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_params(
925 __isl_take isl_space *space);
926 __isl_give isl_space *isl_space_set_from_params(
927 __isl_take isl_space *space);
928 __isl_give isl_space *isl_space_reverse(__isl_take isl_space *space);
929 __isl_give isl_space *isl_space_join(__isl_take isl_space *left,
930 __isl_take isl_space *right);
931 __isl_give isl_space *isl_space_align_params(
932 __isl_take isl_space *space1, __isl_take isl_space *space2)
933 __isl_give isl_space *isl_space_insert_dims(__isl_take isl_space *space,
934 enum isl_dim_type type, unsigned pos, unsigned n);
935 __isl_give isl_space *isl_space_add_dims(__isl_take isl_space *space,
936 enum isl_dim_type type, unsigned n);
937 __isl_give isl_space *isl_space_drop_dims(__isl_take isl_space *space,
938 enum isl_dim_type type, unsigned first, unsigned n);
939 __isl_give isl_space *isl_space_move_dims(__isl_take isl_space *space,
940 enum isl_dim_type dst_type, unsigned dst_pos,
941 enum isl_dim_type src_type, unsigned src_pos,
943 __isl_give isl_space *isl_space_map_from_set(
944 __isl_take isl_space *space);
945 __isl_give isl_space *isl_space_map_from_domain_and_range(
946 __isl_take isl_space *domain,
947 __isl_take isl_space *range);
948 __isl_give isl_space *isl_space_zip(__isl_take isl_space *space);
949 __isl_give isl_space *isl_space_curry(
950 __isl_take isl_space *space);
951 __isl_give isl_space *isl_space_uncurry(
952 __isl_take isl_space *space);
954 Note that if dimensions are added or removed from a space, then
955 the name and the internal structure are lost.
959 A local space is essentially a space with
960 zero or more existentially quantified variables.
961 The local space of a (constraint of a) basic set or relation can be obtained
962 using the following functions.
964 #include <isl/constraint.h>
965 __isl_give isl_local_space *isl_constraint_get_local_space(
966 __isl_keep isl_constraint *constraint);
969 __isl_give isl_local_space *isl_basic_set_get_local_space(
970 __isl_keep isl_basic_set *bset);
973 __isl_give isl_local_space *isl_basic_map_get_local_space(
974 __isl_keep isl_basic_map *bmap);
976 A new local space can be created from a space using
978 #include <isl/local_space.h>
979 __isl_give isl_local_space *isl_local_space_from_space(
980 __isl_take isl_space *space);
982 They can be inspected, modified, copied and freed using the following functions.
984 #include <isl/local_space.h>
985 isl_ctx *isl_local_space_get_ctx(
986 __isl_keep isl_local_space *ls);
987 int isl_local_space_is_set(__isl_keep isl_local_space *ls);
988 int isl_local_space_dim(__isl_keep isl_local_space *ls,
989 enum isl_dim_type type);
990 int isl_local_space_has_dim_id(
991 __isl_keep isl_local_space *ls,
992 enum isl_dim_type type, unsigned pos);
993 __isl_give isl_id *isl_local_space_get_dim_id(
994 __isl_keep isl_local_space *ls,
995 enum isl_dim_type type, unsigned pos);
996 int isl_local_space_has_dim_name(
997 __isl_keep isl_local_space *ls,
998 enum isl_dim_type type, unsigned pos)
999 const char *isl_local_space_get_dim_name(
1000 __isl_keep isl_local_space *ls,
1001 enum isl_dim_type type, unsigned pos);
1002 __isl_give isl_local_space *isl_local_space_set_dim_name(
1003 __isl_take isl_local_space *ls,
1004 enum isl_dim_type type, unsigned pos, const char *s);
1005 __isl_give isl_local_space *isl_local_space_set_dim_id(
1006 __isl_take isl_local_space *ls,
1007 enum isl_dim_type type, unsigned pos,
1008 __isl_take isl_id *id);
1009 __isl_give isl_space *isl_local_space_get_space(
1010 __isl_keep isl_local_space *ls);
1011 __isl_give isl_aff *isl_local_space_get_div(
1012 __isl_keep isl_local_space *ls, int pos);
1013 __isl_give isl_local_space *isl_local_space_copy(
1014 __isl_keep isl_local_space *ls);
1015 void *isl_local_space_free(__isl_take isl_local_space *ls);
1017 Note that C<isl_local_space_get_div> can only be used on local spaces
1020 Two local spaces can be compared using
1022 int isl_local_space_is_equal(__isl_keep isl_local_space *ls1,
1023 __isl_keep isl_local_space *ls2);
1025 Local spaces can be created from other local spaces
1026 using the following functions.
1028 __isl_give isl_local_space *isl_local_space_domain(
1029 __isl_take isl_local_space *ls);
1030 __isl_give isl_local_space *isl_local_space_range(
1031 __isl_take isl_local_space *ls);
1032 __isl_give isl_local_space *isl_local_space_from_domain(
1033 __isl_take isl_local_space *ls);
1034 __isl_give isl_local_space *isl_local_space_intersect(
1035 __isl_take isl_local_space *ls1,
1036 __isl_take isl_local_space *ls2);
1037 __isl_give isl_local_space *isl_local_space_add_dims(
1038 __isl_take isl_local_space *ls,
1039 enum isl_dim_type type, unsigned n);
1040 __isl_give isl_local_space *isl_local_space_insert_dims(
1041 __isl_take isl_local_space *ls,
1042 enum isl_dim_type type, unsigned first, unsigned n);
1043 __isl_give isl_local_space *isl_local_space_drop_dims(
1044 __isl_take isl_local_space *ls,
1045 enum isl_dim_type type, unsigned first, unsigned n);
1047 =head2 Input and Output
1049 C<isl> supports its own input/output format, which is similar
1050 to the C<Omega> format, but also supports the C<PolyLib> format
1053 =head3 C<isl> format
1055 The C<isl> format is similar to that of C<Omega>, but has a different
1056 syntax for describing the parameters and allows for the definition
1057 of an existentially quantified variable as the integer division
1058 of an affine expression.
1059 For example, the set of integers C<i> between C<0> and C<n>
1060 such that C<i % 10 <= 6> can be described as
1062 [n] -> { [i] : exists (a = [i/10] : 0 <= i and i <= n and
1065 A set or relation can have several disjuncts, separated
1066 by the keyword C<or>. Each disjunct is either a conjunction
1067 of constraints or a projection (C<exists>) of a conjunction
1068 of constraints. The constraints are separated by the keyword
1071 =head3 C<PolyLib> format
1073 If the represented set is a union, then the first line
1074 contains a single number representing the number of disjuncts.
1075 Otherwise, a line containing the number C<1> is optional.
1077 Each disjunct is represented by a matrix of constraints.
1078 The first line contains two numbers representing
1079 the number of rows and columns,
1080 where the number of rows is equal to the number of constraints
1081 and the number of columns is equal to two plus the number of variables.
1082 The following lines contain the actual rows of the constraint matrix.
1083 In each row, the first column indicates whether the constraint
1084 is an equality (C<0>) or inequality (C<1>). The final column
1085 corresponds to the constant term.
1087 If the set is parametric, then the coefficients of the parameters
1088 appear in the last columns before the constant column.
1089 The coefficients of any existentially quantified variables appear
1090 between those of the set variables and those of the parameters.
1092 =head3 Extended C<PolyLib> format
1094 The extended C<PolyLib> format is nearly identical to the
1095 C<PolyLib> format. The only difference is that the line
1096 containing the number of rows and columns of a constraint matrix
1097 also contains four additional numbers:
1098 the number of output dimensions, the number of input dimensions,
1099 the number of local dimensions (i.e., the number of existentially
1100 quantified variables) and the number of parameters.
1101 For sets, the number of ``output'' dimensions is equal
1102 to the number of set dimensions, while the number of ``input''
1107 #include <isl/set.h>
1108 __isl_give isl_basic_set *isl_basic_set_read_from_file(
1109 isl_ctx *ctx, FILE *input);
1110 __isl_give isl_basic_set *isl_basic_set_read_from_str(
1111 isl_ctx *ctx, const char *str);
1112 __isl_give isl_set *isl_set_read_from_file(isl_ctx *ctx,
1114 __isl_give isl_set *isl_set_read_from_str(isl_ctx *ctx,
1117 #include <isl/map.h>
1118 __isl_give isl_basic_map *isl_basic_map_read_from_file(
1119 isl_ctx *ctx, FILE *input);
1120 __isl_give isl_basic_map *isl_basic_map_read_from_str(
1121 isl_ctx *ctx, const char *str);
1122 __isl_give isl_map *isl_map_read_from_file(
1123 isl_ctx *ctx, FILE *input);
1124 __isl_give isl_map *isl_map_read_from_str(isl_ctx *ctx,
1127 #include <isl/union_set.h>
1128 __isl_give isl_union_set *isl_union_set_read_from_file(
1129 isl_ctx *ctx, FILE *input);
1130 __isl_give isl_union_set *isl_union_set_read_from_str(
1131 isl_ctx *ctx, const char *str);
1133 #include <isl/union_map.h>
1134 __isl_give isl_union_map *isl_union_map_read_from_file(
1135 isl_ctx *ctx, FILE *input);
1136 __isl_give isl_union_map *isl_union_map_read_from_str(
1137 isl_ctx *ctx, const char *str);
1139 The input format is autodetected and may be either the C<PolyLib> format
1140 or the C<isl> format.
1144 Before anything can be printed, an C<isl_printer> needs to
1147 __isl_give isl_printer *isl_printer_to_file(isl_ctx *ctx,
1149 __isl_give isl_printer *isl_printer_to_str(isl_ctx *ctx);
1150 void *isl_printer_free(__isl_take isl_printer *printer);
1151 __isl_give char *isl_printer_get_str(
1152 __isl_keep isl_printer *printer);
1154 The printer can be inspected using the following functions.
1156 FILE *isl_printer_get_file(
1157 __isl_keep isl_printer *printer);
1158 int isl_printer_get_output_format(
1159 __isl_keep isl_printer *p);
1161 The behavior of the printer can be modified in various ways
1163 __isl_give isl_printer *isl_printer_set_output_format(
1164 __isl_take isl_printer *p, int output_format);
1165 __isl_give isl_printer *isl_printer_set_indent(
1166 __isl_take isl_printer *p, int indent);
1167 __isl_give isl_printer *isl_printer_indent(
1168 __isl_take isl_printer *p, int indent);
1169 __isl_give isl_printer *isl_printer_set_prefix(
1170 __isl_take isl_printer *p, const char *prefix);
1171 __isl_give isl_printer *isl_printer_set_suffix(
1172 __isl_take isl_printer *p, const char *suffix);
1174 The C<output_format> may be either C<ISL_FORMAT_ISL>, C<ISL_FORMAT_OMEGA>,
1175 C<ISL_FORMAT_POLYLIB>, C<ISL_FORMAT_EXT_POLYLIB> or C<ISL_FORMAT_LATEX>
1176 and defaults to C<ISL_FORMAT_ISL>.
1177 Each line in the output is indented by C<indent> (set by
1178 C<isl_printer_set_indent>) spaces
1179 (default: 0), prefixed by C<prefix> and suffixed by C<suffix>.
1180 In the C<PolyLib> format output,
1181 the coefficients of the existentially quantified variables
1182 appear between those of the set variables and those
1184 The function C<isl_printer_indent> increases the indentation
1185 by the specified amount (which may be negative).
1187 To actually print something, use
1189 #include <isl/printer.h>
1190 __isl_give isl_printer *isl_printer_print_double(
1191 __isl_take isl_printer *p, double d);
1193 #include <isl/set.h>
1194 __isl_give isl_printer *isl_printer_print_basic_set(
1195 __isl_take isl_printer *printer,
1196 __isl_keep isl_basic_set *bset);
1197 __isl_give isl_printer *isl_printer_print_set(
1198 __isl_take isl_printer *printer,
1199 __isl_keep isl_set *set);
1201 #include <isl/map.h>
1202 __isl_give isl_printer *isl_printer_print_basic_map(
1203 __isl_take isl_printer *printer,
1204 __isl_keep isl_basic_map *bmap);
1205 __isl_give isl_printer *isl_printer_print_map(
1206 __isl_take isl_printer *printer,
1207 __isl_keep isl_map *map);
1209 #include <isl/union_set.h>
1210 __isl_give isl_printer *isl_printer_print_union_set(
1211 __isl_take isl_printer *p,
1212 __isl_keep isl_union_set *uset);
1214 #include <isl/union_map.h>
1215 __isl_give isl_printer *isl_printer_print_union_map(
1216 __isl_take isl_printer *p,
1217 __isl_keep isl_union_map *umap);
1219 When called on a file printer, the following function flushes
1220 the file. When called on a string printer, the buffer is cleared.
1222 __isl_give isl_printer *isl_printer_flush(
1223 __isl_take isl_printer *p);
1225 =head2 Creating New Sets and Relations
1227 C<isl> has functions for creating some standard sets and relations.
1231 =item * Empty sets and relations
1233 __isl_give isl_basic_set *isl_basic_set_empty(
1234 __isl_take isl_space *space);
1235 __isl_give isl_basic_map *isl_basic_map_empty(
1236 __isl_take isl_space *space);
1237 __isl_give isl_set *isl_set_empty(
1238 __isl_take isl_space *space);
1239 __isl_give isl_map *isl_map_empty(
1240 __isl_take isl_space *space);
1241 __isl_give isl_union_set *isl_union_set_empty(
1242 __isl_take isl_space *space);
1243 __isl_give isl_union_map *isl_union_map_empty(
1244 __isl_take isl_space *space);
1246 For C<isl_union_set>s and C<isl_union_map>s, the space
1247 is only used to specify the parameters.
1249 =item * Universe sets and relations
1251 __isl_give isl_basic_set *isl_basic_set_universe(
1252 __isl_take isl_space *space);
1253 __isl_give isl_basic_map *isl_basic_map_universe(
1254 __isl_take isl_space *space);
1255 __isl_give isl_set *isl_set_universe(
1256 __isl_take isl_space *space);
1257 __isl_give isl_map *isl_map_universe(
1258 __isl_take isl_space *space);
1259 __isl_give isl_union_set *isl_union_set_universe(
1260 __isl_take isl_union_set *uset);
1261 __isl_give isl_union_map *isl_union_map_universe(
1262 __isl_take isl_union_map *umap);
1264 The sets and relations constructed by the functions above
1265 contain all integer values, while those constructed by the
1266 functions below only contain non-negative values.
1268 __isl_give isl_basic_set *isl_basic_set_nat_universe(
1269 __isl_take isl_space *space);
1270 __isl_give isl_basic_map *isl_basic_map_nat_universe(
1271 __isl_take isl_space *space);
1272 __isl_give isl_set *isl_set_nat_universe(
1273 __isl_take isl_space *space);
1274 __isl_give isl_map *isl_map_nat_universe(
1275 __isl_take isl_space *space);
1277 =item * Identity relations
1279 __isl_give isl_basic_map *isl_basic_map_identity(
1280 __isl_take isl_space *space);
1281 __isl_give isl_map *isl_map_identity(
1282 __isl_take isl_space *space);
1284 The number of input and output dimensions in C<space> needs
1287 =item * Lexicographic order
1289 __isl_give isl_map *isl_map_lex_lt(
1290 __isl_take isl_space *set_space);
1291 __isl_give isl_map *isl_map_lex_le(
1292 __isl_take isl_space *set_space);
1293 __isl_give isl_map *isl_map_lex_gt(
1294 __isl_take isl_space *set_space);
1295 __isl_give isl_map *isl_map_lex_ge(
1296 __isl_take isl_space *set_space);
1297 __isl_give isl_map *isl_map_lex_lt_first(
1298 __isl_take isl_space *space, unsigned n);
1299 __isl_give isl_map *isl_map_lex_le_first(
1300 __isl_take isl_space *space, unsigned n);
1301 __isl_give isl_map *isl_map_lex_gt_first(
1302 __isl_take isl_space *space, unsigned n);
1303 __isl_give isl_map *isl_map_lex_ge_first(
1304 __isl_take isl_space *space, unsigned n);
1306 The first four functions take a space for a B<set>
1307 and return relations that express that the elements in the domain
1308 are lexicographically less
1309 (C<isl_map_lex_lt>), less or equal (C<isl_map_lex_le>),
1310 greater (C<isl_map_lex_gt>) or greater or equal (C<isl_map_lex_ge>)
1311 than the elements in the range.
1312 The last four functions take a space for a map
1313 and return relations that express that the first C<n> dimensions
1314 in the domain are lexicographically less
1315 (C<isl_map_lex_lt_first>), less or equal (C<isl_map_lex_le_first>),
1316 greater (C<isl_map_lex_gt_first>) or greater or equal (C<isl_map_lex_ge_first>)
1317 than the first C<n> dimensions in the range.
1321 A basic set or relation can be converted to a set or relation
1322 using the following functions.
1324 __isl_give isl_set *isl_set_from_basic_set(
1325 __isl_take isl_basic_set *bset);
1326 __isl_give isl_map *isl_map_from_basic_map(
1327 __isl_take isl_basic_map *bmap);
1329 Sets and relations can be converted to union sets and relations
1330 using the following functions.
1332 __isl_give isl_union_set *isl_union_set_from_basic_set(
1333 __isl_take isl_basic_set *bset);
1334 __isl_give isl_union_map *isl_union_map_from_basic_map(
1335 __isl_take isl_basic_map *bmap);
1336 __isl_give isl_union_set *isl_union_set_from_set(
1337 __isl_take isl_set *set);
1338 __isl_give isl_union_map *isl_union_map_from_map(
1339 __isl_take isl_map *map);
1341 The inverse conversions below can only be used if the input
1342 union set or relation is known to contain elements in exactly one
1345 __isl_give isl_set *isl_set_from_union_set(
1346 __isl_take isl_union_set *uset);
1347 __isl_give isl_map *isl_map_from_union_map(
1348 __isl_take isl_union_map *umap);
1350 A zero-dimensional (basic) set can be constructed on a given parameter domain
1351 using the following function.
1353 __isl_give isl_basic_set *isl_basic_set_from_params(
1354 __isl_take isl_basic_set *bset);
1355 __isl_give isl_set *isl_set_from_params(
1356 __isl_take isl_set *set);
1358 Sets and relations can be copied and freed again using the following
1361 __isl_give isl_basic_set *isl_basic_set_copy(
1362 __isl_keep isl_basic_set *bset);
1363 __isl_give isl_set *isl_set_copy(__isl_keep isl_set *set);
1364 __isl_give isl_union_set *isl_union_set_copy(
1365 __isl_keep isl_union_set *uset);
1366 __isl_give isl_basic_map *isl_basic_map_copy(
1367 __isl_keep isl_basic_map *bmap);
1368 __isl_give isl_map *isl_map_copy(__isl_keep isl_map *map);
1369 __isl_give isl_union_map *isl_union_map_copy(
1370 __isl_keep isl_union_map *umap);
1371 void *isl_basic_set_free(__isl_take isl_basic_set *bset);
1372 void *isl_set_free(__isl_take isl_set *set);
1373 void *isl_union_set_free(__isl_take isl_union_set *uset);
1374 void *isl_basic_map_free(__isl_take isl_basic_map *bmap);
1375 void *isl_map_free(__isl_take isl_map *map);
1376 void *isl_union_map_free(__isl_take isl_union_map *umap);
1378 Other sets and relations can be constructed by starting
1379 from a universe set or relation, adding equality and/or
1380 inequality constraints and then projecting out the
1381 existentially quantified variables, if any.
1382 Constraints can be constructed, manipulated and
1383 added to (or removed from) (basic) sets and relations
1384 using the following functions.
1386 #include <isl/constraint.h>
1387 __isl_give isl_constraint *isl_equality_alloc(
1388 __isl_take isl_local_space *ls);
1389 __isl_give isl_constraint *isl_inequality_alloc(
1390 __isl_take isl_local_space *ls);
1391 __isl_give isl_constraint *isl_constraint_set_constant_si(
1392 __isl_take isl_constraint *constraint, int v);
1393 __isl_give isl_constraint *isl_constraint_set_constant_val(
1394 __isl_take isl_constraint *constraint,
1395 __isl_take isl_val *v);
1396 __isl_give isl_constraint *isl_constraint_set_coefficient_si(
1397 __isl_take isl_constraint *constraint,
1398 enum isl_dim_type type, int pos, int v);
1399 __isl_give isl_constraint *
1400 isl_constraint_set_coefficient_val(
1401 __isl_take isl_constraint *constraint,
1402 enum isl_dim_type type, int pos, isl_val *v);
1403 __isl_give isl_basic_map *isl_basic_map_add_constraint(
1404 __isl_take isl_basic_map *bmap,
1405 __isl_take isl_constraint *constraint);
1406 __isl_give isl_basic_set *isl_basic_set_add_constraint(
1407 __isl_take isl_basic_set *bset,
1408 __isl_take isl_constraint *constraint);
1409 __isl_give isl_map *isl_map_add_constraint(
1410 __isl_take isl_map *map,
1411 __isl_take isl_constraint *constraint);
1412 __isl_give isl_set *isl_set_add_constraint(
1413 __isl_take isl_set *set,
1414 __isl_take isl_constraint *constraint);
1415 __isl_give isl_basic_set *isl_basic_set_drop_constraint(
1416 __isl_take isl_basic_set *bset,
1417 __isl_take isl_constraint *constraint);
1419 For example, to create a set containing the even integers
1420 between 10 and 42, you would use the following code.
1423 isl_local_space *ls;
1425 isl_basic_set *bset;
1427 space = isl_space_set_alloc(ctx, 0, 2);
1428 bset = isl_basic_set_universe(isl_space_copy(space));
1429 ls = isl_local_space_from_space(space);
1431 c = isl_equality_alloc(isl_local_space_copy(ls));
1432 c = isl_constraint_set_coefficient_si(c, isl_dim_set, 0, -1);
1433 c = isl_constraint_set_coefficient_si(c, isl_dim_set, 1, 2);
1434 bset = isl_basic_set_add_constraint(bset, c);
1436 c = isl_inequality_alloc(isl_local_space_copy(ls));
1437 c = isl_constraint_set_constant_si(c, -10);
1438 c = isl_constraint_set_coefficient_si(c, isl_dim_set, 0, 1);
1439 bset = isl_basic_set_add_constraint(bset, c);
1441 c = isl_inequality_alloc(ls);
1442 c = isl_constraint_set_constant_si(c, 42);
1443 c = isl_constraint_set_coefficient_si(c, isl_dim_set, 0, -1);
1444 bset = isl_basic_set_add_constraint(bset, c);
1446 bset = isl_basic_set_project_out(bset, isl_dim_set, 1, 1);
1450 isl_basic_set *bset;
1451 bset = isl_basic_set_read_from_str(ctx,
1452 "{[i] : exists (a : i = 2a and i >= 10 and i <= 42)}");
1454 A basic set or relation can also be constructed from two matrices
1455 describing the equalities and the inequalities.
1457 __isl_give isl_basic_set *isl_basic_set_from_constraint_matrices(
1458 __isl_take isl_space *space,
1459 __isl_take isl_mat *eq, __isl_take isl_mat *ineq,
1460 enum isl_dim_type c1,
1461 enum isl_dim_type c2, enum isl_dim_type c3,
1462 enum isl_dim_type c4);
1463 __isl_give isl_basic_map *isl_basic_map_from_constraint_matrices(
1464 __isl_take isl_space *space,
1465 __isl_take isl_mat *eq, __isl_take isl_mat *ineq,
1466 enum isl_dim_type c1,
1467 enum isl_dim_type c2, enum isl_dim_type c3,
1468 enum isl_dim_type c4, enum isl_dim_type c5);
1470 The C<isl_dim_type> arguments indicate the order in which
1471 different kinds of variables appear in the input matrices
1472 and should be a permutation of C<isl_dim_cst>, C<isl_dim_param>,
1473 C<isl_dim_set> and C<isl_dim_div> for sets and
1474 of C<isl_dim_cst>, C<isl_dim_param>,
1475 C<isl_dim_in>, C<isl_dim_out> and C<isl_dim_div> for relations.
1477 A (basic or union) set or relation can also be constructed from a
1478 (union) (piecewise) (multiple) affine expression
1479 or a list of affine expressions
1480 (See L<"Piecewise Quasi Affine Expressions"> and
1481 L<"Piecewise Multiple Quasi Affine Expressions">).
1483 __isl_give isl_basic_map *isl_basic_map_from_aff(
1484 __isl_take isl_aff *aff);
1485 __isl_give isl_map *isl_map_from_aff(
1486 __isl_take isl_aff *aff);
1487 __isl_give isl_set *isl_set_from_pw_aff(
1488 __isl_take isl_pw_aff *pwaff);
1489 __isl_give isl_map *isl_map_from_pw_aff(
1490 __isl_take isl_pw_aff *pwaff);
1491 __isl_give isl_basic_map *isl_basic_map_from_aff_list(
1492 __isl_take isl_space *domain_space,
1493 __isl_take isl_aff_list *list);
1494 __isl_give isl_basic_map *isl_basic_map_from_multi_aff(
1495 __isl_take isl_multi_aff *maff)
1496 __isl_give isl_map *isl_map_from_multi_aff(
1497 __isl_take isl_multi_aff *maff)
1498 __isl_give isl_set *isl_set_from_pw_multi_aff(
1499 __isl_take isl_pw_multi_aff *pma);
1500 __isl_give isl_map *isl_map_from_pw_multi_aff(
1501 __isl_take isl_pw_multi_aff *pma);
1502 __isl_give isl_union_map *
1503 isl_union_map_from_union_pw_multi_aff(
1504 __isl_take isl_union_pw_multi_aff *upma);
1506 The C<domain_dim> argument describes the domain of the resulting
1507 basic relation. It is required because the C<list> may consist
1508 of zero affine expressions.
1510 =head2 Inspecting Sets and Relations
1512 Usually, the user should not have to care about the actual constraints
1513 of the sets and maps, but should instead apply the abstract operations
1514 explained in the following sections.
1515 Occasionally, however, it may be required to inspect the individual
1516 coefficients of the constraints. This section explains how to do so.
1517 In these cases, it may also be useful to have C<isl> compute
1518 an explicit representation of the existentially quantified variables.
1520 __isl_give isl_set *isl_set_compute_divs(
1521 __isl_take isl_set *set);
1522 __isl_give isl_map *isl_map_compute_divs(
1523 __isl_take isl_map *map);
1524 __isl_give isl_union_set *isl_union_set_compute_divs(
1525 __isl_take isl_union_set *uset);
1526 __isl_give isl_union_map *isl_union_map_compute_divs(
1527 __isl_take isl_union_map *umap);
1529 This explicit representation defines the existentially quantified
1530 variables as integer divisions of the other variables, possibly
1531 including earlier existentially quantified variables.
1532 An explicitly represented existentially quantified variable therefore
1533 has a unique value when the values of the other variables are known.
1534 If, furthermore, the same existentials, i.e., existentials
1535 with the same explicit representations, should appear in the
1536 same order in each of the disjuncts of a set or map, then the user should call
1537 either of the following functions.
1539 __isl_give isl_set *isl_set_align_divs(
1540 __isl_take isl_set *set);
1541 __isl_give isl_map *isl_map_align_divs(
1542 __isl_take isl_map *map);
1544 Alternatively, the existentially quantified variables can be removed
1545 using the following functions, which compute an overapproximation.
1547 __isl_give isl_basic_set *isl_basic_set_remove_divs(
1548 __isl_take isl_basic_set *bset);
1549 __isl_give isl_basic_map *isl_basic_map_remove_divs(
1550 __isl_take isl_basic_map *bmap);
1551 __isl_give isl_set *isl_set_remove_divs(
1552 __isl_take isl_set *set);
1553 __isl_give isl_map *isl_map_remove_divs(
1554 __isl_take isl_map *map);
1556 It is also possible to only remove those divs that are defined
1557 in terms of a given range of dimensions or only those for which
1558 no explicit representation is known.
1560 __isl_give isl_basic_set *
1561 isl_basic_set_remove_divs_involving_dims(
1562 __isl_take isl_basic_set *bset,
1563 enum isl_dim_type type,
1564 unsigned first, unsigned n);
1565 __isl_give isl_basic_map *
1566 isl_basic_map_remove_divs_involving_dims(
1567 __isl_take isl_basic_map *bmap,
1568 enum isl_dim_type type,
1569 unsigned first, unsigned n);
1570 __isl_give isl_set *isl_set_remove_divs_involving_dims(
1571 __isl_take isl_set *set, enum isl_dim_type type,
1572 unsigned first, unsigned n);
1573 __isl_give isl_map *isl_map_remove_divs_involving_dims(
1574 __isl_take isl_map *map, enum isl_dim_type type,
1575 unsigned first, unsigned n);
1577 __isl_give isl_basic_set *
1578 isl_basic_set_remove_unknown_divs(
1579 __isl_take isl_basic_set *bset);
1580 __isl_give isl_set *isl_set_remove_unknown_divs(
1581 __isl_take isl_set *set);
1582 __isl_give isl_map *isl_map_remove_unknown_divs(
1583 __isl_take isl_map *map);
1585 To iterate over all the sets or maps in a union set or map, use
1587 int isl_union_set_foreach_set(__isl_keep isl_union_set *uset,
1588 int (*fn)(__isl_take isl_set *set, void *user),
1590 int isl_union_map_foreach_map(__isl_keep isl_union_map *umap,
1591 int (*fn)(__isl_take isl_map *map, void *user),
1594 The number of sets or maps in a union set or map can be obtained
1597 int isl_union_set_n_set(__isl_keep isl_union_set *uset);
1598 int isl_union_map_n_map(__isl_keep isl_union_map *umap);
1600 To extract the set or map in a given space from a union, use
1602 __isl_give isl_set *isl_union_set_extract_set(
1603 __isl_keep isl_union_set *uset,
1604 __isl_take isl_space *space);
1605 __isl_give isl_map *isl_union_map_extract_map(
1606 __isl_keep isl_union_map *umap,
1607 __isl_take isl_space *space);
1609 To iterate over all the basic sets or maps in a set or map, use
1611 int isl_set_foreach_basic_set(__isl_keep isl_set *set,
1612 int (*fn)(__isl_take isl_basic_set *bset, void *user),
1614 int isl_map_foreach_basic_map(__isl_keep isl_map *map,
1615 int (*fn)(__isl_take isl_basic_map *bmap, void *user),
1618 The callback function C<fn> should return 0 if successful and
1619 -1 if an error occurs. In the latter case, or if any other error
1620 occurs, the above functions will return -1.
1622 It should be noted that C<isl> does not guarantee that
1623 the basic sets or maps passed to C<fn> are disjoint.
1624 If this is required, then the user should call one of
1625 the following functions first.
1627 __isl_give isl_set *isl_set_make_disjoint(
1628 __isl_take isl_set *set);
1629 __isl_give isl_map *isl_map_make_disjoint(
1630 __isl_take isl_map *map);
1632 The number of basic sets in a set can be obtained
1635 int isl_set_n_basic_set(__isl_keep isl_set *set);
1637 To iterate over the constraints of a basic set or map, use
1639 #include <isl/constraint.h>
1641 int isl_basic_set_n_constraint(
1642 __isl_keep isl_basic_set *bset);
1643 int isl_basic_set_foreach_constraint(
1644 __isl_keep isl_basic_set *bset,
1645 int (*fn)(__isl_take isl_constraint *c, void *user),
1647 int isl_basic_map_foreach_constraint(
1648 __isl_keep isl_basic_map *bmap,
1649 int (*fn)(__isl_take isl_constraint *c, void *user),
1651 void *isl_constraint_free(__isl_take isl_constraint *c);
1653 Again, the callback function C<fn> should return 0 if successful and
1654 -1 if an error occurs. In the latter case, or if any other error
1655 occurs, the above functions will return -1.
1656 The constraint C<c> represents either an equality or an inequality.
1657 Use the following function to find out whether a constraint
1658 represents an equality. If not, it represents an inequality.
1660 int isl_constraint_is_equality(
1661 __isl_keep isl_constraint *constraint);
1663 The coefficients of the constraints can be inspected using
1664 the following functions.
1666 int isl_constraint_is_lower_bound(
1667 __isl_keep isl_constraint *constraint,
1668 enum isl_dim_type type, unsigned pos);
1669 int isl_constraint_is_upper_bound(
1670 __isl_keep isl_constraint *constraint,
1671 enum isl_dim_type type, unsigned pos);
1672 __isl_give isl_val *isl_constraint_get_constant_val(
1673 __isl_keep isl_constraint *constraint);
1674 __isl_give isl_val *isl_constraint_get_coefficient_val(
1675 __isl_keep isl_constraint *constraint,
1676 enum isl_dim_type type, int pos);
1677 int isl_constraint_involves_dims(
1678 __isl_keep isl_constraint *constraint,
1679 enum isl_dim_type type, unsigned first, unsigned n);
1681 The explicit representations of the existentially quantified
1682 variables can be inspected using the following function.
1683 Note that the user is only allowed to use this function
1684 if the inspected set or map is the result of a call
1685 to C<isl_set_compute_divs> or C<isl_map_compute_divs>.
1686 The existentially quantified variable is equal to the floor
1687 of the returned affine expression. The affine expression
1688 itself can be inspected using the functions in
1689 L<"Piecewise Quasi Affine Expressions">.
1691 __isl_give isl_aff *isl_constraint_get_div(
1692 __isl_keep isl_constraint *constraint, int pos);
1694 To obtain the constraints of a basic set or map in matrix
1695 form, use the following functions.
1697 __isl_give isl_mat *isl_basic_set_equalities_matrix(
1698 __isl_keep isl_basic_set *bset,
1699 enum isl_dim_type c1, enum isl_dim_type c2,
1700 enum isl_dim_type c3, enum isl_dim_type c4);
1701 __isl_give isl_mat *isl_basic_set_inequalities_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_map_equalities_matrix(
1706 __isl_keep isl_basic_map *bmap,
1707 enum isl_dim_type c1,
1708 enum isl_dim_type c2, enum isl_dim_type c3,
1709 enum isl_dim_type c4, enum isl_dim_type c5);
1710 __isl_give isl_mat *isl_basic_map_inequalities_matrix(
1711 __isl_keep isl_basic_map *bmap,
1712 enum isl_dim_type c1,
1713 enum isl_dim_type c2, enum isl_dim_type c3,
1714 enum isl_dim_type c4, enum isl_dim_type c5);
1716 The C<isl_dim_type> arguments dictate the order in which
1717 different kinds of variables appear in the resulting matrix
1718 and should be a permutation of C<isl_dim_cst>, C<isl_dim_param>,
1719 C<isl_dim_in>, C<isl_dim_out> and C<isl_dim_div>.
1721 The number of parameters, input, output or set dimensions can
1722 be obtained using the following functions.
1724 unsigned isl_basic_set_dim(__isl_keep isl_basic_set *bset,
1725 enum isl_dim_type type);
1726 unsigned isl_basic_map_dim(__isl_keep isl_basic_map *bmap,
1727 enum isl_dim_type type);
1728 unsigned isl_set_dim(__isl_keep isl_set *set,
1729 enum isl_dim_type type);
1730 unsigned isl_map_dim(__isl_keep isl_map *map,
1731 enum isl_dim_type type);
1733 To check whether the description of a set or relation depends
1734 on one or more given dimensions, it is not necessary to iterate over all
1735 constraints. Instead the following functions can be used.
1737 int isl_basic_set_involves_dims(
1738 __isl_keep isl_basic_set *bset,
1739 enum isl_dim_type type, unsigned first, unsigned n);
1740 int isl_set_involves_dims(__isl_keep isl_set *set,
1741 enum isl_dim_type type, unsigned first, unsigned n);
1742 int isl_basic_map_involves_dims(
1743 __isl_keep isl_basic_map *bmap,
1744 enum isl_dim_type type, unsigned first, unsigned n);
1745 int isl_map_involves_dims(__isl_keep isl_map *map,
1746 enum isl_dim_type type, unsigned first, unsigned n);
1748 Similarly, the following functions can be used to check whether
1749 a given dimension is involved in any lower or upper bound.
1751 int isl_set_dim_has_any_lower_bound(__isl_keep isl_set *set,
1752 enum isl_dim_type type, unsigned pos);
1753 int isl_set_dim_has_any_upper_bound(__isl_keep isl_set *set,
1754 enum isl_dim_type type, unsigned pos);
1756 Note that these functions return true even if there is a bound on
1757 the dimension on only some of the basic sets of C<set>.
1758 To check if they have a bound for all of the basic sets in C<set>,
1759 use the following functions instead.
1761 int isl_set_dim_has_lower_bound(__isl_keep isl_set *set,
1762 enum isl_dim_type type, unsigned pos);
1763 int isl_set_dim_has_upper_bound(__isl_keep isl_set *set,
1764 enum isl_dim_type type, unsigned pos);
1766 The identifiers or names of the domain and range spaces of a set
1767 or relation can be read off or set using the following functions.
1769 __isl_give isl_set *isl_set_set_tuple_id(
1770 __isl_take isl_set *set, __isl_take isl_id *id);
1771 __isl_give isl_set *isl_set_reset_tuple_id(
1772 __isl_take isl_set *set);
1773 int isl_set_has_tuple_id(__isl_keep isl_set *set);
1774 __isl_give isl_id *isl_set_get_tuple_id(
1775 __isl_keep isl_set *set);
1776 __isl_give isl_map *isl_map_set_tuple_id(
1777 __isl_take isl_map *map, enum isl_dim_type type,
1778 __isl_take isl_id *id);
1779 __isl_give isl_map *isl_map_reset_tuple_id(
1780 __isl_take isl_map *map, enum isl_dim_type type);
1781 int isl_map_has_tuple_id(__isl_keep isl_map *map,
1782 enum isl_dim_type type);
1783 __isl_give isl_id *isl_map_get_tuple_id(
1784 __isl_keep isl_map *map, enum isl_dim_type type);
1786 const char *isl_basic_set_get_tuple_name(
1787 __isl_keep isl_basic_set *bset);
1788 __isl_give isl_basic_set *isl_basic_set_set_tuple_name(
1789 __isl_take isl_basic_set *set, const char *s);
1790 int isl_set_has_tuple_name(__isl_keep isl_set *set);
1791 const char *isl_set_get_tuple_name(
1792 __isl_keep isl_set *set);
1793 const char *isl_basic_map_get_tuple_name(
1794 __isl_keep isl_basic_map *bmap,
1795 enum isl_dim_type type);
1796 __isl_give isl_basic_map *isl_basic_map_set_tuple_name(
1797 __isl_take isl_basic_map *bmap,
1798 enum isl_dim_type type, const char *s);
1799 int isl_map_has_tuple_name(__isl_keep isl_map *map,
1800 enum isl_dim_type type);
1801 const char *isl_map_get_tuple_name(
1802 __isl_keep isl_map *map,
1803 enum isl_dim_type type);
1805 As with C<isl_space_get_tuple_name>, the value returned points to
1806 an internal data structure.
1807 The identifiers, positions or names of individual dimensions can be
1808 read off using the following functions.
1810 __isl_give isl_id *isl_basic_set_get_dim_id(
1811 __isl_keep isl_basic_set *bset,
1812 enum isl_dim_type type, unsigned pos);
1813 __isl_give isl_set *isl_set_set_dim_id(
1814 __isl_take isl_set *set, enum isl_dim_type type,
1815 unsigned pos, __isl_take isl_id *id);
1816 int isl_set_has_dim_id(__isl_keep isl_set *set,
1817 enum isl_dim_type type, unsigned pos);
1818 __isl_give isl_id *isl_set_get_dim_id(
1819 __isl_keep isl_set *set, enum isl_dim_type type,
1821 int isl_basic_map_has_dim_id(
1822 __isl_keep isl_basic_map *bmap,
1823 enum isl_dim_type type, unsigned pos);
1824 __isl_give isl_map *isl_map_set_dim_id(
1825 __isl_take isl_map *map, enum isl_dim_type type,
1826 unsigned pos, __isl_take isl_id *id);
1827 int isl_map_has_dim_id(__isl_keep isl_map *map,
1828 enum isl_dim_type type, unsigned pos);
1829 __isl_give isl_id *isl_map_get_dim_id(
1830 __isl_keep isl_map *map, enum isl_dim_type type,
1833 int isl_set_find_dim_by_id(__isl_keep isl_set *set,
1834 enum isl_dim_type type, __isl_keep isl_id *id);
1835 int isl_map_find_dim_by_id(__isl_keep isl_map *map,
1836 enum isl_dim_type type, __isl_keep isl_id *id);
1837 int isl_set_find_dim_by_name(__isl_keep isl_set *set,
1838 enum isl_dim_type type, const char *name);
1839 int isl_map_find_dim_by_name(__isl_keep isl_map *map,
1840 enum isl_dim_type type, const char *name);
1842 const char *isl_constraint_get_dim_name(
1843 __isl_keep isl_constraint *constraint,
1844 enum isl_dim_type type, unsigned pos);
1845 const char *isl_basic_set_get_dim_name(
1846 __isl_keep isl_basic_set *bset,
1847 enum isl_dim_type type, unsigned pos);
1848 int isl_set_has_dim_name(__isl_keep isl_set *set,
1849 enum isl_dim_type type, unsigned pos);
1850 const char *isl_set_get_dim_name(
1851 __isl_keep isl_set *set,
1852 enum isl_dim_type type, unsigned pos);
1853 const char *isl_basic_map_get_dim_name(
1854 __isl_keep isl_basic_map *bmap,
1855 enum isl_dim_type type, unsigned pos);
1856 int isl_map_has_dim_name(__isl_keep isl_map *map,
1857 enum isl_dim_type type, unsigned pos);
1858 const char *isl_map_get_dim_name(
1859 __isl_keep isl_map *map,
1860 enum isl_dim_type type, unsigned pos);
1862 These functions are mostly useful to obtain the identifiers, positions
1863 or names of the parameters. Identifiers of individual dimensions are
1864 essentially only useful for printing. They are ignored by all other
1865 operations and may not be preserved across those operations.
1869 =head3 Unary Properties
1875 The following functions test whether the given set or relation
1876 contains any integer points. The ``plain'' variants do not perform
1877 any computations, but simply check if the given set or relation
1878 is already known to be empty.
1880 int isl_basic_set_plain_is_empty(__isl_keep isl_basic_set *bset);
1881 int isl_basic_set_is_empty(__isl_keep isl_basic_set *bset);
1882 int isl_set_plain_is_empty(__isl_keep isl_set *set);
1883 int isl_set_is_empty(__isl_keep isl_set *set);
1884 int isl_union_set_is_empty(__isl_keep isl_union_set *uset);
1885 int isl_basic_map_plain_is_empty(__isl_keep isl_basic_map *bmap);
1886 int isl_basic_map_is_empty(__isl_keep isl_basic_map *bmap);
1887 int isl_map_plain_is_empty(__isl_keep isl_map *map);
1888 int isl_map_is_empty(__isl_keep isl_map *map);
1889 int isl_union_map_is_empty(__isl_keep isl_union_map *umap);
1891 =item * Universality
1893 int isl_basic_set_is_universe(__isl_keep isl_basic_set *bset);
1894 int isl_basic_map_is_universe(__isl_keep isl_basic_map *bmap);
1895 int isl_set_plain_is_universe(__isl_keep isl_set *set);
1897 =item * Single-valuedness
1899 int isl_basic_map_is_single_valued(
1900 __isl_keep isl_basic_map *bmap);
1901 int isl_map_plain_is_single_valued(
1902 __isl_keep isl_map *map);
1903 int isl_map_is_single_valued(__isl_keep isl_map *map);
1904 int isl_union_map_is_single_valued(__isl_keep isl_union_map *umap);
1908 int isl_map_plain_is_injective(__isl_keep isl_map *map);
1909 int isl_map_is_injective(__isl_keep isl_map *map);
1910 int isl_union_map_plain_is_injective(
1911 __isl_keep isl_union_map *umap);
1912 int isl_union_map_is_injective(
1913 __isl_keep isl_union_map *umap);
1917 int isl_map_is_bijective(__isl_keep isl_map *map);
1918 int isl_union_map_is_bijective(__isl_keep isl_union_map *umap);
1922 __isl_give isl_val *
1923 isl_basic_map_plain_get_val_if_fixed(
1924 __isl_keep isl_basic_map *bmap,
1925 enum isl_dim_type type, unsigned pos);
1926 __isl_give isl_val *isl_set_plain_get_val_if_fixed(
1927 __isl_keep isl_set *set,
1928 enum isl_dim_type type, unsigned pos);
1929 __isl_give isl_val *isl_map_plain_get_val_if_fixed(
1930 __isl_keep isl_map *map,
1931 enum isl_dim_type type, unsigned pos);
1933 If the set or relation obviously lies on a hyperplane where the given dimension
1934 has a fixed value, then return that value.
1935 Otherwise return NaN.
1939 int isl_set_dim_residue_class_val(
1940 __isl_keep isl_set *set,
1941 int pos, __isl_give isl_val **modulo,
1942 __isl_give isl_val **residue);
1944 Check if the values of the given set dimension are equal to a fixed
1945 value modulo some integer value. If so, assign the modulo to C<*modulo>
1946 and the fixed value to C<*residue>. If the given dimension attains only
1947 a single value, then assign C<0> to C<*modulo> and the fixed value to
1949 If the dimension does not attain only a single value and if no modulo
1950 can be found then assign C<1> to C<*modulo> and C<1> to C<*residue>.
1954 To check whether a set is a parameter domain, use this function:
1956 int isl_set_is_params(__isl_keep isl_set *set);
1957 int isl_union_set_is_params(
1958 __isl_keep isl_union_set *uset);
1962 The following functions check whether the domain of the given
1963 (basic) set is a wrapped relation.
1965 int isl_basic_set_is_wrapping(
1966 __isl_keep isl_basic_set *bset);
1967 int isl_set_is_wrapping(__isl_keep isl_set *set);
1969 =item * Internal Product
1971 int isl_basic_map_can_zip(
1972 __isl_keep isl_basic_map *bmap);
1973 int isl_map_can_zip(__isl_keep isl_map *map);
1975 Check whether the product of domain and range of the given relation
1977 i.e., whether both domain and range are nested relations.
1981 int isl_basic_map_can_curry(
1982 __isl_keep isl_basic_map *bmap);
1983 int isl_map_can_curry(__isl_keep isl_map *map);
1985 Check whether the domain of the (basic) relation is a wrapped relation.
1987 int isl_basic_map_can_uncurry(
1988 __isl_keep isl_basic_map *bmap);
1989 int isl_map_can_uncurry(__isl_keep isl_map *map);
1991 Check whether the range of the (basic) relation is a wrapped relation.
1995 =head3 Binary Properties
2001 int isl_set_plain_is_equal(__isl_keep isl_set *set1,
2002 __isl_keep isl_set *set2);
2003 int isl_set_is_equal(__isl_keep isl_set *set1,
2004 __isl_keep isl_set *set2);
2005 int isl_union_set_is_equal(
2006 __isl_keep isl_union_set *uset1,
2007 __isl_keep isl_union_set *uset2);
2008 int isl_basic_map_is_equal(
2009 __isl_keep isl_basic_map *bmap1,
2010 __isl_keep isl_basic_map *bmap2);
2011 int isl_map_is_equal(__isl_keep isl_map *map1,
2012 __isl_keep isl_map *map2);
2013 int isl_map_plain_is_equal(__isl_keep isl_map *map1,
2014 __isl_keep isl_map *map2);
2015 int isl_union_map_is_equal(
2016 __isl_keep isl_union_map *umap1,
2017 __isl_keep isl_union_map *umap2);
2019 =item * Disjointness
2021 int isl_basic_set_is_disjoint(
2022 __isl_keep isl_basic_set *bset1,
2023 __isl_keep isl_basic_set *bset2);
2024 int isl_set_plain_is_disjoint(__isl_keep isl_set *set1,
2025 __isl_keep isl_set *set2);
2026 int isl_set_is_disjoint(__isl_keep isl_set *set1,
2027 __isl_keep isl_set *set2);
2028 int isl_basic_map_is_disjoint(
2029 __isl_keep isl_basic_map *bmap1,
2030 __isl_keep isl_basic_map *bmap2);
2031 int isl_map_is_disjoint(__isl_keep isl_map *map1,
2032 __isl_keep isl_map *map2);
2036 int isl_basic_set_is_subset(
2037 __isl_keep isl_basic_set *bset1,
2038 __isl_keep isl_basic_set *bset2);
2039 int isl_set_is_subset(__isl_keep isl_set *set1,
2040 __isl_keep isl_set *set2);
2041 int isl_set_is_strict_subset(
2042 __isl_keep isl_set *set1,
2043 __isl_keep isl_set *set2);
2044 int isl_union_set_is_subset(
2045 __isl_keep isl_union_set *uset1,
2046 __isl_keep isl_union_set *uset2);
2047 int isl_union_set_is_strict_subset(
2048 __isl_keep isl_union_set *uset1,
2049 __isl_keep isl_union_set *uset2);
2050 int isl_basic_map_is_subset(
2051 __isl_keep isl_basic_map *bmap1,
2052 __isl_keep isl_basic_map *bmap2);
2053 int isl_basic_map_is_strict_subset(
2054 __isl_keep isl_basic_map *bmap1,
2055 __isl_keep isl_basic_map *bmap2);
2056 int isl_map_is_subset(
2057 __isl_keep isl_map *map1,
2058 __isl_keep isl_map *map2);
2059 int isl_map_is_strict_subset(
2060 __isl_keep isl_map *map1,
2061 __isl_keep isl_map *map2);
2062 int isl_union_map_is_subset(
2063 __isl_keep isl_union_map *umap1,
2064 __isl_keep isl_union_map *umap2);
2065 int isl_union_map_is_strict_subset(
2066 __isl_keep isl_union_map *umap1,
2067 __isl_keep isl_union_map *umap2);
2069 Check whether the first argument is a (strict) subset of the
2074 int isl_set_plain_cmp(__isl_keep isl_set *set1,
2075 __isl_keep isl_set *set2);
2077 This function is useful for sorting C<isl_set>s.
2078 The order depends on the internal representation of the inputs.
2079 The order is fixed over different calls to the function (assuming
2080 the internal representation of the inputs has not changed), but may
2081 change over different versions of C<isl>.
2085 =head2 Unary Operations
2091 __isl_give isl_set *isl_set_complement(
2092 __isl_take isl_set *set);
2093 __isl_give isl_map *isl_map_complement(
2094 __isl_take isl_map *map);
2098 __isl_give isl_basic_map *isl_basic_map_reverse(
2099 __isl_take isl_basic_map *bmap);
2100 __isl_give isl_map *isl_map_reverse(
2101 __isl_take isl_map *map);
2102 __isl_give isl_union_map *isl_union_map_reverse(
2103 __isl_take isl_union_map *umap);
2107 __isl_give isl_basic_set *isl_basic_set_project_out(
2108 __isl_take isl_basic_set *bset,
2109 enum isl_dim_type type, unsigned first, unsigned n);
2110 __isl_give isl_basic_map *isl_basic_map_project_out(
2111 __isl_take isl_basic_map *bmap,
2112 enum isl_dim_type type, unsigned first, unsigned n);
2113 __isl_give isl_set *isl_set_project_out(__isl_take isl_set *set,
2114 enum isl_dim_type type, unsigned first, unsigned n);
2115 __isl_give isl_map *isl_map_project_out(__isl_take isl_map *map,
2116 enum isl_dim_type type, unsigned first, unsigned n);
2117 __isl_give isl_basic_set *isl_basic_set_params(
2118 __isl_take isl_basic_set *bset);
2119 __isl_give isl_basic_set *isl_basic_map_domain(
2120 __isl_take isl_basic_map *bmap);
2121 __isl_give isl_basic_set *isl_basic_map_range(
2122 __isl_take isl_basic_map *bmap);
2123 __isl_give isl_set *isl_set_params(__isl_take isl_set *set);
2124 __isl_give isl_set *isl_map_params(__isl_take isl_map *map);
2125 __isl_give isl_set *isl_map_domain(
2126 __isl_take isl_map *bmap);
2127 __isl_give isl_set *isl_map_range(
2128 __isl_take isl_map *map);
2129 __isl_give isl_set *isl_union_set_params(
2130 __isl_take isl_union_set *uset);
2131 __isl_give isl_set *isl_union_map_params(
2132 __isl_take isl_union_map *umap);
2133 __isl_give isl_union_set *isl_union_map_domain(
2134 __isl_take isl_union_map *umap);
2135 __isl_give isl_union_set *isl_union_map_range(
2136 __isl_take isl_union_map *umap);
2138 __isl_give isl_basic_map *isl_basic_map_domain_map(
2139 __isl_take isl_basic_map *bmap);
2140 __isl_give isl_basic_map *isl_basic_map_range_map(
2141 __isl_take isl_basic_map *bmap);
2142 __isl_give isl_map *isl_map_domain_map(__isl_take isl_map *map);
2143 __isl_give isl_map *isl_map_range_map(__isl_take isl_map *map);
2144 __isl_give isl_union_map *isl_union_map_domain_map(
2145 __isl_take isl_union_map *umap);
2146 __isl_give isl_union_map *isl_union_map_range_map(
2147 __isl_take isl_union_map *umap);
2149 The functions above construct a (basic, regular or union) relation
2150 that maps (a wrapped version of) the input relation to its domain or range.
2154 __isl_give isl_basic_set *isl_basic_set_eliminate(
2155 __isl_take isl_basic_set *bset,
2156 enum isl_dim_type type,
2157 unsigned first, unsigned n);
2158 __isl_give isl_set *isl_set_eliminate(
2159 __isl_take isl_set *set, enum isl_dim_type type,
2160 unsigned first, unsigned n);
2161 __isl_give isl_basic_map *isl_basic_map_eliminate(
2162 __isl_take isl_basic_map *bmap,
2163 enum isl_dim_type type,
2164 unsigned first, unsigned n);
2165 __isl_give isl_map *isl_map_eliminate(
2166 __isl_take isl_map *map, enum isl_dim_type type,
2167 unsigned first, unsigned n);
2169 Eliminate the coefficients for the given dimensions from the constraints,
2170 without removing the dimensions.
2174 __isl_give isl_basic_set *isl_basic_set_fix_si(
2175 __isl_take isl_basic_set *bset,
2176 enum isl_dim_type type, unsigned pos, int value);
2177 __isl_give isl_basic_set *isl_basic_set_fix_val(
2178 __isl_take isl_basic_set *bset,
2179 enum isl_dim_type type, unsigned pos,
2180 __isl_take isl_val *v);
2181 __isl_give isl_set *isl_set_fix_si(__isl_take isl_set *set,
2182 enum isl_dim_type type, unsigned pos, int value);
2183 __isl_give isl_set *isl_set_fix_val(
2184 __isl_take isl_set *set,
2185 enum isl_dim_type type, unsigned pos,
2186 __isl_take isl_val *v);
2187 __isl_give isl_basic_map *isl_basic_map_fix_si(
2188 __isl_take isl_basic_map *bmap,
2189 enum isl_dim_type type, unsigned pos, int value);
2190 __isl_give isl_basic_map *isl_basic_map_fix_val(
2191 __isl_take isl_basic_map *bmap,
2192 enum isl_dim_type type, unsigned pos,
2193 __isl_take isl_val *v);
2194 __isl_give isl_map *isl_map_fix_si(__isl_take isl_map *map,
2195 enum isl_dim_type type, unsigned pos, int value);
2196 __isl_give isl_map *isl_map_fix_val(
2197 __isl_take isl_map *map,
2198 enum isl_dim_type type, unsigned pos,
2199 __isl_take isl_val *v);
2201 Intersect the set or relation with the hyperplane where the given
2202 dimension has the fixed given value.
2204 __isl_give isl_basic_map *isl_basic_map_lower_bound_si(
2205 __isl_take isl_basic_map *bmap,
2206 enum isl_dim_type type, unsigned pos, int value);
2207 __isl_give isl_basic_map *isl_basic_map_upper_bound_si(
2208 __isl_take isl_basic_map *bmap,
2209 enum isl_dim_type type, unsigned pos, int value);
2210 __isl_give isl_set *isl_set_lower_bound_si(
2211 __isl_take isl_set *set,
2212 enum isl_dim_type type, unsigned pos, int value);
2213 __isl_give isl_set *isl_set_lower_bound_val(
2214 __isl_take isl_set *set,
2215 enum isl_dim_type type, unsigned pos,
2216 __isl_take isl_val *value);
2217 __isl_give isl_map *isl_map_lower_bound_si(
2218 __isl_take isl_map *map,
2219 enum isl_dim_type type, unsigned pos, int value);
2220 __isl_give isl_set *isl_set_upper_bound_si(
2221 __isl_take isl_set *set,
2222 enum isl_dim_type type, unsigned pos, int value);
2223 __isl_give isl_set *isl_set_upper_bound_val(
2224 __isl_take isl_set *set,
2225 enum isl_dim_type type, unsigned pos,
2226 __isl_take isl_val *value);
2227 __isl_give isl_map *isl_map_upper_bound_si(
2228 __isl_take isl_map *map,
2229 enum isl_dim_type type, unsigned pos, int value);
2231 Intersect the set or relation with the half-space where the given
2232 dimension has a value bounded by the fixed given integer value.
2234 __isl_give isl_set *isl_set_equate(__isl_take isl_set *set,
2235 enum isl_dim_type type1, int pos1,
2236 enum isl_dim_type type2, int pos2);
2237 __isl_give isl_basic_map *isl_basic_map_equate(
2238 __isl_take isl_basic_map *bmap,
2239 enum isl_dim_type type1, int pos1,
2240 enum isl_dim_type type2, int pos2);
2241 __isl_give isl_map *isl_map_equate(__isl_take isl_map *map,
2242 enum isl_dim_type type1, int pos1,
2243 enum isl_dim_type type2, int pos2);
2245 Intersect the set or relation with the hyperplane where the given
2246 dimensions are equal to each other.
2248 __isl_give isl_map *isl_map_oppose(__isl_take isl_map *map,
2249 enum isl_dim_type type1, int pos1,
2250 enum isl_dim_type type2, int pos2);
2252 Intersect the relation with the hyperplane where the given
2253 dimensions have opposite values.
2255 __isl_give isl_basic_map *isl_basic_map_order_ge(
2256 __isl_take isl_basic_map *bmap,
2257 enum isl_dim_type type1, int pos1,
2258 enum isl_dim_type type2, int pos2);
2259 __isl_give isl_map *isl_map_order_lt(__isl_take isl_map *map,
2260 enum isl_dim_type type1, int pos1,
2261 enum isl_dim_type type2, int pos2);
2262 __isl_give isl_basic_map *isl_basic_map_order_gt(
2263 __isl_take isl_basic_map *bmap,
2264 enum isl_dim_type type1, int pos1,
2265 enum isl_dim_type type2, int pos2);
2266 __isl_give isl_map *isl_map_order_gt(__isl_take isl_map *map,
2267 enum isl_dim_type type1, int pos1,
2268 enum isl_dim_type type2, int pos2);
2270 Intersect the relation with the half-space where the given
2271 dimensions satisfy the given ordering.
2275 __isl_give isl_map *isl_set_identity(
2276 __isl_take isl_set *set);
2277 __isl_give isl_union_map *isl_union_set_identity(
2278 __isl_take isl_union_set *uset);
2280 Construct an identity relation on the given (union) set.
2284 __isl_give isl_basic_set *isl_basic_map_deltas(
2285 __isl_take isl_basic_map *bmap);
2286 __isl_give isl_set *isl_map_deltas(__isl_take isl_map *map);
2287 __isl_give isl_union_set *isl_union_map_deltas(
2288 __isl_take isl_union_map *umap);
2290 These functions return a (basic) set containing the differences
2291 between image elements and corresponding domain elements in the input.
2293 __isl_give isl_basic_map *isl_basic_map_deltas_map(
2294 __isl_take isl_basic_map *bmap);
2295 __isl_give isl_map *isl_map_deltas_map(
2296 __isl_take isl_map *map);
2297 __isl_give isl_union_map *isl_union_map_deltas_map(
2298 __isl_take isl_union_map *umap);
2300 The functions above construct a (basic, regular or union) relation
2301 that maps (a wrapped version of) the input relation to its delta set.
2305 Simplify the representation of a set or relation by trying
2306 to combine pairs of basic sets or relations into a single
2307 basic set or relation.
2309 __isl_give isl_set *isl_set_coalesce(__isl_take isl_set *set);
2310 __isl_give isl_map *isl_map_coalesce(__isl_take isl_map *map);
2311 __isl_give isl_union_set *isl_union_set_coalesce(
2312 __isl_take isl_union_set *uset);
2313 __isl_give isl_union_map *isl_union_map_coalesce(
2314 __isl_take isl_union_map *umap);
2316 One of the methods for combining pairs of basic sets or relations
2317 can result in coefficients that are much larger than those that appear
2318 in the constraints of the input. By default, the coefficients are
2319 not allowed to grow larger, but this can be changed by unsetting
2320 the following option.
2322 int isl_options_set_coalesce_bounded_wrapping(
2323 isl_ctx *ctx, int val);
2324 int isl_options_get_coalesce_bounded_wrapping(
2327 =item * Detecting equalities
2329 __isl_give isl_basic_set *isl_basic_set_detect_equalities(
2330 __isl_take isl_basic_set *bset);
2331 __isl_give isl_basic_map *isl_basic_map_detect_equalities(
2332 __isl_take isl_basic_map *bmap);
2333 __isl_give isl_set *isl_set_detect_equalities(
2334 __isl_take isl_set *set);
2335 __isl_give isl_map *isl_map_detect_equalities(
2336 __isl_take isl_map *map);
2337 __isl_give isl_union_set *isl_union_set_detect_equalities(
2338 __isl_take isl_union_set *uset);
2339 __isl_give isl_union_map *isl_union_map_detect_equalities(
2340 __isl_take isl_union_map *umap);
2342 Simplify the representation of a set or relation by detecting implicit
2345 =item * Removing redundant constraints
2347 __isl_give isl_basic_set *isl_basic_set_remove_redundancies(
2348 __isl_take isl_basic_set *bset);
2349 __isl_give isl_set *isl_set_remove_redundancies(
2350 __isl_take isl_set *set);
2351 __isl_give isl_basic_map *isl_basic_map_remove_redundancies(
2352 __isl_take isl_basic_map *bmap);
2353 __isl_give isl_map *isl_map_remove_redundancies(
2354 __isl_take isl_map *map);
2358 __isl_give isl_basic_set *isl_set_convex_hull(
2359 __isl_take isl_set *set);
2360 __isl_give isl_basic_map *isl_map_convex_hull(
2361 __isl_take isl_map *map);
2363 If the input set or relation has any existentially quantified
2364 variables, then the result of these operations is currently undefined.
2368 __isl_give isl_basic_set *
2369 isl_set_unshifted_simple_hull(
2370 __isl_take isl_set *set);
2371 __isl_give isl_basic_map *
2372 isl_map_unshifted_simple_hull(
2373 __isl_take isl_map *map);
2374 __isl_give isl_basic_set *isl_set_simple_hull(
2375 __isl_take isl_set *set);
2376 __isl_give isl_basic_map *isl_map_simple_hull(
2377 __isl_take isl_map *map);
2378 __isl_give isl_union_map *isl_union_map_simple_hull(
2379 __isl_take isl_union_map *umap);
2381 These functions compute a single basic set or relation
2382 that contains the whole input set or relation.
2383 In particular, the output is described by translates
2384 of the constraints describing the basic sets or relations in the input.
2385 In case of C<isl_set_unshifted_simple_hull>, only the original
2386 constraints are used, without any translation.
2390 (See \autoref{s:simple hull}.)
2396 __isl_give isl_basic_set *isl_basic_set_affine_hull(
2397 __isl_take isl_basic_set *bset);
2398 __isl_give isl_basic_set *isl_set_affine_hull(
2399 __isl_take isl_set *set);
2400 __isl_give isl_union_set *isl_union_set_affine_hull(
2401 __isl_take isl_union_set *uset);
2402 __isl_give isl_basic_map *isl_basic_map_affine_hull(
2403 __isl_take isl_basic_map *bmap);
2404 __isl_give isl_basic_map *isl_map_affine_hull(
2405 __isl_take isl_map *map);
2406 __isl_give isl_union_map *isl_union_map_affine_hull(
2407 __isl_take isl_union_map *umap);
2409 In case of union sets and relations, the affine hull is computed
2412 =item * Polyhedral hull
2414 __isl_give isl_basic_set *isl_set_polyhedral_hull(
2415 __isl_take isl_set *set);
2416 __isl_give isl_basic_map *isl_map_polyhedral_hull(
2417 __isl_take isl_map *map);
2418 __isl_give isl_union_set *isl_union_set_polyhedral_hull(
2419 __isl_take isl_union_set *uset);
2420 __isl_give isl_union_map *isl_union_map_polyhedral_hull(
2421 __isl_take isl_union_map *umap);
2423 These functions compute a single basic set or relation
2424 not involving any existentially quantified variables
2425 that contains the whole input set or relation.
2426 In case of union sets and relations, the polyhedral hull is computed
2429 =item * Other approximations
2431 __isl_give isl_basic_set *
2432 isl_basic_set_drop_constraints_involving_dims(
2433 __isl_take isl_basic_set *bset,
2434 enum isl_dim_type type,
2435 unsigned first, unsigned n);
2436 __isl_give isl_basic_map *
2437 isl_basic_map_drop_constraints_involving_dims(
2438 __isl_take isl_basic_map *bmap,
2439 enum isl_dim_type type,
2440 unsigned first, unsigned n);
2441 __isl_give isl_basic_set *
2442 isl_basic_set_drop_constraints_not_involving_dims(
2443 __isl_take isl_basic_set *bset,
2444 enum isl_dim_type type,
2445 unsigned first, unsigned n);
2446 __isl_give isl_set *
2447 isl_set_drop_constraints_involving_dims(
2448 __isl_take isl_set *set,
2449 enum isl_dim_type type,
2450 unsigned first, unsigned n);
2451 __isl_give isl_map *
2452 isl_map_drop_constraints_involving_dims(
2453 __isl_take isl_map *map,
2454 enum isl_dim_type type,
2455 unsigned first, unsigned n);
2457 These functions drop any constraints (not) involving the specified dimensions.
2458 Note that the result depends on the representation of the input.
2462 __isl_give isl_basic_set *isl_basic_set_sample(
2463 __isl_take isl_basic_set *bset);
2464 __isl_give isl_basic_set *isl_set_sample(
2465 __isl_take isl_set *set);
2466 __isl_give isl_basic_map *isl_basic_map_sample(
2467 __isl_take isl_basic_map *bmap);
2468 __isl_give isl_basic_map *isl_map_sample(
2469 __isl_take isl_map *map);
2471 If the input (basic) set or relation is non-empty, then return
2472 a singleton subset of the input. Otherwise, return an empty set.
2474 =item * Optimization
2476 #include <isl/ilp.h>
2477 __isl_give isl_val *isl_basic_set_max_val(
2478 __isl_keep isl_basic_set *bset,
2479 __isl_keep isl_aff *obj);
2480 __isl_give isl_val *isl_set_min_val(
2481 __isl_keep isl_set *set,
2482 __isl_keep isl_aff *obj);
2483 __isl_give isl_val *isl_set_max_val(
2484 __isl_keep isl_set *set,
2485 __isl_keep isl_aff *obj);
2487 Compute the minimum or maximum of the integer affine expression C<obj>
2488 over the points in C<set>, returning the result in C<opt>.
2489 The result is C<NULL> in case of an error, the optimal value in case
2490 there is one, negative infinity or infinity if the problem is unbounded and
2491 NaN if the problem is empty.
2493 =item * Parametric optimization
2495 __isl_give isl_pw_aff *isl_set_dim_min(
2496 __isl_take isl_set *set, int pos);
2497 __isl_give isl_pw_aff *isl_set_dim_max(
2498 __isl_take isl_set *set, int pos);
2499 __isl_give isl_pw_aff *isl_map_dim_max(
2500 __isl_take isl_map *map, int pos);
2502 Compute the minimum or maximum of the given set or output dimension
2503 as a function of the parameters (and input dimensions), but independently
2504 of the other set or output dimensions.
2505 For lexicographic optimization, see L<"Lexicographic Optimization">.
2509 The following functions compute either the set of (rational) coefficient
2510 values of valid constraints for the given set or the set of (rational)
2511 values satisfying the constraints with coefficients from the given set.
2512 Internally, these two sets of functions perform essentially the
2513 same operations, except that the set of coefficients is assumed to
2514 be a cone, while the set of values may be any polyhedron.
2515 The current implementation is based on the Farkas lemma and
2516 Fourier-Motzkin elimination, but this may change or be made optional
2517 in future. In particular, future implementations may use different
2518 dualization algorithms or skip the elimination step.
2520 __isl_give isl_basic_set *isl_basic_set_coefficients(
2521 __isl_take isl_basic_set *bset);
2522 __isl_give isl_basic_set *isl_set_coefficients(
2523 __isl_take isl_set *set);
2524 __isl_give isl_union_set *isl_union_set_coefficients(
2525 __isl_take isl_union_set *bset);
2526 __isl_give isl_basic_set *isl_basic_set_solutions(
2527 __isl_take isl_basic_set *bset);
2528 __isl_give isl_basic_set *isl_set_solutions(
2529 __isl_take isl_set *set);
2530 __isl_give isl_union_set *isl_union_set_solutions(
2531 __isl_take isl_union_set *bset);
2535 __isl_give isl_map *isl_map_fixed_power_val(
2536 __isl_take isl_map *map,
2537 __isl_take isl_val *exp);
2538 __isl_give isl_union_map *
2539 isl_union_map_fixed_power_val(
2540 __isl_take isl_union_map *umap,
2541 __isl_take isl_val *exp);
2543 Compute the given power of C<map>, where C<exp> is assumed to be non-zero.
2544 If the exponent C<exp> is negative, then the -C<exp> th power of the inverse
2545 of C<map> is computed.
2547 __isl_give isl_map *isl_map_power(__isl_take isl_map *map,
2549 __isl_give isl_union_map *isl_union_map_power(
2550 __isl_take isl_union_map *umap, int *exact);
2552 Compute a parametric representation for all positive powers I<k> of C<map>.
2553 The result maps I<k> to a nested relation corresponding to the
2554 I<k>th power of C<map>.
2555 The result may be an overapproximation. If the result is known to be exact,
2556 then C<*exact> is set to C<1>.
2558 =item * Transitive closure
2560 __isl_give isl_map *isl_map_transitive_closure(
2561 __isl_take isl_map *map, int *exact);
2562 __isl_give isl_union_map *isl_union_map_transitive_closure(
2563 __isl_take isl_union_map *umap, int *exact);
2565 Compute the transitive closure of C<map>.
2566 The result may be an overapproximation. If the result is known to be exact,
2567 then C<*exact> is set to C<1>.
2569 =item * Reaching path lengths
2571 __isl_give isl_map *isl_map_reaching_path_lengths(
2572 __isl_take isl_map *map, int *exact);
2574 Compute a relation that maps each element in the range of C<map>
2575 to the lengths of all paths composed of edges in C<map> that
2576 end up in the given element.
2577 The result may be an overapproximation. If the result is known to be exact,
2578 then C<*exact> is set to C<1>.
2579 To compute the I<maximal> path length, the resulting relation
2580 should be postprocessed by C<isl_map_lexmax>.
2581 In particular, if the input relation is a dependence relation
2582 (mapping sources to sinks), then the maximal path length corresponds
2583 to the free schedule.
2584 Note, however, that C<isl_map_lexmax> expects the maximum to be
2585 finite, so if the path lengths are unbounded (possibly due to
2586 the overapproximation), then you will get an error message.
2590 __isl_give isl_basic_set *isl_basic_map_wrap(
2591 __isl_take isl_basic_map *bmap);
2592 __isl_give isl_set *isl_map_wrap(
2593 __isl_take isl_map *map);
2594 __isl_give isl_union_set *isl_union_map_wrap(
2595 __isl_take isl_union_map *umap);
2596 __isl_give isl_basic_map *isl_basic_set_unwrap(
2597 __isl_take isl_basic_set *bset);
2598 __isl_give isl_map *isl_set_unwrap(
2599 __isl_take isl_set *set);
2600 __isl_give isl_union_map *isl_union_set_unwrap(
2601 __isl_take isl_union_set *uset);
2605 Remove any internal structure of domain (and range) of the given
2606 set or relation. If there is any such internal structure in the input,
2607 then the name of the space is also removed.
2609 __isl_give isl_basic_set *isl_basic_set_flatten(
2610 __isl_take isl_basic_set *bset);
2611 __isl_give isl_set *isl_set_flatten(
2612 __isl_take isl_set *set);
2613 __isl_give isl_basic_map *isl_basic_map_flatten_domain(
2614 __isl_take isl_basic_map *bmap);
2615 __isl_give isl_basic_map *isl_basic_map_flatten_range(
2616 __isl_take isl_basic_map *bmap);
2617 __isl_give isl_map *isl_map_flatten_range(
2618 __isl_take isl_map *map);
2619 __isl_give isl_map *isl_map_flatten_domain(
2620 __isl_take isl_map *map);
2621 __isl_give isl_basic_map *isl_basic_map_flatten(
2622 __isl_take isl_basic_map *bmap);
2623 __isl_give isl_map *isl_map_flatten(
2624 __isl_take isl_map *map);
2626 __isl_give isl_map *isl_set_flatten_map(
2627 __isl_take isl_set *set);
2629 The function above constructs a relation
2630 that maps the input set to a flattened version of the set.
2634 Lift the input set to a space with extra dimensions corresponding
2635 to the existentially quantified variables in the input.
2636 In particular, the result lives in a wrapped map where the domain
2637 is the original space and the range corresponds to the original
2638 existentially quantified variables.
2640 __isl_give isl_basic_set *isl_basic_set_lift(
2641 __isl_take isl_basic_set *bset);
2642 __isl_give isl_set *isl_set_lift(
2643 __isl_take isl_set *set);
2644 __isl_give isl_union_set *isl_union_set_lift(
2645 __isl_take isl_union_set *uset);
2647 Given a local space that contains the existentially quantified
2648 variables of a set, a basic relation that, when applied to
2649 a basic set, has essentially the same effect as C<isl_basic_set_lift>,
2650 can be constructed using the following function.
2652 #include <isl/local_space.h>
2653 __isl_give isl_basic_map *isl_local_space_lifting(
2654 __isl_take isl_local_space *ls);
2656 =item * Internal Product
2658 __isl_give isl_basic_map *isl_basic_map_zip(
2659 __isl_take isl_basic_map *bmap);
2660 __isl_give isl_map *isl_map_zip(
2661 __isl_take isl_map *map);
2662 __isl_give isl_union_map *isl_union_map_zip(
2663 __isl_take isl_union_map *umap);
2665 Given a relation with nested relations for domain and range,
2666 interchange the range of the domain with the domain of the range.
2670 __isl_give isl_basic_map *isl_basic_map_curry(
2671 __isl_take isl_basic_map *bmap);
2672 __isl_give isl_basic_map *isl_basic_map_uncurry(
2673 __isl_take isl_basic_map *bmap);
2674 __isl_give isl_map *isl_map_curry(
2675 __isl_take isl_map *map);
2676 __isl_give isl_map *isl_map_uncurry(
2677 __isl_take isl_map *map);
2678 __isl_give isl_union_map *isl_union_map_curry(
2679 __isl_take isl_union_map *umap);
2680 __isl_give isl_union_map *isl_union_map_uncurry(
2681 __isl_take isl_union_map *umap);
2683 Given a relation with a nested relation for domain,
2684 the C<curry> functions
2685 move the range of the nested relation out of the domain
2686 and use it as the domain of a nested relation in the range,
2687 with the original range as range of this nested relation.
2688 The C<uncurry> functions perform the inverse operation.
2690 =item * Aligning parameters
2692 __isl_give isl_basic_set *isl_basic_set_align_params(
2693 __isl_take isl_basic_set *bset,
2694 __isl_take isl_space *model);
2695 __isl_give isl_set *isl_set_align_params(
2696 __isl_take isl_set *set,
2697 __isl_take isl_space *model);
2698 __isl_give isl_basic_map *isl_basic_map_align_params(
2699 __isl_take isl_basic_map *bmap,
2700 __isl_take isl_space *model);
2701 __isl_give isl_map *isl_map_align_params(
2702 __isl_take isl_map *map,
2703 __isl_take isl_space *model);
2705 Change the order of the parameters of the given set or relation
2706 such that the first parameters match those of C<model>.
2707 This may involve the introduction of extra parameters.
2708 All parameters need to be named.
2710 =item * Dimension manipulation
2712 __isl_give isl_basic_set *isl_basic_set_add_dims(
2713 __isl_take isl_basic_set *bset,
2714 enum isl_dim_type type, unsigned n);
2715 __isl_give isl_set *isl_set_add_dims(
2716 __isl_take isl_set *set,
2717 enum isl_dim_type type, unsigned n);
2718 __isl_give isl_map *isl_map_add_dims(
2719 __isl_take isl_map *map,
2720 enum isl_dim_type type, unsigned n);
2721 __isl_give isl_basic_set *isl_basic_set_insert_dims(
2722 __isl_take isl_basic_set *bset,
2723 enum isl_dim_type type, unsigned pos,
2725 __isl_give isl_basic_map *isl_basic_map_insert_dims(
2726 __isl_take isl_basic_map *bmap,
2727 enum isl_dim_type type, unsigned pos,
2729 __isl_give isl_set *isl_set_insert_dims(
2730 __isl_take isl_set *set,
2731 enum isl_dim_type type, unsigned pos, unsigned n);
2732 __isl_give isl_map *isl_map_insert_dims(
2733 __isl_take isl_map *map,
2734 enum isl_dim_type type, unsigned pos, unsigned n);
2735 __isl_give isl_basic_set *isl_basic_set_move_dims(
2736 __isl_take isl_basic_set *bset,
2737 enum isl_dim_type dst_type, unsigned dst_pos,
2738 enum isl_dim_type src_type, unsigned src_pos,
2740 __isl_give isl_basic_map *isl_basic_map_move_dims(
2741 __isl_take isl_basic_map *bmap,
2742 enum isl_dim_type dst_type, unsigned dst_pos,
2743 enum isl_dim_type src_type, unsigned src_pos,
2745 __isl_give isl_set *isl_set_move_dims(
2746 __isl_take isl_set *set,
2747 enum isl_dim_type dst_type, unsigned dst_pos,
2748 enum isl_dim_type src_type, unsigned src_pos,
2750 __isl_give isl_map *isl_map_move_dims(
2751 __isl_take isl_map *map,
2752 enum isl_dim_type dst_type, unsigned dst_pos,
2753 enum isl_dim_type src_type, unsigned src_pos,
2756 It is usually not advisable to directly change the (input or output)
2757 space of a set or a relation as this removes the name and the internal
2758 structure of the space. However, the above functions can be useful
2759 to add new parameters, assuming
2760 C<isl_set_align_params> and C<isl_map_align_params>
2765 =head2 Binary Operations
2767 The two arguments of a binary operation not only need to live
2768 in the same C<isl_ctx>, they currently also need to have
2769 the same (number of) parameters.
2771 =head3 Basic Operations
2775 =item * Intersection
2777 __isl_give isl_basic_set *isl_basic_set_intersect_params(
2778 __isl_take isl_basic_set *bset1,
2779 __isl_take isl_basic_set *bset2);
2780 __isl_give isl_basic_set *isl_basic_set_intersect(
2781 __isl_take isl_basic_set *bset1,
2782 __isl_take isl_basic_set *bset2);
2783 __isl_give isl_set *isl_set_intersect_params(
2784 __isl_take isl_set *set,
2785 __isl_take isl_set *params);
2786 __isl_give isl_set *isl_set_intersect(
2787 __isl_take isl_set *set1,
2788 __isl_take isl_set *set2);
2789 __isl_give isl_union_set *isl_union_set_intersect_params(
2790 __isl_take isl_union_set *uset,
2791 __isl_take isl_set *set);
2792 __isl_give isl_union_map *isl_union_map_intersect_params(
2793 __isl_take isl_union_map *umap,
2794 __isl_take isl_set *set);
2795 __isl_give isl_union_set *isl_union_set_intersect(
2796 __isl_take isl_union_set *uset1,
2797 __isl_take isl_union_set *uset2);
2798 __isl_give isl_basic_map *isl_basic_map_intersect_domain(
2799 __isl_take isl_basic_map *bmap,
2800 __isl_take isl_basic_set *bset);
2801 __isl_give isl_basic_map *isl_basic_map_intersect_range(
2802 __isl_take isl_basic_map *bmap,
2803 __isl_take isl_basic_set *bset);
2804 __isl_give isl_basic_map *isl_basic_map_intersect(
2805 __isl_take isl_basic_map *bmap1,
2806 __isl_take isl_basic_map *bmap2);
2807 __isl_give isl_map *isl_map_intersect_params(
2808 __isl_take isl_map *map,
2809 __isl_take isl_set *params);
2810 __isl_give isl_map *isl_map_intersect_domain(
2811 __isl_take isl_map *map,
2812 __isl_take isl_set *set);
2813 __isl_give isl_map *isl_map_intersect_range(
2814 __isl_take isl_map *map,
2815 __isl_take isl_set *set);
2816 __isl_give isl_map *isl_map_intersect(
2817 __isl_take isl_map *map1,
2818 __isl_take isl_map *map2);
2819 __isl_give isl_union_map *isl_union_map_intersect_domain(
2820 __isl_take isl_union_map *umap,
2821 __isl_take isl_union_set *uset);
2822 __isl_give isl_union_map *isl_union_map_intersect_range(
2823 __isl_take isl_union_map *umap,
2824 __isl_take isl_union_set *uset);
2825 __isl_give isl_union_map *isl_union_map_intersect(
2826 __isl_take isl_union_map *umap1,
2827 __isl_take isl_union_map *umap2);
2829 The second argument to the C<_params> functions needs to be
2830 a parametric (basic) set. For the other functions, a parametric set
2831 for either argument is only allowed if the other argument is
2832 a parametric set as well.
2836 __isl_give isl_set *isl_basic_set_union(
2837 __isl_take isl_basic_set *bset1,
2838 __isl_take isl_basic_set *bset2);
2839 __isl_give isl_map *isl_basic_map_union(
2840 __isl_take isl_basic_map *bmap1,
2841 __isl_take isl_basic_map *bmap2);
2842 __isl_give isl_set *isl_set_union(
2843 __isl_take isl_set *set1,
2844 __isl_take isl_set *set2);
2845 __isl_give isl_map *isl_map_union(
2846 __isl_take isl_map *map1,
2847 __isl_take isl_map *map2);
2848 __isl_give isl_union_set *isl_union_set_union(
2849 __isl_take isl_union_set *uset1,
2850 __isl_take isl_union_set *uset2);
2851 __isl_give isl_union_map *isl_union_map_union(
2852 __isl_take isl_union_map *umap1,
2853 __isl_take isl_union_map *umap2);
2855 =item * Set difference
2857 __isl_give isl_set *isl_set_subtract(
2858 __isl_take isl_set *set1,
2859 __isl_take isl_set *set2);
2860 __isl_give isl_map *isl_map_subtract(
2861 __isl_take isl_map *map1,
2862 __isl_take isl_map *map2);
2863 __isl_give isl_map *isl_map_subtract_domain(
2864 __isl_take isl_map *map,
2865 __isl_take isl_set *dom);
2866 __isl_give isl_map *isl_map_subtract_range(
2867 __isl_take isl_map *map,
2868 __isl_take isl_set *dom);
2869 __isl_give isl_union_set *isl_union_set_subtract(
2870 __isl_take isl_union_set *uset1,
2871 __isl_take isl_union_set *uset2);
2872 __isl_give isl_union_map *isl_union_map_subtract(
2873 __isl_take isl_union_map *umap1,
2874 __isl_take isl_union_map *umap2);
2875 __isl_give isl_union_map *isl_union_map_subtract_domain(
2876 __isl_take isl_union_map *umap,
2877 __isl_take isl_union_set *dom);
2878 __isl_give isl_union_map *isl_union_map_subtract_range(
2879 __isl_take isl_union_map *umap,
2880 __isl_take isl_union_set *dom);
2884 __isl_give isl_basic_set *isl_basic_set_apply(
2885 __isl_take isl_basic_set *bset,
2886 __isl_take isl_basic_map *bmap);
2887 __isl_give isl_set *isl_set_apply(
2888 __isl_take isl_set *set,
2889 __isl_take isl_map *map);
2890 __isl_give isl_union_set *isl_union_set_apply(
2891 __isl_take isl_union_set *uset,
2892 __isl_take isl_union_map *umap);
2893 __isl_give isl_basic_map *isl_basic_map_apply_domain(
2894 __isl_take isl_basic_map *bmap1,
2895 __isl_take isl_basic_map *bmap2);
2896 __isl_give isl_basic_map *isl_basic_map_apply_range(
2897 __isl_take isl_basic_map *bmap1,
2898 __isl_take isl_basic_map *bmap2);
2899 __isl_give isl_map *isl_map_apply_domain(
2900 __isl_take isl_map *map1,
2901 __isl_take isl_map *map2);
2902 __isl_give isl_union_map *isl_union_map_apply_domain(
2903 __isl_take isl_union_map *umap1,
2904 __isl_take isl_union_map *umap2);
2905 __isl_give isl_map *isl_map_apply_range(
2906 __isl_take isl_map *map1,
2907 __isl_take isl_map *map2);
2908 __isl_give isl_union_map *isl_union_map_apply_range(
2909 __isl_take isl_union_map *umap1,
2910 __isl_take isl_union_map *umap2);
2914 __isl_give isl_basic_set *
2915 isl_basic_set_preimage_multi_aff(
2916 __isl_take isl_basic_set *bset,
2917 __isl_take isl_multi_aff *ma);
2918 __isl_give isl_set *isl_set_preimage_multi_aff(
2919 __isl_take isl_set *set,
2920 __isl_take isl_multi_aff *ma);
2921 __isl_give isl_set *isl_set_preimage_pw_multi_aff(
2922 __isl_take isl_set *set,
2923 __isl_take isl_pw_multi_aff *pma);
2924 __isl_give isl_basic_map *
2925 isl_basic_map_preimage_domain_multi_aff(
2926 __isl_take isl_basic_map *bmap,
2927 __isl_take isl_multi_aff *ma);
2928 __isl_give isl_map *isl_map_preimage_domain_multi_aff(
2929 __isl_take isl_map *map,
2930 __isl_take isl_multi_aff *ma);
2931 __isl_give isl_union_map *
2932 isl_union_map_preimage_domain_multi_aff(
2933 __isl_take isl_union_map *umap,
2934 __isl_take isl_multi_aff *ma);
2935 __isl_give isl_basic_map *
2936 isl_basic_map_preimage_range_multi_aff(
2937 __isl_take isl_basic_map *bmap,
2938 __isl_take isl_multi_aff *ma);
2940 These functions compute the preimage of the given set or map domain/range under
2941 the given function. In other words, the expression is plugged
2942 into the set description or into the domain/range of the map.
2943 Objects of types C<isl_multi_aff> and C<isl_pw_multi_aff> are described in
2944 L</"Piecewise Multiple Quasi Affine Expressions">.
2946 =item * Cartesian Product
2948 __isl_give isl_set *isl_set_product(
2949 __isl_take isl_set *set1,
2950 __isl_take isl_set *set2);
2951 __isl_give isl_union_set *isl_union_set_product(
2952 __isl_take isl_union_set *uset1,
2953 __isl_take isl_union_set *uset2);
2954 __isl_give isl_basic_map *isl_basic_map_domain_product(
2955 __isl_take isl_basic_map *bmap1,
2956 __isl_take isl_basic_map *bmap2);
2957 __isl_give isl_basic_map *isl_basic_map_range_product(
2958 __isl_take isl_basic_map *bmap1,
2959 __isl_take isl_basic_map *bmap2);
2960 __isl_give isl_basic_map *isl_basic_map_product(
2961 __isl_take isl_basic_map *bmap1,
2962 __isl_take isl_basic_map *bmap2);
2963 __isl_give isl_map *isl_map_domain_product(
2964 __isl_take isl_map *map1,
2965 __isl_take isl_map *map2);
2966 __isl_give isl_map *isl_map_range_product(
2967 __isl_take isl_map *map1,
2968 __isl_take isl_map *map2);
2969 __isl_give isl_union_map *isl_union_map_domain_product(
2970 __isl_take isl_union_map *umap1,
2971 __isl_take isl_union_map *umap2);
2972 __isl_give isl_union_map *isl_union_map_range_product(
2973 __isl_take isl_union_map *umap1,
2974 __isl_take isl_union_map *umap2);
2975 __isl_give isl_map *isl_map_product(
2976 __isl_take isl_map *map1,
2977 __isl_take isl_map *map2);
2978 __isl_give isl_union_map *isl_union_map_product(
2979 __isl_take isl_union_map *umap1,
2980 __isl_take isl_union_map *umap2);
2982 The above functions compute the cross product of the given
2983 sets or relations. The domains and ranges of the results
2984 are wrapped maps between domains and ranges of the inputs.
2985 To obtain a ``flat'' product, use the following functions
2988 __isl_give isl_basic_set *isl_basic_set_flat_product(
2989 __isl_take isl_basic_set *bset1,
2990 __isl_take isl_basic_set *bset2);
2991 __isl_give isl_set *isl_set_flat_product(
2992 __isl_take isl_set *set1,
2993 __isl_take isl_set *set2);
2994 __isl_give isl_basic_map *isl_basic_map_flat_range_product(
2995 __isl_take isl_basic_map *bmap1,
2996 __isl_take isl_basic_map *bmap2);
2997 __isl_give isl_map *isl_map_flat_domain_product(
2998 __isl_take isl_map *map1,
2999 __isl_take isl_map *map2);
3000 __isl_give isl_map *isl_map_flat_range_product(
3001 __isl_take isl_map *map1,
3002 __isl_take isl_map *map2);
3003 __isl_give isl_union_map *isl_union_map_flat_range_product(
3004 __isl_take isl_union_map *umap1,
3005 __isl_take isl_union_map *umap2);
3006 __isl_give isl_basic_map *isl_basic_map_flat_product(
3007 __isl_take isl_basic_map *bmap1,
3008 __isl_take isl_basic_map *bmap2);
3009 __isl_give isl_map *isl_map_flat_product(
3010 __isl_take isl_map *map1,
3011 __isl_take isl_map *map2);
3013 =item * Simplification
3015 __isl_give isl_basic_set *isl_basic_set_gist(
3016 __isl_take isl_basic_set *bset,
3017 __isl_take isl_basic_set *context);
3018 __isl_give isl_set *isl_set_gist(__isl_take isl_set *set,
3019 __isl_take isl_set *context);
3020 __isl_give isl_set *isl_set_gist_params(
3021 __isl_take isl_set *set,
3022 __isl_take isl_set *context);
3023 __isl_give isl_union_set *isl_union_set_gist(
3024 __isl_take isl_union_set *uset,
3025 __isl_take isl_union_set *context);
3026 __isl_give isl_union_set *isl_union_set_gist_params(
3027 __isl_take isl_union_set *uset,
3028 __isl_take isl_set *set);
3029 __isl_give isl_basic_map *isl_basic_map_gist(
3030 __isl_take isl_basic_map *bmap,
3031 __isl_take isl_basic_map *context);
3032 __isl_give isl_map *isl_map_gist(__isl_take isl_map *map,
3033 __isl_take isl_map *context);
3034 __isl_give isl_map *isl_map_gist_params(
3035 __isl_take isl_map *map,
3036 __isl_take isl_set *context);
3037 __isl_give isl_map *isl_map_gist_domain(
3038 __isl_take isl_map *map,
3039 __isl_take isl_set *context);
3040 __isl_give isl_map *isl_map_gist_range(
3041 __isl_take isl_map *map,
3042 __isl_take isl_set *context);
3043 __isl_give isl_union_map *isl_union_map_gist(
3044 __isl_take isl_union_map *umap,
3045 __isl_take isl_union_map *context);
3046 __isl_give isl_union_map *isl_union_map_gist_params(
3047 __isl_take isl_union_map *umap,
3048 __isl_take isl_set *set);
3049 __isl_give isl_union_map *isl_union_map_gist_domain(
3050 __isl_take isl_union_map *umap,
3051 __isl_take isl_union_set *uset);
3052 __isl_give isl_union_map *isl_union_map_gist_range(
3053 __isl_take isl_union_map *umap,
3054 __isl_take isl_union_set *uset);
3056 The gist operation returns a set or relation that has the
3057 same intersection with the context as the input set or relation.
3058 Any implicit equality in the intersection is made explicit in the result,
3059 while all inequalities that are redundant with respect to the intersection
3061 In case of union sets and relations, the gist operation is performed
3066 =head3 Lexicographic Optimization
3068 Given a (basic) set C<set> (or C<bset>) and a zero-dimensional domain C<dom>,
3069 the following functions
3070 compute a set that contains the lexicographic minimum or maximum
3071 of the elements in C<set> (or C<bset>) for those values of the parameters
3072 that satisfy C<dom>.
3073 If C<empty> is not C<NULL>, then C<*empty> is assigned a set
3074 that contains the parameter values in C<dom> for which C<set> (or C<bset>)
3076 In other words, the union of the parameter values
3077 for which the result is non-empty and of C<*empty>
3080 __isl_give isl_set *isl_basic_set_partial_lexmin(
3081 __isl_take isl_basic_set *bset,
3082 __isl_take isl_basic_set *dom,
3083 __isl_give isl_set **empty);
3084 __isl_give isl_set *isl_basic_set_partial_lexmax(
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_set_partial_lexmin(
3089 __isl_take isl_set *set, __isl_take isl_set *dom,
3090 __isl_give isl_set **empty);
3091 __isl_give isl_set *isl_set_partial_lexmax(
3092 __isl_take isl_set *set, __isl_take isl_set *dom,
3093 __isl_give isl_set **empty);
3095 Given a (basic) set C<set> (or C<bset>), the following functions simply
3096 return a set containing the lexicographic minimum or maximum
3097 of the elements in C<set> (or C<bset>).
3098 In case of union sets, the optimum is computed per space.
3100 __isl_give isl_set *isl_basic_set_lexmin(
3101 __isl_take isl_basic_set *bset);
3102 __isl_give isl_set *isl_basic_set_lexmax(
3103 __isl_take isl_basic_set *bset);
3104 __isl_give isl_set *isl_set_lexmin(
3105 __isl_take isl_set *set);
3106 __isl_give isl_set *isl_set_lexmax(
3107 __isl_take isl_set *set);
3108 __isl_give isl_union_set *isl_union_set_lexmin(
3109 __isl_take isl_union_set *uset);
3110 __isl_give isl_union_set *isl_union_set_lexmax(
3111 __isl_take isl_union_set *uset);
3113 Given a (basic) relation C<map> (or C<bmap>) and a domain C<dom>,
3114 the following functions
3115 compute a relation that maps each element of C<dom>
3116 to the single lexicographic minimum or maximum
3117 of the elements that are associated to that same
3118 element in C<map> (or C<bmap>).
3119 If C<empty> is not C<NULL>, then C<*empty> is assigned a set
3120 that contains the elements in C<dom> that do not map
3121 to any elements in C<map> (or C<bmap>).
3122 In other words, the union of the domain of the result and of C<*empty>
3125 __isl_give isl_map *isl_basic_map_partial_lexmax(
3126 __isl_take isl_basic_map *bmap,
3127 __isl_take isl_basic_set *dom,
3128 __isl_give isl_set **empty);
3129 __isl_give isl_map *isl_basic_map_partial_lexmin(
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_map_partial_lexmax(
3134 __isl_take isl_map *map, __isl_take isl_set *dom,
3135 __isl_give isl_set **empty);
3136 __isl_give isl_map *isl_map_partial_lexmin(
3137 __isl_take isl_map *map, __isl_take isl_set *dom,
3138 __isl_give isl_set **empty);
3140 Given a (basic) map C<map> (or C<bmap>), the following functions simply
3141 return a map mapping each element in the domain of
3142 C<map> (or C<bmap>) to the lexicographic minimum or maximum
3143 of all elements associated to that element.
3144 In case of union relations, the optimum is computed per space.
3146 __isl_give isl_map *isl_basic_map_lexmin(
3147 __isl_take isl_basic_map *bmap);
3148 __isl_give isl_map *isl_basic_map_lexmax(
3149 __isl_take isl_basic_map *bmap);
3150 __isl_give isl_map *isl_map_lexmin(
3151 __isl_take isl_map *map);
3152 __isl_give isl_map *isl_map_lexmax(
3153 __isl_take isl_map *map);
3154 __isl_give isl_union_map *isl_union_map_lexmin(
3155 __isl_take isl_union_map *umap);
3156 __isl_give isl_union_map *isl_union_map_lexmax(
3157 __isl_take isl_union_map *umap);
3159 The following functions return their result in the form of
3160 a piecewise multi-affine expression
3161 (See L<"Piecewise Multiple Quasi Affine Expressions">),
3162 but are otherwise equivalent to the corresponding functions
3163 returning a basic set or relation.
3165 __isl_give isl_pw_multi_aff *
3166 isl_basic_map_lexmin_pw_multi_aff(
3167 __isl_take isl_basic_map *bmap);
3168 __isl_give isl_pw_multi_aff *
3169 isl_basic_set_partial_lexmin_pw_multi_aff(
3170 __isl_take isl_basic_set *bset,
3171 __isl_take isl_basic_set *dom,
3172 __isl_give isl_set **empty);
3173 __isl_give isl_pw_multi_aff *
3174 isl_basic_set_partial_lexmax_pw_multi_aff(
3175 __isl_take isl_basic_set *bset,
3176 __isl_take isl_basic_set *dom,
3177 __isl_give isl_set **empty);
3178 __isl_give isl_pw_multi_aff *
3179 isl_basic_map_partial_lexmin_pw_multi_aff(
3180 __isl_take isl_basic_map *bmap,
3181 __isl_take isl_basic_set *dom,
3182 __isl_give isl_set **empty);
3183 __isl_give isl_pw_multi_aff *
3184 isl_basic_map_partial_lexmax_pw_multi_aff(
3185 __isl_take isl_basic_map *bmap,
3186 __isl_take isl_basic_set *dom,
3187 __isl_give isl_set **empty);
3188 __isl_give isl_pw_multi_aff *isl_set_lexmin_pw_multi_aff(
3189 __isl_take isl_set *set);
3190 __isl_give isl_pw_multi_aff *isl_set_lexmax_pw_multi_aff(
3191 __isl_take isl_set *set);
3192 __isl_give isl_pw_multi_aff *isl_map_lexmin_pw_multi_aff(
3193 __isl_take isl_map *map);
3194 __isl_give isl_pw_multi_aff *isl_map_lexmax_pw_multi_aff(
3195 __isl_take isl_map *map);
3199 Lists are defined over several element types, including
3200 C<isl_val>, C<isl_id>, C<isl_aff>, C<isl_pw_aff>, C<isl_constraint>,
3201 C<isl_basic_set>, C<isl_set>, C<isl_ast_expr> and C<isl_ast_node>.
3202 Here we take lists of C<isl_set>s as an example.
3203 Lists can be created, copied, modified and freed using the following functions.
3205 #include <isl/list.h>
3206 __isl_give isl_set_list *isl_set_list_from_set(
3207 __isl_take isl_set *el);
3208 __isl_give isl_set_list *isl_set_list_alloc(
3209 isl_ctx *ctx, int n);
3210 __isl_give isl_set_list *isl_set_list_copy(
3211 __isl_keep isl_set_list *list);
3212 __isl_give isl_set_list *isl_set_list_insert(
3213 __isl_take isl_set_list *list, unsigned pos,
3214 __isl_take isl_set *el);
3215 __isl_give isl_set_list *isl_set_list_add(
3216 __isl_take isl_set_list *list,
3217 __isl_take isl_set *el);
3218 __isl_give isl_set_list *isl_set_list_drop(
3219 __isl_take isl_set_list *list,
3220 unsigned first, unsigned n);
3221 __isl_give isl_set_list *isl_set_list_set_set(
3222 __isl_take isl_set_list *list, int index,
3223 __isl_take isl_set *set);
3224 __isl_give isl_set_list *isl_set_list_concat(
3225 __isl_take isl_set_list *list1,
3226 __isl_take isl_set_list *list2);
3227 __isl_give isl_set_list *isl_set_list_sort(
3228 __isl_take isl_set_list *list,
3229 int (*cmp)(__isl_keep isl_set *a,
3230 __isl_keep isl_set *b, void *user),
3232 void *isl_set_list_free(__isl_take isl_set_list *list);
3234 C<isl_set_list_alloc> creates an empty list with a capacity for
3235 C<n> elements. C<isl_set_list_from_set> creates a list with a single
3238 Lists can be inspected using the following functions.
3240 #include <isl/list.h>
3241 isl_ctx *isl_set_list_get_ctx(__isl_keep isl_set_list *list);
3242 int isl_set_list_n_set(__isl_keep isl_set_list *list);
3243 __isl_give isl_set *isl_set_list_get_set(
3244 __isl_keep isl_set_list *list, int index);
3245 int isl_set_list_foreach(__isl_keep isl_set_list *list,
3246 int (*fn)(__isl_take isl_set *el, void *user),
3248 int isl_set_list_foreach_scc(__isl_keep isl_set_list *list,
3249 int (*follows)(__isl_keep isl_set *a,
3250 __isl_keep isl_set *b, void *user),
3252 int (*fn)(__isl_take isl_set *el, void *user),
3255 The function C<isl_set_list_foreach_scc> calls C<fn> on each of the
3256 strongly connected components of the graph with as vertices the elements
3257 of C<list> and a directed edge from vertex C<b> to vertex C<a>
3258 iff C<follows(a, b)> returns C<1>. The callbacks C<follows> and C<fn>
3259 should return C<-1> on error.
3261 Lists can be printed using
3263 #include <isl/list.h>
3264 __isl_give isl_printer *isl_printer_print_set_list(
3265 __isl_take isl_printer *p,
3266 __isl_keep isl_set_list *list);
3268 =head2 Multiple Values
3270 An C<isl_multi_val> object represents a sequence of zero or more values,
3271 living in a set space.
3273 An C<isl_multi_val> can be constructed from an C<isl_val_list>
3274 using the following function
3276 #include <isl/val.h>
3277 __isl_give isl_multi_val *isl_multi_val_from_val_list(
3278 __isl_take isl_space *space,
3279 __isl_take isl_val_list *list);
3281 The zero multiple value (with value zero for each set dimension)
3282 can be created using the following function.
3284 #include <isl/val.h>
3285 __isl_give isl_multi_val *isl_multi_val_zero(
3286 __isl_take isl_space *space);
3288 Multiple values can be copied and freed using
3290 #include <isl/val.h>
3291 __isl_give isl_multi_val *isl_multi_val_copy(
3292 __isl_keep isl_multi_val *mv);
3293 void *isl_multi_val_free(__isl_take isl_multi_val *mv);
3295 They can be inspected using
3297 #include <isl/val.h>
3298 isl_ctx *isl_multi_val_get_ctx(
3299 __isl_keep isl_multi_val *mv);
3300 unsigned isl_multi_val_dim(__isl_keep isl_multi_val *mv,
3301 enum isl_dim_type type);
3302 __isl_give isl_val *isl_multi_val_get_val(
3303 __isl_keep isl_multi_val *mv, int pos);
3304 const char *isl_multi_val_get_tuple_name(
3305 __isl_keep isl_multi_val *mv,
3306 enum isl_dim_type type);
3307 int isl_multi_val_has_tuple_id(__isl_keep isl_multi_val *mv,
3308 enum isl_dim_type type);
3310 They can be modified using
3312 #include <isl/val.h>
3313 __isl_give isl_multi_val *isl_multi_val_set_val(
3314 __isl_take isl_multi_val *mv, int pos,
3315 __isl_take isl_val *val);
3316 __isl_give isl_multi_val *isl_multi_val_set_dim_name(
3317 __isl_take isl_multi_val *mv,
3318 enum isl_dim_type type, unsigned pos, const char *s);
3319 __isl_give isl_multi_val *isl_multi_val_set_tuple_name(
3320 __isl_take isl_multi_val *mv,
3321 enum isl_dim_type type, const char *s);
3322 __isl_give isl_multi_val *isl_multi_val_set_tuple_id(
3323 __isl_take isl_multi_val *mv,
3324 enum isl_dim_type type, __isl_take isl_id *id);
3326 __isl_give isl_multi_val *isl_multi_val_insert_dims(
3327 __isl_take isl_multi_val *mv,
3328 enum isl_dim_type type, unsigned first, unsigned n);
3329 __isl_give isl_multi_val *isl_multi_val_add_dims(
3330 __isl_take isl_multi_val *mv,
3331 enum isl_dim_type type, unsigned n);
3332 __isl_give isl_multi_val *isl_multi_val_drop_dims(
3333 __isl_take isl_multi_val *mv,
3334 enum isl_dim_type type, unsigned first, unsigned n);
3338 #include <isl/val.h>
3339 __isl_give isl_multi_val *isl_multi_val_align_params(
3340 __isl_take isl_multi_val *mv,
3341 __isl_take isl_space *model);
3342 __isl_give isl_multi_val *isl_multi_val_range_splice(
3343 __isl_take isl_multi_val *mv1, unsigned pos,
3344 __isl_take isl_multi_val *mv2);
3345 __isl_give isl_multi_val *isl_multi_val_range_product(
3346 __isl_take isl_multi_val *mv1,
3347 __isl_take isl_multi_val *mv2);
3348 __isl_give isl_multi_val *isl_multi_val_flat_range_product(
3349 __isl_take isl_multi_val *mv1,
3350 __isl_take isl_multi_aff *mv2);
3351 __isl_give isl_multi_val *isl_multi_val_add_val(
3352 __isl_take isl_multi_val *mv,
3353 __isl_take isl_val *v);
3354 __isl_give isl_multi_val *isl_multi_val_mod_val(
3355 __isl_take isl_multi_val *mv,
3356 __isl_take isl_val *v);
3357 __isl_give isl_multi_val *isl_multi_val_scale_val(
3358 __isl_take isl_multi_val *mv,
3359 __isl_take isl_val *v);
3360 __isl_give isl_multi_val *isl_multi_val_scale_multi_val(
3361 __isl_take isl_multi_val *mv1,
3362 __isl_take isl_multi_val *mv2);
3364 A multiple value can be printed using
3366 __isl_give isl_printer *isl_printer_print_multi_val(
3367 __isl_take isl_printer *p,
3368 __isl_keep isl_multi_val *mv);
3372 Vectors can be created, copied and freed using the following functions.
3374 #include <isl/vec.h>
3375 __isl_give isl_vec *isl_vec_alloc(isl_ctx *ctx,
3377 __isl_give isl_vec *isl_vec_copy(__isl_keep isl_vec *vec);
3378 void *isl_vec_free(__isl_take isl_vec *vec);
3380 Note that the elements of a newly created vector may have arbitrary values.
3381 The elements can be changed and inspected using the following functions.
3383 isl_ctx *isl_vec_get_ctx(__isl_keep isl_vec *vec);
3384 int isl_vec_size(__isl_keep isl_vec *vec);
3385 __isl_give isl_val *isl_vec_get_element_val(
3386 __isl_keep isl_vec *vec, int pos);
3387 __isl_give isl_vec *isl_vec_set_element_si(
3388 __isl_take isl_vec *vec, int pos, int v);
3389 __isl_give isl_vec *isl_vec_set_element_val(
3390 __isl_take isl_vec *vec, int pos,
3391 __isl_take isl_val *v);
3392 __isl_give isl_vec *isl_vec_set_si(__isl_take isl_vec *vec,
3394 __isl_give isl_vec *isl_vec_set_val(
3395 __isl_take isl_vec *vec, __isl_take isl_val *v);
3396 int isl_vec_cmp_element(__isl_keep isl_vec *vec1,
3397 __isl_keep isl_vec *vec2, int pos);
3399 C<isl_vec_get_element> will return a negative value if anything went wrong.
3400 In that case, the value of C<*v> is undefined.
3402 The following function can be used to concatenate two vectors.
3404 __isl_give isl_vec *isl_vec_concat(__isl_take isl_vec *vec1,
3405 __isl_take isl_vec *vec2);
3409 Matrices can be created, copied and freed using the following functions.
3411 #include <isl/mat.h>
3412 __isl_give isl_mat *isl_mat_alloc(isl_ctx *ctx,
3413 unsigned n_row, unsigned n_col);
3414 __isl_give isl_mat *isl_mat_copy(__isl_keep isl_mat *mat);
3415 void *isl_mat_free(__isl_take isl_mat *mat);
3417 Note that the elements of a newly created matrix may have arbitrary values.
3418 The elements can be changed and inspected using the following functions.
3420 isl_ctx *isl_mat_get_ctx(__isl_keep isl_mat *mat);
3421 int isl_mat_rows(__isl_keep isl_mat *mat);
3422 int isl_mat_cols(__isl_keep isl_mat *mat);
3423 __isl_give isl_val *isl_mat_get_element_val(
3424 __isl_keep isl_mat *mat, int row, int col);
3425 __isl_give isl_mat *isl_mat_set_element_si(__isl_take isl_mat *mat,
3426 int row, int col, int v);
3427 __isl_give isl_mat *isl_mat_set_element_val(
3428 __isl_take isl_mat *mat, int row, int col,
3429 __isl_take isl_val *v);
3431 C<isl_mat_get_element> will return a negative value if anything went wrong.
3432 In that case, the value of C<*v> is undefined.
3434 The following function can be used to compute the (right) inverse
3435 of a matrix, i.e., a matrix such that the product of the original
3436 and the inverse (in that order) is a multiple of the identity matrix.
3437 The input matrix is assumed to be of full row-rank.
3439 __isl_give isl_mat *isl_mat_right_inverse(__isl_take isl_mat *mat);
3441 The following function can be used to compute the (right) kernel
3442 (or null space) of a matrix, i.e., a matrix such that the product of
3443 the original and the kernel (in that order) is the zero matrix.
3445 __isl_give isl_mat *isl_mat_right_kernel(__isl_take isl_mat *mat);
3447 =head2 Piecewise Quasi Affine Expressions
3449 The zero quasi affine expression or the quasi affine expression
3450 that is equal to a given value or
3451 a specified dimension on a given domain can be created using
3453 __isl_give isl_aff *isl_aff_zero_on_domain(
3454 __isl_take isl_local_space *ls);
3455 __isl_give isl_pw_aff *isl_pw_aff_zero_on_domain(
3456 __isl_take isl_local_space *ls);
3457 __isl_give isl_aff *isl_aff_val_on_domain(
3458 __isl_take isl_local_space *ls,
3459 __isl_take isl_val *val);
3460 __isl_give isl_aff *isl_aff_var_on_domain(
3461 __isl_take isl_local_space *ls,
3462 enum isl_dim_type type, unsigned pos);
3463 __isl_give isl_pw_aff *isl_pw_aff_var_on_domain(
3464 __isl_take isl_local_space *ls,
3465 enum isl_dim_type type, unsigned pos);
3467 Note that the space in which the resulting objects live is a map space
3468 with the given space as domain and a one-dimensional range.
3470 An empty piecewise quasi affine expression (one with no cells)
3471 or a piecewise quasi affine expression with a single cell can
3472 be created using the following functions.
3474 #include <isl/aff.h>
3475 __isl_give isl_pw_aff *isl_pw_aff_empty(
3476 __isl_take isl_space *space);
3477 __isl_give isl_pw_aff *isl_pw_aff_alloc(
3478 __isl_take isl_set *set, __isl_take isl_aff *aff);
3479 __isl_give isl_pw_aff *isl_pw_aff_from_aff(
3480 __isl_take isl_aff *aff);
3482 A piecewise quasi affine expression that is equal to 1 on a set
3483 and 0 outside the set can be created using the following function.
3485 #include <isl/aff.h>
3486 __isl_give isl_pw_aff *isl_set_indicator_function(
3487 __isl_take isl_set *set);
3489 Quasi affine expressions can be copied and freed using
3491 #include <isl/aff.h>
3492 __isl_give isl_aff *isl_aff_copy(__isl_keep isl_aff *aff);
3493 void *isl_aff_free(__isl_take isl_aff *aff);
3495 __isl_give isl_pw_aff *isl_pw_aff_copy(
3496 __isl_keep isl_pw_aff *pwaff);
3497 void *isl_pw_aff_free(__isl_take isl_pw_aff *pwaff);
3499 A (rational) bound on a dimension can be extracted from an C<isl_constraint>
3500 using the following function. The constraint is required to have
3501 a non-zero coefficient for the specified dimension.
3503 #include <isl/constraint.h>
3504 __isl_give isl_aff *isl_constraint_get_bound(
3505 __isl_keep isl_constraint *constraint,
3506 enum isl_dim_type type, int pos);
3508 The entire affine expression of the constraint can also be extracted
3509 using the following function.
3511 #include <isl/constraint.h>
3512 __isl_give isl_aff *isl_constraint_get_aff(
3513 __isl_keep isl_constraint *constraint);
3515 Conversely, an equality constraint equating
3516 the affine expression to zero or an inequality constraint enforcing
3517 the affine expression to be non-negative, can be constructed using
3519 __isl_give isl_constraint *isl_equality_from_aff(
3520 __isl_take isl_aff *aff);
3521 __isl_give isl_constraint *isl_inequality_from_aff(
3522 __isl_take isl_aff *aff);
3524 The expression can be inspected using
3526 #include <isl/aff.h>
3527 isl_ctx *isl_aff_get_ctx(__isl_keep isl_aff *aff);
3528 int isl_aff_dim(__isl_keep isl_aff *aff,
3529 enum isl_dim_type type);
3530 __isl_give isl_local_space *isl_aff_get_domain_local_space(
3531 __isl_keep isl_aff *aff);
3532 __isl_give isl_local_space *isl_aff_get_local_space(
3533 __isl_keep isl_aff *aff);
3534 const char *isl_aff_get_dim_name(__isl_keep isl_aff *aff,
3535 enum isl_dim_type type, unsigned pos);
3536 const char *isl_pw_aff_get_dim_name(
3537 __isl_keep isl_pw_aff *pa,
3538 enum isl_dim_type type, unsigned pos);
3539 int isl_pw_aff_has_dim_id(__isl_keep isl_pw_aff *pa,
3540 enum isl_dim_type type, unsigned pos);
3541 __isl_give isl_id *isl_pw_aff_get_dim_id(
3542 __isl_keep isl_pw_aff *pa,
3543 enum isl_dim_type type, unsigned pos);
3544 __isl_give isl_id *isl_pw_aff_get_tuple_id(
3545 __isl_keep isl_pw_aff *pa,
3546 enum isl_dim_type type);
3547 __isl_give isl_val *isl_aff_get_constant_val(
3548 __isl_keep isl_aff *aff);
3549 __isl_give isl_val *isl_aff_get_coefficient_val(
3550 __isl_keep isl_aff *aff,
3551 enum isl_dim_type type, int pos);
3552 __isl_give isl_val *isl_aff_get_denominator_val(
3553 __isl_keep isl_aff *aff);
3554 __isl_give isl_aff *isl_aff_get_div(
3555 __isl_keep isl_aff *aff, int pos);
3557 int isl_pw_aff_n_piece(__isl_keep isl_pw_aff *pwaff);
3558 int isl_pw_aff_foreach_piece(__isl_keep isl_pw_aff *pwaff,
3559 int (*fn)(__isl_take isl_set *set,
3560 __isl_take isl_aff *aff,
3561 void *user), void *user);
3563 int isl_aff_is_cst(__isl_keep isl_aff *aff);
3564 int isl_pw_aff_is_cst(__isl_keep isl_pw_aff *pwaff);
3566 int isl_aff_involves_dims(__isl_keep isl_aff *aff,
3567 enum isl_dim_type type, unsigned first, unsigned n);
3568 int isl_pw_aff_involves_dims(__isl_keep isl_pw_aff *pwaff,
3569 enum isl_dim_type type, unsigned first, unsigned n);
3571 isl_ctx *isl_pw_aff_get_ctx(__isl_keep isl_pw_aff *pwaff);
3572 unsigned isl_pw_aff_dim(__isl_keep isl_pw_aff *pwaff,
3573 enum isl_dim_type type);
3574 int isl_pw_aff_is_empty(__isl_keep isl_pw_aff *pwaff);
3576 It can be modified using
3578 #include <isl/aff.h>
3579 __isl_give isl_pw_aff *isl_pw_aff_set_tuple_id(
3580 __isl_take isl_pw_aff *pwaff,
3581 enum isl_dim_type type, __isl_take isl_id *id);
3582 __isl_give isl_aff *isl_aff_set_dim_name(
3583 __isl_take isl_aff *aff, enum isl_dim_type type,
3584 unsigned pos, const char *s);
3585 __isl_give isl_aff *isl_aff_set_dim_id(
3586 __isl_take isl_aff *aff, enum isl_dim_type type,
3587 unsigned pos, __isl_take isl_id *id);
3588 __isl_give isl_pw_aff *isl_pw_aff_set_dim_id(
3589 __isl_take isl_pw_aff *pma,
3590 enum isl_dim_type type, unsigned pos,
3591 __isl_take isl_id *id);
3592 __isl_give isl_aff *isl_aff_set_constant_si(
3593 __isl_take isl_aff *aff, int v);
3594 __isl_give isl_aff *isl_aff_set_constant_val(
3595 __isl_take isl_aff *aff, __isl_take isl_val *v);
3596 __isl_give isl_aff *isl_aff_set_coefficient_si(
3597 __isl_take isl_aff *aff,
3598 enum isl_dim_type type, int pos, int v);
3599 __isl_give isl_aff *isl_aff_set_coefficient_val(
3600 __isl_take isl_aff *aff,
3601 enum isl_dim_type type, int pos,
3602 __isl_take isl_val *v);
3604 __isl_give isl_aff *isl_aff_add_constant_si(
3605 __isl_take isl_aff *aff, int v);
3606 __isl_give isl_aff *isl_aff_add_constant_val(
3607 __isl_take isl_aff *aff, __isl_take isl_val *v);
3608 __isl_give isl_aff *isl_aff_add_constant_num_si(
3609 __isl_take isl_aff *aff, int v);
3610 __isl_give isl_aff *isl_aff_add_coefficient_si(
3611 __isl_take isl_aff *aff,
3612 enum isl_dim_type type, int pos, int v);
3613 __isl_give isl_aff *isl_aff_add_coefficient_val(
3614 __isl_take isl_aff *aff,
3615 enum isl_dim_type type, int pos,
3616 __isl_take isl_val *v);
3618 __isl_give isl_aff *isl_aff_insert_dims(
3619 __isl_take isl_aff *aff,
3620 enum isl_dim_type type, unsigned first, unsigned n);
3621 __isl_give isl_pw_aff *isl_pw_aff_insert_dims(
3622 __isl_take isl_pw_aff *pwaff,
3623 enum isl_dim_type type, unsigned first, unsigned n);
3624 __isl_give isl_aff *isl_aff_add_dims(
3625 __isl_take isl_aff *aff,
3626 enum isl_dim_type type, unsigned n);
3627 __isl_give isl_pw_aff *isl_pw_aff_add_dims(
3628 __isl_take isl_pw_aff *pwaff,
3629 enum isl_dim_type type, unsigned n);
3630 __isl_give isl_aff *isl_aff_drop_dims(
3631 __isl_take isl_aff *aff,
3632 enum isl_dim_type type, unsigned first, unsigned n);
3633 __isl_give isl_pw_aff *isl_pw_aff_drop_dims(
3634 __isl_take isl_pw_aff *pwaff,
3635 enum isl_dim_type type, unsigned first, unsigned n);
3636 __isl_give isl_aff *isl_aff_move_dims(
3637 __isl_take isl_aff *aff,
3638 enum isl_dim_type dst_type, unsigned dst_pos,
3639 enum isl_dim_type src_type, unsigned src_pos,
3641 __isl_give isl_pw_aff *isl_pw_aff_move_dims(
3642 __isl_take isl_pw_aff *pa,
3643 enum isl_dim_type dst_type, unsigned dst_pos,
3644 enum isl_dim_type src_type, unsigned src_pos,
3647 Note that C<isl_aff_set_constant_si> and C<isl_aff_set_coefficient_si>
3648 set the I<numerator> of the constant or coefficient, while
3649 C<isl_aff_set_constant_val> and C<isl_aff_set_coefficient_val> set
3650 the constant or coefficient as a whole.
3651 The C<add_constant> and C<add_coefficient> functions add an integer
3652 or rational value to
3653 the possibly rational constant or coefficient.
3654 The C<add_constant_num> functions add an integer value to
3657 To check whether an affine expressions is obviously zero
3658 or obviously equal to some other affine expression, use
3660 #include <isl/aff.h>
3661 int isl_aff_plain_is_zero(__isl_keep isl_aff *aff);
3662 int isl_aff_plain_is_equal(__isl_keep isl_aff *aff1,
3663 __isl_keep isl_aff *aff2);
3664 int isl_pw_aff_plain_is_equal(
3665 __isl_keep isl_pw_aff *pwaff1,
3666 __isl_keep isl_pw_aff *pwaff2);
3670 #include <isl/aff.h>
3671 __isl_give isl_aff *isl_aff_add(__isl_take isl_aff *aff1,
3672 __isl_take isl_aff *aff2);
3673 __isl_give isl_pw_aff *isl_pw_aff_add(
3674 __isl_take isl_pw_aff *pwaff1,
3675 __isl_take isl_pw_aff *pwaff2);
3676 __isl_give isl_pw_aff *isl_pw_aff_min(
3677 __isl_take isl_pw_aff *pwaff1,
3678 __isl_take isl_pw_aff *pwaff2);
3679 __isl_give isl_pw_aff *isl_pw_aff_max(
3680 __isl_take isl_pw_aff *pwaff1,
3681 __isl_take isl_pw_aff *pwaff2);
3682 __isl_give isl_aff *isl_aff_sub(__isl_take isl_aff *aff1,
3683 __isl_take isl_aff *aff2);
3684 __isl_give isl_pw_aff *isl_pw_aff_sub(
3685 __isl_take isl_pw_aff *pwaff1,
3686 __isl_take isl_pw_aff *pwaff2);
3687 __isl_give isl_aff *isl_aff_neg(__isl_take isl_aff *aff);
3688 __isl_give isl_pw_aff *isl_pw_aff_neg(
3689 __isl_take isl_pw_aff *pwaff);
3690 __isl_give isl_aff *isl_aff_ceil(__isl_take isl_aff *aff);
3691 __isl_give isl_pw_aff *isl_pw_aff_ceil(
3692 __isl_take isl_pw_aff *pwaff);
3693 __isl_give isl_aff *isl_aff_floor(__isl_take isl_aff *aff);
3694 __isl_give isl_pw_aff *isl_pw_aff_floor(
3695 __isl_take isl_pw_aff *pwaff);
3696 __isl_give isl_aff *isl_aff_mod_val(__isl_take isl_aff *aff,
3697 __isl_take isl_val *mod);
3698 __isl_give isl_pw_aff *isl_pw_aff_mod_val(
3699 __isl_take isl_pw_aff *pa,
3700 __isl_take isl_val *mod);
3701 __isl_give isl_aff *isl_aff_scale_val(__isl_take isl_aff *aff,
3702 __isl_take isl_val *v);
3703 __isl_give isl_pw_aff *isl_pw_aff_scale_val(
3704 __isl_take isl_pw_aff *pa, __isl_take isl_val *v);
3705 __isl_give isl_aff *isl_aff_scale_down_ui(
3706 __isl_take isl_aff *aff, unsigned f);
3707 __isl_give isl_aff *isl_aff_scale_down_val(
3708 __isl_take isl_aff *aff, __isl_take isl_val *v);
3709 __isl_give isl_pw_aff *isl_pw_aff_scale_down_val(
3710 __isl_take isl_pw_aff *pa,
3711 __isl_take isl_val *f);
3713 __isl_give isl_pw_aff *isl_pw_aff_list_min(
3714 __isl_take isl_pw_aff_list *list);
3715 __isl_give isl_pw_aff *isl_pw_aff_list_max(
3716 __isl_take isl_pw_aff_list *list);
3718 __isl_give isl_pw_aff *isl_pw_aff_coalesce(
3719 __isl_take isl_pw_aff *pwqp);
3721 __isl_give isl_aff *isl_aff_align_params(
3722 __isl_take isl_aff *aff,
3723 __isl_take isl_space *model);
3724 __isl_give isl_pw_aff *isl_pw_aff_align_params(
3725 __isl_take isl_pw_aff *pwaff,
3726 __isl_take isl_space *model);
3728 __isl_give isl_aff *isl_aff_project_domain_on_params(
3729 __isl_take isl_aff *aff);
3731 __isl_give isl_aff *isl_aff_gist_params(
3732 __isl_take isl_aff *aff,
3733 __isl_take isl_set *context);
3734 __isl_give isl_aff *isl_aff_gist(__isl_take isl_aff *aff,
3735 __isl_take isl_set *context);
3736 __isl_give isl_pw_aff *isl_pw_aff_gist_params(
3737 __isl_take isl_pw_aff *pwaff,
3738 __isl_take isl_set *context);
3739 __isl_give isl_pw_aff *isl_pw_aff_gist(
3740 __isl_take isl_pw_aff *pwaff,
3741 __isl_take isl_set *context);
3743 __isl_give isl_set *isl_pw_aff_domain(
3744 __isl_take isl_pw_aff *pwaff);
3745 __isl_give isl_pw_aff *isl_pw_aff_intersect_domain(
3746 __isl_take isl_pw_aff *pa,
3747 __isl_take isl_set *set);
3748 __isl_give isl_pw_aff *isl_pw_aff_intersect_params(
3749 __isl_take isl_pw_aff *pa,
3750 __isl_take isl_set *set);
3752 __isl_give isl_aff *isl_aff_mul(__isl_take isl_aff *aff1,
3753 __isl_take isl_aff *aff2);
3754 __isl_give isl_aff *isl_aff_div(__isl_take isl_aff *aff1,
3755 __isl_take isl_aff *aff2);
3756 __isl_give isl_pw_aff *isl_pw_aff_mul(
3757 __isl_take isl_pw_aff *pwaff1,
3758 __isl_take isl_pw_aff *pwaff2);
3759 __isl_give isl_pw_aff *isl_pw_aff_div(
3760 __isl_take isl_pw_aff *pa1,
3761 __isl_take isl_pw_aff *pa2);
3762 __isl_give isl_pw_aff *isl_pw_aff_tdiv_q(
3763 __isl_take isl_pw_aff *pa1,
3764 __isl_take isl_pw_aff *pa2);
3765 __isl_give isl_pw_aff *isl_pw_aff_tdiv_r(
3766 __isl_take isl_pw_aff *pa1,
3767 __isl_take isl_pw_aff *pa2);
3769 When multiplying two affine expressions, at least one of the two needs
3770 to be a constant. Similarly, when dividing an affine expression by another,
3771 the second expression needs to be a constant.
3772 C<isl_pw_aff_tdiv_q> computes the quotient of an integer division with
3773 rounding towards zero. C<isl_pw_aff_tdiv_r> computes the corresponding
3776 #include <isl/aff.h>
3777 __isl_give isl_aff *isl_aff_pullback_multi_aff(
3778 __isl_take isl_aff *aff,
3779 __isl_take isl_multi_aff *ma);
3780 __isl_give isl_pw_aff *isl_pw_aff_pullback_multi_aff(
3781 __isl_take isl_pw_aff *pa,
3782 __isl_take isl_multi_aff *ma);
3783 __isl_give isl_pw_aff *isl_pw_aff_pullback_pw_multi_aff(
3784 __isl_take isl_pw_aff *pa,
3785 __isl_take isl_pw_multi_aff *pma);
3787 These functions precompose the input expression by the given
3788 C<isl_multi_aff> or C<isl_pw_multi_aff>. In other words,
3789 the C<isl_multi_aff> or C<isl_pw_multi_aff> is plugged
3790 into the (piecewise) affine expression.
3791 Objects of type C<isl_multi_aff> are described in
3792 L</"Piecewise Multiple Quasi Affine Expressions">.
3794 #include <isl/aff.h>
3795 __isl_give isl_basic_set *isl_aff_zero_basic_set(
3796 __isl_take isl_aff *aff);
3797 __isl_give isl_basic_set *isl_aff_neg_basic_set(
3798 __isl_take isl_aff *aff);
3799 __isl_give isl_basic_set *isl_aff_le_basic_set(
3800 __isl_take isl_aff *aff1, __isl_take isl_aff *aff2);
3801 __isl_give isl_basic_set *isl_aff_ge_basic_set(
3802 __isl_take isl_aff *aff1, __isl_take isl_aff *aff2);
3803 __isl_give isl_set *isl_pw_aff_eq_set(
3804 __isl_take isl_pw_aff *pwaff1,
3805 __isl_take isl_pw_aff *pwaff2);
3806 __isl_give isl_set *isl_pw_aff_ne_set(
3807 __isl_take isl_pw_aff *pwaff1,
3808 __isl_take isl_pw_aff *pwaff2);
3809 __isl_give isl_set *isl_pw_aff_le_set(
3810 __isl_take isl_pw_aff *pwaff1,
3811 __isl_take isl_pw_aff *pwaff2);
3812 __isl_give isl_set *isl_pw_aff_lt_set(
3813 __isl_take isl_pw_aff *pwaff1,
3814 __isl_take isl_pw_aff *pwaff2);
3815 __isl_give isl_set *isl_pw_aff_ge_set(
3816 __isl_take isl_pw_aff *pwaff1,
3817 __isl_take isl_pw_aff *pwaff2);
3818 __isl_give isl_set *isl_pw_aff_gt_set(
3819 __isl_take isl_pw_aff *pwaff1,
3820 __isl_take isl_pw_aff *pwaff2);
3822 __isl_give isl_set *isl_pw_aff_list_eq_set(
3823 __isl_take isl_pw_aff_list *list1,
3824 __isl_take isl_pw_aff_list *list2);
3825 __isl_give isl_set *isl_pw_aff_list_ne_set(
3826 __isl_take isl_pw_aff_list *list1,
3827 __isl_take isl_pw_aff_list *list2);
3828 __isl_give isl_set *isl_pw_aff_list_le_set(
3829 __isl_take isl_pw_aff_list *list1,
3830 __isl_take isl_pw_aff_list *list2);
3831 __isl_give isl_set *isl_pw_aff_list_lt_set(
3832 __isl_take isl_pw_aff_list *list1,
3833 __isl_take isl_pw_aff_list *list2);
3834 __isl_give isl_set *isl_pw_aff_list_ge_set(
3835 __isl_take isl_pw_aff_list *list1,
3836 __isl_take isl_pw_aff_list *list2);
3837 __isl_give isl_set *isl_pw_aff_list_gt_set(
3838 __isl_take isl_pw_aff_list *list1,
3839 __isl_take isl_pw_aff_list *list2);
3841 The function C<isl_aff_neg_basic_set> returns a basic set
3842 containing those elements in the domain space
3843 of C<aff> where C<aff> is negative.
3844 The function C<isl_aff_ge_basic_set> returns a basic set
3845 containing those elements in the shared space
3846 of C<aff1> and C<aff2> where C<aff1> is greater than or equal to C<aff2>.
3847 The function C<isl_pw_aff_ge_set> returns a set
3848 containing those elements in the shared domain
3849 of C<pwaff1> and C<pwaff2> where C<pwaff1> is greater than or equal to C<pwaff2>.
3850 The functions operating on C<isl_pw_aff_list> apply the corresponding
3851 C<isl_pw_aff> function to each pair of elements in the two lists.
3853 #include <isl/aff.h>
3854 __isl_give isl_set *isl_pw_aff_nonneg_set(
3855 __isl_take isl_pw_aff *pwaff);
3856 __isl_give isl_set *isl_pw_aff_zero_set(
3857 __isl_take isl_pw_aff *pwaff);
3858 __isl_give isl_set *isl_pw_aff_non_zero_set(
3859 __isl_take isl_pw_aff *pwaff);
3861 The function C<isl_pw_aff_nonneg_set> returns a set
3862 containing those elements in the domain
3863 of C<pwaff> where C<pwaff> is non-negative.
3865 #include <isl/aff.h>
3866 __isl_give isl_pw_aff *isl_pw_aff_cond(
3867 __isl_take isl_pw_aff *cond,
3868 __isl_take isl_pw_aff *pwaff_true,
3869 __isl_take isl_pw_aff *pwaff_false);
3871 The function C<isl_pw_aff_cond> performs a conditional operator
3872 and returns an expression that is equal to C<pwaff_true>
3873 for elements where C<cond> is non-zero and equal to C<pwaff_false> for elements
3874 where C<cond> is zero.
3876 #include <isl/aff.h>
3877 __isl_give isl_pw_aff *isl_pw_aff_union_min(
3878 __isl_take isl_pw_aff *pwaff1,
3879 __isl_take isl_pw_aff *pwaff2);
3880 __isl_give isl_pw_aff *isl_pw_aff_union_max(
3881 __isl_take isl_pw_aff *pwaff1,
3882 __isl_take isl_pw_aff *pwaff2);
3883 __isl_give isl_pw_aff *isl_pw_aff_union_add(
3884 __isl_take isl_pw_aff *pwaff1,
3885 __isl_take isl_pw_aff *pwaff2);
3887 The function C<isl_pw_aff_union_max> computes a piecewise quasi-affine
3888 expression with a domain that is the union of those of C<pwaff1> and
3889 C<pwaff2> and such that on each cell, the quasi-affine expression is
3890 the maximum of those of C<pwaff1> and C<pwaff2>. If only one of
3891 C<pwaff1> or C<pwaff2> is defined on a given cell, then the
3892 associated expression is the defined one.
3894 An expression can be read from input using
3896 #include <isl/aff.h>
3897 __isl_give isl_aff *isl_aff_read_from_str(
3898 isl_ctx *ctx, const char *str);
3899 __isl_give isl_pw_aff *isl_pw_aff_read_from_str(
3900 isl_ctx *ctx, const char *str);
3902 An expression can be printed using
3904 #include <isl/aff.h>
3905 __isl_give isl_printer *isl_printer_print_aff(
3906 __isl_take isl_printer *p, __isl_keep isl_aff *aff);
3908 __isl_give isl_printer *isl_printer_print_pw_aff(
3909 __isl_take isl_printer *p,
3910 __isl_keep isl_pw_aff *pwaff);
3912 =head2 Piecewise Multiple Quasi Affine Expressions
3914 An C<isl_multi_aff> object represents a sequence of
3915 zero or more affine expressions, all defined on the same domain space.
3916 Similarly, an C<isl_multi_pw_aff> object represents a sequence of
3917 zero or more piecewise affine expressions.
3919 An C<isl_multi_aff> can be constructed from a single
3920 C<isl_aff> or an C<isl_aff_list> using the
3921 following functions. Similarly for C<isl_multi_pw_aff>.
3923 #include <isl/aff.h>
3924 __isl_give isl_multi_aff *isl_multi_aff_from_aff(
3925 __isl_take isl_aff *aff);
3926 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_from_pw_aff(
3927 __isl_take isl_pw_aff *pa);
3928 __isl_give isl_multi_aff *isl_multi_aff_from_aff_list(
3929 __isl_take isl_space *space,
3930 __isl_take isl_aff_list *list);
3932 An empty piecewise multiple quasi affine expression (one with no cells),
3933 the zero piecewise multiple quasi affine expression (with value zero
3934 for each output dimension),
3935 a piecewise multiple quasi affine expression with a single cell (with
3936 either a universe or a specified domain) or
3937 a zero-dimensional piecewise multiple quasi affine expression
3939 can be created using the following functions.
3941 #include <isl/aff.h>
3942 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_empty(
3943 __isl_take isl_space *space);
3944 __isl_give isl_multi_aff *isl_multi_aff_zero(
3945 __isl_take isl_space *space);
3946 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_zero(
3947 __isl_take isl_space *space);
3948 __isl_give isl_multi_aff *isl_multi_aff_identity(
3949 __isl_take isl_space *space);
3950 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_identity(
3951 __isl_take isl_space *space);
3952 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_identity(
3953 __isl_take isl_space *space);
3954 __isl_give isl_pw_multi_aff *
3955 isl_pw_multi_aff_from_multi_aff(
3956 __isl_take isl_multi_aff *ma);
3957 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_alloc(
3958 __isl_take isl_set *set,
3959 __isl_take isl_multi_aff *maff);
3960 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_from_domain(
3961 __isl_take isl_set *set);
3963 __isl_give isl_union_pw_multi_aff *
3964 isl_union_pw_multi_aff_empty(
3965 __isl_take isl_space *space);
3966 __isl_give isl_union_pw_multi_aff *
3967 isl_union_pw_multi_aff_add_pw_multi_aff(
3968 __isl_take isl_union_pw_multi_aff *upma,
3969 __isl_take isl_pw_multi_aff *pma);
3970 __isl_give isl_union_pw_multi_aff *
3971 isl_union_pw_multi_aff_from_domain(
3972 __isl_take isl_union_set *uset);
3974 A piecewise multiple quasi affine expression can also be initialized
3975 from an C<isl_set> or C<isl_map>, provided the C<isl_set> is a singleton
3976 and the C<isl_map> is single-valued.
3977 In case of a conversion from an C<isl_union_set> or an C<isl_union_map>
3978 to an C<isl_union_pw_multi_aff>, these properties need to hold in each space.
3980 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_from_set(
3981 __isl_take isl_set *set);
3982 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_from_map(
3983 __isl_take isl_map *map);
3985 __isl_give isl_union_pw_multi_aff *
3986 isl_union_pw_multi_aff_from_union_set(
3987 __isl_take isl_union_set *uset);
3988 __isl_give isl_union_pw_multi_aff *
3989 isl_union_pw_multi_aff_from_union_map(
3990 __isl_take isl_union_map *umap);
3992 Multiple quasi affine expressions can be copied and freed using
3994 #include <isl/aff.h>
3995 __isl_give isl_multi_aff *isl_multi_aff_copy(
3996 __isl_keep isl_multi_aff *maff);
3997 void *isl_multi_aff_free(__isl_take isl_multi_aff *maff);
3999 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_copy(
4000 __isl_keep isl_pw_multi_aff *pma);
4001 void *isl_pw_multi_aff_free(
4002 __isl_take isl_pw_multi_aff *pma);
4004 __isl_give isl_union_pw_multi_aff *
4005 isl_union_pw_multi_aff_copy(
4006 __isl_keep isl_union_pw_multi_aff *upma);
4007 void *isl_union_pw_multi_aff_free(
4008 __isl_take isl_union_pw_multi_aff *upma);
4010 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_copy(
4011 __isl_keep isl_multi_pw_aff *mpa);
4012 void *isl_multi_pw_aff_free(
4013 __isl_take isl_multi_pw_aff *mpa);
4015 The expression can be inspected using
4017 #include <isl/aff.h>
4018 isl_ctx *isl_multi_aff_get_ctx(
4019 __isl_keep isl_multi_aff *maff);
4020 isl_ctx *isl_pw_multi_aff_get_ctx(
4021 __isl_keep isl_pw_multi_aff *pma);
4022 isl_ctx *isl_union_pw_multi_aff_get_ctx(
4023 __isl_keep isl_union_pw_multi_aff *upma);
4024 isl_ctx *isl_multi_pw_aff_get_ctx(
4025 __isl_keep isl_multi_pw_aff *mpa);
4026 unsigned isl_multi_aff_dim(__isl_keep isl_multi_aff *maff,
4027 enum isl_dim_type type);
4028 unsigned isl_pw_multi_aff_dim(
4029 __isl_keep isl_pw_multi_aff *pma,
4030 enum isl_dim_type type);
4031 unsigned isl_multi_pw_aff_dim(
4032 __isl_keep isl_multi_pw_aff *mpa,
4033 enum isl_dim_type type);
4034 __isl_give isl_aff *isl_multi_aff_get_aff(
4035 __isl_keep isl_multi_aff *multi, int pos);
4036 __isl_give isl_pw_aff *isl_pw_multi_aff_get_pw_aff(
4037 __isl_keep isl_pw_multi_aff *pma, int pos);
4038 __isl_give isl_pw_aff *isl_multi_pw_aff_get_pw_aff(
4039 __isl_keep isl_multi_pw_aff *mpa, int pos);
4040 const char *isl_pw_multi_aff_get_dim_name(
4041 __isl_keep isl_pw_multi_aff *pma,
4042 enum isl_dim_type type, unsigned pos);
4043 __isl_give isl_id *isl_pw_multi_aff_get_dim_id(
4044 __isl_keep isl_pw_multi_aff *pma,
4045 enum isl_dim_type type, unsigned pos);
4046 const char *isl_multi_aff_get_tuple_name(
4047 __isl_keep isl_multi_aff *multi,
4048 enum isl_dim_type type);
4049 int isl_pw_multi_aff_has_tuple_name(
4050 __isl_keep isl_pw_multi_aff *pma,
4051 enum isl_dim_type type);
4052 const char *isl_pw_multi_aff_get_tuple_name(
4053 __isl_keep isl_pw_multi_aff *pma,
4054 enum isl_dim_type type);
4055 int isl_multi_aff_has_tuple_id(__isl_keep isl_multi_aff *ma,
4056 enum isl_dim_type type);
4057 int isl_pw_multi_aff_has_tuple_id(
4058 __isl_keep isl_pw_multi_aff *pma,
4059 enum isl_dim_type type);
4060 int isl_multi_pw_aff_has_tuple_id(
4061 __isl_keep isl_multi_pw_aff *mpa,
4062 enum isl_dim_type type);
4063 __isl_give isl_id *isl_pw_multi_aff_get_tuple_id(
4064 __isl_keep isl_pw_multi_aff *pma,
4065 enum isl_dim_type type);
4067 int isl_pw_multi_aff_foreach_piece(
4068 __isl_keep isl_pw_multi_aff *pma,
4069 int (*fn)(__isl_take isl_set *set,
4070 __isl_take isl_multi_aff *maff,
4071 void *user), void *user);
4073 int isl_union_pw_multi_aff_foreach_pw_multi_aff(
4074 __isl_keep isl_union_pw_multi_aff *upma,
4075 int (*fn)(__isl_take isl_pw_multi_aff *pma,
4076 void *user), void *user);
4078 It can be modified using
4080 #include <isl/aff.h>
4081 __isl_give isl_multi_aff *isl_multi_aff_set_aff(
4082 __isl_take isl_multi_aff *multi, int pos,
4083 __isl_take isl_aff *aff);
4084 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_set_pw_aff(
4085 __isl_take isl_pw_multi_aff *pma, unsigned pos,
4086 __isl_take isl_pw_aff *pa);
4087 __isl_give isl_multi_aff *isl_multi_aff_set_dim_name(
4088 __isl_take isl_multi_aff *maff,
4089 enum isl_dim_type type, unsigned pos, const char *s);
4090 __isl_give isl_multi_aff *isl_multi_aff_set_tuple_name(
4091 __isl_take isl_multi_aff *maff,
4092 enum isl_dim_type type, const char *s);
4093 __isl_give isl_multi_aff *isl_multi_aff_set_tuple_id(
4094 __isl_take isl_multi_aff *maff,
4095 enum isl_dim_type type, __isl_take isl_id *id);
4096 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_set_tuple_id(
4097 __isl_take isl_pw_multi_aff *pma,
4098 enum isl_dim_type type, __isl_take isl_id *id);
4100 __isl_give isl_multi_pw_aff *
4101 isl_multi_pw_aff_set_dim_name(
4102 __isl_take isl_multi_pw_aff *mpa,
4103 enum isl_dim_type type, unsigned pos, const char *s);
4104 __isl_give isl_multi_pw_aff *
4105 isl_multi_pw_aff_set_tuple_name(
4106 __isl_take isl_multi_pw_aff *mpa,
4107 enum isl_dim_type type, const char *s);
4109 __isl_give isl_multi_aff *isl_multi_aff_insert_dims(
4110 __isl_take isl_multi_aff *ma,
4111 enum isl_dim_type type, unsigned first, unsigned n);
4112 __isl_give isl_multi_aff *isl_multi_aff_add_dims(
4113 __isl_take isl_multi_aff *ma,
4114 enum isl_dim_type type, unsigned n);
4115 __isl_give isl_multi_aff *isl_multi_aff_drop_dims(
4116 __isl_take isl_multi_aff *maff,
4117 enum isl_dim_type type, unsigned first, unsigned n);
4118 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_drop_dims(
4119 __isl_take isl_pw_multi_aff *pma,
4120 enum isl_dim_type type, unsigned first, unsigned n);
4122 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_insert_dims(
4123 __isl_take isl_multi_pw_aff *mpa,
4124 enum isl_dim_type type, unsigned first, unsigned n);
4125 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_add_dims(
4126 __isl_take isl_multi_pw_aff *mpa,
4127 enum isl_dim_type type, unsigned n);
4128 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_move_dims(
4129 __isl_take isl_multi_pw_aff *pma,
4130 enum isl_dim_type dst_type, unsigned dst_pos,
4131 enum isl_dim_type src_type, unsigned src_pos,
4134 To check whether two multiple affine expressions are
4135 obviously equal to each other, use
4137 int isl_multi_aff_plain_is_equal(__isl_keep isl_multi_aff *maff1,
4138 __isl_keep isl_multi_aff *maff2);
4139 int isl_pw_multi_aff_plain_is_equal(
4140 __isl_keep isl_pw_multi_aff *pma1,
4141 __isl_keep isl_pw_multi_aff *pma2);
4145 #include <isl/aff.h>
4146 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_union_lexmin(
4147 __isl_take isl_pw_multi_aff *pma1,
4148 __isl_take isl_pw_multi_aff *pma2);
4149 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_union_lexmax(
4150 __isl_take isl_pw_multi_aff *pma1,
4151 __isl_take isl_pw_multi_aff *pma2);
4152 __isl_give isl_multi_aff *isl_multi_aff_add(
4153 __isl_take isl_multi_aff *maff1,
4154 __isl_take isl_multi_aff *maff2);
4155 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_add(
4156 __isl_take isl_pw_multi_aff *pma1,
4157 __isl_take isl_pw_multi_aff *pma2);
4158 __isl_give isl_union_pw_multi_aff *isl_union_pw_multi_aff_add(
4159 __isl_take isl_union_pw_multi_aff *upma1,
4160 __isl_take isl_union_pw_multi_aff *upma2);
4161 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_union_add(
4162 __isl_take isl_pw_multi_aff *pma1,
4163 __isl_take isl_pw_multi_aff *pma2);
4164 __isl_give isl_multi_aff *isl_multi_aff_sub(
4165 __isl_take isl_multi_aff *ma1,
4166 __isl_take isl_multi_aff *ma2);
4167 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_sub(
4168 __isl_take isl_pw_multi_aff *pma1,
4169 __isl_take isl_pw_multi_aff *pma2);
4170 __isl_give isl_union_pw_multi_aff *isl_union_pw_multi_aff_sub(
4171 __isl_take isl_union_pw_multi_aff *upma1,
4172 __isl_take isl_union_pw_multi_aff *upma2);
4174 C<isl_multi_aff_sub> subtracts the second argument from the first.
4176 __isl_give isl_multi_aff *isl_multi_aff_scale_val(
4177 __isl_take isl_multi_aff *ma,
4178 __isl_take isl_val *v);
4179 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_scale_val(
4180 __isl_take isl_pw_multi_aff *pma,
4181 __isl_take isl_val *v);
4182 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_scale_val(
4183 __isl_take isl_multi_pw_aff *mpa,
4184 __isl_take isl_val *v);
4185 __isl_give isl_multi_aff *isl_multi_aff_scale_multi_val(
4186 __isl_take isl_multi_aff *ma,
4187 __isl_take isl_multi_val *mv);
4188 __isl_give isl_pw_multi_aff *
4189 isl_pw_multi_aff_scale_multi_val(
4190 __isl_take isl_pw_multi_aff *pma,
4191 __isl_take isl_multi_val *mv);
4192 __isl_give isl_multi_pw_aff *
4193 isl_multi_pw_aff_scale_multi_val(
4194 __isl_take isl_multi_pw_aff *mpa,
4195 __isl_take isl_multi_val *mv);
4196 __isl_give isl_union_pw_multi_aff *
4197 isl_union_pw_multi_aff_scale_multi_val(
4198 __isl_take isl_union_pw_multi_aff *upma,
4199 __isl_take isl_multi_val *mv);
4201 C<isl_multi_aff_scale_multi_val> scales the elements of C<ma>
4202 by the corresponding elements of C<mv>.
4204 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_intersect_params(
4205 __isl_take isl_pw_multi_aff *pma,
4206 __isl_take isl_set *set);
4207 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_intersect_domain(
4208 __isl_take isl_pw_multi_aff *pma,
4209 __isl_take isl_set *set);
4210 __isl_give isl_union_pw_multi_aff *
4211 isl_union_pw_multi_aff_intersect_domain(
4212 __isl_take isl_union_pw_multi_aff *upma,
4213 __isl_take isl_union_set *uset);
4214 __isl_give isl_multi_aff *isl_multi_aff_lift(
4215 __isl_take isl_multi_aff *maff,
4216 __isl_give isl_local_space **ls);
4217 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_coalesce(
4218 __isl_take isl_pw_multi_aff *pma);
4219 __isl_give isl_multi_aff *isl_multi_aff_align_params(
4220 __isl_take isl_multi_aff *multi,
4221 __isl_take isl_space *model);
4222 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_align_params(
4223 __isl_take isl_pw_multi_aff *pma,
4224 __isl_take isl_space *model);
4225 __isl_give isl_pw_multi_aff *
4226 isl_pw_multi_aff_project_domain_on_params(
4227 __isl_take isl_pw_multi_aff *pma);
4228 __isl_give isl_multi_aff *isl_multi_aff_gist_params(
4229 __isl_take isl_multi_aff *maff,
4230 __isl_take isl_set *context);
4231 __isl_give isl_multi_aff *isl_multi_aff_gist(
4232 __isl_take isl_multi_aff *maff,
4233 __isl_take isl_set *context);
4234 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_gist_params(
4235 __isl_take isl_pw_multi_aff *pma,
4236 __isl_take isl_set *set);
4237 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_gist(
4238 __isl_take isl_pw_multi_aff *pma,
4239 __isl_take isl_set *set);
4240 __isl_give isl_set *isl_pw_multi_aff_domain(
4241 __isl_take isl_pw_multi_aff *pma);
4242 __isl_give isl_union_set *isl_union_pw_multi_aff_domain(
4243 __isl_take isl_union_pw_multi_aff *upma);
4244 __isl_give isl_multi_aff *isl_multi_aff_range_splice(
4245 __isl_take isl_multi_aff *ma1, unsigned pos,
4246 __isl_take isl_multi_aff *ma2);
4247 __isl_give isl_multi_aff *isl_multi_aff_splice(
4248 __isl_take isl_multi_aff *ma1,
4249 unsigned in_pos, unsigned out_pos,
4250 __isl_take isl_multi_aff *ma2);
4251 __isl_give isl_multi_aff *isl_multi_aff_range_product(
4252 __isl_take isl_multi_aff *ma1,
4253 __isl_take isl_multi_aff *ma2);
4254 __isl_give isl_multi_aff *isl_multi_aff_flat_range_product(
4255 __isl_take isl_multi_aff *ma1,
4256 __isl_take isl_multi_aff *ma2);
4257 __isl_give isl_multi_aff *isl_multi_aff_product(
4258 __isl_take isl_multi_aff *ma1,
4259 __isl_take isl_multi_aff *ma2);
4260 __isl_give isl_pw_multi_aff *
4261 isl_pw_multi_aff_range_product(
4262 __isl_take isl_pw_multi_aff *pma1,
4263 __isl_take isl_pw_multi_aff *pma2);
4264 __isl_give isl_pw_multi_aff *
4265 isl_pw_multi_aff_flat_range_product(
4266 __isl_take isl_pw_multi_aff *pma1,
4267 __isl_take isl_pw_multi_aff *pma2);
4268 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_product(
4269 __isl_take isl_pw_multi_aff *pma1,
4270 __isl_take isl_pw_multi_aff *pma2);
4271 __isl_give isl_union_pw_multi_aff *
4272 isl_union_pw_multi_aff_flat_range_product(
4273 __isl_take isl_union_pw_multi_aff *upma1,
4274 __isl_take isl_union_pw_multi_aff *upma2);
4275 __isl_give isl_multi_pw_aff *
4276 isl_multi_pw_aff_range_splice(
4277 __isl_take isl_multi_pw_aff *mpa1, unsigned pos,
4278 __isl_take isl_multi_pw_aff *mpa2);
4279 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_splice(
4280 __isl_take isl_multi_pw_aff *mpa1,
4281 unsigned in_pos, unsigned out_pos,
4282 __isl_take isl_multi_pw_aff *mpa2);
4283 __isl_give isl_multi_pw_aff *
4284 isl_multi_pw_aff_range_product(
4285 __isl_take isl_multi_pw_aff *mpa1,
4286 __isl_take isl_multi_pw_aff *mpa2);
4287 __isl_give isl_multi_pw_aff *
4288 isl_multi_pw_aff_flat_range_product(
4289 __isl_take isl_multi_pw_aff *mpa1,
4290 __isl_take isl_multi_pw_aff *mpa2);
4292 If the C<ls> argument of C<isl_multi_aff_lift> is not C<NULL>,
4293 then it is assigned the local space that lies at the basis of
4294 the lifting applied.
4296 #include <isl/aff.h>
4297 __isl_give isl_multi_aff *isl_multi_aff_pullback_multi_aff(
4298 __isl_take isl_multi_aff *ma1,
4299 __isl_take isl_multi_aff *ma2);
4300 __isl_give isl_pw_multi_aff *
4301 isl_pw_multi_aff_pullback_multi_aff(
4302 __isl_take isl_pw_multi_aff *pma,
4303 __isl_take isl_multi_aff *ma);
4304 __isl_give isl_pw_multi_aff *
4305 isl_pw_multi_aff_pullback_pw_multi_aff(
4306 __isl_take isl_pw_multi_aff *pma1,
4307 __isl_take isl_pw_multi_aff *pma2);
4309 The function C<isl_multi_aff_pullback_multi_aff> precomposes C<ma1> by C<ma2>.
4310 In other words, C<ma2> is plugged
4313 __isl_give isl_set *isl_multi_aff_lex_le_set(
4314 __isl_take isl_multi_aff *ma1,
4315 __isl_take isl_multi_aff *ma2);
4316 __isl_give isl_set *isl_multi_aff_lex_ge_set(
4317 __isl_take isl_multi_aff *ma1,
4318 __isl_take isl_multi_aff *ma2);
4320 The function C<isl_multi_aff_lex_le_set> returns a set
4321 containing those elements in the shared domain space
4322 where C<ma1> is lexicographically smaller than or
4325 An expression can be read from input using
4327 #include <isl/aff.h>
4328 __isl_give isl_multi_aff *isl_multi_aff_read_from_str(
4329 isl_ctx *ctx, const char *str);
4330 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_read_from_str(
4331 isl_ctx *ctx, const char *str);
4332 __isl_give isl_union_pw_multi_aff *
4333 isl_union_pw_multi_aff_read_from_str(
4334 isl_ctx *ctx, const char *str);
4336 An expression can be printed using
4338 #include <isl/aff.h>
4339 __isl_give isl_printer *isl_printer_print_multi_aff(
4340 __isl_take isl_printer *p,
4341 __isl_keep isl_multi_aff *maff);
4342 __isl_give isl_printer *isl_printer_print_pw_multi_aff(
4343 __isl_take isl_printer *p,
4344 __isl_keep isl_pw_multi_aff *pma);
4345 __isl_give isl_printer *isl_printer_print_union_pw_multi_aff(
4346 __isl_take isl_printer *p,
4347 __isl_keep isl_union_pw_multi_aff *upma);
4348 __isl_give isl_printer *isl_printer_print_multi_pw_aff(
4349 __isl_take isl_printer *p,
4350 __isl_keep isl_multi_pw_aff *mpa);
4354 Points are elements of a set. They can be used to construct
4355 simple sets (boxes) or they can be used to represent the
4356 individual elements of a set.
4357 The zero point (the origin) can be created using
4359 __isl_give isl_point *isl_point_zero(__isl_take isl_space *space);
4361 The coordinates of a point can be inspected, set and changed
4364 __isl_give isl_val *isl_point_get_coordinate_val(
4365 __isl_keep isl_point *pnt,
4366 enum isl_dim_type type, int pos);
4367 __isl_give isl_point *isl_point_set_coordinate_val(
4368 __isl_take isl_point *pnt,
4369 enum isl_dim_type type, int pos,
4370 __isl_take isl_val *v);
4372 __isl_give isl_point *isl_point_add_ui(
4373 __isl_take isl_point *pnt,
4374 enum isl_dim_type type, int pos, unsigned val);
4375 __isl_give isl_point *isl_point_sub_ui(
4376 __isl_take isl_point *pnt,
4377 enum isl_dim_type type, int pos, unsigned val);
4379 Other properties can be obtained using
4381 isl_ctx *isl_point_get_ctx(__isl_keep isl_point *pnt);
4383 Points can be copied or freed using
4385 __isl_give isl_point *isl_point_copy(
4386 __isl_keep isl_point *pnt);
4387 void isl_point_free(__isl_take isl_point *pnt);
4389 A singleton set can be created from a point using
4391 __isl_give isl_basic_set *isl_basic_set_from_point(
4392 __isl_take isl_point *pnt);
4393 __isl_give isl_set *isl_set_from_point(
4394 __isl_take isl_point *pnt);
4396 and a box can be created from two opposite extremal points using
4398 __isl_give isl_basic_set *isl_basic_set_box_from_points(
4399 __isl_take isl_point *pnt1,
4400 __isl_take isl_point *pnt2);
4401 __isl_give isl_set *isl_set_box_from_points(
4402 __isl_take isl_point *pnt1,
4403 __isl_take isl_point *pnt2);
4405 All elements of a B<bounded> (union) set can be enumerated using
4406 the following functions.
4408 int isl_set_foreach_point(__isl_keep isl_set *set,
4409 int (*fn)(__isl_take isl_point *pnt, void *user),
4411 int isl_union_set_foreach_point(__isl_keep isl_union_set *uset,
4412 int (*fn)(__isl_take isl_point *pnt, void *user),
4415 The function C<fn> is called for each integer point in
4416 C<set> with as second argument the last argument of
4417 the C<isl_set_foreach_point> call. The function C<fn>
4418 should return C<0> on success and C<-1> on failure.
4419 In the latter case, C<isl_set_foreach_point> will stop
4420 enumerating and return C<-1> as well.
4421 If the enumeration is performed successfully and to completion,
4422 then C<isl_set_foreach_point> returns C<0>.
4424 To obtain a single point of a (basic) set, use
4426 __isl_give isl_point *isl_basic_set_sample_point(
4427 __isl_take isl_basic_set *bset);
4428 __isl_give isl_point *isl_set_sample_point(
4429 __isl_take isl_set *set);
4431 If C<set> does not contain any (integer) points, then the
4432 resulting point will be ``void'', a property that can be
4435 int isl_point_is_void(__isl_keep isl_point *pnt);
4437 =head2 Piecewise Quasipolynomials
4439 A piecewise quasipolynomial is a particular kind of function that maps
4440 a parametric point to a rational value.
4441 More specifically, a quasipolynomial is a polynomial expression in greatest
4442 integer parts of affine expressions of parameters and variables.
4443 A piecewise quasipolynomial is a subdivision of a given parametric
4444 domain into disjoint cells with a quasipolynomial associated to
4445 each cell. The value of the piecewise quasipolynomial at a given
4446 point is the value of the quasipolynomial associated to the cell
4447 that contains the point. Outside of the union of cells,
4448 the value is assumed to be zero.
4449 For example, the piecewise quasipolynomial
4451 [n] -> { [x] -> ((1 + n) - x) : x <= n and x >= 0 }
4453 maps C<x> to C<1 + n - x> for values of C<x> between C<0> and C<n>.
4454 A given piecewise quasipolynomial has a fixed domain dimension.
4455 Union piecewise quasipolynomials are used to contain piecewise quasipolynomials
4456 defined over different domains.
4457 Piecewise quasipolynomials are mainly used by the C<barvinok>
4458 library for representing the number of elements in a parametric set or map.
4459 For example, the piecewise quasipolynomial above represents
4460 the number of points in the map
4462 [n] -> { [x] -> [y] : x,y >= 0 and 0 <= x + y <= n }
4464 =head3 Input and Output
4466 Piecewise quasipolynomials can be read from input using
4468 __isl_give isl_union_pw_qpolynomial *
4469 isl_union_pw_qpolynomial_read_from_str(
4470 isl_ctx *ctx, const char *str);
4472 Quasipolynomials and piecewise quasipolynomials can be printed
4473 using the following functions.
4475 __isl_give isl_printer *isl_printer_print_qpolynomial(
4476 __isl_take isl_printer *p,
4477 __isl_keep isl_qpolynomial *qp);
4479 __isl_give isl_printer *isl_printer_print_pw_qpolynomial(
4480 __isl_take isl_printer *p,
4481 __isl_keep isl_pw_qpolynomial *pwqp);
4483 __isl_give isl_printer *isl_printer_print_union_pw_qpolynomial(
4484 __isl_take isl_printer *p,
4485 __isl_keep isl_union_pw_qpolynomial *upwqp);
4487 The output format of the printer
4488 needs to be set to either C<ISL_FORMAT_ISL> or C<ISL_FORMAT_C>.
4489 For C<isl_printer_print_union_pw_qpolynomial>, only C<ISL_FORMAT_ISL>
4491 In case of printing in C<ISL_FORMAT_C>, the user may want
4492 to set the names of all dimensions
4494 __isl_give isl_qpolynomial *isl_qpolynomial_set_dim_name(
4495 __isl_take isl_qpolynomial *qp,
4496 enum isl_dim_type type, unsigned pos,
4498 __isl_give isl_pw_qpolynomial *
4499 isl_pw_qpolynomial_set_dim_name(
4500 __isl_take isl_pw_qpolynomial *pwqp,
4501 enum isl_dim_type type, unsigned pos,
4504 =head3 Creating New (Piecewise) Quasipolynomials
4506 Some simple quasipolynomials can be created using the following functions.
4507 More complicated quasipolynomials can be created by applying
4508 operations such as addition and multiplication
4509 on the resulting quasipolynomials
4511 __isl_give isl_qpolynomial *isl_qpolynomial_zero_on_domain(
4512 __isl_take isl_space *domain);
4513 __isl_give isl_qpolynomial *isl_qpolynomial_one_on_domain(
4514 __isl_take isl_space *domain);
4515 __isl_give isl_qpolynomial *isl_qpolynomial_infty_on_domain(
4516 __isl_take isl_space *domain);
4517 __isl_give isl_qpolynomial *isl_qpolynomial_neginfty_on_domain(
4518 __isl_take isl_space *domain);
4519 __isl_give isl_qpolynomial *isl_qpolynomial_nan_on_domain(
4520 __isl_take isl_space *domain);
4521 __isl_give isl_qpolynomial *isl_qpolynomial_val_on_domain(
4522 __isl_take isl_space *domain,
4523 __isl_take isl_val *val);
4524 __isl_give isl_qpolynomial *isl_qpolynomial_var_on_domain(
4525 __isl_take isl_space *domain,
4526 enum isl_dim_type type, unsigned pos);
4527 __isl_give isl_qpolynomial *isl_qpolynomial_from_aff(
4528 __isl_take isl_aff *aff);
4530 Note that the space in which a quasipolynomial lives is a map space
4531 with a one-dimensional range. The C<domain> argument in some of
4532 the functions above corresponds to the domain of this map space.
4534 The zero piecewise quasipolynomial or a piecewise quasipolynomial
4535 with a single cell can be created using the following functions.
4536 Multiple of these single cell piecewise quasipolynomials can
4537 be combined to create more complicated piecewise quasipolynomials.
4539 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_zero(
4540 __isl_take isl_space *space);
4541 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_alloc(
4542 __isl_take isl_set *set,
4543 __isl_take isl_qpolynomial *qp);
4544 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_from_qpolynomial(
4545 __isl_take isl_qpolynomial *qp);
4546 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_from_pw_aff(
4547 __isl_take isl_pw_aff *pwaff);
4549 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_zero(
4550 __isl_take isl_space *space);
4551 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_from_pw_qpolynomial(
4552 __isl_take isl_pw_qpolynomial *pwqp);
4553 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_add_pw_qpolynomial(
4554 __isl_take isl_union_pw_qpolynomial *upwqp,
4555 __isl_take isl_pw_qpolynomial *pwqp);
4557 Quasipolynomials can be copied and freed again using the following
4560 __isl_give isl_qpolynomial *isl_qpolynomial_copy(
4561 __isl_keep isl_qpolynomial *qp);
4562 void *isl_qpolynomial_free(__isl_take isl_qpolynomial *qp);
4564 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_copy(
4565 __isl_keep isl_pw_qpolynomial *pwqp);
4566 void *isl_pw_qpolynomial_free(
4567 __isl_take isl_pw_qpolynomial *pwqp);
4569 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_copy(
4570 __isl_keep isl_union_pw_qpolynomial *upwqp);
4571 void *isl_union_pw_qpolynomial_free(
4572 __isl_take isl_union_pw_qpolynomial *upwqp);
4574 =head3 Inspecting (Piecewise) Quasipolynomials
4576 To iterate over all piecewise quasipolynomials in a union
4577 piecewise quasipolynomial, use the following function
4579 int isl_union_pw_qpolynomial_foreach_pw_qpolynomial(
4580 __isl_keep isl_union_pw_qpolynomial *upwqp,
4581 int (*fn)(__isl_take isl_pw_qpolynomial *pwqp, void *user),
4584 To extract the piecewise quasipolynomial in a given space from a union, use
4586 __isl_give isl_pw_qpolynomial *
4587 isl_union_pw_qpolynomial_extract_pw_qpolynomial(
4588 __isl_keep isl_union_pw_qpolynomial *upwqp,
4589 __isl_take isl_space *space);
4591 To iterate over the cells in a piecewise quasipolynomial,
4592 use either of the following two functions
4594 int isl_pw_qpolynomial_foreach_piece(
4595 __isl_keep isl_pw_qpolynomial *pwqp,
4596 int (*fn)(__isl_take isl_set *set,
4597 __isl_take isl_qpolynomial *qp,
4598 void *user), void *user);
4599 int isl_pw_qpolynomial_foreach_lifted_piece(
4600 __isl_keep isl_pw_qpolynomial *pwqp,
4601 int (*fn)(__isl_take isl_set *set,
4602 __isl_take isl_qpolynomial *qp,
4603 void *user), void *user);
4605 As usual, the function C<fn> should return C<0> on success
4606 and C<-1> on failure. The difference between
4607 C<isl_pw_qpolynomial_foreach_piece> and
4608 C<isl_pw_qpolynomial_foreach_lifted_piece> is that
4609 C<isl_pw_qpolynomial_foreach_lifted_piece> will first
4610 compute unique representations for all existentially quantified
4611 variables and then turn these existentially quantified variables
4612 into extra set variables, adapting the associated quasipolynomial
4613 accordingly. This means that the C<set> passed to C<fn>
4614 will not have any existentially quantified variables, but that
4615 the dimensions of the sets may be different for different
4616 invocations of C<fn>.
4618 The constant term of a quasipolynomial can be extracted using
4620 __isl_give isl_val *isl_qpolynomial_get_constant_val(
4621 __isl_keep isl_qpolynomial *qp);
4623 To iterate over all terms in a quasipolynomial,
4626 int isl_qpolynomial_foreach_term(
4627 __isl_keep isl_qpolynomial *qp,
4628 int (*fn)(__isl_take isl_term *term,
4629 void *user), void *user);
4631 The terms themselves can be inspected and freed using
4634 unsigned isl_term_dim(__isl_keep isl_term *term,
4635 enum isl_dim_type type);
4636 __isl_give isl_val *isl_term_get_coefficient_val(
4637 __isl_keep isl_term *term);
4638 int isl_term_get_exp(__isl_keep isl_term *term,
4639 enum isl_dim_type type, unsigned pos);
4640 __isl_give isl_aff *isl_term_get_div(
4641 __isl_keep isl_term *term, unsigned pos);
4642 void isl_term_free(__isl_take isl_term *term);
4644 Each term is a product of parameters, set variables and
4645 integer divisions. The function C<isl_term_get_exp>
4646 returns the exponent of a given dimensions in the given term.
4648 =head3 Properties of (Piecewise) Quasipolynomials
4650 To check whether two union piecewise quasipolynomials are
4651 obviously equal, use
4653 int isl_union_pw_qpolynomial_plain_is_equal(
4654 __isl_keep isl_union_pw_qpolynomial *upwqp1,
4655 __isl_keep isl_union_pw_qpolynomial *upwqp2);
4657 =head3 Operations on (Piecewise) Quasipolynomials
4659 __isl_give isl_qpolynomial *isl_qpolynomial_scale_val(
4660 __isl_take isl_qpolynomial *qp,
4661 __isl_take isl_val *v);
4662 __isl_give isl_qpolynomial *isl_qpolynomial_neg(
4663 __isl_take isl_qpolynomial *qp);
4664 __isl_give isl_qpolynomial *isl_qpolynomial_add(
4665 __isl_take isl_qpolynomial *qp1,
4666 __isl_take isl_qpolynomial *qp2);
4667 __isl_give isl_qpolynomial *isl_qpolynomial_sub(
4668 __isl_take isl_qpolynomial *qp1,
4669 __isl_take isl_qpolynomial *qp2);
4670 __isl_give isl_qpolynomial *isl_qpolynomial_mul(
4671 __isl_take isl_qpolynomial *qp1,
4672 __isl_take isl_qpolynomial *qp2);
4673 __isl_give isl_qpolynomial *isl_qpolynomial_pow(
4674 __isl_take isl_qpolynomial *qp, unsigned exponent);
4676 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_fix_val(
4677 __isl_take isl_pw_qpolynomial *pwqp,
4678 enum isl_dim_type type, unsigned n,
4679 __isl_take isl_val *v);
4680 __isl_give isl_pw_qpolynomial *
4681 isl_pw_qpolynomial_scale_val(
4682 __isl_take isl_pw_qpolynomial *pwqp,
4683 __isl_take isl_val *v);
4684 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_add(
4685 __isl_take isl_pw_qpolynomial *pwqp1,
4686 __isl_take isl_pw_qpolynomial *pwqp2);
4687 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_sub(
4688 __isl_take isl_pw_qpolynomial *pwqp1,
4689 __isl_take isl_pw_qpolynomial *pwqp2);
4690 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_add_disjoint(
4691 __isl_take isl_pw_qpolynomial *pwqp1,
4692 __isl_take isl_pw_qpolynomial *pwqp2);
4693 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_neg(
4694 __isl_take isl_pw_qpolynomial *pwqp);
4695 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_mul(
4696 __isl_take isl_pw_qpolynomial *pwqp1,
4697 __isl_take isl_pw_qpolynomial *pwqp2);
4698 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_pow(
4699 __isl_take isl_pw_qpolynomial *pwqp, unsigned exponent);
4701 __isl_give isl_union_pw_qpolynomial *
4702 isl_union_pw_qpolynomial_scale_val(
4703 __isl_take isl_union_pw_qpolynomial *upwqp,
4704 __isl_take isl_val *v);
4705 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_add(
4706 __isl_take isl_union_pw_qpolynomial *upwqp1,
4707 __isl_take isl_union_pw_qpolynomial *upwqp2);
4708 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_sub(
4709 __isl_take isl_union_pw_qpolynomial *upwqp1,
4710 __isl_take isl_union_pw_qpolynomial *upwqp2);
4711 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_mul(
4712 __isl_take isl_union_pw_qpolynomial *upwqp1,
4713 __isl_take isl_union_pw_qpolynomial *upwqp2);
4715 __isl_give isl_val *isl_pw_qpolynomial_eval(
4716 __isl_take isl_pw_qpolynomial *pwqp,
4717 __isl_take isl_point *pnt);
4719 __isl_give isl_val *isl_union_pw_qpolynomial_eval(
4720 __isl_take isl_union_pw_qpolynomial *upwqp,
4721 __isl_take isl_point *pnt);
4723 __isl_give isl_set *isl_pw_qpolynomial_domain(
4724 __isl_take isl_pw_qpolynomial *pwqp);
4725 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_intersect_domain(
4726 __isl_take isl_pw_qpolynomial *pwpq,
4727 __isl_take isl_set *set);
4728 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_intersect_params(
4729 __isl_take isl_pw_qpolynomial *pwpq,
4730 __isl_take isl_set *set);
4732 __isl_give isl_union_set *isl_union_pw_qpolynomial_domain(
4733 __isl_take isl_union_pw_qpolynomial *upwqp);
4734 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_intersect_domain(
4735 __isl_take isl_union_pw_qpolynomial *upwpq,
4736 __isl_take isl_union_set *uset);
4737 __isl_give isl_union_pw_qpolynomial *
4738 isl_union_pw_qpolynomial_intersect_params(
4739 __isl_take isl_union_pw_qpolynomial *upwpq,
4740 __isl_take isl_set *set);
4742 __isl_give isl_qpolynomial *isl_qpolynomial_align_params(
4743 __isl_take isl_qpolynomial *qp,
4744 __isl_take isl_space *model);
4746 __isl_give isl_qpolynomial *isl_qpolynomial_project_domain_on_params(
4747 __isl_take isl_qpolynomial *qp);
4748 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_project_domain_on_params(
4749 __isl_take isl_pw_qpolynomial *pwqp);
4751 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_coalesce(
4752 __isl_take isl_union_pw_qpolynomial *upwqp);
4754 __isl_give isl_qpolynomial *isl_qpolynomial_gist_params(
4755 __isl_take isl_qpolynomial *qp,
4756 __isl_take isl_set *context);
4757 __isl_give isl_qpolynomial *isl_qpolynomial_gist(
4758 __isl_take isl_qpolynomial *qp,
4759 __isl_take isl_set *context);
4761 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_gist_params(
4762 __isl_take isl_pw_qpolynomial *pwqp,
4763 __isl_take isl_set *context);
4764 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_gist(
4765 __isl_take isl_pw_qpolynomial *pwqp,
4766 __isl_take isl_set *context);
4768 __isl_give isl_union_pw_qpolynomial *
4769 isl_union_pw_qpolynomial_gist_params(
4770 __isl_take isl_union_pw_qpolynomial *upwqp,
4771 __isl_take isl_set *context);
4772 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_gist(
4773 __isl_take isl_union_pw_qpolynomial *upwqp,
4774 __isl_take isl_union_set *context);
4776 The gist operation applies the gist operation to each of
4777 the cells in the domain of the input piecewise quasipolynomial.
4778 The context is also exploited
4779 to simplify the quasipolynomials associated to each cell.
4781 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_to_polynomial(
4782 __isl_take isl_pw_qpolynomial *pwqp, int sign);
4783 __isl_give isl_union_pw_qpolynomial *
4784 isl_union_pw_qpolynomial_to_polynomial(
4785 __isl_take isl_union_pw_qpolynomial *upwqp, int sign);
4787 Approximate each quasipolynomial by a polynomial. If C<sign> is positive,
4788 the polynomial will be an overapproximation. If C<sign> is negative,
4789 it will be an underapproximation. If C<sign> is zero, the approximation
4790 will lie somewhere in between.
4792 =head2 Bounds on Piecewise Quasipolynomials and Piecewise Quasipolynomial Reductions
4794 A piecewise quasipolynomial reduction is a piecewise
4795 reduction (or fold) of quasipolynomials.
4796 In particular, the reduction can be maximum or a minimum.
4797 The objects are mainly used to represent the result of
4798 an upper or lower bound on a quasipolynomial over its domain,
4799 i.e., as the result of the following function.
4801 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_bound(
4802 __isl_take isl_pw_qpolynomial *pwqp,
4803 enum isl_fold type, int *tight);
4805 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_bound(
4806 __isl_take isl_union_pw_qpolynomial *upwqp,
4807 enum isl_fold type, int *tight);
4809 The C<type> argument may be either C<isl_fold_min> or C<isl_fold_max>.
4810 If C<tight> is not C<NULL>, then C<*tight> is set to C<1>
4811 is the returned bound is known be tight, i.e., for each value
4812 of the parameters there is at least
4813 one element in the domain that reaches the bound.
4814 If the domain of C<pwqp> is not wrapping, then the bound is computed
4815 over all elements in that domain and the result has a purely parametric
4816 domain. If the domain of C<pwqp> is wrapping, then the bound is
4817 computed over the range of the wrapped relation. The domain of the
4818 wrapped relation becomes the domain of the result.
4820 A (piecewise) quasipolynomial reduction can be copied or freed using the
4821 following functions.
4823 __isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_copy(
4824 __isl_keep isl_qpolynomial_fold *fold);
4825 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_copy(
4826 __isl_keep isl_pw_qpolynomial_fold *pwf);
4827 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_copy(
4828 __isl_keep isl_union_pw_qpolynomial_fold *upwf);
4829 void isl_qpolynomial_fold_free(
4830 __isl_take isl_qpolynomial_fold *fold);
4831 void *isl_pw_qpolynomial_fold_free(
4832 __isl_take isl_pw_qpolynomial_fold *pwf);
4833 void *isl_union_pw_qpolynomial_fold_free(
4834 __isl_take isl_union_pw_qpolynomial_fold *upwf);
4836 =head3 Printing Piecewise Quasipolynomial Reductions
4838 Piecewise quasipolynomial reductions can be printed
4839 using the following function.
4841 __isl_give isl_printer *isl_printer_print_pw_qpolynomial_fold(
4842 __isl_take isl_printer *p,
4843 __isl_keep isl_pw_qpolynomial_fold *pwf);
4844 __isl_give isl_printer *isl_printer_print_union_pw_qpolynomial_fold(
4845 __isl_take isl_printer *p,
4846 __isl_keep isl_union_pw_qpolynomial_fold *upwf);
4848 For C<isl_printer_print_pw_qpolynomial_fold>,
4849 output format of the printer
4850 needs to be set to either C<ISL_FORMAT_ISL> or C<ISL_FORMAT_C>.
4851 For C<isl_printer_print_union_pw_qpolynomial_fold>,
4852 output format of the printer
4853 needs to be set to C<ISL_FORMAT_ISL>.
4854 In case of printing in C<ISL_FORMAT_C>, the user may want
4855 to set the names of all dimensions
4857 __isl_give isl_pw_qpolynomial_fold *
4858 isl_pw_qpolynomial_fold_set_dim_name(
4859 __isl_take isl_pw_qpolynomial_fold *pwf,
4860 enum isl_dim_type type, unsigned pos,
4863 =head3 Inspecting (Piecewise) Quasipolynomial Reductions
4865 To iterate over all piecewise quasipolynomial reductions in a union
4866 piecewise quasipolynomial reduction, use the following function
4868 int isl_union_pw_qpolynomial_fold_foreach_pw_qpolynomial_fold(
4869 __isl_keep isl_union_pw_qpolynomial_fold *upwf,
4870 int (*fn)(__isl_take isl_pw_qpolynomial_fold *pwf,
4871 void *user), void *user);
4873 To iterate over the cells in a piecewise quasipolynomial reduction,
4874 use either of the following two functions
4876 int isl_pw_qpolynomial_fold_foreach_piece(
4877 __isl_keep isl_pw_qpolynomial_fold *pwf,
4878 int (*fn)(__isl_take isl_set *set,
4879 __isl_take isl_qpolynomial_fold *fold,
4880 void *user), void *user);
4881 int isl_pw_qpolynomial_fold_foreach_lifted_piece(
4882 __isl_keep isl_pw_qpolynomial_fold *pwf,
4883 int (*fn)(__isl_take isl_set *set,
4884 __isl_take isl_qpolynomial_fold *fold,
4885 void *user), void *user);
4887 See L<Inspecting (Piecewise) Quasipolynomials> for an explanation
4888 of the difference between these two functions.
4890 To iterate over all quasipolynomials in a reduction, use
4892 int isl_qpolynomial_fold_foreach_qpolynomial(
4893 __isl_keep isl_qpolynomial_fold *fold,
4894 int (*fn)(__isl_take isl_qpolynomial *qp,
4895 void *user), void *user);
4897 =head3 Properties of Piecewise Quasipolynomial Reductions
4899 To check whether two union piecewise quasipolynomial reductions are
4900 obviously equal, use
4902 int isl_union_pw_qpolynomial_fold_plain_is_equal(
4903 __isl_keep isl_union_pw_qpolynomial_fold *upwf1,
4904 __isl_keep isl_union_pw_qpolynomial_fold *upwf2);
4906 =head3 Operations on Piecewise Quasipolynomial Reductions
4908 __isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_scale_val(
4909 __isl_take isl_qpolynomial_fold *fold,
4910 __isl_take isl_val *v);
4911 __isl_give isl_pw_qpolynomial_fold *
4912 isl_pw_qpolynomial_fold_scale_val(
4913 __isl_take isl_pw_qpolynomial_fold *pwf,
4914 __isl_take isl_val *v);
4915 __isl_give isl_union_pw_qpolynomial_fold *
4916 isl_union_pw_qpolynomial_fold_scale_val(
4917 __isl_take isl_union_pw_qpolynomial_fold *upwf,
4918 __isl_take isl_val *v);
4920 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_add(
4921 __isl_take isl_pw_qpolynomial_fold *pwf1,
4922 __isl_take isl_pw_qpolynomial_fold *pwf2);
4924 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_fold(
4925 __isl_take isl_pw_qpolynomial_fold *pwf1,
4926 __isl_take isl_pw_qpolynomial_fold *pwf2);
4928 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_fold(
4929 __isl_take isl_union_pw_qpolynomial_fold *upwf1,
4930 __isl_take isl_union_pw_qpolynomial_fold *upwf2);
4932 __isl_give isl_val *isl_pw_qpolynomial_fold_eval(
4933 __isl_take isl_pw_qpolynomial_fold *pwf,
4934 __isl_take isl_point *pnt);
4936 __isl_give isl_val *isl_union_pw_qpolynomial_fold_eval(
4937 __isl_take isl_union_pw_qpolynomial_fold *upwf,
4938 __isl_take isl_point *pnt);
4940 __isl_give isl_pw_qpolynomial_fold *
4941 isl_pw_qpolynomial_fold_intersect_params(
4942 __isl_take isl_pw_qpolynomial_fold *pwf,
4943 __isl_take isl_set *set);
4945 __isl_give isl_union_set *isl_union_pw_qpolynomial_fold_domain(
4946 __isl_take isl_union_pw_qpolynomial_fold *upwf);
4947 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_intersect_domain(
4948 __isl_take isl_union_pw_qpolynomial_fold *upwf,
4949 __isl_take isl_union_set *uset);
4950 __isl_give isl_union_pw_qpolynomial_fold *
4951 isl_union_pw_qpolynomial_fold_intersect_params(
4952 __isl_take isl_union_pw_qpolynomial_fold *upwf,
4953 __isl_take isl_set *set);
4955 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_project_domain_on_params(
4956 __isl_take isl_pw_qpolynomial_fold *pwf);
4958 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_coalesce(
4959 __isl_take isl_pw_qpolynomial_fold *pwf);
4961 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_coalesce(
4962 __isl_take isl_union_pw_qpolynomial_fold *upwf);
4964 __isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_gist_params(
4965 __isl_take isl_qpolynomial_fold *fold,
4966 __isl_take isl_set *context);
4967 __isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_gist(
4968 __isl_take isl_qpolynomial_fold *fold,
4969 __isl_take isl_set *context);
4971 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_gist(
4972 __isl_take isl_pw_qpolynomial_fold *pwf,
4973 __isl_take isl_set *context);
4974 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_gist_params(
4975 __isl_take isl_pw_qpolynomial_fold *pwf,
4976 __isl_take isl_set *context);
4978 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_gist(
4979 __isl_take isl_union_pw_qpolynomial_fold *upwf,
4980 __isl_take isl_union_set *context);
4981 __isl_give isl_union_pw_qpolynomial_fold *
4982 isl_union_pw_qpolynomial_fold_gist_params(
4983 __isl_take isl_union_pw_qpolynomial_fold *upwf,
4984 __isl_take isl_set *context);
4986 The gist operation applies the gist operation to each of
4987 the cells in the domain of the input piecewise quasipolynomial reduction.
4988 In future, the operation will also exploit the context
4989 to simplify the quasipolynomial reductions associated to each cell.
4991 __isl_give isl_pw_qpolynomial_fold *
4992 isl_set_apply_pw_qpolynomial_fold(
4993 __isl_take isl_set *set,
4994 __isl_take isl_pw_qpolynomial_fold *pwf,
4996 __isl_give isl_pw_qpolynomial_fold *
4997 isl_map_apply_pw_qpolynomial_fold(
4998 __isl_take isl_map *map,
4999 __isl_take isl_pw_qpolynomial_fold *pwf,
5001 __isl_give isl_union_pw_qpolynomial_fold *
5002 isl_union_set_apply_union_pw_qpolynomial_fold(
5003 __isl_take isl_union_set *uset,
5004 __isl_take isl_union_pw_qpolynomial_fold *upwf,
5006 __isl_give isl_union_pw_qpolynomial_fold *
5007 isl_union_map_apply_union_pw_qpolynomial_fold(
5008 __isl_take isl_union_map *umap,
5009 __isl_take isl_union_pw_qpolynomial_fold *upwf,
5012 The functions taking a map
5013 compose the given map with the given piecewise quasipolynomial reduction.
5014 That is, compute a bound (of the same type as C<pwf> or C<upwf> itself)
5015 over all elements in the intersection of the range of the map
5016 and the domain of the piecewise quasipolynomial reduction
5017 as a function of an element in the domain of the map.
5018 The functions taking a set compute a bound over all elements in the
5019 intersection of the set and the domain of the
5020 piecewise quasipolynomial reduction.
5022 =head2 Parametric Vertex Enumeration
5024 The parametric vertex enumeration described in this section
5025 is mainly intended to be used internally and by the C<barvinok>
5028 #include <isl/vertices.h>
5029 __isl_give isl_vertices *isl_basic_set_compute_vertices(
5030 __isl_keep isl_basic_set *bset);
5032 The function C<isl_basic_set_compute_vertices> performs the
5033 actual computation of the parametric vertices and the chamber
5034 decomposition and store the result in an C<isl_vertices> object.
5035 This information can be queried by either iterating over all
5036 the vertices or iterating over all the chambers or cells
5037 and then iterating over all vertices that are active on the chamber.
5039 int isl_vertices_foreach_vertex(
5040 __isl_keep isl_vertices *vertices,
5041 int (*fn)(__isl_take isl_vertex *vertex, void *user),
5044 int isl_vertices_foreach_cell(
5045 __isl_keep isl_vertices *vertices,
5046 int (*fn)(__isl_take isl_cell *cell, void *user),
5048 int isl_cell_foreach_vertex(__isl_keep isl_cell *cell,
5049 int (*fn)(__isl_take isl_vertex *vertex, void *user),
5052 Other operations that can be performed on an C<isl_vertices> object are
5055 isl_ctx *isl_vertices_get_ctx(
5056 __isl_keep isl_vertices *vertices);
5057 int isl_vertices_get_n_vertices(
5058 __isl_keep isl_vertices *vertices);
5059 void isl_vertices_free(__isl_take isl_vertices *vertices);
5061 Vertices can be inspected and destroyed using the following functions.
5063 isl_ctx *isl_vertex_get_ctx(__isl_keep isl_vertex *vertex);
5064 int isl_vertex_get_id(__isl_keep isl_vertex *vertex);
5065 __isl_give isl_basic_set *isl_vertex_get_domain(
5066 __isl_keep isl_vertex *vertex);
5067 __isl_give isl_basic_set *isl_vertex_get_expr(
5068 __isl_keep isl_vertex *vertex);
5069 void isl_vertex_free(__isl_take isl_vertex *vertex);
5071 C<isl_vertex_get_expr> returns a singleton parametric set describing
5072 the vertex, while C<isl_vertex_get_domain> returns the activity domain
5074 Note that C<isl_vertex_get_domain> and C<isl_vertex_get_expr> return
5075 B<rational> basic sets, so they should mainly be used for inspection
5076 and should not be mixed with integer sets.
5078 Chambers can be inspected and destroyed using the following functions.
5080 isl_ctx *isl_cell_get_ctx(__isl_keep isl_cell *cell);
5081 __isl_give isl_basic_set *isl_cell_get_domain(
5082 __isl_keep isl_cell *cell);
5083 void isl_cell_free(__isl_take isl_cell *cell);
5085 =head1 Polyhedral Compilation Library
5087 This section collects functionality in C<isl> that has been specifically
5088 designed for use during polyhedral compilation.
5090 =head2 Dependence Analysis
5092 C<isl> contains specialized functionality for performing
5093 array dataflow analysis. That is, given a I<sink> access relation
5094 and a collection of possible I<source> access relations,
5095 C<isl> can compute relations that describe
5096 for each iteration of the sink access, which iteration
5097 of which of the source access relations was the last
5098 to access the same data element before the given iteration
5100 The resulting dependence relations map source iterations
5101 to the corresponding sink iterations.
5102 To compute standard flow dependences, the sink should be
5103 a read, while the sources should be writes.
5104 If any of the source accesses are marked as being I<may>
5105 accesses, then there will be a dependence from the last
5106 I<must> access B<and> from any I<may> access that follows
5107 this last I<must> access.
5108 In particular, if I<all> sources are I<may> accesses,
5109 then memory based dependence analysis is performed.
5110 If, on the other hand, all sources are I<must> accesses,
5111 then value based dependence analysis is performed.
5113 #include <isl/flow.h>
5115 typedef int (*isl_access_level_before)(void *first, void *second);
5117 __isl_give isl_access_info *isl_access_info_alloc(
5118 __isl_take isl_map *sink,
5119 void *sink_user, isl_access_level_before fn,
5121 __isl_give isl_access_info *isl_access_info_add_source(
5122 __isl_take isl_access_info *acc,
5123 __isl_take isl_map *source, int must,
5125 void *isl_access_info_free(__isl_take isl_access_info *acc);
5127 __isl_give isl_flow *isl_access_info_compute_flow(
5128 __isl_take isl_access_info *acc);
5130 int isl_flow_foreach(__isl_keep isl_flow *deps,
5131 int (*fn)(__isl_take isl_map *dep, int must,
5132 void *dep_user, void *user),
5134 __isl_give isl_map *isl_flow_get_no_source(
5135 __isl_keep isl_flow *deps, int must);
5136 void isl_flow_free(__isl_take isl_flow *deps);
5138 The function C<isl_access_info_compute_flow> performs the actual
5139 dependence analysis. The other functions are used to construct
5140 the input for this function or to read off the output.
5142 The input is collected in an C<isl_access_info>, which can
5143 be created through a call to C<isl_access_info_alloc>.
5144 The arguments to this functions are the sink access relation
5145 C<sink>, a token C<sink_user> used to identify the sink
5146 access to the user, a callback function for specifying the
5147 relative order of source and sink accesses, and the number
5148 of source access relations that will be added.
5149 The callback function has type C<int (*)(void *first, void *second)>.
5150 The function is called with two user supplied tokens identifying
5151 either a source or the sink and it should return the shared nesting
5152 level and the relative order of the two accesses.
5153 In particular, let I<n> be the number of loops shared by
5154 the two accesses. If C<first> precedes C<second> textually,
5155 then the function should return I<2 * n + 1>; otherwise,
5156 it should return I<2 * n>.
5157 The sources can be added to the C<isl_access_info> by performing
5158 (at most) C<max_source> calls to C<isl_access_info_add_source>.
5159 C<must> indicates whether the source is a I<must> access
5160 or a I<may> access. Note that a multi-valued access relation
5161 should only be marked I<must> if every iteration in the domain
5162 of the relation accesses I<all> elements in its image.
5163 The C<source_user> token is again used to identify
5164 the source access. The range of the source access relation
5165 C<source> should have the same dimension as the range
5166 of the sink access relation.
5167 The C<isl_access_info_free> function should usually not be
5168 called explicitly, because it is called implicitly by
5169 C<isl_access_info_compute_flow>.
5171 The result of the dependence analysis is collected in an
5172 C<isl_flow>. There may be elements of
5173 the sink access for which no preceding source access could be
5174 found or for which all preceding sources are I<may> accesses.
5175 The relations containing these elements can be obtained through
5176 calls to C<isl_flow_get_no_source>, the first with C<must> set
5177 and the second with C<must> unset.
5178 In the case of standard flow dependence analysis,
5179 with the sink a read and the sources I<must> writes,
5180 the first relation corresponds to the reads from uninitialized
5181 array elements and the second relation is empty.
5182 The actual flow dependences can be extracted using
5183 C<isl_flow_foreach>. This function will call the user-specified
5184 callback function C<fn> for each B<non-empty> dependence between
5185 a source and the sink. The callback function is called
5186 with four arguments, the actual flow dependence relation
5187 mapping source iterations to sink iterations, a boolean that
5188 indicates whether it is a I<must> or I<may> dependence, a token
5189 identifying the source and an additional C<void *> with value
5190 equal to the third argument of the C<isl_flow_foreach> call.
5191 A dependence is marked I<must> if it originates from a I<must>
5192 source and if it is not followed by any I<may> sources.
5194 After finishing with an C<isl_flow>, the user should call
5195 C<isl_flow_free> to free all associated memory.
5197 A higher-level interface to dependence analysis is provided
5198 by the following function.
5200 #include <isl/flow.h>
5202 int isl_union_map_compute_flow(__isl_take isl_union_map *sink,
5203 __isl_take isl_union_map *must_source,
5204 __isl_take isl_union_map *may_source,
5205 __isl_take isl_union_map *schedule,
5206 __isl_give isl_union_map **must_dep,
5207 __isl_give isl_union_map **may_dep,
5208 __isl_give isl_union_map **must_no_source,
5209 __isl_give isl_union_map **may_no_source);
5211 The arrays are identified by the tuple names of the ranges
5212 of the accesses. The iteration domains by the tuple names
5213 of the domains of the accesses and of the schedule.
5214 The relative order of the iteration domains is given by the
5215 schedule. The relations returned through C<must_no_source>
5216 and C<may_no_source> are subsets of C<sink>.
5217 Any of C<must_dep>, C<may_dep>, C<must_no_source>
5218 or C<may_no_source> may be C<NULL>, but a C<NULL> value for
5219 any of the other arguments is treated as an error.
5221 =head3 Interaction with Dependence Analysis
5223 During the dependence analysis, we frequently need to perform
5224 the following operation. Given a relation between sink iterations
5225 and potential source iterations from a particular source domain,
5226 what is the last potential source iteration corresponding to each
5227 sink iteration. It can sometimes be convenient to adjust
5228 the set of potential source iterations before or after each such operation.
5229 The prototypical example is fuzzy array dataflow analysis,
5230 where we need to analyze if, based on data-dependent constraints,
5231 the sink iteration can ever be executed without one or more of
5232 the corresponding potential source iterations being executed.
5233 If so, we can introduce extra parameters and select an unknown
5234 but fixed source iteration from the potential source iterations.
5235 To be able to perform such manipulations, C<isl> provides the following
5238 #include <isl/flow.h>
5240 typedef __isl_give isl_restriction *(*isl_access_restrict)(
5241 __isl_keep isl_map *source_map,
5242 __isl_keep isl_set *sink, void *source_user,
5244 __isl_give isl_access_info *isl_access_info_set_restrict(
5245 __isl_take isl_access_info *acc,
5246 isl_access_restrict fn, void *user);
5248 The function C<isl_access_info_set_restrict> should be called
5249 before calling C<isl_access_info_compute_flow> and registers a callback function
5250 that will be called any time C<isl> is about to compute the last
5251 potential source. The first argument is the (reverse) proto-dependence,
5252 mapping sink iterations to potential source iterations.
5253 The second argument represents the sink iterations for which
5254 we want to compute the last source iteration.
5255 The third argument is the token corresponding to the source
5256 and the final argument is the token passed to C<isl_access_info_set_restrict>.
5257 The callback is expected to return a restriction on either the input or
5258 the output of the operation computing the last potential source.
5259 If the input needs to be restricted then restrictions are needed
5260 for both the source and the sink iterations. The sink iterations
5261 and the potential source iterations will be intersected with these sets.
5262 If the output needs to be restricted then only a restriction on the source
5263 iterations is required.
5264 If any error occurs, the callback should return C<NULL>.
5265 An C<isl_restriction> object can be created, freed and inspected
5266 using the following functions.
5268 #include <isl/flow.h>
5270 __isl_give isl_restriction *isl_restriction_input(
5271 __isl_take isl_set *source_restr,
5272 __isl_take isl_set *sink_restr);
5273 __isl_give isl_restriction *isl_restriction_output(
5274 __isl_take isl_set *source_restr);
5275 __isl_give isl_restriction *isl_restriction_none(
5276 __isl_take isl_map *source_map);
5277 __isl_give isl_restriction *isl_restriction_empty(
5278 __isl_take isl_map *source_map);
5279 void *isl_restriction_free(
5280 __isl_take isl_restriction *restr);
5281 isl_ctx *isl_restriction_get_ctx(
5282 __isl_keep isl_restriction *restr);
5284 C<isl_restriction_none> and C<isl_restriction_empty> are special
5285 cases of C<isl_restriction_input>. C<isl_restriction_none>
5286 is essentially equivalent to
5288 isl_restriction_input(isl_set_universe(
5289 isl_space_range(isl_map_get_space(source_map))),
5291 isl_space_domain(isl_map_get_space(source_map))));
5293 whereas C<isl_restriction_empty> is essentially equivalent to
5295 isl_restriction_input(isl_set_empty(
5296 isl_space_range(isl_map_get_space(source_map))),
5298 isl_space_domain(isl_map_get_space(source_map))));
5302 B<The functionality described in this section is fairly new
5303 and may be subject to change.>
5305 The following function can be used to compute a schedule
5306 for a union of domains.
5307 By default, the algorithm used to construct the schedule is similar
5308 to that of C<Pluto>.
5309 Alternatively, Feautrier's multi-dimensional scheduling algorithm can
5311 The generated schedule respects all C<validity> dependences.
5312 That is, all dependence distances over these dependences in the
5313 scheduled space are lexicographically positive.
5314 The default algorithm tries to minimize the dependence distances over
5315 C<proximity> dependences.
5316 Moreover, it tries to obtain sequences (bands) of schedule dimensions
5317 for groups of domains where the dependence distances have only
5318 non-negative values.
5319 When using Feautrier's algorithm, the C<proximity> dependence
5320 distances are only minimized during the extension to a
5321 full-dimensional schedule.
5323 #include <isl/schedule.h>
5324 __isl_give isl_schedule *isl_union_set_compute_schedule(
5325 __isl_take isl_union_set *domain,
5326 __isl_take isl_union_map *validity,
5327 __isl_take isl_union_map *proximity);
5328 void *isl_schedule_free(__isl_take isl_schedule *sched);
5330 A mapping from the domains to the scheduled space can be obtained
5331 from an C<isl_schedule> using the following function.
5333 __isl_give isl_union_map *isl_schedule_get_map(
5334 __isl_keep isl_schedule *sched);
5336 A representation of the schedule can be printed using
5338 __isl_give isl_printer *isl_printer_print_schedule(
5339 __isl_take isl_printer *p,
5340 __isl_keep isl_schedule *schedule);
5342 A representation of the schedule as a forest of bands can be obtained
5343 using the following function.
5345 __isl_give isl_band_list *isl_schedule_get_band_forest(
5346 __isl_keep isl_schedule *schedule);
5348 The individual bands can be visited in depth-first post-order
5349 using the following function.
5351 #include <isl/schedule.h>
5352 int isl_schedule_foreach_band(
5353 __isl_keep isl_schedule *sched,
5354 int (*fn)(__isl_keep isl_band *band, void *user),
5357 The list can be manipulated as explained in L<"Lists">.
5358 The bands inside the list can be copied and freed using the following
5361 #include <isl/band.h>
5362 __isl_give isl_band *isl_band_copy(
5363 __isl_keep isl_band *band);
5364 void *isl_band_free(__isl_take isl_band *band);
5366 Each band contains zero or more scheduling dimensions.
5367 These are referred to as the members of the band.
5368 The section of the schedule that corresponds to the band is
5369 referred to as the partial schedule of the band.
5370 For those nodes that participate in a band, the outer scheduling
5371 dimensions form the prefix schedule, while the inner scheduling
5372 dimensions form the suffix schedule.
5373 That is, if we take a cut of the band forest, then the union of
5374 the concatenations of the prefix, partial and suffix schedules of
5375 each band in the cut is equal to the entire schedule (modulo
5376 some possible padding at the end with zero scheduling dimensions).
5377 The properties of a band can be inspected using the following functions.
5379 #include <isl/band.h>
5380 isl_ctx *isl_band_get_ctx(__isl_keep isl_band *band);
5382 int isl_band_has_children(__isl_keep isl_band *band);
5383 __isl_give isl_band_list *isl_band_get_children(
5384 __isl_keep isl_band *band);
5386 __isl_give isl_union_map *isl_band_get_prefix_schedule(
5387 __isl_keep isl_band *band);
5388 __isl_give isl_union_map *isl_band_get_partial_schedule(
5389 __isl_keep isl_band *band);
5390 __isl_give isl_union_map *isl_band_get_suffix_schedule(
5391 __isl_keep isl_band *band);
5393 int isl_band_n_member(__isl_keep isl_band *band);
5394 int isl_band_member_is_zero_distance(
5395 __isl_keep isl_band *band, int pos);
5397 int isl_band_list_foreach_band(
5398 __isl_keep isl_band_list *list,
5399 int (*fn)(__isl_keep isl_band *band, void *user),
5402 Note that a scheduling dimension is considered to be ``zero
5403 distance'' if it does not carry any proximity dependences
5405 That is, if the dependence distances of the proximity
5406 dependences are all zero in that direction (for fixed
5407 iterations of outer bands).
5408 Like C<isl_schedule_foreach_band>,
5409 the function C<isl_band_list_foreach_band> calls C<fn> on the bands
5410 in depth-first post-order.
5412 A band can be tiled using the following function.
5414 #include <isl/band.h>
5415 int isl_band_tile(__isl_keep isl_band *band,
5416 __isl_take isl_vec *sizes);
5418 int isl_options_set_tile_scale_tile_loops(isl_ctx *ctx,
5420 int isl_options_get_tile_scale_tile_loops(isl_ctx *ctx);
5421 int isl_options_set_tile_shift_point_loops(isl_ctx *ctx,
5423 int isl_options_get_tile_shift_point_loops(isl_ctx *ctx);
5425 The C<isl_band_tile> function tiles the band using the given tile sizes
5426 inside its schedule.
5427 A new child band is created to represent the point loops and it is
5428 inserted between the modified band and its children.
5429 The C<tile_scale_tile_loops> option specifies whether the tile
5430 loops iterators should be scaled by the tile sizes.
5431 If the C<tile_shift_point_loops> option is set, then the point loops
5432 are shifted to start at zero.
5434 A band can be split into two nested bands using the following function.
5436 int isl_band_split(__isl_keep isl_band *band, int pos);
5438 The resulting outer band contains the first C<pos> dimensions of C<band>
5439 while the inner band contains the remaining dimensions.
5441 A representation of the band can be printed using
5443 #include <isl/band.h>
5444 __isl_give isl_printer *isl_printer_print_band(
5445 __isl_take isl_printer *p,
5446 __isl_keep isl_band *band);
5450 #include <isl/schedule.h>
5451 int isl_options_set_schedule_max_coefficient(
5452 isl_ctx *ctx, int val);
5453 int isl_options_get_schedule_max_coefficient(
5455 int isl_options_set_schedule_max_constant_term(
5456 isl_ctx *ctx, int val);
5457 int isl_options_get_schedule_max_constant_term(
5459 int isl_options_set_schedule_fuse(isl_ctx *ctx, int val);
5460 int isl_options_get_schedule_fuse(isl_ctx *ctx);
5461 int isl_options_set_schedule_maximize_band_depth(
5462 isl_ctx *ctx, int val);
5463 int isl_options_get_schedule_maximize_band_depth(
5465 int isl_options_set_schedule_outer_zero_distance(
5466 isl_ctx *ctx, int val);
5467 int isl_options_get_schedule_outer_zero_distance(
5469 int isl_options_set_schedule_split_scaled(
5470 isl_ctx *ctx, int val);
5471 int isl_options_get_schedule_split_scaled(
5473 int isl_options_set_schedule_algorithm(
5474 isl_ctx *ctx, int val);
5475 int isl_options_get_schedule_algorithm(
5477 int isl_options_set_schedule_separate_components(
5478 isl_ctx *ctx, int val);
5479 int isl_options_get_schedule_separate_components(
5484 =item * schedule_max_coefficient
5486 This option enforces that the coefficients for variable and parameter
5487 dimensions in the calculated schedule are not larger than the specified value.
5488 This option can significantly increase the speed of the scheduling calculation
5489 and may also prevent fusing of unrelated dimensions. A value of -1 means that
5490 this option does not introduce bounds on the variable or parameter
5493 =item * schedule_max_constant_term
5495 This option enforces that the constant coefficients in the calculated schedule
5496 are not larger than the maximal constant term. This option can significantly
5497 increase the speed of the scheduling calculation and may also prevent fusing of
5498 unrelated dimensions. A value of -1 means that this option does not introduce
5499 bounds on the constant coefficients.
5501 =item * schedule_fuse
5503 This option controls the level of fusion.
5504 If this option is set to C<ISL_SCHEDULE_FUSE_MIN>, then loops in the
5505 resulting schedule will be distributed as much as possible.
5506 If this option is set to C<ISL_SCHEDULE_FUSE_MAX>, then C<isl> will
5507 try to fuse loops in the resulting schedule.
5509 =item * schedule_maximize_band_depth
5511 If this option is set, we do not split bands at the point
5512 where we detect splitting is necessary. Instead, we
5513 backtrack and split bands as early as possible. This
5514 reduces the number of splits and maximizes the width of
5515 the bands. Wider bands give more possibilities for tiling.
5516 Note that if the C<schedule_fuse> option is set to C<ISL_SCHEDULE_FUSE_MIN>,
5517 then bands will be split as early as possible, even if there is no need.
5518 The C<schedule_maximize_band_depth> option therefore has no effect in this case.
5520 =item * schedule_outer_zero_distance
5522 If this option is set, then we try to construct schedules
5523 where the outermost scheduling dimension in each band
5524 results in a zero dependence distance over the proximity
5527 =item * schedule_split_scaled
5529 If this option is set, then we try to construct schedules in which the
5530 constant term is split off from the linear part if the linear parts of
5531 the scheduling rows for all nodes in the graphs have a common non-trivial
5533 The constant term is then placed in a separate band and the linear
5536 =item * schedule_algorithm
5538 Selects the scheduling algorithm to be used.
5539 Available scheduling algorithms are C<ISL_SCHEDULE_ALGORITHM_ISL>
5540 and C<ISL_SCHEDULE_ALGORITHM_FEAUTRIER>.
5542 =item * schedule_separate_components
5544 If at any point the dependence graph contains any (weakly connected) components,
5545 then these components are scheduled separately.
5546 If this option is not set, then some iterations of the domains
5547 in these components may be scheduled together.
5548 If this option is set, then the components are given consecutive
5553 =head2 AST Generation
5555 This section describes the C<isl> functionality for generating
5556 ASTs that visit all the elements
5557 in a domain in an order specified by a schedule.
5558 In particular, given a C<isl_union_map>, an AST is generated
5559 that visits all the elements in the domain of the C<isl_union_map>
5560 according to the lexicographic order of the corresponding image
5561 element(s). If the range of the C<isl_union_map> consists of
5562 elements in more than one space, then each of these spaces is handled
5563 separately in an arbitrary order.
5564 It should be noted that the image elements only specify the I<order>
5565 in which the corresponding domain elements should be visited.
5566 No direct relation between the image elements and the loop iterators
5567 in the generated AST should be assumed.
5569 Each AST is generated within a build. The initial build
5570 simply specifies the constraints on the parameters (if any)
5571 and can be created, inspected, copied and freed using the following functions.
5573 #include <isl/ast_build.h>
5574 __isl_give isl_ast_build *isl_ast_build_from_context(
5575 __isl_take isl_set *set);
5576 isl_ctx *isl_ast_build_get_ctx(
5577 __isl_keep isl_ast_build *build);
5578 __isl_give isl_ast_build *isl_ast_build_copy(
5579 __isl_keep isl_ast_build *build);
5580 void *isl_ast_build_free(
5581 __isl_take isl_ast_build *build);
5583 The C<set> argument is usually a parameter set with zero or more parameters.
5584 More C<isl_ast_build> functions are described in L</"Nested AST Generation">
5585 and L</"Fine-grained Control over AST Generation">.
5586 Finally, the AST itself can be constructed using the following
5589 #include <isl/ast_build.h>
5590 __isl_give isl_ast_node *isl_ast_build_ast_from_schedule(
5591 __isl_keep isl_ast_build *build,
5592 __isl_take isl_union_map *schedule);
5594 =head3 Inspecting the AST
5596 The basic properties of an AST node can be obtained as follows.
5598 #include <isl/ast.h>
5599 isl_ctx *isl_ast_node_get_ctx(
5600 __isl_keep isl_ast_node *node);
5601 enum isl_ast_node_type isl_ast_node_get_type(
5602 __isl_keep isl_ast_node *node);
5604 The type of an AST node is one of
5605 C<isl_ast_node_for>,
5607 C<isl_ast_node_block> or
5608 C<isl_ast_node_user>.
5609 An C<isl_ast_node_for> represents a for node.
5610 An C<isl_ast_node_if> represents an if node.
5611 An C<isl_ast_node_block> represents a compound node.
5612 An C<isl_ast_node_user> represents an expression statement.
5613 An expression statement typically corresponds to a domain element, i.e.,
5614 one of the elements that is visited by the AST.
5616 Each type of node has its own additional properties.
5618 #include <isl/ast.h>
5619 __isl_give isl_ast_expr *isl_ast_node_for_get_iterator(
5620 __isl_keep isl_ast_node *node);
5621 __isl_give isl_ast_expr *isl_ast_node_for_get_init(
5622 __isl_keep isl_ast_node *node);
5623 __isl_give isl_ast_expr *isl_ast_node_for_get_cond(
5624 __isl_keep isl_ast_node *node);
5625 __isl_give isl_ast_expr *isl_ast_node_for_get_inc(
5626 __isl_keep isl_ast_node *node);
5627 __isl_give isl_ast_node *isl_ast_node_for_get_body(
5628 __isl_keep isl_ast_node *node);
5629 int isl_ast_node_for_is_degenerate(
5630 __isl_keep isl_ast_node *node);
5632 An C<isl_ast_for> is considered degenerate if it is known to execute
5635 #include <isl/ast.h>
5636 __isl_give isl_ast_expr *isl_ast_node_if_get_cond(
5637 __isl_keep isl_ast_node *node);
5638 __isl_give isl_ast_node *isl_ast_node_if_get_then(
5639 __isl_keep isl_ast_node *node);
5640 int isl_ast_node_if_has_else(
5641 __isl_keep isl_ast_node *node);
5642 __isl_give isl_ast_node *isl_ast_node_if_get_else(
5643 __isl_keep isl_ast_node *node);
5645 __isl_give isl_ast_node_list *
5646 isl_ast_node_block_get_children(
5647 __isl_keep isl_ast_node *node);
5649 __isl_give isl_ast_expr *isl_ast_node_user_get_expr(
5650 __isl_keep isl_ast_node *node);
5652 Each of the returned C<isl_ast_expr>s can in turn be inspected using
5653 the following functions.
5655 #include <isl/ast.h>
5656 isl_ctx *isl_ast_expr_get_ctx(
5657 __isl_keep isl_ast_expr *expr);
5658 enum isl_ast_expr_type isl_ast_expr_get_type(
5659 __isl_keep isl_ast_expr *expr);
5661 The type of an AST expression is one of
5663 C<isl_ast_expr_id> or
5664 C<isl_ast_expr_int>.
5665 An C<isl_ast_expr_op> represents the result of an operation.
5666 An C<isl_ast_expr_id> represents an identifier.
5667 An C<isl_ast_expr_int> represents an integer value.
5669 Each type of expression has its own additional properties.
5671 #include <isl/ast.h>
5672 enum isl_ast_op_type isl_ast_expr_get_op_type(
5673 __isl_keep isl_ast_expr *expr);
5674 int isl_ast_expr_get_op_n_arg(__isl_keep isl_ast_expr *expr);
5675 __isl_give isl_ast_expr *isl_ast_expr_get_op_arg(
5676 __isl_keep isl_ast_expr *expr, int pos);
5677 int isl_ast_node_foreach_ast_op_type(
5678 __isl_keep isl_ast_node *node,
5679 int (*fn)(enum isl_ast_op_type type, void *user),
5682 C<isl_ast_expr_get_op_type> returns the type of the operation
5683 performed. C<isl_ast_expr_get_op_n_arg> returns the number of
5684 arguments. C<isl_ast_expr_get_op_arg> returns the specified
5686 C<isl_ast_node_foreach_ast_op_type> calls C<fn> for each distinct
5687 C<isl_ast_op_type> that appears in C<node>.
5688 The operation type is one of the following.
5692 =item C<isl_ast_op_and>
5694 Logical I<and> of two arguments.
5695 Both arguments can be evaluated.
5697 =item C<isl_ast_op_and_then>
5699 Logical I<and> of two arguments.
5700 The second argument can only be evaluated if the first evaluates to true.
5702 =item C<isl_ast_op_or>
5704 Logical I<or> of two arguments.
5705 Both arguments can be evaluated.
5707 =item C<isl_ast_op_or_else>
5709 Logical I<or> of two arguments.
5710 The second argument can only be evaluated if the first evaluates to false.
5712 =item C<isl_ast_op_max>
5714 Maximum of two or more arguments.
5716 =item C<isl_ast_op_min>
5718 Minimum of two or more arguments.
5720 =item C<isl_ast_op_minus>
5724 =item C<isl_ast_op_add>
5726 Sum of two arguments.
5728 =item C<isl_ast_op_sub>
5730 Difference of two arguments.
5732 =item C<isl_ast_op_mul>
5734 Product of two arguments.
5736 =item C<isl_ast_op_div>
5738 Exact division. That is, the result is known to be an integer.
5740 =item C<isl_ast_op_fdiv_q>
5742 Result of integer division, rounded towards negative
5745 =item C<isl_ast_op_pdiv_q>
5747 Result of integer division, where dividend is known to be non-negative.
5749 =item C<isl_ast_op_pdiv_r>
5751 Remainder of integer division, where dividend is known to be non-negative.
5753 =item C<isl_ast_op_cond>
5755 Conditional operator defined on three arguments.
5756 If the first argument evaluates to true, then the result
5757 is equal to the second argument. Otherwise, the result
5758 is equal to the third argument.
5759 The second and third argument may only be evaluated if
5760 the first argument evaluates to true and false, respectively.
5761 Corresponds to C<a ? b : c> in C.
5763 =item C<isl_ast_op_select>
5765 Conditional operator defined on three arguments.
5766 If the first argument evaluates to true, then the result
5767 is equal to the second argument. Otherwise, the result
5768 is equal to the third argument.
5769 The second and third argument may be evaluated independently
5770 of the value of the first argument.
5771 Corresponds to C<a * b + (1 - a) * c> in C.
5773 =item C<isl_ast_op_eq>
5777 =item C<isl_ast_op_le>
5779 Less than or equal relation.
5781 =item C<isl_ast_op_lt>
5785 =item C<isl_ast_op_ge>
5787 Greater than or equal relation.
5789 =item C<isl_ast_op_gt>
5791 Greater than relation.
5793 =item C<isl_ast_op_call>
5796 The number of arguments of the C<isl_ast_expr> is one more than
5797 the number of arguments in the function call, the first argument
5798 representing the function being called.
5802 #include <isl/ast.h>
5803 __isl_give isl_id *isl_ast_expr_get_id(
5804 __isl_keep isl_ast_expr *expr);
5806 Return the identifier represented by the AST expression.
5808 #include <isl/ast.h>
5809 __isl_give isl_val *isl_ast_expr_get_val(
5810 __isl_keep isl_ast_expr *expr);
5812 Return the integer represented by the AST expression.
5814 =head3 Manipulating and printing the AST
5816 AST nodes can be copied and freed using the following functions.
5818 #include <isl/ast.h>
5819 __isl_give isl_ast_node *isl_ast_node_copy(
5820 __isl_keep isl_ast_node *node);
5821 void *isl_ast_node_free(__isl_take isl_ast_node *node);
5823 AST expressions can be copied and freed using the following functions.
5825 #include <isl/ast.h>
5826 __isl_give isl_ast_expr *isl_ast_expr_copy(
5827 __isl_keep isl_ast_expr *expr);
5828 void *isl_ast_expr_free(__isl_take isl_ast_expr *expr);
5830 New AST expressions can be created either directly or within
5831 the context of an C<isl_ast_build>.
5833 #include <isl/ast.h>
5834 __isl_give isl_ast_expr *isl_ast_expr_from_val(
5835 __isl_take isl_val *v);
5836 __isl_give isl_ast_expr *isl_ast_expr_from_id(
5837 __isl_take isl_id *id);
5838 __isl_give isl_ast_expr *isl_ast_expr_neg(
5839 __isl_take isl_ast_expr *expr);
5840 __isl_give isl_ast_expr *isl_ast_expr_add(
5841 __isl_take isl_ast_expr *expr1,
5842 __isl_take isl_ast_expr *expr2);
5843 __isl_give isl_ast_expr *isl_ast_expr_sub(
5844 __isl_take isl_ast_expr *expr1,
5845 __isl_take isl_ast_expr *expr2);
5846 __isl_give isl_ast_expr *isl_ast_expr_mul(
5847 __isl_take isl_ast_expr *expr1,
5848 __isl_take isl_ast_expr *expr2);
5849 __isl_give isl_ast_expr *isl_ast_expr_div(
5850 __isl_take isl_ast_expr *expr1,
5851 __isl_take isl_ast_expr *expr2);
5852 __isl_give isl_ast_expr *isl_ast_expr_and(
5853 __isl_take isl_ast_expr *expr1,
5854 __isl_take isl_ast_expr *expr2)
5855 __isl_give isl_ast_expr *isl_ast_expr_or(
5856 __isl_take isl_ast_expr *expr1,
5857 __isl_take isl_ast_expr *expr2)
5859 #include <isl/ast_build.h>
5860 __isl_give isl_ast_expr *isl_ast_build_expr_from_pw_aff(
5861 __isl_keep isl_ast_build *build,
5862 __isl_take isl_pw_aff *pa);
5863 __isl_give isl_ast_expr *
5864 isl_ast_build_call_from_pw_multi_aff(
5865 __isl_keep isl_ast_build *build,
5866 __isl_take isl_pw_multi_aff *pma);
5868 The domains of C<pa> and C<pma> should correspond
5869 to the schedule space of C<build>.
5870 The tuple id of C<pma> is used as the function being called.
5872 User specified data can be attached to an C<isl_ast_node> and obtained
5873 from the same C<isl_ast_node> using the following functions.
5875 #include <isl/ast.h>
5876 __isl_give isl_ast_node *isl_ast_node_set_annotation(
5877 __isl_take isl_ast_node *node,
5878 __isl_take isl_id *annotation);
5879 __isl_give isl_id *isl_ast_node_get_annotation(
5880 __isl_keep isl_ast_node *node);
5882 Basic printing can be performed using the following functions.
5884 #include <isl/ast.h>
5885 __isl_give isl_printer *isl_printer_print_ast_expr(
5886 __isl_take isl_printer *p,
5887 __isl_keep isl_ast_expr *expr);
5888 __isl_give isl_printer *isl_printer_print_ast_node(
5889 __isl_take isl_printer *p,
5890 __isl_keep isl_ast_node *node);
5892 More advanced printing can be performed using the following functions.
5894 #include <isl/ast.h>
5895 __isl_give isl_printer *isl_ast_op_type_print_macro(
5896 enum isl_ast_op_type type,
5897 __isl_take isl_printer *p);
5898 __isl_give isl_printer *isl_ast_node_print_macros(
5899 __isl_keep isl_ast_node *node,
5900 __isl_take isl_printer *p);
5901 __isl_give isl_printer *isl_ast_node_print(
5902 __isl_keep isl_ast_node *node,
5903 __isl_take isl_printer *p,
5904 __isl_take isl_ast_print_options *options);
5905 __isl_give isl_printer *isl_ast_node_for_print(
5906 __isl_keep isl_ast_node *node,
5907 __isl_take isl_printer *p,
5908 __isl_take isl_ast_print_options *options);
5909 __isl_give isl_printer *isl_ast_node_if_print(
5910 __isl_keep isl_ast_node *node,
5911 __isl_take isl_printer *p,
5912 __isl_take isl_ast_print_options *options);
5914 While printing an C<isl_ast_node> in C<ISL_FORMAT_C>,
5915 C<isl> may print out an AST that makes use of macros such
5916 as C<floord>, C<min> and C<max>.
5917 C<isl_ast_op_type_print_macro> prints out the macro
5918 corresponding to a specific C<isl_ast_op_type>.
5919 C<isl_ast_node_print_macros> scans the C<isl_ast_node>
5920 for expressions where these macros would be used and prints
5921 out the required macro definitions.
5922 Essentially, C<isl_ast_node_print_macros> calls
5923 C<isl_ast_node_foreach_ast_op_type> with C<isl_ast_op_type_print_macro>
5924 as function argument.
5925 C<isl_ast_node_print>, C<isl_ast_node_for_print> and
5926 C<isl_ast_node_if_print> print an C<isl_ast_node>
5927 in C<ISL_FORMAT_C>, but allow for some extra control
5928 through an C<isl_ast_print_options> object.
5929 This object can be created using the following functions.
5931 #include <isl/ast.h>
5932 __isl_give isl_ast_print_options *
5933 isl_ast_print_options_alloc(isl_ctx *ctx);
5934 __isl_give isl_ast_print_options *
5935 isl_ast_print_options_copy(
5936 __isl_keep isl_ast_print_options *options);
5937 void *isl_ast_print_options_free(
5938 __isl_take isl_ast_print_options *options);
5940 __isl_give isl_ast_print_options *
5941 isl_ast_print_options_set_print_user(
5942 __isl_take isl_ast_print_options *options,
5943 __isl_give isl_printer *(*print_user)(
5944 __isl_take isl_printer *p,
5945 __isl_take isl_ast_print_options *options,
5946 __isl_keep isl_ast_node *node, void *user),
5948 __isl_give isl_ast_print_options *
5949 isl_ast_print_options_set_print_for(
5950 __isl_take isl_ast_print_options *options,
5951 __isl_give isl_printer *(*print_for)(
5952 __isl_take isl_printer *p,
5953 __isl_take isl_ast_print_options *options,
5954 __isl_keep isl_ast_node *node, void *user),
5957 The callback set by C<isl_ast_print_options_set_print_user>
5958 is called whenever a node of type C<isl_ast_node_user> needs to
5960 The callback set by C<isl_ast_print_options_set_print_for>
5961 is called whenever a node of type C<isl_ast_node_for> needs to
5963 Note that C<isl_ast_node_for_print> will I<not> call the
5964 callback set by C<isl_ast_print_options_set_print_for> on the node
5965 on which C<isl_ast_node_for_print> is called, but only on nested
5966 nodes of type C<isl_ast_node_for>. It is therefore safe to
5967 call C<isl_ast_node_for_print> from within the callback set by
5968 C<isl_ast_print_options_set_print_for>.
5970 The following option determines the type to be used for iterators
5971 while printing the AST.
5973 int isl_options_set_ast_iterator_type(
5974 isl_ctx *ctx, const char *val);
5975 const char *isl_options_get_ast_iterator_type(
5980 #include <isl/ast_build.h>
5981 int isl_options_set_ast_build_atomic_upper_bound(
5982 isl_ctx *ctx, int val);
5983 int isl_options_get_ast_build_atomic_upper_bound(
5985 int isl_options_set_ast_build_prefer_pdiv(isl_ctx *ctx,
5987 int isl_options_get_ast_build_prefer_pdiv(isl_ctx *ctx);
5988 int isl_options_set_ast_build_exploit_nested_bounds(
5989 isl_ctx *ctx, int val);
5990 int isl_options_get_ast_build_exploit_nested_bounds(
5992 int isl_options_set_ast_build_group_coscheduled(
5993 isl_ctx *ctx, int val);
5994 int isl_options_get_ast_build_group_coscheduled(
5996 int isl_options_set_ast_build_scale_strides(
5997 isl_ctx *ctx, int val);
5998 int isl_options_get_ast_build_scale_strides(
6000 int isl_options_set_ast_build_allow_else(isl_ctx *ctx,
6002 int isl_options_get_ast_build_allow_else(isl_ctx *ctx);
6003 int isl_options_set_ast_build_allow_or(isl_ctx *ctx,
6005 int isl_options_get_ast_build_allow_or(isl_ctx *ctx);
6009 =item * ast_build_atomic_upper_bound
6011 Generate loop upper bounds that consist of the current loop iterator,
6012 an operator and an expression not involving the iterator.
6013 If this option is not set, then the current loop iterator may appear
6014 several times in the upper bound.
6015 For example, when this option is turned off, AST generation
6018 [n] -> { A[i] -> [i] : 0 <= i <= 100, n }
6022 for (int c0 = 0; c0 <= 100 && n >= c0; c0 += 1)
6025 When the option is turned on, the following AST is generated
6027 for (int c0 = 0; c0 <= min(100, n); c0 += 1)
6030 =item * ast_build_prefer_pdiv
6032 If this option is turned off, then the AST generation will
6033 produce ASTs that may only contain C<isl_ast_op_fdiv_q>
6034 operators, but no C<isl_ast_op_pdiv_q> or
6035 C<isl_ast_op_pdiv_r> operators.
6036 If this options is turned on, then C<isl> will try to convert
6037 some of the C<isl_ast_op_fdiv_q> operators to (expressions containing)
6038 C<isl_ast_op_pdiv_q> or C<isl_ast_op_pdiv_r> operators.
6040 =item * ast_build_exploit_nested_bounds
6042 Simplify conditions based on bounds of nested for loops.
6043 In particular, remove conditions that are implied by the fact
6044 that one or more nested loops have at least one iteration,
6045 meaning that the upper bound is at least as large as the lower bound.
6046 For example, when this option is turned off, AST generation
6049 [N,M] -> { A[i,j] -> [i,j] : 0 <= i <= N and
6055 for (int c0 = 0; c0 <= N; c0 += 1)
6056 for (int c1 = 0; c1 <= M; c1 += 1)
6059 When the option is turned on, the following AST is generated
6061 for (int c0 = 0; c0 <= N; c0 += 1)
6062 for (int c1 = 0; c1 <= M; c1 += 1)
6065 =item * ast_build_group_coscheduled
6067 If two domain elements are assigned the same schedule point, then
6068 they may be executed in any order and they may even appear in different
6069 loops. If this options is set, then the AST generator will make
6070 sure that coscheduled domain elements do not appear in separate parts
6071 of the AST. This is useful in case of nested AST generation
6072 if the outer AST generation is given only part of a schedule
6073 and the inner AST generation should handle the domains that are
6074 coscheduled by this initial part of the schedule together.
6075 For example if an AST is generated for a schedule
6077 { A[i] -> [0]; B[i] -> [0] }
6079 then the C<isl_ast_build_set_create_leaf> callback described
6080 below may get called twice, once for each domain.
6081 Setting this option ensures that the callback is only called once
6082 on both domains together.
6084 =item * ast_build_separation_bounds
6086 This option specifies which bounds to use during separation.
6087 If this option is set to C<ISL_AST_BUILD_SEPARATION_BOUNDS_IMPLICIT>
6088 then all (possibly implicit) bounds on the current dimension will
6089 be used during separation.
6090 If this option is set to C<ISL_AST_BUILD_SEPARATION_BOUNDS_EXPLICIT>
6091 then only those bounds that are explicitly available will
6092 be used during separation.
6094 =item * ast_build_scale_strides
6096 This option specifies whether the AST generator is allowed
6097 to scale down iterators of strided loops.
6099 =item * ast_build_allow_else
6101 This option specifies whether the AST generator is allowed
6102 to construct if statements with else branches.
6104 =item * ast_build_allow_or
6106 This option specifies whether the AST generator is allowed
6107 to construct if conditions with disjunctions.
6111 =head3 Fine-grained Control over AST Generation
6113 Besides specifying the constraints on the parameters,
6114 an C<isl_ast_build> object can be used to control
6115 various aspects of the AST generation process.
6116 The most prominent way of control is through ``options'',
6117 which can be set using the following function.
6119 #include <isl/ast_build.h>
6120 __isl_give isl_ast_build *
6121 isl_ast_build_set_options(
6122 __isl_take isl_ast_build *control,
6123 __isl_take isl_union_map *options);
6125 The options are encoded in an <isl_union_map>.
6126 The domain of this union relation refers to the schedule domain,
6127 i.e., the range of the schedule passed to C<isl_ast_build_ast_from_schedule>.
6128 In the case of nested AST generation (see L</"Nested AST Generation">),
6129 the domain of C<options> should refer to the extra piece of the schedule.
6130 That is, it should be equal to the range of the wrapped relation in the
6131 range of the schedule.
6132 The range of the options can consist of elements in one or more spaces,
6133 the names of which determine the effect of the option.
6134 The values of the range typically also refer to the schedule dimension
6135 to which the option applies. In case of nested AST generation
6136 (see L</"Nested AST Generation">), these values refer to the position
6137 of the schedule dimension within the innermost AST generation.
6138 The constraints on the domain elements of
6139 the option should only refer to this dimension and earlier dimensions.
6140 We consider the following spaces.
6144 =item C<separation_class>
6146 This space is a wrapped relation between two one dimensional spaces.
6147 The input space represents the schedule dimension to which the option
6148 applies and the output space represents the separation class.
6149 While constructing a loop corresponding to the specified schedule
6150 dimension(s), the AST generator will try to generate separate loops
6151 for domain elements that are assigned different classes.
6152 If only some of the elements are assigned a class, then those elements
6153 that are not assigned any class will be treated as belonging to a class
6154 that is separate from the explicitly assigned classes.
6155 The typical use case for this option is to separate full tiles from
6157 The other options, described below, are applied after the separation
6160 As an example, consider the separation into full and partial tiles
6161 of a tiling of a triangular domain.
6162 Take, for example, the domain
6164 { A[i,j] : 0 <= i,j and i + j <= 100 }
6166 and a tiling into tiles of 10 by 10. The input to the AST generator
6167 is then the schedule
6169 { A[i,j] -> [([i/10]),[j/10],i,j] : 0 <= i,j and
6172 Without any options, the following AST is generated
6174 for (int c0 = 0; c0 <= 10; c0 += 1)
6175 for (int c1 = 0; c1 <= -c0 + 10; c1 += 1)
6176 for (int c2 = 10 * c0;
6177 c2 <= min(-10 * c1 + 100, 10 * c0 + 9);
6179 for (int c3 = 10 * c1;
6180 c3 <= min(10 * c1 + 9, -c2 + 100);
6184 Separation into full and partial tiles can be obtained by assigning
6185 a class, say C<0>, to the full tiles. The full tiles are represented by those
6186 values of the first and second schedule dimensions for which there are
6187 values of the third and fourth dimensions to cover an entire tile.
6188 That is, we need to specify the following option
6190 { [a,b,c,d] -> separation_class[[0]->[0]] :
6191 exists b': 0 <= 10a,10b' and
6192 10a+9+10b'+9 <= 100;
6193 [a,b,c,d] -> separation_class[[1]->[0]] :
6194 0 <= 10a,10b and 10a+9+10b+9 <= 100 }
6198 { [a, b, c, d] -> separation_class[[1] -> [0]] :
6199 a >= 0 and b >= 0 and b <= 8 - a;
6200 [a, b, c, d] -> separation_class[[0] -> [0]] :
6203 With this option, the generated AST is as follows
6206 for (int c0 = 0; c0 <= 8; c0 += 1) {
6207 for (int c1 = 0; c1 <= -c0 + 8; c1 += 1)
6208 for (int c2 = 10 * c0;
6209 c2 <= 10 * c0 + 9; c2 += 1)
6210 for (int c3 = 10 * c1;
6211 c3 <= 10 * c1 + 9; c3 += 1)
6213 for (int c1 = -c0 + 9; c1 <= -c0 + 10; c1 += 1)
6214 for (int c2 = 10 * c0;
6215 c2 <= min(-10 * c1 + 100, 10 * c0 + 9);
6217 for (int c3 = 10 * c1;
6218 c3 <= min(-c2 + 100, 10 * c1 + 9);
6222 for (int c0 = 9; c0 <= 10; c0 += 1)
6223 for (int c1 = 0; c1 <= -c0 + 10; c1 += 1)
6224 for (int c2 = 10 * c0;
6225 c2 <= min(-10 * c1 + 100, 10 * c0 + 9);
6227 for (int c3 = 10 * c1;
6228 c3 <= min(10 * c1 + 9, -c2 + 100);
6235 This is a single-dimensional space representing the schedule dimension(s)
6236 to which ``separation'' should be applied. Separation tries to split
6237 a loop into several pieces if this can avoid the generation of guards
6239 See also the C<atomic> option.
6243 This is a single-dimensional space representing the schedule dimension(s)
6244 for which the domains should be considered ``atomic''. That is, the
6245 AST generator will make sure that any given domain space will only appear
6246 in a single loop at the specified level.
6248 Consider the following schedule
6250 { a[i] -> [i] : 0 <= i < 10;
6251 b[i] -> [i+1] : 0 <= i < 10 }
6253 If the following option is specified
6255 { [i] -> separate[x] }
6257 then the following AST will be generated
6261 for (int c0 = 1; c0 <= 9; c0 += 1) {
6268 If, on the other hand, the following option is specified
6270 { [i] -> atomic[x] }
6272 then the following AST will be generated
6274 for (int c0 = 0; c0 <= 10; c0 += 1) {
6281 If neither C<atomic> nor C<separate> is specified, then the AST generator
6282 may produce either of these two results or some intermediate form.
6286 This is a single-dimensional space representing the schedule dimension(s)
6287 that should be I<completely> unrolled.
6288 To obtain a partial unrolling, the user should apply an additional
6289 strip-mining to the schedule and fully unroll the inner loop.
6293 Additional control is available through the following functions.
6295 #include <isl/ast_build.h>
6296 __isl_give isl_ast_build *
6297 isl_ast_build_set_iterators(
6298 __isl_take isl_ast_build *control,
6299 __isl_take isl_id_list *iterators);
6301 The function C<isl_ast_build_set_iterators> allows the user to
6302 specify a list of iterator C<isl_id>s to be used as iterators.
6303 If the input schedule is injective, then
6304 the number of elements in this list should be as large as the dimension
6305 of the schedule space, but no direct correspondence should be assumed
6306 between dimensions and elements.
6307 If the input schedule is not injective, then an additional number
6308 of C<isl_id>s equal to the largest dimension of the input domains
6310 If the number of provided C<isl_id>s is insufficient, then additional
6311 names are automatically generated.
6313 #include <isl/ast_build.h>
6314 __isl_give isl_ast_build *
6315 isl_ast_build_set_create_leaf(
6316 __isl_take isl_ast_build *control,
6317 __isl_give isl_ast_node *(*fn)(
6318 __isl_take isl_ast_build *build,
6319 void *user), void *user);
6322 C<isl_ast_build_set_create_leaf> function allows for the
6323 specification of a callback that should be called whenever the AST
6324 generator arrives at an element of the schedule domain.
6325 The callback should return an AST node that should be inserted
6326 at the corresponding position of the AST. The default action (when
6327 the callback is not set) is to continue generating parts of the AST to scan
6328 all the domain elements associated to the schedule domain element
6329 and to insert user nodes, ``calling'' the domain element, for each of them.
6330 The C<build> argument contains the current state of the C<isl_ast_build>.
6331 To ease nested AST generation (see L</"Nested AST Generation">),
6332 all control information that is
6333 specific to the current AST generation such as the options and
6334 the callbacks has been removed from this C<isl_ast_build>.
6335 The callback would typically return the result of a nested
6337 user defined node created using the following function.
6339 #include <isl/ast.h>
6340 __isl_give isl_ast_node *isl_ast_node_alloc_user(
6341 __isl_take isl_ast_expr *expr);
6343 #include <isl/ast_build.h>
6344 __isl_give isl_ast_build *
6345 isl_ast_build_set_at_each_domain(
6346 __isl_take isl_ast_build *build,
6347 __isl_give isl_ast_node *(*fn)(
6348 __isl_take isl_ast_node *node,
6349 __isl_keep isl_ast_build *build,
6350 void *user), void *user);
6351 __isl_give isl_ast_build *
6352 isl_ast_build_set_before_each_for(
6353 __isl_take isl_ast_build *build,
6354 __isl_give isl_id *(*fn)(
6355 __isl_keep isl_ast_build *build,
6356 void *user), void *user);
6357 __isl_give isl_ast_build *
6358 isl_ast_build_set_after_each_for(
6359 __isl_take isl_ast_build *build,
6360 __isl_give isl_ast_node *(*fn)(
6361 __isl_take isl_ast_node *node,
6362 __isl_keep isl_ast_build *build,
6363 void *user), void *user);
6365 The callback set by C<isl_ast_build_set_at_each_domain> will
6366 be called for each domain AST node.
6367 The callbacks set by C<isl_ast_build_set_before_each_for>
6368 and C<isl_ast_build_set_after_each_for> will be called
6369 for each for AST node. The first will be called in depth-first
6370 pre-order, while the second will be called in depth-first post-order.
6371 Since C<isl_ast_build_set_before_each_for> is called before the for
6372 node is actually constructed, it is only passed an C<isl_ast_build>.
6373 The returned C<isl_id> will be added as an annotation (using
6374 C<isl_ast_node_set_annotation>) to the constructed for node.
6375 In particular, if the user has also specified an C<after_each_for>
6376 callback, then the annotation can be retrieved from the node passed to
6377 that callback using C<isl_ast_node_get_annotation>.
6378 All callbacks should C<NULL> on failure.
6379 The given C<isl_ast_build> can be used to create new
6380 C<isl_ast_expr> objects using C<isl_ast_build_expr_from_pw_aff>
6381 or C<isl_ast_build_call_from_pw_multi_aff>.
6383 =head3 Nested AST Generation
6385 C<isl> allows the user to create an AST within the context
6386 of another AST. These nested ASTs are created using the
6387 same C<isl_ast_build_ast_from_schedule> function that is used to create the
6388 outer AST. The C<build> argument should be an C<isl_ast_build>
6389 passed to a callback set by
6390 C<isl_ast_build_set_create_leaf>.
6391 The space of the range of the C<schedule> argument should refer
6392 to this build. In particular, the space should be a wrapped
6393 relation and the domain of this wrapped relation should be the
6394 same as that of the range of the schedule returned by
6395 C<isl_ast_build_get_schedule> below.
6396 In practice, the new schedule is typically
6397 created by calling C<isl_union_map_range_product> on the old schedule
6398 and some extra piece of the schedule.
6399 The space of the schedule domain is also available from
6400 the C<isl_ast_build>.
6402 #include <isl/ast_build.h>
6403 __isl_give isl_union_map *isl_ast_build_get_schedule(
6404 __isl_keep isl_ast_build *build);
6405 __isl_give isl_space *isl_ast_build_get_schedule_space(
6406 __isl_keep isl_ast_build *build);
6407 __isl_give isl_ast_build *isl_ast_build_restrict(
6408 __isl_take isl_ast_build *build,
6409 __isl_take isl_set *set);
6411 The C<isl_ast_build_get_schedule> function returns a (partial)
6412 schedule for the domains elements for which part of the AST still needs to
6413 be generated in the current build.
6414 In particular, the domain elements are mapped to those iterations of the loops
6415 enclosing the current point of the AST generation inside which
6416 the domain elements are executed.
6417 No direct correspondence between
6418 the input schedule and this schedule should be assumed.
6419 The space obtained from C<isl_ast_build_get_schedule_space> can be used
6420 to create a set for C<isl_ast_build_restrict> to intersect
6421 with the current build. In particular, the set passed to
6422 C<isl_ast_build_restrict> can have additional parameters.
6423 The ids of the set dimensions in the space returned by
6424 C<isl_ast_build_get_schedule_space> correspond to the
6425 iterators of the already generated loops.
6426 The user should not rely on the ids of the output dimensions
6427 of the relations in the union relation returned by
6428 C<isl_ast_build_get_schedule> having any particular value.
6432 Although C<isl> is mainly meant to be used as a library,
6433 it also contains some basic applications that use some
6434 of the functionality of C<isl>.
6435 The input may be specified in either the L<isl format>
6436 or the L<PolyLib format>.
6438 =head2 C<isl_polyhedron_sample>
6440 C<isl_polyhedron_sample> takes a polyhedron as input and prints
6441 an integer element of the polyhedron, if there is any.
6442 The first column in the output is the denominator and is always
6443 equal to 1. If the polyhedron contains no integer points,
6444 then a vector of length zero is printed.
6448 C<isl_pip> takes the same input as the C<example> program
6449 from the C<piplib> distribution, i.e., a set of constraints
6450 on the parameters, a line containing only -1 and finally a set
6451 of constraints on a parametric polyhedron.
6452 The coefficients of the parameters appear in the last columns
6453 (but before the final constant column).
6454 The output is the lexicographic minimum of the parametric polyhedron.
6455 As C<isl> currently does not have its own output format, the output
6456 is just a dump of the internal state.
6458 =head2 C<isl_polyhedron_minimize>
6460 C<isl_polyhedron_minimize> computes the minimum of some linear
6461 or affine objective function over the integer points in a polyhedron.
6462 If an affine objective function
6463 is given, then the constant should appear in the last column.
6465 =head2 C<isl_polytope_scan>
6467 Given a polytope, C<isl_polytope_scan> prints
6468 all integer points in the polytope.
6470 =head2 C<isl_codegen>
6472 Given a schedule, a context set and an options relation,
6473 C<isl_codegen> prints out an AST that scans the domain elements
6474 of the schedule in the order of their image(s) taking into account
6475 the constraints in the context set.