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.
196 C<isl> is released under the MIT license.
200 Permission is hereby granted, free of charge, to any person obtaining a copy of
201 this software and associated documentation files (the "Software"), to deal in
202 the Software without restriction, including without limitation the rights to
203 use, copy, modify, merge, publish, distribute, sublicense, and/or sell copies
204 of the Software, and to permit persons to whom the Software is furnished to do
205 so, subject to the following conditions:
207 The above copyright notice and this permission notice shall be included in all
208 copies or substantial portions of the Software.
210 THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
211 IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
212 FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
213 AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
214 LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
215 OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
220 Note that C<isl> currently requires C<GMP>, which is released
221 under the GNU Lesser General Public License (LGPL). This means
222 that code linked against C<isl> is also linked against LGPL code.
226 The source of C<isl> can be obtained either as a tarball
227 or from the git repository. Both are available from
228 L<http://freshmeat.net/projects/isl/>.
229 The installation process depends on how you obtained
232 =head2 Installation from the git repository
236 =item 1 Clone or update the repository
238 The first time the source is obtained, you need to clone
241 git clone git://repo.or.cz/isl.git
243 To obtain updates, you need to pull in the latest changes
247 =item 2 Generate C<configure>
253 After performing the above steps, continue
254 with the L<Common installation instructions>.
256 =head2 Common installation instructions
260 =item 1 Obtain C<GMP>
262 Building C<isl> requires C<GMP>, including its headers files.
263 Your distribution may not provide these header files by default
264 and you may need to install a package called C<gmp-devel> or something
265 similar. Alternatively, C<GMP> can be built from
266 source, available from L<http://gmplib.org/>.
270 C<isl> uses the standard C<autoconf> C<configure> script.
275 optionally followed by some configure options.
276 A complete list of options can be obtained by running
280 Below we discuss some of the more common options.
282 C<isl> can optionally use C<piplib>, but no
283 C<piplib> functionality is currently used by default.
284 The C<--with-piplib> option can
285 be used to specify which C<piplib>
286 library to use, either an installed version (C<system>),
287 an externally built version (C<build>)
288 or no version (C<no>). The option C<build> is mostly useful
289 in C<configure> scripts of larger projects that bundle both C<isl>
296 Installation prefix for C<isl>
298 =item C<--with-gmp-prefix>
300 Installation prefix for C<GMP> (architecture-independent files).
302 =item C<--with-gmp-exec-prefix>
304 Installation prefix for C<GMP> (architecture-dependent files).
306 =item C<--with-piplib>
308 Which copy of C<piplib> to use, either C<no> (default), C<system> or C<build>.
310 =item C<--with-piplib-prefix>
312 Installation prefix for C<system> C<piplib> (architecture-independent files).
314 =item C<--with-piplib-exec-prefix>
316 Installation prefix for C<system> C<piplib> (architecture-dependent files).
318 =item C<--with-piplib-builddir>
320 Location where C<build> C<piplib> was built.
328 =item 4 Install (optional)
334 =head1 Integer Set Library
336 =head2 Initialization
338 All manipulations of integer sets and relations occur within
339 the context of an C<isl_ctx>.
340 A given C<isl_ctx> can only be used within a single thread.
341 All arguments of a function are required to have been allocated
342 within the same context.
343 There are currently no functions available for moving an object
344 from one C<isl_ctx> to another C<isl_ctx>. This means that
345 there is currently no way of safely moving an object from one
346 thread to another, unless the whole C<isl_ctx> is moved.
348 An C<isl_ctx> can be allocated using C<isl_ctx_alloc> and
349 freed using C<isl_ctx_free>.
350 All objects allocated within an C<isl_ctx> should be freed
351 before the C<isl_ctx> itself is freed.
353 isl_ctx *isl_ctx_alloc();
354 void isl_ctx_free(isl_ctx *ctx);
358 An C<isl_val> represents an integer value, a rational value
359 or one of three special values, infinity, negative infinity and NaN.
360 Some predefined values can be created using the following functions.
363 __isl_give isl_val *isl_val_zero(isl_ctx *ctx);
364 __isl_give isl_val *isl_val_one(isl_ctx *ctx);
365 __isl_give isl_val *isl_val_nan(isl_ctx *ctx);
366 __isl_give isl_val *isl_val_infty(isl_ctx *ctx);
367 __isl_give isl_val *isl_val_neginfty(isl_ctx *ctx);
369 Specific integer values can be created using the following functions.
372 __isl_give isl_val *isl_val_int_from_si(isl_ctx *ctx,
374 __isl_give isl_val *isl_val_int_from_ui(isl_ctx *ctx,
376 __isl_give isl_val *isl_val_int_from_chunks(isl_ctx *ctx,
377 size_t n, size_t size, const void *chunks);
379 The function C<isl_val_int_from_chunks> constructs an C<isl_val>
380 from the C<n> I<digits>, each consisting of C<size> bytes, stored at C<chunks>.
381 The least significant digit is assumed to be stored first.
383 Value objects can be copied and freed using the following functions.
386 __isl_give isl_val *isl_val_copy(__isl_keep isl_val *v);
387 void *isl_val_free(__isl_take isl_val *v);
389 They can be inspected using the following functions.
392 isl_ctx *isl_val_get_ctx(__isl_keep isl_val *val);
393 long isl_val_get_num_si(__isl_keep isl_val *v);
394 long isl_val_get_den_si(__isl_keep isl_val *v);
395 double isl_val_get_d(__isl_keep isl_val *v);
396 size_t isl_val_n_abs_num_chunks(__isl_keep isl_val *v,
398 int isl_val_get_abs_num_chunks(__isl_keep isl_val *v,
399 size_t size, void *chunks);
401 C<isl_val_n_abs_num_chunks> returns the number of I<digits>
402 of C<size> bytes needed to store the absolute value of the
404 C<isl_val_get_abs_num_chunks> stores these digits at C<chunks>,
405 which is assumed to have been preallocated by the caller.
406 The least significant digit is stored first.
407 Note that C<isl_val_get_num_si>, C<isl_val_get_den_si>,
408 C<isl_val_get_d>, C<isl_val_n_abs_num_chunks>
409 and C<isl_val_get_abs_num_chunks> can only be applied to rational values.
411 An C<isl_val> can be modified using the following function.
414 __isl_give isl_val *isl_val_set_si(__isl_take isl_val *v,
417 The following unary properties are defined on C<isl_val>s.
420 int isl_val_sgn(__isl_keep isl_val *v);
421 int isl_val_is_zero(__isl_keep isl_val *v);
422 int isl_val_is_one(__isl_keep isl_val *v);
423 int isl_val_is_negone(__isl_keep isl_val *v);
424 int isl_val_is_nonneg(__isl_keep isl_val *v);
425 int isl_val_is_nonpos(__isl_keep isl_val *v);
426 int isl_val_is_pos(__isl_keep isl_val *v);
427 int isl_val_is_neg(__isl_keep isl_val *v);
428 int isl_val_is_int(__isl_keep isl_val *v);
429 int isl_val_is_rat(__isl_keep isl_val *v);
430 int isl_val_is_nan(__isl_keep isl_val *v);
431 int isl_val_is_infty(__isl_keep isl_val *v);
432 int isl_val_is_neginfty(__isl_keep isl_val *v);
434 Note that the sign of NaN is undefined.
436 The following binary properties are defined on pairs of C<isl_val>s.
439 int isl_val_lt(__isl_keep isl_val *v1,
440 __isl_keep isl_val *v2);
441 int isl_val_le(__isl_keep isl_val *v1,
442 __isl_keep isl_val *v2);
443 int isl_val_gt(__isl_keep isl_val *v1,
444 __isl_keep isl_val *v2);
445 int isl_val_ge(__isl_keep isl_val *v1,
446 __isl_keep isl_val *v2);
447 int isl_val_eq(__isl_keep isl_val *v1,
448 __isl_keep isl_val *v2);
449 int isl_val_ne(__isl_keep isl_val *v1,
450 __isl_keep isl_val *v2);
452 For integer C<isl_val>s we additionally have the following binary property.
455 int isl_val_is_divisible_by(__isl_keep isl_val *v1,
456 __isl_keep isl_val *v2);
458 An C<isl_val> can also be compared to an integer using the following
459 function. The result is undefined for NaN.
462 int isl_val_cmp_si(__isl_keep isl_val *v, long i);
464 The following unary operations are available on C<isl_val>s.
467 __isl_give isl_val *isl_val_abs(__isl_take isl_val *v);
468 __isl_give isl_val *isl_val_neg(__isl_take isl_val *v);
469 __isl_give isl_val *isl_val_floor(__isl_take isl_val *v);
470 __isl_give isl_val *isl_val_ceil(__isl_take isl_val *v);
471 __isl_give isl_val *isl_val_trunc(__isl_take isl_val *v);
473 The following binary operations are available on C<isl_val>s.
476 __isl_give isl_val *isl_val_abs(__isl_take isl_val *v);
477 __isl_give isl_val *isl_val_neg(__isl_take isl_val *v);
478 __isl_give isl_val *isl_val_floor(__isl_take isl_val *v);
479 __isl_give isl_val *isl_val_ceil(__isl_take isl_val *v);
480 __isl_give isl_val *isl_val_trunc(__isl_take isl_val *v);
481 __isl_give isl_val *isl_val_2exp(__isl_take isl_val *v);
482 __isl_give isl_val *isl_val_min(__isl_take isl_val *v1,
483 __isl_take isl_val *v2);
484 __isl_give isl_val *isl_val_max(__isl_take isl_val *v1,
485 __isl_take isl_val *v2);
486 __isl_give isl_val *isl_val_add(__isl_take isl_val *v1,
487 __isl_take isl_val *v2);
488 __isl_give isl_val *isl_val_add_ui(__isl_take isl_val *v1,
490 __isl_give isl_val *isl_val_sub(__isl_take isl_val *v1,
491 __isl_take isl_val *v2);
492 __isl_give isl_val *isl_val_sub_ui(__isl_take isl_val *v1,
494 __isl_give isl_val *isl_val_mul(__isl_take isl_val *v1,
495 __isl_take isl_val *v2);
496 __isl_give isl_val *isl_val_mul_ui(__isl_take isl_val *v1,
498 __isl_give isl_val *isl_val_div(__isl_take isl_val *v1,
499 __isl_take isl_val *v2);
501 On integer values, we additionally have the following operations.
504 __isl_give isl_val *isl_val_2exp(__isl_take isl_val *v);
505 __isl_give isl_val *isl_val_mod(__isl_take isl_val *v1,
506 __isl_take isl_val *v2);
507 __isl_give isl_val *isl_val_gcd(__isl_take isl_val *v1,
508 __isl_take isl_val *v2);
509 __isl_give isl_val *isl_val_gcdext(__isl_take isl_val *v1,
510 __isl_take isl_val *v2, __isl_give isl_val **x,
511 __isl_give isl_val **y);
513 The function C<isl_val_gcdext> returns the greatest common divisor g
514 of C<v1> and C<v2> as well as two integers C<*x> and C<*y> such
515 that C<*x> * C<v1> + C<*y> * C<v2> = g.
517 A value can be read from input using
520 __isl_give isl_val *isl_val_read_from_str(isl_ctx *ctx,
523 A value can be printed using
526 __isl_give isl_printer *isl_printer_print_val(
527 __isl_take isl_printer *p, __isl_keep isl_val *v);
529 =head3 GMP specific functions
531 These functions are only available if C<isl> has been compiled with C<GMP>
534 Specific integer and rational values can be created from C<GMP> values using
535 the following functions.
537 #include <isl/val_gmp.h>
538 __isl_give isl_val *isl_val_int_from_gmp(isl_ctx *ctx,
540 __isl_give isl_val *isl_val_from_gmp(isl_ctx *ctx,
541 const mpz_t n, const mpz_t d);
543 The numerator and denominator of a rational value can be extracted as
544 C<GMP> values using the following functions.
546 #include <isl/val_gmp.h>
547 int isl_val_get_num_gmp(__isl_keep isl_val *v, mpz_t z);
548 int isl_val_get_den_gmp(__isl_keep isl_val *v, mpz_t z);
550 =head2 Sets and Relations
552 C<isl> uses six types of objects for representing sets and relations,
553 C<isl_basic_set>, C<isl_basic_map>, C<isl_set>, C<isl_map>,
554 C<isl_union_set> and C<isl_union_map>.
555 C<isl_basic_set> and C<isl_basic_map> represent sets and relations that
556 can be described as a conjunction of affine constraints, while
557 C<isl_set> and C<isl_map> represent unions of
558 C<isl_basic_set>s and C<isl_basic_map>s, respectively.
559 However, all C<isl_basic_set>s or C<isl_basic_map>s in the union need
560 to live in the same space. C<isl_union_set>s and C<isl_union_map>s
561 represent unions of C<isl_set>s or C<isl_map>s in I<different> spaces,
562 where spaces are considered different if they have a different number
563 of dimensions and/or different names (see L<"Spaces">).
564 The difference between sets and relations (maps) is that sets have
565 one set of variables, while relations have two sets of variables,
566 input variables and output variables.
568 =head2 Memory Management
570 Since a high-level operation on sets and/or relations usually involves
571 several substeps and since the user is usually not interested in
572 the intermediate results, most functions that return a new object
573 will also release all the objects passed as arguments.
574 If the user still wants to use one or more of these arguments
575 after the function call, she should pass along a copy of the
576 object rather than the object itself.
577 The user is then responsible for making sure that the original
578 object gets used somewhere else or is explicitly freed.
580 The arguments and return values of all documented functions are
581 annotated to make clear which arguments are released and which
582 arguments are preserved. In particular, the following annotations
589 C<__isl_give> means that a new object is returned.
590 The user should make sure that the returned pointer is
591 used exactly once as a value for an C<__isl_take> argument.
592 In between, it can be used as a value for as many
593 C<__isl_keep> arguments as the user likes.
594 There is one exception, and that is the case where the
595 pointer returned is C<NULL>. Is this case, the user
596 is free to use it as an C<__isl_take> argument or not.
600 C<__isl_take> means that the object the argument points to
601 is taken over by the function and may no longer be used
602 by the user as an argument to any other function.
603 The pointer value must be one returned by a function
604 returning an C<__isl_give> pointer.
605 If the user passes in a C<NULL> value, then this will
606 be treated as an error in the sense that the function will
607 not perform its usual operation. However, it will still
608 make sure that all the other C<__isl_take> arguments
613 C<__isl_keep> means that the function will only use the object
614 temporarily. After the function has finished, the user
615 can still use it as an argument to other functions.
616 A C<NULL> value will be treated in the same way as
617 a C<NULL> value for an C<__isl_take> argument.
621 =head2 Error Handling
623 C<isl> supports different ways to react in case a runtime error is triggered.
624 Runtime errors arise, e.g., if a function such as C<isl_map_intersect> is called
625 with two maps that have incompatible spaces. There are three possible ways
626 to react on error: to warn, to continue or to abort.
628 The default behavior is to warn. In this mode, C<isl> prints a warning, stores
629 the last error in the corresponding C<isl_ctx> and the function in which the
630 error was triggered returns C<NULL>. An error does not corrupt internal state,
631 such that isl can continue to be used. C<isl> also provides functions to
632 read the last error and to reset the memory that stores the last error. The
633 last error is only stored for information purposes. Its presence does not
634 change the behavior of C<isl>. Hence, resetting an error is not required to
635 continue to use isl, but only to observe new errors.
638 enum isl_error isl_ctx_last_error(isl_ctx *ctx);
639 void isl_ctx_reset_error(isl_ctx *ctx);
641 Another option is to continue on error. This is similar to warn on error mode,
642 except that C<isl> does not print any warning. This allows a program to
643 implement its own error reporting.
645 The last option is to directly abort the execution of the program from within
646 the isl library. This makes it obviously impossible to recover from an error,
647 but it allows to directly spot the error location. By aborting on error,
648 debuggers break at the location the error occurred and can provide a stack
649 trace. Other tools that automatically provide stack traces on abort or that do
650 not want to continue execution after an error was triggered may also prefer to
653 The on error behavior of isl can be specified by calling
654 C<isl_options_set_on_error> or by setting the command line option
655 C<--isl-on-error>. Valid arguments for the function call are
656 C<ISL_ON_ERROR_WARN>, C<ISL_ON_ERROR_CONTINUE> and C<ISL_ON_ERROR_ABORT>. The
657 choices for the command line option are C<warn>, C<continue> and C<abort>.
658 It is also possible to query the current error mode.
660 #include <isl/options.h>
661 int isl_options_set_on_error(isl_ctx *ctx, int val);
662 int isl_options_get_on_error(isl_ctx *ctx);
666 Identifiers are used to identify both individual dimensions
667 and tuples of dimensions. They consist of an optional name and an optional
668 user pointer. The name and the user pointer cannot both be C<NULL>, however.
669 Identifiers with the same name but different pointer values
670 are considered to be distinct.
671 Similarly, identifiers with different names but the same pointer value
672 are also considered to be distinct.
673 Equal identifiers are represented using the same object.
674 Pairs of identifiers can therefore be tested for equality using the
676 Identifiers can be constructed, copied, freed, inspected and printed
677 using the following functions.
680 __isl_give isl_id *isl_id_alloc(isl_ctx *ctx,
681 __isl_keep const char *name, void *user);
682 __isl_give isl_id *isl_id_set_free_user(
683 __isl_take isl_id *id,
684 __isl_give void (*free_user)(void *user));
685 __isl_give isl_id *isl_id_copy(isl_id *id);
686 void *isl_id_free(__isl_take isl_id *id);
688 isl_ctx *isl_id_get_ctx(__isl_keep isl_id *id);
689 void *isl_id_get_user(__isl_keep isl_id *id);
690 __isl_keep const char *isl_id_get_name(__isl_keep isl_id *id);
692 __isl_give isl_printer *isl_printer_print_id(
693 __isl_take isl_printer *p, __isl_keep isl_id *id);
695 The callback set by C<isl_id_set_free_user> is called on the user
696 pointer when the last reference to the C<isl_id> is freed.
697 Note that C<isl_id_get_name> returns a pointer to some internal
698 data structure, so the result can only be used while the
699 corresponding C<isl_id> is alive.
703 Whenever a new set, relation or similiar object is created from scratch,
704 the space in which it lives needs to be specified using an C<isl_space>.
705 Each space involves zero or more parameters and zero, one or two
706 tuples of set or input/output dimensions. The parameters and dimensions
707 are identified by an C<isl_dim_type> and a position.
708 The type C<isl_dim_param> refers to parameters,
709 the type C<isl_dim_set> refers to set dimensions (for spaces
710 with a single tuple of dimensions) and the types C<isl_dim_in>
711 and C<isl_dim_out> refer to input and output dimensions
712 (for spaces with two tuples of dimensions).
713 Local spaces (see L</"Local Spaces">) also contain dimensions
714 of type C<isl_dim_div>.
715 Note that parameters are only identified by their position within
716 a given object. Across different objects, parameters are (usually)
717 identified by their names or identifiers. Only unnamed parameters
718 are identified by their positions across objects. The use of unnamed
719 parameters is discouraged.
721 #include <isl/space.h>
722 __isl_give isl_space *isl_space_alloc(isl_ctx *ctx,
723 unsigned nparam, unsigned n_in, unsigned n_out);
724 __isl_give isl_space *isl_space_params_alloc(isl_ctx *ctx,
726 __isl_give isl_space *isl_space_set_alloc(isl_ctx *ctx,
727 unsigned nparam, unsigned dim);
728 __isl_give isl_space *isl_space_copy(__isl_keep isl_space *space);
729 void *isl_space_free(__isl_take isl_space *space);
730 unsigned isl_space_dim(__isl_keep isl_space *space,
731 enum isl_dim_type type);
733 The space used for creating a parameter domain
734 needs to be created using C<isl_space_params_alloc>.
735 For other sets, the space
736 needs to be created using C<isl_space_set_alloc>, while
737 for a relation, the space
738 needs to be created using C<isl_space_alloc>.
739 C<isl_space_dim> can be used
740 to find out the number of dimensions of each type in
741 a space, where type may be
742 C<isl_dim_param>, C<isl_dim_in> (only for relations),
743 C<isl_dim_out> (only for relations), C<isl_dim_set>
744 (only for sets) or C<isl_dim_all>.
746 To check whether a given space is that of a set or a map
747 or whether it is a parameter space, use these functions:
749 #include <isl/space.h>
750 int isl_space_is_params(__isl_keep isl_space *space);
751 int isl_space_is_set(__isl_keep isl_space *space);
752 int isl_space_is_map(__isl_keep isl_space *space);
754 Spaces can be compared using the following functions:
756 #include <isl/space.h>
757 int isl_space_is_equal(__isl_keep isl_space *space1,
758 __isl_keep isl_space *space2);
759 int isl_space_is_domain(__isl_keep isl_space *space1,
760 __isl_keep isl_space *space2);
761 int isl_space_is_range(__isl_keep isl_space *space1,
762 __isl_keep isl_space *space2);
764 C<isl_space_is_domain> checks whether the first argument is equal
765 to the domain of the second argument. This requires in particular that
766 the first argument is a set space and that the second argument
769 It is often useful to create objects that live in the
770 same space as some other object. This can be accomplished
771 by creating the new objects
772 (see L<Creating New Sets and Relations> or
773 L<Creating New (Piecewise) Quasipolynomials>) based on the space
774 of the original object.
777 __isl_give isl_space *isl_basic_set_get_space(
778 __isl_keep isl_basic_set *bset);
779 __isl_give isl_space *isl_set_get_space(__isl_keep isl_set *set);
781 #include <isl/union_set.h>
782 __isl_give isl_space *isl_union_set_get_space(
783 __isl_keep isl_union_set *uset);
786 __isl_give isl_space *isl_basic_map_get_space(
787 __isl_keep isl_basic_map *bmap);
788 __isl_give isl_space *isl_map_get_space(__isl_keep isl_map *map);
790 #include <isl/union_map.h>
791 __isl_give isl_space *isl_union_map_get_space(
792 __isl_keep isl_union_map *umap);
794 #include <isl/constraint.h>
795 __isl_give isl_space *isl_constraint_get_space(
796 __isl_keep isl_constraint *constraint);
798 #include <isl/polynomial.h>
799 __isl_give isl_space *isl_qpolynomial_get_domain_space(
800 __isl_keep isl_qpolynomial *qp);
801 __isl_give isl_space *isl_qpolynomial_get_space(
802 __isl_keep isl_qpolynomial *qp);
803 __isl_give isl_space *isl_qpolynomial_fold_get_space(
804 __isl_keep isl_qpolynomial_fold *fold);
805 __isl_give isl_space *isl_pw_qpolynomial_get_domain_space(
806 __isl_keep isl_pw_qpolynomial *pwqp);
807 __isl_give isl_space *isl_pw_qpolynomial_get_space(
808 __isl_keep isl_pw_qpolynomial *pwqp);
809 __isl_give isl_space *isl_pw_qpolynomial_fold_get_domain_space(
810 __isl_keep isl_pw_qpolynomial_fold *pwf);
811 __isl_give isl_space *isl_pw_qpolynomial_fold_get_space(
812 __isl_keep isl_pw_qpolynomial_fold *pwf);
813 __isl_give isl_space *isl_union_pw_qpolynomial_get_space(
814 __isl_keep isl_union_pw_qpolynomial *upwqp);
815 __isl_give isl_space *isl_union_pw_qpolynomial_fold_get_space(
816 __isl_keep isl_union_pw_qpolynomial_fold *upwf);
819 __isl_give isl_space *isl_multi_val_get_space(
820 __isl_keep isl_multi_val *mv);
823 __isl_give isl_space *isl_aff_get_domain_space(
824 __isl_keep isl_aff *aff);
825 __isl_give isl_space *isl_aff_get_space(
826 __isl_keep isl_aff *aff);
827 __isl_give isl_space *isl_pw_aff_get_domain_space(
828 __isl_keep isl_pw_aff *pwaff);
829 __isl_give isl_space *isl_pw_aff_get_space(
830 __isl_keep isl_pw_aff *pwaff);
831 __isl_give isl_space *isl_multi_aff_get_domain_space(
832 __isl_keep isl_multi_aff *maff);
833 __isl_give isl_space *isl_multi_aff_get_space(
834 __isl_keep isl_multi_aff *maff);
835 __isl_give isl_space *isl_pw_multi_aff_get_domain_space(
836 __isl_keep isl_pw_multi_aff *pma);
837 __isl_give isl_space *isl_pw_multi_aff_get_space(
838 __isl_keep isl_pw_multi_aff *pma);
839 __isl_give isl_space *isl_union_pw_multi_aff_get_space(
840 __isl_keep isl_union_pw_multi_aff *upma);
841 __isl_give isl_space *isl_multi_pw_aff_get_domain_space(
842 __isl_keep isl_multi_pw_aff *mpa);
843 __isl_give isl_space *isl_multi_pw_aff_get_space(
844 __isl_keep isl_multi_pw_aff *mpa);
846 #include <isl/point.h>
847 __isl_give isl_space *isl_point_get_space(
848 __isl_keep isl_point *pnt);
850 The identifiers or names of the individual dimensions may be set or read off
851 using the following functions.
853 #include <isl/space.h>
854 __isl_give isl_space *isl_space_set_dim_id(
855 __isl_take isl_space *space,
856 enum isl_dim_type type, unsigned pos,
857 __isl_take isl_id *id);
858 int isl_space_has_dim_id(__isl_keep isl_space *space,
859 enum isl_dim_type type, unsigned pos);
860 __isl_give isl_id *isl_space_get_dim_id(
861 __isl_keep isl_space *space,
862 enum isl_dim_type type, unsigned pos);
863 __isl_give isl_space *isl_space_set_dim_name(
864 __isl_take isl_space *space,
865 enum isl_dim_type type, unsigned pos,
866 __isl_keep const char *name);
867 int isl_space_has_dim_name(__isl_keep isl_space *space,
868 enum isl_dim_type type, unsigned pos);
869 __isl_keep const char *isl_space_get_dim_name(
870 __isl_keep isl_space *space,
871 enum isl_dim_type type, unsigned pos);
873 Note that C<isl_space_get_name> returns a pointer to some internal
874 data structure, so the result can only be used while the
875 corresponding C<isl_space> is alive.
876 Also note that every function that operates on two sets or relations
877 requires that both arguments have the same parameters. This also
878 means that if one of the arguments has named parameters, then the
879 other needs to have named parameters too and the names need to match.
880 Pairs of C<isl_set>, C<isl_map>, C<isl_union_set> and/or C<isl_union_map>
881 arguments may have different parameters (as long as they are named),
882 in which case the result will have as parameters the union of the parameters of
885 Given the identifier or name of a dimension (typically a parameter),
886 its position can be obtained from the following function.
888 #include <isl/space.h>
889 int isl_space_find_dim_by_id(__isl_keep isl_space *space,
890 enum isl_dim_type type, __isl_keep isl_id *id);
891 int isl_space_find_dim_by_name(__isl_keep isl_space *space,
892 enum isl_dim_type type, const char *name);
894 The identifiers or names of entire spaces may be set or read off
895 using the following functions.
897 #include <isl/space.h>
898 __isl_give isl_space *isl_space_set_tuple_id(
899 __isl_take isl_space *space,
900 enum isl_dim_type type, __isl_take isl_id *id);
901 __isl_give isl_space *isl_space_reset_tuple_id(
902 __isl_take isl_space *space, enum isl_dim_type type);
903 int isl_space_has_tuple_id(__isl_keep isl_space *space,
904 enum isl_dim_type type);
905 __isl_give isl_id *isl_space_get_tuple_id(
906 __isl_keep isl_space *space, enum isl_dim_type type);
907 __isl_give isl_space *isl_space_set_tuple_name(
908 __isl_take isl_space *space,
909 enum isl_dim_type type, const char *s);
910 int isl_space_has_tuple_name(__isl_keep isl_space *space,
911 enum isl_dim_type type);
912 const char *isl_space_get_tuple_name(__isl_keep isl_space *space,
913 enum isl_dim_type type);
915 The C<type> argument needs to be one of C<isl_dim_in>, C<isl_dim_out>
916 or C<isl_dim_set>. As with C<isl_space_get_name>,
917 the C<isl_space_get_tuple_name> function returns a pointer to some internal
919 Binary operations require the corresponding spaces of their arguments
920 to have the same name.
922 Spaces can be nested. In particular, the domain of a set or
923 the domain or range of a relation can be a nested relation.
924 The following functions can be used to construct and deconstruct
927 #include <isl/space.h>
928 int isl_space_is_wrapping(__isl_keep isl_space *space);
929 __isl_give isl_space *isl_space_wrap(__isl_take isl_space *space);
930 __isl_give isl_space *isl_space_unwrap(__isl_take isl_space *space);
932 The input to C<isl_space_is_wrapping> and C<isl_space_unwrap> should
933 be the space of a set, while that of
934 C<isl_space_wrap> should be the space of a relation.
935 Conversely, the output of C<isl_space_unwrap> is the space
936 of a relation, while that of C<isl_space_wrap> is the space of a set.
938 Spaces can be created from other spaces
939 using the following functions.
941 __isl_give isl_space *isl_space_domain(__isl_take isl_space *space);
942 __isl_give isl_space *isl_space_from_domain(__isl_take isl_space *space);
943 __isl_give isl_space *isl_space_range(__isl_take isl_space *space);
944 __isl_give isl_space *isl_space_from_range(__isl_take isl_space *space);
945 __isl_give isl_space *isl_space_params(
946 __isl_take isl_space *space);
947 __isl_give isl_space *isl_space_set_from_params(
948 __isl_take isl_space *space);
949 __isl_give isl_space *isl_space_reverse(__isl_take isl_space *space);
950 __isl_give isl_space *isl_space_join(__isl_take isl_space *left,
951 __isl_take isl_space *right);
952 __isl_give isl_space *isl_space_align_params(
953 __isl_take isl_space *space1, __isl_take isl_space *space2)
954 __isl_give isl_space *isl_space_insert_dims(__isl_take isl_space *space,
955 enum isl_dim_type type, unsigned pos, unsigned n);
956 __isl_give isl_space *isl_space_add_dims(__isl_take isl_space *space,
957 enum isl_dim_type type, unsigned n);
958 __isl_give isl_space *isl_space_drop_dims(__isl_take isl_space *space,
959 enum isl_dim_type type, unsigned first, unsigned n);
960 __isl_give isl_space *isl_space_move_dims(__isl_take isl_space *space,
961 enum isl_dim_type dst_type, unsigned dst_pos,
962 enum isl_dim_type src_type, unsigned src_pos,
964 __isl_give isl_space *isl_space_map_from_set(
965 __isl_take isl_space *space);
966 __isl_give isl_space *isl_space_map_from_domain_and_range(
967 __isl_take isl_space *domain,
968 __isl_take isl_space *range);
969 __isl_give isl_space *isl_space_zip(__isl_take isl_space *space);
970 __isl_give isl_space *isl_space_curry(
971 __isl_take isl_space *space);
972 __isl_give isl_space *isl_space_uncurry(
973 __isl_take isl_space *space);
975 Note that if dimensions are added or removed from a space, then
976 the name and the internal structure are lost.
980 A local space is essentially a space with
981 zero or more existentially quantified variables.
982 The local space of a (constraint of a) basic set or relation can be obtained
983 using the following functions.
985 #include <isl/constraint.h>
986 __isl_give isl_local_space *isl_constraint_get_local_space(
987 __isl_keep isl_constraint *constraint);
990 __isl_give isl_local_space *isl_basic_set_get_local_space(
991 __isl_keep isl_basic_set *bset);
994 __isl_give isl_local_space *isl_basic_map_get_local_space(
995 __isl_keep isl_basic_map *bmap);
997 A new local space can be created from a space using
999 #include <isl/local_space.h>
1000 __isl_give isl_local_space *isl_local_space_from_space(
1001 __isl_take isl_space *space);
1003 They can be inspected, modified, copied and freed using the following functions.
1005 #include <isl/local_space.h>
1006 isl_ctx *isl_local_space_get_ctx(
1007 __isl_keep isl_local_space *ls);
1008 int isl_local_space_is_set(__isl_keep isl_local_space *ls);
1009 int isl_local_space_dim(__isl_keep isl_local_space *ls,
1010 enum isl_dim_type type);
1011 int isl_local_space_has_dim_id(
1012 __isl_keep isl_local_space *ls,
1013 enum isl_dim_type type, unsigned pos);
1014 __isl_give isl_id *isl_local_space_get_dim_id(
1015 __isl_keep isl_local_space *ls,
1016 enum isl_dim_type type, unsigned pos);
1017 int isl_local_space_has_dim_name(
1018 __isl_keep isl_local_space *ls,
1019 enum isl_dim_type type, unsigned pos)
1020 const char *isl_local_space_get_dim_name(
1021 __isl_keep isl_local_space *ls,
1022 enum isl_dim_type type, unsigned pos);
1023 __isl_give isl_local_space *isl_local_space_set_dim_name(
1024 __isl_take isl_local_space *ls,
1025 enum isl_dim_type type, unsigned pos, const char *s);
1026 __isl_give isl_local_space *isl_local_space_set_dim_id(
1027 __isl_take isl_local_space *ls,
1028 enum isl_dim_type type, unsigned pos,
1029 __isl_take isl_id *id);
1030 __isl_give isl_space *isl_local_space_get_space(
1031 __isl_keep isl_local_space *ls);
1032 __isl_give isl_aff *isl_local_space_get_div(
1033 __isl_keep isl_local_space *ls, int pos);
1034 __isl_give isl_local_space *isl_local_space_copy(
1035 __isl_keep isl_local_space *ls);
1036 void *isl_local_space_free(__isl_take isl_local_space *ls);
1038 Note that C<isl_local_space_get_div> can only be used on local spaces
1041 Two local spaces can be compared using
1043 int isl_local_space_is_equal(__isl_keep isl_local_space *ls1,
1044 __isl_keep isl_local_space *ls2);
1046 Local spaces can be created from other local spaces
1047 using the following functions.
1049 __isl_give isl_local_space *isl_local_space_domain(
1050 __isl_take isl_local_space *ls);
1051 __isl_give isl_local_space *isl_local_space_range(
1052 __isl_take isl_local_space *ls);
1053 __isl_give isl_local_space *isl_local_space_from_domain(
1054 __isl_take isl_local_space *ls);
1055 __isl_give isl_local_space *isl_local_space_intersect(
1056 __isl_take isl_local_space *ls1,
1057 __isl_take isl_local_space *ls2);
1058 __isl_give isl_local_space *isl_local_space_add_dims(
1059 __isl_take isl_local_space *ls,
1060 enum isl_dim_type type, unsigned n);
1061 __isl_give isl_local_space *isl_local_space_insert_dims(
1062 __isl_take isl_local_space *ls,
1063 enum isl_dim_type type, unsigned first, unsigned n);
1064 __isl_give isl_local_space *isl_local_space_drop_dims(
1065 __isl_take isl_local_space *ls,
1066 enum isl_dim_type type, unsigned first, unsigned n);
1068 =head2 Input and Output
1070 C<isl> supports its own input/output format, which is similar
1071 to the C<Omega> format, but also supports the C<PolyLib> format
1074 =head3 C<isl> format
1076 The C<isl> format is similar to that of C<Omega>, but has a different
1077 syntax for describing the parameters and allows for the definition
1078 of an existentially quantified variable as the integer division
1079 of an affine expression.
1080 For example, the set of integers C<i> between C<0> and C<n>
1081 such that C<i % 10 <= 6> can be described as
1083 [n] -> { [i] : exists (a = [i/10] : 0 <= i and i <= n and
1086 A set or relation can have several disjuncts, separated
1087 by the keyword C<or>. Each disjunct is either a conjunction
1088 of constraints or a projection (C<exists>) of a conjunction
1089 of constraints. The constraints are separated by the keyword
1092 =head3 C<PolyLib> format
1094 If the represented set is a union, then the first line
1095 contains a single number representing the number of disjuncts.
1096 Otherwise, a line containing the number C<1> is optional.
1098 Each disjunct is represented by a matrix of constraints.
1099 The first line contains two numbers representing
1100 the number of rows and columns,
1101 where the number of rows is equal to the number of constraints
1102 and the number of columns is equal to two plus the number of variables.
1103 The following lines contain the actual rows of the constraint matrix.
1104 In each row, the first column indicates whether the constraint
1105 is an equality (C<0>) or inequality (C<1>). The final column
1106 corresponds to the constant term.
1108 If the set is parametric, then the coefficients of the parameters
1109 appear in the last columns before the constant column.
1110 The coefficients of any existentially quantified variables appear
1111 between those of the set variables and those of the parameters.
1113 =head3 Extended C<PolyLib> format
1115 The extended C<PolyLib> format is nearly identical to the
1116 C<PolyLib> format. The only difference is that the line
1117 containing the number of rows and columns of a constraint matrix
1118 also contains four additional numbers:
1119 the number of output dimensions, the number of input dimensions,
1120 the number of local dimensions (i.e., the number of existentially
1121 quantified variables) and the number of parameters.
1122 For sets, the number of ``output'' dimensions is equal
1123 to the number of set dimensions, while the number of ``input''
1128 #include <isl/set.h>
1129 __isl_give isl_basic_set *isl_basic_set_read_from_file(
1130 isl_ctx *ctx, FILE *input);
1131 __isl_give isl_basic_set *isl_basic_set_read_from_str(
1132 isl_ctx *ctx, const char *str);
1133 __isl_give isl_set *isl_set_read_from_file(isl_ctx *ctx,
1135 __isl_give isl_set *isl_set_read_from_str(isl_ctx *ctx,
1138 #include <isl/map.h>
1139 __isl_give isl_basic_map *isl_basic_map_read_from_file(
1140 isl_ctx *ctx, FILE *input);
1141 __isl_give isl_basic_map *isl_basic_map_read_from_str(
1142 isl_ctx *ctx, const char *str);
1143 __isl_give isl_map *isl_map_read_from_file(
1144 isl_ctx *ctx, FILE *input);
1145 __isl_give isl_map *isl_map_read_from_str(isl_ctx *ctx,
1148 #include <isl/union_set.h>
1149 __isl_give isl_union_set *isl_union_set_read_from_file(
1150 isl_ctx *ctx, FILE *input);
1151 __isl_give isl_union_set *isl_union_set_read_from_str(
1152 isl_ctx *ctx, const char *str);
1154 #include <isl/union_map.h>
1155 __isl_give isl_union_map *isl_union_map_read_from_file(
1156 isl_ctx *ctx, FILE *input);
1157 __isl_give isl_union_map *isl_union_map_read_from_str(
1158 isl_ctx *ctx, const char *str);
1160 The input format is autodetected and may be either the C<PolyLib> format
1161 or the C<isl> format.
1165 Before anything can be printed, an C<isl_printer> needs to
1168 __isl_give isl_printer *isl_printer_to_file(isl_ctx *ctx,
1170 __isl_give isl_printer *isl_printer_to_str(isl_ctx *ctx);
1171 void *isl_printer_free(__isl_take isl_printer *printer);
1172 __isl_give char *isl_printer_get_str(
1173 __isl_keep isl_printer *printer);
1175 The printer can be inspected using the following functions.
1177 FILE *isl_printer_get_file(
1178 __isl_keep isl_printer *printer);
1179 int isl_printer_get_output_format(
1180 __isl_keep isl_printer *p);
1182 The behavior of the printer can be modified in various ways
1184 __isl_give isl_printer *isl_printer_set_output_format(
1185 __isl_take isl_printer *p, int output_format);
1186 __isl_give isl_printer *isl_printer_set_indent(
1187 __isl_take isl_printer *p, int indent);
1188 __isl_give isl_printer *isl_printer_indent(
1189 __isl_take isl_printer *p, int indent);
1190 __isl_give isl_printer *isl_printer_set_prefix(
1191 __isl_take isl_printer *p, const char *prefix);
1192 __isl_give isl_printer *isl_printer_set_suffix(
1193 __isl_take isl_printer *p, const char *suffix);
1195 The C<output_format> may be either C<ISL_FORMAT_ISL>, C<ISL_FORMAT_OMEGA>,
1196 C<ISL_FORMAT_POLYLIB>, C<ISL_FORMAT_EXT_POLYLIB> or C<ISL_FORMAT_LATEX>
1197 and defaults to C<ISL_FORMAT_ISL>.
1198 Each line in the output is indented by C<indent> (set by
1199 C<isl_printer_set_indent>) spaces
1200 (default: 0), prefixed by C<prefix> and suffixed by C<suffix>.
1201 In the C<PolyLib> format output,
1202 the coefficients of the existentially quantified variables
1203 appear between those of the set variables and those
1205 The function C<isl_printer_indent> increases the indentation
1206 by the specified amount (which may be negative).
1208 To actually print something, use
1210 #include <isl/printer.h>
1211 __isl_give isl_printer *isl_printer_print_double(
1212 __isl_take isl_printer *p, double d);
1214 #include <isl/set.h>
1215 __isl_give isl_printer *isl_printer_print_basic_set(
1216 __isl_take isl_printer *printer,
1217 __isl_keep isl_basic_set *bset);
1218 __isl_give isl_printer *isl_printer_print_set(
1219 __isl_take isl_printer *printer,
1220 __isl_keep isl_set *set);
1222 #include <isl/map.h>
1223 __isl_give isl_printer *isl_printer_print_basic_map(
1224 __isl_take isl_printer *printer,
1225 __isl_keep isl_basic_map *bmap);
1226 __isl_give isl_printer *isl_printer_print_map(
1227 __isl_take isl_printer *printer,
1228 __isl_keep isl_map *map);
1230 #include <isl/union_set.h>
1231 __isl_give isl_printer *isl_printer_print_union_set(
1232 __isl_take isl_printer *p,
1233 __isl_keep isl_union_set *uset);
1235 #include <isl/union_map.h>
1236 __isl_give isl_printer *isl_printer_print_union_map(
1237 __isl_take isl_printer *p,
1238 __isl_keep isl_union_map *umap);
1240 When called on a file printer, the following function flushes
1241 the file. When called on a string printer, the buffer is cleared.
1243 __isl_give isl_printer *isl_printer_flush(
1244 __isl_take isl_printer *p);
1246 =head2 Creating New Sets and Relations
1248 C<isl> has functions for creating some standard sets and relations.
1252 =item * Empty sets and relations
1254 __isl_give isl_basic_set *isl_basic_set_empty(
1255 __isl_take isl_space *space);
1256 __isl_give isl_basic_map *isl_basic_map_empty(
1257 __isl_take isl_space *space);
1258 __isl_give isl_set *isl_set_empty(
1259 __isl_take isl_space *space);
1260 __isl_give isl_map *isl_map_empty(
1261 __isl_take isl_space *space);
1262 __isl_give isl_union_set *isl_union_set_empty(
1263 __isl_take isl_space *space);
1264 __isl_give isl_union_map *isl_union_map_empty(
1265 __isl_take isl_space *space);
1267 For C<isl_union_set>s and C<isl_union_map>s, the space
1268 is only used to specify the parameters.
1270 =item * Universe sets and relations
1272 __isl_give isl_basic_set *isl_basic_set_universe(
1273 __isl_take isl_space *space);
1274 __isl_give isl_basic_map *isl_basic_map_universe(
1275 __isl_take isl_space *space);
1276 __isl_give isl_set *isl_set_universe(
1277 __isl_take isl_space *space);
1278 __isl_give isl_map *isl_map_universe(
1279 __isl_take isl_space *space);
1280 __isl_give isl_union_set *isl_union_set_universe(
1281 __isl_take isl_union_set *uset);
1282 __isl_give isl_union_map *isl_union_map_universe(
1283 __isl_take isl_union_map *umap);
1285 The sets and relations constructed by the functions above
1286 contain all integer values, while those constructed by the
1287 functions below only contain non-negative values.
1289 __isl_give isl_basic_set *isl_basic_set_nat_universe(
1290 __isl_take isl_space *space);
1291 __isl_give isl_basic_map *isl_basic_map_nat_universe(
1292 __isl_take isl_space *space);
1293 __isl_give isl_set *isl_set_nat_universe(
1294 __isl_take isl_space *space);
1295 __isl_give isl_map *isl_map_nat_universe(
1296 __isl_take isl_space *space);
1298 =item * Identity relations
1300 __isl_give isl_basic_map *isl_basic_map_identity(
1301 __isl_take isl_space *space);
1302 __isl_give isl_map *isl_map_identity(
1303 __isl_take isl_space *space);
1305 The number of input and output dimensions in C<space> needs
1308 =item * Lexicographic order
1310 __isl_give isl_map *isl_map_lex_lt(
1311 __isl_take isl_space *set_space);
1312 __isl_give isl_map *isl_map_lex_le(
1313 __isl_take isl_space *set_space);
1314 __isl_give isl_map *isl_map_lex_gt(
1315 __isl_take isl_space *set_space);
1316 __isl_give isl_map *isl_map_lex_ge(
1317 __isl_take isl_space *set_space);
1318 __isl_give isl_map *isl_map_lex_lt_first(
1319 __isl_take isl_space *space, unsigned n);
1320 __isl_give isl_map *isl_map_lex_le_first(
1321 __isl_take isl_space *space, unsigned n);
1322 __isl_give isl_map *isl_map_lex_gt_first(
1323 __isl_take isl_space *space, unsigned n);
1324 __isl_give isl_map *isl_map_lex_ge_first(
1325 __isl_take isl_space *space, unsigned n);
1327 The first four functions take a space for a B<set>
1328 and return relations that express that the elements in the domain
1329 are lexicographically less
1330 (C<isl_map_lex_lt>), less or equal (C<isl_map_lex_le>),
1331 greater (C<isl_map_lex_gt>) or greater or equal (C<isl_map_lex_ge>)
1332 than the elements in the range.
1333 The last four functions take a space for a map
1334 and return relations that express that the first C<n> dimensions
1335 in the domain are lexicographically less
1336 (C<isl_map_lex_lt_first>), less or equal (C<isl_map_lex_le_first>),
1337 greater (C<isl_map_lex_gt_first>) or greater or equal (C<isl_map_lex_ge_first>)
1338 than the first C<n> dimensions in the range.
1342 A basic set or relation can be converted to a set or relation
1343 using the following functions.
1345 __isl_give isl_set *isl_set_from_basic_set(
1346 __isl_take isl_basic_set *bset);
1347 __isl_give isl_map *isl_map_from_basic_map(
1348 __isl_take isl_basic_map *bmap);
1350 Sets and relations can be converted to union sets and relations
1351 using the following functions.
1353 __isl_give isl_union_set *isl_union_set_from_basic_set(
1354 __isl_take isl_basic_set *bset);
1355 __isl_give isl_union_map *isl_union_map_from_basic_map(
1356 __isl_take isl_basic_map *bmap);
1357 __isl_give isl_union_set *isl_union_set_from_set(
1358 __isl_take isl_set *set);
1359 __isl_give isl_union_map *isl_union_map_from_map(
1360 __isl_take isl_map *map);
1362 The inverse conversions below can only be used if the input
1363 union set or relation is known to contain elements in exactly one
1366 __isl_give isl_set *isl_set_from_union_set(
1367 __isl_take isl_union_set *uset);
1368 __isl_give isl_map *isl_map_from_union_map(
1369 __isl_take isl_union_map *umap);
1371 A zero-dimensional (basic) set can be constructed on a given parameter domain
1372 using the following function.
1374 __isl_give isl_basic_set *isl_basic_set_from_params(
1375 __isl_take isl_basic_set *bset);
1376 __isl_give isl_set *isl_set_from_params(
1377 __isl_take isl_set *set);
1379 Sets and relations can be copied and freed again using the following
1382 __isl_give isl_basic_set *isl_basic_set_copy(
1383 __isl_keep isl_basic_set *bset);
1384 __isl_give isl_set *isl_set_copy(__isl_keep isl_set *set);
1385 __isl_give isl_union_set *isl_union_set_copy(
1386 __isl_keep isl_union_set *uset);
1387 __isl_give isl_basic_map *isl_basic_map_copy(
1388 __isl_keep isl_basic_map *bmap);
1389 __isl_give isl_map *isl_map_copy(__isl_keep isl_map *map);
1390 __isl_give isl_union_map *isl_union_map_copy(
1391 __isl_keep isl_union_map *umap);
1392 void *isl_basic_set_free(__isl_take isl_basic_set *bset);
1393 void *isl_set_free(__isl_take isl_set *set);
1394 void *isl_union_set_free(__isl_take isl_union_set *uset);
1395 void *isl_basic_map_free(__isl_take isl_basic_map *bmap);
1396 void *isl_map_free(__isl_take isl_map *map);
1397 void *isl_union_map_free(__isl_take isl_union_map *umap);
1399 Other sets and relations can be constructed by starting
1400 from a universe set or relation, adding equality and/or
1401 inequality constraints and then projecting out the
1402 existentially quantified variables, if any.
1403 Constraints can be constructed, manipulated and
1404 added to (or removed from) (basic) sets and relations
1405 using the following functions.
1407 #include <isl/constraint.h>
1408 __isl_give isl_constraint *isl_equality_alloc(
1409 __isl_take isl_local_space *ls);
1410 __isl_give isl_constraint *isl_inequality_alloc(
1411 __isl_take isl_local_space *ls);
1412 __isl_give isl_constraint *isl_constraint_set_constant_si(
1413 __isl_take isl_constraint *constraint, int v);
1414 __isl_give isl_constraint *isl_constraint_set_constant_val(
1415 __isl_take isl_constraint *constraint,
1416 __isl_take isl_val *v);
1417 __isl_give isl_constraint *isl_constraint_set_coefficient_si(
1418 __isl_take isl_constraint *constraint,
1419 enum isl_dim_type type, int pos, int v);
1420 __isl_give isl_constraint *
1421 isl_constraint_set_coefficient_val(
1422 __isl_take isl_constraint *constraint,
1423 enum isl_dim_type type, int pos, isl_val *v);
1424 __isl_give isl_basic_map *isl_basic_map_add_constraint(
1425 __isl_take isl_basic_map *bmap,
1426 __isl_take isl_constraint *constraint);
1427 __isl_give isl_basic_set *isl_basic_set_add_constraint(
1428 __isl_take isl_basic_set *bset,
1429 __isl_take isl_constraint *constraint);
1430 __isl_give isl_map *isl_map_add_constraint(
1431 __isl_take isl_map *map,
1432 __isl_take isl_constraint *constraint);
1433 __isl_give isl_set *isl_set_add_constraint(
1434 __isl_take isl_set *set,
1435 __isl_take isl_constraint *constraint);
1436 __isl_give isl_basic_set *isl_basic_set_drop_constraint(
1437 __isl_take isl_basic_set *bset,
1438 __isl_take isl_constraint *constraint);
1440 For example, to create a set containing the even integers
1441 between 10 and 42, you would use the following code.
1444 isl_local_space *ls;
1446 isl_basic_set *bset;
1448 space = isl_space_set_alloc(ctx, 0, 2);
1449 bset = isl_basic_set_universe(isl_space_copy(space));
1450 ls = isl_local_space_from_space(space);
1452 c = isl_equality_alloc(isl_local_space_copy(ls));
1453 c = isl_constraint_set_coefficient_si(c, isl_dim_set, 0, -1);
1454 c = isl_constraint_set_coefficient_si(c, isl_dim_set, 1, 2);
1455 bset = isl_basic_set_add_constraint(bset, c);
1457 c = isl_inequality_alloc(isl_local_space_copy(ls));
1458 c = isl_constraint_set_constant_si(c, -10);
1459 c = isl_constraint_set_coefficient_si(c, isl_dim_set, 0, 1);
1460 bset = isl_basic_set_add_constraint(bset, c);
1462 c = isl_inequality_alloc(ls);
1463 c = isl_constraint_set_constant_si(c, 42);
1464 c = isl_constraint_set_coefficient_si(c, isl_dim_set, 0, -1);
1465 bset = isl_basic_set_add_constraint(bset, c);
1467 bset = isl_basic_set_project_out(bset, isl_dim_set, 1, 1);
1471 isl_basic_set *bset;
1472 bset = isl_basic_set_read_from_str(ctx,
1473 "{[i] : exists (a : i = 2a and i >= 10 and i <= 42)}");
1475 A basic set or relation can also be constructed from two matrices
1476 describing the equalities and the inequalities.
1478 __isl_give isl_basic_set *isl_basic_set_from_constraint_matrices(
1479 __isl_take isl_space *space,
1480 __isl_take isl_mat *eq, __isl_take isl_mat *ineq,
1481 enum isl_dim_type c1,
1482 enum isl_dim_type c2, enum isl_dim_type c3,
1483 enum isl_dim_type c4);
1484 __isl_give isl_basic_map *isl_basic_map_from_constraint_matrices(
1485 __isl_take isl_space *space,
1486 __isl_take isl_mat *eq, __isl_take isl_mat *ineq,
1487 enum isl_dim_type c1,
1488 enum isl_dim_type c2, enum isl_dim_type c3,
1489 enum isl_dim_type c4, enum isl_dim_type c5);
1491 The C<isl_dim_type> arguments indicate the order in which
1492 different kinds of variables appear in the input matrices
1493 and should be a permutation of C<isl_dim_cst>, C<isl_dim_param>,
1494 C<isl_dim_set> and C<isl_dim_div> for sets and
1495 of C<isl_dim_cst>, C<isl_dim_param>,
1496 C<isl_dim_in>, C<isl_dim_out> and C<isl_dim_div> for relations.
1498 A (basic or union) set or relation can also be constructed from a
1499 (union) (piecewise) (multiple) affine expression
1500 or a list of affine expressions
1501 (See L<"Piecewise Quasi Affine Expressions"> and
1502 L<"Piecewise Multiple Quasi Affine Expressions">).
1504 __isl_give isl_basic_map *isl_basic_map_from_aff(
1505 __isl_take isl_aff *aff);
1506 __isl_give isl_map *isl_map_from_aff(
1507 __isl_take isl_aff *aff);
1508 __isl_give isl_set *isl_set_from_pw_aff(
1509 __isl_take isl_pw_aff *pwaff);
1510 __isl_give isl_map *isl_map_from_pw_aff(
1511 __isl_take isl_pw_aff *pwaff);
1512 __isl_give isl_basic_map *isl_basic_map_from_aff_list(
1513 __isl_take isl_space *domain_space,
1514 __isl_take isl_aff_list *list);
1515 __isl_give isl_basic_map *isl_basic_map_from_multi_aff(
1516 __isl_take isl_multi_aff *maff)
1517 __isl_give isl_map *isl_map_from_multi_aff(
1518 __isl_take isl_multi_aff *maff)
1519 __isl_give isl_set *isl_set_from_pw_multi_aff(
1520 __isl_take isl_pw_multi_aff *pma);
1521 __isl_give isl_map *isl_map_from_pw_multi_aff(
1522 __isl_take isl_pw_multi_aff *pma);
1523 __isl_give isl_union_map *
1524 isl_union_map_from_union_pw_multi_aff(
1525 __isl_take isl_union_pw_multi_aff *upma);
1527 The C<domain_dim> argument describes the domain of the resulting
1528 basic relation. It is required because the C<list> may consist
1529 of zero affine expressions.
1531 =head2 Inspecting Sets and Relations
1533 Usually, the user should not have to care about the actual constraints
1534 of the sets and maps, but should instead apply the abstract operations
1535 explained in the following sections.
1536 Occasionally, however, it may be required to inspect the individual
1537 coefficients of the constraints. This section explains how to do so.
1538 In these cases, it may also be useful to have C<isl> compute
1539 an explicit representation of the existentially quantified variables.
1541 __isl_give isl_set *isl_set_compute_divs(
1542 __isl_take isl_set *set);
1543 __isl_give isl_map *isl_map_compute_divs(
1544 __isl_take isl_map *map);
1545 __isl_give isl_union_set *isl_union_set_compute_divs(
1546 __isl_take isl_union_set *uset);
1547 __isl_give isl_union_map *isl_union_map_compute_divs(
1548 __isl_take isl_union_map *umap);
1550 This explicit representation defines the existentially quantified
1551 variables as integer divisions of the other variables, possibly
1552 including earlier existentially quantified variables.
1553 An explicitly represented existentially quantified variable therefore
1554 has a unique value when the values of the other variables are known.
1555 If, furthermore, the same existentials, i.e., existentials
1556 with the same explicit representations, should appear in the
1557 same order in each of the disjuncts of a set or map, then the user should call
1558 either of the following functions.
1560 __isl_give isl_set *isl_set_align_divs(
1561 __isl_take isl_set *set);
1562 __isl_give isl_map *isl_map_align_divs(
1563 __isl_take isl_map *map);
1565 Alternatively, the existentially quantified variables can be removed
1566 using the following functions, which compute an overapproximation.
1568 __isl_give isl_basic_set *isl_basic_set_remove_divs(
1569 __isl_take isl_basic_set *bset);
1570 __isl_give isl_basic_map *isl_basic_map_remove_divs(
1571 __isl_take isl_basic_map *bmap);
1572 __isl_give isl_set *isl_set_remove_divs(
1573 __isl_take isl_set *set);
1574 __isl_give isl_map *isl_map_remove_divs(
1575 __isl_take isl_map *map);
1577 It is also possible to only remove those divs that are defined
1578 in terms of a given range of dimensions or only those for which
1579 no explicit representation is known.
1581 __isl_give isl_basic_set *
1582 isl_basic_set_remove_divs_involving_dims(
1583 __isl_take isl_basic_set *bset,
1584 enum isl_dim_type type,
1585 unsigned first, unsigned n);
1586 __isl_give isl_basic_map *
1587 isl_basic_map_remove_divs_involving_dims(
1588 __isl_take isl_basic_map *bmap,
1589 enum isl_dim_type type,
1590 unsigned first, unsigned n);
1591 __isl_give isl_set *isl_set_remove_divs_involving_dims(
1592 __isl_take isl_set *set, enum isl_dim_type type,
1593 unsigned first, unsigned n);
1594 __isl_give isl_map *isl_map_remove_divs_involving_dims(
1595 __isl_take isl_map *map, enum isl_dim_type type,
1596 unsigned first, unsigned n);
1598 __isl_give isl_basic_set *
1599 isl_basic_set_remove_unknown_divs(
1600 __isl_take isl_basic_set *bset);
1601 __isl_give isl_set *isl_set_remove_unknown_divs(
1602 __isl_take isl_set *set);
1603 __isl_give isl_map *isl_map_remove_unknown_divs(
1604 __isl_take isl_map *map);
1606 To iterate over all the sets or maps in a union set or map, use
1608 int isl_union_set_foreach_set(__isl_keep isl_union_set *uset,
1609 int (*fn)(__isl_take isl_set *set, void *user),
1611 int isl_union_map_foreach_map(__isl_keep isl_union_map *umap,
1612 int (*fn)(__isl_take isl_map *map, void *user),
1615 The number of sets or maps in a union set or map can be obtained
1618 int isl_union_set_n_set(__isl_keep isl_union_set *uset);
1619 int isl_union_map_n_map(__isl_keep isl_union_map *umap);
1621 To extract the set or map in a given space from a union, use
1623 __isl_give isl_set *isl_union_set_extract_set(
1624 __isl_keep isl_union_set *uset,
1625 __isl_take isl_space *space);
1626 __isl_give isl_map *isl_union_map_extract_map(
1627 __isl_keep isl_union_map *umap,
1628 __isl_take isl_space *space);
1630 To iterate over all the basic sets or maps in a set or map, use
1632 int isl_set_foreach_basic_set(__isl_keep isl_set *set,
1633 int (*fn)(__isl_take isl_basic_set *bset, void *user),
1635 int isl_map_foreach_basic_map(__isl_keep isl_map *map,
1636 int (*fn)(__isl_take isl_basic_map *bmap, void *user),
1639 The callback function C<fn> should return 0 if successful and
1640 -1 if an error occurs. In the latter case, or if any other error
1641 occurs, the above functions will return -1.
1643 It should be noted that C<isl> does not guarantee that
1644 the basic sets or maps passed to C<fn> are disjoint.
1645 If this is required, then the user should call one of
1646 the following functions first.
1648 __isl_give isl_set *isl_set_make_disjoint(
1649 __isl_take isl_set *set);
1650 __isl_give isl_map *isl_map_make_disjoint(
1651 __isl_take isl_map *map);
1653 The number of basic sets in a set can be obtained
1656 int isl_set_n_basic_set(__isl_keep isl_set *set);
1658 To iterate over the constraints of a basic set or map, use
1660 #include <isl/constraint.h>
1662 int isl_basic_set_n_constraint(
1663 __isl_keep isl_basic_set *bset);
1664 int isl_basic_set_foreach_constraint(
1665 __isl_keep isl_basic_set *bset,
1666 int (*fn)(__isl_take isl_constraint *c, void *user),
1668 int isl_basic_map_foreach_constraint(
1669 __isl_keep isl_basic_map *bmap,
1670 int (*fn)(__isl_take isl_constraint *c, void *user),
1672 void *isl_constraint_free(__isl_take isl_constraint *c);
1674 Again, the callback function C<fn> should return 0 if successful and
1675 -1 if an error occurs. In the latter case, or if any other error
1676 occurs, the above functions will return -1.
1677 The constraint C<c> represents either an equality or an inequality.
1678 Use the following function to find out whether a constraint
1679 represents an equality. If not, it represents an inequality.
1681 int isl_constraint_is_equality(
1682 __isl_keep isl_constraint *constraint);
1684 The coefficients of the constraints can be inspected using
1685 the following functions.
1687 int isl_constraint_is_lower_bound(
1688 __isl_keep isl_constraint *constraint,
1689 enum isl_dim_type type, unsigned pos);
1690 int isl_constraint_is_upper_bound(
1691 __isl_keep isl_constraint *constraint,
1692 enum isl_dim_type type, unsigned pos);
1693 __isl_give isl_val *isl_constraint_get_constant_val(
1694 __isl_keep isl_constraint *constraint);
1695 __isl_give isl_val *isl_constraint_get_coefficient_val(
1696 __isl_keep isl_constraint *constraint,
1697 enum isl_dim_type type, int pos);
1698 int isl_constraint_involves_dims(
1699 __isl_keep isl_constraint *constraint,
1700 enum isl_dim_type type, unsigned first, unsigned n);
1702 The explicit representations of the existentially quantified
1703 variables can be inspected using the following function.
1704 Note that the user is only allowed to use this function
1705 if the inspected set or map is the result of a call
1706 to C<isl_set_compute_divs> or C<isl_map_compute_divs>.
1707 The existentially quantified variable is equal to the floor
1708 of the returned affine expression. The affine expression
1709 itself can be inspected using the functions in
1710 L<"Piecewise Quasi Affine Expressions">.
1712 __isl_give isl_aff *isl_constraint_get_div(
1713 __isl_keep isl_constraint *constraint, int pos);
1715 To obtain the constraints of a basic set or map in matrix
1716 form, use the following functions.
1718 __isl_give isl_mat *isl_basic_set_equalities_matrix(
1719 __isl_keep isl_basic_set *bset,
1720 enum isl_dim_type c1, enum isl_dim_type c2,
1721 enum isl_dim_type c3, enum isl_dim_type c4);
1722 __isl_give isl_mat *isl_basic_set_inequalities_matrix(
1723 __isl_keep isl_basic_set *bset,
1724 enum isl_dim_type c1, enum isl_dim_type c2,
1725 enum isl_dim_type c3, enum isl_dim_type c4);
1726 __isl_give isl_mat *isl_basic_map_equalities_matrix(
1727 __isl_keep isl_basic_map *bmap,
1728 enum isl_dim_type c1,
1729 enum isl_dim_type c2, enum isl_dim_type c3,
1730 enum isl_dim_type c4, enum isl_dim_type c5);
1731 __isl_give isl_mat *isl_basic_map_inequalities_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);
1737 The C<isl_dim_type> arguments dictate the order in which
1738 different kinds of variables appear in the resulting matrix
1739 and should be a permutation of C<isl_dim_cst>, C<isl_dim_param>,
1740 C<isl_dim_in>, C<isl_dim_out> and C<isl_dim_div>.
1742 The number of parameters, input, output or set dimensions can
1743 be obtained using the following functions.
1745 unsigned isl_basic_set_dim(__isl_keep isl_basic_set *bset,
1746 enum isl_dim_type type);
1747 unsigned isl_basic_map_dim(__isl_keep isl_basic_map *bmap,
1748 enum isl_dim_type type);
1749 unsigned isl_set_dim(__isl_keep isl_set *set,
1750 enum isl_dim_type type);
1751 unsigned isl_map_dim(__isl_keep isl_map *map,
1752 enum isl_dim_type type);
1754 To check whether the description of a set or relation depends
1755 on one or more given dimensions, it is not necessary to iterate over all
1756 constraints. Instead the following functions can be used.
1758 int isl_basic_set_involves_dims(
1759 __isl_keep isl_basic_set *bset,
1760 enum isl_dim_type type, unsigned first, unsigned n);
1761 int isl_set_involves_dims(__isl_keep isl_set *set,
1762 enum isl_dim_type type, unsigned first, unsigned n);
1763 int isl_basic_map_involves_dims(
1764 __isl_keep isl_basic_map *bmap,
1765 enum isl_dim_type type, unsigned first, unsigned n);
1766 int isl_map_involves_dims(__isl_keep isl_map *map,
1767 enum isl_dim_type type, unsigned first, unsigned n);
1769 Similarly, the following functions can be used to check whether
1770 a given dimension is involved in any lower or upper bound.
1772 int isl_set_dim_has_any_lower_bound(__isl_keep isl_set *set,
1773 enum isl_dim_type type, unsigned pos);
1774 int isl_set_dim_has_any_upper_bound(__isl_keep isl_set *set,
1775 enum isl_dim_type type, unsigned pos);
1777 Note that these functions return true even if there is a bound on
1778 the dimension on only some of the basic sets of C<set>.
1779 To check if they have a bound for all of the basic sets in C<set>,
1780 use the following functions instead.
1782 int isl_set_dim_has_lower_bound(__isl_keep isl_set *set,
1783 enum isl_dim_type type, unsigned pos);
1784 int isl_set_dim_has_upper_bound(__isl_keep isl_set *set,
1785 enum isl_dim_type type, unsigned pos);
1787 The identifiers or names of the domain and range spaces of a set
1788 or relation can be read off or set using the following functions.
1790 __isl_give isl_set *isl_set_set_tuple_id(
1791 __isl_take isl_set *set, __isl_take isl_id *id);
1792 __isl_give isl_set *isl_set_reset_tuple_id(
1793 __isl_take isl_set *set);
1794 int isl_set_has_tuple_id(__isl_keep isl_set *set);
1795 __isl_give isl_id *isl_set_get_tuple_id(
1796 __isl_keep isl_set *set);
1797 __isl_give isl_map *isl_map_set_tuple_id(
1798 __isl_take isl_map *map, enum isl_dim_type type,
1799 __isl_take isl_id *id);
1800 __isl_give isl_map *isl_map_reset_tuple_id(
1801 __isl_take isl_map *map, enum isl_dim_type type);
1802 int isl_map_has_tuple_id(__isl_keep isl_map *map,
1803 enum isl_dim_type type);
1804 __isl_give isl_id *isl_map_get_tuple_id(
1805 __isl_keep isl_map *map, enum isl_dim_type type);
1807 const char *isl_basic_set_get_tuple_name(
1808 __isl_keep isl_basic_set *bset);
1809 __isl_give isl_basic_set *isl_basic_set_set_tuple_name(
1810 __isl_take isl_basic_set *set, const char *s);
1811 int isl_set_has_tuple_name(__isl_keep isl_set *set);
1812 const char *isl_set_get_tuple_name(
1813 __isl_keep isl_set *set);
1814 const char *isl_basic_map_get_tuple_name(
1815 __isl_keep isl_basic_map *bmap,
1816 enum isl_dim_type type);
1817 __isl_give isl_basic_map *isl_basic_map_set_tuple_name(
1818 __isl_take isl_basic_map *bmap,
1819 enum isl_dim_type type, const char *s);
1820 int isl_map_has_tuple_name(__isl_keep isl_map *map,
1821 enum isl_dim_type type);
1822 const char *isl_map_get_tuple_name(
1823 __isl_keep isl_map *map,
1824 enum isl_dim_type type);
1826 As with C<isl_space_get_tuple_name>, the value returned points to
1827 an internal data structure.
1828 The identifiers, positions or names of individual dimensions can be
1829 read off using the following functions.
1831 __isl_give isl_id *isl_basic_set_get_dim_id(
1832 __isl_keep isl_basic_set *bset,
1833 enum isl_dim_type type, unsigned pos);
1834 __isl_give isl_set *isl_set_set_dim_id(
1835 __isl_take isl_set *set, enum isl_dim_type type,
1836 unsigned pos, __isl_take isl_id *id);
1837 int isl_set_has_dim_id(__isl_keep isl_set *set,
1838 enum isl_dim_type type, unsigned pos);
1839 __isl_give isl_id *isl_set_get_dim_id(
1840 __isl_keep isl_set *set, enum isl_dim_type type,
1842 int isl_basic_map_has_dim_id(
1843 __isl_keep isl_basic_map *bmap,
1844 enum isl_dim_type type, unsigned pos);
1845 __isl_give isl_map *isl_map_set_dim_id(
1846 __isl_take isl_map *map, enum isl_dim_type type,
1847 unsigned pos, __isl_take isl_id *id);
1848 int isl_map_has_dim_id(__isl_keep isl_map *map,
1849 enum isl_dim_type type, unsigned pos);
1850 __isl_give isl_id *isl_map_get_dim_id(
1851 __isl_keep isl_map *map, enum isl_dim_type type,
1854 int isl_set_find_dim_by_id(__isl_keep isl_set *set,
1855 enum isl_dim_type type, __isl_keep isl_id *id);
1856 int isl_map_find_dim_by_id(__isl_keep isl_map *map,
1857 enum isl_dim_type type, __isl_keep isl_id *id);
1858 int isl_set_find_dim_by_name(__isl_keep isl_set *set,
1859 enum isl_dim_type type, const char *name);
1860 int isl_map_find_dim_by_name(__isl_keep isl_map *map,
1861 enum isl_dim_type type, const char *name);
1863 const char *isl_constraint_get_dim_name(
1864 __isl_keep isl_constraint *constraint,
1865 enum isl_dim_type type, unsigned pos);
1866 const char *isl_basic_set_get_dim_name(
1867 __isl_keep isl_basic_set *bset,
1868 enum isl_dim_type type, unsigned pos);
1869 int isl_set_has_dim_name(__isl_keep isl_set *set,
1870 enum isl_dim_type type, unsigned pos);
1871 const char *isl_set_get_dim_name(
1872 __isl_keep isl_set *set,
1873 enum isl_dim_type type, unsigned pos);
1874 const char *isl_basic_map_get_dim_name(
1875 __isl_keep isl_basic_map *bmap,
1876 enum isl_dim_type type, unsigned pos);
1877 int isl_map_has_dim_name(__isl_keep isl_map *map,
1878 enum isl_dim_type type, unsigned pos);
1879 const char *isl_map_get_dim_name(
1880 __isl_keep isl_map *map,
1881 enum isl_dim_type type, unsigned pos);
1883 These functions are mostly useful to obtain the identifiers, positions
1884 or names of the parameters. Identifiers of individual dimensions are
1885 essentially only useful for printing. They are ignored by all other
1886 operations and may not be preserved across those operations.
1890 =head3 Unary Properties
1896 The following functions test whether the given set or relation
1897 contains any integer points. The ``plain'' variants do not perform
1898 any computations, but simply check if the given set or relation
1899 is already known to be empty.
1901 int isl_basic_set_plain_is_empty(__isl_keep isl_basic_set *bset);
1902 int isl_basic_set_is_empty(__isl_keep isl_basic_set *bset);
1903 int isl_set_plain_is_empty(__isl_keep isl_set *set);
1904 int isl_set_is_empty(__isl_keep isl_set *set);
1905 int isl_union_set_is_empty(__isl_keep isl_union_set *uset);
1906 int isl_basic_map_plain_is_empty(__isl_keep isl_basic_map *bmap);
1907 int isl_basic_map_is_empty(__isl_keep isl_basic_map *bmap);
1908 int isl_map_plain_is_empty(__isl_keep isl_map *map);
1909 int isl_map_is_empty(__isl_keep isl_map *map);
1910 int isl_union_map_is_empty(__isl_keep isl_union_map *umap);
1912 =item * Universality
1914 int isl_basic_set_is_universe(__isl_keep isl_basic_set *bset);
1915 int isl_basic_map_is_universe(__isl_keep isl_basic_map *bmap);
1916 int isl_set_plain_is_universe(__isl_keep isl_set *set);
1918 =item * Single-valuedness
1920 int isl_basic_map_is_single_valued(
1921 __isl_keep isl_basic_map *bmap);
1922 int isl_map_plain_is_single_valued(
1923 __isl_keep isl_map *map);
1924 int isl_map_is_single_valued(__isl_keep isl_map *map);
1925 int isl_union_map_is_single_valued(__isl_keep isl_union_map *umap);
1929 int isl_map_plain_is_injective(__isl_keep isl_map *map);
1930 int isl_map_is_injective(__isl_keep isl_map *map);
1931 int isl_union_map_plain_is_injective(
1932 __isl_keep isl_union_map *umap);
1933 int isl_union_map_is_injective(
1934 __isl_keep isl_union_map *umap);
1938 int isl_map_is_bijective(__isl_keep isl_map *map);
1939 int isl_union_map_is_bijective(__isl_keep isl_union_map *umap);
1943 __isl_give isl_val *
1944 isl_basic_map_plain_get_val_if_fixed(
1945 __isl_keep isl_basic_map *bmap,
1946 enum isl_dim_type type, unsigned pos);
1947 __isl_give isl_val *isl_set_plain_get_val_if_fixed(
1948 __isl_keep isl_set *set,
1949 enum isl_dim_type type, unsigned pos);
1950 __isl_give isl_val *isl_map_plain_get_val_if_fixed(
1951 __isl_keep isl_map *map,
1952 enum isl_dim_type type, unsigned pos);
1954 If the set or relation obviously lies on a hyperplane where the given dimension
1955 has a fixed value, then return that value.
1956 Otherwise return NaN.
1960 int isl_set_dim_residue_class_val(
1961 __isl_keep isl_set *set,
1962 int pos, __isl_give isl_val **modulo,
1963 __isl_give isl_val **residue);
1965 Check if the values of the given set dimension are equal to a fixed
1966 value modulo some integer value. If so, assign the modulo to C<*modulo>
1967 and the fixed value to C<*residue>. If the given dimension attains only
1968 a single value, then assign C<0> to C<*modulo> and the fixed value to
1970 If the dimension does not attain only a single value and if no modulo
1971 can be found then assign C<1> to C<*modulo> and C<1> to C<*residue>.
1975 To check whether a set is a parameter domain, use this function:
1977 int isl_set_is_params(__isl_keep isl_set *set);
1978 int isl_union_set_is_params(
1979 __isl_keep isl_union_set *uset);
1983 The following functions check whether the domain of the given
1984 (basic) set is a wrapped relation.
1986 int isl_basic_set_is_wrapping(
1987 __isl_keep isl_basic_set *bset);
1988 int isl_set_is_wrapping(__isl_keep isl_set *set);
1990 =item * Internal Product
1992 int isl_basic_map_can_zip(
1993 __isl_keep isl_basic_map *bmap);
1994 int isl_map_can_zip(__isl_keep isl_map *map);
1996 Check whether the product of domain and range of the given relation
1998 i.e., whether both domain and range are nested relations.
2002 int isl_basic_map_can_curry(
2003 __isl_keep isl_basic_map *bmap);
2004 int isl_map_can_curry(__isl_keep isl_map *map);
2006 Check whether the domain of the (basic) relation is a wrapped relation.
2008 int isl_basic_map_can_uncurry(
2009 __isl_keep isl_basic_map *bmap);
2010 int isl_map_can_uncurry(__isl_keep isl_map *map);
2012 Check whether the range of the (basic) relation is a wrapped relation.
2016 =head3 Binary Properties
2022 int isl_set_plain_is_equal(__isl_keep isl_set *set1,
2023 __isl_keep isl_set *set2);
2024 int isl_set_is_equal(__isl_keep isl_set *set1,
2025 __isl_keep isl_set *set2);
2026 int isl_union_set_is_equal(
2027 __isl_keep isl_union_set *uset1,
2028 __isl_keep isl_union_set *uset2);
2029 int isl_basic_map_is_equal(
2030 __isl_keep isl_basic_map *bmap1,
2031 __isl_keep isl_basic_map *bmap2);
2032 int isl_map_is_equal(__isl_keep isl_map *map1,
2033 __isl_keep isl_map *map2);
2034 int isl_map_plain_is_equal(__isl_keep isl_map *map1,
2035 __isl_keep isl_map *map2);
2036 int isl_union_map_is_equal(
2037 __isl_keep isl_union_map *umap1,
2038 __isl_keep isl_union_map *umap2);
2040 =item * Disjointness
2042 int isl_set_plain_is_disjoint(__isl_keep isl_set *set1,
2043 __isl_keep isl_set *set2);
2044 int isl_set_is_disjoint(__isl_keep isl_set *set1,
2045 __isl_keep isl_set *set2);
2046 int isl_map_is_disjoint(__isl_keep isl_map *map1,
2047 __isl_keep isl_map *map2);
2051 int isl_basic_set_is_subset(
2052 __isl_keep isl_basic_set *bset1,
2053 __isl_keep isl_basic_set *bset2);
2054 int isl_set_is_subset(__isl_keep isl_set *set1,
2055 __isl_keep isl_set *set2);
2056 int isl_set_is_strict_subset(
2057 __isl_keep isl_set *set1,
2058 __isl_keep isl_set *set2);
2059 int isl_union_set_is_subset(
2060 __isl_keep isl_union_set *uset1,
2061 __isl_keep isl_union_set *uset2);
2062 int isl_union_set_is_strict_subset(
2063 __isl_keep isl_union_set *uset1,
2064 __isl_keep isl_union_set *uset2);
2065 int isl_basic_map_is_subset(
2066 __isl_keep isl_basic_map *bmap1,
2067 __isl_keep isl_basic_map *bmap2);
2068 int isl_basic_map_is_strict_subset(
2069 __isl_keep isl_basic_map *bmap1,
2070 __isl_keep isl_basic_map *bmap2);
2071 int isl_map_is_subset(
2072 __isl_keep isl_map *map1,
2073 __isl_keep isl_map *map2);
2074 int isl_map_is_strict_subset(
2075 __isl_keep isl_map *map1,
2076 __isl_keep isl_map *map2);
2077 int isl_union_map_is_subset(
2078 __isl_keep isl_union_map *umap1,
2079 __isl_keep isl_union_map *umap2);
2080 int isl_union_map_is_strict_subset(
2081 __isl_keep isl_union_map *umap1,
2082 __isl_keep isl_union_map *umap2);
2084 Check whether the first argument is a (strict) subset of the
2089 int isl_set_plain_cmp(__isl_keep isl_set *set1,
2090 __isl_keep isl_set *set2);
2092 This function is useful for sorting C<isl_set>s.
2093 The order depends on the internal representation of the inputs.
2094 The order is fixed over different calls to the function (assuming
2095 the internal representation of the inputs has not changed), but may
2096 change over different versions of C<isl>.
2100 =head2 Unary Operations
2106 __isl_give isl_set *isl_set_complement(
2107 __isl_take isl_set *set);
2108 __isl_give isl_map *isl_map_complement(
2109 __isl_take isl_map *map);
2113 __isl_give isl_basic_map *isl_basic_map_reverse(
2114 __isl_take isl_basic_map *bmap);
2115 __isl_give isl_map *isl_map_reverse(
2116 __isl_take isl_map *map);
2117 __isl_give isl_union_map *isl_union_map_reverse(
2118 __isl_take isl_union_map *umap);
2122 __isl_give isl_basic_set *isl_basic_set_project_out(
2123 __isl_take isl_basic_set *bset,
2124 enum isl_dim_type type, unsigned first, unsigned n);
2125 __isl_give isl_basic_map *isl_basic_map_project_out(
2126 __isl_take isl_basic_map *bmap,
2127 enum isl_dim_type type, unsigned first, unsigned n);
2128 __isl_give isl_set *isl_set_project_out(__isl_take isl_set *set,
2129 enum isl_dim_type type, unsigned first, unsigned n);
2130 __isl_give isl_map *isl_map_project_out(__isl_take isl_map *map,
2131 enum isl_dim_type type, unsigned first, unsigned n);
2132 __isl_give isl_basic_set *isl_basic_set_params(
2133 __isl_take isl_basic_set *bset);
2134 __isl_give isl_basic_set *isl_basic_map_domain(
2135 __isl_take isl_basic_map *bmap);
2136 __isl_give isl_basic_set *isl_basic_map_range(
2137 __isl_take isl_basic_map *bmap);
2138 __isl_give isl_set *isl_set_params(__isl_take isl_set *set);
2139 __isl_give isl_set *isl_map_params(__isl_take isl_map *map);
2140 __isl_give isl_set *isl_map_domain(
2141 __isl_take isl_map *bmap);
2142 __isl_give isl_set *isl_map_range(
2143 __isl_take isl_map *map);
2144 __isl_give isl_set *isl_union_set_params(
2145 __isl_take isl_union_set *uset);
2146 __isl_give isl_set *isl_union_map_params(
2147 __isl_take isl_union_map *umap);
2148 __isl_give isl_union_set *isl_union_map_domain(
2149 __isl_take isl_union_map *umap);
2150 __isl_give isl_union_set *isl_union_map_range(
2151 __isl_take isl_union_map *umap);
2153 __isl_give isl_basic_map *isl_basic_map_domain_map(
2154 __isl_take isl_basic_map *bmap);
2155 __isl_give isl_basic_map *isl_basic_map_range_map(
2156 __isl_take isl_basic_map *bmap);
2157 __isl_give isl_map *isl_map_domain_map(__isl_take isl_map *map);
2158 __isl_give isl_map *isl_map_range_map(__isl_take isl_map *map);
2159 __isl_give isl_union_map *isl_union_map_domain_map(
2160 __isl_take isl_union_map *umap);
2161 __isl_give isl_union_map *isl_union_map_range_map(
2162 __isl_take isl_union_map *umap);
2164 The functions above construct a (basic, regular or union) relation
2165 that maps (a wrapped version of) the input relation to its domain or range.
2169 __isl_give isl_basic_set *isl_basic_set_eliminate(
2170 __isl_take isl_basic_set *bset,
2171 enum isl_dim_type type,
2172 unsigned first, unsigned n);
2173 __isl_give isl_set *isl_set_eliminate(
2174 __isl_take isl_set *set, enum isl_dim_type type,
2175 unsigned first, unsigned n);
2176 __isl_give isl_basic_map *isl_basic_map_eliminate(
2177 __isl_take isl_basic_map *bmap,
2178 enum isl_dim_type type,
2179 unsigned first, unsigned n);
2180 __isl_give isl_map *isl_map_eliminate(
2181 __isl_take isl_map *map, enum isl_dim_type type,
2182 unsigned first, unsigned n);
2184 Eliminate the coefficients for the given dimensions from the constraints,
2185 without removing the dimensions.
2189 __isl_give isl_basic_set *isl_basic_set_fix_si(
2190 __isl_take isl_basic_set *bset,
2191 enum isl_dim_type type, unsigned pos, int value);
2192 __isl_give isl_basic_set *isl_basic_set_fix_val(
2193 __isl_take isl_basic_set *bset,
2194 enum isl_dim_type type, unsigned pos,
2195 __isl_take isl_val *v);
2196 __isl_give isl_set *isl_set_fix_si(__isl_take isl_set *set,
2197 enum isl_dim_type type, unsigned pos, int value);
2198 __isl_give isl_set *isl_set_fix_val(
2199 __isl_take isl_set *set,
2200 enum isl_dim_type type, unsigned pos,
2201 __isl_take isl_val *v);
2202 __isl_give isl_basic_map *isl_basic_map_fix_si(
2203 __isl_take isl_basic_map *bmap,
2204 enum isl_dim_type type, unsigned pos, int value);
2205 __isl_give isl_basic_map *isl_basic_map_fix_val(
2206 __isl_take isl_basic_map *bmap,
2207 enum isl_dim_type type, unsigned pos,
2208 __isl_take isl_val *v);
2209 __isl_give isl_map *isl_map_fix_si(__isl_take isl_map *map,
2210 enum isl_dim_type type, unsigned pos, int value);
2211 __isl_give isl_map *isl_map_fix_val(
2212 __isl_take isl_map *map,
2213 enum isl_dim_type type, unsigned pos,
2214 __isl_take isl_val *v);
2216 Intersect the set or relation with the hyperplane where the given
2217 dimension has the fixed given value.
2219 __isl_give isl_basic_map *isl_basic_map_lower_bound_si(
2220 __isl_take isl_basic_map *bmap,
2221 enum isl_dim_type type, unsigned pos, int value);
2222 __isl_give isl_basic_map *isl_basic_map_upper_bound_si(
2223 __isl_take isl_basic_map *bmap,
2224 enum isl_dim_type type, unsigned pos, int value);
2225 __isl_give isl_set *isl_set_lower_bound_si(
2226 __isl_take isl_set *set,
2227 enum isl_dim_type type, unsigned pos, int value);
2228 __isl_give isl_set *isl_set_lower_bound_val(
2229 __isl_take isl_set *set,
2230 enum isl_dim_type type, unsigned pos,
2231 __isl_take isl_val *value);
2232 __isl_give isl_map *isl_map_lower_bound_si(
2233 __isl_take isl_map *map,
2234 enum isl_dim_type type, unsigned pos, int value);
2235 __isl_give isl_set *isl_set_upper_bound_si(
2236 __isl_take isl_set *set,
2237 enum isl_dim_type type, unsigned pos, int value);
2238 __isl_give isl_set *isl_set_upper_bound_val(
2239 __isl_take isl_set *set,
2240 enum isl_dim_type type, unsigned pos,
2241 __isl_take isl_val *value);
2242 __isl_give isl_map *isl_map_upper_bound_si(
2243 __isl_take isl_map *map,
2244 enum isl_dim_type type, unsigned pos, int value);
2246 Intersect the set or relation with the half-space where the given
2247 dimension has a value bounded by the fixed given integer value.
2249 __isl_give isl_set *isl_set_equate(__isl_take isl_set *set,
2250 enum isl_dim_type type1, int pos1,
2251 enum isl_dim_type type2, int pos2);
2252 __isl_give isl_basic_map *isl_basic_map_equate(
2253 __isl_take isl_basic_map *bmap,
2254 enum isl_dim_type type1, int pos1,
2255 enum isl_dim_type type2, int pos2);
2256 __isl_give isl_map *isl_map_equate(__isl_take isl_map *map,
2257 enum isl_dim_type type1, int pos1,
2258 enum isl_dim_type type2, int pos2);
2260 Intersect the set or relation with the hyperplane where the given
2261 dimensions are equal to each other.
2263 __isl_give isl_map *isl_map_oppose(__isl_take isl_map *map,
2264 enum isl_dim_type type1, int pos1,
2265 enum isl_dim_type type2, int pos2);
2267 Intersect the relation with the hyperplane where the given
2268 dimensions have opposite values.
2270 __isl_give isl_basic_map *isl_basic_map_order_ge(
2271 __isl_take isl_basic_map *bmap,
2272 enum isl_dim_type type1, int pos1,
2273 enum isl_dim_type type2, int pos2);
2274 __isl_give isl_map *isl_map_order_lt(__isl_take isl_map *map,
2275 enum isl_dim_type type1, int pos1,
2276 enum isl_dim_type type2, int pos2);
2277 __isl_give isl_basic_map *isl_basic_map_order_gt(
2278 __isl_take isl_basic_map *bmap,
2279 enum isl_dim_type type1, int pos1,
2280 enum isl_dim_type type2, int pos2);
2281 __isl_give isl_map *isl_map_order_gt(__isl_take isl_map *map,
2282 enum isl_dim_type type1, int pos1,
2283 enum isl_dim_type type2, int pos2);
2285 Intersect the relation with the half-space where the given
2286 dimensions satisfy the given ordering.
2290 __isl_give isl_map *isl_set_identity(
2291 __isl_take isl_set *set);
2292 __isl_give isl_union_map *isl_union_set_identity(
2293 __isl_take isl_union_set *uset);
2295 Construct an identity relation on the given (union) set.
2299 __isl_give isl_basic_set *isl_basic_map_deltas(
2300 __isl_take isl_basic_map *bmap);
2301 __isl_give isl_set *isl_map_deltas(__isl_take isl_map *map);
2302 __isl_give isl_union_set *isl_union_map_deltas(
2303 __isl_take isl_union_map *umap);
2305 These functions return a (basic) set containing the differences
2306 between image elements and corresponding domain elements in the input.
2308 __isl_give isl_basic_map *isl_basic_map_deltas_map(
2309 __isl_take isl_basic_map *bmap);
2310 __isl_give isl_map *isl_map_deltas_map(
2311 __isl_take isl_map *map);
2312 __isl_give isl_union_map *isl_union_map_deltas_map(
2313 __isl_take isl_union_map *umap);
2315 The functions above construct a (basic, regular or union) relation
2316 that maps (a wrapped version of) the input relation to its delta set.
2320 Simplify the representation of a set or relation by trying
2321 to combine pairs of basic sets or relations into a single
2322 basic set or relation.
2324 __isl_give isl_set *isl_set_coalesce(__isl_take isl_set *set);
2325 __isl_give isl_map *isl_map_coalesce(__isl_take isl_map *map);
2326 __isl_give isl_union_set *isl_union_set_coalesce(
2327 __isl_take isl_union_set *uset);
2328 __isl_give isl_union_map *isl_union_map_coalesce(
2329 __isl_take isl_union_map *umap);
2331 One of the methods for combining pairs of basic sets or relations
2332 can result in coefficients that are much larger than those that appear
2333 in the constraints of the input. By default, the coefficients are
2334 not allowed to grow larger, but this can be changed by unsetting
2335 the following option.
2337 int isl_options_set_coalesce_bounded_wrapping(
2338 isl_ctx *ctx, int val);
2339 int isl_options_get_coalesce_bounded_wrapping(
2342 =item * Detecting equalities
2344 __isl_give isl_basic_set *isl_basic_set_detect_equalities(
2345 __isl_take isl_basic_set *bset);
2346 __isl_give isl_basic_map *isl_basic_map_detect_equalities(
2347 __isl_take isl_basic_map *bmap);
2348 __isl_give isl_set *isl_set_detect_equalities(
2349 __isl_take isl_set *set);
2350 __isl_give isl_map *isl_map_detect_equalities(
2351 __isl_take isl_map *map);
2352 __isl_give isl_union_set *isl_union_set_detect_equalities(
2353 __isl_take isl_union_set *uset);
2354 __isl_give isl_union_map *isl_union_map_detect_equalities(
2355 __isl_take isl_union_map *umap);
2357 Simplify the representation of a set or relation by detecting implicit
2360 =item * Removing redundant constraints
2362 __isl_give isl_basic_set *isl_basic_set_remove_redundancies(
2363 __isl_take isl_basic_set *bset);
2364 __isl_give isl_set *isl_set_remove_redundancies(
2365 __isl_take isl_set *set);
2366 __isl_give isl_basic_map *isl_basic_map_remove_redundancies(
2367 __isl_take isl_basic_map *bmap);
2368 __isl_give isl_map *isl_map_remove_redundancies(
2369 __isl_take isl_map *map);
2373 __isl_give isl_basic_set *isl_set_convex_hull(
2374 __isl_take isl_set *set);
2375 __isl_give isl_basic_map *isl_map_convex_hull(
2376 __isl_take isl_map *map);
2378 If the input set or relation has any existentially quantified
2379 variables, then the result of these operations is currently undefined.
2383 __isl_give isl_basic_set *
2384 isl_set_unshifted_simple_hull(
2385 __isl_take isl_set *set);
2386 __isl_give isl_basic_map *
2387 isl_map_unshifted_simple_hull(
2388 __isl_take isl_map *map);
2389 __isl_give isl_basic_set *isl_set_simple_hull(
2390 __isl_take isl_set *set);
2391 __isl_give isl_basic_map *isl_map_simple_hull(
2392 __isl_take isl_map *map);
2393 __isl_give isl_union_map *isl_union_map_simple_hull(
2394 __isl_take isl_union_map *umap);
2396 These functions compute a single basic set or relation
2397 that contains the whole input set or relation.
2398 In particular, the output is described by translates
2399 of the constraints describing the basic sets or relations in the input.
2400 In case of C<isl_set_unshifted_simple_hull>, only the original
2401 constraints are used, without any translation.
2405 (See \autoref{s:simple hull}.)
2411 __isl_give isl_basic_set *isl_basic_set_affine_hull(
2412 __isl_take isl_basic_set *bset);
2413 __isl_give isl_basic_set *isl_set_affine_hull(
2414 __isl_take isl_set *set);
2415 __isl_give isl_union_set *isl_union_set_affine_hull(
2416 __isl_take isl_union_set *uset);
2417 __isl_give isl_basic_map *isl_basic_map_affine_hull(
2418 __isl_take isl_basic_map *bmap);
2419 __isl_give isl_basic_map *isl_map_affine_hull(
2420 __isl_take isl_map *map);
2421 __isl_give isl_union_map *isl_union_map_affine_hull(
2422 __isl_take isl_union_map *umap);
2424 In case of union sets and relations, the affine hull is computed
2427 =item * Polyhedral hull
2429 __isl_give isl_basic_set *isl_set_polyhedral_hull(
2430 __isl_take isl_set *set);
2431 __isl_give isl_basic_map *isl_map_polyhedral_hull(
2432 __isl_take isl_map *map);
2433 __isl_give isl_union_set *isl_union_set_polyhedral_hull(
2434 __isl_take isl_union_set *uset);
2435 __isl_give isl_union_map *isl_union_map_polyhedral_hull(
2436 __isl_take isl_union_map *umap);
2438 These functions compute a single basic set or relation
2439 not involving any existentially quantified variables
2440 that contains the whole input set or relation.
2441 In case of union sets and relations, the polyhedral hull is computed
2444 =item * Other approximations
2446 __isl_give isl_basic_set *
2447 isl_basic_set_drop_constraints_involving_dims(
2448 __isl_take isl_basic_set *bset,
2449 enum isl_dim_type type,
2450 unsigned first, unsigned n);
2451 __isl_give isl_basic_map *
2452 isl_basic_map_drop_constraints_involving_dims(
2453 __isl_take isl_basic_map *bmap,
2454 enum isl_dim_type type,
2455 unsigned first, unsigned n);
2456 __isl_give isl_basic_set *
2457 isl_basic_set_drop_constraints_not_involving_dims(
2458 __isl_take isl_basic_set *bset,
2459 enum isl_dim_type type,
2460 unsigned first, unsigned n);
2461 __isl_give isl_set *
2462 isl_set_drop_constraints_involving_dims(
2463 __isl_take isl_set *set,
2464 enum isl_dim_type type,
2465 unsigned first, unsigned n);
2466 __isl_give isl_map *
2467 isl_map_drop_constraints_involving_dims(
2468 __isl_take isl_map *map,
2469 enum isl_dim_type type,
2470 unsigned first, unsigned n);
2472 These functions drop any constraints (not) involving the specified dimensions.
2473 Note that the result depends on the representation of the input.
2477 __isl_give isl_basic_set *isl_basic_set_sample(
2478 __isl_take isl_basic_set *bset);
2479 __isl_give isl_basic_set *isl_set_sample(
2480 __isl_take isl_set *set);
2481 __isl_give isl_basic_map *isl_basic_map_sample(
2482 __isl_take isl_basic_map *bmap);
2483 __isl_give isl_basic_map *isl_map_sample(
2484 __isl_take isl_map *map);
2486 If the input (basic) set or relation is non-empty, then return
2487 a singleton subset of the input. Otherwise, return an empty set.
2489 =item * Optimization
2491 #include <isl/ilp.h>
2492 __isl_give isl_val *isl_basic_set_max_val(
2493 __isl_keep isl_basic_set *bset,
2494 __isl_keep isl_aff *obj);
2495 __isl_give isl_val *isl_set_min_val(
2496 __isl_keep isl_set *set,
2497 __isl_keep isl_aff *obj);
2498 __isl_give isl_val *isl_set_max_val(
2499 __isl_keep isl_set *set,
2500 __isl_keep isl_aff *obj);
2502 Compute the minimum or maximum of the integer affine expression C<obj>
2503 over the points in C<set>, returning the result in C<opt>.
2504 The result is C<NULL> in case of an error, the optimal value in case
2505 there is one, negative infinity or infinity if the problem is unbounded and
2506 NaN if the problem is empty.
2508 =item * Parametric optimization
2510 __isl_give isl_pw_aff *isl_set_dim_min(
2511 __isl_take isl_set *set, int pos);
2512 __isl_give isl_pw_aff *isl_set_dim_max(
2513 __isl_take isl_set *set, int pos);
2514 __isl_give isl_pw_aff *isl_map_dim_max(
2515 __isl_take isl_map *map, int pos);
2517 Compute the minimum or maximum of the given set or output dimension
2518 as a function of the parameters (and input dimensions), but independently
2519 of the other set or output dimensions.
2520 For lexicographic optimization, see L<"Lexicographic Optimization">.
2524 The following functions compute either the set of (rational) coefficient
2525 values of valid constraints for the given set or the set of (rational)
2526 values satisfying the constraints with coefficients from the given set.
2527 Internally, these two sets of functions perform essentially the
2528 same operations, except that the set of coefficients is assumed to
2529 be a cone, while the set of values may be any polyhedron.
2530 The current implementation is based on the Farkas lemma and
2531 Fourier-Motzkin elimination, but this may change or be made optional
2532 in future. In particular, future implementations may use different
2533 dualization algorithms or skip the elimination step.
2535 __isl_give isl_basic_set *isl_basic_set_coefficients(
2536 __isl_take isl_basic_set *bset);
2537 __isl_give isl_basic_set *isl_set_coefficients(
2538 __isl_take isl_set *set);
2539 __isl_give isl_union_set *isl_union_set_coefficients(
2540 __isl_take isl_union_set *bset);
2541 __isl_give isl_basic_set *isl_basic_set_solutions(
2542 __isl_take isl_basic_set *bset);
2543 __isl_give isl_basic_set *isl_set_solutions(
2544 __isl_take isl_set *set);
2545 __isl_give isl_union_set *isl_union_set_solutions(
2546 __isl_take isl_union_set *bset);
2550 __isl_give isl_map *isl_map_fixed_power_val(
2551 __isl_take isl_map *map,
2552 __isl_take isl_val *exp);
2553 __isl_give isl_union_map *
2554 isl_union_map_fixed_power_val(
2555 __isl_take isl_union_map *umap,
2556 __isl_take isl_val *exp);
2558 Compute the given power of C<map>, where C<exp> is assumed to be non-zero.
2559 If the exponent C<exp> is negative, then the -C<exp> th power of the inverse
2560 of C<map> is computed.
2562 __isl_give isl_map *isl_map_power(__isl_take isl_map *map,
2564 __isl_give isl_union_map *isl_union_map_power(
2565 __isl_take isl_union_map *umap, int *exact);
2567 Compute a parametric representation for all positive powers I<k> of C<map>.
2568 The result maps I<k> to a nested relation corresponding to the
2569 I<k>th power of C<map>.
2570 The result may be an overapproximation. If the result is known to be exact,
2571 then C<*exact> is set to C<1>.
2573 =item * Transitive closure
2575 __isl_give isl_map *isl_map_transitive_closure(
2576 __isl_take isl_map *map, int *exact);
2577 __isl_give isl_union_map *isl_union_map_transitive_closure(
2578 __isl_take isl_union_map *umap, int *exact);
2580 Compute the transitive closure of C<map>.
2581 The result may be an overapproximation. If the result is known to be exact,
2582 then C<*exact> is set to C<1>.
2584 =item * Reaching path lengths
2586 __isl_give isl_map *isl_map_reaching_path_lengths(
2587 __isl_take isl_map *map, int *exact);
2589 Compute a relation that maps each element in the range of C<map>
2590 to the lengths of all paths composed of edges in C<map> that
2591 end up in the given element.
2592 The result may be an overapproximation. If the result is known to be exact,
2593 then C<*exact> is set to C<1>.
2594 To compute the I<maximal> path length, the resulting relation
2595 should be postprocessed by C<isl_map_lexmax>.
2596 In particular, if the input relation is a dependence relation
2597 (mapping sources to sinks), then the maximal path length corresponds
2598 to the free schedule.
2599 Note, however, that C<isl_map_lexmax> expects the maximum to be
2600 finite, so if the path lengths are unbounded (possibly due to
2601 the overapproximation), then you will get an error message.
2605 __isl_give isl_basic_set *isl_basic_map_wrap(
2606 __isl_take isl_basic_map *bmap);
2607 __isl_give isl_set *isl_map_wrap(
2608 __isl_take isl_map *map);
2609 __isl_give isl_union_set *isl_union_map_wrap(
2610 __isl_take isl_union_map *umap);
2611 __isl_give isl_basic_map *isl_basic_set_unwrap(
2612 __isl_take isl_basic_set *bset);
2613 __isl_give isl_map *isl_set_unwrap(
2614 __isl_take isl_set *set);
2615 __isl_give isl_union_map *isl_union_set_unwrap(
2616 __isl_take isl_union_set *uset);
2620 Remove any internal structure of domain (and range) of the given
2621 set or relation. If there is any such internal structure in the input,
2622 then the name of the space is also removed.
2624 __isl_give isl_basic_set *isl_basic_set_flatten(
2625 __isl_take isl_basic_set *bset);
2626 __isl_give isl_set *isl_set_flatten(
2627 __isl_take isl_set *set);
2628 __isl_give isl_basic_map *isl_basic_map_flatten_domain(
2629 __isl_take isl_basic_map *bmap);
2630 __isl_give isl_basic_map *isl_basic_map_flatten_range(
2631 __isl_take isl_basic_map *bmap);
2632 __isl_give isl_map *isl_map_flatten_range(
2633 __isl_take isl_map *map);
2634 __isl_give isl_map *isl_map_flatten_domain(
2635 __isl_take isl_map *map);
2636 __isl_give isl_basic_map *isl_basic_map_flatten(
2637 __isl_take isl_basic_map *bmap);
2638 __isl_give isl_map *isl_map_flatten(
2639 __isl_take isl_map *map);
2641 __isl_give isl_map *isl_set_flatten_map(
2642 __isl_take isl_set *set);
2644 The function above constructs a relation
2645 that maps the input set to a flattened version of the set.
2649 Lift the input set to a space with extra dimensions corresponding
2650 to the existentially quantified variables in the input.
2651 In particular, the result lives in a wrapped map where the domain
2652 is the original space and the range corresponds to the original
2653 existentially quantified variables.
2655 __isl_give isl_basic_set *isl_basic_set_lift(
2656 __isl_take isl_basic_set *bset);
2657 __isl_give isl_set *isl_set_lift(
2658 __isl_take isl_set *set);
2659 __isl_give isl_union_set *isl_union_set_lift(
2660 __isl_take isl_union_set *uset);
2662 Given a local space that contains the existentially quantified
2663 variables of a set, a basic relation that, when applied to
2664 a basic set, has essentially the same effect as C<isl_basic_set_lift>,
2665 can be constructed using the following function.
2667 #include <isl/local_space.h>
2668 __isl_give isl_basic_map *isl_local_space_lifting(
2669 __isl_take isl_local_space *ls);
2671 =item * Internal Product
2673 __isl_give isl_basic_map *isl_basic_map_zip(
2674 __isl_take isl_basic_map *bmap);
2675 __isl_give isl_map *isl_map_zip(
2676 __isl_take isl_map *map);
2677 __isl_give isl_union_map *isl_union_map_zip(
2678 __isl_take isl_union_map *umap);
2680 Given a relation with nested relations for domain and range,
2681 interchange the range of the domain with the domain of the range.
2685 __isl_give isl_basic_map *isl_basic_map_curry(
2686 __isl_take isl_basic_map *bmap);
2687 __isl_give isl_basic_map *isl_basic_map_uncurry(
2688 __isl_take isl_basic_map *bmap);
2689 __isl_give isl_map *isl_map_curry(
2690 __isl_take isl_map *map);
2691 __isl_give isl_map *isl_map_uncurry(
2692 __isl_take isl_map *map);
2693 __isl_give isl_union_map *isl_union_map_curry(
2694 __isl_take isl_union_map *umap);
2695 __isl_give isl_union_map *isl_union_map_uncurry(
2696 __isl_take isl_union_map *umap);
2698 Given a relation with a nested relation for domain,
2699 the C<curry> functions
2700 move the range of the nested relation out of the domain
2701 and use it as the domain of a nested relation in the range,
2702 with the original range as range of this nested relation.
2703 The C<uncurry> functions perform the inverse operation.
2705 =item * Aligning parameters
2707 __isl_give isl_basic_set *isl_basic_set_align_params(
2708 __isl_take isl_basic_set *bset,
2709 __isl_take isl_space *model);
2710 __isl_give isl_set *isl_set_align_params(
2711 __isl_take isl_set *set,
2712 __isl_take isl_space *model);
2713 __isl_give isl_basic_map *isl_basic_map_align_params(
2714 __isl_take isl_basic_map *bmap,
2715 __isl_take isl_space *model);
2716 __isl_give isl_map *isl_map_align_params(
2717 __isl_take isl_map *map,
2718 __isl_take isl_space *model);
2720 Change the order of the parameters of the given set or relation
2721 such that the first parameters match those of C<model>.
2722 This may involve the introduction of extra parameters.
2723 All parameters need to be named.
2725 =item * Dimension manipulation
2727 __isl_give isl_basic_set *isl_basic_set_add_dims(
2728 __isl_take isl_basic_set *bset,
2729 enum isl_dim_type type, unsigned n);
2730 __isl_give isl_set *isl_set_add_dims(
2731 __isl_take isl_set *set,
2732 enum isl_dim_type type, unsigned n);
2733 __isl_give isl_map *isl_map_add_dims(
2734 __isl_take isl_map *map,
2735 enum isl_dim_type type, unsigned n);
2736 __isl_give isl_basic_set *isl_basic_set_insert_dims(
2737 __isl_take isl_basic_set *bset,
2738 enum isl_dim_type type, unsigned pos,
2740 __isl_give isl_basic_map *isl_basic_map_insert_dims(
2741 __isl_take isl_basic_map *bmap,
2742 enum isl_dim_type type, unsigned pos,
2744 __isl_give isl_set *isl_set_insert_dims(
2745 __isl_take isl_set *set,
2746 enum isl_dim_type type, unsigned pos, unsigned n);
2747 __isl_give isl_map *isl_map_insert_dims(
2748 __isl_take isl_map *map,
2749 enum isl_dim_type type, unsigned pos, unsigned n);
2750 __isl_give isl_basic_set *isl_basic_set_move_dims(
2751 __isl_take isl_basic_set *bset,
2752 enum isl_dim_type dst_type, unsigned dst_pos,
2753 enum isl_dim_type src_type, unsigned src_pos,
2755 __isl_give isl_basic_map *isl_basic_map_move_dims(
2756 __isl_take isl_basic_map *bmap,
2757 enum isl_dim_type dst_type, unsigned dst_pos,
2758 enum isl_dim_type src_type, unsigned src_pos,
2760 __isl_give isl_set *isl_set_move_dims(
2761 __isl_take isl_set *set,
2762 enum isl_dim_type dst_type, unsigned dst_pos,
2763 enum isl_dim_type src_type, unsigned src_pos,
2765 __isl_give isl_map *isl_map_move_dims(
2766 __isl_take isl_map *map,
2767 enum isl_dim_type dst_type, unsigned dst_pos,
2768 enum isl_dim_type src_type, unsigned src_pos,
2771 It is usually not advisable to directly change the (input or output)
2772 space of a set or a relation as this removes the name and the internal
2773 structure of the space. However, the above functions can be useful
2774 to add new parameters, assuming
2775 C<isl_set_align_params> and C<isl_map_align_params>
2780 =head2 Binary Operations
2782 The two arguments of a binary operation not only need to live
2783 in the same C<isl_ctx>, they currently also need to have
2784 the same (number of) parameters.
2786 =head3 Basic Operations
2790 =item * Intersection
2792 __isl_give isl_basic_set *isl_basic_set_intersect_params(
2793 __isl_take isl_basic_set *bset1,
2794 __isl_take isl_basic_set *bset2);
2795 __isl_give isl_basic_set *isl_basic_set_intersect(
2796 __isl_take isl_basic_set *bset1,
2797 __isl_take isl_basic_set *bset2);
2798 __isl_give isl_set *isl_set_intersect_params(
2799 __isl_take isl_set *set,
2800 __isl_take isl_set *params);
2801 __isl_give isl_set *isl_set_intersect(
2802 __isl_take isl_set *set1,
2803 __isl_take isl_set *set2);
2804 __isl_give isl_union_set *isl_union_set_intersect_params(
2805 __isl_take isl_union_set *uset,
2806 __isl_take isl_set *set);
2807 __isl_give isl_union_map *isl_union_map_intersect_params(
2808 __isl_take isl_union_map *umap,
2809 __isl_take isl_set *set);
2810 __isl_give isl_union_set *isl_union_set_intersect(
2811 __isl_take isl_union_set *uset1,
2812 __isl_take isl_union_set *uset2);
2813 __isl_give isl_basic_map *isl_basic_map_intersect_domain(
2814 __isl_take isl_basic_map *bmap,
2815 __isl_take isl_basic_set *bset);
2816 __isl_give isl_basic_map *isl_basic_map_intersect_range(
2817 __isl_take isl_basic_map *bmap,
2818 __isl_take isl_basic_set *bset);
2819 __isl_give isl_basic_map *isl_basic_map_intersect(
2820 __isl_take isl_basic_map *bmap1,
2821 __isl_take isl_basic_map *bmap2);
2822 __isl_give isl_map *isl_map_intersect_params(
2823 __isl_take isl_map *map,
2824 __isl_take isl_set *params);
2825 __isl_give isl_map *isl_map_intersect_domain(
2826 __isl_take isl_map *map,
2827 __isl_take isl_set *set);
2828 __isl_give isl_map *isl_map_intersect_range(
2829 __isl_take isl_map *map,
2830 __isl_take isl_set *set);
2831 __isl_give isl_map *isl_map_intersect(
2832 __isl_take isl_map *map1,
2833 __isl_take isl_map *map2);
2834 __isl_give isl_union_map *isl_union_map_intersect_domain(
2835 __isl_take isl_union_map *umap,
2836 __isl_take isl_union_set *uset);
2837 __isl_give isl_union_map *isl_union_map_intersect_range(
2838 __isl_take isl_union_map *umap,
2839 __isl_take isl_union_set *uset);
2840 __isl_give isl_union_map *isl_union_map_intersect(
2841 __isl_take isl_union_map *umap1,
2842 __isl_take isl_union_map *umap2);
2844 The second argument to the C<_params> functions needs to be
2845 a parametric (basic) set. For the other functions, a parametric set
2846 for either argument is only allowed if the other argument is
2847 a parametric set as well.
2851 __isl_give isl_set *isl_basic_set_union(
2852 __isl_take isl_basic_set *bset1,
2853 __isl_take isl_basic_set *bset2);
2854 __isl_give isl_map *isl_basic_map_union(
2855 __isl_take isl_basic_map *bmap1,
2856 __isl_take isl_basic_map *bmap2);
2857 __isl_give isl_set *isl_set_union(
2858 __isl_take isl_set *set1,
2859 __isl_take isl_set *set2);
2860 __isl_give isl_map *isl_map_union(
2861 __isl_take isl_map *map1,
2862 __isl_take isl_map *map2);
2863 __isl_give isl_union_set *isl_union_set_union(
2864 __isl_take isl_union_set *uset1,
2865 __isl_take isl_union_set *uset2);
2866 __isl_give isl_union_map *isl_union_map_union(
2867 __isl_take isl_union_map *umap1,
2868 __isl_take isl_union_map *umap2);
2870 =item * Set difference
2872 __isl_give isl_set *isl_set_subtract(
2873 __isl_take isl_set *set1,
2874 __isl_take isl_set *set2);
2875 __isl_give isl_map *isl_map_subtract(
2876 __isl_take isl_map *map1,
2877 __isl_take isl_map *map2);
2878 __isl_give isl_map *isl_map_subtract_domain(
2879 __isl_take isl_map *map,
2880 __isl_take isl_set *dom);
2881 __isl_give isl_map *isl_map_subtract_range(
2882 __isl_take isl_map *map,
2883 __isl_take isl_set *dom);
2884 __isl_give isl_union_set *isl_union_set_subtract(
2885 __isl_take isl_union_set *uset1,
2886 __isl_take isl_union_set *uset2);
2887 __isl_give isl_union_map *isl_union_map_subtract(
2888 __isl_take isl_union_map *umap1,
2889 __isl_take isl_union_map *umap2);
2890 __isl_give isl_union_map *isl_union_map_subtract_domain(
2891 __isl_take isl_union_map *umap,
2892 __isl_take isl_union_set *dom);
2893 __isl_give isl_union_map *isl_union_map_subtract_range(
2894 __isl_take isl_union_map *umap,
2895 __isl_take isl_union_set *dom);
2899 __isl_give isl_basic_set *isl_basic_set_apply(
2900 __isl_take isl_basic_set *bset,
2901 __isl_take isl_basic_map *bmap);
2902 __isl_give isl_set *isl_set_apply(
2903 __isl_take isl_set *set,
2904 __isl_take isl_map *map);
2905 __isl_give isl_union_set *isl_union_set_apply(
2906 __isl_take isl_union_set *uset,
2907 __isl_take isl_union_map *umap);
2908 __isl_give isl_basic_map *isl_basic_map_apply_domain(
2909 __isl_take isl_basic_map *bmap1,
2910 __isl_take isl_basic_map *bmap2);
2911 __isl_give isl_basic_map *isl_basic_map_apply_range(
2912 __isl_take isl_basic_map *bmap1,
2913 __isl_take isl_basic_map *bmap2);
2914 __isl_give isl_map *isl_map_apply_domain(
2915 __isl_take isl_map *map1,
2916 __isl_take isl_map *map2);
2917 __isl_give isl_union_map *isl_union_map_apply_domain(
2918 __isl_take isl_union_map *umap1,
2919 __isl_take isl_union_map *umap2);
2920 __isl_give isl_map *isl_map_apply_range(
2921 __isl_take isl_map *map1,
2922 __isl_take isl_map *map2);
2923 __isl_give isl_union_map *isl_union_map_apply_range(
2924 __isl_take isl_union_map *umap1,
2925 __isl_take isl_union_map *umap2);
2929 __isl_give isl_basic_set *
2930 isl_basic_set_preimage_multi_aff(
2931 __isl_take isl_basic_set *bset,
2932 __isl_take isl_multi_aff *ma);
2933 __isl_give isl_set *isl_set_preimage_multi_aff(
2934 __isl_take isl_set *set,
2935 __isl_take isl_multi_aff *ma);
2936 __isl_give isl_set *isl_set_preimage_pw_multi_aff(
2937 __isl_take isl_set *set,
2938 __isl_take isl_pw_multi_aff *pma);
2939 __isl_give isl_map *isl_map_preimage_domain_multi_aff(
2940 __isl_take isl_map *map,
2941 __isl_take isl_multi_aff *ma);
2942 __isl_give isl_union_map *
2943 isl_union_map_preimage_domain_multi_aff(
2944 __isl_take isl_union_map *umap,
2945 __isl_take isl_multi_aff *ma);
2947 These functions compute the preimage of the given set or map domain under
2948 the given function. In other words, the expression is plugged
2949 into the set description or into the domain of the map.
2950 Objects of types C<isl_multi_aff> and C<isl_pw_multi_aff> are described in
2951 L</"Piecewise Multiple Quasi Affine Expressions">.
2953 =item * Cartesian Product
2955 __isl_give isl_set *isl_set_product(
2956 __isl_take isl_set *set1,
2957 __isl_take isl_set *set2);
2958 __isl_give isl_union_set *isl_union_set_product(
2959 __isl_take isl_union_set *uset1,
2960 __isl_take isl_union_set *uset2);
2961 __isl_give isl_basic_map *isl_basic_map_domain_product(
2962 __isl_take isl_basic_map *bmap1,
2963 __isl_take isl_basic_map *bmap2);
2964 __isl_give isl_basic_map *isl_basic_map_range_product(
2965 __isl_take isl_basic_map *bmap1,
2966 __isl_take isl_basic_map *bmap2);
2967 __isl_give isl_basic_map *isl_basic_map_product(
2968 __isl_take isl_basic_map *bmap1,
2969 __isl_take isl_basic_map *bmap2);
2970 __isl_give isl_map *isl_map_domain_product(
2971 __isl_take isl_map *map1,
2972 __isl_take isl_map *map2);
2973 __isl_give isl_map *isl_map_range_product(
2974 __isl_take isl_map *map1,
2975 __isl_take isl_map *map2);
2976 __isl_give isl_union_map *isl_union_map_domain_product(
2977 __isl_take isl_union_map *umap1,
2978 __isl_take isl_union_map *umap2);
2979 __isl_give isl_union_map *isl_union_map_range_product(
2980 __isl_take isl_union_map *umap1,
2981 __isl_take isl_union_map *umap2);
2982 __isl_give isl_map *isl_map_product(
2983 __isl_take isl_map *map1,
2984 __isl_take isl_map *map2);
2985 __isl_give isl_union_map *isl_union_map_product(
2986 __isl_take isl_union_map *umap1,
2987 __isl_take isl_union_map *umap2);
2989 The above functions compute the cross product of the given
2990 sets or relations. The domains and ranges of the results
2991 are wrapped maps between domains and ranges of the inputs.
2992 To obtain a ``flat'' product, use the following functions
2995 __isl_give isl_basic_set *isl_basic_set_flat_product(
2996 __isl_take isl_basic_set *bset1,
2997 __isl_take isl_basic_set *bset2);
2998 __isl_give isl_set *isl_set_flat_product(
2999 __isl_take isl_set *set1,
3000 __isl_take isl_set *set2);
3001 __isl_give isl_basic_map *isl_basic_map_flat_range_product(
3002 __isl_take isl_basic_map *bmap1,
3003 __isl_take isl_basic_map *bmap2);
3004 __isl_give isl_map *isl_map_flat_domain_product(
3005 __isl_take isl_map *map1,
3006 __isl_take isl_map *map2);
3007 __isl_give isl_map *isl_map_flat_range_product(
3008 __isl_take isl_map *map1,
3009 __isl_take isl_map *map2);
3010 __isl_give isl_union_map *isl_union_map_flat_range_product(
3011 __isl_take isl_union_map *umap1,
3012 __isl_take isl_union_map *umap2);
3013 __isl_give isl_basic_map *isl_basic_map_flat_product(
3014 __isl_take isl_basic_map *bmap1,
3015 __isl_take isl_basic_map *bmap2);
3016 __isl_give isl_map *isl_map_flat_product(
3017 __isl_take isl_map *map1,
3018 __isl_take isl_map *map2);
3020 =item * Simplification
3022 __isl_give isl_basic_set *isl_basic_set_gist(
3023 __isl_take isl_basic_set *bset,
3024 __isl_take isl_basic_set *context);
3025 __isl_give isl_set *isl_set_gist(__isl_take isl_set *set,
3026 __isl_take isl_set *context);
3027 __isl_give isl_set *isl_set_gist_params(
3028 __isl_take isl_set *set,
3029 __isl_take isl_set *context);
3030 __isl_give isl_union_set *isl_union_set_gist(
3031 __isl_take isl_union_set *uset,
3032 __isl_take isl_union_set *context);
3033 __isl_give isl_union_set *isl_union_set_gist_params(
3034 __isl_take isl_union_set *uset,
3035 __isl_take isl_set *set);
3036 __isl_give isl_basic_map *isl_basic_map_gist(
3037 __isl_take isl_basic_map *bmap,
3038 __isl_take isl_basic_map *context);
3039 __isl_give isl_map *isl_map_gist(__isl_take isl_map *map,
3040 __isl_take isl_map *context);
3041 __isl_give isl_map *isl_map_gist_params(
3042 __isl_take isl_map *map,
3043 __isl_take isl_set *context);
3044 __isl_give isl_map *isl_map_gist_domain(
3045 __isl_take isl_map *map,
3046 __isl_take isl_set *context);
3047 __isl_give isl_map *isl_map_gist_range(
3048 __isl_take isl_map *map,
3049 __isl_take isl_set *context);
3050 __isl_give isl_union_map *isl_union_map_gist(
3051 __isl_take isl_union_map *umap,
3052 __isl_take isl_union_map *context);
3053 __isl_give isl_union_map *isl_union_map_gist_params(
3054 __isl_take isl_union_map *umap,
3055 __isl_take isl_set *set);
3056 __isl_give isl_union_map *isl_union_map_gist_domain(
3057 __isl_take isl_union_map *umap,
3058 __isl_take isl_union_set *uset);
3059 __isl_give isl_union_map *isl_union_map_gist_range(
3060 __isl_take isl_union_map *umap,
3061 __isl_take isl_union_set *uset);
3063 The gist operation returns a set or relation that has the
3064 same intersection with the context as the input set or relation.
3065 Any implicit equality in the intersection is made explicit in the result,
3066 while all inequalities that are redundant with respect to the intersection
3068 In case of union sets and relations, the gist operation is performed
3073 =head3 Lexicographic Optimization
3075 Given a (basic) set C<set> (or C<bset>) and a zero-dimensional domain C<dom>,
3076 the following functions
3077 compute a set that contains the lexicographic minimum or maximum
3078 of the elements in C<set> (or C<bset>) for those values of the parameters
3079 that satisfy C<dom>.
3080 If C<empty> is not C<NULL>, then C<*empty> is assigned a set
3081 that contains the parameter values in C<dom> for which C<set> (or C<bset>)
3083 In other words, the union of the parameter values
3084 for which the result is non-empty and of C<*empty>
3087 __isl_give isl_set *isl_basic_set_partial_lexmin(
3088 __isl_take isl_basic_set *bset,
3089 __isl_take isl_basic_set *dom,
3090 __isl_give isl_set **empty);
3091 __isl_give isl_set *isl_basic_set_partial_lexmax(
3092 __isl_take isl_basic_set *bset,
3093 __isl_take isl_basic_set *dom,
3094 __isl_give isl_set **empty);
3095 __isl_give isl_set *isl_set_partial_lexmin(
3096 __isl_take isl_set *set, __isl_take isl_set *dom,
3097 __isl_give isl_set **empty);
3098 __isl_give isl_set *isl_set_partial_lexmax(
3099 __isl_take isl_set *set, __isl_take isl_set *dom,
3100 __isl_give isl_set **empty);
3102 Given a (basic) set C<set> (or C<bset>), the following functions simply
3103 return a set containing the lexicographic minimum or maximum
3104 of the elements in C<set> (or C<bset>).
3105 In case of union sets, the optimum is computed per space.
3107 __isl_give isl_set *isl_basic_set_lexmin(
3108 __isl_take isl_basic_set *bset);
3109 __isl_give isl_set *isl_basic_set_lexmax(
3110 __isl_take isl_basic_set *bset);
3111 __isl_give isl_set *isl_set_lexmin(
3112 __isl_take isl_set *set);
3113 __isl_give isl_set *isl_set_lexmax(
3114 __isl_take isl_set *set);
3115 __isl_give isl_union_set *isl_union_set_lexmin(
3116 __isl_take isl_union_set *uset);
3117 __isl_give isl_union_set *isl_union_set_lexmax(
3118 __isl_take isl_union_set *uset);
3120 Given a (basic) relation C<map> (or C<bmap>) and a domain C<dom>,
3121 the following functions
3122 compute a relation that maps each element of C<dom>
3123 to the single lexicographic minimum or maximum
3124 of the elements that are associated to that same
3125 element in C<map> (or C<bmap>).
3126 If C<empty> is not C<NULL>, then C<*empty> is assigned a set
3127 that contains the elements in C<dom> that do not map
3128 to any elements in C<map> (or C<bmap>).
3129 In other words, the union of the domain of the result and of C<*empty>
3132 __isl_give isl_map *isl_basic_map_partial_lexmax(
3133 __isl_take isl_basic_map *bmap,
3134 __isl_take isl_basic_set *dom,
3135 __isl_give isl_set **empty);
3136 __isl_give isl_map *isl_basic_map_partial_lexmin(
3137 __isl_take isl_basic_map *bmap,
3138 __isl_take isl_basic_set *dom,
3139 __isl_give isl_set **empty);
3140 __isl_give isl_map *isl_map_partial_lexmax(
3141 __isl_take isl_map *map, __isl_take isl_set *dom,
3142 __isl_give isl_set **empty);
3143 __isl_give isl_map *isl_map_partial_lexmin(
3144 __isl_take isl_map *map, __isl_take isl_set *dom,
3145 __isl_give isl_set **empty);
3147 Given a (basic) map C<map> (or C<bmap>), the following functions simply
3148 return a map mapping each element in the domain of
3149 C<map> (or C<bmap>) to the lexicographic minimum or maximum
3150 of all elements associated to that element.
3151 In case of union relations, the optimum is computed per space.
3153 __isl_give isl_map *isl_basic_map_lexmin(
3154 __isl_take isl_basic_map *bmap);
3155 __isl_give isl_map *isl_basic_map_lexmax(
3156 __isl_take isl_basic_map *bmap);
3157 __isl_give isl_map *isl_map_lexmin(
3158 __isl_take isl_map *map);
3159 __isl_give isl_map *isl_map_lexmax(
3160 __isl_take isl_map *map);
3161 __isl_give isl_union_map *isl_union_map_lexmin(
3162 __isl_take isl_union_map *umap);
3163 __isl_give isl_union_map *isl_union_map_lexmax(
3164 __isl_take isl_union_map *umap);
3166 The following functions return their result in the form of
3167 a piecewise multi-affine expression
3168 (See L<"Piecewise Multiple Quasi Affine Expressions">),
3169 but are otherwise equivalent to the corresponding functions
3170 returning a basic set or relation.
3172 __isl_give isl_pw_multi_aff *
3173 isl_basic_map_lexmin_pw_multi_aff(
3174 __isl_take isl_basic_map *bmap);
3175 __isl_give isl_pw_multi_aff *
3176 isl_basic_set_partial_lexmin_pw_multi_aff(
3177 __isl_take isl_basic_set *bset,
3178 __isl_take isl_basic_set *dom,
3179 __isl_give isl_set **empty);
3180 __isl_give isl_pw_multi_aff *
3181 isl_basic_set_partial_lexmax_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_map_partial_lexmin_pw_multi_aff(
3187 __isl_take isl_basic_map *bmap,
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_lexmax_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 *isl_set_lexmin_pw_multi_aff(
3196 __isl_take isl_set *set);
3197 __isl_give isl_pw_multi_aff *isl_set_lexmax_pw_multi_aff(
3198 __isl_take isl_set *set);
3199 __isl_give isl_pw_multi_aff *isl_map_lexmin_pw_multi_aff(
3200 __isl_take isl_map *map);
3201 __isl_give isl_pw_multi_aff *isl_map_lexmax_pw_multi_aff(
3202 __isl_take isl_map *map);
3206 Lists are defined over several element types, including
3207 C<isl_val>, C<isl_id>, C<isl_aff>, C<isl_pw_aff>, C<isl_constraint>,
3208 C<isl_basic_set>, C<isl_set>, C<isl_ast_expr> and C<isl_ast_node>.
3209 Here we take lists of C<isl_set>s as an example.
3210 Lists can be created, copied, modified and freed using the following functions.
3212 #include <isl/list.h>
3213 __isl_give isl_set_list *isl_set_list_from_set(
3214 __isl_take isl_set *el);
3215 __isl_give isl_set_list *isl_set_list_alloc(
3216 isl_ctx *ctx, int n);
3217 __isl_give isl_set_list *isl_set_list_copy(
3218 __isl_keep isl_set_list *list);
3219 __isl_give isl_set_list *isl_set_list_insert(
3220 __isl_take isl_set_list *list, unsigned pos,
3221 __isl_take isl_set *el);
3222 __isl_give isl_set_list *isl_set_list_add(
3223 __isl_take isl_set_list *list,
3224 __isl_take isl_set *el);
3225 __isl_give isl_set_list *isl_set_list_drop(
3226 __isl_take isl_set_list *list,
3227 unsigned first, unsigned n);
3228 __isl_give isl_set_list *isl_set_list_set_set(
3229 __isl_take isl_set_list *list, int index,
3230 __isl_take isl_set *set);
3231 __isl_give isl_set_list *isl_set_list_concat(
3232 __isl_take isl_set_list *list1,
3233 __isl_take isl_set_list *list2);
3234 __isl_give isl_set_list *isl_set_list_sort(
3235 __isl_take isl_set_list *list,
3236 int (*cmp)(__isl_keep isl_set *a,
3237 __isl_keep isl_set *b, void *user),
3239 void *isl_set_list_free(__isl_take isl_set_list *list);
3241 C<isl_set_list_alloc> creates an empty list with a capacity for
3242 C<n> elements. C<isl_set_list_from_set> creates a list with a single
3245 Lists can be inspected using the following functions.
3247 #include <isl/list.h>
3248 isl_ctx *isl_set_list_get_ctx(__isl_keep isl_set_list *list);
3249 int isl_set_list_n_set(__isl_keep isl_set_list *list);
3250 __isl_give isl_set *isl_set_list_get_set(
3251 __isl_keep isl_set_list *list, int index);
3252 int isl_set_list_foreach(__isl_keep isl_set_list *list,
3253 int (*fn)(__isl_take isl_set *el, void *user),
3255 int isl_set_list_foreach_scc(__isl_keep isl_set_list *list,
3256 int (*follows)(__isl_keep isl_set *a,
3257 __isl_keep isl_set *b, void *user),
3259 int (*fn)(__isl_take isl_set *el, void *user),
3262 The function C<isl_set_list_foreach_scc> calls C<fn> on each of the
3263 strongly connected components of the graph with as vertices the elements
3264 of C<list> and a directed edge from vertex C<b> to vertex C<a>
3265 iff C<follows(a, b)> returns C<1>. The callbacks C<follows> and C<fn>
3266 should return C<-1> on error.
3268 Lists can be printed using
3270 #include <isl/list.h>
3271 __isl_give isl_printer *isl_printer_print_set_list(
3272 __isl_take isl_printer *p,
3273 __isl_keep isl_set_list *list);
3275 =head2 Multiple Values
3277 An C<isl_multi_val> object represents a sequence of zero or more values,
3278 living in a set space.
3280 An C<isl_multi_val> can be constructed from an C<isl_val_list>
3281 using the following function
3283 #include <isl/val.h>
3284 __isl_give isl_multi_val *isl_multi_val_from_val_list(
3285 __isl_take isl_space *space,
3286 __isl_take isl_val_list *list);
3288 The zero multiple value (with value zero for each set dimension)
3289 can be created using the following function.
3291 #include <isl/val.h>
3292 __isl_give isl_multi_val *isl_multi_val_zero(
3293 __isl_take isl_space *space);
3295 Multiple values can be copied and freed using
3297 #include <isl/val.h>
3298 __isl_give isl_multi_val *isl_multi_val_copy(
3299 __isl_keep isl_multi_val *mv);
3300 void *isl_multi_val_free(__isl_take isl_multi_val *mv);
3302 They can be inspected using
3304 #include <isl/val.h>
3305 isl_ctx *isl_multi_val_get_ctx(
3306 __isl_keep isl_multi_val *mv);
3307 unsigned isl_multi_val_dim(__isl_keep isl_multi_val *mv,
3308 enum isl_dim_type type);
3309 __isl_give isl_val *isl_multi_val_get_val(
3310 __isl_keep isl_multi_val *mv, int pos);
3311 const char *isl_multi_val_get_tuple_name(
3312 __isl_keep isl_multi_val *mv,
3313 enum isl_dim_type type);
3315 They can be modified using
3317 #include <isl/val.h>
3318 __isl_give isl_multi_val *isl_multi_val_set_val(
3319 __isl_take isl_multi_val *mv, int pos,
3320 __isl_take isl_val *val);
3321 __isl_give isl_multi_val *isl_multi_val_set_dim_name(
3322 __isl_take isl_multi_val *mv,
3323 enum isl_dim_type type, unsigned pos, const char *s);
3324 __isl_give isl_multi_val *isl_multi_val_set_tuple_name(
3325 __isl_take isl_multi_val *mv,
3326 enum isl_dim_type type, const char *s);
3327 __isl_give isl_multi_val *isl_multi_val_set_tuple_id(
3328 __isl_take isl_multi_val *mv,
3329 enum isl_dim_type type, __isl_take isl_id *id);
3331 __isl_give isl_multi_val *isl_multi_val_insert_dims(
3332 __isl_take isl_multi_val *mv,
3333 enum isl_dim_type type, unsigned first, unsigned n);
3334 __isl_give isl_multi_val *isl_multi_val_add_dims(
3335 __isl_take isl_multi_val *mv,
3336 enum isl_dim_type type, unsigned n);
3337 __isl_give isl_multi_val *isl_multi_val_drop_dims(
3338 __isl_take isl_multi_val *mv,
3339 enum isl_dim_type type, unsigned first, unsigned n);
3343 #include <isl/val.h>
3344 __isl_give isl_multi_val *isl_multi_val_align_params(
3345 __isl_take isl_multi_val *mv,
3346 __isl_take isl_space *model);
3347 __isl_give isl_multi_val *isl_multi_val_range_splice(
3348 __isl_take isl_multi_val *mv1, unsigned pos,
3349 __isl_take isl_multi_val *mv2);
3350 __isl_give isl_multi_val *isl_multi_val_range_product(
3351 __isl_take isl_multi_val *mv1,
3352 __isl_take isl_multi_val *mv2);
3353 __isl_give isl_multi_val *isl_multi_val_flat_range_product(
3354 __isl_take isl_multi_val *mv1,
3355 __isl_take isl_multi_aff *mv2);
3356 __isl_give isl_multi_val *isl_multi_val_add_val(
3357 __isl_take isl_multi_val *mv,
3358 __isl_take isl_val *v);
3359 __isl_give isl_multi_val *isl_multi_val_mod_val(
3360 __isl_take isl_multi_val *mv,
3361 __isl_take isl_val *v);
3362 __isl_give isl_multi_val *isl_multi_val_scale_val(
3363 __isl_take isl_multi_val *mv,
3364 __isl_take isl_val *v);
3365 __isl_give isl_multi_val *isl_multi_val_scale_multi_val(
3366 __isl_take isl_multi_val *mv1,
3367 __isl_take isl_multi_val *mv2);
3371 Vectors can be created, copied and freed using the following functions.
3373 #include <isl/vec.h>
3374 __isl_give isl_vec *isl_vec_alloc(isl_ctx *ctx,
3376 __isl_give isl_vec *isl_vec_copy(__isl_keep isl_vec *vec);
3377 void *isl_vec_free(__isl_take isl_vec *vec);
3379 Note that the elements of a newly created vector may have arbitrary values.
3380 The elements can be changed and inspected using the following functions.
3382 isl_ctx *isl_vec_get_ctx(__isl_keep isl_vec *vec);
3383 int isl_vec_size(__isl_keep isl_vec *vec);
3384 __isl_give isl_val *isl_vec_get_element_val(
3385 __isl_keep isl_vec *vec, int pos);
3386 __isl_give isl_vec *isl_vec_set_element_si(
3387 __isl_take isl_vec *vec, int pos, int v);
3388 __isl_give isl_vec *isl_vec_set_element_val(
3389 __isl_take isl_vec *vec, int pos,
3390 __isl_take isl_val *v);
3391 __isl_give isl_vec *isl_vec_set_si(__isl_take isl_vec *vec,
3393 __isl_give isl_vec *isl_vec_set_val(
3394 __isl_take isl_vec *vec, __isl_take isl_val *v);
3395 int isl_vec_cmp_element(__isl_keep isl_vec *vec1,
3396 __isl_keep isl_vec *vec2, int pos);
3398 C<isl_vec_get_element> will return a negative value if anything went wrong.
3399 In that case, the value of C<*v> is undefined.
3401 The following function can be used to concatenate two vectors.
3403 __isl_give isl_vec *isl_vec_concat(__isl_take isl_vec *vec1,
3404 __isl_take isl_vec *vec2);
3408 Matrices can be created, copied and freed using the following functions.
3410 #include <isl/mat.h>
3411 __isl_give isl_mat *isl_mat_alloc(isl_ctx *ctx,
3412 unsigned n_row, unsigned n_col);
3413 __isl_give isl_mat *isl_mat_copy(__isl_keep isl_mat *mat);
3414 void *isl_mat_free(__isl_take isl_mat *mat);
3416 Note that the elements of a newly created matrix may have arbitrary values.
3417 The elements can be changed and inspected using the following functions.
3419 isl_ctx *isl_mat_get_ctx(__isl_keep isl_mat *mat);
3420 int isl_mat_rows(__isl_keep isl_mat *mat);
3421 int isl_mat_cols(__isl_keep isl_mat *mat);
3422 __isl_give isl_val *isl_mat_get_element_val(
3423 __isl_keep isl_mat *mat, int row, int col);
3424 __isl_give isl_mat *isl_mat_set_element_si(__isl_take isl_mat *mat,
3425 int row, int col, int v);
3426 __isl_give isl_mat *isl_mat_set_element_val(
3427 __isl_take isl_mat *mat, int row, int col,
3428 __isl_take isl_val *v);
3430 C<isl_mat_get_element> will return a negative value if anything went wrong.
3431 In that case, the value of C<*v> is undefined.
3433 The following function can be used to compute the (right) inverse
3434 of a matrix, i.e., a matrix such that the product of the original
3435 and the inverse (in that order) is a multiple of the identity matrix.
3436 The input matrix is assumed to be of full row-rank.
3438 __isl_give isl_mat *isl_mat_right_inverse(__isl_take isl_mat *mat);
3440 The following function can be used to compute the (right) kernel
3441 (or null space) of a matrix, i.e., a matrix such that the product of
3442 the original and the kernel (in that order) is the zero matrix.
3444 __isl_give isl_mat *isl_mat_right_kernel(__isl_take isl_mat *mat);
3446 =head2 Piecewise Quasi Affine Expressions
3448 The zero quasi affine expression or the quasi affine expression
3449 that is equal to a specified dimension on a given domain can be created using
3451 __isl_give isl_aff *isl_aff_zero_on_domain(
3452 __isl_take isl_local_space *ls);
3453 __isl_give isl_pw_aff *isl_pw_aff_zero_on_domain(
3454 __isl_take isl_local_space *ls);
3455 __isl_give isl_aff *isl_aff_var_on_domain(
3456 __isl_take isl_local_space *ls,
3457 enum isl_dim_type type, unsigned pos);
3458 __isl_give isl_pw_aff *isl_pw_aff_var_on_domain(
3459 __isl_take isl_local_space *ls,
3460 enum isl_dim_type type, unsigned pos);
3462 Note that the space in which the resulting objects live is a map space
3463 with the given space as domain and a one-dimensional range.
3465 An empty piecewise quasi affine expression (one with no cells)
3466 or a piecewise quasi affine expression with a single cell can
3467 be created using the following functions.
3469 #include <isl/aff.h>
3470 __isl_give isl_pw_aff *isl_pw_aff_empty(
3471 __isl_take isl_space *space);
3472 __isl_give isl_pw_aff *isl_pw_aff_alloc(
3473 __isl_take isl_set *set, __isl_take isl_aff *aff);
3474 __isl_give isl_pw_aff *isl_pw_aff_from_aff(
3475 __isl_take isl_aff *aff);
3477 A piecewise quasi affine expression that is equal to 1 on a set
3478 and 0 outside the set can be created using the following function.
3480 #include <isl/aff.h>
3481 __isl_give isl_pw_aff *isl_set_indicator_function(
3482 __isl_take isl_set *set);
3484 Quasi affine expressions can be copied and freed using
3486 #include <isl/aff.h>
3487 __isl_give isl_aff *isl_aff_copy(__isl_keep isl_aff *aff);
3488 void *isl_aff_free(__isl_take isl_aff *aff);
3490 __isl_give isl_pw_aff *isl_pw_aff_copy(
3491 __isl_keep isl_pw_aff *pwaff);
3492 void *isl_pw_aff_free(__isl_take isl_pw_aff *pwaff);
3494 A (rational) bound on a dimension can be extracted from an C<isl_constraint>
3495 using the following function. The constraint is required to have
3496 a non-zero coefficient for the specified dimension.
3498 #include <isl/constraint.h>
3499 __isl_give isl_aff *isl_constraint_get_bound(
3500 __isl_keep isl_constraint *constraint,
3501 enum isl_dim_type type, int pos);
3503 The entire affine expression of the constraint can also be extracted
3504 using the following function.
3506 #include <isl/constraint.h>
3507 __isl_give isl_aff *isl_constraint_get_aff(
3508 __isl_keep isl_constraint *constraint);
3510 Conversely, an equality constraint equating
3511 the affine expression to zero or an inequality constraint enforcing
3512 the affine expression to be non-negative, can be constructed using
3514 __isl_give isl_constraint *isl_equality_from_aff(
3515 __isl_take isl_aff *aff);
3516 __isl_give isl_constraint *isl_inequality_from_aff(
3517 __isl_take isl_aff *aff);
3519 The expression can be inspected using
3521 #include <isl/aff.h>
3522 isl_ctx *isl_aff_get_ctx(__isl_keep isl_aff *aff);
3523 int isl_aff_dim(__isl_keep isl_aff *aff,
3524 enum isl_dim_type type);
3525 __isl_give isl_local_space *isl_aff_get_domain_local_space(
3526 __isl_keep isl_aff *aff);
3527 __isl_give isl_local_space *isl_aff_get_local_space(
3528 __isl_keep isl_aff *aff);
3529 const char *isl_aff_get_dim_name(__isl_keep isl_aff *aff,
3530 enum isl_dim_type type, unsigned pos);
3531 const char *isl_pw_aff_get_dim_name(
3532 __isl_keep isl_pw_aff *pa,
3533 enum isl_dim_type type, unsigned pos);
3534 int isl_pw_aff_has_dim_id(__isl_keep isl_pw_aff *pa,
3535 enum isl_dim_type type, unsigned pos);
3536 __isl_give isl_id *isl_pw_aff_get_dim_id(
3537 __isl_keep isl_pw_aff *pa,
3538 enum isl_dim_type type, unsigned pos);
3539 __isl_give isl_id *isl_pw_aff_get_tuple_id(
3540 __isl_keep isl_pw_aff *pa,
3541 enum isl_dim_type type);
3542 __isl_give isl_val *isl_aff_get_constant_val(
3543 __isl_keep isl_aff *aff);
3544 __isl_give isl_val *isl_aff_get_coefficient_val(
3545 __isl_keep isl_aff *aff,
3546 enum isl_dim_type type, int pos);
3547 __isl_give isl_val *isl_aff_get_denominator_val(
3548 __isl_keep isl_aff *aff);
3549 __isl_give isl_aff *isl_aff_get_div(
3550 __isl_keep isl_aff *aff, int pos);
3552 int isl_pw_aff_n_piece(__isl_keep isl_pw_aff *pwaff);
3553 int isl_pw_aff_foreach_piece(__isl_keep isl_pw_aff *pwaff,
3554 int (*fn)(__isl_take isl_set *set,
3555 __isl_take isl_aff *aff,
3556 void *user), void *user);
3558 int isl_aff_is_cst(__isl_keep isl_aff *aff);
3559 int isl_pw_aff_is_cst(__isl_keep isl_pw_aff *pwaff);
3561 int isl_aff_involves_dims(__isl_keep isl_aff *aff,
3562 enum isl_dim_type type, unsigned first, unsigned n);
3563 int isl_pw_aff_involves_dims(__isl_keep isl_pw_aff *pwaff,
3564 enum isl_dim_type type, unsigned first, unsigned n);
3566 isl_ctx *isl_pw_aff_get_ctx(__isl_keep isl_pw_aff *pwaff);
3567 unsigned isl_pw_aff_dim(__isl_keep isl_pw_aff *pwaff,
3568 enum isl_dim_type type);
3569 int isl_pw_aff_is_empty(__isl_keep isl_pw_aff *pwaff);
3571 It can be modified using
3573 #include <isl/aff.h>
3574 __isl_give isl_pw_aff *isl_pw_aff_set_tuple_id(
3575 __isl_take isl_pw_aff *pwaff,
3576 enum isl_dim_type type, __isl_take isl_id *id);
3577 __isl_give isl_aff *isl_aff_set_dim_name(
3578 __isl_take isl_aff *aff, enum isl_dim_type type,
3579 unsigned pos, const char *s);
3580 __isl_give isl_aff *isl_aff_set_dim_id(
3581 __isl_take isl_aff *aff, enum isl_dim_type type,
3582 unsigned pos, __isl_take isl_id *id);
3583 __isl_give isl_pw_aff *isl_pw_aff_set_dim_id(
3584 __isl_take isl_pw_aff *pma,
3585 enum isl_dim_type type, unsigned pos,
3586 __isl_take isl_id *id);
3587 __isl_give isl_aff *isl_aff_set_constant_si(
3588 __isl_take isl_aff *aff, int v);
3589 __isl_give isl_aff *isl_aff_set_constant_val(
3590 __isl_take isl_aff *aff, __isl_take isl_val *v);
3591 __isl_give isl_aff *isl_aff_set_coefficient_si(
3592 __isl_take isl_aff *aff,
3593 enum isl_dim_type type, int pos, int v);
3594 __isl_give isl_aff *isl_aff_set_coefficient_val(
3595 __isl_take isl_aff *aff,
3596 enum isl_dim_type type, int pos,
3597 __isl_take isl_val *v);
3599 __isl_give isl_aff *isl_aff_add_constant_si(
3600 __isl_take isl_aff *aff, int v);
3601 __isl_give isl_aff *isl_aff_add_constant_val(
3602 __isl_take isl_aff *aff, __isl_take isl_val *v);
3603 __isl_give isl_aff *isl_aff_add_constant_num_si(
3604 __isl_take isl_aff *aff, int v);
3605 __isl_give isl_aff *isl_aff_add_coefficient_si(
3606 __isl_take isl_aff *aff,
3607 enum isl_dim_type type, int pos, int v);
3608 __isl_give isl_aff *isl_aff_add_coefficient_val(
3609 __isl_take isl_aff *aff,
3610 enum isl_dim_type type, int pos,
3611 __isl_take isl_val *v);
3613 __isl_give isl_aff *isl_aff_insert_dims(
3614 __isl_take isl_aff *aff,
3615 enum isl_dim_type type, unsigned first, unsigned n);
3616 __isl_give isl_pw_aff *isl_pw_aff_insert_dims(
3617 __isl_take isl_pw_aff *pwaff,
3618 enum isl_dim_type type, unsigned first, unsigned n);
3619 __isl_give isl_aff *isl_aff_add_dims(
3620 __isl_take isl_aff *aff,
3621 enum isl_dim_type type, unsigned n);
3622 __isl_give isl_pw_aff *isl_pw_aff_add_dims(
3623 __isl_take isl_pw_aff *pwaff,
3624 enum isl_dim_type type, unsigned n);
3625 __isl_give isl_aff *isl_aff_drop_dims(
3626 __isl_take isl_aff *aff,
3627 enum isl_dim_type type, unsigned first, unsigned n);
3628 __isl_give isl_pw_aff *isl_pw_aff_drop_dims(
3629 __isl_take isl_pw_aff *pwaff,
3630 enum isl_dim_type type, unsigned first, unsigned n);
3632 Note that C<isl_aff_set_constant_si> and C<isl_aff_set_coefficient_si>
3633 set the I<numerator> of the constant or coefficient, while
3634 C<isl_aff_set_constant_val> and C<isl_aff_set_coefficient_val> set
3635 the constant or coefficient as a whole.
3636 The C<add_constant> and C<add_coefficient> functions add an integer
3637 or rational value to
3638 the possibly rational constant or coefficient.
3639 The C<add_constant_num> functions add an integer value to
3642 To check whether an affine expressions is obviously zero
3643 or obviously equal to some other affine expression, use
3645 #include <isl/aff.h>
3646 int isl_aff_plain_is_zero(__isl_keep isl_aff *aff);
3647 int isl_aff_plain_is_equal(__isl_keep isl_aff *aff1,
3648 __isl_keep isl_aff *aff2);
3649 int isl_pw_aff_plain_is_equal(
3650 __isl_keep isl_pw_aff *pwaff1,
3651 __isl_keep isl_pw_aff *pwaff2);
3655 #include <isl/aff.h>
3656 __isl_give isl_aff *isl_aff_add(__isl_take isl_aff *aff1,
3657 __isl_take isl_aff *aff2);
3658 __isl_give isl_pw_aff *isl_pw_aff_add(
3659 __isl_take isl_pw_aff *pwaff1,
3660 __isl_take isl_pw_aff *pwaff2);
3661 __isl_give isl_pw_aff *isl_pw_aff_min(
3662 __isl_take isl_pw_aff *pwaff1,
3663 __isl_take isl_pw_aff *pwaff2);
3664 __isl_give isl_pw_aff *isl_pw_aff_max(
3665 __isl_take isl_pw_aff *pwaff1,
3666 __isl_take isl_pw_aff *pwaff2);
3667 __isl_give isl_aff *isl_aff_sub(__isl_take isl_aff *aff1,
3668 __isl_take isl_aff *aff2);
3669 __isl_give isl_pw_aff *isl_pw_aff_sub(
3670 __isl_take isl_pw_aff *pwaff1,
3671 __isl_take isl_pw_aff *pwaff2);
3672 __isl_give isl_aff *isl_aff_neg(__isl_take isl_aff *aff);
3673 __isl_give isl_pw_aff *isl_pw_aff_neg(
3674 __isl_take isl_pw_aff *pwaff);
3675 __isl_give isl_aff *isl_aff_ceil(__isl_take isl_aff *aff);
3676 __isl_give isl_pw_aff *isl_pw_aff_ceil(
3677 __isl_take isl_pw_aff *pwaff);
3678 __isl_give isl_aff *isl_aff_floor(__isl_take isl_aff *aff);
3679 __isl_give isl_pw_aff *isl_pw_aff_floor(
3680 __isl_take isl_pw_aff *pwaff);
3681 __isl_give isl_aff *isl_aff_mod_val(__isl_take isl_aff *aff,
3682 __isl_take isl_val *mod);
3683 __isl_give isl_pw_aff *isl_pw_aff_mod_val(
3684 __isl_take isl_pw_aff *pa,
3685 __isl_take isl_val *mod);
3686 __isl_give isl_aff *isl_aff_scale_val(__isl_take isl_aff *aff,
3687 __isl_take isl_val *v);
3688 __isl_give isl_pw_aff *isl_pw_aff_scale_val(
3689 __isl_take isl_pw_aff *pa, __isl_take isl_val *v);
3690 __isl_give isl_aff *isl_aff_scale_down_ui(
3691 __isl_take isl_aff *aff, unsigned f);
3692 __isl_give isl_aff *isl_aff_scale_down_val(
3693 __isl_take isl_aff *aff, __isl_take isl_val *v);
3694 __isl_give isl_pw_aff *isl_pw_aff_scale_down_val(
3695 __isl_take isl_pw_aff *pa,
3696 __isl_take isl_val *f);
3698 __isl_give isl_pw_aff *isl_pw_aff_list_min(
3699 __isl_take isl_pw_aff_list *list);
3700 __isl_give isl_pw_aff *isl_pw_aff_list_max(
3701 __isl_take isl_pw_aff_list *list);
3703 __isl_give isl_pw_aff *isl_pw_aff_coalesce(
3704 __isl_take isl_pw_aff *pwqp);
3706 __isl_give isl_aff *isl_aff_align_params(
3707 __isl_take isl_aff *aff,
3708 __isl_take isl_space *model);
3709 __isl_give isl_pw_aff *isl_pw_aff_align_params(
3710 __isl_take isl_pw_aff *pwaff,
3711 __isl_take isl_space *model);
3713 __isl_give isl_aff *isl_aff_project_domain_on_params(
3714 __isl_take isl_aff *aff);
3716 __isl_give isl_aff *isl_aff_gist_params(
3717 __isl_take isl_aff *aff,
3718 __isl_take isl_set *context);
3719 __isl_give isl_aff *isl_aff_gist(__isl_take isl_aff *aff,
3720 __isl_take isl_set *context);
3721 __isl_give isl_pw_aff *isl_pw_aff_gist_params(
3722 __isl_take isl_pw_aff *pwaff,
3723 __isl_take isl_set *context);
3724 __isl_give isl_pw_aff *isl_pw_aff_gist(
3725 __isl_take isl_pw_aff *pwaff,
3726 __isl_take isl_set *context);
3728 __isl_give isl_set *isl_pw_aff_domain(
3729 __isl_take isl_pw_aff *pwaff);
3730 __isl_give isl_pw_aff *isl_pw_aff_intersect_domain(
3731 __isl_take isl_pw_aff *pa,
3732 __isl_take isl_set *set);
3733 __isl_give isl_pw_aff *isl_pw_aff_intersect_params(
3734 __isl_take isl_pw_aff *pa,
3735 __isl_take isl_set *set);
3737 __isl_give isl_aff *isl_aff_mul(__isl_take isl_aff *aff1,
3738 __isl_take isl_aff *aff2);
3739 __isl_give isl_aff *isl_aff_div(__isl_take isl_aff *aff1,
3740 __isl_take isl_aff *aff2);
3741 __isl_give isl_pw_aff *isl_pw_aff_mul(
3742 __isl_take isl_pw_aff *pwaff1,
3743 __isl_take isl_pw_aff *pwaff2);
3744 __isl_give isl_pw_aff *isl_pw_aff_div(
3745 __isl_take isl_pw_aff *pa1,
3746 __isl_take isl_pw_aff *pa2);
3747 __isl_give isl_pw_aff *isl_pw_aff_tdiv_q(
3748 __isl_take isl_pw_aff *pa1,
3749 __isl_take isl_pw_aff *pa2);
3750 __isl_give isl_pw_aff *isl_pw_aff_tdiv_r(
3751 __isl_take isl_pw_aff *pa1,
3752 __isl_take isl_pw_aff *pa2);
3754 When multiplying two affine expressions, at least one of the two needs
3755 to be a constant. Similarly, when dividing an affine expression by another,
3756 the second expression needs to be a constant.
3757 C<isl_pw_aff_tdiv_q> computes the quotient of an integer division with
3758 rounding towards zero. C<isl_pw_aff_tdiv_r> computes the corresponding
3761 #include <isl/aff.h>
3762 __isl_give isl_aff *isl_aff_pullback_multi_aff(
3763 __isl_take isl_aff *aff,
3764 __isl_take isl_multi_aff *ma);
3765 __isl_give isl_pw_aff *isl_pw_aff_pullback_multi_aff(
3766 __isl_take isl_pw_aff *pa,
3767 __isl_take isl_multi_aff *ma);
3768 __isl_give isl_pw_aff *isl_pw_aff_pullback_pw_multi_aff(
3769 __isl_take isl_pw_aff *pa,
3770 __isl_take isl_pw_multi_aff *pma);
3772 These functions precompose the input expression by the given
3773 C<isl_multi_aff> or C<isl_pw_multi_aff>. In other words,
3774 the C<isl_multi_aff> or C<isl_pw_multi_aff> is plugged
3775 into the (piecewise) affine expression.
3776 Objects of type C<isl_multi_aff> are described in
3777 L</"Piecewise Multiple Quasi Affine Expressions">.
3779 #include <isl/aff.h>
3780 __isl_give isl_basic_set *isl_aff_zero_basic_set(
3781 __isl_take isl_aff *aff);
3782 __isl_give isl_basic_set *isl_aff_neg_basic_set(
3783 __isl_take isl_aff *aff);
3784 __isl_give isl_basic_set *isl_aff_le_basic_set(
3785 __isl_take isl_aff *aff1, __isl_take isl_aff *aff2);
3786 __isl_give isl_basic_set *isl_aff_ge_basic_set(
3787 __isl_take isl_aff *aff1, __isl_take isl_aff *aff2);
3788 __isl_give isl_set *isl_pw_aff_eq_set(
3789 __isl_take isl_pw_aff *pwaff1,
3790 __isl_take isl_pw_aff *pwaff2);
3791 __isl_give isl_set *isl_pw_aff_ne_set(
3792 __isl_take isl_pw_aff *pwaff1,
3793 __isl_take isl_pw_aff *pwaff2);
3794 __isl_give isl_set *isl_pw_aff_le_set(
3795 __isl_take isl_pw_aff *pwaff1,
3796 __isl_take isl_pw_aff *pwaff2);
3797 __isl_give isl_set *isl_pw_aff_lt_set(
3798 __isl_take isl_pw_aff *pwaff1,
3799 __isl_take isl_pw_aff *pwaff2);
3800 __isl_give isl_set *isl_pw_aff_ge_set(
3801 __isl_take isl_pw_aff *pwaff1,
3802 __isl_take isl_pw_aff *pwaff2);
3803 __isl_give isl_set *isl_pw_aff_gt_set(
3804 __isl_take isl_pw_aff *pwaff1,
3805 __isl_take isl_pw_aff *pwaff2);
3807 __isl_give isl_set *isl_pw_aff_list_eq_set(
3808 __isl_take isl_pw_aff_list *list1,
3809 __isl_take isl_pw_aff_list *list2);
3810 __isl_give isl_set *isl_pw_aff_list_ne_set(
3811 __isl_take isl_pw_aff_list *list1,
3812 __isl_take isl_pw_aff_list *list2);
3813 __isl_give isl_set *isl_pw_aff_list_le_set(
3814 __isl_take isl_pw_aff_list *list1,
3815 __isl_take isl_pw_aff_list *list2);
3816 __isl_give isl_set *isl_pw_aff_list_lt_set(
3817 __isl_take isl_pw_aff_list *list1,
3818 __isl_take isl_pw_aff_list *list2);
3819 __isl_give isl_set *isl_pw_aff_list_ge_set(
3820 __isl_take isl_pw_aff_list *list1,
3821 __isl_take isl_pw_aff_list *list2);
3822 __isl_give isl_set *isl_pw_aff_list_gt_set(
3823 __isl_take isl_pw_aff_list *list1,
3824 __isl_take isl_pw_aff_list *list2);
3826 The function C<isl_aff_neg_basic_set> returns a basic set
3827 containing those elements in the domain space
3828 of C<aff> where C<aff> is negative.
3829 The function C<isl_aff_ge_basic_set> returns a basic set
3830 containing those elements in the shared space
3831 of C<aff1> and C<aff2> where C<aff1> is greater than or equal to C<aff2>.
3832 The function C<isl_pw_aff_ge_set> returns a set
3833 containing those elements in the shared domain
3834 of C<pwaff1> and C<pwaff2> where C<pwaff1> is greater than or equal to C<pwaff2>.
3835 The functions operating on C<isl_pw_aff_list> apply the corresponding
3836 C<isl_pw_aff> function to each pair of elements in the two lists.
3838 #include <isl/aff.h>
3839 __isl_give isl_set *isl_pw_aff_nonneg_set(
3840 __isl_take isl_pw_aff *pwaff);
3841 __isl_give isl_set *isl_pw_aff_zero_set(
3842 __isl_take isl_pw_aff *pwaff);
3843 __isl_give isl_set *isl_pw_aff_non_zero_set(
3844 __isl_take isl_pw_aff *pwaff);
3846 The function C<isl_pw_aff_nonneg_set> returns a set
3847 containing those elements in the domain
3848 of C<pwaff> where C<pwaff> is non-negative.
3850 #include <isl/aff.h>
3851 __isl_give isl_pw_aff *isl_pw_aff_cond(
3852 __isl_take isl_pw_aff *cond,
3853 __isl_take isl_pw_aff *pwaff_true,
3854 __isl_take isl_pw_aff *pwaff_false);
3856 The function C<isl_pw_aff_cond> performs a conditional operator
3857 and returns an expression that is equal to C<pwaff_true>
3858 for elements where C<cond> is non-zero and equal to C<pwaff_false> for elements
3859 where C<cond> is zero.
3861 #include <isl/aff.h>
3862 __isl_give isl_pw_aff *isl_pw_aff_union_min(
3863 __isl_take isl_pw_aff *pwaff1,
3864 __isl_take isl_pw_aff *pwaff2);
3865 __isl_give isl_pw_aff *isl_pw_aff_union_max(
3866 __isl_take isl_pw_aff *pwaff1,
3867 __isl_take isl_pw_aff *pwaff2);
3868 __isl_give isl_pw_aff *isl_pw_aff_union_add(
3869 __isl_take isl_pw_aff *pwaff1,
3870 __isl_take isl_pw_aff *pwaff2);
3872 The function C<isl_pw_aff_union_max> computes a piecewise quasi-affine
3873 expression with a domain that is the union of those of C<pwaff1> and
3874 C<pwaff2> and such that on each cell, the quasi-affine expression is
3875 the maximum of those of C<pwaff1> and C<pwaff2>. If only one of
3876 C<pwaff1> or C<pwaff2> is defined on a given cell, then the
3877 associated expression is the defined one.
3879 An expression can be read from input using
3881 #include <isl/aff.h>
3882 __isl_give isl_aff *isl_aff_read_from_str(
3883 isl_ctx *ctx, const char *str);
3884 __isl_give isl_pw_aff *isl_pw_aff_read_from_str(
3885 isl_ctx *ctx, const char *str);
3887 An expression can be printed using
3889 #include <isl/aff.h>
3890 __isl_give isl_printer *isl_printer_print_aff(
3891 __isl_take isl_printer *p, __isl_keep isl_aff *aff);
3893 __isl_give isl_printer *isl_printer_print_pw_aff(
3894 __isl_take isl_printer *p,
3895 __isl_keep isl_pw_aff *pwaff);
3897 =head2 Piecewise Multiple Quasi Affine Expressions
3899 An C<isl_multi_aff> object represents a sequence of
3900 zero or more affine expressions, all defined on the same domain space.
3901 Similarly, an C<isl_multi_pw_aff> object represents a sequence of
3902 zero or more piecewise affine expressions.
3904 An C<isl_multi_aff> can be constructed from a single
3905 C<isl_aff> or an C<isl_aff_list> using the
3906 following functions. Similarly for C<isl_multi_pw_aff>.
3908 #include <isl/aff.h>
3909 __isl_give isl_multi_aff *isl_multi_aff_from_aff(
3910 __isl_take isl_aff *aff);
3911 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_from_pw_aff(
3912 __isl_take isl_pw_aff *pa);
3913 __isl_give isl_multi_aff *isl_multi_aff_from_aff_list(
3914 __isl_take isl_space *space,
3915 __isl_take isl_aff_list *list);
3917 An empty piecewise multiple quasi affine expression (one with no cells),
3918 the zero piecewise multiple quasi affine expression (with value zero
3919 for each output dimension),
3920 a piecewise multiple quasi affine expression with a single cell (with
3921 either a universe or a specified domain) or
3922 a zero-dimensional piecewise multiple quasi affine expression
3924 can be created using the following functions.
3926 #include <isl/aff.h>
3927 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_empty(
3928 __isl_take isl_space *space);
3929 __isl_give isl_multi_aff *isl_multi_aff_zero(
3930 __isl_take isl_space *space);
3931 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_zero(
3932 __isl_take isl_space *space);
3933 __isl_give isl_multi_aff *isl_multi_aff_identity(
3934 __isl_take isl_space *space);
3935 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_identity(
3936 __isl_take isl_space *space);
3937 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_identity(
3938 __isl_take isl_space *space);
3939 __isl_give isl_pw_multi_aff *
3940 isl_pw_multi_aff_from_multi_aff(
3941 __isl_take isl_multi_aff *ma);
3942 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_alloc(
3943 __isl_take isl_set *set,
3944 __isl_take isl_multi_aff *maff);
3945 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_from_domain(
3946 __isl_take isl_set *set);
3948 __isl_give isl_union_pw_multi_aff *
3949 isl_union_pw_multi_aff_empty(
3950 __isl_take isl_space *space);
3951 __isl_give isl_union_pw_multi_aff *
3952 isl_union_pw_multi_aff_add_pw_multi_aff(
3953 __isl_take isl_union_pw_multi_aff *upma,
3954 __isl_take isl_pw_multi_aff *pma);
3955 __isl_give isl_union_pw_multi_aff *
3956 isl_union_pw_multi_aff_from_domain(
3957 __isl_take isl_union_set *uset);
3959 A piecewise multiple quasi affine expression can also be initialized
3960 from an C<isl_set> or C<isl_map>, provided the C<isl_set> is a singleton
3961 and the C<isl_map> is single-valued.
3962 In case of a conversion from an C<isl_union_set> or an C<isl_union_map>
3963 to an C<isl_union_pw_multi_aff>, these properties need to hold in each space.
3965 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_from_set(
3966 __isl_take isl_set *set);
3967 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_from_map(
3968 __isl_take isl_map *map);
3970 __isl_give isl_union_pw_multi_aff *
3971 isl_union_pw_multi_aff_from_union_set(
3972 __isl_take isl_union_set *uset);
3973 __isl_give isl_union_pw_multi_aff *
3974 isl_union_pw_multi_aff_from_union_map(
3975 __isl_take isl_union_map *umap);
3977 Multiple quasi affine expressions can be copied and freed using
3979 #include <isl/aff.h>
3980 __isl_give isl_multi_aff *isl_multi_aff_copy(
3981 __isl_keep isl_multi_aff *maff);
3982 void *isl_multi_aff_free(__isl_take isl_multi_aff *maff);
3984 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_copy(
3985 __isl_keep isl_pw_multi_aff *pma);
3986 void *isl_pw_multi_aff_free(
3987 __isl_take isl_pw_multi_aff *pma);
3989 __isl_give isl_union_pw_multi_aff *
3990 isl_union_pw_multi_aff_copy(
3991 __isl_keep isl_union_pw_multi_aff *upma);
3992 void *isl_union_pw_multi_aff_free(
3993 __isl_take isl_union_pw_multi_aff *upma);
3995 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_copy(
3996 __isl_keep isl_multi_pw_aff *mpa);
3997 void *isl_multi_pw_aff_free(
3998 __isl_take isl_multi_pw_aff *mpa);
4000 The expression can be inspected using
4002 #include <isl/aff.h>
4003 isl_ctx *isl_multi_aff_get_ctx(
4004 __isl_keep isl_multi_aff *maff);
4005 isl_ctx *isl_pw_multi_aff_get_ctx(
4006 __isl_keep isl_pw_multi_aff *pma);
4007 isl_ctx *isl_union_pw_multi_aff_get_ctx(
4008 __isl_keep isl_union_pw_multi_aff *upma);
4009 isl_ctx *isl_multi_pw_aff_get_ctx(
4010 __isl_keep isl_multi_pw_aff *mpa);
4011 unsigned isl_multi_aff_dim(__isl_keep isl_multi_aff *maff,
4012 enum isl_dim_type type);
4013 unsigned isl_pw_multi_aff_dim(
4014 __isl_keep isl_pw_multi_aff *pma,
4015 enum isl_dim_type type);
4016 unsigned isl_multi_pw_aff_dim(
4017 __isl_keep isl_multi_pw_aff *mpa,
4018 enum isl_dim_type type);
4019 __isl_give isl_aff *isl_multi_aff_get_aff(
4020 __isl_keep isl_multi_aff *multi, int pos);
4021 __isl_give isl_pw_aff *isl_pw_multi_aff_get_pw_aff(
4022 __isl_keep isl_pw_multi_aff *pma, int pos);
4023 __isl_give isl_pw_aff *isl_multi_pw_aff_get_pw_aff(
4024 __isl_keep isl_multi_pw_aff *mpa, int pos);
4025 const char *isl_pw_multi_aff_get_dim_name(
4026 __isl_keep isl_pw_multi_aff *pma,
4027 enum isl_dim_type type, unsigned pos);
4028 __isl_give isl_id *isl_pw_multi_aff_get_dim_id(
4029 __isl_keep isl_pw_multi_aff *pma,
4030 enum isl_dim_type type, unsigned pos);
4031 const char *isl_multi_aff_get_tuple_name(
4032 __isl_keep isl_multi_aff *multi,
4033 enum isl_dim_type type);
4034 int isl_pw_multi_aff_has_tuple_name(
4035 __isl_keep isl_pw_multi_aff *pma,
4036 enum isl_dim_type type);
4037 const char *isl_pw_multi_aff_get_tuple_name(
4038 __isl_keep isl_pw_multi_aff *pma,
4039 enum isl_dim_type type);
4040 int isl_pw_multi_aff_has_tuple_id(
4041 __isl_keep isl_pw_multi_aff *pma,
4042 enum isl_dim_type type);
4043 __isl_give isl_id *isl_pw_multi_aff_get_tuple_id(
4044 __isl_keep isl_pw_multi_aff *pma,
4045 enum isl_dim_type type);
4047 int isl_pw_multi_aff_foreach_piece(
4048 __isl_keep isl_pw_multi_aff *pma,
4049 int (*fn)(__isl_take isl_set *set,
4050 __isl_take isl_multi_aff *maff,
4051 void *user), void *user);
4053 int isl_union_pw_multi_aff_foreach_pw_multi_aff(
4054 __isl_keep isl_union_pw_multi_aff *upma,
4055 int (*fn)(__isl_take isl_pw_multi_aff *pma,
4056 void *user), void *user);
4058 It can be modified using
4060 #include <isl/aff.h>
4061 __isl_give isl_multi_aff *isl_multi_aff_set_aff(
4062 __isl_take isl_multi_aff *multi, int pos,
4063 __isl_take isl_aff *aff);
4064 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_set_pw_aff(
4065 __isl_take isl_pw_multi_aff *pma, unsigned pos,
4066 __isl_take isl_pw_aff *pa);
4067 __isl_give isl_multi_aff *isl_multi_aff_set_dim_name(
4068 __isl_take isl_multi_aff *maff,
4069 enum isl_dim_type type, unsigned pos, const char *s);
4070 __isl_give isl_multi_aff *isl_multi_aff_set_tuple_name(
4071 __isl_take isl_multi_aff *maff,
4072 enum isl_dim_type type, const char *s);
4073 __isl_give isl_multi_aff *isl_multi_aff_set_tuple_id(
4074 __isl_take isl_multi_aff *maff,
4075 enum isl_dim_type type, __isl_take isl_id *id);
4076 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_set_tuple_id(
4077 __isl_take isl_pw_multi_aff *pma,
4078 enum isl_dim_type type, __isl_take isl_id *id);
4080 __isl_give isl_multi_pw_aff *
4081 isl_multi_pw_aff_set_dim_name(
4082 __isl_take isl_multi_pw_aff *mpa,
4083 enum isl_dim_type type, unsigned pos, const char *s);
4084 __isl_give isl_multi_pw_aff *
4085 isl_multi_pw_aff_set_tuple_name(
4086 __isl_take isl_multi_pw_aff *mpa,
4087 enum isl_dim_type type, const char *s);
4089 __isl_give isl_multi_aff *isl_multi_aff_insert_dims(
4090 __isl_take isl_multi_aff *ma,
4091 enum isl_dim_type type, unsigned first, unsigned n);
4092 __isl_give isl_multi_aff *isl_multi_aff_add_dims(
4093 __isl_take isl_multi_aff *ma,
4094 enum isl_dim_type type, unsigned n);
4095 __isl_give isl_multi_aff *isl_multi_aff_drop_dims(
4096 __isl_take isl_multi_aff *maff,
4097 enum isl_dim_type type, unsigned first, unsigned n);
4098 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_drop_dims(
4099 __isl_take isl_pw_multi_aff *pma,
4100 enum isl_dim_type type, unsigned first, unsigned n);
4102 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_insert_dims(
4103 __isl_take isl_multi_pw_aff *mpa,
4104 enum isl_dim_type type, unsigned first, unsigned n);
4105 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_add_dims(
4106 __isl_take isl_multi_pw_aff *mpa,
4107 enum isl_dim_type type, unsigned n);
4109 To check whether two multiple affine expressions are
4110 obviously equal to each other, use
4112 int isl_multi_aff_plain_is_equal(__isl_keep isl_multi_aff *maff1,
4113 __isl_keep isl_multi_aff *maff2);
4114 int isl_pw_multi_aff_plain_is_equal(
4115 __isl_keep isl_pw_multi_aff *pma1,
4116 __isl_keep isl_pw_multi_aff *pma2);
4120 #include <isl/aff.h>
4121 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_union_lexmin(
4122 __isl_take isl_pw_multi_aff *pma1,
4123 __isl_take isl_pw_multi_aff *pma2);
4124 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_union_lexmax(
4125 __isl_take isl_pw_multi_aff *pma1,
4126 __isl_take isl_pw_multi_aff *pma2);
4127 __isl_give isl_multi_aff *isl_multi_aff_add(
4128 __isl_take isl_multi_aff *maff1,
4129 __isl_take isl_multi_aff *maff2);
4130 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_add(
4131 __isl_take isl_pw_multi_aff *pma1,
4132 __isl_take isl_pw_multi_aff *pma2);
4133 __isl_give isl_union_pw_multi_aff *isl_union_pw_multi_aff_add(
4134 __isl_take isl_union_pw_multi_aff *upma1,
4135 __isl_take isl_union_pw_multi_aff *upma2);
4136 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_union_add(
4137 __isl_take isl_pw_multi_aff *pma1,
4138 __isl_take isl_pw_multi_aff *pma2);
4139 __isl_give isl_multi_aff *isl_multi_aff_sub(
4140 __isl_take isl_multi_aff *ma1,
4141 __isl_take isl_multi_aff *ma2);
4142 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_sub(
4143 __isl_take isl_pw_multi_aff *pma1,
4144 __isl_take isl_pw_multi_aff *pma2);
4145 __isl_give isl_union_pw_multi_aff *isl_union_pw_multi_aff_sub(
4146 __isl_take isl_union_pw_multi_aff *upma1,
4147 __isl_take isl_union_pw_multi_aff *upma2);
4149 C<isl_multi_aff_sub> subtracts the second argument from the first.
4151 __isl_give isl_multi_aff *isl_multi_aff_scale_val(
4152 __isl_take isl_multi_aff *ma,
4153 __isl_take isl_val *v);
4154 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_scale_val(
4155 __isl_take isl_pw_multi_aff *pma,
4156 __isl_take isl_val *v);
4157 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_scale_val(
4158 __isl_take isl_multi_pw_aff *mpa,
4159 __isl_take isl_val *v);
4160 __isl_give isl_multi_aff *isl_multi_aff_scale_multi_val(
4161 __isl_take isl_multi_aff *ma,
4162 __isl_take isl_multi_val *mv);
4163 __isl_give isl_pw_multi_aff *
4164 isl_pw_multi_aff_scale_multi_val(
4165 __isl_take isl_pw_multi_aff *pma,
4166 __isl_take isl_multi_val *mv);
4167 __isl_give isl_multi_pw_aff *
4168 isl_multi_pw_aff_scale_multi_val(
4169 __isl_take isl_multi_pw_aff *mpa,
4170 __isl_take isl_multi_val *mv);
4171 __isl_give isl_union_pw_multi_aff *
4172 isl_union_pw_multi_aff_scale_multi_val(
4173 __isl_take isl_union_pw_multi_aff *upma,
4174 __isl_take isl_multi_val *mv);
4176 C<isl_multi_aff_scale_multi_val> scales the elements of C<ma>
4177 by the corresponding elements of C<mv>.
4179 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_intersect_params(
4180 __isl_take isl_pw_multi_aff *pma,
4181 __isl_take isl_set *set);
4182 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_intersect_domain(
4183 __isl_take isl_pw_multi_aff *pma,
4184 __isl_take isl_set *set);
4185 __isl_give isl_union_pw_multi_aff *
4186 isl_union_pw_multi_aff_intersect_domain(
4187 __isl_take isl_union_pw_multi_aff *upma,
4188 __isl_take isl_union_set *uset);
4189 __isl_give isl_multi_aff *isl_multi_aff_lift(
4190 __isl_take isl_multi_aff *maff,
4191 __isl_give isl_local_space **ls);
4192 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_coalesce(
4193 __isl_take isl_pw_multi_aff *pma);
4194 __isl_give isl_multi_aff *isl_multi_aff_align_params(
4195 __isl_take isl_multi_aff *multi,
4196 __isl_take isl_space *model);
4197 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_align_params(
4198 __isl_take isl_pw_multi_aff *pma,
4199 __isl_take isl_space *model);
4200 __isl_give isl_pw_multi_aff *
4201 isl_pw_multi_aff_project_domain_on_params(
4202 __isl_take isl_pw_multi_aff *pma);
4203 __isl_give isl_multi_aff *isl_multi_aff_gist_params(
4204 __isl_take isl_multi_aff *maff,
4205 __isl_take isl_set *context);
4206 __isl_give isl_multi_aff *isl_multi_aff_gist(
4207 __isl_take isl_multi_aff *maff,
4208 __isl_take isl_set *context);
4209 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_gist_params(
4210 __isl_take isl_pw_multi_aff *pma,
4211 __isl_take isl_set *set);
4212 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_gist(
4213 __isl_take isl_pw_multi_aff *pma,
4214 __isl_take isl_set *set);
4215 __isl_give isl_set *isl_pw_multi_aff_domain(
4216 __isl_take isl_pw_multi_aff *pma);
4217 __isl_give isl_union_set *isl_union_pw_multi_aff_domain(
4218 __isl_take isl_union_pw_multi_aff *upma);
4219 __isl_give isl_multi_aff *isl_multi_aff_range_splice(
4220 __isl_take isl_multi_aff *ma1, unsigned pos,
4221 __isl_take isl_multi_aff *ma2);
4222 __isl_give isl_multi_aff *isl_multi_aff_splice(
4223 __isl_take isl_multi_aff *ma1,
4224 unsigned in_pos, unsigned out_pos,
4225 __isl_take isl_multi_aff *ma2);
4226 __isl_give isl_multi_aff *isl_multi_aff_range_product(
4227 __isl_take isl_multi_aff *ma1,
4228 __isl_take isl_multi_aff *ma2);
4229 __isl_give isl_multi_aff *isl_multi_aff_flat_range_product(
4230 __isl_take isl_multi_aff *ma1,
4231 __isl_take isl_multi_aff *ma2);
4232 __isl_give isl_multi_aff *isl_multi_aff_product(
4233 __isl_take isl_multi_aff *ma1,
4234 __isl_take isl_multi_aff *ma2);
4235 __isl_give isl_pw_multi_aff *
4236 isl_pw_multi_aff_range_product(
4237 __isl_take isl_pw_multi_aff *pma1,
4238 __isl_take isl_pw_multi_aff *pma2);
4239 __isl_give isl_pw_multi_aff *
4240 isl_pw_multi_aff_flat_range_product(
4241 __isl_take isl_pw_multi_aff *pma1,
4242 __isl_take isl_pw_multi_aff *pma2);
4243 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_product(
4244 __isl_take isl_pw_multi_aff *pma1,
4245 __isl_take isl_pw_multi_aff *pma2);
4246 __isl_give isl_union_pw_multi_aff *
4247 isl_union_pw_multi_aff_flat_range_product(
4248 __isl_take isl_union_pw_multi_aff *upma1,
4249 __isl_take isl_union_pw_multi_aff *upma2);
4250 __isl_give isl_multi_pw_aff *
4251 isl_multi_pw_aff_range_splice(
4252 __isl_take isl_multi_pw_aff *mpa1, unsigned pos,
4253 __isl_take isl_multi_pw_aff *mpa2);
4254 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_splice(
4255 __isl_take isl_multi_pw_aff *mpa1,
4256 unsigned in_pos, unsigned out_pos,
4257 __isl_take isl_multi_pw_aff *mpa2);
4258 __isl_give isl_multi_pw_aff *
4259 isl_multi_pw_aff_range_product(
4260 __isl_take isl_multi_pw_aff *mpa1,
4261 __isl_take isl_multi_pw_aff *mpa2);
4262 __isl_give isl_multi_pw_aff *
4263 isl_multi_pw_aff_flat_range_product(
4264 __isl_take isl_multi_pw_aff *mpa1,
4265 __isl_take isl_multi_pw_aff *mpa2);
4267 If the C<ls> argument of C<isl_multi_aff_lift> is not C<NULL>,
4268 then it is assigned the local space that lies at the basis of
4269 the lifting applied.
4271 #include <isl/aff.h>
4272 __isl_give isl_multi_aff *isl_multi_aff_pullback_multi_aff(
4273 __isl_take isl_multi_aff *ma1,
4274 __isl_take isl_multi_aff *ma2);
4275 __isl_give isl_pw_multi_aff *
4276 isl_pw_multi_aff_pullback_multi_aff(
4277 __isl_take isl_pw_multi_aff *pma,
4278 __isl_take isl_multi_aff *ma);
4279 __isl_give isl_pw_multi_aff *
4280 isl_pw_multi_aff_pullback_pw_multi_aff(
4281 __isl_take isl_pw_multi_aff *pma1,
4282 __isl_take isl_pw_multi_aff *pma2);
4284 The function C<isl_multi_aff_pullback_multi_aff> precomposes C<ma1> by C<ma2>.
4285 In other words, C<ma2> is plugged
4288 __isl_give isl_set *isl_multi_aff_lex_le_set(
4289 __isl_take isl_multi_aff *ma1,
4290 __isl_take isl_multi_aff *ma2);
4291 __isl_give isl_set *isl_multi_aff_lex_ge_set(
4292 __isl_take isl_multi_aff *ma1,
4293 __isl_take isl_multi_aff *ma2);
4295 The function C<isl_multi_aff_lex_le_set> returns a set
4296 containing those elements in the shared domain space
4297 where C<ma1> is lexicographically smaller than or
4300 An expression can be read from input using
4302 #include <isl/aff.h>
4303 __isl_give isl_multi_aff *isl_multi_aff_read_from_str(
4304 isl_ctx *ctx, const char *str);
4305 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_read_from_str(
4306 isl_ctx *ctx, const char *str);
4307 __isl_give isl_union_pw_multi_aff *
4308 isl_union_pw_multi_aff_read_from_str(
4309 isl_ctx *ctx, const char *str);
4311 An expression can be printed using
4313 #include <isl/aff.h>
4314 __isl_give isl_printer *isl_printer_print_multi_aff(
4315 __isl_take isl_printer *p,
4316 __isl_keep isl_multi_aff *maff);
4317 __isl_give isl_printer *isl_printer_print_pw_multi_aff(
4318 __isl_take isl_printer *p,
4319 __isl_keep isl_pw_multi_aff *pma);
4320 __isl_give isl_printer *isl_printer_print_union_pw_multi_aff(
4321 __isl_take isl_printer *p,
4322 __isl_keep isl_union_pw_multi_aff *upma);
4323 __isl_give isl_printer *isl_printer_print_multi_pw_aff(
4324 __isl_take isl_printer *p,
4325 __isl_keep isl_multi_pw_aff *mpa);
4329 Points are elements of a set. They can be used to construct
4330 simple sets (boxes) or they can be used to represent the
4331 individual elements of a set.
4332 The zero point (the origin) can be created using
4334 __isl_give isl_point *isl_point_zero(__isl_take isl_space *space);
4336 The coordinates of a point can be inspected, set and changed
4339 __isl_give isl_val *isl_point_get_coordinate_val(
4340 __isl_keep isl_point *pnt,
4341 enum isl_dim_type type, int pos);
4342 __isl_give isl_point *isl_point_set_coordinate_val(
4343 __isl_take isl_point *pnt,
4344 enum isl_dim_type type, int pos,
4345 __isl_take isl_val *v);
4347 __isl_give isl_point *isl_point_add_ui(
4348 __isl_take isl_point *pnt,
4349 enum isl_dim_type type, int pos, unsigned val);
4350 __isl_give isl_point *isl_point_sub_ui(
4351 __isl_take isl_point *pnt,
4352 enum isl_dim_type type, int pos, unsigned val);
4354 Other properties can be obtained using
4356 isl_ctx *isl_point_get_ctx(__isl_keep isl_point *pnt);
4358 Points can be copied or freed using
4360 __isl_give isl_point *isl_point_copy(
4361 __isl_keep isl_point *pnt);
4362 void isl_point_free(__isl_take isl_point *pnt);
4364 A singleton set can be created from a point using
4366 __isl_give isl_basic_set *isl_basic_set_from_point(
4367 __isl_take isl_point *pnt);
4368 __isl_give isl_set *isl_set_from_point(
4369 __isl_take isl_point *pnt);
4371 and a box can be created from two opposite extremal points using
4373 __isl_give isl_basic_set *isl_basic_set_box_from_points(
4374 __isl_take isl_point *pnt1,
4375 __isl_take isl_point *pnt2);
4376 __isl_give isl_set *isl_set_box_from_points(
4377 __isl_take isl_point *pnt1,
4378 __isl_take isl_point *pnt2);
4380 All elements of a B<bounded> (union) set can be enumerated using
4381 the following functions.
4383 int isl_set_foreach_point(__isl_keep isl_set *set,
4384 int (*fn)(__isl_take isl_point *pnt, void *user),
4386 int isl_union_set_foreach_point(__isl_keep isl_union_set *uset,
4387 int (*fn)(__isl_take isl_point *pnt, void *user),
4390 The function C<fn> is called for each integer point in
4391 C<set> with as second argument the last argument of
4392 the C<isl_set_foreach_point> call. The function C<fn>
4393 should return C<0> on success and C<-1> on failure.
4394 In the latter case, C<isl_set_foreach_point> will stop
4395 enumerating and return C<-1> as well.
4396 If the enumeration is performed successfully and to completion,
4397 then C<isl_set_foreach_point> returns C<0>.
4399 To obtain a single point of a (basic) set, use
4401 __isl_give isl_point *isl_basic_set_sample_point(
4402 __isl_take isl_basic_set *bset);
4403 __isl_give isl_point *isl_set_sample_point(
4404 __isl_take isl_set *set);
4406 If C<set> does not contain any (integer) points, then the
4407 resulting point will be ``void'', a property that can be
4410 int isl_point_is_void(__isl_keep isl_point *pnt);
4412 =head2 Piecewise Quasipolynomials
4414 A piecewise quasipolynomial is a particular kind of function that maps
4415 a parametric point to a rational value.
4416 More specifically, a quasipolynomial is a polynomial expression in greatest
4417 integer parts of affine expressions of parameters and variables.
4418 A piecewise quasipolynomial is a subdivision of a given parametric
4419 domain into disjoint cells with a quasipolynomial associated to
4420 each cell. The value of the piecewise quasipolynomial at a given
4421 point is the value of the quasipolynomial associated to the cell
4422 that contains the point. Outside of the union of cells,
4423 the value is assumed to be zero.
4424 For example, the piecewise quasipolynomial
4426 [n] -> { [x] -> ((1 + n) - x) : x <= n and x >= 0 }
4428 maps C<x> to C<1 + n - x> for values of C<x> between C<0> and C<n>.
4429 A given piecewise quasipolynomial has a fixed domain dimension.
4430 Union piecewise quasipolynomials are used to contain piecewise quasipolynomials
4431 defined over different domains.
4432 Piecewise quasipolynomials are mainly used by the C<barvinok>
4433 library for representing the number of elements in a parametric set or map.
4434 For example, the piecewise quasipolynomial above represents
4435 the number of points in the map
4437 [n] -> { [x] -> [y] : x,y >= 0 and 0 <= x + y <= n }
4439 =head3 Input and Output
4441 Piecewise quasipolynomials can be read from input using
4443 __isl_give isl_union_pw_qpolynomial *
4444 isl_union_pw_qpolynomial_read_from_str(
4445 isl_ctx *ctx, const char *str);
4447 Quasipolynomials and piecewise quasipolynomials can be printed
4448 using the following functions.
4450 __isl_give isl_printer *isl_printer_print_qpolynomial(
4451 __isl_take isl_printer *p,
4452 __isl_keep isl_qpolynomial *qp);
4454 __isl_give isl_printer *isl_printer_print_pw_qpolynomial(
4455 __isl_take isl_printer *p,
4456 __isl_keep isl_pw_qpolynomial *pwqp);
4458 __isl_give isl_printer *isl_printer_print_union_pw_qpolynomial(
4459 __isl_take isl_printer *p,
4460 __isl_keep isl_union_pw_qpolynomial *upwqp);
4462 The output format of the printer
4463 needs to be set to either C<ISL_FORMAT_ISL> or C<ISL_FORMAT_C>.
4464 For C<isl_printer_print_union_pw_qpolynomial>, only C<ISL_FORMAT_ISL>
4466 In case of printing in C<ISL_FORMAT_C>, the user may want
4467 to set the names of all dimensions
4469 __isl_give isl_qpolynomial *isl_qpolynomial_set_dim_name(
4470 __isl_take isl_qpolynomial *qp,
4471 enum isl_dim_type type, unsigned pos,
4473 __isl_give isl_pw_qpolynomial *
4474 isl_pw_qpolynomial_set_dim_name(
4475 __isl_take isl_pw_qpolynomial *pwqp,
4476 enum isl_dim_type type, unsigned pos,
4479 =head3 Creating New (Piecewise) Quasipolynomials
4481 Some simple quasipolynomials can be created using the following functions.
4482 More complicated quasipolynomials can be created by applying
4483 operations such as addition and multiplication
4484 on the resulting quasipolynomials
4486 __isl_give isl_qpolynomial *isl_qpolynomial_zero_on_domain(
4487 __isl_take isl_space *domain);
4488 __isl_give isl_qpolynomial *isl_qpolynomial_one_on_domain(
4489 __isl_take isl_space *domain);
4490 __isl_give isl_qpolynomial *isl_qpolynomial_infty_on_domain(
4491 __isl_take isl_space *domain);
4492 __isl_give isl_qpolynomial *isl_qpolynomial_neginfty_on_domain(
4493 __isl_take isl_space *domain);
4494 __isl_give isl_qpolynomial *isl_qpolynomial_nan_on_domain(
4495 __isl_take isl_space *domain);
4496 __isl_give isl_qpolynomial *isl_qpolynomial_val_on_domain(
4497 __isl_take isl_space *domain,
4498 __isl_take isl_val *val);
4499 __isl_give isl_qpolynomial *isl_qpolynomial_var_on_domain(
4500 __isl_take isl_space *domain,
4501 enum isl_dim_type type, unsigned pos);
4502 __isl_give isl_qpolynomial *isl_qpolynomial_from_aff(
4503 __isl_take isl_aff *aff);
4505 Note that the space in which a quasipolynomial lives is a map space
4506 with a one-dimensional range. The C<domain> argument in some of
4507 the functions above corresponds to the domain of this map space.
4509 The zero piecewise quasipolynomial or a piecewise quasipolynomial
4510 with a single cell can be created using the following functions.
4511 Multiple of these single cell piecewise quasipolynomials can
4512 be combined to create more complicated piecewise quasipolynomials.
4514 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_zero(
4515 __isl_take isl_space *space);
4516 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_alloc(
4517 __isl_take isl_set *set,
4518 __isl_take isl_qpolynomial *qp);
4519 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_from_qpolynomial(
4520 __isl_take isl_qpolynomial *qp);
4521 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_from_pw_aff(
4522 __isl_take isl_pw_aff *pwaff);
4524 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_zero(
4525 __isl_take isl_space *space);
4526 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_from_pw_qpolynomial(
4527 __isl_take isl_pw_qpolynomial *pwqp);
4528 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_add_pw_qpolynomial(
4529 __isl_take isl_union_pw_qpolynomial *upwqp,
4530 __isl_take isl_pw_qpolynomial *pwqp);
4532 Quasipolynomials can be copied and freed again using the following
4535 __isl_give isl_qpolynomial *isl_qpolynomial_copy(
4536 __isl_keep isl_qpolynomial *qp);
4537 void *isl_qpolynomial_free(__isl_take isl_qpolynomial *qp);
4539 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_copy(
4540 __isl_keep isl_pw_qpolynomial *pwqp);
4541 void *isl_pw_qpolynomial_free(
4542 __isl_take isl_pw_qpolynomial *pwqp);
4544 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_copy(
4545 __isl_keep isl_union_pw_qpolynomial *upwqp);
4546 void *isl_union_pw_qpolynomial_free(
4547 __isl_take isl_union_pw_qpolynomial *upwqp);
4549 =head3 Inspecting (Piecewise) Quasipolynomials
4551 To iterate over all piecewise quasipolynomials in a union
4552 piecewise quasipolynomial, use the following function
4554 int isl_union_pw_qpolynomial_foreach_pw_qpolynomial(
4555 __isl_keep isl_union_pw_qpolynomial *upwqp,
4556 int (*fn)(__isl_take isl_pw_qpolynomial *pwqp, void *user),
4559 To extract the piecewise quasipolynomial in a given space from a union, use
4561 __isl_give isl_pw_qpolynomial *
4562 isl_union_pw_qpolynomial_extract_pw_qpolynomial(
4563 __isl_keep isl_union_pw_qpolynomial *upwqp,
4564 __isl_take isl_space *space);
4566 To iterate over the cells in a piecewise quasipolynomial,
4567 use either of the following two functions
4569 int isl_pw_qpolynomial_foreach_piece(
4570 __isl_keep isl_pw_qpolynomial *pwqp,
4571 int (*fn)(__isl_take isl_set *set,
4572 __isl_take isl_qpolynomial *qp,
4573 void *user), void *user);
4574 int isl_pw_qpolynomial_foreach_lifted_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);
4580 As usual, the function C<fn> should return C<0> on success
4581 and C<-1> on failure. The difference between
4582 C<isl_pw_qpolynomial_foreach_piece> and
4583 C<isl_pw_qpolynomial_foreach_lifted_piece> is that
4584 C<isl_pw_qpolynomial_foreach_lifted_piece> will first
4585 compute unique representations for all existentially quantified
4586 variables and then turn these existentially quantified variables
4587 into extra set variables, adapting the associated quasipolynomial
4588 accordingly. This means that the C<set> passed to C<fn>
4589 will not have any existentially quantified variables, but that
4590 the dimensions of the sets may be different for different
4591 invocations of C<fn>.
4593 The constant term of a quasipolynomial can be extracted using
4595 __isl_give isl_val *isl_qpolynomial_get_constant_val(
4596 __isl_keep isl_qpolynomial *qp);
4598 To iterate over all terms in a quasipolynomial,
4601 int isl_qpolynomial_foreach_term(
4602 __isl_keep isl_qpolynomial *qp,
4603 int (*fn)(__isl_take isl_term *term,
4604 void *user), void *user);
4606 The terms themselves can be inspected and freed using
4609 unsigned isl_term_dim(__isl_keep isl_term *term,
4610 enum isl_dim_type type);
4611 __isl_give isl_val *isl_term_get_coefficient_val(
4612 __isl_keep isl_term *term);
4613 int isl_term_get_exp(__isl_keep isl_term *term,
4614 enum isl_dim_type type, unsigned pos);
4615 __isl_give isl_aff *isl_term_get_div(
4616 __isl_keep isl_term *term, unsigned pos);
4617 void isl_term_free(__isl_take isl_term *term);
4619 Each term is a product of parameters, set variables and
4620 integer divisions. The function C<isl_term_get_exp>
4621 returns the exponent of a given dimensions in the given term.
4623 =head3 Properties of (Piecewise) Quasipolynomials
4625 To check whether two union piecewise quasipolynomials are
4626 obviously equal, use
4628 int isl_union_pw_qpolynomial_plain_is_equal(
4629 __isl_keep isl_union_pw_qpolynomial *upwqp1,
4630 __isl_keep isl_union_pw_qpolynomial *upwqp2);
4632 =head3 Operations on (Piecewise) Quasipolynomials
4634 __isl_give isl_qpolynomial *isl_qpolynomial_scale_val(
4635 __isl_take isl_qpolynomial *qp,
4636 __isl_take isl_val *v);
4637 __isl_give isl_qpolynomial *isl_qpolynomial_neg(
4638 __isl_take isl_qpolynomial *qp);
4639 __isl_give isl_qpolynomial *isl_qpolynomial_add(
4640 __isl_take isl_qpolynomial *qp1,
4641 __isl_take isl_qpolynomial *qp2);
4642 __isl_give isl_qpolynomial *isl_qpolynomial_sub(
4643 __isl_take isl_qpolynomial *qp1,
4644 __isl_take isl_qpolynomial *qp2);
4645 __isl_give isl_qpolynomial *isl_qpolynomial_mul(
4646 __isl_take isl_qpolynomial *qp1,
4647 __isl_take isl_qpolynomial *qp2);
4648 __isl_give isl_qpolynomial *isl_qpolynomial_pow(
4649 __isl_take isl_qpolynomial *qp, unsigned exponent);
4651 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_fix_val(
4652 __isl_take isl_pw_qpolynomial *pwqp,
4653 enum isl_dim_type type, unsigned n,
4654 __isl_take isl_val *v);
4655 __isl_give isl_pw_qpolynomial *
4656 isl_pw_qpolynomial_scale_val(
4657 __isl_take isl_pw_qpolynomial *pwqp,
4658 __isl_take isl_val *v);
4659 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_add(
4660 __isl_take isl_pw_qpolynomial *pwqp1,
4661 __isl_take isl_pw_qpolynomial *pwqp2);
4662 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_sub(
4663 __isl_take isl_pw_qpolynomial *pwqp1,
4664 __isl_take isl_pw_qpolynomial *pwqp2);
4665 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_add_disjoint(
4666 __isl_take isl_pw_qpolynomial *pwqp1,
4667 __isl_take isl_pw_qpolynomial *pwqp2);
4668 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_neg(
4669 __isl_take isl_pw_qpolynomial *pwqp);
4670 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_mul(
4671 __isl_take isl_pw_qpolynomial *pwqp1,
4672 __isl_take isl_pw_qpolynomial *pwqp2);
4673 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_pow(
4674 __isl_take isl_pw_qpolynomial *pwqp, unsigned exponent);
4676 __isl_give isl_union_pw_qpolynomial *
4677 isl_union_pw_qpolynomial_scale_val(
4678 __isl_take isl_union_pw_qpolynomial *upwqp,
4679 __isl_take isl_val *v);
4680 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_add(
4681 __isl_take isl_union_pw_qpolynomial *upwqp1,
4682 __isl_take isl_union_pw_qpolynomial *upwqp2);
4683 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_sub(
4684 __isl_take isl_union_pw_qpolynomial *upwqp1,
4685 __isl_take isl_union_pw_qpolynomial *upwqp2);
4686 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_mul(
4687 __isl_take isl_union_pw_qpolynomial *upwqp1,
4688 __isl_take isl_union_pw_qpolynomial *upwqp2);
4690 __isl_give isl_qpolynomial *isl_pw_qpolynomial_eval(
4691 __isl_take isl_pw_qpolynomial *pwqp,
4692 __isl_take isl_point *pnt);
4694 __isl_give isl_qpolynomial *isl_union_pw_qpolynomial_eval(
4695 __isl_take isl_union_pw_qpolynomial *upwqp,
4696 __isl_take isl_point *pnt);
4698 __isl_give isl_set *isl_pw_qpolynomial_domain(
4699 __isl_take isl_pw_qpolynomial *pwqp);
4700 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_intersect_domain(
4701 __isl_take isl_pw_qpolynomial *pwpq,
4702 __isl_take isl_set *set);
4703 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_intersect_params(
4704 __isl_take isl_pw_qpolynomial *pwpq,
4705 __isl_take isl_set *set);
4707 __isl_give isl_union_set *isl_union_pw_qpolynomial_domain(
4708 __isl_take isl_union_pw_qpolynomial *upwqp);
4709 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_intersect_domain(
4710 __isl_take isl_union_pw_qpolynomial *upwpq,
4711 __isl_take isl_union_set *uset);
4712 __isl_give isl_union_pw_qpolynomial *
4713 isl_union_pw_qpolynomial_intersect_params(
4714 __isl_take isl_union_pw_qpolynomial *upwpq,
4715 __isl_take isl_set *set);
4717 __isl_give isl_qpolynomial *isl_qpolynomial_align_params(
4718 __isl_take isl_qpolynomial *qp,
4719 __isl_take isl_space *model);
4721 __isl_give isl_qpolynomial *isl_qpolynomial_project_domain_on_params(
4722 __isl_take isl_qpolynomial *qp);
4723 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_project_domain_on_params(
4724 __isl_take isl_pw_qpolynomial *pwqp);
4726 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_coalesce(
4727 __isl_take isl_union_pw_qpolynomial *upwqp);
4729 __isl_give isl_qpolynomial *isl_qpolynomial_gist_params(
4730 __isl_take isl_qpolynomial *qp,
4731 __isl_take isl_set *context);
4732 __isl_give isl_qpolynomial *isl_qpolynomial_gist(
4733 __isl_take isl_qpolynomial *qp,
4734 __isl_take isl_set *context);
4736 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_gist_params(
4737 __isl_take isl_pw_qpolynomial *pwqp,
4738 __isl_take isl_set *context);
4739 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_gist(
4740 __isl_take isl_pw_qpolynomial *pwqp,
4741 __isl_take isl_set *context);
4743 __isl_give isl_union_pw_qpolynomial *
4744 isl_union_pw_qpolynomial_gist_params(
4745 __isl_take isl_union_pw_qpolynomial *upwqp,
4746 __isl_take isl_set *context);
4747 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_gist(
4748 __isl_take isl_union_pw_qpolynomial *upwqp,
4749 __isl_take isl_union_set *context);
4751 The gist operation applies the gist operation to each of
4752 the cells in the domain of the input piecewise quasipolynomial.
4753 The context is also exploited
4754 to simplify the quasipolynomials associated to each cell.
4756 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_to_polynomial(
4757 __isl_take isl_pw_qpolynomial *pwqp, int sign);
4758 __isl_give isl_union_pw_qpolynomial *
4759 isl_union_pw_qpolynomial_to_polynomial(
4760 __isl_take isl_union_pw_qpolynomial *upwqp, int sign);
4762 Approximate each quasipolynomial by a polynomial. If C<sign> is positive,
4763 the polynomial will be an overapproximation. If C<sign> is negative,
4764 it will be an underapproximation. If C<sign> is zero, the approximation
4765 will lie somewhere in between.
4767 =head2 Bounds on Piecewise Quasipolynomials and Piecewise Quasipolynomial Reductions
4769 A piecewise quasipolynomial reduction is a piecewise
4770 reduction (or fold) of quasipolynomials.
4771 In particular, the reduction can be maximum or a minimum.
4772 The objects are mainly used to represent the result of
4773 an upper or lower bound on a quasipolynomial over its domain,
4774 i.e., as the result of the following function.
4776 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_bound(
4777 __isl_take isl_pw_qpolynomial *pwqp,
4778 enum isl_fold type, int *tight);
4780 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_bound(
4781 __isl_take isl_union_pw_qpolynomial *upwqp,
4782 enum isl_fold type, int *tight);
4784 The C<type> argument may be either C<isl_fold_min> or C<isl_fold_max>.
4785 If C<tight> is not C<NULL>, then C<*tight> is set to C<1>
4786 is the returned bound is known be tight, i.e., for each value
4787 of the parameters there is at least
4788 one element in the domain that reaches the bound.
4789 If the domain of C<pwqp> is not wrapping, then the bound is computed
4790 over all elements in that domain and the result has a purely parametric
4791 domain. If the domain of C<pwqp> is wrapping, then the bound is
4792 computed over the range of the wrapped relation. The domain of the
4793 wrapped relation becomes the domain of the result.
4795 A (piecewise) quasipolynomial reduction can be copied or freed using the
4796 following functions.
4798 __isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_copy(
4799 __isl_keep isl_qpolynomial_fold *fold);
4800 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_copy(
4801 __isl_keep isl_pw_qpolynomial_fold *pwf);
4802 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_copy(
4803 __isl_keep isl_union_pw_qpolynomial_fold *upwf);
4804 void isl_qpolynomial_fold_free(
4805 __isl_take isl_qpolynomial_fold *fold);
4806 void *isl_pw_qpolynomial_fold_free(
4807 __isl_take isl_pw_qpolynomial_fold *pwf);
4808 void *isl_union_pw_qpolynomial_fold_free(
4809 __isl_take isl_union_pw_qpolynomial_fold *upwf);
4811 =head3 Printing Piecewise Quasipolynomial Reductions
4813 Piecewise quasipolynomial reductions can be printed
4814 using the following function.
4816 __isl_give isl_printer *isl_printer_print_pw_qpolynomial_fold(
4817 __isl_take isl_printer *p,
4818 __isl_keep isl_pw_qpolynomial_fold *pwf);
4819 __isl_give isl_printer *isl_printer_print_union_pw_qpolynomial_fold(
4820 __isl_take isl_printer *p,
4821 __isl_keep isl_union_pw_qpolynomial_fold *upwf);
4823 For C<isl_printer_print_pw_qpolynomial_fold>,
4824 output format of the printer
4825 needs to be set to either C<ISL_FORMAT_ISL> or C<ISL_FORMAT_C>.
4826 For C<isl_printer_print_union_pw_qpolynomial_fold>,
4827 output format of the printer
4828 needs to be set to C<ISL_FORMAT_ISL>.
4829 In case of printing in C<ISL_FORMAT_C>, the user may want
4830 to set the names of all dimensions
4832 __isl_give isl_pw_qpolynomial_fold *
4833 isl_pw_qpolynomial_fold_set_dim_name(
4834 __isl_take isl_pw_qpolynomial_fold *pwf,
4835 enum isl_dim_type type, unsigned pos,
4838 =head3 Inspecting (Piecewise) Quasipolynomial Reductions
4840 To iterate over all piecewise quasipolynomial reductions in a union
4841 piecewise quasipolynomial reduction, use the following function
4843 int isl_union_pw_qpolynomial_fold_foreach_pw_qpolynomial_fold(
4844 __isl_keep isl_union_pw_qpolynomial_fold *upwf,
4845 int (*fn)(__isl_take isl_pw_qpolynomial_fold *pwf,
4846 void *user), void *user);
4848 To iterate over the cells in a piecewise quasipolynomial reduction,
4849 use either of the following two functions
4851 int isl_pw_qpolynomial_fold_foreach_piece(
4852 __isl_keep isl_pw_qpolynomial_fold *pwf,
4853 int (*fn)(__isl_take isl_set *set,
4854 __isl_take isl_qpolynomial_fold *fold,
4855 void *user), void *user);
4856 int isl_pw_qpolynomial_fold_foreach_lifted_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);
4862 See L<Inspecting (Piecewise) Quasipolynomials> for an explanation
4863 of the difference between these two functions.
4865 To iterate over all quasipolynomials in a reduction, use
4867 int isl_qpolynomial_fold_foreach_qpolynomial(
4868 __isl_keep isl_qpolynomial_fold *fold,
4869 int (*fn)(__isl_take isl_qpolynomial *qp,
4870 void *user), void *user);
4872 =head3 Properties of Piecewise Quasipolynomial Reductions
4874 To check whether two union piecewise quasipolynomial reductions are
4875 obviously equal, use
4877 int isl_union_pw_qpolynomial_fold_plain_is_equal(
4878 __isl_keep isl_union_pw_qpolynomial_fold *upwf1,
4879 __isl_keep isl_union_pw_qpolynomial_fold *upwf2);
4881 =head3 Operations on Piecewise Quasipolynomial Reductions
4883 __isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_scale_val(
4884 __isl_take isl_qpolynomial_fold *fold,
4885 __isl_take isl_val *v);
4886 __isl_give isl_pw_qpolynomial_fold *
4887 isl_pw_qpolynomial_fold_scale_val(
4888 __isl_take isl_pw_qpolynomial_fold *pwf,
4889 __isl_take isl_val *v);
4890 __isl_give isl_union_pw_qpolynomial_fold *
4891 isl_union_pw_qpolynomial_fold_scale_val(
4892 __isl_take isl_union_pw_qpolynomial_fold *upwf,
4893 __isl_take isl_val *v);
4895 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_add(
4896 __isl_take isl_pw_qpolynomial_fold *pwf1,
4897 __isl_take isl_pw_qpolynomial_fold *pwf2);
4899 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_fold(
4900 __isl_take isl_pw_qpolynomial_fold *pwf1,
4901 __isl_take isl_pw_qpolynomial_fold *pwf2);
4903 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_fold(
4904 __isl_take isl_union_pw_qpolynomial_fold *upwf1,
4905 __isl_take isl_union_pw_qpolynomial_fold *upwf2);
4907 __isl_give isl_qpolynomial *isl_pw_qpolynomial_fold_eval(
4908 __isl_take isl_pw_qpolynomial_fold *pwf,
4909 __isl_take isl_point *pnt);
4911 __isl_give isl_qpolynomial *isl_union_pw_qpolynomial_fold_eval(
4912 __isl_take isl_union_pw_qpolynomial_fold *upwf,
4913 __isl_take isl_point *pnt);
4915 __isl_give isl_pw_qpolynomial_fold *
4916 isl_pw_qpolynomial_fold_intersect_params(
4917 __isl_take isl_pw_qpolynomial_fold *pwf,
4918 __isl_take isl_set *set);
4920 __isl_give isl_union_set *isl_union_pw_qpolynomial_fold_domain(
4921 __isl_take isl_union_pw_qpolynomial_fold *upwf);
4922 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_intersect_domain(
4923 __isl_take isl_union_pw_qpolynomial_fold *upwf,
4924 __isl_take isl_union_set *uset);
4925 __isl_give isl_union_pw_qpolynomial_fold *
4926 isl_union_pw_qpolynomial_fold_intersect_params(
4927 __isl_take isl_union_pw_qpolynomial_fold *upwf,
4928 __isl_take isl_set *set);
4930 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_project_domain_on_params(
4931 __isl_take isl_pw_qpolynomial_fold *pwf);
4933 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_coalesce(
4934 __isl_take isl_pw_qpolynomial_fold *pwf);
4936 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_coalesce(
4937 __isl_take isl_union_pw_qpolynomial_fold *upwf);
4939 __isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_gist_params(
4940 __isl_take isl_qpolynomial_fold *fold,
4941 __isl_take isl_set *context);
4942 __isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_gist(
4943 __isl_take isl_qpolynomial_fold *fold,
4944 __isl_take isl_set *context);
4946 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_gist(
4947 __isl_take isl_pw_qpolynomial_fold *pwf,
4948 __isl_take isl_set *context);
4949 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_gist_params(
4950 __isl_take isl_pw_qpolynomial_fold *pwf,
4951 __isl_take isl_set *context);
4953 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_gist(
4954 __isl_take isl_union_pw_qpolynomial_fold *upwf,
4955 __isl_take isl_union_set *context);
4956 __isl_give isl_union_pw_qpolynomial_fold *
4957 isl_union_pw_qpolynomial_fold_gist_params(
4958 __isl_take isl_union_pw_qpolynomial_fold *upwf,
4959 __isl_take isl_set *context);
4961 The gist operation applies the gist operation to each of
4962 the cells in the domain of the input piecewise quasipolynomial reduction.
4963 In future, the operation will also exploit the context
4964 to simplify the quasipolynomial reductions associated to each cell.
4966 __isl_give isl_pw_qpolynomial_fold *
4967 isl_set_apply_pw_qpolynomial_fold(
4968 __isl_take isl_set *set,
4969 __isl_take isl_pw_qpolynomial_fold *pwf,
4971 __isl_give isl_pw_qpolynomial_fold *
4972 isl_map_apply_pw_qpolynomial_fold(
4973 __isl_take isl_map *map,
4974 __isl_take isl_pw_qpolynomial_fold *pwf,
4976 __isl_give isl_union_pw_qpolynomial_fold *
4977 isl_union_set_apply_union_pw_qpolynomial_fold(
4978 __isl_take isl_union_set *uset,
4979 __isl_take isl_union_pw_qpolynomial_fold *upwf,
4981 __isl_give isl_union_pw_qpolynomial_fold *
4982 isl_union_map_apply_union_pw_qpolynomial_fold(
4983 __isl_take isl_union_map *umap,
4984 __isl_take isl_union_pw_qpolynomial_fold *upwf,
4987 The functions taking a map
4988 compose the given map with the given piecewise quasipolynomial reduction.
4989 That is, compute a bound (of the same type as C<pwf> or C<upwf> itself)
4990 over all elements in the intersection of the range of the map
4991 and the domain of the piecewise quasipolynomial reduction
4992 as a function of an element in the domain of the map.
4993 The functions taking a set compute a bound over all elements in the
4994 intersection of the set and the domain of the
4995 piecewise quasipolynomial reduction.
4997 =head2 Parametric Vertex Enumeration
4999 The parametric vertex enumeration described in this section
5000 is mainly intended to be used internally and by the C<barvinok>
5003 #include <isl/vertices.h>
5004 __isl_give isl_vertices *isl_basic_set_compute_vertices(
5005 __isl_keep isl_basic_set *bset);
5007 The function C<isl_basic_set_compute_vertices> performs the
5008 actual computation of the parametric vertices and the chamber
5009 decomposition and store the result in an C<isl_vertices> object.
5010 This information can be queried by either iterating over all
5011 the vertices or iterating over all the chambers or cells
5012 and then iterating over all vertices that are active on the chamber.
5014 int isl_vertices_foreach_vertex(
5015 __isl_keep isl_vertices *vertices,
5016 int (*fn)(__isl_take isl_vertex *vertex, void *user),
5019 int isl_vertices_foreach_cell(
5020 __isl_keep isl_vertices *vertices,
5021 int (*fn)(__isl_take isl_cell *cell, void *user),
5023 int isl_cell_foreach_vertex(__isl_keep isl_cell *cell,
5024 int (*fn)(__isl_take isl_vertex *vertex, void *user),
5027 Other operations that can be performed on an C<isl_vertices> object are
5030 isl_ctx *isl_vertices_get_ctx(
5031 __isl_keep isl_vertices *vertices);
5032 int isl_vertices_get_n_vertices(
5033 __isl_keep isl_vertices *vertices);
5034 void isl_vertices_free(__isl_take isl_vertices *vertices);
5036 Vertices can be inspected and destroyed using the following functions.
5038 isl_ctx *isl_vertex_get_ctx(__isl_keep isl_vertex *vertex);
5039 int isl_vertex_get_id(__isl_keep isl_vertex *vertex);
5040 __isl_give isl_basic_set *isl_vertex_get_domain(
5041 __isl_keep isl_vertex *vertex);
5042 __isl_give isl_basic_set *isl_vertex_get_expr(
5043 __isl_keep isl_vertex *vertex);
5044 void isl_vertex_free(__isl_take isl_vertex *vertex);
5046 C<isl_vertex_get_expr> returns a singleton parametric set describing
5047 the vertex, while C<isl_vertex_get_domain> returns the activity domain
5049 Note that C<isl_vertex_get_domain> and C<isl_vertex_get_expr> return
5050 B<rational> basic sets, so they should mainly be used for inspection
5051 and should not be mixed with integer sets.
5053 Chambers can be inspected and destroyed using the following functions.
5055 isl_ctx *isl_cell_get_ctx(__isl_keep isl_cell *cell);
5056 __isl_give isl_basic_set *isl_cell_get_domain(
5057 __isl_keep isl_cell *cell);
5058 void isl_cell_free(__isl_take isl_cell *cell);
5060 =head1 Polyhedral Compilation Library
5062 This section collects functionality in C<isl> that has been specifically
5063 designed for use during polyhedral compilation.
5065 =head2 Dependence Analysis
5067 C<isl> contains specialized functionality for performing
5068 array dataflow analysis. That is, given a I<sink> access relation
5069 and a collection of possible I<source> access relations,
5070 C<isl> can compute relations that describe
5071 for each iteration of the sink access, which iteration
5072 of which of the source access relations was the last
5073 to access the same data element before the given iteration
5075 The resulting dependence relations map source iterations
5076 to the corresponding sink iterations.
5077 To compute standard flow dependences, the sink should be
5078 a read, while the sources should be writes.
5079 If any of the source accesses are marked as being I<may>
5080 accesses, then there will be a dependence from the last
5081 I<must> access B<and> from any I<may> access that follows
5082 this last I<must> access.
5083 In particular, if I<all> sources are I<may> accesses,
5084 then memory based dependence analysis is performed.
5085 If, on the other hand, all sources are I<must> accesses,
5086 then value based dependence analysis is performed.
5088 #include <isl/flow.h>
5090 typedef int (*isl_access_level_before)(void *first, void *second);
5092 __isl_give isl_access_info *isl_access_info_alloc(
5093 __isl_take isl_map *sink,
5094 void *sink_user, isl_access_level_before fn,
5096 __isl_give isl_access_info *isl_access_info_add_source(
5097 __isl_take isl_access_info *acc,
5098 __isl_take isl_map *source, int must,
5100 void *isl_access_info_free(__isl_take isl_access_info *acc);
5102 __isl_give isl_flow *isl_access_info_compute_flow(
5103 __isl_take isl_access_info *acc);
5105 int isl_flow_foreach(__isl_keep isl_flow *deps,
5106 int (*fn)(__isl_take isl_map *dep, int must,
5107 void *dep_user, void *user),
5109 __isl_give isl_map *isl_flow_get_no_source(
5110 __isl_keep isl_flow *deps, int must);
5111 void isl_flow_free(__isl_take isl_flow *deps);
5113 The function C<isl_access_info_compute_flow> performs the actual
5114 dependence analysis. The other functions are used to construct
5115 the input for this function or to read off the output.
5117 The input is collected in an C<isl_access_info>, which can
5118 be created through a call to C<isl_access_info_alloc>.
5119 The arguments to this functions are the sink access relation
5120 C<sink>, a token C<sink_user> used to identify the sink
5121 access to the user, a callback function for specifying the
5122 relative order of source and sink accesses, and the number
5123 of source access relations that will be added.
5124 The callback function has type C<int (*)(void *first, void *second)>.
5125 The function is called with two user supplied tokens identifying
5126 either a source or the sink and it should return the shared nesting
5127 level and the relative order of the two accesses.
5128 In particular, let I<n> be the number of loops shared by
5129 the two accesses. If C<first> precedes C<second> textually,
5130 then the function should return I<2 * n + 1>; otherwise,
5131 it should return I<2 * n>.
5132 The sources can be added to the C<isl_access_info> by performing
5133 (at most) C<max_source> calls to C<isl_access_info_add_source>.
5134 C<must> indicates whether the source is a I<must> access
5135 or a I<may> access. Note that a multi-valued access relation
5136 should only be marked I<must> if every iteration in the domain
5137 of the relation accesses I<all> elements in its image.
5138 The C<source_user> token is again used to identify
5139 the source access. The range of the source access relation
5140 C<source> should have the same dimension as the range
5141 of the sink access relation.
5142 The C<isl_access_info_free> function should usually not be
5143 called explicitly, because it is called implicitly by
5144 C<isl_access_info_compute_flow>.
5146 The result of the dependence analysis is collected in an
5147 C<isl_flow>. There may be elements of
5148 the sink access for which no preceding source access could be
5149 found or for which all preceding sources are I<may> accesses.
5150 The relations containing these elements can be obtained through
5151 calls to C<isl_flow_get_no_source>, the first with C<must> set
5152 and the second with C<must> unset.
5153 In the case of standard flow dependence analysis,
5154 with the sink a read and the sources I<must> writes,
5155 the first relation corresponds to the reads from uninitialized
5156 array elements and the second relation is empty.
5157 The actual flow dependences can be extracted using
5158 C<isl_flow_foreach>. This function will call the user-specified
5159 callback function C<fn> for each B<non-empty> dependence between
5160 a source and the sink. The callback function is called
5161 with four arguments, the actual flow dependence relation
5162 mapping source iterations to sink iterations, a boolean that
5163 indicates whether it is a I<must> or I<may> dependence, a token
5164 identifying the source and an additional C<void *> with value
5165 equal to the third argument of the C<isl_flow_foreach> call.
5166 A dependence is marked I<must> if it originates from a I<must>
5167 source and if it is not followed by any I<may> sources.
5169 After finishing with an C<isl_flow>, the user should call
5170 C<isl_flow_free> to free all associated memory.
5172 A higher-level interface to dependence analysis is provided
5173 by the following function.
5175 #include <isl/flow.h>
5177 int isl_union_map_compute_flow(__isl_take isl_union_map *sink,
5178 __isl_take isl_union_map *must_source,
5179 __isl_take isl_union_map *may_source,
5180 __isl_take isl_union_map *schedule,
5181 __isl_give isl_union_map **must_dep,
5182 __isl_give isl_union_map **may_dep,
5183 __isl_give isl_union_map **must_no_source,
5184 __isl_give isl_union_map **may_no_source);
5186 The arrays are identified by the tuple names of the ranges
5187 of the accesses. The iteration domains by the tuple names
5188 of the domains of the accesses and of the schedule.
5189 The relative order of the iteration domains is given by the
5190 schedule. The relations returned through C<must_no_source>
5191 and C<may_no_source> are subsets of C<sink>.
5192 Any of C<must_dep>, C<may_dep>, C<must_no_source>
5193 or C<may_no_source> may be C<NULL>, but a C<NULL> value for
5194 any of the other arguments is treated as an error.
5196 =head3 Interaction with Dependence Analysis
5198 During the dependence analysis, we frequently need to perform
5199 the following operation. Given a relation between sink iterations
5200 and potential source iterations from a particular source domain,
5201 what is the last potential source iteration corresponding to each
5202 sink iteration. It can sometimes be convenient to adjust
5203 the set of potential source iterations before or after each such operation.
5204 The prototypical example is fuzzy array dataflow analysis,
5205 where we need to analyze if, based on data-dependent constraints,
5206 the sink iteration can ever be executed without one or more of
5207 the corresponding potential source iterations being executed.
5208 If so, we can introduce extra parameters and select an unknown
5209 but fixed source iteration from the potential source iterations.
5210 To be able to perform such manipulations, C<isl> provides the following
5213 #include <isl/flow.h>
5215 typedef __isl_give isl_restriction *(*isl_access_restrict)(
5216 __isl_keep isl_map *source_map,
5217 __isl_keep isl_set *sink, void *source_user,
5219 __isl_give isl_access_info *isl_access_info_set_restrict(
5220 __isl_take isl_access_info *acc,
5221 isl_access_restrict fn, void *user);
5223 The function C<isl_access_info_set_restrict> should be called
5224 before calling C<isl_access_info_compute_flow> and registers a callback function
5225 that will be called any time C<isl> is about to compute the last
5226 potential source. The first argument is the (reverse) proto-dependence,
5227 mapping sink iterations to potential source iterations.
5228 The second argument represents the sink iterations for which
5229 we want to compute the last source iteration.
5230 The third argument is the token corresponding to the source
5231 and the final argument is the token passed to C<isl_access_info_set_restrict>.
5232 The callback is expected to return a restriction on either the input or
5233 the output of the operation computing the last potential source.
5234 If the input needs to be restricted then restrictions are needed
5235 for both the source and the sink iterations. The sink iterations
5236 and the potential source iterations will be intersected with these sets.
5237 If the output needs to be restricted then only a restriction on the source
5238 iterations is required.
5239 If any error occurs, the callback should return C<NULL>.
5240 An C<isl_restriction> object can be created, freed and inspected
5241 using the following functions.
5243 #include <isl/flow.h>
5245 __isl_give isl_restriction *isl_restriction_input(
5246 __isl_take isl_set *source_restr,
5247 __isl_take isl_set *sink_restr);
5248 __isl_give isl_restriction *isl_restriction_output(
5249 __isl_take isl_set *source_restr);
5250 __isl_give isl_restriction *isl_restriction_none(
5251 __isl_take isl_map *source_map);
5252 __isl_give isl_restriction *isl_restriction_empty(
5253 __isl_take isl_map *source_map);
5254 void *isl_restriction_free(
5255 __isl_take isl_restriction *restr);
5256 isl_ctx *isl_restriction_get_ctx(
5257 __isl_keep isl_restriction *restr);
5259 C<isl_restriction_none> and C<isl_restriction_empty> are special
5260 cases of C<isl_restriction_input>. C<isl_restriction_none>
5261 is essentially equivalent to
5263 isl_restriction_input(isl_set_universe(
5264 isl_space_range(isl_map_get_space(source_map))),
5266 isl_space_domain(isl_map_get_space(source_map))));
5268 whereas C<isl_restriction_empty> is essentially equivalent to
5270 isl_restriction_input(isl_set_empty(
5271 isl_space_range(isl_map_get_space(source_map))),
5273 isl_space_domain(isl_map_get_space(source_map))));
5277 B<The functionality described in this section is fairly new
5278 and may be subject to change.>
5280 The following function can be used to compute a schedule
5281 for a union of domains.
5282 By default, the algorithm used to construct the schedule is similar
5283 to that of C<Pluto>.
5284 Alternatively, Feautrier's multi-dimensional scheduling algorithm can
5286 The generated schedule respects all C<validity> dependences.
5287 That is, all dependence distances over these dependences in the
5288 scheduled space are lexicographically positive.
5289 The default algorithm tries to minimize the dependence distances over
5290 C<proximity> dependences.
5291 Moreover, it tries to obtain sequences (bands) of schedule dimensions
5292 for groups of domains where the dependence distances have only
5293 non-negative values.
5294 When using Feautrier's algorithm, the C<proximity> dependence
5295 distances are only minimized during the extension to a
5296 full-dimensional schedule.
5298 #include <isl/schedule.h>
5299 __isl_give isl_schedule *isl_union_set_compute_schedule(
5300 __isl_take isl_union_set *domain,
5301 __isl_take isl_union_map *validity,
5302 __isl_take isl_union_map *proximity);
5303 void *isl_schedule_free(__isl_take isl_schedule *sched);
5305 A mapping from the domains to the scheduled space can be obtained
5306 from an C<isl_schedule> using the following function.
5308 __isl_give isl_union_map *isl_schedule_get_map(
5309 __isl_keep isl_schedule *sched);
5311 A representation of the schedule can be printed using
5313 __isl_give isl_printer *isl_printer_print_schedule(
5314 __isl_take isl_printer *p,
5315 __isl_keep isl_schedule *schedule);
5317 A representation of the schedule as a forest of bands can be obtained
5318 using the following function.
5320 __isl_give isl_band_list *isl_schedule_get_band_forest(
5321 __isl_keep isl_schedule *schedule);
5323 The individual bands can be visited in depth-first post-order
5324 using the following function.
5326 #include <isl/schedule.h>
5327 int isl_schedule_foreach_band(
5328 __isl_keep isl_schedule *sched,
5329 int (*fn)(__isl_keep isl_band *band, void *user),
5332 The list can be manipulated as explained in L<"Lists">.
5333 The bands inside the list can be copied and freed using the following
5336 #include <isl/band.h>
5337 __isl_give isl_band *isl_band_copy(
5338 __isl_keep isl_band *band);
5339 void *isl_band_free(__isl_take isl_band *band);
5341 Each band contains zero or more scheduling dimensions.
5342 These are referred to as the members of the band.
5343 The section of the schedule that corresponds to the band is
5344 referred to as the partial schedule of the band.
5345 For those nodes that participate in a band, the outer scheduling
5346 dimensions form the prefix schedule, while the inner scheduling
5347 dimensions form the suffix schedule.
5348 That is, if we take a cut of the band forest, then the union of
5349 the concatenations of the prefix, partial and suffix schedules of
5350 each band in the cut is equal to the entire schedule (modulo
5351 some possible padding at the end with zero scheduling dimensions).
5352 The properties of a band can be inspected using the following functions.
5354 #include <isl/band.h>
5355 isl_ctx *isl_band_get_ctx(__isl_keep isl_band *band);
5357 int isl_band_has_children(__isl_keep isl_band *band);
5358 __isl_give isl_band_list *isl_band_get_children(
5359 __isl_keep isl_band *band);
5361 __isl_give isl_union_map *isl_band_get_prefix_schedule(
5362 __isl_keep isl_band *band);
5363 __isl_give isl_union_map *isl_band_get_partial_schedule(
5364 __isl_keep isl_band *band);
5365 __isl_give isl_union_map *isl_band_get_suffix_schedule(
5366 __isl_keep isl_band *band);
5368 int isl_band_n_member(__isl_keep isl_band *band);
5369 int isl_band_member_is_zero_distance(
5370 __isl_keep isl_band *band, int pos);
5372 int isl_band_list_foreach_band(
5373 __isl_keep isl_band_list *list,
5374 int (*fn)(__isl_keep isl_band *band, void *user),
5377 Note that a scheduling dimension is considered to be ``zero
5378 distance'' if it does not carry any proximity dependences
5380 That is, if the dependence distances of the proximity
5381 dependences are all zero in that direction (for fixed
5382 iterations of outer bands).
5383 Like C<isl_schedule_foreach_band>,
5384 the function C<isl_band_list_foreach_band> calls C<fn> on the bands
5385 in depth-first post-order.
5387 A band can be tiled using the following function.
5389 #include <isl/band.h>
5390 int isl_band_tile(__isl_keep isl_band *band,
5391 __isl_take isl_vec *sizes);
5393 int isl_options_set_tile_scale_tile_loops(isl_ctx *ctx,
5395 int isl_options_get_tile_scale_tile_loops(isl_ctx *ctx);
5396 int isl_options_set_tile_shift_point_loops(isl_ctx *ctx,
5398 int isl_options_get_tile_shift_point_loops(isl_ctx *ctx);
5400 The C<isl_band_tile> function tiles the band using the given tile sizes
5401 inside its schedule.
5402 A new child band is created to represent the point loops and it is
5403 inserted between the modified band and its children.
5404 The C<tile_scale_tile_loops> option specifies whether the tile
5405 loops iterators should be scaled by the tile sizes.
5406 If the C<tile_shift_point_loops> option is set, then the point loops
5407 are shifted to start at zero.
5409 A band can be split into two nested bands using the following function.
5411 int isl_band_split(__isl_keep isl_band *band, int pos);
5413 The resulting outer band contains the first C<pos> dimensions of C<band>
5414 while the inner band contains the remaining dimensions.
5416 A representation of the band can be printed using
5418 #include <isl/band.h>
5419 __isl_give isl_printer *isl_printer_print_band(
5420 __isl_take isl_printer *p,
5421 __isl_keep isl_band *band);
5425 #include <isl/schedule.h>
5426 int isl_options_set_schedule_max_coefficient(
5427 isl_ctx *ctx, int val);
5428 int isl_options_get_schedule_max_coefficient(
5430 int isl_options_set_schedule_max_constant_term(
5431 isl_ctx *ctx, int val);
5432 int isl_options_get_schedule_max_constant_term(
5434 int isl_options_set_schedule_fuse(isl_ctx *ctx, int val);
5435 int isl_options_get_schedule_fuse(isl_ctx *ctx);
5436 int isl_options_set_schedule_maximize_band_depth(
5437 isl_ctx *ctx, int val);
5438 int isl_options_get_schedule_maximize_band_depth(
5440 int isl_options_set_schedule_outer_zero_distance(
5441 isl_ctx *ctx, int val);
5442 int isl_options_get_schedule_outer_zero_distance(
5444 int isl_options_set_schedule_split_scaled(
5445 isl_ctx *ctx, int val);
5446 int isl_options_get_schedule_split_scaled(
5448 int isl_options_set_schedule_algorithm(
5449 isl_ctx *ctx, int val);
5450 int isl_options_get_schedule_algorithm(
5452 int isl_options_set_schedule_separate_components(
5453 isl_ctx *ctx, int val);
5454 int isl_options_get_schedule_separate_components(
5459 =item * schedule_max_coefficient
5461 This option enforces that the coefficients for variable and parameter
5462 dimensions in the calculated schedule are not larger than the specified value.
5463 This option can significantly increase the speed of the scheduling calculation
5464 and may also prevent fusing of unrelated dimensions. A value of -1 means that
5465 this option does not introduce bounds on the variable or parameter
5468 =item * schedule_max_constant_term
5470 This option enforces that the constant coefficients in the calculated schedule
5471 are not larger than the maximal constant term. This option can significantly
5472 increase the speed of the scheduling calculation and may also prevent fusing of
5473 unrelated dimensions. A value of -1 means that this option does not introduce
5474 bounds on the constant coefficients.
5476 =item * schedule_fuse
5478 This option controls the level of fusion.
5479 If this option is set to C<ISL_SCHEDULE_FUSE_MIN>, then loops in the
5480 resulting schedule will be distributed as much as possible.
5481 If this option is set to C<ISL_SCHEDULE_FUSE_MAX>, then C<isl> will
5482 try to fuse loops in the resulting schedule.
5484 =item * schedule_maximize_band_depth
5486 If this option is set, we do not split bands at the point
5487 where we detect splitting is necessary. Instead, we
5488 backtrack and split bands as early as possible. This
5489 reduces the number of splits and maximizes the width of
5490 the bands. Wider bands give more possibilities for tiling.
5491 Note that if the C<schedule_fuse> option is set to C<ISL_SCHEDULE_FUSE_MIN>,
5492 then bands will be split as early as possible, even if there is no need.
5493 The C<schedule_maximize_band_depth> option therefore has no effect in this case.
5495 =item * schedule_outer_zero_distance
5497 If this option is set, then we try to construct schedules
5498 where the outermost scheduling dimension in each band
5499 results in a zero dependence distance over the proximity
5502 =item * schedule_split_scaled
5504 If this option is set, then we try to construct schedules in which the
5505 constant term is split off from the linear part if the linear parts of
5506 the scheduling rows for all nodes in the graphs have a common non-trivial
5508 The constant term is then placed in a separate band and the linear
5511 =item * schedule_algorithm
5513 Selects the scheduling algorithm to be used.
5514 Available scheduling algorithms are C<ISL_SCHEDULE_ALGORITHM_ISL>
5515 and C<ISL_SCHEDULE_ALGORITHM_FEAUTRIER>.
5517 =item * schedule_separate_components
5519 If at any point the dependence graph contains any (weakly connected) components,
5520 then these components are scheduled separately.
5521 If this option is not set, then some iterations of the domains
5522 in these components may be scheduled together.
5523 If this option is set, then the components are given consecutive
5528 =head2 AST Generation
5530 This section describes the C<isl> functionality for generating
5531 ASTs that visit all the elements
5532 in a domain in an order specified by a schedule.
5533 In particular, given a C<isl_union_map>, an AST is generated
5534 that visits all the elements in the domain of the C<isl_union_map>
5535 according to the lexicographic order of the corresponding image
5536 element(s). If the range of the C<isl_union_map> consists of
5537 elements in more than one space, then each of these spaces is handled
5538 separately in an arbitrary order.
5539 It should be noted that the image elements only specify the I<order>
5540 in which the corresponding domain elements should be visited.
5541 No direct relation between the image elements and the loop iterators
5542 in the generated AST should be assumed.
5544 Each AST is generated within a build. The initial build
5545 simply specifies the constraints on the parameters (if any)
5546 and can be created, inspected, copied and freed using the following functions.
5548 #include <isl/ast_build.h>
5549 __isl_give isl_ast_build *isl_ast_build_from_context(
5550 __isl_take isl_set *set);
5551 isl_ctx *isl_ast_build_get_ctx(
5552 __isl_keep isl_ast_build *build);
5553 __isl_give isl_ast_build *isl_ast_build_copy(
5554 __isl_keep isl_ast_build *build);
5555 void *isl_ast_build_free(
5556 __isl_take isl_ast_build *build);
5558 The C<set> argument is usually a parameter set with zero or more parameters.
5559 More C<isl_ast_build> functions are described in L</"Nested AST Generation">
5560 and L</"Fine-grained Control over AST Generation">.
5561 Finally, the AST itself can be constructed using the following
5564 #include <isl/ast_build.h>
5565 __isl_give isl_ast_node *isl_ast_build_ast_from_schedule(
5566 __isl_keep isl_ast_build *build,
5567 __isl_take isl_union_map *schedule);
5569 =head3 Inspecting the AST
5571 The basic properties of an AST node can be obtained as follows.
5573 #include <isl/ast.h>
5574 isl_ctx *isl_ast_node_get_ctx(
5575 __isl_keep isl_ast_node *node);
5576 enum isl_ast_node_type isl_ast_node_get_type(
5577 __isl_keep isl_ast_node *node);
5579 The type of an AST node is one of
5580 C<isl_ast_node_for>,
5582 C<isl_ast_node_block> or
5583 C<isl_ast_node_user>.
5584 An C<isl_ast_node_for> represents a for node.
5585 An C<isl_ast_node_if> represents an if node.
5586 An C<isl_ast_node_block> represents a compound node.
5587 An C<isl_ast_node_user> represents an expression statement.
5588 An expression statement typically corresponds to a domain element, i.e.,
5589 one of the elements that is visited by the AST.
5591 Each type of node has its own additional properties.
5593 #include <isl/ast.h>
5594 __isl_give isl_ast_expr *isl_ast_node_for_get_iterator(
5595 __isl_keep isl_ast_node *node);
5596 __isl_give isl_ast_expr *isl_ast_node_for_get_init(
5597 __isl_keep isl_ast_node *node);
5598 __isl_give isl_ast_expr *isl_ast_node_for_get_cond(
5599 __isl_keep isl_ast_node *node);
5600 __isl_give isl_ast_expr *isl_ast_node_for_get_inc(
5601 __isl_keep isl_ast_node *node);
5602 __isl_give isl_ast_node *isl_ast_node_for_get_body(
5603 __isl_keep isl_ast_node *node);
5604 int isl_ast_node_for_is_degenerate(
5605 __isl_keep isl_ast_node *node);
5607 An C<isl_ast_for> is considered degenerate if it is known to execute
5610 #include <isl/ast.h>
5611 __isl_give isl_ast_expr *isl_ast_node_if_get_cond(
5612 __isl_keep isl_ast_node *node);
5613 __isl_give isl_ast_node *isl_ast_node_if_get_then(
5614 __isl_keep isl_ast_node *node);
5615 int isl_ast_node_if_has_else(
5616 __isl_keep isl_ast_node *node);
5617 __isl_give isl_ast_node *isl_ast_node_if_get_else(
5618 __isl_keep isl_ast_node *node);
5620 __isl_give isl_ast_node_list *
5621 isl_ast_node_block_get_children(
5622 __isl_keep isl_ast_node *node);
5624 __isl_give isl_ast_expr *isl_ast_node_user_get_expr(
5625 __isl_keep isl_ast_node *node);
5627 Each of the returned C<isl_ast_expr>s can in turn be inspected using
5628 the following functions.
5630 #include <isl/ast.h>
5631 isl_ctx *isl_ast_expr_get_ctx(
5632 __isl_keep isl_ast_expr *expr);
5633 enum isl_ast_expr_type isl_ast_expr_get_type(
5634 __isl_keep isl_ast_expr *expr);
5636 The type of an AST expression is one of
5638 C<isl_ast_expr_id> or
5639 C<isl_ast_expr_int>.
5640 An C<isl_ast_expr_op> represents the result of an operation.
5641 An C<isl_ast_expr_id> represents an identifier.
5642 An C<isl_ast_expr_int> represents an integer value.
5644 Each type of expression has its own additional properties.
5646 #include <isl/ast.h>
5647 enum isl_ast_op_type isl_ast_expr_get_op_type(
5648 __isl_keep isl_ast_expr *expr);
5649 int isl_ast_expr_get_op_n_arg(__isl_keep isl_ast_expr *expr);
5650 __isl_give isl_ast_expr *isl_ast_expr_get_op_arg(
5651 __isl_keep isl_ast_expr *expr, int pos);
5652 int isl_ast_node_foreach_ast_op_type(
5653 __isl_keep isl_ast_node *node,
5654 int (*fn)(enum isl_ast_op_type type, void *user),
5657 C<isl_ast_expr_get_op_type> returns the type of the operation
5658 performed. C<isl_ast_expr_get_op_n_arg> returns the number of
5659 arguments. C<isl_ast_expr_get_op_arg> returns the specified
5661 C<isl_ast_node_foreach_ast_op_type> calls C<fn> for each distinct
5662 C<isl_ast_op_type> that appears in C<node>.
5663 The operation type is one of the following.
5667 =item C<isl_ast_op_and>
5669 Logical I<and> of two arguments.
5670 Both arguments can be evaluated.
5672 =item C<isl_ast_op_and_then>
5674 Logical I<and> of two arguments.
5675 The second argument can only be evaluated if the first evaluates to true.
5677 =item C<isl_ast_op_or>
5679 Logical I<or> of two arguments.
5680 Both arguments can be evaluated.
5682 =item C<isl_ast_op_or_else>
5684 Logical I<or> of two arguments.
5685 The second argument can only be evaluated if the first evaluates to false.
5687 =item C<isl_ast_op_max>
5689 Maximum of two or more arguments.
5691 =item C<isl_ast_op_min>
5693 Minimum of two or more arguments.
5695 =item C<isl_ast_op_minus>
5699 =item C<isl_ast_op_add>
5701 Sum of two arguments.
5703 =item C<isl_ast_op_sub>
5705 Difference of two arguments.
5707 =item C<isl_ast_op_mul>
5709 Product of two arguments.
5711 =item C<isl_ast_op_div>
5713 Exact division. That is, the result is known to be an integer.
5715 =item C<isl_ast_op_fdiv_q>
5717 Result of integer division, rounded towards negative
5720 =item C<isl_ast_op_pdiv_q>
5722 Result of integer division, where dividend is known to be non-negative.
5724 =item C<isl_ast_op_pdiv_r>
5726 Remainder of integer division, where dividend is known to be non-negative.
5728 =item C<isl_ast_op_cond>
5730 Conditional operator defined on three arguments.
5731 If the first argument evaluates to true, then the result
5732 is equal to the second argument. Otherwise, the result
5733 is equal to the third argument.
5734 The second and third argument may only be evaluated if
5735 the first argument evaluates to true and false, respectively.
5736 Corresponds to C<a ? b : c> in C.
5738 =item C<isl_ast_op_select>
5740 Conditional operator defined on three arguments.
5741 If the first argument evaluates to true, then the result
5742 is equal to the second argument. Otherwise, the result
5743 is equal to the third argument.
5744 The second and third argument may be evaluated independently
5745 of the value of the first argument.
5746 Corresponds to C<a * b + (1 - a) * c> in C.
5748 =item C<isl_ast_op_eq>
5752 =item C<isl_ast_op_le>
5754 Less than or equal relation.
5756 =item C<isl_ast_op_lt>
5760 =item C<isl_ast_op_ge>
5762 Greater than or equal relation.
5764 =item C<isl_ast_op_gt>
5766 Greater than relation.
5768 =item C<isl_ast_op_call>
5771 The number of arguments of the C<isl_ast_expr> is one more than
5772 the number of arguments in the function call, the first argument
5773 representing the function being called.
5777 #include <isl/ast.h>
5778 __isl_give isl_id *isl_ast_expr_get_id(
5779 __isl_keep isl_ast_expr *expr);
5781 Return the identifier represented by the AST expression.
5783 #include <isl/ast.h>
5784 __isl_give isl_val *isl_ast_expr_get_val(
5785 __isl_keep isl_ast_expr *expr);
5787 Return the integer represented by the AST expression.
5789 =head3 Manipulating and printing the AST
5791 AST nodes can be copied and freed using the following functions.
5793 #include <isl/ast.h>
5794 __isl_give isl_ast_node *isl_ast_node_copy(
5795 __isl_keep isl_ast_node *node);
5796 void *isl_ast_node_free(__isl_take isl_ast_node *node);
5798 AST expressions can be copied and freed using the following functions.
5800 #include <isl/ast.h>
5801 __isl_give isl_ast_expr *isl_ast_expr_copy(
5802 __isl_keep isl_ast_expr *expr);
5803 void *isl_ast_expr_free(__isl_take isl_ast_expr *expr);
5805 New AST expressions can be created either directly or within
5806 the context of an C<isl_ast_build>.
5808 #include <isl/ast.h>
5809 __isl_give isl_ast_expr *isl_ast_expr_from_val(
5810 __isl_take isl_val *v);
5811 __isl_give isl_ast_expr *isl_ast_expr_from_id(
5812 __isl_take isl_id *id);
5813 __isl_give isl_ast_expr *isl_ast_expr_neg(
5814 __isl_take isl_ast_expr *expr);
5815 __isl_give isl_ast_expr *isl_ast_expr_add(
5816 __isl_take isl_ast_expr *expr1,
5817 __isl_take isl_ast_expr *expr2);
5818 __isl_give isl_ast_expr *isl_ast_expr_sub(
5819 __isl_take isl_ast_expr *expr1,
5820 __isl_take isl_ast_expr *expr2);
5821 __isl_give isl_ast_expr *isl_ast_expr_mul(
5822 __isl_take isl_ast_expr *expr1,
5823 __isl_take isl_ast_expr *expr2);
5824 __isl_give isl_ast_expr *isl_ast_expr_div(
5825 __isl_take isl_ast_expr *expr1,
5826 __isl_take isl_ast_expr *expr2);
5827 __isl_give isl_ast_expr *isl_ast_expr_and(
5828 __isl_take isl_ast_expr *expr1,
5829 __isl_take isl_ast_expr *expr2)
5830 __isl_give isl_ast_expr *isl_ast_expr_or(
5831 __isl_take isl_ast_expr *expr1,
5832 __isl_take isl_ast_expr *expr2)
5834 #include <isl/ast_build.h>
5835 __isl_give isl_ast_expr *isl_ast_build_expr_from_pw_aff(
5836 __isl_keep isl_ast_build *build,
5837 __isl_take isl_pw_aff *pa);
5838 __isl_give isl_ast_expr *
5839 isl_ast_build_call_from_pw_multi_aff(
5840 __isl_keep isl_ast_build *build,
5841 __isl_take isl_pw_multi_aff *pma);
5843 The domains of C<pa> and C<pma> should correspond
5844 to the schedule space of C<build>.
5845 The tuple id of C<pma> is used as the function being called.
5847 User specified data can be attached to an C<isl_ast_node> and obtained
5848 from the same C<isl_ast_node> using the following functions.
5850 #include <isl/ast.h>
5851 __isl_give isl_ast_node *isl_ast_node_set_annotation(
5852 __isl_take isl_ast_node *node,
5853 __isl_take isl_id *annotation);
5854 __isl_give isl_id *isl_ast_node_get_annotation(
5855 __isl_keep isl_ast_node *node);
5857 Basic printing can be performed using the following functions.
5859 #include <isl/ast.h>
5860 __isl_give isl_printer *isl_printer_print_ast_expr(
5861 __isl_take isl_printer *p,
5862 __isl_keep isl_ast_expr *expr);
5863 __isl_give isl_printer *isl_printer_print_ast_node(
5864 __isl_take isl_printer *p,
5865 __isl_keep isl_ast_node *node);
5867 More advanced printing can be performed using the following functions.
5869 #include <isl/ast.h>
5870 __isl_give isl_printer *isl_ast_op_type_print_macro(
5871 enum isl_ast_op_type type,
5872 __isl_take isl_printer *p);
5873 __isl_give isl_printer *isl_ast_node_print_macros(
5874 __isl_keep isl_ast_node *node,
5875 __isl_take isl_printer *p);
5876 __isl_give isl_printer *isl_ast_node_print(
5877 __isl_keep isl_ast_node *node,
5878 __isl_take isl_printer *p,
5879 __isl_take isl_ast_print_options *options);
5880 __isl_give isl_printer *isl_ast_node_for_print(
5881 __isl_keep isl_ast_node *node,
5882 __isl_take isl_printer *p,
5883 __isl_take isl_ast_print_options *options);
5884 __isl_give isl_printer *isl_ast_node_if_print(
5885 __isl_keep isl_ast_node *node,
5886 __isl_take isl_printer *p,
5887 __isl_take isl_ast_print_options *options);
5889 While printing an C<isl_ast_node> in C<ISL_FORMAT_C>,
5890 C<isl> may print out an AST that makes use of macros such
5891 as C<floord>, C<min> and C<max>.
5892 C<isl_ast_op_type_print_macro> prints out the macro
5893 corresponding to a specific C<isl_ast_op_type>.
5894 C<isl_ast_node_print_macros> scans the C<isl_ast_node>
5895 for expressions where these macros would be used and prints
5896 out the required macro definitions.
5897 Essentially, C<isl_ast_node_print_macros> calls
5898 C<isl_ast_node_foreach_ast_op_type> with C<isl_ast_op_type_print_macro>
5899 as function argument.
5900 C<isl_ast_node_print>, C<isl_ast_node_for_print> and
5901 C<isl_ast_node_if_print> print an C<isl_ast_node>
5902 in C<ISL_FORMAT_C>, but allow for some extra control
5903 through an C<isl_ast_print_options> object.
5904 This object can be created using the following functions.
5906 #include <isl/ast.h>
5907 __isl_give isl_ast_print_options *
5908 isl_ast_print_options_alloc(isl_ctx *ctx);
5909 __isl_give isl_ast_print_options *
5910 isl_ast_print_options_copy(
5911 __isl_keep isl_ast_print_options *options);
5912 void *isl_ast_print_options_free(
5913 __isl_take isl_ast_print_options *options);
5915 __isl_give isl_ast_print_options *
5916 isl_ast_print_options_set_print_user(
5917 __isl_take isl_ast_print_options *options,
5918 __isl_give isl_printer *(*print_user)(
5919 __isl_take isl_printer *p,
5920 __isl_take isl_ast_print_options *options,
5921 __isl_keep isl_ast_node *node, void *user),
5923 __isl_give isl_ast_print_options *
5924 isl_ast_print_options_set_print_for(
5925 __isl_take isl_ast_print_options *options,
5926 __isl_give isl_printer *(*print_for)(
5927 __isl_take isl_printer *p,
5928 __isl_take isl_ast_print_options *options,
5929 __isl_keep isl_ast_node *node, void *user),
5932 The callback set by C<isl_ast_print_options_set_print_user>
5933 is called whenever a node of type C<isl_ast_node_user> needs to
5935 The callback set by C<isl_ast_print_options_set_print_for>
5936 is called whenever a node of type C<isl_ast_node_for> needs to
5938 Note that C<isl_ast_node_for_print> will I<not> call the
5939 callback set by C<isl_ast_print_options_set_print_for> on the node
5940 on which C<isl_ast_node_for_print> is called, but only on nested
5941 nodes of type C<isl_ast_node_for>. It is therefore safe to
5942 call C<isl_ast_node_for_print> from within the callback set by
5943 C<isl_ast_print_options_set_print_for>.
5945 The following option determines the type to be used for iterators
5946 while printing the AST.
5948 int isl_options_set_ast_iterator_type(
5949 isl_ctx *ctx, const char *val);
5950 const char *isl_options_get_ast_iterator_type(
5955 #include <isl/ast_build.h>
5956 int isl_options_set_ast_build_atomic_upper_bound(
5957 isl_ctx *ctx, int val);
5958 int isl_options_get_ast_build_atomic_upper_bound(
5960 int isl_options_set_ast_build_prefer_pdiv(isl_ctx *ctx,
5962 int isl_options_get_ast_build_prefer_pdiv(isl_ctx *ctx);
5963 int isl_options_set_ast_build_exploit_nested_bounds(
5964 isl_ctx *ctx, int val);
5965 int isl_options_get_ast_build_exploit_nested_bounds(
5967 int isl_options_set_ast_build_group_coscheduled(
5968 isl_ctx *ctx, int val);
5969 int isl_options_get_ast_build_group_coscheduled(
5971 int isl_options_set_ast_build_scale_strides(
5972 isl_ctx *ctx, int val);
5973 int isl_options_get_ast_build_scale_strides(
5975 int isl_options_set_ast_build_allow_else(isl_ctx *ctx,
5977 int isl_options_get_ast_build_allow_else(isl_ctx *ctx);
5978 int isl_options_set_ast_build_allow_or(isl_ctx *ctx,
5980 int isl_options_get_ast_build_allow_or(isl_ctx *ctx);
5984 =item * ast_build_atomic_upper_bound
5986 Generate loop upper bounds that consist of the current loop iterator,
5987 an operator and an expression not involving the iterator.
5988 If this option is not set, then the current loop iterator may appear
5989 several times in the upper bound.
5990 For example, when this option is turned off, AST generation
5993 [n] -> { A[i] -> [i] : 0 <= i <= 100, n }
5997 for (int c0 = 0; c0 <= 100 && n >= c0; c0 += 1)
6000 When the option is turned on, the following AST is generated
6002 for (int c0 = 0; c0 <= min(100, n); c0 += 1)
6005 =item * ast_build_prefer_pdiv
6007 If this option is turned off, then the AST generation will
6008 produce ASTs that may only contain C<isl_ast_op_fdiv_q>
6009 operators, but no C<isl_ast_op_pdiv_q> or
6010 C<isl_ast_op_pdiv_r> operators.
6011 If this options is turned on, then C<isl> will try to convert
6012 some of the C<isl_ast_op_fdiv_q> operators to (expressions containing)
6013 C<isl_ast_op_pdiv_q> or C<isl_ast_op_pdiv_r> operators.
6015 =item * ast_build_exploit_nested_bounds
6017 Simplify conditions based on bounds of nested for loops.
6018 In particular, remove conditions that are implied by the fact
6019 that one or more nested loops have at least one iteration,
6020 meaning that the upper bound is at least as large as the lower bound.
6021 For example, when this option is turned off, AST generation
6024 [N,M] -> { A[i,j] -> [i,j] : 0 <= i <= N and
6030 for (int c0 = 0; c0 <= N; c0 += 1)
6031 for (int c1 = 0; c1 <= M; c1 += 1)
6034 When the option is turned on, the following AST is generated
6036 for (int c0 = 0; c0 <= N; c0 += 1)
6037 for (int c1 = 0; c1 <= M; c1 += 1)
6040 =item * ast_build_group_coscheduled
6042 If two domain elements are assigned the same schedule point, then
6043 they may be executed in any order and they may even appear in different
6044 loops. If this options is set, then the AST generator will make
6045 sure that coscheduled domain elements do not appear in separate parts
6046 of the AST. This is useful in case of nested AST generation
6047 if the outer AST generation is given only part of a schedule
6048 and the inner AST generation should handle the domains that are
6049 coscheduled by this initial part of the schedule together.
6050 For example if an AST is generated for a schedule
6052 { A[i] -> [0]; B[i] -> [0] }
6054 then the C<isl_ast_build_set_create_leaf> callback described
6055 below may get called twice, once for each domain.
6056 Setting this option ensures that the callback is only called once
6057 on both domains together.
6059 =item * ast_build_separation_bounds
6061 This option specifies which bounds to use during separation.
6062 If this option is set to C<ISL_AST_BUILD_SEPARATION_BOUNDS_IMPLICIT>
6063 then all (possibly implicit) bounds on the current dimension will
6064 be used during separation.
6065 If this option is set to C<ISL_AST_BUILD_SEPARATION_BOUNDS_EXPLICIT>
6066 then only those bounds that are explicitly available will
6067 be used during separation.
6069 =item * ast_build_scale_strides
6071 This option specifies whether the AST generator is allowed
6072 to scale down iterators of strided loops.
6074 =item * ast_build_allow_else
6076 This option specifies whether the AST generator is allowed
6077 to construct if statements with else branches.
6079 =item * ast_build_allow_or
6081 This option specifies whether the AST generator is allowed
6082 to construct if conditions with disjunctions.
6086 =head3 Fine-grained Control over AST Generation
6088 Besides specifying the constraints on the parameters,
6089 an C<isl_ast_build> object can be used to control
6090 various aspects of the AST generation process.
6091 The most prominent way of control is through ``options'',
6092 which can be set using the following function.
6094 #include <isl/ast_build.h>
6095 __isl_give isl_ast_build *
6096 isl_ast_build_set_options(
6097 __isl_take isl_ast_build *control,
6098 __isl_take isl_union_map *options);
6100 The options are encoded in an <isl_union_map>.
6101 The domain of this union relation refers to the schedule domain,
6102 i.e., the range of the schedule passed to C<isl_ast_build_ast_from_schedule>.
6103 In the case of nested AST generation (see L</"Nested AST Generation">),
6104 the domain of C<options> should refer to the extra piece of the schedule.
6105 That is, it should be equal to the range of the wrapped relation in the
6106 range of the schedule.
6107 The range of the options can consist of elements in one or more spaces,
6108 the names of which determine the effect of the option.
6109 The values of the range typically also refer to the schedule dimension
6110 to which the option applies. In case of nested AST generation
6111 (see L</"Nested AST Generation">), these values refer to the position
6112 of the schedule dimension within the innermost AST generation.
6113 The constraints on the domain elements of
6114 the option should only refer to this dimension and earlier dimensions.
6115 We consider the following spaces.
6119 =item C<separation_class>
6121 This space is a wrapped relation between two one dimensional spaces.
6122 The input space represents the schedule dimension to which the option
6123 applies and the output space represents the separation class.
6124 While constructing a loop corresponding to the specified schedule
6125 dimension(s), the AST generator will try to generate separate loops
6126 for domain elements that are assigned different classes.
6127 If only some of the elements are assigned a class, then those elements
6128 that are not assigned any class will be treated as belonging to a class
6129 that is separate from the explicitly assigned classes.
6130 The typical use case for this option is to separate full tiles from
6132 The other options, described below, are applied after the separation
6135 As an example, consider the separation into full and partial tiles
6136 of a tiling of a triangular domain.
6137 Take, for example, the domain
6139 { A[i,j] : 0 <= i,j and i + j <= 100 }
6141 and a tiling into tiles of 10 by 10. The input to the AST generator
6142 is then the schedule
6144 { A[i,j] -> [([i/10]),[j/10],i,j] : 0 <= i,j and
6147 Without any options, the following AST is generated
6149 for (int c0 = 0; c0 <= 10; c0 += 1)
6150 for (int c1 = 0; c1 <= -c0 + 10; c1 += 1)
6151 for (int c2 = 10 * c0;
6152 c2 <= min(-10 * c1 + 100, 10 * c0 + 9);
6154 for (int c3 = 10 * c1;
6155 c3 <= min(10 * c1 + 9, -c2 + 100);
6159 Separation into full and partial tiles can be obtained by assigning
6160 a class, say C<0>, to the full tiles. The full tiles are represented by those
6161 values of the first and second schedule dimensions for which there are
6162 values of the third and fourth dimensions to cover an entire tile.
6163 That is, we need to specify the following option
6165 { [a,b,c,d] -> separation_class[[0]->[0]] :
6166 exists b': 0 <= 10a,10b' and
6167 10a+9+10b'+9 <= 100;
6168 [a,b,c,d] -> separation_class[[1]->[0]] :
6169 0 <= 10a,10b and 10a+9+10b+9 <= 100 }
6173 { [a, b, c, d] -> separation_class[[1] -> [0]] :
6174 a >= 0 and b >= 0 and b <= 8 - a;
6175 [a, b, c, d] -> separation_class[[0] -> [0]] :
6178 With this option, the generated AST is as follows
6181 for (int c0 = 0; c0 <= 8; c0 += 1) {
6182 for (int c1 = 0; c1 <= -c0 + 8; c1 += 1)
6183 for (int c2 = 10 * c0;
6184 c2 <= 10 * c0 + 9; c2 += 1)
6185 for (int c3 = 10 * c1;
6186 c3 <= 10 * c1 + 9; c3 += 1)
6188 for (int c1 = -c0 + 9; c1 <= -c0 + 10; c1 += 1)
6189 for (int c2 = 10 * c0;
6190 c2 <= min(-10 * c1 + 100, 10 * c0 + 9);
6192 for (int c3 = 10 * c1;
6193 c3 <= min(-c2 + 100, 10 * c1 + 9);
6197 for (int c0 = 9; c0 <= 10; c0 += 1)
6198 for (int c1 = 0; c1 <= -c0 + 10; c1 += 1)
6199 for (int c2 = 10 * c0;
6200 c2 <= min(-10 * c1 + 100, 10 * c0 + 9);
6202 for (int c3 = 10 * c1;
6203 c3 <= min(10 * c1 + 9, -c2 + 100);
6210 This is a single-dimensional space representing the schedule dimension(s)
6211 to which ``separation'' should be applied. Separation tries to split
6212 a loop into several pieces if this can avoid the generation of guards
6214 See also the C<atomic> option.
6218 This is a single-dimensional space representing the schedule dimension(s)
6219 for which the domains should be considered ``atomic''. That is, the
6220 AST generator will make sure that any given domain space will only appear
6221 in a single loop at the specified level.
6223 Consider the following schedule
6225 { a[i] -> [i] : 0 <= i < 10;
6226 b[i] -> [i+1] : 0 <= i < 10 }
6228 If the following option is specified
6230 { [i] -> separate[x] }
6232 then the following AST will be generated
6236 for (int c0 = 1; c0 <= 9; c0 += 1) {
6243 If, on the other hand, the following option is specified
6245 { [i] -> atomic[x] }
6247 then the following AST will be generated
6249 for (int c0 = 0; c0 <= 10; c0 += 1) {
6256 If neither C<atomic> nor C<separate> is specified, then the AST generator
6257 may produce either of these two results or some intermediate form.
6261 This is a single-dimensional space representing the schedule dimension(s)
6262 that should be I<completely> unrolled.
6263 To obtain a partial unrolling, the user should apply an additional
6264 strip-mining to the schedule and fully unroll the inner loop.
6268 Additional control is available through the following functions.
6270 #include <isl/ast_build.h>
6271 __isl_give isl_ast_build *
6272 isl_ast_build_set_iterators(
6273 __isl_take isl_ast_build *control,
6274 __isl_take isl_id_list *iterators);
6276 The function C<isl_ast_build_set_iterators> allows the user to
6277 specify a list of iterator C<isl_id>s to be used as iterators.
6278 If the input schedule is injective, then
6279 the number of elements in this list should be as large as the dimension
6280 of the schedule space, but no direct correspondence should be assumed
6281 between dimensions and elements.
6282 If the input schedule is not injective, then an additional number
6283 of C<isl_id>s equal to the largest dimension of the input domains
6285 If the number of provided C<isl_id>s is insufficient, then additional
6286 names are automatically generated.
6288 #include <isl/ast_build.h>
6289 __isl_give isl_ast_build *
6290 isl_ast_build_set_create_leaf(
6291 __isl_take isl_ast_build *control,
6292 __isl_give isl_ast_node *(*fn)(
6293 __isl_take isl_ast_build *build,
6294 void *user), void *user);
6297 C<isl_ast_build_set_create_leaf> function allows for the
6298 specification of a callback that should be called whenever the AST
6299 generator arrives at an element of the schedule domain.
6300 The callback should return an AST node that should be inserted
6301 at the corresponding position of the AST. The default action (when
6302 the callback is not set) is to continue generating parts of the AST to scan
6303 all the domain elements associated to the schedule domain element
6304 and to insert user nodes, ``calling'' the domain element, for each of them.
6305 The C<build> argument contains the current state of the C<isl_ast_build>.
6306 To ease nested AST generation (see L</"Nested AST Generation">),
6307 all control information that is
6308 specific to the current AST generation such as the options and
6309 the callbacks has been removed from this C<isl_ast_build>.
6310 The callback would typically return the result of a nested
6312 user defined node created using the following function.
6314 #include <isl/ast.h>
6315 __isl_give isl_ast_node *isl_ast_node_alloc_user(
6316 __isl_take isl_ast_expr *expr);
6318 #include <isl/ast_build.h>
6319 __isl_give isl_ast_build *
6320 isl_ast_build_set_at_each_domain(
6321 __isl_take isl_ast_build *build,
6322 __isl_give isl_ast_node *(*fn)(
6323 __isl_take isl_ast_node *node,
6324 __isl_keep isl_ast_build *build,
6325 void *user), void *user);
6326 __isl_give isl_ast_build *
6327 isl_ast_build_set_before_each_for(
6328 __isl_take isl_ast_build *build,
6329 __isl_give isl_id *(*fn)(
6330 __isl_keep isl_ast_build *build,
6331 void *user), void *user);
6332 __isl_give isl_ast_build *
6333 isl_ast_build_set_after_each_for(
6334 __isl_take isl_ast_build *build,
6335 __isl_give isl_ast_node *(*fn)(
6336 __isl_take isl_ast_node *node,
6337 __isl_keep isl_ast_build *build,
6338 void *user), void *user);
6340 The callback set by C<isl_ast_build_set_at_each_domain> will
6341 be called for each domain AST node.
6342 The callbacks set by C<isl_ast_build_set_before_each_for>
6343 and C<isl_ast_build_set_after_each_for> will be called
6344 for each for AST node. The first will be called in depth-first
6345 pre-order, while the second will be called in depth-first post-order.
6346 Since C<isl_ast_build_set_before_each_for> is called before the for
6347 node is actually constructed, it is only passed an C<isl_ast_build>.
6348 The returned C<isl_id> will be added as an annotation (using
6349 C<isl_ast_node_set_annotation>) to the constructed for node.
6350 In particular, if the user has also specified an C<after_each_for>
6351 callback, then the annotation can be retrieved from the node passed to
6352 that callback using C<isl_ast_node_get_annotation>.
6353 All callbacks should C<NULL> on failure.
6354 The given C<isl_ast_build> can be used to create new
6355 C<isl_ast_expr> objects using C<isl_ast_build_expr_from_pw_aff>
6356 or C<isl_ast_build_call_from_pw_multi_aff>.
6358 =head3 Nested AST Generation
6360 C<isl> allows the user to create an AST within the context
6361 of another AST. These nested ASTs are created using the
6362 same C<isl_ast_build_ast_from_schedule> function that is used to create the
6363 outer AST. The C<build> argument should be an C<isl_ast_build>
6364 passed to a callback set by
6365 C<isl_ast_build_set_create_leaf>.
6366 The space of the range of the C<schedule> argument should refer
6367 to this build. In particular, the space should be a wrapped
6368 relation and the domain of this wrapped relation should be the
6369 same as that of the range of the schedule returned by
6370 C<isl_ast_build_get_schedule> below.
6371 In practice, the new schedule is typically
6372 created by calling C<isl_union_map_range_product> on the old schedule
6373 and some extra piece of the schedule.
6374 The space of the schedule domain is also available from
6375 the C<isl_ast_build>.
6377 #include <isl/ast_build.h>
6378 __isl_give isl_union_map *isl_ast_build_get_schedule(
6379 __isl_keep isl_ast_build *build);
6380 __isl_give isl_space *isl_ast_build_get_schedule_space(
6381 __isl_keep isl_ast_build *build);
6382 __isl_give isl_ast_build *isl_ast_build_restrict(
6383 __isl_take isl_ast_build *build,
6384 __isl_take isl_set *set);
6386 The C<isl_ast_build_get_schedule> function returns a (partial)
6387 schedule for the domains elements for which part of the AST still needs to
6388 be generated in the current build.
6389 In particular, the domain elements are mapped to those iterations of the loops
6390 enclosing the current point of the AST generation inside which
6391 the domain elements are executed.
6392 No direct correspondence between
6393 the input schedule and this schedule should be assumed.
6394 The space obtained from C<isl_ast_build_get_schedule_space> can be used
6395 to create a set for C<isl_ast_build_restrict> to intersect
6396 with the current build. In particular, the set passed to
6397 C<isl_ast_build_restrict> can have additional parameters.
6398 The ids of the set dimensions in the space returned by
6399 C<isl_ast_build_get_schedule_space> correspond to the
6400 iterators of the already generated loops.
6401 The user should not rely on the ids of the output dimensions
6402 of the relations in the union relation returned by
6403 C<isl_ast_build_get_schedule> having any particular value.
6407 Although C<isl> is mainly meant to be used as a library,
6408 it also contains some basic applications that use some
6409 of the functionality of C<isl>.
6410 The input may be specified in either the L<isl format>
6411 or the L<PolyLib format>.
6413 =head2 C<isl_polyhedron_sample>
6415 C<isl_polyhedron_sample> takes a polyhedron as input and prints
6416 an integer element of the polyhedron, if there is any.
6417 The first column in the output is the denominator and is always
6418 equal to 1. If the polyhedron contains no integer points,
6419 then a vector of length zero is printed.
6423 C<isl_pip> takes the same input as the C<example> program
6424 from the C<piplib> distribution, i.e., a set of constraints
6425 on the parameters, a line containing only -1 and finally a set
6426 of constraints on a parametric polyhedron.
6427 The coefficients of the parameters appear in the last columns
6428 (but before the final constant column).
6429 The output is the lexicographic minimum of the parametric polyhedron.
6430 As C<isl> currently does not have its own output format, the output
6431 is just a dump of the internal state.
6433 =head2 C<isl_polyhedron_minimize>
6435 C<isl_polyhedron_minimize> computes the minimum of some linear
6436 or affine objective function over the integer points in a polyhedron.
6437 If an affine objective function
6438 is given, then the constant should appear in the last column.
6440 =head2 C<isl_polytope_scan>
6442 Given a polytope, C<isl_polytope_scan> prints
6443 all integer points in the polytope.
6445 =head2 C<isl_codegen>
6447 Given a schedule, a context set and an options relation,
6448 C<isl_codegen> prints out an AST that scans the domain elements
6449 of the schedule in the order of their image(s) taking into account
6450 the constraints in the context set.