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);
342 The user can impose a bound on the number of low-level I<operations>
343 that can be performed by an C<isl_ctx>. This bound can be set and
344 retrieved using the following functions. A bound of zero means that
345 no bound is imposed. The number of operations performed can be
346 reset using C<isl_ctx_reset_operations>. Note that the number
347 of low-level operations needed to perform a high-level computation
348 may differ significantly across different versions
349 of C<isl>, but it should be the same across different platforms
350 for the same version of C<isl>.
352 void isl_ctx_set_max_operations(isl_ctx *ctx,
353 unsigned long max_operations);
354 unsigned long isl_ctx_get_max_operations(isl_ctx *ctx);
355 void isl_ctx_reset_operations(isl_ctx *ctx);
359 An C<isl_val> represents an integer value, a rational value
360 or one of three special values, infinity, negative infinity and NaN.
361 Some predefined values can be created using the following functions.
364 __isl_give isl_val *isl_val_zero(isl_ctx *ctx);
365 __isl_give isl_val *isl_val_one(isl_ctx *ctx);
366 __isl_give isl_val *isl_val_nan(isl_ctx *ctx);
367 __isl_give isl_val *isl_val_infty(isl_ctx *ctx);
368 __isl_give isl_val *isl_val_neginfty(isl_ctx *ctx);
370 Specific integer values can be created using the following functions.
373 __isl_give isl_val *isl_val_int_from_si(isl_ctx *ctx,
375 __isl_give isl_val *isl_val_int_from_ui(isl_ctx *ctx,
377 __isl_give isl_val *isl_val_int_from_chunks(isl_ctx *ctx,
378 size_t n, size_t size, const void *chunks);
380 The function C<isl_val_int_from_chunks> constructs an C<isl_val>
381 from the C<n> I<digits>, each consisting of C<size> bytes, stored at C<chunks>.
382 The least significant digit is assumed to be stored first.
384 Value objects can be copied and freed using the following functions.
387 __isl_give isl_val *isl_val_copy(__isl_keep isl_val *v);
388 void *isl_val_free(__isl_take isl_val *v);
390 They can be inspected using the following functions.
393 isl_ctx *isl_val_get_ctx(__isl_keep isl_val *val);
394 long isl_val_get_num_si(__isl_keep isl_val *v);
395 long isl_val_get_den_si(__isl_keep isl_val *v);
396 double isl_val_get_d(__isl_keep isl_val *v);
397 size_t isl_val_n_abs_num_chunks(__isl_keep isl_val *v,
399 int isl_val_get_abs_num_chunks(__isl_keep isl_val *v,
400 size_t size, void *chunks);
402 C<isl_val_n_abs_num_chunks> returns the number of I<digits>
403 of C<size> bytes needed to store the absolute value of the
405 C<isl_val_get_abs_num_chunks> stores these digits at C<chunks>,
406 which is assumed to have been preallocated by the caller.
407 The least significant digit is stored first.
408 Note that C<isl_val_get_num_si>, C<isl_val_get_den_si>,
409 C<isl_val_get_d>, C<isl_val_n_abs_num_chunks>
410 and C<isl_val_get_abs_num_chunks> can only be applied to rational values.
412 An C<isl_val> can be modified using the following function.
415 __isl_give isl_val *isl_val_set_si(__isl_take isl_val *v,
418 The following unary properties are defined on C<isl_val>s.
421 int isl_val_sgn(__isl_keep isl_val *v);
422 int isl_val_is_zero(__isl_keep isl_val *v);
423 int isl_val_is_one(__isl_keep isl_val *v);
424 int isl_val_is_negone(__isl_keep isl_val *v);
425 int isl_val_is_nonneg(__isl_keep isl_val *v);
426 int isl_val_is_nonpos(__isl_keep isl_val *v);
427 int isl_val_is_pos(__isl_keep isl_val *v);
428 int isl_val_is_neg(__isl_keep isl_val *v);
429 int isl_val_is_int(__isl_keep isl_val *v);
430 int isl_val_is_rat(__isl_keep isl_val *v);
431 int isl_val_is_nan(__isl_keep isl_val *v);
432 int isl_val_is_infty(__isl_keep isl_val *v);
433 int isl_val_is_neginfty(__isl_keep isl_val *v);
435 Note that the sign of NaN is undefined.
437 The following binary properties are defined on pairs of C<isl_val>s.
440 int isl_val_lt(__isl_keep isl_val *v1,
441 __isl_keep isl_val *v2);
442 int isl_val_le(__isl_keep isl_val *v1,
443 __isl_keep isl_val *v2);
444 int isl_val_gt(__isl_keep isl_val *v1,
445 __isl_keep isl_val *v2);
446 int isl_val_ge(__isl_keep isl_val *v1,
447 __isl_keep isl_val *v2);
448 int isl_val_eq(__isl_keep isl_val *v1,
449 __isl_keep isl_val *v2);
450 int isl_val_ne(__isl_keep isl_val *v1,
451 __isl_keep isl_val *v2);
453 For integer C<isl_val>s we additionally have the following binary property.
456 int isl_val_is_divisible_by(__isl_keep isl_val *v1,
457 __isl_keep isl_val *v2);
459 An C<isl_val> can also be compared to an integer using the following
460 function. The result is undefined for NaN.
463 int isl_val_cmp_si(__isl_keep isl_val *v, long i);
465 The following unary operations are available on C<isl_val>s.
468 __isl_give isl_val *isl_val_abs(__isl_take isl_val *v);
469 __isl_give isl_val *isl_val_neg(__isl_take isl_val *v);
470 __isl_give isl_val *isl_val_floor(__isl_take isl_val *v);
471 __isl_give isl_val *isl_val_ceil(__isl_take isl_val *v);
472 __isl_give isl_val *isl_val_trunc(__isl_take isl_val *v);
474 The following binary operations are available on C<isl_val>s.
477 __isl_give isl_val *isl_val_abs(__isl_take isl_val *v);
478 __isl_give isl_val *isl_val_neg(__isl_take isl_val *v);
479 __isl_give isl_val *isl_val_floor(__isl_take isl_val *v);
480 __isl_give isl_val *isl_val_ceil(__isl_take isl_val *v);
481 __isl_give isl_val *isl_val_trunc(__isl_take isl_val *v);
482 __isl_give isl_val *isl_val_2exp(__isl_take isl_val *v);
483 __isl_give isl_val *isl_val_min(__isl_take isl_val *v1,
484 __isl_take isl_val *v2);
485 __isl_give isl_val *isl_val_max(__isl_take isl_val *v1,
486 __isl_take isl_val *v2);
487 __isl_give isl_val *isl_val_add(__isl_take isl_val *v1,
488 __isl_take isl_val *v2);
489 __isl_give isl_val *isl_val_add_ui(__isl_take isl_val *v1,
491 __isl_give isl_val *isl_val_sub(__isl_take isl_val *v1,
492 __isl_take isl_val *v2);
493 __isl_give isl_val *isl_val_sub_ui(__isl_take isl_val *v1,
495 __isl_give isl_val *isl_val_mul(__isl_take isl_val *v1,
496 __isl_take isl_val *v2);
497 __isl_give isl_val *isl_val_mul_ui(__isl_take isl_val *v1,
499 __isl_give isl_val *isl_val_div(__isl_take isl_val *v1,
500 __isl_take isl_val *v2);
502 On integer values, we additionally have the following operations.
505 __isl_give isl_val *isl_val_2exp(__isl_take isl_val *v);
506 __isl_give isl_val *isl_val_mod(__isl_take isl_val *v1,
507 __isl_take isl_val *v2);
508 __isl_give isl_val *isl_val_gcd(__isl_take isl_val *v1,
509 __isl_take isl_val *v2);
510 __isl_give isl_val *isl_val_gcdext(__isl_take isl_val *v1,
511 __isl_take isl_val *v2, __isl_give isl_val **x,
512 __isl_give isl_val **y);
514 The function C<isl_val_gcdext> returns the greatest common divisor g
515 of C<v1> and C<v2> as well as two integers C<*x> and C<*y> such
516 that C<*x> * C<v1> + C<*y> * C<v2> = g.
518 A value can be read from input using
521 __isl_give isl_val *isl_val_read_from_str(isl_ctx *ctx,
524 A value can be printed using
527 __isl_give isl_printer *isl_printer_print_val(
528 __isl_take isl_printer *p, __isl_keep isl_val *v);
530 =head3 GMP specific functions
532 These functions are only available if C<isl> has been compiled with C<GMP>
535 Specific integer and rational values can be created from C<GMP> values using
536 the following functions.
538 #include <isl/val_gmp.h>
539 __isl_give isl_val *isl_val_int_from_gmp(isl_ctx *ctx,
541 __isl_give isl_val *isl_val_from_gmp(isl_ctx *ctx,
542 const mpz_t n, const mpz_t d);
544 The numerator and denominator of a rational value can be extracted as
545 C<GMP> values using the following functions.
547 #include <isl/val_gmp.h>
548 int isl_val_get_num_gmp(__isl_keep isl_val *v, mpz_t z);
549 int isl_val_get_den_gmp(__isl_keep isl_val *v, mpz_t z);
551 =head2 Sets and Relations
553 C<isl> uses six types of objects for representing sets and relations,
554 C<isl_basic_set>, C<isl_basic_map>, C<isl_set>, C<isl_map>,
555 C<isl_union_set> and C<isl_union_map>.
556 C<isl_basic_set> and C<isl_basic_map> represent sets and relations that
557 can be described as a conjunction of affine constraints, while
558 C<isl_set> and C<isl_map> represent unions of
559 C<isl_basic_set>s and C<isl_basic_map>s, respectively.
560 However, all C<isl_basic_set>s or C<isl_basic_map>s in the union need
561 to live in the same space. C<isl_union_set>s and C<isl_union_map>s
562 represent unions of C<isl_set>s or C<isl_map>s in I<different> spaces,
563 where spaces are considered different if they have a different number
564 of dimensions and/or different names (see L<"Spaces">).
565 The difference between sets and relations (maps) is that sets have
566 one set of variables, while relations have two sets of variables,
567 input variables and output variables.
569 =head2 Memory Management
571 Since a high-level operation on sets and/or relations usually involves
572 several substeps and since the user is usually not interested in
573 the intermediate results, most functions that return a new object
574 will also release all the objects passed as arguments.
575 If the user still wants to use one or more of these arguments
576 after the function call, she should pass along a copy of the
577 object rather than the object itself.
578 The user is then responsible for making sure that the original
579 object gets used somewhere else or is explicitly freed.
581 The arguments and return values of all documented functions are
582 annotated to make clear which arguments are released and which
583 arguments are preserved. In particular, the following annotations
590 C<__isl_give> means that a new object is returned.
591 The user should make sure that the returned pointer is
592 used exactly once as a value for an C<__isl_take> argument.
593 In between, it can be used as a value for as many
594 C<__isl_keep> arguments as the user likes.
595 There is one exception, and that is the case where the
596 pointer returned is C<NULL>. Is this case, the user
597 is free to use it as an C<__isl_take> argument or not.
601 C<__isl_take> means that the object the argument points to
602 is taken over by the function and may no longer be used
603 by the user as an argument to any other function.
604 The pointer value must be one returned by a function
605 returning an C<__isl_give> pointer.
606 If the user passes in a C<NULL> value, then this will
607 be treated as an error in the sense that the function will
608 not perform its usual operation. However, it will still
609 make sure that all the other C<__isl_take> arguments
614 C<__isl_keep> means that the function will only use the object
615 temporarily. After the function has finished, the user
616 can still use it as an argument to other functions.
617 A C<NULL> value will be treated in the same way as
618 a C<NULL> value for an C<__isl_take> argument.
622 =head2 Error Handling
624 C<isl> supports different ways to react in case a runtime error is triggered.
625 Runtime errors arise, e.g., if a function such as C<isl_map_intersect> is called
626 with two maps that have incompatible spaces. There are three possible ways
627 to react on error: to warn, to continue or to abort.
629 The default behavior is to warn. In this mode, C<isl> prints a warning, stores
630 the last error in the corresponding C<isl_ctx> and the function in which the
631 error was triggered returns C<NULL>. An error does not corrupt internal state,
632 such that isl can continue to be used. C<isl> also provides functions to
633 read the last error and to reset the memory that stores the last error. The
634 last error is only stored for information purposes. Its presence does not
635 change the behavior of C<isl>. Hence, resetting an error is not required to
636 continue to use isl, but only to observe new errors.
639 enum isl_error isl_ctx_last_error(isl_ctx *ctx);
640 void isl_ctx_reset_error(isl_ctx *ctx);
642 Another option is to continue on error. This is similar to warn on error mode,
643 except that C<isl> does not print any warning. This allows a program to
644 implement its own error reporting.
646 The last option is to directly abort the execution of the program from within
647 the isl library. This makes it obviously impossible to recover from an error,
648 but it allows to directly spot the error location. By aborting on error,
649 debuggers break at the location the error occurred and can provide a stack
650 trace. Other tools that automatically provide stack traces on abort or that do
651 not want to continue execution after an error was triggered may also prefer to
654 The on error behavior of isl can be specified by calling
655 C<isl_options_set_on_error> or by setting the command line option
656 C<--isl-on-error>. Valid arguments for the function call are
657 C<ISL_ON_ERROR_WARN>, C<ISL_ON_ERROR_CONTINUE> and C<ISL_ON_ERROR_ABORT>. The
658 choices for the command line option are C<warn>, C<continue> and C<abort>.
659 It is also possible to query the current error mode.
661 #include <isl/options.h>
662 int isl_options_set_on_error(isl_ctx *ctx, int val);
663 int isl_options_get_on_error(isl_ctx *ctx);
667 Identifiers are used to identify both individual dimensions
668 and tuples of dimensions. They consist of an optional name and an optional
669 user pointer. The name and the user pointer cannot both be C<NULL>, however.
670 Identifiers with the same name but different pointer values
671 are considered to be distinct.
672 Similarly, identifiers with different names but the same pointer value
673 are also considered to be distinct.
674 Equal identifiers are represented using the same object.
675 Pairs of identifiers can therefore be tested for equality using the
677 Identifiers can be constructed, copied, freed, inspected and printed
678 using the following functions.
681 __isl_give isl_id *isl_id_alloc(isl_ctx *ctx,
682 __isl_keep const char *name, void *user);
683 __isl_give isl_id *isl_id_set_free_user(
684 __isl_take isl_id *id,
685 __isl_give void (*free_user)(void *user));
686 __isl_give isl_id *isl_id_copy(isl_id *id);
687 void *isl_id_free(__isl_take isl_id *id);
689 isl_ctx *isl_id_get_ctx(__isl_keep isl_id *id);
690 void *isl_id_get_user(__isl_keep isl_id *id);
691 __isl_keep const char *isl_id_get_name(__isl_keep isl_id *id);
693 __isl_give isl_printer *isl_printer_print_id(
694 __isl_take isl_printer *p, __isl_keep isl_id *id);
696 The callback set by C<isl_id_set_free_user> is called on the user
697 pointer when the last reference to the C<isl_id> is freed.
698 Note that C<isl_id_get_name> returns a pointer to some internal
699 data structure, so the result can only be used while the
700 corresponding C<isl_id> is alive.
704 Whenever a new set, relation or similiar object is created from scratch,
705 the space in which it lives needs to be specified using an C<isl_space>.
706 Each space involves zero or more parameters and zero, one or two
707 tuples of set or input/output dimensions. The parameters and dimensions
708 are identified by an C<isl_dim_type> and a position.
709 The type C<isl_dim_param> refers to parameters,
710 the type C<isl_dim_set> refers to set dimensions (for spaces
711 with a single tuple of dimensions) and the types C<isl_dim_in>
712 and C<isl_dim_out> refer to input and output dimensions
713 (for spaces with two tuples of dimensions).
714 Local spaces (see L</"Local Spaces">) also contain dimensions
715 of type C<isl_dim_div>.
716 Note that parameters are only identified by their position within
717 a given object. Across different objects, parameters are (usually)
718 identified by their names or identifiers. Only unnamed parameters
719 are identified by their positions across objects. The use of unnamed
720 parameters is discouraged.
722 #include <isl/space.h>
723 __isl_give isl_space *isl_space_alloc(isl_ctx *ctx,
724 unsigned nparam, unsigned n_in, unsigned n_out);
725 __isl_give isl_space *isl_space_params_alloc(isl_ctx *ctx,
727 __isl_give isl_space *isl_space_set_alloc(isl_ctx *ctx,
728 unsigned nparam, unsigned dim);
729 __isl_give isl_space *isl_space_copy(__isl_keep isl_space *space);
730 void *isl_space_free(__isl_take isl_space *space);
731 unsigned isl_space_dim(__isl_keep isl_space *space,
732 enum isl_dim_type type);
734 The space used for creating a parameter domain
735 needs to be created using C<isl_space_params_alloc>.
736 For other sets, the space
737 needs to be created using C<isl_space_set_alloc>, while
738 for a relation, the space
739 needs to be created using C<isl_space_alloc>.
740 C<isl_space_dim> can be used
741 to find out the number of dimensions of each type in
742 a space, where type may be
743 C<isl_dim_param>, C<isl_dim_in> (only for relations),
744 C<isl_dim_out> (only for relations), C<isl_dim_set>
745 (only for sets) or C<isl_dim_all>.
747 To check whether a given space is that of a set or a map
748 or whether it is a parameter space, use these functions:
750 #include <isl/space.h>
751 int isl_space_is_params(__isl_keep isl_space *space);
752 int isl_space_is_set(__isl_keep isl_space *space);
753 int isl_space_is_map(__isl_keep isl_space *space);
755 Spaces can be compared using the following functions:
757 #include <isl/space.h>
758 int isl_space_is_equal(__isl_keep isl_space *space1,
759 __isl_keep isl_space *space2);
760 int isl_space_is_domain(__isl_keep isl_space *space1,
761 __isl_keep isl_space *space2);
762 int isl_space_is_range(__isl_keep isl_space *space1,
763 __isl_keep isl_space *space2);
765 C<isl_space_is_domain> checks whether the first argument is equal
766 to the domain of the second argument. This requires in particular that
767 the first argument is a set space and that the second argument
770 It is often useful to create objects that live in the
771 same space as some other object. This can be accomplished
772 by creating the new objects
773 (see L<Creating New Sets and Relations> or
774 L<Creating New (Piecewise) Quasipolynomials>) based on the space
775 of the original object.
778 __isl_give isl_space *isl_basic_set_get_space(
779 __isl_keep isl_basic_set *bset);
780 __isl_give isl_space *isl_set_get_space(__isl_keep isl_set *set);
782 #include <isl/union_set.h>
783 __isl_give isl_space *isl_union_set_get_space(
784 __isl_keep isl_union_set *uset);
787 __isl_give isl_space *isl_basic_map_get_space(
788 __isl_keep isl_basic_map *bmap);
789 __isl_give isl_space *isl_map_get_space(__isl_keep isl_map *map);
791 #include <isl/union_map.h>
792 __isl_give isl_space *isl_union_map_get_space(
793 __isl_keep isl_union_map *umap);
795 #include <isl/constraint.h>
796 __isl_give isl_space *isl_constraint_get_space(
797 __isl_keep isl_constraint *constraint);
799 #include <isl/polynomial.h>
800 __isl_give isl_space *isl_qpolynomial_get_domain_space(
801 __isl_keep isl_qpolynomial *qp);
802 __isl_give isl_space *isl_qpolynomial_get_space(
803 __isl_keep isl_qpolynomial *qp);
804 __isl_give isl_space *isl_qpolynomial_fold_get_space(
805 __isl_keep isl_qpolynomial_fold *fold);
806 __isl_give isl_space *isl_pw_qpolynomial_get_domain_space(
807 __isl_keep isl_pw_qpolynomial *pwqp);
808 __isl_give isl_space *isl_pw_qpolynomial_get_space(
809 __isl_keep isl_pw_qpolynomial *pwqp);
810 __isl_give isl_space *isl_pw_qpolynomial_fold_get_domain_space(
811 __isl_keep isl_pw_qpolynomial_fold *pwf);
812 __isl_give isl_space *isl_pw_qpolynomial_fold_get_space(
813 __isl_keep isl_pw_qpolynomial_fold *pwf);
814 __isl_give isl_space *isl_union_pw_qpolynomial_get_space(
815 __isl_keep isl_union_pw_qpolynomial *upwqp);
816 __isl_give isl_space *isl_union_pw_qpolynomial_fold_get_space(
817 __isl_keep isl_union_pw_qpolynomial_fold *upwf);
820 __isl_give isl_space *isl_multi_val_get_space(
821 __isl_keep isl_multi_val *mv);
824 __isl_give isl_space *isl_aff_get_domain_space(
825 __isl_keep isl_aff *aff);
826 __isl_give isl_space *isl_aff_get_space(
827 __isl_keep isl_aff *aff);
828 __isl_give isl_space *isl_pw_aff_get_domain_space(
829 __isl_keep isl_pw_aff *pwaff);
830 __isl_give isl_space *isl_pw_aff_get_space(
831 __isl_keep isl_pw_aff *pwaff);
832 __isl_give isl_space *isl_multi_aff_get_domain_space(
833 __isl_keep isl_multi_aff *maff);
834 __isl_give isl_space *isl_multi_aff_get_space(
835 __isl_keep isl_multi_aff *maff);
836 __isl_give isl_space *isl_pw_multi_aff_get_domain_space(
837 __isl_keep isl_pw_multi_aff *pma);
838 __isl_give isl_space *isl_pw_multi_aff_get_space(
839 __isl_keep isl_pw_multi_aff *pma);
840 __isl_give isl_space *isl_union_pw_multi_aff_get_space(
841 __isl_keep isl_union_pw_multi_aff *upma);
842 __isl_give isl_space *isl_multi_pw_aff_get_domain_space(
843 __isl_keep isl_multi_pw_aff *mpa);
844 __isl_give isl_space *isl_multi_pw_aff_get_space(
845 __isl_keep isl_multi_pw_aff *mpa);
847 #include <isl/point.h>
848 __isl_give isl_space *isl_point_get_space(
849 __isl_keep isl_point *pnt);
851 The identifiers or names of the individual dimensions may be set or read off
852 using the following functions.
854 #include <isl/space.h>
855 __isl_give isl_space *isl_space_set_dim_id(
856 __isl_take isl_space *space,
857 enum isl_dim_type type, unsigned pos,
858 __isl_take isl_id *id);
859 int isl_space_has_dim_id(__isl_keep isl_space *space,
860 enum isl_dim_type type, unsigned pos);
861 __isl_give isl_id *isl_space_get_dim_id(
862 __isl_keep isl_space *space,
863 enum isl_dim_type type, unsigned pos);
864 __isl_give isl_space *isl_space_set_dim_name(
865 __isl_take isl_space *space,
866 enum isl_dim_type type, unsigned pos,
867 __isl_keep const char *name);
868 int isl_space_has_dim_name(__isl_keep isl_space *space,
869 enum isl_dim_type type, unsigned pos);
870 __isl_keep const char *isl_space_get_dim_name(
871 __isl_keep isl_space *space,
872 enum isl_dim_type type, unsigned pos);
874 Note that C<isl_space_get_name> returns a pointer to some internal
875 data structure, so the result can only be used while the
876 corresponding C<isl_space> is alive.
877 Also note that every function that operates on two sets or relations
878 requires that both arguments have the same parameters. This also
879 means that if one of the arguments has named parameters, then the
880 other needs to have named parameters too and the names need to match.
881 Pairs of C<isl_set>, C<isl_map>, C<isl_union_set> and/or C<isl_union_map>
882 arguments may have different parameters (as long as they are named),
883 in which case the result will have as parameters the union of the parameters of
886 Given the identifier or name of a dimension (typically a parameter),
887 its position can be obtained from the following function.
889 #include <isl/space.h>
890 int isl_space_find_dim_by_id(__isl_keep isl_space *space,
891 enum isl_dim_type type, __isl_keep isl_id *id);
892 int isl_space_find_dim_by_name(__isl_keep isl_space *space,
893 enum isl_dim_type type, const char *name);
895 The identifiers or names of entire spaces may be set or read off
896 using the following functions.
898 #include <isl/space.h>
899 __isl_give isl_space *isl_space_set_tuple_id(
900 __isl_take isl_space *space,
901 enum isl_dim_type type, __isl_take isl_id *id);
902 __isl_give isl_space *isl_space_reset_tuple_id(
903 __isl_take isl_space *space, enum isl_dim_type type);
904 int isl_space_has_tuple_id(__isl_keep isl_space *space,
905 enum isl_dim_type type);
906 __isl_give isl_id *isl_space_get_tuple_id(
907 __isl_keep isl_space *space, enum isl_dim_type type);
908 __isl_give isl_space *isl_space_set_tuple_name(
909 __isl_take isl_space *space,
910 enum isl_dim_type type, const char *s);
911 int isl_space_has_tuple_name(__isl_keep isl_space *space,
912 enum isl_dim_type type);
913 const char *isl_space_get_tuple_name(__isl_keep isl_space *space,
914 enum isl_dim_type type);
916 The C<type> argument needs to be one of C<isl_dim_in>, C<isl_dim_out>
917 or C<isl_dim_set>. As with C<isl_space_get_name>,
918 the C<isl_space_get_tuple_name> function returns a pointer to some internal
920 Binary operations require the corresponding spaces of their arguments
921 to have the same name.
923 To keep the names of all parameters and tuples, but reset the user pointers
924 of all the corresponding identifiers, use the following function.
926 __isl_give isl_space *isl_space_reset_user(
927 __isl_take isl_space *space);
929 Spaces can be nested. In particular, the domain of a set or
930 the domain or range of a relation can be a nested relation.
931 The following functions can be used to construct and deconstruct
934 #include <isl/space.h>
935 int isl_space_is_wrapping(__isl_keep isl_space *space);
936 int isl_space_range_is_wrapping(
937 __isl_keep isl_space *space);
938 __isl_give isl_space *isl_space_wrap(__isl_take isl_space *space);
939 __isl_give isl_space *isl_space_unwrap(__isl_take isl_space *space);
940 __isl_give isl_space *isl_space_product(__isl_take isl_space *space1,
941 __isl_take isl_space *space2);
942 __isl_give isl_space *isl_space_domain_product(
943 __isl_take isl_space *space1,
944 __isl_take isl_space *space2);
945 __isl_give isl_space *isl_space_range_product(
946 __isl_take isl_space *space1,
947 __isl_take isl_space *space2);
948 __isl_give isl_space *isl_space_range_factor_domain(
949 __isl_take isl_space *space);
950 __isl_give isl_space *isl_space_range_factor_range(
951 __isl_take isl_space *space);
953 The input to C<isl_space_is_wrapping> and C<isl_space_unwrap> should
954 be the space of a set, while that of
955 C<isl_space_range_is_wrapping> and
956 C<isl_space_wrap> should be the space of a relation.
957 Conversely, the output of C<isl_space_unwrap> is the space
958 of a relation, while that of C<isl_space_wrap> is the space of a set.
960 C<isl_space_product>, C<isl_space_domain_product>
961 and C<isl_space_range_product> take pairs or relation spaces and
962 produce a single relations space, where either the domain, the range
963 or both domain and range are wrapped spaces of relations between
964 the domains and/or ranges of the input spaces.
965 If the product is only constructed over the domain or the range
966 then the ranges or the domains of the inputs should be the same.
967 The functions C<isl_space_range_factor_domain> and
968 C<isl_space_range_factor_range> extract the two arguments from
969 the result of a call to C<isl_space_range_product>.
971 Spaces can be created from other spaces
972 using the following functions.
974 __isl_give isl_space *isl_space_domain(__isl_take isl_space *space);
975 __isl_give isl_space *isl_space_from_domain(__isl_take isl_space *space);
976 __isl_give isl_space *isl_space_range(__isl_take isl_space *space);
977 __isl_give isl_space *isl_space_from_range(__isl_take isl_space *space);
978 __isl_give isl_space *isl_space_domain_map(
979 __isl_take isl_space *space);
980 __isl_give isl_space *isl_space_range_map(
981 __isl_take isl_space *space);
982 __isl_give isl_space *isl_space_params(
983 __isl_take isl_space *space);
984 __isl_give isl_space *isl_space_set_from_params(
985 __isl_take isl_space *space);
986 __isl_give isl_space *isl_space_reverse(__isl_take isl_space *space);
987 __isl_give isl_space *isl_space_join(__isl_take isl_space *left,
988 __isl_take isl_space *right);
989 __isl_give isl_space *isl_space_align_params(
990 __isl_take isl_space *space1, __isl_take isl_space *space2)
991 __isl_give isl_space *isl_space_insert_dims(__isl_take isl_space *space,
992 enum isl_dim_type type, unsigned pos, unsigned n);
993 __isl_give isl_space *isl_space_add_dims(__isl_take isl_space *space,
994 enum isl_dim_type type, unsigned n);
995 __isl_give isl_space *isl_space_drop_dims(__isl_take isl_space *space,
996 enum isl_dim_type type, unsigned first, unsigned n);
997 __isl_give isl_space *isl_space_move_dims(__isl_take isl_space *space,
998 enum isl_dim_type dst_type, unsigned dst_pos,
999 enum isl_dim_type src_type, unsigned src_pos,
1001 __isl_give isl_space *isl_space_map_from_set(
1002 __isl_take isl_space *space);
1003 __isl_give isl_space *isl_space_map_from_domain_and_range(
1004 __isl_take isl_space *domain,
1005 __isl_take isl_space *range);
1006 __isl_give isl_space *isl_space_zip(__isl_take isl_space *space);
1007 __isl_give isl_space *isl_space_curry(
1008 __isl_take isl_space *space);
1009 __isl_give isl_space *isl_space_uncurry(
1010 __isl_take isl_space *space);
1012 Note that if dimensions are added or removed from a space, then
1013 the name and the internal structure are lost.
1017 A local space is essentially a space with
1018 zero or more existentially quantified variables.
1019 The local space of a (constraint of a) basic set or relation can be obtained
1020 using the following functions.
1022 #include <isl/constraint.h>
1023 __isl_give isl_local_space *isl_constraint_get_local_space(
1024 __isl_keep isl_constraint *constraint);
1026 #include <isl/set.h>
1027 __isl_give isl_local_space *isl_basic_set_get_local_space(
1028 __isl_keep isl_basic_set *bset);
1030 #include <isl/map.h>
1031 __isl_give isl_local_space *isl_basic_map_get_local_space(
1032 __isl_keep isl_basic_map *bmap);
1034 A new local space can be created from a space using
1036 #include <isl/local_space.h>
1037 __isl_give isl_local_space *isl_local_space_from_space(
1038 __isl_take isl_space *space);
1040 They can be inspected, modified, copied and freed using the following functions.
1042 #include <isl/local_space.h>
1043 isl_ctx *isl_local_space_get_ctx(
1044 __isl_keep isl_local_space *ls);
1045 int isl_local_space_is_set(__isl_keep isl_local_space *ls);
1046 int isl_local_space_dim(__isl_keep isl_local_space *ls,
1047 enum isl_dim_type type);
1048 __isl_give isl_local_space *isl_local_space_set_tuple_id(
1049 __isl_take isl_local_space *ls,
1050 enum isl_dim_type type, __isl_take isl_id *id);
1051 int isl_local_space_has_dim_id(
1052 __isl_keep isl_local_space *ls,
1053 enum isl_dim_type type, unsigned pos);
1054 __isl_give isl_id *isl_local_space_get_dim_id(
1055 __isl_keep isl_local_space *ls,
1056 enum isl_dim_type type, unsigned pos);
1057 int isl_local_space_has_dim_name(
1058 __isl_keep isl_local_space *ls,
1059 enum isl_dim_type type, unsigned pos)
1060 const char *isl_local_space_get_dim_name(
1061 __isl_keep isl_local_space *ls,
1062 enum isl_dim_type type, unsigned pos);
1063 __isl_give isl_local_space *isl_local_space_set_dim_name(
1064 __isl_take isl_local_space *ls,
1065 enum isl_dim_type type, unsigned pos, const char *s);
1066 __isl_give isl_local_space *isl_local_space_set_dim_id(
1067 __isl_take isl_local_space *ls,
1068 enum isl_dim_type type, unsigned pos,
1069 __isl_take isl_id *id);
1070 __isl_give isl_space *isl_local_space_get_space(
1071 __isl_keep isl_local_space *ls);
1072 __isl_give isl_aff *isl_local_space_get_div(
1073 __isl_keep isl_local_space *ls, int pos);
1074 __isl_give isl_local_space *isl_local_space_copy(
1075 __isl_keep isl_local_space *ls);
1076 void *isl_local_space_free(__isl_take isl_local_space *ls);
1078 Note that C<isl_local_space_get_div> can only be used on local spaces
1081 Two local spaces can be compared using
1083 int isl_local_space_is_equal(__isl_keep isl_local_space *ls1,
1084 __isl_keep isl_local_space *ls2);
1086 Local spaces can be created from other local spaces
1087 using the following functions.
1089 __isl_give isl_local_space *isl_local_space_domain(
1090 __isl_take isl_local_space *ls);
1091 __isl_give isl_local_space *isl_local_space_range(
1092 __isl_take isl_local_space *ls);
1093 __isl_give isl_local_space *isl_local_space_from_domain(
1094 __isl_take isl_local_space *ls);
1095 __isl_give isl_local_space *isl_local_space_intersect(
1096 __isl_take isl_local_space *ls1,
1097 __isl_take isl_local_space *ls2);
1098 __isl_give isl_local_space *isl_local_space_add_dims(
1099 __isl_take isl_local_space *ls,
1100 enum isl_dim_type type, unsigned n);
1101 __isl_give isl_local_space *isl_local_space_insert_dims(
1102 __isl_take isl_local_space *ls,
1103 enum isl_dim_type type, unsigned first, unsigned n);
1104 __isl_give isl_local_space *isl_local_space_drop_dims(
1105 __isl_take isl_local_space *ls,
1106 enum isl_dim_type type, unsigned first, unsigned n);
1108 =head2 Input and Output
1110 C<isl> supports its own input/output format, which is similar
1111 to the C<Omega> format, but also supports the C<PolyLib> format
1114 =head3 C<isl> format
1116 The C<isl> format is similar to that of C<Omega>, but has a different
1117 syntax for describing the parameters and allows for the definition
1118 of an existentially quantified variable as the integer division
1119 of an affine expression.
1120 For example, the set of integers C<i> between C<0> and C<n>
1121 such that C<i % 10 <= 6> can be described as
1123 [n] -> { [i] : exists (a = [i/10] : 0 <= i and i <= n and
1126 A set or relation can have several disjuncts, separated
1127 by the keyword C<or>. Each disjunct is either a conjunction
1128 of constraints or a projection (C<exists>) of a conjunction
1129 of constraints. The constraints are separated by the keyword
1132 =head3 C<PolyLib> format
1134 If the represented set is a union, then the first line
1135 contains a single number representing the number of disjuncts.
1136 Otherwise, a line containing the number C<1> is optional.
1138 Each disjunct is represented by a matrix of constraints.
1139 The first line contains two numbers representing
1140 the number of rows and columns,
1141 where the number of rows is equal to the number of constraints
1142 and the number of columns is equal to two plus the number of variables.
1143 The following lines contain the actual rows of the constraint matrix.
1144 In each row, the first column indicates whether the constraint
1145 is an equality (C<0>) or inequality (C<1>). The final column
1146 corresponds to the constant term.
1148 If the set is parametric, then the coefficients of the parameters
1149 appear in the last columns before the constant column.
1150 The coefficients of any existentially quantified variables appear
1151 between those of the set variables and those of the parameters.
1153 =head3 Extended C<PolyLib> format
1155 The extended C<PolyLib> format is nearly identical to the
1156 C<PolyLib> format. The only difference is that the line
1157 containing the number of rows and columns of a constraint matrix
1158 also contains four additional numbers:
1159 the number of output dimensions, the number of input dimensions,
1160 the number of local dimensions (i.e., the number of existentially
1161 quantified variables) and the number of parameters.
1162 For sets, the number of ``output'' dimensions is equal
1163 to the number of set dimensions, while the number of ``input''
1168 #include <isl/set.h>
1169 __isl_give isl_basic_set *isl_basic_set_read_from_file(
1170 isl_ctx *ctx, FILE *input);
1171 __isl_give isl_basic_set *isl_basic_set_read_from_str(
1172 isl_ctx *ctx, const char *str);
1173 __isl_give isl_set *isl_set_read_from_file(isl_ctx *ctx,
1175 __isl_give isl_set *isl_set_read_from_str(isl_ctx *ctx,
1178 #include <isl/map.h>
1179 __isl_give isl_basic_map *isl_basic_map_read_from_file(
1180 isl_ctx *ctx, FILE *input);
1181 __isl_give isl_basic_map *isl_basic_map_read_from_str(
1182 isl_ctx *ctx, const char *str);
1183 __isl_give isl_map *isl_map_read_from_file(
1184 isl_ctx *ctx, FILE *input);
1185 __isl_give isl_map *isl_map_read_from_str(isl_ctx *ctx,
1188 #include <isl/union_set.h>
1189 __isl_give isl_union_set *isl_union_set_read_from_file(
1190 isl_ctx *ctx, FILE *input);
1191 __isl_give isl_union_set *isl_union_set_read_from_str(
1192 isl_ctx *ctx, const char *str);
1194 #include <isl/union_map.h>
1195 __isl_give isl_union_map *isl_union_map_read_from_file(
1196 isl_ctx *ctx, FILE *input);
1197 __isl_give isl_union_map *isl_union_map_read_from_str(
1198 isl_ctx *ctx, const char *str);
1200 The input format is autodetected and may be either the C<PolyLib> format
1201 or the C<isl> format.
1205 Before anything can be printed, an C<isl_printer> needs to
1208 __isl_give isl_printer *isl_printer_to_file(isl_ctx *ctx,
1210 __isl_give isl_printer *isl_printer_to_str(isl_ctx *ctx);
1211 void *isl_printer_free(__isl_take isl_printer *printer);
1212 __isl_give char *isl_printer_get_str(
1213 __isl_keep isl_printer *printer);
1215 The printer can be inspected using the following functions.
1217 FILE *isl_printer_get_file(
1218 __isl_keep isl_printer *printer);
1219 int isl_printer_get_output_format(
1220 __isl_keep isl_printer *p);
1222 The behavior of the printer can be modified in various ways
1224 __isl_give isl_printer *isl_printer_set_output_format(
1225 __isl_take isl_printer *p, int output_format);
1226 __isl_give isl_printer *isl_printer_set_indent(
1227 __isl_take isl_printer *p, int indent);
1228 __isl_give isl_printer *isl_printer_indent(
1229 __isl_take isl_printer *p, int indent);
1230 __isl_give isl_printer *isl_printer_set_prefix(
1231 __isl_take isl_printer *p, const char *prefix);
1232 __isl_give isl_printer *isl_printer_set_suffix(
1233 __isl_take isl_printer *p, const char *suffix);
1235 The C<output_format> may be either C<ISL_FORMAT_ISL>, C<ISL_FORMAT_OMEGA>,
1236 C<ISL_FORMAT_POLYLIB>, C<ISL_FORMAT_EXT_POLYLIB> or C<ISL_FORMAT_LATEX>
1237 and defaults to C<ISL_FORMAT_ISL>.
1238 Each line in the output is indented by C<indent> (set by
1239 C<isl_printer_set_indent>) spaces
1240 (default: 0), prefixed by C<prefix> and suffixed by C<suffix>.
1241 In the C<PolyLib> format output,
1242 the coefficients of the existentially quantified variables
1243 appear between those of the set variables and those
1245 The function C<isl_printer_indent> increases the indentation
1246 by the specified amount (which may be negative).
1248 To actually print something, use
1250 #include <isl/printer.h>
1251 __isl_give isl_printer *isl_printer_print_double(
1252 __isl_take isl_printer *p, double d);
1254 #include <isl/set.h>
1255 __isl_give isl_printer *isl_printer_print_basic_set(
1256 __isl_take isl_printer *printer,
1257 __isl_keep isl_basic_set *bset);
1258 __isl_give isl_printer *isl_printer_print_set(
1259 __isl_take isl_printer *printer,
1260 __isl_keep isl_set *set);
1262 #include <isl/map.h>
1263 __isl_give isl_printer *isl_printer_print_basic_map(
1264 __isl_take isl_printer *printer,
1265 __isl_keep isl_basic_map *bmap);
1266 __isl_give isl_printer *isl_printer_print_map(
1267 __isl_take isl_printer *printer,
1268 __isl_keep isl_map *map);
1270 #include <isl/union_set.h>
1271 __isl_give isl_printer *isl_printer_print_union_set(
1272 __isl_take isl_printer *p,
1273 __isl_keep isl_union_set *uset);
1275 #include <isl/union_map.h>
1276 __isl_give isl_printer *isl_printer_print_union_map(
1277 __isl_take isl_printer *p,
1278 __isl_keep isl_union_map *umap);
1280 When called on a file printer, the following function flushes
1281 the file. When called on a string printer, the buffer is cleared.
1283 __isl_give isl_printer *isl_printer_flush(
1284 __isl_take isl_printer *p);
1286 =head2 Creating New Sets and Relations
1288 C<isl> has functions for creating some standard sets and relations.
1292 =item * Empty sets and relations
1294 __isl_give isl_basic_set *isl_basic_set_empty(
1295 __isl_take isl_space *space);
1296 __isl_give isl_basic_map *isl_basic_map_empty(
1297 __isl_take isl_space *space);
1298 __isl_give isl_set *isl_set_empty(
1299 __isl_take isl_space *space);
1300 __isl_give isl_map *isl_map_empty(
1301 __isl_take isl_space *space);
1302 __isl_give isl_union_set *isl_union_set_empty(
1303 __isl_take isl_space *space);
1304 __isl_give isl_union_map *isl_union_map_empty(
1305 __isl_take isl_space *space);
1307 For C<isl_union_set>s and C<isl_union_map>s, the space
1308 is only used to specify the parameters.
1310 =item * Universe sets and relations
1312 __isl_give isl_basic_set *isl_basic_set_universe(
1313 __isl_take isl_space *space);
1314 __isl_give isl_basic_map *isl_basic_map_universe(
1315 __isl_take isl_space *space);
1316 __isl_give isl_set *isl_set_universe(
1317 __isl_take isl_space *space);
1318 __isl_give isl_map *isl_map_universe(
1319 __isl_take isl_space *space);
1320 __isl_give isl_union_set *isl_union_set_universe(
1321 __isl_take isl_union_set *uset);
1322 __isl_give isl_union_map *isl_union_map_universe(
1323 __isl_take isl_union_map *umap);
1325 The sets and relations constructed by the functions above
1326 contain all integer values, while those constructed by the
1327 functions below only contain non-negative values.
1329 __isl_give isl_basic_set *isl_basic_set_nat_universe(
1330 __isl_take isl_space *space);
1331 __isl_give isl_basic_map *isl_basic_map_nat_universe(
1332 __isl_take isl_space *space);
1333 __isl_give isl_set *isl_set_nat_universe(
1334 __isl_take isl_space *space);
1335 __isl_give isl_map *isl_map_nat_universe(
1336 __isl_take isl_space *space);
1338 =item * Identity relations
1340 __isl_give isl_basic_map *isl_basic_map_identity(
1341 __isl_take isl_space *space);
1342 __isl_give isl_map *isl_map_identity(
1343 __isl_take isl_space *space);
1345 The number of input and output dimensions in C<space> needs
1348 =item * Lexicographic order
1350 __isl_give isl_map *isl_map_lex_lt(
1351 __isl_take isl_space *set_space);
1352 __isl_give isl_map *isl_map_lex_le(
1353 __isl_take isl_space *set_space);
1354 __isl_give isl_map *isl_map_lex_gt(
1355 __isl_take isl_space *set_space);
1356 __isl_give isl_map *isl_map_lex_ge(
1357 __isl_take isl_space *set_space);
1358 __isl_give isl_map *isl_map_lex_lt_first(
1359 __isl_take isl_space *space, unsigned n);
1360 __isl_give isl_map *isl_map_lex_le_first(
1361 __isl_take isl_space *space, unsigned n);
1362 __isl_give isl_map *isl_map_lex_gt_first(
1363 __isl_take isl_space *space, unsigned n);
1364 __isl_give isl_map *isl_map_lex_ge_first(
1365 __isl_take isl_space *space, unsigned n);
1367 The first four functions take a space for a B<set>
1368 and return relations that express that the elements in the domain
1369 are lexicographically less
1370 (C<isl_map_lex_lt>), less or equal (C<isl_map_lex_le>),
1371 greater (C<isl_map_lex_gt>) or greater or equal (C<isl_map_lex_ge>)
1372 than the elements in the range.
1373 The last four functions take a space for a map
1374 and return relations that express that the first C<n> dimensions
1375 in the domain are lexicographically less
1376 (C<isl_map_lex_lt_first>), less or equal (C<isl_map_lex_le_first>),
1377 greater (C<isl_map_lex_gt_first>) or greater or equal (C<isl_map_lex_ge_first>)
1378 than the first C<n> dimensions in the range.
1382 A basic set or relation can be converted to a set or relation
1383 using the following functions.
1385 __isl_give isl_set *isl_set_from_basic_set(
1386 __isl_take isl_basic_set *bset);
1387 __isl_give isl_map *isl_map_from_basic_map(
1388 __isl_take isl_basic_map *bmap);
1390 Sets and relations can be converted to union sets and relations
1391 using the following functions.
1393 __isl_give isl_union_set *isl_union_set_from_basic_set(
1394 __isl_take isl_basic_set *bset);
1395 __isl_give isl_union_map *isl_union_map_from_basic_map(
1396 __isl_take isl_basic_map *bmap);
1397 __isl_give isl_union_set *isl_union_set_from_set(
1398 __isl_take isl_set *set);
1399 __isl_give isl_union_map *isl_union_map_from_map(
1400 __isl_take isl_map *map);
1402 The inverse conversions below can only be used if the input
1403 union set or relation is known to contain elements in exactly one
1406 __isl_give isl_set *isl_set_from_union_set(
1407 __isl_take isl_union_set *uset);
1408 __isl_give isl_map *isl_map_from_union_map(
1409 __isl_take isl_union_map *umap);
1411 A zero-dimensional (basic) set can be constructed on a given parameter domain
1412 using the following function.
1414 __isl_give isl_basic_set *isl_basic_set_from_params(
1415 __isl_take isl_basic_set *bset);
1416 __isl_give isl_set *isl_set_from_params(
1417 __isl_take isl_set *set);
1419 Sets and relations can be copied and freed again using the following
1422 __isl_give isl_basic_set *isl_basic_set_copy(
1423 __isl_keep isl_basic_set *bset);
1424 __isl_give isl_set *isl_set_copy(__isl_keep isl_set *set);
1425 __isl_give isl_union_set *isl_union_set_copy(
1426 __isl_keep isl_union_set *uset);
1427 __isl_give isl_basic_map *isl_basic_map_copy(
1428 __isl_keep isl_basic_map *bmap);
1429 __isl_give isl_map *isl_map_copy(__isl_keep isl_map *map);
1430 __isl_give isl_union_map *isl_union_map_copy(
1431 __isl_keep isl_union_map *umap);
1432 void *isl_basic_set_free(__isl_take isl_basic_set *bset);
1433 void *isl_set_free(__isl_take isl_set *set);
1434 void *isl_union_set_free(__isl_take isl_union_set *uset);
1435 void *isl_basic_map_free(__isl_take isl_basic_map *bmap);
1436 void *isl_map_free(__isl_take isl_map *map);
1437 void *isl_union_map_free(__isl_take isl_union_map *umap);
1439 Other sets and relations can be constructed by starting
1440 from a universe set or relation, adding equality and/or
1441 inequality constraints and then projecting out the
1442 existentially quantified variables, if any.
1443 Constraints can be constructed, manipulated and
1444 added to (or removed from) (basic) sets and relations
1445 using the following functions.
1447 #include <isl/constraint.h>
1448 __isl_give isl_constraint *isl_equality_alloc(
1449 __isl_take isl_local_space *ls);
1450 __isl_give isl_constraint *isl_inequality_alloc(
1451 __isl_take isl_local_space *ls);
1452 __isl_give isl_constraint *isl_constraint_set_constant_si(
1453 __isl_take isl_constraint *constraint, int v);
1454 __isl_give isl_constraint *isl_constraint_set_constant_val(
1455 __isl_take isl_constraint *constraint,
1456 __isl_take isl_val *v);
1457 __isl_give isl_constraint *isl_constraint_set_coefficient_si(
1458 __isl_take isl_constraint *constraint,
1459 enum isl_dim_type type, int pos, int v);
1460 __isl_give isl_constraint *
1461 isl_constraint_set_coefficient_val(
1462 __isl_take isl_constraint *constraint,
1463 enum isl_dim_type type, int pos, isl_val *v);
1464 __isl_give isl_basic_map *isl_basic_map_add_constraint(
1465 __isl_take isl_basic_map *bmap,
1466 __isl_take isl_constraint *constraint);
1467 __isl_give isl_basic_set *isl_basic_set_add_constraint(
1468 __isl_take isl_basic_set *bset,
1469 __isl_take isl_constraint *constraint);
1470 __isl_give isl_map *isl_map_add_constraint(
1471 __isl_take isl_map *map,
1472 __isl_take isl_constraint *constraint);
1473 __isl_give isl_set *isl_set_add_constraint(
1474 __isl_take isl_set *set,
1475 __isl_take isl_constraint *constraint);
1476 __isl_give isl_basic_set *isl_basic_set_drop_constraint(
1477 __isl_take isl_basic_set *bset,
1478 __isl_take isl_constraint *constraint);
1480 For example, to create a set containing the even integers
1481 between 10 and 42, you would use the following code.
1484 isl_local_space *ls;
1486 isl_basic_set *bset;
1488 space = isl_space_set_alloc(ctx, 0, 2);
1489 bset = isl_basic_set_universe(isl_space_copy(space));
1490 ls = isl_local_space_from_space(space);
1492 c = isl_equality_alloc(isl_local_space_copy(ls));
1493 c = isl_constraint_set_coefficient_si(c, isl_dim_set, 0, -1);
1494 c = isl_constraint_set_coefficient_si(c, isl_dim_set, 1, 2);
1495 bset = isl_basic_set_add_constraint(bset, c);
1497 c = isl_inequality_alloc(isl_local_space_copy(ls));
1498 c = isl_constraint_set_constant_si(c, -10);
1499 c = isl_constraint_set_coefficient_si(c, isl_dim_set, 0, 1);
1500 bset = isl_basic_set_add_constraint(bset, c);
1502 c = isl_inequality_alloc(ls);
1503 c = isl_constraint_set_constant_si(c, 42);
1504 c = isl_constraint_set_coefficient_si(c, isl_dim_set, 0, -1);
1505 bset = isl_basic_set_add_constraint(bset, c);
1507 bset = isl_basic_set_project_out(bset, isl_dim_set, 1, 1);
1511 isl_basic_set *bset;
1512 bset = isl_basic_set_read_from_str(ctx,
1513 "{[i] : exists (a : i = 2a and i >= 10 and i <= 42)}");
1515 A basic set or relation can also be constructed from two matrices
1516 describing the equalities and the inequalities.
1518 __isl_give isl_basic_set *isl_basic_set_from_constraint_matrices(
1519 __isl_take isl_space *space,
1520 __isl_take isl_mat *eq, __isl_take isl_mat *ineq,
1521 enum isl_dim_type c1,
1522 enum isl_dim_type c2, enum isl_dim_type c3,
1523 enum isl_dim_type c4);
1524 __isl_give isl_basic_map *isl_basic_map_from_constraint_matrices(
1525 __isl_take isl_space *space,
1526 __isl_take isl_mat *eq, __isl_take isl_mat *ineq,
1527 enum isl_dim_type c1,
1528 enum isl_dim_type c2, enum isl_dim_type c3,
1529 enum isl_dim_type c4, enum isl_dim_type c5);
1531 The C<isl_dim_type> arguments indicate the order in which
1532 different kinds of variables appear in the input matrices
1533 and should be a permutation of C<isl_dim_cst>, C<isl_dim_param>,
1534 C<isl_dim_set> and C<isl_dim_div> for sets and
1535 of C<isl_dim_cst>, C<isl_dim_param>,
1536 C<isl_dim_in>, C<isl_dim_out> and C<isl_dim_div> for relations.
1538 A (basic or union) set or relation can also be constructed from a
1539 (union) (piecewise) (multiple) affine expression
1540 or a list of affine expressions
1541 (See L<"Piecewise Quasi Affine Expressions"> and
1542 L<"Piecewise Multiple Quasi Affine Expressions">).
1544 __isl_give isl_basic_map *isl_basic_map_from_aff(
1545 __isl_take isl_aff *aff);
1546 __isl_give isl_map *isl_map_from_aff(
1547 __isl_take isl_aff *aff);
1548 __isl_give isl_set *isl_set_from_pw_aff(
1549 __isl_take isl_pw_aff *pwaff);
1550 __isl_give isl_map *isl_map_from_pw_aff(
1551 __isl_take isl_pw_aff *pwaff);
1552 __isl_give isl_basic_map *isl_basic_map_from_aff_list(
1553 __isl_take isl_space *domain_space,
1554 __isl_take isl_aff_list *list);
1555 __isl_give isl_basic_map *isl_basic_map_from_multi_aff(
1556 __isl_take isl_multi_aff *maff)
1557 __isl_give isl_map *isl_map_from_multi_aff(
1558 __isl_take isl_multi_aff *maff)
1559 __isl_give isl_set *isl_set_from_pw_multi_aff(
1560 __isl_take isl_pw_multi_aff *pma);
1561 __isl_give isl_map *isl_map_from_pw_multi_aff(
1562 __isl_take isl_pw_multi_aff *pma);
1563 __isl_give isl_set *isl_set_from_multi_pw_aff(
1564 __isl_take isl_multi_pw_aff *mpa);
1565 __isl_give isl_map *isl_map_from_multi_pw_aff(
1566 __isl_take isl_multi_pw_aff *mpa);
1567 __isl_give isl_union_map *
1568 isl_union_map_from_union_pw_multi_aff(
1569 __isl_take isl_union_pw_multi_aff *upma);
1571 The C<domain_dim> argument describes the domain of the resulting
1572 basic relation. It is required because the C<list> may consist
1573 of zero affine expressions.
1575 =head2 Inspecting Sets and Relations
1577 Usually, the user should not have to care about the actual constraints
1578 of the sets and maps, but should instead apply the abstract operations
1579 explained in the following sections.
1580 Occasionally, however, it may be required to inspect the individual
1581 coefficients of the constraints. This section explains how to do so.
1582 In these cases, it may also be useful to have C<isl> compute
1583 an explicit representation of the existentially quantified variables.
1585 __isl_give isl_set *isl_set_compute_divs(
1586 __isl_take isl_set *set);
1587 __isl_give isl_map *isl_map_compute_divs(
1588 __isl_take isl_map *map);
1589 __isl_give isl_union_set *isl_union_set_compute_divs(
1590 __isl_take isl_union_set *uset);
1591 __isl_give isl_union_map *isl_union_map_compute_divs(
1592 __isl_take isl_union_map *umap);
1594 This explicit representation defines the existentially quantified
1595 variables as integer divisions of the other variables, possibly
1596 including earlier existentially quantified variables.
1597 An explicitly represented existentially quantified variable therefore
1598 has a unique value when the values of the other variables are known.
1599 If, furthermore, the same existentials, i.e., existentials
1600 with the same explicit representations, should appear in the
1601 same order in each of the disjuncts of a set or map, then the user should call
1602 either of the following functions.
1604 __isl_give isl_set *isl_set_align_divs(
1605 __isl_take isl_set *set);
1606 __isl_give isl_map *isl_map_align_divs(
1607 __isl_take isl_map *map);
1609 Alternatively, the existentially quantified variables can be removed
1610 using the following functions, which compute an overapproximation.
1612 __isl_give isl_basic_set *isl_basic_set_remove_divs(
1613 __isl_take isl_basic_set *bset);
1614 __isl_give isl_basic_map *isl_basic_map_remove_divs(
1615 __isl_take isl_basic_map *bmap);
1616 __isl_give isl_set *isl_set_remove_divs(
1617 __isl_take isl_set *set);
1618 __isl_give isl_map *isl_map_remove_divs(
1619 __isl_take isl_map *map);
1621 It is also possible to only remove those divs that are defined
1622 in terms of a given range of dimensions or only those for which
1623 no explicit representation is known.
1625 __isl_give isl_basic_set *
1626 isl_basic_set_remove_divs_involving_dims(
1627 __isl_take isl_basic_set *bset,
1628 enum isl_dim_type type,
1629 unsigned first, unsigned n);
1630 __isl_give isl_basic_map *
1631 isl_basic_map_remove_divs_involving_dims(
1632 __isl_take isl_basic_map *bmap,
1633 enum isl_dim_type type,
1634 unsigned first, unsigned n);
1635 __isl_give isl_set *isl_set_remove_divs_involving_dims(
1636 __isl_take isl_set *set, enum isl_dim_type type,
1637 unsigned first, unsigned n);
1638 __isl_give isl_map *isl_map_remove_divs_involving_dims(
1639 __isl_take isl_map *map, enum isl_dim_type type,
1640 unsigned first, unsigned n);
1642 __isl_give isl_basic_set *
1643 isl_basic_set_remove_unknown_divs(
1644 __isl_take isl_basic_set *bset);
1645 __isl_give isl_set *isl_set_remove_unknown_divs(
1646 __isl_take isl_set *set);
1647 __isl_give isl_map *isl_map_remove_unknown_divs(
1648 __isl_take isl_map *map);
1650 To iterate over all the sets or maps in a union set or map, use
1652 int isl_union_set_foreach_set(__isl_keep isl_union_set *uset,
1653 int (*fn)(__isl_take isl_set *set, void *user),
1655 int isl_union_map_foreach_map(__isl_keep isl_union_map *umap,
1656 int (*fn)(__isl_take isl_map *map, void *user),
1659 The number of sets or maps in a union set or map can be obtained
1662 int isl_union_set_n_set(__isl_keep isl_union_set *uset);
1663 int isl_union_map_n_map(__isl_keep isl_union_map *umap);
1665 To extract the set or map in a given space from a union, use
1667 __isl_give isl_set *isl_union_set_extract_set(
1668 __isl_keep isl_union_set *uset,
1669 __isl_take isl_space *space);
1670 __isl_give isl_map *isl_union_map_extract_map(
1671 __isl_keep isl_union_map *umap,
1672 __isl_take isl_space *space);
1674 To iterate over all the basic sets or maps in a set or map, use
1676 int isl_set_foreach_basic_set(__isl_keep isl_set *set,
1677 int (*fn)(__isl_take isl_basic_set *bset, void *user),
1679 int isl_map_foreach_basic_map(__isl_keep isl_map *map,
1680 int (*fn)(__isl_take isl_basic_map *bmap, void *user),
1683 The callback function C<fn> should return 0 if successful and
1684 -1 if an error occurs. In the latter case, or if any other error
1685 occurs, the above functions will return -1.
1687 It should be noted that C<isl> does not guarantee that
1688 the basic sets or maps passed to C<fn> are disjoint.
1689 If this is required, then the user should call one of
1690 the following functions first.
1692 __isl_give isl_set *isl_set_make_disjoint(
1693 __isl_take isl_set *set);
1694 __isl_give isl_map *isl_map_make_disjoint(
1695 __isl_take isl_map *map);
1697 The number of basic sets in a set can be obtained
1700 int isl_set_n_basic_set(__isl_keep isl_set *set);
1702 To iterate over the constraints of a basic set or map, use
1704 #include <isl/constraint.h>
1706 int isl_basic_set_n_constraint(
1707 __isl_keep isl_basic_set *bset);
1708 int isl_basic_set_foreach_constraint(
1709 __isl_keep isl_basic_set *bset,
1710 int (*fn)(__isl_take isl_constraint *c, void *user),
1712 int isl_basic_map_foreach_constraint(
1713 __isl_keep isl_basic_map *bmap,
1714 int (*fn)(__isl_take isl_constraint *c, void *user),
1716 void *isl_constraint_free(__isl_take isl_constraint *c);
1718 Again, the callback function C<fn> should return 0 if successful and
1719 -1 if an error occurs. In the latter case, or if any other error
1720 occurs, the above functions will return -1.
1721 The constraint C<c> represents either an equality or an inequality.
1722 Use the following function to find out whether a constraint
1723 represents an equality. If not, it represents an inequality.
1725 int isl_constraint_is_equality(
1726 __isl_keep isl_constraint *constraint);
1728 The coefficients of the constraints can be inspected using
1729 the following functions.
1731 int isl_constraint_is_lower_bound(
1732 __isl_keep isl_constraint *constraint,
1733 enum isl_dim_type type, unsigned pos);
1734 int isl_constraint_is_upper_bound(
1735 __isl_keep isl_constraint *constraint,
1736 enum isl_dim_type type, unsigned pos);
1737 __isl_give isl_val *isl_constraint_get_constant_val(
1738 __isl_keep isl_constraint *constraint);
1739 __isl_give isl_val *isl_constraint_get_coefficient_val(
1740 __isl_keep isl_constraint *constraint,
1741 enum isl_dim_type type, int pos);
1742 int isl_constraint_involves_dims(
1743 __isl_keep isl_constraint *constraint,
1744 enum isl_dim_type type, unsigned first, unsigned n);
1746 The explicit representations of the existentially quantified
1747 variables can be inspected using the following function.
1748 Note that the user is only allowed to use this function
1749 if the inspected set or map is the result of a call
1750 to C<isl_set_compute_divs> or C<isl_map_compute_divs>.
1751 The existentially quantified variable is equal to the floor
1752 of the returned affine expression. The affine expression
1753 itself can be inspected using the functions in
1754 L<"Piecewise Quasi Affine Expressions">.
1756 __isl_give isl_aff *isl_constraint_get_div(
1757 __isl_keep isl_constraint *constraint, int pos);
1759 To obtain the constraints of a basic set or map in matrix
1760 form, use the following functions.
1762 __isl_give isl_mat *isl_basic_set_equalities_matrix(
1763 __isl_keep isl_basic_set *bset,
1764 enum isl_dim_type c1, enum isl_dim_type c2,
1765 enum isl_dim_type c3, enum isl_dim_type c4);
1766 __isl_give isl_mat *isl_basic_set_inequalities_matrix(
1767 __isl_keep isl_basic_set *bset,
1768 enum isl_dim_type c1, enum isl_dim_type c2,
1769 enum isl_dim_type c3, enum isl_dim_type c4);
1770 __isl_give isl_mat *isl_basic_map_equalities_matrix(
1771 __isl_keep isl_basic_map *bmap,
1772 enum isl_dim_type c1,
1773 enum isl_dim_type c2, enum isl_dim_type c3,
1774 enum isl_dim_type c4, enum isl_dim_type c5);
1775 __isl_give isl_mat *isl_basic_map_inequalities_matrix(
1776 __isl_keep isl_basic_map *bmap,
1777 enum isl_dim_type c1,
1778 enum isl_dim_type c2, enum isl_dim_type c3,
1779 enum isl_dim_type c4, enum isl_dim_type c5);
1781 The C<isl_dim_type> arguments dictate the order in which
1782 different kinds of variables appear in the resulting matrix
1783 and should be a permutation of C<isl_dim_cst>, C<isl_dim_param>,
1784 C<isl_dim_in>, C<isl_dim_out> and C<isl_dim_div>.
1786 The number of parameters, input, output or set dimensions can
1787 be obtained using the following functions.
1789 unsigned isl_basic_set_dim(__isl_keep isl_basic_set *bset,
1790 enum isl_dim_type type);
1791 unsigned isl_basic_map_dim(__isl_keep isl_basic_map *bmap,
1792 enum isl_dim_type type);
1793 unsigned isl_set_dim(__isl_keep isl_set *set,
1794 enum isl_dim_type type);
1795 unsigned isl_map_dim(__isl_keep isl_map *map,
1796 enum isl_dim_type type);
1798 To check whether the description of a set or relation depends
1799 on one or more given dimensions, it is not necessary to iterate over all
1800 constraints. Instead the following functions can be used.
1802 int isl_basic_set_involves_dims(
1803 __isl_keep isl_basic_set *bset,
1804 enum isl_dim_type type, unsigned first, unsigned n);
1805 int isl_set_involves_dims(__isl_keep isl_set *set,
1806 enum isl_dim_type type, unsigned first, unsigned n);
1807 int isl_basic_map_involves_dims(
1808 __isl_keep isl_basic_map *bmap,
1809 enum isl_dim_type type, unsigned first, unsigned n);
1810 int isl_map_involves_dims(__isl_keep isl_map *map,
1811 enum isl_dim_type type, unsigned first, unsigned n);
1813 Similarly, the following functions can be used to check whether
1814 a given dimension is involved in any lower or upper bound.
1816 int isl_set_dim_has_any_lower_bound(__isl_keep isl_set *set,
1817 enum isl_dim_type type, unsigned pos);
1818 int isl_set_dim_has_any_upper_bound(__isl_keep isl_set *set,
1819 enum isl_dim_type type, unsigned pos);
1821 Note that these functions return true even if there is a bound on
1822 the dimension on only some of the basic sets of C<set>.
1823 To check if they have a bound for all of the basic sets in C<set>,
1824 use the following functions instead.
1826 int isl_set_dim_has_lower_bound(__isl_keep isl_set *set,
1827 enum isl_dim_type type, unsigned pos);
1828 int isl_set_dim_has_upper_bound(__isl_keep isl_set *set,
1829 enum isl_dim_type type, unsigned pos);
1831 The identifiers or names of the domain and range spaces of a set
1832 or relation can be read off or set using the following functions.
1834 __isl_give isl_basic_set *isl_basic_set_set_tuple_id(
1835 __isl_take isl_basic_set *bset,
1836 __isl_take isl_id *id);
1837 __isl_give isl_set *isl_set_set_tuple_id(
1838 __isl_take isl_set *set, __isl_take isl_id *id);
1839 __isl_give isl_set *isl_set_reset_tuple_id(
1840 __isl_take isl_set *set);
1841 int isl_set_has_tuple_id(__isl_keep isl_set *set);
1842 __isl_give isl_id *isl_set_get_tuple_id(
1843 __isl_keep isl_set *set);
1844 __isl_give isl_basic_map *isl_basic_map_set_tuple_id(
1845 __isl_take isl_basic_map *bmap,
1846 enum isl_dim_type type, __isl_take isl_id *id);
1847 __isl_give isl_map *isl_map_set_tuple_id(
1848 __isl_take isl_map *map, enum isl_dim_type type,
1849 __isl_take isl_id *id);
1850 __isl_give isl_map *isl_map_reset_tuple_id(
1851 __isl_take isl_map *map, enum isl_dim_type type);
1852 int isl_map_has_tuple_id(__isl_keep isl_map *map,
1853 enum isl_dim_type type);
1854 __isl_give isl_id *isl_map_get_tuple_id(
1855 __isl_keep isl_map *map, enum isl_dim_type type);
1857 const char *isl_basic_set_get_tuple_name(
1858 __isl_keep isl_basic_set *bset);
1859 __isl_give isl_basic_set *isl_basic_set_set_tuple_name(
1860 __isl_take isl_basic_set *set, const char *s);
1861 int isl_set_has_tuple_name(__isl_keep isl_set *set);
1862 const char *isl_set_get_tuple_name(
1863 __isl_keep isl_set *set);
1864 const char *isl_basic_map_get_tuple_name(
1865 __isl_keep isl_basic_map *bmap,
1866 enum isl_dim_type type);
1867 __isl_give isl_basic_map *isl_basic_map_set_tuple_name(
1868 __isl_take isl_basic_map *bmap,
1869 enum isl_dim_type type, const char *s);
1870 int isl_map_has_tuple_name(__isl_keep isl_map *map,
1871 enum isl_dim_type type);
1872 const char *isl_map_get_tuple_name(
1873 __isl_keep isl_map *map,
1874 enum isl_dim_type type);
1876 As with C<isl_space_get_tuple_name>, the value returned points to
1877 an internal data structure.
1878 The identifiers, positions or names of individual dimensions can be
1879 read off using the following functions.
1881 __isl_give isl_id *isl_basic_set_get_dim_id(
1882 __isl_keep isl_basic_set *bset,
1883 enum isl_dim_type type, unsigned pos);
1884 __isl_give isl_set *isl_set_set_dim_id(
1885 __isl_take isl_set *set, enum isl_dim_type type,
1886 unsigned pos, __isl_take isl_id *id);
1887 int isl_set_has_dim_id(__isl_keep isl_set *set,
1888 enum isl_dim_type type, unsigned pos);
1889 __isl_give isl_id *isl_set_get_dim_id(
1890 __isl_keep isl_set *set, enum isl_dim_type type,
1892 int isl_basic_map_has_dim_id(
1893 __isl_keep isl_basic_map *bmap,
1894 enum isl_dim_type type, unsigned pos);
1895 __isl_give isl_map *isl_map_set_dim_id(
1896 __isl_take isl_map *map, enum isl_dim_type type,
1897 unsigned pos, __isl_take isl_id *id);
1898 int isl_map_has_dim_id(__isl_keep isl_map *map,
1899 enum isl_dim_type type, unsigned pos);
1900 __isl_give isl_id *isl_map_get_dim_id(
1901 __isl_keep isl_map *map, enum isl_dim_type type,
1904 int isl_set_find_dim_by_id(__isl_keep isl_set *set,
1905 enum isl_dim_type type, __isl_keep isl_id *id);
1906 int isl_map_find_dim_by_id(__isl_keep isl_map *map,
1907 enum isl_dim_type type, __isl_keep isl_id *id);
1908 int isl_set_find_dim_by_name(__isl_keep isl_set *set,
1909 enum isl_dim_type type, const char *name);
1910 int isl_map_find_dim_by_name(__isl_keep isl_map *map,
1911 enum isl_dim_type type, const char *name);
1913 const char *isl_constraint_get_dim_name(
1914 __isl_keep isl_constraint *constraint,
1915 enum isl_dim_type type, unsigned pos);
1916 const char *isl_basic_set_get_dim_name(
1917 __isl_keep isl_basic_set *bset,
1918 enum isl_dim_type type, unsigned pos);
1919 int isl_set_has_dim_name(__isl_keep isl_set *set,
1920 enum isl_dim_type type, unsigned pos);
1921 const char *isl_set_get_dim_name(
1922 __isl_keep isl_set *set,
1923 enum isl_dim_type type, unsigned pos);
1924 const char *isl_basic_map_get_dim_name(
1925 __isl_keep isl_basic_map *bmap,
1926 enum isl_dim_type type, unsigned pos);
1927 int isl_map_has_dim_name(__isl_keep isl_map *map,
1928 enum isl_dim_type type, unsigned pos);
1929 const char *isl_map_get_dim_name(
1930 __isl_keep isl_map *map,
1931 enum isl_dim_type type, unsigned pos);
1933 These functions are mostly useful to obtain the identifiers, positions
1934 or names of the parameters. Identifiers of individual dimensions are
1935 essentially only useful for printing. They are ignored by all other
1936 operations and may not be preserved across those operations.
1938 The user pointers on all parameters and tuples can be reset
1939 using the following functions.
1941 __isl_give isl_set *isl_set_reset_user(
1942 __isl_take isl_set *set);
1943 __isl_give isl_map *isl_map_reset_user(
1944 __isl_take isl_map *map);
1948 =head3 Unary Properties
1954 The following functions test whether the given set or relation
1955 contains any integer points. The ``plain'' variants do not perform
1956 any computations, but simply check if the given set or relation
1957 is already known to be empty.
1959 int isl_basic_set_plain_is_empty(__isl_keep isl_basic_set *bset);
1960 int isl_basic_set_is_empty(__isl_keep isl_basic_set *bset);
1961 int isl_set_plain_is_empty(__isl_keep isl_set *set);
1962 int isl_set_is_empty(__isl_keep isl_set *set);
1963 int isl_union_set_is_empty(__isl_keep isl_union_set *uset);
1964 int isl_basic_map_plain_is_empty(__isl_keep isl_basic_map *bmap);
1965 int isl_basic_map_is_empty(__isl_keep isl_basic_map *bmap);
1966 int isl_map_plain_is_empty(__isl_keep isl_map *map);
1967 int isl_map_is_empty(__isl_keep isl_map *map);
1968 int isl_union_map_is_empty(__isl_keep isl_union_map *umap);
1970 =item * Universality
1972 int isl_basic_set_is_universe(__isl_keep isl_basic_set *bset);
1973 int isl_basic_map_is_universe(__isl_keep isl_basic_map *bmap);
1974 int isl_set_plain_is_universe(__isl_keep isl_set *set);
1976 =item * Single-valuedness
1978 int isl_basic_map_is_single_valued(
1979 __isl_keep isl_basic_map *bmap);
1980 int isl_map_plain_is_single_valued(
1981 __isl_keep isl_map *map);
1982 int isl_map_is_single_valued(__isl_keep isl_map *map);
1983 int isl_union_map_is_single_valued(__isl_keep isl_union_map *umap);
1987 int isl_map_plain_is_injective(__isl_keep isl_map *map);
1988 int isl_map_is_injective(__isl_keep isl_map *map);
1989 int isl_union_map_plain_is_injective(
1990 __isl_keep isl_union_map *umap);
1991 int isl_union_map_is_injective(
1992 __isl_keep isl_union_map *umap);
1996 int isl_map_is_bijective(__isl_keep isl_map *map);
1997 int isl_union_map_is_bijective(__isl_keep isl_union_map *umap);
2001 __isl_give isl_val *
2002 isl_basic_map_plain_get_val_if_fixed(
2003 __isl_keep isl_basic_map *bmap,
2004 enum isl_dim_type type, unsigned pos);
2005 __isl_give isl_val *isl_set_plain_get_val_if_fixed(
2006 __isl_keep isl_set *set,
2007 enum isl_dim_type type, unsigned pos);
2008 __isl_give isl_val *isl_map_plain_get_val_if_fixed(
2009 __isl_keep isl_map *map,
2010 enum isl_dim_type type, unsigned pos);
2012 If the set or relation obviously lies on a hyperplane where the given dimension
2013 has a fixed value, then return that value.
2014 Otherwise return NaN.
2018 int isl_set_dim_residue_class_val(
2019 __isl_keep isl_set *set,
2020 int pos, __isl_give isl_val **modulo,
2021 __isl_give isl_val **residue);
2023 Check if the values of the given set dimension are equal to a fixed
2024 value modulo some integer value. If so, assign the modulo to C<*modulo>
2025 and the fixed value to C<*residue>. If the given dimension attains only
2026 a single value, then assign C<0> to C<*modulo> and the fixed value to
2028 If the dimension does not attain only a single value and if no modulo
2029 can be found then assign C<1> to C<*modulo> and C<1> to C<*residue>.
2033 To check whether a set is a parameter domain, use this function:
2035 int isl_set_is_params(__isl_keep isl_set *set);
2036 int isl_union_set_is_params(
2037 __isl_keep isl_union_set *uset);
2041 The following functions check whether the space of the given
2042 (basic) set or relation range is a wrapped relation.
2044 int isl_basic_set_is_wrapping(
2045 __isl_keep isl_basic_set *bset);
2046 int isl_set_is_wrapping(__isl_keep isl_set *set);
2047 int isl_map_range_is_wrapping(
2048 __isl_keep isl_map *map);
2050 =item * Internal Product
2052 int isl_basic_map_can_zip(
2053 __isl_keep isl_basic_map *bmap);
2054 int isl_map_can_zip(__isl_keep isl_map *map);
2056 Check whether the product of domain and range of the given relation
2058 i.e., whether both domain and range are nested relations.
2062 int isl_basic_map_can_curry(
2063 __isl_keep isl_basic_map *bmap);
2064 int isl_map_can_curry(__isl_keep isl_map *map);
2066 Check whether the domain of the (basic) relation is a wrapped relation.
2068 int isl_basic_map_can_uncurry(
2069 __isl_keep isl_basic_map *bmap);
2070 int isl_map_can_uncurry(__isl_keep isl_map *map);
2072 Check whether the range of the (basic) relation is a wrapped relation.
2076 =head3 Binary Properties
2082 int isl_basic_set_plain_is_equal(
2083 __isl_keep isl_basic_set *bset1,
2084 __isl_keep isl_basic_set *bset2);
2085 int isl_set_plain_is_equal(__isl_keep isl_set *set1,
2086 __isl_keep isl_set *set2);
2087 int isl_set_is_equal(__isl_keep isl_set *set1,
2088 __isl_keep isl_set *set2);
2089 int isl_union_set_is_equal(
2090 __isl_keep isl_union_set *uset1,
2091 __isl_keep isl_union_set *uset2);
2092 int isl_basic_map_is_equal(
2093 __isl_keep isl_basic_map *bmap1,
2094 __isl_keep isl_basic_map *bmap2);
2095 int isl_map_is_equal(__isl_keep isl_map *map1,
2096 __isl_keep isl_map *map2);
2097 int isl_map_plain_is_equal(__isl_keep isl_map *map1,
2098 __isl_keep isl_map *map2);
2099 int isl_union_map_is_equal(
2100 __isl_keep isl_union_map *umap1,
2101 __isl_keep isl_union_map *umap2);
2103 =item * Disjointness
2105 int isl_basic_set_is_disjoint(
2106 __isl_keep isl_basic_set *bset1,
2107 __isl_keep isl_basic_set *bset2);
2108 int isl_set_plain_is_disjoint(__isl_keep isl_set *set1,
2109 __isl_keep isl_set *set2);
2110 int isl_set_is_disjoint(__isl_keep isl_set *set1,
2111 __isl_keep isl_set *set2);
2112 int isl_basic_map_is_disjoint(
2113 __isl_keep isl_basic_map *bmap1,
2114 __isl_keep isl_basic_map *bmap2);
2115 int isl_map_is_disjoint(__isl_keep isl_map *map1,
2116 __isl_keep isl_map *map2);
2120 int isl_basic_set_is_subset(
2121 __isl_keep isl_basic_set *bset1,
2122 __isl_keep isl_basic_set *bset2);
2123 int isl_set_is_subset(__isl_keep isl_set *set1,
2124 __isl_keep isl_set *set2);
2125 int isl_set_is_strict_subset(
2126 __isl_keep isl_set *set1,
2127 __isl_keep isl_set *set2);
2128 int isl_union_set_is_subset(
2129 __isl_keep isl_union_set *uset1,
2130 __isl_keep isl_union_set *uset2);
2131 int isl_union_set_is_strict_subset(
2132 __isl_keep isl_union_set *uset1,
2133 __isl_keep isl_union_set *uset2);
2134 int isl_basic_map_is_subset(
2135 __isl_keep isl_basic_map *bmap1,
2136 __isl_keep isl_basic_map *bmap2);
2137 int isl_basic_map_is_strict_subset(
2138 __isl_keep isl_basic_map *bmap1,
2139 __isl_keep isl_basic_map *bmap2);
2140 int isl_map_is_subset(
2141 __isl_keep isl_map *map1,
2142 __isl_keep isl_map *map2);
2143 int isl_map_is_strict_subset(
2144 __isl_keep isl_map *map1,
2145 __isl_keep isl_map *map2);
2146 int isl_union_map_is_subset(
2147 __isl_keep isl_union_map *umap1,
2148 __isl_keep isl_union_map *umap2);
2149 int isl_union_map_is_strict_subset(
2150 __isl_keep isl_union_map *umap1,
2151 __isl_keep isl_union_map *umap2);
2153 Check whether the first argument is a (strict) subset of the
2158 int isl_set_plain_cmp(__isl_keep isl_set *set1,
2159 __isl_keep isl_set *set2);
2161 This function is useful for sorting C<isl_set>s.
2162 The order depends on the internal representation of the inputs.
2163 The order is fixed over different calls to the function (assuming
2164 the internal representation of the inputs has not changed), but may
2165 change over different versions of C<isl>.
2169 =head2 Unary Operations
2175 __isl_give isl_set *isl_set_complement(
2176 __isl_take isl_set *set);
2177 __isl_give isl_map *isl_map_complement(
2178 __isl_take isl_map *map);
2182 __isl_give isl_basic_map *isl_basic_map_reverse(
2183 __isl_take isl_basic_map *bmap);
2184 __isl_give isl_map *isl_map_reverse(
2185 __isl_take isl_map *map);
2186 __isl_give isl_union_map *isl_union_map_reverse(
2187 __isl_take isl_union_map *umap);
2191 __isl_give isl_basic_set *isl_basic_set_project_out(
2192 __isl_take isl_basic_set *bset,
2193 enum isl_dim_type type, unsigned first, unsigned n);
2194 __isl_give isl_basic_map *isl_basic_map_project_out(
2195 __isl_take isl_basic_map *bmap,
2196 enum isl_dim_type type, unsigned first, unsigned n);
2197 __isl_give isl_set *isl_set_project_out(__isl_take isl_set *set,
2198 enum isl_dim_type type, unsigned first, unsigned n);
2199 __isl_give isl_map *isl_map_project_out(__isl_take isl_map *map,
2200 enum isl_dim_type type, unsigned first, unsigned n);
2201 __isl_give isl_basic_set *isl_basic_set_params(
2202 __isl_take isl_basic_set *bset);
2203 __isl_give isl_basic_set *isl_basic_map_domain(
2204 __isl_take isl_basic_map *bmap);
2205 __isl_give isl_basic_set *isl_basic_map_range(
2206 __isl_take isl_basic_map *bmap);
2207 __isl_give isl_set *isl_set_params(__isl_take isl_set *set);
2208 __isl_give isl_set *isl_map_params(__isl_take isl_map *map);
2209 __isl_give isl_set *isl_map_domain(
2210 __isl_take isl_map *bmap);
2211 __isl_give isl_set *isl_map_range(
2212 __isl_take isl_map *map);
2213 __isl_give isl_set *isl_union_set_params(
2214 __isl_take isl_union_set *uset);
2215 __isl_give isl_set *isl_union_map_params(
2216 __isl_take isl_union_map *umap);
2217 __isl_give isl_union_set *isl_union_map_domain(
2218 __isl_take isl_union_map *umap);
2219 __isl_give isl_union_set *isl_union_map_range(
2220 __isl_take isl_union_map *umap);
2222 __isl_give isl_basic_map *isl_basic_map_domain_map(
2223 __isl_take isl_basic_map *bmap);
2224 __isl_give isl_basic_map *isl_basic_map_range_map(
2225 __isl_take isl_basic_map *bmap);
2226 __isl_give isl_map *isl_map_domain_map(__isl_take isl_map *map);
2227 __isl_give isl_map *isl_map_range_map(__isl_take isl_map *map);
2228 __isl_give isl_union_map *isl_union_map_domain_map(
2229 __isl_take isl_union_map *umap);
2230 __isl_give isl_union_map *isl_union_map_range_map(
2231 __isl_take isl_union_map *umap);
2233 The functions above construct a (basic, regular or union) relation
2234 that maps (a wrapped version of) the input relation to its domain or range.
2238 __isl_give isl_basic_set *isl_basic_set_eliminate(
2239 __isl_take isl_basic_set *bset,
2240 enum isl_dim_type type,
2241 unsigned first, unsigned n);
2242 __isl_give isl_set *isl_set_eliminate(
2243 __isl_take isl_set *set, enum isl_dim_type type,
2244 unsigned first, unsigned n);
2245 __isl_give isl_basic_map *isl_basic_map_eliminate(
2246 __isl_take isl_basic_map *bmap,
2247 enum isl_dim_type type,
2248 unsigned first, unsigned n);
2249 __isl_give isl_map *isl_map_eliminate(
2250 __isl_take isl_map *map, enum isl_dim_type type,
2251 unsigned first, unsigned n);
2253 Eliminate the coefficients for the given dimensions from the constraints,
2254 without removing the dimensions.
2258 __isl_give isl_basic_set *isl_basic_set_fix_si(
2259 __isl_take isl_basic_set *bset,
2260 enum isl_dim_type type, unsigned pos, int value);
2261 __isl_give isl_basic_set *isl_basic_set_fix_val(
2262 __isl_take isl_basic_set *bset,
2263 enum isl_dim_type type, unsigned pos,
2264 __isl_take isl_val *v);
2265 __isl_give isl_set *isl_set_fix_si(__isl_take isl_set *set,
2266 enum isl_dim_type type, unsigned pos, int value);
2267 __isl_give isl_set *isl_set_fix_val(
2268 __isl_take isl_set *set,
2269 enum isl_dim_type type, unsigned pos,
2270 __isl_take isl_val *v);
2271 __isl_give isl_basic_map *isl_basic_map_fix_si(
2272 __isl_take isl_basic_map *bmap,
2273 enum isl_dim_type type, unsigned pos, int value);
2274 __isl_give isl_basic_map *isl_basic_map_fix_val(
2275 __isl_take isl_basic_map *bmap,
2276 enum isl_dim_type type, unsigned pos,
2277 __isl_take isl_val *v);
2278 __isl_give isl_map *isl_map_fix_si(__isl_take isl_map *map,
2279 enum isl_dim_type type, unsigned pos, int value);
2280 __isl_give isl_map *isl_map_fix_val(
2281 __isl_take isl_map *map,
2282 enum isl_dim_type type, unsigned pos,
2283 __isl_take isl_val *v);
2285 Intersect the set or relation with the hyperplane where the given
2286 dimension has the fixed given value.
2288 __isl_give isl_basic_map *isl_basic_map_lower_bound_si(
2289 __isl_take isl_basic_map *bmap,
2290 enum isl_dim_type type, unsigned pos, int value);
2291 __isl_give isl_basic_map *isl_basic_map_upper_bound_si(
2292 __isl_take isl_basic_map *bmap,
2293 enum isl_dim_type type, unsigned pos, int value);
2294 __isl_give isl_set *isl_set_lower_bound_si(
2295 __isl_take isl_set *set,
2296 enum isl_dim_type type, unsigned pos, int value);
2297 __isl_give isl_set *isl_set_lower_bound_val(
2298 __isl_take isl_set *set,
2299 enum isl_dim_type type, unsigned pos,
2300 __isl_take isl_val *value);
2301 __isl_give isl_map *isl_map_lower_bound_si(
2302 __isl_take isl_map *map,
2303 enum isl_dim_type type, unsigned pos, int value);
2304 __isl_give isl_set *isl_set_upper_bound_si(
2305 __isl_take isl_set *set,
2306 enum isl_dim_type type, unsigned pos, int value);
2307 __isl_give isl_set *isl_set_upper_bound_val(
2308 __isl_take isl_set *set,
2309 enum isl_dim_type type, unsigned pos,
2310 __isl_take isl_val *value);
2311 __isl_give isl_map *isl_map_upper_bound_si(
2312 __isl_take isl_map *map,
2313 enum isl_dim_type type, unsigned pos, int value);
2315 Intersect the set or relation with the half-space where the given
2316 dimension has a value bounded by the fixed given integer value.
2318 __isl_give isl_set *isl_set_equate(__isl_take isl_set *set,
2319 enum isl_dim_type type1, int pos1,
2320 enum isl_dim_type type2, int pos2);
2321 __isl_give isl_basic_map *isl_basic_map_equate(
2322 __isl_take isl_basic_map *bmap,
2323 enum isl_dim_type type1, int pos1,
2324 enum isl_dim_type type2, int pos2);
2325 __isl_give isl_map *isl_map_equate(__isl_take isl_map *map,
2326 enum isl_dim_type type1, int pos1,
2327 enum isl_dim_type type2, int pos2);
2329 Intersect the set or relation with the hyperplane where the given
2330 dimensions are equal to each other.
2332 __isl_give isl_map *isl_map_oppose(__isl_take isl_map *map,
2333 enum isl_dim_type type1, int pos1,
2334 enum isl_dim_type type2, int pos2);
2336 Intersect the relation with the hyperplane where the given
2337 dimensions have opposite values.
2339 __isl_give isl_basic_map *isl_basic_map_order_ge(
2340 __isl_take isl_basic_map *bmap,
2341 enum isl_dim_type type1, int pos1,
2342 enum isl_dim_type type2, int pos2);
2343 __isl_give isl_map *isl_map_order_lt(__isl_take isl_map *map,
2344 enum isl_dim_type type1, int pos1,
2345 enum isl_dim_type type2, int pos2);
2346 __isl_give isl_basic_map *isl_basic_map_order_gt(
2347 __isl_take isl_basic_map *bmap,
2348 enum isl_dim_type type1, int pos1,
2349 enum isl_dim_type type2, int pos2);
2350 __isl_give isl_map *isl_map_order_gt(__isl_take isl_map *map,
2351 enum isl_dim_type type1, int pos1,
2352 enum isl_dim_type type2, int pos2);
2354 Intersect the relation with the half-space where the given
2355 dimensions satisfy the given ordering.
2359 __isl_give isl_map *isl_set_identity(
2360 __isl_take isl_set *set);
2361 __isl_give isl_union_map *isl_union_set_identity(
2362 __isl_take isl_union_set *uset);
2364 Construct an identity relation on the given (union) set.
2368 __isl_give isl_basic_set *isl_basic_map_deltas(
2369 __isl_take isl_basic_map *bmap);
2370 __isl_give isl_set *isl_map_deltas(__isl_take isl_map *map);
2371 __isl_give isl_union_set *isl_union_map_deltas(
2372 __isl_take isl_union_map *umap);
2374 These functions return a (basic) set containing the differences
2375 between image elements and corresponding domain elements in the input.
2377 __isl_give isl_basic_map *isl_basic_map_deltas_map(
2378 __isl_take isl_basic_map *bmap);
2379 __isl_give isl_map *isl_map_deltas_map(
2380 __isl_take isl_map *map);
2381 __isl_give isl_union_map *isl_union_map_deltas_map(
2382 __isl_take isl_union_map *umap);
2384 The functions above construct a (basic, regular or union) relation
2385 that maps (a wrapped version of) the input relation to its delta set.
2389 Simplify the representation of a set or relation by trying
2390 to combine pairs of basic sets or relations into a single
2391 basic set or relation.
2393 __isl_give isl_set *isl_set_coalesce(__isl_take isl_set *set);
2394 __isl_give isl_map *isl_map_coalesce(__isl_take isl_map *map);
2395 __isl_give isl_union_set *isl_union_set_coalesce(
2396 __isl_take isl_union_set *uset);
2397 __isl_give isl_union_map *isl_union_map_coalesce(
2398 __isl_take isl_union_map *umap);
2400 One of the methods for combining pairs of basic sets or relations
2401 can result in coefficients that are much larger than those that appear
2402 in the constraints of the input. By default, the coefficients are
2403 not allowed to grow larger, but this can be changed by unsetting
2404 the following option.
2406 int isl_options_set_coalesce_bounded_wrapping(
2407 isl_ctx *ctx, int val);
2408 int isl_options_get_coalesce_bounded_wrapping(
2411 =item * Detecting equalities
2413 __isl_give isl_basic_set *isl_basic_set_detect_equalities(
2414 __isl_take isl_basic_set *bset);
2415 __isl_give isl_basic_map *isl_basic_map_detect_equalities(
2416 __isl_take isl_basic_map *bmap);
2417 __isl_give isl_set *isl_set_detect_equalities(
2418 __isl_take isl_set *set);
2419 __isl_give isl_map *isl_map_detect_equalities(
2420 __isl_take isl_map *map);
2421 __isl_give isl_union_set *isl_union_set_detect_equalities(
2422 __isl_take isl_union_set *uset);
2423 __isl_give isl_union_map *isl_union_map_detect_equalities(
2424 __isl_take isl_union_map *umap);
2426 Simplify the representation of a set or relation by detecting implicit
2429 =item * Removing redundant constraints
2431 __isl_give isl_basic_set *isl_basic_set_remove_redundancies(
2432 __isl_take isl_basic_set *bset);
2433 __isl_give isl_set *isl_set_remove_redundancies(
2434 __isl_take isl_set *set);
2435 __isl_give isl_basic_map *isl_basic_map_remove_redundancies(
2436 __isl_take isl_basic_map *bmap);
2437 __isl_give isl_map *isl_map_remove_redundancies(
2438 __isl_take isl_map *map);
2442 __isl_give isl_basic_set *isl_set_convex_hull(
2443 __isl_take isl_set *set);
2444 __isl_give isl_basic_map *isl_map_convex_hull(
2445 __isl_take isl_map *map);
2447 If the input set or relation has any existentially quantified
2448 variables, then the result of these operations is currently undefined.
2452 __isl_give isl_basic_set *
2453 isl_set_unshifted_simple_hull(
2454 __isl_take isl_set *set);
2455 __isl_give isl_basic_map *
2456 isl_map_unshifted_simple_hull(
2457 __isl_take isl_map *map);
2458 __isl_give isl_basic_set *isl_set_simple_hull(
2459 __isl_take isl_set *set);
2460 __isl_give isl_basic_map *isl_map_simple_hull(
2461 __isl_take isl_map *map);
2462 __isl_give isl_union_map *isl_union_map_simple_hull(
2463 __isl_take isl_union_map *umap);
2465 These functions compute a single basic set or relation
2466 that contains the whole input set or relation.
2467 In particular, the output is described by translates
2468 of the constraints describing the basic sets or relations in the input.
2469 In case of C<isl_set_unshifted_simple_hull>, only the original
2470 constraints are used, without any translation.
2474 (See \autoref{s:simple hull}.)
2480 __isl_give isl_basic_set *isl_basic_set_affine_hull(
2481 __isl_take isl_basic_set *bset);
2482 __isl_give isl_basic_set *isl_set_affine_hull(
2483 __isl_take isl_set *set);
2484 __isl_give isl_union_set *isl_union_set_affine_hull(
2485 __isl_take isl_union_set *uset);
2486 __isl_give isl_basic_map *isl_basic_map_affine_hull(
2487 __isl_take isl_basic_map *bmap);
2488 __isl_give isl_basic_map *isl_map_affine_hull(
2489 __isl_take isl_map *map);
2490 __isl_give isl_union_map *isl_union_map_affine_hull(
2491 __isl_take isl_union_map *umap);
2493 In case of union sets and relations, the affine hull is computed
2496 =item * Polyhedral hull
2498 __isl_give isl_basic_set *isl_set_polyhedral_hull(
2499 __isl_take isl_set *set);
2500 __isl_give isl_basic_map *isl_map_polyhedral_hull(
2501 __isl_take isl_map *map);
2502 __isl_give isl_union_set *isl_union_set_polyhedral_hull(
2503 __isl_take isl_union_set *uset);
2504 __isl_give isl_union_map *isl_union_map_polyhedral_hull(
2505 __isl_take isl_union_map *umap);
2507 These functions compute a single basic set or relation
2508 not involving any existentially quantified variables
2509 that contains the whole input set or relation.
2510 In case of union sets and relations, the polyhedral hull is computed
2513 =item * Other approximations
2515 __isl_give isl_basic_set *
2516 isl_basic_set_drop_constraints_involving_dims(
2517 __isl_take isl_basic_set *bset,
2518 enum isl_dim_type type,
2519 unsigned first, unsigned n);
2520 __isl_give isl_basic_map *
2521 isl_basic_map_drop_constraints_involving_dims(
2522 __isl_take isl_basic_map *bmap,
2523 enum isl_dim_type type,
2524 unsigned first, unsigned n);
2525 __isl_give isl_basic_set *
2526 isl_basic_set_drop_constraints_not_involving_dims(
2527 __isl_take isl_basic_set *bset,
2528 enum isl_dim_type type,
2529 unsigned first, unsigned n);
2530 __isl_give isl_set *
2531 isl_set_drop_constraints_involving_dims(
2532 __isl_take isl_set *set,
2533 enum isl_dim_type type,
2534 unsigned first, unsigned n);
2535 __isl_give isl_map *
2536 isl_map_drop_constraints_involving_dims(
2537 __isl_take isl_map *map,
2538 enum isl_dim_type type,
2539 unsigned first, unsigned n);
2541 These functions drop any constraints (not) involving the specified dimensions.
2542 Note that the result depends on the representation of the input.
2546 __isl_give isl_basic_set *isl_basic_set_sample(
2547 __isl_take isl_basic_set *bset);
2548 __isl_give isl_basic_set *isl_set_sample(
2549 __isl_take isl_set *set);
2550 __isl_give isl_basic_map *isl_basic_map_sample(
2551 __isl_take isl_basic_map *bmap);
2552 __isl_give isl_basic_map *isl_map_sample(
2553 __isl_take isl_map *map);
2555 If the input (basic) set or relation is non-empty, then return
2556 a singleton subset of the input. Otherwise, return an empty set.
2558 =item * Optimization
2560 #include <isl/ilp.h>
2561 __isl_give isl_val *isl_basic_set_max_val(
2562 __isl_keep isl_basic_set *bset,
2563 __isl_keep isl_aff *obj);
2564 __isl_give isl_val *isl_set_min_val(
2565 __isl_keep isl_set *set,
2566 __isl_keep isl_aff *obj);
2567 __isl_give isl_val *isl_set_max_val(
2568 __isl_keep isl_set *set,
2569 __isl_keep isl_aff *obj);
2571 Compute the minimum or maximum of the integer affine expression C<obj>
2572 over the points in C<set>, returning the result in C<opt>.
2573 The result is C<NULL> in case of an error, the optimal value in case
2574 there is one, negative infinity or infinity if the problem is unbounded and
2575 NaN if the problem is empty.
2577 =item * Parametric optimization
2579 __isl_give isl_pw_aff *isl_set_dim_min(
2580 __isl_take isl_set *set, int pos);
2581 __isl_give isl_pw_aff *isl_set_dim_max(
2582 __isl_take isl_set *set, int pos);
2583 __isl_give isl_pw_aff *isl_map_dim_max(
2584 __isl_take isl_map *map, int pos);
2586 Compute the minimum or maximum of the given set or output dimension
2587 as a function of the parameters (and input dimensions), but independently
2588 of the other set or output dimensions.
2589 For lexicographic optimization, see L<"Lexicographic Optimization">.
2593 The following functions compute either the set of (rational) coefficient
2594 values of valid constraints for the given set or the set of (rational)
2595 values satisfying the constraints with coefficients from the given set.
2596 Internally, these two sets of functions perform essentially the
2597 same operations, except that the set of coefficients is assumed to
2598 be a cone, while the set of values may be any polyhedron.
2599 The current implementation is based on the Farkas lemma and
2600 Fourier-Motzkin elimination, but this may change or be made optional
2601 in future. In particular, future implementations may use different
2602 dualization algorithms or skip the elimination step.
2604 __isl_give isl_basic_set *isl_basic_set_coefficients(
2605 __isl_take isl_basic_set *bset);
2606 __isl_give isl_basic_set *isl_set_coefficients(
2607 __isl_take isl_set *set);
2608 __isl_give isl_union_set *isl_union_set_coefficients(
2609 __isl_take isl_union_set *bset);
2610 __isl_give isl_basic_set *isl_basic_set_solutions(
2611 __isl_take isl_basic_set *bset);
2612 __isl_give isl_basic_set *isl_set_solutions(
2613 __isl_take isl_set *set);
2614 __isl_give isl_union_set *isl_union_set_solutions(
2615 __isl_take isl_union_set *bset);
2619 __isl_give isl_map *isl_map_fixed_power_val(
2620 __isl_take isl_map *map,
2621 __isl_take isl_val *exp);
2622 __isl_give isl_union_map *
2623 isl_union_map_fixed_power_val(
2624 __isl_take isl_union_map *umap,
2625 __isl_take isl_val *exp);
2627 Compute the given power of C<map>, where C<exp> is assumed to be non-zero.
2628 If the exponent C<exp> is negative, then the -C<exp> th power of the inverse
2629 of C<map> is computed.
2631 __isl_give isl_map *isl_map_power(__isl_take isl_map *map,
2633 __isl_give isl_union_map *isl_union_map_power(
2634 __isl_take isl_union_map *umap, int *exact);
2636 Compute a parametric representation for all positive powers I<k> of C<map>.
2637 The result maps I<k> to a nested relation corresponding to the
2638 I<k>th power of C<map>.
2639 The result may be an overapproximation. If the result is known to be exact,
2640 then C<*exact> is set to C<1>.
2642 =item * Transitive closure
2644 __isl_give isl_map *isl_map_transitive_closure(
2645 __isl_take isl_map *map, int *exact);
2646 __isl_give isl_union_map *isl_union_map_transitive_closure(
2647 __isl_take isl_union_map *umap, int *exact);
2649 Compute the transitive closure of C<map>.
2650 The result may be an overapproximation. If the result is known to be exact,
2651 then C<*exact> is set to C<1>.
2653 =item * Reaching path lengths
2655 __isl_give isl_map *isl_map_reaching_path_lengths(
2656 __isl_take isl_map *map, int *exact);
2658 Compute a relation that maps each element in the range of C<map>
2659 to the lengths of all paths composed of edges in C<map> that
2660 end up in the given element.
2661 The result may be an overapproximation. If the result is known to be exact,
2662 then C<*exact> is set to C<1>.
2663 To compute the I<maximal> path length, the resulting relation
2664 should be postprocessed by C<isl_map_lexmax>.
2665 In particular, if the input relation is a dependence relation
2666 (mapping sources to sinks), then the maximal path length corresponds
2667 to the free schedule.
2668 Note, however, that C<isl_map_lexmax> expects the maximum to be
2669 finite, so if the path lengths are unbounded (possibly due to
2670 the overapproximation), then you will get an error message.
2674 __isl_give isl_basic_set *isl_basic_map_wrap(
2675 __isl_take isl_basic_map *bmap);
2676 __isl_give isl_set *isl_map_wrap(
2677 __isl_take isl_map *map);
2678 __isl_give isl_union_set *isl_union_map_wrap(
2679 __isl_take isl_union_map *umap);
2680 __isl_give isl_basic_map *isl_basic_set_unwrap(
2681 __isl_take isl_basic_set *bset);
2682 __isl_give isl_map *isl_set_unwrap(
2683 __isl_take isl_set *set);
2684 __isl_give isl_union_map *isl_union_set_unwrap(
2685 __isl_take isl_union_set *uset);
2689 Remove any internal structure of domain (and range) of the given
2690 set or relation. If there is any such internal structure in the input,
2691 then the name of the space is also removed.
2693 __isl_give isl_basic_set *isl_basic_set_flatten(
2694 __isl_take isl_basic_set *bset);
2695 __isl_give isl_set *isl_set_flatten(
2696 __isl_take isl_set *set);
2697 __isl_give isl_basic_map *isl_basic_map_flatten_domain(
2698 __isl_take isl_basic_map *bmap);
2699 __isl_give isl_basic_map *isl_basic_map_flatten_range(
2700 __isl_take isl_basic_map *bmap);
2701 __isl_give isl_map *isl_map_flatten_range(
2702 __isl_take isl_map *map);
2703 __isl_give isl_map *isl_map_flatten_domain(
2704 __isl_take isl_map *map);
2705 __isl_give isl_basic_map *isl_basic_map_flatten(
2706 __isl_take isl_basic_map *bmap);
2707 __isl_give isl_map *isl_map_flatten(
2708 __isl_take isl_map *map);
2710 __isl_give isl_map *isl_set_flatten_map(
2711 __isl_take isl_set *set);
2713 The function above constructs a relation
2714 that maps the input set to a flattened version of the set.
2718 Lift the input set to a space with extra dimensions corresponding
2719 to the existentially quantified variables in the input.
2720 In particular, the result lives in a wrapped map where the domain
2721 is the original space and the range corresponds to the original
2722 existentially quantified variables.
2724 __isl_give isl_basic_set *isl_basic_set_lift(
2725 __isl_take isl_basic_set *bset);
2726 __isl_give isl_set *isl_set_lift(
2727 __isl_take isl_set *set);
2728 __isl_give isl_union_set *isl_union_set_lift(
2729 __isl_take isl_union_set *uset);
2731 Given a local space that contains the existentially quantified
2732 variables of a set, a basic relation that, when applied to
2733 a basic set, has essentially the same effect as C<isl_basic_set_lift>,
2734 can be constructed using the following function.
2736 #include <isl/local_space.h>
2737 __isl_give isl_basic_map *isl_local_space_lifting(
2738 __isl_take isl_local_space *ls);
2740 =item * Internal Product
2742 __isl_give isl_basic_map *isl_basic_map_zip(
2743 __isl_take isl_basic_map *bmap);
2744 __isl_give isl_map *isl_map_zip(
2745 __isl_take isl_map *map);
2746 __isl_give isl_union_map *isl_union_map_zip(
2747 __isl_take isl_union_map *umap);
2749 Given a relation with nested relations for domain and range,
2750 interchange the range of the domain with the domain of the range.
2754 __isl_give isl_basic_map *isl_basic_map_curry(
2755 __isl_take isl_basic_map *bmap);
2756 __isl_give isl_basic_map *isl_basic_map_uncurry(
2757 __isl_take isl_basic_map *bmap);
2758 __isl_give isl_map *isl_map_curry(
2759 __isl_take isl_map *map);
2760 __isl_give isl_map *isl_map_uncurry(
2761 __isl_take isl_map *map);
2762 __isl_give isl_union_map *isl_union_map_curry(
2763 __isl_take isl_union_map *umap);
2764 __isl_give isl_union_map *isl_union_map_uncurry(
2765 __isl_take isl_union_map *umap);
2767 Given a relation with a nested relation for domain,
2768 the C<curry> functions
2769 move the range of the nested relation out of the domain
2770 and use it as the domain of a nested relation in the range,
2771 with the original range as range of this nested relation.
2772 The C<uncurry> functions perform the inverse operation.
2774 =item * Aligning parameters
2776 __isl_give isl_basic_set *isl_basic_set_align_params(
2777 __isl_take isl_basic_set *bset,
2778 __isl_take isl_space *model);
2779 __isl_give isl_set *isl_set_align_params(
2780 __isl_take isl_set *set,
2781 __isl_take isl_space *model);
2782 __isl_give isl_basic_map *isl_basic_map_align_params(
2783 __isl_take isl_basic_map *bmap,
2784 __isl_take isl_space *model);
2785 __isl_give isl_map *isl_map_align_params(
2786 __isl_take isl_map *map,
2787 __isl_take isl_space *model);
2789 Change the order of the parameters of the given set or relation
2790 such that the first parameters match those of C<model>.
2791 This may involve the introduction of extra parameters.
2792 All parameters need to be named.
2794 =item * Dimension manipulation
2796 __isl_give isl_basic_set *isl_basic_set_add_dims(
2797 __isl_take isl_basic_set *bset,
2798 enum isl_dim_type type, unsigned n);
2799 __isl_give isl_set *isl_set_add_dims(
2800 __isl_take isl_set *set,
2801 enum isl_dim_type type, unsigned n);
2802 __isl_give isl_map *isl_map_add_dims(
2803 __isl_take isl_map *map,
2804 enum isl_dim_type type, unsigned n);
2805 __isl_give isl_basic_set *isl_basic_set_insert_dims(
2806 __isl_take isl_basic_set *bset,
2807 enum isl_dim_type type, unsigned pos,
2809 __isl_give isl_basic_map *isl_basic_map_insert_dims(
2810 __isl_take isl_basic_map *bmap,
2811 enum isl_dim_type type, unsigned pos,
2813 __isl_give isl_set *isl_set_insert_dims(
2814 __isl_take isl_set *set,
2815 enum isl_dim_type type, unsigned pos, unsigned n);
2816 __isl_give isl_map *isl_map_insert_dims(
2817 __isl_take isl_map *map,
2818 enum isl_dim_type type, unsigned pos, unsigned n);
2819 __isl_give isl_basic_set *isl_basic_set_move_dims(
2820 __isl_take isl_basic_set *bset,
2821 enum isl_dim_type dst_type, unsigned dst_pos,
2822 enum isl_dim_type src_type, unsigned src_pos,
2824 __isl_give isl_basic_map *isl_basic_map_move_dims(
2825 __isl_take isl_basic_map *bmap,
2826 enum isl_dim_type dst_type, unsigned dst_pos,
2827 enum isl_dim_type src_type, unsigned src_pos,
2829 __isl_give isl_set *isl_set_move_dims(
2830 __isl_take isl_set *set,
2831 enum isl_dim_type dst_type, unsigned dst_pos,
2832 enum isl_dim_type src_type, unsigned src_pos,
2834 __isl_give isl_map *isl_map_move_dims(
2835 __isl_take isl_map *map,
2836 enum isl_dim_type dst_type, unsigned dst_pos,
2837 enum isl_dim_type src_type, unsigned src_pos,
2840 It is usually not advisable to directly change the (input or output)
2841 space of a set or a relation as this removes the name and the internal
2842 structure of the space. However, the above functions can be useful
2843 to add new parameters, assuming
2844 C<isl_set_align_params> and C<isl_map_align_params>
2849 =head2 Binary Operations
2851 The two arguments of a binary operation not only need to live
2852 in the same C<isl_ctx>, they currently also need to have
2853 the same (number of) parameters.
2855 =head3 Basic Operations
2859 =item * Intersection
2861 __isl_give isl_basic_set *isl_basic_set_intersect_params(
2862 __isl_take isl_basic_set *bset1,
2863 __isl_take isl_basic_set *bset2);
2864 __isl_give isl_basic_set *isl_basic_set_intersect(
2865 __isl_take isl_basic_set *bset1,
2866 __isl_take isl_basic_set *bset2);
2867 __isl_give isl_set *isl_set_intersect_params(
2868 __isl_take isl_set *set,
2869 __isl_take isl_set *params);
2870 __isl_give isl_set *isl_set_intersect(
2871 __isl_take isl_set *set1,
2872 __isl_take isl_set *set2);
2873 __isl_give isl_union_set *isl_union_set_intersect_params(
2874 __isl_take isl_union_set *uset,
2875 __isl_take isl_set *set);
2876 __isl_give isl_union_map *isl_union_map_intersect_params(
2877 __isl_take isl_union_map *umap,
2878 __isl_take isl_set *set);
2879 __isl_give isl_union_set *isl_union_set_intersect(
2880 __isl_take isl_union_set *uset1,
2881 __isl_take isl_union_set *uset2);
2882 __isl_give isl_basic_map *isl_basic_map_intersect_domain(
2883 __isl_take isl_basic_map *bmap,
2884 __isl_take isl_basic_set *bset);
2885 __isl_give isl_basic_map *isl_basic_map_intersect_range(
2886 __isl_take isl_basic_map *bmap,
2887 __isl_take isl_basic_set *bset);
2888 __isl_give isl_basic_map *isl_basic_map_intersect(
2889 __isl_take isl_basic_map *bmap1,
2890 __isl_take isl_basic_map *bmap2);
2891 __isl_give isl_map *isl_map_intersect_params(
2892 __isl_take isl_map *map,
2893 __isl_take isl_set *params);
2894 __isl_give isl_map *isl_map_intersect_domain(
2895 __isl_take isl_map *map,
2896 __isl_take isl_set *set);
2897 __isl_give isl_map *isl_map_intersect_range(
2898 __isl_take isl_map *map,
2899 __isl_take isl_set *set);
2900 __isl_give isl_map *isl_map_intersect(
2901 __isl_take isl_map *map1,
2902 __isl_take isl_map *map2);
2903 __isl_give isl_union_map *isl_union_map_intersect_domain(
2904 __isl_take isl_union_map *umap,
2905 __isl_take isl_union_set *uset);
2906 __isl_give isl_union_map *isl_union_map_intersect_range(
2907 __isl_take isl_union_map *umap,
2908 __isl_take isl_union_set *uset);
2909 __isl_give isl_union_map *isl_union_map_intersect(
2910 __isl_take isl_union_map *umap1,
2911 __isl_take isl_union_map *umap2);
2913 The second argument to the C<_params> functions needs to be
2914 a parametric (basic) set. For the other functions, a parametric set
2915 for either argument is only allowed if the other argument is
2916 a parametric set as well.
2920 __isl_give isl_set *isl_basic_set_union(
2921 __isl_take isl_basic_set *bset1,
2922 __isl_take isl_basic_set *bset2);
2923 __isl_give isl_map *isl_basic_map_union(
2924 __isl_take isl_basic_map *bmap1,
2925 __isl_take isl_basic_map *bmap2);
2926 __isl_give isl_set *isl_set_union(
2927 __isl_take isl_set *set1,
2928 __isl_take isl_set *set2);
2929 __isl_give isl_map *isl_map_union(
2930 __isl_take isl_map *map1,
2931 __isl_take isl_map *map2);
2932 __isl_give isl_union_set *isl_union_set_union(
2933 __isl_take isl_union_set *uset1,
2934 __isl_take isl_union_set *uset2);
2935 __isl_give isl_union_map *isl_union_map_union(
2936 __isl_take isl_union_map *umap1,
2937 __isl_take isl_union_map *umap2);
2939 =item * Set difference
2941 __isl_give isl_set *isl_set_subtract(
2942 __isl_take isl_set *set1,
2943 __isl_take isl_set *set2);
2944 __isl_give isl_map *isl_map_subtract(
2945 __isl_take isl_map *map1,
2946 __isl_take isl_map *map2);
2947 __isl_give isl_map *isl_map_subtract_domain(
2948 __isl_take isl_map *map,
2949 __isl_take isl_set *dom);
2950 __isl_give isl_map *isl_map_subtract_range(
2951 __isl_take isl_map *map,
2952 __isl_take isl_set *dom);
2953 __isl_give isl_union_set *isl_union_set_subtract(
2954 __isl_take isl_union_set *uset1,
2955 __isl_take isl_union_set *uset2);
2956 __isl_give isl_union_map *isl_union_map_subtract(
2957 __isl_take isl_union_map *umap1,
2958 __isl_take isl_union_map *umap2);
2959 __isl_give isl_union_map *isl_union_map_subtract_domain(
2960 __isl_take isl_union_map *umap,
2961 __isl_take isl_union_set *dom);
2962 __isl_give isl_union_map *isl_union_map_subtract_range(
2963 __isl_take isl_union_map *umap,
2964 __isl_take isl_union_set *dom);
2968 __isl_give isl_basic_set *isl_basic_set_apply(
2969 __isl_take isl_basic_set *bset,
2970 __isl_take isl_basic_map *bmap);
2971 __isl_give isl_set *isl_set_apply(
2972 __isl_take isl_set *set,
2973 __isl_take isl_map *map);
2974 __isl_give isl_union_set *isl_union_set_apply(
2975 __isl_take isl_union_set *uset,
2976 __isl_take isl_union_map *umap);
2977 __isl_give isl_basic_map *isl_basic_map_apply_domain(
2978 __isl_take isl_basic_map *bmap1,
2979 __isl_take isl_basic_map *bmap2);
2980 __isl_give isl_basic_map *isl_basic_map_apply_range(
2981 __isl_take isl_basic_map *bmap1,
2982 __isl_take isl_basic_map *bmap2);
2983 __isl_give isl_map *isl_map_apply_domain(
2984 __isl_take isl_map *map1,
2985 __isl_take isl_map *map2);
2986 __isl_give isl_union_map *isl_union_map_apply_domain(
2987 __isl_take isl_union_map *umap1,
2988 __isl_take isl_union_map *umap2);
2989 __isl_give isl_map *isl_map_apply_range(
2990 __isl_take isl_map *map1,
2991 __isl_take isl_map *map2);
2992 __isl_give isl_union_map *isl_union_map_apply_range(
2993 __isl_take isl_union_map *umap1,
2994 __isl_take isl_union_map *umap2);
2998 __isl_give isl_basic_set *
2999 isl_basic_set_preimage_multi_aff(
3000 __isl_take isl_basic_set *bset,
3001 __isl_take isl_multi_aff *ma);
3002 __isl_give isl_set *isl_set_preimage_multi_aff(
3003 __isl_take isl_set *set,
3004 __isl_take isl_multi_aff *ma);
3005 __isl_give isl_set *isl_set_preimage_pw_multi_aff(
3006 __isl_take isl_set *set,
3007 __isl_take isl_pw_multi_aff *pma);
3008 __isl_give isl_set *isl_set_preimage_multi_pw_aff(
3009 __isl_take isl_set *set,
3010 __isl_take isl_multi_pw_aff *mpa);
3011 __isl_give isl_basic_map *
3012 isl_basic_map_preimage_domain_multi_aff(
3013 __isl_take isl_basic_map *bmap,
3014 __isl_take isl_multi_aff *ma);
3015 __isl_give isl_map *isl_map_preimage_domain_multi_aff(
3016 __isl_take isl_map *map,
3017 __isl_take isl_multi_aff *ma);
3018 __isl_give isl_map *
3019 isl_map_preimage_domain_pw_multi_aff(
3020 __isl_take isl_map *map,
3021 __isl_take isl_pw_multi_aff *pma);
3022 __isl_give isl_map *
3023 isl_map_preimage_domain_multi_pw_aff(
3024 __isl_take isl_map *map,
3025 __isl_take isl_multi_pw_aff *mpa);
3026 __isl_give isl_union_map *
3027 isl_union_map_preimage_domain_multi_aff(
3028 __isl_take isl_union_map *umap,
3029 __isl_take isl_multi_aff *ma);
3030 __isl_give isl_basic_map *
3031 isl_basic_map_preimage_range_multi_aff(
3032 __isl_take isl_basic_map *bmap,
3033 __isl_take isl_multi_aff *ma);
3035 These functions compute the preimage of the given set or map domain/range under
3036 the given function. In other words, the expression is plugged
3037 into the set description or into the domain/range of the map.
3038 Objects of types C<isl_multi_aff> and C<isl_pw_multi_aff> are described in
3039 L</"Piecewise Multiple Quasi Affine Expressions">.
3041 =item * Cartesian Product
3043 __isl_give isl_set *isl_set_product(
3044 __isl_take isl_set *set1,
3045 __isl_take isl_set *set2);
3046 __isl_give isl_union_set *isl_union_set_product(
3047 __isl_take isl_union_set *uset1,
3048 __isl_take isl_union_set *uset2);
3049 __isl_give isl_basic_map *isl_basic_map_domain_product(
3050 __isl_take isl_basic_map *bmap1,
3051 __isl_take isl_basic_map *bmap2);
3052 __isl_give isl_basic_map *isl_basic_map_range_product(
3053 __isl_take isl_basic_map *bmap1,
3054 __isl_take isl_basic_map *bmap2);
3055 __isl_give isl_basic_map *isl_basic_map_product(
3056 __isl_take isl_basic_map *bmap1,
3057 __isl_take isl_basic_map *bmap2);
3058 __isl_give isl_map *isl_map_domain_product(
3059 __isl_take isl_map *map1,
3060 __isl_take isl_map *map2);
3061 __isl_give isl_map *isl_map_range_product(
3062 __isl_take isl_map *map1,
3063 __isl_take isl_map *map2);
3064 __isl_give isl_union_map *isl_union_map_domain_product(
3065 __isl_take isl_union_map *umap1,
3066 __isl_take isl_union_map *umap2);
3067 __isl_give isl_union_map *isl_union_map_range_product(
3068 __isl_take isl_union_map *umap1,
3069 __isl_take isl_union_map *umap2);
3070 __isl_give isl_map *isl_map_product(
3071 __isl_take isl_map *map1,
3072 __isl_take isl_map *map2);
3073 __isl_give isl_union_map *isl_union_map_product(
3074 __isl_take isl_union_map *umap1,
3075 __isl_take isl_union_map *umap2);
3077 The above functions compute the cross product of the given
3078 sets or relations. The domains and ranges of the results
3079 are wrapped maps between domains and ranges of the inputs.
3080 To obtain a ``flat'' product, use the following functions
3083 __isl_give isl_basic_set *isl_basic_set_flat_product(
3084 __isl_take isl_basic_set *bset1,
3085 __isl_take isl_basic_set *bset2);
3086 __isl_give isl_set *isl_set_flat_product(
3087 __isl_take isl_set *set1,
3088 __isl_take isl_set *set2);
3089 __isl_give isl_basic_map *isl_basic_map_flat_range_product(
3090 __isl_take isl_basic_map *bmap1,
3091 __isl_take isl_basic_map *bmap2);
3092 __isl_give isl_map *isl_map_flat_domain_product(
3093 __isl_take isl_map *map1,
3094 __isl_take isl_map *map2);
3095 __isl_give isl_map *isl_map_flat_range_product(
3096 __isl_take isl_map *map1,
3097 __isl_take isl_map *map2);
3098 __isl_give isl_union_map *isl_union_map_flat_range_product(
3099 __isl_take isl_union_map *umap1,
3100 __isl_take isl_union_map *umap2);
3101 __isl_give isl_basic_map *isl_basic_map_flat_product(
3102 __isl_take isl_basic_map *bmap1,
3103 __isl_take isl_basic_map *bmap2);
3104 __isl_give isl_map *isl_map_flat_product(
3105 __isl_take isl_map *map1,
3106 __isl_take isl_map *map2);
3108 The arguments of a call to C<isl_map_product> can be extracted
3109 from the result using the following two functions.
3111 __isl_give isl_map *isl_map_range_factor_domain(
3112 __isl_take isl_map *map);
3113 __isl_give isl_map *isl_map_range_factor_range(
3114 __isl_take isl_map *map);
3116 =item * Simplification
3118 __isl_give isl_basic_set *isl_basic_set_gist(
3119 __isl_take isl_basic_set *bset,
3120 __isl_take isl_basic_set *context);
3121 __isl_give isl_set *isl_set_gist(__isl_take isl_set *set,
3122 __isl_take isl_set *context);
3123 __isl_give isl_set *isl_set_gist_params(
3124 __isl_take isl_set *set,
3125 __isl_take isl_set *context);
3126 __isl_give isl_union_set *isl_union_set_gist(
3127 __isl_take isl_union_set *uset,
3128 __isl_take isl_union_set *context);
3129 __isl_give isl_union_set *isl_union_set_gist_params(
3130 __isl_take isl_union_set *uset,
3131 __isl_take isl_set *set);
3132 __isl_give isl_basic_map *isl_basic_map_gist(
3133 __isl_take isl_basic_map *bmap,
3134 __isl_take isl_basic_map *context);
3135 __isl_give isl_map *isl_map_gist(__isl_take isl_map *map,
3136 __isl_take isl_map *context);
3137 __isl_give isl_map *isl_map_gist_params(
3138 __isl_take isl_map *map,
3139 __isl_take isl_set *context);
3140 __isl_give isl_map *isl_map_gist_domain(
3141 __isl_take isl_map *map,
3142 __isl_take isl_set *context);
3143 __isl_give isl_map *isl_map_gist_range(
3144 __isl_take isl_map *map,
3145 __isl_take isl_set *context);
3146 __isl_give isl_union_map *isl_union_map_gist(
3147 __isl_take isl_union_map *umap,
3148 __isl_take isl_union_map *context);
3149 __isl_give isl_union_map *isl_union_map_gist_params(
3150 __isl_take isl_union_map *umap,
3151 __isl_take isl_set *set);
3152 __isl_give isl_union_map *isl_union_map_gist_domain(
3153 __isl_take isl_union_map *umap,
3154 __isl_take isl_union_set *uset);
3155 __isl_give isl_union_map *isl_union_map_gist_range(
3156 __isl_take isl_union_map *umap,
3157 __isl_take isl_union_set *uset);
3159 The gist operation returns a set or relation that has the
3160 same intersection with the context as the input set or relation.
3161 Any implicit equality in the intersection is made explicit in the result,
3162 while all inequalities that are redundant with respect to the intersection
3164 In case of union sets and relations, the gist operation is performed
3169 =head3 Lexicographic Optimization
3171 Given a (basic) set C<set> (or C<bset>) and a zero-dimensional domain C<dom>,
3172 the following functions
3173 compute a set that contains the lexicographic minimum or maximum
3174 of the elements in C<set> (or C<bset>) for those values of the parameters
3175 that satisfy C<dom>.
3176 If C<empty> is not C<NULL>, then C<*empty> is assigned a set
3177 that contains the parameter values in C<dom> for which C<set> (or C<bset>)
3179 In other words, the union of the parameter values
3180 for which the result is non-empty and of C<*empty>
3183 __isl_give isl_set *isl_basic_set_partial_lexmin(
3184 __isl_take isl_basic_set *bset,
3185 __isl_take isl_basic_set *dom,
3186 __isl_give isl_set **empty);
3187 __isl_give isl_set *isl_basic_set_partial_lexmax(
3188 __isl_take isl_basic_set *bset,
3189 __isl_take isl_basic_set *dom,
3190 __isl_give isl_set **empty);
3191 __isl_give isl_set *isl_set_partial_lexmin(
3192 __isl_take isl_set *set, __isl_take isl_set *dom,
3193 __isl_give isl_set **empty);
3194 __isl_give isl_set *isl_set_partial_lexmax(
3195 __isl_take isl_set *set, __isl_take isl_set *dom,
3196 __isl_give isl_set **empty);
3198 Given a (basic) set C<set> (or C<bset>), the following functions simply
3199 return a set containing the lexicographic minimum or maximum
3200 of the elements in C<set> (or C<bset>).
3201 In case of union sets, the optimum is computed per space.
3203 __isl_give isl_set *isl_basic_set_lexmin(
3204 __isl_take isl_basic_set *bset);
3205 __isl_give isl_set *isl_basic_set_lexmax(
3206 __isl_take isl_basic_set *bset);
3207 __isl_give isl_set *isl_set_lexmin(
3208 __isl_take isl_set *set);
3209 __isl_give isl_set *isl_set_lexmax(
3210 __isl_take isl_set *set);
3211 __isl_give isl_union_set *isl_union_set_lexmin(
3212 __isl_take isl_union_set *uset);
3213 __isl_give isl_union_set *isl_union_set_lexmax(
3214 __isl_take isl_union_set *uset);
3216 Given a (basic) relation C<map> (or C<bmap>) and a domain C<dom>,
3217 the following functions
3218 compute a relation that maps each element of C<dom>
3219 to the single lexicographic minimum or maximum
3220 of the elements that are associated to that same
3221 element in C<map> (or C<bmap>).
3222 If C<empty> is not C<NULL>, then C<*empty> is assigned a set
3223 that contains the elements in C<dom> that do not map
3224 to any elements in C<map> (or C<bmap>).
3225 In other words, the union of the domain of the result and of C<*empty>
3228 __isl_give isl_map *isl_basic_map_partial_lexmax(
3229 __isl_take isl_basic_map *bmap,
3230 __isl_take isl_basic_set *dom,
3231 __isl_give isl_set **empty);
3232 __isl_give isl_map *isl_basic_map_partial_lexmin(
3233 __isl_take isl_basic_map *bmap,
3234 __isl_take isl_basic_set *dom,
3235 __isl_give isl_set **empty);
3236 __isl_give isl_map *isl_map_partial_lexmax(
3237 __isl_take isl_map *map, __isl_take isl_set *dom,
3238 __isl_give isl_set **empty);
3239 __isl_give isl_map *isl_map_partial_lexmin(
3240 __isl_take isl_map *map, __isl_take isl_set *dom,
3241 __isl_give isl_set **empty);
3243 Given a (basic) map C<map> (or C<bmap>), the following functions simply
3244 return a map mapping each element in the domain of
3245 C<map> (or C<bmap>) to the lexicographic minimum or maximum
3246 of all elements associated to that element.
3247 In case of union relations, the optimum is computed per space.
3249 __isl_give isl_map *isl_basic_map_lexmin(
3250 __isl_take isl_basic_map *bmap);
3251 __isl_give isl_map *isl_basic_map_lexmax(
3252 __isl_take isl_basic_map *bmap);
3253 __isl_give isl_map *isl_map_lexmin(
3254 __isl_take isl_map *map);
3255 __isl_give isl_map *isl_map_lexmax(
3256 __isl_take isl_map *map);
3257 __isl_give isl_union_map *isl_union_map_lexmin(
3258 __isl_take isl_union_map *umap);
3259 __isl_give isl_union_map *isl_union_map_lexmax(
3260 __isl_take isl_union_map *umap);
3262 The following functions return their result in the form of
3263 a piecewise multi-affine expression
3264 (See L<"Piecewise Multiple Quasi Affine Expressions">),
3265 but are otherwise equivalent to the corresponding functions
3266 returning a basic set or relation.
3268 __isl_give isl_pw_multi_aff *
3269 isl_basic_map_lexmin_pw_multi_aff(
3270 __isl_take isl_basic_map *bmap);
3271 __isl_give isl_pw_multi_aff *
3272 isl_basic_set_partial_lexmin_pw_multi_aff(
3273 __isl_take isl_basic_set *bset,
3274 __isl_take isl_basic_set *dom,
3275 __isl_give isl_set **empty);
3276 __isl_give isl_pw_multi_aff *
3277 isl_basic_set_partial_lexmax_pw_multi_aff(
3278 __isl_take isl_basic_set *bset,
3279 __isl_take isl_basic_set *dom,
3280 __isl_give isl_set **empty);
3281 __isl_give isl_pw_multi_aff *
3282 isl_basic_map_partial_lexmin_pw_multi_aff(
3283 __isl_take isl_basic_map *bmap,
3284 __isl_take isl_basic_set *dom,
3285 __isl_give isl_set **empty);
3286 __isl_give isl_pw_multi_aff *
3287 isl_basic_map_partial_lexmax_pw_multi_aff(
3288 __isl_take isl_basic_map *bmap,
3289 __isl_take isl_basic_set *dom,
3290 __isl_give isl_set **empty);
3291 __isl_give isl_pw_multi_aff *isl_set_lexmin_pw_multi_aff(
3292 __isl_take isl_set *set);
3293 __isl_give isl_pw_multi_aff *isl_set_lexmax_pw_multi_aff(
3294 __isl_take isl_set *set);
3295 __isl_give isl_pw_multi_aff *isl_map_lexmin_pw_multi_aff(
3296 __isl_take isl_map *map);
3297 __isl_give isl_pw_multi_aff *isl_map_lexmax_pw_multi_aff(
3298 __isl_take isl_map *map);
3302 Lists are defined over several element types, including
3303 C<isl_val>, C<isl_id>, C<isl_aff>, C<isl_pw_aff>, C<isl_constraint>,
3304 C<isl_basic_set>, C<isl_set>, C<isl_ast_expr> and C<isl_ast_node>.
3305 Here we take lists of C<isl_set>s as an example.
3306 Lists can be created, copied, modified and freed using the following functions.
3308 #include <isl/list.h>
3309 __isl_give isl_set_list *isl_set_list_from_set(
3310 __isl_take isl_set *el);
3311 __isl_give isl_set_list *isl_set_list_alloc(
3312 isl_ctx *ctx, int n);
3313 __isl_give isl_set_list *isl_set_list_copy(
3314 __isl_keep isl_set_list *list);
3315 __isl_give isl_set_list *isl_set_list_insert(
3316 __isl_take isl_set_list *list, unsigned pos,
3317 __isl_take isl_set *el);
3318 __isl_give isl_set_list *isl_set_list_add(
3319 __isl_take isl_set_list *list,
3320 __isl_take isl_set *el);
3321 __isl_give isl_set_list *isl_set_list_drop(
3322 __isl_take isl_set_list *list,
3323 unsigned first, unsigned n);
3324 __isl_give isl_set_list *isl_set_list_set_set(
3325 __isl_take isl_set_list *list, int index,
3326 __isl_take isl_set *set);
3327 __isl_give isl_set_list *isl_set_list_concat(
3328 __isl_take isl_set_list *list1,
3329 __isl_take isl_set_list *list2);
3330 __isl_give isl_set_list *isl_set_list_sort(
3331 __isl_take isl_set_list *list,
3332 int (*cmp)(__isl_keep isl_set *a,
3333 __isl_keep isl_set *b, void *user),
3335 void *isl_set_list_free(__isl_take isl_set_list *list);
3337 C<isl_set_list_alloc> creates an empty list with a capacity for
3338 C<n> elements. C<isl_set_list_from_set> creates a list with a single
3341 Lists can be inspected using the following functions.
3343 #include <isl/list.h>
3344 isl_ctx *isl_set_list_get_ctx(__isl_keep isl_set_list *list);
3345 int isl_set_list_n_set(__isl_keep isl_set_list *list);
3346 __isl_give isl_set *isl_set_list_get_set(
3347 __isl_keep isl_set_list *list, int index);
3348 int isl_set_list_foreach(__isl_keep isl_set_list *list,
3349 int (*fn)(__isl_take isl_set *el, void *user),
3351 int isl_set_list_foreach_scc(__isl_keep isl_set_list *list,
3352 int (*follows)(__isl_keep isl_set *a,
3353 __isl_keep isl_set *b, void *user),
3355 int (*fn)(__isl_take isl_set *el, void *user),
3358 The function C<isl_set_list_foreach_scc> calls C<fn> on each of the
3359 strongly connected components of the graph with as vertices the elements
3360 of C<list> and a directed edge from vertex C<b> to vertex C<a>
3361 iff C<follows(a, b)> returns C<1>. The callbacks C<follows> and C<fn>
3362 should return C<-1> on error.
3364 Lists can be printed using
3366 #include <isl/list.h>
3367 __isl_give isl_printer *isl_printer_print_set_list(
3368 __isl_take isl_printer *p,
3369 __isl_keep isl_set_list *list);
3371 =head2 Associative arrays
3373 Associative arrays map isl objects of a specific type to isl objects
3374 of some (other) specific type. They are defined for several pairs
3375 of types, including (C<isl_map>, C<isl_basic_set>),
3376 (C<isl_id>, C<isl_ast_expr>) and.
3377 (C<isl_id>, C<isl_pw_aff>).
3378 Here, we take associative arrays that map C<isl_id>s to C<isl_ast_expr>s
3381 Associative arrays can be created, copied and freed using
3382 the following functions.
3384 #include <isl/id_to_ast_expr.h>
3385 __isl_give id_to_ast_expr *isl_id_to_ast_expr_alloc(
3386 isl_ctx *ctx, int min_size);
3387 __isl_give id_to_ast_expr *isl_id_to_ast_expr_copy(
3388 __isl_keep id_to_ast_expr *id2expr);
3389 void *isl_id_to_ast_expr_free(
3390 __isl_take id_to_ast_expr *id2expr);
3392 The C<min_size> argument to C<isl_id_to_ast_expr_alloc> can be used
3393 to specify the expected size of the associative array.
3394 The associative array will be grown automatically as needed.
3396 Associative arrays can be inspected using the following functions.
3398 #include <isl/id_to_ast_expr.h>
3399 isl_ctx *isl_id_to_ast_expr_get_ctx(
3400 __isl_keep id_to_ast_expr *id2expr);
3401 int isl_id_to_ast_expr_has(
3402 __isl_keep id_to_ast_expr *id2expr,
3403 __isl_keep isl_id *key);
3404 __isl_give isl_ast_expr *isl_id_to_ast_expr_get(
3405 __isl_keep id_to_ast_expr *id2expr,
3406 __isl_take isl_id *key);
3407 int isl_id_to_ast_expr_foreach(
3408 __isl_keep id_to_ast_expr *id2expr,
3409 int (*fn)(__isl_take isl_id *key,
3410 __isl_take isl_ast_expr *val, void *user),
3413 They can be modified using the following function.
3415 #include <isl/id_to_ast_expr.h>
3416 __isl_give id_to_ast_expr *isl_id_to_ast_expr_set(
3417 __isl_take id_to_ast_expr *id2expr,
3418 __isl_take isl_id *key,
3419 __isl_take isl_ast_expr *val);
3421 Associative arrays can be printed using the following function.
3423 #include <isl/id_to_ast_expr.h>
3424 __isl_give isl_printer *isl_printer_print_id_to_ast_expr(
3425 __isl_take isl_printer *p,
3426 __isl_keep id_to_ast_expr *id2expr);
3428 =head2 Multiple Values
3430 An C<isl_multi_val> object represents a sequence of zero or more values,
3431 living in a set space.
3433 An C<isl_multi_val> can be constructed from an C<isl_val_list>
3434 using the following function
3436 #include <isl/val.h>
3437 __isl_give isl_multi_val *isl_multi_val_from_val_list(
3438 __isl_take isl_space *space,
3439 __isl_take isl_val_list *list);
3441 The zero multiple value (with value zero for each set dimension)
3442 can be created using the following function.
3444 #include <isl/val.h>
3445 __isl_give isl_multi_val *isl_multi_val_zero(
3446 __isl_take isl_space *space);
3448 Multiple values can be copied and freed using
3450 #include <isl/val.h>
3451 __isl_give isl_multi_val *isl_multi_val_copy(
3452 __isl_keep isl_multi_val *mv);
3453 void *isl_multi_val_free(__isl_take isl_multi_val *mv);
3455 They can be inspected using
3457 #include <isl/val.h>
3458 isl_ctx *isl_multi_val_get_ctx(
3459 __isl_keep isl_multi_val *mv);
3460 unsigned isl_multi_val_dim(__isl_keep isl_multi_val *mv,
3461 enum isl_dim_type type);
3462 __isl_give isl_val *isl_multi_val_get_val(
3463 __isl_keep isl_multi_val *mv, int pos);
3464 int isl_multi_val_find_dim_by_id(
3465 __isl_keep isl_multi_val *mv,
3466 enum isl_dim_type type, __isl_keep isl_id *id);
3467 __isl_give isl_id *isl_multi_val_get_dim_id(
3468 __isl_keep isl_multi_val *mv,
3469 enum isl_dim_type type, unsigned pos);
3470 const char *isl_multi_val_get_tuple_name(
3471 __isl_keep isl_multi_val *mv,
3472 enum isl_dim_type type);
3473 int isl_multi_val_has_tuple_id(__isl_keep isl_multi_val *mv,
3474 enum isl_dim_type type);
3475 __isl_give isl_id *isl_multi_val_get_tuple_id(
3476 __isl_keep isl_multi_val *mv,
3477 enum isl_dim_type type);
3478 int isl_multi_val_range_is_wrapping(
3479 __isl_keep isl_multi_val *mv);
3481 They can be modified using
3483 #include <isl/val.h>
3484 __isl_give isl_multi_val *isl_multi_val_set_val(
3485 __isl_take isl_multi_val *mv, int pos,
3486 __isl_take isl_val *val);
3487 __isl_give isl_multi_val *isl_multi_val_set_dim_name(
3488 __isl_take isl_multi_val *mv,
3489 enum isl_dim_type type, unsigned pos, const char *s);
3490 __isl_give isl_multi_val *isl_multi_val_set_dim_id(
3491 __isl_take isl_multi_val *mv,
3492 enum isl_dim_type type, unsigned pos,
3493 __isl_take isl_id *id);
3494 __isl_give isl_multi_val *isl_multi_val_set_tuple_name(
3495 __isl_take isl_multi_val *mv,
3496 enum isl_dim_type type, const char *s);
3497 __isl_give isl_multi_val *isl_multi_val_set_tuple_id(
3498 __isl_take isl_multi_val *mv,
3499 enum isl_dim_type type, __isl_take isl_id *id);
3500 __isl_give isl_multi_val *isl_multi_val_reset_tuple_id(
3501 __isl_take isl_multi_val *mv,
3502 enum isl_dim_type type);
3503 __isl_give isl_multi_val *isl_multi_val_reset_user(
3504 __isl_take isl_multi_val *mv);
3506 __isl_give isl_multi_val *isl_multi_val_insert_dims(
3507 __isl_take isl_multi_val *mv,
3508 enum isl_dim_type type, unsigned first, unsigned n);
3509 __isl_give isl_multi_val *isl_multi_val_add_dims(
3510 __isl_take isl_multi_val *mv,
3511 enum isl_dim_type type, unsigned n);
3512 __isl_give isl_multi_val *isl_multi_val_drop_dims(
3513 __isl_take isl_multi_val *mv,
3514 enum isl_dim_type type, unsigned first, unsigned n);
3518 #include <isl/val.h>
3519 __isl_give isl_multi_val *isl_multi_val_align_params(
3520 __isl_take isl_multi_val *mv,
3521 __isl_take isl_space *model);
3522 __isl_give isl_multi_val *isl_multi_val_from_range(
3523 __isl_take isl_multi_val *mv);
3524 __isl_give isl_multi_val *isl_multi_val_range_splice(
3525 __isl_take isl_multi_val *mv1, unsigned pos,
3526 __isl_take isl_multi_val *mv2);
3527 __isl_give isl_multi_val *isl_multi_val_range_product(
3528 __isl_take isl_multi_val *mv1,
3529 __isl_take isl_multi_val *mv2);
3530 __isl_give isl_multi_val *
3531 isl_multi_val_range_factor_domain(
3532 __isl_take isl_multi_val *mv);
3533 __isl_give isl_multi_val *
3534 isl_multi_val_range_factor_range(
3535 __isl_take isl_multi_val *mv);
3536 __isl_give isl_multi_val *isl_multi_val_flat_range_product(
3537 __isl_take isl_multi_val *mv1,
3538 __isl_take isl_multi_aff *mv2);
3539 __isl_give isl_multi_val *isl_multi_val_product(
3540 __isl_take isl_multi_val *mv1,
3541 __isl_take isl_multi_val *mv2);
3542 __isl_give isl_multi_val *isl_multi_val_add_val(
3543 __isl_take isl_multi_val *mv,
3544 __isl_take isl_val *v);
3545 __isl_give isl_multi_val *isl_multi_val_mod_val(
3546 __isl_take isl_multi_val *mv,
3547 __isl_take isl_val *v);
3548 __isl_give isl_multi_val *isl_multi_val_scale_val(
3549 __isl_take isl_multi_val *mv,
3550 __isl_take isl_val *v);
3551 __isl_give isl_multi_val *isl_multi_val_scale_multi_val(
3552 __isl_take isl_multi_val *mv1,
3553 __isl_take isl_multi_val *mv2);
3554 __isl_give isl_multi_val *
3555 isl_multi_val_scale_down_multi_val(
3556 __isl_take isl_multi_val *mv1,
3557 __isl_take isl_multi_val *mv2);
3559 A multiple value can be printed using
3561 __isl_give isl_printer *isl_printer_print_multi_val(
3562 __isl_take isl_printer *p,
3563 __isl_keep isl_multi_val *mv);
3567 Vectors can be created, copied and freed using the following functions.
3569 #include <isl/vec.h>
3570 __isl_give isl_vec *isl_vec_alloc(isl_ctx *ctx,
3572 __isl_give isl_vec *isl_vec_copy(__isl_keep isl_vec *vec);
3573 void *isl_vec_free(__isl_take isl_vec *vec);
3575 Note that the elements of a newly created vector may have arbitrary values.
3576 The elements can be changed and inspected using the following functions.
3578 isl_ctx *isl_vec_get_ctx(__isl_keep isl_vec *vec);
3579 int isl_vec_size(__isl_keep isl_vec *vec);
3580 __isl_give isl_val *isl_vec_get_element_val(
3581 __isl_keep isl_vec *vec, int pos);
3582 __isl_give isl_vec *isl_vec_set_element_si(
3583 __isl_take isl_vec *vec, int pos, int v);
3584 __isl_give isl_vec *isl_vec_set_element_val(
3585 __isl_take isl_vec *vec, int pos,
3586 __isl_take isl_val *v);
3587 __isl_give isl_vec *isl_vec_set_si(__isl_take isl_vec *vec,
3589 __isl_give isl_vec *isl_vec_set_val(
3590 __isl_take isl_vec *vec, __isl_take isl_val *v);
3591 int isl_vec_cmp_element(__isl_keep isl_vec *vec1,
3592 __isl_keep isl_vec *vec2, int pos);
3594 C<isl_vec_get_element> will return a negative value if anything went wrong.
3595 In that case, the value of C<*v> is undefined.
3597 The following function can be used to concatenate two vectors.
3599 __isl_give isl_vec *isl_vec_concat(__isl_take isl_vec *vec1,
3600 __isl_take isl_vec *vec2);
3604 Matrices can be created, copied and freed using the following functions.
3606 #include <isl/mat.h>
3607 __isl_give isl_mat *isl_mat_alloc(isl_ctx *ctx,
3608 unsigned n_row, unsigned n_col);
3609 __isl_give isl_mat *isl_mat_copy(__isl_keep isl_mat *mat);
3610 void *isl_mat_free(__isl_take isl_mat *mat);
3612 Note that the elements of a newly created matrix may have arbitrary values.
3613 The elements can be changed and inspected using the following functions.
3615 isl_ctx *isl_mat_get_ctx(__isl_keep isl_mat *mat);
3616 int isl_mat_rows(__isl_keep isl_mat *mat);
3617 int isl_mat_cols(__isl_keep isl_mat *mat);
3618 __isl_give isl_val *isl_mat_get_element_val(
3619 __isl_keep isl_mat *mat, int row, int col);
3620 __isl_give isl_mat *isl_mat_set_element_si(__isl_take isl_mat *mat,
3621 int row, int col, int v);
3622 __isl_give isl_mat *isl_mat_set_element_val(
3623 __isl_take isl_mat *mat, int row, int col,
3624 __isl_take isl_val *v);
3626 C<isl_mat_get_element> will return a negative value if anything went wrong.
3627 In that case, the value of C<*v> is undefined.
3629 The following function can be used to compute the (right) inverse
3630 of a matrix, i.e., a matrix such that the product of the original
3631 and the inverse (in that order) is a multiple of the identity matrix.
3632 The input matrix is assumed to be of full row-rank.
3634 __isl_give isl_mat *isl_mat_right_inverse(__isl_take isl_mat *mat);
3636 The following function can be used to compute the (right) kernel
3637 (or null space) of a matrix, i.e., a matrix such that the product of
3638 the original and the kernel (in that order) is the zero matrix.
3640 __isl_give isl_mat *isl_mat_right_kernel(__isl_take isl_mat *mat);
3642 =head2 Piecewise Quasi Affine Expressions
3644 The zero quasi affine expression or the quasi affine expression
3645 that is equal to a given value or
3646 a specified dimension on a given domain can be created using
3648 __isl_give isl_aff *isl_aff_zero_on_domain(
3649 __isl_take isl_local_space *ls);
3650 __isl_give isl_pw_aff *isl_pw_aff_zero_on_domain(
3651 __isl_take isl_local_space *ls);
3652 __isl_give isl_aff *isl_aff_val_on_domain(
3653 __isl_take isl_local_space *ls,
3654 __isl_take isl_val *val);
3655 __isl_give isl_aff *isl_aff_var_on_domain(
3656 __isl_take isl_local_space *ls,
3657 enum isl_dim_type type, unsigned pos);
3658 __isl_give isl_pw_aff *isl_pw_aff_var_on_domain(
3659 __isl_take isl_local_space *ls,
3660 enum isl_dim_type type, unsigned pos);
3662 Note that the space in which the resulting objects live is a map space
3663 with the given space as domain and a one-dimensional range.
3665 An empty piecewise quasi affine expression (one with no cells)
3666 or a piecewise quasi affine expression with a single cell can
3667 be created using the following functions.
3669 #include <isl/aff.h>
3670 __isl_give isl_pw_aff *isl_pw_aff_empty(
3671 __isl_take isl_space *space);
3672 __isl_give isl_pw_aff *isl_pw_aff_alloc(
3673 __isl_take isl_set *set, __isl_take isl_aff *aff);
3674 __isl_give isl_pw_aff *isl_pw_aff_from_aff(
3675 __isl_take isl_aff *aff);
3677 A piecewise quasi affine expression that is equal to 1 on a set
3678 and 0 outside the set can be created using the following function.
3680 #include <isl/aff.h>
3681 __isl_give isl_pw_aff *isl_set_indicator_function(
3682 __isl_take isl_set *set);
3684 Quasi affine expressions can be copied and freed using
3686 #include <isl/aff.h>
3687 __isl_give isl_aff *isl_aff_copy(__isl_keep isl_aff *aff);
3688 void *isl_aff_free(__isl_take isl_aff *aff);
3690 __isl_give isl_pw_aff *isl_pw_aff_copy(
3691 __isl_keep isl_pw_aff *pwaff);
3692 void *isl_pw_aff_free(__isl_take isl_pw_aff *pwaff);
3694 A (rational) bound on a dimension can be extracted from an C<isl_constraint>
3695 using the following function. The constraint is required to have
3696 a non-zero coefficient for the specified dimension.
3698 #include <isl/constraint.h>
3699 __isl_give isl_aff *isl_constraint_get_bound(
3700 __isl_keep isl_constraint *constraint,
3701 enum isl_dim_type type, int pos);
3703 The entire affine expression of the constraint can also be extracted
3704 using the following function.
3706 #include <isl/constraint.h>
3707 __isl_give isl_aff *isl_constraint_get_aff(
3708 __isl_keep isl_constraint *constraint);
3710 Conversely, an equality constraint equating
3711 the affine expression to zero or an inequality constraint enforcing
3712 the affine expression to be non-negative, can be constructed using
3714 __isl_give isl_constraint *isl_equality_from_aff(
3715 __isl_take isl_aff *aff);
3716 __isl_give isl_constraint *isl_inequality_from_aff(
3717 __isl_take isl_aff *aff);
3719 The expression can be inspected using
3721 #include <isl/aff.h>
3722 isl_ctx *isl_aff_get_ctx(__isl_keep isl_aff *aff);
3723 int isl_aff_dim(__isl_keep isl_aff *aff,
3724 enum isl_dim_type type);
3725 __isl_give isl_local_space *isl_aff_get_domain_local_space(
3726 __isl_keep isl_aff *aff);
3727 __isl_give isl_local_space *isl_aff_get_local_space(
3728 __isl_keep isl_aff *aff);
3729 const char *isl_aff_get_dim_name(__isl_keep isl_aff *aff,
3730 enum isl_dim_type type, unsigned pos);
3731 const char *isl_pw_aff_get_dim_name(
3732 __isl_keep isl_pw_aff *pa,
3733 enum isl_dim_type type, unsigned pos);
3734 int isl_pw_aff_has_dim_id(__isl_keep isl_pw_aff *pa,
3735 enum isl_dim_type type, unsigned pos);
3736 __isl_give isl_id *isl_pw_aff_get_dim_id(
3737 __isl_keep isl_pw_aff *pa,
3738 enum isl_dim_type type, unsigned pos);
3739 int isl_pw_aff_has_tuple_id(__isl_keep isl_pw_aff *pa,
3740 enum isl_dim_type type);
3741 __isl_give isl_id *isl_pw_aff_get_tuple_id(
3742 __isl_keep isl_pw_aff *pa,
3743 enum isl_dim_type type);
3744 __isl_give isl_val *isl_aff_get_constant_val(
3745 __isl_keep isl_aff *aff);
3746 __isl_give isl_val *isl_aff_get_coefficient_val(
3747 __isl_keep isl_aff *aff,
3748 enum isl_dim_type type, int pos);
3749 __isl_give isl_val *isl_aff_get_denominator_val(
3750 __isl_keep isl_aff *aff);
3751 __isl_give isl_aff *isl_aff_get_div(
3752 __isl_keep isl_aff *aff, int pos);
3754 int isl_pw_aff_n_piece(__isl_keep isl_pw_aff *pwaff);
3755 int isl_pw_aff_foreach_piece(__isl_keep isl_pw_aff *pwaff,
3756 int (*fn)(__isl_take isl_set *set,
3757 __isl_take isl_aff *aff,
3758 void *user), void *user);
3760 int isl_aff_is_cst(__isl_keep isl_aff *aff);
3761 int isl_pw_aff_is_cst(__isl_keep isl_pw_aff *pwaff);
3763 int isl_aff_involves_dims(__isl_keep isl_aff *aff,
3764 enum isl_dim_type type, unsigned first, unsigned n);
3765 int isl_pw_aff_involves_dims(__isl_keep isl_pw_aff *pwaff,
3766 enum isl_dim_type type, unsigned first, unsigned n);
3768 isl_ctx *isl_pw_aff_get_ctx(__isl_keep isl_pw_aff *pwaff);
3769 unsigned isl_pw_aff_dim(__isl_keep isl_pw_aff *pwaff,
3770 enum isl_dim_type type);
3771 int isl_pw_aff_is_empty(__isl_keep isl_pw_aff *pwaff);
3773 It can be modified using
3775 #include <isl/aff.h>
3776 __isl_give isl_aff *isl_aff_set_tuple_id(
3777 __isl_take isl_aff *aff,
3778 enum isl_dim_type type, __isl_take isl_id *id);
3779 __isl_give isl_pw_aff *isl_pw_aff_set_tuple_id(
3780 __isl_take isl_pw_aff *pwaff,
3781 enum isl_dim_type type, __isl_take isl_id *id);
3782 __isl_give isl_aff *isl_aff_set_dim_name(
3783 __isl_take isl_aff *aff, enum isl_dim_type type,
3784 unsigned pos, const char *s);
3785 __isl_give isl_aff *isl_aff_set_dim_id(
3786 __isl_take isl_aff *aff, enum isl_dim_type type,
3787 unsigned pos, __isl_take isl_id *id);
3788 __isl_give isl_pw_aff *isl_pw_aff_set_dim_id(
3789 __isl_take isl_pw_aff *pma,
3790 enum isl_dim_type type, unsigned pos,
3791 __isl_take isl_id *id);
3792 __isl_give isl_aff *isl_aff_set_constant_si(
3793 __isl_take isl_aff *aff, int v);
3794 __isl_give isl_aff *isl_aff_set_constant_val(
3795 __isl_take isl_aff *aff, __isl_take isl_val *v);
3796 __isl_give isl_aff *isl_aff_set_coefficient_si(
3797 __isl_take isl_aff *aff,
3798 enum isl_dim_type type, int pos, int v);
3799 __isl_give isl_aff *isl_aff_set_coefficient_val(
3800 __isl_take isl_aff *aff,
3801 enum isl_dim_type type, int pos,
3802 __isl_take isl_val *v);
3804 __isl_give isl_aff *isl_aff_add_constant_si(
3805 __isl_take isl_aff *aff, int v);
3806 __isl_give isl_aff *isl_aff_add_constant_val(
3807 __isl_take isl_aff *aff, __isl_take isl_val *v);
3808 __isl_give isl_aff *isl_aff_add_constant_num_si(
3809 __isl_take isl_aff *aff, int v);
3810 __isl_give isl_aff *isl_aff_add_coefficient_si(
3811 __isl_take isl_aff *aff,
3812 enum isl_dim_type type, int pos, int v);
3813 __isl_give isl_aff *isl_aff_add_coefficient_val(
3814 __isl_take isl_aff *aff,
3815 enum isl_dim_type type, int pos,
3816 __isl_take isl_val *v);
3818 __isl_give isl_aff *isl_aff_insert_dims(
3819 __isl_take isl_aff *aff,
3820 enum isl_dim_type type, unsigned first, unsigned n);
3821 __isl_give isl_pw_aff *isl_pw_aff_insert_dims(
3822 __isl_take isl_pw_aff *pwaff,
3823 enum isl_dim_type type, unsigned first, unsigned n);
3824 __isl_give isl_aff *isl_aff_add_dims(
3825 __isl_take isl_aff *aff,
3826 enum isl_dim_type type, unsigned n);
3827 __isl_give isl_pw_aff *isl_pw_aff_add_dims(
3828 __isl_take isl_pw_aff *pwaff,
3829 enum isl_dim_type type, unsigned n);
3830 __isl_give isl_aff *isl_aff_drop_dims(
3831 __isl_take isl_aff *aff,
3832 enum isl_dim_type type, unsigned first, unsigned n);
3833 __isl_give isl_pw_aff *isl_pw_aff_drop_dims(
3834 __isl_take isl_pw_aff *pwaff,
3835 enum isl_dim_type type, unsigned first, unsigned n);
3836 __isl_give isl_aff *isl_aff_move_dims(
3837 __isl_take isl_aff *aff,
3838 enum isl_dim_type dst_type, unsigned dst_pos,
3839 enum isl_dim_type src_type, unsigned src_pos,
3841 __isl_give isl_pw_aff *isl_pw_aff_move_dims(
3842 __isl_take isl_pw_aff *pa,
3843 enum isl_dim_type dst_type, unsigned dst_pos,
3844 enum isl_dim_type src_type, unsigned src_pos,
3847 Note that C<isl_aff_set_constant_si> and C<isl_aff_set_coefficient_si>
3848 set the I<numerator> of the constant or coefficient, while
3849 C<isl_aff_set_constant_val> and C<isl_aff_set_coefficient_val> set
3850 the constant or coefficient as a whole.
3851 The C<add_constant> and C<add_coefficient> functions add an integer
3852 or rational value to
3853 the possibly rational constant or coefficient.
3854 The C<add_constant_num> functions add an integer value to
3857 To check whether an affine expressions is obviously zero
3858 or (obviously) equal to some other affine expression, use
3860 #include <isl/aff.h>
3861 int isl_aff_plain_is_zero(__isl_keep isl_aff *aff);
3862 int isl_aff_plain_is_equal(__isl_keep isl_aff *aff1,
3863 __isl_keep isl_aff *aff2);
3864 int isl_pw_aff_plain_is_equal(
3865 __isl_keep isl_pw_aff *pwaff1,
3866 __isl_keep isl_pw_aff *pwaff2);
3867 int isl_pw_aff_is_equal(__isl_keep isl_pw_aff *pa1,
3868 __isl_keep isl_pw_aff *pa2);
3872 #include <isl/aff.h>
3873 __isl_give isl_aff *isl_aff_add(__isl_take isl_aff *aff1,
3874 __isl_take isl_aff *aff2);
3875 __isl_give isl_pw_aff *isl_pw_aff_add(
3876 __isl_take isl_pw_aff *pwaff1,
3877 __isl_take isl_pw_aff *pwaff2);
3878 __isl_give isl_pw_aff *isl_pw_aff_min(
3879 __isl_take isl_pw_aff *pwaff1,
3880 __isl_take isl_pw_aff *pwaff2);
3881 __isl_give isl_pw_aff *isl_pw_aff_max(
3882 __isl_take isl_pw_aff *pwaff1,
3883 __isl_take isl_pw_aff *pwaff2);
3884 __isl_give isl_aff *isl_aff_sub(__isl_take isl_aff *aff1,
3885 __isl_take isl_aff *aff2);
3886 __isl_give isl_pw_aff *isl_pw_aff_sub(
3887 __isl_take isl_pw_aff *pwaff1,
3888 __isl_take isl_pw_aff *pwaff2);
3889 __isl_give isl_aff *isl_aff_neg(__isl_take isl_aff *aff);
3890 __isl_give isl_pw_aff *isl_pw_aff_neg(
3891 __isl_take isl_pw_aff *pwaff);
3892 __isl_give isl_aff *isl_aff_ceil(__isl_take isl_aff *aff);
3893 __isl_give isl_pw_aff *isl_pw_aff_ceil(
3894 __isl_take isl_pw_aff *pwaff);
3895 __isl_give isl_aff *isl_aff_floor(__isl_take isl_aff *aff);
3896 __isl_give isl_pw_aff *isl_pw_aff_floor(
3897 __isl_take isl_pw_aff *pwaff);
3898 __isl_give isl_aff *isl_aff_mod_val(__isl_take isl_aff *aff,
3899 __isl_take isl_val *mod);
3900 __isl_give isl_pw_aff *isl_pw_aff_mod_val(
3901 __isl_take isl_pw_aff *pa,
3902 __isl_take isl_val *mod);
3903 __isl_give isl_aff *isl_aff_scale_val(__isl_take isl_aff *aff,
3904 __isl_take isl_val *v);
3905 __isl_give isl_pw_aff *isl_pw_aff_scale_val(
3906 __isl_take isl_pw_aff *pa, __isl_take isl_val *v);
3907 __isl_give isl_aff *isl_aff_scale_down_ui(
3908 __isl_take isl_aff *aff, unsigned f);
3909 __isl_give isl_aff *isl_aff_scale_down_val(
3910 __isl_take isl_aff *aff, __isl_take isl_val *v);
3911 __isl_give isl_pw_aff *isl_pw_aff_scale_down_val(
3912 __isl_take isl_pw_aff *pa,
3913 __isl_take isl_val *f);
3915 __isl_give isl_pw_aff *isl_pw_aff_list_min(
3916 __isl_take isl_pw_aff_list *list);
3917 __isl_give isl_pw_aff *isl_pw_aff_list_max(
3918 __isl_take isl_pw_aff_list *list);
3920 __isl_give isl_pw_aff *isl_pw_aff_coalesce(
3921 __isl_take isl_pw_aff *pwqp);
3923 __isl_give isl_aff *isl_aff_align_params(
3924 __isl_take isl_aff *aff,
3925 __isl_take isl_space *model);
3926 __isl_give isl_pw_aff *isl_pw_aff_align_params(
3927 __isl_take isl_pw_aff *pwaff,
3928 __isl_take isl_space *model);
3930 __isl_give isl_aff *isl_aff_project_domain_on_params(
3931 __isl_take isl_aff *aff);
3932 __isl_give isl_pw_aff *isl_pw_aff_from_range(
3933 __isl_take isl_pw_aff *pwa);
3935 __isl_give isl_aff *isl_aff_gist_params(
3936 __isl_take isl_aff *aff,
3937 __isl_take isl_set *context);
3938 __isl_give isl_aff *isl_aff_gist(__isl_take isl_aff *aff,
3939 __isl_take isl_set *context);
3940 __isl_give isl_pw_aff *isl_pw_aff_gist_params(
3941 __isl_take isl_pw_aff *pwaff,
3942 __isl_take isl_set *context);
3943 __isl_give isl_pw_aff *isl_pw_aff_gist(
3944 __isl_take isl_pw_aff *pwaff,
3945 __isl_take isl_set *context);
3947 __isl_give isl_set *isl_pw_aff_domain(
3948 __isl_take isl_pw_aff *pwaff);
3949 __isl_give isl_set *isl_pw_aff_params(
3950 __isl_take isl_pw_aff *pwa);
3951 __isl_give isl_pw_aff *isl_pw_aff_intersect_domain(
3952 __isl_take isl_pw_aff *pa,
3953 __isl_take isl_set *set);
3954 __isl_give isl_pw_aff *isl_pw_aff_intersect_params(
3955 __isl_take isl_pw_aff *pa,
3956 __isl_take isl_set *set);
3958 __isl_give isl_aff *isl_aff_mul(__isl_take isl_aff *aff1,
3959 __isl_take isl_aff *aff2);
3960 __isl_give isl_aff *isl_aff_div(__isl_take isl_aff *aff1,
3961 __isl_take isl_aff *aff2);
3962 __isl_give isl_pw_aff *isl_pw_aff_mul(
3963 __isl_take isl_pw_aff *pwaff1,
3964 __isl_take isl_pw_aff *pwaff2);
3965 __isl_give isl_pw_aff *isl_pw_aff_div(
3966 __isl_take isl_pw_aff *pa1,
3967 __isl_take isl_pw_aff *pa2);
3968 __isl_give isl_pw_aff *isl_pw_aff_tdiv_q(
3969 __isl_take isl_pw_aff *pa1,
3970 __isl_take isl_pw_aff *pa2);
3971 __isl_give isl_pw_aff *isl_pw_aff_tdiv_r(
3972 __isl_take isl_pw_aff *pa1,
3973 __isl_take isl_pw_aff *pa2);
3975 When multiplying two affine expressions, at least one of the two needs
3976 to be a constant. Similarly, when dividing an affine expression by another,
3977 the second expression needs to be a constant.
3978 C<isl_pw_aff_tdiv_q> computes the quotient of an integer division with
3979 rounding towards zero. C<isl_pw_aff_tdiv_r> computes the corresponding
3982 #include <isl/aff.h>
3983 __isl_give isl_aff *isl_aff_pullback_aff(
3984 __isl_take isl_aff *aff1,
3985 __isl_take isl_aff *aff2);
3986 __isl_give isl_aff *isl_aff_pullback_multi_aff(
3987 __isl_take isl_aff *aff,
3988 __isl_take isl_multi_aff *ma);
3989 __isl_give isl_pw_aff *isl_pw_aff_pullback_multi_aff(
3990 __isl_take isl_pw_aff *pa,
3991 __isl_take isl_multi_aff *ma);
3992 __isl_give isl_pw_aff *isl_pw_aff_pullback_pw_multi_aff(
3993 __isl_take isl_pw_aff *pa,
3994 __isl_take isl_pw_multi_aff *pma);
3996 These functions precompose the input expression by the given
3997 C<isl_aff>, C<isl_multi_aff> or C<isl_pw_multi_aff>. In other words,
3998 the C<isl_aff>, C<isl_multi_aff> or C<isl_pw_multi_aff> is plugged
3999 into the (piecewise) affine expression.
4000 Objects of type C<isl_multi_aff> are described in
4001 L</"Piecewise Multiple Quasi Affine Expressions">.
4003 #include <isl/aff.h>
4004 __isl_give isl_basic_set *isl_aff_zero_basic_set(
4005 __isl_take isl_aff *aff);
4006 __isl_give isl_basic_set *isl_aff_neg_basic_set(
4007 __isl_take isl_aff *aff);
4008 __isl_give isl_basic_set *isl_aff_le_basic_set(
4009 __isl_take isl_aff *aff1, __isl_take isl_aff *aff2);
4010 __isl_give isl_basic_set *isl_aff_ge_basic_set(
4011 __isl_take isl_aff *aff1, __isl_take isl_aff *aff2);
4012 __isl_give isl_set *isl_pw_aff_eq_set(
4013 __isl_take isl_pw_aff *pwaff1,
4014 __isl_take isl_pw_aff *pwaff2);
4015 __isl_give isl_set *isl_pw_aff_ne_set(
4016 __isl_take isl_pw_aff *pwaff1,
4017 __isl_take isl_pw_aff *pwaff2);
4018 __isl_give isl_set *isl_pw_aff_le_set(
4019 __isl_take isl_pw_aff *pwaff1,
4020 __isl_take isl_pw_aff *pwaff2);
4021 __isl_give isl_set *isl_pw_aff_lt_set(
4022 __isl_take isl_pw_aff *pwaff1,
4023 __isl_take isl_pw_aff *pwaff2);
4024 __isl_give isl_set *isl_pw_aff_ge_set(
4025 __isl_take isl_pw_aff *pwaff1,
4026 __isl_take isl_pw_aff *pwaff2);
4027 __isl_give isl_set *isl_pw_aff_gt_set(
4028 __isl_take isl_pw_aff *pwaff1,
4029 __isl_take isl_pw_aff *pwaff2);
4031 __isl_give isl_set *isl_pw_aff_list_eq_set(
4032 __isl_take isl_pw_aff_list *list1,
4033 __isl_take isl_pw_aff_list *list2);
4034 __isl_give isl_set *isl_pw_aff_list_ne_set(
4035 __isl_take isl_pw_aff_list *list1,
4036 __isl_take isl_pw_aff_list *list2);
4037 __isl_give isl_set *isl_pw_aff_list_le_set(
4038 __isl_take isl_pw_aff_list *list1,
4039 __isl_take isl_pw_aff_list *list2);
4040 __isl_give isl_set *isl_pw_aff_list_lt_set(
4041 __isl_take isl_pw_aff_list *list1,
4042 __isl_take isl_pw_aff_list *list2);
4043 __isl_give isl_set *isl_pw_aff_list_ge_set(
4044 __isl_take isl_pw_aff_list *list1,
4045 __isl_take isl_pw_aff_list *list2);
4046 __isl_give isl_set *isl_pw_aff_list_gt_set(
4047 __isl_take isl_pw_aff_list *list1,
4048 __isl_take isl_pw_aff_list *list2);
4050 The function C<isl_aff_neg_basic_set> returns a basic set
4051 containing those elements in the domain space
4052 of C<aff> where C<aff> is negative.
4053 The function C<isl_aff_ge_basic_set> returns a basic set
4054 containing those elements in the shared space
4055 of C<aff1> and C<aff2> where C<aff1> is greater than or equal to C<aff2>.
4056 The function C<isl_pw_aff_ge_set> returns a set
4057 containing those elements in the shared domain
4058 of C<pwaff1> and C<pwaff2> where C<pwaff1> is greater than or equal to C<pwaff2>.
4059 The functions operating on C<isl_pw_aff_list> apply the corresponding
4060 C<isl_pw_aff> function to each pair of elements in the two lists.
4062 #include <isl/aff.h>
4063 __isl_give isl_set *isl_pw_aff_nonneg_set(
4064 __isl_take isl_pw_aff *pwaff);
4065 __isl_give isl_set *isl_pw_aff_zero_set(
4066 __isl_take isl_pw_aff *pwaff);
4067 __isl_give isl_set *isl_pw_aff_non_zero_set(
4068 __isl_take isl_pw_aff *pwaff);
4070 The function C<isl_pw_aff_nonneg_set> returns a set
4071 containing those elements in the domain
4072 of C<pwaff> where C<pwaff> is non-negative.
4074 #include <isl/aff.h>
4075 __isl_give isl_pw_aff *isl_pw_aff_cond(
4076 __isl_take isl_pw_aff *cond,
4077 __isl_take isl_pw_aff *pwaff_true,
4078 __isl_take isl_pw_aff *pwaff_false);
4080 The function C<isl_pw_aff_cond> performs a conditional operator
4081 and returns an expression that is equal to C<pwaff_true>
4082 for elements where C<cond> is non-zero and equal to C<pwaff_false> for elements
4083 where C<cond> is zero.
4085 #include <isl/aff.h>
4086 __isl_give isl_pw_aff *isl_pw_aff_union_min(
4087 __isl_take isl_pw_aff *pwaff1,
4088 __isl_take isl_pw_aff *pwaff2);
4089 __isl_give isl_pw_aff *isl_pw_aff_union_max(
4090 __isl_take isl_pw_aff *pwaff1,
4091 __isl_take isl_pw_aff *pwaff2);
4092 __isl_give isl_pw_aff *isl_pw_aff_union_add(
4093 __isl_take isl_pw_aff *pwaff1,
4094 __isl_take isl_pw_aff *pwaff2);
4096 The function C<isl_pw_aff_union_max> computes a piecewise quasi-affine
4097 expression with a domain that is the union of those of C<pwaff1> and
4098 C<pwaff2> and such that on each cell, the quasi-affine expression is
4099 the maximum of those of C<pwaff1> and C<pwaff2>. If only one of
4100 C<pwaff1> or C<pwaff2> is defined on a given cell, then the
4101 associated expression is the defined one.
4103 An expression can be read from input using
4105 #include <isl/aff.h>
4106 __isl_give isl_aff *isl_aff_read_from_str(
4107 isl_ctx *ctx, const char *str);
4108 __isl_give isl_pw_aff *isl_pw_aff_read_from_str(
4109 isl_ctx *ctx, const char *str);
4111 An expression can be printed using
4113 #include <isl/aff.h>
4114 __isl_give isl_printer *isl_printer_print_aff(
4115 __isl_take isl_printer *p, __isl_keep isl_aff *aff);
4117 __isl_give isl_printer *isl_printer_print_pw_aff(
4118 __isl_take isl_printer *p,
4119 __isl_keep isl_pw_aff *pwaff);
4121 =head2 Piecewise Multiple Quasi Affine Expressions
4123 An C<isl_multi_aff> object represents a sequence of
4124 zero or more affine expressions, all defined on the same domain space.
4125 Similarly, an C<isl_multi_pw_aff> object represents a sequence of
4126 zero or more piecewise affine expressions.
4128 An C<isl_multi_aff> can be constructed from a single
4129 C<isl_aff> or an C<isl_aff_list> using the
4130 following functions. Similarly for C<isl_multi_pw_aff>
4131 and C<isl_pw_multi_aff>.
4133 #include <isl/aff.h>
4134 __isl_give isl_multi_aff *isl_multi_aff_from_aff(
4135 __isl_take isl_aff *aff);
4136 __isl_give isl_multi_pw_aff *
4137 isl_multi_pw_aff_from_multi_aff(
4138 __isl_take isl_multi_aff *ma);
4139 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_from_pw_aff(
4140 __isl_take isl_pw_aff *pa);
4141 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_from_pw_aff(
4142 __isl_take isl_pw_aff *pa);
4143 __isl_give isl_multi_aff *isl_multi_aff_from_aff_list(
4144 __isl_take isl_space *space,
4145 __isl_take isl_aff_list *list);
4147 An C<isl_multi_pw_aff> can be converted to an C<isl_pw_multi_aff>
4148 using the function C<isl_pw_multi_aff_from_multi_pw_aff> below.
4149 Note however that the domain
4150 of the result is the intersection of the domains of the input.
4151 The reverse conversion is exact.
4153 #include <isl/aff.h>
4154 __isl_give isl_pw_multi_aff *
4155 isl_pw_multi_aff_from_multi_pw_aff(
4156 __isl_take isl_multi_pw_aff *mpa);
4157 __isl_give isl_multi_pw_aff *
4158 isl_multi_pw_aff_from_pw_multi_aff(
4159 __isl_take isl_pw_multi_aff *pma);
4161 An empty piecewise multiple quasi affine expression (one with no cells),
4162 the zero piecewise multiple quasi affine expression (with value zero
4163 for each output dimension),
4164 a piecewise multiple quasi affine expression with a single cell (with
4165 either a universe or a specified domain) or
4166 a zero-dimensional piecewise multiple quasi affine expression
4168 can be created using the following functions.
4170 #include <isl/aff.h>
4171 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_empty(
4172 __isl_take isl_space *space);
4173 __isl_give isl_multi_aff *isl_multi_aff_zero(
4174 __isl_take isl_space *space);
4175 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_zero(
4176 __isl_take isl_space *space);
4177 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_zero(
4178 __isl_take isl_space *space);
4179 __isl_give isl_multi_aff *isl_multi_aff_identity(
4180 __isl_take isl_space *space);
4181 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_identity(
4182 __isl_take isl_space *space);
4183 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_identity(
4184 __isl_take isl_space *space);
4185 __isl_give isl_multi_aff *isl_multi_aff_domain_map(
4186 __isl_take isl_space *space);
4187 __isl_give isl_multi_aff *isl_multi_aff_range_map(
4188 __isl_take isl_space *space);
4189 __isl_give isl_multi_aff *isl_multi_aff_project_out_map(
4190 __isl_take isl_space *space,
4191 enum isl_dim_type type,
4192 unsigned first, unsigned n);
4193 __isl_give isl_pw_multi_aff *
4194 isl_pw_multi_aff_project_out_map(
4195 __isl_take isl_space *space,
4196 enum isl_dim_type type,
4197 unsigned first, unsigned n);
4198 __isl_give isl_pw_multi_aff *
4199 isl_pw_multi_aff_from_multi_aff(
4200 __isl_take isl_multi_aff *ma);
4201 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_alloc(
4202 __isl_take isl_set *set,
4203 __isl_take isl_multi_aff *maff);
4204 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_from_domain(
4205 __isl_take isl_set *set);
4207 __isl_give isl_union_pw_multi_aff *
4208 isl_union_pw_multi_aff_empty(
4209 __isl_take isl_space *space);
4210 __isl_give isl_union_pw_multi_aff *
4211 isl_union_pw_multi_aff_add_pw_multi_aff(
4212 __isl_take isl_union_pw_multi_aff *upma,
4213 __isl_take isl_pw_multi_aff *pma);
4214 __isl_give isl_union_pw_multi_aff *
4215 isl_union_pw_multi_aff_from_domain(
4216 __isl_take isl_union_set *uset);
4218 A piecewise multiple quasi affine expression can also be initialized
4219 from an C<isl_set> or C<isl_map>, provided the C<isl_set> is a singleton
4220 and the C<isl_map> is single-valued.
4221 In case of a conversion from an C<isl_union_set> or an C<isl_union_map>
4222 to an C<isl_union_pw_multi_aff>, these properties need to hold in each space.
4224 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_from_set(
4225 __isl_take isl_set *set);
4226 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_from_map(
4227 __isl_take isl_map *map);
4229 __isl_give isl_union_pw_multi_aff *
4230 isl_union_pw_multi_aff_from_union_set(
4231 __isl_take isl_union_set *uset);
4232 __isl_give isl_union_pw_multi_aff *
4233 isl_union_pw_multi_aff_from_union_map(
4234 __isl_take isl_union_map *umap);
4236 Multiple quasi affine expressions can be copied and freed using
4238 #include <isl/aff.h>
4239 __isl_give isl_multi_aff *isl_multi_aff_copy(
4240 __isl_keep isl_multi_aff *maff);
4241 void *isl_multi_aff_free(__isl_take isl_multi_aff *maff);
4243 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_copy(
4244 __isl_keep isl_pw_multi_aff *pma);
4245 void *isl_pw_multi_aff_free(
4246 __isl_take isl_pw_multi_aff *pma);
4248 __isl_give isl_union_pw_multi_aff *
4249 isl_union_pw_multi_aff_copy(
4250 __isl_keep isl_union_pw_multi_aff *upma);
4251 void *isl_union_pw_multi_aff_free(
4252 __isl_take isl_union_pw_multi_aff *upma);
4254 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_copy(
4255 __isl_keep isl_multi_pw_aff *mpa);
4256 void *isl_multi_pw_aff_free(
4257 __isl_take isl_multi_pw_aff *mpa);
4259 The expression can be inspected using
4261 #include <isl/aff.h>
4262 isl_ctx *isl_multi_aff_get_ctx(
4263 __isl_keep isl_multi_aff *maff);
4264 isl_ctx *isl_pw_multi_aff_get_ctx(
4265 __isl_keep isl_pw_multi_aff *pma);
4266 isl_ctx *isl_union_pw_multi_aff_get_ctx(
4267 __isl_keep isl_union_pw_multi_aff *upma);
4268 isl_ctx *isl_multi_pw_aff_get_ctx(
4269 __isl_keep isl_multi_pw_aff *mpa);
4270 unsigned isl_multi_aff_dim(__isl_keep isl_multi_aff *maff,
4271 enum isl_dim_type type);
4272 unsigned isl_pw_multi_aff_dim(
4273 __isl_keep isl_pw_multi_aff *pma,
4274 enum isl_dim_type type);
4275 unsigned isl_multi_pw_aff_dim(
4276 __isl_keep isl_multi_pw_aff *mpa,
4277 enum isl_dim_type type);
4278 __isl_give isl_aff *isl_multi_aff_get_aff(
4279 __isl_keep isl_multi_aff *multi, int pos);
4280 __isl_give isl_pw_aff *isl_pw_multi_aff_get_pw_aff(
4281 __isl_keep isl_pw_multi_aff *pma, int pos);
4282 __isl_give isl_pw_aff *isl_multi_pw_aff_get_pw_aff(
4283 __isl_keep isl_multi_pw_aff *mpa, int pos);
4284 int isl_multi_aff_find_dim_by_id(
4285 __isl_keep isl_multi_aff *ma,
4286 enum isl_dim_type type, __isl_keep isl_id *id);
4287 int isl_multi_pw_aff_find_dim_by_id(
4288 __isl_keep isl_multi_pw_aff *mpa,
4289 enum isl_dim_type type, __isl_keep isl_id *id);
4290 const char *isl_pw_multi_aff_get_dim_name(
4291 __isl_keep isl_pw_multi_aff *pma,
4292 enum isl_dim_type type, unsigned pos);
4293 __isl_give isl_id *isl_multi_aff_get_dim_id(
4294 __isl_keep isl_multi_aff *ma,
4295 enum isl_dim_type type, unsigned pos);
4296 __isl_give isl_id *isl_pw_multi_aff_get_dim_id(
4297 __isl_keep isl_pw_multi_aff *pma,
4298 enum isl_dim_type type, unsigned pos);
4299 __isl_give isl_id *isl_multi_pw_aff_get_dim_id(
4300 __isl_keep isl_multi_pw_aff *mpa,
4301 enum isl_dim_type type, unsigned pos);
4302 const char *isl_multi_aff_get_tuple_name(
4303 __isl_keep isl_multi_aff *multi,
4304 enum isl_dim_type type);
4305 int isl_pw_multi_aff_has_tuple_name(
4306 __isl_keep isl_pw_multi_aff *pma,
4307 enum isl_dim_type type);
4308 const char *isl_pw_multi_aff_get_tuple_name(
4309 __isl_keep isl_pw_multi_aff *pma,
4310 enum isl_dim_type type);
4311 int isl_multi_aff_has_tuple_id(__isl_keep isl_multi_aff *ma,
4312 enum isl_dim_type type);
4313 int isl_pw_multi_aff_has_tuple_id(
4314 __isl_keep isl_pw_multi_aff *pma,
4315 enum isl_dim_type type);
4316 int isl_multi_pw_aff_has_tuple_id(
4317 __isl_keep isl_multi_pw_aff *mpa,
4318 enum isl_dim_type type);
4319 __isl_give isl_id *isl_multi_aff_get_tuple_id(
4320 __isl_keep isl_multi_aff *ma,
4321 enum isl_dim_type type);
4322 __isl_give isl_id *isl_pw_multi_aff_get_tuple_id(
4323 __isl_keep isl_pw_multi_aff *pma,
4324 enum isl_dim_type type);
4325 __isl_give isl_id *isl_multi_pw_aff_get_tuple_id(
4326 __isl_keep isl_multi_pw_aff *mpa,
4327 enum isl_dim_type type);
4328 int isl_multi_aff_range_is_wrapping(
4329 __isl_keep isl_multi_aff *ma);
4330 int isl_multi_pw_aff_range_is_wrapping(
4331 __isl_keep isl_multi_pw_aff *mpa);
4333 int isl_pw_multi_aff_foreach_piece(
4334 __isl_keep isl_pw_multi_aff *pma,
4335 int (*fn)(__isl_take isl_set *set,
4336 __isl_take isl_multi_aff *maff,
4337 void *user), void *user);
4339 int isl_union_pw_multi_aff_foreach_pw_multi_aff(
4340 __isl_keep isl_union_pw_multi_aff *upma,
4341 int (*fn)(__isl_take isl_pw_multi_aff *pma,
4342 void *user), void *user);
4344 It can be modified using
4346 #include <isl/aff.h>
4347 __isl_give isl_multi_aff *isl_multi_aff_set_aff(
4348 __isl_take isl_multi_aff *multi, int pos,
4349 __isl_take isl_aff *aff);
4350 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_set_pw_aff(
4351 __isl_take isl_pw_multi_aff *pma, unsigned pos,
4352 __isl_take isl_pw_aff *pa);
4353 __isl_give isl_multi_aff *isl_multi_aff_set_dim_name(
4354 __isl_take isl_multi_aff *maff,
4355 enum isl_dim_type type, unsigned pos, const char *s);
4356 __isl_give isl_multi_aff *isl_multi_aff_set_dim_id(
4357 __isl_take isl_multi_aff *maff,
4358 enum isl_dim_type type, unsigned pos,
4359 __isl_take isl_id *id);
4360 __isl_give isl_multi_aff *isl_multi_aff_set_tuple_name(
4361 __isl_take isl_multi_aff *maff,
4362 enum isl_dim_type type, const char *s);
4363 __isl_give isl_multi_aff *isl_multi_aff_set_tuple_id(
4364 __isl_take isl_multi_aff *maff,
4365 enum isl_dim_type type, __isl_take isl_id *id);
4366 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_set_tuple_id(
4367 __isl_take isl_pw_multi_aff *pma,
4368 enum isl_dim_type type, __isl_take isl_id *id);
4369 __isl_give isl_multi_aff *isl_multi_aff_reset_tuple_id(
4370 __isl_take isl_multi_aff *ma,
4371 enum isl_dim_type type);
4372 __isl_give isl_multi_pw_aff *
4373 isl_multi_pw_aff_reset_tuple_id(
4374 __isl_take isl_multi_pw_aff *mpa,
4375 enum isl_dim_type type);
4376 __isl_give isl_multi_aff *isl_multi_aff_reset_user(
4377 __isl_take isl_multi_aff *ma);
4378 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_reset_user(
4379 __isl_take isl_multi_pw_aff *mpa);
4381 __isl_give isl_multi_pw_aff *
4382 isl_multi_pw_aff_set_dim_name(
4383 __isl_take isl_multi_pw_aff *mpa,
4384 enum isl_dim_type type, unsigned pos, const char *s);
4385 __isl_give isl_multi_pw_aff *
4386 isl_multi_pw_aff_set_dim_id(
4387 __isl_take isl_multi_pw_aff *mpa,
4388 enum isl_dim_type type, unsigned pos,
4389 __isl_take isl_id *id);
4390 __isl_give isl_multi_pw_aff *
4391 isl_multi_pw_aff_set_tuple_name(
4392 __isl_take isl_multi_pw_aff *mpa,
4393 enum isl_dim_type type, const char *s);
4395 __isl_give isl_multi_aff *isl_multi_aff_insert_dims(
4396 __isl_take isl_multi_aff *ma,
4397 enum isl_dim_type type, unsigned first, unsigned n);
4398 __isl_give isl_multi_aff *isl_multi_aff_add_dims(
4399 __isl_take isl_multi_aff *ma,
4400 enum isl_dim_type type, unsigned n);
4401 __isl_give isl_multi_aff *isl_multi_aff_drop_dims(
4402 __isl_take isl_multi_aff *maff,
4403 enum isl_dim_type type, unsigned first, unsigned n);
4404 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_drop_dims(
4405 __isl_take isl_pw_multi_aff *pma,
4406 enum isl_dim_type type, unsigned first, unsigned n);
4408 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_insert_dims(
4409 __isl_take isl_multi_pw_aff *mpa,
4410 enum isl_dim_type type, unsigned first, unsigned n);
4411 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_add_dims(
4412 __isl_take isl_multi_pw_aff *mpa,
4413 enum isl_dim_type type, unsigned n);
4414 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_move_dims(
4415 __isl_take isl_multi_pw_aff *pma,
4416 enum isl_dim_type dst_type, unsigned dst_pos,
4417 enum isl_dim_type src_type, unsigned src_pos,
4420 To check whether two multiple affine expressions are
4421 (obviously) equal to each other, use
4423 int isl_multi_aff_plain_is_equal(__isl_keep isl_multi_aff *maff1,
4424 __isl_keep isl_multi_aff *maff2);
4425 int isl_pw_multi_aff_plain_is_equal(
4426 __isl_keep isl_pw_multi_aff *pma1,
4427 __isl_keep isl_pw_multi_aff *pma2);
4428 int isl_multi_pw_aff_plain_is_equal(
4429 __isl_keep isl_multi_pw_aff *mpa1,
4430 __isl_keep isl_multi_pw_aff *mpa2);
4431 int isl_multi_pw_aff_is_equal(
4432 __isl_keep isl_multi_pw_aff *mpa1,
4433 __isl_keep isl_multi_pw_aff *mpa2);
4437 #include <isl/aff.h>
4438 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_union_lexmin(
4439 __isl_take isl_pw_multi_aff *pma1,
4440 __isl_take isl_pw_multi_aff *pma2);
4441 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_union_lexmax(
4442 __isl_take isl_pw_multi_aff *pma1,
4443 __isl_take isl_pw_multi_aff *pma2);
4444 __isl_give isl_multi_aff *isl_multi_aff_add(
4445 __isl_take isl_multi_aff *maff1,
4446 __isl_take isl_multi_aff *maff2);
4447 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_add(
4448 __isl_take isl_pw_multi_aff *pma1,
4449 __isl_take isl_pw_multi_aff *pma2);
4450 __isl_give isl_union_pw_multi_aff *isl_union_pw_multi_aff_add(
4451 __isl_take isl_union_pw_multi_aff *upma1,
4452 __isl_take isl_union_pw_multi_aff *upma2);
4453 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_union_add(
4454 __isl_take isl_pw_multi_aff *pma1,
4455 __isl_take isl_pw_multi_aff *pma2);
4456 __isl_give isl_multi_aff *isl_multi_aff_sub(
4457 __isl_take isl_multi_aff *ma1,
4458 __isl_take isl_multi_aff *ma2);
4459 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_sub(
4460 __isl_take isl_pw_multi_aff *pma1,
4461 __isl_take isl_pw_multi_aff *pma2);
4462 __isl_give isl_union_pw_multi_aff *isl_union_pw_multi_aff_sub(
4463 __isl_take isl_union_pw_multi_aff *upma1,
4464 __isl_take isl_union_pw_multi_aff *upma2);
4466 C<isl_multi_aff_sub> subtracts the second argument from the first.
4468 __isl_give isl_multi_aff *isl_multi_aff_scale_val(
4469 __isl_take isl_multi_aff *ma,
4470 __isl_take isl_val *v);
4471 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_scale_val(
4472 __isl_take isl_pw_multi_aff *pma,
4473 __isl_take isl_val *v);
4474 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_scale_val(
4475 __isl_take isl_multi_pw_aff *mpa,
4476 __isl_take isl_val *v);
4477 __isl_give isl_multi_aff *isl_multi_aff_scale_multi_val(
4478 __isl_take isl_multi_aff *ma,
4479 __isl_take isl_multi_val *mv);
4480 __isl_give isl_pw_multi_aff *
4481 isl_pw_multi_aff_scale_multi_val(
4482 __isl_take isl_pw_multi_aff *pma,
4483 __isl_take isl_multi_val *mv);
4484 __isl_give isl_multi_pw_aff *
4485 isl_multi_pw_aff_scale_multi_val(
4486 __isl_take isl_multi_pw_aff *mpa,
4487 __isl_take isl_multi_val *mv);
4488 __isl_give isl_union_pw_multi_aff *
4489 isl_union_pw_multi_aff_scale_multi_val(
4490 __isl_take isl_union_pw_multi_aff *upma,
4491 __isl_take isl_multi_val *mv);
4492 __isl_give isl_multi_aff *
4493 isl_multi_aff_scale_down_multi_val(
4494 __isl_take isl_multi_aff *ma,
4495 __isl_take isl_multi_val *mv);
4496 __isl_give isl_multi_pw_aff *
4497 isl_multi_pw_aff_scale_down_multi_val(
4498 __isl_take isl_multi_pw_aff *mpa,
4499 __isl_take isl_multi_val *mv);
4501 C<isl_multi_aff_scale_multi_val> scales the elements of C<ma>
4502 by the corresponding elements of C<mv>.
4504 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_fix_si(
4505 __isl_take isl_pw_multi_aff *pma,
4506 enum isl_dim_type type, unsigned pos, int value);
4507 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_intersect_params(
4508 __isl_take isl_pw_multi_aff *pma,
4509 __isl_take isl_set *set);
4510 __isl_give isl_set *isl_multi_pw_aff_domain(
4511 __isl_take isl_multi_pw_aff *mpa);
4512 __isl_give isl_multi_pw_aff *
4513 isl_multi_pw_aff_intersect_params(
4514 __isl_take isl_multi_pw_aff *mpa,
4515 __isl_take isl_set *set);
4516 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_intersect_domain(
4517 __isl_take isl_pw_multi_aff *pma,
4518 __isl_take isl_set *set);
4519 __isl_give isl_multi_pw_aff *
4520 isl_multi_pw_aff_intersect_domain(
4521 __isl_take isl_multi_pw_aff *mpa,
4522 __isl_take isl_set *domain);
4523 __isl_give isl_union_pw_multi_aff *
4524 isl_union_pw_multi_aff_intersect_domain(
4525 __isl_take isl_union_pw_multi_aff *upma,
4526 __isl_take isl_union_set *uset);
4527 __isl_give isl_multi_aff *isl_multi_aff_lift(
4528 __isl_take isl_multi_aff *maff,
4529 __isl_give isl_local_space **ls);
4530 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_coalesce(
4531 __isl_take isl_pw_multi_aff *pma);
4532 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_coalesce(
4533 __isl_take isl_multi_pw_aff *mpa);
4534 __isl_give isl_multi_aff *isl_multi_aff_align_params(
4535 __isl_take isl_multi_aff *multi,
4536 __isl_take isl_space *model);
4537 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_align_params(
4538 __isl_take isl_pw_multi_aff *pma,
4539 __isl_take isl_space *model);
4540 __isl_give isl_pw_multi_aff *
4541 isl_pw_multi_aff_project_domain_on_params(
4542 __isl_take isl_pw_multi_aff *pma);
4543 __isl_give isl_multi_aff *isl_multi_aff_gist_params(
4544 __isl_take isl_multi_aff *maff,
4545 __isl_take isl_set *context);
4546 __isl_give isl_multi_aff *isl_multi_aff_gist(
4547 __isl_take isl_multi_aff *maff,
4548 __isl_take isl_set *context);
4549 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_gist_params(
4550 __isl_take isl_pw_multi_aff *pma,
4551 __isl_take isl_set *set);
4552 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_gist(
4553 __isl_take isl_pw_multi_aff *pma,
4554 __isl_take isl_set *set);
4555 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_gist_params(
4556 __isl_take isl_multi_pw_aff *mpa,
4557 __isl_take isl_set *set);
4558 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_gist(
4559 __isl_take isl_multi_pw_aff *mpa,
4560 __isl_take isl_set *set);
4561 __isl_give isl_multi_aff *isl_multi_aff_from_range(
4562 __isl_take isl_multi_aff *ma);
4563 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_from_range(
4564 __isl_take isl_multi_pw_aff *mpa);
4565 __isl_give isl_set *isl_pw_multi_aff_domain(
4566 __isl_take isl_pw_multi_aff *pma);
4567 __isl_give isl_union_set *isl_union_pw_multi_aff_domain(
4568 __isl_take isl_union_pw_multi_aff *upma);
4569 __isl_give isl_multi_aff *isl_multi_aff_range_splice(
4570 __isl_take isl_multi_aff *ma1, unsigned pos,
4571 __isl_take isl_multi_aff *ma2);
4572 __isl_give isl_multi_aff *isl_multi_aff_splice(
4573 __isl_take isl_multi_aff *ma1,
4574 unsigned in_pos, unsigned out_pos,
4575 __isl_take isl_multi_aff *ma2);
4576 __isl_give isl_multi_aff *isl_multi_aff_range_product(
4577 __isl_take isl_multi_aff *ma1,
4578 __isl_take isl_multi_aff *ma2);
4579 __isl_give isl_multi_aff *
4580 isl_multi_aff_range_factor_domain(
4581 __isl_take isl_multi_aff *ma);
4582 __isl_give isl_multi_aff *
4583 isl_multi_aff_range_factor_range(
4584 __isl_take isl_multi_aff *ma);
4585 __isl_give isl_multi_aff *isl_multi_aff_flat_range_product(
4586 __isl_take isl_multi_aff *ma1,
4587 __isl_take isl_multi_aff *ma2);
4588 __isl_give isl_multi_aff *isl_multi_aff_product(
4589 __isl_take isl_multi_aff *ma1,
4590 __isl_take isl_multi_aff *ma2);
4591 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_product(
4592 __isl_take isl_multi_pw_aff *mpa1,
4593 __isl_take isl_multi_pw_aff *mpa2);
4594 __isl_give isl_pw_multi_aff *
4595 isl_pw_multi_aff_range_product(
4596 __isl_take isl_pw_multi_aff *pma1,
4597 __isl_take isl_pw_multi_aff *pma2);
4598 __isl_give isl_multi_pw_aff *
4599 isl_multi_pw_aff_range_factor_domain(
4600 __isl_take isl_multi_pw_aff *mpa);
4601 __isl_give isl_multi_pw_aff *
4602 isl_multi_pw_aff_range_factor_range(
4603 __isl_take isl_multi_pw_aff *mpa);
4604 __isl_give isl_pw_multi_aff *
4605 isl_pw_multi_aff_flat_range_product(
4606 __isl_take isl_pw_multi_aff *pma1,
4607 __isl_take isl_pw_multi_aff *pma2);
4608 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_product(
4609 __isl_take isl_pw_multi_aff *pma1,
4610 __isl_take isl_pw_multi_aff *pma2);
4611 __isl_give isl_union_pw_multi_aff *
4612 isl_union_pw_multi_aff_flat_range_product(
4613 __isl_take isl_union_pw_multi_aff *upma1,
4614 __isl_take isl_union_pw_multi_aff *upma2);
4615 __isl_give isl_multi_pw_aff *
4616 isl_multi_pw_aff_range_splice(
4617 __isl_take isl_multi_pw_aff *mpa1, unsigned pos,
4618 __isl_take isl_multi_pw_aff *mpa2);
4619 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_splice(
4620 __isl_take isl_multi_pw_aff *mpa1,
4621 unsigned in_pos, unsigned out_pos,
4622 __isl_take isl_multi_pw_aff *mpa2);
4623 __isl_give isl_multi_pw_aff *
4624 isl_multi_pw_aff_range_product(
4625 __isl_take isl_multi_pw_aff *mpa1,
4626 __isl_take isl_multi_pw_aff *mpa2);
4627 __isl_give isl_multi_pw_aff *
4628 isl_multi_pw_aff_flat_range_product(
4629 __isl_take isl_multi_pw_aff *mpa1,
4630 __isl_take isl_multi_pw_aff *mpa2);
4632 If the C<ls> argument of C<isl_multi_aff_lift> is not C<NULL>,
4633 then it is assigned the local space that lies at the basis of
4634 the lifting applied.
4636 #include <isl/aff.h>
4637 __isl_give isl_multi_aff *isl_multi_aff_pullback_multi_aff(
4638 __isl_take isl_multi_aff *ma1,
4639 __isl_take isl_multi_aff *ma2);
4640 __isl_give isl_pw_multi_aff *
4641 isl_pw_multi_aff_pullback_multi_aff(
4642 __isl_take isl_pw_multi_aff *pma,
4643 __isl_take isl_multi_aff *ma);
4644 __isl_give isl_multi_pw_aff *
4645 isl_multi_pw_aff_pullback_multi_aff(
4646 __isl_take isl_multi_pw_aff *mpa,
4647 __isl_take isl_multi_aff *ma);
4648 __isl_give isl_pw_multi_aff *
4649 isl_pw_multi_aff_pullback_pw_multi_aff(
4650 __isl_take isl_pw_multi_aff *pma1,
4651 __isl_take isl_pw_multi_aff *pma2);
4652 __isl_give isl_multi_pw_aff *
4653 isl_multi_pw_aff_pullback_pw_multi_aff(
4654 __isl_take isl_multi_pw_aff *mpa,
4655 __isl_take isl_pw_multi_aff *pma);
4656 __isl_give isl_multi_pw_aff *
4657 isl_multi_pw_aff_pullback_multi_pw_aff(
4658 __isl_take isl_multi_pw_aff *mpa1,
4659 __isl_take isl_multi_pw_aff *mpa2);
4661 The function C<isl_multi_aff_pullback_multi_aff> precomposes C<ma1> by C<ma2>.
4662 In other words, C<ma2> is plugged
4665 __isl_give isl_set *isl_multi_aff_lex_le_set(
4666 __isl_take isl_multi_aff *ma1,
4667 __isl_take isl_multi_aff *ma2);
4668 __isl_give isl_set *isl_multi_aff_lex_ge_set(
4669 __isl_take isl_multi_aff *ma1,
4670 __isl_take isl_multi_aff *ma2);
4672 The function C<isl_multi_aff_lex_le_set> returns a set
4673 containing those elements in the shared domain space
4674 where C<ma1> is lexicographically smaller than or
4677 An expression can be read from input using
4679 #include <isl/aff.h>
4680 __isl_give isl_multi_aff *isl_multi_aff_read_from_str(
4681 isl_ctx *ctx, const char *str);
4682 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_read_from_str(
4683 isl_ctx *ctx, const char *str);
4684 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_read_from_str(
4685 isl_ctx *ctx, const char *str);
4686 __isl_give isl_union_pw_multi_aff *
4687 isl_union_pw_multi_aff_read_from_str(
4688 isl_ctx *ctx, const char *str);
4690 An expression can be printed using
4692 #include <isl/aff.h>
4693 __isl_give isl_printer *isl_printer_print_multi_aff(
4694 __isl_take isl_printer *p,
4695 __isl_keep isl_multi_aff *maff);
4696 __isl_give isl_printer *isl_printer_print_pw_multi_aff(
4697 __isl_take isl_printer *p,
4698 __isl_keep isl_pw_multi_aff *pma);
4699 __isl_give isl_printer *isl_printer_print_union_pw_multi_aff(
4700 __isl_take isl_printer *p,
4701 __isl_keep isl_union_pw_multi_aff *upma);
4702 __isl_give isl_printer *isl_printer_print_multi_pw_aff(
4703 __isl_take isl_printer *p,
4704 __isl_keep isl_multi_pw_aff *mpa);
4708 Points are elements of a set. They can be used to construct
4709 simple sets (boxes) or they can be used to represent the
4710 individual elements of a set.
4711 The zero point (the origin) can be created using
4713 __isl_give isl_point *isl_point_zero(__isl_take isl_space *space);
4715 The coordinates of a point can be inspected, set and changed
4718 __isl_give isl_val *isl_point_get_coordinate_val(
4719 __isl_keep isl_point *pnt,
4720 enum isl_dim_type type, int pos);
4721 __isl_give isl_point *isl_point_set_coordinate_val(
4722 __isl_take isl_point *pnt,
4723 enum isl_dim_type type, int pos,
4724 __isl_take isl_val *v);
4726 __isl_give isl_point *isl_point_add_ui(
4727 __isl_take isl_point *pnt,
4728 enum isl_dim_type type, int pos, unsigned val);
4729 __isl_give isl_point *isl_point_sub_ui(
4730 __isl_take isl_point *pnt,
4731 enum isl_dim_type type, int pos, unsigned val);
4733 Other properties can be obtained using
4735 isl_ctx *isl_point_get_ctx(__isl_keep isl_point *pnt);
4737 Points can be copied or freed using
4739 __isl_give isl_point *isl_point_copy(
4740 __isl_keep isl_point *pnt);
4741 void isl_point_free(__isl_take isl_point *pnt);
4743 A singleton set can be created from a point using
4745 __isl_give isl_basic_set *isl_basic_set_from_point(
4746 __isl_take isl_point *pnt);
4747 __isl_give isl_set *isl_set_from_point(
4748 __isl_take isl_point *pnt);
4750 and a box can be created from two opposite extremal points using
4752 __isl_give isl_basic_set *isl_basic_set_box_from_points(
4753 __isl_take isl_point *pnt1,
4754 __isl_take isl_point *pnt2);
4755 __isl_give isl_set *isl_set_box_from_points(
4756 __isl_take isl_point *pnt1,
4757 __isl_take isl_point *pnt2);
4759 All elements of a B<bounded> (union) set can be enumerated using
4760 the following functions.
4762 int isl_set_foreach_point(__isl_keep isl_set *set,
4763 int (*fn)(__isl_take isl_point *pnt, void *user),
4765 int isl_union_set_foreach_point(__isl_keep isl_union_set *uset,
4766 int (*fn)(__isl_take isl_point *pnt, void *user),
4769 The function C<fn> is called for each integer point in
4770 C<set> with as second argument the last argument of
4771 the C<isl_set_foreach_point> call. The function C<fn>
4772 should return C<0> on success and C<-1> on failure.
4773 In the latter case, C<isl_set_foreach_point> will stop
4774 enumerating and return C<-1> as well.
4775 If the enumeration is performed successfully and to completion,
4776 then C<isl_set_foreach_point> returns C<0>.
4778 To obtain a single point of a (basic) set, use
4780 __isl_give isl_point *isl_basic_set_sample_point(
4781 __isl_take isl_basic_set *bset);
4782 __isl_give isl_point *isl_set_sample_point(
4783 __isl_take isl_set *set);
4785 If C<set> does not contain any (integer) points, then the
4786 resulting point will be ``void'', a property that can be
4789 int isl_point_is_void(__isl_keep isl_point *pnt);
4791 =head2 Piecewise Quasipolynomials
4793 A piecewise quasipolynomial is a particular kind of function that maps
4794 a parametric point to a rational value.
4795 More specifically, a quasipolynomial is a polynomial expression in greatest
4796 integer parts of affine expressions of parameters and variables.
4797 A piecewise quasipolynomial is a subdivision of a given parametric
4798 domain into disjoint cells with a quasipolynomial associated to
4799 each cell. The value of the piecewise quasipolynomial at a given
4800 point is the value of the quasipolynomial associated to the cell
4801 that contains the point. Outside of the union of cells,
4802 the value is assumed to be zero.
4803 For example, the piecewise quasipolynomial
4805 [n] -> { [x] -> ((1 + n) - x) : x <= n and x >= 0 }
4807 maps C<x> to C<1 + n - x> for values of C<x> between C<0> and C<n>.
4808 A given piecewise quasipolynomial has a fixed domain dimension.
4809 Union piecewise quasipolynomials are used to contain piecewise quasipolynomials
4810 defined over different domains.
4811 Piecewise quasipolynomials are mainly used by the C<barvinok>
4812 library for representing the number of elements in a parametric set or map.
4813 For example, the piecewise quasipolynomial above represents
4814 the number of points in the map
4816 [n] -> { [x] -> [y] : x,y >= 0 and 0 <= x + y <= n }
4818 =head3 Input and Output
4820 Piecewise quasipolynomials can be read from input using
4822 __isl_give isl_union_pw_qpolynomial *
4823 isl_union_pw_qpolynomial_read_from_str(
4824 isl_ctx *ctx, const char *str);
4826 Quasipolynomials and piecewise quasipolynomials can be printed
4827 using the following functions.
4829 __isl_give isl_printer *isl_printer_print_qpolynomial(
4830 __isl_take isl_printer *p,
4831 __isl_keep isl_qpolynomial *qp);
4833 __isl_give isl_printer *isl_printer_print_pw_qpolynomial(
4834 __isl_take isl_printer *p,
4835 __isl_keep isl_pw_qpolynomial *pwqp);
4837 __isl_give isl_printer *isl_printer_print_union_pw_qpolynomial(
4838 __isl_take isl_printer *p,
4839 __isl_keep isl_union_pw_qpolynomial *upwqp);
4841 The output format of the printer
4842 needs to be set to either C<ISL_FORMAT_ISL> or C<ISL_FORMAT_C>.
4843 For C<isl_printer_print_union_pw_qpolynomial>, only C<ISL_FORMAT_ISL>
4845 In case of printing in C<ISL_FORMAT_C>, the user may want
4846 to set the names of all dimensions
4848 __isl_give isl_qpolynomial *isl_qpolynomial_set_dim_name(
4849 __isl_take isl_qpolynomial *qp,
4850 enum isl_dim_type type, unsigned pos,
4852 __isl_give isl_pw_qpolynomial *
4853 isl_pw_qpolynomial_set_dim_name(
4854 __isl_take isl_pw_qpolynomial *pwqp,
4855 enum isl_dim_type type, unsigned pos,
4858 =head3 Creating New (Piecewise) Quasipolynomials
4860 Some simple quasipolynomials can be created using the following functions.
4861 More complicated quasipolynomials can be created by applying
4862 operations such as addition and multiplication
4863 on the resulting quasipolynomials
4865 __isl_give isl_qpolynomial *isl_qpolynomial_zero_on_domain(
4866 __isl_take isl_space *domain);
4867 __isl_give isl_qpolynomial *isl_qpolynomial_one_on_domain(
4868 __isl_take isl_space *domain);
4869 __isl_give isl_qpolynomial *isl_qpolynomial_infty_on_domain(
4870 __isl_take isl_space *domain);
4871 __isl_give isl_qpolynomial *isl_qpolynomial_neginfty_on_domain(
4872 __isl_take isl_space *domain);
4873 __isl_give isl_qpolynomial *isl_qpolynomial_nan_on_domain(
4874 __isl_take isl_space *domain);
4875 __isl_give isl_qpolynomial *isl_qpolynomial_val_on_domain(
4876 __isl_take isl_space *domain,
4877 __isl_take isl_val *val);
4878 __isl_give isl_qpolynomial *isl_qpolynomial_var_on_domain(
4879 __isl_take isl_space *domain,
4880 enum isl_dim_type type, unsigned pos);
4881 __isl_give isl_qpolynomial *isl_qpolynomial_from_aff(
4882 __isl_take isl_aff *aff);
4884 Note that the space in which a quasipolynomial lives is a map space
4885 with a one-dimensional range. The C<domain> argument in some of
4886 the functions above corresponds to the domain of this map space.
4888 The zero piecewise quasipolynomial or a piecewise quasipolynomial
4889 with a single cell can be created using the following functions.
4890 Multiple of these single cell piecewise quasipolynomials can
4891 be combined to create more complicated piecewise quasipolynomials.
4893 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_zero(
4894 __isl_take isl_space *space);
4895 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_alloc(
4896 __isl_take isl_set *set,
4897 __isl_take isl_qpolynomial *qp);
4898 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_from_qpolynomial(
4899 __isl_take isl_qpolynomial *qp);
4900 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_from_pw_aff(
4901 __isl_take isl_pw_aff *pwaff);
4903 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_zero(
4904 __isl_take isl_space *space);
4905 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_from_pw_qpolynomial(
4906 __isl_take isl_pw_qpolynomial *pwqp);
4907 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_add_pw_qpolynomial(
4908 __isl_take isl_union_pw_qpolynomial *upwqp,
4909 __isl_take isl_pw_qpolynomial *pwqp);
4911 Quasipolynomials can be copied and freed again using the following
4914 __isl_give isl_qpolynomial *isl_qpolynomial_copy(
4915 __isl_keep isl_qpolynomial *qp);
4916 void *isl_qpolynomial_free(__isl_take isl_qpolynomial *qp);
4918 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_copy(
4919 __isl_keep isl_pw_qpolynomial *pwqp);
4920 void *isl_pw_qpolynomial_free(
4921 __isl_take isl_pw_qpolynomial *pwqp);
4923 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_copy(
4924 __isl_keep isl_union_pw_qpolynomial *upwqp);
4925 void *isl_union_pw_qpolynomial_free(
4926 __isl_take isl_union_pw_qpolynomial *upwqp);
4928 =head3 Inspecting (Piecewise) Quasipolynomials
4930 To iterate over all piecewise quasipolynomials in a union
4931 piecewise quasipolynomial, use the following function
4933 int isl_union_pw_qpolynomial_foreach_pw_qpolynomial(
4934 __isl_keep isl_union_pw_qpolynomial *upwqp,
4935 int (*fn)(__isl_take isl_pw_qpolynomial *pwqp, void *user),
4938 To extract the piecewise quasipolynomial in a given space from a union, use
4940 __isl_give isl_pw_qpolynomial *
4941 isl_union_pw_qpolynomial_extract_pw_qpolynomial(
4942 __isl_keep isl_union_pw_qpolynomial *upwqp,
4943 __isl_take isl_space *space);
4945 To iterate over the cells in a piecewise quasipolynomial,
4946 use either of the following two functions
4948 int isl_pw_qpolynomial_foreach_piece(
4949 __isl_keep isl_pw_qpolynomial *pwqp,
4950 int (*fn)(__isl_take isl_set *set,
4951 __isl_take isl_qpolynomial *qp,
4952 void *user), void *user);
4953 int isl_pw_qpolynomial_foreach_lifted_piece(
4954 __isl_keep isl_pw_qpolynomial *pwqp,
4955 int (*fn)(__isl_take isl_set *set,
4956 __isl_take isl_qpolynomial *qp,
4957 void *user), void *user);
4959 As usual, the function C<fn> should return C<0> on success
4960 and C<-1> on failure. The difference between
4961 C<isl_pw_qpolynomial_foreach_piece> and
4962 C<isl_pw_qpolynomial_foreach_lifted_piece> is that
4963 C<isl_pw_qpolynomial_foreach_lifted_piece> will first
4964 compute unique representations for all existentially quantified
4965 variables and then turn these existentially quantified variables
4966 into extra set variables, adapting the associated quasipolynomial
4967 accordingly. This means that the C<set> passed to C<fn>
4968 will not have any existentially quantified variables, but that
4969 the dimensions of the sets may be different for different
4970 invocations of C<fn>.
4972 The constant term of a quasipolynomial can be extracted using
4974 __isl_give isl_val *isl_qpolynomial_get_constant_val(
4975 __isl_keep isl_qpolynomial *qp);
4977 To iterate over all terms in a quasipolynomial,
4980 int isl_qpolynomial_foreach_term(
4981 __isl_keep isl_qpolynomial *qp,
4982 int (*fn)(__isl_take isl_term *term,
4983 void *user), void *user);
4985 The terms themselves can be inspected and freed using
4988 unsigned isl_term_dim(__isl_keep isl_term *term,
4989 enum isl_dim_type type);
4990 __isl_give isl_val *isl_term_get_coefficient_val(
4991 __isl_keep isl_term *term);
4992 int isl_term_get_exp(__isl_keep isl_term *term,
4993 enum isl_dim_type type, unsigned pos);
4994 __isl_give isl_aff *isl_term_get_div(
4995 __isl_keep isl_term *term, unsigned pos);
4996 void isl_term_free(__isl_take isl_term *term);
4998 Each term is a product of parameters, set variables and
4999 integer divisions. The function C<isl_term_get_exp>
5000 returns the exponent of a given dimensions in the given term.
5002 =head3 Properties of (Piecewise) Quasipolynomials
5004 To check whether two union piecewise quasipolynomials are
5005 obviously equal, use
5007 int isl_union_pw_qpolynomial_plain_is_equal(
5008 __isl_keep isl_union_pw_qpolynomial *upwqp1,
5009 __isl_keep isl_union_pw_qpolynomial *upwqp2);
5011 =head3 Operations on (Piecewise) Quasipolynomials
5013 __isl_give isl_qpolynomial *isl_qpolynomial_scale_val(
5014 __isl_take isl_qpolynomial *qp,
5015 __isl_take isl_val *v);
5016 __isl_give isl_qpolynomial *isl_qpolynomial_neg(
5017 __isl_take isl_qpolynomial *qp);
5018 __isl_give isl_qpolynomial *isl_qpolynomial_add(
5019 __isl_take isl_qpolynomial *qp1,
5020 __isl_take isl_qpolynomial *qp2);
5021 __isl_give isl_qpolynomial *isl_qpolynomial_sub(
5022 __isl_take isl_qpolynomial *qp1,
5023 __isl_take isl_qpolynomial *qp2);
5024 __isl_give isl_qpolynomial *isl_qpolynomial_mul(
5025 __isl_take isl_qpolynomial *qp1,
5026 __isl_take isl_qpolynomial *qp2);
5027 __isl_give isl_qpolynomial *isl_qpolynomial_pow(
5028 __isl_take isl_qpolynomial *qp, unsigned exponent);
5030 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_fix_val(
5031 __isl_take isl_pw_qpolynomial *pwqp,
5032 enum isl_dim_type type, unsigned n,
5033 __isl_take isl_val *v);
5034 __isl_give isl_pw_qpolynomial *
5035 isl_pw_qpolynomial_scale_val(
5036 __isl_take isl_pw_qpolynomial *pwqp,
5037 __isl_take isl_val *v);
5038 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_add(
5039 __isl_take isl_pw_qpolynomial *pwqp1,
5040 __isl_take isl_pw_qpolynomial *pwqp2);
5041 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_sub(
5042 __isl_take isl_pw_qpolynomial *pwqp1,
5043 __isl_take isl_pw_qpolynomial *pwqp2);
5044 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_add_disjoint(
5045 __isl_take isl_pw_qpolynomial *pwqp1,
5046 __isl_take isl_pw_qpolynomial *pwqp2);
5047 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_neg(
5048 __isl_take isl_pw_qpolynomial *pwqp);
5049 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_mul(
5050 __isl_take isl_pw_qpolynomial *pwqp1,
5051 __isl_take isl_pw_qpolynomial *pwqp2);
5052 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_pow(
5053 __isl_take isl_pw_qpolynomial *pwqp, unsigned exponent);
5055 __isl_give isl_union_pw_qpolynomial *
5056 isl_union_pw_qpolynomial_scale_val(
5057 __isl_take isl_union_pw_qpolynomial *upwqp,
5058 __isl_take isl_val *v);
5059 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_add(
5060 __isl_take isl_union_pw_qpolynomial *upwqp1,
5061 __isl_take isl_union_pw_qpolynomial *upwqp2);
5062 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_sub(
5063 __isl_take isl_union_pw_qpolynomial *upwqp1,
5064 __isl_take isl_union_pw_qpolynomial *upwqp2);
5065 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_mul(
5066 __isl_take isl_union_pw_qpolynomial *upwqp1,
5067 __isl_take isl_union_pw_qpolynomial *upwqp2);
5069 __isl_give isl_val *isl_pw_qpolynomial_eval(
5070 __isl_take isl_pw_qpolynomial *pwqp,
5071 __isl_take isl_point *pnt);
5073 __isl_give isl_val *isl_union_pw_qpolynomial_eval(
5074 __isl_take isl_union_pw_qpolynomial *upwqp,
5075 __isl_take isl_point *pnt);
5077 __isl_give isl_set *isl_pw_qpolynomial_domain(
5078 __isl_take isl_pw_qpolynomial *pwqp);
5079 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_intersect_domain(
5080 __isl_take isl_pw_qpolynomial *pwpq,
5081 __isl_take isl_set *set);
5082 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_intersect_params(
5083 __isl_take isl_pw_qpolynomial *pwpq,
5084 __isl_take isl_set *set);
5086 __isl_give isl_union_set *isl_union_pw_qpolynomial_domain(
5087 __isl_take isl_union_pw_qpolynomial *upwqp);
5088 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_intersect_domain(
5089 __isl_take isl_union_pw_qpolynomial *upwpq,
5090 __isl_take isl_union_set *uset);
5091 __isl_give isl_union_pw_qpolynomial *
5092 isl_union_pw_qpolynomial_intersect_params(
5093 __isl_take isl_union_pw_qpolynomial *upwpq,
5094 __isl_take isl_set *set);
5096 __isl_give isl_qpolynomial *isl_qpolynomial_align_params(
5097 __isl_take isl_qpolynomial *qp,
5098 __isl_take isl_space *model);
5100 __isl_give isl_qpolynomial *isl_qpolynomial_project_domain_on_params(
5101 __isl_take isl_qpolynomial *qp);
5102 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_project_domain_on_params(
5103 __isl_take isl_pw_qpolynomial *pwqp);
5105 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_coalesce(
5106 __isl_take isl_union_pw_qpolynomial *upwqp);
5108 __isl_give isl_qpolynomial *isl_qpolynomial_gist_params(
5109 __isl_take isl_qpolynomial *qp,
5110 __isl_take isl_set *context);
5111 __isl_give isl_qpolynomial *isl_qpolynomial_gist(
5112 __isl_take isl_qpolynomial *qp,
5113 __isl_take isl_set *context);
5115 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_gist_params(
5116 __isl_take isl_pw_qpolynomial *pwqp,
5117 __isl_take isl_set *context);
5118 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_gist(
5119 __isl_take isl_pw_qpolynomial *pwqp,
5120 __isl_take isl_set *context);
5122 __isl_give isl_union_pw_qpolynomial *
5123 isl_union_pw_qpolynomial_gist_params(
5124 __isl_take isl_union_pw_qpolynomial *upwqp,
5125 __isl_take isl_set *context);
5126 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_gist(
5127 __isl_take isl_union_pw_qpolynomial *upwqp,
5128 __isl_take isl_union_set *context);
5130 The gist operation applies the gist operation to each of
5131 the cells in the domain of the input piecewise quasipolynomial.
5132 The context is also exploited
5133 to simplify the quasipolynomials associated to each cell.
5135 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_to_polynomial(
5136 __isl_take isl_pw_qpolynomial *pwqp, int sign);
5137 __isl_give isl_union_pw_qpolynomial *
5138 isl_union_pw_qpolynomial_to_polynomial(
5139 __isl_take isl_union_pw_qpolynomial *upwqp, int sign);
5141 Approximate each quasipolynomial by a polynomial. If C<sign> is positive,
5142 the polynomial will be an overapproximation. If C<sign> is negative,
5143 it will be an underapproximation. If C<sign> is zero, the approximation
5144 will lie somewhere in between.
5146 =head2 Bounds on Piecewise Quasipolynomials and Piecewise Quasipolynomial Reductions
5148 A piecewise quasipolynomial reduction is a piecewise
5149 reduction (or fold) of quasipolynomials.
5150 In particular, the reduction can be maximum or a minimum.
5151 The objects are mainly used to represent the result of
5152 an upper or lower bound on a quasipolynomial over its domain,
5153 i.e., as the result of the following function.
5155 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_bound(
5156 __isl_take isl_pw_qpolynomial *pwqp,
5157 enum isl_fold type, int *tight);
5159 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_bound(
5160 __isl_take isl_union_pw_qpolynomial *upwqp,
5161 enum isl_fold type, int *tight);
5163 The C<type> argument may be either C<isl_fold_min> or C<isl_fold_max>.
5164 If C<tight> is not C<NULL>, then C<*tight> is set to C<1>
5165 is the returned bound is known be tight, i.e., for each value
5166 of the parameters there is at least
5167 one element in the domain that reaches the bound.
5168 If the domain of C<pwqp> is not wrapping, then the bound is computed
5169 over all elements in that domain and the result has a purely parametric
5170 domain. If the domain of C<pwqp> is wrapping, then the bound is
5171 computed over the range of the wrapped relation. The domain of the
5172 wrapped relation becomes the domain of the result.
5174 A (piecewise) quasipolynomial reduction can be copied or freed using the
5175 following functions.
5177 __isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_copy(
5178 __isl_keep isl_qpolynomial_fold *fold);
5179 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_copy(
5180 __isl_keep isl_pw_qpolynomial_fold *pwf);
5181 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_copy(
5182 __isl_keep isl_union_pw_qpolynomial_fold *upwf);
5183 void isl_qpolynomial_fold_free(
5184 __isl_take isl_qpolynomial_fold *fold);
5185 void *isl_pw_qpolynomial_fold_free(
5186 __isl_take isl_pw_qpolynomial_fold *pwf);
5187 void *isl_union_pw_qpolynomial_fold_free(
5188 __isl_take isl_union_pw_qpolynomial_fold *upwf);
5190 =head3 Printing Piecewise Quasipolynomial Reductions
5192 Piecewise quasipolynomial reductions can be printed
5193 using the following function.
5195 __isl_give isl_printer *isl_printer_print_pw_qpolynomial_fold(
5196 __isl_take isl_printer *p,
5197 __isl_keep isl_pw_qpolynomial_fold *pwf);
5198 __isl_give isl_printer *isl_printer_print_union_pw_qpolynomial_fold(
5199 __isl_take isl_printer *p,
5200 __isl_keep isl_union_pw_qpolynomial_fold *upwf);
5202 For C<isl_printer_print_pw_qpolynomial_fold>,
5203 output format of the printer
5204 needs to be set to either C<ISL_FORMAT_ISL> or C<ISL_FORMAT_C>.
5205 For C<isl_printer_print_union_pw_qpolynomial_fold>,
5206 output format of the printer
5207 needs to be set to C<ISL_FORMAT_ISL>.
5208 In case of printing in C<ISL_FORMAT_C>, the user may want
5209 to set the names of all dimensions
5211 __isl_give isl_pw_qpolynomial_fold *
5212 isl_pw_qpolynomial_fold_set_dim_name(
5213 __isl_take isl_pw_qpolynomial_fold *pwf,
5214 enum isl_dim_type type, unsigned pos,
5217 =head3 Inspecting (Piecewise) Quasipolynomial Reductions
5219 To iterate over all piecewise quasipolynomial reductions in a union
5220 piecewise quasipolynomial reduction, use the following function
5222 int isl_union_pw_qpolynomial_fold_foreach_pw_qpolynomial_fold(
5223 __isl_keep isl_union_pw_qpolynomial_fold *upwf,
5224 int (*fn)(__isl_take isl_pw_qpolynomial_fold *pwf,
5225 void *user), void *user);
5227 To iterate over the cells in a piecewise quasipolynomial reduction,
5228 use either of the following two functions
5230 int isl_pw_qpolynomial_fold_foreach_piece(
5231 __isl_keep isl_pw_qpolynomial_fold *pwf,
5232 int (*fn)(__isl_take isl_set *set,
5233 __isl_take isl_qpolynomial_fold *fold,
5234 void *user), void *user);
5235 int isl_pw_qpolynomial_fold_foreach_lifted_piece(
5236 __isl_keep isl_pw_qpolynomial_fold *pwf,
5237 int (*fn)(__isl_take isl_set *set,
5238 __isl_take isl_qpolynomial_fold *fold,
5239 void *user), void *user);
5241 See L<Inspecting (Piecewise) Quasipolynomials> for an explanation
5242 of the difference between these two functions.
5244 To iterate over all quasipolynomials in a reduction, use
5246 int isl_qpolynomial_fold_foreach_qpolynomial(
5247 __isl_keep isl_qpolynomial_fold *fold,
5248 int (*fn)(__isl_take isl_qpolynomial *qp,
5249 void *user), void *user);
5251 =head3 Properties of Piecewise Quasipolynomial Reductions
5253 To check whether two union piecewise quasipolynomial reductions are
5254 obviously equal, use
5256 int isl_union_pw_qpolynomial_fold_plain_is_equal(
5257 __isl_keep isl_union_pw_qpolynomial_fold *upwf1,
5258 __isl_keep isl_union_pw_qpolynomial_fold *upwf2);
5260 =head3 Operations on Piecewise Quasipolynomial Reductions
5262 __isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_scale_val(
5263 __isl_take isl_qpolynomial_fold *fold,
5264 __isl_take isl_val *v);
5265 __isl_give isl_pw_qpolynomial_fold *
5266 isl_pw_qpolynomial_fold_scale_val(
5267 __isl_take isl_pw_qpolynomial_fold *pwf,
5268 __isl_take isl_val *v);
5269 __isl_give isl_union_pw_qpolynomial_fold *
5270 isl_union_pw_qpolynomial_fold_scale_val(
5271 __isl_take isl_union_pw_qpolynomial_fold *upwf,
5272 __isl_take isl_val *v);
5274 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_add(
5275 __isl_take isl_pw_qpolynomial_fold *pwf1,
5276 __isl_take isl_pw_qpolynomial_fold *pwf2);
5278 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_fold(
5279 __isl_take isl_pw_qpolynomial_fold *pwf1,
5280 __isl_take isl_pw_qpolynomial_fold *pwf2);
5282 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_fold(
5283 __isl_take isl_union_pw_qpolynomial_fold *upwf1,
5284 __isl_take isl_union_pw_qpolynomial_fold *upwf2);
5286 __isl_give isl_val *isl_pw_qpolynomial_fold_eval(
5287 __isl_take isl_pw_qpolynomial_fold *pwf,
5288 __isl_take isl_point *pnt);
5290 __isl_give isl_val *isl_union_pw_qpolynomial_fold_eval(
5291 __isl_take isl_union_pw_qpolynomial_fold *upwf,
5292 __isl_take isl_point *pnt);
5294 __isl_give isl_pw_qpolynomial_fold *
5295 isl_pw_qpolynomial_fold_intersect_params(
5296 __isl_take isl_pw_qpolynomial_fold *pwf,
5297 __isl_take isl_set *set);
5299 __isl_give isl_union_set *isl_union_pw_qpolynomial_fold_domain(
5300 __isl_take isl_union_pw_qpolynomial_fold *upwf);
5301 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_intersect_domain(
5302 __isl_take isl_union_pw_qpolynomial_fold *upwf,
5303 __isl_take isl_union_set *uset);
5304 __isl_give isl_union_pw_qpolynomial_fold *
5305 isl_union_pw_qpolynomial_fold_intersect_params(
5306 __isl_take isl_union_pw_qpolynomial_fold *upwf,
5307 __isl_take isl_set *set);
5309 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_project_domain_on_params(
5310 __isl_take isl_pw_qpolynomial_fold *pwf);
5312 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_coalesce(
5313 __isl_take isl_pw_qpolynomial_fold *pwf);
5315 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_coalesce(
5316 __isl_take isl_union_pw_qpolynomial_fold *upwf);
5318 __isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_gist_params(
5319 __isl_take isl_qpolynomial_fold *fold,
5320 __isl_take isl_set *context);
5321 __isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_gist(
5322 __isl_take isl_qpolynomial_fold *fold,
5323 __isl_take isl_set *context);
5325 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_gist(
5326 __isl_take isl_pw_qpolynomial_fold *pwf,
5327 __isl_take isl_set *context);
5328 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_gist_params(
5329 __isl_take isl_pw_qpolynomial_fold *pwf,
5330 __isl_take isl_set *context);
5332 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_gist(
5333 __isl_take isl_union_pw_qpolynomial_fold *upwf,
5334 __isl_take isl_union_set *context);
5335 __isl_give isl_union_pw_qpolynomial_fold *
5336 isl_union_pw_qpolynomial_fold_gist_params(
5337 __isl_take isl_union_pw_qpolynomial_fold *upwf,
5338 __isl_take isl_set *context);
5340 The gist operation applies the gist operation to each of
5341 the cells in the domain of the input piecewise quasipolynomial reduction.
5342 In future, the operation will also exploit the context
5343 to simplify the quasipolynomial reductions associated to each cell.
5345 __isl_give isl_pw_qpolynomial_fold *
5346 isl_set_apply_pw_qpolynomial_fold(
5347 __isl_take isl_set *set,
5348 __isl_take isl_pw_qpolynomial_fold *pwf,
5350 __isl_give isl_pw_qpolynomial_fold *
5351 isl_map_apply_pw_qpolynomial_fold(
5352 __isl_take isl_map *map,
5353 __isl_take isl_pw_qpolynomial_fold *pwf,
5355 __isl_give isl_union_pw_qpolynomial_fold *
5356 isl_union_set_apply_union_pw_qpolynomial_fold(
5357 __isl_take isl_union_set *uset,
5358 __isl_take isl_union_pw_qpolynomial_fold *upwf,
5360 __isl_give isl_union_pw_qpolynomial_fold *
5361 isl_union_map_apply_union_pw_qpolynomial_fold(
5362 __isl_take isl_union_map *umap,
5363 __isl_take isl_union_pw_qpolynomial_fold *upwf,
5366 The functions taking a map
5367 compose the given map with the given piecewise quasipolynomial reduction.
5368 That is, compute a bound (of the same type as C<pwf> or C<upwf> itself)
5369 over all elements in the intersection of the range of the map
5370 and the domain of the piecewise quasipolynomial reduction
5371 as a function of an element in the domain of the map.
5372 The functions taking a set compute a bound over all elements in the
5373 intersection of the set and the domain of the
5374 piecewise quasipolynomial reduction.
5376 =head2 Parametric Vertex Enumeration
5378 The parametric vertex enumeration described in this section
5379 is mainly intended to be used internally and by the C<barvinok>
5382 #include <isl/vertices.h>
5383 __isl_give isl_vertices *isl_basic_set_compute_vertices(
5384 __isl_keep isl_basic_set *bset);
5386 The function C<isl_basic_set_compute_vertices> performs the
5387 actual computation of the parametric vertices and the chamber
5388 decomposition and store the result in an C<isl_vertices> object.
5389 This information can be queried by either iterating over all
5390 the vertices or iterating over all the chambers or cells
5391 and then iterating over all vertices that are active on the chamber.
5393 int isl_vertices_foreach_vertex(
5394 __isl_keep isl_vertices *vertices,
5395 int (*fn)(__isl_take isl_vertex *vertex, void *user),
5398 int isl_vertices_foreach_cell(
5399 __isl_keep isl_vertices *vertices,
5400 int (*fn)(__isl_take isl_cell *cell, void *user),
5402 int isl_cell_foreach_vertex(__isl_keep isl_cell *cell,
5403 int (*fn)(__isl_take isl_vertex *vertex, void *user),
5406 Other operations that can be performed on an C<isl_vertices> object are
5409 isl_ctx *isl_vertices_get_ctx(
5410 __isl_keep isl_vertices *vertices);
5411 int isl_vertices_get_n_vertices(
5412 __isl_keep isl_vertices *vertices);
5413 void isl_vertices_free(__isl_take isl_vertices *vertices);
5415 Vertices can be inspected and destroyed using the following functions.
5417 isl_ctx *isl_vertex_get_ctx(__isl_keep isl_vertex *vertex);
5418 int isl_vertex_get_id(__isl_keep isl_vertex *vertex);
5419 __isl_give isl_basic_set *isl_vertex_get_domain(
5420 __isl_keep isl_vertex *vertex);
5421 __isl_give isl_basic_set *isl_vertex_get_expr(
5422 __isl_keep isl_vertex *vertex);
5423 void isl_vertex_free(__isl_take isl_vertex *vertex);
5425 C<isl_vertex_get_expr> returns a singleton parametric set describing
5426 the vertex, while C<isl_vertex_get_domain> returns the activity domain
5428 Note that C<isl_vertex_get_domain> and C<isl_vertex_get_expr> return
5429 B<rational> basic sets, so they should mainly be used for inspection
5430 and should not be mixed with integer sets.
5432 Chambers can be inspected and destroyed using the following functions.
5434 isl_ctx *isl_cell_get_ctx(__isl_keep isl_cell *cell);
5435 __isl_give isl_basic_set *isl_cell_get_domain(
5436 __isl_keep isl_cell *cell);
5437 void isl_cell_free(__isl_take isl_cell *cell);
5439 =head1 Polyhedral Compilation Library
5441 This section collects functionality in C<isl> that has been specifically
5442 designed for use during polyhedral compilation.
5444 =head2 Dependence Analysis
5446 C<isl> contains specialized functionality for performing
5447 array dataflow analysis. That is, given a I<sink> access relation
5448 and a collection of possible I<source> access relations,
5449 C<isl> can compute relations that describe
5450 for each iteration of the sink access, which iteration
5451 of which of the source access relations was the last
5452 to access the same data element before the given iteration
5454 The resulting dependence relations map source iterations
5455 to the corresponding sink iterations.
5456 To compute standard flow dependences, the sink should be
5457 a read, while the sources should be writes.
5458 If any of the source accesses are marked as being I<may>
5459 accesses, then there will be a dependence from the last
5460 I<must> access B<and> from any I<may> access that follows
5461 this last I<must> access.
5462 In particular, if I<all> sources are I<may> accesses,
5463 then memory based dependence analysis is performed.
5464 If, on the other hand, all sources are I<must> accesses,
5465 then value based dependence analysis is performed.
5467 #include <isl/flow.h>
5469 typedef int (*isl_access_level_before)(void *first, void *second);
5471 __isl_give isl_access_info *isl_access_info_alloc(
5472 __isl_take isl_map *sink,
5473 void *sink_user, isl_access_level_before fn,
5475 __isl_give isl_access_info *isl_access_info_add_source(
5476 __isl_take isl_access_info *acc,
5477 __isl_take isl_map *source, int must,
5479 void *isl_access_info_free(__isl_take isl_access_info *acc);
5481 __isl_give isl_flow *isl_access_info_compute_flow(
5482 __isl_take isl_access_info *acc);
5484 int isl_flow_foreach(__isl_keep isl_flow *deps,
5485 int (*fn)(__isl_take isl_map *dep, int must,
5486 void *dep_user, void *user),
5488 __isl_give isl_map *isl_flow_get_no_source(
5489 __isl_keep isl_flow *deps, int must);
5490 void isl_flow_free(__isl_take isl_flow *deps);
5492 The function C<isl_access_info_compute_flow> performs the actual
5493 dependence analysis. The other functions are used to construct
5494 the input for this function or to read off the output.
5496 The input is collected in an C<isl_access_info>, which can
5497 be created through a call to C<isl_access_info_alloc>.
5498 The arguments to this functions are the sink access relation
5499 C<sink>, a token C<sink_user> used to identify the sink
5500 access to the user, a callback function for specifying the
5501 relative order of source and sink accesses, and the number
5502 of source access relations that will be added.
5503 The callback function has type C<int (*)(void *first, void *second)>.
5504 The function is called with two user supplied tokens identifying
5505 either a source or the sink and it should return the shared nesting
5506 level and the relative order of the two accesses.
5507 In particular, let I<n> be the number of loops shared by
5508 the two accesses. If C<first> precedes C<second> textually,
5509 then the function should return I<2 * n + 1>; otherwise,
5510 it should return I<2 * n>.
5511 The sources can be added to the C<isl_access_info> by performing
5512 (at most) C<max_source> calls to C<isl_access_info_add_source>.
5513 C<must> indicates whether the source is a I<must> access
5514 or a I<may> access. Note that a multi-valued access relation
5515 should only be marked I<must> if every iteration in the domain
5516 of the relation accesses I<all> elements in its image.
5517 The C<source_user> token is again used to identify
5518 the source access. The range of the source access relation
5519 C<source> should have the same dimension as the range
5520 of the sink access relation.
5521 The C<isl_access_info_free> function should usually not be
5522 called explicitly, because it is called implicitly by
5523 C<isl_access_info_compute_flow>.
5525 The result of the dependence analysis is collected in an
5526 C<isl_flow>. There may be elements of
5527 the sink access for which no preceding source access could be
5528 found or for which all preceding sources are I<may> accesses.
5529 The relations containing these elements can be obtained through
5530 calls to C<isl_flow_get_no_source>, the first with C<must> set
5531 and the second with C<must> unset.
5532 In the case of standard flow dependence analysis,
5533 with the sink a read and the sources I<must> writes,
5534 the first relation corresponds to the reads from uninitialized
5535 array elements and the second relation is empty.
5536 The actual flow dependences can be extracted using
5537 C<isl_flow_foreach>. This function will call the user-specified
5538 callback function C<fn> for each B<non-empty> dependence between
5539 a source and the sink. The callback function is called
5540 with four arguments, the actual flow dependence relation
5541 mapping source iterations to sink iterations, a boolean that
5542 indicates whether it is a I<must> or I<may> dependence, a token
5543 identifying the source and an additional C<void *> with value
5544 equal to the third argument of the C<isl_flow_foreach> call.
5545 A dependence is marked I<must> if it originates from a I<must>
5546 source and if it is not followed by any I<may> sources.
5548 After finishing with an C<isl_flow>, the user should call
5549 C<isl_flow_free> to free all associated memory.
5551 A higher-level interface to dependence analysis is provided
5552 by the following function.
5554 #include <isl/flow.h>
5556 int isl_union_map_compute_flow(__isl_take isl_union_map *sink,
5557 __isl_take isl_union_map *must_source,
5558 __isl_take isl_union_map *may_source,
5559 __isl_take isl_union_map *schedule,
5560 __isl_give isl_union_map **must_dep,
5561 __isl_give isl_union_map **may_dep,
5562 __isl_give isl_union_map **must_no_source,
5563 __isl_give isl_union_map **may_no_source);
5565 The arrays are identified by the tuple names of the ranges
5566 of the accesses. The iteration domains by the tuple names
5567 of the domains of the accesses and of the schedule.
5568 The relative order of the iteration domains is given by the
5569 schedule. The relations returned through C<must_no_source>
5570 and C<may_no_source> are subsets of C<sink>.
5571 Any of C<must_dep>, C<may_dep>, C<must_no_source>
5572 or C<may_no_source> may be C<NULL>, but a C<NULL> value for
5573 any of the other arguments is treated as an error.
5575 =head3 Interaction with Dependence Analysis
5577 During the dependence analysis, we frequently need to perform
5578 the following operation. Given a relation between sink iterations
5579 and potential source iterations from a particular source domain,
5580 what is the last potential source iteration corresponding to each
5581 sink iteration. It can sometimes be convenient to adjust
5582 the set of potential source iterations before or after each such operation.
5583 The prototypical example is fuzzy array dataflow analysis,
5584 where we need to analyze if, based on data-dependent constraints,
5585 the sink iteration can ever be executed without one or more of
5586 the corresponding potential source iterations being executed.
5587 If so, we can introduce extra parameters and select an unknown
5588 but fixed source iteration from the potential source iterations.
5589 To be able to perform such manipulations, C<isl> provides the following
5592 #include <isl/flow.h>
5594 typedef __isl_give isl_restriction *(*isl_access_restrict)(
5595 __isl_keep isl_map *source_map,
5596 __isl_keep isl_set *sink, void *source_user,
5598 __isl_give isl_access_info *isl_access_info_set_restrict(
5599 __isl_take isl_access_info *acc,
5600 isl_access_restrict fn, void *user);
5602 The function C<isl_access_info_set_restrict> should be called
5603 before calling C<isl_access_info_compute_flow> and registers a callback function
5604 that will be called any time C<isl> is about to compute the last
5605 potential source. The first argument is the (reverse) proto-dependence,
5606 mapping sink iterations to potential source iterations.
5607 The second argument represents the sink iterations for which
5608 we want to compute the last source iteration.
5609 The third argument is the token corresponding to the source
5610 and the final argument is the token passed to C<isl_access_info_set_restrict>.
5611 The callback is expected to return a restriction on either the input or
5612 the output of the operation computing the last potential source.
5613 If the input needs to be restricted then restrictions are needed
5614 for both the source and the sink iterations. The sink iterations
5615 and the potential source iterations will be intersected with these sets.
5616 If the output needs to be restricted then only a restriction on the source
5617 iterations is required.
5618 If any error occurs, the callback should return C<NULL>.
5619 An C<isl_restriction> object can be created, freed and inspected
5620 using the following functions.
5622 #include <isl/flow.h>
5624 __isl_give isl_restriction *isl_restriction_input(
5625 __isl_take isl_set *source_restr,
5626 __isl_take isl_set *sink_restr);
5627 __isl_give isl_restriction *isl_restriction_output(
5628 __isl_take isl_set *source_restr);
5629 __isl_give isl_restriction *isl_restriction_none(
5630 __isl_take isl_map *source_map);
5631 __isl_give isl_restriction *isl_restriction_empty(
5632 __isl_take isl_map *source_map);
5633 void *isl_restriction_free(
5634 __isl_take isl_restriction *restr);
5635 isl_ctx *isl_restriction_get_ctx(
5636 __isl_keep isl_restriction *restr);
5638 C<isl_restriction_none> and C<isl_restriction_empty> are special
5639 cases of C<isl_restriction_input>. C<isl_restriction_none>
5640 is essentially equivalent to
5642 isl_restriction_input(isl_set_universe(
5643 isl_space_range(isl_map_get_space(source_map))),
5645 isl_space_domain(isl_map_get_space(source_map))));
5647 whereas C<isl_restriction_empty> is essentially equivalent to
5649 isl_restriction_input(isl_set_empty(
5650 isl_space_range(isl_map_get_space(source_map))),
5652 isl_space_domain(isl_map_get_space(source_map))));
5656 B<The functionality described in this section is fairly new
5657 and may be subject to change.>
5659 #include <isl/schedule.h>
5660 __isl_give isl_schedule *
5661 isl_schedule_constraints_compute_schedule(
5662 __isl_take isl_schedule_constraints *sc);
5663 void *isl_schedule_free(__isl_take isl_schedule *sched);
5665 The function C<isl_schedule_constraints_compute_schedule> can be
5666 used to compute a schedule that satisfy the given schedule constraints.
5667 These schedule constraints include the iteration domain for which
5668 a schedule should be computed and dependences between pairs of
5669 iterations. In particular, these dependences include
5670 I<validity> dependences and I<proximity> dependences.
5671 By default, the algorithm used to construct the schedule is similar
5672 to that of C<Pluto>.
5673 Alternatively, Feautrier's multi-dimensional scheduling algorithm can
5675 The generated schedule respects all validity dependences.
5676 That is, all dependence distances over these dependences in the
5677 scheduled space are lexicographically positive.
5678 The default algorithm tries to ensure that the dependence distances
5679 over coincidence constraints are zero and to minimize the
5680 dependence distances over proximity dependences.
5681 Moreover, it tries to obtain sequences (bands) of schedule dimensions
5682 for groups of domains where the dependence distances over validity
5683 dependences have only non-negative values.
5684 When using Feautrier's algorithm, the coincidence and proximity constraints
5685 are only taken into account during the extension to a
5686 full-dimensional schedule.
5688 An C<isl_schedule_constraints> object can be constructed
5689 and manipulated using the following functions.
5691 #include <isl/schedule.h>
5692 __isl_give isl_schedule_constraints *
5693 isl_schedule_constraints_on_domain(
5694 __isl_take isl_union_set *domain);
5695 isl_ctx *isl_schedule_constraints_get_ctx(
5696 __isl_keep isl_schedule_constraints *sc);
5697 __isl_give isl_schedule_constraints *
5698 isl_schedule_constraints_set_validity(
5699 __isl_take isl_schedule_constraints *sc,
5700 __isl_take isl_union_map *validity);
5701 __isl_give isl_schedule_constraints *
5702 isl_schedule_constraints_set_coincidence(
5703 __isl_take isl_schedule_constraints *sc,
5704 __isl_take isl_union_map *coincidence);
5705 __isl_give isl_schedule_constraints *
5706 isl_schedule_constraints_set_proximity(
5707 __isl_take isl_schedule_constraints *sc,
5708 __isl_take isl_union_map *proximity);
5709 __isl_give isl_schedule_constraints *
5710 isl_schedule_constraints_set_conditional_validity(
5711 __isl_take isl_schedule_constraints *sc,
5712 __isl_take isl_union_map *condition,
5713 __isl_take isl_union_map *validity);
5714 void *isl_schedule_constraints_free(
5715 __isl_take isl_schedule_constraints *sc);
5717 The initial C<isl_schedule_constraints> object created by
5718 C<isl_schedule_constraints_on_domain> does not impose any constraints.
5719 That is, it has an empty set of dependences.
5720 The function C<isl_schedule_constraints_set_validity> replaces the
5721 validity dependences, mapping domain elements I<i> to domain
5722 elements that should be scheduled after I<i>.
5723 The function C<isl_schedule_constraints_set_coincidence> replaces the
5724 coincidence dependences, mapping domain elements I<i> to domain
5725 elements that should be scheduled together with I<I>, if possible.
5726 The function C<isl_schedule_constraints_set_proximity> replaces the
5727 proximity dependences, mapping domain elements I<i> to domain
5728 elements that should be scheduled either before I<I>
5729 or as early as possible after I<i>.
5731 The function C<isl_schedule_constraints_set_conditional_validity>
5732 replaces the conditional validity constraints.
5733 A conditional validity constraint is only imposed when any of the corresponding
5734 conditions is satisfied, i.e., when any of them is non-zero.
5735 That is, the scheduler ensures that within each band if the dependence
5736 distances over the condition constraints are not all zero
5737 then all corresponding conditional validity constraints are respected.
5738 A conditional validity constraint corresponds to a condition
5739 if the two are adjacent, i.e., if the domain of one relation intersect
5740 the range of the other relation.
5741 The typical use case of conditional validity constraints is
5742 to allow order constraints between live ranges to be violated
5743 as long as the live ranges themselves are local to the band.
5744 To allow more fine-grained control over which conditions correspond
5745 to which conditional validity constraints, the domains and ranges
5746 of these relations may include I<tags>. That is, the domains and
5747 ranges of those relation may themselves be wrapped relations
5748 where the iteration domain appears in the domain of those wrapped relations
5749 and the range of the wrapped relations can be arbitrarily chosen
5750 by the user. Conditions and conditional validity constraints are only
5751 considere adjacent to each other if the entire wrapped relation matches.
5752 In particular, a relation with a tag will never be considered adjacent
5753 to a relation without a tag.
5755 The following function computes a schedule directly from
5756 an iteration domain and validity and proximity dependences
5757 and is implemented in terms of the functions described above.
5758 The use of C<isl_union_set_compute_schedule> is discouraged.
5760 #include <isl/schedule.h>
5761 __isl_give isl_schedule *isl_union_set_compute_schedule(
5762 __isl_take isl_union_set *domain,
5763 __isl_take isl_union_map *validity,
5764 __isl_take isl_union_map *proximity);
5766 A mapping from the domains to the scheduled space can be obtained
5767 from an C<isl_schedule> using the following function.
5769 __isl_give isl_union_map *isl_schedule_get_map(
5770 __isl_keep isl_schedule *sched);
5772 A representation of the schedule can be printed using
5774 __isl_give isl_printer *isl_printer_print_schedule(
5775 __isl_take isl_printer *p,
5776 __isl_keep isl_schedule *schedule);
5778 A representation of the schedule as a forest of bands can be obtained
5779 using the following function.
5781 __isl_give isl_band_list *isl_schedule_get_band_forest(
5782 __isl_keep isl_schedule *schedule);
5784 The individual bands can be visited in depth-first post-order
5785 using the following function.
5787 #include <isl/schedule.h>
5788 int isl_schedule_foreach_band(
5789 __isl_keep isl_schedule *sched,
5790 int (*fn)(__isl_keep isl_band *band, void *user),
5793 The list can be manipulated as explained in L<"Lists">.
5794 The bands inside the list can be copied and freed using the following
5797 #include <isl/band.h>
5798 __isl_give isl_band *isl_band_copy(
5799 __isl_keep isl_band *band);
5800 void *isl_band_free(__isl_take isl_band *band);
5802 Each band contains zero or more scheduling dimensions.
5803 These are referred to as the members of the band.
5804 The section of the schedule that corresponds to the band is
5805 referred to as the partial schedule of the band.
5806 For those nodes that participate in a band, the outer scheduling
5807 dimensions form the prefix schedule, while the inner scheduling
5808 dimensions form the suffix schedule.
5809 That is, if we take a cut of the band forest, then the union of
5810 the concatenations of the prefix, partial and suffix schedules of
5811 each band in the cut is equal to the entire schedule (modulo
5812 some possible padding at the end with zero scheduling dimensions).
5813 The properties of a band can be inspected using the following functions.
5815 #include <isl/band.h>
5816 isl_ctx *isl_band_get_ctx(__isl_keep isl_band *band);
5818 int isl_band_has_children(__isl_keep isl_band *band);
5819 __isl_give isl_band_list *isl_band_get_children(
5820 __isl_keep isl_band *band);
5822 __isl_give isl_union_map *isl_band_get_prefix_schedule(
5823 __isl_keep isl_band *band);
5824 __isl_give isl_union_map *isl_band_get_partial_schedule(
5825 __isl_keep isl_band *band);
5826 __isl_give isl_union_map *isl_band_get_suffix_schedule(
5827 __isl_keep isl_band *band);
5829 int isl_band_n_member(__isl_keep isl_band *band);
5830 int isl_band_member_is_coincident(
5831 __isl_keep isl_band *band, int pos);
5833 int isl_band_list_foreach_band(
5834 __isl_keep isl_band_list *list,
5835 int (*fn)(__isl_keep isl_band *band, void *user),
5838 Note that a scheduling dimension is considered to be ``coincident''
5839 if it satisfies the coincidence constraints within its band.
5840 That is, if the dependence distances of the coincidence
5841 constraints are all zero in that direction (for fixed
5842 iterations of outer bands).
5843 Like C<isl_schedule_foreach_band>,
5844 the function C<isl_band_list_foreach_band> calls C<fn> on the bands
5845 in depth-first post-order.
5847 A band can be tiled using the following function.
5849 #include <isl/band.h>
5850 int isl_band_tile(__isl_keep isl_band *band,
5851 __isl_take isl_vec *sizes);
5853 int isl_options_set_tile_scale_tile_loops(isl_ctx *ctx,
5855 int isl_options_get_tile_scale_tile_loops(isl_ctx *ctx);
5856 int isl_options_set_tile_shift_point_loops(isl_ctx *ctx,
5858 int isl_options_get_tile_shift_point_loops(isl_ctx *ctx);
5860 The C<isl_band_tile> function tiles the band using the given tile sizes
5861 inside its schedule.
5862 A new child band is created to represent the point loops and it is
5863 inserted between the modified band and its children.
5864 The C<tile_scale_tile_loops> option specifies whether the tile
5865 loops iterators should be scaled by the tile sizes.
5866 If the C<tile_shift_point_loops> option is set, then the point loops
5867 are shifted to start at zero.
5869 A band can be split into two nested bands using the following function.
5871 int isl_band_split(__isl_keep isl_band *band, int pos);
5873 The resulting outer band contains the first C<pos> dimensions of C<band>
5874 while the inner band contains the remaining dimensions.
5876 A representation of the band can be printed using
5878 #include <isl/band.h>
5879 __isl_give isl_printer *isl_printer_print_band(
5880 __isl_take isl_printer *p,
5881 __isl_keep isl_band *band);
5885 #include <isl/schedule.h>
5886 int isl_options_set_schedule_max_coefficient(
5887 isl_ctx *ctx, int val);
5888 int isl_options_get_schedule_max_coefficient(
5890 int isl_options_set_schedule_max_constant_term(
5891 isl_ctx *ctx, int val);
5892 int isl_options_get_schedule_max_constant_term(
5894 int isl_options_set_schedule_fuse(isl_ctx *ctx, int val);
5895 int isl_options_get_schedule_fuse(isl_ctx *ctx);
5896 int isl_options_set_schedule_maximize_band_depth(
5897 isl_ctx *ctx, int val);
5898 int isl_options_get_schedule_maximize_band_depth(
5900 int isl_options_set_schedule_outer_coincidence(
5901 isl_ctx *ctx, int val);
5902 int isl_options_get_schedule_outer_coincidence(
5904 int isl_options_set_schedule_split_scaled(
5905 isl_ctx *ctx, int val);
5906 int isl_options_get_schedule_split_scaled(
5908 int isl_options_set_schedule_algorithm(
5909 isl_ctx *ctx, int val);
5910 int isl_options_get_schedule_algorithm(
5912 int isl_options_set_schedule_separate_components(
5913 isl_ctx *ctx, int val);
5914 int isl_options_get_schedule_separate_components(
5919 =item * schedule_max_coefficient
5921 This option enforces that the coefficients for variable and parameter
5922 dimensions in the calculated schedule are not larger than the specified value.
5923 This option can significantly increase the speed of the scheduling calculation
5924 and may also prevent fusing of unrelated dimensions. A value of -1 means that
5925 this option does not introduce bounds on the variable or parameter
5928 =item * schedule_max_constant_term
5930 This option enforces that the constant coefficients in the calculated schedule
5931 are not larger than the maximal constant term. This option can significantly
5932 increase the speed of the scheduling calculation and may also prevent fusing of
5933 unrelated dimensions. A value of -1 means that this option does not introduce
5934 bounds on the constant coefficients.
5936 =item * schedule_fuse
5938 This option controls the level of fusion.
5939 If this option is set to C<ISL_SCHEDULE_FUSE_MIN>, then loops in the
5940 resulting schedule will be distributed as much as possible.
5941 If this option is set to C<ISL_SCHEDULE_FUSE_MAX>, then C<isl> will
5942 try to fuse loops in the resulting schedule.
5944 =item * schedule_maximize_band_depth
5946 If this option is set, we do not split bands at the point
5947 where we detect splitting is necessary. Instead, we
5948 backtrack and split bands as early as possible. This
5949 reduces the number of splits and maximizes the width of
5950 the bands. Wider bands give more possibilities for tiling.
5951 Note that if the C<schedule_fuse> option is set to C<ISL_SCHEDULE_FUSE_MIN>,
5952 then bands will be split as early as possible, even if there is no need.
5953 The C<schedule_maximize_band_depth> option therefore has no effect in this case.
5955 =item * schedule_outer_coincidence
5957 If this option is set, then we try to construct schedules
5958 where the outermost scheduling dimension in each band
5959 satisfies the coincidence constraints.
5961 =item * schedule_split_scaled
5963 If this option is set, then we try to construct schedules in which the
5964 constant term is split off from the linear part if the linear parts of
5965 the scheduling rows for all nodes in the graphs have a common non-trivial
5967 The constant term is then placed in a separate band and the linear
5970 =item * schedule_algorithm
5972 Selects the scheduling algorithm to be used.
5973 Available scheduling algorithms are C<ISL_SCHEDULE_ALGORITHM_ISL>
5974 and C<ISL_SCHEDULE_ALGORITHM_FEAUTRIER>.
5976 =item * schedule_separate_components
5978 If at any point the dependence graph contains any (weakly connected) components,
5979 then these components are scheduled separately.
5980 If this option is not set, then some iterations of the domains
5981 in these components may be scheduled together.
5982 If this option is set, then the components are given consecutive
5987 =head2 AST Generation
5989 This section describes the C<isl> functionality for generating
5990 ASTs that visit all the elements
5991 in a domain in an order specified by a schedule.
5992 In particular, given a C<isl_union_map>, an AST is generated
5993 that visits all the elements in the domain of the C<isl_union_map>
5994 according to the lexicographic order of the corresponding image
5995 element(s). If the range of the C<isl_union_map> consists of
5996 elements in more than one space, then each of these spaces is handled
5997 separately in an arbitrary order.
5998 It should be noted that the image elements only specify the I<order>
5999 in which the corresponding domain elements should be visited.
6000 No direct relation between the image elements and the loop iterators
6001 in the generated AST should be assumed.
6003 Each AST is generated within a build. The initial build
6004 simply specifies the constraints on the parameters (if any)
6005 and can be created, inspected, copied and freed using the following functions.
6007 #include <isl/ast_build.h>
6008 __isl_give isl_ast_build *isl_ast_build_from_context(
6009 __isl_take isl_set *set);
6010 isl_ctx *isl_ast_build_get_ctx(
6011 __isl_keep isl_ast_build *build);
6012 __isl_give isl_ast_build *isl_ast_build_copy(
6013 __isl_keep isl_ast_build *build);
6014 void *isl_ast_build_free(
6015 __isl_take isl_ast_build *build);
6017 The C<set> argument is usually a parameter set with zero or more parameters.
6018 More C<isl_ast_build> functions are described in L</"Nested AST Generation">
6019 and L</"Fine-grained Control over AST Generation">.
6020 Finally, the AST itself can be constructed using the following
6023 #include <isl/ast_build.h>
6024 __isl_give isl_ast_node *isl_ast_build_ast_from_schedule(
6025 __isl_keep isl_ast_build *build,
6026 __isl_take isl_union_map *schedule);
6028 =head3 Inspecting the AST
6030 The basic properties of an AST node can be obtained as follows.
6032 #include <isl/ast.h>
6033 isl_ctx *isl_ast_node_get_ctx(
6034 __isl_keep isl_ast_node *node);
6035 enum isl_ast_node_type isl_ast_node_get_type(
6036 __isl_keep isl_ast_node *node);
6038 The type of an AST node is one of
6039 C<isl_ast_node_for>,
6041 C<isl_ast_node_block> or
6042 C<isl_ast_node_user>.
6043 An C<isl_ast_node_for> represents a for node.
6044 An C<isl_ast_node_if> represents an if node.
6045 An C<isl_ast_node_block> represents a compound node.
6046 An C<isl_ast_node_user> represents an expression statement.
6047 An expression statement typically corresponds to a domain element, i.e.,
6048 one of the elements that is visited by the AST.
6050 Each type of node has its own additional properties.
6052 #include <isl/ast.h>
6053 __isl_give isl_ast_expr *isl_ast_node_for_get_iterator(
6054 __isl_keep isl_ast_node *node);
6055 __isl_give isl_ast_expr *isl_ast_node_for_get_init(
6056 __isl_keep isl_ast_node *node);
6057 __isl_give isl_ast_expr *isl_ast_node_for_get_cond(
6058 __isl_keep isl_ast_node *node);
6059 __isl_give isl_ast_expr *isl_ast_node_for_get_inc(
6060 __isl_keep isl_ast_node *node);
6061 __isl_give isl_ast_node *isl_ast_node_for_get_body(
6062 __isl_keep isl_ast_node *node);
6063 int isl_ast_node_for_is_degenerate(
6064 __isl_keep isl_ast_node *node);
6066 An C<isl_ast_for> is considered degenerate if it is known to execute
6069 #include <isl/ast.h>
6070 __isl_give isl_ast_expr *isl_ast_node_if_get_cond(
6071 __isl_keep isl_ast_node *node);
6072 __isl_give isl_ast_node *isl_ast_node_if_get_then(
6073 __isl_keep isl_ast_node *node);
6074 int isl_ast_node_if_has_else(
6075 __isl_keep isl_ast_node *node);
6076 __isl_give isl_ast_node *isl_ast_node_if_get_else(
6077 __isl_keep isl_ast_node *node);
6079 __isl_give isl_ast_node_list *
6080 isl_ast_node_block_get_children(
6081 __isl_keep isl_ast_node *node);
6083 __isl_give isl_ast_expr *isl_ast_node_user_get_expr(
6084 __isl_keep isl_ast_node *node);
6086 Each of the returned C<isl_ast_expr>s can in turn be inspected using
6087 the following functions.
6089 #include <isl/ast.h>
6090 isl_ctx *isl_ast_expr_get_ctx(
6091 __isl_keep isl_ast_expr *expr);
6092 enum isl_ast_expr_type isl_ast_expr_get_type(
6093 __isl_keep isl_ast_expr *expr);
6095 The type of an AST expression is one of
6097 C<isl_ast_expr_id> or
6098 C<isl_ast_expr_int>.
6099 An C<isl_ast_expr_op> represents the result of an operation.
6100 An C<isl_ast_expr_id> represents an identifier.
6101 An C<isl_ast_expr_int> represents an integer value.
6103 Each type of expression has its own additional properties.
6105 #include <isl/ast.h>
6106 enum isl_ast_op_type isl_ast_expr_get_op_type(
6107 __isl_keep isl_ast_expr *expr);
6108 int isl_ast_expr_get_op_n_arg(__isl_keep isl_ast_expr *expr);
6109 __isl_give isl_ast_expr *isl_ast_expr_get_op_arg(
6110 __isl_keep isl_ast_expr *expr, int pos);
6111 int isl_ast_node_foreach_ast_op_type(
6112 __isl_keep isl_ast_node *node,
6113 int (*fn)(enum isl_ast_op_type type, void *user),
6116 C<isl_ast_expr_get_op_type> returns the type of the operation
6117 performed. C<isl_ast_expr_get_op_n_arg> returns the number of
6118 arguments. C<isl_ast_expr_get_op_arg> returns the specified
6120 C<isl_ast_node_foreach_ast_op_type> calls C<fn> for each distinct
6121 C<isl_ast_op_type> that appears in C<node>.
6122 The operation type is one of the following.
6126 =item C<isl_ast_op_and>
6128 Logical I<and> of two arguments.
6129 Both arguments can be evaluated.
6131 =item C<isl_ast_op_and_then>
6133 Logical I<and> of two arguments.
6134 The second argument can only be evaluated if the first evaluates to true.
6136 =item C<isl_ast_op_or>
6138 Logical I<or> of two arguments.
6139 Both arguments can be evaluated.
6141 =item C<isl_ast_op_or_else>
6143 Logical I<or> of two arguments.
6144 The second argument can only be evaluated if the first evaluates to false.
6146 =item C<isl_ast_op_max>
6148 Maximum of two or more arguments.
6150 =item C<isl_ast_op_min>
6152 Minimum of two or more arguments.
6154 =item C<isl_ast_op_minus>
6158 =item C<isl_ast_op_add>
6160 Sum of two arguments.
6162 =item C<isl_ast_op_sub>
6164 Difference of two arguments.
6166 =item C<isl_ast_op_mul>
6168 Product of two arguments.
6170 =item C<isl_ast_op_div>
6172 Exact division. That is, the result is known to be an integer.
6174 =item C<isl_ast_op_fdiv_q>
6176 Result of integer division, rounded towards negative
6179 =item C<isl_ast_op_pdiv_q>
6181 Result of integer division, where dividend is known to be non-negative.
6183 =item C<isl_ast_op_pdiv_r>
6185 Remainder of integer division, where dividend is known to be non-negative.
6187 =item C<isl_ast_op_cond>
6189 Conditional operator defined on three arguments.
6190 If the first argument evaluates to true, then the result
6191 is equal to the second argument. Otherwise, the result
6192 is equal to the third argument.
6193 The second and third argument may only be evaluated if
6194 the first argument evaluates to true and false, respectively.
6195 Corresponds to C<a ? b : c> in C.
6197 =item C<isl_ast_op_select>
6199 Conditional operator defined on three arguments.
6200 If the first argument evaluates to true, then the result
6201 is equal to the second argument. Otherwise, the result
6202 is equal to the third argument.
6203 The second and third argument may be evaluated independently
6204 of the value of the first argument.
6205 Corresponds to C<a * b + (1 - a) * c> in C.
6207 =item C<isl_ast_op_eq>
6211 =item C<isl_ast_op_le>
6213 Less than or equal relation.
6215 =item C<isl_ast_op_lt>
6219 =item C<isl_ast_op_ge>
6221 Greater than or equal relation.
6223 =item C<isl_ast_op_gt>
6225 Greater than relation.
6227 =item C<isl_ast_op_call>
6230 The number of arguments of the C<isl_ast_expr> is one more than
6231 the number of arguments in the function call, the first argument
6232 representing the function being called.
6234 =item C<isl_ast_op_access>
6237 The number of arguments of the C<isl_ast_expr> is one more than
6238 the number of index expressions in the array access, the first argument
6239 representing the array being accessed.
6241 =item C<isl_ast_op_member>
6244 This operation has two arguments, a structure and the name of
6245 the member of the structure being accessed.
6249 #include <isl/ast.h>
6250 __isl_give isl_id *isl_ast_expr_get_id(
6251 __isl_keep isl_ast_expr *expr);
6253 Return the identifier represented by the AST expression.
6255 #include <isl/ast.h>
6256 __isl_give isl_val *isl_ast_expr_get_val(
6257 __isl_keep isl_ast_expr *expr);
6259 Return the integer represented by the AST expression.
6261 =head3 Properties of ASTs
6263 #include <isl/ast.h>
6264 int isl_ast_expr_is_equal(__isl_keep isl_ast_expr *expr1,
6265 __isl_keep isl_ast_expr *expr2);
6267 Check if two C<isl_ast_expr>s are equal to each other.
6269 =head3 Manipulating and printing the AST
6271 AST nodes can be copied and freed using the following functions.
6273 #include <isl/ast.h>
6274 __isl_give isl_ast_node *isl_ast_node_copy(
6275 __isl_keep isl_ast_node *node);
6276 void *isl_ast_node_free(__isl_take isl_ast_node *node);
6278 AST expressions can be copied and freed using the following functions.
6280 #include <isl/ast.h>
6281 __isl_give isl_ast_expr *isl_ast_expr_copy(
6282 __isl_keep isl_ast_expr *expr);
6283 void *isl_ast_expr_free(__isl_take isl_ast_expr *expr);
6285 New AST expressions can be created either directly or within
6286 the context of an C<isl_ast_build>.
6288 #include <isl/ast.h>
6289 __isl_give isl_ast_expr *isl_ast_expr_from_val(
6290 __isl_take isl_val *v);
6291 __isl_give isl_ast_expr *isl_ast_expr_from_id(
6292 __isl_take isl_id *id);
6293 __isl_give isl_ast_expr *isl_ast_expr_neg(
6294 __isl_take isl_ast_expr *expr);
6295 __isl_give isl_ast_expr *isl_ast_expr_add(
6296 __isl_take isl_ast_expr *expr1,
6297 __isl_take isl_ast_expr *expr2);
6298 __isl_give isl_ast_expr *isl_ast_expr_sub(
6299 __isl_take isl_ast_expr *expr1,
6300 __isl_take isl_ast_expr *expr2);
6301 __isl_give isl_ast_expr *isl_ast_expr_mul(
6302 __isl_take isl_ast_expr *expr1,
6303 __isl_take isl_ast_expr *expr2);
6304 __isl_give isl_ast_expr *isl_ast_expr_div(
6305 __isl_take isl_ast_expr *expr1,
6306 __isl_take isl_ast_expr *expr2);
6307 __isl_give isl_ast_expr *isl_ast_expr_and(
6308 __isl_take isl_ast_expr *expr1,
6309 __isl_take isl_ast_expr *expr2)
6310 __isl_give isl_ast_expr *isl_ast_expr_or(
6311 __isl_take isl_ast_expr *expr1,
6312 __isl_take isl_ast_expr *expr2)
6313 __isl_give isl_ast_expr *isl_ast_expr_access(
6314 __isl_take isl_ast_expr *array,
6315 __isl_take isl_ast_expr_list *indices);
6317 #include <isl/ast_build.h>
6318 __isl_give isl_ast_expr *isl_ast_build_expr_from_pw_aff(
6319 __isl_keep isl_ast_build *build,
6320 __isl_take isl_pw_aff *pa);
6321 __isl_give isl_ast_expr *
6322 isl_ast_build_access_from_pw_multi_aff(
6323 __isl_keep isl_ast_build *build,
6324 __isl_take isl_pw_multi_aff *pma);
6325 __isl_give isl_ast_expr *
6326 isl_ast_build_access_from_multi_pw_aff(
6327 __isl_keep isl_ast_build *build,
6328 __isl_take isl_multi_pw_aff *mpa);
6329 __isl_give isl_ast_expr *
6330 isl_ast_build_call_from_pw_multi_aff(
6331 __isl_keep isl_ast_build *build,
6332 __isl_take isl_pw_multi_aff *pma);
6333 __isl_give isl_ast_expr *
6334 isl_ast_build_call_from_multi_pw_aff(
6335 __isl_keep isl_ast_build *build,
6336 __isl_take isl_multi_pw_aff *mpa);
6338 The domains of C<pa>, C<mpa> and C<pma> should correspond
6339 to the schedule space of C<build>.
6340 The tuple id of C<mpa> or C<pma> is used as the array being accessed or
6341 the function being called.
6342 If the accessed space is a nested relation, then it is taken
6343 to represent an access of the member specified by the range
6344 of this nested relation of the structure specified by the domain
6345 of the nested relation.
6347 The following functions can be used to modify an C<isl_ast_expr>.
6349 #include <isl/ast.h>
6350 __isl_give isl_ast_expr *isl_ast_expr_set_op_arg(
6351 __isl_take isl_ast_expr *expr, int pos,
6352 __isl_take isl_ast_expr *arg);
6354 Replace the argument of C<expr> at position C<pos> by C<arg>.
6356 #include <isl/ast.h>
6357 __isl_give isl_ast_expr *isl_ast_expr_substitute_ids(
6358 __isl_take isl_ast_expr *expr,
6359 __isl_take isl_id_to_ast_expr *id2expr);
6361 The function C<isl_ast_expr_substitute_ids> replaces the
6362 subexpressions of C<expr> of type C<isl_ast_expr_id>
6363 by the corresponding expression in C<id2expr>, if there is any.
6366 User specified data can be attached to an C<isl_ast_node> and obtained
6367 from the same C<isl_ast_node> using the following functions.
6369 #include <isl/ast.h>
6370 __isl_give isl_ast_node *isl_ast_node_set_annotation(
6371 __isl_take isl_ast_node *node,
6372 __isl_take isl_id *annotation);
6373 __isl_give isl_id *isl_ast_node_get_annotation(
6374 __isl_keep isl_ast_node *node);
6376 Basic printing can be performed using the following functions.
6378 #include <isl/ast.h>
6379 __isl_give isl_printer *isl_printer_print_ast_expr(
6380 __isl_take isl_printer *p,
6381 __isl_keep isl_ast_expr *expr);
6382 __isl_give isl_printer *isl_printer_print_ast_node(
6383 __isl_take isl_printer *p,
6384 __isl_keep isl_ast_node *node);
6386 More advanced printing can be performed using the following functions.
6388 #include <isl/ast.h>
6389 __isl_give isl_printer *isl_ast_op_type_print_macro(
6390 enum isl_ast_op_type type,
6391 __isl_take isl_printer *p);
6392 __isl_give isl_printer *isl_ast_node_print_macros(
6393 __isl_keep isl_ast_node *node,
6394 __isl_take isl_printer *p);
6395 __isl_give isl_printer *isl_ast_node_print(
6396 __isl_keep isl_ast_node *node,
6397 __isl_take isl_printer *p,
6398 __isl_take isl_ast_print_options *options);
6399 __isl_give isl_printer *isl_ast_node_for_print(
6400 __isl_keep isl_ast_node *node,
6401 __isl_take isl_printer *p,
6402 __isl_take isl_ast_print_options *options);
6403 __isl_give isl_printer *isl_ast_node_if_print(
6404 __isl_keep isl_ast_node *node,
6405 __isl_take isl_printer *p,
6406 __isl_take isl_ast_print_options *options);
6408 While printing an C<isl_ast_node> in C<ISL_FORMAT_C>,
6409 C<isl> may print out an AST that makes use of macros such
6410 as C<floord>, C<min> and C<max>.
6411 C<isl_ast_op_type_print_macro> prints out the macro
6412 corresponding to a specific C<isl_ast_op_type>.
6413 C<isl_ast_node_print_macros> scans the C<isl_ast_node>
6414 for expressions where these macros would be used and prints
6415 out the required macro definitions.
6416 Essentially, C<isl_ast_node_print_macros> calls
6417 C<isl_ast_node_foreach_ast_op_type> with C<isl_ast_op_type_print_macro>
6418 as function argument.
6419 C<isl_ast_node_print>, C<isl_ast_node_for_print> and
6420 C<isl_ast_node_if_print> print an C<isl_ast_node>
6421 in C<ISL_FORMAT_C>, but allow for some extra control
6422 through an C<isl_ast_print_options> object.
6423 This object can be created using the following functions.
6425 #include <isl/ast.h>
6426 __isl_give isl_ast_print_options *
6427 isl_ast_print_options_alloc(isl_ctx *ctx);
6428 __isl_give isl_ast_print_options *
6429 isl_ast_print_options_copy(
6430 __isl_keep isl_ast_print_options *options);
6431 void *isl_ast_print_options_free(
6432 __isl_take isl_ast_print_options *options);
6434 __isl_give isl_ast_print_options *
6435 isl_ast_print_options_set_print_user(
6436 __isl_take isl_ast_print_options *options,
6437 __isl_give isl_printer *(*print_user)(
6438 __isl_take isl_printer *p,
6439 __isl_take isl_ast_print_options *options,
6440 __isl_keep isl_ast_node *node, void *user),
6442 __isl_give isl_ast_print_options *
6443 isl_ast_print_options_set_print_for(
6444 __isl_take isl_ast_print_options *options,
6445 __isl_give isl_printer *(*print_for)(
6446 __isl_take isl_printer *p,
6447 __isl_take isl_ast_print_options *options,
6448 __isl_keep isl_ast_node *node, void *user),
6451 The callback set by C<isl_ast_print_options_set_print_user>
6452 is called whenever a node of type C<isl_ast_node_user> needs to
6454 The callback set by C<isl_ast_print_options_set_print_for>
6455 is called whenever a node of type C<isl_ast_node_for> needs to
6457 Note that C<isl_ast_node_for_print> will I<not> call the
6458 callback set by C<isl_ast_print_options_set_print_for> on the node
6459 on which C<isl_ast_node_for_print> is called, but only on nested
6460 nodes of type C<isl_ast_node_for>. It is therefore safe to
6461 call C<isl_ast_node_for_print> from within the callback set by
6462 C<isl_ast_print_options_set_print_for>.
6464 The following option determines the type to be used for iterators
6465 while printing the AST.
6467 int isl_options_set_ast_iterator_type(
6468 isl_ctx *ctx, const char *val);
6469 const char *isl_options_get_ast_iterator_type(
6474 #include <isl/ast_build.h>
6475 int isl_options_set_ast_build_atomic_upper_bound(
6476 isl_ctx *ctx, int val);
6477 int isl_options_get_ast_build_atomic_upper_bound(
6479 int isl_options_set_ast_build_prefer_pdiv(isl_ctx *ctx,
6481 int isl_options_get_ast_build_prefer_pdiv(isl_ctx *ctx);
6482 int isl_options_set_ast_build_exploit_nested_bounds(
6483 isl_ctx *ctx, int val);
6484 int isl_options_get_ast_build_exploit_nested_bounds(
6486 int isl_options_set_ast_build_group_coscheduled(
6487 isl_ctx *ctx, int val);
6488 int isl_options_get_ast_build_group_coscheduled(
6490 int isl_options_set_ast_build_scale_strides(
6491 isl_ctx *ctx, int val);
6492 int isl_options_get_ast_build_scale_strides(
6494 int isl_options_set_ast_build_allow_else(isl_ctx *ctx,
6496 int isl_options_get_ast_build_allow_else(isl_ctx *ctx);
6497 int isl_options_set_ast_build_allow_or(isl_ctx *ctx,
6499 int isl_options_get_ast_build_allow_or(isl_ctx *ctx);
6503 =item * ast_build_atomic_upper_bound
6505 Generate loop upper bounds that consist of the current loop iterator,
6506 an operator and an expression not involving the iterator.
6507 If this option is not set, then the current loop iterator may appear
6508 several times in the upper bound.
6509 For example, when this option is turned off, AST generation
6512 [n] -> { A[i] -> [i] : 0 <= i <= 100, n }
6516 for (int c0 = 0; c0 <= 100 && n >= c0; c0 += 1)
6519 When the option is turned on, the following AST is generated
6521 for (int c0 = 0; c0 <= min(100, n); c0 += 1)
6524 =item * ast_build_prefer_pdiv
6526 If this option is turned off, then the AST generation will
6527 produce ASTs that may only contain C<isl_ast_op_fdiv_q>
6528 operators, but no C<isl_ast_op_pdiv_q> or
6529 C<isl_ast_op_pdiv_r> operators.
6530 If this options is turned on, then C<isl> will try to convert
6531 some of the C<isl_ast_op_fdiv_q> operators to (expressions containing)
6532 C<isl_ast_op_pdiv_q> or C<isl_ast_op_pdiv_r> operators.
6534 =item * ast_build_exploit_nested_bounds
6536 Simplify conditions based on bounds of nested for loops.
6537 In particular, remove conditions that are implied by the fact
6538 that one or more nested loops have at least one iteration,
6539 meaning that the upper bound is at least as large as the lower bound.
6540 For example, when this option is turned off, AST generation
6543 [N,M] -> { A[i,j] -> [i,j] : 0 <= i <= N and
6549 for (int c0 = 0; c0 <= N; c0 += 1)
6550 for (int c1 = 0; c1 <= M; c1 += 1)
6553 When the option is turned on, the following AST is generated
6555 for (int c0 = 0; c0 <= N; c0 += 1)
6556 for (int c1 = 0; c1 <= M; c1 += 1)
6559 =item * ast_build_group_coscheduled
6561 If two domain elements are assigned the same schedule point, then
6562 they may be executed in any order and they may even appear in different
6563 loops. If this options is set, then the AST generator will make
6564 sure that coscheduled domain elements do not appear in separate parts
6565 of the AST. This is useful in case of nested AST generation
6566 if the outer AST generation is given only part of a schedule
6567 and the inner AST generation should handle the domains that are
6568 coscheduled by this initial part of the schedule together.
6569 For example if an AST is generated for a schedule
6571 { A[i] -> [0]; B[i] -> [0] }
6573 then the C<isl_ast_build_set_create_leaf> callback described
6574 below may get called twice, once for each domain.
6575 Setting this option ensures that the callback is only called once
6576 on both domains together.
6578 =item * ast_build_separation_bounds
6580 This option specifies which bounds to use during separation.
6581 If this option is set to C<ISL_AST_BUILD_SEPARATION_BOUNDS_IMPLICIT>
6582 then all (possibly implicit) bounds on the current dimension will
6583 be used during separation.
6584 If this option is set to C<ISL_AST_BUILD_SEPARATION_BOUNDS_EXPLICIT>
6585 then only those bounds that are explicitly available will
6586 be used during separation.
6588 =item * ast_build_scale_strides
6590 This option specifies whether the AST generator is allowed
6591 to scale down iterators of strided loops.
6593 =item * ast_build_allow_else
6595 This option specifies whether the AST generator is allowed
6596 to construct if statements with else branches.
6598 =item * ast_build_allow_or
6600 This option specifies whether the AST generator is allowed
6601 to construct if conditions with disjunctions.
6605 =head3 Fine-grained Control over AST Generation
6607 Besides specifying the constraints on the parameters,
6608 an C<isl_ast_build> object can be used to control
6609 various aspects of the AST generation process.
6610 The most prominent way of control is through ``options'',
6611 which can be set using the following function.
6613 #include <isl/ast_build.h>
6614 __isl_give isl_ast_build *
6615 isl_ast_build_set_options(
6616 __isl_take isl_ast_build *control,
6617 __isl_take isl_union_map *options);
6619 The options are encoded in an <isl_union_map>.
6620 The domain of this union relation refers to the schedule domain,
6621 i.e., the range of the schedule passed to C<isl_ast_build_ast_from_schedule>.
6622 In the case of nested AST generation (see L</"Nested AST Generation">),
6623 the domain of C<options> should refer to the extra piece of the schedule.
6624 That is, it should be equal to the range of the wrapped relation in the
6625 range of the schedule.
6626 The range of the options can consist of elements in one or more spaces,
6627 the names of which determine the effect of the option.
6628 The values of the range typically also refer to the schedule dimension
6629 to which the option applies. In case of nested AST generation
6630 (see L</"Nested AST Generation">), these values refer to the position
6631 of the schedule dimension within the innermost AST generation.
6632 The constraints on the domain elements of
6633 the option should only refer to this dimension and earlier dimensions.
6634 We consider the following spaces.
6638 =item C<separation_class>
6640 This space is a wrapped relation between two one dimensional spaces.
6641 The input space represents the schedule dimension to which the option
6642 applies and the output space represents the separation class.
6643 While constructing a loop corresponding to the specified schedule
6644 dimension(s), the AST generator will try to generate separate loops
6645 for domain elements that are assigned different classes.
6646 If only some of the elements are assigned a class, then those elements
6647 that are not assigned any class will be treated as belonging to a class
6648 that is separate from the explicitly assigned classes.
6649 The typical use case for this option is to separate full tiles from
6651 The other options, described below, are applied after the separation
6654 As an example, consider the separation into full and partial tiles
6655 of a tiling of a triangular domain.
6656 Take, for example, the domain
6658 { A[i,j] : 0 <= i,j and i + j <= 100 }
6660 and a tiling into tiles of 10 by 10. The input to the AST generator
6661 is then the schedule
6663 { A[i,j] -> [([i/10]),[j/10],i,j] : 0 <= i,j and
6666 Without any options, the following AST is generated
6668 for (int c0 = 0; c0 <= 10; c0 += 1)
6669 for (int c1 = 0; c1 <= -c0 + 10; c1 += 1)
6670 for (int c2 = 10 * c0;
6671 c2 <= min(-10 * c1 + 100, 10 * c0 + 9);
6673 for (int c3 = 10 * c1;
6674 c3 <= min(10 * c1 + 9, -c2 + 100);
6678 Separation into full and partial tiles can be obtained by assigning
6679 a class, say C<0>, to the full tiles. The full tiles are represented by those
6680 values of the first and second schedule dimensions for which there are
6681 values of the third and fourth dimensions to cover an entire tile.
6682 That is, we need to specify the following option
6684 { [a,b,c,d] -> separation_class[[0]->[0]] :
6685 exists b': 0 <= 10a,10b' and
6686 10a+9+10b'+9 <= 100;
6687 [a,b,c,d] -> separation_class[[1]->[0]] :
6688 0 <= 10a,10b and 10a+9+10b+9 <= 100 }
6692 { [a, b, c, d] -> separation_class[[1] -> [0]] :
6693 a >= 0 and b >= 0 and b <= 8 - a;
6694 [a, b, c, d] -> separation_class[[0] -> [0]] :
6697 With this option, the generated AST is as follows
6700 for (int c0 = 0; c0 <= 8; c0 += 1) {
6701 for (int c1 = 0; c1 <= -c0 + 8; c1 += 1)
6702 for (int c2 = 10 * c0;
6703 c2 <= 10 * c0 + 9; c2 += 1)
6704 for (int c3 = 10 * c1;
6705 c3 <= 10 * c1 + 9; c3 += 1)
6707 for (int c1 = -c0 + 9; c1 <= -c0 + 10; c1 += 1)
6708 for (int c2 = 10 * c0;
6709 c2 <= min(-10 * c1 + 100, 10 * c0 + 9);
6711 for (int c3 = 10 * c1;
6712 c3 <= min(-c2 + 100, 10 * c1 + 9);
6716 for (int c0 = 9; c0 <= 10; c0 += 1)
6717 for (int c1 = 0; c1 <= -c0 + 10; c1 += 1)
6718 for (int c2 = 10 * c0;
6719 c2 <= min(-10 * c1 + 100, 10 * c0 + 9);
6721 for (int c3 = 10 * c1;
6722 c3 <= min(10 * c1 + 9, -c2 + 100);
6729 This is a single-dimensional space representing the schedule dimension(s)
6730 to which ``separation'' should be applied. Separation tries to split
6731 a loop into several pieces if this can avoid the generation of guards
6733 See also the C<atomic> option.
6737 This is a single-dimensional space representing the schedule dimension(s)
6738 for which the domains should be considered ``atomic''. That is, the
6739 AST generator will make sure that any given domain space will only appear
6740 in a single loop at the specified level.
6742 Consider the following schedule
6744 { a[i] -> [i] : 0 <= i < 10;
6745 b[i] -> [i+1] : 0 <= i < 10 }
6747 If the following option is specified
6749 { [i] -> separate[x] }
6751 then the following AST will be generated
6755 for (int c0 = 1; c0 <= 9; c0 += 1) {
6762 If, on the other hand, the following option is specified
6764 { [i] -> atomic[x] }
6766 then the following AST will be generated
6768 for (int c0 = 0; c0 <= 10; c0 += 1) {
6775 If neither C<atomic> nor C<separate> is specified, then the AST generator
6776 may produce either of these two results or some intermediate form.
6780 This is a single-dimensional space representing the schedule dimension(s)
6781 that should be I<completely> unrolled.
6782 To obtain a partial unrolling, the user should apply an additional
6783 strip-mining to the schedule and fully unroll the inner loop.
6787 Additional control is available through the following functions.
6789 #include <isl/ast_build.h>
6790 __isl_give isl_ast_build *
6791 isl_ast_build_set_iterators(
6792 __isl_take isl_ast_build *control,
6793 __isl_take isl_id_list *iterators);
6795 The function C<isl_ast_build_set_iterators> allows the user to
6796 specify a list of iterator C<isl_id>s to be used as iterators.
6797 If the input schedule is injective, then
6798 the number of elements in this list should be as large as the dimension
6799 of the schedule space, but no direct correspondence should be assumed
6800 between dimensions and elements.
6801 If the input schedule is not injective, then an additional number
6802 of C<isl_id>s equal to the largest dimension of the input domains
6804 If the number of provided C<isl_id>s is insufficient, then additional
6805 names are automatically generated.
6807 #include <isl/ast_build.h>
6808 __isl_give isl_ast_build *
6809 isl_ast_build_set_create_leaf(
6810 __isl_take isl_ast_build *control,
6811 __isl_give isl_ast_node *(*fn)(
6812 __isl_take isl_ast_build *build,
6813 void *user), void *user);
6816 C<isl_ast_build_set_create_leaf> function allows for the
6817 specification of a callback that should be called whenever the AST
6818 generator arrives at an element of the schedule domain.
6819 The callback should return an AST node that should be inserted
6820 at the corresponding position of the AST. The default action (when
6821 the callback is not set) is to continue generating parts of the AST to scan
6822 all the domain elements associated to the schedule domain element
6823 and to insert user nodes, ``calling'' the domain element, for each of them.
6824 The C<build> argument contains the current state of the C<isl_ast_build>.
6825 To ease nested AST generation (see L</"Nested AST Generation">),
6826 all control information that is
6827 specific to the current AST generation such as the options and
6828 the callbacks has been removed from this C<isl_ast_build>.
6829 The callback would typically return the result of a nested
6831 user defined node created using the following function.
6833 #include <isl/ast.h>
6834 __isl_give isl_ast_node *isl_ast_node_alloc_user(
6835 __isl_take isl_ast_expr *expr);
6837 #include <isl/ast_build.h>
6838 __isl_give isl_ast_build *
6839 isl_ast_build_set_at_each_domain(
6840 __isl_take isl_ast_build *build,
6841 __isl_give isl_ast_node *(*fn)(
6842 __isl_take isl_ast_node *node,
6843 __isl_keep isl_ast_build *build,
6844 void *user), void *user);
6845 __isl_give isl_ast_build *
6846 isl_ast_build_set_before_each_for(
6847 __isl_take isl_ast_build *build,
6848 __isl_give isl_id *(*fn)(
6849 __isl_keep isl_ast_build *build,
6850 void *user), void *user);
6851 __isl_give isl_ast_build *
6852 isl_ast_build_set_after_each_for(
6853 __isl_take isl_ast_build *build,
6854 __isl_give isl_ast_node *(*fn)(
6855 __isl_take isl_ast_node *node,
6856 __isl_keep isl_ast_build *build,
6857 void *user), void *user);
6859 The callback set by C<isl_ast_build_set_at_each_domain> will
6860 be called for each domain AST node.
6861 The callbacks set by C<isl_ast_build_set_before_each_for>
6862 and C<isl_ast_build_set_after_each_for> will be called
6863 for each for AST node. The first will be called in depth-first
6864 pre-order, while the second will be called in depth-first post-order.
6865 Since C<isl_ast_build_set_before_each_for> is called before the for
6866 node is actually constructed, it is only passed an C<isl_ast_build>.
6867 The returned C<isl_id> will be added as an annotation (using
6868 C<isl_ast_node_set_annotation>) to the constructed for node.
6869 In particular, if the user has also specified an C<after_each_for>
6870 callback, then the annotation can be retrieved from the node passed to
6871 that callback using C<isl_ast_node_get_annotation>.
6872 All callbacks should C<NULL> on failure.
6873 The given C<isl_ast_build> can be used to create new
6874 C<isl_ast_expr> objects using C<isl_ast_build_expr_from_pw_aff>
6875 or C<isl_ast_build_call_from_pw_multi_aff>.
6877 =head3 Nested AST Generation
6879 C<isl> allows the user to create an AST within the context
6880 of another AST. These nested ASTs are created using the
6881 same C<isl_ast_build_ast_from_schedule> function that is used to create the
6882 outer AST. The C<build> argument should be an C<isl_ast_build>
6883 passed to a callback set by
6884 C<isl_ast_build_set_create_leaf>.
6885 The space of the range of the C<schedule> argument should refer
6886 to this build. In particular, the space should be a wrapped
6887 relation and the domain of this wrapped relation should be the
6888 same as that of the range of the schedule returned by
6889 C<isl_ast_build_get_schedule> below.
6890 In practice, the new schedule is typically
6891 created by calling C<isl_union_map_range_product> on the old schedule
6892 and some extra piece of the schedule.
6893 The space of the schedule domain is also available from
6894 the C<isl_ast_build>.
6896 #include <isl/ast_build.h>
6897 __isl_give isl_union_map *isl_ast_build_get_schedule(
6898 __isl_keep isl_ast_build *build);
6899 __isl_give isl_space *isl_ast_build_get_schedule_space(
6900 __isl_keep isl_ast_build *build);
6901 __isl_give isl_ast_build *isl_ast_build_restrict(
6902 __isl_take isl_ast_build *build,
6903 __isl_take isl_set *set);
6905 The C<isl_ast_build_get_schedule> function returns a (partial)
6906 schedule for the domains elements for which part of the AST still needs to
6907 be generated in the current build.
6908 In particular, the domain elements are mapped to those iterations of the loops
6909 enclosing the current point of the AST generation inside which
6910 the domain elements are executed.
6911 No direct correspondence between
6912 the input schedule and this schedule should be assumed.
6913 The space obtained from C<isl_ast_build_get_schedule_space> can be used
6914 to create a set for C<isl_ast_build_restrict> to intersect
6915 with the current build. In particular, the set passed to
6916 C<isl_ast_build_restrict> can have additional parameters.
6917 The ids of the set dimensions in the space returned by
6918 C<isl_ast_build_get_schedule_space> correspond to the
6919 iterators of the already generated loops.
6920 The user should not rely on the ids of the output dimensions
6921 of the relations in the union relation returned by
6922 C<isl_ast_build_get_schedule> having any particular value.
6926 Although C<isl> is mainly meant to be used as a library,
6927 it also contains some basic applications that use some
6928 of the functionality of C<isl>.
6929 The input may be specified in either the L<isl format>
6930 or the L<PolyLib format>.
6932 =head2 C<isl_polyhedron_sample>
6934 C<isl_polyhedron_sample> takes a polyhedron as input and prints
6935 an integer element of the polyhedron, if there is any.
6936 The first column in the output is the denominator and is always
6937 equal to 1. If the polyhedron contains no integer points,
6938 then a vector of length zero is printed.
6942 C<isl_pip> takes the same input as the C<example> program
6943 from the C<piplib> distribution, i.e., a set of constraints
6944 on the parameters, a line containing only -1 and finally a set
6945 of constraints on a parametric polyhedron.
6946 The coefficients of the parameters appear in the last columns
6947 (but before the final constant column).
6948 The output is the lexicographic minimum of the parametric polyhedron.
6949 As C<isl> currently does not have its own output format, the output
6950 is just a dump of the internal state.
6952 =head2 C<isl_polyhedron_minimize>
6954 C<isl_polyhedron_minimize> computes the minimum of some linear
6955 or affine objective function over the integer points in a polyhedron.
6956 If an affine objective function
6957 is given, then the constant should appear in the last column.
6959 =head2 C<isl_polytope_scan>
6961 Given a polytope, C<isl_polytope_scan> prints
6962 all integer points in the polytope.
6964 =head2 C<isl_codegen>
6966 Given a schedule, a context set and an options relation,
6967 C<isl_codegen> prints out an AST that scans the domain elements
6968 of the schedule in the order of their image(s) taking into account
6969 the constraints in the context set.