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>.
201 C<isl> is released under the MIT license.
205 Permission is hereby granted, free of charge, to any person obtaining a copy of
206 this software and associated documentation files (the "Software"), to deal in
207 the Software without restriction, including without limitation the rights to
208 use, copy, modify, merge, publish, distribute, sublicense, and/or sell copies
209 of the Software, and to permit persons to whom the Software is furnished to do
210 so, subject to the following conditions:
212 The above copyright notice and this permission notice shall be included in all
213 copies or substantial portions of the Software.
215 THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
216 IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
217 FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
218 AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
219 LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
220 OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
225 Note that C<isl> currently requires C<GMP>, which is released
226 under the GNU Lesser General Public License (LGPL). This means
227 that code linked against C<isl> is also linked against LGPL code.
231 The source of C<isl> can be obtained either as a tarball
232 or from the git repository. Both are available from
233 L<http://freshmeat.net/projects/isl/>.
234 The installation process depends on how you obtained
237 =head2 Installation from the git repository
241 =item 1 Clone or update the repository
243 The first time the source is obtained, you need to clone
246 git clone git://repo.or.cz/isl.git
248 To obtain updates, you need to pull in the latest changes
252 =item 2 Generate C<configure>
258 After performing the above steps, continue
259 with the L<Common installation instructions>.
261 =head2 Common installation instructions
265 =item 1 Obtain C<GMP>
267 Building C<isl> requires C<GMP>, including its headers files.
268 Your distribution may not provide these header files by default
269 and you may need to install a package called C<gmp-devel> or something
270 similar. Alternatively, C<GMP> can be built from
271 source, available from L<http://gmplib.org/>.
275 C<isl> uses the standard C<autoconf> C<configure> script.
280 optionally followed by some configure options.
281 A complete list of options can be obtained by running
285 Below we discuss some of the more common options.
291 Installation prefix for C<isl>
293 =item C<--with-gmp-prefix>
295 Installation prefix for C<GMP> (architecture-independent files).
297 =item C<--with-gmp-exec-prefix>
299 Installation prefix for C<GMP> (architecture-dependent files).
307 =item 4 Install (optional)
313 =head1 Integer Set Library
315 =head2 Initialization
317 All manipulations of integer sets and relations occur within
318 the context of an C<isl_ctx>.
319 A given C<isl_ctx> can only be used within a single thread.
320 All arguments of a function are required to have been allocated
321 within the same context.
322 There are currently no functions available for moving an object
323 from one C<isl_ctx> to another C<isl_ctx>. This means that
324 there is currently no way of safely moving an object from one
325 thread to another, unless the whole C<isl_ctx> is moved.
327 An C<isl_ctx> can be allocated using C<isl_ctx_alloc> and
328 freed using C<isl_ctx_free>.
329 All objects allocated within an C<isl_ctx> should be freed
330 before the C<isl_ctx> itself is freed.
332 isl_ctx *isl_ctx_alloc();
333 void isl_ctx_free(isl_ctx *ctx);
337 An C<isl_val> represents an integer value, a rational value
338 or one of three special values, infinity, negative infinity and NaN.
339 Some predefined values can be created using the following functions.
342 __isl_give isl_val *isl_val_zero(isl_ctx *ctx);
343 __isl_give isl_val *isl_val_one(isl_ctx *ctx);
344 __isl_give isl_val *isl_val_nan(isl_ctx *ctx);
345 __isl_give isl_val *isl_val_infty(isl_ctx *ctx);
346 __isl_give isl_val *isl_val_neginfty(isl_ctx *ctx);
348 Specific integer values can be created using the following functions.
351 __isl_give isl_val *isl_val_int_from_si(isl_ctx *ctx,
353 __isl_give isl_val *isl_val_int_from_ui(isl_ctx *ctx,
355 __isl_give isl_val *isl_val_int_from_chunks(isl_ctx *ctx,
356 size_t n, size_t size, const void *chunks);
358 The function C<isl_val_int_from_chunks> constructs an C<isl_val>
359 from the C<n> I<digits>, each consisting of C<size> bytes, stored at C<chunks>.
360 The least significant digit is assumed to be stored first.
362 Value objects can be copied and freed using the following functions.
365 __isl_give isl_val *isl_val_copy(__isl_keep isl_val *v);
366 void *isl_val_free(__isl_take isl_val *v);
368 They can be inspected using the following functions.
371 isl_ctx *isl_val_get_ctx(__isl_keep isl_val *val);
372 long isl_val_get_num_si(__isl_keep isl_val *v);
373 long isl_val_get_den_si(__isl_keep isl_val *v);
374 double isl_val_get_d(__isl_keep isl_val *v);
375 size_t isl_val_n_abs_num_chunks(__isl_keep isl_val *v,
377 int isl_val_get_abs_num_chunks(__isl_keep isl_val *v,
378 size_t size, void *chunks);
380 C<isl_val_n_abs_num_chunks> returns the number of I<digits>
381 of C<size> bytes needed to store the absolute value of the
383 C<isl_val_get_abs_num_chunks> stores these digits at C<chunks>,
384 which is assumed to have been preallocated by the caller.
385 The least significant digit is stored first.
386 Note that C<isl_val_get_num_si>, C<isl_val_get_den_si>,
387 C<isl_val_get_d>, C<isl_val_n_abs_num_chunks>
388 and C<isl_val_get_abs_num_chunks> can only be applied to rational values.
390 An C<isl_val> can be modified using the following function.
393 __isl_give isl_val *isl_val_set_si(__isl_take isl_val *v,
396 The following unary properties are defined on C<isl_val>s.
399 int isl_val_sgn(__isl_keep isl_val *v);
400 int isl_val_is_zero(__isl_keep isl_val *v);
401 int isl_val_is_one(__isl_keep isl_val *v);
402 int isl_val_is_negone(__isl_keep isl_val *v);
403 int isl_val_is_nonneg(__isl_keep isl_val *v);
404 int isl_val_is_nonpos(__isl_keep isl_val *v);
405 int isl_val_is_pos(__isl_keep isl_val *v);
406 int isl_val_is_neg(__isl_keep isl_val *v);
407 int isl_val_is_int(__isl_keep isl_val *v);
408 int isl_val_is_rat(__isl_keep isl_val *v);
409 int isl_val_is_nan(__isl_keep isl_val *v);
410 int isl_val_is_infty(__isl_keep isl_val *v);
411 int isl_val_is_neginfty(__isl_keep isl_val *v);
413 Note that the sign of NaN is undefined.
415 The following binary properties are defined on pairs of C<isl_val>s.
418 int isl_val_lt(__isl_keep isl_val *v1,
419 __isl_keep isl_val *v2);
420 int isl_val_le(__isl_keep isl_val *v1,
421 __isl_keep isl_val *v2);
422 int isl_val_gt(__isl_keep isl_val *v1,
423 __isl_keep isl_val *v2);
424 int isl_val_ge(__isl_keep isl_val *v1,
425 __isl_keep isl_val *v2);
426 int isl_val_eq(__isl_keep isl_val *v1,
427 __isl_keep isl_val *v2);
428 int isl_val_ne(__isl_keep isl_val *v1,
429 __isl_keep isl_val *v2);
431 For integer C<isl_val>s we additionally have the following binary property.
434 int isl_val_is_divisible_by(__isl_keep isl_val *v1,
435 __isl_keep isl_val *v2);
437 An C<isl_val> can also be compared to an integer using the following
438 function. The result is undefined for NaN.
441 int isl_val_cmp_si(__isl_keep isl_val *v, long i);
443 The following unary operations are available on C<isl_val>s.
446 __isl_give isl_val *isl_val_abs(__isl_take isl_val *v);
447 __isl_give isl_val *isl_val_neg(__isl_take isl_val *v);
448 __isl_give isl_val *isl_val_floor(__isl_take isl_val *v);
449 __isl_give isl_val *isl_val_ceil(__isl_take isl_val *v);
450 __isl_give isl_val *isl_val_trunc(__isl_take isl_val *v);
452 The following binary operations are available on C<isl_val>s.
455 __isl_give isl_val *isl_val_abs(__isl_take isl_val *v);
456 __isl_give isl_val *isl_val_neg(__isl_take isl_val *v);
457 __isl_give isl_val *isl_val_floor(__isl_take isl_val *v);
458 __isl_give isl_val *isl_val_ceil(__isl_take isl_val *v);
459 __isl_give isl_val *isl_val_trunc(__isl_take isl_val *v);
460 __isl_give isl_val *isl_val_2exp(__isl_take isl_val *v);
461 __isl_give isl_val *isl_val_min(__isl_take isl_val *v1,
462 __isl_take isl_val *v2);
463 __isl_give isl_val *isl_val_max(__isl_take isl_val *v1,
464 __isl_take isl_val *v2);
465 __isl_give isl_val *isl_val_add(__isl_take isl_val *v1,
466 __isl_take isl_val *v2);
467 __isl_give isl_val *isl_val_add_ui(__isl_take isl_val *v1,
469 __isl_give isl_val *isl_val_sub(__isl_take isl_val *v1,
470 __isl_take isl_val *v2);
471 __isl_give isl_val *isl_val_sub_ui(__isl_take isl_val *v1,
473 __isl_give isl_val *isl_val_mul(__isl_take isl_val *v1,
474 __isl_take isl_val *v2);
475 __isl_give isl_val *isl_val_mul_ui(__isl_take isl_val *v1,
477 __isl_give isl_val *isl_val_div(__isl_take isl_val *v1,
478 __isl_take isl_val *v2);
480 On integer values, we additionally have the following operations.
483 __isl_give isl_val *isl_val_2exp(__isl_take isl_val *v);
484 __isl_give isl_val *isl_val_mod(__isl_take isl_val *v1,
485 __isl_take isl_val *v2);
486 __isl_give isl_val *isl_val_gcd(__isl_take isl_val *v1,
487 __isl_take isl_val *v2);
488 __isl_give isl_val *isl_val_gcdext(__isl_take isl_val *v1,
489 __isl_take isl_val *v2, __isl_give isl_val **x,
490 __isl_give isl_val **y);
492 The function C<isl_val_gcdext> returns the greatest common divisor g
493 of C<v1> and C<v2> as well as two integers C<*x> and C<*y> such
494 that C<*x> * C<v1> + C<*y> * C<v2> = g.
496 A value can be read from input using
499 __isl_give isl_val *isl_val_read_from_str(isl_ctx *ctx,
502 A value can be printed using
505 __isl_give isl_printer *isl_printer_print_val(
506 __isl_take isl_printer *p, __isl_keep isl_val *v);
508 =head3 GMP specific functions
510 These functions are only available if C<isl> has been compiled with C<GMP>
513 Specific integer and rational values can be created from C<GMP> values using
514 the following functions.
516 #include <isl/val_gmp.h>
517 __isl_give isl_val *isl_val_int_from_gmp(isl_ctx *ctx,
519 __isl_give isl_val *isl_val_from_gmp(isl_ctx *ctx,
520 const mpz_t n, const mpz_t d);
522 The numerator and denominator of a rational value can be extracted as
523 C<GMP> values using the following functions.
525 #include <isl/val_gmp.h>
526 int isl_val_get_num_gmp(__isl_keep isl_val *v, mpz_t z);
527 int isl_val_get_den_gmp(__isl_keep isl_val *v, mpz_t z);
529 =head2 Sets and Relations
531 C<isl> uses six types of objects for representing sets and relations,
532 C<isl_basic_set>, C<isl_basic_map>, C<isl_set>, C<isl_map>,
533 C<isl_union_set> and C<isl_union_map>.
534 C<isl_basic_set> and C<isl_basic_map> represent sets and relations that
535 can be described as a conjunction of affine constraints, while
536 C<isl_set> and C<isl_map> represent unions of
537 C<isl_basic_set>s and C<isl_basic_map>s, respectively.
538 However, all C<isl_basic_set>s or C<isl_basic_map>s in the union need
539 to live in the same space. C<isl_union_set>s and C<isl_union_map>s
540 represent unions of C<isl_set>s or C<isl_map>s in I<different> spaces,
541 where spaces are considered different if they have a different number
542 of dimensions and/or different names (see L<"Spaces">).
543 The difference between sets and relations (maps) is that sets have
544 one set of variables, while relations have two sets of variables,
545 input variables and output variables.
547 =head2 Memory Management
549 Since a high-level operation on sets and/or relations usually involves
550 several substeps and since the user is usually not interested in
551 the intermediate results, most functions that return a new object
552 will also release all the objects passed as arguments.
553 If the user still wants to use one or more of these arguments
554 after the function call, she should pass along a copy of the
555 object rather than the object itself.
556 The user is then responsible for making sure that the original
557 object gets used somewhere else or is explicitly freed.
559 The arguments and return values of all documented functions are
560 annotated to make clear which arguments are released and which
561 arguments are preserved. In particular, the following annotations
568 C<__isl_give> means that a new object is returned.
569 The user should make sure that the returned pointer is
570 used exactly once as a value for an C<__isl_take> argument.
571 In between, it can be used as a value for as many
572 C<__isl_keep> arguments as the user likes.
573 There is one exception, and that is the case where the
574 pointer returned is C<NULL>. Is this case, the user
575 is free to use it as an C<__isl_take> argument or not.
579 C<__isl_take> means that the object the argument points to
580 is taken over by the function and may no longer be used
581 by the user as an argument to any other function.
582 The pointer value must be one returned by a function
583 returning an C<__isl_give> pointer.
584 If the user passes in a C<NULL> value, then this will
585 be treated as an error in the sense that the function will
586 not perform its usual operation. However, it will still
587 make sure that all the other C<__isl_take> arguments
592 C<__isl_keep> means that the function will only use the object
593 temporarily. After the function has finished, the user
594 can still use it as an argument to other functions.
595 A C<NULL> value will be treated in the same way as
596 a C<NULL> value for an C<__isl_take> argument.
600 =head2 Error Handling
602 C<isl> supports different ways to react in case a runtime error is triggered.
603 Runtime errors arise, e.g., if a function such as C<isl_map_intersect> is called
604 with two maps that have incompatible spaces. There are three possible ways
605 to react on error: to warn, to continue or to abort.
607 The default behavior is to warn. In this mode, C<isl> prints a warning, stores
608 the last error in the corresponding C<isl_ctx> and the function in which the
609 error was triggered returns C<NULL>. An error does not corrupt internal state,
610 such that isl can continue to be used. C<isl> also provides functions to
611 read the last error and to reset the memory that stores the last error. The
612 last error is only stored for information purposes. Its presence does not
613 change the behavior of C<isl>. Hence, resetting an error is not required to
614 continue to use isl, but only to observe new errors.
617 enum isl_error isl_ctx_last_error(isl_ctx *ctx);
618 void isl_ctx_reset_error(isl_ctx *ctx);
620 Another option is to continue on error. This is similar to warn on error mode,
621 except that C<isl> does not print any warning. This allows a program to
622 implement its own error reporting.
624 The last option is to directly abort the execution of the program from within
625 the isl library. This makes it obviously impossible to recover from an error,
626 but it allows to directly spot the error location. By aborting on error,
627 debuggers break at the location the error occurred and can provide a stack
628 trace. Other tools that automatically provide stack traces on abort or that do
629 not want to continue execution after an error was triggered may also prefer to
632 The on error behavior of isl can be specified by calling
633 C<isl_options_set_on_error> or by setting the command line option
634 C<--isl-on-error>. Valid arguments for the function call are
635 C<ISL_ON_ERROR_WARN>, C<ISL_ON_ERROR_CONTINUE> and C<ISL_ON_ERROR_ABORT>. The
636 choices for the command line option are C<warn>, C<continue> and C<abort>.
637 It is also possible to query the current error mode.
639 #include <isl/options.h>
640 int isl_options_set_on_error(isl_ctx *ctx, int val);
641 int isl_options_get_on_error(isl_ctx *ctx);
645 Identifiers are used to identify both individual dimensions
646 and tuples of dimensions. They consist of an optional name and an optional
647 user pointer. The name and the user pointer cannot both be C<NULL>, however.
648 Identifiers with the same name but different pointer values
649 are considered to be distinct.
650 Similarly, identifiers with different names but the same pointer value
651 are also considered to be distinct.
652 Equal identifiers are represented using the same object.
653 Pairs of identifiers can therefore be tested for equality using the
655 Identifiers can be constructed, copied, freed, inspected and printed
656 using the following functions.
659 __isl_give isl_id *isl_id_alloc(isl_ctx *ctx,
660 __isl_keep const char *name, void *user);
661 __isl_give isl_id *isl_id_set_free_user(
662 __isl_take isl_id *id,
663 __isl_give void (*free_user)(void *user));
664 __isl_give isl_id *isl_id_copy(isl_id *id);
665 void *isl_id_free(__isl_take isl_id *id);
667 isl_ctx *isl_id_get_ctx(__isl_keep isl_id *id);
668 void *isl_id_get_user(__isl_keep isl_id *id);
669 __isl_keep const char *isl_id_get_name(__isl_keep isl_id *id);
671 __isl_give isl_printer *isl_printer_print_id(
672 __isl_take isl_printer *p, __isl_keep isl_id *id);
674 The callback set by C<isl_id_set_free_user> is called on the user
675 pointer when the last reference to the C<isl_id> is freed.
676 Note that C<isl_id_get_name> returns a pointer to some internal
677 data structure, so the result can only be used while the
678 corresponding C<isl_id> is alive.
682 Whenever a new set, relation or similiar object is created from scratch,
683 the space in which it lives needs to be specified using an C<isl_space>.
684 Each space involves zero or more parameters and zero, one or two
685 tuples of set or input/output dimensions. The parameters and dimensions
686 are identified by an C<isl_dim_type> and a position.
687 The type C<isl_dim_param> refers to parameters,
688 the type C<isl_dim_set> refers to set dimensions (for spaces
689 with a single tuple of dimensions) and the types C<isl_dim_in>
690 and C<isl_dim_out> refer to input and output dimensions
691 (for spaces with two tuples of dimensions).
692 Local spaces (see L</"Local Spaces">) also contain dimensions
693 of type C<isl_dim_div>.
694 Note that parameters are only identified by their position within
695 a given object. Across different objects, parameters are (usually)
696 identified by their names or identifiers. Only unnamed parameters
697 are identified by their positions across objects. The use of unnamed
698 parameters is discouraged.
700 #include <isl/space.h>
701 __isl_give isl_space *isl_space_alloc(isl_ctx *ctx,
702 unsigned nparam, unsigned n_in, unsigned n_out);
703 __isl_give isl_space *isl_space_params_alloc(isl_ctx *ctx,
705 __isl_give isl_space *isl_space_set_alloc(isl_ctx *ctx,
706 unsigned nparam, unsigned dim);
707 __isl_give isl_space *isl_space_copy(__isl_keep isl_space *space);
708 void *isl_space_free(__isl_take isl_space *space);
709 unsigned isl_space_dim(__isl_keep isl_space *space,
710 enum isl_dim_type type);
712 The space used for creating a parameter domain
713 needs to be created using C<isl_space_params_alloc>.
714 For other sets, the space
715 needs to be created using C<isl_space_set_alloc>, while
716 for a relation, the space
717 needs to be created using C<isl_space_alloc>.
718 C<isl_space_dim> can be used
719 to find out the number of dimensions of each type in
720 a space, where type may be
721 C<isl_dim_param>, C<isl_dim_in> (only for relations),
722 C<isl_dim_out> (only for relations), C<isl_dim_set>
723 (only for sets) or C<isl_dim_all>.
725 To check whether a given space is that of a set or a map
726 or whether it is a parameter space, use these functions:
728 #include <isl/space.h>
729 int isl_space_is_params(__isl_keep isl_space *space);
730 int isl_space_is_set(__isl_keep isl_space *space);
731 int isl_space_is_map(__isl_keep isl_space *space);
733 Spaces can be compared using the following functions:
735 #include <isl/space.h>
736 int isl_space_is_equal(__isl_keep isl_space *space1,
737 __isl_keep isl_space *space2);
738 int isl_space_is_domain(__isl_keep isl_space *space1,
739 __isl_keep isl_space *space2);
740 int isl_space_is_range(__isl_keep isl_space *space1,
741 __isl_keep isl_space *space2);
743 C<isl_space_is_domain> checks whether the first argument is equal
744 to the domain of the second argument. This requires in particular that
745 the first argument is a set space and that the second argument
748 It is often useful to create objects that live in the
749 same space as some other object. This can be accomplished
750 by creating the new objects
751 (see L<Creating New Sets and Relations> or
752 L<Creating New (Piecewise) Quasipolynomials>) based on the space
753 of the original object.
756 __isl_give isl_space *isl_basic_set_get_space(
757 __isl_keep isl_basic_set *bset);
758 __isl_give isl_space *isl_set_get_space(__isl_keep isl_set *set);
760 #include <isl/union_set.h>
761 __isl_give isl_space *isl_union_set_get_space(
762 __isl_keep isl_union_set *uset);
765 __isl_give isl_space *isl_basic_map_get_space(
766 __isl_keep isl_basic_map *bmap);
767 __isl_give isl_space *isl_map_get_space(__isl_keep isl_map *map);
769 #include <isl/union_map.h>
770 __isl_give isl_space *isl_union_map_get_space(
771 __isl_keep isl_union_map *umap);
773 #include <isl/constraint.h>
774 __isl_give isl_space *isl_constraint_get_space(
775 __isl_keep isl_constraint *constraint);
777 #include <isl/polynomial.h>
778 __isl_give isl_space *isl_qpolynomial_get_domain_space(
779 __isl_keep isl_qpolynomial *qp);
780 __isl_give isl_space *isl_qpolynomial_get_space(
781 __isl_keep isl_qpolynomial *qp);
782 __isl_give isl_space *isl_qpolynomial_fold_get_space(
783 __isl_keep isl_qpolynomial_fold *fold);
784 __isl_give isl_space *isl_pw_qpolynomial_get_domain_space(
785 __isl_keep isl_pw_qpolynomial *pwqp);
786 __isl_give isl_space *isl_pw_qpolynomial_get_space(
787 __isl_keep isl_pw_qpolynomial *pwqp);
788 __isl_give isl_space *isl_pw_qpolynomial_fold_get_domain_space(
789 __isl_keep isl_pw_qpolynomial_fold *pwf);
790 __isl_give isl_space *isl_pw_qpolynomial_fold_get_space(
791 __isl_keep isl_pw_qpolynomial_fold *pwf);
792 __isl_give isl_space *isl_union_pw_qpolynomial_get_space(
793 __isl_keep isl_union_pw_qpolynomial *upwqp);
794 __isl_give isl_space *isl_union_pw_qpolynomial_fold_get_space(
795 __isl_keep isl_union_pw_qpolynomial_fold *upwf);
798 __isl_give isl_space *isl_multi_val_get_space(
799 __isl_keep isl_multi_val *mv);
802 __isl_give isl_space *isl_aff_get_domain_space(
803 __isl_keep isl_aff *aff);
804 __isl_give isl_space *isl_aff_get_space(
805 __isl_keep isl_aff *aff);
806 __isl_give isl_space *isl_pw_aff_get_domain_space(
807 __isl_keep isl_pw_aff *pwaff);
808 __isl_give isl_space *isl_pw_aff_get_space(
809 __isl_keep isl_pw_aff *pwaff);
810 __isl_give isl_space *isl_multi_aff_get_domain_space(
811 __isl_keep isl_multi_aff *maff);
812 __isl_give isl_space *isl_multi_aff_get_space(
813 __isl_keep isl_multi_aff *maff);
814 __isl_give isl_space *isl_pw_multi_aff_get_domain_space(
815 __isl_keep isl_pw_multi_aff *pma);
816 __isl_give isl_space *isl_pw_multi_aff_get_space(
817 __isl_keep isl_pw_multi_aff *pma);
818 __isl_give isl_space *isl_union_pw_multi_aff_get_space(
819 __isl_keep isl_union_pw_multi_aff *upma);
820 __isl_give isl_space *isl_multi_pw_aff_get_domain_space(
821 __isl_keep isl_multi_pw_aff *mpa);
822 __isl_give isl_space *isl_multi_pw_aff_get_space(
823 __isl_keep isl_multi_pw_aff *mpa);
825 #include <isl/point.h>
826 __isl_give isl_space *isl_point_get_space(
827 __isl_keep isl_point *pnt);
829 The identifiers or names of the individual dimensions may be set or read off
830 using the following functions.
832 #include <isl/space.h>
833 __isl_give isl_space *isl_space_set_dim_id(
834 __isl_take isl_space *space,
835 enum isl_dim_type type, unsigned pos,
836 __isl_take isl_id *id);
837 int isl_space_has_dim_id(__isl_keep isl_space *space,
838 enum isl_dim_type type, unsigned pos);
839 __isl_give isl_id *isl_space_get_dim_id(
840 __isl_keep isl_space *space,
841 enum isl_dim_type type, unsigned pos);
842 __isl_give isl_space *isl_space_set_dim_name(
843 __isl_take isl_space *space,
844 enum isl_dim_type type, unsigned pos,
845 __isl_keep const char *name);
846 int isl_space_has_dim_name(__isl_keep isl_space *space,
847 enum isl_dim_type type, unsigned pos);
848 __isl_keep const char *isl_space_get_dim_name(
849 __isl_keep isl_space *space,
850 enum isl_dim_type type, unsigned pos);
852 Note that C<isl_space_get_name> returns a pointer to some internal
853 data structure, so the result can only be used while the
854 corresponding C<isl_space> is alive.
855 Also note that every function that operates on two sets or relations
856 requires that both arguments have the same parameters. This also
857 means that if one of the arguments has named parameters, then the
858 other needs to have named parameters too and the names need to match.
859 Pairs of C<isl_set>, C<isl_map>, C<isl_union_set> and/or C<isl_union_map>
860 arguments may have different parameters (as long as they are named),
861 in which case the result will have as parameters the union of the parameters of
864 Given the identifier or name of a dimension (typically a parameter),
865 its position can be obtained from the following function.
867 #include <isl/space.h>
868 int isl_space_find_dim_by_id(__isl_keep isl_space *space,
869 enum isl_dim_type type, __isl_keep isl_id *id);
870 int isl_space_find_dim_by_name(__isl_keep isl_space *space,
871 enum isl_dim_type type, const char *name);
873 The identifiers or names of entire spaces may be set or read off
874 using the following functions.
876 #include <isl/space.h>
877 __isl_give isl_space *isl_space_set_tuple_id(
878 __isl_take isl_space *space,
879 enum isl_dim_type type, __isl_take isl_id *id);
880 __isl_give isl_space *isl_space_reset_tuple_id(
881 __isl_take isl_space *space, enum isl_dim_type type);
882 int isl_space_has_tuple_id(__isl_keep isl_space *space,
883 enum isl_dim_type type);
884 __isl_give isl_id *isl_space_get_tuple_id(
885 __isl_keep isl_space *space, enum isl_dim_type type);
886 __isl_give isl_space *isl_space_set_tuple_name(
887 __isl_take isl_space *space,
888 enum isl_dim_type type, const char *s);
889 int isl_space_has_tuple_name(__isl_keep isl_space *space,
890 enum isl_dim_type type);
891 const char *isl_space_get_tuple_name(__isl_keep isl_space *space,
892 enum isl_dim_type type);
894 The C<type> argument needs to be one of C<isl_dim_in>, C<isl_dim_out>
895 or C<isl_dim_set>. As with C<isl_space_get_name>,
896 the C<isl_space_get_tuple_name> function returns a pointer to some internal
898 Binary operations require the corresponding spaces of their arguments
899 to have the same name.
901 Spaces can be nested. In particular, the domain of a set or
902 the domain or range of a relation can be a nested relation.
903 The following functions can be used to construct and deconstruct
906 #include <isl/space.h>
907 int isl_space_is_wrapping(__isl_keep isl_space *space);
908 __isl_give isl_space *isl_space_wrap(__isl_take isl_space *space);
909 __isl_give isl_space *isl_space_unwrap(__isl_take isl_space *space);
911 The input to C<isl_space_is_wrapping> and C<isl_space_unwrap> should
912 be the space of a set, while that of
913 C<isl_space_wrap> should be the space of a relation.
914 Conversely, the output of C<isl_space_unwrap> is the space
915 of a relation, while that of C<isl_space_wrap> is the space of a set.
917 Spaces can be created from other spaces
918 using the following functions.
920 __isl_give isl_space *isl_space_domain(__isl_take isl_space *space);
921 __isl_give isl_space *isl_space_from_domain(__isl_take isl_space *space);
922 __isl_give isl_space *isl_space_range(__isl_take isl_space *space);
923 __isl_give isl_space *isl_space_from_range(__isl_take isl_space *space);
924 __isl_give isl_space *isl_space_domain_map(
925 __isl_take isl_space *space);
926 __isl_give isl_space *isl_space_range_map(
927 __isl_take isl_space *space);
928 __isl_give isl_space *isl_space_params(
929 __isl_take isl_space *space);
930 __isl_give isl_space *isl_space_set_from_params(
931 __isl_take isl_space *space);
932 __isl_give isl_space *isl_space_reverse(__isl_take isl_space *space);
933 __isl_give isl_space *isl_space_join(__isl_take isl_space *left,
934 __isl_take isl_space *right);
935 __isl_give isl_space *isl_space_align_params(
936 __isl_take isl_space *space1, __isl_take isl_space *space2)
937 __isl_give isl_space *isl_space_insert_dims(__isl_take isl_space *space,
938 enum isl_dim_type type, unsigned pos, unsigned n);
939 __isl_give isl_space *isl_space_add_dims(__isl_take isl_space *space,
940 enum isl_dim_type type, unsigned n);
941 __isl_give isl_space *isl_space_drop_dims(__isl_take isl_space *space,
942 enum isl_dim_type type, unsigned first, unsigned n);
943 __isl_give isl_space *isl_space_move_dims(__isl_take isl_space *space,
944 enum isl_dim_type dst_type, unsigned dst_pos,
945 enum isl_dim_type src_type, unsigned src_pos,
947 __isl_give isl_space *isl_space_map_from_set(
948 __isl_take isl_space *space);
949 __isl_give isl_space *isl_space_map_from_domain_and_range(
950 __isl_take isl_space *domain,
951 __isl_take isl_space *range);
952 __isl_give isl_space *isl_space_zip(__isl_take isl_space *space);
953 __isl_give isl_space *isl_space_curry(
954 __isl_take isl_space *space);
955 __isl_give isl_space *isl_space_uncurry(
956 __isl_take isl_space *space);
958 Note that if dimensions are added or removed from a space, then
959 the name and the internal structure are lost.
963 A local space is essentially a space with
964 zero or more existentially quantified variables.
965 The local space of a (constraint of a) basic set or relation can be obtained
966 using the following functions.
968 #include <isl/constraint.h>
969 __isl_give isl_local_space *isl_constraint_get_local_space(
970 __isl_keep isl_constraint *constraint);
973 __isl_give isl_local_space *isl_basic_set_get_local_space(
974 __isl_keep isl_basic_set *bset);
977 __isl_give isl_local_space *isl_basic_map_get_local_space(
978 __isl_keep isl_basic_map *bmap);
980 A new local space can be created from a space using
982 #include <isl/local_space.h>
983 __isl_give isl_local_space *isl_local_space_from_space(
984 __isl_take isl_space *space);
986 They can be inspected, modified, copied and freed using the following functions.
988 #include <isl/local_space.h>
989 isl_ctx *isl_local_space_get_ctx(
990 __isl_keep isl_local_space *ls);
991 int isl_local_space_is_set(__isl_keep isl_local_space *ls);
992 int isl_local_space_dim(__isl_keep isl_local_space *ls,
993 enum isl_dim_type type);
994 int isl_local_space_has_dim_id(
995 __isl_keep isl_local_space *ls,
996 enum isl_dim_type type, unsigned pos);
997 __isl_give isl_id *isl_local_space_get_dim_id(
998 __isl_keep isl_local_space *ls,
999 enum isl_dim_type type, unsigned pos);
1000 int isl_local_space_has_dim_name(
1001 __isl_keep isl_local_space *ls,
1002 enum isl_dim_type type, unsigned pos)
1003 const char *isl_local_space_get_dim_name(
1004 __isl_keep isl_local_space *ls,
1005 enum isl_dim_type type, unsigned pos);
1006 __isl_give isl_local_space *isl_local_space_set_dim_name(
1007 __isl_take isl_local_space *ls,
1008 enum isl_dim_type type, unsigned pos, const char *s);
1009 __isl_give isl_local_space *isl_local_space_set_dim_id(
1010 __isl_take isl_local_space *ls,
1011 enum isl_dim_type type, unsigned pos,
1012 __isl_take isl_id *id);
1013 __isl_give isl_space *isl_local_space_get_space(
1014 __isl_keep isl_local_space *ls);
1015 __isl_give isl_aff *isl_local_space_get_div(
1016 __isl_keep isl_local_space *ls, int pos);
1017 __isl_give isl_local_space *isl_local_space_copy(
1018 __isl_keep isl_local_space *ls);
1019 void *isl_local_space_free(__isl_take isl_local_space *ls);
1021 Note that C<isl_local_space_get_div> can only be used on local spaces
1024 Two local spaces can be compared using
1026 int isl_local_space_is_equal(__isl_keep isl_local_space *ls1,
1027 __isl_keep isl_local_space *ls2);
1029 Local spaces can be created from other local spaces
1030 using the following functions.
1032 __isl_give isl_local_space *isl_local_space_domain(
1033 __isl_take isl_local_space *ls);
1034 __isl_give isl_local_space *isl_local_space_range(
1035 __isl_take isl_local_space *ls);
1036 __isl_give isl_local_space *isl_local_space_from_domain(
1037 __isl_take isl_local_space *ls);
1038 __isl_give isl_local_space *isl_local_space_intersect(
1039 __isl_take isl_local_space *ls1,
1040 __isl_take isl_local_space *ls2);
1041 __isl_give isl_local_space *isl_local_space_add_dims(
1042 __isl_take isl_local_space *ls,
1043 enum isl_dim_type type, unsigned n);
1044 __isl_give isl_local_space *isl_local_space_insert_dims(
1045 __isl_take isl_local_space *ls,
1046 enum isl_dim_type type, unsigned first, unsigned n);
1047 __isl_give isl_local_space *isl_local_space_drop_dims(
1048 __isl_take isl_local_space *ls,
1049 enum isl_dim_type type, unsigned first, unsigned n);
1051 =head2 Input and Output
1053 C<isl> supports its own input/output format, which is similar
1054 to the C<Omega> format, but also supports the C<PolyLib> format
1057 =head3 C<isl> format
1059 The C<isl> format is similar to that of C<Omega>, but has a different
1060 syntax for describing the parameters and allows for the definition
1061 of an existentially quantified variable as the integer division
1062 of an affine expression.
1063 For example, the set of integers C<i> between C<0> and C<n>
1064 such that C<i % 10 <= 6> can be described as
1066 [n] -> { [i] : exists (a = [i/10] : 0 <= i and i <= n and
1069 A set or relation can have several disjuncts, separated
1070 by the keyword C<or>. Each disjunct is either a conjunction
1071 of constraints or a projection (C<exists>) of a conjunction
1072 of constraints. The constraints are separated by the keyword
1075 =head3 C<PolyLib> format
1077 If the represented set is a union, then the first line
1078 contains a single number representing the number of disjuncts.
1079 Otherwise, a line containing the number C<1> is optional.
1081 Each disjunct is represented by a matrix of constraints.
1082 The first line contains two numbers representing
1083 the number of rows and columns,
1084 where the number of rows is equal to the number of constraints
1085 and the number of columns is equal to two plus the number of variables.
1086 The following lines contain the actual rows of the constraint matrix.
1087 In each row, the first column indicates whether the constraint
1088 is an equality (C<0>) or inequality (C<1>). The final column
1089 corresponds to the constant term.
1091 If the set is parametric, then the coefficients of the parameters
1092 appear in the last columns before the constant column.
1093 The coefficients of any existentially quantified variables appear
1094 between those of the set variables and those of the parameters.
1096 =head3 Extended C<PolyLib> format
1098 The extended C<PolyLib> format is nearly identical to the
1099 C<PolyLib> format. The only difference is that the line
1100 containing the number of rows and columns of a constraint matrix
1101 also contains four additional numbers:
1102 the number of output dimensions, the number of input dimensions,
1103 the number of local dimensions (i.e., the number of existentially
1104 quantified variables) and the number of parameters.
1105 For sets, the number of ``output'' dimensions is equal
1106 to the number of set dimensions, while the number of ``input''
1111 #include <isl/set.h>
1112 __isl_give isl_basic_set *isl_basic_set_read_from_file(
1113 isl_ctx *ctx, FILE *input);
1114 __isl_give isl_basic_set *isl_basic_set_read_from_str(
1115 isl_ctx *ctx, const char *str);
1116 __isl_give isl_set *isl_set_read_from_file(isl_ctx *ctx,
1118 __isl_give isl_set *isl_set_read_from_str(isl_ctx *ctx,
1121 #include <isl/map.h>
1122 __isl_give isl_basic_map *isl_basic_map_read_from_file(
1123 isl_ctx *ctx, FILE *input);
1124 __isl_give isl_basic_map *isl_basic_map_read_from_str(
1125 isl_ctx *ctx, const char *str);
1126 __isl_give isl_map *isl_map_read_from_file(
1127 isl_ctx *ctx, FILE *input);
1128 __isl_give isl_map *isl_map_read_from_str(isl_ctx *ctx,
1131 #include <isl/union_set.h>
1132 __isl_give isl_union_set *isl_union_set_read_from_file(
1133 isl_ctx *ctx, FILE *input);
1134 __isl_give isl_union_set *isl_union_set_read_from_str(
1135 isl_ctx *ctx, const char *str);
1137 #include <isl/union_map.h>
1138 __isl_give isl_union_map *isl_union_map_read_from_file(
1139 isl_ctx *ctx, FILE *input);
1140 __isl_give isl_union_map *isl_union_map_read_from_str(
1141 isl_ctx *ctx, const char *str);
1143 The input format is autodetected and may be either the C<PolyLib> format
1144 or the C<isl> format.
1148 Before anything can be printed, an C<isl_printer> needs to
1151 __isl_give isl_printer *isl_printer_to_file(isl_ctx *ctx,
1153 __isl_give isl_printer *isl_printer_to_str(isl_ctx *ctx);
1154 void *isl_printer_free(__isl_take isl_printer *printer);
1155 __isl_give char *isl_printer_get_str(
1156 __isl_keep isl_printer *printer);
1158 The printer can be inspected using the following functions.
1160 FILE *isl_printer_get_file(
1161 __isl_keep isl_printer *printer);
1162 int isl_printer_get_output_format(
1163 __isl_keep isl_printer *p);
1165 The behavior of the printer can be modified in various ways
1167 __isl_give isl_printer *isl_printer_set_output_format(
1168 __isl_take isl_printer *p, int output_format);
1169 __isl_give isl_printer *isl_printer_set_indent(
1170 __isl_take isl_printer *p, int indent);
1171 __isl_give isl_printer *isl_printer_indent(
1172 __isl_take isl_printer *p, int indent);
1173 __isl_give isl_printer *isl_printer_set_prefix(
1174 __isl_take isl_printer *p, const char *prefix);
1175 __isl_give isl_printer *isl_printer_set_suffix(
1176 __isl_take isl_printer *p, const char *suffix);
1178 The C<output_format> may be either C<ISL_FORMAT_ISL>, C<ISL_FORMAT_OMEGA>,
1179 C<ISL_FORMAT_POLYLIB>, C<ISL_FORMAT_EXT_POLYLIB> or C<ISL_FORMAT_LATEX>
1180 and defaults to C<ISL_FORMAT_ISL>.
1181 Each line in the output is indented by C<indent> (set by
1182 C<isl_printer_set_indent>) spaces
1183 (default: 0), prefixed by C<prefix> and suffixed by C<suffix>.
1184 In the C<PolyLib> format output,
1185 the coefficients of the existentially quantified variables
1186 appear between those of the set variables and those
1188 The function C<isl_printer_indent> increases the indentation
1189 by the specified amount (which may be negative).
1191 To actually print something, use
1193 #include <isl/printer.h>
1194 __isl_give isl_printer *isl_printer_print_double(
1195 __isl_take isl_printer *p, double d);
1197 #include <isl/set.h>
1198 __isl_give isl_printer *isl_printer_print_basic_set(
1199 __isl_take isl_printer *printer,
1200 __isl_keep isl_basic_set *bset);
1201 __isl_give isl_printer *isl_printer_print_set(
1202 __isl_take isl_printer *printer,
1203 __isl_keep isl_set *set);
1205 #include <isl/map.h>
1206 __isl_give isl_printer *isl_printer_print_basic_map(
1207 __isl_take isl_printer *printer,
1208 __isl_keep isl_basic_map *bmap);
1209 __isl_give isl_printer *isl_printer_print_map(
1210 __isl_take isl_printer *printer,
1211 __isl_keep isl_map *map);
1213 #include <isl/union_set.h>
1214 __isl_give isl_printer *isl_printer_print_union_set(
1215 __isl_take isl_printer *p,
1216 __isl_keep isl_union_set *uset);
1218 #include <isl/union_map.h>
1219 __isl_give isl_printer *isl_printer_print_union_map(
1220 __isl_take isl_printer *p,
1221 __isl_keep isl_union_map *umap);
1223 When called on a file printer, the following function flushes
1224 the file. When called on a string printer, the buffer is cleared.
1226 __isl_give isl_printer *isl_printer_flush(
1227 __isl_take isl_printer *p);
1229 =head2 Creating New Sets and Relations
1231 C<isl> has functions for creating some standard sets and relations.
1235 =item * Empty sets and relations
1237 __isl_give isl_basic_set *isl_basic_set_empty(
1238 __isl_take isl_space *space);
1239 __isl_give isl_basic_map *isl_basic_map_empty(
1240 __isl_take isl_space *space);
1241 __isl_give isl_set *isl_set_empty(
1242 __isl_take isl_space *space);
1243 __isl_give isl_map *isl_map_empty(
1244 __isl_take isl_space *space);
1245 __isl_give isl_union_set *isl_union_set_empty(
1246 __isl_take isl_space *space);
1247 __isl_give isl_union_map *isl_union_map_empty(
1248 __isl_take isl_space *space);
1250 For C<isl_union_set>s and C<isl_union_map>s, the space
1251 is only used to specify the parameters.
1253 =item * Universe sets and relations
1255 __isl_give isl_basic_set *isl_basic_set_universe(
1256 __isl_take isl_space *space);
1257 __isl_give isl_basic_map *isl_basic_map_universe(
1258 __isl_take isl_space *space);
1259 __isl_give isl_set *isl_set_universe(
1260 __isl_take isl_space *space);
1261 __isl_give isl_map *isl_map_universe(
1262 __isl_take isl_space *space);
1263 __isl_give isl_union_set *isl_union_set_universe(
1264 __isl_take isl_union_set *uset);
1265 __isl_give isl_union_map *isl_union_map_universe(
1266 __isl_take isl_union_map *umap);
1268 The sets and relations constructed by the functions above
1269 contain all integer values, while those constructed by the
1270 functions below only contain non-negative values.
1272 __isl_give isl_basic_set *isl_basic_set_nat_universe(
1273 __isl_take isl_space *space);
1274 __isl_give isl_basic_map *isl_basic_map_nat_universe(
1275 __isl_take isl_space *space);
1276 __isl_give isl_set *isl_set_nat_universe(
1277 __isl_take isl_space *space);
1278 __isl_give isl_map *isl_map_nat_universe(
1279 __isl_take isl_space *space);
1281 =item * Identity relations
1283 __isl_give isl_basic_map *isl_basic_map_identity(
1284 __isl_take isl_space *space);
1285 __isl_give isl_map *isl_map_identity(
1286 __isl_take isl_space *space);
1288 The number of input and output dimensions in C<space> needs
1291 =item * Lexicographic order
1293 __isl_give isl_map *isl_map_lex_lt(
1294 __isl_take isl_space *set_space);
1295 __isl_give isl_map *isl_map_lex_le(
1296 __isl_take isl_space *set_space);
1297 __isl_give isl_map *isl_map_lex_gt(
1298 __isl_take isl_space *set_space);
1299 __isl_give isl_map *isl_map_lex_ge(
1300 __isl_take isl_space *set_space);
1301 __isl_give isl_map *isl_map_lex_lt_first(
1302 __isl_take isl_space *space, unsigned n);
1303 __isl_give isl_map *isl_map_lex_le_first(
1304 __isl_take isl_space *space, unsigned n);
1305 __isl_give isl_map *isl_map_lex_gt_first(
1306 __isl_take isl_space *space, unsigned n);
1307 __isl_give isl_map *isl_map_lex_ge_first(
1308 __isl_take isl_space *space, unsigned n);
1310 The first four functions take a space for a B<set>
1311 and return relations that express that the elements in the domain
1312 are lexicographically less
1313 (C<isl_map_lex_lt>), less or equal (C<isl_map_lex_le>),
1314 greater (C<isl_map_lex_gt>) or greater or equal (C<isl_map_lex_ge>)
1315 than the elements in the range.
1316 The last four functions take a space for a map
1317 and return relations that express that the first C<n> dimensions
1318 in the domain are lexicographically less
1319 (C<isl_map_lex_lt_first>), less or equal (C<isl_map_lex_le_first>),
1320 greater (C<isl_map_lex_gt_first>) or greater or equal (C<isl_map_lex_ge_first>)
1321 than the first C<n> dimensions in the range.
1325 A basic set or relation can be converted to a set or relation
1326 using the following functions.
1328 __isl_give isl_set *isl_set_from_basic_set(
1329 __isl_take isl_basic_set *bset);
1330 __isl_give isl_map *isl_map_from_basic_map(
1331 __isl_take isl_basic_map *bmap);
1333 Sets and relations can be converted to union sets and relations
1334 using the following functions.
1336 __isl_give isl_union_set *isl_union_set_from_basic_set(
1337 __isl_take isl_basic_set *bset);
1338 __isl_give isl_union_map *isl_union_map_from_basic_map(
1339 __isl_take isl_basic_map *bmap);
1340 __isl_give isl_union_set *isl_union_set_from_set(
1341 __isl_take isl_set *set);
1342 __isl_give isl_union_map *isl_union_map_from_map(
1343 __isl_take isl_map *map);
1345 The inverse conversions below can only be used if the input
1346 union set or relation is known to contain elements in exactly one
1349 __isl_give isl_set *isl_set_from_union_set(
1350 __isl_take isl_union_set *uset);
1351 __isl_give isl_map *isl_map_from_union_map(
1352 __isl_take isl_union_map *umap);
1354 A zero-dimensional (basic) set can be constructed on a given parameter domain
1355 using the following function.
1357 __isl_give isl_basic_set *isl_basic_set_from_params(
1358 __isl_take isl_basic_set *bset);
1359 __isl_give isl_set *isl_set_from_params(
1360 __isl_take isl_set *set);
1362 Sets and relations can be copied and freed again using the following
1365 __isl_give isl_basic_set *isl_basic_set_copy(
1366 __isl_keep isl_basic_set *bset);
1367 __isl_give isl_set *isl_set_copy(__isl_keep isl_set *set);
1368 __isl_give isl_union_set *isl_union_set_copy(
1369 __isl_keep isl_union_set *uset);
1370 __isl_give isl_basic_map *isl_basic_map_copy(
1371 __isl_keep isl_basic_map *bmap);
1372 __isl_give isl_map *isl_map_copy(__isl_keep isl_map *map);
1373 __isl_give isl_union_map *isl_union_map_copy(
1374 __isl_keep isl_union_map *umap);
1375 void *isl_basic_set_free(__isl_take isl_basic_set *bset);
1376 void *isl_set_free(__isl_take isl_set *set);
1377 void *isl_union_set_free(__isl_take isl_union_set *uset);
1378 void *isl_basic_map_free(__isl_take isl_basic_map *bmap);
1379 void *isl_map_free(__isl_take isl_map *map);
1380 void *isl_union_map_free(__isl_take isl_union_map *umap);
1382 Other sets and relations can be constructed by starting
1383 from a universe set or relation, adding equality and/or
1384 inequality constraints and then projecting out the
1385 existentially quantified variables, if any.
1386 Constraints can be constructed, manipulated and
1387 added to (or removed from) (basic) sets and relations
1388 using the following functions.
1390 #include <isl/constraint.h>
1391 __isl_give isl_constraint *isl_equality_alloc(
1392 __isl_take isl_local_space *ls);
1393 __isl_give isl_constraint *isl_inequality_alloc(
1394 __isl_take isl_local_space *ls);
1395 __isl_give isl_constraint *isl_constraint_set_constant_si(
1396 __isl_take isl_constraint *constraint, int v);
1397 __isl_give isl_constraint *isl_constraint_set_constant_val(
1398 __isl_take isl_constraint *constraint,
1399 __isl_take isl_val *v);
1400 __isl_give isl_constraint *isl_constraint_set_coefficient_si(
1401 __isl_take isl_constraint *constraint,
1402 enum isl_dim_type type, int pos, int v);
1403 __isl_give isl_constraint *
1404 isl_constraint_set_coefficient_val(
1405 __isl_take isl_constraint *constraint,
1406 enum isl_dim_type type, int pos, isl_val *v);
1407 __isl_give isl_basic_map *isl_basic_map_add_constraint(
1408 __isl_take isl_basic_map *bmap,
1409 __isl_take isl_constraint *constraint);
1410 __isl_give isl_basic_set *isl_basic_set_add_constraint(
1411 __isl_take isl_basic_set *bset,
1412 __isl_take isl_constraint *constraint);
1413 __isl_give isl_map *isl_map_add_constraint(
1414 __isl_take isl_map *map,
1415 __isl_take isl_constraint *constraint);
1416 __isl_give isl_set *isl_set_add_constraint(
1417 __isl_take isl_set *set,
1418 __isl_take isl_constraint *constraint);
1419 __isl_give isl_basic_set *isl_basic_set_drop_constraint(
1420 __isl_take isl_basic_set *bset,
1421 __isl_take isl_constraint *constraint);
1423 For example, to create a set containing the even integers
1424 between 10 and 42, you would use the following code.
1427 isl_local_space *ls;
1429 isl_basic_set *bset;
1431 space = isl_space_set_alloc(ctx, 0, 2);
1432 bset = isl_basic_set_universe(isl_space_copy(space));
1433 ls = isl_local_space_from_space(space);
1435 c = isl_equality_alloc(isl_local_space_copy(ls));
1436 c = isl_constraint_set_coefficient_si(c, isl_dim_set, 0, -1);
1437 c = isl_constraint_set_coefficient_si(c, isl_dim_set, 1, 2);
1438 bset = isl_basic_set_add_constraint(bset, c);
1440 c = isl_inequality_alloc(isl_local_space_copy(ls));
1441 c = isl_constraint_set_constant_si(c, -10);
1442 c = isl_constraint_set_coefficient_si(c, isl_dim_set, 0, 1);
1443 bset = isl_basic_set_add_constraint(bset, c);
1445 c = isl_inequality_alloc(ls);
1446 c = isl_constraint_set_constant_si(c, 42);
1447 c = isl_constraint_set_coefficient_si(c, isl_dim_set, 0, -1);
1448 bset = isl_basic_set_add_constraint(bset, c);
1450 bset = isl_basic_set_project_out(bset, isl_dim_set, 1, 1);
1454 isl_basic_set *bset;
1455 bset = isl_basic_set_read_from_str(ctx,
1456 "{[i] : exists (a : i = 2a and i >= 10 and i <= 42)}");
1458 A basic set or relation can also be constructed from two matrices
1459 describing the equalities and the inequalities.
1461 __isl_give isl_basic_set *isl_basic_set_from_constraint_matrices(
1462 __isl_take isl_space *space,
1463 __isl_take isl_mat *eq, __isl_take isl_mat *ineq,
1464 enum isl_dim_type c1,
1465 enum isl_dim_type c2, enum isl_dim_type c3,
1466 enum isl_dim_type c4);
1467 __isl_give isl_basic_map *isl_basic_map_from_constraint_matrices(
1468 __isl_take isl_space *space,
1469 __isl_take isl_mat *eq, __isl_take isl_mat *ineq,
1470 enum isl_dim_type c1,
1471 enum isl_dim_type c2, enum isl_dim_type c3,
1472 enum isl_dim_type c4, enum isl_dim_type c5);
1474 The C<isl_dim_type> arguments indicate the order in which
1475 different kinds of variables appear in the input matrices
1476 and should be a permutation of C<isl_dim_cst>, C<isl_dim_param>,
1477 C<isl_dim_set> and C<isl_dim_div> for sets and
1478 of C<isl_dim_cst>, C<isl_dim_param>,
1479 C<isl_dim_in>, C<isl_dim_out> and C<isl_dim_div> for relations.
1481 A (basic or union) set or relation can also be constructed from a
1482 (union) (piecewise) (multiple) affine expression
1483 or a list of affine expressions
1484 (See L<"Piecewise Quasi Affine Expressions"> and
1485 L<"Piecewise Multiple Quasi Affine Expressions">).
1487 __isl_give isl_basic_map *isl_basic_map_from_aff(
1488 __isl_take isl_aff *aff);
1489 __isl_give isl_map *isl_map_from_aff(
1490 __isl_take isl_aff *aff);
1491 __isl_give isl_set *isl_set_from_pw_aff(
1492 __isl_take isl_pw_aff *pwaff);
1493 __isl_give isl_map *isl_map_from_pw_aff(
1494 __isl_take isl_pw_aff *pwaff);
1495 __isl_give isl_basic_map *isl_basic_map_from_aff_list(
1496 __isl_take isl_space *domain_space,
1497 __isl_take isl_aff_list *list);
1498 __isl_give isl_basic_map *isl_basic_map_from_multi_aff(
1499 __isl_take isl_multi_aff *maff)
1500 __isl_give isl_map *isl_map_from_multi_aff(
1501 __isl_take isl_multi_aff *maff)
1502 __isl_give isl_set *isl_set_from_pw_multi_aff(
1503 __isl_take isl_pw_multi_aff *pma);
1504 __isl_give isl_map *isl_map_from_pw_multi_aff(
1505 __isl_take isl_pw_multi_aff *pma);
1506 __isl_give isl_set *isl_set_from_multi_pw_aff(
1507 __isl_take isl_multi_pw_aff *mpa);
1508 __isl_give isl_map *isl_map_from_multi_pw_aff(
1509 __isl_take isl_multi_pw_aff *mpa);
1510 __isl_give isl_union_map *
1511 isl_union_map_from_union_pw_multi_aff(
1512 __isl_take isl_union_pw_multi_aff *upma);
1514 The C<domain_dim> argument describes the domain of the resulting
1515 basic relation. It is required because the C<list> may consist
1516 of zero affine expressions.
1518 =head2 Inspecting Sets and Relations
1520 Usually, the user should not have to care about the actual constraints
1521 of the sets and maps, but should instead apply the abstract operations
1522 explained in the following sections.
1523 Occasionally, however, it may be required to inspect the individual
1524 coefficients of the constraints. This section explains how to do so.
1525 In these cases, it may also be useful to have C<isl> compute
1526 an explicit representation of the existentially quantified variables.
1528 __isl_give isl_set *isl_set_compute_divs(
1529 __isl_take isl_set *set);
1530 __isl_give isl_map *isl_map_compute_divs(
1531 __isl_take isl_map *map);
1532 __isl_give isl_union_set *isl_union_set_compute_divs(
1533 __isl_take isl_union_set *uset);
1534 __isl_give isl_union_map *isl_union_map_compute_divs(
1535 __isl_take isl_union_map *umap);
1537 This explicit representation defines the existentially quantified
1538 variables as integer divisions of the other variables, possibly
1539 including earlier existentially quantified variables.
1540 An explicitly represented existentially quantified variable therefore
1541 has a unique value when the values of the other variables are known.
1542 If, furthermore, the same existentials, i.e., existentials
1543 with the same explicit representations, should appear in the
1544 same order in each of the disjuncts of a set or map, then the user should call
1545 either of the following functions.
1547 __isl_give isl_set *isl_set_align_divs(
1548 __isl_take isl_set *set);
1549 __isl_give isl_map *isl_map_align_divs(
1550 __isl_take isl_map *map);
1552 Alternatively, the existentially quantified variables can be removed
1553 using the following functions, which compute an overapproximation.
1555 __isl_give isl_basic_set *isl_basic_set_remove_divs(
1556 __isl_take isl_basic_set *bset);
1557 __isl_give isl_basic_map *isl_basic_map_remove_divs(
1558 __isl_take isl_basic_map *bmap);
1559 __isl_give isl_set *isl_set_remove_divs(
1560 __isl_take isl_set *set);
1561 __isl_give isl_map *isl_map_remove_divs(
1562 __isl_take isl_map *map);
1564 It is also possible to only remove those divs that are defined
1565 in terms of a given range of dimensions or only those for which
1566 no explicit representation is known.
1568 __isl_give isl_basic_set *
1569 isl_basic_set_remove_divs_involving_dims(
1570 __isl_take isl_basic_set *bset,
1571 enum isl_dim_type type,
1572 unsigned first, unsigned n);
1573 __isl_give isl_basic_map *
1574 isl_basic_map_remove_divs_involving_dims(
1575 __isl_take isl_basic_map *bmap,
1576 enum isl_dim_type type,
1577 unsigned first, unsigned n);
1578 __isl_give isl_set *isl_set_remove_divs_involving_dims(
1579 __isl_take isl_set *set, enum isl_dim_type type,
1580 unsigned first, unsigned n);
1581 __isl_give isl_map *isl_map_remove_divs_involving_dims(
1582 __isl_take isl_map *map, enum isl_dim_type type,
1583 unsigned first, unsigned n);
1585 __isl_give isl_basic_set *
1586 isl_basic_set_remove_unknown_divs(
1587 __isl_take isl_basic_set *bset);
1588 __isl_give isl_set *isl_set_remove_unknown_divs(
1589 __isl_take isl_set *set);
1590 __isl_give isl_map *isl_map_remove_unknown_divs(
1591 __isl_take isl_map *map);
1593 To iterate over all the sets or maps in a union set or map, use
1595 int isl_union_set_foreach_set(__isl_keep isl_union_set *uset,
1596 int (*fn)(__isl_take isl_set *set, void *user),
1598 int isl_union_map_foreach_map(__isl_keep isl_union_map *umap,
1599 int (*fn)(__isl_take isl_map *map, void *user),
1602 The number of sets or maps in a union set or map can be obtained
1605 int isl_union_set_n_set(__isl_keep isl_union_set *uset);
1606 int isl_union_map_n_map(__isl_keep isl_union_map *umap);
1608 To extract the set or map in a given space from a union, use
1610 __isl_give isl_set *isl_union_set_extract_set(
1611 __isl_keep isl_union_set *uset,
1612 __isl_take isl_space *space);
1613 __isl_give isl_map *isl_union_map_extract_map(
1614 __isl_keep isl_union_map *umap,
1615 __isl_take isl_space *space);
1617 To iterate over all the basic sets or maps in a set or map, use
1619 int isl_set_foreach_basic_set(__isl_keep isl_set *set,
1620 int (*fn)(__isl_take isl_basic_set *bset, void *user),
1622 int isl_map_foreach_basic_map(__isl_keep isl_map *map,
1623 int (*fn)(__isl_take isl_basic_map *bmap, void *user),
1626 The callback function C<fn> should return 0 if successful and
1627 -1 if an error occurs. In the latter case, or if any other error
1628 occurs, the above functions will return -1.
1630 It should be noted that C<isl> does not guarantee that
1631 the basic sets or maps passed to C<fn> are disjoint.
1632 If this is required, then the user should call one of
1633 the following functions first.
1635 __isl_give isl_set *isl_set_make_disjoint(
1636 __isl_take isl_set *set);
1637 __isl_give isl_map *isl_map_make_disjoint(
1638 __isl_take isl_map *map);
1640 The number of basic sets in a set can be obtained
1643 int isl_set_n_basic_set(__isl_keep isl_set *set);
1645 To iterate over the constraints of a basic set or map, use
1647 #include <isl/constraint.h>
1649 int isl_basic_set_n_constraint(
1650 __isl_keep isl_basic_set *bset);
1651 int isl_basic_set_foreach_constraint(
1652 __isl_keep isl_basic_set *bset,
1653 int (*fn)(__isl_take isl_constraint *c, void *user),
1655 int isl_basic_map_foreach_constraint(
1656 __isl_keep isl_basic_map *bmap,
1657 int (*fn)(__isl_take isl_constraint *c, void *user),
1659 void *isl_constraint_free(__isl_take isl_constraint *c);
1661 Again, the callback function C<fn> should return 0 if successful and
1662 -1 if an error occurs. In the latter case, or if any other error
1663 occurs, the above functions will return -1.
1664 The constraint C<c> represents either an equality or an inequality.
1665 Use the following function to find out whether a constraint
1666 represents an equality. If not, it represents an inequality.
1668 int isl_constraint_is_equality(
1669 __isl_keep isl_constraint *constraint);
1671 The coefficients of the constraints can be inspected using
1672 the following functions.
1674 int isl_constraint_is_lower_bound(
1675 __isl_keep isl_constraint *constraint,
1676 enum isl_dim_type type, unsigned pos);
1677 int isl_constraint_is_upper_bound(
1678 __isl_keep isl_constraint *constraint,
1679 enum isl_dim_type type, unsigned pos);
1680 __isl_give isl_val *isl_constraint_get_constant_val(
1681 __isl_keep isl_constraint *constraint);
1682 __isl_give isl_val *isl_constraint_get_coefficient_val(
1683 __isl_keep isl_constraint *constraint,
1684 enum isl_dim_type type, int pos);
1685 int isl_constraint_involves_dims(
1686 __isl_keep isl_constraint *constraint,
1687 enum isl_dim_type type, unsigned first, unsigned n);
1689 The explicit representations of the existentially quantified
1690 variables can be inspected using the following function.
1691 Note that the user is only allowed to use this function
1692 if the inspected set or map is the result of a call
1693 to C<isl_set_compute_divs> or C<isl_map_compute_divs>.
1694 The existentially quantified variable is equal to the floor
1695 of the returned affine expression. The affine expression
1696 itself can be inspected using the functions in
1697 L<"Piecewise Quasi Affine Expressions">.
1699 __isl_give isl_aff *isl_constraint_get_div(
1700 __isl_keep isl_constraint *constraint, int pos);
1702 To obtain the constraints of a basic set or map in matrix
1703 form, use the following functions.
1705 __isl_give isl_mat *isl_basic_set_equalities_matrix(
1706 __isl_keep isl_basic_set *bset,
1707 enum isl_dim_type c1, enum isl_dim_type c2,
1708 enum isl_dim_type c3, enum isl_dim_type c4);
1709 __isl_give isl_mat *isl_basic_set_inequalities_matrix(
1710 __isl_keep isl_basic_set *bset,
1711 enum isl_dim_type c1, enum isl_dim_type c2,
1712 enum isl_dim_type c3, enum isl_dim_type c4);
1713 __isl_give isl_mat *isl_basic_map_equalities_matrix(
1714 __isl_keep isl_basic_map *bmap,
1715 enum isl_dim_type c1,
1716 enum isl_dim_type c2, enum isl_dim_type c3,
1717 enum isl_dim_type c4, enum isl_dim_type c5);
1718 __isl_give isl_mat *isl_basic_map_inequalities_matrix(
1719 __isl_keep isl_basic_map *bmap,
1720 enum isl_dim_type c1,
1721 enum isl_dim_type c2, enum isl_dim_type c3,
1722 enum isl_dim_type c4, enum isl_dim_type c5);
1724 The C<isl_dim_type> arguments dictate the order in which
1725 different kinds of variables appear in the resulting matrix
1726 and should be a permutation of C<isl_dim_cst>, C<isl_dim_param>,
1727 C<isl_dim_in>, C<isl_dim_out> and C<isl_dim_div>.
1729 The number of parameters, input, output or set dimensions can
1730 be obtained using the following functions.
1732 unsigned isl_basic_set_dim(__isl_keep isl_basic_set *bset,
1733 enum isl_dim_type type);
1734 unsigned isl_basic_map_dim(__isl_keep isl_basic_map *bmap,
1735 enum isl_dim_type type);
1736 unsigned isl_set_dim(__isl_keep isl_set *set,
1737 enum isl_dim_type type);
1738 unsigned isl_map_dim(__isl_keep isl_map *map,
1739 enum isl_dim_type type);
1741 To check whether the description of a set or relation depends
1742 on one or more given dimensions, it is not necessary to iterate over all
1743 constraints. Instead the following functions can be used.
1745 int isl_basic_set_involves_dims(
1746 __isl_keep isl_basic_set *bset,
1747 enum isl_dim_type type, unsigned first, unsigned n);
1748 int isl_set_involves_dims(__isl_keep isl_set *set,
1749 enum isl_dim_type type, unsigned first, unsigned n);
1750 int isl_basic_map_involves_dims(
1751 __isl_keep isl_basic_map *bmap,
1752 enum isl_dim_type type, unsigned first, unsigned n);
1753 int isl_map_involves_dims(__isl_keep isl_map *map,
1754 enum isl_dim_type type, unsigned first, unsigned n);
1756 Similarly, the following functions can be used to check whether
1757 a given dimension is involved in any lower or upper bound.
1759 int isl_set_dim_has_any_lower_bound(__isl_keep isl_set *set,
1760 enum isl_dim_type type, unsigned pos);
1761 int isl_set_dim_has_any_upper_bound(__isl_keep isl_set *set,
1762 enum isl_dim_type type, unsigned pos);
1764 Note that these functions return true even if there is a bound on
1765 the dimension on only some of the basic sets of C<set>.
1766 To check if they have a bound for all of the basic sets in C<set>,
1767 use the following functions instead.
1769 int isl_set_dim_has_lower_bound(__isl_keep isl_set *set,
1770 enum isl_dim_type type, unsigned pos);
1771 int isl_set_dim_has_upper_bound(__isl_keep isl_set *set,
1772 enum isl_dim_type type, unsigned pos);
1774 The identifiers or names of the domain and range spaces of a set
1775 or relation can be read off or set using the following functions.
1777 __isl_give isl_set *isl_set_set_tuple_id(
1778 __isl_take isl_set *set, __isl_take isl_id *id);
1779 __isl_give isl_set *isl_set_reset_tuple_id(
1780 __isl_take isl_set *set);
1781 int isl_set_has_tuple_id(__isl_keep isl_set *set);
1782 __isl_give isl_id *isl_set_get_tuple_id(
1783 __isl_keep isl_set *set);
1784 __isl_give isl_map *isl_map_set_tuple_id(
1785 __isl_take isl_map *map, enum isl_dim_type type,
1786 __isl_take isl_id *id);
1787 __isl_give isl_map *isl_map_reset_tuple_id(
1788 __isl_take isl_map *map, enum isl_dim_type type);
1789 int isl_map_has_tuple_id(__isl_keep isl_map *map,
1790 enum isl_dim_type type);
1791 __isl_give isl_id *isl_map_get_tuple_id(
1792 __isl_keep isl_map *map, enum isl_dim_type type);
1794 const char *isl_basic_set_get_tuple_name(
1795 __isl_keep isl_basic_set *bset);
1796 __isl_give isl_basic_set *isl_basic_set_set_tuple_name(
1797 __isl_take isl_basic_set *set, const char *s);
1798 int isl_set_has_tuple_name(__isl_keep isl_set *set);
1799 const char *isl_set_get_tuple_name(
1800 __isl_keep isl_set *set);
1801 const char *isl_basic_map_get_tuple_name(
1802 __isl_keep isl_basic_map *bmap,
1803 enum isl_dim_type type);
1804 __isl_give isl_basic_map *isl_basic_map_set_tuple_name(
1805 __isl_take isl_basic_map *bmap,
1806 enum isl_dim_type type, const char *s);
1807 int isl_map_has_tuple_name(__isl_keep isl_map *map,
1808 enum isl_dim_type type);
1809 const char *isl_map_get_tuple_name(
1810 __isl_keep isl_map *map,
1811 enum isl_dim_type type);
1813 As with C<isl_space_get_tuple_name>, the value returned points to
1814 an internal data structure.
1815 The identifiers, positions or names of individual dimensions can be
1816 read off using the following functions.
1818 __isl_give isl_id *isl_basic_set_get_dim_id(
1819 __isl_keep isl_basic_set *bset,
1820 enum isl_dim_type type, unsigned pos);
1821 __isl_give isl_set *isl_set_set_dim_id(
1822 __isl_take isl_set *set, enum isl_dim_type type,
1823 unsigned pos, __isl_take isl_id *id);
1824 int isl_set_has_dim_id(__isl_keep isl_set *set,
1825 enum isl_dim_type type, unsigned pos);
1826 __isl_give isl_id *isl_set_get_dim_id(
1827 __isl_keep isl_set *set, enum isl_dim_type type,
1829 int isl_basic_map_has_dim_id(
1830 __isl_keep isl_basic_map *bmap,
1831 enum isl_dim_type type, unsigned pos);
1832 __isl_give isl_map *isl_map_set_dim_id(
1833 __isl_take isl_map *map, enum isl_dim_type type,
1834 unsigned pos, __isl_take isl_id *id);
1835 int isl_map_has_dim_id(__isl_keep isl_map *map,
1836 enum isl_dim_type type, unsigned pos);
1837 __isl_give isl_id *isl_map_get_dim_id(
1838 __isl_keep isl_map *map, enum isl_dim_type type,
1841 int isl_set_find_dim_by_id(__isl_keep isl_set *set,
1842 enum isl_dim_type type, __isl_keep isl_id *id);
1843 int isl_map_find_dim_by_id(__isl_keep isl_map *map,
1844 enum isl_dim_type type, __isl_keep isl_id *id);
1845 int isl_set_find_dim_by_name(__isl_keep isl_set *set,
1846 enum isl_dim_type type, const char *name);
1847 int isl_map_find_dim_by_name(__isl_keep isl_map *map,
1848 enum isl_dim_type type, const char *name);
1850 const char *isl_constraint_get_dim_name(
1851 __isl_keep isl_constraint *constraint,
1852 enum isl_dim_type type, unsigned pos);
1853 const char *isl_basic_set_get_dim_name(
1854 __isl_keep isl_basic_set *bset,
1855 enum isl_dim_type type, unsigned pos);
1856 int isl_set_has_dim_name(__isl_keep isl_set *set,
1857 enum isl_dim_type type, unsigned pos);
1858 const char *isl_set_get_dim_name(
1859 __isl_keep isl_set *set,
1860 enum isl_dim_type type, unsigned pos);
1861 const char *isl_basic_map_get_dim_name(
1862 __isl_keep isl_basic_map *bmap,
1863 enum isl_dim_type type, unsigned pos);
1864 int isl_map_has_dim_name(__isl_keep isl_map *map,
1865 enum isl_dim_type type, unsigned pos);
1866 const char *isl_map_get_dim_name(
1867 __isl_keep isl_map *map,
1868 enum isl_dim_type type, unsigned pos);
1870 These functions are mostly useful to obtain the identifiers, positions
1871 or names of the parameters. Identifiers of individual dimensions are
1872 essentially only useful for printing. They are ignored by all other
1873 operations and may not be preserved across those operations.
1877 =head3 Unary Properties
1883 The following functions test whether the given set or relation
1884 contains any integer points. The ``plain'' variants do not perform
1885 any computations, but simply check if the given set or relation
1886 is already known to be empty.
1888 int isl_basic_set_plain_is_empty(__isl_keep isl_basic_set *bset);
1889 int isl_basic_set_is_empty(__isl_keep isl_basic_set *bset);
1890 int isl_set_plain_is_empty(__isl_keep isl_set *set);
1891 int isl_set_is_empty(__isl_keep isl_set *set);
1892 int isl_union_set_is_empty(__isl_keep isl_union_set *uset);
1893 int isl_basic_map_plain_is_empty(__isl_keep isl_basic_map *bmap);
1894 int isl_basic_map_is_empty(__isl_keep isl_basic_map *bmap);
1895 int isl_map_plain_is_empty(__isl_keep isl_map *map);
1896 int isl_map_is_empty(__isl_keep isl_map *map);
1897 int isl_union_map_is_empty(__isl_keep isl_union_map *umap);
1899 =item * Universality
1901 int isl_basic_set_is_universe(__isl_keep isl_basic_set *bset);
1902 int isl_basic_map_is_universe(__isl_keep isl_basic_map *bmap);
1903 int isl_set_plain_is_universe(__isl_keep isl_set *set);
1905 =item * Single-valuedness
1907 int isl_basic_map_is_single_valued(
1908 __isl_keep isl_basic_map *bmap);
1909 int isl_map_plain_is_single_valued(
1910 __isl_keep isl_map *map);
1911 int isl_map_is_single_valued(__isl_keep isl_map *map);
1912 int isl_union_map_is_single_valued(__isl_keep isl_union_map *umap);
1916 int isl_map_plain_is_injective(__isl_keep isl_map *map);
1917 int isl_map_is_injective(__isl_keep isl_map *map);
1918 int isl_union_map_plain_is_injective(
1919 __isl_keep isl_union_map *umap);
1920 int isl_union_map_is_injective(
1921 __isl_keep isl_union_map *umap);
1925 int isl_map_is_bijective(__isl_keep isl_map *map);
1926 int isl_union_map_is_bijective(__isl_keep isl_union_map *umap);
1930 __isl_give isl_val *
1931 isl_basic_map_plain_get_val_if_fixed(
1932 __isl_keep isl_basic_map *bmap,
1933 enum isl_dim_type type, unsigned pos);
1934 __isl_give isl_val *isl_set_plain_get_val_if_fixed(
1935 __isl_keep isl_set *set,
1936 enum isl_dim_type type, unsigned pos);
1937 __isl_give isl_val *isl_map_plain_get_val_if_fixed(
1938 __isl_keep isl_map *map,
1939 enum isl_dim_type type, unsigned pos);
1941 If the set or relation obviously lies on a hyperplane where the given dimension
1942 has a fixed value, then return that value.
1943 Otherwise return NaN.
1947 int isl_set_dim_residue_class_val(
1948 __isl_keep isl_set *set,
1949 int pos, __isl_give isl_val **modulo,
1950 __isl_give isl_val **residue);
1952 Check if the values of the given set dimension are equal to a fixed
1953 value modulo some integer value. If so, assign the modulo to C<*modulo>
1954 and the fixed value to C<*residue>. If the given dimension attains only
1955 a single value, then assign C<0> to C<*modulo> and the fixed value to
1957 If the dimension does not attain only a single value and if no modulo
1958 can be found then assign C<1> to C<*modulo> and C<1> to C<*residue>.
1962 To check whether a set is a parameter domain, use this function:
1964 int isl_set_is_params(__isl_keep isl_set *set);
1965 int isl_union_set_is_params(
1966 __isl_keep isl_union_set *uset);
1970 The following functions check whether the domain of the given
1971 (basic) set is a wrapped relation.
1973 int isl_basic_set_is_wrapping(
1974 __isl_keep isl_basic_set *bset);
1975 int isl_set_is_wrapping(__isl_keep isl_set *set);
1977 =item * Internal Product
1979 int isl_basic_map_can_zip(
1980 __isl_keep isl_basic_map *bmap);
1981 int isl_map_can_zip(__isl_keep isl_map *map);
1983 Check whether the product of domain and range of the given relation
1985 i.e., whether both domain and range are nested relations.
1989 int isl_basic_map_can_curry(
1990 __isl_keep isl_basic_map *bmap);
1991 int isl_map_can_curry(__isl_keep isl_map *map);
1993 Check whether the domain of the (basic) relation is a wrapped relation.
1995 int isl_basic_map_can_uncurry(
1996 __isl_keep isl_basic_map *bmap);
1997 int isl_map_can_uncurry(__isl_keep isl_map *map);
1999 Check whether the range of the (basic) relation is a wrapped relation.
2003 =head3 Binary Properties
2009 int isl_basic_set_plain_is_equal(
2010 __isl_keep isl_basic_set *bset1,
2011 __isl_keep isl_basic_set *bset2);
2012 int isl_set_plain_is_equal(__isl_keep isl_set *set1,
2013 __isl_keep isl_set *set2);
2014 int isl_set_is_equal(__isl_keep isl_set *set1,
2015 __isl_keep isl_set *set2);
2016 int isl_union_set_is_equal(
2017 __isl_keep isl_union_set *uset1,
2018 __isl_keep isl_union_set *uset2);
2019 int isl_basic_map_is_equal(
2020 __isl_keep isl_basic_map *bmap1,
2021 __isl_keep isl_basic_map *bmap2);
2022 int isl_map_is_equal(__isl_keep isl_map *map1,
2023 __isl_keep isl_map *map2);
2024 int isl_map_plain_is_equal(__isl_keep isl_map *map1,
2025 __isl_keep isl_map *map2);
2026 int isl_union_map_is_equal(
2027 __isl_keep isl_union_map *umap1,
2028 __isl_keep isl_union_map *umap2);
2030 =item * Disjointness
2032 int isl_basic_set_is_disjoint(
2033 __isl_keep isl_basic_set *bset1,
2034 __isl_keep isl_basic_set *bset2);
2035 int isl_set_plain_is_disjoint(__isl_keep isl_set *set1,
2036 __isl_keep isl_set *set2);
2037 int isl_set_is_disjoint(__isl_keep isl_set *set1,
2038 __isl_keep isl_set *set2);
2039 int isl_basic_map_is_disjoint(
2040 __isl_keep isl_basic_map *bmap1,
2041 __isl_keep isl_basic_map *bmap2);
2042 int isl_map_is_disjoint(__isl_keep isl_map *map1,
2043 __isl_keep isl_map *map2);
2047 int isl_basic_set_is_subset(
2048 __isl_keep isl_basic_set *bset1,
2049 __isl_keep isl_basic_set *bset2);
2050 int isl_set_is_subset(__isl_keep isl_set *set1,
2051 __isl_keep isl_set *set2);
2052 int isl_set_is_strict_subset(
2053 __isl_keep isl_set *set1,
2054 __isl_keep isl_set *set2);
2055 int isl_union_set_is_subset(
2056 __isl_keep isl_union_set *uset1,
2057 __isl_keep isl_union_set *uset2);
2058 int isl_union_set_is_strict_subset(
2059 __isl_keep isl_union_set *uset1,
2060 __isl_keep isl_union_set *uset2);
2061 int isl_basic_map_is_subset(
2062 __isl_keep isl_basic_map *bmap1,
2063 __isl_keep isl_basic_map *bmap2);
2064 int isl_basic_map_is_strict_subset(
2065 __isl_keep isl_basic_map *bmap1,
2066 __isl_keep isl_basic_map *bmap2);
2067 int isl_map_is_subset(
2068 __isl_keep isl_map *map1,
2069 __isl_keep isl_map *map2);
2070 int isl_map_is_strict_subset(
2071 __isl_keep isl_map *map1,
2072 __isl_keep isl_map *map2);
2073 int isl_union_map_is_subset(
2074 __isl_keep isl_union_map *umap1,
2075 __isl_keep isl_union_map *umap2);
2076 int isl_union_map_is_strict_subset(
2077 __isl_keep isl_union_map *umap1,
2078 __isl_keep isl_union_map *umap2);
2080 Check whether the first argument is a (strict) subset of the
2085 int isl_set_plain_cmp(__isl_keep isl_set *set1,
2086 __isl_keep isl_set *set2);
2088 This function is useful for sorting C<isl_set>s.
2089 The order depends on the internal representation of the inputs.
2090 The order is fixed over different calls to the function (assuming
2091 the internal representation of the inputs has not changed), but may
2092 change over different versions of C<isl>.
2096 =head2 Unary Operations
2102 __isl_give isl_set *isl_set_complement(
2103 __isl_take isl_set *set);
2104 __isl_give isl_map *isl_map_complement(
2105 __isl_take isl_map *map);
2109 __isl_give isl_basic_map *isl_basic_map_reverse(
2110 __isl_take isl_basic_map *bmap);
2111 __isl_give isl_map *isl_map_reverse(
2112 __isl_take isl_map *map);
2113 __isl_give isl_union_map *isl_union_map_reverse(
2114 __isl_take isl_union_map *umap);
2118 __isl_give isl_basic_set *isl_basic_set_project_out(
2119 __isl_take isl_basic_set *bset,
2120 enum isl_dim_type type, unsigned first, unsigned n);
2121 __isl_give isl_basic_map *isl_basic_map_project_out(
2122 __isl_take isl_basic_map *bmap,
2123 enum isl_dim_type type, unsigned first, unsigned n);
2124 __isl_give isl_set *isl_set_project_out(__isl_take isl_set *set,
2125 enum isl_dim_type type, unsigned first, unsigned n);
2126 __isl_give isl_map *isl_map_project_out(__isl_take isl_map *map,
2127 enum isl_dim_type type, unsigned first, unsigned n);
2128 __isl_give isl_basic_set *isl_basic_set_params(
2129 __isl_take isl_basic_set *bset);
2130 __isl_give isl_basic_set *isl_basic_map_domain(
2131 __isl_take isl_basic_map *bmap);
2132 __isl_give isl_basic_set *isl_basic_map_range(
2133 __isl_take isl_basic_map *bmap);
2134 __isl_give isl_set *isl_set_params(__isl_take isl_set *set);
2135 __isl_give isl_set *isl_map_params(__isl_take isl_map *map);
2136 __isl_give isl_set *isl_map_domain(
2137 __isl_take isl_map *bmap);
2138 __isl_give isl_set *isl_map_range(
2139 __isl_take isl_map *map);
2140 __isl_give isl_set *isl_union_set_params(
2141 __isl_take isl_union_set *uset);
2142 __isl_give isl_set *isl_union_map_params(
2143 __isl_take isl_union_map *umap);
2144 __isl_give isl_union_set *isl_union_map_domain(
2145 __isl_take isl_union_map *umap);
2146 __isl_give isl_union_set *isl_union_map_range(
2147 __isl_take isl_union_map *umap);
2149 __isl_give isl_basic_map *isl_basic_map_domain_map(
2150 __isl_take isl_basic_map *bmap);
2151 __isl_give isl_basic_map *isl_basic_map_range_map(
2152 __isl_take isl_basic_map *bmap);
2153 __isl_give isl_map *isl_map_domain_map(__isl_take isl_map *map);
2154 __isl_give isl_map *isl_map_range_map(__isl_take isl_map *map);
2155 __isl_give isl_union_map *isl_union_map_domain_map(
2156 __isl_take isl_union_map *umap);
2157 __isl_give isl_union_map *isl_union_map_range_map(
2158 __isl_take isl_union_map *umap);
2160 The functions above construct a (basic, regular or union) relation
2161 that maps (a wrapped version of) the input relation to its domain or range.
2165 __isl_give isl_basic_set *isl_basic_set_eliminate(
2166 __isl_take isl_basic_set *bset,
2167 enum isl_dim_type type,
2168 unsigned first, unsigned n);
2169 __isl_give isl_set *isl_set_eliminate(
2170 __isl_take isl_set *set, enum isl_dim_type type,
2171 unsigned first, unsigned n);
2172 __isl_give isl_basic_map *isl_basic_map_eliminate(
2173 __isl_take isl_basic_map *bmap,
2174 enum isl_dim_type type,
2175 unsigned first, unsigned n);
2176 __isl_give isl_map *isl_map_eliminate(
2177 __isl_take isl_map *map, enum isl_dim_type type,
2178 unsigned first, unsigned n);
2180 Eliminate the coefficients for the given dimensions from the constraints,
2181 without removing the dimensions.
2185 __isl_give isl_basic_set *isl_basic_set_fix_si(
2186 __isl_take isl_basic_set *bset,
2187 enum isl_dim_type type, unsigned pos, int value);
2188 __isl_give isl_basic_set *isl_basic_set_fix_val(
2189 __isl_take isl_basic_set *bset,
2190 enum isl_dim_type type, unsigned pos,
2191 __isl_take isl_val *v);
2192 __isl_give isl_set *isl_set_fix_si(__isl_take isl_set *set,
2193 enum isl_dim_type type, unsigned pos, int value);
2194 __isl_give isl_set *isl_set_fix_val(
2195 __isl_take isl_set *set,
2196 enum isl_dim_type type, unsigned pos,
2197 __isl_take isl_val *v);
2198 __isl_give isl_basic_map *isl_basic_map_fix_si(
2199 __isl_take isl_basic_map *bmap,
2200 enum isl_dim_type type, unsigned pos, int value);
2201 __isl_give isl_basic_map *isl_basic_map_fix_val(
2202 __isl_take isl_basic_map *bmap,
2203 enum isl_dim_type type, unsigned pos,
2204 __isl_take isl_val *v);
2205 __isl_give isl_map *isl_map_fix_si(__isl_take isl_map *map,
2206 enum isl_dim_type type, unsigned pos, int value);
2207 __isl_give isl_map *isl_map_fix_val(
2208 __isl_take isl_map *map,
2209 enum isl_dim_type type, unsigned pos,
2210 __isl_take isl_val *v);
2212 Intersect the set or relation with the hyperplane where the given
2213 dimension has the fixed given value.
2215 __isl_give isl_basic_map *isl_basic_map_lower_bound_si(
2216 __isl_take isl_basic_map *bmap,
2217 enum isl_dim_type type, unsigned pos, int value);
2218 __isl_give isl_basic_map *isl_basic_map_upper_bound_si(
2219 __isl_take isl_basic_map *bmap,
2220 enum isl_dim_type type, unsigned pos, int value);
2221 __isl_give isl_set *isl_set_lower_bound_si(
2222 __isl_take isl_set *set,
2223 enum isl_dim_type type, unsigned pos, int value);
2224 __isl_give isl_set *isl_set_lower_bound_val(
2225 __isl_take isl_set *set,
2226 enum isl_dim_type type, unsigned pos,
2227 __isl_take isl_val *value);
2228 __isl_give isl_map *isl_map_lower_bound_si(
2229 __isl_take isl_map *map,
2230 enum isl_dim_type type, unsigned pos, int value);
2231 __isl_give isl_set *isl_set_upper_bound_si(
2232 __isl_take isl_set *set,
2233 enum isl_dim_type type, unsigned pos, int value);
2234 __isl_give isl_set *isl_set_upper_bound_val(
2235 __isl_take isl_set *set,
2236 enum isl_dim_type type, unsigned pos,
2237 __isl_take isl_val *value);
2238 __isl_give isl_map *isl_map_upper_bound_si(
2239 __isl_take isl_map *map,
2240 enum isl_dim_type type, unsigned pos, int value);
2242 Intersect the set or relation with the half-space where the given
2243 dimension has a value bounded by the fixed given integer value.
2245 __isl_give isl_set *isl_set_equate(__isl_take isl_set *set,
2246 enum isl_dim_type type1, int pos1,
2247 enum isl_dim_type type2, int pos2);
2248 __isl_give isl_basic_map *isl_basic_map_equate(
2249 __isl_take isl_basic_map *bmap,
2250 enum isl_dim_type type1, int pos1,
2251 enum isl_dim_type type2, int pos2);
2252 __isl_give isl_map *isl_map_equate(__isl_take isl_map *map,
2253 enum isl_dim_type type1, int pos1,
2254 enum isl_dim_type type2, int pos2);
2256 Intersect the set or relation with the hyperplane where the given
2257 dimensions are equal to each other.
2259 __isl_give isl_map *isl_map_oppose(__isl_take isl_map *map,
2260 enum isl_dim_type type1, int pos1,
2261 enum isl_dim_type type2, int pos2);
2263 Intersect the relation with the hyperplane where the given
2264 dimensions have opposite values.
2266 __isl_give isl_basic_map *isl_basic_map_order_ge(
2267 __isl_take isl_basic_map *bmap,
2268 enum isl_dim_type type1, int pos1,
2269 enum isl_dim_type type2, int pos2);
2270 __isl_give isl_map *isl_map_order_lt(__isl_take isl_map *map,
2271 enum isl_dim_type type1, int pos1,
2272 enum isl_dim_type type2, int pos2);
2273 __isl_give isl_basic_map *isl_basic_map_order_gt(
2274 __isl_take isl_basic_map *bmap,
2275 enum isl_dim_type type1, int pos1,
2276 enum isl_dim_type type2, int pos2);
2277 __isl_give isl_map *isl_map_order_gt(__isl_take isl_map *map,
2278 enum isl_dim_type type1, int pos1,
2279 enum isl_dim_type type2, int pos2);
2281 Intersect the relation with the half-space where the given
2282 dimensions satisfy the given ordering.
2286 __isl_give isl_map *isl_set_identity(
2287 __isl_take isl_set *set);
2288 __isl_give isl_union_map *isl_union_set_identity(
2289 __isl_take isl_union_set *uset);
2291 Construct an identity relation on the given (union) set.
2295 __isl_give isl_basic_set *isl_basic_map_deltas(
2296 __isl_take isl_basic_map *bmap);
2297 __isl_give isl_set *isl_map_deltas(__isl_take isl_map *map);
2298 __isl_give isl_union_set *isl_union_map_deltas(
2299 __isl_take isl_union_map *umap);
2301 These functions return a (basic) set containing the differences
2302 between image elements and corresponding domain elements in the input.
2304 __isl_give isl_basic_map *isl_basic_map_deltas_map(
2305 __isl_take isl_basic_map *bmap);
2306 __isl_give isl_map *isl_map_deltas_map(
2307 __isl_take isl_map *map);
2308 __isl_give isl_union_map *isl_union_map_deltas_map(
2309 __isl_take isl_union_map *umap);
2311 The functions above construct a (basic, regular or union) relation
2312 that maps (a wrapped version of) the input relation to its delta set.
2316 Simplify the representation of a set or relation by trying
2317 to combine pairs of basic sets or relations into a single
2318 basic set or relation.
2320 __isl_give isl_set *isl_set_coalesce(__isl_take isl_set *set);
2321 __isl_give isl_map *isl_map_coalesce(__isl_take isl_map *map);
2322 __isl_give isl_union_set *isl_union_set_coalesce(
2323 __isl_take isl_union_set *uset);
2324 __isl_give isl_union_map *isl_union_map_coalesce(
2325 __isl_take isl_union_map *umap);
2327 One of the methods for combining pairs of basic sets or relations
2328 can result in coefficients that are much larger than those that appear
2329 in the constraints of the input. By default, the coefficients are
2330 not allowed to grow larger, but this can be changed by unsetting
2331 the following option.
2333 int isl_options_set_coalesce_bounded_wrapping(
2334 isl_ctx *ctx, int val);
2335 int isl_options_get_coalesce_bounded_wrapping(
2338 =item * Detecting equalities
2340 __isl_give isl_basic_set *isl_basic_set_detect_equalities(
2341 __isl_take isl_basic_set *bset);
2342 __isl_give isl_basic_map *isl_basic_map_detect_equalities(
2343 __isl_take isl_basic_map *bmap);
2344 __isl_give isl_set *isl_set_detect_equalities(
2345 __isl_take isl_set *set);
2346 __isl_give isl_map *isl_map_detect_equalities(
2347 __isl_take isl_map *map);
2348 __isl_give isl_union_set *isl_union_set_detect_equalities(
2349 __isl_take isl_union_set *uset);
2350 __isl_give isl_union_map *isl_union_map_detect_equalities(
2351 __isl_take isl_union_map *umap);
2353 Simplify the representation of a set or relation by detecting implicit
2356 =item * Removing redundant constraints
2358 __isl_give isl_basic_set *isl_basic_set_remove_redundancies(
2359 __isl_take isl_basic_set *bset);
2360 __isl_give isl_set *isl_set_remove_redundancies(
2361 __isl_take isl_set *set);
2362 __isl_give isl_basic_map *isl_basic_map_remove_redundancies(
2363 __isl_take isl_basic_map *bmap);
2364 __isl_give isl_map *isl_map_remove_redundancies(
2365 __isl_take isl_map *map);
2369 __isl_give isl_basic_set *isl_set_convex_hull(
2370 __isl_take isl_set *set);
2371 __isl_give isl_basic_map *isl_map_convex_hull(
2372 __isl_take isl_map *map);
2374 If the input set or relation has any existentially quantified
2375 variables, then the result of these operations is currently undefined.
2379 __isl_give isl_basic_set *
2380 isl_set_unshifted_simple_hull(
2381 __isl_take isl_set *set);
2382 __isl_give isl_basic_map *
2383 isl_map_unshifted_simple_hull(
2384 __isl_take isl_map *map);
2385 __isl_give isl_basic_set *isl_set_simple_hull(
2386 __isl_take isl_set *set);
2387 __isl_give isl_basic_map *isl_map_simple_hull(
2388 __isl_take isl_map *map);
2389 __isl_give isl_union_map *isl_union_map_simple_hull(
2390 __isl_take isl_union_map *umap);
2392 These functions compute a single basic set or relation
2393 that contains the whole input set or relation.
2394 In particular, the output is described by translates
2395 of the constraints describing the basic sets or relations in the input.
2396 In case of C<isl_set_unshifted_simple_hull>, only the original
2397 constraints are used, without any translation.
2401 (See \autoref{s:simple hull}.)
2407 __isl_give isl_basic_set *isl_basic_set_affine_hull(
2408 __isl_take isl_basic_set *bset);
2409 __isl_give isl_basic_set *isl_set_affine_hull(
2410 __isl_take isl_set *set);
2411 __isl_give isl_union_set *isl_union_set_affine_hull(
2412 __isl_take isl_union_set *uset);
2413 __isl_give isl_basic_map *isl_basic_map_affine_hull(
2414 __isl_take isl_basic_map *bmap);
2415 __isl_give isl_basic_map *isl_map_affine_hull(
2416 __isl_take isl_map *map);
2417 __isl_give isl_union_map *isl_union_map_affine_hull(
2418 __isl_take isl_union_map *umap);
2420 In case of union sets and relations, the affine hull is computed
2423 =item * Polyhedral hull
2425 __isl_give isl_basic_set *isl_set_polyhedral_hull(
2426 __isl_take isl_set *set);
2427 __isl_give isl_basic_map *isl_map_polyhedral_hull(
2428 __isl_take isl_map *map);
2429 __isl_give isl_union_set *isl_union_set_polyhedral_hull(
2430 __isl_take isl_union_set *uset);
2431 __isl_give isl_union_map *isl_union_map_polyhedral_hull(
2432 __isl_take isl_union_map *umap);
2434 These functions compute a single basic set or relation
2435 not involving any existentially quantified variables
2436 that contains the whole input set or relation.
2437 In case of union sets and relations, the polyhedral hull is computed
2440 =item * Other approximations
2442 __isl_give isl_basic_set *
2443 isl_basic_set_drop_constraints_involving_dims(
2444 __isl_take isl_basic_set *bset,
2445 enum isl_dim_type type,
2446 unsigned first, unsigned n);
2447 __isl_give isl_basic_map *
2448 isl_basic_map_drop_constraints_involving_dims(
2449 __isl_take isl_basic_map *bmap,
2450 enum isl_dim_type type,
2451 unsigned first, unsigned n);
2452 __isl_give isl_basic_set *
2453 isl_basic_set_drop_constraints_not_involving_dims(
2454 __isl_take isl_basic_set *bset,
2455 enum isl_dim_type type,
2456 unsigned first, unsigned n);
2457 __isl_give isl_set *
2458 isl_set_drop_constraints_involving_dims(
2459 __isl_take isl_set *set,
2460 enum isl_dim_type type,
2461 unsigned first, unsigned n);
2462 __isl_give isl_map *
2463 isl_map_drop_constraints_involving_dims(
2464 __isl_take isl_map *map,
2465 enum isl_dim_type type,
2466 unsigned first, unsigned n);
2468 These functions drop any constraints (not) involving the specified dimensions.
2469 Note that the result depends on the representation of the input.
2473 __isl_give isl_basic_set *isl_basic_set_sample(
2474 __isl_take isl_basic_set *bset);
2475 __isl_give isl_basic_set *isl_set_sample(
2476 __isl_take isl_set *set);
2477 __isl_give isl_basic_map *isl_basic_map_sample(
2478 __isl_take isl_basic_map *bmap);
2479 __isl_give isl_basic_map *isl_map_sample(
2480 __isl_take isl_map *map);
2482 If the input (basic) set or relation is non-empty, then return
2483 a singleton subset of the input. Otherwise, return an empty set.
2485 =item * Optimization
2487 #include <isl/ilp.h>
2488 __isl_give isl_val *isl_basic_set_max_val(
2489 __isl_keep isl_basic_set *bset,
2490 __isl_keep isl_aff *obj);
2491 __isl_give isl_val *isl_set_min_val(
2492 __isl_keep isl_set *set,
2493 __isl_keep isl_aff *obj);
2494 __isl_give isl_val *isl_set_max_val(
2495 __isl_keep isl_set *set,
2496 __isl_keep isl_aff *obj);
2498 Compute the minimum or maximum of the integer affine expression C<obj>
2499 over the points in C<set>, returning the result in C<opt>.
2500 The result is C<NULL> in case of an error, the optimal value in case
2501 there is one, negative infinity or infinity if the problem is unbounded and
2502 NaN if the problem is empty.
2504 =item * Parametric optimization
2506 __isl_give isl_pw_aff *isl_set_dim_min(
2507 __isl_take isl_set *set, int pos);
2508 __isl_give isl_pw_aff *isl_set_dim_max(
2509 __isl_take isl_set *set, int pos);
2510 __isl_give isl_pw_aff *isl_map_dim_max(
2511 __isl_take isl_map *map, int pos);
2513 Compute the minimum or maximum of the given set or output dimension
2514 as a function of the parameters (and input dimensions), but independently
2515 of the other set or output dimensions.
2516 For lexicographic optimization, see L<"Lexicographic Optimization">.
2520 The following functions compute either the set of (rational) coefficient
2521 values of valid constraints for the given set or the set of (rational)
2522 values satisfying the constraints with coefficients from the given set.
2523 Internally, these two sets of functions perform essentially the
2524 same operations, except that the set of coefficients is assumed to
2525 be a cone, while the set of values may be any polyhedron.
2526 The current implementation is based on the Farkas lemma and
2527 Fourier-Motzkin elimination, but this may change or be made optional
2528 in future. In particular, future implementations may use different
2529 dualization algorithms or skip the elimination step.
2531 __isl_give isl_basic_set *isl_basic_set_coefficients(
2532 __isl_take isl_basic_set *bset);
2533 __isl_give isl_basic_set *isl_set_coefficients(
2534 __isl_take isl_set *set);
2535 __isl_give isl_union_set *isl_union_set_coefficients(
2536 __isl_take isl_union_set *bset);
2537 __isl_give isl_basic_set *isl_basic_set_solutions(
2538 __isl_take isl_basic_set *bset);
2539 __isl_give isl_basic_set *isl_set_solutions(
2540 __isl_take isl_set *set);
2541 __isl_give isl_union_set *isl_union_set_solutions(
2542 __isl_take isl_union_set *bset);
2546 __isl_give isl_map *isl_map_fixed_power_val(
2547 __isl_take isl_map *map,
2548 __isl_take isl_val *exp);
2549 __isl_give isl_union_map *
2550 isl_union_map_fixed_power_val(
2551 __isl_take isl_union_map *umap,
2552 __isl_take isl_val *exp);
2554 Compute the given power of C<map>, where C<exp> is assumed to be non-zero.
2555 If the exponent C<exp> is negative, then the -C<exp> th power of the inverse
2556 of C<map> is computed.
2558 __isl_give isl_map *isl_map_power(__isl_take isl_map *map,
2560 __isl_give isl_union_map *isl_union_map_power(
2561 __isl_take isl_union_map *umap, int *exact);
2563 Compute a parametric representation for all positive powers I<k> of C<map>.
2564 The result maps I<k> to a nested relation corresponding to the
2565 I<k>th power of C<map>.
2566 The result may be an overapproximation. If the result is known to be exact,
2567 then C<*exact> is set to C<1>.
2569 =item * Transitive closure
2571 __isl_give isl_map *isl_map_transitive_closure(
2572 __isl_take isl_map *map, int *exact);
2573 __isl_give isl_union_map *isl_union_map_transitive_closure(
2574 __isl_take isl_union_map *umap, int *exact);
2576 Compute the transitive closure of C<map>.
2577 The result may be an overapproximation. If the result is known to be exact,
2578 then C<*exact> is set to C<1>.
2580 =item * Reaching path lengths
2582 __isl_give isl_map *isl_map_reaching_path_lengths(
2583 __isl_take isl_map *map, int *exact);
2585 Compute a relation that maps each element in the range of C<map>
2586 to the lengths of all paths composed of edges in C<map> that
2587 end up in the given element.
2588 The result may be an overapproximation. If the result is known to be exact,
2589 then C<*exact> is set to C<1>.
2590 To compute the I<maximal> path length, the resulting relation
2591 should be postprocessed by C<isl_map_lexmax>.
2592 In particular, if the input relation is a dependence relation
2593 (mapping sources to sinks), then the maximal path length corresponds
2594 to the free schedule.
2595 Note, however, that C<isl_map_lexmax> expects the maximum to be
2596 finite, so if the path lengths are unbounded (possibly due to
2597 the overapproximation), then you will get an error message.
2601 __isl_give isl_basic_set *isl_basic_map_wrap(
2602 __isl_take isl_basic_map *bmap);
2603 __isl_give isl_set *isl_map_wrap(
2604 __isl_take isl_map *map);
2605 __isl_give isl_union_set *isl_union_map_wrap(
2606 __isl_take isl_union_map *umap);
2607 __isl_give isl_basic_map *isl_basic_set_unwrap(
2608 __isl_take isl_basic_set *bset);
2609 __isl_give isl_map *isl_set_unwrap(
2610 __isl_take isl_set *set);
2611 __isl_give isl_union_map *isl_union_set_unwrap(
2612 __isl_take isl_union_set *uset);
2616 Remove any internal structure of domain (and range) of the given
2617 set or relation. If there is any such internal structure in the input,
2618 then the name of the space is also removed.
2620 __isl_give isl_basic_set *isl_basic_set_flatten(
2621 __isl_take isl_basic_set *bset);
2622 __isl_give isl_set *isl_set_flatten(
2623 __isl_take isl_set *set);
2624 __isl_give isl_basic_map *isl_basic_map_flatten_domain(
2625 __isl_take isl_basic_map *bmap);
2626 __isl_give isl_basic_map *isl_basic_map_flatten_range(
2627 __isl_take isl_basic_map *bmap);
2628 __isl_give isl_map *isl_map_flatten_range(
2629 __isl_take isl_map *map);
2630 __isl_give isl_map *isl_map_flatten_domain(
2631 __isl_take isl_map *map);
2632 __isl_give isl_basic_map *isl_basic_map_flatten(
2633 __isl_take isl_basic_map *bmap);
2634 __isl_give isl_map *isl_map_flatten(
2635 __isl_take isl_map *map);
2637 __isl_give isl_map *isl_set_flatten_map(
2638 __isl_take isl_set *set);
2640 The function above constructs a relation
2641 that maps the input set to a flattened version of the set.
2645 Lift the input set to a space with extra dimensions corresponding
2646 to the existentially quantified variables in the input.
2647 In particular, the result lives in a wrapped map where the domain
2648 is the original space and the range corresponds to the original
2649 existentially quantified variables.
2651 __isl_give isl_basic_set *isl_basic_set_lift(
2652 __isl_take isl_basic_set *bset);
2653 __isl_give isl_set *isl_set_lift(
2654 __isl_take isl_set *set);
2655 __isl_give isl_union_set *isl_union_set_lift(
2656 __isl_take isl_union_set *uset);
2658 Given a local space that contains the existentially quantified
2659 variables of a set, a basic relation that, when applied to
2660 a basic set, has essentially the same effect as C<isl_basic_set_lift>,
2661 can be constructed using the following function.
2663 #include <isl/local_space.h>
2664 __isl_give isl_basic_map *isl_local_space_lifting(
2665 __isl_take isl_local_space *ls);
2667 =item * Internal Product
2669 __isl_give isl_basic_map *isl_basic_map_zip(
2670 __isl_take isl_basic_map *bmap);
2671 __isl_give isl_map *isl_map_zip(
2672 __isl_take isl_map *map);
2673 __isl_give isl_union_map *isl_union_map_zip(
2674 __isl_take isl_union_map *umap);
2676 Given a relation with nested relations for domain and range,
2677 interchange the range of the domain with the domain of the range.
2681 __isl_give isl_basic_map *isl_basic_map_curry(
2682 __isl_take isl_basic_map *bmap);
2683 __isl_give isl_basic_map *isl_basic_map_uncurry(
2684 __isl_take isl_basic_map *bmap);
2685 __isl_give isl_map *isl_map_curry(
2686 __isl_take isl_map *map);
2687 __isl_give isl_map *isl_map_uncurry(
2688 __isl_take isl_map *map);
2689 __isl_give isl_union_map *isl_union_map_curry(
2690 __isl_take isl_union_map *umap);
2691 __isl_give isl_union_map *isl_union_map_uncurry(
2692 __isl_take isl_union_map *umap);
2694 Given a relation with a nested relation for domain,
2695 the C<curry> functions
2696 move the range of the nested relation out of the domain
2697 and use it as the domain of a nested relation in the range,
2698 with the original range as range of this nested relation.
2699 The C<uncurry> functions perform the inverse operation.
2701 =item * Aligning parameters
2703 __isl_give isl_basic_set *isl_basic_set_align_params(
2704 __isl_take isl_basic_set *bset,
2705 __isl_take isl_space *model);
2706 __isl_give isl_set *isl_set_align_params(
2707 __isl_take isl_set *set,
2708 __isl_take isl_space *model);
2709 __isl_give isl_basic_map *isl_basic_map_align_params(
2710 __isl_take isl_basic_map *bmap,
2711 __isl_take isl_space *model);
2712 __isl_give isl_map *isl_map_align_params(
2713 __isl_take isl_map *map,
2714 __isl_take isl_space *model);
2716 Change the order of the parameters of the given set or relation
2717 such that the first parameters match those of C<model>.
2718 This may involve the introduction of extra parameters.
2719 All parameters need to be named.
2721 =item * Dimension manipulation
2723 __isl_give isl_basic_set *isl_basic_set_add_dims(
2724 __isl_take isl_basic_set *bset,
2725 enum isl_dim_type type, unsigned n);
2726 __isl_give isl_set *isl_set_add_dims(
2727 __isl_take isl_set *set,
2728 enum isl_dim_type type, unsigned n);
2729 __isl_give isl_map *isl_map_add_dims(
2730 __isl_take isl_map *map,
2731 enum isl_dim_type type, unsigned n);
2732 __isl_give isl_basic_set *isl_basic_set_insert_dims(
2733 __isl_take isl_basic_set *bset,
2734 enum isl_dim_type type, unsigned pos,
2736 __isl_give isl_basic_map *isl_basic_map_insert_dims(
2737 __isl_take isl_basic_map *bmap,
2738 enum isl_dim_type type, unsigned pos,
2740 __isl_give isl_set *isl_set_insert_dims(
2741 __isl_take isl_set *set,
2742 enum isl_dim_type type, unsigned pos, unsigned n);
2743 __isl_give isl_map *isl_map_insert_dims(
2744 __isl_take isl_map *map,
2745 enum isl_dim_type type, unsigned pos, unsigned n);
2746 __isl_give isl_basic_set *isl_basic_set_move_dims(
2747 __isl_take isl_basic_set *bset,
2748 enum isl_dim_type dst_type, unsigned dst_pos,
2749 enum isl_dim_type src_type, unsigned src_pos,
2751 __isl_give isl_basic_map *isl_basic_map_move_dims(
2752 __isl_take isl_basic_map *bmap,
2753 enum isl_dim_type dst_type, unsigned dst_pos,
2754 enum isl_dim_type src_type, unsigned src_pos,
2756 __isl_give isl_set *isl_set_move_dims(
2757 __isl_take isl_set *set,
2758 enum isl_dim_type dst_type, unsigned dst_pos,
2759 enum isl_dim_type src_type, unsigned src_pos,
2761 __isl_give isl_map *isl_map_move_dims(
2762 __isl_take isl_map *map,
2763 enum isl_dim_type dst_type, unsigned dst_pos,
2764 enum isl_dim_type src_type, unsigned src_pos,
2767 It is usually not advisable to directly change the (input or output)
2768 space of a set or a relation as this removes the name and the internal
2769 structure of the space. However, the above functions can be useful
2770 to add new parameters, assuming
2771 C<isl_set_align_params> and C<isl_map_align_params>
2776 =head2 Binary Operations
2778 The two arguments of a binary operation not only need to live
2779 in the same C<isl_ctx>, they currently also need to have
2780 the same (number of) parameters.
2782 =head3 Basic Operations
2786 =item * Intersection
2788 __isl_give isl_basic_set *isl_basic_set_intersect_params(
2789 __isl_take isl_basic_set *bset1,
2790 __isl_take isl_basic_set *bset2);
2791 __isl_give isl_basic_set *isl_basic_set_intersect(
2792 __isl_take isl_basic_set *bset1,
2793 __isl_take isl_basic_set *bset2);
2794 __isl_give isl_set *isl_set_intersect_params(
2795 __isl_take isl_set *set,
2796 __isl_take isl_set *params);
2797 __isl_give isl_set *isl_set_intersect(
2798 __isl_take isl_set *set1,
2799 __isl_take isl_set *set2);
2800 __isl_give isl_union_set *isl_union_set_intersect_params(
2801 __isl_take isl_union_set *uset,
2802 __isl_take isl_set *set);
2803 __isl_give isl_union_map *isl_union_map_intersect_params(
2804 __isl_take isl_union_map *umap,
2805 __isl_take isl_set *set);
2806 __isl_give isl_union_set *isl_union_set_intersect(
2807 __isl_take isl_union_set *uset1,
2808 __isl_take isl_union_set *uset2);
2809 __isl_give isl_basic_map *isl_basic_map_intersect_domain(
2810 __isl_take isl_basic_map *bmap,
2811 __isl_take isl_basic_set *bset);
2812 __isl_give isl_basic_map *isl_basic_map_intersect_range(
2813 __isl_take isl_basic_map *bmap,
2814 __isl_take isl_basic_set *bset);
2815 __isl_give isl_basic_map *isl_basic_map_intersect(
2816 __isl_take isl_basic_map *bmap1,
2817 __isl_take isl_basic_map *bmap2);
2818 __isl_give isl_map *isl_map_intersect_params(
2819 __isl_take isl_map *map,
2820 __isl_take isl_set *params);
2821 __isl_give isl_map *isl_map_intersect_domain(
2822 __isl_take isl_map *map,
2823 __isl_take isl_set *set);
2824 __isl_give isl_map *isl_map_intersect_range(
2825 __isl_take isl_map *map,
2826 __isl_take isl_set *set);
2827 __isl_give isl_map *isl_map_intersect(
2828 __isl_take isl_map *map1,
2829 __isl_take isl_map *map2);
2830 __isl_give isl_union_map *isl_union_map_intersect_domain(
2831 __isl_take isl_union_map *umap,
2832 __isl_take isl_union_set *uset);
2833 __isl_give isl_union_map *isl_union_map_intersect_range(
2834 __isl_take isl_union_map *umap,
2835 __isl_take isl_union_set *uset);
2836 __isl_give isl_union_map *isl_union_map_intersect(
2837 __isl_take isl_union_map *umap1,
2838 __isl_take isl_union_map *umap2);
2840 The second argument to the C<_params> functions needs to be
2841 a parametric (basic) set. For the other functions, a parametric set
2842 for either argument is only allowed if the other argument is
2843 a parametric set as well.
2847 __isl_give isl_set *isl_basic_set_union(
2848 __isl_take isl_basic_set *bset1,
2849 __isl_take isl_basic_set *bset2);
2850 __isl_give isl_map *isl_basic_map_union(
2851 __isl_take isl_basic_map *bmap1,
2852 __isl_take isl_basic_map *bmap2);
2853 __isl_give isl_set *isl_set_union(
2854 __isl_take isl_set *set1,
2855 __isl_take isl_set *set2);
2856 __isl_give isl_map *isl_map_union(
2857 __isl_take isl_map *map1,
2858 __isl_take isl_map *map2);
2859 __isl_give isl_union_set *isl_union_set_union(
2860 __isl_take isl_union_set *uset1,
2861 __isl_take isl_union_set *uset2);
2862 __isl_give isl_union_map *isl_union_map_union(
2863 __isl_take isl_union_map *umap1,
2864 __isl_take isl_union_map *umap2);
2866 =item * Set difference
2868 __isl_give isl_set *isl_set_subtract(
2869 __isl_take isl_set *set1,
2870 __isl_take isl_set *set2);
2871 __isl_give isl_map *isl_map_subtract(
2872 __isl_take isl_map *map1,
2873 __isl_take isl_map *map2);
2874 __isl_give isl_map *isl_map_subtract_domain(
2875 __isl_take isl_map *map,
2876 __isl_take isl_set *dom);
2877 __isl_give isl_map *isl_map_subtract_range(
2878 __isl_take isl_map *map,
2879 __isl_take isl_set *dom);
2880 __isl_give isl_union_set *isl_union_set_subtract(
2881 __isl_take isl_union_set *uset1,
2882 __isl_take isl_union_set *uset2);
2883 __isl_give isl_union_map *isl_union_map_subtract(
2884 __isl_take isl_union_map *umap1,
2885 __isl_take isl_union_map *umap2);
2886 __isl_give isl_union_map *isl_union_map_subtract_domain(
2887 __isl_take isl_union_map *umap,
2888 __isl_take isl_union_set *dom);
2889 __isl_give isl_union_map *isl_union_map_subtract_range(
2890 __isl_take isl_union_map *umap,
2891 __isl_take isl_union_set *dom);
2895 __isl_give isl_basic_set *isl_basic_set_apply(
2896 __isl_take isl_basic_set *bset,
2897 __isl_take isl_basic_map *bmap);
2898 __isl_give isl_set *isl_set_apply(
2899 __isl_take isl_set *set,
2900 __isl_take isl_map *map);
2901 __isl_give isl_union_set *isl_union_set_apply(
2902 __isl_take isl_union_set *uset,
2903 __isl_take isl_union_map *umap);
2904 __isl_give isl_basic_map *isl_basic_map_apply_domain(
2905 __isl_take isl_basic_map *bmap1,
2906 __isl_take isl_basic_map *bmap2);
2907 __isl_give isl_basic_map *isl_basic_map_apply_range(
2908 __isl_take isl_basic_map *bmap1,
2909 __isl_take isl_basic_map *bmap2);
2910 __isl_give isl_map *isl_map_apply_domain(
2911 __isl_take isl_map *map1,
2912 __isl_take isl_map *map2);
2913 __isl_give isl_union_map *isl_union_map_apply_domain(
2914 __isl_take isl_union_map *umap1,
2915 __isl_take isl_union_map *umap2);
2916 __isl_give isl_map *isl_map_apply_range(
2917 __isl_take isl_map *map1,
2918 __isl_take isl_map *map2);
2919 __isl_give isl_union_map *isl_union_map_apply_range(
2920 __isl_take isl_union_map *umap1,
2921 __isl_take isl_union_map *umap2);
2925 __isl_give isl_basic_set *
2926 isl_basic_set_preimage_multi_aff(
2927 __isl_take isl_basic_set *bset,
2928 __isl_take isl_multi_aff *ma);
2929 __isl_give isl_set *isl_set_preimage_multi_aff(
2930 __isl_take isl_set *set,
2931 __isl_take isl_multi_aff *ma);
2932 __isl_give isl_set *isl_set_preimage_pw_multi_aff(
2933 __isl_take isl_set *set,
2934 __isl_take isl_pw_multi_aff *pma);
2935 __isl_give isl_set *isl_set_preimage_multi_pw_aff(
2936 __isl_take isl_set *set,
2937 __isl_take isl_multi_pw_aff *mpa);
2938 __isl_give isl_basic_map *
2939 isl_basic_map_preimage_domain_multi_aff(
2940 __isl_take isl_basic_map *bmap,
2941 __isl_take isl_multi_aff *ma);
2942 __isl_give isl_map *isl_map_preimage_domain_multi_aff(
2943 __isl_take isl_map *map,
2944 __isl_take isl_multi_aff *ma);
2945 __isl_give isl_map *
2946 isl_map_preimage_domain_pw_multi_aff(
2947 __isl_take isl_map *map,
2948 __isl_take isl_pw_multi_aff *pma);
2949 __isl_give isl_map *
2950 isl_map_preimage_domain_multi_pw_aff(
2951 __isl_take isl_map *map,
2952 __isl_take isl_multi_pw_aff *mpa);
2953 __isl_give isl_union_map *
2954 isl_union_map_preimage_domain_multi_aff(
2955 __isl_take isl_union_map *umap,
2956 __isl_take isl_multi_aff *ma);
2957 __isl_give isl_basic_map *
2958 isl_basic_map_preimage_range_multi_aff(
2959 __isl_take isl_basic_map *bmap,
2960 __isl_take isl_multi_aff *ma);
2962 These functions compute the preimage of the given set or map domain/range under
2963 the given function. In other words, the expression is plugged
2964 into the set description or into the domain/range of the map.
2965 Objects of types C<isl_multi_aff> and C<isl_pw_multi_aff> are described in
2966 L</"Piecewise Multiple Quasi Affine Expressions">.
2968 =item * Cartesian Product
2970 __isl_give isl_set *isl_set_product(
2971 __isl_take isl_set *set1,
2972 __isl_take isl_set *set2);
2973 __isl_give isl_union_set *isl_union_set_product(
2974 __isl_take isl_union_set *uset1,
2975 __isl_take isl_union_set *uset2);
2976 __isl_give isl_basic_map *isl_basic_map_domain_product(
2977 __isl_take isl_basic_map *bmap1,
2978 __isl_take isl_basic_map *bmap2);
2979 __isl_give isl_basic_map *isl_basic_map_range_product(
2980 __isl_take isl_basic_map *bmap1,
2981 __isl_take isl_basic_map *bmap2);
2982 __isl_give isl_basic_map *isl_basic_map_product(
2983 __isl_take isl_basic_map *bmap1,
2984 __isl_take isl_basic_map *bmap2);
2985 __isl_give isl_map *isl_map_domain_product(
2986 __isl_take isl_map *map1,
2987 __isl_take isl_map *map2);
2988 __isl_give isl_map *isl_map_range_product(
2989 __isl_take isl_map *map1,
2990 __isl_take isl_map *map2);
2991 __isl_give isl_union_map *isl_union_map_domain_product(
2992 __isl_take isl_union_map *umap1,
2993 __isl_take isl_union_map *umap2);
2994 __isl_give isl_union_map *isl_union_map_range_product(
2995 __isl_take isl_union_map *umap1,
2996 __isl_take isl_union_map *umap2);
2997 __isl_give isl_map *isl_map_product(
2998 __isl_take isl_map *map1,
2999 __isl_take isl_map *map2);
3000 __isl_give isl_union_map *isl_union_map_product(
3001 __isl_take isl_union_map *umap1,
3002 __isl_take isl_union_map *umap2);
3004 The above functions compute the cross product of the given
3005 sets or relations. The domains and ranges of the results
3006 are wrapped maps between domains and ranges of the inputs.
3007 To obtain a ``flat'' product, use the following functions
3010 __isl_give isl_basic_set *isl_basic_set_flat_product(
3011 __isl_take isl_basic_set *bset1,
3012 __isl_take isl_basic_set *bset2);
3013 __isl_give isl_set *isl_set_flat_product(
3014 __isl_take isl_set *set1,
3015 __isl_take isl_set *set2);
3016 __isl_give isl_basic_map *isl_basic_map_flat_range_product(
3017 __isl_take isl_basic_map *bmap1,
3018 __isl_take isl_basic_map *bmap2);
3019 __isl_give isl_map *isl_map_flat_domain_product(
3020 __isl_take isl_map *map1,
3021 __isl_take isl_map *map2);
3022 __isl_give isl_map *isl_map_flat_range_product(
3023 __isl_take isl_map *map1,
3024 __isl_take isl_map *map2);
3025 __isl_give isl_union_map *isl_union_map_flat_range_product(
3026 __isl_take isl_union_map *umap1,
3027 __isl_take isl_union_map *umap2);
3028 __isl_give isl_basic_map *isl_basic_map_flat_product(
3029 __isl_take isl_basic_map *bmap1,
3030 __isl_take isl_basic_map *bmap2);
3031 __isl_give isl_map *isl_map_flat_product(
3032 __isl_take isl_map *map1,
3033 __isl_take isl_map *map2);
3035 =item * Simplification
3037 __isl_give isl_basic_set *isl_basic_set_gist(
3038 __isl_take isl_basic_set *bset,
3039 __isl_take isl_basic_set *context);
3040 __isl_give isl_set *isl_set_gist(__isl_take isl_set *set,
3041 __isl_take isl_set *context);
3042 __isl_give isl_set *isl_set_gist_params(
3043 __isl_take isl_set *set,
3044 __isl_take isl_set *context);
3045 __isl_give isl_union_set *isl_union_set_gist(
3046 __isl_take isl_union_set *uset,
3047 __isl_take isl_union_set *context);
3048 __isl_give isl_union_set *isl_union_set_gist_params(
3049 __isl_take isl_union_set *uset,
3050 __isl_take isl_set *set);
3051 __isl_give isl_basic_map *isl_basic_map_gist(
3052 __isl_take isl_basic_map *bmap,
3053 __isl_take isl_basic_map *context);
3054 __isl_give isl_map *isl_map_gist(__isl_take isl_map *map,
3055 __isl_take isl_map *context);
3056 __isl_give isl_map *isl_map_gist_params(
3057 __isl_take isl_map *map,
3058 __isl_take isl_set *context);
3059 __isl_give isl_map *isl_map_gist_domain(
3060 __isl_take isl_map *map,
3061 __isl_take isl_set *context);
3062 __isl_give isl_map *isl_map_gist_range(
3063 __isl_take isl_map *map,
3064 __isl_take isl_set *context);
3065 __isl_give isl_union_map *isl_union_map_gist(
3066 __isl_take isl_union_map *umap,
3067 __isl_take isl_union_map *context);
3068 __isl_give isl_union_map *isl_union_map_gist_params(
3069 __isl_take isl_union_map *umap,
3070 __isl_take isl_set *set);
3071 __isl_give isl_union_map *isl_union_map_gist_domain(
3072 __isl_take isl_union_map *umap,
3073 __isl_take isl_union_set *uset);
3074 __isl_give isl_union_map *isl_union_map_gist_range(
3075 __isl_take isl_union_map *umap,
3076 __isl_take isl_union_set *uset);
3078 The gist operation returns a set or relation that has the
3079 same intersection with the context as the input set or relation.
3080 Any implicit equality in the intersection is made explicit in the result,
3081 while all inequalities that are redundant with respect to the intersection
3083 In case of union sets and relations, the gist operation is performed
3088 =head3 Lexicographic Optimization
3090 Given a (basic) set C<set> (or C<bset>) and a zero-dimensional domain C<dom>,
3091 the following functions
3092 compute a set that contains the lexicographic minimum or maximum
3093 of the elements in C<set> (or C<bset>) for those values of the parameters
3094 that satisfy C<dom>.
3095 If C<empty> is not C<NULL>, then C<*empty> is assigned a set
3096 that contains the parameter values in C<dom> for which C<set> (or C<bset>)
3098 In other words, the union of the parameter values
3099 for which the result is non-empty and of C<*empty>
3102 __isl_give isl_set *isl_basic_set_partial_lexmin(
3103 __isl_take isl_basic_set *bset,
3104 __isl_take isl_basic_set *dom,
3105 __isl_give isl_set **empty);
3106 __isl_give isl_set *isl_basic_set_partial_lexmax(
3107 __isl_take isl_basic_set *bset,
3108 __isl_take isl_basic_set *dom,
3109 __isl_give isl_set **empty);
3110 __isl_give isl_set *isl_set_partial_lexmin(
3111 __isl_take isl_set *set, __isl_take isl_set *dom,
3112 __isl_give isl_set **empty);
3113 __isl_give isl_set *isl_set_partial_lexmax(
3114 __isl_take isl_set *set, __isl_take isl_set *dom,
3115 __isl_give isl_set **empty);
3117 Given a (basic) set C<set> (or C<bset>), the following functions simply
3118 return a set containing the lexicographic minimum or maximum
3119 of the elements in C<set> (or C<bset>).
3120 In case of union sets, the optimum is computed per space.
3122 __isl_give isl_set *isl_basic_set_lexmin(
3123 __isl_take isl_basic_set *bset);
3124 __isl_give isl_set *isl_basic_set_lexmax(
3125 __isl_take isl_basic_set *bset);
3126 __isl_give isl_set *isl_set_lexmin(
3127 __isl_take isl_set *set);
3128 __isl_give isl_set *isl_set_lexmax(
3129 __isl_take isl_set *set);
3130 __isl_give isl_union_set *isl_union_set_lexmin(
3131 __isl_take isl_union_set *uset);
3132 __isl_give isl_union_set *isl_union_set_lexmax(
3133 __isl_take isl_union_set *uset);
3135 Given a (basic) relation C<map> (or C<bmap>) and a domain C<dom>,
3136 the following functions
3137 compute a relation that maps each element of C<dom>
3138 to the single lexicographic minimum or maximum
3139 of the elements that are associated to that same
3140 element in C<map> (or C<bmap>).
3141 If C<empty> is not C<NULL>, then C<*empty> is assigned a set
3142 that contains the elements in C<dom> that do not map
3143 to any elements in C<map> (or C<bmap>).
3144 In other words, the union of the domain of the result and of C<*empty>
3147 __isl_give isl_map *isl_basic_map_partial_lexmax(
3148 __isl_take isl_basic_map *bmap,
3149 __isl_take isl_basic_set *dom,
3150 __isl_give isl_set **empty);
3151 __isl_give isl_map *isl_basic_map_partial_lexmin(
3152 __isl_take isl_basic_map *bmap,
3153 __isl_take isl_basic_set *dom,
3154 __isl_give isl_set **empty);
3155 __isl_give isl_map *isl_map_partial_lexmax(
3156 __isl_take isl_map *map, __isl_take isl_set *dom,
3157 __isl_give isl_set **empty);
3158 __isl_give isl_map *isl_map_partial_lexmin(
3159 __isl_take isl_map *map, __isl_take isl_set *dom,
3160 __isl_give isl_set **empty);
3162 Given a (basic) map C<map> (or C<bmap>), the following functions simply
3163 return a map mapping each element in the domain of
3164 C<map> (or C<bmap>) to the lexicographic minimum or maximum
3165 of all elements associated to that element.
3166 In case of union relations, the optimum is computed per space.
3168 __isl_give isl_map *isl_basic_map_lexmin(
3169 __isl_take isl_basic_map *bmap);
3170 __isl_give isl_map *isl_basic_map_lexmax(
3171 __isl_take isl_basic_map *bmap);
3172 __isl_give isl_map *isl_map_lexmin(
3173 __isl_take isl_map *map);
3174 __isl_give isl_map *isl_map_lexmax(
3175 __isl_take isl_map *map);
3176 __isl_give isl_union_map *isl_union_map_lexmin(
3177 __isl_take isl_union_map *umap);
3178 __isl_give isl_union_map *isl_union_map_lexmax(
3179 __isl_take isl_union_map *umap);
3181 The following functions return their result in the form of
3182 a piecewise multi-affine expression
3183 (See L<"Piecewise Multiple Quasi Affine Expressions">),
3184 but are otherwise equivalent to the corresponding functions
3185 returning a basic set or relation.
3187 __isl_give isl_pw_multi_aff *
3188 isl_basic_map_lexmin_pw_multi_aff(
3189 __isl_take isl_basic_map *bmap);
3190 __isl_give isl_pw_multi_aff *
3191 isl_basic_set_partial_lexmin_pw_multi_aff(
3192 __isl_take isl_basic_set *bset,
3193 __isl_take isl_basic_set *dom,
3194 __isl_give isl_set **empty);
3195 __isl_give isl_pw_multi_aff *
3196 isl_basic_set_partial_lexmax_pw_multi_aff(
3197 __isl_take isl_basic_set *bset,
3198 __isl_take isl_basic_set *dom,
3199 __isl_give isl_set **empty);
3200 __isl_give isl_pw_multi_aff *
3201 isl_basic_map_partial_lexmin_pw_multi_aff(
3202 __isl_take isl_basic_map *bmap,
3203 __isl_take isl_basic_set *dom,
3204 __isl_give isl_set **empty);
3205 __isl_give isl_pw_multi_aff *
3206 isl_basic_map_partial_lexmax_pw_multi_aff(
3207 __isl_take isl_basic_map *bmap,
3208 __isl_take isl_basic_set *dom,
3209 __isl_give isl_set **empty);
3210 __isl_give isl_pw_multi_aff *isl_set_lexmin_pw_multi_aff(
3211 __isl_take isl_set *set);
3212 __isl_give isl_pw_multi_aff *isl_set_lexmax_pw_multi_aff(
3213 __isl_take isl_set *set);
3214 __isl_give isl_pw_multi_aff *isl_map_lexmin_pw_multi_aff(
3215 __isl_take isl_map *map);
3216 __isl_give isl_pw_multi_aff *isl_map_lexmax_pw_multi_aff(
3217 __isl_take isl_map *map);
3221 Lists are defined over several element types, including
3222 C<isl_val>, C<isl_id>, C<isl_aff>, C<isl_pw_aff>, C<isl_constraint>,
3223 C<isl_basic_set>, C<isl_set>, C<isl_ast_expr> and C<isl_ast_node>.
3224 Here we take lists of C<isl_set>s as an example.
3225 Lists can be created, copied, modified and freed using the following functions.
3227 #include <isl/list.h>
3228 __isl_give isl_set_list *isl_set_list_from_set(
3229 __isl_take isl_set *el);
3230 __isl_give isl_set_list *isl_set_list_alloc(
3231 isl_ctx *ctx, int n);
3232 __isl_give isl_set_list *isl_set_list_copy(
3233 __isl_keep isl_set_list *list);
3234 __isl_give isl_set_list *isl_set_list_insert(
3235 __isl_take isl_set_list *list, unsigned pos,
3236 __isl_take isl_set *el);
3237 __isl_give isl_set_list *isl_set_list_add(
3238 __isl_take isl_set_list *list,
3239 __isl_take isl_set *el);
3240 __isl_give isl_set_list *isl_set_list_drop(
3241 __isl_take isl_set_list *list,
3242 unsigned first, unsigned n);
3243 __isl_give isl_set_list *isl_set_list_set_set(
3244 __isl_take isl_set_list *list, int index,
3245 __isl_take isl_set *set);
3246 __isl_give isl_set_list *isl_set_list_concat(
3247 __isl_take isl_set_list *list1,
3248 __isl_take isl_set_list *list2);
3249 __isl_give isl_set_list *isl_set_list_sort(
3250 __isl_take isl_set_list *list,
3251 int (*cmp)(__isl_keep isl_set *a,
3252 __isl_keep isl_set *b, void *user),
3254 void *isl_set_list_free(__isl_take isl_set_list *list);
3256 C<isl_set_list_alloc> creates an empty list with a capacity for
3257 C<n> elements. C<isl_set_list_from_set> creates a list with a single
3260 Lists can be inspected using the following functions.
3262 #include <isl/list.h>
3263 isl_ctx *isl_set_list_get_ctx(__isl_keep isl_set_list *list);
3264 int isl_set_list_n_set(__isl_keep isl_set_list *list);
3265 __isl_give isl_set *isl_set_list_get_set(
3266 __isl_keep isl_set_list *list, int index);
3267 int isl_set_list_foreach(__isl_keep isl_set_list *list,
3268 int (*fn)(__isl_take isl_set *el, void *user),
3270 int isl_set_list_foreach_scc(__isl_keep isl_set_list *list,
3271 int (*follows)(__isl_keep isl_set *a,
3272 __isl_keep isl_set *b, void *user),
3274 int (*fn)(__isl_take isl_set *el, void *user),
3277 The function C<isl_set_list_foreach_scc> calls C<fn> on each of the
3278 strongly connected components of the graph with as vertices the elements
3279 of C<list> and a directed edge from vertex C<b> to vertex C<a>
3280 iff C<follows(a, b)> returns C<1>. The callbacks C<follows> and C<fn>
3281 should return C<-1> on error.
3283 Lists can be printed using
3285 #include <isl/list.h>
3286 __isl_give isl_printer *isl_printer_print_set_list(
3287 __isl_take isl_printer *p,
3288 __isl_keep isl_set_list *list);
3290 =head2 Associative arrays
3292 Associative arrays map isl objects of a specific type to isl objects
3293 of some (other) specific type. They are defined for several pairs
3294 of types, including (C<isl_map>, C<isl_basic_set>) and
3295 (C<isl_id>, C<isl_ast_expr>).
3296 Here, we take associative arrays that map C<isl_id>s to C<isl_ast_expr>s
3299 Associative arrays can be created, copied and freed using
3300 the following functions.
3302 #include <isl/id_to_ast_expr.h>
3303 __isl_give id_to_ast_expr *isl_id_to_ast_expr_alloc(
3304 isl_ctx *ctx, int min_size);
3305 __isl_give id_to_ast_expr *isl_id_to_ast_expr_copy(
3306 __isl_keep id_to_ast_expr *id2expr);
3307 void *isl_id_to_ast_expr_free(
3308 __isl_take id_to_ast_expr *id2expr);
3310 The C<min_size> argument to C<isl_id_to_ast_expr_alloc> can be used
3311 to specify the expected size of the associative array.
3312 The associative array will be grown automatically as needed.
3314 Associative arrays can be inspected using the following functions.
3316 #include <isl/id_to_ast_expr.h>
3317 isl_ctx *isl_id_to_ast_expr_get_ctx(
3318 __isl_keep id_to_ast_expr *id2expr);
3319 int isl_id_to_ast_expr_has(
3320 __isl_keep id_to_ast_expr *id2expr,
3321 __isl_keep isl_id *key);
3322 __isl_give isl_ast_expr *isl_id_to_ast_expr_get(
3323 __isl_keep id_to_ast_expr *id2expr,
3324 __isl_take isl_id *key);
3325 int isl_id_to_ast_expr_foreach(
3326 __isl_keep id_to_ast_expr *id2expr,
3327 int (*fn)(__isl_take isl_id *key,
3328 __isl_take isl_ast_expr *val, void *user),
3331 They can be modified using the following function.
3333 #include <isl/id_to_ast_expr.h>
3334 __isl_give id_to_ast_expr *isl_id_to_ast_expr_set(
3335 __isl_take id_to_ast_expr *id2expr,
3336 __isl_take isl_id *key,
3337 __isl_take isl_ast_expr *val);
3339 Associative arrays can be printed using the following function.
3341 #include <isl/id_to_ast_expr.h>
3342 __isl_give isl_printer *isl_printer_print_id_to_ast_expr(
3343 __isl_take isl_printer *p,
3344 __isl_keep id_to_ast_expr *id2expr);
3346 =head2 Multiple Values
3348 An C<isl_multi_val> object represents a sequence of zero or more values,
3349 living in a set space.
3351 An C<isl_multi_val> can be constructed from an C<isl_val_list>
3352 using the following function
3354 #include <isl/val.h>
3355 __isl_give isl_multi_val *isl_multi_val_from_val_list(
3356 __isl_take isl_space *space,
3357 __isl_take isl_val_list *list);
3359 The zero multiple value (with value zero for each set dimension)
3360 can be created using the following function.
3362 #include <isl/val.h>
3363 __isl_give isl_multi_val *isl_multi_val_zero(
3364 __isl_take isl_space *space);
3366 Multiple values can be copied and freed using
3368 #include <isl/val.h>
3369 __isl_give isl_multi_val *isl_multi_val_copy(
3370 __isl_keep isl_multi_val *mv);
3371 void *isl_multi_val_free(__isl_take isl_multi_val *mv);
3373 They can be inspected using
3375 #include <isl/val.h>
3376 isl_ctx *isl_multi_val_get_ctx(
3377 __isl_keep isl_multi_val *mv);
3378 unsigned isl_multi_val_dim(__isl_keep isl_multi_val *mv,
3379 enum isl_dim_type type);
3380 __isl_give isl_val *isl_multi_val_get_val(
3381 __isl_keep isl_multi_val *mv, int pos);
3382 int isl_multi_val_find_dim_by_id(
3383 __isl_keep isl_multi_val *mv,
3384 enum isl_dim_type type, __isl_keep isl_id *id);
3385 __isl_give isl_id *isl_multi_val_get_dim_id(
3386 __isl_keep isl_multi_val *mv,
3387 enum isl_dim_type type, unsigned pos);
3388 const char *isl_multi_val_get_tuple_name(
3389 __isl_keep isl_multi_val *mv,
3390 enum isl_dim_type type);
3391 int isl_multi_val_has_tuple_id(__isl_keep isl_multi_val *mv,
3392 enum isl_dim_type type);
3393 __isl_give isl_id *isl_multi_val_get_tuple_id(
3394 __isl_keep isl_multi_val *mv,
3395 enum isl_dim_type type);
3396 __isl_give isl_multi_val *isl_multi_val_reset_tuple_id(
3397 __isl_take isl_multi_val *mv,
3398 enum isl_dim_type type);
3400 They can be modified using
3402 #include <isl/val.h>
3403 __isl_give isl_multi_val *isl_multi_val_set_val(
3404 __isl_take isl_multi_val *mv, int pos,
3405 __isl_take isl_val *val);
3406 __isl_give isl_multi_val *isl_multi_val_set_dim_name(
3407 __isl_take isl_multi_val *mv,
3408 enum isl_dim_type type, unsigned pos, const char *s);
3409 __isl_give isl_multi_val *isl_multi_val_set_dim_id(
3410 __isl_take isl_multi_val *mv,
3411 enum isl_dim_type type, unsigned pos,
3412 __isl_take isl_id *id);
3413 __isl_give isl_multi_val *isl_multi_val_set_tuple_name(
3414 __isl_take isl_multi_val *mv,
3415 enum isl_dim_type type, const char *s);
3416 __isl_give isl_multi_val *isl_multi_val_set_tuple_id(
3417 __isl_take isl_multi_val *mv,
3418 enum isl_dim_type type, __isl_take isl_id *id);
3420 __isl_give isl_multi_val *isl_multi_val_insert_dims(
3421 __isl_take isl_multi_val *mv,
3422 enum isl_dim_type type, unsigned first, unsigned n);
3423 __isl_give isl_multi_val *isl_multi_val_add_dims(
3424 __isl_take isl_multi_val *mv,
3425 enum isl_dim_type type, unsigned n);
3426 __isl_give isl_multi_val *isl_multi_val_drop_dims(
3427 __isl_take isl_multi_val *mv,
3428 enum isl_dim_type type, unsigned first, unsigned n);
3432 #include <isl/val.h>
3433 __isl_give isl_multi_val *isl_multi_val_align_params(
3434 __isl_take isl_multi_val *mv,
3435 __isl_take isl_space *model);
3436 __isl_give isl_multi_val *isl_multi_val_from_range(
3437 __isl_take isl_multi_val *mv);
3438 __isl_give isl_multi_val *isl_multi_val_range_splice(
3439 __isl_take isl_multi_val *mv1, unsigned pos,
3440 __isl_take isl_multi_val *mv2);
3441 __isl_give isl_multi_val *isl_multi_val_range_product(
3442 __isl_take isl_multi_val *mv1,
3443 __isl_take isl_multi_val *mv2);
3444 __isl_give isl_multi_val *isl_multi_val_flat_range_product(
3445 __isl_take isl_multi_val *mv1,
3446 __isl_take isl_multi_aff *mv2);
3447 __isl_give isl_multi_val *isl_multi_val_product(
3448 __isl_take isl_multi_val *mv1,
3449 __isl_take isl_multi_val *mv2);
3450 __isl_give isl_multi_val *isl_multi_val_add_val(
3451 __isl_take isl_multi_val *mv,
3452 __isl_take isl_val *v);
3453 __isl_give isl_multi_val *isl_multi_val_mod_val(
3454 __isl_take isl_multi_val *mv,
3455 __isl_take isl_val *v);
3456 __isl_give isl_multi_val *isl_multi_val_scale_val(
3457 __isl_take isl_multi_val *mv,
3458 __isl_take isl_val *v);
3459 __isl_give isl_multi_val *isl_multi_val_scale_multi_val(
3460 __isl_take isl_multi_val *mv1,
3461 __isl_take isl_multi_val *mv2);
3462 __isl_give isl_multi_val *
3463 isl_multi_val_scale_down_multi_val(
3464 __isl_take isl_multi_val *mv1,
3465 __isl_take isl_multi_val *mv2);
3467 A multiple value can be printed using
3469 __isl_give isl_printer *isl_printer_print_multi_val(
3470 __isl_take isl_printer *p,
3471 __isl_keep isl_multi_val *mv);
3475 Vectors can be created, copied and freed using the following functions.
3477 #include <isl/vec.h>
3478 __isl_give isl_vec *isl_vec_alloc(isl_ctx *ctx,
3480 __isl_give isl_vec *isl_vec_copy(__isl_keep isl_vec *vec);
3481 void *isl_vec_free(__isl_take isl_vec *vec);
3483 Note that the elements of a newly created vector may have arbitrary values.
3484 The elements can be changed and inspected using the following functions.
3486 isl_ctx *isl_vec_get_ctx(__isl_keep isl_vec *vec);
3487 int isl_vec_size(__isl_keep isl_vec *vec);
3488 __isl_give isl_val *isl_vec_get_element_val(
3489 __isl_keep isl_vec *vec, int pos);
3490 __isl_give isl_vec *isl_vec_set_element_si(
3491 __isl_take isl_vec *vec, int pos, int v);
3492 __isl_give isl_vec *isl_vec_set_element_val(
3493 __isl_take isl_vec *vec, int pos,
3494 __isl_take isl_val *v);
3495 __isl_give isl_vec *isl_vec_set_si(__isl_take isl_vec *vec,
3497 __isl_give isl_vec *isl_vec_set_val(
3498 __isl_take isl_vec *vec, __isl_take isl_val *v);
3499 int isl_vec_cmp_element(__isl_keep isl_vec *vec1,
3500 __isl_keep isl_vec *vec2, int pos);
3502 C<isl_vec_get_element> will return a negative value if anything went wrong.
3503 In that case, the value of C<*v> is undefined.
3505 The following function can be used to concatenate two vectors.
3507 __isl_give isl_vec *isl_vec_concat(__isl_take isl_vec *vec1,
3508 __isl_take isl_vec *vec2);
3512 Matrices can be created, copied and freed using the following functions.
3514 #include <isl/mat.h>
3515 __isl_give isl_mat *isl_mat_alloc(isl_ctx *ctx,
3516 unsigned n_row, unsigned n_col);
3517 __isl_give isl_mat *isl_mat_copy(__isl_keep isl_mat *mat);
3518 void *isl_mat_free(__isl_take isl_mat *mat);
3520 Note that the elements of a newly created matrix may have arbitrary values.
3521 The elements can be changed and inspected using the following functions.
3523 isl_ctx *isl_mat_get_ctx(__isl_keep isl_mat *mat);
3524 int isl_mat_rows(__isl_keep isl_mat *mat);
3525 int isl_mat_cols(__isl_keep isl_mat *mat);
3526 __isl_give isl_val *isl_mat_get_element_val(
3527 __isl_keep isl_mat *mat, int row, int col);
3528 __isl_give isl_mat *isl_mat_set_element_si(__isl_take isl_mat *mat,
3529 int row, int col, int v);
3530 __isl_give isl_mat *isl_mat_set_element_val(
3531 __isl_take isl_mat *mat, int row, int col,
3532 __isl_take isl_val *v);
3534 C<isl_mat_get_element> will return a negative value if anything went wrong.
3535 In that case, the value of C<*v> is undefined.
3537 The following function can be used to compute the (right) inverse
3538 of a matrix, i.e., a matrix such that the product of the original
3539 and the inverse (in that order) is a multiple of the identity matrix.
3540 The input matrix is assumed to be of full row-rank.
3542 __isl_give isl_mat *isl_mat_right_inverse(__isl_take isl_mat *mat);
3544 The following function can be used to compute the (right) kernel
3545 (or null space) of a matrix, i.e., a matrix such that the product of
3546 the original and the kernel (in that order) is the zero matrix.
3548 __isl_give isl_mat *isl_mat_right_kernel(__isl_take isl_mat *mat);
3550 =head2 Piecewise Quasi Affine Expressions
3552 The zero quasi affine expression or the quasi affine expression
3553 that is equal to a given value or
3554 a specified dimension on a given domain can be created using
3556 __isl_give isl_aff *isl_aff_zero_on_domain(
3557 __isl_take isl_local_space *ls);
3558 __isl_give isl_pw_aff *isl_pw_aff_zero_on_domain(
3559 __isl_take isl_local_space *ls);
3560 __isl_give isl_aff *isl_aff_val_on_domain(
3561 __isl_take isl_local_space *ls,
3562 __isl_take isl_val *val);
3563 __isl_give isl_aff *isl_aff_var_on_domain(
3564 __isl_take isl_local_space *ls,
3565 enum isl_dim_type type, unsigned pos);
3566 __isl_give isl_pw_aff *isl_pw_aff_var_on_domain(
3567 __isl_take isl_local_space *ls,
3568 enum isl_dim_type type, unsigned pos);
3570 Note that the space in which the resulting objects live is a map space
3571 with the given space as domain and a one-dimensional range.
3573 An empty piecewise quasi affine expression (one with no cells)
3574 or a piecewise quasi affine expression with a single cell can
3575 be created using the following functions.
3577 #include <isl/aff.h>
3578 __isl_give isl_pw_aff *isl_pw_aff_empty(
3579 __isl_take isl_space *space);
3580 __isl_give isl_pw_aff *isl_pw_aff_alloc(
3581 __isl_take isl_set *set, __isl_take isl_aff *aff);
3582 __isl_give isl_pw_aff *isl_pw_aff_from_aff(
3583 __isl_take isl_aff *aff);
3585 A piecewise quasi affine expression that is equal to 1 on a set
3586 and 0 outside the set can be created using the following function.
3588 #include <isl/aff.h>
3589 __isl_give isl_pw_aff *isl_set_indicator_function(
3590 __isl_take isl_set *set);
3592 Quasi affine expressions can be copied and freed using
3594 #include <isl/aff.h>
3595 __isl_give isl_aff *isl_aff_copy(__isl_keep isl_aff *aff);
3596 void *isl_aff_free(__isl_take isl_aff *aff);
3598 __isl_give isl_pw_aff *isl_pw_aff_copy(
3599 __isl_keep isl_pw_aff *pwaff);
3600 void *isl_pw_aff_free(__isl_take isl_pw_aff *pwaff);
3602 A (rational) bound on a dimension can be extracted from an C<isl_constraint>
3603 using the following function. The constraint is required to have
3604 a non-zero coefficient for the specified dimension.
3606 #include <isl/constraint.h>
3607 __isl_give isl_aff *isl_constraint_get_bound(
3608 __isl_keep isl_constraint *constraint,
3609 enum isl_dim_type type, int pos);
3611 The entire affine expression of the constraint can also be extracted
3612 using the following function.
3614 #include <isl/constraint.h>
3615 __isl_give isl_aff *isl_constraint_get_aff(
3616 __isl_keep isl_constraint *constraint);
3618 Conversely, an equality constraint equating
3619 the affine expression to zero or an inequality constraint enforcing
3620 the affine expression to be non-negative, can be constructed using
3622 __isl_give isl_constraint *isl_equality_from_aff(
3623 __isl_take isl_aff *aff);
3624 __isl_give isl_constraint *isl_inequality_from_aff(
3625 __isl_take isl_aff *aff);
3627 The expression can be inspected using
3629 #include <isl/aff.h>
3630 isl_ctx *isl_aff_get_ctx(__isl_keep isl_aff *aff);
3631 int isl_aff_dim(__isl_keep isl_aff *aff,
3632 enum isl_dim_type type);
3633 __isl_give isl_local_space *isl_aff_get_domain_local_space(
3634 __isl_keep isl_aff *aff);
3635 __isl_give isl_local_space *isl_aff_get_local_space(
3636 __isl_keep isl_aff *aff);
3637 const char *isl_aff_get_dim_name(__isl_keep isl_aff *aff,
3638 enum isl_dim_type type, unsigned pos);
3639 const char *isl_pw_aff_get_dim_name(
3640 __isl_keep isl_pw_aff *pa,
3641 enum isl_dim_type type, unsigned pos);
3642 int isl_pw_aff_has_dim_id(__isl_keep isl_pw_aff *pa,
3643 enum isl_dim_type type, unsigned pos);
3644 __isl_give isl_id *isl_pw_aff_get_dim_id(
3645 __isl_keep isl_pw_aff *pa,
3646 enum isl_dim_type type, unsigned pos);
3647 int isl_pw_aff_has_tuple_id(__isl_keep isl_pw_aff *pa,
3648 enum isl_dim_type type);
3649 __isl_give isl_id *isl_pw_aff_get_tuple_id(
3650 __isl_keep isl_pw_aff *pa,
3651 enum isl_dim_type type);
3652 __isl_give isl_val *isl_aff_get_constant_val(
3653 __isl_keep isl_aff *aff);
3654 __isl_give isl_val *isl_aff_get_coefficient_val(
3655 __isl_keep isl_aff *aff,
3656 enum isl_dim_type type, int pos);
3657 __isl_give isl_val *isl_aff_get_denominator_val(
3658 __isl_keep isl_aff *aff);
3659 __isl_give isl_aff *isl_aff_get_div(
3660 __isl_keep isl_aff *aff, int pos);
3662 int isl_pw_aff_n_piece(__isl_keep isl_pw_aff *pwaff);
3663 int isl_pw_aff_foreach_piece(__isl_keep isl_pw_aff *pwaff,
3664 int (*fn)(__isl_take isl_set *set,
3665 __isl_take isl_aff *aff,
3666 void *user), void *user);
3668 int isl_aff_is_cst(__isl_keep isl_aff *aff);
3669 int isl_pw_aff_is_cst(__isl_keep isl_pw_aff *pwaff);
3671 int isl_aff_involves_dims(__isl_keep isl_aff *aff,
3672 enum isl_dim_type type, unsigned first, unsigned n);
3673 int isl_pw_aff_involves_dims(__isl_keep isl_pw_aff *pwaff,
3674 enum isl_dim_type type, unsigned first, unsigned n);
3676 isl_ctx *isl_pw_aff_get_ctx(__isl_keep isl_pw_aff *pwaff);
3677 unsigned isl_pw_aff_dim(__isl_keep isl_pw_aff *pwaff,
3678 enum isl_dim_type type);
3679 int isl_pw_aff_is_empty(__isl_keep isl_pw_aff *pwaff);
3681 It can be modified using
3683 #include <isl/aff.h>
3684 __isl_give isl_pw_aff *isl_pw_aff_set_tuple_id(
3685 __isl_take isl_pw_aff *pwaff,
3686 enum isl_dim_type type, __isl_take isl_id *id);
3687 __isl_give isl_aff *isl_aff_set_dim_name(
3688 __isl_take isl_aff *aff, enum isl_dim_type type,
3689 unsigned pos, const char *s);
3690 __isl_give isl_aff *isl_aff_set_dim_id(
3691 __isl_take isl_aff *aff, enum isl_dim_type type,
3692 unsigned pos, __isl_take isl_id *id);
3693 __isl_give isl_pw_aff *isl_pw_aff_set_dim_id(
3694 __isl_take isl_pw_aff *pma,
3695 enum isl_dim_type type, unsigned pos,
3696 __isl_take isl_id *id);
3697 __isl_give isl_aff *isl_aff_set_constant_si(
3698 __isl_take isl_aff *aff, int v);
3699 __isl_give isl_aff *isl_aff_set_constant_val(
3700 __isl_take isl_aff *aff, __isl_take isl_val *v);
3701 __isl_give isl_aff *isl_aff_set_coefficient_si(
3702 __isl_take isl_aff *aff,
3703 enum isl_dim_type type, int pos, int v);
3704 __isl_give isl_aff *isl_aff_set_coefficient_val(
3705 __isl_take isl_aff *aff,
3706 enum isl_dim_type type, int pos,
3707 __isl_take isl_val *v);
3709 __isl_give isl_aff *isl_aff_add_constant_si(
3710 __isl_take isl_aff *aff, int v);
3711 __isl_give isl_aff *isl_aff_add_constant_val(
3712 __isl_take isl_aff *aff, __isl_take isl_val *v);
3713 __isl_give isl_aff *isl_aff_add_constant_num_si(
3714 __isl_take isl_aff *aff, int v);
3715 __isl_give isl_aff *isl_aff_add_coefficient_si(
3716 __isl_take isl_aff *aff,
3717 enum isl_dim_type type, int pos, int v);
3718 __isl_give isl_aff *isl_aff_add_coefficient_val(
3719 __isl_take isl_aff *aff,
3720 enum isl_dim_type type, int pos,
3721 __isl_take isl_val *v);
3723 __isl_give isl_aff *isl_aff_insert_dims(
3724 __isl_take isl_aff *aff,
3725 enum isl_dim_type type, unsigned first, unsigned n);
3726 __isl_give isl_pw_aff *isl_pw_aff_insert_dims(
3727 __isl_take isl_pw_aff *pwaff,
3728 enum isl_dim_type type, unsigned first, unsigned n);
3729 __isl_give isl_aff *isl_aff_add_dims(
3730 __isl_take isl_aff *aff,
3731 enum isl_dim_type type, unsigned n);
3732 __isl_give isl_pw_aff *isl_pw_aff_add_dims(
3733 __isl_take isl_pw_aff *pwaff,
3734 enum isl_dim_type type, unsigned n);
3735 __isl_give isl_aff *isl_aff_drop_dims(
3736 __isl_take isl_aff *aff,
3737 enum isl_dim_type type, unsigned first, unsigned n);
3738 __isl_give isl_pw_aff *isl_pw_aff_drop_dims(
3739 __isl_take isl_pw_aff *pwaff,
3740 enum isl_dim_type type, unsigned first, unsigned n);
3741 __isl_give isl_aff *isl_aff_move_dims(
3742 __isl_take isl_aff *aff,
3743 enum isl_dim_type dst_type, unsigned dst_pos,
3744 enum isl_dim_type src_type, unsigned src_pos,
3746 __isl_give isl_pw_aff *isl_pw_aff_move_dims(
3747 __isl_take isl_pw_aff *pa,
3748 enum isl_dim_type dst_type, unsigned dst_pos,
3749 enum isl_dim_type src_type, unsigned src_pos,
3752 Note that C<isl_aff_set_constant_si> and C<isl_aff_set_coefficient_si>
3753 set the I<numerator> of the constant or coefficient, while
3754 C<isl_aff_set_constant_val> and C<isl_aff_set_coefficient_val> set
3755 the constant or coefficient as a whole.
3756 The C<add_constant> and C<add_coefficient> functions add an integer
3757 or rational value to
3758 the possibly rational constant or coefficient.
3759 The C<add_constant_num> functions add an integer value to
3762 To check whether an affine expressions is obviously zero
3763 or (obviously) equal to some other affine expression, use
3765 #include <isl/aff.h>
3766 int isl_aff_plain_is_zero(__isl_keep isl_aff *aff);
3767 int isl_aff_plain_is_equal(__isl_keep isl_aff *aff1,
3768 __isl_keep isl_aff *aff2);
3769 int isl_pw_aff_plain_is_equal(
3770 __isl_keep isl_pw_aff *pwaff1,
3771 __isl_keep isl_pw_aff *pwaff2);
3772 int isl_pw_aff_is_equal(__isl_keep isl_pw_aff *pa1,
3773 __isl_keep isl_pw_aff *pa2);
3777 #include <isl/aff.h>
3778 __isl_give isl_aff *isl_aff_add(__isl_take isl_aff *aff1,
3779 __isl_take isl_aff *aff2);
3780 __isl_give isl_pw_aff *isl_pw_aff_add(
3781 __isl_take isl_pw_aff *pwaff1,
3782 __isl_take isl_pw_aff *pwaff2);
3783 __isl_give isl_pw_aff *isl_pw_aff_min(
3784 __isl_take isl_pw_aff *pwaff1,
3785 __isl_take isl_pw_aff *pwaff2);
3786 __isl_give isl_pw_aff *isl_pw_aff_max(
3787 __isl_take isl_pw_aff *pwaff1,
3788 __isl_take isl_pw_aff *pwaff2);
3789 __isl_give isl_aff *isl_aff_sub(__isl_take isl_aff *aff1,
3790 __isl_take isl_aff *aff2);
3791 __isl_give isl_pw_aff *isl_pw_aff_sub(
3792 __isl_take isl_pw_aff *pwaff1,
3793 __isl_take isl_pw_aff *pwaff2);
3794 __isl_give isl_aff *isl_aff_neg(__isl_take isl_aff *aff);
3795 __isl_give isl_pw_aff *isl_pw_aff_neg(
3796 __isl_take isl_pw_aff *pwaff);
3797 __isl_give isl_aff *isl_aff_ceil(__isl_take isl_aff *aff);
3798 __isl_give isl_pw_aff *isl_pw_aff_ceil(
3799 __isl_take isl_pw_aff *pwaff);
3800 __isl_give isl_aff *isl_aff_floor(__isl_take isl_aff *aff);
3801 __isl_give isl_pw_aff *isl_pw_aff_floor(
3802 __isl_take isl_pw_aff *pwaff);
3803 __isl_give isl_aff *isl_aff_mod_val(__isl_take isl_aff *aff,
3804 __isl_take isl_val *mod);
3805 __isl_give isl_pw_aff *isl_pw_aff_mod_val(
3806 __isl_take isl_pw_aff *pa,
3807 __isl_take isl_val *mod);
3808 __isl_give isl_aff *isl_aff_scale_val(__isl_take isl_aff *aff,
3809 __isl_take isl_val *v);
3810 __isl_give isl_pw_aff *isl_pw_aff_scale_val(
3811 __isl_take isl_pw_aff *pa, __isl_take isl_val *v);
3812 __isl_give isl_aff *isl_aff_scale_down_ui(
3813 __isl_take isl_aff *aff, unsigned f);
3814 __isl_give isl_aff *isl_aff_scale_down_val(
3815 __isl_take isl_aff *aff, __isl_take isl_val *v);
3816 __isl_give isl_pw_aff *isl_pw_aff_scale_down_val(
3817 __isl_take isl_pw_aff *pa,
3818 __isl_take isl_val *f);
3820 __isl_give isl_pw_aff *isl_pw_aff_list_min(
3821 __isl_take isl_pw_aff_list *list);
3822 __isl_give isl_pw_aff *isl_pw_aff_list_max(
3823 __isl_take isl_pw_aff_list *list);
3825 __isl_give isl_pw_aff *isl_pw_aff_coalesce(
3826 __isl_take isl_pw_aff *pwqp);
3828 __isl_give isl_aff *isl_aff_align_params(
3829 __isl_take isl_aff *aff,
3830 __isl_take isl_space *model);
3831 __isl_give isl_pw_aff *isl_pw_aff_align_params(
3832 __isl_take isl_pw_aff *pwaff,
3833 __isl_take isl_space *model);
3835 __isl_give isl_aff *isl_aff_project_domain_on_params(
3836 __isl_take isl_aff *aff);
3837 __isl_give isl_pw_aff *isl_pw_aff_from_range(
3838 __isl_take isl_pw_aff *pwa);
3840 __isl_give isl_aff *isl_aff_gist_params(
3841 __isl_take isl_aff *aff,
3842 __isl_take isl_set *context);
3843 __isl_give isl_aff *isl_aff_gist(__isl_take isl_aff *aff,
3844 __isl_take isl_set *context);
3845 __isl_give isl_pw_aff *isl_pw_aff_gist_params(
3846 __isl_take isl_pw_aff *pwaff,
3847 __isl_take isl_set *context);
3848 __isl_give isl_pw_aff *isl_pw_aff_gist(
3849 __isl_take isl_pw_aff *pwaff,
3850 __isl_take isl_set *context);
3852 __isl_give isl_set *isl_pw_aff_domain(
3853 __isl_take isl_pw_aff *pwaff);
3854 __isl_give isl_set *isl_pw_aff_params(
3855 __isl_take isl_pw_aff *pwa);
3856 __isl_give isl_pw_aff *isl_pw_aff_intersect_domain(
3857 __isl_take isl_pw_aff *pa,
3858 __isl_take isl_set *set);
3859 __isl_give isl_pw_aff *isl_pw_aff_intersect_params(
3860 __isl_take isl_pw_aff *pa,
3861 __isl_take isl_set *set);
3863 __isl_give isl_aff *isl_aff_mul(__isl_take isl_aff *aff1,
3864 __isl_take isl_aff *aff2);
3865 __isl_give isl_aff *isl_aff_div(__isl_take isl_aff *aff1,
3866 __isl_take isl_aff *aff2);
3867 __isl_give isl_pw_aff *isl_pw_aff_mul(
3868 __isl_take isl_pw_aff *pwaff1,
3869 __isl_take isl_pw_aff *pwaff2);
3870 __isl_give isl_pw_aff *isl_pw_aff_div(
3871 __isl_take isl_pw_aff *pa1,
3872 __isl_take isl_pw_aff *pa2);
3873 __isl_give isl_pw_aff *isl_pw_aff_tdiv_q(
3874 __isl_take isl_pw_aff *pa1,
3875 __isl_take isl_pw_aff *pa2);
3876 __isl_give isl_pw_aff *isl_pw_aff_tdiv_r(
3877 __isl_take isl_pw_aff *pa1,
3878 __isl_take isl_pw_aff *pa2);
3880 When multiplying two affine expressions, at least one of the two needs
3881 to be a constant. Similarly, when dividing an affine expression by another,
3882 the second expression needs to be a constant.
3883 C<isl_pw_aff_tdiv_q> computes the quotient of an integer division with
3884 rounding towards zero. C<isl_pw_aff_tdiv_r> computes the corresponding
3887 #include <isl/aff.h>
3888 __isl_give isl_aff *isl_aff_pullback_aff(
3889 __isl_take isl_aff *aff1,
3890 __isl_take isl_aff *aff2);
3891 __isl_give isl_aff *isl_aff_pullback_multi_aff(
3892 __isl_take isl_aff *aff,
3893 __isl_take isl_multi_aff *ma);
3894 __isl_give isl_pw_aff *isl_pw_aff_pullback_multi_aff(
3895 __isl_take isl_pw_aff *pa,
3896 __isl_take isl_multi_aff *ma);
3897 __isl_give isl_pw_aff *isl_pw_aff_pullback_pw_multi_aff(
3898 __isl_take isl_pw_aff *pa,
3899 __isl_take isl_pw_multi_aff *pma);
3901 These functions precompose the input expression by the given
3902 C<isl_aff>, C<isl_multi_aff> or C<isl_pw_multi_aff>. In other words,
3903 the C<isl_aff>, C<isl_multi_aff> or C<isl_pw_multi_aff> is plugged
3904 into the (piecewise) affine expression.
3905 Objects of type C<isl_multi_aff> are described in
3906 L</"Piecewise Multiple Quasi Affine Expressions">.
3908 #include <isl/aff.h>
3909 __isl_give isl_basic_set *isl_aff_zero_basic_set(
3910 __isl_take isl_aff *aff);
3911 __isl_give isl_basic_set *isl_aff_neg_basic_set(
3912 __isl_take isl_aff *aff);
3913 __isl_give isl_basic_set *isl_aff_le_basic_set(
3914 __isl_take isl_aff *aff1, __isl_take isl_aff *aff2);
3915 __isl_give isl_basic_set *isl_aff_ge_basic_set(
3916 __isl_take isl_aff *aff1, __isl_take isl_aff *aff2);
3917 __isl_give isl_set *isl_pw_aff_eq_set(
3918 __isl_take isl_pw_aff *pwaff1,
3919 __isl_take isl_pw_aff *pwaff2);
3920 __isl_give isl_set *isl_pw_aff_ne_set(
3921 __isl_take isl_pw_aff *pwaff1,
3922 __isl_take isl_pw_aff *pwaff2);
3923 __isl_give isl_set *isl_pw_aff_le_set(
3924 __isl_take isl_pw_aff *pwaff1,
3925 __isl_take isl_pw_aff *pwaff2);
3926 __isl_give isl_set *isl_pw_aff_lt_set(
3927 __isl_take isl_pw_aff *pwaff1,
3928 __isl_take isl_pw_aff *pwaff2);
3929 __isl_give isl_set *isl_pw_aff_ge_set(
3930 __isl_take isl_pw_aff *pwaff1,
3931 __isl_take isl_pw_aff *pwaff2);
3932 __isl_give isl_set *isl_pw_aff_gt_set(
3933 __isl_take isl_pw_aff *pwaff1,
3934 __isl_take isl_pw_aff *pwaff2);
3936 __isl_give isl_set *isl_pw_aff_list_eq_set(
3937 __isl_take isl_pw_aff_list *list1,
3938 __isl_take isl_pw_aff_list *list2);
3939 __isl_give isl_set *isl_pw_aff_list_ne_set(
3940 __isl_take isl_pw_aff_list *list1,
3941 __isl_take isl_pw_aff_list *list2);
3942 __isl_give isl_set *isl_pw_aff_list_le_set(
3943 __isl_take isl_pw_aff_list *list1,
3944 __isl_take isl_pw_aff_list *list2);
3945 __isl_give isl_set *isl_pw_aff_list_lt_set(
3946 __isl_take isl_pw_aff_list *list1,
3947 __isl_take isl_pw_aff_list *list2);
3948 __isl_give isl_set *isl_pw_aff_list_ge_set(
3949 __isl_take isl_pw_aff_list *list1,
3950 __isl_take isl_pw_aff_list *list2);
3951 __isl_give isl_set *isl_pw_aff_list_gt_set(
3952 __isl_take isl_pw_aff_list *list1,
3953 __isl_take isl_pw_aff_list *list2);
3955 The function C<isl_aff_neg_basic_set> returns a basic set
3956 containing those elements in the domain space
3957 of C<aff> where C<aff> is negative.
3958 The function C<isl_aff_ge_basic_set> returns a basic set
3959 containing those elements in the shared space
3960 of C<aff1> and C<aff2> where C<aff1> is greater than or equal to C<aff2>.
3961 The function C<isl_pw_aff_ge_set> returns a set
3962 containing those elements in the shared domain
3963 of C<pwaff1> and C<pwaff2> where C<pwaff1> is greater than or equal to C<pwaff2>.
3964 The functions operating on C<isl_pw_aff_list> apply the corresponding
3965 C<isl_pw_aff> function to each pair of elements in the two lists.
3967 #include <isl/aff.h>
3968 __isl_give isl_set *isl_pw_aff_nonneg_set(
3969 __isl_take isl_pw_aff *pwaff);
3970 __isl_give isl_set *isl_pw_aff_zero_set(
3971 __isl_take isl_pw_aff *pwaff);
3972 __isl_give isl_set *isl_pw_aff_non_zero_set(
3973 __isl_take isl_pw_aff *pwaff);
3975 The function C<isl_pw_aff_nonneg_set> returns a set
3976 containing those elements in the domain
3977 of C<pwaff> where C<pwaff> is non-negative.
3979 #include <isl/aff.h>
3980 __isl_give isl_pw_aff *isl_pw_aff_cond(
3981 __isl_take isl_pw_aff *cond,
3982 __isl_take isl_pw_aff *pwaff_true,
3983 __isl_take isl_pw_aff *pwaff_false);
3985 The function C<isl_pw_aff_cond> performs a conditional operator
3986 and returns an expression that is equal to C<pwaff_true>
3987 for elements where C<cond> is non-zero and equal to C<pwaff_false> for elements
3988 where C<cond> is zero.
3990 #include <isl/aff.h>
3991 __isl_give isl_pw_aff *isl_pw_aff_union_min(
3992 __isl_take isl_pw_aff *pwaff1,
3993 __isl_take isl_pw_aff *pwaff2);
3994 __isl_give isl_pw_aff *isl_pw_aff_union_max(
3995 __isl_take isl_pw_aff *pwaff1,
3996 __isl_take isl_pw_aff *pwaff2);
3997 __isl_give isl_pw_aff *isl_pw_aff_union_add(
3998 __isl_take isl_pw_aff *pwaff1,
3999 __isl_take isl_pw_aff *pwaff2);
4001 The function C<isl_pw_aff_union_max> computes a piecewise quasi-affine
4002 expression with a domain that is the union of those of C<pwaff1> and
4003 C<pwaff2> and such that on each cell, the quasi-affine expression is
4004 the maximum of those of C<pwaff1> and C<pwaff2>. If only one of
4005 C<pwaff1> or C<pwaff2> is defined on a given cell, then the
4006 associated expression is the defined one.
4008 An expression can be read from input using
4010 #include <isl/aff.h>
4011 __isl_give isl_aff *isl_aff_read_from_str(
4012 isl_ctx *ctx, const char *str);
4013 __isl_give isl_pw_aff *isl_pw_aff_read_from_str(
4014 isl_ctx *ctx, const char *str);
4016 An expression can be printed using
4018 #include <isl/aff.h>
4019 __isl_give isl_printer *isl_printer_print_aff(
4020 __isl_take isl_printer *p, __isl_keep isl_aff *aff);
4022 __isl_give isl_printer *isl_printer_print_pw_aff(
4023 __isl_take isl_printer *p,
4024 __isl_keep isl_pw_aff *pwaff);
4026 =head2 Piecewise Multiple Quasi Affine Expressions
4028 An C<isl_multi_aff> object represents a sequence of
4029 zero or more affine expressions, all defined on the same domain space.
4030 Similarly, an C<isl_multi_pw_aff> object represents a sequence of
4031 zero or more piecewise affine expressions.
4033 An C<isl_multi_aff> can be constructed from a single
4034 C<isl_aff> or an C<isl_aff_list> using the
4035 following functions. Similarly for C<isl_multi_pw_aff>
4036 and C<isl_pw_multi_aff>.
4038 #include <isl/aff.h>
4039 __isl_give isl_multi_aff *isl_multi_aff_from_aff(
4040 __isl_take isl_aff *aff);
4041 __isl_give isl_multi_pw_aff *
4042 isl_multi_pw_aff_from_multi_aff(
4043 __isl_take isl_multi_aff *ma);
4044 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_from_pw_aff(
4045 __isl_take isl_pw_aff *pa);
4046 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_from_pw_aff(
4047 __isl_take isl_pw_aff *pa);
4048 __isl_give isl_multi_aff *isl_multi_aff_from_aff_list(
4049 __isl_take isl_space *space,
4050 __isl_take isl_aff_list *list);
4052 An C<isl_multi_pw_aff> can be converted to an C<isl_pw_multi_aff>
4053 using the function C<isl_pw_multi_aff_from_multi_pw_aff> below.
4054 Note however that the domain
4055 of the result is the intersection of the domains of the input.
4056 The reverse conversion is exact.
4058 #include <isl/aff.h>
4059 __isl_give isl_pw_multi_aff *
4060 isl_pw_multi_aff_from_multi_pw_aff(
4061 __isl_take isl_multi_pw_aff *mpa);
4062 __isl_give isl_multi_pw_aff *
4063 isl_multi_pw_aff_from_pw_multi_aff(
4064 __isl_take isl_pw_multi_aff *pma);
4066 An empty piecewise multiple quasi affine expression (one with no cells),
4067 the zero piecewise multiple quasi affine expression (with value zero
4068 for each output dimension),
4069 a piecewise multiple quasi affine expression with a single cell (with
4070 either a universe or a specified domain) or
4071 a zero-dimensional piecewise multiple quasi affine expression
4073 can be created using the following functions.
4075 #include <isl/aff.h>
4076 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_empty(
4077 __isl_take isl_space *space);
4078 __isl_give isl_multi_aff *isl_multi_aff_zero(
4079 __isl_take isl_space *space);
4080 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_zero(
4081 __isl_take isl_space *space);
4082 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_zero(
4083 __isl_take isl_space *space);
4084 __isl_give isl_multi_aff *isl_multi_aff_identity(
4085 __isl_take isl_space *space);
4086 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_identity(
4087 __isl_take isl_space *space);
4088 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_identity(
4089 __isl_take isl_space *space);
4090 __isl_give isl_multi_aff *isl_multi_aff_domain_map(
4091 __isl_take isl_space *space);
4092 __isl_give isl_multi_aff *isl_multi_aff_range_map(
4093 __isl_take isl_space *space);
4094 __isl_give isl_multi_aff *isl_multi_aff_project_out_map(
4095 __isl_take isl_space *space,
4096 enum isl_dim_type type,
4097 unsigned first, unsigned n);
4098 __isl_give isl_pw_multi_aff *
4099 isl_pw_multi_aff_project_out_map(
4100 __isl_take isl_space *space,
4101 enum isl_dim_type type,
4102 unsigned first, unsigned n);
4103 __isl_give isl_pw_multi_aff *
4104 isl_pw_multi_aff_from_multi_aff(
4105 __isl_take isl_multi_aff *ma);
4106 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_alloc(
4107 __isl_take isl_set *set,
4108 __isl_take isl_multi_aff *maff);
4109 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_from_domain(
4110 __isl_take isl_set *set);
4112 __isl_give isl_union_pw_multi_aff *
4113 isl_union_pw_multi_aff_empty(
4114 __isl_take isl_space *space);
4115 __isl_give isl_union_pw_multi_aff *
4116 isl_union_pw_multi_aff_add_pw_multi_aff(
4117 __isl_take isl_union_pw_multi_aff *upma,
4118 __isl_take isl_pw_multi_aff *pma);
4119 __isl_give isl_union_pw_multi_aff *
4120 isl_union_pw_multi_aff_from_domain(
4121 __isl_take isl_union_set *uset);
4123 A piecewise multiple quasi affine expression can also be initialized
4124 from an C<isl_set> or C<isl_map>, provided the C<isl_set> is a singleton
4125 and the C<isl_map> is single-valued.
4126 In case of a conversion from an C<isl_union_set> or an C<isl_union_map>
4127 to an C<isl_union_pw_multi_aff>, these properties need to hold in each space.
4129 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_from_set(
4130 __isl_take isl_set *set);
4131 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_from_map(
4132 __isl_take isl_map *map);
4134 __isl_give isl_union_pw_multi_aff *
4135 isl_union_pw_multi_aff_from_union_set(
4136 __isl_take isl_union_set *uset);
4137 __isl_give isl_union_pw_multi_aff *
4138 isl_union_pw_multi_aff_from_union_map(
4139 __isl_take isl_union_map *umap);
4141 Multiple quasi affine expressions can be copied and freed using
4143 #include <isl/aff.h>
4144 __isl_give isl_multi_aff *isl_multi_aff_copy(
4145 __isl_keep isl_multi_aff *maff);
4146 void *isl_multi_aff_free(__isl_take isl_multi_aff *maff);
4148 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_copy(
4149 __isl_keep isl_pw_multi_aff *pma);
4150 void *isl_pw_multi_aff_free(
4151 __isl_take isl_pw_multi_aff *pma);
4153 __isl_give isl_union_pw_multi_aff *
4154 isl_union_pw_multi_aff_copy(
4155 __isl_keep isl_union_pw_multi_aff *upma);
4156 void *isl_union_pw_multi_aff_free(
4157 __isl_take isl_union_pw_multi_aff *upma);
4159 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_copy(
4160 __isl_keep isl_multi_pw_aff *mpa);
4161 void *isl_multi_pw_aff_free(
4162 __isl_take isl_multi_pw_aff *mpa);
4164 The expression can be inspected using
4166 #include <isl/aff.h>
4167 isl_ctx *isl_multi_aff_get_ctx(
4168 __isl_keep isl_multi_aff *maff);
4169 isl_ctx *isl_pw_multi_aff_get_ctx(
4170 __isl_keep isl_pw_multi_aff *pma);
4171 isl_ctx *isl_union_pw_multi_aff_get_ctx(
4172 __isl_keep isl_union_pw_multi_aff *upma);
4173 isl_ctx *isl_multi_pw_aff_get_ctx(
4174 __isl_keep isl_multi_pw_aff *mpa);
4175 unsigned isl_multi_aff_dim(__isl_keep isl_multi_aff *maff,
4176 enum isl_dim_type type);
4177 unsigned isl_pw_multi_aff_dim(
4178 __isl_keep isl_pw_multi_aff *pma,
4179 enum isl_dim_type type);
4180 unsigned isl_multi_pw_aff_dim(
4181 __isl_keep isl_multi_pw_aff *mpa,
4182 enum isl_dim_type type);
4183 __isl_give isl_aff *isl_multi_aff_get_aff(
4184 __isl_keep isl_multi_aff *multi, int pos);
4185 __isl_give isl_pw_aff *isl_pw_multi_aff_get_pw_aff(
4186 __isl_keep isl_pw_multi_aff *pma, int pos);
4187 __isl_give isl_pw_aff *isl_multi_pw_aff_get_pw_aff(
4188 __isl_keep isl_multi_pw_aff *mpa, int pos);
4189 int isl_multi_aff_find_dim_by_id(
4190 __isl_keep isl_multi_aff *ma,
4191 enum isl_dim_type type, __isl_keep isl_id *id);
4192 int isl_multi_pw_aff_find_dim_by_id(
4193 __isl_keep isl_multi_pw_aff *mpa,
4194 enum isl_dim_type type, __isl_keep isl_id *id);
4195 const char *isl_pw_multi_aff_get_dim_name(
4196 __isl_keep isl_pw_multi_aff *pma,
4197 enum isl_dim_type type, unsigned pos);
4198 __isl_give isl_id *isl_multi_aff_get_dim_id(
4199 __isl_keep isl_multi_aff *ma,
4200 enum isl_dim_type type, unsigned pos);
4201 __isl_give isl_id *isl_pw_multi_aff_get_dim_id(
4202 __isl_keep isl_pw_multi_aff *pma,
4203 enum isl_dim_type type, unsigned pos);
4204 __isl_give isl_id *isl_multi_pw_aff_get_dim_id(
4205 __isl_keep isl_multi_pw_aff *mpa,
4206 enum isl_dim_type type, unsigned pos);
4207 const char *isl_multi_aff_get_tuple_name(
4208 __isl_keep isl_multi_aff *multi,
4209 enum isl_dim_type type);
4210 int isl_pw_multi_aff_has_tuple_name(
4211 __isl_keep isl_pw_multi_aff *pma,
4212 enum isl_dim_type type);
4213 const char *isl_pw_multi_aff_get_tuple_name(
4214 __isl_keep isl_pw_multi_aff *pma,
4215 enum isl_dim_type type);
4216 int isl_multi_aff_has_tuple_id(__isl_keep isl_multi_aff *ma,
4217 enum isl_dim_type type);
4218 int isl_pw_multi_aff_has_tuple_id(
4219 __isl_keep isl_pw_multi_aff *pma,
4220 enum isl_dim_type type);
4221 int isl_multi_pw_aff_has_tuple_id(
4222 __isl_keep isl_multi_pw_aff *mpa,
4223 enum isl_dim_type type);
4224 __isl_give isl_id *isl_multi_aff_get_tuple_id(
4225 __isl_keep isl_multi_aff *ma,
4226 enum isl_dim_type type);
4227 __isl_give isl_id *isl_pw_multi_aff_get_tuple_id(
4228 __isl_keep isl_pw_multi_aff *pma,
4229 enum isl_dim_type type);
4230 __isl_give isl_id *isl_multi_pw_aff_get_tuple_id(
4231 __isl_keep isl_multi_pw_aff *mpa,
4232 enum isl_dim_type type);
4233 __isl_give isl_multi_aff *isl_multi_aff_reset_tuple_id(
4234 __isl_take isl_multi_aff *ma,
4235 enum isl_dim_type type);
4236 __isl_give isl_multi_pw_aff *
4237 isl_multi_pw_aff_reset_tuple_id(
4238 __isl_take isl_multi_pw_aff *mpa,
4239 enum isl_dim_type type);
4241 int isl_pw_multi_aff_foreach_piece(
4242 __isl_keep isl_pw_multi_aff *pma,
4243 int (*fn)(__isl_take isl_set *set,
4244 __isl_take isl_multi_aff *maff,
4245 void *user), void *user);
4247 int isl_union_pw_multi_aff_foreach_pw_multi_aff(
4248 __isl_keep isl_union_pw_multi_aff *upma,
4249 int (*fn)(__isl_take isl_pw_multi_aff *pma,
4250 void *user), void *user);
4252 It can be modified using
4254 #include <isl/aff.h>
4255 __isl_give isl_multi_aff *isl_multi_aff_set_aff(
4256 __isl_take isl_multi_aff *multi, int pos,
4257 __isl_take isl_aff *aff);
4258 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_set_pw_aff(
4259 __isl_take isl_pw_multi_aff *pma, unsigned pos,
4260 __isl_take isl_pw_aff *pa);
4261 __isl_give isl_multi_aff *isl_multi_aff_set_dim_name(
4262 __isl_take isl_multi_aff *maff,
4263 enum isl_dim_type type, unsigned pos, const char *s);
4264 __isl_give isl_multi_aff *isl_multi_aff_set_dim_id(
4265 __isl_take isl_multi_aff *maff,
4266 enum isl_dim_type type, unsigned pos,
4267 __isl_take isl_id *id);
4268 __isl_give isl_multi_aff *isl_multi_aff_set_tuple_name(
4269 __isl_take isl_multi_aff *maff,
4270 enum isl_dim_type type, const char *s);
4271 __isl_give isl_multi_aff *isl_multi_aff_set_tuple_id(
4272 __isl_take isl_multi_aff *maff,
4273 enum isl_dim_type type, __isl_take isl_id *id);
4274 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_set_tuple_id(
4275 __isl_take isl_pw_multi_aff *pma,
4276 enum isl_dim_type type, __isl_take isl_id *id);
4278 __isl_give isl_multi_pw_aff *
4279 isl_multi_pw_aff_set_dim_name(
4280 __isl_take isl_multi_pw_aff *mpa,
4281 enum isl_dim_type type, unsigned pos, const char *s);
4282 __isl_give isl_multi_pw_aff *
4283 isl_multi_pw_aff_set_dim_id(
4284 __isl_take isl_multi_pw_aff *mpa,
4285 enum isl_dim_type type, unsigned pos,
4286 __isl_take isl_id *id);
4287 __isl_give isl_multi_pw_aff *
4288 isl_multi_pw_aff_set_tuple_name(
4289 __isl_take isl_multi_pw_aff *mpa,
4290 enum isl_dim_type type, const char *s);
4292 __isl_give isl_multi_aff *isl_multi_aff_insert_dims(
4293 __isl_take isl_multi_aff *ma,
4294 enum isl_dim_type type, unsigned first, unsigned n);
4295 __isl_give isl_multi_aff *isl_multi_aff_add_dims(
4296 __isl_take isl_multi_aff *ma,
4297 enum isl_dim_type type, unsigned n);
4298 __isl_give isl_multi_aff *isl_multi_aff_drop_dims(
4299 __isl_take isl_multi_aff *maff,
4300 enum isl_dim_type type, unsigned first, unsigned n);
4301 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_drop_dims(
4302 __isl_take isl_pw_multi_aff *pma,
4303 enum isl_dim_type type, unsigned first, unsigned n);
4305 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_insert_dims(
4306 __isl_take isl_multi_pw_aff *mpa,
4307 enum isl_dim_type type, unsigned first, unsigned n);
4308 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_add_dims(
4309 __isl_take isl_multi_pw_aff *mpa,
4310 enum isl_dim_type type, unsigned n);
4311 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_move_dims(
4312 __isl_take isl_multi_pw_aff *pma,
4313 enum isl_dim_type dst_type, unsigned dst_pos,
4314 enum isl_dim_type src_type, unsigned src_pos,
4317 To check whether two multiple affine expressions are
4318 (obviously) equal to each other, use
4320 int isl_multi_aff_plain_is_equal(__isl_keep isl_multi_aff *maff1,
4321 __isl_keep isl_multi_aff *maff2);
4322 int isl_pw_multi_aff_plain_is_equal(
4323 __isl_keep isl_pw_multi_aff *pma1,
4324 __isl_keep isl_pw_multi_aff *pma2);
4325 int isl_multi_pw_aff_plain_is_equal(
4326 __isl_keep isl_multi_pw_aff *mpa1,
4327 __isl_keep isl_multi_pw_aff *mpa2);
4328 int isl_multi_pw_aff_is_equal(
4329 __isl_keep isl_multi_pw_aff *mpa1,
4330 __isl_keep isl_multi_pw_aff *mpa2);
4334 #include <isl/aff.h>
4335 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_union_lexmin(
4336 __isl_take isl_pw_multi_aff *pma1,
4337 __isl_take isl_pw_multi_aff *pma2);
4338 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_union_lexmax(
4339 __isl_take isl_pw_multi_aff *pma1,
4340 __isl_take isl_pw_multi_aff *pma2);
4341 __isl_give isl_multi_aff *isl_multi_aff_add(
4342 __isl_take isl_multi_aff *maff1,
4343 __isl_take isl_multi_aff *maff2);
4344 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_add(
4345 __isl_take isl_pw_multi_aff *pma1,
4346 __isl_take isl_pw_multi_aff *pma2);
4347 __isl_give isl_union_pw_multi_aff *isl_union_pw_multi_aff_add(
4348 __isl_take isl_union_pw_multi_aff *upma1,
4349 __isl_take isl_union_pw_multi_aff *upma2);
4350 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_union_add(
4351 __isl_take isl_pw_multi_aff *pma1,
4352 __isl_take isl_pw_multi_aff *pma2);
4353 __isl_give isl_multi_aff *isl_multi_aff_sub(
4354 __isl_take isl_multi_aff *ma1,
4355 __isl_take isl_multi_aff *ma2);
4356 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_sub(
4357 __isl_take isl_pw_multi_aff *pma1,
4358 __isl_take isl_pw_multi_aff *pma2);
4359 __isl_give isl_union_pw_multi_aff *isl_union_pw_multi_aff_sub(
4360 __isl_take isl_union_pw_multi_aff *upma1,
4361 __isl_take isl_union_pw_multi_aff *upma2);
4363 C<isl_multi_aff_sub> subtracts the second argument from the first.
4365 __isl_give isl_multi_aff *isl_multi_aff_scale_val(
4366 __isl_take isl_multi_aff *ma,
4367 __isl_take isl_val *v);
4368 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_scale_val(
4369 __isl_take isl_pw_multi_aff *pma,
4370 __isl_take isl_val *v);
4371 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_scale_val(
4372 __isl_take isl_multi_pw_aff *mpa,
4373 __isl_take isl_val *v);
4374 __isl_give isl_multi_aff *isl_multi_aff_scale_multi_val(
4375 __isl_take isl_multi_aff *ma,
4376 __isl_take isl_multi_val *mv);
4377 __isl_give isl_pw_multi_aff *
4378 isl_pw_multi_aff_scale_multi_val(
4379 __isl_take isl_pw_multi_aff *pma,
4380 __isl_take isl_multi_val *mv);
4381 __isl_give isl_multi_pw_aff *
4382 isl_multi_pw_aff_scale_multi_val(
4383 __isl_take isl_multi_pw_aff *mpa,
4384 __isl_take isl_multi_val *mv);
4385 __isl_give isl_union_pw_multi_aff *
4386 isl_union_pw_multi_aff_scale_multi_val(
4387 __isl_take isl_union_pw_multi_aff *upma,
4388 __isl_take isl_multi_val *mv);
4389 __isl_give isl_multi_aff *
4390 isl_multi_aff_scale_down_multi_val(
4391 __isl_take isl_multi_aff *ma,
4392 __isl_take isl_multi_val *mv);
4393 __isl_give isl_multi_pw_aff *
4394 isl_multi_pw_aff_scale_down_multi_val(
4395 __isl_take isl_multi_pw_aff *mpa,
4396 __isl_take isl_multi_val *mv);
4398 C<isl_multi_aff_scale_multi_val> scales the elements of C<ma>
4399 by the corresponding elements of C<mv>.
4401 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_fix_si(
4402 __isl_take isl_pw_multi_aff *pma,
4403 enum isl_dim_type type, unsigned pos, int value);
4404 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_intersect_params(
4405 __isl_take isl_pw_multi_aff *pma,
4406 __isl_take isl_set *set);
4407 __isl_give isl_set *isl_multi_pw_aff_domain(
4408 __isl_take isl_multi_pw_aff *mpa);
4409 __isl_give isl_multi_pw_aff *
4410 isl_multi_pw_aff_intersect_params(
4411 __isl_take isl_multi_pw_aff *mpa,
4412 __isl_take isl_set *set);
4413 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_intersect_domain(
4414 __isl_take isl_pw_multi_aff *pma,
4415 __isl_take isl_set *set);
4416 __isl_give isl_multi_pw_aff *
4417 isl_multi_pw_aff_intersect_domain(
4418 __isl_take isl_multi_pw_aff *mpa,
4419 __isl_take isl_set *domain);
4420 __isl_give isl_union_pw_multi_aff *
4421 isl_union_pw_multi_aff_intersect_domain(
4422 __isl_take isl_union_pw_multi_aff *upma,
4423 __isl_take isl_union_set *uset);
4424 __isl_give isl_multi_aff *isl_multi_aff_lift(
4425 __isl_take isl_multi_aff *maff,
4426 __isl_give isl_local_space **ls);
4427 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_coalesce(
4428 __isl_take isl_pw_multi_aff *pma);
4429 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_coalesce(
4430 __isl_take isl_multi_pw_aff *mpa);
4431 __isl_give isl_multi_aff *isl_multi_aff_align_params(
4432 __isl_take isl_multi_aff *multi,
4433 __isl_take isl_space *model);
4434 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_align_params(
4435 __isl_take isl_pw_multi_aff *pma,
4436 __isl_take isl_space *model);
4437 __isl_give isl_pw_multi_aff *
4438 isl_pw_multi_aff_project_domain_on_params(
4439 __isl_take isl_pw_multi_aff *pma);
4440 __isl_give isl_multi_aff *isl_multi_aff_gist_params(
4441 __isl_take isl_multi_aff *maff,
4442 __isl_take isl_set *context);
4443 __isl_give isl_multi_aff *isl_multi_aff_gist(
4444 __isl_take isl_multi_aff *maff,
4445 __isl_take isl_set *context);
4446 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_gist_params(
4447 __isl_take isl_pw_multi_aff *pma,
4448 __isl_take isl_set *set);
4449 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_gist(
4450 __isl_take isl_pw_multi_aff *pma,
4451 __isl_take isl_set *set);
4452 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_gist_params(
4453 __isl_take isl_multi_pw_aff *mpa,
4454 __isl_take isl_set *set);
4455 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_gist(
4456 __isl_take isl_multi_pw_aff *mpa,
4457 __isl_take isl_set *set);
4458 __isl_give isl_multi_aff *isl_multi_aff_from_range(
4459 __isl_take isl_multi_aff *ma);
4460 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_from_range(
4461 __isl_take isl_multi_pw_aff *mpa);
4462 __isl_give isl_set *isl_pw_multi_aff_domain(
4463 __isl_take isl_pw_multi_aff *pma);
4464 __isl_give isl_union_set *isl_union_pw_multi_aff_domain(
4465 __isl_take isl_union_pw_multi_aff *upma);
4466 __isl_give isl_multi_aff *isl_multi_aff_range_splice(
4467 __isl_take isl_multi_aff *ma1, unsigned pos,
4468 __isl_take isl_multi_aff *ma2);
4469 __isl_give isl_multi_aff *isl_multi_aff_splice(
4470 __isl_take isl_multi_aff *ma1,
4471 unsigned in_pos, unsigned out_pos,
4472 __isl_take isl_multi_aff *ma2);
4473 __isl_give isl_multi_aff *isl_multi_aff_range_product(
4474 __isl_take isl_multi_aff *ma1,
4475 __isl_take isl_multi_aff *ma2);
4476 __isl_give isl_multi_aff *isl_multi_aff_flat_range_product(
4477 __isl_take isl_multi_aff *ma1,
4478 __isl_take isl_multi_aff *ma2);
4479 __isl_give isl_multi_aff *isl_multi_aff_product(
4480 __isl_take isl_multi_aff *ma1,
4481 __isl_take isl_multi_aff *ma2);
4482 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_product(
4483 __isl_take isl_multi_pw_aff *mpa1,
4484 __isl_take isl_multi_pw_aff *mpa2);
4485 __isl_give isl_pw_multi_aff *
4486 isl_pw_multi_aff_range_product(
4487 __isl_take isl_pw_multi_aff *pma1,
4488 __isl_take isl_pw_multi_aff *pma2);
4489 __isl_give isl_pw_multi_aff *
4490 isl_pw_multi_aff_flat_range_product(
4491 __isl_take isl_pw_multi_aff *pma1,
4492 __isl_take isl_pw_multi_aff *pma2);
4493 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_product(
4494 __isl_take isl_pw_multi_aff *pma1,
4495 __isl_take isl_pw_multi_aff *pma2);
4496 __isl_give isl_union_pw_multi_aff *
4497 isl_union_pw_multi_aff_flat_range_product(
4498 __isl_take isl_union_pw_multi_aff *upma1,
4499 __isl_take isl_union_pw_multi_aff *upma2);
4500 __isl_give isl_multi_pw_aff *
4501 isl_multi_pw_aff_range_splice(
4502 __isl_take isl_multi_pw_aff *mpa1, unsigned pos,
4503 __isl_take isl_multi_pw_aff *mpa2);
4504 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_splice(
4505 __isl_take isl_multi_pw_aff *mpa1,
4506 unsigned in_pos, unsigned out_pos,
4507 __isl_take isl_multi_pw_aff *mpa2);
4508 __isl_give isl_multi_pw_aff *
4509 isl_multi_pw_aff_range_product(
4510 __isl_take isl_multi_pw_aff *mpa1,
4511 __isl_take isl_multi_pw_aff *mpa2);
4512 __isl_give isl_multi_pw_aff *
4513 isl_multi_pw_aff_flat_range_product(
4514 __isl_take isl_multi_pw_aff *mpa1,
4515 __isl_take isl_multi_pw_aff *mpa2);
4517 If the C<ls> argument of C<isl_multi_aff_lift> is not C<NULL>,
4518 then it is assigned the local space that lies at the basis of
4519 the lifting applied.
4521 #include <isl/aff.h>
4522 __isl_give isl_multi_aff *isl_multi_aff_pullback_multi_aff(
4523 __isl_take isl_multi_aff *ma1,
4524 __isl_take isl_multi_aff *ma2);
4525 __isl_give isl_pw_multi_aff *
4526 isl_pw_multi_aff_pullback_multi_aff(
4527 __isl_take isl_pw_multi_aff *pma,
4528 __isl_take isl_multi_aff *ma);
4529 __isl_give isl_multi_pw_aff *
4530 isl_multi_pw_aff_pullback_multi_aff(
4531 __isl_take isl_multi_pw_aff *mpa,
4532 __isl_take isl_multi_aff *ma);
4533 __isl_give isl_pw_multi_aff *
4534 isl_pw_multi_aff_pullback_pw_multi_aff(
4535 __isl_take isl_pw_multi_aff *pma1,
4536 __isl_take isl_pw_multi_aff *pma2);
4537 __isl_give isl_multi_pw_aff *
4538 isl_multi_pw_aff_pullback_pw_multi_aff(
4539 __isl_take isl_multi_pw_aff *mpa,
4540 __isl_take isl_pw_multi_aff *pma);
4541 __isl_give isl_multi_pw_aff *
4542 isl_multi_pw_aff_pullback_multi_pw_aff(
4543 __isl_take isl_multi_pw_aff *mpa1,
4544 __isl_take isl_multi_pw_aff *mpa2);
4546 The function C<isl_multi_aff_pullback_multi_aff> precomposes C<ma1> by C<ma2>.
4547 In other words, C<ma2> is plugged
4550 __isl_give isl_set *isl_multi_aff_lex_le_set(
4551 __isl_take isl_multi_aff *ma1,
4552 __isl_take isl_multi_aff *ma2);
4553 __isl_give isl_set *isl_multi_aff_lex_ge_set(
4554 __isl_take isl_multi_aff *ma1,
4555 __isl_take isl_multi_aff *ma2);
4557 The function C<isl_multi_aff_lex_le_set> returns a set
4558 containing those elements in the shared domain space
4559 where C<ma1> is lexicographically smaller than or
4562 An expression can be read from input using
4564 #include <isl/aff.h>
4565 __isl_give isl_multi_aff *isl_multi_aff_read_from_str(
4566 isl_ctx *ctx, const char *str);
4567 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_read_from_str(
4568 isl_ctx *ctx, const char *str);
4569 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_read_from_str(
4570 isl_ctx *ctx, const char *str);
4571 __isl_give isl_union_pw_multi_aff *
4572 isl_union_pw_multi_aff_read_from_str(
4573 isl_ctx *ctx, const char *str);
4575 An expression can be printed using
4577 #include <isl/aff.h>
4578 __isl_give isl_printer *isl_printer_print_multi_aff(
4579 __isl_take isl_printer *p,
4580 __isl_keep isl_multi_aff *maff);
4581 __isl_give isl_printer *isl_printer_print_pw_multi_aff(
4582 __isl_take isl_printer *p,
4583 __isl_keep isl_pw_multi_aff *pma);
4584 __isl_give isl_printer *isl_printer_print_union_pw_multi_aff(
4585 __isl_take isl_printer *p,
4586 __isl_keep isl_union_pw_multi_aff *upma);
4587 __isl_give isl_printer *isl_printer_print_multi_pw_aff(
4588 __isl_take isl_printer *p,
4589 __isl_keep isl_multi_pw_aff *mpa);
4593 Points are elements of a set. They can be used to construct
4594 simple sets (boxes) or they can be used to represent the
4595 individual elements of a set.
4596 The zero point (the origin) can be created using
4598 __isl_give isl_point *isl_point_zero(__isl_take isl_space *space);
4600 The coordinates of a point can be inspected, set and changed
4603 __isl_give isl_val *isl_point_get_coordinate_val(
4604 __isl_keep isl_point *pnt,
4605 enum isl_dim_type type, int pos);
4606 __isl_give isl_point *isl_point_set_coordinate_val(
4607 __isl_take isl_point *pnt,
4608 enum isl_dim_type type, int pos,
4609 __isl_take isl_val *v);
4611 __isl_give isl_point *isl_point_add_ui(
4612 __isl_take isl_point *pnt,
4613 enum isl_dim_type type, int pos, unsigned val);
4614 __isl_give isl_point *isl_point_sub_ui(
4615 __isl_take isl_point *pnt,
4616 enum isl_dim_type type, int pos, unsigned val);
4618 Other properties can be obtained using
4620 isl_ctx *isl_point_get_ctx(__isl_keep isl_point *pnt);
4622 Points can be copied or freed using
4624 __isl_give isl_point *isl_point_copy(
4625 __isl_keep isl_point *pnt);
4626 void isl_point_free(__isl_take isl_point *pnt);
4628 A singleton set can be created from a point using
4630 __isl_give isl_basic_set *isl_basic_set_from_point(
4631 __isl_take isl_point *pnt);
4632 __isl_give isl_set *isl_set_from_point(
4633 __isl_take isl_point *pnt);
4635 and a box can be created from two opposite extremal points using
4637 __isl_give isl_basic_set *isl_basic_set_box_from_points(
4638 __isl_take isl_point *pnt1,
4639 __isl_take isl_point *pnt2);
4640 __isl_give isl_set *isl_set_box_from_points(
4641 __isl_take isl_point *pnt1,
4642 __isl_take isl_point *pnt2);
4644 All elements of a B<bounded> (union) set can be enumerated using
4645 the following functions.
4647 int isl_set_foreach_point(__isl_keep isl_set *set,
4648 int (*fn)(__isl_take isl_point *pnt, void *user),
4650 int isl_union_set_foreach_point(__isl_keep isl_union_set *uset,
4651 int (*fn)(__isl_take isl_point *pnt, void *user),
4654 The function C<fn> is called for each integer point in
4655 C<set> with as second argument the last argument of
4656 the C<isl_set_foreach_point> call. The function C<fn>
4657 should return C<0> on success and C<-1> on failure.
4658 In the latter case, C<isl_set_foreach_point> will stop
4659 enumerating and return C<-1> as well.
4660 If the enumeration is performed successfully and to completion,
4661 then C<isl_set_foreach_point> returns C<0>.
4663 To obtain a single point of a (basic) set, use
4665 __isl_give isl_point *isl_basic_set_sample_point(
4666 __isl_take isl_basic_set *bset);
4667 __isl_give isl_point *isl_set_sample_point(
4668 __isl_take isl_set *set);
4670 If C<set> does not contain any (integer) points, then the
4671 resulting point will be ``void'', a property that can be
4674 int isl_point_is_void(__isl_keep isl_point *pnt);
4676 =head2 Piecewise Quasipolynomials
4678 A piecewise quasipolynomial is a particular kind of function that maps
4679 a parametric point to a rational value.
4680 More specifically, a quasipolynomial is a polynomial expression in greatest
4681 integer parts of affine expressions of parameters and variables.
4682 A piecewise quasipolynomial is a subdivision of a given parametric
4683 domain into disjoint cells with a quasipolynomial associated to
4684 each cell. The value of the piecewise quasipolynomial at a given
4685 point is the value of the quasipolynomial associated to the cell
4686 that contains the point. Outside of the union of cells,
4687 the value is assumed to be zero.
4688 For example, the piecewise quasipolynomial
4690 [n] -> { [x] -> ((1 + n) - x) : x <= n and x >= 0 }
4692 maps C<x> to C<1 + n - x> for values of C<x> between C<0> and C<n>.
4693 A given piecewise quasipolynomial has a fixed domain dimension.
4694 Union piecewise quasipolynomials are used to contain piecewise quasipolynomials
4695 defined over different domains.
4696 Piecewise quasipolynomials are mainly used by the C<barvinok>
4697 library for representing the number of elements in a parametric set or map.
4698 For example, the piecewise quasipolynomial above represents
4699 the number of points in the map
4701 [n] -> { [x] -> [y] : x,y >= 0 and 0 <= x + y <= n }
4703 =head3 Input and Output
4705 Piecewise quasipolynomials can be read from input using
4707 __isl_give isl_union_pw_qpolynomial *
4708 isl_union_pw_qpolynomial_read_from_str(
4709 isl_ctx *ctx, const char *str);
4711 Quasipolynomials and piecewise quasipolynomials can be printed
4712 using the following functions.
4714 __isl_give isl_printer *isl_printer_print_qpolynomial(
4715 __isl_take isl_printer *p,
4716 __isl_keep isl_qpolynomial *qp);
4718 __isl_give isl_printer *isl_printer_print_pw_qpolynomial(
4719 __isl_take isl_printer *p,
4720 __isl_keep isl_pw_qpolynomial *pwqp);
4722 __isl_give isl_printer *isl_printer_print_union_pw_qpolynomial(
4723 __isl_take isl_printer *p,
4724 __isl_keep isl_union_pw_qpolynomial *upwqp);
4726 The output format of the printer
4727 needs to be set to either C<ISL_FORMAT_ISL> or C<ISL_FORMAT_C>.
4728 For C<isl_printer_print_union_pw_qpolynomial>, only C<ISL_FORMAT_ISL>
4730 In case of printing in C<ISL_FORMAT_C>, the user may want
4731 to set the names of all dimensions
4733 __isl_give isl_qpolynomial *isl_qpolynomial_set_dim_name(
4734 __isl_take isl_qpolynomial *qp,
4735 enum isl_dim_type type, unsigned pos,
4737 __isl_give isl_pw_qpolynomial *
4738 isl_pw_qpolynomial_set_dim_name(
4739 __isl_take isl_pw_qpolynomial *pwqp,
4740 enum isl_dim_type type, unsigned pos,
4743 =head3 Creating New (Piecewise) Quasipolynomials
4745 Some simple quasipolynomials can be created using the following functions.
4746 More complicated quasipolynomials can be created by applying
4747 operations such as addition and multiplication
4748 on the resulting quasipolynomials
4750 __isl_give isl_qpolynomial *isl_qpolynomial_zero_on_domain(
4751 __isl_take isl_space *domain);
4752 __isl_give isl_qpolynomial *isl_qpolynomial_one_on_domain(
4753 __isl_take isl_space *domain);
4754 __isl_give isl_qpolynomial *isl_qpolynomial_infty_on_domain(
4755 __isl_take isl_space *domain);
4756 __isl_give isl_qpolynomial *isl_qpolynomial_neginfty_on_domain(
4757 __isl_take isl_space *domain);
4758 __isl_give isl_qpolynomial *isl_qpolynomial_nan_on_domain(
4759 __isl_take isl_space *domain);
4760 __isl_give isl_qpolynomial *isl_qpolynomial_val_on_domain(
4761 __isl_take isl_space *domain,
4762 __isl_take isl_val *val);
4763 __isl_give isl_qpolynomial *isl_qpolynomial_var_on_domain(
4764 __isl_take isl_space *domain,
4765 enum isl_dim_type type, unsigned pos);
4766 __isl_give isl_qpolynomial *isl_qpolynomial_from_aff(
4767 __isl_take isl_aff *aff);
4769 Note that the space in which a quasipolynomial lives is a map space
4770 with a one-dimensional range. The C<domain> argument in some of
4771 the functions above corresponds to the domain of this map space.
4773 The zero piecewise quasipolynomial or a piecewise quasipolynomial
4774 with a single cell can be created using the following functions.
4775 Multiple of these single cell piecewise quasipolynomials can
4776 be combined to create more complicated piecewise quasipolynomials.
4778 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_zero(
4779 __isl_take isl_space *space);
4780 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_alloc(
4781 __isl_take isl_set *set,
4782 __isl_take isl_qpolynomial *qp);
4783 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_from_qpolynomial(
4784 __isl_take isl_qpolynomial *qp);
4785 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_from_pw_aff(
4786 __isl_take isl_pw_aff *pwaff);
4788 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_zero(
4789 __isl_take isl_space *space);
4790 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_from_pw_qpolynomial(
4791 __isl_take isl_pw_qpolynomial *pwqp);
4792 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_add_pw_qpolynomial(
4793 __isl_take isl_union_pw_qpolynomial *upwqp,
4794 __isl_take isl_pw_qpolynomial *pwqp);
4796 Quasipolynomials can be copied and freed again using the following
4799 __isl_give isl_qpolynomial *isl_qpolynomial_copy(
4800 __isl_keep isl_qpolynomial *qp);
4801 void *isl_qpolynomial_free(__isl_take isl_qpolynomial *qp);
4803 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_copy(
4804 __isl_keep isl_pw_qpolynomial *pwqp);
4805 void *isl_pw_qpolynomial_free(
4806 __isl_take isl_pw_qpolynomial *pwqp);
4808 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_copy(
4809 __isl_keep isl_union_pw_qpolynomial *upwqp);
4810 void *isl_union_pw_qpolynomial_free(
4811 __isl_take isl_union_pw_qpolynomial *upwqp);
4813 =head3 Inspecting (Piecewise) Quasipolynomials
4815 To iterate over all piecewise quasipolynomials in a union
4816 piecewise quasipolynomial, use the following function
4818 int isl_union_pw_qpolynomial_foreach_pw_qpolynomial(
4819 __isl_keep isl_union_pw_qpolynomial *upwqp,
4820 int (*fn)(__isl_take isl_pw_qpolynomial *pwqp, void *user),
4823 To extract the piecewise quasipolynomial in a given space from a union, use
4825 __isl_give isl_pw_qpolynomial *
4826 isl_union_pw_qpolynomial_extract_pw_qpolynomial(
4827 __isl_keep isl_union_pw_qpolynomial *upwqp,
4828 __isl_take isl_space *space);
4830 To iterate over the cells in a piecewise quasipolynomial,
4831 use either of the following two functions
4833 int isl_pw_qpolynomial_foreach_piece(
4834 __isl_keep isl_pw_qpolynomial *pwqp,
4835 int (*fn)(__isl_take isl_set *set,
4836 __isl_take isl_qpolynomial *qp,
4837 void *user), void *user);
4838 int isl_pw_qpolynomial_foreach_lifted_piece(
4839 __isl_keep isl_pw_qpolynomial *pwqp,
4840 int (*fn)(__isl_take isl_set *set,
4841 __isl_take isl_qpolynomial *qp,
4842 void *user), void *user);
4844 As usual, the function C<fn> should return C<0> on success
4845 and C<-1> on failure. The difference between
4846 C<isl_pw_qpolynomial_foreach_piece> and
4847 C<isl_pw_qpolynomial_foreach_lifted_piece> is that
4848 C<isl_pw_qpolynomial_foreach_lifted_piece> will first
4849 compute unique representations for all existentially quantified
4850 variables and then turn these existentially quantified variables
4851 into extra set variables, adapting the associated quasipolynomial
4852 accordingly. This means that the C<set> passed to C<fn>
4853 will not have any existentially quantified variables, but that
4854 the dimensions of the sets may be different for different
4855 invocations of C<fn>.
4857 The constant term of a quasipolynomial can be extracted using
4859 __isl_give isl_val *isl_qpolynomial_get_constant_val(
4860 __isl_keep isl_qpolynomial *qp);
4862 To iterate over all terms in a quasipolynomial,
4865 int isl_qpolynomial_foreach_term(
4866 __isl_keep isl_qpolynomial *qp,
4867 int (*fn)(__isl_take isl_term *term,
4868 void *user), void *user);
4870 The terms themselves can be inspected and freed using
4873 unsigned isl_term_dim(__isl_keep isl_term *term,
4874 enum isl_dim_type type);
4875 __isl_give isl_val *isl_term_get_coefficient_val(
4876 __isl_keep isl_term *term);
4877 int isl_term_get_exp(__isl_keep isl_term *term,
4878 enum isl_dim_type type, unsigned pos);
4879 __isl_give isl_aff *isl_term_get_div(
4880 __isl_keep isl_term *term, unsigned pos);
4881 void isl_term_free(__isl_take isl_term *term);
4883 Each term is a product of parameters, set variables and
4884 integer divisions. The function C<isl_term_get_exp>
4885 returns the exponent of a given dimensions in the given term.
4887 =head3 Properties of (Piecewise) Quasipolynomials
4889 To check whether two union piecewise quasipolynomials are
4890 obviously equal, use
4892 int isl_union_pw_qpolynomial_plain_is_equal(
4893 __isl_keep isl_union_pw_qpolynomial *upwqp1,
4894 __isl_keep isl_union_pw_qpolynomial *upwqp2);
4896 =head3 Operations on (Piecewise) Quasipolynomials
4898 __isl_give isl_qpolynomial *isl_qpolynomial_scale_val(
4899 __isl_take isl_qpolynomial *qp,
4900 __isl_take isl_val *v);
4901 __isl_give isl_qpolynomial *isl_qpolynomial_neg(
4902 __isl_take isl_qpolynomial *qp);
4903 __isl_give isl_qpolynomial *isl_qpolynomial_add(
4904 __isl_take isl_qpolynomial *qp1,
4905 __isl_take isl_qpolynomial *qp2);
4906 __isl_give isl_qpolynomial *isl_qpolynomial_sub(
4907 __isl_take isl_qpolynomial *qp1,
4908 __isl_take isl_qpolynomial *qp2);
4909 __isl_give isl_qpolynomial *isl_qpolynomial_mul(
4910 __isl_take isl_qpolynomial *qp1,
4911 __isl_take isl_qpolynomial *qp2);
4912 __isl_give isl_qpolynomial *isl_qpolynomial_pow(
4913 __isl_take isl_qpolynomial *qp, unsigned exponent);
4915 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_fix_val(
4916 __isl_take isl_pw_qpolynomial *pwqp,
4917 enum isl_dim_type type, unsigned n,
4918 __isl_take isl_val *v);
4919 __isl_give isl_pw_qpolynomial *
4920 isl_pw_qpolynomial_scale_val(
4921 __isl_take isl_pw_qpolynomial *pwqp,
4922 __isl_take isl_val *v);
4923 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_add(
4924 __isl_take isl_pw_qpolynomial *pwqp1,
4925 __isl_take isl_pw_qpolynomial *pwqp2);
4926 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_sub(
4927 __isl_take isl_pw_qpolynomial *pwqp1,
4928 __isl_take isl_pw_qpolynomial *pwqp2);
4929 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_add_disjoint(
4930 __isl_take isl_pw_qpolynomial *pwqp1,
4931 __isl_take isl_pw_qpolynomial *pwqp2);
4932 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_neg(
4933 __isl_take isl_pw_qpolynomial *pwqp);
4934 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_mul(
4935 __isl_take isl_pw_qpolynomial *pwqp1,
4936 __isl_take isl_pw_qpolynomial *pwqp2);
4937 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_pow(
4938 __isl_take isl_pw_qpolynomial *pwqp, unsigned exponent);
4940 __isl_give isl_union_pw_qpolynomial *
4941 isl_union_pw_qpolynomial_scale_val(
4942 __isl_take isl_union_pw_qpolynomial *upwqp,
4943 __isl_take isl_val *v);
4944 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_add(
4945 __isl_take isl_union_pw_qpolynomial *upwqp1,
4946 __isl_take isl_union_pw_qpolynomial *upwqp2);
4947 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_sub(
4948 __isl_take isl_union_pw_qpolynomial *upwqp1,
4949 __isl_take isl_union_pw_qpolynomial *upwqp2);
4950 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_mul(
4951 __isl_take isl_union_pw_qpolynomial *upwqp1,
4952 __isl_take isl_union_pw_qpolynomial *upwqp2);
4954 __isl_give isl_val *isl_pw_qpolynomial_eval(
4955 __isl_take isl_pw_qpolynomial *pwqp,
4956 __isl_take isl_point *pnt);
4958 __isl_give isl_val *isl_union_pw_qpolynomial_eval(
4959 __isl_take isl_union_pw_qpolynomial *upwqp,
4960 __isl_take isl_point *pnt);
4962 __isl_give isl_set *isl_pw_qpolynomial_domain(
4963 __isl_take isl_pw_qpolynomial *pwqp);
4964 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_intersect_domain(
4965 __isl_take isl_pw_qpolynomial *pwpq,
4966 __isl_take isl_set *set);
4967 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_intersect_params(
4968 __isl_take isl_pw_qpolynomial *pwpq,
4969 __isl_take isl_set *set);
4971 __isl_give isl_union_set *isl_union_pw_qpolynomial_domain(
4972 __isl_take isl_union_pw_qpolynomial *upwqp);
4973 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_intersect_domain(
4974 __isl_take isl_union_pw_qpolynomial *upwpq,
4975 __isl_take isl_union_set *uset);
4976 __isl_give isl_union_pw_qpolynomial *
4977 isl_union_pw_qpolynomial_intersect_params(
4978 __isl_take isl_union_pw_qpolynomial *upwpq,
4979 __isl_take isl_set *set);
4981 __isl_give isl_qpolynomial *isl_qpolynomial_align_params(
4982 __isl_take isl_qpolynomial *qp,
4983 __isl_take isl_space *model);
4985 __isl_give isl_qpolynomial *isl_qpolynomial_project_domain_on_params(
4986 __isl_take isl_qpolynomial *qp);
4987 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_project_domain_on_params(
4988 __isl_take isl_pw_qpolynomial *pwqp);
4990 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_coalesce(
4991 __isl_take isl_union_pw_qpolynomial *upwqp);
4993 __isl_give isl_qpolynomial *isl_qpolynomial_gist_params(
4994 __isl_take isl_qpolynomial *qp,
4995 __isl_take isl_set *context);
4996 __isl_give isl_qpolynomial *isl_qpolynomial_gist(
4997 __isl_take isl_qpolynomial *qp,
4998 __isl_take isl_set *context);
5000 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_gist_params(
5001 __isl_take isl_pw_qpolynomial *pwqp,
5002 __isl_take isl_set *context);
5003 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_gist(
5004 __isl_take isl_pw_qpolynomial *pwqp,
5005 __isl_take isl_set *context);
5007 __isl_give isl_union_pw_qpolynomial *
5008 isl_union_pw_qpolynomial_gist_params(
5009 __isl_take isl_union_pw_qpolynomial *upwqp,
5010 __isl_take isl_set *context);
5011 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_gist(
5012 __isl_take isl_union_pw_qpolynomial *upwqp,
5013 __isl_take isl_union_set *context);
5015 The gist operation applies the gist operation to each of
5016 the cells in the domain of the input piecewise quasipolynomial.
5017 The context is also exploited
5018 to simplify the quasipolynomials associated to each cell.
5020 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_to_polynomial(
5021 __isl_take isl_pw_qpolynomial *pwqp, int sign);
5022 __isl_give isl_union_pw_qpolynomial *
5023 isl_union_pw_qpolynomial_to_polynomial(
5024 __isl_take isl_union_pw_qpolynomial *upwqp, int sign);
5026 Approximate each quasipolynomial by a polynomial. If C<sign> is positive,
5027 the polynomial will be an overapproximation. If C<sign> is negative,
5028 it will be an underapproximation. If C<sign> is zero, the approximation
5029 will lie somewhere in between.
5031 =head2 Bounds on Piecewise Quasipolynomials and Piecewise Quasipolynomial Reductions
5033 A piecewise quasipolynomial reduction is a piecewise
5034 reduction (or fold) of quasipolynomials.
5035 In particular, the reduction can be maximum or a minimum.
5036 The objects are mainly used to represent the result of
5037 an upper or lower bound on a quasipolynomial over its domain,
5038 i.e., as the result of the following function.
5040 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_bound(
5041 __isl_take isl_pw_qpolynomial *pwqp,
5042 enum isl_fold type, int *tight);
5044 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_bound(
5045 __isl_take isl_union_pw_qpolynomial *upwqp,
5046 enum isl_fold type, int *tight);
5048 The C<type> argument may be either C<isl_fold_min> or C<isl_fold_max>.
5049 If C<tight> is not C<NULL>, then C<*tight> is set to C<1>
5050 is the returned bound is known be tight, i.e., for each value
5051 of the parameters there is at least
5052 one element in the domain that reaches the bound.
5053 If the domain of C<pwqp> is not wrapping, then the bound is computed
5054 over all elements in that domain and the result has a purely parametric
5055 domain. If the domain of C<pwqp> is wrapping, then the bound is
5056 computed over the range of the wrapped relation. The domain of the
5057 wrapped relation becomes the domain of the result.
5059 A (piecewise) quasipolynomial reduction can be copied or freed using the
5060 following functions.
5062 __isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_copy(
5063 __isl_keep isl_qpolynomial_fold *fold);
5064 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_copy(
5065 __isl_keep isl_pw_qpolynomial_fold *pwf);
5066 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_copy(
5067 __isl_keep isl_union_pw_qpolynomial_fold *upwf);
5068 void isl_qpolynomial_fold_free(
5069 __isl_take isl_qpolynomial_fold *fold);
5070 void *isl_pw_qpolynomial_fold_free(
5071 __isl_take isl_pw_qpolynomial_fold *pwf);
5072 void *isl_union_pw_qpolynomial_fold_free(
5073 __isl_take isl_union_pw_qpolynomial_fold *upwf);
5075 =head3 Printing Piecewise Quasipolynomial Reductions
5077 Piecewise quasipolynomial reductions can be printed
5078 using the following function.
5080 __isl_give isl_printer *isl_printer_print_pw_qpolynomial_fold(
5081 __isl_take isl_printer *p,
5082 __isl_keep isl_pw_qpolynomial_fold *pwf);
5083 __isl_give isl_printer *isl_printer_print_union_pw_qpolynomial_fold(
5084 __isl_take isl_printer *p,
5085 __isl_keep isl_union_pw_qpolynomial_fold *upwf);
5087 For C<isl_printer_print_pw_qpolynomial_fold>,
5088 output format of the printer
5089 needs to be set to either C<ISL_FORMAT_ISL> or C<ISL_FORMAT_C>.
5090 For C<isl_printer_print_union_pw_qpolynomial_fold>,
5091 output format of the printer
5092 needs to be set to C<ISL_FORMAT_ISL>.
5093 In case of printing in C<ISL_FORMAT_C>, the user may want
5094 to set the names of all dimensions
5096 __isl_give isl_pw_qpolynomial_fold *
5097 isl_pw_qpolynomial_fold_set_dim_name(
5098 __isl_take isl_pw_qpolynomial_fold *pwf,
5099 enum isl_dim_type type, unsigned pos,
5102 =head3 Inspecting (Piecewise) Quasipolynomial Reductions
5104 To iterate over all piecewise quasipolynomial reductions in a union
5105 piecewise quasipolynomial reduction, use the following function
5107 int isl_union_pw_qpolynomial_fold_foreach_pw_qpolynomial_fold(
5108 __isl_keep isl_union_pw_qpolynomial_fold *upwf,
5109 int (*fn)(__isl_take isl_pw_qpolynomial_fold *pwf,
5110 void *user), void *user);
5112 To iterate over the cells in a piecewise quasipolynomial reduction,
5113 use either of the following two functions
5115 int isl_pw_qpolynomial_fold_foreach_piece(
5116 __isl_keep isl_pw_qpolynomial_fold *pwf,
5117 int (*fn)(__isl_take isl_set *set,
5118 __isl_take isl_qpolynomial_fold *fold,
5119 void *user), void *user);
5120 int isl_pw_qpolynomial_fold_foreach_lifted_piece(
5121 __isl_keep isl_pw_qpolynomial_fold *pwf,
5122 int (*fn)(__isl_take isl_set *set,
5123 __isl_take isl_qpolynomial_fold *fold,
5124 void *user), void *user);
5126 See L<Inspecting (Piecewise) Quasipolynomials> for an explanation
5127 of the difference between these two functions.
5129 To iterate over all quasipolynomials in a reduction, use
5131 int isl_qpolynomial_fold_foreach_qpolynomial(
5132 __isl_keep isl_qpolynomial_fold *fold,
5133 int (*fn)(__isl_take isl_qpolynomial *qp,
5134 void *user), void *user);
5136 =head3 Properties of Piecewise Quasipolynomial Reductions
5138 To check whether two union piecewise quasipolynomial reductions are
5139 obviously equal, use
5141 int isl_union_pw_qpolynomial_fold_plain_is_equal(
5142 __isl_keep isl_union_pw_qpolynomial_fold *upwf1,
5143 __isl_keep isl_union_pw_qpolynomial_fold *upwf2);
5145 =head3 Operations on Piecewise Quasipolynomial Reductions
5147 __isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_scale_val(
5148 __isl_take isl_qpolynomial_fold *fold,
5149 __isl_take isl_val *v);
5150 __isl_give isl_pw_qpolynomial_fold *
5151 isl_pw_qpolynomial_fold_scale_val(
5152 __isl_take isl_pw_qpolynomial_fold *pwf,
5153 __isl_take isl_val *v);
5154 __isl_give isl_union_pw_qpolynomial_fold *
5155 isl_union_pw_qpolynomial_fold_scale_val(
5156 __isl_take isl_union_pw_qpolynomial_fold *upwf,
5157 __isl_take isl_val *v);
5159 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_add(
5160 __isl_take isl_pw_qpolynomial_fold *pwf1,
5161 __isl_take isl_pw_qpolynomial_fold *pwf2);
5163 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_fold(
5164 __isl_take isl_pw_qpolynomial_fold *pwf1,
5165 __isl_take isl_pw_qpolynomial_fold *pwf2);
5167 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_fold(
5168 __isl_take isl_union_pw_qpolynomial_fold *upwf1,
5169 __isl_take isl_union_pw_qpolynomial_fold *upwf2);
5171 __isl_give isl_val *isl_pw_qpolynomial_fold_eval(
5172 __isl_take isl_pw_qpolynomial_fold *pwf,
5173 __isl_take isl_point *pnt);
5175 __isl_give isl_val *isl_union_pw_qpolynomial_fold_eval(
5176 __isl_take isl_union_pw_qpolynomial_fold *upwf,
5177 __isl_take isl_point *pnt);
5179 __isl_give isl_pw_qpolynomial_fold *
5180 isl_pw_qpolynomial_fold_intersect_params(
5181 __isl_take isl_pw_qpolynomial_fold *pwf,
5182 __isl_take isl_set *set);
5184 __isl_give isl_union_set *isl_union_pw_qpolynomial_fold_domain(
5185 __isl_take isl_union_pw_qpolynomial_fold *upwf);
5186 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_intersect_domain(
5187 __isl_take isl_union_pw_qpolynomial_fold *upwf,
5188 __isl_take isl_union_set *uset);
5189 __isl_give isl_union_pw_qpolynomial_fold *
5190 isl_union_pw_qpolynomial_fold_intersect_params(
5191 __isl_take isl_union_pw_qpolynomial_fold *upwf,
5192 __isl_take isl_set *set);
5194 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_project_domain_on_params(
5195 __isl_take isl_pw_qpolynomial_fold *pwf);
5197 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_coalesce(
5198 __isl_take isl_pw_qpolynomial_fold *pwf);
5200 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_coalesce(
5201 __isl_take isl_union_pw_qpolynomial_fold *upwf);
5203 __isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_gist_params(
5204 __isl_take isl_qpolynomial_fold *fold,
5205 __isl_take isl_set *context);
5206 __isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_gist(
5207 __isl_take isl_qpolynomial_fold *fold,
5208 __isl_take isl_set *context);
5210 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_gist(
5211 __isl_take isl_pw_qpolynomial_fold *pwf,
5212 __isl_take isl_set *context);
5213 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_gist_params(
5214 __isl_take isl_pw_qpolynomial_fold *pwf,
5215 __isl_take isl_set *context);
5217 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_gist(
5218 __isl_take isl_union_pw_qpolynomial_fold *upwf,
5219 __isl_take isl_union_set *context);
5220 __isl_give isl_union_pw_qpolynomial_fold *
5221 isl_union_pw_qpolynomial_fold_gist_params(
5222 __isl_take isl_union_pw_qpolynomial_fold *upwf,
5223 __isl_take isl_set *context);
5225 The gist operation applies the gist operation to each of
5226 the cells in the domain of the input piecewise quasipolynomial reduction.
5227 In future, the operation will also exploit the context
5228 to simplify the quasipolynomial reductions associated to each cell.
5230 __isl_give isl_pw_qpolynomial_fold *
5231 isl_set_apply_pw_qpolynomial_fold(
5232 __isl_take isl_set *set,
5233 __isl_take isl_pw_qpolynomial_fold *pwf,
5235 __isl_give isl_pw_qpolynomial_fold *
5236 isl_map_apply_pw_qpolynomial_fold(
5237 __isl_take isl_map *map,
5238 __isl_take isl_pw_qpolynomial_fold *pwf,
5240 __isl_give isl_union_pw_qpolynomial_fold *
5241 isl_union_set_apply_union_pw_qpolynomial_fold(
5242 __isl_take isl_union_set *uset,
5243 __isl_take isl_union_pw_qpolynomial_fold *upwf,
5245 __isl_give isl_union_pw_qpolynomial_fold *
5246 isl_union_map_apply_union_pw_qpolynomial_fold(
5247 __isl_take isl_union_map *umap,
5248 __isl_take isl_union_pw_qpolynomial_fold *upwf,
5251 The functions taking a map
5252 compose the given map with the given piecewise quasipolynomial reduction.
5253 That is, compute a bound (of the same type as C<pwf> or C<upwf> itself)
5254 over all elements in the intersection of the range of the map
5255 and the domain of the piecewise quasipolynomial reduction
5256 as a function of an element in the domain of the map.
5257 The functions taking a set compute a bound over all elements in the
5258 intersection of the set and the domain of the
5259 piecewise quasipolynomial reduction.
5261 =head2 Parametric Vertex Enumeration
5263 The parametric vertex enumeration described in this section
5264 is mainly intended to be used internally and by the C<barvinok>
5267 #include <isl/vertices.h>
5268 __isl_give isl_vertices *isl_basic_set_compute_vertices(
5269 __isl_keep isl_basic_set *bset);
5271 The function C<isl_basic_set_compute_vertices> performs the
5272 actual computation of the parametric vertices and the chamber
5273 decomposition and store the result in an C<isl_vertices> object.
5274 This information can be queried by either iterating over all
5275 the vertices or iterating over all the chambers or cells
5276 and then iterating over all vertices that are active on the chamber.
5278 int isl_vertices_foreach_vertex(
5279 __isl_keep isl_vertices *vertices,
5280 int (*fn)(__isl_take isl_vertex *vertex, void *user),
5283 int isl_vertices_foreach_cell(
5284 __isl_keep isl_vertices *vertices,
5285 int (*fn)(__isl_take isl_cell *cell, void *user),
5287 int isl_cell_foreach_vertex(__isl_keep isl_cell *cell,
5288 int (*fn)(__isl_take isl_vertex *vertex, void *user),
5291 Other operations that can be performed on an C<isl_vertices> object are
5294 isl_ctx *isl_vertices_get_ctx(
5295 __isl_keep isl_vertices *vertices);
5296 int isl_vertices_get_n_vertices(
5297 __isl_keep isl_vertices *vertices);
5298 void isl_vertices_free(__isl_take isl_vertices *vertices);
5300 Vertices can be inspected and destroyed using the following functions.
5302 isl_ctx *isl_vertex_get_ctx(__isl_keep isl_vertex *vertex);
5303 int isl_vertex_get_id(__isl_keep isl_vertex *vertex);
5304 __isl_give isl_basic_set *isl_vertex_get_domain(
5305 __isl_keep isl_vertex *vertex);
5306 __isl_give isl_basic_set *isl_vertex_get_expr(
5307 __isl_keep isl_vertex *vertex);
5308 void isl_vertex_free(__isl_take isl_vertex *vertex);
5310 C<isl_vertex_get_expr> returns a singleton parametric set describing
5311 the vertex, while C<isl_vertex_get_domain> returns the activity domain
5313 Note that C<isl_vertex_get_domain> and C<isl_vertex_get_expr> return
5314 B<rational> basic sets, so they should mainly be used for inspection
5315 and should not be mixed with integer sets.
5317 Chambers can be inspected and destroyed using the following functions.
5319 isl_ctx *isl_cell_get_ctx(__isl_keep isl_cell *cell);
5320 __isl_give isl_basic_set *isl_cell_get_domain(
5321 __isl_keep isl_cell *cell);
5322 void isl_cell_free(__isl_take isl_cell *cell);
5324 =head1 Polyhedral Compilation Library
5326 This section collects functionality in C<isl> that has been specifically
5327 designed for use during polyhedral compilation.
5329 =head2 Dependence Analysis
5331 C<isl> contains specialized functionality for performing
5332 array dataflow analysis. That is, given a I<sink> access relation
5333 and a collection of possible I<source> access relations,
5334 C<isl> can compute relations that describe
5335 for each iteration of the sink access, which iteration
5336 of which of the source access relations was the last
5337 to access the same data element before the given iteration
5339 The resulting dependence relations map source iterations
5340 to the corresponding sink iterations.
5341 To compute standard flow dependences, the sink should be
5342 a read, while the sources should be writes.
5343 If any of the source accesses are marked as being I<may>
5344 accesses, then there will be a dependence from the last
5345 I<must> access B<and> from any I<may> access that follows
5346 this last I<must> access.
5347 In particular, if I<all> sources are I<may> accesses,
5348 then memory based dependence analysis is performed.
5349 If, on the other hand, all sources are I<must> accesses,
5350 then value based dependence analysis is performed.
5352 #include <isl/flow.h>
5354 typedef int (*isl_access_level_before)(void *first, void *second);
5356 __isl_give isl_access_info *isl_access_info_alloc(
5357 __isl_take isl_map *sink,
5358 void *sink_user, isl_access_level_before fn,
5360 __isl_give isl_access_info *isl_access_info_add_source(
5361 __isl_take isl_access_info *acc,
5362 __isl_take isl_map *source, int must,
5364 void *isl_access_info_free(__isl_take isl_access_info *acc);
5366 __isl_give isl_flow *isl_access_info_compute_flow(
5367 __isl_take isl_access_info *acc);
5369 int isl_flow_foreach(__isl_keep isl_flow *deps,
5370 int (*fn)(__isl_take isl_map *dep, int must,
5371 void *dep_user, void *user),
5373 __isl_give isl_map *isl_flow_get_no_source(
5374 __isl_keep isl_flow *deps, int must);
5375 void isl_flow_free(__isl_take isl_flow *deps);
5377 The function C<isl_access_info_compute_flow> performs the actual
5378 dependence analysis. The other functions are used to construct
5379 the input for this function or to read off the output.
5381 The input is collected in an C<isl_access_info>, which can
5382 be created through a call to C<isl_access_info_alloc>.
5383 The arguments to this functions are the sink access relation
5384 C<sink>, a token C<sink_user> used to identify the sink
5385 access to the user, a callback function for specifying the
5386 relative order of source and sink accesses, and the number
5387 of source access relations that will be added.
5388 The callback function has type C<int (*)(void *first, void *second)>.
5389 The function is called with two user supplied tokens identifying
5390 either a source or the sink and it should return the shared nesting
5391 level and the relative order of the two accesses.
5392 In particular, let I<n> be the number of loops shared by
5393 the two accesses. If C<first> precedes C<second> textually,
5394 then the function should return I<2 * n + 1>; otherwise,
5395 it should return I<2 * n>.
5396 The sources can be added to the C<isl_access_info> by performing
5397 (at most) C<max_source> calls to C<isl_access_info_add_source>.
5398 C<must> indicates whether the source is a I<must> access
5399 or a I<may> access. Note that a multi-valued access relation
5400 should only be marked I<must> if every iteration in the domain
5401 of the relation accesses I<all> elements in its image.
5402 The C<source_user> token is again used to identify
5403 the source access. The range of the source access relation
5404 C<source> should have the same dimension as the range
5405 of the sink access relation.
5406 The C<isl_access_info_free> function should usually not be
5407 called explicitly, because it is called implicitly by
5408 C<isl_access_info_compute_flow>.
5410 The result of the dependence analysis is collected in an
5411 C<isl_flow>. There may be elements of
5412 the sink access for which no preceding source access could be
5413 found or for which all preceding sources are I<may> accesses.
5414 The relations containing these elements can be obtained through
5415 calls to C<isl_flow_get_no_source>, the first with C<must> set
5416 and the second with C<must> unset.
5417 In the case of standard flow dependence analysis,
5418 with the sink a read and the sources I<must> writes,
5419 the first relation corresponds to the reads from uninitialized
5420 array elements and the second relation is empty.
5421 The actual flow dependences can be extracted using
5422 C<isl_flow_foreach>. This function will call the user-specified
5423 callback function C<fn> for each B<non-empty> dependence between
5424 a source and the sink. The callback function is called
5425 with four arguments, the actual flow dependence relation
5426 mapping source iterations to sink iterations, a boolean that
5427 indicates whether it is a I<must> or I<may> dependence, a token
5428 identifying the source and an additional C<void *> with value
5429 equal to the third argument of the C<isl_flow_foreach> call.
5430 A dependence is marked I<must> if it originates from a I<must>
5431 source and if it is not followed by any I<may> sources.
5433 After finishing with an C<isl_flow>, the user should call
5434 C<isl_flow_free> to free all associated memory.
5436 A higher-level interface to dependence analysis is provided
5437 by the following function.
5439 #include <isl/flow.h>
5441 int isl_union_map_compute_flow(__isl_take isl_union_map *sink,
5442 __isl_take isl_union_map *must_source,
5443 __isl_take isl_union_map *may_source,
5444 __isl_take isl_union_map *schedule,
5445 __isl_give isl_union_map **must_dep,
5446 __isl_give isl_union_map **may_dep,
5447 __isl_give isl_union_map **must_no_source,
5448 __isl_give isl_union_map **may_no_source);
5450 The arrays are identified by the tuple names of the ranges
5451 of the accesses. The iteration domains by the tuple names
5452 of the domains of the accesses and of the schedule.
5453 The relative order of the iteration domains is given by the
5454 schedule. The relations returned through C<must_no_source>
5455 and C<may_no_source> are subsets of C<sink>.
5456 Any of C<must_dep>, C<may_dep>, C<must_no_source>
5457 or C<may_no_source> may be C<NULL>, but a C<NULL> value for
5458 any of the other arguments is treated as an error.
5460 =head3 Interaction with Dependence Analysis
5462 During the dependence analysis, we frequently need to perform
5463 the following operation. Given a relation between sink iterations
5464 and potential source iterations from a particular source domain,
5465 what is the last potential source iteration corresponding to each
5466 sink iteration. It can sometimes be convenient to adjust
5467 the set of potential source iterations before or after each such operation.
5468 The prototypical example is fuzzy array dataflow analysis,
5469 where we need to analyze if, based on data-dependent constraints,
5470 the sink iteration can ever be executed without one or more of
5471 the corresponding potential source iterations being executed.
5472 If so, we can introduce extra parameters and select an unknown
5473 but fixed source iteration from the potential source iterations.
5474 To be able to perform such manipulations, C<isl> provides the following
5477 #include <isl/flow.h>
5479 typedef __isl_give isl_restriction *(*isl_access_restrict)(
5480 __isl_keep isl_map *source_map,
5481 __isl_keep isl_set *sink, void *source_user,
5483 __isl_give isl_access_info *isl_access_info_set_restrict(
5484 __isl_take isl_access_info *acc,
5485 isl_access_restrict fn, void *user);
5487 The function C<isl_access_info_set_restrict> should be called
5488 before calling C<isl_access_info_compute_flow> and registers a callback function
5489 that will be called any time C<isl> is about to compute the last
5490 potential source. The first argument is the (reverse) proto-dependence,
5491 mapping sink iterations to potential source iterations.
5492 The second argument represents the sink iterations for which
5493 we want to compute the last source iteration.
5494 The third argument is the token corresponding to the source
5495 and the final argument is the token passed to C<isl_access_info_set_restrict>.
5496 The callback is expected to return a restriction on either the input or
5497 the output of the operation computing the last potential source.
5498 If the input needs to be restricted then restrictions are needed
5499 for both the source and the sink iterations. The sink iterations
5500 and the potential source iterations will be intersected with these sets.
5501 If the output needs to be restricted then only a restriction on the source
5502 iterations is required.
5503 If any error occurs, the callback should return C<NULL>.
5504 An C<isl_restriction> object can be created, freed and inspected
5505 using the following functions.
5507 #include <isl/flow.h>
5509 __isl_give isl_restriction *isl_restriction_input(
5510 __isl_take isl_set *source_restr,
5511 __isl_take isl_set *sink_restr);
5512 __isl_give isl_restriction *isl_restriction_output(
5513 __isl_take isl_set *source_restr);
5514 __isl_give isl_restriction *isl_restriction_none(
5515 __isl_take isl_map *source_map);
5516 __isl_give isl_restriction *isl_restriction_empty(
5517 __isl_take isl_map *source_map);
5518 void *isl_restriction_free(
5519 __isl_take isl_restriction *restr);
5520 isl_ctx *isl_restriction_get_ctx(
5521 __isl_keep isl_restriction *restr);
5523 C<isl_restriction_none> and C<isl_restriction_empty> are special
5524 cases of C<isl_restriction_input>. C<isl_restriction_none>
5525 is essentially equivalent to
5527 isl_restriction_input(isl_set_universe(
5528 isl_space_range(isl_map_get_space(source_map))),
5530 isl_space_domain(isl_map_get_space(source_map))));
5532 whereas C<isl_restriction_empty> is essentially equivalent to
5534 isl_restriction_input(isl_set_empty(
5535 isl_space_range(isl_map_get_space(source_map))),
5537 isl_space_domain(isl_map_get_space(source_map))));
5541 B<The functionality described in this section is fairly new
5542 and may be subject to change.>
5544 The following function can be used to compute a schedule
5545 for a union of domains.
5546 By default, the algorithm used to construct the schedule is similar
5547 to that of C<Pluto>.
5548 Alternatively, Feautrier's multi-dimensional scheduling algorithm can
5550 The generated schedule respects all C<validity> dependences.
5551 That is, all dependence distances over these dependences in the
5552 scheduled space are lexicographically positive.
5553 The default algorithm tries to minimize the dependence distances over
5554 C<proximity> dependences.
5555 Moreover, it tries to obtain sequences (bands) of schedule dimensions
5556 for groups of domains where the dependence distances have only
5557 non-negative values.
5558 When using Feautrier's algorithm, the C<proximity> dependence
5559 distances are only minimized during the extension to a
5560 full-dimensional schedule.
5562 #include <isl/schedule.h>
5563 __isl_give isl_schedule *isl_union_set_compute_schedule(
5564 __isl_take isl_union_set *domain,
5565 __isl_take isl_union_map *validity,
5566 __isl_take isl_union_map *proximity);
5567 void *isl_schedule_free(__isl_take isl_schedule *sched);
5569 A mapping from the domains to the scheduled space can be obtained
5570 from an C<isl_schedule> using the following function.
5572 __isl_give isl_union_map *isl_schedule_get_map(
5573 __isl_keep isl_schedule *sched);
5575 A representation of the schedule can be printed using
5577 __isl_give isl_printer *isl_printer_print_schedule(
5578 __isl_take isl_printer *p,
5579 __isl_keep isl_schedule *schedule);
5581 A representation of the schedule as a forest of bands can be obtained
5582 using the following function.
5584 __isl_give isl_band_list *isl_schedule_get_band_forest(
5585 __isl_keep isl_schedule *schedule);
5587 The individual bands can be visited in depth-first post-order
5588 using the following function.
5590 #include <isl/schedule.h>
5591 int isl_schedule_foreach_band(
5592 __isl_keep isl_schedule *sched,
5593 int (*fn)(__isl_keep isl_band *band, void *user),
5596 The list can be manipulated as explained in L<"Lists">.
5597 The bands inside the list can be copied and freed using the following
5600 #include <isl/band.h>
5601 __isl_give isl_band *isl_band_copy(
5602 __isl_keep isl_band *band);
5603 void *isl_band_free(__isl_take isl_band *band);
5605 Each band contains zero or more scheduling dimensions.
5606 These are referred to as the members of the band.
5607 The section of the schedule that corresponds to the band is
5608 referred to as the partial schedule of the band.
5609 For those nodes that participate in a band, the outer scheduling
5610 dimensions form the prefix schedule, while the inner scheduling
5611 dimensions form the suffix schedule.
5612 That is, if we take a cut of the band forest, then the union of
5613 the concatenations of the prefix, partial and suffix schedules of
5614 each band in the cut is equal to the entire schedule (modulo
5615 some possible padding at the end with zero scheduling dimensions).
5616 The properties of a band can be inspected using the following functions.
5618 #include <isl/band.h>
5619 isl_ctx *isl_band_get_ctx(__isl_keep isl_band *band);
5621 int isl_band_has_children(__isl_keep isl_band *band);
5622 __isl_give isl_band_list *isl_band_get_children(
5623 __isl_keep isl_band *band);
5625 __isl_give isl_union_map *isl_band_get_prefix_schedule(
5626 __isl_keep isl_band *band);
5627 __isl_give isl_union_map *isl_band_get_partial_schedule(
5628 __isl_keep isl_band *band);
5629 __isl_give isl_union_map *isl_band_get_suffix_schedule(
5630 __isl_keep isl_band *band);
5632 int isl_band_n_member(__isl_keep isl_band *band);
5633 int isl_band_member_is_zero_distance(
5634 __isl_keep isl_band *band, int pos);
5636 int isl_band_list_foreach_band(
5637 __isl_keep isl_band_list *list,
5638 int (*fn)(__isl_keep isl_band *band, void *user),
5641 Note that a scheduling dimension is considered to be ``zero
5642 distance'' if it does not carry any proximity dependences
5644 That is, if the dependence distances of the proximity
5645 dependences are all zero in that direction (for fixed
5646 iterations of outer bands).
5647 Like C<isl_schedule_foreach_band>,
5648 the function C<isl_band_list_foreach_band> calls C<fn> on the bands
5649 in depth-first post-order.
5651 A band can be tiled using the following function.
5653 #include <isl/band.h>
5654 int isl_band_tile(__isl_keep isl_band *band,
5655 __isl_take isl_vec *sizes);
5657 int isl_options_set_tile_scale_tile_loops(isl_ctx *ctx,
5659 int isl_options_get_tile_scale_tile_loops(isl_ctx *ctx);
5660 int isl_options_set_tile_shift_point_loops(isl_ctx *ctx,
5662 int isl_options_get_tile_shift_point_loops(isl_ctx *ctx);
5664 The C<isl_band_tile> function tiles the band using the given tile sizes
5665 inside its schedule.
5666 A new child band is created to represent the point loops and it is
5667 inserted between the modified band and its children.
5668 The C<tile_scale_tile_loops> option specifies whether the tile
5669 loops iterators should be scaled by the tile sizes.
5670 If the C<tile_shift_point_loops> option is set, then the point loops
5671 are shifted to start at zero.
5673 A band can be split into two nested bands using the following function.
5675 int isl_band_split(__isl_keep isl_band *band, int pos);
5677 The resulting outer band contains the first C<pos> dimensions of C<band>
5678 while the inner band contains the remaining dimensions.
5680 A representation of the band can be printed using
5682 #include <isl/band.h>
5683 __isl_give isl_printer *isl_printer_print_band(
5684 __isl_take isl_printer *p,
5685 __isl_keep isl_band *band);
5689 #include <isl/schedule.h>
5690 int isl_options_set_schedule_max_coefficient(
5691 isl_ctx *ctx, int val);
5692 int isl_options_get_schedule_max_coefficient(
5694 int isl_options_set_schedule_max_constant_term(
5695 isl_ctx *ctx, int val);
5696 int isl_options_get_schedule_max_constant_term(
5698 int isl_options_set_schedule_fuse(isl_ctx *ctx, int val);
5699 int isl_options_get_schedule_fuse(isl_ctx *ctx);
5700 int isl_options_set_schedule_maximize_band_depth(
5701 isl_ctx *ctx, int val);
5702 int isl_options_get_schedule_maximize_band_depth(
5704 int isl_options_set_schedule_outer_zero_distance(
5705 isl_ctx *ctx, int val);
5706 int isl_options_get_schedule_outer_zero_distance(
5708 int isl_options_set_schedule_split_scaled(
5709 isl_ctx *ctx, int val);
5710 int isl_options_get_schedule_split_scaled(
5712 int isl_options_set_schedule_algorithm(
5713 isl_ctx *ctx, int val);
5714 int isl_options_get_schedule_algorithm(
5716 int isl_options_set_schedule_separate_components(
5717 isl_ctx *ctx, int val);
5718 int isl_options_get_schedule_separate_components(
5723 =item * schedule_max_coefficient
5725 This option enforces that the coefficients for variable and parameter
5726 dimensions in the calculated schedule are not larger than the specified value.
5727 This option can significantly increase the speed of the scheduling calculation
5728 and may also prevent fusing of unrelated dimensions. A value of -1 means that
5729 this option does not introduce bounds on the variable or parameter
5732 =item * schedule_max_constant_term
5734 This option enforces that the constant coefficients in the calculated schedule
5735 are not larger than the maximal constant term. This option can significantly
5736 increase the speed of the scheduling calculation and may also prevent fusing of
5737 unrelated dimensions. A value of -1 means that this option does not introduce
5738 bounds on the constant coefficients.
5740 =item * schedule_fuse
5742 This option controls the level of fusion.
5743 If this option is set to C<ISL_SCHEDULE_FUSE_MIN>, then loops in the
5744 resulting schedule will be distributed as much as possible.
5745 If this option is set to C<ISL_SCHEDULE_FUSE_MAX>, then C<isl> will
5746 try to fuse loops in the resulting schedule.
5748 =item * schedule_maximize_band_depth
5750 If this option is set, we do not split bands at the point
5751 where we detect splitting is necessary. Instead, we
5752 backtrack and split bands as early as possible. This
5753 reduces the number of splits and maximizes the width of
5754 the bands. Wider bands give more possibilities for tiling.
5755 Note that if the C<schedule_fuse> option is set to C<ISL_SCHEDULE_FUSE_MIN>,
5756 then bands will be split as early as possible, even if there is no need.
5757 The C<schedule_maximize_band_depth> option therefore has no effect in this case.
5759 =item * schedule_outer_zero_distance
5761 If this option is set, then we try to construct schedules
5762 where the outermost scheduling dimension in each band
5763 results in a zero dependence distance over the proximity
5766 =item * schedule_split_scaled
5768 If this option is set, then we try to construct schedules in which the
5769 constant term is split off from the linear part if the linear parts of
5770 the scheduling rows for all nodes in the graphs have a common non-trivial
5772 The constant term is then placed in a separate band and the linear
5775 =item * schedule_algorithm
5777 Selects the scheduling algorithm to be used.
5778 Available scheduling algorithms are C<ISL_SCHEDULE_ALGORITHM_ISL>
5779 and C<ISL_SCHEDULE_ALGORITHM_FEAUTRIER>.
5781 =item * schedule_separate_components
5783 If at any point the dependence graph contains any (weakly connected) components,
5784 then these components are scheduled separately.
5785 If this option is not set, then some iterations of the domains
5786 in these components may be scheduled together.
5787 If this option is set, then the components are given consecutive
5792 =head2 AST Generation
5794 This section describes the C<isl> functionality for generating
5795 ASTs that visit all the elements
5796 in a domain in an order specified by a schedule.
5797 In particular, given a C<isl_union_map>, an AST is generated
5798 that visits all the elements in the domain of the C<isl_union_map>
5799 according to the lexicographic order of the corresponding image
5800 element(s). If the range of the C<isl_union_map> consists of
5801 elements in more than one space, then each of these spaces is handled
5802 separately in an arbitrary order.
5803 It should be noted that the image elements only specify the I<order>
5804 in which the corresponding domain elements should be visited.
5805 No direct relation between the image elements and the loop iterators
5806 in the generated AST should be assumed.
5808 Each AST is generated within a build. The initial build
5809 simply specifies the constraints on the parameters (if any)
5810 and can be created, inspected, copied and freed using the following functions.
5812 #include <isl/ast_build.h>
5813 __isl_give isl_ast_build *isl_ast_build_from_context(
5814 __isl_take isl_set *set);
5815 isl_ctx *isl_ast_build_get_ctx(
5816 __isl_keep isl_ast_build *build);
5817 __isl_give isl_ast_build *isl_ast_build_copy(
5818 __isl_keep isl_ast_build *build);
5819 void *isl_ast_build_free(
5820 __isl_take isl_ast_build *build);
5822 The C<set> argument is usually a parameter set with zero or more parameters.
5823 More C<isl_ast_build> functions are described in L</"Nested AST Generation">
5824 and L</"Fine-grained Control over AST Generation">.
5825 Finally, the AST itself can be constructed using the following
5828 #include <isl/ast_build.h>
5829 __isl_give isl_ast_node *isl_ast_build_ast_from_schedule(
5830 __isl_keep isl_ast_build *build,
5831 __isl_take isl_union_map *schedule);
5833 =head3 Inspecting the AST
5835 The basic properties of an AST node can be obtained as follows.
5837 #include <isl/ast.h>
5838 isl_ctx *isl_ast_node_get_ctx(
5839 __isl_keep isl_ast_node *node);
5840 enum isl_ast_node_type isl_ast_node_get_type(
5841 __isl_keep isl_ast_node *node);
5843 The type of an AST node is one of
5844 C<isl_ast_node_for>,
5846 C<isl_ast_node_block> or
5847 C<isl_ast_node_user>.
5848 An C<isl_ast_node_for> represents a for node.
5849 An C<isl_ast_node_if> represents an if node.
5850 An C<isl_ast_node_block> represents a compound node.
5851 An C<isl_ast_node_user> represents an expression statement.
5852 An expression statement typically corresponds to a domain element, i.e.,
5853 one of the elements that is visited by the AST.
5855 Each type of node has its own additional properties.
5857 #include <isl/ast.h>
5858 __isl_give isl_ast_expr *isl_ast_node_for_get_iterator(
5859 __isl_keep isl_ast_node *node);
5860 __isl_give isl_ast_expr *isl_ast_node_for_get_init(
5861 __isl_keep isl_ast_node *node);
5862 __isl_give isl_ast_expr *isl_ast_node_for_get_cond(
5863 __isl_keep isl_ast_node *node);
5864 __isl_give isl_ast_expr *isl_ast_node_for_get_inc(
5865 __isl_keep isl_ast_node *node);
5866 __isl_give isl_ast_node *isl_ast_node_for_get_body(
5867 __isl_keep isl_ast_node *node);
5868 int isl_ast_node_for_is_degenerate(
5869 __isl_keep isl_ast_node *node);
5871 An C<isl_ast_for> is considered degenerate if it is known to execute
5874 #include <isl/ast.h>
5875 __isl_give isl_ast_expr *isl_ast_node_if_get_cond(
5876 __isl_keep isl_ast_node *node);
5877 __isl_give isl_ast_node *isl_ast_node_if_get_then(
5878 __isl_keep isl_ast_node *node);
5879 int isl_ast_node_if_has_else(
5880 __isl_keep isl_ast_node *node);
5881 __isl_give isl_ast_node *isl_ast_node_if_get_else(
5882 __isl_keep isl_ast_node *node);
5884 __isl_give isl_ast_node_list *
5885 isl_ast_node_block_get_children(
5886 __isl_keep isl_ast_node *node);
5888 __isl_give isl_ast_expr *isl_ast_node_user_get_expr(
5889 __isl_keep isl_ast_node *node);
5891 Each of the returned C<isl_ast_expr>s can in turn be inspected using
5892 the following functions.
5894 #include <isl/ast.h>
5895 isl_ctx *isl_ast_expr_get_ctx(
5896 __isl_keep isl_ast_expr *expr);
5897 enum isl_ast_expr_type isl_ast_expr_get_type(
5898 __isl_keep isl_ast_expr *expr);
5900 The type of an AST expression is one of
5902 C<isl_ast_expr_id> or
5903 C<isl_ast_expr_int>.
5904 An C<isl_ast_expr_op> represents the result of an operation.
5905 An C<isl_ast_expr_id> represents an identifier.
5906 An C<isl_ast_expr_int> represents an integer value.
5908 Each type of expression has its own additional properties.
5910 #include <isl/ast.h>
5911 enum isl_ast_op_type isl_ast_expr_get_op_type(
5912 __isl_keep isl_ast_expr *expr);
5913 int isl_ast_expr_get_op_n_arg(__isl_keep isl_ast_expr *expr);
5914 __isl_give isl_ast_expr *isl_ast_expr_get_op_arg(
5915 __isl_keep isl_ast_expr *expr, int pos);
5916 int isl_ast_node_foreach_ast_op_type(
5917 __isl_keep isl_ast_node *node,
5918 int (*fn)(enum isl_ast_op_type type, void *user),
5921 C<isl_ast_expr_get_op_type> returns the type of the operation
5922 performed. C<isl_ast_expr_get_op_n_arg> returns the number of
5923 arguments. C<isl_ast_expr_get_op_arg> returns the specified
5925 C<isl_ast_node_foreach_ast_op_type> calls C<fn> for each distinct
5926 C<isl_ast_op_type> that appears in C<node>.
5927 The operation type is one of the following.
5931 =item C<isl_ast_op_and>
5933 Logical I<and> of two arguments.
5934 Both arguments can be evaluated.
5936 =item C<isl_ast_op_and_then>
5938 Logical I<and> of two arguments.
5939 The second argument can only be evaluated if the first evaluates to true.
5941 =item C<isl_ast_op_or>
5943 Logical I<or> of two arguments.
5944 Both arguments can be evaluated.
5946 =item C<isl_ast_op_or_else>
5948 Logical I<or> of two arguments.
5949 The second argument can only be evaluated if the first evaluates to false.
5951 =item C<isl_ast_op_max>
5953 Maximum of two or more arguments.
5955 =item C<isl_ast_op_min>
5957 Minimum of two or more arguments.
5959 =item C<isl_ast_op_minus>
5963 =item C<isl_ast_op_add>
5965 Sum of two arguments.
5967 =item C<isl_ast_op_sub>
5969 Difference of two arguments.
5971 =item C<isl_ast_op_mul>
5973 Product of two arguments.
5975 =item C<isl_ast_op_div>
5977 Exact division. That is, the result is known to be an integer.
5979 =item C<isl_ast_op_fdiv_q>
5981 Result of integer division, rounded towards negative
5984 =item C<isl_ast_op_pdiv_q>
5986 Result of integer division, where dividend is known to be non-negative.
5988 =item C<isl_ast_op_pdiv_r>
5990 Remainder of integer division, where dividend is known to be non-negative.
5992 =item C<isl_ast_op_cond>
5994 Conditional operator defined on three arguments.
5995 If the first argument evaluates to true, then the result
5996 is equal to the second argument. Otherwise, the result
5997 is equal to the third argument.
5998 The second and third argument may only be evaluated if
5999 the first argument evaluates to true and false, respectively.
6000 Corresponds to C<a ? b : c> in C.
6002 =item C<isl_ast_op_select>
6004 Conditional operator defined on three arguments.
6005 If the first argument evaluates to true, then the result
6006 is equal to the second argument. Otherwise, the result
6007 is equal to the third argument.
6008 The second and third argument may be evaluated independently
6009 of the value of the first argument.
6010 Corresponds to C<a * b + (1 - a) * c> in C.
6012 =item C<isl_ast_op_eq>
6016 =item C<isl_ast_op_le>
6018 Less than or equal relation.
6020 =item C<isl_ast_op_lt>
6024 =item C<isl_ast_op_ge>
6026 Greater than or equal relation.
6028 =item C<isl_ast_op_gt>
6030 Greater than relation.
6032 =item C<isl_ast_op_call>
6035 The number of arguments of the C<isl_ast_expr> is one more than
6036 the number of arguments in the function call, the first argument
6037 representing the function being called.
6039 =item C<isl_ast_op_access>
6042 The number of arguments of the C<isl_ast_expr> is one more than
6043 the number of index expressions in the array access, the first argument
6044 representing the array being accessed.
6048 #include <isl/ast.h>
6049 __isl_give isl_id *isl_ast_expr_get_id(
6050 __isl_keep isl_ast_expr *expr);
6052 Return the identifier represented by the AST expression.
6054 #include <isl/ast.h>
6055 __isl_give isl_val *isl_ast_expr_get_val(
6056 __isl_keep isl_ast_expr *expr);
6058 Return the integer represented by the AST expression.
6060 =head3 Properties of ASTs
6062 #include <isl/ast.h>
6063 int isl_ast_expr_is_equal(__isl_keep isl_ast_expr *expr1,
6064 __isl_keep isl_ast_expr *expr2);
6066 Check if two C<isl_ast_expr>s are equal to each other.
6068 =head3 Manipulating and printing the AST
6070 AST nodes can be copied and freed using the following functions.
6072 #include <isl/ast.h>
6073 __isl_give isl_ast_node *isl_ast_node_copy(
6074 __isl_keep isl_ast_node *node);
6075 void *isl_ast_node_free(__isl_take isl_ast_node *node);
6077 AST expressions can be copied and freed using the following functions.
6079 #include <isl/ast.h>
6080 __isl_give isl_ast_expr *isl_ast_expr_copy(
6081 __isl_keep isl_ast_expr *expr);
6082 void *isl_ast_expr_free(__isl_take isl_ast_expr *expr);
6084 New AST expressions can be created either directly or within
6085 the context of an C<isl_ast_build>.
6087 #include <isl/ast.h>
6088 __isl_give isl_ast_expr *isl_ast_expr_from_val(
6089 __isl_take isl_val *v);
6090 __isl_give isl_ast_expr *isl_ast_expr_from_id(
6091 __isl_take isl_id *id);
6092 __isl_give isl_ast_expr *isl_ast_expr_neg(
6093 __isl_take isl_ast_expr *expr);
6094 __isl_give isl_ast_expr *isl_ast_expr_add(
6095 __isl_take isl_ast_expr *expr1,
6096 __isl_take isl_ast_expr *expr2);
6097 __isl_give isl_ast_expr *isl_ast_expr_sub(
6098 __isl_take isl_ast_expr *expr1,
6099 __isl_take isl_ast_expr *expr2);
6100 __isl_give isl_ast_expr *isl_ast_expr_mul(
6101 __isl_take isl_ast_expr *expr1,
6102 __isl_take isl_ast_expr *expr2);
6103 __isl_give isl_ast_expr *isl_ast_expr_div(
6104 __isl_take isl_ast_expr *expr1,
6105 __isl_take isl_ast_expr *expr2);
6106 __isl_give isl_ast_expr *isl_ast_expr_and(
6107 __isl_take isl_ast_expr *expr1,
6108 __isl_take isl_ast_expr *expr2)
6109 __isl_give isl_ast_expr *isl_ast_expr_or(
6110 __isl_take isl_ast_expr *expr1,
6111 __isl_take isl_ast_expr *expr2)
6113 #include <isl/ast_build.h>
6114 __isl_give isl_ast_expr *isl_ast_build_expr_from_pw_aff(
6115 __isl_keep isl_ast_build *build,
6116 __isl_take isl_pw_aff *pa);
6117 __isl_give isl_ast_expr *
6118 isl_ast_build_access_from_pw_multi_aff(
6119 __isl_keep isl_ast_build *build,
6120 __isl_take isl_pw_multi_aff *pma);
6121 __isl_give isl_ast_expr *
6122 isl_ast_build_access_from_multi_pw_aff(
6123 __isl_keep isl_ast_build *build,
6124 __isl_take isl_multi_pw_aff *mpa);
6125 __isl_give isl_ast_expr *
6126 isl_ast_build_call_from_pw_multi_aff(
6127 __isl_keep isl_ast_build *build,
6128 __isl_take isl_pw_multi_aff *pma);
6129 __isl_give isl_ast_expr *
6130 isl_ast_build_call_from_multi_pw_aff(
6131 __isl_keep isl_ast_build *build,
6132 __isl_take isl_multi_pw_aff *mpa);
6134 The domains of C<pa>, C<mpa> and C<pma> should correspond
6135 to the schedule space of C<build>.
6136 The tuple id of C<mpa> or C<pma> is used as the array being accessed or
6137 the function being called.
6139 User specified data can be attached to an C<isl_ast_node> and obtained
6140 from the same C<isl_ast_node> using the following functions.
6142 #include <isl/ast.h>
6143 __isl_give isl_ast_node *isl_ast_node_set_annotation(
6144 __isl_take isl_ast_node *node,
6145 __isl_take isl_id *annotation);
6146 __isl_give isl_id *isl_ast_node_get_annotation(
6147 __isl_keep isl_ast_node *node);
6149 Basic printing can be performed using the following functions.
6151 #include <isl/ast.h>
6152 __isl_give isl_printer *isl_printer_print_ast_expr(
6153 __isl_take isl_printer *p,
6154 __isl_keep isl_ast_expr *expr);
6155 __isl_give isl_printer *isl_printer_print_ast_node(
6156 __isl_take isl_printer *p,
6157 __isl_keep isl_ast_node *node);
6159 More advanced printing can be performed using the following functions.
6161 #include <isl/ast.h>
6162 __isl_give isl_printer *isl_ast_op_type_print_macro(
6163 enum isl_ast_op_type type,
6164 __isl_take isl_printer *p);
6165 __isl_give isl_printer *isl_ast_node_print_macros(
6166 __isl_keep isl_ast_node *node,
6167 __isl_take isl_printer *p);
6168 __isl_give isl_printer *isl_ast_node_print(
6169 __isl_keep isl_ast_node *node,
6170 __isl_take isl_printer *p,
6171 __isl_take isl_ast_print_options *options);
6172 __isl_give isl_printer *isl_ast_node_for_print(
6173 __isl_keep isl_ast_node *node,
6174 __isl_take isl_printer *p,
6175 __isl_take isl_ast_print_options *options);
6176 __isl_give isl_printer *isl_ast_node_if_print(
6177 __isl_keep isl_ast_node *node,
6178 __isl_take isl_printer *p,
6179 __isl_take isl_ast_print_options *options);
6181 While printing an C<isl_ast_node> in C<ISL_FORMAT_C>,
6182 C<isl> may print out an AST that makes use of macros such
6183 as C<floord>, C<min> and C<max>.
6184 C<isl_ast_op_type_print_macro> prints out the macro
6185 corresponding to a specific C<isl_ast_op_type>.
6186 C<isl_ast_node_print_macros> scans the C<isl_ast_node>
6187 for expressions where these macros would be used and prints
6188 out the required macro definitions.
6189 Essentially, C<isl_ast_node_print_macros> calls
6190 C<isl_ast_node_foreach_ast_op_type> with C<isl_ast_op_type_print_macro>
6191 as function argument.
6192 C<isl_ast_node_print>, C<isl_ast_node_for_print> and
6193 C<isl_ast_node_if_print> print an C<isl_ast_node>
6194 in C<ISL_FORMAT_C>, but allow for some extra control
6195 through an C<isl_ast_print_options> object.
6196 This object can be created using the following functions.
6198 #include <isl/ast.h>
6199 __isl_give isl_ast_print_options *
6200 isl_ast_print_options_alloc(isl_ctx *ctx);
6201 __isl_give isl_ast_print_options *
6202 isl_ast_print_options_copy(
6203 __isl_keep isl_ast_print_options *options);
6204 void *isl_ast_print_options_free(
6205 __isl_take isl_ast_print_options *options);
6207 __isl_give isl_ast_print_options *
6208 isl_ast_print_options_set_print_user(
6209 __isl_take isl_ast_print_options *options,
6210 __isl_give isl_printer *(*print_user)(
6211 __isl_take isl_printer *p,
6212 __isl_take isl_ast_print_options *options,
6213 __isl_keep isl_ast_node *node, void *user),
6215 __isl_give isl_ast_print_options *
6216 isl_ast_print_options_set_print_for(
6217 __isl_take isl_ast_print_options *options,
6218 __isl_give isl_printer *(*print_for)(
6219 __isl_take isl_printer *p,
6220 __isl_take isl_ast_print_options *options,
6221 __isl_keep isl_ast_node *node, void *user),
6224 The callback set by C<isl_ast_print_options_set_print_user>
6225 is called whenever a node of type C<isl_ast_node_user> needs to
6227 The callback set by C<isl_ast_print_options_set_print_for>
6228 is called whenever a node of type C<isl_ast_node_for> needs to
6230 Note that C<isl_ast_node_for_print> will I<not> call the
6231 callback set by C<isl_ast_print_options_set_print_for> on the node
6232 on which C<isl_ast_node_for_print> is called, but only on nested
6233 nodes of type C<isl_ast_node_for>. It is therefore safe to
6234 call C<isl_ast_node_for_print> from within the callback set by
6235 C<isl_ast_print_options_set_print_for>.
6237 The following option determines the type to be used for iterators
6238 while printing the AST.
6240 int isl_options_set_ast_iterator_type(
6241 isl_ctx *ctx, const char *val);
6242 const char *isl_options_get_ast_iterator_type(
6247 #include <isl/ast_build.h>
6248 int isl_options_set_ast_build_atomic_upper_bound(
6249 isl_ctx *ctx, int val);
6250 int isl_options_get_ast_build_atomic_upper_bound(
6252 int isl_options_set_ast_build_prefer_pdiv(isl_ctx *ctx,
6254 int isl_options_get_ast_build_prefer_pdiv(isl_ctx *ctx);
6255 int isl_options_set_ast_build_exploit_nested_bounds(
6256 isl_ctx *ctx, int val);
6257 int isl_options_get_ast_build_exploit_nested_bounds(
6259 int isl_options_set_ast_build_group_coscheduled(
6260 isl_ctx *ctx, int val);
6261 int isl_options_get_ast_build_group_coscheduled(
6263 int isl_options_set_ast_build_scale_strides(
6264 isl_ctx *ctx, int val);
6265 int isl_options_get_ast_build_scale_strides(
6267 int isl_options_set_ast_build_allow_else(isl_ctx *ctx,
6269 int isl_options_get_ast_build_allow_else(isl_ctx *ctx);
6270 int isl_options_set_ast_build_allow_or(isl_ctx *ctx,
6272 int isl_options_get_ast_build_allow_or(isl_ctx *ctx);
6276 =item * ast_build_atomic_upper_bound
6278 Generate loop upper bounds that consist of the current loop iterator,
6279 an operator and an expression not involving the iterator.
6280 If this option is not set, then the current loop iterator may appear
6281 several times in the upper bound.
6282 For example, when this option is turned off, AST generation
6285 [n] -> { A[i] -> [i] : 0 <= i <= 100, n }
6289 for (int c0 = 0; c0 <= 100 && n >= c0; c0 += 1)
6292 When the option is turned on, the following AST is generated
6294 for (int c0 = 0; c0 <= min(100, n); c0 += 1)
6297 =item * ast_build_prefer_pdiv
6299 If this option is turned off, then the AST generation will
6300 produce ASTs that may only contain C<isl_ast_op_fdiv_q>
6301 operators, but no C<isl_ast_op_pdiv_q> or
6302 C<isl_ast_op_pdiv_r> operators.
6303 If this options is turned on, then C<isl> will try to convert
6304 some of the C<isl_ast_op_fdiv_q> operators to (expressions containing)
6305 C<isl_ast_op_pdiv_q> or C<isl_ast_op_pdiv_r> operators.
6307 =item * ast_build_exploit_nested_bounds
6309 Simplify conditions based on bounds of nested for loops.
6310 In particular, remove conditions that are implied by the fact
6311 that one or more nested loops have at least one iteration,
6312 meaning that the upper bound is at least as large as the lower bound.
6313 For example, when this option is turned off, AST generation
6316 [N,M] -> { A[i,j] -> [i,j] : 0 <= i <= N and
6322 for (int c0 = 0; c0 <= N; c0 += 1)
6323 for (int c1 = 0; c1 <= M; c1 += 1)
6326 When the option is turned on, the following AST is generated
6328 for (int c0 = 0; c0 <= N; c0 += 1)
6329 for (int c1 = 0; c1 <= M; c1 += 1)
6332 =item * ast_build_group_coscheduled
6334 If two domain elements are assigned the same schedule point, then
6335 they may be executed in any order and they may even appear in different
6336 loops. If this options is set, then the AST generator will make
6337 sure that coscheduled domain elements do not appear in separate parts
6338 of the AST. This is useful in case of nested AST generation
6339 if the outer AST generation is given only part of a schedule
6340 and the inner AST generation should handle the domains that are
6341 coscheduled by this initial part of the schedule together.
6342 For example if an AST is generated for a schedule
6344 { A[i] -> [0]; B[i] -> [0] }
6346 then the C<isl_ast_build_set_create_leaf> callback described
6347 below may get called twice, once for each domain.
6348 Setting this option ensures that the callback is only called once
6349 on both domains together.
6351 =item * ast_build_separation_bounds
6353 This option specifies which bounds to use during separation.
6354 If this option is set to C<ISL_AST_BUILD_SEPARATION_BOUNDS_IMPLICIT>
6355 then all (possibly implicit) bounds on the current dimension will
6356 be used during separation.
6357 If this option is set to C<ISL_AST_BUILD_SEPARATION_BOUNDS_EXPLICIT>
6358 then only those bounds that are explicitly available will
6359 be used during separation.
6361 =item * ast_build_scale_strides
6363 This option specifies whether the AST generator is allowed
6364 to scale down iterators of strided loops.
6366 =item * ast_build_allow_else
6368 This option specifies whether the AST generator is allowed
6369 to construct if statements with else branches.
6371 =item * ast_build_allow_or
6373 This option specifies whether the AST generator is allowed
6374 to construct if conditions with disjunctions.
6378 =head3 Fine-grained Control over AST Generation
6380 Besides specifying the constraints on the parameters,
6381 an C<isl_ast_build> object can be used to control
6382 various aspects of the AST generation process.
6383 The most prominent way of control is through ``options'',
6384 which can be set using the following function.
6386 #include <isl/ast_build.h>
6387 __isl_give isl_ast_build *
6388 isl_ast_build_set_options(
6389 __isl_take isl_ast_build *control,
6390 __isl_take isl_union_map *options);
6392 The options are encoded in an <isl_union_map>.
6393 The domain of this union relation refers to the schedule domain,
6394 i.e., the range of the schedule passed to C<isl_ast_build_ast_from_schedule>.
6395 In the case of nested AST generation (see L</"Nested AST Generation">),
6396 the domain of C<options> should refer to the extra piece of the schedule.
6397 That is, it should be equal to the range of the wrapped relation in the
6398 range of the schedule.
6399 The range of the options can consist of elements in one or more spaces,
6400 the names of which determine the effect of the option.
6401 The values of the range typically also refer to the schedule dimension
6402 to which the option applies. In case of nested AST generation
6403 (see L</"Nested AST Generation">), these values refer to the position
6404 of the schedule dimension within the innermost AST generation.
6405 The constraints on the domain elements of
6406 the option should only refer to this dimension and earlier dimensions.
6407 We consider the following spaces.
6411 =item C<separation_class>
6413 This space is a wrapped relation between two one dimensional spaces.
6414 The input space represents the schedule dimension to which the option
6415 applies and the output space represents the separation class.
6416 While constructing a loop corresponding to the specified schedule
6417 dimension(s), the AST generator will try to generate separate loops
6418 for domain elements that are assigned different classes.
6419 If only some of the elements are assigned a class, then those elements
6420 that are not assigned any class will be treated as belonging to a class
6421 that is separate from the explicitly assigned classes.
6422 The typical use case for this option is to separate full tiles from
6424 The other options, described below, are applied after the separation
6427 As an example, consider the separation into full and partial tiles
6428 of a tiling of a triangular domain.
6429 Take, for example, the domain
6431 { A[i,j] : 0 <= i,j and i + j <= 100 }
6433 and a tiling into tiles of 10 by 10. The input to the AST generator
6434 is then the schedule
6436 { A[i,j] -> [([i/10]),[j/10],i,j] : 0 <= i,j and
6439 Without any options, the following AST is generated
6441 for (int c0 = 0; c0 <= 10; c0 += 1)
6442 for (int c1 = 0; c1 <= -c0 + 10; c1 += 1)
6443 for (int c2 = 10 * c0;
6444 c2 <= min(-10 * c1 + 100, 10 * c0 + 9);
6446 for (int c3 = 10 * c1;
6447 c3 <= min(10 * c1 + 9, -c2 + 100);
6451 Separation into full and partial tiles can be obtained by assigning
6452 a class, say C<0>, to the full tiles. The full tiles are represented by those
6453 values of the first and second schedule dimensions for which there are
6454 values of the third and fourth dimensions to cover an entire tile.
6455 That is, we need to specify the following option
6457 { [a,b,c,d] -> separation_class[[0]->[0]] :
6458 exists b': 0 <= 10a,10b' and
6459 10a+9+10b'+9 <= 100;
6460 [a,b,c,d] -> separation_class[[1]->[0]] :
6461 0 <= 10a,10b and 10a+9+10b+9 <= 100 }
6465 { [a, b, c, d] -> separation_class[[1] -> [0]] :
6466 a >= 0 and b >= 0 and b <= 8 - a;
6467 [a, b, c, d] -> separation_class[[0] -> [0]] :
6470 With this option, the generated AST is as follows
6473 for (int c0 = 0; c0 <= 8; c0 += 1) {
6474 for (int c1 = 0; c1 <= -c0 + 8; c1 += 1)
6475 for (int c2 = 10 * c0;
6476 c2 <= 10 * c0 + 9; c2 += 1)
6477 for (int c3 = 10 * c1;
6478 c3 <= 10 * c1 + 9; c3 += 1)
6480 for (int c1 = -c0 + 9; c1 <= -c0 + 10; c1 += 1)
6481 for (int c2 = 10 * c0;
6482 c2 <= min(-10 * c1 + 100, 10 * c0 + 9);
6484 for (int c3 = 10 * c1;
6485 c3 <= min(-c2 + 100, 10 * c1 + 9);
6489 for (int c0 = 9; c0 <= 10; c0 += 1)
6490 for (int c1 = 0; c1 <= -c0 + 10; c1 += 1)
6491 for (int c2 = 10 * c0;
6492 c2 <= min(-10 * c1 + 100, 10 * c0 + 9);
6494 for (int c3 = 10 * c1;
6495 c3 <= min(10 * c1 + 9, -c2 + 100);
6502 This is a single-dimensional space representing the schedule dimension(s)
6503 to which ``separation'' should be applied. Separation tries to split
6504 a loop into several pieces if this can avoid the generation of guards
6506 See also the C<atomic> option.
6510 This is a single-dimensional space representing the schedule dimension(s)
6511 for which the domains should be considered ``atomic''. That is, the
6512 AST generator will make sure that any given domain space will only appear
6513 in a single loop at the specified level.
6515 Consider the following schedule
6517 { a[i] -> [i] : 0 <= i < 10;
6518 b[i] -> [i+1] : 0 <= i < 10 }
6520 If the following option is specified
6522 { [i] -> separate[x] }
6524 then the following AST will be generated
6528 for (int c0 = 1; c0 <= 9; c0 += 1) {
6535 If, on the other hand, the following option is specified
6537 { [i] -> atomic[x] }
6539 then the following AST will be generated
6541 for (int c0 = 0; c0 <= 10; c0 += 1) {
6548 If neither C<atomic> nor C<separate> is specified, then the AST generator
6549 may produce either of these two results or some intermediate form.
6553 This is a single-dimensional space representing the schedule dimension(s)
6554 that should be I<completely> unrolled.
6555 To obtain a partial unrolling, the user should apply an additional
6556 strip-mining to the schedule and fully unroll the inner loop.
6560 Additional control is available through the following functions.
6562 #include <isl/ast_build.h>
6563 __isl_give isl_ast_build *
6564 isl_ast_build_set_iterators(
6565 __isl_take isl_ast_build *control,
6566 __isl_take isl_id_list *iterators);
6568 The function C<isl_ast_build_set_iterators> allows the user to
6569 specify a list of iterator C<isl_id>s to be used as iterators.
6570 If the input schedule is injective, then
6571 the number of elements in this list should be as large as the dimension
6572 of the schedule space, but no direct correspondence should be assumed
6573 between dimensions and elements.
6574 If the input schedule is not injective, then an additional number
6575 of C<isl_id>s equal to the largest dimension of the input domains
6577 If the number of provided C<isl_id>s is insufficient, then additional
6578 names are automatically generated.
6580 #include <isl/ast_build.h>
6581 __isl_give isl_ast_build *
6582 isl_ast_build_set_create_leaf(
6583 __isl_take isl_ast_build *control,
6584 __isl_give isl_ast_node *(*fn)(
6585 __isl_take isl_ast_build *build,
6586 void *user), void *user);
6589 C<isl_ast_build_set_create_leaf> function allows for the
6590 specification of a callback that should be called whenever the AST
6591 generator arrives at an element of the schedule domain.
6592 The callback should return an AST node that should be inserted
6593 at the corresponding position of the AST. The default action (when
6594 the callback is not set) is to continue generating parts of the AST to scan
6595 all the domain elements associated to the schedule domain element
6596 and to insert user nodes, ``calling'' the domain element, for each of them.
6597 The C<build> argument contains the current state of the C<isl_ast_build>.
6598 To ease nested AST generation (see L</"Nested AST Generation">),
6599 all control information that is
6600 specific to the current AST generation such as the options and
6601 the callbacks has been removed from this C<isl_ast_build>.
6602 The callback would typically return the result of a nested
6604 user defined node created using the following function.
6606 #include <isl/ast.h>
6607 __isl_give isl_ast_node *isl_ast_node_alloc_user(
6608 __isl_take isl_ast_expr *expr);
6610 #include <isl/ast_build.h>
6611 __isl_give isl_ast_build *
6612 isl_ast_build_set_at_each_domain(
6613 __isl_take isl_ast_build *build,
6614 __isl_give isl_ast_node *(*fn)(
6615 __isl_take isl_ast_node *node,
6616 __isl_keep isl_ast_build *build,
6617 void *user), void *user);
6618 __isl_give isl_ast_build *
6619 isl_ast_build_set_before_each_for(
6620 __isl_take isl_ast_build *build,
6621 __isl_give isl_id *(*fn)(
6622 __isl_keep isl_ast_build *build,
6623 void *user), void *user);
6624 __isl_give isl_ast_build *
6625 isl_ast_build_set_after_each_for(
6626 __isl_take isl_ast_build *build,
6627 __isl_give isl_ast_node *(*fn)(
6628 __isl_take isl_ast_node *node,
6629 __isl_keep isl_ast_build *build,
6630 void *user), void *user);
6632 The callback set by C<isl_ast_build_set_at_each_domain> will
6633 be called for each domain AST node.
6634 The callbacks set by C<isl_ast_build_set_before_each_for>
6635 and C<isl_ast_build_set_after_each_for> will be called
6636 for each for AST node. The first will be called in depth-first
6637 pre-order, while the second will be called in depth-first post-order.
6638 Since C<isl_ast_build_set_before_each_for> is called before the for
6639 node is actually constructed, it is only passed an C<isl_ast_build>.
6640 The returned C<isl_id> will be added as an annotation (using
6641 C<isl_ast_node_set_annotation>) to the constructed for node.
6642 In particular, if the user has also specified an C<after_each_for>
6643 callback, then the annotation can be retrieved from the node passed to
6644 that callback using C<isl_ast_node_get_annotation>.
6645 All callbacks should C<NULL> on failure.
6646 The given C<isl_ast_build> can be used to create new
6647 C<isl_ast_expr> objects using C<isl_ast_build_expr_from_pw_aff>
6648 or C<isl_ast_build_call_from_pw_multi_aff>.
6650 =head3 Nested AST Generation
6652 C<isl> allows the user to create an AST within the context
6653 of another AST. These nested ASTs are created using the
6654 same C<isl_ast_build_ast_from_schedule> function that is used to create the
6655 outer AST. The C<build> argument should be an C<isl_ast_build>
6656 passed to a callback set by
6657 C<isl_ast_build_set_create_leaf>.
6658 The space of the range of the C<schedule> argument should refer
6659 to this build. In particular, the space should be a wrapped
6660 relation and the domain of this wrapped relation should be the
6661 same as that of the range of the schedule returned by
6662 C<isl_ast_build_get_schedule> below.
6663 In practice, the new schedule is typically
6664 created by calling C<isl_union_map_range_product> on the old schedule
6665 and some extra piece of the schedule.
6666 The space of the schedule domain is also available from
6667 the C<isl_ast_build>.
6669 #include <isl/ast_build.h>
6670 __isl_give isl_union_map *isl_ast_build_get_schedule(
6671 __isl_keep isl_ast_build *build);
6672 __isl_give isl_space *isl_ast_build_get_schedule_space(
6673 __isl_keep isl_ast_build *build);
6674 __isl_give isl_ast_build *isl_ast_build_restrict(
6675 __isl_take isl_ast_build *build,
6676 __isl_take isl_set *set);
6678 The C<isl_ast_build_get_schedule> function returns a (partial)
6679 schedule for the domains elements for which part of the AST still needs to
6680 be generated in the current build.
6681 In particular, the domain elements are mapped to those iterations of the loops
6682 enclosing the current point of the AST generation inside which
6683 the domain elements are executed.
6684 No direct correspondence between
6685 the input schedule and this schedule should be assumed.
6686 The space obtained from C<isl_ast_build_get_schedule_space> can be used
6687 to create a set for C<isl_ast_build_restrict> to intersect
6688 with the current build. In particular, the set passed to
6689 C<isl_ast_build_restrict> can have additional parameters.
6690 The ids of the set dimensions in the space returned by
6691 C<isl_ast_build_get_schedule_space> correspond to the
6692 iterators of the already generated loops.
6693 The user should not rely on the ids of the output dimensions
6694 of the relations in the union relation returned by
6695 C<isl_ast_build_get_schedule> having any particular value.
6699 Although C<isl> is mainly meant to be used as a library,
6700 it also contains some basic applications that use some
6701 of the functionality of C<isl>.
6702 The input may be specified in either the L<isl format>
6703 or the L<PolyLib format>.
6705 =head2 C<isl_polyhedron_sample>
6707 C<isl_polyhedron_sample> takes a polyhedron as input and prints
6708 an integer element of the polyhedron, if there is any.
6709 The first column in the output is the denominator and is always
6710 equal to 1. If the polyhedron contains no integer points,
6711 then a vector of length zero is printed.
6715 C<isl_pip> takes the same input as the C<example> program
6716 from the C<piplib> distribution, i.e., a set of constraints
6717 on the parameters, a line containing only -1 and finally a set
6718 of constraints on a parametric polyhedron.
6719 The coefficients of the parameters appear in the last columns
6720 (but before the final constant column).
6721 The output is the lexicographic minimum of the parametric polyhedron.
6722 As C<isl> currently does not have its own output format, the output
6723 is just a dump of the internal state.
6725 =head2 C<isl_polyhedron_minimize>
6727 C<isl_polyhedron_minimize> computes the minimum of some linear
6728 or affine objective function over the integer points in a polyhedron.
6729 If an affine objective function
6730 is given, then the constant should appear in the last column.
6732 =head2 C<isl_polytope_scan>
6734 Given a polytope, C<isl_polytope_scan> prints
6735 all integer points in the polytope.
6737 =head2 C<isl_codegen>
6739 Given a schedule, a context set and an options relation,
6740 C<isl_codegen> prints out an AST that scans the domain elements
6741 of the schedule in the order of their image(s) taking into account
6742 the constraints in the context set.