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 int isl_local_space_has_dim_id(
1034 __isl_keep isl_local_space *ls,
1035 enum isl_dim_type type, unsigned pos);
1036 __isl_give isl_id *isl_local_space_get_dim_id(
1037 __isl_keep isl_local_space *ls,
1038 enum isl_dim_type type, unsigned pos);
1039 int isl_local_space_has_dim_name(
1040 __isl_keep isl_local_space *ls,
1041 enum isl_dim_type type, unsigned pos)
1042 const char *isl_local_space_get_dim_name(
1043 __isl_keep isl_local_space *ls,
1044 enum isl_dim_type type, unsigned pos);
1045 __isl_give isl_local_space *isl_local_space_set_dim_name(
1046 __isl_take isl_local_space *ls,
1047 enum isl_dim_type type, unsigned pos, const char *s);
1048 __isl_give isl_local_space *isl_local_space_set_dim_id(
1049 __isl_take isl_local_space *ls,
1050 enum isl_dim_type type, unsigned pos,
1051 __isl_take isl_id *id);
1052 __isl_give isl_space *isl_local_space_get_space(
1053 __isl_keep isl_local_space *ls);
1054 __isl_give isl_aff *isl_local_space_get_div(
1055 __isl_keep isl_local_space *ls, int pos);
1056 __isl_give isl_local_space *isl_local_space_copy(
1057 __isl_keep isl_local_space *ls);
1058 void *isl_local_space_free(__isl_take isl_local_space *ls);
1060 Note that C<isl_local_space_get_div> can only be used on local spaces
1063 Two local spaces can be compared using
1065 int isl_local_space_is_equal(__isl_keep isl_local_space *ls1,
1066 __isl_keep isl_local_space *ls2);
1068 Local spaces can be created from other local spaces
1069 using the following functions.
1071 __isl_give isl_local_space *isl_local_space_domain(
1072 __isl_take isl_local_space *ls);
1073 __isl_give isl_local_space *isl_local_space_range(
1074 __isl_take isl_local_space *ls);
1075 __isl_give isl_local_space *isl_local_space_from_domain(
1076 __isl_take isl_local_space *ls);
1077 __isl_give isl_local_space *isl_local_space_intersect(
1078 __isl_take isl_local_space *ls1,
1079 __isl_take isl_local_space *ls2);
1080 __isl_give isl_local_space *isl_local_space_add_dims(
1081 __isl_take isl_local_space *ls,
1082 enum isl_dim_type type, unsigned n);
1083 __isl_give isl_local_space *isl_local_space_insert_dims(
1084 __isl_take isl_local_space *ls,
1085 enum isl_dim_type type, unsigned first, unsigned n);
1086 __isl_give isl_local_space *isl_local_space_drop_dims(
1087 __isl_take isl_local_space *ls,
1088 enum isl_dim_type type, unsigned first, unsigned n);
1090 =head2 Input and Output
1092 C<isl> supports its own input/output format, which is similar
1093 to the C<Omega> format, but also supports the C<PolyLib> format
1096 =head3 C<isl> format
1098 The C<isl> format is similar to that of C<Omega>, but has a different
1099 syntax for describing the parameters and allows for the definition
1100 of an existentially quantified variable as the integer division
1101 of an affine expression.
1102 For example, the set of integers C<i> between C<0> and C<n>
1103 such that C<i % 10 <= 6> can be described as
1105 [n] -> { [i] : exists (a = [i/10] : 0 <= i and i <= n and
1108 A set or relation can have several disjuncts, separated
1109 by the keyword C<or>. Each disjunct is either a conjunction
1110 of constraints or a projection (C<exists>) of a conjunction
1111 of constraints. The constraints are separated by the keyword
1114 =head3 C<PolyLib> format
1116 If the represented set is a union, then the first line
1117 contains a single number representing the number of disjuncts.
1118 Otherwise, a line containing the number C<1> is optional.
1120 Each disjunct is represented by a matrix of constraints.
1121 The first line contains two numbers representing
1122 the number of rows and columns,
1123 where the number of rows is equal to the number of constraints
1124 and the number of columns is equal to two plus the number of variables.
1125 The following lines contain the actual rows of the constraint matrix.
1126 In each row, the first column indicates whether the constraint
1127 is an equality (C<0>) or inequality (C<1>). The final column
1128 corresponds to the constant term.
1130 If the set is parametric, then the coefficients of the parameters
1131 appear in the last columns before the constant column.
1132 The coefficients of any existentially quantified variables appear
1133 between those of the set variables and those of the parameters.
1135 =head3 Extended C<PolyLib> format
1137 The extended C<PolyLib> format is nearly identical to the
1138 C<PolyLib> format. The only difference is that the line
1139 containing the number of rows and columns of a constraint matrix
1140 also contains four additional numbers:
1141 the number of output dimensions, the number of input dimensions,
1142 the number of local dimensions (i.e., the number of existentially
1143 quantified variables) and the number of parameters.
1144 For sets, the number of ``output'' dimensions is equal
1145 to the number of set dimensions, while the number of ``input''
1150 #include <isl/set.h>
1151 __isl_give isl_basic_set *isl_basic_set_read_from_file(
1152 isl_ctx *ctx, FILE *input);
1153 __isl_give isl_basic_set *isl_basic_set_read_from_str(
1154 isl_ctx *ctx, const char *str);
1155 __isl_give isl_set *isl_set_read_from_file(isl_ctx *ctx,
1157 __isl_give isl_set *isl_set_read_from_str(isl_ctx *ctx,
1160 #include <isl/map.h>
1161 __isl_give isl_basic_map *isl_basic_map_read_from_file(
1162 isl_ctx *ctx, FILE *input);
1163 __isl_give isl_basic_map *isl_basic_map_read_from_str(
1164 isl_ctx *ctx, const char *str);
1165 __isl_give isl_map *isl_map_read_from_file(
1166 isl_ctx *ctx, FILE *input);
1167 __isl_give isl_map *isl_map_read_from_str(isl_ctx *ctx,
1170 #include <isl/union_set.h>
1171 __isl_give isl_union_set *isl_union_set_read_from_file(
1172 isl_ctx *ctx, FILE *input);
1173 __isl_give isl_union_set *isl_union_set_read_from_str(
1174 isl_ctx *ctx, const char *str);
1176 #include <isl/union_map.h>
1177 __isl_give isl_union_map *isl_union_map_read_from_file(
1178 isl_ctx *ctx, FILE *input);
1179 __isl_give isl_union_map *isl_union_map_read_from_str(
1180 isl_ctx *ctx, const char *str);
1182 The input format is autodetected and may be either the C<PolyLib> format
1183 or the C<isl> format.
1187 Before anything can be printed, an C<isl_printer> needs to
1190 __isl_give isl_printer *isl_printer_to_file(isl_ctx *ctx,
1192 __isl_give isl_printer *isl_printer_to_str(isl_ctx *ctx);
1193 void *isl_printer_free(__isl_take isl_printer *printer);
1194 __isl_give char *isl_printer_get_str(
1195 __isl_keep isl_printer *printer);
1197 The printer can be inspected using the following functions.
1199 FILE *isl_printer_get_file(
1200 __isl_keep isl_printer *printer);
1201 int isl_printer_get_output_format(
1202 __isl_keep isl_printer *p);
1204 The behavior of the printer can be modified in various ways
1206 __isl_give isl_printer *isl_printer_set_output_format(
1207 __isl_take isl_printer *p, int output_format);
1208 __isl_give isl_printer *isl_printer_set_indent(
1209 __isl_take isl_printer *p, int indent);
1210 __isl_give isl_printer *isl_printer_indent(
1211 __isl_take isl_printer *p, int indent);
1212 __isl_give isl_printer *isl_printer_set_prefix(
1213 __isl_take isl_printer *p, const char *prefix);
1214 __isl_give isl_printer *isl_printer_set_suffix(
1215 __isl_take isl_printer *p, const char *suffix);
1217 The C<output_format> may be either C<ISL_FORMAT_ISL>, C<ISL_FORMAT_OMEGA>,
1218 C<ISL_FORMAT_POLYLIB>, C<ISL_FORMAT_EXT_POLYLIB> or C<ISL_FORMAT_LATEX>
1219 and defaults to C<ISL_FORMAT_ISL>.
1220 Each line in the output is indented by C<indent> (set by
1221 C<isl_printer_set_indent>) spaces
1222 (default: 0), prefixed by C<prefix> and suffixed by C<suffix>.
1223 In the C<PolyLib> format output,
1224 the coefficients of the existentially quantified variables
1225 appear between those of the set variables and those
1227 The function C<isl_printer_indent> increases the indentation
1228 by the specified amount (which may be negative).
1230 To actually print something, use
1232 #include <isl/printer.h>
1233 __isl_give isl_printer *isl_printer_print_double(
1234 __isl_take isl_printer *p, double d);
1236 #include <isl/set.h>
1237 __isl_give isl_printer *isl_printer_print_basic_set(
1238 __isl_take isl_printer *printer,
1239 __isl_keep isl_basic_set *bset);
1240 __isl_give isl_printer *isl_printer_print_set(
1241 __isl_take isl_printer *printer,
1242 __isl_keep isl_set *set);
1244 #include <isl/map.h>
1245 __isl_give isl_printer *isl_printer_print_basic_map(
1246 __isl_take isl_printer *printer,
1247 __isl_keep isl_basic_map *bmap);
1248 __isl_give isl_printer *isl_printer_print_map(
1249 __isl_take isl_printer *printer,
1250 __isl_keep isl_map *map);
1252 #include <isl/union_set.h>
1253 __isl_give isl_printer *isl_printer_print_union_set(
1254 __isl_take isl_printer *p,
1255 __isl_keep isl_union_set *uset);
1257 #include <isl/union_map.h>
1258 __isl_give isl_printer *isl_printer_print_union_map(
1259 __isl_take isl_printer *p,
1260 __isl_keep isl_union_map *umap);
1262 When called on a file printer, the following function flushes
1263 the file. When called on a string printer, the buffer is cleared.
1265 __isl_give isl_printer *isl_printer_flush(
1266 __isl_take isl_printer *p);
1268 =head2 Creating New Sets and Relations
1270 C<isl> has functions for creating some standard sets and relations.
1274 =item * Empty sets and relations
1276 __isl_give isl_basic_set *isl_basic_set_empty(
1277 __isl_take isl_space *space);
1278 __isl_give isl_basic_map *isl_basic_map_empty(
1279 __isl_take isl_space *space);
1280 __isl_give isl_set *isl_set_empty(
1281 __isl_take isl_space *space);
1282 __isl_give isl_map *isl_map_empty(
1283 __isl_take isl_space *space);
1284 __isl_give isl_union_set *isl_union_set_empty(
1285 __isl_take isl_space *space);
1286 __isl_give isl_union_map *isl_union_map_empty(
1287 __isl_take isl_space *space);
1289 For C<isl_union_set>s and C<isl_union_map>s, the space
1290 is only used to specify the parameters.
1292 =item * Universe sets and relations
1294 __isl_give isl_basic_set *isl_basic_set_universe(
1295 __isl_take isl_space *space);
1296 __isl_give isl_basic_map *isl_basic_map_universe(
1297 __isl_take isl_space *space);
1298 __isl_give isl_set *isl_set_universe(
1299 __isl_take isl_space *space);
1300 __isl_give isl_map *isl_map_universe(
1301 __isl_take isl_space *space);
1302 __isl_give isl_union_set *isl_union_set_universe(
1303 __isl_take isl_union_set *uset);
1304 __isl_give isl_union_map *isl_union_map_universe(
1305 __isl_take isl_union_map *umap);
1307 The sets and relations constructed by the functions above
1308 contain all integer values, while those constructed by the
1309 functions below only contain non-negative values.
1311 __isl_give isl_basic_set *isl_basic_set_nat_universe(
1312 __isl_take isl_space *space);
1313 __isl_give isl_basic_map *isl_basic_map_nat_universe(
1314 __isl_take isl_space *space);
1315 __isl_give isl_set *isl_set_nat_universe(
1316 __isl_take isl_space *space);
1317 __isl_give isl_map *isl_map_nat_universe(
1318 __isl_take isl_space *space);
1320 =item * Identity relations
1322 __isl_give isl_basic_map *isl_basic_map_identity(
1323 __isl_take isl_space *space);
1324 __isl_give isl_map *isl_map_identity(
1325 __isl_take isl_space *space);
1327 The number of input and output dimensions in C<space> needs
1330 =item * Lexicographic order
1332 __isl_give isl_map *isl_map_lex_lt(
1333 __isl_take isl_space *set_space);
1334 __isl_give isl_map *isl_map_lex_le(
1335 __isl_take isl_space *set_space);
1336 __isl_give isl_map *isl_map_lex_gt(
1337 __isl_take isl_space *set_space);
1338 __isl_give isl_map *isl_map_lex_ge(
1339 __isl_take isl_space *set_space);
1340 __isl_give isl_map *isl_map_lex_lt_first(
1341 __isl_take isl_space *space, unsigned n);
1342 __isl_give isl_map *isl_map_lex_le_first(
1343 __isl_take isl_space *space, unsigned n);
1344 __isl_give isl_map *isl_map_lex_gt_first(
1345 __isl_take isl_space *space, unsigned n);
1346 __isl_give isl_map *isl_map_lex_ge_first(
1347 __isl_take isl_space *space, unsigned n);
1349 The first four functions take a space for a B<set>
1350 and return relations that express that the elements in the domain
1351 are lexicographically less
1352 (C<isl_map_lex_lt>), less or equal (C<isl_map_lex_le>),
1353 greater (C<isl_map_lex_gt>) or greater or equal (C<isl_map_lex_ge>)
1354 than the elements in the range.
1355 The last four functions take a space for a map
1356 and return relations that express that the first C<n> dimensions
1357 in the domain are lexicographically less
1358 (C<isl_map_lex_lt_first>), less or equal (C<isl_map_lex_le_first>),
1359 greater (C<isl_map_lex_gt_first>) or greater or equal (C<isl_map_lex_ge_first>)
1360 than the first C<n> dimensions in the range.
1364 A basic set or relation can be converted to a set or relation
1365 using the following functions.
1367 __isl_give isl_set *isl_set_from_basic_set(
1368 __isl_take isl_basic_set *bset);
1369 __isl_give isl_map *isl_map_from_basic_map(
1370 __isl_take isl_basic_map *bmap);
1372 Sets and relations can be converted to union sets and relations
1373 using the following functions.
1375 __isl_give isl_union_set *isl_union_set_from_basic_set(
1376 __isl_take isl_basic_set *bset);
1377 __isl_give isl_union_map *isl_union_map_from_basic_map(
1378 __isl_take isl_basic_map *bmap);
1379 __isl_give isl_union_set *isl_union_set_from_set(
1380 __isl_take isl_set *set);
1381 __isl_give isl_union_map *isl_union_map_from_map(
1382 __isl_take isl_map *map);
1384 The inverse conversions below can only be used if the input
1385 union set or relation is known to contain elements in exactly one
1388 __isl_give isl_set *isl_set_from_union_set(
1389 __isl_take isl_union_set *uset);
1390 __isl_give isl_map *isl_map_from_union_map(
1391 __isl_take isl_union_map *umap);
1393 A zero-dimensional (basic) set can be constructed on a given parameter domain
1394 using the following function.
1396 __isl_give isl_basic_set *isl_basic_set_from_params(
1397 __isl_take isl_basic_set *bset);
1398 __isl_give isl_set *isl_set_from_params(
1399 __isl_take isl_set *set);
1401 Sets and relations can be copied and freed again using the following
1404 __isl_give isl_basic_set *isl_basic_set_copy(
1405 __isl_keep isl_basic_set *bset);
1406 __isl_give isl_set *isl_set_copy(__isl_keep isl_set *set);
1407 __isl_give isl_union_set *isl_union_set_copy(
1408 __isl_keep isl_union_set *uset);
1409 __isl_give isl_basic_map *isl_basic_map_copy(
1410 __isl_keep isl_basic_map *bmap);
1411 __isl_give isl_map *isl_map_copy(__isl_keep isl_map *map);
1412 __isl_give isl_union_map *isl_union_map_copy(
1413 __isl_keep isl_union_map *umap);
1414 void *isl_basic_set_free(__isl_take isl_basic_set *bset);
1415 void *isl_set_free(__isl_take isl_set *set);
1416 void *isl_union_set_free(__isl_take isl_union_set *uset);
1417 void *isl_basic_map_free(__isl_take isl_basic_map *bmap);
1418 void *isl_map_free(__isl_take isl_map *map);
1419 void *isl_union_map_free(__isl_take isl_union_map *umap);
1421 Other sets and relations can be constructed by starting
1422 from a universe set or relation, adding equality and/or
1423 inequality constraints and then projecting out the
1424 existentially quantified variables, if any.
1425 Constraints can be constructed, manipulated and
1426 added to (or removed from) (basic) sets and relations
1427 using the following functions.
1429 #include <isl/constraint.h>
1430 __isl_give isl_constraint *isl_equality_alloc(
1431 __isl_take isl_local_space *ls);
1432 __isl_give isl_constraint *isl_inequality_alloc(
1433 __isl_take isl_local_space *ls);
1434 __isl_give isl_constraint *isl_constraint_set_constant_si(
1435 __isl_take isl_constraint *constraint, int v);
1436 __isl_give isl_constraint *isl_constraint_set_constant_val(
1437 __isl_take isl_constraint *constraint,
1438 __isl_take isl_val *v);
1439 __isl_give isl_constraint *isl_constraint_set_coefficient_si(
1440 __isl_take isl_constraint *constraint,
1441 enum isl_dim_type type, int pos, int v);
1442 __isl_give isl_constraint *
1443 isl_constraint_set_coefficient_val(
1444 __isl_take isl_constraint *constraint,
1445 enum isl_dim_type type, int pos, isl_val *v);
1446 __isl_give isl_basic_map *isl_basic_map_add_constraint(
1447 __isl_take isl_basic_map *bmap,
1448 __isl_take isl_constraint *constraint);
1449 __isl_give isl_basic_set *isl_basic_set_add_constraint(
1450 __isl_take isl_basic_set *bset,
1451 __isl_take isl_constraint *constraint);
1452 __isl_give isl_map *isl_map_add_constraint(
1453 __isl_take isl_map *map,
1454 __isl_take isl_constraint *constraint);
1455 __isl_give isl_set *isl_set_add_constraint(
1456 __isl_take isl_set *set,
1457 __isl_take isl_constraint *constraint);
1458 __isl_give isl_basic_set *isl_basic_set_drop_constraint(
1459 __isl_take isl_basic_set *bset,
1460 __isl_take isl_constraint *constraint);
1462 For example, to create a set containing the even integers
1463 between 10 and 42, you would use the following code.
1466 isl_local_space *ls;
1468 isl_basic_set *bset;
1470 space = isl_space_set_alloc(ctx, 0, 2);
1471 bset = isl_basic_set_universe(isl_space_copy(space));
1472 ls = isl_local_space_from_space(space);
1474 c = isl_equality_alloc(isl_local_space_copy(ls));
1475 c = isl_constraint_set_coefficient_si(c, isl_dim_set, 0, -1);
1476 c = isl_constraint_set_coefficient_si(c, isl_dim_set, 1, 2);
1477 bset = isl_basic_set_add_constraint(bset, c);
1479 c = isl_inequality_alloc(isl_local_space_copy(ls));
1480 c = isl_constraint_set_constant_si(c, -10);
1481 c = isl_constraint_set_coefficient_si(c, isl_dim_set, 0, 1);
1482 bset = isl_basic_set_add_constraint(bset, c);
1484 c = isl_inequality_alloc(ls);
1485 c = isl_constraint_set_constant_si(c, 42);
1486 c = isl_constraint_set_coefficient_si(c, isl_dim_set, 0, -1);
1487 bset = isl_basic_set_add_constraint(bset, c);
1489 bset = isl_basic_set_project_out(bset, isl_dim_set, 1, 1);
1493 isl_basic_set *bset;
1494 bset = isl_basic_set_read_from_str(ctx,
1495 "{[i] : exists (a : i = 2a and i >= 10 and i <= 42)}");
1497 A basic set or relation can also be constructed from two matrices
1498 describing the equalities and the inequalities.
1500 __isl_give isl_basic_set *isl_basic_set_from_constraint_matrices(
1501 __isl_take isl_space *space,
1502 __isl_take isl_mat *eq, __isl_take isl_mat *ineq,
1503 enum isl_dim_type c1,
1504 enum isl_dim_type c2, enum isl_dim_type c3,
1505 enum isl_dim_type c4);
1506 __isl_give isl_basic_map *isl_basic_map_from_constraint_matrices(
1507 __isl_take isl_space *space,
1508 __isl_take isl_mat *eq, __isl_take isl_mat *ineq,
1509 enum isl_dim_type c1,
1510 enum isl_dim_type c2, enum isl_dim_type c3,
1511 enum isl_dim_type c4, enum isl_dim_type c5);
1513 The C<isl_dim_type> arguments indicate the order in which
1514 different kinds of variables appear in the input matrices
1515 and should be a permutation of C<isl_dim_cst>, C<isl_dim_param>,
1516 C<isl_dim_set> and C<isl_dim_div> for sets and
1517 of C<isl_dim_cst>, C<isl_dim_param>,
1518 C<isl_dim_in>, C<isl_dim_out> and C<isl_dim_div> for relations.
1520 A (basic or union) set or relation can also be constructed from a
1521 (union) (piecewise) (multiple) affine expression
1522 or a list of affine expressions
1523 (See L<"Piecewise Quasi Affine Expressions"> and
1524 L<"Piecewise Multiple Quasi Affine Expressions">).
1526 __isl_give isl_basic_map *isl_basic_map_from_aff(
1527 __isl_take isl_aff *aff);
1528 __isl_give isl_map *isl_map_from_aff(
1529 __isl_take isl_aff *aff);
1530 __isl_give isl_set *isl_set_from_pw_aff(
1531 __isl_take isl_pw_aff *pwaff);
1532 __isl_give isl_map *isl_map_from_pw_aff(
1533 __isl_take isl_pw_aff *pwaff);
1534 __isl_give isl_basic_map *isl_basic_map_from_aff_list(
1535 __isl_take isl_space *domain_space,
1536 __isl_take isl_aff_list *list);
1537 __isl_give isl_basic_map *isl_basic_map_from_multi_aff(
1538 __isl_take isl_multi_aff *maff)
1539 __isl_give isl_map *isl_map_from_multi_aff(
1540 __isl_take isl_multi_aff *maff)
1541 __isl_give isl_set *isl_set_from_pw_multi_aff(
1542 __isl_take isl_pw_multi_aff *pma);
1543 __isl_give isl_map *isl_map_from_pw_multi_aff(
1544 __isl_take isl_pw_multi_aff *pma);
1545 __isl_give isl_set *isl_set_from_multi_pw_aff(
1546 __isl_take isl_multi_pw_aff *mpa);
1547 __isl_give isl_map *isl_map_from_multi_pw_aff(
1548 __isl_take isl_multi_pw_aff *mpa);
1549 __isl_give isl_union_map *
1550 isl_union_map_from_union_pw_multi_aff(
1551 __isl_take isl_union_pw_multi_aff *upma);
1553 The C<domain_dim> argument describes the domain of the resulting
1554 basic relation. It is required because the C<list> may consist
1555 of zero affine expressions.
1557 =head2 Inspecting Sets and Relations
1559 Usually, the user should not have to care about the actual constraints
1560 of the sets and maps, but should instead apply the abstract operations
1561 explained in the following sections.
1562 Occasionally, however, it may be required to inspect the individual
1563 coefficients of the constraints. This section explains how to do so.
1564 In these cases, it may also be useful to have C<isl> compute
1565 an explicit representation of the existentially quantified variables.
1567 __isl_give isl_set *isl_set_compute_divs(
1568 __isl_take isl_set *set);
1569 __isl_give isl_map *isl_map_compute_divs(
1570 __isl_take isl_map *map);
1571 __isl_give isl_union_set *isl_union_set_compute_divs(
1572 __isl_take isl_union_set *uset);
1573 __isl_give isl_union_map *isl_union_map_compute_divs(
1574 __isl_take isl_union_map *umap);
1576 This explicit representation defines the existentially quantified
1577 variables as integer divisions of the other variables, possibly
1578 including earlier existentially quantified variables.
1579 An explicitly represented existentially quantified variable therefore
1580 has a unique value when the values of the other variables are known.
1581 If, furthermore, the same existentials, i.e., existentials
1582 with the same explicit representations, should appear in the
1583 same order in each of the disjuncts of a set or map, then the user should call
1584 either of the following functions.
1586 __isl_give isl_set *isl_set_align_divs(
1587 __isl_take isl_set *set);
1588 __isl_give isl_map *isl_map_align_divs(
1589 __isl_take isl_map *map);
1591 Alternatively, the existentially quantified variables can be removed
1592 using the following functions, which compute an overapproximation.
1594 __isl_give isl_basic_set *isl_basic_set_remove_divs(
1595 __isl_take isl_basic_set *bset);
1596 __isl_give isl_basic_map *isl_basic_map_remove_divs(
1597 __isl_take isl_basic_map *bmap);
1598 __isl_give isl_set *isl_set_remove_divs(
1599 __isl_take isl_set *set);
1600 __isl_give isl_map *isl_map_remove_divs(
1601 __isl_take isl_map *map);
1603 It is also possible to only remove those divs that are defined
1604 in terms of a given range of dimensions or only those for which
1605 no explicit representation is known.
1607 __isl_give isl_basic_set *
1608 isl_basic_set_remove_divs_involving_dims(
1609 __isl_take isl_basic_set *bset,
1610 enum isl_dim_type type,
1611 unsigned first, unsigned n);
1612 __isl_give isl_basic_map *
1613 isl_basic_map_remove_divs_involving_dims(
1614 __isl_take isl_basic_map *bmap,
1615 enum isl_dim_type type,
1616 unsigned first, unsigned n);
1617 __isl_give isl_set *isl_set_remove_divs_involving_dims(
1618 __isl_take isl_set *set, enum isl_dim_type type,
1619 unsigned first, unsigned n);
1620 __isl_give isl_map *isl_map_remove_divs_involving_dims(
1621 __isl_take isl_map *map, enum isl_dim_type type,
1622 unsigned first, unsigned n);
1624 __isl_give isl_basic_set *
1625 isl_basic_set_remove_unknown_divs(
1626 __isl_take isl_basic_set *bset);
1627 __isl_give isl_set *isl_set_remove_unknown_divs(
1628 __isl_take isl_set *set);
1629 __isl_give isl_map *isl_map_remove_unknown_divs(
1630 __isl_take isl_map *map);
1632 To iterate over all the sets or maps in a union set or map, use
1634 int isl_union_set_foreach_set(__isl_keep isl_union_set *uset,
1635 int (*fn)(__isl_take isl_set *set, void *user),
1637 int isl_union_map_foreach_map(__isl_keep isl_union_map *umap,
1638 int (*fn)(__isl_take isl_map *map, void *user),
1641 The number of sets or maps in a union set or map can be obtained
1644 int isl_union_set_n_set(__isl_keep isl_union_set *uset);
1645 int isl_union_map_n_map(__isl_keep isl_union_map *umap);
1647 To extract the set or map in a given space from a union, use
1649 __isl_give isl_set *isl_union_set_extract_set(
1650 __isl_keep isl_union_set *uset,
1651 __isl_take isl_space *space);
1652 __isl_give isl_map *isl_union_map_extract_map(
1653 __isl_keep isl_union_map *umap,
1654 __isl_take isl_space *space);
1656 To iterate over all the basic sets or maps in a set or map, use
1658 int isl_set_foreach_basic_set(__isl_keep isl_set *set,
1659 int (*fn)(__isl_take isl_basic_set *bset, void *user),
1661 int isl_map_foreach_basic_map(__isl_keep isl_map *map,
1662 int (*fn)(__isl_take isl_basic_map *bmap, void *user),
1665 The callback function C<fn> should return 0 if successful and
1666 -1 if an error occurs. In the latter case, or if any other error
1667 occurs, the above functions will return -1.
1669 It should be noted that C<isl> does not guarantee that
1670 the basic sets or maps passed to C<fn> are disjoint.
1671 If this is required, then the user should call one of
1672 the following functions first.
1674 __isl_give isl_set *isl_set_make_disjoint(
1675 __isl_take isl_set *set);
1676 __isl_give isl_map *isl_map_make_disjoint(
1677 __isl_take isl_map *map);
1679 The number of basic sets in a set can be obtained
1682 int isl_set_n_basic_set(__isl_keep isl_set *set);
1684 To iterate over the constraints of a basic set or map, use
1686 #include <isl/constraint.h>
1688 int isl_basic_set_n_constraint(
1689 __isl_keep isl_basic_set *bset);
1690 int isl_basic_set_foreach_constraint(
1691 __isl_keep isl_basic_set *bset,
1692 int (*fn)(__isl_take isl_constraint *c, void *user),
1694 int isl_basic_map_foreach_constraint(
1695 __isl_keep isl_basic_map *bmap,
1696 int (*fn)(__isl_take isl_constraint *c, void *user),
1698 void *isl_constraint_free(__isl_take isl_constraint *c);
1700 Again, the callback function C<fn> should return 0 if successful and
1701 -1 if an error occurs. In the latter case, or if any other error
1702 occurs, the above functions will return -1.
1703 The constraint C<c> represents either an equality or an inequality.
1704 Use the following function to find out whether a constraint
1705 represents an equality. If not, it represents an inequality.
1707 int isl_constraint_is_equality(
1708 __isl_keep isl_constraint *constraint);
1710 The coefficients of the constraints can be inspected using
1711 the following functions.
1713 int isl_constraint_is_lower_bound(
1714 __isl_keep isl_constraint *constraint,
1715 enum isl_dim_type type, unsigned pos);
1716 int isl_constraint_is_upper_bound(
1717 __isl_keep isl_constraint *constraint,
1718 enum isl_dim_type type, unsigned pos);
1719 __isl_give isl_val *isl_constraint_get_constant_val(
1720 __isl_keep isl_constraint *constraint);
1721 __isl_give isl_val *isl_constraint_get_coefficient_val(
1722 __isl_keep isl_constraint *constraint,
1723 enum isl_dim_type type, int pos);
1724 int isl_constraint_involves_dims(
1725 __isl_keep isl_constraint *constraint,
1726 enum isl_dim_type type, unsigned first, unsigned n);
1728 The explicit representations of the existentially quantified
1729 variables can be inspected using the following function.
1730 Note that the user is only allowed to use this function
1731 if the inspected set or map is the result of a call
1732 to C<isl_set_compute_divs> or C<isl_map_compute_divs>.
1733 The existentially quantified variable is equal to the floor
1734 of the returned affine expression. The affine expression
1735 itself can be inspected using the functions in
1736 L<"Piecewise Quasi Affine Expressions">.
1738 __isl_give isl_aff *isl_constraint_get_div(
1739 __isl_keep isl_constraint *constraint, int pos);
1741 To obtain the constraints of a basic set or map in matrix
1742 form, use the following functions.
1744 __isl_give isl_mat *isl_basic_set_equalities_matrix(
1745 __isl_keep isl_basic_set *bset,
1746 enum isl_dim_type c1, enum isl_dim_type c2,
1747 enum isl_dim_type c3, enum isl_dim_type c4);
1748 __isl_give isl_mat *isl_basic_set_inequalities_matrix(
1749 __isl_keep isl_basic_set *bset,
1750 enum isl_dim_type c1, enum isl_dim_type c2,
1751 enum isl_dim_type c3, enum isl_dim_type c4);
1752 __isl_give isl_mat *isl_basic_map_equalities_matrix(
1753 __isl_keep isl_basic_map *bmap,
1754 enum isl_dim_type c1,
1755 enum isl_dim_type c2, enum isl_dim_type c3,
1756 enum isl_dim_type c4, enum isl_dim_type c5);
1757 __isl_give isl_mat *isl_basic_map_inequalities_matrix(
1758 __isl_keep isl_basic_map *bmap,
1759 enum isl_dim_type c1,
1760 enum isl_dim_type c2, enum isl_dim_type c3,
1761 enum isl_dim_type c4, enum isl_dim_type c5);
1763 The C<isl_dim_type> arguments dictate the order in which
1764 different kinds of variables appear in the resulting matrix
1765 and should be a permutation of C<isl_dim_cst>, C<isl_dim_param>,
1766 C<isl_dim_in>, C<isl_dim_out> and C<isl_dim_div>.
1768 The number of parameters, input, output or set dimensions can
1769 be obtained using the following functions.
1771 unsigned isl_basic_set_dim(__isl_keep isl_basic_set *bset,
1772 enum isl_dim_type type);
1773 unsigned isl_basic_map_dim(__isl_keep isl_basic_map *bmap,
1774 enum isl_dim_type type);
1775 unsigned isl_set_dim(__isl_keep isl_set *set,
1776 enum isl_dim_type type);
1777 unsigned isl_map_dim(__isl_keep isl_map *map,
1778 enum isl_dim_type type);
1780 To check whether the description of a set or relation depends
1781 on one or more given dimensions, it is not necessary to iterate over all
1782 constraints. Instead the following functions can be used.
1784 int isl_basic_set_involves_dims(
1785 __isl_keep isl_basic_set *bset,
1786 enum isl_dim_type type, unsigned first, unsigned n);
1787 int isl_set_involves_dims(__isl_keep isl_set *set,
1788 enum isl_dim_type type, unsigned first, unsigned n);
1789 int isl_basic_map_involves_dims(
1790 __isl_keep isl_basic_map *bmap,
1791 enum isl_dim_type type, unsigned first, unsigned n);
1792 int isl_map_involves_dims(__isl_keep isl_map *map,
1793 enum isl_dim_type type, unsigned first, unsigned n);
1795 Similarly, the following functions can be used to check whether
1796 a given dimension is involved in any lower or upper bound.
1798 int isl_set_dim_has_any_lower_bound(__isl_keep isl_set *set,
1799 enum isl_dim_type type, unsigned pos);
1800 int isl_set_dim_has_any_upper_bound(__isl_keep isl_set *set,
1801 enum isl_dim_type type, unsigned pos);
1803 Note that these functions return true even if there is a bound on
1804 the dimension on only some of the basic sets of C<set>.
1805 To check if they have a bound for all of the basic sets in C<set>,
1806 use the following functions instead.
1808 int isl_set_dim_has_lower_bound(__isl_keep isl_set *set,
1809 enum isl_dim_type type, unsigned pos);
1810 int isl_set_dim_has_upper_bound(__isl_keep isl_set *set,
1811 enum isl_dim_type type, unsigned pos);
1813 The identifiers or names of the domain and range spaces of a set
1814 or relation can be read off or set using the following functions.
1816 __isl_give isl_basic_set *isl_basic_set_set_tuple_id(
1817 __isl_take isl_basic_set *bset,
1818 __isl_take isl_id *id);
1819 __isl_give isl_set *isl_set_set_tuple_id(
1820 __isl_take isl_set *set, __isl_take isl_id *id);
1821 __isl_give isl_set *isl_set_reset_tuple_id(
1822 __isl_take isl_set *set);
1823 int isl_set_has_tuple_id(__isl_keep isl_set *set);
1824 __isl_give isl_id *isl_set_get_tuple_id(
1825 __isl_keep isl_set *set);
1826 __isl_give isl_basic_map *isl_basic_map_set_tuple_id(
1827 __isl_take isl_basic_map *bmap,
1828 enum isl_dim_type type, __isl_take isl_id *id);
1829 __isl_give isl_map *isl_map_set_tuple_id(
1830 __isl_take isl_map *map, enum isl_dim_type type,
1831 __isl_take isl_id *id);
1832 __isl_give isl_map *isl_map_reset_tuple_id(
1833 __isl_take isl_map *map, enum isl_dim_type type);
1834 int isl_map_has_tuple_id(__isl_keep isl_map *map,
1835 enum isl_dim_type type);
1836 __isl_give isl_id *isl_map_get_tuple_id(
1837 __isl_keep isl_map *map, enum isl_dim_type type);
1839 const char *isl_basic_set_get_tuple_name(
1840 __isl_keep isl_basic_set *bset);
1841 __isl_give isl_basic_set *isl_basic_set_set_tuple_name(
1842 __isl_take isl_basic_set *set, const char *s);
1843 int isl_set_has_tuple_name(__isl_keep isl_set *set);
1844 const char *isl_set_get_tuple_name(
1845 __isl_keep isl_set *set);
1846 const char *isl_basic_map_get_tuple_name(
1847 __isl_keep isl_basic_map *bmap,
1848 enum isl_dim_type type);
1849 __isl_give isl_basic_map *isl_basic_map_set_tuple_name(
1850 __isl_take isl_basic_map *bmap,
1851 enum isl_dim_type type, const char *s);
1852 int isl_map_has_tuple_name(__isl_keep isl_map *map,
1853 enum isl_dim_type type);
1854 const char *isl_map_get_tuple_name(
1855 __isl_keep isl_map *map,
1856 enum isl_dim_type type);
1858 As with C<isl_space_get_tuple_name>, the value returned points to
1859 an internal data structure.
1860 The identifiers, positions or names of individual dimensions can be
1861 read off using the following functions.
1863 __isl_give isl_id *isl_basic_set_get_dim_id(
1864 __isl_keep isl_basic_set *bset,
1865 enum isl_dim_type type, unsigned pos);
1866 __isl_give isl_set *isl_set_set_dim_id(
1867 __isl_take isl_set *set, enum isl_dim_type type,
1868 unsigned pos, __isl_take isl_id *id);
1869 int isl_set_has_dim_id(__isl_keep isl_set *set,
1870 enum isl_dim_type type, unsigned pos);
1871 __isl_give isl_id *isl_set_get_dim_id(
1872 __isl_keep isl_set *set, enum isl_dim_type type,
1874 int isl_basic_map_has_dim_id(
1875 __isl_keep isl_basic_map *bmap,
1876 enum isl_dim_type type, unsigned pos);
1877 __isl_give isl_map *isl_map_set_dim_id(
1878 __isl_take isl_map *map, enum isl_dim_type type,
1879 unsigned pos, __isl_take isl_id *id);
1880 int isl_map_has_dim_id(__isl_keep isl_map *map,
1881 enum isl_dim_type type, unsigned pos);
1882 __isl_give isl_id *isl_map_get_dim_id(
1883 __isl_keep isl_map *map, enum isl_dim_type type,
1886 int isl_set_find_dim_by_id(__isl_keep isl_set *set,
1887 enum isl_dim_type type, __isl_keep isl_id *id);
1888 int isl_map_find_dim_by_id(__isl_keep isl_map *map,
1889 enum isl_dim_type type, __isl_keep isl_id *id);
1890 int isl_set_find_dim_by_name(__isl_keep isl_set *set,
1891 enum isl_dim_type type, const char *name);
1892 int isl_map_find_dim_by_name(__isl_keep isl_map *map,
1893 enum isl_dim_type type, const char *name);
1895 const char *isl_constraint_get_dim_name(
1896 __isl_keep isl_constraint *constraint,
1897 enum isl_dim_type type, unsigned pos);
1898 const char *isl_basic_set_get_dim_name(
1899 __isl_keep isl_basic_set *bset,
1900 enum isl_dim_type type, unsigned pos);
1901 int isl_set_has_dim_name(__isl_keep isl_set *set,
1902 enum isl_dim_type type, unsigned pos);
1903 const char *isl_set_get_dim_name(
1904 __isl_keep isl_set *set,
1905 enum isl_dim_type type, unsigned pos);
1906 const char *isl_basic_map_get_dim_name(
1907 __isl_keep isl_basic_map *bmap,
1908 enum isl_dim_type type, unsigned pos);
1909 int isl_map_has_dim_name(__isl_keep isl_map *map,
1910 enum isl_dim_type type, unsigned pos);
1911 const char *isl_map_get_dim_name(
1912 __isl_keep isl_map *map,
1913 enum isl_dim_type type, unsigned pos);
1915 These functions are mostly useful to obtain the identifiers, positions
1916 or names of the parameters. Identifiers of individual dimensions are
1917 essentially only useful for printing. They are ignored by all other
1918 operations and may not be preserved across those operations.
1920 The user pointers on all parameters and tuples can be reset
1921 using the following functions.
1923 __isl_give isl_set *isl_set_reset_user(
1924 __isl_take isl_set *set);
1925 __isl_give isl_map *isl_map_reset_user(
1926 __isl_take isl_map *map);
1930 =head3 Unary Properties
1936 The following functions test whether the given set or relation
1937 contains any integer points. The ``plain'' variants do not perform
1938 any computations, but simply check if the given set or relation
1939 is already known to be empty.
1941 int isl_basic_set_plain_is_empty(__isl_keep isl_basic_set *bset);
1942 int isl_basic_set_is_empty(__isl_keep isl_basic_set *bset);
1943 int isl_set_plain_is_empty(__isl_keep isl_set *set);
1944 int isl_set_is_empty(__isl_keep isl_set *set);
1945 int isl_union_set_is_empty(__isl_keep isl_union_set *uset);
1946 int isl_basic_map_plain_is_empty(__isl_keep isl_basic_map *bmap);
1947 int isl_basic_map_is_empty(__isl_keep isl_basic_map *bmap);
1948 int isl_map_plain_is_empty(__isl_keep isl_map *map);
1949 int isl_map_is_empty(__isl_keep isl_map *map);
1950 int isl_union_map_is_empty(__isl_keep isl_union_map *umap);
1952 =item * Universality
1954 int isl_basic_set_is_universe(__isl_keep isl_basic_set *bset);
1955 int isl_basic_map_is_universe(__isl_keep isl_basic_map *bmap);
1956 int isl_set_plain_is_universe(__isl_keep isl_set *set);
1958 =item * Single-valuedness
1960 int isl_basic_map_is_single_valued(
1961 __isl_keep isl_basic_map *bmap);
1962 int isl_map_plain_is_single_valued(
1963 __isl_keep isl_map *map);
1964 int isl_map_is_single_valued(__isl_keep isl_map *map);
1965 int isl_union_map_is_single_valued(__isl_keep isl_union_map *umap);
1969 int isl_map_plain_is_injective(__isl_keep isl_map *map);
1970 int isl_map_is_injective(__isl_keep isl_map *map);
1971 int isl_union_map_plain_is_injective(
1972 __isl_keep isl_union_map *umap);
1973 int isl_union_map_is_injective(
1974 __isl_keep isl_union_map *umap);
1978 int isl_map_is_bijective(__isl_keep isl_map *map);
1979 int isl_union_map_is_bijective(__isl_keep isl_union_map *umap);
1983 __isl_give isl_val *
1984 isl_basic_map_plain_get_val_if_fixed(
1985 __isl_keep isl_basic_map *bmap,
1986 enum isl_dim_type type, unsigned pos);
1987 __isl_give isl_val *isl_set_plain_get_val_if_fixed(
1988 __isl_keep isl_set *set,
1989 enum isl_dim_type type, unsigned pos);
1990 __isl_give isl_val *isl_map_plain_get_val_if_fixed(
1991 __isl_keep isl_map *map,
1992 enum isl_dim_type type, unsigned pos);
1994 If the set or relation obviously lies on a hyperplane where the given dimension
1995 has a fixed value, then return that value.
1996 Otherwise return NaN.
2000 int isl_set_dim_residue_class_val(
2001 __isl_keep isl_set *set,
2002 int pos, __isl_give isl_val **modulo,
2003 __isl_give isl_val **residue);
2005 Check if the values of the given set dimension are equal to a fixed
2006 value modulo some integer value. If so, assign the modulo to C<*modulo>
2007 and the fixed value to C<*residue>. If the given dimension attains only
2008 a single value, then assign C<0> to C<*modulo> and the fixed value to
2010 If the dimension does not attain only a single value and if no modulo
2011 can be found then assign C<1> to C<*modulo> and C<1> to C<*residue>.
2015 To check whether a set is a parameter domain, use this function:
2017 int isl_set_is_params(__isl_keep isl_set *set);
2018 int isl_union_set_is_params(
2019 __isl_keep isl_union_set *uset);
2023 The following functions check whether the space of the given
2024 (basic) set or relation range is a wrapped relation.
2026 int isl_basic_set_is_wrapping(
2027 __isl_keep isl_basic_set *bset);
2028 int isl_set_is_wrapping(__isl_keep isl_set *set);
2029 int isl_map_range_is_wrapping(
2030 __isl_keep isl_map *map);
2032 =item * Internal Product
2034 int isl_basic_map_can_zip(
2035 __isl_keep isl_basic_map *bmap);
2036 int isl_map_can_zip(__isl_keep isl_map *map);
2038 Check whether the product of domain and range of the given relation
2040 i.e., whether both domain and range are nested relations.
2044 int isl_basic_map_can_curry(
2045 __isl_keep isl_basic_map *bmap);
2046 int isl_map_can_curry(__isl_keep isl_map *map);
2048 Check whether the domain of the (basic) relation is a wrapped relation.
2050 int isl_basic_map_can_uncurry(
2051 __isl_keep isl_basic_map *bmap);
2052 int isl_map_can_uncurry(__isl_keep isl_map *map);
2054 Check whether the range of the (basic) relation is a wrapped relation.
2058 =head3 Binary Properties
2064 int isl_basic_set_plain_is_equal(
2065 __isl_keep isl_basic_set *bset1,
2066 __isl_keep isl_basic_set *bset2);
2067 int isl_set_plain_is_equal(__isl_keep isl_set *set1,
2068 __isl_keep isl_set *set2);
2069 int isl_set_is_equal(__isl_keep isl_set *set1,
2070 __isl_keep isl_set *set2);
2071 int isl_union_set_is_equal(
2072 __isl_keep isl_union_set *uset1,
2073 __isl_keep isl_union_set *uset2);
2074 int isl_basic_map_is_equal(
2075 __isl_keep isl_basic_map *bmap1,
2076 __isl_keep isl_basic_map *bmap2);
2077 int isl_map_is_equal(__isl_keep isl_map *map1,
2078 __isl_keep isl_map *map2);
2079 int isl_map_plain_is_equal(__isl_keep isl_map *map1,
2080 __isl_keep isl_map *map2);
2081 int isl_union_map_is_equal(
2082 __isl_keep isl_union_map *umap1,
2083 __isl_keep isl_union_map *umap2);
2085 =item * Disjointness
2087 int isl_basic_set_is_disjoint(
2088 __isl_keep isl_basic_set *bset1,
2089 __isl_keep isl_basic_set *bset2);
2090 int isl_set_plain_is_disjoint(__isl_keep isl_set *set1,
2091 __isl_keep isl_set *set2);
2092 int isl_set_is_disjoint(__isl_keep isl_set *set1,
2093 __isl_keep isl_set *set2);
2094 int isl_basic_map_is_disjoint(
2095 __isl_keep isl_basic_map *bmap1,
2096 __isl_keep isl_basic_map *bmap2);
2097 int isl_map_is_disjoint(__isl_keep isl_map *map1,
2098 __isl_keep isl_map *map2);
2102 int isl_basic_set_is_subset(
2103 __isl_keep isl_basic_set *bset1,
2104 __isl_keep isl_basic_set *bset2);
2105 int isl_set_is_subset(__isl_keep isl_set *set1,
2106 __isl_keep isl_set *set2);
2107 int isl_set_is_strict_subset(
2108 __isl_keep isl_set *set1,
2109 __isl_keep isl_set *set2);
2110 int isl_union_set_is_subset(
2111 __isl_keep isl_union_set *uset1,
2112 __isl_keep isl_union_set *uset2);
2113 int isl_union_set_is_strict_subset(
2114 __isl_keep isl_union_set *uset1,
2115 __isl_keep isl_union_set *uset2);
2116 int isl_basic_map_is_subset(
2117 __isl_keep isl_basic_map *bmap1,
2118 __isl_keep isl_basic_map *bmap2);
2119 int isl_basic_map_is_strict_subset(
2120 __isl_keep isl_basic_map *bmap1,
2121 __isl_keep isl_basic_map *bmap2);
2122 int isl_map_is_subset(
2123 __isl_keep isl_map *map1,
2124 __isl_keep isl_map *map2);
2125 int isl_map_is_strict_subset(
2126 __isl_keep isl_map *map1,
2127 __isl_keep isl_map *map2);
2128 int isl_union_map_is_subset(
2129 __isl_keep isl_union_map *umap1,
2130 __isl_keep isl_union_map *umap2);
2131 int isl_union_map_is_strict_subset(
2132 __isl_keep isl_union_map *umap1,
2133 __isl_keep isl_union_map *umap2);
2135 Check whether the first argument is a (strict) subset of the
2140 int isl_set_plain_cmp(__isl_keep isl_set *set1,
2141 __isl_keep isl_set *set2);
2143 This function is useful for sorting C<isl_set>s.
2144 The order depends on the internal representation of the inputs.
2145 The order is fixed over different calls to the function (assuming
2146 the internal representation of the inputs has not changed), but may
2147 change over different versions of C<isl>.
2151 =head2 Unary Operations
2157 __isl_give isl_set *isl_set_complement(
2158 __isl_take isl_set *set);
2159 __isl_give isl_map *isl_map_complement(
2160 __isl_take isl_map *map);
2164 __isl_give isl_basic_map *isl_basic_map_reverse(
2165 __isl_take isl_basic_map *bmap);
2166 __isl_give isl_map *isl_map_reverse(
2167 __isl_take isl_map *map);
2168 __isl_give isl_union_map *isl_union_map_reverse(
2169 __isl_take isl_union_map *umap);
2173 __isl_give isl_basic_set *isl_basic_set_project_out(
2174 __isl_take isl_basic_set *bset,
2175 enum isl_dim_type type, unsigned first, unsigned n);
2176 __isl_give isl_basic_map *isl_basic_map_project_out(
2177 __isl_take isl_basic_map *bmap,
2178 enum isl_dim_type type, unsigned first, unsigned n);
2179 __isl_give isl_set *isl_set_project_out(__isl_take isl_set *set,
2180 enum isl_dim_type type, unsigned first, unsigned n);
2181 __isl_give isl_map *isl_map_project_out(__isl_take isl_map *map,
2182 enum isl_dim_type type, unsigned first, unsigned n);
2183 __isl_give isl_basic_set *isl_basic_set_params(
2184 __isl_take isl_basic_set *bset);
2185 __isl_give isl_basic_set *isl_basic_map_domain(
2186 __isl_take isl_basic_map *bmap);
2187 __isl_give isl_basic_set *isl_basic_map_range(
2188 __isl_take isl_basic_map *bmap);
2189 __isl_give isl_set *isl_set_params(__isl_take isl_set *set);
2190 __isl_give isl_set *isl_map_params(__isl_take isl_map *map);
2191 __isl_give isl_set *isl_map_domain(
2192 __isl_take isl_map *bmap);
2193 __isl_give isl_set *isl_map_range(
2194 __isl_take isl_map *map);
2195 __isl_give isl_set *isl_union_set_params(
2196 __isl_take isl_union_set *uset);
2197 __isl_give isl_set *isl_union_map_params(
2198 __isl_take isl_union_map *umap);
2199 __isl_give isl_union_set *isl_union_map_domain(
2200 __isl_take isl_union_map *umap);
2201 __isl_give isl_union_set *isl_union_map_range(
2202 __isl_take isl_union_map *umap);
2204 __isl_give isl_basic_map *isl_basic_map_domain_map(
2205 __isl_take isl_basic_map *bmap);
2206 __isl_give isl_basic_map *isl_basic_map_range_map(
2207 __isl_take isl_basic_map *bmap);
2208 __isl_give isl_map *isl_map_domain_map(__isl_take isl_map *map);
2209 __isl_give isl_map *isl_map_range_map(__isl_take isl_map *map);
2210 __isl_give isl_union_map *isl_union_map_domain_map(
2211 __isl_take isl_union_map *umap);
2212 __isl_give isl_union_map *isl_union_map_range_map(
2213 __isl_take isl_union_map *umap);
2215 The functions above construct a (basic, regular or union) relation
2216 that maps (a wrapped version of) the input relation to its domain or range.
2220 __isl_give isl_basic_set *isl_basic_set_eliminate(
2221 __isl_take isl_basic_set *bset,
2222 enum isl_dim_type type,
2223 unsigned first, unsigned n);
2224 __isl_give isl_set *isl_set_eliminate(
2225 __isl_take isl_set *set, enum isl_dim_type type,
2226 unsigned first, unsigned n);
2227 __isl_give isl_basic_map *isl_basic_map_eliminate(
2228 __isl_take isl_basic_map *bmap,
2229 enum isl_dim_type type,
2230 unsigned first, unsigned n);
2231 __isl_give isl_map *isl_map_eliminate(
2232 __isl_take isl_map *map, enum isl_dim_type type,
2233 unsigned first, unsigned n);
2235 Eliminate the coefficients for the given dimensions from the constraints,
2236 without removing the dimensions.
2240 __isl_give isl_basic_set *isl_basic_set_fix_si(
2241 __isl_take isl_basic_set *bset,
2242 enum isl_dim_type type, unsigned pos, int value);
2243 __isl_give isl_basic_set *isl_basic_set_fix_val(
2244 __isl_take isl_basic_set *bset,
2245 enum isl_dim_type type, unsigned pos,
2246 __isl_take isl_val *v);
2247 __isl_give isl_set *isl_set_fix_si(__isl_take isl_set *set,
2248 enum isl_dim_type type, unsigned pos, int value);
2249 __isl_give isl_set *isl_set_fix_val(
2250 __isl_take isl_set *set,
2251 enum isl_dim_type type, unsigned pos,
2252 __isl_take isl_val *v);
2253 __isl_give isl_basic_map *isl_basic_map_fix_si(
2254 __isl_take isl_basic_map *bmap,
2255 enum isl_dim_type type, unsigned pos, int value);
2256 __isl_give isl_basic_map *isl_basic_map_fix_val(
2257 __isl_take isl_basic_map *bmap,
2258 enum isl_dim_type type, unsigned pos,
2259 __isl_take isl_val *v);
2260 __isl_give isl_map *isl_map_fix_si(__isl_take isl_map *map,
2261 enum isl_dim_type type, unsigned pos, int value);
2262 __isl_give isl_map *isl_map_fix_val(
2263 __isl_take isl_map *map,
2264 enum isl_dim_type type, unsigned pos,
2265 __isl_take isl_val *v);
2267 Intersect the set or relation with the hyperplane where the given
2268 dimension has the fixed given value.
2270 __isl_give isl_basic_map *isl_basic_map_lower_bound_si(
2271 __isl_take isl_basic_map *bmap,
2272 enum isl_dim_type type, unsigned pos, int value);
2273 __isl_give isl_basic_map *isl_basic_map_upper_bound_si(
2274 __isl_take isl_basic_map *bmap,
2275 enum isl_dim_type type, unsigned pos, int value);
2276 __isl_give isl_set *isl_set_lower_bound_si(
2277 __isl_take isl_set *set,
2278 enum isl_dim_type type, unsigned pos, int value);
2279 __isl_give isl_set *isl_set_lower_bound_val(
2280 __isl_take isl_set *set,
2281 enum isl_dim_type type, unsigned pos,
2282 __isl_take isl_val *value);
2283 __isl_give isl_map *isl_map_lower_bound_si(
2284 __isl_take isl_map *map,
2285 enum isl_dim_type type, unsigned pos, int value);
2286 __isl_give isl_set *isl_set_upper_bound_si(
2287 __isl_take isl_set *set,
2288 enum isl_dim_type type, unsigned pos, int value);
2289 __isl_give isl_set *isl_set_upper_bound_val(
2290 __isl_take isl_set *set,
2291 enum isl_dim_type type, unsigned pos,
2292 __isl_take isl_val *value);
2293 __isl_give isl_map *isl_map_upper_bound_si(
2294 __isl_take isl_map *map,
2295 enum isl_dim_type type, unsigned pos, int value);
2297 Intersect the set or relation with the half-space where the given
2298 dimension has a value bounded by the fixed given integer value.
2300 __isl_give isl_set *isl_set_equate(__isl_take isl_set *set,
2301 enum isl_dim_type type1, int pos1,
2302 enum isl_dim_type type2, int pos2);
2303 __isl_give isl_basic_map *isl_basic_map_equate(
2304 __isl_take isl_basic_map *bmap,
2305 enum isl_dim_type type1, int pos1,
2306 enum isl_dim_type type2, int pos2);
2307 __isl_give isl_map *isl_map_equate(__isl_take isl_map *map,
2308 enum isl_dim_type type1, int pos1,
2309 enum isl_dim_type type2, int pos2);
2311 Intersect the set or relation with the hyperplane where the given
2312 dimensions are equal to each other.
2314 __isl_give isl_map *isl_map_oppose(__isl_take isl_map *map,
2315 enum isl_dim_type type1, int pos1,
2316 enum isl_dim_type type2, int pos2);
2318 Intersect the relation with the hyperplane where the given
2319 dimensions have opposite values.
2321 __isl_give isl_basic_map *isl_basic_map_order_ge(
2322 __isl_take isl_basic_map *bmap,
2323 enum isl_dim_type type1, int pos1,
2324 enum isl_dim_type type2, int pos2);
2325 __isl_give isl_map *isl_map_order_lt(__isl_take isl_map *map,
2326 enum isl_dim_type type1, int pos1,
2327 enum isl_dim_type type2, int pos2);
2328 __isl_give isl_basic_map *isl_basic_map_order_gt(
2329 __isl_take isl_basic_map *bmap,
2330 enum isl_dim_type type1, int pos1,
2331 enum isl_dim_type type2, int pos2);
2332 __isl_give isl_map *isl_map_order_gt(__isl_take isl_map *map,
2333 enum isl_dim_type type1, int pos1,
2334 enum isl_dim_type type2, int pos2);
2336 Intersect the relation with the half-space where the given
2337 dimensions satisfy the given ordering.
2341 __isl_give isl_map *isl_set_identity(
2342 __isl_take isl_set *set);
2343 __isl_give isl_union_map *isl_union_set_identity(
2344 __isl_take isl_union_set *uset);
2346 Construct an identity relation on the given (union) set.
2350 __isl_give isl_basic_set *isl_basic_map_deltas(
2351 __isl_take isl_basic_map *bmap);
2352 __isl_give isl_set *isl_map_deltas(__isl_take isl_map *map);
2353 __isl_give isl_union_set *isl_union_map_deltas(
2354 __isl_take isl_union_map *umap);
2356 These functions return a (basic) set containing the differences
2357 between image elements and corresponding domain elements in the input.
2359 __isl_give isl_basic_map *isl_basic_map_deltas_map(
2360 __isl_take isl_basic_map *bmap);
2361 __isl_give isl_map *isl_map_deltas_map(
2362 __isl_take isl_map *map);
2363 __isl_give isl_union_map *isl_union_map_deltas_map(
2364 __isl_take isl_union_map *umap);
2366 The functions above construct a (basic, regular or union) relation
2367 that maps (a wrapped version of) the input relation to its delta set.
2371 Simplify the representation of a set or relation by trying
2372 to combine pairs of basic sets or relations into a single
2373 basic set or relation.
2375 __isl_give isl_set *isl_set_coalesce(__isl_take isl_set *set);
2376 __isl_give isl_map *isl_map_coalesce(__isl_take isl_map *map);
2377 __isl_give isl_union_set *isl_union_set_coalesce(
2378 __isl_take isl_union_set *uset);
2379 __isl_give isl_union_map *isl_union_map_coalesce(
2380 __isl_take isl_union_map *umap);
2382 One of the methods for combining pairs of basic sets or relations
2383 can result in coefficients that are much larger than those that appear
2384 in the constraints of the input. By default, the coefficients are
2385 not allowed to grow larger, but this can be changed by unsetting
2386 the following option.
2388 int isl_options_set_coalesce_bounded_wrapping(
2389 isl_ctx *ctx, int val);
2390 int isl_options_get_coalesce_bounded_wrapping(
2393 =item * Detecting equalities
2395 __isl_give isl_basic_set *isl_basic_set_detect_equalities(
2396 __isl_take isl_basic_set *bset);
2397 __isl_give isl_basic_map *isl_basic_map_detect_equalities(
2398 __isl_take isl_basic_map *bmap);
2399 __isl_give isl_set *isl_set_detect_equalities(
2400 __isl_take isl_set *set);
2401 __isl_give isl_map *isl_map_detect_equalities(
2402 __isl_take isl_map *map);
2403 __isl_give isl_union_set *isl_union_set_detect_equalities(
2404 __isl_take isl_union_set *uset);
2405 __isl_give isl_union_map *isl_union_map_detect_equalities(
2406 __isl_take isl_union_map *umap);
2408 Simplify the representation of a set or relation by detecting implicit
2411 =item * Removing redundant constraints
2413 __isl_give isl_basic_set *isl_basic_set_remove_redundancies(
2414 __isl_take isl_basic_set *bset);
2415 __isl_give isl_set *isl_set_remove_redundancies(
2416 __isl_take isl_set *set);
2417 __isl_give isl_basic_map *isl_basic_map_remove_redundancies(
2418 __isl_take isl_basic_map *bmap);
2419 __isl_give isl_map *isl_map_remove_redundancies(
2420 __isl_take isl_map *map);
2424 __isl_give isl_basic_set *isl_set_convex_hull(
2425 __isl_take isl_set *set);
2426 __isl_give isl_basic_map *isl_map_convex_hull(
2427 __isl_take isl_map *map);
2429 If the input set or relation has any existentially quantified
2430 variables, then the result of these operations is currently undefined.
2434 __isl_give isl_basic_set *
2435 isl_set_unshifted_simple_hull(
2436 __isl_take isl_set *set);
2437 __isl_give isl_basic_map *
2438 isl_map_unshifted_simple_hull(
2439 __isl_take isl_map *map);
2440 __isl_give isl_basic_set *isl_set_simple_hull(
2441 __isl_take isl_set *set);
2442 __isl_give isl_basic_map *isl_map_simple_hull(
2443 __isl_take isl_map *map);
2444 __isl_give isl_union_map *isl_union_map_simple_hull(
2445 __isl_take isl_union_map *umap);
2447 These functions compute a single basic set or relation
2448 that contains the whole input set or relation.
2449 In particular, the output is described by translates
2450 of the constraints describing the basic sets or relations in the input.
2451 In case of C<isl_set_unshifted_simple_hull>, only the original
2452 constraints are used, without any translation.
2456 (See \autoref{s:simple hull}.)
2462 __isl_give isl_basic_set *isl_basic_set_affine_hull(
2463 __isl_take isl_basic_set *bset);
2464 __isl_give isl_basic_set *isl_set_affine_hull(
2465 __isl_take isl_set *set);
2466 __isl_give isl_union_set *isl_union_set_affine_hull(
2467 __isl_take isl_union_set *uset);
2468 __isl_give isl_basic_map *isl_basic_map_affine_hull(
2469 __isl_take isl_basic_map *bmap);
2470 __isl_give isl_basic_map *isl_map_affine_hull(
2471 __isl_take isl_map *map);
2472 __isl_give isl_union_map *isl_union_map_affine_hull(
2473 __isl_take isl_union_map *umap);
2475 In case of union sets and relations, the affine hull is computed
2478 =item * Polyhedral hull
2480 __isl_give isl_basic_set *isl_set_polyhedral_hull(
2481 __isl_take isl_set *set);
2482 __isl_give isl_basic_map *isl_map_polyhedral_hull(
2483 __isl_take isl_map *map);
2484 __isl_give isl_union_set *isl_union_set_polyhedral_hull(
2485 __isl_take isl_union_set *uset);
2486 __isl_give isl_union_map *isl_union_map_polyhedral_hull(
2487 __isl_take isl_union_map *umap);
2489 These functions compute a single basic set or relation
2490 not involving any existentially quantified variables
2491 that contains the whole input set or relation.
2492 In case of union sets and relations, the polyhedral hull is computed
2495 =item * Other approximations
2497 __isl_give isl_basic_set *
2498 isl_basic_set_drop_constraints_involving_dims(
2499 __isl_take isl_basic_set *bset,
2500 enum isl_dim_type type,
2501 unsigned first, unsigned n);
2502 __isl_give isl_basic_map *
2503 isl_basic_map_drop_constraints_involving_dims(
2504 __isl_take isl_basic_map *bmap,
2505 enum isl_dim_type type,
2506 unsigned first, unsigned n);
2507 __isl_give isl_basic_set *
2508 isl_basic_set_drop_constraints_not_involving_dims(
2509 __isl_take isl_basic_set *bset,
2510 enum isl_dim_type type,
2511 unsigned first, unsigned n);
2512 __isl_give isl_set *
2513 isl_set_drop_constraints_involving_dims(
2514 __isl_take isl_set *set,
2515 enum isl_dim_type type,
2516 unsigned first, unsigned n);
2517 __isl_give isl_map *
2518 isl_map_drop_constraints_involving_dims(
2519 __isl_take isl_map *map,
2520 enum isl_dim_type type,
2521 unsigned first, unsigned n);
2523 These functions drop any constraints (not) involving the specified dimensions.
2524 Note that the result depends on the representation of the input.
2528 __isl_give isl_basic_set *isl_basic_set_sample(
2529 __isl_take isl_basic_set *bset);
2530 __isl_give isl_basic_set *isl_set_sample(
2531 __isl_take isl_set *set);
2532 __isl_give isl_basic_map *isl_basic_map_sample(
2533 __isl_take isl_basic_map *bmap);
2534 __isl_give isl_basic_map *isl_map_sample(
2535 __isl_take isl_map *map);
2537 If the input (basic) set or relation is non-empty, then return
2538 a singleton subset of the input. Otherwise, return an empty set.
2540 =item * Optimization
2542 #include <isl/ilp.h>
2543 __isl_give isl_val *isl_basic_set_max_val(
2544 __isl_keep isl_basic_set *bset,
2545 __isl_keep isl_aff *obj);
2546 __isl_give isl_val *isl_set_min_val(
2547 __isl_keep isl_set *set,
2548 __isl_keep isl_aff *obj);
2549 __isl_give isl_val *isl_set_max_val(
2550 __isl_keep isl_set *set,
2551 __isl_keep isl_aff *obj);
2553 Compute the minimum or maximum of the integer affine expression C<obj>
2554 over the points in C<set>, returning the result in C<opt>.
2555 The result is C<NULL> in case of an error, the optimal value in case
2556 there is one, negative infinity or infinity if the problem is unbounded and
2557 NaN if the problem is empty.
2559 =item * Parametric optimization
2561 __isl_give isl_pw_aff *isl_set_dim_min(
2562 __isl_take isl_set *set, int pos);
2563 __isl_give isl_pw_aff *isl_set_dim_max(
2564 __isl_take isl_set *set, int pos);
2565 __isl_give isl_pw_aff *isl_map_dim_max(
2566 __isl_take isl_map *map, int pos);
2568 Compute the minimum or maximum of the given set or output dimension
2569 as a function of the parameters (and input dimensions), but independently
2570 of the other set or output dimensions.
2571 For lexicographic optimization, see L<"Lexicographic Optimization">.
2575 The following functions compute either the set of (rational) coefficient
2576 values of valid constraints for the given set or the set of (rational)
2577 values satisfying the constraints with coefficients from the given set.
2578 Internally, these two sets of functions perform essentially the
2579 same operations, except that the set of coefficients is assumed to
2580 be a cone, while the set of values may be any polyhedron.
2581 The current implementation is based on the Farkas lemma and
2582 Fourier-Motzkin elimination, but this may change or be made optional
2583 in future. In particular, future implementations may use different
2584 dualization algorithms or skip the elimination step.
2586 __isl_give isl_basic_set *isl_basic_set_coefficients(
2587 __isl_take isl_basic_set *bset);
2588 __isl_give isl_basic_set *isl_set_coefficients(
2589 __isl_take isl_set *set);
2590 __isl_give isl_union_set *isl_union_set_coefficients(
2591 __isl_take isl_union_set *bset);
2592 __isl_give isl_basic_set *isl_basic_set_solutions(
2593 __isl_take isl_basic_set *bset);
2594 __isl_give isl_basic_set *isl_set_solutions(
2595 __isl_take isl_set *set);
2596 __isl_give isl_union_set *isl_union_set_solutions(
2597 __isl_take isl_union_set *bset);
2601 __isl_give isl_map *isl_map_fixed_power_val(
2602 __isl_take isl_map *map,
2603 __isl_take isl_val *exp);
2604 __isl_give isl_union_map *
2605 isl_union_map_fixed_power_val(
2606 __isl_take isl_union_map *umap,
2607 __isl_take isl_val *exp);
2609 Compute the given power of C<map>, where C<exp> is assumed to be non-zero.
2610 If the exponent C<exp> is negative, then the -C<exp> th power of the inverse
2611 of C<map> is computed.
2613 __isl_give isl_map *isl_map_power(__isl_take isl_map *map,
2615 __isl_give isl_union_map *isl_union_map_power(
2616 __isl_take isl_union_map *umap, int *exact);
2618 Compute a parametric representation for all positive powers I<k> of C<map>.
2619 The result maps I<k> to a nested relation corresponding to the
2620 I<k>th power of C<map>.
2621 The result may be an overapproximation. If the result is known to be exact,
2622 then C<*exact> is set to C<1>.
2624 =item * Transitive closure
2626 __isl_give isl_map *isl_map_transitive_closure(
2627 __isl_take isl_map *map, int *exact);
2628 __isl_give isl_union_map *isl_union_map_transitive_closure(
2629 __isl_take isl_union_map *umap, int *exact);
2631 Compute the transitive closure of C<map>.
2632 The result may be an overapproximation. If the result is known to be exact,
2633 then C<*exact> is set to C<1>.
2635 =item * Reaching path lengths
2637 __isl_give isl_map *isl_map_reaching_path_lengths(
2638 __isl_take isl_map *map, int *exact);
2640 Compute a relation that maps each element in the range of C<map>
2641 to the lengths of all paths composed of edges in C<map> that
2642 end up in the given element.
2643 The result may be an overapproximation. If the result is known to be exact,
2644 then C<*exact> is set to C<1>.
2645 To compute the I<maximal> path length, the resulting relation
2646 should be postprocessed by C<isl_map_lexmax>.
2647 In particular, if the input relation is a dependence relation
2648 (mapping sources to sinks), then the maximal path length corresponds
2649 to the free schedule.
2650 Note, however, that C<isl_map_lexmax> expects the maximum to be
2651 finite, so if the path lengths are unbounded (possibly due to
2652 the overapproximation), then you will get an error message.
2656 __isl_give isl_basic_set *isl_basic_map_wrap(
2657 __isl_take isl_basic_map *bmap);
2658 __isl_give isl_set *isl_map_wrap(
2659 __isl_take isl_map *map);
2660 __isl_give isl_union_set *isl_union_map_wrap(
2661 __isl_take isl_union_map *umap);
2662 __isl_give isl_basic_map *isl_basic_set_unwrap(
2663 __isl_take isl_basic_set *bset);
2664 __isl_give isl_map *isl_set_unwrap(
2665 __isl_take isl_set *set);
2666 __isl_give isl_union_map *isl_union_set_unwrap(
2667 __isl_take isl_union_set *uset);
2671 Remove any internal structure of domain (and range) of the given
2672 set or relation. If there is any such internal structure in the input,
2673 then the name of the space is also removed.
2675 __isl_give isl_basic_set *isl_basic_set_flatten(
2676 __isl_take isl_basic_set *bset);
2677 __isl_give isl_set *isl_set_flatten(
2678 __isl_take isl_set *set);
2679 __isl_give isl_basic_map *isl_basic_map_flatten_domain(
2680 __isl_take isl_basic_map *bmap);
2681 __isl_give isl_basic_map *isl_basic_map_flatten_range(
2682 __isl_take isl_basic_map *bmap);
2683 __isl_give isl_map *isl_map_flatten_range(
2684 __isl_take isl_map *map);
2685 __isl_give isl_map *isl_map_flatten_domain(
2686 __isl_take isl_map *map);
2687 __isl_give isl_basic_map *isl_basic_map_flatten(
2688 __isl_take isl_basic_map *bmap);
2689 __isl_give isl_map *isl_map_flatten(
2690 __isl_take isl_map *map);
2692 __isl_give isl_map *isl_set_flatten_map(
2693 __isl_take isl_set *set);
2695 The function above constructs a relation
2696 that maps the input set to a flattened version of the set.
2700 Lift the input set to a space with extra dimensions corresponding
2701 to the existentially quantified variables in the input.
2702 In particular, the result lives in a wrapped map where the domain
2703 is the original space and the range corresponds to the original
2704 existentially quantified variables.
2706 __isl_give isl_basic_set *isl_basic_set_lift(
2707 __isl_take isl_basic_set *bset);
2708 __isl_give isl_set *isl_set_lift(
2709 __isl_take isl_set *set);
2710 __isl_give isl_union_set *isl_union_set_lift(
2711 __isl_take isl_union_set *uset);
2713 Given a local space that contains the existentially quantified
2714 variables of a set, a basic relation that, when applied to
2715 a basic set, has essentially the same effect as C<isl_basic_set_lift>,
2716 can be constructed using the following function.
2718 #include <isl/local_space.h>
2719 __isl_give isl_basic_map *isl_local_space_lifting(
2720 __isl_take isl_local_space *ls);
2722 =item * Internal Product
2724 __isl_give isl_basic_map *isl_basic_map_zip(
2725 __isl_take isl_basic_map *bmap);
2726 __isl_give isl_map *isl_map_zip(
2727 __isl_take isl_map *map);
2728 __isl_give isl_union_map *isl_union_map_zip(
2729 __isl_take isl_union_map *umap);
2731 Given a relation with nested relations for domain and range,
2732 interchange the range of the domain with the domain of the range.
2736 __isl_give isl_basic_map *isl_basic_map_curry(
2737 __isl_take isl_basic_map *bmap);
2738 __isl_give isl_basic_map *isl_basic_map_uncurry(
2739 __isl_take isl_basic_map *bmap);
2740 __isl_give isl_map *isl_map_curry(
2741 __isl_take isl_map *map);
2742 __isl_give isl_map *isl_map_uncurry(
2743 __isl_take isl_map *map);
2744 __isl_give isl_union_map *isl_union_map_curry(
2745 __isl_take isl_union_map *umap);
2746 __isl_give isl_union_map *isl_union_map_uncurry(
2747 __isl_take isl_union_map *umap);
2749 Given a relation with a nested relation for domain,
2750 the C<curry> functions
2751 move the range of the nested relation out of the domain
2752 and use it as the domain of a nested relation in the range,
2753 with the original range as range of this nested relation.
2754 The C<uncurry> functions perform the inverse operation.
2756 =item * Aligning parameters
2758 __isl_give isl_basic_set *isl_basic_set_align_params(
2759 __isl_take isl_basic_set *bset,
2760 __isl_take isl_space *model);
2761 __isl_give isl_set *isl_set_align_params(
2762 __isl_take isl_set *set,
2763 __isl_take isl_space *model);
2764 __isl_give isl_basic_map *isl_basic_map_align_params(
2765 __isl_take isl_basic_map *bmap,
2766 __isl_take isl_space *model);
2767 __isl_give isl_map *isl_map_align_params(
2768 __isl_take isl_map *map,
2769 __isl_take isl_space *model);
2771 Change the order of the parameters of the given set or relation
2772 such that the first parameters match those of C<model>.
2773 This may involve the introduction of extra parameters.
2774 All parameters need to be named.
2776 =item * Dimension manipulation
2778 __isl_give isl_basic_set *isl_basic_set_add_dims(
2779 __isl_take isl_basic_set *bset,
2780 enum isl_dim_type type, unsigned n);
2781 __isl_give isl_set *isl_set_add_dims(
2782 __isl_take isl_set *set,
2783 enum isl_dim_type type, unsigned n);
2784 __isl_give isl_map *isl_map_add_dims(
2785 __isl_take isl_map *map,
2786 enum isl_dim_type type, unsigned n);
2787 __isl_give isl_basic_set *isl_basic_set_insert_dims(
2788 __isl_take isl_basic_set *bset,
2789 enum isl_dim_type type, unsigned pos,
2791 __isl_give isl_basic_map *isl_basic_map_insert_dims(
2792 __isl_take isl_basic_map *bmap,
2793 enum isl_dim_type type, unsigned pos,
2795 __isl_give isl_set *isl_set_insert_dims(
2796 __isl_take isl_set *set,
2797 enum isl_dim_type type, unsigned pos, unsigned n);
2798 __isl_give isl_map *isl_map_insert_dims(
2799 __isl_take isl_map *map,
2800 enum isl_dim_type type, unsigned pos, unsigned n);
2801 __isl_give isl_basic_set *isl_basic_set_move_dims(
2802 __isl_take isl_basic_set *bset,
2803 enum isl_dim_type dst_type, unsigned dst_pos,
2804 enum isl_dim_type src_type, unsigned src_pos,
2806 __isl_give isl_basic_map *isl_basic_map_move_dims(
2807 __isl_take isl_basic_map *bmap,
2808 enum isl_dim_type dst_type, unsigned dst_pos,
2809 enum isl_dim_type src_type, unsigned src_pos,
2811 __isl_give isl_set *isl_set_move_dims(
2812 __isl_take isl_set *set,
2813 enum isl_dim_type dst_type, unsigned dst_pos,
2814 enum isl_dim_type src_type, unsigned src_pos,
2816 __isl_give isl_map *isl_map_move_dims(
2817 __isl_take isl_map *map,
2818 enum isl_dim_type dst_type, unsigned dst_pos,
2819 enum isl_dim_type src_type, unsigned src_pos,
2822 It is usually not advisable to directly change the (input or output)
2823 space of a set or a relation as this removes the name and the internal
2824 structure of the space. However, the above functions can be useful
2825 to add new parameters, assuming
2826 C<isl_set_align_params> and C<isl_map_align_params>
2831 =head2 Binary Operations
2833 The two arguments of a binary operation not only need to live
2834 in the same C<isl_ctx>, they currently also need to have
2835 the same (number of) parameters.
2837 =head3 Basic Operations
2841 =item * Intersection
2843 __isl_give isl_basic_set *isl_basic_set_intersect_params(
2844 __isl_take isl_basic_set *bset1,
2845 __isl_take isl_basic_set *bset2);
2846 __isl_give isl_basic_set *isl_basic_set_intersect(
2847 __isl_take isl_basic_set *bset1,
2848 __isl_take isl_basic_set *bset2);
2849 __isl_give isl_set *isl_set_intersect_params(
2850 __isl_take isl_set *set,
2851 __isl_take isl_set *params);
2852 __isl_give isl_set *isl_set_intersect(
2853 __isl_take isl_set *set1,
2854 __isl_take isl_set *set2);
2855 __isl_give isl_union_set *isl_union_set_intersect_params(
2856 __isl_take isl_union_set *uset,
2857 __isl_take isl_set *set);
2858 __isl_give isl_union_map *isl_union_map_intersect_params(
2859 __isl_take isl_union_map *umap,
2860 __isl_take isl_set *set);
2861 __isl_give isl_union_set *isl_union_set_intersect(
2862 __isl_take isl_union_set *uset1,
2863 __isl_take isl_union_set *uset2);
2864 __isl_give isl_basic_map *isl_basic_map_intersect_domain(
2865 __isl_take isl_basic_map *bmap,
2866 __isl_take isl_basic_set *bset);
2867 __isl_give isl_basic_map *isl_basic_map_intersect_range(
2868 __isl_take isl_basic_map *bmap,
2869 __isl_take isl_basic_set *bset);
2870 __isl_give isl_basic_map *isl_basic_map_intersect(
2871 __isl_take isl_basic_map *bmap1,
2872 __isl_take isl_basic_map *bmap2);
2873 __isl_give isl_map *isl_map_intersect_params(
2874 __isl_take isl_map *map,
2875 __isl_take isl_set *params);
2876 __isl_give isl_map *isl_map_intersect_domain(
2877 __isl_take isl_map *map,
2878 __isl_take isl_set *set);
2879 __isl_give isl_map *isl_map_intersect_range(
2880 __isl_take isl_map *map,
2881 __isl_take isl_set *set);
2882 __isl_give isl_map *isl_map_intersect(
2883 __isl_take isl_map *map1,
2884 __isl_take isl_map *map2);
2885 __isl_give isl_union_map *isl_union_map_intersect_domain(
2886 __isl_take isl_union_map *umap,
2887 __isl_take isl_union_set *uset);
2888 __isl_give isl_union_map *isl_union_map_intersect_range(
2889 __isl_take isl_union_map *umap,
2890 __isl_take isl_union_set *uset);
2891 __isl_give isl_union_map *isl_union_map_intersect(
2892 __isl_take isl_union_map *umap1,
2893 __isl_take isl_union_map *umap2);
2895 The second argument to the C<_params> functions needs to be
2896 a parametric (basic) set. For the other functions, a parametric set
2897 for either argument is only allowed if the other argument is
2898 a parametric set as well.
2902 __isl_give isl_set *isl_basic_set_union(
2903 __isl_take isl_basic_set *bset1,
2904 __isl_take isl_basic_set *bset2);
2905 __isl_give isl_map *isl_basic_map_union(
2906 __isl_take isl_basic_map *bmap1,
2907 __isl_take isl_basic_map *bmap2);
2908 __isl_give isl_set *isl_set_union(
2909 __isl_take isl_set *set1,
2910 __isl_take isl_set *set2);
2911 __isl_give isl_map *isl_map_union(
2912 __isl_take isl_map *map1,
2913 __isl_take isl_map *map2);
2914 __isl_give isl_union_set *isl_union_set_union(
2915 __isl_take isl_union_set *uset1,
2916 __isl_take isl_union_set *uset2);
2917 __isl_give isl_union_map *isl_union_map_union(
2918 __isl_take isl_union_map *umap1,
2919 __isl_take isl_union_map *umap2);
2921 =item * Set difference
2923 __isl_give isl_set *isl_set_subtract(
2924 __isl_take isl_set *set1,
2925 __isl_take isl_set *set2);
2926 __isl_give isl_map *isl_map_subtract(
2927 __isl_take isl_map *map1,
2928 __isl_take isl_map *map2);
2929 __isl_give isl_map *isl_map_subtract_domain(
2930 __isl_take isl_map *map,
2931 __isl_take isl_set *dom);
2932 __isl_give isl_map *isl_map_subtract_range(
2933 __isl_take isl_map *map,
2934 __isl_take isl_set *dom);
2935 __isl_give isl_union_set *isl_union_set_subtract(
2936 __isl_take isl_union_set *uset1,
2937 __isl_take isl_union_set *uset2);
2938 __isl_give isl_union_map *isl_union_map_subtract(
2939 __isl_take isl_union_map *umap1,
2940 __isl_take isl_union_map *umap2);
2941 __isl_give isl_union_map *isl_union_map_subtract_domain(
2942 __isl_take isl_union_map *umap,
2943 __isl_take isl_union_set *dom);
2944 __isl_give isl_union_map *isl_union_map_subtract_range(
2945 __isl_take isl_union_map *umap,
2946 __isl_take isl_union_set *dom);
2950 __isl_give isl_basic_set *isl_basic_set_apply(
2951 __isl_take isl_basic_set *bset,
2952 __isl_take isl_basic_map *bmap);
2953 __isl_give isl_set *isl_set_apply(
2954 __isl_take isl_set *set,
2955 __isl_take isl_map *map);
2956 __isl_give isl_union_set *isl_union_set_apply(
2957 __isl_take isl_union_set *uset,
2958 __isl_take isl_union_map *umap);
2959 __isl_give isl_basic_map *isl_basic_map_apply_domain(
2960 __isl_take isl_basic_map *bmap1,
2961 __isl_take isl_basic_map *bmap2);
2962 __isl_give isl_basic_map *isl_basic_map_apply_range(
2963 __isl_take isl_basic_map *bmap1,
2964 __isl_take isl_basic_map *bmap2);
2965 __isl_give isl_map *isl_map_apply_domain(
2966 __isl_take isl_map *map1,
2967 __isl_take isl_map *map2);
2968 __isl_give isl_union_map *isl_union_map_apply_domain(
2969 __isl_take isl_union_map *umap1,
2970 __isl_take isl_union_map *umap2);
2971 __isl_give isl_map *isl_map_apply_range(
2972 __isl_take isl_map *map1,
2973 __isl_take isl_map *map2);
2974 __isl_give isl_union_map *isl_union_map_apply_range(
2975 __isl_take isl_union_map *umap1,
2976 __isl_take isl_union_map *umap2);
2980 __isl_give isl_basic_set *
2981 isl_basic_set_preimage_multi_aff(
2982 __isl_take isl_basic_set *bset,
2983 __isl_take isl_multi_aff *ma);
2984 __isl_give isl_set *isl_set_preimage_multi_aff(
2985 __isl_take isl_set *set,
2986 __isl_take isl_multi_aff *ma);
2987 __isl_give isl_set *isl_set_preimage_pw_multi_aff(
2988 __isl_take isl_set *set,
2989 __isl_take isl_pw_multi_aff *pma);
2990 __isl_give isl_set *isl_set_preimage_multi_pw_aff(
2991 __isl_take isl_set *set,
2992 __isl_take isl_multi_pw_aff *mpa);
2993 __isl_give isl_basic_map *
2994 isl_basic_map_preimage_domain_multi_aff(
2995 __isl_take isl_basic_map *bmap,
2996 __isl_take isl_multi_aff *ma);
2997 __isl_give isl_map *isl_map_preimage_domain_multi_aff(
2998 __isl_take isl_map *map,
2999 __isl_take isl_multi_aff *ma);
3000 __isl_give isl_map *
3001 isl_map_preimage_domain_pw_multi_aff(
3002 __isl_take isl_map *map,
3003 __isl_take isl_pw_multi_aff *pma);
3004 __isl_give isl_map *
3005 isl_map_preimage_domain_multi_pw_aff(
3006 __isl_take isl_map *map,
3007 __isl_take isl_multi_pw_aff *mpa);
3008 __isl_give isl_union_map *
3009 isl_union_map_preimage_domain_multi_aff(
3010 __isl_take isl_union_map *umap,
3011 __isl_take isl_multi_aff *ma);
3012 __isl_give isl_basic_map *
3013 isl_basic_map_preimage_range_multi_aff(
3014 __isl_take isl_basic_map *bmap,
3015 __isl_take isl_multi_aff *ma);
3017 These functions compute the preimage of the given set or map domain/range under
3018 the given function. In other words, the expression is plugged
3019 into the set description or into the domain/range of the map.
3020 Objects of types C<isl_multi_aff> and C<isl_pw_multi_aff> are described in
3021 L</"Piecewise Multiple Quasi Affine Expressions">.
3023 =item * Cartesian Product
3025 __isl_give isl_set *isl_set_product(
3026 __isl_take isl_set *set1,
3027 __isl_take isl_set *set2);
3028 __isl_give isl_union_set *isl_union_set_product(
3029 __isl_take isl_union_set *uset1,
3030 __isl_take isl_union_set *uset2);
3031 __isl_give isl_basic_map *isl_basic_map_domain_product(
3032 __isl_take isl_basic_map *bmap1,
3033 __isl_take isl_basic_map *bmap2);
3034 __isl_give isl_basic_map *isl_basic_map_range_product(
3035 __isl_take isl_basic_map *bmap1,
3036 __isl_take isl_basic_map *bmap2);
3037 __isl_give isl_basic_map *isl_basic_map_product(
3038 __isl_take isl_basic_map *bmap1,
3039 __isl_take isl_basic_map *bmap2);
3040 __isl_give isl_map *isl_map_domain_product(
3041 __isl_take isl_map *map1,
3042 __isl_take isl_map *map2);
3043 __isl_give isl_map *isl_map_range_product(
3044 __isl_take isl_map *map1,
3045 __isl_take isl_map *map2);
3046 __isl_give isl_union_map *isl_union_map_domain_product(
3047 __isl_take isl_union_map *umap1,
3048 __isl_take isl_union_map *umap2);
3049 __isl_give isl_union_map *isl_union_map_range_product(
3050 __isl_take isl_union_map *umap1,
3051 __isl_take isl_union_map *umap2);
3052 __isl_give isl_map *isl_map_product(
3053 __isl_take isl_map *map1,
3054 __isl_take isl_map *map2);
3055 __isl_give isl_union_map *isl_union_map_product(
3056 __isl_take isl_union_map *umap1,
3057 __isl_take isl_union_map *umap2);
3059 The above functions compute the cross product of the given
3060 sets or relations. The domains and ranges of the results
3061 are wrapped maps between domains and ranges of the inputs.
3062 To obtain a ``flat'' product, use the following functions
3065 __isl_give isl_basic_set *isl_basic_set_flat_product(
3066 __isl_take isl_basic_set *bset1,
3067 __isl_take isl_basic_set *bset2);
3068 __isl_give isl_set *isl_set_flat_product(
3069 __isl_take isl_set *set1,
3070 __isl_take isl_set *set2);
3071 __isl_give isl_basic_map *isl_basic_map_flat_range_product(
3072 __isl_take isl_basic_map *bmap1,
3073 __isl_take isl_basic_map *bmap2);
3074 __isl_give isl_map *isl_map_flat_domain_product(
3075 __isl_take isl_map *map1,
3076 __isl_take isl_map *map2);
3077 __isl_give isl_map *isl_map_flat_range_product(
3078 __isl_take isl_map *map1,
3079 __isl_take isl_map *map2);
3080 __isl_give isl_union_map *isl_union_map_flat_range_product(
3081 __isl_take isl_union_map *umap1,
3082 __isl_take isl_union_map *umap2);
3083 __isl_give isl_basic_map *isl_basic_map_flat_product(
3084 __isl_take isl_basic_map *bmap1,
3085 __isl_take isl_basic_map *bmap2);
3086 __isl_give isl_map *isl_map_flat_product(
3087 __isl_take isl_map *map1,
3088 __isl_take isl_map *map2);
3090 The arguments of a call to C<isl_map_product> can be extracted
3091 from the result using the following two functions.
3093 __isl_give isl_map *isl_map_range_factor_domain(
3094 __isl_take isl_map *map);
3095 __isl_give isl_map *isl_map_range_factor_range(
3096 __isl_take isl_map *map);
3098 =item * Simplification
3100 __isl_give isl_basic_set *isl_basic_set_gist(
3101 __isl_take isl_basic_set *bset,
3102 __isl_take isl_basic_set *context);
3103 __isl_give isl_set *isl_set_gist(__isl_take isl_set *set,
3104 __isl_take isl_set *context);
3105 __isl_give isl_set *isl_set_gist_params(
3106 __isl_take isl_set *set,
3107 __isl_take isl_set *context);
3108 __isl_give isl_union_set *isl_union_set_gist(
3109 __isl_take isl_union_set *uset,
3110 __isl_take isl_union_set *context);
3111 __isl_give isl_union_set *isl_union_set_gist_params(
3112 __isl_take isl_union_set *uset,
3113 __isl_take isl_set *set);
3114 __isl_give isl_basic_map *isl_basic_map_gist(
3115 __isl_take isl_basic_map *bmap,
3116 __isl_take isl_basic_map *context);
3117 __isl_give isl_map *isl_map_gist(__isl_take isl_map *map,
3118 __isl_take isl_map *context);
3119 __isl_give isl_map *isl_map_gist_params(
3120 __isl_take isl_map *map,
3121 __isl_take isl_set *context);
3122 __isl_give isl_map *isl_map_gist_domain(
3123 __isl_take isl_map *map,
3124 __isl_take isl_set *context);
3125 __isl_give isl_map *isl_map_gist_range(
3126 __isl_take isl_map *map,
3127 __isl_take isl_set *context);
3128 __isl_give isl_union_map *isl_union_map_gist(
3129 __isl_take isl_union_map *umap,
3130 __isl_take isl_union_map *context);
3131 __isl_give isl_union_map *isl_union_map_gist_params(
3132 __isl_take isl_union_map *umap,
3133 __isl_take isl_set *set);
3134 __isl_give isl_union_map *isl_union_map_gist_domain(
3135 __isl_take isl_union_map *umap,
3136 __isl_take isl_union_set *uset);
3137 __isl_give isl_union_map *isl_union_map_gist_range(
3138 __isl_take isl_union_map *umap,
3139 __isl_take isl_union_set *uset);
3141 The gist operation returns a set or relation that has the
3142 same intersection with the context as the input set or relation.
3143 Any implicit equality in the intersection is made explicit in the result,
3144 while all inequalities that are redundant with respect to the intersection
3146 In case of union sets and relations, the gist operation is performed
3151 =head3 Lexicographic Optimization
3153 Given a (basic) set C<set> (or C<bset>) and a zero-dimensional domain C<dom>,
3154 the following functions
3155 compute a set that contains the lexicographic minimum or maximum
3156 of the elements in C<set> (or C<bset>) for those values of the parameters
3157 that satisfy C<dom>.
3158 If C<empty> is not C<NULL>, then C<*empty> is assigned a set
3159 that contains the parameter values in C<dom> for which C<set> (or C<bset>)
3161 In other words, the union of the parameter values
3162 for which the result is non-empty and of C<*empty>
3165 __isl_give isl_set *isl_basic_set_partial_lexmin(
3166 __isl_take isl_basic_set *bset,
3167 __isl_take isl_basic_set *dom,
3168 __isl_give isl_set **empty);
3169 __isl_give isl_set *isl_basic_set_partial_lexmax(
3170 __isl_take isl_basic_set *bset,
3171 __isl_take isl_basic_set *dom,
3172 __isl_give isl_set **empty);
3173 __isl_give isl_set *isl_set_partial_lexmin(
3174 __isl_take isl_set *set, __isl_take isl_set *dom,
3175 __isl_give isl_set **empty);
3176 __isl_give isl_set *isl_set_partial_lexmax(
3177 __isl_take isl_set *set, __isl_take isl_set *dom,
3178 __isl_give isl_set **empty);
3180 Given a (basic) set C<set> (or C<bset>), the following functions simply
3181 return a set containing the lexicographic minimum or maximum
3182 of the elements in C<set> (or C<bset>).
3183 In case of union sets, the optimum is computed per space.
3185 __isl_give isl_set *isl_basic_set_lexmin(
3186 __isl_take isl_basic_set *bset);
3187 __isl_give isl_set *isl_basic_set_lexmax(
3188 __isl_take isl_basic_set *bset);
3189 __isl_give isl_set *isl_set_lexmin(
3190 __isl_take isl_set *set);
3191 __isl_give isl_set *isl_set_lexmax(
3192 __isl_take isl_set *set);
3193 __isl_give isl_union_set *isl_union_set_lexmin(
3194 __isl_take isl_union_set *uset);
3195 __isl_give isl_union_set *isl_union_set_lexmax(
3196 __isl_take isl_union_set *uset);
3198 Given a (basic) relation C<map> (or C<bmap>) and a domain C<dom>,
3199 the following functions
3200 compute a relation that maps each element of C<dom>
3201 to the single lexicographic minimum or maximum
3202 of the elements that are associated to that same
3203 element in C<map> (or C<bmap>).
3204 If C<empty> is not C<NULL>, then C<*empty> is assigned a set
3205 that contains the elements in C<dom> that do not map
3206 to any elements in C<map> (or C<bmap>).
3207 In other words, the union of the domain of the result and of C<*empty>
3210 __isl_give isl_map *isl_basic_map_partial_lexmax(
3211 __isl_take isl_basic_map *bmap,
3212 __isl_take isl_basic_set *dom,
3213 __isl_give isl_set **empty);
3214 __isl_give isl_map *isl_basic_map_partial_lexmin(
3215 __isl_take isl_basic_map *bmap,
3216 __isl_take isl_basic_set *dom,
3217 __isl_give isl_set **empty);
3218 __isl_give isl_map *isl_map_partial_lexmax(
3219 __isl_take isl_map *map, __isl_take isl_set *dom,
3220 __isl_give isl_set **empty);
3221 __isl_give isl_map *isl_map_partial_lexmin(
3222 __isl_take isl_map *map, __isl_take isl_set *dom,
3223 __isl_give isl_set **empty);
3225 Given a (basic) map C<map> (or C<bmap>), the following functions simply
3226 return a map mapping each element in the domain of
3227 C<map> (or C<bmap>) to the lexicographic minimum or maximum
3228 of all elements associated to that element.
3229 In case of union relations, the optimum is computed per space.
3231 __isl_give isl_map *isl_basic_map_lexmin(
3232 __isl_take isl_basic_map *bmap);
3233 __isl_give isl_map *isl_basic_map_lexmax(
3234 __isl_take isl_basic_map *bmap);
3235 __isl_give isl_map *isl_map_lexmin(
3236 __isl_take isl_map *map);
3237 __isl_give isl_map *isl_map_lexmax(
3238 __isl_take isl_map *map);
3239 __isl_give isl_union_map *isl_union_map_lexmin(
3240 __isl_take isl_union_map *umap);
3241 __isl_give isl_union_map *isl_union_map_lexmax(
3242 __isl_take isl_union_map *umap);
3244 The following functions return their result in the form of
3245 a piecewise multi-affine expression
3246 (See L<"Piecewise Multiple Quasi Affine Expressions">),
3247 but are otherwise equivalent to the corresponding functions
3248 returning a basic set or relation.
3250 __isl_give isl_pw_multi_aff *
3251 isl_basic_map_lexmin_pw_multi_aff(
3252 __isl_take isl_basic_map *bmap);
3253 __isl_give isl_pw_multi_aff *
3254 isl_basic_set_partial_lexmin_pw_multi_aff(
3255 __isl_take isl_basic_set *bset,
3256 __isl_take isl_basic_set *dom,
3257 __isl_give isl_set **empty);
3258 __isl_give isl_pw_multi_aff *
3259 isl_basic_set_partial_lexmax_pw_multi_aff(
3260 __isl_take isl_basic_set *bset,
3261 __isl_take isl_basic_set *dom,
3262 __isl_give isl_set **empty);
3263 __isl_give isl_pw_multi_aff *
3264 isl_basic_map_partial_lexmin_pw_multi_aff(
3265 __isl_take isl_basic_map *bmap,
3266 __isl_take isl_basic_set *dom,
3267 __isl_give isl_set **empty);
3268 __isl_give isl_pw_multi_aff *
3269 isl_basic_map_partial_lexmax_pw_multi_aff(
3270 __isl_take isl_basic_map *bmap,
3271 __isl_take isl_basic_set *dom,
3272 __isl_give isl_set **empty);
3273 __isl_give isl_pw_multi_aff *isl_set_lexmin_pw_multi_aff(
3274 __isl_take isl_set *set);
3275 __isl_give isl_pw_multi_aff *isl_set_lexmax_pw_multi_aff(
3276 __isl_take isl_set *set);
3277 __isl_give isl_pw_multi_aff *isl_map_lexmin_pw_multi_aff(
3278 __isl_take isl_map *map);
3279 __isl_give isl_pw_multi_aff *isl_map_lexmax_pw_multi_aff(
3280 __isl_take isl_map *map);
3284 Lists are defined over several element types, including
3285 C<isl_val>, C<isl_id>, C<isl_aff>, C<isl_pw_aff>, C<isl_constraint>,
3286 C<isl_basic_set>, C<isl_set>, C<isl_ast_expr> and C<isl_ast_node>.
3287 Here we take lists of C<isl_set>s as an example.
3288 Lists can be created, copied, modified and freed using the following functions.
3290 #include <isl/list.h>
3291 __isl_give isl_set_list *isl_set_list_from_set(
3292 __isl_take isl_set *el);
3293 __isl_give isl_set_list *isl_set_list_alloc(
3294 isl_ctx *ctx, int n);
3295 __isl_give isl_set_list *isl_set_list_copy(
3296 __isl_keep isl_set_list *list);
3297 __isl_give isl_set_list *isl_set_list_insert(
3298 __isl_take isl_set_list *list, unsigned pos,
3299 __isl_take isl_set *el);
3300 __isl_give isl_set_list *isl_set_list_add(
3301 __isl_take isl_set_list *list,
3302 __isl_take isl_set *el);
3303 __isl_give isl_set_list *isl_set_list_drop(
3304 __isl_take isl_set_list *list,
3305 unsigned first, unsigned n);
3306 __isl_give isl_set_list *isl_set_list_set_set(
3307 __isl_take isl_set_list *list, int index,
3308 __isl_take isl_set *set);
3309 __isl_give isl_set_list *isl_set_list_concat(
3310 __isl_take isl_set_list *list1,
3311 __isl_take isl_set_list *list2);
3312 __isl_give isl_set_list *isl_set_list_sort(
3313 __isl_take isl_set_list *list,
3314 int (*cmp)(__isl_keep isl_set *a,
3315 __isl_keep isl_set *b, void *user),
3317 void *isl_set_list_free(__isl_take isl_set_list *list);
3319 C<isl_set_list_alloc> creates an empty list with a capacity for
3320 C<n> elements. C<isl_set_list_from_set> creates a list with a single
3323 Lists can be inspected using the following functions.
3325 #include <isl/list.h>
3326 isl_ctx *isl_set_list_get_ctx(__isl_keep isl_set_list *list);
3327 int isl_set_list_n_set(__isl_keep isl_set_list *list);
3328 __isl_give isl_set *isl_set_list_get_set(
3329 __isl_keep isl_set_list *list, int index);
3330 int isl_set_list_foreach(__isl_keep isl_set_list *list,
3331 int (*fn)(__isl_take isl_set *el, void *user),
3333 int isl_set_list_foreach_scc(__isl_keep isl_set_list *list,
3334 int (*follows)(__isl_keep isl_set *a,
3335 __isl_keep isl_set *b, void *user),
3337 int (*fn)(__isl_take isl_set *el, void *user),
3340 The function C<isl_set_list_foreach_scc> calls C<fn> on each of the
3341 strongly connected components of the graph with as vertices the elements
3342 of C<list> and a directed edge from vertex C<b> to vertex C<a>
3343 iff C<follows(a, b)> returns C<1>. The callbacks C<follows> and C<fn>
3344 should return C<-1> on error.
3346 Lists can be printed using
3348 #include <isl/list.h>
3349 __isl_give isl_printer *isl_printer_print_set_list(
3350 __isl_take isl_printer *p,
3351 __isl_keep isl_set_list *list);
3353 =head2 Associative arrays
3355 Associative arrays map isl objects of a specific type to isl objects
3356 of some (other) specific type. They are defined for several pairs
3357 of types, including (C<isl_map>, C<isl_basic_set>),
3358 (C<isl_id>, C<isl_ast_expr>) and.
3359 (C<isl_id>, C<isl_pw_aff>).
3360 Here, we take associative arrays that map C<isl_id>s to C<isl_ast_expr>s
3363 Associative arrays can be created, copied and freed using
3364 the following functions.
3366 #include <isl/id_to_ast_expr.h>
3367 __isl_give id_to_ast_expr *isl_id_to_ast_expr_alloc(
3368 isl_ctx *ctx, int min_size);
3369 __isl_give id_to_ast_expr *isl_id_to_ast_expr_copy(
3370 __isl_keep id_to_ast_expr *id2expr);
3371 void *isl_id_to_ast_expr_free(
3372 __isl_take id_to_ast_expr *id2expr);
3374 The C<min_size> argument to C<isl_id_to_ast_expr_alloc> can be used
3375 to specify the expected size of the associative array.
3376 The associative array will be grown automatically as needed.
3378 Associative arrays can be inspected using the following functions.
3380 #include <isl/id_to_ast_expr.h>
3381 isl_ctx *isl_id_to_ast_expr_get_ctx(
3382 __isl_keep id_to_ast_expr *id2expr);
3383 int isl_id_to_ast_expr_has(
3384 __isl_keep id_to_ast_expr *id2expr,
3385 __isl_keep isl_id *key);
3386 __isl_give isl_ast_expr *isl_id_to_ast_expr_get(
3387 __isl_keep id_to_ast_expr *id2expr,
3388 __isl_take isl_id *key);
3389 int isl_id_to_ast_expr_foreach(
3390 __isl_keep id_to_ast_expr *id2expr,
3391 int (*fn)(__isl_take isl_id *key,
3392 __isl_take isl_ast_expr *val, void *user),
3395 They can be modified using the following function.
3397 #include <isl/id_to_ast_expr.h>
3398 __isl_give id_to_ast_expr *isl_id_to_ast_expr_set(
3399 __isl_take id_to_ast_expr *id2expr,
3400 __isl_take isl_id *key,
3401 __isl_take isl_ast_expr *val);
3403 Associative arrays can be printed using the following function.
3405 #include <isl/id_to_ast_expr.h>
3406 __isl_give isl_printer *isl_printer_print_id_to_ast_expr(
3407 __isl_take isl_printer *p,
3408 __isl_keep id_to_ast_expr *id2expr);
3410 =head2 Multiple Values
3412 An C<isl_multi_val> object represents a sequence of zero or more values,
3413 living in a set space.
3415 An C<isl_multi_val> can be constructed from an C<isl_val_list>
3416 using the following function
3418 #include <isl/val.h>
3419 __isl_give isl_multi_val *isl_multi_val_from_val_list(
3420 __isl_take isl_space *space,
3421 __isl_take isl_val_list *list);
3423 The zero multiple value (with value zero for each set dimension)
3424 can be created using the following function.
3426 #include <isl/val.h>
3427 __isl_give isl_multi_val *isl_multi_val_zero(
3428 __isl_take isl_space *space);
3430 Multiple values can be copied and freed using
3432 #include <isl/val.h>
3433 __isl_give isl_multi_val *isl_multi_val_copy(
3434 __isl_keep isl_multi_val *mv);
3435 void *isl_multi_val_free(__isl_take isl_multi_val *mv);
3437 They can be inspected using
3439 #include <isl/val.h>
3440 isl_ctx *isl_multi_val_get_ctx(
3441 __isl_keep isl_multi_val *mv);
3442 unsigned isl_multi_val_dim(__isl_keep isl_multi_val *mv,
3443 enum isl_dim_type type);
3444 __isl_give isl_val *isl_multi_val_get_val(
3445 __isl_keep isl_multi_val *mv, int pos);
3446 int isl_multi_val_find_dim_by_id(
3447 __isl_keep isl_multi_val *mv,
3448 enum isl_dim_type type, __isl_keep isl_id *id);
3449 __isl_give isl_id *isl_multi_val_get_dim_id(
3450 __isl_keep isl_multi_val *mv,
3451 enum isl_dim_type type, unsigned pos);
3452 const char *isl_multi_val_get_tuple_name(
3453 __isl_keep isl_multi_val *mv,
3454 enum isl_dim_type type);
3455 int isl_multi_val_has_tuple_id(__isl_keep isl_multi_val *mv,
3456 enum isl_dim_type type);
3457 __isl_give isl_id *isl_multi_val_get_tuple_id(
3458 __isl_keep isl_multi_val *mv,
3459 enum isl_dim_type type);
3460 int isl_multi_val_range_is_wrapping(
3461 __isl_keep isl_multi_val *mv);
3463 They can be modified using
3465 #include <isl/val.h>
3466 __isl_give isl_multi_val *isl_multi_val_set_val(
3467 __isl_take isl_multi_val *mv, int pos,
3468 __isl_take isl_val *val);
3469 __isl_give isl_multi_val *isl_multi_val_set_dim_name(
3470 __isl_take isl_multi_val *mv,
3471 enum isl_dim_type type, unsigned pos, const char *s);
3472 __isl_give isl_multi_val *isl_multi_val_set_dim_id(
3473 __isl_take isl_multi_val *mv,
3474 enum isl_dim_type type, unsigned pos,
3475 __isl_take isl_id *id);
3476 __isl_give isl_multi_val *isl_multi_val_set_tuple_name(
3477 __isl_take isl_multi_val *mv,
3478 enum isl_dim_type type, const char *s);
3479 __isl_give isl_multi_val *isl_multi_val_set_tuple_id(
3480 __isl_take isl_multi_val *mv,
3481 enum isl_dim_type type, __isl_take isl_id *id);
3482 __isl_give isl_multi_val *isl_multi_val_reset_tuple_id(
3483 __isl_take isl_multi_val *mv,
3484 enum isl_dim_type type);
3485 __isl_give isl_multi_val *isl_multi_val_reset_user(
3486 __isl_take isl_multi_val *mv);
3488 __isl_give isl_multi_val *isl_multi_val_insert_dims(
3489 __isl_take isl_multi_val *mv,
3490 enum isl_dim_type type, unsigned first, unsigned n);
3491 __isl_give isl_multi_val *isl_multi_val_add_dims(
3492 __isl_take isl_multi_val *mv,
3493 enum isl_dim_type type, unsigned n);
3494 __isl_give isl_multi_val *isl_multi_val_drop_dims(
3495 __isl_take isl_multi_val *mv,
3496 enum isl_dim_type type, unsigned first, unsigned n);
3500 #include <isl/val.h>
3501 __isl_give isl_multi_val *isl_multi_val_align_params(
3502 __isl_take isl_multi_val *mv,
3503 __isl_take isl_space *model);
3504 __isl_give isl_multi_val *isl_multi_val_from_range(
3505 __isl_take isl_multi_val *mv);
3506 __isl_give isl_multi_val *isl_multi_val_range_splice(
3507 __isl_take isl_multi_val *mv1, unsigned pos,
3508 __isl_take isl_multi_val *mv2);
3509 __isl_give isl_multi_val *isl_multi_val_range_product(
3510 __isl_take isl_multi_val *mv1,
3511 __isl_take isl_multi_val *mv2);
3512 __isl_give isl_multi_val *
3513 isl_multi_val_range_factor_domain(
3514 __isl_take isl_multi_val *mv);
3515 __isl_give isl_multi_val *
3516 isl_multi_val_range_factor_range(
3517 __isl_take isl_multi_val *mv);
3518 __isl_give isl_multi_val *isl_multi_val_flat_range_product(
3519 __isl_take isl_multi_val *mv1,
3520 __isl_take isl_multi_aff *mv2);
3521 __isl_give isl_multi_val *isl_multi_val_product(
3522 __isl_take isl_multi_val *mv1,
3523 __isl_take isl_multi_val *mv2);
3524 __isl_give isl_multi_val *isl_multi_val_add_val(
3525 __isl_take isl_multi_val *mv,
3526 __isl_take isl_val *v);
3527 __isl_give isl_multi_val *isl_multi_val_mod_val(
3528 __isl_take isl_multi_val *mv,
3529 __isl_take isl_val *v);
3530 __isl_give isl_multi_val *isl_multi_val_scale_val(
3531 __isl_take isl_multi_val *mv,
3532 __isl_take isl_val *v);
3533 __isl_give isl_multi_val *isl_multi_val_scale_multi_val(
3534 __isl_take isl_multi_val *mv1,
3535 __isl_take isl_multi_val *mv2);
3536 __isl_give isl_multi_val *
3537 isl_multi_val_scale_down_multi_val(
3538 __isl_take isl_multi_val *mv1,
3539 __isl_take isl_multi_val *mv2);
3541 A multiple value can be printed using
3543 __isl_give isl_printer *isl_printer_print_multi_val(
3544 __isl_take isl_printer *p,
3545 __isl_keep isl_multi_val *mv);
3549 Vectors can be created, copied and freed using the following functions.
3551 #include <isl/vec.h>
3552 __isl_give isl_vec *isl_vec_alloc(isl_ctx *ctx,
3554 __isl_give isl_vec *isl_vec_copy(__isl_keep isl_vec *vec);
3555 void *isl_vec_free(__isl_take isl_vec *vec);
3557 Note that the elements of a newly created vector may have arbitrary values.
3558 The elements can be changed and inspected using the following functions.
3560 isl_ctx *isl_vec_get_ctx(__isl_keep isl_vec *vec);
3561 int isl_vec_size(__isl_keep isl_vec *vec);
3562 __isl_give isl_val *isl_vec_get_element_val(
3563 __isl_keep isl_vec *vec, int pos);
3564 __isl_give isl_vec *isl_vec_set_element_si(
3565 __isl_take isl_vec *vec, int pos, int v);
3566 __isl_give isl_vec *isl_vec_set_element_val(
3567 __isl_take isl_vec *vec, int pos,
3568 __isl_take isl_val *v);
3569 __isl_give isl_vec *isl_vec_set_si(__isl_take isl_vec *vec,
3571 __isl_give isl_vec *isl_vec_set_val(
3572 __isl_take isl_vec *vec, __isl_take isl_val *v);
3573 int isl_vec_cmp_element(__isl_keep isl_vec *vec1,
3574 __isl_keep isl_vec *vec2, int pos);
3576 C<isl_vec_get_element> will return a negative value if anything went wrong.
3577 In that case, the value of C<*v> is undefined.
3579 The following function can be used to concatenate two vectors.
3581 __isl_give isl_vec *isl_vec_concat(__isl_take isl_vec *vec1,
3582 __isl_take isl_vec *vec2);
3586 Matrices can be created, copied and freed using the following functions.
3588 #include <isl/mat.h>
3589 __isl_give isl_mat *isl_mat_alloc(isl_ctx *ctx,
3590 unsigned n_row, unsigned n_col);
3591 __isl_give isl_mat *isl_mat_copy(__isl_keep isl_mat *mat);
3592 void *isl_mat_free(__isl_take isl_mat *mat);
3594 Note that the elements of a newly created matrix may have arbitrary values.
3595 The elements can be changed and inspected using the following functions.
3597 isl_ctx *isl_mat_get_ctx(__isl_keep isl_mat *mat);
3598 int isl_mat_rows(__isl_keep isl_mat *mat);
3599 int isl_mat_cols(__isl_keep isl_mat *mat);
3600 __isl_give isl_val *isl_mat_get_element_val(
3601 __isl_keep isl_mat *mat, int row, int col);
3602 __isl_give isl_mat *isl_mat_set_element_si(__isl_take isl_mat *mat,
3603 int row, int col, int v);
3604 __isl_give isl_mat *isl_mat_set_element_val(
3605 __isl_take isl_mat *mat, int row, int col,
3606 __isl_take isl_val *v);
3608 C<isl_mat_get_element> will return a negative value if anything went wrong.
3609 In that case, the value of C<*v> is undefined.
3611 The following function can be used to compute the (right) inverse
3612 of a matrix, i.e., a matrix such that the product of the original
3613 and the inverse (in that order) is a multiple of the identity matrix.
3614 The input matrix is assumed to be of full row-rank.
3616 __isl_give isl_mat *isl_mat_right_inverse(__isl_take isl_mat *mat);
3618 The following function can be used to compute the (right) kernel
3619 (or null space) of a matrix, i.e., a matrix such that the product of
3620 the original and the kernel (in that order) is the zero matrix.
3622 __isl_give isl_mat *isl_mat_right_kernel(__isl_take isl_mat *mat);
3624 =head2 Piecewise Quasi Affine Expressions
3626 The zero quasi affine expression or the quasi affine expression
3627 that is equal to a given value or
3628 a specified dimension on a given domain can be created using
3630 __isl_give isl_aff *isl_aff_zero_on_domain(
3631 __isl_take isl_local_space *ls);
3632 __isl_give isl_pw_aff *isl_pw_aff_zero_on_domain(
3633 __isl_take isl_local_space *ls);
3634 __isl_give isl_aff *isl_aff_val_on_domain(
3635 __isl_take isl_local_space *ls,
3636 __isl_take isl_val *val);
3637 __isl_give isl_aff *isl_aff_var_on_domain(
3638 __isl_take isl_local_space *ls,
3639 enum isl_dim_type type, unsigned pos);
3640 __isl_give isl_pw_aff *isl_pw_aff_var_on_domain(
3641 __isl_take isl_local_space *ls,
3642 enum isl_dim_type type, unsigned pos);
3644 Note that the space in which the resulting objects live is a map space
3645 with the given space as domain and a one-dimensional range.
3647 An empty piecewise quasi affine expression (one with no cells)
3648 or a piecewise quasi affine expression with a single cell can
3649 be created using the following functions.
3651 #include <isl/aff.h>
3652 __isl_give isl_pw_aff *isl_pw_aff_empty(
3653 __isl_take isl_space *space);
3654 __isl_give isl_pw_aff *isl_pw_aff_alloc(
3655 __isl_take isl_set *set, __isl_take isl_aff *aff);
3656 __isl_give isl_pw_aff *isl_pw_aff_from_aff(
3657 __isl_take isl_aff *aff);
3659 A piecewise quasi affine expression that is equal to 1 on a set
3660 and 0 outside the set can be created using the following function.
3662 #include <isl/aff.h>
3663 __isl_give isl_pw_aff *isl_set_indicator_function(
3664 __isl_take isl_set *set);
3666 Quasi affine expressions can be copied and freed using
3668 #include <isl/aff.h>
3669 __isl_give isl_aff *isl_aff_copy(__isl_keep isl_aff *aff);
3670 void *isl_aff_free(__isl_take isl_aff *aff);
3672 __isl_give isl_pw_aff *isl_pw_aff_copy(
3673 __isl_keep isl_pw_aff *pwaff);
3674 void *isl_pw_aff_free(__isl_take isl_pw_aff *pwaff);
3676 A (rational) bound on a dimension can be extracted from an C<isl_constraint>
3677 using the following function. The constraint is required to have
3678 a non-zero coefficient for the specified dimension.
3680 #include <isl/constraint.h>
3681 __isl_give isl_aff *isl_constraint_get_bound(
3682 __isl_keep isl_constraint *constraint,
3683 enum isl_dim_type type, int pos);
3685 The entire affine expression of the constraint can also be extracted
3686 using the following function.
3688 #include <isl/constraint.h>
3689 __isl_give isl_aff *isl_constraint_get_aff(
3690 __isl_keep isl_constraint *constraint);
3692 Conversely, an equality constraint equating
3693 the affine expression to zero or an inequality constraint enforcing
3694 the affine expression to be non-negative, can be constructed using
3696 __isl_give isl_constraint *isl_equality_from_aff(
3697 __isl_take isl_aff *aff);
3698 __isl_give isl_constraint *isl_inequality_from_aff(
3699 __isl_take isl_aff *aff);
3701 The expression can be inspected using
3703 #include <isl/aff.h>
3704 isl_ctx *isl_aff_get_ctx(__isl_keep isl_aff *aff);
3705 int isl_aff_dim(__isl_keep isl_aff *aff,
3706 enum isl_dim_type type);
3707 __isl_give isl_local_space *isl_aff_get_domain_local_space(
3708 __isl_keep isl_aff *aff);
3709 __isl_give isl_local_space *isl_aff_get_local_space(
3710 __isl_keep isl_aff *aff);
3711 const char *isl_aff_get_dim_name(__isl_keep isl_aff *aff,
3712 enum isl_dim_type type, unsigned pos);
3713 const char *isl_pw_aff_get_dim_name(
3714 __isl_keep isl_pw_aff *pa,
3715 enum isl_dim_type type, unsigned pos);
3716 int isl_pw_aff_has_dim_id(__isl_keep isl_pw_aff *pa,
3717 enum isl_dim_type type, unsigned pos);
3718 __isl_give isl_id *isl_pw_aff_get_dim_id(
3719 __isl_keep isl_pw_aff *pa,
3720 enum isl_dim_type type, unsigned pos);
3721 int isl_pw_aff_has_tuple_id(__isl_keep isl_pw_aff *pa,
3722 enum isl_dim_type type);
3723 __isl_give isl_id *isl_pw_aff_get_tuple_id(
3724 __isl_keep isl_pw_aff *pa,
3725 enum isl_dim_type type);
3726 __isl_give isl_val *isl_aff_get_constant_val(
3727 __isl_keep isl_aff *aff);
3728 __isl_give isl_val *isl_aff_get_coefficient_val(
3729 __isl_keep isl_aff *aff,
3730 enum isl_dim_type type, int pos);
3731 __isl_give isl_val *isl_aff_get_denominator_val(
3732 __isl_keep isl_aff *aff);
3733 __isl_give isl_aff *isl_aff_get_div(
3734 __isl_keep isl_aff *aff, int pos);
3736 int isl_pw_aff_n_piece(__isl_keep isl_pw_aff *pwaff);
3737 int isl_pw_aff_foreach_piece(__isl_keep isl_pw_aff *pwaff,
3738 int (*fn)(__isl_take isl_set *set,
3739 __isl_take isl_aff *aff,
3740 void *user), void *user);
3742 int isl_aff_is_cst(__isl_keep isl_aff *aff);
3743 int isl_pw_aff_is_cst(__isl_keep isl_pw_aff *pwaff);
3745 int isl_aff_involves_dims(__isl_keep isl_aff *aff,
3746 enum isl_dim_type type, unsigned first, unsigned n);
3747 int isl_pw_aff_involves_dims(__isl_keep isl_pw_aff *pwaff,
3748 enum isl_dim_type type, unsigned first, unsigned n);
3750 isl_ctx *isl_pw_aff_get_ctx(__isl_keep isl_pw_aff *pwaff);
3751 unsigned isl_pw_aff_dim(__isl_keep isl_pw_aff *pwaff,
3752 enum isl_dim_type type);
3753 int isl_pw_aff_is_empty(__isl_keep isl_pw_aff *pwaff);
3755 It can be modified using
3757 #include <isl/aff.h>
3758 __isl_give isl_pw_aff *isl_pw_aff_set_tuple_id(
3759 __isl_take isl_pw_aff *pwaff,
3760 enum isl_dim_type type, __isl_take isl_id *id);
3761 __isl_give isl_aff *isl_aff_set_dim_name(
3762 __isl_take isl_aff *aff, enum isl_dim_type type,
3763 unsigned pos, const char *s);
3764 __isl_give isl_aff *isl_aff_set_dim_id(
3765 __isl_take isl_aff *aff, enum isl_dim_type type,
3766 unsigned pos, __isl_take isl_id *id);
3767 __isl_give isl_pw_aff *isl_pw_aff_set_dim_id(
3768 __isl_take isl_pw_aff *pma,
3769 enum isl_dim_type type, unsigned pos,
3770 __isl_take isl_id *id);
3771 __isl_give isl_aff *isl_aff_set_constant_si(
3772 __isl_take isl_aff *aff, int v);
3773 __isl_give isl_aff *isl_aff_set_constant_val(
3774 __isl_take isl_aff *aff, __isl_take isl_val *v);
3775 __isl_give isl_aff *isl_aff_set_coefficient_si(
3776 __isl_take isl_aff *aff,
3777 enum isl_dim_type type, int pos, int v);
3778 __isl_give isl_aff *isl_aff_set_coefficient_val(
3779 __isl_take isl_aff *aff,
3780 enum isl_dim_type type, int pos,
3781 __isl_take isl_val *v);
3783 __isl_give isl_aff *isl_aff_add_constant_si(
3784 __isl_take isl_aff *aff, int v);
3785 __isl_give isl_aff *isl_aff_add_constant_val(
3786 __isl_take isl_aff *aff, __isl_take isl_val *v);
3787 __isl_give isl_aff *isl_aff_add_constant_num_si(
3788 __isl_take isl_aff *aff, int v);
3789 __isl_give isl_aff *isl_aff_add_coefficient_si(
3790 __isl_take isl_aff *aff,
3791 enum isl_dim_type type, int pos, int v);
3792 __isl_give isl_aff *isl_aff_add_coefficient_val(
3793 __isl_take isl_aff *aff,
3794 enum isl_dim_type type, int pos,
3795 __isl_take isl_val *v);
3797 __isl_give isl_aff *isl_aff_insert_dims(
3798 __isl_take isl_aff *aff,
3799 enum isl_dim_type type, unsigned first, unsigned n);
3800 __isl_give isl_pw_aff *isl_pw_aff_insert_dims(
3801 __isl_take isl_pw_aff *pwaff,
3802 enum isl_dim_type type, unsigned first, unsigned n);
3803 __isl_give isl_aff *isl_aff_add_dims(
3804 __isl_take isl_aff *aff,
3805 enum isl_dim_type type, unsigned n);
3806 __isl_give isl_pw_aff *isl_pw_aff_add_dims(
3807 __isl_take isl_pw_aff *pwaff,
3808 enum isl_dim_type type, unsigned n);
3809 __isl_give isl_aff *isl_aff_drop_dims(
3810 __isl_take isl_aff *aff,
3811 enum isl_dim_type type, unsigned first, unsigned n);
3812 __isl_give isl_pw_aff *isl_pw_aff_drop_dims(
3813 __isl_take isl_pw_aff *pwaff,
3814 enum isl_dim_type type, unsigned first, unsigned n);
3815 __isl_give isl_aff *isl_aff_move_dims(
3816 __isl_take isl_aff *aff,
3817 enum isl_dim_type dst_type, unsigned dst_pos,
3818 enum isl_dim_type src_type, unsigned src_pos,
3820 __isl_give isl_pw_aff *isl_pw_aff_move_dims(
3821 __isl_take isl_pw_aff *pa,
3822 enum isl_dim_type dst_type, unsigned dst_pos,
3823 enum isl_dim_type src_type, unsigned src_pos,
3826 Note that C<isl_aff_set_constant_si> and C<isl_aff_set_coefficient_si>
3827 set the I<numerator> of the constant or coefficient, while
3828 C<isl_aff_set_constant_val> and C<isl_aff_set_coefficient_val> set
3829 the constant or coefficient as a whole.
3830 The C<add_constant> and C<add_coefficient> functions add an integer
3831 or rational value to
3832 the possibly rational constant or coefficient.
3833 The C<add_constant_num> functions add an integer value to
3836 To check whether an affine expressions is obviously zero
3837 or (obviously) equal to some other affine expression, use
3839 #include <isl/aff.h>
3840 int isl_aff_plain_is_zero(__isl_keep isl_aff *aff);
3841 int isl_aff_plain_is_equal(__isl_keep isl_aff *aff1,
3842 __isl_keep isl_aff *aff2);
3843 int isl_pw_aff_plain_is_equal(
3844 __isl_keep isl_pw_aff *pwaff1,
3845 __isl_keep isl_pw_aff *pwaff2);
3846 int isl_pw_aff_is_equal(__isl_keep isl_pw_aff *pa1,
3847 __isl_keep isl_pw_aff *pa2);
3851 #include <isl/aff.h>
3852 __isl_give isl_aff *isl_aff_add(__isl_take isl_aff *aff1,
3853 __isl_take isl_aff *aff2);
3854 __isl_give isl_pw_aff *isl_pw_aff_add(
3855 __isl_take isl_pw_aff *pwaff1,
3856 __isl_take isl_pw_aff *pwaff2);
3857 __isl_give isl_pw_aff *isl_pw_aff_min(
3858 __isl_take isl_pw_aff *pwaff1,
3859 __isl_take isl_pw_aff *pwaff2);
3860 __isl_give isl_pw_aff *isl_pw_aff_max(
3861 __isl_take isl_pw_aff *pwaff1,
3862 __isl_take isl_pw_aff *pwaff2);
3863 __isl_give isl_aff *isl_aff_sub(__isl_take isl_aff *aff1,
3864 __isl_take isl_aff *aff2);
3865 __isl_give isl_pw_aff *isl_pw_aff_sub(
3866 __isl_take isl_pw_aff *pwaff1,
3867 __isl_take isl_pw_aff *pwaff2);
3868 __isl_give isl_aff *isl_aff_neg(__isl_take isl_aff *aff);
3869 __isl_give isl_pw_aff *isl_pw_aff_neg(
3870 __isl_take isl_pw_aff *pwaff);
3871 __isl_give isl_aff *isl_aff_ceil(__isl_take isl_aff *aff);
3872 __isl_give isl_pw_aff *isl_pw_aff_ceil(
3873 __isl_take isl_pw_aff *pwaff);
3874 __isl_give isl_aff *isl_aff_floor(__isl_take isl_aff *aff);
3875 __isl_give isl_pw_aff *isl_pw_aff_floor(
3876 __isl_take isl_pw_aff *pwaff);
3877 __isl_give isl_aff *isl_aff_mod_val(__isl_take isl_aff *aff,
3878 __isl_take isl_val *mod);
3879 __isl_give isl_pw_aff *isl_pw_aff_mod_val(
3880 __isl_take isl_pw_aff *pa,
3881 __isl_take isl_val *mod);
3882 __isl_give isl_aff *isl_aff_scale_val(__isl_take isl_aff *aff,
3883 __isl_take isl_val *v);
3884 __isl_give isl_pw_aff *isl_pw_aff_scale_val(
3885 __isl_take isl_pw_aff *pa, __isl_take isl_val *v);
3886 __isl_give isl_aff *isl_aff_scale_down_ui(
3887 __isl_take isl_aff *aff, unsigned f);
3888 __isl_give isl_aff *isl_aff_scale_down_val(
3889 __isl_take isl_aff *aff, __isl_take isl_val *v);
3890 __isl_give isl_pw_aff *isl_pw_aff_scale_down_val(
3891 __isl_take isl_pw_aff *pa,
3892 __isl_take isl_val *f);
3894 __isl_give isl_pw_aff *isl_pw_aff_list_min(
3895 __isl_take isl_pw_aff_list *list);
3896 __isl_give isl_pw_aff *isl_pw_aff_list_max(
3897 __isl_take isl_pw_aff_list *list);
3899 __isl_give isl_pw_aff *isl_pw_aff_coalesce(
3900 __isl_take isl_pw_aff *pwqp);
3902 __isl_give isl_aff *isl_aff_align_params(
3903 __isl_take isl_aff *aff,
3904 __isl_take isl_space *model);
3905 __isl_give isl_pw_aff *isl_pw_aff_align_params(
3906 __isl_take isl_pw_aff *pwaff,
3907 __isl_take isl_space *model);
3909 __isl_give isl_aff *isl_aff_project_domain_on_params(
3910 __isl_take isl_aff *aff);
3911 __isl_give isl_pw_aff *isl_pw_aff_from_range(
3912 __isl_take isl_pw_aff *pwa);
3914 __isl_give isl_aff *isl_aff_gist_params(
3915 __isl_take isl_aff *aff,
3916 __isl_take isl_set *context);
3917 __isl_give isl_aff *isl_aff_gist(__isl_take isl_aff *aff,
3918 __isl_take isl_set *context);
3919 __isl_give isl_pw_aff *isl_pw_aff_gist_params(
3920 __isl_take isl_pw_aff *pwaff,
3921 __isl_take isl_set *context);
3922 __isl_give isl_pw_aff *isl_pw_aff_gist(
3923 __isl_take isl_pw_aff *pwaff,
3924 __isl_take isl_set *context);
3926 __isl_give isl_set *isl_pw_aff_domain(
3927 __isl_take isl_pw_aff *pwaff);
3928 __isl_give isl_set *isl_pw_aff_params(
3929 __isl_take isl_pw_aff *pwa);
3930 __isl_give isl_pw_aff *isl_pw_aff_intersect_domain(
3931 __isl_take isl_pw_aff *pa,
3932 __isl_take isl_set *set);
3933 __isl_give isl_pw_aff *isl_pw_aff_intersect_params(
3934 __isl_take isl_pw_aff *pa,
3935 __isl_take isl_set *set);
3937 __isl_give isl_aff *isl_aff_mul(__isl_take isl_aff *aff1,
3938 __isl_take isl_aff *aff2);
3939 __isl_give isl_aff *isl_aff_div(__isl_take isl_aff *aff1,
3940 __isl_take isl_aff *aff2);
3941 __isl_give isl_pw_aff *isl_pw_aff_mul(
3942 __isl_take isl_pw_aff *pwaff1,
3943 __isl_take isl_pw_aff *pwaff2);
3944 __isl_give isl_pw_aff *isl_pw_aff_div(
3945 __isl_take isl_pw_aff *pa1,
3946 __isl_take isl_pw_aff *pa2);
3947 __isl_give isl_pw_aff *isl_pw_aff_tdiv_q(
3948 __isl_take isl_pw_aff *pa1,
3949 __isl_take isl_pw_aff *pa2);
3950 __isl_give isl_pw_aff *isl_pw_aff_tdiv_r(
3951 __isl_take isl_pw_aff *pa1,
3952 __isl_take isl_pw_aff *pa2);
3954 When multiplying two affine expressions, at least one of the two needs
3955 to be a constant. Similarly, when dividing an affine expression by another,
3956 the second expression needs to be a constant.
3957 C<isl_pw_aff_tdiv_q> computes the quotient of an integer division with
3958 rounding towards zero. C<isl_pw_aff_tdiv_r> computes the corresponding
3961 #include <isl/aff.h>
3962 __isl_give isl_aff *isl_aff_pullback_aff(
3963 __isl_take isl_aff *aff1,
3964 __isl_take isl_aff *aff2);
3965 __isl_give isl_aff *isl_aff_pullback_multi_aff(
3966 __isl_take isl_aff *aff,
3967 __isl_take isl_multi_aff *ma);
3968 __isl_give isl_pw_aff *isl_pw_aff_pullback_multi_aff(
3969 __isl_take isl_pw_aff *pa,
3970 __isl_take isl_multi_aff *ma);
3971 __isl_give isl_pw_aff *isl_pw_aff_pullback_pw_multi_aff(
3972 __isl_take isl_pw_aff *pa,
3973 __isl_take isl_pw_multi_aff *pma);
3975 These functions precompose the input expression by the given
3976 C<isl_aff>, C<isl_multi_aff> or C<isl_pw_multi_aff>. In other words,
3977 the C<isl_aff>, C<isl_multi_aff> or C<isl_pw_multi_aff> is plugged
3978 into the (piecewise) affine expression.
3979 Objects of type C<isl_multi_aff> are described in
3980 L</"Piecewise Multiple Quasi Affine Expressions">.
3982 #include <isl/aff.h>
3983 __isl_give isl_basic_set *isl_aff_zero_basic_set(
3984 __isl_take isl_aff *aff);
3985 __isl_give isl_basic_set *isl_aff_neg_basic_set(
3986 __isl_take isl_aff *aff);
3987 __isl_give isl_basic_set *isl_aff_le_basic_set(
3988 __isl_take isl_aff *aff1, __isl_take isl_aff *aff2);
3989 __isl_give isl_basic_set *isl_aff_ge_basic_set(
3990 __isl_take isl_aff *aff1, __isl_take isl_aff *aff2);
3991 __isl_give isl_set *isl_pw_aff_eq_set(
3992 __isl_take isl_pw_aff *pwaff1,
3993 __isl_take isl_pw_aff *pwaff2);
3994 __isl_give isl_set *isl_pw_aff_ne_set(
3995 __isl_take isl_pw_aff *pwaff1,
3996 __isl_take isl_pw_aff *pwaff2);
3997 __isl_give isl_set *isl_pw_aff_le_set(
3998 __isl_take isl_pw_aff *pwaff1,
3999 __isl_take isl_pw_aff *pwaff2);
4000 __isl_give isl_set *isl_pw_aff_lt_set(
4001 __isl_take isl_pw_aff *pwaff1,
4002 __isl_take isl_pw_aff *pwaff2);
4003 __isl_give isl_set *isl_pw_aff_ge_set(
4004 __isl_take isl_pw_aff *pwaff1,
4005 __isl_take isl_pw_aff *pwaff2);
4006 __isl_give isl_set *isl_pw_aff_gt_set(
4007 __isl_take isl_pw_aff *pwaff1,
4008 __isl_take isl_pw_aff *pwaff2);
4010 __isl_give isl_set *isl_pw_aff_list_eq_set(
4011 __isl_take isl_pw_aff_list *list1,
4012 __isl_take isl_pw_aff_list *list2);
4013 __isl_give isl_set *isl_pw_aff_list_ne_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_le_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_lt_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_ge_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_gt_set(
4026 __isl_take isl_pw_aff_list *list1,
4027 __isl_take isl_pw_aff_list *list2);
4029 The function C<isl_aff_neg_basic_set> returns a basic set
4030 containing those elements in the domain space
4031 of C<aff> where C<aff> is negative.
4032 The function C<isl_aff_ge_basic_set> returns a basic set
4033 containing those elements in the shared space
4034 of C<aff1> and C<aff2> where C<aff1> is greater than or equal to C<aff2>.
4035 The function C<isl_pw_aff_ge_set> returns a set
4036 containing those elements in the shared domain
4037 of C<pwaff1> and C<pwaff2> where C<pwaff1> is greater than or equal to C<pwaff2>.
4038 The functions operating on C<isl_pw_aff_list> apply the corresponding
4039 C<isl_pw_aff> function to each pair of elements in the two lists.
4041 #include <isl/aff.h>
4042 __isl_give isl_set *isl_pw_aff_nonneg_set(
4043 __isl_take isl_pw_aff *pwaff);
4044 __isl_give isl_set *isl_pw_aff_zero_set(
4045 __isl_take isl_pw_aff *pwaff);
4046 __isl_give isl_set *isl_pw_aff_non_zero_set(
4047 __isl_take isl_pw_aff *pwaff);
4049 The function C<isl_pw_aff_nonneg_set> returns a set
4050 containing those elements in the domain
4051 of C<pwaff> where C<pwaff> is non-negative.
4053 #include <isl/aff.h>
4054 __isl_give isl_pw_aff *isl_pw_aff_cond(
4055 __isl_take isl_pw_aff *cond,
4056 __isl_take isl_pw_aff *pwaff_true,
4057 __isl_take isl_pw_aff *pwaff_false);
4059 The function C<isl_pw_aff_cond> performs a conditional operator
4060 and returns an expression that is equal to C<pwaff_true>
4061 for elements where C<cond> is non-zero and equal to C<pwaff_false> for elements
4062 where C<cond> is zero.
4064 #include <isl/aff.h>
4065 __isl_give isl_pw_aff *isl_pw_aff_union_min(
4066 __isl_take isl_pw_aff *pwaff1,
4067 __isl_take isl_pw_aff *pwaff2);
4068 __isl_give isl_pw_aff *isl_pw_aff_union_max(
4069 __isl_take isl_pw_aff *pwaff1,
4070 __isl_take isl_pw_aff *pwaff2);
4071 __isl_give isl_pw_aff *isl_pw_aff_union_add(
4072 __isl_take isl_pw_aff *pwaff1,
4073 __isl_take isl_pw_aff *pwaff2);
4075 The function C<isl_pw_aff_union_max> computes a piecewise quasi-affine
4076 expression with a domain that is the union of those of C<pwaff1> and
4077 C<pwaff2> and such that on each cell, the quasi-affine expression is
4078 the maximum of those of C<pwaff1> and C<pwaff2>. If only one of
4079 C<pwaff1> or C<pwaff2> is defined on a given cell, then the
4080 associated expression is the defined one.
4082 An expression can be read from input using
4084 #include <isl/aff.h>
4085 __isl_give isl_aff *isl_aff_read_from_str(
4086 isl_ctx *ctx, const char *str);
4087 __isl_give isl_pw_aff *isl_pw_aff_read_from_str(
4088 isl_ctx *ctx, const char *str);
4090 An expression can be printed using
4092 #include <isl/aff.h>
4093 __isl_give isl_printer *isl_printer_print_aff(
4094 __isl_take isl_printer *p, __isl_keep isl_aff *aff);
4096 __isl_give isl_printer *isl_printer_print_pw_aff(
4097 __isl_take isl_printer *p,
4098 __isl_keep isl_pw_aff *pwaff);
4100 =head2 Piecewise Multiple Quasi Affine Expressions
4102 An C<isl_multi_aff> object represents a sequence of
4103 zero or more affine expressions, all defined on the same domain space.
4104 Similarly, an C<isl_multi_pw_aff> object represents a sequence of
4105 zero or more piecewise affine expressions.
4107 An C<isl_multi_aff> can be constructed from a single
4108 C<isl_aff> or an C<isl_aff_list> using the
4109 following functions. Similarly for C<isl_multi_pw_aff>
4110 and C<isl_pw_multi_aff>.
4112 #include <isl/aff.h>
4113 __isl_give isl_multi_aff *isl_multi_aff_from_aff(
4114 __isl_take isl_aff *aff);
4115 __isl_give isl_multi_pw_aff *
4116 isl_multi_pw_aff_from_multi_aff(
4117 __isl_take isl_multi_aff *ma);
4118 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_from_pw_aff(
4119 __isl_take isl_pw_aff *pa);
4120 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_from_pw_aff(
4121 __isl_take isl_pw_aff *pa);
4122 __isl_give isl_multi_aff *isl_multi_aff_from_aff_list(
4123 __isl_take isl_space *space,
4124 __isl_take isl_aff_list *list);
4126 An C<isl_multi_pw_aff> can be converted to an C<isl_pw_multi_aff>
4127 using the function C<isl_pw_multi_aff_from_multi_pw_aff> below.
4128 Note however that the domain
4129 of the result is the intersection of the domains of the input.
4130 The reverse conversion is exact.
4132 #include <isl/aff.h>
4133 __isl_give isl_pw_multi_aff *
4134 isl_pw_multi_aff_from_multi_pw_aff(
4135 __isl_take isl_multi_pw_aff *mpa);
4136 __isl_give isl_multi_pw_aff *
4137 isl_multi_pw_aff_from_pw_multi_aff(
4138 __isl_take isl_pw_multi_aff *pma);
4140 An empty piecewise multiple quasi affine expression (one with no cells),
4141 the zero piecewise multiple quasi affine expression (with value zero
4142 for each output dimension),
4143 a piecewise multiple quasi affine expression with a single cell (with
4144 either a universe or a specified domain) or
4145 a zero-dimensional piecewise multiple quasi affine expression
4147 can be created using the following functions.
4149 #include <isl/aff.h>
4150 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_empty(
4151 __isl_take isl_space *space);
4152 __isl_give isl_multi_aff *isl_multi_aff_zero(
4153 __isl_take isl_space *space);
4154 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_zero(
4155 __isl_take isl_space *space);
4156 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_zero(
4157 __isl_take isl_space *space);
4158 __isl_give isl_multi_aff *isl_multi_aff_identity(
4159 __isl_take isl_space *space);
4160 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_identity(
4161 __isl_take isl_space *space);
4162 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_identity(
4163 __isl_take isl_space *space);
4164 __isl_give isl_multi_aff *isl_multi_aff_domain_map(
4165 __isl_take isl_space *space);
4166 __isl_give isl_multi_aff *isl_multi_aff_range_map(
4167 __isl_take isl_space *space);
4168 __isl_give isl_multi_aff *isl_multi_aff_project_out_map(
4169 __isl_take isl_space *space,
4170 enum isl_dim_type type,
4171 unsigned first, unsigned n);
4172 __isl_give isl_pw_multi_aff *
4173 isl_pw_multi_aff_project_out_map(
4174 __isl_take isl_space *space,
4175 enum isl_dim_type type,
4176 unsigned first, unsigned n);
4177 __isl_give isl_pw_multi_aff *
4178 isl_pw_multi_aff_from_multi_aff(
4179 __isl_take isl_multi_aff *ma);
4180 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_alloc(
4181 __isl_take isl_set *set,
4182 __isl_take isl_multi_aff *maff);
4183 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_from_domain(
4184 __isl_take isl_set *set);
4186 __isl_give isl_union_pw_multi_aff *
4187 isl_union_pw_multi_aff_empty(
4188 __isl_take isl_space *space);
4189 __isl_give isl_union_pw_multi_aff *
4190 isl_union_pw_multi_aff_add_pw_multi_aff(
4191 __isl_take isl_union_pw_multi_aff *upma,
4192 __isl_take isl_pw_multi_aff *pma);
4193 __isl_give isl_union_pw_multi_aff *
4194 isl_union_pw_multi_aff_from_domain(
4195 __isl_take isl_union_set *uset);
4197 A piecewise multiple quasi affine expression can also be initialized
4198 from an C<isl_set> or C<isl_map>, provided the C<isl_set> is a singleton
4199 and the C<isl_map> is single-valued.
4200 In case of a conversion from an C<isl_union_set> or an C<isl_union_map>
4201 to an C<isl_union_pw_multi_aff>, these properties need to hold in each space.
4203 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_from_set(
4204 __isl_take isl_set *set);
4205 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_from_map(
4206 __isl_take isl_map *map);
4208 __isl_give isl_union_pw_multi_aff *
4209 isl_union_pw_multi_aff_from_union_set(
4210 __isl_take isl_union_set *uset);
4211 __isl_give isl_union_pw_multi_aff *
4212 isl_union_pw_multi_aff_from_union_map(
4213 __isl_take isl_union_map *umap);
4215 Multiple quasi affine expressions can be copied and freed using
4217 #include <isl/aff.h>
4218 __isl_give isl_multi_aff *isl_multi_aff_copy(
4219 __isl_keep isl_multi_aff *maff);
4220 void *isl_multi_aff_free(__isl_take isl_multi_aff *maff);
4222 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_copy(
4223 __isl_keep isl_pw_multi_aff *pma);
4224 void *isl_pw_multi_aff_free(
4225 __isl_take isl_pw_multi_aff *pma);
4227 __isl_give isl_union_pw_multi_aff *
4228 isl_union_pw_multi_aff_copy(
4229 __isl_keep isl_union_pw_multi_aff *upma);
4230 void *isl_union_pw_multi_aff_free(
4231 __isl_take isl_union_pw_multi_aff *upma);
4233 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_copy(
4234 __isl_keep isl_multi_pw_aff *mpa);
4235 void *isl_multi_pw_aff_free(
4236 __isl_take isl_multi_pw_aff *mpa);
4238 The expression can be inspected using
4240 #include <isl/aff.h>
4241 isl_ctx *isl_multi_aff_get_ctx(
4242 __isl_keep isl_multi_aff *maff);
4243 isl_ctx *isl_pw_multi_aff_get_ctx(
4244 __isl_keep isl_pw_multi_aff *pma);
4245 isl_ctx *isl_union_pw_multi_aff_get_ctx(
4246 __isl_keep isl_union_pw_multi_aff *upma);
4247 isl_ctx *isl_multi_pw_aff_get_ctx(
4248 __isl_keep isl_multi_pw_aff *mpa);
4249 unsigned isl_multi_aff_dim(__isl_keep isl_multi_aff *maff,
4250 enum isl_dim_type type);
4251 unsigned isl_pw_multi_aff_dim(
4252 __isl_keep isl_pw_multi_aff *pma,
4253 enum isl_dim_type type);
4254 unsigned isl_multi_pw_aff_dim(
4255 __isl_keep isl_multi_pw_aff *mpa,
4256 enum isl_dim_type type);
4257 __isl_give isl_aff *isl_multi_aff_get_aff(
4258 __isl_keep isl_multi_aff *multi, int pos);
4259 __isl_give isl_pw_aff *isl_pw_multi_aff_get_pw_aff(
4260 __isl_keep isl_pw_multi_aff *pma, int pos);
4261 __isl_give isl_pw_aff *isl_multi_pw_aff_get_pw_aff(
4262 __isl_keep isl_multi_pw_aff *mpa, int pos);
4263 int isl_multi_aff_find_dim_by_id(
4264 __isl_keep isl_multi_aff *ma,
4265 enum isl_dim_type type, __isl_keep isl_id *id);
4266 int isl_multi_pw_aff_find_dim_by_id(
4267 __isl_keep isl_multi_pw_aff *mpa,
4268 enum isl_dim_type type, __isl_keep isl_id *id);
4269 const char *isl_pw_multi_aff_get_dim_name(
4270 __isl_keep isl_pw_multi_aff *pma,
4271 enum isl_dim_type type, unsigned pos);
4272 __isl_give isl_id *isl_multi_aff_get_dim_id(
4273 __isl_keep isl_multi_aff *ma,
4274 enum isl_dim_type type, unsigned pos);
4275 __isl_give isl_id *isl_pw_multi_aff_get_dim_id(
4276 __isl_keep isl_pw_multi_aff *pma,
4277 enum isl_dim_type type, unsigned pos);
4278 __isl_give isl_id *isl_multi_pw_aff_get_dim_id(
4279 __isl_keep isl_multi_pw_aff *mpa,
4280 enum isl_dim_type type, unsigned pos);
4281 const char *isl_multi_aff_get_tuple_name(
4282 __isl_keep isl_multi_aff *multi,
4283 enum isl_dim_type type);
4284 int isl_pw_multi_aff_has_tuple_name(
4285 __isl_keep isl_pw_multi_aff *pma,
4286 enum isl_dim_type type);
4287 const char *isl_pw_multi_aff_get_tuple_name(
4288 __isl_keep isl_pw_multi_aff *pma,
4289 enum isl_dim_type type);
4290 int isl_multi_aff_has_tuple_id(__isl_keep isl_multi_aff *ma,
4291 enum isl_dim_type type);
4292 int isl_pw_multi_aff_has_tuple_id(
4293 __isl_keep isl_pw_multi_aff *pma,
4294 enum isl_dim_type type);
4295 int isl_multi_pw_aff_has_tuple_id(
4296 __isl_keep isl_multi_pw_aff *mpa,
4297 enum isl_dim_type type);
4298 __isl_give isl_id *isl_multi_aff_get_tuple_id(
4299 __isl_keep isl_multi_aff *ma,
4300 enum isl_dim_type type);
4301 __isl_give isl_id *isl_pw_multi_aff_get_tuple_id(
4302 __isl_keep isl_pw_multi_aff *pma,
4303 enum isl_dim_type type);
4304 __isl_give isl_id *isl_multi_pw_aff_get_tuple_id(
4305 __isl_keep isl_multi_pw_aff *mpa,
4306 enum isl_dim_type type);
4307 int isl_multi_aff_range_is_wrapping(
4308 __isl_keep isl_multi_aff *ma);
4309 int isl_multi_pw_aff_range_is_wrapping(
4310 __isl_keep isl_multi_pw_aff *mpa);
4312 int isl_pw_multi_aff_foreach_piece(
4313 __isl_keep isl_pw_multi_aff *pma,
4314 int (*fn)(__isl_take isl_set *set,
4315 __isl_take isl_multi_aff *maff,
4316 void *user), void *user);
4318 int isl_union_pw_multi_aff_foreach_pw_multi_aff(
4319 __isl_keep isl_union_pw_multi_aff *upma,
4320 int (*fn)(__isl_take isl_pw_multi_aff *pma,
4321 void *user), void *user);
4323 It can be modified using
4325 #include <isl/aff.h>
4326 __isl_give isl_multi_aff *isl_multi_aff_set_aff(
4327 __isl_take isl_multi_aff *multi, int pos,
4328 __isl_take isl_aff *aff);
4329 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_set_pw_aff(
4330 __isl_take isl_pw_multi_aff *pma, unsigned pos,
4331 __isl_take isl_pw_aff *pa);
4332 __isl_give isl_multi_aff *isl_multi_aff_set_dim_name(
4333 __isl_take isl_multi_aff *maff,
4334 enum isl_dim_type type, unsigned pos, const char *s);
4335 __isl_give isl_multi_aff *isl_multi_aff_set_dim_id(
4336 __isl_take isl_multi_aff *maff,
4337 enum isl_dim_type type, unsigned pos,
4338 __isl_take isl_id *id);
4339 __isl_give isl_multi_aff *isl_multi_aff_set_tuple_name(
4340 __isl_take isl_multi_aff *maff,
4341 enum isl_dim_type type, const char *s);
4342 __isl_give isl_multi_aff *isl_multi_aff_set_tuple_id(
4343 __isl_take isl_multi_aff *maff,
4344 enum isl_dim_type type, __isl_take isl_id *id);
4345 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_set_tuple_id(
4346 __isl_take isl_pw_multi_aff *pma,
4347 enum isl_dim_type type, __isl_take isl_id *id);
4348 __isl_give isl_multi_aff *isl_multi_aff_reset_tuple_id(
4349 __isl_take isl_multi_aff *ma,
4350 enum isl_dim_type type);
4351 __isl_give isl_multi_pw_aff *
4352 isl_multi_pw_aff_reset_tuple_id(
4353 __isl_take isl_multi_pw_aff *mpa,
4354 enum isl_dim_type type);
4355 __isl_give isl_multi_aff *isl_multi_aff_reset_user(
4356 __isl_take isl_multi_aff *ma);
4357 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_reset_user(
4358 __isl_take isl_multi_pw_aff *mpa);
4360 __isl_give isl_multi_pw_aff *
4361 isl_multi_pw_aff_set_dim_name(
4362 __isl_take isl_multi_pw_aff *mpa,
4363 enum isl_dim_type type, unsigned pos, const char *s);
4364 __isl_give isl_multi_pw_aff *
4365 isl_multi_pw_aff_set_dim_id(
4366 __isl_take isl_multi_pw_aff *mpa,
4367 enum isl_dim_type type, unsigned pos,
4368 __isl_take isl_id *id);
4369 __isl_give isl_multi_pw_aff *
4370 isl_multi_pw_aff_set_tuple_name(
4371 __isl_take isl_multi_pw_aff *mpa,
4372 enum isl_dim_type type, const char *s);
4374 __isl_give isl_multi_aff *isl_multi_aff_insert_dims(
4375 __isl_take isl_multi_aff *ma,
4376 enum isl_dim_type type, unsigned first, unsigned n);
4377 __isl_give isl_multi_aff *isl_multi_aff_add_dims(
4378 __isl_take isl_multi_aff *ma,
4379 enum isl_dim_type type, unsigned n);
4380 __isl_give isl_multi_aff *isl_multi_aff_drop_dims(
4381 __isl_take isl_multi_aff *maff,
4382 enum isl_dim_type type, unsigned first, unsigned n);
4383 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_drop_dims(
4384 __isl_take isl_pw_multi_aff *pma,
4385 enum isl_dim_type type, unsigned first, unsigned n);
4387 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_insert_dims(
4388 __isl_take isl_multi_pw_aff *mpa,
4389 enum isl_dim_type type, unsigned first, unsigned n);
4390 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_add_dims(
4391 __isl_take isl_multi_pw_aff *mpa,
4392 enum isl_dim_type type, unsigned n);
4393 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_move_dims(
4394 __isl_take isl_multi_pw_aff *pma,
4395 enum isl_dim_type dst_type, unsigned dst_pos,
4396 enum isl_dim_type src_type, unsigned src_pos,
4399 To check whether two multiple affine expressions are
4400 (obviously) equal to each other, use
4402 int isl_multi_aff_plain_is_equal(__isl_keep isl_multi_aff *maff1,
4403 __isl_keep isl_multi_aff *maff2);
4404 int isl_pw_multi_aff_plain_is_equal(
4405 __isl_keep isl_pw_multi_aff *pma1,
4406 __isl_keep isl_pw_multi_aff *pma2);
4407 int isl_multi_pw_aff_plain_is_equal(
4408 __isl_keep isl_multi_pw_aff *mpa1,
4409 __isl_keep isl_multi_pw_aff *mpa2);
4410 int isl_multi_pw_aff_is_equal(
4411 __isl_keep isl_multi_pw_aff *mpa1,
4412 __isl_keep isl_multi_pw_aff *mpa2);
4416 #include <isl/aff.h>
4417 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_union_lexmin(
4418 __isl_take isl_pw_multi_aff *pma1,
4419 __isl_take isl_pw_multi_aff *pma2);
4420 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_union_lexmax(
4421 __isl_take isl_pw_multi_aff *pma1,
4422 __isl_take isl_pw_multi_aff *pma2);
4423 __isl_give isl_multi_aff *isl_multi_aff_add(
4424 __isl_take isl_multi_aff *maff1,
4425 __isl_take isl_multi_aff *maff2);
4426 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_add(
4427 __isl_take isl_pw_multi_aff *pma1,
4428 __isl_take isl_pw_multi_aff *pma2);
4429 __isl_give isl_union_pw_multi_aff *isl_union_pw_multi_aff_add(
4430 __isl_take isl_union_pw_multi_aff *upma1,
4431 __isl_take isl_union_pw_multi_aff *upma2);
4432 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_union_add(
4433 __isl_take isl_pw_multi_aff *pma1,
4434 __isl_take isl_pw_multi_aff *pma2);
4435 __isl_give isl_multi_aff *isl_multi_aff_sub(
4436 __isl_take isl_multi_aff *ma1,
4437 __isl_take isl_multi_aff *ma2);
4438 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_sub(
4439 __isl_take isl_pw_multi_aff *pma1,
4440 __isl_take isl_pw_multi_aff *pma2);
4441 __isl_give isl_union_pw_multi_aff *isl_union_pw_multi_aff_sub(
4442 __isl_take isl_union_pw_multi_aff *upma1,
4443 __isl_take isl_union_pw_multi_aff *upma2);
4445 C<isl_multi_aff_sub> subtracts the second argument from the first.
4447 __isl_give isl_multi_aff *isl_multi_aff_scale_val(
4448 __isl_take isl_multi_aff *ma,
4449 __isl_take isl_val *v);
4450 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_scale_val(
4451 __isl_take isl_pw_multi_aff *pma,
4452 __isl_take isl_val *v);
4453 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_scale_val(
4454 __isl_take isl_multi_pw_aff *mpa,
4455 __isl_take isl_val *v);
4456 __isl_give isl_multi_aff *isl_multi_aff_scale_multi_val(
4457 __isl_take isl_multi_aff *ma,
4458 __isl_take isl_multi_val *mv);
4459 __isl_give isl_pw_multi_aff *
4460 isl_pw_multi_aff_scale_multi_val(
4461 __isl_take isl_pw_multi_aff *pma,
4462 __isl_take isl_multi_val *mv);
4463 __isl_give isl_multi_pw_aff *
4464 isl_multi_pw_aff_scale_multi_val(
4465 __isl_take isl_multi_pw_aff *mpa,
4466 __isl_take isl_multi_val *mv);
4467 __isl_give isl_union_pw_multi_aff *
4468 isl_union_pw_multi_aff_scale_multi_val(
4469 __isl_take isl_union_pw_multi_aff *upma,
4470 __isl_take isl_multi_val *mv);
4471 __isl_give isl_multi_aff *
4472 isl_multi_aff_scale_down_multi_val(
4473 __isl_take isl_multi_aff *ma,
4474 __isl_take isl_multi_val *mv);
4475 __isl_give isl_multi_pw_aff *
4476 isl_multi_pw_aff_scale_down_multi_val(
4477 __isl_take isl_multi_pw_aff *mpa,
4478 __isl_take isl_multi_val *mv);
4480 C<isl_multi_aff_scale_multi_val> scales the elements of C<ma>
4481 by the corresponding elements of C<mv>.
4483 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_fix_si(
4484 __isl_take isl_pw_multi_aff *pma,
4485 enum isl_dim_type type, unsigned pos, int value);
4486 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_intersect_params(
4487 __isl_take isl_pw_multi_aff *pma,
4488 __isl_take isl_set *set);
4489 __isl_give isl_set *isl_multi_pw_aff_domain(
4490 __isl_take isl_multi_pw_aff *mpa);
4491 __isl_give isl_multi_pw_aff *
4492 isl_multi_pw_aff_intersect_params(
4493 __isl_take isl_multi_pw_aff *mpa,
4494 __isl_take isl_set *set);
4495 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_intersect_domain(
4496 __isl_take isl_pw_multi_aff *pma,
4497 __isl_take isl_set *set);
4498 __isl_give isl_multi_pw_aff *
4499 isl_multi_pw_aff_intersect_domain(
4500 __isl_take isl_multi_pw_aff *mpa,
4501 __isl_take isl_set *domain);
4502 __isl_give isl_union_pw_multi_aff *
4503 isl_union_pw_multi_aff_intersect_domain(
4504 __isl_take isl_union_pw_multi_aff *upma,
4505 __isl_take isl_union_set *uset);
4506 __isl_give isl_multi_aff *isl_multi_aff_lift(
4507 __isl_take isl_multi_aff *maff,
4508 __isl_give isl_local_space **ls);
4509 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_coalesce(
4510 __isl_take isl_pw_multi_aff *pma);
4511 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_coalesce(
4512 __isl_take isl_multi_pw_aff *mpa);
4513 __isl_give isl_multi_aff *isl_multi_aff_align_params(
4514 __isl_take isl_multi_aff *multi,
4515 __isl_take isl_space *model);
4516 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_align_params(
4517 __isl_take isl_pw_multi_aff *pma,
4518 __isl_take isl_space *model);
4519 __isl_give isl_pw_multi_aff *
4520 isl_pw_multi_aff_project_domain_on_params(
4521 __isl_take isl_pw_multi_aff *pma);
4522 __isl_give isl_multi_aff *isl_multi_aff_gist_params(
4523 __isl_take isl_multi_aff *maff,
4524 __isl_take isl_set *context);
4525 __isl_give isl_multi_aff *isl_multi_aff_gist(
4526 __isl_take isl_multi_aff *maff,
4527 __isl_take isl_set *context);
4528 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_gist_params(
4529 __isl_take isl_pw_multi_aff *pma,
4530 __isl_take isl_set *set);
4531 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_gist(
4532 __isl_take isl_pw_multi_aff *pma,
4533 __isl_take isl_set *set);
4534 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_gist_params(
4535 __isl_take isl_multi_pw_aff *mpa,
4536 __isl_take isl_set *set);
4537 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_gist(
4538 __isl_take isl_multi_pw_aff *mpa,
4539 __isl_take isl_set *set);
4540 __isl_give isl_multi_aff *isl_multi_aff_from_range(
4541 __isl_take isl_multi_aff *ma);
4542 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_from_range(
4543 __isl_take isl_multi_pw_aff *mpa);
4544 __isl_give isl_set *isl_pw_multi_aff_domain(
4545 __isl_take isl_pw_multi_aff *pma);
4546 __isl_give isl_union_set *isl_union_pw_multi_aff_domain(
4547 __isl_take isl_union_pw_multi_aff *upma);
4548 __isl_give isl_multi_aff *isl_multi_aff_range_splice(
4549 __isl_take isl_multi_aff *ma1, unsigned pos,
4550 __isl_take isl_multi_aff *ma2);
4551 __isl_give isl_multi_aff *isl_multi_aff_splice(
4552 __isl_take isl_multi_aff *ma1,
4553 unsigned in_pos, unsigned out_pos,
4554 __isl_take isl_multi_aff *ma2);
4555 __isl_give isl_multi_aff *isl_multi_aff_range_product(
4556 __isl_take isl_multi_aff *ma1,
4557 __isl_take isl_multi_aff *ma2);
4558 __isl_give isl_multi_aff *
4559 isl_multi_aff_range_factor_domain(
4560 __isl_take isl_multi_aff *ma);
4561 __isl_give isl_multi_aff *
4562 isl_multi_aff_range_factor_range(
4563 __isl_take isl_multi_aff *ma);
4564 __isl_give isl_multi_aff *isl_multi_aff_flat_range_product(
4565 __isl_take isl_multi_aff *ma1,
4566 __isl_take isl_multi_aff *ma2);
4567 __isl_give isl_multi_aff *isl_multi_aff_product(
4568 __isl_take isl_multi_aff *ma1,
4569 __isl_take isl_multi_aff *ma2);
4570 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_product(
4571 __isl_take isl_multi_pw_aff *mpa1,
4572 __isl_take isl_multi_pw_aff *mpa2);
4573 __isl_give isl_pw_multi_aff *
4574 isl_pw_multi_aff_range_product(
4575 __isl_take isl_pw_multi_aff *pma1,
4576 __isl_take isl_pw_multi_aff *pma2);
4577 __isl_give isl_multi_pw_aff *
4578 isl_multi_pw_aff_range_factor_domain(
4579 __isl_take isl_multi_pw_aff *mpa);
4580 __isl_give isl_multi_pw_aff *
4581 isl_multi_pw_aff_range_factor_range(
4582 __isl_take isl_multi_pw_aff *mpa);
4583 __isl_give isl_pw_multi_aff *
4584 isl_pw_multi_aff_flat_range_product(
4585 __isl_take isl_pw_multi_aff *pma1,
4586 __isl_take isl_pw_multi_aff *pma2);
4587 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_product(
4588 __isl_take isl_pw_multi_aff *pma1,
4589 __isl_take isl_pw_multi_aff *pma2);
4590 __isl_give isl_union_pw_multi_aff *
4591 isl_union_pw_multi_aff_flat_range_product(
4592 __isl_take isl_union_pw_multi_aff *upma1,
4593 __isl_take isl_union_pw_multi_aff *upma2);
4594 __isl_give isl_multi_pw_aff *
4595 isl_multi_pw_aff_range_splice(
4596 __isl_take isl_multi_pw_aff *mpa1, unsigned pos,
4597 __isl_take isl_multi_pw_aff *mpa2);
4598 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_splice(
4599 __isl_take isl_multi_pw_aff *mpa1,
4600 unsigned in_pos, unsigned out_pos,
4601 __isl_take isl_multi_pw_aff *mpa2);
4602 __isl_give isl_multi_pw_aff *
4603 isl_multi_pw_aff_range_product(
4604 __isl_take isl_multi_pw_aff *mpa1,
4605 __isl_take isl_multi_pw_aff *mpa2);
4606 __isl_give isl_multi_pw_aff *
4607 isl_multi_pw_aff_flat_range_product(
4608 __isl_take isl_multi_pw_aff *mpa1,
4609 __isl_take isl_multi_pw_aff *mpa2);
4611 If the C<ls> argument of C<isl_multi_aff_lift> is not C<NULL>,
4612 then it is assigned the local space that lies at the basis of
4613 the lifting applied.
4615 #include <isl/aff.h>
4616 __isl_give isl_multi_aff *isl_multi_aff_pullback_multi_aff(
4617 __isl_take isl_multi_aff *ma1,
4618 __isl_take isl_multi_aff *ma2);
4619 __isl_give isl_pw_multi_aff *
4620 isl_pw_multi_aff_pullback_multi_aff(
4621 __isl_take isl_pw_multi_aff *pma,
4622 __isl_take isl_multi_aff *ma);
4623 __isl_give isl_multi_pw_aff *
4624 isl_multi_pw_aff_pullback_multi_aff(
4625 __isl_take isl_multi_pw_aff *mpa,
4626 __isl_take isl_multi_aff *ma);
4627 __isl_give isl_pw_multi_aff *
4628 isl_pw_multi_aff_pullback_pw_multi_aff(
4629 __isl_take isl_pw_multi_aff *pma1,
4630 __isl_take isl_pw_multi_aff *pma2);
4631 __isl_give isl_multi_pw_aff *
4632 isl_multi_pw_aff_pullback_pw_multi_aff(
4633 __isl_take isl_multi_pw_aff *mpa,
4634 __isl_take isl_pw_multi_aff *pma);
4635 __isl_give isl_multi_pw_aff *
4636 isl_multi_pw_aff_pullback_multi_pw_aff(
4637 __isl_take isl_multi_pw_aff *mpa1,
4638 __isl_take isl_multi_pw_aff *mpa2);
4640 The function C<isl_multi_aff_pullback_multi_aff> precomposes C<ma1> by C<ma2>.
4641 In other words, C<ma2> is plugged
4644 __isl_give isl_set *isl_multi_aff_lex_le_set(
4645 __isl_take isl_multi_aff *ma1,
4646 __isl_take isl_multi_aff *ma2);
4647 __isl_give isl_set *isl_multi_aff_lex_ge_set(
4648 __isl_take isl_multi_aff *ma1,
4649 __isl_take isl_multi_aff *ma2);
4651 The function C<isl_multi_aff_lex_le_set> returns a set
4652 containing those elements in the shared domain space
4653 where C<ma1> is lexicographically smaller than or
4656 An expression can be read from input using
4658 #include <isl/aff.h>
4659 __isl_give isl_multi_aff *isl_multi_aff_read_from_str(
4660 isl_ctx *ctx, const char *str);
4661 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_read_from_str(
4662 isl_ctx *ctx, const char *str);
4663 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_read_from_str(
4664 isl_ctx *ctx, const char *str);
4665 __isl_give isl_union_pw_multi_aff *
4666 isl_union_pw_multi_aff_read_from_str(
4667 isl_ctx *ctx, const char *str);
4669 An expression can be printed using
4671 #include <isl/aff.h>
4672 __isl_give isl_printer *isl_printer_print_multi_aff(
4673 __isl_take isl_printer *p,
4674 __isl_keep isl_multi_aff *maff);
4675 __isl_give isl_printer *isl_printer_print_pw_multi_aff(
4676 __isl_take isl_printer *p,
4677 __isl_keep isl_pw_multi_aff *pma);
4678 __isl_give isl_printer *isl_printer_print_union_pw_multi_aff(
4679 __isl_take isl_printer *p,
4680 __isl_keep isl_union_pw_multi_aff *upma);
4681 __isl_give isl_printer *isl_printer_print_multi_pw_aff(
4682 __isl_take isl_printer *p,
4683 __isl_keep isl_multi_pw_aff *mpa);
4687 Points are elements of a set. They can be used to construct
4688 simple sets (boxes) or they can be used to represent the
4689 individual elements of a set.
4690 The zero point (the origin) can be created using
4692 __isl_give isl_point *isl_point_zero(__isl_take isl_space *space);
4694 The coordinates of a point can be inspected, set and changed
4697 __isl_give isl_val *isl_point_get_coordinate_val(
4698 __isl_keep isl_point *pnt,
4699 enum isl_dim_type type, int pos);
4700 __isl_give isl_point *isl_point_set_coordinate_val(
4701 __isl_take isl_point *pnt,
4702 enum isl_dim_type type, int pos,
4703 __isl_take isl_val *v);
4705 __isl_give isl_point *isl_point_add_ui(
4706 __isl_take isl_point *pnt,
4707 enum isl_dim_type type, int pos, unsigned val);
4708 __isl_give isl_point *isl_point_sub_ui(
4709 __isl_take isl_point *pnt,
4710 enum isl_dim_type type, int pos, unsigned val);
4712 Other properties can be obtained using
4714 isl_ctx *isl_point_get_ctx(__isl_keep isl_point *pnt);
4716 Points can be copied or freed using
4718 __isl_give isl_point *isl_point_copy(
4719 __isl_keep isl_point *pnt);
4720 void isl_point_free(__isl_take isl_point *pnt);
4722 A singleton set can be created from a point using
4724 __isl_give isl_basic_set *isl_basic_set_from_point(
4725 __isl_take isl_point *pnt);
4726 __isl_give isl_set *isl_set_from_point(
4727 __isl_take isl_point *pnt);
4729 and a box can be created from two opposite extremal points using
4731 __isl_give isl_basic_set *isl_basic_set_box_from_points(
4732 __isl_take isl_point *pnt1,
4733 __isl_take isl_point *pnt2);
4734 __isl_give isl_set *isl_set_box_from_points(
4735 __isl_take isl_point *pnt1,
4736 __isl_take isl_point *pnt2);
4738 All elements of a B<bounded> (union) set can be enumerated using
4739 the following functions.
4741 int isl_set_foreach_point(__isl_keep isl_set *set,
4742 int (*fn)(__isl_take isl_point *pnt, void *user),
4744 int isl_union_set_foreach_point(__isl_keep isl_union_set *uset,
4745 int (*fn)(__isl_take isl_point *pnt, void *user),
4748 The function C<fn> is called for each integer point in
4749 C<set> with as second argument the last argument of
4750 the C<isl_set_foreach_point> call. The function C<fn>
4751 should return C<0> on success and C<-1> on failure.
4752 In the latter case, C<isl_set_foreach_point> will stop
4753 enumerating and return C<-1> as well.
4754 If the enumeration is performed successfully and to completion,
4755 then C<isl_set_foreach_point> returns C<0>.
4757 To obtain a single point of a (basic) set, use
4759 __isl_give isl_point *isl_basic_set_sample_point(
4760 __isl_take isl_basic_set *bset);
4761 __isl_give isl_point *isl_set_sample_point(
4762 __isl_take isl_set *set);
4764 If C<set> does not contain any (integer) points, then the
4765 resulting point will be ``void'', a property that can be
4768 int isl_point_is_void(__isl_keep isl_point *pnt);
4770 =head2 Piecewise Quasipolynomials
4772 A piecewise quasipolynomial is a particular kind of function that maps
4773 a parametric point to a rational value.
4774 More specifically, a quasipolynomial is a polynomial expression in greatest
4775 integer parts of affine expressions of parameters and variables.
4776 A piecewise quasipolynomial is a subdivision of a given parametric
4777 domain into disjoint cells with a quasipolynomial associated to
4778 each cell. The value of the piecewise quasipolynomial at a given
4779 point is the value of the quasipolynomial associated to the cell
4780 that contains the point. Outside of the union of cells,
4781 the value is assumed to be zero.
4782 For example, the piecewise quasipolynomial
4784 [n] -> { [x] -> ((1 + n) - x) : x <= n and x >= 0 }
4786 maps C<x> to C<1 + n - x> for values of C<x> between C<0> and C<n>.
4787 A given piecewise quasipolynomial has a fixed domain dimension.
4788 Union piecewise quasipolynomials are used to contain piecewise quasipolynomials
4789 defined over different domains.
4790 Piecewise quasipolynomials are mainly used by the C<barvinok>
4791 library for representing the number of elements in a parametric set or map.
4792 For example, the piecewise quasipolynomial above represents
4793 the number of points in the map
4795 [n] -> { [x] -> [y] : x,y >= 0 and 0 <= x + y <= n }
4797 =head3 Input and Output
4799 Piecewise quasipolynomials can be read from input using
4801 __isl_give isl_union_pw_qpolynomial *
4802 isl_union_pw_qpolynomial_read_from_str(
4803 isl_ctx *ctx, const char *str);
4805 Quasipolynomials and piecewise quasipolynomials can be printed
4806 using the following functions.
4808 __isl_give isl_printer *isl_printer_print_qpolynomial(
4809 __isl_take isl_printer *p,
4810 __isl_keep isl_qpolynomial *qp);
4812 __isl_give isl_printer *isl_printer_print_pw_qpolynomial(
4813 __isl_take isl_printer *p,
4814 __isl_keep isl_pw_qpolynomial *pwqp);
4816 __isl_give isl_printer *isl_printer_print_union_pw_qpolynomial(
4817 __isl_take isl_printer *p,
4818 __isl_keep isl_union_pw_qpolynomial *upwqp);
4820 The output format of the printer
4821 needs to be set to either C<ISL_FORMAT_ISL> or C<ISL_FORMAT_C>.
4822 For C<isl_printer_print_union_pw_qpolynomial>, only C<ISL_FORMAT_ISL>
4824 In case of printing in C<ISL_FORMAT_C>, the user may want
4825 to set the names of all dimensions
4827 __isl_give isl_qpolynomial *isl_qpolynomial_set_dim_name(
4828 __isl_take isl_qpolynomial *qp,
4829 enum isl_dim_type type, unsigned pos,
4831 __isl_give isl_pw_qpolynomial *
4832 isl_pw_qpolynomial_set_dim_name(
4833 __isl_take isl_pw_qpolynomial *pwqp,
4834 enum isl_dim_type type, unsigned pos,
4837 =head3 Creating New (Piecewise) Quasipolynomials
4839 Some simple quasipolynomials can be created using the following functions.
4840 More complicated quasipolynomials can be created by applying
4841 operations such as addition and multiplication
4842 on the resulting quasipolynomials
4844 __isl_give isl_qpolynomial *isl_qpolynomial_zero_on_domain(
4845 __isl_take isl_space *domain);
4846 __isl_give isl_qpolynomial *isl_qpolynomial_one_on_domain(
4847 __isl_take isl_space *domain);
4848 __isl_give isl_qpolynomial *isl_qpolynomial_infty_on_domain(
4849 __isl_take isl_space *domain);
4850 __isl_give isl_qpolynomial *isl_qpolynomial_neginfty_on_domain(
4851 __isl_take isl_space *domain);
4852 __isl_give isl_qpolynomial *isl_qpolynomial_nan_on_domain(
4853 __isl_take isl_space *domain);
4854 __isl_give isl_qpolynomial *isl_qpolynomial_val_on_domain(
4855 __isl_take isl_space *domain,
4856 __isl_take isl_val *val);
4857 __isl_give isl_qpolynomial *isl_qpolynomial_var_on_domain(
4858 __isl_take isl_space *domain,
4859 enum isl_dim_type type, unsigned pos);
4860 __isl_give isl_qpolynomial *isl_qpolynomial_from_aff(
4861 __isl_take isl_aff *aff);
4863 Note that the space in which a quasipolynomial lives is a map space
4864 with a one-dimensional range. The C<domain> argument in some of
4865 the functions above corresponds to the domain of this map space.
4867 The zero piecewise quasipolynomial or a piecewise quasipolynomial
4868 with a single cell can be created using the following functions.
4869 Multiple of these single cell piecewise quasipolynomials can
4870 be combined to create more complicated piecewise quasipolynomials.
4872 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_zero(
4873 __isl_take isl_space *space);
4874 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_alloc(
4875 __isl_take isl_set *set,
4876 __isl_take isl_qpolynomial *qp);
4877 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_from_qpolynomial(
4878 __isl_take isl_qpolynomial *qp);
4879 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_from_pw_aff(
4880 __isl_take isl_pw_aff *pwaff);
4882 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_zero(
4883 __isl_take isl_space *space);
4884 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_from_pw_qpolynomial(
4885 __isl_take isl_pw_qpolynomial *pwqp);
4886 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_add_pw_qpolynomial(
4887 __isl_take isl_union_pw_qpolynomial *upwqp,
4888 __isl_take isl_pw_qpolynomial *pwqp);
4890 Quasipolynomials can be copied and freed again using the following
4893 __isl_give isl_qpolynomial *isl_qpolynomial_copy(
4894 __isl_keep isl_qpolynomial *qp);
4895 void *isl_qpolynomial_free(__isl_take isl_qpolynomial *qp);
4897 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_copy(
4898 __isl_keep isl_pw_qpolynomial *pwqp);
4899 void *isl_pw_qpolynomial_free(
4900 __isl_take isl_pw_qpolynomial *pwqp);
4902 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_copy(
4903 __isl_keep isl_union_pw_qpolynomial *upwqp);
4904 void *isl_union_pw_qpolynomial_free(
4905 __isl_take isl_union_pw_qpolynomial *upwqp);
4907 =head3 Inspecting (Piecewise) Quasipolynomials
4909 To iterate over all piecewise quasipolynomials in a union
4910 piecewise quasipolynomial, use the following function
4912 int isl_union_pw_qpolynomial_foreach_pw_qpolynomial(
4913 __isl_keep isl_union_pw_qpolynomial *upwqp,
4914 int (*fn)(__isl_take isl_pw_qpolynomial *pwqp, void *user),
4917 To extract the piecewise quasipolynomial in a given space from a union, use
4919 __isl_give isl_pw_qpolynomial *
4920 isl_union_pw_qpolynomial_extract_pw_qpolynomial(
4921 __isl_keep isl_union_pw_qpolynomial *upwqp,
4922 __isl_take isl_space *space);
4924 To iterate over the cells in a piecewise quasipolynomial,
4925 use either of the following two functions
4927 int isl_pw_qpolynomial_foreach_piece(
4928 __isl_keep isl_pw_qpolynomial *pwqp,
4929 int (*fn)(__isl_take isl_set *set,
4930 __isl_take isl_qpolynomial *qp,
4931 void *user), void *user);
4932 int isl_pw_qpolynomial_foreach_lifted_piece(
4933 __isl_keep isl_pw_qpolynomial *pwqp,
4934 int (*fn)(__isl_take isl_set *set,
4935 __isl_take isl_qpolynomial *qp,
4936 void *user), void *user);
4938 As usual, the function C<fn> should return C<0> on success
4939 and C<-1> on failure. The difference between
4940 C<isl_pw_qpolynomial_foreach_piece> and
4941 C<isl_pw_qpolynomial_foreach_lifted_piece> is that
4942 C<isl_pw_qpolynomial_foreach_lifted_piece> will first
4943 compute unique representations for all existentially quantified
4944 variables and then turn these existentially quantified variables
4945 into extra set variables, adapting the associated quasipolynomial
4946 accordingly. This means that the C<set> passed to C<fn>
4947 will not have any existentially quantified variables, but that
4948 the dimensions of the sets may be different for different
4949 invocations of C<fn>.
4951 The constant term of a quasipolynomial can be extracted using
4953 __isl_give isl_val *isl_qpolynomial_get_constant_val(
4954 __isl_keep isl_qpolynomial *qp);
4956 To iterate over all terms in a quasipolynomial,
4959 int isl_qpolynomial_foreach_term(
4960 __isl_keep isl_qpolynomial *qp,
4961 int (*fn)(__isl_take isl_term *term,
4962 void *user), void *user);
4964 The terms themselves can be inspected and freed using
4967 unsigned isl_term_dim(__isl_keep isl_term *term,
4968 enum isl_dim_type type);
4969 __isl_give isl_val *isl_term_get_coefficient_val(
4970 __isl_keep isl_term *term);
4971 int isl_term_get_exp(__isl_keep isl_term *term,
4972 enum isl_dim_type type, unsigned pos);
4973 __isl_give isl_aff *isl_term_get_div(
4974 __isl_keep isl_term *term, unsigned pos);
4975 void isl_term_free(__isl_take isl_term *term);
4977 Each term is a product of parameters, set variables and
4978 integer divisions. The function C<isl_term_get_exp>
4979 returns the exponent of a given dimensions in the given term.
4981 =head3 Properties of (Piecewise) Quasipolynomials
4983 To check whether two union piecewise quasipolynomials are
4984 obviously equal, use
4986 int isl_union_pw_qpolynomial_plain_is_equal(
4987 __isl_keep isl_union_pw_qpolynomial *upwqp1,
4988 __isl_keep isl_union_pw_qpolynomial *upwqp2);
4990 =head3 Operations on (Piecewise) Quasipolynomials
4992 __isl_give isl_qpolynomial *isl_qpolynomial_scale_val(
4993 __isl_take isl_qpolynomial *qp,
4994 __isl_take isl_val *v);
4995 __isl_give isl_qpolynomial *isl_qpolynomial_neg(
4996 __isl_take isl_qpolynomial *qp);
4997 __isl_give isl_qpolynomial *isl_qpolynomial_add(
4998 __isl_take isl_qpolynomial *qp1,
4999 __isl_take isl_qpolynomial *qp2);
5000 __isl_give isl_qpolynomial *isl_qpolynomial_sub(
5001 __isl_take isl_qpolynomial *qp1,
5002 __isl_take isl_qpolynomial *qp2);
5003 __isl_give isl_qpolynomial *isl_qpolynomial_mul(
5004 __isl_take isl_qpolynomial *qp1,
5005 __isl_take isl_qpolynomial *qp2);
5006 __isl_give isl_qpolynomial *isl_qpolynomial_pow(
5007 __isl_take isl_qpolynomial *qp, unsigned exponent);
5009 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_fix_val(
5010 __isl_take isl_pw_qpolynomial *pwqp,
5011 enum isl_dim_type type, unsigned n,
5012 __isl_take isl_val *v);
5013 __isl_give isl_pw_qpolynomial *
5014 isl_pw_qpolynomial_scale_val(
5015 __isl_take isl_pw_qpolynomial *pwqp,
5016 __isl_take isl_val *v);
5017 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_add(
5018 __isl_take isl_pw_qpolynomial *pwqp1,
5019 __isl_take isl_pw_qpolynomial *pwqp2);
5020 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_sub(
5021 __isl_take isl_pw_qpolynomial *pwqp1,
5022 __isl_take isl_pw_qpolynomial *pwqp2);
5023 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_add_disjoint(
5024 __isl_take isl_pw_qpolynomial *pwqp1,
5025 __isl_take isl_pw_qpolynomial *pwqp2);
5026 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_neg(
5027 __isl_take isl_pw_qpolynomial *pwqp);
5028 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_mul(
5029 __isl_take isl_pw_qpolynomial *pwqp1,
5030 __isl_take isl_pw_qpolynomial *pwqp2);
5031 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_pow(
5032 __isl_take isl_pw_qpolynomial *pwqp, unsigned exponent);
5034 __isl_give isl_union_pw_qpolynomial *
5035 isl_union_pw_qpolynomial_scale_val(
5036 __isl_take isl_union_pw_qpolynomial *upwqp,
5037 __isl_take isl_val *v);
5038 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_add(
5039 __isl_take isl_union_pw_qpolynomial *upwqp1,
5040 __isl_take isl_union_pw_qpolynomial *upwqp2);
5041 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_sub(
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_mul(
5045 __isl_take isl_union_pw_qpolynomial *upwqp1,
5046 __isl_take isl_union_pw_qpolynomial *upwqp2);
5048 __isl_give isl_val *isl_pw_qpolynomial_eval(
5049 __isl_take isl_pw_qpolynomial *pwqp,
5050 __isl_take isl_point *pnt);
5052 __isl_give isl_val *isl_union_pw_qpolynomial_eval(
5053 __isl_take isl_union_pw_qpolynomial *upwqp,
5054 __isl_take isl_point *pnt);
5056 __isl_give isl_set *isl_pw_qpolynomial_domain(
5057 __isl_take isl_pw_qpolynomial *pwqp);
5058 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_intersect_domain(
5059 __isl_take isl_pw_qpolynomial *pwpq,
5060 __isl_take isl_set *set);
5061 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_intersect_params(
5062 __isl_take isl_pw_qpolynomial *pwpq,
5063 __isl_take isl_set *set);
5065 __isl_give isl_union_set *isl_union_pw_qpolynomial_domain(
5066 __isl_take isl_union_pw_qpolynomial *upwqp);
5067 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_intersect_domain(
5068 __isl_take isl_union_pw_qpolynomial *upwpq,
5069 __isl_take isl_union_set *uset);
5070 __isl_give isl_union_pw_qpolynomial *
5071 isl_union_pw_qpolynomial_intersect_params(
5072 __isl_take isl_union_pw_qpolynomial *upwpq,
5073 __isl_take isl_set *set);
5075 __isl_give isl_qpolynomial *isl_qpolynomial_align_params(
5076 __isl_take isl_qpolynomial *qp,
5077 __isl_take isl_space *model);
5079 __isl_give isl_qpolynomial *isl_qpolynomial_project_domain_on_params(
5080 __isl_take isl_qpolynomial *qp);
5081 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_project_domain_on_params(
5082 __isl_take isl_pw_qpolynomial *pwqp);
5084 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_coalesce(
5085 __isl_take isl_union_pw_qpolynomial *upwqp);
5087 __isl_give isl_qpolynomial *isl_qpolynomial_gist_params(
5088 __isl_take isl_qpolynomial *qp,
5089 __isl_take isl_set *context);
5090 __isl_give isl_qpolynomial *isl_qpolynomial_gist(
5091 __isl_take isl_qpolynomial *qp,
5092 __isl_take isl_set *context);
5094 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_gist_params(
5095 __isl_take isl_pw_qpolynomial *pwqp,
5096 __isl_take isl_set *context);
5097 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_gist(
5098 __isl_take isl_pw_qpolynomial *pwqp,
5099 __isl_take isl_set *context);
5101 __isl_give isl_union_pw_qpolynomial *
5102 isl_union_pw_qpolynomial_gist_params(
5103 __isl_take isl_union_pw_qpolynomial *upwqp,
5104 __isl_take isl_set *context);
5105 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_gist(
5106 __isl_take isl_union_pw_qpolynomial *upwqp,
5107 __isl_take isl_union_set *context);
5109 The gist operation applies the gist operation to each of
5110 the cells in the domain of the input piecewise quasipolynomial.
5111 The context is also exploited
5112 to simplify the quasipolynomials associated to each cell.
5114 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_to_polynomial(
5115 __isl_take isl_pw_qpolynomial *pwqp, int sign);
5116 __isl_give isl_union_pw_qpolynomial *
5117 isl_union_pw_qpolynomial_to_polynomial(
5118 __isl_take isl_union_pw_qpolynomial *upwqp, int sign);
5120 Approximate each quasipolynomial by a polynomial. If C<sign> is positive,
5121 the polynomial will be an overapproximation. If C<sign> is negative,
5122 it will be an underapproximation. If C<sign> is zero, the approximation
5123 will lie somewhere in between.
5125 =head2 Bounds on Piecewise Quasipolynomials and Piecewise Quasipolynomial Reductions
5127 A piecewise quasipolynomial reduction is a piecewise
5128 reduction (or fold) of quasipolynomials.
5129 In particular, the reduction can be maximum or a minimum.
5130 The objects are mainly used to represent the result of
5131 an upper or lower bound on a quasipolynomial over its domain,
5132 i.e., as the result of the following function.
5134 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_bound(
5135 __isl_take isl_pw_qpolynomial *pwqp,
5136 enum isl_fold type, int *tight);
5138 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_bound(
5139 __isl_take isl_union_pw_qpolynomial *upwqp,
5140 enum isl_fold type, int *tight);
5142 The C<type> argument may be either C<isl_fold_min> or C<isl_fold_max>.
5143 If C<tight> is not C<NULL>, then C<*tight> is set to C<1>
5144 is the returned bound is known be tight, i.e., for each value
5145 of the parameters there is at least
5146 one element in the domain that reaches the bound.
5147 If the domain of C<pwqp> is not wrapping, then the bound is computed
5148 over all elements in that domain and the result has a purely parametric
5149 domain. If the domain of C<pwqp> is wrapping, then the bound is
5150 computed over the range of the wrapped relation. The domain of the
5151 wrapped relation becomes the domain of the result.
5153 A (piecewise) quasipolynomial reduction can be copied or freed using the
5154 following functions.
5156 __isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_copy(
5157 __isl_keep isl_qpolynomial_fold *fold);
5158 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_copy(
5159 __isl_keep isl_pw_qpolynomial_fold *pwf);
5160 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_copy(
5161 __isl_keep isl_union_pw_qpolynomial_fold *upwf);
5162 void isl_qpolynomial_fold_free(
5163 __isl_take isl_qpolynomial_fold *fold);
5164 void *isl_pw_qpolynomial_fold_free(
5165 __isl_take isl_pw_qpolynomial_fold *pwf);
5166 void *isl_union_pw_qpolynomial_fold_free(
5167 __isl_take isl_union_pw_qpolynomial_fold *upwf);
5169 =head3 Printing Piecewise Quasipolynomial Reductions
5171 Piecewise quasipolynomial reductions can be printed
5172 using the following function.
5174 __isl_give isl_printer *isl_printer_print_pw_qpolynomial_fold(
5175 __isl_take isl_printer *p,
5176 __isl_keep isl_pw_qpolynomial_fold *pwf);
5177 __isl_give isl_printer *isl_printer_print_union_pw_qpolynomial_fold(
5178 __isl_take isl_printer *p,
5179 __isl_keep isl_union_pw_qpolynomial_fold *upwf);
5181 For C<isl_printer_print_pw_qpolynomial_fold>,
5182 output format of the printer
5183 needs to be set to either C<ISL_FORMAT_ISL> or C<ISL_FORMAT_C>.
5184 For C<isl_printer_print_union_pw_qpolynomial_fold>,
5185 output format of the printer
5186 needs to be set to C<ISL_FORMAT_ISL>.
5187 In case of printing in C<ISL_FORMAT_C>, the user may want
5188 to set the names of all dimensions
5190 __isl_give isl_pw_qpolynomial_fold *
5191 isl_pw_qpolynomial_fold_set_dim_name(
5192 __isl_take isl_pw_qpolynomial_fold *pwf,
5193 enum isl_dim_type type, unsigned pos,
5196 =head3 Inspecting (Piecewise) Quasipolynomial Reductions
5198 To iterate over all piecewise quasipolynomial reductions in a union
5199 piecewise quasipolynomial reduction, use the following function
5201 int isl_union_pw_qpolynomial_fold_foreach_pw_qpolynomial_fold(
5202 __isl_keep isl_union_pw_qpolynomial_fold *upwf,
5203 int (*fn)(__isl_take isl_pw_qpolynomial_fold *pwf,
5204 void *user), void *user);
5206 To iterate over the cells in a piecewise quasipolynomial reduction,
5207 use either of the following two functions
5209 int isl_pw_qpolynomial_fold_foreach_piece(
5210 __isl_keep isl_pw_qpolynomial_fold *pwf,
5211 int (*fn)(__isl_take isl_set *set,
5212 __isl_take isl_qpolynomial_fold *fold,
5213 void *user), void *user);
5214 int isl_pw_qpolynomial_fold_foreach_lifted_piece(
5215 __isl_keep isl_pw_qpolynomial_fold *pwf,
5216 int (*fn)(__isl_take isl_set *set,
5217 __isl_take isl_qpolynomial_fold *fold,
5218 void *user), void *user);
5220 See L<Inspecting (Piecewise) Quasipolynomials> for an explanation
5221 of the difference between these two functions.
5223 To iterate over all quasipolynomials in a reduction, use
5225 int isl_qpolynomial_fold_foreach_qpolynomial(
5226 __isl_keep isl_qpolynomial_fold *fold,
5227 int (*fn)(__isl_take isl_qpolynomial *qp,
5228 void *user), void *user);
5230 =head3 Properties of Piecewise Quasipolynomial Reductions
5232 To check whether two union piecewise quasipolynomial reductions are
5233 obviously equal, use
5235 int isl_union_pw_qpolynomial_fold_plain_is_equal(
5236 __isl_keep isl_union_pw_qpolynomial_fold *upwf1,
5237 __isl_keep isl_union_pw_qpolynomial_fold *upwf2);
5239 =head3 Operations on Piecewise Quasipolynomial Reductions
5241 __isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_scale_val(
5242 __isl_take isl_qpolynomial_fold *fold,
5243 __isl_take isl_val *v);
5244 __isl_give isl_pw_qpolynomial_fold *
5245 isl_pw_qpolynomial_fold_scale_val(
5246 __isl_take isl_pw_qpolynomial_fold *pwf,
5247 __isl_take isl_val *v);
5248 __isl_give isl_union_pw_qpolynomial_fold *
5249 isl_union_pw_qpolynomial_fold_scale_val(
5250 __isl_take isl_union_pw_qpolynomial_fold *upwf,
5251 __isl_take isl_val *v);
5253 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_add(
5254 __isl_take isl_pw_qpolynomial_fold *pwf1,
5255 __isl_take isl_pw_qpolynomial_fold *pwf2);
5257 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_fold(
5258 __isl_take isl_pw_qpolynomial_fold *pwf1,
5259 __isl_take isl_pw_qpolynomial_fold *pwf2);
5261 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_fold(
5262 __isl_take isl_union_pw_qpolynomial_fold *upwf1,
5263 __isl_take isl_union_pw_qpolynomial_fold *upwf2);
5265 __isl_give isl_val *isl_pw_qpolynomial_fold_eval(
5266 __isl_take isl_pw_qpolynomial_fold *pwf,
5267 __isl_take isl_point *pnt);
5269 __isl_give isl_val *isl_union_pw_qpolynomial_fold_eval(
5270 __isl_take isl_union_pw_qpolynomial_fold *upwf,
5271 __isl_take isl_point *pnt);
5273 __isl_give isl_pw_qpolynomial_fold *
5274 isl_pw_qpolynomial_fold_intersect_params(
5275 __isl_take isl_pw_qpolynomial_fold *pwf,
5276 __isl_take isl_set *set);
5278 __isl_give isl_union_set *isl_union_pw_qpolynomial_fold_domain(
5279 __isl_take isl_union_pw_qpolynomial_fold *upwf);
5280 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_intersect_domain(
5281 __isl_take isl_union_pw_qpolynomial_fold *upwf,
5282 __isl_take isl_union_set *uset);
5283 __isl_give isl_union_pw_qpolynomial_fold *
5284 isl_union_pw_qpolynomial_fold_intersect_params(
5285 __isl_take isl_union_pw_qpolynomial_fold *upwf,
5286 __isl_take isl_set *set);
5288 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_project_domain_on_params(
5289 __isl_take isl_pw_qpolynomial_fold *pwf);
5291 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_coalesce(
5292 __isl_take isl_pw_qpolynomial_fold *pwf);
5294 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_coalesce(
5295 __isl_take isl_union_pw_qpolynomial_fold *upwf);
5297 __isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_gist_params(
5298 __isl_take isl_qpolynomial_fold *fold,
5299 __isl_take isl_set *context);
5300 __isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_gist(
5301 __isl_take isl_qpolynomial_fold *fold,
5302 __isl_take isl_set *context);
5304 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_gist(
5305 __isl_take isl_pw_qpolynomial_fold *pwf,
5306 __isl_take isl_set *context);
5307 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_gist_params(
5308 __isl_take isl_pw_qpolynomial_fold *pwf,
5309 __isl_take isl_set *context);
5311 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_gist(
5312 __isl_take isl_union_pw_qpolynomial_fold *upwf,
5313 __isl_take isl_union_set *context);
5314 __isl_give isl_union_pw_qpolynomial_fold *
5315 isl_union_pw_qpolynomial_fold_gist_params(
5316 __isl_take isl_union_pw_qpolynomial_fold *upwf,
5317 __isl_take isl_set *context);
5319 The gist operation applies the gist operation to each of
5320 the cells in the domain of the input piecewise quasipolynomial reduction.
5321 In future, the operation will also exploit the context
5322 to simplify the quasipolynomial reductions associated to each cell.
5324 __isl_give isl_pw_qpolynomial_fold *
5325 isl_set_apply_pw_qpolynomial_fold(
5326 __isl_take isl_set *set,
5327 __isl_take isl_pw_qpolynomial_fold *pwf,
5329 __isl_give isl_pw_qpolynomial_fold *
5330 isl_map_apply_pw_qpolynomial_fold(
5331 __isl_take isl_map *map,
5332 __isl_take isl_pw_qpolynomial_fold *pwf,
5334 __isl_give isl_union_pw_qpolynomial_fold *
5335 isl_union_set_apply_union_pw_qpolynomial_fold(
5336 __isl_take isl_union_set *uset,
5337 __isl_take isl_union_pw_qpolynomial_fold *upwf,
5339 __isl_give isl_union_pw_qpolynomial_fold *
5340 isl_union_map_apply_union_pw_qpolynomial_fold(
5341 __isl_take isl_union_map *umap,
5342 __isl_take isl_union_pw_qpolynomial_fold *upwf,
5345 The functions taking a map
5346 compose the given map with the given piecewise quasipolynomial reduction.
5347 That is, compute a bound (of the same type as C<pwf> or C<upwf> itself)
5348 over all elements in the intersection of the range of the map
5349 and the domain of the piecewise quasipolynomial reduction
5350 as a function of an element in the domain of the map.
5351 The functions taking a set compute a bound over all elements in the
5352 intersection of the set and the domain of the
5353 piecewise quasipolynomial reduction.
5355 =head2 Parametric Vertex Enumeration
5357 The parametric vertex enumeration described in this section
5358 is mainly intended to be used internally and by the C<barvinok>
5361 #include <isl/vertices.h>
5362 __isl_give isl_vertices *isl_basic_set_compute_vertices(
5363 __isl_keep isl_basic_set *bset);
5365 The function C<isl_basic_set_compute_vertices> performs the
5366 actual computation of the parametric vertices and the chamber
5367 decomposition and store the result in an C<isl_vertices> object.
5368 This information can be queried by either iterating over all
5369 the vertices or iterating over all the chambers or cells
5370 and then iterating over all vertices that are active on the chamber.
5372 int isl_vertices_foreach_vertex(
5373 __isl_keep isl_vertices *vertices,
5374 int (*fn)(__isl_take isl_vertex *vertex, void *user),
5377 int isl_vertices_foreach_cell(
5378 __isl_keep isl_vertices *vertices,
5379 int (*fn)(__isl_take isl_cell *cell, void *user),
5381 int isl_cell_foreach_vertex(__isl_keep isl_cell *cell,
5382 int (*fn)(__isl_take isl_vertex *vertex, void *user),
5385 Other operations that can be performed on an C<isl_vertices> object are
5388 isl_ctx *isl_vertices_get_ctx(
5389 __isl_keep isl_vertices *vertices);
5390 int isl_vertices_get_n_vertices(
5391 __isl_keep isl_vertices *vertices);
5392 void isl_vertices_free(__isl_take isl_vertices *vertices);
5394 Vertices can be inspected and destroyed using the following functions.
5396 isl_ctx *isl_vertex_get_ctx(__isl_keep isl_vertex *vertex);
5397 int isl_vertex_get_id(__isl_keep isl_vertex *vertex);
5398 __isl_give isl_basic_set *isl_vertex_get_domain(
5399 __isl_keep isl_vertex *vertex);
5400 __isl_give isl_basic_set *isl_vertex_get_expr(
5401 __isl_keep isl_vertex *vertex);
5402 void isl_vertex_free(__isl_take isl_vertex *vertex);
5404 C<isl_vertex_get_expr> returns a singleton parametric set describing
5405 the vertex, while C<isl_vertex_get_domain> returns the activity domain
5407 Note that C<isl_vertex_get_domain> and C<isl_vertex_get_expr> return
5408 B<rational> basic sets, so they should mainly be used for inspection
5409 and should not be mixed with integer sets.
5411 Chambers can be inspected and destroyed using the following functions.
5413 isl_ctx *isl_cell_get_ctx(__isl_keep isl_cell *cell);
5414 __isl_give isl_basic_set *isl_cell_get_domain(
5415 __isl_keep isl_cell *cell);
5416 void isl_cell_free(__isl_take isl_cell *cell);
5418 =head1 Polyhedral Compilation Library
5420 This section collects functionality in C<isl> that has been specifically
5421 designed for use during polyhedral compilation.
5423 =head2 Dependence Analysis
5425 C<isl> contains specialized functionality for performing
5426 array dataflow analysis. That is, given a I<sink> access relation
5427 and a collection of possible I<source> access relations,
5428 C<isl> can compute relations that describe
5429 for each iteration of the sink access, which iteration
5430 of which of the source access relations was the last
5431 to access the same data element before the given iteration
5433 The resulting dependence relations map source iterations
5434 to the corresponding sink iterations.
5435 To compute standard flow dependences, the sink should be
5436 a read, while the sources should be writes.
5437 If any of the source accesses are marked as being I<may>
5438 accesses, then there will be a dependence from the last
5439 I<must> access B<and> from any I<may> access that follows
5440 this last I<must> access.
5441 In particular, if I<all> sources are I<may> accesses,
5442 then memory based dependence analysis is performed.
5443 If, on the other hand, all sources are I<must> accesses,
5444 then value based dependence analysis is performed.
5446 #include <isl/flow.h>
5448 typedef int (*isl_access_level_before)(void *first, void *second);
5450 __isl_give isl_access_info *isl_access_info_alloc(
5451 __isl_take isl_map *sink,
5452 void *sink_user, isl_access_level_before fn,
5454 __isl_give isl_access_info *isl_access_info_add_source(
5455 __isl_take isl_access_info *acc,
5456 __isl_take isl_map *source, int must,
5458 void *isl_access_info_free(__isl_take isl_access_info *acc);
5460 __isl_give isl_flow *isl_access_info_compute_flow(
5461 __isl_take isl_access_info *acc);
5463 int isl_flow_foreach(__isl_keep isl_flow *deps,
5464 int (*fn)(__isl_take isl_map *dep, int must,
5465 void *dep_user, void *user),
5467 __isl_give isl_map *isl_flow_get_no_source(
5468 __isl_keep isl_flow *deps, int must);
5469 void isl_flow_free(__isl_take isl_flow *deps);
5471 The function C<isl_access_info_compute_flow> performs the actual
5472 dependence analysis. The other functions are used to construct
5473 the input for this function or to read off the output.
5475 The input is collected in an C<isl_access_info>, which can
5476 be created through a call to C<isl_access_info_alloc>.
5477 The arguments to this functions are the sink access relation
5478 C<sink>, a token C<sink_user> used to identify the sink
5479 access to the user, a callback function for specifying the
5480 relative order of source and sink accesses, and the number
5481 of source access relations that will be added.
5482 The callback function has type C<int (*)(void *first, void *second)>.
5483 The function is called with two user supplied tokens identifying
5484 either a source or the sink and it should return the shared nesting
5485 level and the relative order of the two accesses.
5486 In particular, let I<n> be the number of loops shared by
5487 the two accesses. If C<first> precedes C<second> textually,
5488 then the function should return I<2 * n + 1>; otherwise,
5489 it should return I<2 * n>.
5490 The sources can be added to the C<isl_access_info> by performing
5491 (at most) C<max_source> calls to C<isl_access_info_add_source>.
5492 C<must> indicates whether the source is a I<must> access
5493 or a I<may> access. Note that a multi-valued access relation
5494 should only be marked I<must> if every iteration in the domain
5495 of the relation accesses I<all> elements in its image.
5496 The C<source_user> token is again used to identify
5497 the source access. The range of the source access relation
5498 C<source> should have the same dimension as the range
5499 of the sink access relation.
5500 The C<isl_access_info_free> function should usually not be
5501 called explicitly, because it is called implicitly by
5502 C<isl_access_info_compute_flow>.
5504 The result of the dependence analysis is collected in an
5505 C<isl_flow>. There may be elements of
5506 the sink access for which no preceding source access could be
5507 found or for which all preceding sources are I<may> accesses.
5508 The relations containing these elements can be obtained through
5509 calls to C<isl_flow_get_no_source>, the first with C<must> set
5510 and the second with C<must> unset.
5511 In the case of standard flow dependence analysis,
5512 with the sink a read and the sources I<must> writes,
5513 the first relation corresponds to the reads from uninitialized
5514 array elements and the second relation is empty.
5515 The actual flow dependences can be extracted using
5516 C<isl_flow_foreach>. This function will call the user-specified
5517 callback function C<fn> for each B<non-empty> dependence between
5518 a source and the sink. The callback function is called
5519 with four arguments, the actual flow dependence relation
5520 mapping source iterations to sink iterations, a boolean that
5521 indicates whether it is a I<must> or I<may> dependence, a token
5522 identifying the source and an additional C<void *> with value
5523 equal to the third argument of the C<isl_flow_foreach> call.
5524 A dependence is marked I<must> if it originates from a I<must>
5525 source and if it is not followed by any I<may> sources.
5527 After finishing with an C<isl_flow>, the user should call
5528 C<isl_flow_free> to free all associated memory.
5530 A higher-level interface to dependence analysis is provided
5531 by the following function.
5533 #include <isl/flow.h>
5535 int isl_union_map_compute_flow(__isl_take isl_union_map *sink,
5536 __isl_take isl_union_map *must_source,
5537 __isl_take isl_union_map *may_source,
5538 __isl_take isl_union_map *schedule,
5539 __isl_give isl_union_map **must_dep,
5540 __isl_give isl_union_map **may_dep,
5541 __isl_give isl_union_map **must_no_source,
5542 __isl_give isl_union_map **may_no_source);
5544 The arrays are identified by the tuple names of the ranges
5545 of the accesses. The iteration domains by the tuple names
5546 of the domains of the accesses and of the schedule.
5547 The relative order of the iteration domains is given by the
5548 schedule. The relations returned through C<must_no_source>
5549 and C<may_no_source> are subsets of C<sink>.
5550 Any of C<must_dep>, C<may_dep>, C<must_no_source>
5551 or C<may_no_source> may be C<NULL>, but a C<NULL> value for
5552 any of the other arguments is treated as an error.
5554 =head3 Interaction with Dependence Analysis
5556 During the dependence analysis, we frequently need to perform
5557 the following operation. Given a relation between sink iterations
5558 and potential source iterations from a particular source domain,
5559 what is the last potential source iteration corresponding to each
5560 sink iteration. It can sometimes be convenient to adjust
5561 the set of potential source iterations before or after each such operation.
5562 The prototypical example is fuzzy array dataflow analysis,
5563 where we need to analyze if, based on data-dependent constraints,
5564 the sink iteration can ever be executed without one or more of
5565 the corresponding potential source iterations being executed.
5566 If so, we can introduce extra parameters and select an unknown
5567 but fixed source iteration from the potential source iterations.
5568 To be able to perform such manipulations, C<isl> provides the following
5571 #include <isl/flow.h>
5573 typedef __isl_give isl_restriction *(*isl_access_restrict)(
5574 __isl_keep isl_map *source_map,
5575 __isl_keep isl_set *sink, void *source_user,
5577 __isl_give isl_access_info *isl_access_info_set_restrict(
5578 __isl_take isl_access_info *acc,
5579 isl_access_restrict fn, void *user);
5581 The function C<isl_access_info_set_restrict> should be called
5582 before calling C<isl_access_info_compute_flow> and registers a callback function
5583 that will be called any time C<isl> is about to compute the last
5584 potential source. The first argument is the (reverse) proto-dependence,
5585 mapping sink iterations to potential source iterations.
5586 The second argument represents the sink iterations for which
5587 we want to compute the last source iteration.
5588 The third argument is the token corresponding to the source
5589 and the final argument is the token passed to C<isl_access_info_set_restrict>.
5590 The callback is expected to return a restriction on either the input or
5591 the output of the operation computing the last potential source.
5592 If the input needs to be restricted then restrictions are needed
5593 for both the source and the sink iterations. The sink iterations
5594 and the potential source iterations will be intersected with these sets.
5595 If the output needs to be restricted then only a restriction on the source
5596 iterations is required.
5597 If any error occurs, the callback should return C<NULL>.
5598 An C<isl_restriction> object can be created, freed and inspected
5599 using the following functions.
5601 #include <isl/flow.h>
5603 __isl_give isl_restriction *isl_restriction_input(
5604 __isl_take isl_set *source_restr,
5605 __isl_take isl_set *sink_restr);
5606 __isl_give isl_restriction *isl_restriction_output(
5607 __isl_take isl_set *source_restr);
5608 __isl_give isl_restriction *isl_restriction_none(
5609 __isl_take isl_map *source_map);
5610 __isl_give isl_restriction *isl_restriction_empty(
5611 __isl_take isl_map *source_map);
5612 void *isl_restriction_free(
5613 __isl_take isl_restriction *restr);
5614 isl_ctx *isl_restriction_get_ctx(
5615 __isl_keep isl_restriction *restr);
5617 C<isl_restriction_none> and C<isl_restriction_empty> are special
5618 cases of C<isl_restriction_input>. C<isl_restriction_none>
5619 is essentially equivalent to
5621 isl_restriction_input(isl_set_universe(
5622 isl_space_range(isl_map_get_space(source_map))),
5624 isl_space_domain(isl_map_get_space(source_map))));
5626 whereas C<isl_restriction_empty> is essentially equivalent to
5628 isl_restriction_input(isl_set_empty(
5629 isl_space_range(isl_map_get_space(source_map))),
5631 isl_space_domain(isl_map_get_space(source_map))));
5635 B<The functionality described in this section is fairly new
5636 and may be subject to change.>
5638 #include <isl/schedule.h>
5639 __isl_give isl_schedule *
5640 isl_schedule_constraints_compute_schedule(
5641 __isl_take isl_schedule_constraints *sc);
5642 void *isl_schedule_free(__isl_take isl_schedule *sched);
5644 The function C<isl_schedule_constraints_compute_schedule> can be
5645 used to compute a schedule that satisfy the given schedule constraints.
5646 These schedule constraints include the iteration domain for which
5647 a schedule should be computed and dependences between pairs of
5648 iterations. In particular, these dependences include
5649 I<validity> dependences and I<proximity> dependences.
5650 By default, the algorithm used to construct the schedule is similar
5651 to that of C<Pluto>.
5652 Alternatively, Feautrier's multi-dimensional scheduling algorithm can
5654 The generated schedule respects all validity dependences.
5655 That is, all dependence distances over these dependences in the
5656 scheduled space are lexicographically positive.
5657 The default algorithm tries to ensure that the dependence distances
5658 over coincidence constraints are zero and to minimize the
5659 dependence distances over proximity dependences.
5660 Moreover, it tries to obtain sequences (bands) of schedule dimensions
5661 for groups of domains where the dependence distances over validity
5662 dependences have only non-negative values.
5663 When using Feautrier's algorithm, the coincidence and proximity constraints
5664 are only taken into account during the extension to a
5665 full-dimensional schedule.
5667 An C<isl_schedule_constraints> object can be constructed
5668 and manipulated using the following functions.
5670 #include <isl/schedule.h>
5671 __isl_give isl_schedule_constraints *
5672 isl_schedule_constraints_on_domain(
5673 __isl_take isl_union_set *domain);
5674 isl_ctx *isl_schedule_constraints_get_ctx(
5675 __isl_keep isl_schedule_constraints *sc);
5676 __isl_give isl_schedule_constraints *
5677 isl_schedule_constraints_set_validity(
5678 __isl_take isl_schedule_constraints *sc,
5679 __isl_take isl_union_map *validity);
5680 __isl_give isl_schedule_constraints *
5681 isl_schedule_constraints_set_coincidence(
5682 __isl_take isl_schedule_constraints *sc,
5683 __isl_take isl_union_map *coincidence);
5684 __isl_give isl_schedule_constraints *
5685 isl_schedule_constraints_set_proximity(
5686 __isl_take isl_schedule_constraints *sc,
5687 __isl_take isl_union_map *proximity);
5688 __isl_give isl_schedule_constraints *
5689 isl_schedule_constraints_set_conditional_validity(
5690 __isl_take isl_schedule_constraints *sc,
5691 __isl_take isl_union_map *condition,
5692 __isl_take isl_union_map *validity);
5693 void *isl_schedule_constraints_free(
5694 __isl_take isl_schedule_constraints *sc);
5696 The initial C<isl_schedule_constraints> object created by
5697 C<isl_schedule_constraints_on_domain> does not impose any constraints.
5698 That is, it has an empty set of dependences.
5699 The function C<isl_schedule_constraints_set_validity> replaces the
5700 validity dependences, mapping domain elements I<i> to domain
5701 elements that should be scheduled after I<i>.
5702 The function C<isl_schedule_constraints_set_coincidence> replaces the
5703 coincidence dependences, mapping domain elements I<i> to domain
5704 elements that should be scheduled together with I<I>, if possible.
5705 The function C<isl_schedule_constraints_set_proximity> replaces the
5706 proximity dependences, mapping domain elements I<i> to domain
5707 elements that should be scheduled either before I<I>
5708 or as early as possible after I<i>.
5710 The function C<isl_schedule_constraints_set_conditional_validity>
5711 replaces the conditional validity constraints.
5712 A conditional validity constraint is only imposed when any of the corresponding
5713 conditions is satisfied, i.e., when any of them is non-zero.
5714 That is, the scheduler ensures that within each band if the dependence
5715 distances over the condition constraints are not all zero
5716 then all corresponding conditional validity constraints are respected.
5717 A conditional validity constraint corresponds to a condition
5718 if the two are adjacent, i.e., if the domain of one relation intersect
5719 the range of the other relation.
5720 The typical use case of conditional validity constraints is
5721 to allow order constraints between live ranges to be violated
5722 as long as the live ranges themselves are local to the band.
5723 To allow more fine-grained control over which conditions correspond
5724 to which conditional validity constraints, the domains and ranges
5725 of these relations may include I<tags>. That is, the domains and
5726 ranges of those relation may themselves be wrapped relations
5727 where the iteration domain appears in the domain of those wrapped relations
5728 and the range of the wrapped relations can be arbitrarily chosen
5729 by the user. Conditions and conditional validity constraints are only
5730 considere adjacent to each other if the entire wrapped relation matches.
5731 In particular, a relation with a tag will never be considered adjacent
5732 to a relation without a tag.
5734 The following function computes a schedule directly from
5735 an iteration domain and validity and proximity dependences
5736 and is implemented in terms of the functions described above.
5737 The use of C<isl_union_set_compute_schedule> is discouraged.
5739 #include <isl/schedule.h>
5740 __isl_give isl_schedule *isl_union_set_compute_schedule(
5741 __isl_take isl_union_set *domain,
5742 __isl_take isl_union_map *validity,
5743 __isl_take isl_union_map *proximity);
5745 A mapping from the domains to the scheduled space can be obtained
5746 from an C<isl_schedule> using the following function.
5748 __isl_give isl_union_map *isl_schedule_get_map(
5749 __isl_keep isl_schedule *sched);
5751 A representation of the schedule can be printed using
5753 __isl_give isl_printer *isl_printer_print_schedule(
5754 __isl_take isl_printer *p,
5755 __isl_keep isl_schedule *schedule);
5757 A representation of the schedule as a forest of bands can be obtained
5758 using the following function.
5760 __isl_give isl_band_list *isl_schedule_get_band_forest(
5761 __isl_keep isl_schedule *schedule);
5763 The individual bands can be visited in depth-first post-order
5764 using the following function.
5766 #include <isl/schedule.h>
5767 int isl_schedule_foreach_band(
5768 __isl_keep isl_schedule *sched,
5769 int (*fn)(__isl_keep isl_band *band, void *user),
5772 The list can be manipulated as explained in L<"Lists">.
5773 The bands inside the list can be copied and freed using the following
5776 #include <isl/band.h>
5777 __isl_give isl_band *isl_band_copy(
5778 __isl_keep isl_band *band);
5779 void *isl_band_free(__isl_take isl_band *band);
5781 Each band contains zero or more scheduling dimensions.
5782 These are referred to as the members of the band.
5783 The section of the schedule that corresponds to the band is
5784 referred to as the partial schedule of the band.
5785 For those nodes that participate in a band, the outer scheduling
5786 dimensions form the prefix schedule, while the inner scheduling
5787 dimensions form the suffix schedule.
5788 That is, if we take a cut of the band forest, then the union of
5789 the concatenations of the prefix, partial and suffix schedules of
5790 each band in the cut is equal to the entire schedule (modulo
5791 some possible padding at the end with zero scheduling dimensions).
5792 The properties of a band can be inspected using the following functions.
5794 #include <isl/band.h>
5795 isl_ctx *isl_band_get_ctx(__isl_keep isl_band *band);
5797 int isl_band_has_children(__isl_keep isl_band *band);
5798 __isl_give isl_band_list *isl_band_get_children(
5799 __isl_keep isl_band *band);
5801 __isl_give isl_union_map *isl_band_get_prefix_schedule(
5802 __isl_keep isl_band *band);
5803 __isl_give isl_union_map *isl_band_get_partial_schedule(
5804 __isl_keep isl_band *band);
5805 __isl_give isl_union_map *isl_band_get_suffix_schedule(
5806 __isl_keep isl_band *band);
5808 int isl_band_n_member(__isl_keep isl_band *band);
5809 int isl_band_member_is_coincident(
5810 __isl_keep isl_band *band, int pos);
5812 int isl_band_list_foreach_band(
5813 __isl_keep isl_band_list *list,
5814 int (*fn)(__isl_keep isl_band *band, void *user),
5817 Note that a scheduling dimension is considered to be ``coincident''
5818 if it satisfies the coincidence constraints within its band.
5819 That is, if the dependence distances of the coincidence
5820 constraints are all zero in that direction (for fixed
5821 iterations of outer bands).
5822 Like C<isl_schedule_foreach_band>,
5823 the function C<isl_band_list_foreach_band> calls C<fn> on the bands
5824 in depth-first post-order.
5826 A band can be tiled using the following function.
5828 #include <isl/band.h>
5829 int isl_band_tile(__isl_keep isl_band *band,
5830 __isl_take isl_vec *sizes);
5832 int isl_options_set_tile_scale_tile_loops(isl_ctx *ctx,
5834 int isl_options_get_tile_scale_tile_loops(isl_ctx *ctx);
5835 int isl_options_set_tile_shift_point_loops(isl_ctx *ctx,
5837 int isl_options_get_tile_shift_point_loops(isl_ctx *ctx);
5839 The C<isl_band_tile> function tiles the band using the given tile sizes
5840 inside its schedule.
5841 A new child band is created to represent the point loops and it is
5842 inserted between the modified band and its children.
5843 The C<tile_scale_tile_loops> option specifies whether the tile
5844 loops iterators should be scaled by the tile sizes.
5845 If the C<tile_shift_point_loops> option is set, then the point loops
5846 are shifted to start at zero.
5848 A band can be split into two nested bands using the following function.
5850 int isl_band_split(__isl_keep isl_band *band, int pos);
5852 The resulting outer band contains the first C<pos> dimensions of C<band>
5853 while the inner band contains the remaining dimensions.
5855 A representation of the band can be printed using
5857 #include <isl/band.h>
5858 __isl_give isl_printer *isl_printer_print_band(
5859 __isl_take isl_printer *p,
5860 __isl_keep isl_band *band);
5864 #include <isl/schedule.h>
5865 int isl_options_set_schedule_max_coefficient(
5866 isl_ctx *ctx, int val);
5867 int isl_options_get_schedule_max_coefficient(
5869 int isl_options_set_schedule_max_constant_term(
5870 isl_ctx *ctx, int val);
5871 int isl_options_get_schedule_max_constant_term(
5873 int isl_options_set_schedule_fuse(isl_ctx *ctx, int val);
5874 int isl_options_get_schedule_fuse(isl_ctx *ctx);
5875 int isl_options_set_schedule_maximize_band_depth(
5876 isl_ctx *ctx, int val);
5877 int isl_options_get_schedule_maximize_band_depth(
5879 int isl_options_set_schedule_outer_coincidence(
5880 isl_ctx *ctx, int val);
5881 int isl_options_get_schedule_outer_coincidence(
5883 int isl_options_set_schedule_split_scaled(
5884 isl_ctx *ctx, int val);
5885 int isl_options_get_schedule_split_scaled(
5887 int isl_options_set_schedule_algorithm(
5888 isl_ctx *ctx, int val);
5889 int isl_options_get_schedule_algorithm(
5891 int isl_options_set_schedule_separate_components(
5892 isl_ctx *ctx, int val);
5893 int isl_options_get_schedule_separate_components(
5898 =item * schedule_max_coefficient
5900 This option enforces that the coefficients for variable and parameter
5901 dimensions in the calculated schedule are not larger than the specified value.
5902 This option can significantly increase the speed of the scheduling calculation
5903 and may also prevent fusing of unrelated dimensions. A value of -1 means that
5904 this option does not introduce bounds on the variable or parameter
5907 =item * schedule_max_constant_term
5909 This option enforces that the constant coefficients in the calculated schedule
5910 are not larger than the maximal constant term. This option can significantly
5911 increase the speed of the scheduling calculation and may also prevent fusing of
5912 unrelated dimensions. A value of -1 means that this option does not introduce
5913 bounds on the constant coefficients.
5915 =item * schedule_fuse
5917 This option controls the level of fusion.
5918 If this option is set to C<ISL_SCHEDULE_FUSE_MIN>, then loops in the
5919 resulting schedule will be distributed as much as possible.
5920 If this option is set to C<ISL_SCHEDULE_FUSE_MAX>, then C<isl> will
5921 try to fuse loops in the resulting schedule.
5923 =item * schedule_maximize_band_depth
5925 If this option is set, we do not split bands at the point
5926 where we detect splitting is necessary. Instead, we
5927 backtrack and split bands as early as possible. This
5928 reduces the number of splits and maximizes the width of
5929 the bands. Wider bands give more possibilities for tiling.
5930 Note that if the C<schedule_fuse> option is set to C<ISL_SCHEDULE_FUSE_MIN>,
5931 then bands will be split as early as possible, even if there is no need.
5932 The C<schedule_maximize_band_depth> option therefore has no effect in this case.
5934 =item * schedule_outer_coincidence
5936 If this option is set, then we try to construct schedules
5937 where the outermost scheduling dimension in each band
5938 satisfies the coincidence constraints.
5940 =item * schedule_split_scaled
5942 If this option is set, then we try to construct schedules in which the
5943 constant term is split off from the linear part if the linear parts of
5944 the scheduling rows for all nodes in the graphs have a common non-trivial
5946 The constant term is then placed in a separate band and the linear
5949 =item * schedule_algorithm
5951 Selects the scheduling algorithm to be used.
5952 Available scheduling algorithms are C<ISL_SCHEDULE_ALGORITHM_ISL>
5953 and C<ISL_SCHEDULE_ALGORITHM_FEAUTRIER>.
5955 =item * schedule_separate_components
5957 If at any point the dependence graph contains any (weakly connected) components,
5958 then these components are scheduled separately.
5959 If this option is not set, then some iterations of the domains
5960 in these components may be scheduled together.
5961 If this option is set, then the components are given consecutive
5966 =head2 AST Generation
5968 This section describes the C<isl> functionality for generating
5969 ASTs that visit all the elements
5970 in a domain in an order specified by a schedule.
5971 In particular, given a C<isl_union_map>, an AST is generated
5972 that visits all the elements in the domain of the C<isl_union_map>
5973 according to the lexicographic order of the corresponding image
5974 element(s). If the range of the C<isl_union_map> consists of
5975 elements in more than one space, then each of these spaces is handled
5976 separately in an arbitrary order.
5977 It should be noted that the image elements only specify the I<order>
5978 in which the corresponding domain elements should be visited.
5979 No direct relation between the image elements and the loop iterators
5980 in the generated AST should be assumed.
5982 Each AST is generated within a build. The initial build
5983 simply specifies the constraints on the parameters (if any)
5984 and can be created, inspected, copied and freed using the following functions.
5986 #include <isl/ast_build.h>
5987 __isl_give isl_ast_build *isl_ast_build_from_context(
5988 __isl_take isl_set *set);
5989 isl_ctx *isl_ast_build_get_ctx(
5990 __isl_keep isl_ast_build *build);
5991 __isl_give isl_ast_build *isl_ast_build_copy(
5992 __isl_keep isl_ast_build *build);
5993 void *isl_ast_build_free(
5994 __isl_take isl_ast_build *build);
5996 The C<set> argument is usually a parameter set with zero or more parameters.
5997 More C<isl_ast_build> functions are described in L</"Nested AST Generation">
5998 and L</"Fine-grained Control over AST Generation">.
5999 Finally, the AST itself can be constructed using the following
6002 #include <isl/ast_build.h>
6003 __isl_give isl_ast_node *isl_ast_build_ast_from_schedule(
6004 __isl_keep isl_ast_build *build,
6005 __isl_take isl_union_map *schedule);
6007 =head3 Inspecting the AST
6009 The basic properties of an AST node can be obtained as follows.
6011 #include <isl/ast.h>
6012 isl_ctx *isl_ast_node_get_ctx(
6013 __isl_keep isl_ast_node *node);
6014 enum isl_ast_node_type isl_ast_node_get_type(
6015 __isl_keep isl_ast_node *node);
6017 The type of an AST node is one of
6018 C<isl_ast_node_for>,
6020 C<isl_ast_node_block> or
6021 C<isl_ast_node_user>.
6022 An C<isl_ast_node_for> represents a for node.
6023 An C<isl_ast_node_if> represents an if node.
6024 An C<isl_ast_node_block> represents a compound node.
6025 An C<isl_ast_node_user> represents an expression statement.
6026 An expression statement typically corresponds to a domain element, i.e.,
6027 one of the elements that is visited by the AST.
6029 Each type of node has its own additional properties.
6031 #include <isl/ast.h>
6032 __isl_give isl_ast_expr *isl_ast_node_for_get_iterator(
6033 __isl_keep isl_ast_node *node);
6034 __isl_give isl_ast_expr *isl_ast_node_for_get_init(
6035 __isl_keep isl_ast_node *node);
6036 __isl_give isl_ast_expr *isl_ast_node_for_get_cond(
6037 __isl_keep isl_ast_node *node);
6038 __isl_give isl_ast_expr *isl_ast_node_for_get_inc(
6039 __isl_keep isl_ast_node *node);
6040 __isl_give isl_ast_node *isl_ast_node_for_get_body(
6041 __isl_keep isl_ast_node *node);
6042 int isl_ast_node_for_is_degenerate(
6043 __isl_keep isl_ast_node *node);
6045 An C<isl_ast_for> is considered degenerate if it is known to execute
6048 #include <isl/ast.h>
6049 __isl_give isl_ast_expr *isl_ast_node_if_get_cond(
6050 __isl_keep isl_ast_node *node);
6051 __isl_give isl_ast_node *isl_ast_node_if_get_then(
6052 __isl_keep isl_ast_node *node);
6053 int isl_ast_node_if_has_else(
6054 __isl_keep isl_ast_node *node);
6055 __isl_give isl_ast_node *isl_ast_node_if_get_else(
6056 __isl_keep isl_ast_node *node);
6058 __isl_give isl_ast_node_list *
6059 isl_ast_node_block_get_children(
6060 __isl_keep isl_ast_node *node);
6062 __isl_give isl_ast_expr *isl_ast_node_user_get_expr(
6063 __isl_keep isl_ast_node *node);
6065 Each of the returned C<isl_ast_expr>s can in turn be inspected using
6066 the following functions.
6068 #include <isl/ast.h>
6069 isl_ctx *isl_ast_expr_get_ctx(
6070 __isl_keep isl_ast_expr *expr);
6071 enum isl_ast_expr_type isl_ast_expr_get_type(
6072 __isl_keep isl_ast_expr *expr);
6074 The type of an AST expression is one of
6076 C<isl_ast_expr_id> or
6077 C<isl_ast_expr_int>.
6078 An C<isl_ast_expr_op> represents the result of an operation.
6079 An C<isl_ast_expr_id> represents an identifier.
6080 An C<isl_ast_expr_int> represents an integer value.
6082 Each type of expression has its own additional properties.
6084 #include <isl/ast.h>
6085 enum isl_ast_op_type isl_ast_expr_get_op_type(
6086 __isl_keep isl_ast_expr *expr);
6087 int isl_ast_expr_get_op_n_arg(__isl_keep isl_ast_expr *expr);
6088 __isl_give isl_ast_expr *isl_ast_expr_get_op_arg(
6089 __isl_keep isl_ast_expr *expr, int pos);
6090 int isl_ast_node_foreach_ast_op_type(
6091 __isl_keep isl_ast_node *node,
6092 int (*fn)(enum isl_ast_op_type type, void *user),
6095 C<isl_ast_expr_get_op_type> returns the type of the operation
6096 performed. C<isl_ast_expr_get_op_n_arg> returns the number of
6097 arguments. C<isl_ast_expr_get_op_arg> returns the specified
6099 C<isl_ast_node_foreach_ast_op_type> calls C<fn> for each distinct
6100 C<isl_ast_op_type> that appears in C<node>.
6101 The operation type is one of the following.
6105 =item C<isl_ast_op_and>
6107 Logical I<and> of two arguments.
6108 Both arguments can be evaluated.
6110 =item C<isl_ast_op_and_then>
6112 Logical I<and> of two arguments.
6113 The second argument can only be evaluated if the first evaluates to true.
6115 =item C<isl_ast_op_or>
6117 Logical I<or> of two arguments.
6118 Both arguments can be evaluated.
6120 =item C<isl_ast_op_or_else>
6122 Logical I<or> of two arguments.
6123 The second argument can only be evaluated if the first evaluates to false.
6125 =item C<isl_ast_op_max>
6127 Maximum of two or more arguments.
6129 =item C<isl_ast_op_min>
6131 Minimum of two or more arguments.
6133 =item C<isl_ast_op_minus>
6137 =item C<isl_ast_op_add>
6139 Sum of two arguments.
6141 =item C<isl_ast_op_sub>
6143 Difference of two arguments.
6145 =item C<isl_ast_op_mul>
6147 Product of two arguments.
6149 =item C<isl_ast_op_div>
6151 Exact division. That is, the result is known to be an integer.
6153 =item C<isl_ast_op_fdiv_q>
6155 Result of integer division, rounded towards negative
6158 =item C<isl_ast_op_pdiv_q>
6160 Result of integer division, where dividend is known to be non-negative.
6162 =item C<isl_ast_op_pdiv_r>
6164 Remainder of integer division, where dividend is known to be non-negative.
6166 =item C<isl_ast_op_cond>
6168 Conditional operator defined on three arguments.
6169 If the first argument evaluates to true, then the result
6170 is equal to the second argument. Otherwise, the result
6171 is equal to the third argument.
6172 The second and third argument may only be evaluated if
6173 the first argument evaluates to true and false, respectively.
6174 Corresponds to C<a ? b : c> in C.
6176 =item C<isl_ast_op_select>
6178 Conditional operator defined on three arguments.
6179 If the first argument evaluates to true, then the result
6180 is equal to the second argument. Otherwise, the result
6181 is equal to the third argument.
6182 The second and third argument may be evaluated independently
6183 of the value of the first argument.
6184 Corresponds to C<a * b + (1 - a) * c> in C.
6186 =item C<isl_ast_op_eq>
6190 =item C<isl_ast_op_le>
6192 Less than or equal relation.
6194 =item C<isl_ast_op_lt>
6198 =item C<isl_ast_op_ge>
6200 Greater than or equal relation.
6202 =item C<isl_ast_op_gt>
6204 Greater than relation.
6206 =item C<isl_ast_op_call>
6209 The number of arguments of the C<isl_ast_expr> is one more than
6210 the number of arguments in the function call, the first argument
6211 representing the function being called.
6213 =item C<isl_ast_op_access>
6216 The number of arguments of the C<isl_ast_expr> is one more than
6217 the number of index expressions in the array access, the first argument
6218 representing the array being accessed.
6220 =item C<isl_ast_op_member>
6223 This operation has two arguments, a structure and the name of
6224 the member of the structure being accessed.
6228 #include <isl/ast.h>
6229 __isl_give isl_id *isl_ast_expr_get_id(
6230 __isl_keep isl_ast_expr *expr);
6232 Return the identifier represented by the AST expression.
6234 #include <isl/ast.h>
6235 __isl_give isl_val *isl_ast_expr_get_val(
6236 __isl_keep isl_ast_expr *expr);
6238 Return the integer represented by the AST expression.
6240 =head3 Properties of ASTs
6242 #include <isl/ast.h>
6243 int isl_ast_expr_is_equal(__isl_keep isl_ast_expr *expr1,
6244 __isl_keep isl_ast_expr *expr2);
6246 Check if two C<isl_ast_expr>s are equal to each other.
6248 =head3 Manipulating and printing the AST
6250 AST nodes can be copied and freed using the following functions.
6252 #include <isl/ast.h>
6253 __isl_give isl_ast_node *isl_ast_node_copy(
6254 __isl_keep isl_ast_node *node);
6255 void *isl_ast_node_free(__isl_take isl_ast_node *node);
6257 AST expressions can be copied and freed using the following functions.
6259 #include <isl/ast.h>
6260 __isl_give isl_ast_expr *isl_ast_expr_copy(
6261 __isl_keep isl_ast_expr *expr);
6262 void *isl_ast_expr_free(__isl_take isl_ast_expr *expr);
6264 New AST expressions can be created either directly or within
6265 the context of an C<isl_ast_build>.
6267 #include <isl/ast.h>
6268 __isl_give isl_ast_expr *isl_ast_expr_from_val(
6269 __isl_take isl_val *v);
6270 __isl_give isl_ast_expr *isl_ast_expr_from_id(
6271 __isl_take isl_id *id);
6272 __isl_give isl_ast_expr *isl_ast_expr_neg(
6273 __isl_take isl_ast_expr *expr);
6274 __isl_give isl_ast_expr *isl_ast_expr_add(
6275 __isl_take isl_ast_expr *expr1,
6276 __isl_take isl_ast_expr *expr2);
6277 __isl_give isl_ast_expr *isl_ast_expr_sub(
6278 __isl_take isl_ast_expr *expr1,
6279 __isl_take isl_ast_expr *expr2);
6280 __isl_give isl_ast_expr *isl_ast_expr_mul(
6281 __isl_take isl_ast_expr *expr1,
6282 __isl_take isl_ast_expr *expr2);
6283 __isl_give isl_ast_expr *isl_ast_expr_div(
6284 __isl_take isl_ast_expr *expr1,
6285 __isl_take isl_ast_expr *expr2);
6286 __isl_give isl_ast_expr *isl_ast_expr_and(
6287 __isl_take isl_ast_expr *expr1,
6288 __isl_take isl_ast_expr *expr2)
6289 __isl_give isl_ast_expr *isl_ast_expr_or(
6290 __isl_take isl_ast_expr *expr1,
6291 __isl_take isl_ast_expr *expr2)
6292 __isl_give isl_ast_expr *isl_ast_expr_access(
6293 __isl_take isl_ast_expr *array,
6294 __isl_take isl_ast_expr_list *indices);
6296 #include <isl/ast_build.h>
6297 __isl_give isl_ast_expr *isl_ast_build_expr_from_pw_aff(
6298 __isl_keep isl_ast_build *build,
6299 __isl_take isl_pw_aff *pa);
6300 __isl_give isl_ast_expr *
6301 isl_ast_build_access_from_pw_multi_aff(
6302 __isl_keep isl_ast_build *build,
6303 __isl_take isl_pw_multi_aff *pma);
6304 __isl_give isl_ast_expr *
6305 isl_ast_build_access_from_multi_pw_aff(
6306 __isl_keep isl_ast_build *build,
6307 __isl_take isl_multi_pw_aff *mpa);
6308 __isl_give isl_ast_expr *
6309 isl_ast_build_call_from_pw_multi_aff(
6310 __isl_keep isl_ast_build *build,
6311 __isl_take isl_pw_multi_aff *pma);
6312 __isl_give isl_ast_expr *
6313 isl_ast_build_call_from_multi_pw_aff(
6314 __isl_keep isl_ast_build *build,
6315 __isl_take isl_multi_pw_aff *mpa);
6317 The domains of C<pa>, C<mpa> and C<pma> should correspond
6318 to the schedule space of C<build>.
6319 The tuple id of C<mpa> or C<pma> is used as the array being accessed or
6320 the function being called.
6321 If the accessed space is a nested relation, then it is taken
6322 to represent an access of the member specified by the range
6323 of this nested relation of the structure specified by the domain
6324 of the nested relation.
6326 The following functions can be used to modify an C<isl_ast_expr>.
6328 #include <isl/ast.h>
6329 __isl_give isl_ast_expr *isl_ast_expr_set_op_arg(
6330 __isl_take isl_ast_expr *expr, int pos,
6331 __isl_take isl_ast_expr *arg);
6333 Replace the argument of C<expr> at position C<pos> by C<arg>.
6335 #include <isl/ast.h>
6336 __isl_give isl_ast_expr *isl_ast_expr_substitute_ids(
6337 __isl_take isl_ast_expr *expr,
6338 __isl_take isl_id_to_ast_expr *id2expr);
6340 The function C<isl_ast_expr_substitute_ids> replaces the
6341 subexpressions of C<expr> of type C<isl_ast_expr_id>
6342 by the corresponding expression in C<id2expr>, if there is any.
6345 User specified data can be attached to an C<isl_ast_node> and obtained
6346 from the same C<isl_ast_node> using the following functions.
6348 #include <isl/ast.h>
6349 __isl_give isl_ast_node *isl_ast_node_set_annotation(
6350 __isl_take isl_ast_node *node,
6351 __isl_take isl_id *annotation);
6352 __isl_give isl_id *isl_ast_node_get_annotation(
6353 __isl_keep isl_ast_node *node);
6355 Basic printing can be performed using the following functions.
6357 #include <isl/ast.h>
6358 __isl_give isl_printer *isl_printer_print_ast_expr(
6359 __isl_take isl_printer *p,
6360 __isl_keep isl_ast_expr *expr);
6361 __isl_give isl_printer *isl_printer_print_ast_node(
6362 __isl_take isl_printer *p,
6363 __isl_keep isl_ast_node *node);
6365 More advanced printing can be performed using the following functions.
6367 #include <isl/ast.h>
6368 __isl_give isl_printer *isl_ast_op_type_print_macro(
6369 enum isl_ast_op_type type,
6370 __isl_take isl_printer *p);
6371 __isl_give isl_printer *isl_ast_node_print_macros(
6372 __isl_keep isl_ast_node *node,
6373 __isl_take isl_printer *p);
6374 __isl_give isl_printer *isl_ast_node_print(
6375 __isl_keep isl_ast_node *node,
6376 __isl_take isl_printer *p,
6377 __isl_take isl_ast_print_options *options);
6378 __isl_give isl_printer *isl_ast_node_for_print(
6379 __isl_keep isl_ast_node *node,
6380 __isl_take isl_printer *p,
6381 __isl_take isl_ast_print_options *options);
6382 __isl_give isl_printer *isl_ast_node_if_print(
6383 __isl_keep isl_ast_node *node,
6384 __isl_take isl_printer *p,
6385 __isl_take isl_ast_print_options *options);
6387 While printing an C<isl_ast_node> in C<ISL_FORMAT_C>,
6388 C<isl> may print out an AST that makes use of macros such
6389 as C<floord>, C<min> and C<max>.
6390 C<isl_ast_op_type_print_macro> prints out the macro
6391 corresponding to a specific C<isl_ast_op_type>.
6392 C<isl_ast_node_print_macros> scans the C<isl_ast_node>
6393 for expressions where these macros would be used and prints
6394 out the required macro definitions.
6395 Essentially, C<isl_ast_node_print_macros> calls
6396 C<isl_ast_node_foreach_ast_op_type> with C<isl_ast_op_type_print_macro>
6397 as function argument.
6398 C<isl_ast_node_print>, C<isl_ast_node_for_print> and
6399 C<isl_ast_node_if_print> print an C<isl_ast_node>
6400 in C<ISL_FORMAT_C>, but allow for some extra control
6401 through an C<isl_ast_print_options> object.
6402 This object can be created using the following functions.
6404 #include <isl/ast.h>
6405 __isl_give isl_ast_print_options *
6406 isl_ast_print_options_alloc(isl_ctx *ctx);
6407 __isl_give isl_ast_print_options *
6408 isl_ast_print_options_copy(
6409 __isl_keep isl_ast_print_options *options);
6410 void *isl_ast_print_options_free(
6411 __isl_take isl_ast_print_options *options);
6413 __isl_give isl_ast_print_options *
6414 isl_ast_print_options_set_print_user(
6415 __isl_take isl_ast_print_options *options,
6416 __isl_give isl_printer *(*print_user)(
6417 __isl_take isl_printer *p,
6418 __isl_take isl_ast_print_options *options,
6419 __isl_keep isl_ast_node *node, void *user),
6421 __isl_give isl_ast_print_options *
6422 isl_ast_print_options_set_print_for(
6423 __isl_take isl_ast_print_options *options,
6424 __isl_give isl_printer *(*print_for)(
6425 __isl_take isl_printer *p,
6426 __isl_take isl_ast_print_options *options,
6427 __isl_keep isl_ast_node *node, void *user),
6430 The callback set by C<isl_ast_print_options_set_print_user>
6431 is called whenever a node of type C<isl_ast_node_user> needs to
6433 The callback set by C<isl_ast_print_options_set_print_for>
6434 is called whenever a node of type C<isl_ast_node_for> needs to
6436 Note that C<isl_ast_node_for_print> will I<not> call the
6437 callback set by C<isl_ast_print_options_set_print_for> on the node
6438 on which C<isl_ast_node_for_print> is called, but only on nested
6439 nodes of type C<isl_ast_node_for>. It is therefore safe to
6440 call C<isl_ast_node_for_print> from within the callback set by
6441 C<isl_ast_print_options_set_print_for>.
6443 The following option determines the type to be used for iterators
6444 while printing the AST.
6446 int isl_options_set_ast_iterator_type(
6447 isl_ctx *ctx, const char *val);
6448 const char *isl_options_get_ast_iterator_type(
6453 #include <isl/ast_build.h>
6454 int isl_options_set_ast_build_atomic_upper_bound(
6455 isl_ctx *ctx, int val);
6456 int isl_options_get_ast_build_atomic_upper_bound(
6458 int isl_options_set_ast_build_prefer_pdiv(isl_ctx *ctx,
6460 int isl_options_get_ast_build_prefer_pdiv(isl_ctx *ctx);
6461 int isl_options_set_ast_build_exploit_nested_bounds(
6462 isl_ctx *ctx, int val);
6463 int isl_options_get_ast_build_exploit_nested_bounds(
6465 int isl_options_set_ast_build_group_coscheduled(
6466 isl_ctx *ctx, int val);
6467 int isl_options_get_ast_build_group_coscheduled(
6469 int isl_options_set_ast_build_scale_strides(
6470 isl_ctx *ctx, int val);
6471 int isl_options_get_ast_build_scale_strides(
6473 int isl_options_set_ast_build_allow_else(isl_ctx *ctx,
6475 int isl_options_get_ast_build_allow_else(isl_ctx *ctx);
6476 int isl_options_set_ast_build_allow_or(isl_ctx *ctx,
6478 int isl_options_get_ast_build_allow_or(isl_ctx *ctx);
6482 =item * ast_build_atomic_upper_bound
6484 Generate loop upper bounds that consist of the current loop iterator,
6485 an operator and an expression not involving the iterator.
6486 If this option is not set, then the current loop iterator may appear
6487 several times in the upper bound.
6488 For example, when this option is turned off, AST generation
6491 [n] -> { A[i] -> [i] : 0 <= i <= 100, n }
6495 for (int c0 = 0; c0 <= 100 && n >= c0; c0 += 1)
6498 When the option is turned on, the following AST is generated
6500 for (int c0 = 0; c0 <= min(100, n); c0 += 1)
6503 =item * ast_build_prefer_pdiv
6505 If this option is turned off, then the AST generation will
6506 produce ASTs that may only contain C<isl_ast_op_fdiv_q>
6507 operators, but no C<isl_ast_op_pdiv_q> or
6508 C<isl_ast_op_pdiv_r> operators.
6509 If this options is turned on, then C<isl> will try to convert
6510 some of the C<isl_ast_op_fdiv_q> operators to (expressions containing)
6511 C<isl_ast_op_pdiv_q> or C<isl_ast_op_pdiv_r> operators.
6513 =item * ast_build_exploit_nested_bounds
6515 Simplify conditions based on bounds of nested for loops.
6516 In particular, remove conditions that are implied by the fact
6517 that one or more nested loops have at least one iteration,
6518 meaning that the upper bound is at least as large as the lower bound.
6519 For example, when this option is turned off, AST generation
6522 [N,M] -> { A[i,j] -> [i,j] : 0 <= i <= N and
6528 for (int c0 = 0; c0 <= N; c0 += 1)
6529 for (int c1 = 0; c1 <= M; c1 += 1)
6532 When the option is turned on, the following AST is generated
6534 for (int c0 = 0; c0 <= N; c0 += 1)
6535 for (int c1 = 0; c1 <= M; c1 += 1)
6538 =item * ast_build_group_coscheduled
6540 If two domain elements are assigned the same schedule point, then
6541 they may be executed in any order and they may even appear in different
6542 loops. If this options is set, then the AST generator will make
6543 sure that coscheduled domain elements do not appear in separate parts
6544 of the AST. This is useful in case of nested AST generation
6545 if the outer AST generation is given only part of a schedule
6546 and the inner AST generation should handle the domains that are
6547 coscheduled by this initial part of the schedule together.
6548 For example if an AST is generated for a schedule
6550 { A[i] -> [0]; B[i] -> [0] }
6552 then the C<isl_ast_build_set_create_leaf> callback described
6553 below may get called twice, once for each domain.
6554 Setting this option ensures that the callback is only called once
6555 on both domains together.
6557 =item * ast_build_separation_bounds
6559 This option specifies which bounds to use during separation.
6560 If this option is set to C<ISL_AST_BUILD_SEPARATION_BOUNDS_IMPLICIT>
6561 then all (possibly implicit) bounds on the current dimension will
6562 be used during separation.
6563 If this option is set to C<ISL_AST_BUILD_SEPARATION_BOUNDS_EXPLICIT>
6564 then only those bounds that are explicitly available will
6565 be used during separation.
6567 =item * ast_build_scale_strides
6569 This option specifies whether the AST generator is allowed
6570 to scale down iterators of strided loops.
6572 =item * ast_build_allow_else
6574 This option specifies whether the AST generator is allowed
6575 to construct if statements with else branches.
6577 =item * ast_build_allow_or
6579 This option specifies whether the AST generator is allowed
6580 to construct if conditions with disjunctions.
6584 =head3 Fine-grained Control over AST Generation
6586 Besides specifying the constraints on the parameters,
6587 an C<isl_ast_build> object can be used to control
6588 various aspects of the AST generation process.
6589 The most prominent way of control is through ``options'',
6590 which can be set using the following function.
6592 #include <isl/ast_build.h>
6593 __isl_give isl_ast_build *
6594 isl_ast_build_set_options(
6595 __isl_take isl_ast_build *control,
6596 __isl_take isl_union_map *options);
6598 The options are encoded in an <isl_union_map>.
6599 The domain of this union relation refers to the schedule domain,
6600 i.e., the range of the schedule passed to C<isl_ast_build_ast_from_schedule>.
6601 In the case of nested AST generation (see L</"Nested AST Generation">),
6602 the domain of C<options> should refer to the extra piece of the schedule.
6603 That is, it should be equal to the range of the wrapped relation in the
6604 range of the schedule.
6605 The range of the options can consist of elements in one or more spaces,
6606 the names of which determine the effect of the option.
6607 The values of the range typically also refer to the schedule dimension
6608 to which the option applies. In case of nested AST generation
6609 (see L</"Nested AST Generation">), these values refer to the position
6610 of the schedule dimension within the innermost AST generation.
6611 The constraints on the domain elements of
6612 the option should only refer to this dimension and earlier dimensions.
6613 We consider the following spaces.
6617 =item C<separation_class>
6619 This space is a wrapped relation between two one dimensional spaces.
6620 The input space represents the schedule dimension to which the option
6621 applies and the output space represents the separation class.
6622 While constructing a loop corresponding to the specified schedule
6623 dimension(s), the AST generator will try to generate separate loops
6624 for domain elements that are assigned different classes.
6625 If only some of the elements are assigned a class, then those elements
6626 that are not assigned any class will be treated as belonging to a class
6627 that is separate from the explicitly assigned classes.
6628 The typical use case for this option is to separate full tiles from
6630 The other options, described below, are applied after the separation
6633 As an example, consider the separation into full and partial tiles
6634 of a tiling of a triangular domain.
6635 Take, for example, the domain
6637 { A[i,j] : 0 <= i,j and i + j <= 100 }
6639 and a tiling into tiles of 10 by 10. The input to the AST generator
6640 is then the schedule
6642 { A[i,j] -> [([i/10]),[j/10],i,j] : 0 <= i,j and
6645 Without any options, the following AST is generated
6647 for (int c0 = 0; c0 <= 10; c0 += 1)
6648 for (int c1 = 0; c1 <= -c0 + 10; c1 += 1)
6649 for (int c2 = 10 * c0;
6650 c2 <= min(-10 * c1 + 100, 10 * c0 + 9);
6652 for (int c3 = 10 * c1;
6653 c3 <= min(10 * c1 + 9, -c2 + 100);
6657 Separation into full and partial tiles can be obtained by assigning
6658 a class, say C<0>, to the full tiles. The full tiles are represented by those
6659 values of the first and second schedule dimensions for which there are
6660 values of the third and fourth dimensions to cover an entire tile.
6661 That is, we need to specify the following option
6663 { [a,b,c,d] -> separation_class[[0]->[0]] :
6664 exists b': 0 <= 10a,10b' and
6665 10a+9+10b'+9 <= 100;
6666 [a,b,c,d] -> separation_class[[1]->[0]] :
6667 0 <= 10a,10b and 10a+9+10b+9 <= 100 }
6671 { [a, b, c, d] -> separation_class[[1] -> [0]] :
6672 a >= 0 and b >= 0 and b <= 8 - a;
6673 [a, b, c, d] -> separation_class[[0] -> [0]] :
6676 With this option, the generated AST is as follows
6679 for (int c0 = 0; c0 <= 8; c0 += 1) {
6680 for (int c1 = 0; c1 <= -c0 + 8; c1 += 1)
6681 for (int c2 = 10 * c0;
6682 c2 <= 10 * c0 + 9; c2 += 1)
6683 for (int c3 = 10 * c1;
6684 c3 <= 10 * c1 + 9; c3 += 1)
6686 for (int c1 = -c0 + 9; c1 <= -c0 + 10; c1 += 1)
6687 for (int c2 = 10 * c0;
6688 c2 <= min(-10 * c1 + 100, 10 * c0 + 9);
6690 for (int c3 = 10 * c1;
6691 c3 <= min(-c2 + 100, 10 * c1 + 9);
6695 for (int c0 = 9; c0 <= 10; c0 += 1)
6696 for (int c1 = 0; c1 <= -c0 + 10; c1 += 1)
6697 for (int c2 = 10 * c0;
6698 c2 <= min(-10 * c1 + 100, 10 * c0 + 9);
6700 for (int c3 = 10 * c1;
6701 c3 <= min(10 * c1 + 9, -c2 + 100);
6708 This is a single-dimensional space representing the schedule dimension(s)
6709 to which ``separation'' should be applied. Separation tries to split
6710 a loop into several pieces if this can avoid the generation of guards
6712 See also the C<atomic> option.
6716 This is a single-dimensional space representing the schedule dimension(s)
6717 for which the domains should be considered ``atomic''. That is, the
6718 AST generator will make sure that any given domain space will only appear
6719 in a single loop at the specified level.
6721 Consider the following schedule
6723 { a[i] -> [i] : 0 <= i < 10;
6724 b[i] -> [i+1] : 0 <= i < 10 }
6726 If the following option is specified
6728 { [i] -> separate[x] }
6730 then the following AST will be generated
6734 for (int c0 = 1; c0 <= 9; c0 += 1) {
6741 If, on the other hand, the following option is specified
6743 { [i] -> atomic[x] }
6745 then the following AST will be generated
6747 for (int c0 = 0; c0 <= 10; c0 += 1) {
6754 If neither C<atomic> nor C<separate> is specified, then the AST generator
6755 may produce either of these two results or some intermediate form.
6759 This is a single-dimensional space representing the schedule dimension(s)
6760 that should be I<completely> unrolled.
6761 To obtain a partial unrolling, the user should apply an additional
6762 strip-mining to the schedule and fully unroll the inner loop.
6766 Additional control is available through the following functions.
6768 #include <isl/ast_build.h>
6769 __isl_give isl_ast_build *
6770 isl_ast_build_set_iterators(
6771 __isl_take isl_ast_build *control,
6772 __isl_take isl_id_list *iterators);
6774 The function C<isl_ast_build_set_iterators> allows the user to
6775 specify a list of iterator C<isl_id>s to be used as iterators.
6776 If the input schedule is injective, then
6777 the number of elements in this list should be as large as the dimension
6778 of the schedule space, but no direct correspondence should be assumed
6779 between dimensions and elements.
6780 If the input schedule is not injective, then an additional number
6781 of C<isl_id>s equal to the largest dimension of the input domains
6783 If the number of provided C<isl_id>s is insufficient, then additional
6784 names are automatically generated.
6786 #include <isl/ast_build.h>
6787 __isl_give isl_ast_build *
6788 isl_ast_build_set_create_leaf(
6789 __isl_take isl_ast_build *control,
6790 __isl_give isl_ast_node *(*fn)(
6791 __isl_take isl_ast_build *build,
6792 void *user), void *user);
6795 C<isl_ast_build_set_create_leaf> function allows for the
6796 specification of a callback that should be called whenever the AST
6797 generator arrives at an element of the schedule domain.
6798 The callback should return an AST node that should be inserted
6799 at the corresponding position of the AST. The default action (when
6800 the callback is not set) is to continue generating parts of the AST to scan
6801 all the domain elements associated to the schedule domain element
6802 and to insert user nodes, ``calling'' the domain element, for each of them.
6803 The C<build> argument contains the current state of the C<isl_ast_build>.
6804 To ease nested AST generation (see L</"Nested AST Generation">),
6805 all control information that is
6806 specific to the current AST generation such as the options and
6807 the callbacks has been removed from this C<isl_ast_build>.
6808 The callback would typically return the result of a nested
6810 user defined node created using the following function.
6812 #include <isl/ast.h>
6813 __isl_give isl_ast_node *isl_ast_node_alloc_user(
6814 __isl_take isl_ast_expr *expr);
6816 #include <isl/ast_build.h>
6817 __isl_give isl_ast_build *
6818 isl_ast_build_set_at_each_domain(
6819 __isl_take isl_ast_build *build,
6820 __isl_give isl_ast_node *(*fn)(
6821 __isl_take isl_ast_node *node,
6822 __isl_keep isl_ast_build *build,
6823 void *user), void *user);
6824 __isl_give isl_ast_build *
6825 isl_ast_build_set_before_each_for(
6826 __isl_take isl_ast_build *build,
6827 __isl_give isl_id *(*fn)(
6828 __isl_keep isl_ast_build *build,
6829 void *user), void *user);
6830 __isl_give isl_ast_build *
6831 isl_ast_build_set_after_each_for(
6832 __isl_take isl_ast_build *build,
6833 __isl_give isl_ast_node *(*fn)(
6834 __isl_take isl_ast_node *node,
6835 __isl_keep isl_ast_build *build,
6836 void *user), void *user);
6838 The callback set by C<isl_ast_build_set_at_each_domain> will
6839 be called for each domain AST node.
6840 The callbacks set by C<isl_ast_build_set_before_each_for>
6841 and C<isl_ast_build_set_after_each_for> will be called
6842 for each for AST node. The first will be called in depth-first
6843 pre-order, while the second will be called in depth-first post-order.
6844 Since C<isl_ast_build_set_before_each_for> is called before the for
6845 node is actually constructed, it is only passed an C<isl_ast_build>.
6846 The returned C<isl_id> will be added as an annotation (using
6847 C<isl_ast_node_set_annotation>) to the constructed for node.
6848 In particular, if the user has also specified an C<after_each_for>
6849 callback, then the annotation can be retrieved from the node passed to
6850 that callback using C<isl_ast_node_get_annotation>.
6851 All callbacks should C<NULL> on failure.
6852 The given C<isl_ast_build> can be used to create new
6853 C<isl_ast_expr> objects using C<isl_ast_build_expr_from_pw_aff>
6854 or C<isl_ast_build_call_from_pw_multi_aff>.
6856 =head3 Nested AST Generation
6858 C<isl> allows the user to create an AST within the context
6859 of another AST. These nested ASTs are created using the
6860 same C<isl_ast_build_ast_from_schedule> function that is used to create the
6861 outer AST. The C<build> argument should be an C<isl_ast_build>
6862 passed to a callback set by
6863 C<isl_ast_build_set_create_leaf>.
6864 The space of the range of the C<schedule> argument should refer
6865 to this build. In particular, the space should be a wrapped
6866 relation and the domain of this wrapped relation should be the
6867 same as that of the range of the schedule returned by
6868 C<isl_ast_build_get_schedule> below.
6869 In practice, the new schedule is typically
6870 created by calling C<isl_union_map_range_product> on the old schedule
6871 and some extra piece of the schedule.
6872 The space of the schedule domain is also available from
6873 the C<isl_ast_build>.
6875 #include <isl/ast_build.h>
6876 __isl_give isl_union_map *isl_ast_build_get_schedule(
6877 __isl_keep isl_ast_build *build);
6878 __isl_give isl_space *isl_ast_build_get_schedule_space(
6879 __isl_keep isl_ast_build *build);
6880 __isl_give isl_ast_build *isl_ast_build_restrict(
6881 __isl_take isl_ast_build *build,
6882 __isl_take isl_set *set);
6884 The C<isl_ast_build_get_schedule> function returns a (partial)
6885 schedule for the domains elements for which part of the AST still needs to
6886 be generated in the current build.
6887 In particular, the domain elements are mapped to those iterations of the loops
6888 enclosing the current point of the AST generation inside which
6889 the domain elements are executed.
6890 No direct correspondence between
6891 the input schedule and this schedule should be assumed.
6892 The space obtained from C<isl_ast_build_get_schedule_space> can be used
6893 to create a set for C<isl_ast_build_restrict> to intersect
6894 with the current build. In particular, the set passed to
6895 C<isl_ast_build_restrict> can have additional parameters.
6896 The ids of the set dimensions in the space returned by
6897 C<isl_ast_build_get_schedule_space> correspond to the
6898 iterators of the already generated loops.
6899 The user should not rely on the ids of the output dimensions
6900 of the relations in the union relation returned by
6901 C<isl_ast_build_get_schedule> having any particular value.
6905 Although C<isl> is mainly meant to be used as a library,
6906 it also contains some basic applications that use some
6907 of the functionality of C<isl>.
6908 The input may be specified in either the L<isl format>
6909 or the L<PolyLib format>.
6911 =head2 C<isl_polyhedron_sample>
6913 C<isl_polyhedron_sample> takes a polyhedron as input and prints
6914 an integer element of the polyhedron, if there is any.
6915 The first column in the output is the denominator and is always
6916 equal to 1. If the polyhedron contains no integer points,
6917 then a vector of length zero is printed.
6921 C<isl_pip> takes the same input as the C<example> program
6922 from the C<piplib> distribution, i.e., a set of constraints
6923 on the parameters, a line containing only -1 and finally a set
6924 of constraints on a parametric polyhedron.
6925 The coefficients of the parameters appear in the last columns
6926 (but before the final constant column).
6927 The output is the lexicographic minimum of the parametric polyhedron.
6928 As C<isl> currently does not have its own output format, the output
6929 is just a dump of the internal state.
6931 =head2 C<isl_polyhedron_minimize>
6933 C<isl_polyhedron_minimize> computes the minimum of some linear
6934 or affine objective function over the integer points in a polyhedron.
6935 If an affine objective function
6936 is given, then the constant should appear in the last column.
6938 =head2 C<isl_polytope_scan>
6940 Given a polytope, C<isl_polytope_scan> prints
6941 all integer points in the polytope.
6943 =head2 C<isl_codegen>
6945 Given a schedule, a context set and an options relation,
6946 C<isl_codegen> prints out an AST that scans the domain elements
6947 of the schedule in the order of their image(s) taking into account
6948 the constraints in the context set.