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_set *isl_set_set_tuple_id(
1817 __isl_take isl_set *set, __isl_take isl_id *id);
1818 __isl_give isl_set *isl_set_reset_tuple_id(
1819 __isl_take isl_set *set);
1820 int isl_set_has_tuple_id(__isl_keep isl_set *set);
1821 __isl_give isl_id *isl_set_get_tuple_id(
1822 __isl_keep isl_set *set);
1823 __isl_give isl_map *isl_map_set_tuple_id(
1824 __isl_take isl_map *map, enum isl_dim_type type,
1825 __isl_take isl_id *id);
1826 __isl_give isl_map *isl_map_reset_tuple_id(
1827 __isl_take isl_map *map, enum isl_dim_type type);
1828 int isl_map_has_tuple_id(__isl_keep isl_map *map,
1829 enum isl_dim_type type);
1830 __isl_give isl_id *isl_map_get_tuple_id(
1831 __isl_keep isl_map *map, enum isl_dim_type type);
1833 const char *isl_basic_set_get_tuple_name(
1834 __isl_keep isl_basic_set *bset);
1835 __isl_give isl_basic_set *isl_basic_set_set_tuple_name(
1836 __isl_take isl_basic_set *set, const char *s);
1837 int isl_set_has_tuple_name(__isl_keep isl_set *set);
1838 const char *isl_set_get_tuple_name(
1839 __isl_keep isl_set *set);
1840 const char *isl_basic_map_get_tuple_name(
1841 __isl_keep isl_basic_map *bmap,
1842 enum isl_dim_type type);
1843 __isl_give isl_basic_map *isl_basic_map_set_tuple_name(
1844 __isl_take isl_basic_map *bmap,
1845 enum isl_dim_type type, const char *s);
1846 int isl_map_has_tuple_name(__isl_keep isl_map *map,
1847 enum isl_dim_type type);
1848 const char *isl_map_get_tuple_name(
1849 __isl_keep isl_map *map,
1850 enum isl_dim_type type);
1852 As with C<isl_space_get_tuple_name>, the value returned points to
1853 an internal data structure.
1854 The identifiers, positions or names of individual dimensions can be
1855 read off using the following functions.
1857 __isl_give isl_id *isl_basic_set_get_dim_id(
1858 __isl_keep isl_basic_set *bset,
1859 enum isl_dim_type type, unsigned pos);
1860 __isl_give isl_set *isl_set_set_dim_id(
1861 __isl_take isl_set *set, enum isl_dim_type type,
1862 unsigned pos, __isl_take isl_id *id);
1863 int isl_set_has_dim_id(__isl_keep isl_set *set,
1864 enum isl_dim_type type, unsigned pos);
1865 __isl_give isl_id *isl_set_get_dim_id(
1866 __isl_keep isl_set *set, enum isl_dim_type type,
1868 int isl_basic_map_has_dim_id(
1869 __isl_keep isl_basic_map *bmap,
1870 enum isl_dim_type type, unsigned pos);
1871 __isl_give isl_map *isl_map_set_dim_id(
1872 __isl_take isl_map *map, enum isl_dim_type type,
1873 unsigned pos, __isl_take isl_id *id);
1874 int isl_map_has_dim_id(__isl_keep isl_map *map,
1875 enum isl_dim_type type, unsigned pos);
1876 __isl_give isl_id *isl_map_get_dim_id(
1877 __isl_keep isl_map *map, enum isl_dim_type type,
1880 int isl_set_find_dim_by_id(__isl_keep isl_set *set,
1881 enum isl_dim_type type, __isl_keep isl_id *id);
1882 int isl_map_find_dim_by_id(__isl_keep isl_map *map,
1883 enum isl_dim_type type, __isl_keep isl_id *id);
1884 int isl_set_find_dim_by_name(__isl_keep isl_set *set,
1885 enum isl_dim_type type, const char *name);
1886 int isl_map_find_dim_by_name(__isl_keep isl_map *map,
1887 enum isl_dim_type type, const char *name);
1889 const char *isl_constraint_get_dim_name(
1890 __isl_keep isl_constraint *constraint,
1891 enum isl_dim_type type, unsigned pos);
1892 const char *isl_basic_set_get_dim_name(
1893 __isl_keep isl_basic_set *bset,
1894 enum isl_dim_type type, unsigned pos);
1895 int isl_set_has_dim_name(__isl_keep isl_set *set,
1896 enum isl_dim_type type, unsigned pos);
1897 const char *isl_set_get_dim_name(
1898 __isl_keep isl_set *set,
1899 enum isl_dim_type type, unsigned pos);
1900 const char *isl_basic_map_get_dim_name(
1901 __isl_keep isl_basic_map *bmap,
1902 enum isl_dim_type type, unsigned pos);
1903 int isl_map_has_dim_name(__isl_keep isl_map *map,
1904 enum isl_dim_type type, unsigned pos);
1905 const char *isl_map_get_dim_name(
1906 __isl_keep isl_map *map,
1907 enum isl_dim_type type, unsigned pos);
1909 These functions are mostly useful to obtain the identifiers, positions
1910 or names of the parameters. Identifiers of individual dimensions are
1911 essentially only useful for printing. They are ignored by all other
1912 operations and may not be preserved across those operations.
1914 The user pointers on all parameters and tuples can be reset
1915 using the following functions.
1917 __isl_give isl_set *isl_set_reset_user(
1918 __isl_take isl_set *set);
1919 __isl_give isl_map *isl_map_reset_user(
1920 __isl_take isl_map *map);
1924 =head3 Unary Properties
1930 The following functions test whether the given set or relation
1931 contains any integer points. The ``plain'' variants do not perform
1932 any computations, but simply check if the given set or relation
1933 is already known to be empty.
1935 int isl_basic_set_plain_is_empty(__isl_keep isl_basic_set *bset);
1936 int isl_basic_set_is_empty(__isl_keep isl_basic_set *bset);
1937 int isl_set_plain_is_empty(__isl_keep isl_set *set);
1938 int isl_set_is_empty(__isl_keep isl_set *set);
1939 int isl_union_set_is_empty(__isl_keep isl_union_set *uset);
1940 int isl_basic_map_plain_is_empty(__isl_keep isl_basic_map *bmap);
1941 int isl_basic_map_is_empty(__isl_keep isl_basic_map *bmap);
1942 int isl_map_plain_is_empty(__isl_keep isl_map *map);
1943 int isl_map_is_empty(__isl_keep isl_map *map);
1944 int isl_union_map_is_empty(__isl_keep isl_union_map *umap);
1946 =item * Universality
1948 int isl_basic_set_is_universe(__isl_keep isl_basic_set *bset);
1949 int isl_basic_map_is_universe(__isl_keep isl_basic_map *bmap);
1950 int isl_set_plain_is_universe(__isl_keep isl_set *set);
1952 =item * Single-valuedness
1954 int isl_basic_map_is_single_valued(
1955 __isl_keep isl_basic_map *bmap);
1956 int isl_map_plain_is_single_valued(
1957 __isl_keep isl_map *map);
1958 int isl_map_is_single_valued(__isl_keep isl_map *map);
1959 int isl_union_map_is_single_valued(__isl_keep isl_union_map *umap);
1963 int isl_map_plain_is_injective(__isl_keep isl_map *map);
1964 int isl_map_is_injective(__isl_keep isl_map *map);
1965 int isl_union_map_plain_is_injective(
1966 __isl_keep isl_union_map *umap);
1967 int isl_union_map_is_injective(
1968 __isl_keep isl_union_map *umap);
1972 int isl_map_is_bijective(__isl_keep isl_map *map);
1973 int isl_union_map_is_bijective(__isl_keep isl_union_map *umap);
1977 __isl_give isl_val *
1978 isl_basic_map_plain_get_val_if_fixed(
1979 __isl_keep isl_basic_map *bmap,
1980 enum isl_dim_type type, unsigned pos);
1981 __isl_give isl_val *isl_set_plain_get_val_if_fixed(
1982 __isl_keep isl_set *set,
1983 enum isl_dim_type type, unsigned pos);
1984 __isl_give isl_val *isl_map_plain_get_val_if_fixed(
1985 __isl_keep isl_map *map,
1986 enum isl_dim_type type, unsigned pos);
1988 If the set or relation obviously lies on a hyperplane where the given dimension
1989 has a fixed value, then return that value.
1990 Otherwise return NaN.
1994 int isl_set_dim_residue_class_val(
1995 __isl_keep isl_set *set,
1996 int pos, __isl_give isl_val **modulo,
1997 __isl_give isl_val **residue);
1999 Check if the values of the given set dimension are equal to a fixed
2000 value modulo some integer value. If so, assign the modulo to C<*modulo>
2001 and the fixed value to C<*residue>. If the given dimension attains only
2002 a single value, then assign C<0> to C<*modulo> and the fixed value to
2004 If the dimension does not attain only a single value and if no modulo
2005 can be found then assign C<1> to C<*modulo> and C<1> to C<*residue>.
2009 To check whether a set is a parameter domain, use this function:
2011 int isl_set_is_params(__isl_keep isl_set *set);
2012 int isl_union_set_is_params(
2013 __isl_keep isl_union_set *uset);
2017 The following functions check whether the space of the given
2018 (basic) set or relation range is a wrapped relation.
2020 int isl_basic_set_is_wrapping(
2021 __isl_keep isl_basic_set *bset);
2022 int isl_set_is_wrapping(__isl_keep isl_set *set);
2023 int isl_map_range_is_wrapping(
2024 __isl_keep isl_map *map);
2026 =item * Internal Product
2028 int isl_basic_map_can_zip(
2029 __isl_keep isl_basic_map *bmap);
2030 int isl_map_can_zip(__isl_keep isl_map *map);
2032 Check whether the product of domain and range of the given relation
2034 i.e., whether both domain and range are nested relations.
2038 int isl_basic_map_can_curry(
2039 __isl_keep isl_basic_map *bmap);
2040 int isl_map_can_curry(__isl_keep isl_map *map);
2042 Check whether the domain of the (basic) relation is a wrapped relation.
2044 int isl_basic_map_can_uncurry(
2045 __isl_keep isl_basic_map *bmap);
2046 int isl_map_can_uncurry(__isl_keep isl_map *map);
2048 Check whether the range of the (basic) relation is a wrapped relation.
2052 =head3 Binary Properties
2058 int isl_basic_set_plain_is_equal(
2059 __isl_keep isl_basic_set *bset1,
2060 __isl_keep isl_basic_set *bset2);
2061 int isl_set_plain_is_equal(__isl_keep isl_set *set1,
2062 __isl_keep isl_set *set2);
2063 int isl_set_is_equal(__isl_keep isl_set *set1,
2064 __isl_keep isl_set *set2);
2065 int isl_union_set_is_equal(
2066 __isl_keep isl_union_set *uset1,
2067 __isl_keep isl_union_set *uset2);
2068 int isl_basic_map_is_equal(
2069 __isl_keep isl_basic_map *bmap1,
2070 __isl_keep isl_basic_map *bmap2);
2071 int isl_map_is_equal(__isl_keep isl_map *map1,
2072 __isl_keep isl_map *map2);
2073 int isl_map_plain_is_equal(__isl_keep isl_map *map1,
2074 __isl_keep isl_map *map2);
2075 int isl_union_map_is_equal(
2076 __isl_keep isl_union_map *umap1,
2077 __isl_keep isl_union_map *umap2);
2079 =item * Disjointness
2081 int isl_basic_set_is_disjoint(
2082 __isl_keep isl_basic_set *bset1,
2083 __isl_keep isl_basic_set *bset2);
2084 int isl_set_plain_is_disjoint(__isl_keep isl_set *set1,
2085 __isl_keep isl_set *set2);
2086 int isl_set_is_disjoint(__isl_keep isl_set *set1,
2087 __isl_keep isl_set *set2);
2088 int isl_basic_map_is_disjoint(
2089 __isl_keep isl_basic_map *bmap1,
2090 __isl_keep isl_basic_map *bmap2);
2091 int isl_map_is_disjoint(__isl_keep isl_map *map1,
2092 __isl_keep isl_map *map2);
2096 int isl_basic_set_is_subset(
2097 __isl_keep isl_basic_set *bset1,
2098 __isl_keep isl_basic_set *bset2);
2099 int isl_set_is_subset(__isl_keep isl_set *set1,
2100 __isl_keep isl_set *set2);
2101 int isl_set_is_strict_subset(
2102 __isl_keep isl_set *set1,
2103 __isl_keep isl_set *set2);
2104 int isl_union_set_is_subset(
2105 __isl_keep isl_union_set *uset1,
2106 __isl_keep isl_union_set *uset2);
2107 int isl_union_set_is_strict_subset(
2108 __isl_keep isl_union_set *uset1,
2109 __isl_keep isl_union_set *uset2);
2110 int isl_basic_map_is_subset(
2111 __isl_keep isl_basic_map *bmap1,
2112 __isl_keep isl_basic_map *bmap2);
2113 int isl_basic_map_is_strict_subset(
2114 __isl_keep isl_basic_map *bmap1,
2115 __isl_keep isl_basic_map *bmap2);
2116 int isl_map_is_subset(
2117 __isl_keep isl_map *map1,
2118 __isl_keep isl_map *map2);
2119 int isl_map_is_strict_subset(
2120 __isl_keep isl_map *map1,
2121 __isl_keep isl_map *map2);
2122 int isl_union_map_is_subset(
2123 __isl_keep isl_union_map *umap1,
2124 __isl_keep isl_union_map *umap2);
2125 int isl_union_map_is_strict_subset(
2126 __isl_keep isl_union_map *umap1,
2127 __isl_keep isl_union_map *umap2);
2129 Check whether the first argument is a (strict) subset of the
2134 int isl_set_plain_cmp(__isl_keep isl_set *set1,
2135 __isl_keep isl_set *set2);
2137 This function is useful for sorting C<isl_set>s.
2138 The order depends on the internal representation of the inputs.
2139 The order is fixed over different calls to the function (assuming
2140 the internal representation of the inputs has not changed), but may
2141 change over different versions of C<isl>.
2145 =head2 Unary Operations
2151 __isl_give isl_set *isl_set_complement(
2152 __isl_take isl_set *set);
2153 __isl_give isl_map *isl_map_complement(
2154 __isl_take isl_map *map);
2158 __isl_give isl_basic_map *isl_basic_map_reverse(
2159 __isl_take isl_basic_map *bmap);
2160 __isl_give isl_map *isl_map_reverse(
2161 __isl_take isl_map *map);
2162 __isl_give isl_union_map *isl_union_map_reverse(
2163 __isl_take isl_union_map *umap);
2167 __isl_give isl_basic_set *isl_basic_set_project_out(
2168 __isl_take isl_basic_set *bset,
2169 enum isl_dim_type type, unsigned first, unsigned n);
2170 __isl_give isl_basic_map *isl_basic_map_project_out(
2171 __isl_take isl_basic_map *bmap,
2172 enum isl_dim_type type, unsigned first, unsigned n);
2173 __isl_give isl_set *isl_set_project_out(__isl_take isl_set *set,
2174 enum isl_dim_type type, unsigned first, unsigned n);
2175 __isl_give isl_map *isl_map_project_out(__isl_take isl_map *map,
2176 enum isl_dim_type type, unsigned first, unsigned n);
2177 __isl_give isl_basic_set *isl_basic_set_params(
2178 __isl_take isl_basic_set *bset);
2179 __isl_give isl_basic_set *isl_basic_map_domain(
2180 __isl_take isl_basic_map *bmap);
2181 __isl_give isl_basic_set *isl_basic_map_range(
2182 __isl_take isl_basic_map *bmap);
2183 __isl_give isl_set *isl_set_params(__isl_take isl_set *set);
2184 __isl_give isl_set *isl_map_params(__isl_take isl_map *map);
2185 __isl_give isl_set *isl_map_domain(
2186 __isl_take isl_map *bmap);
2187 __isl_give isl_set *isl_map_range(
2188 __isl_take isl_map *map);
2189 __isl_give isl_set *isl_union_set_params(
2190 __isl_take isl_union_set *uset);
2191 __isl_give isl_set *isl_union_map_params(
2192 __isl_take isl_union_map *umap);
2193 __isl_give isl_union_set *isl_union_map_domain(
2194 __isl_take isl_union_map *umap);
2195 __isl_give isl_union_set *isl_union_map_range(
2196 __isl_take isl_union_map *umap);
2198 __isl_give isl_basic_map *isl_basic_map_domain_map(
2199 __isl_take isl_basic_map *bmap);
2200 __isl_give isl_basic_map *isl_basic_map_range_map(
2201 __isl_take isl_basic_map *bmap);
2202 __isl_give isl_map *isl_map_domain_map(__isl_take isl_map *map);
2203 __isl_give isl_map *isl_map_range_map(__isl_take isl_map *map);
2204 __isl_give isl_union_map *isl_union_map_domain_map(
2205 __isl_take isl_union_map *umap);
2206 __isl_give isl_union_map *isl_union_map_range_map(
2207 __isl_take isl_union_map *umap);
2209 The functions above construct a (basic, regular or union) relation
2210 that maps (a wrapped version of) the input relation to its domain or range.
2214 __isl_give isl_basic_set *isl_basic_set_eliminate(
2215 __isl_take isl_basic_set *bset,
2216 enum isl_dim_type type,
2217 unsigned first, unsigned n);
2218 __isl_give isl_set *isl_set_eliminate(
2219 __isl_take isl_set *set, enum isl_dim_type type,
2220 unsigned first, unsigned n);
2221 __isl_give isl_basic_map *isl_basic_map_eliminate(
2222 __isl_take isl_basic_map *bmap,
2223 enum isl_dim_type type,
2224 unsigned first, unsigned n);
2225 __isl_give isl_map *isl_map_eliminate(
2226 __isl_take isl_map *map, enum isl_dim_type type,
2227 unsigned first, unsigned n);
2229 Eliminate the coefficients for the given dimensions from the constraints,
2230 without removing the dimensions.
2234 __isl_give isl_basic_set *isl_basic_set_fix_si(
2235 __isl_take isl_basic_set *bset,
2236 enum isl_dim_type type, unsigned pos, int value);
2237 __isl_give isl_basic_set *isl_basic_set_fix_val(
2238 __isl_take isl_basic_set *bset,
2239 enum isl_dim_type type, unsigned pos,
2240 __isl_take isl_val *v);
2241 __isl_give isl_set *isl_set_fix_si(__isl_take isl_set *set,
2242 enum isl_dim_type type, unsigned pos, int value);
2243 __isl_give isl_set *isl_set_fix_val(
2244 __isl_take isl_set *set,
2245 enum isl_dim_type type, unsigned pos,
2246 __isl_take isl_val *v);
2247 __isl_give isl_basic_map *isl_basic_map_fix_si(
2248 __isl_take isl_basic_map *bmap,
2249 enum isl_dim_type type, unsigned pos, int value);
2250 __isl_give isl_basic_map *isl_basic_map_fix_val(
2251 __isl_take isl_basic_map *bmap,
2252 enum isl_dim_type type, unsigned pos,
2253 __isl_take isl_val *v);
2254 __isl_give isl_map *isl_map_fix_si(__isl_take isl_map *map,
2255 enum isl_dim_type type, unsigned pos, int value);
2256 __isl_give isl_map *isl_map_fix_val(
2257 __isl_take isl_map *map,
2258 enum isl_dim_type type, unsigned pos,
2259 __isl_take isl_val *v);
2261 Intersect the set or relation with the hyperplane where the given
2262 dimension has the fixed given value.
2264 __isl_give isl_basic_map *isl_basic_map_lower_bound_si(
2265 __isl_take isl_basic_map *bmap,
2266 enum isl_dim_type type, unsigned pos, int value);
2267 __isl_give isl_basic_map *isl_basic_map_upper_bound_si(
2268 __isl_take isl_basic_map *bmap,
2269 enum isl_dim_type type, unsigned pos, int value);
2270 __isl_give isl_set *isl_set_lower_bound_si(
2271 __isl_take isl_set *set,
2272 enum isl_dim_type type, unsigned pos, int value);
2273 __isl_give isl_set *isl_set_lower_bound_val(
2274 __isl_take isl_set *set,
2275 enum isl_dim_type type, unsigned pos,
2276 __isl_take isl_val *value);
2277 __isl_give isl_map *isl_map_lower_bound_si(
2278 __isl_take isl_map *map,
2279 enum isl_dim_type type, unsigned pos, int value);
2280 __isl_give isl_set *isl_set_upper_bound_si(
2281 __isl_take isl_set *set,
2282 enum isl_dim_type type, unsigned pos, int value);
2283 __isl_give isl_set *isl_set_upper_bound_val(
2284 __isl_take isl_set *set,
2285 enum isl_dim_type type, unsigned pos,
2286 __isl_take isl_val *value);
2287 __isl_give isl_map *isl_map_upper_bound_si(
2288 __isl_take isl_map *map,
2289 enum isl_dim_type type, unsigned pos, int value);
2291 Intersect the set or relation with the half-space where the given
2292 dimension has a value bounded by the fixed given integer value.
2294 __isl_give isl_set *isl_set_equate(__isl_take isl_set *set,
2295 enum isl_dim_type type1, int pos1,
2296 enum isl_dim_type type2, int pos2);
2297 __isl_give isl_basic_map *isl_basic_map_equate(
2298 __isl_take isl_basic_map *bmap,
2299 enum isl_dim_type type1, int pos1,
2300 enum isl_dim_type type2, int pos2);
2301 __isl_give isl_map *isl_map_equate(__isl_take isl_map *map,
2302 enum isl_dim_type type1, int pos1,
2303 enum isl_dim_type type2, int pos2);
2305 Intersect the set or relation with the hyperplane where the given
2306 dimensions are equal to each other.
2308 __isl_give isl_map *isl_map_oppose(__isl_take isl_map *map,
2309 enum isl_dim_type type1, int pos1,
2310 enum isl_dim_type type2, int pos2);
2312 Intersect the relation with the hyperplane where the given
2313 dimensions have opposite values.
2315 __isl_give isl_basic_map *isl_basic_map_order_ge(
2316 __isl_take isl_basic_map *bmap,
2317 enum isl_dim_type type1, int pos1,
2318 enum isl_dim_type type2, int pos2);
2319 __isl_give isl_map *isl_map_order_lt(__isl_take isl_map *map,
2320 enum isl_dim_type type1, int pos1,
2321 enum isl_dim_type type2, int pos2);
2322 __isl_give isl_basic_map *isl_basic_map_order_gt(
2323 __isl_take isl_basic_map *bmap,
2324 enum isl_dim_type type1, int pos1,
2325 enum isl_dim_type type2, int pos2);
2326 __isl_give isl_map *isl_map_order_gt(__isl_take isl_map *map,
2327 enum isl_dim_type type1, int pos1,
2328 enum isl_dim_type type2, int pos2);
2330 Intersect the relation with the half-space where the given
2331 dimensions satisfy the given ordering.
2335 __isl_give isl_map *isl_set_identity(
2336 __isl_take isl_set *set);
2337 __isl_give isl_union_map *isl_union_set_identity(
2338 __isl_take isl_union_set *uset);
2340 Construct an identity relation on the given (union) set.
2344 __isl_give isl_basic_set *isl_basic_map_deltas(
2345 __isl_take isl_basic_map *bmap);
2346 __isl_give isl_set *isl_map_deltas(__isl_take isl_map *map);
2347 __isl_give isl_union_set *isl_union_map_deltas(
2348 __isl_take isl_union_map *umap);
2350 These functions return a (basic) set containing the differences
2351 between image elements and corresponding domain elements in the input.
2353 __isl_give isl_basic_map *isl_basic_map_deltas_map(
2354 __isl_take isl_basic_map *bmap);
2355 __isl_give isl_map *isl_map_deltas_map(
2356 __isl_take isl_map *map);
2357 __isl_give isl_union_map *isl_union_map_deltas_map(
2358 __isl_take isl_union_map *umap);
2360 The functions above construct a (basic, regular or union) relation
2361 that maps (a wrapped version of) the input relation to its delta set.
2365 Simplify the representation of a set or relation by trying
2366 to combine pairs of basic sets or relations into a single
2367 basic set or relation.
2369 __isl_give isl_set *isl_set_coalesce(__isl_take isl_set *set);
2370 __isl_give isl_map *isl_map_coalesce(__isl_take isl_map *map);
2371 __isl_give isl_union_set *isl_union_set_coalesce(
2372 __isl_take isl_union_set *uset);
2373 __isl_give isl_union_map *isl_union_map_coalesce(
2374 __isl_take isl_union_map *umap);
2376 One of the methods for combining pairs of basic sets or relations
2377 can result in coefficients that are much larger than those that appear
2378 in the constraints of the input. By default, the coefficients are
2379 not allowed to grow larger, but this can be changed by unsetting
2380 the following option.
2382 int isl_options_set_coalesce_bounded_wrapping(
2383 isl_ctx *ctx, int val);
2384 int isl_options_get_coalesce_bounded_wrapping(
2387 =item * Detecting equalities
2389 __isl_give isl_basic_set *isl_basic_set_detect_equalities(
2390 __isl_take isl_basic_set *bset);
2391 __isl_give isl_basic_map *isl_basic_map_detect_equalities(
2392 __isl_take isl_basic_map *bmap);
2393 __isl_give isl_set *isl_set_detect_equalities(
2394 __isl_take isl_set *set);
2395 __isl_give isl_map *isl_map_detect_equalities(
2396 __isl_take isl_map *map);
2397 __isl_give isl_union_set *isl_union_set_detect_equalities(
2398 __isl_take isl_union_set *uset);
2399 __isl_give isl_union_map *isl_union_map_detect_equalities(
2400 __isl_take isl_union_map *umap);
2402 Simplify the representation of a set or relation by detecting implicit
2405 =item * Removing redundant constraints
2407 __isl_give isl_basic_set *isl_basic_set_remove_redundancies(
2408 __isl_take isl_basic_set *bset);
2409 __isl_give isl_set *isl_set_remove_redundancies(
2410 __isl_take isl_set *set);
2411 __isl_give isl_basic_map *isl_basic_map_remove_redundancies(
2412 __isl_take isl_basic_map *bmap);
2413 __isl_give isl_map *isl_map_remove_redundancies(
2414 __isl_take isl_map *map);
2418 __isl_give isl_basic_set *isl_set_convex_hull(
2419 __isl_take isl_set *set);
2420 __isl_give isl_basic_map *isl_map_convex_hull(
2421 __isl_take isl_map *map);
2423 If the input set or relation has any existentially quantified
2424 variables, then the result of these operations is currently undefined.
2428 __isl_give isl_basic_set *
2429 isl_set_unshifted_simple_hull(
2430 __isl_take isl_set *set);
2431 __isl_give isl_basic_map *
2432 isl_map_unshifted_simple_hull(
2433 __isl_take isl_map *map);
2434 __isl_give isl_basic_set *isl_set_simple_hull(
2435 __isl_take isl_set *set);
2436 __isl_give isl_basic_map *isl_map_simple_hull(
2437 __isl_take isl_map *map);
2438 __isl_give isl_union_map *isl_union_map_simple_hull(
2439 __isl_take isl_union_map *umap);
2441 These functions compute a single basic set or relation
2442 that contains the whole input set or relation.
2443 In particular, the output is described by translates
2444 of the constraints describing the basic sets or relations in the input.
2445 In case of C<isl_set_unshifted_simple_hull>, only the original
2446 constraints are used, without any translation.
2450 (See \autoref{s:simple hull}.)
2456 __isl_give isl_basic_set *isl_basic_set_affine_hull(
2457 __isl_take isl_basic_set *bset);
2458 __isl_give isl_basic_set *isl_set_affine_hull(
2459 __isl_take isl_set *set);
2460 __isl_give isl_union_set *isl_union_set_affine_hull(
2461 __isl_take isl_union_set *uset);
2462 __isl_give isl_basic_map *isl_basic_map_affine_hull(
2463 __isl_take isl_basic_map *bmap);
2464 __isl_give isl_basic_map *isl_map_affine_hull(
2465 __isl_take isl_map *map);
2466 __isl_give isl_union_map *isl_union_map_affine_hull(
2467 __isl_take isl_union_map *umap);
2469 In case of union sets and relations, the affine hull is computed
2472 =item * Polyhedral hull
2474 __isl_give isl_basic_set *isl_set_polyhedral_hull(
2475 __isl_take isl_set *set);
2476 __isl_give isl_basic_map *isl_map_polyhedral_hull(
2477 __isl_take isl_map *map);
2478 __isl_give isl_union_set *isl_union_set_polyhedral_hull(
2479 __isl_take isl_union_set *uset);
2480 __isl_give isl_union_map *isl_union_map_polyhedral_hull(
2481 __isl_take isl_union_map *umap);
2483 These functions compute a single basic set or relation
2484 not involving any existentially quantified variables
2485 that contains the whole input set or relation.
2486 In case of union sets and relations, the polyhedral hull is computed
2489 =item * Other approximations
2491 __isl_give isl_basic_set *
2492 isl_basic_set_drop_constraints_involving_dims(
2493 __isl_take isl_basic_set *bset,
2494 enum isl_dim_type type,
2495 unsigned first, unsigned n);
2496 __isl_give isl_basic_map *
2497 isl_basic_map_drop_constraints_involving_dims(
2498 __isl_take isl_basic_map *bmap,
2499 enum isl_dim_type type,
2500 unsigned first, unsigned n);
2501 __isl_give isl_basic_set *
2502 isl_basic_set_drop_constraints_not_involving_dims(
2503 __isl_take isl_basic_set *bset,
2504 enum isl_dim_type type,
2505 unsigned first, unsigned n);
2506 __isl_give isl_set *
2507 isl_set_drop_constraints_involving_dims(
2508 __isl_take isl_set *set,
2509 enum isl_dim_type type,
2510 unsigned first, unsigned n);
2511 __isl_give isl_map *
2512 isl_map_drop_constraints_involving_dims(
2513 __isl_take isl_map *map,
2514 enum isl_dim_type type,
2515 unsigned first, unsigned n);
2517 These functions drop any constraints (not) involving the specified dimensions.
2518 Note that the result depends on the representation of the input.
2522 __isl_give isl_basic_set *isl_basic_set_sample(
2523 __isl_take isl_basic_set *bset);
2524 __isl_give isl_basic_set *isl_set_sample(
2525 __isl_take isl_set *set);
2526 __isl_give isl_basic_map *isl_basic_map_sample(
2527 __isl_take isl_basic_map *bmap);
2528 __isl_give isl_basic_map *isl_map_sample(
2529 __isl_take isl_map *map);
2531 If the input (basic) set or relation is non-empty, then return
2532 a singleton subset of the input. Otherwise, return an empty set.
2534 =item * Optimization
2536 #include <isl/ilp.h>
2537 __isl_give isl_val *isl_basic_set_max_val(
2538 __isl_keep isl_basic_set *bset,
2539 __isl_keep isl_aff *obj);
2540 __isl_give isl_val *isl_set_min_val(
2541 __isl_keep isl_set *set,
2542 __isl_keep isl_aff *obj);
2543 __isl_give isl_val *isl_set_max_val(
2544 __isl_keep isl_set *set,
2545 __isl_keep isl_aff *obj);
2547 Compute the minimum or maximum of the integer affine expression C<obj>
2548 over the points in C<set>, returning the result in C<opt>.
2549 The result is C<NULL> in case of an error, the optimal value in case
2550 there is one, negative infinity or infinity if the problem is unbounded and
2551 NaN if the problem is empty.
2553 =item * Parametric optimization
2555 __isl_give isl_pw_aff *isl_set_dim_min(
2556 __isl_take isl_set *set, int pos);
2557 __isl_give isl_pw_aff *isl_set_dim_max(
2558 __isl_take isl_set *set, int pos);
2559 __isl_give isl_pw_aff *isl_map_dim_max(
2560 __isl_take isl_map *map, int pos);
2562 Compute the minimum or maximum of the given set or output dimension
2563 as a function of the parameters (and input dimensions), but independently
2564 of the other set or output dimensions.
2565 For lexicographic optimization, see L<"Lexicographic Optimization">.
2569 The following functions compute either the set of (rational) coefficient
2570 values of valid constraints for the given set or the set of (rational)
2571 values satisfying the constraints with coefficients from the given set.
2572 Internally, these two sets of functions perform essentially the
2573 same operations, except that the set of coefficients is assumed to
2574 be a cone, while the set of values may be any polyhedron.
2575 The current implementation is based on the Farkas lemma and
2576 Fourier-Motzkin elimination, but this may change or be made optional
2577 in future. In particular, future implementations may use different
2578 dualization algorithms or skip the elimination step.
2580 __isl_give isl_basic_set *isl_basic_set_coefficients(
2581 __isl_take isl_basic_set *bset);
2582 __isl_give isl_basic_set *isl_set_coefficients(
2583 __isl_take isl_set *set);
2584 __isl_give isl_union_set *isl_union_set_coefficients(
2585 __isl_take isl_union_set *bset);
2586 __isl_give isl_basic_set *isl_basic_set_solutions(
2587 __isl_take isl_basic_set *bset);
2588 __isl_give isl_basic_set *isl_set_solutions(
2589 __isl_take isl_set *set);
2590 __isl_give isl_union_set *isl_union_set_solutions(
2591 __isl_take isl_union_set *bset);
2595 __isl_give isl_map *isl_map_fixed_power_val(
2596 __isl_take isl_map *map,
2597 __isl_take isl_val *exp);
2598 __isl_give isl_union_map *
2599 isl_union_map_fixed_power_val(
2600 __isl_take isl_union_map *umap,
2601 __isl_take isl_val *exp);
2603 Compute the given power of C<map>, where C<exp> is assumed to be non-zero.
2604 If the exponent C<exp> is negative, then the -C<exp> th power of the inverse
2605 of C<map> is computed.
2607 __isl_give isl_map *isl_map_power(__isl_take isl_map *map,
2609 __isl_give isl_union_map *isl_union_map_power(
2610 __isl_take isl_union_map *umap, int *exact);
2612 Compute a parametric representation for all positive powers I<k> of C<map>.
2613 The result maps I<k> to a nested relation corresponding to the
2614 I<k>th power of C<map>.
2615 The result may be an overapproximation. If the result is known to be exact,
2616 then C<*exact> is set to C<1>.
2618 =item * Transitive closure
2620 __isl_give isl_map *isl_map_transitive_closure(
2621 __isl_take isl_map *map, int *exact);
2622 __isl_give isl_union_map *isl_union_map_transitive_closure(
2623 __isl_take isl_union_map *umap, int *exact);
2625 Compute the transitive closure of C<map>.
2626 The result may be an overapproximation. If the result is known to be exact,
2627 then C<*exact> is set to C<1>.
2629 =item * Reaching path lengths
2631 __isl_give isl_map *isl_map_reaching_path_lengths(
2632 __isl_take isl_map *map, int *exact);
2634 Compute a relation that maps each element in the range of C<map>
2635 to the lengths of all paths composed of edges in C<map> that
2636 end up in the given element.
2637 The result may be an overapproximation. If the result is known to be exact,
2638 then C<*exact> is set to C<1>.
2639 To compute the I<maximal> path length, the resulting relation
2640 should be postprocessed by C<isl_map_lexmax>.
2641 In particular, if the input relation is a dependence relation
2642 (mapping sources to sinks), then the maximal path length corresponds
2643 to the free schedule.
2644 Note, however, that C<isl_map_lexmax> expects the maximum to be
2645 finite, so if the path lengths are unbounded (possibly due to
2646 the overapproximation), then you will get an error message.
2650 __isl_give isl_basic_set *isl_basic_map_wrap(
2651 __isl_take isl_basic_map *bmap);
2652 __isl_give isl_set *isl_map_wrap(
2653 __isl_take isl_map *map);
2654 __isl_give isl_union_set *isl_union_map_wrap(
2655 __isl_take isl_union_map *umap);
2656 __isl_give isl_basic_map *isl_basic_set_unwrap(
2657 __isl_take isl_basic_set *bset);
2658 __isl_give isl_map *isl_set_unwrap(
2659 __isl_take isl_set *set);
2660 __isl_give isl_union_map *isl_union_set_unwrap(
2661 __isl_take isl_union_set *uset);
2665 Remove any internal structure of domain (and range) of the given
2666 set or relation. If there is any such internal structure in the input,
2667 then the name of the space is also removed.
2669 __isl_give isl_basic_set *isl_basic_set_flatten(
2670 __isl_take isl_basic_set *bset);
2671 __isl_give isl_set *isl_set_flatten(
2672 __isl_take isl_set *set);
2673 __isl_give isl_basic_map *isl_basic_map_flatten_domain(
2674 __isl_take isl_basic_map *bmap);
2675 __isl_give isl_basic_map *isl_basic_map_flatten_range(
2676 __isl_take isl_basic_map *bmap);
2677 __isl_give isl_map *isl_map_flatten_range(
2678 __isl_take isl_map *map);
2679 __isl_give isl_map *isl_map_flatten_domain(
2680 __isl_take isl_map *map);
2681 __isl_give isl_basic_map *isl_basic_map_flatten(
2682 __isl_take isl_basic_map *bmap);
2683 __isl_give isl_map *isl_map_flatten(
2684 __isl_take isl_map *map);
2686 __isl_give isl_map *isl_set_flatten_map(
2687 __isl_take isl_set *set);
2689 The function above constructs a relation
2690 that maps the input set to a flattened version of the set.
2694 Lift the input set to a space with extra dimensions corresponding
2695 to the existentially quantified variables in the input.
2696 In particular, the result lives in a wrapped map where the domain
2697 is the original space and the range corresponds to the original
2698 existentially quantified variables.
2700 __isl_give isl_basic_set *isl_basic_set_lift(
2701 __isl_take isl_basic_set *bset);
2702 __isl_give isl_set *isl_set_lift(
2703 __isl_take isl_set *set);
2704 __isl_give isl_union_set *isl_union_set_lift(
2705 __isl_take isl_union_set *uset);
2707 Given a local space that contains the existentially quantified
2708 variables of a set, a basic relation that, when applied to
2709 a basic set, has essentially the same effect as C<isl_basic_set_lift>,
2710 can be constructed using the following function.
2712 #include <isl/local_space.h>
2713 __isl_give isl_basic_map *isl_local_space_lifting(
2714 __isl_take isl_local_space *ls);
2716 =item * Internal Product
2718 __isl_give isl_basic_map *isl_basic_map_zip(
2719 __isl_take isl_basic_map *bmap);
2720 __isl_give isl_map *isl_map_zip(
2721 __isl_take isl_map *map);
2722 __isl_give isl_union_map *isl_union_map_zip(
2723 __isl_take isl_union_map *umap);
2725 Given a relation with nested relations for domain and range,
2726 interchange the range of the domain with the domain of the range.
2730 __isl_give isl_basic_map *isl_basic_map_curry(
2731 __isl_take isl_basic_map *bmap);
2732 __isl_give isl_basic_map *isl_basic_map_uncurry(
2733 __isl_take isl_basic_map *bmap);
2734 __isl_give isl_map *isl_map_curry(
2735 __isl_take isl_map *map);
2736 __isl_give isl_map *isl_map_uncurry(
2737 __isl_take isl_map *map);
2738 __isl_give isl_union_map *isl_union_map_curry(
2739 __isl_take isl_union_map *umap);
2740 __isl_give isl_union_map *isl_union_map_uncurry(
2741 __isl_take isl_union_map *umap);
2743 Given a relation with a nested relation for domain,
2744 the C<curry> functions
2745 move the range of the nested relation out of the domain
2746 and use it as the domain of a nested relation in the range,
2747 with the original range as range of this nested relation.
2748 The C<uncurry> functions perform the inverse operation.
2750 =item * Aligning parameters
2752 __isl_give isl_basic_set *isl_basic_set_align_params(
2753 __isl_take isl_basic_set *bset,
2754 __isl_take isl_space *model);
2755 __isl_give isl_set *isl_set_align_params(
2756 __isl_take isl_set *set,
2757 __isl_take isl_space *model);
2758 __isl_give isl_basic_map *isl_basic_map_align_params(
2759 __isl_take isl_basic_map *bmap,
2760 __isl_take isl_space *model);
2761 __isl_give isl_map *isl_map_align_params(
2762 __isl_take isl_map *map,
2763 __isl_take isl_space *model);
2765 Change the order of the parameters of the given set or relation
2766 such that the first parameters match those of C<model>.
2767 This may involve the introduction of extra parameters.
2768 All parameters need to be named.
2770 =item * Dimension manipulation
2772 __isl_give isl_basic_set *isl_basic_set_add_dims(
2773 __isl_take isl_basic_set *bset,
2774 enum isl_dim_type type, unsigned n);
2775 __isl_give isl_set *isl_set_add_dims(
2776 __isl_take isl_set *set,
2777 enum isl_dim_type type, unsigned n);
2778 __isl_give isl_map *isl_map_add_dims(
2779 __isl_take isl_map *map,
2780 enum isl_dim_type type, unsigned n);
2781 __isl_give isl_basic_set *isl_basic_set_insert_dims(
2782 __isl_take isl_basic_set *bset,
2783 enum isl_dim_type type, unsigned pos,
2785 __isl_give isl_basic_map *isl_basic_map_insert_dims(
2786 __isl_take isl_basic_map *bmap,
2787 enum isl_dim_type type, unsigned pos,
2789 __isl_give isl_set *isl_set_insert_dims(
2790 __isl_take isl_set *set,
2791 enum isl_dim_type type, unsigned pos, unsigned n);
2792 __isl_give isl_map *isl_map_insert_dims(
2793 __isl_take isl_map *map,
2794 enum isl_dim_type type, unsigned pos, unsigned n);
2795 __isl_give isl_basic_set *isl_basic_set_move_dims(
2796 __isl_take isl_basic_set *bset,
2797 enum isl_dim_type dst_type, unsigned dst_pos,
2798 enum isl_dim_type src_type, unsigned src_pos,
2800 __isl_give isl_basic_map *isl_basic_map_move_dims(
2801 __isl_take isl_basic_map *bmap,
2802 enum isl_dim_type dst_type, unsigned dst_pos,
2803 enum isl_dim_type src_type, unsigned src_pos,
2805 __isl_give isl_set *isl_set_move_dims(
2806 __isl_take isl_set *set,
2807 enum isl_dim_type dst_type, unsigned dst_pos,
2808 enum isl_dim_type src_type, unsigned src_pos,
2810 __isl_give isl_map *isl_map_move_dims(
2811 __isl_take isl_map *map,
2812 enum isl_dim_type dst_type, unsigned dst_pos,
2813 enum isl_dim_type src_type, unsigned src_pos,
2816 It is usually not advisable to directly change the (input or output)
2817 space of a set or a relation as this removes the name and the internal
2818 structure of the space. However, the above functions can be useful
2819 to add new parameters, assuming
2820 C<isl_set_align_params> and C<isl_map_align_params>
2825 =head2 Binary Operations
2827 The two arguments of a binary operation not only need to live
2828 in the same C<isl_ctx>, they currently also need to have
2829 the same (number of) parameters.
2831 =head3 Basic Operations
2835 =item * Intersection
2837 __isl_give isl_basic_set *isl_basic_set_intersect_params(
2838 __isl_take isl_basic_set *bset1,
2839 __isl_take isl_basic_set *bset2);
2840 __isl_give isl_basic_set *isl_basic_set_intersect(
2841 __isl_take isl_basic_set *bset1,
2842 __isl_take isl_basic_set *bset2);
2843 __isl_give isl_set *isl_set_intersect_params(
2844 __isl_take isl_set *set,
2845 __isl_take isl_set *params);
2846 __isl_give isl_set *isl_set_intersect(
2847 __isl_take isl_set *set1,
2848 __isl_take isl_set *set2);
2849 __isl_give isl_union_set *isl_union_set_intersect_params(
2850 __isl_take isl_union_set *uset,
2851 __isl_take isl_set *set);
2852 __isl_give isl_union_map *isl_union_map_intersect_params(
2853 __isl_take isl_union_map *umap,
2854 __isl_take isl_set *set);
2855 __isl_give isl_union_set *isl_union_set_intersect(
2856 __isl_take isl_union_set *uset1,
2857 __isl_take isl_union_set *uset2);
2858 __isl_give isl_basic_map *isl_basic_map_intersect_domain(
2859 __isl_take isl_basic_map *bmap,
2860 __isl_take isl_basic_set *bset);
2861 __isl_give isl_basic_map *isl_basic_map_intersect_range(
2862 __isl_take isl_basic_map *bmap,
2863 __isl_take isl_basic_set *bset);
2864 __isl_give isl_basic_map *isl_basic_map_intersect(
2865 __isl_take isl_basic_map *bmap1,
2866 __isl_take isl_basic_map *bmap2);
2867 __isl_give isl_map *isl_map_intersect_params(
2868 __isl_take isl_map *map,
2869 __isl_take isl_set *params);
2870 __isl_give isl_map *isl_map_intersect_domain(
2871 __isl_take isl_map *map,
2872 __isl_take isl_set *set);
2873 __isl_give isl_map *isl_map_intersect_range(
2874 __isl_take isl_map *map,
2875 __isl_take isl_set *set);
2876 __isl_give isl_map *isl_map_intersect(
2877 __isl_take isl_map *map1,
2878 __isl_take isl_map *map2);
2879 __isl_give isl_union_map *isl_union_map_intersect_domain(
2880 __isl_take isl_union_map *umap,
2881 __isl_take isl_union_set *uset);
2882 __isl_give isl_union_map *isl_union_map_intersect_range(
2883 __isl_take isl_union_map *umap,
2884 __isl_take isl_union_set *uset);
2885 __isl_give isl_union_map *isl_union_map_intersect(
2886 __isl_take isl_union_map *umap1,
2887 __isl_take isl_union_map *umap2);
2889 The second argument to the C<_params> functions needs to be
2890 a parametric (basic) set. For the other functions, a parametric set
2891 for either argument is only allowed if the other argument is
2892 a parametric set as well.
2896 __isl_give isl_set *isl_basic_set_union(
2897 __isl_take isl_basic_set *bset1,
2898 __isl_take isl_basic_set *bset2);
2899 __isl_give isl_map *isl_basic_map_union(
2900 __isl_take isl_basic_map *bmap1,
2901 __isl_take isl_basic_map *bmap2);
2902 __isl_give isl_set *isl_set_union(
2903 __isl_take isl_set *set1,
2904 __isl_take isl_set *set2);
2905 __isl_give isl_map *isl_map_union(
2906 __isl_take isl_map *map1,
2907 __isl_take isl_map *map2);
2908 __isl_give isl_union_set *isl_union_set_union(
2909 __isl_take isl_union_set *uset1,
2910 __isl_take isl_union_set *uset2);
2911 __isl_give isl_union_map *isl_union_map_union(
2912 __isl_take isl_union_map *umap1,
2913 __isl_take isl_union_map *umap2);
2915 =item * Set difference
2917 __isl_give isl_set *isl_set_subtract(
2918 __isl_take isl_set *set1,
2919 __isl_take isl_set *set2);
2920 __isl_give isl_map *isl_map_subtract(
2921 __isl_take isl_map *map1,
2922 __isl_take isl_map *map2);
2923 __isl_give isl_map *isl_map_subtract_domain(
2924 __isl_take isl_map *map,
2925 __isl_take isl_set *dom);
2926 __isl_give isl_map *isl_map_subtract_range(
2927 __isl_take isl_map *map,
2928 __isl_take isl_set *dom);
2929 __isl_give isl_union_set *isl_union_set_subtract(
2930 __isl_take isl_union_set *uset1,
2931 __isl_take isl_union_set *uset2);
2932 __isl_give isl_union_map *isl_union_map_subtract(
2933 __isl_take isl_union_map *umap1,
2934 __isl_take isl_union_map *umap2);
2935 __isl_give isl_union_map *isl_union_map_subtract_domain(
2936 __isl_take isl_union_map *umap,
2937 __isl_take isl_union_set *dom);
2938 __isl_give isl_union_map *isl_union_map_subtract_range(
2939 __isl_take isl_union_map *umap,
2940 __isl_take isl_union_set *dom);
2944 __isl_give isl_basic_set *isl_basic_set_apply(
2945 __isl_take isl_basic_set *bset,
2946 __isl_take isl_basic_map *bmap);
2947 __isl_give isl_set *isl_set_apply(
2948 __isl_take isl_set *set,
2949 __isl_take isl_map *map);
2950 __isl_give isl_union_set *isl_union_set_apply(
2951 __isl_take isl_union_set *uset,
2952 __isl_take isl_union_map *umap);
2953 __isl_give isl_basic_map *isl_basic_map_apply_domain(
2954 __isl_take isl_basic_map *bmap1,
2955 __isl_take isl_basic_map *bmap2);
2956 __isl_give isl_basic_map *isl_basic_map_apply_range(
2957 __isl_take isl_basic_map *bmap1,
2958 __isl_take isl_basic_map *bmap2);
2959 __isl_give isl_map *isl_map_apply_domain(
2960 __isl_take isl_map *map1,
2961 __isl_take isl_map *map2);
2962 __isl_give isl_union_map *isl_union_map_apply_domain(
2963 __isl_take isl_union_map *umap1,
2964 __isl_take isl_union_map *umap2);
2965 __isl_give isl_map *isl_map_apply_range(
2966 __isl_take isl_map *map1,
2967 __isl_take isl_map *map2);
2968 __isl_give isl_union_map *isl_union_map_apply_range(
2969 __isl_take isl_union_map *umap1,
2970 __isl_take isl_union_map *umap2);
2974 __isl_give isl_basic_set *
2975 isl_basic_set_preimage_multi_aff(
2976 __isl_take isl_basic_set *bset,
2977 __isl_take isl_multi_aff *ma);
2978 __isl_give isl_set *isl_set_preimage_multi_aff(
2979 __isl_take isl_set *set,
2980 __isl_take isl_multi_aff *ma);
2981 __isl_give isl_set *isl_set_preimage_pw_multi_aff(
2982 __isl_take isl_set *set,
2983 __isl_take isl_pw_multi_aff *pma);
2984 __isl_give isl_set *isl_set_preimage_multi_pw_aff(
2985 __isl_take isl_set *set,
2986 __isl_take isl_multi_pw_aff *mpa);
2987 __isl_give isl_basic_map *
2988 isl_basic_map_preimage_domain_multi_aff(
2989 __isl_take isl_basic_map *bmap,
2990 __isl_take isl_multi_aff *ma);
2991 __isl_give isl_map *isl_map_preimage_domain_multi_aff(
2992 __isl_take isl_map *map,
2993 __isl_take isl_multi_aff *ma);
2994 __isl_give isl_map *
2995 isl_map_preimage_domain_pw_multi_aff(
2996 __isl_take isl_map *map,
2997 __isl_take isl_pw_multi_aff *pma);
2998 __isl_give isl_map *
2999 isl_map_preimage_domain_multi_pw_aff(
3000 __isl_take isl_map *map,
3001 __isl_take isl_multi_pw_aff *mpa);
3002 __isl_give isl_union_map *
3003 isl_union_map_preimage_domain_multi_aff(
3004 __isl_take isl_union_map *umap,
3005 __isl_take isl_multi_aff *ma);
3006 __isl_give isl_basic_map *
3007 isl_basic_map_preimage_range_multi_aff(
3008 __isl_take isl_basic_map *bmap,
3009 __isl_take isl_multi_aff *ma);
3011 These functions compute the preimage of the given set or map domain/range under
3012 the given function. In other words, the expression is plugged
3013 into the set description or into the domain/range of the map.
3014 Objects of types C<isl_multi_aff> and C<isl_pw_multi_aff> are described in
3015 L</"Piecewise Multiple Quasi Affine Expressions">.
3017 =item * Cartesian Product
3019 __isl_give isl_set *isl_set_product(
3020 __isl_take isl_set *set1,
3021 __isl_take isl_set *set2);
3022 __isl_give isl_union_set *isl_union_set_product(
3023 __isl_take isl_union_set *uset1,
3024 __isl_take isl_union_set *uset2);
3025 __isl_give isl_basic_map *isl_basic_map_domain_product(
3026 __isl_take isl_basic_map *bmap1,
3027 __isl_take isl_basic_map *bmap2);
3028 __isl_give isl_basic_map *isl_basic_map_range_product(
3029 __isl_take isl_basic_map *bmap1,
3030 __isl_take isl_basic_map *bmap2);
3031 __isl_give isl_basic_map *isl_basic_map_product(
3032 __isl_take isl_basic_map *bmap1,
3033 __isl_take isl_basic_map *bmap2);
3034 __isl_give isl_map *isl_map_domain_product(
3035 __isl_take isl_map *map1,
3036 __isl_take isl_map *map2);
3037 __isl_give isl_map *isl_map_range_product(
3038 __isl_take isl_map *map1,
3039 __isl_take isl_map *map2);
3040 __isl_give isl_union_map *isl_union_map_domain_product(
3041 __isl_take isl_union_map *umap1,
3042 __isl_take isl_union_map *umap2);
3043 __isl_give isl_union_map *isl_union_map_range_product(
3044 __isl_take isl_union_map *umap1,
3045 __isl_take isl_union_map *umap2);
3046 __isl_give isl_map *isl_map_product(
3047 __isl_take isl_map *map1,
3048 __isl_take isl_map *map2);
3049 __isl_give isl_union_map *isl_union_map_product(
3050 __isl_take isl_union_map *umap1,
3051 __isl_take isl_union_map *umap2);
3053 The above functions compute the cross product of the given
3054 sets or relations. The domains and ranges of the results
3055 are wrapped maps between domains and ranges of the inputs.
3056 To obtain a ``flat'' product, use the following functions
3059 __isl_give isl_basic_set *isl_basic_set_flat_product(
3060 __isl_take isl_basic_set *bset1,
3061 __isl_take isl_basic_set *bset2);
3062 __isl_give isl_set *isl_set_flat_product(
3063 __isl_take isl_set *set1,
3064 __isl_take isl_set *set2);
3065 __isl_give isl_basic_map *isl_basic_map_flat_range_product(
3066 __isl_take isl_basic_map *bmap1,
3067 __isl_take isl_basic_map *bmap2);
3068 __isl_give isl_map *isl_map_flat_domain_product(
3069 __isl_take isl_map *map1,
3070 __isl_take isl_map *map2);
3071 __isl_give isl_map *isl_map_flat_range_product(
3072 __isl_take isl_map *map1,
3073 __isl_take isl_map *map2);
3074 __isl_give isl_union_map *isl_union_map_flat_range_product(
3075 __isl_take isl_union_map *umap1,
3076 __isl_take isl_union_map *umap2);
3077 __isl_give isl_basic_map *isl_basic_map_flat_product(
3078 __isl_take isl_basic_map *bmap1,
3079 __isl_take isl_basic_map *bmap2);
3080 __isl_give isl_map *isl_map_flat_product(
3081 __isl_take isl_map *map1,
3082 __isl_take isl_map *map2);
3084 The arguments of a call to C<isl_map_product> can be extracted
3085 from the result using the following two functions.
3087 __isl_give isl_map *isl_map_range_factor_domain(
3088 __isl_take isl_map *map);
3089 __isl_give isl_map *isl_map_range_factor_range(
3090 __isl_take isl_map *map);
3092 =item * Simplification
3094 __isl_give isl_basic_set *isl_basic_set_gist(
3095 __isl_take isl_basic_set *bset,
3096 __isl_take isl_basic_set *context);
3097 __isl_give isl_set *isl_set_gist(__isl_take isl_set *set,
3098 __isl_take isl_set *context);
3099 __isl_give isl_set *isl_set_gist_params(
3100 __isl_take isl_set *set,
3101 __isl_take isl_set *context);
3102 __isl_give isl_union_set *isl_union_set_gist(
3103 __isl_take isl_union_set *uset,
3104 __isl_take isl_union_set *context);
3105 __isl_give isl_union_set *isl_union_set_gist_params(
3106 __isl_take isl_union_set *uset,
3107 __isl_take isl_set *set);
3108 __isl_give isl_basic_map *isl_basic_map_gist(
3109 __isl_take isl_basic_map *bmap,
3110 __isl_take isl_basic_map *context);
3111 __isl_give isl_map *isl_map_gist(__isl_take isl_map *map,
3112 __isl_take isl_map *context);
3113 __isl_give isl_map *isl_map_gist_params(
3114 __isl_take isl_map *map,
3115 __isl_take isl_set *context);
3116 __isl_give isl_map *isl_map_gist_domain(
3117 __isl_take isl_map *map,
3118 __isl_take isl_set *context);
3119 __isl_give isl_map *isl_map_gist_range(
3120 __isl_take isl_map *map,
3121 __isl_take isl_set *context);
3122 __isl_give isl_union_map *isl_union_map_gist(
3123 __isl_take isl_union_map *umap,
3124 __isl_take isl_union_map *context);
3125 __isl_give isl_union_map *isl_union_map_gist_params(
3126 __isl_take isl_union_map *umap,
3127 __isl_take isl_set *set);
3128 __isl_give isl_union_map *isl_union_map_gist_domain(
3129 __isl_take isl_union_map *umap,
3130 __isl_take isl_union_set *uset);
3131 __isl_give isl_union_map *isl_union_map_gist_range(
3132 __isl_take isl_union_map *umap,
3133 __isl_take isl_union_set *uset);
3135 The gist operation returns a set or relation that has the
3136 same intersection with the context as the input set or relation.
3137 Any implicit equality in the intersection is made explicit in the result,
3138 while all inequalities that are redundant with respect to the intersection
3140 In case of union sets and relations, the gist operation is performed
3145 =head3 Lexicographic Optimization
3147 Given a (basic) set C<set> (or C<bset>) and a zero-dimensional domain C<dom>,
3148 the following functions
3149 compute a set that contains the lexicographic minimum or maximum
3150 of the elements in C<set> (or C<bset>) for those values of the parameters
3151 that satisfy C<dom>.
3152 If C<empty> is not C<NULL>, then C<*empty> is assigned a set
3153 that contains the parameter values in C<dom> for which C<set> (or C<bset>)
3155 In other words, the union of the parameter values
3156 for which the result is non-empty and of C<*empty>
3159 __isl_give isl_set *isl_basic_set_partial_lexmin(
3160 __isl_take isl_basic_set *bset,
3161 __isl_take isl_basic_set *dom,
3162 __isl_give isl_set **empty);
3163 __isl_give isl_set *isl_basic_set_partial_lexmax(
3164 __isl_take isl_basic_set *bset,
3165 __isl_take isl_basic_set *dom,
3166 __isl_give isl_set **empty);
3167 __isl_give isl_set *isl_set_partial_lexmin(
3168 __isl_take isl_set *set, __isl_take isl_set *dom,
3169 __isl_give isl_set **empty);
3170 __isl_give isl_set *isl_set_partial_lexmax(
3171 __isl_take isl_set *set, __isl_take isl_set *dom,
3172 __isl_give isl_set **empty);
3174 Given a (basic) set C<set> (or C<bset>), the following functions simply
3175 return a set containing the lexicographic minimum or maximum
3176 of the elements in C<set> (or C<bset>).
3177 In case of union sets, the optimum is computed per space.
3179 __isl_give isl_set *isl_basic_set_lexmin(
3180 __isl_take isl_basic_set *bset);
3181 __isl_give isl_set *isl_basic_set_lexmax(
3182 __isl_take isl_basic_set *bset);
3183 __isl_give isl_set *isl_set_lexmin(
3184 __isl_take isl_set *set);
3185 __isl_give isl_set *isl_set_lexmax(
3186 __isl_take isl_set *set);
3187 __isl_give isl_union_set *isl_union_set_lexmin(
3188 __isl_take isl_union_set *uset);
3189 __isl_give isl_union_set *isl_union_set_lexmax(
3190 __isl_take isl_union_set *uset);
3192 Given a (basic) relation C<map> (or C<bmap>) and a domain C<dom>,
3193 the following functions
3194 compute a relation that maps each element of C<dom>
3195 to the single lexicographic minimum or maximum
3196 of the elements that are associated to that same
3197 element in C<map> (or C<bmap>).
3198 If C<empty> is not C<NULL>, then C<*empty> is assigned a set
3199 that contains the elements in C<dom> that do not map
3200 to any elements in C<map> (or C<bmap>).
3201 In other words, the union of the domain of the result and of C<*empty>
3204 __isl_give isl_map *isl_basic_map_partial_lexmax(
3205 __isl_take isl_basic_map *bmap,
3206 __isl_take isl_basic_set *dom,
3207 __isl_give isl_set **empty);
3208 __isl_give isl_map *isl_basic_map_partial_lexmin(
3209 __isl_take isl_basic_map *bmap,
3210 __isl_take isl_basic_set *dom,
3211 __isl_give isl_set **empty);
3212 __isl_give isl_map *isl_map_partial_lexmax(
3213 __isl_take isl_map *map, __isl_take isl_set *dom,
3214 __isl_give isl_set **empty);
3215 __isl_give isl_map *isl_map_partial_lexmin(
3216 __isl_take isl_map *map, __isl_take isl_set *dom,
3217 __isl_give isl_set **empty);
3219 Given a (basic) map C<map> (or C<bmap>), the following functions simply
3220 return a map mapping each element in the domain of
3221 C<map> (or C<bmap>) to the lexicographic minimum or maximum
3222 of all elements associated to that element.
3223 In case of union relations, the optimum is computed per space.
3225 __isl_give isl_map *isl_basic_map_lexmin(
3226 __isl_take isl_basic_map *bmap);
3227 __isl_give isl_map *isl_basic_map_lexmax(
3228 __isl_take isl_basic_map *bmap);
3229 __isl_give isl_map *isl_map_lexmin(
3230 __isl_take isl_map *map);
3231 __isl_give isl_map *isl_map_lexmax(
3232 __isl_take isl_map *map);
3233 __isl_give isl_union_map *isl_union_map_lexmin(
3234 __isl_take isl_union_map *umap);
3235 __isl_give isl_union_map *isl_union_map_lexmax(
3236 __isl_take isl_union_map *umap);
3238 The following functions return their result in the form of
3239 a piecewise multi-affine expression
3240 (See L<"Piecewise Multiple Quasi Affine Expressions">),
3241 but are otherwise equivalent to the corresponding functions
3242 returning a basic set or relation.
3244 __isl_give isl_pw_multi_aff *
3245 isl_basic_map_lexmin_pw_multi_aff(
3246 __isl_take isl_basic_map *bmap);
3247 __isl_give isl_pw_multi_aff *
3248 isl_basic_set_partial_lexmin_pw_multi_aff(
3249 __isl_take isl_basic_set *bset,
3250 __isl_take isl_basic_set *dom,
3251 __isl_give isl_set **empty);
3252 __isl_give isl_pw_multi_aff *
3253 isl_basic_set_partial_lexmax_pw_multi_aff(
3254 __isl_take isl_basic_set *bset,
3255 __isl_take isl_basic_set *dom,
3256 __isl_give isl_set **empty);
3257 __isl_give isl_pw_multi_aff *
3258 isl_basic_map_partial_lexmin_pw_multi_aff(
3259 __isl_take isl_basic_map *bmap,
3260 __isl_take isl_basic_set *dom,
3261 __isl_give isl_set **empty);
3262 __isl_give isl_pw_multi_aff *
3263 isl_basic_map_partial_lexmax_pw_multi_aff(
3264 __isl_take isl_basic_map *bmap,
3265 __isl_take isl_basic_set *dom,
3266 __isl_give isl_set **empty);
3267 __isl_give isl_pw_multi_aff *isl_set_lexmin_pw_multi_aff(
3268 __isl_take isl_set *set);
3269 __isl_give isl_pw_multi_aff *isl_set_lexmax_pw_multi_aff(
3270 __isl_take isl_set *set);
3271 __isl_give isl_pw_multi_aff *isl_map_lexmin_pw_multi_aff(
3272 __isl_take isl_map *map);
3273 __isl_give isl_pw_multi_aff *isl_map_lexmax_pw_multi_aff(
3274 __isl_take isl_map *map);
3278 Lists are defined over several element types, including
3279 C<isl_val>, C<isl_id>, C<isl_aff>, C<isl_pw_aff>, C<isl_constraint>,
3280 C<isl_basic_set>, C<isl_set>, C<isl_ast_expr> and C<isl_ast_node>.
3281 Here we take lists of C<isl_set>s as an example.
3282 Lists can be created, copied, modified and freed using the following functions.
3284 #include <isl/list.h>
3285 __isl_give isl_set_list *isl_set_list_from_set(
3286 __isl_take isl_set *el);
3287 __isl_give isl_set_list *isl_set_list_alloc(
3288 isl_ctx *ctx, int n);
3289 __isl_give isl_set_list *isl_set_list_copy(
3290 __isl_keep isl_set_list *list);
3291 __isl_give isl_set_list *isl_set_list_insert(
3292 __isl_take isl_set_list *list, unsigned pos,
3293 __isl_take isl_set *el);
3294 __isl_give isl_set_list *isl_set_list_add(
3295 __isl_take isl_set_list *list,
3296 __isl_take isl_set *el);
3297 __isl_give isl_set_list *isl_set_list_drop(
3298 __isl_take isl_set_list *list,
3299 unsigned first, unsigned n);
3300 __isl_give isl_set_list *isl_set_list_set_set(
3301 __isl_take isl_set_list *list, int index,
3302 __isl_take isl_set *set);
3303 __isl_give isl_set_list *isl_set_list_concat(
3304 __isl_take isl_set_list *list1,
3305 __isl_take isl_set_list *list2);
3306 __isl_give isl_set_list *isl_set_list_sort(
3307 __isl_take isl_set_list *list,
3308 int (*cmp)(__isl_keep isl_set *a,
3309 __isl_keep isl_set *b, void *user),
3311 void *isl_set_list_free(__isl_take isl_set_list *list);
3313 C<isl_set_list_alloc> creates an empty list with a capacity for
3314 C<n> elements. C<isl_set_list_from_set> creates a list with a single
3317 Lists can be inspected using the following functions.
3319 #include <isl/list.h>
3320 isl_ctx *isl_set_list_get_ctx(__isl_keep isl_set_list *list);
3321 int isl_set_list_n_set(__isl_keep isl_set_list *list);
3322 __isl_give isl_set *isl_set_list_get_set(
3323 __isl_keep isl_set_list *list, int index);
3324 int isl_set_list_foreach(__isl_keep isl_set_list *list,
3325 int (*fn)(__isl_take isl_set *el, void *user),
3327 int isl_set_list_foreach_scc(__isl_keep isl_set_list *list,
3328 int (*follows)(__isl_keep isl_set *a,
3329 __isl_keep isl_set *b, void *user),
3331 int (*fn)(__isl_take isl_set *el, void *user),
3334 The function C<isl_set_list_foreach_scc> calls C<fn> on each of the
3335 strongly connected components of the graph with as vertices the elements
3336 of C<list> and a directed edge from vertex C<b> to vertex C<a>
3337 iff C<follows(a, b)> returns C<1>. The callbacks C<follows> and C<fn>
3338 should return C<-1> on error.
3340 Lists can be printed using
3342 #include <isl/list.h>
3343 __isl_give isl_printer *isl_printer_print_set_list(
3344 __isl_take isl_printer *p,
3345 __isl_keep isl_set_list *list);
3347 =head2 Associative arrays
3349 Associative arrays map isl objects of a specific type to isl objects
3350 of some (other) specific type. They are defined for several pairs
3351 of types, including (C<isl_map>, C<isl_basic_set>),
3352 (C<isl_id>, C<isl_ast_expr>) and.
3353 (C<isl_id>, C<isl_pw_aff>).
3354 Here, we take associative arrays that map C<isl_id>s to C<isl_ast_expr>s
3357 Associative arrays can be created, copied and freed using
3358 the following functions.
3360 #include <isl/id_to_ast_expr.h>
3361 __isl_give id_to_ast_expr *isl_id_to_ast_expr_alloc(
3362 isl_ctx *ctx, int min_size);
3363 __isl_give id_to_ast_expr *isl_id_to_ast_expr_copy(
3364 __isl_keep id_to_ast_expr *id2expr);
3365 void *isl_id_to_ast_expr_free(
3366 __isl_take id_to_ast_expr *id2expr);
3368 The C<min_size> argument to C<isl_id_to_ast_expr_alloc> can be used
3369 to specify the expected size of the associative array.
3370 The associative array will be grown automatically as needed.
3372 Associative arrays can be inspected using the following functions.
3374 #include <isl/id_to_ast_expr.h>
3375 isl_ctx *isl_id_to_ast_expr_get_ctx(
3376 __isl_keep id_to_ast_expr *id2expr);
3377 int isl_id_to_ast_expr_has(
3378 __isl_keep id_to_ast_expr *id2expr,
3379 __isl_keep isl_id *key);
3380 __isl_give isl_ast_expr *isl_id_to_ast_expr_get(
3381 __isl_keep id_to_ast_expr *id2expr,
3382 __isl_take isl_id *key);
3383 int isl_id_to_ast_expr_foreach(
3384 __isl_keep id_to_ast_expr *id2expr,
3385 int (*fn)(__isl_take isl_id *key,
3386 __isl_take isl_ast_expr *val, void *user),
3389 They can be modified using the following function.
3391 #include <isl/id_to_ast_expr.h>
3392 __isl_give id_to_ast_expr *isl_id_to_ast_expr_set(
3393 __isl_take id_to_ast_expr *id2expr,
3394 __isl_take isl_id *key,
3395 __isl_take isl_ast_expr *val);
3397 Associative arrays can be printed using the following function.
3399 #include <isl/id_to_ast_expr.h>
3400 __isl_give isl_printer *isl_printer_print_id_to_ast_expr(
3401 __isl_take isl_printer *p,
3402 __isl_keep id_to_ast_expr *id2expr);
3404 =head2 Multiple Values
3406 An C<isl_multi_val> object represents a sequence of zero or more values,
3407 living in a set space.
3409 An C<isl_multi_val> can be constructed from an C<isl_val_list>
3410 using the following function
3412 #include <isl/val.h>
3413 __isl_give isl_multi_val *isl_multi_val_from_val_list(
3414 __isl_take isl_space *space,
3415 __isl_take isl_val_list *list);
3417 The zero multiple value (with value zero for each set dimension)
3418 can be created using the following function.
3420 #include <isl/val.h>
3421 __isl_give isl_multi_val *isl_multi_val_zero(
3422 __isl_take isl_space *space);
3424 Multiple values can be copied and freed using
3426 #include <isl/val.h>
3427 __isl_give isl_multi_val *isl_multi_val_copy(
3428 __isl_keep isl_multi_val *mv);
3429 void *isl_multi_val_free(__isl_take isl_multi_val *mv);
3431 They can be inspected using
3433 #include <isl/val.h>
3434 isl_ctx *isl_multi_val_get_ctx(
3435 __isl_keep isl_multi_val *mv);
3436 unsigned isl_multi_val_dim(__isl_keep isl_multi_val *mv,
3437 enum isl_dim_type type);
3438 __isl_give isl_val *isl_multi_val_get_val(
3439 __isl_keep isl_multi_val *mv, int pos);
3440 int isl_multi_val_find_dim_by_id(
3441 __isl_keep isl_multi_val *mv,
3442 enum isl_dim_type type, __isl_keep isl_id *id);
3443 __isl_give isl_id *isl_multi_val_get_dim_id(
3444 __isl_keep isl_multi_val *mv,
3445 enum isl_dim_type type, unsigned pos);
3446 const char *isl_multi_val_get_tuple_name(
3447 __isl_keep isl_multi_val *mv,
3448 enum isl_dim_type type);
3449 int isl_multi_val_has_tuple_id(__isl_keep isl_multi_val *mv,
3450 enum isl_dim_type type);
3451 __isl_give isl_id *isl_multi_val_get_tuple_id(
3452 __isl_keep isl_multi_val *mv,
3453 enum isl_dim_type type);
3454 int isl_multi_val_range_is_wrapping(
3455 __isl_keep isl_multi_val *mv);
3457 They can be modified using
3459 #include <isl/val.h>
3460 __isl_give isl_multi_val *isl_multi_val_set_val(
3461 __isl_take isl_multi_val *mv, int pos,
3462 __isl_take isl_val *val);
3463 __isl_give isl_multi_val *isl_multi_val_set_dim_name(
3464 __isl_take isl_multi_val *mv,
3465 enum isl_dim_type type, unsigned pos, const char *s);
3466 __isl_give isl_multi_val *isl_multi_val_set_dim_id(
3467 __isl_take isl_multi_val *mv,
3468 enum isl_dim_type type, unsigned pos,
3469 __isl_take isl_id *id);
3470 __isl_give isl_multi_val *isl_multi_val_set_tuple_name(
3471 __isl_take isl_multi_val *mv,
3472 enum isl_dim_type type, const char *s);
3473 __isl_give isl_multi_val *isl_multi_val_set_tuple_id(
3474 __isl_take isl_multi_val *mv,
3475 enum isl_dim_type type, __isl_take isl_id *id);
3476 __isl_give isl_multi_val *isl_multi_val_reset_tuple_id(
3477 __isl_take isl_multi_val *mv,
3478 enum isl_dim_type type);
3479 __isl_give isl_multi_val *isl_multi_val_reset_user(
3480 __isl_take isl_multi_val *mv);
3482 __isl_give isl_multi_val *isl_multi_val_insert_dims(
3483 __isl_take isl_multi_val *mv,
3484 enum isl_dim_type type, unsigned first, unsigned n);
3485 __isl_give isl_multi_val *isl_multi_val_add_dims(
3486 __isl_take isl_multi_val *mv,
3487 enum isl_dim_type type, unsigned n);
3488 __isl_give isl_multi_val *isl_multi_val_drop_dims(
3489 __isl_take isl_multi_val *mv,
3490 enum isl_dim_type type, unsigned first, unsigned n);
3494 #include <isl/val.h>
3495 __isl_give isl_multi_val *isl_multi_val_align_params(
3496 __isl_take isl_multi_val *mv,
3497 __isl_take isl_space *model);
3498 __isl_give isl_multi_val *isl_multi_val_from_range(
3499 __isl_take isl_multi_val *mv);
3500 __isl_give isl_multi_val *isl_multi_val_range_splice(
3501 __isl_take isl_multi_val *mv1, unsigned pos,
3502 __isl_take isl_multi_val *mv2);
3503 __isl_give isl_multi_val *isl_multi_val_range_product(
3504 __isl_take isl_multi_val *mv1,
3505 __isl_take isl_multi_val *mv2);
3506 __isl_give isl_multi_val *
3507 isl_multi_val_range_factor_domain(
3508 __isl_take isl_multi_val *mv);
3509 __isl_give isl_multi_val *
3510 isl_multi_val_range_factor_range(
3511 __isl_take isl_multi_val *mv);
3512 __isl_give isl_multi_val *isl_multi_val_flat_range_product(
3513 __isl_take isl_multi_val *mv1,
3514 __isl_take isl_multi_aff *mv2);
3515 __isl_give isl_multi_val *isl_multi_val_product(
3516 __isl_take isl_multi_val *mv1,
3517 __isl_take isl_multi_val *mv2);
3518 __isl_give isl_multi_val *isl_multi_val_add_val(
3519 __isl_take isl_multi_val *mv,
3520 __isl_take isl_val *v);
3521 __isl_give isl_multi_val *isl_multi_val_mod_val(
3522 __isl_take isl_multi_val *mv,
3523 __isl_take isl_val *v);
3524 __isl_give isl_multi_val *isl_multi_val_scale_val(
3525 __isl_take isl_multi_val *mv,
3526 __isl_take isl_val *v);
3527 __isl_give isl_multi_val *isl_multi_val_scale_multi_val(
3528 __isl_take isl_multi_val *mv1,
3529 __isl_take isl_multi_val *mv2);
3530 __isl_give isl_multi_val *
3531 isl_multi_val_scale_down_multi_val(
3532 __isl_take isl_multi_val *mv1,
3533 __isl_take isl_multi_val *mv2);
3535 A multiple value can be printed using
3537 __isl_give isl_printer *isl_printer_print_multi_val(
3538 __isl_take isl_printer *p,
3539 __isl_keep isl_multi_val *mv);
3543 Vectors can be created, copied and freed using the following functions.
3545 #include <isl/vec.h>
3546 __isl_give isl_vec *isl_vec_alloc(isl_ctx *ctx,
3548 __isl_give isl_vec *isl_vec_copy(__isl_keep isl_vec *vec);
3549 void *isl_vec_free(__isl_take isl_vec *vec);
3551 Note that the elements of a newly created vector may have arbitrary values.
3552 The elements can be changed and inspected using the following functions.
3554 isl_ctx *isl_vec_get_ctx(__isl_keep isl_vec *vec);
3555 int isl_vec_size(__isl_keep isl_vec *vec);
3556 __isl_give isl_val *isl_vec_get_element_val(
3557 __isl_keep isl_vec *vec, int pos);
3558 __isl_give isl_vec *isl_vec_set_element_si(
3559 __isl_take isl_vec *vec, int pos, int v);
3560 __isl_give isl_vec *isl_vec_set_element_val(
3561 __isl_take isl_vec *vec, int pos,
3562 __isl_take isl_val *v);
3563 __isl_give isl_vec *isl_vec_set_si(__isl_take isl_vec *vec,
3565 __isl_give isl_vec *isl_vec_set_val(
3566 __isl_take isl_vec *vec, __isl_take isl_val *v);
3567 int isl_vec_cmp_element(__isl_keep isl_vec *vec1,
3568 __isl_keep isl_vec *vec2, int pos);
3570 C<isl_vec_get_element> will return a negative value if anything went wrong.
3571 In that case, the value of C<*v> is undefined.
3573 The following function can be used to concatenate two vectors.
3575 __isl_give isl_vec *isl_vec_concat(__isl_take isl_vec *vec1,
3576 __isl_take isl_vec *vec2);
3580 Matrices can be created, copied and freed using the following functions.
3582 #include <isl/mat.h>
3583 __isl_give isl_mat *isl_mat_alloc(isl_ctx *ctx,
3584 unsigned n_row, unsigned n_col);
3585 __isl_give isl_mat *isl_mat_copy(__isl_keep isl_mat *mat);
3586 void *isl_mat_free(__isl_take isl_mat *mat);
3588 Note that the elements of a newly created matrix may have arbitrary values.
3589 The elements can be changed and inspected using the following functions.
3591 isl_ctx *isl_mat_get_ctx(__isl_keep isl_mat *mat);
3592 int isl_mat_rows(__isl_keep isl_mat *mat);
3593 int isl_mat_cols(__isl_keep isl_mat *mat);
3594 __isl_give isl_val *isl_mat_get_element_val(
3595 __isl_keep isl_mat *mat, int row, int col);
3596 __isl_give isl_mat *isl_mat_set_element_si(__isl_take isl_mat *mat,
3597 int row, int col, int v);
3598 __isl_give isl_mat *isl_mat_set_element_val(
3599 __isl_take isl_mat *mat, int row, int col,
3600 __isl_take isl_val *v);
3602 C<isl_mat_get_element> will return a negative value if anything went wrong.
3603 In that case, the value of C<*v> is undefined.
3605 The following function can be used to compute the (right) inverse
3606 of a matrix, i.e., a matrix such that the product of the original
3607 and the inverse (in that order) is a multiple of the identity matrix.
3608 The input matrix is assumed to be of full row-rank.
3610 __isl_give isl_mat *isl_mat_right_inverse(__isl_take isl_mat *mat);
3612 The following function can be used to compute the (right) kernel
3613 (or null space) of a matrix, i.e., a matrix such that the product of
3614 the original and the kernel (in that order) is the zero matrix.
3616 __isl_give isl_mat *isl_mat_right_kernel(__isl_take isl_mat *mat);
3618 =head2 Piecewise Quasi Affine Expressions
3620 The zero quasi affine expression or the quasi affine expression
3621 that is equal to a given value or
3622 a specified dimension on a given domain can be created using
3624 __isl_give isl_aff *isl_aff_zero_on_domain(
3625 __isl_take isl_local_space *ls);
3626 __isl_give isl_pw_aff *isl_pw_aff_zero_on_domain(
3627 __isl_take isl_local_space *ls);
3628 __isl_give isl_aff *isl_aff_val_on_domain(
3629 __isl_take isl_local_space *ls,
3630 __isl_take isl_val *val);
3631 __isl_give isl_aff *isl_aff_var_on_domain(
3632 __isl_take isl_local_space *ls,
3633 enum isl_dim_type type, unsigned pos);
3634 __isl_give isl_pw_aff *isl_pw_aff_var_on_domain(
3635 __isl_take isl_local_space *ls,
3636 enum isl_dim_type type, unsigned pos);
3638 Note that the space in which the resulting objects live is a map space
3639 with the given space as domain and a one-dimensional range.
3641 An empty piecewise quasi affine expression (one with no cells)
3642 or a piecewise quasi affine expression with a single cell can
3643 be created using the following functions.
3645 #include <isl/aff.h>
3646 __isl_give isl_pw_aff *isl_pw_aff_empty(
3647 __isl_take isl_space *space);
3648 __isl_give isl_pw_aff *isl_pw_aff_alloc(
3649 __isl_take isl_set *set, __isl_take isl_aff *aff);
3650 __isl_give isl_pw_aff *isl_pw_aff_from_aff(
3651 __isl_take isl_aff *aff);
3653 A piecewise quasi affine expression that is equal to 1 on a set
3654 and 0 outside the set can be created using the following function.
3656 #include <isl/aff.h>
3657 __isl_give isl_pw_aff *isl_set_indicator_function(
3658 __isl_take isl_set *set);
3660 Quasi affine expressions can be copied and freed using
3662 #include <isl/aff.h>
3663 __isl_give isl_aff *isl_aff_copy(__isl_keep isl_aff *aff);
3664 void *isl_aff_free(__isl_take isl_aff *aff);
3666 __isl_give isl_pw_aff *isl_pw_aff_copy(
3667 __isl_keep isl_pw_aff *pwaff);
3668 void *isl_pw_aff_free(__isl_take isl_pw_aff *pwaff);
3670 A (rational) bound on a dimension can be extracted from an C<isl_constraint>
3671 using the following function. The constraint is required to have
3672 a non-zero coefficient for the specified dimension.
3674 #include <isl/constraint.h>
3675 __isl_give isl_aff *isl_constraint_get_bound(
3676 __isl_keep isl_constraint *constraint,
3677 enum isl_dim_type type, int pos);
3679 The entire affine expression of the constraint can also be extracted
3680 using the following function.
3682 #include <isl/constraint.h>
3683 __isl_give isl_aff *isl_constraint_get_aff(
3684 __isl_keep isl_constraint *constraint);
3686 Conversely, an equality constraint equating
3687 the affine expression to zero or an inequality constraint enforcing
3688 the affine expression to be non-negative, can be constructed using
3690 __isl_give isl_constraint *isl_equality_from_aff(
3691 __isl_take isl_aff *aff);
3692 __isl_give isl_constraint *isl_inequality_from_aff(
3693 __isl_take isl_aff *aff);
3695 The expression can be inspected using
3697 #include <isl/aff.h>
3698 isl_ctx *isl_aff_get_ctx(__isl_keep isl_aff *aff);
3699 int isl_aff_dim(__isl_keep isl_aff *aff,
3700 enum isl_dim_type type);
3701 __isl_give isl_local_space *isl_aff_get_domain_local_space(
3702 __isl_keep isl_aff *aff);
3703 __isl_give isl_local_space *isl_aff_get_local_space(
3704 __isl_keep isl_aff *aff);
3705 const char *isl_aff_get_dim_name(__isl_keep isl_aff *aff,
3706 enum isl_dim_type type, unsigned pos);
3707 const char *isl_pw_aff_get_dim_name(
3708 __isl_keep isl_pw_aff *pa,
3709 enum isl_dim_type type, unsigned pos);
3710 int isl_pw_aff_has_dim_id(__isl_keep isl_pw_aff *pa,
3711 enum isl_dim_type type, unsigned pos);
3712 __isl_give isl_id *isl_pw_aff_get_dim_id(
3713 __isl_keep isl_pw_aff *pa,
3714 enum isl_dim_type type, unsigned pos);
3715 int isl_pw_aff_has_tuple_id(__isl_keep isl_pw_aff *pa,
3716 enum isl_dim_type type);
3717 __isl_give isl_id *isl_pw_aff_get_tuple_id(
3718 __isl_keep isl_pw_aff *pa,
3719 enum isl_dim_type type);
3720 __isl_give isl_val *isl_aff_get_constant_val(
3721 __isl_keep isl_aff *aff);
3722 __isl_give isl_val *isl_aff_get_coefficient_val(
3723 __isl_keep isl_aff *aff,
3724 enum isl_dim_type type, int pos);
3725 __isl_give isl_val *isl_aff_get_denominator_val(
3726 __isl_keep isl_aff *aff);
3727 __isl_give isl_aff *isl_aff_get_div(
3728 __isl_keep isl_aff *aff, int pos);
3730 int isl_pw_aff_n_piece(__isl_keep isl_pw_aff *pwaff);
3731 int isl_pw_aff_foreach_piece(__isl_keep isl_pw_aff *pwaff,
3732 int (*fn)(__isl_take isl_set *set,
3733 __isl_take isl_aff *aff,
3734 void *user), void *user);
3736 int isl_aff_is_cst(__isl_keep isl_aff *aff);
3737 int isl_pw_aff_is_cst(__isl_keep isl_pw_aff *pwaff);
3739 int isl_aff_involves_dims(__isl_keep isl_aff *aff,
3740 enum isl_dim_type type, unsigned first, unsigned n);
3741 int isl_pw_aff_involves_dims(__isl_keep isl_pw_aff *pwaff,
3742 enum isl_dim_type type, unsigned first, unsigned n);
3744 isl_ctx *isl_pw_aff_get_ctx(__isl_keep isl_pw_aff *pwaff);
3745 unsigned isl_pw_aff_dim(__isl_keep isl_pw_aff *pwaff,
3746 enum isl_dim_type type);
3747 int isl_pw_aff_is_empty(__isl_keep isl_pw_aff *pwaff);
3749 It can be modified using
3751 #include <isl/aff.h>
3752 __isl_give isl_pw_aff *isl_pw_aff_set_tuple_id(
3753 __isl_take isl_pw_aff *pwaff,
3754 enum isl_dim_type type, __isl_take isl_id *id);
3755 __isl_give isl_aff *isl_aff_set_dim_name(
3756 __isl_take isl_aff *aff, enum isl_dim_type type,
3757 unsigned pos, const char *s);
3758 __isl_give isl_aff *isl_aff_set_dim_id(
3759 __isl_take isl_aff *aff, enum isl_dim_type type,
3760 unsigned pos, __isl_take isl_id *id);
3761 __isl_give isl_pw_aff *isl_pw_aff_set_dim_id(
3762 __isl_take isl_pw_aff *pma,
3763 enum isl_dim_type type, unsigned pos,
3764 __isl_take isl_id *id);
3765 __isl_give isl_aff *isl_aff_set_constant_si(
3766 __isl_take isl_aff *aff, int v);
3767 __isl_give isl_aff *isl_aff_set_constant_val(
3768 __isl_take isl_aff *aff, __isl_take isl_val *v);
3769 __isl_give isl_aff *isl_aff_set_coefficient_si(
3770 __isl_take isl_aff *aff,
3771 enum isl_dim_type type, int pos, int v);
3772 __isl_give isl_aff *isl_aff_set_coefficient_val(
3773 __isl_take isl_aff *aff,
3774 enum isl_dim_type type, int pos,
3775 __isl_take isl_val *v);
3777 __isl_give isl_aff *isl_aff_add_constant_si(
3778 __isl_take isl_aff *aff, int v);
3779 __isl_give isl_aff *isl_aff_add_constant_val(
3780 __isl_take isl_aff *aff, __isl_take isl_val *v);
3781 __isl_give isl_aff *isl_aff_add_constant_num_si(
3782 __isl_take isl_aff *aff, int v);
3783 __isl_give isl_aff *isl_aff_add_coefficient_si(
3784 __isl_take isl_aff *aff,
3785 enum isl_dim_type type, int pos, int v);
3786 __isl_give isl_aff *isl_aff_add_coefficient_val(
3787 __isl_take isl_aff *aff,
3788 enum isl_dim_type type, int pos,
3789 __isl_take isl_val *v);
3791 __isl_give isl_aff *isl_aff_insert_dims(
3792 __isl_take isl_aff *aff,
3793 enum isl_dim_type type, unsigned first, unsigned n);
3794 __isl_give isl_pw_aff *isl_pw_aff_insert_dims(
3795 __isl_take isl_pw_aff *pwaff,
3796 enum isl_dim_type type, unsigned first, unsigned n);
3797 __isl_give isl_aff *isl_aff_add_dims(
3798 __isl_take isl_aff *aff,
3799 enum isl_dim_type type, unsigned n);
3800 __isl_give isl_pw_aff *isl_pw_aff_add_dims(
3801 __isl_take isl_pw_aff *pwaff,
3802 enum isl_dim_type type, unsigned n);
3803 __isl_give isl_aff *isl_aff_drop_dims(
3804 __isl_take isl_aff *aff,
3805 enum isl_dim_type type, unsigned first, unsigned n);
3806 __isl_give isl_pw_aff *isl_pw_aff_drop_dims(
3807 __isl_take isl_pw_aff *pwaff,
3808 enum isl_dim_type type, unsigned first, unsigned n);
3809 __isl_give isl_aff *isl_aff_move_dims(
3810 __isl_take isl_aff *aff,
3811 enum isl_dim_type dst_type, unsigned dst_pos,
3812 enum isl_dim_type src_type, unsigned src_pos,
3814 __isl_give isl_pw_aff *isl_pw_aff_move_dims(
3815 __isl_take isl_pw_aff *pa,
3816 enum isl_dim_type dst_type, unsigned dst_pos,
3817 enum isl_dim_type src_type, unsigned src_pos,
3820 Note that C<isl_aff_set_constant_si> and C<isl_aff_set_coefficient_si>
3821 set the I<numerator> of the constant or coefficient, while
3822 C<isl_aff_set_constant_val> and C<isl_aff_set_coefficient_val> set
3823 the constant or coefficient as a whole.
3824 The C<add_constant> and C<add_coefficient> functions add an integer
3825 or rational value to
3826 the possibly rational constant or coefficient.
3827 The C<add_constant_num> functions add an integer value to
3830 To check whether an affine expressions is obviously zero
3831 or (obviously) equal to some other affine expression, use
3833 #include <isl/aff.h>
3834 int isl_aff_plain_is_zero(__isl_keep isl_aff *aff);
3835 int isl_aff_plain_is_equal(__isl_keep isl_aff *aff1,
3836 __isl_keep isl_aff *aff2);
3837 int isl_pw_aff_plain_is_equal(
3838 __isl_keep isl_pw_aff *pwaff1,
3839 __isl_keep isl_pw_aff *pwaff2);
3840 int isl_pw_aff_is_equal(__isl_keep isl_pw_aff *pa1,
3841 __isl_keep isl_pw_aff *pa2);
3845 #include <isl/aff.h>
3846 __isl_give isl_aff *isl_aff_add(__isl_take isl_aff *aff1,
3847 __isl_take isl_aff *aff2);
3848 __isl_give isl_pw_aff *isl_pw_aff_add(
3849 __isl_take isl_pw_aff *pwaff1,
3850 __isl_take isl_pw_aff *pwaff2);
3851 __isl_give isl_pw_aff *isl_pw_aff_min(
3852 __isl_take isl_pw_aff *pwaff1,
3853 __isl_take isl_pw_aff *pwaff2);
3854 __isl_give isl_pw_aff *isl_pw_aff_max(
3855 __isl_take isl_pw_aff *pwaff1,
3856 __isl_take isl_pw_aff *pwaff2);
3857 __isl_give isl_aff *isl_aff_sub(__isl_take isl_aff *aff1,
3858 __isl_take isl_aff *aff2);
3859 __isl_give isl_pw_aff *isl_pw_aff_sub(
3860 __isl_take isl_pw_aff *pwaff1,
3861 __isl_take isl_pw_aff *pwaff2);
3862 __isl_give isl_aff *isl_aff_neg(__isl_take isl_aff *aff);
3863 __isl_give isl_pw_aff *isl_pw_aff_neg(
3864 __isl_take isl_pw_aff *pwaff);
3865 __isl_give isl_aff *isl_aff_ceil(__isl_take isl_aff *aff);
3866 __isl_give isl_pw_aff *isl_pw_aff_ceil(
3867 __isl_take isl_pw_aff *pwaff);
3868 __isl_give isl_aff *isl_aff_floor(__isl_take isl_aff *aff);
3869 __isl_give isl_pw_aff *isl_pw_aff_floor(
3870 __isl_take isl_pw_aff *pwaff);
3871 __isl_give isl_aff *isl_aff_mod_val(__isl_take isl_aff *aff,
3872 __isl_take isl_val *mod);
3873 __isl_give isl_pw_aff *isl_pw_aff_mod_val(
3874 __isl_take isl_pw_aff *pa,
3875 __isl_take isl_val *mod);
3876 __isl_give isl_aff *isl_aff_scale_val(__isl_take isl_aff *aff,
3877 __isl_take isl_val *v);
3878 __isl_give isl_pw_aff *isl_pw_aff_scale_val(
3879 __isl_take isl_pw_aff *pa, __isl_take isl_val *v);
3880 __isl_give isl_aff *isl_aff_scale_down_ui(
3881 __isl_take isl_aff *aff, unsigned f);
3882 __isl_give isl_aff *isl_aff_scale_down_val(
3883 __isl_take isl_aff *aff, __isl_take isl_val *v);
3884 __isl_give isl_pw_aff *isl_pw_aff_scale_down_val(
3885 __isl_take isl_pw_aff *pa,
3886 __isl_take isl_val *f);
3888 __isl_give isl_pw_aff *isl_pw_aff_list_min(
3889 __isl_take isl_pw_aff_list *list);
3890 __isl_give isl_pw_aff *isl_pw_aff_list_max(
3891 __isl_take isl_pw_aff_list *list);
3893 __isl_give isl_pw_aff *isl_pw_aff_coalesce(
3894 __isl_take isl_pw_aff *pwqp);
3896 __isl_give isl_aff *isl_aff_align_params(
3897 __isl_take isl_aff *aff,
3898 __isl_take isl_space *model);
3899 __isl_give isl_pw_aff *isl_pw_aff_align_params(
3900 __isl_take isl_pw_aff *pwaff,
3901 __isl_take isl_space *model);
3903 __isl_give isl_aff *isl_aff_project_domain_on_params(
3904 __isl_take isl_aff *aff);
3905 __isl_give isl_pw_aff *isl_pw_aff_from_range(
3906 __isl_take isl_pw_aff *pwa);
3908 __isl_give isl_aff *isl_aff_gist_params(
3909 __isl_take isl_aff *aff,
3910 __isl_take isl_set *context);
3911 __isl_give isl_aff *isl_aff_gist(__isl_take isl_aff *aff,
3912 __isl_take isl_set *context);
3913 __isl_give isl_pw_aff *isl_pw_aff_gist_params(
3914 __isl_take isl_pw_aff *pwaff,
3915 __isl_take isl_set *context);
3916 __isl_give isl_pw_aff *isl_pw_aff_gist(
3917 __isl_take isl_pw_aff *pwaff,
3918 __isl_take isl_set *context);
3920 __isl_give isl_set *isl_pw_aff_domain(
3921 __isl_take isl_pw_aff *pwaff);
3922 __isl_give isl_set *isl_pw_aff_params(
3923 __isl_take isl_pw_aff *pwa);
3924 __isl_give isl_pw_aff *isl_pw_aff_intersect_domain(
3925 __isl_take isl_pw_aff *pa,
3926 __isl_take isl_set *set);
3927 __isl_give isl_pw_aff *isl_pw_aff_intersect_params(
3928 __isl_take isl_pw_aff *pa,
3929 __isl_take isl_set *set);
3931 __isl_give isl_aff *isl_aff_mul(__isl_take isl_aff *aff1,
3932 __isl_take isl_aff *aff2);
3933 __isl_give isl_aff *isl_aff_div(__isl_take isl_aff *aff1,
3934 __isl_take isl_aff *aff2);
3935 __isl_give isl_pw_aff *isl_pw_aff_mul(
3936 __isl_take isl_pw_aff *pwaff1,
3937 __isl_take isl_pw_aff *pwaff2);
3938 __isl_give isl_pw_aff *isl_pw_aff_div(
3939 __isl_take isl_pw_aff *pa1,
3940 __isl_take isl_pw_aff *pa2);
3941 __isl_give isl_pw_aff *isl_pw_aff_tdiv_q(
3942 __isl_take isl_pw_aff *pa1,
3943 __isl_take isl_pw_aff *pa2);
3944 __isl_give isl_pw_aff *isl_pw_aff_tdiv_r(
3945 __isl_take isl_pw_aff *pa1,
3946 __isl_take isl_pw_aff *pa2);
3948 When multiplying two affine expressions, at least one of the two needs
3949 to be a constant. Similarly, when dividing an affine expression by another,
3950 the second expression needs to be a constant.
3951 C<isl_pw_aff_tdiv_q> computes the quotient of an integer division with
3952 rounding towards zero. C<isl_pw_aff_tdiv_r> computes the corresponding
3955 #include <isl/aff.h>
3956 __isl_give isl_aff *isl_aff_pullback_aff(
3957 __isl_take isl_aff *aff1,
3958 __isl_take isl_aff *aff2);
3959 __isl_give isl_aff *isl_aff_pullback_multi_aff(
3960 __isl_take isl_aff *aff,
3961 __isl_take isl_multi_aff *ma);
3962 __isl_give isl_pw_aff *isl_pw_aff_pullback_multi_aff(
3963 __isl_take isl_pw_aff *pa,
3964 __isl_take isl_multi_aff *ma);
3965 __isl_give isl_pw_aff *isl_pw_aff_pullback_pw_multi_aff(
3966 __isl_take isl_pw_aff *pa,
3967 __isl_take isl_pw_multi_aff *pma);
3969 These functions precompose the input expression by the given
3970 C<isl_aff>, C<isl_multi_aff> or C<isl_pw_multi_aff>. In other words,
3971 the C<isl_aff>, C<isl_multi_aff> or C<isl_pw_multi_aff> is plugged
3972 into the (piecewise) affine expression.
3973 Objects of type C<isl_multi_aff> are described in
3974 L</"Piecewise Multiple Quasi Affine Expressions">.
3976 #include <isl/aff.h>
3977 __isl_give isl_basic_set *isl_aff_zero_basic_set(
3978 __isl_take isl_aff *aff);
3979 __isl_give isl_basic_set *isl_aff_neg_basic_set(
3980 __isl_take isl_aff *aff);
3981 __isl_give isl_basic_set *isl_aff_le_basic_set(
3982 __isl_take isl_aff *aff1, __isl_take isl_aff *aff2);
3983 __isl_give isl_basic_set *isl_aff_ge_basic_set(
3984 __isl_take isl_aff *aff1, __isl_take isl_aff *aff2);
3985 __isl_give isl_set *isl_pw_aff_eq_set(
3986 __isl_take isl_pw_aff *pwaff1,
3987 __isl_take isl_pw_aff *pwaff2);
3988 __isl_give isl_set *isl_pw_aff_ne_set(
3989 __isl_take isl_pw_aff *pwaff1,
3990 __isl_take isl_pw_aff *pwaff2);
3991 __isl_give isl_set *isl_pw_aff_le_set(
3992 __isl_take isl_pw_aff *pwaff1,
3993 __isl_take isl_pw_aff *pwaff2);
3994 __isl_give isl_set *isl_pw_aff_lt_set(
3995 __isl_take isl_pw_aff *pwaff1,
3996 __isl_take isl_pw_aff *pwaff2);
3997 __isl_give isl_set *isl_pw_aff_ge_set(
3998 __isl_take isl_pw_aff *pwaff1,
3999 __isl_take isl_pw_aff *pwaff2);
4000 __isl_give isl_set *isl_pw_aff_gt_set(
4001 __isl_take isl_pw_aff *pwaff1,
4002 __isl_take isl_pw_aff *pwaff2);
4004 __isl_give isl_set *isl_pw_aff_list_eq_set(
4005 __isl_take isl_pw_aff_list *list1,
4006 __isl_take isl_pw_aff_list *list2);
4007 __isl_give isl_set *isl_pw_aff_list_ne_set(
4008 __isl_take isl_pw_aff_list *list1,
4009 __isl_take isl_pw_aff_list *list2);
4010 __isl_give isl_set *isl_pw_aff_list_le_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_lt_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_ge_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_gt_set(
4020 __isl_take isl_pw_aff_list *list1,
4021 __isl_take isl_pw_aff_list *list2);
4023 The function C<isl_aff_neg_basic_set> returns a basic set
4024 containing those elements in the domain space
4025 of C<aff> where C<aff> is negative.
4026 The function C<isl_aff_ge_basic_set> returns a basic set
4027 containing those elements in the shared space
4028 of C<aff1> and C<aff2> where C<aff1> is greater than or equal to C<aff2>.
4029 The function C<isl_pw_aff_ge_set> returns a set
4030 containing those elements in the shared domain
4031 of C<pwaff1> and C<pwaff2> where C<pwaff1> is greater than or equal to C<pwaff2>.
4032 The functions operating on C<isl_pw_aff_list> apply the corresponding
4033 C<isl_pw_aff> function to each pair of elements in the two lists.
4035 #include <isl/aff.h>
4036 __isl_give isl_set *isl_pw_aff_nonneg_set(
4037 __isl_take isl_pw_aff *pwaff);
4038 __isl_give isl_set *isl_pw_aff_zero_set(
4039 __isl_take isl_pw_aff *pwaff);
4040 __isl_give isl_set *isl_pw_aff_non_zero_set(
4041 __isl_take isl_pw_aff *pwaff);
4043 The function C<isl_pw_aff_nonneg_set> returns a set
4044 containing those elements in the domain
4045 of C<pwaff> where C<pwaff> is non-negative.
4047 #include <isl/aff.h>
4048 __isl_give isl_pw_aff *isl_pw_aff_cond(
4049 __isl_take isl_pw_aff *cond,
4050 __isl_take isl_pw_aff *pwaff_true,
4051 __isl_take isl_pw_aff *pwaff_false);
4053 The function C<isl_pw_aff_cond> performs a conditional operator
4054 and returns an expression that is equal to C<pwaff_true>
4055 for elements where C<cond> is non-zero and equal to C<pwaff_false> for elements
4056 where C<cond> is zero.
4058 #include <isl/aff.h>
4059 __isl_give isl_pw_aff *isl_pw_aff_union_min(
4060 __isl_take isl_pw_aff *pwaff1,
4061 __isl_take isl_pw_aff *pwaff2);
4062 __isl_give isl_pw_aff *isl_pw_aff_union_max(
4063 __isl_take isl_pw_aff *pwaff1,
4064 __isl_take isl_pw_aff *pwaff2);
4065 __isl_give isl_pw_aff *isl_pw_aff_union_add(
4066 __isl_take isl_pw_aff *pwaff1,
4067 __isl_take isl_pw_aff *pwaff2);
4069 The function C<isl_pw_aff_union_max> computes a piecewise quasi-affine
4070 expression with a domain that is the union of those of C<pwaff1> and
4071 C<pwaff2> and such that on each cell, the quasi-affine expression is
4072 the maximum of those of C<pwaff1> and C<pwaff2>. If only one of
4073 C<pwaff1> or C<pwaff2> is defined on a given cell, then the
4074 associated expression is the defined one.
4076 An expression can be read from input using
4078 #include <isl/aff.h>
4079 __isl_give isl_aff *isl_aff_read_from_str(
4080 isl_ctx *ctx, const char *str);
4081 __isl_give isl_pw_aff *isl_pw_aff_read_from_str(
4082 isl_ctx *ctx, const char *str);
4084 An expression can be printed using
4086 #include <isl/aff.h>
4087 __isl_give isl_printer *isl_printer_print_aff(
4088 __isl_take isl_printer *p, __isl_keep isl_aff *aff);
4090 __isl_give isl_printer *isl_printer_print_pw_aff(
4091 __isl_take isl_printer *p,
4092 __isl_keep isl_pw_aff *pwaff);
4094 =head2 Piecewise Multiple Quasi Affine Expressions
4096 An C<isl_multi_aff> object represents a sequence of
4097 zero or more affine expressions, all defined on the same domain space.
4098 Similarly, an C<isl_multi_pw_aff> object represents a sequence of
4099 zero or more piecewise affine expressions.
4101 An C<isl_multi_aff> can be constructed from a single
4102 C<isl_aff> or an C<isl_aff_list> using the
4103 following functions. Similarly for C<isl_multi_pw_aff>
4104 and C<isl_pw_multi_aff>.
4106 #include <isl/aff.h>
4107 __isl_give isl_multi_aff *isl_multi_aff_from_aff(
4108 __isl_take isl_aff *aff);
4109 __isl_give isl_multi_pw_aff *
4110 isl_multi_pw_aff_from_multi_aff(
4111 __isl_take isl_multi_aff *ma);
4112 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_from_pw_aff(
4113 __isl_take isl_pw_aff *pa);
4114 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_from_pw_aff(
4115 __isl_take isl_pw_aff *pa);
4116 __isl_give isl_multi_aff *isl_multi_aff_from_aff_list(
4117 __isl_take isl_space *space,
4118 __isl_take isl_aff_list *list);
4120 An C<isl_multi_pw_aff> can be converted to an C<isl_pw_multi_aff>
4121 using the function C<isl_pw_multi_aff_from_multi_pw_aff> below.
4122 Note however that the domain
4123 of the result is the intersection of the domains of the input.
4124 The reverse conversion is exact.
4126 #include <isl/aff.h>
4127 __isl_give isl_pw_multi_aff *
4128 isl_pw_multi_aff_from_multi_pw_aff(
4129 __isl_take isl_multi_pw_aff *mpa);
4130 __isl_give isl_multi_pw_aff *
4131 isl_multi_pw_aff_from_pw_multi_aff(
4132 __isl_take isl_pw_multi_aff *pma);
4134 An empty piecewise multiple quasi affine expression (one with no cells),
4135 the zero piecewise multiple quasi affine expression (with value zero
4136 for each output dimension),
4137 a piecewise multiple quasi affine expression with a single cell (with
4138 either a universe or a specified domain) or
4139 a zero-dimensional piecewise multiple quasi affine expression
4141 can be created using the following functions.
4143 #include <isl/aff.h>
4144 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_empty(
4145 __isl_take isl_space *space);
4146 __isl_give isl_multi_aff *isl_multi_aff_zero(
4147 __isl_take isl_space *space);
4148 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_zero(
4149 __isl_take isl_space *space);
4150 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_zero(
4151 __isl_take isl_space *space);
4152 __isl_give isl_multi_aff *isl_multi_aff_identity(
4153 __isl_take isl_space *space);
4154 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_identity(
4155 __isl_take isl_space *space);
4156 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_identity(
4157 __isl_take isl_space *space);
4158 __isl_give isl_multi_aff *isl_multi_aff_domain_map(
4159 __isl_take isl_space *space);
4160 __isl_give isl_multi_aff *isl_multi_aff_range_map(
4161 __isl_take isl_space *space);
4162 __isl_give isl_multi_aff *isl_multi_aff_project_out_map(
4163 __isl_take isl_space *space,
4164 enum isl_dim_type type,
4165 unsigned first, unsigned n);
4166 __isl_give isl_pw_multi_aff *
4167 isl_pw_multi_aff_project_out_map(
4168 __isl_take isl_space *space,
4169 enum isl_dim_type type,
4170 unsigned first, unsigned n);
4171 __isl_give isl_pw_multi_aff *
4172 isl_pw_multi_aff_from_multi_aff(
4173 __isl_take isl_multi_aff *ma);
4174 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_alloc(
4175 __isl_take isl_set *set,
4176 __isl_take isl_multi_aff *maff);
4177 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_from_domain(
4178 __isl_take isl_set *set);
4180 __isl_give isl_union_pw_multi_aff *
4181 isl_union_pw_multi_aff_empty(
4182 __isl_take isl_space *space);
4183 __isl_give isl_union_pw_multi_aff *
4184 isl_union_pw_multi_aff_add_pw_multi_aff(
4185 __isl_take isl_union_pw_multi_aff *upma,
4186 __isl_take isl_pw_multi_aff *pma);
4187 __isl_give isl_union_pw_multi_aff *
4188 isl_union_pw_multi_aff_from_domain(
4189 __isl_take isl_union_set *uset);
4191 A piecewise multiple quasi affine expression can also be initialized
4192 from an C<isl_set> or C<isl_map>, provided the C<isl_set> is a singleton
4193 and the C<isl_map> is single-valued.
4194 In case of a conversion from an C<isl_union_set> or an C<isl_union_map>
4195 to an C<isl_union_pw_multi_aff>, these properties need to hold in each space.
4197 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_from_set(
4198 __isl_take isl_set *set);
4199 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_from_map(
4200 __isl_take isl_map *map);
4202 __isl_give isl_union_pw_multi_aff *
4203 isl_union_pw_multi_aff_from_union_set(
4204 __isl_take isl_union_set *uset);
4205 __isl_give isl_union_pw_multi_aff *
4206 isl_union_pw_multi_aff_from_union_map(
4207 __isl_take isl_union_map *umap);
4209 Multiple quasi affine expressions can be copied and freed using
4211 #include <isl/aff.h>
4212 __isl_give isl_multi_aff *isl_multi_aff_copy(
4213 __isl_keep isl_multi_aff *maff);
4214 void *isl_multi_aff_free(__isl_take isl_multi_aff *maff);
4216 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_copy(
4217 __isl_keep isl_pw_multi_aff *pma);
4218 void *isl_pw_multi_aff_free(
4219 __isl_take isl_pw_multi_aff *pma);
4221 __isl_give isl_union_pw_multi_aff *
4222 isl_union_pw_multi_aff_copy(
4223 __isl_keep isl_union_pw_multi_aff *upma);
4224 void *isl_union_pw_multi_aff_free(
4225 __isl_take isl_union_pw_multi_aff *upma);
4227 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_copy(
4228 __isl_keep isl_multi_pw_aff *mpa);
4229 void *isl_multi_pw_aff_free(
4230 __isl_take isl_multi_pw_aff *mpa);
4232 The expression can be inspected using
4234 #include <isl/aff.h>
4235 isl_ctx *isl_multi_aff_get_ctx(
4236 __isl_keep isl_multi_aff *maff);
4237 isl_ctx *isl_pw_multi_aff_get_ctx(
4238 __isl_keep isl_pw_multi_aff *pma);
4239 isl_ctx *isl_union_pw_multi_aff_get_ctx(
4240 __isl_keep isl_union_pw_multi_aff *upma);
4241 isl_ctx *isl_multi_pw_aff_get_ctx(
4242 __isl_keep isl_multi_pw_aff *mpa);
4243 unsigned isl_multi_aff_dim(__isl_keep isl_multi_aff *maff,
4244 enum isl_dim_type type);
4245 unsigned isl_pw_multi_aff_dim(
4246 __isl_keep isl_pw_multi_aff *pma,
4247 enum isl_dim_type type);
4248 unsigned isl_multi_pw_aff_dim(
4249 __isl_keep isl_multi_pw_aff *mpa,
4250 enum isl_dim_type type);
4251 __isl_give isl_aff *isl_multi_aff_get_aff(
4252 __isl_keep isl_multi_aff *multi, int pos);
4253 __isl_give isl_pw_aff *isl_pw_multi_aff_get_pw_aff(
4254 __isl_keep isl_pw_multi_aff *pma, int pos);
4255 __isl_give isl_pw_aff *isl_multi_pw_aff_get_pw_aff(
4256 __isl_keep isl_multi_pw_aff *mpa, int pos);
4257 int isl_multi_aff_find_dim_by_id(
4258 __isl_keep isl_multi_aff *ma,
4259 enum isl_dim_type type, __isl_keep isl_id *id);
4260 int isl_multi_pw_aff_find_dim_by_id(
4261 __isl_keep isl_multi_pw_aff *mpa,
4262 enum isl_dim_type type, __isl_keep isl_id *id);
4263 const char *isl_pw_multi_aff_get_dim_name(
4264 __isl_keep isl_pw_multi_aff *pma,
4265 enum isl_dim_type type, unsigned pos);
4266 __isl_give isl_id *isl_multi_aff_get_dim_id(
4267 __isl_keep isl_multi_aff *ma,
4268 enum isl_dim_type type, unsigned pos);
4269 __isl_give isl_id *isl_pw_multi_aff_get_dim_id(
4270 __isl_keep isl_pw_multi_aff *pma,
4271 enum isl_dim_type type, unsigned pos);
4272 __isl_give isl_id *isl_multi_pw_aff_get_dim_id(
4273 __isl_keep isl_multi_pw_aff *mpa,
4274 enum isl_dim_type type, unsigned pos);
4275 const char *isl_multi_aff_get_tuple_name(
4276 __isl_keep isl_multi_aff *multi,
4277 enum isl_dim_type type);
4278 int isl_pw_multi_aff_has_tuple_name(
4279 __isl_keep isl_pw_multi_aff *pma,
4280 enum isl_dim_type type);
4281 const char *isl_pw_multi_aff_get_tuple_name(
4282 __isl_keep isl_pw_multi_aff *pma,
4283 enum isl_dim_type type);
4284 int isl_multi_aff_has_tuple_id(__isl_keep isl_multi_aff *ma,
4285 enum isl_dim_type type);
4286 int isl_pw_multi_aff_has_tuple_id(
4287 __isl_keep isl_pw_multi_aff *pma,
4288 enum isl_dim_type type);
4289 int isl_multi_pw_aff_has_tuple_id(
4290 __isl_keep isl_multi_pw_aff *mpa,
4291 enum isl_dim_type type);
4292 __isl_give isl_id *isl_multi_aff_get_tuple_id(
4293 __isl_keep isl_multi_aff *ma,
4294 enum isl_dim_type type);
4295 __isl_give isl_id *isl_pw_multi_aff_get_tuple_id(
4296 __isl_keep isl_pw_multi_aff *pma,
4297 enum isl_dim_type type);
4298 __isl_give isl_id *isl_multi_pw_aff_get_tuple_id(
4299 __isl_keep isl_multi_pw_aff *mpa,
4300 enum isl_dim_type type);
4301 int isl_multi_aff_range_is_wrapping(
4302 __isl_keep isl_multi_aff *ma);
4303 int isl_multi_pw_aff_range_is_wrapping(
4304 __isl_keep isl_multi_pw_aff *mpa);
4306 int isl_pw_multi_aff_foreach_piece(
4307 __isl_keep isl_pw_multi_aff *pma,
4308 int (*fn)(__isl_take isl_set *set,
4309 __isl_take isl_multi_aff *maff,
4310 void *user), void *user);
4312 int isl_union_pw_multi_aff_foreach_pw_multi_aff(
4313 __isl_keep isl_union_pw_multi_aff *upma,
4314 int (*fn)(__isl_take isl_pw_multi_aff *pma,
4315 void *user), void *user);
4317 It can be modified using
4319 #include <isl/aff.h>
4320 __isl_give isl_multi_aff *isl_multi_aff_set_aff(
4321 __isl_take isl_multi_aff *multi, int pos,
4322 __isl_take isl_aff *aff);
4323 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_set_pw_aff(
4324 __isl_take isl_pw_multi_aff *pma, unsigned pos,
4325 __isl_take isl_pw_aff *pa);
4326 __isl_give isl_multi_aff *isl_multi_aff_set_dim_name(
4327 __isl_take isl_multi_aff *maff,
4328 enum isl_dim_type type, unsigned pos, const char *s);
4329 __isl_give isl_multi_aff *isl_multi_aff_set_dim_id(
4330 __isl_take isl_multi_aff *maff,
4331 enum isl_dim_type type, unsigned pos,
4332 __isl_take isl_id *id);
4333 __isl_give isl_multi_aff *isl_multi_aff_set_tuple_name(
4334 __isl_take isl_multi_aff *maff,
4335 enum isl_dim_type type, const char *s);
4336 __isl_give isl_multi_aff *isl_multi_aff_set_tuple_id(
4337 __isl_take isl_multi_aff *maff,
4338 enum isl_dim_type type, __isl_take isl_id *id);
4339 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_set_tuple_id(
4340 __isl_take isl_pw_multi_aff *pma,
4341 enum isl_dim_type type, __isl_take isl_id *id);
4342 __isl_give isl_multi_aff *isl_multi_aff_reset_tuple_id(
4343 __isl_take isl_multi_aff *ma,
4344 enum isl_dim_type type);
4345 __isl_give isl_multi_pw_aff *
4346 isl_multi_pw_aff_reset_tuple_id(
4347 __isl_take isl_multi_pw_aff *mpa,
4348 enum isl_dim_type type);
4349 __isl_give isl_multi_aff *isl_multi_aff_reset_user(
4350 __isl_take isl_multi_aff *ma);
4351 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_reset_user(
4352 __isl_take isl_multi_pw_aff *mpa);
4354 __isl_give isl_multi_pw_aff *
4355 isl_multi_pw_aff_set_dim_name(
4356 __isl_take isl_multi_pw_aff *mpa,
4357 enum isl_dim_type type, unsigned pos, const char *s);
4358 __isl_give isl_multi_pw_aff *
4359 isl_multi_pw_aff_set_dim_id(
4360 __isl_take isl_multi_pw_aff *mpa,
4361 enum isl_dim_type type, unsigned pos,
4362 __isl_take isl_id *id);
4363 __isl_give isl_multi_pw_aff *
4364 isl_multi_pw_aff_set_tuple_name(
4365 __isl_take isl_multi_pw_aff *mpa,
4366 enum isl_dim_type type, const char *s);
4368 __isl_give isl_multi_aff *isl_multi_aff_insert_dims(
4369 __isl_take isl_multi_aff *ma,
4370 enum isl_dim_type type, unsigned first, unsigned n);
4371 __isl_give isl_multi_aff *isl_multi_aff_add_dims(
4372 __isl_take isl_multi_aff *ma,
4373 enum isl_dim_type type, unsigned n);
4374 __isl_give isl_multi_aff *isl_multi_aff_drop_dims(
4375 __isl_take isl_multi_aff *maff,
4376 enum isl_dim_type type, unsigned first, unsigned n);
4377 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_drop_dims(
4378 __isl_take isl_pw_multi_aff *pma,
4379 enum isl_dim_type type, unsigned first, unsigned n);
4381 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_insert_dims(
4382 __isl_take isl_multi_pw_aff *mpa,
4383 enum isl_dim_type type, unsigned first, unsigned n);
4384 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_add_dims(
4385 __isl_take isl_multi_pw_aff *mpa,
4386 enum isl_dim_type type, unsigned n);
4387 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_move_dims(
4388 __isl_take isl_multi_pw_aff *pma,
4389 enum isl_dim_type dst_type, unsigned dst_pos,
4390 enum isl_dim_type src_type, unsigned src_pos,
4393 To check whether two multiple affine expressions are
4394 (obviously) equal to each other, use
4396 int isl_multi_aff_plain_is_equal(__isl_keep isl_multi_aff *maff1,
4397 __isl_keep isl_multi_aff *maff2);
4398 int isl_pw_multi_aff_plain_is_equal(
4399 __isl_keep isl_pw_multi_aff *pma1,
4400 __isl_keep isl_pw_multi_aff *pma2);
4401 int isl_multi_pw_aff_plain_is_equal(
4402 __isl_keep isl_multi_pw_aff *mpa1,
4403 __isl_keep isl_multi_pw_aff *mpa2);
4404 int isl_multi_pw_aff_is_equal(
4405 __isl_keep isl_multi_pw_aff *mpa1,
4406 __isl_keep isl_multi_pw_aff *mpa2);
4410 #include <isl/aff.h>
4411 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_union_lexmin(
4412 __isl_take isl_pw_multi_aff *pma1,
4413 __isl_take isl_pw_multi_aff *pma2);
4414 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_union_lexmax(
4415 __isl_take isl_pw_multi_aff *pma1,
4416 __isl_take isl_pw_multi_aff *pma2);
4417 __isl_give isl_multi_aff *isl_multi_aff_add(
4418 __isl_take isl_multi_aff *maff1,
4419 __isl_take isl_multi_aff *maff2);
4420 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_add(
4421 __isl_take isl_pw_multi_aff *pma1,
4422 __isl_take isl_pw_multi_aff *pma2);
4423 __isl_give isl_union_pw_multi_aff *isl_union_pw_multi_aff_add(
4424 __isl_take isl_union_pw_multi_aff *upma1,
4425 __isl_take isl_union_pw_multi_aff *upma2);
4426 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_union_add(
4427 __isl_take isl_pw_multi_aff *pma1,
4428 __isl_take isl_pw_multi_aff *pma2);
4429 __isl_give isl_multi_aff *isl_multi_aff_sub(
4430 __isl_take isl_multi_aff *ma1,
4431 __isl_take isl_multi_aff *ma2);
4432 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_sub(
4433 __isl_take isl_pw_multi_aff *pma1,
4434 __isl_take isl_pw_multi_aff *pma2);
4435 __isl_give isl_union_pw_multi_aff *isl_union_pw_multi_aff_sub(
4436 __isl_take isl_union_pw_multi_aff *upma1,
4437 __isl_take isl_union_pw_multi_aff *upma2);
4439 C<isl_multi_aff_sub> subtracts the second argument from the first.
4441 __isl_give isl_multi_aff *isl_multi_aff_scale_val(
4442 __isl_take isl_multi_aff *ma,
4443 __isl_take isl_val *v);
4444 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_scale_val(
4445 __isl_take isl_pw_multi_aff *pma,
4446 __isl_take isl_val *v);
4447 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_scale_val(
4448 __isl_take isl_multi_pw_aff *mpa,
4449 __isl_take isl_val *v);
4450 __isl_give isl_multi_aff *isl_multi_aff_scale_multi_val(
4451 __isl_take isl_multi_aff *ma,
4452 __isl_take isl_multi_val *mv);
4453 __isl_give isl_pw_multi_aff *
4454 isl_pw_multi_aff_scale_multi_val(
4455 __isl_take isl_pw_multi_aff *pma,
4456 __isl_take isl_multi_val *mv);
4457 __isl_give isl_multi_pw_aff *
4458 isl_multi_pw_aff_scale_multi_val(
4459 __isl_take isl_multi_pw_aff *mpa,
4460 __isl_take isl_multi_val *mv);
4461 __isl_give isl_union_pw_multi_aff *
4462 isl_union_pw_multi_aff_scale_multi_val(
4463 __isl_take isl_union_pw_multi_aff *upma,
4464 __isl_take isl_multi_val *mv);
4465 __isl_give isl_multi_aff *
4466 isl_multi_aff_scale_down_multi_val(
4467 __isl_take isl_multi_aff *ma,
4468 __isl_take isl_multi_val *mv);
4469 __isl_give isl_multi_pw_aff *
4470 isl_multi_pw_aff_scale_down_multi_val(
4471 __isl_take isl_multi_pw_aff *mpa,
4472 __isl_take isl_multi_val *mv);
4474 C<isl_multi_aff_scale_multi_val> scales the elements of C<ma>
4475 by the corresponding elements of C<mv>.
4477 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_fix_si(
4478 __isl_take isl_pw_multi_aff *pma,
4479 enum isl_dim_type type, unsigned pos, int value);
4480 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_intersect_params(
4481 __isl_take isl_pw_multi_aff *pma,
4482 __isl_take isl_set *set);
4483 __isl_give isl_set *isl_multi_pw_aff_domain(
4484 __isl_take isl_multi_pw_aff *mpa);
4485 __isl_give isl_multi_pw_aff *
4486 isl_multi_pw_aff_intersect_params(
4487 __isl_take isl_multi_pw_aff *mpa,
4488 __isl_take isl_set *set);
4489 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_intersect_domain(
4490 __isl_take isl_pw_multi_aff *pma,
4491 __isl_take isl_set *set);
4492 __isl_give isl_multi_pw_aff *
4493 isl_multi_pw_aff_intersect_domain(
4494 __isl_take isl_multi_pw_aff *mpa,
4495 __isl_take isl_set *domain);
4496 __isl_give isl_union_pw_multi_aff *
4497 isl_union_pw_multi_aff_intersect_domain(
4498 __isl_take isl_union_pw_multi_aff *upma,
4499 __isl_take isl_union_set *uset);
4500 __isl_give isl_multi_aff *isl_multi_aff_lift(
4501 __isl_take isl_multi_aff *maff,
4502 __isl_give isl_local_space **ls);
4503 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_coalesce(
4504 __isl_take isl_pw_multi_aff *pma);
4505 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_coalesce(
4506 __isl_take isl_multi_pw_aff *mpa);
4507 __isl_give isl_multi_aff *isl_multi_aff_align_params(
4508 __isl_take isl_multi_aff *multi,
4509 __isl_take isl_space *model);
4510 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_align_params(
4511 __isl_take isl_pw_multi_aff *pma,
4512 __isl_take isl_space *model);
4513 __isl_give isl_pw_multi_aff *
4514 isl_pw_multi_aff_project_domain_on_params(
4515 __isl_take isl_pw_multi_aff *pma);
4516 __isl_give isl_multi_aff *isl_multi_aff_gist_params(
4517 __isl_take isl_multi_aff *maff,
4518 __isl_take isl_set *context);
4519 __isl_give isl_multi_aff *isl_multi_aff_gist(
4520 __isl_take isl_multi_aff *maff,
4521 __isl_take isl_set *context);
4522 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_gist_params(
4523 __isl_take isl_pw_multi_aff *pma,
4524 __isl_take isl_set *set);
4525 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_gist(
4526 __isl_take isl_pw_multi_aff *pma,
4527 __isl_take isl_set *set);
4528 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_gist_params(
4529 __isl_take isl_multi_pw_aff *mpa,
4530 __isl_take isl_set *set);
4531 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_gist(
4532 __isl_take isl_multi_pw_aff *mpa,
4533 __isl_take isl_set *set);
4534 __isl_give isl_multi_aff *isl_multi_aff_from_range(
4535 __isl_take isl_multi_aff *ma);
4536 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_from_range(
4537 __isl_take isl_multi_pw_aff *mpa);
4538 __isl_give isl_set *isl_pw_multi_aff_domain(
4539 __isl_take isl_pw_multi_aff *pma);
4540 __isl_give isl_union_set *isl_union_pw_multi_aff_domain(
4541 __isl_take isl_union_pw_multi_aff *upma);
4542 __isl_give isl_multi_aff *isl_multi_aff_range_splice(
4543 __isl_take isl_multi_aff *ma1, unsigned pos,
4544 __isl_take isl_multi_aff *ma2);
4545 __isl_give isl_multi_aff *isl_multi_aff_splice(
4546 __isl_take isl_multi_aff *ma1,
4547 unsigned in_pos, unsigned out_pos,
4548 __isl_take isl_multi_aff *ma2);
4549 __isl_give isl_multi_aff *isl_multi_aff_range_product(
4550 __isl_take isl_multi_aff *ma1,
4551 __isl_take isl_multi_aff *ma2);
4552 __isl_give isl_multi_aff *
4553 isl_multi_aff_range_factor_domain(
4554 __isl_take isl_multi_aff *ma);
4555 __isl_give isl_multi_aff *
4556 isl_multi_aff_range_factor_range(
4557 __isl_take isl_multi_aff *ma);
4558 __isl_give isl_multi_aff *isl_multi_aff_flat_range_product(
4559 __isl_take isl_multi_aff *ma1,
4560 __isl_take isl_multi_aff *ma2);
4561 __isl_give isl_multi_aff *isl_multi_aff_product(
4562 __isl_take isl_multi_aff *ma1,
4563 __isl_take isl_multi_aff *ma2);
4564 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_product(
4565 __isl_take isl_multi_pw_aff *mpa1,
4566 __isl_take isl_multi_pw_aff *mpa2);
4567 __isl_give isl_pw_multi_aff *
4568 isl_pw_multi_aff_range_product(
4569 __isl_take isl_pw_multi_aff *pma1,
4570 __isl_take isl_pw_multi_aff *pma2);
4571 __isl_give isl_multi_pw_aff *
4572 isl_multi_pw_aff_range_factor_domain(
4573 __isl_take isl_multi_pw_aff *mpa);
4574 __isl_give isl_multi_pw_aff *
4575 isl_multi_pw_aff_range_factor_range(
4576 __isl_take isl_multi_pw_aff *mpa);
4577 __isl_give isl_pw_multi_aff *
4578 isl_pw_multi_aff_flat_range_product(
4579 __isl_take isl_pw_multi_aff *pma1,
4580 __isl_take isl_pw_multi_aff *pma2);
4581 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_product(
4582 __isl_take isl_pw_multi_aff *pma1,
4583 __isl_take isl_pw_multi_aff *pma2);
4584 __isl_give isl_union_pw_multi_aff *
4585 isl_union_pw_multi_aff_flat_range_product(
4586 __isl_take isl_union_pw_multi_aff *upma1,
4587 __isl_take isl_union_pw_multi_aff *upma2);
4588 __isl_give isl_multi_pw_aff *
4589 isl_multi_pw_aff_range_splice(
4590 __isl_take isl_multi_pw_aff *mpa1, unsigned pos,
4591 __isl_take isl_multi_pw_aff *mpa2);
4592 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_splice(
4593 __isl_take isl_multi_pw_aff *mpa1,
4594 unsigned in_pos, unsigned out_pos,
4595 __isl_take isl_multi_pw_aff *mpa2);
4596 __isl_give isl_multi_pw_aff *
4597 isl_multi_pw_aff_range_product(
4598 __isl_take isl_multi_pw_aff *mpa1,
4599 __isl_take isl_multi_pw_aff *mpa2);
4600 __isl_give isl_multi_pw_aff *
4601 isl_multi_pw_aff_flat_range_product(
4602 __isl_take isl_multi_pw_aff *mpa1,
4603 __isl_take isl_multi_pw_aff *mpa2);
4605 If the C<ls> argument of C<isl_multi_aff_lift> is not C<NULL>,
4606 then it is assigned the local space that lies at the basis of
4607 the lifting applied.
4609 #include <isl/aff.h>
4610 __isl_give isl_multi_aff *isl_multi_aff_pullback_multi_aff(
4611 __isl_take isl_multi_aff *ma1,
4612 __isl_take isl_multi_aff *ma2);
4613 __isl_give isl_pw_multi_aff *
4614 isl_pw_multi_aff_pullback_multi_aff(
4615 __isl_take isl_pw_multi_aff *pma,
4616 __isl_take isl_multi_aff *ma);
4617 __isl_give isl_multi_pw_aff *
4618 isl_multi_pw_aff_pullback_multi_aff(
4619 __isl_take isl_multi_pw_aff *mpa,
4620 __isl_take isl_multi_aff *ma);
4621 __isl_give isl_pw_multi_aff *
4622 isl_pw_multi_aff_pullback_pw_multi_aff(
4623 __isl_take isl_pw_multi_aff *pma1,
4624 __isl_take isl_pw_multi_aff *pma2);
4625 __isl_give isl_multi_pw_aff *
4626 isl_multi_pw_aff_pullback_pw_multi_aff(
4627 __isl_take isl_multi_pw_aff *mpa,
4628 __isl_take isl_pw_multi_aff *pma);
4629 __isl_give isl_multi_pw_aff *
4630 isl_multi_pw_aff_pullback_multi_pw_aff(
4631 __isl_take isl_multi_pw_aff *mpa1,
4632 __isl_take isl_multi_pw_aff *mpa2);
4634 The function C<isl_multi_aff_pullback_multi_aff> precomposes C<ma1> by C<ma2>.
4635 In other words, C<ma2> is plugged
4638 __isl_give isl_set *isl_multi_aff_lex_le_set(
4639 __isl_take isl_multi_aff *ma1,
4640 __isl_take isl_multi_aff *ma2);
4641 __isl_give isl_set *isl_multi_aff_lex_ge_set(
4642 __isl_take isl_multi_aff *ma1,
4643 __isl_take isl_multi_aff *ma2);
4645 The function C<isl_multi_aff_lex_le_set> returns a set
4646 containing those elements in the shared domain space
4647 where C<ma1> is lexicographically smaller than or
4650 An expression can be read from input using
4652 #include <isl/aff.h>
4653 __isl_give isl_multi_aff *isl_multi_aff_read_from_str(
4654 isl_ctx *ctx, const char *str);
4655 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_read_from_str(
4656 isl_ctx *ctx, const char *str);
4657 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_read_from_str(
4658 isl_ctx *ctx, const char *str);
4659 __isl_give isl_union_pw_multi_aff *
4660 isl_union_pw_multi_aff_read_from_str(
4661 isl_ctx *ctx, const char *str);
4663 An expression can be printed using
4665 #include <isl/aff.h>
4666 __isl_give isl_printer *isl_printer_print_multi_aff(
4667 __isl_take isl_printer *p,
4668 __isl_keep isl_multi_aff *maff);
4669 __isl_give isl_printer *isl_printer_print_pw_multi_aff(
4670 __isl_take isl_printer *p,
4671 __isl_keep isl_pw_multi_aff *pma);
4672 __isl_give isl_printer *isl_printer_print_union_pw_multi_aff(
4673 __isl_take isl_printer *p,
4674 __isl_keep isl_union_pw_multi_aff *upma);
4675 __isl_give isl_printer *isl_printer_print_multi_pw_aff(
4676 __isl_take isl_printer *p,
4677 __isl_keep isl_multi_pw_aff *mpa);
4681 Points are elements of a set. They can be used to construct
4682 simple sets (boxes) or they can be used to represent the
4683 individual elements of a set.
4684 The zero point (the origin) can be created using
4686 __isl_give isl_point *isl_point_zero(__isl_take isl_space *space);
4688 The coordinates of a point can be inspected, set and changed
4691 __isl_give isl_val *isl_point_get_coordinate_val(
4692 __isl_keep isl_point *pnt,
4693 enum isl_dim_type type, int pos);
4694 __isl_give isl_point *isl_point_set_coordinate_val(
4695 __isl_take isl_point *pnt,
4696 enum isl_dim_type type, int pos,
4697 __isl_take isl_val *v);
4699 __isl_give isl_point *isl_point_add_ui(
4700 __isl_take isl_point *pnt,
4701 enum isl_dim_type type, int pos, unsigned val);
4702 __isl_give isl_point *isl_point_sub_ui(
4703 __isl_take isl_point *pnt,
4704 enum isl_dim_type type, int pos, unsigned val);
4706 Other properties can be obtained using
4708 isl_ctx *isl_point_get_ctx(__isl_keep isl_point *pnt);
4710 Points can be copied or freed using
4712 __isl_give isl_point *isl_point_copy(
4713 __isl_keep isl_point *pnt);
4714 void isl_point_free(__isl_take isl_point *pnt);
4716 A singleton set can be created from a point using
4718 __isl_give isl_basic_set *isl_basic_set_from_point(
4719 __isl_take isl_point *pnt);
4720 __isl_give isl_set *isl_set_from_point(
4721 __isl_take isl_point *pnt);
4723 and a box can be created from two opposite extremal points using
4725 __isl_give isl_basic_set *isl_basic_set_box_from_points(
4726 __isl_take isl_point *pnt1,
4727 __isl_take isl_point *pnt2);
4728 __isl_give isl_set *isl_set_box_from_points(
4729 __isl_take isl_point *pnt1,
4730 __isl_take isl_point *pnt2);
4732 All elements of a B<bounded> (union) set can be enumerated using
4733 the following functions.
4735 int isl_set_foreach_point(__isl_keep isl_set *set,
4736 int (*fn)(__isl_take isl_point *pnt, void *user),
4738 int isl_union_set_foreach_point(__isl_keep isl_union_set *uset,
4739 int (*fn)(__isl_take isl_point *pnt, void *user),
4742 The function C<fn> is called for each integer point in
4743 C<set> with as second argument the last argument of
4744 the C<isl_set_foreach_point> call. The function C<fn>
4745 should return C<0> on success and C<-1> on failure.
4746 In the latter case, C<isl_set_foreach_point> will stop
4747 enumerating and return C<-1> as well.
4748 If the enumeration is performed successfully and to completion,
4749 then C<isl_set_foreach_point> returns C<0>.
4751 To obtain a single point of a (basic) set, use
4753 __isl_give isl_point *isl_basic_set_sample_point(
4754 __isl_take isl_basic_set *bset);
4755 __isl_give isl_point *isl_set_sample_point(
4756 __isl_take isl_set *set);
4758 If C<set> does not contain any (integer) points, then the
4759 resulting point will be ``void'', a property that can be
4762 int isl_point_is_void(__isl_keep isl_point *pnt);
4764 =head2 Piecewise Quasipolynomials
4766 A piecewise quasipolynomial is a particular kind of function that maps
4767 a parametric point to a rational value.
4768 More specifically, a quasipolynomial is a polynomial expression in greatest
4769 integer parts of affine expressions of parameters and variables.
4770 A piecewise quasipolynomial is a subdivision of a given parametric
4771 domain into disjoint cells with a quasipolynomial associated to
4772 each cell. The value of the piecewise quasipolynomial at a given
4773 point is the value of the quasipolynomial associated to the cell
4774 that contains the point. Outside of the union of cells,
4775 the value is assumed to be zero.
4776 For example, the piecewise quasipolynomial
4778 [n] -> { [x] -> ((1 + n) - x) : x <= n and x >= 0 }
4780 maps C<x> to C<1 + n - x> for values of C<x> between C<0> and C<n>.
4781 A given piecewise quasipolynomial has a fixed domain dimension.
4782 Union piecewise quasipolynomials are used to contain piecewise quasipolynomials
4783 defined over different domains.
4784 Piecewise quasipolynomials are mainly used by the C<barvinok>
4785 library for representing the number of elements in a parametric set or map.
4786 For example, the piecewise quasipolynomial above represents
4787 the number of points in the map
4789 [n] -> { [x] -> [y] : x,y >= 0 and 0 <= x + y <= n }
4791 =head3 Input and Output
4793 Piecewise quasipolynomials can be read from input using
4795 __isl_give isl_union_pw_qpolynomial *
4796 isl_union_pw_qpolynomial_read_from_str(
4797 isl_ctx *ctx, const char *str);
4799 Quasipolynomials and piecewise quasipolynomials can be printed
4800 using the following functions.
4802 __isl_give isl_printer *isl_printer_print_qpolynomial(
4803 __isl_take isl_printer *p,
4804 __isl_keep isl_qpolynomial *qp);
4806 __isl_give isl_printer *isl_printer_print_pw_qpolynomial(
4807 __isl_take isl_printer *p,
4808 __isl_keep isl_pw_qpolynomial *pwqp);
4810 __isl_give isl_printer *isl_printer_print_union_pw_qpolynomial(
4811 __isl_take isl_printer *p,
4812 __isl_keep isl_union_pw_qpolynomial *upwqp);
4814 The output format of the printer
4815 needs to be set to either C<ISL_FORMAT_ISL> or C<ISL_FORMAT_C>.
4816 For C<isl_printer_print_union_pw_qpolynomial>, only C<ISL_FORMAT_ISL>
4818 In case of printing in C<ISL_FORMAT_C>, the user may want
4819 to set the names of all dimensions
4821 __isl_give isl_qpolynomial *isl_qpolynomial_set_dim_name(
4822 __isl_take isl_qpolynomial *qp,
4823 enum isl_dim_type type, unsigned pos,
4825 __isl_give isl_pw_qpolynomial *
4826 isl_pw_qpolynomial_set_dim_name(
4827 __isl_take isl_pw_qpolynomial *pwqp,
4828 enum isl_dim_type type, unsigned pos,
4831 =head3 Creating New (Piecewise) Quasipolynomials
4833 Some simple quasipolynomials can be created using the following functions.
4834 More complicated quasipolynomials can be created by applying
4835 operations such as addition and multiplication
4836 on the resulting quasipolynomials
4838 __isl_give isl_qpolynomial *isl_qpolynomial_zero_on_domain(
4839 __isl_take isl_space *domain);
4840 __isl_give isl_qpolynomial *isl_qpolynomial_one_on_domain(
4841 __isl_take isl_space *domain);
4842 __isl_give isl_qpolynomial *isl_qpolynomial_infty_on_domain(
4843 __isl_take isl_space *domain);
4844 __isl_give isl_qpolynomial *isl_qpolynomial_neginfty_on_domain(
4845 __isl_take isl_space *domain);
4846 __isl_give isl_qpolynomial *isl_qpolynomial_nan_on_domain(
4847 __isl_take isl_space *domain);
4848 __isl_give isl_qpolynomial *isl_qpolynomial_val_on_domain(
4849 __isl_take isl_space *domain,
4850 __isl_take isl_val *val);
4851 __isl_give isl_qpolynomial *isl_qpolynomial_var_on_domain(
4852 __isl_take isl_space *domain,
4853 enum isl_dim_type type, unsigned pos);
4854 __isl_give isl_qpolynomial *isl_qpolynomial_from_aff(
4855 __isl_take isl_aff *aff);
4857 Note that the space in which a quasipolynomial lives is a map space
4858 with a one-dimensional range. The C<domain> argument in some of
4859 the functions above corresponds to the domain of this map space.
4861 The zero piecewise quasipolynomial or a piecewise quasipolynomial
4862 with a single cell can be created using the following functions.
4863 Multiple of these single cell piecewise quasipolynomials can
4864 be combined to create more complicated piecewise quasipolynomials.
4866 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_zero(
4867 __isl_take isl_space *space);
4868 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_alloc(
4869 __isl_take isl_set *set,
4870 __isl_take isl_qpolynomial *qp);
4871 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_from_qpolynomial(
4872 __isl_take isl_qpolynomial *qp);
4873 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_from_pw_aff(
4874 __isl_take isl_pw_aff *pwaff);
4876 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_zero(
4877 __isl_take isl_space *space);
4878 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_from_pw_qpolynomial(
4879 __isl_take isl_pw_qpolynomial *pwqp);
4880 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_add_pw_qpolynomial(
4881 __isl_take isl_union_pw_qpolynomial *upwqp,
4882 __isl_take isl_pw_qpolynomial *pwqp);
4884 Quasipolynomials can be copied and freed again using the following
4887 __isl_give isl_qpolynomial *isl_qpolynomial_copy(
4888 __isl_keep isl_qpolynomial *qp);
4889 void *isl_qpolynomial_free(__isl_take isl_qpolynomial *qp);
4891 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_copy(
4892 __isl_keep isl_pw_qpolynomial *pwqp);
4893 void *isl_pw_qpolynomial_free(
4894 __isl_take isl_pw_qpolynomial *pwqp);
4896 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_copy(
4897 __isl_keep isl_union_pw_qpolynomial *upwqp);
4898 void *isl_union_pw_qpolynomial_free(
4899 __isl_take isl_union_pw_qpolynomial *upwqp);
4901 =head3 Inspecting (Piecewise) Quasipolynomials
4903 To iterate over all piecewise quasipolynomials in a union
4904 piecewise quasipolynomial, use the following function
4906 int isl_union_pw_qpolynomial_foreach_pw_qpolynomial(
4907 __isl_keep isl_union_pw_qpolynomial *upwqp,
4908 int (*fn)(__isl_take isl_pw_qpolynomial *pwqp, void *user),
4911 To extract the piecewise quasipolynomial in a given space from a union, use
4913 __isl_give isl_pw_qpolynomial *
4914 isl_union_pw_qpolynomial_extract_pw_qpolynomial(
4915 __isl_keep isl_union_pw_qpolynomial *upwqp,
4916 __isl_take isl_space *space);
4918 To iterate over the cells in a piecewise quasipolynomial,
4919 use either of the following two functions
4921 int isl_pw_qpolynomial_foreach_piece(
4922 __isl_keep isl_pw_qpolynomial *pwqp,
4923 int (*fn)(__isl_take isl_set *set,
4924 __isl_take isl_qpolynomial *qp,
4925 void *user), void *user);
4926 int isl_pw_qpolynomial_foreach_lifted_piece(
4927 __isl_keep isl_pw_qpolynomial *pwqp,
4928 int (*fn)(__isl_take isl_set *set,
4929 __isl_take isl_qpolynomial *qp,
4930 void *user), void *user);
4932 As usual, the function C<fn> should return C<0> on success
4933 and C<-1> on failure. The difference between
4934 C<isl_pw_qpolynomial_foreach_piece> and
4935 C<isl_pw_qpolynomial_foreach_lifted_piece> is that
4936 C<isl_pw_qpolynomial_foreach_lifted_piece> will first
4937 compute unique representations for all existentially quantified
4938 variables and then turn these existentially quantified variables
4939 into extra set variables, adapting the associated quasipolynomial
4940 accordingly. This means that the C<set> passed to C<fn>
4941 will not have any existentially quantified variables, but that
4942 the dimensions of the sets may be different for different
4943 invocations of C<fn>.
4945 The constant term of a quasipolynomial can be extracted using
4947 __isl_give isl_val *isl_qpolynomial_get_constant_val(
4948 __isl_keep isl_qpolynomial *qp);
4950 To iterate over all terms in a quasipolynomial,
4953 int isl_qpolynomial_foreach_term(
4954 __isl_keep isl_qpolynomial *qp,
4955 int (*fn)(__isl_take isl_term *term,
4956 void *user), void *user);
4958 The terms themselves can be inspected and freed using
4961 unsigned isl_term_dim(__isl_keep isl_term *term,
4962 enum isl_dim_type type);
4963 __isl_give isl_val *isl_term_get_coefficient_val(
4964 __isl_keep isl_term *term);
4965 int isl_term_get_exp(__isl_keep isl_term *term,
4966 enum isl_dim_type type, unsigned pos);
4967 __isl_give isl_aff *isl_term_get_div(
4968 __isl_keep isl_term *term, unsigned pos);
4969 void isl_term_free(__isl_take isl_term *term);
4971 Each term is a product of parameters, set variables and
4972 integer divisions. The function C<isl_term_get_exp>
4973 returns the exponent of a given dimensions in the given term.
4975 =head3 Properties of (Piecewise) Quasipolynomials
4977 To check whether two union piecewise quasipolynomials are
4978 obviously equal, use
4980 int isl_union_pw_qpolynomial_plain_is_equal(
4981 __isl_keep isl_union_pw_qpolynomial *upwqp1,
4982 __isl_keep isl_union_pw_qpolynomial *upwqp2);
4984 =head3 Operations on (Piecewise) Quasipolynomials
4986 __isl_give isl_qpolynomial *isl_qpolynomial_scale_val(
4987 __isl_take isl_qpolynomial *qp,
4988 __isl_take isl_val *v);
4989 __isl_give isl_qpolynomial *isl_qpolynomial_neg(
4990 __isl_take isl_qpolynomial *qp);
4991 __isl_give isl_qpolynomial *isl_qpolynomial_add(
4992 __isl_take isl_qpolynomial *qp1,
4993 __isl_take isl_qpolynomial *qp2);
4994 __isl_give isl_qpolynomial *isl_qpolynomial_sub(
4995 __isl_take isl_qpolynomial *qp1,
4996 __isl_take isl_qpolynomial *qp2);
4997 __isl_give isl_qpolynomial *isl_qpolynomial_mul(
4998 __isl_take isl_qpolynomial *qp1,
4999 __isl_take isl_qpolynomial *qp2);
5000 __isl_give isl_qpolynomial *isl_qpolynomial_pow(
5001 __isl_take isl_qpolynomial *qp, unsigned exponent);
5003 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_fix_val(
5004 __isl_take isl_pw_qpolynomial *pwqp,
5005 enum isl_dim_type type, unsigned n,
5006 __isl_take isl_val *v);
5007 __isl_give isl_pw_qpolynomial *
5008 isl_pw_qpolynomial_scale_val(
5009 __isl_take isl_pw_qpolynomial *pwqp,
5010 __isl_take isl_val *v);
5011 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_add(
5012 __isl_take isl_pw_qpolynomial *pwqp1,
5013 __isl_take isl_pw_qpolynomial *pwqp2);
5014 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_sub(
5015 __isl_take isl_pw_qpolynomial *pwqp1,
5016 __isl_take isl_pw_qpolynomial *pwqp2);
5017 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_add_disjoint(
5018 __isl_take isl_pw_qpolynomial *pwqp1,
5019 __isl_take isl_pw_qpolynomial *pwqp2);
5020 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_neg(
5021 __isl_take isl_pw_qpolynomial *pwqp);
5022 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_mul(
5023 __isl_take isl_pw_qpolynomial *pwqp1,
5024 __isl_take isl_pw_qpolynomial *pwqp2);
5025 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_pow(
5026 __isl_take isl_pw_qpolynomial *pwqp, unsigned exponent);
5028 __isl_give isl_union_pw_qpolynomial *
5029 isl_union_pw_qpolynomial_scale_val(
5030 __isl_take isl_union_pw_qpolynomial *upwqp,
5031 __isl_take isl_val *v);
5032 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_add(
5033 __isl_take isl_union_pw_qpolynomial *upwqp1,
5034 __isl_take isl_union_pw_qpolynomial *upwqp2);
5035 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_sub(
5036 __isl_take isl_union_pw_qpolynomial *upwqp1,
5037 __isl_take isl_union_pw_qpolynomial *upwqp2);
5038 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_mul(
5039 __isl_take isl_union_pw_qpolynomial *upwqp1,
5040 __isl_take isl_union_pw_qpolynomial *upwqp2);
5042 __isl_give isl_val *isl_pw_qpolynomial_eval(
5043 __isl_take isl_pw_qpolynomial *pwqp,
5044 __isl_take isl_point *pnt);
5046 __isl_give isl_val *isl_union_pw_qpolynomial_eval(
5047 __isl_take isl_union_pw_qpolynomial *upwqp,
5048 __isl_take isl_point *pnt);
5050 __isl_give isl_set *isl_pw_qpolynomial_domain(
5051 __isl_take isl_pw_qpolynomial *pwqp);
5052 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_intersect_domain(
5053 __isl_take isl_pw_qpolynomial *pwpq,
5054 __isl_take isl_set *set);
5055 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_intersect_params(
5056 __isl_take isl_pw_qpolynomial *pwpq,
5057 __isl_take isl_set *set);
5059 __isl_give isl_union_set *isl_union_pw_qpolynomial_domain(
5060 __isl_take isl_union_pw_qpolynomial *upwqp);
5061 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_intersect_domain(
5062 __isl_take isl_union_pw_qpolynomial *upwpq,
5063 __isl_take isl_union_set *uset);
5064 __isl_give isl_union_pw_qpolynomial *
5065 isl_union_pw_qpolynomial_intersect_params(
5066 __isl_take isl_union_pw_qpolynomial *upwpq,
5067 __isl_take isl_set *set);
5069 __isl_give isl_qpolynomial *isl_qpolynomial_align_params(
5070 __isl_take isl_qpolynomial *qp,
5071 __isl_take isl_space *model);
5073 __isl_give isl_qpolynomial *isl_qpolynomial_project_domain_on_params(
5074 __isl_take isl_qpolynomial *qp);
5075 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_project_domain_on_params(
5076 __isl_take isl_pw_qpolynomial *pwqp);
5078 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_coalesce(
5079 __isl_take isl_union_pw_qpolynomial *upwqp);
5081 __isl_give isl_qpolynomial *isl_qpolynomial_gist_params(
5082 __isl_take isl_qpolynomial *qp,
5083 __isl_take isl_set *context);
5084 __isl_give isl_qpolynomial *isl_qpolynomial_gist(
5085 __isl_take isl_qpolynomial *qp,
5086 __isl_take isl_set *context);
5088 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_gist_params(
5089 __isl_take isl_pw_qpolynomial *pwqp,
5090 __isl_take isl_set *context);
5091 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_gist(
5092 __isl_take isl_pw_qpolynomial *pwqp,
5093 __isl_take isl_set *context);
5095 __isl_give isl_union_pw_qpolynomial *
5096 isl_union_pw_qpolynomial_gist_params(
5097 __isl_take isl_union_pw_qpolynomial *upwqp,
5098 __isl_take isl_set *context);
5099 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_gist(
5100 __isl_take isl_union_pw_qpolynomial *upwqp,
5101 __isl_take isl_union_set *context);
5103 The gist operation applies the gist operation to each of
5104 the cells in the domain of the input piecewise quasipolynomial.
5105 The context is also exploited
5106 to simplify the quasipolynomials associated to each cell.
5108 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_to_polynomial(
5109 __isl_take isl_pw_qpolynomial *pwqp, int sign);
5110 __isl_give isl_union_pw_qpolynomial *
5111 isl_union_pw_qpolynomial_to_polynomial(
5112 __isl_take isl_union_pw_qpolynomial *upwqp, int sign);
5114 Approximate each quasipolynomial by a polynomial. If C<sign> is positive,
5115 the polynomial will be an overapproximation. If C<sign> is negative,
5116 it will be an underapproximation. If C<sign> is zero, the approximation
5117 will lie somewhere in between.
5119 =head2 Bounds on Piecewise Quasipolynomials and Piecewise Quasipolynomial Reductions
5121 A piecewise quasipolynomial reduction is a piecewise
5122 reduction (or fold) of quasipolynomials.
5123 In particular, the reduction can be maximum or a minimum.
5124 The objects are mainly used to represent the result of
5125 an upper or lower bound on a quasipolynomial over its domain,
5126 i.e., as the result of the following function.
5128 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_bound(
5129 __isl_take isl_pw_qpolynomial *pwqp,
5130 enum isl_fold type, int *tight);
5132 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_bound(
5133 __isl_take isl_union_pw_qpolynomial *upwqp,
5134 enum isl_fold type, int *tight);
5136 The C<type> argument may be either C<isl_fold_min> or C<isl_fold_max>.
5137 If C<tight> is not C<NULL>, then C<*tight> is set to C<1>
5138 is the returned bound is known be tight, i.e., for each value
5139 of the parameters there is at least
5140 one element in the domain that reaches the bound.
5141 If the domain of C<pwqp> is not wrapping, then the bound is computed
5142 over all elements in that domain and the result has a purely parametric
5143 domain. If the domain of C<pwqp> is wrapping, then the bound is
5144 computed over the range of the wrapped relation. The domain of the
5145 wrapped relation becomes the domain of the result.
5147 A (piecewise) quasipolynomial reduction can be copied or freed using the
5148 following functions.
5150 __isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_copy(
5151 __isl_keep isl_qpolynomial_fold *fold);
5152 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_copy(
5153 __isl_keep isl_pw_qpolynomial_fold *pwf);
5154 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_copy(
5155 __isl_keep isl_union_pw_qpolynomial_fold *upwf);
5156 void isl_qpolynomial_fold_free(
5157 __isl_take isl_qpolynomial_fold *fold);
5158 void *isl_pw_qpolynomial_fold_free(
5159 __isl_take isl_pw_qpolynomial_fold *pwf);
5160 void *isl_union_pw_qpolynomial_fold_free(
5161 __isl_take isl_union_pw_qpolynomial_fold *upwf);
5163 =head3 Printing Piecewise Quasipolynomial Reductions
5165 Piecewise quasipolynomial reductions can be printed
5166 using the following function.
5168 __isl_give isl_printer *isl_printer_print_pw_qpolynomial_fold(
5169 __isl_take isl_printer *p,
5170 __isl_keep isl_pw_qpolynomial_fold *pwf);
5171 __isl_give isl_printer *isl_printer_print_union_pw_qpolynomial_fold(
5172 __isl_take isl_printer *p,
5173 __isl_keep isl_union_pw_qpolynomial_fold *upwf);
5175 For C<isl_printer_print_pw_qpolynomial_fold>,
5176 output format of the printer
5177 needs to be set to either C<ISL_FORMAT_ISL> or C<ISL_FORMAT_C>.
5178 For C<isl_printer_print_union_pw_qpolynomial_fold>,
5179 output format of the printer
5180 needs to be set to C<ISL_FORMAT_ISL>.
5181 In case of printing in C<ISL_FORMAT_C>, the user may want
5182 to set the names of all dimensions
5184 __isl_give isl_pw_qpolynomial_fold *
5185 isl_pw_qpolynomial_fold_set_dim_name(
5186 __isl_take isl_pw_qpolynomial_fold *pwf,
5187 enum isl_dim_type type, unsigned pos,
5190 =head3 Inspecting (Piecewise) Quasipolynomial Reductions
5192 To iterate over all piecewise quasipolynomial reductions in a union
5193 piecewise quasipolynomial reduction, use the following function
5195 int isl_union_pw_qpolynomial_fold_foreach_pw_qpolynomial_fold(
5196 __isl_keep isl_union_pw_qpolynomial_fold *upwf,
5197 int (*fn)(__isl_take isl_pw_qpolynomial_fold *pwf,
5198 void *user), void *user);
5200 To iterate over the cells in a piecewise quasipolynomial reduction,
5201 use either of the following two functions
5203 int isl_pw_qpolynomial_fold_foreach_piece(
5204 __isl_keep isl_pw_qpolynomial_fold *pwf,
5205 int (*fn)(__isl_take isl_set *set,
5206 __isl_take isl_qpolynomial_fold *fold,
5207 void *user), void *user);
5208 int isl_pw_qpolynomial_fold_foreach_lifted_piece(
5209 __isl_keep isl_pw_qpolynomial_fold *pwf,
5210 int (*fn)(__isl_take isl_set *set,
5211 __isl_take isl_qpolynomial_fold *fold,
5212 void *user), void *user);
5214 See L<Inspecting (Piecewise) Quasipolynomials> for an explanation
5215 of the difference between these two functions.
5217 To iterate over all quasipolynomials in a reduction, use
5219 int isl_qpolynomial_fold_foreach_qpolynomial(
5220 __isl_keep isl_qpolynomial_fold *fold,
5221 int (*fn)(__isl_take isl_qpolynomial *qp,
5222 void *user), void *user);
5224 =head3 Properties of Piecewise Quasipolynomial Reductions
5226 To check whether two union piecewise quasipolynomial reductions are
5227 obviously equal, use
5229 int isl_union_pw_qpolynomial_fold_plain_is_equal(
5230 __isl_keep isl_union_pw_qpolynomial_fold *upwf1,
5231 __isl_keep isl_union_pw_qpolynomial_fold *upwf2);
5233 =head3 Operations on Piecewise Quasipolynomial Reductions
5235 __isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_scale_val(
5236 __isl_take isl_qpolynomial_fold *fold,
5237 __isl_take isl_val *v);
5238 __isl_give isl_pw_qpolynomial_fold *
5239 isl_pw_qpolynomial_fold_scale_val(
5240 __isl_take isl_pw_qpolynomial_fold *pwf,
5241 __isl_take isl_val *v);
5242 __isl_give isl_union_pw_qpolynomial_fold *
5243 isl_union_pw_qpolynomial_fold_scale_val(
5244 __isl_take isl_union_pw_qpolynomial_fold *upwf,
5245 __isl_take isl_val *v);
5247 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_add(
5248 __isl_take isl_pw_qpolynomial_fold *pwf1,
5249 __isl_take isl_pw_qpolynomial_fold *pwf2);
5251 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_fold(
5252 __isl_take isl_pw_qpolynomial_fold *pwf1,
5253 __isl_take isl_pw_qpolynomial_fold *pwf2);
5255 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_fold(
5256 __isl_take isl_union_pw_qpolynomial_fold *upwf1,
5257 __isl_take isl_union_pw_qpolynomial_fold *upwf2);
5259 __isl_give isl_val *isl_pw_qpolynomial_fold_eval(
5260 __isl_take isl_pw_qpolynomial_fold *pwf,
5261 __isl_take isl_point *pnt);
5263 __isl_give isl_val *isl_union_pw_qpolynomial_fold_eval(
5264 __isl_take isl_union_pw_qpolynomial_fold *upwf,
5265 __isl_take isl_point *pnt);
5267 __isl_give isl_pw_qpolynomial_fold *
5268 isl_pw_qpolynomial_fold_intersect_params(
5269 __isl_take isl_pw_qpolynomial_fold *pwf,
5270 __isl_take isl_set *set);
5272 __isl_give isl_union_set *isl_union_pw_qpolynomial_fold_domain(
5273 __isl_take isl_union_pw_qpolynomial_fold *upwf);
5274 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_intersect_domain(
5275 __isl_take isl_union_pw_qpolynomial_fold *upwf,
5276 __isl_take isl_union_set *uset);
5277 __isl_give isl_union_pw_qpolynomial_fold *
5278 isl_union_pw_qpolynomial_fold_intersect_params(
5279 __isl_take isl_union_pw_qpolynomial_fold *upwf,
5280 __isl_take isl_set *set);
5282 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_project_domain_on_params(
5283 __isl_take isl_pw_qpolynomial_fold *pwf);
5285 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_coalesce(
5286 __isl_take isl_pw_qpolynomial_fold *pwf);
5288 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_coalesce(
5289 __isl_take isl_union_pw_qpolynomial_fold *upwf);
5291 __isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_gist_params(
5292 __isl_take isl_qpolynomial_fold *fold,
5293 __isl_take isl_set *context);
5294 __isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_gist(
5295 __isl_take isl_qpolynomial_fold *fold,
5296 __isl_take isl_set *context);
5298 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_gist(
5299 __isl_take isl_pw_qpolynomial_fold *pwf,
5300 __isl_take isl_set *context);
5301 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_gist_params(
5302 __isl_take isl_pw_qpolynomial_fold *pwf,
5303 __isl_take isl_set *context);
5305 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_gist(
5306 __isl_take isl_union_pw_qpolynomial_fold *upwf,
5307 __isl_take isl_union_set *context);
5308 __isl_give isl_union_pw_qpolynomial_fold *
5309 isl_union_pw_qpolynomial_fold_gist_params(
5310 __isl_take isl_union_pw_qpolynomial_fold *upwf,
5311 __isl_take isl_set *context);
5313 The gist operation applies the gist operation to each of
5314 the cells in the domain of the input piecewise quasipolynomial reduction.
5315 In future, the operation will also exploit the context
5316 to simplify the quasipolynomial reductions associated to each cell.
5318 __isl_give isl_pw_qpolynomial_fold *
5319 isl_set_apply_pw_qpolynomial_fold(
5320 __isl_take isl_set *set,
5321 __isl_take isl_pw_qpolynomial_fold *pwf,
5323 __isl_give isl_pw_qpolynomial_fold *
5324 isl_map_apply_pw_qpolynomial_fold(
5325 __isl_take isl_map *map,
5326 __isl_take isl_pw_qpolynomial_fold *pwf,
5328 __isl_give isl_union_pw_qpolynomial_fold *
5329 isl_union_set_apply_union_pw_qpolynomial_fold(
5330 __isl_take isl_union_set *uset,
5331 __isl_take isl_union_pw_qpolynomial_fold *upwf,
5333 __isl_give isl_union_pw_qpolynomial_fold *
5334 isl_union_map_apply_union_pw_qpolynomial_fold(
5335 __isl_take isl_union_map *umap,
5336 __isl_take isl_union_pw_qpolynomial_fold *upwf,
5339 The functions taking a map
5340 compose the given map with the given piecewise quasipolynomial reduction.
5341 That is, compute a bound (of the same type as C<pwf> or C<upwf> itself)
5342 over all elements in the intersection of the range of the map
5343 and the domain of the piecewise quasipolynomial reduction
5344 as a function of an element in the domain of the map.
5345 The functions taking a set compute a bound over all elements in the
5346 intersection of the set and the domain of the
5347 piecewise quasipolynomial reduction.
5349 =head2 Parametric Vertex Enumeration
5351 The parametric vertex enumeration described in this section
5352 is mainly intended to be used internally and by the C<barvinok>
5355 #include <isl/vertices.h>
5356 __isl_give isl_vertices *isl_basic_set_compute_vertices(
5357 __isl_keep isl_basic_set *bset);
5359 The function C<isl_basic_set_compute_vertices> performs the
5360 actual computation of the parametric vertices and the chamber
5361 decomposition and store the result in an C<isl_vertices> object.
5362 This information can be queried by either iterating over all
5363 the vertices or iterating over all the chambers or cells
5364 and then iterating over all vertices that are active on the chamber.
5366 int isl_vertices_foreach_vertex(
5367 __isl_keep isl_vertices *vertices,
5368 int (*fn)(__isl_take isl_vertex *vertex, void *user),
5371 int isl_vertices_foreach_cell(
5372 __isl_keep isl_vertices *vertices,
5373 int (*fn)(__isl_take isl_cell *cell, void *user),
5375 int isl_cell_foreach_vertex(__isl_keep isl_cell *cell,
5376 int (*fn)(__isl_take isl_vertex *vertex, void *user),
5379 Other operations that can be performed on an C<isl_vertices> object are
5382 isl_ctx *isl_vertices_get_ctx(
5383 __isl_keep isl_vertices *vertices);
5384 int isl_vertices_get_n_vertices(
5385 __isl_keep isl_vertices *vertices);
5386 void isl_vertices_free(__isl_take isl_vertices *vertices);
5388 Vertices can be inspected and destroyed using the following functions.
5390 isl_ctx *isl_vertex_get_ctx(__isl_keep isl_vertex *vertex);
5391 int isl_vertex_get_id(__isl_keep isl_vertex *vertex);
5392 __isl_give isl_basic_set *isl_vertex_get_domain(
5393 __isl_keep isl_vertex *vertex);
5394 __isl_give isl_basic_set *isl_vertex_get_expr(
5395 __isl_keep isl_vertex *vertex);
5396 void isl_vertex_free(__isl_take isl_vertex *vertex);
5398 C<isl_vertex_get_expr> returns a singleton parametric set describing
5399 the vertex, while C<isl_vertex_get_domain> returns the activity domain
5401 Note that C<isl_vertex_get_domain> and C<isl_vertex_get_expr> return
5402 B<rational> basic sets, so they should mainly be used for inspection
5403 and should not be mixed with integer sets.
5405 Chambers can be inspected and destroyed using the following functions.
5407 isl_ctx *isl_cell_get_ctx(__isl_keep isl_cell *cell);
5408 __isl_give isl_basic_set *isl_cell_get_domain(
5409 __isl_keep isl_cell *cell);
5410 void isl_cell_free(__isl_take isl_cell *cell);
5412 =head1 Polyhedral Compilation Library
5414 This section collects functionality in C<isl> that has been specifically
5415 designed for use during polyhedral compilation.
5417 =head2 Dependence Analysis
5419 C<isl> contains specialized functionality for performing
5420 array dataflow analysis. That is, given a I<sink> access relation
5421 and a collection of possible I<source> access relations,
5422 C<isl> can compute relations that describe
5423 for each iteration of the sink access, which iteration
5424 of which of the source access relations was the last
5425 to access the same data element before the given iteration
5427 The resulting dependence relations map source iterations
5428 to the corresponding sink iterations.
5429 To compute standard flow dependences, the sink should be
5430 a read, while the sources should be writes.
5431 If any of the source accesses are marked as being I<may>
5432 accesses, then there will be a dependence from the last
5433 I<must> access B<and> from any I<may> access that follows
5434 this last I<must> access.
5435 In particular, if I<all> sources are I<may> accesses,
5436 then memory based dependence analysis is performed.
5437 If, on the other hand, all sources are I<must> accesses,
5438 then value based dependence analysis is performed.
5440 #include <isl/flow.h>
5442 typedef int (*isl_access_level_before)(void *first, void *second);
5444 __isl_give isl_access_info *isl_access_info_alloc(
5445 __isl_take isl_map *sink,
5446 void *sink_user, isl_access_level_before fn,
5448 __isl_give isl_access_info *isl_access_info_add_source(
5449 __isl_take isl_access_info *acc,
5450 __isl_take isl_map *source, int must,
5452 void *isl_access_info_free(__isl_take isl_access_info *acc);
5454 __isl_give isl_flow *isl_access_info_compute_flow(
5455 __isl_take isl_access_info *acc);
5457 int isl_flow_foreach(__isl_keep isl_flow *deps,
5458 int (*fn)(__isl_take isl_map *dep, int must,
5459 void *dep_user, void *user),
5461 __isl_give isl_map *isl_flow_get_no_source(
5462 __isl_keep isl_flow *deps, int must);
5463 void isl_flow_free(__isl_take isl_flow *deps);
5465 The function C<isl_access_info_compute_flow> performs the actual
5466 dependence analysis. The other functions are used to construct
5467 the input for this function or to read off the output.
5469 The input is collected in an C<isl_access_info>, which can
5470 be created through a call to C<isl_access_info_alloc>.
5471 The arguments to this functions are the sink access relation
5472 C<sink>, a token C<sink_user> used to identify the sink
5473 access to the user, a callback function for specifying the
5474 relative order of source and sink accesses, and the number
5475 of source access relations that will be added.
5476 The callback function has type C<int (*)(void *first, void *second)>.
5477 The function is called with two user supplied tokens identifying
5478 either a source or the sink and it should return the shared nesting
5479 level and the relative order of the two accesses.
5480 In particular, let I<n> be the number of loops shared by
5481 the two accesses. If C<first> precedes C<second> textually,
5482 then the function should return I<2 * n + 1>; otherwise,
5483 it should return I<2 * n>.
5484 The sources can be added to the C<isl_access_info> by performing
5485 (at most) C<max_source> calls to C<isl_access_info_add_source>.
5486 C<must> indicates whether the source is a I<must> access
5487 or a I<may> access. Note that a multi-valued access relation
5488 should only be marked I<must> if every iteration in the domain
5489 of the relation accesses I<all> elements in its image.
5490 The C<source_user> token is again used to identify
5491 the source access. The range of the source access relation
5492 C<source> should have the same dimension as the range
5493 of the sink access relation.
5494 The C<isl_access_info_free> function should usually not be
5495 called explicitly, because it is called implicitly by
5496 C<isl_access_info_compute_flow>.
5498 The result of the dependence analysis is collected in an
5499 C<isl_flow>. There may be elements of
5500 the sink access for which no preceding source access could be
5501 found or for which all preceding sources are I<may> accesses.
5502 The relations containing these elements can be obtained through
5503 calls to C<isl_flow_get_no_source>, the first with C<must> set
5504 and the second with C<must> unset.
5505 In the case of standard flow dependence analysis,
5506 with the sink a read and the sources I<must> writes,
5507 the first relation corresponds to the reads from uninitialized
5508 array elements and the second relation is empty.
5509 The actual flow dependences can be extracted using
5510 C<isl_flow_foreach>. This function will call the user-specified
5511 callback function C<fn> for each B<non-empty> dependence between
5512 a source and the sink. The callback function is called
5513 with four arguments, the actual flow dependence relation
5514 mapping source iterations to sink iterations, a boolean that
5515 indicates whether it is a I<must> or I<may> dependence, a token
5516 identifying the source and an additional C<void *> with value
5517 equal to the third argument of the C<isl_flow_foreach> call.
5518 A dependence is marked I<must> if it originates from a I<must>
5519 source and if it is not followed by any I<may> sources.
5521 After finishing with an C<isl_flow>, the user should call
5522 C<isl_flow_free> to free all associated memory.
5524 A higher-level interface to dependence analysis is provided
5525 by the following function.
5527 #include <isl/flow.h>
5529 int isl_union_map_compute_flow(__isl_take isl_union_map *sink,
5530 __isl_take isl_union_map *must_source,
5531 __isl_take isl_union_map *may_source,
5532 __isl_take isl_union_map *schedule,
5533 __isl_give isl_union_map **must_dep,
5534 __isl_give isl_union_map **may_dep,
5535 __isl_give isl_union_map **must_no_source,
5536 __isl_give isl_union_map **may_no_source);
5538 The arrays are identified by the tuple names of the ranges
5539 of the accesses. The iteration domains by the tuple names
5540 of the domains of the accesses and of the schedule.
5541 The relative order of the iteration domains is given by the
5542 schedule. The relations returned through C<must_no_source>
5543 and C<may_no_source> are subsets of C<sink>.
5544 Any of C<must_dep>, C<may_dep>, C<must_no_source>
5545 or C<may_no_source> may be C<NULL>, but a C<NULL> value for
5546 any of the other arguments is treated as an error.
5548 =head3 Interaction with Dependence Analysis
5550 During the dependence analysis, we frequently need to perform
5551 the following operation. Given a relation between sink iterations
5552 and potential source iterations from a particular source domain,
5553 what is the last potential source iteration corresponding to each
5554 sink iteration. It can sometimes be convenient to adjust
5555 the set of potential source iterations before or after each such operation.
5556 The prototypical example is fuzzy array dataflow analysis,
5557 where we need to analyze if, based on data-dependent constraints,
5558 the sink iteration can ever be executed without one or more of
5559 the corresponding potential source iterations being executed.
5560 If so, we can introduce extra parameters and select an unknown
5561 but fixed source iteration from the potential source iterations.
5562 To be able to perform such manipulations, C<isl> provides the following
5565 #include <isl/flow.h>
5567 typedef __isl_give isl_restriction *(*isl_access_restrict)(
5568 __isl_keep isl_map *source_map,
5569 __isl_keep isl_set *sink, void *source_user,
5571 __isl_give isl_access_info *isl_access_info_set_restrict(
5572 __isl_take isl_access_info *acc,
5573 isl_access_restrict fn, void *user);
5575 The function C<isl_access_info_set_restrict> should be called
5576 before calling C<isl_access_info_compute_flow> and registers a callback function
5577 that will be called any time C<isl> is about to compute the last
5578 potential source. The first argument is the (reverse) proto-dependence,
5579 mapping sink iterations to potential source iterations.
5580 The second argument represents the sink iterations for which
5581 we want to compute the last source iteration.
5582 The third argument is the token corresponding to the source
5583 and the final argument is the token passed to C<isl_access_info_set_restrict>.
5584 The callback is expected to return a restriction on either the input or
5585 the output of the operation computing the last potential source.
5586 If the input needs to be restricted then restrictions are needed
5587 for both the source and the sink iterations. The sink iterations
5588 and the potential source iterations will be intersected with these sets.
5589 If the output needs to be restricted then only a restriction on the source
5590 iterations is required.
5591 If any error occurs, the callback should return C<NULL>.
5592 An C<isl_restriction> object can be created, freed and inspected
5593 using the following functions.
5595 #include <isl/flow.h>
5597 __isl_give isl_restriction *isl_restriction_input(
5598 __isl_take isl_set *source_restr,
5599 __isl_take isl_set *sink_restr);
5600 __isl_give isl_restriction *isl_restriction_output(
5601 __isl_take isl_set *source_restr);
5602 __isl_give isl_restriction *isl_restriction_none(
5603 __isl_take isl_map *source_map);
5604 __isl_give isl_restriction *isl_restriction_empty(
5605 __isl_take isl_map *source_map);
5606 void *isl_restriction_free(
5607 __isl_take isl_restriction *restr);
5608 isl_ctx *isl_restriction_get_ctx(
5609 __isl_keep isl_restriction *restr);
5611 C<isl_restriction_none> and C<isl_restriction_empty> are special
5612 cases of C<isl_restriction_input>. C<isl_restriction_none>
5613 is essentially equivalent to
5615 isl_restriction_input(isl_set_universe(
5616 isl_space_range(isl_map_get_space(source_map))),
5618 isl_space_domain(isl_map_get_space(source_map))));
5620 whereas C<isl_restriction_empty> is essentially equivalent to
5622 isl_restriction_input(isl_set_empty(
5623 isl_space_range(isl_map_get_space(source_map))),
5625 isl_space_domain(isl_map_get_space(source_map))));
5629 B<The functionality described in this section is fairly new
5630 and may be subject to change.>
5632 #include <isl/schedule.h>
5633 __isl_give isl_schedule *
5634 isl_schedule_constraints_compute_schedule(
5635 __isl_take isl_schedule_constraints *sc);
5636 void *isl_schedule_free(__isl_take isl_schedule *sched);
5638 The function C<isl_schedule_constraints_compute_schedule> can be
5639 used to compute a schedule that satisfy the given schedule constraints.
5640 These schedule constraints include the iteration domain for which
5641 a schedule should be computed and dependences between pairs of
5642 iterations. In particular, these dependences include
5643 I<validity> dependences and I<proximity> dependences.
5644 By default, the algorithm used to construct the schedule is similar
5645 to that of C<Pluto>.
5646 Alternatively, Feautrier's multi-dimensional scheduling algorithm can
5648 The generated schedule respects all validity dependences.
5649 That is, all dependence distances over these dependences in the
5650 scheduled space are lexicographically positive.
5651 The default algorithm tries to ensure that the dependence distances
5652 over coincidence constraints are zero and to minimize the
5653 dependence distances over proximity dependences.
5654 Moreover, it tries to obtain sequences (bands) of schedule dimensions
5655 for groups of domains where the dependence distances over validity
5656 dependences have only non-negative values.
5657 When using Feautrier's algorithm, the coincidence and proximity constraints
5658 are only taken into account during the extension to a
5659 full-dimensional schedule.
5661 An C<isl_schedule_constraints> object can be constructed
5662 and manipulated using the following functions.
5664 #include <isl/schedule.h>
5665 __isl_give isl_schedule_constraints *
5666 isl_schedule_constraints_on_domain(
5667 __isl_take isl_union_set *domain);
5668 isl_ctx *isl_schedule_constraints_get_ctx(
5669 __isl_keep isl_schedule_constraints *sc);
5670 __isl_give isl_schedule_constraints *
5671 isl_schedule_constraints_set_validity(
5672 __isl_take isl_schedule_constraints *sc,
5673 __isl_take isl_union_map *validity);
5674 __isl_give isl_schedule_constraints *
5675 isl_schedule_constraints_set_coincidence(
5676 __isl_take isl_schedule_constraints *sc,
5677 __isl_take isl_union_map *coincidence);
5678 __isl_give isl_schedule_constraints *
5679 isl_schedule_constraints_set_proximity(
5680 __isl_take isl_schedule_constraints *sc,
5681 __isl_take isl_union_map *proximity);
5682 __isl_give isl_schedule_constraints *
5683 isl_schedule_constraints_set_conditional_validity(
5684 __isl_take isl_schedule_constraints *sc,
5685 __isl_take isl_union_map *condition,
5686 __isl_take isl_union_map *validity);
5687 void *isl_schedule_constraints_free(
5688 __isl_take isl_schedule_constraints *sc);
5690 The initial C<isl_schedule_constraints> object created by
5691 C<isl_schedule_constraints_on_domain> does not impose any constraints.
5692 That is, it has an empty set of dependences.
5693 The function C<isl_schedule_constraints_set_validity> replaces the
5694 validity dependences, mapping domain elements I<i> to domain
5695 elements that should be scheduled after I<i>.
5696 The function C<isl_schedule_constraints_set_coincidence> replaces the
5697 coincidence dependences, mapping domain elements I<i> to domain
5698 elements that should be scheduled together with I<I>, if possible.
5699 The function C<isl_schedule_constraints_set_proximity> replaces the
5700 proximity dependences, mapping domain elements I<i> to domain
5701 elements that should be scheduled either before I<I>
5702 or as early as possible after I<i>.
5704 The function C<isl_schedule_constraints_set_conditional_validity>
5705 replaces the conditional validity constraints.
5706 A conditional validity constraint is only imposed when any of the corresponding
5707 conditions is satisfied, i.e., when any of them is non-zero.
5708 That is, the scheduler ensures that within each band if the dependence
5709 distances over the condition constraints are not all zero
5710 then all corresponding conditional validity constraints are respected.
5711 A conditional validity constraint corresponds to a condition
5712 if the two are adjacent, i.e., if the domain of one relation intersect
5713 the range of the other relation.
5714 The typical use case of conditional validity constraints is
5715 to allow order constraints between live ranges to be violated
5716 as long as the live ranges themselves are local to the band.
5717 To allow more fine-grained control over which conditions correspond
5718 to which conditional validity constraints, the domains and ranges
5719 of these relations may include I<tags>. That is, the domains and
5720 ranges of those relation may themselves be wrapped relations
5721 where the iteration domain appears in the domain of those wrapped relations
5722 and the range of the wrapped relations can be arbitrarily chosen
5723 by the user. Conditions and conditional validity constraints are only
5724 considere adjacent to each other if the entire wrapped relation matches.
5725 In particular, a relation with a tag will never be considered adjacent
5726 to a relation without a tag.
5728 The following function computes a schedule directly from
5729 an iteration domain and validity and proximity dependences
5730 and is implemented in terms of the functions described above.
5731 The use of C<isl_union_set_compute_schedule> is discouraged.
5733 #include <isl/schedule.h>
5734 __isl_give isl_schedule *isl_union_set_compute_schedule(
5735 __isl_take isl_union_set *domain,
5736 __isl_take isl_union_map *validity,
5737 __isl_take isl_union_map *proximity);
5739 A mapping from the domains to the scheduled space can be obtained
5740 from an C<isl_schedule> using the following function.
5742 __isl_give isl_union_map *isl_schedule_get_map(
5743 __isl_keep isl_schedule *sched);
5745 A representation of the schedule can be printed using
5747 __isl_give isl_printer *isl_printer_print_schedule(
5748 __isl_take isl_printer *p,
5749 __isl_keep isl_schedule *schedule);
5751 A representation of the schedule as a forest of bands can be obtained
5752 using the following function.
5754 __isl_give isl_band_list *isl_schedule_get_band_forest(
5755 __isl_keep isl_schedule *schedule);
5757 The individual bands can be visited in depth-first post-order
5758 using the following function.
5760 #include <isl/schedule.h>
5761 int isl_schedule_foreach_band(
5762 __isl_keep isl_schedule *sched,
5763 int (*fn)(__isl_keep isl_band *band, void *user),
5766 The list can be manipulated as explained in L<"Lists">.
5767 The bands inside the list can be copied and freed using the following
5770 #include <isl/band.h>
5771 __isl_give isl_band *isl_band_copy(
5772 __isl_keep isl_band *band);
5773 void *isl_band_free(__isl_take isl_band *band);
5775 Each band contains zero or more scheduling dimensions.
5776 These are referred to as the members of the band.
5777 The section of the schedule that corresponds to the band is
5778 referred to as the partial schedule of the band.
5779 For those nodes that participate in a band, the outer scheduling
5780 dimensions form the prefix schedule, while the inner scheduling
5781 dimensions form the suffix schedule.
5782 That is, if we take a cut of the band forest, then the union of
5783 the concatenations of the prefix, partial and suffix schedules of
5784 each band in the cut is equal to the entire schedule (modulo
5785 some possible padding at the end with zero scheduling dimensions).
5786 The properties of a band can be inspected using the following functions.
5788 #include <isl/band.h>
5789 isl_ctx *isl_band_get_ctx(__isl_keep isl_band *band);
5791 int isl_band_has_children(__isl_keep isl_band *band);
5792 __isl_give isl_band_list *isl_band_get_children(
5793 __isl_keep isl_band *band);
5795 __isl_give isl_union_map *isl_band_get_prefix_schedule(
5796 __isl_keep isl_band *band);
5797 __isl_give isl_union_map *isl_band_get_partial_schedule(
5798 __isl_keep isl_band *band);
5799 __isl_give isl_union_map *isl_band_get_suffix_schedule(
5800 __isl_keep isl_band *band);
5802 int isl_band_n_member(__isl_keep isl_band *band);
5803 int isl_band_member_is_coincident(
5804 __isl_keep isl_band *band, int pos);
5806 int isl_band_list_foreach_band(
5807 __isl_keep isl_band_list *list,
5808 int (*fn)(__isl_keep isl_band *band, void *user),
5811 Note that a scheduling dimension is considered to be ``coincident''
5812 if it satisfies the coincidence constraints within its band.
5813 That is, if the dependence distances of the coincidence
5814 constraints are all zero in that direction (for fixed
5815 iterations of outer bands).
5816 Like C<isl_schedule_foreach_band>,
5817 the function C<isl_band_list_foreach_band> calls C<fn> on the bands
5818 in depth-first post-order.
5820 A band can be tiled using the following function.
5822 #include <isl/band.h>
5823 int isl_band_tile(__isl_keep isl_band *band,
5824 __isl_take isl_vec *sizes);
5826 int isl_options_set_tile_scale_tile_loops(isl_ctx *ctx,
5828 int isl_options_get_tile_scale_tile_loops(isl_ctx *ctx);
5829 int isl_options_set_tile_shift_point_loops(isl_ctx *ctx,
5831 int isl_options_get_tile_shift_point_loops(isl_ctx *ctx);
5833 The C<isl_band_tile> function tiles the band using the given tile sizes
5834 inside its schedule.
5835 A new child band is created to represent the point loops and it is
5836 inserted between the modified band and its children.
5837 The C<tile_scale_tile_loops> option specifies whether the tile
5838 loops iterators should be scaled by the tile sizes.
5839 If the C<tile_shift_point_loops> option is set, then the point loops
5840 are shifted to start at zero.
5842 A band can be split into two nested bands using the following function.
5844 int isl_band_split(__isl_keep isl_band *band, int pos);
5846 The resulting outer band contains the first C<pos> dimensions of C<band>
5847 while the inner band contains the remaining dimensions.
5849 A representation of the band can be printed using
5851 #include <isl/band.h>
5852 __isl_give isl_printer *isl_printer_print_band(
5853 __isl_take isl_printer *p,
5854 __isl_keep isl_band *band);
5858 #include <isl/schedule.h>
5859 int isl_options_set_schedule_max_coefficient(
5860 isl_ctx *ctx, int val);
5861 int isl_options_get_schedule_max_coefficient(
5863 int isl_options_set_schedule_max_constant_term(
5864 isl_ctx *ctx, int val);
5865 int isl_options_get_schedule_max_constant_term(
5867 int isl_options_set_schedule_fuse(isl_ctx *ctx, int val);
5868 int isl_options_get_schedule_fuse(isl_ctx *ctx);
5869 int isl_options_set_schedule_maximize_band_depth(
5870 isl_ctx *ctx, int val);
5871 int isl_options_get_schedule_maximize_band_depth(
5873 int isl_options_set_schedule_outer_coincidence(
5874 isl_ctx *ctx, int val);
5875 int isl_options_get_schedule_outer_coincidence(
5877 int isl_options_set_schedule_split_scaled(
5878 isl_ctx *ctx, int val);
5879 int isl_options_get_schedule_split_scaled(
5881 int isl_options_set_schedule_algorithm(
5882 isl_ctx *ctx, int val);
5883 int isl_options_get_schedule_algorithm(
5885 int isl_options_set_schedule_separate_components(
5886 isl_ctx *ctx, int val);
5887 int isl_options_get_schedule_separate_components(
5892 =item * schedule_max_coefficient
5894 This option enforces that the coefficients for variable and parameter
5895 dimensions in the calculated schedule are not larger than the specified value.
5896 This option can significantly increase the speed of the scheduling calculation
5897 and may also prevent fusing of unrelated dimensions. A value of -1 means that
5898 this option does not introduce bounds on the variable or parameter
5901 =item * schedule_max_constant_term
5903 This option enforces that the constant coefficients in the calculated schedule
5904 are not larger than the maximal constant term. This option can significantly
5905 increase the speed of the scheduling calculation and may also prevent fusing of
5906 unrelated dimensions. A value of -1 means that this option does not introduce
5907 bounds on the constant coefficients.
5909 =item * schedule_fuse
5911 This option controls the level of fusion.
5912 If this option is set to C<ISL_SCHEDULE_FUSE_MIN>, then loops in the
5913 resulting schedule will be distributed as much as possible.
5914 If this option is set to C<ISL_SCHEDULE_FUSE_MAX>, then C<isl> will
5915 try to fuse loops in the resulting schedule.
5917 =item * schedule_maximize_band_depth
5919 If this option is set, we do not split bands at the point
5920 where we detect splitting is necessary. Instead, we
5921 backtrack and split bands as early as possible. This
5922 reduces the number of splits and maximizes the width of
5923 the bands. Wider bands give more possibilities for tiling.
5924 Note that if the C<schedule_fuse> option is set to C<ISL_SCHEDULE_FUSE_MIN>,
5925 then bands will be split as early as possible, even if there is no need.
5926 The C<schedule_maximize_band_depth> option therefore has no effect in this case.
5928 =item * schedule_outer_coincidence
5930 If this option is set, then we try to construct schedules
5931 where the outermost scheduling dimension in each band
5932 satisfies the coincidence constraints.
5934 =item * schedule_split_scaled
5936 If this option is set, then we try to construct schedules in which the
5937 constant term is split off from the linear part if the linear parts of
5938 the scheduling rows for all nodes in the graphs have a common non-trivial
5940 The constant term is then placed in a separate band and the linear
5943 =item * schedule_algorithm
5945 Selects the scheduling algorithm to be used.
5946 Available scheduling algorithms are C<ISL_SCHEDULE_ALGORITHM_ISL>
5947 and C<ISL_SCHEDULE_ALGORITHM_FEAUTRIER>.
5949 =item * schedule_separate_components
5951 If at any point the dependence graph contains any (weakly connected) components,
5952 then these components are scheduled separately.
5953 If this option is not set, then some iterations of the domains
5954 in these components may be scheduled together.
5955 If this option is set, then the components are given consecutive
5960 =head2 AST Generation
5962 This section describes the C<isl> functionality for generating
5963 ASTs that visit all the elements
5964 in a domain in an order specified by a schedule.
5965 In particular, given a C<isl_union_map>, an AST is generated
5966 that visits all the elements in the domain of the C<isl_union_map>
5967 according to the lexicographic order of the corresponding image
5968 element(s). If the range of the C<isl_union_map> consists of
5969 elements in more than one space, then each of these spaces is handled
5970 separately in an arbitrary order.
5971 It should be noted that the image elements only specify the I<order>
5972 in which the corresponding domain elements should be visited.
5973 No direct relation between the image elements and the loop iterators
5974 in the generated AST should be assumed.
5976 Each AST is generated within a build. The initial build
5977 simply specifies the constraints on the parameters (if any)
5978 and can be created, inspected, copied and freed using the following functions.
5980 #include <isl/ast_build.h>
5981 __isl_give isl_ast_build *isl_ast_build_from_context(
5982 __isl_take isl_set *set);
5983 isl_ctx *isl_ast_build_get_ctx(
5984 __isl_keep isl_ast_build *build);
5985 __isl_give isl_ast_build *isl_ast_build_copy(
5986 __isl_keep isl_ast_build *build);
5987 void *isl_ast_build_free(
5988 __isl_take isl_ast_build *build);
5990 The C<set> argument is usually a parameter set with zero or more parameters.
5991 More C<isl_ast_build> functions are described in L</"Nested AST Generation">
5992 and L</"Fine-grained Control over AST Generation">.
5993 Finally, the AST itself can be constructed using the following
5996 #include <isl/ast_build.h>
5997 __isl_give isl_ast_node *isl_ast_build_ast_from_schedule(
5998 __isl_keep isl_ast_build *build,
5999 __isl_take isl_union_map *schedule);
6001 =head3 Inspecting the AST
6003 The basic properties of an AST node can be obtained as follows.
6005 #include <isl/ast.h>
6006 isl_ctx *isl_ast_node_get_ctx(
6007 __isl_keep isl_ast_node *node);
6008 enum isl_ast_node_type isl_ast_node_get_type(
6009 __isl_keep isl_ast_node *node);
6011 The type of an AST node is one of
6012 C<isl_ast_node_for>,
6014 C<isl_ast_node_block> or
6015 C<isl_ast_node_user>.
6016 An C<isl_ast_node_for> represents a for node.
6017 An C<isl_ast_node_if> represents an if node.
6018 An C<isl_ast_node_block> represents a compound node.
6019 An C<isl_ast_node_user> represents an expression statement.
6020 An expression statement typically corresponds to a domain element, i.e.,
6021 one of the elements that is visited by the AST.
6023 Each type of node has its own additional properties.
6025 #include <isl/ast.h>
6026 __isl_give isl_ast_expr *isl_ast_node_for_get_iterator(
6027 __isl_keep isl_ast_node *node);
6028 __isl_give isl_ast_expr *isl_ast_node_for_get_init(
6029 __isl_keep isl_ast_node *node);
6030 __isl_give isl_ast_expr *isl_ast_node_for_get_cond(
6031 __isl_keep isl_ast_node *node);
6032 __isl_give isl_ast_expr *isl_ast_node_for_get_inc(
6033 __isl_keep isl_ast_node *node);
6034 __isl_give isl_ast_node *isl_ast_node_for_get_body(
6035 __isl_keep isl_ast_node *node);
6036 int isl_ast_node_for_is_degenerate(
6037 __isl_keep isl_ast_node *node);
6039 An C<isl_ast_for> is considered degenerate if it is known to execute
6042 #include <isl/ast.h>
6043 __isl_give isl_ast_expr *isl_ast_node_if_get_cond(
6044 __isl_keep isl_ast_node *node);
6045 __isl_give isl_ast_node *isl_ast_node_if_get_then(
6046 __isl_keep isl_ast_node *node);
6047 int isl_ast_node_if_has_else(
6048 __isl_keep isl_ast_node *node);
6049 __isl_give isl_ast_node *isl_ast_node_if_get_else(
6050 __isl_keep isl_ast_node *node);
6052 __isl_give isl_ast_node_list *
6053 isl_ast_node_block_get_children(
6054 __isl_keep isl_ast_node *node);
6056 __isl_give isl_ast_expr *isl_ast_node_user_get_expr(
6057 __isl_keep isl_ast_node *node);
6059 Each of the returned C<isl_ast_expr>s can in turn be inspected using
6060 the following functions.
6062 #include <isl/ast.h>
6063 isl_ctx *isl_ast_expr_get_ctx(
6064 __isl_keep isl_ast_expr *expr);
6065 enum isl_ast_expr_type isl_ast_expr_get_type(
6066 __isl_keep isl_ast_expr *expr);
6068 The type of an AST expression is one of
6070 C<isl_ast_expr_id> or
6071 C<isl_ast_expr_int>.
6072 An C<isl_ast_expr_op> represents the result of an operation.
6073 An C<isl_ast_expr_id> represents an identifier.
6074 An C<isl_ast_expr_int> represents an integer value.
6076 Each type of expression has its own additional properties.
6078 #include <isl/ast.h>
6079 enum isl_ast_op_type isl_ast_expr_get_op_type(
6080 __isl_keep isl_ast_expr *expr);
6081 int isl_ast_expr_get_op_n_arg(__isl_keep isl_ast_expr *expr);
6082 __isl_give isl_ast_expr *isl_ast_expr_get_op_arg(
6083 __isl_keep isl_ast_expr *expr, int pos);
6084 int isl_ast_node_foreach_ast_op_type(
6085 __isl_keep isl_ast_node *node,
6086 int (*fn)(enum isl_ast_op_type type, void *user),
6089 C<isl_ast_expr_get_op_type> returns the type of the operation
6090 performed. C<isl_ast_expr_get_op_n_arg> returns the number of
6091 arguments. C<isl_ast_expr_get_op_arg> returns the specified
6093 C<isl_ast_node_foreach_ast_op_type> calls C<fn> for each distinct
6094 C<isl_ast_op_type> that appears in C<node>.
6095 The operation type is one of the following.
6099 =item C<isl_ast_op_and>
6101 Logical I<and> of two arguments.
6102 Both arguments can be evaluated.
6104 =item C<isl_ast_op_and_then>
6106 Logical I<and> of two arguments.
6107 The second argument can only be evaluated if the first evaluates to true.
6109 =item C<isl_ast_op_or>
6111 Logical I<or> of two arguments.
6112 Both arguments can be evaluated.
6114 =item C<isl_ast_op_or_else>
6116 Logical I<or> of two arguments.
6117 The second argument can only be evaluated if the first evaluates to false.
6119 =item C<isl_ast_op_max>
6121 Maximum of two or more arguments.
6123 =item C<isl_ast_op_min>
6125 Minimum of two or more arguments.
6127 =item C<isl_ast_op_minus>
6131 =item C<isl_ast_op_add>
6133 Sum of two arguments.
6135 =item C<isl_ast_op_sub>
6137 Difference of two arguments.
6139 =item C<isl_ast_op_mul>
6141 Product of two arguments.
6143 =item C<isl_ast_op_div>
6145 Exact division. That is, the result is known to be an integer.
6147 =item C<isl_ast_op_fdiv_q>
6149 Result of integer division, rounded towards negative
6152 =item C<isl_ast_op_pdiv_q>
6154 Result of integer division, where dividend is known to be non-negative.
6156 =item C<isl_ast_op_pdiv_r>
6158 Remainder of integer division, where dividend is known to be non-negative.
6160 =item C<isl_ast_op_cond>
6162 Conditional operator defined on three arguments.
6163 If the first argument evaluates to true, then the result
6164 is equal to the second argument. Otherwise, the result
6165 is equal to the third argument.
6166 The second and third argument may only be evaluated if
6167 the first argument evaluates to true and false, respectively.
6168 Corresponds to C<a ? b : c> in C.
6170 =item C<isl_ast_op_select>
6172 Conditional operator defined on three arguments.
6173 If the first argument evaluates to true, then the result
6174 is equal to the second argument. Otherwise, the result
6175 is equal to the third argument.
6176 The second and third argument may be evaluated independently
6177 of the value of the first argument.
6178 Corresponds to C<a * b + (1 - a) * c> in C.
6180 =item C<isl_ast_op_eq>
6184 =item C<isl_ast_op_le>
6186 Less than or equal relation.
6188 =item C<isl_ast_op_lt>
6192 =item C<isl_ast_op_ge>
6194 Greater than or equal relation.
6196 =item C<isl_ast_op_gt>
6198 Greater than relation.
6200 =item C<isl_ast_op_call>
6203 The number of arguments of the C<isl_ast_expr> is one more than
6204 the number of arguments in the function call, the first argument
6205 representing the function being called.
6207 =item C<isl_ast_op_access>
6210 The number of arguments of the C<isl_ast_expr> is one more than
6211 the number of index expressions in the array access, the first argument
6212 representing the array being accessed.
6214 =item C<isl_ast_op_member>
6217 This operation has two arguments, a structure and the name of
6218 the member of the structure being accessed.
6222 #include <isl/ast.h>
6223 __isl_give isl_id *isl_ast_expr_get_id(
6224 __isl_keep isl_ast_expr *expr);
6226 Return the identifier represented by the AST expression.
6228 #include <isl/ast.h>
6229 __isl_give isl_val *isl_ast_expr_get_val(
6230 __isl_keep isl_ast_expr *expr);
6232 Return the integer represented by the AST expression.
6234 =head3 Properties of ASTs
6236 #include <isl/ast.h>
6237 int isl_ast_expr_is_equal(__isl_keep isl_ast_expr *expr1,
6238 __isl_keep isl_ast_expr *expr2);
6240 Check if two C<isl_ast_expr>s are equal to each other.
6242 =head3 Manipulating and printing the AST
6244 AST nodes can be copied and freed using the following functions.
6246 #include <isl/ast.h>
6247 __isl_give isl_ast_node *isl_ast_node_copy(
6248 __isl_keep isl_ast_node *node);
6249 void *isl_ast_node_free(__isl_take isl_ast_node *node);
6251 AST expressions can be copied and freed using the following functions.
6253 #include <isl/ast.h>
6254 __isl_give isl_ast_expr *isl_ast_expr_copy(
6255 __isl_keep isl_ast_expr *expr);
6256 void *isl_ast_expr_free(__isl_take isl_ast_expr *expr);
6258 New AST expressions can be created either directly or within
6259 the context of an C<isl_ast_build>.
6261 #include <isl/ast.h>
6262 __isl_give isl_ast_expr *isl_ast_expr_from_val(
6263 __isl_take isl_val *v);
6264 __isl_give isl_ast_expr *isl_ast_expr_from_id(
6265 __isl_take isl_id *id);
6266 __isl_give isl_ast_expr *isl_ast_expr_neg(
6267 __isl_take isl_ast_expr *expr);
6268 __isl_give isl_ast_expr *isl_ast_expr_add(
6269 __isl_take isl_ast_expr *expr1,
6270 __isl_take isl_ast_expr *expr2);
6271 __isl_give isl_ast_expr *isl_ast_expr_sub(
6272 __isl_take isl_ast_expr *expr1,
6273 __isl_take isl_ast_expr *expr2);
6274 __isl_give isl_ast_expr *isl_ast_expr_mul(
6275 __isl_take isl_ast_expr *expr1,
6276 __isl_take isl_ast_expr *expr2);
6277 __isl_give isl_ast_expr *isl_ast_expr_div(
6278 __isl_take isl_ast_expr *expr1,
6279 __isl_take isl_ast_expr *expr2);
6280 __isl_give isl_ast_expr *isl_ast_expr_and(
6281 __isl_take isl_ast_expr *expr1,
6282 __isl_take isl_ast_expr *expr2)
6283 __isl_give isl_ast_expr *isl_ast_expr_or(
6284 __isl_take isl_ast_expr *expr1,
6285 __isl_take isl_ast_expr *expr2)
6286 __isl_give isl_ast_expr *isl_ast_expr_access(
6287 __isl_take isl_ast_expr *array,
6288 __isl_take isl_ast_expr_list *indices);
6290 #include <isl/ast_build.h>
6291 __isl_give isl_ast_expr *isl_ast_build_expr_from_pw_aff(
6292 __isl_keep isl_ast_build *build,
6293 __isl_take isl_pw_aff *pa);
6294 __isl_give isl_ast_expr *
6295 isl_ast_build_access_from_pw_multi_aff(
6296 __isl_keep isl_ast_build *build,
6297 __isl_take isl_pw_multi_aff *pma);
6298 __isl_give isl_ast_expr *
6299 isl_ast_build_access_from_multi_pw_aff(
6300 __isl_keep isl_ast_build *build,
6301 __isl_take isl_multi_pw_aff *mpa);
6302 __isl_give isl_ast_expr *
6303 isl_ast_build_call_from_pw_multi_aff(
6304 __isl_keep isl_ast_build *build,
6305 __isl_take isl_pw_multi_aff *pma);
6306 __isl_give isl_ast_expr *
6307 isl_ast_build_call_from_multi_pw_aff(
6308 __isl_keep isl_ast_build *build,
6309 __isl_take isl_multi_pw_aff *mpa);
6311 The domains of C<pa>, C<mpa> and C<pma> should correspond
6312 to the schedule space of C<build>.
6313 The tuple id of C<mpa> or C<pma> is used as the array being accessed or
6314 the function being called.
6315 If the accessed space is a nested relation, then it is taken
6316 to represent an access of the member specified by the range
6317 of this nested relation of the structure specified by the domain
6318 of the nested relation.
6320 The following functions can be used to modify an C<isl_ast_expr>.
6322 #include <isl/ast.h>
6323 __isl_give isl_ast_expr *isl_ast_expr_set_op_arg(
6324 __isl_take isl_ast_expr *expr, int pos,
6325 __isl_take isl_ast_expr *arg);
6327 Replace the argument of C<expr> at position C<pos> by C<arg>.
6329 #include <isl/ast.h>
6330 __isl_give isl_ast_expr *isl_ast_expr_substitute_ids(
6331 __isl_take isl_ast_expr *expr,
6332 __isl_take isl_id_to_ast_expr *id2expr);
6334 The function C<isl_ast_expr_substitute_ids> replaces the
6335 subexpressions of C<expr> of type C<isl_ast_expr_id>
6336 by the corresponding expression in C<id2expr>, if there is any.
6339 User specified data can be attached to an C<isl_ast_node> and obtained
6340 from the same C<isl_ast_node> using the following functions.
6342 #include <isl/ast.h>
6343 __isl_give isl_ast_node *isl_ast_node_set_annotation(
6344 __isl_take isl_ast_node *node,
6345 __isl_take isl_id *annotation);
6346 __isl_give isl_id *isl_ast_node_get_annotation(
6347 __isl_keep isl_ast_node *node);
6349 Basic printing can be performed using the following functions.
6351 #include <isl/ast.h>
6352 __isl_give isl_printer *isl_printer_print_ast_expr(
6353 __isl_take isl_printer *p,
6354 __isl_keep isl_ast_expr *expr);
6355 __isl_give isl_printer *isl_printer_print_ast_node(
6356 __isl_take isl_printer *p,
6357 __isl_keep isl_ast_node *node);
6359 More advanced printing can be performed using the following functions.
6361 #include <isl/ast.h>
6362 __isl_give isl_printer *isl_ast_op_type_print_macro(
6363 enum isl_ast_op_type type,
6364 __isl_take isl_printer *p);
6365 __isl_give isl_printer *isl_ast_node_print_macros(
6366 __isl_keep isl_ast_node *node,
6367 __isl_take isl_printer *p);
6368 __isl_give isl_printer *isl_ast_node_print(
6369 __isl_keep isl_ast_node *node,
6370 __isl_take isl_printer *p,
6371 __isl_take isl_ast_print_options *options);
6372 __isl_give isl_printer *isl_ast_node_for_print(
6373 __isl_keep isl_ast_node *node,
6374 __isl_take isl_printer *p,
6375 __isl_take isl_ast_print_options *options);
6376 __isl_give isl_printer *isl_ast_node_if_print(
6377 __isl_keep isl_ast_node *node,
6378 __isl_take isl_printer *p,
6379 __isl_take isl_ast_print_options *options);
6381 While printing an C<isl_ast_node> in C<ISL_FORMAT_C>,
6382 C<isl> may print out an AST that makes use of macros such
6383 as C<floord>, C<min> and C<max>.
6384 C<isl_ast_op_type_print_macro> prints out the macro
6385 corresponding to a specific C<isl_ast_op_type>.
6386 C<isl_ast_node_print_macros> scans the C<isl_ast_node>
6387 for expressions where these macros would be used and prints
6388 out the required macro definitions.
6389 Essentially, C<isl_ast_node_print_macros> calls
6390 C<isl_ast_node_foreach_ast_op_type> with C<isl_ast_op_type_print_macro>
6391 as function argument.
6392 C<isl_ast_node_print>, C<isl_ast_node_for_print> and
6393 C<isl_ast_node_if_print> print an C<isl_ast_node>
6394 in C<ISL_FORMAT_C>, but allow for some extra control
6395 through an C<isl_ast_print_options> object.
6396 This object can be created using the following functions.
6398 #include <isl/ast.h>
6399 __isl_give isl_ast_print_options *
6400 isl_ast_print_options_alloc(isl_ctx *ctx);
6401 __isl_give isl_ast_print_options *
6402 isl_ast_print_options_copy(
6403 __isl_keep isl_ast_print_options *options);
6404 void *isl_ast_print_options_free(
6405 __isl_take isl_ast_print_options *options);
6407 __isl_give isl_ast_print_options *
6408 isl_ast_print_options_set_print_user(
6409 __isl_take isl_ast_print_options *options,
6410 __isl_give isl_printer *(*print_user)(
6411 __isl_take isl_printer *p,
6412 __isl_take isl_ast_print_options *options,
6413 __isl_keep isl_ast_node *node, void *user),
6415 __isl_give isl_ast_print_options *
6416 isl_ast_print_options_set_print_for(
6417 __isl_take isl_ast_print_options *options,
6418 __isl_give isl_printer *(*print_for)(
6419 __isl_take isl_printer *p,
6420 __isl_take isl_ast_print_options *options,
6421 __isl_keep isl_ast_node *node, void *user),
6424 The callback set by C<isl_ast_print_options_set_print_user>
6425 is called whenever a node of type C<isl_ast_node_user> needs to
6427 The callback set by C<isl_ast_print_options_set_print_for>
6428 is called whenever a node of type C<isl_ast_node_for> needs to
6430 Note that C<isl_ast_node_for_print> will I<not> call the
6431 callback set by C<isl_ast_print_options_set_print_for> on the node
6432 on which C<isl_ast_node_for_print> is called, but only on nested
6433 nodes of type C<isl_ast_node_for>. It is therefore safe to
6434 call C<isl_ast_node_for_print> from within the callback set by
6435 C<isl_ast_print_options_set_print_for>.
6437 The following option determines the type to be used for iterators
6438 while printing the AST.
6440 int isl_options_set_ast_iterator_type(
6441 isl_ctx *ctx, const char *val);
6442 const char *isl_options_get_ast_iterator_type(
6447 #include <isl/ast_build.h>
6448 int isl_options_set_ast_build_atomic_upper_bound(
6449 isl_ctx *ctx, int val);
6450 int isl_options_get_ast_build_atomic_upper_bound(
6452 int isl_options_set_ast_build_prefer_pdiv(isl_ctx *ctx,
6454 int isl_options_get_ast_build_prefer_pdiv(isl_ctx *ctx);
6455 int isl_options_set_ast_build_exploit_nested_bounds(
6456 isl_ctx *ctx, int val);
6457 int isl_options_get_ast_build_exploit_nested_bounds(
6459 int isl_options_set_ast_build_group_coscheduled(
6460 isl_ctx *ctx, int val);
6461 int isl_options_get_ast_build_group_coscheduled(
6463 int isl_options_set_ast_build_scale_strides(
6464 isl_ctx *ctx, int val);
6465 int isl_options_get_ast_build_scale_strides(
6467 int isl_options_set_ast_build_allow_else(isl_ctx *ctx,
6469 int isl_options_get_ast_build_allow_else(isl_ctx *ctx);
6470 int isl_options_set_ast_build_allow_or(isl_ctx *ctx,
6472 int isl_options_get_ast_build_allow_or(isl_ctx *ctx);
6476 =item * ast_build_atomic_upper_bound
6478 Generate loop upper bounds that consist of the current loop iterator,
6479 an operator and an expression not involving the iterator.
6480 If this option is not set, then the current loop iterator may appear
6481 several times in the upper bound.
6482 For example, when this option is turned off, AST generation
6485 [n] -> { A[i] -> [i] : 0 <= i <= 100, n }
6489 for (int c0 = 0; c0 <= 100 && n >= c0; c0 += 1)
6492 When the option is turned on, the following AST is generated
6494 for (int c0 = 0; c0 <= min(100, n); c0 += 1)
6497 =item * ast_build_prefer_pdiv
6499 If this option is turned off, then the AST generation will
6500 produce ASTs that may only contain C<isl_ast_op_fdiv_q>
6501 operators, but no C<isl_ast_op_pdiv_q> or
6502 C<isl_ast_op_pdiv_r> operators.
6503 If this options is turned on, then C<isl> will try to convert
6504 some of the C<isl_ast_op_fdiv_q> operators to (expressions containing)
6505 C<isl_ast_op_pdiv_q> or C<isl_ast_op_pdiv_r> operators.
6507 =item * ast_build_exploit_nested_bounds
6509 Simplify conditions based on bounds of nested for loops.
6510 In particular, remove conditions that are implied by the fact
6511 that one or more nested loops have at least one iteration,
6512 meaning that the upper bound is at least as large as the lower bound.
6513 For example, when this option is turned off, AST generation
6516 [N,M] -> { A[i,j] -> [i,j] : 0 <= i <= N and
6522 for (int c0 = 0; c0 <= N; c0 += 1)
6523 for (int c1 = 0; c1 <= M; c1 += 1)
6526 When the option is turned on, the following AST is generated
6528 for (int c0 = 0; c0 <= N; c0 += 1)
6529 for (int c1 = 0; c1 <= M; c1 += 1)
6532 =item * ast_build_group_coscheduled
6534 If two domain elements are assigned the same schedule point, then
6535 they may be executed in any order and they may even appear in different
6536 loops. If this options is set, then the AST generator will make
6537 sure that coscheduled domain elements do not appear in separate parts
6538 of the AST. This is useful in case of nested AST generation
6539 if the outer AST generation is given only part of a schedule
6540 and the inner AST generation should handle the domains that are
6541 coscheduled by this initial part of the schedule together.
6542 For example if an AST is generated for a schedule
6544 { A[i] -> [0]; B[i] -> [0] }
6546 then the C<isl_ast_build_set_create_leaf> callback described
6547 below may get called twice, once for each domain.
6548 Setting this option ensures that the callback is only called once
6549 on both domains together.
6551 =item * ast_build_separation_bounds
6553 This option specifies which bounds to use during separation.
6554 If this option is set to C<ISL_AST_BUILD_SEPARATION_BOUNDS_IMPLICIT>
6555 then all (possibly implicit) bounds on the current dimension will
6556 be used during separation.
6557 If this option is set to C<ISL_AST_BUILD_SEPARATION_BOUNDS_EXPLICIT>
6558 then only those bounds that are explicitly available will
6559 be used during separation.
6561 =item * ast_build_scale_strides
6563 This option specifies whether the AST generator is allowed
6564 to scale down iterators of strided loops.
6566 =item * ast_build_allow_else
6568 This option specifies whether the AST generator is allowed
6569 to construct if statements with else branches.
6571 =item * ast_build_allow_or
6573 This option specifies whether the AST generator is allowed
6574 to construct if conditions with disjunctions.
6578 =head3 Fine-grained Control over AST Generation
6580 Besides specifying the constraints on the parameters,
6581 an C<isl_ast_build> object can be used to control
6582 various aspects of the AST generation process.
6583 The most prominent way of control is through ``options'',
6584 which can be set using the following function.
6586 #include <isl/ast_build.h>
6587 __isl_give isl_ast_build *
6588 isl_ast_build_set_options(
6589 __isl_take isl_ast_build *control,
6590 __isl_take isl_union_map *options);
6592 The options are encoded in an <isl_union_map>.
6593 The domain of this union relation refers to the schedule domain,
6594 i.e., the range of the schedule passed to C<isl_ast_build_ast_from_schedule>.
6595 In the case of nested AST generation (see L</"Nested AST Generation">),
6596 the domain of C<options> should refer to the extra piece of the schedule.
6597 That is, it should be equal to the range of the wrapped relation in the
6598 range of the schedule.
6599 The range of the options can consist of elements in one or more spaces,
6600 the names of which determine the effect of the option.
6601 The values of the range typically also refer to the schedule dimension
6602 to which the option applies. In case of nested AST generation
6603 (see L</"Nested AST Generation">), these values refer to the position
6604 of the schedule dimension within the innermost AST generation.
6605 The constraints on the domain elements of
6606 the option should only refer to this dimension and earlier dimensions.
6607 We consider the following spaces.
6611 =item C<separation_class>
6613 This space is a wrapped relation between two one dimensional spaces.
6614 The input space represents the schedule dimension to which the option
6615 applies and the output space represents the separation class.
6616 While constructing a loop corresponding to the specified schedule
6617 dimension(s), the AST generator will try to generate separate loops
6618 for domain elements that are assigned different classes.
6619 If only some of the elements are assigned a class, then those elements
6620 that are not assigned any class will be treated as belonging to a class
6621 that is separate from the explicitly assigned classes.
6622 The typical use case for this option is to separate full tiles from
6624 The other options, described below, are applied after the separation
6627 As an example, consider the separation into full and partial tiles
6628 of a tiling of a triangular domain.
6629 Take, for example, the domain
6631 { A[i,j] : 0 <= i,j and i + j <= 100 }
6633 and a tiling into tiles of 10 by 10. The input to the AST generator
6634 is then the schedule
6636 { A[i,j] -> [([i/10]),[j/10],i,j] : 0 <= i,j and
6639 Without any options, the following AST is generated
6641 for (int c0 = 0; c0 <= 10; c0 += 1)
6642 for (int c1 = 0; c1 <= -c0 + 10; c1 += 1)
6643 for (int c2 = 10 * c0;
6644 c2 <= min(-10 * c1 + 100, 10 * c0 + 9);
6646 for (int c3 = 10 * c1;
6647 c3 <= min(10 * c1 + 9, -c2 + 100);
6651 Separation into full and partial tiles can be obtained by assigning
6652 a class, say C<0>, to the full tiles. The full tiles are represented by those
6653 values of the first and second schedule dimensions for which there are
6654 values of the third and fourth dimensions to cover an entire tile.
6655 That is, we need to specify the following option
6657 { [a,b,c,d] -> separation_class[[0]->[0]] :
6658 exists b': 0 <= 10a,10b' and
6659 10a+9+10b'+9 <= 100;
6660 [a,b,c,d] -> separation_class[[1]->[0]] :
6661 0 <= 10a,10b and 10a+9+10b+9 <= 100 }
6665 { [a, b, c, d] -> separation_class[[1] -> [0]] :
6666 a >= 0 and b >= 0 and b <= 8 - a;
6667 [a, b, c, d] -> separation_class[[0] -> [0]] :
6670 With this option, the generated AST is as follows
6673 for (int c0 = 0; c0 <= 8; c0 += 1) {
6674 for (int c1 = 0; c1 <= -c0 + 8; c1 += 1)
6675 for (int c2 = 10 * c0;
6676 c2 <= 10 * c0 + 9; c2 += 1)
6677 for (int c3 = 10 * c1;
6678 c3 <= 10 * c1 + 9; c3 += 1)
6680 for (int c1 = -c0 + 9; c1 <= -c0 + 10; c1 += 1)
6681 for (int c2 = 10 * c0;
6682 c2 <= min(-10 * c1 + 100, 10 * c0 + 9);
6684 for (int c3 = 10 * c1;
6685 c3 <= min(-c2 + 100, 10 * c1 + 9);
6689 for (int c0 = 9; c0 <= 10; c0 += 1)
6690 for (int c1 = 0; c1 <= -c0 + 10; c1 += 1)
6691 for (int c2 = 10 * c0;
6692 c2 <= min(-10 * c1 + 100, 10 * c0 + 9);
6694 for (int c3 = 10 * c1;
6695 c3 <= min(10 * c1 + 9, -c2 + 100);
6702 This is a single-dimensional space representing the schedule dimension(s)
6703 to which ``separation'' should be applied. Separation tries to split
6704 a loop into several pieces if this can avoid the generation of guards
6706 See also the C<atomic> option.
6710 This is a single-dimensional space representing the schedule dimension(s)
6711 for which the domains should be considered ``atomic''. That is, the
6712 AST generator will make sure that any given domain space will only appear
6713 in a single loop at the specified level.
6715 Consider the following schedule
6717 { a[i] -> [i] : 0 <= i < 10;
6718 b[i] -> [i+1] : 0 <= i < 10 }
6720 If the following option is specified
6722 { [i] -> separate[x] }
6724 then the following AST will be generated
6728 for (int c0 = 1; c0 <= 9; c0 += 1) {
6735 If, on the other hand, the following option is specified
6737 { [i] -> atomic[x] }
6739 then the following AST will be generated
6741 for (int c0 = 0; c0 <= 10; c0 += 1) {
6748 If neither C<atomic> nor C<separate> is specified, then the AST generator
6749 may produce either of these two results or some intermediate form.
6753 This is a single-dimensional space representing the schedule dimension(s)
6754 that should be I<completely> unrolled.
6755 To obtain a partial unrolling, the user should apply an additional
6756 strip-mining to the schedule and fully unroll the inner loop.
6760 Additional control is available through the following functions.
6762 #include <isl/ast_build.h>
6763 __isl_give isl_ast_build *
6764 isl_ast_build_set_iterators(
6765 __isl_take isl_ast_build *control,
6766 __isl_take isl_id_list *iterators);
6768 The function C<isl_ast_build_set_iterators> allows the user to
6769 specify a list of iterator C<isl_id>s to be used as iterators.
6770 If the input schedule is injective, then
6771 the number of elements in this list should be as large as the dimension
6772 of the schedule space, but no direct correspondence should be assumed
6773 between dimensions and elements.
6774 If the input schedule is not injective, then an additional number
6775 of C<isl_id>s equal to the largest dimension of the input domains
6777 If the number of provided C<isl_id>s is insufficient, then additional
6778 names are automatically generated.
6780 #include <isl/ast_build.h>
6781 __isl_give isl_ast_build *
6782 isl_ast_build_set_create_leaf(
6783 __isl_take isl_ast_build *control,
6784 __isl_give isl_ast_node *(*fn)(
6785 __isl_take isl_ast_build *build,
6786 void *user), void *user);
6789 C<isl_ast_build_set_create_leaf> function allows for the
6790 specification of a callback that should be called whenever the AST
6791 generator arrives at an element of the schedule domain.
6792 The callback should return an AST node that should be inserted
6793 at the corresponding position of the AST. The default action (when
6794 the callback is not set) is to continue generating parts of the AST to scan
6795 all the domain elements associated to the schedule domain element
6796 and to insert user nodes, ``calling'' the domain element, for each of them.
6797 The C<build> argument contains the current state of the C<isl_ast_build>.
6798 To ease nested AST generation (see L</"Nested AST Generation">),
6799 all control information that is
6800 specific to the current AST generation such as the options and
6801 the callbacks has been removed from this C<isl_ast_build>.
6802 The callback would typically return the result of a nested
6804 user defined node created using the following function.
6806 #include <isl/ast.h>
6807 __isl_give isl_ast_node *isl_ast_node_alloc_user(
6808 __isl_take isl_ast_expr *expr);
6810 #include <isl/ast_build.h>
6811 __isl_give isl_ast_build *
6812 isl_ast_build_set_at_each_domain(
6813 __isl_take isl_ast_build *build,
6814 __isl_give isl_ast_node *(*fn)(
6815 __isl_take isl_ast_node *node,
6816 __isl_keep isl_ast_build *build,
6817 void *user), void *user);
6818 __isl_give isl_ast_build *
6819 isl_ast_build_set_before_each_for(
6820 __isl_take isl_ast_build *build,
6821 __isl_give isl_id *(*fn)(
6822 __isl_keep isl_ast_build *build,
6823 void *user), void *user);
6824 __isl_give isl_ast_build *
6825 isl_ast_build_set_after_each_for(
6826 __isl_take isl_ast_build *build,
6827 __isl_give isl_ast_node *(*fn)(
6828 __isl_take isl_ast_node *node,
6829 __isl_keep isl_ast_build *build,
6830 void *user), void *user);
6832 The callback set by C<isl_ast_build_set_at_each_domain> will
6833 be called for each domain AST node.
6834 The callbacks set by C<isl_ast_build_set_before_each_for>
6835 and C<isl_ast_build_set_after_each_for> will be called
6836 for each for AST node. The first will be called in depth-first
6837 pre-order, while the second will be called in depth-first post-order.
6838 Since C<isl_ast_build_set_before_each_for> is called before the for
6839 node is actually constructed, it is only passed an C<isl_ast_build>.
6840 The returned C<isl_id> will be added as an annotation (using
6841 C<isl_ast_node_set_annotation>) to the constructed for node.
6842 In particular, if the user has also specified an C<after_each_for>
6843 callback, then the annotation can be retrieved from the node passed to
6844 that callback using C<isl_ast_node_get_annotation>.
6845 All callbacks should C<NULL> on failure.
6846 The given C<isl_ast_build> can be used to create new
6847 C<isl_ast_expr> objects using C<isl_ast_build_expr_from_pw_aff>
6848 or C<isl_ast_build_call_from_pw_multi_aff>.
6850 =head3 Nested AST Generation
6852 C<isl> allows the user to create an AST within the context
6853 of another AST. These nested ASTs are created using the
6854 same C<isl_ast_build_ast_from_schedule> function that is used to create the
6855 outer AST. The C<build> argument should be an C<isl_ast_build>
6856 passed to a callback set by
6857 C<isl_ast_build_set_create_leaf>.
6858 The space of the range of the C<schedule> argument should refer
6859 to this build. In particular, the space should be a wrapped
6860 relation and the domain of this wrapped relation should be the
6861 same as that of the range of the schedule returned by
6862 C<isl_ast_build_get_schedule> below.
6863 In practice, the new schedule is typically
6864 created by calling C<isl_union_map_range_product> on the old schedule
6865 and some extra piece of the schedule.
6866 The space of the schedule domain is also available from
6867 the C<isl_ast_build>.
6869 #include <isl/ast_build.h>
6870 __isl_give isl_union_map *isl_ast_build_get_schedule(
6871 __isl_keep isl_ast_build *build);
6872 __isl_give isl_space *isl_ast_build_get_schedule_space(
6873 __isl_keep isl_ast_build *build);
6874 __isl_give isl_ast_build *isl_ast_build_restrict(
6875 __isl_take isl_ast_build *build,
6876 __isl_take isl_set *set);
6878 The C<isl_ast_build_get_schedule> function returns a (partial)
6879 schedule for the domains elements for which part of the AST still needs to
6880 be generated in the current build.
6881 In particular, the domain elements are mapped to those iterations of the loops
6882 enclosing the current point of the AST generation inside which
6883 the domain elements are executed.
6884 No direct correspondence between
6885 the input schedule and this schedule should be assumed.
6886 The space obtained from C<isl_ast_build_get_schedule_space> can be used
6887 to create a set for C<isl_ast_build_restrict> to intersect
6888 with the current build. In particular, the set passed to
6889 C<isl_ast_build_restrict> can have additional parameters.
6890 The ids of the set dimensions in the space returned by
6891 C<isl_ast_build_get_schedule_space> correspond to the
6892 iterators of the already generated loops.
6893 The user should not rely on the ids of the output dimensions
6894 of the relations in the union relation returned by
6895 C<isl_ast_build_get_schedule> having any particular value.
6899 Although C<isl> is mainly meant to be used as a library,
6900 it also contains some basic applications that use some
6901 of the functionality of C<isl>.
6902 The input may be specified in either the L<isl format>
6903 or the L<PolyLib format>.
6905 =head2 C<isl_polyhedron_sample>
6907 C<isl_polyhedron_sample> takes a polyhedron as input and prints
6908 an integer element of the polyhedron, if there is any.
6909 The first column in the output is the denominator and is always
6910 equal to 1. If the polyhedron contains no integer points,
6911 then a vector of length zero is printed.
6915 C<isl_pip> takes the same input as the C<example> program
6916 from the C<piplib> distribution, i.e., a set of constraints
6917 on the parameters, a line containing only -1 and finally a set
6918 of constraints on a parametric polyhedron.
6919 The coefficients of the parameters appear in the last columns
6920 (but before the final constant column).
6921 The output is the lexicographic minimum of the parametric polyhedron.
6922 As C<isl> currently does not have its own output format, the output
6923 is just a dump of the internal state.
6925 =head2 C<isl_polyhedron_minimize>
6927 C<isl_polyhedron_minimize> computes the minimum of some linear
6928 or affine objective function over the integer points in a polyhedron.
6929 If an affine objective function
6930 is given, then the constant should appear in the last column.
6932 =head2 C<isl_polytope_scan>
6934 Given a polytope, C<isl_polytope_scan> prints
6935 all integer points in the polytope.
6937 =head2 C<isl_codegen>
6939 Given a schedule, a context set and an options relation,
6940 C<isl_codegen> prints out an AST that scans the domain elements
6941 of the schedule in the order of their image(s) taking into account
6942 the constraints in the context set.