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_union_map *
1507 isl_union_map_from_union_pw_multi_aff(
1508 __isl_take isl_union_pw_multi_aff *upma);
1510 The C<domain_dim> argument describes the domain of the resulting
1511 basic relation. It is required because the C<list> may consist
1512 of zero affine expressions.
1514 =head2 Inspecting Sets and Relations
1516 Usually, the user should not have to care about the actual constraints
1517 of the sets and maps, but should instead apply the abstract operations
1518 explained in the following sections.
1519 Occasionally, however, it may be required to inspect the individual
1520 coefficients of the constraints. This section explains how to do so.
1521 In these cases, it may also be useful to have C<isl> compute
1522 an explicit representation of the existentially quantified variables.
1524 __isl_give isl_set *isl_set_compute_divs(
1525 __isl_take isl_set *set);
1526 __isl_give isl_map *isl_map_compute_divs(
1527 __isl_take isl_map *map);
1528 __isl_give isl_union_set *isl_union_set_compute_divs(
1529 __isl_take isl_union_set *uset);
1530 __isl_give isl_union_map *isl_union_map_compute_divs(
1531 __isl_take isl_union_map *umap);
1533 This explicit representation defines the existentially quantified
1534 variables as integer divisions of the other variables, possibly
1535 including earlier existentially quantified variables.
1536 An explicitly represented existentially quantified variable therefore
1537 has a unique value when the values of the other variables are known.
1538 If, furthermore, the same existentials, i.e., existentials
1539 with the same explicit representations, should appear in the
1540 same order in each of the disjuncts of a set or map, then the user should call
1541 either of the following functions.
1543 __isl_give isl_set *isl_set_align_divs(
1544 __isl_take isl_set *set);
1545 __isl_give isl_map *isl_map_align_divs(
1546 __isl_take isl_map *map);
1548 Alternatively, the existentially quantified variables can be removed
1549 using the following functions, which compute an overapproximation.
1551 __isl_give isl_basic_set *isl_basic_set_remove_divs(
1552 __isl_take isl_basic_set *bset);
1553 __isl_give isl_basic_map *isl_basic_map_remove_divs(
1554 __isl_take isl_basic_map *bmap);
1555 __isl_give isl_set *isl_set_remove_divs(
1556 __isl_take isl_set *set);
1557 __isl_give isl_map *isl_map_remove_divs(
1558 __isl_take isl_map *map);
1560 It is also possible to only remove those divs that are defined
1561 in terms of a given range of dimensions or only those for which
1562 no explicit representation is known.
1564 __isl_give isl_basic_set *
1565 isl_basic_set_remove_divs_involving_dims(
1566 __isl_take isl_basic_set *bset,
1567 enum isl_dim_type type,
1568 unsigned first, unsigned n);
1569 __isl_give isl_basic_map *
1570 isl_basic_map_remove_divs_involving_dims(
1571 __isl_take isl_basic_map *bmap,
1572 enum isl_dim_type type,
1573 unsigned first, unsigned n);
1574 __isl_give isl_set *isl_set_remove_divs_involving_dims(
1575 __isl_take isl_set *set, enum isl_dim_type type,
1576 unsigned first, unsigned n);
1577 __isl_give isl_map *isl_map_remove_divs_involving_dims(
1578 __isl_take isl_map *map, enum isl_dim_type type,
1579 unsigned first, unsigned n);
1581 __isl_give isl_basic_set *
1582 isl_basic_set_remove_unknown_divs(
1583 __isl_take isl_basic_set *bset);
1584 __isl_give isl_set *isl_set_remove_unknown_divs(
1585 __isl_take isl_set *set);
1586 __isl_give isl_map *isl_map_remove_unknown_divs(
1587 __isl_take isl_map *map);
1589 To iterate over all the sets or maps in a union set or map, use
1591 int isl_union_set_foreach_set(__isl_keep isl_union_set *uset,
1592 int (*fn)(__isl_take isl_set *set, void *user),
1594 int isl_union_map_foreach_map(__isl_keep isl_union_map *umap,
1595 int (*fn)(__isl_take isl_map *map, void *user),
1598 The number of sets or maps in a union set or map can be obtained
1601 int isl_union_set_n_set(__isl_keep isl_union_set *uset);
1602 int isl_union_map_n_map(__isl_keep isl_union_map *umap);
1604 To extract the set or map in a given space from a union, use
1606 __isl_give isl_set *isl_union_set_extract_set(
1607 __isl_keep isl_union_set *uset,
1608 __isl_take isl_space *space);
1609 __isl_give isl_map *isl_union_map_extract_map(
1610 __isl_keep isl_union_map *umap,
1611 __isl_take isl_space *space);
1613 To iterate over all the basic sets or maps in a set or map, use
1615 int isl_set_foreach_basic_set(__isl_keep isl_set *set,
1616 int (*fn)(__isl_take isl_basic_set *bset, void *user),
1618 int isl_map_foreach_basic_map(__isl_keep isl_map *map,
1619 int (*fn)(__isl_take isl_basic_map *bmap, void *user),
1622 The callback function C<fn> should return 0 if successful and
1623 -1 if an error occurs. In the latter case, or if any other error
1624 occurs, the above functions will return -1.
1626 It should be noted that C<isl> does not guarantee that
1627 the basic sets or maps passed to C<fn> are disjoint.
1628 If this is required, then the user should call one of
1629 the following functions first.
1631 __isl_give isl_set *isl_set_make_disjoint(
1632 __isl_take isl_set *set);
1633 __isl_give isl_map *isl_map_make_disjoint(
1634 __isl_take isl_map *map);
1636 The number of basic sets in a set can be obtained
1639 int isl_set_n_basic_set(__isl_keep isl_set *set);
1641 To iterate over the constraints of a basic set or map, use
1643 #include <isl/constraint.h>
1645 int isl_basic_set_n_constraint(
1646 __isl_keep isl_basic_set *bset);
1647 int isl_basic_set_foreach_constraint(
1648 __isl_keep isl_basic_set *bset,
1649 int (*fn)(__isl_take isl_constraint *c, void *user),
1651 int isl_basic_map_foreach_constraint(
1652 __isl_keep isl_basic_map *bmap,
1653 int (*fn)(__isl_take isl_constraint *c, void *user),
1655 void *isl_constraint_free(__isl_take isl_constraint *c);
1657 Again, the callback function C<fn> should return 0 if successful and
1658 -1 if an error occurs. In the latter case, or if any other error
1659 occurs, the above functions will return -1.
1660 The constraint C<c> represents either an equality or an inequality.
1661 Use the following function to find out whether a constraint
1662 represents an equality. If not, it represents an inequality.
1664 int isl_constraint_is_equality(
1665 __isl_keep isl_constraint *constraint);
1667 The coefficients of the constraints can be inspected using
1668 the following functions.
1670 int isl_constraint_is_lower_bound(
1671 __isl_keep isl_constraint *constraint,
1672 enum isl_dim_type type, unsigned pos);
1673 int isl_constraint_is_upper_bound(
1674 __isl_keep isl_constraint *constraint,
1675 enum isl_dim_type type, unsigned pos);
1676 __isl_give isl_val *isl_constraint_get_constant_val(
1677 __isl_keep isl_constraint *constraint);
1678 __isl_give isl_val *isl_constraint_get_coefficient_val(
1679 __isl_keep isl_constraint *constraint,
1680 enum isl_dim_type type, int pos);
1681 int isl_constraint_involves_dims(
1682 __isl_keep isl_constraint *constraint,
1683 enum isl_dim_type type, unsigned first, unsigned n);
1685 The explicit representations of the existentially quantified
1686 variables can be inspected using the following function.
1687 Note that the user is only allowed to use this function
1688 if the inspected set or map is the result of a call
1689 to C<isl_set_compute_divs> or C<isl_map_compute_divs>.
1690 The existentially quantified variable is equal to the floor
1691 of the returned affine expression. The affine expression
1692 itself can be inspected using the functions in
1693 L<"Piecewise Quasi Affine Expressions">.
1695 __isl_give isl_aff *isl_constraint_get_div(
1696 __isl_keep isl_constraint *constraint, int pos);
1698 To obtain the constraints of a basic set or map in matrix
1699 form, use the following functions.
1701 __isl_give isl_mat *isl_basic_set_equalities_matrix(
1702 __isl_keep isl_basic_set *bset,
1703 enum isl_dim_type c1, enum isl_dim_type c2,
1704 enum isl_dim_type c3, enum isl_dim_type c4);
1705 __isl_give isl_mat *isl_basic_set_inequalities_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_map_equalities_matrix(
1710 __isl_keep isl_basic_map *bmap,
1711 enum isl_dim_type c1,
1712 enum isl_dim_type c2, enum isl_dim_type c3,
1713 enum isl_dim_type c4, enum isl_dim_type c5);
1714 __isl_give isl_mat *isl_basic_map_inequalities_matrix(
1715 __isl_keep isl_basic_map *bmap,
1716 enum isl_dim_type c1,
1717 enum isl_dim_type c2, enum isl_dim_type c3,
1718 enum isl_dim_type c4, enum isl_dim_type c5);
1720 The C<isl_dim_type> arguments dictate the order in which
1721 different kinds of variables appear in the resulting matrix
1722 and should be a permutation of C<isl_dim_cst>, C<isl_dim_param>,
1723 C<isl_dim_in>, C<isl_dim_out> and C<isl_dim_div>.
1725 The number of parameters, input, output or set dimensions can
1726 be obtained using the following functions.
1728 unsigned isl_basic_set_dim(__isl_keep isl_basic_set *bset,
1729 enum isl_dim_type type);
1730 unsigned isl_basic_map_dim(__isl_keep isl_basic_map *bmap,
1731 enum isl_dim_type type);
1732 unsigned isl_set_dim(__isl_keep isl_set *set,
1733 enum isl_dim_type type);
1734 unsigned isl_map_dim(__isl_keep isl_map *map,
1735 enum isl_dim_type type);
1737 To check whether the description of a set or relation depends
1738 on one or more given dimensions, it is not necessary to iterate over all
1739 constraints. Instead the following functions can be used.
1741 int isl_basic_set_involves_dims(
1742 __isl_keep isl_basic_set *bset,
1743 enum isl_dim_type type, unsigned first, unsigned n);
1744 int isl_set_involves_dims(__isl_keep isl_set *set,
1745 enum isl_dim_type type, unsigned first, unsigned n);
1746 int isl_basic_map_involves_dims(
1747 __isl_keep isl_basic_map *bmap,
1748 enum isl_dim_type type, unsigned first, unsigned n);
1749 int isl_map_involves_dims(__isl_keep isl_map *map,
1750 enum isl_dim_type type, unsigned first, unsigned n);
1752 Similarly, the following functions can be used to check whether
1753 a given dimension is involved in any lower or upper bound.
1755 int isl_set_dim_has_any_lower_bound(__isl_keep isl_set *set,
1756 enum isl_dim_type type, unsigned pos);
1757 int isl_set_dim_has_any_upper_bound(__isl_keep isl_set *set,
1758 enum isl_dim_type type, unsigned pos);
1760 Note that these functions return true even if there is a bound on
1761 the dimension on only some of the basic sets of C<set>.
1762 To check if they have a bound for all of the basic sets in C<set>,
1763 use the following functions instead.
1765 int isl_set_dim_has_lower_bound(__isl_keep isl_set *set,
1766 enum isl_dim_type type, unsigned pos);
1767 int isl_set_dim_has_upper_bound(__isl_keep isl_set *set,
1768 enum isl_dim_type type, unsigned pos);
1770 The identifiers or names of the domain and range spaces of a set
1771 or relation can be read off or set using the following functions.
1773 __isl_give isl_set *isl_set_set_tuple_id(
1774 __isl_take isl_set *set, __isl_take isl_id *id);
1775 __isl_give isl_set *isl_set_reset_tuple_id(
1776 __isl_take isl_set *set);
1777 int isl_set_has_tuple_id(__isl_keep isl_set *set);
1778 __isl_give isl_id *isl_set_get_tuple_id(
1779 __isl_keep isl_set *set);
1780 __isl_give isl_map *isl_map_set_tuple_id(
1781 __isl_take isl_map *map, enum isl_dim_type type,
1782 __isl_take isl_id *id);
1783 __isl_give isl_map *isl_map_reset_tuple_id(
1784 __isl_take isl_map *map, enum isl_dim_type type);
1785 int isl_map_has_tuple_id(__isl_keep isl_map *map,
1786 enum isl_dim_type type);
1787 __isl_give isl_id *isl_map_get_tuple_id(
1788 __isl_keep isl_map *map, enum isl_dim_type type);
1790 const char *isl_basic_set_get_tuple_name(
1791 __isl_keep isl_basic_set *bset);
1792 __isl_give isl_basic_set *isl_basic_set_set_tuple_name(
1793 __isl_take isl_basic_set *set, const char *s);
1794 int isl_set_has_tuple_name(__isl_keep isl_set *set);
1795 const char *isl_set_get_tuple_name(
1796 __isl_keep isl_set *set);
1797 const char *isl_basic_map_get_tuple_name(
1798 __isl_keep isl_basic_map *bmap,
1799 enum isl_dim_type type);
1800 __isl_give isl_basic_map *isl_basic_map_set_tuple_name(
1801 __isl_take isl_basic_map *bmap,
1802 enum isl_dim_type type, const char *s);
1803 int isl_map_has_tuple_name(__isl_keep isl_map *map,
1804 enum isl_dim_type type);
1805 const char *isl_map_get_tuple_name(
1806 __isl_keep isl_map *map,
1807 enum isl_dim_type type);
1809 As with C<isl_space_get_tuple_name>, the value returned points to
1810 an internal data structure.
1811 The identifiers, positions or names of individual dimensions can be
1812 read off using the following functions.
1814 __isl_give isl_id *isl_basic_set_get_dim_id(
1815 __isl_keep isl_basic_set *bset,
1816 enum isl_dim_type type, unsigned pos);
1817 __isl_give isl_set *isl_set_set_dim_id(
1818 __isl_take isl_set *set, enum isl_dim_type type,
1819 unsigned pos, __isl_take isl_id *id);
1820 int isl_set_has_dim_id(__isl_keep isl_set *set,
1821 enum isl_dim_type type, unsigned pos);
1822 __isl_give isl_id *isl_set_get_dim_id(
1823 __isl_keep isl_set *set, enum isl_dim_type type,
1825 int isl_basic_map_has_dim_id(
1826 __isl_keep isl_basic_map *bmap,
1827 enum isl_dim_type type, unsigned pos);
1828 __isl_give isl_map *isl_map_set_dim_id(
1829 __isl_take isl_map *map, enum isl_dim_type type,
1830 unsigned pos, __isl_take isl_id *id);
1831 int isl_map_has_dim_id(__isl_keep isl_map *map,
1832 enum isl_dim_type type, unsigned pos);
1833 __isl_give isl_id *isl_map_get_dim_id(
1834 __isl_keep isl_map *map, enum isl_dim_type type,
1837 int isl_set_find_dim_by_id(__isl_keep isl_set *set,
1838 enum isl_dim_type type, __isl_keep isl_id *id);
1839 int isl_map_find_dim_by_id(__isl_keep isl_map *map,
1840 enum isl_dim_type type, __isl_keep isl_id *id);
1841 int isl_set_find_dim_by_name(__isl_keep isl_set *set,
1842 enum isl_dim_type type, const char *name);
1843 int isl_map_find_dim_by_name(__isl_keep isl_map *map,
1844 enum isl_dim_type type, const char *name);
1846 const char *isl_constraint_get_dim_name(
1847 __isl_keep isl_constraint *constraint,
1848 enum isl_dim_type type, unsigned pos);
1849 const char *isl_basic_set_get_dim_name(
1850 __isl_keep isl_basic_set *bset,
1851 enum isl_dim_type type, unsigned pos);
1852 int isl_set_has_dim_name(__isl_keep isl_set *set,
1853 enum isl_dim_type type, unsigned pos);
1854 const char *isl_set_get_dim_name(
1855 __isl_keep isl_set *set,
1856 enum isl_dim_type type, unsigned pos);
1857 const char *isl_basic_map_get_dim_name(
1858 __isl_keep isl_basic_map *bmap,
1859 enum isl_dim_type type, unsigned pos);
1860 int isl_map_has_dim_name(__isl_keep isl_map *map,
1861 enum isl_dim_type type, unsigned pos);
1862 const char *isl_map_get_dim_name(
1863 __isl_keep isl_map *map,
1864 enum isl_dim_type type, unsigned pos);
1866 These functions are mostly useful to obtain the identifiers, positions
1867 or names of the parameters. Identifiers of individual dimensions are
1868 essentially only useful for printing. They are ignored by all other
1869 operations and may not be preserved across those operations.
1873 =head3 Unary Properties
1879 The following functions test whether the given set or relation
1880 contains any integer points. The ``plain'' variants do not perform
1881 any computations, but simply check if the given set or relation
1882 is already known to be empty.
1884 int isl_basic_set_plain_is_empty(__isl_keep isl_basic_set *bset);
1885 int isl_basic_set_is_empty(__isl_keep isl_basic_set *bset);
1886 int isl_set_plain_is_empty(__isl_keep isl_set *set);
1887 int isl_set_is_empty(__isl_keep isl_set *set);
1888 int isl_union_set_is_empty(__isl_keep isl_union_set *uset);
1889 int isl_basic_map_plain_is_empty(__isl_keep isl_basic_map *bmap);
1890 int isl_basic_map_is_empty(__isl_keep isl_basic_map *bmap);
1891 int isl_map_plain_is_empty(__isl_keep isl_map *map);
1892 int isl_map_is_empty(__isl_keep isl_map *map);
1893 int isl_union_map_is_empty(__isl_keep isl_union_map *umap);
1895 =item * Universality
1897 int isl_basic_set_is_universe(__isl_keep isl_basic_set *bset);
1898 int isl_basic_map_is_universe(__isl_keep isl_basic_map *bmap);
1899 int isl_set_plain_is_universe(__isl_keep isl_set *set);
1901 =item * Single-valuedness
1903 int isl_basic_map_is_single_valued(
1904 __isl_keep isl_basic_map *bmap);
1905 int isl_map_plain_is_single_valued(
1906 __isl_keep isl_map *map);
1907 int isl_map_is_single_valued(__isl_keep isl_map *map);
1908 int isl_union_map_is_single_valued(__isl_keep isl_union_map *umap);
1912 int isl_map_plain_is_injective(__isl_keep isl_map *map);
1913 int isl_map_is_injective(__isl_keep isl_map *map);
1914 int isl_union_map_plain_is_injective(
1915 __isl_keep isl_union_map *umap);
1916 int isl_union_map_is_injective(
1917 __isl_keep isl_union_map *umap);
1921 int isl_map_is_bijective(__isl_keep isl_map *map);
1922 int isl_union_map_is_bijective(__isl_keep isl_union_map *umap);
1926 __isl_give isl_val *
1927 isl_basic_map_plain_get_val_if_fixed(
1928 __isl_keep isl_basic_map *bmap,
1929 enum isl_dim_type type, unsigned pos);
1930 __isl_give isl_val *isl_set_plain_get_val_if_fixed(
1931 __isl_keep isl_set *set,
1932 enum isl_dim_type type, unsigned pos);
1933 __isl_give isl_val *isl_map_plain_get_val_if_fixed(
1934 __isl_keep isl_map *map,
1935 enum isl_dim_type type, unsigned pos);
1937 If the set or relation obviously lies on a hyperplane where the given dimension
1938 has a fixed value, then return that value.
1939 Otherwise return NaN.
1943 int isl_set_dim_residue_class_val(
1944 __isl_keep isl_set *set,
1945 int pos, __isl_give isl_val **modulo,
1946 __isl_give isl_val **residue);
1948 Check if the values of the given set dimension are equal to a fixed
1949 value modulo some integer value. If so, assign the modulo to C<*modulo>
1950 and the fixed value to C<*residue>. If the given dimension attains only
1951 a single value, then assign C<0> to C<*modulo> and the fixed value to
1953 If the dimension does not attain only a single value and if no modulo
1954 can be found then assign C<1> to C<*modulo> and C<1> to C<*residue>.
1958 To check whether a set is a parameter domain, use this function:
1960 int isl_set_is_params(__isl_keep isl_set *set);
1961 int isl_union_set_is_params(
1962 __isl_keep isl_union_set *uset);
1966 The following functions check whether the domain of the given
1967 (basic) set is a wrapped relation.
1969 int isl_basic_set_is_wrapping(
1970 __isl_keep isl_basic_set *bset);
1971 int isl_set_is_wrapping(__isl_keep isl_set *set);
1973 =item * Internal Product
1975 int isl_basic_map_can_zip(
1976 __isl_keep isl_basic_map *bmap);
1977 int isl_map_can_zip(__isl_keep isl_map *map);
1979 Check whether the product of domain and range of the given relation
1981 i.e., whether both domain and range are nested relations.
1985 int isl_basic_map_can_curry(
1986 __isl_keep isl_basic_map *bmap);
1987 int isl_map_can_curry(__isl_keep isl_map *map);
1989 Check whether the domain of the (basic) relation is a wrapped relation.
1991 int isl_basic_map_can_uncurry(
1992 __isl_keep isl_basic_map *bmap);
1993 int isl_map_can_uncurry(__isl_keep isl_map *map);
1995 Check whether the range of the (basic) relation is a wrapped relation.
1999 =head3 Binary Properties
2005 int isl_set_plain_is_equal(__isl_keep isl_set *set1,
2006 __isl_keep isl_set *set2);
2007 int isl_set_is_equal(__isl_keep isl_set *set1,
2008 __isl_keep isl_set *set2);
2009 int isl_union_set_is_equal(
2010 __isl_keep isl_union_set *uset1,
2011 __isl_keep isl_union_set *uset2);
2012 int isl_basic_map_is_equal(
2013 __isl_keep isl_basic_map *bmap1,
2014 __isl_keep isl_basic_map *bmap2);
2015 int isl_map_is_equal(__isl_keep isl_map *map1,
2016 __isl_keep isl_map *map2);
2017 int isl_map_plain_is_equal(__isl_keep isl_map *map1,
2018 __isl_keep isl_map *map2);
2019 int isl_union_map_is_equal(
2020 __isl_keep isl_union_map *umap1,
2021 __isl_keep isl_union_map *umap2);
2023 =item * Disjointness
2025 int isl_basic_set_is_disjoint(
2026 __isl_keep isl_basic_set *bset1,
2027 __isl_keep isl_basic_set *bset2);
2028 int isl_set_plain_is_disjoint(__isl_keep isl_set *set1,
2029 __isl_keep isl_set *set2);
2030 int isl_set_is_disjoint(__isl_keep isl_set *set1,
2031 __isl_keep isl_set *set2);
2032 int isl_basic_map_is_disjoint(
2033 __isl_keep isl_basic_map *bmap1,
2034 __isl_keep isl_basic_map *bmap2);
2035 int isl_map_is_disjoint(__isl_keep isl_map *map1,
2036 __isl_keep isl_map *map2);
2040 int isl_basic_set_is_subset(
2041 __isl_keep isl_basic_set *bset1,
2042 __isl_keep isl_basic_set *bset2);
2043 int isl_set_is_subset(__isl_keep isl_set *set1,
2044 __isl_keep isl_set *set2);
2045 int isl_set_is_strict_subset(
2046 __isl_keep isl_set *set1,
2047 __isl_keep isl_set *set2);
2048 int isl_union_set_is_subset(
2049 __isl_keep isl_union_set *uset1,
2050 __isl_keep isl_union_set *uset2);
2051 int isl_union_set_is_strict_subset(
2052 __isl_keep isl_union_set *uset1,
2053 __isl_keep isl_union_set *uset2);
2054 int isl_basic_map_is_subset(
2055 __isl_keep isl_basic_map *bmap1,
2056 __isl_keep isl_basic_map *bmap2);
2057 int isl_basic_map_is_strict_subset(
2058 __isl_keep isl_basic_map *bmap1,
2059 __isl_keep isl_basic_map *bmap2);
2060 int isl_map_is_subset(
2061 __isl_keep isl_map *map1,
2062 __isl_keep isl_map *map2);
2063 int isl_map_is_strict_subset(
2064 __isl_keep isl_map *map1,
2065 __isl_keep isl_map *map2);
2066 int isl_union_map_is_subset(
2067 __isl_keep isl_union_map *umap1,
2068 __isl_keep isl_union_map *umap2);
2069 int isl_union_map_is_strict_subset(
2070 __isl_keep isl_union_map *umap1,
2071 __isl_keep isl_union_map *umap2);
2073 Check whether the first argument is a (strict) subset of the
2078 int isl_set_plain_cmp(__isl_keep isl_set *set1,
2079 __isl_keep isl_set *set2);
2081 This function is useful for sorting C<isl_set>s.
2082 The order depends on the internal representation of the inputs.
2083 The order is fixed over different calls to the function (assuming
2084 the internal representation of the inputs has not changed), but may
2085 change over different versions of C<isl>.
2089 =head2 Unary Operations
2095 __isl_give isl_set *isl_set_complement(
2096 __isl_take isl_set *set);
2097 __isl_give isl_map *isl_map_complement(
2098 __isl_take isl_map *map);
2102 __isl_give isl_basic_map *isl_basic_map_reverse(
2103 __isl_take isl_basic_map *bmap);
2104 __isl_give isl_map *isl_map_reverse(
2105 __isl_take isl_map *map);
2106 __isl_give isl_union_map *isl_union_map_reverse(
2107 __isl_take isl_union_map *umap);
2111 __isl_give isl_basic_set *isl_basic_set_project_out(
2112 __isl_take isl_basic_set *bset,
2113 enum isl_dim_type type, unsigned first, unsigned n);
2114 __isl_give isl_basic_map *isl_basic_map_project_out(
2115 __isl_take isl_basic_map *bmap,
2116 enum isl_dim_type type, unsigned first, unsigned n);
2117 __isl_give isl_set *isl_set_project_out(__isl_take isl_set *set,
2118 enum isl_dim_type type, unsigned first, unsigned n);
2119 __isl_give isl_map *isl_map_project_out(__isl_take isl_map *map,
2120 enum isl_dim_type type, unsigned first, unsigned n);
2121 __isl_give isl_basic_set *isl_basic_set_params(
2122 __isl_take isl_basic_set *bset);
2123 __isl_give isl_basic_set *isl_basic_map_domain(
2124 __isl_take isl_basic_map *bmap);
2125 __isl_give isl_basic_set *isl_basic_map_range(
2126 __isl_take isl_basic_map *bmap);
2127 __isl_give isl_set *isl_set_params(__isl_take isl_set *set);
2128 __isl_give isl_set *isl_map_params(__isl_take isl_map *map);
2129 __isl_give isl_set *isl_map_domain(
2130 __isl_take isl_map *bmap);
2131 __isl_give isl_set *isl_map_range(
2132 __isl_take isl_map *map);
2133 __isl_give isl_set *isl_union_set_params(
2134 __isl_take isl_union_set *uset);
2135 __isl_give isl_set *isl_union_map_params(
2136 __isl_take isl_union_map *umap);
2137 __isl_give isl_union_set *isl_union_map_domain(
2138 __isl_take isl_union_map *umap);
2139 __isl_give isl_union_set *isl_union_map_range(
2140 __isl_take isl_union_map *umap);
2142 __isl_give isl_basic_map *isl_basic_map_domain_map(
2143 __isl_take isl_basic_map *bmap);
2144 __isl_give isl_basic_map *isl_basic_map_range_map(
2145 __isl_take isl_basic_map *bmap);
2146 __isl_give isl_map *isl_map_domain_map(__isl_take isl_map *map);
2147 __isl_give isl_map *isl_map_range_map(__isl_take isl_map *map);
2148 __isl_give isl_union_map *isl_union_map_domain_map(
2149 __isl_take isl_union_map *umap);
2150 __isl_give isl_union_map *isl_union_map_range_map(
2151 __isl_take isl_union_map *umap);
2153 The functions above construct a (basic, regular or union) relation
2154 that maps (a wrapped version of) the input relation to its domain or range.
2158 __isl_give isl_basic_set *isl_basic_set_eliminate(
2159 __isl_take isl_basic_set *bset,
2160 enum isl_dim_type type,
2161 unsigned first, unsigned n);
2162 __isl_give isl_set *isl_set_eliminate(
2163 __isl_take isl_set *set, enum isl_dim_type type,
2164 unsigned first, unsigned n);
2165 __isl_give isl_basic_map *isl_basic_map_eliminate(
2166 __isl_take isl_basic_map *bmap,
2167 enum isl_dim_type type,
2168 unsigned first, unsigned n);
2169 __isl_give isl_map *isl_map_eliminate(
2170 __isl_take isl_map *map, enum isl_dim_type type,
2171 unsigned first, unsigned n);
2173 Eliminate the coefficients for the given dimensions from the constraints,
2174 without removing the dimensions.
2178 __isl_give isl_basic_set *isl_basic_set_fix_si(
2179 __isl_take isl_basic_set *bset,
2180 enum isl_dim_type type, unsigned pos, int value);
2181 __isl_give isl_basic_set *isl_basic_set_fix_val(
2182 __isl_take isl_basic_set *bset,
2183 enum isl_dim_type type, unsigned pos,
2184 __isl_take isl_val *v);
2185 __isl_give isl_set *isl_set_fix_si(__isl_take isl_set *set,
2186 enum isl_dim_type type, unsigned pos, int value);
2187 __isl_give isl_set *isl_set_fix_val(
2188 __isl_take isl_set *set,
2189 enum isl_dim_type type, unsigned pos,
2190 __isl_take isl_val *v);
2191 __isl_give isl_basic_map *isl_basic_map_fix_si(
2192 __isl_take isl_basic_map *bmap,
2193 enum isl_dim_type type, unsigned pos, int value);
2194 __isl_give isl_basic_map *isl_basic_map_fix_val(
2195 __isl_take isl_basic_map *bmap,
2196 enum isl_dim_type type, unsigned pos,
2197 __isl_take isl_val *v);
2198 __isl_give isl_map *isl_map_fix_si(__isl_take isl_map *map,
2199 enum isl_dim_type type, unsigned pos, int value);
2200 __isl_give isl_map *isl_map_fix_val(
2201 __isl_take isl_map *map,
2202 enum isl_dim_type type, unsigned pos,
2203 __isl_take isl_val *v);
2205 Intersect the set or relation with the hyperplane where the given
2206 dimension has the fixed given value.
2208 __isl_give isl_basic_map *isl_basic_map_lower_bound_si(
2209 __isl_take isl_basic_map *bmap,
2210 enum isl_dim_type type, unsigned pos, int value);
2211 __isl_give isl_basic_map *isl_basic_map_upper_bound_si(
2212 __isl_take isl_basic_map *bmap,
2213 enum isl_dim_type type, unsigned pos, int value);
2214 __isl_give isl_set *isl_set_lower_bound_si(
2215 __isl_take isl_set *set,
2216 enum isl_dim_type type, unsigned pos, int value);
2217 __isl_give isl_set *isl_set_lower_bound_val(
2218 __isl_take isl_set *set,
2219 enum isl_dim_type type, unsigned pos,
2220 __isl_take isl_val *value);
2221 __isl_give isl_map *isl_map_lower_bound_si(
2222 __isl_take isl_map *map,
2223 enum isl_dim_type type, unsigned pos, int value);
2224 __isl_give isl_set *isl_set_upper_bound_si(
2225 __isl_take isl_set *set,
2226 enum isl_dim_type type, unsigned pos, int value);
2227 __isl_give isl_set *isl_set_upper_bound_val(
2228 __isl_take isl_set *set,
2229 enum isl_dim_type type, unsigned pos,
2230 __isl_take isl_val *value);
2231 __isl_give isl_map *isl_map_upper_bound_si(
2232 __isl_take isl_map *map,
2233 enum isl_dim_type type, unsigned pos, int value);
2235 Intersect the set or relation with the half-space where the given
2236 dimension has a value bounded by the fixed given integer value.
2238 __isl_give isl_set *isl_set_equate(__isl_take isl_set *set,
2239 enum isl_dim_type type1, int pos1,
2240 enum isl_dim_type type2, int pos2);
2241 __isl_give isl_basic_map *isl_basic_map_equate(
2242 __isl_take isl_basic_map *bmap,
2243 enum isl_dim_type type1, int pos1,
2244 enum isl_dim_type type2, int pos2);
2245 __isl_give isl_map *isl_map_equate(__isl_take isl_map *map,
2246 enum isl_dim_type type1, int pos1,
2247 enum isl_dim_type type2, int pos2);
2249 Intersect the set or relation with the hyperplane where the given
2250 dimensions are equal to each other.
2252 __isl_give isl_map *isl_map_oppose(__isl_take isl_map *map,
2253 enum isl_dim_type type1, int pos1,
2254 enum isl_dim_type type2, int pos2);
2256 Intersect the relation with the hyperplane where the given
2257 dimensions have opposite values.
2259 __isl_give isl_basic_map *isl_basic_map_order_ge(
2260 __isl_take isl_basic_map *bmap,
2261 enum isl_dim_type type1, int pos1,
2262 enum isl_dim_type type2, int pos2);
2263 __isl_give isl_map *isl_map_order_lt(__isl_take isl_map *map,
2264 enum isl_dim_type type1, int pos1,
2265 enum isl_dim_type type2, int pos2);
2266 __isl_give isl_basic_map *isl_basic_map_order_gt(
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_gt(__isl_take isl_map *map,
2271 enum isl_dim_type type1, int pos1,
2272 enum isl_dim_type type2, int pos2);
2274 Intersect the relation with the half-space where the given
2275 dimensions satisfy the given ordering.
2279 __isl_give isl_map *isl_set_identity(
2280 __isl_take isl_set *set);
2281 __isl_give isl_union_map *isl_union_set_identity(
2282 __isl_take isl_union_set *uset);
2284 Construct an identity relation on the given (union) set.
2288 __isl_give isl_basic_set *isl_basic_map_deltas(
2289 __isl_take isl_basic_map *bmap);
2290 __isl_give isl_set *isl_map_deltas(__isl_take isl_map *map);
2291 __isl_give isl_union_set *isl_union_map_deltas(
2292 __isl_take isl_union_map *umap);
2294 These functions return a (basic) set containing the differences
2295 between image elements and corresponding domain elements in the input.
2297 __isl_give isl_basic_map *isl_basic_map_deltas_map(
2298 __isl_take isl_basic_map *bmap);
2299 __isl_give isl_map *isl_map_deltas_map(
2300 __isl_take isl_map *map);
2301 __isl_give isl_union_map *isl_union_map_deltas_map(
2302 __isl_take isl_union_map *umap);
2304 The functions above construct a (basic, regular or union) relation
2305 that maps (a wrapped version of) the input relation to its delta set.
2309 Simplify the representation of a set or relation by trying
2310 to combine pairs of basic sets or relations into a single
2311 basic set or relation.
2313 __isl_give isl_set *isl_set_coalesce(__isl_take isl_set *set);
2314 __isl_give isl_map *isl_map_coalesce(__isl_take isl_map *map);
2315 __isl_give isl_union_set *isl_union_set_coalesce(
2316 __isl_take isl_union_set *uset);
2317 __isl_give isl_union_map *isl_union_map_coalesce(
2318 __isl_take isl_union_map *umap);
2320 One of the methods for combining pairs of basic sets or relations
2321 can result in coefficients that are much larger than those that appear
2322 in the constraints of the input. By default, the coefficients are
2323 not allowed to grow larger, but this can be changed by unsetting
2324 the following option.
2326 int isl_options_set_coalesce_bounded_wrapping(
2327 isl_ctx *ctx, int val);
2328 int isl_options_get_coalesce_bounded_wrapping(
2331 =item * Detecting equalities
2333 __isl_give isl_basic_set *isl_basic_set_detect_equalities(
2334 __isl_take isl_basic_set *bset);
2335 __isl_give isl_basic_map *isl_basic_map_detect_equalities(
2336 __isl_take isl_basic_map *bmap);
2337 __isl_give isl_set *isl_set_detect_equalities(
2338 __isl_take isl_set *set);
2339 __isl_give isl_map *isl_map_detect_equalities(
2340 __isl_take isl_map *map);
2341 __isl_give isl_union_set *isl_union_set_detect_equalities(
2342 __isl_take isl_union_set *uset);
2343 __isl_give isl_union_map *isl_union_map_detect_equalities(
2344 __isl_take isl_union_map *umap);
2346 Simplify the representation of a set or relation by detecting implicit
2349 =item * Removing redundant constraints
2351 __isl_give isl_basic_set *isl_basic_set_remove_redundancies(
2352 __isl_take isl_basic_set *bset);
2353 __isl_give isl_set *isl_set_remove_redundancies(
2354 __isl_take isl_set *set);
2355 __isl_give isl_basic_map *isl_basic_map_remove_redundancies(
2356 __isl_take isl_basic_map *bmap);
2357 __isl_give isl_map *isl_map_remove_redundancies(
2358 __isl_take isl_map *map);
2362 __isl_give isl_basic_set *isl_set_convex_hull(
2363 __isl_take isl_set *set);
2364 __isl_give isl_basic_map *isl_map_convex_hull(
2365 __isl_take isl_map *map);
2367 If the input set or relation has any existentially quantified
2368 variables, then the result of these operations is currently undefined.
2372 __isl_give isl_basic_set *
2373 isl_set_unshifted_simple_hull(
2374 __isl_take isl_set *set);
2375 __isl_give isl_basic_map *
2376 isl_map_unshifted_simple_hull(
2377 __isl_take isl_map *map);
2378 __isl_give isl_basic_set *isl_set_simple_hull(
2379 __isl_take isl_set *set);
2380 __isl_give isl_basic_map *isl_map_simple_hull(
2381 __isl_take isl_map *map);
2382 __isl_give isl_union_map *isl_union_map_simple_hull(
2383 __isl_take isl_union_map *umap);
2385 These functions compute a single basic set or relation
2386 that contains the whole input set or relation.
2387 In particular, the output is described by translates
2388 of the constraints describing the basic sets or relations in the input.
2389 In case of C<isl_set_unshifted_simple_hull>, only the original
2390 constraints are used, without any translation.
2394 (See \autoref{s:simple hull}.)
2400 __isl_give isl_basic_set *isl_basic_set_affine_hull(
2401 __isl_take isl_basic_set *bset);
2402 __isl_give isl_basic_set *isl_set_affine_hull(
2403 __isl_take isl_set *set);
2404 __isl_give isl_union_set *isl_union_set_affine_hull(
2405 __isl_take isl_union_set *uset);
2406 __isl_give isl_basic_map *isl_basic_map_affine_hull(
2407 __isl_take isl_basic_map *bmap);
2408 __isl_give isl_basic_map *isl_map_affine_hull(
2409 __isl_take isl_map *map);
2410 __isl_give isl_union_map *isl_union_map_affine_hull(
2411 __isl_take isl_union_map *umap);
2413 In case of union sets and relations, the affine hull is computed
2416 =item * Polyhedral hull
2418 __isl_give isl_basic_set *isl_set_polyhedral_hull(
2419 __isl_take isl_set *set);
2420 __isl_give isl_basic_map *isl_map_polyhedral_hull(
2421 __isl_take isl_map *map);
2422 __isl_give isl_union_set *isl_union_set_polyhedral_hull(
2423 __isl_take isl_union_set *uset);
2424 __isl_give isl_union_map *isl_union_map_polyhedral_hull(
2425 __isl_take isl_union_map *umap);
2427 These functions compute a single basic set or relation
2428 not involving any existentially quantified variables
2429 that contains the whole input set or relation.
2430 In case of union sets and relations, the polyhedral hull is computed
2433 =item * Other approximations
2435 __isl_give isl_basic_set *
2436 isl_basic_set_drop_constraints_involving_dims(
2437 __isl_take isl_basic_set *bset,
2438 enum isl_dim_type type,
2439 unsigned first, unsigned n);
2440 __isl_give isl_basic_map *
2441 isl_basic_map_drop_constraints_involving_dims(
2442 __isl_take isl_basic_map *bmap,
2443 enum isl_dim_type type,
2444 unsigned first, unsigned n);
2445 __isl_give isl_basic_set *
2446 isl_basic_set_drop_constraints_not_involving_dims(
2447 __isl_take isl_basic_set *bset,
2448 enum isl_dim_type type,
2449 unsigned first, unsigned n);
2450 __isl_give isl_set *
2451 isl_set_drop_constraints_involving_dims(
2452 __isl_take isl_set *set,
2453 enum isl_dim_type type,
2454 unsigned first, unsigned n);
2455 __isl_give isl_map *
2456 isl_map_drop_constraints_involving_dims(
2457 __isl_take isl_map *map,
2458 enum isl_dim_type type,
2459 unsigned first, unsigned n);
2461 These functions drop any constraints (not) involving the specified dimensions.
2462 Note that the result depends on the representation of the input.
2466 __isl_give isl_basic_set *isl_basic_set_sample(
2467 __isl_take isl_basic_set *bset);
2468 __isl_give isl_basic_set *isl_set_sample(
2469 __isl_take isl_set *set);
2470 __isl_give isl_basic_map *isl_basic_map_sample(
2471 __isl_take isl_basic_map *bmap);
2472 __isl_give isl_basic_map *isl_map_sample(
2473 __isl_take isl_map *map);
2475 If the input (basic) set or relation is non-empty, then return
2476 a singleton subset of the input. Otherwise, return an empty set.
2478 =item * Optimization
2480 #include <isl/ilp.h>
2481 __isl_give isl_val *isl_basic_set_max_val(
2482 __isl_keep isl_basic_set *bset,
2483 __isl_keep isl_aff *obj);
2484 __isl_give isl_val *isl_set_min_val(
2485 __isl_keep isl_set *set,
2486 __isl_keep isl_aff *obj);
2487 __isl_give isl_val *isl_set_max_val(
2488 __isl_keep isl_set *set,
2489 __isl_keep isl_aff *obj);
2491 Compute the minimum or maximum of the integer affine expression C<obj>
2492 over the points in C<set>, returning the result in C<opt>.
2493 The result is C<NULL> in case of an error, the optimal value in case
2494 there is one, negative infinity or infinity if the problem is unbounded and
2495 NaN if the problem is empty.
2497 =item * Parametric optimization
2499 __isl_give isl_pw_aff *isl_set_dim_min(
2500 __isl_take isl_set *set, int pos);
2501 __isl_give isl_pw_aff *isl_set_dim_max(
2502 __isl_take isl_set *set, int pos);
2503 __isl_give isl_pw_aff *isl_map_dim_max(
2504 __isl_take isl_map *map, int pos);
2506 Compute the minimum or maximum of the given set or output dimension
2507 as a function of the parameters (and input dimensions), but independently
2508 of the other set or output dimensions.
2509 For lexicographic optimization, see L<"Lexicographic Optimization">.
2513 The following functions compute either the set of (rational) coefficient
2514 values of valid constraints for the given set or the set of (rational)
2515 values satisfying the constraints with coefficients from the given set.
2516 Internally, these two sets of functions perform essentially the
2517 same operations, except that the set of coefficients is assumed to
2518 be a cone, while the set of values may be any polyhedron.
2519 The current implementation is based on the Farkas lemma and
2520 Fourier-Motzkin elimination, but this may change or be made optional
2521 in future. In particular, future implementations may use different
2522 dualization algorithms or skip the elimination step.
2524 __isl_give isl_basic_set *isl_basic_set_coefficients(
2525 __isl_take isl_basic_set *bset);
2526 __isl_give isl_basic_set *isl_set_coefficients(
2527 __isl_take isl_set *set);
2528 __isl_give isl_union_set *isl_union_set_coefficients(
2529 __isl_take isl_union_set *bset);
2530 __isl_give isl_basic_set *isl_basic_set_solutions(
2531 __isl_take isl_basic_set *bset);
2532 __isl_give isl_basic_set *isl_set_solutions(
2533 __isl_take isl_set *set);
2534 __isl_give isl_union_set *isl_union_set_solutions(
2535 __isl_take isl_union_set *bset);
2539 __isl_give isl_map *isl_map_fixed_power_val(
2540 __isl_take isl_map *map,
2541 __isl_take isl_val *exp);
2542 __isl_give isl_union_map *
2543 isl_union_map_fixed_power_val(
2544 __isl_take isl_union_map *umap,
2545 __isl_take isl_val *exp);
2547 Compute the given power of C<map>, where C<exp> is assumed to be non-zero.
2548 If the exponent C<exp> is negative, then the -C<exp> th power of the inverse
2549 of C<map> is computed.
2551 __isl_give isl_map *isl_map_power(__isl_take isl_map *map,
2553 __isl_give isl_union_map *isl_union_map_power(
2554 __isl_take isl_union_map *umap, int *exact);
2556 Compute a parametric representation for all positive powers I<k> of C<map>.
2557 The result maps I<k> to a nested relation corresponding to the
2558 I<k>th power of C<map>.
2559 The result may be an overapproximation. If the result is known to be exact,
2560 then C<*exact> is set to C<1>.
2562 =item * Transitive closure
2564 __isl_give isl_map *isl_map_transitive_closure(
2565 __isl_take isl_map *map, int *exact);
2566 __isl_give isl_union_map *isl_union_map_transitive_closure(
2567 __isl_take isl_union_map *umap, int *exact);
2569 Compute the transitive closure of C<map>.
2570 The result may be an overapproximation. If the result is known to be exact,
2571 then C<*exact> is set to C<1>.
2573 =item * Reaching path lengths
2575 __isl_give isl_map *isl_map_reaching_path_lengths(
2576 __isl_take isl_map *map, int *exact);
2578 Compute a relation that maps each element in the range of C<map>
2579 to the lengths of all paths composed of edges in C<map> that
2580 end up in the given element.
2581 The result may be an overapproximation. If the result is known to be exact,
2582 then C<*exact> is set to C<1>.
2583 To compute the I<maximal> path length, the resulting relation
2584 should be postprocessed by C<isl_map_lexmax>.
2585 In particular, if the input relation is a dependence relation
2586 (mapping sources to sinks), then the maximal path length corresponds
2587 to the free schedule.
2588 Note, however, that C<isl_map_lexmax> expects the maximum to be
2589 finite, so if the path lengths are unbounded (possibly due to
2590 the overapproximation), then you will get an error message.
2594 __isl_give isl_basic_set *isl_basic_map_wrap(
2595 __isl_take isl_basic_map *bmap);
2596 __isl_give isl_set *isl_map_wrap(
2597 __isl_take isl_map *map);
2598 __isl_give isl_union_set *isl_union_map_wrap(
2599 __isl_take isl_union_map *umap);
2600 __isl_give isl_basic_map *isl_basic_set_unwrap(
2601 __isl_take isl_basic_set *bset);
2602 __isl_give isl_map *isl_set_unwrap(
2603 __isl_take isl_set *set);
2604 __isl_give isl_union_map *isl_union_set_unwrap(
2605 __isl_take isl_union_set *uset);
2609 Remove any internal structure of domain (and range) of the given
2610 set or relation. If there is any such internal structure in the input,
2611 then the name of the space is also removed.
2613 __isl_give isl_basic_set *isl_basic_set_flatten(
2614 __isl_take isl_basic_set *bset);
2615 __isl_give isl_set *isl_set_flatten(
2616 __isl_take isl_set *set);
2617 __isl_give isl_basic_map *isl_basic_map_flatten_domain(
2618 __isl_take isl_basic_map *bmap);
2619 __isl_give isl_basic_map *isl_basic_map_flatten_range(
2620 __isl_take isl_basic_map *bmap);
2621 __isl_give isl_map *isl_map_flatten_range(
2622 __isl_take isl_map *map);
2623 __isl_give isl_map *isl_map_flatten_domain(
2624 __isl_take isl_map *map);
2625 __isl_give isl_basic_map *isl_basic_map_flatten(
2626 __isl_take isl_basic_map *bmap);
2627 __isl_give isl_map *isl_map_flatten(
2628 __isl_take isl_map *map);
2630 __isl_give isl_map *isl_set_flatten_map(
2631 __isl_take isl_set *set);
2633 The function above constructs a relation
2634 that maps the input set to a flattened version of the set.
2638 Lift the input set to a space with extra dimensions corresponding
2639 to the existentially quantified variables in the input.
2640 In particular, the result lives in a wrapped map where the domain
2641 is the original space and the range corresponds to the original
2642 existentially quantified variables.
2644 __isl_give isl_basic_set *isl_basic_set_lift(
2645 __isl_take isl_basic_set *bset);
2646 __isl_give isl_set *isl_set_lift(
2647 __isl_take isl_set *set);
2648 __isl_give isl_union_set *isl_union_set_lift(
2649 __isl_take isl_union_set *uset);
2651 Given a local space that contains the existentially quantified
2652 variables of a set, a basic relation that, when applied to
2653 a basic set, has essentially the same effect as C<isl_basic_set_lift>,
2654 can be constructed using the following function.
2656 #include <isl/local_space.h>
2657 __isl_give isl_basic_map *isl_local_space_lifting(
2658 __isl_take isl_local_space *ls);
2660 =item * Internal Product
2662 __isl_give isl_basic_map *isl_basic_map_zip(
2663 __isl_take isl_basic_map *bmap);
2664 __isl_give isl_map *isl_map_zip(
2665 __isl_take isl_map *map);
2666 __isl_give isl_union_map *isl_union_map_zip(
2667 __isl_take isl_union_map *umap);
2669 Given a relation with nested relations for domain and range,
2670 interchange the range of the domain with the domain of the range.
2674 __isl_give isl_basic_map *isl_basic_map_curry(
2675 __isl_take isl_basic_map *bmap);
2676 __isl_give isl_basic_map *isl_basic_map_uncurry(
2677 __isl_take isl_basic_map *bmap);
2678 __isl_give isl_map *isl_map_curry(
2679 __isl_take isl_map *map);
2680 __isl_give isl_map *isl_map_uncurry(
2681 __isl_take isl_map *map);
2682 __isl_give isl_union_map *isl_union_map_curry(
2683 __isl_take isl_union_map *umap);
2684 __isl_give isl_union_map *isl_union_map_uncurry(
2685 __isl_take isl_union_map *umap);
2687 Given a relation with a nested relation for domain,
2688 the C<curry> functions
2689 move the range of the nested relation out of the domain
2690 and use it as the domain of a nested relation in the range,
2691 with the original range as range of this nested relation.
2692 The C<uncurry> functions perform the inverse operation.
2694 =item * Aligning parameters
2696 __isl_give isl_basic_set *isl_basic_set_align_params(
2697 __isl_take isl_basic_set *bset,
2698 __isl_take isl_space *model);
2699 __isl_give isl_set *isl_set_align_params(
2700 __isl_take isl_set *set,
2701 __isl_take isl_space *model);
2702 __isl_give isl_basic_map *isl_basic_map_align_params(
2703 __isl_take isl_basic_map *bmap,
2704 __isl_take isl_space *model);
2705 __isl_give isl_map *isl_map_align_params(
2706 __isl_take isl_map *map,
2707 __isl_take isl_space *model);
2709 Change the order of the parameters of the given set or relation
2710 such that the first parameters match those of C<model>.
2711 This may involve the introduction of extra parameters.
2712 All parameters need to be named.
2714 =item * Dimension manipulation
2716 __isl_give isl_basic_set *isl_basic_set_add_dims(
2717 __isl_take isl_basic_set *bset,
2718 enum isl_dim_type type, unsigned n);
2719 __isl_give isl_set *isl_set_add_dims(
2720 __isl_take isl_set *set,
2721 enum isl_dim_type type, unsigned n);
2722 __isl_give isl_map *isl_map_add_dims(
2723 __isl_take isl_map *map,
2724 enum isl_dim_type type, unsigned n);
2725 __isl_give isl_basic_set *isl_basic_set_insert_dims(
2726 __isl_take isl_basic_set *bset,
2727 enum isl_dim_type type, unsigned pos,
2729 __isl_give isl_basic_map *isl_basic_map_insert_dims(
2730 __isl_take isl_basic_map *bmap,
2731 enum isl_dim_type type, unsigned pos,
2733 __isl_give isl_set *isl_set_insert_dims(
2734 __isl_take isl_set *set,
2735 enum isl_dim_type type, unsigned pos, unsigned n);
2736 __isl_give isl_map *isl_map_insert_dims(
2737 __isl_take isl_map *map,
2738 enum isl_dim_type type, unsigned pos, unsigned n);
2739 __isl_give isl_basic_set *isl_basic_set_move_dims(
2740 __isl_take isl_basic_set *bset,
2741 enum isl_dim_type dst_type, unsigned dst_pos,
2742 enum isl_dim_type src_type, unsigned src_pos,
2744 __isl_give isl_basic_map *isl_basic_map_move_dims(
2745 __isl_take isl_basic_map *bmap,
2746 enum isl_dim_type dst_type, unsigned dst_pos,
2747 enum isl_dim_type src_type, unsigned src_pos,
2749 __isl_give isl_set *isl_set_move_dims(
2750 __isl_take isl_set *set,
2751 enum isl_dim_type dst_type, unsigned dst_pos,
2752 enum isl_dim_type src_type, unsigned src_pos,
2754 __isl_give isl_map *isl_map_move_dims(
2755 __isl_take isl_map *map,
2756 enum isl_dim_type dst_type, unsigned dst_pos,
2757 enum isl_dim_type src_type, unsigned src_pos,
2760 It is usually not advisable to directly change the (input or output)
2761 space of a set or a relation as this removes the name and the internal
2762 structure of the space. However, the above functions can be useful
2763 to add new parameters, assuming
2764 C<isl_set_align_params> and C<isl_map_align_params>
2769 =head2 Binary Operations
2771 The two arguments of a binary operation not only need to live
2772 in the same C<isl_ctx>, they currently also need to have
2773 the same (number of) parameters.
2775 =head3 Basic Operations
2779 =item * Intersection
2781 __isl_give isl_basic_set *isl_basic_set_intersect_params(
2782 __isl_take isl_basic_set *bset1,
2783 __isl_take isl_basic_set *bset2);
2784 __isl_give isl_basic_set *isl_basic_set_intersect(
2785 __isl_take isl_basic_set *bset1,
2786 __isl_take isl_basic_set *bset2);
2787 __isl_give isl_set *isl_set_intersect_params(
2788 __isl_take isl_set *set,
2789 __isl_take isl_set *params);
2790 __isl_give isl_set *isl_set_intersect(
2791 __isl_take isl_set *set1,
2792 __isl_take isl_set *set2);
2793 __isl_give isl_union_set *isl_union_set_intersect_params(
2794 __isl_take isl_union_set *uset,
2795 __isl_take isl_set *set);
2796 __isl_give isl_union_map *isl_union_map_intersect_params(
2797 __isl_take isl_union_map *umap,
2798 __isl_take isl_set *set);
2799 __isl_give isl_union_set *isl_union_set_intersect(
2800 __isl_take isl_union_set *uset1,
2801 __isl_take isl_union_set *uset2);
2802 __isl_give isl_basic_map *isl_basic_map_intersect_domain(
2803 __isl_take isl_basic_map *bmap,
2804 __isl_take isl_basic_set *bset);
2805 __isl_give isl_basic_map *isl_basic_map_intersect_range(
2806 __isl_take isl_basic_map *bmap,
2807 __isl_take isl_basic_set *bset);
2808 __isl_give isl_basic_map *isl_basic_map_intersect(
2809 __isl_take isl_basic_map *bmap1,
2810 __isl_take isl_basic_map *bmap2);
2811 __isl_give isl_map *isl_map_intersect_params(
2812 __isl_take isl_map *map,
2813 __isl_take isl_set *params);
2814 __isl_give isl_map *isl_map_intersect_domain(
2815 __isl_take isl_map *map,
2816 __isl_take isl_set *set);
2817 __isl_give isl_map *isl_map_intersect_range(
2818 __isl_take isl_map *map,
2819 __isl_take isl_set *set);
2820 __isl_give isl_map *isl_map_intersect(
2821 __isl_take isl_map *map1,
2822 __isl_take isl_map *map2);
2823 __isl_give isl_union_map *isl_union_map_intersect_domain(
2824 __isl_take isl_union_map *umap,
2825 __isl_take isl_union_set *uset);
2826 __isl_give isl_union_map *isl_union_map_intersect_range(
2827 __isl_take isl_union_map *umap,
2828 __isl_take isl_union_set *uset);
2829 __isl_give isl_union_map *isl_union_map_intersect(
2830 __isl_take isl_union_map *umap1,
2831 __isl_take isl_union_map *umap2);
2833 The second argument to the C<_params> functions needs to be
2834 a parametric (basic) set. For the other functions, a parametric set
2835 for either argument is only allowed if the other argument is
2836 a parametric set as well.
2840 __isl_give isl_set *isl_basic_set_union(
2841 __isl_take isl_basic_set *bset1,
2842 __isl_take isl_basic_set *bset2);
2843 __isl_give isl_map *isl_basic_map_union(
2844 __isl_take isl_basic_map *bmap1,
2845 __isl_take isl_basic_map *bmap2);
2846 __isl_give isl_set *isl_set_union(
2847 __isl_take isl_set *set1,
2848 __isl_take isl_set *set2);
2849 __isl_give isl_map *isl_map_union(
2850 __isl_take isl_map *map1,
2851 __isl_take isl_map *map2);
2852 __isl_give isl_union_set *isl_union_set_union(
2853 __isl_take isl_union_set *uset1,
2854 __isl_take isl_union_set *uset2);
2855 __isl_give isl_union_map *isl_union_map_union(
2856 __isl_take isl_union_map *umap1,
2857 __isl_take isl_union_map *umap2);
2859 =item * Set difference
2861 __isl_give isl_set *isl_set_subtract(
2862 __isl_take isl_set *set1,
2863 __isl_take isl_set *set2);
2864 __isl_give isl_map *isl_map_subtract(
2865 __isl_take isl_map *map1,
2866 __isl_take isl_map *map2);
2867 __isl_give isl_map *isl_map_subtract_domain(
2868 __isl_take isl_map *map,
2869 __isl_take isl_set *dom);
2870 __isl_give isl_map *isl_map_subtract_range(
2871 __isl_take isl_map *map,
2872 __isl_take isl_set *dom);
2873 __isl_give isl_union_set *isl_union_set_subtract(
2874 __isl_take isl_union_set *uset1,
2875 __isl_take isl_union_set *uset2);
2876 __isl_give isl_union_map *isl_union_map_subtract(
2877 __isl_take isl_union_map *umap1,
2878 __isl_take isl_union_map *umap2);
2879 __isl_give isl_union_map *isl_union_map_subtract_domain(
2880 __isl_take isl_union_map *umap,
2881 __isl_take isl_union_set *dom);
2882 __isl_give isl_union_map *isl_union_map_subtract_range(
2883 __isl_take isl_union_map *umap,
2884 __isl_take isl_union_set *dom);
2888 __isl_give isl_basic_set *isl_basic_set_apply(
2889 __isl_take isl_basic_set *bset,
2890 __isl_take isl_basic_map *bmap);
2891 __isl_give isl_set *isl_set_apply(
2892 __isl_take isl_set *set,
2893 __isl_take isl_map *map);
2894 __isl_give isl_union_set *isl_union_set_apply(
2895 __isl_take isl_union_set *uset,
2896 __isl_take isl_union_map *umap);
2897 __isl_give isl_basic_map *isl_basic_map_apply_domain(
2898 __isl_take isl_basic_map *bmap1,
2899 __isl_take isl_basic_map *bmap2);
2900 __isl_give isl_basic_map *isl_basic_map_apply_range(
2901 __isl_take isl_basic_map *bmap1,
2902 __isl_take isl_basic_map *bmap2);
2903 __isl_give isl_map *isl_map_apply_domain(
2904 __isl_take isl_map *map1,
2905 __isl_take isl_map *map2);
2906 __isl_give isl_union_map *isl_union_map_apply_domain(
2907 __isl_take isl_union_map *umap1,
2908 __isl_take isl_union_map *umap2);
2909 __isl_give isl_map *isl_map_apply_range(
2910 __isl_take isl_map *map1,
2911 __isl_take isl_map *map2);
2912 __isl_give isl_union_map *isl_union_map_apply_range(
2913 __isl_take isl_union_map *umap1,
2914 __isl_take isl_union_map *umap2);
2918 __isl_give isl_basic_set *
2919 isl_basic_set_preimage_multi_aff(
2920 __isl_take isl_basic_set *bset,
2921 __isl_take isl_multi_aff *ma);
2922 __isl_give isl_set *isl_set_preimage_multi_aff(
2923 __isl_take isl_set *set,
2924 __isl_take isl_multi_aff *ma);
2925 __isl_give isl_set *isl_set_preimage_pw_multi_aff(
2926 __isl_take isl_set *set,
2927 __isl_take isl_pw_multi_aff *pma);
2928 __isl_give isl_basic_map *
2929 isl_basic_map_preimage_domain_multi_aff(
2930 __isl_take isl_basic_map *bmap,
2931 __isl_take isl_multi_aff *ma);
2932 __isl_give isl_map *isl_map_preimage_domain_multi_aff(
2933 __isl_take isl_map *map,
2934 __isl_take isl_multi_aff *ma);
2935 __isl_give isl_union_map *
2936 isl_union_map_preimage_domain_multi_aff(
2937 __isl_take isl_union_map *umap,
2938 __isl_take isl_multi_aff *ma);
2939 __isl_give isl_basic_map *
2940 isl_basic_map_preimage_range_multi_aff(
2941 __isl_take isl_basic_map *bmap,
2942 __isl_take isl_multi_aff *ma);
2944 These functions compute the preimage of the given set or map domain/range under
2945 the given function. In other words, the expression is plugged
2946 into the set description or into the domain/range of the map.
2947 Objects of types C<isl_multi_aff> and C<isl_pw_multi_aff> are described in
2948 L</"Piecewise Multiple Quasi Affine Expressions">.
2950 =item * Cartesian Product
2952 __isl_give isl_set *isl_set_product(
2953 __isl_take isl_set *set1,
2954 __isl_take isl_set *set2);
2955 __isl_give isl_union_set *isl_union_set_product(
2956 __isl_take isl_union_set *uset1,
2957 __isl_take isl_union_set *uset2);
2958 __isl_give isl_basic_map *isl_basic_map_domain_product(
2959 __isl_take isl_basic_map *bmap1,
2960 __isl_take isl_basic_map *bmap2);
2961 __isl_give isl_basic_map *isl_basic_map_range_product(
2962 __isl_take isl_basic_map *bmap1,
2963 __isl_take isl_basic_map *bmap2);
2964 __isl_give isl_basic_map *isl_basic_map_product(
2965 __isl_take isl_basic_map *bmap1,
2966 __isl_take isl_basic_map *bmap2);
2967 __isl_give isl_map *isl_map_domain_product(
2968 __isl_take isl_map *map1,
2969 __isl_take isl_map *map2);
2970 __isl_give isl_map *isl_map_range_product(
2971 __isl_take isl_map *map1,
2972 __isl_take isl_map *map2);
2973 __isl_give isl_union_map *isl_union_map_domain_product(
2974 __isl_take isl_union_map *umap1,
2975 __isl_take isl_union_map *umap2);
2976 __isl_give isl_union_map *isl_union_map_range_product(
2977 __isl_take isl_union_map *umap1,
2978 __isl_take isl_union_map *umap2);
2979 __isl_give isl_map *isl_map_product(
2980 __isl_take isl_map *map1,
2981 __isl_take isl_map *map2);
2982 __isl_give isl_union_map *isl_union_map_product(
2983 __isl_take isl_union_map *umap1,
2984 __isl_take isl_union_map *umap2);
2986 The above functions compute the cross product of the given
2987 sets or relations. The domains and ranges of the results
2988 are wrapped maps between domains and ranges of the inputs.
2989 To obtain a ``flat'' product, use the following functions
2992 __isl_give isl_basic_set *isl_basic_set_flat_product(
2993 __isl_take isl_basic_set *bset1,
2994 __isl_take isl_basic_set *bset2);
2995 __isl_give isl_set *isl_set_flat_product(
2996 __isl_take isl_set *set1,
2997 __isl_take isl_set *set2);
2998 __isl_give isl_basic_map *isl_basic_map_flat_range_product(
2999 __isl_take isl_basic_map *bmap1,
3000 __isl_take isl_basic_map *bmap2);
3001 __isl_give isl_map *isl_map_flat_domain_product(
3002 __isl_take isl_map *map1,
3003 __isl_take isl_map *map2);
3004 __isl_give isl_map *isl_map_flat_range_product(
3005 __isl_take isl_map *map1,
3006 __isl_take isl_map *map2);
3007 __isl_give isl_union_map *isl_union_map_flat_range_product(
3008 __isl_take isl_union_map *umap1,
3009 __isl_take isl_union_map *umap2);
3010 __isl_give isl_basic_map *isl_basic_map_flat_product(
3011 __isl_take isl_basic_map *bmap1,
3012 __isl_take isl_basic_map *bmap2);
3013 __isl_give isl_map *isl_map_flat_product(
3014 __isl_take isl_map *map1,
3015 __isl_take isl_map *map2);
3017 =item * Simplification
3019 __isl_give isl_basic_set *isl_basic_set_gist(
3020 __isl_take isl_basic_set *bset,
3021 __isl_take isl_basic_set *context);
3022 __isl_give isl_set *isl_set_gist(__isl_take isl_set *set,
3023 __isl_take isl_set *context);
3024 __isl_give isl_set *isl_set_gist_params(
3025 __isl_take isl_set *set,
3026 __isl_take isl_set *context);
3027 __isl_give isl_union_set *isl_union_set_gist(
3028 __isl_take isl_union_set *uset,
3029 __isl_take isl_union_set *context);
3030 __isl_give isl_union_set *isl_union_set_gist_params(
3031 __isl_take isl_union_set *uset,
3032 __isl_take isl_set *set);
3033 __isl_give isl_basic_map *isl_basic_map_gist(
3034 __isl_take isl_basic_map *bmap,
3035 __isl_take isl_basic_map *context);
3036 __isl_give isl_map *isl_map_gist(__isl_take isl_map *map,
3037 __isl_take isl_map *context);
3038 __isl_give isl_map *isl_map_gist_params(
3039 __isl_take isl_map *map,
3040 __isl_take isl_set *context);
3041 __isl_give isl_map *isl_map_gist_domain(
3042 __isl_take isl_map *map,
3043 __isl_take isl_set *context);
3044 __isl_give isl_map *isl_map_gist_range(
3045 __isl_take isl_map *map,
3046 __isl_take isl_set *context);
3047 __isl_give isl_union_map *isl_union_map_gist(
3048 __isl_take isl_union_map *umap,
3049 __isl_take isl_union_map *context);
3050 __isl_give isl_union_map *isl_union_map_gist_params(
3051 __isl_take isl_union_map *umap,
3052 __isl_take isl_set *set);
3053 __isl_give isl_union_map *isl_union_map_gist_domain(
3054 __isl_take isl_union_map *umap,
3055 __isl_take isl_union_set *uset);
3056 __isl_give isl_union_map *isl_union_map_gist_range(
3057 __isl_take isl_union_map *umap,
3058 __isl_take isl_union_set *uset);
3060 The gist operation returns a set or relation that has the
3061 same intersection with the context as the input set or relation.
3062 Any implicit equality in the intersection is made explicit in the result,
3063 while all inequalities that are redundant with respect to the intersection
3065 In case of union sets and relations, the gist operation is performed
3070 =head3 Lexicographic Optimization
3072 Given a (basic) set C<set> (or C<bset>) and a zero-dimensional domain C<dom>,
3073 the following functions
3074 compute a set that contains the lexicographic minimum or maximum
3075 of the elements in C<set> (or C<bset>) for those values of the parameters
3076 that satisfy C<dom>.
3077 If C<empty> is not C<NULL>, then C<*empty> is assigned a set
3078 that contains the parameter values in C<dom> for which C<set> (or C<bset>)
3080 In other words, the union of the parameter values
3081 for which the result is non-empty and of C<*empty>
3084 __isl_give isl_set *isl_basic_set_partial_lexmin(
3085 __isl_take isl_basic_set *bset,
3086 __isl_take isl_basic_set *dom,
3087 __isl_give isl_set **empty);
3088 __isl_give isl_set *isl_basic_set_partial_lexmax(
3089 __isl_take isl_basic_set *bset,
3090 __isl_take isl_basic_set *dom,
3091 __isl_give isl_set **empty);
3092 __isl_give isl_set *isl_set_partial_lexmin(
3093 __isl_take isl_set *set, __isl_take isl_set *dom,
3094 __isl_give isl_set **empty);
3095 __isl_give isl_set *isl_set_partial_lexmax(
3096 __isl_take isl_set *set, __isl_take isl_set *dom,
3097 __isl_give isl_set **empty);
3099 Given a (basic) set C<set> (or C<bset>), the following functions simply
3100 return a set containing the lexicographic minimum or maximum
3101 of the elements in C<set> (or C<bset>).
3102 In case of union sets, the optimum is computed per space.
3104 __isl_give isl_set *isl_basic_set_lexmin(
3105 __isl_take isl_basic_set *bset);
3106 __isl_give isl_set *isl_basic_set_lexmax(
3107 __isl_take isl_basic_set *bset);
3108 __isl_give isl_set *isl_set_lexmin(
3109 __isl_take isl_set *set);
3110 __isl_give isl_set *isl_set_lexmax(
3111 __isl_take isl_set *set);
3112 __isl_give isl_union_set *isl_union_set_lexmin(
3113 __isl_take isl_union_set *uset);
3114 __isl_give isl_union_set *isl_union_set_lexmax(
3115 __isl_take isl_union_set *uset);
3117 Given a (basic) relation C<map> (or C<bmap>) and a domain C<dom>,
3118 the following functions
3119 compute a relation that maps each element of C<dom>
3120 to the single lexicographic minimum or maximum
3121 of the elements that are associated to that same
3122 element in C<map> (or C<bmap>).
3123 If C<empty> is not C<NULL>, then C<*empty> is assigned a set
3124 that contains the elements in C<dom> that do not map
3125 to any elements in C<map> (or C<bmap>).
3126 In other words, the union of the domain of the result and of C<*empty>
3129 __isl_give isl_map *isl_basic_map_partial_lexmax(
3130 __isl_take isl_basic_map *bmap,
3131 __isl_take isl_basic_set *dom,
3132 __isl_give isl_set **empty);
3133 __isl_give isl_map *isl_basic_map_partial_lexmin(
3134 __isl_take isl_basic_map *bmap,
3135 __isl_take isl_basic_set *dom,
3136 __isl_give isl_set **empty);
3137 __isl_give isl_map *isl_map_partial_lexmax(
3138 __isl_take isl_map *map, __isl_take isl_set *dom,
3139 __isl_give isl_set **empty);
3140 __isl_give isl_map *isl_map_partial_lexmin(
3141 __isl_take isl_map *map, __isl_take isl_set *dom,
3142 __isl_give isl_set **empty);
3144 Given a (basic) map C<map> (or C<bmap>), the following functions simply
3145 return a map mapping each element in the domain of
3146 C<map> (or C<bmap>) to the lexicographic minimum or maximum
3147 of all elements associated to that element.
3148 In case of union relations, the optimum is computed per space.
3150 __isl_give isl_map *isl_basic_map_lexmin(
3151 __isl_take isl_basic_map *bmap);
3152 __isl_give isl_map *isl_basic_map_lexmax(
3153 __isl_take isl_basic_map *bmap);
3154 __isl_give isl_map *isl_map_lexmin(
3155 __isl_take isl_map *map);
3156 __isl_give isl_map *isl_map_lexmax(
3157 __isl_take isl_map *map);
3158 __isl_give isl_union_map *isl_union_map_lexmin(
3159 __isl_take isl_union_map *umap);
3160 __isl_give isl_union_map *isl_union_map_lexmax(
3161 __isl_take isl_union_map *umap);
3163 The following functions return their result in the form of
3164 a piecewise multi-affine expression
3165 (See L<"Piecewise Multiple Quasi Affine Expressions">),
3166 but are otherwise equivalent to the corresponding functions
3167 returning a basic set or relation.
3169 __isl_give isl_pw_multi_aff *
3170 isl_basic_map_lexmin_pw_multi_aff(
3171 __isl_take isl_basic_map *bmap);
3172 __isl_give isl_pw_multi_aff *
3173 isl_basic_set_partial_lexmin_pw_multi_aff(
3174 __isl_take isl_basic_set *bset,
3175 __isl_take isl_basic_set *dom,
3176 __isl_give isl_set **empty);
3177 __isl_give isl_pw_multi_aff *
3178 isl_basic_set_partial_lexmax_pw_multi_aff(
3179 __isl_take isl_basic_set *bset,
3180 __isl_take isl_basic_set *dom,
3181 __isl_give isl_set **empty);
3182 __isl_give isl_pw_multi_aff *
3183 isl_basic_map_partial_lexmin_pw_multi_aff(
3184 __isl_take isl_basic_map *bmap,
3185 __isl_take isl_basic_set *dom,
3186 __isl_give isl_set **empty);
3187 __isl_give isl_pw_multi_aff *
3188 isl_basic_map_partial_lexmax_pw_multi_aff(
3189 __isl_take isl_basic_map *bmap,
3190 __isl_take isl_basic_set *dom,
3191 __isl_give isl_set **empty);
3192 __isl_give isl_pw_multi_aff *isl_set_lexmin_pw_multi_aff(
3193 __isl_take isl_set *set);
3194 __isl_give isl_pw_multi_aff *isl_set_lexmax_pw_multi_aff(
3195 __isl_take isl_set *set);
3196 __isl_give isl_pw_multi_aff *isl_map_lexmin_pw_multi_aff(
3197 __isl_take isl_map *map);
3198 __isl_give isl_pw_multi_aff *isl_map_lexmax_pw_multi_aff(
3199 __isl_take isl_map *map);
3203 Lists are defined over several element types, including
3204 C<isl_val>, C<isl_id>, C<isl_aff>, C<isl_pw_aff>, C<isl_constraint>,
3205 C<isl_basic_set>, C<isl_set>, C<isl_ast_expr> and C<isl_ast_node>.
3206 Here we take lists of C<isl_set>s as an example.
3207 Lists can be created, copied, modified and freed using the following functions.
3209 #include <isl/list.h>
3210 __isl_give isl_set_list *isl_set_list_from_set(
3211 __isl_take isl_set *el);
3212 __isl_give isl_set_list *isl_set_list_alloc(
3213 isl_ctx *ctx, int n);
3214 __isl_give isl_set_list *isl_set_list_copy(
3215 __isl_keep isl_set_list *list);
3216 __isl_give isl_set_list *isl_set_list_insert(
3217 __isl_take isl_set_list *list, unsigned pos,
3218 __isl_take isl_set *el);
3219 __isl_give isl_set_list *isl_set_list_add(
3220 __isl_take isl_set_list *list,
3221 __isl_take isl_set *el);
3222 __isl_give isl_set_list *isl_set_list_drop(
3223 __isl_take isl_set_list *list,
3224 unsigned first, unsigned n);
3225 __isl_give isl_set_list *isl_set_list_set_set(
3226 __isl_take isl_set_list *list, int index,
3227 __isl_take isl_set *set);
3228 __isl_give isl_set_list *isl_set_list_concat(
3229 __isl_take isl_set_list *list1,
3230 __isl_take isl_set_list *list2);
3231 __isl_give isl_set_list *isl_set_list_sort(
3232 __isl_take isl_set_list *list,
3233 int (*cmp)(__isl_keep isl_set *a,
3234 __isl_keep isl_set *b, void *user),
3236 void *isl_set_list_free(__isl_take isl_set_list *list);
3238 C<isl_set_list_alloc> creates an empty list with a capacity for
3239 C<n> elements. C<isl_set_list_from_set> creates a list with a single
3242 Lists can be inspected using the following functions.
3244 #include <isl/list.h>
3245 isl_ctx *isl_set_list_get_ctx(__isl_keep isl_set_list *list);
3246 int isl_set_list_n_set(__isl_keep isl_set_list *list);
3247 __isl_give isl_set *isl_set_list_get_set(
3248 __isl_keep isl_set_list *list, int index);
3249 int isl_set_list_foreach(__isl_keep isl_set_list *list,
3250 int (*fn)(__isl_take isl_set *el, void *user),
3252 int isl_set_list_foreach_scc(__isl_keep isl_set_list *list,
3253 int (*follows)(__isl_keep isl_set *a,
3254 __isl_keep isl_set *b, void *user),
3256 int (*fn)(__isl_take isl_set *el, void *user),
3259 The function C<isl_set_list_foreach_scc> calls C<fn> on each of the
3260 strongly connected components of the graph with as vertices the elements
3261 of C<list> and a directed edge from vertex C<b> to vertex C<a>
3262 iff C<follows(a, b)> returns C<1>. The callbacks C<follows> and C<fn>
3263 should return C<-1> on error.
3265 Lists can be printed using
3267 #include <isl/list.h>
3268 __isl_give isl_printer *isl_printer_print_set_list(
3269 __isl_take isl_printer *p,
3270 __isl_keep isl_set_list *list);
3272 =head2 Multiple Values
3274 An C<isl_multi_val> object represents a sequence of zero or more values,
3275 living in a set space.
3277 An C<isl_multi_val> can be constructed from an C<isl_val_list>
3278 using the following function
3280 #include <isl/val.h>
3281 __isl_give isl_multi_val *isl_multi_val_from_val_list(
3282 __isl_take isl_space *space,
3283 __isl_take isl_val_list *list);
3285 The zero multiple value (with value zero for each set dimension)
3286 can be created using the following function.
3288 #include <isl/val.h>
3289 __isl_give isl_multi_val *isl_multi_val_zero(
3290 __isl_take isl_space *space);
3292 Multiple values can be copied and freed using
3294 #include <isl/val.h>
3295 __isl_give isl_multi_val *isl_multi_val_copy(
3296 __isl_keep isl_multi_val *mv);
3297 void *isl_multi_val_free(__isl_take isl_multi_val *mv);
3299 They can be inspected using
3301 #include <isl/val.h>
3302 isl_ctx *isl_multi_val_get_ctx(
3303 __isl_keep isl_multi_val *mv);
3304 unsigned isl_multi_val_dim(__isl_keep isl_multi_val *mv,
3305 enum isl_dim_type type);
3306 __isl_give isl_val *isl_multi_val_get_val(
3307 __isl_keep isl_multi_val *mv, int pos);
3308 int isl_multi_val_find_dim_by_id(
3309 __isl_keep isl_multi_val *mv,
3310 enum isl_dim_type type, __isl_keep isl_id *id);
3311 __isl_give isl_id *isl_multi_val_get_dim_id(
3312 __isl_keep isl_multi_val *mv,
3313 enum isl_dim_type type, unsigned pos);
3314 const char *isl_multi_val_get_tuple_name(
3315 __isl_keep isl_multi_val *mv,
3316 enum isl_dim_type type);
3317 int isl_multi_val_has_tuple_id(__isl_keep isl_multi_val *mv,
3318 enum isl_dim_type type);
3319 __isl_give isl_id *isl_multi_val_get_tuple_id(
3320 __isl_keep isl_multi_val *mv,
3321 enum isl_dim_type type);
3322 __isl_give isl_multi_val *isl_multi_val_reset_tuple_id(
3323 __isl_take isl_multi_val *mv,
3324 enum isl_dim_type type);
3326 They can be modified using
3328 #include <isl/val.h>
3329 __isl_give isl_multi_val *isl_multi_val_set_val(
3330 __isl_take isl_multi_val *mv, int pos,
3331 __isl_take isl_val *val);
3332 __isl_give isl_multi_val *isl_multi_val_set_dim_name(
3333 __isl_take isl_multi_val *mv,
3334 enum isl_dim_type type, unsigned pos, const char *s);
3335 __isl_give isl_multi_val *isl_multi_val_set_dim_id(
3336 __isl_take isl_multi_val *mv,
3337 enum isl_dim_type type, unsigned pos,
3338 __isl_take isl_id *id);
3339 __isl_give isl_multi_val *isl_multi_val_set_tuple_name(
3340 __isl_take isl_multi_val *mv,
3341 enum isl_dim_type type, const char *s);
3342 __isl_give isl_multi_val *isl_multi_val_set_tuple_id(
3343 __isl_take isl_multi_val *mv,
3344 enum isl_dim_type type, __isl_take isl_id *id);
3346 __isl_give isl_multi_val *isl_multi_val_insert_dims(
3347 __isl_take isl_multi_val *mv,
3348 enum isl_dim_type type, unsigned first, unsigned n);
3349 __isl_give isl_multi_val *isl_multi_val_add_dims(
3350 __isl_take isl_multi_val *mv,
3351 enum isl_dim_type type, unsigned n);
3352 __isl_give isl_multi_val *isl_multi_val_drop_dims(
3353 __isl_take isl_multi_val *mv,
3354 enum isl_dim_type type, unsigned first, unsigned n);
3358 #include <isl/val.h>
3359 __isl_give isl_multi_val *isl_multi_val_align_params(
3360 __isl_take isl_multi_val *mv,
3361 __isl_take isl_space *model);
3362 __isl_give isl_multi_val *isl_multi_val_from_range(
3363 __isl_take isl_multi_val *mv);
3364 __isl_give isl_multi_val *isl_multi_val_range_splice(
3365 __isl_take isl_multi_val *mv1, unsigned pos,
3366 __isl_take isl_multi_val *mv2);
3367 __isl_give isl_multi_val *isl_multi_val_range_product(
3368 __isl_take isl_multi_val *mv1,
3369 __isl_take isl_multi_val *mv2);
3370 __isl_give isl_multi_val *isl_multi_val_flat_range_product(
3371 __isl_take isl_multi_val *mv1,
3372 __isl_take isl_multi_aff *mv2);
3373 __isl_give isl_multi_val *isl_multi_val_add_val(
3374 __isl_take isl_multi_val *mv,
3375 __isl_take isl_val *v);
3376 __isl_give isl_multi_val *isl_multi_val_mod_val(
3377 __isl_take isl_multi_val *mv,
3378 __isl_take isl_val *v);
3379 __isl_give isl_multi_val *isl_multi_val_scale_val(
3380 __isl_take isl_multi_val *mv,
3381 __isl_take isl_val *v);
3382 __isl_give isl_multi_val *isl_multi_val_scale_multi_val(
3383 __isl_take isl_multi_val *mv1,
3384 __isl_take isl_multi_val *mv2);
3385 __isl_give isl_multi_val *
3386 isl_multi_val_scale_down_multi_val(
3387 __isl_take isl_multi_val *mv1,
3388 __isl_take isl_multi_val *mv2);
3390 A multiple value can be printed using
3392 __isl_give isl_printer *isl_printer_print_multi_val(
3393 __isl_take isl_printer *p,
3394 __isl_keep isl_multi_val *mv);
3398 Vectors can be created, copied and freed using the following functions.
3400 #include <isl/vec.h>
3401 __isl_give isl_vec *isl_vec_alloc(isl_ctx *ctx,
3403 __isl_give isl_vec *isl_vec_copy(__isl_keep isl_vec *vec);
3404 void *isl_vec_free(__isl_take isl_vec *vec);
3406 Note that the elements of a newly created vector may have arbitrary values.
3407 The elements can be changed and inspected using the following functions.
3409 isl_ctx *isl_vec_get_ctx(__isl_keep isl_vec *vec);
3410 int isl_vec_size(__isl_keep isl_vec *vec);
3411 __isl_give isl_val *isl_vec_get_element_val(
3412 __isl_keep isl_vec *vec, int pos);
3413 __isl_give isl_vec *isl_vec_set_element_si(
3414 __isl_take isl_vec *vec, int pos, int v);
3415 __isl_give isl_vec *isl_vec_set_element_val(
3416 __isl_take isl_vec *vec, int pos,
3417 __isl_take isl_val *v);
3418 __isl_give isl_vec *isl_vec_set_si(__isl_take isl_vec *vec,
3420 __isl_give isl_vec *isl_vec_set_val(
3421 __isl_take isl_vec *vec, __isl_take isl_val *v);
3422 int isl_vec_cmp_element(__isl_keep isl_vec *vec1,
3423 __isl_keep isl_vec *vec2, int pos);
3425 C<isl_vec_get_element> will return a negative value if anything went wrong.
3426 In that case, the value of C<*v> is undefined.
3428 The following function can be used to concatenate two vectors.
3430 __isl_give isl_vec *isl_vec_concat(__isl_take isl_vec *vec1,
3431 __isl_take isl_vec *vec2);
3435 Matrices can be created, copied and freed using the following functions.
3437 #include <isl/mat.h>
3438 __isl_give isl_mat *isl_mat_alloc(isl_ctx *ctx,
3439 unsigned n_row, unsigned n_col);
3440 __isl_give isl_mat *isl_mat_copy(__isl_keep isl_mat *mat);
3441 void *isl_mat_free(__isl_take isl_mat *mat);
3443 Note that the elements of a newly created matrix may have arbitrary values.
3444 The elements can be changed and inspected using the following functions.
3446 isl_ctx *isl_mat_get_ctx(__isl_keep isl_mat *mat);
3447 int isl_mat_rows(__isl_keep isl_mat *mat);
3448 int isl_mat_cols(__isl_keep isl_mat *mat);
3449 __isl_give isl_val *isl_mat_get_element_val(
3450 __isl_keep isl_mat *mat, int row, int col);
3451 __isl_give isl_mat *isl_mat_set_element_si(__isl_take isl_mat *mat,
3452 int row, int col, int v);
3453 __isl_give isl_mat *isl_mat_set_element_val(
3454 __isl_take isl_mat *mat, int row, int col,
3455 __isl_take isl_val *v);
3457 C<isl_mat_get_element> will return a negative value if anything went wrong.
3458 In that case, the value of C<*v> is undefined.
3460 The following function can be used to compute the (right) inverse
3461 of a matrix, i.e., a matrix such that the product of the original
3462 and the inverse (in that order) is a multiple of the identity matrix.
3463 The input matrix is assumed to be of full row-rank.
3465 __isl_give isl_mat *isl_mat_right_inverse(__isl_take isl_mat *mat);
3467 The following function can be used to compute the (right) kernel
3468 (or null space) of a matrix, i.e., a matrix such that the product of
3469 the original and the kernel (in that order) is the zero matrix.
3471 __isl_give isl_mat *isl_mat_right_kernel(__isl_take isl_mat *mat);
3473 =head2 Piecewise Quasi Affine Expressions
3475 The zero quasi affine expression or the quasi affine expression
3476 that is equal to a given value or
3477 a specified dimension on a given domain can be created using
3479 __isl_give isl_aff *isl_aff_zero_on_domain(
3480 __isl_take isl_local_space *ls);
3481 __isl_give isl_pw_aff *isl_pw_aff_zero_on_domain(
3482 __isl_take isl_local_space *ls);
3483 __isl_give isl_aff *isl_aff_val_on_domain(
3484 __isl_take isl_local_space *ls,
3485 __isl_take isl_val *val);
3486 __isl_give isl_aff *isl_aff_var_on_domain(
3487 __isl_take isl_local_space *ls,
3488 enum isl_dim_type type, unsigned pos);
3489 __isl_give isl_pw_aff *isl_pw_aff_var_on_domain(
3490 __isl_take isl_local_space *ls,
3491 enum isl_dim_type type, unsigned pos);
3493 Note that the space in which the resulting objects live is a map space
3494 with the given space as domain and a one-dimensional range.
3496 An empty piecewise quasi affine expression (one with no cells)
3497 or a piecewise quasi affine expression with a single cell can
3498 be created using the following functions.
3500 #include <isl/aff.h>
3501 __isl_give isl_pw_aff *isl_pw_aff_empty(
3502 __isl_take isl_space *space);
3503 __isl_give isl_pw_aff *isl_pw_aff_alloc(
3504 __isl_take isl_set *set, __isl_take isl_aff *aff);
3505 __isl_give isl_pw_aff *isl_pw_aff_from_aff(
3506 __isl_take isl_aff *aff);
3508 A piecewise quasi affine expression that is equal to 1 on a set
3509 and 0 outside the set can be created using the following function.
3511 #include <isl/aff.h>
3512 __isl_give isl_pw_aff *isl_set_indicator_function(
3513 __isl_take isl_set *set);
3515 Quasi affine expressions can be copied and freed using
3517 #include <isl/aff.h>
3518 __isl_give isl_aff *isl_aff_copy(__isl_keep isl_aff *aff);
3519 void *isl_aff_free(__isl_take isl_aff *aff);
3521 __isl_give isl_pw_aff *isl_pw_aff_copy(
3522 __isl_keep isl_pw_aff *pwaff);
3523 void *isl_pw_aff_free(__isl_take isl_pw_aff *pwaff);
3525 A (rational) bound on a dimension can be extracted from an C<isl_constraint>
3526 using the following function. The constraint is required to have
3527 a non-zero coefficient for the specified dimension.
3529 #include <isl/constraint.h>
3530 __isl_give isl_aff *isl_constraint_get_bound(
3531 __isl_keep isl_constraint *constraint,
3532 enum isl_dim_type type, int pos);
3534 The entire affine expression of the constraint can also be extracted
3535 using the following function.
3537 #include <isl/constraint.h>
3538 __isl_give isl_aff *isl_constraint_get_aff(
3539 __isl_keep isl_constraint *constraint);
3541 Conversely, an equality constraint equating
3542 the affine expression to zero or an inequality constraint enforcing
3543 the affine expression to be non-negative, can be constructed using
3545 __isl_give isl_constraint *isl_equality_from_aff(
3546 __isl_take isl_aff *aff);
3547 __isl_give isl_constraint *isl_inequality_from_aff(
3548 __isl_take isl_aff *aff);
3550 The expression can be inspected using
3552 #include <isl/aff.h>
3553 isl_ctx *isl_aff_get_ctx(__isl_keep isl_aff *aff);
3554 int isl_aff_dim(__isl_keep isl_aff *aff,
3555 enum isl_dim_type type);
3556 __isl_give isl_local_space *isl_aff_get_domain_local_space(
3557 __isl_keep isl_aff *aff);
3558 __isl_give isl_local_space *isl_aff_get_local_space(
3559 __isl_keep isl_aff *aff);
3560 const char *isl_aff_get_dim_name(__isl_keep isl_aff *aff,
3561 enum isl_dim_type type, unsigned pos);
3562 const char *isl_pw_aff_get_dim_name(
3563 __isl_keep isl_pw_aff *pa,
3564 enum isl_dim_type type, unsigned pos);
3565 int isl_pw_aff_has_dim_id(__isl_keep isl_pw_aff *pa,
3566 enum isl_dim_type type, unsigned pos);
3567 __isl_give isl_id *isl_pw_aff_get_dim_id(
3568 __isl_keep isl_pw_aff *pa,
3569 enum isl_dim_type type, unsigned pos);
3570 __isl_give isl_id *isl_pw_aff_get_tuple_id(
3571 __isl_keep isl_pw_aff *pa,
3572 enum isl_dim_type type);
3573 __isl_give isl_val *isl_aff_get_constant_val(
3574 __isl_keep isl_aff *aff);
3575 __isl_give isl_val *isl_aff_get_coefficient_val(
3576 __isl_keep isl_aff *aff,
3577 enum isl_dim_type type, int pos);
3578 __isl_give isl_val *isl_aff_get_denominator_val(
3579 __isl_keep isl_aff *aff);
3580 __isl_give isl_aff *isl_aff_get_div(
3581 __isl_keep isl_aff *aff, int pos);
3583 int isl_pw_aff_n_piece(__isl_keep isl_pw_aff *pwaff);
3584 int isl_pw_aff_foreach_piece(__isl_keep isl_pw_aff *pwaff,
3585 int (*fn)(__isl_take isl_set *set,
3586 __isl_take isl_aff *aff,
3587 void *user), void *user);
3589 int isl_aff_is_cst(__isl_keep isl_aff *aff);
3590 int isl_pw_aff_is_cst(__isl_keep isl_pw_aff *pwaff);
3592 int isl_aff_involves_dims(__isl_keep isl_aff *aff,
3593 enum isl_dim_type type, unsigned first, unsigned n);
3594 int isl_pw_aff_involves_dims(__isl_keep isl_pw_aff *pwaff,
3595 enum isl_dim_type type, unsigned first, unsigned n);
3597 isl_ctx *isl_pw_aff_get_ctx(__isl_keep isl_pw_aff *pwaff);
3598 unsigned isl_pw_aff_dim(__isl_keep isl_pw_aff *pwaff,
3599 enum isl_dim_type type);
3600 int isl_pw_aff_is_empty(__isl_keep isl_pw_aff *pwaff);
3602 It can be modified using
3604 #include <isl/aff.h>
3605 __isl_give isl_pw_aff *isl_pw_aff_set_tuple_id(
3606 __isl_take isl_pw_aff *pwaff,
3607 enum isl_dim_type type, __isl_take isl_id *id);
3608 __isl_give isl_aff *isl_aff_set_dim_name(
3609 __isl_take isl_aff *aff, enum isl_dim_type type,
3610 unsigned pos, const char *s);
3611 __isl_give isl_aff *isl_aff_set_dim_id(
3612 __isl_take isl_aff *aff, enum isl_dim_type type,
3613 unsigned pos, __isl_take isl_id *id);
3614 __isl_give isl_pw_aff *isl_pw_aff_set_dim_id(
3615 __isl_take isl_pw_aff *pma,
3616 enum isl_dim_type type, unsigned pos,
3617 __isl_take isl_id *id);
3618 __isl_give isl_aff *isl_aff_set_constant_si(
3619 __isl_take isl_aff *aff, int v);
3620 __isl_give isl_aff *isl_aff_set_constant_val(
3621 __isl_take isl_aff *aff, __isl_take isl_val *v);
3622 __isl_give isl_aff *isl_aff_set_coefficient_si(
3623 __isl_take isl_aff *aff,
3624 enum isl_dim_type type, int pos, int v);
3625 __isl_give isl_aff *isl_aff_set_coefficient_val(
3626 __isl_take isl_aff *aff,
3627 enum isl_dim_type type, int pos,
3628 __isl_take isl_val *v);
3630 __isl_give isl_aff *isl_aff_add_constant_si(
3631 __isl_take isl_aff *aff, int v);
3632 __isl_give isl_aff *isl_aff_add_constant_val(
3633 __isl_take isl_aff *aff, __isl_take isl_val *v);
3634 __isl_give isl_aff *isl_aff_add_constant_num_si(
3635 __isl_take isl_aff *aff, int v);
3636 __isl_give isl_aff *isl_aff_add_coefficient_si(
3637 __isl_take isl_aff *aff,
3638 enum isl_dim_type type, int pos, int v);
3639 __isl_give isl_aff *isl_aff_add_coefficient_val(
3640 __isl_take isl_aff *aff,
3641 enum isl_dim_type type, int pos,
3642 __isl_take isl_val *v);
3644 __isl_give isl_aff *isl_aff_insert_dims(
3645 __isl_take isl_aff *aff,
3646 enum isl_dim_type type, unsigned first, unsigned n);
3647 __isl_give isl_pw_aff *isl_pw_aff_insert_dims(
3648 __isl_take isl_pw_aff *pwaff,
3649 enum isl_dim_type type, unsigned first, unsigned n);
3650 __isl_give isl_aff *isl_aff_add_dims(
3651 __isl_take isl_aff *aff,
3652 enum isl_dim_type type, unsigned n);
3653 __isl_give isl_pw_aff *isl_pw_aff_add_dims(
3654 __isl_take isl_pw_aff *pwaff,
3655 enum isl_dim_type type, unsigned n);
3656 __isl_give isl_aff *isl_aff_drop_dims(
3657 __isl_take isl_aff *aff,
3658 enum isl_dim_type type, unsigned first, unsigned n);
3659 __isl_give isl_pw_aff *isl_pw_aff_drop_dims(
3660 __isl_take isl_pw_aff *pwaff,
3661 enum isl_dim_type type, unsigned first, unsigned n);
3662 __isl_give isl_aff *isl_aff_move_dims(
3663 __isl_take isl_aff *aff,
3664 enum isl_dim_type dst_type, unsigned dst_pos,
3665 enum isl_dim_type src_type, unsigned src_pos,
3667 __isl_give isl_pw_aff *isl_pw_aff_move_dims(
3668 __isl_take isl_pw_aff *pa,
3669 enum isl_dim_type dst_type, unsigned dst_pos,
3670 enum isl_dim_type src_type, unsigned src_pos,
3673 Note that C<isl_aff_set_constant_si> and C<isl_aff_set_coefficient_si>
3674 set the I<numerator> of the constant or coefficient, while
3675 C<isl_aff_set_constant_val> and C<isl_aff_set_coefficient_val> set
3676 the constant or coefficient as a whole.
3677 The C<add_constant> and C<add_coefficient> functions add an integer
3678 or rational value to
3679 the possibly rational constant or coefficient.
3680 The C<add_constant_num> functions add an integer value to
3683 To check whether an affine expressions is obviously zero
3684 or obviously equal to some other affine expression, use
3686 #include <isl/aff.h>
3687 int isl_aff_plain_is_zero(__isl_keep isl_aff *aff);
3688 int isl_aff_plain_is_equal(__isl_keep isl_aff *aff1,
3689 __isl_keep isl_aff *aff2);
3690 int isl_pw_aff_plain_is_equal(
3691 __isl_keep isl_pw_aff *pwaff1,
3692 __isl_keep isl_pw_aff *pwaff2);
3696 #include <isl/aff.h>
3697 __isl_give isl_aff *isl_aff_add(__isl_take isl_aff *aff1,
3698 __isl_take isl_aff *aff2);
3699 __isl_give isl_pw_aff *isl_pw_aff_add(
3700 __isl_take isl_pw_aff *pwaff1,
3701 __isl_take isl_pw_aff *pwaff2);
3702 __isl_give isl_pw_aff *isl_pw_aff_min(
3703 __isl_take isl_pw_aff *pwaff1,
3704 __isl_take isl_pw_aff *pwaff2);
3705 __isl_give isl_pw_aff *isl_pw_aff_max(
3706 __isl_take isl_pw_aff *pwaff1,
3707 __isl_take isl_pw_aff *pwaff2);
3708 __isl_give isl_aff *isl_aff_sub(__isl_take isl_aff *aff1,
3709 __isl_take isl_aff *aff2);
3710 __isl_give isl_pw_aff *isl_pw_aff_sub(
3711 __isl_take isl_pw_aff *pwaff1,
3712 __isl_take isl_pw_aff *pwaff2);
3713 __isl_give isl_aff *isl_aff_neg(__isl_take isl_aff *aff);
3714 __isl_give isl_pw_aff *isl_pw_aff_neg(
3715 __isl_take isl_pw_aff *pwaff);
3716 __isl_give isl_aff *isl_aff_ceil(__isl_take isl_aff *aff);
3717 __isl_give isl_pw_aff *isl_pw_aff_ceil(
3718 __isl_take isl_pw_aff *pwaff);
3719 __isl_give isl_aff *isl_aff_floor(__isl_take isl_aff *aff);
3720 __isl_give isl_pw_aff *isl_pw_aff_floor(
3721 __isl_take isl_pw_aff *pwaff);
3722 __isl_give isl_aff *isl_aff_mod_val(__isl_take isl_aff *aff,
3723 __isl_take isl_val *mod);
3724 __isl_give isl_pw_aff *isl_pw_aff_mod_val(
3725 __isl_take isl_pw_aff *pa,
3726 __isl_take isl_val *mod);
3727 __isl_give isl_aff *isl_aff_scale_val(__isl_take isl_aff *aff,
3728 __isl_take isl_val *v);
3729 __isl_give isl_pw_aff *isl_pw_aff_scale_val(
3730 __isl_take isl_pw_aff *pa, __isl_take isl_val *v);
3731 __isl_give isl_aff *isl_aff_scale_down_ui(
3732 __isl_take isl_aff *aff, unsigned f);
3733 __isl_give isl_aff *isl_aff_scale_down_val(
3734 __isl_take isl_aff *aff, __isl_take isl_val *v);
3735 __isl_give isl_pw_aff *isl_pw_aff_scale_down_val(
3736 __isl_take isl_pw_aff *pa,
3737 __isl_take isl_val *f);
3739 __isl_give isl_pw_aff *isl_pw_aff_list_min(
3740 __isl_take isl_pw_aff_list *list);
3741 __isl_give isl_pw_aff *isl_pw_aff_list_max(
3742 __isl_take isl_pw_aff_list *list);
3744 __isl_give isl_pw_aff *isl_pw_aff_coalesce(
3745 __isl_take isl_pw_aff *pwqp);
3747 __isl_give isl_aff *isl_aff_align_params(
3748 __isl_take isl_aff *aff,
3749 __isl_take isl_space *model);
3750 __isl_give isl_pw_aff *isl_pw_aff_align_params(
3751 __isl_take isl_pw_aff *pwaff,
3752 __isl_take isl_space *model);
3754 __isl_give isl_aff *isl_aff_project_domain_on_params(
3755 __isl_take isl_aff *aff);
3757 __isl_give isl_aff *isl_aff_gist_params(
3758 __isl_take isl_aff *aff,
3759 __isl_take isl_set *context);
3760 __isl_give isl_aff *isl_aff_gist(__isl_take isl_aff *aff,
3761 __isl_take isl_set *context);
3762 __isl_give isl_pw_aff *isl_pw_aff_gist_params(
3763 __isl_take isl_pw_aff *pwaff,
3764 __isl_take isl_set *context);
3765 __isl_give isl_pw_aff *isl_pw_aff_gist(
3766 __isl_take isl_pw_aff *pwaff,
3767 __isl_take isl_set *context);
3769 __isl_give isl_set *isl_pw_aff_domain(
3770 __isl_take isl_pw_aff *pwaff);
3771 __isl_give isl_pw_aff *isl_pw_aff_intersect_domain(
3772 __isl_take isl_pw_aff *pa,
3773 __isl_take isl_set *set);
3774 __isl_give isl_pw_aff *isl_pw_aff_intersect_params(
3775 __isl_take isl_pw_aff *pa,
3776 __isl_take isl_set *set);
3778 __isl_give isl_aff *isl_aff_mul(__isl_take isl_aff *aff1,
3779 __isl_take isl_aff *aff2);
3780 __isl_give isl_aff *isl_aff_div(__isl_take isl_aff *aff1,
3781 __isl_take isl_aff *aff2);
3782 __isl_give isl_pw_aff *isl_pw_aff_mul(
3783 __isl_take isl_pw_aff *pwaff1,
3784 __isl_take isl_pw_aff *pwaff2);
3785 __isl_give isl_pw_aff *isl_pw_aff_div(
3786 __isl_take isl_pw_aff *pa1,
3787 __isl_take isl_pw_aff *pa2);
3788 __isl_give isl_pw_aff *isl_pw_aff_tdiv_q(
3789 __isl_take isl_pw_aff *pa1,
3790 __isl_take isl_pw_aff *pa2);
3791 __isl_give isl_pw_aff *isl_pw_aff_tdiv_r(
3792 __isl_take isl_pw_aff *pa1,
3793 __isl_take isl_pw_aff *pa2);
3795 When multiplying two affine expressions, at least one of the two needs
3796 to be a constant. Similarly, when dividing an affine expression by another,
3797 the second expression needs to be a constant.
3798 C<isl_pw_aff_tdiv_q> computes the quotient of an integer division with
3799 rounding towards zero. C<isl_pw_aff_tdiv_r> computes the corresponding
3802 #include <isl/aff.h>
3803 __isl_give isl_aff *isl_aff_pullback_multi_aff(
3804 __isl_take isl_aff *aff,
3805 __isl_take isl_multi_aff *ma);
3806 __isl_give isl_pw_aff *isl_pw_aff_pullback_multi_aff(
3807 __isl_take isl_pw_aff *pa,
3808 __isl_take isl_multi_aff *ma);
3809 __isl_give isl_pw_aff *isl_pw_aff_pullback_pw_multi_aff(
3810 __isl_take isl_pw_aff *pa,
3811 __isl_take isl_pw_multi_aff *pma);
3813 These functions precompose the input expression by the given
3814 C<isl_multi_aff> or C<isl_pw_multi_aff>. In other words,
3815 the C<isl_multi_aff> or C<isl_pw_multi_aff> is plugged
3816 into the (piecewise) affine expression.
3817 Objects of type C<isl_multi_aff> are described in
3818 L</"Piecewise Multiple Quasi Affine Expressions">.
3820 #include <isl/aff.h>
3821 __isl_give isl_basic_set *isl_aff_zero_basic_set(
3822 __isl_take isl_aff *aff);
3823 __isl_give isl_basic_set *isl_aff_neg_basic_set(
3824 __isl_take isl_aff *aff);
3825 __isl_give isl_basic_set *isl_aff_le_basic_set(
3826 __isl_take isl_aff *aff1, __isl_take isl_aff *aff2);
3827 __isl_give isl_basic_set *isl_aff_ge_basic_set(
3828 __isl_take isl_aff *aff1, __isl_take isl_aff *aff2);
3829 __isl_give isl_set *isl_pw_aff_eq_set(
3830 __isl_take isl_pw_aff *pwaff1,
3831 __isl_take isl_pw_aff *pwaff2);
3832 __isl_give isl_set *isl_pw_aff_ne_set(
3833 __isl_take isl_pw_aff *pwaff1,
3834 __isl_take isl_pw_aff *pwaff2);
3835 __isl_give isl_set *isl_pw_aff_le_set(
3836 __isl_take isl_pw_aff *pwaff1,
3837 __isl_take isl_pw_aff *pwaff2);
3838 __isl_give isl_set *isl_pw_aff_lt_set(
3839 __isl_take isl_pw_aff *pwaff1,
3840 __isl_take isl_pw_aff *pwaff2);
3841 __isl_give isl_set *isl_pw_aff_ge_set(
3842 __isl_take isl_pw_aff *pwaff1,
3843 __isl_take isl_pw_aff *pwaff2);
3844 __isl_give isl_set *isl_pw_aff_gt_set(
3845 __isl_take isl_pw_aff *pwaff1,
3846 __isl_take isl_pw_aff *pwaff2);
3848 __isl_give isl_set *isl_pw_aff_list_eq_set(
3849 __isl_take isl_pw_aff_list *list1,
3850 __isl_take isl_pw_aff_list *list2);
3851 __isl_give isl_set *isl_pw_aff_list_ne_set(
3852 __isl_take isl_pw_aff_list *list1,
3853 __isl_take isl_pw_aff_list *list2);
3854 __isl_give isl_set *isl_pw_aff_list_le_set(
3855 __isl_take isl_pw_aff_list *list1,
3856 __isl_take isl_pw_aff_list *list2);
3857 __isl_give isl_set *isl_pw_aff_list_lt_set(
3858 __isl_take isl_pw_aff_list *list1,
3859 __isl_take isl_pw_aff_list *list2);
3860 __isl_give isl_set *isl_pw_aff_list_ge_set(
3861 __isl_take isl_pw_aff_list *list1,
3862 __isl_take isl_pw_aff_list *list2);
3863 __isl_give isl_set *isl_pw_aff_list_gt_set(
3864 __isl_take isl_pw_aff_list *list1,
3865 __isl_take isl_pw_aff_list *list2);
3867 The function C<isl_aff_neg_basic_set> returns a basic set
3868 containing those elements in the domain space
3869 of C<aff> where C<aff> is negative.
3870 The function C<isl_aff_ge_basic_set> returns a basic set
3871 containing those elements in the shared space
3872 of C<aff1> and C<aff2> where C<aff1> is greater than or equal to C<aff2>.
3873 The function C<isl_pw_aff_ge_set> returns a set
3874 containing those elements in the shared domain
3875 of C<pwaff1> and C<pwaff2> where C<pwaff1> is greater than or equal to C<pwaff2>.
3876 The functions operating on C<isl_pw_aff_list> apply the corresponding
3877 C<isl_pw_aff> function to each pair of elements in the two lists.
3879 #include <isl/aff.h>
3880 __isl_give isl_set *isl_pw_aff_nonneg_set(
3881 __isl_take isl_pw_aff *pwaff);
3882 __isl_give isl_set *isl_pw_aff_zero_set(
3883 __isl_take isl_pw_aff *pwaff);
3884 __isl_give isl_set *isl_pw_aff_non_zero_set(
3885 __isl_take isl_pw_aff *pwaff);
3887 The function C<isl_pw_aff_nonneg_set> returns a set
3888 containing those elements in the domain
3889 of C<pwaff> where C<pwaff> is non-negative.
3891 #include <isl/aff.h>
3892 __isl_give isl_pw_aff *isl_pw_aff_cond(
3893 __isl_take isl_pw_aff *cond,
3894 __isl_take isl_pw_aff *pwaff_true,
3895 __isl_take isl_pw_aff *pwaff_false);
3897 The function C<isl_pw_aff_cond> performs a conditional operator
3898 and returns an expression that is equal to C<pwaff_true>
3899 for elements where C<cond> is non-zero and equal to C<pwaff_false> for elements
3900 where C<cond> is zero.
3902 #include <isl/aff.h>
3903 __isl_give isl_pw_aff *isl_pw_aff_union_min(
3904 __isl_take isl_pw_aff *pwaff1,
3905 __isl_take isl_pw_aff *pwaff2);
3906 __isl_give isl_pw_aff *isl_pw_aff_union_max(
3907 __isl_take isl_pw_aff *pwaff1,
3908 __isl_take isl_pw_aff *pwaff2);
3909 __isl_give isl_pw_aff *isl_pw_aff_union_add(
3910 __isl_take isl_pw_aff *pwaff1,
3911 __isl_take isl_pw_aff *pwaff2);
3913 The function C<isl_pw_aff_union_max> computes a piecewise quasi-affine
3914 expression with a domain that is the union of those of C<pwaff1> and
3915 C<pwaff2> and such that on each cell, the quasi-affine expression is
3916 the maximum of those of C<pwaff1> and C<pwaff2>. If only one of
3917 C<pwaff1> or C<pwaff2> is defined on a given cell, then the
3918 associated expression is the defined one.
3920 An expression can be read from input using
3922 #include <isl/aff.h>
3923 __isl_give isl_aff *isl_aff_read_from_str(
3924 isl_ctx *ctx, const char *str);
3925 __isl_give isl_pw_aff *isl_pw_aff_read_from_str(
3926 isl_ctx *ctx, const char *str);
3928 An expression can be printed using
3930 #include <isl/aff.h>
3931 __isl_give isl_printer *isl_printer_print_aff(
3932 __isl_take isl_printer *p, __isl_keep isl_aff *aff);
3934 __isl_give isl_printer *isl_printer_print_pw_aff(
3935 __isl_take isl_printer *p,
3936 __isl_keep isl_pw_aff *pwaff);
3938 =head2 Piecewise Multiple Quasi Affine Expressions
3940 An C<isl_multi_aff> object represents a sequence of
3941 zero or more affine expressions, all defined on the same domain space.
3942 Similarly, an C<isl_multi_pw_aff> object represents a sequence of
3943 zero or more piecewise affine expressions.
3945 An C<isl_multi_aff> can be constructed from a single
3946 C<isl_aff> or an C<isl_aff_list> using the
3947 following functions. Similarly for C<isl_multi_pw_aff>.
3949 #include <isl/aff.h>
3950 __isl_give isl_multi_aff *isl_multi_aff_from_aff(
3951 __isl_take isl_aff *aff);
3952 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_from_pw_aff(
3953 __isl_take isl_pw_aff *pa);
3954 __isl_give isl_multi_aff *isl_multi_aff_from_aff_list(
3955 __isl_take isl_space *space,
3956 __isl_take isl_aff_list *list);
3958 An empty piecewise multiple quasi affine expression (one with no cells),
3959 the zero piecewise multiple quasi affine expression (with value zero
3960 for each output dimension),
3961 a piecewise multiple quasi affine expression with a single cell (with
3962 either a universe or a specified domain) or
3963 a zero-dimensional piecewise multiple quasi affine expression
3965 can be created using the following functions.
3967 #include <isl/aff.h>
3968 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_empty(
3969 __isl_take isl_space *space);
3970 __isl_give isl_multi_aff *isl_multi_aff_zero(
3971 __isl_take isl_space *space);
3972 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_zero(
3973 __isl_take isl_space *space);
3974 __isl_give isl_multi_aff *isl_multi_aff_identity(
3975 __isl_take isl_space *space);
3976 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_identity(
3977 __isl_take isl_space *space);
3978 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_identity(
3979 __isl_take isl_space *space);
3980 __isl_give isl_multi_aff *isl_multi_aff_domain_map(
3981 __isl_take isl_space *space);
3982 __isl_give isl_pw_multi_aff *
3983 isl_pw_multi_aff_from_multi_aff(
3984 __isl_take isl_multi_aff *ma);
3985 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_alloc(
3986 __isl_take isl_set *set,
3987 __isl_take isl_multi_aff *maff);
3988 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_from_domain(
3989 __isl_take isl_set *set);
3991 __isl_give isl_union_pw_multi_aff *
3992 isl_union_pw_multi_aff_empty(
3993 __isl_take isl_space *space);
3994 __isl_give isl_union_pw_multi_aff *
3995 isl_union_pw_multi_aff_add_pw_multi_aff(
3996 __isl_take isl_union_pw_multi_aff *upma,
3997 __isl_take isl_pw_multi_aff *pma);
3998 __isl_give isl_union_pw_multi_aff *
3999 isl_union_pw_multi_aff_from_domain(
4000 __isl_take isl_union_set *uset);
4002 A piecewise multiple quasi affine expression can also be initialized
4003 from an C<isl_set> or C<isl_map>, provided the C<isl_set> is a singleton
4004 and the C<isl_map> is single-valued.
4005 In case of a conversion from an C<isl_union_set> or an C<isl_union_map>
4006 to an C<isl_union_pw_multi_aff>, these properties need to hold in each space.
4008 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_from_set(
4009 __isl_take isl_set *set);
4010 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_from_map(
4011 __isl_take isl_map *map);
4013 __isl_give isl_union_pw_multi_aff *
4014 isl_union_pw_multi_aff_from_union_set(
4015 __isl_take isl_union_set *uset);
4016 __isl_give isl_union_pw_multi_aff *
4017 isl_union_pw_multi_aff_from_union_map(
4018 __isl_take isl_union_map *umap);
4020 Multiple quasi affine expressions can be copied and freed using
4022 #include <isl/aff.h>
4023 __isl_give isl_multi_aff *isl_multi_aff_copy(
4024 __isl_keep isl_multi_aff *maff);
4025 void *isl_multi_aff_free(__isl_take isl_multi_aff *maff);
4027 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_copy(
4028 __isl_keep isl_pw_multi_aff *pma);
4029 void *isl_pw_multi_aff_free(
4030 __isl_take isl_pw_multi_aff *pma);
4032 __isl_give isl_union_pw_multi_aff *
4033 isl_union_pw_multi_aff_copy(
4034 __isl_keep isl_union_pw_multi_aff *upma);
4035 void *isl_union_pw_multi_aff_free(
4036 __isl_take isl_union_pw_multi_aff *upma);
4038 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_copy(
4039 __isl_keep isl_multi_pw_aff *mpa);
4040 void *isl_multi_pw_aff_free(
4041 __isl_take isl_multi_pw_aff *mpa);
4043 The expression can be inspected using
4045 #include <isl/aff.h>
4046 isl_ctx *isl_multi_aff_get_ctx(
4047 __isl_keep isl_multi_aff *maff);
4048 isl_ctx *isl_pw_multi_aff_get_ctx(
4049 __isl_keep isl_pw_multi_aff *pma);
4050 isl_ctx *isl_union_pw_multi_aff_get_ctx(
4051 __isl_keep isl_union_pw_multi_aff *upma);
4052 isl_ctx *isl_multi_pw_aff_get_ctx(
4053 __isl_keep isl_multi_pw_aff *mpa);
4054 unsigned isl_multi_aff_dim(__isl_keep isl_multi_aff *maff,
4055 enum isl_dim_type type);
4056 unsigned isl_pw_multi_aff_dim(
4057 __isl_keep isl_pw_multi_aff *pma,
4058 enum isl_dim_type type);
4059 unsigned isl_multi_pw_aff_dim(
4060 __isl_keep isl_multi_pw_aff *mpa,
4061 enum isl_dim_type type);
4062 __isl_give isl_aff *isl_multi_aff_get_aff(
4063 __isl_keep isl_multi_aff *multi, int pos);
4064 __isl_give isl_pw_aff *isl_pw_multi_aff_get_pw_aff(
4065 __isl_keep isl_pw_multi_aff *pma, int pos);
4066 __isl_give isl_pw_aff *isl_multi_pw_aff_get_pw_aff(
4067 __isl_keep isl_multi_pw_aff *mpa, int pos);
4068 int isl_multi_aff_find_dim_by_id(
4069 __isl_keep isl_multi_aff *ma,
4070 enum isl_dim_type type, __isl_keep isl_id *id);
4071 int isl_multi_pw_aff_find_dim_by_id(
4072 __isl_keep isl_multi_pw_aff *mpa,
4073 enum isl_dim_type type, __isl_keep isl_id *id);
4074 const char *isl_pw_multi_aff_get_dim_name(
4075 __isl_keep isl_pw_multi_aff *pma,
4076 enum isl_dim_type type, unsigned pos);
4077 __isl_give isl_id *isl_multi_aff_get_dim_id(
4078 __isl_keep isl_multi_aff *ma,
4079 enum isl_dim_type type, unsigned pos);
4080 __isl_give isl_id *isl_pw_multi_aff_get_dim_id(
4081 __isl_keep isl_pw_multi_aff *pma,
4082 enum isl_dim_type type, unsigned pos);
4083 __isl_give isl_id *isl_multi_pw_aff_get_dim_id(
4084 __isl_keep isl_multi_pw_aff *mpa,
4085 enum isl_dim_type type, unsigned pos);
4086 const char *isl_multi_aff_get_tuple_name(
4087 __isl_keep isl_multi_aff *multi,
4088 enum isl_dim_type type);
4089 int isl_pw_multi_aff_has_tuple_name(
4090 __isl_keep isl_pw_multi_aff *pma,
4091 enum isl_dim_type type);
4092 const char *isl_pw_multi_aff_get_tuple_name(
4093 __isl_keep isl_pw_multi_aff *pma,
4094 enum isl_dim_type type);
4095 int isl_multi_aff_has_tuple_id(__isl_keep isl_multi_aff *ma,
4096 enum isl_dim_type type);
4097 int isl_pw_multi_aff_has_tuple_id(
4098 __isl_keep isl_pw_multi_aff *pma,
4099 enum isl_dim_type type);
4100 int isl_multi_pw_aff_has_tuple_id(
4101 __isl_keep isl_multi_pw_aff *mpa,
4102 enum isl_dim_type type);
4103 __isl_give isl_id *isl_multi_aff_get_tuple_id(
4104 __isl_keep isl_multi_aff *ma,
4105 enum isl_dim_type type);
4106 __isl_give isl_id *isl_pw_multi_aff_get_tuple_id(
4107 __isl_keep isl_pw_multi_aff *pma,
4108 enum isl_dim_type type);
4109 __isl_give isl_id *isl_multi_pw_aff_get_tuple_id(
4110 __isl_keep isl_multi_pw_aff *mpa,
4111 enum isl_dim_type type);
4112 __isl_give isl_multi_aff *isl_multi_aff_reset_tuple_id(
4113 __isl_take isl_multi_aff *ma,
4114 enum isl_dim_type type);
4115 __isl_give isl_multi_pw_aff *
4116 isl_multi_pw_aff_reset_tuple_id(
4117 __isl_take isl_multi_pw_aff *mpa,
4118 enum isl_dim_type type);
4120 int isl_pw_multi_aff_foreach_piece(
4121 __isl_keep isl_pw_multi_aff *pma,
4122 int (*fn)(__isl_take isl_set *set,
4123 __isl_take isl_multi_aff *maff,
4124 void *user), void *user);
4126 int isl_union_pw_multi_aff_foreach_pw_multi_aff(
4127 __isl_keep isl_union_pw_multi_aff *upma,
4128 int (*fn)(__isl_take isl_pw_multi_aff *pma,
4129 void *user), void *user);
4131 It can be modified using
4133 #include <isl/aff.h>
4134 __isl_give isl_multi_aff *isl_multi_aff_set_aff(
4135 __isl_take isl_multi_aff *multi, int pos,
4136 __isl_take isl_aff *aff);
4137 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_set_pw_aff(
4138 __isl_take isl_pw_multi_aff *pma, unsigned pos,
4139 __isl_take isl_pw_aff *pa);
4140 __isl_give isl_multi_aff *isl_multi_aff_set_dim_name(
4141 __isl_take isl_multi_aff *maff,
4142 enum isl_dim_type type, unsigned pos, const char *s);
4143 __isl_give isl_multi_aff *isl_multi_aff_set_dim_id(
4144 __isl_take isl_multi_aff *maff,
4145 enum isl_dim_type type, unsigned pos,
4146 __isl_take isl_id *id);
4147 __isl_give isl_multi_aff *isl_multi_aff_set_tuple_name(
4148 __isl_take isl_multi_aff *maff,
4149 enum isl_dim_type type, const char *s);
4150 __isl_give isl_multi_aff *isl_multi_aff_set_tuple_id(
4151 __isl_take isl_multi_aff *maff,
4152 enum isl_dim_type type, __isl_take isl_id *id);
4153 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_set_tuple_id(
4154 __isl_take isl_pw_multi_aff *pma,
4155 enum isl_dim_type type, __isl_take isl_id *id);
4157 __isl_give isl_multi_pw_aff *
4158 isl_multi_pw_aff_set_dim_name(
4159 __isl_take isl_multi_pw_aff *mpa,
4160 enum isl_dim_type type, unsigned pos, const char *s);
4161 __isl_give isl_multi_pw_aff *
4162 isl_multi_pw_aff_set_dim_id(
4163 __isl_take isl_multi_pw_aff *mpa,
4164 enum isl_dim_type type, unsigned pos,
4165 __isl_take isl_id *id);
4166 __isl_give isl_multi_pw_aff *
4167 isl_multi_pw_aff_set_tuple_name(
4168 __isl_take isl_multi_pw_aff *mpa,
4169 enum isl_dim_type type, const char *s);
4171 __isl_give isl_multi_aff *isl_multi_aff_insert_dims(
4172 __isl_take isl_multi_aff *ma,
4173 enum isl_dim_type type, unsigned first, unsigned n);
4174 __isl_give isl_multi_aff *isl_multi_aff_add_dims(
4175 __isl_take isl_multi_aff *ma,
4176 enum isl_dim_type type, unsigned n);
4177 __isl_give isl_multi_aff *isl_multi_aff_drop_dims(
4178 __isl_take isl_multi_aff *maff,
4179 enum isl_dim_type type, unsigned first, unsigned n);
4180 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_drop_dims(
4181 __isl_take isl_pw_multi_aff *pma,
4182 enum isl_dim_type type, unsigned first, unsigned n);
4184 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_insert_dims(
4185 __isl_take isl_multi_pw_aff *mpa,
4186 enum isl_dim_type type, unsigned first, unsigned n);
4187 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_add_dims(
4188 __isl_take isl_multi_pw_aff *mpa,
4189 enum isl_dim_type type, unsigned n);
4190 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_move_dims(
4191 __isl_take isl_multi_pw_aff *pma,
4192 enum isl_dim_type dst_type, unsigned dst_pos,
4193 enum isl_dim_type src_type, unsigned src_pos,
4196 To check whether two multiple affine expressions are
4197 obviously equal to each other, use
4199 int isl_multi_aff_plain_is_equal(__isl_keep isl_multi_aff *maff1,
4200 __isl_keep isl_multi_aff *maff2);
4201 int isl_pw_multi_aff_plain_is_equal(
4202 __isl_keep isl_pw_multi_aff *pma1,
4203 __isl_keep isl_pw_multi_aff *pma2);
4207 #include <isl/aff.h>
4208 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_union_lexmin(
4209 __isl_take isl_pw_multi_aff *pma1,
4210 __isl_take isl_pw_multi_aff *pma2);
4211 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_union_lexmax(
4212 __isl_take isl_pw_multi_aff *pma1,
4213 __isl_take isl_pw_multi_aff *pma2);
4214 __isl_give isl_multi_aff *isl_multi_aff_add(
4215 __isl_take isl_multi_aff *maff1,
4216 __isl_take isl_multi_aff *maff2);
4217 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_add(
4218 __isl_take isl_pw_multi_aff *pma1,
4219 __isl_take isl_pw_multi_aff *pma2);
4220 __isl_give isl_union_pw_multi_aff *isl_union_pw_multi_aff_add(
4221 __isl_take isl_union_pw_multi_aff *upma1,
4222 __isl_take isl_union_pw_multi_aff *upma2);
4223 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_union_add(
4224 __isl_take isl_pw_multi_aff *pma1,
4225 __isl_take isl_pw_multi_aff *pma2);
4226 __isl_give isl_multi_aff *isl_multi_aff_sub(
4227 __isl_take isl_multi_aff *ma1,
4228 __isl_take isl_multi_aff *ma2);
4229 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_sub(
4230 __isl_take isl_pw_multi_aff *pma1,
4231 __isl_take isl_pw_multi_aff *pma2);
4232 __isl_give isl_union_pw_multi_aff *isl_union_pw_multi_aff_sub(
4233 __isl_take isl_union_pw_multi_aff *upma1,
4234 __isl_take isl_union_pw_multi_aff *upma2);
4236 C<isl_multi_aff_sub> subtracts the second argument from the first.
4238 __isl_give isl_multi_aff *isl_multi_aff_scale_val(
4239 __isl_take isl_multi_aff *ma,
4240 __isl_take isl_val *v);
4241 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_scale_val(
4242 __isl_take isl_pw_multi_aff *pma,
4243 __isl_take isl_val *v);
4244 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_scale_val(
4245 __isl_take isl_multi_pw_aff *mpa,
4246 __isl_take isl_val *v);
4247 __isl_give isl_multi_aff *isl_multi_aff_scale_multi_val(
4248 __isl_take isl_multi_aff *ma,
4249 __isl_take isl_multi_val *mv);
4250 __isl_give isl_pw_multi_aff *
4251 isl_pw_multi_aff_scale_multi_val(
4252 __isl_take isl_pw_multi_aff *pma,
4253 __isl_take isl_multi_val *mv);
4254 __isl_give isl_multi_pw_aff *
4255 isl_multi_pw_aff_scale_multi_val(
4256 __isl_take isl_multi_pw_aff *mpa,
4257 __isl_take isl_multi_val *mv);
4258 __isl_give isl_union_pw_multi_aff *
4259 isl_union_pw_multi_aff_scale_multi_val(
4260 __isl_take isl_union_pw_multi_aff *upma,
4261 __isl_take isl_multi_val *mv);
4262 __isl_give isl_multi_aff *
4263 isl_multi_aff_scale_down_multi_val(
4264 __isl_take isl_multi_aff *ma,
4265 __isl_take isl_multi_val *mv);
4266 __isl_give isl_multi_pw_aff *
4267 isl_multi_pw_aff_scale_down_multi_val(
4268 __isl_take isl_multi_pw_aff *mpa,
4269 __isl_take isl_multi_val *mv);
4271 C<isl_multi_aff_scale_multi_val> scales the elements of C<ma>
4272 by the corresponding elements of C<mv>.
4274 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_intersect_params(
4275 __isl_take isl_pw_multi_aff *pma,
4276 __isl_take isl_set *set);
4277 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_intersect_domain(
4278 __isl_take isl_pw_multi_aff *pma,
4279 __isl_take isl_set *set);
4280 __isl_give isl_union_pw_multi_aff *
4281 isl_union_pw_multi_aff_intersect_domain(
4282 __isl_take isl_union_pw_multi_aff *upma,
4283 __isl_take isl_union_set *uset);
4284 __isl_give isl_multi_aff *isl_multi_aff_lift(
4285 __isl_take isl_multi_aff *maff,
4286 __isl_give isl_local_space **ls);
4287 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_coalesce(
4288 __isl_take isl_pw_multi_aff *pma);
4289 __isl_give isl_multi_aff *isl_multi_aff_align_params(
4290 __isl_take isl_multi_aff *multi,
4291 __isl_take isl_space *model);
4292 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_align_params(
4293 __isl_take isl_pw_multi_aff *pma,
4294 __isl_take isl_space *model);
4295 __isl_give isl_pw_multi_aff *
4296 isl_pw_multi_aff_project_domain_on_params(
4297 __isl_take isl_pw_multi_aff *pma);
4298 __isl_give isl_multi_aff *isl_multi_aff_gist_params(
4299 __isl_take isl_multi_aff *maff,
4300 __isl_take isl_set *context);
4301 __isl_give isl_multi_aff *isl_multi_aff_gist(
4302 __isl_take isl_multi_aff *maff,
4303 __isl_take isl_set *context);
4304 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_gist_params(
4305 __isl_take isl_pw_multi_aff *pma,
4306 __isl_take isl_set *set);
4307 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_gist(
4308 __isl_take isl_pw_multi_aff *pma,
4309 __isl_take isl_set *set);
4310 __isl_give isl_multi_aff *isl_multi_aff_from_range(
4311 __isl_take isl_multi_aff *ma);
4312 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_from_range(
4313 __isl_take isl_multi_pw_aff *mpa);
4314 __isl_give isl_set *isl_pw_multi_aff_domain(
4315 __isl_take isl_pw_multi_aff *pma);
4316 __isl_give isl_union_set *isl_union_pw_multi_aff_domain(
4317 __isl_take isl_union_pw_multi_aff *upma);
4318 __isl_give isl_multi_aff *isl_multi_aff_range_splice(
4319 __isl_take isl_multi_aff *ma1, unsigned pos,
4320 __isl_take isl_multi_aff *ma2);
4321 __isl_give isl_multi_aff *isl_multi_aff_splice(
4322 __isl_take isl_multi_aff *ma1,
4323 unsigned in_pos, unsigned out_pos,
4324 __isl_take isl_multi_aff *ma2);
4325 __isl_give isl_multi_aff *isl_multi_aff_range_product(
4326 __isl_take isl_multi_aff *ma1,
4327 __isl_take isl_multi_aff *ma2);
4328 __isl_give isl_multi_aff *isl_multi_aff_flat_range_product(
4329 __isl_take isl_multi_aff *ma1,
4330 __isl_take isl_multi_aff *ma2);
4331 __isl_give isl_multi_aff *isl_multi_aff_product(
4332 __isl_take isl_multi_aff *ma1,
4333 __isl_take isl_multi_aff *ma2);
4334 __isl_give isl_pw_multi_aff *
4335 isl_pw_multi_aff_range_product(
4336 __isl_take isl_pw_multi_aff *pma1,
4337 __isl_take isl_pw_multi_aff *pma2);
4338 __isl_give isl_pw_multi_aff *
4339 isl_pw_multi_aff_flat_range_product(
4340 __isl_take isl_pw_multi_aff *pma1,
4341 __isl_take isl_pw_multi_aff *pma2);
4342 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_product(
4343 __isl_take isl_pw_multi_aff *pma1,
4344 __isl_take isl_pw_multi_aff *pma2);
4345 __isl_give isl_union_pw_multi_aff *
4346 isl_union_pw_multi_aff_flat_range_product(
4347 __isl_take isl_union_pw_multi_aff *upma1,
4348 __isl_take isl_union_pw_multi_aff *upma2);
4349 __isl_give isl_multi_pw_aff *
4350 isl_multi_pw_aff_range_splice(
4351 __isl_take isl_multi_pw_aff *mpa1, unsigned pos,
4352 __isl_take isl_multi_pw_aff *mpa2);
4353 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_splice(
4354 __isl_take isl_multi_pw_aff *mpa1,
4355 unsigned in_pos, unsigned out_pos,
4356 __isl_take isl_multi_pw_aff *mpa2);
4357 __isl_give isl_multi_pw_aff *
4358 isl_multi_pw_aff_range_product(
4359 __isl_take isl_multi_pw_aff *mpa1,
4360 __isl_take isl_multi_pw_aff *mpa2);
4361 __isl_give isl_multi_pw_aff *
4362 isl_multi_pw_aff_flat_range_product(
4363 __isl_take isl_multi_pw_aff *mpa1,
4364 __isl_take isl_multi_pw_aff *mpa2);
4366 If the C<ls> argument of C<isl_multi_aff_lift> is not C<NULL>,
4367 then it is assigned the local space that lies at the basis of
4368 the lifting applied.
4370 #include <isl/aff.h>
4371 __isl_give isl_multi_aff *isl_multi_aff_pullback_multi_aff(
4372 __isl_take isl_multi_aff *ma1,
4373 __isl_take isl_multi_aff *ma2);
4374 __isl_give isl_pw_multi_aff *
4375 isl_pw_multi_aff_pullback_multi_aff(
4376 __isl_take isl_pw_multi_aff *pma,
4377 __isl_take isl_multi_aff *ma);
4378 __isl_give isl_pw_multi_aff *
4379 isl_pw_multi_aff_pullback_pw_multi_aff(
4380 __isl_take isl_pw_multi_aff *pma1,
4381 __isl_take isl_pw_multi_aff *pma2);
4383 The function C<isl_multi_aff_pullback_multi_aff> precomposes C<ma1> by C<ma2>.
4384 In other words, C<ma2> is plugged
4387 __isl_give isl_set *isl_multi_aff_lex_le_set(
4388 __isl_take isl_multi_aff *ma1,
4389 __isl_take isl_multi_aff *ma2);
4390 __isl_give isl_set *isl_multi_aff_lex_ge_set(
4391 __isl_take isl_multi_aff *ma1,
4392 __isl_take isl_multi_aff *ma2);
4394 The function C<isl_multi_aff_lex_le_set> returns a set
4395 containing those elements in the shared domain space
4396 where C<ma1> is lexicographically smaller than or
4399 An expression can be read from input using
4401 #include <isl/aff.h>
4402 __isl_give isl_multi_aff *isl_multi_aff_read_from_str(
4403 isl_ctx *ctx, const char *str);
4404 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_read_from_str(
4405 isl_ctx *ctx, const char *str);
4406 __isl_give isl_union_pw_multi_aff *
4407 isl_union_pw_multi_aff_read_from_str(
4408 isl_ctx *ctx, const char *str);
4410 An expression can be printed using
4412 #include <isl/aff.h>
4413 __isl_give isl_printer *isl_printer_print_multi_aff(
4414 __isl_take isl_printer *p,
4415 __isl_keep isl_multi_aff *maff);
4416 __isl_give isl_printer *isl_printer_print_pw_multi_aff(
4417 __isl_take isl_printer *p,
4418 __isl_keep isl_pw_multi_aff *pma);
4419 __isl_give isl_printer *isl_printer_print_union_pw_multi_aff(
4420 __isl_take isl_printer *p,
4421 __isl_keep isl_union_pw_multi_aff *upma);
4422 __isl_give isl_printer *isl_printer_print_multi_pw_aff(
4423 __isl_take isl_printer *p,
4424 __isl_keep isl_multi_pw_aff *mpa);
4428 Points are elements of a set. They can be used to construct
4429 simple sets (boxes) or they can be used to represent the
4430 individual elements of a set.
4431 The zero point (the origin) can be created using
4433 __isl_give isl_point *isl_point_zero(__isl_take isl_space *space);
4435 The coordinates of a point can be inspected, set and changed
4438 __isl_give isl_val *isl_point_get_coordinate_val(
4439 __isl_keep isl_point *pnt,
4440 enum isl_dim_type type, int pos);
4441 __isl_give isl_point *isl_point_set_coordinate_val(
4442 __isl_take isl_point *pnt,
4443 enum isl_dim_type type, int pos,
4444 __isl_take isl_val *v);
4446 __isl_give isl_point *isl_point_add_ui(
4447 __isl_take isl_point *pnt,
4448 enum isl_dim_type type, int pos, unsigned val);
4449 __isl_give isl_point *isl_point_sub_ui(
4450 __isl_take isl_point *pnt,
4451 enum isl_dim_type type, int pos, unsigned val);
4453 Other properties can be obtained using
4455 isl_ctx *isl_point_get_ctx(__isl_keep isl_point *pnt);
4457 Points can be copied or freed using
4459 __isl_give isl_point *isl_point_copy(
4460 __isl_keep isl_point *pnt);
4461 void isl_point_free(__isl_take isl_point *pnt);
4463 A singleton set can be created from a point using
4465 __isl_give isl_basic_set *isl_basic_set_from_point(
4466 __isl_take isl_point *pnt);
4467 __isl_give isl_set *isl_set_from_point(
4468 __isl_take isl_point *pnt);
4470 and a box can be created from two opposite extremal points using
4472 __isl_give isl_basic_set *isl_basic_set_box_from_points(
4473 __isl_take isl_point *pnt1,
4474 __isl_take isl_point *pnt2);
4475 __isl_give isl_set *isl_set_box_from_points(
4476 __isl_take isl_point *pnt1,
4477 __isl_take isl_point *pnt2);
4479 All elements of a B<bounded> (union) set can be enumerated using
4480 the following functions.
4482 int isl_set_foreach_point(__isl_keep isl_set *set,
4483 int (*fn)(__isl_take isl_point *pnt, void *user),
4485 int isl_union_set_foreach_point(__isl_keep isl_union_set *uset,
4486 int (*fn)(__isl_take isl_point *pnt, void *user),
4489 The function C<fn> is called for each integer point in
4490 C<set> with as second argument the last argument of
4491 the C<isl_set_foreach_point> call. The function C<fn>
4492 should return C<0> on success and C<-1> on failure.
4493 In the latter case, C<isl_set_foreach_point> will stop
4494 enumerating and return C<-1> as well.
4495 If the enumeration is performed successfully and to completion,
4496 then C<isl_set_foreach_point> returns C<0>.
4498 To obtain a single point of a (basic) set, use
4500 __isl_give isl_point *isl_basic_set_sample_point(
4501 __isl_take isl_basic_set *bset);
4502 __isl_give isl_point *isl_set_sample_point(
4503 __isl_take isl_set *set);
4505 If C<set> does not contain any (integer) points, then the
4506 resulting point will be ``void'', a property that can be
4509 int isl_point_is_void(__isl_keep isl_point *pnt);
4511 =head2 Piecewise Quasipolynomials
4513 A piecewise quasipolynomial is a particular kind of function that maps
4514 a parametric point to a rational value.
4515 More specifically, a quasipolynomial is a polynomial expression in greatest
4516 integer parts of affine expressions of parameters and variables.
4517 A piecewise quasipolynomial is a subdivision of a given parametric
4518 domain into disjoint cells with a quasipolynomial associated to
4519 each cell. The value of the piecewise quasipolynomial at a given
4520 point is the value of the quasipolynomial associated to the cell
4521 that contains the point. Outside of the union of cells,
4522 the value is assumed to be zero.
4523 For example, the piecewise quasipolynomial
4525 [n] -> { [x] -> ((1 + n) - x) : x <= n and x >= 0 }
4527 maps C<x> to C<1 + n - x> for values of C<x> between C<0> and C<n>.
4528 A given piecewise quasipolynomial has a fixed domain dimension.
4529 Union piecewise quasipolynomials are used to contain piecewise quasipolynomials
4530 defined over different domains.
4531 Piecewise quasipolynomials are mainly used by the C<barvinok>
4532 library for representing the number of elements in a parametric set or map.
4533 For example, the piecewise quasipolynomial above represents
4534 the number of points in the map
4536 [n] -> { [x] -> [y] : x,y >= 0 and 0 <= x + y <= n }
4538 =head3 Input and Output
4540 Piecewise quasipolynomials can be read from input using
4542 __isl_give isl_union_pw_qpolynomial *
4543 isl_union_pw_qpolynomial_read_from_str(
4544 isl_ctx *ctx, const char *str);
4546 Quasipolynomials and piecewise quasipolynomials can be printed
4547 using the following functions.
4549 __isl_give isl_printer *isl_printer_print_qpolynomial(
4550 __isl_take isl_printer *p,
4551 __isl_keep isl_qpolynomial *qp);
4553 __isl_give isl_printer *isl_printer_print_pw_qpolynomial(
4554 __isl_take isl_printer *p,
4555 __isl_keep isl_pw_qpolynomial *pwqp);
4557 __isl_give isl_printer *isl_printer_print_union_pw_qpolynomial(
4558 __isl_take isl_printer *p,
4559 __isl_keep isl_union_pw_qpolynomial *upwqp);
4561 The output format of the printer
4562 needs to be set to either C<ISL_FORMAT_ISL> or C<ISL_FORMAT_C>.
4563 For C<isl_printer_print_union_pw_qpolynomial>, only C<ISL_FORMAT_ISL>
4565 In case of printing in C<ISL_FORMAT_C>, the user may want
4566 to set the names of all dimensions
4568 __isl_give isl_qpolynomial *isl_qpolynomial_set_dim_name(
4569 __isl_take isl_qpolynomial *qp,
4570 enum isl_dim_type type, unsigned pos,
4572 __isl_give isl_pw_qpolynomial *
4573 isl_pw_qpolynomial_set_dim_name(
4574 __isl_take isl_pw_qpolynomial *pwqp,
4575 enum isl_dim_type type, unsigned pos,
4578 =head3 Creating New (Piecewise) Quasipolynomials
4580 Some simple quasipolynomials can be created using the following functions.
4581 More complicated quasipolynomials can be created by applying
4582 operations such as addition and multiplication
4583 on the resulting quasipolynomials
4585 __isl_give isl_qpolynomial *isl_qpolynomial_zero_on_domain(
4586 __isl_take isl_space *domain);
4587 __isl_give isl_qpolynomial *isl_qpolynomial_one_on_domain(
4588 __isl_take isl_space *domain);
4589 __isl_give isl_qpolynomial *isl_qpolynomial_infty_on_domain(
4590 __isl_take isl_space *domain);
4591 __isl_give isl_qpolynomial *isl_qpolynomial_neginfty_on_domain(
4592 __isl_take isl_space *domain);
4593 __isl_give isl_qpolynomial *isl_qpolynomial_nan_on_domain(
4594 __isl_take isl_space *domain);
4595 __isl_give isl_qpolynomial *isl_qpolynomial_val_on_domain(
4596 __isl_take isl_space *domain,
4597 __isl_take isl_val *val);
4598 __isl_give isl_qpolynomial *isl_qpolynomial_var_on_domain(
4599 __isl_take isl_space *domain,
4600 enum isl_dim_type type, unsigned pos);
4601 __isl_give isl_qpolynomial *isl_qpolynomial_from_aff(
4602 __isl_take isl_aff *aff);
4604 Note that the space in which a quasipolynomial lives is a map space
4605 with a one-dimensional range. The C<domain> argument in some of
4606 the functions above corresponds to the domain of this map space.
4608 The zero piecewise quasipolynomial or a piecewise quasipolynomial
4609 with a single cell can be created using the following functions.
4610 Multiple of these single cell piecewise quasipolynomials can
4611 be combined to create more complicated piecewise quasipolynomials.
4613 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_zero(
4614 __isl_take isl_space *space);
4615 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_alloc(
4616 __isl_take isl_set *set,
4617 __isl_take isl_qpolynomial *qp);
4618 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_from_qpolynomial(
4619 __isl_take isl_qpolynomial *qp);
4620 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_from_pw_aff(
4621 __isl_take isl_pw_aff *pwaff);
4623 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_zero(
4624 __isl_take isl_space *space);
4625 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_from_pw_qpolynomial(
4626 __isl_take isl_pw_qpolynomial *pwqp);
4627 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_add_pw_qpolynomial(
4628 __isl_take isl_union_pw_qpolynomial *upwqp,
4629 __isl_take isl_pw_qpolynomial *pwqp);
4631 Quasipolynomials can be copied and freed again using the following
4634 __isl_give isl_qpolynomial *isl_qpolynomial_copy(
4635 __isl_keep isl_qpolynomial *qp);
4636 void *isl_qpolynomial_free(__isl_take isl_qpolynomial *qp);
4638 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_copy(
4639 __isl_keep isl_pw_qpolynomial *pwqp);
4640 void *isl_pw_qpolynomial_free(
4641 __isl_take isl_pw_qpolynomial *pwqp);
4643 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_copy(
4644 __isl_keep isl_union_pw_qpolynomial *upwqp);
4645 void *isl_union_pw_qpolynomial_free(
4646 __isl_take isl_union_pw_qpolynomial *upwqp);
4648 =head3 Inspecting (Piecewise) Quasipolynomials
4650 To iterate over all piecewise quasipolynomials in a union
4651 piecewise quasipolynomial, use the following function
4653 int isl_union_pw_qpolynomial_foreach_pw_qpolynomial(
4654 __isl_keep isl_union_pw_qpolynomial *upwqp,
4655 int (*fn)(__isl_take isl_pw_qpolynomial *pwqp, void *user),
4658 To extract the piecewise quasipolynomial in a given space from a union, use
4660 __isl_give isl_pw_qpolynomial *
4661 isl_union_pw_qpolynomial_extract_pw_qpolynomial(
4662 __isl_keep isl_union_pw_qpolynomial *upwqp,
4663 __isl_take isl_space *space);
4665 To iterate over the cells in a piecewise quasipolynomial,
4666 use either of the following two functions
4668 int isl_pw_qpolynomial_foreach_piece(
4669 __isl_keep isl_pw_qpolynomial *pwqp,
4670 int (*fn)(__isl_take isl_set *set,
4671 __isl_take isl_qpolynomial *qp,
4672 void *user), void *user);
4673 int isl_pw_qpolynomial_foreach_lifted_piece(
4674 __isl_keep isl_pw_qpolynomial *pwqp,
4675 int (*fn)(__isl_take isl_set *set,
4676 __isl_take isl_qpolynomial *qp,
4677 void *user), void *user);
4679 As usual, the function C<fn> should return C<0> on success
4680 and C<-1> on failure. The difference between
4681 C<isl_pw_qpolynomial_foreach_piece> and
4682 C<isl_pw_qpolynomial_foreach_lifted_piece> is that
4683 C<isl_pw_qpolynomial_foreach_lifted_piece> will first
4684 compute unique representations for all existentially quantified
4685 variables and then turn these existentially quantified variables
4686 into extra set variables, adapting the associated quasipolynomial
4687 accordingly. This means that the C<set> passed to C<fn>
4688 will not have any existentially quantified variables, but that
4689 the dimensions of the sets may be different for different
4690 invocations of C<fn>.
4692 The constant term of a quasipolynomial can be extracted using
4694 __isl_give isl_val *isl_qpolynomial_get_constant_val(
4695 __isl_keep isl_qpolynomial *qp);
4697 To iterate over all terms in a quasipolynomial,
4700 int isl_qpolynomial_foreach_term(
4701 __isl_keep isl_qpolynomial *qp,
4702 int (*fn)(__isl_take isl_term *term,
4703 void *user), void *user);
4705 The terms themselves can be inspected and freed using
4708 unsigned isl_term_dim(__isl_keep isl_term *term,
4709 enum isl_dim_type type);
4710 __isl_give isl_val *isl_term_get_coefficient_val(
4711 __isl_keep isl_term *term);
4712 int isl_term_get_exp(__isl_keep isl_term *term,
4713 enum isl_dim_type type, unsigned pos);
4714 __isl_give isl_aff *isl_term_get_div(
4715 __isl_keep isl_term *term, unsigned pos);
4716 void isl_term_free(__isl_take isl_term *term);
4718 Each term is a product of parameters, set variables and
4719 integer divisions. The function C<isl_term_get_exp>
4720 returns the exponent of a given dimensions in the given term.
4722 =head3 Properties of (Piecewise) Quasipolynomials
4724 To check whether two union piecewise quasipolynomials are
4725 obviously equal, use
4727 int isl_union_pw_qpolynomial_plain_is_equal(
4728 __isl_keep isl_union_pw_qpolynomial *upwqp1,
4729 __isl_keep isl_union_pw_qpolynomial *upwqp2);
4731 =head3 Operations on (Piecewise) Quasipolynomials
4733 __isl_give isl_qpolynomial *isl_qpolynomial_scale_val(
4734 __isl_take isl_qpolynomial *qp,
4735 __isl_take isl_val *v);
4736 __isl_give isl_qpolynomial *isl_qpolynomial_neg(
4737 __isl_take isl_qpolynomial *qp);
4738 __isl_give isl_qpolynomial *isl_qpolynomial_add(
4739 __isl_take isl_qpolynomial *qp1,
4740 __isl_take isl_qpolynomial *qp2);
4741 __isl_give isl_qpolynomial *isl_qpolynomial_sub(
4742 __isl_take isl_qpolynomial *qp1,
4743 __isl_take isl_qpolynomial *qp2);
4744 __isl_give isl_qpolynomial *isl_qpolynomial_mul(
4745 __isl_take isl_qpolynomial *qp1,
4746 __isl_take isl_qpolynomial *qp2);
4747 __isl_give isl_qpolynomial *isl_qpolynomial_pow(
4748 __isl_take isl_qpolynomial *qp, unsigned exponent);
4750 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_fix_val(
4751 __isl_take isl_pw_qpolynomial *pwqp,
4752 enum isl_dim_type type, unsigned n,
4753 __isl_take isl_val *v);
4754 __isl_give isl_pw_qpolynomial *
4755 isl_pw_qpolynomial_scale_val(
4756 __isl_take isl_pw_qpolynomial *pwqp,
4757 __isl_take isl_val *v);
4758 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_add(
4759 __isl_take isl_pw_qpolynomial *pwqp1,
4760 __isl_take isl_pw_qpolynomial *pwqp2);
4761 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_sub(
4762 __isl_take isl_pw_qpolynomial *pwqp1,
4763 __isl_take isl_pw_qpolynomial *pwqp2);
4764 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_add_disjoint(
4765 __isl_take isl_pw_qpolynomial *pwqp1,
4766 __isl_take isl_pw_qpolynomial *pwqp2);
4767 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_neg(
4768 __isl_take isl_pw_qpolynomial *pwqp);
4769 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_mul(
4770 __isl_take isl_pw_qpolynomial *pwqp1,
4771 __isl_take isl_pw_qpolynomial *pwqp2);
4772 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_pow(
4773 __isl_take isl_pw_qpolynomial *pwqp, unsigned exponent);
4775 __isl_give isl_union_pw_qpolynomial *
4776 isl_union_pw_qpolynomial_scale_val(
4777 __isl_take isl_union_pw_qpolynomial *upwqp,
4778 __isl_take isl_val *v);
4779 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_add(
4780 __isl_take isl_union_pw_qpolynomial *upwqp1,
4781 __isl_take isl_union_pw_qpolynomial *upwqp2);
4782 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_sub(
4783 __isl_take isl_union_pw_qpolynomial *upwqp1,
4784 __isl_take isl_union_pw_qpolynomial *upwqp2);
4785 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_mul(
4786 __isl_take isl_union_pw_qpolynomial *upwqp1,
4787 __isl_take isl_union_pw_qpolynomial *upwqp2);
4789 __isl_give isl_val *isl_pw_qpolynomial_eval(
4790 __isl_take isl_pw_qpolynomial *pwqp,
4791 __isl_take isl_point *pnt);
4793 __isl_give isl_val *isl_union_pw_qpolynomial_eval(
4794 __isl_take isl_union_pw_qpolynomial *upwqp,
4795 __isl_take isl_point *pnt);
4797 __isl_give isl_set *isl_pw_qpolynomial_domain(
4798 __isl_take isl_pw_qpolynomial *pwqp);
4799 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_intersect_domain(
4800 __isl_take isl_pw_qpolynomial *pwpq,
4801 __isl_take isl_set *set);
4802 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_intersect_params(
4803 __isl_take isl_pw_qpolynomial *pwpq,
4804 __isl_take isl_set *set);
4806 __isl_give isl_union_set *isl_union_pw_qpolynomial_domain(
4807 __isl_take isl_union_pw_qpolynomial *upwqp);
4808 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_intersect_domain(
4809 __isl_take isl_union_pw_qpolynomial *upwpq,
4810 __isl_take isl_union_set *uset);
4811 __isl_give isl_union_pw_qpolynomial *
4812 isl_union_pw_qpolynomial_intersect_params(
4813 __isl_take isl_union_pw_qpolynomial *upwpq,
4814 __isl_take isl_set *set);
4816 __isl_give isl_qpolynomial *isl_qpolynomial_align_params(
4817 __isl_take isl_qpolynomial *qp,
4818 __isl_take isl_space *model);
4820 __isl_give isl_qpolynomial *isl_qpolynomial_project_domain_on_params(
4821 __isl_take isl_qpolynomial *qp);
4822 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_project_domain_on_params(
4823 __isl_take isl_pw_qpolynomial *pwqp);
4825 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_coalesce(
4826 __isl_take isl_union_pw_qpolynomial *upwqp);
4828 __isl_give isl_qpolynomial *isl_qpolynomial_gist_params(
4829 __isl_take isl_qpolynomial *qp,
4830 __isl_take isl_set *context);
4831 __isl_give isl_qpolynomial *isl_qpolynomial_gist(
4832 __isl_take isl_qpolynomial *qp,
4833 __isl_take isl_set *context);
4835 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_gist_params(
4836 __isl_take isl_pw_qpolynomial *pwqp,
4837 __isl_take isl_set *context);
4838 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_gist(
4839 __isl_take isl_pw_qpolynomial *pwqp,
4840 __isl_take isl_set *context);
4842 __isl_give isl_union_pw_qpolynomial *
4843 isl_union_pw_qpolynomial_gist_params(
4844 __isl_take isl_union_pw_qpolynomial *upwqp,
4845 __isl_take isl_set *context);
4846 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_gist(
4847 __isl_take isl_union_pw_qpolynomial *upwqp,
4848 __isl_take isl_union_set *context);
4850 The gist operation applies the gist operation to each of
4851 the cells in the domain of the input piecewise quasipolynomial.
4852 The context is also exploited
4853 to simplify the quasipolynomials associated to each cell.
4855 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_to_polynomial(
4856 __isl_take isl_pw_qpolynomial *pwqp, int sign);
4857 __isl_give isl_union_pw_qpolynomial *
4858 isl_union_pw_qpolynomial_to_polynomial(
4859 __isl_take isl_union_pw_qpolynomial *upwqp, int sign);
4861 Approximate each quasipolynomial by a polynomial. If C<sign> is positive,
4862 the polynomial will be an overapproximation. If C<sign> is negative,
4863 it will be an underapproximation. If C<sign> is zero, the approximation
4864 will lie somewhere in between.
4866 =head2 Bounds on Piecewise Quasipolynomials and Piecewise Quasipolynomial Reductions
4868 A piecewise quasipolynomial reduction is a piecewise
4869 reduction (or fold) of quasipolynomials.
4870 In particular, the reduction can be maximum or a minimum.
4871 The objects are mainly used to represent the result of
4872 an upper or lower bound on a quasipolynomial over its domain,
4873 i.e., as the result of the following function.
4875 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_bound(
4876 __isl_take isl_pw_qpolynomial *pwqp,
4877 enum isl_fold type, int *tight);
4879 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_bound(
4880 __isl_take isl_union_pw_qpolynomial *upwqp,
4881 enum isl_fold type, int *tight);
4883 The C<type> argument may be either C<isl_fold_min> or C<isl_fold_max>.
4884 If C<tight> is not C<NULL>, then C<*tight> is set to C<1>
4885 is the returned bound is known be tight, i.e., for each value
4886 of the parameters there is at least
4887 one element in the domain that reaches the bound.
4888 If the domain of C<pwqp> is not wrapping, then the bound is computed
4889 over all elements in that domain and the result has a purely parametric
4890 domain. If the domain of C<pwqp> is wrapping, then the bound is
4891 computed over the range of the wrapped relation. The domain of the
4892 wrapped relation becomes the domain of the result.
4894 A (piecewise) quasipolynomial reduction can be copied or freed using the
4895 following functions.
4897 __isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_copy(
4898 __isl_keep isl_qpolynomial_fold *fold);
4899 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_copy(
4900 __isl_keep isl_pw_qpolynomial_fold *pwf);
4901 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_copy(
4902 __isl_keep isl_union_pw_qpolynomial_fold *upwf);
4903 void isl_qpolynomial_fold_free(
4904 __isl_take isl_qpolynomial_fold *fold);
4905 void *isl_pw_qpolynomial_fold_free(
4906 __isl_take isl_pw_qpolynomial_fold *pwf);
4907 void *isl_union_pw_qpolynomial_fold_free(
4908 __isl_take isl_union_pw_qpolynomial_fold *upwf);
4910 =head3 Printing Piecewise Quasipolynomial Reductions
4912 Piecewise quasipolynomial reductions can be printed
4913 using the following function.
4915 __isl_give isl_printer *isl_printer_print_pw_qpolynomial_fold(
4916 __isl_take isl_printer *p,
4917 __isl_keep isl_pw_qpolynomial_fold *pwf);
4918 __isl_give isl_printer *isl_printer_print_union_pw_qpolynomial_fold(
4919 __isl_take isl_printer *p,
4920 __isl_keep isl_union_pw_qpolynomial_fold *upwf);
4922 For C<isl_printer_print_pw_qpolynomial_fold>,
4923 output format of the printer
4924 needs to be set to either C<ISL_FORMAT_ISL> or C<ISL_FORMAT_C>.
4925 For C<isl_printer_print_union_pw_qpolynomial_fold>,
4926 output format of the printer
4927 needs to be set to C<ISL_FORMAT_ISL>.
4928 In case of printing in C<ISL_FORMAT_C>, the user may want
4929 to set the names of all dimensions
4931 __isl_give isl_pw_qpolynomial_fold *
4932 isl_pw_qpolynomial_fold_set_dim_name(
4933 __isl_take isl_pw_qpolynomial_fold *pwf,
4934 enum isl_dim_type type, unsigned pos,
4937 =head3 Inspecting (Piecewise) Quasipolynomial Reductions
4939 To iterate over all piecewise quasipolynomial reductions in a union
4940 piecewise quasipolynomial reduction, use the following function
4942 int isl_union_pw_qpolynomial_fold_foreach_pw_qpolynomial_fold(
4943 __isl_keep isl_union_pw_qpolynomial_fold *upwf,
4944 int (*fn)(__isl_take isl_pw_qpolynomial_fold *pwf,
4945 void *user), void *user);
4947 To iterate over the cells in a piecewise quasipolynomial reduction,
4948 use either of the following two functions
4950 int isl_pw_qpolynomial_fold_foreach_piece(
4951 __isl_keep isl_pw_qpolynomial_fold *pwf,
4952 int (*fn)(__isl_take isl_set *set,
4953 __isl_take isl_qpolynomial_fold *fold,
4954 void *user), void *user);
4955 int isl_pw_qpolynomial_fold_foreach_lifted_piece(
4956 __isl_keep isl_pw_qpolynomial_fold *pwf,
4957 int (*fn)(__isl_take isl_set *set,
4958 __isl_take isl_qpolynomial_fold *fold,
4959 void *user), void *user);
4961 See L<Inspecting (Piecewise) Quasipolynomials> for an explanation
4962 of the difference between these two functions.
4964 To iterate over all quasipolynomials in a reduction, use
4966 int isl_qpolynomial_fold_foreach_qpolynomial(
4967 __isl_keep isl_qpolynomial_fold *fold,
4968 int (*fn)(__isl_take isl_qpolynomial *qp,
4969 void *user), void *user);
4971 =head3 Properties of Piecewise Quasipolynomial Reductions
4973 To check whether two union piecewise quasipolynomial reductions are
4974 obviously equal, use
4976 int isl_union_pw_qpolynomial_fold_plain_is_equal(
4977 __isl_keep isl_union_pw_qpolynomial_fold *upwf1,
4978 __isl_keep isl_union_pw_qpolynomial_fold *upwf2);
4980 =head3 Operations on Piecewise Quasipolynomial Reductions
4982 __isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_scale_val(
4983 __isl_take isl_qpolynomial_fold *fold,
4984 __isl_take isl_val *v);
4985 __isl_give isl_pw_qpolynomial_fold *
4986 isl_pw_qpolynomial_fold_scale_val(
4987 __isl_take isl_pw_qpolynomial_fold *pwf,
4988 __isl_take isl_val *v);
4989 __isl_give isl_union_pw_qpolynomial_fold *
4990 isl_union_pw_qpolynomial_fold_scale_val(
4991 __isl_take isl_union_pw_qpolynomial_fold *upwf,
4992 __isl_take isl_val *v);
4994 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_add(
4995 __isl_take isl_pw_qpolynomial_fold *pwf1,
4996 __isl_take isl_pw_qpolynomial_fold *pwf2);
4998 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_fold(
4999 __isl_take isl_pw_qpolynomial_fold *pwf1,
5000 __isl_take isl_pw_qpolynomial_fold *pwf2);
5002 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_fold(
5003 __isl_take isl_union_pw_qpolynomial_fold *upwf1,
5004 __isl_take isl_union_pw_qpolynomial_fold *upwf2);
5006 __isl_give isl_val *isl_pw_qpolynomial_fold_eval(
5007 __isl_take isl_pw_qpolynomial_fold *pwf,
5008 __isl_take isl_point *pnt);
5010 __isl_give isl_val *isl_union_pw_qpolynomial_fold_eval(
5011 __isl_take isl_union_pw_qpolynomial_fold *upwf,
5012 __isl_take isl_point *pnt);
5014 __isl_give isl_pw_qpolynomial_fold *
5015 isl_pw_qpolynomial_fold_intersect_params(
5016 __isl_take isl_pw_qpolynomial_fold *pwf,
5017 __isl_take isl_set *set);
5019 __isl_give isl_union_set *isl_union_pw_qpolynomial_fold_domain(
5020 __isl_take isl_union_pw_qpolynomial_fold *upwf);
5021 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_intersect_domain(
5022 __isl_take isl_union_pw_qpolynomial_fold *upwf,
5023 __isl_take isl_union_set *uset);
5024 __isl_give isl_union_pw_qpolynomial_fold *
5025 isl_union_pw_qpolynomial_fold_intersect_params(
5026 __isl_take isl_union_pw_qpolynomial_fold *upwf,
5027 __isl_take isl_set *set);
5029 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_project_domain_on_params(
5030 __isl_take isl_pw_qpolynomial_fold *pwf);
5032 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_coalesce(
5033 __isl_take isl_pw_qpolynomial_fold *pwf);
5035 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_coalesce(
5036 __isl_take isl_union_pw_qpolynomial_fold *upwf);
5038 __isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_gist_params(
5039 __isl_take isl_qpolynomial_fold *fold,
5040 __isl_take isl_set *context);
5041 __isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_gist(
5042 __isl_take isl_qpolynomial_fold *fold,
5043 __isl_take isl_set *context);
5045 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_gist(
5046 __isl_take isl_pw_qpolynomial_fold *pwf,
5047 __isl_take isl_set *context);
5048 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_gist_params(
5049 __isl_take isl_pw_qpolynomial_fold *pwf,
5050 __isl_take isl_set *context);
5052 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_gist(
5053 __isl_take isl_union_pw_qpolynomial_fold *upwf,
5054 __isl_take isl_union_set *context);
5055 __isl_give isl_union_pw_qpolynomial_fold *
5056 isl_union_pw_qpolynomial_fold_gist_params(
5057 __isl_take isl_union_pw_qpolynomial_fold *upwf,
5058 __isl_take isl_set *context);
5060 The gist operation applies the gist operation to each of
5061 the cells in the domain of the input piecewise quasipolynomial reduction.
5062 In future, the operation will also exploit the context
5063 to simplify the quasipolynomial reductions associated to each cell.
5065 __isl_give isl_pw_qpolynomial_fold *
5066 isl_set_apply_pw_qpolynomial_fold(
5067 __isl_take isl_set *set,
5068 __isl_take isl_pw_qpolynomial_fold *pwf,
5070 __isl_give isl_pw_qpolynomial_fold *
5071 isl_map_apply_pw_qpolynomial_fold(
5072 __isl_take isl_map *map,
5073 __isl_take isl_pw_qpolynomial_fold *pwf,
5075 __isl_give isl_union_pw_qpolynomial_fold *
5076 isl_union_set_apply_union_pw_qpolynomial_fold(
5077 __isl_take isl_union_set *uset,
5078 __isl_take isl_union_pw_qpolynomial_fold *upwf,
5080 __isl_give isl_union_pw_qpolynomial_fold *
5081 isl_union_map_apply_union_pw_qpolynomial_fold(
5082 __isl_take isl_union_map *umap,
5083 __isl_take isl_union_pw_qpolynomial_fold *upwf,
5086 The functions taking a map
5087 compose the given map with the given piecewise quasipolynomial reduction.
5088 That is, compute a bound (of the same type as C<pwf> or C<upwf> itself)
5089 over all elements in the intersection of the range of the map
5090 and the domain of the piecewise quasipolynomial reduction
5091 as a function of an element in the domain of the map.
5092 The functions taking a set compute a bound over all elements in the
5093 intersection of the set and the domain of the
5094 piecewise quasipolynomial reduction.
5096 =head2 Parametric Vertex Enumeration
5098 The parametric vertex enumeration described in this section
5099 is mainly intended to be used internally and by the C<barvinok>
5102 #include <isl/vertices.h>
5103 __isl_give isl_vertices *isl_basic_set_compute_vertices(
5104 __isl_keep isl_basic_set *bset);
5106 The function C<isl_basic_set_compute_vertices> performs the
5107 actual computation of the parametric vertices and the chamber
5108 decomposition and store the result in an C<isl_vertices> object.
5109 This information can be queried by either iterating over all
5110 the vertices or iterating over all the chambers or cells
5111 and then iterating over all vertices that are active on the chamber.
5113 int isl_vertices_foreach_vertex(
5114 __isl_keep isl_vertices *vertices,
5115 int (*fn)(__isl_take isl_vertex *vertex, void *user),
5118 int isl_vertices_foreach_cell(
5119 __isl_keep isl_vertices *vertices,
5120 int (*fn)(__isl_take isl_cell *cell, void *user),
5122 int isl_cell_foreach_vertex(__isl_keep isl_cell *cell,
5123 int (*fn)(__isl_take isl_vertex *vertex, void *user),
5126 Other operations that can be performed on an C<isl_vertices> object are
5129 isl_ctx *isl_vertices_get_ctx(
5130 __isl_keep isl_vertices *vertices);
5131 int isl_vertices_get_n_vertices(
5132 __isl_keep isl_vertices *vertices);
5133 void isl_vertices_free(__isl_take isl_vertices *vertices);
5135 Vertices can be inspected and destroyed using the following functions.
5137 isl_ctx *isl_vertex_get_ctx(__isl_keep isl_vertex *vertex);
5138 int isl_vertex_get_id(__isl_keep isl_vertex *vertex);
5139 __isl_give isl_basic_set *isl_vertex_get_domain(
5140 __isl_keep isl_vertex *vertex);
5141 __isl_give isl_basic_set *isl_vertex_get_expr(
5142 __isl_keep isl_vertex *vertex);
5143 void isl_vertex_free(__isl_take isl_vertex *vertex);
5145 C<isl_vertex_get_expr> returns a singleton parametric set describing
5146 the vertex, while C<isl_vertex_get_domain> returns the activity domain
5148 Note that C<isl_vertex_get_domain> and C<isl_vertex_get_expr> return
5149 B<rational> basic sets, so they should mainly be used for inspection
5150 and should not be mixed with integer sets.
5152 Chambers can be inspected and destroyed using the following functions.
5154 isl_ctx *isl_cell_get_ctx(__isl_keep isl_cell *cell);
5155 __isl_give isl_basic_set *isl_cell_get_domain(
5156 __isl_keep isl_cell *cell);
5157 void isl_cell_free(__isl_take isl_cell *cell);
5159 =head1 Polyhedral Compilation Library
5161 This section collects functionality in C<isl> that has been specifically
5162 designed for use during polyhedral compilation.
5164 =head2 Dependence Analysis
5166 C<isl> contains specialized functionality for performing
5167 array dataflow analysis. That is, given a I<sink> access relation
5168 and a collection of possible I<source> access relations,
5169 C<isl> can compute relations that describe
5170 for each iteration of the sink access, which iteration
5171 of which of the source access relations was the last
5172 to access the same data element before the given iteration
5174 The resulting dependence relations map source iterations
5175 to the corresponding sink iterations.
5176 To compute standard flow dependences, the sink should be
5177 a read, while the sources should be writes.
5178 If any of the source accesses are marked as being I<may>
5179 accesses, then there will be a dependence from the last
5180 I<must> access B<and> from any I<may> access that follows
5181 this last I<must> access.
5182 In particular, if I<all> sources are I<may> accesses,
5183 then memory based dependence analysis is performed.
5184 If, on the other hand, all sources are I<must> accesses,
5185 then value based dependence analysis is performed.
5187 #include <isl/flow.h>
5189 typedef int (*isl_access_level_before)(void *first, void *second);
5191 __isl_give isl_access_info *isl_access_info_alloc(
5192 __isl_take isl_map *sink,
5193 void *sink_user, isl_access_level_before fn,
5195 __isl_give isl_access_info *isl_access_info_add_source(
5196 __isl_take isl_access_info *acc,
5197 __isl_take isl_map *source, int must,
5199 void *isl_access_info_free(__isl_take isl_access_info *acc);
5201 __isl_give isl_flow *isl_access_info_compute_flow(
5202 __isl_take isl_access_info *acc);
5204 int isl_flow_foreach(__isl_keep isl_flow *deps,
5205 int (*fn)(__isl_take isl_map *dep, int must,
5206 void *dep_user, void *user),
5208 __isl_give isl_map *isl_flow_get_no_source(
5209 __isl_keep isl_flow *deps, int must);
5210 void isl_flow_free(__isl_take isl_flow *deps);
5212 The function C<isl_access_info_compute_flow> performs the actual
5213 dependence analysis. The other functions are used to construct
5214 the input for this function or to read off the output.
5216 The input is collected in an C<isl_access_info>, which can
5217 be created through a call to C<isl_access_info_alloc>.
5218 The arguments to this functions are the sink access relation
5219 C<sink>, a token C<sink_user> used to identify the sink
5220 access to the user, a callback function for specifying the
5221 relative order of source and sink accesses, and the number
5222 of source access relations that will be added.
5223 The callback function has type C<int (*)(void *first, void *second)>.
5224 The function is called with two user supplied tokens identifying
5225 either a source or the sink and it should return the shared nesting
5226 level and the relative order of the two accesses.
5227 In particular, let I<n> be the number of loops shared by
5228 the two accesses. If C<first> precedes C<second> textually,
5229 then the function should return I<2 * n + 1>; otherwise,
5230 it should return I<2 * n>.
5231 The sources can be added to the C<isl_access_info> by performing
5232 (at most) C<max_source> calls to C<isl_access_info_add_source>.
5233 C<must> indicates whether the source is a I<must> access
5234 or a I<may> access. Note that a multi-valued access relation
5235 should only be marked I<must> if every iteration in the domain
5236 of the relation accesses I<all> elements in its image.
5237 The C<source_user> token is again used to identify
5238 the source access. The range of the source access relation
5239 C<source> should have the same dimension as the range
5240 of the sink access relation.
5241 The C<isl_access_info_free> function should usually not be
5242 called explicitly, because it is called implicitly by
5243 C<isl_access_info_compute_flow>.
5245 The result of the dependence analysis is collected in an
5246 C<isl_flow>. There may be elements of
5247 the sink access for which no preceding source access could be
5248 found or for which all preceding sources are I<may> accesses.
5249 The relations containing these elements can be obtained through
5250 calls to C<isl_flow_get_no_source>, the first with C<must> set
5251 and the second with C<must> unset.
5252 In the case of standard flow dependence analysis,
5253 with the sink a read and the sources I<must> writes,
5254 the first relation corresponds to the reads from uninitialized
5255 array elements and the second relation is empty.
5256 The actual flow dependences can be extracted using
5257 C<isl_flow_foreach>. This function will call the user-specified
5258 callback function C<fn> for each B<non-empty> dependence between
5259 a source and the sink. The callback function is called
5260 with four arguments, the actual flow dependence relation
5261 mapping source iterations to sink iterations, a boolean that
5262 indicates whether it is a I<must> or I<may> dependence, a token
5263 identifying the source and an additional C<void *> with value
5264 equal to the third argument of the C<isl_flow_foreach> call.
5265 A dependence is marked I<must> if it originates from a I<must>
5266 source and if it is not followed by any I<may> sources.
5268 After finishing with an C<isl_flow>, the user should call
5269 C<isl_flow_free> to free all associated memory.
5271 A higher-level interface to dependence analysis is provided
5272 by the following function.
5274 #include <isl/flow.h>
5276 int isl_union_map_compute_flow(__isl_take isl_union_map *sink,
5277 __isl_take isl_union_map *must_source,
5278 __isl_take isl_union_map *may_source,
5279 __isl_take isl_union_map *schedule,
5280 __isl_give isl_union_map **must_dep,
5281 __isl_give isl_union_map **may_dep,
5282 __isl_give isl_union_map **must_no_source,
5283 __isl_give isl_union_map **may_no_source);
5285 The arrays are identified by the tuple names of the ranges
5286 of the accesses. The iteration domains by the tuple names
5287 of the domains of the accesses and of the schedule.
5288 The relative order of the iteration domains is given by the
5289 schedule. The relations returned through C<must_no_source>
5290 and C<may_no_source> are subsets of C<sink>.
5291 Any of C<must_dep>, C<may_dep>, C<must_no_source>
5292 or C<may_no_source> may be C<NULL>, but a C<NULL> value for
5293 any of the other arguments is treated as an error.
5295 =head3 Interaction with Dependence Analysis
5297 During the dependence analysis, we frequently need to perform
5298 the following operation. Given a relation between sink iterations
5299 and potential source iterations from a particular source domain,
5300 what is the last potential source iteration corresponding to each
5301 sink iteration. It can sometimes be convenient to adjust
5302 the set of potential source iterations before or after each such operation.
5303 The prototypical example is fuzzy array dataflow analysis,
5304 where we need to analyze if, based on data-dependent constraints,
5305 the sink iteration can ever be executed without one or more of
5306 the corresponding potential source iterations being executed.
5307 If so, we can introduce extra parameters and select an unknown
5308 but fixed source iteration from the potential source iterations.
5309 To be able to perform such manipulations, C<isl> provides the following
5312 #include <isl/flow.h>
5314 typedef __isl_give isl_restriction *(*isl_access_restrict)(
5315 __isl_keep isl_map *source_map,
5316 __isl_keep isl_set *sink, void *source_user,
5318 __isl_give isl_access_info *isl_access_info_set_restrict(
5319 __isl_take isl_access_info *acc,
5320 isl_access_restrict fn, void *user);
5322 The function C<isl_access_info_set_restrict> should be called
5323 before calling C<isl_access_info_compute_flow> and registers a callback function
5324 that will be called any time C<isl> is about to compute the last
5325 potential source. The first argument is the (reverse) proto-dependence,
5326 mapping sink iterations to potential source iterations.
5327 The second argument represents the sink iterations for which
5328 we want to compute the last source iteration.
5329 The third argument is the token corresponding to the source
5330 and the final argument is the token passed to C<isl_access_info_set_restrict>.
5331 The callback is expected to return a restriction on either the input or
5332 the output of the operation computing the last potential source.
5333 If the input needs to be restricted then restrictions are needed
5334 for both the source and the sink iterations. The sink iterations
5335 and the potential source iterations will be intersected with these sets.
5336 If the output needs to be restricted then only a restriction on the source
5337 iterations is required.
5338 If any error occurs, the callback should return C<NULL>.
5339 An C<isl_restriction> object can be created, freed and inspected
5340 using the following functions.
5342 #include <isl/flow.h>
5344 __isl_give isl_restriction *isl_restriction_input(
5345 __isl_take isl_set *source_restr,
5346 __isl_take isl_set *sink_restr);
5347 __isl_give isl_restriction *isl_restriction_output(
5348 __isl_take isl_set *source_restr);
5349 __isl_give isl_restriction *isl_restriction_none(
5350 __isl_take isl_map *source_map);
5351 __isl_give isl_restriction *isl_restriction_empty(
5352 __isl_take isl_map *source_map);
5353 void *isl_restriction_free(
5354 __isl_take isl_restriction *restr);
5355 isl_ctx *isl_restriction_get_ctx(
5356 __isl_keep isl_restriction *restr);
5358 C<isl_restriction_none> and C<isl_restriction_empty> are special
5359 cases of C<isl_restriction_input>. C<isl_restriction_none>
5360 is essentially equivalent to
5362 isl_restriction_input(isl_set_universe(
5363 isl_space_range(isl_map_get_space(source_map))),
5365 isl_space_domain(isl_map_get_space(source_map))));
5367 whereas C<isl_restriction_empty> is essentially equivalent to
5369 isl_restriction_input(isl_set_empty(
5370 isl_space_range(isl_map_get_space(source_map))),
5372 isl_space_domain(isl_map_get_space(source_map))));
5376 B<The functionality described in this section is fairly new
5377 and may be subject to change.>
5379 The following function can be used to compute a schedule
5380 for a union of domains.
5381 By default, the algorithm used to construct the schedule is similar
5382 to that of C<Pluto>.
5383 Alternatively, Feautrier's multi-dimensional scheduling algorithm can
5385 The generated schedule respects all C<validity> dependences.
5386 That is, all dependence distances over these dependences in the
5387 scheduled space are lexicographically positive.
5388 The default algorithm tries to minimize the dependence distances over
5389 C<proximity> dependences.
5390 Moreover, it tries to obtain sequences (bands) of schedule dimensions
5391 for groups of domains where the dependence distances have only
5392 non-negative values.
5393 When using Feautrier's algorithm, the C<proximity> dependence
5394 distances are only minimized during the extension to a
5395 full-dimensional schedule.
5397 #include <isl/schedule.h>
5398 __isl_give isl_schedule *isl_union_set_compute_schedule(
5399 __isl_take isl_union_set *domain,
5400 __isl_take isl_union_map *validity,
5401 __isl_take isl_union_map *proximity);
5402 void *isl_schedule_free(__isl_take isl_schedule *sched);
5404 A mapping from the domains to the scheduled space can be obtained
5405 from an C<isl_schedule> using the following function.
5407 __isl_give isl_union_map *isl_schedule_get_map(
5408 __isl_keep isl_schedule *sched);
5410 A representation of the schedule can be printed using
5412 __isl_give isl_printer *isl_printer_print_schedule(
5413 __isl_take isl_printer *p,
5414 __isl_keep isl_schedule *schedule);
5416 A representation of the schedule as a forest of bands can be obtained
5417 using the following function.
5419 __isl_give isl_band_list *isl_schedule_get_band_forest(
5420 __isl_keep isl_schedule *schedule);
5422 The individual bands can be visited in depth-first post-order
5423 using the following function.
5425 #include <isl/schedule.h>
5426 int isl_schedule_foreach_band(
5427 __isl_keep isl_schedule *sched,
5428 int (*fn)(__isl_keep isl_band *band, void *user),
5431 The list can be manipulated as explained in L<"Lists">.
5432 The bands inside the list can be copied and freed using the following
5435 #include <isl/band.h>
5436 __isl_give isl_band *isl_band_copy(
5437 __isl_keep isl_band *band);
5438 void *isl_band_free(__isl_take isl_band *band);
5440 Each band contains zero or more scheduling dimensions.
5441 These are referred to as the members of the band.
5442 The section of the schedule that corresponds to the band is
5443 referred to as the partial schedule of the band.
5444 For those nodes that participate in a band, the outer scheduling
5445 dimensions form the prefix schedule, while the inner scheduling
5446 dimensions form the suffix schedule.
5447 That is, if we take a cut of the band forest, then the union of
5448 the concatenations of the prefix, partial and suffix schedules of
5449 each band in the cut is equal to the entire schedule (modulo
5450 some possible padding at the end with zero scheduling dimensions).
5451 The properties of a band can be inspected using the following functions.
5453 #include <isl/band.h>
5454 isl_ctx *isl_band_get_ctx(__isl_keep isl_band *band);
5456 int isl_band_has_children(__isl_keep isl_band *band);
5457 __isl_give isl_band_list *isl_band_get_children(
5458 __isl_keep isl_band *band);
5460 __isl_give isl_union_map *isl_band_get_prefix_schedule(
5461 __isl_keep isl_band *band);
5462 __isl_give isl_union_map *isl_band_get_partial_schedule(
5463 __isl_keep isl_band *band);
5464 __isl_give isl_union_map *isl_band_get_suffix_schedule(
5465 __isl_keep isl_band *band);
5467 int isl_band_n_member(__isl_keep isl_band *band);
5468 int isl_band_member_is_zero_distance(
5469 __isl_keep isl_band *band, int pos);
5471 int isl_band_list_foreach_band(
5472 __isl_keep isl_band_list *list,
5473 int (*fn)(__isl_keep isl_band *band, void *user),
5476 Note that a scheduling dimension is considered to be ``zero
5477 distance'' if it does not carry any proximity dependences
5479 That is, if the dependence distances of the proximity
5480 dependences are all zero in that direction (for fixed
5481 iterations of outer bands).
5482 Like C<isl_schedule_foreach_band>,
5483 the function C<isl_band_list_foreach_band> calls C<fn> on the bands
5484 in depth-first post-order.
5486 A band can be tiled using the following function.
5488 #include <isl/band.h>
5489 int isl_band_tile(__isl_keep isl_band *band,
5490 __isl_take isl_vec *sizes);
5492 int isl_options_set_tile_scale_tile_loops(isl_ctx *ctx,
5494 int isl_options_get_tile_scale_tile_loops(isl_ctx *ctx);
5495 int isl_options_set_tile_shift_point_loops(isl_ctx *ctx,
5497 int isl_options_get_tile_shift_point_loops(isl_ctx *ctx);
5499 The C<isl_band_tile> function tiles the band using the given tile sizes
5500 inside its schedule.
5501 A new child band is created to represent the point loops and it is
5502 inserted between the modified band and its children.
5503 The C<tile_scale_tile_loops> option specifies whether the tile
5504 loops iterators should be scaled by the tile sizes.
5505 If the C<tile_shift_point_loops> option is set, then the point loops
5506 are shifted to start at zero.
5508 A band can be split into two nested bands using the following function.
5510 int isl_band_split(__isl_keep isl_band *band, int pos);
5512 The resulting outer band contains the first C<pos> dimensions of C<band>
5513 while the inner band contains the remaining dimensions.
5515 A representation of the band can be printed using
5517 #include <isl/band.h>
5518 __isl_give isl_printer *isl_printer_print_band(
5519 __isl_take isl_printer *p,
5520 __isl_keep isl_band *band);
5524 #include <isl/schedule.h>
5525 int isl_options_set_schedule_max_coefficient(
5526 isl_ctx *ctx, int val);
5527 int isl_options_get_schedule_max_coefficient(
5529 int isl_options_set_schedule_max_constant_term(
5530 isl_ctx *ctx, int val);
5531 int isl_options_get_schedule_max_constant_term(
5533 int isl_options_set_schedule_fuse(isl_ctx *ctx, int val);
5534 int isl_options_get_schedule_fuse(isl_ctx *ctx);
5535 int isl_options_set_schedule_maximize_band_depth(
5536 isl_ctx *ctx, int val);
5537 int isl_options_get_schedule_maximize_band_depth(
5539 int isl_options_set_schedule_outer_zero_distance(
5540 isl_ctx *ctx, int val);
5541 int isl_options_get_schedule_outer_zero_distance(
5543 int isl_options_set_schedule_split_scaled(
5544 isl_ctx *ctx, int val);
5545 int isl_options_get_schedule_split_scaled(
5547 int isl_options_set_schedule_algorithm(
5548 isl_ctx *ctx, int val);
5549 int isl_options_get_schedule_algorithm(
5551 int isl_options_set_schedule_separate_components(
5552 isl_ctx *ctx, int val);
5553 int isl_options_get_schedule_separate_components(
5558 =item * schedule_max_coefficient
5560 This option enforces that the coefficients for variable and parameter
5561 dimensions in the calculated schedule are not larger than the specified value.
5562 This option can significantly increase the speed of the scheduling calculation
5563 and may also prevent fusing of unrelated dimensions. A value of -1 means that
5564 this option does not introduce bounds on the variable or parameter
5567 =item * schedule_max_constant_term
5569 This option enforces that the constant coefficients in the calculated schedule
5570 are not larger than the maximal constant term. This option can significantly
5571 increase the speed of the scheduling calculation and may also prevent fusing of
5572 unrelated dimensions. A value of -1 means that this option does not introduce
5573 bounds on the constant coefficients.
5575 =item * schedule_fuse
5577 This option controls the level of fusion.
5578 If this option is set to C<ISL_SCHEDULE_FUSE_MIN>, then loops in the
5579 resulting schedule will be distributed as much as possible.
5580 If this option is set to C<ISL_SCHEDULE_FUSE_MAX>, then C<isl> will
5581 try to fuse loops in the resulting schedule.
5583 =item * schedule_maximize_band_depth
5585 If this option is set, we do not split bands at the point
5586 where we detect splitting is necessary. Instead, we
5587 backtrack and split bands as early as possible. This
5588 reduces the number of splits and maximizes the width of
5589 the bands. Wider bands give more possibilities for tiling.
5590 Note that if the C<schedule_fuse> option is set to C<ISL_SCHEDULE_FUSE_MIN>,
5591 then bands will be split as early as possible, even if there is no need.
5592 The C<schedule_maximize_band_depth> option therefore has no effect in this case.
5594 =item * schedule_outer_zero_distance
5596 If this option is set, then we try to construct schedules
5597 where the outermost scheduling dimension in each band
5598 results in a zero dependence distance over the proximity
5601 =item * schedule_split_scaled
5603 If this option is set, then we try to construct schedules in which the
5604 constant term is split off from the linear part if the linear parts of
5605 the scheduling rows for all nodes in the graphs have a common non-trivial
5607 The constant term is then placed in a separate band and the linear
5610 =item * schedule_algorithm
5612 Selects the scheduling algorithm to be used.
5613 Available scheduling algorithms are C<ISL_SCHEDULE_ALGORITHM_ISL>
5614 and C<ISL_SCHEDULE_ALGORITHM_FEAUTRIER>.
5616 =item * schedule_separate_components
5618 If at any point the dependence graph contains any (weakly connected) components,
5619 then these components are scheduled separately.
5620 If this option is not set, then some iterations of the domains
5621 in these components may be scheduled together.
5622 If this option is set, then the components are given consecutive
5627 =head2 AST Generation
5629 This section describes the C<isl> functionality for generating
5630 ASTs that visit all the elements
5631 in a domain in an order specified by a schedule.
5632 In particular, given a C<isl_union_map>, an AST is generated
5633 that visits all the elements in the domain of the C<isl_union_map>
5634 according to the lexicographic order of the corresponding image
5635 element(s). If the range of the C<isl_union_map> consists of
5636 elements in more than one space, then each of these spaces is handled
5637 separately in an arbitrary order.
5638 It should be noted that the image elements only specify the I<order>
5639 in which the corresponding domain elements should be visited.
5640 No direct relation between the image elements and the loop iterators
5641 in the generated AST should be assumed.
5643 Each AST is generated within a build. The initial build
5644 simply specifies the constraints on the parameters (if any)
5645 and can be created, inspected, copied and freed using the following functions.
5647 #include <isl/ast_build.h>
5648 __isl_give isl_ast_build *isl_ast_build_from_context(
5649 __isl_take isl_set *set);
5650 isl_ctx *isl_ast_build_get_ctx(
5651 __isl_keep isl_ast_build *build);
5652 __isl_give isl_ast_build *isl_ast_build_copy(
5653 __isl_keep isl_ast_build *build);
5654 void *isl_ast_build_free(
5655 __isl_take isl_ast_build *build);
5657 The C<set> argument is usually a parameter set with zero or more parameters.
5658 More C<isl_ast_build> functions are described in L</"Nested AST Generation">
5659 and L</"Fine-grained Control over AST Generation">.
5660 Finally, the AST itself can be constructed using the following
5663 #include <isl/ast_build.h>
5664 __isl_give isl_ast_node *isl_ast_build_ast_from_schedule(
5665 __isl_keep isl_ast_build *build,
5666 __isl_take isl_union_map *schedule);
5668 =head3 Inspecting the AST
5670 The basic properties of an AST node can be obtained as follows.
5672 #include <isl/ast.h>
5673 isl_ctx *isl_ast_node_get_ctx(
5674 __isl_keep isl_ast_node *node);
5675 enum isl_ast_node_type isl_ast_node_get_type(
5676 __isl_keep isl_ast_node *node);
5678 The type of an AST node is one of
5679 C<isl_ast_node_for>,
5681 C<isl_ast_node_block> or
5682 C<isl_ast_node_user>.
5683 An C<isl_ast_node_for> represents a for node.
5684 An C<isl_ast_node_if> represents an if node.
5685 An C<isl_ast_node_block> represents a compound node.
5686 An C<isl_ast_node_user> represents an expression statement.
5687 An expression statement typically corresponds to a domain element, i.e.,
5688 one of the elements that is visited by the AST.
5690 Each type of node has its own additional properties.
5692 #include <isl/ast.h>
5693 __isl_give isl_ast_expr *isl_ast_node_for_get_iterator(
5694 __isl_keep isl_ast_node *node);
5695 __isl_give isl_ast_expr *isl_ast_node_for_get_init(
5696 __isl_keep isl_ast_node *node);
5697 __isl_give isl_ast_expr *isl_ast_node_for_get_cond(
5698 __isl_keep isl_ast_node *node);
5699 __isl_give isl_ast_expr *isl_ast_node_for_get_inc(
5700 __isl_keep isl_ast_node *node);
5701 __isl_give isl_ast_node *isl_ast_node_for_get_body(
5702 __isl_keep isl_ast_node *node);
5703 int isl_ast_node_for_is_degenerate(
5704 __isl_keep isl_ast_node *node);
5706 An C<isl_ast_for> is considered degenerate if it is known to execute
5709 #include <isl/ast.h>
5710 __isl_give isl_ast_expr *isl_ast_node_if_get_cond(
5711 __isl_keep isl_ast_node *node);
5712 __isl_give isl_ast_node *isl_ast_node_if_get_then(
5713 __isl_keep isl_ast_node *node);
5714 int isl_ast_node_if_has_else(
5715 __isl_keep isl_ast_node *node);
5716 __isl_give isl_ast_node *isl_ast_node_if_get_else(
5717 __isl_keep isl_ast_node *node);
5719 __isl_give isl_ast_node_list *
5720 isl_ast_node_block_get_children(
5721 __isl_keep isl_ast_node *node);
5723 __isl_give isl_ast_expr *isl_ast_node_user_get_expr(
5724 __isl_keep isl_ast_node *node);
5726 Each of the returned C<isl_ast_expr>s can in turn be inspected using
5727 the following functions.
5729 #include <isl/ast.h>
5730 isl_ctx *isl_ast_expr_get_ctx(
5731 __isl_keep isl_ast_expr *expr);
5732 enum isl_ast_expr_type isl_ast_expr_get_type(
5733 __isl_keep isl_ast_expr *expr);
5735 The type of an AST expression is one of
5737 C<isl_ast_expr_id> or
5738 C<isl_ast_expr_int>.
5739 An C<isl_ast_expr_op> represents the result of an operation.
5740 An C<isl_ast_expr_id> represents an identifier.
5741 An C<isl_ast_expr_int> represents an integer value.
5743 Each type of expression has its own additional properties.
5745 #include <isl/ast.h>
5746 enum isl_ast_op_type isl_ast_expr_get_op_type(
5747 __isl_keep isl_ast_expr *expr);
5748 int isl_ast_expr_get_op_n_arg(__isl_keep isl_ast_expr *expr);
5749 __isl_give isl_ast_expr *isl_ast_expr_get_op_arg(
5750 __isl_keep isl_ast_expr *expr, int pos);
5751 int isl_ast_node_foreach_ast_op_type(
5752 __isl_keep isl_ast_node *node,
5753 int (*fn)(enum isl_ast_op_type type, void *user),
5756 C<isl_ast_expr_get_op_type> returns the type of the operation
5757 performed. C<isl_ast_expr_get_op_n_arg> returns the number of
5758 arguments. C<isl_ast_expr_get_op_arg> returns the specified
5760 C<isl_ast_node_foreach_ast_op_type> calls C<fn> for each distinct
5761 C<isl_ast_op_type> that appears in C<node>.
5762 The operation type is one of the following.
5766 =item C<isl_ast_op_and>
5768 Logical I<and> of two arguments.
5769 Both arguments can be evaluated.
5771 =item C<isl_ast_op_and_then>
5773 Logical I<and> of two arguments.
5774 The second argument can only be evaluated if the first evaluates to true.
5776 =item C<isl_ast_op_or>
5778 Logical I<or> of two arguments.
5779 Both arguments can be evaluated.
5781 =item C<isl_ast_op_or_else>
5783 Logical I<or> of two arguments.
5784 The second argument can only be evaluated if the first evaluates to false.
5786 =item C<isl_ast_op_max>
5788 Maximum of two or more arguments.
5790 =item C<isl_ast_op_min>
5792 Minimum of two or more arguments.
5794 =item C<isl_ast_op_minus>
5798 =item C<isl_ast_op_add>
5800 Sum of two arguments.
5802 =item C<isl_ast_op_sub>
5804 Difference of two arguments.
5806 =item C<isl_ast_op_mul>
5808 Product of two arguments.
5810 =item C<isl_ast_op_div>
5812 Exact division. That is, the result is known to be an integer.
5814 =item C<isl_ast_op_fdiv_q>
5816 Result of integer division, rounded towards negative
5819 =item C<isl_ast_op_pdiv_q>
5821 Result of integer division, where dividend is known to be non-negative.
5823 =item C<isl_ast_op_pdiv_r>
5825 Remainder of integer division, where dividend is known to be non-negative.
5827 =item C<isl_ast_op_cond>
5829 Conditional operator defined on three arguments.
5830 If the first argument evaluates to true, then the result
5831 is equal to the second argument. Otherwise, the result
5832 is equal to the third argument.
5833 The second and third argument may only be evaluated if
5834 the first argument evaluates to true and false, respectively.
5835 Corresponds to C<a ? b : c> in C.
5837 =item C<isl_ast_op_select>
5839 Conditional operator defined on three arguments.
5840 If the first argument evaluates to true, then the result
5841 is equal to the second argument. Otherwise, the result
5842 is equal to the third argument.
5843 The second and third argument may be evaluated independently
5844 of the value of the first argument.
5845 Corresponds to C<a * b + (1 - a) * c> in C.
5847 =item C<isl_ast_op_eq>
5851 =item C<isl_ast_op_le>
5853 Less than or equal relation.
5855 =item C<isl_ast_op_lt>
5859 =item C<isl_ast_op_ge>
5861 Greater than or equal relation.
5863 =item C<isl_ast_op_gt>
5865 Greater than relation.
5867 =item C<isl_ast_op_call>
5870 The number of arguments of the C<isl_ast_expr> is one more than
5871 the number of arguments in the function call, the first argument
5872 representing the function being called.
5876 #include <isl/ast.h>
5877 __isl_give isl_id *isl_ast_expr_get_id(
5878 __isl_keep isl_ast_expr *expr);
5880 Return the identifier represented by the AST expression.
5882 #include <isl/ast.h>
5883 __isl_give isl_val *isl_ast_expr_get_val(
5884 __isl_keep isl_ast_expr *expr);
5886 Return the integer represented by the AST expression.
5888 =head3 Manipulating and printing the AST
5890 AST nodes can be copied and freed using the following functions.
5892 #include <isl/ast.h>
5893 __isl_give isl_ast_node *isl_ast_node_copy(
5894 __isl_keep isl_ast_node *node);
5895 void *isl_ast_node_free(__isl_take isl_ast_node *node);
5897 AST expressions can be copied and freed using the following functions.
5899 #include <isl/ast.h>
5900 __isl_give isl_ast_expr *isl_ast_expr_copy(
5901 __isl_keep isl_ast_expr *expr);
5902 void *isl_ast_expr_free(__isl_take isl_ast_expr *expr);
5904 New AST expressions can be created either directly or within
5905 the context of an C<isl_ast_build>.
5907 #include <isl/ast.h>
5908 __isl_give isl_ast_expr *isl_ast_expr_from_val(
5909 __isl_take isl_val *v);
5910 __isl_give isl_ast_expr *isl_ast_expr_from_id(
5911 __isl_take isl_id *id);
5912 __isl_give isl_ast_expr *isl_ast_expr_neg(
5913 __isl_take isl_ast_expr *expr);
5914 __isl_give isl_ast_expr *isl_ast_expr_add(
5915 __isl_take isl_ast_expr *expr1,
5916 __isl_take isl_ast_expr *expr2);
5917 __isl_give isl_ast_expr *isl_ast_expr_sub(
5918 __isl_take isl_ast_expr *expr1,
5919 __isl_take isl_ast_expr *expr2);
5920 __isl_give isl_ast_expr *isl_ast_expr_mul(
5921 __isl_take isl_ast_expr *expr1,
5922 __isl_take isl_ast_expr *expr2);
5923 __isl_give isl_ast_expr *isl_ast_expr_div(
5924 __isl_take isl_ast_expr *expr1,
5925 __isl_take isl_ast_expr *expr2);
5926 __isl_give isl_ast_expr *isl_ast_expr_and(
5927 __isl_take isl_ast_expr *expr1,
5928 __isl_take isl_ast_expr *expr2)
5929 __isl_give isl_ast_expr *isl_ast_expr_or(
5930 __isl_take isl_ast_expr *expr1,
5931 __isl_take isl_ast_expr *expr2)
5933 #include <isl/ast_build.h>
5934 __isl_give isl_ast_expr *isl_ast_build_expr_from_pw_aff(
5935 __isl_keep isl_ast_build *build,
5936 __isl_take isl_pw_aff *pa);
5937 __isl_give isl_ast_expr *
5938 isl_ast_build_call_from_pw_multi_aff(
5939 __isl_keep isl_ast_build *build,
5940 __isl_take isl_pw_multi_aff *pma);
5942 The domains of C<pa> and C<pma> should correspond
5943 to the schedule space of C<build>.
5944 The tuple id of C<pma> is used as the function being called.
5946 User specified data can be attached to an C<isl_ast_node> and obtained
5947 from the same C<isl_ast_node> using the following functions.
5949 #include <isl/ast.h>
5950 __isl_give isl_ast_node *isl_ast_node_set_annotation(
5951 __isl_take isl_ast_node *node,
5952 __isl_take isl_id *annotation);
5953 __isl_give isl_id *isl_ast_node_get_annotation(
5954 __isl_keep isl_ast_node *node);
5956 Basic printing can be performed using the following functions.
5958 #include <isl/ast.h>
5959 __isl_give isl_printer *isl_printer_print_ast_expr(
5960 __isl_take isl_printer *p,
5961 __isl_keep isl_ast_expr *expr);
5962 __isl_give isl_printer *isl_printer_print_ast_node(
5963 __isl_take isl_printer *p,
5964 __isl_keep isl_ast_node *node);
5966 More advanced printing can be performed using the following functions.
5968 #include <isl/ast.h>
5969 __isl_give isl_printer *isl_ast_op_type_print_macro(
5970 enum isl_ast_op_type type,
5971 __isl_take isl_printer *p);
5972 __isl_give isl_printer *isl_ast_node_print_macros(
5973 __isl_keep isl_ast_node *node,
5974 __isl_take isl_printer *p);
5975 __isl_give isl_printer *isl_ast_node_print(
5976 __isl_keep isl_ast_node *node,
5977 __isl_take isl_printer *p,
5978 __isl_take isl_ast_print_options *options);
5979 __isl_give isl_printer *isl_ast_node_for_print(
5980 __isl_keep isl_ast_node *node,
5981 __isl_take isl_printer *p,
5982 __isl_take isl_ast_print_options *options);
5983 __isl_give isl_printer *isl_ast_node_if_print(
5984 __isl_keep isl_ast_node *node,
5985 __isl_take isl_printer *p,
5986 __isl_take isl_ast_print_options *options);
5988 While printing an C<isl_ast_node> in C<ISL_FORMAT_C>,
5989 C<isl> may print out an AST that makes use of macros such
5990 as C<floord>, C<min> and C<max>.
5991 C<isl_ast_op_type_print_macro> prints out the macro
5992 corresponding to a specific C<isl_ast_op_type>.
5993 C<isl_ast_node_print_macros> scans the C<isl_ast_node>
5994 for expressions where these macros would be used and prints
5995 out the required macro definitions.
5996 Essentially, C<isl_ast_node_print_macros> calls
5997 C<isl_ast_node_foreach_ast_op_type> with C<isl_ast_op_type_print_macro>
5998 as function argument.
5999 C<isl_ast_node_print>, C<isl_ast_node_for_print> and
6000 C<isl_ast_node_if_print> print an C<isl_ast_node>
6001 in C<ISL_FORMAT_C>, but allow for some extra control
6002 through an C<isl_ast_print_options> object.
6003 This object can be created using the following functions.
6005 #include <isl/ast.h>
6006 __isl_give isl_ast_print_options *
6007 isl_ast_print_options_alloc(isl_ctx *ctx);
6008 __isl_give isl_ast_print_options *
6009 isl_ast_print_options_copy(
6010 __isl_keep isl_ast_print_options *options);
6011 void *isl_ast_print_options_free(
6012 __isl_take isl_ast_print_options *options);
6014 __isl_give isl_ast_print_options *
6015 isl_ast_print_options_set_print_user(
6016 __isl_take isl_ast_print_options *options,
6017 __isl_give isl_printer *(*print_user)(
6018 __isl_take isl_printer *p,
6019 __isl_take isl_ast_print_options *options,
6020 __isl_keep isl_ast_node *node, void *user),
6022 __isl_give isl_ast_print_options *
6023 isl_ast_print_options_set_print_for(
6024 __isl_take isl_ast_print_options *options,
6025 __isl_give isl_printer *(*print_for)(
6026 __isl_take isl_printer *p,
6027 __isl_take isl_ast_print_options *options,
6028 __isl_keep isl_ast_node *node, void *user),
6031 The callback set by C<isl_ast_print_options_set_print_user>
6032 is called whenever a node of type C<isl_ast_node_user> needs to
6034 The callback set by C<isl_ast_print_options_set_print_for>
6035 is called whenever a node of type C<isl_ast_node_for> needs to
6037 Note that C<isl_ast_node_for_print> will I<not> call the
6038 callback set by C<isl_ast_print_options_set_print_for> on the node
6039 on which C<isl_ast_node_for_print> is called, but only on nested
6040 nodes of type C<isl_ast_node_for>. It is therefore safe to
6041 call C<isl_ast_node_for_print> from within the callback set by
6042 C<isl_ast_print_options_set_print_for>.
6044 The following option determines the type to be used for iterators
6045 while printing the AST.
6047 int isl_options_set_ast_iterator_type(
6048 isl_ctx *ctx, const char *val);
6049 const char *isl_options_get_ast_iterator_type(
6054 #include <isl/ast_build.h>
6055 int isl_options_set_ast_build_atomic_upper_bound(
6056 isl_ctx *ctx, int val);
6057 int isl_options_get_ast_build_atomic_upper_bound(
6059 int isl_options_set_ast_build_prefer_pdiv(isl_ctx *ctx,
6061 int isl_options_get_ast_build_prefer_pdiv(isl_ctx *ctx);
6062 int isl_options_set_ast_build_exploit_nested_bounds(
6063 isl_ctx *ctx, int val);
6064 int isl_options_get_ast_build_exploit_nested_bounds(
6066 int isl_options_set_ast_build_group_coscheduled(
6067 isl_ctx *ctx, int val);
6068 int isl_options_get_ast_build_group_coscheduled(
6070 int isl_options_set_ast_build_scale_strides(
6071 isl_ctx *ctx, int val);
6072 int isl_options_get_ast_build_scale_strides(
6074 int isl_options_set_ast_build_allow_else(isl_ctx *ctx,
6076 int isl_options_get_ast_build_allow_else(isl_ctx *ctx);
6077 int isl_options_set_ast_build_allow_or(isl_ctx *ctx,
6079 int isl_options_get_ast_build_allow_or(isl_ctx *ctx);
6083 =item * ast_build_atomic_upper_bound
6085 Generate loop upper bounds that consist of the current loop iterator,
6086 an operator and an expression not involving the iterator.
6087 If this option is not set, then the current loop iterator may appear
6088 several times in the upper bound.
6089 For example, when this option is turned off, AST generation
6092 [n] -> { A[i] -> [i] : 0 <= i <= 100, n }
6096 for (int c0 = 0; c0 <= 100 && n >= c0; c0 += 1)
6099 When the option is turned on, the following AST is generated
6101 for (int c0 = 0; c0 <= min(100, n); c0 += 1)
6104 =item * ast_build_prefer_pdiv
6106 If this option is turned off, then the AST generation will
6107 produce ASTs that may only contain C<isl_ast_op_fdiv_q>
6108 operators, but no C<isl_ast_op_pdiv_q> or
6109 C<isl_ast_op_pdiv_r> operators.
6110 If this options is turned on, then C<isl> will try to convert
6111 some of the C<isl_ast_op_fdiv_q> operators to (expressions containing)
6112 C<isl_ast_op_pdiv_q> or C<isl_ast_op_pdiv_r> operators.
6114 =item * ast_build_exploit_nested_bounds
6116 Simplify conditions based on bounds of nested for loops.
6117 In particular, remove conditions that are implied by the fact
6118 that one or more nested loops have at least one iteration,
6119 meaning that the upper bound is at least as large as the lower bound.
6120 For example, when this option is turned off, AST generation
6123 [N,M] -> { A[i,j] -> [i,j] : 0 <= i <= N and
6129 for (int c0 = 0; c0 <= N; c0 += 1)
6130 for (int c1 = 0; c1 <= M; c1 += 1)
6133 When the option is turned on, the following AST is generated
6135 for (int c0 = 0; c0 <= N; c0 += 1)
6136 for (int c1 = 0; c1 <= M; c1 += 1)
6139 =item * ast_build_group_coscheduled
6141 If two domain elements are assigned the same schedule point, then
6142 they may be executed in any order and they may even appear in different
6143 loops. If this options is set, then the AST generator will make
6144 sure that coscheduled domain elements do not appear in separate parts
6145 of the AST. This is useful in case of nested AST generation
6146 if the outer AST generation is given only part of a schedule
6147 and the inner AST generation should handle the domains that are
6148 coscheduled by this initial part of the schedule together.
6149 For example if an AST is generated for a schedule
6151 { A[i] -> [0]; B[i] -> [0] }
6153 then the C<isl_ast_build_set_create_leaf> callback described
6154 below may get called twice, once for each domain.
6155 Setting this option ensures that the callback is only called once
6156 on both domains together.
6158 =item * ast_build_separation_bounds
6160 This option specifies which bounds to use during separation.
6161 If this option is set to C<ISL_AST_BUILD_SEPARATION_BOUNDS_IMPLICIT>
6162 then all (possibly implicit) bounds on the current dimension will
6163 be used during separation.
6164 If this option is set to C<ISL_AST_BUILD_SEPARATION_BOUNDS_EXPLICIT>
6165 then only those bounds that are explicitly available will
6166 be used during separation.
6168 =item * ast_build_scale_strides
6170 This option specifies whether the AST generator is allowed
6171 to scale down iterators of strided loops.
6173 =item * ast_build_allow_else
6175 This option specifies whether the AST generator is allowed
6176 to construct if statements with else branches.
6178 =item * ast_build_allow_or
6180 This option specifies whether the AST generator is allowed
6181 to construct if conditions with disjunctions.
6185 =head3 Fine-grained Control over AST Generation
6187 Besides specifying the constraints on the parameters,
6188 an C<isl_ast_build> object can be used to control
6189 various aspects of the AST generation process.
6190 The most prominent way of control is through ``options'',
6191 which can be set using the following function.
6193 #include <isl/ast_build.h>
6194 __isl_give isl_ast_build *
6195 isl_ast_build_set_options(
6196 __isl_take isl_ast_build *control,
6197 __isl_take isl_union_map *options);
6199 The options are encoded in an <isl_union_map>.
6200 The domain of this union relation refers to the schedule domain,
6201 i.e., the range of the schedule passed to C<isl_ast_build_ast_from_schedule>.
6202 In the case of nested AST generation (see L</"Nested AST Generation">),
6203 the domain of C<options> should refer to the extra piece of the schedule.
6204 That is, it should be equal to the range of the wrapped relation in the
6205 range of the schedule.
6206 The range of the options can consist of elements in one or more spaces,
6207 the names of which determine the effect of the option.
6208 The values of the range typically also refer to the schedule dimension
6209 to which the option applies. In case of nested AST generation
6210 (see L</"Nested AST Generation">), these values refer to the position
6211 of the schedule dimension within the innermost AST generation.
6212 The constraints on the domain elements of
6213 the option should only refer to this dimension and earlier dimensions.
6214 We consider the following spaces.
6218 =item C<separation_class>
6220 This space is a wrapped relation between two one dimensional spaces.
6221 The input space represents the schedule dimension to which the option
6222 applies and the output space represents the separation class.
6223 While constructing a loop corresponding to the specified schedule
6224 dimension(s), the AST generator will try to generate separate loops
6225 for domain elements that are assigned different classes.
6226 If only some of the elements are assigned a class, then those elements
6227 that are not assigned any class will be treated as belonging to a class
6228 that is separate from the explicitly assigned classes.
6229 The typical use case for this option is to separate full tiles from
6231 The other options, described below, are applied after the separation
6234 As an example, consider the separation into full and partial tiles
6235 of a tiling of a triangular domain.
6236 Take, for example, the domain
6238 { A[i,j] : 0 <= i,j and i + j <= 100 }
6240 and a tiling into tiles of 10 by 10. The input to the AST generator
6241 is then the schedule
6243 { A[i,j] -> [([i/10]),[j/10],i,j] : 0 <= i,j and
6246 Without any options, the following AST is generated
6248 for (int c0 = 0; c0 <= 10; c0 += 1)
6249 for (int c1 = 0; c1 <= -c0 + 10; c1 += 1)
6250 for (int c2 = 10 * c0;
6251 c2 <= min(-10 * c1 + 100, 10 * c0 + 9);
6253 for (int c3 = 10 * c1;
6254 c3 <= min(10 * c1 + 9, -c2 + 100);
6258 Separation into full and partial tiles can be obtained by assigning
6259 a class, say C<0>, to the full tiles. The full tiles are represented by those
6260 values of the first and second schedule dimensions for which there are
6261 values of the third and fourth dimensions to cover an entire tile.
6262 That is, we need to specify the following option
6264 { [a,b,c,d] -> separation_class[[0]->[0]] :
6265 exists b': 0 <= 10a,10b' and
6266 10a+9+10b'+9 <= 100;
6267 [a,b,c,d] -> separation_class[[1]->[0]] :
6268 0 <= 10a,10b and 10a+9+10b+9 <= 100 }
6272 { [a, b, c, d] -> separation_class[[1] -> [0]] :
6273 a >= 0 and b >= 0 and b <= 8 - a;
6274 [a, b, c, d] -> separation_class[[0] -> [0]] :
6277 With this option, the generated AST is as follows
6280 for (int c0 = 0; c0 <= 8; c0 += 1) {
6281 for (int c1 = 0; c1 <= -c0 + 8; c1 += 1)
6282 for (int c2 = 10 * c0;
6283 c2 <= 10 * c0 + 9; c2 += 1)
6284 for (int c3 = 10 * c1;
6285 c3 <= 10 * c1 + 9; c3 += 1)
6287 for (int c1 = -c0 + 9; c1 <= -c0 + 10; c1 += 1)
6288 for (int c2 = 10 * c0;
6289 c2 <= min(-10 * c1 + 100, 10 * c0 + 9);
6291 for (int c3 = 10 * c1;
6292 c3 <= min(-c2 + 100, 10 * c1 + 9);
6296 for (int c0 = 9; c0 <= 10; c0 += 1)
6297 for (int c1 = 0; c1 <= -c0 + 10; c1 += 1)
6298 for (int c2 = 10 * c0;
6299 c2 <= min(-10 * c1 + 100, 10 * c0 + 9);
6301 for (int c3 = 10 * c1;
6302 c3 <= min(10 * c1 + 9, -c2 + 100);
6309 This is a single-dimensional space representing the schedule dimension(s)
6310 to which ``separation'' should be applied. Separation tries to split
6311 a loop into several pieces if this can avoid the generation of guards
6313 See also the C<atomic> option.
6317 This is a single-dimensional space representing the schedule dimension(s)
6318 for which the domains should be considered ``atomic''. That is, the
6319 AST generator will make sure that any given domain space will only appear
6320 in a single loop at the specified level.
6322 Consider the following schedule
6324 { a[i] -> [i] : 0 <= i < 10;
6325 b[i] -> [i+1] : 0 <= i < 10 }
6327 If the following option is specified
6329 { [i] -> separate[x] }
6331 then the following AST will be generated
6335 for (int c0 = 1; c0 <= 9; c0 += 1) {
6342 If, on the other hand, the following option is specified
6344 { [i] -> atomic[x] }
6346 then the following AST will be generated
6348 for (int c0 = 0; c0 <= 10; c0 += 1) {
6355 If neither C<atomic> nor C<separate> is specified, then the AST generator
6356 may produce either of these two results or some intermediate form.
6360 This is a single-dimensional space representing the schedule dimension(s)
6361 that should be I<completely> unrolled.
6362 To obtain a partial unrolling, the user should apply an additional
6363 strip-mining to the schedule and fully unroll the inner loop.
6367 Additional control is available through the following functions.
6369 #include <isl/ast_build.h>
6370 __isl_give isl_ast_build *
6371 isl_ast_build_set_iterators(
6372 __isl_take isl_ast_build *control,
6373 __isl_take isl_id_list *iterators);
6375 The function C<isl_ast_build_set_iterators> allows the user to
6376 specify a list of iterator C<isl_id>s to be used as iterators.
6377 If the input schedule is injective, then
6378 the number of elements in this list should be as large as the dimension
6379 of the schedule space, but no direct correspondence should be assumed
6380 between dimensions and elements.
6381 If the input schedule is not injective, then an additional number
6382 of C<isl_id>s equal to the largest dimension of the input domains
6384 If the number of provided C<isl_id>s is insufficient, then additional
6385 names are automatically generated.
6387 #include <isl/ast_build.h>
6388 __isl_give isl_ast_build *
6389 isl_ast_build_set_create_leaf(
6390 __isl_take isl_ast_build *control,
6391 __isl_give isl_ast_node *(*fn)(
6392 __isl_take isl_ast_build *build,
6393 void *user), void *user);
6396 C<isl_ast_build_set_create_leaf> function allows for the
6397 specification of a callback that should be called whenever the AST
6398 generator arrives at an element of the schedule domain.
6399 The callback should return an AST node that should be inserted
6400 at the corresponding position of the AST. The default action (when
6401 the callback is not set) is to continue generating parts of the AST to scan
6402 all the domain elements associated to the schedule domain element
6403 and to insert user nodes, ``calling'' the domain element, for each of them.
6404 The C<build> argument contains the current state of the C<isl_ast_build>.
6405 To ease nested AST generation (see L</"Nested AST Generation">),
6406 all control information that is
6407 specific to the current AST generation such as the options and
6408 the callbacks has been removed from this C<isl_ast_build>.
6409 The callback would typically return the result of a nested
6411 user defined node created using the following function.
6413 #include <isl/ast.h>
6414 __isl_give isl_ast_node *isl_ast_node_alloc_user(
6415 __isl_take isl_ast_expr *expr);
6417 #include <isl/ast_build.h>
6418 __isl_give isl_ast_build *
6419 isl_ast_build_set_at_each_domain(
6420 __isl_take isl_ast_build *build,
6421 __isl_give isl_ast_node *(*fn)(
6422 __isl_take isl_ast_node *node,
6423 __isl_keep isl_ast_build *build,
6424 void *user), void *user);
6425 __isl_give isl_ast_build *
6426 isl_ast_build_set_before_each_for(
6427 __isl_take isl_ast_build *build,
6428 __isl_give isl_id *(*fn)(
6429 __isl_keep isl_ast_build *build,
6430 void *user), void *user);
6431 __isl_give isl_ast_build *
6432 isl_ast_build_set_after_each_for(
6433 __isl_take isl_ast_build *build,
6434 __isl_give isl_ast_node *(*fn)(
6435 __isl_take isl_ast_node *node,
6436 __isl_keep isl_ast_build *build,
6437 void *user), void *user);
6439 The callback set by C<isl_ast_build_set_at_each_domain> will
6440 be called for each domain AST node.
6441 The callbacks set by C<isl_ast_build_set_before_each_for>
6442 and C<isl_ast_build_set_after_each_for> will be called
6443 for each for AST node. The first will be called in depth-first
6444 pre-order, while the second will be called in depth-first post-order.
6445 Since C<isl_ast_build_set_before_each_for> is called before the for
6446 node is actually constructed, it is only passed an C<isl_ast_build>.
6447 The returned C<isl_id> will be added as an annotation (using
6448 C<isl_ast_node_set_annotation>) to the constructed for node.
6449 In particular, if the user has also specified an C<after_each_for>
6450 callback, then the annotation can be retrieved from the node passed to
6451 that callback using C<isl_ast_node_get_annotation>.
6452 All callbacks should C<NULL> on failure.
6453 The given C<isl_ast_build> can be used to create new
6454 C<isl_ast_expr> objects using C<isl_ast_build_expr_from_pw_aff>
6455 or C<isl_ast_build_call_from_pw_multi_aff>.
6457 =head3 Nested AST Generation
6459 C<isl> allows the user to create an AST within the context
6460 of another AST. These nested ASTs are created using the
6461 same C<isl_ast_build_ast_from_schedule> function that is used to create the
6462 outer AST. The C<build> argument should be an C<isl_ast_build>
6463 passed to a callback set by
6464 C<isl_ast_build_set_create_leaf>.
6465 The space of the range of the C<schedule> argument should refer
6466 to this build. In particular, the space should be a wrapped
6467 relation and the domain of this wrapped relation should be the
6468 same as that of the range of the schedule returned by
6469 C<isl_ast_build_get_schedule> below.
6470 In practice, the new schedule is typically
6471 created by calling C<isl_union_map_range_product> on the old schedule
6472 and some extra piece of the schedule.
6473 The space of the schedule domain is also available from
6474 the C<isl_ast_build>.
6476 #include <isl/ast_build.h>
6477 __isl_give isl_union_map *isl_ast_build_get_schedule(
6478 __isl_keep isl_ast_build *build);
6479 __isl_give isl_space *isl_ast_build_get_schedule_space(
6480 __isl_keep isl_ast_build *build);
6481 __isl_give isl_ast_build *isl_ast_build_restrict(
6482 __isl_take isl_ast_build *build,
6483 __isl_take isl_set *set);
6485 The C<isl_ast_build_get_schedule> function returns a (partial)
6486 schedule for the domains elements for which part of the AST still needs to
6487 be generated in the current build.
6488 In particular, the domain elements are mapped to those iterations of the loops
6489 enclosing the current point of the AST generation inside which
6490 the domain elements are executed.
6491 No direct correspondence between
6492 the input schedule and this schedule should be assumed.
6493 The space obtained from C<isl_ast_build_get_schedule_space> can be used
6494 to create a set for C<isl_ast_build_restrict> to intersect
6495 with the current build. In particular, the set passed to
6496 C<isl_ast_build_restrict> can have additional parameters.
6497 The ids of the set dimensions in the space returned by
6498 C<isl_ast_build_get_schedule_space> correspond to the
6499 iterators of the already generated loops.
6500 The user should not rely on the ids of the output dimensions
6501 of the relations in the union relation returned by
6502 C<isl_ast_build_get_schedule> having any particular value.
6506 Although C<isl> is mainly meant to be used as a library,
6507 it also contains some basic applications that use some
6508 of the functionality of C<isl>.
6509 The input may be specified in either the L<isl format>
6510 or the L<PolyLib format>.
6512 =head2 C<isl_polyhedron_sample>
6514 C<isl_polyhedron_sample> takes a polyhedron as input and prints
6515 an integer element of the polyhedron, if there is any.
6516 The first column in the output is the denominator and is always
6517 equal to 1. If the polyhedron contains no integer points,
6518 then a vector of length zero is printed.
6522 C<isl_pip> takes the same input as the C<example> program
6523 from the C<piplib> distribution, i.e., a set of constraints
6524 on the parameters, a line containing only -1 and finally a set
6525 of constraints on a parametric polyhedron.
6526 The coefficients of the parameters appear in the last columns
6527 (but before the final constant column).
6528 The output is the lexicographic minimum of the parametric polyhedron.
6529 As C<isl> currently does not have its own output format, the output
6530 is just a dump of the internal state.
6532 =head2 C<isl_polyhedron_minimize>
6534 C<isl_polyhedron_minimize> computes the minimum of some linear
6535 or affine objective function over the integer points in a polyhedron.
6536 If an affine objective function
6537 is given, then the constant should appear in the last column.
6539 =head2 C<isl_polytope_scan>
6541 Given a polytope, C<isl_polytope_scan> prints
6542 all integer points in the polytope.
6544 =head2 C<isl_codegen>
6546 Given a schedule, a context set and an options relation,
6547 C<isl_codegen> prints out an AST that scans the domain elements
6548 of the schedule in the order of their image(s) taking into account
6549 the constraints in the context set.