3 C<isl> is a thread-safe C library for manipulating
4 sets and relations of integer points bounded by affine constraints.
5 The descriptions of the sets and relations may involve
6 both parameters and existentially quantified variables.
7 All computations are performed in exact integer arithmetic
9 The C<isl> library offers functionality that is similar
10 to that offered by the C<Omega> and C<Omega+> libraries,
11 but the underlying algorithms are in most cases completely different.
13 The library is by no means complete and some fairly basic
14 functionality is still missing.
15 Still, even in its current form, the library has been successfully
16 used as a backend polyhedral library for the polyhedral
17 scanner C<CLooG> and as part of an equivalence checker of
18 static affine programs.
19 For bug reports, feature requests and questions,
20 visit the the discussion group at
21 L<http://groups.google.com/group/isl-development>.
23 =head2 Backward Incompatible Changes
25 =head3 Changes since isl-0.02
29 =item * The old printing functions have been deprecated
30 and replaced by C<isl_printer> functions, see L<Input and Output>.
32 =item * Most functions related to dependence analysis have acquired
33 an extra C<must> argument. To obtain the old behavior, this argument
34 should be given the value 1. See L<Dependence Analysis>.
38 =head3 Changes since isl-0.03
42 =item * The function C<isl_pw_qpolynomial_fold_add> has been
43 renamed to C<isl_pw_qpolynomial_fold_fold>.
44 Similarly, C<isl_union_pw_qpolynomial_fold_add> has been
45 renamed to C<isl_union_pw_qpolynomial_fold_fold>.
49 =head3 Changes since isl-0.04
53 =item * All header files have been renamed from C<isl_header.h>
58 =head3 Changes since isl-0.05
62 =item * The functions C<isl_printer_print_basic_set> and
63 C<isl_printer_print_basic_map> no longer print a newline.
65 =item * The functions C<isl_flow_get_no_source>
66 and C<isl_union_map_compute_flow> now return
67 the accesses for which no source could be found instead of
68 the iterations where those accesses occur.
70 =item * The functions C<isl_basic_map_identity> and
71 C<isl_map_identity> now take a B<map> space as input. An old call
72 C<isl_map_identity(space)> can be rewritten to
73 C<isl_map_identity(isl_space_map_from_set(space))>.
75 =item * The function C<isl_map_power> no longer takes
76 a parameter position as input. Instead, the exponent
77 is now expressed as the domain of the resulting relation.
81 =head3 Changes since isl-0.06
85 =item * The format of C<isl_printer_print_qpolynomial>'s
86 C<ISL_FORMAT_ISL> output has changed.
87 Use C<ISL_FORMAT_C> to obtain the old output.
89 =item * The C<*_fast_*> functions have been renamed to C<*_plain_*>.
90 Some of the old names have been kept for backward compatibility,
91 but they will be removed in the future.
95 =head3 Changes since isl-0.07
99 =item * The function C<isl_pw_aff_max> has been renamed to
100 C<isl_pw_aff_union_max>.
101 Similarly, the function C<isl_pw_aff_add> has been renamed to
102 C<isl_pw_aff_union_add>.
104 =item * The C<isl_dim> type has been renamed to C<isl_space>
105 along with the associated functions.
106 Some of the old names have been kept for backward compatibility,
107 but they will be removed in the future.
109 =item * Spaces of maps, sets and parameter domains are now
110 treated differently. The distinction between map spaces and set spaces
111 has always been made on a conceptual level, but proper use of such spaces
112 was never checked. Furthermore, up until isl-0.07 there was no way
113 of explicitly creating a parameter space. These can now be created
114 directly using C<isl_space_params_alloc> or from other spaces using
117 =item * The space in which C<isl_aff>, C<isl_pw_aff>, C<isl_qpolynomial>,
118 C<isl_pw_qpolynomial>, C<isl_qpolynomial_fold> and C<isl_pw_qpolynomial_fold>
119 objects live is now a map space
120 instead of a set space. This means, for example, that the dimensions
121 of the domain of an C<isl_aff> are now considered to be of type
122 C<isl_dim_in> instead of C<isl_dim_set>. Extra functions have been
123 added to obtain the domain space. Some of the constructors still
124 take a domain space and have therefore been renamed.
126 =item * The functions C<isl_equality_alloc> and C<isl_inequality_alloc>
127 now take an C<isl_local_space> instead of an C<isl_space>.
128 An C<isl_local_space> can be created from an C<isl_space>
129 using C<isl_local_space_from_space>.
131 =item * The C<isl_div> type has been removed. Functions that used
132 to return an C<isl_div> now return an C<isl_aff>.
133 Note that the space of an C<isl_aff> is that of relation.
134 When replacing a call to C<isl_div_get_coefficient> by a call to
135 C<isl_aff_get_coefficient> any C<isl_dim_set> argument needs
136 to be replaced by C<isl_dim_in>.
137 A call to C<isl_aff_from_div> can be replaced by a call
139 A call to C<isl_qpolynomial_div(div)> call be replaced by
142 isl_qpolynomial_from_aff(isl_aff_floor(div))
144 The function C<isl_constraint_div> has also been renamed
145 to C<isl_constraint_get_div>.
147 =item * The C<nparam> argument has been removed from
148 C<isl_map_read_from_str> and similar functions.
149 When reading input in the original PolyLib format,
150 the result will have no parameters.
151 If parameters are expected, the caller may want to perform
152 dimension manipulation on the result.
156 =head3 Changes since isl-0.09
160 =item * The C<schedule_split_parallel> option has been replaced
161 by the C<schedule_split_scaled> option.
163 =item * The first argument of C<isl_pw_aff_cond> is now
164 an C<isl_pw_aff> instead of an C<isl_set>.
165 A call C<isl_pw_aff_cond(a, b, c)> can be replaced by
167 isl_pw_aff_cond(isl_set_indicator_function(a), b, c)
171 =head3 Changes since isl-0.10
175 =item * The functions C<isl_set_dim_has_lower_bound> and
176 C<isl_set_dim_has_upper_bound> have been renamed to
177 C<isl_set_dim_has_any_lower_bound> and
178 C<isl_set_dim_has_any_upper_bound>.
179 The new C<isl_set_dim_has_lower_bound> and
180 C<isl_set_dim_has_upper_bound> have slightly different meanings.
184 =head3 Changes since isl-0.12
188 =item * C<isl_int> has been replaced by C<isl_val>.
189 Some of the old functions are still available in C<isl/deprecated/*.h>
190 but they will be removed in the future.
192 =item * The functions C<isl_pw_qpolynomial_eval>,
193 C<isl_union_pw_qpolynomial_eval>, C<isl_pw_qpolynomial_fold_eval>
194 and C<isl_union_pw_qpolynomial_fold_eval> have been changed to return
195 an C<isl_val> instead of an C<isl_qpolynomial>.
197 =item * The function C<isl_band_member_is_zero_distance>
198 has been removed. Essentially the same functionality is available
199 through C<isl_band_member_is_coincident>, except that is requires
200 setting up coincidence constraints.
201 The option C<schedule_outer_zero_distance> has accordingly been
202 replaced by the option C<schedule_outer_coincidence>.
208 C<isl> is released under the MIT license.
212 Permission is hereby granted, free of charge, to any person obtaining a copy of
213 this software and associated documentation files (the "Software"), to deal in
214 the Software without restriction, including without limitation the rights to
215 use, copy, modify, merge, publish, distribute, sublicense, and/or sell copies
216 of the Software, and to permit persons to whom the Software is furnished to do
217 so, subject to the following conditions:
219 The above copyright notice and this permission notice shall be included in all
220 copies or substantial portions of the Software.
222 THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
223 IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
224 FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
225 AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
226 LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
227 OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
232 Note that C<isl> currently requires C<GMP>, which is released
233 under the GNU Lesser General Public License (LGPL). This means
234 that code linked against C<isl> is also linked against LGPL code.
238 The source of C<isl> can be obtained either as a tarball
239 or from the git repository. Both are available from
240 L<http://freshmeat.net/projects/isl/>.
241 The installation process depends on how you obtained
244 =head2 Installation from the git repository
248 =item 1 Clone or update the repository
250 The first time the source is obtained, you need to clone
253 git clone git://repo.or.cz/isl.git
255 To obtain updates, you need to pull in the latest changes
259 =item 2 Generate C<configure>
265 After performing the above steps, continue
266 with the L<Common installation instructions>.
268 =head2 Common installation instructions
272 =item 1 Obtain C<GMP>
274 Building C<isl> requires C<GMP>, including its headers files.
275 Your distribution may not provide these header files by default
276 and you may need to install a package called C<gmp-devel> or something
277 similar. Alternatively, C<GMP> can be built from
278 source, available from L<http://gmplib.org/>.
282 C<isl> uses the standard C<autoconf> C<configure> script.
287 optionally followed by some configure options.
288 A complete list of options can be obtained by running
292 Below we discuss some of the more common options.
298 Installation prefix for C<isl>
300 =item C<--with-gmp-prefix>
302 Installation prefix for C<GMP> (architecture-independent files).
304 =item C<--with-gmp-exec-prefix>
306 Installation prefix for C<GMP> (architecture-dependent files).
314 =item 4 Install (optional)
320 =head1 Integer Set Library
322 =head2 Initialization
324 All manipulations of integer sets and relations occur within
325 the context of an C<isl_ctx>.
326 A given C<isl_ctx> can only be used within a single thread.
327 All arguments of a function are required to have been allocated
328 within the same context.
329 There are currently no functions available for moving an object
330 from one C<isl_ctx> to another C<isl_ctx>. This means that
331 there is currently no way of safely moving an object from one
332 thread to another, unless the whole C<isl_ctx> is moved.
334 An C<isl_ctx> can be allocated using C<isl_ctx_alloc> and
335 freed using C<isl_ctx_free>.
336 All objects allocated within an C<isl_ctx> should be freed
337 before the C<isl_ctx> itself is freed.
339 isl_ctx *isl_ctx_alloc();
340 void isl_ctx_free(isl_ctx *ctx);
344 An C<isl_val> represents an integer value, a rational value
345 or one of three special values, infinity, negative infinity and NaN.
346 Some predefined values can be created using the following functions.
349 __isl_give isl_val *isl_val_zero(isl_ctx *ctx);
350 __isl_give isl_val *isl_val_one(isl_ctx *ctx);
351 __isl_give isl_val *isl_val_nan(isl_ctx *ctx);
352 __isl_give isl_val *isl_val_infty(isl_ctx *ctx);
353 __isl_give isl_val *isl_val_neginfty(isl_ctx *ctx);
355 Specific integer values can be created using the following functions.
358 __isl_give isl_val *isl_val_int_from_si(isl_ctx *ctx,
360 __isl_give isl_val *isl_val_int_from_ui(isl_ctx *ctx,
362 __isl_give isl_val *isl_val_int_from_chunks(isl_ctx *ctx,
363 size_t n, size_t size, const void *chunks);
365 The function C<isl_val_int_from_chunks> constructs an C<isl_val>
366 from the C<n> I<digits>, each consisting of C<size> bytes, stored at C<chunks>.
367 The least significant digit is assumed to be stored first.
369 Value objects can be copied and freed using the following functions.
372 __isl_give isl_val *isl_val_copy(__isl_keep isl_val *v);
373 void *isl_val_free(__isl_take isl_val *v);
375 They can be inspected using the following functions.
378 isl_ctx *isl_val_get_ctx(__isl_keep isl_val *val);
379 long isl_val_get_num_si(__isl_keep isl_val *v);
380 long isl_val_get_den_si(__isl_keep isl_val *v);
381 double isl_val_get_d(__isl_keep isl_val *v);
382 size_t isl_val_n_abs_num_chunks(__isl_keep isl_val *v,
384 int isl_val_get_abs_num_chunks(__isl_keep isl_val *v,
385 size_t size, void *chunks);
387 C<isl_val_n_abs_num_chunks> returns the number of I<digits>
388 of C<size> bytes needed to store the absolute value of the
390 C<isl_val_get_abs_num_chunks> stores these digits at C<chunks>,
391 which is assumed to have been preallocated by the caller.
392 The least significant digit is stored first.
393 Note that C<isl_val_get_num_si>, C<isl_val_get_den_si>,
394 C<isl_val_get_d>, C<isl_val_n_abs_num_chunks>
395 and C<isl_val_get_abs_num_chunks> can only be applied to rational values.
397 An C<isl_val> can be modified using the following function.
400 __isl_give isl_val *isl_val_set_si(__isl_take isl_val *v,
403 The following unary properties are defined on C<isl_val>s.
406 int isl_val_sgn(__isl_keep isl_val *v);
407 int isl_val_is_zero(__isl_keep isl_val *v);
408 int isl_val_is_one(__isl_keep isl_val *v);
409 int isl_val_is_negone(__isl_keep isl_val *v);
410 int isl_val_is_nonneg(__isl_keep isl_val *v);
411 int isl_val_is_nonpos(__isl_keep isl_val *v);
412 int isl_val_is_pos(__isl_keep isl_val *v);
413 int isl_val_is_neg(__isl_keep isl_val *v);
414 int isl_val_is_int(__isl_keep isl_val *v);
415 int isl_val_is_rat(__isl_keep isl_val *v);
416 int isl_val_is_nan(__isl_keep isl_val *v);
417 int isl_val_is_infty(__isl_keep isl_val *v);
418 int isl_val_is_neginfty(__isl_keep isl_val *v);
420 Note that the sign of NaN is undefined.
422 The following binary properties are defined on pairs of C<isl_val>s.
425 int isl_val_lt(__isl_keep isl_val *v1,
426 __isl_keep isl_val *v2);
427 int isl_val_le(__isl_keep isl_val *v1,
428 __isl_keep isl_val *v2);
429 int isl_val_gt(__isl_keep isl_val *v1,
430 __isl_keep isl_val *v2);
431 int isl_val_ge(__isl_keep isl_val *v1,
432 __isl_keep isl_val *v2);
433 int isl_val_eq(__isl_keep isl_val *v1,
434 __isl_keep isl_val *v2);
435 int isl_val_ne(__isl_keep isl_val *v1,
436 __isl_keep isl_val *v2);
438 For integer C<isl_val>s we additionally have the following binary property.
441 int isl_val_is_divisible_by(__isl_keep isl_val *v1,
442 __isl_keep isl_val *v2);
444 An C<isl_val> can also be compared to an integer using the following
445 function. The result is undefined for NaN.
448 int isl_val_cmp_si(__isl_keep isl_val *v, long i);
450 The following unary operations are available on C<isl_val>s.
453 __isl_give isl_val *isl_val_abs(__isl_take isl_val *v);
454 __isl_give isl_val *isl_val_neg(__isl_take isl_val *v);
455 __isl_give isl_val *isl_val_floor(__isl_take isl_val *v);
456 __isl_give isl_val *isl_val_ceil(__isl_take isl_val *v);
457 __isl_give isl_val *isl_val_trunc(__isl_take isl_val *v);
459 The following binary operations are available on C<isl_val>s.
462 __isl_give isl_val *isl_val_abs(__isl_take isl_val *v);
463 __isl_give isl_val *isl_val_neg(__isl_take isl_val *v);
464 __isl_give isl_val *isl_val_floor(__isl_take isl_val *v);
465 __isl_give isl_val *isl_val_ceil(__isl_take isl_val *v);
466 __isl_give isl_val *isl_val_trunc(__isl_take isl_val *v);
467 __isl_give isl_val *isl_val_2exp(__isl_take isl_val *v);
468 __isl_give isl_val *isl_val_min(__isl_take isl_val *v1,
469 __isl_take isl_val *v2);
470 __isl_give isl_val *isl_val_max(__isl_take isl_val *v1,
471 __isl_take isl_val *v2);
472 __isl_give isl_val *isl_val_add(__isl_take isl_val *v1,
473 __isl_take isl_val *v2);
474 __isl_give isl_val *isl_val_add_ui(__isl_take isl_val *v1,
476 __isl_give isl_val *isl_val_sub(__isl_take isl_val *v1,
477 __isl_take isl_val *v2);
478 __isl_give isl_val *isl_val_sub_ui(__isl_take isl_val *v1,
480 __isl_give isl_val *isl_val_mul(__isl_take isl_val *v1,
481 __isl_take isl_val *v2);
482 __isl_give isl_val *isl_val_mul_ui(__isl_take isl_val *v1,
484 __isl_give isl_val *isl_val_div(__isl_take isl_val *v1,
485 __isl_take isl_val *v2);
487 On integer values, we additionally have the following operations.
490 __isl_give isl_val *isl_val_2exp(__isl_take isl_val *v);
491 __isl_give isl_val *isl_val_mod(__isl_take isl_val *v1,
492 __isl_take isl_val *v2);
493 __isl_give isl_val *isl_val_gcd(__isl_take isl_val *v1,
494 __isl_take isl_val *v2);
495 __isl_give isl_val *isl_val_gcdext(__isl_take isl_val *v1,
496 __isl_take isl_val *v2, __isl_give isl_val **x,
497 __isl_give isl_val **y);
499 The function C<isl_val_gcdext> returns the greatest common divisor g
500 of C<v1> and C<v2> as well as two integers C<*x> and C<*y> such
501 that C<*x> * C<v1> + C<*y> * C<v2> = g.
503 A value can be read from input using
506 __isl_give isl_val *isl_val_read_from_str(isl_ctx *ctx,
509 A value can be printed using
512 __isl_give isl_printer *isl_printer_print_val(
513 __isl_take isl_printer *p, __isl_keep isl_val *v);
515 =head3 GMP specific functions
517 These functions are only available if C<isl> has been compiled with C<GMP>
520 Specific integer and rational values can be created from C<GMP> values using
521 the following functions.
523 #include <isl/val_gmp.h>
524 __isl_give isl_val *isl_val_int_from_gmp(isl_ctx *ctx,
526 __isl_give isl_val *isl_val_from_gmp(isl_ctx *ctx,
527 const mpz_t n, const mpz_t d);
529 The numerator and denominator of a rational value can be extracted as
530 C<GMP> values using the following functions.
532 #include <isl/val_gmp.h>
533 int isl_val_get_num_gmp(__isl_keep isl_val *v, mpz_t z);
534 int isl_val_get_den_gmp(__isl_keep isl_val *v, mpz_t z);
536 =head2 Sets and Relations
538 C<isl> uses six types of objects for representing sets and relations,
539 C<isl_basic_set>, C<isl_basic_map>, C<isl_set>, C<isl_map>,
540 C<isl_union_set> and C<isl_union_map>.
541 C<isl_basic_set> and C<isl_basic_map> represent sets and relations that
542 can be described as a conjunction of affine constraints, while
543 C<isl_set> and C<isl_map> represent unions of
544 C<isl_basic_set>s and C<isl_basic_map>s, respectively.
545 However, all C<isl_basic_set>s or C<isl_basic_map>s in the union need
546 to live in the same space. C<isl_union_set>s and C<isl_union_map>s
547 represent unions of C<isl_set>s or C<isl_map>s in I<different> spaces,
548 where spaces are considered different if they have a different number
549 of dimensions and/or different names (see L<"Spaces">).
550 The difference between sets and relations (maps) is that sets have
551 one set of variables, while relations have two sets of variables,
552 input variables and output variables.
554 =head2 Memory Management
556 Since a high-level operation on sets and/or relations usually involves
557 several substeps and since the user is usually not interested in
558 the intermediate results, most functions that return a new object
559 will also release all the objects passed as arguments.
560 If the user still wants to use one or more of these arguments
561 after the function call, she should pass along a copy of the
562 object rather than the object itself.
563 The user is then responsible for making sure that the original
564 object gets used somewhere else or is explicitly freed.
566 The arguments and return values of all documented functions are
567 annotated to make clear which arguments are released and which
568 arguments are preserved. In particular, the following annotations
575 C<__isl_give> means that a new object is returned.
576 The user should make sure that the returned pointer is
577 used exactly once as a value for an C<__isl_take> argument.
578 In between, it can be used as a value for as many
579 C<__isl_keep> arguments as the user likes.
580 There is one exception, and that is the case where the
581 pointer returned is C<NULL>. Is this case, the user
582 is free to use it as an C<__isl_take> argument or not.
586 C<__isl_take> means that the object the argument points to
587 is taken over by the function and may no longer be used
588 by the user as an argument to any other function.
589 The pointer value must be one returned by a function
590 returning an C<__isl_give> pointer.
591 If the user passes in a C<NULL> value, then this will
592 be treated as an error in the sense that the function will
593 not perform its usual operation. However, it will still
594 make sure that all the other C<__isl_take> arguments
599 C<__isl_keep> means that the function will only use the object
600 temporarily. After the function has finished, the user
601 can still use it as an argument to other functions.
602 A C<NULL> value will be treated in the same way as
603 a C<NULL> value for an C<__isl_take> argument.
607 =head2 Error Handling
609 C<isl> supports different ways to react in case a runtime error is triggered.
610 Runtime errors arise, e.g., if a function such as C<isl_map_intersect> is called
611 with two maps that have incompatible spaces. There are three possible ways
612 to react on error: to warn, to continue or to abort.
614 The default behavior is to warn. In this mode, C<isl> prints a warning, stores
615 the last error in the corresponding C<isl_ctx> and the function in which the
616 error was triggered returns C<NULL>. An error does not corrupt internal state,
617 such that isl can continue to be used. C<isl> also provides functions to
618 read the last error and to reset the memory that stores the last error. The
619 last error is only stored for information purposes. Its presence does not
620 change the behavior of C<isl>. Hence, resetting an error is not required to
621 continue to use isl, but only to observe new errors.
624 enum isl_error isl_ctx_last_error(isl_ctx *ctx);
625 void isl_ctx_reset_error(isl_ctx *ctx);
627 Another option is to continue on error. This is similar to warn on error mode,
628 except that C<isl> does not print any warning. This allows a program to
629 implement its own error reporting.
631 The last option is to directly abort the execution of the program from within
632 the isl library. This makes it obviously impossible to recover from an error,
633 but it allows to directly spot the error location. By aborting on error,
634 debuggers break at the location the error occurred and can provide a stack
635 trace. Other tools that automatically provide stack traces on abort or that do
636 not want to continue execution after an error was triggered may also prefer to
639 The on error behavior of isl can be specified by calling
640 C<isl_options_set_on_error> or by setting the command line option
641 C<--isl-on-error>. Valid arguments for the function call are
642 C<ISL_ON_ERROR_WARN>, C<ISL_ON_ERROR_CONTINUE> and C<ISL_ON_ERROR_ABORT>. The
643 choices for the command line option are C<warn>, C<continue> and C<abort>.
644 It is also possible to query the current error mode.
646 #include <isl/options.h>
647 int isl_options_set_on_error(isl_ctx *ctx, int val);
648 int isl_options_get_on_error(isl_ctx *ctx);
652 Identifiers are used to identify both individual dimensions
653 and tuples of dimensions. They consist of an optional name and an optional
654 user pointer. The name and the user pointer cannot both be C<NULL>, however.
655 Identifiers with the same name but different pointer values
656 are considered to be distinct.
657 Similarly, identifiers with different names but the same pointer value
658 are also considered to be distinct.
659 Equal identifiers are represented using the same object.
660 Pairs of identifiers can therefore be tested for equality using the
662 Identifiers can be constructed, copied, freed, inspected and printed
663 using the following functions.
666 __isl_give isl_id *isl_id_alloc(isl_ctx *ctx,
667 __isl_keep const char *name, void *user);
668 __isl_give isl_id *isl_id_set_free_user(
669 __isl_take isl_id *id,
670 __isl_give void (*free_user)(void *user));
671 __isl_give isl_id *isl_id_copy(isl_id *id);
672 void *isl_id_free(__isl_take isl_id *id);
674 isl_ctx *isl_id_get_ctx(__isl_keep isl_id *id);
675 void *isl_id_get_user(__isl_keep isl_id *id);
676 __isl_keep const char *isl_id_get_name(__isl_keep isl_id *id);
678 __isl_give isl_printer *isl_printer_print_id(
679 __isl_take isl_printer *p, __isl_keep isl_id *id);
681 The callback set by C<isl_id_set_free_user> is called on the user
682 pointer when the last reference to the C<isl_id> is freed.
683 Note that C<isl_id_get_name> returns a pointer to some internal
684 data structure, so the result can only be used while the
685 corresponding C<isl_id> is alive.
689 Whenever a new set, relation or similiar object is created from scratch,
690 the space in which it lives needs to be specified using an C<isl_space>.
691 Each space involves zero or more parameters and zero, one or two
692 tuples of set or input/output dimensions. The parameters and dimensions
693 are identified by an C<isl_dim_type> and a position.
694 The type C<isl_dim_param> refers to parameters,
695 the type C<isl_dim_set> refers to set dimensions (for spaces
696 with a single tuple of dimensions) and the types C<isl_dim_in>
697 and C<isl_dim_out> refer to input and output dimensions
698 (for spaces with two tuples of dimensions).
699 Local spaces (see L</"Local Spaces">) also contain dimensions
700 of type C<isl_dim_div>.
701 Note that parameters are only identified by their position within
702 a given object. Across different objects, parameters are (usually)
703 identified by their names or identifiers. Only unnamed parameters
704 are identified by their positions across objects. The use of unnamed
705 parameters is discouraged.
707 #include <isl/space.h>
708 __isl_give isl_space *isl_space_alloc(isl_ctx *ctx,
709 unsigned nparam, unsigned n_in, unsigned n_out);
710 __isl_give isl_space *isl_space_params_alloc(isl_ctx *ctx,
712 __isl_give isl_space *isl_space_set_alloc(isl_ctx *ctx,
713 unsigned nparam, unsigned dim);
714 __isl_give isl_space *isl_space_copy(__isl_keep isl_space *space);
715 void *isl_space_free(__isl_take isl_space *space);
716 unsigned isl_space_dim(__isl_keep isl_space *space,
717 enum isl_dim_type type);
719 The space used for creating a parameter domain
720 needs to be created using C<isl_space_params_alloc>.
721 For other sets, the space
722 needs to be created using C<isl_space_set_alloc>, while
723 for a relation, the space
724 needs to be created using C<isl_space_alloc>.
725 C<isl_space_dim> can be used
726 to find out the number of dimensions of each type in
727 a space, where type may be
728 C<isl_dim_param>, C<isl_dim_in> (only for relations),
729 C<isl_dim_out> (only for relations), C<isl_dim_set>
730 (only for sets) or C<isl_dim_all>.
732 To check whether a given space is that of a set or a map
733 or whether it is a parameter space, use these functions:
735 #include <isl/space.h>
736 int isl_space_is_params(__isl_keep isl_space *space);
737 int isl_space_is_set(__isl_keep isl_space *space);
738 int isl_space_is_map(__isl_keep isl_space *space);
740 Spaces can be compared using the following functions:
742 #include <isl/space.h>
743 int isl_space_is_equal(__isl_keep isl_space *space1,
744 __isl_keep isl_space *space2);
745 int isl_space_is_domain(__isl_keep isl_space *space1,
746 __isl_keep isl_space *space2);
747 int isl_space_is_range(__isl_keep isl_space *space1,
748 __isl_keep isl_space *space2);
750 C<isl_space_is_domain> checks whether the first argument is equal
751 to the domain of the second argument. This requires in particular that
752 the first argument is a set space and that the second argument
755 It is often useful to create objects that live in the
756 same space as some other object. This can be accomplished
757 by creating the new objects
758 (see L<Creating New Sets and Relations> or
759 L<Creating New (Piecewise) Quasipolynomials>) based on the space
760 of the original object.
763 __isl_give isl_space *isl_basic_set_get_space(
764 __isl_keep isl_basic_set *bset);
765 __isl_give isl_space *isl_set_get_space(__isl_keep isl_set *set);
767 #include <isl/union_set.h>
768 __isl_give isl_space *isl_union_set_get_space(
769 __isl_keep isl_union_set *uset);
772 __isl_give isl_space *isl_basic_map_get_space(
773 __isl_keep isl_basic_map *bmap);
774 __isl_give isl_space *isl_map_get_space(__isl_keep isl_map *map);
776 #include <isl/union_map.h>
777 __isl_give isl_space *isl_union_map_get_space(
778 __isl_keep isl_union_map *umap);
780 #include <isl/constraint.h>
781 __isl_give isl_space *isl_constraint_get_space(
782 __isl_keep isl_constraint *constraint);
784 #include <isl/polynomial.h>
785 __isl_give isl_space *isl_qpolynomial_get_domain_space(
786 __isl_keep isl_qpolynomial *qp);
787 __isl_give isl_space *isl_qpolynomial_get_space(
788 __isl_keep isl_qpolynomial *qp);
789 __isl_give isl_space *isl_qpolynomial_fold_get_space(
790 __isl_keep isl_qpolynomial_fold *fold);
791 __isl_give isl_space *isl_pw_qpolynomial_get_domain_space(
792 __isl_keep isl_pw_qpolynomial *pwqp);
793 __isl_give isl_space *isl_pw_qpolynomial_get_space(
794 __isl_keep isl_pw_qpolynomial *pwqp);
795 __isl_give isl_space *isl_pw_qpolynomial_fold_get_domain_space(
796 __isl_keep isl_pw_qpolynomial_fold *pwf);
797 __isl_give isl_space *isl_pw_qpolynomial_fold_get_space(
798 __isl_keep isl_pw_qpolynomial_fold *pwf);
799 __isl_give isl_space *isl_union_pw_qpolynomial_get_space(
800 __isl_keep isl_union_pw_qpolynomial *upwqp);
801 __isl_give isl_space *isl_union_pw_qpolynomial_fold_get_space(
802 __isl_keep isl_union_pw_qpolynomial_fold *upwf);
805 __isl_give isl_space *isl_multi_val_get_space(
806 __isl_keep isl_multi_val *mv);
809 __isl_give isl_space *isl_aff_get_domain_space(
810 __isl_keep isl_aff *aff);
811 __isl_give isl_space *isl_aff_get_space(
812 __isl_keep isl_aff *aff);
813 __isl_give isl_space *isl_pw_aff_get_domain_space(
814 __isl_keep isl_pw_aff *pwaff);
815 __isl_give isl_space *isl_pw_aff_get_space(
816 __isl_keep isl_pw_aff *pwaff);
817 __isl_give isl_space *isl_multi_aff_get_domain_space(
818 __isl_keep isl_multi_aff *maff);
819 __isl_give isl_space *isl_multi_aff_get_space(
820 __isl_keep isl_multi_aff *maff);
821 __isl_give isl_space *isl_pw_multi_aff_get_domain_space(
822 __isl_keep isl_pw_multi_aff *pma);
823 __isl_give isl_space *isl_pw_multi_aff_get_space(
824 __isl_keep isl_pw_multi_aff *pma);
825 __isl_give isl_space *isl_union_pw_multi_aff_get_space(
826 __isl_keep isl_union_pw_multi_aff *upma);
827 __isl_give isl_space *isl_multi_pw_aff_get_domain_space(
828 __isl_keep isl_multi_pw_aff *mpa);
829 __isl_give isl_space *isl_multi_pw_aff_get_space(
830 __isl_keep isl_multi_pw_aff *mpa);
832 #include <isl/point.h>
833 __isl_give isl_space *isl_point_get_space(
834 __isl_keep isl_point *pnt);
836 The identifiers or names of the individual dimensions may be set or read off
837 using the following functions.
839 #include <isl/space.h>
840 __isl_give isl_space *isl_space_set_dim_id(
841 __isl_take isl_space *space,
842 enum isl_dim_type type, unsigned pos,
843 __isl_take isl_id *id);
844 int isl_space_has_dim_id(__isl_keep isl_space *space,
845 enum isl_dim_type type, unsigned pos);
846 __isl_give isl_id *isl_space_get_dim_id(
847 __isl_keep isl_space *space,
848 enum isl_dim_type type, unsigned pos);
849 __isl_give isl_space *isl_space_set_dim_name(
850 __isl_take isl_space *space,
851 enum isl_dim_type type, unsigned pos,
852 __isl_keep const char *name);
853 int isl_space_has_dim_name(__isl_keep isl_space *space,
854 enum isl_dim_type type, unsigned pos);
855 __isl_keep const char *isl_space_get_dim_name(
856 __isl_keep isl_space *space,
857 enum isl_dim_type type, unsigned pos);
859 Note that C<isl_space_get_name> returns a pointer to some internal
860 data structure, so the result can only be used while the
861 corresponding C<isl_space> is alive.
862 Also note that every function that operates on two sets or relations
863 requires that both arguments have the same parameters. This also
864 means that if one of the arguments has named parameters, then the
865 other needs to have named parameters too and the names need to match.
866 Pairs of C<isl_set>, C<isl_map>, C<isl_union_set> and/or C<isl_union_map>
867 arguments may have different parameters (as long as they are named),
868 in which case the result will have as parameters the union of the parameters of
871 Given the identifier or name of a dimension (typically a parameter),
872 its position can be obtained from the following function.
874 #include <isl/space.h>
875 int isl_space_find_dim_by_id(__isl_keep isl_space *space,
876 enum isl_dim_type type, __isl_keep isl_id *id);
877 int isl_space_find_dim_by_name(__isl_keep isl_space *space,
878 enum isl_dim_type type, const char *name);
880 The identifiers or names of entire spaces may be set or read off
881 using the following functions.
883 #include <isl/space.h>
884 __isl_give isl_space *isl_space_set_tuple_id(
885 __isl_take isl_space *space,
886 enum isl_dim_type type, __isl_take isl_id *id);
887 __isl_give isl_space *isl_space_reset_tuple_id(
888 __isl_take isl_space *space, enum isl_dim_type type);
889 int isl_space_has_tuple_id(__isl_keep isl_space *space,
890 enum isl_dim_type type);
891 __isl_give isl_id *isl_space_get_tuple_id(
892 __isl_keep isl_space *space, enum isl_dim_type type);
893 __isl_give isl_space *isl_space_set_tuple_name(
894 __isl_take isl_space *space,
895 enum isl_dim_type type, const char *s);
896 int isl_space_has_tuple_name(__isl_keep isl_space *space,
897 enum isl_dim_type type);
898 const char *isl_space_get_tuple_name(__isl_keep isl_space *space,
899 enum isl_dim_type type);
901 The C<type> argument needs to be one of C<isl_dim_in>, C<isl_dim_out>
902 or C<isl_dim_set>. As with C<isl_space_get_name>,
903 the C<isl_space_get_tuple_name> function returns a pointer to some internal
905 Binary operations require the corresponding spaces of their arguments
906 to have the same name.
908 To keep the names of all parameters and tuples, but reset the user pointers
909 of all the corresponding identifiers, use the following function.
911 __isl_give isl_space *isl_space_reset_user(
912 __isl_take isl_space *space);
914 Spaces can be nested. In particular, the domain of a set or
915 the domain or range of a relation can be a nested relation.
916 The following functions can be used to construct and deconstruct
919 #include <isl/space.h>
920 int isl_space_is_wrapping(__isl_keep isl_space *space);
921 int isl_space_range_is_wrapping(
922 __isl_keep isl_space *space);
923 __isl_give isl_space *isl_space_wrap(__isl_take isl_space *space);
924 __isl_give isl_space *isl_space_unwrap(__isl_take isl_space *space);
925 __isl_give isl_space *isl_space_product(__isl_take isl_space *space1,
926 __isl_take isl_space *space2);
927 __isl_give isl_space *isl_space_domain_product(
928 __isl_take isl_space *space1,
929 __isl_take isl_space *space2);
930 __isl_give isl_space *isl_space_range_product(
931 __isl_take isl_space *space1,
932 __isl_take isl_space *space2);
933 __isl_give isl_space *isl_space_range_factor_domain(
934 __isl_take isl_space *space);
935 __isl_give isl_space *isl_space_range_factor_range(
936 __isl_take isl_space *space);
938 The input to C<isl_space_is_wrapping> and C<isl_space_unwrap> should
939 be the space of a set, while that of
940 C<isl_space_range_is_wrapping> and
941 C<isl_space_wrap> should be the space of a relation.
942 Conversely, the output of C<isl_space_unwrap> is the space
943 of a relation, while that of C<isl_space_wrap> is the space of a set.
945 C<isl_space_product>, C<isl_space_domain_product>
946 and C<isl_space_range_product> take pairs or relation spaces and
947 produce a single relations space, where either the domain, the range
948 or both domain and range are wrapped spaces of relations between
949 the domains and/or ranges of the input spaces.
950 If the product is only constructed over the domain or the range
951 then the ranges or the domains of the inputs should be the same.
952 The functions C<isl_space_range_factor_domain> and
953 C<isl_space_range_factor_range> extract the two arguments from
954 the result of a call to C<isl_space_range_product>.
956 Spaces can be created from other spaces
957 using the following functions.
959 __isl_give isl_space *isl_space_domain(__isl_take isl_space *space);
960 __isl_give isl_space *isl_space_from_domain(__isl_take isl_space *space);
961 __isl_give isl_space *isl_space_range(__isl_take isl_space *space);
962 __isl_give isl_space *isl_space_from_range(__isl_take isl_space *space);
963 __isl_give isl_space *isl_space_domain_map(
964 __isl_take isl_space *space);
965 __isl_give isl_space *isl_space_range_map(
966 __isl_take isl_space *space);
967 __isl_give isl_space *isl_space_params(
968 __isl_take isl_space *space);
969 __isl_give isl_space *isl_space_set_from_params(
970 __isl_take isl_space *space);
971 __isl_give isl_space *isl_space_reverse(__isl_take isl_space *space);
972 __isl_give isl_space *isl_space_join(__isl_take isl_space *left,
973 __isl_take isl_space *right);
974 __isl_give isl_space *isl_space_align_params(
975 __isl_take isl_space *space1, __isl_take isl_space *space2)
976 __isl_give isl_space *isl_space_insert_dims(__isl_take isl_space *space,
977 enum isl_dim_type type, unsigned pos, unsigned n);
978 __isl_give isl_space *isl_space_add_dims(__isl_take isl_space *space,
979 enum isl_dim_type type, unsigned n);
980 __isl_give isl_space *isl_space_drop_dims(__isl_take isl_space *space,
981 enum isl_dim_type type, unsigned first, unsigned n);
982 __isl_give isl_space *isl_space_move_dims(__isl_take isl_space *space,
983 enum isl_dim_type dst_type, unsigned dst_pos,
984 enum isl_dim_type src_type, unsigned src_pos,
986 __isl_give isl_space *isl_space_map_from_set(
987 __isl_take isl_space *space);
988 __isl_give isl_space *isl_space_map_from_domain_and_range(
989 __isl_take isl_space *domain,
990 __isl_take isl_space *range);
991 __isl_give isl_space *isl_space_zip(__isl_take isl_space *space);
992 __isl_give isl_space *isl_space_curry(
993 __isl_take isl_space *space);
994 __isl_give isl_space *isl_space_uncurry(
995 __isl_take isl_space *space);
997 Note that if dimensions are added or removed from a space, then
998 the name and the internal structure are lost.
1002 A local space is essentially a space with
1003 zero or more existentially quantified variables.
1004 The local space of a (constraint of a) basic set or relation can be obtained
1005 using the following functions.
1007 #include <isl/constraint.h>
1008 __isl_give isl_local_space *isl_constraint_get_local_space(
1009 __isl_keep isl_constraint *constraint);
1011 #include <isl/set.h>
1012 __isl_give isl_local_space *isl_basic_set_get_local_space(
1013 __isl_keep isl_basic_set *bset);
1015 #include <isl/map.h>
1016 __isl_give isl_local_space *isl_basic_map_get_local_space(
1017 __isl_keep isl_basic_map *bmap);
1019 A new local space can be created from a space using
1021 #include <isl/local_space.h>
1022 __isl_give isl_local_space *isl_local_space_from_space(
1023 __isl_take isl_space *space);
1025 They can be inspected, modified, copied and freed using the following functions.
1027 #include <isl/local_space.h>
1028 isl_ctx *isl_local_space_get_ctx(
1029 __isl_keep isl_local_space *ls);
1030 int isl_local_space_is_set(__isl_keep isl_local_space *ls);
1031 int isl_local_space_dim(__isl_keep isl_local_space *ls,
1032 enum isl_dim_type type);
1033 __isl_give isl_local_space *isl_local_space_set_tuple_id(
1034 __isl_take isl_local_space *ls,
1035 enum isl_dim_type type, __isl_take isl_id *id);
1036 int isl_local_space_has_dim_id(
1037 __isl_keep isl_local_space *ls,
1038 enum isl_dim_type type, unsigned pos);
1039 __isl_give isl_id *isl_local_space_get_dim_id(
1040 __isl_keep isl_local_space *ls,
1041 enum isl_dim_type type, unsigned pos);
1042 int isl_local_space_has_dim_name(
1043 __isl_keep isl_local_space *ls,
1044 enum isl_dim_type type, unsigned pos)
1045 const char *isl_local_space_get_dim_name(
1046 __isl_keep isl_local_space *ls,
1047 enum isl_dim_type type, unsigned pos);
1048 __isl_give isl_local_space *isl_local_space_set_dim_name(
1049 __isl_take isl_local_space *ls,
1050 enum isl_dim_type type, unsigned pos, const char *s);
1051 __isl_give isl_local_space *isl_local_space_set_dim_id(
1052 __isl_take isl_local_space *ls,
1053 enum isl_dim_type type, unsigned pos,
1054 __isl_take isl_id *id);
1055 __isl_give isl_space *isl_local_space_get_space(
1056 __isl_keep isl_local_space *ls);
1057 __isl_give isl_aff *isl_local_space_get_div(
1058 __isl_keep isl_local_space *ls, int pos);
1059 __isl_give isl_local_space *isl_local_space_copy(
1060 __isl_keep isl_local_space *ls);
1061 void *isl_local_space_free(__isl_take isl_local_space *ls);
1063 Note that C<isl_local_space_get_div> can only be used on local spaces
1066 Two local spaces can be compared using
1068 int isl_local_space_is_equal(__isl_keep isl_local_space *ls1,
1069 __isl_keep isl_local_space *ls2);
1071 Local spaces can be created from other local spaces
1072 using the following functions.
1074 __isl_give isl_local_space *isl_local_space_domain(
1075 __isl_take isl_local_space *ls);
1076 __isl_give isl_local_space *isl_local_space_range(
1077 __isl_take isl_local_space *ls);
1078 __isl_give isl_local_space *isl_local_space_from_domain(
1079 __isl_take isl_local_space *ls);
1080 __isl_give isl_local_space *isl_local_space_intersect(
1081 __isl_take isl_local_space *ls1,
1082 __isl_take isl_local_space *ls2);
1083 __isl_give isl_local_space *isl_local_space_add_dims(
1084 __isl_take isl_local_space *ls,
1085 enum isl_dim_type type, unsigned n);
1086 __isl_give isl_local_space *isl_local_space_insert_dims(
1087 __isl_take isl_local_space *ls,
1088 enum isl_dim_type type, unsigned first, unsigned n);
1089 __isl_give isl_local_space *isl_local_space_drop_dims(
1090 __isl_take isl_local_space *ls,
1091 enum isl_dim_type type, unsigned first, unsigned n);
1093 =head2 Input and Output
1095 C<isl> supports its own input/output format, which is similar
1096 to the C<Omega> format, but also supports the C<PolyLib> format
1099 =head3 C<isl> format
1101 The C<isl> format is similar to that of C<Omega>, but has a different
1102 syntax for describing the parameters and allows for the definition
1103 of an existentially quantified variable as the integer division
1104 of an affine expression.
1105 For example, the set of integers C<i> between C<0> and C<n>
1106 such that C<i % 10 <= 6> can be described as
1108 [n] -> { [i] : exists (a = [i/10] : 0 <= i and i <= n and
1111 A set or relation can have several disjuncts, separated
1112 by the keyword C<or>. Each disjunct is either a conjunction
1113 of constraints or a projection (C<exists>) of a conjunction
1114 of constraints. The constraints are separated by the keyword
1117 =head3 C<PolyLib> format
1119 If the represented set is a union, then the first line
1120 contains a single number representing the number of disjuncts.
1121 Otherwise, a line containing the number C<1> is optional.
1123 Each disjunct is represented by a matrix of constraints.
1124 The first line contains two numbers representing
1125 the number of rows and columns,
1126 where the number of rows is equal to the number of constraints
1127 and the number of columns is equal to two plus the number of variables.
1128 The following lines contain the actual rows of the constraint matrix.
1129 In each row, the first column indicates whether the constraint
1130 is an equality (C<0>) or inequality (C<1>). The final column
1131 corresponds to the constant term.
1133 If the set is parametric, then the coefficients of the parameters
1134 appear in the last columns before the constant column.
1135 The coefficients of any existentially quantified variables appear
1136 between those of the set variables and those of the parameters.
1138 =head3 Extended C<PolyLib> format
1140 The extended C<PolyLib> format is nearly identical to the
1141 C<PolyLib> format. The only difference is that the line
1142 containing the number of rows and columns of a constraint matrix
1143 also contains four additional numbers:
1144 the number of output dimensions, the number of input dimensions,
1145 the number of local dimensions (i.e., the number of existentially
1146 quantified variables) and the number of parameters.
1147 For sets, the number of ``output'' dimensions is equal
1148 to the number of set dimensions, while the number of ``input''
1153 #include <isl/set.h>
1154 __isl_give isl_basic_set *isl_basic_set_read_from_file(
1155 isl_ctx *ctx, FILE *input);
1156 __isl_give isl_basic_set *isl_basic_set_read_from_str(
1157 isl_ctx *ctx, const char *str);
1158 __isl_give isl_set *isl_set_read_from_file(isl_ctx *ctx,
1160 __isl_give isl_set *isl_set_read_from_str(isl_ctx *ctx,
1163 #include <isl/map.h>
1164 __isl_give isl_basic_map *isl_basic_map_read_from_file(
1165 isl_ctx *ctx, FILE *input);
1166 __isl_give isl_basic_map *isl_basic_map_read_from_str(
1167 isl_ctx *ctx, const char *str);
1168 __isl_give isl_map *isl_map_read_from_file(
1169 isl_ctx *ctx, FILE *input);
1170 __isl_give isl_map *isl_map_read_from_str(isl_ctx *ctx,
1173 #include <isl/union_set.h>
1174 __isl_give isl_union_set *isl_union_set_read_from_file(
1175 isl_ctx *ctx, FILE *input);
1176 __isl_give isl_union_set *isl_union_set_read_from_str(
1177 isl_ctx *ctx, const char *str);
1179 #include <isl/union_map.h>
1180 __isl_give isl_union_map *isl_union_map_read_from_file(
1181 isl_ctx *ctx, FILE *input);
1182 __isl_give isl_union_map *isl_union_map_read_from_str(
1183 isl_ctx *ctx, const char *str);
1185 The input format is autodetected and may be either the C<PolyLib> format
1186 or the C<isl> format.
1190 Before anything can be printed, an C<isl_printer> needs to
1193 __isl_give isl_printer *isl_printer_to_file(isl_ctx *ctx,
1195 __isl_give isl_printer *isl_printer_to_str(isl_ctx *ctx);
1196 void *isl_printer_free(__isl_take isl_printer *printer);
1197 __isl_give char *isl_printer_get_str(
1198 __isl_keep isl_printer *printer);
1200 The printer can be inspected using the following functions.
1202 FILE *isl_printer_get_file(
1203 __isl_keep isl_printer *printer);
1204 int isl_printer_get_output_format(
1205 __isl_keep isl_printer *p);
1207 The behavior of the printer can be modified in various ways
1209 __isl_give isl_printer *isl_printer_set_output_format(
1210 __isl_take isl_printer *p, int output_format);
1211 __isl_give isl_printer *isl_printer_set_indent(
1212 __isl_take isl_printer *p, int indent);
1213 __isl_give isl_printer *isl_printer_indent(
1214 __isl_take isl_printer *p, int indent);
1215 __isl_give isl_printer *isl_printer_set_prefix(
1216 __isl_take isl_printer *p, const char *prefix);
1217 __isl_give isl_printer *isl_printer_set_suffix(
1218 __isl_take isl_printer *p, const char *suffix);
1220 The C<output_format> may be either C<ISL_FORMAT_ISL>, C<ISL_FORMAT_OMEGA>,
1221 C<ISL_FORMAT_POLYLIB>, C<ISL_FORMAT_EXT_POLYLIB> or C<ISL_FORMAT_LATEX>
1222 and defaults to C<ISL_FORMAT_ISL>.
1223 Each line in the output is indented by C<indent> (set by
1224 C<isl_printer_set_indent>) spaces
1225 (default: 0), prefixed by C<prefix> and suffixed by C<suffix>.
1226 In the C<PolyLib> format output,
1227 the coefficients of the existentially quantified variables
1228 appear between those of the set variables and those
1230 The function C<isl_printer_indent> increases the indentation
1231 by the specified amount (which may be negative).
1233 To actually print something, use
1235 #include <isl/printer.h>
1236 __isl_give isl_printer *isl_printer_print_double(
1237 __isl_take isl_printer *p, double d);
1239 #include <isl/set.h>
1240 __isl_give isl_printer *isl_printer_print_basic_set(
1241 __isl_take isl_printer *printer,
1242 __isl_keep isl_basic_set *bset);
1243 __isl_give isl_printer *isl_printer_print_set(
1244 __isl_take isl_printer *printer,
1245 __isl_keep isl_set *set);
1247 #include <isl/map.h>
1248 __isl_give isl_printer *isl_printer_print_basic_map(
1249 __isl_take isl_printer *printer,
1250 __isl_keep isl_basic_map *bmap);
1251 __isl_give isl_printer *isl_printer_print_map(
1252 __isl_take isl_printer *printer,
1253 __isl_keep isl_map *map);
1255 #include <isl/union_set.h>
1256 __isl_give isl_printer *isl_printer_print_union_set(
1257 __isl_take isl_printer *p,
1258 __isl_keep isl_union_set *uset);
1260 #include <isl/union_map.h>
1261 __isl_give isl_printer *isl_printer_print_union_map(
1262 __isl_take isl_printer *p,
1263 __isl_keep isl_union_map *umap);
1265 When called on a file printer, the following function flushes
1266 the file. When called on a string printer, the buffer is cleared.
1268 __isl_give isl_printer *isl_printer_flush(
1269 __isl_take isl_printer *p);
1271 =head2 Creating New Sets and Relations
1273 C<isl> has functions for creating some standard sets and relations.
1277 =item * Empty sets and relations
1279 __isl_give isl_basic_set *isl_basic_set_empty(
1280 __isl_take isl_space *space);
1281 __isl_give isl_basic_map *isl_basic_map_empty(
1282 __isl_take isl_space *space);
1283 __isl_give isl_set *isl_set_empty(
1284 __isl_take isl_space *space);
1285 __isl_give isl_map *isl_map_empty(
1286 __isl_take isl_space *space);
1287 __isl_give isl_union_set *isl_union_set_empty(
1288 __isl_take isl_space *space);
1289 __isl_give isl_union_map *isl_union_map_empty(
1290 __isl_take isl_space *space);
1292 For C<isl_union_set>s and C<isl_union_map>s, the space
1293 is only used to specify the parameters.
1295 =item * Universe sets and relations
1297 __isl_give isl_basic_set *isl_basic_set_universe(
1298 __isl_take isl_space *space);
1299 __isl_give isl_basic_map *isl_basic_map_universe(
1300 __isl_take isl_space *space);
1301 __isl_give isl_set *isl_set_universe(
1302 __isl_take isl_space *space);
1303 __isl_give isl_map *isl_map_universe(
1304 __isl_take isl_space *space);
1305 __isl_give isl_union_set *isl_union_set_universe(
1306 __isl_take isl_union_set *uset);
1307 __isl_give isl_union_map *isl_union_map_universe(
1308 __isl_take isl_union_map *umap);
1310 The sets and relations constructed by the functions above
1311 contain all integer values, while those constructed by the
1312 functions below only contain non-negative values.
1314 __isl_give isl_basic_set *isl_basic_set_nat_universe(
1315 __isl_take isl_space *space);
1316 __isl_give isl_basic_map *isl_basic_map_nat_universe(
1317 __isl_take isl_space *space);
1318 __isl_give isl_set *isl_set_nat_universe(
1319 __isl_take isl_space *space);
1320 __isl_give isl_map *isl_map_nat_universe(
1321 __isl_take isl_space *space);
1323 =item * Identity relations
1325 __isl_give isl_basic_map *isl_basic_map_identity(
1326 __isl_take isl_space *space);
1327 __isl_give isl_map *isl_map_identity(
1328 __isl_take isl_space *space);
1330 The number of input and output dimensions in C<space> needs
1333 =item * Lexicographic order
1335 __isl_give isl_map *isl_map_lex_lt(
1336 __isl_take isl_space *set_space);
1337 __isl_give isl_map *isl_map_lex_le(
1338 __isl_take isl_space *set_space);
1339 __isl_give isl_map *isl_map_lex_gt(
1340 __isl_take isl_space *set_space);
1341 __isl_give isl_map *isl_map_lex_ge(
1342 __isl_take isl_space *set_space);
1343 __isl_give isl_map *isl_map_lex_lt_first(
1344 __isl_take isl_space *space, unsigned n);
1345 __isl_give isl_map *isl_map_lex_le_first(
1346 __isl_take isl_space *space, unsigned n);
1347 __isl_give isl_map *isl_map_lex_gt_first(
1348 __isl_take isl_space *space, unsigned n);
1349 __isl_give isl_map *isl_map_lex_ge_first(
1350 __isl_take isl_space *space, unsigned n);
1352 The first four functions take a space for a B<set>
1353 and return relations that express that the elements in the domain
1354 are lexicographically less
1355 (C<isl_map_lex_lt>), less or equal (C<isl_map_lex_le>),
1356 greater (C<isl_map_lex_gt>) or greater or equal (C<isl_map_lex_ge>)
1357 than the elements in the range.
1358 The last four functions take a space for a map
1359 and return relations that express that the first C<n> dimensions
1360 in the domain are lexicographically less
1361 (C<isl_map_lex_lt_first>), less or equal (C<isl_map_lex_le_first>),
1362 greater (C<isl_map_lex_gt_first>) or greater or equal (C<isl_map_lex_ge_first>)
1363 than the first C<n> dimensions in the range.
1367 A basic set or relation can be converted to a set or relation
1368 using the following functions.
1370 __isl_give isl_set *isl_set_from_basic_set(
1371 __isl_take isl_basic_set *bset);
1372 __isl_give isl_map *isl_map_from_basic_map(
1373 __isl_take isl_basic_map *bmap);
1375 Sets and relations can be converted to union sets and relations
1376 using the following functions.
1378 __isl_give isl_union_set *isl_union_set_from_basic_set(
1379 __isl_take isl_basic_set *bset);
1380 __isl_give isl_union_map *isl_union_map_from_basic_map(
1381 __isl_take isl_basic_map *bmap);
1382 __isl_give isl_union_set *isl_union_set_from_set(
1383 __isl_take isl_set *set);
1384 __isl_give isl_union_map *isl_union_map_from_map(
1385 __isl_take isl_map *map);
1387 The inverse conversions below can only be used if the input
1388 union set or relation is known to contain elements in exactly one
1391 __isl_give isl_set *isl_set_from_union_set(
1392 __isl_take isl_union_set *uset);
1393 __isl_give isl_map *isl_map_from_union_map(
1394 __isl_take isl_union_map *umap);
1396 A zero-dimensional (basic) set can be constructed on a given parameter domain
1397 using the following function.
1399 __isl_give isl_basic_set *isl_basic_set_from_params(
1400 __isl_take isl_basic_set *bset);
1401 __isl_give isl_set *isl_set_from_params(
1402 __isl_take isl_set *set);
1404 Sets and relations can be copied and freed again using the following
1407 __isl_give isl_basic_set *isl_basic_set_copy(
1408 __isl_keep isl_basic_set *bset);
1409 __isl_give isl_set *isl_set_copy(__isl_keep isl_set *set);
1410 __isl_give isl_union_set *isl_union_set_copy(
1411 __isl_keep isl_union_set *uset);
1412 __isl_give isl_basic_map *isl_basic_map_copy(
1413 __isl_keep isl_basic_map *bmap);
1414 __isl_give isl_map *isl_map_copy(__isl_keep isl_map *map);
1415 __isl_give isl_union_map *isl_union_map_copy(
1416 __isl_keep isl_union_map *umap);
1417 void *isl_basic_set_free(__isl_take isl_basic_set *bset);
1418 void *isl_set_free(__isl_take isl_set *set);
1419 void *isl_union_set_free(__isl_take isl_union_set *uset);
1420 void *isl_basic_map_free(__isl_take isl_basic_map *bmap);
1421 void *isl_map_free(__isl_take isl_map *map);
1422 void *isl_union_map_free(__isl_take isl_union_map *umap);
1424 Other sets and relations can be constructed by starting
1425 from a universe set or relation, adding equality and/or
1426 inequality constraints and then projecting out the
1427 existentially quantified variables, if any.
1428 Constraints can be constructed, manipulated and
1429 added to (or removed from) (basic) sets and relations
1430 using the following functions.
1432 #include <isl/constraint.h>
1433 __isl_give isl_constraint *isl_equality_alloc(
1434 __isl_take isl_local_space *ls);
1435 __isl_give isl_constraint *isl_inequality_alloc(
1436 __isl_take isl_local_space *ls);
1437 __isl_give isl_constraint *isl_constraint_set_constant_si(
1438 __isl_take isl_constraint *constraint, int v);
1439 __isl_give isl_constraint *isl_constraint_set_constant_val(
1440 __isl_take isl_constraint *constraint,
1441 __isl_take isl_val *v);
1442 __isl_give isl_constraint *isl_constraint_set_coefficient_si(
1443 __isl_take isl_constraint *constraint,
1444 enum isl_dim_type type, int pos, int v);
1445 __isl_give isl_constraint *
1446 isl_constraint_set_coefficient_val(
1447 __isl_take isl_constraint *constraint,
1448 enum isl_dim_type type, int pos, isl_val *v);
1449 __isl_give isl_basic_map *isl_basic_map_add_constraint(
1450 __isl_take isl_basic_map *bmap,
1451 __isl_take isl_constraint *constraint);
1452 __isl_give isl_basic_set *isl_basic_set_add_constraint(
1453 __isl_take isl_basic_set *bset,
1454 __isl_take isl_constraint *constraint);
1455 __isl_give isl_map *isl_map_add_constraint(
1456 __isl_take isl_map *map,
1457 __isl_take isl_constraint *constraint);
1458 __isl_give isl_set *isl_set_add_constraint(
1459 __isl_take isl_set *set,
1460 __isl_take isl_constraint *constraint);
1461 __isl_give isl_basic_set *isl_basic_set_drop_constraint(
1462 __isl_take isl_basic_set *bset,
1463 __isl_take isl_constraint *constraint);
1465 For example, to create a set containing the even integers
1466 between 10 and 42, you would use the following code.
1469 isl_local_space *ls;
1471 isl_basic_set *bset;
1473 space = isl_space_set_alloc(ctx, 0, 2);
1474 bset = isl_basic_set_universe(isl_space_copy(space));
1475 ls = isl_local_space_from_space(space);
1477 c = isl_equality_alloc(isl_local_space_copy(ls));
1478 c = isl_constraint_set_coefficient_si(c, isl_dim_set, 0, -1);
1479 c = isl_constraint_set_coefficient_si(c, isl_dim_set, 1, 2);
1480 bset = isl_basic_set_add_constraint(bset, c);
1482 c = isl_inequality_alloc(isl_local_space_copy(ls));
1483 c = isl_constraint_set_constant_si(c, -10);
1484 c = isl_constraint_set_coefficient_si(c, isl_dim_set, 0, 1);
1485 bset = isl_basic_set_add_constraint(bset, c);
1487 c = isl_inequality_alloc(ls);
1488 c = isl_constraint_set_constant_si(c, 42);
1489 c = isl_constraint_set_coefficient_si(c, isl_dim_set, 0, -1);
1490 bset = isl_basic_set_add_constraint(bset, c);
1492 bset = isl_basic_set_project_out(bset, isl_dim_set, 1, 1);
1496 isl_basic_set *bset;
1497 bset = isl_basic_set_read_from_str(ctx,
1498 "{[i] : exists (a : i = 2a and i >= 10 and i <= 42)}");
1500 A basic set or relation can also be constructed from two matrices
1501 describing the equalities and the inequalities.
1503 __isl_give isl_basic_set *isl_basic_set_from_constraint_matrices(
1504 __isl_take isl_space *space,
1505 __isl_take isl_mat *eq, __isl_take isl_mat *ineq,
1506 enum isl_dim_type c1,
1507 enum isl_dim_type c2, enum isl_dim_type c3,
1508 enum isl_dim_type c4);
1509 __isl_give isl_basic_map *isl_basic_map_from_constraint_matrices(
1510 __isl_take isl_space *space,
1511 __isl_take isl_mat *eq, __isl_take isl_mat *ineq,
1512 enum isl_dim_type c1,
1513 enum isl_dim_type c2, enum isl_dim_type c3,
1514 enum isl_dim_type c4, enum isl_dim_type c5);
1516 The C<isl_dim_type> arguments indicate the order in which
1517 different kinds of variables appear in the input matrices
1518 and should be a permutation of C<isl_dim_cst>, C<isl_dim_param>,
1519 C<isl_dim_set> and C<isl_dim_div> for sets and
1520 of C<isl_dim_cst>, C<isl_dim_param>,
1521 C<isl_dim_in>, C<isl_dim_out> and C<isl_dim_div> for relations.
1523 A (basic or union) set or relation can also be constructed from a
1524 (union) (piecewise) (multiple) affine expression
1525 or a list of affine expressions
1526 (See L<"Piecewise Quasi Affine Expressions"> and
1527 L<"Piecewise Multiple Quasi Affine Expressions">).
1529 __isl_give isl_basic_map *isl_basic_map_from_aff(
1530 __isl_take isl_aff *aff);
1531 __isl_give isl_map *isl_map_from_aff(
1532 __isl_take isl_aff *aff);
1533 __isl_give isl_set *isl_set_from_pw_aff(
1534 __isl_take isl_pw_aff *pwaff);
1535 __isl_give isl_map *isl_map_from_pw_aff(
1536 __isl_take isl_pw_aff *pwaff);
1537 __isl_give isl_basic_map *isl_basic_map_from_aff_list(
1538 __isl_take isl_space *domain_space,
1539 __isl_take isl_aff_list *list);
1540 __isl_give isl_basic_map *isl_basic_map_from_multi_aff(
1541 __isl_take isl_multi_aff *maff)
1542 __isl_give isl_map *isl_map_from_multi_aff(
1543 __isl_take isl_multi_aff *maff)
1544 __isl_give isl_set *isl_set_from_pw_multi_aff(
1545 __isl_take isl_pw_multi_aff *pma);
1546 __isl_give isl_map *isl_map_from_pw_multi_aff(
1547 __isl_take isl_pw_multi_aff *pma);
1548 __isl_give isl_set *isl_set_from_multi_pw_aff(
1549 __isl_take isl_multi_pw_aff *mpa);
1550 __isl_give isl_map *isl_map_from_multi_pw_aff(
1551 __isl_take isl_multi_pw_aff *mpa);
1552 __isl_give isl_union_map *
1553 isl_union_map_from_union_pw_multi_aff(
1554 __isl_take isl_union_pw_multi_aff *upma);
1556 The C<domain_dim> argument describes the domain of the resulting
1557 basic relation. It is required because the C<list> may consist
1558 of zero affine expressions.
1560 =head2 Inspecting Sets and Relations
1562 Usually, the user should not have to care about the actual constraints
1563 of the sets and maps, but should instead apply the abstract operations
1564 explained in the following sections.
1565 Occasionally, however, it may be required to inspect the individual
1566 coefficients of the constraints. This section explains how to do so.
1567 In these cases, it may also be useful to have C<isl> compute
1568 an explicit representation of the existentially quantified variables.
1570 __isl_give isl_set *isl_set_compute_divs(
1571 __isl_take isl_set *set);
1572 __isl_give isl_map *isl_map_compute_divs(
1573 __isl_take isl_map *map);
1574 __isl_give isl_union_set *isl_union_set_compute_divs(
1575 __isl_take isl_union_set *uset);
1576 __isl_give isl_union_map *isl_union_map_compute_divs(
1577 __isl_take isl_union_map *umap);
1579 This explicit representation defines the existentially quantified
1580 variables as integer divisions of the other variables, possibly
1581 including earlier existentially quantified variables.
1582 An explicitly represented existentially quantified variable therefore
1583 has a unique value when the values of the other variables are known.
1584 If, furthermore, the same existentials, i.e., existentials
1585 with the same explicit representations, should appear in the
1586 same order in each of the disjuncts of a set or map, then the user should call
1587 either of the following functions.
1589 __isl_give isl_set *isl_set_align_divs(
1590 __isl_take isl_set *set);
1591 __isl_give isl_map *isl_map_align_divs(
1592 __isl_take isl_map *map);
1594 Alternatively, the existentially quantified variables can be removed
1595 using the following functions, which compute an overapproximation.
1597 __isl_give isl_basic_set *isl_basic_set_remove_divs(
1598 __isl_take isl_basic_set *bset);
1599 __isl_give isl_basic_map *isl_basic_map_remove_divs(
1600 __isl_take isl_basic_map *bmap);
1601 __isl_give isl_set *isl_set_remove_divs(
1602 __isl_take isl_set *set);
1603 __isl_give isl_map *isl_map_remove_divs(
1604 __isl_take isl_map *map);
1606 It is also possible to only remove those divs that are defined
1607 in terms of a given range of dimensions or only those for which
1608 no explicit representation is known.
1610 __isl_give isl_basic_set *
1611 isl_basic_set_remove_divs_involving_dims(
1612 __isl_take isl_basic_set *bset,
1613 enum isl_dim_type type,
1614 unsigned first, unsigned n);
1615 __isl_give isl_basic_map *
1616 isl_basic_map_remove_divs_involving_dims(
1617 __isl_take isl_basic_map *bmap,
1618 enum isl_dim_type type,
1619 unsigned first, unsigned n);
1620 __isl_give isl_set *isl_set_remove_divs_involving_dims(
1621 __isl_take isl_set *set, enum isl_dim_type type,
1622 unsigned first, unsigned n);
1623 __isl_give isl_map *isl_map_remove_divs_involving_dims(
1624 __isl_take isl_map *map, enum isl_dim_type type,
1625 unsigned first, unsigned n);
1627 __isl_give isl_basic_set *
1628 isl_basic_set_remove_unknown_divs(
1629 __isl_take isl_basic_set *bset);
1630 __isl_give isl_set *isl_set_remove_unknown_divs(
1631 __isl_take isl_set *set);
1632 __isl_give isl_map *isl_map_remove_unknown_divs(
1633 __isl_take isl_map *map);
1635 To iterate over all the sets or maps in a union set or map, use
1637 int isl_union_set_foreach_set(__isl_keep isl_union_set *uset,
1638 int (*fn)(__isl_take isl_set *set, void *user),
1640 int isl_union_map_foreach_map(__isl_keep isl_union_map *umap,
1641 int (*fn)(__isl_take isl_map *map, void *user),
1644 The number of sets or maps in a union set or map can be obtained
1647 int isl_union_set_n_set(__isl_keep isl_union_set *uset);
1648 int isl_union_map_n_map(__isl_keep isl_union_map *umap);
1650 To extract the set or map in a given space from a union, use
1652 __isl_give isl_set *isl_union_set_extract_set(
1653 __isl_keep isl_union_set *uset,
1654 __isl_take isl_space *space);
1655 __isl_give isl_map *isl_union_map_extract_map(
1656 __isl_keep isl_union_map *umap,
1657 __isl_take isl_space *space);
1659 To iterate over all the basic sets or maps in a set or map, use
1661 int isl_set_foreach_basic_set(__isl_keep isl_set *set,
1662 int (*fn)(__isl_take isl_basic_set *bset, void *user),
1664 int isl_map_foreach_basic_map(__isl_keep isl_map *map,
1665 int (*fn)(__isl_take isl_basic_map *bmap, void *user),
1668 The callback function C<fn> should return 0 if successful and
1669 -1 if an error occurs. In the latter case, or if any other error
1670 occurs, the above functions will return -1.
1672 It should be noted that C<isl> does not guarantee that
1673 the basic sets or maps passed to C<fn> are disjoint.
1674 If this is required, then the user should call one of
1675 the following functions first.
1677 __isl_give isl_set *isl_set_make_disjoint(
1678 __isl_take isl_set *set);
1679 __isl_give isl_map *isl_map_make_disjoint(
1680 __isl_take isl_map *map);
1682 The number of basic sets in a set can be obtained
1685 int isl_set_n_basic_set(__isl_keep isl_set *set);
1687 To iterate over the constraints of a basic set or map, use
1689 #include <isl/constraint.h>
1691 int isl_basic_set_n_constraint(
1692 __isl_keep isl_basic_set *bset);
1693 int isl_basic_set_foreach_constraint(
1694 __isl_keep isl_basic_set *bset,
1695 int (*fn)(__isl_take isl_constraint *c, void *user),
1697 int isl_basic_map_foreach_constraint(
1698 __isl_keep isl_basic_map *bmap,
1699 int (*fn)(__isl_take isl_constraint *c, void *user),
1701 void *isl_constraint_free(__isl_take isl_constraint *c);
1703 Again, the callback function C<fn> should return 0 if successful and
1704 -1 if an error occurs. In the latter case, or if any other error
1705 occurs, the above functions will return -1.
1706 The constraint C<c> represents either an equality or an inequality.
1707 Use the following function to find out whether a constraint
1708 represents an equality. If not, it represents an inequality.
1710 int isl_constraint_is_equality(
1711 __isl_keep isl_constraint *constraint);
1713 The coefficients of the constraints can be inspected using
1714 the following functions.
1716 int isl_constraint_is_lower_bound(
1717 __isl_keep isl_constraint *constraint,
1718 enum isl_dim_type type, unsigned pos);
1719 int isl_constraint_is_upper_bound(
1720 __isl_keep isl_constraint *constraint,
1721 enum isl_dim_type type, unsigned pos);
1722 __isl_give isl_val *isl_constraint_get_constant_val(
1723 __isl_keep isl_constraint *constraint);
1724 __isl_give isl_val *isl_constraint_get_coefficient_val(
1725 __isl_keep isl_constraint *constraint,
1726 enum isl_dim_type type, int pos);
1727 int isl_constraint_involves_dims(
1728 __isl_keep isl_constraint *constraint,
1729 enum isl_dim_type type, unsigned first, unsigned n);
1731 The explicit representations of the existentially quantified
1732 variables can be inspected using the following function.
1733 Note that the user is only allowed to use this function
1734 if the inspected set or map is the result of a call
1735 to C<isl_set_compute_divs> or C<isl_map_compute_divs>.
1736 The existentially quantified variable is equal to the floor
1737 of the returned affine expression. The affine expression
1738 itself can be inspected using the functions in
1739 L<"Piecewise Quasi Affine Expressions">.
1741 __isl_give isl_aff *isl_constraint_get_div(
1742 __isl_keep isl_constraint *constraint, int pos);
1744 To obtain the constraints of a basic set or map in matrix
1745 form, use the following functions.
1747 __isl_give isl_mat *isl_basic_set_equalities_matrix(
1748 __isl_keep isl_basic_set *bset,
1749 enum isl_dim_type c1, enum isl_dim_type c2,
1750 enum isl_dim_type c3, enum isl_dim_type c4);
1751 __isl_give isl_mat *isl_basic_set_inequalities_matrix(
1752 __isl_keep isl_basic_set *bset,
1753 enum isl_dim_type c1, enum isl_dim_type c2,
1754 enum isl_dim_type c3, enum isl_dim_type c4);
1755 __isl_give isl_mat *isl_basic_map_equalities_matrix(
1756 __isl_keep isl_basic_map *bmap,
1757 enum isl_dim_type c1,
1758 enum isl_dim_type c2, enum isl_dim_type c3,
1759 enum isl_dim_type c4, enum isl_dim_type c5);
1760 __isl_give isl_mat *isl_basic_map_inequalities_matrix(
1761 __isl_keep isl_basic_map *bmap,
1762 enum isl_dim_type c1,
1763 enum isl_dim_type c2, enum isl_dim_type c3,
1764 enum isl_dim_type c4, enum isl_dim_type c5);
1766 The C<isl_dim_type> arguments dictate the order in which
1767 different kinds of variables appear in the resulting matrix
1768 and should be a permutation of C<isl_dim_cst>, C<isl_dim_param>,
1769 C<isl_dim_in>, C<isl_dim_out> and C<isl_dim_div>.
1771 The number of parameters, input, output or set dimensions can
1772 be obtained using the following functions.
1774 unsigned isl_basic_set_dim(__isl_keep isl_basic_set *bset,
1775 enum isl_dim_type type);
1776 unsigned isl_basic_map_dim(__isl_keep isl_basic_map *bmap,
1777 enum isl_dim_type type);
1778 unsigned isl_set_dim(__isl_keep isl_set *set,
1779 enum isl_dim_type type);
1780 unsigned isl_map_dim(__isl_keep isl_map *map,
1781 enum isl_dim_type type);
1783 To check whether the description of a set or relation depends
1784 on one or more given dimensions, it is not necessary to iterate over all
1785 constraints. Instead the following functions can be used.
1787 int isl_basic_set_involves_dims(
1788 __isl_keep isl_basic_set *bset,
1789 enum isl_dim_type type, unsigned first, unsigned n);
1790 int isl_set_involves_dims(__isl_keep isl_set *set,
1791 enum isl_dim_type type, unsigned first, unsigned n);
1792 int isl_basic_map_involves_dims(
1793 __isl_keep isl_basic_map *bmap,
1794 enum isl_dim_type type, unsigned first, unsigned n);
1795 int isl_map_involves_dims(__isl_keep isl_map *map,
1796 enum isl_dim_type type, unsigned first, unsigned n);
1798 Similarly, the following functions can be used to check whether
1799 a given dimension is involved in any lower or upper bound.
1801 int isl_set_dim_has_any_lower_bound(__isl_keep isl_set *set,
1802 enum isl_dim_type type, unsigned pos);
1803 int isl_set_dim_has_any_upper_bound(__isl_keep isl_set *set,
1804 enum isl_dim_type type, unsigned pos);
1806 Note that these functions return true even if there is a bound on
1807 the dimension on only some of the basic sets of C<set>.
1808 To check if they have a bound for all of the basic sets in C<set>,
1809 use the following functions instead.
1811 int isl_set_dim_has_lower_bound(__isl_keep isl_set *set,
1812 enum isl_dim_type type, unsigned pos);
1813 int isl_set_dim_has_upper_bound(__isl_keep isl_set *set,
1814 enum isl_dim_type type, unsigned pos);
1816 The identifiers or names of the domain and range spaces of a set
1817 or relation can be read off or set using the following functions.
1819 __isl_give isl_basic_set *isl_basic_set_set_tuple_id(
1820 __isl_take isl_basic_set *bset,
1821 __isl_take isl_id *id);
1822 __isl_give isl_set *isl_set_set_tuple_id(
1823 __isl_take isl_set *set, __isl_take isl_id *id);
1824 __isl_give isl_set *isl_set_reset_tuple_id(
1825 __isl_take isl_set *set);
1826 int isl_set_has_tuple_id(__isl_keep isl_set *set);
1827 __isl_give isl_id *isl_set_get_tuple_id(
1828 __isl_keep isl_set *set);
1829 __isl_give isl_basic_map *isl_basic_map_set_tuple_id(
1830 __isl_take isl_basic_map *bmap,
1831 enum isl_dim_type type, __isl_take isl_id *id);
1832 __isl_give isl_map *isl_map_set_tuple_id(
1833 __isl_take isl_map *map, enum isl_dim_type type,
1834 __isl_take isl_id *id);
1835 __isl_give isl_map *isl_map_reset_tuple_id(
1836 __isl_take isl_map *map, enum isl_dim_type type);
1837 int isl_map_has_tuple_id(__isl_keep isl_map *map,
1838 enum isl_dim_type type);
1839 __isl_give isl_id *isl_map_get_tuple_id(
1840 __isl_keep isl_map *map, enum isl_dim_type type);
1842 const char *isl_basic_set_get_tuple_name(
1843 __isl_keep isl_basic_set *bset);
1844 __isl_give isl_basic_set *isl_basic_set_set_tuple_name(
1845 __isl_take isl_basic_set *set, const char *s);
1846 int isl_set_has_tuple_name(__isl_keep isl_set *set);
1847 const char *isl_set_get_tuple_name(
1848 __isl_keep isl_set *set);
1849 const char *isl_basic_map_get_tuple_name(
1850 __isl_keep isl_basic_map *bmap,
1851 enum isl_dim_type type);
1852 __isl_give isl_basic_map *isl_basic_map_set_tuple_name(
1853 __isl_take isl_basic_map *bmap,
1854 enum isl_dim_type type, const char *s);
1855 int isl_map_has_tuple_name(__isl_keep isl_map *map,
1856 enum isl_dim_type type);
1857 const char *isl_map_get_tuple_name(
1858 __isl_keep isl_map *map,
1859 enum isl_dim_type type);
1861 As with C<isl_space_get_tuple_name>, the value returned points to
1862 an internal data structure.
1863 The identifiers, positions or names of individual dimensions can be
1864 read off using the following functions.
1866 __isl_give isl_id *isl_basic_set_get_dim_id(
1867 __isl_keep isl_basic_set *bset,
1868 enum isl_dim_type type, unsigned pos);
1869 __isl_give isl_set *isl_set_set_dim_id(
1870 __isl_take isl_set *set, enum isl_dim_type type,
1871 unsigned pos, __isl_take isl_id *id);
1872 int isl_set_has_dim_id(__isl_keep isl_set *set,
1873 enum isl_dim_type type, unsigned pos);
1874 __isl_give isl_id *isl_set_get_dim_id(
1875 __isl_keep isl_set *set, enum isl_dim_type type,
1877 int isl_basic_map_has_dim_id(
1878 __isl_keep isl_basic_map *bmap,
1879 enum isl_dim_type type, unsigned pos);
1880 __isl_give isl_map *isl_map_set_dim_id(
1881 __isl_take isl_map *map, enum isl_dim_type type,
1882 unsigned pos, __isl_take isl_id *id);
1883 int isl_map_has_dim_id(__isl_keep isl_map *map,
1884 enum isl_dim_type type, unsigned pos);
1885 __isl_give isl_id *isl_map_get_dim_id(
1886 __isl_keep isl_map *map, enum isl_dim_type type,
1889 int isl_set_find_dim_by_id(__isl_keep isl_set *set,
1890 enum isl_dim_type type, __isl_keep isl_id *id);
1891 int isl_map_find_dim_by_id(__isl_keep isl_map *map,
1892 enum isl_dim_type type, __isl_keep isl_id *id);
1893 int isl_set_find_dim_by_name(__isl_keep isl_set *set,
1894 enum isl_dim_type type, const char *name);
1895 int isl_map_find_dim_by_name(__isl_keep isl_map *map,
1896 enum isl_dim_type type, const char *name);
1898 const char *isl_constraint_get_dim_name(
1899 __isl_keep isl_constraint *constraint,
1900 enum isl_dim_type type, unsigned pos);
1901 const char *isl_basic_set_get_dim_name(
1902 __isl_keep isl_basic_set *bset,
1903 enum isl_dim_type type, unsigned pos);
1904 int isl_set_has_dim_name(__isl_keep isl_set *set,
1905 enum isl_dim_type type, unsigned pos);
1906 const char *isl_set_get_dim_name(
1907 __isl_keep isl_set *set,
1908 enum isl_dim_type type, unsigned pos);
1909 const char *isl_basic_map_get_dim_name(
1910 __isl_keep isl_basic_map *bmap,
1911 enum isl_dim_type type, unsigned pos);
1912 int isl_map_has_dim_name(__isl_keep isl_map *map,
1913 enum isl_dim_type type, unsigned pos);
1914 const char *isl_map_get_dim_name(
1915 __isl_keep isl_map *map,
1916 enum isl_dim_type type, unsigned pos);
1918 These functions are mostly useful to obtain the identifiers, positions
1919 or names of the parameters. Identifiers of individual dimensions are
1920 essentially only useful for printing. They are ignored by all other
1921 operations and may not be preserved across those operations.
1923 The user pointers on all parameters and tuples can be reset
1924 using the following functions.
1926 __isl_give isl_set *isl_set_reset_user(
1927 __isl_take isl_set *set);
1928 __isl_give isl_map *isl_map_reset_user(
1929 __isl_take isl_map *map);
1933 =head3 Unary Properties
1939 The following functions test whether the given set or relation
1940 contains any integer points. The ``plain'' variants do not perform
1941 any computations, but simply check if the given set or relation
1942 is already known to be empty.
1944 int isl_basic_set_plain_is_empty(__isl_keep isl_basic_set *bset);
1945 int isl_basic_set_is_empty(__isl_keep isl_basic_set *bset);
1946 int isl_set_plain_is_empty(__isl_keep isl_set *set);
1947 int isl_set_is_empty(__isl_keep isl_set *set);
1948 int isl_union_set_is_empty(__isl_keep isl_union_set *uset);
1949 int isl_basic_map_plain_is_empty(__isl_keep isl_basic_map *bmap);
1950 int isl_basic_map_is_empty(__isl_keep isl_basic_map *bmap);
1951 int isl_map_plain_is_empty(__isl_keep isl_map *map);
1952 int isl_map_is_empty(__isl_keep isl_map *map);
1953 int isl_union_map_is_empty(__isl_keep isl_union_map *umap);
1955 =item * Universality
1957 int isl_basic_set_is_universe(__isl_keep isl_basic_set *bset);
1958 int isl_basic_map_is_universe(__isl_keep isl_basic_map *bmap);
1959 int isl_set_plain_is_universe(__isl_keep isl_set *set);
1961 =item * Single-valuedness
1963 int isl_basic_map_is_single_valued(
1964 __isl_keep isl_basic_map *bmap);
1965 int isl_map_plain_is_single_valued(
1966 __isl_keep isl_map *map);
1967 int isl_map_is_single_valued(__isl_keep isl_map *map);
1968 int isl_union_map_is_single_valued(__isl_keep isl_union_map *umap);
1972 int isl_map_plain_is_injective(__isl_keep isl_map *map);
1973 int isl_map_is_injective(__isl_keep isl_map *map);
1974 int isl_union_map_plain_is_injective(
1975 __isl_keep isl_union_map *umap);
1976 int isl_union_map_is_injective(
1977 __isl_keep isl_union_map *umap);
1981 int isl_map_is_bijective(__isl_keep isl_map *map);
1982 int isl_union_map_is_bijective(__isl_keep isl_union_map *umap);
1986 __isl_give isl_val *
1987 isl_basic_map_plain_get_val_if_fixed(
1988 __isl_keep isl_basic_map *bmap,
1989 enum isl_dim_type type, unsigned pos);
1990 __isl_give isl_val *isl_set_plain_get_val_if_fixed(
1991 __isl_keep isl_set *set,
1992 enum isl_dim_type type, unsigned pos);
1993 __isl_give isl_val *isl_map_plain_get_val_if_fixed(
1994 __isl_keep isl_map *map,
1995 enum isl_dim_type type, unsigned pos);
1997 If the set or relation obviously lies on a hyperplane where the given dimension
1998 has a fixed value, then return that value.
1999 Otherwise return NaN.
2003 int isl_set_dim_residue_class_val(
2004 __isl_keep isl_set *set,
2005 int pos, __isl_give isl_val **modulo,
2006 __isl_give isl_val **residue);
2008 Check if the values of the given set dimension are equal to a fixed
2009 value modulo some integer value. If so, assign the modulo to C<*modulo>
2010 and the fixed value to C<*residue>. If the given dimension attains only
2011 a single value, then assign C<0> to C<*modulo> and the fixed value to
2013 If the dimension does not attain only a single value and if no modulo
2014 can be found then assign C<1> to C<*modulo> and C<1> to C<*residue>.
2018 To check whether a set is a parameter domain, use this function:
2020 int isl_set_is_params(__isl_keep isl_set *set);
2021 int isl_union_set_is_params(
2022 __isl_keep isl_union_set *uset);
2026 The following functions check whether the space of the given
2027 (basic) set or relation range is a wrapped relation.
2029 int isl_basic_set_is_wrapping(
2030 __isl_keep isl_basic_set *bset);
2031 int isl_set_is_wrapping(__isl_keep isl_set *set);
2032 int isl_map_range_is_wrapping(
2033 __isl_keep isl_map *map);
2035 =item * Internal Product
2037 int isl_basic_map_can_zip(
2038 __isl_keep isl_basic_map *bmap);
2039 int isl_map_can_zip(__isl_keep isl_map *map);
2041 Check whether the product of domain and range of the given relation
2043 i.e., whether both domain and range are nested relations.
2047 int isl_basic_map_can_curry(
2048 __isl_keep isl_basic_map *bmap);
2049 int isl_map_can_curry(__isl_keep isl_map *map);
2051 Check whether the domain of the (basic) relation is a wrapped relation.
2053 int isl_basic_map_can_uncurry(
2054 __isl_keep isl_basic_map *bmap);
2055 int isl_map_can_uncurry(__isl_keep isl_map *map);
2057 Check whether the range of the (basic) relation is a wrapped relation.
2061 =head3 Binary Properties
2067 int isl_basic_set_plain_is_equal(
2068 __isl_keep isl_basic_set *bset1,
2069 __isl_keep isl_basic_set *bset2);
2070 int isl_set_plain_is_equal(__isl_keep isl_set *set1,
2071 __isl_keep isl_set *set2);
2072 int isl_set_is_equal(__isl_keep isl_set *set1,
2073 __isl_keep isl_set *set2);
2074 int isl_union_set_is_equal(
2075 __isl_keep isl_union_set *uset1,
2076 __isl_keep isl_union_set *uset2);
2077 int isl_basic_map_is_equal(
2078 __isl_keep isl_basic_map *bmap1,
2079 __isl_keep isl_basic_map *bmap2);
2080 int isl_map_is_equal(__isl_keep isl_map *map1,
2081 __isl_keep isl_map *map2);
2082 int isl_map_plain_is_equal(__isl_keep isl_map *map1,
2083 __isl_keep isl_map *map2);
2084 int isl_union_map_is_equal(
2085 __isl_keep isl_union_map *umap1,
2086 __isl_keep isl_union_map *umap2);
2088 =item * Disjointness
2090 int isl_basic_set_is_disjoint(
2091 __isl_keep isl_basic_set *bset1,
2092 __isl_keep isl_basic_set *bset2);
2093 int isl_set_plain_is_disjoint(__isl_keep isl_set *set1,
2094 __isl_keep isl_set *set2);
2095 int isl_set_is_disjoint(__isl_keep isl_set *set1,
2096 __isl_keep isl_set *set2);
2097 int isl_basic_map_is_disjoint(
2098 __isl_keep isl_basic_map *bmap1,
2099 __isl_keep isl_basic_map *bmap2);
2100 int isl_map_is_disjoint(__isl_keep isl_map *map1,
2101 __isl_keep isl_map *map2);
2105 int isl_basic_set_is_subset(
2106 __isl_keep isl_basic_set *bset1,
2107 __isl_keep isl_basic_set *bset2);
2108 int isl_set_is_subset(__isl_keep isl_set *set1,
2109 __isl_keep isl_set *set2);
2110 int isl_set_is_strict_subset(
2111 __isl_keep isl_set *set1,
2112 __isl_keep isl_set *set2);
2113 int isl_union_set_is_subset(
2114 __isl_keep isl_union_set *uset1,
2115 __isl_keep isl_union_set *uset2);
2116 int isl_union_set_is_strict_subset(
2117 __isl_keep isl_union_set *uset1,
2118 __isl_keep isl_union_set *uset2);
2119 int isl_basic_map_is_subset(
2120 __isl_keep isl_basic_map *bmap1,
2121 __isl_keep isl_basic_map *bmap2);
2122 int isl_basic_map_is_strict_subset(
2123 __isl_keep isl_basic_map *bmap1,
2124 __isl_keep isl_basic_map *bmap2);
2125 int isl_map_is_subset(
2126 __isl_keep isl_map *map1,
2127 __isl_keep isl_map *map2);
2128 int isl_map_is_strict_subset(
2129 __isl_keep isl_map *map1,
2130 __isl_keep isl_map *map2);
2131 int isl_union_map_is_subset(
2132 __isl_keep isl_union_map *umap1,
2133 __isl_keep isl_union_map *umap2);
2134 int isl_union_map_is_strict_subset(
2135 __isl_keep isl_union_map *umap1,
2136 __isl_keep isl_union_map *umap2);
2138 Check whether the first argument is a (strict) subset of the
2143 int isl_set_plain_cmp(__isl_keep isl_set *set1,
2144 __isl_keep isl_set *set2);
2146 This function is useful for sorting C<isl_set>s.
2147 The order depends on the internal representation of the inputs.
2148 The order is fixed over different calls to the function (assuming
2149 the internal representation of the inputs has not changed), but may
2150 change over different versions of C<isl>.
2154 =head2 Unary Operations
2160 __isl_give isl_set *isl_set_complement(
2161 __isl_take isl_set *set);
2162 __isl_give isl_map *isl_map_complement(
2163 __isl_take isl_map *map);
2167 __isl_give isl_basic_map *isl_basic_map_reverse(
2168 __isl_take isl_basic_map *bmap);
2169 __isl_give isl_map *isl_map_reverse(
2170 __isl_take isl_map *map);
2171 __isl_give isl_union_map *isl_union_map_reverse(
2172 __isl_take isl_union_map *umap);
2176 __isl_give isl_basic_set *isl_basic_set_project_out(
2177 __isl_take isl_basic_set *bset,
2178 enum isl_dim_type type, unsigned first, unsigned n);
2179 __isl_give isl_basic_map *isl_basic_map_project_out(
2180 __isl_take isl_basic_map *bmap,
2181 enum isl_dim_type type, unsigned first, unsigned n);
2182 __isl_give isl_set *isl_set_project_out(__isl_take isl_set *set,
2183 enum isl_dim_type type, unsigned first, unsigned n);
2184 __isl_give isl_map *isl_map_project_out(__isl_take isl_map *map,
2185 enum isl_dim_type type, unsigned first, unsigned n);
2186 __isl_give isl_basic_set *isl_basic_set_params(
2187 __isl_take isl_basic_set *bset);
2188 __isl_give isl_basic_set *isl_basic_map_domain(
2189 __isl_take isl_basic_map *bmap);
2190 __isl_give isl_basic_set *isl_basic_map_range(
2191 __isl_take isl_basic_map *bmap);
2192 __isl_give isl_set *isl_set_params(__isl_take isl_set *set);
2193 __isl_give isl_set *isl_map_params(__isl_take isl_map *map);
2194 __isl_give isl_set *isl_map_domain(
2195 __isl_take isl_map *bmap);
2196 __isl_give isl_set *isl_map_range(
2197 __isl_take isl_map *map);
2198 __isl_give isl_set *isl_union_set_params(
2199 __isl_take isl_union_set *uset);
2200 __isl_give isl_set *isl_union_map_params(
2201 __isl_take isl_union_map *umap);
2202 __isl_give isl_union_set *isl_union_map_domain(
2203 __isl_take isl_union_map *umap);
2204 __isl_give isl_union_set *isl_union_map_range(
2205 __isl_take isl_union_map *umap);
2207 __isl_give isl_basic_map *isl_basic_map_domain_map(
2208 __isl_take isl_basic_map *bmap);
2209 __isl_give isl_basic_map *isl_basic_map_range_map(
2210 __isl_take isl_basic_map *bmap);
2211 __isl_give isl_map *isl_map_domain_map(__isl_take isl_map *map);
2212 __isl_give isl_map *isl_map_range_map(__isl_take isl_map *map);
2213 __isl_give isl_union_map *isl_union_map_domain_map(
2214 __isl_take isl_union_map *umap);
2215 __isl_give isl_union_map *isl_union_map_range_map(
2216 __isl_take isl_union_map *umap);
2218 The functions above construct a (basic, regular or union) relation
2219 that maps (a wrapped version of) the input relation to its domain or range.
2223 __isl_give isl_basic_set *isl_basic_set_eliminate(
2224 __isl_take isl_basic_set *bset,
2225 enum isl_dim_type type,
2226 unsigned first, unsigned n);
2227 __isl_give isl_set *isl_set_eliminate(
2228 __isl_take isl_set *set, enum isl_dim_type type,
2229 unsigned first, unsigned n);
2230 __isl_give isl_basic_map *isl_basic_map_eliminate(
2231 __isl_take isl_basic_map *bmap,
2232 enum isl_dim_type type,
2233 unsigned first, unsigned n);
2234 __isl_give isl_map *isl_map_eliminate(
2235 __isl_take isl_map *map, enum isl_dim_type type,
2236 unsigned first, unsigned n);
2238 Eliminate the coefficients for the given dimensions from the constraints,
2239 without removing the dimensions.
2243 __isl_give isl_basic_set *isl_basic_set_fix_si(
2244 __isl_take isl_basic_set *bset,
2245 enum isl_dim_type type, unsigned pos, int value);
2246 __isl_give isl_basic_set *isl_basic_set_fix_val(
2247 __isl_take isl_basic_set *bset,
2248 enum isl_dim_type type, unsigned pos,
2249 __isl_take isl_val *v);
2250 __isl_give isl_set *isl_set_fix_si(__isl_take isl_set *set,
2251 enum isl_dim_type type, unsigned pos, int value);
2252 __isl_give isl_set *isl_set_fix_val(
2253 __isl_take isl_set *set,
2254 enum isl_dim_type type, unsigned pos,
2255 __isl_take isl_val *v);
2256 __isl_give isl_basic_map *isl_basic_map_fix_si(
2257 __isl_take isl_basic_map *bmap,
2258 enum isl_dim_type type, unsigned pos, int value);
2259 __isl_give isl_basic_map *isl_basic_map_fix_val(
2260 __isl_take isl_basic_map *bmap,
2261 enum isl_dim_type type, unsigned pos,
2262 __isl_take isl_val *v);
2263 __isl_give isl_map *isl_map_fix_si(__isl_take isl_map *map,
2264 enum isl_dim_type type, unsigned pos, int value);
2265 __isl_give isl_map *isl_map_fix_val(
2266 __isl_take isl_map *map,
2267 enum isl_dim_type type, unsigned pos,
2268 __isl_take isl_val *v);
2270 Intersect the set or relation with the hyperplane where the given
2271 dimension has the fixed given value.
2273 __isl_give isl_basic_map *isl_basic_map_lower_bound_si(
2274 __isl_take isl_basic_map *bmap,
2275 enum isl_dim_type type, unsigned pos, int value);
2276 __isl_give isl_basic_map *isl_basic_map_upper_bound_si(
2277 __isl_take isl_basic_map *bmap,
2278 enum isl_dim_type type, unsigned pos, int value);
2279 __isl_give isl_set *isl_set_lower_bound_si(
2280 __isl_take isl_set *set,
2281 enum isl_dim_type type, unsigned pos, int value);
2282 __isl_give isl_set *isl_set_lower_bound_val(
2283 __isl_take isl_set *set,
2284 enum isl_dim_type type, unsigned pos,
2285 __isl_take isl_val *value);
2286 __isl_give isl_map *isl_map_lower_bound_si(
2287 __isl_take isl_map *map,
2288 enum isl_dim_type type, unsigned pos, int value);
2289 __isl_give isl_set *isl_set_upper_bound_si(
2290 __isl_take isl_set *set,
2291 enum isl_dim_type type, unsigned pos, int value);
2292 __isl_give isl_set *isl_set_upper_bound_val(
2293 __isl_take isl_set *set,
2294 enum isl_dim_type type, unsigned pos,
2295 __isl_take isl_val *value);
2296 __isl_give isl_map *isl_map_upper_bound_si(
2297 __isl_take isl_map *map,
2298 enum isl_dim_type type, unsigned pos, int value);
2300 Intersect the set or relation with the half-space where the given
2301 dimension has a value bounded by the fixed given integer value.
2303 __isl_give isl_set *isl_set_equate(__isl_take isl_set *set,
2304 enum isl_dim_type type1, int pos1,
2305 enum isl_dim_type type2, int pos2);
2306 __isl_give isl_basic_map *isl_basic_map_equate(
2307 __isl_take isl_basic_map *bmap,
2308 enum isl_dim_type type1, int pos1,
2309 enum isl_dim_type type2, int pos2);
2310 __isl_give isl_map *isl_map_equate(__isl_take isl_map *map,
2311 enum isl_dim_type type1, int pos1,
2312 enum isl_dim_type type2, int pos2);
2314 Intersect the set or relation with the hyperplane where the given
2315 dimensions are equal to each other.
2317 __isl_give isl_map *isl_map_oppose(__isl_take isl_map *map,
2318 enum isl_dim_type type1, int pos1,
2319 enum isl_dim_type type2, int pos2);
2321 Intersect the relation with the hyperplane where the given
2322 dimensions have opposite values.
2324 __isl_give isl_basic_map *isl_basic_map_order_ge(
2325 __isl_take isl_basic_map *bmap,
2326 enum isl_dim_type type1, int pos1,
2327 enum isl_dim_type type2, int pos2);
2328 __isl_give isl_map *isl_map_order_lt(__isl_take isl_map *map,
2329 enum isl_dim_type type1, int pos1,
2330 enum isl_dim_type type2, int pos2);
2331 __isl_give isl_basic_map *isl_basic_map_order_gt(
2332 __isl_take isl_basic_map *bmap,
2333 enum isl_dim_type type1, int pos1,
2334 enum isl_dim_type type2, int pos2);
2335 __isl_give isl_map *isl_map_order_gt(__isl_take isl_map *map,
2336 enum isl_dim_type type1, int pos1,
2337 enum isl_dim_type type2, int pos2);
2339 Intersect the relation with the half-space where the given
2340 dimensions satisfy the given ordering.
2344 __isl_give isl_map *isl_set_identity(
2345 __isl_take isl_set *set);
2346 __isl_give isl_union_map *isl_union_set_identity(
2347 __isl_take isl_union_set *uset);
2349 Construct an identity relation on the given (union) set.
2353 __isl_give isl_basic_set *isl_basic_map_deltas(
2354 __isl_take isl_basic_map *bmap);
2355 __isl_give isl_set *isl_map_deltas(__isl_take isl_map *map);
2356 __isl_give isl_union_set *isl_union_map_deltas(
2357 __isl_take isl_union_map *umap);
2359 These functions return a (basic) set containing the differences
2360 between image elements and corresponding domain elements in the input.
2362 __isl_give isl_basic_map *isl_basic_map_deltas_map(
2363 __isl_take isl_basic_map *bmap);
2364 __isl_give isl_map *isl_map_deltas_map(
2365 __isl_take isl_map *map);
2366 __isl_give isl_union_map *isl_union_map_deltas_map(
2367 __isl_take isl_union_map *umap);
2369 The functions above construct a (basic, regular or union) relation
2370 that maps (a wrapped version of) the input relation to its delta set.
2374 Simplify the representation of a set or relation by trying
2375 to combine pairs of basic sets or relations into a single
2376 basic set or relation.
2378 __isl_give isl_set *isl_set_coalesce(__isl_take isl_set *set);
2379 __isl_give isl_map *isl_map_coalesce(__isl_take isl_map *map);
2380 __isl_give isl_union_set *isl_union_set_coalesce(
2381 __isl_take isl_union_set *uset);
2382 __isl_give isl_union_map *isl_union_map_coalesce(
2383 __isl_take isl_union_map *umap);
2385 One of the methods for combining pairs of basic sets or relations
2386 can result in coefficients that are much larger than those that appear
2387 in the constraints of the input. By default, the coefficients are
2388 not allowed to grow larger, but this can be changed by unsetting
2389 the following option.
2391 int isl_options_set_coalesce_bounded_wrapping(
2392 isl_ctx *ctx, int val);
2393 int isl_options_get_coalesce_bounded_wrapping(
2396 =item * Detecting equalities
2398 __isl_give isl_basic_set *isl_basic_set_detect_equalities(
2399 __isl_take isl_basic_set *bset);
2400 __isl_give isl_basic_map *isl_basic_map_detect_equalities(
2401 __isl_take isl_basic_map *bmap);
2402 __isl_give isl_set *isl_set_detect_equalities(
2403 __isl_take isl_set *set);
2404 __isl_give isl_map *isl_map_detect_equalities(
2405 __isl_take isl_map *map);
2406 __isl_give isl_union_set *isl_union_set_detect_equalities(
2407 __isl_take isl_union_set *uset);
2408 __isl_give isl_union_map *isl_union_map_detect_equalities(
2409 __isl_take isl_union_map *umap);
2411 Simplify the representation of a set or relation by detecting implicit
2414 =item * Removing redundant constraints
2416 __isl_give isl_basic_set *isl_basic_set_remove_redundancies(
2417 __isl_take isl_basic_set *bset);
2418 __isl_give isl_set *isl_set_remove_redundancies(
2419 __isl_take isl_set *set);
2420 __isl_give isl_basic_map *isl_basic_map_remove_redundancies(
2421 __isl_take isl_basic_map *bmap);
2422 __isl_give isl_map *isl_map_remove_redundancies(
2423 __isl_take isl_map *map);
2427 __isl_give isl_basic_set *isl_set_convex_hull(
2428 __isl_take isl_set *set);
2429 __isl_give isl_basic_map *isl_map_convex_hull(
2430 __isl_take isl_map *map);
2432 If the input set or relation has any existentially quantified
2433 variables, then the result of these operations is currently undefined.
2437 __isl_give isl_basic_set *
2438 isl_set_unshifted_simple_hull(
2439 __isl_take isl_set *set);
2440 __isl_give isl_basic_map *
2441 isl_map_unshifted_simple_hull(
2442 __isl_take isl_map *map);
2443 __isl_give isl_basic_set *isl_set_simple_hull(
2444 __isl_take isl_set *set);
2445 __isl_give isl_basic_map *isl_map_simple_hull(
2446 __isl_take isl_map *map);
2447 __isl_give isl_union_map *isl_union_map_simple_hull(
2448 __isl_take isl_union_map *umap);
2450 These functions compute a single basic set or relation
2451 that contains the whole input set or relation.
2452 In particular, the output is described by translates
2453 of the constraints describing the basic sets or relations in the input.
2454 In case of C<isl_set_unshifted_simple_hull>, only the original
2455 constraints are used, without any translation.
2459 (See \autoref{s:simple hull}.)
2465 __isl_give isl_basic_set *isl_basic_set_affine_hull(
2466 __isl_take isl_basic_set *bset);
2467 __isl_give isl_basic_set *isl_set_affine_hull(
2468 __isl_take isl_set *set);
2469 __isl_give isl_union_set *isl_union_set_affine_hull(
2470 __isl_take isl_union_set *uset);
2471 __isl_give isl_basic_map *isl_basic_map_affine_hull(
2472 __isl_take isl_basic_map *bmap);
2473 __isl_give isl_basic_map *isl_map_affine_hull(
2474 __isl_take isl_map *map);
2475 __isl_give isl_union_map *isl_union_map_affine_hull(
2476 __isl_take isl_union_map *umap);
2478 In case of union sets and relations, the affine hull is computed
2481 =item * Polyhedral hull
2483 __isl_give isl_basic_set *isl_set_polyhedral_hull(
2484 __isl_take isl_set *set);
2485 __isl_give isl_basic_map *isl_map_polyhedral_hull(
2486 __isl_take isl_map *map);
2487 __isl_give isl_union_set *isl_union_set_polyhedral_hull(
2488 __isl_take isl_union_set *uset);
2489 __isl_give isl_union_map *isl_union_map_polyhedral_hull(
2490 __isl_take isl_union_map *umap);
2492 These functions compute a single basic set or relation
2493 not involving any existentially quantified variables
2494 that contains the whole input set or relation.
2495 In case of union sets and relations, the polyhedral hull is computed
2498 =item * Other approximations
2500 __isl_give isl_basic_set *
2501 isl_basic_set_drop_constraints_involving_dims(
2502 __isl_take isl_basic_set *bset,
2503 enum isl_dim_type type,
2504 unsigned first, unsigned n);
2505 __isl_give isl_basic_map *
2506 isl_basic_map_drop_constraints_involving_dims(
2507 __isl_take isl_basic_map *bmap,
2508 enum isl_dim_type type,
2509 unsigned first, unsigned n);
2510 __isl_give isl_basic_set *
2511 isl_basic_set_drop_constraints_not_involving_dims(
2512 __isl_take isl_basic_set *bset,
2513 enum isl_dim_type type,
2514 unsigned first, unsigned n);
2515 __isl_give isl_set *
2516 isl_set_drop_constraints_involving_dims(
2517 __isl_take isl_set *set,
2518 enum isl_dim_type type,
2519 unsigned first, unsigned n);
2520 __isl_give isl_map *
2521 isl_map_drop_constraints_involving_dims(
2522 __isl_take isl_map *map,
2523 enum isl_dim_type type,
2524 unsigned first, unsigned n);
2526 These functions drop any constraints (not) involving the specified dimensions.
2527 Note that the result depends on the representation of the input.
2531 __isl_give isl_basic_set *isl_basic_set_sample(
2532 __isl_take isl_basic_set *bset);
2533 __isl_give isl_basic_set *isl_set_sample(
2534 __isl_take isl_set *set);
2535 __isl_give isl_basic_map *isl_basic_map_sample(
2536 __isl_take isl_basic_map *bmap);
2537 __isl_give isl_basic_map *isl_map_sample(
2538 __isl_take isl_map *map);
2540 If the input (basic) set or relation is non-empty, then return
2541 a singleton subset of the input. Otherwise, return an empty set.
2543 =item * Optimization
2545 #include <isl/ilp.h>
2546 __isl_give isl_val *isl_basic_set_max_val(
2547 __isl_keep isl_basic_set *bset,
2548 __isl_keep isl_aff *obj);
2549 __isl_give isl_val *isl_set_min_val(
2550 __isl_keep isl_set *set,
2551 __isl_keep isl_aff *obj);
2552 __isl_give isl_val *isl_set_max_val(
2553 __isl_keep isl_set *set,
2554 __isl_keep isl_aff *obj);
2556 Compute the minimum or maximum of the integer affine expression C<obj>
2557 over the points in C<set>, returning the result in C<opt>.
2558 The result is C<NULL> in case of an error, the optimal value in case
2559 there is one, negative infinity or infinity if the problem is unbounded and
2560 NaN if the problem is empty.
2562 =item * Parametric optimization
2564 __isl_give isl_pw_aff *isl_set_dim_min(
2565 __isl_take isl_set *set, int pos);
2566 __isl_give isl_pw_aff *isl_set_dim_max(
2567 __isl_take isl_set *set, int pos);
2568 __isl_give isl_pw_aff *isl_map_dim_max(
2569 __isl_take isl_map *map, int pos);
2571 Compute the minimum or maximum of the given set or output dimension
2572 as a function of the parameters (and input dimensions), but independently
2573 of the other set or output dimensions.
2574 For lexicographic optimization, see L<"Lexicographic Optimization">.
2578 The following functions compute either the set of (rational) coefficient
2579 values of valid constraints for the given set or the set of (rational)
2580 values satisfying the constraints with coefficients from the given set.
2581 Internally, these two sets of functions perform essentially the
2582 same operations, except that the set of coefficients is assumed to
2583 be a cone, while the set of values may be any polyhedron.
2584 The current implementation is based on the Farkas lemma and
2585 Fourier-Motzkin elimination, but this may change or be made optional
2586 in future. In particular, future implementations may use different
2587 dualization algorithms or skip the elimination step.
2589 __isl_give isl_basic_set *isl_basic_set_coefficients(
2590 __isl_take isl_basic_set *bset);
2591 __isl_give isl_basic_set *isl_set_coefficients(
2592 __isl_take isl_set *set);
2593 __isl_give isl_union_set *isl_union_set_coefficients(
2594 __isl_take isl_union_set *bset);
2595 __isl_give isl_basic_set *isl_basic_set_solutions(
2596 __isl_take isl_basic_set *bset);
2597 __isl_give isl_basic_set *isl_set_solutions(
2598 __isl_take isl_set *set);
2599 __isl_give isl_union_set *isl_union_set_solutions(
2600 __isl_take isl_union_set *bset);
2604 __isl_give isl_map *isl_map_fixed_power_val(
2605 __isl_take isl_map *map,
2606 __isl_take isl_val *exp);
2607 __isl_give isl_union_map *
2608 isl_union_map_fixed_power_val(
2609 __isl_take isl_union_map *umap,
2610 __isl_take isl_val *exp);
2612 Compute the given power of C<map>, where C<exp> is assumed to be non-zero.
2613 If the exponent C<exp> is negative, then the -C<exp> th power of the inverse
2614 of C<map> is computed.
2616 __isl_give isl_map *isl_map_power(__isl_take isl_map *map,
2618 __isl_give isl_union_map *isl_union_map_power(
2619 __isl_take isl_union_map *umap, int *exact);
2621 Compute a parametric representation for all positive powers I<k> of C<map>.
2622 The result maps I<k> to a nested relation corresponding to the
2623 I<k>th power of C<map>.
2624 The result may be an overapproximation. If the result is known to be exact,
2625 then C<*exact> is set to C<1>.
2627 =item * Transitive closure
2629 __isl_give isl_map *isl_map_transitive_closure(
2630 __isl_take isl_map *map, int *exact);
2631 __isl_give isl_union_map *isl_union_map_transitive_closure(
2632 __isl_take isl_union_map *umap, int *exact);
2634 Compute the transitive closure of C<map>.
2635 The result may be an overapproximation. If the result is known to be exact,
2636 then C<*exact> is set to C<1>.
2638 =item * Reaching path lengths
2640 __isl_give isl_map *isl_map_reaching_path_lengths(
2641 __isl_take isl_map *map, int *exact);
2643 Compute a relation that maps each element in the range of C<map>
2644 to the lengths of all paths composed of edges in C<map> that
2645 end up in the given element.
2646 The result may be an overapproximation. If the result is known to be exact,
2647 then C<*exact> is set to C<1>.
2648 To compute the I<maximal> path length, the resulting relation
2649 should be postprocessed by C<isl_map_lexmax>.
2650 In particular, if the input relation is a dependence relation
2651 (mapping sources to sinks), then the maximal path length corresponds
2652 to the free schedule.
2653 Note, however, that C<isl_map_lexmax> expects the maximum to be
2654 finite, so if the path lengths are unbounded (possibly due to
2655 the overapproximation), then you will get an error message.
2659 __isl_give isl_basic_set *isl_basic_map_wrap(
2660 __isl_take isl_basic_map *bmap);
2661 __isl_give isl_set *isl_map_wrap(
2662 __isl_take isl_map *map);
2663 __isl_give isl_union_set *isl_union_map_wrap(
2664 __isl_take isl_union_map *umap);
2665 __isl_give isl_basic_map *isl_basic_set_unwrap(
2666 __isl_take isl_basic_set *bset);
2667 __isl_give isl_map *isl_set_unwrap(
2668 __isl_take isl_set *set);
2669 __isl_give isl_union_map *isl_union_set_unwrap(
2670 __isl_take isl_union_set *uset);
2674 Remove any internal structure of domain (and range) of the given
2675 set or relation. If there is any such internal structure in the input,
2676 then the name of the space is also removed.
2678 __isl_give isl_basic_set *isl_basic_set_flatten(
2679 __isl_take isl_basic_set *bset);
2680 __isl_give isl_set *isl_set_flatten(
2681 __isl_take isl_set *set);
2682 __isl_give isl_basic_map *isl_basic_map_flatten_domain(
2683 __isl_take isl_basic_map *bmap);
2684 __isl_give isl_basic_map *isl_basic_map_flatten_range(
2685 __isl_take isl_basic_map *bmap);
2686 __isl_give isl_map *isl_map_flatten_range(
2687 __isl_take isl_map *map);
2688 __isl_give isl_map *isl_map_flatten_domain(
2689 __isl_take isl_map *map);
2690 __isl_give isl_basic_map *isl_basic_map_flatten(
2691 __isl_take isl_basic_map *bmap);
2692 __isl_give isl_map *isl_map_flatten(
2693 __isl_take isl_map *map);
2695 __isl_give isl_map *isl_set_flatten_map(
2696 __isl_take isl_set *set);
2698 The function above constructs a relation
2699 that maps the input set to a flattened version of the set.
2703 Lift the input set to a space with extra dimensions corresponding
2704 to the existentially quantified variables in the input.
2705 In particular, the result lives in a wrapped map where the domain
2706 is the original space and the range corresponds to the original
2707 existentially quantified variables.
2709 __isl_give isl_basic_set *isl_basic_set_lift(
2710 __isl_take isl_basic_set *bset);
2711 __isl_give isl_set *isl_set_lift(
2712 __isl_take isl_set *set);
2713 __isl_give isl_union_set *isl_union_set_lift(
2714 __isl_take isl_union_set *uset);
2716 Given a local space that contains the existentially quantified
2717 variables of a set, a basic relation that, when applied to
2718 a basic set, has essentially the same effect as C<isl_basic_set_lift>,
2719 can be constructed using the following function.
2721 #include <isl/local_space.h>
2722 __isl_give isl_basic_map *isl_local_space_lifting(
2723 __isl_take isl_local_space *ls);
2725 =item * Internal Product
2727 __isl_give isl_basic_map *isl_basic_map_zip(
2728 __isl_take isl_basic_map *bmap);
2729 __isl_give isl_map *isl_map_zip(
2730 __isl_take isl_map *map);
2731 __isl_give isl_union_map *isl_union_map_zip(
2732 __isl_take isl_union_map *umap);
2734 Given a relation with nested relations for domain and range,
2735 interchange the range of the domain with the domain of the range.
2739 __isl_give isl_basic_map *isl_basic_map_curry(
2740 __isl_take isl_basic_map *bmap);
2741 __isl_give isl_basic_map *isl_basic_map_uncurry(
2742 __isl_take isl_basic_map *bmap);
2743 __isl_give isl_map *isl_map_curry(
2744 __isl_take isl_map *map);
2745 __isl_give isl_map *isl_map_uncurry(
2746 __isl_take isl_map *map);
2747 __isl_give isl_union_map *isl_union_map_curry(
2748 __isl_take isl_union_map *umap);
2749 __isl_give isl_union_map *isl_union_map_uncurry(
2750 __isl_take isl_union_map *umap);
2752 Given a relation with a nested relation for domain,
2753 the C<curry> functions
2754 move the range of the nested relation out of the domain
2755 and use it as the domain of a nested relation in the range,
2756 with the original range as range of this nested relation.
2757 The C<uncurry> functions perform the inverse operation.
2759 =item * Aligning parameters
2761 __isl_give isl_basic_set *isl_basic_set_align_params(
2762 __isl_take isl_basic_set *bset,
2763 __isl_take isl_space *model);
2764 __isl_give isl_set *isl_set_align_params(
2765 __isl_take isl_set *set,
2766 __isl_take isl_space *model);
2767 __isl_give isl_basic_map *isl_basic_map_align_params(
2768 __isl_take isl_basic_map *bmap,
2769 __isl_take isl_space *model);
2770 __isl_give isl_map *isl_map_align_params(
2771 __isl_take isl_map *map,
2772 __isl_take isl_space *model);
2774 Change the order of the parameters of the given set or relation
2775 such that the first parameters match those of C<model>.
2776 This may involve the introduction of extra parameters.
2777 All parameters need to be named.
2779 =item * Dimension manipulation
2781 __isl_give isl_basic_set *isl_basic_set_add_dims(
2782 __isl_take isl_basic_set *bset,
2783 enum isl_dim_type type, unsigned n);
2784 __isl_give isl_set *isl_set_add_dims(
2785 __isl_take isl_set *set,
2786 enum isl_dim_type type, unsigned n);
2787 __isl_give isl_map *isl_map_add_dims(
2788 __isl_take isl_map *map,
2789 enum isl_dim_type type, unsigned n);
2790 __isl_give isl_basic_set *isl_basic_set_insert_dims(
2791 __isl_take isl_basic_set *bset,
2792 enum isl_dim_type type, unsigned pos,
2794 __isl_give isl_basic_map *isl_basic_map_insert_dims(
2795 __isl_take isl_basic_map *bmap,
2796 enum isl_dim_type type, unsigned pos,
2798 __isl_give isl_set *isl_set_insert_dims(
2799 __isl_take isl_set *set,
2800 enum isl_dim_type type, unsigned pos, unsigned n);
2801 __isl_give isl_map *isl_map_insert_dims(
2802 __isl_take isl_map *map,
2803 enum isl_dim_type type, unsigned pos, unsigned n);
2804 __isl_give isl_basic_set *isl_basic_set_move_dims(
2805 __isl_take isl_basic_set *bset,
2806 enum isl_dim_type dst_type, unsigned dst_pos,
2807 enum isl_dim_type src_type, unsigned src_pos,
2809 __isl_give isl_basic_map *isl_basic_map_move_dims(
2810 __isl_take isl_basic_map *bmap,
2811 enum isl_dim_type dst_type, unsigned dst_pos,
2812 enum isl_dim_type src_type, unsigned src_pos,
2814 __isl_give isl_set *isl_set_move_dims(
2815 __isl_take isl_set *set,
2816 enum isl_dim_type dst_type, unsigned dst_pos,
2817 enum isl_dim_type src_type, unsigned src_pos,
2819 __isl_give isl_map *isl_map_move_dims(
2820 __isl_take isl_map *map,
2821 enum isl_dim_type dst_type, unsigned dst_pos,
2822 enum isl_dim_type src_type, unsigned src_pos,
2825 It is usually not advisable to directly change the (input or output)
2826 space of a set or a relation as this removes the name and the internal
2827 structure of the space. However, the above functions can be useful
2828 to add new parameters, assuming
2829 C<isl_set_align_params> and C<isl_map_align_params>
2834 =head2 Binary Operations
2836 The two arguments of a binary operation not only need to live
2837 in the same C<isl_ctx>, they currently also need to have
2838 the same (number of) parameters.
2840 =head3 Basic Operations
2844 =item * Intersection
2846 __isl_give isl_basic_set *isl_basic_set_intersect_params(
2847 __isl_take isl_basic_set *bset1,
2848 __isl_take isl_basic_set *bset2);
2849 __isl_give isl_basic_set *isl_basic_set_intersect(
2850 __isl_take isl_basic_set *bset1,
2851 __isl_take isl_basic_set *bset2);
2852 __isl_give isl_set *isl_set_intersect_params(
2853 __isl_take isl_set *set,
2854 __isl_take isl_set *params);
2855 __isl_give isl_set *isl_set_intersect(
2856 __isl_take isl_set *set1,
2857 __isl_take isl_set *set2);
2858 __isl_give isl_union_set *isl_union_set_intersect_params(
2859 __isl_take isl_union_set *uset,
2860 __isl_take isl_set *set);
2861 __isl_give isl_union_map *isl_union_map_intersect_params(
2862 __isl_take isl_union_map *umap,
2863 __isl_take isl_set *set);
2864 __isl_give isl_union_set *isl_union_set_intersect(
2865 __isl_take isl_union_set *uset1,
2866 __isl_take isl_union_set *uset2);
2867 __isl_give isl_basic_map *isl_basic_map_intersect_domain(
2868 __isl_take isl_basic_map *bmap,
2869 __isl_take isl_basic_set *bset);
2870 __isl_give isl_basic_map *isl_basic_map_intersect_range(
2871 __isl_take isl_basic_map *bmap,
2872 __isl_take isl_basic_set *bset);
2873 __isl_give isl_basic_map *isl_basic_map_intersect(
2874 __isl_take isl_basic_map *bmap1,
2875 __isl_take isl_basic_map *bmap2);
2876 __isl_give isl_map *isl_map_intersect_params(
2877 __isl_take isl_map *map,
2878 __isl_take isl_set *params);
2879 __isl_give isl_map *isl_map_intersect_domain(
2880 __isl_take isl_map *map,
2881 __isl_take isl_set *set);
2882 __isl_give isl_map *isl_map_intersect_range(
2883 __isl_take isl_map *map,
2884 __isl_take isl_set *set);
2885 __isl_give isl_map *isl_map_intersect(
2886 __isl_take isl_map *map1,
2887 __isl_take isl_map *map2);
2888 __isl_give isl_union_map *isl_union_map_intersect_domain(
2889 __isl_take isl_union_map *umap,
2890 __isl_take isl_union_set *uset);
2891 __isl_give isl_union_map *isl_union_map_intersect_range(
2892 __isl_take isl_union_map *umap,
2893 __isl_take isl_union_set *uset);
2894 __isl_give isl_union_map *isl_union_map_intersect(
2895 __isl_take isl_union_map *umap1,
2896 __isl_take isl_union_map *umap2);
2898 The second argument to the C<_params> functions needs to be
2899 a parametric (basic) set. For the other functions, a parametric set
2900 for either argument is only allowed if the other argument is
2901 a parametric set as well.
2905 __isl_give isl_set *isl_basic_set_union(
2906 __isl_take isl_basic_set *bset1,
2907 __isl_take isl_basic_set *bset2);
2908 __isl_give isl_map *isl_basic_map_union(
2909 __isl_take isl_basic_map *bmap1,
2910 __isl_take isl_basic_map *bmap2);
2911 __isl_give isl_set *isl_set_union(
2912 __isl_take isl_set *set1,
2913 __isl_take isl_set *set2);
2914 __isl_give isl_map *isl_map_union(
2915 __isl_take isl_map *map1,
2916 __isl_take isl_map *map2);
2917 __isl_give isl_union_set *isl_union_set_union(
2918 __isl_take isl_union_set *uset1,
2919 __isl_take isl_union_set *uset2);
2920 __isl_give isl_union_map *isl_union_map_union(
2921 __isl_take isl_union_map *umap1,
2922 __isl_take isl_union_map *umap2);
2924 =item * Set difference
2926 __isl_give isl_set *isl_set_subtract(
2927 __isl_take isl_set *set1,
2928 __isl_take isl_set *set2);
2929 __isl_give isl_map *isl_map_subtract(
2930 __isl_take isl_map *map1,
2931 __isl_take isl_map *map2);
2932 __isl_give isl_map *isl_map_subtract_domain(
2933 __isl_take isl_map *map,
2934 __isl_take isl_set *dom);
2935 __isl_give isl_map *isl_map_subtract_range(
2936 __isl_take isl_map *map,
2937 __isl_take isl_set *dom);
2938 __isl_give isl_union_set *isl_union_set_subtract(
2939 __isl_take isl_union_set *uset1,
2940 __isl_take isl_union_set *uset2);
2941 __isl_give isl_union_map *isl_union_map_subtract(
2942 __isl_take isl_union_map *umap1,
2943 __isl_take isl_union_map *umap2);
2944 __isl_give isl_union_map *isl_union_map_subtract_domain(
2945 __isl_take isl_union_map *umap,
2946 __isl_take isl_union_set *dom);
2947 __isl_give isl_union_map *isl_union_map_subtract_range(
2948 __isl_take isl_union_map *umap,
2949 __isl_take isl_union_set *dom);
2953 __isl_give isl_basic_set *isl_basic_set_apply(
2954 __isl_take isl_basic_set *bset,
2955 __isl_take isl_basic_map *bmap);
2956 __isl_give isl_set *isl_set_apply(
2957 __isl_take isl_set *set,
2958 __isl_take isl_map *map);
2959 __isl_give isl_union_set *isl_union_set_apply(
2960 __isl_take isl_union_set *uset,
2961 __isl_take isl_union_map *umap);
2962 __isl_give isl_basic_map *isl_basic_map_apply_domain(
2963 __isl_take isl_basic_map *bmap1,
2964 __isl_take isl_basic_map *bmap2);
2965 __isl_give isl_basic_map *isl_basic_map_apply_range(
2966 __isl_take isl_basic_map *bmap1,
2967 __isl_take isl_basic_map *bmap2);
2968 __isl_give isl_map *isl_map_apply_domain(
2969 __isl_take isl_map *map1,
2970 __isl_take isl_map *map2);
2971 __isl_give isl_union_map *isl_union_map_apply_domain(
2972 __isl_take isl_union_map *umap1,
2973 __isl_take isl_union_map *umap2);
2974 __isl_give isl_map *isl_map_apply_range(
2975 __isl_take isl_map *map1,
2976 __isl_take isl_map *map2);
2977 __isl_give isl_union_map *isl_union_map_apply_range(
2978 __isl_take isl_union_map *umap1,
2979 __isl_take isl_union_map *umap2);
2983 __isl_give isl_basic_set *
2984 isl_basic_set_preimage_multi_aff(
2985 __isl_take isl_basic_set *bset,
2986 __isl_take isl_multi_aff *ma);
2987 __isl_give isl_set *isl_set_preimage_multi_aff(
2988 __isl_take isl_set *set,
2989 __isl_take isl_multi_aff *ma);
2990 __isl_give isl_set *isl_set_preimage_pw_multi_aff(
2991 __isl_take isl_set *set,
2992 __isl_take isl_pw_multi_aff *pma);
2993 __isl_give isl_set *isl_set_preimage_multi_pw_aff(
2994 __isl_take isl_set *set,
2995 __isl_take isl_multi_pw_aff *mpa);
2996 __isl_give isl_basic_map *
2997 isl_basic_map_preimage_domain_multi_aff(
2998 __isl_take isl_basic_map *bmap,
2999 __isl_take isl_multi_aff *ma);
3000 __isl_give isl_map *isl_map_preimage_domain_multi_aff(
3001 __isl_take isl_map *map,
3002 __isl_take isl_multi_aff *ma);
3003 __isl_give isl_map *
3004 isl_map_preimage_domain_pw_multi_aff(
3005 __isl_take isl_map *map,
3006 __isl_take isl_pw_multi_aff *pma);
3007 __isl_give isl_map *
3008 isl_map_preimage_domain_multi_pw_aff(
3009 __isl_take isl_map *map,
3010 __isl_take isl_multi_pw_aff *mpa);
3011 __isl_give isl_union_map *
3012 isl_union_map_preimage_domain_multi_aff(
3013 __isl_take isl_union_map *umap,
3014 __isl_take isl_multi_aff *ma);
3015 __isl_give isl_basic_map *
3016 isl_basic_map_preimage_range_multi_aff(
3017 __isl_take isl_basic_map *bmap,
3018 __isl_take isl_multi_aff *ma);
3020 These functions compute the preimage of the given set or map domain/range under
3021 the given function. In other words, the expression is plugged
3022 into the set description or into the domain/range of the map.
3023 Objects of types C<isl_multi_aff> and C<isl_pw_multi_aff> are described in
3024 L</"Piecewise Multiple Quasi Affine Expressions">.
3026 =item * Cartesian Product
3028 __isl_give isl_set *isl_set_product(
3029 __isl_take isl_set *set1,
3030 __isl_take isl_set *set2);
3031 __isl_give isl_union_set *isl_union_set_product(
3032 __isl_take isl_union_set *uset1,
3033 __isl_take isl_union_set *uset2);
3034 __isl_give isl_basic_map *isl_basic_map_domain_product(
3035 __isl_take isl_basic_map *bmap1,
3036 __isl_take isl_basic_map *bmap2);
3037 __isl_give isl_basic_map *isl_basic_map_range_product(
3038 __isl_take isl_basic_map *bmap1,
3039 __isl_take isl_basic_map *bmap2);
3040 __isl_give isl_basic_map *isl_basic_map_product(
3041 __isl_take isl_basic_map *bmap1,
3042 __isl_take isl_basic_map *bmap2);
3043 __isl_give isl_map *isl_map_domain_product(
3044 __isl_take isl_map *map1,
3045 __isl_take isl_map *map2);
3046 __isl_give isl_map *isl_map_range_product(
3047 __isl_take isl_map *map1,
3048 __isl_take isl_map *map2);
3049 __isl_give isl_union_map *isl_union_map_domain_product(
3050 __isl_take isl_union_map *umap1,
3051 __isl_take isl_union_map *umap2);
3052 __isl_give isl_union_map *isl_union_map_range_product(
3053 __isl_take isl_union_map *umap1,
3054 __isl_take isl_union_map *umap2);
3055 __isl_give isl_map *isl_map_product(
3056 __isl_take isl_map *map1,
3057 __isl_take isl_map *map2);
3058 __isl_give isl_union_map *isl_union_map_product(
3059 __isl_take isl_union_map *umap1,
3060 __isl_take isl_union_map *umap2);
3062 The above functions compute the cross product of the given
3063 sets or relations. The domains and ranges of the results
3064 are wrapped maps between domains and ranges of the inputs.
3065 To obtain a ``flat'' product, use the following functions
3068 __isl_give isl_basic_set *isl_basic_set_flat_product(
3069 __isl_take isl_basic_set *bset1,
3070 __isl_take isl_basic_set *bset2);
3071 __isl_give isl_set *isl_set_flat_product(
3072 __isl_take isl_set *set1,
3073 __isl_take isl_set *set2);
3074 __isl_give isl_basic_map *isl_basic_map_flat_range_product(
3075 __isl_take isl_basic_map *bmap1,
3076 __isl_take isl_basic_map *bmap2);
3077 __isl_give isl_map *isl_map_flat_domain_product(
3078 __isl_take isl_map *map1,
3079 __isl_take isl_map *map2);
3080 __isl_give isl_map *isl_map_flat_range_product(
3081 __isl_take isl_map *map1,
3082 __isl_take isl_map *map2);
3083 __isl_give isl_union_map *isl_union_map_flat_range_product(
3084 __isl_take isl_union_map *umap1,
3085 __isl_take isl_union_map *umap2);
3086 __isl_give isl_basic_map *isl_basic_map_flat_product(
3087 __isl_take isl_basic_map *bmap1,
3088 __isl_take isl_basic_map *bmap2);
3089 __isl_give isl_map *isl_map_flat_product(
3090 __isl_take isl_map *map1,
3091 __isl_take isl_map *map2);
3093 The arguments of a call to C<isl_map_product> can be extracted
3094 from the result using the following two functions.
3096 __isl_give isl_map *isl_map_range_factor_domain(
3097 __isl_take isl_map *map);
3098 __isl_give isl_map *isl_map_range_factor_range(
3099 __isl_take isl_map *map);
3101 =item * Simplification
3103 __isl_give isl_basic_set *isl_basic_set_gist(
3104 __isl_take isl_basic_set *bset,
3105 __isl_take isl_basic_set *context);
3106 __isl_give isl_set *isl_set_gist(__isl_take isl_set *set,
3107 __isl_take isl_set *context);
3108 __isl_give isl_set *isl_set_gist_params(
3109 __isl_take isl_set *set,
3110 __isl_take isl_set *context);
3111 __isl_give isl_union_set *isl_union_set_gist(
3112 __isl_take isl_union_set *uset,
3113 __isl_take isl_union_set *context);
3114 __isl_give isl_union_set *isl_union_set_gist_params(
3115 __isl_take isl_union_set *uset,
3116 __isl_take isl_set *set);
3117 __isl_give isl_basic_map *isl_basic_map_gist(
3118 __isl_take isl_basic_map *bmap,
3119 __isl_take isl_basic_map *context);
3120 __isl_give isl_map *isl_map_gist(__isl_take isl_map *map,
3121 __isl_take isl_map *context);
3122 __isl_give isl_map *isl_map_gist_params(
3123 __isl_take isl_map *map,
3124 __isl_take isl_set *context);
3125 __isl_give isl_map *isl_map_gist_domain(
3126 __isl_take isl_map *map,
3127 __isl_take isl_set *context);
3128 __isl_give isl_map *isl_map_gist_range(
3129 __isl_take isl_map *map,
3130 __isl_take isl_set *context);
3131 __isl_give isl_union_map *isl_union_map_gist(
3132 __isl_take isl_union_map *umap,
3133 __isl_take isl_union_map *context);
3134 __isl_give isl_union_map *isl_union_map_gist_params(
3135 __isl_take isl_union_map *umap,
3136 __isl_take isl_set *set);
3137 __isl_give isl_union_map *isl_union_map_gist_domain(
3138 __isl_take isl_union_map *umap,
3139 __isl_take isl_union_set *uset);
3140 __isl_give isl_union_map *isl_union_map_gist_range(
3141 __isl_take isl_union_map *umap,
3142 __isl_take isl_union_set *uset);
3144 The gist operation returns a set or relation that has the
3145 same intersection with the context as the input set or relation.
3146 Any implicit equality in the intersection is made explicit in the result,
3147 while all inequalities that are redundant with respect to the intersection
3149 In case of union sets and relations, the gist operation is performed
3154 =head3 Lexicographic Optimization
3156 Given a (basic) set C<set> (or C<bset>) and a zero-dimensional domain C<dom>,
3157 the following functions
3158 compute a set that contains the lexicographic minimum or maximum
3159 of the elements in C<set> (or C<bset>) for those values of the parameters
3160 that satisfy C<dom>.
3161 If C<empty> is not C<NULL>, then C<*empty> is assigned a set
3162 that contains the parameter values in C<dom> for which C<set> (or C<bset>)
3164 In other words, the union of the parameter values
3165 for which the result is non-empty and of C<*empty>
3168 __isl_give isl_set *isl_basic_set_partial_lexmin(
3169 __isl_take isl_basic_set *bset,
3170 __isl_take isl_basic_set *dom,
3171 __isl_give isl_set **empty);
3172 __isl_give isl_set *isl_basic_set_partial_lexmax(
3173 __isl_take isl_basic_set *bset,
3174 __isl_take isl_basic_set *dom,
3175 __isl_give isl_set **empty);
3176 __isl_give isl_set *isl_set_partial_lexmin(
3177 __isl_take isl_set *set, __isl_take isl_set *dom,
3178 __isl_give isl_set **empty);
3179 __isl_give isl_set *isl_set_partial_lexmax(
3180 __isl_take isl_set *set, __isl_take isl_set *dom,
3181 __isl_give isl_set **empty);
3183 Given a (basic) set C<set> (or C<bset>), the following functions simply
3184 return a set containing the lexicographic minimum or maximum
3185 of the elements in C<set> (or C<bset>).
3186 In case of union sets, the optimum is computed per space.
3188 __isl_give isl_set *isl_basic_set_lexmin(
3189 __isl_take isl_basic_set *bset);
3190 __isl_give isl_set *isl_basic_set_lexmax(
3191 __isl_take isl_basic_set *bset);
3192 __isl_give isl_set *isl_set_lexmin(
3193 __isl_take isl_set *set);
3194 __isl_give isl_set *isl_set_lexmax(
3195 __isl_take isl_set *set);
3196 __isl_give isl_union_set *isl_union_set_lexmin(
3197 __isl_take isl_union_set *uset);
3198 __isl_give isl_union_set *isl_union_set_lexmax(
3199 __isl_take isl_union_set *uset);
3201 Given a (basic) relation C<map> (or C<bmap>) and a domain C<dom>,
3202 the following functions
3203 compute a relation that maps each element of C<dom>
3204 to the single lexicographic minimum or maximum
3205 of the elements that are associated to that same
3206 element in C<map> (or C<bmap>).
3207 If C<empty> is not C<NULL>, then C<*empty> is assigned a set
3208 that contains the elements in C<dom> that do not map
3209 to any elements in C<map> (or C<bmap>).
3210 In other words, the union of the domain of the result and of C<*empty>
3213 __isl_give isl_map *isl_basic_map_partial_lexmax(
3214 __isl_take isl_basic_map *bmap,
3215 __isl_take isl_basic_set *dom,
3216 __isl_give isl_set **empty);
3217 __isl_give isl_map *isl_basic_map_partial_lexmin(
3218 __isl_take isl_basic_map *bmap,
3219 __isl_take isl_basic_set *dom,
3220 __isl_give isl_set **empty);
3221 __isl_give isl_map *isl_map_partial_lexmax(
3222 __isl_take isl_map *map, __isl_take isl_set *dom,
3223 __isl_give isl_set **empty);
3224 __isl_give isl_map *isl_map_partial_lexmin(
3225 __isl_take isl_map *map, __isl_take isl_set *dom,
3226 __isl_give isl_set **empty);
3228 Given a (basic) map C<map> (or C<bmap>), the following functions simply
3229 return a map mapping each element in the domain of
3230 C<map> (or C<bmap>) to the lexicographic minimum or maximum
3231 of all elements associated to that element.
3232 In case of union relations, the optimum is computed per space.
3234 __isl_give isl_map *isl_basic_map_lexmin(
3235 __isl_take isl_basic_map *bmap);
3236 __isl_give isl_map *isl_basic_map_lexmax(
3237 __isl_take isl_basic_map *bmap);
3238 __isl_give isl_map *isl_map_lexmin(
3239 __isl_take isl_map *map);
3240 __isl_give isl_map *isl_map_lexmax(
3241 __isl_take isl_map *map);
3242 __isl_give isl_union_map *isl_union_map_lexmin(
3243 __isl_take isl_union_map *umap);
3244 __isl_give isl_union_map *isl_union_map_lexmax(
3245 __isl_take isl_union_map *umap);
3247 The following functions return their result in the form of
3248 a piecewise multi-affine expression
3249 (See L<"Piecewise Multiple Quasi Affine Expressions">),
3250 but are otherwise equivalent to the corresponding functions
3251 returning a basic set or relation.
3253 __isl_give isl_pw_multi_aff *
3254 isl_basic_map_lexmin_pw_multi_aff(
3255 __isl_take isl_basic_map *bmap);
3256 __isl_give isl_pw_multi_aff *
3257 isl_basic_set_partial_lexmin_pw_multi_aff(
3258 __isl_take isl_basic_set *bset,
3259 __isl_take isl_basic_set *dom,
3260 __isl_give isl_set **empty);
3261 __isl_give isl_pw_multi_aff *
3262 isl_basic_set_partial_lexmax_pw_multi_aff(
3263 __isl_take isl_basic_set *bset,
3264 __isl_take isl_basic_set *dom,
3265 __isl_give isl_set **empty);
3266 __isl_give isl_pw_multi_aff *
3267 isl_basic_map_partial_lexmin_pw_multi_aff(
3268 __isl_take isl_basic_map *bmap,
3269 __isl_take isl_basic_set *dom,
3270 __isl_give isl_set **empty);
3271 __isl_give isl_pw_multi_aff *
3272 isl_basic_map_partial_lexmax_pw_multi_aff(
3273 __isl_take isl_basic_map *bmap,
3274 __isl_take isl_basic_set *dom,
3275 __isl_give isl_set **empty);
3276 __isl_give isl_pw_multi_aff *isl_set_lexmin_pw_multi_aff(
3277 __isl_take isl_set *set);
3278 __isl_give isl_pw_multi_aff *isl_set_lexmax_pw_multi_aff(
3279 __isl_take isl_set *set);
3280 __isl_give isl_pw_multi_aff *isl_map_lexmin_pw_multi_aff(
3281 __isl_take isl_map *map);
3282 __isl_give isl_pw_multi_aff *isl_map_lexmax_pw_multi_aff(
3283 __isl_take isl_map *map);
3287 Lists are defined over several element types, including
3288 C<isl_val>, C<isl_id>, C<isl_aff>, C<isl_pw_aff>, C<isl_constraint>,
3289 C<isl_basic_set>, C<isl_set>, C<isl_ast_expr> and C<isl_ast_node>.
3290 Here we take lists of C<isl_set>s as an example.
3291 Lists can be created, copied, modified and freed using the following functions.
3293 #include <isl/list.h>
3294 __isl_give isl_set_list *isl_set_list_from_set(
3295 __isl_take isl_set *el);
3296 __isl_give isl_set_list *isl_set_list_alloc(
3297 isl_ctx *ctx, int n);
3298 __isl_give isl_set_list *isl_set_list_copy(
3299 __isl_keep isl_set_list *list);
3300 __isl_give isl_set_list *isl_set_list_insert(
3301 __isl_take isl_set_list *list, unsigned pos,
3302 __isl_take isl_set *el);
3303 __isl_give isl_set_list *isl_set_list_add(
3304 __isl_take isl_set_list *list,
3305 __isl_take isl_set *el);
3306 __isl_give isl_set_list *isl_set_list_drop(
3307 __isl_take isl_set_list *list,
3308 unsigned first, unsigned n);
3309 __isl_give isl_set_list *isl_set_list_set_set(
3310 __isl_take isl_set_list *list, int index,
3311 __isl_take isl_set *set);
3312 __isl_give isl_set_list *isl_set_list_concat(
3313 __isl_take isl_set_list *list1,
3314 __isl_take isl_set_list *list2);
3315 __isl_give isl_set_list *isl_set_list_sort(
3316 __isl_take isl_set_list *list,
3317 int (*cmp)(__isl_keep isl_set *a,
3318 __isl_keep isl_set *b, void *user),
3320 void *isl_set_list_free(__isl_take isl_set_list *list);
3322 C<isl_set_list_alloc> creates an empty list with a capacity for
3323 C<n> elements. C<isl_set_list_from_set> creates a list with a single
3326 Lists can be inspected using the following functions.
3328 #include <isl/list.h>
3329 isl_ctx *isl_set_list_get_ctx(__isl_keep isl_set_list *list);
3330 int isl_set_list_n_set(__isl_keep isl_set_list *list);
3331 __isl_give isl_set *isl_set_list_get_set(
3332 __isl_keep isl_set_list *list, int index);
3333 int isl_set_list_foreach(__isl_keep isl_set_list *list,
3334 int (*fn)(__isl_take isl_set *el, void *user),
3336 int isl_set_list_foreach_scc(__isl_keep isl_set_list *list,
3337 int (*follows)(__isl_keep isl_set *a,
3338 __isl_keep isl_set *b, void *user),
3340 int (*fn)(__isl_take isl_set *el, void *user),
3343 The function C<isl_set_list_foreach_scc> calls C<fn> on each of the
3344 strongly connected components of the graph with as vertices the elements
3345 of C<list> and a directed edge from vertex C<b> to vertex C<a>
3346 iff C<follows(a, b)> returns C<1>. The callbacks C<follows> and C<fn>
3347 should return C<-1> on error.
3349 Lists can be printed using
3351 #include <isl/list.h>
3352 __isl_give isl_printer *isl_printer_print_set_list(
3353 __isl_take isl_printer *p,
3354 __isl_keep isl_set_list *list);
3356 =head2 Associative arrays
3358 Associative arrays map isl objects of a specific type to isl objects
3359 of some (other) specific type. They are defined for several pairs
3360 of types, including (C<isl_map>, C<isl_basic_set>),
3361 (C<isl_id>, C<isl_ast_expr>) and.
3362 (C<isl_id>, C<isl_pw_aff>).
3363 Here, we take associative arrays that map C<isl_id>s to C<isl_ast_expr>s
3366 Associative arrays can be created, copied and freed using
3367 the following functions.
3369 #include <isl/id_to_ast_expr.h>
3370 __isl_give id_to_ast_expr *isl_id_to_ast_expr_alloc(
3371 isl_ctx *ctx, int min_size);
3372 __isl_give id_to_ast_expr *isl_id_to_ast_expr_copy(
3373 __isl_keep id_to_ast_expr *id2expr);
3374 void *isl_id_to_ast_expr_free(
3375 __isl_take id_to_ast_expr *id2expr);
3377 The C<min_size> argument to C<isl_id_to_ast_expr_alloc> can be used
3378 to specify the expected size of the associative array.
3379 The associative array will be grown automatically as needed.
3381 Associative arrays can be inspected using the following functions.
3383 #include <isl/id_to_ast_expr.h>
3384 isl_ctx *isl_id_to_ast_expr_get_ctx(
3385 __isl_keep id_to_ast_expr *id2expr);
3386 int isl_id_to_ast_expr_has(
3387 __isl_keep id_to_ast_expr *id2expr,
3388 __isl_keep isl_id *key);
3389 __isl_give isl_ast_expr *isl_id_to_ast_expr_get(
3390 __isl_keep id_to_ast_expr *id2expr,
3391 __isl_take isl_id *key);
3392 int isl_id_to_ast_expr_foreach(
3393 __isl_keep id_to_ast_expr *id2expr,
3394 int (*fn)(__isl_take isl_id *key,
3395 __isl_take isl_ast_expr *val, void *user),
3398 They can be modified using the following function.
3400 #include <isl/id_to_ast_expr.h>
3401 __isl_give id_to_ast_expr *isl_id_to_ast_expr_set(
3402 __isl_take id_to_ast_expr *id2expr,
3403 __isl_take isl_id *key,
3404 __isl_take isl_ast_expr *val);
3406 Associative arrays can be printed using the following function.
3408 #include <isl/id_to_ast_expr.h>
3409 __isl_give isl_printer *isl_printer_print_id_to_ast_expr(
3410 __isl_take isl_printer *p,
3411 __isl_keep id_to_ast_expr *id2expr);
3413 =head2 Multiple Values
3415 An C<isl_multi_val> object represents a sequence of zero or more values,
3416 living in a set space.
3418 An C<isl_multi_val> can be constructed from an C<isl_val_list>
3419 using the following function
3421 #include <isl/val.h>
3422 __isl_give isl_multi_val *isl_multi_val_from_val_list(
3423 __isl_take isl_space *space,
3424 __isl_take isl_val_list *list);
3426 The zero multiple value (with value zero for each set dimension)
3427 can be created using the following function.
3429 #include <isl/val.h>
3430 __isl_give isl_multi_val *isl_multi_val_zero(
3431 __isl_take isl_space *space);
3433 Multiple values can be copied and freed using
3435 #include <isl/val.h>
3436 __isl_give isl_multi_val *isl_multi_val_copy(
3437 __isl_keep isl_multi_val *mv);
3438 void *isl_multi_val_free(__isl_take isl_multi_val *mv);
3440 They can be inspected using
3442 #include <isl/val.h>
3443 isl_ctx *isl_multi_val_get_ctx(
3444 __isl_keep isl_multi_val *mv);
3445 unsigned isl_multi_val_dim(__isl_keep isl_multi_val *mv,
3446 enum isl_dim_type type);
3447 __isl_give isl_val *isl_multi_val_get_val(
3448 __isl_keep isl_multi_val *mv, int pos);
3449 int isl_multi_val_find_dim_by_id(
3450 __isl_keep isl_multi_val *mv,
3451 enum isl_dim_type type, __isl_keep isl_id *id);
3452 __isl_give isl_id *isl_multi_val_get_dim_id(
3453 __isl_keep isl_multi_val *mv,
3454 enum isl_dim_type type, unsigned pos);
3455 const char *isl_multi_val_get_tuple_name(
3456 __isl_keep isl_multi_val *mv,
3457 enum isl_dim_type type);
3458 int isl_multi_val_has_tuple_id(__isl_keep isl_multi_val *mv,
3459 enum isl_dim_type type);
3460 __isl_give isl_id *isl_multi_val_get_tuple_id(
3461 __isl_keep isl_multi_val *mv,
3462 enum isl_dim_type type);
3463 int isl_multi_val_range_is_wrapping(
3464 __isl_keep isl_multi_val *mv);
3466 They can be modified using
3468 #include <isl/val.h>
3469 __isl_give isl_multi_val *isl_multi_val_set_val(
3470 __isl_take isl_multi_val *mv, int pos,
3471 __isl_take isl_val *val);
3472 __isl_give isl_multi_val *isl_multi_val_set_dim_name(
3473 __isl_take isl_multi_val *mv,
3474 enum isl_dim_type type, unsigned pos, const char *s);
3475 __isl_give isl_multi_val *isl_multi_val_set_dim_id(
3476 __isl_take isl_multi_val *mv,
3477 enum isl_dim_type type, unsigned pos,
3478 __isl_take isl_id *id);
3479 __isl_give isl_multi_val *isl_multi_val_set_tuple_name(
3480 __isl_take isl_multi_val *mv,
3481 enum isl_dim_type type, const char *s);
3482 __isl_give isl_multi_val *isl_multi_val_set_tuple_id(
3483 __isl_take isl_multi_val *mv,
3484 enum isl_dim_type type, __isl_take isl_id *id);
3485 __isl_give isl_multi_val *isl_multi_val_reset_tuple_id(
3486 __isl_take isl_multi_val *mv,
3487 enum isl_dim_type type);
3488 __isl_give isl_multi_val *isl_multi_val_reset_user(
3489 __isl_take isl_multi_val *mv);
3491 __isl_give isl_multi_val *isl_multi_val_insert_dims(
3492 __isl_take isl_multi_val *mv,
3493 enum isl_dim_type type, unsigned first, unsigned n);
3494 __isl_give isl_multi_val *isl_multi_val_add_dims(
3495 __isl_take isl_multi_val *mv,
3496 enum isl_dim_type type, unsigned n);
3497 __isl_give isl_multi_val *isl_multi_val_drop_dims(
3498 __isl_take isl_multi_val *mv,
3499 enum isl_dim_type type, unsigned first, unsigned n);
3503 #include <isl/val.h>
3504 __isl_give isl_multi_val *isl_multi_val_align_params(
3505 __isl_take isl_multi_val *mv,
3506 __isl_take isl_space *model);
3507 __isl_give isl_multi_val *isl_multi_val_from_range(
3508 __isl_take isl_multi_val *mv);
3509 __isl_give isl_multi_val *isl_multi_val_range_splice(
3510 __isl_take isl_multi_val *mv1, unsigned pos,
3511 __isl_take isl_multi_val *mv2);
3512 __isl_give isl_multi_val *isl_multi_val_range_product(
3513 __isl_take isl_multi_val *mv1,
3514 __isl_take isl_multi_val *mv2);
3515 __isl_give isl_multi_val *
3516 isl_multi_val_range_factor_domain(
3517 __isl_take isl_multi_val *mv);
3518 __isl_give isl_multi_val *
3519 isl_multi_val_range_factor_range(
3520 __isl_take isl_multi_val *mv);
3521 __isl_give isl_multi_val *isl_multi_val_flat_range_product(
3522 __isl_take isl_multi_val *mv1,
3523 __isl_take isl_multi_aff *mv2);
3524 __isl_give isl_multi_val *isl_multi_val_product(
3525 __isl_take isl_multi_val *mv1,
3526 __isl_take isl_multi_val *mv2);
3527 __isl_give isl_multi_val *isl_multi_val_add_val(
3528 __isl_take isl_multi_val *mv,
3529 __isl_take isl_val *v);
3530 __isl_give isl_multi_val *isl_multi_val_mod_val(
3531 __isl_take isl_multi_val *mv,
3532 __isl_take isl_val *v);
3533 __isl_give isl_multi_val *isl_multi_val_scale_val(
3534 __isl_take isl_multi_val *mv,
3535 __isl_take isl_val *v);
3536 __isl_give isl_multi_val *isl_multi_val_scale_multi_val(
3537 __isl_take isl_multi_val *mv1,
3538 __isl_take isl_multi_val *mv2);
3539 __isl_give isl_multi_val *
3540 isl_multi_val_scale_down_multi_val(
3541 __isl_take isl_multi_val *mv1,
3542 __isl_take isl_multi_val *mv2);
3544 A multiple value can be printed using
3546 __isl_give isl_printer *isl_printer_print_multi_val(
3547 __isl_take isl_printer *p,
3548 __isl_keep isl_multi_val *mv);
3552 Vectors can be created, copied and freed using the following functions.
3554 #include <isl/vec.h>
3555 __isl_give isl_vec *isl_vec_alloc(isl_ctx *ctx,
3557 __isl_give isl_vec *isl_vec_copy(__isl_keep isl_vec *vec);
3558 void *isl_vec_free(__isl_take isl_vec *vec);
3560 Note that the elements of a newly created vector may have arbitrary values.
3561 The elements can be changed and inspected using the following functions.
3563 isl_ctx *isl_vec_get_ctx(__isl_keep isl_vec *vec);
3564 int isl_vec_size(__isl_keep isl_vec *vec);
3565 __isl_give isl_val *isl_vec_get_element_val(
3566 __isl_keep isl_vec *vec, int pos);
3567 __isl_give isl_vec *isl_vec_set_element_si(
3568 __isl_take isl_vec *vec, int pos, int v);
3569 __isl_give isl_vec *isl_vec_set_element_val(
3570 __isl_take isl_vec *vec, int pos,
3571 __isl_take isl_val *v);
3572 __isl_give isl_vec *isl_vec_set_si(__isl_take isl_vec *vec,
3574 __isl_give isl_vec *isl_vec_set_val(
3575 __isl_take isl_vec *vec, __isl_take isl_val *v);
3576 int isl_vec_cmp_element(__isl_keep isl_vec *vec1,
3577 __isl_keep isl_vec *vec2, int pos);
3579 C<isl_vec_get_element> will return a negative value if anything went wrong.
3580 In that case, the value of C<*v> is undefined.
3582 The following function can be used to concatenate two vectors.
3584 __isl_give isl_vec *isl_vec_concat(__isl_take isl_vec *vec1,
3585 __isl_take isl_vec *vec2);
3589 Matrices can be created, copied and freed using the following functions.
3591 #include <isl/mat.h>
3592 __isl_give isl_mat *isl_mat_alloc(isl_ctx *ctx,
3593 unsigned n_row, unsigned n_col);
3594 __isl_give isl_mat *isl_mat_copy(__isl_keep isl_mat *mat);
3595 void *isl_mat_free(__isl_take isl_mat *mat);
3597 Note that the elements of a newly created matrix may have arbitrary values.
3598 The elements can be changed and inspected using the following functions.
3600 isl_ctx *isl_mat_get_ctx(__isl_keep isl_mat *mat);
3601 int isl_mat_rows(__isl_keep isl_mat *mat);
3602 int isl_mat_cols(__isl_keep isl_mat *mat);
3603 __isl_give isl_val *isl_mat_get_element_val(
3604 __isl_keep isl_mat *mat, int row, int col);
3605 __isl_give isl_mat *isl_mat_set_element_si(__isl_take isl_mat *mat,
3606 int row, int col, int v);
3607 __isl_give isl_mat *isl_mat_set_element_val(
3608 __isl_take isl_mat *mat, int row, int col,
3609 __isl_take isl_val *v);
3611 C<isl_mat_get_element> will return a negative value if anything went wrong.
3612 In that case, the value of C<*v> is undefined.
3614 The following function can be used to compute the (right) inverse
3615 of a matrix, i.e., a matrix such that the product of the original
3616 and the inverse (in that order) is a multiple of the identity matrix.
3617 The input matrix is assumed to be of full row-rank.
3619 __isl_give isl_mat *isl_mat_right_inverse(__isl_take isl_mat *mat);
3621 The following function can be used to compute the (right) kernel
3622 (or null space) of a matrix, i.e., a matrix such that the product of
3623 the original and the kernel (in that order) is the zero matrix.
3625 __isl_give isl_mat *isl_mat_right_kernel(__isl_take isl_mat *mat);
3627 =head2 Piecewise Quasi Affine Expressions
3629 The zero quasi affine expression or the quasi affine expression
3630 that is equal to a given value or
3631 a specified dimension on a given domain can be created using
3633 __isl_give isl_aff *isl_aff_zero_on_domain(
3634 __isl_take isl_local_space *ls);
3635 __isl_give isl_pw_aff *isl_pw_aff_zero_on_domain(
3636 __isl_take isl_local_space *ls);
3637 __isl_give isl_aff *isl_aff_val_on_domain(
3638 __isl_take isl_local_space *ls,
3639 __isl_take isl_val *val);
3640 __isl_give isl_aff *isl_aff_var_on_domain(
3641 __isl_take isl_local_space *ls,
3642 enum isl_dim_type type, unsigned pos);
3643 __isl_give isl_pw_aff *isl_pw_aff_var_on_domain(
3644 __isl_take isl_local_space *ls,
3645 enum isl_dim_type type, unsigned pos);
3647 Note that the space in which the resulting objects live is a map space
3648 with the given space as domain and a one-dimensional range.
3650 An empty piecewise quasi affine expression (one with no cells)
3651 or a piecewise quasi affine expression with a single cell can
3652 be created using the following functions.
3654 #include <isl/aff.h>
3655 __isl_give isl_pw_aff *isl_pw_aff_empty(
3656 __isl_take isl_space *space);
3657 __isl_give isl_pw_aff *isl_pw_aff_alloc(
3658 __isl_take isl_set *set, __isl_take isl_aff *aff);
3659 __isl_give isl_pw_aff *isl_pw_aff_from_aff(
3660 __isl_take isl_aff *aff);
3662 A piecewise quasi affine expression that is equal to 1 on a set
3663 and 0 outside the set can be created using the following function.
3665 #include <isl/aff.h>
3666 __isl_give isl_pw_aff *isl_set_indicator_function(
3667 __isl_take isl_set *set);
3669 Quasi affine expressions can be copied and freed using
3671 #include <isl/aff.h>
3672 __isl_give isl_aff *isl_aff_copy(__isl_keep isl_aff *aff);
3673 void *isl_aff_free(__isl_take isl_aff *aff);
3675 __isl_give isl_pw_aff *isl_pw_aff_copy(
3676 __isl_keep isl_pw_aff *pwaff);
3677 void *isl_pw_aff_free(__isl_take isl_pw_aff *pwaff);
3679 A (rational) bound on a dimension can be extracted from an C<isl_constraint>
3680 using the following function. The constraint is required to have
3681 a non-zero coefficient for the specified dimension.
3683 #include <isl/constraint.h>
3684 __isl_give isl_aff *isl_constraint_get_bound(
3685 __isl_keep isl_constraint *constraint,
3686 enum isl_dim_type type, int pos);
3688 The entire affine expression of the constraint can also be extracted
3689 using the following function.
3691 #include <isl/constraint.h>
3692 __isl_give isl_aff *isl_constraint_get_aff(
3693 __isl_keep isl_constraint *constraint);
3695 Conversely, an equality constraint equating
3696 the affine expression to zero or an inequality constraint enforcing
3697 the affine expression to be non-negative, can be constructed using
3699 __isl_give isl_constraint *isl_equality_from_aff(
3700 __isl_take isl_aff *aff);
3701 __isl_give isl_constraint *isl_inequality_from_aff(
3702 __isl_take isl_aff *aff);
3704 The expression can be inspected using
3706 #include <isl/aff.h>
3707 isl_ctx *isl_aff_get_ctx(__isl_keep isl_aff *aff);
3708 int isl_aff_dim(__isl_keep isl_aff *aff,
3709 enum isl_dim_type type);
3710 __isl_give isl_local_space *isl_aff_get_domain_local_space(
3711 __isl_keep isl_aff *aff);
3712 __isl_give isl_local_space *isl_aff_get_local_space(
3713 __isl_keep isl_aff *aff);
3714 const char *isl_aff_get_dim_name(__isl_keep isl_aff *aff,
3715 enum isl_dim_type type, unsigned pos);
3716 const char *isl_pw_aff_get_dim_name(
3717 __isl_keep isl_pw_aff *pa,
3718 enum isl_dim_type type, unsigned pos);
3719 int isl_pw_aff_has_dim_id(__isl_keep isl_pw_aff *pa,
3720 enum isl_dim_type type, unsigned pos);
3721 __isl_give isl_id *isl_pw_aff_get_dim_id(
3722 __isl_keep isl_pw_aff *pa,
3723 enum isl_dim_type type, unsigned pos);
3724 int isl_pw_aff_has_tuple_id(__isl_keep isl_pw_aff *pa,
3725 enum isl_dim_type type);
3726 __isl_give isl_id *isl_pw_aff_get_tuple_id(
3727 __isl_keep isl_pw_aff *pa,
3728 enum isl_dim_type type);
3729 __isl_give isl_val *isl_aff_get_constant_val(
3730 __isl_keep isl_aff *aff);
3731 __isl_give isl_val *isl_aff_get_coefficient_val(
3732 __isl_keep isl_aff *aff,
3733 enum isl_dim_type type, int pos);
3734 __isl_give isl_val *isl_aff_get_denominator_val(
3735 __isl_keep isl_aff *aff);
3736 __isl_give isl_aff *isl_aff_get_div(
3737 __isl_keep isl_aff *aff, int pos);
3739 int isl_pw_aff_n_piece(__isl_keep isl_pw_aff *pwaff);
3740 int isl_pw_aff_foreach_piece(__isl_keep isl_pw_aff *pwaff,
3741 int (*fn)(__isl_take isl_set *set,
3742 __isl_take isl_aff *aff,
3743 void *user), void *user);
3745 int isl_aff_is_cst(__isl_keep isl_aff *aff);
3746 int isl_pw_aff_is_cst(__isl_keep isl_pw_aff *pwaff);
3748 int isl_aff_involves_dims(__isl_keep isl_aff *aff,
3749 enum isl_dim_type type, unsigned first, unsigned n);
3750 int isl_pw_aff_involves_dims(__isl_keep isl_pw_aff *pwaff,
3751 enum isl_dim_type type, unsigned first, unsigned n);
3753 isl_ctx *isl_pw_aff_get_ctx(__isl_keep isl_pw_aff *pwaff);
3754 unsigned isl_pw_aff_dim(__isl_keep isl_pw_aff *pwaff,
3755 enum isl_dim_type type);
3756 int isl_pw_aff_is_empty(__isl_keep isl_pw_aff *pwaff);
3758 It can be modified using
3760 #include <isl/aff.h>
3761 __isl_give isl_pw_aff *isl_pw_aff_set_tuple_id(
3762 __isl_take isl_pw_aff *pwaff,
3763 enum isl_dim_type type, __isl_take isl_id *id);
3764 __isl_give isl_aff *isl_aff_set_dim_name(
3765 __isl_take isl_aff *aff, enum isl_dim_type type,
3766 unsigned pos, const char *s);
3767 __isl_give isl_aff *isl_aff_set_dim_id(
3768 __isl_take isl_aff *aff, enum isl_dim_type type,
3769 unsigned pos, __isl_take isl_id *id);
3770 __isl_give isl_pw_aff *isl_pw_aff_set_dim_id(
3771 __isl_take isl_pw_aff *pma,
3772 enum isl_dim_type type, unsigned pos,
3773 __isl_take isl_id *id);
3774 __isl_give isl_aff *isl_aff_set_constant_si(
3775 __isl_take isl_aff *aff, int v);
3776 __isl_give isl_aff *isl_aff_set_constant_val(
3777 __isl_take isl_aff *aff, __isl_take isl_val *v);
3778 __isl_give isl_aff *isl_aff_set_coefficient_si(
3779 __isl_take isl_aff *aff,
3780 enum isl_dim_type type, int pos, int v);
3781 __isl_give isl_aff *isl_aff_set_coefficient_val(
3782 __isl_take isl_aff *aff,
3783 enum isl_dim_type type, int pos,
3784 __isl_take isl_val *v);
3786 __isl_give isl_aff *isl_aff_add_constant_si(
3787 __isl_take isl_aff *aff, int v);
3788 __isl_give isl_aff *isl_aff_add_constant_val(
3789 __isl_take isl_aff *aff, __isl_take isl_val *v);
3790 __isl_give isl_aff *isl_aff_add_constant_num_si(
3791 __isl_take isl_aff *aff, int v);
3792 __isl_give isl_aff *isl_aff_add_coefficient_si(
3793 __isl_take isl_aff *aff,
3794 enum isl_dim_type type, int pos, int v);
3795 __isl_give isl_aff *isl_aff_add_coefficient_val(
3796 __isl_take isl_aff *aff,
3797 enum isl_dim_type type, int pos,
3798 __isl_take isl_val *v);
3800 __isl_give isl_aff *isl_aff_insert_dims(
3801 __isl_take isl_aff *aff,
3802 enum isl_dim_type type, unsigned first, unsigned n);
3803 __isl_give isl_pw_aff *isl_pw_aff_insert_dims(
3804 __isl_take isl_pw_aff *pwaff,
3805 enum isl_dim_type type, unsigned first, unsigned n);
3806 __isl_give isl_aff *isl_aff_add_dims(
3807 __isl_take isl_aff *aff,
3808 enum isl_dim_type type, unsigned n);
3809 __isl_give isl_pw_aff *isl_pw_aff_add_dims(
3810 __isl_take isl_pw_aff *pwaff,
3811 enum isl_dim_type type, unsigned n);
3812 __isl_give isl_aff *isl_aff_drop_dims(
3813 __isl_take isl_aff *aff,
3814 enum isl_dim_type type, unsigned first, unsigned n);
3815 __isl_give isl_pw_aff *isl_pw_aff_drop_dims(
3816 __isl_take isl_pw_aff *pwaff,
3817 enum isl_dim_type type, unsigned first, unsigned n);
3818 __isl_give isl_aff *isl_aff_move_dims(
3819 __isl_take isl_aff *aff,
3820 enum isl_dim_type dst_type, unsigned dst_pos,
3821 enum isl_dim_type src_type, unsigned src_pos,
3823 __isl_give isl_pw_aff *isl_pw_aff_move_dims(
3824 __isl_take isl_pw_aff *pa,
3825 enum isl_dim_type dst_type, unsigned dst_pos,
3826 enum isl_dim_type src_type, unsigned src_pos,
3829 Note that C<isl_aff_set_constant_si> and C<isl_aff_set_coefficient_si>
3830 set the I<numerator> of the constant or coefficient, while
3831 C<isl_aff_set_constant_val> and C<isl_aff_set_coefficient_val> set
3832 the constant or coefficient as a whole.
3833 The C<add_constant> and C<add_coefficient> functions add an integer
3834 or rational value to
3835 the possibly rational constant or coefficient.
3836 The C<add_constant_num> functions add an integer value to
3839 To check whether an affine expressions is obviously zero
3840 or (obviously) equal to some other affine expression, use
3842 #include <isl/aff.h>
3843 int isl_aff_plain_is_zero(__isl_keep isl_aff *aff);
3844 int isl_aff_plain_is_equal(__isl_keep isl_aff *aff1,
3845 __isl_keep isl_aff *aff2);
3846 int isl_pw_aff_plain_is_equal(
3847 __isl_keep isl_pw_aff *pwaff1,
3848 __isl_keep isl_pw_aff *pwaff2);
3849 int isl_pw_aff_is_equal(__isl_keep isl_pw_aff *pa1,
3850 __isl_keep isl_pw_aff *pa2);
3854 #include <isl/aff.h>
3855 __isl_give isl_aff *isl_aff_add(__isl_take isl_aff *aff1,
3856 __isl_take isl_aff *aff2);
3857 __isl_give isl_pw_aff *isl_pw_aff_add(
3858 __isl_take isl_pw_aff *pwaff1,
3859 __isl_take isl_pw_aff *pwaff2);
3860 __isl_give isl_pw_aff *isl_pw_aff_min(
3861 __isl_take isl_pw_aff *pwaff1,
3862 __isl_take isl_pw_aff *pwaff2);
3863 __isl_give isl_pw_aff *isl_pw_aff_max(
3864 __isl_take isl_pw_aff *pwaff1,
3865 __isl_take isl_pw_aff *pwaff2);
3866 __isl_give isl_aff *isl_aff_sub(__isl_take isl_aff *aff1,
3867 __isl_take isl_aff *aff2);
3868 __isl_give isl_pw_aff *isl_pw_aff_sub(
3869 __isl_take isl_pw_aff *pwaff1,
3870 __isl_take isl_pw_aff *pwaff2);
3871 __isl_give isl_aff *isl_aff_neg(__isl_take isl_aff *aff);
3872 __isl_give isl_pw_aff *isl_pw_aff_neg(
3873 __isl_take isl_pw_aff *pwaff);
3874 __isl_give isl_aff *isl_aff_ceil(__isl_take isl_aff *aff);
3875 __isl_give isl_pw_aff *isl_pw_aff_ceil(
3876 __isl_take isl_pw_aff *pwaff);
3877 __isl_give isl_aff *isl_aff_floor(__isl_take isl_aff *aff);
3878 __isl_give isl_pw_aff *isl_pw_aff_floor(
3879 __isl_take isl_pw_aff *pwaff);
3880 __isl_give isl_aff *isl_aff_mod_val(__isl_take isl_aff *aff,
3881 __isl_take isl_val *mod);
3882 __isl_give isl_pw_aff *isl_pw_aff_mod_val(
3883 __isl_take isl_pw_aff *pa,
3884 __isl_take isl_val *mod);
3885 __isl_give isl_aff *isl_aff_scale_val(__isl_take isl_aff *aff,
3886 __isl_take isl_val *v);
3887 __isl_give isl_pw_aff *isl_pw_aff_scale_val(
3888 __isl_take isl_pw_aff *pa, __isl_take isl_val *v);
3889 __isl_give isl_aff *isl_aff_scale_down_ui(
3890 __isl_take isl_aff *aff, unsigned f);
3891 __isl_give isl_aff *isl_aff_scale_down_val(
3892 __isl_take isl_aff *aff, __isl_take isl_val *v);
3893 __isl_give isl_pw_aff *isl_pw_aff_scale_down_val(
3894 __isl_take isl_pw_aff *pa,
3895 __isl_take isl_val *f);
3897 __isl_give isl_pw_aff *isl_pw_aff_list_min(
3898 __isl_take isl_pw_aff_list *list);
3899 __isl_give isl_pw_aff *isl_pw_aff_list_max(
3900 __isl_take isl_pw_aff_list *list);
3902 __isl_give isl_pw_aff *isl_pw_aff_coalesce(
3903 __isl_take isl_pw_aff *pwqp);
3905 __isl_give isl_aff *isl_aff_align_params(
3906 __isl_take isl_aff *aff,
3907 __isl_take isl_space *model);
3908 __isl_give isl_pw_aff *isl_pw_aff_align_params(
3909 __isl_take isl_pw_aff *pwaff,
3910 __isl_take isl_space *model);
3912 __isl_give isl_aff *isl_aff_project_domain_on_params(
3913 __isl_take isl_aff *aff);
3914 __isl_give isl_pw_aff *isl_pw_aff_from_range(
3915 __isl_take isl_pw_aff *pwa);
3917 __isl_give isl_aff *isl_aff_gist_params(
3918 __isl_take isl_aff *aff,
3919 __isl_take isl_set *context);
3920 __isl_give isl_aff *isl_aff_gist(__isl_take isl_aff *aff,
3921 __isl_take isl_set *context);
3922 __isl_give isl_pw_aff *isl_pw_aff_gist_params(
3923 __isl_take isl_pw_aff *pwaff,
3924 __isl_take isl_set *context);
3925 __isl_give isl_pw_aff *isl_pw_aff_gist(
3926 __isl_take isl_pw_aff *pwaff,
3927 __isl_take isl_set *context);
3929 __isl_give isl_set *isl_pw_aff_domain(
3930 __isl_take isl_pw_aff *pwaff);
3931 __isl_give isl_set *isl_pw_aff_params(
3932 __isl_take isl_pw_aff *pwa);
3933 __isl_give isl_pw_aff *isl_pw_aff_intersect_domain(
3934 __isl_take isl_pw_aff *pa,
3935 __isl_take isl_set *set);
3936 __isl_give isl_pw_aff *isl_pw_aff_intersect_params(
3937 __isl_take isl_pw_aff *pa,
3938 __isl_take isl_set *set);
3940 __isl_give isl_aff *isl_aff_mul(__isl_take isl_aff *aff1,
3941 __isl_take isl_aff *aff2);
3942 __isl_give isl_aff *isl_aff_div(__isl_take isl_aff *aff1,
3943 __isl_take isl_aff *aff2);
3944 __isl_give isl_pw_aff *isl_pw_aff_mul(
3945 __isl_take isl_pw_aff *pwaff1,
3946 __isl_take isl_pw_aff *pwaff2);
3947 __isl_give isl_pw_aff *isl_pw_aff_div(
3948 __isl_take isl_pw_aff *pa1,
3949 __isl_take isl_pw_aff *pa2);
3950 __isl_give isl_pw_aff *isl_pw_aff_tdiv_q(
3951 __isl_take isl_pw_aff *pa1,
3952 __isl_take isl_pw_aff *pa2);
3953 __isl_give isl_pw_aff *isl_pw_aff_tdiv_r(
3954 __isl_take isl_pw_aff *pa1,
3955 __isl_take isl_pw_aff *pa2);
3957 When multiplying two affine expressions, at least one of the two needs
3958 to be a constant. Similarly, when dividing an affine expression by another,
3959 the second expression needs to be a constant.
3960 C<isl_pw_aff_tdiv_q> computes the quotient of an integer division with
3961 rounding towards zero. C<isl_pw_aff_tdiv_r> computes the corresponding
3964 #include <isl/aff.h>
3965 __isl_give isl_aff *isl_aff_pullback_aff(
3966 __isl_take isl_aff *aff1,
3967 __isl_take isl_aff *aff2);
3968 __isl_give isl_aff *isl_aff_pullback_multi_aff(
3969 __isl_take isl_aff *aff,
3970 __isl_take isl_multi_aff *ma);
3971 __isl_give isl_pw_aff *isl_pw_aff_pullback_multi_aff(
3972 __isl_take isl_pw_aff *pa,
3973 __isl_take isl_multi_aff *ma);
3974 __isl_give isl_pw_aff *isl_pw_aff_pullback_pw_multi_aff(
3975 __isl_take isl_pw_aff *pa,
3976 __isl_take isl_pw_multi_aff *pma);
3978 These functions precompose the input expression by the given
3979 C<isl_aff>, C<isl_multi_aff> or C<isl_pw_multi_aff>. In other words,
3980 the C<isl_aff>, C<isl_multi_aff> or C<isl_pw_multi_aff> is plugged
3981 into the (piecewise) affine expression.
3982 Objects of type C<isl_multi_aff> are described in
3983 L</"Piecewise Multiple Quasi Affine Expressions">.
3985 #include <isl/aff.h>
3986 __isl_give isl_basic_set *isl_aff_zero_basic_set(
3987 __isl_take isl_aff *aff);
3988 __isl_give isl_basic_set *isl_aff_neg_basic_set(
3989 __isl_take isl_aff *aff);
3990 __isl_give isl_basic_set *isl_aff_le_basic_set(
3991 __isl_take isl_aff *aff1, __isl_take isl_aff *aff2);
3992 __isl_give isl_basic_set *isl_aff_ge_basic_set(
3993 __isl_take isl_aff *aff1, __isl_take isl_aff *aff2);
3994 __isl_give isl_set *isl_pw_aff_eq_set(
3995 __isl_take isl_pw_aff *pwaff1,
3996 __isl_take isl_pw_aff *pwaff2);
3997 __isl_give isl_set *isl_pw_aff_ne_set(
3998 __isl_take isl_pw_aff *pwaff1,
3999 __isl_take isl_pw_aff *pwaff2);
4000 __isl_give isl_set *isl_pw_aff_le_set(
4001 __isl_take isl_pw_aff *pwaff1,
4002 __isl_take isl_pw_aff *pwaff2);
4003 __isl_give isl_set *isl_pw_aff_lt_set(
4004 __isl_take isl_pw_aff *pwaff1,
4005 __isl_take isl_pw_aff *pwaff2);
4006 __isl_give isl_set *isl_pw_aff_ge_set(
4007 __isl_take isl_pw_aff *pwaff1,
4008 __isl_take isl_pw_aff *pwaff2);
4009 __isl_give isl_set *isl_pw_aff_gt_set(
4010 __isl_take isl_pw_aff *pwaff1,
4011 __isl_take isl_pw_aff *pwaff2);
4013 __isl_give isl_set *isl_pw_aff_list_eq_set(
4014 __isl_take isl_pw_aff_list *list1,
4015 __isl_take isl_pw_aff_list *list2);
4016 __isl_give isl_set *isl_pw_aff_list_ne_set(
4017 __isl_take isl_pw_aff_list *list1,
4018 __isl_take isl_pw_aff_list *list2);
4019 __isl_give isl_set *isl_pw_aff_list_le_set(
4020 __isl_take isl_pw_aff_list *list1,
4021 __isl_take isl_pw_aff_list *list2);
4022 __isl_give isl_set *isl_pw_aff_list_lt_set(
4023 __isl_take isl_pw_aff_list *list1,
4024 __isl_take isl_pw_aff_list *list2);
4025 __isl_give isl_set *isl_pw_aff_list_ge_set(
4026 __isl_take isl_pw_aff_list *list1,
4027 __isl_take isl_pw_aff_list *list2);
4028 __isl_give isl_set *isl_pw_aff_list_gt_set(
4029 __isl_take isl_pw_aff_list *list1,
4030 __isl_take isl_pw_aff_list *list2);
4032 The function C<isl_aff_neg_basic_set> returns a basic set
4033 containing those elements in the domain space
4034 of C<aff> where C<aff> is negative.
4035 The function C<isl_aff_ge_basic_set> returns a basic set
4036 containing those elements in the shared space
4037 of C<aff1> and C<aff2> where C<aff1> is greater than or equal to C<aff2>.
4038 The function C<isl_pw_aff_ge_set> returns a set
4039 containing those elements in the shared domain
4040 of C<pwaff1> and C<pwaff2> where C<pwaff1> is greater than or equal to C<pwaff2>.
4041 The functions operating on C<isl_pw_aff_list> apply the corresponding
4042 C<isl_pw_aff> function to each pair of elements in the two lists.
4044 #include <isl/aff.h>
4045 __isl_give isl_set *isl_pw_aff_nonneg_set(
4046 __isl_take isl_pw_aff *pwaff);
4047 __isl_give isl_set *isl_pw_aff_zero_set(
4048 __isl_take isl_pw_aff *pwaff);
4049 __isl_give isl_set *isl_pw_aff_non_zero_set(
4050 __isl_take isl_pw_aff *pwaff);
4052 The function C<isl_pw_aff_nonneg_set> returns a set
4053 containing those elements in the domain
4054 of C<pwaff> where C<pwaff> is non-negative.
4056 #include <isl/aff.h>
4057 __isl_give isl_pw_aff *isl_pw_aff_cond(
4058 __isl_take isl_pw_aff *cond,
4059 __isl_take isl_pw_aff *pwaff_true,
4060 __isl_take isl_pw_aff *pwaff_false);
4062 The function C<isl_pw_aff_cond> performs a conditional operator
4063 and returns an expression that is equal to C<pwaff_true>
4064 for elements where C<cond> is non-zero and equal to C<pwaff_false> for elements
4065 where C<cond> is zero.
4067 #include <isl/aff.h>
4068 __isl_give isl_pw_aff *isl_pw_aff_union_min(
4069 __isl_take isl_pw_aff *pwaff1,
4070 __isl_take isl_pw_aff *pwaff2);
4071 __isl_give isl_pw_aff *isl_pw_aff_union_max(
4072 __isl_take isl_pw_aff *pwaff1,
4073 __isl_take isl_pw_aff *pwaff2);
4074 __isl_give isl_pw_aff *isl_pw_aff_union_add(
4075 __isl_take isl_pw_aff *pwaff1,
4076 __isl_take isl_pw_aff *pwaff2);
4078 The function C<isl_pw_aff_union_max> computes a piecewise quasi-affine
4079 expression with a domain that is the union of those of C<pwaff1> and
4080 C<pwaff2> and such that on each cell, the quasi-affine expression is
4081 the maximum of those of C<pwaff1> and C<pwaff2>. If only one of
4082 C<pwaff1> or C<pwaff2> is defined on a given cell, then the
4083 associated expression is the defined one.
4085 An expression can be read from input using
4087 #include <isl/aff.h>
4088 __isl_give isl_aff *isl_aff_read_from_str(
4089 isl_ctx *ctx, const char *str);
4090 __isl_give isl_pw_aff *isl_pw_aff_read_from_str(
4091 isl_ctx *ctx, const char *str);
4093 An expression can be printed using
4095 #include <isl/aff.h>
4096 __isl_give isl_printer *isl_printer_print_aff(
4097 __isl_take isl_printer *p, __isl_keep isl_aff *aff);
4099 __isl_give isl_printer *isl_printer_print_pw_aff(
4100 __isl_take isl_printer *p,
4101 __isl_keep isl_pw_aff *pwaff);
4103 =head2 Piecewise Multiple Quasi Affine Expressions
4105 An C<isl_multi_aff> object represents a sequence of
4106 zero or more affine expressions, all defined on the same domain space.
4107 Similarly, an C<isl_multi_pw_aff> object represents a sequence of
4108 zero or more piecewise affine expressions.
4110 An C<isl_multi_aff> can be constructed from a single
4111 C<isl_aff> or an C<isl_aff_list> using the
4112 following functions. Similarly for C<isl_multi_pw_aff>
4113 and C<isl_pw_multi_aff>.
4115 #include <isl/aff.h>
4116 __isl_give isl_multi_aff *isl_multi_aff_from_aff(
4117 __isl_take isl_aff *aff);
4118 __isl_give isl_multi_pw_aff *
4119 isl_multi_pw_aff_from_multi_aff(
4120 __isl_take isl_multi_aff *ma);
4121 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_from_pw_aff(
4122 __isl_take isl_pw_aff *pa);
4123 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_from_pw_aff(
4124 __isl_take isl_pw_aff *pa);
4125 __isl_give isl_multi_aff *isl_multi_aff_from_aff_list(
4126 __isl_take isl_space *space,
4127 __isl_take isl_aff_list *list);
4129 An C<isl_multi_pw_aff> can be converted to an C<isl_pw_multi_aff>
4130 using the function C<isl_pw_multi_aff_from_multi_pw_aff> below.
4131 Note however that the domain
4132 of the result is the intersection of the domains of the input.
4133 The reverse conversion is exact.
4135 #include <isl/aff.h>
4136 __isl_give isl_pw_multi_aff *
4137 isl_pw_multi_aff_from_multi_pw_aff(
4138 __isl_take isl_multi_pw_aff *mpa);
4139 __isl_give isl_multi_pw_aff *
4140 isl_multi_pw_aff_from_pw_multi_aff(
4141 __isl_take isl_pw_multi_aff *pma);
4143 An empty piecewise multiple quasi affine expression (one with no cells),
4144 the zero piecewise multiple quasi affine expression (with value zero
4145 for each output dimension),
4146 a piecewise multiple quasi affine expression with a single cell (with
4147 either a universe or a specified domain) or
4148 a zero-dimensional piecewise multiple quasi affine expression
4150 can be created using the following functions.
4152 #include <isl/aff.h>
4153 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_empty(
4154 __isl_take isl_space *space);
4155 __isl_give isl_multi_aff *isl_multi_aff_zero(
4156 __isl_take isl_space *space);
4157 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_zero(
4158 __isl_take isl_space *space);
4159 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_zero(
4160 __isl_take isl_space *space);
4161 __isl_give isl_multi_aff *isl_multi_aff_identity(
4162 __isl_take isl_space *space);
4163 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_identity(
4164 __isl_take isl_space *space);
4165 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_identity(
4166 __isl_take isl_space *space);
4167 __isl_give isl_multi_aff *isl_multi_aff_domain_map(
4168 __isl_take isl_space *space);
4169 __isl_give isl_multi_aff *isl_multi_aff_range_map(
4170 __isl_take isl_space *space);
4171 __isl_give isl_multi_aff *isl_multi_aff_project_out_map(
4172 __isl_take isl_space *space,
4173 enum isl_dim_type type,
4174 unsigned first, unsigned n);
4175 __isl_give isl_pw_multi_aff *
4176 isl_pw_multi_aff_project_out_map(
4177 __isl_take isl_space *space,
4178 enum isl_dim_type type,
4179 unsigned first, unsigned n);
4180 __isl_give isl_pw_multi_aff *
4181 isl_pw_multi_aff_from_multi_aff(
4182 __isl_take isl_multi_aff *ma);
4183 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_alloc(
4184 __isl_take isl_set *set,
4185 __isl_take isl_multi_aff *maff);
4186 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_from_domain(
4187 __isl_take isl_set *set);
4189 __isl_give isl_union_pw_multi_aff *
4190 isl_union_pw_multi_aff_empty(
4191 __isl_take isl_space *space);
4192 __isl_give isl_union_pw_multi_aff *
4193 isl_union_pw_multi_aff_add_pw_multi_aff(
4194 __isl_take isl_union_pw_multi_aff *upma,
4195 __isl_take isl_pw_multi_aff *pma);
4196 __isl_give isl_union_pw_multi_aff *
4197 isl_union_pw_multi_aff_from_domain(
4198 __isl_take isl_union_set *uset);
4200 A piecewise multiple quasi affine expression can also be initialized
4201 from an C<isl_set> or C<isl_map>, provided the C<isl_set> is a singleton
4202 and the C<isl_map> is single-valued.
4203 In case of a conversion from an C<isl_union_set> or an C<isl_union_map>
4204 to an C<isl_union_pw_multi_aff>, these properties need to hold in each space.
4206 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_from_set(
4207 __isl_take isl_set *set);
4208 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_from_map(
4209 __isl_take isl_map *map);
4211 __isl_give isl_union_pw_multi_aff *
4212 isl_union_pw_multi_aff_from_union_set(
4213 __isl_take isl_union_set *uset);
4214 __isl_give isl_union_pw_multi_aff *
4215 isl_union_pw_multi_aff_from_union_map(
4216 __isl_take isl_union_map *umap);
4218 Multiple quasi affine expressions can be copied and freed using
4220 #include <isl/aff.h>
4221 __isl_give isl_multi_aff *isl_multi_aff_copy(
4222 __isl_keep isl_multi_aff *maff);
4223 void *isl_multi_aff_free(__isl_take isl_multi_aff *maff);
4225 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_copy(
4226 __isl_keep isl_pw_multi_aff *pma);
4227 void *isl_pw_multi_aff_free(
4228 __isl_take isl_pw_multi_aff *pma);
4230 __isl_give isl_union_pw_multi_aff *
4231 isl_union_pw_multi_aff_copy(
4232 __isl_keep isl_union_pw_multi_aff *upma);
4233 void *isl_union_pw_multi_aff_free(
4234 __isl_take isl_union_pw_multi_aff *upma);
4236 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_copy(
4237 __isl_keep isl_multi_pw_aff *mpa);
4238 void *isl_multi_pw_aff_free(
4239 __isl_take isl_multi_pw_aff *mpa);
4241 The expression can be inspected using
4243 #include <isl/aff.h>
4244 isl_ctx *isl_multi_aff_get_ctx(
4245 __isl_keep isl_multi_aff *maff);
4246 isl_ctx *isl_pw_multi_aff_get_ctx(
4247 __isl_keep isl_pw_multi_aff *pma);
4248 isl_ctx *isl_union_pw_multi_aff_get_ctx(
4249 __isl_keep isl_union_pw_multi_aff *upma);
4250 isl_ctx *isl_multi_pw_aff_get_ctx(
4251 __isl_keep isl_multi_pw_aff *mpa);
4252 unsigned isl_multi_aff_dim(__isl_keep isl_multi_aff *maff,
4253 enum isl_dim_type type);
4254 unsigned isl_pw_multi_aff_dim(
4255 __isl_keep isl_pw_multi_aff *pma,
4256 enum isl_dim_type type);
4257 unsigned isl_multi_pw_aff_dim(
4258 __isl_keep isl_multi_pw_aff *mpa,
4259 enum isl_dim_type type);
4260 __isl_give isl_aff *isl_multi_aff_get_aff(
4261 __isl_keep isl_multi_aff *multi, int pos);
4262 __isl_give isl_pw_aff *isl_pw_multi_aff_get_pw_aff(
4263 __isl_keep isl_pw_multi_aff *pma, int pos);
4264 __isl_give isl_pw_aff *isl_multi_pw_aff_get_pw_aff(
4265 __isl_keep isl_multi_pw_aff *mpa, int pos);
4266 int isl_multi_aff_find_dim_by_id(
4267 __isl_keep isl_multi_aff *ma,
4268 enum isl_dim_type type, __isl_keep isl_id *id);
4269 int isl_multi_pw_aff_find_dim_by_id(
4270 __isl_keep isl_multi_pw_aff *mpa,
4271 enum isl_dim_type type, __isl_keep isl_id *id);
4272 const char *isl_pw_multi_aff_get_dim_name(
4273 __isl_keep isl_pw_multi_aff *pma,
4274 enum isl_dim_type type, unsigned pos);
4275 __isl_give isl_id *isl_multi_aff_get_dim_id(
4276 __isl_keep isl_multi_aff *ma,
4277 enum isl_dim_type type, unsigned pos);
4278 __isl_give isl_id *isl_pw_multi_aff_get_dim_id(
4279 __isl_keep isl_pw_multi_aff *pma,
4280 enum isl_dim_type type, unsigned pos);
4281 __isl_give isl_id *isl_multi_pw_aff_get_dim_id(
4282 __isl_keep isl_multi_pw_aff *mpa,
4283 enum isl_dim_type type, unsigned pos);
4284 const char *isl_multi_aff_get_tuple_name(
4285 __isl_keep isl_multi_aff *multi,
4286 enum isl_dim_type type);
4287 int isl_pw_multi_aff_has_tuple_name(
4288 __isl_keep isl_pw_multi_aff *pma,
4289 enum isl_dim_type type);
4290 const char *isl_pw_multi_aff_get_tuple_name(
4291 __isl_keep isl_pw_multi_aff *pma,
4292 enum isl_dim_type type);
4293 int isl_multi_aff_has_tuple_id(__isl_keep isl_multi_aff *ma,
4294 enum isl_dim_type type);
4295 int isl_pw_multi_aff_has_tuple_id(
4296 __isl_keep isl_pw_multi_aff *pma,
4297 enum isl_dim_type type);
4298 int isl_multi_pw_aff_has_tuple_id(
4299 __isl_keep isl_multi_pw_aff *mpa,
4300 enum isl_dim_type type);
4301 __isl_give isl_id *isl_multi_aff_get_tuple_id(
4302 __isl_keep isl_multi_aff *ma,
4303 enum isl_dim_type type);
4304 __isl_give isl_id *isl_pw_multi_aff_get_tuple_id(
4305 __isl_keep isl_pw_multi_aff *pma,
4306 enum isl_dim_type type);
4307 __isl_give isl_id *isl_multi_pw_aff_get_tuple_id(
4308 __isl_keep isl_multi_pw_aff *mpa,
4309 enum isl_dim_type type);
4310 int isl_multi_aff_range_is_wrapping(
4311 __isl_keep isl_multi_aff *ma);
4312 int isl_multi_pw_aff_range_is_wrapping(
4313 __isl_keep isl_multi_pw_aff *mpa);
4315 int isl_pw_multi_aff_foreach_piece(
4316 __isl_keep isl_pw_multi_aff *pma,
4317 int (*fn)(__isl_take isl_set *set,
4318 __isl_take isl_multi_aff *maff,
4319 void *user), void *user);
4321 int isl_union_pw_multi_aff_foreach_pw_multi_aff(
4322 __isl_keep isl_union_pw_multi_aff *upma,
4323 int (*fn)(__isl_take isl_pw_multi_aff *pma,
4324 void *user), void *user);
4326 It can be modified using
4328 #include <isl/aff.h>
4329 __isl_give isl_multi_aff *isl_multi_aff_set_aff(
4330 __isl_take isl_multi_aff *multi, int pos,
4331 __isl_take isl_aff *aff);
4332 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_set_pw_aff(
4333 __isl_take isl_pw_multi_aff *pma, unsigned pos,
4334 __isl_take isl_pw_aff *pa);
4335 __isl_give isl_multi_aff *isl_multi_aff_set_dim_name(
4336 __isl_take isl_multi_aff *maff,
4337 enum isl_dim_type type, unsigned pos, const char *s);
4338 __isl_give isl_multi_aff *isl_multi_aff_set_dim_id(
4339 __isl_take isl_multi_aff *maff,
4340 enum isl_dim_type type, unsigned pos,
4341 __isl_take isl_id *id);
4342 __isl_give isl_multi_aff *isl_multi_aff_set_tuple_name(
4343 __isl_take isl_multi_aff *maff,
4344 enum isl_dim_type type, const char *s);
4345 __isl_give isl_multi_aff *isl_multi_aff_set_tuple_id(
4346 __isl_take isl_multi_aff *maff,
4347 enum isl_dim_type type, __isl_take isl_id *id);
4348 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_set_tuple_id(
4349 __isl_take isl_pw_multi_aff *pma,
4350 enum isl_dim_type type, __isl_take isl_id *id);
4351 __isl_give isl_multi_aff *isl_multi_aff_reset_tuple_id(
4352 __isl_take isl_multi_aff *ma,
4353 enum isl_dim_type type);
4354 __isl_give isl_multi_pw_aff *
4355 isl_multi_pw_aff_reset_tuple_id(
4356 __isl_take isl_multi_pw_aff *mpa,
4357 enum isl_dim_type type);
4358 __isl_give isl_multi_aff *isl_multi_aff_reset_user(
4359 __isl_take isl_multi_aff *ma);
4360 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_reset_user(
4361 __isl_take isl_multi_pw_aff *mpa);
4363 __isl_give isl_multi_pw_aff *
4364 isl_multi_pw_aff_set_dim_name(
4365 __isl_take isl_multi_pw_aff *mpa,
4366 enum isl_dim_type type, unsigned pos, const char *s);
4367 __isl_give isl_multi_pw_aff *
4368 isl_multi_pw_aff_set_dim_id(
4369 __isl_take isl_multi_pw_aff *mpa,
4370 enum isl_dim_type type, unsigned pos,
4371 __isl_take isl_id *id);
4372 __isl_give isl_multi_pw_aff *
4373 isl_multi_pw_aff_set_tuple_name(
4374 __isl_take isl_multi_pw_aff *mpa,
4375 enum isl_dim_type type, const char *s);
4377 __isl_give isl_multi_aff *isl_multi_aff_insert_dims(
4378 __isl_take isl_multi_aff *ma,
4379 enum isl_dim_type type, unsigned first, unsigned n);
4380 __isl_give isl_multi_aff *isl_multi_aff_add_dims(
4381 __isl_take isl_multi_aff *ma,
4382 enum isl_dim_type type, unsigned n);
4383 __isl_give isl_multi_aff *isl_multi_aff_drop_dims(
4384 __isl_take isl_multi_aff *maff,
4385 enum isl_dim_type type, unsigned first, unsigned n);
4386 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_drop_dims(
4387 __isl_take isl_pw_multi_aff *pma,
4388 enum isl_dim_type type, unsigned first, unsigned n);
4390 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_insert_dims(
4391 __isl_take isl_multi_pw_aff *mpa,
4392 enum isl_dim_type type, unsigned first, unsigned n);
4393 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_add_dims(
4394 __isl_take isl_multi_pw_aff *mpa,
4395 enum isl_dim_type type, unsigned n);
4396 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_move_dims(
4397 __isl_take isl_multi_pw_aff *pma,
4398 enum isl_dim_type dst_type, unsigned dst_pos,
4399 enum isl_dim_type src_type, unsigned src_pos,
4402 To check whether two multiple affine expressions are
4403 (obviously) equal to each other, use
4405 int isl_multi_aff_plain_is_equal(__isl_keep isl_multi_aff *maff1,
4406 __isl_keep isl_multi_aff *maff2);
4407 int isl_pw_multi_aff_plain_is_equal(
4408 __isl_keep isl_pw_multi_aff *pma1,
4409 __isl_keep isl_pw_multi_aff *pma2);
4410 int isl_multi_pw_aff_plain_is_equal(
4411 __isl_keep isl_multi_pw_aff *mpa1,
4412 __isl_keep isl_multi_pw_aff *mpa2);
4413 int isl_multi_pw_aff_is_equal(
4414 __isl_keep isl_multi_pw_aff *mpa1,
4415 __isl_keep isl_multi_pw_aff *mpa2);
4419 #include <isl/aff.h>
4420 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_union_lexmin(
4421 __isl_take isl_pw_multi_aff *pma1,
4422 __isl_take isl_pw_multi_aff *pma2);
4423 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_union_lexmax(
4424 __isl_take isl_pw_multi_aff *pma1,
4425 __isl_take isl_pw_multi_aff *pma2);
4426 __isl_give isl_multi_aff *isl_multi_aff_add(
4427 __isl_take isl_multi_aff *maff1,
4428 __isl_take isl_multi_aff *maff2);
4429 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_add(
4430 __isl_take isl_pw_multi_aff *pma1,
4431 __isl_take isl_pw_multi_aff *pma2);
4432 __isl_give isl_union_pw_multi_aff *isl_union_pw_multi_aff_add(
4433 __isl_take isl_union_pw_multi_aff *upma1,
4434 __isl_take isl_union_pw_multi_aff *upma2);
4435 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_union_add(
4436 __isl_take isl_pw_multi_aff *pma1,
4437 __isl_take isl_pw_multi_aff *pma2);
4438 __isl_give isl_multi_aff *isl_multi_aff_sub(
4439 __isl_take isl_multi_aff *ma1,
4440 __isl_take isl_multi_aff *ma2);
4441 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_sub(
4442 __isl_take isl_pw_multi_aff *pma1,
4443 __isl_take isl_pw_multi_aff *pma2);
4444 __isl_give isl_union_pw_multi_aff *isl_union_pw_multi_aff_sub(
4445 __isl_take isl_union_pw_multi_aff *upma1,
4446 __isl_take isl_union_pw_multi_aff *upma2);
4448 C<isl_multi_aff_sub> subtracts the second argument from the first.
4450 __isl_give isl_multi_aff *isl_multi_aff_scale_val(
4451 __isl_take isl_multi_aff *ma,
4452 __isl_take isl_val *v);
4453 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_scale_val(
4454 __isl_take isl_pw_multi_aff *pma,
4455 __isl_take isl_val *v);
4456 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_scale_val(
4457 __isl_take isl_multi_pw_aff *mpa,
4458 __isl_take isl_val *v);
4459 __isl_give isl_multi_aff *isl_multi_aff_scale_multi_val(
4460 __isl_take isl_multi_aff *ma,
4461 __isl_take isl_multi_val *mv);
4462 __isl_give isl_pw_multi_aff *
4463 isl_pw_multi_aff_scale_multi_val(
4464 __isl_take isl_pw_multi_aff *pma,
4465 __isl_take isl_multi_val *mv);
4466 __isl_give isl_multi_pw_aff *
4467 isl_multi_pw_aff_scale_multi_val(
4468 __isl_take isl_multi_pw_aff *mpa,
4469 __isl_take isl_multi_val *mv);
4470 __isl_give isl_union_pw_multi_aff *
4471 isl_union_pw_multi_aff_scale_multi_val(
4472 __isl_take isl_union_pw_multi_aff *upma,
4473 __isl_take isl_multi_val *mv);
4474 __isl_give isl_multi_aff *
4475 isl_multi_aff_scale_down_multi_val(
4476 __isl_take isl_multi_aff *ma,
4477 __isl_take isl_multi_val *mv);
4478 __isl_give isl_multi_pw_aff *
4479 isl_multi_pw_aff_scale_down_multi_val(
4480 __isl_take isl_multi_pw_aff *mpa,
4481 __isl_take isl_multi_val *mv);
4483 C<isl_multi_aff_scale_multi_val> scales the elements of C<ma>
4484 by the corresponding elements of C<mv>.
4486 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_fix_si(
4487 __isl_take isl_pw_multi_aff *pma,
4488 enum isl_dim_type type, unsigned pos, int value);
4489 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_intersect_params(
4490 __isl_take isl_pw_multi_aff *pma,
4491 __isl_take isl_set *set);
4492 __isl_give isl_set *isl_multi_pw_aff_domain(
4493 __isl_take isl_multi_pw_aff *mpa);
4494 __isl_give isl_multi_pw_aff *
4495 isl_multi_pw_aff_intersect_params(
4496 __isl_take isl_multi_pw_aff *mpa,
4497 __isl_take isl_set *set);
4498 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_intersect_domain(
4499 __isl_take isl_pw_multi_aff *pma,
4500 __isl_take isl_set *set);
4501 __isl_give isl_multi_pw_aff *
4502 isl_multi_pw_aff_intersect_domain(
4503 __isl_take isl_multi_pw_aff *mpa,
4504 __isl_take isl_set *domain);
4505 __isl_give isl_union_pw_multi_aff *
4506 isl_union_pw_multi_aff_intersect_domain(
4507 __isl_take isl_union_pw_multi_aff *upma,
4508 __isl_take isl_union_set *uset);
4509 __isl_give isl_multi_aff *isl_multi_aff_lift(
4510 __isl_take isl_multi_aff *maff,
4511 __isl_give isl_local_space **ls);
4512 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_coalesce(
4513 __isl_take isl_pw_multi_aff *pma);
4514 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_coalesce(
4515 __isl_take isl_multi_pw_aff *mpa);
4516 __isl_give isl_multi_aff *isl_multi_aff_align_params(
4517 __isl_take isl_multi_aff *multi,
4518 __isl_take isl_space *model);
4519 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_align_params(
4520 __isl_take isl_pw_multi_aff *pma,
4521 __isl_take isl_space *model);
4522 __isl_give isl_pw_multi_aff *
4523 isl_pw_multi_aff_project_domain_on_params(
4524 __isl_take isl_pw_multi_aff *pma);
4525 __isl_give isl_multi_aff *isl_multi_aff_gist_params(
4526 __isl_take isl_multi_aff *maff,
4527 __isl_take isl_set *context);
4528 __isl_give isl_multi_aff *isl_multi_aff_gist(
4529 __isl_take isl_multi_aff *maff,
4530 __isl_take isl_set *context);
4531 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_gist_params(
4532 __isl_take isl_pw_multi_aff *pma,
4533 __isl_take isl_set *set);
4534 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_gist(
4535 __isl_take isl_pw_multi_aff *pma,
4536 __isl_take isl_set *set);
4537 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_gist_params(
4538 __isl_take isl_multi_pw_aff *mpa,
4539 __isl_take isl_set *set);
4540 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_gist(
4541 __isl_take isl_multi_pw_aff *mpa,
4542 __isl_take isl_set *set);
4543 __isl_give isl_multi_aff *isl_multi_aff_from_range(
4544 __isl_take isl_multi_aff *ma);
4545 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_from_range(
4546 __isl_take isl_multi_pw_aff *mpa);
4547 __isl_give isl_set *isl_pw_multi_aff_domain(
4548 __isl_take isl_pw_multi_aff *pma);
4549 __isl_give isl_union_set *isl_union_pw_multi_aff_domain(
4550 __isl_take isl_union_pw_multi_aff *upma);
4551 __isl_give isl_multi_aff *isl_multi_aff_range_splice(
4552 __isl_take isl_multi_aff *ma1, unsigned pos,
4553 __isl_take isl_multi_aff *ma2);
4554 __isl_give isl_multi_aff *isl_multi_aff_splice(
4555 __isl_take isl_multi_aff *ma1,
4556 unsigned in_pos, unsigned out_pos,
4557 __isl_take isl_multi_aff *ma2);
4558 __isl_give isl_multi_aff *isl_multi_aff_range_product(
4559 __isl_take isl_multi_aff *ma1,
4560 __isl_take isl_multi_aff *ma2);
4561 __isl_give isl_multi_aff *
4562 isl_multi_aff_range_factor_domain(
4563 __isl_take isl_multi_aff *ma);
4564 __isl_give isl_multi_aff *
4565 isl_multi_aff_range_factor_range(
4566 __isl_take isl_multi_aff *ma);
4567 __isl_give isl_multi_aff *isl_multi_aff_flat_range_product(
4568 __isl_take isl_multi_aff *ma1,
4569 __isl_take isl_multi_aff *ma2);
4570 __isl_give isl_multi_aff *isl_multi_aff_product(
4571 __isl_take isl_multi_aff *ma1,
4572 __isl_take isl_multi_aff *ma2);
4573 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_product(
4574 __isl_take isl_multi_pw_aff *mpa1,
4575 __isl_take isl_multi_pw_aff *mpa2);
4576 __isl_give isl_pw_multi_aff *
4577 isl_pw_multi_aff_range_product(
4578 __isl_take isl_pw_multi_aff *pma1,
4579 __isl_take isl_pw_multi_aff *pma2);
4580 __isl_give isl_multi_pw_aff *
4581 isl_multi_pw_aff_range_factor_domain(
4582 __isl_take isl_multi_pw_aff *mpa);
4583 __isl_give isl_multi_pw_aff *
4584 isl_multi_pw_aff_range_factor_range(
4585 __isl_take isl_multi_pw_aff *mpa);
4586 __isl_give isl_pw_multi_aff *
4587 isl_pw_multi_aff_flat_range_product(
4588 __isl_take isl_pw_multi_aff *pma1,
4589 __isl_take isl_pw_multi_aff *pma2);
4590 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_product(
4591 __isl_take isl_pw_multi_aff *pma1,
4592 __isl_take isl_pw_multi_aff *pma2);
4593 __isl_give isl_union_pw_multi_aff *
4594 isl_union_pw_multi_aff_flat_range_product(
4595 __isl_take isl_union_pw_multi_aff *upma1,
4596 __isl_take isl_union_pw_multi_aff *upma2);
4597 __isl_give isl_multi_pw_aff *
4598 isl_multi_pw_aff_range_splice(
4599 __isl_take isl_multi_pw_aff *mpa1, unsigned pos,
4600 __isl_take isl_multi_pw_aff *mpa2);
4601 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_splice(
4602 __isl_take isl_multi_pw_aff *mpa1,
4603 unsigned in_pos, unsigned out_pos,
4604 __isl_take isl_multi_pw_aff *mpa2);
4605 __isl_give isl_multi_pw_aff *
4606 isl_multi_pw_aff_range_product(
4607 __isl_take isl_multi_pw_aff *mpa1,
4608 __isl_take isl_multi_pw_aff *mpa2);
4609 __isl_give isl_multi_pw_aff *
4610 isl_multi_pw_aff_flat_range_product(
4611 __isl_take isl_multi_pw_aff *mpa1,
4612 __isl_take isl_multi_pw_aff *mpa2);
4614 If the C<ls> argument of C<isl_multi_aff_lift> is not C<NULL>,
4615 then it is assigned the local space that lies at the basis of
4616 the lifting applied.
4618 #include <isl/aff.h>
4619 __isl_give isl_multi_aff *isl_multi_aff_pullback_multi_aff(
4620 __isl_take isl_multi_aff *ma1,
4621 __isl_take isl_multi_aff *ma2);
4622 __isl_give isl_pw_multi_aff *
4623 isl_pw_multi_aff_pullback_multi_aff(
4624 __isl_take isl_pw_multi_aff *pma,
4625 __isl_take isl_multi_aff *ma);
4626 __isl_give isl_multi_pw_aff *
4627 isl_multi_pw_aff_pullback_multi_aff(
4628 __isl_take isl_multi_pw_aff *mpa,
4629 __isl_take isl_multi_aff *ma);
4630 __isl_give isl_pw_multi_aff *
4631 isl_pw_multi_aff_pullback_pw_multi_aff(
4632 __isl_take isl_pw_multi_aff *pma1,
4633 __isl_take isl_pw_multi_aff *pma2);
4634 __isl_give isl_multi_pw_aff *
4635 isl_multi_pw_aff_pullback_pw_multi_aff(
4636 __isl_take isl_multi_pw_aff *mpa,
4637 __isl_take isl_pw_multi_aff *pma);
4638 __isl_give isl_multi_pw_aff *
4639 isl_multi_pw_aff_pullback_multi_pw_aff(
4640 __isl_take isl_multi_pw_aff *mpa1,
4641 __isl_take isl_multi_pw_aff *mpa2);
4643 The function C<isl_multi_aff_pullback_multi_aff> precomposes C<ma1> by C<ma2>.
4644 In other words, C<ma2> is plugged
4647 __isl_give isl_set *isl_multi_aff_lex_le_set(
4648 __isl_take isl_multi_aff *ma1,
4649 __isl_take isl_multi_aff *ma2);
4650 __isl_give isl_set *isl_multi_aff_lex_ge_set(
4651 __isl_take isl_multi_aff *ma1,
4652 __isl_take isl_multi_aff *ma2);
4654 The function C<isl_multi_aff_lex_le_set> returns a set
4655 containing those elements in the shared domain space
4656 where C<ma1> is lexicographically smaller than or
4659 An expression can be read from input using
4661 #include <isl/aff.h>
4662 __isl_give isl_multi_aff *isl_multi_aff_read_from_str(
4663 isl_ctx *ctx, const char *str);
4664 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_read_from_str(
4665 isl_ctx *ctx, const char *str);
4666 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_read_from_str(
4667 isl_ctx *ctx, const char *str);
4668 __isl_give isl_union_pw_multi_aff *
4669 isl_union_pw_multi_aff_read_from_str(
4670 isl_ctx *ctx, const char *str);
4672 An expression can be printed using
4674 #include <isl/aff.h>
4675 __isl_give isl_printer *isl_printer_print_multi_aff(
4676 __isl_take isl_printer *p,
4677 __isl_keep isl_multi_aff *maff);
4678 __isl_give isl_printer *isl_printer_print_pw_multi_aff(
4679 __isl_take isl_printer *p,
4680 __isl_keep isl_pw_multi_aff *pma);
4681 __isl_give isl_printer *isl_printer_print_union_pw_multi_aff(
4682 __isl_take isl_printer *p,
4683 __isl_keep isl_union_pw_multi_aff *upma);
4684 __isl_give isl_printer *isl_printer_print_multi_pw_aff(
4685 __isl_take isl_printer *p,
4686 __isl_keep isl_multi_pw_aff *mpa);
4690 Points are elements of a set. They can be used to construct
4691 simple sets (boxes) or they can be used to represent the
4692 individual elements of a set.
4693 The zero point (the origin) can be created using
4695 __isl_give isl_point *isl_point_zero(__isl_take isl_space *space);
4697 The coordinates of a point can be inspected, set and changed
4700 __isl_give isl_val *isl_point_get_coordinate_val(
4701 __isl_keep isl_point *pnt,
4702 enum isl_dim_type type, int pos);
4703 __isl_give isl_point *isl_point_set_coordinate_val(
4704 __isl_take isl_point *pnt,
4705 enum isl_dim_type type, int pos,
4706 __isl_take isl_val *v);
4708 __isl_give isl_point *isl_point_add_ui(
4709 __isl_take isl_point *pnt,
4710 enum isl_dim_type type, int pos, unsigned val);
4711 __isl_give isl_point *isl_point_sub_ui(
4712 __isl_take isl_point *pnt,
4713 enum isl_dim_type type, int pos, unsigned val);
4715 Other properties can be obtained using
4717 isl_ctx *isl_point_get_ctx(__isl_keep isl_point *pnt);
4719 Points can be copied or freed using
4721 __isl_give isl_point *isl_point_copy(
4722 __isl_keep isl_point *pnt);
4723 void isl_point_free(__isl_take isl_point *pnt);
4725 A singleton set can be created from a point using
4727 __isl_give isl_basic_set *isl_basic_set_from_point(
4728 __isl_take isl_point *pnt);
4729 __isl_give isl_set *isl_set_from_point(
4730 __isl_take isl_point *pnt);
4732 and a box can be created from two opposite extremal points using
4734 __isl_give isl_basic_set *isl_basic_set_box_from_points(
4735 __isl_take isl_point *pnt1,
4736 __isl_take isl_point *pnt2);
4737 __isl_give isl_set *isl_set_box_from_points(
4738 __isl_take isl_point *pnt1,
4739 __isl_take isl_point *pnt2);
4741 All elements of a B<bounded> (union) set can be enumerated using
4742 the following functions.
4744 int isl_set_foreach_point(__isl_keep isl_set *set,
4745 int (*fn)(__isl_take isl_point *pnt, void *user),
4747 int isl_union_set_foreach_point(__isl_keep isl_union_set *uset,
4748 int (*fn)(__isl_take isl_point *pnt, void *user),
4751 The function C<fn> is called for each integer point in
4752 C<set> with as second argument the last argument of
4753 the C<isl_set_foreach_point> call. The function C<fn>
4754 should return C<0> on success and C<-1> on failure.
4755 In the latter case, C<isl_set_foreach_point> will stop
4756 enumerating and return C<-1> as well.
4757 If the enumeration is performed successfully and to completion,
4758 then C<isl_set_foreach_point> returns C<0>.
4760 To obtain a single point of a (basic) set, use
4762 __isl_give isl_point *isl_basic_set_sample_point(
4763 __isl_take isl_basic_set *bset);
4764 __isl_give isl_point *isl_set_sample_point(
4765 __isl_take isl_set *set);
4767 If C<set> does not contain any (integer) points, then the
4768 resulting point will be ``void'', a property that can be
4771 int isl_point_is_void(__isl_keep isl_point *pnt);
4773 =head2 Piecewise Quasipolynomials
4775 A piecewise quasipolynomial is a particular kind of function that maps
4776 a parametric point to a rational value.
4777 More specifically, a quasipolynomial is a polynomial expression in greatest
4778 integer parts of affine expressions of parameters and variables.
4779 A piecewise quasipolynomial is a subdivision of a given parametric
4780 domain into disjoint cells with a quasipolynomial associated to
4781 each cell. The value of the piecewise quasipolynomial at a given
4782 point is the value of the quasipolynomial associated to the cell
4783 that contains the point. Outside of the union of cells,
4784 the value is assumed to be zero.
4785 For example, the piecewise quasipolynomial
4787 [n] -> { [x] -> ((1 + n) - x) : x <= n and x >= 0 }
4789 maps C<x> to C<1 + n - x> for values of C<x> between C<0> and C<n>.
4790 A given piecewise quasipolynomial has a fixed domain dimension.
4791 Union piecewise quasipolynomials are used to contain piecewise quasipolynomials
4792 defined over different domains.
4793 Piecewise quasipolynomials are mainly used by the C<barvinok>
4794 library for representing the number of elements in a parametric set or map.
4795 For example, the piecewise quasipolynomial above represents
4796 the number of points in the map
4798 [n] -> { [x] -> [y] : x,y >= 0 and 0 <= x + y <= n }
4800 =head3 Input and Output
4802 Piecewise quasipolynomials can be read from input using
4804 __isl_give isl_union_pw_qpolynomial *
4805 isl_union_pw_qpolynomial_read_from_str(
4806 isl_ctx *ctx, const char *str);
4808 Quasipolynomials and piecewise quasipolynomials can be printed
4809 using the following functions.
4811 __isl_give isl_printer *isl_printer_print_qpolynomial(
4812 __isl_take isl_printer *p,
4813 __isl_keep isl_qpolynomial *qp);
4815 __isl_give isl_printer *isl_printer_print_pw_qpolynomial(
4816 __isl_take isl_printer *p,
4817 __isl_keep isl_pw_qpolynomial *pwqp);
4819 __isl_give isl_printer *isl_printer_print_union_pw_qpolynomial(
4820 __isl_take isl_printer *p,
4821 __isl_keep isl_union_pw_qpolynomial *upwqp);
4823 The output format of the printer
4824 needs to be set to either C<ISL_FORMAT_ISL> or C<ISL_FORMAT_C>.
4825 For C<isl_printer_print_union_pw_qpolynomial>, only C<ISL_FORMAT_ISL>
4827 In case of printing in C<ISL_FORMAT_C>, the user may want
4828 to set the names of all dimensions
4830 __isl_give isl_qpolynomial *isl_qpolynomial_set_dim_name(
4831 __isl_take isl_qpolynomial *qp,
4832 enum isl_dim_type type, unsigned pos,
4834 __isl_give isl_pw_qpolynomial *
4835 isl_pw_qpolynomial_set_dim_name(
4836 __isl_take isl_pw_qpolynomial *pwqp,
4837 enum isl_dim_type type, unsigned pos,
4840 =head3 Creating New (Piecewise) Quasipolynomials
4842 Some simple quasipolynomials can be created using the following functions.
4843 More complicated quasipolynomials can be created by applying
4844 operations such as addition and multiplication
4845 on the resulting quasipolynomials
4847 __isl_give isl_qpolynomial *isl_qpolynomial_zero_on_domain(
4848 __isl_take isl_space *domain);
4849 __isl_give isl_qpolynomial *isl_qpolynomial_one_on_domain(
4850 __isl_take isl_space *domain);
4851 __isl_give isl_qpolynomial *isl_qpolynomial_infty_on_domain(
4852 __isl_take isl_space *domain);
4853 __isl_give isl_qpolynomial *isl_qpolynomial_neginfty_on_domain(
4854 __isl_take isl_space *domain);
4855 __isl_give isl_qpolynomial *isl_qpolynomial_nan_on_domain(
4856 __isl_take isl_space *domain);
4857 __isl_give isl_qpolynomial *isl_qpolynomial_val_on_domain(
4858 __isl_take isl_space *domain,
4859 __isl_take isl_val *val);
4860 __isl_give isl_qpolynomial *isl_qpolynomial_var_on_domain(
4861 __isl_take isl_space *domain,
4862 enum isl_dim_type type, unsigned pos);
4863 __isl_give isl_qpolynomial *isl_qpolynomial_from_aff(
4864 __isl_take isl_aff *aff);
4866 Note that the space in which a quasipolynomial lives is a map space
4867 with a one-dimensional range. The C<domain> argument in some of
4868 the functions above corresponds to the domain of this map space.
4870 The zero piecewise quasipolynomial or a piecewise quasipolynomial
4871 with a single cell can be created using the following functions.
4872 Multiple of these single cell piecewise quasipolynomials can
4873 be combined to create more complicated piecewise quasipolynomials.
4875 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_zero(
4876 __isl_take isl_space *space);
4877 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_alloc(
4878 __isl_take isl_set *set,
4879 __isl_take isl_qpolynomial *qp);
4880 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_from_qpolynomial(
4881 __isl_take isl_qpolynomial *qp);
4882 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_from_pw_aff(
4883 __isl_take isl_pw_aff *pwaff);
4885 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_zero(
4886 __isl_take isl_space *space);
4887 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_from_pw_qpolynomial(
4888 __isl_take isl_pw_qpolynomial *pwqp);
4889 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_add_pw_qpolynomial(
4890 __isl_take isl_union_pw_qpolynomial *upwqp,
4891 __isl_take isl_pw_qpolynomial *pwqp);
4893 Quasipolynomials can be copied and freed again using the following
4896 __isl_give isl_qpolynomial *isl_qpolynomial_copy(
4897 __isl_keep isl_qpolynomial *qp);
4898 void *isl_qpolynomial_free(__isl_take isl_qpolynomial *qp);
4900 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_copy(
4901 __isl_keep isl_pw_qpolynomial *pwqp);
4902 void *isl_pw_qpolynomial_free(
4903 __isl_take isl_pw_qpolynomial *pwqp);
4905 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_copy(
4906 __isl_keep isl_union_pw_qpolynomial *upwqp);
4907 void *isl_union_pw_qpolynomial_free(
4908 __isl_take isl_union_pw_qpolynomial *upwqp);
4910 =head3 Inspecting (Piecewise) Quasipolynomials
4912 To iterate over all piecewise quasipolynomials in a union
4913 piecewise quasipolynomial, use the following function
4915 int isl_union_pw_qpolynomial_foreach_pw_qpolynomial(
4916 __isl_keep isl_union_pw_qpolynomial *upwqp,
4917 int (*fn)(__isl_take isl_pw_qpolynomial *pwqp, void *user),
4920 To extract the piecewise quasipolynomial in a given space from a union, use
4922 __isl_give isl_pw_qpolynomial *
4923 isl_union_pw_qpolynomial_extract_pw_qpolynomial(
4924 __isl_keep isl_union_pw_qpolynomial *upwqp,
4925 __isl_take isl_space *space);
4927 To iterate over the cells in a piecewise quasipolynomial,
4928 use either of the following two functions
4930 int isl_pw_qpolynomial_foreach_piece(
4931 __isl_keep isl_pw_qpolynomial *pwqp,
4932 int (*fn)(__isl_take isl_set *set,
4933 __isl_take isl_qpolynomial *qp,
4934 void *user), void *user);
4935 int isl_pw_qpolynomial_foreach_lifted_piece(
4936 __isl_keep isl_pw_qpolynomial *pwqp,
4937 int (*fn)(__isl_take isl_set *set,
4938 __isl_take isl_qpolynomial *qp,
4939 void *user), void *user);
4941 As usual, the function C<fn> should return C<0> on success
4942 and C<-1> on failure. The difference between
4943 C<isl_pw_qpolynomial_foreach_piece> and
4944 C<isl_pw_qpolynomial_foreach_lifted_piece> is that
4945 C<isl_pw_qpolynomial_foreach_lifted_piece> will first
4946 compute unique representations for all existentially quantified
4947 variables and then turn these existentially quantified variables
4948 into extra set variables, adapting the associated quasipolynomial
4949 accordingly. This means that the C<set> passed to C<fn>
4950 will not have any existentially quantified variables, but that
4951 the dimensions of the sets may be different for different
4952 invocations of C<fn>.
4954 The constant term of a quasipolynomial can be extracted using
4956 __isl_give isl_val *isl_qpolynomial_get_constant_val(
4957 __isl_keep isl_qpolynomial *qp);
4959 To iterate over all terms in a quasipolynomial,
4962 int isl_qpolynomial_foreach_term(
4963 __isl_keep isl_qpolynomial *qp,
4964 int (*fn)(__isl_take isl_term *term,
4965 void *user), void *user);
4967 The terms themselves can be inspected and freed using
4970 unsigned isl_term_dim(__isl_keep isl_term *term,
4971 enum isl_dim_type type);
4972 __isl_give isl_val *isl_term_get_coefficient_val(
4973 __isl_keep isl_term *term);
4974 int isl_term_get_exp(__isl_keep isl_term *term,
4975 enum isl_dim_type type, unsigned pos);
4976 __isl_give isl_aff *isl_term_get_div(
4977 __isl_keep isl_term *term, unsigned pos);
4978 void isl_term_free(__isl_take isl_term *term);
4980 Each term is a product of parameters, set variables and
4981 integer divisions. The function C<isl_term_get_exp>
4982 returns the exponent of a given dimensions in the given term.
4984 =head3 Properties of (Piecewise) Quasipolynomials
4986 To check whether two union piecewise quasipolynomials are
4987 obviously equal, use
4989 int isl_union_pw_qpolynomial_plain_is_equal(
4990 __isl_keep isl_union_pw_qpolynomial *upwqp1,
4991 __isl_keep isl_union_pw_qpolynomial *upwqp2);
4993 =head3 Operations on (Piecewise) Quasipolynomials
4995 __isl_give isl_qpolynomial *isl_qpolynomial_scale_val(
4996 __isl_take isl_qpolynomial *qp,
4997 __isl_take isl_val *v);
4998 __isl_give isl_qpolynomial *isl_qpolynomial_neg(
4999 __isl_take isl_qpolynomial *qp);
5000 __isl_give isl_qpolynomial *isl_qpolynomial_add(
5001 __isl_take isl_qpolynomial *qp1,
5002 __isl_take isl_qpolynomial *qp2);
5003 __isl_give isl_qpolynomial *isl_qpolynomial_sub(
5004 __isl_take isl_qpolynomial *qp1,
5005 __isl_take isl_qpolynomial *qp2);
5006 __isl_give isl_qpolynomial *isl_qpolynomial_mul(
5007 __isl_take isl_qpolynomial *qp1,
5008 __isl_take isl_qpolynomial *qp2);
5009 __isl_give isl_qpolynomial *isl_qpolynomial_pow(
5010 __isl_take isl_qpolynomial *qp, unsigned exponent);
5012 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_fix_val(
5013 __isl_take isl_pw_qpolynomial *pwqp,
5014 enum isl_dim_type type, unsigned n,
5015 __isl_take isl_val *v);
5016 __isl_give isl_pw_qpolynomial *
5017 isl_pw_qpolynomial_scale_val(
5018 __isl_take isl_pw_qpolynomial *pwqp,
5019 __isl_take isl_val *v);
5020 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_add(
5021 __isl_take isl_pw_qpolynomial *pwqp1,
5022 __isl_take isl_pw_qpolynomial *pwqp2);
5023 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_sub(
5024 __isl_take isl_pw_qpolynomial *pwqp1,
5025 __isl_take isl_pw_qpolynomial *pwqp2);
5026 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_add_disjoint(
5027 __isl_take isl_pw_qpolynomial *pwqp1,
5028 __isl_take isl_pw_qpolynomial *pwqp2);
5029 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_neg(
5030 __isl_take isl_pw_qpolynomial *pwqp);
5031 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_mul(
5032 __isl_take isl_pw_qpolynomial *pwqp1,
5033 __isl_take isl_pw_qpolynomial *pwqp2);
5034 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_pow(
5035 __isl_take isl_pw_qpolynomial *pwqp, unsigned exponent);
5037 __isl_give isl_union_pw_qpolynomial *
5038 isl_union_pw_qpolynomial_scale_val(
5039 __isl_take isl_union_pw_qpolynomial *upwqp,
5040 __isl_take isl_val *v);
5041 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_add(
5042 __isl_take isl_union_pw_qpolynomial *upwqp1,
5043 __isl_take isl_union_pw_qpolynomial *upwqp2);
5044 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_sub(
5045 __isl_take isl_union_pw_qpolynomial *upwqp1,
5046 __isl_take isl_union_pw_qpolynomial *upwqp2);
5047 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_mul(
5048 __isl_take isl_union_pw_qpolynomial *upwqp1,
5049 __isl_take isl_union_pw_qpolynomial *upwqp2);
5051 __isl_give isl_val *isl_pw_qpolynomial_eval(
5052 __isl_take isl_pw_qpolynomial *pwqp,
5053 __isl_take isl_point *pnt);
5055 __isl_give isl_val *isl_union_pw_qpolynomial_eval(
5056 __isl_take isl_union_pw_qpolynomial *upwqp,
5057 __isl_take isl_point *pnt);
5059 __isl_give isl_set *isl_pw_qpolynomial_domain(
5060 __isl_take isl_pw_qpolynomial *pwqp);
5061 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_intersect_domain(
5062 __isl_take isl_pw_qpolynomial *pwpq,
5063 __isl_take isl_set *set);
5064 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_intersect_params(
5065 __isl_take isl_pw_qpolynomial *pwpq,
5066 __isl_take isl_set *set);
5068 __isl_give isl_union_set *isl_union_pw_qpolynomial_domain(
5069 __isl_take isl_union_pw_qpolynomial *upwqp);
5070 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_intersect_domain(
5071 __isl_take isl_union_pw_qpolynomial *upwpq,
5072 __isl_take isl_union_set *uset);
5073 __isl_give isl_union_pw_qpolynomial *
5074 isl_union_pw_qpolynomial_intersect_params(
5075 __isl_take isl_union_pw_qpolynomial *upwpq,
5076 __isl_take isl_set *set);
5078 __isl_give isl_qpolynomial *isl_qpolynomial_align_params(
5079 __isl_take isl_qpolynomial *qp,
5080 __isl_take isl_space *model);
5082 __isl_give isl_qpolynomial *isl_qpolynomial_project_domain_on_params(
5083 __isl_take isl_qpolynomial *qp);
5084 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_project_domain_on_params(
5085 __isl_take isl_pw_qpolynomial *pwqp);
5087 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_coalesce(
5088 __isl_take isl_union_pw_qpolynomial *upwqp);
5090 __isl_give isl_qpolynomial *isl_qpolynomial_gist_params(
5091 __isl_take isl_qpolynomial *qp,
5092 __isl_take isl_set *context);
5093 __isl_give isl_qpolynomial *isl_qpolynomial_gist(
5094 __isl_take isl_qpolynomial *qp,
5095 __isl_take isl_set *context);
5097 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_gist_params(
5098 __isl_take isl_pw_qpolynomial *pwqp,
5099 __isl_take isl_set *context);
5100 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_gist(
5101 __isl_take isl_pw_qpolynomial *pwqp,
5102 __isl_take isl_set *context);
5104 __isl_give isl_union_pw_qpolynomial *
5105 isl_union_pw_qpolynomial_gist_params(
5106 __isl_take isl_union_pw_qpolynomial *upwqp,
5107 __isl_take isl_set *context);
5108 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_gist(
5109 __isl_take isl_union_pw_qpolynomial *upwqp,
5110 __isl_take isl_union_set *context);
5112 The gist operation applies the gist operation to each of
5113 the cells in the domain of the input piecewise quasipolynomial.
5114 The context is also exploited
5115 to simplify the quasipolynomials associated to each cell.
5117 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_to_polynomial(
5118 __isl_take isl_pw_qpolynomial *pwqp, int sign);
5119 __isl_give isl_union_pw_qpolynomial *
5120 isl_union_pw_qpolynomial_to_polynomial(
5121 __isl_take isl_union_pw_qpolynomial *upwqp, int sign);
5123 Approximate each quasipolynomial by a polynomial. If C<sign> is positive,
5124 the polynomial will be an overapproximation. If C<sign> is negative,
5125 it will be an underapproximation. If C<sign> is zero, the approximation
5126 will lie somewhere in between.
5128 =head2 Bounds on Piecewise Quasipolynomials and Piecewise Quasipolynomial Reductions
5130 A piecewise quasipolynomial reduction is a piecewise
5131 reduction (or fold) of quasipolynomials.
5132 In particular, the reduction can be maximum or a minimum.
5133 The objects are mainly used to represent the result of
5134 an upper or lower bound on a quasipolynomial over its domain,
5135 i.e., as the result of the following function.
5137 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_bound(
5138 __isl_take isl_pw_qpolynomial *pwqp,
5139 enum isl_fold type, int *tight);
5141 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_bound(
5142 __isl_take isl_union_pw_qpolynomial *upwqp,
5143 enum isl_fold type, int *tight);
5145 The C<type> argument may be either C<isl_fold_min> or C<isl_fold_max>.
5146 If C<tight> is not C<NULL>, then C<*tight> is set to C<1>
5147 is the returned bound is known be tight, i.e., for each value
5148 of the parameters there is at least
5149 one element in the domain that reaches the bound.
5150 If the domain of C<pwqp> is not wrapping, then the bound is computed
5151 over all elements in that domain and the result has a purely parametric
5152 domain. If the domain of C<pwqp> is wrapping, then the bound is
5153 computed over the range of the wrapped relation. The domain of the
5154 wrapped relation becomes the domain of the result.
5156 A (piecewise) quasipolynomial reduction can be copied or freed using the
5157 following functions.
5159 __isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_copy(
5160 __isl_keep isl_qpolynomial_fold *fold);
5161 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_copy(
5162 __isl_keep isl_pw_qpolynomial_fold *pwf);
5163 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_copy(
5164 __isl_keep isl_union_pw_qpolynomial_fold *upwf);
5165 void isl_qpolynomial_fold_free(
5166 __isl_take isl_qpolynomial_fold *fold);
5167 void *isl_pw_qpolynomial_fold_free(
5168 __isl_take isl_pw_qpolynomial_fold *pwf);
5169 void *isl_union_pw_qpolynomial_fold_free(
5170 __isl_take isl_union_pw_qpolynomial_fold *upwf);
5172 =head3 Printing Piecewise Quasipolynomial Reductions
5174 Piecewise quasipolynomial reductions can be printed
5175 using the following function.
5177 __isl_give isl_printer *isl_printer_print_pw_qpolynomial_fold(
5178 __isl_take isl_printer *p,
5179 __isl_keep isl_pw_qpolynomial_fold *pwf);
5180 __isl_give isl_printer *isl_printer_print_union_pw_qpolynomial_fold(
5181 __isl_take isl_printer *p,
5182 __isl_keep isl_union_pw_qpolynomial_fold *upwf);
5184 For C<isl_printer_print_pw_qpolynomial_fold>,
5185 output format of the printer
5186 needs to be set to either C<ISL_FORMAT_ISL> or C<ISL_FORMAT_C>.
5187 For C<isl_printer_print_union_pw_qpolynomial_fold>,
5188 output format of the printer
5189 needs to be set to C<ISL_FORMAT_ISL>.
5190 In case of printing in C<ISL_FORMAT_C>, the user may want
5191 to set the names of all dimensions
5193 __isl_give isl_pw_qpolynomial_fold *
5194 isl_pw_qpolynomial_fold_set_dim_name(
5195 __isl_take isl_pw_qpolynomial_fold *pwf,
5196 enum isl_dim_type type, unsigned pos,
5199 =head3 Inspecting (Piecewise) Quasipolynomial Reductions
5201 To iterate over all piecewise quasipolynomial reductions in a union
5202 piecewise quasipolynomial reduction, use the following function
5204 int isl_union_pw_qpolynomial_fold_foreach_pw_qpolynomial_fold(
5205 __isl_keep isl_union_pw_qpolynomial_fold *upwf,
5206 int (*fn)(__isl_take isl_pw_qpolynomial_fold *pwf,
5207 void *user), void *user);
5209 To iterate over the cells in a piecewise quasipolynomial reduction,
5210 use either of the following two functions
5212 int isl_pw_qpolynomial_fold_foreach_piece(
5213 __isl_keep isl_pw_qpolynomial_fold *pwf,
5214 int (*fn)(__isl_take isl_set *set,
5215 __isl_take isl_qpolynomial_fold *fold,
5216 void *user), void *user);
5217 int isl_pw_qpolynomial_fold_foreach_lifted_piece(
5218 __isl_keep isl_pw_qpolynomial_fold *pwf,
5219 int (*fn)(__isl_take isl_set *set,
5220 __isl_take isl_qpolynomial_fold *fold,
5221 void *user), void *user);
5223 See L<Inspecting (Piecewise) Quasipolynomials> for an explanation
5224 of the difference between these two functions.
5226 To iterate over all quasipolynomials in a reduction, use
5228 int isl_qpolynomial_fold_foreach_qpolynomial(
5229 __isl_keep isl_qpolynomial_fold *fold,
5230 int (*fn)(__isl_take isl_qpolynomial *qp,
5231 void *user), void *user);
5233 =head3 Properties of Piecewise Quasipolynomial Reductions
5235 To check whether two union piecewise quasipolynomial reductions are
5236 obviously equal, use
5238 int isl_union_pw_qpolynomial_fold_plain_is_equal(
5239 __isl_keep isl_union_pw_qpolynomial_fold *upwf1,
5240 __isl_keep isl_union_pw_qpolynomial_fold *upwf2);
5242 =head3 Operations on Piecewise Quasipolynomial Reductions
5244 __isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_scale_val(
5245 __isl_take isl_qpolynomial_fold *fold,
5246 __isl_take isl_val *v);
5247 __isl_give isl_pw_qpolynomial_fold *
5248 isl_pw_qpolynomial_fold_scale_val(
5249 __isl_take isl_pw_qpolynomial_fold *pwf,
5250 __isl_take isl_val *v);
5251 __isl_give isl_union_pw_qpolynomial_fold *
5252 isl_union_pw_qpolynomial_fold_scale_val(
5253 __isl_take isl_union_pw_qpolynomial_fold *upwf,
5254 __isl_take isl_val *v);
5256 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_add(
5257 __isl_take isl_pw_qpolynomial_fold *pwf1,
5258 __isl_take isl_pw_qpolynomial_fold *pwf2);
5260 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_fold(
5261 __isl_take isl_pw_qpolynomial_fold *pwf1,
5262 __isl_take isl_pw_qpolynomial_fold *pwf2);
5264 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_fold(
5265 __isl_take isl_union_pw_qpolynomial_fold *upwf1,
5266 __isl_take isl_union_pw_qpolynomial_fold *upwf2);
5268 __isl_give isl_val *isl_pw_qpolynomial_fold_eval(
5269 __isl_take isl_pw_qpolynomial_fold *pwf,
5270 __isl_take isl_point *pnt);
5272 __isl_give isl_val *isl_union_pw_qpolynomial_fold_eval(
5273 __isl_take isl_union_pw_qpolynomial_fold *upwf,
5274 __isl_take isl_point *pnt);
5276 __isl_give isl_pw_qpolynomial_fold *
5277 isl_pw_qpolynomial_fold_intersect_params(
5278 __isl_take isl_pw_qpolynomial_fold *pwf,
5279 __isl_take isl_set *set);
5281 __isl_give isl_union_set *isl_union_pw_qpolynomial_fold_domain(
5282 __isl_take isl_union_pw_qpolynomial_fold *upwf);
5283 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_intersect_domain(
5284 __isl_take isl_union_pw_qpolynomial_fold *upwf,
5285 __isl_take isl_union_set *uset);
5286 __isl_give isl_union_pw_qpolynomial_fold *
5287 isl_union_pw_qpolynomial_fold_intersect_params(
5288 __isl_take isl_union_pw_qpolynomial_fold *upwf,
5289 __isl_take isl_set *set);
5291 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_project_domain_on_params(
5292 __isl_take isl_pw_qpolynomial_fold *pwf);
5294 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_coalesce(
5295 __isl_take isl_pw_qpolynomial_fold *pwf);
5297 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_coalesce(
5298 __isl_take isl_union_pw_qpolynomial_fold *upwf);
5300 __isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_gist_params(
5301 __isl_take isl_qpolynomial_fold *fold,
5302 __isl_take isl_set *context);
5303 __isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_gist(
5304 __isl_take isl_qpolynomial_fold *fold,
5305 __isl_take isl_set *context);
5307 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_gist(
5308 __isl_take isl_pw_qpolynomial_fold *pwf,
5309 __isl_take isl_set *context);
5310 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_gist_params(
5311 __isl_take isl_pw_qpolynomial_fold *pwf,
5312 __isl_take isl_set *context);
5314 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_gist(
5315 __isl_take isl_union_pw_qpolynomial_fold *upwf,
5316 __isl_take isl_union_set *context);
5317 __isl_give isl_union_pw_qpolynomial_fold *
5318 isl_union_pw_qpolynomial_fold_gist_params(
5319 __isl_take isl_union_pw_qpolynomial_fold *upwf,
5320 __isl_take isl_set *context);
5322 The gist operation applies the gist operation to each of
5323 the cells in the domain of the input piecewise quasipolynomial reduction.
5324 In future, the operation will also exploit the context
5325 to simplify the quasipolynomial reductions associated to each cell.
5327 __isl_give isl_pw_qpolynomial_fold *
5328 isl_set_apply_pw_qpolynomial_fold(
5329 __isl_take isl_set *set,
5330 __isl_take isl_pw_qpolynomial_fold *pwf,
5332 __isl_give isl_pw_qpolynomial_fold *
5333 isl_map_apply_pw_qpolynomial_fold(
5334 __isl_take isl_map *map,
5335 __isl_take isl_pw_qpolynomial_fold *pwf,
5337 __isl_give isl_union_pw_qpolynomial_fold *
5338 isl_union_set_apply_union_pw_qpolynomial_fold(
5339 __isl_take isl_union_set *uset,
5340 __isl_take isl_union_pw_qpolynomial_fold *upwf,
5342 __isl_give isl_union_pw_qpolynomial_fold *
5343 isl_union_map_apply_union_pw_qpolynomial_fold(
5344 __isl_take isl_union_map *umap,
5345 __isl_take isl_union_pw_qpolynomial_fold *upwf,
5348 The functions taking a map
5349 compose the given map with the given piecewise quasipolynomial reduction.
5350 That is, compute a bound (of the same type as C<pwf> or C<upwf> itself)
5351 over all elements in the intersection of the range of the map
5352 and the domain of the piecewise quasipolynomial reduction
5353 as a function of an element in the domain of the map.
5354 The functions taking a set compute a bound over all elements in the
5355 intersection of the set and the domain of the
5356 piecewise quasipolynomial reduction.
5358 =head2 Parametric Vertex Enumeration
5360 The parametric vertex enumeration described in this section
5361 is mainly intended to be used internally and by the C<barvinok>
5364 #include <isl/vertices.h>
5365 __isl_give isl_vertices *isl_basic_set_compute_vertices(
5366 __isl_keep isl_basic_set *bset);
5368 The function C<isl_basic_set_compute_vertices> performs the
5369 actual computation of the parametric vertices and the chamber
5370 decomposition and store the result in an C<isl_vertices> object.
5371 This information can be queried by either iterating over all
5372 the vertices or iterating over all the chambers or cells
5373 and then iterating over all vertices that are active on the chamber.
5375 int isl_vertices_foreach_vertex(
5376 __isl_keep isl_vertices *vertices,
5377 int (*fn)(__isl_take isl_vertex *vertex, void *user),
5380 int isl_vertices_foreach_cell(
5381 __isl_keep isl_vertices *vertices,
5382 int (*fn)(__isl_take isl_cell *cell, void *user),
5384 int isl_cell_foreach_vertex(__isl_keep isl_cell *cell,
5385 int (*fn)(__isl_take isl_vertex *vertex, void *user),
5388 Other operations that can be performed on an C<isl_vertices> object are
5391 isl_ctx *isl_vertices_get_ctx(
5392 __isl_keep isl_vertices *vertices);
5393 int isl_vertices_get_n_vertices(
5394 __isl_keep isl_vertices *vertices);
5395 void isl_vertices_free(__isl_take isl_vertices *vertices);
5397 Vertices can be inspected and destroyed using the following functions.
5399 isl_ctx *isl_vertex_get_ctx(__isl_keep isl_vertex *vertex);
5400 int isl_vertex_get_id(__isl_keep isl_vertex *vertex);
5401 __isl_give isl_basic_set *isl_vertex_get_domain(
5402 __isl_keep isl_vertex *vertex);
5403 __isl_give isl_basic_set *isl_vertex_get_expr(
5404 __isl_keep isl_vertex *vertex);
5405 void isl_vertex_free(__isl_take isl_vertex *vertex);
5407 C<isl_vertex_get_expr> returns a singleton parametric set describing
5408 the vertex, while C<isl_vertex_get_domain> returns the activity domain
5410 Note that C<isl_vertex_get_domain> and C<isl_vertex_get_expr> return
5411 B<rational> basic sets, so they should mainly be used for inspection
5412 and should not be mixed with integer sets.
5414 Chambers can be inspected and destroyed using the following functions.
5416 isl_ctx *isl_cell_get_ctx(__isl_keep isl_cell *cell);
5417 __isl_give isl_basic_set *isl_cell_get_domain(
5418 __isl_keep isl_cell *cell);
5419 void isl_cell_free(__isl_take isl_cell *cell);
5421 =head1 Polyhedral Compilation Library
5423 This section collects functionality in C<isl> that has been specifically
5424 designed for use during polyhedral compilation.
5426 =head2 Dependence Analysis
5428 C<isl> contains specialized functionality for performing
5429 array dataflow analysis. That is, given a I<sink> access relation
5430 and a collection of possible I<source> access relations,
5431 C<isl> can compute relations that describe
5432 for each iteration of the sink access, which iteration
5433 of which of the source access relations was the last
5434 to access the same data element before the given iteration
5436 The resulting dependence relations map source iterations
5437 to the corresponding sink iterations.
5438 To compute standard flow dependences, the sink should be
5439 a read, while the sources should be writes.
5440 If any of the source accesses are marked as being I<may>
5441 accesses, then there will be a dependence from the last
5442 I<must> access B<and> from any I<may> access that follows
5443 this last I<must> access.
5444 In particular, if I<all> sources are I<may> accesses,
5445 then memory based dependence analysis is performed.
5446 If, on the other hand, all sources are I<must> accesses,
5447 then value based dependence analysis is performed.
5449 #include <isl/flow.h>
5451 typedef int (*isl_access_level_before)(void *first, void *second);
5453 __isl_give isl_access_info *isl_access_info_alloc(
5454 __isl_take isl_map *sink,
5455 void *sink_user, isl_access_level_before fn,
5457 __isl_give isl_access_info *isl_access_info_add_source(
5458 __isl_take isl_access_info *acc,
5459 __isl_take isl_map *source, int must,
5461 void *isl_access_info_free(__isl_take isl_access_info *acc);
5463 __isl_give isl_flow *isl_access_info_compute_flow(
5464 __isl_take isl_access_info *acc);
5466 int isl_flow_foreach(__isl_keep isl_flow *deps,
5467 int (*fn)(__isl_take isl_map *dep, int must,
5468 void *dep_user, void *user),
5470 __isl_give isl_map *isl_flow_get_no_source(
5471 __isl_keep isl_flow *deps, int must);
5472 void isl_flow_free(__isl_take isl_flow *deps);
5474 The function C<isl_access_info_compute_flow> performs the actual
5475 dependence analysis. The other functions are used to construct
5476 the input for this function or to read off the output.
5478 The input is collected in an C<isl_access_info>, which can
5479 be created through a call to C<isl_access_info_alloc>.
5480 The arguments to this functions are the sink access relation
5481 C<sink>, a token C<sink_user> used to identify the sink
5482 access to the user, a callback function for specifying the
5483 relative order of source and sink accesses, and the number
5484 of source access relations that will be added.
5485 The callback function has type C<int (*)(void *first, void *second)>.
5486 The function is called with two user supplied tokens identifying
5487 either a source or the sink and it should return the shared nesting
5488 level and the relative order of the two accesses.
5489 In particular, let I<n> be the number of loops shared by
5490 the two accesses. If C<first> precedes C<second> textually,
5491 then the function should return I<2 * n + 1>; otherwise,
5492 it should return I<2 * n>.
5493 The sources can be added to the C<isl_access_info> by performing
5494 (at most) C<max_source> calls to C<isl_access_info_add_source>.
5495 C<must> indicates whether the source is a I<must> access
5496 or a I<may> access. Note that a multi-valued access relation
5497 should only be marked I<must> if every iteration in the domain
5498 of the relation accesses I<all> elements in its image.
5499 The C<source_user> token is again used to identify
5500 the source access. The range of the source access relation
5501 C<source> should have the same dimension as the range
5502 of the sink access relation.
5503 The C<isl_access_info_free> function should usually not be
5504 called explicitly, because it is called implicitly by
5505 C<isl_access_info_compute_flow>.
5507 The result of the dependence analysis is collected in an
5508 C<isl_flow>. There may be elements of
5509 the sink access for which no preceding source access could be
5510 found or for which all preceding sources are I<may> accesses.
5511 The relations containing these elements can be obtained through
5512 calls to C<isl_flow_get_no_source>, the first with C<must> set
5513 and the second with C<must> unset.
5514 In the case of standard flow dependence analysis,
5515 with the sink a read and the sources I<must> writes,
5516 the first relation corresponds to the reads from uninitialized
5517 array elements and the second relation is empty.
5518 The actual flow dependences can be extracted using
5519 C<isl_flow_foreach>. This function will call the user-specified
5520 callback function C<fn> for each B<non-empty> dependence between
5521 a source and the sink. The callback function is called
5522 with four arguments, the actual flow dependence relation
5523 mapping source iterations to sink iterations, a boolean that
5524 indicates whether it is a I<must> or I<may> dependence, a token
5525 identifying the source and an additional C<void *> with value
5526 equal to the third argument of the C<isl_flow_foreach> call.
5527 A dependence is marked I<must> if it originates from a I<must>
5528 source and if it is not followed by any I<may> sources.
5530 After finishing with an C<isl_flow>, the user should call
5531 C<isl_flow_free> to free all associated memory.
5533 A higher-level interface to dependence analysis is provided
5534 by the following function.
5536 #include <isl/flow.h>
5538 int isl_union_map_compute_flow(__isl_take isl_union_map *sink,
5539 __isl_take isl_union_map *must_source,
5540 __isl_take isl_union_map *may_source,
5541 __isl_take isl_union_map *schedule,
5542 __isl_give isl_union_map **must_dep,
5543 __isl_give isl_union_map **may_dep,
5544 __isl_give isl_union_map **must_no_source,
5545 __isl_give isl_union_map **may_no_source);
5547 The arrays are identified by the tuple names of the ranges
5548 of the accesses. The iteration domains by the tuple names
5549 of the domains of the accesses and of the schedule.
5550 The relative order of the iteration domains is given by the
5551 schedule. The relations returned through C<must_no_source>
5552 and C<may_no_source> are subsets of C<sink>.
5553 Any of C<must_dep>, C<may_dep>, C<must_no_source>
5554 or C<may_no_source> may be C<NULL>, but a C<NULL> value for
5555 any of the other arguments is treated as an error.
5557 =head3 Interaction with Dependence Analysis
5559 During the dependence analysis, we frequently need to perform
5560 the following operation. Given a relation between sink iterations
5561 and potential source iterations from a particular source domain,
5562 what is the last potential source iteration corresponding to each
5563 sink iteration. It can sometimes be convenient to adjust
5564 the set of potential source iterations before or after each such operation.
5565 The prototypical example is fuzzy array dataflow analysis,
5566 where we need to analyze if, based on data-dependent constraints,
5567 the sink iteration can ever be executed without one or more of
5568 the corresponding potential source iterations being executed.
5569 If so, we can introduce extra parameters and select an unknown
5570 but fixed source iteration from the potential source iterations.
5571 To be able to perform such manipulations, C<isl> provides the following
5574 #include <isl/flow.h>
5576 typedef __isl_give isl_restriction *(*isl_access_restrict)(
5577 __isl_keep isl_map *source_map,
5578 __isl_keep isl_set *sink, void *source_user,
5580 __isl_give isl_access_info *isl_access_info_set_restrict(
5581 __isl_take isl_access_info *acc,
5582 isl_access_restrict fn, void *user);
5584 The function C<isl_access_info_set_restrict> should be called
5585 before calling C<isl_access_info_compute_flow> and registers a callback function
5586 that will be called any time C<isl> is about to compute the last
5587 potential source. The first argument is the (reverse) proto-dependence,
5588 mapping sink iterations to potential source iterations.
5589 The second argument represents the sink iterations for which
5590 we want to compute the last source iteration.
5591 The third argument is the token corresponding to the source
5592 and the final argument is the token passed to C<isl_access_info_set_restrict>.
5593 The callback is expected to return a restriction on either the input or
5594 the output of the operation computing the last potential source.
5595 If the input needs to be restricted then restrictions are needed
5596 for both the source and the sink iterations. The sink iterations
5597 and the potential source iterations will be intersected with these sets.
5598 If the output needs to be restricted then only a restriction on the source
5599 iterations is required.
5600 If any error occurs, the callback should return C<NULL>.
5601 An C<isl_restriction> object can be created, freed and inspected
5602 using the following functions.
5604 #include <isl/flow.h>
5606 __isl_give isl_restriction *isl_restriction_input(
5607 __isl_take isl_set *source_restr,
5608 __isl_take isl_set *sink_restr);
5609 __isl_give isl_restriction *isl_restriction_output(
5610 __isl_take isl_set *source_restr);
5611 __isl_give isl_restriction *isl_restriction_none(
5612 __isl_take isl_map *source_map);
5613 __isl_give isl_restriction *isl_restriction_empty(
5614 __isl_take isl_map *source_map);
5615 void *isl_restriction_free(
5616 __isl_take isl_restriction *restr);
5617 isl_ctx *isl_restriction_get_ctx(
5618 __isl_keep isl_restriction *restr);
5620 C<isl_restriction_none> and C<isl_restriction_empty> are special
5621 cases of C<isl_restriction_input>. C<isl_restriction_none>
5622 is essentially equivalent to
5624 isl_restriction_input(isl_set_universe(
5625 isl_space_range(isl_map_get_space(source_map))),
5627 isl_space_domain(isl_map_get_space(source_map))));
5629 whereas C<isl_restriction_empty> is essentially equivalent to
5631 isl_restriction_input(isl_set_empty(
5632 isl_space_range(isl_map_get_space(source_map))),
5634 isl_space_domain(isl_map_get_space(source_map))));
5638 B<The functionality described in this section is fairly new
5639 and may be subject to change.>
5641 #include <isl/schedule.h>
5642 __isl_give isl_schedule *
5643 isl_schedule_constraints_compute_schedule(
5644 __isl_take isl_schedule_constraints *sc);
5645 void *isl_schedule_free(__isl_take isl_schedule *sched);
5647 The function C<isl_schedule_constraints_compute_schedule> can be
5648 used to compute a schedule that satisfy the given schedule constraints.
5649 These schedule constraints include the iteration domain for which
5650 a schedule should be computed and dependences between pairs of
5651 iterations. In particular, these dependences include
5652 I<validity> dependences and I<proximity> dependences.
5653 By default, the algorithm used to construct the schedule is similar
5654 to that of C<Pluto>.
5655 Alternatively, Feautrier's multi-dimensional scheduling algorithm can
5657 The generated schedule respects all validity dependences.
5658 That is, all dependence distances over these dependences in the
5659 scheduled space are lexicographically positive.
5660 The default algorithm tries to ensure that the dependence distances
5661 over coincidence constraints are zero and to minimize the
5662 dependence distances over proximity dependences.
5663 Moreover, it tries to obtain sequences (bands) of schedule dimensions
5664 for groups of domains where the dependence distances over validity
5665 dependences have only non-negative values.
5666 When using Feautrier's algorithm, the coincidence and proximity constraints
5667 are only taken into account during the extension to a
5668 full-dimensional schedule.
5670 An C<isl_schedule_constraints> object can be constructed
5671 and manipulated using the following functions.
5673 #include <isl/schedule.h>
5674 __isl_give isl_schedule_constraints *
5675 isl_schedule_constraints_on_domain(
5676 __isl_take isl_union_set *domain);
5677 isl_ctx *isl_schedule_constraints_get_ctx(
5678 __isl_keep isl_schedule_constraints *sc);
5679 __isl_give isl_schedule_constraints *
5680 isl_schedule_constraints_set_validity(
5681 __isl_take isl_schedule_constraints *sc,
5682 __isl_take isl_union_map *validity);
5683 __isl_give isl_schedule_constraints *
5684 isl_schedule_constraints_set_coincidence(
5685 __isl_take isl_schedule_constraints *sc,
5686 __isl_take isl_union_map *coincidence);
5687 __isl_give isl_schedule_constraints *
5688 isl_schedule_constraints_set_proximity(
5689 __isl_take isl_schedule_constraints *sc,
5690 __isl_take isl_union_map *proximity);
5691 __isl_give isl_schedule_constraints *
5692 isl_schedule_constraints_set_conditional_validity(
5693 __isl_take isl_schedule_constraints *sc,
5694 __isl_take isl_union_map *condition,
5695 __isl_take isl_union_map *validity);
5696 void *isl_schedule_constraints_free(
5697 __isl_take isl_schedule_constraints *sc);
5699 The initial C<isl_schedule_constraints> object created by
5700 C<isl_schedule_constraints_on_domain> does not impose any constraints.
5701 That is, it has an empty set of dependences.
5702 The function C<isl_schedule_constraints_set_validity> replaces the
5703 validity dependences, mapping domain elements I<i> to domain
5704 elements that should be scheduled after I<i>.
5705 The function C<isl_schedule_constraints_set_coincidence> replaces the
5706 coincidence dependences, mapping domain elements I<i> to domain
5707 elements that should be scheduled together with I<I>, if possible.
5708 The function C<isl_schedule_constraints_set_proximity> replaces the
5709 proximity dependences, mapping domain elements I<i> to domain
5710 elements that should be scheduled either before I<I>
5711 or as early as possible after I<i>.
5713 The function C<isl_schedule_constraints_set_conditional_validity>
5714 replaces the conditional validity constraints.
5715 A conditional validity constraint is only imposed when any of the corresponding
5716 conditions is satisfied, i.e., when any of them is non-zero.
5717 That is, the scheduler ensures that within each band if the dependence
5718 distances over the condition constraints are not all zero
5719 then all corresponding conditional validity constraints are respected.
5720 A conditional validity constraint corresponds to a condition
5721 if the two are adjacent, i.e., if the domain of one relation intersect
5722 the range of the other relation.
5723 The typical use case of conditional validity constraints is
5724 to allow order constraints between live ranges to be violated
5725 as long as the live ranges themselves are local to the band.
5726 To allow more fine-grained control over which conditions correspond
5727 to which conditional validity constraints, the domains and ranges
5728 of these relations may include I<tags>. That is, the domains and
5729 ranges of those relation may themselves be wrapped relations
5730 where the iteration domain appears in the domain of those wrapped relations
5731 and the range of the wrapped relations can be arbitrarily chosen
5732 by the user. Conditions and conditional validity constraints are only
5733 considere adjacent to each other if the entire wrapped relation matches.
5734 In particular, a relation with a tag will never be considered adjacent
5735 to a relation without a tag.
5737 The following function computes a schedule directly from
5738 an iteration domain and validity and proximity dependences
5739 and is implemented in terms of the functions described above.
5740 The use of C<isl_union_set_compute_schedule> is discouraged.
5742 #include <isl/schedule.h>
5743 __isl_give isl_schedule *isl_union_set_compute_schedule(
5744 __isl_take isl_union_set *domain,
5745 __isl_take isl_union_map *validity,
5746 __isl_take isl_union_map *proximity);
5748 A mapping from the domains to the scheduled space can be obtained
5749 from an C<isl_schedule> using the following function.
5751 __isl_give isl_union_map *isl_schedule_get_map(
5752 __isl_keep isl_schedule *sched);
5754 A representation of the schedule can be printed using
5756 __isl_give isl_printer *isl_printer_print_schedule(
5757 __isl_take isl_printer *p,
5758 __isl_keep isl_schedule *schedule);
5760 A representation of the schedule as a forest of bands can be obtained
5761 using the following function.
5763 __isl_give isl_band_list *isl_schedule_get_band_forest(
5764 __isl_keep isl_schedule *schedule);
5766 The individual bands can be visited in depth-first post-order
5767 using the following function.
5769 #include <isl/schedule.h>
5770 int isl_schedule_foreach_band(
5771 __isl_keep isl_schedule *sched,
5772 int (*fn)(__isl_keep isl_band *band, void *user),
5775 The list can be manipulated as explained in L<"Lists">.
5776 The bands inside the list can be copied and freed using the following
5779 #include <isl/band.h>
5780 __isl_give isl_band *isl_band_copy(
5781 __isl_keep isl_band *band);
5782 void *isl_band_free(__isl_take isl_band *band);
5784 Each band contains zero or more scheduling dimensions.
5785 These are referred to as the members of the band.
5786 The section of the schedule that corresponds to the band is
5787 referred to as the partial schedule of the band.
5788 For those nodes that participate in a band, the outer scheduling
5789 dimensions form the prefix schedule, while the inner scheduling
5790 dimensions form the suffix schedule.
5791 That is, if we take a cut of the band forest, then the union of
5792 the concatenations of the prefix, partial and suffix schedules of
5793 each band in the cut is equal to the entire schedule (modulo
5794 some possible padding at the end with zero scheduling dimensions).
5795 The properties of a band can be inspected using the following functions.
5797 #include <isl/band.h>
5798 isl_ctx *isl_band_get_ctx(__isl_keep isl_band *band);
5800 int isl_band_has_children(__isl_keep isl_band *band);
5801 __isl_give isl_band_list *isl_band_get_children(
5802 __isl_keep isl_band *band);
5804 __isl_give isl_union_map *isl_band_get_prefix_schedule(
5805 __isl_keep isl_band *band);
5806 __isl_give isl_union_map *isl_band_get_partial_schedule(
5807 __isl_keep isl_band *band);
5808 __isl_give isl_union_map *isl_band_get_suffix_schedule(
5809 __isl_keep isl_band *band);
5811 int isl_band_n_member(__isl_keep isl_band *band);
5812 int isl_band_member_is_coincident(
5813 __isl_keep isl_band *band, int pos);
5815 int isl_band_list_foreach_band(
5816 __isl_keep isl_band_list *list,
5817 int (*fn)(__isl_keep isl_band *band, void *user),
5820 Note that a scheduling dimension is considered to be ``coincident''
5821 if it satisfies the coincidence constraints within its band.
5822 That is, if the dependence distances of the coincidence
5823 constraints are all zero in that direction (for fixed
5824 iterations of outer bands).
5825 Like C<isl_schedule_foreach_band>,
5826 the function C<isl_band_list_foreach_band> calls C<fn> on the bands
5827 in depth-first post-order.
5829 A band can be tiled using the following function.
5831 #include <isl/band.h>
5832 int isl_band_tile(__isl_keep isl_band *band,
5833 __isl_take isl_vec *sizes);
5835 int isl_options_set_tile_scale_tile_loops(isl_ctx *ctx,
5837 int isl_options_get_tile_scale_tile_loops(isl_ctx *ctx);
5838 int isl_options_set_tile_shift_point_loops(isl_ctx *ctx,
5840 int isl_options_get_tile_shift_point_loops(isl_ctx *ctx);
5842 The C<isl_band_tile> function tiles the band using the given tile sizes
5843 inside its schedule.
5844 A new child band is created to represent the point loops and it is
5845 inserted between the modified band and its children.
5846 The C<tile_scale_tile_loops> option specifies whether the tile
5847 loops iterators should be scaled by the tile sizes.
5848 If the C<tile_shift_point_loops> option is set, then the point loops
5849 are shifted to start at zero.
5851 A band can be split into two nested bands using the following function.
5853 int isl_band_split(__isl_keep isl_band *band, int pos);
5855 The resulting outer band contains the first C<pos> dimensions of C<band>
5856 while the inner band contains the remaining dimensions.
5858 A representation of the band can be printed using
5860 #include <isl/band.h>
5861 __isl_give isl_printer *isl_printer_print_band(
5862 __isl_take isl_printer *p,
5863 __isl_keep isl_band *band);
5867 #include <isl/schedule.h>
5868 int isl_options_set_schedule_max_coefficient(
5869 isl_ctx *ctx, int val);
5870 int isl_options_get_schedule_max_coefficient(
5872 int isl_options_set_schedule_max_constant_term(
5873 isl_ctx *ctx, int val);
5874 int isl_options_get_schedule_max_constant_term(
5876 int isl_options_set_schedule_fuse(isl_ctx *ctx, int val);
5877 int isl_options_get_schedule_fuse(isl_ctx *ctx);
5878 int isl_options_set_schedule_maximize_band_depth(
5879 isl_ctx *ctx, int val);
5880 int isl_options_get_schedule_maximize_band_depth(
5882 int isl_options_set_schedule_outer_coincidence(
5883 isl_ctx *ctx, int val);
5884 int isl_options_get_schedule_outer_coincidence(
5886 int isl_options_set_schedule_split_scaled(
5887 isl_ctx *ctx, int val);
5888 int isl_options_get_schedule_split_scaled(
5890 int isl_options_set_schedule_algorithm(
5891 isl_ctx *ctx, int val);
5892 int isl_options_get_schedule_algorithm(
5894 int isl_options_set_schedule_separate_components(
5895 isl_ctx *ctx, int val);
5896 int isl_options_get_schedule_separate_components(
5901 =item * schedule_max_coefficient
5903 This option enforces that the coefficients for variable and parameter
5904 dimensions in the calculated schedule are not larger than the specified value.
5905 This option can significantly increase the speed of the scheduling calculation
5906 and may also prevent fusing of unrelated dimensions. A value of -1 means that
5907 this option does not introduce bounds on the variable or parameter
5910 =item * schedule_max_constant_term
5912 This option enforces that the constant coefficients in the calculated schedule
5913 are not larger than the maximal constant term. This option can significantly
5914 increase the speed of the scheduling calculation and may also prevent fusing of
5915 unrelated dimensions. A value of -1 means that this option does not introduce
5916 bounds on the constant coefficients.
5918 =item * schedule_fuse
5920 This option controls the level of fusion.
5921 If this option is set to C<ISL_SCHEDULE_FUSE_MIN>, then loops in the
5922 resulting schedule will be distributed as much as possible.
5923 If this option is set to C<ISL_SCHEDULE_FUSE_MAX>, then C<isl> will
5924 try to fuse loops in the resulting schedule.
5926 =item * schedule_maximize_band_depth
5928 If this option is set, we do not split bands at the point
5929 where we detect splitting is necessary. Instead, we
5930 backtrack and split bands as early as possible. This
5931 reduces the number of splits and maximizes the width of
5932 the bands. Wider bands give more possibilities for tiling.
5933 Note that if the C<schedule_fuse> option is set to C<ISL_SCHEDULE_FUSE_MIN>,
5934 then bands will be split as early as possible, even if there is no need.
5935 The C<schedule_maximize_band_depth> option therefore has no effect in this case.
5937 =item * schedule_outer_coincidence
5939 If this option is set, then we try to construct schedules
5940 where the outermost scheduling dimension in each band
5941 satisfies the coincidence constraints.
5943 =item * schedule_split_scaled
5945 If this option is set, then we try to construct schedules in which the
5946 constant term is split off from the linear part if the linear parts of
5947 the scheduling rows for all nodes in the graphs have a common non-trivial
5949 The constant term is then placed in a separate band and the linear
5952 =item * schedule_algorithm
5954 Selects the scheduling algorithm to be used.
5955 Available scheduling algorithms are C<ISL_SCHEDULE_ALGORITHM_ISL>
5956 and C<ISL_SCHEDULE_ALGORITHM_FEAUTRIER>.
5958 =item * schedule_separate_components
5960 If at any point the dependence graph contains any (weakly connected) components,
5961 then these components are scheduled separately.
5962 If this option is not set, then some iterations of the domains
5963 in these components may be scheduled together.
5964 If this option is set, then the components are given consecutive
5969 =head2 AST Generation
5971 This section describes the C<isl> functionality for generating
5972 ASTs that visit all the elements
5973 in a domain in an order specified by a schedule.
5974 In particular, given a C<isl_union_map>, an AST is generated
5975 that visits all the elements in the domain of the C<isl_union_map>
5976 according to the lexicographic order of the corresponding image
5977 element(s). If the range of the C<isl_union_map> consists of
5978 elements in more than one space, then each of these spaces is handled
5979 separately in an arbitrary order.
5980 It should be noted that the image elements only specify the I<order>
5981 in which the corresponding domain elements should be visited.
5982 No direct relation between the image elements and the loop iterators
5983 in the generated AST should be assumed.
5985 Each AST is generated within a build. The initial build
5986 simply specifies the constraints on the parameters (if any)
5987 and can be created, inspected, copied and freed using the following functions.
5989 #include <isl/ast_build.h>
5990 __isl_give isl_ast_build *isl_ast_build_from_context(
5991 __isl_take isl_set *set);
5992 isl_ctx *isl_ast_build_get_ctx(
5993 __isl_keep isl_ast_build *build);
5994 __isl_give isl_ast_build *isl_ast_build_copy(
5995 __isl_keep isl_ast_build *build);
5996 void *isl_ast_build_free(
5997 __isl_take isl_ast_build *build);
5999 The C<set> argument is usually a parameter set with zero or more parameters.
6000 More C<isl_ast_build> functions are described in L</"Nested AST Generation">
6001 and L</"Fine-grained Control over AST Generation">.
6002 Finally, the AST itself can be constructed using the following
6005 #include <isl/ast_build.h>
6006 __isl_give isl_ast_node *isl_ast_build_ast_from_schedule(
6007 __isl_keep isl_ast_build *build,
6008 __isl_take isl_union_map *schedule);
6010 =head3 Inspecting the AST
6012 The basic properties of an AST node can be obtained as follows.
6014 #include <isl/ast.h>
6015 isl_ctx *isl_ast_node_get_ctx(
6016 __isl_keep isl_ast_node *node);
6017 enum isl_ast_node_type isl_ast_node_get_type(
6018 __isl_keep isl_ast_node *node);
6020 The type of an AST node is one of
6021 C<isl_ast_node_for>,
6023 C<isl_ast_node_block> or
6024 C<isl_ast_node_user>.
6025 An C<isl_ast_node_for> represents a for node.
6026 An C<isl_ast_node_if> represents an if node.
6027 An C<isl_ast_node_block> represents a compound node.
6028 An C<isl_ast_node_user> represents an expression statement.
6029 An expression statement typically corresponds to a domain element, i.e.,
6030 one of the elements that is visited by the AST.
6032 Each type of node has its own additional properties.
6034 #include <isl/ast.h>
6035 __isl_give isl_ast_expr *isl_ast_node_for_get_iterator(
6036 __isl_keep isl_ast_node *node);
6037 __isl_give isl_ast_expr *isl_ast_node_for_get_init(
6038 __isl_keep isl_ast_node *node);
6039 __isl_give isl_ast_expr *isl_ast_node_for_get_cond(
6040 __isl_keep isl_ast_node *node);
6041 __isl_give isl_ast_expr *isl_ast_node_for_get_inc(
6042 __isl_keep isl_ast_node *node);
6043 __isl_give isl_ast_node *isl_ast_node_for_get_body(
6044 __isl_keep isl_ast_node *node);
6045 int isl_ast_node_for_is_degenerate(
6046 __isl_keep isl_ast_node *node);
6048 An C<isl_ast_for> is considered degenerate if it is known to execute
6051 #include <isl/ast.h>
6052 __isl_give isl_ast_expr *isl_ast_node_if_get_cond(
6053 __isl_keep isl_ast_node *node);
6054 __isl_give isl_ast_node *isl_ast_node_if_get_then(
6055 __isl_keep isl_ast_node *node);
6056 int isl_ast_node_if_has_else(
6057 __isl_keep isl_ast_node *node);
6058 __isl_give isl_ast_node *isl_ast_node_if_get_else(
6059 __isl_keep isl_ast_node *node);
6061 __isl_give isl_ast_node_list *
6062 isl_ast_node_block_get_children(
6063 __isl_keep isl_ast_node *node);
6065 __isl_give isl_ast_expr *isl_ast_node_user_get_expr(
6066 __isl_keep isl_ast_node *node);
6068 Each of the returned C<isl_ast_expr>s can in turn be inspected using
6069 the following functions.
6071 #include <isl/ast.h>
6072 isl_ctx *isl_ast_expr_get_ctx(
6073 __isl_keep isl_ast_expr *expr);
6074 enum isl_ast_expr_type isl_ast_expr_get_type(
6075 __isl_keep isl_ast_expr *expr);
6077 The type of an AST expression is one of
6079 C<isl_ast_expr_id> or
6080 C<isl_ast_expr_int>.
6081 An C<isl_ast_expr_op> represents the result of an operation.
6082 An C<isl_ast_expr_id> represents an identifier.
6083 An C<isl_ast_expr_int> represents an integer value.
6085 Each type of expression has its own additional properties.
6087 #include <isl/ast.h>
6088 enum isl_ast_op_type isl_ast_expr_get_op_type(
6089 __isl_keep isl_ast_expr *expr);
6090 int isl_ast_expr_get_op_n_arg(__isl_keep isl_ast_expr *expr);
6091 __isl_give isl_ast_expr *isl_ast_expr_get_op_arg(
6092 __isl_keep isl_ast_expr *expr, int pos);
6093 int isl_ast_node_foreach_ast_op_type(
6094 __isl_keep isl_ast_node *node,
6095 int (*fn)(enum isl_ast_op_type type, void *user),
6098 C<isl_ast_expr_get_op_type> returns the type of the operation
6099 performed. C<isl_ast_expr_get_op_n_arg> returns the number of
6100 arguments. C<isl_ast_expr_get_op_arg> returns the specified
6102 C<isl_ast_node_foreach_ast_op_type> calls C<fn> for each distinct
6103 C<isl_ast_op_type> that appears in C<node>.
6104 The operation type is one of the following.
6108 =item C<isl_ast_op_and>
6110 Logical I<and> of two arguments.
6111 Both arguments can be evaluated.
6113 =item C<isl_ast_op_and_then>
6115 Logical I<and> of two arguments.
6116 The second argument can only be evaluated if the first evaluates to true.
6118 =item C<isl_ast_op_or>
6120 Logical I<or> of two arguments.
6121 Both arguments can be evaluated.
6123 =item C<isl_ast_op_or_else>
6125 Logical I<or> of two arguments.
6126 The second argument can only be evaluated if the first evaluates to false.
6128 =item C<isl_ast_op_max>
6130 Maximum of two or more arguments.
6132 =item C<isl_ast_op_min>
6134 Minimum of two or more arguments.
6136 =item C<isl_ast_op_minus>
6140 =item C<isl_ast_op_add>
6142 Sum of two arguments.
6144 =item C<isl_ast_op_sub>
6146 Difference of two arguments.
6148 =item C<isl_ast_op_mul>
6150 Product of two arguments.
6152 =item C<isl_ast_op_div>
6154 Exact division. That is, the result is known to be an integer.
6156 =item C<isl_ast_op_fdiv_q>
6158 Result of integer division, rounded towards negative
6161 =item C<isl_ast_op_pdiv_q>
6163 Result of integer division, where dividend is known to be non-negative.
6165 =item C<isl_ast_op_pdiv_r>
6167 Remainder of integer division, where dividend is known to be non-negative.
6169 =item C<isl_ast_op_cond>
6171 Conditional operator defined on three arguments.
6172 If the first argument evaluates to true, then the result
6173 is equal to the second argument. Otherwise, the result
6174 is equal to the third argument.
6175 The second and third argument may only be evaluated if
6176 the first argument evaluates to true and false, respectively.
6177 Corresponds to C<a ? b : c> in C.
6179 =item C<isl_ast_op_select>
6181 Conditional operator defined on three arguments.
6182 If the first argument evaluates to true, then the result
6183 is equal to the second argument. Otherwise, the result
6184 is equal to the third argument.
6185 The second and third argument may be evaluated independently
6186 of the value of the first argument.
6187 Corresponds to C<a * b + (1 - a) * c> in C.
6189 =item C<isl_ast_op_eq>
6193 =item C<isl_ast_op_le>
6195 Less than or equal relation.
6197 =item C<isl_ast_op_lt>
6201 =item C<isl_ast_op_ge>
6203 Greater than or equal relation.
6205 =item C<isl_ast_op_gt>
6207 Greater than relation.
6209 =item C<isl_ast_op_call>
6212 The number of arguments of the C<isl_ast_expr> is one more than
6213 the number of arguments in the function call, the first argument
6214 representing the function being called.
6216 =item C<isl_ast_op_access>
6219 The number of arguments of the C<isl_ast_expr> is one more than
6220 the number of index expressions in the array access, the first argument
6221 representing the array being accessed.
6223 =item C<isl_ast_op_member>
6226 This operation has two arguments, a structure and the name of
6227 the member of the structure being accessed.
6231 #include <isl/ast.h>
6232 __isl_give isl_id *isl_ast_expr_get_id(
6233 __isl_keep isl_ast_expr *expr);
6235 Return the identifier represented by the AST expression.
6237 #include <isl/ast.h>
6238 __isl_give isl_val *isl_ast_expr_get_val(
6239 __isl_keep isl_ast_expr *expr);
6241 Return the integer represented by the AST expression.
6243 =head3 Properties of ASTs
6245 #include <isl/ast.h>
6246 int isl_ast_expr_is_equal(__isl_keep isl_ast_expr *expr1,
6247 __isl_keep isl_ast_expr *expr2);
6249 Check if two C<isl_ast_expr>s are equal to each other.
6251 =head3 Manipulating and printing the AST
6253 AST nodes can be copied and freed using the following functions.
6255 #include <isl/ast.h>
6256 __isl_give isl_ast_node *isl_ast_node_copy(
6257 __isl_keep isl_ast_node *node);
6258 void *isl_ast_node_free(__isl_take isl_ast_node *node);
6260 AST expressions can be copied and freed using the following functions.
6262 #include <isl/ast.h>
6263 __isl_give isl_ast_expr *isl_ast_expr_copy(
6264 __isl_keep isl_ast_expr *expr);
6265 void *isl_ast_expr_free(__isl_take isl_ast_expr *expr);
6267 New AST expressions can be created either directly or within
6268 the context of an C<isl_ast_build>.
6270 #include <isl/ast.h>
6271 __isl_give isl_ast_expr *isl_ast_expr_from_val(
6272 __isl_take isl_val *v);
6273 __isl_give isl_ast_expr *isl_ast_expr_from_id(
6274 __isl_take isl_id *id);
6275 __isl_give isl_ast_expr *isl_ast_expr_neg(
6276 __isl_take isl_ast_expr *expr);
6277 __isl_give isl_ast_expr *isl_ast_expr_add(
6278 __isl_take isl_ast_expr *expr1,
6279 __isl_take isl_ast_expr *expr2);
6280 __isl_give isl_ast_expr *isl_ast_expr_sub(
6281 __isl_take isl_ast_expr *expr1,
6282 __isl_take isl_ast_expr *expr2);
6283 __isl_give isl_ast_expr *isl_ast_expr_mul(
6284 __isl_take isl_ast_expr *expr1,
6285 __isl_take isl_ast_expr *expr2);
6286 __isl_give isl_ast_expr *isl_ast_expr_div(
6287 __isl_take isl_ast_expr *expr1,
6288 __isl_take isl_ast_expr *expr2);
6289 __isl_give isl_ast_expr *isl_ast_expr_and(
6290 __isl_take isl_ast_expr *expr1,
6291 __isl_take isl_ast_expr *expr2)
6292 __isl_give isl_ast_expr *isl_ast_expr_or(
6293 __isl_take isl_ast_expr *expr1,
6294 __isl_take isl_ast_expr *expr2)
6295 __isl_give isl_ast_expr *isl_ast_expr_access(
6296 __isl_take isl_ast_expr *array,
6297 __isl_take isl_ast_expr_list *indices);
6299 #include <isl/ast_build.h>
6300 __isl_give isl_ast_expr *isl_ast_build_expr_from_pw_aff(
6301 __isl_keep isl_ast_build *build,
6302 __isl_take isl_pw_aff *pa);
6303 __isl_give isl_ast_expr *
6304 isl_ast_build_access_from_pw_multi_aff(
6305 __isl_keep isl_ast_build *build,
6306 __isl_take isl_pw_multi_aff *pma);
6307 __isl_give isl_ast_expr *
6308 isl_ast_build_access_from_multi_pw_aff(
6309 __isl_keep isl_ast_build *build,
6310 __isl_take isl_multi_pw_aff *mpa);
6311 __isl_give isl_ast_expr *
6312 isl_ast_build_call_from_pw_multi_aff(
6313 __isl_keep isl_ast_build *build,
6314 __isl_take isl_pw_multi_aff *pma);
6315 __isl_give isl_ast_expr *
6316 isl_ast_build_call_from_multi_pw_aff(
6317 __isl_keep isl_ast_build *build,
6318 __isl_take isl_multi_pw_aff *mpa);
6320 The domains of C<pa>, C<mpa> and C<pma> should correspond
6321 to the schedule space of C<build>.
6322 The tuple id of C<mpa> or C<pma> is used as the array being accessed or
6323 the function being called.
6324 If the accessed space is a nested relation, then it is taken
6325 to represent an access of the member specified by the range
6326 of this nested relation of the structure specified by the domain
6327 of the nested relation.
6329 The following functions can be used to modify an C<isl_ast_expr>.
6331 #include <isl/ast.h>
6332 __isl_give isl_ast_expr *isl_ast_expr_set_op_arg(
6333 __isl_take isl_ast_expr *expr, int pos,
6334 __isl_take isl_ast_expr *arg);
6336 Replace the argument of C<expr> at position C<pos> by C<arg>.
6338 #include <isl/ast.h>
6339 __isl_give isl_ast_expr *isl_ast_expr_substitute_ids(
6340 __isl_take isl_ast_expr *expr,
6341 __isl_take isl_id_to_ast_expr *id2expr);
6343 The function C<isl_ast_expr_substitute_ids> replaces the
6344 subexpressions of C<expr> of type C<isl_ast_expr_id>
6345 by the corresponding expression in C<id2expr>, if there is any.
6348 User specified data can be attached to an C<isl_ast_node> and obtained
6349 from the same C<isl_ast_node> using the following functions.
6351 #include <isl/ast.h>
6352 __isl_give isl_ast_node *isl_ast_node_set_annotation(
6353 __isl_take isl_ast_node *node,
6354 __isl_take isl_id *annotation);
6355 __isl_give isl_id *isl_ast_node_get_annotation(
6356 __isl_keep isl_ast_node *node);
6358 Basic printing can be performed using the following functions.
6360 #include <isl/ast.h>
6361 __isl_give isl_printer *isl_printer_print_ast_expr(
6362 __isl_take isl_printer *p,
6363 __isl_keep isl_ast_expr *expr);
6364 __isl_give isl_printer *isl_printer_print_ast_node(
6365 __isl_take isl_printer *p,
6366 __isl_keep isl_ast_node *node);
6368 More advanced printing can be performed using the following functions.
6370 #include <isl/ast.h>
6371 __isl_give isl_printer *isl_ast_op_type_print_macro(
6372 enum isl_ast_op_type type,
6373 __isl_take isl_printer *p);
6374 __isl_give isl_printer *isl_ast_node_print_macros(
6375 __isl_keep isl_ast_node *node,
6376 __isl_take isl_printer *p);
6377 __isl_give isl_printer *isl_ast_node_print(
6378 __isl_keep isl_ast_node *node,
6379 __isl_take isl_printer *p,
6380 __isl_take isl_ast_print_options *options);
6381 __isl_give isl_printer *isl_ast_node_for_print(
6382 __isl_keep isl_ast_node *node,
6383 __isl_take isl_printer *p,
6384 __isl_take isl_ast_print_options *options);
6385 __isl_give isl_printer *isl_ast_node_if_print(
6386 __isl_keep isl_ast_node *node,
6387 __isl_take isl_printer *p,
6388 __isl_take isl_ast_print_options *options);
6390 While printing an C<isl_ast_node> in C<ISL_FORMAT_C>,
6391 C<isl> may print out an AST that makes use of macros such
6392 as C<floord>, C<min> and C<max>.
6393 C<isl_ast_op_type_print_macro> prints out the macro
6394 corresponding to a specific C<isl_ast_op_type>.
6395 C<isl_ast_node_print_macros> scans the C<isl_ast_node>
6396 for expressions where these macros would be used and prints
6397 out the required macro definitions.
6398 Essentially, C<isl_ast_node_print_macros> calls
6399 C<isl_ast_node_foreach_ast_op_type> with C<isl_ast_op_type_print_macro>
6400 as function argument.
6401 C<isl_ast_node_print>, C<isl_ast_node_for_print> and
6402 C<isl_ast_node_if_print> print an C<isl_ast_node>
6403 in C<ISL_FORMAT_C>, but allow for some extra control
6404 through an C<isl_ast_print_options> object.
6405 This object can be created using the following functions.
6407 #include <isl/ast.h>
6408 __isl_give isl_ast_print_options *
6409 isl_ast_print_options_alloc(isl_ctx *ctx);
6410 __isl_give isl_ast_print_options *
6411 isl_ast_print_options_copy(
6412 __isl_keep isl_ast_print_options *options);
6413 void *isl_ast_print_options_free(
6414 __isl_take isl_ast_print_options *options);
6416 __isl_give isl_ast_print_options *
6417 isl_ast_print_options_set_print_user(
6418 __isl_take isl_ast_print_options *options,
6419 __isl_give isl_printer *(*print_user)(
6420 __isl_take isl_printer *p,
6421 __isl_take isl_ast_print_options *options,
6422 __isl_keep isl_ast_node *node, void *user),
6424 __isl_give isl_ast_print_options *
6425 isl_ast_print_options_set_print_for(
6426 __isl_take isl_ast_print_options *options,
6427 __isl_give isl_printer *(*print_for)(
6428 __isl_take isl_printer *p,
6429 __isl_take isl_ast_print_options *options,
6430 __isl_keep isl_ast_node *node, void *user),
6433 The callback set by C<isl_ast_print_options_set_print_user>
6434 is called whenever a node of type C<isl_ast_node_user> needs to
6436 The callback set by C<isl_ast_print_options_set_print_for>
6437 is called whenever a node of type C<isl_ast_node_for> needs to
6439 Note that C<isl_ast_node_for_print> will I<not> call the
6440 callback set by C<isl_ast_print_options_set_print_for> on the node
6441 on which C<isl_ast_node_for_print> is called, but only on nested
6442 nodes of type C<isl_ast_node_for>. It is therefore safe to
6443 call C<isl_ast_node_for_print> from within the callback set by
6444 C<isl_ast_print_options_set_print_for>.
6446 The following option determines the type to be used for iterators
6447 while printing the AST.
6449 int isl_options_set_ast_iterator_type(
6450 isl_ctx *ctx, const char *val);
6451 const char *isl_options_get_ast_iterator_type(
6456 #include <isl/ast_build.h>
6457 int isl_options_set_ast_build_atomic_upper_bound(
6458 isl_ctx *ctx, int val);
6459 int isl_options_get_ast_build_atomic_upper_bound(
6461 int isl_options_set_ast_build_prefer_pdiv(isl_ctx *ctx,
6463 int isl_options_get_ast_build_prefer_pdiv(isl_ctx *ctx);
6464 int isl_options_set_ast_build_exploit_nested_bounds(
6465 isl_ctx *ctx, int val);
6466 int isl_options_get_ast_build_exploit_nested_bounds(
6468 int isl_options_set_ast_build_group_coscheduled(
6469 isl_ctx *ctx, int val);
6470 int isl_options_get_ast_build_group_coscheduled(
6472 int isl_options_set_ast_build_scale_strides(
6473 isl_ctx *ctx, int val);
6474 int isl_options_get_ast_build_scale_strides(
6476 int isl_options_set_ast_build_allow_else(isl_ctx *ctx,
6478 int isl_options_get_ast_build_allow_else(isl_ctx *ctx);
6479 int isl_options_set_ast_build_allow_or(isl_ctx *ctx,
6481 int isl_options_get_ast_build_allow_or(isl_ctx *ctx);
6485 =item * ast_build_atomic_upper_bound
6487 Generate loop upper bounds that consist of the current loop iterator,
6488 an operator and an expression not involving the iterator.
6489 If this option is not set, then the current loop iterator may appear
6490 several times in the upper bound.
6491 For example, when this option is turned off, AST generation
6494 [n] -> { A[i] -> [i] : 0 <= i <= 100, n }
6498 for (int c0 = 0; c0 <= 100 && n >= c0; c0 += 1)
6501 When the option is turned on, the following AST is generated
6503 for (int c0 = 0; c0 <= min(100, n); c0 += 1)
6506 =item * ast_build_prefer_pdiv
6508 If this option is turned off, then the AST generation will
6509 produce ASTs that may only contain C<isl_ast_op_fdiv_q>
6510 operators, but no C<isl_ast_op_pdiv_q> or
6511 C<isl_ast_op_pdiv_r> operators.
6512 If this options is turned on, then C<isl> will try to convert
6513 some of the C<isl_ast_op_fdiv_q> operators to (expressions containing)
6514 C<isl_ast_op_pdiv_q> or C<isl_ast_op_pdiv_r> operators.
6516 =item * ast_build_exploit_nested_bounds
6518 Simplify conditions based on bounds of nested for loops.
6519 In particular, remove conditions that are implied by the fact
6520 that one or more nested loops have at least one iteration,
6521 meaning that the upper bound is at least as large as the lower bound.
6522 For example, when this option is turned off, AST generation
6525 [N,M] -> { A[i,j] -> [i,j] : 0 <= i <= N and
6531 for (int c0 = 0; c0 <= N; c0 += 1)
6532 for (int c1 = 0; c1 <= M; c1 += 1)
6535 When the option is turned on, the following AST is generated
6537 for (int c0 = 0; c0 <= N; c0 += 1)
6538 for (int c1 = 0; c1 <= M; c1 += 1)
6541 =item * ast_build_group_coscheduled
6543 If two domain elements are assigned the same schedule point, then
6544 they may be executed in any order and they may even appear in different
6545 loops. If this options is set, then the AST generator will make
6546 sure that coscheduled domain elements do not appear in separate parts
6547 of the AST. This is useful in case of nested AST generation
6548 if the outer AST generation is given only part of a schedule
6549 and the inner AST generation should handle the domains that are
6550 coscheduled by this initial part of the schedule together.
6551 For example if an AST is generated for a schedule
6553 { A[i] -> [0]; B[i] -> [0] }
6555 then the C<isl_ast_build_set_create_leaf> callback described
6556 below may get called twice, once for each domain.
6557 Setting this option ensures that the callback is only called once
6558 on both domains together.
6560 =item * ast_build_separation_bounds
6562 This option specifies which bounds to use during separation.
6563 If this option is set to C<ISL_AST_BUILD_SEPARATION_BOUNDS_IMPLICIT>
6564 then all (possibly implicit) bounds on the current dimension will
6565 be used during separation.
6566 If this option is set to C<ISL_AST_BUILD_SEPARATION_BOUNDS_EXPLICIT>
6567 then only those bounds that are explicitly available will
6568 be used during separation.
6570 =item * ast_build_scale_strides
6572 This option specifies whether the AST generator is allowed
6573 to scale down iterators of strided loops.
6575 =item * ast_build_allow_else
6577 This option specifies whether the AST generator is allowed
6578 to construct if statements with else branches.
6580 =item * ast_build_allow_or
6582 This option specifies whether the AST generator is allowed
6583 to construct if conditions with disjunctions.
6587 =head3 Fine-grained Control over AST Generation
6589 Besides specifying the constraints on the parameters,
6590 an C<isl_ast_build> object can be used to control
6591 various aspects of the AST generation process.
6592 The most prominent way of control is through ``options'',
6593 which can be set using the following function.
6595 #include <isl/ast_build.h>
6596 __isl_give isl_ast_build *
6597 isl_ast_build_set_options(
6598 __isl_take isl_ast_build *control,
6599 __isl_take isl_union_map *options);
6601 The options are encoded in an <isl_union_map>.
6602 The domain of this union relation refers to the schedule domain,
6603 i.e., the range of the schedule passed to C<isl_ast_build_ast_from_schedule>.
6604 In the case of nested AST generation (see L</"Nested AST Generation">),
6605 the domain of C<options> should refer to the extra piece of the schedule.
6606 That is, it should be equal to the range of the wrapped relation in the
6607 range of the schedule.
6608 The range of the options can consist of elements in one or more spaces,
6609 the names of which determine the effect of the option.
6610 The values of the range typically also refer to the schedule dimension
6611 to which the option applies. In case of nested AST generation
6612 (see L</"Nested AST Generation">), these values refer to the position
6613 of the schedule dimension within the innermost AST generation.
6614 The constraints on the domain elements of
6615 the option should only refer to this dimension and earlier dimensions.
6616 We consider the following spaces.
6620 =item C<separation_class>
6622 This space is a wrapped relation between two one dimensional spaces.
6623 The input space represents the schedule dimension to which the option
6624 applies and the output space represents the separation class.
6625 While constructing a loop corresponding to the specified schedule
6626 dimension(s), the AST generator will try to generate separate loops
6627 for domain elements that are assigned different classes.
6628 If only some of the elements are assigned a class, then those elements
6629 that are not assigned any class will be treated as belonging to a class
6630 that is separate from the explicitly assigned classes.
6631 The typical use case for this option is to separate full tiles from
6633 The other options, described below, are applied after the separation
6636 As an example, consider the separation into full and partial tiles
6637 of a tiling of a triangular domain.
6638 Take, for example, the domain
6640 { A[i,j] : 0 <= i,j and i + j <= 100 }
6642 and a tiling into tiles of 10 by 10. The input to the AST generator
6643 is then the schedule
6645 { A[i,j] -> [([i/10]),[j/10],i,j] : 0 <= i,j and
6648 Without any options, the following AST is generated
6650 for (int c0 = 0; c0 <= 10; c0 += 1)
6651 for (int c1 = 0; c1 <= -c0 + 10; c1 += 1)
6652 for (int c2 = 10 * c0;
6653 c2 <= min(-10 * c1 + 100, 10 * c0 + 9);
6655 for (int c3 = 10 * c1;
6656 c3 <= min(10 * c1 + 9, -c2 + 100);
6660 Separation into full and partial tiles can be obtained by assigning
6661 a class, say C<0>, to the full tiles. The full tiles are represented by those
6662 values of the first and second schedule dimensions for which there are
6663 values of the third and fourth dimensions to cover an entire tile.
6664 That is, we need to specify the following option
6666 { [a,b,c,d] -> separation_class[[0]->[0]] :
6667 exists b': 0 <= 10a,10b' and
6668 10a+9+10b'+9 <= 100;
6669 [a,b,c,d] -> separation_class[[1]->[0]] :
6670 0 <= 10a,10b and 10a+9+10b+9 <= 100 }
6674 { [a, b, c, d] -> separation_class[[1] -> [0]] :
6675 a >= 0 and b >= 0 and b <= 8 - a;
6676 [a, b, c, d] -> separation_class[[0] -> [0]] :
6679 With this option, the generated AST is as follows
6682 for (int c0 = 0; c0 <= 8; c0 += 1) {
6683 for (int c1 = 0; c1 <= -c0 + 8; c1 += 1)
6684 for (int c2 = 10 * c0;
6685 c2 <= 10 * c0 + 9; c2 += 1)
6686 for (int c3 = 10 * c1;
6687 c3 <= 10 * c1 + 9; c3 += 1)
6689 for (int c1 = -c0 + 9; c1 <= -c0 + 10; c1 += 1)
6690 for (int c2 = 10 * c0;
6691 c2 <= min(-10 * c1 + 100, 10 * c0 + 9);
6693 for (int c3 = 10 * c1;
6694 c3 <= min(-c2 + 100, 10 * c1 + 9);
6698 for (int c0 = 9; c0 <= 10; c0 += 1)
6699 for (int c1 = 0; c1 <= -c0 + 10; c1 += 1)
6700 for (int c2 = 10 * c0;
6701 c2 <= min(-10 * c1 + 100, 10 * c0 + 9);
6703 for (int c3 = 10 * c1;
6704 c3 <= min(10 * c1 + 9, -c2 + 100);
6711 This is a single-dimensional space representing the schedule dimension(s)
6712 to which ``separation'' should be applied. Separation tries to split
6713 a loop into several pieces if this can avoid the generation of guards
6715 See also the C<atomic> option.
6719 This is a single-dimensional space representing the schedule dimension(s)
6720 for which the domains should be considered ``atomic''. That is, the
6721 AST generator will make sure that any given domain space will only appear
6722 in a single loop at the specified level.
6724 Consider the following schedule
6726 { a[i] -> [i] : 0 <= i < 10;
6727 b[i] -> [i+1] : 0 <= i < 10 }
6729 If the following option is specified
6731 { [i] -> separate[x] }
6733 then the following AST will be generated
6737 for (int c0 = 1; c0 <= 9; c0 += 1) {
6744 If, on the other hand, the following option is specified
6746 { [i] -> atomic[x] }
6748 then the following AST will be generated
6750 for (int c0 = 0; c0 <= 10; c0 += 1) {
6757 If neither C<atomic> nor C<separate> is specified, then the AST generator
6758 may produce either of these two results or some intermediate form.
6762 This is a single-dimensional space representing the schedule dimension(s)
6763 that should be I<completely> unrolled.
6764 To obtain a partial unrolling, the user should apply an additional
6765 strip-mining to the schedule and fully unroll the inner loop.
6769 Additional control is available through the following functions.
6771 #include <isl/ast_build.h>
6772 __isl_give isl_ast_build *
6773 isl_ast_build_set_iterators(
6774 __isl_take isl_ast_build *control,
6775 __isl_take isl_id_list *iterators);
6777 The function C<isl_ast_build_set_iterators> allows the user to
6778 specify a list of iterator C<isl_id>s to be used as iterators.
6779 If the input schedule is injective, then
6780 the number of elements in this list should be as large as the dimension
6781 of the schedule space, but no direct correspondence should be assumed
6782 between dimensions and elements.
6783 If the input schedule is not injective, then an additional number
6784 of C<isl_id>s equal to the largest dimension of the input domains
6786 If the number of provided C<isl_id>s is insufficient, then additional
6787 names are automatically generated.
6789 #include <isl/ast_build.h>
6790 __isl_give isl_ast_build *
6791 isl_ast_build_set_create_leaf(
6792 __isl_take isl_ast_build *control,
6793 __isl_give isl_ast_node *(*fn)(
6794 __isl_take isl_ast_build *build,
6795 void *user), void *user);
6798 C<isl_ast_build_set_create_leaf> function allows for the
6799 specification of a callback that should be called whenever the AST
6800 generator arrives at an element of the schedule domain.
6801 The callback should return an AST node that should be inserted
6802 at the corresponding position of the AST. The default action (when
6803 the callback is not set) is to continue generating parts of the AST to scan
6804 all the domain elements associated to the schedule domain element
6805 and to insert user nodes, ``calling'' the domain element, for each of them.
6806 The C<build> argument contains the current state of the C<isl_ast_build>.
6807 To ease nested AST generation (see L</"Nested AST Generation">),
6808 all control information that is
6809 specific to the current AST generation such as the options and
6810 the callbacks has been removed from this C<isl_ast_build>.
6811 The callback would typically return the result of a nested
6813 user defined node created using the following function.
6815 #include <isl/ast.h>
6816 __isl_give isl_ast_node *isl_ast_node_alloc_user(
6817 __isl_take isl_ast_expr *expr);
6819 #include <isl/ast_build.h>
6820 __isl_give isl_ast_build *
6821 isl_ast_build_set_at_each_domain(
6822 __isl_take isl_ast_build *build,
6823 __isl_give isl_ast_node *(*fn)(
6824 __isl_take isl_ast_node *node,
6825 __isl_keep isl_ast_build *build,
6826 void *user), void *user);
6827 __isl_give isl_ast_build *
6828 isl_ast_build_set_before_each_for(
6829 __isl_take isl_ast_build *build,
6830 __isl_give isl_id *(*fn)(
6831 __isl_keep isl_ast_build *build,
6832 void *user), void *user);
6833 __isl_give isl_ast_build *
6834 isl_ast_build_set_after_each_for(
6835 __isl_take isl_ast_build *build,
6836 __isl_give isl_ast_node *(*fn)(
6837 __isl_take isl_ast_node *node,
6838 __isl_keep isl_ast_build *build,
6839 void *user), void *user);
6841 The callback set by C<isl_ast_build_set_at_each_domain> will
6842 be called for each domain AST node.
6843 The callbacks set by C<isl_ast_build_set_before_each_for>
6844 and C<isl_ast_build_set_after_each_for> will be called
6845 for each for AST node. The first will be called in depth-first
6846 pre-order, while the second will be called in depth-first post-order.
6847 Since C<isl_ast_build_set_before_each_for> is called before the for
6848 node is actually constructed, it is only passed an C<isl_ast_build>.
6849 The returned C<isl_id> will be added as an annotation (using
6850 C<isl_ast_node_set_annotation>) to the constructed for node.
6851 In particular, if the user has also specified an C<after_each_for>
6852 callback, then the annotation can be retrieved from the node passed to
6853 that callback using C<isl_ast_node_get_annotation>.
6854 All callbacks should C<NULL> on failure.
6855 The given C<isl_ast_build> can be used to create new
6856 C<isl_ast_expr> objects using C<isl_ast_build_expr_from_pw_aff>
6857 or C<isl_ast_build_call_from_pw_multi_aff>.
6859 =head3 Nested AST Generation
6861 C<isl> allows the user to create an AST within the context
6862 of another AST. These nested ASTs are created using the
6863 same C<isl_ast_build_ast_from_schedule> function that is used to create the
6864 outer AST. The C<build> argument should be an C<isl_ast_build>
6865 passed to a callback set by
6866 C<isl_ast_build_set_create_leaf>.
6867 The space of the range of the C<schedule> argument should refer
6868 to this build. In particular, the space should be a wrapped
6869 relation and the domain of this wrapped relation should be the
6870 same as that of the range of the schedule returned by
6871 C<isl_ast_build_get_schedule> below.
6872 In practice, the new schedule is typically
6873 created by calling C<isl_union_map_range_product> on the old schedule
6874 and some extra piece of the schedule.
6875 The space of the schedule domain is also available from
6876 the C<isl_ast_build>.
6878 #include <isl/ast_build.h>
6879 __isl_give isl_union_map *isl_ast_build_get_schedule(
6880 __isl_keep isl_ast_build *build);
6881 __isl_give isl_space *isl_ast_build_get_schedule_space(
6882 __isl_keep isl_ast_build *build);
6883 __isl_give isl_ast_build *isl_ast_build_restrict(
6884 __isl_take isl_ast_build *build,
6885 __isl_take isl_set *set);
6887 The C<isl_ast_build_get_schedule> function returns a (partial)
6888 schedule for the domains elements for which part of the AST still needs to
6889 be generated in the current build.
6890 In particular, the domain elements are mapped to those iterations of the loops
6891 enclosing the current point of the AST generation inside which
6892 the domain elements are executed.
6893 No direct correspondence between
6894 the input schedule and this schedule should be assumed.
6895 The space obtained from C<isl_ast_build_get_schedule_space> can be used
6896 to create a set for C<isl_ast_build_restrict> to intersect
6897 with the current build. In particular, the set passed to
6898 C<isl_ast_build_restrict> can have additional parameters.
6899 The ids of the set dimensions in the space returned by
6900 C<isl_ast_build_get_schedule_space> correspond to the
6901 iterators of the already generated loops.
6902 The user should not rely on the ids of the output dimensions
6903 of the relations in the union relation returned by
6904 C<isl_ast_build_get_schedule> having any particular value.
6908 Although C<isl> is mainly meant to be used as a library,
6909 it also contains some basic applications that use some
6910 of the functionality of C<isl>.
6911 The input may be specified in either the L<isl format>
6912 or the L<PolyLib format>.
6914 =head2 C<isl_polyhedron_sample>
6916 C<isl_polyhedron_sample> takes a polyhedron as input and prints
6917 an integer element of the polyhedron, if there is any.
6918 The first column in the output is the denominator and is always
6919 equal to 1. If the polyhedron contains no integer points,
6920 then a vector of length zero is printed.
6924 C<isl_pip> takes the same input as the C<example> program
6925 from the C<piplib> distribution, i.e., a set of constraints
6926 on the parameters, a line containing only -1 and finally a set
6927 of constraints on a parametric polyhedron.
6928 The coefficients of the parameters appear in the last columns
6929 (but before the final constant column).
6930 The output is the lexicographic minimum of the parametric polyhedron.
6931 As C<isl> currently does not have its own output format, the output
6932 is just a dump of the internal state.
6934 =head2 C<isl_polyhedron_minimize>
6936 C<isl_polyhedron_minimize> computes the minimum of some linear
6937 or affine objective function over the integer points in a polyhedron.
6938 If an affine objective function
6939 is given, then the constant should appear in the last column.
6941 =head2 C<isl_polytope_scan>
6943 Given a polytope, C<isl_polytope_scan> prints
6944 all integer points in the polytope.
6946 =head2 C<isl_codegen>
6948 Given a schedule, a context set and an options relation,
6949 C<isl_codegen> prints out an AST that scans the domain elements
6950 of the schedule in the order of their image(s) taking into account
6951 the constraints in the context set.