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 #include <isl/set.h>
3065 __isl_give isl_basic_set *
3066 isl_basic_set_preimage_multi_aff(
3067 __isl_take isl_basic_set *bset,
3068 __isl_take isl_multi_aff *ma);
3069 __isl_give isl_set *isl_set_preimage_multi_aff(
3070 __isl_take isl_set *set,
3071 __isl_take isl_multi_aff *ma);
3072 __isl_give isl_set *isl_set_preimage_pw_multi_aff(
3073 __isl_take isl_set *set,
3074 __isl_take isl_pw_multi_aff *pma);
3075 __isl_give isl_set *isl_set_preimage_multi_pw_aff(
3076 __isl_take isl_set *set,
3077 __isl_take isl_multi_pw_aff *mpa);
3079 #include <isl/map.h>
3080 __isl_give isl_basic_map *
3081 isl_basic_map_preimage_domain_multi_aff(
3082 __isl_take isl_basic_map *bmap,
3083 __isl_take isl_multi_aff *ma);
3084 __isl_give isl_map *isl_map_preimage_domain_multi_aff(
3085 __isl_take isl_map *map,
3086 __isl_take isl_multi_aff *ma);
3087 __isl_give isl_map *
3088 isl_map_preimage_domain_pw_multi_aff(
3089 __isl_take isl_map *map,
3090 __isl_take isl_pw_multi_aff *pma);
3091 __isl_give isl_map *
3092 isl_map_preimage_range_pw_multi_aff(
3093 __isl_take isl_map *map,
3094 __isl_take isl_pw_multi_aff *pma);
3095 __isl_give isl_map *
3096 isl_map_preimage_domain_multi_pw_aff(
3097 __isl_take isl_map *map,
3098 __isl_take isl_multi_pw_aff *mpa);
3099 __isl_give isl_basic_map *
3100 isl_basic_map_preimage_range_multi_aff(
3101 __isl_take isl_basic_map *bmap,
3102 __isl_take isl_multi_aff *ma);
3104 #include <isl/union_map.h>
3105 __isl_give isl_union_map *
3106 isl_union_map_preimage_domain_multi_aff(
3107 __isl_take isl_union_map *umap,
3108 __isl_take isl_multi_aff *ma);
3110 These functions compute the preimage of the given set or map domain/range under
3111 the given function. In other words, the expression is plugged
3112 into the set description or into the domain/range of the map.
3113 Objects of types C<isl_multi_aff> and C<isl_pw_multi_aff> are described in
3114 L</"Piecewise Multiple Quasi Affine Expressions">.
3116 =item * Cartesian Product
3118 #include <isl/space.h>
3119 __isl_give isl_space *isl_space_product(
3120 __isl_take isl_space *space1,
3121 __isl_take isl_space *space2);
3122 __isl_give isl_space *isl_space_domain_product(
3123 __isl_take isl_space *space1,
3124 __isl_take isl_space *space2);
3125 __isl_give isl_space *isl_space_range_product(
3126 __isl_take isl_space *space1,
3127 __isl_take isl_space *space2);
3130 C<isl_space_product>, C<isl_space_domain_product>
3131 and C<isl_space_range_product> take pairs or relation spaces and
3132 produce a single relations space, where either the domain, the range
3133 or both domain and range are wrapped spaces of relations between
3134 the domains and/or ranges of the input spaces.
3135 If the product is only constructed over the domain or the range
3136 then the ranges or the domains of the inputs should be the same.
3138 #include <isl/set.h>
3139 __isl_give isl_set *isl_set_product(
3140 __isl_take isl_set *set1,
3141 __isl_take isl_set *set2);
3143 #include <isl/map.h>
3144 __isl_give isl_basic_map *isl_basic_map_domain_product(
3145 __isl_take isl_basic_map *bmap1,
3146 __isl_take isl_basic_map *bmap2);
3147 __isl_give isl_basic_map *isl_basic_map_range_product(
3148 __isl_take isl_basic_map *bmap1,
3149 __isl_take isl_basic_map *bmap2);
3150 __isl_give isl_basic_map *isl_basic_map_product(
3151 __isl_take isl_basic_map *bmap1,
3152 __isl_take isl_basic_map *bmap2);
3153 __isl_give isl_map *isl_map_domain_product(
3154 __isl_take isl_map *map1,
3155 __isl_take isl_map *map2);
3156 __isl_give isl_map *isl_map_range_product(
3157 __isl_take isl_map *map1,
3158 __isl_take isl_map *map2);
3159 __isl_give isl_map *isl_map_product(
3160 __isl_take isl_map *map1,
3161 __isl_take isl_map *map2);
3163 #include <isl/union_set.h>
3164 __isl_give isl_union_set *isl_union_set_product(
3165 __isl_take isl_union_set *uset1,
3166 __isl_take isl_union_set *uset2);
3168 #include <isl/union_map.h>
3169 __isl_give isl_union_map *isl_union_map_domain_product(
3170 __isl_take isl_union_map *umap1,
3171 __isl_take isl_union_map *umap2);
3172 __isl_give isl_union_map *isl_union_map_range_product(
3173 __isl_take isl_union_map *umap1,
3174 __isl_take isl_union_map *umap2);
3175 __isl_give isl_union_map *isl_union_map_product(
3176 __isl_take isl_union_map *umap1,
3177 __isl_take isl_union_map *umap2);
3179 The above functions compute the cross product of the given
3180 sets or relations. The domains and ranges of the results
3181 are wrapped maps between domains and ranges of the inputs.
3182 To obtain a ``flat'' product, use the following functions
3185 __isl_give isl_basic_set *isl_basic_set_flat_product(
3186 __isl_take isl_basic_set *bset1,
3187 __isl_take isl_basic_set *bset2);
3188 __isl_give isl_set *isl_set_flat_product(
3189 __isl_take isl_set *set1,
3190 __isl_take isl_set *set2);
3191 __isl_give isl_basic_map *isl_basic_map_flat_range_product(
3192 __isl_take isl_basic_map *bmap1,
3193 __isl_take isl_basic_map *bmap2);
3194 __isl_give isl_map *isl_map_flat_domain_product(
3195 __isl_take isl_map *map1,
3196 __isl_take isl_map *map2);
3197 __isl_give isl_map *isl_map_flat_range_product(
3198 __isl_take isl_map *map1,
3199 __isl_take isl_map *map2);
3200 __isl_give isl_union_map *isl_union_map_flat_range_product(
3201 __isl_take isl_union_map *umap1,
3202 __isl_take isl_union_map *umap2);
3203 __isl_give isl_basic_map *isl_basic_map_flat_product(
3204 __isl_take isl_basic_map *bmap1,
3205 __isl_take isl_basic_map *bmap2);
3206 __isl_give isl_map *isl_map_flat_product(
3207 __isl_take isl_map *map1,
3208 __isl_take isl_map *map2);
3210 #include <isl/space.h>
3211 __isl_give isl_space *isl_space_domain_factor_domain(
3212 __isl_take isl_space *space);
3213 __isl_give isl_space *isl_space_range_factor_domain(
3214 __isl_take isl_space *space);
3215 __isl_give isl_space *isl_space_range_factor_range(
3216 __isl_take isl_space *space);
3218 The functions C<isl_space_range_factor_domain> and
3219 C<isl_space_range_factor_range> extract the two arguments from
3220 the result of a call to C<isl_space_range_product>.
3222 The arguments of a call to C<isl_map_range_product> can be extracted
3223 from the result using the following two functions.
3225 #include <isl/map.h>
3226 __isl_give isl_map *isl_map_range_factor_domain(
3227 __isl_take isl_map *map);
3228 __isl_give isl_map *isl_map_range_factor_range(
3229 __isl_take isl_map *map);
3231 =item * Simplification
3233 __isl_give isl_basic_set *isl_basic_set_gist(
3234 __isl_take isl_basic_set *bset,
3235 __isl_take isl_basic_set *context);
3236 __isl_give isl_set *isl_set_gist(__isl_take isl_set *set,
3237 __isl_take isl_set *context);
3238 __isl_give isl_set *isl_set_gist_params(
3239 __isl_take isl_set *set,
3240 __isl_take isl_set *context);
3241 __isl_give isl_union_set *isl_union_set_gist(
3242 __isl_take isl_union_set *uset,
3243 __isl_take isl_union_set *context);
3244 __isl_give isl_union_set *isl_union_set_gist_params(
3245 __isl_take isl_union_set *uset,
3246 __isl_take isl_set *set);
3247 __isl_give isl_basic_map *isl_basic_map_gist(
3248 __isl_take isl_basic_map *bmap,
3249 __isl_take isl_basic_map *context);
3250 __isl_give isl_map *isl_map_gist(__isl_take isl_map *map,
3251 __isl_take isl_map *context);
3252 __isl_give isl_map *isl_map_gist_params(
3253 __isl_take isl_map *map,
3254 __isl_take isl_set *context);
3255 __isl_give isl_map *isl_map_gist_domain(
3256 __isl_take isl_map *map,
3257 __isl_take isl_set *context);
3258 __isl_give isl_map *isl_map_gist_range(
3259 __isl_take isl_map *map,
3260 __isl_take isl_set *context);
3261 __isl_give isl_union_map *isl_union_map_gist(
3262 __isl_take isl_union_map *umap,
3263 __isl_take isl_union_map *context);
3264 __isl_give isl_union_map *isl_union_map_gist_params(
3265 __isl_take isl_union_map *umap,
3266 __isl_take isl_set *set);
3267 __isl_give isl_union_map *isl_union_map_gist_domain(
3268 __isl_take isl_union_map *umap,
3269 __isl_take isl_union_set *uset);
3270 __isl_give isl_union_map *isl_union_map_gist_range(
3271 __isl_take isl_union_map *umap,
3272 __isl_take isl_union_set *uset);
3274 The gist operation returns a set or relation that has the
3275 same intersection with the context as the input set or relation.
3276 Any implicit equality in the intersection is made explicit in the result,
3277 while all inequalities that are redundant with respect to the intersection
3279 In case of union sets and relations, the gist operation is performed
3284 =head3 Lexicographic Optimization
3286 Given a (basic) set C<set> (or C<bset>) and a zero-dimensional domain C<dom>,
3287 the following functions
3288 compute a set that contains the lexicographic minimum or maximum
3289 of the elements in C<set> (or C<bset>) for those values of the parameters
3290 that satisfy C<dom>.
3291 If C<empty> is not C<NULL>, then C<*empty> is assigned a set
3292 that contains the parameter values in C<dom> for which C<set> (or C<bset>)
3294 In other words, the union of the parameter values
3295 for which the result is non-empty and of C<*empty>
3298 __isl_give isl_set *isl_basic_set_partial_lexmin(
3299 __isl_take isl_basic_set *bset,
3300 __isl_take isl_basic_set *dom,
3301 __isl_give isl_set **empty);
3302 __isl_give isl_set *isl_basic_set_partial_lexmax(
3303 __isl_take isl_basic_set *bset,
3304 __isl_take isl_basic_set *dom,
3305 __isl_give isl_set **empty);
3306 __isl_give isl_set *isl_set_partial_lexmin(
3307 __isl_take isl_set *set, __isl_take isl_set *dom,
3308 __isl_give isl_set **empty);
3309 __isl_give isl_set *isl_set_partial_lexmax(
3310 __isl_take isl_set *set, __isl_take isl_set *dom,
3311 __isl_give isl_set **empty);
3313 Given a (basic) set C<set> (or C<bset>), the following functions simply
3314 return a set containing the lexicographic minimum or maximum
3315 of the elements in C<set> (or C<bset>).
3316 In case of union sets, the optimum is computed per space.
3318 __isl_give isl_set *isl_basic_set_lexmin(
3319 __isl_take isl_basic_set *bset);
3320 __isl_give isl_set *isl_basic_set_lexmax(
3321 __isl_take isl_basic_set *bset);
3322 __isl_give isl_set *isl_set_lexmin(
3323 __isl_take isl_set *set);
3324 __isl_give isl_set *isl_set_lexmax(
3325 __isl_take isl_set *set);
3326 __isl_give isl_union_set *isl_union_set_lexmin(
3327 __isl_take isl_union_set *uset);
3328 __isl_give isl_union_set *isl_union_set_lexmax(
3329 __isl_take isl_union_set *uset);
3331 Given a (basic) relation C<map> (or C<bmap>) and a domain C<dom>,
3332 the following functions
3333 compute a relation that maps each element of C<dom>
3334 to the single lexicographic minimum or maximum
3335 of the elements that are associated to that same
3336 element in C<map> (or C<bmap>).
3337 If C<empty> is not C<NULL>, then C<*empty> is assigned a set
3338 that contains the elements in C<dom> that do not map
3339 to any elements in C<map> (or C<bmap>).
3340 In other words, the union of the domain of the result and of C<*empty>
3343 __isl_give isl_map *isl_basic_map_partial_lexmax(
3344 __isl_take isl_basic_map *bmap,
3345 __isl_take isl_basic_set *dom,
3346 __isl_give isl_set **empty);
3347 __isl_give isl_map *isl_basic_map_partial_lexmin(
3348 __isl_take isl_basic_map *bmap,
3349 __isl_take isl_basic_set *dom,
3350 __isl_give isl_set **empty);
3351 __isl_give isl_map *isl_map_partial_lexmax(
3352 __isl_take isl_map *map, __isl_take isl_set *dom,
3353 __isl_give isl_set **empty);
3354 __isl_give isl_map *isl_map_partial_lexmin(
3355 __isl_take isl_map *map, __isl_take isl_set *dom,
3356 __isl_give isl_set **empty);
3358 Given a (basic) map C<map> (or C<bmap>), the following functions simply
3359 return a map mapping each element in the domain of
3360 C<map> (or C<bmap>) to the lexicographic minimum or maximum
3361 of all elements associated to that element.
3362 In case of union relations, the optimum is computed per space.
3364 __isl_give isl_map *isl_basic_map_lexmin(
3365 __isl_take isl_basic_map *bmap);
3366 __isl_give isl_map *isl_basic_map_lexmax(
3367 __isl_take isl_basic_map *bmap);
3368 __isl_give isl_map *isl_map_lexmin(
3369 __isl_take isl_map *map);
3370 __isl_give isl_map *isl_map_lexmax(
3371 __isl_take isl_map *map);
3372 __isl_give isl_union_map *isl_union_map_lexmin(
3373 __isl_take isl_union_map *umap);
3374 __isl_give isl_union_map *isl_union_map_lexmax(
3375 __isl_take isl_union_map *umap);
3377 The following functions return their result in the form of
3378 a piecewise multi-affine expression
3379 (See L<"Piecewise Multiple Quasi Affine Expressions">),
3380 but are otherwise equivalent to the corresponding functions
3381 returning a basic set or relation.
3383 __isl_give isl_pw_multi_aff *
3384 isl_basic_map_lexmin_pw_multi_aff(
3385 __isl_take isl_basic_map *bmap);
3386 __isl_give isl_pw_multi_aff *
3387 isl_basic_set_partial_lexmin_pw_multi_aff(
3388 __isl_take isl_basic_set *bset,
3389 __isl_take isl_basic_set *dom,
3390 __isl_give isl_set **empty);
3391 __isl_give isl_pw_multi_aff *
3392 isl_basic_set_partial_lexmax_pw_multi_aff(
3393 __isl_take isl_basic_set *bset,
3394 __isl_take isl_basic_set *dom,
3395 __isl_give isl_set **empty);
3396 __isl_give isl_pw_multi_aff *
3397 isl_basic_map_partial_lexmin_pw_multi_aff(
3398 __isl_take isl_basic_map *bmap,
3399 __isl_take isl_basic_set *dom,
3400 __isl_give isl_set **empty);
3401 __isl_give isl_pw_multi_aff *
3402 isl_basic_map_partial_lexmax_pw_multi_aff(
3403 __isl_take isl_basic_map *bmap,
3404 __isl_take isl_basic_set *dom,
3405 __isl_give isl_set **empty);
3406 __isl_give isl_pw_multi_aff *isl_set_lexmin_pw_multi_aff(
3407 __isl_take isl_set *set);
3408 __isl_give isl_pw_multi_aff *isl_set_lexmax_pw_multi_aff(
3409 __isl_take isl_set *set);
3410 __isl_give isl_pw_multi_aff *isl_map_lexmin_pw_multi_aff(
3411 __isl_take isl_map *map);
3412 __isl_give isl_pw_multi_aff *isl_map_lexmax_pw_multi_aff(
3413 __isl_take isl_map *map);
3417 Lists are defined over several element types, including
3418 C<isl_val>, C<isl_id>, C<isl_aff>, C<isl_pw_aff>, C<isl_constraint>,
3419 C<isl_basic_set>, C<isl_set>, C<isl_ast_expr> and C<isl_ast_node>.
3420 Here we take lists of C<isl_set>s as an example.
3421 Lists can be created, copied, modified and freed using the following functions.
3423 #include <isl/list.h>
3424 __isl_give isl_set_list *isl_set_list_from_set(
3425 __isl_take isl_set *el);
3426 __isl_give isl_set_list *isl_set_list_alloc(
3427 isl_ctx *ctx, int n);
3428 __isl_give isl_set_list *isl_set_list_copy(
3429 __isl_keep isl_set_list *list);
3430 __isl_give isl_set_list *isl_set_list_insert(
3431 __isl_take isl_set_list *list, unsigned pos,
3432 __isl_take isl_set *el);
3433 __isl_give isl_set_list *isl_set_list_add(
3434 __isl_take isl_set_list *list,
3435 __isl_take isl_set *el);
3436 __isl_give isl_set_list *isl_set_list_drop(
3437 __isl_take isl_set_list *list,
3438 unsigned first, unsigned n);
3439 __isl_give isl_set_list *isl_set_list_set_set(
3440 __isl_take isl_set_list *list, int index,
3441 __isl_take isl_set *set);
3442 __isl_give isl_set_list *isl_set_list_concat(
3443 __isl_take isl_set_list *list1,
3444 __isl_take isl_set_list *list2);
3445 __isl_give isl_set_list *isl_set_list_sort(
3446 __isl_take isl_set_list *list,
3447 int (*cmp)(__isl_keep isl_set *a,
3448 __isl_keep isl_set *b, void *user),
3450 void *isl_set_list_free(__isl_take isl_set_list *list);
3452 C<isl_set_list_alloc> creates an empty list with a capacity for
3453 C<n> elements. C<isl_set_list_from_set> creates a list with a single
3456 Lists can be inspected using the following functions.
3458 #include <isl/list.h>
3459 isl_ctx *isl_set_list_get_ctx(__isl_keep isl_set_list *list);
3460 int isl_set_list_n_set(__isl_keep isl_set_list *list);
3461 __isl_give isl_set *isl_set_list_get_set(
3462 __isl_keep isl_set_list *list, int index);
3463 int isl_set_list_foreach(__isl_keep isl_set_list *list,
3464 int (*fn)(__isl_take isl_set *el, void *user),
3466 int isl_set_list_foreach_scc(__isl_keep isl_set_list *list,
3467 int (*follows)(__isl_keep isl_set *a,
3468 __isl_keep isl_set *b, void *user),
3470 int (*fn)(__isl_take isl_set *el, void *user),
3473 The function C<isl_set_list_foreach_scc> calls C<fn> on each of the
3474 strongly connected components of the graph with as vertices the elements
3475 of C<list> and a directed edge from vertex C<b> to vertex C<a>
3476 iff C<follows(a, b)> returns C<1>. The callbacks C<follows> and C<fn>
3477 should return C<-1> on error.
3479 Lists can be printed using
3481 #include <isl/list.h>
3482 __isl_give isl_printer *isl_printer_print_set_list(
3483 __isl_take isl_printer *p,
3484 __isl_keep isl_set_list *list);
3486 =head2 Associative arrays
3488 Associative arrays map isl objects of a specific type to isl objects
3489 of some (other) specific type. They are defined for several pairs
3490 of types, including (C<isl_map>, C<isl_basic_set>),
3491 (C<isl_id>, C<isl_ast_expr>) and.
3492 (C<isl_id>, C<isl_pw_aff>).
3493 Here, we take associative arrays that map C<isl_id>s to C<isl_ast_expr>s
3496 Associative arrays can be created, copied and freed using
3497 the following functions.
3499 #include <isl/id_to_ast_expr.h>
3500 __isl_give id_to_ast_expr *isl_id_to_ast_expr_alloc(
3501 isl_ctx *ctx, int min_size);
3502 __isl_give id_to_ast_expr *isl_id_to_ast_expr_copy(
3503 __isl_keep id_to_ast_expr *id2expr);
3504 void *isl_id_to_ast_expr_free(
3505 __isl_take id_to_ast_expr *id2expr);
3507 The C<min_size> argument to C<isl_id_to_ast_expr_alloc> can be used
3508 to specify the expected size of the associative array.
3509 The associative array will be grown automatically as needed.
3511 Associative arrays can be inspected using the following functions.
3513 #include <isl/id_to_ast_expr.h>
3514 isl_ctx *isl_id_to_ast_expr_get_ctx(
3515 __isl_keep id_to_ast_expr *id2expr);
3516 int isl_id_to_ast_expr_has(
3517 __isl_keep id_to_ast_expr *id2expr,
3518 __isl_keep isl_id *key);
3519 __isl_give isl_ast_expr *isl_id_to_ast_expr_get(
3520 __isl_keep id_to_ast_expr *id2expr,
3521 __isl_take isl_id *key);
3522 int isl_id_to_ast_expr_foreach(
3523 __isl_keep id_to_ast_expr *id2expr,
3524 int (*fn)(__isl_take isl_id *key,
3525 __isl_take isl_ast_expr *val, void *user),
3528 They can be modified using the following function.
3530 #include <isl/id_to_ast_expr.h>
3531 __isl_give id_to_ast_expr *isl_id_to_ast_expr_set(
3532 __isl_take id_to_ast_expr *id2expr,
3533 __isl_take isl_id *key,
3534 __isl_take isl_ast_expr *val);
3535 __isl_give id_to_ast_expr *isl_id_to_ast_expr_drop(
3536 __isl_take id_to_ast_expr *id2expr,
3537 __isl_take isl_id *key);
3539 Associative arrays can be printed using the following function.
3541 #include <isl/id_to_ast_expr.h>
3542 __isl_give isl_printer *isl_printer_print_id_to_ast_expr(
3543 __isl_take isl_printer *p,
3544 __isl_keep id_to_ast_expr *id2expr);
3546 =head2 Multiple Values
3548 An C<isl_multi_val> object represents a sequence of zero or more values,
3549 living in a set space.
3551 An C<isl_multi_val> can be constructed from an C<isl_val_list>
3552 using the following function
3554 #include <isl/val.h>
3555 __isl_give isl_multi_val *isl_multi_val_from_val_list(
3556 __isl_take isl_space *space,
3557 __isl_take isl_val_list *list);
3559 The zero multiple value (with value zero for each set dimension)
3560 can be created using the following function.
3562 #include <isl/val.h>
3563 __isl_give isl_multi_val *isl_multi_val_zero(
3564 __isl_take isl_space *space);
3566 Multiple values can be copied and freed using
3568 #include <isl/val.h>
3569 __isl_give isl_multi_val *isl_multi_val_copy(
3570 __isl_keep isl_multi_val *mv);
3571 void *isl_multi_val_free(__isl_take isl_multi_val *mv);
3573 They can be inspected using
3575 #include <isl/val.h>
3576 isl_ctx *isl_multi_val_get_ctx(
3577 __isl_keep isl_multi_val *mv);
3578 unsigned isl_multi_val_dim(__isl_keep isl_multi_val *mv,
3579 enum isl_dim_type type);
3580 __isl_give isl_val *isl_multi_val_get_val(
3581 __isl_keep isl_multi_val *mv, int pos);
3582 int isl_multi_val_find_dim_by_id(
3583 __isl_keep isl_multi_val *mv,
3584 enum isl_dim_type type, __isl_keep isl_id *id);
3585 __isl_give isl_id *isl_multi_val_get_dim_id(
3586 __isl_keep isl_multi_val *mv,
3587 enum isl_dim_type type, unsigned pos);
3588 const char *isl_multi_val_get_tuple_name(
3589 __isl_keep isl_multi_val *mv,
3590 enum isl_dim_type type);
3591 int isl_multi_val_has_tuple_id(__isl_keep isl_multi_val *mv,
3592 enum isl_dim_type type);
3593 __isl_give isl_id *isl_multi_val_get_tuple_id(
3594 __isl_keep isl_multi_val *mv,
3595 enum isl_dim_type type);
3596 int isl_multi_val_range_is_wrapping(
3597 __isl_keep isl_multi_val *mv);
3599 They can be modified using
3601 #include <isl/val.h>
3602 __isl_give isl_multi_val *isl_multi_val_set_val(
3603 __isl_take isl_multi_val *mv, int pos,
3604 __isl_take isl_val *val);
3605 __isl_give isl_multi_val *isl_multi_val_set_dim_name(
3606 __isl_take isl_multi_val *mv,
3607 enum isl_dim_type type, unsigned pos, const char *s);
3608 __isl_give isl_multi_val *isl_multi_val_set_dim_id(
3609 __isl_take isl_multi_val *mv,
3610 enum isl_dim_type type, unsigned pos,
3611 __isl_take isl_id *id);
3612 __isl_give isl_multi_val *isl_multi_val_set_tuple_name(
3613 __isl_take isl_multi_val *mv,
3614 enum isl_dim_type type, const char *s);
3615 __isl_give isl_multi_val *isl_multi_val_set_tuple_id(
3616 __isl_take isl_multi_val *mv,
3617 enum isl_dim_type type, __isl_take isl_id *id);
3618 __isl_give isl_multi_val *isl_multi_val_reset_tuple_id(
3619 __isl_take isl_multi_val *mv,
3620 enum isl_dim_type type);
3621 __isl_give isl_multi_val *isl_multi_val_reset_user(
3622 __isl_take isl_multi_val *mv);
3624 __isl_give isl_multi_val *isl_multi_val_insert_dims(
3625 __isl_take isl_multi_val *mv,
3626 enum isl_dim_type type, unsigned first, unsigned n);
3627 __isl_give isl_multi_val *isl_multi_val_add_dims(
3628 __isl_take isl_multi_val *mv,
3629 enum isl_dim_type type, unsigned n);
3630 __isl_give isl_multi_val *isl_multi_val_drop_dims(
3631 __isl_take isl_multi_val *mv,
3632 enum isl_dim_type type, unsigned first, unsigned n);
3636 #include <isl/val.h>
3637 __isl_give isl_multi_val *isl_multi_val_align_params(
3638 __isl_take isl_multi_val *mv,
3639 __isl_take isl_space *model);
3640 __isl_give isl_multi_val *isl_multi_val_from_range(
3641 __isl_take isl_multi_val *mv);
3642 __isl_give isl_multi_val *isl_multi_val_range_splice(
3643 __isl_take isl_multi_val *mv1, unsigned pos,
3644 __isl_take isl_multi_val *mv2);
3645 __isl_give isl_multi_val *isl_multi_val_range_product(
3646 __isl_take isl_multi_val *mv1,
3647 __isl_take isl_multi_val *mv2);
3648 __isl_give isl_multi_val *
3649 isl_multi_val_range_factor_domain(
3650 __isl_take isl_multi_val *mv);
3651 __isl_give isl_multi_val *
3652 isl_multi_val_range_factor_range(
3653 __isl_take isl_multi_val *mv);
3654 __isl_give isl_multi_val *isl_multi_val_flat_range_product(
3655 __isl_take isl_multi_val *mv1,
3656 __isl_take isl_multi_aff *mv2);
3657 __isl_give isl_multi_val *isl_multi_val_product(
3658 __isl_take isl_multi_val *mv1,
3659 __isl_take isl_multi_val *mv2);
3660 __isl_give isl_multi_val *isl_multi_val_add_val(
3661 __isl_take isl_multi_val *mv,
3662 __isl_take isl_val *v);
3663 __isl_give isl_multi_val *isl_multi_val_mod_val(
3664 __isl_take isl_multi_val *mv,
3665 __isl_take isl_val *v);
3666 __isl_give isl_multi_val *isl_multi_val_scale_val(
3667 __isl_take isl_multi_val *mv,
3668 __isl_take isl_val *v);
3669 __isl_give isl_multi_val *isl_multi_val_scale_multi_val(
3670 __isl_take isl_multi_val *mv1,
3671 __isl_take isl_multi_val *mv2);
3672 __isl_give isl_multi_val *
3673 isl_multi_val_scale_down_multi_val(
3674 __isl_take isl_multi_val *mv1,
3675 __isl_take isl_multi_val *mv2);
3677 A multiple value can be printed using
3679 __isl_give isl_printer *isl_printer_print_multi_val(
3680 __isl_take isl_printer *p,
3681 __isl_keep isl_multi_val *mv);
3685 Vectors can be created, copied and freed using the following functions.
3687 #include <isl/vec.h>
3688 __isl_give isl_vec *isl_vec_alloc(isl_ctx *ctx,
3690 __isl_give isl_vec *isl_vec_copy(__isl_keep isl_vec *vec);
3691 void *isl_vec_free(__isl_take isl_vec *vec);
3693 Note that the elements of a newly created vector may have arbitrary values.
3694 The elements can be changed and inspected using the following functions.
3696 isl_ctx *isl_vec_get_ctx(__isl_keep isl_vec *vec);
3697 int isl_vec_size(__isl_keep isl_vec *vec);
3698 __isl_give isl_val *isl_vec_get_element_val(
3699 __isl_keep isl_vec *vec, int pos);
3700 __isl_give isl_vec *isl_vec_set_element_si(
3701 __isl_take isl_vec *vec, int pos, int v);
3702 __isl_give isl_vec *isl_vec_set_element_val(
3703 __isl_take isl_vec *vec, int pos,
3704 __isl_take isl_val *v);
3705 __isl_give isl_vec *isl_vec_set_si(__isl_take isl_vec *vec,
3707 __isl_give isl_vec *isl_vec_set_val(
3708 __isl_take isl_vec *vec, __isl_take isl_val *v);
3709 int isl_vec_cmp_element(__isl_keep isl_vec *vec1,
3710 __isl_keep isl_vec *vec2, int pos);
3712 C<isl_vec_get_element> will return a negative value if anything went wrong.
3713 In that case, the value of C<*v> is undefined.
3715 The following function can be used to concatenate two vectors.
3717 __isl_give isl_vec *isl_vec_concat(__isl_take isl_vec *vec1,
3718 __isl_take isl_vec *vec2);
3722 Matrices can be created, copied and freed using the following functions.
3724 #include <isl/mat.h>
3725 __isl_give isl_mat *isl_mat_alloc(isl_ctx *ctx,
3726 unsigned n_row, unsigned n_col);
3727 __isl_give isl_mat *isl_mat_copy(__isl_keep isl_mat *mat);
3728 void *isl_mat_free(__isl_take isl_mat *mat);
3730 Note that the elements of a newly created matrix may have arbitrary values.
3731 The elements can be changed and inspected using the following functions.
3733 isl_ctx *isl_mat_get_ctx(__isl_keep isl_mat *mat);
3734 int isl_mat_rows(__isl_keep isl_mat *mat);
3735 int isl_mat_cols(__isl_keep isl_mat *mat);
3736 __isl_give isl_val *isl_mat_get_element_val(
3737 __isl_keep isl_mat *mat, int row, int col);
3738 __isl_give isl_mat *isl_mat_set_element_si(__isl_take isl_mat *mat,
3739 int row, int col, int v);
3740 __isl_give isl_mat *isl_mat_set_element_val(
3741 __isl_take isl_mat *mat, int row, int col,
3742 __isl_take isl_val *v);
3744 C<isl_mat_get_element> will return a negative value if anything went wrong.
3745 In that case, the value of C<*v> is undefined.
3747 The following function can be used to compute the (right) inverse
3748 of a matrix, i.e., a matrix such that the product of the original
3749 and the inverse (in that order) is a multiple of the identity matrix.
3750 The input matrix is assumed to be of full row-rank.
3752 __isl_give isl_mat *isl_mat_right_inverse(__isl_take isl_mat *mat);
3754 The following function can be used to compute the (right) kernel
3755 (or null space) of a matrix, i.e., a matrix such that the product of
3756 the original and the kernel (in that order) is the zero matrix.
3758 __isl_give isl_mat *isl_mat_right_kernel(__isl_take isl_mat *mat);
3760 =head2 Piecewise Quasi Affine Expressions
3762 The zero quasi affine expression or the quasi affine expression
3763 that is equal to a given value or
3764 a specified dimension on a given domain can be created using
3766 __isl_give isl_aff *isl_aff_zero_on_domain(
3767 __isl_take isl_local_space *ls);
3768 __isl_give isl_pw_aff *isl_pw_aff_zero_on_domain(
3769 __isl_take isl_local_space *ls);
3770 __isl_give isl_aff *isl_aff_val_on_domain(
3771 __isl_take isl_local_space *ls,
3772 __isl_take isl_val *val);
3773 __isl_give isl_aff *isl_aff_var_on_domain(
3774 __isl_take isl_local_space *ls,
3775 enum isl_dim_type type, unsigned pos);
3776 __isl_give isl_pw_aff *isl_pw_aff_var_on_domain(
3777 __isl_take isl_local_space *ls,
3778 enum isl_dim_type type, unsigned pos);
3780 Note that the space in which the resulting objects live is a map space
3781 with the given space as domain and a one-dimensional range.
3783 An empty piecewise quasi affine expression (one with no cells)
3784 or a piecewise quasi affine expression with a single cell can
3785 be created using the following functions.
3787 #include <isl/aff.h>
3788 __isl_give isl_pw_aff *isl_pw_aff_empty(
3789 __isl_take isl_space *space);
3790 __isl_give isl_pw_aff *isl_pw_aff_alloc(
3791 __isl_take isl_set *set, __isl_take isl_aff *aff);
3792 __isl_give isl_pw_aff *isl_pw_aff_from_aff(
3793 __isl_take isl_aff *aff);
3795 A piecewise quasi affine expression that is equal to 1 on a set
3796 and 0 outside the set can be created using the following function.
3798 #include <isl/aff.h>
3799 __isl_give isl_pw_aff *isl_set_indicator_function(
3800 __isl_take isl_set *set);
3802 Quasi affine expressions can be copied and freed using
3804 #include <isl/aff.h>
3805 __isl_give isl_aff *isl_aff_copy(__isl_keep isl_aff *aff);
3806 void *isl_aff_free(__isl_take isl_aff *aff);
3808 __isl_give isl_pw_aff *isl_pw_aff_copy(
3809 __isl_keep isl_pw_aff *pwaff);
3810 void *isl_pw_aff_free(__isl_take isl_pw_aff *pwaff);
3812 A (rational) bound on a dimension can be extracted from an C<isl_constraint>
3813 using the following function. The constraint is required to have
3814 a non-zero coefficient for the specified dimension.
3816 #include <isl/constraint.h>
3817 __isl_give isl_aff *isl_constraint_get_bound(
3818 __isl_keep isl_constraint *constraint,
3819 enum isl_dim_type type, int pos);
3821 The entire affine expression of the constraint can also be extracted
3822 using the following function.
3824 #include <isl/constraint.h>
3825 __isl_give isl_aff *isl_constraint_get_aff(
3826 __isl_keep isl_constraint *constraint);
3828 Conversely, an equality constraint equating
3829 the affine expression to zero or an inequality constraint enforcing
3830 the affine expression to be non-negative, can be constructed using
3832 __isl_give isl_constraint *isl_equality_from_aff(
3833 __isl_take isl_aff *aff);
3834 __isl_give isl_constraint *isl_inequality_from_aff(
3835 __isl_take isl_aff *aff);
3837 The expression can be inspected using
3839 #include <isl/aff.h>
3840 isl_ctx *isl_aff_get_ctx(__isl_keep isl_aff *aff);
3841 int isl_aff_dim(__isl_keep isl_aff *aff,
3842 enum isl_dim_type type);
3843 __isl_give isl_local_space *isl_aff_get_domain_local_space(
3844 __isl_keep isl_aff *aff);
3845 __isl_give isl_local_space *isl_aff_get_local_space(
3846 __isl_keep isl_aff *aff);
3847 const char *isl_aff_get_dim_name(__isl_keep isl_aff *aff,
3848 enum isl_dim_type type, unsigned pos);
3849 const char *isl_pw_aff_get_dim_name(
3850 __isl_keep isl_pw_aff *pa,
3851 enum isl_dim_type type, unsigned pos);
3852 int isl_pw_aff_has_dim_id(__isl_keep isl_pw_aff *pa,
3853 enum isl_dim_type type, unsigned pos);
3854 __isl_give isl_id *isl_pw_aff_get_dim_id(
3855 __isl_keep isl_pw_aff *pa,
3856 enum isl_dim_type type, unsigned pos);
3857 int isl_pw_aff_has_tuple_id(__isl_keep isl_pw_aff *pa,
3858 enum isl_dim_type type);
3859 __isl_give isl_id *isl_pw_aff_get_tuple_id(
3860 __isl_keep isl_pw_aff *pa,
3861 enum isl_dim_type type);
3862 __isl_give isl_val *isl_aff_get_constant_val(
3863 __isl_keep isl_aff *aff);
3864 __isl_give isl_val *isl_aff_get_coefficient_val(
3865 __isl_keep isl_aff *aff,
3866 enum isl_dim_type type, int pos);
3867 __isl_give isl_val *isl_aff_get_denominator_val(
3868 __isl_keep isl_aff *aff);
3869 __isl_give isl_aff *isl_aff_get_div(
3870 __isl_keep isl_aff *aff, int pos);
3872 int isl_pw_aff_n_piece(__isl_keep isl_pw_aff *pwaff);
3873 int isl_pw_aff_foreach_piece(__isl_keep isl_pw_aff *pwaff,
3874 int (*fn)(__isl_take isl_set *set,
3875 __isl_take isl_aff *aff,
3876 void *user), void *user);
3878 int isl_aff_is_cst(__isl_keep isl_aff *aff);
3879 int isl_pw_aff_is_cst(__isl_keep isl_pw_aff *pwaff);
3881 int isl_aff_involves_dims(__isl_keep isl_aff *aff,
3882 enum isl_dim_type type, unsigned first, unsigned n);
3883 int isl_pw_aff_involves_dims(__isl_keep isl_pw_aff *pwaff,
3884 enum isl_dim_type type, unsigned first, unsigned n);
3886 isl_ctx *isl_pw_aff_get_ctx(__isl_keep isl_pw_aff *pwaff);
3887 unsigned isl_pw_aff_dim(__isl_keep isl_pw_aff *pwaff,
3888 enum isl_dim_type type);
3889 int isl_pw_aff_is_empty(__isl_keep isl_pw_aff *pwaff);
3891 It can be modified using
3893 #include <isl/aff.h>
3894 __isl_give isl_aff *isl_aff_set_tuple_id(
3895 __isl_take isl_aff *aff,
3896 enum isl_dim_type type, __isl_take isl_id *id);
3897 __isl_give isl_pw_aff *isl_pw_aff_set_tuple_id(
3898 __isl_take isl_pw_aff *pwaff,
3899 enum isl_dim_type type, __isl_take isl_id *id);
3900 __isl_give isl_aff *isl_aff_set_dim_name(
3901 __isl_take isl_aff *aff, enum isl_dim_type type,
3902 unsigned pos, const char *s);
3903 __isl_give isl_aff *isl_aff_set_dim_id(
3904 __isl_take isl_aff *aff, enum isl_dim_type type,
3905 unsigned pos, __isl_take isl_id *id);
3906 __isl_give isl_pw_aff *isl_pw_aff_set_dim_id(
3907 __isl_take isl_pw_aff *pma,
3908 enum isl_dim_type type, unsigned pos,
3909 __isl_take isl_id *id);
3910 __isl_give isl_aff *isl_aff_set_constant_si(
3911 __isl_take isl_aff *aff, int v);
3912 __isl_give isl_aff *isl_aff_set_constant_val(
3913 __isl_take isl_aff *aff, __isl_take isl_val *v);
3914 __isl_give isl_aff *isl_aff_set_coefficient_si(
3915 __isl_take isl_aff *aff,
3916 enum isl_dim_type type, int pos, int v);
3917 __isl_give isl_aff *isl_aff_set_coefficient_val(
3918 __isl_take isl_aff *aff,
3919 enum isl_dim_type type, int pos,
3920 __isl_take isl_val *v);
3922 __isl_give isl_aff *isl_aff_add_constant_si(
3923 __isl_take isl_aff *aff, int v);
3924 __isl_give isl_aff *isl_aff_add_constant_val(
3925 __isl_take isl_aff *aff, __isl_take isl_val *v);
3926 __isl_give isl_aff *isl_aff_add_constant_num_si(
3927 __isl_take isl_aff *aff, int v);
3928 __isl_give isl_aff *isl_aff_add_coefficient_si(
3929 __isl_take isl_aff *aff,
3930 enum isl_dim_type type, int pos, int v);
3931 __isl_give isl_aff *isl_aff_add_coefficient_val(
3932 __isl_take isl_aff *aff,
3933 enum isl_dim_type type, int pos,
3934 __isl_take isl_val *v);
3936 __isl_give isl_aff *isl_aff_insert_dims(
3937 __isl_take isl_aff *aff,
3938 enum isl_dim_type type, unsigned first, unsigned n);
3939 __isl_give isl_pw_aff *isl_pw_aff_insert_dims(
3940 __isl_take isl_pw_aff *pwaff,
3941 enum isl_dim_type type, unsigned first, unsigned n);
3942 __isl_give isl_aff *isl_aff_add_dims(
3943 __isl_take isl_aff *aff,
3944 enum isl_dim_type type, unsigned n);
3945 __isl_give isl_pw_aff *isl_pw_aff_add_dims(
3946 __isl_take isl_pw_aff *pwaff,
3947 enum isl_dim_type type, unsigned n);
3948 __isl_give isl_aff *isl_aff_drop_dims(
3949 __isl_take isl_aff *aff,
3950 enum isl_dim_type type, unsigned first, unsigned n);
3951 __isl_give isl_pw_aff *isl_pw_aff_drop_dims(
3952 __isl_take isl_pw_aff *pwaff,
3953 enum isl_dim_type type, unsigned first, unsigned n);
3954 __isl_give isl_aff *isl_aff_move_dims(
3955 __isl_take isl_aff *aff,
3956 enum isl_dim_type dst_type, unsigned dst_pos,
3957 enum isl_dim_type src_type, unsigned src_pos,
3959 __isl_give isl_pw_aff *isl_pw_aff_move_dims(
3960 __isl_take isl_pw_aff *pa,
3961 enum isl_dim_type dst_type, unsigned dst_pos,
3962 enum isl_dim_type src_type, unsigned src_pos,
3965 Note that C<isl_aff_set_constant_si> and C<isl_aff_set_coefficient_si>
3966 set the I<numerator> of the constant or coefficient, while
3967 C<isl_aff_set_constant_val> and C<isl_aff_set_coefficient_val> set
3968 the constant or coefficient as a whole.
3969 The C<add_constant> and C<add_coefficient> functions add an integer
3970 or rational value to
3971 the possibly rational constant or coefficient.
3972 The C<add_constant_num> functions add an integer value to
3975 To check whether an affine expressions is obviously zero
3976 or (obviously) equal to some other affine expression, use
3978 #include <isl/aff.h>
3979 int isl_aff_plain_is_zero(__isl_keep isl_aff *aff);
3980 int isl_aff_plain_is_equal(__isl_keep isl_aff *aff1,
3981 __isl_keep isl_aff *aff2);
3982 int isl_pw_aff_plain_is_equal(
3983 __isl_keep isl_pw_aff *pwaff1,
3984 __isl_keep isl_pw_aff *pwaff2);
3985 int isl_pw_aff_is_equal(__isl_keep isl_pw_aff *pa1,
3986 __isl_keep isl_pw_aff *pa2);
3990 #include <isl/aff.h>
3991 __isl_give isl_aff *isl_aff_add(__isl_take isl_aff *aff1,
3992 __isl_take isl_aff *aff2);
3993 __isl_give isl_pw_aff *isl_pw_aff_add(
3994 __isl_take isl_pw_aff *pwaff1,
3995 __isl_take isl_pw_aff *pwaff2);
3996 __isl_give isl_pw_aff *isl_pw_aff_min(
3997 __isl_take isl_pw_aff *pwaff1,
3998 __isl_take isl_pw_aff *pwaff2);
3999 __isl_give isl_pw_aff *isl_pw_aff_max(
4000 __isl_take isl_pw_aff *pwaff1,
4001 __isl_take isl_pw_aff *pwaff2);
4002 __isl_give isl_aff *isl_aff_sub(__isl_take isl_aff *aff1,
4003 __isl_take isl_aff *aff2);
4004 __isl_give isl_pw_aff *isl_pw_aff_sub(
4005 __isl_take isl_pw_aff *pwaff1,
4006 __isl_take isl_pw_aff *pwaff2);
4007 __isl_give isl_aff *isl_aff_neg(__isl_take isl_aff *aff);
4008 __isl_give isl_pw_aff *isl_pw_aff_neg(
4009 __isl_take isl_pw_aff *pwaff);
4010 __isl_give isl_aff *isl_aff_ceil(__isl_take isl_aff *aff);
4011 __isl_give isl_pw_aff *isl_pw_aff_ceil(
4012 __isl_take isl_pw_aff *pwaff);
4013 __isl_give isl_aff *isl_aff_floor(__isl_take isl_aff *aff);
4014 __isl_give isl_pw_aff *isl_pw_aff_floor(
4015 __isl_take isl_pw_aff *pwaff);
4016 __isl_give isl_aff *isl_aff_mod_val(__isl_take isl_aff *aff,
4017 __isl_take isl_val *mod);
4018 __isl_give isl_pw_aff *isl_pw_aff_mod_val(
4019 __isl_take isl_pw_aff *pa,
4020 __isl_take isl_val *mod);
4021 __isl_give isl_aff *isl_aff_scale_val(__isl_take isl_aff *aff,
4022 __isl_take isl_val *v);
4023 __isl_give isl_pw_aff *isl_pw_aff_scale_val(
4024 __isl_take isl_pw_aff *pa, __isl_take isl_val *v);
4025 __isl_give isl_aff *isl_aff_scale_down_ui(
4026 __isl_take isl_aff *aff, unsigned f);
4027 __isl_give isl_aff *isl_aff_scale_down_val(
4028 __isl_take isl_aff *aff, __isl_take isl_val *v);
4029 __isl_give isl_pw_aff *isl_pw_aff_scale_down_val(
4030 __isl_take isl_pw_aff *pa,
4031 __isl_take isl_val *f);
4033 __isl_give isl_pw_aff *isl_pw_aff_list_min(
4034 __isl_take isl_pw_aff_list *list);
4035 __isl_give isl_pw_aff *isl_pw_aff_list_max(
4036 __isl_take isl_pw_aff_list *list);
4038 __isl_give isl_pw_aff *isl_pw_aff_coalesce(
4039 __isl_take isl_pw_aff *pwqp);
4041 __isl_give isl_aff *isl_aff_align_params(
4042 __isl_take isl_aff *aff,
4043 __isl_take isl_space *model);
4044 __isl_give isl_pw_aff *isl_pw_aff_align_params(
4045 __isl_take isl_pw_aff *pwaff,
4046 __isl_take isl_space *model);
4048 __isl_give isl_aff *isl_aff_project_domain_on_params(
4049 __isl_take isl_aff *aff);
4050 __isl_give isl_pw_aff *isl_pw_aff_from_range(
4051 __isl_take isl_pw_aff *pwa);
4053 __isl_give isl_aff *isl_aff_gist_params(
4054 __isl_take isl_aff *aff,
4055 __isl_take isl_set *context);
4056 __isl_give isl_aff *isl_aff_gist(__isl_take isl_aff *aff,
4057 __isl_take isl_set *context);
4058 __isl_give isl_pw_aff *isl_pw_aff_gist_params(
4059 __isl_take isl_pw_aff *pwaff,
4060 __isl_take isl_set *context);
4061 __isl_give isl_pw_aff *isl_pw_aff_gist(
4062 __isl_take isl_pw_aff *pwaff,
4063 __isl_take isl_set *context);
4065 __isl_give isl_set *isl_pw_aff_domain(
4066 __isl_take isl_pw_aff *pwaff);
4067 __isl_give isl_set *isl_pw_aff_params(
4068 __isl_take isl_pw_aff *pwa);
4069 __isl_give isl_pw_aff *isl_pw_aff_intersect_domain(
4070 __isl_take isl_pw_aff *pa,
4071 __isl_take isl_set *set);
4072 __isl_give isl_pw_aff *isl_pw_aff_intersect_params(
4073 __isl_take isl_pw_aff *pa,
4074 __isl_take isl_set *set);
4076 __isl_give isl_aff *isl_aff_mul(__isl_take isl_aff *aff1,
4077 __isl_take isl_aff *aff2);
4078 __isl_give isl_aff *isl_aff_div(__isl_take isl_aff *aff1,
4079 __isl_take isl_aff *aff2);
4080 __isl_give isl_pw_aff *isl_pw_aff_mul(
4081 __isl_take isl_pw_aff *pwaff1,
4082 __isl_take isl_pw_aff *pwaff2);
4083 __isl_give isl_pw_aff *isl_pw_aff_div(
4084 __isl_take isl_pw_aff *pa1,
4085 __isl_take isl_pw_aff *pa2);
4086 __isl_give isl_pw_aff *isl_pw_aff_tdiv_q(
4087 __isl_take isl_pw_aff *pa1,
4088 __isl_take isl_pw_aff *pa2);
4089 __isl_give isl_pw_aff *isl_pw_aff_tdiv_r(
4090 __isl_take isl_pw_aff *pa1,
4091 __isl_take isl_pw_aff *pa2);
4093 When multiplying two affine expressions, at least one of the two needs
4094 to be a constant. Similarly, when dividing an affine expression by another,
4095 the second expression needs to be a constant.
4096 C<isl_pw_aff_tdiv_q> computes the quotient of an integer division with
4097 rounding towards zero. C<isl_pw_aff_tdiv_r> computes the corresponding
4100 #include <isl/aff.h>
4101 __isl_give isl_aff *isl_aff_pullback_aff(
4102 __isl_take isl_aff *aff1,
4103 __isl_take isl_aff *aff2);
4104 __isl_give isl_aff *isl_aff_pullback_multi_aff(
4105 __isl_take isl_aff *aff,
4106 __isl_take isl_multi_aff *ma);
4107 __isl_give isl_pw_aff *isl_pw_aff_pullback_multi_aff(
4108 __isl_take isl_pw_aff *pa,
4109 __isl_take isl_multi_aff *ma);
4110 __isl_give isl_pw_aff *isl_pw_aff_pullback_pw_multi_aff(
4111 __isl_take isl_pw_aff *pa,
4112 __isl_take isl_pw_multi_aff *pma);
4113 __isl_give isl_pw_aff *isl_pw_aff_pullback_multi_pw_aff(
4114 __isl_take isl_pw_aff *pa,
4115 __isl_take isl_multi_pw_aff *mpa);
4117 These functions precompose the input expression by the given
4118 C<isl_aff>, C<isl_multi_aff> or C<isl_pw_multi_aff>. In other words,
4119 the C<isl_aff>, C<isl_multi_aff> or C<isl_pw_multi_aff> is plugged
4120 into the (piecewise) affine expression.
4121 Objects of type C<isl_multi_aff> are described in
4122 L</"Piecewise Multiple Quasi Affine Expressions">.
4124 #include <isl/aff.h>
4125 __isl_give isl_basic_set *isl_aff_zero_basic_set(
4126 __isl_take isl_aff *aff);
4127 __isl_give isl_basic_set *isl_aff_neg_basic_set(
4128 __isl_take isl_aff *aff);
4129 __isl_give isl_basic_set *isl_aff_le_basic_set(
4130 __isl_take isl_aff *aff1, __isl_take isl_aff *aff2);
4131 __isl_give isl_basic_set *isl_aff_ge_basic_set(
4132 __isl_take isl_aff *aff1, __isl_take isl_aff *aff2);
4133 __isl_give isl_set *isl_pw_aff_eq_set(
4134 __isl_take isl_pw_aff *pwaff1,
4135 __isl_take isl_pw_aff *pwaff2);
4136 __isl_give isl_set *isl_pw_aff_ne_set(
4137 __isl_take isl_pw_aff *pwaff1,
4138 __isl_take isl_pw_aff *pwaff2);
4139 __isl_give isl_set *isl_pw_aff_le_set(
4140 __isl_take isl_pw_aff *pwaff1,
4141 __isl_take isl_pw_aff *pwaff2);
4142 __isl_give isl_set *isl_pw_aff_lt_set(
4143 __isl_take isl_pw_aff *pwaff1,
4144 __isl_take isl_pw_aff *pwaff2);
4145 __isl_give isl_set *isl_pw_aff_ge_set(
4146 __isl_take isl_pw_aff *pwaff1,
4147 __isl_take isl_pw_aff *pwaff2);
4148 __isl_give isl_set *isl_pw_aff_gt_set(
4149 __isl_take isl_pw_aff *pwaff1,
4150 __isl_take isl_pw_aff *pwaff2);
4152 __isl_give isl_set *isl_pw_aff_list_eq_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_ne_set(
4156 __isl_take isl_pw_aff_list *list1,
4157 __isl_take isl_pw_aff_list *list2);
4158 __isl_give isl_set *isl_pw_aff_list_le_set(
4159 __isl_take isl_pw_aff_list *list1,
4160 __isl_take isl_pw_aff_list *list2);
4161 __isl_give isl_set *isl_pw_aff_list_lt_set(
4162 __isl_take isl_pw_aff_list *list1,
4163 __isl_take isl_pw_aff_list *list2);
4164 __isl_give isl_set *isl_pw_aff_list_ge_set(
4165 __isl_take isl_pw_aff_list *list1,
4166 __isl_take isl_pw_aff_list *list2);
4167 __isl_give isl_set *isl_pw_aff_list_gt_set(
4168 __isl_take isl_pw_aff_list *list1,
4169 __isl_take isl_pw_aff_list *list2);
4171 The function C<isl_aff_neg_basic_set> returns a basic set
4172 containing those elements in the domain space
4173 of C<aff> where C<aff> is negative.
4174 The function C<isl_aff_ge_basic_set> returns a basic set
4175 containing those elements in the shared space
4176 of C<aff1> and C<aff2> where C<aff1> is greater than or equal to C<aff2>.
4177 The function C<isl_pw_aff_ge_set> returns a set
4178 containing those elements in the shared domain
4179 of C<pwaff1> and C<pwaff2> where C<pwaff1> is greater than or equal to C<pwaff2>.
4180 The functions operating on C<isl_pw_aff_list> apply the corresponding
4181 C<isl_pw_aff> function to each pair of elements in the two lists.
4183 #include <isl/aff.h>
4184 __isl_give isl_set *isl_pw_aff_nonneg_set(
4185 __isl_take isl_pw_aff *pwaff);
4186 __isl_give isl_set *isl_pw_aff_zero_set(
4187 __isl_take isl_pw_aff *pwaff);
4188 __isl_give isl_set *isl_pw_aff_non_zero_set(
4189 __isl_take isl_pw_aff *pwaff);
4191 The function C<isl_pw_aff_nonneg_set> returns a set
4192 containing those elements in the domain
4193 of C<pwaff> where C<pwaff> is non-negative.
4195 #include <isl/aff.h>
4196 __isl_give isl_pw_aff *isl_pw_aff_cond(
4197 __isl_take isl_pw_aff *cond,
4198 __isl_take isl_pw_aff *pwaff_true,
4199 __isl_take isl_pw_aff *pwaff_false);
4201 The function C<isl_pw_aff_cond> performs a conditional operator
4202 and returns an expression that is equal to C<pwaff_true>
4203 for elements where C<cond> is non-zero and equal to C<pwaff_false> for elements
4204 where C<cond> is zero.
4206 #include <isl/aff.h>
4207 __isl_give isl_pw_aff *isl_pw_aff_union_min(
4208 __isl_take isl_pw_aff *pwaff1,
4209 __isl_take isl_pw_aff *pwaff2);
4210 __isl_give isl_pw_aff *isl_pw_aff_union_max(
4211 __isl_take isl_pw_aff *pwaff1,
4212 __isl_take isl_pw_aff *pwaff2);
4213 __isl_give isl_pw_aff *isl_pw_aff_union_add(
4214 __isl_take isl_pw_aff *pwaff1,
4215 __isl_take isl_pw_aff *pwaff2);
4217 The function C<isl_pw_aff_union_max> computes a piecewise quasi-affine
4218 expression with a domain that is the union of those of C<pwaff1> and
4219 C<pwaff2> and such that on each cell, the quasi-affine expression is
4220 the maximum of those of C<pwaff1> and C<pwaff2>. If only one of
4221 C<pwaff1> or C<pwaff2> is defined on a given cell, then the
4222 associated expression is the defined one.
4224 An expression can be read from input using
4226 #include <isl/aff.h>
4227 __isl_give isl_aff *isl_aff_read_from_str(
4228 isl_ctx *ctx, const char *str);
4229 __isl_give isl_pw_aff *isl_pw_aff_read_from_str(
4230 isl_ctx *ctx, const char *str);
4232 An expression can be printed using
4234 #include <isl/aff.h>
4235 __isl_give isl_printer *isl_printer_print_aff(
4236 __isl_take isl_printer *p, __isl_keep isl_aff *aff);
4238 __isl_give isl_printer *isl_printer_print_pw_aff(
4239 __isl_take isl_printer *p,
4240 __isl_keep isl_pw_aff *pwaff);
4242 =head2 Piecewise Multiple Quasi Affine Expressions
4244 An C<isl_multi_aff> object represents a sequence of
4245 zero or more affine expressions, all defined on the same domain space.
4246 Similarly, an C<isl_multi_pw_aff> object represents a sequence of
4247 zero or more piecewise affine expressions.
4249 An C<isl_multi_aff> can be constructed from a single
4250 C<isl_aff> or an C<isl_aff_list> using the
4251 following functions. Similarly for C<isl_multi_pw_aff>
4252 and C<isl_pw_multi_aff>.
4254 #include <isl/aff.h>
4255 __isl_give isl_multi_aff *isl_multi_aff_from_aff(
4256 __isl_take isl_aff *aff);
4257 __isl_give isl_multi_pw_aff *
4258 isl_multi_pw_aff_from_multi_aff(
4259 __isl_take isl_multi_aff *ma);
4260 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_from_pw_aff(
4261 __isl_take isl_pw_aff *pa);
4262 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_from_pw_aff(
4263 __isl_take isl_pw_aff *pa);
4264 __isl_give isl_multi_aff *isl_multi_aff_from_aff_list(
4265 __isl_take isl_space *space,
4266 __isl_take isl_aff_list *list);
4268 An C<isl_multi_pw_aff> can be converted to an C<isl_pw_multi_aff>
4269 using the function C<isl_pw_multi_aff_from_multi_pw_aff> below.
4270 Note however that the domain
4271 of the result is the intersection of the domains of the input.
4272 The reverse conversion is exact.
4274 #include <isl/aff.h>
4275 __isl_give isl_pw_multi_aff *
4276 isl_pw_multi_aff_from_multi_pw_aff(
4277 __isl_take isl_multi_pw_aff *mpa);
4278 __isl_give isl_multi_pw_aff *
4279 isl_multi_pw_aff_from_pw_multi_aff(
4280 __isl_take isl_pw_multi_aff *pma);
4282 An empty piecewise multiple quasi affine expression (one with no cells),
4283 the zero piecewise multiple quasi affine expression (with value zero
4284 for each output dimension),
4285 a piecewise multiple quasi affine expression with a single cell (with
4286 either a universe or a specified domain) or
4287 a zero-dimensional piecewise multiple quasi affine expression
4289 can be created using the following functions.
4291 #include <isl/aff.h>
4292 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_empty(
4293 __isl_take isl_space *space);
4294 __isl_give isl_multi_aff *isl_multi_aff_zero(
4295 __isl_take isl_space *space);
4296 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_zero(
4297 __isl_take isl_space *space);
4298 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_zero(
4299 __isl_take isl_space *space);
4300 __isl_give isl_multi_aff *isl_multi_aff_identity(
4301 __isl_take isl_space *space);
4302 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_identity(
4303 __isl_take isl_space *space);
4304 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_identity(
4305 __isl_take isl_space *space);
4306 __isl_give isl_multi_aff *isl_multi_aff_domain_map(
4307 __isl_take isl_space *space);
4308 __isl_give isl_multi_aff *isl_multi_aff_range_map(
4309 __isl_take isl_space *space);
4310 __isl_give isl_multi_aff *isl_multi_aff_project_out_map(
4311 __isl_take isl_space *space,
4312 enum isl_dim_type type,
4313 unsigned first, unsigned n);
4314 __isl_give isl_pw_multi_aff *
4315 isl_pw_multi_aff_project_out_map(
4316 __isl_take isl_space *space,
4317 enum isl_dim_type type,
4318 unsigned first, unsigned n);
4319 __isl_give isl_pw_multi_aff *
4320 isl_pw_multi_aff_from_multi_aff(
4321 __isl_take isl_multi_aff *ma);
4322 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_alloc(
4323 __isl_take isl_set *set,
4324 __isl_take isl_multi_aff *maff);
4325 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_from_domain(
4326 __isl_take isl_set *set);
4328 __isl_give isl_union_pw_multi_aff *
4329 isl_union_pw_multi_aff_empty(
4330 __isl_take isl_space *space);
4331 __isl_give isl_union_pw_multi_aff *
4332 isl_union_pw_multi_aff_add_pw_multi_aff(
4333 __isl_take isl_union_pw_multi_aff *upma,
4334 __isl_take isl_pw_multi_aff *pma);
4335 __isl_give isl_union_pw_multi_aff *
4336 isl_union_pw_multi_aff_from_domain(
4337 __isl_take isl_union_set *uset);
4339 A piecewise multiple quasi affine expression can also be initialized
4340 from an C<isl_set> or C<isl_map>, provided the C<isl_set> is a singleton
4341 and the C<isl_map> is single-valued.
4342 In case of a conversion from an C<isl_union_set> or an C<isl_union_map>
4343 to an C<isl_union_pw_multi_aff>, these properties need to hold in each space.
4345 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_from_set(
4346 __isl_take isl_set *set);
4347 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_from_map(
4348 __isl_take isl_map *map);
4350 __isl_give isl_union_pw_multi_aff *
4351 isl_union_pw_multi_aff_from_union_set(
4352 __isl_take isl_union_set *uset);
4353 __isl_give isl_union_pw_multi_aff *
4354 isl_union_pw_multi_aff_from_union_map(
4355 __isl_take isl_union_map *umap);
4357 Multiple quasi affine expressions can be copied and freed using
4359 #include <isl/aff.h>
4360 __isl_give isl_multi_aff *isl_multi_aff_copy(
4361 __isl_keep isl_multi_aff *maff);
4362 void *isl_multi_aff_free(__isl_take isl_multi_aff *maff);
4364 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_copy(
4365 __isl_keep isl_pw_multi_aff *pma);
4366 void *isl_pw_multi_aff_free(
4367 __isl_take isl_pw_multi_aff *pma);
4369 __isl_give isl_union_pw_multi_aff *
4370 isl_union_pw_multi_aff_copy(
4371 __isl_keep isl_union_pw_multi_aff *upma);
4372 void *isl_union_pw_multi_aff_free(
4373 __isl_take isl_union_pw_multi_aff *upma);
4375 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_copy(
4376 __isl_keep isl_multi_pw_aff *mpa);
4377 void *isl_multi_pw_aff_free(
4378 __isl_take isl_multi_pw_aff *mpa);
4380 The expression can be inspected using
4382 #include <isl/aff.h>
4383 isl_ctx *isl_multi_aff_get_ctx(
4384 __isl_keep isl_multi_aff *maff);
4385 isl_ctx *isl_pw_multi_aff_get_ctx(
4386 __isl_keep isl_pw_multi_aff *pma);
4387 isl_ctx *isl_union_pw_multi_aff_get_ctx(
4388 __isl_keep isl_union_pw_multi_aff *upma);
4389 isl_ctx *isl_multi_pw_aff_get_ctx(
4390 __isl_keep isl_multi_pw_aff *mpa);
4392 int isl_multi_aff_involves_dims(
4393 __isl_keep isl_multi_aff *ma,
4394 enum isl_dim_type type, unsigned first, unsigned n);
4395 int isl_multi_pw_aff_involves_dims(
4396 __isl_keep isl_multi_pw_aff *mpa,
4397 enum isl_dim_type type, unsigned first, unsigned n);
4399 unsigned isl_multi_aff_dim(__isl_keep isl_multi_aff *maff,
4400 enum isl_dim_type type);
4401 unsigned isl_pw_multi_aff_dim(
4402 __isl_keep isl_pw_multi_aff *pma,
4403 enum isl_dim_type type);
4404 unsigned isl_multi_pw_aff_dim(
4405 __isl_keep isl_multi_pw_aff *mpa,
4406 enum isl_dim_type type);
4407 __isl_give isl_aff *isl_multi_aff_get_aff(
4408 __isl_keep isl_multi_aff *multi, int pos);
4409 __isl_give isl_pw_aff *isl_pw_multi_aff_get_pw_aff(
4410 __isl_keep isl_pw_multi_aff *pma, int pos);
4411 __isl_give isl_pw_aff *isl_multi_pw_aff_get_pw_aff(
4412 __isl_keep isl_multi_pw_aff *mpa, int pos);
4413 int isl_multi_aff_find_dim_by_id(
4414 __isl_keep isl_multi_aff *ma,
4415 enum isl_dim_type type, __isl_keep isl_id *id);
4416 int isl_multi_pw_aff_find_dim_by_id(
4417 __isl_keep isl_multi_pw_aff *mpa,
4418 enum isl_dim_type type, __isl_keep isl_id *id);
4419 const char *isl_pw_multi_aff_get_dim_name(
4420 __isl_keep isl_pw_multi_aff *pma,
4421 enum isl_dim_type type, unsigned pos);
4422 __isl_give isl_id *isl_multi_aff_get_dim_id(
4423 __isl_keep isl_multi_aff *ma,
4424 enum isl_dim_type type, unsigned pos);
4425 __isl_give isl_id *isl_pw_multi_aff_get_dim_id(
4426 __isl_keep isl_pw_multi_aff *pma,
4427 enum isl_dim_type type, unsigned pos);
4428 __isl_give isl_id *isl_multi_pw_aff_get_dim_id(
4429 __isl_keep isl_multi_pw_aff *mpa,
4430 enum isl_dim_type type, unsigned pos);
4431 const char *isl_multi_aff_get_tuple_name(
4432 __isl_keep isl_multi_aff *multi,
4433 enum isl_dim_type type);
4434 int isl_pw_multi_aff_has_tuple_name(
4435 __isl_keep isl_pw_multi_aff *pma,
4436 enum isl_dim_type type);
4437 const char *isl_pw_multi_aff_get_tuple_name(
4438 __isl_keep isl_pw_multi_aff *pma,
4439 enum isl_dim_type type);
4440 int isl_multi_aff_has_tuple_id(__isl_keep isl_multi_aff *ma,
4441 enum isl_dim_type type);
4442 int isl_pw_multi_aff_has_tuple_id(
4443 __isl_keep isl_pw_multi_aff *pma,
4444 enum isl_dim_type type);
4445 int isl_multi_pw_aff_has_tuple_id(
4446 __isl_keep isl_multi_pw_aff *mpa,
4447 enum isl_dim_type type);
4448 __isl_give isl_id *isl_multi_aff_get_tuple_id(
4449 __isl_keep isl_multi_aff *ma,
4450 enum isl_dim_type type);
4451 __isl_give isl_id *isl_pw_multi_aff_get_tuple_id(
4452 __isl_keep isl_pw_multi_aff *pma,
4453 enum isl_dim_type type);
4454 __isl_give isl_id *isl_multi_pw_aff_get_tuple_id(
4455 __isl_keep isl_multi_pw_aff *mpa,
4456 enum isl_dim_type type);
4457 int isl_multi_aff_range_is_wrapping(
4458 __isl_keep isl_multi_aff *ma);
4459 int isl_multi_pw_aff_range_is_wrapping(
4460 __isl_keep isl_multi_pw_aff *mpa);
4462 int isl_pw_multi_aff_foreach_piece(
4463 __isl_keep isl_pw_multi_aff *pma,
4464 int (*fn)(__isl_take isl_set *set,
4465 __isl_take isl_multi_aff *maff,
4466 void *user), void *user);
4468 int isl_union_pw_multi_aff_foreach_pw_multi_aff(
4469 __isl_keep isl_union_pw_multi_aff *upma,
4470 int (*fn)(__isl_take isl_pw_multi_aff *pma,
4471 void *user), void *user);
4473 It can be modified using
4475 #include <isl/aff.h>
4476 __isl_give isl_multi_aff *isl_multi_aff_set_aff(
4477 __isl_take isl_multi_aff *multi, int pos,
4478 __isl_take isl_aff *aff);
4479 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_set_pw_aff(
4480 __isl_take isl_pw_multi_aff *pma, unsigned pos,
4481 __isl_take isl_pw_aff *pa);
4482 __isl_give isl_multi_aff *isl_multi_aff_set_dim_name(
4483 __isl_take isl_multi_aff *maff,
4484 enum isl_dim_type type, unsigned pos, const char *s);
4485 __isl_give isl_multi_aff *isl_multi_aff_set_dim_id(
4486 __isl_take isl_multi_aff *maff,
4487 enum isl_dim_type type, unsigned pos,
4488 __isl_take isl_id *id);
4489 __isl_give isl_multi_aff *isl_multi_aff_set_tuple_name(
4490 __isl_take isl_multi_aff *maff,
4491 enum isl_dim_type type, const char *s);
4492 __isl_give isl_multi_aff *isl_multi_aff_set_tuple_id(
4493 __isl_take isl_multi_aff *maff,
4494 enum isl_dim_type type, __isl_take isl_id *id);
4495 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_set_tuple_id(
4496 __isl_take isl_pw_multi_aff *pma,
4497 enum isl_dim_type type, __isl_take isl_id *id);
4498 __isl_give isl_multi_aff *isl_multi_aff_reset_tuple_id(
4499 __isl_take isl_multi_aff *ma,
4500 enum isl_dim_type type);
4501 __isl_give isl_multi_pw_aff *
4502 isl_multi_pw_aff_reset_tuple_id(
4503 __isl_take isl_multi_pw_aff *mpa,
4504 enum isl_dim_type type);
4505 __isl_give isl_multi_aff *isl_multi_aff_reset_user(
4506 __isl_take isl_multi_aff *ma);
4507 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_reset_user(
4508 __isl_take isl_multi_pw_aff *mpa);
4510 __isl_give isl_multi_pw_aff *
4511 isl_multi_pw_aff_set_dim_name(
4512 __isl_take isl_multi_pw_aff *mpa,
4513 enum isl_dim_type type, unsigned pos, const char *s);
4514 __isl_give isl_multi_pw_aff *
4515 isl_multi_pw_aff_set_dim_id(
4516 __isl_take isl_multi_pw_aff *mpa,
4517 enum isl_dim_type type, unsigned pos,
4518 __isl_take isl_id *id);
4519 __isl_give isl_multi_pw_aff *
4520 isl_multi_pw_aff_set_tuple_name(
4521 __isl_take isl_multi_pw_aff *mpa,
4522 enum isl_dim_type type, const char *s);
4524 __isl_give isl_multi_aff *isl_multi_aff_flatten_domain(
4525 __isl_take isl_multi_aff *ma);
4527 __isl_give isl_multi_aff *isl_multi_aff_insert_dims(
4528 __isl_take isl_multi_aff *ma,
4529 enum isl_dim_type type, unsigned first, unsigned n);
4530 __isl_give isl_multi_aff *isl_multi_aff_add_dims(
4531 __isl_take isl_multi_aff *ma,
4532 enum isl_dim_type type, unsigned n);
4533 __isl_give isl_multi_aff *isl_multi_aff_drop_dims(
4534 __isl_take isl_multi_aff *maff,
4535 enum isl_dim_type type, unsigned first, unsigned n);
4536 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_drop_dims(
4537 __isl_take isl_pw_multi_aff *pma,
4538 enum isl_dim_type type, unsigned first, unsigned n);
4540 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_insert_dims(
4541 __isl_take isl_multi_pw_aff *mpa,
4542 enum isl_dim_type type, unsigned first, unsigned n);
4543 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_add_dims(
4544 __isl_take isl_multi_pw_aff *mpa,
4545 enum isl_dim_type type, unsigned n);
4546 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_move_dims(
4547 __isl_take isl_multi_pw_aff *pma,
4548 enum isl_dim_type dst_type, unsigned dst_pos,
4549 enum isl_dim_type src_type, unsigned src_pos,
4552 To check whether two multiple affine expressions are
4553 (obviously) equal to each other, use
4555 int isl_multi_aff_plain_is_equal(__isl_keep isl_multi_aff *maff1,
4556 __isl_keep isl_multi_aff *maff2);
4557 int isl_pw_multi_aff_plain_is_equal(
4558 __isl_keep isl_pw_multi_aff *pma1,
4559 __isl_keep isl_pw_multi_aff *pma2);
4560 int isl_multi_pw_aff_plain_is_equal(
4561 __isl_keep isl_multi_pw_aff *mpa1,
4562 __isl_keep isl_multi_pw_aff *mpa2);
4563 int isl_multi_pw_aff_is_equal(
4564 __isl_keep isl_multi_pw_aff *mpa1,
4565 __isl_keep isl_multi_pw_aff *mpa2);
4569 #include <isl/aff.h>
4570 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_union_lexmin(
4571 __isl_take isl_pw_multi_aff *pma1,
4572 __isl_take isl_pw_multi_aff *pma2);
4573 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_union_lexmax(
4574 __isl_take isl_pw_multi_aff *pma1,
4575 __isl_take isl_pw_multi_aff *pma2);
4576 __isl_give isl_multi_aff *isl_multi_aff_add(
4577 __isl_take isl_multi_aff *maff1,
4578 __isl_take isl_multi_aff *maff2);
4579 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_add(
4580 __isl_take isl_pw_multi_aff *pma1,
4581 __isl_take isl_pw_multi_aff *pma2);
4582 __isl_give isl_union_pw_multi_aff *isl_union_pw_multi_aff_add(
4583 __isl_take isl_union_pw_multi_aff *upma1,
4584 __isl_take isl_union_pw_multi_aff *upma2);
4585 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_union_add(
4586 __isl_take isl_pw_multi_aff *pma1,
4587 __isl_take isl_pw_multi_aff *pma2);
4588 __isl_give isl_multi_aff *isl_multi_aff_sub(
4589 __isl_take isl_multi_aff *ma1,
4590 __isl_take isl_multi_aff *ma2);
4591 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_sub(
4592 __isl_take isl_pw_multi_aff *pma1,
4593 __isl_take isl_pw_multi_aff *pma2);
4594 __isl_give isl_union_pw_multi_aff *isl_union_pw_multi_aff_sub(
4595 __isl_take isl_union_pw_multi_aff *upma1,
4596 __isl_take isl_union_pw_multi_aff *upma2);
4598 C<isl_multi_aff_sub> subtracts the second argument from the first.
4600 __isl_give isl_multi_aff *isl_multi_aff_scale_val(
4601 __isl_take isl_multi_aff *ma,
4602 __isl_take isl_val *v);
4603 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_scale_val(
4604 __isl_take isl_pw_multi_aff *pma,
4605 __isl_take isl_val *v);
4606 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_scale_val(
4607 __isl_take isl_multi_pw_aff *mpa,
4608 __isl_take isl_val *v);
4609 __isl_give isl_multi_aff *isl_multi_aff_scale_multi_val(
4610 __isl_take isl_multi_aff *ma,
4611 __isl_take isl_multi_val *mv);
4612 __isl_give isl_pw_multi_aff *
4613 isl_pw_multi_aff_scale_multi_val(
4614 __isl_take isl_pw_multi_aff *pma,
4615 __isl_take isl_multi_val *mv);
4616 __isl_give isl_multi_pw_aff *
4617 isl_multi_pw_aff_scale_multi_val(
4618 __isl_take isl_multi_pw_aff *mpa,
4619 __isl_take isl_multi_val *mv);
4620 __isl_give isl_union_pw_multi_aff *
4621 isl_union_pw_multi_aff_scale_multi_val(
4622 __isl_take isl_union_pw_multi_aff *upma,
4623 __isl_take isl_multi_val *mv);
4624 __isl_give isl_multi_aff *
4625 isl_multi_aff_scale_down_multi_val(
4626 __isl_take isl_multi_aff *ma,
4627 __isl_take isl_multi_val *mv);
4628 __isl_give isl_multi_pw_aff *
4629 isl_multi_pw_aff_scale_down_multi_val(
4630 __isl_take isl_multi_pw_aff *mpa,
4631 __isl_take isl_multi_val *mv);
4633 C<isl_multi_aff_scale_multi_val> scales the elements of C<ma>
4634 by the corresponding elements of C<mv>.
4636 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_fix_si(
4637 __isl_take isl_pw_multi_aff *pma,
4638 enum isl_dim_type type, unsigned pos, int value);
4639 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_intersect_params(
4640 __isl_take isl_pw_multi_aff *pma,
4641 __isl_take isl_set *set);
4642 __isl_give isl_set *isl_multi_pw_aff_domain(
4643 __isl_take isl_multi_pw_aff *mpa);
4644 __isl_give isl_multi_pw_aff *
4645 isl_multi_pw_aff_intersect_params(
4646 __isl_take isl_multi_pw_aff *mpa,
4647 __isl_take isl_set *set);
4648 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_intersect_domain(
4649 __isl_take isl_pw_multi_aff *pma,
4650 __isl_take isl_set *set);
4651 __isl_give isl_multi_pw_aff *
4652 isl_multi_pw_aff_intersect_domain(
4653 __isl_take isl_multi_pw_aff *mpa,
4654 __isl_take isl_set *domain);
4655 __isl_give isl_union_pw_multi_aff *
4656 isl_union_pw_multi_aff_intersect_domain(
4657 __isl_take isl_union_pw_multi_aff *upma,
4658 __isl_take isl_union_set *uset);
4659 __isl_give isl_multi_aff *isl_multi_aff_lift(
4660 __isl_take isl_multi_aff *maff,
4661 __isl_give isl_local_space **ls);
4662 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_coalesce(
4663 __isl_take isl_pw_multi_aff *pma);
4664 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_coalesce(
4665 __isl_take isl_multi_pw_aff *mpa);
4666 __isl_give isl_multi_aff *isl_multi_aff_align_params(
4667 __isl_take isl_multi_aff *multi,
4668 __isl_take isl_space *model);
4669 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_align_params(
4670 __isl_take isl_pw_multi_aff *pma,
4671 __isl_take isl_space *model);
4672 __isl_give isl_pw_multi_aff *
4673 isl_pw_multi_aff_project_domain_on_params(
4674 __isl_take isl_pw_multi_aff *pma);
4675 __isl_give isl_multi_aff *isl_multi_aff_gist_params(
4676 __isl_take isl_multi_aff *maff,
4677 __isl_take isl_set *context);
4678 __isl_give isl_multi_aff *isl_multi_aff_gist(
4679 __isl_take isl_multi_aff *maff,
4680 __isl_take isl_set *context);
4681 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_gist_params(
4682 __isl_take isl_pw_multi_aff *pma,
4683 __isl_take isl_set *set);
4684 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_gist(
4685 __isl_take isl_pw_multi_aff *pma,
4686 __isl_take isl_set *set);
4687 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_gist_params(
4688 __isl_take isl_multi_pw_aff *mpa,
4689 __isl_take isl_set *set);
4690 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_gist(
4691 __isl_take isl_multi_pw_aff *mpa,
4692 __isl_take isl_set *set);
4693 __isl_give isl_multi_aff *isl_multi_aff_from_range(
4694 __isl_take isl_multi_aff *ma);
4695 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_from_range(
4696 __isl_take isl_multi_pw_aff *mpa);
4697 __isl_give isl_set *isl_pw_multi_aff_domain(
4698 __isl_take isl_pw_multi_aff *pma);
4699 __isl_give isl_union_set *isl_union_pw_multi_aff_domain(
4700 __isl_take isl_union_pw_multi_aff *upma);
4701 __isl_give isl_multi_aff *isl_multi_aff_range_splice(
4702 __isl_take isl_multi_aff *ma1, unsigned pos,
4703 __isl_take isl_multi_aff *ma2);
4704 __isl_give isl_multi_aff *isl_multi_aff_splice(
4705 __isl_take isl_multi_aff *ma1,
4706 unsigned in_pos, unsigned out_pos,
4707 __isl_take isl_multi_aff *ma2);
4708 __isl_give isl_multi_aff *isl_multi_aff_range_product(
4709 __isl_take isl_multi_aff *ma1,
4710 __isl_take isl_multi_aff *ma2);
4711 __isl_give isl_multi_aff *
4712 isl_multi_aff_range_factor_domain(
4713 __isl_take isl_multi_aff *ma);
4714 __isl_give isl_multi_aff *
4715 isl_multi_aff_range_factor_range(
4716 __isl_take isl_multi_aff *ma);
4717 __isl_give isl_multi_aff *isl_multi_aff_flat_range_product(
4718 __isl_take isl_multi_aff *ma1,
4719 __isl_take isl_multi_aff *ma2);
4720 __isl_give isl_multi_aff *isl_multi_aff_product(
4721 __isl_take isl_multi_aff *ma1,
4722 __isl_take isl_multi_aff *ma2);
4723 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_product(
4724 __isl_take isl_multi_pw_aff *mpa1,
4725 __isl_take isl_multi_pw_aff *mpa2);
4726 __isl_give isl_pw_multi_aff *
4727 isl_pw_multi_aff_range_product(
4728 __isl_take isl_pw_multi_aff *pma1,
4729 __isl_take isl_pw_multi_aff *pma2);
4730 __isl_give isl_multi_pw_aff *
4731 isl_multi_pw_aff_range_factor_domain(
4732 __isl_take isl_multi_pw_aff *mpa);
4733 __isl_give isl_multi_pw_aff *
4734 isl_multi_pw_aff_range_factor_range(
4735 __isl_take isl_multi_pw_aff *mpa);
4736 __isl_give isl_pw_multi_aff *
4737 isl_pw_multi_aff_flat_range_product(
4738 __isl_take isl_pw_multi_aff *pma1,
4739 __isl_take isl_pw_multi_aff *pma2);
4740 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_product(
4741 __isl_take isl_pw_multi_aff *pma1,
4742 __isl_take isl_pw_multi_aff *pma2);
4743 __isl_give isl_union_pw_multi_aff *
4744 isl_union_pw_multi_aff_flat_range_product(
4745 __isl_take isl_union_pw_multi_aff *upma1,
4746 __isl_take isl_union_pw_multi_aff *upma2);
4747 __isl_give isl_multi_pw_aff *
4748 isl_multi_pw_aff_range_splice(
4749 __isl_take isl_multi_pw_aff *mpa1, unsigned pos,
4750 __isl_take isl_multi_pw_aff *mpa2);
4751 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_splice(
4752 __isl_take isl_multi_pw_aff *mpa1,
4753 unsigned in_pos, unsigned out_pos,
4754 __isl_take isl_multi_pw_aff *mpa2);
4755 __isl_give isl_multi_pw_aff *
4756 isl_multi_pw_aff_range_product(
4757 __isl_take isl_multi_pw_aff *mpa1,
4758 __isl_take isl_multi_pw_aff *mpa2);
4759 __isl_give isl_multi_pw_aff *
4760 isl_multi_pw_aff_flat_range_product(
4761 __isl_take isl_multi_pw_aff *mpa1,
4762 __isl_take isl_multi_pw_aff *mpa2);
4764 If the C<ls> argument of C<isl_multi_aff_lift> is not C<NULL>,
4765 then it is assigned the local space that lies at the basis of
4766 the lifting applied.
4768 #include <isl/aff.h>
4769 __isl_give isl_multi_aff *isl_multi_aff_pullback_multi_aff(
4770 __isl_take isl_multi_aff *ma1,
4771 __isl_take isl_multi_aff *ma2);
4772 __isl_give isl_pw_multi_aff *
4773 isl_pw_multi_aff_pullback_multi_aff(
4774 __isl_take isl_pw_multi_aff *pma,
4775 __isl_take isl_multi_aff *ma);
4776 __isl_give isl_multi_pw_aff *
4777 isl_multi_pw_aff_pullback_multi_aff(
4778 __isl_take isl_multi_pw_aff *mpa,
4779 __isl_take isl_multi_aff *ma);
4780 __isl_give isl_pw_multi_aff *
4781 isl_pw_multi_aff_pullback_pw_multi_aff(
4782 __isl_take isl_pw_multi_aff *pma1,
4783 __isl_take isl_pw_multi_aff *pma2);
4784 __isl_give isl_multi_pw_aff *
4785 isl_multi_pw_aff_pullback_pw_multi_aff(
4786 __isl_take isl_multi_pw_aff *mpa,
4787 __isl_take isl_pw_multi_aff *pma);
4788 __isl_give isl_multi_pw_aff *
4789 isl_multi_pw_aff_pullback_multi_pw_aff(
4790 __isl_take isl_multi_pw_aff *mpa1,
4791 __isl_take isl_multi_pw_aff *mpa2);
4793 The function C<isl_multi_aff_pullback_multi_aff> precomposes C<ma1> by C<ma2>.
4794 In other words, C<ma2> is plugged
4797 __isl_give isl_set *isl_multi_aff_lex_le_set(
4798 __isl_take isl_multi_aff *ma1,
4799 __isl_take isl_multi_aff *ma2);
4800 __isl_give isl_set *isl_multi_aff_lex_ge_set(
4801 __isl_take isl_multi_aff *ma1,
4802 __isl_take isl_multi_aff *ma2);
4804 The function C<isl_multi_aff_lex_le_set> returns a set
4805 containing those elements in the shared domain space
4806 where C<ma1> is lexicographically smaller than or
4809 An expression can be read from input using
4811 #include <isl/aff.h>
4812 __isl_give isl_multi_aff *isl_multi_aff_read_from_str(
4813 isl_ctx *ctx, const char *str);
4814 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_read_from_str(
4815 isl_ctx *ctx, const char *str);
4816 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_read_from_str(
4817 isl_ctx *ctx, const char *str);
4818 __isl_give isl_union_pw_multi_aff *
4819 isl_union_pw_multi_aff_read_from_str(
4820 isl_ctx *ctx, const char *str);
4822 An expression can be printed using
4824 #include <isl/aff.h>
4825 __isl_give isl_printer *isl_printer_print_multi_aff(
4826 __isl_take isl_printer *p,
4827 __isl_keep isl_multi_aff *maff);
4828 __isl_give isl_printer *isl_printer_print_pw_multi_aff(
4829 __isl_take isl_printer *p,
4830 __isl_keep isl_pw_multi_aff *pma);
4831 __isl_give isl_printer *isl_printer_print_union_pw_multi_aff(
4832 __isl_take isl_printer *p,
4833 __isl_keep isl_union_pw_multi_aff *upma);
4834 __isl_give isl_printer *isl_printer_print_multi_pw_aff(
4835 __isl_take isl_printer *p,
4836 __isl_keep isl_multi_pw_aff *mpa);
4840 Points are elements of a set. They can be used to construct
4841 simple sets (boxes) or they can be used to represent the
4842 individual elements of a set.
4843 The zero point (the origin) can be created using
4845 __isl_give isl_point *isl_point_zero(__isl_take isl_space *space);
4847 The coordinates of a point can be inspected, set and changed
4850 __isl_give isl_val *isl_point_get_coordinate_val(
4851 __isl_keep isl_point *pnt,
4852 enum isl_dim_type type, int pos);
4853 __isl_give isl_point *isl_point_set_coordinate_val(
4854 __isl_take isl_point *pnt,
4855 enum isl_dim_type type, int pos,
4856 __isl_take isl_val *v);
4858 __isl_give isl_point *isl_point_add_ui(
4859 __isl_take isl_point *pnt,
4860 enum isl_dim_type type, int pos, unsigned val);
4861 __isl_give isl_point *isl_point_sub_ui(
4862 __isl_take isl_point *pnt,
4863 enum isl_dim_type type, int pos, unsigned val);
4865 Other properties can be obtained using
4867 isl_ctx *isl_point_get_ctx(__isl_keep isl_point *pnt);
4869 Points can be copied or freed using
4871 __isl_give isl_point *isl_point_copy(
4872 __isl_keep isl_point *pnt);
4873 void isl_point_free(__isl_take isl_point *pnt);
4875 A singleton set can be created from a point using
4877 __isl_give isl_basic_set *isl_basic_set_from_point(
4878 __isl_take isl_point *pnt);
4879 __isl_give isl_set *isl_set_from_point(
4880 __isl_take isl_point *pnt);
4882 and a box can be created from two opposite extremal points using
4884 __isl_give isl_basic_set *isl_basic_set_box_from_points(
4885 __isl_take isl_point *pnt1,
4886 __isl_take isl_point *pnt2);
4887 __isl_give isl_set *isl_set_box_from_points(
4888 __isl_take isl_point *pnt1,
4889 __isl_take isl_point *pnt2);
4891 All elements of a B<bounded> (union) set can be enumerated using
4892 the following functions.
4894 int isl_set_foreach_point(__isl_keep isl_set *set,
4895 int (*fn)(__isl_take isl_point *pnt, void *user),
4897 int isl_union_set_foreach_point(__isl_keep isl_union_set *uset,
4898 int (*fn)(__isl_take isl_point *pnt, void *user),
4901 The function C<fn> is called for each integer point in
4902 C<set> with as second argument the last argument of
4903 the C<isl_set_foreach_point> call. The function C<fn>
4904 should return C<0> on success and C<-1> on failure.
4905 In the latter case, C<isl_set_foreach_point> will stop
4906 enumerating and return C<-1> as well.
4907 If the enumeration is performed successfully and to completion,
4908 then C<isl_set_foreach_point> returns C<0>.
4910 To obtain a single point of a (basic) set, use
4912 __isl_give isl_point *isl_basic_set_sample_point(
4913 __isl_take isl_basic_set *bset);
4914 __isl_give isl_point *isl_set_sample_point(
4915 __isl_take isl_set *set);
4917 If C<set> does not contain any (integer) points, then the
4918 resulting point will be ``void'', a property that can be
4921 int isl_point_is_void(__isl_keep isl_point *pnt);
4923 =head2 Piecewise Quasipolynomials
4925 A piecewise quasipolynomial is a particular kind of function that maps
4926 a parametric point to a rational value.
4927 More specifically, a quasipolynomial is a polynomial expression in greatest
4928 integer parts of affine expressions of parameters and variables.
4929 A piecewise quasipolynomial is a subdivision of a given parametric
4930 domain into disjoint cells with a quasipolynomial associated to
4931 each cell. The value of the piecewise quasipolynomial at a given
4932 point is the value of the quasipolynomial associated to the cell
4933 that contains the point. Outside of the union of cells,
4934 the value is assumed to be zero.
4935 For example, the piecewise quasipolynomial
4937 [n] -> { [x] -> ((1 + n) - x) : x <= n and x >= 0 }
4939 maps C<x> to C<1 + n - x> for values of C<x> between C<0> and C<n>.
4940 A given piecewise quasipolynomial has a fixed domain dimension.
4941 Union piecewise quasipolynomials are used to contain piecewise quasipolynomials
4942 defined over different domains.
4943 Piecewise quasipolynomials are mainly used by the C<barvinok>
4944 library for representing the number of elements in a parametric set or map.
4945 For example, the piecewise quasipolynomial above represents
4946 the number of points in the map
4948 [n] -> { [x] -> [y] : x,y >= 0 and 0 <= x + y <= n }
4950 =head3 Input and Output
4952 Piecewise quasipolynomials can be read from input using
4954 __isl_give isl_union_pw_qpolynomial *
4955 isl_union_pw_qpolynomial_read_from_str(
4956 isl_ctx *ctx, const char *str);
4958 Quasipolynomials and piecewise quasipolynomials can be printed
4959 using the following functions.
4961 __isl_give isl_printer *isl_printer_print_qpolynomial(
4962 __isl_take isl_printer *p,
4963 __isl_keep isl_qpolynomial *qp);
4965 __isl_give isl_printer *isl_printer_print_pw_qpolynomial(
4966 __isl_take isl_printer *p,
4967 __isl_keep isl_pw_qpolynomial *pwqp);
4969 __isl_give isl_printer *isl_printer_print_union_pw_qpolynomial(
4970 __isl_take isl_printer *p,
4971 __isl_keep isl_union_pw_qpolynomial *upwqp);
4973 The output format of the printer
4974 needs to be set to either C<ISL_FORMAT_ISL> or C<ISL_FORMAT_C>.
4975 For C<isl_printer_print_union_pw_qpolynomial>, only C<ISL_FORMAT_ISL>
4977 In case of printing in C<ISL_FORMAT_C>, the user may want
4978 to set the names of all dimensions
4980 __isl_give isl_qpolynomial *isl_qpolynomial_set_dim_name(
4981 __isl_take isl_qpolynomial *qp,
4982 enum isl_dim_type type, unsigned pos,
4984 __isl_give isl_pw_qpolynomial *
4985 isl_pw_qpolynomial_set_dim_name(
4986 __isl_take isl_pw_qpolynomial *pwqp,
4987 enum isl_dim_type type, unsigned pos,
4990 =head3 Creating New (Piecewise) Quasipolynomials
4992 Some simple quasipolynomials can be created using the following functions.
4993 More complicated quasipolynomials can be created by applying
4994 operations such as addition and multiplication
4995 on the resulting quasipolynomials
4997 __isl_give isl_qpolynomial *isl_qpolynomial_zero_on_domain(
4998 __isl_take isl_space *domain);
4999 __isl_give isl_qpolynomial *isl_qpolynomial_one_on_domain(
5000 __isl_take isl_space *domain);
5001 __isl_give isl_qpolynomial *isl_qpolynomial_infty_on_domain(
5002 __isl_take isl_space *domain);
5003 __isl_give isl_qpolynomial *isl_qpolynomial_neginfty_on_domain(
5004 __isl_take isl_space *domain);
5005 __isl_give isl_qpolynomial *isl_qpolynomial_nan_on_domain(
5006 __isl_take isl_space *domain);
5007 __isl_give isl_qpolynomial *isl_qpolynomial_val_on_domain(
5008 __isl_take isl_space *domain,
5009 __isl_take isl_val *val);
5010 __isl_give isl_qpolynomial *isl_qpolynomial_var_on_domain(
5011 __isl_take isl_space *domain,
5012 enum isl_dim_type type, unsigned pos);
5013 __isl_give isl_qpolynomial *isl_qpolynomial_from_aff(
5014 __isl_take isl_aff *aff);
5016 Note that the space in which a quasipolynomial lives is a map space
5017 with a one-dimensional range. The C<domain> argument in some of
5018 the functions above corresponds to the domain of this map space.
5020 The zero piecewise quasipolynomial or a piecewise quasipolynomial
5021 with a single cell can be created using the following functions.
5022 Multiple of these single cell piecewise quasipolynomials can
5023 be combined to create more complicated piecewise quasipolynomials.
5025 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_zero(
5026 __isl_take isl_space *space);
5027 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_alloc(
5028 __isl_take isl_set *set,
5029 __isl_take isl_qpolynomial *qp);
5030 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_from_qpolynomial(
5031 __isl_take isl_qpolynomial *qp);
5032 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_from_pw_aff(
5033 __isl_take isl_pw_aff *pwaff);
5035 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_zero(
5036 __isl_take isl_space *space);
5037 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_from_pw_qpolynomial(
5038 __isl_take isl_pw_qpolynomial *pwqp);
5039 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_add_pw_qpolynomial(
5040 __isl_take isl_union_pw_qpolynomial *upwqp,
5041 __isl_take isl_pw_qpolynomial *pwqp);
5043 Quasipolynomials can be copied and freed again using the following
5046 __isl_give isl_qpolynomial *isl_qpolynomial_copy(
5047 __isl_keep isl_qpolynomial *qp);
5048 void *isl_qpolynomial_free(__isl_take isl_qpolynomial *qp);
5050 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_copy(
5051 __isl_keep isl_pw_qpolynomial *pwqp);
5052 void *isl_pw_qpolynomial_free(
5053 __isl_take isl_pw_qpolynomial *pwqp);
5055 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_copy(
5056 __isl_keep isl_union_pw_qpolynomial *upwqp);
5057 void *isl_union_pw_qpolynomial_free(
5058 __isl_take isl_union_pw_qpolynomial *upwqp);
5060 =head3 Inspecting (Piecewise) Quasipolynomials
5062 To iterate over all piecewise quasipolynomials in a union
5063 piecewise quasipolynomial, use the following function
5065 int isl_union_pw_qpolynomial_foreach_pw_qpolynomial(
5066 __isl_keep isl_union_pw_qpolynomial *upwqp,
5067 int (*fn)(__isl_take isl_pw_qpolynomial *pwqp, void *user),
5070 To extract the piecewise quasipolynomial in a given space from a union, use
5072 __isl_give isl_pw_qpolynomial *
5073 isl_union_pw_qpolynomial_extract_pw_qpolynomial(
5074 __isl_keep isl_union_pw_qpolynomial *upwqp,
5075 __isl_take isl_space *space);
5077 To iterate over the cells in a piecewise quasipolynomial,
5078 use either of the following two functions
5080 int isl_pw_qpolynomial_foreach_piece(
5081 __isl_keep isl_pw_qpolynomial *pwqp,
5082 int (*fn)(__isl_take isl_set *set,
5083 __isl_take isl_qpolynomial *qp,
5084 void *user), void *user);
5085 int isl_pw_qpolynomial_foreach_lifted_piece(
5086 __isl_keep isl_pw_qpolynomial *pwqp,
5087 int (*fn)(__isl_take isl_set *set,
5088 __isl_take isl_qpolynomial *qp,
5089 void *user), void *user);
5091 As usual, the function C<fn> should return C<0> on success
5092 and C<-1> on failure. The difference between
5093 C<isl_pw_qpolynomial_foreach_piece> and
5094 C<isl_pw_qpolynomial_foreach_lifted_piece> is that
5095 C<isl_pw_qpolynomial_foreach_lifted_piece> will first
5096 compute unique representations for all existentially quantified
5097 variables and then turn these existentially quantified variables
5098 into extra set variables, adapting the associated quasipolynomial
5099 accordingly. This means that the C<set> passed to C<fn>
5100 will not have any existentially quantified variables, but that
5101 the dimensions of the sets may be different for different
5102 invocations of C<fn>.
5104 The constant term of a quasipolynomial can be extracted using
5106 __isl_give isl_val *isl_qpolynomial_get_constant_val(
5107 __isl_keep isl_qpolynomial *qp);
5109 To iterate over all terms in a quasipolynomial,
5112 int isl_qpolynomial_foreach_term(
5113 __isl_keep isl_qpolynomial *qp,
5114 int (*fn)(__isl_take isl_term *term,
5115 void *user), void *user);
5117 The terms themselves can be inspected and freed using
5120 unsigned isl_term_dim(__isl_keep isl_term *term,
5121 enum isl_dim_type type);
5122 __isl_give isl_val *isl_term_get_coefficient_val(
5123 __isl_keep isl_term *term);
5124 int isl_term_get_exp(__isl_keep isl_term *term,
5125 enum isl_dim_type type, unsigned pos);
5126 __isl_give isl_aff *isl_term_get_div(
5127 __isl_keep isl_term *term, unsigned pos);
5128 void isl_term_free(__isl_take isl_term *term);
5130 Each term is a product of parameters, set variables and
5131 integer divisions. The function C<isl_term_get_exp>
5132 returns the exponent of a given dimensions in the given term.
5134 =head3 Properties of (Piecewise) Quasipolynomials
5136 To check whether two union piecewise quasipolynomials are
5137 obviously equal, use
5139 int isl_union_pw_qpolynomial_plain_is_equal(
5140 __isl_keep isl_union_pw_qpolynomial *upwqp1,
5141 __isl_keep isl_union_pw_qpolynomial *upwqp2);
5143 =head3 Operations on (Piecewise) Quasipolynomials
5145 __isl_give isl_qpolynomial *isl_qpolynomial_scale_val(
5146 __isl_take isl_qpolynomial *qp,
5147 __isl_take isl_val *v);
5148 __isl_give isl_qpolynomial *isl_qpolynomial_neg(
5149 __isl_take isl_qpolynomial *qp);
5150 __isl_give isl_qpolynomial *isl_qpolynomial_add(
5151 __isl_take isl_qpolynomial *qp1,
5152 __isl_take isl_qpolynomial *qp2);
5153 __isl_give isl_qpolynomial *isl_qpolynomial_sub(
5154 __isl_take isl_qpolynomial *qp1,
5155 __isl_take isl_qpolynomial *qp2);
5156 __isl_give isl_qpolynomial *isl_qpolynomial_mul(
5157 __isl_take isl_qpolynomial *qp1,
5158 __isl_take isl_qpolynomial *qp2);
5159 __isl_give isl_qpolynomial *isl_qpolynomial_pow(
5160 __isl_take isl_qpolynomial *qp, unsigned exponent);
5162 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_fix_val(
5163 __isl_take isl_pw_qpolynomial *pwqp,
5164 enum isl_dim_type type, unsigned n,
5165 __isl_take isl_val *v);
5166 __isl_give isl_pw_qpolynomial *
5167 isl_pw_qpolynomial_scale_val(
5168 __isl_take isl_pw_qpolynomial *pwqp,
5169 __isl_take isl_val *v);
5170 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_add(
5171 __isl_take isl_pw_qpolynomial *pwqp1,
5172 __isl_take isl_pw_qpolynomial *pwqp2);
5173 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_sub(
5174 __isl_take isl_pw_qpolynomial *pwqp1,
5175 __isl_take isl_pw_qpolynomial *pwqp2);
5176 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_add_disjoint(
5177 __isl_take isl_pw_qpolynomial *pwqp1,
5178 __isl_take isl_pw_qpolynomial *pwqp2);
5179 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_neg(
5180 __isl_take isl_pw_qpolynomial *pwqp);
5181 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_mul(
5182 __isl_take isl_pw_qpolynomial *pwqp1,
5183 __isl_take isl_pw_qpolynomial *pwqp2);
5184 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_pow(
5185 __isl_take isl_pw_qpolynomial *pwqp, unsigned exponent);
5187 __isl_give isl_union_pw_qpolynomial *
5188 isl_union_pw_qpolynomial_scale_val(
5189 __isl_take isl_union_pw_qpolynomial *upwqp,
5190 __isl_take isl_val *v);
5191 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_add(
5192 __isl_take isl_union_pw_qpolynomial *upwqp1,
5193 __isl_take isl_union_pw_qpolynomial *upwqp2);
5194 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_sub(
5195 __isl_take isl_union_pw_qpolynomial *upwqp1,
5196 __isl_take isl_union_pw_qpolynomial *upwqp2);
5197 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_mul(
5198 __isl_take isl_union_pw_qpolynomial *upwqp1,
5199 __isl_take isl_union_pw_qpolynomial *upwqp2);
5201 __isl_give isl_val *isl_pw_qpolynomial_eval(
5202 __isl_take isl_pw_qpolynomial *pwqp,
5203 __isl_take isl_point *pnt);
5205 __isl_give isl_val *isl_union_pw_qpolynomial_eval(
5206 __isl_take isl_union_pw_qpolynomial *upwqp,
5207 __isl_take isl_point *pnt);
5209 __isl_give isl_set *isl_pw_qpolynomial_domain(
5210 __isl_take isl_pw_qpolynomial *pwqp);
5211 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_intersect_domain(
5212 __isl_take isl_pw_qpolynomial *pwpq,
5213 __isl_take isl_set *set);
5214 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_intersect_params(
5215 __isl_take isl_pw_qpolynomial *pwpq,
5216 __isl_take isl_set *set);
5218 __isl_give isl_union_set *isl_union_pw_qpolynomial_domain(
5219 __isl_take isl_union_pw_qpolynomial *upwqp);
5220 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_intersect_domain(
5221 __isl_take isl_union_pw_qpolynomial *upwpq,
5222 __isl_take isl_union_set *uset);
5223 __isl_give isl_union_pw_qpolynomial *
5224 isl_union_pw_qpolynomial_intersect_params(
5225 __isl_take isl_union_pw_qpolynomial *upwpq,
5226 __isl_take isl_set *set);
5228 __isl_give isl_qpolynomial *isl_qpolynomial_align_params(
5229 __isl_take isl_qpolynomial *qp,
5230 __isl_take isl_space *model);
5232 __isl_give isl_qpolynomial *isl_qpolynomial_project_domain_on_params(
5233 __isl_take isl_qpolynomial *qp);
5234 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_project_domain_on_params(
5235 __isl_take isl_pw_qpolynomial *pwqp);
5237 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_coalesce(
5238 __isl_take isl_union_pw_qpolynomial *upwqp);
5240 __isl_give isl_qpolynomial *isl_qpolynomial_gist_params(
5241 __isl_take isl_qpolynomial *qp,
5242 __isl_take isl_set *context);
5243 __isl_give isl_qpolynomial *isl_qpolynomial_gist(
5244 __isl_take isl_qpolynomial *qp,
5245 __isl_take isl_set *context);
5247 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_gist_params(
5248 __isl_take isl_pw_qpolynomial *pwqp,
5249 __isl_take isl_set *context);
5250 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_gist(
5251 __isl_take isl_pw_qpolynomial *pwqp,
5252 __isl_take isl_set *context);
5254 __isl_give isl_union_pw_qpolynomial *
5255 isl_union_pw_qpolynomial_gist_params(
5256 __isl_take isl_union_pw_qpolynomial *upwqp,
5257 __isl_take isl_set *context);
5258 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_gist(
5259 __isl_take isl_union_pw_qpolynomial *upwqp,
5260 __isl_take isl_union_set *context);
5262 The gist operation applies the gist operation to each of
5263 the cells in the domain of the input piecewise quasipolynomial.
5264 The context is also exploited
5265 to simplify the quasipolynomials associated to each cell.
5267 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_to_polynomial(
5268 __isl_take isl_pw_qpolynomial *pwqp, int sign);
5269 __isl_give isl_union_pw_qpolynomial *
5270 isl_union_pw_qpolynomial_to_polynomial(
5271 __isl_take isl_union_pw_qpolynomial *upwqp, int sign);
5273 Approximate each quasipolynomial by a polynomial. If C<sign> is positive,
5274 the polynomial will be an overapproximation. If C<sign> is negative,
5275 it will be an underapproximation. If C<sign> is zero, the approximation
5276 will lie somewhere in between.
5278 =head2 Bounds on Piecewise Quasipolynomials and Piecewise Quasipolynomial Reductions
5280 A piecewise quasipolynomial reduction is a piecewise
5281 reduction (or fold) of quasipolynomials.
5282 In particular, the reduction can be maximum or a minimum.
5283 The objects are mainly used to represent the result of
5284 an upper or lower bound on a quasipolynomial over its domain,
5285 i.e., as the result of the following function.
5287 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_bound(
5288 __isl_take isl_pw_qpolynomial *pwqp,
5289 enum isl_fold type, int *tight);
5291 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_bound(
5292 __isl_take isl_union_pw_qpolynomial *upwqp,
5293 enum isl_fold type, int *tight);
5295 The C<type> argument may be either C<isl_fold_min> or C<isl_fold_max>.
5296 If C<tight> is not C<NULL>, then C<*tight> is set to C<1>
5297 is the returned bound is known be tight, i.e., for each value
5298 of the parameters there is at least
5299 one element in the domain that reaches the bound.
5300 If the domain of C<pwqp> is not wrapping, then the bound is computed
5301 over all elements in that domain and the result has a purely parametric
5302 domain. If the domain of C<pwqp> is wrapping, then the bound is
5303 computed over the range of the wrapped relation. The domain of the
5304 wrapped relation becomes the domain of the result.
5306 A (piecewise) quasipolynomial reduction can be copied or freed using the
5307 following functions.
5309 __isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_copy(
5310 __isl_keep isl_qpolynomial_fold *fold);
5311 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_copy(
5312 __isl_keep isl_pw_qpolynomial_fold *pwf);
5313 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_copy(
5314 __isl_keep isl_union_pw_qpolynomial_fold *upwf);
5315 void isl_qpolynomial_fold_free(
5316 __isl_take isl_qpolynomial_fold *fold);
5317 void *isl_pw_qpolynomial_fold_free(
5318 __isl_take isl_pw_qpolynomial_fold *pwf);
5319 void *isl_union_pw_qpolynomial_fold_free(
5320 __isl_take isl_union_pw_qpolynomial_fold *upwf);
5322 =head3 Printing Piecewise Quasipolynomial Reductions
5324 Piecewise quasipolynomial reductions can be printed
5325 using the following function.
5327 __isl_give isl_printer *isl_printer_print_pw_qpolynomial_fold(
5328 __isl_take isl_printer *p,
5329 __isl_keep isl_pw_qpolynomial_fold *pwf);
5330 __isl_give isl_printer *isl_printer_print_union_pw_qpolynomial_fold(
5331 __isl_take isl_printer *p,
5332 __isl_keep isl_union_pw_qpolynomial_fold *upwf);
5334 For C<isl_printer_print_pw_qpolynomial_fold>,
5335 output format of the printer
5336 needs to be set to either C<ISL_FORMAT_ISL> or C<ISL_FORMAT_C>.
5337 For C<isl_printer_print_union_pw_qpolynomial_fold>,
5338 output format of the printer
5339 needs to be set to C<ISL_FORMAT_ISL>.
5340 In case of printing in C<ISL_FORMAT_C>, the user may want
5341 to set the names of all dimensions
5343 __isl_give isl_pw_qpolynomial_fold *
5344 isl_pw_qpolynomial_fold_set_dim_name(
5345 __isl_take isl_pw_qpolynomial_fold *pwf,
5346 enum isl_dim_type type, unsigned pos,
5349 =head3 Inspecting (Piecewise) Quasipolynomial Reductions
5351 To iterate over all piecewise quasipolynomial reductions in a union
5352 piecewise quasipolynomial reduction, use the following function
5354 int isl_union_pw_qpolynomial_fold_foreach_pw_qpolynomial_fold(
5355 __isl_keep isl_union_pw_qpolynomial_fold *upwf,
5356 int (*fn)(__isl_take isl_pw_qpolynomial_fold *pwf,
5357 void *user), void *user);
5359 To iterate over the cells in a piecewise quasipolynomial reduction,
5360 use either of the following two functions
5362 int isl_pw_qpolynomial_fold_foreach_piece(
5363 __isl_keep isl_pw_qpolynomial_fold *pwf,
5364 int (*fn)(__isl_take isl_set *set,
5365 __isl_take isl_qpolynomial_fold *fold,
5366 void *user), void *user);
5367 int isl_pw_qpolynomial_fold_foreach_lifted_piece(
5368 __isl_keep isl_pw_qpolynomial_fold *pwf,
5369 int (*fn)(__isl_take isl_set *set,
5370 __isl_take isl_qpolynomial_fold *fold,
5371 void *user), void *user);
5373 See L<Inspecting (Piecewise) Quasipolynomials> for an explanation
5374 of the difference between these two functions.
5376 To iterate over all quasipolynomials in a reduction, use
5378 int isl_qpolynomial_fold_foreach_qpolynomial(
5379 __isl_keep isl_qpolynomial_fold *fold,
5380 int (*fn)(__isl_take isl_qpolynomial *qp,
5381 void *user), void *user);
5383 =head3 Properties of Piecewise Quasipolynomial Reductions
5385 To check whether two union piecewise quasipolynomial reductions are
5386 obviously equal, use
5388 int isl_union_pw_qpolynomial_fold_plain_is_equal(
5389 __isl_keep isl_union_pw_qpolynomial_fold *upwf1,
5390 __isl_keep isl_union_pw_qpolynomial_fold *upwf2);
5392 =head3 Operations on Piecewise Quasipolynomial Reductions
5394 __isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_scale_val(
5395 __isl_take isl_qpolynomial_fold *fold,
5396 __isl_take isl_val *v);
5397 __isl_give isl_pw_qpolynomial_fold *
5398 isl_pw_qpolynomial_fold_scale_val(
5399 __isl_take isl_pw_qpolynomial_fold *pwf,
5400 __isl_take isl_val *v);
5401 __isl_give isl_union_pw_qpolynomial_fold *
5402 isl_union_pw_qpolynomial_fold_scale_val(
5403 __isl_take isl_union_pw_qpolynomial_fold *upwf,
5404 __isl_take isl_val *v);
5406 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_add(
5407 __isl_take isl_pw_qpolynomial_fold *pwf1,
5408 __isl_take isl_pw_qpolynomial_fold *pwf2);
5410 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_fold(
5411 __isl_take isl_pw_qpolynomial_fold *pwf1,
5412 __isl_take isl_pw_qpolynomial_fold *pwf2);
5414 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_fold(
5415 __isl_take isl_union_pw_qpolynomial_fold *upwf1,
5416 __isl_take isl_union_pw_qpolynomial_fold *upwf2);
5418 __isl_give isl_val *isl_pw_qpolynomial_fold_eval(
5419 __isl_take isl_pw_qpolynomial_fold *pwf,
5420 __isl_take isl_point *pnt);
5422 __isl_give isl_val *isl_union_pw_qpolynomial_fold_eval(
5423 __isl_take isl_union_pw_qpolynomial_fold *upwf,
5424 __isl_take isl_point *pnt);
5426 __isl_give isl_pw_qpolynomial_fold *
5427 isl_pw_qpolynomial_fold_intersect_params(
5428 __isl_take isl_pw_qpolynomial_fold *pwf,
5429 __isl_take isl_set *set);
5431 __isl_give isl_union_set *isl_union_pw_qpolynomial_fold_domain(
5432 __isl_take isl_union_pw_qpolynomial_fold *upwf);
5433 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_intersect_domain(
5434 __isl_take isl_union_pw_qpolynomial_fold *upwf,
5435 __isl_take isl_union_set *uset);
5436 __isl_give isl_union_pw_qpolynomial_fold *
5437 isl_union_pw_qpolynomial_fold_intersect_params(
5438 __isl_take isl_union_pw_qpolynomial_fold *upwf,
5439 __isl_take isl_set *set);
5441 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_project_domain_on_params(
5442 __isl_take isl_pw_qpolynomial_fold *pwf);
5444 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_coalesce(
5445 __isl_take isl_pw_qpolynomial_fold *pwf);
5447 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_coalesce(
5448 __isl_take isl_union_pw_qpolynomial_fold *upwf);
5450 __isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_gist_params(
5451 __isl_take isl_qpolynomial_fold *fold,
5452 __isl_take isl_set *context);
5453 __isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_gist(
5454 __isl_take isl_qpolynomial_fold *fold,
5455 __isl_take isl_set *context);
5457 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_gist(
5458 __isl_take isl_pw_qpolynomial_fold *pwf,
5459 __isl_take isl_set *context);
5460 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_gist_params(
5461 __isl_take isl_pw_qpolynomial_fold *pwf,
5462 __isl_take isl_set *context);
5464 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_gist(
5465 __isl_take isl_union_pw_qpolynomial_fold *upwf,
5466 __isl_take isl_union_set *context);
5467 __isl_give isl_union_pw_qpolynomial_fold *
5468 isl_union_pw_qpolynomial_fold_gist_params(
5469 __isl_take isl_union_pw_qpolynomial_fold *upwf,
5470 __isl_take isl_set *context);
5472 The gist operation applies the gist operation to each of
5473 the cells in the domain of the input piecewise quasipolynomial reduction.
5474 In future, the operation will also exploit the context
5475 to simplify the quasipolynomial reductions associated to each cell.
5477 __isl_give isl_pw_qpolynomial_fold *
5478 isl_set_apply_pw_qpolynomial_fold(
5479 __isl_take isl_set *set,
5480 __isl_take isl_pw_qpolynomial_fold *pwf,
5482 __isl_give isl_pw_qpolynomial_fold *
5483 isl_map_apply_pw_qpolynomial_fold(
5484 __isl_take isl_map *map,
5485 __isl_take isl_pw_qpolynomial_fold *pwf,
5487 __isl_give isl_union_pw_qpolynomial_fold *
5488 isl_union_set_apply_union_pw_qpolynomial_fold(
5489 __isl_take isl_union_set *uset,
5490 __isl_take isl_union_pw_qpolynomial_fold *upwf,
5492 __isl_give isl_union_pw_qpolynomial_fold *
5493 isl_union_map_apply_union_pw_qpolynomial_fold(
5494 __isl_take isl_union_map *umap,
5495 __isl_take isl_union_pw_qpolynomial_fold *upwf,
5498 The functions taking a map
5499 compose the given map with the given piecewise quasipolynomial reduction.
5500 That is, compute a bound (of the same type as C<pwf> or C<upwf> itself)
5501 over all elements in the intersection of the range of the map
5502 and the domain of the piecewise quasipolynomial reduction
5503 as a function of an element in the domain of the map.
5504 The functions taking a set compute a bound over all elements in the
5505 intersection of the set and the domain of the
5506 piecewise quasipolynomial reduction.
5508 =head2 Parametric Vertex Enumeration
5510 The parametric vertex enumeration described in this section
5511 is mainly intended to be used internally and by the C<barvinok>
5514 #include <isl/vertices.h>
5515 __isl_give isl_vertices *isl_basic_set_compute_vertices(
5516 __isl_keep isl_basic_set *bset);
5518 The function C<isl_basic_set_compute_vertices> performs the
5519 actual computation of the parametric vertices and the chamber
5520 decomposition and store the result in an C<isl_vertices> object.
5521 This information can be queried by either iterating over all
5522 the vertices or iterating over all the chambers or cells
5523 and then iterating over all vertices that are active on the chamber.
5525 int isl_vertices_foreach_vertex(
5526 __isl_keep isl_vertices *vertices,
5527 int (*fn)(__isl_take isl_vertex *vertex, void *user),
5530 int isl_vertices_foreach_cell(
5531 __isl_keep isl_vertices *vertices,
5532 int (*fn)(__isl_take isl_cell *cell, void *user),
5534 int isl_cell_foreach_vertex(__isl_keep isl_cell *cell,
5535 int (*fn)(__isl_take isl_vertex *vertex, void *user),
5538 Other operations that can be performed on an C<isl_vertices> object are
5541 isl_ctx *isl_vertices_get_ctx(
5542 __isl_keep isl_vertices *vertices);
5543 int isl_vertices_get_n_vertices(
5544 __isl_keep isl_vertices *vertices);
5545 void isl_vertices_free(__isl_take isl_vertices *vertices);
5547 Vertices can be inspected and destroyed using the following functions.
5549 isl_ctx *isl_vertex_get_ctx(__isl_keep isl_vertex *vertex);
5550 int isl_vertex_get_id(__isl_keep isl_vertex *vertex);
5551 __isl_give isl_basic_set *isl_vertex_get_domain(
5552 __isl_keep isl_vertex *vertex);
5553 __isl_give isl_basic_set *isl_vertex_get_expr(
5554 __isl_keep isl_vertex *vertex);
5555 void isl_vertex_free(__isl_take isl_vertex *vertex);
5557 C<isl_vertex_get_expr> returns a singleton parametric set describing
5558 the vertex, while C<isl_vertex_get_domain> returns the activity domain
5560 Note that C<isl_vertex_get_domain> and C<isl_vertex_get_expr> return
5561 B<rational> basic sets, so they should mainly be used for inspection
5562 and should not be mixed with integer sets.
5564 Chambers can be inspected and destroyed using the following functions.
5566 isl_ctx *isl_cell_get_ctx(__isl_keep isl_cell *cell);
5567 __isl_give isl_basic_set *isl_cell_get_domain(
5568 __isl_keep isl_cell *cell);
5569 void isl_cell_free(__isl_take isl_cell *cell);
5571 =head1 Polyhedral Compilation Library
5573 This section collects functionality in C<isl> that has been specifically
5574 designed for use during polyhedral compilation.
5576 =head2 Dependence Analysis
5578 C<isl> contains specialized functionality for performing
5579 array dataflow analysis. That is, given a I<sink> access relation
5580 and a collection of possible I<source> access relations,
5581 C<isl> can compute relations that describe
5582 for each iteration of the sink access, which iteration
5583 of which of the source access relations was the last
5584 to access the same data element before the given iteration
5586 The resulting dependence relations map source iterations
5587 to the corresponding sink iterations.
5588 To compute standard flow dependences, the sink should be
5589 a read, while the sources should be writes.
5590 If any of the source accesses are marked as being I<may>
5591 accesses, then there will be a dependence from the last
5592 I<must> access B<and> from any I<may> access that follows
5593 this last I<must> access.
5594 In particular, if I<all> sources are I<may> accesses,
5595 then memory based dependence analysis is performed.
5596 If, on the other hand, all sources are I<must> accesses,
5597 then value based dependence analysis is performed.
5599 #include <isl/flow.h>
5601 typedef int (*isl_access_level_before)(void *first, void *second);
5603 __isl_give isl_access_info *isl_access_info_alloc(
5604 __isl_take isl_map *sink,
5605 void *sink_user, isl_access_level_before fn,
5607 __isl_give isl_access_info *isl_access_info_add_source(
5608 __isl_take isl_access_info *acc,
5609 __isl_take isl_map *source, int must,
5611 void *isl_access_info_free(__isl_take isl_access_info *acc);
5613 __isl_give isl_flow *isl_access_info_compute_flow(
5614 __isl_take isl_access_info *acc);
5616 int isl_flow_foreach(__isl_keep isl_flow *deps,
5617 int (*fn)(__isl_take isl_map *dep, int must,
5618 void *dep_user, void *user),
5620 __isl_give isl_map *isl_flow_get_no_source(
5621 __isl_keep isl_flow *deps, int must);
5622 void isl_flow_free(__isl_take isl_flow *deps);
5624 The function C<isl_access_info_compute_flow> performs the actual
5625 dependence analysis. The other functions are used to construct
5626 the input for this function or to read off the output.
5628 The input is collected in an C<isl_access_info>, which can
5629 be created through a call to C<isl_access_info_alloc>.
5630 The arguments to this functions are the sink access relation
5631 C<sink>, a token C<sink_user> used to identify the sink
5632 access to the user, a callback function for specifying the
5633 relative order of source and sink accesses, and the number
5634 of source access relations that will be added.
5635 The callback function has type C<int (*)(void *first, void *second)>.
5636 The function is called with two user supplied tokens identifying
5637 either a source or the sink and it should return the shared nesting
5638 level and the relative order of the two accesses.
5639 In particular, let I<n> be the number of loops shared by
5640 the two accesses. If C<first> precedes C<second> textually,
5641 then the function should return I<2 * n + 1>; otherwise,
5642 it should return I<2 * n>.
5643 The sources can be added to the C<isl_access_info> by performing
5644 (at most) C<max_source> calls to C<isl_access_info_add_source>.
5645 C<must> indicates whether the source is a I<must> access
5646 or a I<may> access. Note that a multi-valued access relation
5647 should only be marked I<must> if every iteration in the domain
5648 of the relation accesses I<all> elements in its image.
5649 The C<source_user> token is again used to identify
5650 the source access. The range of the source access relation
5651 C<source> should have the same dimension as the range
5652 of the sink access relation.
5653 The C<isl_access_info_free> function should usually not be
5654 called explicitly, because it is called implicitly by
5655 C<isl_access_info_compute_flow>.
5657 The result of the dependence analysis is collected in an
5658 C<isl_flow>. There may be elements of
5659 the sink access for which no preceding source access could be
5660 found or for which all preceding sources are I<may> accesses.
5661 The relations containing these elements can be obtained through
5662 calls to C<isl_flow_get_no_source>, the first with C<must> set
5663 and the second with C<must> unset.
5664 In the case of standard flow dependence analysis,
5665 with the sink a read and the sources I<must> writes,
5666 the first relation corresponds to the reads from uninitialized
5667 array elements and the second relation is empty.
5668 The actual flow dependences can be extracted using
5669 C<isl_flow_foreach>. This function will call the user-specified
5670 callback function C<fn> for each B<non-empty> dependence between
5671 a source and the sink. The callback function is called
5672 with four arguments, the actual flow dependence relation
5673 mapping source iterations to sink iterations, a boolean that
5674 indicates whether it is a I<must> or I<may> dependence, a token
5675 identifying the source and an additional C<void *> with value
5676 equal to the third argument of the C<isl_flow_foreach> call.
5677 A dependence is marked I<must> if it originates from a I<must>
5678 source and if it is not followed by any I<may> sources.
5680 After finishing with an C<isl_flow>, the user should call
5681 C<isl_flow_free> to free all associated memory.
5683 A higher-level interface to dependence analysis is provided
5684 by the following function.
5686 #include <isl/flow.h>
5688 int isl_union_map_compute_flow(__isl_take isl_union_map *sink,
5689 __isl_take isl_union_map *must_source,
5690 __isl_take isl_union_map *may_source,
5691 __isl_take isl_union_map *schedule,
5692 __isl_give isl_union_map **must_dep,
5693 __isl_give isl_union_map **may_dep,
5694 __isl_give isl_union_map **must_no_source,
5695 __isl_give isl_union_map **may_no_source);
5697 The arrays are identified by the tuple names of the ranges
5698 of the accesses. The iteration domains by the tuple names
5699 of the domains of the accesses and of the schedule.
5700 The relative order of the iteration domains is given by the
5701 schedule. The relations returned through C<must_no_source>
5702 and C<may_no_source> are subsets of C<sink>.
5703 Any of C<must_dep>, C<may_dep>, C<must_no_source>
5704 or C<may_no_source> may be C<NULL>, but a C<NULL> value for
5705 any of the other arguments is treated as an error.
5707 =head3 Interaction with Dependence Analysis
5709 During the dependence analysis, we frequently need to perform
5710 the following operation. Given a relation between sink iterations
5711 and potential source iterations from a particular source domain,
5712 what is the last potential source iteration corresponding to each
5713 sink iteration. It can sometimes be convenient to adjust
5714 the set of potential source iterations before or after each such operation.
5715 The prototypical example is fuzzy array dataflow analysis,
5716 where we need to analyze if, based on data-dependent constraints,
5717 the sink iteration can ever be executed without one or more of
5718 the corresponding potential source iterations being executed.
5719 If so, we can introduce extra parameters and select an unknown
5720 but fixed source iteration from the potential source iterations.
5721 To be able to perform such manipulations, C<isl> provides the following
5724 #include <isl/flow.h>
5726 typedef __isl_give isl_restriction *(*isl_access_restrict)(
5727 __isl_keep isl_map *source_map,
5728 __isl_keep isl_set *sink, void *source_user,
5730 __isl_give isl_access_info *isl_access_info_set_restrict(
5731 __isl_take isl_access_info *acc,
5732 isl_access_restrict fn, void *user);
5734 The function C<isl_access_info_set_restrict> should be called
5735 before calling C<isl_access_info_compute_flow> and registers a callback function
5736 that will be called any time C<isl> is about to compute the last
5737 potential source. The first argument is the (reverse) proto-dependence,
5738 mapping sink iterations to potential source iterations.
5739 The second argument represents the sink iterations for which
5740 we want to compute the last source iteration.
5741 The third argument is the token corresponding to the source
5742 and the final argument is the token passed to C<isl_access_info_set_restrict>.
5743 The callback is expected to return a restriction on either the input or
5744 the output of the operation computing the last potential source.
5745 If the input needs to be restricted then restrictions are needed
5746 for both the source and the sink iterations. The sink iterations
5747 and the potential source iterations will be intersected with these sets.
5748 If the output needs to be restricted then only a restriction on the source
5749 iterations is required.
5750 If any error occurs, the callback should return C<NULL>.
5751 An C<isl_restriction> object can be created, freed and inspected
5752 using the following functions.
5754 #include <isl/flow.h>
5756 __isl_give isl_restriction *isl_restriction_input(
5757 __isl_take isl_set *source_restr,
5758 __isl_take isl_set *sink_restr);
5759 __isl_give isl_restriction *isl_restriction_output(
5760 __isl_take isl_set *source_restr);
5761 __isl_give isl_restriction *isl_restriction_none(
5762 __isl_take isl_map *source_map);
5763 __isl_give isl_restriction *isl_restriction_empty(
5764 __isl_take isl_map *source_map);
5765 void *isl_restriction_free(
5766 __isl_take isl_restriction *restr);
5767 isl_ctx *isl_restriction_get_ctx(
5768 __isl_keep isl_restriction *restr);
5770 C<isl_restriction_none> and C<isl_restriction_empty> are special
5771 cases of C<isl_restriction_input>. C<isl_restriction_none>
5772 is essentially equivalent to
5774 isl_restriction_input(isl_set_universe(
5775 isl_space_range(isl_map_get_space(source_map))),
5777 isl_space_domain(isl_map_get_space(source_map))));
5779 whereas C<isl_restriction_empty> is essentially equivalent to
5781 isl_restriction_input(isl_set_empty(
5782 isl_space_range(isl_map_get_space(source_map))),
5784 isl_space_domain(isl_map_get_space(source_map))));
5788 B<The functionality described in this section is fairly new
5789 and may be subject to change.>
5791 #include <isl/schedule.h>
5792 __isl_give isl_schedule *
5793 isl_schedule_constraints_compute_schedule(
5794 __isl_take isl_schedule_constraints *sc);
5795 void *isl_schedule_free(__isl_take isl_schedule *sched);
5797 The function C<isl_schedule_constraints_compute_schedule> can be
5798 used to compute a schedule that satisfy the given schedule constraints.
5799 These schedule constraints include the iteration domain for which
5800 a schedule should be computed and dependences between pairs of
5801 iterations. In particular, these dependences include
5802 I<validity> dependences and I<proximity> dependences.
5803 By default, the algorithm used to construct the schedule is similar
5804 to that of C<Pluto>.
5805 Alternatively, Feautrier's multi-dimensional scheduling algorithm can
5807 The generated schedule respects all validity dependences.
5808 That is, all dependence distances over these dependences in the
5809 scheduled space are lexicographically positive.
5810 The default algorithm tries to ensure that the dependence distances
5811 over coincidence constraints are zero and to minimize the
5812 dependence distances over proximity dependences.
5813 Moreover, it tries to obtain sequences (bands) of schedule dimensions
5814 for groups of domains where the dependence distances over validity
5815 dependences have only non-negative values.
5816 When using Feautrier's algorithm, the coincidence and proximity constraints
5817 are only taken into account during the extension to a
5818 full-dimensional schedule.
5820 An C<isl_schedule_constraints> object can be constructed
5821 and manipulated using the following functions.
5823 #include <isl/schedule.h>
5824 __isl_give isl_schedule_constraints *
5825 isl_schedule_constraints_copy(
5826 __isl_keep isl_schedule_constraints *sc);
5827 __isl_give isl_schedule_constraints *
5828 isl_schedule_constraints_on_domain(
5829 __isl_take isl_union_set *domain);
5830 isl_ctx *isl_schedule_constraints_get_ctx(
5831 __isl_keep isl_schedule_constraints *sc);
5832 __isl_give isl_schedule_constraints *
5833 isl_schedule_constraints_set_validity(
5834 __isl_take isl_schedule_constraints *sc,
5835 __isl_take isl_union_map *validity);
5836 __isl_give isl_schedule_constraints *
5837 isl_schedule_constraints_set_coincidence(
5838 __isl_take isl_schedule_constraints *sc,
5839 __isl_take isl_union_map *coincidence);
5840 __isl_give isl_schedule_constraints *
5841 isl_schedule_constraints_set_proximity(
5842 __isl_take isl_schedule_constraints *sc,
5843 __isl_take isl_union_map *proximity);
5844 __isl_give isl_schedule_constraints *
5845 isl_schedule_constraints_set_conditional_validity(
5846 __isl_take isl_schedule_constraints *sc,
5847 __isl_take isl_union_map *condition,
5848 __isl_take isl_union_map *validity);
5849 void *isl_schedule_constraints_free(
5850 __isl_take isl_schedule_constraints *sc);
5852 The initial C<isl_schedule_constraints> object created by
5853 C<isl_schedule_constraints_on_domain> does not impose any constraints.
5854 That is, it has an empty set of dependences.
5855 The function C<isl_schedule_constraints_set_validity> replaces the
5856 validity dependences, mapping domain elements I<i> to domain
5857 elements that should be scheduled after I<i>.
5858 The function C<isl_schedule_constraints_set_coincidence> replaces the
5859 coincidence dependences, mapping domain elements I<i> to domain
5860 elements that should be scheduled together with I<I>, if possible.
5861 The function C<isl_schedule_constraints_set_proximity> replaces the
5862 proximity dependences, mapping domain elements I<i> to domain
5863 elements that should be scheduled either before I<I>
5864 or as early as possible after I<i>.
5866 The function C<isl_schedule_constraints_set_conditional_validity>
5867 replaces the conditional validity constraints.
5868 A conditional validity constraint is only imposed when any of the corresponding
5869 conditions is satisfied, i.e., when any of them is non-zero.
5870 That is, the scheduler ensures that within each band if the dependence
5871 distances over the condition constraints are not all zero
5872 then all corresponding conditional validity constraints are respected.
5873 A conditional validity constraint corresponds to a condition
5874 if the two are adjacent, i.e., if the domain of one relation intersect
5875 the range of the other relation.
5876 The typical use case of conditional validity constraints is
5877 to allow order constraints between live ranges to be violated
5878 as long as the live ranges themselves are local to the band.
5879 To allow more fine-grained control over which conditions correspond
5880 to which conditional validity constraints, the domains and ranges
5881 of these relations may include I<tags>. That is, the domains and
5882 ranges of those relation may themselves be wrapped relations
5883 where the iteration domain appears in the domain of those wrapped relations
5884 and the range of the wrapped relations can be arbitrarily chosen
5885 by the user. Conditions and conditional validity constraints are only
5886 considere adjacent to each other if the entire wrapped relation matches.
5887 In particular, a relation with a tag will never be considered adjacent
5888 to a relation without a tag.
5890 The following function computes a schedule directly from
5891 an iteration domain and validity and proximity dependences
5892 and is implemented in terms of the functions described above.
5893 The use of C<isl_union_set_compute_schedule> is discouraged.
5895 #include <isl/schedule.h>
5896 __isl_give isl_schedule *isl_union_set_compute_schedule(
5897 __isl_take isl_union_set *domain,
5898 __isl_take isl_union_map *validity,
5899 __isl_take isl_union_map *proximity);
5901 A mapping from the domains to the scheduled space can be obtained
5902 from an C<isl_schedule> using the following function.
5904 __isl_give isl_union_map *isl_schedule_get_map(
5905 __isl_keep isl_schedule *sched);
5907 A representation of the schedule can be printed using
5909 __isl_give isl_printer *isl_printer_print_schedule(
5910 __isl_take isl_printer *p,
5911 __isl_keep isl_schedule *schedule);
5913 A representation of the schedule as a forest of bands can be obtained
5914 using the following function.
5916 __isl_give isl_band_list *isl_schedule_get_band_forest(
5917 __isl_keep isl_schedule *schedule);
5919 The individual bands can be visited in depth-first post-order
5920 using the following function.
5922 #include <isl/schedule.h>
5923 int isl_schedule_foreach_band(
5924 __isl_keep isl_schedule *sched,
5925 int (*fn)(__isl_keep isl_band *band, void *user),
5928 The list can be manipulated as explained in L<"Lists">.
5929 The bands inside the list can be copied and freed using the following
5932 #include <isl/band.h>
5933 __isl_give isl_band *isl_band_copy(
5934 __isl_keep isl_band *band);
5935 void *isl_band_free(__isl_take isl_band *band);
5937 Each band contains zero or more scheduling dimensions.
5938 These are referred to as the members of the band.
5939 The section of the schedule that corresponds to the band is
5940 referred to as the partial schedule of the band.
5941 For those nodes that participate in a band, the outer scheduling
5942 dimensions form the prefix schedule, while the inner scheduling
5943 dimensions form the suffix schedule.
5944 That is, if we take a cut of the band forest, then the union of
5945 the concatenations of the prefix, partial and suffix schedules of
5946 each band in the cut is equal to the entire schedule (modulo
5947 some possible padding at the end with zero scheduling dimensions).
5948 The properties of a band can be inspected using the following functions.
5950 #include <isl/band.h>
5951 isl_ctx *isl_band_get_ctx(__isl_keep isl_band *band);
5953 int isl_band_has_children(__isl_keep isl_band *band);
5954 __isl_give isl_band_list *isl_band_get_children(
5955 __isl_keep isl_band *band);
5957 __isl_give isl_union_map *isl_band_get_prefix_schedule(
5958 __isl_keep isl_band *band);
5959 __isl_give isl_union_map *isl_band_get_partial_schedule(
5960 __isl_keep isl_band *band);
5961 __isl_give isl_union_map *isl_band_get_suffix_schedule(
5962 __isl_keep isl_band *band);
5964 int isl_band_n_member(__isl_keep isl_band *band);
5965 int isl_band_member_is_coincident(
5966 __isl_keep isl_band *band, int pos);
5968 int isl_band_list_foreach_band(
5969 __isl_keep isl_band_list *list,
5970 int (*fn)(__isl_keep isl_band *band, void *user),
5973 Note that a scheduling dimension is considered to be ``coincident''
5974 if it satisfies the coincidence constraints within its band.
5975 That is, if the dependence distances of the coincidence
5976 constraints are all zero in that direction (for fixed
5977 iterations of outer bands).
5978 Like C<isl_schedule_foreach_band>,
5979 the function C<isl_band_list_foreach_band> calls C<fn> on the bands
5980 in depth-first post-order.
5982 A band can be tiled using the following function.
5984 #include <isl/band.h>
5985 int isl_band_tile(__isl_keep isl_band *band,
5986 __isl_take isl_vec *sizes);
5988 int isl_options_set_tile_scale_tile_loops(isl_ctx *ctx,
5990 int isl_options_get_tile_scale_tile_loops(isl_ctx *ctx);
5991 int isl_options_set_tile_shift_point_loops(isl_ctx *ctx,
5993 int isl_options_get_tile_shift_point_loops(isl_ctx *ctx);
5995 The C<isl_band_tile> function tiles the band using the given tile sizes
5996 inside its schedule.
5997 A new child band is created to represent the point loops and it is
5998 inserted between the modified band and its children.
5999 The C<tile_scale_tile_loops> option specifies whether the tile
6000 loops iterators should be scaled by the tile sizes.
6001 If the C<tile_shift_point_loops> option is set, then the point loops
6002 are shifted to start at zero.
6004 A band can be split into two nested bands using the following function.
6006 int isl_band_split(__isl_keep isl_band *band, int pos);
6008 The resulting outer band contains the first C<pos> dimensions of C<band>
6009 while the inner band contains the remaining dimensions.
6011 A representation of the band can be printed using
6013 #include <isl/band.h>
6014 __isl_give isl_printer *isl_printer_print_band(
6015 __isl_take isl_printer *p,
6016 __isl_keep isl_band *band);
6020 #include <isl/schedule.h>
6021 int isl_options_set_schedule_max_coefficient(
6022 isl_ctx *ctx, int val);
6023 int isl_options_get_schedule_max_coefficient(
6025 int isl_options_set_schedule_max_constant_term(
6026 isl_ctx *ctx, int val);
6027 int isl_options_get_schedule_max_constant_term(
6029 int isl_options_set_schedule_fuse(isl_ctx *ctx, int val);
6030 int isl_options_get_schedule_fuse(isl_ctx *ctx);
6031 int isl_options_set_schedule_maximize_band_depth(
6032 isl_ctx *ctx, int val);
6033 int isl_options_get_schedule_maximize_band_depth(
6035 int isl_options_set_schedule_outer_coincidence(
6036 isl_ctx *ctx, int val);
6037 int isl_options_get_schedule_outer_coincidence(
6039 int isl_options_set_schedule_split_scaled(
6040 isl_ctx *ctx, int val);
6041 int isl_options_get_schedule_split_scaled(
6043 int isl_options_set_schedule_algorithm(
6044 isl_ctx *ctx, int val);
6045 int isl_options_get_schedule_algorithm(
6047 int isl_options_set_schedule_separate_components(
6048 isl_ctx *ctx, int val);
6049 int isl_options_get_schedule_separate_components(
6054 =item * schedule_max_coefficient
6056 This option enforces that the coefficients for variable and parameter
6057 dimensions in the calculated schedule are not larger than the specified value.
6058 This option can significantly increase the speed of the scheduling calculation
6059 and may also prevent fusing of unrelated dimensions. A value of -1 means that
6060 this option does not introduce bounds on the variable or parameter
6063 =item * schedule_max_constant_term
6065 This option enforces that the constant coefficients in the calculated schedule
6066 are not larger than the maximal constant term. This option can significantly
6067 increase the speed of the scheduling calculation and may also prevent fusing of
6068 unrelated dimensions. A value of -1 means that this option does not introduce
6069 bounds on the constant coefficients.
6071 =item * schedule_fuse
6073 This option controls the level of fusion.
6074 If this option is set to C<ISL_SCHEDULE_FUSE_MIN>, then loops in the
6075 resulting schedule will be distributed as much as possible.
6076 If this option is set to C<ISL_SCHEDULE_FUSE_MAX>, then C<isl> will
6077 try to fuse loops in the resulting schedule.
6079 =item * schedule_maximize_band_depth
6081 If this option is set, we do not split bands at the point
6082 where we detect splitting is necessary. Instead, we
6083 backtrack and split bands as early as possible. This
6084 reduces the number of splits and maximizes the width of
6085 the bands. Wider bands give more possibilities for tiling.
6086 Note that if the C<schedule_fuse> option is set to C<ISL_SCHEDULE_FUSE_MIN>,
6087 then bands will be split as early as possible, even if there is no need.
6088 The C<schedule_maximize_band_depth> option therefore has no effect in this case.
6090 =item * schedule_outer_coincidence
6092 If this option is set, then we try to construct schedules
6093 where the outermost scheduling dimension in each band
6094 satisfies the coincidence constraints.
6096 =item * schedule_split_scaled
6098 If this option is set, then we try to construct schedules in which the
6099 constant term is split off from the linear part if the linear parts of
6100 the scheduling rows for all nodes in the graphs have a common non-trivial
6102 The constant term is then placed in a separate band and the linear
6105 =item * schedule_algorithm
6107 Selects the scheduling algorithm to be used.
6108 Available scheduling algorithms are C<ISL_SCHEDULE_ALGORITHM_ISL>
6109 and C<ISL_SCHEDULE_ALGORITHM_FEAUTRIER>.
6111 =item * schedule_separate_components
6113 If at any point the dependence graph contains any (weakly connected) components,
6114 then these components are scheduled separately.
6115 If this option is not set, then some iterations of the domains
6116 in these components may be scheduled together.
6117 If this option is set, then the components are given consecutive
6122 =head2 AST Generation
6124 This section describes the C<isl> functionality for generating
6125 ASTs that visit all the elements
6126 in a domain in an order specified by a schedule.
6127 In particular, given a C<isl_union_map>, an AST is generated
6128 that visits all the elements in the domain of the C<isl_union_map>
6129 according to the lexicographic order of the corresponding image
6130 element(s). If the range of the C<isl_union_map> consists of
6131 elements in more than one space, then each of these spaces is handled
6132 separately in an arbitrary order.
6133 It should be noted that the image elements only specify the I<order>
6134 in which the corresponding domain elements should be visited.
6135 No direct relation between the image elements and the loop iterators
6136 in the generated AST should be assumed.
6138 Each AST is generated within a build. The initial build
6139 simply specifies the constraints on the parameters (if any)
6140 and can be created, inspected, copied and freed using the following functions.
6142 #include <isl/ast_build.h>
6143 __isl_give isl_ast_build *isl_ast_build_from_context(
6144 __isl_take isl_set *set);
6145 isl_ctx *isl_ast_build_get_ctx(
6146 __isl_keep isl_ast_build *build);
6147 __isl_give isl_ast_build *isl_ast_build_copy(
6148 __isl_keep isl_ast_build *build);
6149 void *isl_ast_build_free(
6150 __isl_take isl_ast_build *build);
6152 The C<set> argument is usually a parameter set with zero or more parameters.
6153 More C<isl_ast_build> functions are described in L</"Nested AST Generation">
6154 and L</"Fine-grained Control over AST Generation">.
6155 Finally, the AST itself can be constructed using the following
6158 #include <isl/ast_build.h>
6159 __isl_give isl_ast_node *isl_ast_build_ast_from_schedule(
6160 __isl_keep isl_ast_build *build,
6161 __isl_take isl_union_map *schedule);
6163 =head3 Inspecting the AST
6165 The basic properties of an AST node can be obtained as follows.
6167 #include <isl/ast.h>
6168 isl_ctx *isl_ast_node_get_ctx(
6169 __isl_keep isl_ast_node *node);
6170 enum isl_ast_node_type isl_ast_node_get_type(
6171 __isl_keep isl_ast_node *node);
6173 The type of an AST node is one of
6174 C<isl_ast_node_for>,
6176 C<isl_ast_node_block> or
6177 C<isl_ast_node_user>.
6178 An C<isl_ast_node_for> represents a for node.
6179 An C<isl_ast_node_if> represents an if node.
6180 An C<isl_ast_node_block> represents a compound node.
6181 An C<isl_ast_node_user> represents an expression statement.
6182 An expression statement typically corresponds to a domain element, i.e.,
6183 one of the elements that is visited by the AST.
6185 Each type of node has its own additional properties.
6187 #include <isl/ast.h>
6188 __isl_give isl_ast_expr *isl_ast_node_for_get_iterator(
6189 __isl_keep isl_ast_node *node);
6190 __isl_give isl_ast_expr *isl_ast_node_for_get_init(
6191 __isl_keep isl_ast_node *node);
6192 __isl_give isl_ast_expr *isl_ast_node_for_get_cond(
6193 __isl_keep isl_ast_node *node);
6194 __isl_give isl_ast_expr *isl_ast_node_for_get_inc(
6195 __isl_keep isl_ast_node *node);
6196 __isl_give isl_ast_node *isl_ast_node_for_get_body(
6197 __isl_keep isl_ast_node *node);
6198 int isl_ast_node_for_is_degenerate(
6199 __isl_keep isl_ast_node *node);
6201 An C<isl_ast_for> is considered degenerate if it is known to execute
6204 #include <isl/ast.h>
6205 __isl_give isl_ast_expr *isl_ast_node_if_get_cond(
6206 __isl_keep isl_ast_node *node);
6207 __isl_give isl_ast_node *isl_ast_node_if_get_then(
6208 __isl_keep isl_ast_node *node);
6209 int isl_ast_node_if_has_else(
6210 __isl_keep isl_ast_node *node);
6211 __isl_give isl_ast_node *isl_ast_node_if_get_else(
6212 __isl_keep isl_ast_node *node);
6214 __isl_give isl_ast_node_list *
6215 isl_ast_node_block_get_children(
6216 __isl_keep isl_ast_node *node);
6218 __isl_give isl_ast_expr *isl_ast_node_user_get_expr(
6219 __isl_keep isl_ast_node *node);
6221 Each of the returned C<isl_ast_expr>s can in turn be inspected using
6222 the following functions.
6224 #include <isl/ast.h>
6225 isl_ctx *isl_ast_expr_get_ctx(
6226 __isl_keep isl_ast_expr *expr);
6227 enum isl_ast_expr_type isl_ast_expr_get_type(
6228 __isl_keep isl_ast_expr *expr);
6230 The type of an AST expression is one of
6232 C<isl_ast_expr_id> or
6233 C<isl_ast_expr_int>.
6234 An C<isl_ast_expr_op> represents the result of an operation.
6235 An C<isl_ast_expr_id> represents an identifier.
6236 An C<isl_ast_expr_int> represents an integer value.
6238 Each type of expression has its own additional properties.
6240 #include <isl/ast.h>
6241 enum isl_ast_op_type isl_ast_expr_get_op_type(
6242 __isl_keep isl_ast_expr *expr);
6243 int isl_ast_expr_get_op_n_arg(__isl_keep isl_ast_expr *expr);
6244 __isl_give isl_ast_expr *isl_ast_expr_get_op_arg(
6245 __isl_keep isl_ast_expr *expr, int pos);
6246 int isl_ast_node_foreach_ast_op_type(
6247 __isl_keep isl_ast_node *node,
6248 int (*fn)(enum isl_ast_op_type type, void *user),
6251 C<isl_ast_expr_get_op_type> returns the type of the operation
6252 performed. C<isl_ast_expr_get_op_n_arg> returns the number of
6253 arguments. C<isl_ast_expr_get_op_arg> returns the specified
6255 C<isl_ast_node_foreach_ast_op_type> calls C<fn> for each distinct
6256 C<isl_ast_op_type> that appears in C<node>.
6257 The operation type is one of the following.
6261 =item C<isl_ast_op_and>
6263 Logical I<and> of two arguments.
6264 Both arguments can be evaluated.
6266 =item C<isl_ast_op_and_then>
6268 Logical I<and> of two arguments.
6269 The second argument can only be evaluated if the first evaluates to true.
6271 =item C<isl_ast_op_or>
6273 Logical I<or> of two arguments.
6274 Both arguments can be evaluated.
6276 =item C<isl_ast_op_or_else>
6278 Logical I<or> of two arguments.
6279 The second argument can only be evaluated if the first evaluates to false.
6281 =item C<isl_ast_op_max>
6283 Maximum of two or more arguments.
6285 =item C<isl_ast_op_min>
6287 Minimum of two or more arguments.
6289 =item C<isl_ast_op_minus>
6293 =item C<isl_ast_op_add>
6295 Sum of two arguments.
6297 =item C<isl_ast_op_sub>
6299 Difference of two arguments.
6301 =item C<isl_ast_op_mul>
6303 Product of two arguments.
6305 =item C<isl_ast_op_div>
6307 Exact division. That is, the result is known to be an integer.
6309 =item C<isl_ast_op_fdiv_q>
6311 Result of integer division, rounded towards negative
6314 =item C<isl_ast_op_pdiv_q>
6316 Result of integer division, where dividend is known to be non-negative.
6318 =item C<isl_ast_op_pdiv_r>
6320 Remainder of integer division, where dividend is known to be non-negative.
6322 =item C<isl_ast_op_cond>
6324 Conditional operator defined on three arguments.
6325 If the first argument evaluates to true, then the result
6326 is equal to the second argument. Otherwise, the result
6327 is equal to the third argument.
6328 The second and third argument may only be evaluated if
6329 the first argument evaluates to true and false, respectively.
6330 Corresponds to C<a ? b : c> in C.
6332 =item C<isl_ast_op_select>
6334 Conditional operator defined on three arguments.
6335 If the first argument evaluates to true, then the result
6336 is equal to the second argument. Otherwise, the result
6337 is equal to the third argument.
6338 The second and third argument may be evaluated independently
6339 of the value of the first argument.
6340 Corresponds to C<a * b + (1 - a) * c> in C.
6342 =item C<isl_ast_op_eq>
6346 =item C<isl_ast_op_le>
6348 Less than or equal relation.
6350 =item C<isl_ast_op_lt>
6354 =item C<isl_ast_op_ge>
6356 Greater than or equal relation.
6358 =item C<isl_ast_op_gt>
6360 Greater than relation.
6362 =item C<isl_ast_op_call>
6365 The number of arguments of the C<isl_ast_expr> is one more than
6366 the number of arguments in the function call, the first argument
6367 representing the function being called.
6369 =item C<isl_ast_op_access>
6372 The number of arguments of the C<isl_ast_expr> is one more than
6373 the number of index expressions in the array access, the first argument
6374 representing the array being accessed.
6376 =item C<isl_ast_op_member>
6379 This operation has two arguments, a structure and the name of
6380 the member of the structure being accessed.
6384 #include <isl/ast.h>
6385 __isl_give isl_id *isl_ast_expr_get_id(
6386 __isl_keep isl_ast_expr *expr);
6388 Return the identifier represented by the AST expression.
6390 #include <isl/ast.h>
6391 __isl_give isl_val *isl_ast_expr_get_val(
6392 __isl_keep isl_ast_expr *expr);
6394 Return the integer represented by the AST expression.
6396 =head3 Properties of ASTs
6398 #include <isl/ast.h>
6399 int isl_ast_expr_is_equal(__isl_keep isl_ast_expr *expr1,
6400 __isl_keep isl_ast_expr *expr2);
6402 Check if two C<isl_ast_expr>s are equal to each other.
6404 =head3 Manipulating and printing the AST
6406 AST nodes can be copied and freed using the following functions.
6408 #include <isl/ast.h>
6409 __isl_give isl_ast_node *isl_ast_node_copy(
6410 __isl_keep isl_ast_node *node);
6411 void *isl_ast_node_free(__isl_take isl_ast_node *node);
6413 AST expressions can be copied and freed using the following functions.
6415 #include <isl/ast.h>
6416 __isl_give isl_ast_expr *isl_ast_expr_copy(
6417 __isl_keep isl_ast_expr *expr);
6418 void *isl_ast_expr_free(__isl_take isl_ast_expr *expr);
6420 New AST expressions can be created either directly or within
6421 the context of an C<isl_ast_build>.
6423 #include <isl/ast.h>
6424 __isl_give isl_ast_expr *isl_ast_expr_from_val(
6425 __isl_take isl_val *v);
6426 __isl_give isl_ast_expr *isl_ast_expr_from_id(
6427 __isl_take isl_id *id);
6428 __isl_give isl_ast_expr *isl_ast_expr_neg(
6429 __isl_take isl_ast_expr *expr);
6430 __isl_give isl_ast_expr *isl_ast_expr_add(
6431 __isl_take isl_ast_expr *expr1,
6432 __isl_take isl_ast_expr *expr2);
6433 __isl_give isl_ast_expr *isl_ast_expr_sub(
6434 __isl_take isl_ast_expr *expr1,
6435 __isl_take isl_ast_expr *expr2);
6436 __isl_give isl_ast_expr *isl_ast_expr_mul(
6437 __isl_take isl_ast_expr *expr1,
6438 __isl_take isl_ast_expr *expr2);
6439 __isl_give isl_ast_expr *isl_ast_expr_div(
6440 __isl_take isl_ast_expr *expr1,
6441 __isl_take isl_ast_expr *expr2);
6442 __isl_give isl_ast_expr *isl_ast_expr_and(
6443 __isl_take isl_ast_expr *expr1,
6444 __isl_take isl_ast_expr *expr2)
6445 __isl_give isl_ast_expr *isl_ast_expr_or(
6446 __isl_take isl_ast_expr *expr1,
6447 __isl_take isl_ast_expr *expr2)
6448 __isl_give isl_ast_expr *isl_ast_expr_access(
6449 __isl_take isl_ast_expr *array,
6450 __isl_take isl_ast_expr_list *indices);
6452 #include <isl/ast_build.h>
6453 __isl_give isl_ast_expr *isl_ast_build_expr_from_pw_aff(
6454 __isl_keep isl_ast_build *build,
6455 __isl_take isl_pw_aff *pa);
6456 __isl_give isl_ast_expr *
6457 isl_ast_build_access_from_pw_multi_aff(
6458 __isl_keep isl_ast_build *build,
6459 __isl_take isl_pw_multi_aff *pma);
6460 __isl_give isl_ast_expr *
6461 isl_ast_build_access_from_multi_pw_aff(
6462 __isl_keep isl_ast_build *build,
6463 __isl_take isl_multi_pw_aff *mpa);
6464 __isl_give isl_ast_expr *
6465 isl_ast_build_call_from_pw_multi_aff(
6466 __isl_keep isl_ast_build *build,
6467 __isl_take isl_pw_multi_aff *pma);
6468 __isl_give isl_ast_expr *
6469 isl_ast_build_call_from_multi_pw_aff(
6470 __isl_keep isl_ast_build *build,
6471 __isl_take isl_multi_pw_aff *mpa);
6473 The domains of C<pa>, C<mpa> and C<pma> should correspond
6474 to the schedule space of C<build>.
6475 The tuple id of C<mpa> or C<pma> is used as the array being accessed or
6476 the function being called.
6477 If the accessed space is a nested relation, then it is taken
6478 to represent an access of the member specified by the range
6479 of this nested relation of the structure specified by the domain
6480 of the nested relation.
6482 The following functions can be used to modify an C<isl_ast_expr>.
6484 #include <isl/ast.h>
6485 __isl_give isl_ast_expr *isl_ast_expr_set_op_arg(
6486 __isl_take isl_ast_expr *expr, int pos,
6487 __isl_take isl_ast_expr *arg);
6489 Replace the argument of C<expr> at position C<pos> by C<arg>.
6491 #include <isl/ast.h>
6492 __isl_give isl_ast_expr *isl_ast_expr_substitute_ids(
6493 __isl_take isl_ast_expr *expr,
6494 __isl_take isl_id_to_ast_expr *id2expr);
6496 The function C<isl_ast_expr_substitute_ids> replaces the
6497 subexpressions of C<expr> of type C<isl_ast_expr_id>
6498 by the corresponding expression in C<id2expr>, if there is any.
6501 User specified data can be attached to an C<isl_ast_node> and obtained
6502 from the same C<isl_ast_node> using the following functions.
6504 #include <isl/ast.h>
6505 __isl_give isl_ast_node *isl_ast_node_set_annotation(
6506 __isl_take isl_ast_node *node,
6507 __isl_take isl_id *annotation);
6508 __isl_give isl_id *isl_ast_node_get_annotation(
6509 __isl_keep isl_ast_node *node);
6511 Basic printing can be performed using the following functions.
6513 #include <isl/ast.h>
6514 __isl_give isl_printer *isl_printer_print_ast_expr(
6515 __isl_take isl_printer *p,
6516 __isl_keep isl_ast_expr *expr);
6517 __isl_give isl_printer *isl_printer_print_ast_node(
6518 __isl_take isl_printer *p,
6519 __isl_keep isl_ast_node *node);
6521 More advanced printing can be performed using the following functions.
6523 #include <isl/ast.h>
6524 __isl_give isl_printer *isl_ast_op_type_print_macro(
6525 enum isl_ast_op_type type,
6526 __isl_take isl_printer *p);
6527 __isl_give isl_printer *isl_ast_node_print_macros(
6528 __isl_keep isl_ast_node *node,
6529 __isl_take isl_printer *p);
6530 __isl_give isl_printer *isl_ast_node_print(
6531 __isl_keep isl_ast_node *node,
6532 __isl_take isl_printer *p,
6533 __isl_take isl_ast_print_options *options);
6534 __isl_give isl_printer *isl_ast_node_for_print(
6535 __isl_keep isl_ast_node *node,
6536 __isl_take isl_printer *p,
6537 __isl_take isl_ast_print_options *options);
6538 __isl_give isl_printer *isl_ast_node_if_print(
6539 __isl_keep isl_ast_node *node,
6540 __isl_take isl_printer *p,
6541 __isl_take isl_ast_print_options *options);
6543 While printing an C<isl_ast_node> in C<ISL_FORMAT_C>,
6544 C<isl> may print out an AST that makes use of macros such
6545 as C<floord>, C<min> and C<max>.
6546 C<isl_ast_op_type_print_macro> prints out the macro
6547 corresponding to a specific C<isl_ast_op_type>.
6548 C<isl_ast_node_print_macros> scans the C<isl_ast_node>
6549 for expressions where these macros would be used and prints
6550 out the required macro definitions.
6551 Essentially, C<isl_ast_node_print_macros> calls
6552 C<isl_ast_node_foreach_ast_op_type> with C<isl_ast_op_type_print_macro>
6553 as function argument.
6554 C<isl_ast_node_print>, C<isl_ast_node_for_print> and
6555 C<isl_ast_node_if_print> print an C<isl_ast_node>
6556 in C<ISL_FORMAT_C>, but allow for some extra control
6557 through an C<isl_ast_print_options> object.
6558 This object can be created using the following functions.
6560 #include <isl/ast.h>
6561 __isl_give isl_ast_print_options *
6562 isl_ast_print_options_alloc(isl_ctx *ctx);
6563 __isl_give isl_ast_print_options *
6564 isl_ast_print_options_copy(
6565 __isl_keep isl_ast_print_options *options);
6566 void *isl_ast_print_options_free(
6567 __isl_take isl_ast_print_options *options);
6569 __isl_give isl_ast_print_options *
6570 isl_ast_print_options_set_print_user(
6571 __isl_take isl_ast_print_options *options,
6572 __isl_give isl_printer *(*print_user)(
6573 __isl_take isl_printer *p,
6574 __isl_take isl_ast_print_options *options,
6575 __isl_keep isl_ast_node *node, void *user),
6577 __isl_give isl_ast_print_options *
6578 isl_ast_print_options_set_print_for(
6579 __isl_take isl_ast_print_options *options,
6580 __isl_give isl_printer *(*print_for)(
6581 __isl_take isl_printer *p,
6582 __isl_take isl_ast_print_options *options,
6583 __isl_keep isl_ast_node *node, void *user),
6586 The callback set by C<isl_ast_print_options_set_print_user>
6587 is called whenever a node of type C<isl_ast_node_user> needs to
6589 The callback set by C<isl_ast_print_options_set_print_for>
6590 is called whenever a node of type C<isl_ast_node_for> needs to
6592 Note that C<isl_ast_node_for_print> will I<not> call the
6593 callback set by C<isl_ast_print_options_set_print_for> on the node
6594 on which C<isl_ast_node_for_print> is called, but only on nested
6595 nodes of type C<isl_ast_node_for>. It is therefore safe to
6596 call C<isl_ast_node_for_print> from within the callback set by
6597 C<isl_ast_print_options_set_print_for>.
6599 The following option determines the type to be used for iterators
6600 while printing the AST.
6602 int isl_options_set_ast_iterator_type(
6603 isl_ctx *ctx, const char *val);
6604 const char *isl_options_get_ast_iterator_type(
6609 #include <isl/ast_build.h>
6610 int isl_options_set_ast_build_atomic_upper_bound(
6611 isl_ctx *ctx, int val);
6612 int isl_options_get_ast_build_atomic_upper_bound(
6614 int isl_options_set_ast_build_prefer_pdiv(isl_ctx *ctx,
6616 int isl_options_get_ast_build_prefer_pdiv(isl_ctx *ctx);
6617 int isl_options_set_ast_build_exploit_nested_bounds(
6618 isl_ctx *ctx, int val);
6619 int isl_options_get_ast_build_exploit_nested_bounds(
6621 int isl_options_set_ast_build_group_coscheduled(
6622 isl_ctx *ctx, int val);
6623 int isl_options_get_ast_build_group_coscheduled(
6625 int isl_options_set_ast_build_scale_strides(
6626 isl_ctx *ctx, int val);
6627 int isl_options_get_ast_build_scale_strides(
6629 int isl_options_set_ast_build_allow_else(isl_ctx *ctx,
6631 int isl_options_get_ast_build_allow_else(isl_ctx *ctx);
6632 int isl_options_set_ast_build_allow_or(isl_ctx *ctx,
6634 int isl_options_get_ast_build_allow_or(isl_ctx *ctx);
6638 =item * ast_build_atomic_upper_bound
6640 Generate loop upper bounds that consist of the current loop iterator,
6641 an operator and an expression not involving the iterator.
6642 If this option is not set, then the current loop iterator may appear
6643 several times in the upper bound.
6644 For example, when this option is turned off, AST generation
6647 [n] -> { A[i] -> [i] : 0 <= i <= 100, n }
6651 for (int c0 = 0; c0 <= 100 && n >= c0; c0 += 1)
6654 When the option is turned on, the following AST is generated
6656 for (int c0 = 0; c0 <= min(100, n); c0 += 1)
6659 =item * ast_build_prefer_pdiv
6661 If this option is turned off, then the AST generation will
6662 produce ASTs that may only contain C<isl_ast_op_fdiv_q>
6663 operators, but no C<isl_ast_op_pdiv_q> or
6664 C<isl_ast_op_pdiv_r> operators.
6665 If this options is turned on, then C<isl> will try to convert
6666 some of the C<isl_ast_op_fdiv_q> operators to (expressions containing)
6667 C<isl_ast_op_pdiv_q> or C<isl_ast_op_pdiv_r> operators.
6669 =item * ast_build_exploit_nested_bounds
6671 Simplify conditions based on bounds of nested for loops.
6672 In particular, remove conditions that are implied by the fact
6673 that one or more nested loops have at least one iteration,
6674 meaning that the upper bound is at least as large as the lower bound.
6675 For example, when this option is turned off, AST generation
6678 [N,M] -> { A[i,j] -> [i,j] : 0 <= i <= N and
6684 for (int c0 = 0; c0 <= N; c0 += 1)
6685 for (int c1 = 0; c1 <= M; c1 += 1)
6688 When the option is turned on, the following AST is generated
6690 for (int c0 = 0; c0 <= N; c0 += 1)
6691 for (int c1 = 0; c1 <= M; c1 += 1)
6694 =item * ast_build_group_coscheduled
6696 If two domain elements are assigned the same schedule point, then
6697 they may be executed in any order and they may even appear in different
6698 loops. If this options is set, then the AST generator will make
6699 sure that coscheduled domain elements do not appear in separate parts
6700 of the AST. This is useful in case of nested AST generation
6701 if the outer AST generation is given only part of a schedule
6702 and the inner AST generation should handle the domains that are
6703 coscheduled by this initial part of the schedule together.
6704 For example if an AST is generated for a schedule
6706 { A[i] -> [0]; B[i] -> [0] }
6708 then the C<isl_ast_build_set_create_leaf> callback described
6709 below may get called twice, once for each domain.
6710 Setting this option ensures that the callback is only called once
6711 on both domains together.
6713 =item * ast_build_separation_bounds
6715 This option specifies which bounds to use during separation.
6716 If this option is set to C<ISL_AST_BUILD_SEPARATION_BOUNDS_IMPLICIT>
6717 then all (possibly implicit) bounds on the current dimension will
6718 be used during separation.
6719 If this option is set to C<ISL_AST_BUILD_SEPARATION_BOUNDS_EXPLICIT>
6720 then only those bounds that are explicitly available will
6721 be used during separation.
6723 =item * ast_build_scale_strides
6725 This option specifies whether the AST generator is allowed
6726 to scale down iterators of strided loops.
6728 =item * ast_build_allow_else
6730 This option specifies whether the AST generator is allowed
6731 to construct if statements with else branches.
6733 =item * ast_build_allow_or
6735 This option specifies whether the AST generator is allowed
6736 to construct if conditions with disjunctions.
6740 =head3 Fine-grained Control over AST Generation
6742 Besides specifying the constraints on the parameters,
6743 an C<isl_ast_build> object can be used to control
6744 various aspects of the AST generation process.
6745 The most prominent way of control is through ``options'',
6746 which can be set using the following function.
6748 #include <isl/ast_build.h>
6749 __isl_give isl_ast_build *
6750 isl_ast_build_set_options(
6751 __isl_take isl_ast_build *control,
6752 __isl_take isl_union_map *options);
6754 The options are encoded in an <isl_union_map>.
6755 The domain of this union relation refers to the schedule domain,
6756 i.e., the range of the schedule passed to C<isl_ast_build_ast_from_schedule>.
6757 In the case of nested AST generation (see L</"Nested AST Generation">),
6758 the domain of C<options> should refer to the extra piece of the schedule.
6759 That is, it should be equal to the range of the wrapped relation in the
6760 range of the schedule.
6761 The range of the options can consist of elements in one or more spaces,
6762 the names of which determine the effect of the option.
6763 The values of the range typically also refer to the schedule dimension
6764 to which the option applies. In case of nested AST generation
6765 (see L</"Nested AST Generation">), these values refer to the position
6766 of the schedule dimension within the innermost AST generation.
6767 The constraints on the domain elements of
6768 the option should only refer to this dimension and earlier dimensions.
6769 We consider the following spaces.
6773 =item C<separation_class>
6775 This space is a wrapped relation between two one dimensional spaces.
6776 The input space represents the schedule dimension to which the option
6777 applies and the output space represents the separation class.
6778 While constructing a loop corresponding to the specified schedule
6779 dimension(s), the AST generator will try to generate separate loops
6780 for domain elements that are assigned different classes.
6781 If only some of the elements are assigned a class, then those elements
6782 that are not assigned any class will be treated as belonging to a class
6783 that is separate from the explicitly assigned classes.
6784 The typical use case for this option is to separate full tiles from
6786 The other options, described below, are applied after the separation
6789 As an example, consider the separation into full and partial tiles
6790 of a tiling of a triangular domain.
6791 Take, for example, the domain
6793 { A[i,j] : 0 <= i,j and i + j <= 100 }
6795 and a tiling into tiles of 10 by 10. The input to the AST generator
6796 is then the schedule
6798 { A[i,j] -> [([i/10]),[j/10],i,j] : 0 <= i,j and
6801 Without any options, the following AST is generated
6803 for (int c0 = 0; c0 <= 10; c0 += 1)
6804 for (int c1 = 0; c1 <= -c0 + 10; c1 += 1)
6805 for (int c2 = 10 * c0;
6806 c2 <= min(-10 * c1 + 100, 10 * c0 + 9);
6808 for (int c3 = 10 * c1;
6809 c3 <= min(10 * c1 + 9, -c2 + 100);
6813 Separation into full and partial tiles can be obtained by assigning
6814 a class, say C<0>, to the full tiles. The full tiles are represented by those
6815 values of the first and second schedule dimensions for which there are
6816 values of the third and fourth dimensions to cover an entire tile.
6817 That is, we need to specify the following option
6819 { [a,b,c,d] -> separation_class[[0]->[0]] :
6820 exists b': 0 <= 10a,10b' and
6821 10a+9+10b'+9 <= 100;
6822 [a,b,c,d] -> separation_class[[1]->[0]] :
6823 0 <= 10a,10b and 10a+9+10b+9 <= 100 }
6827 { [a, b, c, d] -> separation_class[[1] -> [0]] :
6828 a >= 0 and b >= 0 and b <= 8 - a;
6829 [a, b, c, d] -> separation_class[[0] -> [0]] :
6832 With this option, the generated AST is as follows
6835 for (int c0 = 0; c0 <= 8; c0 += 1) {
6836 for (int c1 = 0; c1 <= -c0 + 8; c1 += 1)
6837 for (int c2 = 10 * c0;
6838 c2 <= 10 * c0 + 9; c2 += 1)
6839 for (int c3 = 10 * c1;
6840 c3 <= 10 * c1 + 9; c3 += 1)
6842 for (int c1 = -c0 + 9; c1 <= -c0 + 10; c1 += 1)
6843 for (int c2 = 10 * c0;
6844 c2 <= min(-10 * c1 + 100, 10 * c0 + 9);
6846 for (int c3 = 10 * c1;
6847 c3 <= min(-c2 + 100, 10 * c1 + 9);
6851 for (int c0 = 9; c0 <= 10; c0 += 1)
6852 for (int c1 = 0; c1 <= -c0 + 10; c1 += 1)
6853 for (int c2 = 10 * c0;
6854 c2 <= min(-10 * c1 + 100, 10 * c0 + 9);
6856 for (int c3 = 10 * c1;
6857 c3 <= min(10 * c1 + 9, -c2 + 100);
6864 This is a single-dimensional space representing the schedule dimension(s)
6865 to which ``separation'' should be applied. Separation tries to split
6866 a loop into several pieces if this can avoid the generation of guards
6868 See also the C<atomic> option.
6872 This is a single-dimensional space representing the schedule dimension(s)
6873 for which the domains should be considered ``atomic''. That is, the
6874 AST generator will make sure that any given domain space will only appear
6875 in a single loop at the specified level.
6877 Consider the following schedule
6879 { a[i] -> [i] : 0 <= i < 10;
6880 b[i] -> [i+1] : 0 <= i < 10 }
6882 If the following option is specified
6884 { [i] -> separate[x] }
6886 then the following AST will be generated
6890 for (int c0 = 1; c0 <= 9; c0 += 1) {
6897 If, on the other hand, the following option is specified
6899 { [i] -> atomic[x] }
6901 then the following AST will be generated
6903 for (int c0 = 0; c0 <= 10; c0 += 1) {
6910 If neither C<atomic> nor C<separate> is specified, then the AST generator
6911 may produce either of these two results or some intermediate form.
6915 This is a single-dimensional space representing the schedule dimension(s)
6916 that should be I<completely> unrolled.
6917 To obtain a partial unrolling, the user should apply an additional
6918 strip-mining to the schedule and fully unroll the inner loop.
6922 Additional control is available through the following functions.
6924 #include <isl/ast_build.h>
6925 __isl_give isl_ast_build *
6926 isl_ast_build_set_iterators(
6927 __isl_take isl_ast_build *control,
6928 __isl_take isl_id_list *iterators);
6930 The function C<isl_ast_build_set_iterators> allows the user to
6931 specify a list of iterator C<isl_id>s to be used as iterators.
6932 If the input schedule is injective, then
6933 the number of elements in this list should be as large as the dimension
6934 of the schedule space, but no direct correspondence should be assumed
6935 between dimensions and elements.
6936 If the input schedule is not injective, then an additional number
6937 of C<isl_id>s equal to the largest dimension of the input domains
6939 If the number of provided C<isl_id>s is insufficient, then additional
6940 names are automatically generated.
6942 #include <isl/ast_build.h>
6943 __isl_give isl_ast_build *
6944 isl_ast_build_set_create_leaf(
6945 __isl_take isl_ast_build *control,
6946 __isl_give isl_ast_node *(*fn)(
6947 __isl_take isl_ast_build *build,
6948 void *user), void *user);
6951 C<isl_ast_build_set_create_leaf> function allows for the
6952 specification of a callback that should be called whenever the AST
6953 generator arrives at an element of the schedule domain.
6954 The callback should return an AST node that should be inserted
6955 at the corresponding position of the AST. The default action (when
6956 the callback is not set) is to continue generating parts of the AST to scan
6957 all the domain elements associated to the schedule domain element
6958 and to insert user nodes, ``calling'' the domain element, for each of them.
6959 The C<build> argument contains the current state of the C<isl_ast_build>.
6960 To ease nested AST generation (see L</"Nested AST Generation">),
6961 all control information that is
6962 specific to the current AST generation such as the options and
6963 the callbacks has been removed from this C<isl_ast_build>.
6964 The callback would typically return the result of a nested
6966 user defined node created using the following function.
6968 #include <isl/ast.h>
6969 __isl_give isl_ast_node *isl_ast_node_alloc_user(
6970 __isl_take isl_ast_expr *expr);
6972 #include <isl/ast_build.h>
6973 __isl_give isl_ast_build *
6974 isl_ast_build_set_at_each_domain(
6975 __isl_take isl_ast_build *build,
6976 __isl_give isl_ast_node *(*fn)(
6977 __isl_take isl_ast_node *node,
6978 __isl_keep isl_ast_build *build,
6979 void *user), void *user);
6980 __isl_give isl_ast_build *
6981 isl_ast_build_set_before_each_for(
6982 __isl_take isl_ast_build *build,
6983 __isl_give isl_id *(*fn)(
6984 __isl_keep isl_ast_build *build,
6985 void *user), void *user);
6986 __isl_give isl_ast_build *
6987 isl_ast_build_set_after_each_for(
6988 __isl_take isl_ast_build *build,
6989 __isl_give isl_ast_node *(*fn)(
6990 __isl_take isl_ast_node *node,
6991 __isl_keep isl_ast_build *build,
6992 void *user), void *user);
6994 The callback set by C<isl_ast_build_set_at_each_domain> will
6995 be called for each domain AST node.
6996 The callbacks set by C<isl_ast_build_set_before_each_for>
6997 and C<isl_ast_build_set_after_each_for> will be called
6998 for each for AST node. The first will be called in depth-first
6999 pre-order, while the second will be called in depth-first post-order.
7000 Since C<isl_ast_build_set_before_each_for> is called before the for
7001 node is actually constructed, it is only passed an C<isl_ast_build>.
7002 The returned C<isl_id> will be added as an annotation (using
7003 C<isl_ast_node_set_annotation>) to the constructed for node.
7004 In particular, if the user has also specified an C<after_each_for>
7005 callback, then the annotation can be retrieved from the node passed to
7006 that callback using C<isl_ast_node_get_annotation>.
7007 All callbacks should C<NULL> on failure.
7008 The given C<isl_ast_build> can be used to create new
7009 C<isl_ast_expr> objects using C<isl_ast_build_expr_from_pw_aff>
7010 or C<isl_ast_build_call_from_pw_multi_aff>.
7012 =head3 Nested AST Generation
7014 C<isl> allows the user to create an AST within the context
7015 of another AST. These nested ASTs are created using the
7016 same C<isl_ast_build_ast_from_schedule> function that is used to create the
7017 outer AST. The C<build> argument should be an C<isl_ast_build>
7018 passed to a callback set by
7019 C<isl_ast_build_set_create_leaf>.
7020 The space of the range of the C<schedule> argument should refer
7021 to this build. In particular, the space should be a wrapped
7022 relation and the domain of this wrapped relation should be the
7023 same as that of the range of the schedule returned by
7024 C<isl_ast_build_get_schedule> below.
7025 In practice, the new schedule is typically
7026 created by calling C<isl_union_map_range_product> on the old schedule
7027 and some extra piece of the schedule.
7028 The space of the schedule domain is also available from
7029 the C<isl_ast_build>.
7031 #include <isl/ast_build.h>
7032 __isl_give isl_union_map *isl_ast_build_get_schedule(
7033 __isl_keep isl_ast_build *build);
7034 __isl_give isl_space *isl_ast_build_get_schedule_space(
7035 __isl_keep isl_ast_build *build);
7036 __isl_give isl_ast_build *isl_ast_build_restrict(
7037 __isl_take isl_ast_build *build,
7038 __isl_take isl_set *set);
7040 The C<isl_ast_build_get_schedule> function returns a (partial)
7041 schedule for the domains elements for which part of the AST still needs to
7042 be generated in the current build.
7043 In particular, the domain elements are mapped to those iterations of the loops
7044 enclosing the current point of the AST generation inside which
7045 the domain elements are executed.
7046 No direct correspondence between
7047 the input schedule and this schedule should be assumed.
7048 The space obtained from C<isl_ast_build_get_schedule_space> can be used
7049 to create a set for C<isl_ast_build_restrict> to intersect
7050 with the current build. In particular, the set passed to
7051 C<isl_ast_build_restrict> can have additional parameters.
7052 The ids of the set dimensions in the space returned by
7053 C<isl_ast_build_get_schedule_space> correspond to the
7054 iterators of the already generated loops.
7055 The user should not rely on the ids of the output dimensions
7056 of the relations in the union relation returned by
7057 C<isl_ast_build_get_schedule> having any particular value.
7061 Although C<isl> is mainly meant to be used as a library,
7062 it also contains some basic applications that use some
7063 of the functionality of C<isl>.
7064 The input may be specified in either the L<isl format>
7065 or the L<PolyLib format>.
7067 =head2 C<isl_polyhedron_sample>
7069 C<isl_polyhedron_sample> takes a polyhedron as input and prints
7070 an integer element of the polyhedron, if there is any.
7071 The first column in the output is the denominator and is always
7072 equal to 1. If the polyhedron contains no integer points,
7073 then a vector of length zero is printed.
7077 C<isl_pip> takes the same input as the C<example> program
7078 from the C<piplib> distribution, i.e., a set of constraints
7079 on the parameters, a line containing only -1 and finally a set
7080 of constraints on a parametric polyhedron.
7081 The coefficients of the parameters appear in the last columns
7082 (but before the final constant column).
7083 The output is the lexicographic minimum of the parametric polyhedron.
7084 As C<isl> currently does not have its own output format, the output
7085 is just a dump of the internal state.
7087 =head2 C<isl_polyhedron_minimize>
7089 C<isl_polyhedron_minimize> computes the minimum of some linear
7090 or affine objective function over the integer points in a polyhedron.
7091 If an affine objective function
7092 is given, then the constant should appear in the last column.
7094 =head2 C<isl_polytope_scan>
7096 Given a polytope, C<isl_polytope_scan> prints
7097 all integer points in the polytope.
7099 =head2 C<isl_codegen>
7101 Given a schedule, a context set and an options relation,
7102 C<isl_codegen> prints out an AST that scans the domain elements
7103 of the schedule in the order of their image(s) taking into account
7104 the constraints in the context set.