3 C<isl> is a thread-safe C library for manipulating
4 sets and relations of integer points bounded by affine constraints.
5 The descriptions of the sets and relations may involve
6 both parameters and existentially quantified variables.
7 All computations are performed in exact integer arithmetic
9 The C<isl> library offers functionality that is similar
10 to that offered by the C<Omega> and C<Omega+> libraries,
11 but the underlying algorithms are in most cases completely different.
13 The library is by no means complete and some fairly basic
14 functionality is still missing.
15 Still, even in its current form, the library has been successfully
16 used as a backend polyhedral library for the polyhedral
17 scanner C<CLooG> and as part of an equivalence checker of
18 static affine programs.
19 For bug reports, feature requests and questions,
20 visit the the discussion group at
21 L<http://groups.google.com/group/isl-development>.
23 =head2 Backward Incompatible Changes
25 =head3 Changes since isl-0.02
29 =item * The old printing functions have been deprecated
30 and replaced by C<isl_printer> functions, see L<Input and Output>.
32 =item * Most functions related to dependence analysis have acquired
33 an extra C<must> argument. To obtain the old behavior, this argument
34 should be given the value 1. See L<Dependence Analysis>.
38 =head3 Changes since isl-0.03
42 =item * The function C<isl_pw_qpolynomial_fold_add> has been
43 renamed to C<isl_pw_qpolynomial_fold_fold>.
44 Similarly, C<isl_union_pw_qpolynomial_fold_add> has been
45 renamed to C<isl_union_pw_qpolynomial_fold_fold>.
49 =head3 Changes since isl-0.04
53 =item * All header files have been renamed from C<isl_header.h>
58 =head3 Changes since isl-0.05
62 =item * The functions C<isl_printer_print_basic_set> and
63 C<isl_printer_print_basic_map> no longer print a newline.
65 =item * The functions C<isl_flow_get_no_source>
66 and C<isl_union_map_compute_flow> now return
67 the accesses for which no source could be found instead of
68 the iterations where those accesses occur.
70 =item * The functions C<isl_basic_map_identity> and
71 C<isl_map_identity> now take a B<map> space as input. An old call
72 C<isl_map_identity(space)> can be rewritten to
73 C<isl_map_identity(isl_space_map_from_set(space))>.
75 =item * The function C<isl_map_power> no longer takes
76 a parameter position as input. Instead, the exponent
77 is now expressed as the domain of the resulting relation.
81 =head3 Changes since isl-0.06
85 =item * The format of C<isl_printer_print_qpolynomial>'s
86 C<ISL_FORMAT_ISL> output has changed.
87 Use C<ISL_FORMAT_C> to obtain the old output.
89 =item * The C<*_fast_*> functions have been renamed to C<*_plain_*>.
90 Some of the old names have been kept for backward compatibility,
91 but they will be removed in the future.
95 =head3 Changes since isl-0.07
99 =item * The function C<isl_pw_aff_max> has been renamed to
100 C<isl_pw_aff_union_max>.
101 Similarly, the function C<isl_pw_aff_add> has been renamed to
102 C<isl_pw_aff_union_add>.
104 =item * The C<isl_dim> type has been renamed to C<isl_space>
105 along with the associated functions.
106 Some of the old names have been kept for backward compatibility,
107 but they will be removed in the future.
109 =item * Spaces of maps, sets and parameter domains are now
110 treated differently. The distinction between map spaces and set spaces
111 has always been made on a conceptual level, but proper use of such spaces
112 was never checked. Furthermore, up until isl-0.07 there was no way
113 of explicitly creating a parameter space. These can now be created
114 directly using C<isl_space_params_alloc> or from other spaces using
117 =item * The space in which C<isl_aff>, C<isl_pw_aff>, C<isl_qpolynomial>,
118 C<isl_pw_qpolynomial>, C<isl_qpolynomial_fold> and C<isl_pw_qpolynomial_fold>
119 objects live is now a map space
120 instead of a set space. This means, for example, that the dimensions
121 of the domain of an C<isl_aff> are now considered to be of type
122 C<isl_dim_in> instead of C<isl_dim_set>. Extra functions have been
123 added to obtain the domain space. Some of the constructors still
124 take a domain space and have therefore been renamed.
126 =item * The functions C<isl_equality_alloc> and C<isl_inequality_alloc>
127 now take an C<isl_local_space> instead of an C<isl_space>.
128 An C<isl_local_space> can be created from an C<isl_space>
129 using C<isl_local_space_from_space>.
131 =item * The C<isl_div> type has been removed. Functions that used
132 to return an C<isl_div> now return an C<isl_aff>.
133 Note that the space of an C<isl_aff> is that of relation.
134 When replacing a call to C<isl_div_get_coefficient> by a call to
135 C<isl_aff_get_coefficient> any C<isl_dim_set> argument needs
136 to be replaced by C<isl_dim_in>.
137 A call to C<isl_aff_from_div> can be replaced by a call
139 A call to C<isl_qpolynomial_div(div)> call be replaced by
142 isl_qpolynomial_from_aff(isl_aff_floor(div))
144 The function C<isl_constraint_div> has also been renamed
145 to C<isl_constraint_get_div>.
147 =item * The C<nparam> argument has been removed from
148 C<isl_map_read_from_str> and similar functions.
149 When reading input in the original PolyLib format,
150 the result will have no parameters.
151 If parameters are expected, the caller may want to perform
152 dimension manipulation on the result.
156 =head3 Changes since isl-0.09
160 =item * The C<schedule_split_parallel> option has been replaced
161 by the C<schedule_split_scaled> option.
163 =item * The first argument of C<isl_pw_aff_cond> is now
164 an C<isl_pw_aff> instead of an C<isl_set>.
165 A call C<isl_pw_aff_cond(a, b, c)> can be replaced by
167 isl_pw_aff_cond(isl_set_indicator_function(a), b, c)
171 =head3 Changes since isl-0.10
175 =item * The functions C<isl_set_dim_has_lower_bound> and
176 C<isl_set_dim_has_upper_bound> have been renamed to
177 C<isl_set_dim_has_any_lower_bound> and
178 C<isl_set_dim_has_any_upper_bound>.
179 The new C<isl_set_dim_has_lower_bound> and
180 C<isl_set_dim_has_upper_bound> have slightly different meanings.
184 =head3 Changes since isl-0.12
188 =item * C<isl_int> has been replaced by C<isl_val>.
189 Some of the old functions are still available in C<isl/deprecated/*.h>
190 but they will be removed in the future.
192 =item * The functions C<isl_pw_qpolynomial_eval>,
193 C<isl_union_pw_qpolynomial_eval>, C<isl_pw_qpolynomial_fold_eval>
194 and C<isl_union_pw_qpolynomial_fold_eval> have been changed to return
195 an C<isl_val> instead of an C<isl_qpolynomial>.
201 C<isl> is released under the MIT license.
205 Permission is hereby granted, free of charge, to any person obtaining a copy of
206 this software and associated documentation files (the "Software"), to deal in
207 the Software without restriction, including without limitation the rights to
208 use, copy, modify, merge, publish, distribute, sublicense, and/or sell copies
209 of the Software, and to permit persons to whom the Software is furnished to do
210 so, subject to the following conditions:
212 The above copyright notice and this permission notice shall be included in all
213 copies or substantial portions of the Software.
215 THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
216 IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
217 FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
218 AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
219 LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
220 OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
225 Note that C<isl> currently requires C<GMP>, which is released
226 under the GNU Lesser General Public License (LGPL). This means
227 that code linked against C<isl> is also linked against LGPL code.
231 The source of C<isl> can be obtained either as a tarball
232 or from the git repository. Both are available from
233 L<http://freshmeat.net/projects/isl/>.
234 The installation process depends on how you obtained
237 =head2 Installation from the git repository
241 =item 1 Clone or update the repository
243 The first time the source is obtained, you need to clone
246 git clone git://repo.or.cz/isl.git
248 To obtain updates, you need to pull in the latest changes
252 =item 2 Generate C<configure>
258 After performing the above steps, continue
259 with the L<Common installation instructions>.
261 =head2 Common installation instructions
265 =item 1 Obtain C<GMP>
267 Building C<isl> requires C<GMP>, including its headers files.
268 Your distribution may not provide these header files by default
269 and you may need to install a package called C<gmp-devel> or something
270 similar. Alternatively, C<GMP> can be built from
271 source, available from L<http://gmplib.org/>.
275 C<isl> uses the standard C<autoconf> C<configure> script.
280 optionally followed by some configure options.
281 A complete list of options can be obtained by running
285 Below we discuss some of the more common options.
287 C<isl> can optionally use C<piplib>, but no
288 C<piplib> functionality is currently used by default.
289 The C<--with-piplib> option can
290 be used to specify which C<piplib>
291 library to use, either an installed version (C<system>),
292 an externally built version (C<build>)
293 or no version (C<no>). The option C<build> is mostly useful
294 in C<configure> scripts of larger projects that bundle both C<isl>
301 Installation prefix for C<isl>
303 =item C<--with-gmp-prefix>
305 Installation prefix for C<GMP> (architecture-independent files).
307 =item C<--with-gmp-exec-prefix>
309 Installation prefix for C<GMP> (architecture-dependent files).
311 =item C<--with-piplib>
313 Which copy of C<piplib> to use, either C<no> (default), C<system> or C<build>.
315 =item C<--with-piplib-prefix>
317 Installation prefix for C<system> C<piplib> (architecture-independent files).
319 =item C<--with-piplib-exec-prefix>
321 Installation prefix for C<system> C<piplib> (architecture-dependent files).
323 =item C<--with-piplib-builddir>
325 Location where C<build> C<piplib> was built.
333 =item 4 Install (optional)
339 =head1 Integer Set Library
341 =head2 Initialization
343 All manipulations of integer sets and relations occur within
344 the context of an C<isl_ctx>.
345 A given C<isl_ctx> can only be used within a single thread.
346 All arguments of a function are required to have been allocated
347 within the same context.
348 There are currently no functions available for moving an object
349 from one C<isl_ctx> to another C<isl_ctx>. This means that
350 there is currently no way of safely moving an object from one
351 thread to another, unless the whole C<isl_ctx> is moved.
353 An C<isl_ctx> can be allocated using C<isl_ctx_alloc> and
354 freed using C<isl_ctx_free>.
355 All objects allocated within an C<isl_ctx> should be freed
356 before the C<isl_ctx> itself is freed.
358 isl_ctx *isl_ctx_alloc();
359 void isl_ctx_free(isl_ctx *ctx);
363 An C<isl_val> represents an integer value, a rational value
364 or one of three special values, infinity, negative infinity and NaN.
365 Some predefined values can be created using the following functions.
368 __isl_give isl_val *isl_val_zero(isl_ctx *ctx);
369 __isl_give isl_val *isl_val_one(isl_ctx *ctx);
370 __isl_give isl_val *isl_val_nan(isl_ctx *ctx);
371 __isl_give isl_val *isl_val_infty(isl_ctx *ctx);
372 __isl_give isl_val *isl_val_neginfty(isl_ctx *ctx);
374 Specific integer values can be created using the following functions.
377 __isl_give isl_val *isl_val_int_from_si(isl_ctx *ctx,
379 __isl_give isl_val *isl_val_int_from_ui(isl_ctx *ctx,
381 __isl_give isl_val *isl_val_int_from_chunks(isl_ctx *ctx,
382 size_t n, size_t size, const void *chunks);
384 The function C<isl_val_int_from_chunks> constructs an C<isl_val>
385 from the C<n> I<digits>, each consisting of C<size> bytes, stored at C<chunks>.
386 The least significant digit is assumed to be stored first.
388 Value objects can be copied and freed using the following functions.
391 __isl_give isl_val *isl_val_copy(__isl_keep isl_val *v);
392 void *isl_val_free(__isl_take isl_val *v);
394 They can be inspected using the following functions.
397 isl_ctx *isl_val_get_ctx(__isl_keep isl_val *val);
398 long isl_val_get_num_si(__isl_keep isl_val *v);
399 long isl_val_get_den_si(__isl_keep isl_val *v);
400 double isl_val_get_d(__isl_keep isl_val *v);
401 size_t isl_val_n_abs_num_chunks(__isl_keep isl_val *v,
403 int isl_val_get_abs_num_chunks(__isl_keep isl_val *v,
404 size_t size, void *chunks);
406 C<isl_val_n_abs_num_chunks> returns the number of I<digits>
407 of C<size> bytes needed to store the absolute value of the
409 C<isl_val_get_abs_num_chunks> stores these digits at C<chunks>,
410 which is assumed to have been preallocated by the caller.
411 The least significant digit is stored first.
412 Note that C<isl_val_get_num_si>, C<isl_val_get_den_si>,
413 C<isl_val_get_d>, C<isl_val_n_abs_num_chunks>
414 and C<isl_val_get_abs_num_chunks> can only be applied to rational values.
416 An C<isl_val> can be modified using the following function.
419 __isl_give isl_val *isl_val_set_si(__isl_take isl_val *v,
422 The following unary properties are defined on C<isl_val>s.
425 int isl_val_sgn(__isl_keep isl_val *v);
426 int isl_val_is_zero(__isl_keep isl_val *v);
427 int isl_val_is_one(__isl_keep isl_val *v);
428 int isl_val_is_negone(__isl_keep isl_val *v);
429 int isl_val_is_nonneg(__isl_keep isl_val *v);
430 int isl_val_is_nonpos(__isl_keep isl_val *v);
431 int isl_val_is_pos(__isl_keep isl_val *v);
432 int isl_val_is_neg(__isl_keep isl_val *v);
433 int isl_val_is_int(__isl_keep isl_val *v);
434 int isl_val_is_rat(__isl_keep isl_val *v);
435 int isl_val_is_nan(__isl_keep isl_val *v);
436 int isl_val_is_infty(__isl_keep isl_val *v);
437 int isl_val_is_neginfty(__isl_keep isl_val *v);
439 Note that the sign of NaN is undefined.
441 The following binary properties are defined on pairs of C<isl_val>s.
444 int isl_val_lt(__isl_keep isl_val *v1,
445 __isl_keep isl_val *v2);
446 int isl_val_le(__isl_keep isl_val *v1,
447 __isl_keep isl_val *v2);
448 int isl_val_gt(__isl_keep isl_val *v1,
449 __isl_keep isl_val *v2);
450 int isl_val_ge(__isl_keep isl_val *v1,
451 __isl_keep isl_val *v2);
452 int isl_val_eq(__isl_keep isl_val *v1,
453 __isl_keep isl_val *v2);
454 int isl_val_ne(__isl_keep isl_val *v1,
455 __isl_keep isl_val *v2);
457 For integer C<isl_val>s we additionally have the following binary property.
460 int isl_val_is_divisible_by(__isl_keep isl_val *v1,
461 __isl_keep isl_val *v2);
463 An C<isl_val> can also be compared to an integer using the following
464 function. The result is undefined for NaN.
467 int isl_val_cmp_si(__isl_keep isl_val *v, long i);
469 The following unary operations are available on C<isl_val>s.
472 __isl_give isl_val *isl_val_abs(__isl_take isl_val *v);
473 __isl_give isl_val *isl_val_neg(__isl_take isl_val *v);
474 __isl_give isl_val *isl_val_floor(__isl_take isl_val *v);
475 __isl_give isl_val *isl_val_ceil(__isl_take isl_val *v);
476 __isl_give isl_val *isl_val_trunc(__isl_take isl_val *v);
478 The following binary operations are available on C<isl_val>s.
481 __isl_give isl_val *isl_val_abs(__isl_take isl_val *v);
482 __isl_give isl_val *isl_val_neg(__isl_take isl_val *v);
483 __isl_give isl_val *isl_val_floor(__isl_take isl_val *v);
484 __isl_give isl_val *isl_val_ceil(__isl_take isl_val *v);
485 __isl_give isl_val *isl_val_trunc(__isl_take isl_val *v);
486 __isl_give isl_val *isl_val_2exp(__isl_take isl_val *v);
487 __isl_give isl_val *isl_val_min(__isl_take isl_val *v1,
488 __isl_take isl_val *v2);
489 __isl_give isl_val *isl_val_max(__isl_take isl_val *v1,
490 __isl_take isl_val *v2);
491 __isl_give isl_val *isl_val_add(__isl_take isl_val *v1,
492 __isl_take isl_val *v2);
493 __isl_give isl_val *isl_val_add_ui(__isl_take isl_val *v1,
495 __isl_give isl_val *isl_val_sub(__isl_take isl_val *v1,
496 __isl_take isl_val *v2);
497 __isl_give isl_val *isl_val_sub_ui(__isl_take isl_val *v1,
499 __isl_give isl_val *isl_val_mul(__isl_take isl_val *v1,
500 __isl_take isl_val *v2);
501 __isl_give isl_val *isl_val_mul_ui(__isl_take isl_val *v1,
503 __isl_give isl_val *isl_val_div(__isl_take isl_val *v1,
504 __isl_take isl_val *v2);
506 On integer values, we additionally have the following operations.
509 __isl_give isl_val *isl_val_2exp(__isl_take isl_val *v);
510 __isl_give isl_val *isl_val_mod(__isl_take isl_val *v1,
511 __isl_take isl_val *v2);
512 __isl_give isl_val *isl_val_gcd(__isl_take isl_val *v1,
513 __isl_take isl_val *v2);
514 __isl_give isl_val *isl_val_gcdext(__isl_take isl_val *v1,
515 __isl_take isl_val *v2, __isl_give isl_val **x,
516 __isl_give isl_val **y);
518 The function C<isl_val_gcdext> returns the greatest common divisor g
519 of C<v1> and C<v2> as well as two integers C<*x> and C<*y> such
520 that C<*x> * C<v1> + C<*y> * C<v2> = g.
522 A value can be read from input using
525 __isl_give isl_val *isl_val_read_from_str(isl_ctx *ctx,
528 A value can be printed using
531 __isl_give isl_printer *isl_printer_print_val(
532 __isl_take isl_printer *p, __isl_keep isl_val *v);
534 =head3 GMP specific functions
536 These functions are only available if C<isl> has been compiled with C<GMP>
539 Specific integer and rational values can be created from C<GMP> values using
540 the following functions.
542 #include <isl/val_gmp.h>
543 __isl_give isl_val *isl_val_int_from_gmp(isl_ctx *ctx,
545 __isl_give isl_val *isl_val_from_gmp(isl_ctx *ctx,
546 const mpz_t n, const mpz_t d);
548 The numerator and denominator of a rational value can be extracted as
549 C<GMP> values using the following functions.
551 #include <isl/val_gmp.h>
552 int isl_val_get_num_gmp(__isl_keep isl_val *v, mpz_t z);
553 int isl_val_get_den_gmp(__isl_keep isl_val *v, mpz_t z);
555 =head2 Sets and Relations
557 C<isl> uses six types of objects for representing sets and relations,
558 C<isl_basic_set>, C<isl_basic_map>, C<isl_set>, C<isl_map>,
559 C<isl_union_set> and C<isl_union_map>.
560 C<isl_basic_set> and C<isl_basic_map> represent sets and relations that
561 can be described as a conjunction of affine constraints, while
562 C<isl_set> and C<isl_map> represent unions of
563 C<isl_basic_set>s and C<isl_basic_map>s, respectively.
564 However, all C<isl_basic_set>s or C<isl_basic_map>s in the union need
565 to live in the same space. C<isl_union_set>s and C<isl_union_map>s
566 represent unions of C<isl_set>s or C<isl_map>s in I<different> spaces,
567 where spaces are considered different if they have a different number
568 of dimensions and/or different names (see L<"Spaces">).
569 The difference between sets and relations (maps) is that sets have
570 one set of variables, while relations have two sets of variables,
571 input variables and output variables.
573 =head2 Memory Management
575 Since a high-level operation on sets and/or relations usually involves
576 several substeps and since the user is usually not interested in
577 the intermediate results, most functions that return a new object
578 will also release all the objects passed as arguments.
579 If the user still wants to use one or more of these arguments
580 after the function call, she should pass along a copy of the
581 object rather than the object itself.
582 The user is then responsible for making sure that the original
583 object gets used somewhere else or is explicitly freed.
585 The arguments and return values of all documented functions are
586 annotated to make clear which arguments are released and which
587 arguments are preserved. In particular, the following annotations
594 C<__isl_give> means that a new object is returned.
595 The user should make sure that the returned pointer is
596 used exactly once as a value for an C<__isl_take> argument.
597 In between, it can be used as a value for as many
598 C<__isl_keep> arguments as the user likes.
599 There is one exception, and that is the case where the
600 pointer returned is C<NULL>. Is this case, the user
601 is free to use it as an C<__isl_take> argument or not.
605 C<__isl_take> means that the object the argument points to
606 is taken over by the function and may no longer be used
607 by the user as an argument to any other function.
608 The pointer value must be one returned by a function
609 returning an C<__isl_give> pointer.
610 If the user passes in a C<NULL> value, then this will
611 be treated as an error in the sense that the function will
612 not perform its usual operation. However, it will still
613 make sure that all the other C<__isl_take> arguments
618 C<__isl_keep> means that the function will only use the object
619 temporarily. After the function has finished, the user
620 can still use it as an argument to other functions.
621 A C<NULL> value will be treated in the same way as
622 a C<NULL> value for an C<__isl_take> argument.
626 =head2 Error Handling
628 C<isl> supports different ways to react in case a runtime error is triggered.
629 Runtime errors arise, e.g., if a function such as C<isl_map_intersect> is called
630 with two maps that have incompatible spaces. There are three possible ways
631 to react on error: to warn, to continue or to abort.
633 The default behavior is to warn. In this mode, C<isl> prints a warning, stores
634 the last error in the corresponding C<isl_ctx> and the function in which the
635 error was triggered returns C<NULL>. An error does not corrupt internal state,
636 such that isl can continue to be used. C<isl> also provides functions to
637 read the last error and to reset the memory that stores the last error. The
638 last error is only stored for information purposes. Its presence does not
639 change the behavior of C<isl>. Hence, resetting an error is not required to
640 continue to use isl, but only to observe new errors.
643 enum isl_error isl_ctx_last_error(isl_ctx *ctx);
644 void isl_ctx_reset_error(isl_ctx *ctx);
646 Another option is to continue on error. This is similar to warn on error mode,
647 except that C<isl> does not print any warning. This allows a program to
648 implement its own error reporting.
650 The last option is to directly abort the execution of the program from within
651 the isl library. This makes it obviously impossible to recover from an error,
652 but it allows to directly spot the error location. By aborting on error,
653 debuggers break at the location the error occurred and can provide a stack
654 trace. Other tools that automatically provide stack traces on abort or that do
655 not want to continue execution after an error was triggered may also prefer to
658 The on error behavior of isl can be specified by calling
659 C<isl_options_set_on_error> or by setting the command line option
660 C<--isl-on-error>. Valid arguments for the function call are
661 C<ISL_ON_ERROR_WARN>, C<ISL_ON_ERROR_CONTINUE> and C<ISL_ON_ERROR_ABORT>. The
662 choices for the command line option are C<warn>, C<continue> and C<abort>.
663 It is also possible to query the current error mode.
665 #include <isl/options.h>
666 int isl_options_set_on_error(isl_ctx *ctx, int val);
667 int isl_options_get_on_error(isl_ctx *ctx);
671 Identifiers are used to identify both individual dimensions
672 and tuples of dimensions. They consist of an optional name and an optional
673 user pointer. The name and the user pointer cannot both be C<NULL>, however.
674 Identifiers with the same name but different pointer values
675 are considered to be distinct.
676 Similarly, identifiers with different names but the same pointer value
677 are also considered to be distinct.
678 Equal identifiers are represented using the same object.
679 Pairs of identifiers can therefore be tested for equality using the
681 Identifiers can be constructed, copied, freed, inspected and printed
682 using the following functions.
685 __isl_give isl_id *isl_id_alloc(isl_ctx *ctx,
686 __isl_keep const char *name, void *user);
687 __isl_give isl_id *isl_id_set_free_user(
688 __isl_take isl_id *id,
689 __isl_give void (*free_user)(void *user));
690 __isl_give isl_id *isl_id_copy(isl_id *id);
691 void *isl_id_free(__isl_take isl_id *id);
693 isl_ctx *isl_id_get_ctx(__isl_keep isl_id *id);
694 void *isl_id_get_user(__isl_keep isl_id *id);
695 __isl_keep const char *isl_id_get_name(__isl_keep isl_id *id);
697 __isl_give isl_printer *isl_printer_print_id(
698 __isl_take isl_printer *p, __isl_keep isl_id *id);
700 The callback set by C<isl_id_set_free_user> is called on the user
701 pointer when the last reference to the C<isl_id> is freed.
702 Note that C<isl_id_get_name> returns a pointer to some internal
703 data structure, so the result can only be used while the
704 corresponding C<isl_id> is alive.
708 Whenever a new set, relation or similiar object is created from scratch,
709 the space in which it lives needs to be specified using an C<isl_space>.
710 Each space involves zero or more parameters and zero, one or two
711 tuples of set or input/output dimensions. The parameters and dimensions
712 are identified by an C<isl_dim_type> and a position.
713 The type C<isl_dim_param> refers to parameters,
714 the type C<isl_dim_set> refers to set dimensions (for spaces
715 with a single tuple of dimensions) and the types C<isl_dim_in>
716 and C<isl_dim_out> refer to input and output dimensions
717 (for spaces with two tuples of dimensions).
718 Local spaces (see L</"Local Spaces">) also contain dimensions
719 of type C<isl_dim_div>.
720 Note that parameters are only identified by their position within
721 a given object. Across different objects, parameters are (usually)
722 identified by their names or identifiers. Only unnamed parameters
723 are identified by their positions across objects. The use of unnamed
724 parameters is discouraged.
726 #include <isl/space.h>
727 __isl_give isl_space *isl_space_alloc(isl_ctx *ctx,
728 unsigned nparam, unsigned n_in, unsigned n_out);
729 __isl_give isl_space *isl_space_params_alloc(isl_ctx *ctx,
731 __isl_give isl_space *isl_space_set_alloc(isl_ctx *ctx,
732 unsigned nparam, unsigned dim);
733 __isl_give isl_space *isl_space_copy(__isl_keep isl_space *space);
734 void *isl_space_free(__isl_take isl_space *space);
735 unsigned isl_space_dim(__isl_keep isl_space *space,
736 enum isl_dim_type type);
738 The space used for creating a parameter domain
739 needs to be created using C<isl_space_params_alloc>.
740 For other sets, the space
741 needs to be created using C<isl_space_set_alloc>, while
742 for a relation, the space
743 needs to be created using C<isl_space_alloc>.
744 C<isl_space_dim> can be used
745 to find out the number of dimensions of each type in
746 a space, where type may be
747 C<isl_dim_param>, C<isl_dim_in> (only for relations),
748 C<isl_dim_out> (only for relations), C<isl_dim_set>
749 (only for sets) or C<isl_dim_all>.
751 To check whether a given space is that of a set or a map
752 or whether it is a parameter space, use these functions:
754 #include <isl/space.h>
755 int isl_space_is_params(__isl_keep isl_space *space);
756 int isl_space_is_set(__isl_keep isl_space *space);
757 int isl_space_is_map(__isl_keep isl_space *space);
759 Spaces can be compared using the following functions:
761 #include <isl/space.h>
762 int isl_space_is_equal(__isl_keep isl_space *space1,
763 __isl_keep isl_space *space2);
764 int isl_space_is_domain(__isl_keep isl_space *space1,
765 __isl_keep isl_space *space2);
766 int isl_space_is_range(__isl_keep isl_space *space1,
767 __isl_keep isl_space *space2);
769 C<isl_space_is_domain> checks whether the first argument is equal
770 to the domain of the second argument. This requires in particular that
771 the first argument is a set space and that the second argument
774 It is often useful to create objects that live in the
775 same space as some other object. This can be accomplished
776 by creating the new objects
777 (see L<Creating New Sets and Relations> or
778 L<Creating New (Piecewise) Quasipolynomials>) based on the space
779 of the original object.
782 __isl_give isl_space *isl_basic_set_get_space(
783 __isl_keep isl_basic_set *bset);
784 __isl_give isl_space *isl_set_get_space(__isl_keep isl_set *set);
786 #include <isl/union_set.h>
787 __isl_give isl_space *isl_union_set_get_space(
788 __isl_keep isl_union_set *uset);
791 __isl_give isl_space *isl_basic_map_get_space(
792 __isl_keep isl_basic_map *bmap);
793 __isl_give isl_space *isl_map_get_space(__isl_keep isl_map *map);
795 #include <isl/union_map.h>
796 __isl_give isl_space *isl_union_map_get_space(
797 __isl_keep isl_union_map *umap);
799 #include <isl/constraint.h>
800 __isl_give isl_space *isl_constraint_get_space(
801 __isl_keep isl_constraint *constraint);
803 #include <isl/polynomial.h>
804 __isl_give isl_space *isl_qpolynomial_get_domain_space(
805 __isl_keep isl_qpolynomial *qp);
806 __isl_give isl_space *isl_qpolynomial_get_space(
807 __isl_keep isl_qpolynomial *qp);
808 __isl_give isl_space *isl_qpolynomial_fold_get_space(
809 __isl_keep isl_qpolynomial_fold *fold);
810 __isl_give isl_space *isl_pw_qpolynomial_get_domain_space(
811 __isl_keep isl_pw_qpolynomial *pwqp);
812 __isl_give isl_space *isl_pw_qpolynomial_get_space(
813 __isl_keep isl_pw_qpolynomial *pwqp);
814 __isl_give isl_space *isl_pw_qpolynomial_fold_get_domain_space(
815 __isl_keep isl_pw_qpolynomial_fold *pwf);
816 __isl_give isl_space *isl_pw_qpolynomial_fold_get_space(
817 __isl_keep isl_pw_qpolynomial_fold *pwf);
818 __isl_give isl_space *isl_union_pw_qpolynomial_get_space(
819 __isl_keep isl_union_pw_qpolynomial *upwqp);
820 __isl_give isl_space *isl_union_pw_qpolynomial_fold_get_space(
821 __isl_keep isl_union_pw_qpolynomial_fold *upwf);
824 __isl_give isl_space *isl_multi_val_get_space(
825 __isl_keep isl_multi_val *mv);
828 __isl_give isl_space *isl_aff_get_domain_space(
829 __isl_keep isl_aff *aff);
830 __isl_give isl_space *isl_aff_get_space(
831 __isl_keep isl_aff *aff);
832 __isl_give isl_space *isl_pw_aff_get_domain_space(
833 __isl_keep isl_pw_aff *pwaff);
834 __isl_give isl_space *isl_pw_aff_get_space(
835 __isl_keep isl_pw_aff *pwaff);
836 __isl_give isl_space *isl_multi_aff_get_domain_space(
837 __isl_keep isl_multi_aff *maff);
838 __isl_give isl_space *isl_multi_aff_get_space(
839 __isl_keep isl_multi_aff *maff);
840 __isl_give isl_space *isl_pw_multi_aff_get_domain_space(
841 __isl_keep isl_pw_multi_aff *pma);
842 __isl_give isl_space *isl_pw_multi_aff_get_space(
843 __isl_keep isl_pw_multi_aff *pma);
844 __isl_give isl_space *isl_union_pw_multi_aff_get_space(
845 __isl_keep isl_union_pw_multi_aff *upma);
846 __isl_give isl_space *isl_multi_pw_aff_get_domain_space(
847 __isl_keep isl_multi_pw_aff *mpa);
848 __isl_give isl_space *isl_multi_pw_aff_get_space(
849 __isl_keep isl_multi_pw_aff *mpa);
851 #include <isl/point.h>
852 __isl_give isl_space *isl_point_get_space(
853 __isl_keep isl_point *pnt);
855 The identifiers or names of the individual dimensions may be set or read off
856 using the following functions.
858 #include <isl/space.h>
859 __isl_give isl_space *isl_space_set_dim_id(
860 __isl_take isl_space *space,
861 enum isl_dim_type type, unsigned pos,
862 __isl_take isl_id *id);
863 int isl_space_has_dim_id(__isl_keep isl_space *space,
864 enum isl_dim_type type, unsigned pos);
865 __isl_give isl_id *isl_space_get_dim_id(
866 __isl_keep isl_space *space,
867 enum isl_dim_type type, unsigned pos);
868 __isl_give isl_space *isl_space_set_dim_name(
869 __isl_take isl_space *space,
870 enum isl_dim_type type, unsigned pos,
871 __isl_keep const char *name);
872 int isl_space_has_dim_name(__isl_keep isl_space *space,
873 enum isl_dim_type type, unsigned pos);
874 __isl_keep const char *isl_space_get_dim_name(
875 __isl_keep isl_space *space,
876 enum isl_dim_type type, unsigned pos);
878 Note that C<isl_space_get_name> returns a pointer to some internal
879 data structure, so the result can only be used while the
880 corresponding C<isl_space> is alive.
881 Also note that every function that operates on two sets or relations
882 requires that both arguments have the same parameters. This also
883 means that if one of the arguments has named parameters, then the
884 other needs to have named parameters too and the names need to match.
885 Pairs of C<isl_set>, C<isl_map>, C<isl_union_set> and/or C<isl_union_map>
886 arguments may have different parameters (as long as they are named),
887 in which case the result will have as parameters the union of the parameters of
890 Given the identifier or name of a dimension (typically a parameter),
891 its position can be obtained from the following function.
893 #include <isl/space.h>
894 int isl_space_find_dim_by_id(__isl_keep isl_space *space,
895 enum isl_dim_type type, __isl_keep isl_id *id);
896 int isl_space_find_dim_by_name(__isl_keep isl_space *space,
897 enum isl_dim_type type, const char *name);
899 The identifiers or names of entire spaces may be set or read off
900 using the following functions.
902 #include <isl/space.h>
903 __isl_give isl_space *isl_space_set_tuple_id(
904 __isl_take isl_space *space,
905 enum isl_dim_type type, __isl_take isl_id *id);
906 __isl_give isl_space *isl_space_reset_tuple_id(
907 __isl_take isl_space *space, enum isl_dim_type type);
908 int isl_space_has_tuple_id(__isl_keep isl_space *space,
909 enum isl_dim_type type);
910 __isl_give isl_id *isl_space_get_tuple_id(
911 __isl_keep isl_space *space, enum isl_dim_type type);
912 __isl_give isl_space *isl_space_set_tuple_name(
913 __isl_take isl_space *space,
914 enum isl_dim_type type, const char *s);
915 int isl_space_has_tuple_name(__isl_keep isl_space *space,
916 enum isl_dim_type type);
917 const char *isl_space_get_tuple_name(__isl_keep isl_space *space,
918 enum isl_dim_type type);
920 The C<type> argument needs to be one of C<isl_dim_in>, C<isl_dim_out>
921 or C<isl_dim_set>. As with C<isl_space_get_name>,
922 the C<isl_space_get_tuple_name> function returns a pointer to some internal
924 Binary operations require the corresponding spaces of their arguments
925 to have the same name.
927 Spaces can be nested. In particular, the domain of a set or
928 the domain or range of a relation can be a nested relation.
929 The following functions can be used to construct and deconstruct
932 #include <isl/space.h>
933 int isl_space_is_wrapping(__isl_keep isl_space *space);
934 __isl_give isl_space *isl_space_wrap(__isl_take isl_space *space);
935 __isl_give isl_space *isl_space_unwrap(__isl_take isl_space *space);
937 The input to C<isl_space_is_wrapping> and C<isl_space_unwrap> should
938 be the space of a set, while that of
939 C<isl_space_wrap> should be the space of a relation.
940 Conversely, the output of C<isl_space_unwrap> is the space
941 of a relation, while that of C<isl_space_wrap> is the space of a set.
943 Spaces can be created from other spaces
944 using the following functions.
946 __isl_give isl_space *isl_space_domain(__isl_take isl_space *space);
947 __isl_give isl_space *isl_space_from_domain(__isl_take isl_space *space);
948 __isl_give isl_space *isl_space_range(__isl_take isl_space *space);
949 __isl_give isl_space *isl_space_from_range(__isl_take isl_space *space);
950 __isl_give isl_space *isl_space_params(
951 __isl_take isl_space *space);
952 __isl_give isl_space *isl_space_set_from_params(
953 __isl_take isl_space *space);
954 __isl_give isl_space *isl_space_reverse(__isl_take isl_space *space);
955 __isl_give isl_space *isl_space_join(__isl_take isl_space *left,
956 __isl_take isl_space *right);
957 __isl_give isl_space *isl_space_align_params(
958 __isl_take isl_space *space1, __isl_take isl_space *space2)
959 __isl_give isl_space *isl_space_insert_dims(__isl_take isl_space *space,
960 enum isl_dim_type type, unsigned pos, unsigned n);
961 __isl_give isl_space *isl_space_add_dims(__isl_take isl_space *space,
962 enum isl_dim_type type, unsigned n);
963 __isl_give isl_space *isl_space_drop_dims(__isl_take isl_space *space,
964 enum isl_dim_type type, unsigned first, unsigned n);
965 __isl_give isl_space *isl_space_move_dims(__isl_take isl_space *space,
966 enum isl_dim_type dst_type, unsigned dst_pos,
967 enum isl_dim_type src_type, unsigned src_pos,
969 __isl_give isl_space *isl_space_map_from_set(
970 __isl_take isl_space *space);
971 __isl_give isl_space *isl_space_map_from_domain_and_range(
972 __isl_take isl_space *domain,
973 __isl_take isl_space *range);
974 __isl_give isl_space *isl_space_zip(__isl_take isl_space *space);
975 __isl_give isl_space *isl_space_curry(
976 __isl_take isl_space *space);
977 __isl_give isl_space *isl_space_uncurry(
978 __isl_take isl_space *space);
980 Note that if dimensions are added or removed from a space, then
981 the name and the internal structure are lost.
985 A local space is essentially a space with
986 zero or more existentially quantified variables.
987 The local space of a (constraint of a) basic set or relation can be obtained
988 using the following functions.
990 #include <isl/constraint.h>
991 __isl_give isl_local_space *isl_constraint_get_local_space(
992 __isl_keep isl_constraint *constraint);
995 __isl_give isl_local_space *isl_basic_set_get_local_space(
996 __isl_keep isl_basic_set *bset);
999 __isl_give isl_local_space *isl_basic_map_get_local_space(
1000 __isl_keep isl_basic_map *bmap);
1002 A new local space can be created from a space using
1004 #include <isl/local_space.h>
1005 __isl_give isl_local_space *isl_local_space_from_space(
1006 __isl_take isl_space *space);
1008 They can be inspected, modified, copied and freed using the following functions.
1010 #include <isl/local_space.h>
1011 isl_ctx *isl_local_space_get_ctx(
1012 __isl_keep isl_local_space *ls);
1013 int isl_local_space_is_set(__isl_keep isl_local_space *ls);
1014 int isl_local_space_dim(__isl_keep isl_local_space *ls,
1015 enum isl_dim_type type);
1016 int isl_local_space_has_dim_id(
1017 __isl_keep isl_local_space *ls,
1018 enum isl_dim_type type, unsigned pos);
1019 __isl_give isl_id *isl_local_space_get_dim_id(
1020 __isl_keep isl_local_space *ls,
1021 enum isl_dim_type type, unsigned pos);
1022 int isl_local_space_has_dim_name(
1023 __isl_keep isl_local_space *ls,
1024 enum isl_dim_type type, unsigned pos)
1025 const char *isl_local_space_get_dim_name(
1026 __isl_keep isl_local_space *ls,
1027 enum isl_dim_type type, unsigned pos);
1028 __isl_give isl_local_space *isl_local_space_set_dim_name(
1029 __isl_take isl_local_space *ls,
1030 enum isl_dim_type type, unsigned pos, const char *s);
1031 __isl_give isl_local_space *isl_local_space_set_dim_id(
1032 __isl_take isl_local_space *ls,
1033 enum isl_dim_type type, unsigned pos,
1034 __isl_take isl_id *id);
1035 __isl_give isl_space *isl_local_space_get_space(
1036 __isl_keep isl_local_space *ls);
1037 __isl_give isl_aff *isl_local_space_get_div(
1038 __isl_keep isl_local_space *ls, int pos);
1039 __isl_give isl_local_space *isl_local_space_copy(
1040 __isl_keep isl_local_space *ls);
1041 void *isl_local_space_free(__isl_take isl_local_space *ls);
1043 Note that C<isl_local_space_get_div> can only be used on local spaces
1046 Two local spaces can be compared using
1048 int isl_local_space_is_equal(__isl_keep isl_local_space *ls1,
1049 __isl_keep isl_local_space *ls2);
1051 Local spaces can be created from other local spaces
1052 using the following functions.
1054 __isl_give isl_local_space *isl_local_space_domain(
1055 __isl_take isl_local_space *ls);
1056 __isl_give isl_local_space *isl_local_space_range(
1057 __isl_take isl_local_space *ls);
1058 __isl_give isl_local_space *isl_local_space_from_domain(
1059 __isl_take isl_local_space *ls);
1060 __isl_give isl_local_space *isl_local_space_intersect(
1061 __isl_take isl_local_space *ls1,
1062 __isl_take isl_local_space *ls2);
1063 __isl_give isl_local_space *isl_local_space_add_dims(
1064 __isl_take isl_local_space *ls,
1065 enum isl_dim_type type, unsigned n);
1066 __isl_give isl_local_space *isl_local_space_insert_dims(
1067 __isl_take isl_local_space *ls,
1068 enum isl_dim_type type, unsigned first, unsigned n);
1069 __isl_give isl_local_space *isl_local_space_drop_dims(
1070 __isl_take isl_local_space *ls,
1071 enum isl_dim_type type, unsigned first, unsigned n);
1073 =head2 Input and Output
1075 C<isl> supports its own input/output format, which is similar
1076 to the C<Omega> format, but also supports the C<PolyLib> format
1079 =head3 C<isl> format
1081 The C<isl> format is similar to that of C<Omega>, but has a different
1082 syntax for describing the parameters and allows for the definition
1083 of an existentially quantified variable as the integer division
1084 of an affine expression.
1085 For example, the set of integers C<i> between C<0> and C<n>
1086 such that C<i % 10 <= 6> can be described as
1088 [n] -> { [i] : exists (a = [i/10] : 0 <= i and i <= n and
1091 A set or relation can have several disjuncts, separated
1092 by the keyword C<or>. Each disjunct is either a conjunction
1093 of constraints or a projection (C<exists>) of a conjunction
1094 of constraints. The constraints are separated by the keyword
1097 =head3 C<PolyLib> format
1099 If the represented set is a union, then the first line
1100 contains a single number representing the number of disjuncts.
1101 Otherwise, a line containing the number C<1> is optional.
1103 Each disjunct is represented by a matrix of constraints.
1104 The first line contains two numbers representing
1105 the number of rows and columns,
1106 where the number of rows is equal to the number of constraints
1107 and the number of columns is equal to two plus the number of variables.
1108 The following lines contain the actual rows of the constraint matrix.
1109 In each row, the first column indicates whether the constraint
1110 is an equality (C<0>) or inequality (C<1>). The final column
1111 corresponds to the constant term.
1113 If the set is parametric, then the coefficients of the parameters
1114 appear in the last columns before the constant column.
1115 The coefficients of any existentially quantified variables appear
1116 between those of the set variables and those of the parameters.
1118 =head3 Extended C<PolyLib> format
1120 The extended C<PolyLib> format is nearly identical to the
1121 C<PolyLib> format. The only difference is that the line
1122 containing the number of rows and columns of a constraint matrix
1123 also contains four additional numbers:
1124 the number of output dimensions, the number of input dimensions,
1125 the number of local dimensions (i.e., the number of existentially
1126 quantified variables) and the number of parameters.
1127 For sets, the number of ``output'' dimensions is equal
1128 to the number of set dimensions, while the number of ``input''
1133 #include <isl/set.h>
1134 __isl_give isl_basic_set *isl_basic_set_read_from_file(
1135 isl_ctx *ctx, FILE *input);
1136 __isl_give isl_basic_set *isl_basic_set_read_from_str(
1137 isl_ctx *ctx, const char *str);
1138 __isl_give isl_set *isl_set_read_from_file(isl_ctx *ctx,
1140 __isl_give isl_set *isl_set_read_from_str(isl_ctx *ctx,
1143 #include <isl/map.h>
1144 __isl_give isl_basic_map *isl_basic_map_read_from_file(
1145 isl_ctx *ctx, FILE *input);
1146 __isl_give isl_basic_map *isl_basic_map_read_from_str(
1147 isl_ctx *ctx, const char *str);
1148 __isl_give isl_map *isl_map_read_from_file(
1149 isl_ctx *ctx, FILE *input);
1150 __isl_give isl_map *isl_map_read_from_str(isl_ctx *ctx,
1153 #include <isl/union_set.h>
1154 __isl_give isl_union_set *isl_union_set_read_from_file(
1155 isl_ctx *ctx, FILE *input);
1156 __isl_give isl_union_set *isl_union_set_read_from_str(
1157 isl_ctx *ctx, const char *str);
1159 #include <isl/union_map.h>
1160 __isl_give isl_union_map *isl_union_map_read_from_file(
1161 isl_ctx *ctx, FILE *input);
1162 __isl_give isl_union_map *isl_union_map_read_from_str(
1163 isl_ctx *ctx, const char *str);
1165 The input format is autodetected and may be either the C<PolyLib> format
1166 or the C<isl> format.
1170 Before anything can be printed, an C<isl_printer> needs to
1173 __isl_give isl_printer *isl_printer_to_file(isl_ctx *ctx,
1175 __isl_give isl_printer *isl_printer_to_str(isl_ctx *ctx);
1176 void *isl_printer_free(__isl_take isl_printer *printer);
1177 __isl_give char *isl_printer_get_str(
1178 __isl_keep isl_printer *printer);
1180 The printer can be inspected using the following functions.
1182 FILE *isl_printer_get_file(
1183 __isl_keep isl_printer *printer);
1184 int isl_printer_get_output_format(
1185 __isl_keep isl_printer *p);
1187 The behavior of the printer can be modified in various ways
1189 __isl_give isl_printer *isl_printer_set_output_format(
1190 __isl_take isl_printer *p, int output_format);
1191 __isl_give isl_printer *isl_printer_set_indent(
1192 __isl_take isl_printer *p, int indent);
1193 __isl_give isl_printer *isl_printer_indent(
1194 __isl_take isl_printer *p, int indent);
1195 __isl_give isl_printer *isl_printer_set_prefix(
1196 __isl_take isl_printer *p, const char *prefix);
1197 __isl_give isl_printer *isl_printer_set_suffix(
1198 __isl_take isl_printer *p, const char *suffix);
1200 The C<output_format> may be either C<ISL_FORMAT_ISL>, C<ISL_FORMAT_OMEGA>,
1201 C<ISL_FORMAT_POLYLIB>, C<ISL_FORMAT_EXT_POLYLIB> or C<ISL_FORMAT_LATEX>
1202 and defaults to C<ISL_FORMAT_ISL>.
1203 Each line in the output is indented by C<indent> (set by
1204 C<isl_printer_set_indent>) spaces
1205 (default: 0), prefixed by C<prefix> and suffixed by C<suffix>.
1206 In the C<PolyLib> format output,
1207 the coefficients of the existentially quantified variables
1208 appear between those of the set variables and those
1210 The function C<isl_printer_indent> increases the indentation
1211 by the specified amount (which may be negative).
1213 To actually print something, use
1215 #include <isl/printer.h>
1216 __isl_give isl_printer *isl_printer_print_double(
1217 __isl_take isl_printer *p, double d);
1219 #include <isl/set.h>
1220 __isl_give isl_printer *isl_printer_print_basic_set(
1221 __isl_take isl_printer *printer,
1222 __isl_keep isl_basic_set *bset);
1223 __isl_give isl_printer *isl_printer_print_set(
1224 __isl_take isl_printer *printer,
1225 __isl_keep isl_set *set);
1227 #include <isl/map.h>
1228 __isl_give isl_printer *isl_printer_print_basic_map(
1229 __isl_take isl_printer *printer,
1230 __isl_keep isl_basic_map *bmap);
1231 __isl_give isl_printer *isl_printer_print_map(
1232 __isl_take isl_printer *printer,
1233 __isl_keep isl_map *map);
1235 #include <isl/union_set.h>
1236 __isl_give isl_printer *isl_printer_print_union_set(
1237 __isl_take isl_printer *p,
1238 __isl_keep isl_union_set *uset);
1240 #include <isl/union_map.h>
1241 __isl_give isl_printer *isl_printer_print_union_map(
1242 __isl_take isl_printer *p,
1243 __isl_keep isl_union_map *umap);
1245 When called on a file printer, the following function flushes
1246 the file. When called on a string printer, the buffer is cleared.
1248 __isl_give isl_printer *isl_printer_flush(
1249 __isl_take isl_printer *p);
1251 =head2 Creating New Sets and Relations
1253 C<isl> has functions for creating some standard sets and relations.
1257 =item * Empty sets and relations
1259 __isl_give isl_basic_set *isl_basic_set_empty(
1260 __isl_take isl_space *space);
1261 __isl_give isl_basic_map *isl_basic_map_empty(
1262 __isl_take isl_space *space);
1263 __isl_give isl_set *isl_set_empty(
1264 __isl_take isl_space *space);
1265 __isl_give isl_map *isl_map_empty(
1266 __isl_take isl_space *space);
1267 __isl_give isl_union_set *isl_union_set_empty(
1268 __isl_take isl_space *space);
1269 __isl_give isl_union_map *isl_union_map_empty(
1270 __isl_take isl_space *space);
1272 For C<isl_union_set>s and C<isl_union_map>s, the space
1273 is only used to specify the parameters.
1275 =item * Universe sets and relations
1277 __isl_give isl_basic_set *isl_basic_set_universe(
1278 __isl_take isl_space *space);
1279 __isl_give isl_basic_map *isl_basic_map_universe(
1280 __isl_take isl_space *space);
1281 __isl_give isl_set *isl_set_universe(
1282 __isl_take isl_space *space);
1283 __isl_give isl_map *isl_map_universe(
1284 __isl_take isl_space *space);
1285 __isl_give isl_union_set *isl_union_set_universe(
1286 __isl_take isl_union_set *uset);
1287 __isl_give isl_union_map *isl_union_map_universe(
1288 __isl_take isl_union_map *umap);
1290 The sets and relations constructed by the functions above
1291 contain all integer values, while those constructed by the
1292 functions below only contain non-negative values.
1294 __isl_give isl_basic_set *isl_basic_set_nat_universe(
1295 __isl_take isl_space *space);
1296 __isl_give isl_basic_map *isl_basic_map_nat_universe(
1297 __isl_take isl_space *space);
1298 __isl_give isl_set *isl_set_nat_universe(
1299 __isl_take isl_space *space);
1300 __isl_give isl_map *isl_map_nat_universe(
1301 __isl_take isl_space *space);
1303 =item * Identity relations
1305 __isl_give isl_basic_map *isl_basic_map_identity(
1306 __isl_take isl_space *space);
1307 __isl_give isl_map *isl_map_identity(
1308 __isl_take isl_space *space);
1310 The number of input and output dimensions in C<space> needs
1313 =item * Lexicographic order
1315 __isl_give isl_map *isl_map_lex_lt(
1316 __isl_take isl_space *set_space);
1317 __isl_give isl_map *isl_map_lex_le(
1318 __isl_take isl_space *set_space);
1319 __isl_give isl_map *isl_map_lex_gt(
1320 __isl_take isl_space *set_space);
1321 __isl_give isl_map *isl_map_lex_ge(
1322 __isl_take isl_space *set_space);
1323 __isl_give isl_map *isl_map_lex_lt_first(
1324 __isl_take isl_space *space, unsigned n);
1325 __isl_give isl_map *isl_map_lex_le_first(
1326 __isl_take isl_space *space, unsigned n);
1327 __isl_give isl_map *isl_map_lex_gt_first(
1328 __isl_take isl_space *space, unsigned n);
1329 __isl_give isl_map *isl_map_lex_ge_first(
1330 __isl_take isl_space *space, unsigned n);
1332 The first four functions take a space for a B<set>
1333 and return relations that express that the elements in the domain
1334 are lexicographically less
1335 (C<isl_map_lex_lt>), less or equal (C<isl_map_lex_le>),
1336 greater (C<isl_map_lex_gt>) or greater or equal (C<isl_map_lex_ge>)
1337 than the elements in the range.
1338 The last four functions take a space for a map
1339 and return relations that express that the first C<n> dimensions
1340 in the domain are lexicographically less
1341 (C<isl_map_lex_lt_first>), less or equal (C<isl_map_lex_le_first>),
1342 greater (C<isl_map_lex_gt_first>) or greater or equal (C<isl_map_lex_ge_first>)
1343 than the first C<n> dimensions in the range.
1347 A basic set or relation can be converted to a set or relation
1348 using the following functions.
1350 __isl_give isl_set *isl_set_from_basic_set(
1351 __isl_take isl_basic_set *bset);
1352 __isl_give isl_map *isl_map_from_basic_map(
1353 __isl_take isl_basic_map *bmap);
1355 Sets and relations can be converted to union sets and relations
1356 using the following functions.
1358 __isl_give isl_union_set *isl_union_set_from_basic_set(
1359 __isl_take isl_basic_set *bset);
1360 __isl_give isl_union_map *isl_union_map_from_basic_map(
1361 __isl_take isl_basic_map *bmap);
1362 __isl_give isl_union_set *isl_union_set_from_set(
1363 __isl_take isl_set *set);
1364 __isl_give isl_union_map *isl_union_map_from_map(
1365 __isl_take isl_map *map);
1367 The inverse conversions below can only be used if the input
1368 union set or relation is known to contain elements in exactly one
1371 __isl_give isl_set *isl_set_from_union_set(
1372 __isl_take isl_union_set *uset);
1373 __isl_give isl_map *isl_map_from_union_map(
1374 __isl_take isl_union_map *umap);
1376 A zero-dimensional (basic) set can be constructed on a given parameter domain
1377 using the following function.
1379 __isl_give isl_basic_set *isl_basic_set_from_params(
1380 __isl_take isl_basic_set *bset);
1381 __isl_give isl_set *isl_set_from_params(
1382 __isl_take isl_set *set);
1384 Sets and relations can be copied and freed again using the following
1387 __isl_give isl_basic_set *isl_basic_set_copy(
1388 __isl_keep isl_basic_set *bset);
1389 __isl_give isl_set *isl_set_copy(__isl_keep isl_set *set);
1390 __isl_give isl_union_set *isl_union_set_copy(
1391 __isl_keep isl_union_set *uset);
1392 __isl_give isl_basic_map *isl_basic_map_copy(
1393 __isl_keep isl_basic_map *bmap);
1394 __isl_give isl_map *isl_map_copy(__isl_keep isl_map *map);
1395 __isl_give isl_union_map *isl_union_map_copy(
1396 __isl_keep isl_union_map *umap);
1397 void *isl_basic_set_free(__isl_take isl_basic_set *bset);
1398 void *isl_set_free(__isl_take isl_set *set);
1399 void *isl_union_set_free(__isl_take isl_union_set *uset);
1400 void *isl_basic_map_free(__isl_take isl_basic_map *bmap);
1401 void *isl_map_free(__isl_take isl_map *map);
1402 void *isl_union_map_free(__isl_take isl_union_map *umap);
1404 Other sets and relations can be constructed by starting
1405 from a universe set or relation, adding equality and/or
1406 inequality constraints and then projecting out the
1407 existentially quantified variables, if any.
1408 Constraints can be constructed, manipulated and
1409 added to (or removed from) (basic) sets and relations
1410 using the following functions.
1412 #include <isl/constraint.h>
1413 __isl_give isl_constraint *isl_equality_alloc(
1414 __isl_take isl_local_space *ls);
1415 __isl_give isl_constraint *isl_inequality_alloc(
1416 __isl_take isl_local_space *ls);
1417 __isl_give isl_constraint *isl_constraint_set_constant_si(
1418 __isl_take isl_constraint *constraint, int v);
1419 __isl_give isl_constraint *isl_constraint_set_constant_val(
1420 __isl_take isl_constraint *constraint,
1421 __isl_take isl_val *v);
1422 __isl_give isl_constraint *isl_constraint_set_coefficient_si(
1423 __isl_take isl_constraint *constraint,
1424 enum isl_dim_type type, int pos, int v);
1425 __isl_give isl_constraint *
1426 isl_constraint_set_coefficient_val(
1427 __isl_take isl_constraint *constraint,
1428 enum isl_dim_type type, int pos, isl_val *v);
1429 __isl_give isl_basic_map *isl_basic_map_add_constraint(
1430 __isl_take isl_basic_map *bmap,
1431 __isl_take isl_constraint *constraint);
1432 __isl_give isl_basic_set *isl_basic_set_add_constraint(
1433 __isl_take isl_basic_set *bset,
1434 __isl_take isl_constraint *constraint);
1435 __isl_give isl_map *isl_map_add_constraint(
1436 __isl_take isl_map *map,
1437 __isl_take isl_constraint *constraint);
1438 __isl_give isl_set *isl_set_add_constraint(
1439 __isl_take isl_set *set,
1440 __isl_take isl_constraint *constraint);
1441 __isl_give isl_basic_set *isl_basic_set_drop_constraint(
1442 __isl_take isl_basic_set *bset,
1443 __isl_take isl_constraint *constraint);
1445 For example, to create a set containing the even integers
1446 between 10 and 42, you would use the following code.
1449 isl_local_space *ls;
1451 isl_basic_set *bset;
1453 space = isl_space_set_alloc(ctx, 0, 2);
1454 bset = isl_basic_set_universe(isl_space_copy(space));
1455 ls = isl_local_space_from_space(space);
1457 c = isl_equality_alloc(isl_local_space_copy(ls));
1458 c = isl_constraint_set_coefficient_si(c, isl_dim_set, 0, -1);
1459 c = isl_constraint_set_coefficient_si(c, isl_dim_set, 1, 2);
1460 bset = isl_basic_set_add_constraint(bset, c);
1462 c = isl_inequality_alloc(isl_local_space_copy(ls));
1463 c = isl_constraint_set_constant_si(c, -10);
1464 c = isl_constraint_set_coefficient_si(c, isl_dim_set, 0, 1);
1465 bset = isl_basic_set_add_constraint(bset, c);
1467 c = isl_inequality_alloc(ls);
1468 c = isl_constraint_set_constant_si(c, 42);
1469 c = isl_constraint_set_coefficient_si(c, isl_dim_set, 0, -1);
1470 bset = isl_basic_set_add_constraint(bset, c);
1472 bset = isl_basic_set_project_out(bset, isl_dim_set, 1, 1);
1476 isl_basic_set *bset;
1477 bset = isl_basic_set_read_from_str(ctx,
1478 "{[i] : exists (a : i = 2a and i >= 10 and i <= 42)}");
1480 A basic set or relation can also be constructed from two matrices
1481 describing the equalities and the inequalities.
1483 __isl_give isl_basic_set *isl_basic_set_from_constraint_matrices(
1484 __isl_take isl_space *space,
1485 __isl_take isl_mat *eq, __isl_take isl_mat *ineq,
1486 enum isl_dim_type c1,
1487 enum isl_dim_type c2, enum isl_dim_type c3,
1488 enum isl_dim_type c4);
1489 __isl_give isl_basic_map *isl_basic_map_from_constraint_matrices(
1490 __isl_take isl_space *space,
1491 __isl_take isl_mat *eq, __isl_take isl_mat *ineq,
1492 enum isl_dim_type c1,
1493 enum isl_dim_type c2, enum isl_dim_type c3,
1494 enum isl_dim_type c4, enum isl_dim_type c5);
1496 The C<isl_dim_type> arguments indicate the order in which
1497 different kinds of variables appear in the input matrices
1498 and should be a permutation of C<isl_dim_cst>, C<isl_dim_param>,
1499 C<isl_dim_set> and C<isl_dim_div> for sets and
1500 of C<isl_dim_cst>, C<isl_dim_param>,
1501 C<isl_dim_in>, C<isl_dim_out> and C<isl_dim_div> for relations.
1503 A (basic or union) set or relation can also be constructed from a
1504 (union) (piecewise) (multiple) affine expression
1505 or a list of affine expressions
1506 (See L<"Piecewise Quasi Affine Expressions"> and
1507 L<"Piecewise Multiple Quasi Affine Expressions">).
1509 __isl_give isl_basic_map *isl_basic_map_from_aff(
1510 __isl_take isl_aff *aff);
1511 __isl_give isl_map *isl_map_from_aff(
1512 __isl_take isl_aff *aff);
1513 __isl_give isl_set *isl_set_from_pw_aff(
1514 __isl_take isl_pw_aff *pwaff);
1515 __isl_give isl_map *isl_map_from_pw_aff(
1516 __isl_take isl_pw_aff *pwaff);
1517 __isl_give isl_basic_map *isl_basic_map_from_aff_list(
1518 __isl_take isl_space *domain_space,
1519 __isl_take isl_aff_list *list);
1520 __isl_give isl_basic_map *isl_basic_map_from_multi_aff(
1521 __isl_take isl_multi_aff *maff)
1522 __isl_give isl_map *isl_map_from_multi_aff(
1523 __isl_take isl_multi_aff *maff)
1524 __isl_give isl_set *isl_set_from_pw_multi_aff(
1525 __isl_take isl_pw_multi_aff *pma);
1526 __isl_give isl_map *isl_map_from_pw_multi_aff(
1527 __isl_take isl_pw_multi_aff *pma);
1528 __isl_give isl_union_map *
1529 isl_union_map_from_union_pw_multi_aff(
1530 __isl_take isl_union_pw_multi_aff *upma);
1532 The C<domain_dim> argument describes the domain of the resulting
1533 basic relation. It is required because the C<list> may consist
1534 of zero affine expressions.
1536 =head2 Inspecting Sets and Relations
1538 Usually, the user should not have to care about the actual constraints
1539 of the sets and maps, but should instead apply the abstract operations
1540 explained in the following sections.
1541 Occasionally, however, it may be required to inspect the individual
1542 coefficients of the constraints. This section explains how to do so.
1543 In these cases, it may also be useful to have C<isl> compute
1544 an explicit representation of the existentially quantified variables.
1546 __isl_give isl_set *isl_set_compute_divs(
1547 __isl_take isl_set *set);
1548 __isl_give isl_map *isl_map_compute_divs(
1549 __isl_take isl_map *map);
1550 __isl_give isl_union_set *isl_union_set_compute_divs(
1551 __isl_take isl_union_set *uset);
1552 __isl_give isl_union_map *isl_union_map_compute_divs(
1553 __isl_take isl_union_map *umap);
1555 This explicit representation defines the existentially quantified
1556 variables as integer divisions of the other variables, possibly
1557 including earlier existentially quantified variables.
1558 An explicitly represented existentially quantified variable therefore
1559 has a unique value when the values of the other variables are known.
1560 If, furthermore, the same existentials, i.e., existentials
1561 with the same explicit representations, should appear in the
1562 same order in each of the disjuncts of a set or map, then the user should call
1563 either of the following functions.
1565 __isl_give isl_set *isl_set_align_divs(
1566 __isl_take isl_set *set);
1567 __isl_give isl_map *isl_map_align_divs(
1568 __isl_take isl_map *map);
1570 Alternatively, the existentially quantified variables can be removed
1571 using the following functions, which compute an overapproximation.
1573 __isl_give isl_basic_set *isl_basic_set_remove_divs(
1574 __isl_take isl_basic_set *bset);
1575 __isl_give isl_basic_map *isl_basic_map_remove_divs(
1576 __isl_take isl_basic_map *bmap);
1577 __isl_give isl_set *isl_set_remove_divs(
1578 __isl_take isl_set *set);
1579 __isl_give isl_map *isl_map_remove_divs(
1580 __isl_take isl_map *map);
1582 It is also possible to only remove those divs that are defined
1583 in terms of a given range of dimensions or only those for which
1584 no explicit representation is known.
1586 __isl_give isl_basic_set *
1587 isl_basic_set_remove_divs_involving_dims(
1588 __isl_take isl_basic_set *bset,
1589 enum isl_dim_type type,
1590 unsigned first, unsigned n);
1591 __isl_give isl_basic_map *
1592 isl_basic_map_remove_divs_involving_dims(
1593 __isl_take isl_basic_map *bmap,
1594 enum isl_dim_type type,
1595 unsigned first, unsigned n);
1596 __isl_give isl_set *isl_set_remove_divs_involving_dims(
1597 __isl_take isl_set *set, enum isl_dim_type type,
1598 unsigned first, unsigned n);
1599 __isl_give isl_map *isl_map_remove_divs_involving_dims(
1600 __isl_take isl_map *map, enum isl_dim_type type,
1601 unsigned first, unsigned n);
1603 __isl_give isl_basic_set *
1604 isl_basic_set_remove_unknown_divs(
1605 __isl_take isl_basic_set *bset);
1606 __isl_give isl_set *isl_set_remove_unknown_divs(
1607 __isl_take isl_set *set);
1608 __isl_give isl_map *isl_map_remove_unknown_divs(
1609 __isl_take isl_map *map);
1611 To iterate over all the sets or maps in a union set or map, use
1613 int isl_union_set_foreach_set(__isl_keep isl_union_set *uset,
1614 int (*fn)(__isl_take isl_set *set, void *user),
1616 int isl_union_map_foreach_map(__isl_keep isl_union_map *umap,
1617 int (*fn)(__isl_take isl_map *map, void *user),
1620 The number of sets or maps in a union set or map can be obtained
1623 int isl_union_set_n_set(__isl_keep isl_union_set *uset);
1624 int isl_union_map_n_map(__isl_keep isl_union_map *umap);
1626 To extract the set or map in a given space from a union, use
1628 __isl_give isl_set *isl_union_set_extract_set(
1629 __isl_keep isl_union_set *uset,
1630 __isl_take isl_space *space);
1631 __isl_give isl_map *isl_union_map_extract_map(
1632 __isl_keep isl_union_map *umap,
1633 __isl_take isl_space *space);
1635 To iterate over all the basic sets or maps in a set or map, use
1637 int isl_set_foreach_basic_set(__isl_keep isl_set *set,
1638 int (*fn)(__isl_take isl_basic_set *bset, void *user),
1640 int isl_map_foreach_basic_map(__isl_keep isl_map *map,
1641 int (*fn)(__isl_take isl_basic_map *bmap, void *user),
1644 The callback function C<fn> should return 0 if successful and
1645 -1 if an error occurs. In the latter case, or if any other error
1646 occurs, the above functions will return -1.
1648 It should be noted that C<isl> does not guarantee that
1649 the basic sets or maps passed to C<fn> are disjoint.
1650 If this is required, then the user should call one of
1651 the following functions first.
1653 __isl_give isl_set *isl_set_make_disjoint(
1654 __isl_take isl_set *set);
1655 __isl_give isl_map *isl_map_make_disjoint(
1656 __isl_take isl_map *map);
1658 The number of basic sets in a set can be obtained
1661 int isl_set_n_basic_set(__isl_keep isl_set *set);
1663 To iterate over the constraints of a basic set or map, use
1665 #include <isl/constraint.h>
1667 int isl_basic_set_n_constraint(
1668 __isl_keep isl_basic_set *bset);
1669 int isl_basic_set_foreach_constraint(
1670 __isl_keep isl_basic_set *bset,
1671 int (*fn)(__isl_take isl_constraint *c, void *user),
1673 int isl_basic_map_foreach_constraint(
1674 __isl_keep isl_basic_map *bmap,
1675 int (*fn)(__isl_take isl_constraint *c, void *user),
1677 void *isl_constraint_free(__isl_take isl_constraint *c);
1679 Again, the callback function C<fn> should return 0 if successful and
1680 -1 if an error occurs. In the latter case, or if any other error
1681 occurs, the above functions will return -1.
1682 The constraint C<c> represents either an equality or an inequality.
1683 Use the following function to find out whether a constraint
1684 represents an equality. If not, it represents an inequality.
1686 int isl_constraint_is_equality(
1687 __isl_keep isl_constraint *constraint);
1689 The coefficients of the constraints can be inspected using
1690 the following functions.
1692 int isl_constraint_is_lower_bound(
1693 __isl_keep isl_constraint *constraint,
1694 enum isl_dim_type type, unsigned pos);
1695 int isl_constraint_is_upper_bound(
1696 __isl_keep isl_constraint *constraint,
1697 enum isl_dim_type type, unsigned pos);
1698 __isl_give isl_val *isl_constraint_get_constant_val(
1699 __isl_keep isl_constraint *constraint);
1700 __isl_give isl_val *isl_constraint_get_coefficient_val(
1701 __isl_keep isl_constraint *constraint,
1702 enum isl_dim_type type, int pos);
1703 int isl_constraint_involves_dims(
1704 __isl_keep isl_constraint *constraint,
1705 enum isl_dim_type type, unsigned first, unsigned n);
1707 The explicit representations of the existentially quantified
1708 variables can be inspected using the following function.
1709 Note that the user is only allowed to use this function
1710 if the inspected set or map is the result of a call
1711 to C<isl_set_compute_divs> or C<isl_map_compute_divs>.
1712 The existentially quantified variable is equal to the floor
1713 of the returned affine expression. The affine expression
1714 itself can be inspected using the functions in
1715 L<"Piecewise Quasi Affine Expressions">.
1717 __isl_give isl_aff *isl_constraint_get_div(
1718 __isl_keep isl_constraint *constraint, int pos);
1720 To obtain the constraints of a basic set or map in matrix
1721 form, use the following functions.
1723 __isl_give isl_mat *isl_basic_set_equalities_matrix(
1724 __isl_keep isl_basic_set *bset,
1725 enum isl_dim_type c1, enum isl_dim_type c2,
1726 enum isl_dim_type c3, enum isl_dim_type c4);
1727 __isl_give isl_mat *isl_basic_set_inequalities_matrix(
1728 __isl_keep isl_basic_set *bset,
1729 enum isl_dim_type c1, enum isl_dim_type c2,
1730 enum isl_dim_type c3, enum isl_dim_type c4);
1731 __isl_give isl_mat *isl_basic_map_equalities_matrix(
1732 __isl_keep isl_basic_map *bmap,
1733 enum isl_dim_type c1,
1734 enum isl_dim_type c2, enum isl_dim_type c3,
1735 enum isl_dim_type c4, enum isl_dim_type c5);
1736 __isl_give isl_mat *isl_basic_map_inequalities_matrix(
1737 __isl_keep isl_basic_map *bmap,
1738 enum isl_dim_type c1,
1739 enum isl_dim_type c2, enum isl_dim_type c3,
1740 enum isl_dim_type c4, enum isl_dim_type c5);
1742 The C<isl_dim_type> arguments dictate the order in which
1743 different kinds of variables appear in the resulting matrix
1744 and should be a permutation of C<isl_dim_cst>, C<isl_dim_param>,
1745 C<isl_dim_in>, C<isl_dim_out> and C<isl_dim_div>.
1747 The number of parameters, input, output or set dimensions can
1748 be obtained using the following functions.
1750 unsigned isl_basic_set_dim(__isl_keep isl_basic_set *bset,
1751 enum isl_dim_type type);
1752 unsigned isl_basic_map_dim(__isl_keep isl_basic_map *bmap,
1753 enum isl_dim_type type);
1754 unsigned isl_set_dim(__isl_keep isl_set *set,
1755 enum isl_dim_type type);
1756 unsigned isl_map_dim(__isl_keep isl_map *map,
1757 enum isl_dim_type type);
1759 To check whether the description of a set or relation depends
1760 on one or more given dimensions, it is not necessary to iterate over all
1761 constraints. Instead the following functions can be used.
1763 int isl_basic_set_involves_dims(
1764 __isl_keep isl_basic_set *bset,
1765 enum isl_dim_type type, unsigned first, unsigned n);
1766 int isl_set_involves_dims(__isl_keep isl_set *set,
1767 enum isl_dim_type type, unsigned first, unsigned n);
1768 int isl_basic_map_involves_dims(
1769 __isl_keep isl_basic_map *bmap,
1770 enum isl_dim_type type, unsigned first, unsigned n);
1771 int isl_map_involves_dims(__isl_keep isl_map *map,
1772 enum isl_dim_type type, unsigned first, unsigned n);
1774 Similarly, the following functions can be used to check whether
1775 a given dimension is involved in any lower or upper bound.
1777 int isl_set_dim_has_any_lower_bound(__isl_keep isl_set *set,
1778 enum isl_dim_type type, unsigned pos);
1779 int isl_set_dim_has_any_upper_bound(__isl_keep isl_set *set,
1780 enum isl_dim_type type, unsigned pos);
1782 Note that these functions return true even if there is a bound on
1783 the dimension on only some of the basic sets of C<set>.
1784 To check if they have a bound for all of the basic sets in C<set>,
1785 use the following functions instead.
1787 int isl_set_dim_has_lower_bound(__isl_keep isl_set *set,
1788 enum isl_dim_type type, unsigned pos);
1789 int isl_set_dim_has_upper_bound(__isl_keep isl_set *set,
1790 enum isl_dim_type type, unsigned pos);
1792 The identifiers or names of the domain and range spaces of a set
1793 or relation can be read off or set using the following functions.
1795 __isl_give isl_set *isl_set_set_tuple_id(
1796 __isl_take isl_set *set, __isl_take isl_id *id);
1797 __isl_give isl_set *isl_set_reset_tuple_id(
1798 __isl_take isl_set *set);
1799 int isl_set_has_tuple_id(__isl_keep isl_set *set);
1800 __isl_give isl_id *isl_set_get_tuple_id(
1801 __isl_keep isl_set *set);
1802 __isl_give isl_map *isl_map_set_tuple_id(
1803 __isl_take isl_map *map, enum isl_dim_type type,
1804 __isl_take isl_id *id);
1805 __isl_give isl_map *isl_map_reset_tuple_id(
1806 __isl_take isl_map *map, enum isl_dim_type type);
1807 int isl_map_has_tuple_id(__isl_keep isl_map *map,
1808 enum isl_dim_type type);
1809 __isl_give isl_id *isl_map_get_tuple_id(
1810 __isl_keep isl_map *map, enum isl_dim_type type);
1812 const char *isl_basic_set_get_tuple_name(
1813 __isl_keep isl_basic_set *bset);
1814 __isl_give isl_basic_set *isl_basic_set_set_tuple_name(
1815 __isl_take isl_basic_set *set, const char *s);
1816 int isl_set_has_tuple_name(__isl_keep isl_set *set);
1817 const char *isl_set_get_tuple_name(
1818 __isl_keep isl_set *set);
1819 const char *isl_basic_map_get_tuple_name(
1820 __isl_keep isl_basic_map *bmap,
1821 enum isl_dim_type type);
1822 __isl_give isl_basic_map *isl_basic_map_set_tuple_name(
1823 __isl_take isl_basic_map *bmap,
1824 enum isl_dim_type type, const char *s);
1825 int isl_map_has_tuple_name(__isl_keep isl_map *map,
1826 enum isl_dim_type type);
1827 const char *isl_map_get_tuple_name(
1828 __isl_keep isl_map *map,
1829 enum isl_dim_type type);
1831 As with C<isl_space_get_tuple_name>, the value returned points to
1832 an internal data structure.
1833 The identifiers, positions or names of individual dimensions can be
1834 read off using the following functions.
1836 __isl_give isl_id *isl_basic_set_get_dim_id(
1837 __isl_keep isl_basic_set *bset,
1838 enum isl_dim_type type, unsigned pos);
1839 __isl_give isl_set *isl_set_set_dim_id(
1840 __isl_take isl_set *set, enum isl_dim_type type,
1841 unsigned pos, __isl_take isl_id *id);
1842 int isl_set_has_dim_id(__isl_keep isl_set *set,
1843 enum isl_dim_type type, unsigned pos);
1844 __isl_give isl_id *isl_set_get_dim_id(
1845 __isl_keep isl_set *set, enum isl_dim_type type,
1847 int isl_basic_map_has_dim_id(
1848 __isl_keep isl_basic_map *bmap,
1849 enum isl_dim_type type, unsigned pos);
1850 __isl_give isl_map *isl_map_set_dim_id(
1851 __isl_take isl_map *map, enum isl_dim_type type,
1852 unsigned pos, __isl_take isl_id *id);
1853 int isl_map_has_dim_id(__isl_keep isl_map *map,
1854 enum isl_dim_type type, unsigned pos);
1855 __isl_give isl_id *isl_map_get_dim_id(
1856 __isl_keep isl_map *map, enum isl_dim_type type,
1859 int isl_set_find_dim_by_id(__isl_keep isl_set *set,
1860 enum isl_dim_type type, __isl_keep isl_id *id);
1861 int isl_map_find_dim_by_id(__isl_keep isl_map *map,
1862 enum isl_dim_type type, __isl_keep isl_id *id);
1863 int isl_set_find_dim_by_name(__isl_keep isl_set *set,
1864 enum isl_dim_type type, const char *name);
1865 int isl_map_find_dim_by_name(__isl_keep isl_map *map,
1866 enum isl_dim_type type, const char *name);
1868 const char *isl_constraint_get_dim_name(
1869 __isl_keep isl_constraint *constraint,
1870 enum isl_dim_type type, unsigned pos);
1871 const char *isl_basic_set_get_dim_name(
1872 __isl_keep isl_basic_set *bset,
1873 enum isl_dim_type type, unsigned pos);
1874 int isl_set_has_dim_name(__isl_keep isl_set *set,
1875 enum isl_dim_type type, unsigned pos);
1876 const char *isl_set_get_dim_name(
1877 __isl_keep isl_set *set,
1878 enum isl_dim_type type, unsigned pos);
1879 const char *isl_basic_map_get_dim_name(
1880 __isl_keep isl_basic_map *bmap,
1881 enum isl_dim_type type, unsigned pos);
1882 int isl_map_has_dim_name(__isl_keep isl_map *map,
1883 enum isl_dim_type type, unsigned pos);
1884 const char *isl_map_get_dim_name(
1885 __isl_keep isl_map *map,
1886 enum isl_dim_type type, unsigned pos);
1888 These functions are mostly useful to obtain the identifiers, positions
1889 or names of the parameters. Identifiers of individual dimensions are
1890 essentially only useful for printing. They are ignored by all other
1891 operations and may not be preserved across those operations.
1895 =head3 Unary Properties
1901 The following functions test whether the given set or relation
1902 contains any integer points. The ``plain'' variants do not perform
1903 any computations, but simply check if the given set or relation
1904 is already known to be empty.
1906 int isl_basic_set_plain_is_empty(__isl_keep isl_basic_set *bset);
1907 int isl_basic_set_is_empty(__isl_keep isl_basic_set *bset);
1908 int isl_set_plain_is_empty(__isl_keep isl_set *set);
1909 int isl_set_is_empty(__isl_keep isl_set *set);
1910 int isl_union_set_is_empty(__isl_keep isl_union_set *uset);
1911 int isl_basic_map_plain_is_empty(__isl_keep isl_basic_map *bmap);
1912 int isl_basic_map_is_empty(__isl_keep isl_basic_map *bmap);
1913 int isl_map_plain_is_empty(__isl_keep isl_map *map);
1914 int isl_map_is_empty(__isl_keep isl_map *map);
1915 int isl_union_map_is_empty(__isl_keep isl_union_map *umap);
1917 =item * Universality
1919 int isl_basic_set_is_universe(__isl_keep isl_basic_set *bset);
1920 int isl_basic_map_is_universe(__isl_keep isl_basic_map *bmap);
1921 int isl_set_plain_is_universe(__isl_keep isl_set *set);
1923 =item * Single-valuedness
1925 int isl_basic_map_is_single_valued(
1926 __isl_keep isl_basic_map *bmap);
1927 int isl_map_plain_is_single_valued(
1928 __isl_keep isl_map *map);
1929 int isl_map_is_single_valued(__isl_keep isl_map *map);
1930 int isl_union_map_is_single_valued(__isl_keep isl_union_map *umap);
1934 int isl_map_plain_is_injective(__isl_keep isl_map *map);
1935 int isl_map_is_injective(__isl_keep isl_map *map);
1936 int isl_union_map_plain_is_injective(
1937 __isl_keep isl_union_map *umap);
1938 int isl_union_map_is_injective(
1939 __isl_keep isl_union_map *umap);
1943 int isl_map_is_bijective(__isl_keep isl_map *map);
1944 int isl_union_map_is_bijective(__isl_keep isl_union_map *umap);
1948 __isl_give isl_val *
1949 isl_basic_map_plain_get_val_if_fixed(
1950 __isl_keep isl_basic_map *bmap,
1951 enum isl_dim_type type, unsigned pos);
1952 __isl_give isl_val *isl_set_plain_get_val_if_fixed(
1953 __isl_keep isl_set *set,
1954 enum isl_dim_type type, unsigned pos);
1955 __isl_give isl_val *isl_map_plain_get_val_if_fixed(
1956 __isl_keep isl_map *map,
1957 enum isl_dim_type type, unsigned pos);
1959 If the set or relation obviously lies on a hyperplane where the given dimension
1960 has a fixed value, then return that value.
1961 Otherwise return NaN.
1965 int isl_set_dim_residue_class_val(
1966 __isl_keep isl_set *set,
1967 int pos, __isl_give isl_val **modulo,
1968 __isl_give isl_val **residue);
1970 Check if the values of the given set dimension are equal to a fixed
1971 value modulo some integer value. If so, assign the modulo to C<*modulo>
1972 and the fixed value to C<*residue>. If the given dimension attains only
1973 a single value, then assign C<0> to C<*modulo> and the fixed value to
1975 If the dimension does not attain only a single value and if no modulo
1976 can be found then assign C<1> to C<*modulo> and C<1> to C<*residue>.
1980 To check whether a set is a parameter domain, use this function:
1982 int isl_set_is_params(__isl_keep isl_set *set);
1983 int isl_union_set_is_params(
1984 __isl_keep isl_union_set *uset);
1988 The following functions check whether the domain of the given
1989 (basic) set is a wrapped relation.
1991 int isl_basic_set_is_wrapping(
1992 __isl_keep isl_basic_set *bset);
1993 int isl_set_is_wrapping(__isl_keep isl_set *set);
1995 =item * Internal Product
1997 int isl_basic_map_can_zip(
1998 __isl_keep isl_basic_map *bmap);
1999 int isl_map_can_zip(__isl_keep isl_map *map);
2001 Check whether the product of domain and range of the given relation
2003 i.e., whether both domain and range are nested relations.
2007 int isl_basic_map_can_curry(
2008 __isl_keep isl_basic_map *bmap);
2009 int isl_map_can_curry(__isl_keep isl_map *map);
2011 Check whether the domain of the (basic) relation is a wrapped relation.
2013 int isl_basic_map_can_uncurry(
2014 __isl_keep isl_basic_map *bmap);
2015 int isl_map_can_uncurry(__isl_keep isl_map *map);
2017 Check whether the range of the (basic) relation is a wrapped relation.
2021 =head3 Binary Properties
2027 int isl_set_plain_is_equal(__isl_keep isl_set *set1,
2028 __isl_keep isl_set *set2);
2029 int isl_set_is_equal(__isl_keep isl_set *set1,
2030 __isl_keep isl_set *set2);
2031 int isl_union_set_is_equal(
2032 __isl_keep isl_union_set *uset1,
2033 __isl_keep isl_union_set *uset2);
2034 int isl_basic_map_is_equal(
2035 __isl_keep isl_basic_map *bmap1,
2036 __isl_keep isl_basic_map *bmap2);
2037 int isl_map_is_equal(__isl_keep isl_map *map1,
2038 __isl_keep isl_map *map2);
2039 int isl_map_plain_is_equal(__isl_keep isl_map *map1,
2040 __isl_keep isl_map *map2);
2041 int isl_union_map_is_equal(
2042 __isl_keep isl_union_map *umap1,
2043 __isl_keep isl_union_map *umap2);
2045 =item * Disjointness
2047 int isl_set_plain_is_disjoint(__isl_keep isl_set *set1,
2048 __isl_keep isl_set *set2);
2049 int isl_set_is_disjoint(__isl_keep isl_set *set1,
2050 __isl_keep isl_set *set2);
2051 int isl_map_is_disjoint(__isl_keep isl_map *map1,
2052 __isl_keep isl_map *map2);
2056 int isl_basic_set_is_subset(
2057 __isl_keep isl_basic_set *bset1,
2058 __isl_keep isl_basic_set *bset2);
2059 int isl_set_is_subset(__isl_keep isl_set *set1,
2060 __isl_keep isl_set *set2);
2061 int isl_set_is_strict_subset(
2062 __isl_keep isl_set *set1,
2063 __isl_keep isl_set *set2);
2064 int isl_union_set_is_subset(
2065 __isl_keep isl_union_set *uset1,
2066 __isl_keep isl_union_set *uset2);
2067 int isl_union_set_is_strict_subset(
2068 __isl_keep isl_union_set *uset1,
2069 __isl_keep isl_union_set *uset2);
2070 int isl_basic_map_is_subset(
2071 __isl_keep isl_basic_map *bmap1,
2072 __isl_keep isl_basic_map *bmap2);
2073 int isl_basic_map_is_strict_subset(
2074 __isl_keep isl_basic_map *bmap1,
2075 __isl_keep isl_basic_map *bmap2);
2076 int isl_map_is_subset(
2077 __isl_keep isl_map *map1,
2078 __isl_keep isl_map *map2);
2079 int isl_map_is_strict_subset(
2080 __isl_keep isl_map *map1,
2081 __isl_keep isl_map *map2);
2082 int isl_union_map_is_subset(
2083 __isl_keep isl_union_map *umap1,
2084 __isl_keep isl_union_map *umap2);
2085 int isl_union_map_is_strict_subset(
2086 __isl_keep isl_union_map *umap1,
2087 __isl_keep isl_union_map *umap2);
2089 Check whether the first argument is a (strict) subset of the
2094 int isl_set_plain_cmp(__isl_keep isl_set *set1,
2095 __isl_keep isl_set *set2);
2097 This function is useful for sorting C<isl_set>s.
2098 The order depends on the internal representation of the inputs.
2099 The order is fixed over different calls to the function (assuming
2100 the internal representation of the inputs has not changed), but may
2101 change over different versions of C<isl>.
2105 =head2 Unary Operations
2111 __isl_give isl_set *isl_set_complement(
2112 __isl_take isl_set *set);
2113 __isl_give isl_map *isl_map_complement(
2114 __isl_take isl_map *map);
2118 __isl_give isl_basic_map *isl_basic_map_reverse(
2119 __isl_take isl_basic_map *bmap);
2120 __isl_give isl_map *isl_map_reverse(
2121 __isl_take isl_map *map);
2122 __isl_give isl_union_map *isl_union_map_reverse(
2123 __isl_take isl_union_map *umap);
2127 __isl_give isl_basic_set *isl_basic_set_project_out(
2128 __isl_take isl_basic_set *bset,
2129 enum isl_dim_type type, unsigned first, unsigned n);
2130 __isl_give isl_basic_map *isl_basic_map_project_out(
2131 __isl_take isl_basic_map *bmap,
2132 enum isl_dim_type type, unsigned first, unsigned n);
2133 __isl_give isl_set *isl_set_project_out(__isl_take isl_set *set,
2134 enum isl_dim_type type, unsigned first, unsigned n);
2135 __isl_give isl_map *isl_map_project_out(__isl_take isl_map *map,
2136 enum isl_dim_type type, unsigned first, unsigned n);
2137 __isl_give isl_basic_set *isl_basic_set_params(
2138 __isl_take isl_basic_set *bset);
2139 __isl_give isl_basic_set *isl_basic_map_domain(
2140 __isl_take isl_basic_map *bmap);
2141 __isl_give isl_basic_set *isl_basic_map_range(
2142 __isl_take isl_basic_map *bmap);
2143 __isl_give isl_set *isl_set_params(__isl_take isl_set *set);
2144 __isl_give isl_set *isl_map_params(__isl_take isl_map *map);
2145 __isl_give isl_set *isl_map_domain(
2146 __isl_take isl_map *bmap);
2147 __isl_give isl_set *isl_map_range(
2148 __isl_take isl_map *map);
2149 __isl_give isl_set *isl_union_set_params(
2150 __isl_take isl_union_set *uset);
2151 __isl_give isl_set *isl_union_map_params(
2152 __isl_take isl_union_map *umap);
2153 __isl_give isl_union_set *isl_union_map_domain(
2154 __isl_take isl_union_map *umap);
2155 __isl_give isl_union_set *isl_union_map_range(
2156 __isl_take isl_union_map *umap);
2158 __isl_give isl_basic_map *isl_basic_map_domain_map(
2159 __isl_take isl_basic_map *bmap);
2160 __isl_give isl_basic_map *isl_basic_map_range_map(
2161 __isl_take isl_basic_map *bmap);
2162 __isl_give isl_map *isl_map_domain_map(__isl_take isl_map *map);
2163 __isl_give isl_map *isl_map_range_map(__isl_take isl_map *map);
2164 __isl_give isl_union_map *isl_union_map_domain_map(
2165 __isl_take isl_union_map *umap);
2166 __isl_give isl_union_map *isl_union_map_range_map(
2167 __isl_take isl_union_map *umap);
2169 The functions above construct a (basic, regular or union) relation
2170 that maps (a wrapped version of) the input relation to its domain or range.
2174 __isl_give isl_basic_set *isl_basic_set_eliminate(
2175 __isl_take isl_basic_set *bset,
2176 enum isl_dim_type type,
2177 unsigned first, unsigned n);
2178 __isl_give isl_set *isl_set_eliminate(
2179 __isl_take isl_set *set, enum isl_dim_type type,
2180 unsigned first, unsigned n);
2181 __isl_give isl_basic_map *isl_basic_map_eliminate(
2182 __isl_take isl_basic_map *bmap,
2183 enum isl_dim_type type,
2184 unsigned first, unsigned n);
2185 __isl_give isl_map *isl_map_eliminate(
2186 __isl_take isl_map *map, enum isl_dim_type type,
2187 unsigned first, unsigned n);
2189 Eliminate the coefficients for the given dimensions from the constraints,
2190 without removing the dimensions.
2194 __isl_give isl_basic_set *isl_basic_set_fix_si(
2195 __isl_take isl_basic_set *bset,
2196 enum isl_dim_type type, unsigned pos, int value);
2197 __isl_give isl_basic_set *isl_basic_set_fix_val(
2198 __isl_take isl_basic_set *bset,
2199 enum isl_dim_type type, unsigned pos,
2200 __isl_take isl_val *v);
2201 __isl_give isl_set *isl_set_fix_si(__isl_take isl_set *set,
2202 enum isl_dim_type type, unsigned pos, int value);
2203 __isl_give isl_set *isl_set_fix_val(
2204 __isl_take isl_set *set,
2205 enum isl_dim_type type, unsigned pos,
2206 __isl_take isl_val *v);
2207 __isl_give isl_basic_map *isl_basic_map_fix_si(
2208 __isl_take isl_basic_map *bmap,
2209 enum isl_dim_type type, unsigned pos, int value);
2210 __isl_give isl_basic_map *isl_basic_map_fix_val(
2211 __isl_take isl_basic_map *bmap,
2212 enum isl_dim_type type, unsigned pos,
2213 __isl_take isl_val *v);
2214 __isl_give isl_map *isl_map_fix_si(__isl_take isl_map *map,
2215 enum isl_dim_type type, unsigned pos, int value);
2216 __isl_give isl_map *isl_map_fix_val(
2217 __isl_take isl_map *map,
2218 enum isl_dim_type type, unsigned pos,
2219 __isl_take isl_val *v);
2221 Intersect the set or relation with the hyperplane where the given
2222 dimension has the fixed given value.
2224 __isl_give isl_basic_map *isl_basic_map_lower_bound_si(
2225 __isl_take isl_basic_map *bmap,
2226 enum isl_dim_type type, unsigned pos, int value);
2227 __isl_give isl_basic_map *isl_basic_map_upper_bound_si(
2228 __isl_take isl_basic_map *bmap,
2229 enum isl_dim_type type, unsigned pos, int value);
2230 __isl_give isl_set *isl_set_lower_bound_si(
2231 __isl_take isl_set *set,
2232 enum isl_dim_type type, unsigned pos, int value);
2233 __isl_give isl_set *isl_set_lower_bound_val(
2234 __isl_take isl_set *set,
2235 enum isl_dim_type type, unsigned pos,
2236 __isl_take isl_val *value);
2237 __isl_give isl_map *isl_map_lower_bound_si(
2238 __isl_take isl_map *map,
2239 enum isl_dim_type type, unsigned pos, int value);
2240 __isl_give isl_set *isl_set_upper_bound_si(
2241 __isl_take isl_set *set,
2242 enum isl_dim_type type, unsigned pos, int value);
2243 __isl_give isl_set *isl_set_upper_bound_val(
2244 __isl_take isl_set *set,
2245 enum isl_dim_type type, unsigned pos,
2246 __isl_take isl_val *value);
2247 __isl_give isl_map *isl_map_upper_bound_si(
2248 __isl_take isl_map *map,
2249 enum isl_dim_type type, unsigned pos, int value);
2251 Intersect the set or relation with the half-space where the given
2252 dimension has a value bounded by the fixed given integer value.
2254 __isl_give isl_set *isl_set_equate(__isl_take isl_set *set,
2255 enum isl_dim_type type1, int pos1,
2256 enum isl_dim_type type2, int pos2);
2257 __isl_give isl_basic_map *isl_basic_map_equate(
2258 __isl_take isl_basic_map *bmap,
2259 enum isl_dim_type type1, int pos1,
2260 enum isl_dim_type type2, int pos2);
2261 __isl_give isl_map *isl_map_equate(__isl_take isl_map *map,
2262 enum isl_dim_type type1, int pos1,
2263 enum isl_dim_type type2, int pos2);
2265 Intersect the set or relation with the hyperplane where the given
2266 dimensions are equal to each other.
2268 __isl_give isl_map *isl_map_oppose(__isl_take isl_map *map,
2269 enum isl_dim_type type1, int pos1,
2270 enum isl_dim_type type2, int pos2);
2272 Intersect the relation with the hyperplane where the given
2273 dimensions have opposite values.
2275 __isl_give isl_basic_map *isl_basic_map_order_ge(
2276 __isl_take isl_basic_map *bmap,
2277 enum isl_dim_type type1, int pos1,
2278 enum isl_dim_type type2, int pos2);
2279 __isl_give isl_map *isl_map_order_lt(__isl_take isl_map *map,
2280 enum isl_dim_type type1, int pos1,
2281 enum isl_dim_type type2, int pos2);
2282 __isl_give isl_basic_map *isl_basic_map_order_gt(
2283 __isl_take isl_basic_map *bmap,
2284 enum isl_dim_type type1, int pos1,
2285 enum isl_dim_type type2, int pos2);
2286 __isl_give isl_map *isl_map_order_gt(__isl_take isl_map *map,
2287 enum isl_dim_type type1, int pos1,
2288 enum isl_dim_type type2, int pos2);
2290 Intersect the relation with the half-space where the given
2291 dimensions satisfy the given ordering.
2295 __isl_give isl_map *isl_set_identity(
2296 __isl_take isl_set *set);
2297 __isl_give isl_union_map *isl_union_set_identity(
2298 __isl_take isl_union_set *uset);
2300 Construct an identity relation on the given (union) set.
2304 __isl_give isl_basic_set *isl_basic_map_deltas(
2305 __isl_take isl_basic_map *bmap);
2306 __isl_give isl_set *isl_map_deltas(__isl_take isl_map *map);
2307 __isl_give isl_union_set *isl_union_map_deltas(
2308 __isl_take isl_union_map *umap);
2310 These functions return a (basic) set containing the differences
2311 between image elements and corresponding domain elements in the input.
2313 __isl_give isl_basic_map *isl_basic_map_deltas_map(
2314 __isl_take isl_basic_map *bmap);
2315 __isl_give isl_map *isl_map_deltas_map(
2316 __isl_take isl_map *map);
2317 __isl_give isl_union_map *isl_union_map_deltas_map(
2318 __isl_take isl_union_map *umap);
2320 The functions above construct a (basic, regular or union) relation
2321 that maps (a wrapped version of) the input relation to its delta set.
2325 Simplify the representation of a set or relation by trying
2326 to combine pairs of basic sets or relations into a single
2327 basic set or relation.
2329 __isl_give isl_set *isl_set_coalesce(__isl_take isl_set *set);
2330 __isl_give isl_map *isl_map_coalesce(__isl_take isl_map *map);
2331 __isl_give isl_union_set *isl_union_set_coalesce(
2332 __isl_take isl_union_set *uset);
2333 __isl_give isl_union_map *isl_union_map_coalesce(
2334 __isl_take isl_union_map *umap);
2336 One of the methods for combining pairs of basic sets or relations
2337 can result in coefficients that are much larger than those that appear
2338 in the constraints of the input. By default, the coefficients are
2339 not allowed to grow larger, but this can be changed by unsetting
2340 the following option.
2342 int isl_options_set_coalesce_bounded_wrapping(
2343 isl_ctx *ctx, int val);
2344 int isl_options_get_coalesce_bounded_wrapping(
2347 =item * Detecting equalities
2349 __isl_give isl_basic_set *isl_basic_set_detect_equalities(
2350 __isl_take isl_basic_set *bset);
2351 __isl_give isl_basic_map *isl_basic_map_detect_equalities(
2352 __isl_take isl_basic_map *bmap);
2353 __isl_give isl_set *isl_set_detect_equalities(
2354 __isl_take isl_set *set);
2355 __isl_give isl_map *isl_map_detect_equalities(
2356 __isl_take isl_map *map);
2357 __isl_give isl_union_set *isl_union_set_detect_equalities(
2358 __isl_take isl_union_set *uset);
2359 __isl_give isl_union_map *isl_union_map_detect_equalities(
2360 __isl_take isl_union_map *umap);
2362 Simplify the representation of a set or relation by detecting implicit
2365 =item * Removing redundant constraints
2367 __isl_give isl_basic_set *isl_basic_set_remove_redundancies(
2368 __isl_take isl_basic_set *bset);
2369 __isl_give isl_set *isl_set_remove_redundancies(
2370 __isl_take isl_set *set);
2371 __isl_give isl_basic_map *isl_basic_map_remove_redundancies(
2372 __isl_take isl_basic_map *bmap);
2373 __isl_give isl_map *isl_map_remove_redundancies(
2374 __isl_take isl_map *map);
2378 __isl_give isl_basic_set *isl_set_convex_hull(
2379 __isl_take isl_set *set);
2380 __isl_give isl_basic_map *isl_map_convex_hull(
2381 __isl_take isl_map *map);
2383 If the input set or relation has any existentially quantified
2384 variables, then the result of these operations is currently undefined.
2388 __isl_give isl_basic_set *
2389 isl_set_unshifted_simple_hull(
2390 __isl_take isl_set *set);
2391 __isl_give isl_basic_map *
2392 isl_map_unshifted_simple_hull(
2393 __isl_take isl_map *map);
2394 __isl_give isl_basic_set *isl_set_simple_hull(
2395 __isl_take isl_set *set);
2396 __isl_give isl_basic_map *isl_map_simple_hull(
2397 __isl_take isl_map *map);
2398 __isl_give isl_union_map *isl_union_map_simple_hull(
2399 __isl_take isl_union_map *umap);
2401 These functions compute a single basic set or relation
2402 that contains the whole input set or relation.
2403 In particular, the output is described by translates
2404 of the constraints describing the basic sets or relations in the input.
2405 In case of C<isl_set_unshifted_simple_hull>, only the original
2406 constraints are used, without any translation.
2410 (See \autoref{s:simple hull}.)
2416 __isl_give isl_basic_set *isl_basic_set_affine_hull(
2417 __isl_take isl_basic_set *bset);
2418 __isl_give isl_basic_set *isl_set_affine_hull(
2419 __isl_take isl_set *set);
2420 __isl_give isl_union_set *isl_union_set_affine_hull(
2421 __isl_take isl_union_set *uset);
2422 __isl_give isl_basic_map *isl_basic_map_affine_hull(
2423 __isl_take isl_basic_map *bmap);
2424 __isl_give isl_basic_map *isl_map_affine_hull(
2425 __isl_take isl_map *map);
2426 __isl_give isl_union_map *isl_union_map_affine_hull(
2427 __isl_take isl_union_map *umap);
2429 In case of union sets and relations, the affine hull is computed
2432 =item * Polyhedral hull
2434 __isl_give isl_basic_set *isl_set_polyhedral_hull(
2435 __isl_take isl_set *set);
2436 __isl_give isl_basic_map *isl_map_polyhedral_hull(
2437 __isl_take isl_map *map);
2438 __isl_give isl_union_set *isl_union_set_polyhedral_hull(
2439 __isl_take isl_union_set *uset);
2440 __isl_give isl_union_map *isl_union_map_polyhedral_hull(
2441 __isl_take isl_union_map *umap);
2443 These functions compute a single basic set or relation
2444 not involving any existentially quantified variables
2445 that contains the whole input set or relation.
2446 In case of union sets and relations, the polyhedral hull is computed
2449 =item * Other approximations
2451 __isl_give isl_basic_set *
2452 isl_basic_set_drop_constraints_involving_dims(
2453 __isl_take isl_basic_set *bset,
2454 enum isl_dim_type type,
2455 unsigned first, unsigned n);
2456 __isl_give isl_basic_map *
2457 isl_basic_map_drop_constraints_involving_dims(
2458 __isl_take isl_basic_map *bmap,
2459 enum isl_dim_type type,
2460 unsigned first, unsigned n);
2461 __isl_give isl_basic_set *
2462 isl_basic_set_drop_constraints_not_involving_dims(
2463 __isl_take isl_basic_set *bset,
2464 enum isl_dim_type type,
2465 unsigned first, unsigned n);
2466 __isl_give isl_set *
2467 isl_set_drop_constraints_involving_dims(
2468 __isl_take isl_set *set,
2469 enum isl_dim_type type,
2470 unsigned first, unsigned n);
2471 __isl_give isl_map *
2472 isl_map_drop_constraints_involving_dims(
2473 __isl_take isl_map *map,
2474 enum isl_dim_type type,
2475 unsigned first, unsigned n);
2477 These functions drop any constraints (not) involving the specified dimensions.
2478 Note that the result depends on the representation of the input.
2482 __isl_give isl_basic_set *isl_basic_set_sample(
2483 __isl_take isl_basic_set *bset);
2484 __isl_give isl_basic_set *isl_set_sample(
2485 __isl_take isl_set *set);
2486 __isl_give isl_basic_map *isl_basic_map_sample(
2487 __isl_take isl_basic_map *bmap);
2488 __isl_give isl_basic_map *isl_map_sample(
2489 __isl_take isl_map *map);
2491 If the input (basic) set or relation is non-empty, then return
2492 a singleton subset of the input. Otherwise, return an empty set.
2494 =item * Optimization
2496 #include <isl/ilp.h>
2497 __isl_give isl_val *isl_basic_set_max_val(
2498 __isl_keep isl_basic_set *bset,
2499 __isl_keep isl_aff *obj);
2500 __isl_give isl_val *isl_set_min_val(
2501 __isl_keep isl_set *set,
2502 __isl_keep isl_aff *obj);
2503 __isl_give isl_val *isl_set_max_val(
2504 __isl_keep isl_set *set,
2505 __isl_keep isl_aff *obj);
2507 Compute the minimum or maximum of the integer affine expression C<obj>
2508 over the points in C<set>, returning the result in C<opt>.
2509 The result is C<NULL> in case of an error, the optimal value in case
2510 there is one, negative infinity or infinity if the problem is unbounded and
2511 NaN if the problem is empty.
2513 =item * Parametric optimization
2515 __isl_give isl_pw_aff *isl_set_dim_min(
2516 __isl_take isl_set *set, int pos);
2517 __isl_give isl_pw_aff *isl_set_dim_max(
2518 __isl_take isl_set *set, int pos);
2519 __isl_give isl_pw_aff *isl_map_dim_max(
2520 __isl_take isl_map *map, int pos);
2522 Compute the minimum or maximum of the given set or output dimension
2523 as a function of the parameters (and input dimensions), but independently
2524 of the other set or output dimensions.
2525 For lexicographic optimization, see L<"Lexicographic Optimization">.
2529 The following functions compute either the set of (rational) coefficient
2530 values of valid constraints for the given set or the set of (rational)
2531 values satisfying the constraints with coefficients from the given set.
2532 Internally, these two sets of functions perform essentially the
2533 same operations, except that the set of coefficients is assumed to
2534 be a cone, while the set of values may be any polyhedron.
2535 The current implementation is based on the Farkas lemma and
2536 Fourier-Motzkin elimination, but this may change or be made optional
2537 in future. In particular, future implementations may use different
2538 dualization algorithms or skip the elimination step.
2540 __isl_give isl_basic_set *isl_basic_set_coefficients(
2541 __isl_take isl_basic_set *bset);
2542 __isl_give isl_basic_set *isl_set_coefficients(
2543 __isl_take isl_set *set);
2544 __isl_give isl_union_set *isl_union_set_coefficients(
2545 __isl_take isl_union_set *bset);
2546 __isl_give isl_basic_set *isl_basic_set_solutions(
2547 __isl_take isl_basic_set *bset);
2548 __isl_give isl_basic_set *isl_set_solutions(
2549 __isl_take isl_set *set);
2550 __isl_give isl_union_set *isl_union_set_solutions(
2551 __isl_take isl_union_set *bset);
2555 __isl_give isl_map *isl_map_fixed_power_val(
2556 __isl_take isl_map *map,
2557 __isl_take isl_val *exp);
2558 __isl_give isl_union_map *
2559 isl_union_map_fixed_power_val(
2560 __isl_take isl_union_map *umap,
2561 __isl_take isl_val *exp);
2563 Compute the given power of C<map>, where C<exp> is assumed to be non-zero.
2564 If the exponent C<exp> is negative, then the -C<exp> th power of the inverse
2565 of C<map> is computed.
2567 __isl_give isl_map *isl_map_power(__isl_take isl_map *map,
2569 __isl_give isl_union_map *isl_union_map_power(
2570 __isl_take isl_union_map *umap, int *exact);
2572 Compute a parametric representation for all positive powers I<k> of C<map>.
2573 The result maps I<k> to a nested relation corresponding to the
2574 I<k>th power of C<map>.
2575 The result may be an overapproximation. If the result is known to be exact,
2576 then C<*exact> is set to C<1>.
2578 =item * Transitive closure
2580 __isl_give isl_map *isl_map_transitive_closure(
2581 __isl_take isl_map *map, int *exact);
2582 __isl_give isl_union_map *isl_union_map_transitive_closure(
2583 __isl_take isl_union_map *umap, int *exact);
2585 Compute the transitive closure of C<map>.
2586 The result may be an overapproximation. If the result is known to be exact,
2587 then C<*exact> is set to C<1>.
2589 =item * Reaching path lengths
2591 __isl_give isl_map *isl_map_reaching_path_lengths(
2592 __isl_take isl_map *map, int *exact);
2594 Compute a relation that maps each element in the range of C<map>
2595 to the lengths of all paths composed of edges in C<map> that
2596 end up in the given element.
2597 The result may be an overapproximation. If the result is known to be exact,
2598 then C<*exact> is set to C<1>.
2599 To compute the I<maximal> path length, the resulting relation
2600 should be postprocessed by C<isl_map_lexmax>.
2601 In particular, if the input relation is a dependence relation
2602 (mapping sources to sinks), then the maximal path length corresponds
2603 to the free schedule.
2604 Note, however, that C<isl_map_lexmax> expects the maximum to be
2605 finite, so if the path lengths are unbounded (possibly due to
2606 the overapproximation), then you will get an error message.
2610 __isl_give isl_basic_set *isl_basic_map_wrap(
2611 __isl_take isl_basic_map *bmap);
2612 __isl_give isl_set *isl_map_wrap(
2613 __isl_take isl_map *map);
2614 __isl_give isl_union_set *isl_union_map_wrap(
2615 __isl_take isl_union_map *umap);
2616 __isl_give isl_basic_map *isl_basic_set_unwrap(
2617 __isl_take isl_basic_set *bset);
2618 __isl_give isl_map *isl_set_unwrap(
2619 __isl_take isl_set *set);
2620 __isl_give isl_union_map *isl_union_set_unwrap(
2621 __isl_take isl_union_set *uset);
2625 Remove any internal structure of domain (and range) of the given
2626 set or relation. If there is any such internal structure in the input,
2627 then the name of the space is also removed.
2629 __isl_give isl_basic_set *isl_basic_set_flatten(
2630 __isl_take isl_basic_set *bset);
2631 __isl_give isl_set *isl_set_flatten(
2632 __isl_take isl_set *set);
2633 __isl_give isl_basic_map *isl_basic_map_flatten_domain(
2634 __isl_take isl_basic_map *bmap);
2635 __isl_give isl_basic_map *isl_basic_map_flatten_range(
2636 __isl_take isl_basic_map *bmap);
2637 __isl_give isl_map *isl_map_flatten_range(
2638 __isl_take isl_map *map);
2639 __isl_give isl_map *isl_map_flatten_domain(
2640 __isl_take isl_map *map);
2641 __isl_give isl_basic_map *isl_basic_map_flatten(
2642 __isl_take isl_basic_map *bmap);
2643 __isl_give isl_map *isl_map_flatten(
2644 __isl_take isl_map *map);
2646 __isl_give isl_map *isl_set_flatten_map(
2647 __isl_take isl_set *set);
2649 The function above constructs a relation
2650 that maps the input set to a flattened version of the set.
2654 Lift the input set to a space with extra dimensions corresponding
2655 to the existentially quantified variables in the input.
2656 In particular, the result lives in a wrapped map where the domain
2657 is the original space and the range corresponds to the original
2658 existentially quantified variables.
2660 __isl_give isl_basic_set *isl_basic_set_lift(
2661 __isl_take isl_basic_set *bset);
2662 __isl_give isl_set *isl_set_lift(
2663 __isl_take isl_set *set);
2664 __isl_give isl_union_set *isl_union_set_lift(
2665 __isl_take isl_union_set *uset);
2667 Given a local space that contains the existentially quantified
2668 variables of a set, a basic relation that, when applied to
2669 a basic set, has essentially the same effect as C<isl_basic_set_lift>,
2670 can be constructed using the following function.
2672 #include <isl/local_space.h>
2673 __isl_give isl_basic_map *isl_local_space_lifting(
2674 __isl_take isl_local_space *ls);
2676 =item * Internal Product
2678 __isl_give isl_basic_map *isl_basic_map_zip(
2679 __isl_take isl_basic_map *bmap);
2680 __isl_give isl_map *isl_map_zip(
2681 __isl_take isl_map *map);
2682 __isl_give isl_union_map *isl_union_map_zip(
2683 __isl_take isl_union_map *umap);
2685 Given a relation with nested relations for domain and range,
2686 interchange the range of the domain with the domain of the range.
2690 __isl_give isl_basic_map *isl_basic_map_curry(
2691 __isl_take isl_basic_map *bmap);
2692 __isl_give isl_basic_map *isl_basic_map_uncurry(
2693 __isl_take isl_basic_map *bmap);
2694 __isl_give isl_map *isl_map_curry(
2695 __isl_take isl_map *map);
2696 __isl_give isl_map *isl_map_uncurry(
2697 __isl_take isl_map *map);
2698 __isl_give isl_union_map *isl_union_map_curry(
2699 __isl_take isl_union_map *umap);
2700 __isl_give isl_union_map *isl_union_map_uncurry(
2701 __isl_take isl_union_map *umap);
2703 Given a relation with a nested relation for domain,
2704 the C<curry> functions
2705 move the range of the nested relation out of the domain
2706 and use it as the domain of a nested relation in the range,
2707 with the original range as range of this nested relation.
2708 The C<uncurry> functions perform the inverse operation.
2710 =item * Aligning parameters
2712 __isl_give isl_basic_set *isl_basic_set_align_params(
2713 __isl_take isl_basic_set *bset,
2714 __isl_take isl_space *model);
2715 __isl_give isl_set *isl_set_align_params(
2716 __isl_take isl_set *set,
2717 __isl_take isl_space *model);
2718 __isl_give isl_basic_map *isl_basic_map_align_params(
2719 __isl_take isl_basic_map *bmap,
2720 __isl_take isl_space *model);
2721 __isl_give isl_map *isl_map_align_params(
2722 __isl_take isl_map *map,
2723 __isl_take isl_space *model);
2725 Change the order of the parameters of the given set or relation
2726 such that the first parameters match those of C<model>.
2727 This may involve the introduction of extra parameters.
2728 All parameters need to be named.
2730 =item * Dimension manipulation
2732 __isl_give isl_basic_set *isl_basic_set_add_dims(
2733 __isl_take isl_basic_set *bset,
2734 enum isl_dim_type type, unsigned n);
2735 __isl_give isl_set *isl_set_add_dims(
2736 __isl_take isl_set *set,
2737 enum isl_dim_type type, unsigned n);
2738 __isl_give isl_map *isl_map_add_dims(
2739 __isl_take isl_map *map,
2740 enum isl_dim_type type, unsigned n);
2741 __isl_give isl_basic_set *isl_basic_set_insert_dims(
2742 __isl_take isl_basic_set *bset,
2743 enum isl_dim_type type, unsigned pos,
2745 __isl_give isl_basic_map *isl_basic_map_insert_dims(
2746 __isl_take isl_basic_map *bmap,
2747 enum isl_dim_type type, unsigned pos,
2749 __isl_give isl_set *isl_set_insert_dims(
2750 __isl_take isl_set *set,
2751 enum isl_dim_type type, unsigned pos, unsigned n);
2752 __isl_give isl_map *isl_map_insert_dims(
2753 __isl_take isl_map *map,
2754 enum isl_dim_type type, unsigned pos, unsigned n);
2755 __isl_give isl_basic_set *isl_basic_set_move_dims(
2756 __isl_take isl_basic_set *bset,
2757 enum isl_dim_type dst_type, unsigned dst_pos,
2758 enum isl_dim_type src_type, unsigned src_pos,
2760 __isl_give isl_basic_map *isl_basic_map_move_dims(
2761 __isl_take isl_basic_map *bmap,
2762 enum isl_dim_type dst_type, unsigned dst_pos,
2763 enum isl_dim_type src_type, unsigned src_pos,
2765 __isl_give isl_set *isl_set_move_dims(
2766 __isl_take isl_set *set,
2767 enum isl_dim_type dst_type, unsigned dst_pos,
2768 enum isl_dim_type src_type, unsigned src_pos,
2770 __isl_give isl_map *isl_map_move_dims(
2771 __isl_take isl_map *map,
2772 enum isl_dim_type dst_type, unsigned dst_pos,
2773 enum isl_dim_type src_type, unsigned src_pos,
2776 It is usually not advisable to directly change the (input or output)
2777 space of a set or a relation as this removes the name and the internal
2778 structure of the space. However, the above functions can be useful
2779 to add new parameters, assuming
2780 C<isl_set_align_params> and C<isl_map_align_params>
2785 =head2 Binary Operations
2787 The two arguments of a binary operation not only need to live
2788 in the same C<isl_ctx>, they currently also need to have
2789 the same (number of) parameters.
2791 =head3 Basic Operations
2795 =item * Intersection
2797 __isl_give isl_basic_set *isl_basic_set_intersect_params(
2798 __isl_take isl_basic_set *bset1,
2799 __isl_take isl_basic_set *bset2);
2800 __isl_give isl_basic_set *isl_basic_set_intersect(
2801 __isl_take isl_basic_set *bset1,
2802 __isl_take isl_basic_set *bset2);
2803 __isl_give isl_set *isl_set_intersect_params(
2804 __isl_take isl_set *set,
2805 __isl_take isl_set *params);
2806 __isl_give isl_set *isl_set_intersect(
2807 __isl_take isl_set *set1,
2808 __isl_take isl_set *set2);
2809 __isl_give isl_union_set *isl_union_set_intersect_params(
2810 __isl_take isl_union_set *uset,
2811 __isl_take isl_set *set);
2812 __isl_give isl_union_map *isl_union_map_intersect_params(
2813 __isl_take isl_union_map *umap,
2814 __isl_take isl_set *set);
2815 __isl_give isl_union_set *isl_union_set_intersect(
2816 __isl_take isl_union_set *uset1,
2817 __isl_take isl_union_set *uset2);
2818 __isl_give isl_basic_map *isl_basic_map_intersect_domain(
2819 __isl_take isl_basic_map *bmap,
2820 __isl_take isl_basic_set *bset);
2821 __isl_give isl_basic_map *isl_basic_map_intersect_range(
2822 __isl_take isl_basic_map *bmap,
2823 __isl_take isl_basic_set *bset);
2824 __isl_give isl_basic_map *isl_basic_map_intersect(
2825 __isl_take isl_basic_map *bmap1,
2826 __isl_take isl_basic_map *bmap2);
2827 __isl_give isl_map *isl_map_intersect_params(
2828 __isl_take isl_map *map,
2829 __isl_take isl_set *params);
2830 __isl_give isl_map *isl_map_intersect_domain(
2831 __isl_take isl_map *map,
2832 __isl_take isl_set *set);
2833 __isl_give isl_map *isl_map_intersect_range(
2834 __isl_take isl_map *map,
2835 __isl_take isl_set *set);
2836 __isl_give isl_map *isl_map_intersect(
2837 __isl_take isl_map *map1,
2838 __isl_take isl_map *map2);
2839 __isl_give isl_union_map *isl_union_map_intersect_domain(
2840 __isl_take isl_union_map *umap,
2841 __isl_take isl_union_set *uset);
2842 __isl_give isl_union_map *isl_union_map_intersect_range(
2843 __isl_take isl_union_map *umap,
2844 __isl_take isl_union_set *uset);
2845 __isl_give isl_union_map *isl_union_map_intersect(
2846 __isl_take isl_union_map *umap1,
2847 __isl_take isl_union_map *umap2);
2849 The second argument to the C<_params> functions needs to be
2850 a parametric (basic) set. For the other functions, a parametric set
2851 for either argument is only allowed if the other argument is
2852 a parametric set as well.
2856 __isl_give isl_set *isl_basic_set_union(
2857 __isl_take isl_basic_set *bset1,
2858 __isl_take isl_basic_set *bset2);
2859 __isl_give isl_map *isl_basic_map_union(
2860 __isl_take isl_basic_map *bmap1,
2861 __isl_take isl_basic_map *bmap2);
2862 __isl_give isl_set *isl_set_union(
2863 __isl_take isl_set *set1,
2864 __isl_take isl_set *set2);
2865 __isl_give isl_map *isl_map_union(
2866 __isl_take isl_map *map1,
2867 __isl_take isl_map *map2);
2868 __isl_give isl_union_set *isl_union_set_union(
2869 __isl_take isl_union_set *uset1,
2870 __isl_take isl_union_set *uset2);
2871 __isl_give isl_union_map *isl_union_map_union(
2872 __isl_take isl_union_map *umap1,
2873 __isl_take isl_union_map *umap2);
2875 =item * Set difference
2877 __isl_give isl_set *isl_set_subtract(
2878 __isl_take isl_set *set1,
2879 __isl_take isl_set *set2);
2880 __isl_give isl_map *isl_map_subtract(
2881 __isl_take isl_map *map1,
2882 __isl_take isl_map *map2);
2883 __isl_give isl_map *isl_map_subtract_domain(
2884 __isl_take isl_map *map,
2885 __isl_take isl_set *dom);
2886 __isl_give isl_map *isl_map_subtract_range(
2887 __isl_take isl_map *map,
2888 __isl_take isl_set *dom);
2889 __isl_give isl_union_set *isl_union_set_subtract(
2890 __isl_take isl_union_set *uset1,
2891 __isl_take isl_union_set *uset2);
2892 __isl_give isl_union_map *isl_union_map_subtract(
2893 __isl_take isl_union_map *umap1,
2894 __isl_take isl_union_map *umap2);
2895 __isl_give isl_union_map *isl_union_map_subtract_domain(
2896 __isl_take isl_union_map *umap,
2897 __isl_take isl_union_set *dom);
2898 __isl_give isl_union_map *isl_union_map_subtract_range(
2899 __isl_take isl_union_map *umap,
2900 __isl_take isl_union_set *dom);
2904 __isl_give isl_basic_set *isl_basic_set_apply(
2905 __isl_take isl_basic_set *bset,
2906 __isl_take isl_basic_map *bmap);
2907 __isl_give isl_set *isl_set_apply(
2908 __isl_take isl_set *set,
2909 __isl_take isl_map *map);
2910 __isl_give isl_union_set *isl_union_set_apply(
2911 __isl_take isl_union_set *uset,
2912 __isl_take isl_union_map *umap);
2913 __isl_give isl_basic_map *isl_basic_map_apply_domain(
2914 __isl_take isl_basic_map *bmap1,
2915 __isl_take isl_basic_map *bmap2);
2916 __isl_give isl_basic_map *isl_basic_map_apply_range(
2917 __isl_take isl_basic_map *bmap1,
2918 __isl_take isl_basic_map *bmap2);
2919 __isl_give isl_map *isl_map_apply_domain(
2920 __isl_take isl_map *map1,
2921 __isl_take isl_map *map2);
2922 __isl_give isl_union_map *isl_union_map_apply_domain(
2923 __isl_take isl_union_map *umap1,
2924 __isl_take isl_union_map *umap2);
2925 __isl_give isl_map *isl_map_apply_range(
2926 __isl_take isl_map *map1,
2927 __isl_take isl_map *map2);
2928 __isl_give isl_union_map *isl_union_map_apply_range(
2929 __isl_take isl_union_map *umap1,
2930 __isl_take isl_union_map *umap2);
2934 __isl_give isl_basic_set *
2935 isl_basic_set_preimage_multi_aff(
2936 __isl_take isl_basic_set *bset,
2937 __isl_take isl_multi_aff *ma);
2938 __isl_give isl_set *isl_set_preimage_multi_aff(
2939 __isl_take isl_set *set,
2940 __isl_take isl_multi_aff *ma);
2941 __isl_give isl_set *isl_set_preimage_pw_multi_aff(
2942 __isl_take isl_set *set,
2943 __isl_take isl_pw_multi_aff *pma);
2944 __isl_give isl_map *isl_map_preimage_domain_multi_aff(
2945 __isl_take isl_map *map,
2946 __isl_take isl_multi_aff *ma);
2947 __isl_give isl_union_map *
2948 isl_union_map_preimage_domain_multi_aff(
2949 __isl_take isl_union_map *umap,
2950 __isl_take isl_multi_aff *ma);
2952 These functions compute the preimage of the given set or map domain under
2953 the given function. In other words, the expression is plugged
2954 into the set description or into the domain of the map.
2955 Objects of types C<isl_multi_aff> and C<isl_pw_multi_aff> are described in
2956 L</"Piecewise Multiple Quasi Affine Expressions">.
2958 =item * Cartesian Product
2960 __isl_give isl_set *isl_set_product(
2961 __isl_take isl_set *set1,
2962 __isl_take isl_set *set2);
2963 __isl_give isl_union_set *isl_union_set_product(
2964 __isl_take isl_union_set *uset1,
2965 __isl_take isl_union_set *uset2);
2966 __isl_give isl_basic_map *isl_basic_map_domain_product(
2967 __isl_take isl_basic_map *bmap1,
2968 __isl_take isl_basic_map *bmap2);
2969 __isl_give isl_basic_map *isl_basic_map_range_product(
2970 __isl_take isl_basic_map *bmap1,
2971 __isl_take isl_basic_map *bmap2);
2972 __isl_give isl_basic_map *isl_basic_map_product(
2973 __isl_take isl_basic_map *bmap1,
2974 __isl_take isl_basic_map *bmap2);
2975 __isl_give isl_map *isl_map_domain_product(
2976 __isl_take isl_map *map1,
2977 __isl_take isl_map *map2);
2978 __isl_give isl_map *isl_map_range_product(
2979 __isl_take isl_map *map1,
2980 __isl_take isl_map *map2);
2981 __isl_give isl_union_map *isl_union_map_domain_product(
2982 __isl_take isl_union_map *umap1,
2983 __isl_take isl_union_map *umap2);
2984 __isl_give isl_union_map *isl_union_map_range_product(
2985 __isl_take isl_union_map *umap1,
2986 __isl_take isl_union_map *umap2);
2987 __isl_give isl_map *isl_map_product(
2988 __isl_take isl_map *map1,
2989 __isl_take isl_map *map2);
2990 __isl_give isl_union_map *isl_union_map_product(
2991 __isl_take isl_union_map *umap1,
2992 __isl_take isl_union_map *umap2);
2994 The above functions compute the cross product of the given
2995 sets or relations. The domains and ranges of the results
2996 are wrapped maps between domains and ranges of the inputs.
2997 To obtain a ``flat'' product, use the following functions
3000 __isl_give isl_basic_set *isl_basic_set_flat_product(
3001 __isl_take isl_basic_set *bset1,
3002 __isl_take isl_basic_set *bset2);
3003 __isl_give isl_set *isl_set_flat_product(
3004 __isl_take isl_set *set1,
3005 __isl_take isl_set *set2);
3006 __isl_give isl_basic_map *isl_basic_map_flat_range_product(
3007 __isl_take isl_basic_map *bmap1,
3008 __isl_take isl_basic_map *bmap2);
3009 __isl_give isl_map *isl_map_flat_domain_product(
3010 __isl_take isl_map *map1,
3011 __isl_take isl_map *map2);
3012 __isl_give isl_map *isl_map_flat_range_product(
3013 __isl_take isl_map *map1,
3014 __isl_take isl_map *map2);
3015 __isl_give isl_union_map *isl_union_map_flat_range_product(
3016 __isl_take isl_union_map *umap1,
3017 __isl_take isl_union_map *umap2);
3018 __isl_give isl_basic_map *isl_basic_map_flat_product(
3019 __isl_take isl_basic_map *bmap1,
3020 __isl_take isl_basic_map *bmap2);
3021 __isl_give isl_map *isl_map_flat_product(
3022 __isl_take isl_map *map1,
3023 __isl_take isl_map *map2);
3025 =item * Simplification
3027 __isl_give isl_basic_set *isl_basic_set_gist(
3028 __isl_take isl_basic_set *bset,
3029 __isl_take isl_basic_set *context);
3030 __isl_give isl_set *isl_set_gist(__isl_take isl_set *set,
3031 __isl_take isl_set *context);
3032 __isl_give isl_set *isl_set_gist_params(
3033 __isl_take isl_set *set,
3034 __isl_take isl_set *context);
3035 __isl_give isl_union_set *isl_union_set_gist(
3036 __isl_take isl_union_set *uset,
3037 __isl_take isl_union_set *context);
3038 __isl_give isl_union_set *isl_union_set_gist_params(
3039 __isl_take isl_union_set *uset,
3040 __isl_take isl_set *set);
3041 __isl_give isl_basic_map *isl_basic_map_gist(
3042 __isl_take isl_basic_map *bmap,
3043 __isl_take isl_basic_map *context);
3044 __isl_give isl_map *isl_map_gist(__isl_take isl_map *map,
3045 __isl_take isl_map *context);
3046 __isl_give isl_map *isl_map_gist_params(
3047 __isl_take isl_map *map,
3048 __isl_take isl_set *context);
3049 __isl_give isl_map *isl_map_gist_domain(
3050 __isl_take isl_map *map,
3051 __isl_take isl_set *context);
3052 __isl_give isl_map *isl_map_gist_range(
3053 __isl_take isl_map *map,
3054 __isl_take isl_set *context);
3055 __isl_give isl_union_map *isl_union_map_gist(
3056 __isl_take isl_union_map *umap,
3057 __isl_take isl_union_map *context);
3058 __isl_give isl_union_map *isl_union_map_gist_params(
3059 __isl_take isl_union_map *umap,
3060 __isl_take isl_set *set);
3061 __isl_give isl_union_map *isl_union_map_gist_domain(
3062 __isl_take isl_union_map *umap,
3063 __isl_take isl_union_set *uset);
3064 __isl_give isl_union_map *isl_union_map_gist_range(
3065 __isl_take isl_union_map *umap,
3066 __isl_take isl_union_set *uset);
3068 The gist operation returns a set or relation that has the
3069 same intersection with the context as the input set or relation.
3070 Any implicit equality in the intersection is made explicit in the result,
3071 while all inequalities that are redundant with respect to the intersection
3073 In case of union sets and relations, the gist operation is performed
3078 =head3 Lexicographic Optimization
3080 Given a (basic) set C<set> (or C<bset>) and a zero-dimensional domain C<dom>,
3081 the following functions
3082 compute a set that contains the lexicographic minimum or maximum
3083 of the elements in C<set> (or C<bset>) for those values of the parameters
3084 that satisfy C<dom>.
3085 If C<empty> is not C<NULL>, then C<*empty> is assigned a set
3086 that contains the parameter values in C<dom> for which C<set> (or C<bset>)
3088 In other words, the union of the parameter values
3089 for which the result is non-empty and of C<*empty>
3092 __isl_give isl_set *isl_basic_set_partial_lexmin(
3093 __isl_take isl_basic_set *bset,
3094 __isl_take isl_basic_set *dom,
3095 __isl_give isl_set **empty);
3096 __isl_give isl_set *isl_basic_set_partial_lexmax(
3097 __isl_take isl_basic_set *bset,
3098 __isl_take isl_basic_set *dom,
3099 __isl_give isl_set **empty);
3100 __isl_give isl_set *isl_set_partial_lexmin(
3101 __isl_take isl_set *set, __isl_take isl_set *dom,
3102 __isl_give isl_set **empty);
3103 __isl_give isl_set *isl_set_partial_lexmax(
3104 __isl_take isl_set *set, __isl_take isl_set *dom,
3105 __isl_give isl_set **empty);
3107 Given a (basic) set C<set> (or C<bset>), the following functions simply
3108 return a set containing the lexicographic minimum or maximum
3109 of the elements in C<set> (or C<bset>).
3110 In case of union sets, the optimum is computed per space.
3112 __isl_give isl_set *isl_basic_set_lexmin(
3113 __isl_take isl_basic_set *bset);
3114 __isl_give isl_set *isl_basic_set_lexmax(
3115 __isl_take isl_basic_set *bset);
3116 __isl_give isl_set *isl_set_lexmin(
3117 __isl_take isl_set *set);
3118 __isl_give isl_set *isl_set_lexmax(
3119 __isl_take isl_set *set);
3120 __isl_give isl_union_set *isl_union_set_lexmin(
3121 __isl_take isl_union_set *uset);
3122 __isl_give isl_union_set *isl_union_set_lexmax(
3123 __isl_take isl_union_set *uset);
3125 Given a (basic) relation C<map> (or C<bmap>) and a domain C<dom>,
3126 the following functions
3127 compute a relation that maps each element of C<dom>
3128 to the single lexicographic minimum or maximum
3129 of the elements that are associated to that same
3130 element in C<map> (or C<bmap>).
3131 If C<empty> is not C<NULL>, then C<*empty> is assigned a set
3132 that contains the elements in C<dom> that do not map
3133 to any elements in C<map> (or C<bmap>).
3134 In other words, the union of the domain of the result and of C<*empty>
3137 __isl_give isl_map *isl_basic_map_partial_lexmax(
3138 __isl_take isl_basic_map *bmap,
3139 __isl_take isl_basic_set *dom,
3140 __isl_give isl_set **empty);
3141 __isl_give isl_map *isl_basic_map_partial_lexmin(
3142 __isl_take isl_basic_map *bmap,
3143 __isl_take isl_basic_set *dom,
3144 __isl_give isl_set **empty);
3145 __isl_give isl_map *isl_map_partial_lexmax(
3146 __isl_take isl_map *map, __isl_take isl_set *dom,
3147 __isl_give isl_set **empty);
3148 __isl_give isl_map *isl_map_partial_lexmin(
3149 __isl_take isl_map *map, __isl_take isl_set *dom,
3150 __isl_give isl_set **empty);
3152 Given a (basic) map C<map> (or C<bmap>), the following functions simply
3153 return a map mapping each element in the domain of
3154 C<map> (or C<bmap>) to the lexicographic minimum or maximum
3155 of all elements associated to that element.
3156 In case of union relations, the optimum is computed per space.
3158 __isl_give isl_map *isl_basic_map_lexmin(
3159 __isl_take isl_basic_map *bmap);
3160 __isl_give isl_map *isl_basic_map_lexmax(
3161 __isl_take isl_basic_map *bmap);
3162 __isl_give isl_map *isl_map_lexmin(
3163 __isl_take isl_map *map);
3164 __isl_give isl_map *isl_map_lexmax(
3165 __isl_take isl_map *map);
3166 __isl_give isl_union_map *isl_union_map_lexmin(
3167 __isl_take isl_union_map *umap);
3168 __isl_give isl_union_map *isl_union_map_lexmax(
3169 __isl_take isl_union_map *umap);
3171 The following functions return their result in the form of
3172 a piecewise multi-affine expression
3173 (See L<"Piecewise Multiple Quasi Affine Expressions">),
3174 but are otherwise equivalent to the corresponding functions
3175 returning a basic set or relation.
3177 __isl_give isl_pw_multi_aff *
3178 isl_basic_map_lexmin_pw_multi_aff(
3179 __isl_take isl_basic_map *bmap);
3180 __isl_give isl_pw_multi_aff *
3181 isl_basic_set_partial_lexmin_pw_multi_aff(
3182 __isl_take isl_basic_set *bset,
3183 __isl_take isl_basic_set *dom,
3184 __isl_give isl_set **empty);
3185 __isl_give isl_pw_multi_aff *
3186 isl_basic_set_partial_lexmax_pw_multi_aff(
3187 __isl_take isl_basic_set *bset,
3188 __isl_take isl_basic_set *dom,
3189 __isl_give isl_set **empty);
3190 __isl_give isl_pw_multi_aff *
3191 isl_basic_map_partial_lexmin_pw_multi_aff(
3192 __isl_take isl_basic_map *bmap,
3193 __isl_take isl_basic_set *dom,
3194 __isl_give isl_set **empty);
3195 __isl_give isl_pw_multi_aff *
3196 isl_basic_map_partial_lexmax_pw_multi_aff(
3197 __isl_take isl_basic_map *bmap,
3198 __isl_take isl_basic_set *dom,
3199 __isl_give isl_set **empty);
3200 __isl_give isl_pw_multi_aff *isl_set_lexmin_pw_multi_aff(
3201 __isl_take isl_set *set);
3202 __isl_give isl_pw_multi_aff *isl_set_lexmax_pw_multi_aff(
3203 __isl_take isl_set *set);
3204 __isl_give isl_pw_multi_aff *isl_map_lexmin_pw_multi_aff(
3205 __isl_take isl_map *map);
3206 __isl_give isl_pw_multi_aff *isl_map_lexmax_pw_multi_aff(
3207 __isl_take isl_map *map);
3211 Lists are defined over several element types, including
3212 C<isl_val>, C<isl_id>, C<isl_aff>, C<isl_pw_aff>, C<isl_constraint>,
3213 C<isl_basic_set>, C<isl_set>, C<isl_ast_expr> and C<isl_ast_node>.
3214 Here we take lists of C<isl_set>s as an example.
3215 Lists can be created, copied, modified and freed using the following functions.
3217 #include <isl/list.h>
3218 __isl_give isl_set_list *isl_set_list_from_set(
3219 __isl_take isl_set *el);
3220 __isl_give isl_set_list *isl_set_list_alloc(
3221 isl_ctx *ctx, int n);
3222 __isl_give isl_set_list *isl_set_list_copy(
3223 __isl_keep isl_set_list *list);
3224 __isl_give isl_set_list *isl_set_list_insert(
3225 __isl_take isl_set_list *list, unsigned pos,
3226 __isl_take isl_set *el);
3227 __isl_give isl_set_list *isl_set_list_add(
3228 __isl_take isl_set_list *list,
3229 __isl_take isl_set *el);
3230 __isl_give isl_set_list *isl_set_list_drop(
3231 __isl_take isl_set_list *list,
3232 unsigned first, unsigned n);
3233 __isl_give isl_set_list *isl_set_list_set_set(
3234 __isl_take isl_set_list *list, int index,
3235 __isl_take isl_set *set);
3236 __isl_give isl_set_list *isl_set_list_concat(
3237 __isl_take isl_set_list *list1,
3238 __isl_take isl_set_list *list2);
3239 __isl_give isl_set_list *isl_set_list_sort(
3240 __isl_take isl_set_list *list,
3241 int (*cmp)(__isl_keep isl_set *a,
3242 __isl_keep isl_set *b, void *user),
3244 void *isl_set_list_free(__isl_take isl_set_list *list);
3246 C<isl_set_list_alloc> creates an empty list with a capacity for
3247 C<n> elements. C<isl_set_list_from_set> creates a list with a single
3250 Lists can be inspected using the following functions.
3252 #include <isl/list.h>
3253 isl_ctx *isl_set_list_get_ctx(__isl_keep isl_set_list *list);
3254 int isl_set_list_n_set(__isl_keep isl_set_list *list);
3255 __isl_give isl_set *isl_set_list_get_set(
3256 __isl_keep isl_set_list *list, int index);
3257 int isl_set_list_foreach(__isl_keep isl_set_list *list,
3258 int (*fn)(__isl_take isl_set *el, void *user),
3260 int isl_set_list_foreach_scc(__isl_keep isl_set_list *list,
3261 int (*follows)(__isl_keep isl_set *a,
3262 __isl_keep isl_set *b, void *user),
3264 int (*fn)(__isl_take isl_set *el, void *user),
3267 The function C<isl_set_list_foreach_scc> calls C<fn> on each of the
3268 strongly connected components of the graph with as vertices the elements
3269 of C<list> and a directed edge from vertex C<b> to vertex C<a>
3270 iff C<follows(a, b)> returns C<1>. The callbacks C<follows> and C<fn>
3271 should return C<-1> on error.
3273 Lists can be printed using
3275 #include <isl/list.h>
3276 __isl_give isl_printer *isl_printer_print_set_list(
3277 __isl_take isl_printer *p,
3278 __isl_keep isl_set_list *list);
3280 =head2 Multiple Values
3282 An C<isl_multi_val> object represents a sequence of zero or more values,
3283 living in a set space.
3285 An C<isl_multi_val> can be constructed from an C<isl_val_list>
3286 using the following function
3288 #include <isl/val.h>
3289 __isl_give isl_multi_val *isl_multi_val_from_val_list(
3290 __isl_take isl_space *space,
3291 __isl_take isl_val_list *list);
3293 The zero multiple value (with value zero for each set dimension)
3294 can be created using the following function.
3296 #include <isl/val.h>
3297 __isl_give isl_multi_val *isl_multi_val_zero(
3298 __isl_take isl_space *space);
3300 Multiple values can be copied and freed using
3302 #include <isl/val.h>
3303 __isl_give isl_multi_val *isl_multi_val_copy(
3304 __isl_keep isl_multi_val *mv);
3305 void *isl_multi_val_free(__isl_take isl_multi_val *mv);
3307 They can be inspected using
3309 #include <isl/val.h>
3310 isl_ctx *isl_multi_val_get_ctx(
3311 __isl_keep isl_multi_val *mv);
3312 unsigned isl_multi_val_dim(__isl_keep isl_multi_val *mv,
3313 enum isl_dim_type type);
3314 __isl_give isl_val *isl_multi_val_get_val(
3315 __isl_keep isl_multi_val *mv, int pos);
3316 const char *isl_multi_val_get_tuple_name(
3317 __isl_keep isl_multi_val *mv,
3318 enum isl_dim_type type);
3320 They can be modified using
3322 #include <isl/val.h>
3323 __isl_give isl_multi_val *isl_multi_val_set_val(
3324 __isl_take isl_multi_val *mv, int pos,
3325 __isl_take isl_val *val);
3326 __isl_give isl_multi_val *isl_multi_val_set_dim_name(
3327 __isl_take isl_multi_val *mv,
3328 enum isl_dim_type type, unsigned pos, const char *s);
3329 __isl_give isl_multi_val *isl_multi_val_set_tuple_name(
3330 __isl_take isl_multi_val *mv,
3331 enum isl_dim_type type, const char *s);
3332 __isl_give isl_multi_val *isl_multi_val_set_tuple_id(
3333 __isl_take isl_multi_val *mv,
3334 enum isl_dim_type type, __isl_take isl_id *id);
3336 __isl_give isl_multi_val *isl_multi_val_insert_dims(
3337 __isl_take isl_multi_val *mv,
3338 enum isl_dim_type type, unsigned first, unsigned n);
3339 __isl_give isl_multi_val *isl_multi_val_add_dims(
3340 __isl_take isl_multi_val *mv,
3341 enum isl_dim_type type, unsigned n);
3342 __isl_give isl_multi_val *isl_multi_val_drop_dims(
3343 __isl_take isl_multi_val *mv,
3344 enum isl_dim_type type, unsigned first, unsigned n);
3348 #include <isl/val.h>
3349 __isl_give isl_multi_val *isl_multi_val_align_params(
3350 __isl_take isl_multi_val *mv,
3351 __isl_take isl_space *model);
3352 __isl_give isl_multi_val *isl_multi_val_range_splice(
3353 __isl_take isl_multi_val *mv1, unsigned pos,
3354 __isl_take isl_multi_val *mv2);
3355 __isl_give isl_multi_val *isl_multi_val_range_product(
3356 __isl_take isl_multi_val *mv1,
3357 __isl_take isl_multi_val *mv2);
3358 __isl_give isl_multi_val *isl_multi_val_flat_range_product(
3359 __isl_take isl_multi_val *mv1,
3360 __isl_take isl_multi_aff *mv2);
3361 __isl_give isl_multi_val *isl_multi_val_add_val(
3362 __isl_take isl_multi_val *mv,
3363 __isl_take isl_val *v);
3364 __isl_give isl_multi_val *isl_multi_val_mod_val(
3365 __isl_take isl_multi_val *mv,
3366 __isl_take isl_val *v);
3367 __isl_give isl_multi_val *isl_multi_val_scale_val(
3368 __isl_take isl_multi_val *mv,
3369 __isl_take isl_val *v);
3370 __isl_give isl_multi_val *isl_multi_val_scale_multi_val(
3371 __isl_take isl_multi_val *mv1,
3372 __isl_take isl_multi_val *mv2);
3376 Vectors can be created, copied and freed using the following functions.
3378 #include <isl/vec.h>
3379 __isl_give isl_vec *isl_vec_alloc(isl_ctx *ctx,
3381 __isl_give isl_vec *isl_vec_copy(__isl_keep isl_vec *vec);
3382 void *isl_vec_free(__isl_take isl_vec *vec);
3384 Note that the elements of a newly created vector may have arbitrary values.
3385 The elements can be changed and inspected using the following functions.
3387 isl_ctx *isl_vec_get_ctx(__isl_keep isl_vec *vec);
3388 int isl_vec_size(__isl_keep isl_vec *vec);
3389 __isl_give isl_val *isl_vec_get_element_val(
3390 __isl_keep isl_vec *vec, int pos);
3391 __isl_give isl_vec *isl_vec_set_element_si(
3392 __isl_take isl_vec *vec, int pos, int v);
3393 __isl_give isl_vec *isl_vec_set_element_val(
3394 __isl_take isl_vec *vec, int pos,
3395 __isl_take isl_val *v);
3396 __isl_give isl_vec *isl_vec_set_si(__isl_take isl_vec *vec,
3398 __isl_give isl_vec *isl_vec_set_val(
3399 __isl_take isl_vec *vec, __isl_take isl_val *v);
3400 int isl_vec_cmp_element(__isl_keep isl_vec *vec1,
3401 __isl_keep isl_vec *vec2, int pos);
3403 C<isl_vec_get_element> will return a negative value if anything went wrong.
3404 In that case, the value of C<*v> is undefined.
3406 The following function can be used to concatenate two vectors.
3408 __isl_give isl_vec *isl_vec_concat(__isl_take isl_vec *vec1,
3409 __isl_take isl_vec *vec2);
3413 Matrices can be created, copied and freed using the following functions.
3415 #include <isl/mat.h>
3416 __isl_give isl_mat *isl_mat_alloc(isl_ctx *ctx,
3417 unsigned n_row, unsigned n_col);
3418 __isl_give isl_mat *isl_mat_copy(__isl_keep isl_mat *mat);
3419 void *isl_mat_free(__isl_take isl_mat *mat);
3421 Note that the elements of a newly created matrix may have arbitrary values.
3422 The elements can be changed and inspected using the following functions.
3424 isl_ctx *isl_mat_get_ctx(__isl_keep isl_mat *mat);
3425 int isl_mat_rows(__isl_keep isl_mat *mat);
3426 int isl_mat_cols(__isl_keep isl_mat *mat);
3427 __isl_give isl_val *isl_mat_get_element_val(
3428 __isl_keep isl_mat *mat, int row, int col);
3429 __isl_give isl_mat *isl_mat_set_element_si(__isl_take isl_mat *mat,
3430 int row, int col, int v);
3431 __isl_give isl_mat *isl_mat_set_element_val(
3432 __isl_take isl_mat *mat, int row, int col,
3433 __isl_take isl_val *v);
3435 C<isl_mat_get_element> will return a negative value if anything went wrong.
3436 In that case, the value of C<*v> is undefined.
3438 The following function can be used to compute the (right) inverse
3439 of a matrix, i.e., a matrix such that the product of the original
3440 and the inverse (in that order) is a multiple of the identity matrix.
3441 The input matrix is assumed to be of full row-rank.
3443 __isl_give isl_mat *isl_mat_right_inverse(__isl_take isl_mat *mat);
3445 The following function can be used to compute the (right) kernel
3446 (or null space) of a matrix, i.e., a matrix such that the product of
3447 the original and the kernel (in that order) is the zero matrix.
3449 __isl_give isl_mat *isl_mat_right_kernel(__isl_take isl_mat *mat);
3451 =head2 Piecewise Quasi Affine Expressions
3453 The zero quasi affine expression or the quasi affine expression
3454 that is equal to a specified dimension on a given domain can be created using
3456 __isl_give isl_aff *isl_aff_zero_on_domain(
3457 __isl_take isl_local_space *ls);
3458 __isl_give isl_pw_aff *isl_pw_aff_zero_on_domain(
3459 __isl_take isl_local_space *ls);
3460 __isl_give isl_aff *isl_aff_var_on_domain(
3461 __isl_take isl_local_space *ls,
3462 enum isl_dim_type type, unsigned pos);
3463 __isl_give isl_pw_aff *isl_pw_aff_var_on_domain(
3464 __isl_take isl_local_space *ls,
3465 enum isl_dim_type type, unsigned pos);
3467 Note that the space in which the resulting objects live is a map space
3468 with the given space as domain and a one-dimensional range.
3470 An empty piecewise quasi affine expression (one with no cells)
3471 or a piecewise quasi affine expression with a single cell can
3472 be created using the following functions.
3474 #include <isl/aff.h>
3475 __isl_give isl_pw_aff *isl_pw_aff_empty(
3476 __isl_take isl_space *space);
3477 __isl_give isl_pw_aff *isl_pw_aff_alloc(
3478 __isl_take isl_set *set, __isl_take isl_aff *aff);
3479 __isl_give isl_pw_aff *isl_pw_aff_from_aff(
3480 __isl_take isl_aff *aff);
3482 A piecewise quasi affine expression that is equal to 1 on a set
3483 and 0 outside the set can be created using the following function.
3485 #include <isl/aff.h>
3486 __isl_give isl_pw_aff *isl_set_indicator_function(
3487 __isl_take isl_set *set);
3489 Quasi affine expressions can be copied and freed using
3491 #include <isl/aff.h>
3492 __isl_give isl_aff *isl_aff_copy(__isl_keep isl_aff *aff);
3493 void *isl_aff_free(__isl_take isl_aff *aff);
3495 __isl_give isl_pw_aff *isl_pw_aff_copy(
3496 __isl_keep isl_pw_aff *pwaff);
3497 void *isl_pw_aff_free(__isl_take isl_pw_aff *pwaff);
3499 A (rational) bound on a dimension can be extracted from an C<isl_constraint>
3500 using the following function. The constraint is required to have
3501 a non-zero coefficient for the specified dimension.
3503 #include <isl/constraint.h>
3504 __isl_give isl_aff *isl_constraint_get_bound(
3505 __isl_keep isl_constraint *constraint,
3506 enum isl_dim_type type, int pos);
3508 The entire affine expression of the constraint can also be extracted
3509 using the following function.
3511 #include <isl/constraint.h>
3512 __isl_give isl_aff *isl_constraint_get_aff(
3513 __isl_keep isl_constraint *constraint);
3515 Conversely, an equality constraint equating
3516 the affine expression to zero or an inequality constraint enforcing
3517 the affine expression to be non-negative, can be constructed using
3519 __isl_give isl_constraint *isl_equality_from_aff(
3520 __isl_take isl_aff *aff);
3521 __isl_give isl_constraint *isl_inequality_from_aff(
3522 __isl_take isl_aff *aff);
3524 The expression can be inspected using
3526 #include <isl/aff.h>
3527 isl_ctx *isl_aff_get_ctx(__isl_keep isl_aff *aff);
3528 int isl_aff_dim(__isl_keep isl_aff *aff,
3529 enum isl_dim_type type);
3530 __isl_give isl_local_space *isl_aff_get_domain_local_space(
3531 __isl_keep isl_aff *aff);
3532 __isl_give isl_local_space *isl_aff_get_local_space(
3533 __isl_keep isl_aff *aff);
3534 const char *isl_aff_get_dim_name(__isl_keep isl_aff *aff,
3535 enum isl_dim_type type, unsigned pos);
3536 const char *isl_pw_aff_get_dim_name(
3537 __isl_keep isl_pw_aff *pa,
3538 enum isl_dim_type type, unsigned pos);
3539 int isl_pw_aff_has_dim_id(__isl_keep isl_pw_aff *pa,
3540 enum isl_dim_type type, unsigned pos);
3541 __isl_give isl_id *isl_pw_aff_get_dim_id(
3542 __isl_keep isl_pw_aff *pa,
3543 enum isl_dim_type type, unsigned pos);
3544 __isl_give isl_id *isl_pw_aff_get_tuple_id(
3545 __isl_keep isl_pw_aff *pa,
3546 enum isl_dim_type type);
3547 __isl_give isl_val *isl_aff_get_constant_val(
3548 __isl_keep isl_aff *aff);
3549 __isl_give isl_val *isl_aff_get_coefficient_val(
3550 __isl_keep isl_aff *aff,
3551 enum isl_dim_type type, int pos);
3552 __isl_give isl_val *isl_aff_get_denominator_val(
3553 __isl_keep isl_aff *aff);
3554 __isl_give isl_aff *isl_aff_get_div(
3555 __isl_keep isl_aff *aff, int pos);
3557 int isl_pw_aff_n_piece(__isl_keep isl_pw_aff *pwaff);
3558 int isl_pw_aff_foreach_piece(__isl_keep isl_pw_aff *pwaff,
3559 int (*fn)(__isl_take isl_set *set,
3560 __isl_take isl_aff *aff,
3561 void *user), void *user);
3563 int isl_aff_is_cst(__isl_keep isl_aff *aff);
3564 int isl_pw_aff_is_cst(__isl_keep isl_pw_aff *pwaff);
3566 int isl_aff_involves_dims(__isl_keep isl_aff *aff,
3567 enum isl_dim_type type, unsigned first, unsigned n);
3568 int isl_pw_aff_involves_dims(__isl_keep isl_pw_aff *pwaff,
3569 enum isl_dim_type type, unsigned first, unsigned n);
3571 isl_ctx *isl_pw_aff_get_ctx(__isl_keep isl_pw_aff *pwaff);
3572 unsigned isl_pw_aff_dim(__isl_keep isl_pw_aff *pwaff,
3573 enum isl_dim_type type);
3574 int isl_pw_aff_is_empty(__isl_keep isl_pw_aff *pwaff);
3576 It can be modified using
3578 #include <isl/aff.h>
3579 __isl_give isl_pw_aff *isl_pw_aff_set_tuple_id(
3580 __isl_take isl_pw_aff *pwaff,
3581 enum isl_dim_type type, __isl_take isl_id *id);
3582 __isl_give isl_aff *isl_aff_set_dim_name(
3583 __isl_take isl_aff *aff, enum isl_dim_type type,
3584 unsigned pos, const char *s);
3585 __isl_give isl_aff *isl_aff_set_dim_id(
3586 __isl_take isl_aff *aff, enum isl_dim_type type,
3587 unsigned pos, __isl_take isl_id *id);
3588 __isl_give isl_pw_aff *isl_pw_aff_set_dim_id(
3589 __isl_take isl_pw_aff *pma,
3590 enum isl_dim_type type, unsigned pos,
3591 __isl_take isl_id *id);
3592 __isl_give isl_aff *isl_aff_set_constant_si(
3593 __isl_take isl_aff *aff, int v);
3594 __isl_give isl_aff *isl_aff_set_constant_val(
3595 __isl_take isl_aff *aff, __isl_take isl_val *v);
3596 __isl_give isl_aff *isl_aff_set_coefficient_si(
3597 __isl_take isl_aff *aff,
3598 enum isl_dim_type type, int pos, int v);
3599 __isl_give isl_aff *isl_aff_set_coefficient_val(
3600 __isl_take isl_aff *aff,
3601 enum isl_dim_type type, int pos,
3602 __isl_take isl_val *v);
3604 __isl_give isl_aff *isl_aff_add_constant_si(
3605 __isl_take isl_aff *aff, int v);
3606 __isl_give isl_aff *isl_aff_add_constant_val(
3607 __isl_take isl_aff *aff, __isl_take isl_val *v);
3608 __isl_give isl_aff *isl_aff_add_constant_num_si(
3609 __isl_take isl_aff *aff, int v);
3610 __isl_give isl_aff *isl_aff_add_coefficient_si(
3611 __isl_take isl_aff *aff,
3612 enum isl_dim_type type, int pos, int v);
3613 __isl_give isl_aff *isl_aff_add_coefficient_val(
3614 __isl_take isl_aff *aff,
3615 enum isl_dim_type type, int pos,
3616 __isl_take isl_val *v);
3618 __isl_give isl_aff *isl_aff_insert_dims(
3619 __isl_take isl_aff *aff,
3620 enum isl_dim_type type, unsigned first, unsigned n);
3621 __isl_give isl_pw_aff *isl_pw_aff_insert_dims(
3622 __isl_take isl_pw_aff *pwaff,
3623 enum isl_dim_type type, unsigned first, unsigned n);
3624 __isl_give isl_aff *isl_aff_add_dims(
3625 __isl_take isl_aff *aff,
3626 enum isl_dim_type type, unsigned n);
3627 __isl_give isl_pw_aff *isl_pw_aff_add_dims(
3628 __isl_take isl_pw_aff *pwaff,
3629 enum isl_dim_type type, unsigned n);
3630 __isl_give isl_aff *isl_aff_drop_dims(
3631 __isl_take isl_aff *aff,
3632 enum isl_dim_type type, unsigned first, unsigned n);
3633 __isl_give isl_pw_aff *isl_pw_aff_drop_dims(
3634 __isl_take isl_pw_aff *pwaff,
3635 enum isl_dim_type type, unsigned first, unsigned n);
3637 Note that C<isl_aff_set_constant_si> and C<isl_aff_set_coefficient_si>
3638 set the I<numerator> of the constant or coefficient, while
3639 C<isl_aff_set_constant_val> and C<isl_aff_set_coefficient_val> set
3640 the constant or coefficient as a whole.
3641 The C<add_constant> and C<add_coefficient> functions add an integer
3642 or rational value to
3643 the possibly rational constant or coefficient.
3644 The C<add_constant_num> functions add an integer value to
3647 To check whether an affine expressions is obviously zero
3648 or obviously equal to some other affine expression, use
3650 #include <isl/aff.h>
3651 int isl_aff_plain_is_zero(__isl_keep isl_aff *aff);
3652 int isl_aff_plain_is_equal(__isl_keep isl_aff *aff1,
3653 __isl_keep isl_aff *aff2);
3654 int isl_pw_aff_plain_is_equal(
3655 __isl_keep isl_pw_aff *pwaff1,
3656 __isl_keep isl_pw_aff *pwaff2);
3660 #include <isl/aff.h>
3661 __isl_give isl_aff *isl_aff_add(__isl_take isl_aff *aff1,
3662 __isl_take isl_aff *aff2);
3663 __isl_give isl_pw_aff *isl_pw_aff_add(
3664 __isl_take isl_pw_aff *pwaff1,
3665 __isl_take isl_pw_aff *pwaff2);
3666 __isl_give isl_pw_aff *isl_pw_aff_min(
3667 __isl_take isl_pw_aff *pwaff1,
3668 __isl_take isl_pw_aff *pwaff2);
3669 __isl_give isl_pw_aff *isl_pw_aff_max(
3670 __isl_take isl_pw_aff *pwaff1,
3671 __isl_take isl_pw_aff *pwaff2);
3672 __isl_give isl_aff *isl_aff_sub(__isl_take isl_aff *aff1,
3673 __isl_take isl_aff *aff2);
3674 __isl_give isl_pw_aff *isl_pw_aff_sub(
3675 __isl_take isl_pw_aff *pwaff1,
3676 __isl_take isl_pw_aff *pwaff2);
3677 __isl_give isl_aff *isl_aff_neg(__isl_take isl_aff *aff);
3678 __isl_give isl_pw_aff *isl_pw_aff_neg(
3679 __isl_take isl_pw_aff *pwaff);
3680 __isl_give isl_aff *isl_aff_ceil(__isl_take isl_aff *aff);
3681 __isl_give isl_pw_aff *isl_pw_aff_ceil(
3682 __isl_take isl_pw_aff *pwaff);
3683 __isl_give isl_aff *isl_aff_floor(__isl_take isl_aff *aff);
3684 __isl_give isl_pw_aff *isl_pw_aff_floor(
3685 __isl_take isl_pw_aff *pwaff);
3686 __isl_give isl_aff *isl_aff_mod_val(__isl_take isl_aff *aff,
3687 __isl_take isl_val *mod);
3688 __isl_give isl_pw_aff *isl_pw_aff_mod_val(
3689 __isl_take isl_pw_aff *pa,
3690 __isl_take isl_val *mod);
3691 __isl_give isl_aff *isl_aff_scale_val(__isl_take isl_aff *aff,
3692 __isl_take isl_val *v);
3693 __isl_give isl_pw_aff *isl_pw_aff_scale_val(
3694 __isl_take isl_pw_aff *pa, __isl_take isl_val *v);
3695 __isl_give isl_aff *isl_aff_scale_down_ui(
3696 __isl_take isl_aff *aff, unsigned f);
3697 __isl_give isl_aff *isl_aff_scale_down_val(
3698 __isl_take isl_aff *aff, __isl_take isl_val *v);
3699 __isl_give isl_pw_aff *isl_pw_aff_scale_down_val(
3700 __isl_take isl_pw_aff *pa,
3701 __isl_take isl_val *f);
3703 __isl_give isl_pw_aff *isl_pw_aff_list_min(
3704 __isl_take isl_pw_aff_list *list);
3705 __isl_give isl_pw_aff *isl_pw_aff_list_max(
3706 __isl_take isl_pw_aff_list *list);
3708 __isl_give isl_pw_aff *isl_pw_aff_coalesce(
3709 __isl_take isl_pw_aff *pwqp);
3711 __isl_give isl_aff *isl_aff_align_params(
3712 __isl_take isl_aff *aff,
3713 __isl_take isl_space *model);
3714 __isl_give isl_pw_aff *isl_pw_aff_align_params(
3715 __isl_take isl_pw_aff *pwaff,
3716 __isl_take isl_space *model);
3718 __isl_give isl_aff *isl_aff_project_domain_on_params(
3719 __isl_take isl_aff *aff);
3721 __isl_give isl_aff *isl_aff_gist_params(
3722 __isl_take isl_aff *aff,
3723 __isl_take isl_set *context);
3724 __isl_give isl_aff *isl_aff_gist(__isl_take isl_aff *aff,
3725 __isl_take isl_set *context);
3726 __isl_give isl_pw_aff *isl_pw_aff_gist_params(
3727 __isl_take isl_pw_aff *pwaff,
3728 __isl_take isl_set *context);
3729 __isl_give isl_pw_aff *isl_pw_aff_gist(
3730 __isl_take isl_pw_aff *pwaff,
3731 __isl_take isl_set *context);
3733 __isl_give isl_set *isl_pw_aff_domain(
3734 __isl_take isl_pw_aff *pwaff);
3735 __isl_give isl_pw_aff *isl_pw_aff_intersect_domain(
3736 __isl_take isl_pw_aff *pa,
3737 __isl_take isl_set *set);
3738 __isl_give isl_pw_aff *isl_pw_aff_intersect_params(
3739 __isl_take isl_pw_aff *pa,
3740 __isl_take isl_set *set);
3742 __isl_give isl_aff *isl_aff_mul(__isl_take isl_aff *aff1,
3743 __isl_take isl_aff *aff2);
3744 __isl_give isl_aff *isl_aff_div(__isl_take isl_aff *aff1,
3745 __isl_take isl_aff *aff2);
3746 __isl_give isl_pw_aff *isl_pw_aff_mul(
3747 __isl_take isl_pw_aff *pwaff1,
3748 __isl_take isl_pw_aff *pwaff2);
3749 __isl_give isl_pw_aff *isl_pw_aff_div(
3750 __isl_take isl_pw_aff *pa1,
3751 __isl_take isl_pw_aff *pa2);
3752 __isl_give isl_pw_aff *isl_pw_aff_tdiv_q(
3753 __isl_take isl_pw_aff *pa1,
3754 __isl_take isl_pw_aff *pa2);
3755 __isl_give isl_pw_aff *isl_pw_aff_tdiv_r(
3756 __isl_take isl_pw_aff *pa1,
3757 __isl_take isl_pw_aff *pa2);
3759 When multiplying two affine expressions, at least one of the two needs
3760 to be a constant. Similarly, when dividing an affine expression by another,
3761 the second expression needs to be a constant.
3762 C<isl_pw_aff_tdiv_q> computes the quotient of an integer division with
3763 rounding towards zero. C<isl_pw_aff_tdiv_r> computes the corresponding
3766 #include <isl/aff.h>
3767 __isl_give isl_aff *isl_aff_pullback_multi_aff(
3768 __isl_take isl_aff *aff,
3769 __isl_take isl_multi_aff *ma);
3770 __isl_give isl_pw_aff *isl_pw_aff_pullback_multi_aff(
3771 __isl_take isl_pw_aff *pa,
3772 __isl_take isl_multi_aff *ma);
3773 __isl_give isl_pw_aff *isl_pw_aff_pullback_pw_multi_aff(
3774 __isl_take isl_pw_aff *pa,
3775 __isl_take isl_pw_multi_aff *pma);
3777 These functions precompose the input expression by the given
3778 C<isl_multi_aff> or C<isl_pw_multi_aff>. In other words,
3779 the C<isl_multi_aff> or C<isl_pw_multi_aff> is plugged
3780 into the (piecewise) affine expression.
3781 Objects of type C<isl_multi_aff> are described in
3782 L</"Piecewise Multiple Quasi Affine Expressions">.
3784 #include <isl/aff.h>
3785 __isl_give isl_basic_set *isl_aff_zero_basic_set(
3786 __isl_take isl_aff *aff);
3787 __isl_give isl_basic_set *isl_aff_neg_basic_set(
3788 __isl_take isl_aff *aff);
3789 __isl_give isl_basic_set *isl_aff_le_basic_set(
3790 __isl_take isl_aff *aff1, __isl_take isl_aff *aff2);
3791 __isl_give isl_basic_set *isl_aff_ge_basic_set(
3792 __isl_take isl_aff *aff1, __isl_take isl_aff *aff2);
3793 __isl_give isl_set *isl_pw_aff_eq_set(
3794 __isl_take isl_pw_aff *pwaff1,
3795 __isl_take isl_pw_aff *pwaff2);
3796 __isl_give isl_set *isl_pw_aff_ne_set(
3797 __isl_take isl_pw_aff *pwaff1,
3798 __isl_take isl_pw_aff *pwaff2);
3799 __isl_give isl_set *isl_pw_aff_le_set(
3800 __isl_take isl_pw_aff *pwaff1,
3801 __isl_take isl_pw_aff *pwaff2);
3802 __isl_give isl_set *isl_pw_aff_lt_set(
3803 __isl_take isl_pw_aff *pwaff1,
3804 __isl_take isl_pw_aff *pwaff2);
3805 __isl_give isl_set *isl_pw_aff_ge_set(
3806 __isl_take isl_pw_aff *pwaff1,
3807 __isl_take isl_pw_aff *pwaff2);
3808 __isl_give isl_set *isl_pw_aff_gt_set(
3809 __isl_take isl_pw_aff *pwaff1,
3810 __isl_take isl_pw_aff *pwaff2);
3812 __isl_give isl_set *isl_pw_aff_list_eq_set(
3813 __isl_take isl_pw_aff_list *list1,
3814 __isl_take isl_pw_aff_list *list2);
3815 __isl_give isl_set *isl_pw_aff_list_ne_set(
3816 __isl_take isl_pw_aff_list *list1,
3817 __isl_take isl_pw_aff_list *list2);
3818 __isl_give isl_set *isl_pw_aff_list_le_set(
3819 __isl_take isl_pw_aff_list *list1,
3820 __isl_take isl_pw_aff_list *list2);
3821 __isl_give isl_set *isl_pw_aff_list_lt_set(
3822 __isl_take isl_pw_aff_list *list1,
3823 __isl_take isl_pw_aff_list *list2);
3824 __isl_give isl_set *isl_pw_aff_list_ge_set(
3825 __isl_take isl_pw_aff_list *list1,
3826 __isl_take isl_pw_aff_list *list2);
3827 __isl_give isl_set *isl_pw_aff_list_gt_set(
3828 __isl_take isl_pw_aff_list *list1,
3829 __isl_take isl_pw_aff_list *list2);
3831 The function C<isl_aff_neg_basic_set> returns a basic set
3832 containing those elements in the domain space
3833 of C<aff> where C<aff> is negative.
3834 The function C<isl_aff_ge_basic_set> returns a basic set
3835 containing those elements in the shared space
3836 of C<aff1> and C<aff2> where C<aff1> is greater than or equal to C<aff2>.
3837 The function C<isl_pw_aff_ge_set> returns a set
3838 containing those elements in the shared domain
3839 of C<pwaff1> and C<pwaff2> where C<pwaff1> is greater than or equal to C<pwaff2>.
3840 The functions operating on C<isl_pw_aff_list> apply the corresponding
3841 C<isl_pw_aff> function to each pair of elements in the two lists.
3843 #include <isl/aff.h>
3844 __isl_give isl_set *isl_pw_aff_nonneg_set(
3845 __isl_take isl_pw_aff *pwaff);
3846 __isl_give isl_set *isl_pw_aff_zero_set(
3847 __isl_take isl_pw_aff *pwaff);
3848 __isl_give isl_set *isl_pw_aff_non_zero_set(
3849 __isl_take isl_pw_aff *pwaff);
3851 The function C<isl_pw_aff_nonneg_set> returns a set
3852 containing those elements in the domain
3853 of C<pwaff> where C<pwaff> is non-negative.
3855 #include <isl/aff.h>
3856 __isl_give isl_pw_aff *isl_pw_aff_cond(
3857 __isl_take isl_pw_aff *cond,
3858 __isl_take isl_pw_aff *pwaff_true,
3859 __isl_take isl_pw_aff *pwaff_false);
3861 The function C<isl_pw_aff_cond> performs a conditional operator
3862 and returns an expression that is equal to C<pwaff_true>
3863 for elements where C<cond> is non-zero and equal to C<pwaff_false> for elements
3864 where C<cond> is zero.
3866 #include <isl/aff.h>
3867 __isl_give isl_pw_aff *isl_pw_aff_union_min(
3868 __isl_take isl_pw_aff *pwaff1,
3869 __isl_take isl_pw_aff *pwaff2);
3870 __isl_give isl_pw_aff *isl_pw_aff_union_max(
3871 __isl_take isl_pw_aff *pwaff1,
3872 __isl_take isl_pw_aff *pwaff2);
3873 __isl_give isl_pw_aff *isl_pw_aff_union_add(
3874 __isl_take isl_pw_aff *pwaff1,
3875 __isl_take isl_pw_aff *pwaff2);
3877 The function C<isl_pw_aff_union_max> computes a piecewise quasi-affine
3878 expression with a domain that is the union of those of C<pwaff1> and
3879 C<pwaff2> and such that on each cell, the quasi-affine expression is
3880 the maximum of those of C<pwaff1> and C<pwaff2>. If only one of
3881 C<pwaff1> or C<pwaff2> is defined on a given cell, then the
3882 associated expression is the defined one.
3884 An expression can be read from input using
3886 #include <isl/aff.h>
3887 __isl_give isl_aff *isl_aff_read_from_str(
3888 isl_ctx *ctx, const char *str);
3889 __isl_give isl_pw_aff *isl_pw_aff_read_from_str(
3890 isl_ctx *ctx, const char *str);
3892 An expression can be printed using
3894 #include <isl/aff.h>
3895 __isl_give isl_printer *isl_printer_print_aff(
3896 __isl_take isl_printer *p, __isl_keep isl_aff *aff);
3898 __isl_give isl_printer *isl_printer_print_pw_aff(
3899 __isl_take isl_printer *p,
3900 __isl_keep isl_pw_aff *pwaff);
3902 =head2 Piecewise Multiple Quasi Affine Expressions
3904 An C<isl_multi_aff> object represents a sequence of
3905 zero or more affine expressions, all defined on the same domain space.
3906 Similarly, an C<isl_multi_pw_aff> object represents a sequence of
3907 zero or more piecewise affine expressions.
3909 An C<isl_multi_aff> can be constructed from a single
3910 C<isl_aff> or an C<isl_aff_list> using the
3911 following functions. Similarly for C<isl_multi_pw_aff>.
3913 #include <isl/aff.h>
3914 __isl_give isl_multi_aff *isl_multi_aff_from_aff(
3915 __isl_take isl_aff *aff);
3916 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_from_pw_aff(
3917 __isl_take isl_pw_aff *pa);
3918 __isl_give isl_multi_aff *isl_multi_aff_from_aff_list(
3919 __isl_take isl_space *space,
3920 __isl_take isl_aff_list *list);
3922 An empty piecewise multiple quasi affine expression (one with no cells),
3923 the zero piecewise multiple quasi affine expression (with value zero
3924 for each output dimension),
3925 a piecewise multiple quasi affine expression with a single cell (with
3926 either a universe or a specified domain) or
3927 a zero-dimensional piecewise multiple quasi affine expression
3929 can be created using the following functions.
3931 #include <isl/aff.h>
3932 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_empty(
3933 __isl_take isl_space *space);
3934 __isl_give isl_multi_aff *isl_multi_aff_zero(
3935 __isl_take isl_space *space);
3936 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_zero(
3937 __isl_take isl_space *space);
3938 __isl_give isl_multi_aff *isl_multi_aff_identity(
3939 __isl_take isl_space *space);
3940 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_identity(
3941 __isl_take isl_space *space);
3942 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_identity(
3943 __isl_take isl_space *space);
3944 __isl_give isl_pw_multi_aff *
3945 isl_pw_multi_aff_from_multi_aff(
3946 __isl_take isl_multi_aff *ma);
3947 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_alloc(
3948 __isl_take isl_set *set,
3949 __isl_take isl_multi_aff *maff);
3950 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_from_domain(
3951 __isl_take isl_set *set);
3953 __isl_give isl_union_pw_multi_aff *
3954 isl_union_pw_multi_aff_empty(
3955 __isl_take isl_space *space);
3956 __isl_give isl_union_pw_multi_aff *
3957 isl_union_pw_multi_aff_add_pw_multi_aff(
3958 __isl_take isl_union_pw_multi_aff *upma,
3959 __isl_take isl_pw_multi_aff *pma);
3960 __isl_give isl_union_pw_multi_aff *
3961 isl_union_pw_multi_aff_from_domain(
3962 __isl_take isl_union_set *uset);
3964 A piecewise multiple quasi affine expression can also be initialized
3965 from an C<isl_set> or C<isl_map>, provided the C<isl_set> is a singleton
3966 and the C<isl_map> is single-valued.
3967 In case of a conversion from an C<isl_union_set> or an C<isl_union_map>
3968 to an C<isl_union_pw_multi_aff>, these properties need to hold in each space.
3970 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_from_set(
3971 __isl_take isl_set *set);
3972 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_from_map(
3973 __isl_take isl_map *map);
3975 __isl_give isl_union_pw_multi_aff *
3976 isl_union_pw_multi_aff_from_union_set(
3977 __isl_take isl_union_set *uset);
3978 __isl_give isl_union_pw_multi_aff *
3979 isl_union_pw_multi_aff_from_union_map(
3980 __isl_take isl_union_map *umap);
3982 Multiple quasi affine expressions can be copied and freed using
3984 #include <isl/aff.h>
3985 __isl_give isl_multi_aff *isl_multi_aff_copy(
3986 __isl_keep isl_multi_aff *maff);
3987 void *isl_multi_aff_free(__isl_take isl_multi_aff *maff);
3989 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_copy(
3990 __isl_keep isl_pw_multi_aff *pma);
3991 void *isl_pw_multi_aff_free(
3992 __isl_take isl_pw_multi_aff *pma);
3994 __isl_give isl_union_pw_multi_aff *
3995 isl_union_pw_multi_aff_copy(
3996 __isl_keep isl_union_pw_multi_aff *upma);
3997 void *isl_union_pw_multi_aff_free(
3998 __isl_take isl_union_pw_multi_aff *upma);
4000 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_copy(
4001 __isl_keep isl_multi_pw_aff *mpa);
4002 void *isl_multi_pw_aff_free(
4003 __isl_take isl_multi_pw_aff *mpa);
4005 The expression can be inspected using
4007 #include <isl/aff.h>
4008 isl_ctx *isl_multi_aff_get_ctx(
4009 __isl_keep isl_multi_aff *maff);
4010 isl_ctx *isl_pw_multi_aff_get_ctx(
4011 __isl_keep isl_pw_multi_aff *pma);
4012 isl_ctx *isl_union_pw_multi_aff_get_ctx(
4013 __isl_keep isl_union_pw_multi_aff *upma);
4014 isl_ctx *isl_multi_pw_aff_get_ctx(
4015 __isl_keep isl_multi_pw_aff *mpa);
4016 unsigned isl_multi_aff_dim(__isl_keep isl_multi_aff *maff,
4017 enum isl_dim_type type);
4018 unsigned isl_pw_multi_aff_dim(
4019 __isl_keep isl_pw_multi_aff *pma,
4020 enum isl_dim_type type);
4021 unsigned isl_multi_pw_aff_dim(
4022 __isl_keep isl_multi_pw_aff *mpa,
4023 enum isl_dim_type type);
4024 __isl_give isl_aff *isl_multi_aff_get_aff(
4025 __isl_keep isl_multi_aff *multi, int pos);
4026 __isl_give isl_pw_aff *isl_pw_multi_aff_get_pw_aff(
4027 __isl_keep isl_pw_multi_aff *pma, int pos);
4028 __isl_give isl_pw_aff *isl_multi_pw_aff_get_pw_aff(
4029 __isl_keep isl_multi_pw_aff *mpa, int pos);
4030 const char *isl_pw_multi_aff_get_dim_name(
4031 __isl_keep isl_pw_multi_aff *pma,
4032 enum isl_dim_type type, unsigned pos);
4033 __isl_give isl_id *isl_pw_multi_aff_get_dim_id(
4034 __isl_keep isl_pw_multi_aff *pma,
4035 enum isl_dim_type type, unsigned pos);
4036 const char *isl_multi_aff_get_tuple_name(
4037 __isl_keep isl_multi_aff *multi,
4038 enum isl_dim_type type);
4039 int isl_pw_multi_aff_has_tuple_name(
4040 __isl_keep isl_pw_multi_aff *pma,
4041 enum isl_dim_type type);
4042 const char *isl_pw_multi_aff_get_tuple_name(
4043 __isl_keep isl_pw_multi_aff *pma,
4044 enum isl_dim_type type);
4045 int isl_pw_multi_aff_has_tuple_id(
4046 __isl_keep isl_pw_multi_aff *pma,
4047 enum isl_dim_type type);
4048 __isl_give isl_id *isl_pw_multi_aff_get_tuple_id(
4049 __isl_keep isl_pw_multi_aff *pma,
4050 enum isl_dim_type type);
4052 int isl_pw_multi_aff_foreach_piece(
4053 __isl_keep isl_pw_multi_aff *pma,
4054 int (*fn)(__isl_take isl_set *set,
4055 __isl_take isl_multi_aff *maff,
4056 void *user), void *user);
4058 int isl_union_pw_multi_aff_foreach_pw_multi_aff(
4059 __isl_keep isl_union_pw_multi_aff *upma,
4060 int (*fn)(__isl_take isl_pw_multi_aff *pma,
4061 void *user), void *user);
4063 It can be modified using
4065 #include <isl/aff.h>
4066 __isl_give isl_multi_aff *isl_multi_aff_set_aff(
4067 __isl_take isl_multi_aff *multi, int pos,
4068 __isl_take isl_aff *aff);
4069 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_set_pw_aff(
4070 __isl_take isl_pw_multi_aff *pma, unsigned pos,
4071 __isl_take isl_pw_aff *pa);
4072 __isl_give isl_multi_aff *isl_multi_aff_set_dim_name(
4073 __isl_take isl_multi_aff *maff,
4074 enum isl_dim_type type, unsigned pos, const char *s);
4075 __isl_give isl_multi_aff *isl_multi_aff_set_tuple_name(
4076 __isl_take isl_multi_aff *maff,
4077 enum isl_dim_type type, const char *s);
4078 __isl_give isl_multi_aff *isl_multi_aff_set_tuple_id(
4079 __isl_take isl_multi_aff *maff,
4080 enum isl_dim_type type, __isl_take isl_id *id);
4081 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_set_tuple_id(
4082 __isl_take isl_pw_multi_aff *pma,
4083 enum isl_dim_type type, __isl_take isl_id *id);
4085 __isl_give isl_multi_pw_aff *
4086 isl_multi_pw_aff_set_dim_name(
4087 __isl_take isl_multi_pw_aff *mpa,
4088 enum isl_dim_type type, unsigned pos, const char *s);
4089 __isl_give isl_multi_pw_aff *
4090 isl_multi_pw_aff_set_tuple_name(
4091 __isl_take isl_multi_pw_aff *mpa,
4092 enum isl_dim_type type, const char *s);
4094 __isl_give isl_multi_aff *isl_multi_aff_insert_dims(
4095 __isl_take isl_multi_aff *ma,
4096 enum isl_dim_type type, unsigned first, unsigned n);
4097 __isl_give isl_multi_aff *isl_multi_aff_add_dims(
4098 __isl_take isl_multi_aff *ma,
4099 enum isl_dim_type type, unsigned n);
4100 __isl_give isl_multi_aff *isl_multi_aff_drop_dims(
4101 __isl_take isl_multi_aff *maff,
4102 enum isl_dim_type type, unsigned first, unsigned n);
4103 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_drop_dims(
4104 __isl_take isl_pw_multi_aff *pma,
4105 enum isl_dim_type type, unsigned first, unsigned n);
4107 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_insert_dims(
4108 __isl_take isl_multi_pw_aff *mpa,
4109 enum isl_dim_type type, unsigned first, unsigned n);
4110 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_add_dims(
4111 __isl_take isl_multi_pw_aff *mpa,
4112 enum isl_dim_type type, unsigned n);
4114 To check whether two multiple affine expressions are
4115 obviously equal to each other, use
4117 int isl_multi_aff_plain_is_equal(__isl_keep isl_multi_aff *maff1,
4118 __isl_keep isl_multi_aff *maff2);
4119 int isl_pw_multi_aff_plain_is_equal(
4120 __isl_keep isl_pw_multi_aff *pma1,
4121 __isl_keep isl_pw_multi_aff *pma2);
4125 #include <isl/aff.h>
4126 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_union_lexmin(
4127 __isl_take isl_pw_multi_aff *pma1,
4128 __isl_take isl_pw_multi_aff *pma2);
4129 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_union_lexmax(
4130 __isl_take isl_pw_multi_aff *pma1,
4131 __isl_take isl_pw_multi_aff *pma2);
4132 __isl_give isl_multi_aff *isl_multi_aff_add(
4133 __isl_take isl_multi_aff *maff1,
4134 __isl_take isl_multi_aff *maff2);
4135 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_add(
4136 __isl_take isl_pw_multi_aff *pma1,
4137 __isl_take isl_pw_multi_aff *pma2);
4138 __isl_give isl_union_pw_multi_aff *isl_union_pw_multi_aff_add(
4139 __isl_take isl_union_pw_multi_aff *upma1,
4140 __isl_take isl_union_pw_multi_aff *upma2);
4141 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_union_add(
4142 __isl_take isl_pw_multi_aff *pma1,
4143 __isl_take isl_pw_multi_aff *pma2);
4144 __isl_give isl_multi_aff *isl_multi_aff_sub(
4145 __isl_take isl_multi_aff *ma1,
4146 __isl_take isl_multi_aff *ma2);
4147 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_sub(
4148 __isl_take isl_pw_multi_aff *pma1,
4149 __isl_take isl_pw_multi_aff *pma2);
4150 __isl_give isl_union_pw_multi_aff *isl_union_pw_multi_aff_sub(
4151 __isl_take isl_union_pw_multi_aff *upma1,
4152 __isl_take isl_union_pw_multi_aff *upma2);
4154 C<isl_multi_aff_sub> subtracts the second argument from the first.
4156 __isl_give isl_multi_aff *isl_multi_aff_scale_val(
4157 __isl_take isl_multi_aff *ma,
4158 __isl_take isl_val *v);
4159 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_scale_val(
4160 __isl_take isl_pw_multi_aff *pma,
4161 __isl_take isl_val *v);
4162 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_scale_val(
4163 __isl_take isl_multi_pw_aff *mpa,
4164 __isl_take isl_val *v);
4165 __isl_give isl_multi_aff *isl_multi_aff_scale_multi_val(
4166 __isl_take isl_multi_aff *ma,
4167 __isl_take isl_multi_val *mv);
4168 __isl_give isl_pw_multi_aff *
4169 isl_pw_multi_aff_scale_multi_val(
4170 __isl_take isl_pw_multi_aff *pma,
4171 __isl_take isl_multi_val *mv);
4172 __isl_give isl_multi_pw_aff *
4173 isl_multi_pw_aff_scale_multi_val(
4174 __isl_take isl_multi_pw_aff *mpa,
4175 __isl_take isl_multi_val *mv);
4176 __isl_give isl_union_pw_multi_aff *
4177 isl_union_pw_multi_aff_scale_multi_val(
4178 __isl_take isl_union_pw_multi_aff *upma,
4179 __isl_take isl_multi_val *mv);
4181 C<isl_multi_aff_scale_multi_val> scales the elements of C<ma>
4182 by the corresponding elements of C<mv>.
4184 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_intersect_params(
4185 __isl_take isl_pw_multi_aff *pma,
4186 __isl_take isl_set *set);
4187 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_intersect_domain(
4188 __isl_take isl_pw_multi_aff *pma,
4189 __isl_take isl_set *set);
4190 __isl_give isl_union_pw_multi_aff *
4191 isl_union_pw_multi_aff_intersect_domain(
4192 __isl_take isl_union_pw_multi_aff *upma,
4193 __isl_take isl_union_set *uset);
4194 __isl_give isl_multi_aff *isl_multi_aff_lift(
4195 __isl_take isl_multi_aff *maff,
4196 __isl_give isl_local_space **ls);
4197 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_coalesce(
4198 __isl_take isl_pw_multi_aff *pma);
4199 __isl_give isl_multi_aff *isl_multi_aff_align_params(
4200 __isl_take isl_multi_aff *multi,
4201 __isl_take isl_space *model);
4202 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_align_params(
4203 __isl_take isl_pw_multi_aff *pma,
4204 __isl_take isl_space *model);
4205 __isl_give isl_pw_multi_aff *
4206 isl_pw_multi_aff_project_domain_on_params(
4207 __isl_take isl_pw_multi_aff *pma);
4208 __isl_give isl_multi_aff *isl_multi_aff_gist_params(
4209 __isl_take isl_multi_aff *maff,
4210 __isl_take isl_set *context);
4211 __isl_give isl_multi_aff *isl_multi_aff_gist(
4212 __isl_take isl_multi_aff *maff,
4213 __isl_take isl_set *context);
4214 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_gist_params(
4215 __isl_take isl_pw_multi_aff *pma,
4216 __isl_take isl_set *set);
4217 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_gist(
4218 __isl_take isl_pw_multi_aff *pma,
4219 __isl_take isl_set *set);
4220 __isl_give isl_set *isl_pw_multi_aff_domain(
4221 __isl_take isl_pw_multi_aff *pma);
4222 __isl_give isl_union_set *isl_union_pw_multi_aff_domain(
4223 __isl_take isl_union_pw_multi_aff *upma);
4224 __isl_give isl_multi_aff *isl_multi_aff_range_splice(
4225 __isl_take isl_multi_aff *ma1, unsigned pos,
4226 __isl_take isl_multi_aff *ma2);
4227 __isl_give isl_multi_aff *isl_multi_aff_splice(
4228 __isl_take isl_multi_aff *ma1,
4229 unsigned in_pos, unsigned out_pos,
4230 __isl_take isl_multi_aff *ma2);
4231 __isl_give isl_multi_aff *isl_multi_aff_range_product(
4232 __isl_take isl_multi_aff *ma1,
4233 __isl_take isl_multi_aff *ma2);
4234 __isl_give isl_multi_aff *isl_multi_aff_flat_range_product(
4235 __isl_take isl_multi_aff *ma1,
4236 __isl_take isl_multi_aff *ma2);
4237 __isl_give isl_multi_aff *isl_multi_aff_product(
4238 __isl_take isl_multi_aff *ma1,
4239 __isl_take isl_multi_aff *ma2);
4240 __isl_give isl_pw_multi_aff *
4241 isl_pw_multi_aff_range_product(
4242 __isl_take isl_pw_multi_aff *pma1,
4243 __isl_take isl_pw_multi_aff *pma2);
4244 __isl_give isl_pw_multi_aff *
4245 isl_pw_multi_aff_flat_range_product(
4246 __isl_take isl_pw_multi_aff *pma1,
4247 __isl_take isl_pw_multi_aff *pma2);
4248 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_product(
4249 __isl_take isl_pw_multi_aff *pma1,
4250 __isl_take isl_pw_multi_aff *pma2);
4251 __isl_give isl_union_pw_multi_aff *
4252 isl_union_pw_multi_aff_flat_range_product(
4253 __isl_take isl_union_pw_multi_aff *upma1,
4254 __isl_take isl_union_pw_multi_aff *upma2);
4255 __isl_give isl_multi_pw_aff *
4256 isl_multi_pw_aff_range_splice(
4257 __isl_take isl_multi_pw_aff *mpa1, unsigned pos,
4258 __isl_take isl_multi_pw_aff *mpa2);
4259 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_splice(
4260 __isl_take isl_multi_pw_aff *mpa1,
4261 unsigned in_pos, unsigned out_pos,
4262 __isl_take isl_multi_pw_aff *mpa2);
4263 __isl_give isl_multi_pw_aff *
4264 isl_multi_pw_aff_range_product(
4265 __isl_take isl_multi_pw_aff *mpa1,
4266 __isl_take isl_multi_pw_aff *mpa2);
4267 __isl_give isl_multi_pw_aff *
4268 isl_multi_pw_aff_flat_range_product(
4269 __isl_take isl_multi_pw_aff *mpa1,
4270 __isl_take isl_multi_pw_aff *mpa2);
4272 If the C<ls> argument of C<isl_multi_aff_lift> is not C<NULL>,
4273 then it is assigned the local space that lies at the basis of
4274 the lifting applied.
4276 #include <isl/aff.h>
4277 __isl_give isl_multi_aff *isl_multi_aff_pullback_multi_aff(
4278 __isl_take isl_multi_aff *ma1,
4279 __isl_take isl_multi_aff *ma2);
4280 __isl_give isl_pw_multi_aff *
4281 isl_pw_multi_aff_pullback_multi_aff(
4282 __isl_take isl_pw_multi_aff *pma,
4283 __isl_take isl_multi_aff *ma);
4284 __isl_give isl_pw_multi_aff *
4285 isl_pw_multi_aff_pullback_pw_multi_aff(
4286 __isl_take isl_pw_multi_aff *pma1,
4287 __isl_take isl_pw_multi_aff *pma2);
4289 The function C<isl_multi_aff_pullback_multi_aff> precomposes C<ma1> by C<ma2>.
4290 In other words, C<ma2> is plugged
4293 __isl_give isl_set *isl_multi_aff_lex_le_set(
4294 __isl_take isl_multi_aff *ma1,
4295 __isl_take isl_multi_aff *ma2);
4296 __isl_give isl_set *isl_multi_aff_lex_ge_set(
4297 __isl_take isl_multi_aff *ma1,
4298 __isl_take isl_multi_aff *ma2);
4300 The function C<isl_multi_aff_lex_le_set> returns a set
4301 containing those elements in the shared domain space
4302 where C<ma1> is lexicographically smaller than or
4305 An expression can be read from input using
4307 #include <isl/aff.h>
4308 __isl_give isl_multi_aff *isl_multi_aff_read_from_str(
4309 isl_ctx *ctx, const char *str);
4310 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_read_from_str(
4311 isl_ctx *ctx, const char *str);
4312 __isl_give isl_union_pw_multi_aff *
4313 isl_union_pw_multi_aff_read_from_str(
4314 isl_ctx *ctx, const char *str);
4316 An expression can be printed using
4318 #include <isl/aff.h>
4319 __isl_give isl_printer *isl_printer_print_multi_aff(
4320 __isl_take isl_printer *p,
4321 __isl_keep isl_multi_aff *maff);
4322 __isl_give isl_printer *isl_printer_print_pw_multi_aff(
4323 __isl_take isl_printer *p,
4324 __isl_keep isl_pw_multi_aff *pma);
4325 __isl_give isl_printer *isl_printer_print_union_pw_multi_aff(
4326 __isl_take isl_printer *p,
4327 __isl_keep isl_union_pw_multi_aff *upma);
4328 __isl_give isl_printer *isl_printer_print_multi_pw_aff(
4329 __isl_take isl_printer *p,
4330 __isl_keep isl_multi_pw_aff *mpa);
4334 Points are elements of a set. They can be used to construct
4335 simple sets (boxes) or they can be used to represent the
4336 individual elements of a set.
4337 The zero point (the origin) can be created using
4339 __isl_give isl_point *isl_point_zero(__isl_take isl_space *space);
4341 The coordinates of a point can be inspected, set and changed
4344 __isl_give isl_val *isl_point_get_coordinate_val(
4345 __isl_keep isl_point *pnt,
4346 enum isl_dim_type type, int pos);
4347 __isl_give isl_point *isl_point_set_coordinate_val(
4348 __isl_take isl_point *pnt,
4349 enum isl_dim_type type, int pos,
4350 __isl_take isl_val *v);
4352 __isl_give isl_point *isl_point_add_ui(
4353 __isl_take isl_point *pnt,
4354 enum isl_dim_type type, int pos, unsigned val);
4355 __isl_give isl_point *isl_point_sub_ui(
4356 __isl_take isl_point *pnt,
4357 enum isl_dim_type type, int pos, unsigned val);
4359 Other properties can be obtained using
4361 isl_ctx *isl_point_get_ctx(__isl_keep isl_point *pnt);
4363 Points can be copied or freed using
4365 __isl_give isl_point *isl_point_copy(
4366 __isl_keep isl_point *pnt);
4367 void isl_point_free(__isl_take isl_point *pnt);
4369 A singleton set can be created from a point using
4371 __isl_give isl_basic_set *isl_basic_set_from_point(
4372 __isl_take isl_point *pnt);
4373 __isl_give isl_set *isl_set_from_point(
4374 __isl_take isl_point *pnt);
4376 and a box can be created from two opposite extremal points using
4378 __isl_give isl_basic_set *isl_basic_set_box_from_points(
4379 __isl_take isl_point *pnt1,
4380 __isl_take isl_point *pnt2);
4381 __isl_give isl_set *isl_set_box_from_points(
4382 __isl_take isl_point *pnt1,
4383 __isl_take isl_point *pnt2);
4385 All elements of a B<bounded> (union) set can be enumerated using
4386 the following functions.
4388 int isl_set_foreach_point(__isl_keep isl_set *set,
4389 int (*fn)(__isl_take isl_point *pnt, void *user),
4391 int isl_union_set_foreach_point(__isl_keep isl_union_set *uset,
4392 int (*fn)(__isl_take isl_point *pnt, void *user),
4395 The function C<fn> is called for each integer point in
4396 C<set> with as second argument the last argument of
4397 the C<isl_set_foreach_point> call. The function C<fn>
4398 should return C<0> on success and C<-1> on failure.
4399 In the latter case, C<isl_set_foreach_point> will stop
4400 enumerating and return C<-1> as well.
4401 If the enumeration is performed successfully and to completion,
4402 then C<isl_set_foreach_point> returns C<0>.
4404 To obtain a single point of a (basic) set, use
4406 __isl_give isl_point *isl_basic_set_sample_point(
4407 __isl_take isl_basic_set *bset);
4408 __isl_give isl_point *isl_set_sample_point(
4409 __isl_take isl_set *set);
4411 If C<set> does not contain any (integer) points, then the
4412 resulting point will be ``void'', a property that can be
4415 int isl_point_is_void(__isl_keep isl_point *pnt);
4417 =head2 Piecewise Quasipolynomials
4419 A piecewise quasipolynomial is a particular kind of function that maps
4420 a parametric point to a rational value.
4421 More specifically, a quasipolynomial is a polynomial expression in greatest
4422 integer parts of affine expressions of parameters and variables.
4423 A piecewise quasipolynomial is a subdivision of a given parametric
4424 domain into disjoint cells with a quasipolynomial associated to
4425 each cell. The value of the piecewise quasipolynomial at a given
4426 point is the value of the quasipolynomial associated to the cell
4427 that contains the point. Outside of the union of cells,
4428 the value is assumed to be zero.
4429 For example, the piecewise quasipolynomial
4431 [n] -> { [x] -> ((1 + n) - x) : x <= n and x >= 0 }
4433 maps C<x> to C<1 + n - x> for values of C<x> between C<0> and C<n>.
4434 A given piecewise quasipolynomial has a fixed domain dimension.
4435 Union piecewise quasipolynomials are used to contain piecewise quasipolynomials
4436 defined over different domains.
4437 Piecewise quasipolynomials are mainly used by the C<barvinok>
4438 library for representing the number of elements in a parametric set or map.
4439 For example, the piecewise quasipolynomial above represents
4440 the number of points in the map
4442 [n] -> { [x] -> [y] : x,y >= 0 and 0 <= x + y <= n }
4444 =head3 Input and Output
4446 Piecewise quasipolynomials can be read from input using
4448 __isl_give isl_union_pw_qpolynomial *
4449 isl_union_pw_qpolynomial_read_from_str(
4450 isl_ctx *ctx, const char *str);
4452 Quasipolynomials and piecewise quasipolynomials can be printed
4453 using the following functions.
4455 __isl_give isl_printer *isl_printer_print_qpolynomial(
4456 __isl_take isl_printer *p,
4457 __isl_keep isl_qpolynomial *qp);
4459 __isl_give isl_printer *isl_printer_print_pw_qpolynomial(
4460 __isl_take isl_printer *p,
4461 __isl_keep isl_pw_qpolynomial *pwqp);
4463 __isl_give isl_printer *isl_printer_print_union_pw_qpolynomial(
4464 __isl_take isl_printer *p,
4465 __isl_keep isl_union_pw_qpolynomial *upwqp);
4467 The output format of the printer
4468 needs to be set to either C<ISL_FORMAT_ISL> or C<ISL_FORMAT_C>.
4469 For C<isl_printer_print_union_pw_qpolynomial>, only C<ISL_FORMAT_ISL>
4471 In case of printing in C<ISL_FORMAT_C>, the user may want
4472 to set the names of all dimensions
4474 __isl_give isl_qpolynomial *isl_qpolynomial_set_dim_name(
4475 __isl_take isl_qpolynomial *qp,
4476 enum isl_dim_type type, unsigned pos,
4478 __isl_give isl_pw_qpolynomial *
4479 isl_pw_qpolynomial_set_dim_name(
4480 __isl_take isl_pw_qpolynomial *pwqp,
4481 enum isl_dim_type type, unsigned pos,
4484 =head3 Creating New (Piecewise) Quasipolynomials
4486 Some simple quasipolynomials can be created using the following functions.
4487 More complicated quasipolynomials can be created by applying
4488 operations such as addition and multiplication
4489 on the resulting quasipolynomials
4491 __isl_give isl_qpolynomial *isl_qpolynomial_zero_on_domain(
4492 __isl_take isl_space *domain);
4493 __isl_give isl_qpolynomial *isl_qpolynomial_one_on_domain(
4494 __isl_take isl_space *domain);
4495 __isl_give isl_qpolynomial *isl_qpolynomial_infty_on_domain(
4496 __isl_take isl_space *domain);
4497 __isl_give isl_qpolynomial *isl_qpolynomial_neginfty_on_domain(
4498 __isl_take isl_space *domain);
4499 __isl_give isl_qpolynomial *isl_qpolynomial_nan_on_domain(
4500 __isl_take isl_space *domain);
4501 __isl_give isl_qpolynomial *isl_qpolynomial_val_on_domain(
4502 __isl_take isl_space *domain,
4503 __isl_take isl_val *val);
4504 __isl_give isl_qpolynomial *isl_qpolynomial_var_on_domain(
4505 __isl_take isl_space *domain,
4506 enum isl_dim_type type, unsigned pos);
4507 __isl_give isl_qpolynomial *isl_qpolynomial_from_aff(
4508 __isl_take isl_aff *aff);
4510 Note that the space in which a quasipolynomial lives is a map space
4511 with a one-dimensional range. The C<domain> argument in some of
4512 the functions above corresponds to the domain of this map space.
4514 The zero piecewise quasipolynomial or a piecewise quasipolynomial
4515 with a single cell can be created using the following functions.
4516 Multiple of these single cell piecewise quasipolynomials can
4517 be combined to create more complicated piecewise quasipolynomials.
4519 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_zero(
4520 __isl_take isl_space *space);
4521 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_alloc(
4522 __isl_take isl_set *set,
4523 __isl_take isl_qpolynomial *qp);
4524 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_from_qpolynomial(
4525 __isl_take isl_qpolynomial *qp);
4526 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_from_pw_aff(
4527 __isl_take isl_pw_aff *pwaff);
4529 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_zero(
4530 __isl_take isl_space *space);
4531 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_from_pw_qpolynomial(
4532 __isl_take isl_pw_qpolynomial *pwqp);
4533 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_add_pw_qpolynomial(
4534 __isl_take isl_union_pw_qpolynomial *upwqp,
4535 __isl_take isl_pw_qpolynomial *pwqp);
4537 Quasipolynomials can be copied and freed again using the following
4540 __isl_give isl_qpolynomial *isl_qpolynomial_copy(
4541 __isl_keep isl_qpolynomial *qp);
4542 void *isl_qpolynomial_free(__isl_take isl_qpolynomial *qp);
4544 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_copy(
4545 __isl_keep isl_pw_qpolynomial *pwqp);
4546 void *isl_pw_qpolynomial_free(
4547 __isl_take isl_pw_qpolynomial *pwqp);
4549 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_copy(
4550 __isl_keep isl_union_pw_qpolynomial *upwqp);
4551 void *isl_union_pw_qpolynomial_free(
4552 __isl_take isl_union_pw_qpolynomial *upwqp);
4554 =head3 Inspecting (Piecewise) Quasipolynomials
4556 To iterate over all piecewise quasipolynomials in a union
4557 piecewise quasipolynomial, use the following function
4559 int isl_union_pw_qpolynomial_foreach_pw_qpolynomial(
4560 __isl_keep isl_union_pw_qpolynomial *upwqp,
4561 int (*fn)(__isl_take isl_pw_qpolynomial *pwqp, void *user),
4564 To extract the piecewise quasipolynomial in a given space from a union, use
4566 __isl_give isl_pw_qpolynomial *
4567 isl_union_pw_qpolynomial_extract_pw_qpolynomial(
4568 __isl_keep isl_union_pw_qpolynomial *upwqp,
4569 __isl_take isl_space *space);
4571 To iterate over the cells in a piecewise quasipolynomial,
4572 use either of the following two functions
4574 int isl_pw_qpolynomial_foreach_piece(
4575 __isl_keep isl_pw_qpolynomial *pwqp,
4576 int (*fn)(__isl_take isl_set *set,
4577 __isl_take isl_qpolynomial *qp,
4578 void *user), void *user);
4579 int isl_pw_qpolynomial_foreach_lifted_piece(
4580 __isl_keep isl_pw_qpolynomial *pwqp,
4581 int (*fn)(__isl_take isl_set *set,
4582 __isl_take isl_qpolynomial *qp,
4583 void *user), void *user);
4585 As usual, the function C<fn> should return C<0> on success
4586 and C<-1> on failure. The difference between
4587 C<isl_pw_qpolynomial_foreach_piece> and
4588 C<isl_pw_qpolynomial_foreach_lifted_piece> is that
4589 C<isl_pw_qpolynomial_foreach_lifted_piece> will first
4590 compute unique representations for all existentially quantified
4591 variables and then turn these existentially quantified variables
4592 into extra set variables, adapting the associated quasipolynomial
4593 accordingly. This means that the C<set> passed to C<fn>
4594 will not have any existentially quantified variables, but that
4595 the dimensions of the sets may be different for different
4596 invocations of C<fn>.
4598 The constant term of a quasipolynomial can be extracted using
4600 __isl_give isl_val *isl_qpolynomial_get_constant_val(
4601 __isl_keep isl_qpolynomial *qp);
4603 To iterate over all terms in a quasipolynomial,
4606 int isl_qpolynomial_foreach_term(
4607 __isl_keep isl_qpolynomial *qp,
4608 int (*fn)(__isl_take isl_term *term,
4609 void *user), void *user);
4611 The terms themselves can be inspected and freed using
4614 unsigned isl_term_dim(__isl_keep isl_term *term,
4615 enum isl_dim_type type);
4616 __isl_give isl_val *isl_term_get_coefficient_val(
4617 __isl_keep isl_term *term);
4618 int isl_term_get_exp(__isl_keep isl_term *term,
4619 enum isl_dim_type type, unsigned pos);
4620 __isl_give isl_aff *isl_term_get_div(
4621 __isl_keep isl_term *term, unsigned pos);
4622 void isl_term_free(__isl_take isl_term *term);
4624 Each term is a product of parameters, set variables and
4625 integer divisions. The function C<isl_term_get_exp>
4626 returns the exponent of a given dimensions in the given term.
4628 =head3 Properties of (Piecewise) Quasipolynomials
4630 To check whether two union piecewise quasipolynomials are
4631 obviously equal, use
4633 int isl_union_pw_qpolynomial_plain_is_equal(
4634 __isl_keep isl_union_pw_qpolynomial *upwqp1,
4635 __isl_keep isl_union_pw_qpolynomial *upwqp2);
4637 =head3 Operations on (Piecewise) Quasipolynomials
4639 __isl_give isl_qpolynomial *isl_qpolynomial_scale_val(
4640 __isl_take isl_qpolynomial *qp,
4641 __isl_take isl_val *v);
4642 __isl_give isl_qpolynomial *isl_qpolynomial_neg(
4643 __isl_take isl_qpolynomial *qp);
4644 __isl_give isl_qpolynomial *isl_qpolynomial_add(
4645 __isl_take isl_qpolynomial *qp1,
4646 __isl_take isl_qpolynomial *qp2);
4647 __isl_give isl_qpolynomial *isl_qpolynomial_sub(
4648 __isl_take isl_qpolynomial *qp1,
4649 __isl_take isl_qpolynomial *qp2);
4650 __isl_give isl_qpolynomial *isl_qpolynomial_mul(
4651 __isl_take isl_qpolynomial *qp1,
4652 __isl_take isl_qpolynomial *qp2);
4653 __isl_give isl_qpolynomial *isl_qpolynomial_pow(
4654 __isl_take isl_qpolynomial *qp, unsigned exponent);
4656 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_fix_val(
4657 __isl_take isl_pw_qpolynomial *pwqp,
4658 enum isl_dim_type type, unsigned n,
4659 __isl_take isl_val *v);
4660 __isl_give isl_pw_qpolynomial *
4661 isl_pw_qpolynomial_scale_val(
4662 __isl_take isl_pw_qpolynomial *pwqp,
4663 __isl_take isl_val *v);
4664 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_add(
4665 __isl_take isl_pw_qpolynomial *pwqp1,
4666 __isl_take isl_pw_qpolynomial *pwqp2);
4667 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_sub(
4668 __isl_take isl_pw_qpolynomial *pwqp1,
4669 __isl_take isl_pw_qpolynomial *pwqp2);
4670 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_add_disjoint(
4671 __isl_take isl_pw_qpolynomial *pwqp1,
4672 __isl_take isl_pw_qpolynomial *pwqp2);
4673 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_neg(
4674 __isl_take isl_pw_qpolynomial *pwqp);
4675 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_mul(
4676 __isl_take isl_pw_qpolynomial *pwqp1,
4677 __isl_take isl_pw_qpolynomial *pwqp2);
4678 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_pow(
4679 __isl_take isl_pw_qpolynomial *pwqp, unsigned exponent);
4681 __isl_give isl_union_pw_qpolynomial *
4682 isl_union_pw_qpolynomial_scale_val(
4683 __isl_take isl_union_pw_qpolynomial *upwqp,
4684 __isl_take isl_val *v);
4685 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_add(
4686 __isl_take isl_union_pw_qpolynomial *upwqp1,
4687 __isl_take isl_union_pw_qpolynomial *upwqp2);
4688 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_sub(
4689 __isl_take isl_union_pw_qpolynomial *upwqp1,
4690 __isl_take isl_union_pw_qpolynomial *upwqp2);
4691 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_mul(
4692 __isl_take isl_union_pw_qpolynomial *upwqp1,
4693 __isl_take isl_union_pw_qpolynomial *upwqp2);
4695 __isl_give isl_val *isl_pw_qpolynomial_eval(
4696 __isl_take isl_pw_qpolynomial *pwqp,
4697 __isl_take isl_point *pnt);
4699 __isl_give isl_val *isl_union_pw_qpolynomial_eval(
4700 __isl_take isl_union_pw_qpolynomial *upwqp,
4701 __isl_take isl_point *pnt);
4703 __isl_give isl_set *isl_pw_qpolynomial_domain(
4704 __isl_take isl_pw_qpolynomial *pwqp);
4705 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_intersect_domain(
4706 __isl_take isl_pw_qpolynomial *pwpq,
4707 __isl_take isl_set *set);
4708 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_intersect_params(
4709 __isl_take isl_pw_qpolynomial *pwpq,
4710 __isl_take isl_set *set);
4712 __isl_give isl_union_set *isl_union_pw_qpolynomial_domain(
4713 __isl_take isl_union_pw_qpolynomial *upwqp);
4714 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_intersect_domain(
4715 __isl_take isl_union_pw_qpolynomial *upwpq,
4716 __isl_take isl_union_set *uset);
4717 __isl_give isl_union_pw_qpolynomial *
4718 isl_union_pw_qpolynomial_intersect_params(
4719 __isl_take isl_union_pw_qpolynomial *upwpq,
4720 __isl_take isl_set *set);
4722 __isl_give isl_qpolynomial *isl_qpolynomial_align_params(
4723 __isl_take isl_qpolynomial *qp,
4724 __isl_take isl_space *model);
4726 __isl_give isl_qpolynomial *isl_qpolynomial_project_domain_on_params(
4727 __isl_take isl_qpolynomial *qp);
4728 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_project_domain_on_params(
4729 __isl_take isl_pw_qpolynomial *pwqp);
4731 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_coalesce(
4732 __isl_take isl_union_pw_qpolynomial *upwqp);
4734 __isl_give isl_qpolynomial *isl_qpolynomial_gist_params(
4735 __isl_take isl_qpolynomial *qp,
4736 __isl_take isl_set *context);
4737 __isl_give isl_qpolynomial *isl_qpolynomial_gist(
4738 __isl_take isl_qpolynomial *qp,
4739 __isl_take isl_set *context);
4741 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_gist_params(
4742 __isl_take isl_pw_qpolynomial *pwqp,
4743 __isl_take isl_set *context);
4744 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_gist(
4745 __isl_take isl_pw_qpolynomial *pwqp,
4746 __isl_take isl_set *context);
4748 __isl_give isl_union_pw_qpolynomial *
4749 isl_union_pw_qpolynomial_gist_params(
4750 __isl_take isl_union_pw_qpolynomial *upwqp,
4751 __isl_take isl_set *context);
4752 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_gist(
4753 __isl_take isl_union_pw_qpolynomial *upwqp,
4754 __isl_take isl_union_set *context);
4756 The gist operation applies the gist operation to each of
4757 the cells in the domain of the input piecewise quasipolynomial.
4758 The context is also exploited
4759 to simplify the quasipolynomials associated to each cell.
4761 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_to_polynomial(
4762 __isl_take isl_pw_qpolynomial *pwqp, int sign);
4763 __isl_give isl_union_pw_qpolynomial *
4764 isl_union_pw_qpolynomial_to_polynomial(
4765 __isl_take isl_union_pw_qpolynomial *upwqp, int sign);
4767 Approximate each quasipolynomial by a polynomial. If C<sign> is positive,
4768 the polynomial will be an overapproximation. If C<sign> is negative,
4769 it will be an underapproximation. If C<sign> is zero, the approximation
4770 will lie somewhere in between.
4772 =head2 Bounds on Piecewise Quasipolynomials and Piecewise Quasipolynomial Reductions
4774 A piecewise quasipolynomial reduction is a piecewise
4775 reduction (or fold) of quasipolynomials.
4776 In particular, the reduction can be maximum or a minimum.
4777 The objects are mainly used to represent the result of
4778 an upper or lower bound on a quasipolynomial over its domain,
4779 i.e., as the result of the following function.
4781 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_bound(
4782 __isl_take isl_pw_qpolynomial *pwqp,
4783 enum isl_fold type, int *tight);
4785 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_bound(
4786 __isl_take isl_union_pw_qpolynomial *upwqp,
4787 enum isl_fold type, int *tight);
4789 The C<type> argument may be either C<isl_fold_min> or C<isl_fold_max>.
4790 If C<tight> is not C<NULL>, then C<*tight> is set to C<1>
4791 is the returned bound is known be tight, i.e., for each value
4792 of the parameters there is at least
4793 one element in the domain that reaches the bound.
4794 If the domain of C<pwqp> is not wrapping, then the bound is computed
4795 over all elements in that domain and the result has a purely parametric
4796 domain. If the domain of C<pwqp> is wrapping, then the bound is
4797 computed over the range of the wrapped relation. The domain of the
4798 wrapped relation becomes the domain of the result.
4800 A (piecewise) quasipolynomial reduction can be copied or freed using the
4801 following functions.
4803 __isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_copy(
4804 __isl_keep isl_qpolynomial_fold *fold);
4805 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_copy(
4806 __isl_keep isl_pw_qpolynomial_fold *pwf);
4807 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_copy(
4808 __isl_keep isl_union_pw_qpolynomial_fold *upwf);
4809 void isl_qpolynomial_fold_free(
4810 __isl_take isl_qpolynomial_fold *fold);
4811 void *isl_pw_qpolynomial_fold_free(
4812 __isl_take isl_pw_qpolynomial_fold *pwf);
4813 void *isl_union_pw_qpolynomial_fold_free(
4814 __isl_take isl_union_pw_qpolynomial_fold *upwf);
4816 =head3 Printing Piecewise Quasipolynomial Reductions
4818 Piecewise quasipolynomial reductions can be printed
4819 using the following function.
4821 __isl_give isl_printer *isl_printer_print_pw_qpolynomial_fold(
4822 __isl_take isl_printer *p,
4823 __isl_keep isl_pw_qpolynomial_fold *pwf);
4824 __isl_give isl_printer *isl_printer_print_union_pw_qpolynomial_fold(
4825 __isl_take isl_printer *p,
4826 __isl_keep isl_union_pw_qpolynomial_fold *upwf);
4828 For C<isl_printer_print_pw_qpolynomial_fold>,
4829 output format of the printer
4830 needs to be set to either C<ISL_FORMAT_ISL> or C<ISL_FORMAT_C>.
4831 For C<isl_printer_print_union_pw_qpolynomial_fold>,
4832 output format of the printer
4833 needs to be set to C<ISL_FORMAT_ISL>.
4834 In case of printing in C<ISL_FORMAT_C>, the user may want
4835 to set the names of all dimensions
4837 __isl_give isl_pw_qpolynomial_fold *
4838 isl_pw_qpolynomial_fold_set_dim_name(
4839 __isl_take isl_pw_qpolynomial_fold *pwf,
4840 enum isl_dim_type type, unsigned pos,
4843 =head3 Inspecting (Piecewise) Quasipolynomial Reductions
4845 To iterate over all piecewise quasipolynomial reductions in a union
4846 piecewise quasipolynomial reduction, use the following function
4848 int isl_union_pw_qpolynomial_fold_foreach_pw_qpolynomial_fold(
4849 __isl_keep isl_union_pw_qpolynomial_fold *upwf,
4850 int (*fn)(__isl_take isl_pw_qpolynomial_fold *pwf,
4851 void *user), void *user);
4853 To iterate over the cells in a piecewise quasipolynomial reduction,
4854 use either of the following two functions
4856 int isl_pw_qpolynomial_fold_foreach_piece(
4857 __isl_keep isl_pw_qpolynomial_fold *pwf,
4858 int (*fn)(__isl_take isl_set *set,
4859 __isl_take isl_qpolynomial_fold *fold,
4860 void *user), void *user);
4861 int isl_pw_qpolynomial_fold_foreach_lifted_piece(
4862 __isl_keep isl_pw_qpolynomial_fold *pwf,
4863 int (*fn)(__isl_take isl_set *set,
4864 __isl_take isl_qpolynomial_fold *fold,
4865 void *user), void *user);
4867 See L<Inspecting (Piecewise) Quasipolynomials> for an explanation
4868 of the difference between these two functions.
4870 To iterate over all quasipolynomials in a reduction, use
4872 int isl_qpolynomial_fold_foreach_qpolynomial(
4873 __isl_keep isl_qpolynomial_fold *fold,
4874 int (*fn)(__isl_take isl_qpolynomial *qp,
4875 void *user), void *user);
4877 =head3 Properties of Piecewise Quasipolynomial Reductions
4879 To check whether two union piecewise quasipolynomial reductions are
4880 obviously equal, use
4882 int isl_union_pw_qpolynomial_fold_plain_is_equal(
4883 __isl_keep isl_union_pw_qpolynomial_fold *upwf1,
4884 __isl_keep isl_union_pw_qpolynomial_fold *upwf2);
4886 =head3 Operations on Piecewise Quasipolynomial Reductions
4888 __isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_scale_val(
4889 __isl_take isl_qpolynomial_fold *fold,
4890 __isl_take isl_val *v);
4891 __isl_give isl_pw_qpolynomial_fold *
4892 isl_pw_qpolynomial_fold_scale_val(
4893 __isl_take isl_pw_qpolynomial_fold *pwf,
4894 __isl_take isl_val *v);
4895 __isl_give isl_union_pw_qpolynomial_fold *
4896 isl_union_pw_qpolynomial_fold_scale_val(
4897 __isl_take isl_union_pw_qpolynomial_fold *upwf,
4898 __isl_take isl_val *v);
4900 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_add(
4901 __isl_take isl_pw_qpolynomial_fold *pwf1,
4902 __isl_take isl_pw_qpolynomial_fold *pwf2);
4904 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_fold(
4905 __isl_take isl_pw_qpolynomial_fold *pwf1,
4906 __isl_take isl_pw_qpolynomial_fold *pwf2);
4908 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_fold(
4909 __isl_take isl_union_pw_qpolynomial_fold *upwf1,
4910 __isl_take isl_union_pw_qpolynomial_fold *upwf2);
4912 __isl_give isl_val *isl_pw_qpolynomial_fold_eval(
4913 __isl_take isl_pw_qpolynomial_fold *pwf,
4914 __isl_take isl_point *pnt);
4916 __isl_give isl_val *isl_union_pw_qpolynomial_fold_eval(
4917 __isl_take isl_union_pw_qpolynomial_fold *upwf,
4918 __isl_take isl_point *pnt);
4920 __isl_give isl_pw_qpolynomial_fold *
4921 isl_pw_qpolynomial_fold_intersect_params(
4922 __isl_take isl_pw_qpolynomial_fold *pwf,
4923 __isl_take isl_set *set);
4925 __isl_give isl_union_set *isl_union_pw_qpolynomial_fold_domain(
4926 __isl_take isl_union_pw_qpolynomial_fold *upwf);
4927 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_intersect_domain(
4928 __isl_take isl_union_pw_qpolynomial_fold *upwf,
4929 __isl_take isl_union_set *uset);
4930 __isl_give isl_union_pw_qpolynomial_fold *
4931 isl_union_pw_qpolynomial_fold_intersect_params(
4932 __isl_take isl_union_pw_qpolynomial_fold *upwf,
4933 __isl_take isl_set *set);
4935 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_project_domain_on_params(
4936 __isl_take isl_pw_qpolynomial_fold *pwf);
4938 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_coalesce(
4939 __isl_take isl_pw_qpolynomial_fold *pwf);
4941 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_coalesce(
4942 __isl_take isl_union_pw_qpolynomial_fold *upwf);
4944 __isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_gist_params(
4945 __isl_take isl_qpolynomial_fold *fold,
4946 __isl_take isl_set *context);
4947 __isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_gist(
4948 __isl_take isl_qpolynomial_fold *fold,
4949 __isl_take isl_set *context);
4951 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_gist(
4952 __isl_take isl_pw_qpolynomial_fold *pwf,
4953 __isl_take isl_set *context);
4954 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_gist_params(
4955 __isl_take isl_pw_qpolynomial_fold *pwf,
4956 __isl_take isl_set *context);
4958 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_gist(
4959 __isl_take isl_union_pw_qpolynomial_fold *upwf,
4960 __isl_take isl_union_set *context);
4961 __isl_give isl_union_pw_qpolynomial_fold *
4962 isl_union_pw_qpolynomial_fold_gist_params(
4963 __isl_take isl_union_pw_qpolynomial_fold *upwf,
4964 __isl_take isl_set *context);
4966 The gist operation applies the gist operation to each of
4967 the cells in the domain of the input piecewise quasipolynomial reduction.
4968 In future, the operation will also exploit the context
4969 to simplify the quasipolynomial reductions associated to each cell.
4971 __isl_give isl_pw_qpolynomial_fold *
4972 isl_set_apply_pw_qpolynomial_fold(
4973 __isl_take isl_set *set,
4974 __isl_take isl_pw_qpolynomial_fold *pwf,
4976 __isl_give isl_pw_qpolynomial_fold *
4977 isl_map_apply_pw_qpolynomial_fold(
4978 __isl_take isl_map *map,
4979 __isl_take isl_pw_qpolynomial_fold *pwf,
4981 __isl_give isl_union_pw_qpolynomial_fold *
4982 isl_union_set_apply_union_pw_qpolynomial_fold(
4983 __isl_take isl_union_set *uset,
4984 __isl_take isl_union_pw_qpolynomial_fold *upwf,
4986 __isl_give isl_union_pw_qpolynomial_fold *
4987 isl_union_map_apply_union_pw_qpolynomial_fold(
4988 __isl_take isl_union_map *umap,
4989 __isl_take isl_union_pw_qpolynomial_fold *upwf,
4992 The functions taking a map
4993 compose the given map with the given piecewise quasipolynomial reduction.
4994 That is, compute a bound (of the same type as C<pwf> or C<upwf> itself)
4995 over all elements in the intersection of the range of the map
4996 and the domain of the piecewise quasipolynomial reduction
4997 as a function of an element in the domain of the map.
4998 The functions taking a set compute a bound over all elements in the
4999 intersection of the set and the domain of the
5000 piecewise quasipolynomial reduction.
5002 =head2 Parametric Vertex Enumeration
5004 The parametric vertex enumeration described in this section
5005 is mainly intended to be used internally and by the C<barvinok>
5008 #include <isl/vertices.h>
5009 __isl_give isl_vertices *isl_basic_set_compute_vertices(
5010 __isl_keep isl_basic_set *bset);
5012 The function C<isl_basic_set_compute_vertices> performs the
5013 actual computation of the parametric vertices and the chamber
5014 decomposition and store the result in an C<isl_vertices> object.
5015 This information can be queried by either iterating over all
5016 the vertices or iterating over all the chambers or cells
5017 and then iterating over all vertices that are active on the chamber.
5019 int isl_vertices_foreach_vertex(
5020 __isl_keep isl_vertices *vertices,
5021 int (*fn)(__isl_take isl_vertex *vertex, void *user),
5024 int isl_vertices_foreach_cell(
5025 __isl_keep isl_vertices *vertices,
5026 int (*fn)(__isl_take isl_cell *cell, void *user),
5028 int isl_cell_foreach_vertex(__isl_keep isl_cell *cell,
5029 int (*fn)(__isl_take isl_vertex *vertex, void *user),
5032 Other operations that can be performed on an C<isl_vertices> object are
5035 isl_ctx *isl_vertices_get_ctx(
5036 __isl_keep isl_vertices *vertices);
5037 int isl_vertices_get_n_vertices(
5038 __isl_keep isl_vertices *vertices);
5039 void isl_vertices_free(__isl_take isl_vertices *vertices);
5041 Vertices can be inspected and destroyed using the following functions.
5043 isl_ctx *isl_vertex_get_ctx(__isl_keep isl_vertex *vertex);
5044 int isl_vertex_get_id(__isl_keep isl_vertex *vertex);
5045 __isl_give isl_basic_set *isl_vertex_get_domain(
5046 __isl_keep isl_vertex *vertex);
5047 __isl_give isl_basic_set *isl_vertex_get_expr(
5048 __isl_keep isl_vertex *vertex);
5049 void isl_vertex_free(__isl_take isl_vertex *vertex);
5051 C<isl_vertex_get_expr> returns a singleton parametric set describing
5052 the vertex, while C<isl_vertex_get_domain> returns the activity domain
5054 Note that C<isl_vertex_get_domain> and C<isl_vertex_get_expr> return
5055 B<rational> basic sets, so they should mainly be used for inspection
5056 and should not be mixed with integer sets.
5058 Chambers can be inspected and destroyed using the following functions.
5060 isl_ctx *isl_cell_get_ctx(__isl_keep isl_cell *cell);
5061 __isl_give isl_basic_set *isl_cell_get_domain(
5062 __isl_keep isl_cell *cell);
5063 void isl_cell_free(__isl_take isl_cell *cell);
5065 =head1 Polyhedral Compilation Library
5067 This section collects functionality in C<isl> that has been specifically
5068 designed for use during polyhedral compilation.
5070 =head2 Dependence Analysis
5072 C<isl> contains specialized functionality for performing
5073 array dataflow analysis. That is, given a I<sink> access relation
5074 and a collection of possible I<source> access relations,
5075 C<isl> can compute relations that describe
5076 for each iteration of the sink access, which iteration
5077 of which of the source access relations was the last
5078 to access the same data element before the given iteration
5080 The resulting dependence relations map source iterations
5081 to the corresponding sink iterations.
5082 To compute standard flow dependences, the sink should be
5083 a read, while the sources should be writes.
5084 If any of the source accesses are marked as being I<may>
5085 accesses, then there will be a dependence from the last
5086 I<must> access B<and> from any I<may> access that follows
5087 this last I<must> access.
5088 In particular, if I<all> sources are I<may> accesses,
5089 then memory based dependence analysis is performed.
5090 If, on the other hand, all sources are I<must> accesses,
5091 then value based dependence analysis is performed.
5093 #include <isl/flow.h>
5095 typedef int (*isl_access_level_before)(void *first, void *second);
5097 __isl_give isl_access_info *isl_access_info_alloc(
5098 __isl_take isl_map *sink,
5099 void *sink_user, isl_access_level_before fn,
5101 __isl_give isl_access_info *isl_access_info_add_source(
5102 __isl_take isl_access_info *acc,
5103 __isl_take isl_map *source, int must,
5105 void *isl_access_info_free(__isl_take isl_access_info *acc);
5107 __isl_give isl_flow *isl_access_info_compute_flow(
5108 __isl_take isl_access_info *acc);
5110 int isl_flow_foreach(__isl_keep isl_flow *deps,
5111 int (*fn)(__isl_take isl_map *dep, int must,
5112 void *dep_user, void *user),
5114 __isl_give isl_map *isl_flow_get_no_source(
5115 __isl_keep isl_flow *deps, int must);
5116 void isl_flow_free(__isl_take isl_flow *deps);
5118 The function C<isl_access_info_compute_flow> performs the actual
5119 dependence analysis. The other functions are used to construct
5120 the input for this function or to read off the output.
5122 The input is collected in an C<isl_access_info>, which can
5123 be created through a call to C<isl_access_info_alloc>.
5124 The arguments to this functions are the sink access relation
5125 C<sink>, a token C<sink_user> used to identify the sink
5126 access to the user, a callback function for specifying the
5127 relative order of source and sink accesses, and the number
5128 of source access relations that will be added.
5129 The callback function has type C<int (*)(void *first, void *second)>.
5130 The function is called with two user supplied tokens identifying
5131 either a source or the sink and it should return the shared nesting
5132 level and the relative order of the two accesses.
5133 In particular, let I<n> be the number of loops shared by
5134 the two accesses. If C<first> precedes C<second> textually,
5135 then the function should return I<2 * n + 1>; otherwise,
5136 it should return I<2 * n>.
5137 The sources can be added to the C<isl_access_info> by performing
5138 (at most) C<max_source> calls to C<isl_access_info_add_source>.
5139 C<must> indicates whether the source is a I<must> access
5140 or a I<may> access. Note that a multi-valued access relation
5141 should only be marked I<must> if every iteration in the domain
5142 of the relation accesses I<all> elements in its image.
5143 The C<source_user> token is again used to identify
5144 the source access. The range of the source access relation
5145 C<source> should have the same dimension as the range
5146 of the sink access relation.
5147 The C<isl_access_info_free> function should usually not be
5148 called explicitly, because it is called implicitly by
5149 C<isl_access_info_compute_flow>.
5151 The result of the dependence analysis is collected in an
5152 C<isl_flow>. There may be elements of
5153 the sink access for which no preceding source access could be
5154 found or for which all preceding sources are I<may> accesses.
5155 The relations containing these elements can be obtained through
5156 calls to C<isl_flow_get_no_source>, the first with C<must> set
5157 and the second with C<must> unset.
5158 In the case of standard flow dependence analysis,
5159 with the sink a read and the sources I<must> writes,
5160 the first relation corresponds to the reads from uninitialized
5161 array elements and the second relation is empty.
5162 The actual flow dependences can be extracted using
5163 C<isl_flow_foreach>. This function will call the user-specified
5164 callback function C<fn> for each B<non-empty> dependence between
5165 a source and the sink. The callback function is called
5166 with four arguments, the actual flow dependence relation
5167 mapping source iterations to sink iterations, a boolean that
5168 indicates whether it is a I<must> or I<may> dependence, a token
5169 identifying the source and an additional C<void *> with value
5170 equal to the third argument of the C<isl_flow_foreach> call.
5171 A dependence is marked I<must> if it originates from a I<must>
5172 source and if it is not followed by any I<may> sources.
5174 After finishing with an C<isl_flow>, the user should call
5175 C<isl_flow_free> to free all associated memory.
5177 A higher-level interface to dependence analysis is provided
5178 by the following function.
5180 #include <isl/flow.h>
5182 int isl_union_map_compute_flow(__isl_take isl_union_map *sink,
5183 __isl_take isl_union_map *must_source,
5184 __isl_take isl_union_map *may_source,
5185 __isl_take isl_union_map *schedule,
5186 __isl_give isl_union_map **must_dep,
5187 __isl_give isl_union_map **may_dep,
5188 __isl_give isl_union_map **must_no_source,
5189 __isl_give isl_union_map **may_no_source);
5191 The arrays are identified by the tuple names of the ranges
5192 of the accesses. The iteration domains by the tuple names
5193 of the domains of the accesses and of the schedule.
5194 The relative order of the iteration domains is given by the
5195 schedule. The relations returned through C<must_no_source>
5196 and C<may_no_source> are subsets of C<sink>.
5197 Any of C<must_dep>, C<may_dep>, C<must_no_source>
5198 or C<may_no_source> may be C<NULL>, but a C<NULL> value for
5199 any of the other arguments is treated as an error.
5201 =head3 Interaction with Dependence Analysis
5203 During the dependence analysis, we frequently need to perform
5204 the following operation. Given a relation between sink iterations
5205 and potential source iterations from a particular source domain,
5206 what is the last potential source iteration corresponding to each
5207 sink iteration. It can sometimes be convenient to adjust
5208 the set of potential source iterations before or after each such operation.
5209 The prototypical example is fuzzy array dataflow analysis,
5210 where we need to analyze if, based on data-dependent constraints,
5211 the sink iteration can ever be executed without one or more of
5212 the corresponding potential source iterations being executed.
5213 If so, we can introduce extra parameters and select an unknown
5214 but fixed source iteration from the potential source iterations.
5215 To be able to perform such manipulations, C<isl> provides the following
5218 #include <isl/flow.h>
5220 typedef __isl_give isl_restriction *(*isl_access_restrict)(
5221 __isl_keep isl_map *source_map,
5222 __isl_keep isl_set *sink, void *source_user,
5224 __isl_give isl_access_info *isl_access_info_set_restrict(
5225 __isl_take isl_access_info *acc,
5226 isl_access_restrict fn, void *user);
5228 The function C<isl_access_info_set_restrict> should be called
5229 before calling C<isl_access_info_compute_flow> and registers a callback function
5230 that will be called any time C<isl> is about to compute the last
5231 potential source. The first argument is the (reverse) proto-dependence,
5232 mapping sink iterations to potential source iterations.
5233 The second argument represents the sink iterations for which
5234 we want to compute the last source iteration.
5235 The third argument is the token corresponding to the source
5236 and the final argument is the token passed to C<isl_access_info_set_restrict>.
5237 The callback is expected to return a restriction on either the input or
5238 the output of the operation computing the last potential source.
5239 If the input needs to be restricted then restrictions are needed
5240 for both the source and the sink iterations. The sink iterations
5241 and the potential source iterations will be intersected with these sets.
5242 If the output needs to be restricted then only a restriction on the source
5243 iterations is required.
5244 If any error occurs, the callback should return C<NULL>.
5245 An C<isl_restriction> object can be created, freed and inspected
5246 using the following functions.
5248 #include <isl/flow.h>
5250 __isl_give isl_restriction *isl_restriction_input(
5251 __isl_take isl_set *source_restr,
5252 __isl_take isl_set *sink_restr);
5253 __isl_give isl_restriction *isl_restriction_output(
5254 __isl_take isl_set *source_restr);
5255 __isl_give isl_restriction *isl_restriction_none(
5256 __isl_take isl_map *source_map);
5257 __isl_give isl_restriction *isl_restriction_empty(
5258 __isl_take isl_map *source_map);
5259 void *isl_restriction_free(
5260 __isl_take isl_restriction *restr);
5261 isl_ctx *isl_restriction_get_ctx(
5262 __isl_keep isl_restriction *restr);
5264 C<isl_restriction_none> and C<isl_restriction_empty> are special
5265 cases of C<isl_restriction_input>. C<isl_restriction_none>
5266 is essentially equivalent to
5268 isl_restriction_input(isl_set_universe(
5269 isl_space_range(isl_map_get_space(source_map))),
5271 isl_space_domain(isl_map_get_space(source_map))));
5273 whereas C<isl_restriction_empty> is essentially equivalent to
5275 isl_restriction_input(isl_set_empty(
5276 isl_space_range(isl_map_get_space(source_map))),
5278 isl_space_domain(isl_map_get_space(source_map))));
5282 B<The functionality described in this section is fairly new
5283 and may be subject to change.>
5285 The following function can be used to compute a schedule
5286 for a union of domains.
5287 By default, the algorithm used to construct the schedule is similar
5288 to that of C<Pluto>.
5289 Alternatively, Feautrier's multi-dimensional scheduling algorithm can
5291 The generated schedule respects all C<validity> dependences.
5292 That is, all dependence distances over these dependences in the
5293 scheduled space are lexicographically positive.
5294 The default algorithm tries to minimize the dependence distances over
5295 C<proximity> dependences.
5296 Moreover, it tries to obtain sequences (bands) of schedule dimensions
5297 for groups of domains where the dependence distances have only
5298 non-negative values.
5299 When using Feautrier's algorithm, the C<proximity> dependence
5300 distances are only minimized during the extension to a
5301 full-dimensional schedule.
5303 #include <isl/schedule.h>
5304 __isl_give isl_schedule *isl_union_set_compute_schedule(
5305 __isl_take isl_union_set *domain,
5306 __isl_take isl_union_map *validity,
5307 __isl_take isl_union_map *proximity);
5308 void *isl_schedule_free(__isl_take isl_schedule *sched);
5310 A mapping from the domains to the scheduled space can be obtained
5311 from an C<isl_schedule> using the following function.
5313 __isl_give isl_union_map *isl_schedule_get_map(
5314 __isl_keep isl_schedule *sched);
5316 A representation of the schedule can be printed using
5318 __isl_give isl_printer *isl_printer_print_schedule(
5319 __isl_take isl_printer *p,
5320 __isl_keep isl_schedule *schedule);
5322 A representation of the schedule as a forest of bands can be obtained
5323 using the following function.
5325 __isl_give isl_band_list *isl_schedule_get_band_forest(
5326 __isl_keep isl_schedule *schedule);
5328 The individual bands can be visited in depth-first post-order
5329 using the following function.
5331 #include <isl/schedule.h>
5332 int isl_schedule_foreach_band(
5333 __isl_keep isl_schedule *sched,
5334 int (*fn)(__isl_keep isl_band *band, void *user),
5337 The list can be manipulated as explained in L<"Lists">.
5338 The bands inside the list can be copied and freed using the following
5341 #include <isl/band.h>
5342 __isl_give isl_band *isl_band_copy(
5343 __isl_keep isl_band *band);
5344 void *isl_band_free(__isl_take isl_band *band);
5346 Each band contains zero or more scheduling dimensions.
5347 These are referred to as the members of the band.
5348 The section of the schedule that corresponds to the band is
5349 referred to as the partial schedule of the band.
5350 For those nodes that participate in a band, the outer scheduling
5351 dimensions form the prefix schedule, while the inner scheduling
5352 dimensions form the suffix schedule.
5353 That is, if we take a cut of the band forest, then the union of
5354 the concatenations of the prefix, partial and suffix schedules of
5355 each band in the cut is equal to the entire schedule (modulo
5356 some possible padding at the end with zero scheduling dimensions).
5357 The properties of a band can be inspected using the following functions.
5359 #include <isl/band.h>
5360 isl_ctx *isl_band_get_ctx(__isl_keep isl_band *band);
5362 int isl_band_has_children(__isl_keep isl_band *band);
5363 __isl_give isl_band_list *isl_band_get_children(
5364 __isl_keep isl_band *band);
5366 __isl_give isl_union_map *isl_band_get_prefix_schedule(
5367 __isl_keep isl_band *band);
5368 __isl_give isl_union_map *isl_band_get_partial_schedule(
5369 __isl_keep isl_band *band);
5370 __isl_give isl_union_map *isl_band_get_suffix_schedule(
5371 __isl_keep isl_band *band);
5373 int isl_band_n_member(__isl_keep isl_band *band);
5374 int isl_band_member_is_zero_distance(
5375 __isl_keep isl_band *band, int pos);
5377 int isl_band_list_foreach_band(
5378 __isl_keep isl_band_list *list,
5379 int (*fn)(__isl_keep isl_band *band, void *user),
5382 Note that a scheduling dimension is considered to be ``zero
5383 distance'' if it does not carry any proximity dependences
5385 That is, if the dependence distances of the proximity
5386 dependences are all zero in that direction (for fixed
5387 iterations of outer bands).
5388 Like C<isl_schedule_foreach_band>,
5389 the function C<isl_band_list_foreach_band> calls C<fn> on the bands
5390 in depth-first post-order.
5392 A band can be tiled using the following function.
5394 #include <isl/band.h>
5395 int isl_band_tile(__isl_keep isl_band *band,
5396 __isl_take isl_vec *sizes);
5398 int isl_options_set_tile_scale_tile_loops(isl_ctx *ctx,
5400 int isl_options_get_tile_scale_tile_loops(isl_ctx *ctx);
5401 int isl_options_set_tile_shift_point_loops(isl_ctx *ctx,
5403 int isl_options_get_tile_shift_point_loops(isl_ctx *ctx);
5405 The C<isl_band_tile> function tiles the band using the given tile sizes
5406 inside its schedule.
5407 A new child band is created to represent the point loops and it is
5408 inserted between the modified band and its children.
5409 The C<tile_scale_tile_loops> option specifies whether the tile
5410 loops iterators should be scaled by the tile sizes.
5411 If the C<tile_shift_point_loops> option is set, then the point loops
5412 are shifted to start at zero.
5414 A band can be split into two nested bands using the following function.
5416 int isl_band_split(__isl_keep isl_band *band, int pos);
5418 The resulting outer band contains the first C<pos> dimensions of C<band>
5419 while the inner band contains the remaining dimensions.
5421 A representation of the band can be printed using
5423 #include <isl/band.h>
5424 __isl_give isl_printer *isl_printer_print_band(
5425 __isl_take isl_printer *p,
5426 __isl_keep isl_band *band);
5430 #include <isl/schedule.h>
5431 int isl_options_set_schedule_max_coefficient(
5432 isl_ctx *ctx, int val);
5433 int isl_options_get_schedule_max_coefficient(
5435 int isl_options_set_schedule_max_constant_term(
5436 isl_ctx *ctx, int val);
5437 int isl_options_get_schedule_max_constant_term(
5439 int isl_options_set_schedule_fuse(isl_ctx *ctx, int val);
5440 int isl_options_get_schedule_fuse(isl_ctx *ctx);
5441 int isl_options_set_schedule_maximize_band_depth(
5442 isl_ctx *ctx, int val);
5443 int isl_options_get_schedule_maximize_band_depth(
5445 int isl_options_set_schedule_outer_zero_distance(
5446 isl_ctx *ctx, int val);
5447 int isl_options_get_schedule_outer_zero_distance(
5449 int isl_options_set_schedule_split_scaled(
5450 isl_ctx *ctx, int val);
5451 int isl_options_get_schedule_split_scaled(
5453 int isl_options_set_schedule_algorithm(
5454 isl_ctx *ctx, int val);
5455 int isl_options_get_schedule_algorithm(
5457 int isl_options_set_schedule_separate_components(
5458 isl_ctx *ctx, int val);
5459 int isl_options_get_schedule_separate_components(
5464 =item * schedule_max_coefficient
5466 This option enforces that the coefficients for variable and parameter
5467 dimensions in the calculated schedule are not larger than the specified value.
5468 This option can significantly increase the speed of the scheduling calculation
5469 and may also prevent fusing of unrelated dimensions. A value of -1 means that
5470 this option does not introduce bounds on the variable or parameter
5473 =item * schedule_max_constant_term
5475 This option enforces that the constant coefficients in the calculated schedule
5476 are not larger than the maximal constant term. This option can significantly
5477 increase the speed of the scheduling calculation and may also prevent fusing of
5478 unrelated dimensions. A value of -1 means that this option does not introduce
5479 bounds on the constant coefficients.
5481 =item * schedule_fuse
5483 This option controls the level of fusion.
5484 If this option is set to C<ISL_SCHEDULE_FUSE_MIN>, then loops in the
5485 resulting schedule will be distributed as much as possible.
5486 If this option is set to C<ISL_SCHEDULE_FUSE_MAX>, then C<isl> will
5487 try to fuse loops in the resulting schedule.
5489 =item * schedule_maximize_band_depth
5491 If this option is set, we do not split bands at the point
5492 where we detect splitting is necessary. Instead, we
5493 backtrack and split bands as early as possible. This
5494 reduces the number of splits and maximizes the width of
5495 the bands. Wider bands give more possibilities for tiling.
5496 Note that if the C<schedule_fuse> option is set to C<ISL_SCHEDULE_FUSE_MIN>,
5497 then bands will be split as early as possible, even if there is no need.
5498 The C<schedule_maximize_band_depth> option therefore has no effect in this case.
5500 =item * schedule_outer_zero_distance
5502 If this option is set, then we try to construct schedules
5503 where the outermost scheduling dimension in each band
5504 results in a zero dependence distance over the proximity
5507 =item * schedule_split_scaled
5509 If this option is set, then we try to construct schedules in which the
5510 constant term is split off from the linear part if the linear parts of
5511 the scheduling rows for all nodes in the graphs have a common non-trivial
5513 The constant term is then placed in a separate band and the linear
5516 =item * schedule_algorithm
5518 Selects the scheduling algorithm to be used.
5519 Available scheduling algorithms are C<ISL_SCHEDULE_ALGORITHM_ISL>
5520 and C<ISL_SCHEDULE_ALGORITHM_FEAUTRIER>.
5522 =item * schedule_separate_components
5524 If at any point the dependence graph contains any (weakly connected) components,
5525 then these components are scheduled separately.
5526 If this option is not set, then some iterations of the domains
5527 in these components may be scheduled together.
5528 If this option is set, then the components are given consecutive
5533 =head2 AST Generation
5535 This section describes the C<isl> functionality for generating
5536 ASTs that visit all the elements
5537 in a domain in an order specified by a schedule.
5538 In particular, given a C<isl_union_map>, an AST is generated
5539 that visits all the elements in the domain of the C<isl_union_map>
5540 according to the lexicographic order of the corresponding image
5541 element(s). If the range of the C<isl_union_map> consists of
5542 elements in more than one space, then each of these spaces is handled
5543 separately in an arbitrary order.
5544 It should be noted that the image elements only specify the I<order>
5545 in which the corresponding domain elements should be visited.
5546 No direct relation between the image elements and the loop iterators
5547 in the generated AST should be assumed.
5549 Each AST is generated within a build. The initial build
5550 simply specifies the constraints on the parameters (if any)
5551 and can be created, inspected, copied and freed using the following functions.
5553 #include <isl/ast_build.h>
5554 __isl_give isl_ast_build *isl_ast_build_from_context(
5555 __isl_take isl_set *set);
5556 isl_ctx *isl_ast_build_get_ctx(
5557 __isl_keep isl_ast_build *build);
5558 __isl_give isl_ast_build *isl_ast_build_copy(
5559 __isl_keep isl_ast_build *build);
5560 void *isl_ast_build_free(
5561 __isl_take isl_ast_build *build);
5563 The C<set> argument is usually a parameter set with zero or more parameters.
5564 More C<isl_ast_build> functions are described in L</"Nested AST Generation">
5565 and L</"Fine-grained Control over AST Generation">.
5566 Finally, the AST itself can be constructed using the following
5569 #include <isl/ast_build.h>
5570 __isl_give isl_ast_node *isl_ast_build_ast_from_schedule(
5571 __isl_keep isl_ast_build *build,
5572 __isl_take isl_union_map *schedule);
5574 =head3 Inspecting the AST
5576 The basic properties of an AST node can be obtained as follows.
5578 #include <isl/ast.h>
5579 isl_ctx *isl_ast_node_get_ctx(
5580 __isl_keep isl_ast_node *node);
5581 enum isl_ast_node_type isl_ast_node_get_type(
5582 __isl_keep isl_ast_node *node);
5584 The type of an AST node is one of
5585 C<isl_ast_node_for>,
5587 C<isl_ast_node_block> or
5588 C<isl_ast_node_user>.
5589 An C<isl_ast_node_for> represents a for node.
5590 An C<isl_ast_node_if> represents an if node.
5591 An C<isl_ast_node_block> represents a compound node.
5592 An C<isl_ast_node_user> represents an expression statement.
5593 An expression statement typically corresponds to a domain element, i.e.,
5594 one of the elements that is visited by the AST.
5596 Each type of node has its own additional properties.
5598 #include <isl/ast.h>
5599 __isl_give isl_ast_expr *isl_ast_node_for_get_iterator(
5600 __isl_keep isl_ast_node *node);
5601 __isl_give isl_ast_expr *isl_ast_node_for_get_init(
5602 __isl_keep isl_ast_node *node);
5603 __isl_give isl_ast_expr *isl_ast_node_for_get_cond(
5604 __isl_keep isl_ast_node *node);
5605 __isl_give isl_ast_expr *isl_ast_node_for_get_inc(
5606 __isl_keep isl_ast_node *node);
5607 __isl_give isl_ast_node *isl_ast_node_for_get_body(
5608 __isl_keep isl_ast_node *node);
5609 int isl_ast_node_for_is_degenerate(
5610 __isl_keep isl_ast_node *node);
5612 An C<isl_ast_for> is considered degenerate if it is known to execute
5615 #include <isl/ast.h>
5616 __isl_give isl_ast_expr *isl_ast_node_if_get_cond(
5617 __isl_keep isl_ast_node *node);
5618 __isl_give isl_ast_node *isl_ast_node_if_get_then(
5619 __isl_keep isl_ast_node *node);
5620 int isl_ast_node_if_has_else(
5621 __isl_keep isl_ast_node *node);
5622 __isl_give isl_ast_node *isl_ast_node_if_get_else(
5623 __isl_keep isl_ast_node *node);
5625 __isl_give isl_ast_node_list *
5626 isl_ast_node_block_get_children(
5627 __isl_keep isl_ast_node *node);
5629 __isl_give isl_ast_expr *isl_ast_node_user_get_expr(
5630 __isl_keep isl_ast_node *node);
5632 Each of the returned C<isl_ast_expr>s can in turn be inspected using
5633 the following functions.
5635 #include <isl/ast.h>
5636 isl_ctx *isl_ast_expr_get_ctx(
5637 __isl_keep isl_ast_expr *expr);
5638 enum isl_ast_expr_type isl_ast_expr_get_type(
5639 __isl_keep isl_ast_expr *expr);
5641 The type of an AST expression is one of
5643 C<isl_ast_expr_id> or
5644 C<isl_ast_expr_int>.
5645 An C<isl_ast_expr_op> represents the result of an operation.
5646 An C<isl_ast_expr_id> represents an identifier.
5647 An C<isl_ast_expr_int> represents an integer value.
5649 Each type of expression has its own additional properties.
5651 #include <isl/ast.h>
5652 enum isl_ast_op_type isl_ast_expr_get_op_type(
5653 __isl_keep isl_ast_expr *expr);
5654 int isl_ast_expr_get_op_n_arg(__isl_keep isl_ast_expr *expr);
5655 __isl_give isl_ast_expr *isl_ast_expr_get_op_arg(
5656 __isl_keep isl_ast_expr *expr, int pos);
5657 int isl_ast_node_foreach_ast_op_type(
5658 __isl_keep isl_ast_node *node,
5659 int (*fn)(enum isl_ast_op_type type, void *user),
5662 C<isl_ast_expr_get_op_type> returns the type of the operation
5663 performed. C<isl_ast_expr_get_op_n_arg> returns the number of
5664 arguments. C<isl_ast_expr_get_op_arg> returns the specified
5666 C<isl_ast_node_foreach_ast_op_type> calls C<fn> for each distinct
5667 C<isl_ast_op_type> that appears in C<node>.
5668 The operation type is one of the following.
5672 =item C<isl_ast_op_and>
5674 Logical I<and> of two arguments.
5675 Both arguments can be evaluated.
5677 =item C<isl_ast_op_and_then>
5679 Logical I<and> of two arguments.
5680 The second argument can only be evaluated if the first evaluates to true.
5682 =item C<isl_ast_op_or>
5684 Logical I<or> of two arguments.
5685 Both arguments can be evaluated.
5687 =item C<isl_ast_op_or_else>
5689 Logical I<or> of two arguments.
5690 The second argument can only be evaluated if the first evaluates to false.
5692 =item C<isl_ast_op_max>
5694 Maximum of two or more arguments.
5696 =item C<isl_ast_op_min>
5698 Minimum of two or more arguments.
5700 =item C<isl_ast_op_minus>
5704 =item C<isl_ast_op_add>
5706 Sum of two arguments.
5708 =item C<isl_ast_op_sub>
5710 Difference of two arguments.
5712 =item C<isl_ast_op_mul>
5714 Product of two arguments.
5716 =item C<isl_ast_op_div>
5718 Exact division. That is, the result is known to be an integer.
5720 =item C<isl_ast_op_fdiv_q>
5722 Result of integer division, rounded towards negative
5725 =item C<isl_ast_op_pdiv_q>
5727 Result of integer division, where dividend is known to be non-negative.
5729 =item C<isl_ast_op_pdiv_r>
5731 Remainder of integer division, where dividend is known to be non-negative.
5733 =item C<isl_ast_op_cond>
5735 Conditional operator defined on three arguments.
5736 If the first argument evaluates to true, then the result
5737 is equal to the second argument. Otherwise, the result
5738 is equal to the third argument.
5739 The second and third argument may only be evaluated if
5740 the first argument evaluates to true and false, respectively.
5741 Corresponds to C<a ? b : c> in C.
5743 =item C<isl_ast_op_select>
5745 Conditional operator defined on three arguments.
5746 If the first argument evaluates to true, then the result
5747 is equal to the second argument. Otherwise, the result
5748 is equal to the third argument.
5749 The second and third argument may be evaluated independently
5750 of the value of the first argument.
5751 Corresponds to C<a * b + (1 - a) * c> in C.
5753 =item C<isl_ast_op_eq>
5757 =item C<isl_ast_op_le>
5759 Less than or equal relation.
5761 =item C<isl_ast_op_lt>
5765 =item C<isl_ast_op_ge>
5767 Greater than or equal relation.
5769 =item C<isl_ast_op_gt>
5771 Greater than relation.
5773 =item C<isl_ast_op_call>
5776 The number of arguments of the C<isl_ast_expr> is one more than
5777 the number of arguments in the function call, the first argument
5778 representing the function being called.
5782 #include <isl/ast.h>
5783 __isl_give isl_id *isl_ast_expr_get_id(
5784 __isl_keep isl_ast_expr *expr);
5786 Return the identifier represented by the AST expression.
5788 #include <isl/ast.h>
5789 __isl_give isl_val *isl_ast_expr_get_val(
5790 __isl_keep isl_ast_expr *expr);
5792 Return the integer represented by the AST expression.
5794 =head3 Manipulating and printing the AST
5796 AST nodes can be copied and freed using the following functions.
5798 #include <isl/ast.h>
5799 __isl_give isl_ast_node *isl_ast_node_copy(
5800 __isl_keep isl_ast_node *node);
5801 void *isl_ast_node_free(__isl_take isl_ast_node *node);
5803 AST expressions can be copied and freed using the following functions.
5805 #include <isl/ast.h>
5806 __isl_give isl_ast_expr *isl_ast_expr_copy(
5807 __isl_keep isl_ast_expr *expr);
5808 void *isl_ast_expr_free(__isl_take isl_ast_expr *expr);
5810 New AST expressions can be created either directly or within
5811 the context of an C<isl_ast_build>.
5813 #include <isl/ast.h>
5814 __isl_give isl_ast_expr *isl_ast_expr_from_val(
5815 __isl_take isl_val *v);
5816 __isl_give isl_ast_expr *isl_ast_expr_from_id(
5817 __isl_take isl_id *id);
5818 __isl_give isl_ast_expr *isl_ast_expr_neg(
5819 __isl_take isl_ast_expr *expr);
5820 __isl_give isl_ast_expr *isl_ast_expr_add(
5821 __isl_take isl_ast_expr *expr1,
5822 __isl_take isl_ast_expr *expr2);
5823 __isl_give isl_ast_expr *isl_ast_expr_sub(
5824 __isl_take isl_ast_expr *expr1,
5825 __isl_take isl_ast_expr *expr2);
5826 __isl_give isl_ast_expr *isl_ast_expr_mul(
5827 __isl_take isl_ast_expr *expr1,
5828 __isl_take isl_ast_expr *expr2);
5829 __isl_give isl_ast_expr *isl_ast_expr_div(
5830 __isl_take isl_ast_expr *expr1,
5831 __isl_take isl_ast_expr *expr2);
5832 __isl_give isl_ast_expr *isl_ast_expr_and(
5833 __isl_take isl_ast_expr *expr1,
5834 __isl_take isl_ast_expr *expr2)
5835 __isl_give isl_ast_expr *isl_ast_expr_or(
5836 __isl_take isl_ast_expr *expr1,
5837 __isl_take isl_ast_expr *expr2)
5839 #include <isl/ast_build.h>
5840 __isl_give isl_ast_expr *isl_ast_build_expr_from_pw_aff(
5841 __isl_keep isl_ast_build *build,
5842 __isl_take isl_pw_aff *pa);
5843 __isl_give isl_ast_expr *
5844 isl_ast_build_call_from_pw_multi_aff(
5845 __isl_keep isl_ast_build *build,
5846 __isl_take isl_pw_multi_aff *pma);
5848 The domains of C<pa> and C<pma> should correspond
5849 to the schedule space of C<build>.
5850 The tuple id of C<pma> is used as the function being called.
5852 User specified data can be attached to an C<isl_ast_node> and obtained
5853 from the same C<isl_ast_node> using the following functions.
5855 #include <isl/ast.h>
5856 __isl_give isl_ast_node *isl_ast_node_set_annotation(
5857 __isl_take isl_ast_node *node,
5858 __isl_take isl_id *annotation);
5859 __isl_give isl_id *isl_ast_node_get_annotation(
5860 __isl_keep isl_ast_node *node);
5862 Basic printing can be performed using the following functions.
5864 #include <isl/ast.h>
5865 __isl_give isl_printer *isl_printer_print_ast_expr(
5866 __isl_take isl_printer *p,
5867 __isl_keep isl_ast_expr *expr);
5868 __isl_give isl_printer *isl_printer_print_ast_node(
5869 __isl_take isl_printer *p,
5870 __isl_keep isl_ast_node *node);
5872 More advanced printing can be performed using the following functions.
5874 #include <isl/ast.h>
5875 __isl_give isl_printer *isl_ast_op_type_print_macro(
5876 enum isl_ast_op_type type,
5877 __isl_take isl_printer *p);
5878 __isl_give isl_printer *isl_ast_node_print_macros(
5879 __isl_keep isl_ast_node *node,
5880 __isl_take isl_printer *p);
5881 __isl_give isl_printer *isl_ast_node_print(
5882 __isl_keep isl_ast_node *node,
5883 __isl_take isl_printer *p,
5884 __isl_take isl_ast_print_options *options);
5885 __isl_give isl_printer *isl_ast_node_for_print(
5886 __isl_keep isl_ast_node *node,
5887 __isl_take isl_printer *p,
5888 __isl_take isl_ast_print_options *options);
5889 __isl_give isl_printer *isl_ast_node_if_print(
5890 __isl_keep isl_ast_node *node,
5891 __isl_take isl_printer *p,
5892 __isl_take isl_ast_print_options *options);
5894 While printing an C<isl_ast_node> in C<ISL_FORMAT_C>,
5895 C<isl> may print out an AST that makes use of macros such
5896 as C<floord>, C<min> and C<max>.
5897 C<isl_ast_op_type_print_macro> prints out the macro
5898 corresponding to a specific C<isl_ast_op_type>.
5899 C<isl_ast_node_print_macros> scans the C<isl_ast_node>
5900 for expressions where these macros would be used and prints
5901 out the required macro definitions.
5902 Essentially, C<isl_ast_node_print_macros> calls
5903 C<isl_ast_node_foreach_ast_op_type> with C<isl_ast_op_type_print_macro>
5904 as function argument.
5905 C<isl_ast_node_print>, C<isl_ast_node_for_print> and
5906 C<isl_ast_node_if_print> print an C<isl_ast_node>
5907 in C<ISL_FORMAT_C>, but allow for some extra control
5908 through an C<isl_ast_print_options> object.
5909 This object can be created using the following functions.
5911 #include <isl/ast.h>
5912 __isl_give isl_ast_print_options *
5913 isl_ast_print_options_alloc(isl_ctx *ctx);
5914 __isl_give isl_ast_print_options *
5915 isl_ast_print_options_copy(
5916 __isl_keep isl_ast_print_options *options);
5917 void *isl_ast_print_options_free(
5918 __isl_take isl_ast_print_options *options);
5920 __isl_give isl_ast_print_options *
5921 isl_ast_print_options_set_print_user(
5922 __isl_take isl_ast_print_options *options,
5923 __isl_give isl_printer *(*print_user)(
5924 __isl_take isl_printer *p,
5925 __isl_take isl_ast_print_options *options,
5926 __isl_keep isl_ast_node *node, void *user),
5928 __isl_give isl_ast_print_options *
5929 isl_ast_print_options_set_print_for(
5930 __isl_take isl_ast_print_options *options,
5931 __isl_give isl_printer *(*print_for)(
5932 __isl_take isl_printer *p,
5933 __isl_take isl_ast_print_options *options,
5934 __isl_keep isl_ast_node *node, void *user),
5937 The callback set by C<isl_ast_print_options_set_print_user>
5938 is called whenever a node of type C<isl_ast_node_user> needs to
5940 The callback set by C<isl_ast_print_options_set_print_for>
5941 is called whenever a node of type C<isl_ast_node_for> needs to
5943 Note that C<isl_ast_node_for_print> will I<not> call the
5944 callback set by C<isl_ast_print_options_set_print_for> on the node
5945 on which C<isl_ast_node_for_print> is called, but only on nested
5946 nodes of type C<isl_ast_node_for>. It is therefore safe to
5947 call C<isl_ast_node_for_print> from within the callback set by
5948 C<isl_ast_print_options_set_print_for>.
5950 The following option determines the type to be used for iterators
5951 while printing the AST.
5953 int isl_options_set_ast_iterator_type(
5954 isl_ctx *ctx, const char *val);
5955 const char *isl_options_get_ast_iterator_type(
5960 #include <isl/ast_build.h>
5961 int isl_options_set_ast_build_atomic_upper_bound(
5962 isl_ctx *ctx, int val);
5963 int isl_options_get_ast_build_atomic_upper_bound(
5965 int isl_options_set_ast_build_prefer_pdiv(isl_ctx *ctx,
5967 int isl_options_get_ast_build_prefer_pdiv(isl_ctx *ctx);
5968 int isl_options_set_ast_build_exploit_nested_bounds(
5969 isl_ctx *ctx, int val);
5970 int isl_options_get_ast_build_exploit_nested_bounds(
5972 int isl_options_set_ast_build_group_coscheduled(
5973 isl_ctx *ctx, int val);
5974 int isl_options_get_ast_build_group_coscheduled(
5976 int isl_options_set_ast_build_scale_strides(
5977 isl_ctx *ctx, int val);
5978 int isl_options_get_ast_build_scale_strides(
5980 int isl_options_set_ast_build_allow_else(isl_ctx *ctx,
5982 int isl_options_get_ast_build_allow_else(isl_ctx *ctx);
5983 int isl_options_set_ast_build_allow_or(isl_ctx *ctx,
5985 int isl_options_get_ast_build_allow_or(isl_ctx *ctx);
5989 =item * ast_build_atomic_upper_bound
5991 Generate loop upper bounds that consist of the current loop iterator,
5992 an operator and an expression not involving the iterator.
5993 If this option is not set, then the current loop iterator may appear
5994 several times in the upper bound.
5995 For example, when this option is turned off, AST generation
5998 [n] -> { A[i] -> [i] : 0 <= i <= 100, n }
6002 for (int c0 = 0; c0 <= 100 && n >= c0; c0 += 1)
6005 When the option is turned on, the following AST is generated
6007 for (int c0 = 0; c0 <= min(100, n); c0 += 1)
6010 =item * ast_build_prefer_pdiv
6012 If this option is turned off, then the AST generation will
6013 produce ASTs that may only contain C<isl_ast_op_fdiv_q>
6014 operators, but no C<isl_ast_op_pdiv_q> or
6015 C<isl_ast_op_pdiv_r> operators.
6016 If this options is turned on, then C<isl> will try to convert
6017 some of the C<isl_ast_op_fdiv_q> operators to (expressions containing)
6018 C<isl_ast_op_pdiv_q> or C<isl_ast_op_pdiv_r> operators.
6020 =item * ast_build_exploit_nested_bounds
6022 Simplify conditions based on bounds of nested for loops.
6023 In particular, remove conditions that are implied by the fact
6024 that one or more nested loops have at least one iteration,
6025 meaning that the upper bound is at least as large as the lower bound.
6026 For example, when this option is turned off, AST generation
6029 [N,M] -> { A[i,j] -> [i,j] : 0 <= i <= N and
6035 for (int c0 = 0; c0 <= N; c0 += 1)
6036 for (int c1 = 0; c1 <= M; c1 += 1)
6039 When the option is turned on, the following AST is generated
6041 for (int c0 = 0; c0 <= N; c0 += 1)
6042 for (int c1 = 0; c1 <= M; c1 += 1)
6045 =item * ast_build_group_coscheduled
6047 If two domain elements are assigned the same schedule point, then
6048 they may be executed in any order and they may even appear in different
6049 loops. If this options is set, then the AST generator will make
6050 sure that coscheduled domain elements do not appear in separate parts
6051 of the AST. This is useful in case of nested AST generation
6052 if the outer AST generation is given only part of a schedule
6053 and the inner AST generation should handle the domains that are
6054 coscheduled by this initial part of the schedule together.
6055 For example if an AST is generated for a schedule
6057 { A[i] -> [0]; B[i] -> [0] }
6059 then the C<isl_ast_build_set_create_leaf> callback described
6060 below may get called twice, once for each domain.
6061 Setting this option ensures that the callback is only called once
6062 on both domains together.
6064 =item * ast_build_separation_bounds
6066 This option specifies which bounds to use during separation.
6067 If this option is set to C<ISL_AST_BUILD_SEPARATION_BOUNDS_IMPLICIT>
6068 then all (possibly implicit) bounds on the current dimension will
6069 be used during separation.
6070 If this option is set to C<ISL_AST_BUILD_SEPARATION_BOUNDS_EXPLICIT>
6071 then only those bounds that are explicitly available will
6072 be used during separation.
6074 =item * ast_build_scale_strides
6076 This option specifies whether the AST generator is allowed
6077 to scale down iterators of strided loops.
6079 =item * ast_build_allow_else
6081 This option specifies whether the AST generator is allowed
6082 to construct if statements with else branches.
6084 =item * ast_build_allow_or
6086 This option specifies whether the AST generator is allowed
6087 to construct if conditions with disjunctions.
6091 =head3 Fine-grained Control over AST Generation
6093 Besides specifying the constraints on the parameters,
6094 an C<isl_ast_build> object can be used to control
6095 various aspects of the AST generation process.
6096 The most prominent way of control is through ``options'',
6097 which can be set using the following function.
6099 #include <isl/ast_build.h>
6100 __isl_give isl_ast_build *
6101 isl_ast_build_set_options(
6102 __isl_take isl_ast_build *control,
6103 __isl_take isl_union_map *options);
6105 The options are encoded in an <isl_union_map>.
6106 The domain of this union relation refers to the schedule domain,
6107 i.e., the range of the schedule passed to C<isl_ast_build_ast_from_schedule>.
6108 In the case of nested AST generation (see L</"Nested AST Generation">),
6109 the domain of C<options> should refer to the extra piece of the schedule.
6110 That is, it should be equal to the range of the wrapped relation in the
6111 range of the schedule.
6112 The range of the options can consist of elements in one or more spaces,
6113 the names of which determine the effect of the option.
6114 The values of the range typically also refer to the schedule dimension
6115 to which the option applies. In case of nested AST generation
6116 (see L</"Nested AST Generation">), these values refer to the position
6117 of the schedule dimension within the innermost AST generation.
6118 The constraints on the domain elements of
6119 the option should only refer to this dimension and earlier dimensions.
6120 We consider the following spaces.
6124 =item C<separation_class>
6126 This space is a wrapped relation between two one dimensional spaces.
6127 The input space represents the schedule dimension to which the option
6128 applies and the output space represents the separation class.
6129 While constructing a loop corresponding to the specified schedule
6130 dimension(s), the AST generator will try to generate separate loops
6131 for domain elements that are assigned different classes.
6132 If only some of the elements are assigned a class, then those elements
6133 that are not assigned any class will be treated as belonging to a class
6134 that is separate from the explicitly assigned classes.
6135 The typical use case for this option is to separate full tiles from
6137 The other options, described below, are applied after the separation
6140 As an example, consider the separation into full and partial tiles
6141 of a tiling of a triangular domain.
6142 Take, for example, the domain
6144 { A[i,j] : 0 <= i,j and i + j <= 100 }
6146 and a tiling into tiles of 10 by 10. The input to the AST generator
6147 is then the schedule
6149 { A[i,j] -> [([i/10]),[j/10],i,j] : 0 <= i,j and
6152 Without any options, the following AST is generated
6154 for (int c0 = 0; c0 <= 10; c0 += 1)
6155 for (int c1 = 0; c1 <= -c0 + 10; c1 += 1)
6156 for (int c2 = 10 * c0;
6157 c2 <= min(-10 * c1 + 100, 10 * c0 + 9);
6159 for (int c3 = 10 * c1;
6160 c3 <= min(10 * c1 + 9, -c2 + 100);
6164 Separation into full and partial tiles can be obtained by assigning
6165 a class, say C<0>, to the full tiles. The full tiles are represented by those
6166 values of the first and second schedule dimensions for which there are
6167 values of the third and fourth dimensions to cover an entire tile.
6168 That is, we need to specify the following option
6170 { [a,b,c,d] -> separation_class[[0]->[0]] :
6171 exists b': 0 <= 10a,10b' and
6172 10a+9+10b'+9 <= 100;
6173 [a,b,c,d] -> separation_class[[1]->[0]] :
6174 0 <= 10a,10b and 10a+9+10b+9 <= 100 }
6178 { [a, b, c, d] -> separation_class[[1] -> [0]] :
6179 a >= 0 and b >= 0 and b <= 8 - a;
6180 [a, b, c, d] -> separation_class[[0] -> [0]] :
6183 With this option, the generated AST is as follows
6186 for (int c0 = 0; c0 <= 8; c0 += 1) {
6187 for (int c1 = 0; c1 <= -c0 + 8; c1 += 1)
6188 for (int c2 = 10 * c0;
6189 c2 <= 10 * c0 + 9; c2 += 1)
6190 for (int c3 = 10 * c1;
6191 c3 <= 10 * c1 + 9; c3 += 1)
6193 for (int c1 = -c0 + 9; c1 <= -c0 + 10; c1 += 1)
6194 for (int c2 = 10 * c0;
6195 c2 <= min(-10 * c1 + 100, 10 * c0 + 9);
6197 for (int c3 = 10 * c1;
6198 c3 <= min(-c2 + 100, 10 * c1 + 9);
6202 for (int c0 = 9; c0 <= 10; c0 += 1)
6203 for (int c1 = 0; c1 <= -c0 + 10; c1 += 1)
6204 for (int c2 = 10 * c0;
6205 c2 <= min(-10 * c1 + 100, 10 * c0 + 9);
6207 for (int c3 = 10 * c1;
6208 c3 <= min(10 * c1 + 9, -c2 + 100);
6215 This is a single-dimensional space representing the schedule dimension(s)
6216 to which ``separation'' should be applied. Separation tries to split
6217 a loop into several pieces if this can avoid the generation of guards
6219 See also the C<atomic> option.
6223 This is a single-dimensional space representing the schedule dimension(s)
6224 for which the domains should be considered ``atomic''. That is, the
6225 AST generator will make sure that any given domain space will only appear
6226 in a single loop at the specified level.
6228 Consider the following schedule
6230 { a[i] -> [i] : 0 <= i < 10;
6231 b[i] -> [i+1] : 0 <= i < 10 }
6233 If the following option is specified
6235 { [i] -> separate[x] }
6237 then the following AST will be generated
6241 for (int c0 = 1; c0 <= 9; c0 += 1) {
6248 If, on the other hand, the following option is specified
6250 { [i] -> atomic[x] }
6252 then the following AST will be generated
6254 for (int c0 = 0; c0 <= 10; c0 += 1) {
6261 If neither C<atomic> nor C<separate> is specified, then the AST generator
6262 may produce either of these two results or some intermediate form.
6266 This is a single-dimensional space representing the schedule dimension(s)
6267 that should be I<completely> unrolled.
6268 To obtain a partial unrolling, the user should apply an additional
6269 strip-mining to the schedule and fully unroll the inner loop.
6273 Additional control is available through the following functions.
6275 #include <isl/ast_build.h>
6276 __isl_give isl_ast_build *
6277 isl_ast_build_set_iterators(
6278 __isl_take isl_ast_build *control,
6279 __isl_take isl_id_list *iterators);
6281 The function C<isl_ast_build_set_iterators> allows the user to
6282 specify a list of iterator C<isl_id>s to be used as iterators.
6283 If the input schedule is injective, then
6284 the number of elements in this list should be as large as the dimension
6285 of the schedule space, but no direct correspondence should be assumed
6286 between dimensions and elements.
6287 If the input schedule is not injective, then an additional number
6288 of C<isl_id>s equal to the largest dimension of the input domains
6290 If the number of provided C<isl_id>s is insufficient, then additional
6291 names are automatically generated.
6293 #include <isl/ast_build.h>
6294 __isl_give isl_ast_build *
6295 isl_ast_build_set_create_leaf(
6296 __isl_take isl_ast_build *control,
6297 __isl_give isl_ast_node *(*fn)(
6298 __isl_take isl_ast_build *build,
6299 void *user), void *user);
6302 C<isl_ast_build_set_create_leaf> function allows for the
6303 specification of a callback that should be called whenever the AST
6304 generator arrives at an element of the schedule domain.
6305 The callback should return an AST node that should be inserted
6306 at the corresponding position of the AST. The default action (when
6307 the callback is not set) is to continue generating parts of the AST to scan
6308 all the domain elements associated to the schedule domain element
6309 and to insert user nodes, ``calling'' the domain element, for each of them.
6310 The C<build> argument contains the current state of the C<isl_ast_build>.
6311 To ease nested AST generation (see L</"Nested AST Generation">),
6312 all control information that is
6313 specific to the current AST generation such as the options and
6314 the callbacks has been removed from this C<isl_ast_build>.
6315 The callback would typically return the result of a nested
6317 user defined node created using the following function.
6319 #include <isl/ast.h>
6320 __isl_give isl_ast_node *isl_ast_node_alloc_user(
6321 __isl_take isl_ast_expr *expr);
6323 #include <isl/ast_build.h>
6324 __isl_give isl_ast_build *
6325 isl_ast_build_set_at_each_domain(
6326 __isl_take isl_ast_build *build,
6327 __isl_give isl_ast_node *(*fn)(
6328 __isl_take isl_ast_node *node,
6329 __isl_keep isl_ast_build *build,
6330 void *user), void *user);
6331 __isl_give isl_ast_build *
6332 isl_ast_build_set_before_each_for(
6333 __isl_take isl_ast_build *build,
6334 __isl_give isl_id *(*fn)(
6335 __isl_keep isl_ast_build *build,
6336 void *user), void *user);
6337 __isl_give isl_ast_build *
6338 isl_ast_build_set_after_each_for(
6339 __isl_take isl_ast_build *build,
6340 __isl_give isl_ast_node *(*fn)(
6341 __isl_take isl_ast_node *node,
6342 __isl_keep isl_ast_build *build,
6343 void *user), void *user);
6345 The callback set by C<isl_ast_build_set_at_each_domain> will
6346 be called for each domain AST node.
6347 The callbacks set by C<isl_ast_build_set_before_each_for>
6348 and C<isl_ast_build_set_after_each_for> will be called
6349 for each for AST node. The first will be called in depth-first
6350 pre-order, while the second will be called in depth-first post-order.
6351 Since C<isl_ast_build_set_before_each_for> is called before the for
6352 node is actually constructed, it is only passed an C<isl_ast_build>.
6353 The returned C<isl_id> will be added as an annotation (using
6354 C<isl_ast_node_set_annotation>) to the constructed for node.
6355 In particular, if the user has also specified an C<after_each_for>
6356 callback, then the annotation can be retrieved from the node passed to
6357 that callback using C<isl_ast_node_get_annotation>.
6358 All callbacks should C<NULL> on failure.
6359 The given C<isl_ast_build> can be used to create new
6360 C<isl_ast_expr> objects using C<isl_ast_build_expr_from_pw_aff>
6361 or C<isl_ast_build_call_from_pw_multi_aff>.
6363 =head3 Nested AST Generation
6365 C<isl> allows the user to create an AST within the context
6366 of another AST. These nested ASTs are created using the
6367 same C<isl_ast_build_ast_from_schedule> function that is used to create the
6368 outer AST. The C<build> argument should be an C<isl_ast_build>
6369 passed to a callback set by
6370 C<isl_ast_build_set_create_leaf>.
6371 The space of the range of the C<schedule> argument should refer
6372 to this build. In particular, the space should be a wrapped
6373 relation and the domain of this wrapped relation should be the
6374 same as that of the range of the schedule returned by
6375 C<isl_ast_build_get_schedule> below.
6376 In practice, the new schedule is typically
6377 created by calling C<isl_union_map_range_product> on the old schedule
6378 and some extra piece of the schedule.
6379 The space of the schedule domain is also available from
6380 the C<isl_ast_build>.
6382 #include <isl/ast_build.h>
6383 __isl_give isl_union_map *isl_ast_build_get_schedule(
6384 __isl_keep isl_ast_build *build);
6385 __isl_give isl_space *isl_ast_build_get_schedule_space(
6386 __isl_keep isl_ast_build *build);
6387 __isl_give isl_ast_build *isl_ast_build_restrict(
6388 __isl_take isl_ast_build *build,
6389 __isl_take isl_set *set);
6391 The C<isl_ast_build_get_schedule> function returns a (partial)
6392 schedule for the domains elements for which part of the AST still needs to
6393 be generated in the current build.
6394 In particular, the domain elements are mapped to those iterations of the loops
6395 enclosing the current point of the AST generation inside which
6396 the domain elements are executed.
6397 No direct correspondence between
6398 the input schedule and this schedule should be assumed.
6399 The space obtained from C<isl_ast_build_get_schedule_space> can be used
6400 to create a set for C<isl_ast_build_restrict> to intersect
6401 with the current build. In particular, the set passed to
6402 C<isl_ast_build_restrict> can have additional parameters.
6403 The ids of the set dimensions in the space returned by
6404 C<isl_ast_build_get_schedule_space> correspond to the
6405 iterators of the already generated loops.
6406 The user should not rely on the ids of the output dimensions
6407 of the relations in the union relation returned by
6408 C<isl_ast_build_get_schedule> having any particular value.
6412 Although C<isl> is mainly meant to be used as a library,
6413 it also contains some basic applications that use some
6414 of the functionality of C<isl>.
6415 The input may be specified in either the L<isl format>
6416 or the L<PolyLib format>.
6418 =head2 C<isl_polyhedron_sample>
6420 C<isl_polyhedron_sample> takes a polyhedron as input and prints
6421 an integer element of the polyhedron, if there is any.
6422 The first column in the output is the denominator and is always
6423 equal to 1. If the polyhedron contains no integer points,
6424 then a vector of length zero is printed.
6428 C<isl_pip> takes the same input as the C<example> program
6429 from the C<piplib> distribution, i.e., a set of constraints
6430 on the parameters, a line containing only -1 and finally a set
6431 of constraints on a parametric polyhedron.
6432 The coefficients of the parameters appear in the last columns
6433 (but before the final constant column).
6434 The output is the lexicographic minimum of the parametric polyhedron.
6435 As C<isl> currently does not have its own output format, the output
6436 is just a dump of the internal state.
6438 =head2 C<isl_polyhedron_minimize>
6440 C<isl_polyhedron_minimize> computes the minimum of some linear
6441 or affine objective function over the integer points in a polyhedron.
6442 If an affine objective function
6443 is given, then the constant should appear in the last column.
6445 =head2 C<isl_polytope_scan>
6447 Given a polytope, C<isl_polytope_scan> prints
6448 all integer points in the polytope.
6450 =head2 C<isl_codegen>
6452 Given a schedule, a context set and an options relation,
6453 C<isl_codegen> prints out an AST that scans the domain elements
6454 of the schedule in the order of their image(s) taking into account
6455 the constraints in the context set.