750 C<isl_restriction_none> and C<isl_restriction_empty> are special
5751 cases of C<isl_restriction_input>. C<isl_restriction_none>
5752 is essentially equivalent to
5754 isl_restriction_input(isl_set_universe(
5755 isl_space_range(isl_map_get_space(source_map))),
5757 isl_space_domain(isl_map_get_space(source_map))));
5759 whereas C<isl_restriction_empty> is essentially equivalent to
5761 isl_restriction_input(isl_set_empty(
5762 isl_space_range(isl_map_get_space(source_map))),
5764 isl_space_domain(isl_map_get_space(source_map))));
5768 B<The functionality described in this section is fairly new
5769 and may be subject to change.>
5771 #include <isl/schedule.h>
5772 __isl_give isl_schedule *
5773 isl_schedule_constraints_compute_schedule(
5774 __isl_take isl_schedule_constraints *sc);
5775 void *isl_schedule_free(__isl_take isl_schedule *sched);
5777 The function C<isl_schedule_constraints_compute_schedule> can be
5778 used to compute a schedule that satisfy the given schedule constraints.
5779 These schedule constraints include the iteration domain for which
5780 a schedule should be computed and dependences between pairs of
5781 iterations. In particular, these dependences include
5782 I<validity> dependences and I<proximity> dependences.
5783 By default, the algorithm used to construct the schedule is similar
5784 to that of C<Pluto>.
5785 Alternatively, Feautrier's multi-dimensional scheduling algorithm can
5787 The generated schedule respects all validity dependences.
5788 That is, all dependence distances over these dependences in the
5789 scheduled space are lexicographically positive.
5790 The default algorithm tries to ensure that the dependence distances
5791 over coincidence constraints are zero and to minimize the
5792 dependence distances over proximity dependences.
5793 Moreover, it tries to obtain sequences (bands) of schedule dimensions
5794 for groups of domains where the dependence distances over validity
5795 dependences have only non-negative values.
5796 When using Feautrier's algorithm, the coincidence and proximity constraints
5797 are only taken into account during the extension to a
5798 full-dimensional schedule.
5800 An C<isl_schedule_constraints> object can be constructed
5801 and manipulated using the following functions.
5803 #include <isl/schedule.h>
5804 __isl_give isl_schedule_constraints *
5805 isl_schedule_constraints_copy(
5806 __isl_keep isl_schedule_constraints *sc);
5807 __isl_give isl_schedule_constraints *
5808 isl_schedule_constraints_on_domain(
5809 __isl_take isl_union_set *domain);
5810 isl_ctx *isl_schedule_constraints_get_ctx(
5811 __isl_keep isl_schedule_constraints *sc);
5812 __isl_give isl_schedule_constraints *
5813 isl_schedule_constraints_set_validity(
5814 __isl_take isl_schedule_constraints *sc,
5815 __isl_take isl_union_map *validity);
5816 __isl_give isl_schedule_constraints *
5817 isl_schedule_constraints_set_coincidence(
5818 __isl_take isl_schedule_constraints *sc,
5819 __isl_take isl_union_map *coincidence);
5820 __isl_give isl_schedule_constraints *
5821 isl_schedule_constraints_set_proximity(
5822 __isl_take isl_schedule_constraints *sc,
5823 __isl_take isl_union_map *proximity);
5824 __isl_give isl_schedule_constraints *
5825 isl_schedule_constraints_set_conditional_validity(
5826 __isl_take isl_schedule_constraints *sc,
5827 __isl_take isl_union_map *condition,
5828 __isl_take isl_union_map *validity);
5829 void *isl_schedule_constraints_free(
5830 __isl_take isl_schedule_constraints *sc);
5832 The initial C<isl_schedule_constraints> object created by
5833 C<isl_schedule_constraints_on_domain> does not impose any constraints.
5834 That is, it has an empty set of dependences.
5835 The function C<isl_schedule_constraints_set_validity> replaces the
5836 validity dependences, mapping domain elements I<i> to domain
5837 elements that should be scheduled after I<i>.
5838 The function C<isl_schedule_constraints_set_coincidence> replaces the
5839 coincidence dependences, mapping domain elements I<i> to domain
5840 elements that should be scheduled together with I<I>, if possible.
5841 The function C<isl_schedule_constraints_set_proximity> replaces the
5842 proximity dependences, mapping domain elements I<i> to domain
5843 elements that should be scheduled either before I<I>
5844 or as early as possible after I<i>.
5846 The function C<isl_schedule_constraints_set_conditional_validity>
5847 replaces the conditional validity constraints.
5848 A conditional validity constraint is only imposed when any of the corresponding
5849 conditions is satisfied, i.e., when any of them is non-zero.
5850 That is, the scheduler ensures that within each band if the dependence
5851 distances over the condition constraints are not all zero
5852 then all corresponding conditional validity constraints are respected.
5853 A conditional validity constraint corresponds to a condition
5854 if the two are adjacent, i.e., if the domain of one relation intersect
5855 the range of the other relation.
5856 The typical use case of conditional validity constraints is
5857 to allow order constraints between live ranges to be violated
5858 as long as the live ranges themselves are local to the band.
5859 To allow more fine-grained control over which conditions correspond
5860 to which conditional validity constraints, the domains and ranges
5861 of these relations may include I<tags>. That is, the domains and
5862 ranges of those relation may themselves be wrapped relations
5863 where the iteration domain appears in the domain of those wrapped relations
5864 and the range of the wrapped relations can be arbitrarily chosen
5865 by the user. Conditions and conditional validity constraints are only
5866 considere adjacent to each other if the entire wrapped relation matches.
5867 In particular, a relation with a tag will never be considered adjacent
5868 to a relation without a tag.
5870 The following function computes a schedule directly from
5871 an iteration domain and validity and proximity dependences
5872 and is implemented in terms of the functions described above.
5873 The use of C<isl_union_set_compute_schedule> is discouraged.
5875 #include <isl/schedule.h>
5876 __isl_give isl_schedule *isl_union_set_compute_schedule(
5877 __isl_take isl_union_set *domain,
5878 __isl_take isl_union_map *validity,
5879 __isl_take isl_union_map *proximity);
5881 A mapping from the domains to the scheduled space can be obtained
5882 from an C<isl_schedule> using the following function.
5884 __isl_give isl_union_map *isl_schedule_get_map(
5885 __isl_keep isl_schedule *sched);
5887 A representation of the schedule can be printed using
5889 __isl_give isl_printer *isl_printer_print_schedule(
5890 __isl_take isl_printer *p,
5891 __isl_keep isl_schedule *schedule);
5893 A representation of the schedule as a forest of bands can be obtained
5894 using the following function.
5896 __isl_give isl_band_list *isl_schedule_get_band_forest(
5897 __isl_keep isl_schedule *schedule);
5899 The individual bands can be visited in depth-first post-order
5900 using the following function.
5902 #include <isl/schedule.h>
5903 int isl_schedule_foreach_band(
5904 __isl_keep isl_schedule *sched,
5905 int (*fn)(__isl_keep isl_band *band, void *user),
5908 The list can be manipulated as explained in L<"Lists">.
5909 The bands inside the list can be copied and freed using the following
5912 #include <isl/band.h>
5913 __isl_give isl_band *isl_band_copy(
5914 __isl_keep isl_band *band);
5915 void *isl_band_free(__isl_take isl_band *band);
5917 Each band contains zero or more scheduling dimensions.
5918 These are referred to as the members of the band.
5919 The section of the schedule that corresponds to the band is
5920 referred to as the partial schedule of the band.
5921 For those nodes that participate in a band, the outer scheduling
5922 dimensions form the prefix schedule, while the inner scheduling
5923 dimensions form the suffix schedule.
5924 That is, if we take a cut of the band forest, then the union of
5925 the concatenations of the prefix, partial and suffix schedules of
5926 each band in the cut is equal to the entire schedule (modulo
5927 some possible padding at the end with zero scheduling dimensions).
5928 The properties of a band can be inspected using the following functions.
5930 #include <isl/band.h>
5931 isl_ctx *isl_band_get_ctx(__isl_keep isl_band *band);
5933 int isl_band_has_children(__isl_keep isl_band *band);
5934 __isl_give isl_band_list *isl_band_get_children(
5935 __isl_keep isl_band *band);
5937 __isl_give isl_union_map *isl_band_get_prefix_schedule(
5938 __isl_keep isl_band *band);
5939 __isl_give isl_union_map *isl_band_get_partial_schedule(
5940 __isl_keep isl_band *band);
5941 __isl_give isl_union_map *isl_band_get_suffix_schedule(
5942 __isl_keep isl_band *band);
5944 int isl_band_n_member(__isl_keep isl_band *band);
5945 int isl_band_member_is_coincident(
5946 __isl_keep isl_band *band, int pos);
5948 int isl_band_list_foreach_band(
5949 __isl_keep isl_band_list *list,
5950 int (*fn)(__isl_keep isl_band *band, void *user),
5953 Note that a scheduling dimension is considered to be ``coincident''
5954 if it satisfies the coincidence constraints within its band.
5955 That is, if the dependence distances of the coincidence
5956 constraints are all zero in that direction (for fixed
5957 iterations of outer bands).
5958 Like C<isl_schedule_foreach_band>,
5959 the function C<isl_band_list_foreach_band> calls C<fn> on the bands
5960 in depth-first post-order.
5962 A band can be tiled using the following function.
5964 #include <isl/band.h>
5965 int isl_band_tile(__isl_keep isl_band *band,
5966 __isl_take isl_vec *sizes);
5968 int isl_options_set_tile_scale_tile_loops(isl_ctx *ctx,
5970 int isl_options_get_tile_scale_tile_loops(isl_ctx *ctx);
5971 int isl_options_set_tile_shift_point_loops(isl_ctx *ctx,
5973 int isl_options_get_tile_shift_point_loops(isl_ctx *ctx);
5975 The C<isl_band_tile> function tiles the band using the given tile sizes
5976 inside its schedule.
5977 A new child band is created to represent the point loops and it is
5978 inserted between the modified band and its children.
5979 The C<tile_scale_tile_loops> option specifies whether the tile
5980 loops iterators should be scaled by the tile sizes.
5981 If the C<tile_shift_point_loops> option is set, then the point loops
5982 are shifted to start at zero.
5984 A band can be split into two nested bands using the following function.
5986 int isl_band_split(__isl_keep isl_band *band, int pos);
5988 The resulting outer band contains the first C<pos> dimensions of C<band>
5989 while the inner band contains the remaining dimensions.
5991 A representation of the band can be printed using
5993 #include <isl/band.h>
5994 __isl_give isl_printer *isl_printer_print_band(
5995 __isl_take isl_printer *p,
5996 __isl_keep isl_band *band);
6000 #include <isl/schedule.h>
6001 int isl_options_set_schedule_max_coefficient(
6002 isl_ctx *ctx, int val);
6003 int isl_options_get_schedule_max_coefficient(
6005 int isl_options_set_schedule_max_constant_term(
6006 isl_ctx *ctx, int val);
6007 int isl_options_get_schedule_max_constant_term(
6009 int isl_options_set_schedule_fuse(isl_ctx *ctx, int val);
6010 int isl_options_get_schedule_fuse(isl_ctx *ctx);
6011 int isl_options_set_schedule_maximize_band_depth(
6012 isl_ctx *ctx, int val);
6013 int isl_options_get_schedule_maximize_band_depth(
6015 int isl_options_set_schedule_outer_coincidence(
6016 isl_ctx *ctx, int val);
6017 int isl_options_get_schedule_outer_coincidence(
6019 int isl_options_set_schedule_split_scaled(
6020 isl_ctx *ctx, int val);
6021 int isl_options_get_schedule_split_scaled(
6023 int isl_options_set_schedule_algorithm(
6024 isl_ctx *ctx, int val);
6025 int isl_options_get_schedule_algorithm(
6027 int isl_options_set_schedule_separate_components(
6028 isl_ctx *ctx, int val);
6029 int isl_options_get_schedule_separate_components(
6034 =item * schedule_max_coefficient
6036 This option enforces that the coefficients for variable and parameter
6037 dimensions in the calculated schedule are not larger than the specified value.
6038 This option can significantly increase the speed of the scheduling calculation
6039 and may also prevent fusing of unrelated dimensions. A value of -1 means that
6040 this option does not introduce bounds on the variable or parameter
6043 =item * schedule_max_constant_term
6045 This option enforces that the constant coefficients in the calculated schedule
6046 are not larger than the maximal constant term. This option can significantly
6047 increase the speed of the scheduling calculation and may also prevent fusing of
6048 unrelated dimensions. A value of -1 means that this option does not introduce
6049 bounds on the constant coefficients.
6051 =item * schedule_fuse
6053 This option controls the level of fusion.
6054 If this option is set to C<ISL_SCHEDULE_FUSE_MIN>, then loops in the
6055 resulting schedule will be distributed as much as possible.
6056 If this option is set to C<ISL_SCHEDULE_FUSE_MAX>, then C<isl> will
6057 try to fuse loops in the resulting schedule.
6059 =item * schedule_maximize_band_depth
6061 If this option is set, we do not split bands at the point
6062 where we detect splitting is necessary. Instead, we
6063 backtrack and split bands as early as possible. This
6064 reduces the number of splits and maximizes the width of
6065 the bands. Wider bands give more possibilities for tiling.
6066 Note that if the C<schedule_fuse> option is set to C<ISL_SCHEDULE_FUSE_MIN>,
6067 then bands will be split as early as possible, even if there is no need.
6068 The C<schedule_maximize_band_depth> option therefore has no effect in this case.
6070 =item * schedule_outer_coincidence
6072 If this option is set, then we try to construct schedules
6073 where the outermost scheduling dimension in each band
6074 satisfies the coincidence constraints.
6076 =item * schedule_split_scaled
6078 If this option is set, then we try to construct schedules in which the
6079 constant term is split off from the linear part if the linear parts of
6080 the scheduling rows for all nodes in the graphs have a common non-trivial
6082 The constant term is then placed in a separate band and the linear
6085 =item * schedule_algorithm
6087 Selects the scheduling algorithm to be used.
6088 Available scheduling algorithms are C<ISL_SCHEDULE_ALGORITHM_ISL>
6089 and C<ISL_SCHEDULE_ALGORITHM_FEAUTRIER>.
6091 =item * schedule_separate_components
6093 If at any point the dependence graph contains any (weakly connected) components,
6094 then these components are scheduled separately.
6095 If this option is not set, then some iterations of the domains
6096 in these components may be scheduled together.
6097 If this option is set, then the components are given consecutive
6102 =head2 AST Generation
6104 This section describes the C<isl> functionality for generating
6105 ASTs that visit all the elements
6106 in a domain in an order specified by a schedule.
6107 In particular, given a C<isl_union_map>, an AST is generated
6108 that visits all the elements in the domain of the C<isl_union_map>
6109 according to the lexicographic order of the corresponding image
6110 element(s). If the range of the C<isl_union_map> consists of
6111 elements in more than one space, then each of these spaces is handled
6112 separately in an arbitrary order.
6113 It should be noted that the image elements only specify the I<order>
6114 in which the corresponding domain elements should be visited.
6115 No direct relation between the image elements and the loop iterators
6116 in the generated AST should be assumed.
6118 Each AST is generated within a build. The initial build
6119 simply specifies the constraints on the parameters (if any)
6120 and can be created, inspected, copied and freed using the following functions.
6122 #include <isl/ast_build.h>
6123 __isl_give isl_ast_build *isl_ast_build_from_context(
6124 __isl_take isl_set *set);
6125 isl_ctx *isl_ast_build_get_ctx(
6126 __isl_keep isl_ast_build *build);
6127 __isl_give isl_ast_build *isl_ast_build_copy(
6128 __isl_keep isl_ast_build *build);
6129 void *isl_ast_build_free(
6130 __isl_take isl_ast_build *build);
6132 The C<set> argument is usually a parameter set with zero or more parameters.
6133 More C<isl_ast_build> functions are described in L</"Nested AST Generation">
6134 and L</"Fine-grained Control over AST Generation">.
6135 Finally, the AST itself can be constructed using the following
6138 #include <isl/ast_build.h>
6139 __isl_give isl_ast_node *isl_ast_build_ast_from_schedule(
6140 __isl_keep isl_ast_build *build,
6141 __isl_take isl_union_map *schedule);
6143 =head3 Inspecting the AST
6145 The basic properties of an AST node can be obtained as follows.
6147 #include <isl/ast.h>
6148 isl_ctx *isl_ast_node_get_ctx(
6149 __isl_keep isl_ast_node *node);
6150 enum isl_ast_node_type isl_ast_node_get_type(
6151 __isl_keep isl_ast_node *node);
6153 The type of an AST node is one of
6154 C<isl_ast_node_for>,
6156 C<isl_ast_node_block> or
6157 C<isl_ast_node_user>.
6158 An C<isl_ast_node_for> represents a for node.
6159 An C<isl_ast_node_if> represents an if node.
6160 An C<isl_ast_node_block> represents a compound node.
6161 An C<isl_ast_node_user> represents an expression statement.
6162 An expression statement typically corresponds to a domain element, i.e.,
6163 one of the elements that is visited by the AST.
6165 Each type of node has its own additional properties.
6167 #include <isl/ast.h>
6168 __isl_give isl_ast_expr *isl_ast_node_for_get_iterator(
6169 __isl_keep isl_ast_node *node);
6170 __isl_give isl_ast_expr *isl_ast_node_for_get_init(
6171 __isl_keep isl_ast_node *node);
6172 __isl_give isl_ast_expr *isl_ast_node_for_get_cond(
6173 __isl_keep isl_ast_node *node);
6174 __isl_give isl_ast_expr *isl_ast_node_for_get_inc(
6175 __isl_keep isl_ast_node *node);
6176 __isl_give isl_ast_node *isl_ast_node_for_get_body(
6177 __isl_keep isl_ast_node *node);
6178 int isl_ast_node_for_is_degenerate(
6179 __isl_keep isl_ast_node *node);
6181 An C<isl_ast_for> is considered degenerate if it is known to execute
6184 #include <isl/ast.h>
6185 __isl_give isl_ast_expr *isl_ast_node_if_get_cond(
6186 __isl_keep isl_ast_node *node);
6187 __isl_give isl_ast_node *isl_ast_node_if_get_then(
6188 __isl_keep isl_ast_node *node);
6189 int isl_ast_node_if_has_else(
6190 __isl_keep isl_ast_node *node);
6191 __isl_give isl_ast_node *isl_ast_node_if_get_else(
6192 __isl_keep isl_ast_node *node);
6194 __isl_give isl_ast_node_list *
6195 isl_ast_node_block_get_children(
6196 __isl_keep isl_ast_node *node);
6198 __isl_give isl_ast_expr *isl_ast_node_user_get_expr(
6199 __isl_keep isl_ast_node *node);
6201 Each of the returned C<isl_ast_expr>s can in turn be inspected using
6202 the following functions.
6204 #include <isl/ast.h>
6205 isl_ctx *isl_ast_expr_get_ctx(
6206 __isl_keep isl_ast_expr *expr);
6207 enum isl_ast_expr_type isl_ast_expr_get_type(
6208 __isl_keep isl_ast_expr *expr);
6210 The type of an AST expression is one of
6212 C<isl_ast_expr_id> or
6213 C<isl_ast_expr_int>.
6214 An C<isl_ast_expr_op> represents the result of an operation.
6215 An C<isl_ast_expr_id> represents an identifier.
6216 An C<isl_ast_expr_int> represents an integer value.
6218 Each type of expression has its own additional properties.
6220 #include <isl/ast.h>
6221 enum isl_ast_op_type isl_ast_expr_get_op_type(
6222 __isl_keep isl_ast_expr *expr);
6223 int isl_ast_expr_get_op_n_arg(__isl_keep isl_ast_expr *expr);
6224 __isl_give isl_ast_expr *isl_ast_expr_get_op_arg(
6225 __isl_keep isl_ast_expr *expr, int pos);
6226 int isl_ast_node_foreach_ast_op_type(
6227 __isl_keep isl_ast_node *node,
6228 int (*fn)(enum isl_ast_op_type type, void *user),
6231 C<isl_ast_expr_get_op_type> returns the type of the operation
6232 performed. C<isl_ast_expr_get_op_n_arg> returns the number of
6233 arguments. C<isl_ast_expr_get_op_arg> returns the specified
6235 C<isl_ast_node_foreach_ast_op_type> calls C<fn> for each distinct
6236 C<isl_ast_op_type> that appears in C<node>.
6237 The operation type is one of the following.
6241 =item C<isl_ast_op_and>
6243 Logical I<and> of two arguments.
6244 Both arguments can be evaluated.
6246 =item C<isl_ast_op_and_then>
6248 Logical I<and> of two arguments.
6249 The second argument can only be evaluated if the first evaluates to true.
6251 =item C<isl_ast_op_or>
6253 Logical I<or> of two arguments.
6254 Both arguments can be evaluated.
6256 =item C<isl_ast_op_or_else>
6258 Logical I<or> of two arguments.
6259 The second argument can only be evaluated if the first evaluates to false.
6261 =item C<isl_ast_op_max>
6263 Maximum of two or more arguments.
6265 =item C<isl_ast_op_min>
6267 Minimum of two or more arguments.
6269 =item C<isl_ast_op_minus>
6273 =item C<isl_ast_op_add>
6275 Sum of two arguments.
6277 =item C<isl_ast_op_sub>
6279 Difference of two arguments.
6281 =item C<isl_ast_op_mul>
6283 Product of two arguments.
6285 =item C<isl_ast_op_div>
6287 Exact division. That is, the result is known to be an integer.
6289 =item C<isl_ast_op_fdiv_q>
6291 Result of integer division, rounded towards negative
6294 =item C<isl_ast_op_pdiv_q>
6296 Result of integer division, where dividend is known to be non-negative.
6298 =item C<isl_ast_op_pdiv_r>
6300 Remainder of integer division, where dividend is known to be non-negative.
6302 =item C<isl_ast_op_cond>
6304 Conditional operator defined on three arguments.
6305 If the first argument evaluates to true, then the result
6306 is equal to the second argument. Otherwise, the result
6307 is equal to the third argument.
6308 The second and third argument may only be evaluated if
6309 the first argument evaluates to true and false, respectively.
6310 Corresponds to C<a ? b : c> in C.
6312 =item C<isl_ast_op_select>
6314 Conditional operator defined on three arguments.
6315 If the first argument evaluates to true, then the result
6316 is equal to the second argument. Otherwise, the result
6317 is equal to the third argument.
6318 The second and third argument may be evaluated independently
6319 of the value of the first argument.
6320 Corresponds to C<a * b + (1 - a) * c> in C.
6322 =item C<isl_ast_op_eq>
6326 =item C<isl_ast_op_le>
6328 Less than or equal relation.
6330 =item C<isl_ast_op_lt>
6334 =item C<isl_ast_op_ge>
6336 Greater than or equal relation.
6338 =item C<isl_ast_op_gt>
6340 Greater than relation.
6342 =item C<isl_ast_op_call>
6345 The number of arguments of the C<isl_ast_expr> is one more than
6346 the number of arguments in the function call, the first argument
6347 representing the function being called.
6349 =item C<isl_ast_op_access>
6352 The number of arguments of the C<isl_ast_expr> is one more than
6353 the number of index expressions in the array access, the first argument
6354 representing the array being accessed.
6356 =item C<isl_ast_op_member>
6359 This operation has two arguments, a structure and the name of
6360 the member of the structure being accessed.
6364 #include <isl/ast.h>
6365 __isl_give isl_id *isl_ast_expr_get_id(
6366 __isl_keep isl_ast_expr *expr);
6368 Return the identifier represented by the AST expression.
6370 #include <isl/ast.h>
6371 __isl_give isl_val *isl_ast_expr_get_val(
6372 __isl_keep isl_ast_expr *expr);
6374 Return the integer represented by the AST expression.
6376 =head3 Properties of ASTs
6378 #include <isl/ast.h>
6379 int isl_ast_expr_is_equal(__isl_keep isl_ast_expr *expr1,
6380 __isl_keep isl_ast_expr *expr2);
6382 Check if two C<isl_ast_expr>s are equal to each other.
6384 =head3 Manipulating and printing the AST
6386 AST nodes can be copied and freed using the following functions.
6388 #include <isl/ast.h>
6389 __isl_give isl_ast_node *isl_ast_node_copy(
6390 __isl_keep isl_ast_node *node);
6391 void *isl_ast_node_free(__isl_take isl_ast_node *node);
6393 AST expressions can be copied and freed using the following functions.
6395 #include <isl/ast.h>
6396 __isl_give isl_ast_expr *isl_ast_expr_copy(
6397 __isl_keep isl_ast_expr *expr);
6398 void *isl_ast_expr_free(__isl_take isl_ast_expr *expr);
6400 New AST expressions can be created either directly or within
6401 the context of an C<isl_ast_build>.
6403 #include <isl/ast.h>
6404 __isl_give isl_ast_expr *isl_ast_expr_from_val(
6405 __isl_take isl_val *v);
6406 __isl_give isl_ast_expr *isl_ast_expr_from_id(
6407 __isl_take isl_id *id);
6408 __isl_give isl_ast_expr *isl_ast_expr_neg(
6409 __isl_take isl_ast_expr *expr);
6410 __isl_give isl_ast_expr *isl_ast_expr_add(
6411 __isl_take isl_ast_expr *expr1,
6412 __isl_take isl_ast_expr *expr2);
6413 __isl_give isl_ast_expr *isl_ast_expr_sub(
6414 __isl_take isl_ast_expr *expr1,
6415 __isl_take isl_ast_expr *expr2);
6416 __isl_give isl_ast_expr *isl_ast_expr_mul(
6417 __isl_take isl_ast_expr *expr1,
6418 __isl_take isl_ast_expr *expr2);
6419 __isl_give isl_ast_expr *isl_ast_expr_div(
6420 __isl_take isl_ast_expr *expr1,
6421 __isl_take isl_ast_expr *expr2);
6422 __isl_give isl_ast_expr *isl_ast_expr_and(
6423 __isl_take isl_ast_expr *expr1,
6424 __isl_take isl_ast_expr *expr2)
6425 __isl_give isl_ast_expr *isl_ast_expr_or(
6426 __isl_take isl_ast_expr *expr1,
6427 __isl_take isl_ast_expr *expr2)
6428 __isl_give isl_ast_expr *isl_ast_expr_access(
6429 __isl_take isl_ast_expr *array,
6430 __isl_take isl_ast_expr_list *indices);
6432 #include <isl/ast_build.h>
6433 __isl_give isl_ast_expr *isl_ast_build_expr_from_pw_aff(
6434 __isl_keep isl_ast_build *build,
6435 __isl_take isl_pw_aff *pa);
6436 __isl_give isl_ast_expr *
6437 isl_ast_build_access_from_pw_multi_aff(
6438 __isl_keep isl_ast_build *build,
6439 __isl_take isl_pw_multi_aff *pma);
6440 __isl_give isl_ast_expr *
6441 isl_ast_build_access_from_multi_pw_aff(
6442 __isl_keep isl_ast_build *build,
6443 __isl_take isl_multi_pw_aff *mpa);
6444 __isl_give isl_ast_expr *
6445 isl_ast_build_call_from_pw_multi_aff(
6446 __isl_keep isl_ast_build *build,
6447 __isl_take isl_pw_multi_aff *pma);
6448 __isl_give isl_ast_expr *
6449 isl_ast_build_call_from_multi_pw_aff(
6450 __isl_keep isl_ast_build *build,
6451 __isl_take isl_multi_pw_aff *mpa);
6453 The domains of C<pa>, C<mpa> and C<pma> should correspond
6454 to the schedule space of C<build>.
6455 The tuple id of C<mpa> or C<pma> is used as the array being accessed or
6456 the function being called.
6457 If the accessed space is a nested relation, then it is taken
6458 to represent an access of the member specified by the range
6459 of this nested relation of the structure specified by the domain
6460 of the nested relation.
6462 The following functions can be used to modify an C<isl_ast_expr>.
6464 #include <isl/ast.h>
6465 __isl_give isl_ast_expr *isl_ast_expr_set_op_arg(
6466 __isl_take isl_ast_expr *expr, int pos,
6467 __isl_take isl_ast_expr *arg);
6469 Replace the argument of C<expr> at position C<pos> by C<arg>.
6471 #include <isl/ast.h>
6472 __isl_give isl_ast_expr *isl_ast_expr_substitute_ids(
6473 __isl_take isl_ast_expr *expr,
6474 __isl_take isl_id_to_ast_expr *id2expr);
6476 The function C<isl_ast_expr_substitute_ids> replaces the
6477 subexpressions of C<expr> of type C<isl_ast_expr_id>
6478 by the corresponding expression in C<id2expr>, if there is any.
6481 User specified data can be attached to an C<isl_ast_node> and obtained
6482 from the same C<isl_ast_node> using the following functions.
6484 #include <isl/ast.h>
6485 __isl_give isl_ast_node *isl_ast_node_set_annotation(
6486 __isl_take isl_ast_node *node,
6487 __isl_take isl_id *annotation);
6488 __isl_give isl_id *isl_ast_node_get_annotation(
6489 __isl_keep isl_ast_node *node);
6491 Basic printing can be performed using the following functions.
6493 #include <isl/ast.h>
6494 __isl_give isl_printer *isl_printer_print_ast_expr(
6495 __isl_take isl_printer *p,
6496 __isl_keep isl_ast_expr *expr);
6497 __isl_give isl_printer *isl_printer_print_ast_node(
6498 __isl_take isl_printer *p,
6499 __isl_keep isl_ast_node *node);
6501 More advanced printing can be performed using the following functions.
6503 #include <isl/ast.h>
6504 __isl_give isl_printer *isl_ast_op_type_print_macro(
6505 enum isl_ast_op_type type,
6506 __isl_take isl_printer *p);
6507 __isl_give isl_printer *isl_ast_node_print_macros(
6508 __isl_keep isl_ast_node *node,
6509 __isl_take isl_printer *p);
6510 __isl_give isl_printer *isl_ast_node_print(
6511 __isl_keep isl_ast_node *node,
6512 __isl_take isl_printer *p,
6513 __isl_take isl_ast_print_options *options);
6514 __isl_give isl_printer *isl_ast_node_for_print(
6515 __isl_keep isl_ast_node *node,
6516 __isl_take isl_printer *p,
6517 __isl_take isl_ast_print_options *options);
6518 __isl_give isl_printer *isl_ast_node_if_print(
6519 __isl_keep isl_ast_node *node,
6520 __isl_take isl_printer *p,
6521 __isl_take isl_ast_print_options *options);
6523 While printing an C<isl_ast_node> in C<ISL_FORMAT_C>,
6524 C<isl> may print out an AST that makes use of macros such
6525 as C<floord>, C<min> and C<max>.
6526 C<isl_ast_op_type_print_macro> prints out the macro
6527 corresponding to a specific C<isl_ast_op_type>.
6528 C<isl_ast_node_print_macros> scans the C<isl_ast_node>
6529 for expressions where these macros would be used and prints
6530 out the required macro definitions.
6531 Essentially, C<isl_ast_node_print_macros> calls
6532 C<isl_ast_node_foreach_ast_op_type> with C<isl_ast_op_type_print_macro>
6533 as function argument.
6534 C<isl_ast_node_print>, C<isl_ast_node_for_print> and
6535 C<isl_ast_node_if_print> print an C<isl_ast_node>
6536 in C<ISL_FORMAT_C>, but allow for some extra control
6537 through an C<isl_ast_print_options> object.
6538 This object can be created using the following functions.
6540 #include <isl/ast.h>
6541 __isl_give isl_ast_print_options *
6542 isl_ast_print_options_alloc(isl_ctx *ctx);
6543 __isl_give isl_ast_print_options *
6544 isl_ast_print_options_copy(
6545 __isl_keep isl_ast_print_options *options);
6546 void *isl_ast_print_options_free(
6547 __isl_take isl_ast_print_options *options);
6549 __isl_give isl_ast_print_options *
6550 isl_ast_print_options_set_print_user(
6551 __isl_take isl_ast_print_options *options,
6552 __isl_give isl_printer *(*print_user)(
6553 __isl_take isl_printer *p,
6554 __isl_take isl_ast_print_options *options,
6555 __isl_keep isl_ast_node *node, void *user),
6557 __isl_give isl_ast_print_options *
6558 isl_ast_print_options_set_print_for(
6559 __isl_take isl_ast_print_options *options,
6560 __isl_give isl_printer *(*print_for)(
6561 __isl_take isl_printer *p,
6562 __isl_take isl_ast_print_options *options,
6563 __isl_keep isl_ast_node *node, void *user),
6566 The callback set by C<isl_ast_print_options_set_print_user>
6567 is called whenever a node of type C<isl_ast_node_user> needs to
6569 The callback set by C<isl_ast_print_options_set_print_for>
6570 is called whenever a node of type C<isl_ast_node_for> needs to
6572 Note that C<isl_ast_node_for_print> will I<not> call the
6573 callback set by C<isl_ast_print_options_set_print_for> on the node
6574 on which C<isl_ast_node_for_print> is called, but only on nested
6575 nodes of type C<isl_ast_node_for>. It is therefore safe to
6576 call C<isl_ast_node_for_print> from within the callback set by
6577 C<isl_ast_print_options_set_print_for>.
6579 The following option determines the type to be used for iterators
6580 while printing the AST.
6582 int isl_options_set_ast_iterator_type(
6583 isl_ctx *ctx, const char *val);
6584 const char *isl_options_get_ast_iterator_type(
6589 #include <isl/ast_build.h>
6590 int isl_options_set_ast_build_atomic_upper_bound(
6591 isl_ctx *ctx, int val);
6592 int isl_options_get_ast_build_atomic_upper_bound(
6594 int isl_options_set_ast_build_prefer_pdiv(isl_ctx *ctx,
6596 int isl_options_get_ast_build_prefer_pdiv(isl_ctx *ctx);
6597 int isl_options_set_ast_build_exploit_nested_bounds(
6598 isl_ctx *ctx, int val);
6599 int isl_options_get_ast_build_exploit_nested_bounds(
6601 int isl_options_set_ast_build_group_coscheduled(
6602 isl_ctx *ctx, int val);
6603 int isl_options_get_ast_build_group_coscheduled(
6605 int isl_options_set_ast_build_scale_strides(
6606 isl_ctx *ctx, int val);
6607 int isl_options_get_ast_build_scale_strides(
6609 int isl_options_set_ast_build_allow_else(isl_ctx *ctx,
6611 int isl_options_get_ast_build_allow_else(isl_ctx *ctx);
6612 int isl_options_set_ast_build_allow_or(isl_ctx *ctx,
6614 int isl_options_get_ast_build_allow_or(isl_ctx *ctx);
6618 =item * ast_build_atomic_upper_bound
6620 Generate loop upper bounds that consist of the current loop iterator,
6621 an operator and an expression not involving the iterator.
6622 If this option is not set, then the current loop iterator may appear
6623 several times in the upper bound.
6624 For example, when this option is turned off, AST generation
6627 [n] -> { A[i] -> [i] : 0 <= i <= 100, n }
6631 for (int c0 = 0; c0 <= 100 && n >= c0; c0 += 1)
6634 When the option is turned on, the following AST is generated
6636 for (int c0 = 0; c0 <= min(100, n); c0 += 1)
6639 =item * ast_build_prefer_pdiv
6641 If this option is turned off, then the AST generation will
6642 produce ASTs that may only contain C<isl_ast_op_fdiv_q>
6643 operators, but no C<isl_ast_op_pdiv_q> or
6644 C<isl_ast_op_pdiv_r> operators.
6645 If this options is turned on, then C<isl> will try to convert
6646 some of the C<isl_ast_op_fdiv_q> operators to (expressions containing)
6647 C<isl_ast_op_pdiv_q> or C<isl_ast_op_pdiv_r> operators.
6649 =item * ast_build_exploit_nested_bounds
6651 Simplify conditions based on bounds of nested for loops.
6652 In particular, remove conditions that are implied by the fact
6653 that one or more nested loops have at least one iteration,
6654 meaning that the upper bound is at least as large as the lower bound.
6655 For example, when this option is turned off, AST generation
6658 [N,M] -> { A[i,j] -> [i,j] : 0 <= i <= N and
6664 for (int c0 = 0; c0 <= N; c0 += 1)
6665 for (int c1 = 0; c1 <= M; c1 += 1)
6668 When the option is turned on, the following AST is generated
6670 for (int c0 = 0; c0 <= N; c0 += 1)
6671 for (int c1 = 0; c1 <= M; c1 += 1)
6674 =item * ast_build_group_coscheduled
6676 If two domain elements are assigned the same schedule point, then
6677 they may be executed in any order and they may even appear in different
6678 loops. If this options is set, then the AST generator will make
6679 sure that coscheduled domain elements do not appear in separate parts
6680 of the AST. This is useful in case of nested AST generation
6681 if the outer AST generation is given only part of a schedule
6682 and the inner AST generation should handle the domains that are
6683 coscheduled by this initial part of the schedule together.
6684 For example if an AST is generated for a schedule
6686 { A[i] -> [0]; B[i] -> [0] }
6688 then the C<isl_ast_build_set_create_leaf> callback described
6689 below may get called twice, once for each domain.
6690 Setting this option ensures that the callback is only called once
6691 on both domains together.
6693 =item * ast_build_separation_bounds
6695 This option specifies which bounds to use during separation.
6696 If this option is set to C<ISL_AST_BUILD_SEPARATION_BOUNDS_IMPLICIT>
6697 then all (possibly implicit) bounds on the current dimension will
6698 be used during separation.
6699 If this option is set to C<ISL_AST_BUILD_SEPARATION_BOUNDS_EXPLICIT>
6700 then only those bounds that are explicitly available will
6701 be used during separation.
6703 =item * ast_build_scale_strides
6705 This option specifies whether the AST generator is allowed
6706 to scale down iterators of strided loops.
6708 =item * ast_build_allow_else
6710 This option specifies whether the AST generator is allowed
6711 to construct if statements with else branches.
6713 =item * ast_build_allow_or
6715 This option specifies whether the AST generator is allowed
6716 to construct if conditions with disjunctions.
6720 =head3 Fine-grained Control over AST Generation
6722 Besides specifying the constraints on the parameters,
6723 an C<isl_ast_build> object can be used to control
6724 various aspects of the AST generation process.
6725 The most prominent way of control is through ``options'',
6726 which can be set using the following function.
6728 #include <isl/ast_build.h>
6729 __isl_give isl_ast_build *
6730 isl_ast_build_set_options(
6731 __isl_take isl_ast_build *control,
6732 __isl_take isl_union_map *options);
6734 The options are encoded in an <isl_union_map>.
6735 The domain of this union relation refers to the schedule domain,
6736 i.e., the range of the schedule passed to C<isl_ast_build_ast_from_schedule>.
6737 In the case of nested AST generation (see L</"Nested AST Generation">),
6738 the domain of C<options> should refer to the extra piece of the schedule.
6739 That is, it should be equal to the range of the wrapped relation in the
6740 range of the schedule.
6741 The range of the options can consist of elements in one or more spaces,
6742 the names of which determine the effect of the option.
6743 The values of the range typically also refer to the schedule dimension
6744 to which the option applies. In case of nested AST generation
6745 (see L</"Nested AST Generation">), these values refer to the position
6746 of the schedule dimension within the innermost AST generation.
6747 The constraints on the domain elements of
6748 the option should only refer to this dimension and earlier dimensions.
6749 We consider the following spaces.
6753 =item C<separation_class>
6755 This space is a wrapped relation between two one dimensional spaces.
6756 The input space represents the schedule dimension to which the option
6757 applies and the output space represents the separation class.
6758 While constructing a loop corresponding to the specified schedule
6759 dimension(s), the AST generator will try to generate separate loops
6760 for domain elements that are assigned different classes.
6761 If only some of the elements are assigned a class, then those elements
6762 that are not assigned any class will be treated as belonging to a class
6763 that is separate from the explicitly assigned classes.
6764 The typical use case for this option is to separate full tiles from
6766 The other options, described below, are applied after the separation
6769 As an example, consider the separation into full and partial tiles
6770 of a tiling of a triangular domain.
6771 Take, for example, the domain
6773 { A[i,j] : 0 <= i,j and i + j <= 100 }
6775 and a tiling into tiles of 10 by 10. The input to the AST generator
6776 is then the schedule
6778 { A[i,j] -> [([i/10]),[j/10],i,j] : 0 <= i,j and
6781 Without any options, the following AST is generated
6783 for (int c0 = 0; c0 <= 10; c0 += 1)
6784 for (int c1 = 0; c1 <= -c0 + 10; c1 += 1)
6785 for (int c2 = 10 * c0;
6786 c2 <= min(-10 * c1 + 100, 10 * c0 + 9);
6788 for (int c3 = 10 * c1;
6789 c3 <= min(10 * c1 + 9, -c2 + 100);
6793 Separation into full and partial tiles can be obtained by assigning
6794 a class, say C<0>, to the full tiles. The full tiles are represented by those
6795 values of the first and second schedule dimensions for which there are
6796 values of the third and fourth dimensions to cover an entire tile.
6797 That is, we need to specify the following option
6799 { [a,b,c,d] -> separation_class[[0]->[0]] :
6800 exists b': 0 <= 10a,10b' and
6801 10a+9+10b'+9 <= 100;
6802 [a,b,c,d] -> separation_class[[1]->[0]] :
6803 0 <= 10a,10b and 10a+9+10b+9 <= 100 }
6807 { [a, b, c, d] -> separation_class[[1] -> [0]] :
6808 a >= 0 and b >= 0 and b <= 8 - a;
6809 [a, b, c, d] -> separation_class[[0] -> [0]] :
6812 With this option, the generated AST is as follows
6815 for (int c0 = 0; c0 <= 8; c0 += 1) {
6816 for (int c1 = 0; c1 <= -c0 + 8; c1 += 1)
6817 for (int c2 = 10 * c0;
6818 c2 <= 10 * c0 + 9; c2 += 1)
6819 for (int c3 = 10 * c1;
6820 c3 <= 10 * c1 + 9; c3 += 1)
6822 for (int c1 = -c0 + 9; c1 <= -c0 + 10; c1 += 1)
6823 for (int c2 = 10 * c0;
6824 c2 <= min(-10 * c1 + 100, 10 * c0 + 9);
6826 for (int c3 = 10 * c1;
6827 c3 <= min(-c2 + 100, 10 * c1 + 9);
6831 for (int c0 = 9; c0 <= 10; c0 += 1)
6832 for (int c1 = 0; c1 <= -c0 + 10; c1 += 1)
6833 for (int c2 = 10 * c0;
6834 c2 <= min(-10 * c1 + 100, 10 * c0 + 9);
6836 for (int c3 = 10 * c1;
6837 c3 <= min(10 * c1 + 9, -c2 + 100);
6844 This is a single-dimensional space representing the schedule dimension(s)
6845 to which ``separation'' should be applied. Separation tries to split
6846 a loop into several pieces if this can avoid the generation of guards
6848 See also the C<atomic> option.
6852 This is a single-dimensional space representing the schedule dimension(s)
6853 for which the domains should be considered ``atomic''. That is, the
6854 AST generator will make sure that any given domain space will only appear
6855 in a single loop at the specified level.
6857 Consider the following schedule
6859 { a[i] -> [i] : 0 <= i < 10;
6860 b[i] -> [i+1] : 0 <= i < 10 }
6862 If the following option is specified
6864 { [i] -> separate[x] }
6866 then the following AST will be generated
6870 for (int c0 = 1; c0 <= 9; c0 += 1) {
6877 If, on the other hand, the following option is specified
6879 { [i] -> atomic[x] }
6881 then the following AST will be generated
6883 for (int c0 = 0; c0 <= 10; c0 += 1) {
6890 If neither C<atomic> nor C<separate> is specified, then the AST generator
6891 may produce either of these two results or some intermediate form.
6895 This is a single-dimensional space representing the schedule dimension(s)
6896 that should be I<completely> unrolled.
6897 To obtain a partial unrolling, the user should apply an additional
6898 strip-mining to the schedule and fully unroll the inner loop.
6902 Additional control is available through the following functions.
6904 #include <isl/ast_build.h>
6905 __isl_give isl_ast_build *
6906 isl_ast_build_set_iterators(
6907 __isl_take isl_ast_build *control,
6908 __isl_take isl_id_list *iterators);
6910 The function C<isl_ast_build_set_iterators> allows the user to
6911 specify a list of iterator C<isl_id>s to be used as iterators.
6912 If the input schedule is injective, then
6913 the number of elements in this list should be as large as the dimension
6914 of the schedule space, but no direct correspondence should be assumed
6915 between dimensions and elements.
6916 If the input schedule is not injective, then an additional number
6917 of C<isl_id>s equal to the largest dimension of the input domains
6919 If the number of provided C<isl_id>s is insufficient, then additional
6920 names are automatically generated.
6922 #include <isl/ast_build.h>
6923 __isl_give isl_ast_build *
6924 isl_ast_build_set_create_leaf(
6925 __isl_take isl_ast_build *control,
6926 __isl_give isl_ast_node *(*fn)(
6927 __isl_take isl_ast_build *build,
6928 void *user), void *user);
6931 C<isl_ast_build_set_create_leaf> function allows for the
6932 specification of a callback that should be called whenever the AST
6933 generator arrives at an element of the schedule domain.
6934 The callback should return an AST node that should be inserted
6935 at the corresponding position of the AST. The default action (when
6936 the callback is not set) is to continue generating parts of the AST to scan
6937 all the domain elements associated to the schedule domain element
6938 and to insert user nodes, ``calling'' the domain element, for each of them.
6939 The C<build> argument contains the current state of the C<isl_ast_build>.
6940 To ease nested AST generation (see L</"Nested AST Generation">),
6941 all control information that is
6942 specific to the current AST generation such as the options and
6943 the callbacks has been removed from this C<isl_ast_build>.
6944 The callback would typically return the result of a nested
6946 user defined node created using the following function.
6948 #include <isl/ast.h>
6949 __isl_give isl_ast_node *isl_ast_node_alloc_user(
6950 __isl_take isl_ast_expr *expr);
6952 #include <isl/ast_build.h>
6953 __isl_give isl_ast_build *
6954 isl_ast_build_set_at_each_domain(
6955 __isl_take isl_ast_build *build,
6956 __isl_give isl_ast_node *(*fn)(
6957 __isl_take isl_ast_node *node,
6958 __isl_keep isl_ast_build *build,
6959 void *user), void *user);
6960 __isl_give isl_ast_build *
6961 isl_ast_build_set_before_each_for(
6962 __isl_take isl_ast_build *build,
6963 __isl_give isl_id *(*fn)(
6964 __isl_keep isl_ast_build *build,
6965 void *user), void *user);
6966 __isl_give isl_ast_build *
6967 isl_ast_build_set_after_each_for(
6968 __isl_take isl_ast_build *build,
6969 __isl_give isl_ast_node *(*fn)(
6970 __isl_take isl_ast_node *node,
6971 __isl_keep isl_ast_build *build,
6972 void *user), void *user);
6974 The callback set by C<isl_ast_build_set_at_each_domain> will
6975 be called for each domain AST node.
6976 The callbacks set by C<isl_ast_build_set_before_each_for>
6977 and C<isl_ast_build_set_after_each_for> will be called
6978 for each for AST node. The first will be called in depth-first
6979 pre-order, while the second will be called in depth-first post-order.
6980 Since C<isl_ast_build_set_before_each_for> is called before the for
6981 node is actually constructed, it is only passed an C<isl_ast_build>.
6982 The returned C<isl_id> will be added as an annotation (using
6983 C<isl_ast_node_set_annotation>) to the constructed for node.
6984 In particular, if the user has also specified an C<after_each_for>
6985 callback, then the annotation can be retrieved from the node passed to
6986 that callback using C<isl_ast_node_get_annotation>.
6987 All callbacks should C<NULL> on failure.
6988 The given C<isl_ast_build> can be used to create new
6989 C<isl_ast_expr> objects using C<isl_ast_build_expr_from_pw_aff>
6990 or C<isl_ast_build_call_from_pw_multi_aff>.
6992 =head3 Nested AST Generation
6994 C<isl> allows the user to create an AST within the context
6995 of another AST. These nested ASTs are created using the
6996 same C<isl_ast_build_ast_from_schedule> function that is used to create the
6997 outer AST. The C<build> argument should be an C<isl_ast_build>
6998 passed to a callback set by
6999 C<isl_ast_build_set_create_leaf>.
7000 The space of the range of the C<schedule> argument should refer
7001 to this build. In particular, the space should be a wrapped
7002 relation and the domain of this wrapped relation should be the
7003 same as that of the range of the schedule returned by
7004 C<isl_ast_build_get_schedule> below.
7005 In practice, the new schedule is typically
7006 created by calling C<isl_union_map_range_product> on the old schedule
7007 and some extra piece of the schedule.
7008 The space of the schedule domain is also available from
7009 the C<isl_ast_build>.
7011 #include <isl/ast_build.h>
7012 __isl_give isl_union_map *isl_ast_build_get_schedule(
7013 __isl_keep isl_ast_build *build);
7014 __isl_give isl_space *isl_ast_build_get_schedule_space(
7015 __isl_keep isl_ast_build *build);
7016 __isl_give isl_ast_build *isl_ast_build_restrict(
7017 __isl_take isl_ast_build *build,
7018 __isl_take isl_set *set);
7020 The C<isl_ast_build_get_schedule> function returns a (partial)
7021 schedule for the domains elements for which part of the AST still needs to
7022 be generated in the current build.
7023 In particular, the domain elements are mapped to those iterations of the loops
7024 enclosing the current point of the AST generation inside which
7025 the domain elements are executed.
7026 No direct correspondence between
7027 the input schedule and this schedule should be assumed.
7028 The space obtained from C<isl_ast_build_get_schedule_space> can be used
7029 to create a set for C<isl_ast_build_restrict> to intersect
7030 with the current build. In particular, the set passed to
7031 C<isl_ast_build_restrict> can have additional parameters.
7032 The ids of the set dimensions in the space returned by
7033 C<isl_ast_build_get_schedule_space> correspond to the
7034 iterators of the already generated loops.
7035 The user should not rely on the ids of the output dimensions
7036 of the relations in the union relation returned by
7037 C<isl_ast_build_get_schedule> having any particular value.
7041 Although C<isl> is mainly meant to be used as a library,
7042 it also contains some basic applications that use some
7043 of the functionality of C<isl>.
7044 The input may be specified in either the L<isl format>
7045 or the L<PolyLib format>.
7047 =head2 C<isl_polyhedron_sample>
7049 C<isl_polyhedron_sample> takes a polyhedron as input and prints
7050 an integer element of the polyhedron, if there is any.
7051 The first column in the output is the denominator and is always
7052 equal to 1. If the polyhedron contains no integer points,
7053 then a vector of length zero is printed.
7057 C<isl_pip> takes the same input as the C<example> program
7058 from the C<piplib> distribution, i.e., a set of constraints
7059 on the parameters, a line containing only -1 and finally a set
7060 of constraints on a parametric polyhedron.
7061 The coefficients of the parameters appear in the last columns
7062 (but before the final constant column).
7063 The output is the lexicographic minimum of the parametric polyhedron.
7064 As C<isl> currently does not have its own output format, the output
7065 is just a dump of the internal state.
7067 =head2 C<isl_polyhedron_minimize>
7069 C<isl_polyhedron_minimize> computes the minimum of some linear
7070 or affine objective function over the integer points in a polyhedron.
7071 If an affine objective function
7072 is given, then the constant should appear in the last column.
7074 =head2 C<isl_polytope_scan>
7076 Given a polytope, C<isl_polytope_scan> prints
7077 all integer points in the polytope.
7079 =head2 C<isl_codegen>
7081 Given a schedule, a context set and an options relation,
7082 C<isl_codegen> prints out an AST that scans the domain elements
7083 of the schedule in the order of their image(s) taking into account
7084 the constraints in the context set.