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 following functions.
1057 __isl_give isl_local_space *isl_local_space_domain(
1058 __isl_take isl_local_space *ls);
1059 __isl_give isl_local_space *isl_local_space_range(
1060 __isl_take isl_local_space *ls);
1061 __isl_give isl_local_space *isl_local_space_from_domain(
1062 __isl_take isl_local_space *ls);
1063 __isl_give isl_local_space *isl_local_space_intersect(
1064 __isl_take isl_local_space *ls1,
1065 __isl_take isl_local_space *ls2);
1066 __isl_give isl_local_space *isl_local_space_add_dims(
1067 __isl_take isl_local_space *ls,
1068 enum isl_dim_type type, unsigned n);
1069 __isl_give isl_local_space *isl_local_space_insert_dims(
1070 __isl_take isl_local_space *ls,
1071 enum isl_dim_type type, unsigned first, unsigned n);
1072 __isl_give isl_local_space *isl_local_space_drop_dims(
1073 __isl_take isl_local_space *ls,
1074 enum isl_dim_type type, unsigned first, unsigned n);
1076 =head2 Input and Output
1078 C<isl> supports its own input/output format, which is similar
1079 to the C<Omega> format, but also supports the C<PolyLib> format
1082 =head3 C<isl> format
1084 The C<isl> format is similar to that of C<Omega>, but has a different
1085 syntax for describing the parameters and allows for the definition
1086 of an existentially quantified variable as the integer division
1087 of an affine expression.
1088 For example, the set of integers C<i> between C<0> and C<n>
1089 such that C<i % 10 <= 6> can be described as
1091 [n] -> { [i] : exists (a = [i/10] : 0 <= i and i <= n and
1094 A set or relation can have several disjuncts, separated
1095 by the keyword C<or>. Each disjunct is either a conjunction
1096 of constraints or a projection (C<exists>) of a conjunction
1097 of constraints. The constraints are separated by the keyword
1100 =head3 C<PolyLib> format
1102 If the represented set is a union, then the first line
1103 contains a single number representing the number of disjuncts.
1104 Otherwise, a line containing the number C<1> is optional.
1106 Each disjunct is represented by a matrix of constraints.
1107 The first line contains two numbers representing
1108 the number of rows and columns,
1109 where the number of rows is equal to the number of constraints
1110 and the number of columns is equal to two plus the number of variables.
1111 The following lines contain the actual rows of the constraint matrix.
1112 In each row, the first column indicates whether the constraint
1113 is an equality (C<0>) or inequality (C<1>). The final column
1114 corresponds to the constant term.
1116 If the set is parametric, then the coefficients of the parameters
1117 appear in the last columns before the constant column.
1118 The coefficients of any existentially quantified variables appear
1119 between those of the set variables and those of the parameters.
1121 =head3 Extended C<PolyLib> format
1123 The extended C<PolyLib> format is nearly identical to the
1124 C<PolyLib> format. The only difference is that the line
1125 containing the number of rows and columns of a constraint matrix
1126 also contains four additional numbers:
1127 the number of output dimensions, the number of input dimensions,
1128 the number of local dimensions (i.e., the number of existentially
1129 quantified variables) and the number of parameters.
1130 For sets, the number of ``output'' dimensions is equal
1131 to the number of set dimensions, while the number of ``input''
1136 #include <isl/set.h>
1137 __isl_give isl_basic_set *isl_basic_set_read_from_file(
1138 isl_ctx *ctx, FILE *input);
1139 __isl_give isl_basic_set *isl_basic_set_read_from_str(
1140 isl_ctx *ctx, const char *str);
1141 __isl_give isl_set *isl_set_read_from_file(isl_ctx *ctx,
1143 __isl_give isl_set *isl_set_read_from_str(isl_ctx *ctx,
1146 #include <isl/map.h>
1147 __isl_give isl_basic_map *isl_basic_map_read_from_file(
1148 isl_ctx *ctx, FILE *input);
1149 __isl_give isl_basic_map *isl_basic_map_read_from_str(
1150 isl_ctx *ctx, const char *str);
1151 __isl_give isl_map *isl_map_read_from_file(
1152 isl_ctx *ctx, FILE *input);
1153 __isl_give isl_map *isl_map_read_from_str(isl_ctx *ctx,
1156 #include <isl/union_set.h>
1157 __isl_give isl_union_set *isl_union_set_read_from_file(
1158 isl_ctx *ctx, FILE *input);
1159 __isl_give isl_union_set *isl_union_set_read_from_str(
1160 isl_ctx *ctx, const char *str);
1162 #include <isl/union_map.h>
1163 __isl_give isl_union_map *isl_union_map_read_from_file(
1164 isl_ctx *ctx, FILE *input);
1165 __isl_give isl_union_map *isl_union_map_read_from_str(
1166 isl_ctx *ctx, const char *str);
1168 The input format is autodetected and may be either the C<PolyLib> format
1169 or the C<isl> format.
1173 Before anything can be printed, an C<isl_printer> needs to
1176 __isl_give isl_printer *isl_printer_to_file(isl_ctx *ctx,
1178 __isl_give isl_printer *isl_printer_to_str(isl_ctx *ctx);
1179 void *isl_printer_free(__isl_take isl_printer *printer);
1180 __isl_give char *isl_printer_get_str(
1181 __isl_keep isl_printer *printer);
1183 The printer can be inspected using the following functions.
1185 FILE *isl_printer_get_file(
1186 __isl_keep isl_printer *printer);
1187 int isl_printer_get_output_format(
1188 __isl_keep isl_printer *p);
1190 The behavior of the printer can be modified in various ways
1192 __isl_give isl_printer *isl_printer_set_output_format(
1193 __isl_take isl_printer *p, int output_format);
1194 __isl_give isl_printer *isl_printer_set_indent(
1195 __isl_take isl_printer *p, int indent);
1196 __isl_give isl_printer *isl_printer_indent(
1197 __isl_take isl_printer *p, int indent);
1198 __isl_give isl_printer *isl_printer_set_prefix(
1199 __isl_take isl_printer *p, const char *prefix);
1200 __isl_give isl_printer *isl_printer_set_suffix(
1201 __isl_take isl_printer *p, const char *suffix);
1203 The C<output_format> may be either C<ISL_FORMAT_ISL>, C<ISL_FORMAT_OMEGA>,
1204 C<ISL_FORMAT_POLYLIB>, C<ISL_FORMAT_EXT_POLYLIB> or C<ISL_FORMAT_LATEX>
1205 and defaults to C<ISL_FORMAT_ISL>.
1206 Each line in the output is indented by C<indent> (set by
1207 C<isl_printer_set_indent>) spaces
1208 (default: 0), prefixed by C<prefix> and suffixed by C<suffix>.
1209 In the C<PolyLib> format output,
1210 the coefficients of the existentially quantified variables
1211 appear between those of the set variables and those
1213 The function C<isl_printer_indent> increases the indentation
1214 by the specified amount (which may be negative).
1216 To actually print something, use
1218 #include <isl/printer.h>
1219 __isl_give isl_printer *isl_printer_print_double(
1220 __isl_take isl_printer *p, double d);
1222 #include <isl/set.h>
1223 __isl_give isl_printer *isl_printer_print_basic_set(
1224 __isl_take isl_printer *printer,
1225 __isl_keep isl_basic_set *bset);
1226 __isl_give isl_printer *isl_printer_print_set(
1227 __isl_take isl_printer *printer,
1228 __isl_keep isl_set *set);
1230 #include <isl/map.h>
1231 __isl_give isl_printer *isl_printer_print_basic_map(
1232 __isl_take isl_printer *printer,
1233 __isl_keep isl_basic_map *bmap);
1234 __isl_give isl_printer *isl_printer_print_map(
1235 __isl_take isl_printer *printer,
1236 __isl_keep isl_map *map);
1238 #include <isl/union_set.h>
1239 __isl_give isl_printer *isl_printer_print_union_set(
1240 __isl_take isl_printer *p,
1241 __isl_keep isl_union_set *uset);
1243 #include <isl/union_map.h>
1244 __isl_give isl_printer *isl_printer_print_union_map(
1245 __isl_take isl_printer *p,
1246 __isl_keep isl_union_map *umap);
1248 When called on a file printer, the following function flushes
1249 the file. When called on a string printer, the buffer is cleared.
1251 __isl_give isl_printer *isl_printer_flush(
1252 __isl_take isl_printer *p);
1254 =head2 Creating New Sets and Relations
1256 C<isl> has functions for creating some standard sets and relations.
1260 =item * Empty sets and relations
1262 __isl_give isl_basic_set *isl_basic_set_empty(
1263 __isl_take isl_space *space);
1264 __isl_give isl_basic_map *isl_basic_map_empty(
1265 __isl_take isl_space *space);
1266 __isl_give isl_set *isl_set_empty(
1267 __isl_take isl_space *space);
1268 __isl_give isl_map *isl_map_empty(
1269 __isl_take isl_space *space);
1270 __isl_give isl_union_set *isl_union_set_empty(
1271 __isl_take isl_space *space);
1272 __isl_give isl_union_map *isl_union_map_empty(
1273 __isl_take isl_space *space);
1275 For C<isl_union_set>s and C<isl_union_map>s, the space
1276 is only used to specify the parameters.
1278 =item * Universe sets and relations
1280 __isl_give isl_basic_set *isl_basic_set_universe(
1281 __isl_take isl_space *space);
1282 __isl_give isl_basic_map *isl_basic_map_universe(
1283 __isl_take isl_space *space);
1284 __isl_give isl_set *isl_set_universe(
1285 __isl_take isl_space *space);
1286 __isl_give isl_map *isl_map_universe(
1287 __isl_take isl_space *space);
1288 __isl_give isl_union_set *isl_union_set_universe(
1289 __isl_take isl_union_set *uset);
1290 __isl_give isl_union_map *isl_union_map_universe(
1291 __isl_take isl_union_map *umap);
1293 The sets and relations constructed by the functions above
1294 contain all integer values, while those constructed by the
1295 functions below only contain non-negative values.
1297 __isl_give isl_basic_set *isl_basic_set_nat_universe(
1298 __isl_take isl_space *space);
1299 __isl_give isl_basic_map *isl_basic_map_nat_universe(
1300 __isl_take isl_space *space);
1301 __isl_give isl_set *isl_set_nat_universe(
1302 __isl_take isl_space *space);
1303 __isl_give isl_map *isl_map_nat_universe(
1304 __isl_take isl_space *space);
1306 =item * Identity relations
1308 __isl_give isl_basic_map *isl_basic_map_identity(
1309 __isl_take isl_space *space);
1310 __isl_give isl_map *isl_map_identity(
1311 __isl_take isl_space *space);
1313 The number of input and output dimensions in C<space> needs
1316 =item * Lexicographic order
1318 __isl_give isl_map *isl_map_lex_lt(
1319 __isl_take isl_space *set_space);
1320 __isl_give isl_map *isl_map_lex_le(
1321 __isl_take isl_space *set_space);
1322 __isl_give isl_map *isl_map_lex_gt(
1323 __isl_take isl_space *set_space);
1324 __isl_give isl_map *isl_map_lex_ge(
1325 __isl_take isl_space *set_space);
1326 __isl_give isl_map *isl_map_lex_lt_first(
1327 __isl_take isl_space *space, unsigned n);
1328 __isl_give isl_map *isl_map_lex_le_first(
1329 __isl_take isl_space *space, unsigned n);
1330 __isl_give isl_map *isl_map_lex_gt_first(
1331 __isl_take isl_space *space, unsigned n);
1332 __isl_give isl_map *isl_map_lex_ge_first(
1333 __isl_take isl_space *space, unsigned n);
1335 The first four functions take a space for a B<set>
1336 and return relations that express that the elements in the domain
1337 are lexicographically less
1338 (C<isl_map_lex_lt>), less or equal (C<isl_map_lex_le>),
1339 greater (C<isl_map_lex_gt>) or greater or equal (C<isl_map_lex_ge>)
1340 than the elements in the range.
1341 The last four functions take a space for a map
1342 and return relations that express that the first C<n> dimensions
1343 in the domain are lexicographically less
1344 (C<isl_map_lex_lt_first>), less or equal (C<isl_map_lex_le_first>),
1345 greater (C<isl_map_lex_gt_first>) or greater or equal (C<isl_map_lex_ge_first>)
1346 than the first C<n> dimensions in the range.
1350 A basic set or relation can be converted to a set or relation
1351 using the following functions.
1353 __isl_give isl_set *isl_set_from_basic_set(
1354 __isl_take isl_basic_set *bset);
1355 __isl_give isl_map *isl_map_from_basic_map(
1356 __isl_take isl_basic_map *bmap);
1358 Sets and relations can be converted to union sets and relations
1359 using the following functions.
1361 __isl_give isl_union_set *isl_union_set_from_basic_set(
1362 __isl_take isl_basic_set *bset);
1363 __isl_give isl_union_map *isl_union_map_from_basic_map(
1364 __isl_take isl_basic_map *bmap);
1365 __isl_give isl_union_set *isl_union_set_from_set(
1366 __isl_take isl_set *set);
1367 __isl_give isl_union_map *isl_union_map_from_map(
1368 __isl_take isl_map *map);
1370 The inverse conversions below can only be used if the input
1371 union set or relation is known to contain elements in exactly one
1374 __isl_give isl_set *isl_set_from_union_set(
1375 __isl_take isl_union_set *uset);
1376 __isl_give isl_map *isl_map_from_union_map(
1377 __isl_take isl_union_map *umap);
1379 A zero-dimensional (basic) set can be constructed on a given parameter domain
1380 using the following function.
1382 __isl_give isl_basic_set *isl_basic_set_from_params(
1383 __isl_take isl_basic_set *bset);
1384 __isl_give isl_set *isl_set_from_params(
1385 __isl_take isl_set *set);
1387 Sets and relations can be copied and freed again using the following
1390 __isl_give isl_basic_set *isl_basic_set_copy(
1391 __isl_keep isl_basic_set *bset);
1392 __isl_give isl_set *isl_set_copy(__isl_keep isl_set *set);
1393 __isl_give isl_union_set *isl_union_set_copy(
1394 __isl_keep isl_union_set *uset);
1395 __isl_give isl_basic_map *isl_basic_map_copy(
1396 __isl_keep isl_basic_map *bmap);
1397 __isl_give isl_map *isl_map_copy(__isl_keep isl_map *map);
1398 __isl_give isl_union_map *isl_union_map_copy(
1399 __isl_keep isl_union_map *umap);
1400 void *isl_basic_set_free(__isl_take isl_basic_set *bset);
1401 void *isl_set_free(__isl_take isl_set *set);
1402 void *isl_union_set_free(__isl_take isl_union_set *uset);
1403 void *isl_basic_map_free(__isl_take isl_basic_map *bmap);
1404 void *isl_map_free(__isl_take isl_map *map);
1405 void *isl_union_map_free(__isl_take isl_union_map *umap);
1407 Other sets and relations can be constructed by starting
1408 from a universe set or relation, adding equality and/or
1409 inequality constraints and then projecting out the
1410 existentially quantified variables, if any.
1411 Constraints can be constructed, manipulated and
1412 added to (or removed from) (basic) sets and relations
1413 using the following functions.
1415 #include <isl/constraint.h>
1416 __isl_give isl_constraint *isl_equality_alloc(
1417 __isl_take isl_local_space *ls);
1418 __isl_give isl_constraint *isl_inequality_alloc(
1419 __isl_take isl_local_space *ls);
1420 __isl_give isl_constraint *isl_constraint_set_constant_si(
1421 __isl_take isl_constraint *constraint, int v);
1422 __isl_give isl_constraint *isl_constraint_set_constant_val(
1423 __isl_take isl_constraint *constraint,
1424 __isl_take isl_val *v);
1425 __isl_give isl_constraint *isl_constraint_set_coefficient_si(
1426 __isl_take isl_constraint *constraint,
1427 enum isl_dim_type type, int pos, int v);
1428 __isl_give isl_constraint *
1429 isl_constraint_set_coefficient_val(
1430 __isl_take isl_constraint *constraint,
1431 enum isl_dim_type type, int pos,
1432 __isl_take isl_val *v);
1433 __isl_give isl_basic_map *isl_basic_map_add_constraint(
1434 __isl_take isl_basic_map *bmap,
1435 __isl_take isl_constraint *constraint);
1436 __isl_give isl_basic_set *isl_basic_set_add_constraint(
1437 __isl_take isl_basic_set *bset,
1438 __isl_take isl_constraint *constraint);
1439 __isl_give isl_map *isl_map_add_constraint(
1440 __isl_take isl_map *map,
1441 __isl_take isl_constraint *constraint);
1442 __isl_give isl_set *isl_set_add_constraint(
1443 __isl_take isl_set *set,
1444 __isl_take isl_constraint *constraint);
1445 __isl_give isl_basic_set *isl_basic_set_drop_constraint(
1446 __isl_take isl_basic_set *bset,
1447 __isl_take isl_constraint *constraint);
1449 For example, to create a set containing the even integers
1450 between 10 and 42, you would use the following code.
1453 isl_local_space *ls;
1455 isl_basic_set *bset;
1457 space = isl_space_set_alloc(ctx, 0, 2);
1458 bset = isl_basic_set_universe(isl_space_copy(space));
1459 ls = isl_local_space_from_space(space);
1461 c = isl_equality_alloc(isl_local_space_copy(ls));
1462 c = isl_constraint_set_coefficient_si(c, isl_dim_set, 0, -1);
1463 c = isl_constraint_set_coefficient_si(c, isl_dim_set, 1, 2);
1464 bset = isl_basic_set_add_constraint(bset, c);
1466 c = isl_inequality_alloc(isl_local_space_copy(ls));
1467 c = isl_constraint_set_constant_si(c, -10);
1468 c = isl_constraint_set_coefficient_si(c, isl_dim_set, 0, 1);
1469 bset = isl_basic_set_add_constraint(bset, c);
1471 c = isl_inequality_alloc(ls);
1472 c = isl_constraint_set_constant_si(c, 42);
1473 c = isl_constraint_set_coefficient_si(c, isl_dim_set, 0, -1);
1474 bset = isl_basic_set_add_constraint(bset, c);
1476 bset = isl_basic_set_project_out(bset, isl_dim_set, 1, 1);
1480 isl_basic_set *bset;
1481 bset = isl_basic_set_read_from_str(ctx,
1482 "{[i] : exists (a : i = 2a and i >= 10 and i <= 42)}");
1484 A basic set or relation can also be constructed from two matrices
1485 describing the equalities and the inequalities.
1487 __isl_give isl_basic_set *isl_basic_set_from_constraint_matrices(
1488 __isl_take isl_space *space,
1489 __isl_take isl_mat *eq, __isl_take isl_mat *ineq,
1490 enum isl_dim_type c1,
1491 enum isl_dim_type c2, enum isl_dim_type c3,
1492 enum isl_dim_type c4);
1493 __isl_give isl_basic_map *isl_basic_map_from_constraint_matrices(
1494 __isl_take isl_space *space,
1495 __isl_take isl_mat *eq, __isl_take isl_mat *ineq,
1496 enum isl_dim_type c1,
1497 enum isl_dim_type c2, enum isl_dim_type c3,
1498 enum isl_dim_type c4, enum isl_dim_type c5);
1500 The C<isl_dim_type> arguments indicate the order in which
1501 different kinds of variables appear in the input matrices
1502 and should be a permutation of C<isl_dim_cst>, C<isl_dim_param>,
1503 C<isl_dim_set> and C<isl_dim_div> for sets and
1504 of C<isl_dim_cst>, C<isl_dim_param>,
1505 C<isl_dim_in>, C<isl_dim_out> and C<isl_dim_div> for relations.
1507 A (basic or union) set or relation can also be constructed from a
1508 (union) (piecewise) (multiple) affine expression
1509 or a list of affine expressions
1510 (See L<"Piecewise Quasi Affine Expressions"> and
1511 L<"Piecewise Multiple Quasi Affine Expressions">).
1513 __isl_give isl_basic_map *isl_basic_map_from_aff(
1514 __isl_take isl_aff *aff);
1515 __isl_give isl_map *isl_map_from_aff(
1516 __isl_take isl_aff *aff);
1517 __isl_give isl_set *isl_set_from_pw_aff(
1518 __isl_take isl_pw_aff *pwaff);
1519 __isl_give isl_map *isl_map_from_pw_aff(
1520 __isl_take isl_pw_aff *pwaff);
1521 __isl_give isl_basic_map *isl_basic_map_from_aff_list(
1522 __isl_take isl_space *domain_space,
1523 __isl_take isl_aff_list *list);
1524 __isl_give isl_basic_map *isl_basic_map_from_multi_aff(
1525 __isl_take isl_multi_aff *maff)
1526 __isl_give isl_map *isl_map_from_multi_aff(
1527 __isl_take isl_multi_aff *maff)
1528 __isl_give isl_set *isl_set_from_pw_multi_aff(
1529 __isl_take isl_pw_multi_aff *pma);
1530 __isl_give isl_map *isl_map_from_pw_multi_aff(
1531 __isl_take isl_pw_multi_aff *pma);
1532 __isl_give isl_set *isl_set_from_multi_pw_aff(
1533 __isl_take isl_multi_pw_aff *mpa);
1534 __isl_give isl_map *isl_map_from_multi_pw_aff(
1535 __isl_take isl_multi_pw_aff *mpa);
1536 __isl_give isl_union_map *
1537 isl_union_map_from_union_pw_multi_aff(
1538 __isl_take isl_union_pw_multi_aff *upma);
1540 The C<domain_space> argument describes the domain of the resulting
1541 basic relation. It is required because the C<list> may consist
1542 of zero affine expressions.
1544 =head2 Inspecting Sets and Relations
1546 Usually, the user should not have to care about the actual constraints
1547 of the sets and maps, but should instead apply the abstract operations
1548 explained in the following sections.
1549 Occasionally, however, it may be required to inspect the individual
1550 coefficients of the constraints. This section explains how to do so.
1551 In these cases, it may also be useful to have C<isl> compute
1552 an explicit representation of the existentially quantified variables.
1554 __isl_give isl_set *isl_set_compute_divs(
1555 __isl_take isl_set *set);
1556 __isl_give isl_map *isl_map_compute_divs(
1557 __isl_take isl_map *map);
1558 __isl_give isl_union_set *isl_union_set_compute_divs(
1559 __isl_take isl_union_set *uset);
1560 __isl_give isl_union_map *isl_union_map_compute_divs(
1561 __isl_take isl_union_map *umap);
1563 This explicit representation defines the existentially quantified
1564 variables as integer divisions of the other variables, possibly
1565 including earlier existentially quantified variables.
1566 An explicitly represented existentially quantified variable therefore
1567 has a unique value when the values of the other variables are known.
1568 If, furthermore, the same existentials, i.e., existentials
1569 with the same explicit representations, should appear in the
1570 same order in each of the disjuncts of a set or map, then the user should call
1571 either of the following functions.
1573 __isl_give isl_set *isl_set_align_divs(
1574 __isl_take isl_set *set);
1575 __isl_give isl_map *isl_map_align_divs(
1576 __isl_take isl_map *map);
1578 Alternatively, the existentially quantified variables can be removed
1579 using the following functions, which compute an overapproximation.
1581 __isl_give isl_basic_set *isl_basic_set_remove_divs(
1582 __isl_take isl_basic_set *bset);
1583 __isl_give isl_basic_map *isl_basic_map_remove_divs(
1584 __isl_take isl_basic_map *bmap);
1585 __isl_give isl_set *isl_set_remove_divs(
1586 __isl_take isl_set *set);
1587 __isl_give isl_map *isl_map_remove_divs(
1588 __isl_take isl_map *map);
1590 It is also possible to only remove those divs that are defined
1591 in terms of a given range of dimensions or only those for which
1592 no explicit representation is known.
1594 __isl_give isl_basic_set *
1595 isl_basic_set_remove_divs_involving_dims(
1596 __isl_take isl_basic_set *bset,
1597 enum isl_dim_type type,
1598 unsigned first, unsigned n);
1599 __isl_give isl_basic_map *
1600 isl_basic_map_remove_divs_involving_dims(
1601 __isl_take isl_basic_map *bmap,
1602 enum isl_dim_type type,
1603 unsigned first, unsigned n);
1604 __isl_give isl_set *isl_set_remove_divs_involving_dims(
1605 __isl_take isl_set *set, enum isl_dim_type type,
1606 unsigned first, unsigned n);
1607 __isl_give isl_map *isl_map_remove_divs_involving_dims(
1608 __isl_take isl_map *map, enum isl_dim_type type,
1609 unsigned first, unsigned n);
1611 __isl_give isl_basic_set *
1612 isl_basic_set_remove_unknown_divs(
1613 __isl_take isl_basic_set *bset);
1614 __isl_give isl_set *isl_set_remove_unknown_divs(
1615 __isl_take isl_set *set);
1616 __isl_give isl_map *isl_map_remove_unknown_divs(
1617 __isl_take isl_map *map);
1619 To iterate over all the sets or maps in a union set or map, use
1621 int isl_union_set_foreach_set(__isl_keep isl_union_set *uset,
1622 int (*fn)(__isl_take isl_set *set, void *user),
1624 int isl_union_map_foreach_map(__isl_keep isl_union_map *umap,
1625 int (*fn)(__isl_take isl_map *map, void *user),
1628 The number of sets or maps in a union set or map can be obtained
1631 int isl_union_set_n_set(__isl_keep isl_union_set *uset);
1632 int isl_union_map_n_map(__isl_keep isl_union_map *umap);
1634 To extract the set or map in a given space from a union, use
1636 __isl_give isl_set *isl_union_set_extract_set(
1637 __isl_keep isl_union_set *uset,
1638 __isl_take isl_space *space);
1639 __isl_give isl_map *isl_union_map_extract_map(
1640 __isl_keep isl_union_map *umap,
1641 __isl_take isl_space *space);
1643 To iterate over all the basic sets or maps in a set or map, use
1645 int isl_set_foreach_basic_set(__isl_keep isl_set *set,
1646 int (*fn)(__isl_take isl_basic_set *bset, void *user),
1648 int isl_map_foreach_basic_map(__isl_keep isl_map *map,
1649 int (*fn)(__isl_take isl_basic_map *bmap, void *user),
1652 The callback function C<fn> should return 0 if successful and
1653 -1 if an error occurs. In the latter case, or if any other error
1654 occurs, the above functions will return -1.
1656 It should be noted that C<isl> does not guarantee that
1657 the basic sets or maps passed to C<fn> are disjoint.
1658 If this is required, then the user should call one of
1659 the following functions first.
1661 __isl_give isl_set *isl_set_make_disjoint(
1662 __isl_take isl_set *set);
1663 __isl_give isl_map *isl_map_make_disjoint(
1664 __isl_take isl_map *map);
1666 The number of basic sets in a set can be obtained
1669 int isl_set_n_basic_set(__isl_keep isl_set *set);
1671 To iterate over the constraints of a basic set or map, use
1673 #include <isl/constraint.h>
1675 int isl_basic_set_n_constraint(
1676 __isl_keep isl_basic_set *bset);
1677 int isl_basic_set_foreach_constraint(
1678 __isl_keep isl_basic_set *bset,
1679 int (*fn)(__isl_take isl_constraint *c, void *user),
1681 int isl_basic_map_foreach_constraint(
1682 __isl_keep isl_basic_map *bmap,
1683 int (*fn)(__isl_take isl_constraint *c, void *user),
1685 void *isl_constraint_free(__isl_take isl_constraint *c);
1687 Again, the callback function C<fn> should return 0 if successful and
1688 -1 if an error occurs. In the latter case, or if any other error
1689 occurs, the above functions will return -1.
1690 The constraint C<c> represents either an equality or an inequality.
1691 Use the following function to find out whether a constraint
1692 represents an equality. If not, it represents an inequality.
1694 int isl_constraint_is_equality(
1695 __isl_keep isl_constraint *constraint);
1697 The coefficients of the constraints can be inspected using
1698 the following functions.
1700 int isl_constraint_is_lower_bound(
1701 __isl_keep isl_constraint *constraint,
1702 enum isl_dim_type type, unsigned pos);
1703 int isl_constraint_is_upper_bound(
1704 __isl_keep isl_constraint *constraint,
1705 enum isl_dim_type type, unsigned pos);
1706 __isl_give isl_val *isl_constraint_get_constant_val(
1707 __isl_keep isl_constraint *constraint);
1708 __isl_give isl_val *isl_constraint_get_coefficient_val(
1709 __isl_keep isl_constraint *constraint,
1710 enum isl_dim_type type, int pos);
1711 int isl_constraint_involves_dims(
1712 __isl_keep isl_constraint *constraint,
1713 enum isl_dim_type type, unsigned first, unsigned n);
1715 The explicit representations of the existentially quantified
1716 variables can be inspected using the following function.
1717 Note that the user is only allowed to use this function
1718 if the inspected set or map is the result of a call
1719 to C<isl_set_compute_divs> or C<isl_map_compute_divs>.
1720 The existentially quantified variable is equal to the floor
1721 of the returned affine expression. The affine expression
1722 itself can be inspected using the functions in
1723 L<"Piecewise Quasi Affine Expressions">.
1725 __isl_give isl_aff *isl_constraint_get_div(
1726 __isl_keep isl_constraint *constraint, int pos);
1728 To obtain the constraints of a basic set or map in matrix
1729 form, use the following functions.
1731 __isl_give isl_mat *isl_basic_set_equalities_matrix(
1732 __isl_keep isl_basic_set *bset,
1733 enum isl_dim_type c1, enum isl_dim_type c2,
1734 enum isl_dim_type c3, enum isl_dim_type c4);
1735 __isl_give isl_mat *isl_basic_set_inequalities_matrix(
1736 __isl_keep isl_basic_set *bset,
1737 enum isl_dim_type c1, enum isl_dim_type c2,
1738 enum isl_dim_type c3, enum isl_dim_type c4);
1739 __isl_give isl_mat *isl_basic_map_equalities_matrix(
1740 __isl_keep isl_basic_map *bmap,
1741 enum isl_dim_type c1,
1742 enum isl_dim_type c2, enum isl_dim_type c3,
1743 enum isl_dim_type c4, enum isl_dim_type c5);
1744 __isl_give isl_mat *isl_basic_map_inequalities_matrix(
1745 __isl_keep isl_basic_map *bmap,
1746 enum isl_dim_type c1,
1747 enum isl_dim_type c2, enum isl_dim_type c3,
1748 enum isl_dim_type c4, enum isl_dim_type c5);
1750 The C<isl_dim_type> arguments dictate the order in which
1751 different kinds of variables appear in the resulting matrix
1752 and should be a permutation of C<isl_dim_cst>, C<isl_dim_param>,
1753 C<isl_dim_in>, C<isl_dim_out> and C<isl_dim_div>.
1755 The number of parameters, input, output or set dimensions can
1756 be obtained using the following functions.
1758 unsigned isl_basic_set_dim(__isl_keep isl_basic_set *bset,
1759 enum isl_dim_type type);
1760 unsigned isl_basic_map_dim(__isl_keep isl_basic_map *bmap,
1761 enum isl_dim_type type);
1762 unsigned isl_set_dim(__isl_keep isl_set *set,
1763 enum isl_dim_type type);
1764 unsigned isl_map_dim(__isl_keep isl_map *map,
1765 enum isl_dim_type type);
1767 To check whether the description of a set or relation depends
1768 on one or more given dimensions, it is not necessary to iterate over all
1769 constraints. Instead the following functions can be used.
1771 int isl_basic_set_involves_dims(
1772 __isl_keep isl_basic_set *bset,
1773 enum isl_dim_type type, unsigned first, unsigned n);
1774 int isl_set_involves_dims(__isl_keep isl_set *set,
1775 enum isl_dim_type type, unsigned first, unsigned n);
1776 int isl_basic_map_involves_dims(
1777 __isl_keep isl_basic_map *bmap,
1778 enum isl_dim_type type, unsigned first, unsigned n);
1779 int isl_map_involves_dims(__isl_keep isl_map *map,
1780 enum isl_dim_type type, unsigned first, unsigned n);
1782 Similarly, the following functions can be used to check whether
1783 a given dimension is involved in any lower or upper bound.
1785 int isl_set_dim_has_any_lower_bound(__isl_keep isl_set *set,
1786 enum isl_dim_type type, unsigned pos);
1787 int isl_set_dim_has_any_upper_bound(__isl_keep isl_set *set,
1788 enum isl_dim_type type, unsigned pos);
1790 Note that these functions return true even if there is a bound on
1791 the dimension on only some of the basic sets of C<set>.
1792 To check if they have a bound for all of the basic sets in C<set>,
1793 use the following functions instead.
1795 int isl_set_dim_has_lower_bound(__isl_keep isl_set *set,
1796 enum isl_dim_type type, unsigned pos);
1797 int isl_set_dim_has_upper_bound(__isl_keep isl_set *set,
1798 enum isl_dim_type type, unsigned pos);
1800 The identifiers or names of the domain and range spaces of a set
1801 or relation can be read off or set using the following functions.
1803 __isl_give isl_basic_set *isl_basic_set_set_tuple_id(
1804 __isl_take isl_basic_set *bset,
1805 __isl_take isl_id *id);
1806 __isl_give isl_set *isl_set_set_tuple_id(
1807 __isl_take isl_set *set, __isl_take isl_id *id);
1808 __isl_give isl_set *isl_set_reset_tuple_id(
1809 __isl_take isl_set *set);
1810 int isl_set_has_tuple_id(__isl_keep isl_set *set);
1811 __isl_give isl_id *isl_set_get_tuple_id(
1812 __isl_keep isl_set *set);
1813 __isl_give isl_basic_map *isl_basic_map_set_tuple_id(
1814 __isl_take isl_basic_map *bmap,
1815 enum isl_dim_type type, __isl_take isl_id *id);
1816 __isl_give isl_map *isl_map_set_tuple_id(
1817 __isl_take isl_map *map, enum isl_dim_type type,
1818 __isl_take isl_id *id);
1819 __isl_give isl_map *isl_map_reset_tuple_id(
1820 __isl_take isl_map *map, enum isl_dim_type type);
1821 int isl_map_has_tuple_id(__isl_keep isl_map *map,
1822 enum isl_dim_type type);
1823 __isl_give isl_id *isl_map_get_tuple_id(
1824 __isl_keep isl_map *map, enum isl_dim_type type);
1826 const char *isl_basic_set_get_tuple_name(
1827 __isl_keep isl_basic_set *bset);
1828 __isl_give isl_basic_set *isl_basic_set_set_tuple_name(
1829 __isl_take isl_basic_set *set, const char *s);
1830 int isl_set_has_tuple_name(__isl_keep isl_set *set);
1831 const char *isl_set_get_tuple_name(
1832 __isl_keep isl_set *set);
1833 const char *isl_basic_map_get_tuple_name(
1834 __isl_keep isl_basic_map *bmap,
1835 enum isl_dim_type type);
1836 __isl_give isl_basic_map *isl_basic_map_set_tuple_name(
1837 __isl_take isl_basic_map *bmap,
1838 enum isl_dim_type type, const char *s);
1839 int isl_map_has_tuple_name(__isl_keep isl_map *map,
1840 enum isl_dim_type type);
1841 const char *isl_map_get_tuple_name(
1842 __isl_keep isl_map *map,
1843 enum isl_dim_type type);
1845 As with C<isl_space_get_tuple_name>, the value returned points to
1846 an internal data structure.
1847 The identifiers, positions or names of individual dimensions can be
1848 read off using the following functions.
1850 __isl_give isl_id *isl_basic_set_get_dim_id(
1851 __isl_keep isl_basic_set *bset,
1852 enum isl_dim_type type, unsigned pos);
1853 __isl_give isl_set *isl_set_set_dim_id(
1854 __isl_take isl_set *set, enum isl_dim_type type,
1855 unsigned pos, __isl_take isl_id *id);
1856 int isl_set_has_dim_id(__isl_keep isl_set *set,
1857 enum isl_dim_type type, unsigned pos);
1858 __isl_give isl_id *isl_set_get_dim_id(
1859 __isl_keep isl_set *set, enum isl_dim_type type,
1861 int isl_basic_map_has_dim_id(
1862 __isl_keep isl_basic_map *bmap,
1863 enum isl_dim_type type, unsigned pos);
1864 __isl_give isl_map *isl_map_set_dim_id(
1865 __isl_take isl_map *map, enum isl_dim_type type,
1866 unsigned pos, __isl_take isl_id *id);
1867 int isl_map_has_dim_id(__isl_keep isl_map *map,
1868 enum isl_dim_type type, unsigned pos);
1869 __isl_give isl_id *isl_map_get_dim_id(
1870 __isl_keep isl_map *map, enum isl_dim_type type,
1873 int isl_set_find_dim_by_id(__isl_keep isl_set *set,
1874 enum isl_dim_type type, __isl_keep isl_id *id);
1875 int isl_map_find_dim_by_id(__isl_keep isl_map *map,
1876 enum isl_dim_type type, __isl_keep isl_id *id);
1877 int isl_set_find_dim_by_name(__isl_keep isl_set *set,
1878 enum isl_dim_type type, const char *name);
1879 int isl_map_find_dim_by_name(__isl_keep isl_map *map,
1880 enum isl_dim_type type, const char *name);
1882 const char *isl_constraint_get_dim_name(
1883 __isl_keep isl_constraint *constraint,
1884 enum isl_dim_type type, unsigned pos);
1885 const char *isl_basic_set_get_dim_name(
1886 __isl_keep isl_basic_set *bset,
1887 enum isl_dim_type type, unsigned pos);
1888 int isl_set_has_dim_name(__isl_keep isl_set *set,
1889 enum isl_dim_type type, unsigned pos);
1890 const char *isl_set_get_dim_name(
1891 __isl_keep isl_set *set,
1892 enum isl_dim_type type, unsigned pos);
1893 const char *isl_basic_map_get_dim_name(
1894 __isl_keep isl_basic_map *bmap,
1895 enum isl_dim_type type, unsigned pos);
1896 int isl_map_has_dim_name(__isl_keep isl_map *map,
1897 enum isl_dim_type type, unsigned pos);
1898 const char *isl_map_get_dim_name(
1899 __isl_keep isl_map *map,
1900 enum isl_dim_type type, unsigned pos);
1902 These functions are mostly useful to obtain the identifiers, positions
1903 or names of the parameters. Identifiers of individual dimensions are
1904 essentially only useful for printing. They are ignored by all other
1905 operations and may not be preserved across those operations.
1907 The user pointers on all parameters and tuples can be reset
1908 using the following functions.
1910 __isl_give isl_set *isl_set_reset_user(
1911 __isl_take isl_set *set);
1912 __isl_give isl_map *isl_map_reset_user(
1913 __isl_take isl_map *map);
1917 =head3 Unary Properties
1923 The following functions test whether the given set or relation
1924 contains any integer points. The ``plain'' variants do not perform
1925 any computations, but simply check if the given set or relation
1926 is already known to be empty.
1928 int isl_basic_set_plain_is_empty(__isl_keep isl_basic_set *bset);
1929 int isl_basic_set_is_empty(__isl_keep isl_basic_set *bset);
1930 int isl_set_plain_is_empty(__isl_keep isl_set *set);
1931 int isl_set_is_empty(__isl_keep isl_set *set);
1932 int isl_union_set_is_empty(__isl_keep isl_union_set *uset);
1933 int isl_basic_map_plain_is_empty(__isl_keep isl_basic_map *bmap);
1934 int isl_basic_map_is_empty(__isl_keep isl_basic_map *bmap);
1935 int isl_map_plain_is_empty(__isl_keep isl_map *map);
1936 int isl_map_is_empty(__isl_keep isl_map *map);
1937 int isl_union_map_is_empty(__isl_keep isl_union_map *umap);
1939 =item * Universality
1941 int isl_basic_set_is_universe(__isl_keep isl_basic_set *bset);
1942 int isl_basic_map_is_universe(__isl_keep isl_basic_map *bmap);
1943 int isl_set_plain_is_universe(__isl_keep isl_set *set);
1945 =item * Single-valuedness
1947 int isl_basic_map_is_single_valued(
1948 __isl_keep isl_basic_map *bmap);
1949 int isl_map_plain_is_single_valued(
1950 __isl_keep isl_map *map);
1951 int isl_map_is_single_valued(__isl_keep isl_map *map);
1952 int isl_union_map_is_single_valued(__isl_keep isl_union_map *umap);
1956 int isl_map_plain_is_injective(__isl_keep isl_map *map);
1957 int isl_map_is_injective(__isl_keep isl_map *map);
1958 int isl_union_map_plain_is_injective(
1959 __isl_keep isl_union_map *umap);
1960 int isl_union_map_is_injective(
1961 __isl_keep isl_union_map *umap);
1965 int isl_map_is_bijective(__isl_keep isl_map *map);
1966 int isl_union_map_is_bijective(__isl_keep isl_union_map *umap);
1970 __isl_give isl_val *
1971 isl_basic_map_plain_get_val_if_fixed(
1972 __isl_keep isl_basic_map *bmap,
1973 enum isl_dim_type type, unsigned pos);
1974 __isl_give isl_val *isl_set_plain_get_val_if_fixed(
1975 __isl_keep isl_set *set,
1976 enum isl_dim_type type, unsigned pos);
1977 __isl_give isl_val *isl_map_plain_get_val_if_fixed(
1978 __isl_keep isl_map *map,
1979 enum isl_dim_type type, unsigned pos);
1981 If the set or relation obviously lies on a hyperplane where the given dimension
1982 has a fixed value, then return that value.
1983 Otherwise return NaN.
1987 int isl_set_dim_residue_class_val(
1988 __isl_keep isl_set *set,
1989 int pos, __isl_give isl_val **modulo,
1990 __isl_give isl_val **residue);
1992 Check if the values of the given set dimension are equal to a fixed
1993 value modulo some integer value. If so, assign the modulo to C<*modulo>
1994 and the fixed value to C<*residue>. If the given dimension attains only
1995 a single value, then assign C<0> to C<*modulo> and the fixed value to
1997 If the dimension does not attain only a single value and if no modulo
1998 can be found then assign C<1> to C<*modulo> and C<1> to C<*residue>.
2002 To check whether a set is a parameter domain, use this function:
2004 int isl_set_is_params(__isl_keep isl_set *set);
2005 int isl_union_set_is_params(
2006 __isl_keep isl_union_set *uset);
2010 The following functions check whether the space of the given
2011 (basic) set or relation range is a wrapped relation.
2013 #include <isl/space.h>
2014 int isl_space_is_wrapping(
2015 __isl_keep isl_space *space);
2016 int isl_space_domain_is_wrapping(
2017 __isl_keep isl_space *space);
2018 int isl_space_range_is_wrapping(
2019 __isl_keep isl_space *space);
2021 #include <isl/set.h>
2022 int isl_basic_set_is_wrapping(
2023 __isl_keep isl_basic_set *bset);
2024 int isl_set_is_wrapping(__isl_keep isl_set *set);
2026 #include <isl/map.h>
2027 int isl_map_range_is_wrapping(
2028 __isl_keep isl_map *map);
2030 The input to C<isl_space_is_wrapping> should
2031 be the space of a set, while that of
2032 C<isl_space_domain_is_wrapping> and
2033 C<isl_space_range_is_wrapping> should be the space of a relation.
2035 =item * Internal Product
2037 int isl_basic_map_can_zip(
2038 __isl_keep isl_basic_map *bmap);
2039 int isl_map_can_zip(__isl_keep isl_map *map);
2041 Check whether the product of domain and range of the given relation
2043 i.e., whether both domain and range are nested relations.
2047 int isl_basic_map_can_curry(
2048 __isl_keep isl_basic_map *bmap);
2049 int isl_map_can_curry(__isl_keep isl_map *map);
2051 Check whether the domain of the (basic) relation is a wrapped relation.
2053 int isl_basic_map_can_uncurry(
2054 __isl_keep isl_basic_map *bmap);
2055 int isl_map_can_uncurry(__isl_keep isl_map *map);
2057 Check whether the range of the (basic) relation is a wrapped relation.
2061 =head3 Binary Properties
2067 int isl_basic_set_plain_is_equal(
2068 __isl_keep isl_basic_set *bset1,
2069 __isl_keep isl_basic_set *bset2);
2070 int isl_set_plain_is_equal(__isl_keep isl_set *set1,
2071 __isl_keep isl_set *set2);
2072 int isl_set_is_equal(__isl_keep isl_set *set1,
2073 __isl_keep isl_set *set2);
2074 int isl_union_set_is_equal(
2075 __isl_keep isl_union_set *uset1,
2076 __isl_keep isl_union_set *uset2);
2077 int isl_basic_map_is_equal(
2078 __isl_keep isl_basic_map *bmap1,
2079 __isl_keep isl_basic_map *bmap2);
2080 int isl_map_is_equal(__isl_keep isl_map *map1,
2081 __isl_keep isl_map *map2);
2082 int isl_map_plain_is_equal(__isl_keep isl_map *map1,
2083 __isl_keep isl_map *map2);
2084 int isl_union_map_is_equal(
2085 __isl_keep isl_union_map *umap1,
2086 __isl_keep isl_union_map *umap2);
2088 =item * Disjointness
2090 int isl_basic_set_is_disjoint(
2091 __isl_keep isl_basic_set *bset1,
2092 __isl_keep isl_basic_set *bset2);
2093 int isl_set_plain_is_disjoint(__isl_keep isl_set *set1,
2094 __isl_keep isl_set *set2);
2095 int isl_set_is_disjoint(__isl_keep isl_set *set1,
2096 __isl_keep isl_set *set2);
2097 int isl_basic_map_is_disjoint(
2098 __isl_keep isl_basic_map *bmap1,
2099 __isl_keep isl_basic_map *bmap2);
2100 int isl_map_is_disjoint(__isl_keep isl_map *map1,
2101 __isl_keep isl_map *map2);
2105 int isl_basic_set_is_subset(
2106 __isl_keep isl_basic_set *bset1,
2107 __isl_keep isl_basic_set *bset2);
2108 int isl_set_is_subset(__isl_keep isl_set *set1,
2109 __isl_keep isl_set *set2);
2110 int isl_set_is_strict_subset(
2111 __isl_keep isl_set *set1,
2112 __isl_keep isl_set *set2);
2113 int isl_union_set_is_subset(
2114 __isl_keep isl_union_set *uset1,
2115 __isl_keep isl_union_set *uset2);
2116 int isl_union_set_is_strict_subset(
2117 __isl_keep isl_union_set *uset1,
2118 __isl_keep isl_union_set *uset2);
2119 int isl_basic_map_is_subset(
2120 __isl_keep isl_basic_map *bmap1,
2121 __isl_keep isl_basic_map *bmap2);
2122 int isl_basic_map_is_strict_subset(
2123 __isl_keep isl_basic_map *bmap1,
2124 __isl_keep isl_basic_map *bmap2);
2125 int isl_map_is_subset(
2126 __isl_keep isl_map *map1,
2127 __isl_keep isl_map *map2);
2128 int isl_map_is_strict_subset(
2129 __isl_keep isl_map *map1,
2130 __isl_keep isl_map *map2);
2131 int isl_union_map_is_subset(
2132 __isl_keep isl_union_map *umap1,
2133 __isl_keep isl_union_map *umap2);
2134 int isl_union_map_is_strict_subset(
2135 __isl_keep isl_union_map *umap1,
2136 __isl_keep isl_union_map *umap2);
2138 Check whether the first argument is a (strict) subset of the
2143 int isl_set_plain_cmp(__isl_keep isl_set *set1,
2144 __isl_keep isl_set *set2);
2146 This function is useful for sorting C<isl_set>s.
2147 The order depends on the internal representation of the inputs.
2148 The order is fixed over different calls to the function (assuming
2149 the internal representation of the inputs has not changed), but may
2150 change over different versions of C<isl>.
2154 =head2 Unary Operations
2160 __isl_give isl_set *isl_set_complement(
2161 __isl_take isl_set *set);
2162 __isl_give isl_map *isl_map_complement(
2163 __isl_take isl_map *map);
2167 __isl_give isl_basic_map *isl_basic_map_reverse(
2168 __isl_take isl_basic_map *bmap);
2169 __isl_give isl_map *isl_map_reverse(
2170 __isl_take isl_map *map);
2171 __isl_give isl_union_map *isl_union_map_reverse(
2172 __isl_take isl_union_map *umap);
2176 __isl_give isl_basic_set *isl_basic_set_project_out(
2177 __isl_take isl_basic_set *bset,
2178 enum isl_dim_type type, unsigned first, unsigned n);
2179 __isl_give isl_basic_map *isl_basic_map_project_out(
2180 __isl_take isl_basic_map *bmap,
2181 enum isl_dim_type type, unsigned first, unsigned n);
2182 __isl_give isl_set *isl_set_project_out(__isl_take isl_set *set,
2183 enum isl_dim_type type, unsigned first, unsigned n);
2184 __isl_give isl_map *isl_map_project_out(__isl_take isl_map *map,
2185 enum isl_dim_type type, unsigned first, unsigned n);
2186 __isl_give isl_basic_set *isl_basic_set_params(
2187 __isl_take isl_basic_set *bset);
2188 __isl_give isl_basic_set *isl_basic_map_domain(
2189 __isl_take isl_basic_map *bmap);
2190 __isl_give isl_basic_set *isl_basic_map_range(
2191 __isl_take isl_basic_map *bmap);
2192 __isl_give isl_set *isl_set_params(__isl_take isl_set *set);
2193 __isl_give isl_set *isl_map_params(__isl_take isl_map *map);
2194 __isl_give isl_set *isl_map_domain(
2195 __isl_take isl_map *bmap);
2196 __isl_give isl_set *isl_map_range(
2197 __isl_take isl_map *map);
2198 __isl_give isl_set *isl_union_set_params(
2199 __isl_take isl_union_set *uset);
2200 __isl_give isl_set *isl_union_map_params(
2201 __isl_take isl_union_map *umap);
2202 __isl_give isl_union_set *isl_union_map_domain(
2203 __isl_take isl_union_map *umap);
2204 __isl_give isl_union_set *isl_union_map_range(
2205 __isl_take isl_union_map *umap);
2207 __isl_give isl_basic_map *isl_basic_map_domain_map(
2208 __isl_take isl_basic_map *bmap);
2209 __isl_give isl_basic_map *isl_basic_map_range_map(
2210 __isl_take isl_basic_map *bmap);
2211 __isl_give isl_map *isl_map_domain_map(__isl_take isl_map *map);
2212 __isl_give isl_map *isl_map_range_map(__isl_take isl_map *map);
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/map.h>
2244 __isl_give isl_map *isl_map_from_domain(
2245 __isl_take isl_set *set);
2246 __isl_give isl_map *isl_map_from_range(
2247 __isl_take isl_set *set);
2249 Create a relation with the given set as domain or range.
2250 The range or domain of the created relation is a zero-dimensional
2251 flat anonymous space.
2255 __isl_give isl_basic_set *isl_basic_set_fix_si(
2256 __isl_take isl_basic_set *bset,
2257 enum isl_dim_type type, unsigned pos, int value);
2258 __isl_give isl_basic_set *isl_basic_set_fix_val(
2259 __isl_take isl_basic_set *bset,
2260 enum isl_dim_type type, unsigned pos,
2261 __isl_take isl_val *v);
2262 __isl_give isl_set *isl_set_fix_si(__isl_take isl_set *set,
2263 enum isl_dim_type type, unsigned pos, int value);
2264 __isl_give isl_set *isl_set_fix_val(
2265 __isl_take isl_set *set,
2266 enum isl_dim_type type, unsigned pos,
2267 __isl_take isl_val *v);
2268 __isl_give isl_basic_map *isl_basic_map_fix_si(
2269 __isl_take isl_basic_map *bmap,
2270 enum isl_dim_type type, unsigned pos, int value);
2271 __isl_give isl_basic_map *isl_basic_map_fix_val(
2272 __isl_take isl_basic_map *bmap,
2273 enum isl_dim_type type, unsigned pos,
2274 __isl_take isl_val *v);
2275 __isl_give isl_map *isl_map_fix_si(__isl_take isl_map *map,
2276 enum isl_dim_type type, unsigned pos, int value);
2277 __isl_give isl_map *isl_map_fix_val(
2278 __isl_take isl_map *map,
2279 enum isl_dim_type type, unsigned pos,
2280 __isl_take isl_val *v);
2282 Intersect the set or relation with the hyperplane where the given
2283 dimension has the fixed given value.
2285 __isl_give isl_basic_map *isl_basic_map_lower_bound_si(
2286 __isl_take isl_basic_map *bmap,
2287 enum isl_dim_type type, unsigned pos, int value);
2288 __isl_give isl_basic_map *isl_basic_map_upper_bound_si(
2289 __isl_take isl_basic_map *bmap,
2290 enum isl_dim_type type, unsigned pos, int value);
2291 __isl_give isl_set *isl_set_lower_bound_si(
2292 __isl_take isl_set *set,
2293 enum isl_dim_type type, unsigned pos, int value);
2294 __isl_give isl_set *isl_set_lower_bound_val(
2295 __isl_take isl_set *set,
2296 enum isl_dim_type type, unsigned pos,
2297 __isl_take isl_val *value);
2298 __isl_give isl_map *isl_map_lower_bound_si(
2299 __isl_take isl_map *map,
2300 enum isl_dim_type type, unsigned pos, int value);
2301 __isl_give isl_set *isl_set_upper_bound_si(
2302 __isl_take isl_set *set,
2303 enum isl_dim_type type, unsigned pos, int value);
2304 __isl_give isl_set *isl_set_upper_bound_val(
2305 __isl_take isl_set *set,
2306 enum isl_dim_type type, unsigned pos,
2307 __isl_take isl_val *value);
2308 __isl_give isl_map *isl_map_upper_bound_si(
2309 __isl_take isl_map *map,
2310 enum isl_dim_type type, unsigned pos, int value);
2312 Intersect the set or relation with the half-space where the given
2313 dimension has a value bounded by the fixed given integer value.
2315 __isl_give isl_set *isl_set_equate(__isl_take isl_set *set,
2316 enum isl_dim_type type1, int pos1,
2317 enum isl_dim_type type2, int pos2);
2318 __isl_give isl_basic_map *isl_basic_map_equate(
2319 __isl_take isl_basic_map *bmap,
2320 enum isl_dim_type type1, int pos1,
2321 enum isl_dim_type type2, int pos2);
2322 __isl_give isl_map *isl_map_equate(__isl_take isl_map *map,
2323 enum isl_dim_type type1, int pos1,
2324 enum isl_dim_type type2, int pos2);
2326 Intersect the set or relation with the hyperplane where the given
2327 dimensions are equal to each other.
2329 __isl_give isl_map *isl_map_oppose(__isl_take isl_map *map,
2330 enum isl_dim_type type1, int pos1,
2331 enum isl_dim_type type2, int pos2);
2333 Intersect the relation with the hyperplane where the given
2334 dimensions have opposite values.
2336 __isl_give isl_map *isl_map_order_le(
2337 __isl_take isl_map *map,
2338 enum isl_dim_type type1, int pos1,
2339 enum isl_dim_type type2, int pos2);
2340 __isl_give isl_basic_map *isl_basic_map_order_ge(
2341 __isl_take isl_basic_map *bmap,
2342 enum isl_dim_type type1, int pos1,
2343 enum isl_dim_type type2, int pos2);
2344 __isl_give isl_map *isl_map_order_ge(
2345 __isl_take isl_map *map,
2346 enum isl_dim_type type1, int pos1,
2347 enum isl_dim_type type2, int pos2);
2348 __isl_give isl_map *isl_map_order_lt(__isl_take isl_map *map,
2349 enum isl_dim_type type1, int pos1,
2350 enum isl_dim_type type2, int pos2);
2351 __isl_give isl_basic_map *isl_basic_map_order_gt(
2352 __isl_take isl_basic_map *bmap,
2353 enum isl_dim_type type1, int pos1,
2354 enum isl_dim_type type2, int pos2);
2355 __isl_give isl_map *isl_map_order_gt(__isl_take isl_map *map,
2356 enum isl_dim_type type1, int pos1,
2357 enum isl_dim_type type2, int pos2);
2359 Intersect the relation with the half-space where the given
2360 dimensions satisfy the given ordering.
2364 __isl_give isl_map *isl_set_identity(
2365 __isl_take isl_set *set);
2366 __isl_give isl_union_map *isl_union_set_identity(
2367 __isl_take isl_union_set *uset);
2369 Construct an identity relation on the given (union) set.
2373 __isl_give isl_basic_set *isl_basic_map_deltas(
2374 __isl_take isl_basic_map *bmap);
2375 __isl_give isl_set *isl_map_deltas(__isl_take isl_map *map);
2376 __isl_give isl_union_set *isl_union_map_deltas(
2377 __isl_take isl_union_map *umap);
2379 These functions return a (basic) set containing the differences
2380 between image elements and corresponding domain elements in the input.
2382 __isl_give isl_basic_map *isl_basic_map_deltas_map(
2383 __isl_take isl_basic_map *bmap);
2384 __isl_give isl_map *isl_map_deltas_map(
2385 __isl_take isl_map *map);
2386 __isl_give isl_union_map *isl_union_map_deltas_map(
2387 __isl_take isl_union_map *umap);
2389 The functions above construct a (basic, regular or union) relation
2390 that maps (a wrapped version of) the input relation to its delta set.
2394 Simplify the representation of a set or relation by trying
2395 to combine pairs of basic sets or relations into a single
2396 basic set or relation.
2398 __isl_give isl_set *isl_set_coalesce(__isl_take isl_set *set);
2399 __isl_give isl_map *isl_map_coalesce(__isl_take isl_map *map);
2400 __isl_give isl_union_set *isl_union_set_coalesce(
2401 __isl_take isl_union_set *uset);
2402 __isl_give isl_union_map *isl_union_map_coalesce(
2403 __isl_take isl_union_map *umap);
2405 One of the methods for combining pairs of basic sets or relations
2406 can result in coefficients that are much larger than those that appear
2407 in the constraints of the input. By default, the coefficients are
2408 not allowed to grow larger, but this can be changed by unsetting
2409 the following option.
2411 int isl_options_set_coalesce_bounded_wrapping(
2412 isl_ctx *ctx, int val);
2413 int isl_options_get_coalesce_bounded_wrapping(
2416 =item * Detecting equalities
2418 __isl_give isl_basic_set *isl_basic_set_detect_equalities(
2419 __isl_take isl_basic_set *bset);
2420 __isl_give isl_basic_map *isl_basic_map_detect_equalities(
2421 __isl_take isl_basic_map *bmap);
2422 __isl_give isl_set *isl_set_detect_equalities(
2423 __isl_take isl_set *set);
2424 __isl_give isl_map *isl_map_detect_equalities(
2425 __isl_take isl_map *map);
2426 __isl_give isl_union_set *isl_union_set_detect_equalities(
2427 __isl_take isl_union_set *uset);
2428 __isl_give isl_union_map *isl_union_map_detect_equalities(
2429 __isl_take isl_union_map *umap);
2431 Simplify the representation of a set or relation by detecting implicit
2434 =item * Removing redundant constraints
2436 __isl_give isl_basic_set *isl_basic_set_remove_redundancies(
2437 __isl_take isl_basic_set *bset);
2438 __isl_give isl_set *isl_set_remove_redundancies(
2439 __isl_take isl_set *set);
2440 __isl_give isl_basic_map *isl_basic_map_remove_redundancies(
2441 __isl_take isl_basic_map *bmap);
2442 __isl_give isl_map *isl_map_remove_redundancies(
2443 __isl_take isl_map *map);
2447 __isl_give isl_basic_set *isl_set_convex_hull(
2448 __isl_take isl_set *set);
2449 __isl_give isl_basic_map *isl_map_convex_hull(
2450 __isl_take isl_map *map);
2452 If the input set or relation has any existentially quantified
2453 variables, then the result of these operations is currently undefined.
2457 __isl_give isl_basic_set *
2458 isl_set_unshifted_simple_hull(
2459 __isl_take isl_set *set);
2460 __isl_give isl_basic_map *
2461 isl_map_unshifted_simple_hull(
2462 __isl_take isl_map *map);
2463 __isl_give isl_basic_set *isl_set_simple_hull(
2464 __isl_take isl_set *set);
2465 __isl_give isl_basic_map *isl_map_simple_hull(
2466 __isl_take isl_map *map);
2467 __isl_give isl_union_map *isl_union_map_simple_hull(
2468 __isl_take isl_union_map *umap);
2470 These functions compute a single basic set or relation
2471 that contains the whole input set or relation.
2472 In particular, the output is described by translates
2473 of the constraints describing the basic sets or relations in the input.
2474 In case of C<isl_set_unshifted_simple_hull>, only the original
2475 constraints are used, without any translation.
2479 (See \autoref{s:simple hull}.)
2485 __isl_give isl_basic_set *isl_basic_set_affine_hull(
2486 __isl_take isl_basic_set *bset);
2487 __isl_give isl_basic_set *isl_set_affine_hull(
2488 __isl_take isl_set *set);
2489 __isl_give isl_union_set *isl_union_set_affine_hull(
2490 __isl_take isl_union_set *uset);
2491 __isl_give isl_basic_map *isl_basic_map_affine_hull(
2492 __isl_take isl_basic_map *bmap);
2493 __isl_give isl_basic_map *isl_map_affine_hull(
2494 __isl_take isl_map *map);
2495 __isl_give isl_union_map *isl_union_map_affine_hull(
2496 __isl_take isl_union_map *umap);
2498 In case of union sets and relations, the affine hull is computed
2501 =item * Polyhedral hull
2503 __isl_give isl_basic_set *isl_set_polyhedral_hull(
2504 __isl_take isl_set *set);
2505 __isl_give isl_basic_map *isl_map_polyhedral_hull(
2506 __isl_take isl_map *map);
2507 __isl_give isl_union_set *isl_union_set_polyhedral_hull(
2508 __isl_take isl_union_set *uset);
2509 __isl_give isl_union_map *isl_union_map_polyhedral_hull(
2510 __isl_take isl_union_map *umap);
2512 These functions compute a single basic set or relation
2513 not involving any existentially quantified variables
2514 that contains the whole input set or relation.
2515 In case of union sets and relations, the polyhedral hull is computed
2518 =item * Other approximations
2520 __isl_give isl_basic_set *
2521 isl_basic_set_drop_constraints_involving_dims(
2522 __isl_take isl_basic_set *bset,
2523 enum isl_dim_type type,
2524 unsigned first, unsigned n);
2525 __isl_give isl_basic_map *
2526 isl_basic_map_drop_constraints_involving_dims(
2527 __isl_take isl_basic_map *bmap,
2528 enum isl_dim_type type,
2529 unsigned first, unsigned n);
2530 __isl_give isl_basic_set *
2531 isl_basic_set_drop_constraints_not_involving_dims(
2532 __isl_take isl_basic_set *bset,
2533 enum isl_dim_type type,
2534 unsigned first, unsigned n);
2535 __isl_give isl_set *
2536 isl_set_drop_constraints_involving_dims(
2537 __isl_take isl_set *set,
2538 enum isl_dim_type type,
2539 unsigned first, unsigned n);
2540 __isl_give isl_map *
2541 isl_map_drop_constraints_involving_dims(
2542 __isl_take isl_map *map,
2543 enum isl_dim_type type,
2544 unsigned first, unsigned n);
2546 These functions drop any constraints (not) involving the specified dimensions.
2547 Note that the result depends on the representation of the input.
2551 __isl_give isl_basic_set *isl_basic_set_sample(
2552 __isl_take isl_basic_set *bset);
2553 __isl_give isl_basic_set *isl_set_sample(
2554 __isl_take isl_set *set);
2555 __isl_give isl_basic_map *isl_basic_map_sample(
2556 __isl_take isl_basic_map *bmap);
2557 __isl_give isl_basic_map *isl_map_sample(
2558 __isl_take isl_map *map);
2560 If the input (basic) set or relation is non-empty, then return
2561 a singleton subset of the input. Otherwise, return an empty set.
2563 =item * Optimization
2565 #include <isl/ilp.h>
2566 __isl_give isl_val *isl_basic_set_max_val(
2567 __isl_keep isl_basic_set *bset,
2568 __isl_keep isl_aff *obj);
2569 __isl_give isl_val *isl_set_min_val(
2570 __isl_keep isl_set *set,
2571 __isl_keep isl_aff *obj);
2572 __isl_give isl_val *isl_set_max_val(
2573 __isl_keep isl_set *set,
2574 __isl_keep isl_aff *obj);
2576 Compute the minimum or maximum of the integer affine expression C<obj>
2577 over the points in C<set>, returning the result in C<opt>.
2578 The result is C<NULL> in case of an error, the optimal value in case
2579 there is one, negative infinity or infinity if the problem is unbounded and
2580 NaN if the problem is empty.
2582 =item * Parametric optimization
2584 __isl_give isl_pw_aff *isl_set_dim_min(
2585 __isl_take isl_set *set, int pos);
2586 __isl_give isl_pw_aff *isl_set_dim_max(
2587 __isl_take isl_set *set, int pos);
2588 __isl_give isl_pw_aff *isl_map_dim_max(
2589 __isl_take isl_map *map, int pos);
2591 Compute the minimum or maximum of the given set or output dimension
2592 as a function of the parameters (and input dimensions), but independently
2593 of the other set or output dimensions.
2594 For lexicographic optimization, see L<"Lexicographic Optimization">.
2598 The following functions compute either the set of (rational) coefficient
2599 values of valid constraints for the given set or the set of (rational)
2600 values satisfying the constraints with coefficients from the given set.
2601 Internally, these two sets of functions perform essentially the
2602 same operations, except that the set of coefficients is assumed to
2603 be a cone, while the set of values may be any polyhedron.
2604 The current implementation is based on the Farkas lemma and
2605 Fourier-Motzkin elimination, but this may change or be made optional
2606 in future. In particular, future implementations may use different
2607 dualization algorithms or skip the elimination step.
2609 __isl_give isl_basic_set *isl_basic_set_coefficients(
2610 __isl_take isl_basic_set *bset);
2611 __isl_give isl_basic_set *isl_set_coefficients(
2612 __isl_take isl_set *set);
2613 __isl_give isl_union_set *isl_union_set_coefficients(
2614 __isl_take isl_union_set *bset);
2615 __isl_give isl_basic_set *isl_basic_set_solutions(
2616 __isl_take isl_basic_set *bset);
2617 __isl_give isl_basic_set *isl_set_solutions(
2618 __isl_take isl_set *set);
2619 __isl_give isl_union_set *isl_union_set_solutions(
2620 __isl_take isl_union_set *bset);
2624 __isl_give isl_map *isl_map_fixed_power_val(
2625 __isl_take isl_map *map,
2626 __isl_take isl_val *exp);
2627 __isl_give isl_union_map *
2628 isl_union_map_fixed_power_val(
2629 __isl_take isl_union_map *umap,
2630 __isl_take isl_val *exp);
2632 Compute the given power of C<map>, where C<exp> is assumed to be non-zero.
2633 If the exponent C<exp> is negative, then the -C<exp> th power of the inverse
2634 of C<map> is computed.
2636 __isl_give isl_map *isl_map_power(__isl_take isl_map *map,
2638 __isl_give isl_union_map *isl_union_map_power(
2639 __isl_take isl_union_map *umap, int *exact);
2641 Compute a parametric representation for all positive powers I<k> of C<map>.
2642 The result maps I<k> to a nested relation corresponding to the
2643 I<k>th power of C<map>.
2644 The result may be an overapproximation. If the result is known to be exact,
2645 then C<*exact> is set to C<1>.
2647 =item * Transitive closure
2649 __isl_give isl_map *isl_map_transitive_closure(
2650 __isl_take isl_map *map, int *exact);
2651 __isl_give isl_union_map *isl_union_map_transitive_closure(
2652 __isl_take isl_union_map *umap, int *exact);
2654 Compute the transitive closure of C<map>.
2655 The result may be an overapproximation. If the result is known to be exact,
2656 then C<*exact> is set to C<1>.
2658 =item * Reaching path lengths
2660 __isl_give isl_map *isl_map_reaching_path_lengths(
2661 __isl_take isl_map *map, int *exact);
2663 Compute a relation that maps each element in the range of C<map>
2664 to the lengths of all paths composed of edges in C<map> that
2665 end up in the given element.
2666 The result may be an overapproximation. If the result is known to be exact,
2667 then C<*exact> is set to C<1>.
2668 To compute the I<maximal> path length, the resulting relation
2669 should be postprocessed by C<isl_map_lexmax>.
2670 In particular, if the input relation is a dependence relation
2671 (mapping sources to sinks), then the maximal path length corresponds
2672 to the free schedule.
2673 Note, however, that C<isl_map_lexmax> expects the maximum to be
2674 finite, so if the path lengths are unbounded (possibly due to
2675 the overapproximation), then you will get an error message.
2679 #include <isl/space.h>
2680 __isl_give isl_space *isl_space_wrap(
2681 __isl_take isl_space *space);
2682 __isl_give isl_space *isl_space_unwrap(
2683 __isl_take isl_space *space);
2685 #include <isl/set.h>
2686 __isl_give isl_basic_map *isl_basic_set_unwrap(
2687 __isl_take isl_basic_set *bset);
2688 __isl_give isl_map *isl_set_unwrap(
2689 __isl_take isl_set *set);
2691 #include <isl/map.h>
2692 __isl_give isl_basic_set *isl_basic_map_wrap(
2693 __isl_take isl_basic_map *bmap);
2694 __isl_give isl_set *isl_map_wrap(
2695 __isl_take isl_map *map);
2697 #include <isl/union_set.h>
2698 __isl_give isl_union_map *isl_union_set_unwrap(
2699 __isl_take isl_union_set *uset);
2701 #include <isl/union_map.h>
2702 __isl_give isl_union_set *isl_union_map_wrap(
2703 __isl_take isl_union_map *umap);
2705 The input to C<isl_space_unwrap> should
2706 be the space of a set, while that of
2707 C<isl_space_wrap> should be the space of a relation.
2708 Conversely, the output of C<isl_space_unwrap> is the space
2709 of a relation, while that of C<isl_space_wrap> is the space of a set.
2713 Remove any internal structure of domain (and range) of the given
2714 set or relation. If there is any such internal structure in the input,
2715 then the name of the space is also removed.
2717 __isl_give isl_basic_set *isl_basic_set_flatten(
2718 __isl_take isl_basic_set *bset);
2719 __isl_give isl_set *isl_set_flatten(
2720 __isl_take isl_set *set);
2721 __isl_give isl_basic_map *isl_basic_map_flatten_domain(
2722 __isl_take isl_basic_map *bmap);
2723 __isl_give isl_basic_map *isl_basic_map_flatten_range(
2724 __isl_take isl_basic_map *bmap);
2725 __isl_give isl_map *isl_map_flatten_range(
2726 __isl_take isl_map *map);
2727 __isl_give isl_map *isl_map_flatten_domain(
2728 __isl_take isl_map *map);
2729 __isl_give isl_basic_map *isl_basic_map_flatten(
2730 __isl_take isl_basic_map *bmap);
2731 __isl_give isl_map *isl_map_flatten(
2732 __isl_take isl_map *map);
2734 __isl_give isl_map *isl_set_flatten_map(
2735 __isl_take isl_set *set);
2737 The function above constructs a relation
2738 that maps the input set to a flattened version of the set.
2742 Lift the input set to a space with extra dimensions corresponding
2743 to the existentially quantified variables in the input.
2744 In particular, the result lives in a wrapped map where the domain
2745 is the original space and the range corresponds to the original
2746 existentially quantified variables.
2748 __isl_give isl_basic_set *isl_basic_set_lift(
2749 __isl_take isl_basic_set *bset);
2750 __isl_give isl_set *isl_set_lift(
2751 __isl_take isl_set *set);
2752 __isl_give isl_union_set *isl_union_set_lift(
2753 __isl_take isl_union_set *uset);
2755 Given a local space that contains the existentially quantified
2756 variables of a set, a basic relation that, when applied to
2757 a basic set, has essentially the same effect as C<isl_basic_set_lift>,
2758 can be constructed using the following function.
2760 #include <isl/local_space.h>
2761 __isl_give isl_basic_map *isl_local_space_lifting(
2762 __isl_take isl_local_space *ls);
2764 =item * Internal Product
2766 __isl_give isl_basic_map *isl_basic_map_zip(
2767 __isl_take isl_basic_map *bmap);
2768 __isl_give isl_map *isl_map_zip(
2769 __isl_take isl_map *map);
2770 __isl_give isl_union_map *isl_union_map_zip(
2771 __isl_take isl_union_map *umap);
2773 Given a relation with nested relations for domain and range,
2774 interchange the range of the domain with the domain of the range.
2778 __isl_give isl_basic_map *isl_basic_map_curry(
2779 __isl_take isl_basic_map *bmap);
2780 __isl_give isl_basic_map *isl_basic_map_uncurry(
2781 __isl_take isl_basic_map *bmap);
2782 __isl_give isl_map *isl_map_curry(
2783 __isl_take isl_map *map);
2784 __isl_give isl_map *isl_map_uncurry(
2785 __isl_take isl_map *map);
2786 __isl_give isl_union_map *isl_union_map_curry(
2787 __isl_take isl_union_map *umap);
2788 __isl_give isl_union_map *isl_union_map_uncurry(
2789 __isl_take isl_union_map *umap);
2791 Given a relation with a nested relation for domain,
2792 the C<curry> functions
2793 move the range of the nested relation out of the domain
2794 and use it as the domain of a nested relation in the range,
2795 with the original range as range of this nested relation.
2796 The C<uncurry> functions perform the inverse operation.
2798 =item * Aligning parameters
2800 __isl_give isl_basic_set *isl_basic_set_align_params(
2801 __isl_take isl_basic_set *bset,
2802 __isl_take isl_space *model);
2803 __isl_give isl_set *isl_set_align_params(
2804 __isl_take isl_set *set,
2805 __isl_take isl_space *model);
2806 __isl_give isl_basic_map *isl_basic_map_align_params(
2807 __isl_take isl_basic_map *bmap,
2808 __isl_take isl_space *model);
2809 __isl_give isl_map *isl_map_align_params(
2810 __isl_take isl_map *map,
2811 __isl_take isl_space *model);
2813 Change the order of the parameters of the given set or relation
2814 such that the first parameters match those of C<model>.
2815 This may involve the introduction of extra parameters.
2816 All parameters need to be named.
2818 =item * Dimension manipulation
2820 __isl_give isl_basic_set *isl_basic_set_add_dims(
2821 __isl_take isl_basic_set *bset,
2822 enum isl_dim_type type, unsigned n);
2823 __isl_give isl_set *isl_set_add_dims(
2824 __isl_take isl_set *set,
2825 enum isl_dim_type type, unsigned n);
2826 __isl_give isl_map *isl_map_add_dims(
2827 __isl_take isl_map *map,
2828 enum isl_dim_type type, unsigned n);
2829 __isl_give isl_basic_set *isl_basic_set_insert_dims(
2830 __isl_take isl_basic_set *bset,
2831 enum isl_dim_type type, unsigned pos,
2833 __isl_give isl_basic_map *isl_basic_map_insert_dims(
2834 __isl_take isl_basic_map *bmap,
2835 enum isl_dim_type type, unsigned pos,
2837 __isl_give isl_set *isl_set_insert_dims(
2838 __isl_take isl_set *set,
2839 enum isl_dim_type type, unsigned pos, unsigned n);
2840 __isl_give isl_map *isl_map_insert_dims(
2841 __isl_take isl_map *map,
2842 enum isl_dim_type type, unsigned pos, unsigned n);
2843 __isl_give isl_basic_set *isl_basic_set_move_dims(
2844 __isl_take isl_basic_set *bset,
2845 enum isl_dim_type dst_type, unsigned dst_pos,
2846 enum isl_dim_type src_type, unsigned src_pos,
2848 __isl_give isl_basic_map *isl_basic_map_move_dims(
2849 __isl_take isl_basic_map *bmap,
2850 enum isl_dim_type dst_type, unsigned dst_pos,
2851 enum isl_dim_type src_type, unsigned src_pos,
2853 __isl_give isl_set *isl_set_move_dims(
2854 __isl_take isl_set *set,
2855 enum isl_dim_type dst_type, unsigned dst_pos,
2856 enum isl_dim_type src_type, unsigned src_pos,
2858 __isl_give isl_map *isl_map_move_dims(
2859 __isl_take isl_map *map,
2860 enum isl_dim_type dst_type, unsigned dst_pos,
2861 enum isl_dim_type src_type, unsigned src_pos,
2864 It is usually not advisable to directly change the (input or output)
2865 space of a set or a relation as this removes the name and the internal
2866 structure of the space. However, the above functions can be useful
2867 to add new parameters, assuming
2868 C<isl_set_align_params> and C<isl_map_align_params>
2873 =head2 Binary Operations
2875 The two arguments of a binary operation not only need to live
2876 in the same C<isl_ctx>, they currently also need to have
2877 the same (number of) parameters.
2879 =head3 Basic Operations
2883 =item * Intersection
2885 __isl_give isl_basic_set *isl_basic_set_intersect_params(
2886 __isl_take isl_basic_set *bset1,
2887 __isl_take isl_basic_set *bset2);
2888 __isl_give isl_basic_set *isl_basic_set_intersect(
2889 __isl_take isl_basic_set *bset1,
2890 __isl_take isl_basic_set *bset2);
2891 __isl_give isl_set *isl_set_intersect_params(
2892 __isl_take isl_set *set,
2893 __isl_take isl_set *params);
2894 __isl_give isl_set *isl_set_intersect(
2895 __isl_take isl_set *set1,
2896 __isl_take isl_set *set2);
2897 __isl_give isl_union_set *isl_union_set_intersect_params(
2898 __isl_take isl_union_set *uset,
2899 __isl_take isl_set *set);
2900 __isl_give isl_union_map *isl_union_map_intersect_params(
2901 __isl_take isl_union_map *umap,
2902 __isl_take isl_set *set);
2903 __isl_give isl_union_set *isl_union_set_intersect(
2904 __isl_take isl_union_set *uset1,
2905 __isl_take isl_union_set *uset2);
2906 __isl_give isl_basic_map *isl_basic_map_intersect_domain(
2907 __isl_take isl_basic_map *bmap,
2908 __isl_take isl_basic_set *bset);
2909 __isl_give isl_basic_map *isl_basic_map_intersect_range(
2910 __isl_take isl_basic_map *bmap,
2911 __isl_take isl_basic_set *bset);
2912 __isl_give isl_basic_map *isl_basic_map_intersect(
2913 __isl_take isl_basic_map *bmap1,
2914 __isl_take isl_basic_map *bmap2);
2915 __isl_give isl_map *isl_map_intersect_params(
2916 __isl_take isl_map *map,
2917 __isl_take isl_set *params);
2918 __isl_give isl_map *isl_map_intersect_domain(
2919 __isl_take isl_map *map,
2920 __isl_take isl_set *set);
2921 __isl_give isl_map *isl_map_intersect_range(
2922 __isl_take isl_map *map,
2923 __isl_take isl_set *set);
2924 __isl_give isl_map *isl_map_intersect(
2925 __isl_take isl_map *map1,
2926 __isl_take isl_map *map2);
2927 __isl_give isl_union_map *isl_union_map_intersect_domain(
2928 __isl_take isl_union_map *umap,
2929 __isl_take isl_union_set *uset);
2930 __isl_give isl_union_map *isl_union_map_intersect_range(
2931 __isl_take isl_union_map *umap,
2932 __isl_take isl_union_set *uset);
2933 __isl_give isl_union_map *isl_union_map_intersect(
2934 __isl_take isl_union_map *umap1,
2935 __isl_take isl_union_map *umap2);
2937 The second argument to the C<_params> functions needs to be
2938 a parametric (basic) set. For the other functions, a parametric set
2939 for either argument is only allowed if the other argument is
2940 a parametric set as well.
2944 __isl_give isl_set *isl_basic_set_union(
2945 __isl_take isl_basic_set *bset1,
2946 __isl_take isl_basic_set *bset2);
2947 __isl_give isl_map *isl_basic_map_union(
2948 __isl_take isl_basic_map *bmap1,
2949 __isl_take isl_basic_map *bmap2);
2950 __isl_give isl_set *isl_set_union(
2951 __isl_take isl_set *set1,
2952 __isl_take isl_set *set2);
2953 __isl_give isl_map *isl_map_union(
2954 __isl_take isl_map *map1,
2955 __isl_take isl_map *map2);
2956 __isl_give isl_union_set *isl_union_set_union(
2957 __isl_take isl_union_set *uset1,
2958 __isl_take isl_union_set *uset2);
2959 __isl_give isl_union_map *isl_union_map_union(
2960 __isl_take isl_union_map *umap1,
2961 __isl_take isl_union_map *umap2);
2963 =item * Set difference
2965 __isl_give isl_set *isl_set_subtract(
2966 __isl_take isl_set *set1,
2967 __isl_take isl_set *set2);
2968 __isl_give isl_map *isl_map_subtract(
2969 __isl_take isl_map *map1,
2970 __isl_take isl_map *map2);
2971 __isl_give isl_map *isl_map_subtract_domain(
2972 __isl_take isl_map *map,
2973 __isl_take isl_set *dom);
2974 __isl_give isl_map *isl_map_subtract_range(
2975 __isl_take isl_map *map,
2976 __isl_take isl_set *dom);
2977 __isl_give isl_union_set *isl_union_set_subtract(
2978 __isl_take isl_union_set *uset1,
2979 __isl_take isl_union_set *uset2);
2980 __isl_give isl_union_map *isl_union_map_subtract(
2981 __isl_take isl_union_map *umap1,
2982 __isl_take isl_union_map *umap2);
2983 __isl_give isl_union_map *isl_union_map_subtract_domain(
2984 __isl_take isl_union_map *umap,
2985 __isl_take isl_union_set *dom);
2986 __isl_give isl_union_map *isl_union_map_subtract_range(
2987 __isl_take isl_union_map *umap,
2988 __isl_take isl_union_set *dom);
2992 __isl_give isl_basic_set *isl_basic_set_apply(
2993 __isl_take isl_basic_set *bset,
2994 __isl_take isl_basic_map *bmap);
2995 __isl_give isl_set *isl_set_apply(
2996 __isl_take isl_set *set,
2997 __isl_take isl_map *map);
2998 __isl_give isl_union_set *isl_union_set_apply(
2999 __isl_take isl_union_set *uset,
3000 __isl_take isl_union_map *umap);
3001 __isl_give isl_basic_map *isl_basic_map_apply_domain(
3002 __isl_take isl_basic_map *bmap1,
3003 __isl_take isl_basic_map *bmap2);
3004 __isl_give isl_basic_map *isl_basic_map_apply_range(
3005 __isl_take isl_basic_map *bmap1,
3006 __isl_take isl_basic_map *bmap2);
3007 __isl_give isl_map *isl_map_apply_domain(
3008 __isl_take isl_map *map1,
3009 __isl_take isl_map *map2);
3010 __isl_give isl_union_map *isl_union_map_apply_domain(
3011 __isl_take isl_union_map *umap1,
3012 __isl_take isl_union_map *umap2);
3013 __isl_give isl_map *isl_map_apply_range(
3014 __isl_take isl_map *map1,
3015 __isl_take isl_map *map2);
3016 __isl_give isl_union_map *isl_union_map_apply_range(
3017 __isl_take isl_union_map *umap1,
3018 __isl_take isl_union_map *umap2);
3022 __isl_give isl_basic_set *
3023 isl_basic_set_preimage_multi_aff(
3024 __isl_take isl_basic_set *bset,
3025 __isl_take isl_multi_aff *ma);
3026 __isl_give isl_set *isl_set_preimage_multi_aff(
3027 __isl_take isl_set *set,
3028 __isl_take isl_multi_aff *ma);
3029 __isl_give isl_set *isl_set_preimage_pw_multi_aff(
3030 __isl_take isl_set *set,
3031 __isl_take isl_pw_multi_aff *pma);
3032 __isl_give isl_set *isl_set_preimage_multi_pw_aff(
3033 __isl_take isl_set *set,
3034 __isl_take isl_multi_pw_aff *mpa);
3035 __isl_give isl_basic_map *
3036 isl_basic_map_preimage_domain_multi_aff(
3037 __isl_take isl_basic_map *bmap,
3038 __isl_take isl_multi_aff *ma);
3039 __isl_give isl_map *isl_map_preimage_domain_multi_aff(
3040 __isl_take isl_map *map,
3041 __isl_take isl_multi_aff *ma);
3042 __isl_give isl_map *
3043 isl_map_preimage_domain_pw_multi_aff(
3044 __isl_take isl_map *map,
3045 __isl_take isl_pw_multi_aff *pma);
3046 __isl_give isl_map *
3047 isl_map_preimage_domain_multi_pw_aff(
3048 __isl_take isl_map *map,
3049 __isl_take isl_multi_pw_aff *mpa);
3050 __isl_give isl_union_map *
3051 isl_union_map_preimage_domain_multi_aff(
3052 __isl_take isl_union_map *umap,
3053 __isl_take isl_multi_aff *ma);
3054 __isl_give isl_basic_map *
3055 isl_basic_map_preimage_range_multi_aff(
3056 __isl_take isl_basic_map *bmap,
3057 __isl_take isl_multi_aff *ma);
3059 These functions compute the preimage of the given set or map domain/range under
3060 the given function. In other words, the expression is plugged
3061 into the set description or into the domain/range of the map.
3062 Objects of types C<isl_multi_aff> and C<isl_pw_multi_aff> are described in
3063 L</"Piecewise Multiple Quasi Affine Expressions">.
3065 =item * Cartesian Product
3067 #include <isl/space.h>
3068 __isl_give isl_space *isl_space_product(
3069 __isl_take isl_space *space1,
3070 __isl_take isl_space *space2);
3071 __isl_give isl_space *isl_space_domain_product(
3072 __isl_take isl_space *space1,
3073 __isl_take isl_space *space2);
3074 __isl_give isl_space *isl_space_range_product(
3075 __isl_take isl_space *space1,
3076 __isl_take isl_space *space2);
3079 C<isl_space_product>, C<isl_space_domain_product>
3080 and C<isl_space_range_product> take pairs or relation spaces and
3081 produce a single relations space, where either the domain, the range
3082 or both domain and range are wrapped spaces of relations between
3083 the domains and/or ranges of the input spaces.
3084 If the product is only constructed over the domain or the range
3085 then the ranges or the domains of the inputs should be the same.
3087 #include <isl/set.h>
3088 __isl_give isl_set *isl_set_product(
3089 __isl_take isl_set *set1,
3090 __isl_take isl_set *set2);
3092 #include <isl/map.h>
3093 __isl_give isl_basic_map *isl_basic_map_domain_product(
3094 __isl_take isl_basic_map *bmap1,
3095 __isl_take isl_basic_map *bmap2);
3096 __isl_give isl_basic_map *isl_basic_map_range_product(
3097 __isl_take isl_basic_map *bmap1,
3098 __isl_take isl_basic_map *bmap2);
3099 __isl_give isl_basic_map *isl_basic_map_product(
3100 __isl_take isl_basic_map *bmap1,
3101 __isl_take isl_basic_map *bmap2);
3102 __isl_give isl_map *isl_map_domain_product(
3103 __isl_take isl_map *map1,
3104 __isl_take isl_map *map2);
3105 __isl_give isl_map *isl_map_range_product(
3106 __isl_take isl_map *map1,
3107 __isl_take isl_map *map2);
3108 __isl_give isl_map *isl_map_product(
3109 __isl_take isl_map *map1,
3110 __isl_take isl_map *map2);
3112 #include <isl/union_set.h>
3113 __isl_give isl_union_set *isl_union_set_product(
3114 __isl_take isl_union_set *uset1,
3115 __isl_take isl_union_set *uset2);
3117 #include <isl/union_map.h>
3118 __isl_give isl_union_map *isl_union_map_domain_product(
3119 __isl_take isl_union_map *umap1,
3120 __isl_take isl_union_map *umap2);
3121 __isl_give isl_union_map *isl_union_map_range_product(
3122 __isl_take isl_union_map *umap1,
3123 __isl_take isl_union_map *umap2);
3124 __isl_give isl_union_map *isl_union_map_product(
3125 __isl_take isl_union_map *umap1,
3126 __isl_take isl_union_map *umap2);
3128 The above functions compute the cross product of the given
3129 sets or relations. The domains and ranges of the results
3130 are wrapped maps between domains and ranges of the inputs.
3131 To obtain a ``flat'' product, use the following functions
3134 __isl_give isl_basic_set *isl_basic_set_flat_product(
3135 __isl_take isl_basic_set *bset1,
3136 __isl_take isl_basic_set *bset2);
3137 __isl_give isl_set *isl_set_flat_product(
3138 __isl_take isl_set *set1,
3139 __isl_take isl_set *set2);
3140 __isl_give isl_basic_map *isl_basic_map_flat_range_product(
3141 __isl_take isl_basic_map *bmap1,
3142 __isl_take isl_basic_map *bmap2);
3143 __isl_give isl_map *isl_map_flat_domain_product(
3144 __isl_take isl_map *map1,
3145 __isl_take isl_map *map2);
3146 __isl_give isl_map *isl_map_flat_range_product(
3147 __isl_take isl_map *map1,
3148 __isl_take isl_map *map2);
3149 __isl_give isl_union_map *isl_union_map_flat_range_product(
3150 __isl_take isl_union_map *umap1,
3151 __isl_take isl_union_map *umap2);
3152 __isl_give isl_basic_map *isl_basic_map_flat_product(
3153 __isl_take isl_basic_map *bmap1,
3154 __isl_take isl_basic_map *bmap2);
3155 __isl_give isl_map *isl_map_flat_product(
3156 __isl_take isl_map *map1,
3157 __isl_take isl_map *map2);
3159 #include <isl/space.h>
3160 __isl_give isl_space *isl_space_range_factor_domain(
3161 __isl_take isl_space *space);
3162 __isl_give isl_space *isl_space_range_factor_range(
3163 __isl_take isl_space *space);
3165 The functions C<isl_space_range_factor_domain> and
3166 C<isl_space_range_factor_range> extract the two arguments from
3167 the result of a call to C<isl_space_range_product>.
3169 The arguments of a call to C<isl_map_range_product> can be extracted
3170 from the result using the following two functions.
3172 #include <isl/map.h>
3173 __isl_give isl_map *isl_map_range_factor_domain(
3174 __isl_take isl_map *map);
3175 __isl_give isl_map *isl_map_range_factor_range(
3176 __isl_take isl_map *map);
3178 =item * Simplification
3180 __isl_give isl_basic_set *isl_basic_set_gist(
3181 __isl_take isl_basic_set *bset,
3182 __isl_take isl_basic_set *context);
3183 __isl_give isl_set *isl_set_gist(__isl_take isl_set *set,
3184 __isl_take isl_set *context);
3185 __isl_give isl_set *isl_set_gist_params(
3186 __isl_take isl_set *set,
3187 __isl_take isl_set *context);
3188 __isl_give isl_union_set *isl_union_set_gist(
3189 __isl_take isl_union_set *uset,
3190 __isl_take isl_union_set *context);
3191 __isl_give isl_union_set *isl_union_set_gist_params(
3192 __isl_take isl_union_set *uset,
3193 __isl_take isl_set *set);
3194 __isl_give isl_basic_map *isl_basic_map_gist(
3195 __isl_take isl_basic_map *bmap,
3196 __isl_take isl_basic_map *context);
3197 __isl_give isl_map *isl_map_gist(__isl_take isl_map *map,
3198 __isl_take isl_map *context);
3199 __isl_give isl_map *isl_map_gist_params(
3200 __isl_take isl_map *map,
3201 __isl_take isl_set *context);
3202 __isl_give isl_map *isl_map_gist_domain(
3203 __isl_take isl_map *map,
3204 __isl_take isl_set *context);
3205 __isl_give isl_map *isl_map_gist_range(
3206 __isl_take isl_map *map,
3207 __isl_take isl_set *context);
3208 __isl_give isl_union_map *isl_union_map_gist(
3209 __isl_take isl_union_map *umap,
3210 __isl_take isl_union_map *context);
3211 __isl_give isl_union_map *isl_union_map_gist_params(
3212 __isl_take isl_union_map *umap,
3213 __isl_take isl_set *set);
3214 __isl_give isl_union_map *isl_union_map_gist_domain(
3215 __isl_take isl_union_map *umap,
3216 __isl_take isl_union_set *uset);
3217 __isl_give isl_union_map *isl_union_map_gist_range(
3218 __isl_take isl_union_map *umap,
3219 __isl_take isl_union_set *uset);
3221 The gist operation returns a set or relation that has the
3222 same intersection with the context as the input set or relation.
3223 Any implicit equality in the intersection is made explicit in the result,
3224 while all inequalities that are redundant with respect to the intersection
3226 In case of union sets and relations, the gist operation is performed
3231 =head3 Lexicographic Optimization
3233 Given a (basic) set C<set> (or C<bset>) and a zero-dimensional domain C<dom>,
3234 the following functions
3235 compute a set that contains the lexicographic minimum or maximum
3236 of the elements in C<set> (or C<bset>) for those values of the parameters
3237 that satisfy C<dom>.
3238 If C<empty> is not C<NULL>, then C<*empty> is assigned a set
3239 that contains the parameter values in C<dom> for which C<set> (or C<bset>)
3241 In other words, the union of the parameter values
3242 for which the result is non-empty and of C<*empty>
3245 __isl_give isl_set *isl_basic_set_partial_lexmin(
3246 __isl_take isl_basic_set *bset,
3247 __isl_take isl_basic_set *dom,
3248 __isl_give isl_set **empty);
3249 __isl_give isl_set *isl_basic_set_partial_lexmax(
3250 __isl_take isl_basic_set *bset,
3251 __isl_take isl_basic_set *dom,
3252 __isl_give isl_set **empty);
3253 __isl_give isl_set *isl_set_partial_lexmin(
3254 __isl_take isl_set *set, __isl_take isl_set *dom,
3255 __isl_give isl_set **empty);
3256 __isl_give isl_set *isl_set_partial_lexmax(
3257 __isl_take isl_set *set, __isl_take isl_set *dom,
3258 __isl_give isl_set **empty);
3260 Given a (basic) set C<set> (or C<bset>), the following functions simply
3261 return a set containing the lexicographic minimum or maximum
3262 of the elements in C<set> (or C<bset>).
3263 In case of union sets, the optimum is computed per space.
3265 __isl_give isl_set *isl_basic_set_lexmin(
3266 __isl_take isl_basic_set *bset);
3267 __isl_give isl_set *isl_basic_set_lexmax(
3268 __isl_take isl_basic_set *bset);
3269 __isl_give isl_set *isl_set_lexmin(
3270 __isl_take isl_set *set);
3271 __isl_give isl_set *isl_set_lexmax(
3272 __isl_take isl_set *set);
3273 __isl_give isl_union_set *isl_union_set_lexmin(
3274 __isl_take isl_union_set *uset);
3275 __isl_give isl_union_set *isl_union_set_lexmax(
3276 __isl_take isl_union_set *uset);
3278 Given a (basic) relation C<map> (or C<bmap>) and a domain C<dom>,
3279 the following functions
3280 compute a relation that maps each element of C<dom>
3281 to the single lexicographic minimum or maximum
3282 of the elements that are associated to that same
3283 element in C<map> (or C<bmap>).
3284 If C<empty> is not C<NULL>, then C<*empty> is assigned a set
3285 that contains the elements in C<dom> that do not map
3286 to any elements in C<map> (or C<bmap>).
3287 In other words, the union of the domain of the result and of C<*empty>
3290 __isl_give isl_map *isl_basic_map_partial_lexmax(
3291 __isl_take isl_basic_map *bmap,
3292 __isl_take isl_basic_set *dom,
3293 __isl_give isl_set **empty);
3294 __isl_give isl_map *isl_basic_map_partial_lexmin(
3295 __isl_take isl_basic_map *bmap,
3296 __isl_take isl_basic_set *dom,
3297 __isl_give isl_set **empty);
3298 __isl_give isl_map *isl_map_partial_lexmax(
3299 __isl_take isl_map *map, __isl_take isl_set *dom,
3300 __isl_give isl_set **empty);
3301 __isl_give isl_map *isl_map_partial_lexmin(
3302 __isl_take isl_map *map, __isl_take isl_set *dom,
3303 __isl_give isl_set **empty);
3305 Given a (basic) map C<map> (or C<bmap>), the following functions simply
3306 return a map mapping each element in the domain of
3307 C<map> (or C<bmap>) to the lexicographic minimum or maximum
3308 of all elements associated to that element.
3309 In case of union relations, the optimum is computed per space.
3311 __isl_give isl_map *isl_basic_map_lexmin(
3312 __isl_take isl_basic_map *bmap);
3313 __isl_give isl_map *isl_basic_map_lexmax(
3314 __isl_take isl_basic_map *bmap);
3315 __isl_give isl_map *isl_map_lexmin(
3316 __isl_take isl_map *map);
3317 __isl_give isl_map *isl_map_lexmax(
3318 __isl_take isl_map *map);
3319 __isl_give isl_union_map *isl_union_map_lexmin(
3320 __isl_take isl_union_map *umap);
3321 __isl_give isl_union_map *isl_union_map_lexmax(
3322 __isl_take isl_union_map *umap);
3324 The following functions return their result in the form of
3325 a piecewise multi-affine expression
3326 (See L<"Piecewise Multiple Quasi Affine Expressions">),
3327 but are otherwise equivalent to the corresponding functions
3328 returning a basic set or relation.
3330 __isl_give isl_pw_multi_aff *
3331 isl_basic_map_lexmin_pw_multi_aff(
3332 __isl_take isl_basic_map *bmap);
3333 __isl_give isl_pw_multi_aff *
3334 isl_basic_set_partial_lexmin_pw_multi_aff(
3335 __isl_take isl_basic_set *bset,
3336 __isl_take isl_basic_set *dom,
3337 __isl_give isl_set **empty);
3338 __isl_give isl_pw_multi_aff *
3339 isl_basic_set_partial_lexmax_pw_multi_aff(
3340 __isl_take isl_basic_set *bset,
3341 __isl_take isl_basic_set *dom,
3342 __isl_give isl_set **empty);
3343 __isl_give isl_pw_multi_aff *
3344 isl_basic_map_partial_lexmin_pw_multi_aff(
3345 __isl_take isl_basic_map *bmap,
3346 __isl_take isl_basic_set *dom,
3347 __isl_give isl_set **empty);
3348 __isl_give isl_pw_multi_aff *
3349 isl_basic_map_partial_lexmax_pw_multi_aff(
3350 __isl_take isl_basic_map *bmap,
3351 __isl_take isl_basic_set *dom,
3352 __isl_give isl_set **empty);
3353 __isl_give isl_pw_multi_aff *isl_set_lexmin_pw_multi_aff(
3354 __isl_take isl_set *set);
3355 __isl_give isl_pw_multi_aff *isl_set_lexmax_pw_multi_aff(
3356 __isl_take isl_set *set);
3357 __isl_give isl_pw_multi_aff *isl_map_lexmin_pw_multi_aff(
3358 __isl_take isl_map *map);
3359 __isl_give isl_pw_multi_aff *isl_map_lexmax_pw_multi_aff(
3360 __isl_take isl_map *map);
3364 Lists are defined over several element types, including
3365 C<isl_val>, C<isl_id>, C<isl_aff>, C<isl_pw_aff>, C<isl_constraint>,
3366 C<isl_basic_set>, C<isl_set>, C<isl_ast_expr> and C<isl_ast_node>.
3367 Here we take lists of C<isl_set>s as an example.
3368 Lists can be created, copied, modified and freed using the following functions.
3370 #include <isl/list.h>
3371 __isl_give isl_set_list *isl_set_list_from_set(
3372 __isl_take isl_set *el);
3373 __isl_give isl_set_list *isl_set_list_alloc(
3374 isl_ctx *ctx, int n);
3375 __isl_give isl_set_list *isl_set_list_copy(
3376 __isl_keep isl_set_list *list);
3377 __isl_give isl_set_list *isl_set_list_insert(
3378 __isl_take isl_set_list *list, unsigned pos,
3379 __isl_take isl_set *el);
3380 __isl_give isl_set_list *isl_set_list_add(
3381 __isl_take isl_set_list *list,
3382 __isl_take isl_set *el);
3383 __isl_give isl_set_list *isl_set_list_drop(
3384 __isl_take isl_set_list *list,
3385 unsigned first, unsigned n);
3386 __isl_give isl_set_list *isl_set_list_set_set(
3387 __isl_take isl_set_list *list, int index,
3388 __isl_take isl_set *set);
3389 __isl_give isl_set_list *isl_set_list_concat(
3390 __isl_take isl_set_list *list1,
3391 __isl_take isl_set_list *list2);
3392 __isl_give isl_set_list *isl_set_list_sort(
3393 __isl_take isl_set_list *list,
3394 int (*cmp)(__isl_keep isl_set *a,
3395 __isl_keep isl_set *b, void *user),
3397 void *isl_set_list_free(__isl_take isl_set_list *list);
3399 C<isl_set_list_alloc> creates an empty list with a capacity for
3400 C<n> elements. C<isl_set_list_from_set> creates a list with a single
3403 Lists can be inspected using the following functions.
3405 #include <isl/list.h>
3406 isl_ctx *isl_set_list_get_ctx(__isl_keep isl_set_list *list);
3407 int isl_set_list_n_set(__isl_keep isl_set_list *list);
3408 __isl_give isl_set *isl_set_list_get_set(
3409 __isl_keep isl_set_list *list, int index);
3410 int isl_set_list_foreach(__isl_keep isl_set_list *list,
3411 int (*fn)(__isl_take isl_set *el, void *user),
3413 int isl_set_list_foreach_scc(__isl_keep isl_set_list *list,
3414 int (*follows)(__isl_keep isl_set *a,
3415 __isl_keep isl_set *b, void *user),
3417 int (*fn)(__isl_take isl_set *el, void *user),
3420 The function C<isl_set_list_foreach_scc> calls C<fn> on each of the
3421 strongly connected components of the graph with as vertices the elements
3422 of C<list> and a directed edge from vertex C<b> to vertex C<a>
3423 iff C<follows(a, b)> returns C<1>. The callbacks C<follows> and C<fn>
3424 should return C<-1> on error.
3426 Lists can be printed using
3428 #include <isl/list.h>
3429 __isl_give isl_printer *isl_printer_print_set_list(
3430 __isl_take isl_printer *p,
3431 __isl_keep isl_set_list *list);
3433 =head2 Associative arrays
3435 Associative arrays map isl objects of a specific type to isl objects
3436 of some (other) specific type. They are defined for several pairs
3437 of types, including (C<isl_map>, C<isl_basic_set>),
3438 (C<isl_id>, C<isl_ast_expr>) and.
3439 (C<isl_id>, C<isl_pw_aff>).
3440 Here, we take associative arrays that map C<isl_id>s to C<isl_ast_expr>s
3443 Associative arrays can be created, copied and freed using
3444 the following functions.
3446 #include <isl/id_to_ast_expr.h>
3447 __isl_give id_to_ast_expr *isl_id_to_ast_expr_alloc(
3448 isl_ctx *ctx, int min_size);
3449 __isl_give id_to_ast_expr *isl_id_to_ast_expr_copy(
3450 __isl_keep id_to_ast_expr *id2expr);
3451 void *isl_id_to_ast_expr_free(
3452 __isl_take id_to_ast_expr *id2expr);
3454 The C<min_size> argument to C<isl_id_to_ast_expr_alloc> can be used
3455 to specify the expected size of the associative array.
3456 The associative array will be grown automatically as needed.
3458 Associative arrays can be inspected using the following functions.
3460 #include <isl/id_to_ast_expr.h>
3461 isl_ctx *isl_id_to_ast_expr_get_ctx(
3462 __isl_keep id_to_ast_expr *id2expr);
3463 int isl_id_to_ast_expr_has(
3464 __isl_keep id_to_ast_expr *id2expr,
3465 __isl_keep isl_id *key);
3466 __isl_give isl_ast_expr *isl_id_to_ast_expr_get(
3467 __isl_keep id_to_ast_expr *id2expr,
3468 __isl_take isl_id *key);
3469 int isl_id_to_ast_expr_foreach(
3470 __isl_keep id_to_ast_expr *id2expr,
3471 int (*fn)(__isl_take isl_id *key,
3472 __isl_take isl_ast_expr *val, void *user),
3475 They can be modified using the following function.
3477 #include <isl/id_to_ast_expr.h>
3478 __isl_give id_to_ast_expr *isl_id_to_ast_expr_set(
3479 __isl_take id_to_ast_expr *id2expr,
3480 __isl_take isl_id *key,
3481 __isl_take isl_ast_expr *val);
3482 __isl_give id_to_ast_expr *isl_id_to_ast_expr_drop(
3483 __isl_take id_to_ast_expr *id2expr,
3484 __isl_take isl_id *key);
3486 Associative arrays can be printed using the following function.
3488 #include <isl/id_to_ast_expr.h>
3489 __isl_give isl_printer *isl_printer_print_id_to_ast_expr(
3490 __isl_take isl_printer *p,
3491 __isl_keep id_to_ast_expr *id2expr);
3493 =head2 Multiple Values
3495 An C<isl_multi_val> object represents a sequence of zero or more values,
3496 living in a set space.
3498 An C<isl_multi_val> can be constructed from an C<isl_val_list>
3499 using the following function
3501 #include <isl/val.h>
3502 __isl_give isl_multi_val *isl_multi_val_from_val_list(
3503 __isl_take isl_space *space,
3504 __isl_take isl_val_list *list);
3506 The zero multiple value (with value zero for each set dimension)
3507 can be created using the following function.
3509 #include <isl/val.h>
3510 __isl_give isl_multi_val *isl_multi_val_zero(
3511 __isl_take isl_space *space);
3513 Multiple values can be copied and freed using
3515 #include <isl/val.h>
3516 __isl_give isl_multi_val *isl_multi_val_copy(
3517 __isl_keep isl_multi_val *mv);
3518 void *isl_multi_val_free(__isl_take isl_multi_val *mv);
3520 They can be inspected using
3522 #include <isl/val.h>
3523 isl_ctx *isl_multi_val_get_ctx(
3524 __isl_keep isl_multi_val *mv);
3525 unsigned isl_multi_val_dim(__isl_keep isl_multi_val *mv,
3526 enum isl_dim_type type);
3527 __isl_give isl_val *isl_multi_val_get_val(
3528 __isl_keep isl_multi_val *mv, int pos);
3529 int isl_multi_val_find_dim_by_id(
3530 __isl_keep isl_multi_val *mv,
3531 enum isl_dim_type type, __isl_keep isl_id *id);
3532 __isl_give isl_id *isl_multi_val_get_dim_id(
3533 __isl_keep isl_multi_val *mv,
3534 enum isl_dim_type type, unsigned pos);
3535 const char *isl_multi_val_get_tuple_name(
3536 __isl_keep isl_multi_val *mv,
3537 enum isl_dim_type type);
3538 int isl_multi_val_has_tuple_id(__isl_keep isl_multi_val *mv,
3539 enum isl_dim_type type);
3540 __isl_give isl_id *isl_multi_val_get_tuple_id(
3541 __isl_keep isl_multi_val *mv,
3542 enum isl_dim_type type);
3543 int isl_multi_val_range_is_wrapping(
3544 __isl_keep isl_multi_val *mv);
3546 They can be modified using
3548 #include <isl/val.h>
3549 __isl_give isl_multi_val *isl_multi_val_set_val(
3550 __isl_take isl_multi_val *mv, int pos,
3551 __isl_take isl_val *val);
3552 __isl_give isl_multi_val *isl_multi_val_set_dim_name(
3553 __isl_take isl_multi_val *mv,
3554 enum isl_dim_type type, unsigned pos, const char *s);
3555 __isl_give isl_multi_val *isl_multi_val_set_dim_id(
3556 __isl_take isl_multi_val *mv,
3557 enum isl_dim_type type, unsigned pos,
3558 __isl_take isl_id *id);
3559 __isl_give isl_multi_val *isl_multi_val_set_tuple_name(
3560 __isl_take isl_multi_val *mv,
3561 enum isl_dim_type type, const char *s);
3562 __isl_give isl_multi_val *isl_multi_val_set_tuple_id(
3563 __isl_take isl_multi_val *mv,
3564 enum isl_dim_type type, __isl_take isl_id *id);
3565 __isl_give isl_multi_val *isl_multi_val_reset_tuple_id(
3566 __isl_take isl_multi_val *mv,
3567 enum isl_dim_type type);
3568 __isl_give isl_multi_val *isl_multi_val_reset_user(
3569 __isl_take isl_multi_val *mv);
3571 __isl_give isl_multi_val *isl_multi_val_insert_dims(
3572 __isl_take isl_multi_val *mv,
3573 enum isl_dim_type type, unsigned first, unsigned n);
3574 __isl_give isl_multi_val *isl_multi_val_add_dims(
3575 __isl_take isl_multi_val *mv,
3576 enum isl_dim_type type, unsigned n);
3577 __isl_give isl_multi_val *isl_multi_val_drop_dims(
3578 __isl_take isl_multi_val *mv,
3579 enum isl_dim_type type, unsigned first, unsigned n);
3583 #include <isl/val.h>
3584 __isl_give isl_multi_val *isl_multi_val_align_params(
3585 __isl_take isl_multi_val *mv,
3586 __isl_take isl_space *model);
3587 __isl_give isl_multi_val *isl_multi_val_from_range(
3588 __isl_take isl_multi_val *mv);
3589 __isl_give isl_multi_val *isl_multi_val_range_splice(
3590 __isl_take isl_multi_val *mv1, unsigned pos,
3591 __isl_take isl_multi_val *mv2);
3592 __isl_give isl_multi_val *isl_multi_val_range_product(
3593 __isl_take isl_multi_val *mv1,
3594 __isl_take isl_multi_val *mv2);
3595 __isl_give isl_multi_val *
3596 isl_multi_val_range_factor_domain(
3597 __isl_take isl_multi_val *mv);
3598 __isl_give isl_multi_val *
3599 isl_multi_val_range_factor_range(
3600 __isl_take isl_multi_val *mv);
3601 __isl_give isl_multi_val *isl_multi_val_flat_range_product(
3602 __isl_take isl_multi_val *mv1,
3603 __isl_take isl_multi_aff *mv2);
3604 __isl_give isl_multi_val *isl_multi_val_product(
3605 __isl_take isl_multi_val *mv1,
3606 __isl_take isl_multi_val *mv2);
3607 __isl_give isl_multi_val *isl_multi_val_add_val(
3608 __isl_take isl_multi_val *mv,
3609 __isl_take isl_val *v);
3610 __isl_give isl_multi_val *isl_multi_val_mod_val(
3611 __isl_take isl_multi_val *mv,
3612 __isl_take isl_val *v);
3613 __isl_give isl_multi_val *isl_multi_val_scale_val(
3614 __isl_take isl_multi_val *mv,
3615 __isl_take isl_val *v);
3616 __isl_give isl_multi_val *isl_multi_val_scale_multi_val(
3617 __isl_take isl_multi_val *mv1,
3618 __isl_take isl_multi_val *mv2);
3619 __isl_give isl_multi_val *
3620 isl_multi_val_scale_down_multi_val(
3621 __isl_take isl_multi_val *mv1,
3622 __isl_take isl_multi_val *mv2);
3624 A multiple value can be printed using
3626 __isl_give isl_printer *isl_printer_print_multi_val(
3627 __isl_take isl_printer *p,
3628 __isl_keep isl_multi_val *mv);
3632 Vectors can be created, copied and freed using the following functions.
3634 #include <isl/vec.h>
3635 __isl_give isl_vec *isl_vec_alloc(isl_ctx *ctx,
3637 __isl_give isl_vec *isl_vec_copy(__isl_keep isl_vec *vec);
3638 void *isl_vec_free(__isl_take isl_vec *vec);
3640 Note that the elements of a newly created vector may have arbitrary values.
3641 The elements can be changed and inspected using the following functions.
3643 isl_ctx *isl_vec_get_ctx(__isl_keep isl_vec *vec);
3644 int isl_vec_size(__isl_keep isl_vec *vec);
3645 __isl_give isl_val *isl_vec_get_element_val(
3646 __isl_keep isl_vec *vec, int pos);
3647 __isl_give isl_vec *isl_vec_set_element_si(
3648 __isl_take isl_vec *vec, int pos, int v);
3649 __isl_give isl_vec *isl_vec_set_element_val(
3650 __isl_take isl_vec *vec, int pos,
3651 __isl_take isl_val *v);
3652 __isl_give isl_vec *isl_vec_set_si(__isl_take isl_vec *vec,
3654 __isl_give isl_vec *isl_vec_set_val(
3655 __isl_take isl_vec *vec, __isl_take isl_val *v);
3656 int isl_vec_cmp_element(__isl_keep isl_vec *vec1,
3657 __isl_keep isl_vec *vec2, int pos);
3659 C<isl_vec_get_element> will return a negative value if anything went wrong.
3660 In that case, the value of C<*v> is undefined.
3662 The following function can be used to concatenate two vectors.
3664 __isl_give isl_vec *isl_vec_concat(__isl_take isl_vec *vec1,
3665 __isl_take isl_vec *vec2);
3669 Matrices can be created, copied and freed using the following functions.
3671 #include <isl/mat.h>
3672 __isl_give isl_mat *isl_mat_alloc(isl_ctx *ctx,
3673 unsigned n_row, unsigned n_col);
3674 __isl_give isl_mat *isl_mat_copy(__isl_keep isl_mat *mat);
3675 void *isl_mat_free(__isl_take isl_mat *mat);
3677 Note that the elements of a newly created matrix may have arbitrary values.
3678 The elements can be changed and inspected using the following functions.
3680 isl_ctx *isl_mat_get_ctx(__isl_keep isl_mat *mat);
3681 int isl_mat_rows(__isl_keep isl_mat *mat);
3682 int isl_mat_cols(__isl_keep isl_mat *mat);
3683 __isl_give isl_val *isl_mat_get_element_val(
3684 __isl_keep isl_mat *mat, int row, int col);
3685 __isl_give isl_mat *isl_mat_set_element_si(__isl_take isl_mat *mat,
3686 int row, int col, int v);
3687 __isl_give isl_mat *isl_mat_set_element_val(
3688 __isl_take isl_mat *mat, int row, int col,
3689 __isl_take isl_val *v);
3691 C<isl_mat_get_element> will return a negative value if anything went wrong.
3692 In that case, the value of C<*v> is undefined.
3694 The following function can be used to compute the (right) inverse
3695 of a matrix, i.e., a matrix such that the product of the original
3696 and the inverse (in that order) is a multiple of the identity matrix.
3697 The input matrix is assumed to be of full row-rank.
3699 __isl_give isl_mat *isl_mat_right_inverse(__isl_take isl_mat *mat);
3701 The following function can be used to compute the (right) kernel
3702 (or null space) of a matrix, i.e., a matrix such that the product of
3703 the original and the kernel (in that order) is the zero matrix.
3705 __isl_give isl_mat *isl_mat_right_kernel(__isl_take isl_mat *mat);
3707 =head2 Piecewise Quasi Affine Expressions
3709 The zero quasi affine expression or the quasi affine expression
3710 that is equal to a given value or
3711 a specified dimension on a given domain can be created using
3713 __isl_give isl_aff *isl_aff_zero_on_domain(
3714 __isl_take isl_local_space *ls);
3715 __isl_give isl_pw_aff *isl_pw_aff_zero_on_domain(
3716 __isl_take isl_local_space *ls);
3717 __isl_give isl_aff *isl_aff_val_on_domain(
3718 __isl_take isl_local_space *ls,
3719 __isl_take isl_val *val);
3720 __isl_give isl_aff *isl_aff_var_on_domain(
3721 __isl_take isl_local_space *ls,
3722 enum isl_dim_type type, unsigned pos);
3723 __isl_give isl_pw_aff *isl_pw_aff_var_on_domain(
3724 __isl_take isl_local_space *ls,
3725 enum isl_dim_type type, unsigned pos);
3727 Note that the space in which the resulting objects live is a map space
3728 with the given space as domain and a one-dimensional range.
3730 An empty piecewise quasi affine expression (one with no cells)
3731 or a piecewise quasi affine expression with a single cell can
3732 be created using the following functions.
3734 #include <isl/aff.h>
3735 __isl_give isl_pw_aff *isl_pw_aff_empty(
3736 __isl_take isl_space *space);
3737 __isl_give isl_pw_aff *isl_pw_aff_alloc(
3738 __isl_take isl_set *set, __isl_take isl_aff *aff);
3739 __isl_give isl_pw_aff *isl_pw_aff_from_aff(
3740 __isl_take isl_aff *aff);
3742 A piecewise quasi affine expression that is equal to 1 on a set
3743 and 0 outside the set can be created using the following function.
3745 #include <isl/aff.h>
3746 __isl_give isl_pw_aff *isl_set_indicator_function(
3747 __isl_take isl_set *set);
3749 Quasi affine expressions can be copied and freed using
3751 #include <isl/aff.h>
3752 __isl_give isl_aff *isl_aff_copy(__isl_keep isl_aff *aff);
3753 void *isl_aff_free(__isl_take isl_aff *aff);
3755 __isl_give isl_pw_aff *isl_pw_aff_copy(
3756 __isl_keep isl_pw_aff *pwaff);
3757 void *isl_pw_aff_free(__isl_take isl_pw_aff *pwaff);
3759 A (rational) bound on a dimension can be extracted from an C<isl_constraint>
3760 using the following function. The constraint is required to have
3761 a non-zero coefficient for the specified dimension.
3763 #include <isl/constraint.h>
3764 __isl_give isl_aff *isl_constraint_get_bound(
3765 __isl_keep isl_constraint *constraint,
3766 enum isl_dim_type type, int pos);
3768 The entire affine expression of the constraint can also be extracted
3769 using the following function.
3771 #include <isl/constraint.h>
3772 __isl_give isl_aff *isl_constraint_get_aff(
3773 __isl_keep isl_constraint *constraint);
3775 Conversely, an equality constraint equating
3776 the affine expression to zero or an inequality constraint enforcing
3777 the affine expression to be non-negative, can be constructed using
3779 __isl_give isl_constraint *isl_equality_from_aff(
3780 __isl_take isl_aff *aff);
3781 __isl_give isl_constraint *isl_inequality_from_aff(
3782 __isl_take isl_aff *aff);
3784 The expression can be inspected using
3786 #include <isl/aff.h>
3787 isl_ctx *isl_aff_get_ctx(__isl_keep isl_aff *aff);
3788 int isl_aff_dim(__isl_keep isl_aff *aff,
3789 enum isl_dim_type type);
3790 __isl_give isl_local_space *isl_aff_get_domain_local_space(
3791 __isl_keep isl_aff *aff);
3792 __isl_give isl_local_space *isl_aff_get_local_space(
3793 __isl_keep isl_aff *aff);
3794 const char *isl_aff_get_dim_name(__isl_keep isl_aff *aff,
3795 enum isl_dim_type type, unsigned pos);
3796 const char *isl_pw_aff_get_dim_name(
3797 __isl_keep isl_pw_aff *pa,
3798 enum isl_dim_type type, unsigned pos);
3799 int isl_pw_aff_has_dim_id(__isl_keep isl_pw_aff *pa,
3800 enum isl_dim_type type, unsigned pos);
3801 __isl_give isl_id *isl_pw_aff_get_dim_id(
3802 __isl_keep isl_pw_aff *pa,
3803 enum isl_dim_type type, unsigned pos);
3804 int isl_pw_aff_has_tuple_id(__isl_keep isl_pw_aff *pa,
3805 enum isl_dim_type type);
3806 __isl_give isl_id *isl_pw_aff_get_tuple_id(
3807 __isl_keep isl_pw_aff *pa,
3808 enum isl_dim_type type);
3809 __isl_give isl_val *isl_aff_get_constant_val(
3810 __isl_keep isl_aff *aff);
3811 __isl_give isl_val *isl_aff_get_coefficient_val(
3812 __isl_keep isl_aff *aff,
3813 enum isl_dim_type type, int pos);
3814 __isl_give isl_val *isl_aff_get_denominator_val(
3815 __isl_keep isl_aff *aff);
3816 __isl_give isl_aff *isl_aff_get_div(
3817 __isl_keep isl_aff *aff, int pos);
3819 int isl_pw_aff_n_piece(__isl_keep isl_pw_aff *pwaff);
3820 int isl_pw_aff_foreach_piece(__isl_keep isl_pw_aff *pwaff,
3821 int (*fn)(__isl_take isl_set *set,
3822 __isl_take isl_aff *aff,
3823 void *user), void *user);
3825 int isl_aff_is_cst(__isl_keep isl_aff *aff);
3826 int isl_pw_aff_is_cst(__isl_keep isl_pw_aff *pwaff);
3828 int isl_aff_involves_dims(__isl_keep isl_aff *aff,
3829 enum isl_dim_type type, unsigned first, unsigned n);
3830 int isl_pw_aff_involves_dims(__isl_keep isl_pw_aff *pwaff,
3831 enum isl_dim_type type, unsigned first, unsigned n);
3833 isl_ctx *isl_pw_aff_get_ctx(__isl_keep isl_pw_aff *pwaff);
3834 unsigned isl_pw_aff_dim(__isl_keep isl_pw_aff *pwaff,
3835 enum isl_dim_type type);
3836 int isl_pw_aff_is_empty(__isl_keep isl_pw_aff *pwaff);
3838 It can be modified using
3840 #include <isl/aff.h>
3841 __isl_give isl_aff *isl_aff_set_tuple_id(
3842 __isl_take isl_aff *aff,
3843 enum isl_dim_type type, __isl_take isl_id *id);
3844 __isl_give isl_pw_aff *isl_pw_aff_set_tuple_id(
3845 __isl_take isl_pw_aff *pwaff,
3846 enum isl_dim_type type, __isl_take isl_id *id);
3847 __isl_give isl_aff *isl_aff_set_dim_name(
3848 __isl_take isl_aff *aff, enum isl_dim_type type,
3849 unsigned pos, const char *s);
3850 __isl_give isl_aff *isl_aff_set_dim_id(
3851 __isl_take isl_aff *aff, enum isl_dim_type type,
3852 unsigned pos, __isl_take isl_id *id);
3853 __isl_give isl_pw_aff *isl_pw_aff_set_dim_id(
3854 __isl_take isl_pw_aff *pma,
3855 enum isl_dim_type type, unsigned pos,
3856 __isl_take isl_id *id);
3857 __isl_give isl_aff *isl_aff_set_constant_si(
3858 __isl_take isl_aff *aff, int v);
3859 __isl_give isl_aff *isl_aff_set_constant_val(
3860 __isl_take isl_aff *aff, __isl_take isl_val *v);
3861 __isl_give isl_aff *isl_aff_set_coefficient_si(
3862 __isl_take isl_aff *aff,
3863 enum isl_dim_type type, int pos, int v);
3864 __isl_give isl_aff *isl_aff_set_coefficient_val(
3865 __isl_take isl_aff *aff,
3866 enum isl_dim_type type, int pos,
3867 __isl_take isl_val *v);
3869 __isl_give isl_aff *isl_aff_add_constant_si(
3870 __isl_take isl_aff *aff, int v);
3871 __isl_give isl_aff *isl_aff_add_constant_val(
3872 __isl_take isl_aff *aff, __isl_take isl_val *v);
3873 __isl_give isl_aff *isl_aff_add_constant_num_si(
3874 __isl_take isl_aff *aff, int v);
3875 __isl_give isl_aff *isl_aff_add_coefficient_si(
3876 __isl_take isl_aff *aff,
3877 enum isl_dim_type type, int pos, int v);
3878 __isl_give isl_aff *isl_aff_add_coefficient_val(
3879 __isl_take isl_aff *aff,
3880 enum isl_dim_type type, int pos,
3881 __isl_take isl_val *v);
3883 __isl_give isl_aff *isl_aff_insert_dims(
3884 __isl_take isl_aff *aff,
3885 enum isl_dim_type type, unsigned first, unsigned n);
3886 __isl_give isl_pw_aff *isl_pw_aff_insert_dims(
3887 __isl_take isl_pw_aff *pwaff,
3888 enum isl_dim_type type, unsigned first, unsigned n);
3889 __isl_give isl_aff *isl_aff_add_dims(
3890 __isl_take isl_aff *aff,
3891 enum isl_dim_type type, unsigned n);
3892 __isl_give isl_pw_aff *isl_pw_aff_add_dims(
3893 __isl_take isl_pw_aff *pwaff,
3894 enum isl_dim_type type, unsigned n);
3895 __isl_give isl_aff *isl_aff_drop_dims(
3896 __isl_take isl_aff *aff,
3897 enum isl_dim_type type, unsigned first, unsigned n);
3898 __isl_give isl_pw_aff *isl_pw_aff_drop_dims(
3899 __isl_take isl_pw_aff *pwaff,
3900 enum isl_dim_type type, unsigned first, unsigned n);
3901 __isl_give isl_aff *isl_aff_move_dims(
3902 __isl_take isl_aff *aff,
3903 enum isl_dim_type dst_type, unsigned dst_pos,
3904 enum isl_dim_type src_type, unsigned src_pos,
3906 __isl_give isl_pw_aff *isl_pw_aff_move_dims(
3907 __isl_take isl_pw_aff *pa,
3908 enum isl_dim_type dst_type, unsigned dst_pos,
3909 enum isl_dim_type src_type, unsigned src_pos,
3912 Note that C<isl_aff_set_constant_si> and C<isl_aff_set_coefficient_si>
3913 set the I<numerator> of the constant or coefficient, while
3914 C<isl_aff_set_constant_val> and C<isl_aff_set_coefficient_val> set
3915 the constant or coefficient as a whole.
3916 The C<add_constant> and C<add_coefficient> functions add an integer
3917 or rational value to
3918 the possibly rational constant or coefficient.
3919 The C<add_constant_num> functions add an integer value to
3922 To check whether an affine expressions is obviously zero
3923 or (obviously) equal to some other affine expression, use
3925 #include <isl/aff.h>
3926 int isl_aff_plain_is_zero(__isl_keep isl_aff *aff);
3927 int isl_aff_plain_is_equal(__isl_keep isl_aff *aff1,
3928 __isl_keep isl_aff *aff2);
3929 int isl_pw_aff_plain_is_equal(
3930 __isl_keep isl_pw_aff *pwaff1,
3931 __isl_keep isl_pw_aff *pwaff2);
3932 int isl_pw_aff_is_equal(__isl_keep isl_pw_aff *pa1,
3933 __isl_keep isl_pw_aff *pa2);
3937 #include <isl/aff.h>
3938 __isl_give isl_aff *isl_aff_add(__isl_take isl_aff *aff1,
3939 __isl_take isl_aff *aff2);
3940 __isl_give isl_pw_aff *isl_pw_aff_add(
3941 __isl_take isl_pw_aff *pwaff1,
3942 __isl_take isl_pw_aff *pwaff2);
3943 __isl_give isl_pw_aff *isl_pw_aff_min(
3944 __isl_take isl_pw_aff *pwaff1,
3945 __isl_take isl_pw_aff *pwaff2);
3946 __isl_give isl_pw_aff *isl_pw_aff_max(
3947 __isl_take isl_pw_aff *pwaff1,
3948 __isl_take isl_pw_aff *pwaff2);
3949 __isl_give isl_aff *isl_aff_sub(__isl_take isl_aff *aff1,
3950 __isl_take isl_aff *aff2);
3951 __isl_give isl_pw_aff *isl_pw_aff_sub(
3952 __isl_take isl_pw_aff *pwaff1,
3953 __isl_take isl_pw_aff *pwaff2);
3954 __isl_give isl_aff *isl_aff_neg(__isl_take isl_aff *aff);
3955 __isl_give isl_pw_aff *isl_pw_aff_neg(
3956 __isl_take isl_pw_aff *pwaff);
3957 __isl_give isl_aff *isl_aff_ceil(__isl_take isl_aff *aff);
3958 __isl_give isl_pw_aff *isl_pw_aff_ceil(
3959 __isl_take isl_pw_aff *pwaff);
3960 __isl_give isl_aff *isl_aff_floor(__isl_take isl_aff *aff);
3961 __isl_give isl_pw_aff *isl_pw_aff_floor(
3962 __isl_take isl_pw_aff *pwaff);
3963 __isl_give isl_aff *isl_aff_mod_val(__isl_take isl_aff *aff,
3964 __isl_take isl_val *mod);
3965 __isl_give isl_pw_aff *isl_pw_aff_mod_val(
3966 __isl_take isl_pw_aff *pa,
3967 __isl_take isl_val *mod);
3968 __isl_give isl_aff *isl_aff_scale_val(__isl_take isl_aff *aff,
3969 __isl_take isl_val *v);
3970 __isl_give isl_pw_aff *isl_pw_aff_scale_val(
3971 __isl_take isl_pw_aff *pa, __isl_take isl_val *v);
3972 __isl_give isl_aff *isl_aff_scale_down_ui(
3973 __isl_take isl_aff *aff, unsigned f);
3974 __isl_give isl_aff *isl_aff_scale_down_val(
3975 __isl_take isl_aff *aff, __isl_take isl_val *v);
3976 __isl_give isl_pw_aff *isl_pw_aff_scale_down_val(
3977 __isl_take isl_pw_aff *pa,
3978 __isl_take isl_val *f);
3980 __isl_give isl_pw_aff *isl_pw_aff_list_min(
3981 __isl_take isl_pw_aff_list *list);
3982 __isl_give isl_pw_aff *isl_pw_aff_list_max(
3983 __isl_take isl_pw_aff_list *list);
3985 __isl_give isl_pw_aff *isl_pw_aff_coalesce(
3986 __isl_take isl_pw_aff *pwqp);
3988 __isl_give isl_aff *isl_aff_align_params(
3989 __isl_take isl_aff *aff,
3990 __isl_take isl_space *model);
3991 __isl_give isl_pw_aff *isl_pw_aff_align_params(
3992 __isl_take isl_pw_aff *pwaff,
3993 __isl_take isl_space *model);
3995 __isl_give isl_aff *isl_aff_project_domain_on_params(
3996 __isl_take isl_aff *aff);
3997 __isl_give isl_pw_aff *isl_pw_aff_from_range(
3998 __isl_take isl_pw_aff *pwa);
4000 __isl_give isl_aff *isl_aff_gist_params(
4001 __isl_take isl_aff *aff,
4002 __isl_take isl_set *context);
4003 __isl_give isl_aff *isl_aff_gist(__isl_take isl_aff *aff,
4004 __isl_take isl_set *context);
4005 __isl_give isl_pw_aff *isl_pw_aff_gist_params(
4006 __isl_take isl_pw_aff *pwaff,
4007 __isl_take isl_set *context);
4008 __isl_give isl_pw_aff *isl_pw_aff_gist(
4009 __isl_take isl_pw_aff *pwaff,
4010 __isl_take isl_set *context);
4012 __isl_give isl_set *isl_pw_aff_domain(
4013 __isl_take isl_pw_aff *pwaff);
4014 __isl_give isl_set *isl_pw_aff_params(
4015 __isl_take isl_pw_aff *pwa);
4016 __isl_give isl_pw_aff *isl_pw_aff_intersect_domain(
4017 __isl_take isl_pw_aff *pa,
4018 __isl_take isl_set *set);
4019 __isl_give isl_pw_aff *isl_pw_aff_intersect_params(
4020 __isl_take isl_pw_aff *pa,
4021 __isl_take isl_set *set);
4023 __isl_give isl_aff *isl_aff_mul(__isl_take isl_aff *aff1,
4024 __isl_take isl_aff *aff2);
4025 __isl_give isl_aff *isl_aff_div(__isl_take isl_aff *aff1,
4026 __isl_take isl_aff *aff2);
4027 __isl_give isl_pw_aff *isl_pw_aff_mul(
4028 __isl_take isl_pw_aff *pwaff1,
4029 __isl_take isl_pw_aff *pwaff2);
4030 __isl_give isl_pw_aff *isl_pw_aff_div(
4031 __isl_take isl_pw_aff *pa1,
4032 __isl_take isl_pw_aff *pa2);
4033 __isl_give isl_pw_aff *isl_pw_aff_tdiv_q(
4034 __isl_take isl_pw_aff *pa1,
4035 __isl_take isl_pw_aff *pa2);
4036 __isl_give isl_pw_aff *isl_pw_aff_tdiv_r(
4037 __isl_take isl_pw_aff *pa1,
4038 __isl_take isl_pw_aff *pa2);
4040 When multiplying two affine expressions, at least one of the two needs
4041 to be a constant. Similarly, when dividing an affine expression by another,
4042 the second expression needs to be a constant.
4043 C<isl_pw_aff_tdiv_q> computes the quotient of an integer division with
4044 rounding towards zero. C<isl_pw_aff_tdiv_r> computes the corresponding
4047 #include <isl/aff.h>
4048 __isl_give isl_aff *isl_aff_pullback_aff(
4049 __isl_take isl_aff *aff1,
4050 __isl_take isl_aff *aff2);
4051 __isl_give isl_aff *isl_aff_pullback_multi_aff(
4052 __isl_take isl_aff *aff,
4053 __isl_take isl_multi_aff *ma);
4054 __isl_give isl_pw_aff *isl_pw_aff_pullback_multi_aff(
4055 __isl_take isl_pw_aff *pa,
4056 __isl_take isl_multi_aff *ma);
4057 __isl_give isl_pw_aff *isl_pw_aff_pullback_pw_multi_aff(
4058 __isl_take isl_pw_aff *pa,
4059 __isl_take isl_pw_multi_aff *pma);
4061 These functions precompose the input expression by the given
4062 C<isl_aff>, C<isl_multi_aff> or C<isl_pw_multi_aff>. In other words,
4063 the C<isl_aff>, C<isl_multi_aff> or C<isl_pw_multi_aff> is plugged
4064 into the (piecewise) affine expression.
4065 Objects of type C<isl_multi_aff> are described in
4066 L</"Piecewise Multiple Quasi Affine Expressions">.
4068 #include <isl/aff.h>
4069 __isl_give isl_basic_set *isl_aff_zero_basic_set(
4070 __isl_take isl_aff *aff);
4071 __isl_give isl_basic_set *isl_aff_neg_basic_set(
4072 __isl_take isl_aff *aff);
4073 __isl_give isl_basic_set *isl_aff_le_basic_set(
4074 __isl_take isl_aff *aff1, __isl_take isl_aff *aff2);
4075 __isl_give isl_basic_set *isl_aff_ge_basic_set(
4076 __isl_take isl_aff *aff1, __isl_take isl_aff *aff2);
4077 __isl_give isl_set *isl_pw_aff_eq_set(
4078 __isl_take isl_pw_aff *pwaff1,
4079 __isl_take isl_pw_aff *pwaff2);
4080 __isl_give isl_set *isl_pw_aff_ne_set(
4081 __isl_take isl_pw_aff *pwaff1,
4082 __isl_take isl_pw_aff *pwaff2);
4083 __isl_give isl_set *isl_pw_aff_le_set(
4084 __isl_take isl_pw_aff *pwaff1,
4085 __isl_take isl_pw_aff *pwaff2);
4086 __isl_give isl_set *isl_pw_aff_lt_set(
4087 __isl_take isl_pw_aff *pwaff1,
4088 __isl_take isl_pw_aff *pwaff2);
4089 __isl_give isl_set *isl_pw_aff_ge_set(
4090 __isl_take isl_pw_aff *pwaff1,
4091 __isl_take isl_pw_aff *pwaff2);
4092 __isl_give isl_set *isl_pw_aff_gt_set(
4093 __isl_take isl_pw_aff *pwaff1,
4094 __isl_take isl_pw_aff *pwaff2);
4096 __isl_give isl_set *isl_pw_aff_list_eq_set(
4097 __isl_take isl_pw_aff_list *list1,
4098 __isl_take isl_pw_aff_list *list2);
4099 __isl_give isl_set *isl_pw_aff_list_ne_set(
4100 __isl_take isl_pw_aff_list *list1,
4101 __isl_take isl_pw_aff_list *list2);
4102 __isl_give isl_set *isl_pw_aff_list_le_set(
4103 __isl_take isl_pw_aff_list *list1,
4104 __isl_take isl_pw_aff_list *list2);
4105 __isl_give isl_set *isl_pw_aff_list_lt_set(
4106 __isl_take isl_pw_aff_list *list1,
4107 __isl_take isl_pw_aff_list *list2);
4108 __isl_give isl_set *isl_pw_aff_list_ge_set(
4109 __isl_take isl_pw_aff_list *list1,
4110 __isl_take isl_pw_aff_list *list2);
4111 __isl_give isl_set *isl_pw_aff_list_gt_set(
4112 __isl_take isl_pw_aff_list *list1,
4113 __isl_take isl_pw_aff_list *list2);
4115 The function C<isl_aff_neg_basic_set> returns a basic set
4116 containing those elements in the domain space
4117 of C<aff> where C<aff> is negative.
4118 The function C<isl_aff_ge_basic_set> returns a basic set
4119 containing those elements in the shared space
4120 of C<aff1> and C<aff2> where C<aff1> is greater than or equal to C<aff2>.
4121 The function C<isl_pw_aff_ge_set> returns a set
4122 containing those elements in the shared domain
4123 of C<pwaff1> and C<pwaff2> where C<pwaff1> is greater than or equal to C<pwaff2>.
4124 The functions operating on C<isl_pw_aff_list> apply the corresponding
4125 C<isl_pw_aff> function to each pair of elements in the two lists.
4127 #include <isl/aff.h>
4128 __isl_give isl_set *isl_pw_aff_nonneg_set(
4129 __isl_take isl_pw_aff *pwaff);
4130 __isl_give isl_set *isl_pw_aff_zero_set(
4131 __isl_take isl_pw_aff *pwaff);
4132 __isl_give isl_set *isl_pw_aff_non_zero_set(
4133 __isl_take isl_pw_aff *pwaff);
4135 The function C<isl_pw_aff_nonneg_set> returns a set
4136 containing those elements in the domain
4137 of C<pwaff> where C<pwaff> is non-negative.
4139 #include <isl/aff.h>
4140 __isl_give isl_pw_aff *isl_pw_aff_cond(
4141 __isl_take isl_pw_aff *cond,
4142 __isl_take isl_pw_aff *pwaff_true,
4143 __isl_take isl_pw_aff *pwaff_false);
4145 The function C<isl_pw_aff_cond> performs a conditional operator
4146 and returns an expression that is equal to C<pwaff_true>
4147 for elements where C<cond> is non-zero and equal to C<pwaff_false> for elements
4148 where C<cond> is zero.
4150 #include <isl/aff.h>
4151 __isl_give isl_pw_aff *isl_pw_aff_union_min(
4152 __isl_take isl_pw_aff *pwaff1,
4153 __isl_take isl_pw_aff *pwaff2);
4154 __isl_give isl_pw_aff *isl_pw_aff_union_max(
4155 __isl_take isl_pw_aff *pwaff1,
4156 __isl_take isl_pw_aff *pwaff2);
4157 __isl_give isl_pw_aff *isl_pw_aff_union_add(
4158 __isl_take isl_pw_aff *pwaff1,
4159 __isl_take isl_pw_aff *pwaff2);
4161 The function C<isl_pw_aff_union_max> computes a piecewise quasi-affine
4162 expression with a domain that is the union of those of C<pwaff1> and
4163 C<pwaff2> and such that on each cell, the quasi-affine expression is
4164 the maximum of those of C<pwaff1> and C<pwaff2>. If only one of
4165 C<pwaff1> or C<pwaff2> is defined on a given cell, then the
4166 associated expression is the defined one.
4168 An expression can be read from input using
4170 #include <isl/aff.h>
4171 __isl_give isl_aff *isl_aff_read_from_str(
4172 isl_ctx *ctx, const char *str);
4173 __isl_give isl_pw_aff *isl_pw_aff_read_from_str(
4174 isl_ctx *ctx, const char *str);
4176 An expression can be printed using
4178 #include <isl/aff.h>
4179 __isl_give isl_printer *isl_printer_print_aff(
4180 __isl_take isl_printer *p, __isl_keep isl_aff *aff);
4182 __isl_give isl_printer *isl_printer_print_pw_aff(
4183 __isl_take isl_printer *p,
4184 __isl_keep isl_pw_aff *pwaff);
4186 =head2 Piecewise Multiple Quasi Affine Expressions
4188 An C<isl_multi_aff> object represents a sequence of
4189 zero or more affine expressions, all defined on the same domain space.
4190 Similarly, an C<isl_multi_pw_aff> object represents a sequence of
4191 zero or more piecewise affine expressions.
4193 An C<isl_multi_aff> can be constructed from a single
4194 C<isl_aff> or an C<isl_aff_list> using the
4195 following functions. Similarly for C<isl_multi_pw_aff>
4196 and C<isl_pw_multi_aff>.
4198 #include <isl/aff.h>
4199 __isl_give isl_multi_aff *isl_multi_aff_from_aff(
4200 __isl_take isl_aff *aff);
4201 __isl_give isl_multi_pw_aff *
4202 isl_multi_pw_aff_from_multi_aff(
4203 __isl_take isl_multi_aff *ma);
4204 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_from_pw_aff(
4205 __isl_take isl_pw_aff *pa);
4206 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_from_pw_aff(
4207 __isl_take isl_pw_aff *pa);
4208 __isl_give isl_multi_aff *isl_multi_aff_from_aff_list(
4209 __isl_take isl_space *space,
4210 __isl_take isl_aff_list *list);
4212 An C<isl_multi_pw_aff> can be converted to an C<isl_pw_multi_aff>
4213 using the function C<isl_pw_multi_aff_from_multi_pw_aff> below.
4214 Note however that the domain
4215 of the result is the intersection of the domains of the input.
4216 The reverse conversion is exact.
4218 #include <isl/aff.h>
4219 __isl_give isl_pw_multi_aff *
4220 isl_pw_multi_aff_from_multi_pw_aff(
4221 __isl_take isl_multi_pw_aff *mpa);
4222 __isl_give isl_multi_pw_aff *
4223 isl_multi_pw_aff_from_pw_multi_aff(
4224 __isl_take isl_pw_multi_aff *pma);
4226 An empty piecewise multiple quasi affine expression (one with no cells),
4227 the zero piecewise multiple quasi affine expression (with value zero
4228 for each output dimension),
4229 a piecewise multiple quasi affine expression with a single cell (with
4230 either a universe or a specified domain) or
4231 a zero-dimensional piecewise multiple quasi affine expression
4233 can be created using the following functions.
4235 #include <isl/aff.h>
4236 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_empty(
4237 __isl_take isl_space *space);
4238 __isl_give isl_multi_aff *isl_multi_aff_zero(
4239 __isl_take isl_space *space);
4240 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_zero(
4241 __isl_take isl_space *space);
4242 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_zero(
4243 __isl_take isl_space *space);
4244 __isl_give isl_multi_aff *isl_multi_aff_identity(
4245 __isl_take isl_space *space);
4246 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_identity(
4247 __isl_take isl_space *space);
4248 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_identity(
4249 __isl_take isl_space *space);
4250 __isl_give isl_multi_aff *isl_multi_aff_domain_map(
4251 __isl_take isl_space *space);
4252 __isl_give isl_multi_aff *isl_multi_aff_range_map(
4253 __isl_take isl_space *space);
4254 __isl_give isl_multi_aff *isl_multi_aff_project_out_map(
4255 __isl_take isl_space *space,
4256 enum isl_dim_type type,
4257 unsigned first, unsigned n);
4258 __isl_give isl_pw_multi_aff *
4259 isl_pw_multi_aff_project_out_map(
4260 __isl_take isl_space *space,
4261 enum isl_dim_type type,
4262 unsigned first, unsigned n);
4263 __isl_give isl_pw_multi_aff *
4264 isl_pw_multi_aff_from_multi_aff(
4265 __isl_take isl_multi_aff *ma);
4266 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_alloc(
4267 __isl_take isl_set *set,
4268 __isl_take isl_multi_aff *maff);
4269 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_from_domain(
4270 __isl_take isl_set *set);
4272 __isl_give isl_union_pw_multi_aff *
4273 isl_union_pw_multi_aff_empty(
4274 __isl_take isl_space *space);
4275 __isl_give isl_union_pw_multi_aff *
4276 isl_union_pw_multi_aff_add_pw_multi_aff(
4277 __isl_take isl_union_pw_multi_aff *upma,
4278 __isl_take isl_pw_multi_aff *pma);
4279 __isl_give isl_union_pw_multi_aff *
4280 isl_union_pw_multi_aff_from_domain(
4281 __isl_take isl_union_set *uset);
4283 A piecewise multiple quasi affine expression can also be initialized
4284 from an C<isl_set> or C<isl_map>, provided the C<isl_set> is a singleton
4285 and the C<isl_map> is single-valued.
4286 In case of a conversion from an C<isl_union_set> or an C<isl_union_map>
4287 to an C<isl_union_pw_multi_aff>, these properties need to hold in each space.
4289 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_from_set(
4290 __isl_take isl_set *set);
4291 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_from_map(
4292 __isl_take isl_map *map);
4294 __isl_give isl_union_pw_multi_aff *
4295 isl_union_pw_multi_aff_from_union_set(
4296 __isl_take isl_union_set *uset);
4297 __isl_give isl_union_pw_multi_aff *
4298 isl_union_pw_multi_aff_from_union_map(
4299 __isl_take isl_union_map *umap);
4301 Multiple quasi affine expressions can be copied and freed using
4303 #include <isl/aff.h>
4304 __isl_give isl_multi_aff *isl_multi_aff_copy(
4305 __isl_keep isl_multi_aff *maff);
4306 void *isl_multi_aff_free(__isl_take isl_multi_aff *maff);
4308 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_copy(
4309 __isl_keep isl_pw_multi_aff *pma);
4310 void *isl_pw_multi_aff_free(
4311 __isl_take isl_pw_multi_aff *pma);
4313 __isl_give isl_union_pw_multi_aff *
4314 isl_union_pw_multi_aff_copy(
4315 __isl_keep isl_union_pw_multi_aff *upma);
4316 void *isl_union_pw_multi_aff_free(
4317 __isl_take isl_union_pw_multi_aff *upma);
4319 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_copy(
4320 __isl_keep isl_multi_pw_aff *mpa);
4321 void *isl_multi_pw_aff_free(
4322 __isl_take isl_multi_pw_aff *mpa);
4324 The expression can be inspected using
4326 #include <isl/aff.h>
4327 isl_ctx *isl_multi_aff_get_ctx(
4328 __isl_keep isl_multi_aff *maff);
4329 isl_ctx *isl_pw_multi_aff_get_ctx(
4330 __isl_keep isl_pw_multi_aff *pma);
4331 isl_ctx *isl_union_pw_multi_aff_get_ctx(
4332 __isl_keep isl_union_pw_multi_aff *upma);
4333 isl_ctx *isl_multi_pw_aff_get_ctx(
4334 __isl_keep isl_multi_pw_aff *mpa);
4335 unsigned isl_multi_aff_dim(__isl_keep isl_multi_aff *maff,
4336 enum isl_dim_type type);
4337 unsigned isl_pw_multi_aff_dim(
4338 __isl_keep isl_pw_multi_aff *pma,
4339 enum isl_dim_type type);
4340 unsigned isl_multi_pw_aff_dim(
4341 __isl_keep isl_multi_pw_aff *mpa,
4342 enum isl_dim_type type);
4343 __isl_give isl_aff *isl_multi_aff_get_aff(
4344 __isl_keep isl_multi_aff *multi, int pos);
4345 __isl_give isl_pw_aff *isl_pw_multi_aff_get_pw_aff(
4346 __isl_keep isl_pw_multi_aff *pma, int pos);
4347 __isl_give isl_pw_aff *isl_multi_pw_aff_get_pw_aff(
4348 __isl_keep isl_multi_pw_aff *mpa, int pos);
4349 int isl_multi_aff_find_dim_by_id(
4350 __isl_keep isl_multi_aff *ma,
4351 enum isl_dim_type type, __isl_keep isl_id *id);
4352 int isl_multi_pw_aff_find_dim_by_id(
4353 __isl_keep isl_multi_pw_aff *mpa,
4354 enum isl_dim_type type, __isl_keep isl_id *id);
4355 const char *isl_pw_multi_aff_get_dim_name(
4356 __isl_keep isl_pw_multi_aff *pma,
4357 enum isl_dim_type type, unsigned pos);
4358 __isl_give isl_id *isl_multi_aff_get_dim_id(
4359 __isl_keep isl_multi_aff *ma,
4360 enum isl_dim_type type, unsigned pos);
4361 __isl_give isl_id *isl_pw_multi_aff_get_dim_id(
4362 __isl_keep isl_pw_multi_aff *pma,
4363 enum isl_dim_type type, unsigned pos);
4364 __isl_give isl_id *isl_multi_pw_aff_get_dim_id(
4365 __isl_keep isl_multi_pw_aff *mpa,
4366 enum isl_dim_type type, unsigned pos);
4367 const char *isl_multi_aff_get_tuple_name(
4368 __isl_keep isl_multi_aff *multi,
4369 enum isl_dim_type type);
4370 int isl_pw_multi_aff_has_tuple_name(
4371 __isl_keep isl_pw_multi_aff *pma,
4372 enum isl_dim_type type);
4373 const char *isl_pw_multi_aff_get_tuple_name(
4374 __isl_keep isl_pw_multi_aff *pma,
4375 enum isl_dim_type type);
4376 int isl_multi_aff_has_tuple_id(__isl_keep isl_multi_aff *ma,
4377 enum isl_dim_type type);
4378 int isl_pw_multi_aff_has_tuple_id(
4379 __isl_keep isl_pw_multi_aff *pma,
4380 enum isl_dim_type type);
4381 int isl_multi_pw_aff_has_tuple_id(
4382 __isl_keep isl_multi_pw_aff *mpa,
4383 enum isl_dim_type type);
4384 __isl_give isl_id *isl_multi_aff_get_tuple_id(
4385 __isl_keep isl_multi_aff *ma,
4386 enum isl_dim_type type);
4387 __isl_give isl_id *isl_pw_multi_aff_get_tuple_id(
4388 __isl_keep isl_pw_multi_aff *pma,
4389 enum isl_dim_type type);
4390 __isl_give isl_id *isl_multi_pw_aff_get_tuple_id(
4391 __isl_keep isl_multi_pw_aff *mpa,
4392 enum isl_dim_type type);
4393 int isl_multi_aff_range_is_wrapping(
4394 __isl_keep isl_multi_aff *ma);
4395 int isl_multi_pw_aff_range_is_wrapping(
4396 __isl_keep isl_multi_pw_aff *mpa);
4398 int isl_pw_multi_aff_foreach_piece(
4399 __isl_keep isl_pw_multi_aff *pma,
4400 int (*fn)(__isl_take isl_set *set,
4401 __isl_take isl_multi_aff *maff,
4402 void *user), void *user);
4404 int isl_union_pw_multi_aff_foreach_pw_multi_aff(
4405 __isl_keep isl_union_pw_multi_aff *upma,
4406 int (*fn)(__isl_take isl_pw_multi_aff *pma,
4407 void *user), void *user);
4409 It can be modified using
4411 #include <isl/aff.h>
4412 __isl_give isl_multi_aff *isl_multi_aff_set_aff(
4413 __isl_take isl_multi_aff *multi, int pos,
4414 __isl_take isl_aff *aff);
4415 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_set_pw_aff(
4416 __isl_take isl_pw_multi_aff *pma, unsigned pos,
4417 __isl_take isl_pw_aff *pa);
4418 __isl_give isl_multi_aff *isl_multi_aff_set_dim_name(
4419 __isl_take isl_multi_aff *maff,
4420 enum isl_dim_type type, unsigned pos, const char *s);
4421 __isl_give isl_multi_aff *isl_multi_aff_set_dim_id(
4422 __isl_take isl_multi_aff *maff,
4423 enum isl_dim_type type, unsigned pos,
4424 __isl_take isl_id *id);
4425 __isl_give isl_multi_aff *isl_multi_aff_set_tuple_name(
4426 __isl_take isl_multi_aff *maff,
4427 enum isl_dim_type type, const char *s);
4428 __isl_give isl_multi_aff *isl_multi_aff_set_tuple_id(
4429 __isl_take isl_multi_aff *maff,
4430 enum isl_dim_type type, __isl_take isl_id *id);
4431 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_set_tuple_id(
4432 __isl_take isl_pw_multi_aff *pma,
4433 enum isl_dim_type type, __isl_take isl_id *id);
4434 __isl_give isl_multi_aff *isl_multi_aff_reset_tuple_id(
4435 __isl_take isl_multi_aff *ma,
4436 enum isl_dim_type type);
4437 __isl_give isl_multi_pw_aff *
4438 isl_multi_pw_aff_reset_tuple_id(
4439 __isl_take isl_multi_pw_aff *mpa,
4440 enum isl_dim_type type);
4441 __isl_give isl_multi_aff *isl_multi_aff_reset_user(
4442 __isl_take isl_multi_aff *ma);
4443 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_reset_user(
4444 __isl_take isl_multi_pw_aff *mpa);
4446 __isl_give isl_multi_pw_aff *
4447 isl_multi_pw_aff_set_dim_name(
4448 __isl_take isl_multi_pw_aff *mpa,
4449 enum isl_dim_type type, unsigned pos, const char *s);
4450 __isl_give isl_multi_pw_aff *
4451 isl_multi_pw_aff_set_dim_id(
4452 __isl_take isl_multi_pw_aff *mpa,
4453 enum isl_dim_type type, unsigned pos,
4454 __isl_take isl_id *id);
4455 __isl_give isl_multi_pw_aff *
4456 isl_multi_pw_aff_set_tuple_name(
4457 __isl_take isl_multi_pw_aff *mpa,
4458 enum isl_dim_type type, const char *s);
4460 __isl_give isl_multi_aff *isl_multi_aff_insert_dims(
4461 __isl_take isl_multi_aff *ma,
4462 enum isl_dim_type type, unsigned first, unsigned n);
4463 __isl_give isl_multi_aff *isl_multi_aff_add_dims(
4464 __isl_take isl_multi_aff *ma,
4465 enum isl_dim_type type, unsigned n);
4466 __isl_give isl_multi_aff *isl_multi_aff_drop_dims(
4467 __isl_take isl_multi_aff *maff,
4468 enum isl_dim_type type, unsigned first, unsigned n);
4469 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_drop_dims(
4470 __isl_take isl_pw_multi_aff *pma,
4471 enum isl_dim_type type, unsigned first, unsigned n);
4473 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_insert_dims(
4474 __isl_take isl_multi_pw_aff *mpa,
4475 enum isl_dim_type type, unsigned first, unsigned n);
4476 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_add_dims(
4477 __isl_take isl_multi_pw_aff *mpa,
4478 enum isl_dim_type type, unsigned n);
4479 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_move_dims(
4480 __isl_take isl_multi_pw_aff *pma,
4481 enum isl_dim_type dst_type, unsigned dst_pos,
4482 enum isl_dim_type src_type, unsigned src_pos,
4485 To check whether two multiple affine expressions are
4486 (obviously) equal to each other, use
4488 int isl_multi_aff_plain_is_equal(__isl_keep isl_multi_aff *maff1,
4489 __isl_keep isl_multi_aff *maff2);
4490 int isl_pw_multi_aff_plain_is_equal(
4491 __isl_keep isl_pw_multi_aff *pma1,
4492 __isl_keep isl_pw_multi_aff *pma2);
4493 int isl_multi_pw_aff_plain_is_equal(
4494 __isl_keep isl_multi_pw_aff *mpa1,
4495 __isl_keep isl_multi_pw_aff *mpa2);
4496 int isl_multi_pw_aff_is_equal(
4497 __isl_keep isl_multi_pw_aff *mpa1,
4498 __isl_keep isl_multi_pw_aff *mpa2);
4502 #include <isl/aff.h>
4503 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_union_lexmin(
4504 __isl_take isl_pw_multi_aff *pma1,
4505 __isl_take isl_pw_multi_aff *pma2);
4506 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_union_lexmax(
4507 __isl_take isl_pw_multi_aff *pma1,
4508 __isl_take isl_pw_multi_aff *pma2);
4509 __isl_give isl_multi_aff *isl_multi_aff_add(
4510 __isl_take isl_multi_aff *maff1,
4511 __isl_take isl_multi_aff *maff2);
4512 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_add(
4513 __isl_take isl_pw_multi_aff *pma1,
4514 __isl_take isl_pw_multi_aff *pma2);
4515 __isl_give isl_union_pw_multi_aff *isl_union_pw_multi_aff_add(
4516 __isl_take isl_union_pw_multi_aff *upma1,
4517 __isl_take isl_union_pw_multi_aff *upma2);
4518 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_union_add(
4519 __isl_take isl_pw_multi_aff *pma1,
4520 __isl_take isl_pw_multi_aff *pma2);
4521 __isl_give isl_multi_aff *isl_multi_aff_sub(
4522 __isl_take isl_multi_aff *ma1,
4523 __isl_take isl_multi_aff *ma2);
4524 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_sub(
4525 __isl_take isl_pw_multi_aff *pma1,
4526 __isl_take isl_pw_multi_aff *pma2);
4527 __isl_give isl_union_pw_multi_aff *isl_union_pw_multi_aff_sub(
4528 __isl_take isl_union_pw_multi_aff *upma1,
4529 __isl_take isl_union_pw_multi_aff *upma2);
4531 C<isl_multi_aff_sub> subtracts the second argument from the first.
4533 __isl_give isl_multi_aff *isl_multi_aff_scale_val(
4534 __isl_take isl_multi_aff *ma,
4535 __isl_take isl_val *v);
4536 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_scale_val(
4537 __isl_take isl_pw_multi_aff *pma,
4538 __isl_take isl_val *v);
4539 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_scale_val(
4540 __isl_take isl_multi_pw_aff *mpa,
4541 __isl_take isl_val *v);
4542 __isl_give isl_multi_aff *isl_multi_aff_scale_multi_val(
4543 __isl_take isl_multi_aff *ma,
4544 __isl_take isl_multi_val *mv);
4545 __isl_give isl_pw_multi_aff *
4546 isl_pw_multi_aff_scale_multi_val(
4547 __isl_take isl_pw_multi_aff *pma,
4548 __isl_take isl_multi_val *mv);
4549 __isl_give isl_multi_pw_aff *
4550 isl_multi_pw_aff_scale_multi_val(
4551 __isl_take isl_multi_pw_aff *mpa,
4552 __isl_take isl_multi_val *mv);
4553 __isl_give isl_union_pw_multi_aff *
4554 isl_union_pw_multi_aff_scale_multi_val(
4555 __isl_take isl_union_pw_multi_aff *upma,
4556 __isl_take isl_multi_val *mv);
4557 __isl_give isl_multi_aff *
4558 isl_multi_aff_scale_down_multi_val(
4559 __isl_take isl_multi_aff *ma,
4560 __isl_take isl_multi_val *mv);
4561 __isl_give isl_multi_pw_aff *
4562 isl_multi_pw_aff_scale_down_multi_val(
4563 __isl_take isl_multi_pw_aff *mpa,
4564 __isl_take isl_multi_val *mv);
4566 C<isl_multi_aff_scale_multi_val> scales the elements of C<ma>
4567 by the corresponding elements of C<mv>.
4569 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_fix_si(
4570 __isl_take isl_pw_multi_aff *pma,
4571 enum isl_dim_type type, unsigned pos, int value);
4572 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_intersect_params(
4573 __isl_take isl_pw_multi_aff *pma,
4574 __isl_take isl_set *set);
4575 __isl_give isl_set *isl_multi_pw_aff_domain(
4576 __isl_take isl_multi_pw_aff *mpa);
4577 __isl_give isl_multi_pw_aff *
4578 isl_multi_pw_aff_intersect_params(
4579 __isl_take isl_multi_pw_aff *mpa,
4580 __isl_take isl_set *set);
4581 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_intersect_domain(
4582 __isl_take isl_pw_multi_aff *pma,
4583 __isl_take isl_set *set);
4584 __isl_give isl_multi_pw_aff *
4585 isl_multi_pw_aff_intersect_domain(
4586 __isl_take isl_multi_pw_aff *mpa,
4587 __isl_take isl_set *domain);
4588 __isl_give isl_union_pw_multi_aff *
4589 isl_union_pw_multi_aff_intersect_domain(
4590 __isl_take isl_union_pw_multi_aff *upma,
4591 __isl_take isl_union_set *uset);
4592 __isl_give isl_multi_aff *isl_multi_aff_lift(
4593 __isl_take isl_multi_aff *maff,
4594 __isl_give isl_local_space **ls);
4595 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_coalesce(
4596 __isl_take isl_pw_multi_aff *pma);
4597 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_coalesce(
4598 __isl_take isl_multi_pw_aff *mpa);
4599 __isl_give isl_multi_aff *isl_multi_aff_align_params(
4600 __isl_take isl_multi_aff *multi,
4601 __isl_take isl_space *model);
4602 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_align_params(
4603 __isl_take isl_pw_multi_aff *pma,
4604 __isl_take isl_space *model);
4605 __isl_give isl_pw_multi_aff *
4606 isl_pw_multi_aff_project_domain_on_params(
4607 __isl_take isl_pw_multi_aff *pma);
4608 __isl_give isl_multi_aff *isl_multi_aff_gist_params(
4609 __isl_take isl_multi_aff *maff,
4610 __isl_take isl_set *context);
4611 __isl_give isl_multi_aff *isl_multi_aff_gist(
4612 __isl_take isl_multi_aff *maff,
4613 __isl_take isl_set *context);
4614 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_gist_params(
4615 __isl_take isl_pw_multi_aff *pma,
4616 __isl_take isl_set *set);
4617 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_gist(
4618 __isl_take isl_pw_multi_aff *pma,
4619 __isl_take isl_set *set);
4620 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_gist_params(
4621 __isl_take isl_multi_pw_aff *mpa,
4622 __isl_take isl_set *set);
4623 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_gist(
4624 __isl_take isl_multi_pw_aff *mpa,
4625 __isl_take isl_set *set);
4626 __isl_give isl_multi_aff *isl_multi_aff_from_range(
4627 __isl_take isl_multi_aff *ma);
4628 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_from_range(
4629 __isl_take isl_multi_pw_aff *mpa);
4630 __isl_give isl_set *isl_pw_multi_aff_domain(
4631 __isl_take isl_pw_multi_aff *pma);
4632 __isl_give isl_union_set *isl_union_pw_multi_aff_domain(
4633 __isl_take isl_union_pw_multi_aff *upma);
4634 __isl_give isl_multi_aff *isl_multi_aff_range_splice(
4635 __isl_take isl_multi_aff *ma1, unsigned pos,
4636 __isl_take isl_multi_aff *ma2);
4637 __isl_give isl_multi_aff *isl_multi_aff_splice(
4638 __isl_take isl_multi_aff *ma1,
4639 unsigned in_pos, unsigned out_pos,
4640 __isl_take isl_multi_aff *ma2);
4641 __isl_give isl_multi_aff *isl_multi_aff_range_product(
4642 __isl_take isl_multi_aff *ma1,
4643 __isl_take isl_multi_aff *ma2);
4644 __isl_give isl_multi_aff *
4645 isl_multi_aff_range_factor_domain(
4646 __isl_take isl_multi_aff *ma);
4647 __isl_give isl_multi_aff *
4648 isl_multi_aff_range_factor_range(
4649 __isl_take isl_multi_aff *ma);
4650 __isl_give isl_multi_aff *isl_multi_aff_flat_range_product(
4651 __isl_take isl_multi_aff *ma1,
4652 __isl_take isl_multi_aff *ma2);
4653 __isl_give isl_multi_aff *isl_multi_aff_product(
4654 __isl_take isl_multi_aff *ma1,
4655 __isl_take isl_multi_aff *ma2);
4656 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_product(
4657 __isl_take isl_multi_pw_aff *mpa1,
4658 __isl_take isl_multi_pw_aff *mpa2);
4659 __isl_give isl_pw_multi_aff *
4660 isl_pw_multi_aff_range_product(
4661 __isl_take isl_pw_multi_aff *pma1,
4662 __isl_take isl_pw_multi_aff *pma2);
4663 __isl_give isl_multi_pw_aff *
4664 isl_multi_pw_aff_range_factor_domain(
4665 __isl_take isl_multi_pw_aff *mpa);
4666 __isl_give isl_multi_pw_aff *
4667 isl_multi_pw_aff_range_factor_range(
4668 __isl_take isl_multi_pw_aff *mpa);
4669 __isl_give isl_pw_multi_aff *
4670 isl_pw_multi_aff_flat_range_product(
4671 __isl_take isl_pw_multi_aff *pma1,
4672 __isl_take isl_pw_multi_aff *pma2);
4673 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_product(
4674 __isl_take isl_pw_multi_aff *pma1,
4675 __isl_take isl_pw_multi_aff *pma2);
4676 __isl_give isl_union_pw_multi_aff *
4677 isl_union_pw_multi_aff_flat_range_product(
4678 __isl_take isl_union_pw_multi_aff *upma1,
4679 __isl_take isl_union_pw_multi_aff *upma2);
4680 __isl_give isl_multi_pw_aff *
4681 isl_multi_pw_aff_range_splice(
4682 __isl_take isl_multi_pw_aff *mpa1, unsigned pos,
4683 __isl_take isl_multi_pw_aff *mpa2);
4684 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_splice(
4685 __isl_take isl_multi_pw_aff *mpa1,
4686 unsigned in_pos, unsigned out_pos,
4687 __isl_take isl_multi_pw_aff *mpa2);
4688 __isl_give isl_multi_pw_aff *
4689 isl_multi_pw_aff_range_product(
4690 __isl_take isl_multi_pw_aff *mpa1,
4691 __isl_take isl_multi_pw_aff *mpa2);
4692 __isl_give isl_multi_pw_aff *
4693 isl_multi_pw_aff_flat_range_product(
4694 __isl_take isl_multi_pw_aff *mpa1,
4695 __isl_take isl_multi_pw_aff *mpa2);
4697 If the C<ls> argument of C<isl_multi_aff_lift> is not C<NULL>,
4698 then it is assigned the local space that lies at the basis of
4699 the lifting applied.
4701 #include <isl/aff.h>
4702 __isl_give isl_multi_aff *isl_multi_aff_pullback_multi_aff(
4703 __isl_take isl_multi_aff *ma1,
4704 __isl_take isl_multi_aff *ma2);
4705 __isl_give isl_pw_multi_aff *
4706 isl_pw_multi_aff_pullback_multi_aff(
4707 __isl_take isl_pw_multi_aff *pma,
4708 __isl_take isl_multi_aff *ma);
4709 __isl_give isl_multi_pw_aff *
4710 isl_multi_pw_aff_pullback_multi_aff(
4711 __isl_take isl_multi_pw_aff *mpa,
4712 __isl_take isl_multi_aff *ma);
4713 __isl_give isl_pw_multi_aff *
4714 isl_pw_multi_aff_pullback_pw_multi_aff(
4715 __isl_take isl_pw_multi_aff *pma1,
4716 __isl_take isl_pw_multi_aff *pma2);
4717 __isl_give isl_multi_pw_aff *
4718 isl_multi_pw_aff_pullback_pw_multi_aff(
4719 __isl_take isl_multi_pw_aff *mpa,
4720 __isl_take isl_pw_multi_aff *pma);
4721 __isl_give isl_multi_pw_aff *
4722 isl_multi_pw_aff_pullback_multi_pw_aff(
4723 __isl_take isl_multi_pw_aff *mpa1,
4724 __isl_take isl_multi_pw_aff *mpa2);
4726 The function C<isl_multi_aff_pullback_multi_aff> precomposes C<ma1> by C<ma2>.
4727 In other words, C<ma2> is plugged
4730 __isl_give isl_set *isl_multi_aff_lex_le_set(
4731 __isl_take isl_multi_aff *ma1,
4732 __isl_take isl_multi_aff *ma2);
4733 __isl_give isl_set *isl_multi_aff_lex_ge_set(
4734 __isl_take isl_multi_aff *ma1,
4735 __isl_take isl_multi_aff *ma2);
4737 The function C<isl_multi_aff_lex_le_set> returns a set
4738 containing those elements in the shared domain space
4739 where C<ma1> is lexicographically smaller than or
4742 An expression can be read from input using
4744 #include <isl/aff.h>
4745 __isl_give isl_multi_aff *isl_multi_aff_read_from_str(
4746 isl_ctx *ctx, const char *str);
4747 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_read_from_str(
4748 isl_ctx *ctx, const char *str);
4749 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_read_from_str(
4750 isl_ctx *ctx, const char *str);
4751 __isl_give isl_union_pw_multi_aff *
4752 isl_union_pw_multi_aff_read_from_str(
4753 isl_ctx *ctx, const char *str);
4755 An expression can be printed using
4757 #include <isl/aff.h>
4758 __isl_give isl_printer *isl_printer_print_multi_aff(
4759 __isl_take isl_printer *p,
4760 __isl_keep isl_multi_aff *maff);
4761 __isl_give isl_printer *isl_printer_print_pw_multi_aff(
4762 __isl_take isl_printer *p,
4763 __isl_keep isl_pw_multi_aff *pma);
4764 __isl_give isl_printer *isl_printer_print_union_pw_multi_aff(
4765 __isl_take isl_printer *p,
4766 __isl_keep isl_union_pw_multi_aff *upma);
4767 __isl_give isl_printer *isl_printer_print_multi_pw_aff(
4768 __isl_take isl_printer *p,
4769 __isl_keep isl_multi_pw_aff *mpa);
4773 Points are elements of a set. They can be used to construct
4774 simple sets (boxes) or they can be used to represent the
4775 individual elements of a set.
4776 The zero point (the origin) can be created using
4778 __isl_give isl_point *isl_point_zero(__isl_take isl_space *space);
4780 The coordinates of a point can be inspected, set and changed
4783 __isl_give isl_val *isl_point_get_coordinate_val(
4784 __isl_keep isl_point *pnt,
4785 enum isl_dim_type type, int pos);
4786 __isl_give isl_point *isl_point_set_coordinate_val(
4787 __isl_take isl_point *pnt,
4788 enum isl_dim_type type, int pos,
4789 __isl_take isl_val *v);
4791 __isl_give isl_point *isl_point_add_ui(
4792 __isl_take isl_point *pnt,
4793 enum isl_dim_type type, int pos, unsigned val);
4794 __isl_give isl_point *isl_point_sub_ui(
4795 __isl_take isl_point *pnt,
4796 enum isl_dim_type type, int pos, unsigned val);
4798 Other properties can be obtained using
4800 isl_ctx *isl_point_get_ctx(__isl_keep isl_point *pnt);
4802 Points can be copied or freed using
4804 __isl_give isl_point *isl_point_copy(
4805 __isl_keep isl_point *pnt);
4806 void isl_point_free(__isl_take isl_point *pnt);
4808 A singleton set can be created from a point using
4810 __isl_give isl_basic_set *isl_basic_set_from_point(
4811 __isl_take isl_point *pnt);
4812 __isl_give isl_set *isl_set_from_point(
4813 __isl_take isl_point *pnt);
4815 and a box can be created from two opposite extremal points using
4817 __isl_give isl_basic_set *isl_basic_set_box_from_points(
4818 __isl_take isl_point *pnt1,
4819 __isl_take isl_point *pnt2);
4820 __isl_give isl_set *isl_set_box_from_points(
4821 __isl_take isl_point *pnt1,
4822 __isl_take isl_point *pnt2);
4824 All elements of a B<bounded> (union) set can be enumerated using
4825 the following functions.
4827 int isl_set_foreach_point(__isl_keep isl_set *set,
4828 int (*fn)(__isl_take isl_point *pnt, void *user),
4830 int isl_union_set_foreach_point(__isl_keep isl_union_set *uset,
4831 int (*fn)(__isl_take isl_point *pnt, void *user),
4834 The function C<fn> is called for each integer point in
4835 C<set> with as second argument the last argument of
4836 the C<isl_set_foreach_point> call. The function C<fn>
4837 should return C<0> on success and C<-1> on failure.
4838 In the latter case, C<isl_set_foreach_point> will stop
4839 enumerating and return C<-1> as well.
4840 If the enumeration is performed successfully and to completion,
4841 then C<isl_set_foreach_point> returns C<0>.
4843 To obtain a single point of a (basic) set, use
4845 __isl_give isl_point *isl_basic_set_sample_point(
4846 __isl_take isl_basic_set *bset);
4847 __isl_give isl_point *isl_set_sample_point(
4848 __isl_take isl_set *set);
4850 If C<set> does not contain any (integer) points, then the
4851 resulting point will be ``void'', a property that can be
4854 int isl_point_is_void(__isl_keep isl_point *pnt);
4856 =head2 Piecewise Quasipolynomials
4858 A piecewise quasipolynomial is a particular kind of function that maps
4859 a parametric point to a rational value.
4860 More specifically, a quasipolynomial is a polynomial expression in greatest
4861 integer parts of affine expressions of parameters and variables.
4862 A piecewise quasipolynomial is a subdivision of a given parametric
4863 domain into disjoint cells with a quasipolynomial associated to
4864 each cell. The value of the piecewise quasipolynomial at a given
4865 point is the value of the quasipolynomial associated to the cell
4866 that contains the point. Outside of the union of cells,
4867 the value is assumed to be zero.
4868 For example, the piecewise quasipolynomial
4870 [n] -> { [x] -> ((1 + n) - x) : x <= n and x >= 0 }
4872 maps C<x> to C<1 + n - x> for values of C<x> between C<0> and C<n>.
4873 A given piecewise quasipolynomial has a fixed domain dimension.
4874 Union piecewise quasipolynomials are used to contain piecewise quasipolynomials
4875 defined over different domains.
4876 Piecewise quasipolynomials are mainly used by the C<barvinok>
4877 library for representing the number of elements in a parametric set or map.
4878 For example, the piecewise quasipolynomial above represents
4879 the number of points in the map
4881 [n] -> { [x] -> [y] : x,y >= 0 and 0 <= x + y <= n }
4883 =head3 Input and Output
4885 Piecewise quasipolynomials can be read from input using
4887 __isl_give isl_union_pw_qpolynomial *
4888 isl_union_pw_qpolynomial_read_from_str(
4889 isl_ctx *ctx, const char *str);
4891 Quasipolynomials and piecewise quasipolynomials can be printed
4892 using the following functions.
4894 __isl_give isl_printer *isl_printer_print_qpolynomial(
4895 __isl_take isl_printer *p,
4896 __isl_keep isl_qpolynomial *qp);
4898 __isl_give isl_printer *isl_printer_print_pw_qpolynomial(
4899 __isl_take isl_printer *p,
4900 __isl_keep isl_pw_qpolynomial *pwqp);
4902 __isl_give isl_printer *isl_printer_print_union_pw_qpolynomial(
4903 __isl_take isl_printer *p,
4904 __isl_keep isl_union_pw_qpolynomial *upwqp);
4906 The output format of the printer
4907 needs to be set to either C<ISL_FORMAT_ISL> or C<ISL_FORMAT_C>.
4908 For C<isl_printer_print_union_pw_qpolynomial>, only C<ISL_FORMAT_ISL>
4910 In case of printing in C<ISL_FORMAT_C>, the user may want
4911 to set the names of all dimensions
4913 __isl_give isl_qpolynomial *isl_qpolynomial_set_dim_name(
4914 __isl_take isl_qpolynomial *qp,
4915 enum isl_dim_type type, unsigned pos,
4917 __isl_give isl_pw_qpolynomial *
4918 isl_pw_qpolynomial_set_dim_name(
4919 __isl_take isl_pw_qpolynomial *pwqp,
4920 enum isl_dim_type type, unsigned pos,
4923 =head3 Creating New (Piecewise) Quasipolynomials
4925 Some simple quasipolynomials can be created using the following functions.
4926 More complicated quasipolynomials can be created by applying
4927 operations such as addition and multiplication
4928 on the resulting quasipolynomials
4930 __isl_give isl_qpolynomial *isl_qpolynomial_zero_on_domain(
4931 __isl_take isl_space *domain);
4932 __isl_give isl_qpolynomial *isl_qpolynomial_one_on_domain(
4933 __isl_take isl_space *domain);
4934 __isl_give isl_qpolynomial *isl_qpolynomial_infty_on_domain(
4935 __isl_take isl_space *domain);
4936 __isl_give isl_qpolynomial *isl_qpolynomial_neginfty_on_domain(
4937 __isl_take isl_space *domain);
4938 __isl_give isl_qpolynomial *isl_qpolynomial_nan_on_domain(
4939 __isl_take isl_space *domain);
4940 __isl_give isl_qpolynomial *isl_qpolynomial_val_on_domain(
4941 __isl_take isl_space *domain,
4942 __isl_take isl_val *val);
4943 __isl_give isl_qpolynomial *isl_qpolynomial_var_on_domain(
4944 __isl_take isl_space *domain,
4945 enum isl_dim_type type, unsigned pos);
4946 __isl_give isl_qpolynomial *isl_qpolynomial_from_aff(
4947 __isl_take isl_aff *aff);
4949 Note that the space in which a quasipolynomial lives is a map space
4950 with a one-dimensional range. The C<domain> argument in some of
4951 the functions above corresponds to the domain of this map space.
4953 The zero piecewise quasipolynomial or a piecewise quasipolynomial
4954 with a single cell can be created using the following functions.
4955 Multiple of these single cell piecewise quasipolynomials can
4956 be combined to create more complicated piecewise quasipolynomials.
4958 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_zero(
4959 __isl_take isl_space *space);
4960 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_alloc(
4961 __isl_take isl_set *set,
4962 __isl_take isl_qpolynomial *qp);
4963 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_from_qpolynomial(
4964 __isl_take isl_qpolynomial *qp);
4965 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_from_pw_aff(
4966 __isl_take isl_pw_aff *pwaff);
4968 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_zero(
4969 __isl_take isl_space *space);
4970 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_from_pw_qpolynomial(
4971 __isl_take isl_pw_qpolynomial *pwqp);
4972 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_add_pw_qpolynomial(
4973 __isl_take isl_union_pw_qpolynomial *upwqp,
4974 __isl_take isl_pw_qpolynomial *pwqp);
4976 Quasipolynomials can be copied and freed again using the following
4979 __isl_give isl_qpolynomial *isl_qpolynomial_copy(
4980 __isl_keep isl_qpolynomial *qp);
4981 void *isl_qpolynomial_free(__isl_take isl_qpolynomial *qp);
4983 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_copy(
4984 __isl_keep isl_pw_qpolynomial *pwqp);
4985 void *isl_pw_qpolynomial_free(
4986 __isl_take isl_pw_qpolynomial *pwqp);
4988 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_copy(
4989 __isl_keep isl_union_pw_qpolynomial *upwqp);
4990 void *isl_union_pw_qpolynomial_free(
4991 __isl_take isl_union_pw_qpolynomial *upwqp);
4993 =head3 Inspecting (Piecewise) Quasipolynomials
4995 To iterate over all piecewise quasipolynomials in a union
4996 piecewise quasipolynomial, use the following function
4998 int isl_union_pw_qpolynomial_foreach_pw_qpolynomial(
4999 __isl_keep isl_union_pw_qpolynomial *upwqp,
5000 int (*fn)(__isl_take isl_pw_qpolynomial *pwqp, void *user),
5003 To extract the piecewise quasipolynomial in a given space from a union, use
5005 __isl_give isl_pw_qpolynomial *
5006 isl_union_pw_qpolynomial_extract_pw_qpolynomial(
5007 __isl_keep isl_union_pw_qpolynomial *upwqp,
5008 __isl_take isl_space *space);
5010 To iterate over the cells in a piecewise quasipolynomial,
5011 use either of the following two functions
5013 int isl_pw_qpolynomial_foreach_piece(
5014 __isl_keep isl_pw_qpolynomial *pwqp,
5015 int (*fn)(__isl_take isl_set *set,
5016 __isl_take isl_qpolynomial *qp,
5017 void *user), void *user);
5018 int isl_pw_qpolynomial_foreach_lifted_piece(
5019 __isl_keep isl_pw_qpolynomial *pwqp,
5020 int (*fn)(__isl_take isl_set *set,
5021 __isl_take isl_qpolynomial *qp,
5022 void *user), void *user);
5024 As usual, the function C<fn> should return C<0> on success
5025 and C<-1> on failure. The difference between
5026 C<isl_pw_qpolynomial_foreach_piece> and
5027 C<isl_pw_qpolynomial_foreach_lifted_piece> is that
5028 C<isl_pw_qpolynomial_foreach_lifted_piece> will first
5029 compute unique representations for all existentially quantified
5030 variables and then turn these existentially quantified variables
5031 into extra set variables, adapting the associated quasipolynomial
5032 accordingly. This means that the C<set> passed to C<fn>
5033 will not have any existentially quantified variables, but that
5034 the dimensions of the sets may be different for different
5035 invocations of C<fn>.
5037 The constant term of a quasipolynomial can be extracted using
5039 __isl_give isl_val *isl_qpolynomial_get_constant_val(
5040 __isl_keep isl_qpolynomial *qp);
5042 To iterate over all terms in a quasipolynomial,
5045 int isl_qpolynomial_foreach_term(
5046 __isl_keep isl_qpolynomial *qp,
5047 int (*fn)(__isl_take isl_term *term,
5048 void *user), void *user);
5050 The terms themselves can be inspected and freed using
5053 unsigned isl_term_dim(__isl_keep isl_term *term,
5054 enum isl_dim_type type);
5055 __isl_give isl_val *isl_term_get_coefficient_val(
5056 __isl_keep isl_term *term);
5057 int isl_term_get_exp(__isl_keep isl_term *term,
5058 enum isl_dim_type type, unsigned pos);
5059 __isl_give isl_aff *isl_term_get_div(
5060 __isl_keep isl_term *term, unsigned pos);
5061 void isl_term_free(__isl_take isl_term *term);
5063 Each term is a product of parameters, set variables and
5064 integer divisions. The function C<isl_term_get_exp>
5065 returns the exponent of a given dimensions in the given term.
5067 =head3 Properties of (Piecewise) Quasipolynomials
5069 To check whether two union piecewise quasipolynomials are
5070 obviously equal, use
5072 int isl_union_pw_qpolynomial_plain_is_equal(
5073 __isl_keep isl_union_pw_qpolynomial *upwqp1,
5074 __isl_keep isl_union_pw_qpolynomial *upwqp2);
5076 =head3 Operations on (Piecewise) Quasipolynomials
5078 __isl_give isl_qpolynomial *isl_qpolynomial_scale_val(
5079 __isl_take isl_qpolynomial *qp,
5080 __isl_take isl_val *v);
5081 __isl_give isl_qpolynomial *isl_qpolynomial_neg(
5082 __isl_take isl_qpolynomial *qp);
5083 __isl_give isl_qpolynomial *isl_qpolynomial_add(
5084 __isl_take isl_qpolynomial *qp1,
5085 __isl_take isl_qpolynomial *qp2);
5086 __isl_give isl_qpolynomial *isl_qpolynomial_sub(
5087 __isl_take isl_qpolynomial *qp1,
5088 __isl_take isl_qpolynomial *qp2);
5089 __isl_give isl_qpolynomial *isl_qpolynomial_mul(
5090 __isl_take isl_qpolynomial *qp1,
5091 __isl_take isl_qpolynomial *qp2);
5092 __isl_give isl_qpolynomial *isl_qpolynomial_pow(
5093 __isl_take isl_qpolynomial *qp, unsigned exponent);
5095 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_fix_val(
5096 __isl_take isl_pw_qpolynomial *pwqp,
5097 enum isl_dim_type type, unsigned n,
5098 __isl_take isl_val *v);
5099 __isl_give isl_pw_qpolynomial *
5100 isl_pw_qpolynomial_scale_val(
5101 __isl_take isl_pw_qpolynomial *pwqp,
5102 __isl_take isl_val *v);
5103 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_add(
5104 __isl_take isl_pw_qpolynomial *pwqp1,
5105 __isl_take isl_pw_qpolynomial *pwqp2);
5106 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_sub(
5107 __isl_take isl_pw_qpolynomial *pwqp1,
5108 __isl_take isl_pw_qpolynomial *pwqp2);
5109 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_add_disjoint(
5110 __isl_take isl_pw_qpolynomial *pwqp1,
5111 __isl_take isl_pw_qpolynomial *pwqp2);
5112 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_neg(
5113 __isl_take isl_pw_qpolynomial *pwqp);
5114 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_mul(
5115 __isl_take isl_pw_qpolynomial *pwqp1,
5116 __isl_take isl_pw_qpolynomial *pwqp2);
5117 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_pow(
5118 __isl_take isl_pw_qpolynomial *pwqp, unsigned exponent);
5120 __isl_give isl_union_pw_qpolynomial *
5121 isl_union_pw_qpolynomial_scale_val(
5122 __isl_take isl_union_pw_qpolynomial *upwqp,
5123 __isl_take isl_val *v);
5124 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_add(
5125 __isl_take isl_union_pw_qpolynomial *upwqp1,
5126 __isl_take isl_union_pw_qpolynomial *upwqp2);
5127 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_sub(
5128 __isl_take isl_union_pw_qpolynomial *upwqp1,
5129 __isl_take isl_union_pw_qpolynomial *upwqp2);
5130 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_mul(
5131 __isl_take isl_union_pw_qpolynomial *upwqp1,
5132 __isl_take isl_union_pw_qpolynomial *upwqp2);
5134 __isl_give isl_val *isl_pw_qpolynomial_eval(
5135 __isl_take isl_pw_qpolynomial *pwqp,
5136 __isl_take isl_point *pnt);
5138 __isl_give isl_val *isl_union_pw_qpolynomial_eval(
5139 __isl_take isl_union_pw_qpolynomial *upwqp,
5140 __isl_take isl_point *pnt);
5142 __isl_give isl_set *isl_pw_qpolynomial_domain(
5143 __isl_take isl_pw_qpolynomial *pwqp);
5144 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_intersect_domain(
5145 __isl_take isl_pw_qpolynomial *pwpq,
5146 __isl_take isl_set *set);
5147 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_intersect_params(
5148 __isl_take isl_pw_qpolynomial *pwpq,
5149 __isl_take isl_set *set);
5151 __isl_give isl_union_set *isl_union_pw_qpolynomial_domain(
5152 __isl_take isl_union_pw_qpolynomial *upwqp);
5153 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_intersect_domain(
5154 __isl_take isl_union_pw_qpolynomial *upwpq,
5155 __isl_take isl_union_set *uset);
5156 __isl_give isl_union_pw_qpolynomial *
5157 isl_union_pw_qpolynomial_intersect_params(
5158 __isl_take isl_union_pw_qpolynomial *upwpq,
5159 __isl_take isl_set *set);
5161 __isl_give isl_qpolynomial *isl_qpolynomial_align_params(
5162 __isl_take isl_qpolynomial *qp,
5163 __isl_take isl_space *model);
5165 __isl_give isl_qpolynomial *isl_qpolynomial_project_domain_on_params(
5166 __isl_take isl_qpolynomial *qp);
5167 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_project_domain_on_params(
5168 __isl_take isl_pw_qpolynomial *pwqp);
5170 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_coalesce(
5171 __isl_take isl_union_pw_qpolynomial *upwqp);
5173 __isl_give isl_qpolynomial *isl_qpolynomial_gist_params(
5174 __isl_take isl_qpolynomial *qp,
5175 __isl_take isl_set *context);
5176 __isl_give isl_qpolynomial *isl_qpolynomial_gist(
5177 __isl_take isl_qpolynomial *qp,
5178 __isl_take isl_set *context);
5180 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_gist_params(
5181 __isl_take isl_pw_qpolynomial *pwqp,
5182 __isl_take isl_set *context);
5183 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_gist(
5184 __isl_take isl_pw_qpolynomial *pwqp,
5185 __isl_take isl_set *context);
5187 __isl_give isl_union_pw_qpolynomial *
5188 isl_union_pw_qpolynomial_gist_params(
5189 __isl_take isl_union_pw_qpolynomial *upwqp,
5190 __isl_take isl_set *context);
5191 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_gist(
5192 __isl_take isl_union_pw_qpolynomial *upwqp,
5193 __isl_take isl_union_set *context);
5195 The gist operation applies the gist operation to each of
5196 the cells in the domain of the input piecewise quasipolynomial.
5197 The context is also exploited
5198 to simplify the quasipolynomials associated to each cell.
5200 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_to_polynomial(
5201 __isl_take isl_pw_qpolynomial *pwqp, int sign);
5202 __isl_give isl_union_pw_qpolynomial *
5203 isl_union_pw_qpolynomial_to_polynomial(
5204 __isl_take isl_union_pw_qpolynomial *upwqp, int sign);
5206 Approximate each quasipolynomial by a polynomial. If C<sign> is positive,
5207 the polynomial will be an overapproximation. If C<sign> is negative,
5208 it will be an underapproximation. If C<sign> is zero, the approximation
5209 will lie somewhere in between.
5211 =head2 Bounds on Piecewise Quasipolynomials and Piecewise Quasipolynomial Reductions
5213 A piecewise quasipolynomial reduction is a piecewise
5214 reduction (or fold) of quasipolynomials.
5215 In particular, the reduction can be maximum or a minimum.
5216 The objects are mainly used to represent the result of
5217 an upper or lower bound on a quasipolynomial over its domain,
5218 i.e., as the result of the following function.
5220 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_bound(
5221 __isl_take isl_pw_qpolynomial *pwqp,
5222 enum isl_fold type, int *tight);
5224 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_bound(
5225 __isl_take isl_union_pw_qpolynomial *upwqp,
5226 enum isl_fold type, int *tight);
5228 The C<type> argument may be either C<isl_fold_min> or C<isl_fold_max>.
5229 If C<tight> is not C<NULL>, then C<*tight> is set to C<1>
5230 is the returned bound is known be tight, i.e., for each value
5231 of the parameters there is at least
5232 one element in the domain that reaches the bound.
5233 If the domain of C<pwqp> is not wrapping, then the bound is computed
5234 over all elements in that domain and the result has a purely parametric
5235 domain. If the domain of C<pwqp> is wrapping, then the bound is
5236 computed over the range of the wrapped relation. The domain of the
5237 wrapped relation becomes the domain of the result.
5239 A (piecewise) quasipolynomial reduction can be copied or freed using the
5240 following functions.
5242 __isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_copy(
5243 __isl_keep isl_qpolynomial_fold *fold);
5244 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_copy(
5245 __isl_keep isl_pw_qpolynomial_fold *pwf);
5246 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_copy(
5247 __isl_keep isl_union_pw_qpolynomial_fold *upwf);
5248 void isl_qpolynomial_fold_free(
5249 __isl_take isl_qpolynomial_fold *fold);
5250 void *isl_pw_qpolynomial_fold_free(
5251 __isl_take isl_pw_qpolynomial_fold *pwf);
5252 void *isl_union_pw_qpolynomial_fold_free(
5253 __isl_take isl_union_pw_qpolynomial_fold *upwf);
5255 =head3 Printing Piecewise Quasipolynomial Reductions
5257 Piecewise quasipolynomial reductions can be printed
5258 using the following function.
5260 __isl_give isl_printer *isl_printer_print_pw_qpolynomial_fold(
5261 __isl_take isl_printer *p,
5262 __isl_keep isl_pw_qpolynomial_fold *pwf);
5263 __isl_give isl_printer *isl_printer_print_union_pw_qpolynomial_fold(
5264 __isl_take isl_printer *p,
5265 __isl_keep isl_union_pw_qpolynomial_fold *upwf);
5267 For C<isl_printer_print_pw_qpolynomial_fold>,
5268 output format of the printer
5269 needs to be set to either C<ISL_FORMAT_ISL> or C<ISL_FORMAT_C>.
5270 For C<isl_printer_print_union_pw_qpolynomial_fold>,
5271 output format of the printer
5272 needs to be set to C<ISL_FORMAT_ISL>.
5273 In case of printing in C<ISL_FORMAT_C>, the user may want
5274 to set the names of all dimensions
5276 __isl_give isl_pw_qpolynomial_fold *
5277 isl_pw_qpolynomial_fold_set_dim_name(
5278 __isl_take isl_pw_qpolynomial_fold *pwf,
5279 enum isl_dim_type type, unsigned pos,
5282 =head3 Inspecting (Piecewise) Quasipolynomial Reductions
5284 To iterate over all piecewise quasipolynomial reductions in a union
5285 piecewise quasipolynomial reduction, use the following function
5287 int isl_union_pw_qpolynomial_fold_foreach_pw_qpolynomial_fold(
5288 __isl_keep isl_union_pw_qpolynomial_fold *upwf,
5289 int (*fn)(__isl_take isl_pw_qpolynomial_fold *pwf,
5290 void *user), void *user);
5292 To iterate over the cells in a piecewise quasipolynomial reduction,
5293 use either of the following two functions
5295 int isl_pw_qpolynomial_fold_foreach_piece(
5296 __isl_keep isl_pw_qpolynomial_fold *pwf,
5297 int (*fn)(__isl_take isl_set *set,
5298 __isl_take isl_qpolynomial_fold *fold,
5299 void *user), void *user);
5300 int isl_pw_qpolynomial_fold_foreach_lifted_piece(
5301 __isl_keep isl_pw_qpolynomial_fold *pwf,
5302 int (*fn)(__isl_take isl_set *set,
5303 __isl_take isl_qpolynomial_fold *fold,
5304 void *user), void *user);
5306 See L<Inspecting (Piecewise) Quasipolynomials> for an explanation
5307 of the difference between these two functions.
5309 To iterate over all quasipolynomials in a reduction, use
5311 int isl_qpolynomial_fold_foreach_qpolynomial(
5312 __isl_keep isl_qpolynomial_fold *fold,
5313 int (*fn)(__isl_take isl_qpolynomial *qp,
5314 void *user), void *user);
5316 =head3 Properties of Piecewise Quasipolynomial Reductions
5318 To check whether two union piecewise quasipolynomial reductions are
5319 obviously equal, use
5321 int isl_union_pw_qpolynomial_fold_plain_is_equal(
5322 __isl_keep isl_union_pw_qpolynomial_fold *upwf1,
5323 __isl_keep isl_union_pw_qpolynomial_fold *upwf2);
5325 =head3 Operations on Piecewise Quasipolynomial Reductions
5327 __isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_scale_val(
5328 __isl_take isl_qpolynomial_fold *fold,
5329 __isl_take isl_val *v);
5330 __isl_give isl_pw_qpolynomial_fold *
5331 isl_pw_qpolynomial_fold_scale_val(
5332 __isl_take isl_pw_qpolynomial_fold *pwf,
5333 __isl_take isl_val *v);
5334 __isl_give isl_union_pw_qpolynomial_fold *
5335 isl_union_pw_qpolynomial_fold_scale_val(
5336 __isl_take isl_union_pw_qpolynomial_fold *upwf,
5337 __isl_take isl_val *v);
5339 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_add(
5340 __isl_take isl_pw_qpolynomial_fold *pwf1,
5341 __isl_take isl_pw_qpolynomial_fold *pwf2);
5343 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_fold(
5344 __isl_take isl_pw_qpolynomial_fold *pwf1,
5345 __isl_take isl_pw_qpolynomial_fold *pwf2);
5347 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_fold(
5348 __isl_take isl_union_pw_qpolynomial_fold *upwf1,
5349 __isl_take isl_union_pw_qpolynomial_fold *upwf2);
5351 __isl_give isl_val *isl_pw_qpolynomial_fold_eval(
5352 __isl_take isl_pw_qpolynomial_fold *pwf,
5353 __isl_take isl_point *pnt);
5355 __isl_give isl_val *isl_union_pw_qpolynomial_fold_eval(
5356 __isl_take isl_union_pw_qpolynomial_fold *upwf,
5357 __isl_take isl_point *pnt);
5359 __isl_give isl_pw_qpolynomial_fold *
5360 isl_pw_qpolynomial_fold_intersect_params(
5361 __isl_take isl_pw_qpolynomial_fold *pwf,
5362 __isl_take isl_set *set);
5364 __isl_give isl_union_set *isl_union_pw_qpolynomial_fold_domain(
5365 __isl_take isl_union_pw_qpolynomial_fold *upwf);
5366 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_intersect_domain(
5367 __isl_take isl_union_pw_qpolynomial_fold *upwf,
5368 __isl_take isl_union_set *uset);
5369 __isl_give isl_union_pw_qpolynomial_fold *
5370 isl_union_pw_qpolynomial_fold_intersect_params(
5371 __isl_take isl_union_pw_qpolynomial_fold *upwf,
5372 __isl_take isl_set *set);
5374 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_project_domain_on_params(
5375 __isl_take isl_pw_qpolynomial_fold *pwf);
5377 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_coalesce(
5378 __isl_take isl_pw_qpolynomial_fold *pwf);
5380 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_coalesce(
5381 __isl_take isl_union_pw_qpolynomial_fold *upwf);
5383 __isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_gist_params(
5384 __isl_take isl_qpolynomial_fold *fold,
5385 __isl_take isl_set *context);
5386 __isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_gist(
5387 __isl_take isl_qpolynomial_fold *fold,
5388 __isl_take isl_set *context);
5390 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_gist(
5391 __isl_take isl_pw_qpolynomial_fold *pwf,
5392 __isl_take isl_set *context);
5393 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_gist_params(
5394 __isl_take isl_pw_qpolynomial_fold *pwf,
5395 __isl_take isl_set *context);
5397 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_gist(
5398 __isl_take isl_union_pw_qpolynomial_fold *upwf,
5399 __isl_take isl_union_set *context);
5400 __isl_give isl_union_pw_qpolynomial_fold *
5401 isl_union_pw_qpolynomial_fold_gist_params(
5402 __isl_take isl_union_pw_qpolynomial_fold *upwf,
5403 __isl_take isl_set *context);
5405 The gist operation applies the gist operation to each of
5406 the cells in the domain of the input piecewise quasipolynomial reduction.
5407 In future, the operation will also exploit the context
5408 to simplify the quasipolynomial reductions associated to each cell.
5410 __isl_give isl_pw_qpolynomial_fold *
5411 isl_set_apply_pw_qpolynomial_fold(
5412 __isl_take isl_set *set,
5413 __isl_take isl_pw_qpolynomial_fold *pwf,
5415 __isl_give isl_pw_qpolynomial_fold *
5416 isl_map_apply_pw_qpolynomial_fold(
5417 __isl_take isl_map *map,
5418 __isl_take isl_pw_qpolynomial_fold *pwf,
5420 __isl_give isl_union_pw_qpolynomial_fold *
5421 isl_union_set_apply_union_pw_qpolynomial_fold(
5422 __isl_take isl_union_set *uset,
5423 __isl_take isl_union_pw_qpolynomial_fold *upwf,
5425 __isl_give isl_union_pw_qpolynomial_fold *
5426 isl_union_map_apply_union_pw_qpolynomial_fold(
5427 __isl_take isl_union_map *umap,
5428 __isl_take isl_union_pw_qpolynomial_fold *upwf,
5431 The functions taking a map
5432 compose the given map with the given piecewise quasipolynomial reduction.
5433 That is, compute a bound (of the same type as C<pwf> or C<upwf> itself)
5434 over all elements in the intersection of the range of the map
5435 and the domain of the piecewise quasipolynomial reduction
5436 as a function of an element in the domain of the map.
5437 The functions taking a set compute a bound over all elements in the
5438 intersection of the set and the domain of the
5439 piecewise quasipolynomial reduction.
5441 =head2 Parametric Vertex Enumeration
5443 The parametric vertex enumeration described in this section
5444 is mainly intended to be used internally and by the C<barvinok>
5447 #include <isl/vertices.h>
5448 __isl_give isl_vertices *isl_basic_set_compute_vertices(
5449 __isl_keep isl_basic_set *bset);
5451 The function C<isl_basic_set_compute_vertices> performs the
5452 actual computation of the parametric vertices and the chamber
5453 decomposition and store the result in an C<isl_vertices> object.
5454 This information can be queried by either iterating over all
5455 the vertices or iterating over all the chambers or cells
5456 and then iterating over all vertices that are active on the chamber.
5458 int isl_vertices_foreach_vertex(
5459 __isl_keep isl_vertices *vertices,
5460 int (*fn)(__isl_take isl_vertex *vertex, void *user),
5463 int isl_vertices_foreach_cell(
5464 __isl_keep isl_vertices *vertices,
5465 int (*fn)(__isl_take isl_cell *cell, void *user),
5467 int isl_cell_foreach_vertex(__isl_keep isl_cell *cell,
5468 int (*fn)(__isl_take isl_vertex *vertex, void *user),
5471 Other operations that can be performed on an C<isl_vertices> object are
5474 isl_ctx *isl_vertices_get_ctx(
5475 __isl_keep isl_vertices *vertices);
5476 int isl_vertices_get_n_vertices(
5477 __isl_keep isl_vertices *vertices);
5478 void isl_vertices_free(__isl_take isl_vertices *vertices);
5480 Vertices can be inspected and destroyed using the following functions.
5482 isl_ctx *isl_vertex_get_ctx(__isl_keep isl_vertex *vertex);
5483 int isl_vertex_get_id(__isl_keep isl_vertex *vertex);
5484 __isl_give isl_basic_set *isl_vertex_get_domain(
5485 __isl_keep isl_vertex *vertex);
5486 __isl_give isl_basic_set *isl_vertex_get_expr(
5487 __isl_keep isl_vertex *vertex);
5488 void isl_vertex_free(__isl_take isl_vertex *vertex);
5490 C<isl_vertex_get_expr> returns a singleton parametric set describing
5491 the vertex, while C<isl_vertex_get_domain> returns the activity domain
5493 Note that C<isl_vertex_get_domain> and C<isl_vertex_get_expr> return
5494 B<rational> basic sets, so they should mainly be used for inspection
5495 and should not be mixed with integer sets.
5497 Chambers can be inspected and destroyed using the following functions.
5499 isl_ctx *isl_cell_get_ctx(__isl_keep isl_cell *cell);
5500 __isl_give isl_basic_set *isl_cell_get_domain(
5501 __isl_keep isl_cell *cell);
5502 void isl_cell_free(__isl_take isl_cell *cell);
5504 =head1 Polyhedral Compilation Library
5506 This section collects functionality in C<isl> that has been specifically
5507 designed for use during polyhedral compilation.
5509 =head2 Dependence Analysis
5511 C<isl> contains specialized functionality for performing
5512 array dataflow analysis. That is, given a I<sink> access relation
5513 and a collection of possible I<source> access relations,
5514 C<isl> can compute relations that describe
5515 for each iteration of the sink access, which iteration
5516 of which of the source access relations was the last
5517 to access the same data element before the given iteration
5519 The resulting dependence relations map source iterations
5520 to the corresponding sink iterations.
5521 To compute standard flow dependences, the sink should be
5522 a read, while the sources should be writes.
5523 If any of the source accesses are marked as being I<may>
5524 accesses, then there will be a dependence from the last
5525 I<must> access B<and> from any I<may> access that follows
5526 this last I<must> access.
5527 In particular, if I<all> sources are I<may> accesses,
5528 then memory based dependence analysis is performed.
5529 If, on the other hand, all sources are I<must> accesses,
5530 then value based dependence analysis is performed.
5532 #include <isl/flow.h>
5534 typedef int (*isl_access_level_before)(void *first, void *second);
5536 __isl_give isl_access_info *isl_access_info_alloc(
5537 __isl_take isl_map *sink,
5538 void *sink_user, isl_access_level_before fn,
5540 __isl_give isl_access_info *isl_access_info_add_source(
5541 __isl_take isl_access_info *acc,
5542 __isl_take isl_map *source, int must,
5544 void *isl_access_info_free(__isl_take isl_access_info *acc);
5546 __isl_give isl_flow *isl_access_info_compute_flow(
5547 __isl_take isl_access_info *acc);
5549 int isl_flow_foreach(__isl_keep isl_flow *deps,
5550 int (*fn)(__isl_take isl_map *dep, int must,
5551 void *dep_user, void *user),
5553 __isl_give isl_map *isl_flow_get_no_source(
5554 __isl_keep isl_flow *deps, int must);
5555 void isl_flow_free(__isl_take isl_flow *deps);
5557 The function C<isl_access_info_compute_flow> performs the actual
5558 dependence analysis. The other functions are used to construct
5559 the input for this function or to read off the output.
5561 The input is collected in an C<isl_access_info>, which can
5562 be created through a call to C<isl_access_info_alloc>.
5563 The arguments to this functions are the sink access relation
5564 C<sink>, a token C<sink_user> used to identify the sink
5565 access to the user, a callback function for specifying the
5566 relative order of source and sink accesses, and the number
5567 of source access relations that will be added.
5568 The callback function has type C<int (*)(void *first, void *second)>.
5569 The function is called with two user supplied tokens identifying
5570 either a source or the sink and it should return the shared nesting
5571 level and the relative order of the two accesses.
5572 In particular, let I<n> be the number of loops shared by
5573 the two accesses. If C<first> precedes C<second> textually,
5574 then the function should return I<2 * n + 1>; otherwise,
5575 it should return I<2 * n>.
5576 The sources can be added to the C<isl_access_info> by performing
5577 (at most) C<max_source> calls to C<isl_access_info_add_source>.
5578 C<must> indicates whether the source is a I<must> access
5579 or a I<may> access. Note that a multi-valued access relation
5580 should only be marked I<must> if every iteration in the domain
5581 of the relation accesses I<all> elements in its image.
5582 The C<source_user> token is again used to identify
5583 the source access. The range of the source access relation
5584 C<source> should have the same dimension as the range
5585 of the sink access relation.
5586 The C<isl_access_info_free> function should usually not be
5587 called explicitly, because it is called implicitly by
5588 C<isl_access_info_compute_flow>.
5590 The result of the dependence analysis is collected in an
5591 C<isl_flow>. There may be elements of
5592 the sink access for which no preceding source access could be
5593 found or for which all preceding sources are I<may> accesses.
5594 The relations containing these elements can be obtained through
5595 calls to C<isl_flow_get_no_source>, the first with C<must> set
5596 and the second with C<must> unset.
5597 In the case of standard flow dependence analysis,
5598 with the sink a read and the sources I<must> writes,
5599 the first relation corresponds to the reads from uninitialized
5600 array elements and the second relation is empty.
5601 The actual flow dependences can be extracted using
5602 C<isl_flow_foreach>. This function will call the user-specified
5603 callback function C<fn> for each B<non-empty> dependence between
5604 a source and the sink. The callback function is called
5605 with four arguments, the actual flow dependence relation
5606 mapping source iterations to sink iterations, a boolean that
5607 indicates whether it is a I<must> or I<may> dependence, a token
5608 identifying the source and an additional C<void *> with value
5609 equal to the third argument of the C<isl_flow_foreach> call.
5610 A dependence is marked I<must> if it originates from a I<must>
5611 source and if it is not followed by any I<may> sources.
5613 After finishing with an C<isl_flow>, the user should call
5614 C<isl_flow_free> to free all associated memory.
5616 A higher-level interface to dependence analysis is provided
5617 by the following function.
5619 #include <isl/flow.h>
5621 int isl_union_map_compute_flow(__isl_take isl_union_map *sink,
5622 __isl_take isl_union_map *must_source,
5623 __isl_take isl_union_map *may_source,
5624 __isl_take isl_union_map *schedule,
5625 __isl_give isl_union_map **must_dep,
5626 __isl_give isl_union_map **may_dep,
5627 __isl_give isl_union_map **must_no_source,
5628 __isl_give isl_union_map **may_no_source);
5630 The arrays are identified by the tuple names of the ranges
5631 of the accesses. The iteration domains by the tuple names
5632 of the domains of the accesses and of the schedule.
5633 The relative order of the iteration domains is given by the
5634 schedule. The relations returned through C<must_no_source>
5635 and C<may_no_source> are subsets of C<sink>.
5636 Any of C<must_dep>, C<may_dep>, C<must_no_source>
5637 or C<may_no_source> may be C<NULL>, but a C<NULL> value for
5638 any of the other arguments is treated as an error.
5640 =head3 Interaction with Dependence Analysis
5642 During the dependence analysis, we frequently need to perform
5643 the following operation. Given a relation between sink iterations
5644 and potential source iterations from a particular source domain,
5645 what is the last potential source iteration corresponding to each
5646 sink iteration. It can sometimes be convenient to adjust
5647 the set of potential source iterations before or after each such operation.
5648 The prototypical example is fuzzy array dataflow analysis,
5649 where we need to analyze if, based on data-dependent constraints,
5650 the sink iteration can ever be executed without one or more of
5651 the corresponding potential source iterations being executed.
5652 If so, we can introduce extra parameters and select an unknown
5653 but fixed source iteration from the potential source iterations.
5654 To be able to perform such manipulations, C<isl> provides the following
5657 #include <isl/flow.h>
5659 typedef __isl_give isl_restriction *(*isl_access_restrict)(
5660 __isl_keep isl_map *source_map,
5661 __isl_keep isl_set *sink, void *source_user,
5663 __isl_give isl_access_info *isl_access_info_set_restrict(
5664 __isl_take isl_access_info *acc,
5665 isl_access_restrict fn, void *user);
5667 The function C<isl_access_info_set_restrict> should be called
5668 before calling C<isl_access_info_compute_flow> and registers a callback function
5669 that will be called any time C<isl> is about to compute the last
5670 potential source. The first argument is the (reverse) proto-dependence,
5671 mapping sink iterations to potential source iterations.
5672 The second argument represents the sink iterations for which
5673 we want to compute the last source iteration.
5674 The third argument is the token corresponding to the source
5675 and the final argument is the token passed to C<isl_access_info_set_restrict>.
5676 The callback is expected to return a restriction on either the input or
5677 the output of the operation computing the last potential source.
5678 If the input needs to be restricted then restrictions are needed
5679 for both the source and the sink iterations. The sink iterations
5680 and the potential source iterations will be intersected with these sets.
5681 If the output needs to be restricted then only a restriction on the source
5682 iterations is required.
5683 If any error occurs, the callback should return C<NULL>.
5684 An C<isl_restriction> object can be created, freed and inspected
5685 using the following functions.
5687 #include <isl/flow.h>
5689 __isl_give isl_restriction *isl_restriction_input(
5690 __isl_take isl_set *source_restr,
5691 __isl_take isl_set *sink_restr);
5692 __isl_give isl_restriction *isl_restriction_output(
5693 __isl_take isl_set *source_restr);
5694 __isl_give isl_restriction *isl_restriction_none(
5695 __isl_take isl_map *source_map);
5696 __isl_give isl_restriction *isl_restriction_empty(
5697 __isl_take isl_map *source_map);
5698 void *isl_restriction_free(
5699 __isl_take isl_restriction *restr);
5700 isl_ctx *isl_restriction_get_ctx(
5701 __isl_keep isl_restriction *restr);
5703 C<isl_restriction_none> and C<isl_restriction_empty> are special
5704 cases of C<isl_restriction_input>. C<isl_restriction_none>
5705 is essentially equivalent to
5707 isl_restriction_input(isl_set_universe(
5708 isl_space_range(isl_map_get_space(source_map))),
5710 isl_space_domain(isl_map_get_space(source_map))));
5712 whereas C<isl_restriction_empty> is essentially equivalent to
5714 isl_restriction_input(isl_set_empty(
5715 isl_space_range(isl_map_get_space(source_map))),
5717 isl_space_domain(isl_map_get_space(source_map))));
5721 B<The functionality described in this section is fairly new
5722 and may be subject to change.>
5724 #include <isl/schedule.h>
5725 __isl_give isl_schedule *
5726 isl_schedule_constraints_compute_schedule(
5727 __isl_take isl_schedule_constraints *sc);
5728 void *isl_schedule_free(__isl_take isl_schedule *sched);
5730 The function C<isl_schedule_constraints_compute_schedule> can be
5731 used to compute a schedule that satisfy the given schedule constraints.
5732 These schedule constraints include the iteration domain for which
5733 a schedule should be computed and dependences between pairs of
5734 iterations. In particular, these dependences include
5735 I<validity> dependences and I<proximity> dependences.
5736 By default, the algorithm used to construct the schedule is similar
5737 to that of C<Pluto>.
5738 Alternatively, Feautrier's multi-dimensional scheduling algorithm can
5740 The generated schedule respects all validity dependences.
5741 That is, all dependence distances over these dependences in the
5742 scheduled space are lexicographically positive.
5743 The default algorithm tries to ensure that the dependence distances
5744 over coincidence constraints are zero and to minimize the
5745 dependence distances over proximity dependences.
5746 Moreover, it tries to obtain sequences (bands) of schedule dimensions
5747 for groups of domains where the dependence distances over validity
5748 dependences have only non-negative values.
5749 When using Feautrier's algorithm, the coincidence and proximity constraints
5750 are only taken into account during the extension to a
5751 full-dimensional schedule.
5753 An C<isl_schedule_constraints> object can be constructed
5754 and manipulated using the following functions.
5756 #include <isl/schedule.h>
5757 __isl_give isl_schedule_constraints *
5758 isl_schedule_constraints_copy(
5759 __isl_keep isl_schedule_constraints *sc);
5760 __isl_give isl_schedule_constraints *
5761 isl_schedule_constraints_on_domain(
5762 __isl_take isl_union_set *domain);
5763 isl_ctx *isl_schedule_constraints_get_ctx(
5764 __isl_keep isl_schedule_constraints *sc);
5765 __isl_give isl_schedule_constraints *
5766 isl_schedule_constraints_set_validity(
5767 __isl_take isl_schedule_constraints *sc,
5768 __isl_take isl_union_map *validity);
5769 __isl_give isl_schedule_constraints *
5770 isl_schedule_constraints_set_coincidence(
5771 __isl_take isl_schedule_constraints *sc,
5772 __isl_take isl_union_map *coincidence);
5773 __isl_give isl_schedule_constraints *
5774 isl_schedule_constraints_set_proximity(
5775 __isl_take isl_schedule_constraints *sc,
5776 __isl_take isl_union_map *proximity);
5777 __isl_give isl_schedule_constraints *
5778 isl_schedule_constraints_set_conditional_validity(
5779 __isl_take isl_schedule_constraints *sc,
5780 __isl_take isl_union_map *condition,
5781 __isl_take isl_union_map *validity);
5782 void *isl_schedule_constraints_free(
5783 __isl_take isl_schedule_constraints *sc);
5785 The initial C<isl_schedule_constraints> object created by
5786 C<isl_schedule_constraints_on_domain> does not impose any constraints.
5787 That is, it has an empty set of dependences.
5788 The function C<isl_schedule_constraints_set_validity> replaces the
5789 validity dependences, mapping domain elements I<i> to domain
5790 elements that should be scheduled after I<i>.
5791 The function C<isl_schedule_constraints_set_coincidence> replaces the
5792 coincidence dependences, mapping domain elements I<i> to domain
5793 elements that should be scheduled together with I<I>, if possible.
5794 The function C<isl_schedule_constraints_set_proximity> replaces the
5795 proximity dependences, mapping domain elements I<i> to domain
5796 elements that should be scheduled either before I<I>
5797 or as early as possible after I<i>.
5799 The function C<isl_schedule_constraints_set_conditional_validity>
5800 replaces the conditional validity constraints.
5801 A conditional validity constraint is only imposed when any of the corresponding
5802 conditions is satisfied, i.e., when any of them is non-zero.
5803 That is, the scheduler ensures that within each band if the dependence
5804 distances over the condition constraints are not all zero
5805 then all corresponding conditional validity constraints are respected.
5806 A conditional validity constraint corresponds to a condition
5807 if the two are adjacent, i.e., if the domain of one relation intersect
5808 the range of the other relation.
5809 The typical use case of conditional validity constraints is
5810 to allow order constraints between live ranges to be violated
5811 as long as the live ranges themselves are local to the band.
5812 To allow more fine-grained control over which conditions correspond
5813 to which conditional validity constraints, the domains and ranges
5814 of these relations may include I<tags>. That is, the domains and
5815 ranges of those relation may themselves be wrapped relations
5816 where the iteration domain appears in the domain of those wrapped relations
5817 and the range of the wrapped relations can be arbitrarily chosen
5818 by the user. Conditions and conditional validity constraints are only
5819 considere adjacent to each other if the entire wrapped relation matches.
5820 In particular, a relation with a tag will never be considered adjacent
5821 to a relation without a tag.
5823 The following function computes a schedule directly from
5824 an iteration domain and validity and proximity dependences
5825 and is implemented in terms of the functions described above.
5826 The use of C<isl_union_set_compute_schedule> is discouraged.
5828 #include <isl/schedule.h>
5829 __isl_give isl_schedule *isl_union_set_compute_schedule(
5830 __isl_take isl_union_set *domain,
5831 __isl_take isl_union_map *validity,
5832 __isl_take isl_union_map *proximity);
5834 A mapping from the domains to the scheduled space can be obtained
5835 from an C<isl_schedule> using the following function.
5837 __isl_give isl_union_map *isl_schedule_get_map(
5838 __isl_keep isl_schedule *sched);
5840 A representation of the schedule can be printed using
5842 __isl_give isl_printer *isl_printer_print_schedule(
5843 __isl_take isl_printer *p,
5844 __isl_keep isl_schedule *schedule);
5846 A representation of the schedule as a forest of bands can be obtained
5847 using the following function.
5849 __isl_give isl_band_list *isl_schedule_get_band_forest(
5850 __isl_keep isl_schedule *schedule);
5852 The individual bands can be visited in depth-first post-order
5853 using the following function.
5855 #include <isl/schedule.h>
5856 int isl_schedule_foreach_band(
5857 __isl_keep isl_schedule *sched,
5858 int (*fn)(__isl_keep isl_band *band, void *user),
5861 The list can be manipulated as explained in L<"Lists">.
5862 The bands inside the list can be copied and freed using the following
5865 #include <isl/band.h>
5866 __isl_give isl_band *isl_band_copy(
5867 __isl_keep isl_band *band);
5868 void *isl_band_free(__isl_take isl_band *band);
5870 Each band contains zero or more scheduling dimensions.
5871 These are referred to as the members of the band.
5872 The section of the schedule that corresponds to the band is
5873 referred to as the partial schedule of the band.
5874 For those nodes that participate in a band, the outer scheduling
5875 dimensions form the prefix schedule, while the inner scheduling
5876 dimensions form the suffix schedule.
5877 That is, if we take a cut of the band forest, then the union of
5878 the concatenations of the prefix, partial and suffix schedules of
5879 each band in the cut is equal to the entire schedule (modulo
5880 some possible padding at the end with zero scheduling dimensions).
5881 The properties of a band can be inspected using the following functions.
5883 #include <isl/band.h>
5884 isl_ctx *isl_band_get_ctx(__isl_keep isl_band *band);
5886 int isl_band_has_children(__isl_keep isl_band *band);
5887 __isl_give isl_band_list *isl_band_get_children(
5888 __isl_keep isl_band *band);
5890 __isl_give isl_union_map *isl_band_get_prefix_schedule(
5891 __isl_keep isl_band *band);
5892 __isl_give isl_union_map *isl_band_get_partial_schedule(
5893 __isl_keep isl_band *band);
5894 __isl_give isl_union_map *isl_band_get_suffix_schedule(
5895 __isl_keep isl_band *band);
5897 int isl_band_n_member(__isl_keep isl_band *band);
5898 int isl_band_member_is_coincident(
5899 __isl_keep isl_band *band, int pos);
5901 int isl_band_list_foreach_band(
5902 __isl_keep isl_band_list *list,
5903 int (*fn)(__isl_keep isl_band *band, void *user),
5906 Note that a scheduling dimension is considered to be ``coincident''
5907 if it satisfies the coincidence constraints within its band.
5908 That is, if the dependence distances of the coincidence
5909 constraints are all zero in that direction (for fixed
5910 iterations of outer bands).
5911 Like C<isl_schedule_foreach_band>,
5912 the function C<isl_band_list_foreach_band> calls C<fn> on the bands
5913 in depth-first post-order.
5915 A band can be tiled using the following function.
5917 #include <isl/band.h>
5918 int isl_band_tile(__isl_keep isl_band *band,
5919 __isl_take isl_vec *sizes);
5921 int isl_options_set_tile_scale_tile_loops(isl_ctx *ctx,
5923 int isl_options_get_tile_scale_tile_loops(isl_ctx *ctx);
5924 int isl_options_set_tile_shift_point_loops(isl_ctx *ctx,
5926 int isl_options_get_tile_shift_point_loops(isl_ctx *ctx);
5928 The C<isl_band_tile> function tiles the band using the given tile sizes
5929 inside its schedule.
5930 A new child band is created to represent the point loops and it is
5931 inserted between the modified band and its children.
5932 The C<tile_scale_tile_loops> option specifies whether the tile
5933 loops iterators should be scaled by the tile sizes.
5934 If the C<tile_shift_point_loops> option is set, then the point loops
5935 are shifted to start at zero.
5937 A band can be split into two nested bands using the following function.
5939 int isl_band_split(__isl_keep isl_band *band, int pos);
5941 The resulting outer band contains the first C<pos> dimensions of C<band>
5942 while the inner band contains the remaining dimensions.
5944 A representation of the band can be printed using
5946 #include <isl/band.h>
5947 __isl_give isl_printer *isl_printer_print_band(
5948 __isl_take isl_printer *p,
5949 __isl_keep isl_band *band);
5953 #include <isl/schedule.h>
5954 int isl_options_set_schedule_max_coefficient(
5955 isl_ctx *ctx, int val);
5956 int isl_options_get_schedule_max_coefficient(
5958 int isl_options_set_schedule_max_constant_term(
5959 isl_ctx *ctx, int val);
5960 int isl_options_get_schedule_max_constant_term(
5962 int isl_options_set_schedule_fuse(isl_ctx *ctx, int val);
5963 int isl_options_get_schedule_fuse(isl_ctx *ctx);
5964 int isl_options_set_schedule_maximize_band_depth(
5965 isl_ctx *ctx, int val);
5966 int isl_options_get_schedule_maximize_band_depth(
5968 int isl_options_set_schedule_outer_coincidence(
5969 isl_ctx *ctx, int val);
5970 int isl_options_get_schedule_outer_coincidence(
5972 int isl_options_set_schedule_split_scaled(
5973 isl_ctx *ctx, int val);
5974 int isl_options_get_schedule_split_scaled(
5976 int isl_options_set_schedule_algorithm(
5977 isl_ctx *ctx, int val);
5978 int isl_options_get_schedule_algorithm(
5980 int isl_options_set_schedule_separate_components(
5981 isl_ctx *ctx, int val);
5982 int isl_options_get_schedule_separate_components(
5987 =item * schedule_max_coefficient
5989 This option enforces that the coefficients for variable and parameter
5990 dimensions in the calculated schedule are not larger than the specified value.
5991 This option can significantly increase the speed of the scheduling calculation
5992 and may also prevent fusing of unrelated dimensions. A value of -1 means that
5993 this option does not introduce bounds on the variable or parameter
5996 =item * schedule_max_constant_term
5998 This option enforces that the constant coefficients in the calculated schedule
5999 are not larger than the maximal constant term. This option can significantly
6000 increase the speed of the scheduling calculation and may also prevent fusing of
6001 unrelated dimensions. A value of -1 means that this option does not introduce
6002 bounds on the constant coefficients.
6004 =item * schedule_fuse
6006 This option controls the level of fusion.
6007 If this option is set to C<ISL_SCHEDULE_FUSE_MIN>, then loops in the
6008 resulting schedule will be distributed as much as possible.
6009 If this option is set to C<ISL_SCHEDULE_FUSE_MAX>, then C<isl> will
6010 try to fuse loops in the resulting schedule.
6012 =item * schedule_maximize_band_depth
6014 If this option is set, we do not split bands at the point
6015 where we detect splitting is necessary. Instead, we
6016 backtrack and split bands as early as possible. This
6017 reduces the number of splits and maximizes the width of
6018 the bands. Wider bands give more possibilities for tiling.
6019 Note that if the C<schedule_fuse> option is set to C<ISL_SCHEDULE_FUSE_MIN>,
6020 then bands will be split as early as possible, even if there is no need.
6021 The C<schedule_maximize_band_depth> option therefore has no effect in this case.
6023 =item * schedule_outer_coincidence
6025 If this option is set, then we try to construct schedules
6026 where the outermost scheduling dimension in each band
6027 satisfies the coincidence constraints.
6029 =item * schedule_split_scaled
6031 If this option is set, then we try to construct schedules in which the
6032 constant term is split off from the linear part if the linear parts of
6033 the scheduling rows for all nodes in the graphs have a common non-trivial
6035 The constant term is then placed in a separate band and the linear
6038 =item * schedule_algorithm
6040 Selects the scheduling algorithm to be used.
6041 Available scheduling algorithms are C<ISL_SCHEDULE_ALGORITHM_ISL>
6042 and C<ISL_SCHEDULE_ALGORITHM_FEAUTRIER>.
6044 =item * schedule_separate_components
6046 If at any point the dependence graph contains any (weakly connected) components,
6047 then these components are scheduled separately.
6048 If this option is not set, then some iterations of the domains
6049 in these components may be scheduled together.
6050 If this option is set, then the components are given consecutive
6055 =head2 AST Generation
6057 This section describes the C<isl> functionality for generating
6058 ASTs that visit all the elements
6059 in a domain in an order specified by a schedule.
6060 In particular, given a C<isl_union_map>, an AST is generated
6061 that visits all the elements in the domain of the C<isl_union_map>
6062 according to the lexicographic order of the corresponding image
6063 element(s). If the range of the C<isl_union_map> consists of
6064 elements in more than one space, then each of these spaces is handled
6065 separately in an arbitrary order.
6066 It should be noted that the image elements only specify the I<order>
6067 in which the corresponding domain elements should be visited.
6068 No direct relation between the image elements and the loop iterators
6069 in the generated AST should be assumed.
6071 Each AST is generated within a build. The initial build
6072 simply specifies the constraints on the parameters (if any)
6073 and can be created, inspected, copied and freed using the following functions.
6075 #include <isl/ast_build.h>
6076 __isl_give isl_ast_build *isl_ast_build_from_context(
6077 __isl_take isl_set *set);
6078 isl_ctx *isl_ast_build_get_ctx(
6079 __isl_keep isl_ast_build *build);
6080 __isl_give isl_ast_build *isl_ast_build_copy(
6081 __isl_keep isl_ast_build *build);
6082 void *isl_ast_build_free(
6083 __isl_take isl_ast_build *build);
6085 The C<set> argument is usually a parameter set with zero or more parameters.
6086 More C<isl_ast_build> functions are described in L</"Nested AST Generation">
6087 and L</"Fine-grained Control over AST Generation">.
6088 Finally, the AST itself can be constructed using the following
6091 #include <isl/ast_build.h>
6092 __isl_give isl_ast_node *isl_ast_build_ast_from_schedule(
6093 __isl_keep isl_ast_build *build,
6094 __isl_take isl_union_map *schedule);
6096 =head3 Inspecting the AST
6098 The basic properties of an AST node can be obtained as follows.
6100 #include <isl/ast.h>
6101 isl_ctx *isl_ast_node_get_ctx(
6102 __isl_keep isl_ast_node *node);
6103 enum isl_ast_node_type isl_ast_node_get_type(
6104 __isl_keep isl_ast_node *node);
6106 The type of an AST node is one of
6107 C<isl_ast_node_for>,
6109 C<isl_ast_node_block> or
6110 C<isl_ast_node_user>.
6111 An C<isl_ast_node_for> represents a for node.
6112 An C<isl_ast_node_if> represents an if node.
6113 An C<isl_ast_node_block> represents a compound node.
6114 An C<isl_ast_node_user> represents an expression statement.
6115 An expression statement typically corresponds to a domain element, i.e.,
6116 one of the elements that is visited by the AST.
6118 Each type of node has its own additional properties.
6120 #include <isl/ast.h>
6121 __isl_give isl_ast_expr *isl_ast_node_for_get_iterator(
6122 __isl_keep isl_ast_node *node);
6123 __isl_give isl_ast_expr *isl_ast_node_for_get_init(
6124 __isl_keep isl_ast_node *node);
6125 __isl_give isl_ast_expr *isl_ast_node_for_get_cond(
6126 __isl_keep isl_ast_node *node);
6127 __isl_give isl_ast_expr *isl_ast_node_for_get_inc(
6128 __isl_keep isl_ast_node *node);
6129 __isl_give isl_ast_node *isl_ast_node_for_get_body(
6130 __isl_keep isl_ast_node *node);
6131 int isl_ast_node_for_is_degenerate(
6132 __isl_keep isl_ast_node *node);
6134 An C<isl_ast_for> is considered degenerate if it is known to execute
6137 #include <isl/ast.h>
6138 __isl_give isl_ast_expr *isl_ast_node_if_get_cond(
6139 __isl_keep isl_ast_node *node);
6140 __isl_give isl_ast_node *isl_ast_node_if_get_then(
6141 __isl_keep isl_ast_node *node);
6142 int isl_ast_node_if_has_else(
6143 __isl_keep isl_ast_node *node);
6144 __isl_give isl_ast_node *isl_ast_node_if_get_else(
6145 __isl_keep isl_ast_node *node);
6147 __isl_give isl_ast_node_list *
6148 isl_ast_node_block_get_children(
6149 __isl_keep isl_ast_node *node);
6151 __isl_give isl_ast_expr *isl_ast_node_user_get_expr(
6152 __isl_keep isl_ast_node *node);
6154 Each of the returned C<isl_ast_expr>s can in turn be inspected using
6155 the following functions.
6157 #include <isl/ast.h>
6158 isl_ctx *isl_ast_expr_get_ctx(
6159 __isl_keep isl_ast_expr *expr);
6160 enum isl_ast_expr_type isl_ast_expr_get_type(
6161 __isl_keep isl_ast_expr *expr);
6163 The type of an AST expression is one of
6165 C<isl_ast_expr_id> or
6166 C<isl_ast_expr_int>.
6167 An C<isl_ast_expr_op> represents the result of an operation.
6168 An C<isl_ast_expr_id> represents an identifier.
6169 An C<isl_ast_expr_int> represents an integer value.
6171 Each type of expression has its own additional properties.
6173 #include <isl/ast.h>
6174 enum isl_ast_op_type isl_ast_expr_get_op_type(
6175 __isl_keep isl_ast_expr *expr);
6176 int isl_ast_expr_get_op_n_arg(__isl_keep isl_ast_expr *expr);
6177 __isl_give isl_ast_expr *isl_ast_expr_get_op_arg(
6178 __isl_keep isl_ast_expr *expr, int pos);
6179 int isl_ast_node_foreach_ast_op_type(
6180 __isl_keep isl_ast_node *node,
6181 int (*fn)(enum isl_ast_op_type type, void *user),
6184 C<isl_ast_expr_get_op_type> returns the type of the operation
6185 performed. C<isl_ast_expr_get_op_n_arg> returns the number of
6186 arguments. C<isl_ast_expr_get_op_arg> returns the specified
6188 C<isl_ast_node_foreach_ast_op_type> calls C<fn> for each distinct
6189 C<isl_ast_op_type> that appears in C<node>.
6190 The operation type is one of the following.
6194 =item C<isl_ast_op_and>
6196 Logical I<and> of two arguments.
6197 Both arguments can be evaluated.
6199 =item C<isl_ast_op_and_then>
6201 Logical I<and> of two arguments.
6202 The second argument can only be evaluated if the first evaluates to true.
6204 =item C<isl_ast_op_or>
6206 Logical I<or> of two arguments.
6207 Both arguments can be evaluated.
6209 =item C<isl_ast_op_or_else>
6211 Logical I<or> of two arguments.
6212 The second argument can only be evaluated if the first evaluates to false.
6214 =item C<isl_ast_op_max>
6216 Maximum of two or more arguments.
6218 =item C<isl_ast_op_min>
6220 Minimum of two or more arguments.
6222 =item C<isl_ast_op_minus>
6226 =item C<isl_ast_op_add>
6228 Sum of two arguments.
6230 =item C<isl_ast_op_sub>
6232 Difference of two arguments.
6234 =item C<isl_ast_op_mul>
6236 Product of two arguments.
6238 =item C<isl_ast_op_div>
6240 Exact division. That is, the result is known to be an integer.
6242 =item C<isl_ast_op_fdiv_q>
6244 Result of integer division, rounded towards negative
6247 =item C<isl_ast_op_pdiv_q>
6249 Result of integer division, where dividend is known to be non-negative.
6251 =item C<isl_ast_op_pdiv_r>
6253 Remainder of integer division, where dividend is known to be non-negative.
6255 =item C<isl_ast_op_cond>
6257 Conditional operator defined on three arguments.
6258 If the first argument evaluates to true, then the result
6259 is equal to the second argument. Otherwise, the result
6260 is equal to the third argument.
6261 The second and third argument may only be evaluated if
6262 the first argument evaluates to true and false, respectively.
6263 Corresponds to C<a ? b : c> in C.
6265 =item C<isl_ast_op_select>
6267 Conditional operator defined on three arguments.
6268 If the first argument evaluates to true, then the result
6269 is equal to the second argument. Otherwise, the result
6270 is equal to the third argument.
6271 The second and third argument may be evaluated independently
6272 of the value of the first argument.
6273 Corresponds to C<a * b + (1 - a) * c> in C.
6275 =item C<isl_ast_op_eq>
6279 =item C<isl_ast_op_le>
6281 Less than or equal relation.
6283 =item C<isl_ast_op_lt>
6287 =item C<isl_ast_op_ge>
6289 Greater than or equal relation.
6291 =item C<isl_ast_op_gt>
6293 Greater than relation.
6295 =item C<isl_ast_op_call>
6298 The number of arguments of the C<isl_ast_expr> is one more than
6299 the number of arguments in the function call, the first argument
6300 representing the function being called.
6302 =item C<isl_ast_op_access>
6305 The number of arguments of the C<isl_ast_expr> is one more than
6306 the number of index expressions in the array access, the first argument
6307 representing the array being accessed.
6309 =item C<isl_ast_op_member>
6312 This operation has two arguments, a structure and the name of
6313 the member of the structure being accessed.
6317 #include <isl/ast.h>
6318 __isl_give isl_id *isl_ast_expr_get_id(
6319 __isl_keep isl_ast_expr *expr);
6321 Return the identifier represented by the AST expression.
6323 #include <isl/ast.h>
6324 __isl_give isl_val *isl_ast_expr_get_val(
6325 __isl_keep isl_ast_expr *expr);
6327 Return the integer represented by the AST expression.
6329 =head3 Properties of ASTs
6331 #include <isl/ast.h>
6332 int isl_ast_expr_is_equal(__isl_keep isl_ast_expr *expr1,
6333 __isl_keep isl_ast_expr *expr2);
6335 Check if two C<isl_ast_expr>s are equal to each other.
6337 =head3 Manipulating and printing the AST
6339 AST nodes can be copied and freed using the following functions.
6341 #include <isl/ast.h>
6342 __isl_give isl_ast_node *isl_ast_node_copy(
6343 __isl_keep isl_ast_node *node);
6344 void *isl_ast_node_free(__isl_take isl_ast_node *node);
6346 AST expressions can be copied and freed using the following functions.
6348 #include <isl/ast.h>
6349 __isl_give isl_ast_expr *isl_ast_expr_copy(
6350 __isl_keep isl_ast_expr *expr);
6351 void *isl_ast_expr_free(__isl_take isl_ast_expr *expr);
6353 New AST expressions can be created either directly or within
6354 the context of an C<isl_ast_build>.
6356 #include <isl/ast.h>
6357 __isl_give isl_ast_expr *isl_ast_expr_from_val(
6358 __isl_take isl_val *v);
6359 __isl_give isl_ast_expr *isl_ast_expr_from_id(
6360 __isl_take isl_id *id);
6361 __isl_give isl_ast_expr *isl_ast_expr_neg(
6362 __isl_take isl_ast_expr *expr);
6363 __isl_give isl_ast_expr *isl_ast_expr_add(
6364 __isl_take isl_ast_expr *expr1,
6365 __isl_take isl_ast_expr *expr2);
6366 __isl_give isl_ast_expr *isl_ast_expr_sub(
6367 __isl_take isl_ast_expr *expr1,
6368 __isl_take isl_ast_expr *expr2);
6369 __isl_give isl_ast_expr *isl_ast_expr_mul(
6370 __isl_take isl_ast_expr *expr1,
6371 __isl_take isl_ast_expr *expr2);
6372 __isl_give isl_ast_expr *isl_ast_expr_div(
6373 __isl_take isl_ast_expr *expr1,
6374 __isl_take isl_ast_expr *expr2);
6375 __isl_give isl_ast_expr *isl_ast_expr_and(
6376 __isl_take isl_ast_expr *expr1,
6377 __isl_take isl_ast_expr *expr2)
6378 __isl_give isl_ast_expr *isl_ast_expr_or(
6379 __isl_take isl_ast_expr *expr1,
6380 __isl_take isl_ast_expr *expr2)
6381 __isl_give isl_ast_expr *isl_ast_expr_access(
6382 __isl_take isl_ast_expr *array,
6383 __isl_take isl_ast_expr_list *indices);
6385 #include <isl/ast_build.h>
6386 __isl_give isl_ast_expr *isl_ast_build_expr_from_pw_aff(
6387 __isl_keep isl_ast_build *build,
6388 __isl_take isl_pw_aff *pa);
6389 __isl_give isl_ast_expr *
6390 isl_ast_build_access_from_pw_multi_aff(
6391 __isl_keep isl_ast_build *build,
6392 __isl_take isl_pw_multi_aff *pma);
6393 __isl_give isl_ast_expr *
6394 isl_ast_build_access_from_multi_pw_aff(
6395 __isl_keep isl_ast_build *build,
6396 __isl_take isl_multi_pw_aff *mpa);
6397 __isl_give isl_ast_expr *
6398 isl_ast_build_call_from_pw_multi_aff(
6399 __isl_keep isl_ast_build *build,
6400 __isl_take isl_pw_multi_aff *pma);
6401 __isl_give isl_ast_expr *
6402 isl_ast_build_call_from_multi_pw_aff(
6403 __isl_keep isl_ast_build *build,
6404 __isl_take isl_multi_pw_aff *mpa);
6406 The domains of C<pa>, C<mpa> and C<pma> should correspond
6407 to the schedule space of C<build>.
6408 The tuple id of C<mpa> or C<pma> is used as the array being accessed or
6409 the function being called.
6410 If the accessed space is a nested relation, then it is taken
6411 to represent an access of the member specified by the range
6412 of this nested relation of the structure specified by the domain
6413 of the nested relation.
6415 The following functions can be used to modify an C<isl_ast_expr>.
6417 #include <isl/ast.h>
6418 __isl_give isl_ast_expr *isl_ast_expr_set_op_arg(
6419 __isl_take isl_ast_expr *expr, int pos,
6420 __isl_take isl_ast_expr *arg);
6422 Replace the argument of C<expr> at position C<pos> by C<arg>.
6424 #include <isl/ast.h>
6425 __isl_give isl_ast_expr *isl_ast_expr_substitute_ids(
6426 __isl_take isl_ast_expr *expr,
6427 __isl_take isl_id_to_ast_expr *id2expr);
6429 The function C<isl_ast_expr_substitute_ids> replaces the
6430 subexpressions of C<expr> of type C<isl_ast_expr_id>
6431 by the corresponding expression in C<id2expr>, if there is any.
6434 User specified data can be attached to an C<isl_ast_node> and obtained
6435 from the same C<isl_ast_node> using the following functions.
6437 #include <isl/ast.h>
6438 __isl_give isl_ast_node *isl_ast_node_set_annotation(
6439 __isl_take isl_ast_node *node,
6440 __isl_take isl_id *annotation);
6441 __isl_give isl_id *isl_ast_node_get_annotation(
6442 __isl_keep isl_ast_node *node);
6444 Basic printing can be performed using the following functions.
6446 #include <isl/ast.h>
6447 __isl_give isl_printer *isl_printer_print_ast_expr(
6448 __isl_take isl_printer *p,
6449 __isl_keep isl_ast_expr *expr);
6450 __isl_give isl_printer *isl_printer_print_ast_node(
6451 __isl_take isl_printer *p,
6452 __isl_keep isl_ast_node *node);
6454 More advanced printing can be performed using the following functions.
6456 #include <isl/ast.h>
6457 __isl_give isl_printer *isl_ast_op_type_print_macro(
6458 enum isl_ast_op_type type,
6459 __isl_take isl_printer *p);
6460 __isl_give isl_printer *isl_ast_node_print_macros(
6461 __isl_keep isl_ast_node *node,
6462 __isl_take isl_printer *p);
6463 __isl_give isl_printer *isl_ast_node_print(
6464 __isl_keep isl_ast_node *node,
6465 __isl_take isl_printer *p,
6466 __isl_take isl_ast_print_options *options);
6467 __isl_give isl_printer *isl_ast_node_for_print(
6468 __isl_keep isl_ast_node *node,
6469 __isl_take isl_printer *p,
6470 __isl_take isl_ast_print_options *options);
6471 __isl_give isl_printer *isl_ast_node_if_print(
6472 __isl_keep isl_ast_node *node,
6473 __isl_take isl_printer *p,
6474 __isl_take isl_ast_print_options *options);
6476 While printing an C<isl_ast_node> in C<ISL_FORMAT_C>,
6477 C<isl> may print out an AST that makes use of macros such
6478 as C<floord>, C<min> and C<max>.
6479 C<isl_ast_op_type_print_macro> prints out the macro
6480 corresponding to a specific C<isl_ast_op_type>.
6481 C<isl_ast_node_print_macros> scans the C<isl_ast_node>
6482 for expressions where these macros would be used and prints
6483 out the required macro definitions.
6484 Essentially, C<isl_ast_node_print_macros> calls
6485 C<isl_ast_node_foreach_ast_op_type> with C<isl_ast_op_type_print_macro>
6486 as function argument.
6487 C<isl_ast_node_print>, C<isl_ast_node_for_print> and
6488 C<isl_ast_node_if_print> print an C<isl_ast_node>
6489 in C<ISL_FORMAT_C>, but allow for some extra control
6490 through an C<isl_ast_print_options> object.
6491 This object can be created using the following functions.
6493 #include <isl/ast.h>
6494 __isl_give isl_ast_print_options *
6495 isl_ast_print_options_alloc(isl_ctx *ctx);
6496 __isl_give isl_ast_print_options *
6497 isl_ast_print_options_copy(
6498 __isl_keep isl_ast_print_options *options);
6499 void *isl_ast_print_options_free(
6500 __isl_take isl_ast_print_options *options);
6502 __isl_give isl_ast_print_options *
6503 isl_ast_print_options_set_print_user(
6504 __isl_take isl_ast_print_options *options,
6505 __isl_give isl_printer *(*print_user)(
6506 __isl_take isl_printer *p,
6507 __isl_take isl_ast_print_options *options,
6508 __isl_keep isl_ast_node *node, void *user),
6510 __isl_give isl_ast_print_options *
6511 isl_ast_print_options_set_print_for(
6512 __isl_take isl_ast_print_options *options,
6513 __isl_give isl_printer *(*print_for)(
6514 __isl_take isl_printer *p,
6515 __isl_take isl_ast_print_options *options,
6516 __isl_keep isl_ast_node *node, void *user),
6519 The callback set by C<isl_ast_print_options_set_print_user>
6520 is called whenever a node of type C<isl_ast_node_user> needs to
6522 The callback set by C<isl_ast_print_options_set_print_for>
6523 is called whenever a node of type C<isl_ast_node_for> needs to
6525 Note that C<isl_ast_node_for_print> will I<not> call the
6526 callback set by C<isl_ast_print_options_set_print_for> on the node
6527 on which C<isl_ast_node_for_print> is called, but only on nested
6528 nodes of type C<isl_ast_node_for>. It is therefore safe to
6529 call C<isl_ast_node_for_print> from within the callback set by
6530 C<isl_ast_print_options_set_print_for>.
6532 The following option determines the type to be used for iterators
6533 while printing the AST.
6535 int isl_options_set_ast_iterator_type(
6536 isl_ctx *ctx, const char *val);
6537 const char *isl_options_get_ast_iterator_type(
6542 #include <isl/ast_build.h>
6543 int isl_options_set_ast_build_atomic_upper_bound(
6544 isl_ctx *ctx, int val);
6545 int isl_options_get_ast_build_atomic_upper_bound(
6547 int isl_options_set_ast_build_prefer_pdiv(isl_ctx *ctx,
6549 int isl_options_get_ast_build_prefer_pdiv(isl_ctx *ctx);
6550 int isl_options_set_ast_build_exploit_nested_bounds(
6551 isl_ctx *ctx, int val);
6552 int isl_options_get_ast_build_exploit_nested_bounds(
6554 int isl_options_set_ast_build_group_coscheduled(
6555 isl_ctx *ctx, int val);
6556 int isl_options_get_ast_build_group_coscheduled(
6558 int isl_options_set_ast_build_scale_strides(
6559 isl_ctx *ctx, int val);
6560 int isl_options_get_ast_build_scale_strides(
6562 int isl_options_set_ast_build_allow_else(isl_ctx *ctx,
6564 int isl_options_get_ast_build_allow_else(isl_ctx *ctx);
6565 int isl_options_set_ast_build_allow_or(isl_ctx *ctx,
6567 int isl_options_get_ast_build_allow_or(isl_ctx *ctx);
6571 =item * ast_build_atomic_upper_bound
6573 Generate loop upper bounds that consist of the current loop iterator,
6574 an operator and an expression not involving the iterator.
6575 If this option is not set, then the current loop iterator may appear
6576 several times in the upper bound.
6577 For example, when this option is turned off, AST generation
6580 [n] -> { A[i] -> [i] : 0 <= i <= 100, n }
6584 for (int c0 = 0; c0 <= 100 && n >= c0; c0 += 1)
6587 When the option is turned on, the following AST is generated
6589 for (int c0 = 0; c0 <= min(100, n); c0 += 1)
6592 =item * ast_build_prefer_pdiv
6594 If this option is turned off, then the AST generation will
6595 produce ASTs that may only contain C<isl_ast_op_fdiv_q>
6596 operators, but no C<isl_ast_op_pdiv_q> or
6597 C<isl_ast_op_pdiv_r> operators.
6598 If this options is turned on, then C<isl> will try to convert
6599 some of the C<isl_ast_op_fdiv_q> operators to (expressions containing)
6600 C<isl_ast_op_pdiv_q> or C<isl_ast_op_pdiv_r> operators.
6602 =item * ast_build_exploit_nested_bounds
6604 Simplify conditions based on bounds of nested for loops.
6605 In particular, remove conditions that are implied by the fact
6606 that one or more nested loops have at least one iteration,
6607 meaning that the upper bound is at least as large as the lower bound.
6608 For example, when this option is turned off, AST generation
6611 [N,M] -> { A[i,j] -> [i,j] : 0 <= i <= N and
6617 for (int c0 = 0; c0 <= N; c0 += 1)
6618 for (int c1 = 0; c1 <= M; c1 += 1)
6621 When the option is turned on, the following AST is generated
6623 for (int c0 = 0; c0 <= N; c0 += 1)
6624 for (int c1 = 0; c1 <= M; c1 += 1)
6627 =item * ast_build_group_coscheduled
6629 If two domain elements are assigned the same schedule point, then
6630 they may be executed in any order and they may even appear in different
6631 loops. If this options is set, then the AST generator will make
6632 sure that coscheduled domain elements do not appear in separate parts
6633 of the AST. This is useful in case of nested AST generation
6634 if the outer AST generation is given only part of a schedule
6635 and the inner AST generation should handle the domains that are
6636 coscheduled by this initial part of the schedule together.
6637 For example if an AST is generated for a schedule
6639 { A[i] -> [0]; B[i] -> [0] }
6641 then the C<isl_ast_build_set_create_leaf> callback described
6642 below may get called twice, once for each domain.
6643 Setting this option ensures that the callback is only called once
6644 on both domains together.
6646 =item * ast_build_separation_bounds
6648 This option specifies which bounds to use during separation.
6649 If this option is set to C<ISL_AST_BUILD_SEPARATION_BOUNDS_IMPLICIT>
6650 then all (possibly implicit) bounds on the current dimension will
6651 be used during separation.
6652 If this option is set to C<ISL_AST_BUILD_SEPARATION_BOUNDS_EXPLICIT>
6653 then only those bounds that are explicitly available will
6654 be used during separation.
6656 =item * ast_build_scale_strides
6658 This option specifies whether the AST generator is allowed
6659 to scale down iterators of strided loops.
6661 =item * ast_build_allow_else
6663 This option specifies whether the AST generator is allowed
6664 to construct if statements with else branches.
6666 =item * ast_build_allow_or
6668 This option specifies whether the AST generator is allowed
6669 to construct if conditions with disjunctions.
6673 =head3 Fine-grained Control over AST Generation
6675 Besides specifying the constraints on the parameters,
6676 an C<isl_ast_build> object can be used to control
6677 various aspects of the AST generation process.
6678 The most prominent way of control is through ``options'',
6679 which can be set using the following function.
6681 #include <isl/ast_build.h>
6682 __isl_give isl_ast_build *
6683 isl_ast_build_set_options(
6684 __isl_take isl_ast_build *control,
6685 __isl_take isl_union_map *options);
6687 The options are encoded in an <isl_union_map>.
6688 The domain of this union relation refers to the schedule domain,
6689 i.e., the range of the schedule passed to C<isl_ast_build_ast_from_schedule>.
6690 In the case of nested AST generation (see L</"Nested AST Generation">),
6691 the domain of C<options> should refer to the extra piece of the schedule.
6692 That is, it should be equal to the range of the wrapped relation in the
6693 range of the schedule.
6694 The range of the options can consist of elements in one or more spaces,
6695 the names of which determine the effect of the option.
6696 The values of the range typically also refer to the schedule dimension
6697 to which the option applies. In case of nested AST generation
6698 (see L</"Nested AST Generation">), these values refer to the position
6699 of the schedule dimension within the innermost AST generation.
6700 The constraints on the domain elements of
6701 the option should only refer to this dimension and earlier dimensions.
6702 We consider the following spaces.
6706 =item C<separation_class>
6708 This space is a wrapped relation between two one dimensional spaces.
6709 The input space represents the schedule dimension to which the option
6710 applies and the output space represents the separation class.
6711 While constructing a loop corresponding to the specified schedule
6712 dimension(s), the AST generator will try to generate separate loops
6713 for domain elements that are assigned different classes.
6714 If only some of the elements are assigned a class, then those elements
6715 that are not assigned any class will be treated as belonging to a class
6716 that is separate from the explicitly assigned classes.
6717 The typical use case for this option is to separate full tiles from
6719 The other options, described below, are applied after the separation
6722 As an example, consider the separation into full and partial tiles
6723 of a tiling of a triangular domain.
6724 Take, for example, the domain
6726 { A[i,j] : 0 <= i,j and i + j <= 100 }
6728 and a tiling into tiles of 10 by 10. The input to the AST generator
6729 is then the schedule
6731 { A[i,j] -> [([i/10]),[j/10],i,j] : 0 <= i,j and
6734 Without any options, the following AST is generated
6736 for (int c0 = 0; c0 <= 10; c0 += 1)
6737 for (int c1 = 0; c1 <= -c0 + 10; c1 += 1)
6738 for (int c2 = 10 * c0;
6739 c2 <= min(-10 * c1 + 100, 10 * c0 + 9);
6741 for (int c3 = 10 * c1;
6742 c3 <= min(10 * c1 + 9, -c2 + 100);
6746 Separation into full and partial tiles can be obtained by assigning
6747 a class, say C<0>, to the full tiles. The full tiles are represented by those
6748 values of the first and second schedule dimensions for which there are
6749 values of the third and fourth dimensions to cover an entire tile.
6750 That is, we need to specify the following option
6752 { [a,b,c,d] -> separation_class[[0]->[0]] :
6753 exists b': 0 <= 10a,10b' and
6754 10a+9+10b'+9 <= 100;
6755 [a,b,c,d] -> separation_class[[1]->[0]] :
6756 0 <= 10a,10b and 10a+9+10b+9 <= 100 }
6760 { [a, b, c, d] -> separation_class[[1] -> [0]] :
6761 a >= 0 and b >= 0 and b <= 8 - a;
6762 [a, b, c, d] -> separation_class[[0] -> [0]] :
6765 With this option, the generated AST is as follows
6768 for (int c0 = 0; c0 <= 8; c0 += 1) {
6769 for (int c1 = 0; c1 <= -c0 + 8; c1 += 1)
6770 for (int c2 = 10 * c0;
6771 c2 <= 10 * c0 + 9; c2 += 1)
6772 for (int c3 = 10 * c1;
6773 c3 <= 10 * c1 + 9; c3 += 1)
6775 for (int c1 = -c0 + 9; c1 <= -c0 + 10; c1 += 1)
6776 for (int c2 = 10 * c0;
6777 c2 <= min(-10 * c1 + 100, 10 * c0 + 9);
6779 for (int c3 = 10 * c1;
6780 c3 <= min(-c2 + 100, 10 * c1 + 9);
6784 for (int c0 = 9; c0 <= 10; c0 += 1)
6785 for (int c1 = 0; c1 <= -c0 + 10; c1 += 1)
6786 for (int c2 = 10 * c0;
6787 c2 <= min(-10 * c1 + 100, 10 * c0 + 9);
6789 for (int c3 = 10 * c1;
6790 c3 <= min(10 * c1 + 9, -c2 + 100);
6797 This is a single-dimensional space representing the schedule dimension(s)
6798 to which ``separation'' should be applied. Separation tries to split
6799 a loop into several pieces if this can avoid the generation of guards
6801 See also the C<atomic> option.
6805 This is a single-dimensional space representing the schedule dimension(s)
6806 for which the domains should be considered ``atomic''. That is, the
6807 AST generator will make sure that any given domain space will only appear
6808 in a single loop at the specified level.
6810 Consider the following schedule
6812 { a[i] -> [i] : 0 <= i < 10;
6813 b[i] -> [i+1] : 0 <= i < 10 }
6815 If the following option is specified
6817 { [i] -> separate[x] }
6819 then the following AST will be generated
6823 for (int c0 = 1; c0 <= 9; c0 += 1) {
6830 If, on the other hand, the following option is specified
6832 { [i] -> atomic[x] }
6834 then the following AST will be generated
6836 for (int c0 = 0; c0 <= 10; c0 += 1) {
6843 If neither C<atomic> nor C<separate> is specified, then the AST generator
6844 may produce either of these two results or some intermediate form.
6848 This is a single-dimensional space representing the schedule dimension(s)
6849 that should be I<completely> unrolled.
6850 To obtain a partial unrolling, the user should apply an additional
6851 strip-mining to the schedule and fully unroll the inner loop.
6855 Additional control is available through the following functions.
6857 #include <isl/ast_build.h>
6858 __isl_give isl_ast_build *
6859 isl_ast_build_set_iterators(
6860 __isl_take isl_ast_build *control,
6861 __isl_take isl_id_list *iterators);
6863 The function C<isl_ast_build_set_iterators> allows the user to
6864 specify a list of iterator C<isl_id>s to be used as iterators.
6865 If the input schedule is injective, then
6866 the number of elements in this list should be as large as the dimension
6867 of the schedule space, but no direct correspondence should be assumed
6868 between dimensions and elements.
6869 If the input schedule is not injective, then an additional number
6870 of C<isl_id>s equal to the largest dimension of the input domains
6872 If the number of provided C<isl_id>s is insufficient, then additional
6873 names are automatically generated.
6875 #include <isl/ast_build.h>
6876 __isl_give isl_ast_build *
6877 isl_ast_build_set_create_leaf(
6878 __isl_take isl_ast_build *control,
6879 __isl_give isl_ast_node *(*fn)(
6880 __isl_take isl_ast_build *build,
6881 void *user), void *user);
6884 C<isl_ast_build_set_create_leaf> function allows for the
6885 specification of a callback that should be called whenever the AST
6886 generator arrives at an element of the schedule domain.
6887 The callback should return an AST node that should be inserted
6888 at the corresponding position of the AST. The default action (when
6889 the callback is not set) is to continue generating parts of the AST to scan
6890 all the domain elements associated to the schedule domain element
6891 and to insert user nodes, ``calling'' the domain element, for each of them.
6892 The C<build> argument contains the current state of the C<isl_ast_build>.
6893 To ease nested AST generation (see L</"Nested AST Generation">),
6894 all control information that is
6895 specific to the current AST generation such as the options and
6896 the callbacks has been removed from this C<isl_ast_build>.
6897 The callback would typically return the result of a nested
6899 user defined node created using the following function.
6901 #include <isl/ast.h>
6902 __isl_give isl_ast_node *isl_ast_node_alloc_user(
6903 __isl_take isl_ast_expr *expr);
6905 #include <isl/ast_build.h>
6906 __isl_give isl_ast_build *
6907 isl_ast_build_set_at_each_domain(
6908 __isl_take isl_ast_build *build,
6909 __isl_give isl_ast_node *(*fn)(
6910 __isl_take isl_ast_node *node,
6911 __isl_keep isl_ast_build *build,
6912 void *user), void *user);
6913 __isl_give isl_ast_build *
6914 isl_ast_build_set_before_each_for(
6915 __isl_take isl_ast_build *build,
6916 __isl_give isl_id *(*fn)(
6917 __isl_keep isl_ast_build *build,
6918 void *user), void *user);
6919 __isl_give isl_ast_build *
6920 isl_ast_build_set_after_each_for(
6921 __isl_take isl_ast_build *build,
6922 __isl_give isl_ast_node *(*fn)(
6923 __isl_take isl_ast_node *node,
6924 __isl_keep isl_ast_build *build,
6925 void *user), void *user);
6927 The callback set by C<isl_ast_build_set_at_each_domain> will
6928 be called for each domain AST node.
6929 The callbacks set by C<isl_ast_build_set_before_each_for>
6930 and C<isl_ast_build_set_after_each_for> will be called
6931 for each for AST node. The first will be called in depth-first
6932 pre-order, while the second will be called in depth-first post-order.
6933 Since C<isl_ast_build_set_before_each_for> is called before the for
6934 node is actually constructed, it is only passed an C<isl_ast_build>.
6935 The returned C<isl_id> will be added as an annotation (using
6936 C<isl_ast_node_set_annotation>) to the constructed for node.
6937 In particular, if the user has also specified an C<after_each_for>
6938 callback, then the annotation can be retrieved from the node passed to
6939 that callback using C<isl_ast_node_get_annotation>.
6940 All callbacks should C<NULL> on failure.
6941 The given C<isl_ast_build> can be used to create new
6942 C<isl_ast_expr> objects using C<isl_ast_build_expr_from_pw_aff>
6943 or C<isl_ast_build_call_from_pw_multi_aff>.
6945 =head3 Nested AST Generation
6947 C<isl> allows the user to create an AST within the context
6948 of another AST. These nested ASTs are created using the
6949 same C<isl_ast_build_ast_from_schedule> function that is used to create the
6950 outer AST. The C<build> argument should be an C<isl_ast_build>
6951 passed to a callback set by
6952 C<isl_ast_build_set_create_leaf>.
6953 The space of the range of the C<schedule> argument should refer
6954 to this build. In particular, the space should be a wrapped
6955 relation and the domain of this wrapped relation should be the
6956 same as that of the range of the schedule returned by
6957 C<isl_ast_build_get_schedule> below.
6958 In practice, the new schedule is typically
6959 created by calling C<isl_union_map_range_product> on the old schedule
6960 and some extra piece of the schedule.
6961 The space of the schedule domain is also available from
6962 the C<isl_ast_build>.
6964 #include <isl/ast_build.h>
6965 __isl_give isl_union_map *isl_ast_build_get_schedule(
6966 __isl_keep isl_ast_build *build);
6967 __isl_give isl_space *isl_ast_build_get_schedule_space(
6968 __isl_keep isl_ast_build *build);
6969 __isl_give isl_ast_build *isl_ast_build_restrict(
6970 __isl_take isl_ast_build *build,
6971 __isl_take isl_set *set);
6973 The C<isl_ast_build_get_schedule> function returns a (partial)
6974 schedule for the domains elements for which part of the AST still needs to
6975 be generated in the current build.
6976 In particular, the domain elements are mapped to those iterations of the loops
6977 enclosing the current point of the AST generation inside which
6978 the domain elements are executed.
6979 No direct correspondence between
6980 the input schedule and this schedule should be assumed.
6981 The space obtained from C<isl_ast_build_get_schedule_space> can be used
6982 to create a set for C<isl_ast_build_restrict> to intersect
6983 with the current build. In particular, the set passed to
6984 C<isl_ast_build_restrict> can have additional parameters.
6985 The ids of the set dimensions in the space returned by
6986 C<isl_ast_build_get_schedule_space> correspond to the
6987 iterators of the already generated loops.
6988 The user should not rely on the ids of the output dimensions
6989 of the relations in the union relation returned by
6990 C<isl_ast_build_get_schedule> having any particular value.
6994 Although C<isl> is mainly meant to be used as a library,
6995 it also contains some basic applications that use some
6996 of the functionality of C<isl>.
6997 The input may be specified in either the L<isl format>
6998 or the L<PolyLib format>.
7000 =head2 C<isl_polyhedron_sample>
7002 C<isl_polyhedron_sample> takes a polyhedron as input and prints
7003 an integer element of the polyhedron, if there is any.
7004 The first column in the output is the denominator and is always
7005 equal to 1. If the polyhedron contains no integer points,
7006 then a vector of length zero is printed.
7010 C<isl_pip> takes the same input as the C<example> program
7011 from the C<piplib> distribution, i.e., a set of constraints
7012 on the parameters, a line containing only -1 and finally a set
7013 of constraints on a parametric polyhedron.
7014 The coefficients of the parameters appear in the last columns
7015 (but before the final constant column).
7016 The output is the lexicographic minimum of the parametric polyhedron.
7017 As C<isl> currently does not have its own output format, the output
7018 is just a dump of the internal state.
7020 =head2 C<isl_polyhedron_minimize>
7022 C<isl_polyhedron_minimize> computes the minimum of some linear
7023 or affine objective function over the integer points in a polyhedron.
7024 If an affine objective function
7025 is given, then the constant should appear in the last column.
7027 =head2 C<isl_polytope_scan>
7029 Given a polytope, C<isl_polytope_scan> prints
7030 all integer points in the polytope.
7032 =head2 C<isl_codegen>
7034 Given a schedule, a context set and an options relation,
7035 C<isl_codegen> prints out an AST that scans the domain elements
7036 of the schedule in the order of their image(s) taking into account
7037 the constraints in the context set.