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 The following functions can be used to construct and deconstruct
935 #include <isl/space.h>
936 int isl_space_is_wrapping(__isl_keep isl_space *space);
937 int isl_space_range_is_wrapping(
938 __isl_keep isl_space *space);
939 __isl_give isl_space *isl_space_wrap(__isl_take isl_space *space);
940 __isl_give isl_space *isl_space_unwrap(__isl_take isl_space *space);
941 __isl_give isl_space *isl_space_product(__isl_take isl_space *space1,
942 __isl_take isl_space *space2);
943 __isl_give isl_space *isl_space_domain_product(
944 __isl_take isl_space *space1,
945 __isl_take isl_space *space2);
946 __isl_give isl_space *isl_space_range_product(
947 __isl_take isl_space *space1,
948 __isl_take isl_space *space2);
949 __isl_give isl_space *isl_space_range_factor_domain(
950 __isl_take isl_space *space);
951 __isl_give isl_space *isl_space_range_factor_range(
952 __isl_take isl_space *space);
954 The input to C<isl_space_is_wrapping> and C<isl_space_unwrap> should
955 be the space of a set, while that of
956 C<isl_space_range_is_wrapping> and
957 C<isl_space_wrap> should be the space of a relation.
958 Conversely, the output of C<isl_space_unwrap> is the space
959 of a relation, while that of C<isl_space_wrap> is the space of a set.
961 C<isl_space_product>, C<isl_space_domain_product>
962 and C<isl_space_range_product> take pairs or relation spaces and
963 produce a single relations space, where either the domain, the range
964 or both domain and range are wrapped spaces of relations between
965 the domains and/or ranges of the input spaces.
966 If the product is only constructed over the domain or the range
967 then the ranges or the domains of the inputs should be the same.
968 The functions C<isl_space_range_factor_domain> and
969 C<isl_space_range_factor_range> extract the two arguments from
970 the result of a call to C<isl_space_range_product>.
972 Spaces can be created from other spaces
973 using the following functions.
975 __isl_give isl_space *isl_space_domain(__isl_take isl_space *space);
976 __isl_give isl_space *isl_space_from_domain(__isl_take isl_space *space);
977 __isl_give isl_space *isl_space_range(__isl_take isl_space *space);
978 __isl_give isl_space *isl_space_from_range(__isl_take isl_space *space);
979 __isl_give isl_space *isl_space_domain_map(
980 __isl_take isl_space *space);
981 __isl_give isl_space *isl_space_range_map(
982 __isl_take isl_space *space);
983 __isl_give isl_space *isl_space_params(
984 __isl_take isl_space *space);
985 __isl_give isl_space *isl_space_set_from_params(
986 __isl_take isl_space *space);
987 __isl_give isl_space *isl_space_reverse(__isl_take isl_space *space);
988 __isl_give isl_space *isl_space_join(__isl_take isl_space *left,
989 __isl_take isl_space *right);
990 __isl_give isl_space *isl_space_align_params(
991 __isl_take isl_space *space1, __isl_take isl_space *space2)
992 __isl_give isl_space *isl_space_insert_dims(__isl_take isl_space *space,
993 enum isl_dim_type type, unsigned pos, unsigned n);
994 __isl_give isl_space *isl_space_add_dims(__isl_take isl_space *space,
995 enum isl_dim_type type, unsigned n);
996 __isl_give isl_space *isl_space_drop_dims(__isl_take isl_space *space,
997 enum isl_dim_type type, unsigned first, unsigned n);
998 __isl_give isl_space *isl_space_move_dims(__isl_take isl_space *space,
999 enum isl_dim_type dst_type, unsigned dst_pos,
1000 enum isl_dim_type src_type, unsigned src_pos,
1002 __isl_give isl_space *isl_space_map_from_set(
1003 __isl_take isl_space *space);
1004 __isl_give isl_space *isl_space_map_from_domain_and_range(
1005 __isl_take isl_space *domain,
1006 __isl_take isl_space *range);
1007 __isl_give isl_space *isl_space_zip(__isl_take isl_space *space);
1008 __isl_give isl_space *isl_space_curry(
1009 __isl_take isl_space *space);
1010 __isl_give isl_space *isl_space_uncurry(
1011 __isl_take isl_space *space);
1013 Note that if dimensions are added or removed from a space, then
1014 the name and the internal structure are lost.
1018 A local space is essentially a space with
1019 zero or more existentially quantified variables.
1020 The local space of a (constraint of a) basic set or relation can be obtained
1021 using the following functions.
1023 #include <isl/constraint.h>
1024 __isl_give isl_local_space *isl_constraint_get_local_space(
1025 __isl_keep isl_constraint *constraint);
1027 #include <isl/set.h>
1028 __isl_give isl_local_space *isl_basic_set_get_local_space(
1029 __isl_keep isl_basic_set *bset);
1031 #include <isl/map.h>
1032 __isl_give isl_local_space *isl_basic_map_get_local_space(
1033 __isl_keep isl_basic_map *bmap);
1035 A new local space can be created from a space using
1037 #include <isl/local_space.h>
1038 __isl_give isl_local_space *isl_local_space_from_space(
1039 __isl_take isl_space *space);
1041 They can be inspected, modified, copied and freed using the following functions.
1043 #include <isl/local_space.h>
1044 isl_ctx *isl_local_space_get_ctx(
1045 __isl_keep isl_local_space *ls);
1046 int isl_local_space_is_set(__isl_keep isl_local_space *ls);
1047 int isl_local_space_dim(__isl_keep isl_local_space *ls,
1048 enum isl_dim_type type);
1049 __isl_give isl_local_space *isl_local_space_set_tuple_id(
1050 __isl_take isl_local_space *ls,
1051 enum isl_dim_type type, __isl_take isl_id *id);
1052 int isl_local_space_has_dim_id(
1053 __isl_keep isl_local_space *ls,
1054 enum isl_dim_type type, unsigned pos);
1055 __isl_give isl_id *isl_local_space_get_dim_id(
1056 __isl_keep isl_local_space *ls,
1057 enum isl_dim_type type, unsigned pos);
1058 int isl_local_space_has_dim_name(
1059 __isl_keep isl_local_space *ls,
1060 enum isl_dim_type type, unsigned pos)
1061 const char *isl_local_space_get_dim_name(
1062 __isl_keep isl_local_space *ls,
1063 enum isl_dim_type type, unsigned pos);
1064 __isl_give isl_local_space *isl_local_space_set_dim_name(
1065 __isl_take isl_local_space *ls,
1066 enum isl_dim_type type, unsigned pos, const char *s);
1067 __isl_give isl_local_space *isl_local_space_set_dim_id(
1068 __isl_take isl_local_space *ls,
1069 enum isl_dim_type type, unsigned pos,
1070 __isl_take isl_id *id);
1071 __isl_give isl_space *isl_local_space_get_space(
1072 __isl_keep isl_local_space *ls);
1073 __isl_give isl_aff *isl_local_space_get_div(
1074 __isl_keep isl_local_space *ls, int pos);
1075 __isl_give isl_local_space *isl_local_space_copy(
1076 __isl_keep isl_local_space *ls);
1077 void *isl_local_space_free(__isl_take isl_local_space *ls);
1079 Note that C<isl_local_space_get_div> can only be used on local spaces
1082 Two local spaces can be compared using
1084 int isl_local_space_is_equal(__isl_keep isl_local_space *ls1,
1085 __isl_keep isl_local_space *ls2);
1087 Local spaces can be created from other local spaces
1088 using the following functions.
1090 __isl_give isl_local_space *isl_local_space_domain(
1091 __isl_take isl_local_space *ls);
1092 __isl_give isl_local_space *isl_local_space_range(
1093 __isl_take isl_local_space *ls);
1094 __isl_give isl_local_space *isl_local_space_from_domain(
1095 __isl_take isl_local_space *ls);
1096 __isl_give isl_local_space *isl_local_space_intersect(
1097 __isl_take isl_local_space *ls1,
1098 __isl_take isl_local_space *ls2);
1099 __isl_give isl_local_space *isl_local_space_add_dims(
1100 __isl_take isl_local_space *ls,
1101 enum isl_dim_type type, unsigned n);
1102 __isl_give isl_local_space *isl_local_space_insert_dims(
1103 __isl_take isl_local_space *ls,
1104 enum isl_dim_type type, unsigned first, unsigned n);
1105 __isl_give isl_local_space *isl_local_space_drop_dims(
1106 __isl_take isl_local_space *ls,
1107 enum isl_dim_type type, unsigned first, unsigned n);
1109 =head2 Input and Output
1111 C<isl> supports its own input/output format, which is similar
1112 to the C<Omega> format, but also supports the C<PolyLib> format
1115 =head3 C<isl> format
1117 The C<isl> format is similar to that of C<Omega>, but has a different
1118 syntax for describing the parameters and allows for the definition
1119 of an existentially quantified variable as the integer division
1120 of an affine expression.
1121 For example, the set of integers C<i> between C<0> and C<n>
1122 such that C<i % 10 <= 6> can be described as
1124 [n] -> { [i] : exists (a = [i/10] : 0 <= i and i <= n and
1127 A set or relation can have several disjuncts, separated
1128 by the keyword C<or>. Each disjunct is either a conjunction
1129 of constraints or a projection (C<exists>) of a conjunction
1130 of constraints. The constraints are separated by the keyword
1133 =head3 C<PolyLib> format
1135 If the represented set is a union, then the first line
1136 contains a single number representing the number of disjuncts.
1137 Otherwise, a line containing the number C<1> is optional.
1139 Each disjunct is represented by a matrix of constraints.
1140 The first line contains two numbers representing
1141 the number of rows and columns,
1142 where the number of rows is equal to the number of constraints
1143 and the number of columns is equal to two plus the number of variables.
1144 The following lines contain the actual rows of the constraint matrix.
1145 In each row, the first column indicates whether the constraint
1146 is an equality (C<0>) or inequality (C<1>). The final column
1147 corresponds to the constant term.
1149 If the set is parametric, then the coefficients of the parameters
1150 appear in the last columns before the constant column.
1151 The coefficients of any existentially quantified variables appear
1152 between those of the set variables and those of the parameters.
1154 =head3 Extended C<PolyLib> format
1156 The extended C<PolyLib> format is nearly identical to the
1157 C<PolyLib> format. The only difference is that the line
1158 containing the number of rows and columns of a constraint matrix
1159 also contains four additional numbers:
1160 the number of output dimensions, the number of input dimensions,
1161 the number of local dimensions (i.e., the number of existentially
1162 quantified variables) and the number of parameters.
1163 For sets, the number of ``output'' dimensions is equal
1164 to the number of set dimensions, while the number of ``input''
1169 #include <isl/set.h>
1170 __isl_give isl_basic_set *isl_basic_set_read_from_file(
1171 isl_ctx *ctx, FILE *input);
1172 __isl_give isl_basic_set *isl_basic_set_read_from_str(
1173 isl_ctx *ctx, const char *str);
1174 __isl_give isl_set *isl_set_read_from_file(isl_ctx *ctx,
1176 __isl_give isl_set *isl_set_read_from_str(isl_ctx *ctx,
1179 #include <isl/map.h>
1180 __isl_give isl_basic_map *isl_basic_map_read_from_file(
1181 isl_ctx *ctx, FILE *input);
1182 __isl_give isl_basic_map *isl_basic_map_read_from_str(
1183 isl_ctx *ctx, const char *str);
1184 __isl_give isl_map *isl_map_read_from_file(
1185 isl_ctx *ctx, FILE *input);
1186 __isl_give isl_map *isl_map_read_from_str(isl_ctx *ctx,
1189 #include <isl/union_set.h>
1190 __isl_give isl_union_set *isl_union_set_read_from_file(
1191 isl_ctx *ctx, FILE *input);
1192 __isl_give isl_union_set *isl_union_set_read_from_str(
1193 isl_ctx *ctx, const char *str);
1195 #include <isl/union_map.h>
1196 __isl_give isl_union_map *isl_union_map_read_from_file(
1197 isl_ctx *ctx, FILE *input);
1198 __isl_give isl_union_map *isl_union_map_read_from_str(
1199 isl_ctx *ctx, const char *str);
1201 The input format is autodetected and may be either the C<PolyLib> format
1202 or the C<isl> format.
1206 Before anything can be printed, an C<isl_printer> needs to
1209 __isl_give isl_printer *isl_printer_to_file(isl_ctx *ctx,
1211 __isl_give isl_printer *isl_printer_to_str(isl_ctx *ctx);
1212 void *isl_printer_free(__isl_take isl_printer *printer);
1213 __isl_give char *isl_printer_get_str(
1214 __isl_keep isl_printer *printer);
1216 The printer can be inspected using the following functions.
1218 FILE *isl_printer_get_file(
1219 __isl_keep isl_printer *printer);
1220 int isl_printer_get_output_format(
1221 __isl_keep isl_printer *p);
1223 The behavior of the printer can be modified in various ways
1225 __isl_give isl_printer *isl_printer_set_output_format(
1226 __isl_take isl_printer *p, int output_format);
1227 __isl_give isl_printer *isl_printer_set_indent(
1228 __isl_take isl_printer *p, int indent);
1229 __isl_give isl_printer *isl_printer_indent(
1230 __isl_take isl_printer *p, int indent);
1231 __isl_give isl_printer *isl_printer_set_prefix(
1232 __isl_take isl_printer *p, const char *prefix);
1233 __isl_give isl_printer *isl_printer_set_suffix(
1234 __isl_take isl_printer *p, const char *suffix);
1236 The C<output_format> may be either C<ISL_FORMAT_ISL>, C<ISL_FORMAT_OMEGA>,
1237 C<ISL_FORMAT_POLYLIB>, C<ISL_FORMAT_EXT_POLYLIB> or C<ISL_FORMAT_LATEX>
1238 and defaults to C<ISL_FORMAT_ISL>.
1239 Each line in the output is indented by C<indent> (set by
1240 C<isl_printer_set_indent>) spaces
1241 (default: 0), prefixed by C<prefix> and suffixed by C<suffix>.
1242 In the C<PolyLib> format output,
1243 the coefficients of the existentially quantified variables
1244 appear between those of the set variables and those
1246 The function C<isl_printer_indent> increases the indentation
1247 by the specified amount (which may be negative).
1249 To actually print something, use
1251 #include <isl/printer.h>
1252 __isl_give isl_printer *isl_printer_print_double(
1253 __isl_take isl_printer *p, double d);
1255 #include <isl/set.h>
1256 __isl_give isl_printer *isl_printer_print_basic_set(
1257 __isl_take isl_printer *printer,
1258 __isl_keep isl_basic_set *bset);
1259 __isl_give isl_printer *isl_printer_print_set(
1260 __isl_take isl_printer *printer,
1261 __isl_keep isl_set *set);
1263 #include <isl/map.h>
1264 __isl_give isl_printer *isl_printer_print_basic_map(
1265 __isl_take isl_printer *printer,
1266 __isl_keep isl_basic_map *bmap);
1267 __isl_give isl_printer *isl_printer_print_map(
1268 __isl_take isl_printer *printer,
1269 __isl_keep isl_map *map);
1271 #include <isl/union_set.h>
1272 __isl_give isl_printer *isl_printer_print_union_set(
1273 __isl_take isl_printer *p,
1274 __isl_keep isl_union_set *uset);
1276 #include <isl/union_map.h>
1277 __isl_give isl_printer *isl_printer_print_union_map(
1278 __isl_take isl_printer *p,
1279 __isl_keep isl_union_map *umap);
1281 When called on a file printer, the following function flushes
1282 the file. When called on a string printer, the buffer is cleared.
1284 __isl_give isl_printer *isl_printer_flush(
1285 __isl_take isl_printer *p);
1287 =head2 Creating New Sets and Relations
1289 C<isl> has functions for creating some standard sets and relations.
1293 =item * Empty sets and relations
1295 __isl_give isl_basic_set *isl_basic_set_empty(
1296 __isl_take isl_space *space);
1297 __isl_give isl_basic_map *isl_basic_map_empty(
1298 __isl_take isl_space *space);
1299 __isl_give isl_set *isl_set_empty(
1300 __isl_take isl_space *space);
1301 __isl_give isl_map *isl_map_empty(
1302 __isl_take isl_space *space);
1303 __isl_give isl_union_set *isl_union_set_empty(
1304 __isl_take isl_space *space);
1305 __isl_give isl_union_map *isl_union_map_empty(
1306 __isl_take isl_space *space);
1308 For C<isl_union_set>s and C<isl_union_map>s, the space
1309 is only used to specify the parameters.
1311 =item * Universe sets and relations
1313 __isl_give isl_basic_set *isl_basic_set_universe(
1314 __isl_take isl_space *space);
1315 __isl_give isl_basic_map *isl_basic_map_universe(
1316 __isl_take isl_space *space);
1317 __isl_give isl_set *isl_set_universe(
1318 __isl_take isl_space *space);
1319 __isl_give isl_map *isl_map_universe(
1320 __isl_take isl_space *space);
1321 __isl_give isl_union_set *isl_union_set_universe(
1322 __isl_take isl_union_set *uset);
1323 __isl_give isl_union_map *isl_union_map_universe(
1324 __isl_take isl_union_map *umap);
1326 The sets and relations constructed by the functions above
1327 contain all integer values, while those constructed by the
1328 functions below only contain non-negative values.
1330 __isl_give isl_basic_set *isl_basic_set_nat_universe(
1331 __isl_take isl_space *space);
1332 __isl_give isl_basic_map *isl_basic_map_nat_universe(
1333 __isl_take isl_space *space);
1334 __isl_give isl_set *isl_set_nat_universe(
1335 __isl_take isl_space *space);
1336 __isl_give isl_map *isl_map_nat_universe(
1337 __isl_take isl_space *space);
1339 =item * Identity relations
1341 __isl_give isl_basic_map *isl_basic_map_identity(
1342 __isl_take isl_space *space);
1343 __isl_give isl_map *isl_map_identity(
1344 __isl_take isl_space *space);
1346 The number of input and output dimensions in C<space> needs
1349 =item * Lexicographic order
1351 __isl_give isl_map *isl_map_lex_lt(
1352 __isl_take isl_space *set_space);
1353 __isl_give isl_map *isl_map_lex_le(
1354 __isl_take isl_space *set_space);
1355 __isl_give isl_map *isl_map_lex_gt(
1356 __isl_take isl_space *set_space);
1357 __isl_give isl_map *isl_map_lex_ge(
1358 __isl_take isl_space *set_space);
1359 __isl_give isl_map *isl_map_lex_lt_first(
1360 __isl_take isl_space *space, unsigned n);
1361 __isl_give isl_map *isl_map_lex_le_first(
1362 __isl_take isl_space *space, unsigned n);
1363 __isl_give isl_map *isl_map_lex_gt_first(
1364 __isl_take isl_space *space, unsigned n);
1365 __isl_give isl_map *isl_map_lex_ge_first(
1366 __isl_take isl_space *space, unsigned n);
1368 The first four functions take a space for a B<set>
1369 and return relations that express that the elements in the domain
1370 are lexicographically less
1371 (C<isl_map_lex_lt>), less or equal (C<isl_map_lex_le>),
1372 greater (C<isl_map_lex_gt>) or greater or equal (C<isl_map_lex_ge>)
1373 than the elements in the range.
1374 The last four functions take a space for a map
1375 and return relations that express that the first C<n> dimensions
1376 in the domain are lexicographically less
1377 (C<isl_map_lex_lt_first>), less or equal (C<isl_map_lex_le_first>),
1378 greater (C<isl_map_lex_gt_first>) or greater or equal (C<isl_map_lex_ge_first>)
1379 than the first C<n> dimensions in the range.
1383 A basic set or relation can be converted to a set or relation
1384 using the following functions.
1386 __isl_give isl_set *isl_set_from_basic_set(
1387 __isl_take isl_basic_set *bset);
1388 __isl_give isl_map *isl_map_from_basic_map(
1389 __isl_take isl_basic_map *bmap);
1391 Sets and relations can be converted to union sets and relations
1392 using the following functions.
1394 __isl_give isl_union_set *isl_union_set_from_basic_set(
1395 __isl_take isl_basic_set *bset);
1396 __isl_give isl_union_map *isl_union_map_from_basic_map(
1397 __isl_take isl_basic_map *bmap);
1398 __isl_give isl_union_set *isl_union_set_from_set(
1399 __isl_take isl_set *set);
1400 __isl_give isl_union_map *isl_union_map_from_map(
1401 __isl_take isl_map *map);
1403 The inverse conversions below can only be used if the input
1404 union set or relation is known to contain elements in exactly one
1407 __isl_give isl_set *isl_set_from_union_set(
1408 __isl_take isl_union_set *uset);
1409 __isl_give isl_map *isl_map_from_union_map(
1410 __isl_take isl_union_map *umap);
1412 A zero-dimensional (basic) set can be constructed on a given parameter domain
1413 using the following function.
1415 __isl_give isl_basic_set *isl_basic_set_from_params(
1416 __isl_take isl_basic_set *bset);
1417 __isl_give isl_set *isl_set_from_params(
1418 __isl_take isl_set *set);
1420 Sets and relations can be copied and freed again using the following
1423 __isl_give isl_basic_set *isl_basic_set_copy(
1424 __isl_keep isl_basic_set *bset);
1425 __isl_give isl_set *isl_set_copy(__isl_keep isl_set *set);
1426 __isl_give isl_union_set *isl_union_set_copy(
1427 __isl_keep isl_union_set *uset);
1428 __isl_give isl_basic_map *isl_basic_map_copy(
1429 __isl_keep isl_basic_map *bmap);
1430 __isl_give isl_map *isl_map_copy(__isl_keep isl_map *map);
1431 __isl_give isl_union_map *isl_union_map_copy(
1432 __isl_keep isl_union_map *umap);
1433 void *isl_basic_set_free(__isl_take isl_basic_set *bset);
1434 void *isl_set_free(__isl_take isl_set *set);
1435 void *isl_union_set_free(__isl_take isl_union_set *uset);
1436 void *isl_basic_map_free(__isl_take isl_basic_map *bmap);
1437 void *isl_map_free(__isl_take isl_map *map);
1438 void *isl_union_map_free(__isl_take isl_union_map *umap);
1440 Other sets and relations can be constructed by starting
1441 from a universe set or relation, adding equality and/or
1442 inequality constraints and then projecting out the
1443 existentially quantified variables, if any.
1444 Constraints can be constructed, manipulated and
1445 added to (or removed from) (basic) sets and relations
1446 using the following functions.
1448 #include <isl/constraint.h>
1449 __isl_give isl_constraint *isl_equality_alloc(
1450 __isl_take isl_local_space *ls);
1451 __isl_give isl_constraint *isl_inequality_alloc(
1452 __isl_take isl_local_space *ls);
1453 __isl_give isl_constraint *isl_constraint_set_constant_si(
1454 __isl_take isl_constraint *constraint, int v);
1455 __isl_give isl_constraint *isl_constraint_set_constant_val(
1456 __isl_take isl_constraint *constraint,
1457 __isl_take isl_val *v);
1458 __isl_give isl_constraint *isl_constraint_set_coefficient_si(
1459 __isl_take isl_constraint *constraint,
1460 enum isl_dim_type type, int pos, int v);
1461 __isl_give isl_constraint *
1462 isl_constraint_set_coefficient_val(
1463 __isl_take isl_constraint *constraint,
1464 enum isl_dim_type type, int pos,
1465 __isl_take isl_val *v);
1466 __isl_give isl_basic_map *isl_basic_map_add_constraint(
1467 __isl_take isl_basic_map *bmap,
1468 __isl_take isl_constraint *constraint);
1469 __isl_give isl_basic_set *isl_basic_set_add_constraint(
1470 __isl_take isl_basic_set *bset,
1471 __isl_take isl_constraint *constraint);
1472 __isl_give isl_map *isl_map_add_constraint(
1473 __isl_take isl_map *map,
1474 __isl_take isl_constraint *constraint);
1475 __isl_give isl_set *isl_set_add_constraint(
1476 __isl_take isl_set *set,
1477 __isl_take isl_constraint *constraint);
1478 __isl_give isl_basic_set *isl_basic_set_drop_constraint(
1479 __isl_take isl_basic_set *bset,
1480 __isl_take isl_constraint *constraint);
1482 For example, to create a set containing the even integers
1483 between 10 and 42, you would use the following code.
1486 isl_local_space *ls;
1488 isl_basic_set *bset;
1490 space = isl_space_set_alloc(ctx, 0, 2);
1491 bset = isl_basic_set_universe(isl_space_copy(space));
1492 ls = isl_local_space_from_space(space);
1494 c = isl_equality_alloc(isl_local_space_copy(ls));
1495 c = isl_constraint_set_coefficient_si(c, isl_dim_set, 0, -1);
1496 c = isl_constraint_set_coefficient_si(c, isl_dim_set, 1, 2);
1497 bset = isl_basic_set_add_constraint(bset, c);
1499 c = isl_inequality_alloc(isl_local_space_copy(ls));
1500 c = isl_constraint_set_constant_si(c, -10);
1501 c = isl_constraint_set_coefficient_si(c, isl_dim_set, 0, 1);
1502 bset = isl_basic_set_add_constraint(bset, c);
1504 c = isl_inequality_alloc(ls);
1505 c = isl_constraint_set_constant_si(c, 42);
1506 c = isl_constraint_set_coefficient_si(c, isl_dim_set, 0, -1);
1507 bset = isl_basic_set_add_constraint(bset, c);
1509 bset = isl_basic_set_project_out(bset, isl_dim_set, 1, 1);
1513 isl_basic_set *bset;
1514 bset = isl_basic_set_read_from_str(ctx,
1515 "{[i] : exists (a : i = 2a and i >= 10 and i <= 42)}");
1517 A basic set or relation can also be constructed from two matrices
1518 describing the equalities and the inequalities.
1520 __isl_give isl_basic_set *isl_basic_set_from_constraint_matrices(
1521 __isl_take isl_space *space,
1522 __isl_take isl_mat *eq, __isl_take isl_mat *ineq,
1523 enum isl_dim_type c1,
1524 enum isl_dim_type c2, enum isl_dim_type c3,
1525 enum isl_dim_type c4);
1526 __isl_give isl_basic_map *isl_basic_map_from_constraint_matrices(
1527 __isl_take isl_space *space,
1528 __isl_take isl_mat *eq, __isl_take isl_mat *ineq,
1529 enum isl_dim_type c1,
1530 enum isl_dim_type c2, enum isl_dim_type c3,
1531 enum isl_dim_type c4, enum isl_dim_type c5);
1533 The C<isl_dim_type> arguments indicate the order in which
1534 different kinds of variables appear in the input matrices
1535 and should be a permutation of C<isl_dim_cst>, C<isl_dim_param>,
1536 C<isl_dim_set> and C<isl_dim_div> for sets and
1537 of C<isl_dim_cst>, C<isl_dim_param>,
1538 C<isl_dim_in>, C<isl_dim_out> and C<isl_dim_div> for relations.
1540 A (basic or union) set or relation can also be constructed from a
1541 (union) (piecewise) (multiple) affine expression
1542 or a list of affine expressions
1543 (See L<"Piecewise Quasi Affine Expressions"> and
1544 L<"Piecewise Multiple Quasi Affine Expressions">).
1546 __isl_give isl_basic_map *isl_basic_map_from_aff(
1547 __isl_take isl_aff *aff);
1548 __isl_give isl_map *isl_map_from_aff(
1549 __isl_take isl_aff *aff);
1550 __isl_give isl_set *isl_set_from_pw_aff(
1551 __isl_take isl_pw_aff *pwaff);
1552 __isl_give isl_map *isl_map_from_pw_aff(
1553 __isl_take isl_pw_aff *pwaff);
1554 __isl_give isl_basic_map *isl_basic_map_from_aff_list(
1555 __isl_take isl_space *domain_space,
1556 __isl_take isl_aff_list *list);
1557 __isl_give isl_basic_map *isl_basic_map_from_multi_aff(
1558 __isl_take isl_multi_aff *maff)
1559 __isl_give isl_map *isl_map_from_multi_aff(
1560 __isl_take isl_multi_aff *maff)
1561 __isl_give isl_set *isl_set_from_pw_multi_aff(
1562 __isl_take isl_pw_multi_aff *pma);
1563 __isl_give isl_map *isl_map_from_pw_multi_aff(
1564 __isl_take isl_pw_multi_aff *pma);
1565 __isl_give isl_set *isl_set_from_multi_pw_aff(
1566 __isl_take isl_multi_pw_aff *mpa);
1567 __isl_give isl_map *isl_map_from_multi_pw_aff(
1568 __isl_take isl_multi_pw_aff *mpa);
1569 __isl_give isl_union_map *
1570 isl_union_map_from_union_pw_multi_aff(
1571 __isl_take isl_union_pw_multi_aff *upma);
1573 The C<domain_space> argument describes the domain of the resulting
1574 basic relation. It is required because the C<list> may consist
1575 of zero affine expressions.
1577 =head2 Inspecting Sets and Relations
1579 Usually, the user should not have to care about the actual constraints
1580 of the sets and maps, but should instead apply the abstract operations
1581 explained in the following sections.
1582 Occasionally, however, it may be required to inspect the individual
1583 coefficients of the constraints. This section explains how to do so.
1584 In these cases, it may also be useful to have C<isl> compute
1585 an explicit representation of the existentially quantified variables.
1587 __isl_give isl_set *isl_set_compute_divs(
1588 __isl_take isl_set *set);
1589 __isl_give isl_map *isl_map_compute_divs(
1590 __isl_take isl_map *map);
1591 __isl_give isl_union_set *isl_union_set_compute_divs(
1592 __isl_take isl_union_set *uset);
1593 __isl_give isl_union_map *isl_union_map_compute_divs(
1594 __isl_take isl_union_map *umap);
1596 This explicit representation defines the existentially quantified
1597 variables as integer divisions of the other variables, possibly
1598 including earlier existentially quantified variables.
1599 An explicitly represented existentially quantified variable therefore
1600 has a unique value when the values of the other variables are known.
1601 If, furthermore, the same existentials, i.e., existentials
1602 with the same explicit representations, should appear in the
1603 same order in each of the disjuncts of a set or map, then the user should call
1604 either of the following functions.
1606 __isl_give isl_set *isl_set_align_divs(
1607 __isl_take isl_set *set);
1608 __isl_give isl_map *isl_map_align_divs(
1609 __isl_take isl_map *map);
1611 Alternatively, the existentially quantified variables can be removed
1612 using the following functions, which compute an overapproximation.
1614 __isl_give isl_basic_set *isl_basic_set_remove_divs(
1615 __isl_take isl_basic_set *bset);
1616 __isl_give isl_basic_map *isl_basic_map_remove_divs(
1617 __isl_take isl_basic_map *bmap);
1618 __isl_give isl_set *isl_set_remove_divs(
1619 __isl_take isl_set *set);
1620 __isl_give isl_map *isl_map_remove_divs(
1621 __isl_take isl_map *map);
1623 It is also possible to only remove those divs that are defined
1624 in terms of a given range of dimensions or only those for which
1625 no explicit representation is known.
1627 __isl_give isl_basic_set *
1628 isl_basic_set_remove_divs_involving_dims(
1629 __isl_take isl_basic_set *bset,
1630 enum isl_dim_type type,
1631 unsigned first, unsigned n);
1632 __isl_give isl_basic_map *
1633 isl_basic_map_remove_divs_involving_dims(
1634 __isl_take isl_basic_map *bmap,
1635 enum isl_dim_type type,
1636 unsigned first, unsigned n);
1637 __isl_give isl_set *isl_set_remove_divs_involving_dims(
1638 __isl_take isl_set *set, enum isl_dim_type type,
1639 unsigned first, unsigned n);
1640 __isl_give isl_map *isl_map_remove_divs_involving_dims(
1641 __isl_take isl_map *map, enum isl_dim_type type,
1642 unsigned first, unsigned n);
1644 __isl_give isl_basic_set *
1645 isl_basic_set_remove_unknown_divs(
1646 __isl_take isl_basic_set *bset);
1647 __isl_give isl_set *isl_set_remove_unknown_divs(
1648 __isl_take isl_set *set);
1649 __isl_give isl_map *isl_map_remove_unknown_divs(
1650 __isl_take isl_map *map);
1652 To iterate over all the sets or maps in a union set or map, use
1654 int isl_union_set_foreach_set(__isl_keep isl_union_set *uset,
1655 int (*fn)(__isl_take isl_set *set, void *user),
1657 int isl_union_map_foreach_map(__isl_keep isl_union_map *umap,
1658 int (*fn)(__isl_take isl_map *map, void *user),
1661 The number of sets or maps in a union set or map can be obtained
1664 int isl_union_set_n_set(__isl_keep isl_union_set *uset);
1665 int isl_union_map_n_map(__isl_keep isl_union_map *umap);
1667 To extract the set or map in a given space from a union, use
1669 __isl_give isl_set *isl_union_set_extract_set(
1670 __isl_keep isl_union_set *uset,
1671 __isl_take isl_space *space);
1672 __isl_give isl_map *isl_union_map_extract_map(
1673 __isl_keep isl_union_map *umap,
1674 __isl_take isl_space *space);
1676 To iterate over all the basic sets or maps in a set or map, use
1678 int isl_set_foreach_basic_set(__isl_keep isl_set *set,
1679 int (*fn)(__isl_take isl_basic_set *bset, void *user),
1681 int isl_map_foreach_basic_map(__isl_keep isl_map *map,
1682 int (*fn)(__isl_take isl_basic_map *bmap, void *user),
1685 The callback function C<fn> should return 0 if successful and
1686 -1 if an error occurs. In the latter case, or if any other error
1687 occurs, the above functions will return -1.
1689 It should be noted that C<isl> does not guarantee that
1690 the basic sets or maps passed to C<fn> are disjoint.
1691 If this is required, then the user should call one of
1692 the following functions first.
1694 __isl_give isl_set *isl_set_make_disjoint(
1695 __isl_take isl_set *set);
1696 __isl_give isl_map *isl_map_make_disjoint(
1697 __isl_take isl_map *map);
1699 The number of basic sets in a set can be obtained
1702 int isl_set_n_basic_set(__isl_keep isl_set *set);
1704 To iterate over the constraints of a basic set or map, use
1706 #include <isl/constraint.h>
1708 int isl_basic_set_n_constraint(
1709 __isl_keep isl_basic_set *bset);
1710 int isl_basic_set_foreach_constraint(
1711 __isl_keep isl_basic_set *bset,
1712 int (*fn)(__isl_take isl_constraint *c, void *user),
1714 int isl_basic_map_foreach_constraint(
1715 __isl_keep isl_basic_map *bmap,
1716 int (*fn)(__isl_take isl_constraint *c, void *user),
1718 void *isl_constraint_free(__isl_take isl_constraint *c);
1720 Again, the callback function C<fn> should return 0 if successful and
1721 -1 if an error occurs. In the latter case, or if any other error
1722 occurs, the above functions will return -1.
1723 The constraint C<c> represents either an equality or an inequality.
1724 Use the following function to find out whether a constraint
1725 represents an equality. If not, it represents an inequality.
1727 int isl_constraint_is_equality(
1728 __isl_keep isl_constraint *constraint);
1730 The coefficients of the constraints can be inspected using
1731 the following functions.
1733 int isl_constraint_is_lower_bound(
1734 __isl_keep isl_constraint *constraint,
1735 enum isl_dim_type type, unsigned pos);
1736 int isl_constraint_is_upper_bound(
1737 __isl_keep isl_constraint *constraint,
1738 enum isl_dim_type type, unsigned pos);
1739 __isl_give isl_val *isl_constraint_get_constant_val(
1740 __isl_keep isl_constraint *constraint);
1741 __isl_give isl_val *isl_constraint_get_coefficient_val(
1742 __isl_keep isl_constraint *constraint,
1743 enum isl_dim_type type, int pos);
1744 int isl_constraint_involves_dims(
1745 __isl_keep isl_constraint *constraint,
1746 enum isl_dim_type type, unsigned first, unsigned n);
1748 The explicit representations of the existentially quantified
1749 variables can be inspected using the following function.
1750 Note that the user is only allowed to use this function
1751 if the inspected set or map is the result of a call
1752 to C<isl_set_compute_divs> or C<isl_map_compute_divs>.
1753 The existentially quantified variable is equal to the floor
1754 of the returned affine expression. The affine expression
1755 itself can be inspected using the functions in
1756 L<"Piecewise Quasi Affine Expressions">.
1758 __isl_give isl_aff *isl_constraint_get_div(
1759 __isl_keep isl_constraint *constraint, int pos);
1761 To obtain the constraints of a basic set or map in matrix
1762 form, use the following functions.
1764 __isl_give isl_mat *isl_basic_set_equalities_matrix(
1765 __isl_keep isl_basic_set *bset,
1766 enum isl_dim_type c1, enum isl_dim_type c2,
1767 enum isl_dim_type c3, enum isl_dim_type c4);
1768 __isl_give isl_mat *isl_basic_set_inequalities_matrix(
1769 __isl_keep isl_basic_set *bset,
1770 enum isl_dim_type c1, enum isl_dim_type c2,
1771 enum isl_dim_type c3, enum isl_dim_type c4);
1772 __isl_give isl_mat *isl_basic_map_equalities_matrix(
1773 __isl_keep isl_basic_map *bmap,
1774 enum isl_dim_type c1,
1775 enum isl_dim_type c2, enum isl_dim_type c3,
1776 enum isl_dim_type c4, enum isl_dim_type c5);
1777 __isl_give isl_mat *isl_basic_map_inequalities_matrix(
1778 __isl_keep isl_basic_map *bmap,
1779 enum isl_dim_type c1,
1780 enum isl_dim_type c2, enum isl_dim_type c3,
1781 enum isl_dim_type c4, enum isl_dim_type c5);
1783 The C<isl_dim_type> arguments dictate the order in which
1784 different kinds of variables appear in the resulting matrix
1785 and should be a permutation of C<isl_dim_cst>, C<isl_dim_param>,
1786 C<isl_dim_in>, C<isl_dim_out> and C<isl_dim_div>.
1788 The number of parameters, input, output or set dimensions can
1789 be obtained using the following functions.
1791 unsigned isl_basic_set_dim(__isl_keep isl_basic_set *bset,
1792 enum isl_dim_type type);
1793 unsigned isl_basic_map_dim(__isl_keep isl_basic_map *bmap,
1794 enum isl_dim_type type);
1795 unsigned isl_set_dim(__isl_keep isl_set *set,
1796 enum isl_dim_type type);
1797 unsigned isl_map_dim(__isl_keep isl_map *map,
1798 enum isl_dim_type type);
1800 To check whether the description of a set or relation depends
1801 on one or more given dimensions, it is not necessary to iterate over all
1802 constraints. Instead the following functions can be used.
1804 int isl_basic_set_involves_dims(
1805 __isl_keep isl_basic_set *bset,
1806 enum isl_dim_type type, unsigned first, unsigned n);
1807 int isl_set_involves_dims(__isl_keep isl_set *set,
1808 enum isl_dim_type type, unsigned first, unsigned n);
1809 int isl_basic_map_involves_dims(
1810 __isl_keep isl_basic_map *bmap,
1811 enum isl_dim_type type, unsigned first, unsigned n);
1812 int isl_map_involves_dims(__isl_keep isl_map *map,
1813 enum isl_dim_type type, unsigned first, unsigned n);
1815 Similarly, the following functions can be used to check whether
1816 a given dimension is involved in any lower or upper bound.
1818 int isl_set_dim_has_any_lower_bound(__isl_keep isl_set *set,
1819 enum isl_dim_type type, unsigned pos);
1820 int isl_set_dim_has_any_upper_bound(__isl_keep isl_set *set,
1821 enum isl_dim_type type, unsigned pos);
1823 Note that these functions return true even if there is a bound on
1824 the dimension on only some of the basic sets of C<set>.
1825 To check if they have a bound for all of the basic sets in C<set>,
1826 use the following functions instead.
1828 int isl_set_dim_has_lower_bound(__isl_keep isl_set *set,
1829 enum isl_dim_type type, unsigned pos);
1830 int isl_set_dim_has_upper_bound(__isl_keep isl_set *set,
1831 enum isl_dim_type type, unsigned pos);
1833 The identifiers or names of the domain and range spaces of a set
1834 or relation can be read off or set using the following functions.
1836 __isl_give isl_basic_set *isl_basic_set_set_tuple_id(
1837 __isl_take isl_basic_set *bset,
1838 __isl_take isl_id *id);
1839 __isl_give isl_set *isl_set_set_tuple_id(
1840 __isl_take isl_set *set, __isl_take isl_id *id);
1841 __isl_give isl_set *isl_set_reset_tuple_id(
1842 __isl_take isl_set *set);
1843 int isl_set_has_tuple_id(__isl_keep isl_set *set);
1844 __isl_give isl_id *isl_set_get_tuple_id(
1845 __isl_keep isl_set *set);
1846 __isl_give isl_basic_map *isl_basic_map_set_tuple_id(
1847 __isl_take isl_basic_map *bmap,
1848 enum isl_dim_type type, __isl_take isl_id *id);
1849 __isl_give isl_map *isl_map_set_tuple_id(
1850 __isl_take isl_map *map, enum isl_dim_type type,
1851 __isl_take isl_id *id);
1852 __isl_give isl_map *isl_map_reset_tuple_id(
1853 __isl_take isl_map *map, enum isl_dim_type type);
1854 int isl_map_has_tuple_id(__isl_keep isl_map *map,
1855 enum isl_dim_type type);
1856 __isl_give isl_id *isl_map_get_tuple_id(
1857 __isl_keep isl_map *map, enum isl_dim_type type);
1859 const char *isl_basic_set_get_tuple_name(
1860 __isl_keep isl_basic_set *bset);
1861 __isl_give isl_basic_set *isl_basic_set_set_tuple_name(
1862 __isl_take isl_basic_set *set, const char *s);
1863 int isl_set_has_tuple_name(__isl_keep isl_set *set);
1864 const char *isl_set_get_tuple_name(
1865 __isl_keep isl_set *set);
1866 const char *isl_basic_map_get_tuple_name(
1867 __isl_keep isl_basic_map *bmap,
1868 enum isl_dim_type type);
1869 __isl_give isl_basic_map *isl_basic_map_set_tuple_name(
1870 __isl_take isl_basic_map *bmap,
1871 enum isl_dim_type type, const char *s);
1872 int isl_map_has_tuple_name(__isl_keep isl_map *map,
1873 enum isl_dim_type type);
1874 const char *isl_map_get_tuple_name(
1875 __isl_keep isl_map *map,
1876 enum isl_dim_type type);
1878 As with C<isl_space_get_tuple_name>, the value returned points to
1879 an internal data structure.
1880 The identifiers, positions or names of individual dimensions can be
1881 read off using the following functions.
1883 __isl_give isl_id *isl_basic_set_get_dim_id(
1884 __isl_keep isl_basic_set *bset,
1885 enum isl_dim_type type, unsigned pos);
1886 __isl_give isl_set *isl_set_set_dim_id(
1887 __isl_take isl_set *set, enum isl_dim_type type,
1888 unsigned pos, __isl_take isl_id *id);
1889 int isl_set_has_dim_id(__isl_keep isl_set *set,
1890 enum isl_dim_type type, unsigned pos);
1891 __isl_give isl_id *isl_set_get_dim_id(
1892 __isl_keep isl_set *set, enum isl_dim_type type,
1894 int isl_basic_map_has_dim_id(
1895 __isl_keep isl_basic_map *bmap,
1896 enum isl_dim_type type, unsigned pos);
1897 __isl_give isl_map *isl_map_set_dim_id(
1898 __isl_take isl_map *map, enum isl_dim_type type,
1899 unsigned pos, __isl_take isl_id *id);
1900 int isl_map_has_dim_id(__isl_keep isl_map *map,
1901 enum isl_dim_type type, unsigned pos);
1902 __isl_give isl_id *isl_map_get_dim_id(
1903 __isl_keep isl_map *map, enum isl_dim_type type,
1906 int isl_set_find_dim_by_id(__isl_keep isl_set *set,
1907 enum isl_dim_type type, __isl_keep isl_id *id);
1908 int isl_map_find_dim_by_id(__isl_keep isl_map *map,
1909 enum isl_dim_type type, __isl_keep isl_id *id);
1910 int isl_set_find_dim_by_name(__isl_keep isl_set *set,
1911 enum isl_dim_type type, const char *name);
1912 int isl_map_find_dim_by_name(__isl_keep isl_map *map,
1913 enum isl_dim_type type, const char *name);
1915 const char *isl_constraint_get_dim_name(
1916 __isl_keep isl_constraint *constraint,
1917 enum isl_dim_type type, unsigned pos);
1918 const char *isl_basic_set_get_dim_name(
1919 __isl_keep isl_basic_set *bset,
1920 enum isl_dim_type type, unsigned pos);
1921 int isl_set_has_dim_name(__isl_keep isl_set *set,
1922 enum isl_dim_type type, unsigned pos);
1923 const char *isl_set_get_dim_name(
1924 __isl_keep isl_set *set,
1925 enum isl_dim_type type, unsigned pos);
1926 const char *isl_basic_map_get_dim_name(
1927 __isl_keep isl_basic_map *bmap,
1928 enum isl_dim_type type, unsigned pos);
1929 int isl_map_has_dim_name(__isl_keep isl_map *map,
1930 enum isl_dim_type type, unsigned pos);
1931 const char *isl_map_get_dim_name(
1932 __isl_keep isl_map *map,
1933 enum isl_dim_type type, unsigned pos);
1935 These functions are mostly useful to obtain the identifiers, positions
1936 or names of the parameters. Identifiers of individual dimensions are
1937 essentially only useful for printing. They are ignored by all other
1938 operations and may not be preserved across those operations.
1940 The user pointers on all parameters and tuples can be reset
1941 using the following functions.
1943 __isl_give isl_set *isl_set_reset_user(
1944 __isl_take isl_set *set);
1945 __isl_give isl_map *isl_map_reset_user(
1946 __isl_take isl_map *map);
1950 =head3 Unary Properties
1956 The following functions test whether the given set or relation
1957 contains any integer points. The ``plain'' variants do not perform
1958 any computations, but simply check if the given set or relation
1959 is already known to be empty.
1961 int isl_basic_set_plain_is_empty(__isl_keep isl_basic_set *bset);
1962 int isl_basic_set_is_empty(__isl_keep isl_basic_set *bset);
1963 int isl_set_plain_is_empty(__isl_keep isl_set *set);
1964 int isl_set_is_empty(__isl_keep isl_set *set);
1965 int isl_union_set_is_empty(__isl_keep isl_union_set *uset);
1966 int isl_basic_map_plain_is_empty(__isl_keep isl_basic_map *bmap);
1967 int isl_basic_map_is_empty(__isl_keep isl_basic_map *bmap);
1968 int isl_map_plain_is_empty(__isl_keep isl_map *map);
1969 int isl_map_is_empty(__isl_keep isl_map *map);
1970 int isl_union_map_is_empty(__isl_keep isl_union_map *umap);
1972 =item * Universality
1974 int isl_basic_set_is_universe(__isl_keep isl_basic_set *bset);
1975 int isl_basic_map_is_universe(__isl_keep isl_basic_map *bmap);
1976 int isl_set_plain_is_universe(__isl_keep isl_set *set);
1978 =item * Single-valuedness
1980 int isl_basic_map_is_single_valued(
1981 __isl_keep isl_basic_map *bmap);
1982 int isl_map_plain_is_single_valued(
1983 __isl_keep isl_map *map);
1984 int isl_map_is_single_valued(__isl_keep isl_map *map);
1985 int isl_union_map_is_single_valued(__isl_keep isl_union_map *umap);
1989 int isl_map_plain_is_injective(__isl_keep isl_map *map);
1990 int isl_map_is_injective(__isl_keep isl_map *map);
1991 int isl_union_map_plain_is_injective(
1992 __isl_keep isl_union_map *umap);
1993 int isl_union_map_is_injective(
1994 __isl_keep isl_union_map *umap);
1998 int isl_map_is_bijective(__isl_keep isl_map *map);
1999 int isl_union_map_is_bijective(__isl_keep isl_union_map *umap);
2003 __isl_give isl_val *
2004 isl_basic_map_plain_get_val_if_fixed(
2005 __isl_keep isl_basic_map *bmap,
2006 enum isl_dim_type type, unsigned pos);
2007 __isl_give isl_val *isl_set_plain_get_val_if_fixed(
2008 __isl_keep isl_set *set,
2009 enum isl_dim_type type, unsigned pos);
2010 __isl_give isl_val *isl_map_plain_get_val_if_fixed(
2011 __isl_keep isl_map *map,
2012 enum isl_dim_type type, unsigned pos);
2014 If the set or relation obviously lies on a hyperplane where the given dimension
2015 has a fixed value, then return that value.
2016 Otherwise return NaN.
2020 int isl_set_dim_residue_class_val(
2021 __isl_keep isl_set *set,
2022 int pos, __isl_give isl_val **modulo,
2023 __isl_give isl_val **residue);
2025 Check if the values of the given set dimension are equal to a fixed
2026 value modulo some integer value. If so, assign the modulo to C<*modulo>
2027 and the fixed value to C<*residue>. If the given dimension attains only
2028 a single value, then assign C<0> to C<*modulo> and the fixed value to
2030 If the dimension does not attain only a single value and if no modulo
2031 can be found then assign C<1> to C<*modulo> and C<1> to C<*residue>.
2035 To check whether a set is a parameter domain, use this function:
2037 int isl_set_is_params(__isl_keep isl_set *set);
2038 int isl_union_set_is_params(
2039 __isl_keep isl_union_set *uset);
2043 The following functions check whether the space of the given
2044 (basic) set or relation range is a wrapped relation.
2046 int isl_basic_set_is_wrapping(
2047 __isl_keep isl_basic_set *bset);
2048 int isl_set_is_wrapping(__isl_keep isl_set *set);
2049 int isl_map_range_is_wrapping(
2050 __isl_keep isl_map *map);
2052 =item * Internal Product
2054 int isl_basic_map_can_zip(
2055 __isl_keep isl_basic_map *bmap);
2056 int isl_map_can_zip(__isl_keep isl_map *map);
2058 Check whether the product of domain and range of the given relation
2060 i.e., whether both domain and range are nested relations.
2064 int isl_basic_map_can_curry(
2065 __isl_keep isl_basic_map *bmap);
2066 int isl_map_can_curry(__isl_keep isl_map *map);
2068 Check whether the domain of the (basic) relation is a wrapped relation.
2070 int isl_basic_map_can_uncurry(
2071 __isl_keep isl_basic_map *bmap);
2072 int isl_map_can_uncurry(__isl_keep isl_map *map);
2074 Check whether the range of the (basic) relation is a wrapped relation.
2078 =head3 Binary Properties
2084 int isl_basic_set_plain_is_equal(
2085 __isl_keep isl_basic_set *bset1,
2086 __isl_keep isl_basic_set *bset2);
2087 int isl_set_plain_is_equal(__isl_keep isl_set *set1,
2088 __isl_keep isl_set *set2);
2089 int isl_set_is_equal(__isl_keep isl_set *set1,
2090 __isl_keep isl_set *set2);
2091 int isl_union_set_is_equal(
2092 __isl_keep isl_union_set *uset1,
2093 __isl_keep isl_union_set *uset2);
2094 int isl_basic_map_is_equal(
2095 __isl_keep isl_basic_map *bmap1,
2096 __isl_keep isl_basic_map *bmap2);
2097 int isl_map_is_equal(__isl_keep isl_map *map1,
2098 __isl_keep isl_map *map2);
2099 int isl_map_plain_is_equal(__isl_keep isl_map *map1,
2100 __isl_keep isl_map *map2);
2101 int isl_union_map_is_equal(
2102 __isl_keep isl_union_map *umap1,
2103 __isl_keep isl_union_map *umap2);
2105 =item * Disjointness
2107 int isl_basic_set_is_disjoint(
2108 __isl_keep isl_basic_set *bset1,
2109 __isl_keep isl_basic_set *bset2);
2110 int isl_set_plain_is_disjoint(__isl_keep isl_set *set1,
2111 __isl_keep isl_set *set2);
2112 int isl_set_is_disjoint(__isl_keep isl_set *set1,
2113 __isl_keep isl_set *set2);
2114 int isl_basic_map_is_disjoint(
2115 __isl_keep isl_basic_map *bmap1,
2116 __isl_keep isl_basic_map *bmap2);
2117 int isl_map_is_disjoint(__isl_keep isl_map *map1,
2118 __isl_keep isl_map *map2);
2122 int isl_basic_set_is_subset(
2123 __isl_keep isl_basic_set *bset1,
2124 __isl_keep isl_basic_set *bset2);
2125 int isl_set_is_subset(__isl_keep isl_set *set1,
2126 __isl_keep isl_set *set2);
2127 int isl_set_is_strict_subset(
2128 __isl_keep isl_set *set1,
2129 __isl_keep isl_set *set2);
2130 int isl_union_set_is_subset(
2131 __isl_keep isl_union_set *uset1,
2132 __isl_keep isl_union_set *uset2);
2133 int isl_union_set_is_strict_subset(
2134 __isl_keep isl_union_set *uset1,
2135 __isl_keep isl_union_set *uset2);
2136 int isl_basic_map_is_subset(
2137 __isl_keep isl_basic_map *bmap1,
2138 __isl_keep isl_basic_map *bmap2);
2139 int isl_basic_map_is_strict_subset(
2140 __isl_keep isl_basic_map *bmap1,
2141 __isl_keep isl_basic_map *bmap2);
2142 int isl_map_is_subset(
2143 __isl_keep isl_map *map1,
2144 __isl_keep isl_map *map2);
2145 int isl_map_is_strict_subset(
2146 __isl_keep isl_map *map1,
2147 __isl_keep isl_map *map2);
2148 int isl_union_map_is_subset(
2149 __isl_keep isl_union_map *umap1,
2150 __isl_keep isl_union_map *umap2);
2151 int isl_union_map_is_strict_subset(
2152 __isl_keep isl_union_map *umap1,
2153 __isl_keep isl_union_map *umap2);
2155 Check whether the first argument is a (strict) subset of the
2160 int isl_set_plain_cmp(__isl_keep isl_set *set1,
2161 __isl_keep isl_set *set2);
2163 This function is useful for sorting C<isl_set>s.
2164 The order depends on the internal representation of the inputs.
2165 The order is fixed over different calls to the function (assuming
2166 the internal representation of the inputs has not changed), but may
2167 change over different versions of C<isl>.
2171 =head2 Unary Operations
2177 __isl_give isl_set *isl_set_complement(
2178 __isl_take isl_set *set);
2179 __isl_give isl_map *isl_map_complement(
2180 __isl_take isl_map *map);
2184 __isl_give isl_basic_map *isl_basic_map_reverse(
2185 __isl_take isl_basic_map *bmap);
2186 __isl_give isl_map *isl_map_reverse(
2187 __isl_take isl_map *map);
2188 __isl_give isl_union_map *isl_union_map_reverse(
2189 __isl_take isl_union_map *umap);
2193 __isl_give isl_basic_set *isl_basic_set_project_out(
2194 __isl_take isl_basic_set *bset,
2195 enum isl_dim_type type, unsigned first, unsigned n);
2196 __isl_give isl_basic_map *isl_basic_map_project_out(
2197 __isl_take isl_basic_map *bmap,
2198 enum isl_dim_type type, unsigned first, unsigned n);
2199 __isl_give isl_set *isl_set_project_out(__isl_take isl_set *set,
2200 enum isl_dim_type type, unsigned first, unsigned n);
2201 __isl_give isl_map *isl_map_project_out(__isl_take isl_map *map,
2202 enum isl_dim_type type, unsigned first, unsigned n);
2203 __isl_give isl_basic_set *isl_basic_set_params(
2204 __isl_take isl_basic_set *bset);
2205 __isl_give isl_basic_set *isl_basic_map_domain(
2206 __isl_take isl_basic_map *bmap);
2207 __isl_give isl_basic_set *isl_basic_map_range(
2208 __isl_take isl_basic_map *bmap);
2209 __isl_give isl_set *isl_set_params(__isl_take isl_set *set);
2210 __isl_give isl_set *isl_map_params(__isl_take isl_map *map);
2211 __isl_give isl_set *isl_map_domain(
2212 __isl_take isl_map *bmap);
2213 __isl_give isl_set *isl_map_range(
2214 __isl_take isl_map *map);
2215 __isl_give isl_set *isl_union_set_params(
2216 __isl_take isl_union_set *uset);
2217 __isl_give isl_set *isl_union_map_params(
2218 __isl_take isl_union_map *umap);
2219 __isl_give isl_union_set *isl_union_map_domain(
2220 __isl_take isl_union_map *umap);
2221 __isl_give isl_union_set *isl_union_map_range(
2222 __isl_take isl_union_map *umap);
2224 __isl_give isl_basic_map *isl_basic_map_domain_map(
2225 __isl_take isl_basic_map *bmap);
2226 __isl_give isl_basic_map *isl_basic_map_range_map(
2227 __isl_take isl_basic_map *bmap);
2228 __isl_give isl_map *isl_map_domain_map(__isl_take isl_map *map);
2229 __isl_give isl_map *isl_map_range_map(__isl_take isl_map *map);
2230 __isl_give isl_union_map *isl_union_map_domain_map(
2231 __isl_take isl_union_map *umap);
2232 __isl_give isl_union_map *isl_union_map_range_map(
2233 __isl_take isl_union_map *umap);
2235 The functions above construct a (basic, regular or union) relation
2236 that maps (a wrapped version of) the input relation to its domain or range.
2240 __isl_give isl_basic_set *isl_basic_set_eliminate(
2241 __isl_take isl_basic_set *bset,
2242 enum isl_dim_type type,
2243 unsigned first, unsigned n);
2244 __isl_give isl_set *isl_set_eliminate(
2245 __isl_take isl_set *set, enum isl_dim_type type,
2246 unsigned first, unsigned n);
2247 __isl_give isl_basic_map *isl_basic_map_eliminate(
2248 __isl_take isl_basic_map *bmap,
2249 enum isl_dim_type type,
2250 unsigned first, unsigned n);
2251 __isl_give isl_map *isl_map_eliminate(
2252 __isl_take isl_map *map, enum isl_dim_type type,
2253 unsigned first, unsigned n);
2255 Eliminate the coefficients for the given dimensions from the constraints,
2256 without removing the dimensions.
2258 =item * Constructing a relation from a set
2260 #include <isl/map.h>
2261 __isl_give isl_map *isl_map_from_domain(
2262 __isl_take isl_set *set);
2263 __isl_give isl_map *isl_map_from_range(
2264 __isl_take isl_set *set);
2266 Create a relation with the given set as domain or range.
2267 The range or domain of the created relation is a zero-dimensional
2268 flat anonymous space.
2272 __isl_give isl_basic_set *isl_basic_set_fix_si(
2273 __isl_take isl_basic_set *bset,
2274 enum isl_dim_type type, unsigned pos, int value);
2275 __isl_give isl_basic_set *isl_basic_set_fix_val(
2276 __isl_take isl_basic_set *bset,
2277 enum isl_dim_type type, unsigned pos,
2278 __isl_take isl_val *v);
2279 __isl_give isl_set *isl_set_fix_si(__isl_take isl_set *set,
2280 enum isl_dim_type type, unsigned pos, int value);
2281 __isl_give isl_set *isl_set_fix_val(
2282 __isl_take isl_set *set,
2283 enum isl_dim_type type, unsigned pos,
2284 __isl_take isl_val *v);
2285 __isl_give isl_basic_map *isl_basic_map_fix_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_fix_val(
2289 __isl_take isl_basic_map *bmap,
2290 enum isl_dim_type type, unsigned pos,
2291 __isl_take isl_val *v);
2292 __isl_give isl_map *isl_map_fix_si(__isl_take isl_map *map,
2293 enum isl_dim_type type, unsigned pos, int value);
2294 __isl_give isl_map *isl_map_fix_val(
2295 __isl_take isl_map *map,
2296 enum isl_dim_type type, unsigned pos,
2297 __isl_take isl_val *v);
2299 Intersect the set or relation with the hyperplane where the given
2300 dimension has the fixed given value.
2302 __isl_give isl_basic_map *isl_basic_map_lower_bound_si(
2303 __isl_take isl_basic_map *bmap,
2304 enum isl_dim_type type, unsigned pos, int value);
2305 __isl_give isl_basic_map *isl_basic_map_upper_bound_si(
2306 __isl_take isl_basic_map *bmap,
2307 enum isl_dim_type type, unsigned pos, int value);
2308 __isl_give isl_set *isl_set_lower_bound_si(
2309 __isl_take isl_set *set,
2310 enum isl_dim_type type, unsigned pos, int value);
2311 __isl_give isl_set *isl_set_lower_bound_val(
2312 __isl_take isl_set *set,
2313 enum isl_dim_type type, unsigned pos,
2314 __isl_take isl_val *value);
2315 __isl_give isl_map *isl_map_lower_bound_si(
2316 __isl_take isl_map *map,
2317 enum isl_dim_type type, unsigned pos, int value);
2318 __isl_give isl_set *isl_set_upper_bound_si(
2319 __isl_take isl_set *set,
2320 enum isl_dim_type type, unsigned pos, int value);
2321 __isl_give isl_set *isl_set_upper_bound_val(
2322 __isl_take isl_set *set,
2323 enum isl_dim_type type, unsigned pos,
2324 __isl_take isl_val *value);
2325 __isl_give isl_map *isl_map_upper_bound_si(
2326 __isl_take isl_map *map,
2327 enum isl_dim_type type, unsigned pos, int value);
2329 Intersect the set or relation with the half-space where the given
2330 dimension has a value bounded by the fixed given integer value.
2332 __isl_give isl_set *isl_set_equate(__isl_take isl_set *set,
2333 enum isl_dim_type type1, int pos1,
2334 enum isl_dim_type type2, int pos2);
2335 __isl_give isl_basic_map *isl_basic_map_equate(
2336 __isl_take isl_basic_map *bmap,
2337 enum isl_dim_type type1, int pos1,
2338 enum isl_dim_type type2, int pos2);
2339 __isl_give isl_map *isl_map_equate(__isl_take isl_map *map,
2340 enum isl_dim_type type1, int pos1,
2341 enum isl_dim_type type2, int pos2);
2343 Intersect the set or relation with the hyperplane where the given
2344 dimensions are equal to each other.
2346 __isl_give isl_map *isl_map_oppose(__isl_take isl_map *map,
2347 enum isl_dim_type type1, int pos1,
2348 enum isl_dim_type type2, int pos2);
2350 Intersect the relation with the hyperplane where the given
2351 dimensions have opposite values.
2353 __isl_give isl_map *isl_map_order_le(
2354 __isl_take isl_map *map,
2355 enum isl_dim_type type1, int pos1,
2356 enum isl_dim_type type2, int pos2);
2357 __isl_give isl_basic_map *isl_basic_map_order_ge(
2358 __isl_take isl_basic_map *bmap,
2359 enum isl_dim_type type1, int pos1,
2360 enum isl_dim_type type2, int pos2);
2361 __isl_give isl_map *isl_map_order_ge(
2362 __isl_take isl_map *map,
2363 enum isl_dim_type type1, int pos1,
2364 enum isl_dim_type type2, int pos2);
2365 __isl_give isl_map *isl_map_order_lt(__isl_take isl_map *map,
2366 enum isl_dim_type type1, int pos1,
2367 enum isl_dim_type type2, int pos2);
2368 __isl_give isl_basic_map *isl_basic_map_order_gt(
2369 __isl_take isl_basic_map *bmap,
2370 enum isl_dim_type type1, int pos1,
2371 enum isl_dim_type type2, int pos2);
2372 __isl_give isl_map *isl_map_order_gt(__isl_take isl_map *map,
2373 enum isl_dim_type type1, int pos1,
2374 enum isl_dim_type type2, int pos2);
2376 Intersect the relation with the half-space where the given
2377 dimensions satisfy the given ordering.
2381 __isl_give isl_map *isl_set_identity(
2382 __isl_take isl_set *set);
2383 __isl_give isl_union_map *isl_union_set_identity(
2384 __isl_take isl_union_set *uset);
2386 Construct an identity relation on the given (union) set.
2390 __isl_give isl_basic_set *isl_basic_map_deltas(
2391 __isl_take isl_basic_map *bmap);
2392 __isl_give isl_set *isl_map_deltas(__isl_take isl_map *map);
2393 __isl_give isl_union_set *isl_union_map_deltas(
2394 __isl_take isl_union_map *umap);
2396 These functions return a (basic) set containing the differences
2397 between image elements and corresponding domain elements in the input.
2399 __isl_give isl_basic_map *isl_basic_map_deltas_map(
2400 __isl_take isl_basic_map *bmap);
2401 __isl_give isl_map *isl_map_deltas_map(
2402 __isl_take isl_map *map);
2403 __isl_give isl_union_map *isl_union_map_deltas_map(
2404 __isl_take isl_union_map *umap);
2406 The functions above construct a (basic, regular or union) relation
2407 that maps (a wrapped version of) the input relation to its delta set.
2411 Simplify the representation of a set or relation by trying
2412 to combine pairs of basic sets or relations into a single
2413 basic set or relation.
2415 __isl_give isl_set *isl_set_coalesce(__isl_take isl_set *set);
2416 __isl_give isl_map *isl_map_coalesce(__isl_take isl_map *map);
2417 __isl_give isl_union_set *isl_union_set_coalesce(
2418 __isl_take isl_union_set *uset);
2419 __isl_give isl_union_map *isl_union_map_coalesce(
2420 __isl_take isl_union_map *umap);
2422 One of the methods for combining pairs of basic sets or relations
2423 can result in coefficients that are much larger than those that appear
2424 in the constraints of the input. By default, the coefficients are
2425 not allowed to grow larger, but this can be changed by unsetting
2426 the following option.
2428 int isl_options_set_coalesce_bounded_wrapping(
2429 isl_ctx *ctx, int val);
2430 int isl_options_get_coalesce_bounded_wrapping(
2433 =item * Detecting equalities
2435 __isl_give isl_basic_set *isl_basic_set_detect_equalities(
2436 __isl_take isl_basic_set *bset);
2437 __isl_give isl_basic_map *isl_basic_map_detect_equalities(
2438 __isl_take isl_basic_map *bmap);
2439 __isl_give isl_set *isl_set_detect_equalities(
2440 __isl_take isl_set *set);
2441 __isl_give isl_map *isl_map_detect_equalities(
2442 __isl_take isl_map *map);
2443 __isl_give isl_union_set *isl_union_set_detect_equalities(
2444 __isl_take isl_union_set *uset);
2445 __isl_give isl_union_map *isl_union_map_detect_equalities(
2446 __isl_take isl_union_map *umap);
2448 Simplify the representation of a set or relation by detecting implicit
2451 =item * Removing redundant constraints
2453 __isl_give isl_basic_set *isl_basic_set_remove_redundancies(
2454 __isl_take isl_basic_set *bset);
2455 __isl_give isl_set *isl_set_remove_redundancies(
2456 __isl_take isl_set *set);
2457 __isl_give isl_basic_map *isl_basic_map_remove_redundancies(
2458 __isl_take isl_basic_map *bmap);
2459 __isl_give isl_map *isl_map_remove_redundancies(
2460 __isl_take isl_map *map);
2464 __isl_give isl_basic_set *isl_set_convex_hull(
2465 __isl_take isl_set *set);
2466 __isl_give isl_basic_map *isl_map_convex_hull(
2467 __isl_take isl_map *map);
2469 If the input set or relation has any existentially quantified
2470 variables, then the result of these operations is currently undefined.
2474 __isl_give isl_basic_set *
2475 isl_set_unshifted_simple_hull(
2476 __isl_take isl_set *set);
2477 __isl_give isl_basic_map *
2478 isl_map_unshifted_simple_hull(
2479 __isl_take isl_map *map);
2480 __isl_give isl_basic_set *isl_set_simple_hull(
2481 __isl_take isl_set *set);
2482 __isl_give isl_basic_map *isl_map_simple_hull(
2483 __isl_take isl_map *map);
2484 __isl_give isl_union_map *isl_union_map_simple_hull(
2485 __isl_take isl_union_map *umap);
2487 These functions compute a single basic set or relation
2488 that contains the whole input set or relation.
2489 In particular, the output is described by translates
2490 of the constraints describing the basic sets or relations in the input.
2491 In case of C<isl_set_unshifted_simple_hull>, only the original
2492 constraints are used, without any translation.
2496 (See \autoref{s:simple hull}.)
2502 __isl_give isl_basic_set *isl_basic_set_affine_hull(
2503 __isl_take isl_basic_set *bset);
2504 __isl_give isl_basic_set *isl_set_affine_hull(
2505 __isl_take isl_set *set);
2506 __isl_give isl_union_set *isl_union_set_affine_hull(
2507 __isl_take isl_union_set *uset);
2508 __isl_give isl_basic_map *isl_basic_map_affine_hull(
2509 __isl_take isl_basic_map *bmap);
2510 __isl_give isl_basic_map *isl_map_affine_hull(
2511 __isl_take isl_map *map);
2512 __isl_give isl_union_map *isl_union_map_affine_hull(
2513 __isl_take isl_union_map *umap);
2515 In case of union sets and relations, the affine hull is computed
2518 =item * Polyhedral hull
2520 __isl_give isl_basic_set *isl_set_polyhedral_hull(
2521 __isl_take isl_set *set);
2522 __isl_give isl_basic_map *isl_map_polyhedral_hull(
2523 __isl_take isl_map *map);
2524 __isl_give isl_union_set *isl_union_set_polyhedral_hull(
2525 __isl_take isl_union_set *uset);
2526 __isl_give isl_union_map *isl_union_map_polyhedral_hull(
2527 __isl_take isl_union_map *umap);
2529 These functions compute a single basic set or relation
2530 not involving any existentially quantified variables
2531 that contains the whole input set or relation.
2532 In case of union sets and relations, the polyhedral hull is computed
2535 =item * Other approximations
2537 __isl_give isl_basic_set *
2538 isl_basic_set_drop_constraints_involving_dims(
2539 __isl_take isl_basic_set *bset,
2540 enum isl_dim_type type,
2541 unsigned first, unsigned n);
2542 __isl_give isl_basic_map *
2543 isl_basic_map_drop_constraints_involving_dims(
2544 __isl_take isl_basic_map *bmap,
2545 enum isl_dim_type type,
2546 unsigned first, unsigned n);
2547 __isl_give isl_basic_set *
2548 isl_basic_set_drop_constraints_not_involving_dims(
2549 __isl_take isl_basic_set *bset,
2550 enum isl_dim_type type,
2551 unsigned first, unsigned n);
2552 __isl_give isl_set *
2553 isl_set_drop_constraints_involving_dims(
2554 __isl_take isl_set *set,
2555 enum isl_dim_type type,
2556 unsigned first, unsigned n);
2557 __isl_give isl_map *
2558 isl_map_drop_constraints_involving_dims(
2559 __isl_take isl_map *map,
2560 enum isl_dim_type type,
2561 unsigned first, unsigned n);
2563 These functions drop any constraints (not) involving the specified dimensions.
2564 Note that the result depends on the representation of the input.
2568 __isl_give isl_basic_set *isl_basic_set_sample(
2569 __isl_take isl_basic_set *bset);
2570 __isl_give isl_basic_set *isl_set_sample(
2571 __isl_take isl_set *set);
2572 __isl_give isl_basic_map *isl_basic_map_sample(
2573 __isl_take isl_basic_map *bmap);
2574 __isl_give isl_basic_map *isl_map_sample(
2575 __isl_take isl_map *map);
2577 If the input (basic) set or relation is non-empty, then return
2578 a singleton subset of the input. Otherwise, return an empty set.
2580 =item * Optimization
2582 #include <isl/ilp.h>
2583 __isl_give isl_val *isl_basic_set_max_val(
2584 __isl_keep isl_basic_set *bset,
2585 __isl_keep isl_aff *obj);
2586 __isl_give isl_val *isl_set_min_val(
2587 __isl_keep isl_set *set,
2588 __isl_keep isl_aff *obj);
2589 __isl_give isl_val *isl_set_max_val(
2590 __isl_keep isl_set *set,
2591 __isl_keep isl_aff *obj);
2593 Compute the minimum or maximum of the integer affine expression C<obj>
2594 over the points in C<set>, returning the result in C<opt>.
2595 The result is C<NULL> in case of an error, the optimal value in case
2596 there is one, negative infinity or infinity if the problem is unbounded and
2597 NaN if the problem is empty.
2599 =item * Parametric optimization
2601 __isl_give isl_pw_aff *isl_set_dim_min(
2602 __isl_take isl_set *set, int pos);
2603 __isl_give isl_pw_aff *isl_set_dim_max(
2604 __isl_take isl_set *set, int pos);
2605 __isl_give isl_pw_aff *isl_map_dim_max(
2606 __isl_take isl_map *map, int pos);
2608 Compute the minimum or maximum of the given set or output dimension
2609 as a function of the parameters (and input dimensions), but independently
2610 of the other set or output dimensions.
2611 For lexicographic optimization, see L<"Lexicographic Optimization">.
2615 The following functions compute either the set of (rational) coefficient
2616 values of valid constraints for the given set or the set of (rational)
2617 values satisfying the constraints with coefficients from the given set.
2618 Internally, these two sets of functions perform essentially the
2619 same operations, except that the set of coefficients is assumed to
2620 be a cone, while the set of values may be any polyhedron.
2621 The current implementation is based on the Farkas lemma and
2622 Fourier-Motzkin elimination, but this may change or be made optional
2623 in future. In particular, future implementations may use different
2624 dualization algorithms or skip the elimination step.
2626 __isl_give isl_basic_set *isl_basic_set_coefficients(
2627 __isl_take isl_basic_set *bset);
2628 __isl_give isl_basic_set *isl_set_coefficients(
2629 __isl_take isl_set *set);
2630 __isl_give isl_union_set *isl_union_set_coefficients(
2631 __isl_take isl_union_set *bset);
2632 __isl_give isl_basic_set *isl_basic_set_solutions(
2633 __isl_take isl_basic_set *bset);
2634 __isl_give isl_basic_set *isl_set_solutions(
2635 __isl_take isl_set *set);
2636 __isl_give isl_union_set *isl_union_set_solutions(
2637 __isl_take isl_union_set *bset);
2641 __isl_give isl_map *isl_map_fixed_power_val(
2642 __isl_take isl_map *map,
2643 __isl_take isl_val *exp);
2644 __isl_give isl_union_map *
2645 isl_union_map_fixed_power_val(
2646 __isl_take isl_union_map *umap,
2647 __isl_take isl_val *exp);
2649 Compute the given power of C<map>, where C<exp> is assumed to be non-zero.
2650 If the exponent C<exp> is negative, then the -C<exp> th power of the inverse
2651 of C<map> is computed.
2653 __isl_give isl_map *isl_map_power(__isl_take isl_map *map,
2655 __isl_give isl_union_map *isl_union_map_power(
2656 __isl_take isl_union_map *umap, int *exact);
2658 Compute a parametric representation for all positive powers I<k> of C<map>.
2659 The result maps I<k> to a nested relation corresponding to the
2660 I<k>th power of C<map>.
2661 The result may be an overapproximation. If the result is known to be exact,
2662 then C<*exact> is set to C<1>.
2664 =item * Transitive closure
2666 __isl_give isl_map *isl_map_transitive_closure(
2667 __isl_take isl_map *map, int *exact);
2668 __isl_give isl_union_map *isl_union_map_transitive_closure(
2669 __isl_take isl_union_map *umap, int *exact);
2671 Compute the transitive closure of C<map>.
2672 The result may be an overapproximation. If the result is known to be exact,
2673 then C<*exact> is set to C<1>.
2675 =item * Reaching path lengths
2677 __isl_give isl_map *isl_map_reaching_path_lengths(
2678 __isl_take isl_map *map, int *exact);
2680 Compute a relation that maps each element in the range of C<map>
2681 to the lengths of all paths composed of edges in C<map> that
2682 end up in the given element.
2683 The result may be an overapproximation. If the result is known to be exact,
2684 then C<*exact> is set to C<1>.
2685 To compute the I<maximal> path length, the resulting relation
2686 should be postprocessed by C<isl_map_lexmax>.
2687 In particular, if the input relation is a dependence relation
2688 (mapping sources to sinks), then the maximal path length corresponds
2689 to the free schedule.
2690 Note, however, that C<isl_map_lexmax> expects the maximum to be
2691 finite, so if the path lengths are unbounded (possibly due to
2692 the overapproximation), then you will get an error message.
2696 __isl_give isl_basic_set *isl_basic_map_wrap(
2697 __isl_take isl_basic_map *bmap);
2698 __isl_give isl_set *isl_map_wrap(
2699 __isl_take isl_map *map);
2700 __isl_give isl_union_set *isl_union_map_wrap(
2701 __isl_take isl_union_map *umap);
2702 __isl_give isl_basic_map *isl_basic_set_unwrap(
2703 __isl_take isl_basic_set *bset);
2704 __isl_give isl_map *isl_set_unwrap(
2705 __isl_take isl_set *set);
2706 __isl_give isl_union_map *isl_union_set_unwrap(
2707 __isl_take isl_union_set *uset);
2711 Remove any internal structure of domain (and range) of the given
2712 set or relation. If there is any such internal structure in the input,
2713 then the name of the space is also removed.
2715 __isl_give isl_basic_set *isl_basic_set_flatten(
2716 __isl_take isl_basic_set *bset);
2717 __isl_give isl_set *isl_set_flatten(
2718 __isl_take isl_set *set);
2719 __isl_give isl_basic_map *isl_basic_map_flatten_domain(
2720 __isl_take isl_basic_map *bmap);
2721 __isl_give isl_basic_map *isl_basic_map_flatten_range(
2722 __isl_take isl_basic_map *bmap);
2723 __isl_give isl_map *isl_map_flatten_range(
2724 __isl_take isl_map *map);
2725 __isl_give isl_map *isl_map_flatten_domain(
2726 __isl_take isl_map *map);
2727 __isl_give isl_basic_map *isl_basic_map_flatten(
2728 __isl_take isl_basic_map *bmap);
2729 __isl_give isl_map *isl_map_flatten(
2730 __isl_take isl_map *map);
2732 __isl_give isl_map *isl_set_flatten_map(
2733 __isl_take isl_set *set);
2735 The function above constructs a relation
2736 that maps the input set to a flattened version of the set.
2740 Lift the input set to a space with extra dimensions corresponding
2741 to the existentially quantified variables in the input.
2742 In particular, the result lives in a wrapped map where the domain
2743 is the original space and the range corresponds to the original
2744 existentially quantified variables.
2746 __isl_give isl_basic_set *isl_basic_set_lift(
2747 __isl_take isl_basic_set *bset);
2748 __isl_give isl_set *isl_set_lift(
2749 __isl_take isl_set *set);
2750 __isl_give isl_union_set *isl_union_set_lift(
2751 __isl_take isl_union_set *uset);
2753 Given a local space that contains the existentially quantified
2754 variables of a set, a basic relation that, when applied to
2755 a basic set, has essentially the same effect as C<isl_basic_set_lift>,
2756 can be constructed using the following function.
2758 #include <isl/local_space.h>
2759 __isl_give isl_basic_map *isl_local_space_lifting(
2760 __isl_take isl_local_space *ls);
2762 =item * Internal Product
2764 __isl_give isl_basic_map *isl_basic_map_zip(
2765 __isl_take isl_basic_map *bmap);
2766 __isl_give isl_map *isl_map_zip(
2767 __isl_take isl_map *map);
2768 __isl_give isl_union_map *isl_union_map_zip(
2769 __isl_take isl_union_map *umap);
2771 Given a relation with nested relations for domain and range,
2772 interchange the range of the domain with the domain of the range.
2776 __isl_give isl_basic_map *isl_basic_map_curry(
2777 __isl_take isl_basic_map *bmap);
2778 __isl_give isl_basic_map *isl_basic_map_uncurry(
2779 __isl_take isl_basic_map *bmap);
2780 __isl_give isl_map *isl_map_curry(
2781 __isl_take isl_map *map);
2782 __isl_give isl_map *isl_map_uncurry(
2783 __isl_take isl_map *map);
2784 __isl_give isl_union_map *isl_union_map_curry(
2785 __isl_take isl_union_map *umap);
2786 __isl_give isl_union_map *isl_union_map_uncurry(
2787 __isl_take isl_union_map *umap);
2789 Given a relation with a nested relation for domain,
2790 the C<curry> functions
2791 move the range of the nested relation out of the domain
2792 and use it as the domain of a nested relation in the range,
2793 with the original range as range of this nested relation.
2794 The C<uncurry> functions perform the inverse operation.
2796 =item * Aligning parameters
2798 __isl_give isl_basic_set *isl_basic_set_align_params(
2799 __isl_take isl_basic_set *bset,
2800 __isl_take isl_space *model);
2801 __isl_give isl_set *isl_set_align_params(
2802 __isl_take isl_set *set,
2803 __isl_take isl_space *model);
2804 __isl_give isl_basic_map *isl_basic_map_align_params(
2805 __isl_take isl_basic_map *bmap,
2806 __isl_take isl_space *model);
2807 __isl_give isl_map *isl_map_align_params(
2808 __isl_take isl_map *map,
2809 __isl_take isl_space *model);
2811 Change the order of the parameters of the given set or relation
2812 such that the first parameters match those of C<model>.
2813 This may involve the introduction of extra parameters.
2814 All parameters need to be named.
2816 =item * Dimension manipulation
2818 __isl_give isl_basic_set *isl_basic_set_add_dims(
2819 __isl_take isl_basic_set *bset,
2820 enum isl_dim_type type, unsigned n);
2821 __isl_give isl_set *isl_set_add_dims(
2822 __isl_take isl_set *set,
2823 enum isl_dim_type type, unsigned n);
2824 __isl_give isl_map *isl_map_add_dims(
2825 __isl_take isl_map *map,
2826 enum isl_dim_type type, unsigned n);
2827 __isl_give isl_basic_set *isl_basic_set_insert_dims(
2828 __isl_take isl_basic_set *bset,
2829 enum isl_dim_type type, unsigned pos,
2831 __isl_give isl_basic_map *isl_basic_map_insert_dims(
2832 __isl_take isl_basic_map *bmap,
2833 enum isl_dim_type type, unsigned pos,
2835 __isl_give isl_set *isl_set_insert_dims(
2836 __isl_take isl_set *set,
2837 enum isl_dim_type type, unsigned pos, unsigned n);
2838 __isl_give isl_map *isl_map_insert_dims(
2839 __isl_take isl_map *map,
2840 enum isl_dim_type type, unsigned pos, unsigned n);
2841 __isl_give isl_basic_set *isl_basic_set_move_dims(
2842 __isl_take isl_basic_set *bset,
2843 enum isl_dim_type dst_type, unsigned dst_pos,
2844 enum isl_dim_type src_type, unsigned src_pos,
2846 __isl_give isl_basic_map *isl_basic_map_move_dims(
2847 __isl_take isl_basic_map *bmap,
2848 enum isl_dim_type dst_type, unsigned dst_pos,
2849 enum isl_dim_type src_type, unsigned src_pos,
2851 __isl_give isl_set *isl_set_move_dims(
2852 __isl_take isl_set *set,
2853 enum isl_dim_type dst_type, unsigned dst_pos,
2854 enum isl_dim_type src_type, unsigned src_pos,
2856 __isl_give isl_map *isl_map_move_dims(
2857 __isl_take isl_map *map,
2858 enum isl_dim_type dst_type, unsigned dst_pos,
2859 enum isl_dim_type src_type, unsigned src_pos,
2862 It is usually not advisable to directly change the (input or output)
2863 space of a set or a relation as this removes the name and the internal
2864 structure of the space. However, the above functions can be useful
2865 to add new parameters, assuming
2866 C<isl_set_align_params> and C<isl_map_align_params>
2871 =head2 Binary Operations
2873 The two arguments of a binary operation not only need to live
2874 in the same C<isl_ctx>, they currently also need to have
2875 the same (number of) parameters.
2877 =head3 Basic Operations
2881 =item * Intersection
2883 __isl_give isl_basic_set *isl_basic_set_intersect_params(
2884 __isl_take isl_basic_set *bset1,
2885 __isl_take isl_basic_set *bset2);
2886 __isl_give isl_basic_set *isl_basic_set_intersect(
2887 __isl_take isl_basic_set *bset1,
2888 __isl_take isl_basic_set *bset2);
2889 __isl_give isl_set *isl_set_intersect_params(
2890 __isl_take isl_set *set,
2891 __isl_take isl_set *params);
2892 __isl_give isl_set *isl_set_intersect(
2893 __isl_take isl_set *set1,
2894 __isl_take isl_set *set2);
2895 __isl_give isl_union_set *isl_union_set_intersect_params(
2896 __isl_take isl_union_set *uset,
2897 __isl_take isl_set *set);
2898 __isl_give isl_union_map *isl_union_map_intersect_params(
2899 __isl_take isl_union_map *umap,
2900 __isl_take isl_set *set);
2901 __isl_give isl_union_set *isl_union_set_intersect(
2902 __isl_take isl_union_set *uset1,
2903 __isl_take isl_union_set *uset2);
2904 __isl_give isl_basic_map *isl_basic_map_intersect_domain(
2905 __isl_take isl_basic_map *bmap,
2906 __isl_take isl_basic_set *bset);
2907 __isl_give isl_basic_map *isl_basic_map_intersect_range(
2908 __isl_take isl_basic_map *bmap,
2909 __isl_take isl_basic_set *bset);
2910 __isl_give isl_basic_map *isl_basic_map_intersect(
2911 __isl_take isl_basic_map *bmap1,
2912 __isl_take isl_basic_map *bmap2);
2913 __isl_give isl_map *isl_map_intersect_params(
2914 __isl_take isl_map *map,
2915 __isl_take isl_set *params);
2916 __isl_give isl_map *isl_map_intersect_domain(
2917 __isl_take isl_map *map,
2918 __isl_take isl_set *set);
2919 __isl_give isl_map *isl_map_intersect_range(
2920 __isl_take isl_map *map,
2921 __isl_take isl_set *set);
2922 __isl_give isl_map *isl_map_intersect(
2923 __isl_take isl_map *map1,
2924 __isl_take isl_map *map2);
2925 __isl_give isl_union_map *isl_union_map_intersect_domain(
2926 __isl_take isl_union_map *umap,
2927 __isl_take isl_union_set *uset);
2928 __isl_give isl_union_map *isl_union_map_intersect_range(
2929 __isl_take isl_union_map *umap,
2930 __isl_take isl_union_set *uset);
2931 __isl_give isl_union_map *isl_union_map_intersect(
2932 __isl_take isl_union_map *umap1,
2933 __isl_take isl_union_map *umap2);
2935 The second argument to the C<_params> functions needs to be
2936 a parametric (basic) set. For the other functions, a parametric set
2937 for either argument is only allowed if the other argument is
2938 a parametric set as well.
2942 __isl_give isl_set *isl_basic_set_union(
2943 __isl_take isl_basic_set *bset1,
2944 __isl_take isl_basic_set *bset2);
2945 __isl_give isl_map *isl_basic_map_union(
2946 __isl_take isl_basic_map *bmap1,
2947 __isl_take isl_basic_map *bmap2);
2948 __isl_give isl_set *isl_set_union(
2949 __isl_take isl_set *set1,
2950 __isl_take isl_set *set2);
2951 __isl_give isl_map *isl_map_union(
2952 __isl_take isl_map *map1,
2953 __isl_take isl_map *map2);
2954 __isl_give isl_union_set *isl_union_set_union(
2955 __isl_take isl_union_set *uset1,
2956 __isl_take isl_union_set *uset2);
2957 __isl_give isl_union_map *isl_union_map_union(
2958 __isl_take isl_union_map *umap1,
2959 __isl_take isl_union_map *umap2);
2961 =item * Set difference
2963 __isl_give isl_set *isl_set_subtract(
2964 __isl_take isl_set *set1,
2965 __isl_take isl_set *set2);
2966 __isl_give isl_map *isl_map_subtract(
2967 __isl_take isl_map *map1,
2968 __isl_take isl_map *map2);
2969 __isl_give isl_map *isl_map_subtract_domain(
2970 __isl_take isl_map *map,
2971 __isl_take isl_set *dom);
2972 __isl_give isl_map *isl_map_subtract_range(
2973 __isl_take isl_map *map,
2974 __isl_take isl_set *dom);
2975 __isl_give isl_union_set *isl_union_set_subtract(
2976 __isl_take isl_union_set *uset1,
2977 __isl_take isl_union_set *uset2);
2978 __isl_give isl_union_map *isl_union_map_subtract(
2979 __isl_take isl_union_map *umap1,
2980 __isl_take isl_union_map *umap2);
2981 __isl_give isl_union_map *isl_union_map_subtract_domain(
2982 __isl_take isl_union_map *umap,
2983 __isl_take isl_union_set *dom);
2984 __isl_give isl_union_map *isl_union_map_subtract_range(
2985 __isl_take isl_union_map *umap,
2986 __isl_take isl_union_set *dom);
2990 __isl_give isl_basic_set *isl_basic_set_apply(
2991 __isl_take isl_basic_set *bset,
2992 __isl_take isl_basic_map *bmap);
2993 __isl_give isl_set *isl_set_apply(
2994 __isl_take isl_set *set,
2995 __isl_take isl_map *map);
2996 __isl_give isl_union_set *isl_union_set_apply(
2997 __isl_take isl_union_set *uset,
2998 __isl_take isl_union_map *umap);
2999 __isl_give isl_basic_map *isl_basic_map_apply_domain(
3000 __isl_take isl_basic_map *bmap1,
3001 __isl_take isl_basic_map *bmap2);
3002 __isl_give isl_basic_map *isl_basic_map_apply_range(
3003 __isl_take isl_basic_map *bmap1,
3004 __isl_take isl_basic_map *bmap2);
3005 __isl_give isl_map *isl_map_apply_domain(
3006 __isl_take isl_map *map1,
3007 __isl_take isl_map *map2);
3008 __isl_give isl_union_map *isl_union_map_apply_domain(
3009 __isl_take isl_union_map *umap1,
3010 __isl_take isl_union_map *umap2);
3011 __isl_give isl_map *isl_map_apply_range(
3012 __isl_take isl_map *map1,
3013 __isl_take isl_map *map2);
3014 __isl_give isl_union_map *isl_union_map_apply_range(
3015 __isl_take isl_union_map *umap1,
3016 __isl_take isl_union_map *umap2);
3020 __isl_give isl_basic_set *
3021 isl_basic_set_preimage_multi_aff(
3022 __isl_take isl_basic_set *bset,
3023 __isl_take isl_multi_aff *ma);
3024 __isl_give isl_set *isl_set_preimage_multi_aff(
3025 __isl_take isl_set *set,
3026 __isl_take isl_multi_aff *ma);
3027 __isl_give isl_set *isl_set_preimage_pw_multi_aff(
3028 __isl_take isl_set *set,
3029 __isl_take isl_pw_multi_aff *pma);
3030 __isl_give isl_set *isl_set_preimage_multi_pw_aff(
3031 __isl_take isl_set *set,
3032 __isl_take isl_multi_pw_aff *mpa);
3033 __isl_give isl_basic_map *
3034 isl_basic_map_preimage_domain_multi_aff(
3035 __isl_take isl_basic_map *bmap,
3036 __isl_take isl_multi_aff *ma);
3037 __isl_give isl_map *isl_map_preimage_domain_multi_aff(
3038 __isl_take isl_map *map,
3039 __isl_take isl_multi_aff *ma);
3040 __isl_give isl_map *
3041 isl_map_preimage_domain_pw_multi_aff(
3042 __isl_take isl_map *map,
3043 __isl_take isl_pw_multi_aff *pma);
3044 __isl_give isl_map *
3045 isl_map_preimage_domain_multi_pw_aff(
3046 __isl_take isl_map *map,
3047 __isl_take isl_multi_pw_aff *mpa);
3048 __isl_give isl_union_map *
3049 isl_union_map_preimage_domain_multi_aff(
3050 __isl_take isl_union_map *umap,
3051 __isl_take isl_multi_aff *ma);
3052 __isl_give isl_basic_map *
3053 isl_basic_map_preimage_range_multi_aff(
3054 __isl_take isl_basic_map *bmap,
3055 __isl_take isl_multi_aff *ma);
3057 These functions compute the preimage of the given set or map domain/range under
3058 the given function. In other words, the expression is plugged
3059 into the set description or into the domain/range of the map.
3060 Objects of types C<isl_multi_aff> and C<isl_pw_multi_aff> are described in
3061 L</"Piecewise Multiple Quasi Affine Expressions">.
3063 =item * Cartesian Product
3065 __isl_give isl_set *isl_set_product(
3066 __isl_take isl_set *set1,
3067 __isl_take isl_set *set2);
3068 __isl_give isl_union_set *isl_union_set_product(
3069 __isl_take isl_union_set *uset1,
3070 __isl_take isl_union_set *uset2);
3071 __isl_give isl_basic_map *isl_basic_map_domain_product(
3072 __isl_take isl_basic_map *bmap1,
3073 __isl_take isl_basic_map *bmap2);
3074 __isl_give isl_basic_map *isl_basic_map_range_product(
3075 __isl_take isl_basic_map *bmap1,
3076 __isl_take isl_basic_map *bmap2);
3077 __isl_give isl_basic_map *isl_basic_map_product(
3078 __isl_take isl_basic_map *bmap1,
3079 __isl_take isl_basic_map *bmap2);
3080 __isl_give isl_map *isl_map_domain_product(
3081 __isl_take isl_map *map1,
3082 __isl_take isl_map *map2);
3083 __isl_give isl_map *isl_map_range_product(
3084 __isl_take isl_map *map1,
3085 __isl_take isl_map *map2);
3086 __isl_give isl_union_map *isl_union_map_domain_product(
3087 __isl_take isl_union_map *umap1,
3088 __isl_take isl_union_map *umap2);
3089 __isl_give isl_union_map *isl_union_map_range_product(
3090 __isl_take isl_union_map *umap1,
3091 __isl_take isl_union_map *umap2);
3092 __isl_give isl_map *isl_map_product(
3093 __isl_take isl_map *map1,
3094 __isl_take isl_map *map2);
3095 __isl_give isl_union_map *isl_union_map_product(
3096 __isl_take isl_union_map *umap1,
3097 __isl_take isl_union_map *umap2);
3099 The above functions compute the cross product of the given
3100 sets or relations. The domains and ranges of the results
3101 are wrapped maps between domains and ranges of the inputs.
3102 To obtain a ``flat'' product, use the following functions
3105 __isl_give isl_basic_set *isl_basic_set_flat_product(
3106 __isl_take isl_basic_set *bset1,
3107 __isl_take isl_basic_set *bset2);
3108 __isl_give isl_set *isl_set_flat_product(
3109 __isl_take isl_set *set1,
3110 __isl_take isl_set *set2);
3111 __isl_give isl_basic_map *isl_basic_map_flat_range_product(
3112 __isl_take isl_basic_map *bmap1,
3113 __isl_take isl_basic_map *bmap2);
3114 __isl_give isl_map *isl_map_flat_domain_product(
3115 __isl_take isl_map *map1,
3116 __isl_take isl_map *map2);
3117 __isl_give isl_map *isl_map_flat_range_product(
3118 __isl_take isl_map *map1,
3119 __isl_take isl_map *map2);
3120 __isl_give isl_union_map *isl_union_map_flat_range_product(
3121 __isl_take isl_union_map *umap1,
3122 __isl_take isl_union_map *umap2);
3123 __isl_give isl_basic_map *isl_basic_map_flat_product(
3124 __isl_take isl_basic_map *bmap1,
3125 __isl_take isl_basic_map *bmap2);
3126 __isl_give isl_map *isl_map_flat_product(
3127 __isl_take isl_map *map1,
3128 __isl_take isl_map *map2);
3130 The arguments of a call to C<isl_map_product> can be extracted
3131 from the result using the following two functions.
3133 __isl_give isl_map *isl_map_range_factor_domain(
3134 __isl_take isl_map *map);
3135 __isl_give isl_map *isl_map_range_factor_range(
3136 __isl_take isl_map *map);
3138 =item * Simplification
3140 __isl_give isl_basic_set *isl_basic_set_gist(
3141 __isl_take isl_basic_set *bset,
3142 __isl_take isl_basic_set *context);
3143 __isl_give isl_set *isl_set_gist(__isl_take isl_set *set,
3144 __isl_take isl_set *context);
3145 __isl_give isl_set *isl_set_gist_params(
3146 __isl_take isl_set *set,
3147 __isl_take isl_set *context);
3148 __isl_give isl_union_set *isl_union_set_gist(
3149 __isl_take isl_union_set *uset,
3150 __isl_take isl_union_set *context);
3151 __isl_give isl_union_set *isl_union_set_gist_params(
3152 __isl_take isl_union_set *uset,
3153 __isl_take isl_set *set);
3154 __isl_give isl_basic_map *isl_basic_map_gist(
3155 __isl_take isl_basic_map *bmap,
3156 __isl_take isl_basic_map *context);
3157 __isl_give isl_map *isl_map_gist(__isl_take isl_map *map,
3158 __isl_take isl_map *context);
3159 __isl_give isl_map *isl_map_gist_params(
3160 __isl_take isl_map *map,
3161 __isl_take isl_set *context);
3162 __isl_give isl_map *isl_map_gist_domain(
3163 __isl_take isl_map *map,
3164 __isl_take isl_set *context);
3165 __isl_give isl_map *isl_map_gist_range(
3166 __isl_take isl_map *map,
3167 __isl_take isl_set *context);
3168 __isl_give isl_union_map *isl_union_map_gist(
3169 __isl_take isl_union_map *umap,
3170 __isl_take isl_union_map *context);
3171 __isl_give isl_union_map *isl_union_map_gist_params(
3172 __isl_take isl_union_map *umap,
3173 __isl_take isl_set *set);
3174 __isl_give isl_union_map *isl_union_map_gist_domain(
3175 __isl_take isl_union_map *umap,
3176 __isl_take isl_union_set *uset);
3177 __isl_give isl_union_map *isl_union_map_gist_range(
3178 __isl_take isl_union_map *umap,
3179 __isl_take isl_union_set *uset);
3181 The gist operation returns a set or relation that has the
3182 same intersection with the context as the input set or relation.
3183 Any implicit equality in the intersection is made explicit in the result,
3184 while all inequalities that are redundant with respect to the intersection
3186 In case of union sets and relations, the gist operation is performed
3191 =head3 Lexicographic Optimization
3193 Given a (basic) set C<set> (or C<bset>) and a zero-dimensional domain C<dom>,
3194 the following functions
3195 compute a set that contains the lexicographic minimum or maximum
3196 of the elements in C<set> (or C<bset>) for those values of the parameters
3197 that satisfy C<dom>.
3198 If C<empty> is not C<NULL>, then C<*empty> is assigned a set
3199 that contains the parameter values in C<dom> for which C<set> (or C<bset>)
3201 In other words, the union of the parameter values
3202 for which the result is non-empty and of C<*empty>
3205 __isl_give isl_set *isl_basic_set_partial_lexmin(
3206 __isl_take isl_basic_set *bset,
3207 __isl_take isl_basic_set *dom,
3208 __isl_give isl_set **empty);
3209 __isl_give isl_set *isl_basic_set_partial_lexmax(
3210 __isl_take isl_basic_set *bset,
3211 __isl_take isl_basic_set *dom,
3212 __isl_give isl_set **empty);
3213 __isl_give isl_set *isl_set_partial_lexmin(
3214 __isl_take isl_set *set, __isl_take isl_set *dom,
3215 __isl_give isl_set **empty);
3216 __isl_give isl_set *isl_set_partial_lexmax(
3217 __isl_take isl_set *set, __isl_take isl_set *dom,
3218 __isl_give isl_set **empty);
3220 Given a (basic) set C<set> (or C<bset>), the following functions simply
3221 return a set containing the lexicographic minimum or maximum
3222 of the elements in C<set> (or C<bset>).
3223 In case of union sets, the optimum is computed per space.
3225 __isl_give isl_set *isl_basic_set_lexmin(
3226 __isl_take isl_basic_set *bset);
3227 __isl_give isl_set *isl_basic_set_lexmax(
3228 __isl_take isl_basic_set *bset);
3229 __isl_give isl_set *isl_set_lexmin(
3230 __isl_take isl_set *set);
3231 __isl_give isl_set *isl_set_lexmax(
3232 __isl_take isl_set *set);
3233 __isl_give isl_union_set *isl_union_set_lexmin(
3234 __isl_take isl_union_set *uset);
3235 __isl_give isl_union_set *isl_union_set_lexmax(
3236 __isl_take isl_union_set *uset);
3238 Given a (basic) relation C<map> (or C<bmap>) and a domain C<dom>,
3239 the following functions
3240 compute a relation that maps each element of C<dom>
3241 to the single lexicographic minimum or maximum
3242 of the elements that are associated to that same
3243 element in C<map> (or C<bmap>).
3244 If C<empty> is not C<NULL>, then C<*empty> is assigned a set
3245 that contains the elements in C<dom> that do not map
3246 to any elements in C<map> (or C<bmap>).
3247 In other words, the union of the domain of the result and of C<*empty>
3250 __isl_give isl_map *isl_basic_map_partial_lexmax(
3251 __isl_take isl_basic_map *bmap,
3252 __isl_take isl_basic_set *dom,
3253 __isl_give isl_set **empty);
3254 __isl_give isl_map *isl_basic_map_partial_lexmin(
3255 __isl_take isl_basic_map *bmap,
3256 __isl_take isl_basic_set *dom,
3257 __isl_give isl_set **empty);
3258 __isl_give isl_map *isl_map_partial_lexmax(
3259 __isl_take isl_map *map, __isl_take isl_set *dom,
3260 __isl_give isl_set **empty);
3261 __isl_give isl_map *isl_map_partial_lexmin(
3262 __isl_take isl_map *map, __isl_take isl_set *dom,
3263 __isl_give isl_set **empty);
3265 Given a (basic) map C<map> (or C<bmap>), the following functions simply
3266 return a map mapping each element in the domain of
3267 C<map> (or C<bmap>) to the lexicographic minimum or maximum
3268 of all elements associated to that element.
3269 In case of union relations, the optimum is computed per space.
3271 __isl_give isl_map *isl_basic_map_lexmin(
3272 __isl_take isl_basic_map *bmap);
3273 __isl_give isl_map *isl_basic_map_lexmax(
3274 __isl_take isl_basic_map *bmap);
3275 __isl_give isl_map *isl_map_lexmin(
3276 __isl_take isl_map *map);
3277 __isl_give isl_map *isl_map_lexmax(
3278 __isl_take isl_map *map);
3279 __isl_give isl_union_map *isl_union_map_lexmin(
3280 __isl_take isl_union_map *umap);
3281 __isl_give isl_union_map *isl_union_map_lexmax(
3282 __isl_take isl_union_map *umap);
3284 The following functions return their result in the form of
3285 a piecewise multi-affine expression
3286 (See L<"Piecewise Multiple Quasi Affine Expressions">),
3287 but are otherwise equivalent to the corresponding functions
3288 returning a basic set or relation.
3290 __isl_give isl_pw_multi_aff *
3291 isl_basic_map_lexmin_pw_multi_aff(
3292 __isl_take isl_basic_map *bmap);
3293 __isl_give isl_pw_multi_aff *
3294 isl_basic_set_partial_lexmin_pw_multi_aff(
3295 __isl_take isl_basic_set *bset,
3296 __isl_take isl_basic_set *dom,
3297 __isl_give isl_set **empty);
3298 __isl_give isl_pw_multi_aff *
3299 isl_basic_set_partial_lexmax_pw_multi_aff(
3300 __isl_take isl_basic_set *bset,
3301 __isl_take isl_basic_set *dom,
3302 __isl_give isl_set **empty);
3303 __isl_give isl_pw_multi_aff *
3304 isl_basic_map_partial_lexmin_pw_multi_aff(
3305 __isl_take isl_basic_map *bmap,
3306 __isl_take isl_basic_set *dom,
3307 __isl_give isl_set **empty);
3308 __isl_give isl_pw_multi_aff *
3309 isl_basic_map_partial_lexmax_pw_multi_aff(
3310 __isl_take isl_basic_map *bmap,
3311 __isl_take isl_basic_set *dom,
3312 __isl_give isl_set **empty);
3313 __isl_give isl_pw_multi_aff *isl_set_lexmin_pw_multi_aff(
3314 __isl_take isl_set *set);
3315 __isl_give isl_pw_multi_aff *isl_set_lexmax_pw_multi_aff(
3316 __isl_take isl_set *set);
3317 __isl_give isl_pw_multi_aff *isl_map_lexmin_pw_multi_aff(
3318 __isl_take isl_map *map);
3319 __isl_give isl_pw_multi_aff *isl_map_lexmax_pw_multi_aff(
3320 __isl_take isl_map *map);
3324 Lists are defined over several element types, including
3325 C<isl_val>, C<isl_id>, C<isl_aff>, C<isl_pw_aff>, C<isl_constraint>,
3326 C<isl_basic_set>, C<isl_set>, C<isl_ast_expr> and C<isl_ast_node>.
3327 Here we take lists of C<isl_set>s as an example.
3328 Lists can be created, copied, modified and freed using the following functions.
3330 #include <isl/list.h>
3331 __isl_give isl_set_list *isl_set_list_from_set(
3332 __isl_take isl_set *el);
3333 __isl_give isl_set_list *isl_set_list_alloc(
3334 isl_ctx *ctx, int n);
3335 __isl_give isl_set_list *isl_set_list_copy(
3336 __isl_keep isl_set_list *list);
3337 __isl_give isl_set_list *isl_set_list_insert(
3338 __isl_take isl_set_list *list, unsigned pos,
3339 __isl_take isl_set *el);
3340 __isl_give isl_set_list *isl_set_list_add(
3341 __isl_take isl_set_list *list,
3342 __isl_take isl_set *el);
3343 __isl_give isl_set_list *isl_set_list_drop(
3344 __isl_take isl_set_list *list,
3345 unsigned first, unsigned n);
3346 __isl_give isl_set_list *isl_set_list_set_set(
3347 __isl_take isl_set_list *list, int index,
3348 __isl_take isl_set *set);
3349 __isl_give isl_set_list *isl_set_list_concat(
3350 __isl_take isl_set_list *list1,
3351 __isl_take isl_set_list *list2);
3352 __isl_give isl_set_list *isl_set_list_sort(
3353 __isl_take isl_set_list *list,
3354 int (*cmp)(__isl_keep isl_set *a,
3355 __isl_keep isl_set *b, void *user),
3357 void *isl_set_list_free(__isl_take isl_set_list *list);
3359 C<isl_set_list_alloc> creates an empty list with a capacity for
3360 C<n> elements. C<isl_set_list_from_set> creates a list with a single
3363 Lists can be inspected using the following functions.
3365 #include <isl/list.h>
3366 isl_ctx *isl_set_list_get_ctx(__isl_keep isl_set_list *list);
3367 int isl_set_list_n_set(__isl_keep isl_set_list *list);
3368 __isl_give isl_set *isl_set_list_get_set(
3369 __isl_keep isl_set_list *list, int index);
3370 int isl_set_list_foreach(__isl_keep isl_set_list *list,
3371 int (*fn)(__isl_take isl_set *el, void *user),
3373 int isl_set_list_foreach_scc(__isl_keep isl_set_list *list,
3374 int (*follows)(__isl_keep isl_set *a,
3375 __isl_keep isl_set *b, void *user),
3377 int (*fn)(__isl_take isl_set *el, void *user),
3380 The function C<isl_set_list_foreach_scc> calls C<fn> on each of the
3381 strongly connected components of the graph with as vertices the elements
3382 of C<list> and a directed edge from vertex C<b> to vertex C<a>
3383 iff C<follows(a, b)> returns C<1>. The callbacks C<follows> and C<fn>
3384 should return C<-1> on error.
3386 Lists can be printed using
3388 #include <isl/list.h>
3389 __isl_give isl_printer *isl_printer_print_set_list(
3390 __isl_take isl_printer *p,
3391 __isl_keep isl_set_list *list);
3393 =head2 Associative arrays
3395 Associative arrays map isl objects of a specific type to isl objects
3396 of some (other) specific type. They are defined for several pairs
3397 of types, including (C<isl_map>, C<isl_basic_set>),
3398 (C<isl_id>, C<isl_ast_expr>) and.
3399 (C<isl_id>, C<isl_pw_aff>).
3400 Here, we take associative arrays that map C<isl_id>s to C<isl_ast_expr>s
3403 Associative arrays can be created, copied and freed using
3404 the following functions.
3406 #include <isl/id_to_ast_expr.h>
3407 __isl_give id_to_ast_expr *isl_id_to_ast_expr_alloc(
3408 isl_ctx *ctx, int min_size);
3409 __isl_give id_to_ast_expr *isl_id_to_ast_expr_copy(
3410 __isl_keep id_to_ast_expr *id2expr);
3411 void *isl_id_to_ast_expr_free(
3412 __isl_take id_to_ast_expr *id2expr);
3414 The C<min_size> argument to C<isl_id_to_ast_expr_alloc> can be used
3415 to specify the expected size of the associative array.
3416 The associative array will be grown automatically as needed.
3418 Associative arrays can be inspected using the following functions.
3420 #include <isl/id_to_ast_expr.h>
3421 isl_ctx *isl_id_to_ast_expr_get_ctx(
3422 __isl_keep id_to_ast_expr *id2expr);
3423 int isl_id_to_ast_expr_has(
3424 __isl_keep id_to_ast_expr *id2expr,
3425 __isl_keep isl_id *key);
3426 __isl_give isl_ast_expr *isl_id_to_ast_expr_get(
3427 __isl_keep id_to_ast_expr *id2expr,
3428 __isl_take isl_id *key);
3429 int isl_id_to_ast_expr_foreach(
3430 __isl_keep id_to_ast_expr *id2expr,
3431 int (*fn)(__isl_take isl_id *key,
3432 __isl_take isl_ast_expr *val, void *user),
3435 They can be modified using the following function.
3437 #include <isl/id_to_ast_expr.h>
3438 __isl_give id_to_ast_expr *isl_id_to_ast_expr_set(
3439 __isl_take id_to_ast_expr *id2expr,
3440 __isl_take isl_id *key,
3441 __isl_take isl_ast_expr *val);
3442 __isl_give id_to_ast_expr *isl_id_to_ast_expr_drop(
3443 __isl_take id_to_ast_expr *id2expr,
3444 __isl_take isl_id *key);
3446 Associative arrays can be printed using the following function.
3448 #include <isl/id_to_ast_expr.h>
3449 __isl_give isl_printer *isl_printer_print_id_to_ast_expr(
3450 __isl_take isl_printer *p,
3451 __isl_keep id_to_ast_expr *id2expr);
3453 =head2 Multiple Values
3455 An C<isl_multi_val> object represents a sequence of zero or more values,
3456 living in a set space.
3458 An C<isl_multi_val> can be constructed from an C<isl_val_list>
3459 using the following function
3461 #include <isl/val.h>
3462 __isl_give isl_multi_val *isl_multi_val_from_val_list(
3463 __isl_take isl_space *space,
3464 __isl_take isl_val_list *list);
3466 The zero multiple value (with value zero for each set dimension)
3467 can be created using the following function.
3469 #include <isl/val.h>
3470 __isl_give isl_multi_val *isl_multi_val_zero(
3471 __isl_take isl_space *space);
3473 Multiple values can be copied and freed using
3475 #include <isl/val.h>
3476 __isl_give isl_multi_val *isl_multi_val_copy(
3477 __isl_keep isl_multi_val *mv);
3478 void *isl_multi_val_free(__isl_take isl_multi_val *mv);
3480 They can be inspected using
3482 #include <isl/val.h>
3483 isl_ctx *isl_multi_val_get_ctx(
3484 __isl_keep isl_multi_val *mv);
3485 unsigned isl_multi_val_dim(__isl_keep isl_multi_val *mv,
3486 enum isl_dim_type type);
3487 __isl_give isl_val *isl_multi_val_get_val(
3488 __isl_keep isl_multi_val *mv, int pos);
3489 int isl_multi_val_find_dim_by_id(
3490 __isl_keep isl_multi_val *mv,
3491 enum isl_dim_type type, __isl_keep isl_id *id);
3492 __isl_give isl_id *isl_multi_val_get_dim_id(
3493 __isl_keep isl_multi_val *mv,
3494 enum isl_dim_type type, unsigned pos);
3495 const char *isl_multi_val_get_tuple_name(
3496 __isl_keep isl_multi_val *mv,
3497 enum isl_dim_type type);
3498 int isl_multi_val_has_tuple_id(__isl_keep isl_multi_val *mv,
3499 enum isl_dim_type type);
3500 __isl_give isl_id *isl_multi_val_get_tuple_id(
3501 __isl_keep isl_multi_val *mv,
3502 enum isl_dim_type type);
3503 int isl_multi_val_range_is_wrapping(
3504 __isl_keep isl_multi_val *mv);
3506 They can be modified using
3508 #include <isl/val.h>
3509 __isl_give isl_multi_val *isl_multi_val_set_val(
3510 __isl_take isl_multi_val *mv, int pos,
3511 __isl_take isl_val *val);
3512 __isl_give isl_multi_val *isl_multi_val_set_dim_name(
3513 __isl_take isl_multi_val *mv,
3514 enum isl_dim_type type, unsigned pos, const char *s);
3515 __isl_give isl_multi_val *isl_multi_val_set_dim_id(
3516 __isl_take isl_multi_val *mv,
3517 enum isl_dim_type type, unsigned pos,
3518 __isl_take isl_id *id);
3519 __isl_give isl_multi_val *isl_multi_val_set_tuple_name(
3520 __isl_take isl_multi_val *mv,
3521 enum isl_dim_type type, const char *s);
3522 __isl_give isl_multi_val *isl_multi_val_set_tuple_id(
3523 __isl_take isl_multi_val *mv,
3524 enum isl_dim_type type, __isl_take isl_id *id);
3525 __isl_give isl_multi_val *isl_multi_val_reset_tuple_id(
3526 __isl_take isl_multi_val *mv,
3527 enum isl_dim_type type);
3528 __isl_give isl_multi_val *isl_multi_val_reset_user(
3529 __isl_take isl_multi_val *mv);
3531 __isl_give isl_multi_val *isl_multi_val_insert_dims(
3532 __isl_take isl_multi_val *mv,
3533 enum isl_dim_type type, unsigned first, unsigned n);
3534 __isl_give isl_multi_val *isl_multi_val_add_dims(
3535 __isl_take isl_multi_val *mv,
3536 enum isl_dim_type type, unsigned n);
3537 __isl_give isl_multi_val *isl_multi_val_drop_dims(
3538 __isl_take isl_multi_val *mv,
3539 enum isl_dim_type type, unsigned first, unsigned n);
3543 #include <isl/val.h>
3544 __isl_give isl_multi_val *isl_multi_val_align_params(
3545 __isl_take isl_multi_val *mv,
3546 __isl_take isl_space *model);
3547 __isl_give isl_multi_val *isl_multi_val_from_range(
3548 __isl_take isl_multi_val *mv);
3549 __isl_give isl_multi_val *isl_multi_val_range_splice(
3550 __isl_take isl_multi_val *mv1, unsigned pos,
3551 __isl_take isl_multi_val *mv2);
3552 __isl_give isl_multi_val *isl_multi_val_range_product(
3553 __isl_take isl_multi_val *mv1,
3554 __isl_take isl_multi_val *mv2);
3555 __isl_give isl_multi_val *
3556 isl_multi_val_range_factor_domain(
3557 __isl_take isl_multi_val *mv);
3558 __isl_give isl_multi_val *
3559 isl_multi_val_range_factor_range(
3560 __isl_take isl_multi_val *mv);
3561 __isl_give isl_multi_val *isl_multi_val_flat_range_product(
3562 __isl_take isl_multi_val *mv1,
3563 __isl_take isl_multi_aff *mv2);
3564 __isl_give isl_multi_val *isl_multi_val_product(
3565 __isl_take isl_multi_val *mv1,
3566 __isl_take isl_multi_val *mv2);
3567 __isl_give isl_multi_val *isl_multi_val_add_val(
3568 __isl_take isl_multi_val *mv,
3569 __isl_take isl_val *v);
3570 __isl_give isl_multi_val *isl_multi_val_mod_val(
3571 __isl_take isl_multi_val *mv,
3572 __isl_take isl_val *v);
3573 __isl_give isl_multi_val *isl_multi_val_scale_val(
3574 __isl_take isl_multi_val *mv,
3575 __isl_take isl_val *v);
3576 __isl_give isl_multi_val *isl_multi_val_scale_multi_val(
3577 __isl_take isl_multi_val *mv1,
3578 __isl_take isl_multi_val *mv2);
3579 __isl_give isl_multi_val *
3580 isl_multi_val_scale_down_multi_val(
3581 __isl_take isl_multi_val *mv1,
3582 __isl_take isl_multi_val *mv2);
3584 A multiple value can be printed using
3586 __isl_give isl_printer *isl_printer_print_multi_val(
3587 __isl_take isl_printer *p,
3588 __isl_keep isl_multi_val *mv);
3592 Vectors can be created, copied and freed using the following functions.
3594 #include <isl/vec.h>
3595 __isl_give isl_vec *isl_vec_alloc(isl_ctx *ctx,
3597 __isl_give isl_vec *isl_vec_copy(__isl_keep isl_vec *vec);
3598 void *isl_vec_free(__isl_take isl_vec *vec);
3600 Note that the elements of a newly created vector may have arbitrary values.
3601 The elements can be changed and inspected using the following functions.
3603 isl_ctx *isl_vec_get_ctx(__isl_keep isl_vec *vec);
3604 int isl_vec_size(__isl_keep isl_vec *vec);
3605 __isl_give isl_val *isl_vec_get_element_val(
3606 __isl_keep isl_vec *vec, int pos);
3607 __isl_give isl_vec *isl_vec_set_element_si(
3608 __isl_take isl_vec *vec, int pos, int v);
3609 __isl_give isl_vec *isl_vec_set_element_val(
3610 __isl_take isl_vec *vec, int pos,
3611 __isl_take isl_val *v);
3612 __isl_give isl_vec *isl_vec_set_si(__isl_take isl_vec *vec,
3614 __isl_give isl_vec *isl_vec_set_val(
3615 __isl_take isl_vec *vec, __isl_take isl_val *v);
3616 int isl_vec_cmp_element(__isl_keep isl_vec *vec1,
3617 __isl_keep isl_vec *vec2, int pos);
3619 C<isl_vec_get_element> will return a negative value if anything went wrong.
3620 In that case, the value of C<*v> is undefined.
3622 The following function can be used to concatenate two vectors.
3624 __isl_give isl_vec *isl_vec_concat(__isl_take isl_vec *vec1,
3625 __isl_take isl_vec *vec2);
3629 Matrices can be created, copied and freed using the following functions.
3631 #include <isl/mat.h>
3632 __isl_give isl_mat *isl_mat_alloc(isl_ctx *ctx,
3633 unsigned n_row, unsigned n_col);
3634 __isl_give isl_mat *isl_mat_copy(__isl_keep isl_mat *mat);
3635 void *isl_mat_free(__isl_take isl_mat *mat);
3637 Note that the elements of a newly created matrix may have arbitrary values.
3638 The elements can be changed and inspected using the following functions.
3640 isl_ctx *isl_mat_get_ctx(__isl_keep isl_mat *mat);
3641 int isl_mat_rows(__isl_keep isl_mat *mat);
3642 int isl_mat_cols(__isl_keep isl_mat *mat);
3643 __isl_give isl_val *isl_mat_get_element_val(
3644 __isl_keep isl_mat *mat, int row, int col);
3645 __isl_give isl_mat *isl_mat_set_element_si(__isl_take isl_mat *mat,
3646 int row, int col, int v);
3647 __isl_give isl_mat *isl_mat_set_element_val(
3648 __isl_take isl_mat *mat, int row, int col,
3649 __isl_take isl_val *v);
3651 C<isl_mat_get_element> will return a negative value if anything went wrong.
3652 In that case, the value of C<*v> is undefined.
3654 The following function can be used to compute the (right) inverse
3655 of a matrix, i.e., a matrix such that the product of the original
3656 and the inverse (in that order) is a multiple of the identity matrix.
3657 The input matrix is assumed to be of full row-rank.
3659 __isl_give isl_mat *isl_mat_right_inverse(__isl_take isl_mat *mat);
3661 The following function can be used to compute the (right) kernel
3662 (or null space) of a matrix, i.e., a matrix such that the product of
3663 the original and the kernel (in that order) is the zero matrix.
3665 __isl_give isl_mat *isl_mat_right_kernel(__isl_take isl_mat *mat);
3667 =head2 Piecewise Quasi Affine Expressions
3669 The zero quasi affine expression or the quasi affine expression
3670 that is equal to a given value or
3671 a specified dimension on a given domain can be created using
3673 __isl_give isl_aff *isl_aff_zero_on_domain(
3674 __isl_take isl_local_space *ls);
3675 __isl_give isl_pw_aff *isl_pw_aff_zero_on_domain(
3676 __isl_take isl_local_space *ls);
3677 __isl_give isl_aff *isl_aff_val_on_domain(
3678 __isl_take isl_local_space *ls,
3679 __isl_take isl_val *val);
3680 __isl_give isl_aff *isl_aff_var_on_domain(
3681 __isl_take isl_local_space *ls,
3682 enum isl_dim_type type, unsigned pos);
3683 __isl_give isl_pw_aff *isl_pw_aff_var_on_domain(
3684 __isl_take isl_local_space *ls,
3685 enum isl_dim_type type, unsigned pos);
3687 Note that the space in which the resulting objects live is a map space
3688 with the given space as domain and a one-dimensional range.
3690 An empty piecewise quasi affine expression (one with no cells)
3691 or a piecewise quasi affine expression with a single cell can
3692 be created using the following functions.
3694 #include <isl/aff.h>
3695 __isl_give isl_pw_aff *isl_pw_aff_empty(
3696 __isl_take isl_space *space);
3697 __isl_give isl_pw_aff *isl_pw_aff_alloc(
3698 __isl_take isl_set *set, __isl_take isl_aff *aff);
3699 __isl_give isl_pw_aff *isl_pw_aff_from_aff(
3700 __isl_take isl_aff *aff);
3702 A piecewise quasi affine expression that is equal to 1 on a set
3703 and 0 outside the set can be created using the following function.
3705 #include <isl/aff.h>
3706 __isl_give isl_pw_aff *isl_set_indicator_function(
3707 __isl_take isl_set *set);
3709 Quasi affine expressions can be copied and freed using
3711 #include <isl/aff.h>
3712 __isl_give isl_aff *isl_aff_copy(__isl_keep isl_aff *aff);
3713 void *isl_aff_free(__isl_take isl_aff *aff);
3715 __isl_give isl_pw_aff *isl_pw_aff_copy(
3716 __isl_keep isl_pw_aff *pwaff);
3717 void *isl_pw_aff_free(__isl_take isl_pw_aff *pwaff);
3719 A (rational) bound on a dimension can be extracted from an C<isl_constraint>
3720 using the following function. The constraint is required to have
3721 a non-zero coefficient for the specified dimension.
3723 #include <isl/constraint.h>
3724 __isl_give isl_aff *isl_constraint_get_bound(
3725 __isl_keep isl_constraint *constraint,
3726 enum isl_dim_type type, int pos);
3728 The entire affine expression of the constraint can also be extracted
3729 using the following function.
3731 #include <isl/constraint.h>
3732 __isl_give isl_aff *isl_constraint_get_aff(
3733 __isl_keep isl_constraint *constraint);
3735 Conversely, an equality constraint equating
3736 the affine expression to zero or an inequality constraint enforcing
3737 the affine expression to be non-negative, can be constructed using
3739 __isl_give isl_constraint *isl_equality_from_aff(
3740 __isl_take isl_aff *aff);
3741 __isl_give isl_constraint *isl_inequality_from_aff(
3742 __isl_take isl_aff *aff);
3744 The expression can be inspected using
3746 #include <isl/aff.h>
3747 isl_ctx *isl_aff_get_ctx(__isl_keep isl_aff *aff);
3748 int isl_aff_dim(__isl_keep isl_aff *aff,
3749 enum isl_dim_type type);
3750 __isl_give isl_local_space *isl_aff_get_domain_local_space(
3751 __isl_keep isl_aff *aff);
3752 __isl_give isl_local_space *isl_aff_get_local_space(
3753 __isl_keep isl_aff *aff);
3754 const char *isl_aff_get_dim_name(__isl_keep isl_aff *aff,
3755 enum isl_dim_type type, unsigned pos);
3756 const char *isl_pw_aff_get_dim_name(
3757 __isl_keep isl_pw_aff *pa,
3758 enum isl_dim_type type, unsigned pos);
3759 int isl_pw_aff_has_dim_id(__isl_keep isl_pw_aff *pa,
3760 enum isl_dim_type type, unsigned pos);
3761 __isl_give isl_id *isl_pw_aff_get_dim_id(
3762 __isl_keep isl_pw_aff *pa,
3763 enum isl_dim_type type, unsigned pos);
3764 int isl_pw_aff_has_tuple_id(__isl_keep isl_pw_aff *pa,
3765 enum isl_dim_type type);
3766 __isl_give isl_id *isl_pw_aff_get_tuple_id(
3767 __isl_keep isl_pw_aff *pa,
3768 enum isl_dim_type type);
3769 __isl_give isl_val *isl_aff_get_constant_val(
3770 __isl_keep isl_aff *aff);
3771 __isl_give isl_val *isl_aff_get_coefficient_val(
3772 __isl_keep isl_aff *aff,
3773 enum isl_dim_type type, int pos);
3774 __isl_give isl_val *isl_aff_get_denominator_val(
3775 __isl_keep isl_aff *aff);
3776 __isl_give isl_aff *isl_aff_get_div(
3777 __isl_keep isl_aff *aff, int pos);
3779 int isl_pw_aff_n_piece(__isl_keep isl_pw_aff *pwaff);
3780 int isl_pw_aff_foreach_piece(__isl_keep isl_pw_aff *pwaff,
3781 int (*fn)(__isl_take isl_set *set,
3782 __isl_take isl_aff *aff,
3783 void *user), void *user);
3785 int isl_aff_is_cst(__isl_keep isl_aff *aff);
3786 int isl_pw_aff_is_cst(__isl_keep isl_pw_aff *pwaff);
3788 int isl_aff_involves_dims(__isl_keep isl_aff *aff,
3789 enum isl_dim_type type, unsigned first, unsigned n);
3790 int isl_pw_aff_involves_dims(__isl_keep isl_pw_aff *pwaff,
3791 enum isl_dim_type type, unsigned first, unsigned n);
3793 isl_ctx *isl_pw_aff_get_ctx(__isl_keep isl_pw_aff *pwaff);
3794 unsigned isl_pw_aff_dim(__isl_keep isl_pw_aff *pwaff,
3795 enum isl_dim_type type);
3796 int isl_pw_aff_is_empty(__isl_keep isl_pw_aff *pwaff);
3798 It can be modified using
3800 #include <isl/aff.h>
3801 __isl_give isl_aff *isl_aff_set_tuple_id(
3802 __isl_take isl_aff *aff,
3803 enum isl_dim_type type, __isl_take isl_id *id);
3804 __isl_give isl_pw_aff *isl_pw_aff_set_tuple_id(
3805 __isl_take isl_pw_aff *pwaff,
3806 enum isl_dim_type type, __isl_take isl_id *id);
3807 __isl_give isl_aff *isl_aff_set_dim_name(
3808 __isl_take isl_aff *aff, enum isl_dim_type type,
3809 unsigned pos, const char *s);
3810 __isl_give isl_aff *isl_aff_set_dim_id(
3811 __isl_take isl_aff *aff, enum isl_dim_type type,
3812 unsigned pos, __isl_take isl_id *id);
3813 __isl_give isl_pw_aff *isl_pw_aff_set_dim_id(
3814 __isl_take isl_pw_aff *pma,
3815 enum isl_dim_type type, unsigned pos,
3816 __isl_take isl_id *id);
3817 __isl_give isl_aff *isl_aff_set_constant_si(
3818 __isl_take isl_aff *aff, int v);
3819 __isl_give isl_aff *isl_aff_set_constant_val(
3820 __isl_take isl_aff *aff, __isl_take isl_val *v);
3821 __isl_give isl_aff *isl_aff_set_coefficient_si(
3822 __isl_take isl_aff *aff,
3823 enum isl_dim_type type, int pos, int v);
3824 __isl_give isl_aff *isl_aff_set_coefficient_val(
3825 __isl_take isl_aff *aff,
3826 enum isl_dim_type type, int pos,
3827 __isl_take isl_val *v);
3829 __isl_give isl_aff *isl_aff_add_constant_si(
3830 __isl_take isl_aff *aff, int v);
3831 __isl_give isl_aff *isl_aff_add_constant_val(
3832 __isl_take isl_aff *aff, __isl_take isl_val *v);
3833 __isl_give isl_aff *isl_aff_add_constant_num_si(
3834 __isl_take isl_aff *aff, int v);
3835 __isl_give isl_aff *isl_aff_add_coefficient_si(
3836 __isl_take isl_aff *aff,
3837 enum isl_dim_type type, int pos, int v);
3838 __isl_give isl_aff *isl_aff_add_coefficient_val(
3839 __isl_take isl_aff *aff,
3840 enum isl_dim_type type, int pos,
3841 __isl_take isl_val *v);
3843 __isl_give isl_aff *isl_aff_insert_dims(
3844 __isl_take isl_aff *aff,
3845 enum isl_dim_type type, unsigned first, unsigned n);
3846 __isl_give isl_pw_aff *isl_pw_aff_insert_dims(
3847 __isl_take isl_pw_aff *pwaff,
3848 enum isl_dim_type type, unsigned first, unsigned n);
3849 __isl_give isl_aff *isl_aff_add_dims(
3850 __isl_take isl_aff *aff,
3851 enum isl_dim_type type, unsigned n);
3852 __isl_give isl_pw_aff *isl_pw_aff_add_dims(
3853 __isl_take isl_pw_aff *pwaff,
3854 enum isl_dim_type type, unsigned n);
3855 __isl_give isl_aff *isl_aff_drop_dims(
3856 __isl_take isl_aff *aff,
3857 enum isl_dim_type type, unsigned first, unsigned n);
3858 __isl_give isl_pw_aff *isl_pw_aff_drop_dims(
3859 __isl_take isl_pw_aff *pwaff,
3860 enum isl_dim_type type, unsigned first, unsigned n);
3861 __isl_give isl_aff *isl_aff_move_dims(
3862 __isl_take isl_aff *aff,
3863 enum isl_dim_type dst_type, unsigned dst_pos,
3864 enum isl_dim_type src_type, unsigned src_pos,
3866 __isl_give isl_pw_aff *isl_pw_aff_move_dims(
3867 __isl_take isl_pw_aff *pa,
3868 enum isl_dim_type dst_type, unsigned dst_pos,
3869 enum isl_dim_type src_type, unsigned src_pos,
3872 Note that C<isl_aff_set_constant_si> and C<isl_aff_set_coefficient_si>
3873 set the I<numerator> of the constant or coefficient, while
3874 C<isl_aff_set_constant_val> and C<isl_aff_set_coefficient_val> set
3875 the constant or coefficient as a whole.
3876 The C<add_constant> and C<add_coefficient> functions add an integer
3877 or rational value to
3878 the possibly rational constant or coefficient.
3879 The C<add_constant_num> functions add an integer value to
3882 To check whether an affine expressions is obviously zero
3883 or (obviously) equal to some other affine expression, use
3885 #include <isl/aff.h>
3886 int isl_aff_plain_is_zero(__isl_keep isl_aff *aff);
3887 int isl_aff_plain_is_equal(__isl_keep isl_aff *aff1,
3888 __isl_keep isl_aff *aff2);
3889 int isl_pw_aff_plain_is_equal(
3890 __isl_keep isl_pw_aff *pwaff1,
3891 __isl_keep isl_pw_aff *pwaff2);
3892 int isl_pw_aff_is_equal(__isl_keep isl_pw_aff *pa1,
3893 __isl_keep isl_pw_aff *pa2);
3897 #include <isl/aff.h>
3898 __isl_give isl_aff *isl_aff_add(__isl_take isl_aff *aff1,
3899 __isl_take isl_aff *aff2);
3900 __isl_give isl_pw_aff *isl_pw_aff_add(
3901 __isl_take isl_pw_aff *pwaff1,
3902 __isl_take isl_pw_aff *pwaff2);
3903 __isl_give isl_pw_aff *isl_pw_aff_min(
3904 __isl_take isl_pw_aff *pwaff1,
3905 __isl_take isl_pw_aff *pwaff2);
3906 __isl_give isl_pw_aff *isl_pw_aff_max(
3907 __isl_take isl_pw_aff *pwaff1,
3908 __isl_take isl_pw_aff *pwaff2);
3909 __isl_give isl_aff *isl_aff_sub(__isl_take isl_aff *aff1,
3910 __isl_take isl_aff *aff2);
3911 __isl_give isl_pw_aff *isl_pw_aff_sub(
3912 __isl_take isl_pw_aff *pwaff1,
3913 __isl_take isl_pw_aff *pwaff2);
3914 __isl_give isl_aff *isl_aff_neg(__isl_take isl_aff *aff);
3915 __isl_give isl_pw_aff *isl_pw_aff_neg(
3916 __isl_take isl_pw_aff *pwaff);
3917 __isl_give isl_aff *isl_aff_ceil(__isl_take isl_aff *aff);
3918 __isl_give isl_pw_aff *isl_pw_aff_ceil(
3919 __isl_take isl_pw_aff *pwaff);
3920 __isl_give isl_aff *isl_aff_floor(__isl_take isl_aff *aff);
3921 __isl_give isl_pw_aff *isl_pw_aff_floor(
3922 __isl_take isl_pw_aff *pwaff);
3923 __isl_give isl_aff *isl_aff_mod_val(__isl_take isl_aff *aff,
3924 __isl_take isl_val *mod);
3925 __isl_give isl_pw_aff *isl_pw_aff_mod_val(
3926 __isl_take isl_pw_aff *pa,
3927 __isl_take isl_val *mod);
3928 __isl_give isl_aff *isl_aff_scale_val(__isl_take isl_aff *aff,
3929 __isl_take isl_val *v);
3930 __isl_give isl_pw_aff *isl_pw_aff_scale_val(
3931 __isl_take isl_pw_aff *pa, __isl_take isl_val *v);
3932 __isl_give isl_aff *isl_aff_scale_down_ui(
3933 __isl_take isl_aff *aff, unsigned f);
3934 __isl_give isl_aff *isl_aff_scale_down_val(
3935 __isl_take isl_aff *aff, __isl_take isl_val *v);
3936 __isl_give isl_pw_aff *isl_pw_aff_scale_down_val(
3937 __isl_take isl_pw_aff *pa,
3938 __isl_take isl_val *f);
3940 __isl_give isl_pw_aff *isl_pw_aff_list_min(
3941 __isl_take isl_pw_aff_list *list);
3942 __isl_give isl_pw_aff *isl_pw_aff_list_max(
3943 __isl_take isl_pw_aff_list *list);
3945 __isl_give isl_pw_aff *isl_pw_aff_coalesce(
3946 __isl_take isl_pw_aff *pwqp);
3948 __isl_give isl_aff *isl_aff_align_params(
3949 __isl_take isl_aff *aff,
3950 __isl_take isl_space *model);
3951 __isl_give isl_pw_aff *isl_pw_aff_align_params(
3952 __isl_take isl_pw_aff *pwaff,
3953 __isl_take isl_space *model);
3955 __isl_give isl_aff *isl_aff_project_domain_on_params(
3956 __isl_take isl_aff *aff);
3957 __isl_give isl_pw_aff *isl_pw_aff_from_range(
3958 __isl_take isl_pw_aff *pwa);
3960 __isl_give isl_aff *isl_aff_gist_params(
3961 __isl_take isl_aff *aff,
3962 __isl_take isl_set *context);
3963 __isl_give isl_aff *isl_aff_gist(__isl_take isl_aff *aff,
3964 __isl_take isl_set *context);
3965 __isl_give isl_pw_aff *isl_pw_aff_gist_params(
3966 __isl_take isl_pw_aff *pwaff,
3967 __isl_take isl_set *context);
3968 __isl_give isl_pw_aff *isl_pw_aff_gist(
3969 __isl_take isl_pw_aff *pwaff,
3970 __isl_take isl_set *context);
3972 __isl_give isl_set *isl_pw_aff_domain(
3973 __isl_take isl_pw_aff *pwaff);
3974 __isl_give isl_set *isl_pw_aff_params(
3975 __isl_take isl_pw_aff *pwa);
3976 __isl_give isl_pw_aff *isl_pw_aff_intersect_domain(
3977 __isl_take isl_pw_aff *pa,
3978 __isl_take isl_set *set);
3979 __isl_give isl_pw_aff *isl_pw_aff_intersect_params(
3980 __isl_take isl_pw_aff *pa,
3981 __isl_take isl_set *set);
3983 __isl_give isl_aff *isl_aff_mul(__isl_take isl_aff *aff1,
3984 __isl_take isl_aff *aff2);
3985 __isl_give isl_aff *isl_aff_div(__isl_take isl_aff *aff1,
3986 __isl_take isl_aff *aff2);
3987 __isl_give isl_pw_aff *isl_pw_aff_mul(
3988 __isl_take isl_pw_aff *pwaff1,
3989 __isl_take isl_pw_aff *pwaff2);
3990 __isl_give isl_pw_aff *isl_pw_aff_div(
3991 __isl_take isl_pw_aff *pa1,
3992 __isl_take isl_pw_aff *pa2);
3993 __isl_give isl_pw_aff *isl_pw_aff_tdiv_q(
3994 __isl_take isl_pw_aff *pa1,
3995 __isl_take isl_pw_aff *pa2);
3996 __isl_give isl_pw_aff *isl_pw_aff_tdiv_r(
3997 __isl_take isl_pw_aff *pa1,
3998 __isl_take isl_pw_aff *pa2);
4000 When multiplying two affine expressions, at least one of the two needs
4001 to be a constant. Similarly, when dividing an affine expression by another,
4002 the second expression needs to be a constant.
4003 C<isl_pw_aff_tdiv_q> computes the quotient of an integer division with
4004 rounding towards zero. C<isl_pw_aff_tdiv_r> computes the corresponding
4007 #include <isl/aff.h>
4008 __isl_give isl_aff *isl_aff_pullback_aff(
4009 __isl_take isl_aff *aff1,
4010 __isl_take isl_aff *aff2);
4011 __isl_give isl_aff *isl_aff_pullback_multi_aff(
4012 __isl_take isl_aff *aff,
4013 __isl_take isl_multi_aff *ma);
4014 __isl_give isl_pw_aff *isl_pw_aff_pullback_multi_aff(
4015 __isl_take isl_pw_aff *pa,
4016 __isl_take isl_multi_aff *ma);
4017 __isl_give isl_pw_aff *isl_pw_aff_pullback_pw_multi_aff(
4018 __isl_take isl_pw_aff *pa,
4019 __isl_take isl_pw_multi_aff *pma);
4021 These functions precompose the input expression by the given
4022 C<isl_aff>, C<isl_multi_aff> or C<isl_pw_multi_aff>. In other words,
4023 the C<isl_aff>, C<isl_multi_aff> or C<isl_pw_multi_aff> is plugged
4024 into the (piecewise) affine expression.
4025 Objects of type C<isl_multi_aff> are described in
4026 L</"Piecewise Multiple Quasi Affine Expressions">.
4028 #include <isl/aff.h>
4029 __isl_give isl_basic_set *isl_aff_zero_basic_set(
4030 __isl_take isl_aff *aff);
4031 __isl_give isl_basic_set *isl_aff_neg_basic_set(
4032 __isl_take isl_aff *aff);
4033 __isl_give isl_basic_set *isl_aff_le_basic_set(
4034 __isl_take isl_aff *aff1, __isl_take isl_aff *aff2);
4035 __isl_give isl_basic_set *isl_aff_ge_basic_set(
4036 __isl_take isl_aff *aff1, __isl_take isl_aff *aff2);
4037 __isl_give isl_set *isl_pw_aff_eq_set(
4038 __isl_take isl_pw_aff *pwaff1,
4039 __isl_take isl_pw_aff *pwaff2);
4040 __isl_give isl_set *isl_pw_aff_ne_set(
4041 __isl_take isl_pw_aff *pwaff1,
4042 __isl_take isl_pw_aff *pwaff2);
4043 __isl_give isl_set *isl_pw_aff_le_set(
4044 __isl_take isl_pw_aff *pwaff1,
4045 __isl_take isl_pw_aff *pwaff2);
4046 __isl_give isl_set *isl_pw_aff_lt_set(
4047 __isl_take isl_pw_aff *pwaff1,
4048 __isl_take isl_pw_aff *pwaff2);
4049 __isl_give isl_set *isl_pw_aff_ge_set(
4050 __isl_take isl_pw_aff *pwaff1,
4051 __isl_take isl_pw_aff *pwaff2);
4052 __isl_give isl_set *isl_pw_aff_gt_set(
4053 __isl_take isl_pw_aff *pwaff1,
4054 __isl_take isl_pw_aff *pwaff2);
4056 __isl_give isl_set *isl_pw_aff_list_eq_set(
4057 __isl_take isl_pw_aff_list *list1,
4058 __isl_take isl_pw_aff_list *list2);
4059 __isl_give isl_set *isl_pw_aff_list_ne_set(
4060 __isl_take isl_pw_aff_list *list1,
4061 __isl_take isl_pw_aff_list *list2);
4062 __isl_give isl_set *isl_pw_aff_list_le_set(
4063 __isl_take isl_pw_aff_list *list1,
4064 __isl_take isl_pw_aff_list *list2);
4065 __isl_give isl_set *isl_pw_aff_list_lt_set(
4066 __isl_take isl_pw_aff_list *list1,
4067 __isl_take isl_pw_aff_list *list2);
4068 __isl_give isl_set *isl_pw_aff_list_ge_set(
4069 __isl_take isl_pw_aff_list *list1,
4070 __isl_take isl_pw_aff_list *list2);
4071 __isl_give isl_set *isl_pw_aff_list_gt_set(
4072 __isl_take isl_pw_aff_list *list1,
4073 __isl_take isl_pw_aff_list *list2);
4075 The function C<isl_aff_neg_basic_set> returns a basic set
4076 containing those elements in the domain space
4077 of C<aff> where C<aff> is negative.
4078 The function C<isl_aff_ge_basic_set> returns a basic set
4079 containing those elements in the shared space
4080 of C<aff1> and C<aff2> where C<aff1> is greater than or equal to C<aff2>.
4081 The function C<isl_pw_aff_ge_set> returns a set
4082 containing those elements in the shared domain
4083 of C<pwaff1> and C<pwaff2> where C<pwaff1> is greater than or equal to C<pwaff2>.
4084 The functions operating on C<isl_pw_aff_list> apply the corresponding
4085 C<isl_pw_aff> function to each pair of elements in the two lists.
4087 #include <isl/aff.h>
4088 __isl_give isl_set *isl_pw_aff_nonneg_set(
4089 __isl_take isl_pw_aff *pwaff);
4090 __isl_give isl_set *isl_pw_aff_zero_set(
4091 __isl_take isl_pw_aff *pwaff);
4092 __isl_give isl_set *isl_pw_aff_non_zero_set(
4093 __isl_take isl_pw_aff *pwaff);
4095 The function C<isl_pw_aff_nonneg_set> returns a set
4096 containing those elements in the domain
4097 of C<pwaff> where C<pwaff> is non-negative.
4099 #include <isl/aff.h>
4100 __isl_give isl_pw_aff *isl_pw_aff_cond(
4101 __isl_take isl_pw_aff *cond,
4102 __isl_take isl_pw_aff *pwaff_true,
4103 __isl_take isl_pw_aff *pwaff_false);
4105 The function C<isl_pw_aff_cond> performs a conditional operator
4106 and returns an expression that is equal to C<pwaff_true>
4107 for elements where C<cond> is non-zero and equal to C<pwaff_false> for elements
4108 where C<cond> is zero.
4110 #include <isl/aff.h>
4111 __isl_give isl_pw_aff *isl_pw_aff_union_min(
4112 __isl_take isl_pw_aff *pwaff1,
4113 __isl_take isl_pw_aff *pwaff2);
4114 __isl_give isl_pw_aff *isl_pw_aff_union_max(
4115 __isl_take isl_pw_aff *pwaff1,
4116 __isl_take isl_pw_aff *pwaff2);
4117 __isl_give isl_pw_aff *isl_pw_aff_union_add(
4118 __isl_take isl_pw_aff *pwaff1,
4119 __isl_take isl_pw_aff *pwaff2);
4121 The function C<isl_pw_aff_union_max> computes a piecewise quasi-affine
4122 expression with a domain that is the union of those of C<pwaff1> and
4123 C<pwaff2> and such that on each cell, the quasi-affine expression is
4124 the maximum of those of C<pwaff1> and C<pwaff2>. If only one of
4125 C<pwaff1> or C<pwaff2> is defined on a given cell, then the
4126 associated expression is the defined one.
4128 An expression can be read from input using
4130 #include <isl/aff.h>
4131 __isl_give isl_aff *isl_aff_read_from_str(
4132 isl_ctx *ctx, const char *str);
4133 __isl_give isl_pw_aff *isl_pw_aff_read_from_str(
4134 isl_ctx *ctx, const char *str);
4136 An expression can be printed using
4138 #include <isl/aff.h>
4139 __isl_give isl_printer *isl_printer_print_aff(
4140 __isl_take isl_printer *p, __isl_keep isl_aff *aff);
4142 __isl_give isl_printer *isl_printer_print_pw_aff(
4143 __isl_take isl_printer *p,
4144 __isl_keep isl_pw_aff *pwaff);
4146 =head2 Piecewise Multiple Quasi Affine Expressions
4148 An C<isl_multi_aff> object represents a sequence of
4149 zero or more affine expressions, all defined on the same domain space.
4150 Similarly, an C<isl_multi_pw_aff> object represents a sequence of
4151 zero or more piecewise affine expressions.
4153 An C<isl_multi_aff> can be constructed from a single
4154 C<isl_aff> or an C<isl_aff_list> using the
4155 following functions. Similarly for C<isl_multi_pw_aff>
4156 and C<isl_pw_multi_aff>.
4158 #include <isl/aff.h>
4159 __isl_give isl_multi_aff *isl_multi_aff_from_aff(
4160 __isl_take isl_aff *aff);
4161 __isl_give isl_multi_pw_aff *
4162 isl_multi_pw_aff_from_multi_aff(
4163 __isl_take isl_multi_aff *ma);
4164 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_from_pw_aff(
4165 __isl_take isl_pw_aff *pa);
4166 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_from_pw_aff(
4167 __isl_take isl_pw_aff *pa);
4168 __isl_give isl_multi_aff *isl_multi_aff_from_aff_list(
4169 __isl_take isl_space *space,
4170 __isl_take isl_aff_list *list);
4172 An C<isl_multi_pw_aff> can be converted to an C<isl_pw_multi_aff>
4173 using the function C<isl_pw_multi_aff_from_multi_pw_aff> below.
4174 Note however that the domain
4175 of the result is the intersection of the domains of the input.
4176 The reverse conversion is exact.
4178 #include <isl/aff.h>
4179 __isl_give isl_pw_multi_aff *
4180 isl_pw_multi_aff_from_multi_pw_aff(
4181 __isl_take isl_multi_pw_aff *mpa);
4182 __isl_give isl_multi_pw_aff *
4183 isl_multi_pw_aff_from_pw_multi_aff(
4184 __isl_take isl_pw_multi_aff *pma);
4186 An empty piecewise multiple quasi affine expression (one with no cells),
4187 the zero piecewise multiple quasi affine expression (with value zero
4188 for each output dimension),
4189 a piecewise multiple quasi affine expression with a single cell (with
4190 either a universe or a specified domain) or
4191 a zero-dimensional piecewise multiple quasi affine expression
4193 can be created using the following functions.
4195 #include <isl/aff.h>
4196 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_empty(
4197 __isl_take isl_space *space);
4198 __isl_give isl_multi_aff *isl_multi_aff_zero(
4199 __isl_take isl_space *space);
4200 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_zero(
4201 __isl_take isl_space *space);
4202 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_zero(
4203 __isl_take isl_space *space);
4204 __isl_give isl_multi_aff *isl_multi_aff_identity(
4205 __isl_take isl_space *space);
4206 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_identity(
4207 __isl_take isl_space *space);
4208 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_identity(
4209 __isl_take isl_space *space);
4210 __isl_give isl_multi_aff *isl_multi_aff_domain_map(
4211 __isl_take isl_space *space);
4212 __isl_give isl_multi_aff *isl_multi_aff_range_map(
4213 __isl_take isl_space *space);
4214 __isl_give isl_multi_aff *isl_multi_aff_project_out_map(
4215 __isl_take isl_space *space,
4216 enum isl_dim_type type,
4217 unsigned first, unsigned n);
4218 __isl_give isl_pw_multi_aff *
4219 isl_pw_multi_aff_project_out_map(
4220 __isl_take isl_space *space,
4221 enum isl_dim_type type,
4222 unsigned first, unsigned n);
4223 __isl_give isl_pw_multi_aff *
4224 isl_pw_multi_aff_from_multi_aff(
4225 __isl_take isl_multi_aff *ma);
4226 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_alloc(
4227 __isl_take isl_set *set,
4228 __isl_take isl_multi_aff *maff);
4229 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_from_domain(
4230 __isl_take isl_set *set);
4232 __isl_give isl_union_pw_multi_aff *
4233 isl_union_pw_multi_aff_empty(
4234 __isl_take isl_space *space);
4235 __isl_give isl_union_pw_multi_aff *
4236 isl_union_pw_multi_aff_add_pw_multi_aff(
4237 __isl_take isl_union_pw_multi_aff *upma,
4238 __isl_take isl_pw_multi_aff *pma);
4239 __isl_give isl_union_pw_multi_aff *
4240 isl_union_pw_multi_aff_from_domain(
4241 __isl_take isl_union_set *uset);
4243 A piecewise multiple quasi affine expression can also be initialized
4244 from an C<isl_set> or C<isl_map>, provided the C<isl_set> is a singleton
4245 and the C<isl_map> is single-valued.
4246 In case of a conversion from an C<isl_union_set> or an C<isl_union_map>
4247 to an C<isl_union_pw_multi_aff>, these properties need to hold in each space.
4249 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_from_set(
4250 __isl_take isl_set *set);
4251 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_from_map(
4252 __isl_take isl_map *map);
4254 __isl_give isl_union_pw_multi_aff *
4255 isl_union_pw_multi_aff_from_union_set(
4256 __isl_take isl_union_set *uset);
4257 __isl_give isl_union_pw_multi_aff *
4258 isl_union_pw_multi_aff_from_union_map(
4259 __isl_take isl_union_map *umap);
4261 Multiple quasi affine expressions can be copied and freed using
4263 #include <isl/aff.h>
4264 __isl_give isl_multi_aff *isl_multi_aff_copy(
4265 __isl_keep isl_multi_aff *maff);
4266 void *isl_multi_aff_free(__isl_take isl_multi_aff *maff);
4268 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_copy(
4269 __isl_keep isl_pw_multi_aff *pma);
4270 void *isl_pw_multi_aff_free(
4271 __isl_take isl_pw_multi_aff *pma);
4273 __isl_give isl_union_pw_multi_aff *
4274 isl_union_pw_multi_aff_copy(
4275 __isl_keep isl_union_pw_multi_aff *upma);
4276 void *isl_union_pw_multi_aff_free(
4277 __isl_take isl_union_pw_multi_aff *upma);
4279 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_copy(
4280 __isl_keep isl_multi_pw_aff *mpa);
4281 void *isl_multi_pw_aff_free(
4282 __isl_take isl_multi_pw_aff *mpa);
4284 The expression can be inspected using
4286 #include <isl/aff.h>
4287 isl_ctx *isl_multi_aff_get_ctx(
4288 __isl_keep isl_multi_aff *maff);
4289 isl_ctx *isl_pw_multi_aff_get_ctx(
4290 __isl_keep isl_pw_multi_aff *pma);
4291 isl_ctx *isl_union_pw_multi_aff_get_ctx(
4292 __isl_keep isl_union_pw_multi_aff *upma);
4293 isl_ctx *isl_multi_pw_aff_get_ctx(
4294 __isl_keep isl_multi_pw_aff *mpa);
4295 unsigned isl_multi_aff_dim(__isl_keep isl_multi_aff *maff,
4296 enum isl_dim_type type);
4297 unsigned isl_pw_multi_aff_dim(
4298 __isl_keep isl_pw_multi_aff *pma,
4299 enum isl_dim_type type);
4300 unsigned isl_multi_pw_aff_dim(
4301 __isl_keep isl_multi_pw_aff *mpa,
4302 enum isl_dim_type type);
4303 __isl_give isl_aff *isl_multi_aff_get_aff(
4304 __isl_keep isl_multi_aff *multi, int pos);
4305 __isl_give isl_pw_aff *isl_pw_multi_aff_get_pw_aff(
4306 __isl_keep isl_pw_multi_aff *pma, int pos);
4307 __isl_give isl_pw_aff *isl_multi_pw_aff_get_pw_aff(
4308 __isl_keep isl_multi_pw_aff *mpa, int pos);
4309 int isl_multi_aff_find_dim_by_id(
4310 __isl_keep isl_multi_aff *ma,
4311 enum isl_dim_type type, __isl_keep isl_id *id);
4312 int isl_multi_pw_aff_find_dim_by_id(
4313 __isl_keep isl_multi_pw_aff *mpa,
4314 enum isl_dim_type type, __isl_keep isl_id *id);
4315 const char *isl_pw_multi_aff_get_dim_name(
4316 __isl_keep isl_pw_multi_aff *pma,
4317 enum isl_dim_type type, unsigned pos);
4318 __isl_give isl_id *isl_multi_aff_get_dim_id(
4319 __isl_keep isl_multi_aff *ma,
4320 enum isl_dim_type type, unsigned pos);
4321 __isl_give isl_id *isl_pw_multi_aff_get_dim_id(
4322 __isl_keep isl_pw_multi_aff *pma,
4323 enum isl_dim_type type, unsigned pos);
4324 __isl_give isl_id *isl_multi_pw_aff_get_dim_id(
4325 __isl_keep isl_multi_pw_aff *mpa,
4326 enum isl_dim_type type, unsigned pos);
4327 const char *isl_multi_aff_get_tuple_name(
4328 __isl_keep isl_multi_aff *multi,
4329 enum isl_dim_type type);
4330 int isl_pw_multi_aff_has_tuple_name(
4331 __isl_keep isl_pw_multi_aff *pma,
4332 enum isl_dim_type type);
4333 const char *isl_pw_multi_aff_get_tuple_name(
4334 __isl_keep isl_pw_multi_aff *pma,
4335 enum isl_dim_type type);
4336 int isl_multi_aff_has_tuple_id(__isl_keep isl_multi_aff *ma,
4337 enum isl_dim_type type);
4338 int isl_pw_multi_aff_has_tuple_id(
4339 __isl_keep isl_pw_multi_aff *pma,
4340 enum isl_dim_type type);
4341 int isl_multi_pw_aff_has_tuple_id(
4342 __isl_keep isl_multi_pw_aff *mpa,
4343 enum isl_dim_type type);
4344 __isl_give isl_id *isl_multi_aff_get_tuple_id(
4345 __isl_keep isl_multi_aff *ma,
4346 enum isl_dim_type type);
4347 __isl_give isl_id *isl_pw_multi_aff_get_tuple_id(
4348 __isl_keep isl_pw_multi_aff *pma,
4349 enum isl_dim_type type);
4350 __isl_give isl_id *isl_multi_pw_aff_get_tuple_id(
4351 __isl_keep isl_multi_pw_aff *mpa,
4352 enum isl_dim_type type);
4353 int isl_multi_aff_range_is_wrapping(
4354 __isl_keep isl_multi_aff *ma);
4355 int isl_multi_pw_aff_range_is_wrapping(
4356 __isl_keep isl_multi_pw_aff *mpa);
4358 int isl_pw_multi_aff_foreach_piece(
4359 __isl_keep isl_pw_multi_aff *pma,
4360 int (*fn)(__isl_take isl_set *set,
4361 __isl_take isl_multi_aff *maff,
4362 void *user), void *user);
4364 int isl_union_pw_multi_aff_foreach_pw_multi_aff(
4365 __isl_keep isl_union_pw_multi_aff *upma,
4366 int (*fn)(__isl_take isl_pw_multi_aff *pma,
4367 void *user), void *user);
4369 It can be modified using
4371 #include <isl/aff.h>
4372 __isl_give isl_multi_aff *isl_multi_aff_set_aff(
4373 __isl_take isl_multi_aff *multi, int pos,
4374 __isl_take isl_aff *aff);
4375 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_set_pw_aff(
4376 __isl_take isl_pw_multi_aff *pma, unsigned pos,
4377 __isl_take isl_pw_aff *pa);
4378 __isl_give isl_multi_aff *isl_multi_aff_set_dim_name(
4379 __isl_take isl_multi_aff *maff,
4380 enum isl_dim_type type, unsigned pos, const char *s);
4381 __isl_give isl_multi_aff *isl_multi_aff_set_dim_id(
4382 __isl_take isl_multi_aff *maff,
4383 enum isl_dim_type type, unsigned pos,
4384 __isl_take isl_id *id);
4385 __isl_give isl_multi_aff *isl_multi_aff_set_tuple_name(
4386 __isl_take isl_multi_aff *maff,
4387 enum isl_dim_type type, const char *s);
4388 __isl_give isl_multi_aff *isl_multi_aff_set_tuple_id(
4389 __isl_take isl_multi_aff *maff,
4390 enum isl_dim_type type, __isl_take isl_id *id);
4391 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_set_tuple_id(
4392 __isl_take isl_pw_multi_aff *pma,
4393 enum isl_dim_type type, __isl_take isl_id *id);
4394 __isl_give isl_multi_aff *isl_multi_aff_reset_tuple_id(
4395 __isl_take isl_multi_aff *ma,
4396 enum isl_dim_type type);
4397 __isl_give isl_multi_pw_aff *
4398 isl_multi_pw_aff_reset_tuple_id(
4399 __isl_take isl_multi_pw_aff *mpa,
4400 enum isl_dim_type type);
4401 __isl_give isl_multi_aff *isl_multi_aff_reset_user(
4402 __isl_take isl_multi_aff *ma);
4403 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_reset_user(
4404 __isl_take isl_multi_pw_aff *mpa);
4406 __isl_give isl_multi_pw_aff *
4407 isl_multi_pw_aff_set_dim_name(
4408 __isl_take isl_multi_pw_aff *mpa,
4409 enum isl_dim_type type, unsigned pos, const char *s);
4410 __isl_give isl_multi_pw_aff *
4411 isl_multi_pw_aff_set_dim_id(
4412 __isl_take isl_multi_pw_aff *mpa,
4413 enum isl_dim_type type, unsigned pos,
4414 __isl_take isl_id *id);
4415 __isl_give isl_multi_pw_aff *
4416 isl_multi_pw_aff_set_tuple_name(
4417 __isl_take isl_multi_pw_aff *mpa,
4418 enum isl_dim_type type, const char *s);
4420 __isl_give isl_multi_aff *isl_multi_aff_insert_dims(
4421 __isl_take isl_multi_aff *ma,
4422 enum isl_dim_type type, unsigned first, unsigned n);
4423 __isl_give isl_multi_aff *isl_multi_aff_add_dims(
4424 __isl_take isl_multi_aff *ma,
4425 enum isl_dim_type type, unsigned n);
4426 __isl_give isl_multi_aff *isl_multi_aff_drop_dims(
4427 __isl_take isl_multi_aff *maff,
4428 enum isl_dim_type type, unsigned first, unsigned n);
4429 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_drop_dims(
4430 __isl_take isl_pw_multi_aff *pma,
4431 enum isl_dim_type type, unsigned first, unsigned n);
4433 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_insert_dims(
4434 __isl_take isl_multi_pw_aff *mpa,
4435 enum isl_dim_type type, unsigned first, unsigned n);
4436 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_add_dims(
4437 __isl_take isl_multi_pw_aff *mpa,
4438 enum isl_dim_type type, unsigned n);
4439 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_move_dims(
4440 __isl_take isl_multi_pw_aff *pma,
4441 enum isl_dim_type dst_type, unsigned dst_pos,
4442 enum isl_dim_type src_type, unsigned src_pos,
4445 To check whether two multiple affine expressions are
4446 (obviously) equal to each other, use
4448 int isl_multi_aff_plain_is_equal(__isl_keep isl_multi_aff *maff1,
4449 __isl_keep isl_multi_aff *maff2);
4450 int isl_pw_multi_aff_plain_is_equal(
4451 __isl_keep isl_pw_multi_aff *pma1,
4452 __isl_keep isl_pw_multi_aff *pma2);
4453 int isl_multi_pw_aff_plain_is_equal(
4454 __isl_keep isl_multi_pw_aff *mpa1,
4455 __isl_keep isl_multi_pw_aff *mpa2);
4456 int isl_multi_pw_aff_is_equal(
4457 __isl_keep isl_multi_pw_aff *mpa1,
4458 __isl_keep isl_multi_pw_aff *mpa2);
4462 #include <isl/aff.h>
4463 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_union_lexmin(
4464 __isl_take isl_pw_multi_aff *pma1,
4465 __isl_take isl_pw_multi_aff *pma2);
4466 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_union_lexmax(
4467 __isl_take isl_pw_multi_aff *pma1,
4468 __isl_take isl_pw_multi_aff *pma2);
4469 __isl_give isl_multi_aff *isl_multi_aff_add(
4470 __isl_take isl_multi_aff *maff1,
4471 __isl_take isl_multi_aff *maff2);
4472 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_add(
4473 __isl_take isl_pw_multi_aff *pma1,
4474 __isl_take isl_pw_multi_aff *pma2);
4475 __isl_give isl_union_pw_multi_aff *isl_union_pw_multi_aff_add(
4476 __isl_take isl_union_pw_multi_aff *upma1,
4477 __isl_take isl_union_pw_multi_aff *upma2);
4478 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_union_add(
4479 __isl_take isl_pw_multi_aff *pma1,
4480 __isl_take isl_pw_multi_aff *pma2);
4481 __isl_give isl_multi_aff *isl_multi_aff_sub(
4482 __isl_take isl_multi_aff *ma1,
4483 __isl_take isl_multi_aff *ma2);
4484 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_sub(
4485 __isl_take isl_pw_multi_aff *pma1,
4486 __isl_take isl_pw_multi_aff *pma2);
4487 __isl_give isl_union_pw_multi_aff *isl_union_pw_multi_aff_sub(
4488 __isl_take isl_union_pw_multi_aff *upma1,
4489 __isl_take isl_union_pw_multi_aff *upma2);
4491 C<isl_multi_aff_sub> subtracts the second argument from the first.
4493 __isl_give isl_multi_aff *isl_multi_aff_scale_val(
4494 __isl_take isl_multi_aff *ma,
4495 __isl_take isl_val *v);
4496 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_scale_val(
4497 __isl_take isl_pw_multi_aff *pma,
4498 __isl_take isl_val *v);
4499 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_scale_val(
4500 __isl_take isl_multi_pw_aff *mpa,
4501 __isl_take isl_val *v);
4502 __isl_give isl_multi_aff *isl_multi_aff_scale_multi_val(
4503 __isl_take isl_multi_aff *ma,
4504 __isl_take isl_multi_val *mv);
4505 __isl_give isl_pw_multi_aff *
4506 isl_pw_multi_aff_scale_multi_val(
4507 __isl_take isl_pw_multi_aff *pma,
4508 __isl_take isl_multi_val *mv);
4509 __isl_give isl_multi_pw_aff *
4510 isl_multi_pw_aff_scale_multi_val(
4511 __isl_take isl_multi_pw_aff *mpa,
4512 __isl_take isl_multi_val *mv);
4513 __isl_give isl_union_pw_multi_aff *
4514 isl_union_pw_multi_aff_scale_multi_val(
4515 __isl_take isl_union_pw_multi_aff *upma,
4516 __isl_take isl_multi_val *mv);
4517 __isl_give isl_multi_aff *
4518 isl_multi_aff_scale_down_multi_val(
4519 __isl_take isl_multi_aff *ma,
4520 __isl_take isl_multi_val *mv);
4521 __isl_give isl_multi_pw_aff *
4522 isl_multi_pw_aff_scale_down_multi_val(
4523 __isl_take isl_multi_pw_aff *mpa,
4524 __isl_take isl_multi_val *mv);
4526 C<isl_multi_aff_scale_multi_val> scales the elements of C<ma>
4527 by the corresponding elements of C<mv>.
4529 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_fix_si(
4530 __isl_take isl_pw_multi_aff *pma,
4531 enum isl_dim_type type, unsigned pos, int value);
4532 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_intersect_params(
4533 __isl_take isl_pw_multi_aff *pma,
4534 __isl_take isl_set *set);
4535 __isl_give isl_set *isl_multi_pw_aff_domain(
4536 __isl_take isl_multi_pw_aff *mpa);
4537 __isl_give isl_multi_pw_aff *
4538 isl_multi_pw_aff_intersect_params(
4539 __isl_take isl_multi_pw_aff *mpa,
4540 __isl_take isl_set *set);
4541 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_intersect_domain(
4542 __isl_take isl_pw_multi_aff *pma,
4543 __isl_take isl_set *set);
4544 __isl_give isl_multi_pw_aff *
4545 isl_multi_pw_aff_intersect_domain(
4546 __isl_take isl_multi_pw_aff *mpa,
4547 __isl_take isl_set *domain);
4548 __isl_give isl_union_pw_multi_aff *
4549 isl_union_pw_multi_aff_intersect_domain(
4550 __isl_take isl_union_pw_multi_aff *upma,
4551 __isl_take isl_union_set *uset);
4552 __isl_give isl_multi_aff *isl_multi_aff_lift(
4553 __isl_take isl_multi_aff *maff,
4554 __isl_give isl_local_space **ls);
4555 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_coalesce(
4556 __isl_take isl_pw_multi_aff *pma);
4557 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_coalesce(
4558 __isl_take isl_multi_pw_aff *mpa);
4559 __isl_give isl_multi_aff *isl_multi_aff_align_params(
4560 __isl_take isl_multi_aff *multi,
4561 __isl_take isl_space *model);
4562 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_align_params(
4563 __isl_take isl_pw_multi_aff *pma,
4564 __isl_take isl_space *model);
4565 __isl_give isl_pw_multi_aff *
4566 isl_pw_multi_aff_project_domain_on_params(
4567 __isl_take isl_pw_multi_aff *pma);
4568 __isl_give isl_multi_aff *isl_multi_aff_gist_params(
4569 __isl_take isl_multi_aff *maff,
4570 __isl_take isl_set *context);
4571 __isl_give isl_multi_aff *isl_multi_aff_gist(
4572 __isl_take isl_multi_aff *maff,
4573 __isl_take isl_set *context);
4574 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_gist_params(
4575 __isl_take isl_pw_multi_aff *pma,
4576 __isl_take isl_set *set);
4577 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_gist(
4578 __isl_take isl_pw_multi_aff *pma,
4579 __isl_take isl_set *set);
4580 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_gist_params(
4581 __isl_take isl_multi_pw_aff *mpa,
4582 __isl_take isl_set *set);
4583 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_gist(
4584 __isl_take isl_multi_pw_aff *mpa,
4585 __isl_take isl_set *set);
4586 __isl_give isl_multi_aff *isl_multi_aff_from_range(
4587 __isl_take isl_multi_aff *ma);
4588 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_from_range(
4589 __isl_take isl_multi_pw_aff *mpa);
4590 __isl_give isl_set *isl_pw_multi_aff_domain(
4591 __isl_take isl_pw_multi_aff *pma);
4592 __isl_give isl_union_set *isl_union_pw_multi_aff_domain(
4593 __isl_take isl_union_pw_multi_aff *upma);
4594 __isl_give isl_multi_aff *isl_multi_aff_range_splice(
4595 __isl_take isl_multi_aff *ma1, unsigned pos,
4596 __isl_take isl_multi_aff *ma2);
4597 __isl_give isl_multi_aff *isl_multi_aff_splice(
4598 __isl_take isl_multi_aff *ma1,
4599 unsigned in_pos, unsigned out_pos,
4600 __isl_take isl_multi_aff *ma2);
4601 __isl_give isl_multi_aff *isl_multi_aff_range_product(
4602 __isl_take isl_multi_aff *ma1,
4603 __isl_take isl_multi_aff *ma2);
4604 __isl_give isl_multi_aff *
4605 isl_multi_aff_range_factor_domain(
4606 __isl_take isl_multi_aff *ma);
4607 __isl_give isl_multi_aff *
4608 isl_multi_aff_range_factor_range(
4609 __isl_take isl_multi_aff *ma);
4610 __isl_give isl_multi_aff *isl_multi_aff_flat_range_product(
4611 __isl_take isl_multi_aff *ma1,
4612 __isl_take isl_multi_aff *ma2);
4613 __isl_give isl_multi_aff *isl_multi_aff_product(
4614 __isl_take isl_multi_aff *ma1,
4615 __isl_take isl_multi_aff *ma2);
4616 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_product(
4617 __isl_take isl_multi_pw_aff *mpa1,
4618 __isl_take isl_multi_pw_aff *mpa2);
4619 __isl_give isl_pw_multi_aff *
4620 isl_pw_multi_aff_range_product(
4621 __isl_take isl_pw_multi_aff *pma1,
4622 __isl_take isl_pw_multi_aff *pma2);
4623 __isl_give isl_multi_pw_aff *
4624 isl_multi_pw_aff_range_factor_domain(
4625 __isl_take isl_multi_pw_aff *mpa);
4626 __isl_give isl_multi_pw_aff *
4627 isl_multi_pw_aff_range_factor_range(
4628 __isl_take isl_multi_pw_aff *mpa);
4629 __isl_give isl_pw_multi_aff *
4630 isl_pw_multi_aff_flat_range_product(
4631 __isl_take isl_pw_multi_aff *pma1,
4632 __isl_take isl_pw_multi_aff *pma2);
4633 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_product(
4634 __isl_take isl_pw_multi_aff *pma1,
4635 __isl_take isl_pw_multi_aff *pma2);
4636 __isl_give isl_union_pw_multi_aff *
4637 isl_union_pw_multi_aff_flat_range_product(
4638 __isl_take isl_union_pw_multi_aff *upma1,
4639 __isl_take isl_union_pw_multi_aff *upma2);
4640 __isl_give isl_multi_pw_aff *
4641 isl_multi_pw_aff_range_splice(
4642 __isl_take isl_multi_pw_aff *mpa1, unsigned pos,
4643 __isl_take isl_multi_pw_aff *mpa2);
4644 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_splice(
4645 __isl_take isl_multi_pw_aff *mpa1,
4646 unsigned in_pos, unsigned out_pos,
4647 __isl_take isl_multi_pw_aff *mpa2);
4648 __isl_give isl_multi_pw_aff *
4649 isl_multi_pw_aff_range_product(
4650 __isl_take isl_multi_pw_aff *mpa1,
4651 __isl_take isl_multi_pw_aff *mpa2);
4652 __isl_give isl_multi_pw_aff *
4653 isl_multi_pw_aff_flat_range_product(
4654 __isl_take isl_multi_pw_aff *mpa1,
4655 __isl_take isl_multi_pw_aff *mpa2);
4657 If the C<ls> argument of C<isl_multi_aff_lift> is not C<NULL>,
4658 then it is assigned the local space that lies at the basis of
4659 the lifting applied.
4661 #include <isl/aff.h>
4662 __isl_give isl_multi_aff *isl_multi_aff_pullback_multi_aff(
4663 __isl_take isl_multi_aff *ma1,
4664 __isl_take isl_multi_aff *ma2);
4665 __isl_give isl_pw_multi_aff *
4666 isl_pw_multi_aff_pullback_multi_aff(
4667 __isl_take isl_pw_multi_aff *pma,
4668 __isl_take isl_multi_aff *ma);
4669 __isl_give isl_multi_pw_aff *
4670 isl_multi_pw_aff_pullback_multi_aff(
4671 __isl_take isl_multi_pw_aff *mpa,
4672 __isl_take isl_multi_aff *ma);
4673 __isl_give isl_pw_multi_aff *
4674 isl_pw_multi_aff_pullback_pw_multi_aff(
4675 __isl_take isl_pw_multi_aff *pma1,
4676 __isl_take isl_pw_multi_aff *pma2);
4677 __isl_give isl_multi_pw_aff *
4678 isl_multi_pw_aff_pullback_pw_multi_aff(
4679 __isl_take isl_multi_pw_aff *mpa,
4680 __isl_take isl_pw_multi_aff *pma);
4681 __isl_give isl_multi_pw_aff *
4682 isl_multi_pw_aff_pullback_multi_pw_aff(
4683 __isl_take isl_multi_pw_aff *mpa1,
4684 __isl_take isl_multi_pw_aff *mpa2);
4686 The function C<isl_multi_aff_pullback_multi_aff> precomposes C<ma1> by C<ma2>.
4687 In other words, C<ma2> is plugged
4690 __isl_give isl_set *isl_multi_aff_lex_le_set(
4691 __isl_take isl_multi_aff *ma1,
4692 __isl_take isl_multi_aff *ma2);
4693 __isl_give isl_set *isl_multi_aff_lex_ge_set(
4694 __isl_take isl_multi_aff *ma1,
4695 __isl_take isl_multi_aff *ma2);
4697 The function C<isl_multi_aff_lex_le_set> returns a set
4698 containing those elements in the shared domain space
4699 where C<ma1> is lexicographically smaller than or
4702 An expression can be read from input using
4704 #include <isl/aff.h>
4705 __isl_give isl_multi_aff *isl_multi_aff_read_from_str(
4706 isl_ctx *ctx, const char *str);
4707 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_read_from_str(
4708 isl_ctx *ctx, const char *str);
4709 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_read_from_str(
4710 isl_ctx *ctx, const char *str);
4711 __isl_give isl_union_pw_multi_aff *
4712 isl_union_pw_multi_aff_read_from_str(
4713 isl_ctx *ctx, const char *str);
4715 An expression can be printed using
4717 #include <isl/aff.h>
4718 __isl_give isl_printer *isl_printer_print_multi_aff(
4719 __isl_take isl_printer *p,
4720 __isl_keep isl_multi_aff *maff);
4721 __isl_give isl_printer *isl_printer_print_pw_multi_aff(
4722 __isl_take isl_printer *p,
4723 __isl_keep isl_pw_multi_aff *pma);
4724 __isl_give isl_printer *isl_printer_print_union_pw_multi_aff(
4725 __isl_take isl_printer *p,
4726 __isl_keep isl_union_pw_multi_aff *upma);
4727 __isl_give isl_printer *isl_printer_print_multi_pw_aff(
4728 __isl_take isl_printer *p,
4729 __isl_keep isl_multi_pw_aff *mpa);
4733 Points are elements of a set. They can be used to construct
4734 simple sets (boxes) or they can be used to represent the
4735 individual elements of a set.
4736 The zero point (the origin) can be created using
4738 __isl_give isl_point *isl_point_zero(__isl_take isl_space *space);
4740 The coordinates of a point can be inspected, set and changed
4743 __isl_give isl_val *isl_point_get_coordinate_val(
4744 __isl_keep isl_point *pnt,
4745 enum isl_dim_type type, int pos);
4746 __isl_give isl_point *isl_point_set_coordinate_val(
4747 __isl_take isl_point *pnt,
4748 enum isl_dim_type type, int pos,
4749 __isl_take isl_val *v);
4751 __isl_give isl_point *isl_point_add_ui(
4752 __isl_take isl_point *pnt,
4753 enum isl_dim_type type, int pos, unsigned val);
4754 __isl_give isl_point *isl_point_sub_ui(
4755 __isl_take isl_point *pnt,
4756 enum isl_dim_type type, int pos, unsigned val);
4758 Other properties can be obtained using
4760 isl_ctx *isl_point_get_ctx(__isl_keep isl_point *pnt);
4762 Points can be copied or freed using
4764 __isl_give isl_point *isl_point_copy(
4765 __isl_keep isl_point *pnt);
4766 void isl_point_free(__isl_take isl_point *pnt);
4768 A singleton set can be created from a point using
4770 __isl_give isl_basic_set *isl_basic_set_from_point(
4771 __isl_take isl_point *pnt);
4772 __isl_give isl_set *isl_set_from_point(
4773 __isl_take isl_point *pnt);
4775 and a box can be created from two opposite extremal points using
4777 __isl_give isl_basic_set *isl_basic_set_box_from_points(
4778 __isl_take isl_point *pnt1,
4779 __isl_take isl_point *pnt2);
4780 __isl_give isl_set *isl_set_box_from_points(
4781 __isl_take isl_point *pnt1,
4782 __isl_take isl_point *pnt2);
4784 All elements of a B<bounded> (union) set can be enumerated using
4785 the following functions.
4787 int isl_set_foreach_point(__isl_keep isl_set *set,
4788 int (*fn)(__isl_take isl_point *pnt, void *user),
4790 int isl_union_set_foreach_point(__isl_keep isl_union_set *uset,
4791 int (*fn)(__isl_take isl_point *pnt, void *user),
4794 The function C<fn> is called for each integer point in
4795 C<set> with as second argument the last argument of
4796 the C<isl_set_foreach_point> call. The function C<fn>
4797 should return C<0> on success and C<-1> on failure.
4798 In the latter case, C<isl_set_foreach_point> will stop
4799 enumerating and return C<-1> as well.
4800 If the enumeration is performed successfully and to completion,
4801 then C<isl_set_foreach_point> returns C<0>.
4803 To obtain a single point of a (basic) set, use
4805 __isl_give isl_point *isl_basic_set_sample_point(
4806 __isl_take isl_basic_set *bset);
4807 __isl_give isl_point *isl_set_sample_point(
4808 __isl_take isl_set *set);
4810 If C<set> does not contain any (integer) points, then the
4811 resulting point will be ``void'', a property that can be
4814 int isl_point_is_void(__isl_keep isl_point *pnt);
4816 =head2 Piecewise Quasipolynomials
4818 A piecewise quasipolynomial is a particular kind of function that maps
4819 a parametric point to a rational value.
4820 More specifically, a quasipolynomial is a polynomial expression in greatest
4821 integer parts of affine expressions of parameters and variables.
4822 A piecewise quasipolynomial is a subdivision of a given parametric
4823 domain into disjoint cells with a quasipolynomial associated to
4824 each cell. The value of the piecewise quasipolynomial at a given
4825 point is the value of the quasipolynomial associated to the cell
4826 that contains the point. Outside of the union of cells,
4827 the value is assumed to be zero.
4828 For example, the piecewise quasipolynomial
4830 [n] -> { [x] -> ((1 + n) - x) : x <= n and x >= 0 }
4832 maps C<x> to C<1 + n - x> for values of C<x> between C<0> and C<n>.
4833 A given piecewise quasipolynomial has a fixed domain dimension.
4834 Union piecewise quasipolynomials are used to contain piecewise quasipolynomials
4835 defined over different domains.
4836 Piecewise quasipolynomials are mainly used by the C<barvinok>
4837 library for representing the number of elements in a parametric set or map.
4838 For example, the piecewise quasipolynomial above represents
4839 the number of points in the map
4841 [n] -> { [x] -> [y] : x,y >= 0 and 0 <= x + y <= n }
4843 =head3 Input and Output
4845 Piecewise quasipolynomials can be read from input using
4847 __isl_give isl_union_pw_qpolynomial *
4848 isl_union_pw_qpolynomial_read_from_str(
4849 isl_ctx *ctx, const char *str);
4851 Quasipolynomials and piecewise quasipolynomials can be printed
4852 using the following functions.
4854 __isl_give isl_printer *isl_printer_print_qpolynomial(
4855 __isl_take isl_printer *p,
4856 __isl_keep isl_qpolynomial *qp);
4858 __isl_give isl_printer *isl_printer_print_pw_qpolynomial(
4859 __isl_take isl_printer *p,
4860 __isl_keep isl_pw_qpolynomial *pwqp);
4862 __isl_give isl_printer *isl_printer_print_union_pw_qpolynomial(
4863 __isl_take isl_printer *p,
4864 __isl_keep isl_union_pw_qpolynomial *upwqp);
4866 The output format of the printer
4867 needs to be set to either C<ISL_FORMAT_ISL> or C<ISL_FORMAT_C>.
4868 For C<isl_printer_print_union_pw_qpolynomial>, only C<ISL_FORMAT_ISL>
4870 In case of printing in C<ISL_FORMAT_C>, the user may want
4871 to set the names of all dimensions
4873 __isl_give isl_qpolynomial *isl_qpolynomial_set_dim_name(
4874 __isl_take isl_qpolynomial *qp,
4875 enum isl_dim_type type, unsigned pos,
4877 __isl_give isl_pw_qpolynomial *
4878 isl_pw_qpolynomial_set_dim_name(
4879 __isl_take isl_pw_qpolynomial *pwqp,
4880 enum isl_dim_type type, unsigned pos,
4883 =head3 Creating New (Piecewise) Quasipolynomials
4885 Some simple quasipolynomials can be created using the following functions.
4886 More complicated quasipolynomials can be created by applying
4887 operations such as addition and multiplication
4888 on the resulting quasipolynomials
4890 __isl_give isl_qpolynomial *isl_qpolynomial_zero_on_domain(
4891 __isl_take isl_space *domain);
4892 __isl_give isl_qpolynomial *isl_qpolynomial_one_on_domain(
4893 __isl_take isl_space *domain);
4894 __isl_give isl_qpolynomial *isl_qpolynomial_infty_on_domain(
4895 __isl_take isl_space *domain);
4896 __isl_give isl_qpolynomial *isl_qpolynomial_neginfty_on_domain(
4897 __isl_take isl_space *domain);
4898 __isl_give isl_qpolynomial *isl_qpolynomial_nan_on_domain(
4899 __isl_take isl_space *domain);
4900 __isl_give isl_qpolynomial *isl_qpolynomial_val_on_domain(
4901 __isl_take isl_space *domain,
4902 __isl_take isl_val *val);
4903 __isl_give isl_qpolynomial *isl_qpolynomial_var_on_domain(
4904 __isl_take isl_space *domain,
4905 enum isl_dim_type type, unsigned pos);
4906 __isl_give isl_qpolynomial *isl_qpolynomial_from_aff(
4907 __isl_take isl_aff *aff);
4909 Note that the space in which a quasipolynomial lives is a map space
4910 with a one-dimensional range. The C<domain> argument in some of
4911 the functions above corresponds to the domain of this map space.
4913 The zero piecewise quasipolynomial or a piecewise quasipolynomial
4914 with a single cell can be created using the following functions.
4915 Multiple of these single cell piecewise quasipolynomials can
4916 be combined to create more complicated piecewise quasipolynomials.
4918 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_zero(
4919 __isl_take isl_space *space);
4920 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_alloc(
4921 __isl_take isl_set *set,
4922 __isl_take isl_qpolynomial *qp);
4923 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_from_qpolynomial(
4924 __isl_take isl_qpolynomial *qp);
4925 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_from_pw_aff(
4926 __isl_take isl_pw_aff *pwaff);
4928 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_zero(
4929 __isl_take isl_space *space);
4930 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_from_pw_qpolynomial(
4931 __isl_take isl_pw_qpolynomial *pwqp);
4932 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_add_pw_qpolynomial(
4933 __isl_take isl_union_pw_qpolynomial *upwqp,
4934 __isl_take isl_pw_qpolynomial *pwqp);
4936 Quasipolynomials can be copied and freed again using the following
4939 __isl_give isl_qpolynomial *isl_qpolynomial_copy(
4940 __isl_keep isl_qpolynomial *qp);
4941 void *isl_qpolynomial_free(__isl_take isl_qpolynomial *qp);
4943 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_copy(
4944 __isl_keep isl_pw_qpolynomial *pwqp);
4945 void *isl_pw_qpolynomial_free(
4946 __isl_take isl_pw_qpolynomial *pwqp);
4948 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_copy(
4949 __isl_keep isl_union_pw_qpolynomial *upwqp);
4950 void *isl_union_pw_qpolynomial_free(
4951 __isl_take isl_union_pw_qpolynomial *upwqp);
4953 =head3 Inspecting (Piecewise) Quasipolynomials
4955 To iterate over all piecewise quasipolynomials in a union
4956 piecewise quasipolynomial, use the following function
4958 int isl_union_pw_qpolynomial_foreach_pw_qpolynomial(
4959 __isl_keep isl_union_pw_qpolynomial *upwqp,
4960 int (*fn)(__isl_take isl_pw_qpolynomial *pwqp, void *user),
4963 To extract the piecewise quasipolynomial in a given space from a union, use
4965 __isl_give isl_pw_qpolynomial *
4966 isl_union_pw_qpolynomial_extract_pw_qpolynomial(
4967 __isl_keep isl_union_pw_qpolynomial *upwqp,
4968 __isl_take isl_space *space);
4970 To iterate over the cells in a piecewise quasipolynomial,
4971 use either of the following two functions
4973 int isl_pw_qpolynomial_foreach_piece(
4974 __isl_keep isl_pw_qpolynomial *pwqp,
4975 int (*fn)(__isl_take isl_set *set,
4976 __isl_take isl_qpolynomial *qp,
4977 void *user), void *user);
4978 int isl_pw_qpolynomial_foreach_lifted_piece(
4979 __isl_keep isl_pw_qpolynomial *pwqp,
4980 int (*fn)(__isl_take isl_set *set,
4981 __isl_take isl_qpolynomial *qp,
4982 void *user), void *user);
4984 As usual, the function C<fn> should return C<0> on success
4985 and C<-1> on failure. The difference between
4986 C<isl_pw_qpolynomial_foreach_piece> and
4987 C<isl_pw_qpolynomial_foreach_lifted_piece> is that
4988 C<isl_pw_qpolynomial_foreach_lifted_piece> will first
4989 compute unique representations for all existentially quantified
4990 variables and then turn these existentially quantified variables
4991 into extra set variables, adapting the associated quasipolynomial
4992 accordingly. This means that the C<set> passed to C<fn>
4993 will not have any existentially quantified variables, but that
4994 the dimensions of the sets may be different for different
4995 invocations of C<fn>.
4997 The constant term of a quasipolynomial can be extracted using
4999 __isl_give isl_val *isl_qpolynomial_get_constant_val(
5000 __isl_keep isl_qpolynomial *qp);
5002 To iterate over all terms in a quasipolynomial,
5005 int isl_qpolynomial_foreach_term(
5006 __isl_keep isl_qpolynomial *qp,
5007 int (*fn)(__isl_take isl_term *term,
5008 void *user), void *user);
5010 The terms themselves can be inspected and freed using
5013 unsigned isl_term_dim(__isl_keep isl_term *term,
5014 enum isl_dim_type type);
5015 __isl_give isl_val *isl_term_get_coefficient_val(
5016 __isl_keep isl_term *term);
5017 int isl_term_get_exp(__isl_keep isl_term *term,
5018 enum isl_dim_type type, unsigned pos);
5019 __isl_give isl_aff *isl_term_get_div(
5020 __isl_keep isl_term *term, unsigned pos);
5021 void isl_term_free(__isl_take isl_term *term);
5023 Each term is a product of parameters, set variables and
5024 integer divisions. The function C<isl_term_get_exp>
5025 returns the exponent of a given dimensions in the given term.
5027 =head3 Properties of (Piecewise) Quasipolynomials
5029 To check whether two union piecewise quasipolynomials are
5030 obviously equal, use
5032 int isl_union_pw_qpolynomial_plain_is_equal(
5033 __isl_keep isl_union_pw_qpolynomial *upwqp1,
5034 __isl_keep isl_union_pw_qpolynomial *upwqp2);
5036 =head3 Operations on (Piecewise) Quasipolynomials
5038 __isl_give isl_qpolynomial *isl_qpolynomial_scale_val(
5039 __isl_take isl_qpolynomial *qp,
5040 __isl_take isl_val *v);
5041 __isl_give isl_qpolynomial *isl_qpolynomial_neg(
5042 __isl_take isl_qpolynomial *qp);
5043 __isl_give isl_qpolynomial *isl_qpolynomial_add(
5044 __isl_take isl_qpolynomial *qp1,
5045 __isl_take isl_qpolynomial *qp2);
5046 __isl_give isl_qpolynomial *isl_qpolynomial_sub(
5047 __isl_take isl_qpolynomial *qp1,
5048 __isl_take isl_qpolynomial *qp2);
5049 __isl_give isl_qpolynomial *isl_qpolynomial_mul(
5050 __isl_take isl_qpolynomial *qp1,
5051 __isl_take isl_qpolynomial *qp2);
5052 __isl_give isl_qpolynomial *isl_qpolynomial_pow(
5053 __isl_take isl_qpolynomial *qp, unsigned exponent);
5055 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_fix_val(
5056 __isl_take isl_pw_qpolynomial *pwqp,
5057 enum isl_dim_type type, unsigned n,
5058 __isl_take isl_val *v);
5059 __isl_give isl_pw_qpolynomial *
5060 isl_pw_qpolynomial_scale_val(
5061 __isl_take isl_pw_qpolynomial *pwqp,
5062 __isl_take isl_val *v);
5063 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_add(
5064 __isl_take isl_pw_qpolynomial *pwqp1,
5065 __isl_take isl_pw_qpolynomial *pwqp2);
5066 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_sub(
5067 __isl_take isl_pw_qpolynomial *pwqp1,
5068 __isl_take isl_pw_qpolynomial *pwqp2);
5069 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_add_disjoint(
5070 __isl_take isl_pw_qpolynomial *pwqp1,
5071 __isl_take isl_pw_qpolynomial *pwqp2);
5072 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_neg(
5073 __isl_take isl_pw_qpolynomial *pwqp);
5074 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_mul(
5075 __isl_take isl_pw_qpolynomial *pwqp1,
5076 __isl_take isl_pw_qpolynomial *pwqp2);
5077 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_pow(
5078 __isl_take isl_pw_qpolynomial *pwqp, unsigned exponent);
5080 __isl_give isl_union_pw_qpolynomial *
5081 isl_union_pw_qpolynomial_scale_val(
5082 __isl_take isl_union_pw_qpolynomial *upwqp,
5083 __isl_take isl_val *v);
5084 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_add(
5085 __isl_take isl_union_pw_qpolynomial *upwqp1,
5086 __isl_take isl_union_pw_qpolynomial *upwqp2);
5087 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_sub(
5088 __isl_take isl_union_pw_qpolynomial *upwqp1,
5089 __isl_take isl_union_pw_qpolynomial *upwqp2);
5090 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_mul(
5091 __isl_take isl_union_pw_qpolynomial *upwqp1,
5092 __isl_take isl_union_pw_qpolynomial *upwqp2);
5094 __isl_give isl_val *isl_pw_qpolynomial_eval(
5095 __isl_take isl_pw_qpolynomial *pwqp,
5096 __isl_take isl_point *pnt);
5098 __isl_give isl_val *isl_union_pw_qpolynomial_eval(
5099 __isl_take isl_union_pw_qpolynomial *upwqp,
5100 __isl_take isl_point *pnt);
5102 __isl_give isl_set *isl_pw_qpolynomial_domain(
5103 __isl_take isl_pw_qpolynomial *pwqp);
5104 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_intersect_domain(
5105 __isl_take isl_pw_qpolynomial *pwpq,
5106 __isl_take isl_set *set);
5107 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_intersect_params(
5108 __isl_take isl_pw_qpolynomial *pwpq,
5109 __isl_take isl_set *set);
5111 __isl_give isl_union_set *isl_union_pw_qpolynomial_domain(
5112 __isl_take isl_union_pw_qpolynomial *upwqp);
5113 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_intersect_domain(
5114 __isl_take isl_union_pw_qpolynomial *upwpq,
5115 __isl_take isl_union_set *uset);
5116 __isl_give isl_union_pw_qpolynomial *
5117 isl_union_pw_qpolynomial_intersect_params(
5118 __isl_take isl_union_pw_qpolynomial *upwpq,
5119 __isl_take isl_set *set);
5121 __isl_give isl_qpolynomial *isl_qpolynomial_align_params(
5122 __isl_take isl_qpolynomial *qp,
5123 __isl_take isl_space *model);
5125 __isl_give isl_qpolynomial *isl_qpolynomial_project_domain_on_params(
5126 __isl_take isl_qpolynomial *qp);
5127 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_project_domain_on_params(
5128 __isl_take isl_pw_qpolynomial *pwqp);
5130 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_coalesce(
5131 __isl_take isl_union_pw_qpolynomial *upwqp);
5133 __isl_give isl_qpolynomial *isl_qpolynomial_gist_params(
5134 __isl_take isl_qpolynomial *qp,
5135 __isl_take isl_set *context);
5136 __isl_give isl_qpolynomial *isl_qpolynomial_gist(
5137 __isl_take isl_qpolynomial *qp,
5138 __isl_take isl_set *context);
5140 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_gist_params(
5141 __isl_take isl_pw_qpolynomial *pwqp,
5142 __isl_take isl_set *context);
5143 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_gist(
5144 __isl_take isl_pw_qpolynomial *pwqp,
5145 __isl_take isl_set *context);
5147 __isl_give isl_union_pw_qpolynomial *
5148 isl_union_pw_qpolynomial_gist_params(
5149 __isl_take isl_union_pw_qpolynomial *upwqp,
5150 __isl_take isl_set *context);
5151 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_gist(
5152 __isl_take isl_union_pw_qpolynomial *upwqp,
5153 __isl_take isl_union_set *context);
5155 The gist operation applies the gist operation to each of
5156 the cells in the domain of the input piecewise quasipolynomial.
5157 The context is also exploited
5158 to simplify the quasipolynomials associated to each cell.
5160 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_to_polynomial(
5161 __isl_take isl_pw_qpolynomial *pwqp, int sign);
5162 __isl_give isl_union_pw_qpolynomial *
5163 isl_union_pw_qpolynomial_to_polynomial(
5164 __isl_take isl_union_pw_qpolynomial *upwqp, int sign);
5166 Approximate each quasipolynomial by a polynomial. If C<sign> is positive,
5167 the polynomial will be an overapproximation. If C<sign> is negative,
5168 it will be an underapproximation. If C<sign> is zero, the approximation
5169 will lie somewhere in between.
5171 =head2 Bounds on Piecewise Quasipolynomials and Piecewise Quasipolynomial Reductions
5173 A piecewise quasipolynomial reduction is a piecewise
5174 reduction (or fold) of quasipolynomials.
5175 In particular, the reduction can be maximum or a minimum.
5176 The objects are mainly used to represent the result of
5177 an upper or lower bound on a quasipolynomial over its domain,
5178 i.e., as the result of the following function.
5180 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_bound(
5181 __isl_take isl_pw_qpolynomial *pwqp,
5182 enum isl_fold type, int *tight);
5184 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_bound(
5185 __isl_take isl_union_pw_qpolynomial *upwqp,
5186 enum isl_fold type, int *tight);
5188 The C<type> argument may be either C<isl_fold_min> or C<isl_fold_max>.
5189 If C<tight> is not C<NULL>, then C<*tight> is set to C<1>
5190 is the returned bound is known be tight, i.e., for each value
5191 of the parameters there is at least
5192 one element in the domain that reaches the bound.
5193 If the domain of C<pwqp> is not wrapping, then the bound is computed
5194 over all elements in that domain and the result has a purely parametric
5195 domain. If the domain of C<pwqp> is wrapping, then the bound is
5196 computed over the range of the wrapped relation. The domain of the
5197 wrapped relation becomes the domain of the result.
5199 A (piecewise) quasipolynomial reduction can be copied or freed using the
5200 following functions.
5202 __isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_copy(
5203 __isl_keep isl_qpolynomial_fold *fold);
5204 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_copy(
5205 __isl_keep isl_pw_qpolynomial_fold *pwf);
5206 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_copy(
5207 __isl_keep isl_union_pw_qpolynomial_fold *upwf);
5208 void isl_qpolynomial_fold_free(
5209 __isl_take isl_qpolynomial_fold *fold);
5210 void *isl_pw_qpolynomial_fold_free(
5211 __isl_take isl_pw_qpolynomial_fold *pwf);
5212 void *isl_union_pw_qpolynomial_fold_free(
5213 __isl_take isl_union_pw_qpolynomial_fold *upwf);
5215 =head3 Printing Piecewise Quasipolynomial Reductions
5217 Piecewise quasipolynomial reductions can be printed
5218 using the following function.
5220 __isl_give isl_printer *isl_printer_print_pw_qpolynomial_fold(
5221 __isl_take isl_printer *p,
5222 __isl_keep isl_pw_qpolynomial_fold *pwf);
5223 __isl_give isl_printer *isl_printer_print_union_pw_qpolynomial_fold(
5224 __isl_take isl_printer *p,
5225 __isl_keep isl_union_pw_qpolynomial_fold *upwf);
5227 For C<isl_printer_print_pw_qpolynomial_fold>,
5228 output format of the printer
5229 needs to be set to either C<ISL_FORMAT_ISL> or C<ISL_FORMAT_C>.
5230 For C<isl_printer_print_union_pw_qpolynomial_fold>,
5231 output format of the printer
5232 needs to be set to C<ISL_FORMAT_ISL>.
5233 In case of printing in C<ISL_FORMAT_C>, the user may want
5234 to set the names of all dimensions
5236 __isl_give isl_pw_qpolynomial_fold *
5237 isl_pw_qpolynomial_fold_set_dim_name(
5238 __isl_take isl_pw_qpolynomial_fold *pwf,
5239 enum isl_dim_type type, unsigned pos,
5242 =head3 Inspecting (Piecewise) Quasipolynomial Reductions
5244 To iterate over all piecewise quasipolynomial reductions in a union
5245 piecewise quasipolynomial reduction, use the following function
5247 int isl_union_pw_qpolynomial_fold_foreach_pw_qpolynomial_fold(
5248 __isl_keep isl_union_pw_qpolynomial_fold *upwf,
5249 int (*fn)(__isl_take isl_pw_qpolynomial_fold *pwf,
5250 void *user), void *user);
5252 To iterate over the cells in a piecewise quasipolynomial reduction,
5253 use either of the following two functions
5255 int isl_pw_qpolynomial_fold_foreach_piece(
5256 __isl_keep isl_pw_qpolynomial_fold *pwf,
5257 int (*fn)(__isl_take isl_set *set,
5258 __isl_take isl_qpolynomial_fold *fold,
5259 void *user), void *user);
5260 int isl_pw_qpolynomial_fold_foreach_lifted_piece(
5261 __isl_keep isl_pw_qpolynomial_fold *pwf,
5262 int (*fn)(__isl_take isl_set *set,
5263 __isl_take isl_qpolynomial_fold *fold,
5264 void *user), void *user);
5266 See L<Inspecting (Piecewise) Quasipolynomials> for an explanation
5267 of the difference between these two functions.
5269 To iterate over all quasipolynomials in a reduction, use
5271 int isl_qpolynomial_fold_foreach_qpolynomial(
5272 __isl_keep isl_qpolynomial_fold *fold,
5273 int (*fn)(__isl_take isl_qpolynomial *qp,
5274 void *user), void *user);
5276 =head3 Properties of Piecewise Quasipolynomial Reductions
5278 To check whether two union piecewise quasipolynomial reductions are
5279 obviously equal, use
5281 int isl_union_pw_qpolynomial_fold_plain_is_equal(
5282 __isl_keep isl_union_pw_qpolynomial_fold *upwf1,
5283 __isl_keep isl_union_pw_qpolynomial_fold *upwf2);
5285 =head3 Operations on Piecewise Quasipolynomial Reductions
5287 __isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_scale_val(
5288 __isl_take isl_qpolynomial_fold *fold,
5289 __isl_take isl_val *v);
5290 __isl_give isl_pw_qpolynomial_fold *
5291 isl_pw_qpolynomial_fold_scale_val(
5292 __isl_take isl_pw_qpolynomial_fold *pwf,
5293 __isl_take isl_val *v);
5294 __isl_give isl_union_pw_qpolynomial_fold *
5295 isl_union_pw_qpolynomial_fold_scale_val(
5296 __isl_take isl_union_pw_qpolynomial_fold *upwf,
5297 __isl_take isl_val *v);
5299 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_add(
5300 __isl_take isl_pw_qpolynomial_fold *pwf1,
5301 __isl_take isl_pw_qpolynomial_fold *pwf2);
5303 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_fold(
5304 __isl_take isl_pw_qpolynomial_fold *pwf1,
5305 __isl_take isl_pw_qpolynomial_fold *pwf2);
5307 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_fold(
5308 __isl_take isl_union_pw_qpolynomial_fold *upwf1,
5309 __isl_take isl_union_pw_qpolynomial_fold *upwf2);
5311 __isl_give isl_val *isl_pw_qpolynomial_fold_eval(
5312 __isl_take isl_pw_qpolynomial_fold *pwf,
5313 __isl_take isl_point *pnt);
5315 __isl_give isl_val *isl_union_pw_qpolynomial_fold_eval(
5316 __isl_take isl_union_pw_qpolynomial_fold *upwf,
5317 __isl_take isl_point *pnt);
5319 __isl_give isl_pw_qpolynomial_fold *
5320 isl_pw_qpolynomial_fold_intersect_params(
5321 __isl_take isl_pw_qpolynomial_fold *pwf,
5322 __isl_take isl_set *set);
5324 __isl_give isl_union_set *isl_union_pw_qpolynomial_fold_domain(
5325 __isl_take isl_union_pw_qpolynomial_fold *upwf);
5326 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_intersect_domain(
5327 __isl_take isl_union_pw_qpolynomial_fold *upwf,
5328 __isl_take isl_union_set *uset);
5329 __isl_give isl_union_pw_qpolynomial_fold *
5330 isl_union_pw_qpolynomial_fold_intersect_params(
5331 __isl_take isl_union_pw_qpolynomial_fold *upwf,
5332 __isl_take isl_set *set);
5334 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_project_domain_on_params(
5335 __isl_take isl_pw_qpolynomial_fold *pwf);
5337 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_coalesce(
5338 __isl_take isl_pw_qpolynomial_fold *pwf);
5340 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_coalesce(
5341 __isl_take isl_union_pw_qpolynomial_fold *upwf);
5343 __isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_gist_params(
5344 __isl_take isl_qpolynomial_fold *fold,
5345 __isl_take isl_set *context);
5346 __isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_gist(
5347 __isl_take isl_qpolynomial_fold *fold,
5348 __isl_take isl_set *context);
5350 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_gist(
5351 __isl_take isl_pw_qpolynomial_fold *pwf,
5352 __isl_take isl_set *context);
5353 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_gist_params(
5354 __isl_take isl_pw_qpolynomial_fold *pwf,
5355 __isl_take isl_set *context);
5357 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_gist(
5358 __isl_take isl_union_pw_qpolynomial_fold *upwf,
5359 __isl_take isl_union_set *context);
5360 __isl_give isl_union_pw_qpolynomial_fold *
5361 isl_union_pw_qpolynomial_fold_gist_params(
5362 __isl_take isl_union_pw_qpolynomial_fold *upwf,
5363 __isl_take isl_set *context);
5365 The gist operation applies the gist operation to each of
5366 the cells in the domain of the input piecewise quasipolynomial reduction.
5367 In future, the operation will also exploit the context
5368 to simplify the quasipolynomial reductions associated to each cell.
5370 __isl_give isl_pw_qpolynomial_fold *
5371 isl_set_apply_pw_qpolynomial_fold(
5372 __isl_take isl_set *set,
5373 __isl_take isl_pw_qpolynomial_fold *pwf,
5375 __isl_give isl_pw_qpolynomial_fold *
5376 isl_map_apply_pw_qpolynomial_fold(
5377 __isl_take isl_map *map,
5378 __isl_take isl_pw_qpolynomial_fold *pwf,
5380 __isl_give isl_union_pw_qpolynomial_fold *
5381 isl_union_set_apply_union_pw_qpolynomial_fold(
5382 __isl_take isl_union_set *uset,
5383 __isl_take isl_union_pw_qpolynomial_fold *upwf,
5385 __isl_give isl_union_pw_qpolynomial_fold *
5386 isl_union_map_apply_union_pw_qpolynomial_fold(
5387 __isl_take isl_union_map *umap,
5388 __isl_take isl_union_pw_qpolynomial_fold *upwf,
5391 The functions taking a map
5392 compose the given map with the given piecewise quasipolynomial reduction.
5393 That is, compute a bound (of the same type as C<pwf> or C<upwf> itself)
5394 over all elements in the intersection of the range of the map
5395 and the domain of the piecewise quasipolynomial reduction
5396 as a function of an element in the domain of the map.
5397 The functions taking a set compute a bound over all elements in the
5398 intersection of the set and the domain of the
5399 piecewise quasipolynomial reduction.
5401 =head2 Parametric Vertex Enumeration
5403 The parametric vertex enumeration described in this section
5404 is mainly intended to be used internally and by the C<barvinok>
5407 #include <isl/vertices.h>
5408 __isl_give isl_vertices *isl_basic_set_compute_vertices(
5409 __isl_keep isl_basic_set *bset);
5411 The function C<isl_basic_set_compute_vertices> performs the
5412 actual computation of the parametric vertices and the chamber
5413 decomposition and store the result in an C<isl_vertices> object.
5414 This information can be queried by either iterating over all
5415 the vertices or iterating over all the chambers or cells
5416 and then iterating over all vertices that are active on the chamber.
5418 int isl_vertices_foreach_vertex(
5419 __isl_keep isl_vertices *vertices,
5420 int (*fn)(__isl_take isl_vertex *vertex, void *user),
5423 int isl_vertices_foreach_cell(
5424 __isl_keep isl_vertices *vertices,
5425 int (*fn)(__isl_take isl_cell *cell, void *user),
5427 int isl_cell_foreach_vertex(__isl_keep isl_cell *cell,
5428 int (*fn)(__isl_take isl_vertex *vertex, void *user),
5431 Other operations that can be performed on an C<isl_vertices> object are
5434 isl_ctx *isl_vertices_get_ctx(
5435 __isl_keep isl_vertices *vertices);
5436 int isl_vertices_get_n_vertices(
5437 __isl_keep isl_vertices *vertices);
5438 void isl_vertices_free(__isl_take isl_vertices *vertices);
5440 Vertices can be inspected and destroyed using the following functions.
5442 isl_ctx *isl_vertex_get_ctx(__isl_keep isl_vertex *vertex);
5443 int isl_vertex_get_id(__isl_keep isl_vertex *vertex);
5444 __isl_give isl_basic_set *isl_vertex_get_domain(
5445 __isl_keep isl_vertex *vertex);
5446 __isl_give isl_basic_set *isl_vertex_get_expr(
5447 __isl_keep isl_vertex *vertex);
5448 void isl_vertex_free(__isl_take isl_vertex *vertex);
5450 C<isl_vertex_get_expr> returns a singleton parametric set describing
5451 the vertex, while C<isl_vertex_get_domain> returns the activity domain
5453 Note that C<isl_vertex_get_domain> and C<isl_vertex_get_expr> return
5454 B<rational> basic sets, so they should mainly be used for inspection
5455 and should not be mixed with integer sets.
5457 Chambers can be inspected and destroyed using the following functions.
5459 isl_ctx *isl_cell_get_ctx(__isl_keep isl_cell *cell);
5460 __isl_give isl_basic_set *isl_cell_get_domain(
5461 __isl_keep isl_cell *cell);
5462 void isl_cell_free(__isl_take isl_cell *cell);
5464 =head1 Polyhedral Compilation Library
5466 This section collects functionality in C<isl> that has been specifically
5467 designed for use during polyhedral compilation.
5469 =head2 Dependence Analysis
5471 C<isl> contains specialized functionality for performing
5472 array dataflow analysis. That is, given a I<sink> access relation
5473 and a collection of possible I<source> access relations,
5474 C<isl> can compute relations that describe
5475 for each iteration of the sink access, which iteration
5476 of which of the source access relations was the last
5477 to access the same data element before the given iteration
5479 The resulting dependence relations map source iterations
5480 to the corresponding sink iterations.
5481 To compute standard flow dependences, the sink should be
5482 a read, while the sources should be writes.
5483 If any of the source accesses are marked as being I<may>
5484 accesses, then there will be a dependence from the last
5485 I<must> access B<and> from any I<may> access that follows
5486 this last I<must> access.
5487 In particular, if I<all> sources are I<may> accesses,
5488 then memory based dependence analysis is performed.
5489 If, on the other hand, all sources are I<must> accesses,
5490 then value based dependence analysis is performed.
5492 #include <isl/flow.h>
5494 typedef int (*isl_access_level_before)(void *first, void *second);
5496 __isl_give isl_access_info *isl_access_info_alloc(
5497 __isl_take isl_map *sink,
5498 void *sink_user, isl_access_level_before fn,
5500 __isl_give isl_access_info *isl_access_info_add_source(
5501 __isl_take isl_access_info *acc,
5502 __isl_take isl_map *source, int must,
5504 void *isl_access_info_free(__isl_take isl_access_info *acc);
5506 __isl_give isl_flow *isl_access_info_compute_flow(
5507 __isl_take isl_access_info *acc);
5509 int isl_flow_foreach(__isl_keep isl_flow *deps,
5510 int (*fn)(__isl_take isl_map *dep, int must,
5511 void *dep_user, void *user),
5513 __isl_give isl_map *isl_flow_get_no_source(
5514 __isl_keep isl_flow *deps, int must);
5515 void isl_flow_free(__isl_take isl_flow *deps);
5517 The function C<isl_access_info_compute_flow> performs the actual
5518 dependence analysis. The other functions are used to construct
5519 the input for this function or to read off the output.
5521 The input is collected in an C<isl_access_info>, which can
5522 be created through a call to C<isl_access_info_alloc>.
5523 The arguments to this functions are the sink access relation
5524 C<sink>, a token C<sink_user> used to identify the sink
5525 access to the user, a callback function for specifying the
5526 relative order of source and sink accesses, and the number
5527 of source access relations that will be added.
5528 The callback function has type C<int (*)(void *first, void *second)>.
5529 The function is called with two user supplied tokens identifying
5530 either a source or the sink and it should return the shared nesting
5531 level and the relative order of the two accesses.
5532 In particular, let I<n> be the number of loops shared by
5533 the two accesses. If C<first> precedes C<second> textually,
5534 then the function should return I<2 * n + 1>; otherwise,
5535 it should return I<2 * n>.
5536 The sources can be added to the C<isl_access_info> by performing
5537 (at most) C<max_source> calls to C<isl_access_info_add_source>.
5538 C<must> indicates whether the source is a I<must> access
5539 or a I<may> access. Note that a multi-valued access relation
5540 should only be marked I<must> if every iteration in the domain
5541 of the relation accesses I<all> elements in its image.
5542 The C<source_user> token is again used to identify
5543 the source access. The range of the source access relation
5544 C<source> should have the same dimension as the range
5545 of the sink access relation.
5546 The C<isl_access_info_free> function should usually not be
5547 called explicitly, because it is called implicitly by
5548 C<isl_access_info_compute_flow>.
5550 The result of the dependence analysis is collected in an
5551 C<isl_flow>. There may be elements of
5552 the sink access for which no preceding source access could be
5553 found or for which all preceding sources are I<may> accesses.
5554 The relations containing these elements can be obtained through
5555 calls to C<isl_flow_get_no_source>, the first with C<must> set
5556 and the second with C<must> unset.
5557 In the case of standard flow dependence analysis,
5558 with the sink a read and the sources I<must> writes,
5559 the first relation corresponds to the reads from uninitialized
5560 array elements and the second relation is empty.
5561 The actual flow dependences can be extracted using
5562 C<isl_flow_foreach>. This function will call the user-specified
5563 callback function C<fn> for each B<non-empty> dependence between
5564 a source and the sink. The callback function is called
5565 with four arguments, the actual flow dependence relation
5566 mapping source iterations to sink iterations, a boolean that
5567 indicates whether it is a I<must> or I<may> dependence, a token
5568 identifying the source and an additional C<void *> with value
5569 equal to the third argument of the C<isl_flow_foreach> call.
5570 A dependence is marked I<must> if it originates from a I<must>
5571 source and if it is not followed by any I<may> sources.
5573 After finishing with an C<isl_flow>, the user should call
5574 C<isl_flow_free> to free all associated memory.
5576 A higher-level interface to dependence analysis is provided
5577 by the following function.
5579 #include <isl/flow.h>
5581 int isl_union_map_compute_flow(__isl_take isl_union_map *sink,
5582 __isl_take isl_union_map *must_source,
5583 __isl_take isl_union_map *may_source,
5584 __isl_take isl_union_map *schedule,
5585 __isl_give isl_union_map **must_dep,
5586 __isl_give isl_union_map **may_dep,
5587 __isl_give isl_union_map **must_no_source,
5588 __isl_give isl_union_map **may_no_source);
5590 The arrays are identified by the tuple names of the ranges
5591 of the accesses. The iteration domains by the tuple names
5592 of the domains of the accesses and of the schedule.
5593 The relative order of the iteration domains is given by the
5594 schedule. The relations returned through C<must_no_source>
5595 and C<may_no_source> are subsets of C<sink>.
5596 Any of C<must_dep>, C<may_dep>, C<must_no_source>
5597 or C<may_no_source> may be C<NULL>, but a C<NULL> value for
5598 any of the other arguments is treated as an error.
5600 =head3 Interaction with Dependence Analysis
5602 During the dependence analysis, we frequently need to perform
5603 the following operation. Given a relation between sink iterations
5604 and potential source iterations from a particular source domain,
5605 what is the last potential source iteration corresponding to each
5606 sink iteration. It can sometimes be convenient to adjust
5607 the set of potential source iterations before or after each such operation.
5608 The prototypical example is fuzzy array dataflow analysis,
5609 where we need to analyze if, based on data-dependent constraints,
5610 the sink iteration can ever be executed without one or more of
5611 the corresponding potential source iterations being executed.
5612 If so, we can introduce extra parameters and select an unknown
5613 but fixed source iteration from the potential source iterations.
5614 To be able to perform such manipulations, C<isl> provides the following
5617 #include <isl/flow.h>
5619 typedef __isl_give isl_restriction *(*isl_access_restrict)(
5620 __isl_keep isl_map *source_map,
5621 __isl_keep isl_set *sink, void *source_user,
5623 __isl_give isl_access_info *isl_access_info_set_restrict(
5624 __isl_take isl_access_info *acc,
5625 isl_access_restrict fn, void *user);
5627 The function C<isl_access_info_set_restrict> should be called
5628 before calling C<isl_access_info_compute_flow> and registers a callback function
5629 that will be called any time C<isl> is about to compute the last
5630 potential source. The first argument is the (reverse) proto-dependence,
5631 mapping sink iterations to potential source iterations.
5632 The second argument represents the sink iterations for which
5633 we want to compute the last source iteration.
5634 The third argument is the token corresponding to the source
5635 and the final argument is the token passed to C<isl_access_info_set_restrict>.
5636 The callback is expected to return a restriction on either the input or
5637 the output of the operation computing the last potential source.
5638 If the input needs to be restricted then restrictions are needed
5639 for both the source and the sink iterations. The sink iterations
5640 and the potential source iterations will be intersected with these sets.
5641 If the output needs to be restricted then only a restriction on the source
5642 iterations is required.
5643 If any error occurs, the callback should return C<NULL>.
5644 An C<isl_restriction> object can be created, freed and inspected
5645 using the following functions.
5647 #include <isl/flow.h>
5649 __isl_give isl_restriction *isl_restriction_input(
5650 __isl_take isl_set *source_restr,
5651 __isl_take isl_set *sink_restr);
5652 __isl_give isl_restriction *isl_restriction_output(
5653 __isl_take isl_set *source_restr);
5654 __isl_give isl_restriction *isl_restriction_none(
5655 __isl_take isl_map *source_map);
5656 __isl_give isl_restriction *isl_restriction_empty(
5657 __isl_take isl_map *source_map);
5658 void *isl_restriction_free(
5659 __isl_take isl_restriction *restr);
5660 isl_ctx *isl_restriction_get_ctx(
5661 __isl_keep isl_restriction *restr);
5663 C<isl_restriction_none> and C<isl_restriction_empty> are special
5664 cases of C<isl_restriction_input>. C<isl_restriction_none>
5665 is essentially equivalent to
5667 isl_restriction_input(isl_set_universe(
5668 isl_space_range(isl_map_get_space(source_map))),
5670 isl_space_domain(isl_map_get_space(source_map))));
5672 whereas C<isl_restriction_empty> is essentially equivalent to
5674 isl_restriction_input(isl_set_empty(
5675 isl_space_range(isl_map_get_space(source_map))),
5677 isl_space_domain(isl_map_get_space(source_map))));
5681 B<The functionality described in this section is fairly new
5682 and may be subject to change.>
5684 #include <isl/schedule.h>
5685 __isl_give isl_schedule *
5686 isl_schedule_constraints_compute_schedule(
5687 __isl_take isl_schedule_constraints *sc);
5688 void *isl_schedule_free(__isl_take isl_schedule *sched);
5690 The function C<isl_schedule_constraints_compute_schedule> can be
5691 used to compute a schedule that satisfy the given schedule constraints.
5692 These schedule constraints include the iteration domain for which
5693 a schedule should be computed and dependences between pairs of
5694 iterations. In particular, these dependences include
5695 I<validity> dependences and I<proximity> dependences.
5696 By default, the algorithm used to construct the schedule is similar
5697 to that of C<Pluto>.
5698 Alternatively, Feautrier's multi-dimensional scheduling algorithm can
5700 The generated schedule respects all validity dependences.
5701 That is, all dependence distances over these dependences in the
5702 scheduled space are lexicographically positive.
5703 The default algorithm tries to ensure that the dependence distances
5704 over coincidence constraints are zero and to minimize the
5705 dependence distances over proximity dependences.
5706 Moreover, it tries to obtain sequences (bands) of schedule dimensions
5707 for groups of domains where the dependence distances over validity
5708 dependences have only non-negative values.
5709 When using Feautrier's algorithm, the coincidence and proximity constraints
5710 are only taken into account during the extension to a
5711 full-dimensional schedule.
5713 An C<isl_schedule_constraints> object can be constructed
5714 and manipulated using the following functions.
5716 #include <isl/schedule.h>
5717 __isl_give isl_schedule_constraints *
5718 isl_schedule_constraints_copy(
5719 __isl_keep isl_schedule_constraints *sc);
5720 __isl_give isl_schedule_constraints *
5721 isl_schedule_constraints_on_domain(
5722 __isl_take isl_union_set *domain);
5723 isl_ctx *isl_schedule_constraints_get_ctx(
5724 __isl_keep isl_schedule_constraints *sc);
5725 __isl_give isl_schedule_constraints *
5726 isl_schedule_constraints_set_validity(
5727 __isl_take isl_schedule_constraints *sc,
5728 __isl_take isl_union_map *validity);
5729 __isl_give isl_schedule_constraints *
5730 isl_schedule_constraints_set_coincidence(
5731 __isl_take isl_schedule_constraints *sc,
5732 __isl_take isl_union_map *coincidence);
5733 __isl_give isl_schedule_constraints *
5734 isl_schedule_constraints_set_proximity(
5735 __isl_take isl_schedule_constraints *sc,
5736 __isl_take isl_union_map *proximity);
5737 __isl_give isl_schedule_constraints *
5738 isl_schedule_constraints_set_conditional_validity(
5739 __isl_take isl_schedule_constraints *sc,
5740 __isl_take isl_union_map *condition,
5741 __isl_take isl_union_map *validity);
5742 void *isl_schedule_constraints_free(
5743 __isl_take isl_schedule_constraints *sc);
5745 The initial C<isl_schedule_constraints> object created by
5746 C<isl_schedule_constraints_on_domain> does not impose any constraints.
5747 That is, it has an empty set of dependences.
5748 The function C<isl_schedule_constraints_set_validity> replaces the
5749 validity dependences, mapping domain elements I<i> to domain
5750 elements that should be scheduled after I<i>.
5751 The function C<isl_schedule_constraints_set_coincidence> replaces the
5752 coincidence dependences, mapping domain elements I<i> to domain
5753 elements that should be scheduled together with I<I>, if possible.
5754 The function C<isl_schedule_constraints_set_proximity> replaces the
5755 proximity dependences, mapping domain elements I<i> to domain
5756 elements that should be scheduled either before I<I>
5757 or as early as possible after I<i>.
5759 The function C<isl_schedule_constraints_set_conditional_validity>
5760 replaces the conditional validity constraints.
5761 A conditional validity constraint is only imposed when any of the corresponding
5762 conditions is satisfied, i.e., when any of them is non-zero.
5763 That is, the scheduler ensures that within each band if the dependence
5764 distances over the condition constraints are not all zero
5765 then all corresponding conditional validity constraints are respected.
5766 A conditional validity constraint corresponds to a condition
5767 if the two are adjacent, i.e., if the domain of one relation intersect
5768 the range of the other relation.
5769 The typical use case of conditional validity constraints is
5770 to allow order constraints between live ranges to be violated
5771 as long as the live ranges themselves are local to the band.
5772 To allow more fine-grained control over which conditions correspond
5773 to which conditional validity constraints, the domains and ranges
5774 of these relations may include I<tags>. That is, the domains and
5775 ranges of those relation may themselves be wrapped relations
5776 where the iteration domain appears in the domain of those wrapped relations
5777 and the range of the wrapped relations can be arbitrarily chosen
5778 by the user. Conditions and conditional validity constraints are only
5779 considere adjacent to each other if the entire wrapped relation matches.
5780 In particular, a relation with a tag will never be considered adjacent
5781 to a relation without a tag.
5783 The following function computes a schedule directly from
5784 an iteration domain and validity and proximity dependences
5785 and is implemented in terms of the functions described above.
5786 The use of C<isl_union_set_compute_schedule> is discouraged.
5788 #include <isl/schedule.h>
5789 __isl_give isl_schedule *isl_union_set_compute_schedule(
5790 __isl_take isl_union_set *domain,
5791 __isl_take isl_union_map *validity,
5792 __isl_take isl_union_map *proximity);
5794 A mapping from the domains to the scheduled space can be obtained
5795 from an C<isl_schedule> using the following function.
5797 __isl_give isl_union_map *isl_schedule_get_map(
5798 __isl_keep isl_schedule *sched);
5800 A representation of the schedule can be printed using
5802 __isl_give isl_printer *isl_printer_print_schedule(
5803 __isl_take isl_printer *p,
5804 __isl_keep isl_schedule *schedule);
5806 A representation of the schedule as a forest of bands can be obtained
5807 using the following function.
5809 __isl_give isl_band_list *isl_schedule_get_band_forest(
5810 __isl_keep isl_schedule *schedule);
5812 The individual bands can be visited in depth-first post-order
5813 using the following function.
5815 #include <isl/schedule.h>
5816 int isl_schedule_foreach_band(
5817 __isl_keep isl_schedule *sched,
5818 int (*fn)(__isl_keep isl_band *band, void *user),
5821 The list can be manipulated as explained in L<"Lists">.
5822 The bands inside the list can be copied and freed using the following
5825 #include <isl/band.h>
5826 __isl_give isl_band *isl_band_copy(
5827 __isl_keep isl_band *band);
5828 void *isl_band_free(__isl_take isl_band *band);
5830 Each band contains zero or more scheduling dimensions.
5831 These are referred to as the members of the band.
5832 The section of the schedule that corresponds to the band is
5833 referred to as the partial schedule of the band.
5834 For those nodes that participate in a band, the outer scheduling
5835 dimensions form the prefix schedule, while the inner scheduling
5836 dimensions form the suffix schedule.
5837 That is, if we take a cut of the band forest, then the union of
5838 the concatenations of the prefix, partial and suffix schedules of
5839 each band in the cut is equal to the entire schedule (modulo
5840 some possible padding at the end with zero scheduling dimensions).
5841 The properties of a band can be inspected using the following functions.
5843 #include <isl/band.h>
5844 isl_ctx *isl_band_get_ctx(__isl_keep isl_band *band);
5846 int isl_band_has_children(__isl_keep isl_band *band);
5847 __isl_give isl_band_list *isl_band_get_children(
5848 __isl_keep isl_band *band);
5850 __isl_give isl_union_map *isl_band_get_prefix_schedule(
5851 __isl_keep isl_band *band);
5852 __isl_give isl_union_map *isl_band_get_partial_schedule(
5853 __isl_keep isl_band *band);
5854 __isl_give isl_union_map *isl_band_get_suffix_schedule(
5855 __isl_keep isl_band *band);
5857 int isl_band_n_member(__isl_keep isl_band *band);
5858 int isl_band_member_is_coincident(
5859 __isl_keep isl_band *band, int pos);
5861 int isl_band_list_foreach_band(
5862 __isl_keep isl_band_list *list,
5863 int (*fn)(__isl_keep isl_band *band, void *user),
5866 Note that a scheduling dimension is considered to be ``coincident''
5867 if it satisfies the coincidence constraints within its band.
5868 That is, if the dependence distances of the coincidence
5869 constraints are all zero in that direction (for fixed
5870 iterations of outer bands).
5871 Like C<isl_schedule_foreach_band>,
5872 the function C<isl_band_list_foreach_band> calls C<fn> on the bands
5873 in depth-first post-order.
5875 A band can be tiled using the following function.
5877 #include <isl/band.h>
5878 int isl_band_tile(__isl_keep isl_band *band,
5879 __isl_take isl_vec *sizes);
5881 int isl_options_set_tile_scale_tile_loops(isl_ctx *ctx,
5883 int isl_options_get_tile_scale_tile_loops(isl_ctx *ctx);
5884 int isl_options_set_tile_shift_point_loops(isl_ctx *ctx,
5886 int isl_options_get_tile_shift_point_loops(isl_ctx *ctx);
5888 The C<isl_band_tile> function tiles the band using the given tile sizes
5889 inside its schedule.
5890 A new child band is created to represent the point loops and it is
5891 inserted between the modified band and its children.
5892 The C<tile_scale_tile_loops> option specifies whether the tile
5893 loops iterators should be scaled by the tile sizes.
5894 If the C<tile_shift_point_loops> option is set, then the point loops
5895 are shifted to start at zero.
5897 A band can be split into two nested bands using the following function.
5899 int isl_band_split(__isl_keep isl_band *band, int pos);
5901 The resulting outer band contains the first C<pos> dimensions of C<band>
5902 while the inner band contains the remaining dimensions.
5904 A representation of the band can be printed using
5906 #include <isl/band.h>
5907 __isl_give isl_printer *isl_printer_print_band(
5908 __isl_take isl_printer *p,
5909 __isl_keep isl_band *band);
5913 #include <isl/schedule.h>
5914 int isl_options_set_schedule_max_coefficient(
5915 isl_ctx *ctx, int val);
5916 int isl_options_get_schedule_max_coefficient(
5918 int isl_options_set_schedule_max_constant_term(
5919 isl_ctx *ctx, int val);
5920 int isl_options_get_schedule_max_constant_term(
5922 int isl_options_set_schedule_fuse(isl_ctx *ctx, int val);
5923 int isl_options_get_schedule_fuse(isl_ctx *ctx);
5924 int isl_options_set_schedule_maximize_band_depth(
5925 isl_ctx *ctx, int val);
5926 int isl_options_get_schedule_maximize_band_depth(
5928 int isl_options_set_schedule_outer_coincidence(
5929 isl_ctx *ctx, int val);
5930 int isl_options_get_schedule_outer_coincidence(
5932 int isl_options_set_schedule_split_scaled(
5933 isl_ctx *ctx, int val);
5934 int isl_options_get_schedule_split_scaled(
5936 int isl_options_set_schedule_algorithm(
5937 isl_ctx *ctx, int val);
5938 int isl_options_get_schedule_algorithm(
5940 int isl_options_set_schedule_separate_components(
5941 isl_ctx *ctx, int val);
5942 int isl_options_get_schedule_separate_components(
5947 =item * schedule_max_coefficient
5949 This option enforces that the coefficients for variable and parameter
5950 dimensions in the calculated schedule are not larger than the specified value.
5951 This option can significantly increase the speed of the scheduling calculation
5952 and may also prevent fusing of unrelated dimensions. A value of -1 means that
5953 this option does not introduce bounds on the variable or parameter
5956 =item * schedule_max_constant_term
5958 This option enforces that the constant coefficients in the calculated schedule
5959 are not larger than the maximal constant term. This option can significantly
5960 increase the speed of the scheduling calculation and may also prevent fusing of
5961 unrelated dimensions. A value of -1 means that this option does not introduce
5962 bounds on the constant coefficients.
5964 =item * schedule_fuse
5966 This option controls the level of fusion.
5967 If this option is set to C<ISL_SCHEDULE_FUSE_MIN>, then loops in the
5968 resulting schedule will be distributed as much as possible.
5969 If this option is set to C<ISL_SCHEDULE_FUSE_MAX>, then C<isl> will
5970 try to fuse loops in the resulting schedule.
5972 =item * schedule_maximize_band_depth
5974 If this option is set, we do not split bands at the point
5975 where we detect splitting is necessary. Instead, we
5976 backtrack and split bands as early as possible. This
5977 reduces the number of splits and maximizes the width of
5978 the bands. Wider bands give more possibilities for tiling.
5979 Note that if the C<schedule_fuse> option is set to C<ISL_SCHEDULE_FUSE_MIN>,
5980 then bands will be split as early as possible, even if there is no need.
5981 The C<schedule_maximize_band_depth> option therefore has no effect in this case.
5983 =item * schedule_outer_coincidence
5985 If this option is set, then we try to construct schedules
5986 where the outermost scheduling dimension in each band
5987 satisfies the coincidence constraints.
5989 =item * schedule_split_scaled
5991 If this option is set, then we try to construct schedules in which the
5992 constant term is split off from the linear part if the linear parts of
5993 the scheduling rows for all nodes in the graphs have a common non-trivial
5995 The constant term is then placed in a separate band and the linear
5998 =item * schedule_algorithm
6000 Selects the scheduling algorithm to be used.
6001 Available scheduling algorithms are C<ISL_SCHEDULE_ALGORITHM_ISL>
6002 and C<ISL_SCHEDULE_ALGORITHM_FEAUTRIER>.
6004 =item * schedule_separate_components
6006 If at any point the dependence graph contains any (weakly connected) components,
6007 then these components are scheduled separately.
6008 If this option is not set, then some iterations of the domains
6009 in these components may be scheduled together.
6010 If this option is set, then the components are given consecutive
6015 =head2 AST Generation
6017 This section describes the C<isl> functionality for generating
6018 ASTs that visit all the elements
6019 in a domain in an order specified by a schedule.
6020 In particular, given a C<isl_union_map>, an AST is generated
6021 that visits all the elements in the domain of the C<isl_union_map>
6022 according to the lexicographic order of the corresponding image
6023 element(s). If the range of the C<isl_union_map> consists of
6024 elements in more than one space, then each of these spaces is handled
6025 separately in an arbitrary order.
6026 It should be noted that the image elements only specify the I<order>
6027 in which the corresponding domain elements should be visited.
6028 No direct relation between the image elements and the loop iterators
6029 in the generated AST should be assumed.
6031 Each AST is generated within a build. The initial build
6032 simply specifies the constraints on the parameters (if any)
6033 and can be created, inspected, copied and freed using the following functions.
6035 #include <isl/ast_build.h>
6036 __isl_give isl_ast_build *isl_ast_build_from_context(
6037 __isl_take isl_set *set);
6038 isl_ctx *isl_ast_build_get_ctx(
6039 __isl_keep isl_ast_build *build);
6040 __isl_give isl_ast_build *isl_ast_build_copy(
6041 __isl_keep isl_ast_build *build);
6042 void *isl_ast_build_free(
6043 __isl_take isl_ast_build *build);
6045 The C<set> argument is usually a parameter set with zero or more parameters.
6046 More C<isl_ast_build> functions are described in L</"Nested AST Generation">
6047 and L</"Fine-grained Control over AST Generation">.
6048 Finally, the AST itself can be constructed using the following
6051 #include <isl/ast_build.h>
6052 __isl_give isl_ast_node *isl_ast_build_ast_from_schedule(
6053 __isl_keep isl_ast_build *build,
6054 __isl_take isl_union_map *schedule);
6056 =head3 Inspecting the AST
6058 The basic properties of an AST node can be obtained as follows.
6060 #include <isl/ast.h>
6061 isl_ctx *isl_ast_node_get_ctx(
6062 __isl_keep isl_ast_node *node);
6063 enum isl_ast_node_type isl_ast_node_get_type(
6064 __isl_keep isl_ast_node *node);
6066 The type of an AST node is one of
6067 C<isl_ast_node_for>,
6069 C<isl_ast_node_block> or
6070 C<isl_ast_node_user>.
6071 An C<isl_ast_node_for> represents a for node.
6072 An C<isl_ast_node_if> represents an if node.
6073 An C<isl_ast_node_block> represents a compound node.
6074 An C<isl_ast_node_user> represents an expression statement.
6075 An expression statement typically corresponds to a domain element, i.e.,
6076 one of the elements that is visited by the AST.
6078 Each type of node has its own additional properties.
6080 #include <isl/ast.h>
6081 __isl_give isl_ast_expr *isl_ast_node_for_get_iterator(
6082 __isl_keep isl_ast_node *node);
6083 __isl_give isl_ast_expr *isl_ast_node_for_get_init(
6084 __isl_keep isl_ast_node *node);
6085 __isl_give isl_ast_expr *isl_ast_node_for_get_cond(
6086 __isl_keep isl_ast_node *node);
6087 __isl_give isl_ast_expr *isl_ast_node_for_get_inc(
6088 __isl_keep isl_ast_node *node);
6089 __isl_give isl_ast_node *isl_ast_node_for_get_body(
6090 __isl_keep isl_ast_node *node);
6091 int isl_ast_node_for_is_degenerate(
6092 __isl_keep isl_ast_node *node);
6094 An C<isl_ast_for> is considered degenerate if it is known to execute
6097 #include <isl/ast.h>
6098 __isl_give isl_ast_expr *isl_ast_node_if_get_cond(
6099 __isl_keep isl_ast_node *node);
6100 __isl_give isl_ast_node *isl_ast_node_if_get_then(
6101 __isl_keep isl_ast_node *node);
6102 int isl_ast_node_if_has_else(
6103 __isl_keep isl_ast_node *node);
6104 __isl_give isl_ast_node *isl_ast_node_if_get_else(
6105 __isl_keep isl_ast_node *node);
6107 __isl_give isl_ast_node_list *
6108 isl_ast_node_block_get_children(
6109 __isl_keep isl_ast_node *node);
6111 __isl_give isl_ast_expr *isl_ast_node_user_get_expr(
6112 __isl_keep isl_ast_node *node);
6114 Each of the returned C<isl_ast_expr>s can in turn be inspected using
6115 the following functions.
6117 #include <isl/ast.h>
6118 isl_ctx *isl_ast_expr_get_ctx(
6119 __isl_keep isl_ast_expr *expr);
6120 enum isl_ast_expr_type isl_ast_expr_get_type(
6121 __isl_keep isl_ast_expr *expr);
6123 The type of an AST expression is one of
6125 C<isl_ast_expr_id> or
6126 C<isl_ast_expr_int>.
6127 An C<isl_ast_expr_op> represents the result of an operation.
6128 An C<isl_ast_expr_id> represents an identifier.
6129 An C<isl_ast_expr_int> represents an integer value.
6131 Each type of expression has its own additional properties.
6133 #include <isl/ast.h>
6134 enum isl_ast_op_type isl_ast_expr_get_op_type(
6135 __isl_keep isl_ast_expr *expr);
6136 int isl_ast_expr_get_op_n_arg(__isl_keep isl_ast_expr *expr);
6137 __isl_give isl_ast_expr *isl_ast_expr_get_op_arg(
6138 __isl_keep isl_ast_expr *expr, int pos);
6139 int isl_ast_node_foreach_ast_op_type(
6140 __isl_keep isl_ast_node *node,
6141 int (*fn)(enum isl_ast_op_type type, void *user),
6144 C<isl_ast_expr_get_op_type> returns the type of the operation
6145 performed. C<isl_ast_expr_get_op_n_arg> returns the number of
6146 arguments. C<isl_ast_expr_get_op_arg> returns the specified
6148 C<isl_ast_node_foreach_ast_op_type> calls C<fn> for each distinct
6149 C<isl_ast_op_type> that appears in C<node>.
6150 The operation type is one of the following.
6154 =item C<isl_ast_op_and>
6156 Logical I<and> of two arguments.
6157 Both arguments can be evaluated.
6159 =item C<isl_ast_op_and_then>
6161 Logical I<and> of two arguments.
6162 The second argument can only be evaluated if the first evaluates to true.
6164 =item C<isl_ast_op_or>
6166 Logical I<or> of two arguments.
6167 Both arguments can be evaluated.
6169 =item C<isl_ast_op_or_else>
6171 Logical I<or> of two arguments.
6172 The second argument can only be evaluated if the first evaluates to false.
6174 =item C<isl_ast_op_max>
6176 Maximum of two or more arguments.
6178 =item C<isl_ast_op_min>
6180 Minimum of two or more arguments.
6182 =item C<isl_ast_op_minus>
6186 =item C<isl_ast_op_add>
6188 Sum of two arguments.
6190 =item C<isl_ast_op_sub>
6192 Difference of two arguments.
6194 =item C<isl_ast_op_mul>
6196 Product of two arguments.
6198 =item C<isl_ast_op_div>
6200 Exact division. That is, the result is known to be an integer.
6202 =item C<isl_ast_op_fdiv_q>
6204 Result of integer division, rounded towards negative
6207 =item C<isl_ast_op_pdiv_q>
6209 Result of integer division, where dividend is known to be non-negative.
6211 =item C<isl_ast_op_pdiv_r>
6213 Remainder of integer division, where dividend is known to be non-negative.
6215 =item C<isl_ast_op_cond>
6217 Conditional operator defined on three arguments.
6218 If the first argument evaluates to true, then the result
6219 is equal to the second argument. Otherwise, the result
6220 is equal to the third argument.
6221 The second and third argument may only be evaluated if
6222 the first argument evaluates to true and false, respectively.
6223 Corresponds to C<a ? b : c> in C.
6225 =item C<isl_ast_op_select>
6227 Conditional operator defined on three arguments.
6228 If the first argument evaluates to true, then the result
6229 is equal to the second argument. Otherwise, the result
6230 is equal to the third argument.
6231 The second and third argument may be evaluated independently
6232 of the value of the first argument.
6233 Corresponds to C<a * b + (1 - a) * c> in C.
6235 =item C<isl_ast_op_eq>
6239 =item C<isl_ast_op_le>
6241 Less than or equal relation.
6243 =item C<isl_ast_op_lt>
6247 =item C<isl_ast_op_ge>
6249 Greater than or equal relation.
6251 =item C<isl_ast_op_gt>
6253 Greater than relation.
6255 =item C<isl_ast_op_call>
6258 The number of arguments of the C<isl_ast_expr> is one more than
6259 the number of arguments in the function call, the first argument
6260 representing the function being called.
6262 =item C<isl_ast_op_access>
6265 The number of arguments of the C<isl_ast_expr> is one more than
6266 the number of index expressions in the array access, the first argument
6267 representing the array being accessed.
6269 =item C<isl_ast_op_member>
6272 This operation has two arguments, a structure and the name of
6273 the member of the structure being accessed.
6277 #include <isl/ast.h>
6278 __isl_give isl_id *isl_ast_expr_get_id(
6279 __isl_keep isl_ast_expr *expr);
6281 Return the identifier represented by the AST expression.
6283 #include <isl/ast.h>
6284 __isl_give isl_val *isl_ast_expr_get_val(
6285 __isl_keep isl_ast_expr *expr);
6287 Return the integer represented by the AST expression.
6289 =head3 Properties of ASTs
6291 #include <isl/ast.h>
6292 int isl_ast_expr_is_equal(__isl_keep isl_ast_expr *expr1,
6293 __isl_keep isl_ast_expr *expr2);
6295 Check if two C<isl_ast_expr>s are equal to each other.
6297 =head3 Manipulating and printing the AST
6299 AST nodes can be copied and freed using the following functions.
6301 #include <isl/ast.h>
6302 __isl_give isl_ast_node *isl_ast_node_copy(
6303 __isl_keep isl_ast_node *node);
6304 void *isl_ast_node_free(__isl_take isl_ast_node *node);
6306 AST expressions can be copied and freed using the following functions.
6308 #include <isl/ast.h>
6309 __isl_give isl_ast_expr *isl_ast_expr_copy(
6310 __isl_keep isl_ast_expr *expr);
6311 void *isl_ast_expr_free(__isl_take isl_ast_expr *expr);
6313 New AST expressions can be created either directly or within
6314 the context of an C<isl_ast_build>.
6316 #include <isl/ast.h>
6317 __isl_give isl_ast_expr *isl_ast_expr_from_val(
6318 __isl_take isl_val *v);
6319 __isl_give isl_ast_expr *isl_ast_expr_from_id(
6320 __isl_take isl_id *id);
6321 __isl_give isl_ast_expr *isl_ast_expr_neg(
6322 __isl_take isl_ast_expr *expr);
6323 __isl_give isl_ast_expr *isl_ast_expr_add(
6324 __isl_take isl_ast_expr *expr1,
6325 __isl_take isl_ast_expr *expr2);
6326 __isl_give isl_ast_expr *isl_ast_expr_sub(
6327 __isl_take isl_ast_expr *expr1,
6328 __isl_take isl_ast_expr *expr2);
6329 __isl_give isl_ast_expr *isl_ast_expr_mul(
6330 __isl_take isl_ast_expr *expr1,
6331 __isl_take isl_ast_expr *expr2);
6332 __isl_give isl_ast_expr *isl_ast_expr_div(
6333 __isl_take isl_ast_expr *expr1,
6334 __isl_take isl_ast_expr *expr2);
6335 __isl_give isl_ast_expr *isl_ast_expr_and(
6336 __isl_take isl_ast_expr *expr1,
6337 __isl_take isl_ast_expr *expr2)
6338 __isl_give isl_ast_expr *isl_ast_expr_or(
6339 __isl_take isl_ast_expr *expr1,
6340 __isl_take isl_ast_expr *expr2)
6341 __isl_give isl_ast_expr *isl_ast_expr_access(
6342 __isl_take isl_ast_expr *array,
6343 __isl_take isl_ast_expr_list *indices);
6345 #include <isl/ast_build.h>
6346 __isl_give isl_ast_expr *isl_ast_build_expr_from_pw_aff(
6347 __isl_keep isl_ast_build *build,
6348 __isl_take isl_pw_aff *pa);
6349 __isl_give isl_ast_expr *
6350 isl_ast_build_access_from_pw_multi_aff(
6351 __isl_keep isl_ast_build *build,
6352 __isl_take isl_pw_multi_aff *pma);
6353 __isl_give isl_ast_expr *
6354 isl_ast_build_access_from_multi_pw_aff(
6355 __isl_keep isl_ast_build *build,
6356 __isl_take isl_multi_pw_aff *mpa);
6357 __isl_give isl_ast_expr *
6358 isl_ast_build_call_from_pw_multi_aff(
6359 __isl_keep isl_ast_build *build,
6360 __isl_take isl_pw_multi_aff *pma);
6361 __isl_give isl_ast_expr *
6362 isl_ast_build_call_from_multi_pw_aff(
6363 __isl_keep isl_ast_build *build,
6364 __isl_take isl_multi_pw_aff *mpa);
6366 The domains of C<pa>, C<mpa> and C<pma> should correspond
6367 to the schedule space of C<build>.
6368 The tuple id of C<mpa> or C<pma> is used as the array being accessed or
6369 the function being called.
6370 If the accessed space is a nested relation, then it is taken
6371 to represent an access of the member specified by the range
6372 of this nested relation of the structure specified by the domain
6373 of the nested relation.
6375 The following functions can be used to modify an C<isl_ast_expr>.
6377 #include <isl/ast.h>
6378 __isl_give isl_ast_expr *isl_ast_expr_set_op_arg(
6379 __isl_take isl_ast_expr *expr, int pos,
6380 __isl_take isl_ast_expr *arg);
6382 Replace the argument of C<expr> at position C<pos> by C<arg>.
6384 #include <isl/ast.h>
6385 __isl_give isl_ast_expr *isl_ast_expr_substitute_ids(
6386 __isl_take isl_ast_expr *expr,
6387 __isl_take isl_id_to_ast_expr *id2expr);
6389 The function C<isl_ast_expr_substitute_ids> replaces the
6390 subexpressions of C<expr> of type C<isl_ast_expr_id>
6391 by the corresponding expression in C<id2expr>, if there is any.
6394 User specified data can be attached to an C<isl_ast_node> and obtained
6395 from the same C<isl_ast_node> using the following functions.
6397 #include <isl/ast.h>
6398 __isl_give isl_ast_node *isl_ast_node_set_annotation(
6399 __isl_take isl_ast_node *node,
6400 __isl_take isl_id *annotation);
6401 __isl_give isl_id *isl_ast_node_get_annotation(
6402 __isl_keep isl_ast_node *node);
6404 Basic printing can be performed using the following functions.
6406 #include <isl/ast.h>
6407 __isl_give isl_printer *isl_printer_print_ast_expr(
6408 __isl_take isl_printer *p,
6409 __isl_keep isl_ast_expr *expr);
6410 __isl_give isl_printer *isl_printer_print_ast_node(
6411 __isl_take isl_printer *p,
6412 __isl_keep isl_ast_node *node);
6414 More advanced printing can be performed using the following functions.
6416 #include <isl/ast.h>
6417 __isl_give isl_printer *isl_ast_op_type_print_macro(
6418 enum isl_ast_op_type type,
6419 __isl_take isl_printer *p);
6420 __isl_give isl_printer *isl_ast_node_print_macros(
6421 __isl_keep isl_ast_node *node,
6422 __isl_take isl_printer *p);
6423 __isl_give isl_printer *isl_ast_node_print(
6424 __isl_keep isl_ast_node *node,
6425 __isl_take isl_printer *p,
6426 __isl_take isl_ast_print_options *options);
6427 __isl_give isl_printer *isl_ast_node_for_print(
6428 __isl_keep isl_ast_node *node,
6429 __isl_take isl_printer *p,
6430 __isl_take isl_ast_print_options *options);
6431 __isl_give isl_printer *isl_ast_node_if_print(
6432 __isl_keep isl_ast_node *node,
6433 __isl_take isl_printer *p,
6434 __isl_take isl_ast_print_options *options);
6436 While printing an C<isl_ast_node> in C<ISL_FORMAT_C>,
6437 C<isl> may print out an AST that makes use of macros such
6438 as C<floord>, C<min> and C<max>.
6439 C<isl_ast_op_type_print_macro> prints out the macro
6440 corresponding to a specific C<isl_ast_op_type>.
6441 C<isl_ast_node_print_macros> scans the C<isl_ast_node>
6442 for expressions where these macros would be used and prints
6443 out the required macro definitions.
6444 Essentially, C<isl_ast_node_print_macros> calls
6445 C<isl_ast_node_foreach_ast_op_type> with C<isl_ast_op_type_print_macro>
6446 as function argument.
6447 C<isl_ast_node_print>, C<isl_ast_node_for_print> and
6448 C<isl_ast_node_if_print> print an C<isl_ast_node>
6449 in C<ISL_FORMAT_C>, but allow for some extra control
6450 through an C<isl_ast_print_options> object.
6451 This object can be created using the following functions.
6453 #include <isl/ast.h>
6454 __isl_give isl_ast_print_options *
6455 isl_ast_print_options_alloc(isl_ctx *ctx);
6456 __isl_give isl_ast_print_options *
6457 isl_ast_print_options_copy(
6458 __isl_keep isl_ast_print_options *options);
6459 void *isl_ast_print_options_free(
6460 __isl_take isl_ast_print_options *options);
6462 __isl_give isl_ast_print_options *
6463 isl_ast_print_options_set_print_user(
6464 __isl_take isl_ast_print_options *options,
6465 __isl_give isl_printer *(*print_user)(
6466 __isl_take isl_printer *p,
6467 __isl_take isl_ast_print_options *options,
6468 __isl_keep isl_ast_node *node, void *user),
6470 __isl_give isl_ast_print_options *
6471 isl_ast_print_options_set_print_for(
6472 __isl_take isl_ast_print_options *options,
6473 __isl_give isl_printer *(*print_for)(
6474 __isl_take isl_printer *p,
6475 __isl_take isl_ast_print_options *options,
6476 __isl_keep isl_ast_node *node, void *user),
6479 The callback set by C<isl_ast_print_options_set_print_user>
6480 is called whenever a node of type C<isl_ast_node_user> needs to
6482 The callback set by C<isl_ast_print_options_set_print_for>
6483 is called whenever a node of type C<isl_ast_node_for> needs to
6485 Note that C<isl_ast_node_for_print> will I<not> call the
6486 callback set by C<isl_ast_print_options_set_print_for> on the node
6487 on which C<isl_ast_node_for_print> is called, but only on nested
6488 nodes of type C<isl_ast_node_for>. It is therefore safe to
6489 call C<isl_ast_node_for_print> from within the callback set by
6490 C<isl_ast_print_options_set_print_for>.
6492 The following option determines the type to be used for iterators
6493 while printing the AST.
6495 int isl_options_set_ast_iterator_type(
6496 isl_ctx *ctx, const char *val);
6497 const char *isl_options_get_ast_iterator_type(
6502 #include <isl/ast_build.h>
6503 int isl_options_set_ast_build_atomic_upper_bound(
6504 isl_ctx *ctx, int val);
6505 int isl_options_get_ast_build_atomic_upper_bound(
6507 int isl_options_set_ast_build_prefer_pdiv(isl_ctx *ctx,
6509 int isl_options_get_ast_build_prefer_pdiv(isl_ctx *ctx);
6510 int isl_options_set_ast_build_exploit_nested_bounds(
6511 isl_ctx *ctx, int val);
6512 int isl_options_get_ast_build_exploit_nested_bounds(
6514 int isl_options_set_ast_build_group_coscheduled(
6515 isl_ctx *ctx, int val);
6516 int isl_options_get_ast_build_group_coscheduled(
6518 int isl_options_set_ast_build_scale_strides(
6519 isl_ctx *ctx, int val);
6520 int isl_options_get_ast_build_scale_strides(
6522 int isl_options_set_ast_build_allow_else(isl_ctx *ctx,
6524 int isl_options_get_ast_build_allow_else(isl_ctx *ctx);
6525 int isl_options_set_ast_build_allow_or(isl_ctx *ctx,
6527 int isl_options_get_ast_build_allow_or(isl_ctx *ctx);
6531 =item * ast_build_atomic_upper_bound
6533 Generate loop upper bounds that consist of the current loop iterator,
6534 an operator and an expression not involving the iterator.
6535 If this option is not set, then the current loop iterator may appear
6536 several times in the upper bound.
6537 For example, when this option is turned off, AST generation
6540 [n] -> { A[i] -> [i] : 0 <= i <= 100, n }
6544 for (int c0 = 0; c0 <= 100 && n >= c0; c0 += 1)
6547 When the option is turned on, the following AST is generated
6549 for (int c0 = 0; c0 <= min(100, n); c0 += 1)
6552 =item * ast_build_prefer_pdiv
6554 If this option is turned off, then the AST generation will
6555 produce ASTs that may only contain C<isl_ast_op_fdiv_q>
6556 operators, but no C<isl_ast_op_pdiv_q> or
6557 C<isl_ast_op_pdiv_r> operators.
6558 If this options is turned on, then C<isl> will try to convert
6559 some of the C<isl_ast_op_fdiv_q> operators to (expressions containing)
6560 C<isl_ast_op_pdiv_q> or C<isl_ast_op_pdiv_r> operators.
6562 =item * ast_build_exploit_nested_bounds
6564 Simplify conditions based on bounds of nested for loops.
6565 In particular, remove conditions that are implied by the fact
6566 that one or more nested loops have at least one iteration,
6567 meaning that the upper bound is at least as large as the lower bound.
6568 For example, when this option is turned off, AST generation
6571 [N,M] -> { A[i,j] -> [i,j] : 0 <= i <= N and
6577 for (int c0 = 0; c0 <= N; c0 += 1)
6578 for (int c1 = 0; c1 <= M; c1 += 1)
6581 When the option is turned on, the following AST is generated
6583 for (int c0 = 0; c0 <= N; c0 += 1)
6584 for (int c1 = 0; c1 <= M; c1 += 1)
6587 =item * ast_build_group_coscheduled
6589 If two domain elements are assigned the same schedule point, then
6590 they may be executed in any order and they may even appear in different
6591 loops. If this options is set, then the AST generator will make
6592 sure that coscheduled domain elements do not appear in separate parts
6593 of the AST. This is useful in case of nested AST generation
6594 if the outer AST generation is given only part of a schedule
6595 and the inner AST generation should handle the domains that are
6596 coscheduled by this initial part of the schedule together.
6597 For example if an AST is generated for a schedule
6599 { A[i] -> [0]; B[i] -> [0] }
6601 then the C<isl_ast_build_set_create_leaf> callback described
6602 below may get called twice, once for each domain.
6603 Setting this option ensures that the callback is only called once
6604 on both domains together.
6606 =item * ast_build_separation_bounds
6608 This option specifies which bounds to use during separation.
6609 If this option is set to C<ISL_AST_BUILD_SEPARATION_BOUNDS_IMPLICIT>
6610 then all (possibly implicit) bounds on the current dimension will
6611 be used during separation.
6612 If this option is set to C<ISL_AST_BUILD_SEPARATION_BOUNDS_EXPLICIT>
6613 then only those bounds that are explicitly available will
6614 be used during separation.
6616 =item * ast_build_scale_strides
6618 This option specifies whether the AST generator is allowed
6619 to scale down iterators of strided loops.
6621 =item * ast_build_allow_else
6623 This option specifies whether the AST generator is allowed
6624 to construct if statements with else branches.
6626 =item * ast_build_allow_or
6628 This option specifies whether the AST generator is allowed
6629 to construct if conditions with disjunctions.
6633 =head3 Fine-grained Control over AST Generation
6635 Besides specifying the constraints on the parameters,
6636 an C<isl_ast_build> object can be used to control
6637 various aspects of the AST generation process.
6638 The most prominent way of control is through ``options'',
6639 which can be set using the following function.
6641 #include <isl/ast_build.h>
6642 __isl_give isl_ast_build *
6643 isl_ast_build_set_options(
6644 __isl_take isl_ast_build *control,
6645 __isl_take isl_union_map *options);
6647 The options are encoded in an <isl_union_map>.
6648 The domain of this union relation refers to the schedule domain,
6649 i.e., the range of the schedule passed to C<isl_ast_build_ast_from_schedule>.
6650 In the case of nested AST generation (see L</"Nested AST Generation">),
6651 the domain of C<options> should refer to the extra piece of the schedule.
6652 That is, it should be equal to the range of the wrapped relation in the
6653 range of the schedule.
6654 The range of the options can consist of elements in one or more spaces,
6655 the names of which determine the effect of the option.
6656 The values of the range typically also refer to the schedule dimension
6657 to which the option applies. In case of nested AST generation
6658 (see L</"Nested AST Generation">), these values refer to the position
6659 of the schedule dimension within the innermost AST generation.
6660 The constraints on the domain elements of
6661 the option should only refer to this dimension and earlier dimensions.
6662 We consider the following spaces.
6666 =item C<separation_class>
6668 This space is a wrapped relation between two one dimensional spaces.
6669 The input space represents the schedule dimension to which the option
6670 applies and the output space represents the separation class.
6671 While constructing a loop corresponding to the specified schedule
6672 dimension(s), the AST generator will try to generate separate loops
6673 for domain elements that are assigned different classes.
6674 If only some of the elements are assigned a class, then those elements
6675 that are not assigned any class will be treated as belonging to a class
6676 that is separate from the explicitly assigned classes.
6677 The typical use case for this option is to separate full tiles from
6679 The other options, described below, are applied after the separation
6682 As an example, consider the separation into full and partial tiles
6683 of a tiling of a triangular domain.
6684 Take, for example, the domain
6686 { A[i,j] : 0 <= i,j and i + j <= 100 }
6688 and a tiling into tiles of 10 by 10. The input to the AST generator
6689 is then the schedule
6691 { A[i,j] -> [([i/10]),[j/10],i,j] : 0 <= i,j and
6694 Without any options, the following AST is generated
6696 for (int c0 = 0; c0 <= 10; c0 += 1)
6697 for (int c1 = 0; c1 <= -c0 + 10; c1 += 1)
6698 for (int c2 = 10 * c0;
6699 c2 <= min(-10 * c1 + 100, 10 * c0 + 9);
6701 for (int c3 = 10 * c1;
6702 c3 <= min(10 * c1 + 9, -c2 + 100);
6706 Separation into full and partial tiles can be obtained by assigning
6707 a class, say C<0>, to the full tiles. The full tiles are represented by those
6708 values of the first and second schedule dimensions for which there are
6709 values of the third and fourth dimensions to cover an entire tile.
6710 That is, we need to specify the following option
6712 { [a,b,c,d] -> separation_class[[0]->[0]] :
6713 exists b': 0 <= 10a,10b' and
6714 10a+9+10b'+9 <= 100;
6715 [a,b,c,d] -> separation_class[[1]->[0]] :
6716 0 <= 10a,10b and 10a+9+10b+9 <= 100 }
6720 { [a, b, c, d] -> separation_class[[1] -> [0]] :
6721 a >= 0 and b >= 0 and b <= 8 - a;
6722 [a, b, c, d] -> separation_class[[0] -> [0]] :
6725 With this option, the generated AST is as follows
6728 for (int c0 = 0; c0 <= 8; c0 += 1) {
6729 for (int c1 = 0; c1 <= -c0 + 8; c1 += 1)
6730 for (int c2 = 10 * c0;
6731 c2 <= 10 * c0 + 9; c2 += 1)
6732 for (int c3 = 10 * c1;
6733 c3 <= 10 * c1 + 9; c3 += 1)
6735 for (int c1 = -c0 + 9; c1 <= -c0 + 10; c1 += 1)
6736 for (int c2 = 10 * c0;
6737 c2 <= min(-10 * c1 + 100, 10 * c0 + 9);
6739 for (int c3 = 10 * c1;
6740 c3 <= min(-c2 + 100, 10 * c1 + 9);
6744 for (int c0 = 9; c0 <= 10; c0 += 1)
6745 for (int c1 = 0; c1 <= -c0 + 10; c1 += 1)
6746 for (int c2 = 10 * c0;
6747 c2 <= min(-10 * c1 + 100, 10 * c0 + 9);
6749 for (int c3 = 10 * c1;
6750 c3 <= min(10 * c1 + 9, -c2 + 100);
6757 This is a single-dimensional space representing the schedule dimension(s)
6758 to which ``separation'' should be applied. Separation tries to split
6759 a loop into several pieces if this can avoid the generation of guards
6761 See also the C<atomic> option.
6765 This is a single-dimensional space representing the schedule dimension(s)
6766 for which the domains should be considered ``atomic''. That is, the
6767 AST generator will make sure that any given domain space will only appear
6768 in a single loop at the specified level.
6770 Consider the following schedule
6772 { a[i] -> [i] : 0 <= i < 10;
6773 b[i] -> [i+1] : 0 <= i < 10 }
6775 If the following option is specified
6777 { [i] -> separate[x] }
6779 then the following AST will be generated
6783 for (int c0 = 1; c0 <= 9; c0 += 1) {
6790 If, on the other hand, the following option is specified
6792 { [i] -> atomic[x] }
6794 then the following AST will be generated
6796 for (int c0 = 0; c0 <= 10; c0 += 1) {
6803 If neither C<atomic> nor C<separate> is specified, then the AST generator
6804 may produce either of these two results or some intermediate form.
6808 This is a single-dimensional space representing the schedule dimension(s)
6809 that should be I<completely> unrolled.
6810 To obtain a partial unrolling, the user should apply an additional
6811 strip-mining to the schedule and fully unroll the inner loop.
6815 Additional control is available through the following functions.
6817 #include <isl/ast_build.h>
6818 __isl_give isl_ast_build *
6819 isl_ast_build_set_iterators(
6820 __isl_take isl_ast_build *control,
6821 __isl_take isl_id_list *iterators);
6823 The function C<isl_ast_build_set_iterators> allows the user to
6824 specify a list of iterator C<isl_id>s to be used as iterators.
6825 If the input schedule is injective, then
6826 the number of elements in this list should be as large as the dimension
6827 of the schedule space, but no direct correspondence should be assumed
6828 between dimensions and elements.
6829 If the input schedule is not injective, then an additional number
6830 of C<isl_id>s equal to the largest dimension of the input domains
6832 If the number of provided C<isl_id>s is insufficient, then additional
6833 names are automatically generated.
6835 #include <isl/ast_build.h>
6836 __isl_give isl_ast_build *
6837 isl_ast_build_set_create_leaf(
6838 __isl_take isl_ast_build *control,
6839 __isl_give isl_ast_node *(*fn)(
6840 __isl_take isl_ast_build *build,
6841 void *user), void *user);
6844 C<isl_ast_build_set_create_leaf> function allows for the
6845 specification of a callback that should be called whenever the AST
6846 generator arrives at an element of the schedule domain.
6847 The callback should return an AST node that should be inserted
6848 at the corresponding position of the AST. The default action (when
6849 the callback is not set) is to continue generating parts of the AST to scan
6850 all the domain elements associated to the schedule domain element
6851 and to insert user nodes, ``calling'' the domain element, for each of them.
6852 The C<build> argument contains the current state of the C<isl_ast_build>.
6853 To ease nested AST generation (see L</"Nested AST Generation">),
6854 all control information that is
6855 specific to the current AST generation such as the options and
6856 the callbacks has been removed from this C<isl_ast_build>.
6857 The callback would typically return the result of a nested
6859 user defined node created using the following function.
6861 #include <isl/ast.h>
6862 __isl_give isl_ast_node *isl_ast_node_alloc_user(
6863 __isl_take isl_ast_expr *expr);
6865 #include <isl/ast_build.h>
6866 __isl_give isl_ast_build *
6867 isl_ast_build_set_at_each_domain(
6868 __isl_take isl_ast_build *build,
6869 __isl_give isl_ast_node *(*fn)(
6870 __isl_take isl_ast_node *node,
6871 __isl_keep isl_ast_build *build,
6872 void *user), void *user);
6873 __isl_give isl_ast_build *
6874 isl_ast_build_set_before_each_for(
6875 __isl_take isl_ast_build *build,
6876 __isl_give isl_id *(*fn)(
6877 __isl_keep isl_ast_build *build,
6878 void *user), void *user);
6879 __isl_give isl_ast_build *
6880 isl_ast_build_set_after_each_for(
6881 __isl_take isl_ast_build *build,
6882 __isl_give isl_ast_node *(*fn)(
6883 __isl_take isl_ast_node *node,
6884 __isl_keep isl_ast_build *build,
6885 void *user), void *user);
6887 The callback set by C<isl_ast_build_set_at_each_domain> will
6888 be called for each domain AST node.
6889 The callbacks set by C<isl_ast_build_set_before_each_for>
6890 and C<isl_ast_build_set_after_each_for> will be called
6891 for each for AST node. The first will be called in depth-first
6892 pre-order, while the second will be called in depth-first post-order.
6893 Since C<isl_ast_build_set_before_each_for> is called before the for
6894 node is actually constructed, it is only passed an C<isl_ast_build>.
6895 The returned C<isl_id> will be added as an annotation (using
6896 C<isl_ast_node_set_annotation>) to the constructed for node.
6897 In particular, if the user has also specified an C<after_each_for>
6898 callback, then the annotation can be retrieved from the node passed to
6899 that callback using C<isl_ast_node_get_annotation>.
6900 All callbacks should C<NULL> on failure.
6901 The given C<isl_ast_build> can be used to create new
6902 C<isl_ast_expr> objects using C<isl_ast_build_expr_from_pw_aff>
6903 or C<isl_ast_build_call_from_pw_multi_aff>.
6905 =head3 Nested AST Generation
6907 C<isl> allows the user to create an AST within the context
6908 of another AST. These nested ASTs are created using the
6909 same C<isl_ast_build_ast_from_schedule> function that is used to create the
6910 outer AST. The C<build> argument should be an C<isl_ast_build>
6911 passed to a callback set by
6912 C<isl_ast_build_set_create_leaf>.
6913 The space of the range of the C<schedule> argument should refer
6914 to this build. In particular, the space should be a wrapped
6915 relation and the domain of this wrapped relation should be the
6916 same as that of the range of the schedule returned by
6917 C<isl_ast_build_get_schedule> below.
6918 In practice, the new schedule is typically
6919 created by calling C<isl_union_map_range_product> on the old schedule
6920 and some extra piece of the schedule.
6921 The space of the schedule domain is also available from
6922 the C<isl_ast_build>.
6924 #include <isl/ast_build.h>
6925 __isl_give isl_union_map *isl_ast_build_get_schedule(
6926 __isl_keep isl_ast_build *build);
6927 __isl_give isl_space *isl_ast_build_get_schedule_space(
6928 __isl_keep isl_ast_build *build);
6929 __isl_give isl_ast_build *isl_ast_build_restrict(
6930 __isl_take isl_ast_build *build,
6931 __isl_take isl_set *set);
6933 The C<isl_ast_build_get_schedule> function returns a (partial)
6934 schedule for the domains elements for which part of the AST still needs to
6935 be generated in the current build.
6936 In particular, the domain elements are mapped to those iterations of the loops
6937 enclosing the current point of the AST generation inside which
6938 the domain elements are executed.
6939 No direct correspondence between
6940 the input schedule and this schedule should be assumed.
6941 The space obtained from C<isl_ast_build_get_schedule_space> can be used
6942 to create a set for C<isl_ast_build_restrict> to intersect
6943 with the current build. In particular, the set passed to
6944 C<isl_ast_build_restrict> can have additional parameters.
6945 The ids of the set dimensions in the space returned by
6946 C<isl_ast_build_get_schedule_space> correspond to the
6947 iterators of the already generated loops.
6948 The user should not rely on the ids of the output dimensions
6949 of the relations in the union relation returned by
6950 C<isl_ast_build_get_schedule> having any particular value.
6954 Although C<isl> is mainly meant to be used as a library,
6955 it also contains some basic applications that use some
6956 of the functionality of C<isl>.
6957 The input may be specified in either the L<isl format>
6958 or the L<PolyLib format>.
6960 =head2 C<isl_polyhedron_sample>
6962 C<isl_polyhedron_sample> takes a polyhedron as input and prints
6963 an integer element of the polyhedron, if there is any.
6964 The first column in the output is the denominator and is always
6965 equal to 1. If the polyhedron contains no integer points,
6966 then a vector of length zero is printed.
6970 C<isl_pip> takes the same input as the C<example> program
6971 from the C<piplib> distribution, i.e., a set of constraints
6972 on the parameters, a line containing only -1 and finally a set
6973 of constraints on a parametric polyhedron.
6974 The coefficients of the parameters appear in the last columns
6975 (but before the final constant column).
6976 The output is the lexicographic minimum of the parametric polyhedron.
6977 As C<isl> currently does not have its own output format, the output
6978 is just a dump of the internal state.
6980 =head2 C<isl_polyhedron_minimize>
6982 C<isl_polyhedron_minimize> computes the minimum of some linear
6983 or affine objective function over the integer points in a polyhedron.
6984 If an affine objective function
6985 is given, then the constant should appear in the last column.
6987 =head2 C<isl_polytope_scan>
6989 Given a polytope, C<isl_polytope_scan> prints
6990 all integer points in the polytope.
6992 =head2 C<isl_codegen>
6994 Given a schedule, a context set and an options relation,
6995 C<isl_codegen> prints out an AST that scans the domain elements
6996 of the schedule in the order of their image(s) taking into account
6997 the constraints in the context set.