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.
186 C<isl> is released under the MIT license.
190 Permission is hereby granted, free of charge, to any person obtaining a copy of
191 this software and associated documentation files (the "Software"), to deal in
192 the Software without restriction, including without limitation the rights to
193 use, copy, modify, merge, publish, distribute, sublicense, and/or sell copies
194 of the Software, and to permit persons to whom the Software is furnished to do
195 so, subject to the following conditions:
197 The above copyright notice and this permission notice shall be included in all
198 copies or substantial portions of the Software.
200 THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
201 IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
202 FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
203 AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
204 LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
205 OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
210 Note that C<isl> currently requires C<GMP>, which is released
211 under the GNU Lesser General Public License (LGPL). This means
212 that code linked against C<isl> is also linked against LGPL code.
216 The source of C<isl> can be obtained either as a tarball
217 or from the git repository. Both are available from
218 L<http://freshmeat.net/projects/isl/>.
219 The installation process depends on how you obtained
222 =head2 Installation from the git repository
226 =item 1 Clone or update the repository
228 The first time the source is obtained, you need to clone
231 git clone git://repo.or.cz/isl.git
233 To obtain updates, you need to pull in the latest changes
237 =item 2 Generate C<configure>
243 After performing the above steps, continue
244 with the L<Common installation instructions>.
246 =head2 Common installation instructions
250 =item 1 Obtain C<GMP>
252 Building C<isl> requires C<GMP>, including its headers files.
253 Your distribution may not provide these header files by default
254 and you may need to install a package called C<gmp-devel> or something
255 similar. Alternatively, C<GMP> can be built from
256 source, available from L<http://gmplib.org/>.
260 C<isl> uses the standard C<autoconf> C<configure> script.
265 optionally followed by some configure options.
266 A complete list of options can be obtained by running
270 Below we discuss some of the more common options.
272 C<isl> can optionally use C<piplib>, but no
273 C<piplib> functionality is currently used by default.
274 The C<--with-piplib> option can
275 be used to specify which C<piplib>
276 library to use, either an installed version (C<system>),
277 an externally built version (C<build>)
278 or no version (C<no>). The option C<build> is mostly useful
279 in C<configure> scripts of larger projects that bundle both C<isl>
286 Installation prefix for C<isl>
288 =item C<--with-gmp-prefix>
290 Installation prefix for C<GMP> (architecture-independent files).
292 =item C<--with-gmp-exec-prefix>
294 Installation prefix for C<GMP> (architecture-dependent files).
296 =item C<--with-piplib>
298 Which copy of C<piplib> to use, either C<no> (default), C<system> or C<build>.
300 =item C<--with-piplib-prefix>
302 Installation prefix for C<system> C<piplib> (architecture-independent files).
304 =item C<--with-piplib-exec-prefix>
306 Installation prefix for C<system> C<piplib> (architecture-dependent files).
308 =item C<--with-piplib-builddir>
310 Location where C<build> C<piplib> was built.
318 =item 4 Install (optional)
324 =head1 Integer Set Library
326 =head2 Initialization
328 All manipulations of integer sets and relations occur within
329 the context of an C<isl_ctx>.
330 A given C<isl_ctx> can only be used within a single thread.
331 All arguments of a function are required to have been allocated
332 within the same context.
333 There are currently no functions available for moving an object
334 from one C<isl_ctx> to another C<isl_ctx>. This means that
335 there is currently no way of safely moving an object from one
336 thread to another, unless the whole C<isl_ctx> is moved.
338 An C<isl_ctx> can be allocated using C<isl_ctx_alloc> and
339 freed using C<isl_ctx_free>.
340 All objects allocated within an C<isl_ctx> should be freed
341 before the C<isl_ctx> itself is freed.
343 isl_ctx *isl_ctx_alloc();
344 void isl_ctx_free(isl_ctx *ctx);
348 An C<isl_val> represents an integer value, a rational value
349 or one of three special values, infinity, negative infinity and NaN.
350 Some predefined values can be created using the following functions.
353 __isl_give isl_val *isl_val_zero(isl_ctx *ctx);
354 __isl_give isl_val *isl_val_one(isl_ctx *ctx);
355 __isl_give isl_val *isl_val_nan(isl_ctx *ctx);
356 __isl_give isl_val *isl_val_infty(isl_ctx *ctx);
357 __isl_give isl_val *isl_val_neginfty(isl_ctx *ctx);
359 Specific integer values can be created using the following functions.
362 __isl_give isl_val *isl_val_int_from_si(isl_ctx *ctx,
364 __isl_give isl_val *isl_val_int_from_ui(isl_ctx *ctx,
367 They can be copied and freed using the following functions.
370 __isl_give isl_val *isl_val_copy(__isl_keep isl_val *v);
371 void *isl_val_free(__isl_take isl_val *v);
373 They can be inspected using the following functions.
376 isl_ctx *isl_val_get_ctx(__isl_keep isl_val *val);
377 long isl_val_get_num_si(__isl_keep isl_val *v);
378 long isl_val_get_den_si(__isl_keep isl_val *v);
379 double isl_val_get_d(__isl_keep isl_val *v);
381 Note that C<isl_val_get_num_si>, C<isl_val_get_den_si> and
382 C<isl_val_get_d> can only be applied to rational values.
384 An C<isl_val> can be modified using the following function.
387 __isl_give isl_val *isl_val_set_si(__isl_take isl_val *v,
390 The following unary properties are defined on C<isl_val>s.
393 int isl_val_sgn(__isl_keep isl_val *v);
394 int isl_val_is_zero(__isl_keep isl_val *v);
395 int isl_val_is_one(__isl_keep isl_val *v);
396 int isl_val_is_negone(__isl_keep isl_val *v);
397 int isl_val_is_nonneg(__isl_keep isl_val *v);
398 int isl_val_is_nonpos(__isl_keep isl_val *v);
399 int isl_val_is_pos(__isl_keep isl_val *v);
400 int isl_val_is_neg(__isl_keep isl_val *v);
401 int isl_val_is_int(__isl_keep isl_val *v);
402 int isl_val_is_rat(__isl_keep isl_val *v);
403 int isl_val_is_nan(__isl_keep isl_val *v);
404 int isl_val_is_infty(__isl_keep isl_val *v);
405 int isl_val_is_neginfty(__isl_keep isl_val *v);
407 Note that the sign of NaN is undefined.
409 The following binary properties are defined on pairs of C<isl_val>s.
412 int isl_val_lt(__isl_keep isl_val *v1,
413 __isl_keep isl_val *v2);
414 int isl_val_le(__isl_keep isl_val *v1,
415 __isl_keep isl_val *v2);
416 int isl_val_gt(__isl_keep isl_val *v1,
417 __isl_keep isl_val *v2);
418 int isl_val_ge(__isl_keep isl_val *v1,
419 __isl_keep isl_val *v2);
420 int isl_val_eq(__isl_keep isl_val *v1,
421 __isl_keep isl_val *v2);
422 int isl_val_ne(__isl_keep isl_val *v1,
423 __isl_keep isl_val *v2);
425 For integer C<isl_val>s we additionally have the following binary property.
428 int isl_val_is_divisible_by(__isl_keep isl_val *v1,
429 __isl_keep isl_val *v2);
431 An C<isl_val> can also be compared to an integer using the following
432 function. The result is undefined for NaN.
435 int isl_val_cmp_si(__isl_keep isl_val *v, long i);
437 The following unary operations are available on C<isl_val>s.
440 __isl_give isl_val *isl_val_abs(__isl_take isl_val *v);
441 __isl_give isl_val *isl_val_neg(__isl_take isl_val *v);
442 __isl_give isl_val *isl_val_floor(__isl_take isl_val *v);
443 __isl_give isl_val *isl_val_ceil(__isl_take isl_val *v);
444 __isl_give isl_val *isl_val_trunc(__isl_take isl_val *v);
446 The following binary operations are available on C<isl_val>s.
449 __isl_give isl_val *isl_val_abs(__isl_take isl_val *v);
450 __isl_give isl_val *isl_val_neg(__isl_take isl_val *v);
451 __isl_give isl_val *isl_val_floor(__isl_take isl_val *v);
452 __isl_give isl_val *isl_val_ceil(__isl_take isl_val *v);
453 __isl_give isl_val *isl_val_trunc(__isl_take isl_val *v);
454 __isl_give isl_val *isl_val_2exp(__isl_take isl_val *v);
455 __isl_give isl_val *isl_val_min(__isl_take isl_val *v1,
456 __isl_take isl_val *v2);
457 __isl_give isl_val *isl_val_max(__isl_take isl_val *v1,
458 __isl_take isl_val *v2);
459 __isl_give isl_val *isl_val_add(__isl_take isl_val *v1,
460 __isl_take isl_val *v2);
461 __isl_give isl_val *isl_val_add_ui(__isl_take isl_val *v1,
463 __isl_give isl_val *isl_val_sub(__isl_take isl_val *v1,
464 __isl_take isl_val *v2);
465 __isl_give isl_val *isl_val_sub_ui(__isl_take isl_val *v1,
467 __isl_give isl_val *isl_val_mul(__isl_take isl_val *v1,
468 __isl_take isl_val *v2);
469 __isl_give isl_val *isl_val_mul_ui(__isl_take isl_val *v1,
471 __isl_give isl_val *isl_val_div(__isl_take isl_val *v1,
472 __isl_take isl_val *v2);
474 On integer values, we additionally have the following operations.
477 __isl_give isl_val *isl_val_2exp(__isl_take isl_val *v);
478 __isl_give isl_val *isl_val_mod(__isl_take isl_val *v1,
479 __isl_take isl_val *v2);
480 __isl_give isl_val *isl_val_gcd(__isl_take isl_val *v1,
481 __isl_take isl_val *v2);
482 __isl_give isl_val *isl_val_gcdext(__isl_take isl_val *v1,
483 __isl_take isl_val *v2, __isl_give isl_val **x,
484 __isl_give isl_val **y);
486 The function C<isl_val_gcdext> returns the greatest common divisor g
487 of C<v1> and C<v2> as well as two integers C<*x> and C<*y> such
488 that C<*x> * C<v1> + C<*y> * C<v2> = g.
490 A value can be read from input using
493 __isl_give isl_val *isl_val_read_from_str(isl_ctx *ctx,
496 A value can be printed using
499 __isl_give isl_printer *isl_printer_print_val(
500 __isl_take isl_printer *p, __isl_keep isl_val *v);
502 =head2 Integers (obsolescent)
504 All operations on integers, mainly the coefficients
505 of the constraints describing the sets and relations,
506 are performed in exact integer arithmetic using C<GMP>.
507 However, to allow future versions of C<isl> to optionally
508 support fixed integer arithmetic, all calls to C<GMP>
509 are wrapped inside C<isl> specific macros.
510 The basic type is C<isl_int> and the operations below
511 are available on this type.
512 The meanings of these operations are essentially the same
513 as their C<GMP> C<mpz_> counterparts.
514 As always with C<GMP> types, C<isl_int>s need to be
515 initialized with C<isl_int_init> before they can be used
516 and they need to be released with C<isl_int_clear>
518 The user should not assume that an C<isl_int> is represented
519 as a C<mpz_t>, but should instead explicitly convert between
520 C<mpz_t>s and C<isl_int>s using C<isl_int_set_gmp> and
521 C<isl_int_get_gmp> whenever a C<mpz_t> is required.
525 =item isl_int_init(i)
527 =item isl_int_clear(i)
529 =item isl_int_set(r,i)
531 =item isl_int_set_si(r,i)
533 =item isl_int_set_gmp(r,g)
535 =item isl_int_get_gmp(i,g)
537 =item isl_int_abs(r,i)
539 =item isl_int_neg(r,i)
541 =item isl_int_swap(i,j)
543 =item isl_int_swap_or_set(i,j)
545 =item isl_int_add_ui(r,i,j)
547 =item isl_int_sub_ui(r,i,j)
549 =item isl_int_add(r,i,j)
551 =item isl_int_sub(r,i,j)
553 =item isl_int_mul(r,i,j)
555 =item isl_int_mul_ui(r,i,j)
557 =item isl_int_addmul(r,i,j)
559 =item isl_int_submul(r,i,j)
561 =item isl_int_gcd(r,i,j)
563 =item isl_int_lcm(r,i,j)
565 =item isl_int_divexact(r,i,j)
567 =item isl_int_cdiv_q(r,i,j)
569 =item isl_int_fdiv_q(r,i,j)
571 =item isl_int_fdiv_r(r,i,j)
573 =item isl_int_fdiv_q_ui(r,i,j)
575 =item isl_int_read(r,s)
577 =item isl_int_print(out,i,width)
581 =item isl_int_cmp(i,j)
583 =item isl_int_cmp_si(i,si)
585 =item isl_int_eq(i,j)
587 =item isl_int_ne(i,j)
589 =item isl_int_lt(i,j)
591 =item isl_int_le(i,j)
593 =item isl_int_gt(i,j)
595 =item isl_int_ge(i,j)
597 =item isl_int_abs_eq(i,j)
599 =item isl_int_abs_ne(i,j)
601 =item isl_int_abs_lt(i,j)
603 =item isl_int_abs_gt(i,j)
605 =item isl_int_abs_ge(i,j)
607 =item isl_int_is_zero(i)
609 =item isl_int_is_one(i)
611 =item isl_int_is_negone(i)
613 =item isl_int_is_pos(i)
615 =item isl_int_is_neg(i)
617 =item isl_int_is_nonpos(i)
619 =item isl_int_is_nonneg(i)
621 =item isl_int_is_divisible_by(i,j)
625 =head2 Sets and Relations
627 C<isl> uses six types of objects for representing sets and relations,
628 C<isl_basic_set>, C<isl_basic_map>, C<isl_set>, C<isl_map>,
629 C<isl_union_set> and C<isl_union_map>.
630 C<isl_basic_set> and C<isl_basic_map> represent sets and relations that
631 can be described as a conjunction of affine constraints, while
632 C<isl_set> and C<isl_map> represent unions of
633 C<isl_basic_set>s and C<isl_basic_map>s, respectively.
634 However, all C<isl_basic_set>s or C<isl_basic_map>s in the union need
635 to live in the same space. C<isl_union_set>s and C<isl_union_map>s
636 represent unions of C<isl_set>s or C<isl_map>s in I<different> spaces,
637 where spaces are considered different if they have a different number
638 of dimensions and/or different names (see L<"Spaces">).
639 The difference between sets and relations (maps) is that sets have
640 one set of variables, while relations have two sets of variables,
641 input variables and output variables.
643 =head2 Memory Management
645 Since a high-level operation on sets and/or relations usually involves
646 several substeps and since the user is usually not interested in
647 the intermediate results, most functions that return a new object
648 will also release all the objects passed as arguments.
649 If the user still wants to use one or more of these arguments
650 after the function call, she should pass along a copy of the
651 object rather than the object itself.
652 The user is then responsible for making sure that the original
653 object gets used somewhere else or is explicitly freed.
655 The arguments and return values of all documented functions are
656 annotated to make clear which arguments are released and which
657 arguments are preserved. In particular, the following annotations
664 C<__isl_give> means that a new object is returned.
665 The user should make sure that the returned pointer is
666 used exactly once as a value for an C<__isl_take> argument.
667 In between, it can be used as a value for as many
668 C<__isl_keep> arguments as the user likes.
669 There is one exception, and that is the case where the
670 pointer returned is C<NULL>. Is this case, the user
671 is free to use it as an C<__isl_take> argument or not.
675 C<__isl_take> means that the object the argument points to
676 is taken over by the function and may no longer be used
677 by the user as an argument to any other function.
678 The pointer value must be one returned by a function
679 returning an C<__isl_give> pointer.
680 If the user passes in a C<NULL> value, then this will
681 be treated as an error in the sense that the function will
682 not perform its usual operation. However, it will still
683 make sure that all the other C<__isl_take> arguments
688 C<__isl_keep> means that the function will only use the object
689 temporarily. After the function has finished, the user
690 can still use it as an argument to other functions.
691 A C<NULL> value will be treated in the same way as
692 a C<NULL> value for an C<__isl_take> argument.
696 =head2 Error Handling
698 C<isl> supports different ways to react in case a runtime error is triggered.
699 Runtime errors arise, e.g., if a function such as C<isl_map_intersect> is called
700 with two maps that have incompatible spaces. There are three possible ways
701 to react on error: to warn, to continue or to abort.
703 The default behavior is to warn. In this mode, C<isl> prints a warning, stores
704 the last error in the corresponding C<isl_ctx> and the function in which the
705 error was triggered returns C<NULL>. An error does not corrupt internal state,
706 such that isl can continue to be used. C<isl> also provides functions to
707 read the last error and to reset the memory that stores the last error. The
708 last error is only stored for information purposes. Its presence does not
709 change the behavior of C<isl>. Hence, resetting an error is not required to
710 continue to use isl, but only to observe new errors.
713 enum isl_error isl_ctx_last_error(isl_ctx *ctx);
714 void isl_ctx_reset_error(isl_ctx *ctx);
716 Another option is to continue on error. This is similar to warn on error mode,
717 except that C<isl> does not print any warning. This allows a program to
718 implement its own error reporting.
720 The last option is to directly abort the execution of the program from within
721 the isl library. This makes it obviously impossible to recover from an error,
722 but it allows to directly spot the error location. By aborting on error,
723 debuggers break at the location the error occurred and can provide a stack
724 trace. Other tools that automatically provide stack traces on abort or that do
725 not want to continue execution after an error was triggered may also prefer to
728 The on error behavior of isl can be specified by calling
729 C<isl_options_set_on_error> or by setting the command line option
730 C<--isl-on-error>. Valid arguments for the function call are
731 C<ISL_ON_ERROR_WARN>, C<ISL_ON_ERROR_CONTINUE> and C<ISL_ON_ERROR_ABORT>. The
732 choices for the command line option are C<warn>, C<continue> and C<abort>.
733 It is also possible to query the current error mode.
735 #include <isl/options.h>
736 int isl_options_set_on_error(isl_ctx *ctx, int val);
737 int isl_options_get_on_error(isl_ctx *ctx);
741 Identifiers are used to identify both individual dimensions
742 and tuples of dimensions. They consist of an optional name and an optional
743 user pointer. The name and the user pointer cannot both be C<NULL>, however.
744 Identifiers with the same name but different pointer values
745 are considered to be distinct.
746 Similarly, identifiers with different names but the same pointer value
747 are also considered to be distinct.
748 Equal identifiers are represented using the same object.
749 Pairs of identifiers can therefore be tested for equality using the
751 Identifiers can be constructed, copied, freed, inspected and printed
752 using the following functions.
755 __isl_give isl_id *isl_id_alloc(isl_ctx *ctx,
756 __isl_keep const char *name, void *user);
757 __isl_give isl_id *isl_id_set_free_user(
758 __isl_take isl_id *id,
759 __isl_give void (*free_user)(void *user));
760 __isl_give isl_id *isl_id_copy(isl_id *id);
761 void *isl_id_free(__isl_take isl_id *id);
763 isl_ctx *isl_id_get_ctx(__isl_keep isl_id *id);
764 void *isl_id_get_user(__isl_keep isl_id *id);
765 __isl_keep const char *isl_id_get_name(__isl_keep isl_id *id);
767 __isl_give isl_printer *isl_printer_print_id(
768 __isl_take isl_printer *p, __isl_keep isl_id *id);
770 The callback set by C<isl_id_set_free_user> is called on the user
771 pointer when the last reference to the C<isl_id> is freed.
772 Note that C<isl_id_get_name> returns a pointer to some internal
773 data structure, so the result can only be used while the
774 corresponding C<isl_id> is alive.
778 Whenever a new set, relation or similiar object is created from scratch,
779 the space in which it lives needs to be specified using an C<isl_space>.
780 Each space involves zero or more parameters and zero, one or two
781 tuples of set or input/output dimensions. The parameters and dimensions
782 are identified by an C<isl_dim_type> and a position.
783 The type C<isl_dim_param> refers to parameters,
784 the type C<isl_dim_set> refers to set dimensions (for spaces
785 with a single tuple of dimensions) and the types C<isl_dim_in>
786 and C<isl_dim_out> refer to input and output dimensions
787 (for spaces with two tuples of dimensions).
788 Local spaces (see L</"Local Spaces">) also contain dimensions
789 of type C<isl_dim_div>.
790 Note that parameters are only identified by their position within
791 a given object. Across different objects, parameters are (usually)
792 identified by their names or identifiers. Only unnamed parameters
793 are identified by their positions across objects. The use of unnamed
794 parameters is discouraged.
796 #include <isl/space.h>
797 __isl_give isl_space *isl_space_alloc(isl_ctx *ctx,
798 unsigned nparam, unsigned n_in, unsigned n_out);
799 __isl_give isl_space *isl_space_params_alloc(isl_ctx *ctx,
801 __isl_give isl_space *isl_space_set_alloc(isl_ctx *ctx,
802 unsigned nparam, unsigned dim);
803 __isl_give isl_space *isl_space_copy(__isl_keep isl_space *space);
804 void *isl_space_free(__isl_take isl_space *space);
805 unsigned isl_space_dim(__isl_keep isl_space *space,
806 enum isl_dim_type type);
808 The space used for creating a parameter domain
809 needs to be created using C<isl_space_params_alloc>.
810 For other sets, the space
811 needs to be created using C<isl_space_set_alloc>, while
812 for a relation, the space
813 needs to be created using C<isl_space_alloc>.
814 C<isl_space_dim> can be used
815 to find out the number of dimensions of each type in
816 a space, where type may be
817 C<isl_dim_param>, C<isl_dim_in> (only for relations),
818 C<isl_dim_out> (only for relations), C<isl_dim_set>
819 (only for sets) or C<isl_dim_all>.
821 To check whether a given space is that of a set or a map
822 or whether it is a parameter space, use these functions:
824 #include <isl/space.h>
825 int isl_space_is_params(__isl_keep isl_space *space);
826 int isl_space_is_set(__isl_keep isl_space *space);
827 int isl_space_is_map(__isl_keep isl_space *space);
829 Spaces can be compared using the following functions:
831 #include <isl/space.h>
832 int isl_space_is_equal(__isl_keep isl_space *space1,
833 __isl_keep isl_space *space2);
834 int isl_space_is_domain(__isl_keep isl_space *space1,
835 __isl_keep isl_space *space2);
836 int isl_space_is_range(__isl_keep isl_space *space1,
837 __isl_keep isl_space *space2);
839 C<isl_space_is_domain> checks whether the first argument is equal
840 to the domain of the second argument. This requires in particular that
841 the first argument is a set space and that the second argument
844 It is often useful to create objects that live in the
845 same space as some other object. This can be accomplished
846 by creating the new objects
847 (see L<Creating New Sets and Relations> or
848 L<Creating New (Piecewise) Quasipolynomials>) based on the space
849 of the original object.
852 __isl_give isl_space *isl_basic_set_get_space(
853 __isl_keep isl_basic_set *bset);
854 __isl_give isl_space *isl_set_get_space(__isl_keep isl_set *set);
856 #include <isl/union_set.h>
857 __isl_give isl_space *isl_union_set_get_space(
858 __isl_keep isl_union_set *uset);
861 __isl_give isl_space *isl_basic_map_get_space(
862 __isl_keep isl_basic_map *bmap);
863 __isl_give isl_space *isl_map_get_space(__isl_keep isl_map *map);
865 #include <isl/union_map.h>
866 __isl_give isl_space *isl_union_map_get_space(
867 __isl_keep isl_union_map *umap);
869 #include <isl/constraint.h>
870 __isl_give isl_space *isl_constraint_get_space(
871 __isl_keep isl_constraint *constraint);
873 #include <isl/polynomial.h>
874 __isl_give isl_space *isl_qpolynomial_get_domain_space(
875 __isl_keep isl_qpolynomial *qp);
876 __isl_give isl_space *isl_qpolynomial_get_space(
877 __isl_keep isl_qpolynomial *qp);
878 __isl_give isl_space *isl_qpolynomial_fold_get_space(
879 __isl_keep isl_qpolynomial_fold *fold);
880 __isl_give isl_space *isl_pw_qpolynomial_get_domain_space(
881 __isl_keep isl_pw_qpolynomial *pwqp);
882 __isl_give isl_space *isl_pw_qpolynomial_get_space(
883 __isl_keep isl_pw_qpolynomial *pwqp);
884 __isl_give isl_space *isl_pw_qpolynomial_fold_get_domain_space(
885 __isl_keep isl_pw_qpolynomial_fold *pwf);
886 __isl_give isl_space *isl_pw_qpolynomial_fold_get_space(
887 __isl_keep isl_pw_qpolynomial_fold *pwf);
888 __isl_give isl_space *isl_union_pw_qpolynomial_get_space(
889 __isl_keep isl_union_pw_qpolynomial *upwqp);
890 __isl_give isl_space *isl_union_pw_qpolynomial_fold_get_space(
891 __isl_keep isl_union_pw_qpolynomial_fold *upwf);
894 __isl_give isl_space *isl_aff_get_domain_space(
895 __isl_keep isl_aff *aff);
896 __isl_give isl_space *isl_aff_get_space(
897 __isl_keep isl_aff *aff);
898 __isl_give isl_space *isl_pw_aff_get_domain_space(
899 __isl_keep isl_pw_aff *pwaff);
900 __isl_give isl_space *isl_pw_aff_get_space(
901 __isl_keep isl_pw_aff *pwaff);
902 __isl_give isl_space *isl_multi_aff_get_domain_space(
903 __isl_keep isl_multi_aff *maff);
904 __isl_give isl_space *isl_multi_aff_get_space(
905 __isl_keep isl_multi_aff *maff);
906 __isl_give isl_space *isl_pw_multi_aff_get_domain_space(
907 __isl_keep isl_pw_multi_aff *pma);
908 __isl_give isl_space *isl_pw_multi_aff_get_space(
909 __isl_keep isl_pw_multi_aff *pma);
910 __isl_give isl_space *isl_union_pw_multi_aff_get_space(
911 __isl_keep isl_union_pw_multi_aff *upma);
912 __isl_give isl_space *isl_multi_pw_aff_get_domain_space(
913 __isl_keep isl_multi_pw_aff *mpa);
914 __isl_give isl_space *isl_multi_pw_aff_get_space(
915 __isl_keep isl_multi_pw_aff *mpa);
917 #include <isl/point.h>
918 __isl_give isl_space *isl_point_get_space(
919 __isl_keep isl_point *pnt);
921 The identifiers or names of the individual dimensions may be set or read off
922 using the following functions.
924 #include <isl/space.h>
925 __isl_give isl_space *isl_space_set_dim_id(
926 __isl_take isl_space *space,
927 enum isl_dim_type type, unsigned pos,
928 __isl_take isl_id *id);
929 int isl_space_has_dim_id(__isl_keep isl_space *space,
930 enum isl_dim_type type, unsigned pos);
931 __isl_give isl_id *isl_space_get_dim_id(
932 __isl_keep isl_space *space,
933 enum isl_dim_type type, unsigned pos);
934 __isl_give isl_space *isl_space_set_dim_name(
935 __isl_take isl_space *space,
936 enum isl_dim_type type, unsigned pos,
937 __isl_keep const char *name);
938 int isl_space_has_dim_name(__isl_keep isl_space *space,
939 enum isl_dim_type type, unsigned pos);
940 __isl_keep const char *isl_space_get_dim_name(
941 __isl_keep isl_space *space,
942 enum isl_dim_type type, unsigned pos);
944 Note that C<isl_space_get_name> returns a pointer to some internal
945 data structure, so the result can only be used while the
946 corresponding C<isl_space> is alive.
947 Also note that every function that operates on two sets or relations
948 requires that both arguments have the same parameters. This also
949 means that if one of the arguments has named parameters, then the
950 other needs to have named parameters too and the names need to match.
951 Pairs of C<isl_set>, C<isl_map>, C<isl_union_set> and/or C<isl_union_map>
952 arguments may have different parameters (as long as they are named),
953 in which case the result will have as parameters the union of the parameters of
956 Given the identifier or name of a dimension (typically a parameter),
957 its position can be obtained from the following function.
959 #include <isl/space.h>
960 int isl_space_find_dim_by_id(__isl_keep isl_space *space,
961 enum isl_dim_type type, __isl_keep isl_id *id);
962 int isl_space_find_dim_by_name(__isl_keep isl_space *space,
963 enum isl_dim_type type, const char *name);
965 The identifiers or names of entire spaces may be set or read off
966 using the following functions.
968 #include <isl/space.h>
969 __isl_give isl_space *isl_space_set_tuple_id(
970 __isl_take isl_space *space,
971 enum isl_dim_type type, __isl_take isl_id *id);
972 __isl_give isl_space *isl_space_reset_tuple_id(
973 __isl_take isl_space *space, enum isl_dim_type type);
974 int isl_space_has_tuple_id(__isl_keep isl_space *space,
975 enum isl_dim_type type);
976 __isl_give isl_id *isl_space_get_tuple_id(
977 __isl_keep isl_space *space, enum isl_dim_type type);
978 __isl_give isl_space *isl_space_set_tuple_name(
979 __isl_take isl_space *space,
980 enum isl_dim_type type, const char *s);
981 int isl_space_has_tuple_name(__isl_keep isl_space *space,
982 enum isl_dim_type type);
983 const char *isl_space_get_tuple_name(__isl_keep isl_space *space,
984 enum isl_dim_type type);
986 The C<type> argument needs to be one of C<isl_dim_in>, C<isl_dim_out>
987 or C<isl_dim_set>. As with C<isl_space_get_name>,
988 the C<isl_space_get_tuple_name> function returns a pointer to some internal
990 Binary operations require the corresponding spaces of their arguments
991 to have the same name.
993 Spaces can be nested. In particular, the domain of a set or
994 the domain or range of a relation can be a nested relation.
995 The following functions can be used to construct and deconstruct
998 #include <isl/space.h>
999 int isl_space_is_wrapping(__isl_keep isl_space *space);
1000 __isl_give isl_space *isl_space_wrap(__isl_take isl_space *space);
1001 __isl_give isl_space *isl_space_unwrap(__isl_take isl_space *space);
1003 The input to C<isl_space_is_wrapping> and C<isl_space_unwrap> should
1004 be the space of a set, while that of
1005 C<isl_space_wrap> should be the space of a relation.
1006 Conversely, the output of C<isl_space_unwrap> is the space
1007 of a relation, while that of C<isl_space_wrap> is the space of a set.
1009 Spaces can be created from other spaces
1010 using the following functions.
1012 __isl_give isl_space *isl_space_domain(__isl_take isl_space *space);
1013 __isl_give isl_space *isl_space_from_domain(__isl_take isl_space *space);
1014 __isl_give isl_space *isl_space_range(__isl_take isl_space *space);
1015 __isl_give isl_space *isl_space_from_range(__isl_take isl_space *space);
1016 __isl_give isl_space *isl_space_params(
1017 __isl_take isl_space *space);
1018 __isl_give isl_space *isl_space_set_from_params(
1019 __isl_take isl_space *space);
1020 __isl_give isl_space *isl_space_reverse(__isl_take isl_space *space);
1021 __isl_give isl_space *isl_space_join(__isl_take isl_space *left,
1022 __isl_take isl_space *right);
1023 __isl_give isl_space *isl_space_align_params(
1024 __isl_take isl_space *space1, __isl_take isl_space *space2)
1025 __isl_give isl_space *isl_space_insert_dims(__isl_take isl_space *space,
1026 enum isl_dim_type type, unsigned pos, unsigned n);
1027 __isl_give isl_space *isl_space_add_dims(__isl_take isl_space *space,
1028 enum isl_dim_type type, unsigned n);
1029 __isl_give isl_space *isl_space_drop_dims(__isl_take isl_space *space,
1030 enum isl_dim_type type, unsigned first, unsigned n);
1031 __isl_give isl_space *isl_space_move_dims(__isl_take isl_space *space,
1032 enum isl_dim_type dst_type, unsigned dst_pos,
1033 enum isl_dim_type src_type, unsigned src_pos,
1035 __isl_give isl_space *isl_space_map_from_set(
1036 __isl_take isl_space *space);
1037 __isl_give isl_space *isl_space_map_from_domain_and_range(
1038 __isl_take isl_space *domain,
1039 __isl_take isl_space *range);
1040 __isl_give isl_space *isl_space_zip(__isl_take isl_space *space);
1041 __isl_give isl_space *isl_space_curry(
1042 __isl_take isl_space *space);
1043 __isl_give isl_space *isl_space_uncurry(
1044 __isl_take isl_space *space);
1046 Note that if dimensions are added or removed from a space, then
1047 the name and the internal structure are lost.
1051 A local space is essentially a space with
1052 zero or more existentially quantified variables.
1053 The local space of a (constraint of a) basic set or relation can be obtained
1054 using the following functions.
1056 #include <isl/constraint.h>
1057 __isl_give isl_local_space *isl_constraint_get_local_space(
1058 __isl_keep isl_constraint *constraint);
1060 #include <isl/set.h>
1061 __isl_give isl_local_space *isl_basic_set_get_local_space(
1062 __isl_keep isl_basic_set *bset);
1064 #include <isl/map.h>
1065 __isl_give isl_local_space *isl_basic_map_get_local_space(
1066 __isl_keep isl_basic_map *bmap);
1068 A new local space can be created from a space using
1070 #include <isl/local_space.h>
1071 __isl_give isl_local_space *isl_local_space_from_space(
1072 __isl_take isl_space *space);
1074 They can be inspected, modified, copied and freed using the following functions.
1076 #include <isl/local_space.h>
1077 isl_ctx *isl_local_space_get_ctx(
1078 __isl_keep isl_local_space *ls);
1079 int isl_local_space_is_set(__isl_keep isl_local_space *ls);
1080 int isl_local_space_dim(__isl_keep isl_local_space *ls,
1081 enum isl_dim_type type);
1082 int isl_local_space_has_dim_id(
1083 __isl_keep isl_local_space *ls,
1084 enum isl_dim_type type, unsigned pos);
1085 __isl_give isl_id *isl_local_space_get_dim_id(
1086 __isl_keep isl_local_space *ls,
1087 enum isl_dim_type type, unsigned pos);
1088 int isl_local_space_has_dim_name(
1089 __isl_keep isl_local_space *ls,
1090 enum isl_dim_type type, unsigned pos)
1091 const char *isl_local_space_get_dim_name(
1092 __isl_keep isl_local_space *ls,
1093 enum isl_dim_type type, unsigned pos);
1094 __isl_give isl_local_space *isl_local_space_set_dim_name(
1095 __isl_take isl_local_space *ls,
1096 enum isl_dim_type type, unsigned pos, const char *s);
1097 __isl_give isl_local_space *isl_local_space_set_dim_id(
1098 __isl_take isl_local_space *ls,
1099 enum isl_dim_type type, unsigned pos,
1100 __isl_take isl_id *id);
1101 __isl_give isl_space *isl_local_space_get_space(
1102 __isl_keep isl_local_space *ls);
1103 __isl_give isl_aff *isl_local_space_get_div(
1104 __isl_keep isl_local_space *ls, int pos);
1105 __isl_give isl_local_space *isl_local_space_copy(
1106 __isl_keep isl_local_space *ls);
1107 void *isl_local_space_free(__isl_take isl_local_space *ls);
1109 Note that C<isl_local_space_get_div> can only be used on local spaces
1112 Two local spaces can be compared using
1114 int isl_local_space_is_equal(__isl_keep isl_local_space *ls1,
1115 __isl_keep isl_local_space *ls2);
1117 Local spaces can be created from other local spaces
1118 using the following functions.
1120 __isl_give isl_local_space *isl_local_space_domain(
1121 __isl_take isl_local_space *ls);
1122 __isl_give isl_local_space *isl_local_space_range(
1123 __isl_take isl_local_space *ls);
1124 __isl_give isl_local_space *isl_local_space_from_domain(
1125 __isl_take isl_local_space *ls);
1126 __isl_give isl_local_space *isl_local_space_intersect(
1127 __isl_take isl_local_space *ls1,
1128 __isl_take isl_local_space *ls2);
1129 __isl_give isl_local_space *isl_local_space_add_dims(
1130 __isl_take isl_local_space *ls,
1131 enum isl_dim_type type, unsigned n);
1132 __isl_give isl_local_space *isl_local_space_insert_dims(
1133 __isl_take isl_local_space *ls,
1134 enum isl_dim_type type, unsigned first, unsigned n);
1135 __isl_give isl_local_space *isl_local_space_drop_dims(
1136 __isl_take isl_local_space *ls,
1137 enum isl_dim_type type, unsigned first, unsigned n);
1139 =head2 Input and Output
1141 C<isl> supports its own input/output format, which is similar
1142 to the C<Omega> format, but also supports the C<PolyLib> format
1145 =head3 C<isl> format
1147 The C<isl> format is similar to that of C<Omega>, but has a different
1148 syntax for describing the parameters and allows for the definition
1149 of an existentially quantified variable as the integer division
1150 of an affine expression.
1151 For example, the set of integers C<i> between C<0> and C<n>
1152 such that C<i % 10 <= 6> can be described as
1154 [n] -> { [i] : exists (a = [i/10] : 0 <= i and i <= n and
1157 A set or relation can have several disjuncts, separated
1158 by the keyword C<or>. Each disjunct is either a conjunction
1159 of constraints or a projection (C<exists>) of a conjunction
1160 of constraints. The constraints are separated by the keyword
1163 =head3 C<PolyLib> format
1165 If the represented set is a union, then the first line
1166 contains a single number representing the number of disjuncts.
1167 Otherwise, a line containing the number C<1> is optional.
1169 Each disjunct is represented by a matrix of constraints.
1170 The first line contains two numbers representing
1171 the number of rows and columns,
1172 where the number of rows is equal to the number of constraints
1173 and the number of columns is equal to two plus the number of variables.
1174 The following lines contain the actual rows of the constraint matrix.
1175 In each row, the first column indicates whether the constraint
1176 is an equality (C<0>) or inequality (C<1>). The final column
1177 corresponds to the constant term.
1179 If the set is parametric, then the coefficients of the parameters
1180 appear in the last columns before the constant column.
1181 The coefficients of any existentially quantified variables appear
1182 between those of the set variables and those of the parameters.
1184 =head3 Extended C<PolyLib> format
1186 The extended C<PolyLib> format is nearly identical to the
1187 C<PolyLib> format. The only difference is that the line
1188 containing the number of rows and columns of a constraint matrix
1189 also contains four additional numbers:
1190 the number of output dimensions, the number of input dimensions,
1191 the number of local dimensions (i.e., the number of existentially
1192 quantified variables) and the number of parameters.
1193 For sets, the number of ``output'' dimensions is equal
1194 to the number of set dimensions, while the number of ``input''
1199 #include <isl/set.h>
1200 __isl_give isl_basic_set *isl_basic_set_read_from_file(
1201 isl_ctx *ctx, FILE *input);
1202 __isl_give isl_basic_set *isl_basic_set_read_from_str(
1203 isl_ctx *ctx, const char *str);
1204 __isl_give isl_set *isl_set_read_from_file(isl_ctx *ctx,
1206 __isl_give isl_set *isl_set_read_from_str(isl_ctx *ctx,
1209 #include <isl/map.h>
1210 __isl_give isl_basic_map *isl_basic_map_read_from_file(
1211 isl_ctx *ctx, FILE *input);
1212 __isl_give isl_basic_map *isl_basic_map_read_from_str(
1213 isl_ctx *ctx, const char *str);
1214 __isl_give isl_map *isl_map_read_from_file(
1215 isl_ctx *ctx, FILE *input);
1216 __isl_give isl_map *isl_map_read_from_str(isl_ctx *ctx,
1219 #include <isl/union_set.h>
1220 __isl_give isl_union_set *isl_union_set_read_from_file(
1221 isl_ctx *ctx, FILE *input);
1222 __isl_give isl_union_set *isl_union_set_read_from_str(
1223 isl_ctx *ctx, const char *str);
1225 #include <isl/union_map.h>
1226 __isl_give isl_union_map *isl_union_map_read_from_file(
1227 isl_ctx *ctx, FILE *input);
1228 __isl_give isl_union_map *isl_union_map_read_from_str(
1229 isl_ctx *ctx, const char *str);
1231 The input format is autodetected and may be either the C<PolyLib> format
1232 or the C<isl> format.
1236 Before anything can be printed, an C<isl_printer> needs to
1239 __isl_give isl_printer *isl_printer_to_file(isl_ctx *ctx,
1241 __isl_give isl_printer *isl_printer_to_str(isl_ctx *ctx);
1242 void *isl_printer_free(__isl_take isl_printer *printer);
1243 __isl_give char *isl_printer_get_str(
1244 __isl_keep isl_printer *printer);
1246 The printer can be inspected using the following functions.
1248 FILE *isl_printer_get_file(
1249 __isl_keep isl_printer *printer);
1250 int isl_printer_get_output_format(
1251 __isl_keep isl_printer *p);
1253 The behavior of the printer can be modified in various ways
1255 __isl_give isl_printer *isl_printer_set_output_format(
1256 __isl_take isl_printer *p, int output_format);
1257 __isl_give isl_printer *isl_printer_set_indent(
1258 __isl_take isl_printer *p, int indent);
1259 __isl_give isl_printer *isl_printer_indent(
1260 __isl_take isl_printer *p, int indent);
1261 __isl_give isl_printer *isl_printer_set_prefix(
1262 __isl_take isl_printer *p, const char *prefix);
1263 __isl_give isl_printer *isl_printer_set_suffix(
1264 __isl_take isl_printer *p, const char *suffix);
1266 The C<output_format> may be either C<ISL_FORMAT_ISL>, C<ISL_FORMAT_OMEGA>,
1267 C<ISL_FORMAT_POLYLIB>, C<ISL_FORMAT_EXT_POLYLIB> or C<ISL_FORMAT_LATEX>
1268 and defaults to C<ISL_FORMAT_ISL>.
1269 Each line in the output is indented by C<indent> (set by
1270 C<isl_printer_set_indent>) spaces
1271 (default: 0), prefixed by C<prefix> and suffixed by C<suffix>.
1272 In the C<PolyLib> format output,
1273 the coefficients of the existentially quantified variables
1274 appear between those of the set variables and those
1276 The function C<isl_printer_indent> increases the indentation
1277 by the specified amount (which may be negative).
1279 To actually print something, use
1281 #include <isl/printer.h>
1282 __isl_give isl_printer *isl_printer_print_double(
1283 __isl_take isl_printer *p, double d);
1285 #include <isl/set.h>
1286 __isl_give isl_printer *isl_printer_print_basic_set(
1287 __isl_take isl_printer *printer,
1288 __isl_keep isl_basic_set *bset);
1289 __isl_give isl_printer *isl_printer_print_set(
1290 __isl_take isl_printer *printer,
1291 __isl_keep isl_set *set);
1293 #include <isl/map.h>
1294 __isl_give isl_printer *isl_printer_print_basic_map(
1295 __isl_take isl_printer *printer,
1296 __isl_keep isl_basic_map *bmap);
1297 __isl_give isl_printer *isl_printer_print_map(
1298 __isl_take isl_printer *printer,
1299 __isl_keep isl_map *map);
1301 #include <isl/union_set.h>
1302 __isl_give isl_printer *isl_printer_print_union_set(
1303 __isl_take isl_printer *p,
1304 __isl_keep isl_union_set *uset);
1306 #include <isl/union_map.h>
1307 __isl_give isl_printer *isl_printer_print_union_map(
1308 __isl_take isl_printer *p,
1309 __isl_keep isl_union_map *umap);
1311 When called on a file printer, the following function flushes
1312 the file. When called on a string printer, the buffer is cleared.
1314 __isl_give isl_printer *isl_printer_flush(
1315 __isl_take isl_printer *p);
1317 =head2 Creating New Sets and Relations
1319 C<isl> has functions for creating some standard sets and relations.
1323 =item * Empty sets and relations
1325 __isl_give isl_basic_set *isl_basic_set_empty(
1326 __isl_take isl_space *space);
1327 __isl_give isl_basic_map *isl_basic_map_empty(
1328 __isl_take isl_space *space);
1329 __isl_give isl_set *isl_set_empty(
1330 __isl_take isl_space *space);
1331 __isl_give isl_map *isl_map_empty(
1332 __isl_take isl_space *space);
1333 __isl_give isl_union_set *isl_union_set_empty(
1334 __isl_take isl_space *space);
1335 __isl_give isl_union_map *isl_union_map_empty(
1336 __isl_take isl_space *space);
1338 For C<isl_union_set>s and C<isl_union_map>s, the space
1339 is only used to specify the parameters.
1341 =item * Universe sets and relations
1343 __isl_give isl_basic_set *isl_basic_set_universe(
1344 __isl_take isl_space *space);
1345 __isl_give isl_basic_map *isl_basic_map_universe(
1346 __isl_take isl_space *space);
1347 __isl_give isl_set *isl_set_universe(
1348 __isl_take isl_space *space);
1349 __isl_give isl_map *isl_map_universe(
1350 __isl_take isl_space *space);
1351 __isl_give isl_union_set *isl_union_set_universe(
1352 __isl_take isl_union_set *uset);
1353 __isl_give isl_union_map *isl_union_map_universe(
1354 __isl_take isl_union_map *umap);
1356 The sets and relations constructed by the functions above
1357 contain all integer values, while those constructed by the
1358 functions below only contain non-negative values.
1360 __isl_give isl_basic_set *isl_basic_set_nat_universe(
1361 __isl_take isl_space *space);
1362 __isl_give isl_basic_map *isl_basic_map_nat_universe(
1363 __isl_take isl_space *space);
1364 __isl_give isl_set *isl_set_nat_universe(
1365 __isl_take isl_space *space);
1366 __isl_give isl_map *isl_map_nat_universe(
1367 __isl_take isl_space *space);
1369 =item * Identity relations
1371 __isl_give isl_basic_map *isl_basic_map_identity(
1372 __isl_take isl_space *space);
1373 __isl_give isl_map *isl_map_identity(
1374 __isl_take isl_space *space);
1376 The number of input and output dimensions in C<space> needs
1379 =item * Lexicographic order
1381 __isl_give isl_map *isl_map_lex_lt(
1382 __isl_take isl_space *set_space);
1383 __isl_give isl_map *isl_map_lex_le(
1384 __isl_take isl_space *set_space);
1385 __isl_give isl_map *isl_map_lex_gt(
1386 __isl_take isl_space *set_space);
1387 __isl_give isl_map *isl_map_lex_ge(
1388 __isl_take isl_space *set_space);
1389 __isl_give isl_map *isl_map_lex_lt_first(
1390 __isl_take isl_space *space, unsigned n);
1391 __isl_give isl_map *isl_map_lex_le_first(
1392 __isl_take isl_space *space, unsigned n);
1393 __isl_give isl_map *isl_map_lex_gt_first(
1394 __isl_take isl_space *space, unsigned n);
1395 __isl_give isl_map *isl_map_lex_ge_first(
1396 __isl_take isl_space *space, unsigned n);
1398 The first four functions take a space for a B<set>
1399 and return relations that express that the elements in the domain
1400 are lexicographically less
1401 (C<isl_map_lex_lt>), less or equal (C<isl_map_lex_le>),
1402 greater (C<isl_map_lex_gt>) or greater or equal (C<isl_map_lex_ge>)
1403 than the elements in the range.
1404 The last four functions take a space for a map
1405 and return relations that express that the first C<n> dimensions
1406 in the domain are lexicographically less
1407 (C<isl_map_lex_lt_first>), less or equal (C<isl_map_lex_le_first>),
1408 greater (C<isl_map_lex_gt_first>) or greater or equal (C<isl_map_lex_ge_first>)
1409 than the first C<n> dimensions in the range.
1413 A basic set or relation can be converted to a set or relation
1414 using the following functions.
1416 __isl_give isl_set *isl_set_from_basic_set(
1417 __isl_take isl_basic_set *bset);
1418 __isl_give isl_map *isl_map_from_basic_map(
1419 __isl_take isl_basic_map *bmap);
1421 Sets and relations can be converted to union sets and relations
1422 using the following functions.
1424 __isl_give isl_union_set *isl_union_set_from_basic_set(
1425 __isl_take isl_basic_set *bset);
1426 __isl_give isl_union_map *isl_union_map_from_basic_map(
1427 __isl_take isl_basic_map *bmap);
1428 __isl_give isl_union_set *isl_union_set_from_set(
1429 __isl_take isl_set *set);
1430 __isl_give isl_union_map *isl_union_map_from_map(
1431 __isl_take isl_map *map);
1433 The inverse conversions below can only be used if the input
1434 union set or relation is known to contain elements in exactly one
1437 __isl_give isl_set *isl_set_from_union_set(
1438 __isl_take isl_union_set *uset);
1439 __isl_give isl_map *isl_map_from_union_map(
1440 __isl_take isl_union_map *umap);
1442 A zero-dimensional (basic) set can be constructed on a given parameter domain
1443 using the following function.
1445 __isl_give isl_basic_set *isl_basic_set_from_params(
1446 __isl_take isl_basic_set *bset);
1447 __isl_give isl_set *isl_set_from_params(
1448 __isl_take isl_set *set);
1450 Sets and relations can be copied and freed again using the following
1453 __isl_give isl_basic_set *isl_basic_set_copy(
1454 __isl_keep isl_basic_set *bset);
1455 __isl_give isl_set *isl_set_copy(__isl_keep isl_set *set);
1456 __isl_give isl_union_set *isl_union_set_copy(
1457 __isl_keep isl_union_set *uset);
1458 __isl_give isl_basic_map *isl_basic_map_copy(
1459 __isl_keep isl_basic_map *bmap);
1460 __isl_give isl_map *isl_map_copy(__isl_keep isl_map *map);
1461 __isl_give isl_union_map *isl_union_map_copy(
1462 __isl_keep isl_union_map *umap);
1463 void *isl_basic_set_free(__isl_take isl_basic_set *bset);
1464 void *isl_set_free(__isl_take isl_set *set);
1465 void *isl_union_set_free(__isl_take isl_union_set *uset);
1466 void *isl_basic_map_free(__isl_take isl_basic_map *bmap);
1467 void *isl_map_free(__isl_take isl_map *map);
1468 void *isl_union_map_free(__isl_take isl_union_map *umap);
1470 Other sets and relations can be constructed by starting
1471 from a universe set or relation, adding equality and/or
1472 inequality constraints and then projecting out the
1473 existentially quantified variables, if any.
1474 Constraints can be constructed, manipulated and
1475 added to (or removed from) (basic) sets and relations
1476 using the following functions.
1478 #include <isl/constraint.h>
1479 __isl_give isl_constraint *isl_equality_alloc(
1480 __isl_take isl_local_space *ls);
1481 __isl_give isl_constraint *isl_inequality_alloc(
1482 __isl_take isl_local_space *ls);
1483 __isl_give isl_constraint *isl_constraint_set_constant(
1484 __isl_take isl_constraint *constraint, isl_int v);
1485 __isl_give isl_constraint *isl_constraint_set_constant_si(
1486 __isl_take isl_constraint *constraint, int v);
1487 __isl_give isl_constraint *isl_constraint_set_coefficient(
1488 __isl_take isl_constraint *constraint,
1489 enum isl_dim_type type, int pos, isl_int v);
1490 __isl_give isl_constraint *isl_constraint_set_coefficient_si(
1491 __isl_take isl_constraint *constraint,
1492 enum isl_dim_type type, int pos, int v);
1493 __isl_give isl_basic_map *isl_basic_map_add_constraint(
1494 __isl_take isl_basic_map *bmap,
1495 __isl_take isl_constraint *constraint);
1496 __isl_give isl_basic_set *isl_basic_set_add_constraint(
1497 __isl_take isl_basic_set *bset,
1498 __isl_take isl_constraint *constraint);
1499 __isl_give isl_map *isl_map_add_constraint(
1500 __isl_take isl_map *map,
1501 __isl_take isl_constraint *constraint);
1502 __isl_give isl_set *isl_set_add_constraint(
1503 __isl_take isl_set *set,
1504 __isl_take isl_constraint *constraint);
1505 __isl_give isl_basic_set *isl_basic_set_drop_constraint(
1506 __isl_take isl_basic_set *bset,
1507 __isl_take isl_constraint *constraint);
1509 For example, to create a set containing the even integers
1510 between 10 and 42, you would use the following code.
1513 isl_local_space *ls;
1515 isl_basic_set *bset;
1517 space = isl_space_set_alloc(ctx, 0, 2);
1518 bset = isl_basic_set_universe(isl_space_copy(space));
1519 ls = isl_local_space_from_space(space);
1521 c = isl_equality_alloc(isl_local_space_copy(ls));
1522 c = isl_constraint_set_coefficient_si(c, isl_dim_set, 0, -1);
1523 c = isl_constraint_set_coefficient_si(c, isl_dim_set, 1, 2);
1524 bset = isl_basic_set_add_constraint(bset, c);
1526 c = isl_inequality_alloc(isl_local_space_copy(ls));
1527 c = isl_constraint_set_constant_si(c, -10);
1528 c = isl_constraint_set_coefficient_si(c, isl_dim_set, 0, 1);
1529 bset = isl_basic_set_add_constraint(bset, c);
1531 c = isl_inequality_alloc(ls);
1532 c = isl_constraint_set_constant_si(c, 42);
1533 c = isl_constraint_set_coefficient_si(c, isl_dim_set, 0, -1);
1534 bset = isl_basic_set_add_constraint(bset, c);
1536 bset = isl_basic_set_project_out(bset, isl_dim_set, 1, 1);
1540 isl_basic_set *bset;
1541 bset = isl_basic_set_read_from_str(ctx,
1542 "{[i] : exists (a : i = 2a and i >= 10 and i <= 42)}");
1544 A basic set or relation can also be constructed from two matrices
1545 describing the equalities and the inequalities.
1547 __isl_give isl_basic_set *isl_basic_set_from_constraint_matrices(
1548 __isl_take isl_space *space,
1549 __isl_take isl_mat *eq, __isl_take isl_mat *ineq,
1550 enum isl_dim_type c1,
1551 enum isl_dim_type c2, enum isl_dim_type c3,
1552 enum isl_dim_type c4);
1553 __isl_give isl_basic_map *isl_basic_map_from_constraint_matrices(
1554 __isl_take isl_space *space,
1555 __isl_take isl_mat *eq, __isl_take isl_mat *ineq,
1556 enum isl_dim_type c1,
1557 enum isl_dim_type c2, enum isl_dim_type c3,
1558 enum isl_dim_type c4, enum isl_dim_type c5);
1560 The C<isl_dim_type> arguments indicate the order in which
1561 different kinds of variables appear in the input matrices
1562 and should be a permutation of C<isl_dim_cst>, C<isl_dim_param>,
1563 C<isl_dim_set> and C<isl_dim_div> for sets and
1564 of C<isl_dim_cst>, C<isl_dim_param>,
1565 C<isl_dim_in>, C<isl_dim_out> and C<isl_dim_div> for relations.
1567 A (basic or union) set or relation can also be constructed from a
1568 (union) (piecewise) (multiple) affine expression
1569 or a list of affine expressions
1570 (See L<"Piecewise Quasi Affine Expressions"> and
1571 L<"Piecewise Multiple Quasi Affine Expressions">).
1573 __isl_give isl_basic_map *isl_basic_map_from_aff(
1574 __isl_take isl_aff *aff);
1575 __isl_give isl_map *isl_map_from_aff(
1576 __isl_take isl_aff *aff);
1577 __isl_give isl_set *isl_set_from_pw_aff(
1578 __isl_take isl_pw_aff *pwaff);
1579 __isl_give isl_map *isl_map_from_pw_aff(
1580 __isl_take isl_pw_aff *pwaff);
1581 __isl_give isl_basic_map *isl_basic_map_from_aff_list(
1582 __isl_take isl_space *domain_space,
1583 __isl_take isl_aff_list *list);
1584 __isl_give isl_basic_map *isl_basic_map_from_multi_aff(
1585 __isl_take isl_multi_aff *maff)
1586 __isl_give isl_map *isl_map_from_multi_aff(
1587 __isl_take isl_multi_aff *maff)
1588 __isl_give isl_set *isl_set_from_pw_multi_aff(
1589 __isl_take isl_pw_multi_aff *pma);
1590 __isl_give isl_map *isl_map_from_pw_multi_aff(
1591 __isl_take isl_pw_multi_aff *pma);
1592 __isl_give isl_union_map *
1593 isl_union_map_from_union_pw_multi_aff(
1594 __isl_take isl_union_pw_multi_aff *upma);
1596 The C<domain_dim> argument describes the domain of the resulting
1597 basic relation. It is required because the C<list> may consist
1598 of zero affine expressions.
1600 =head2 Inspecting Sets and Relations
1602 Usually, the user should not have to care about the actual constraints
1603 of the sets and maps, but should instead apply the abstract operations
1604 explained in the following sections.
1605 Occasionally, however, it may be required to inspect the individual
1606 coefficients of the constraints. This section explains how to do so.
1607 In these cases, it may also be useful to have C<isl> compute
1608 an explicit representation of the existentially quantified variables.
1610 __isl_give isl_set *isl_set_compute_divs(
1611 __isl_take isl_set *set);
1612 __isl_give isl_map *isl_map_compute_divs(
1613 __isl_take isl_map *map);
1614 __isl_give isl_union_set *isl_union_set_compute_divs(
1615 __isl_take isl_union_set *uset);
1616 __isl_give isl_union_map *isl_union_map_compute_divs(
1617 __isl_take isl_union_map *umap);
1619 This explicit representation defines the existentially quantified
1620 variables as integer divisions of the other variables, possibly
1621 including earlier existentially quantified variables.
1622 An explicitly represented existentially quantified variable therefore
1623 has a unique value when the values of the other variables are known.
1624 If, furthermore, the same existentials, i.e., existentials
1625 with the same explicit representations, should appear in the
1626 same order in each of the disjuncts of a set or map, then the user should call
1627 either of the following functions.
1629 __isl_give isl_set *isl_set_align_divs(
1630 __isl_take isl_set *set);
1631 __isl_give isl_map *isl_map_align_divs(
1632 __isl_take isl_map *map);
1634 Alternatively, the existentially quantified variables can be removed
1635 using the following functions, which compute an overapproximation.
1637 __isl_give isl_basic_set *isl_basic_set_remove_divs(
1638 __isl_take isl_basic_set *bset);
1639 __isl_give isl_basic_map *isl_basic_map_remove_divs(
1640 __isl_take isl_basic_map *bmap);
1641 __isl_give isl_set *isl_set_remove_divs(
1642 __isl_take isl_set *set);
1643 __isl_give isl_map *isl_map_remove_divs(
1644 __isl_take isl_map *map);
1646 It is also possible to only remove those divs that are defined
1647 in terms of a given range of dimensions or only those for which
1648 no explicit representation is known.
1650 __isl_give isl_basic_set *
1651 isl_basic_set_remove_divs_involving_dims(
1652 __isl_take isl_basic_set *bset,
1653 enum isl_dim_type type,
1654 unsigned first, unsigned n);
1655 __isl_give isl_basic_map *
1656 isl_basic_map_remove_divs_involving_dims(
1657 __isl_take isl_basic_map *bmap,
1658 enum isl_dim_type type,
1659 unsigned first, unsigned n);
1660 __isl_give isl_set *isl_set_remove_divs_involving_dims(
1661 __isl_take isl_set *set, enum isl_dim_type type,
1662 unsigned first, unsigned n);
1663 __isl_give isl_map *isl_map_remove_divs_involving_dims(
1664 __isl_take isl_map *map, enum isl_dim_type type,
1665 unsigned first, unsigned n);
1667 __isl_give isl_basic_set *
1668 isl_basic_set_remove_unknown_divs(
1669 __isl_take isl_basic_set *bset);
1670 __isl_give isl_set *isl_set_remove_unknown_divs(
1671 __isl_take isl_set *set);
1672 __isl_give isl_map *isl_map_remove_unknown_divs(
1673 __isl_take isl_map *map);
1675 To iterate over all the sets or maps in a union set or map, use
1677 int isl_union_set_foreach_set(__isl_keep isl_union_set *uset,
1678 int (*fn)(__isl_take isl_set *set, void *user),
1680 int isl_union_map_foreach_map(__isl_keep isl_union_map *umap,
1681 int (*fn)(__isl_take isl_map *map, void *user),
1684 The number of sets or maps in a union set or map can be obtained
1687 int isl_union_set_n_set(__isl_keep isl_union_set *uset);
1688 int isl_union_map_n_map(__isl_keep isl_union_map *umap);
1690 To extract the set or map in a given space from a union, use
1692 __isl_give isl_set *isl_union_set_extract_set(
1693 __isl_keep isl_union_set *uset,
1694 __isl_take isl_space *space);
1695 __isl_give isl_map *isl_union_map_extract_map(
1696 __isl_keep isl_union_map *umap,
1697 __isl_take isl_space *space);
1699 To iterate over all the basic sets or maps in a set or map, use
1701 int isl_set_foreach_basic_set(__isl_keep isl_set *set,
1702 int (*fn)(__isl_take isl_basic_set *bset, void *user),
1704 int isl_map_foreach_basic_map(__isl_keep isl_map *map,
1705 int (*fn)(__isl_take isl_basic_map *bmap, void *user),
1708 The callback function C<fn> should return 0 if successful and
1709 -1 if an error occurs. In the latter case, or if any other error
1710 occurs, the above functions will return -1.
1712 It should be noted that C<isl> does not guarantee that
1713 the basic sets or maps passed to C<fn> are disjoint.
1714 If this is required, then the user should call one of
1715 the following functions first.
1717 __isl_give isl_set *isl_set_make_disjoint(
1718 __isl_take isl_set *set);
1719 __isl_give isl_map *isl_map_make_disjoint(
1720 __isl_take isl_map *map);
1722 The number of basic sets in a set can be obtained
1725 int isl_set_n_basic_set(__isl_keep isl_set *set);
1727 To iterate over the constraints of a basic set or map, use
1729 #include <isl/constraint.h>
1731 int isl_basic_set_n_constraint(
1732 __isl_keep isl_basic_set *bset);
1733 int isl_basic_set_foreach_constraint(
1734 __isl_keep isl_basic_set *bset,
1735 int (*fn)(__isl_take isl_constraint *c, void *user),
1737 int isl_basic_map_foreach_constraint(
1738 __isl_keep isl_basic_map *bmap,
1739 int (*fn)(__isl_take isl_constraint *c, void *user),
1741 void *isl_constraint_free(__isl_take isl_constraint *c);
1743 Again, the callback function C<fn> should return 0 if successful and
1744 -1 if an error occurs. In the latter case, or if any other error
1745 occurs, the above functions will return -1.
1746 The constraint C<c> represents either an equality or an inequality.
1747 Use the following function to find out whether a constraint
1748 represents an equality. If not, it represents an inequality.
1750 int isl_constraint_is_equality(
1751 __isl_keep isl_constraint *constraint);
1753 The coefficients of the constraints can be inspected using
1754 the following functions.
1756 int isl_constraint_is_lower_bound(
1757 __isl_keep isl_constraint *constraint,
1758 enum isl_dim_type type, unsigned pos);
1759 int isl_constraint_is_upper_bound(
1760 __isl_keep isl_constraint *constraint,
1761 enum isl_dim_type type, unsigned pos);
1762 void isl_constraint_get_constant(
1763 __isl_keep isl_constraint *constraint, isl_int *v);
1764 void isl_constraint_get_coefficient(
1765 __isl_keep isl_constraint *constraint,
1766 enum isl_dim_type type, int pos, isl_int *v);
1767 int isl_constraint_involves_dims(
1768 __isl_keep isl_constraint *constraint,
1769 enum isl_dim_type type, unsigned first, unsigned n);
1771 The explicit representations of the existentially quantified
1772 variables can be inspected using the following function.
1773 Note that the user is only allowed to use this function
1774 if the inspected set or map is the result of a call
1775 to C<isl_set_compute_divs> or C<isl_map_compute_divs>.
1776 The existentially quantified variable is equal to the floor
1777 of the returned affine expression. The affine expression
1778 itself can be inspected using the functions in
1779 L<"Piecewise Quasi Affine Expressions">.
1781 __isl_give isl_aff *isl_constraint_get_div(
1782 __isl_keep isl_constraint *constraint, int pos);
1784 To obtain the constraints of a basic set or map in matrix
1785 form, use the following functions.
1787 __isl_give isl_mat *isl_basic_set_equalities_matrix(
1788 __isl_keep isl_basic_set *bset,
1789 enum isl_dim_type c1, enum isl_dim_type c2,
1790 enum isl_dim_type c3, enum isl_dim_type c4);
1791 __isl_give isl_mat *isl_basic_set_inequalities_matrix(
1792 __isl_keep isl_basic_set *bset,
1793 enum isl_dim_type c1, enum isl_dim_type c2,
1794 enum isl_dim_type c3, enum isl_dim_type c4);
1795 __isl_give isl_mat *isl_basic_map_equalities_matrix(
1796 __isl_keep isl_basic_map *bmap,
1797 enum isl_dim_type c1,
1798 enum isl_dim_type c2, enum isl_dim_type c3,
1799 enum isl_dim_type c4, enum isl_dim_type c5);
1800 __isl_give isl_mat *isl_basic_map_inequalities_matrix(
1801 __isl_keep isl_basic_map *bmap,
1802 enum isl_dim_type c1,
1803 enum isl_dim_type c2, enum isl_dim_type c3,
1804 enum isl_dim_type c4, enum isl_dim_type c5);
1806 The C<isl_dim_type> arguments dictate the order in which
1807 different kinds of variables appear in the resulting matrix
1808 and should be a permutation of C<isl_dim_cst>, C<isl_dim_param>,
1809 C<isl_dim_in>, C<isl_dim_out> and C<isl_dim_div>.
1811 The number of parameters, input, output or set dimensions can
1812 be obtained using the following functions.
1814 unsigned isl_basic_set_dim(__isl_keep isl_basic_set *bset,
1815 enum isl_dim_type type);
1816 unsigned isl_basic_map_dim(__isl_keep isl_basic_map *bmap,
1817 enum isl_dim_type type);
1818 unsigned isl_set_dim(__isl_keep isl_set *set,
1819 enum isl_dim_type type);
1820 unsigned isl_map_dim(__isl_keep isl_map *map,
1821 enum isl_dim_type type);
1823 To check whether the description of a set or relation depends
1824 on one or more given dimensions, it is not necessary to iterate over all
1825 constraints. Instead the following functions can be used.
1827 int isl_basic_set_involves_dims(
1828 __isl_keep isl_basic_set *bset,
1829 enum isl_dim_type type, unsigned first, unsigned n);
1830 int isl_set_involves_dims(__isl_keep isl_set *set,
1831 enum isl_dim_type type, unsigned first, unsigned n);
1832 int isl_basic_map_involves_dims(
1833 __isl_keep isl_basic_map *bmap,
1834 enum isl_dim_type type, unsigned first, unsigned n);
1835 int isl_map_involves_dims(__isl_keep isl_map *map,
1836 enum isl_dim_type type, unsigned first, unsigned n);
1838 Similarly, the following functions can be used to check whether
1839 a given dimension is involved in any lower or upper bound.
1841 int isl_set_dim_has_any_lower_bound(__isl_keep isl_set *set,
1842 enum isl_dim_type type, unsigned pos);
1843 int isl_set_dim_has_any_upper_bound(__isl_keep isl_set *set,
1844 enum isl_dim_type type, unsigned pos);
1846 Note that these functions return true even if there is a bound on
1847 the dimension on only some of the basic sets of C<set>.
1848 To check if they have a bound for all of the basic sets in C<set>,
1849 use the following functions instead.
1851 int isl_set_dim_has_lower_bound(__isl_keep isl_set *set,
1852 enum isl_dim_type type, unsigned pos);
1853 int isl_set_dim_has_upper_bound(__isl_keep isl_set *set,
1854 enum isl_dim_type type, unsigned pos);
1856 The identifiers or names of the domain and range spaces of a set
1857 or relation can be read off or set using the following functions.
1859 __isl_give isl_set *isl_set_set_tuple_id(
1860 __isl_take isl_set *set, __isl_take isl_id *id);
1861 __isl_give isl_set *isl_set_reset_tuple_id(
1862 __isl_take isl_set *set);
1863 int isl_set_has_tuple_id(__isl_keep isl_set *set);
1864 __isl_give isl_id *isl_set_get_tuple_id(
1865 __isl_keep isl_set *set);
1866 __isl_give isl_map *isl_map_set_tuple_id(
1867 __isl_take isl_map *map, enum isl_dim_type type,
1868 __isl_take isl_id *id);
1869 __isl_give isl_map *isl_map_reset_tuple_id(
1870 __isl_take isl_map *map, enum isl_dim_type type);
1871 int isl_map_has_tuple_id(__isl_keep isl_map *map,
1872 enum isl_dim_type type);
1873 __isl_give isl_id *isl_map_get_tuple_id(
1874 __isl_keep isl_map *map, enum isl_dim_type type);
1876 const char *isl_basic_set_get_tuple_name(
1877 __isl_keep isl_basic_set *bset);
1878 __isl_give isl_basic_set *isl_basic_set_set_tuple_name(
1879 __isl_take isl_basic_set *set, const char *s);
1880 int isl_set_has_tuple_name(__isl_keep isl_set *set);
1881 const char *isl_set_get_tuple_name(
1882 __isl_keep isl_set *set);
1883 const char *isl_basic_map_get_tuple_name(
1884 __isl_keep isl_basic_map *bmap,
1885 enum isl_dim_type type);
1886 __isl_give isl_basic_map *isl_basic_map_set_tuple_name(
1887 __isl_take isl_basic_map *bmap,
1888 enum isl_dim_type type, const char *s);
1889 int isl_map_has_tuple_name(__isl_keep isl_map *map,
1890 enum isl_dim_type type);
1891 const char *isl_map_get_tuple_name(
1892 __isl_keep isl_map *map,
1893 enum isl_dim_type type);
1895 As with C<isl_space_get_tuple_name>, the value returned points to
1896 an internal data structure.
1897 The identifiers, positions or names of individual dimensions can be
1898 read off using the following functions.
1900 __isl_give isl_id *isl_basic_set_get_dim_id(
1901 __isl_keep isl_basic_set *bset,
1902 enum isl_dim_type type, unsigned pos);
1903 __isl_give isl_set *isl_set_set_dim_id(
1904 __isl_take isl_set *set, enum isl_dim_type type,
1905 unsigned pos, __isl_take isl_id *id);
1906 int isl_set_has_dim_id(__isl_keep isl_set *set,
1907 enum isl_dim_type type, unsigned pos);
1908 __isl_give isl_id *isl_set_get_dim_id(
1909 __isl_keep isl_set *set, enum isl_dim_type type,
1911 int isl_basic_map_has_dim_id(
1912 __isl_keep isl_basic_map *bmap,
1913 enum isl_dim_type type, unsigned pos);
1914 __isl_give isl_map *isl_map_set_dim_id(
1915 __isl_take isl_map *map, enum isl_dim_type type,
1916 unsigned pos, __isl_take isl_id *id);
1917 int isl_map_has_dim_id(__isl_keep isl_map *map,
1918 enum isl_dim_type type, unsigned pos);
1919 __isl_give isl_id *isl_map_get_dim_id(
1920 __isl_keep isl_map *map, enum isl_dim_type type,
1923 int isl_set_find_dim_by_id(__isl_keep isl_set *set,
1924 enum isl_dim_type type, __isl_keep isl_id *id);
1925 int isl_map_find_dim_by_id(__isl_keep isl_map *map,
1926 enum isl_dim_type type, __isl_keep isl_id *id);
1927 int isl_set_find_dim_by_name(__isl_keep isl_set *set,
1928 enum isl_dim_type type, const char *name);
1929 int isl_map_find_dim_by_name(__isl_keep isl_map *map,
1930 enum isl_dim_type type, const char *name);
1932 const char *isl_constraint_get_dim_name(
1933 __isl_keep isl_constraint *constraint,
1934 enum isl_dim_type type, unsigned pos);
1935 const char *isl_basic_set_get_dim_name(
1936 __isl_keep isl_basic_set *bset,
1937 enum isl_dim_type type, unsigned pos);
1938 int isl_set_has_dim_name(__isl_keep isl_set *set,
1939 enum isl_dim_type type, unsigned pos);
1940 const char *isl_set_get_dim_name(
1941 __isl_keep isl_set *set,
1942 enum isl_dim_type type, unsigned pos);
1943 const char *isl_basic_map_get_dim_name(
1944 __isl_keep isl_basic_map *bmap,
1945 enum isl_dim_type type, unsigned pos);
1946 int isl_map_has_dim_name(__isl_keep isl_map *map,
1947 enum isl_dim_type type, unsigned pos);
1948 const char *isl_map_get_dim_name(
1949 __isl_keep isl_map *map,
1950 enum isl_dim_type type, unsigned pos);
1952 These functions are mostly useful to obtain the identifiers, positions
1953 or names of the parameters. Identifiers of individual dimensions are
1954 essentially only useful for printing. They are ignored by all other
1955 operations and may not be preserved across those operations.
1959 =head3 Unary Properties
1965 The following functions test whether the given set or relation
1966 contains any integer points. The ``plain'' variants do not perform
1967 any computations, but simply check if the given set or relation
1968 is already known to be empty.
1970 int isl_basic_set_plain_is_empty(__isl_keep isl_basic_set *bset);
1971 int isl_basic_set_is_empty(__isl_keep isl_basic_set *bset);
1972 int isl_set_plain_is_empty(__isl_keep isl_set *set);
1973 int isl_set_is_empty(__isl_keep isl_set *set);
1974 int isl_union_set_is_empty(__isl_keep isl_union_set *uset);
1975 int isl_basic_map_plain_is_empty(__isl_keep isl_basic_map *bmap);
1976 int isl_basic_map_is_empty(__isl_keep isl_basic_map *bmap);
1977 int isl_map_plain_is_empty(__isl_keep isl_map *map);
1978 int isl_map_is_empty(__isl_keep isl_map *map);
1979 int isl_union_map_is_empty(__isl_keep isl_union_map *umap);
1981 =item * Universality
1983 int isl_basic_set_is_universe(__isl_keep isl_basic_set *bset);
1984 int isl_basic_map_is_universe(__isl_keep isl_basic_map *bmap);
1985 int isl_set_plain_is_universe(__isl_keep isl_set *set);
1987 =item * Single-valuedness
1989 int isl_basic_map_is_single_valued(
1990 __isl_keep isl_basic_map *bmap);
1991 int isl_map_plain_is_single_valued(
1992 __isl_keep isl_map *map);
1993 int isl_map_is_single_valued(__isl_keep isl_map *map);
1994 int isl_union_map_is_single_valued(__isl_keep isl_union_map *umap);
1998 int isl_map_plain_is_injective(__isl_keep isl_map *map);
1999 int isl_map_is_injective(__isl_keep isl_map *map);
2000 int isl_union_map_plain_is_injective(
2001 __isl_keep isl_union_map *umap);
2002 int isl_union_map_is_injective(
2003 __isl_keep isl_union_map *umap);
2007 int isl_map_is_bijective(__isl_keep isl_map *map);
2008 int isl_union_map_is_bijective(__isl_keep isl_union_map *umap);
2012 int isl_basic_map_plain_is_fixed(
2013 __isl_keep isl_basic_map *bmap,
2014 enum isl_dim_type type, unsigned pos,
2016 int isl_set_plain_is_fixed(__isl_keep isl_set *set,
2017 enum isl_dim_type type, unsigned pos,
2019 int isl_map_plain_is_fixed(__isl_keep isl_map *map,
2020 enum isl_dim_type type, unsigned pos,
2023 Check if the relation obviously lies on a hyperplane where the given dimension
2024 has a fixed value and if so, return that value in C<*val>.
2028 To check whether a set is a parameter domain, use this function:
2030 int isl_set_is_params(__isl_keep isl_set *set);
2031 int isl_union_set_is_params(
2032 __isl_keep isl_union_set *uset);
2036 The following functions check whether the domain of the given
2037 (basic) set is a wrapped relation.
2039 int isl_basic_set_is_wrapping(
2040 __isl_keep isl_basic_set *bset);
2041 int isl_set_is_wrapping(__isl_keep isl_set *set);
2043 =item * Internal Product
2045 int isl_basic_map_can_zip(
2046 __isl_keep isl_basic_map *bmap);
2047 int isl_map_can_zip(__isl_keep isl_map *map);
2049 Check whether the product of domain and range of the given relation
2051 i.e., whether both domain and range are nested relations.
2055 int isl_basic_map_can_curry(
2056 __isl_keep isl_basic_map *bmap);
2057 int isl_map_can_curry(__isl_keep isl_map *map);
2059 Check whether the domain of the (basic) relation is a wrapped relation.
2061 int isl_basic_map_can_uncurry(
2062 __isl_keep isl_basic_map *bmap);
2063 int isl_map_can_uncurry(__isl_keep isl_map *map);
2065 Check whether the range of the (basic) relation is a wrapped relation.
2069 =head3 Binary Properties
2075 int isl_set_plain_is_equal(__isl_keep isl_set *set1,
2076 __isl_keep isl_set *set2);
2077 int isl_set_is_equal(__isl_keep isl_set *set1,
2078 __isl_keep isl_set *set2);
2079 int isl_union_set_is_equal(
2080 __isl_keep isl_union_set *uset1,
2081 __isl_keep isl_union_set *uset2);
2082 int isl_basic_map_is_equal(
2083 __isl_keep isl_basic_map *bmap1,
2084 __isl_keep isl_basic_map *bmap2);
2085 int isl_map_is_equal(__isl_keep isl_map *map1,
2086 __isl_keep isl_map *map2);
2087 int isl_map_plain_is_equal(__isl_keep isl_map *map1,
2088 __isl_keep isl_map *map2);
2089 int isl_union_map_is_equal(
2090 __isl_keep isl_union_map *umap1,
2091 __isl_keep isl_union_map *umap2);
2093 =item * Disjointness
2095 int isl_set_plain_is_disjoint(__isl_keep isl_set *set1,
2096 __isl_keep isl_set *set2);
2097 int isl_set_is_disjoint(__isl_keep isl_set *set1,
2098 __isl_keep isl_set *set2);
2099 int isl_map_is_disjoint(__isl_keep isl_map *map1,
2100 __isl_keep isl_map *map2);
2104 int isl_basic_set_is_subset(
2105 __isl_keep isl_basic_set *bset1,
2106 __isl_keep isl_basic_set *bset2);
2107 int isl_set_is_subset(__isl_keep isl_set *set1,
2108 __isl_keep isl_set *set2);
2109 int isl_set_is_strict_subset(
2110 __isl_keep isl_set *set1,
2111 __isl_keep isl_set *set2);
2112 int isl_union_set_is_subset(
2113 __isl_keep isl_union_set *uset1,
2114 __isl_keep isl_union_set *uset2);
2115 int isl_union_set_is_strict_subset(
2116 __isl_keep isl_union_set *uset1,
2117 __isl_keep isl_union_set *uset2);
2118 int isl_basic_map_is_subset(
2119 __isl_keep isl_basic_map *bmap1,
2120 __isl_keep isl_basic_map *bmap2);
2121 int isl_basic_map_is_strict_subset(
2122 __isl_keep isl_basic_map *bmap1,
2123 __isl_keep isl_basic_map *bmap2);
2124 int isl_map_is_subset(
2125 __isl_keep isl_map *map1,
2126 __isl_keep isl_map *map2);
2127 int isl_map_is_strict_subset(
2128 __isl_keep isl_map *map1,
2129 __isl_keep isl_map *map2);
2130 int isl_union_map_is_subset(
2131 __isl_keep isl_union_map *umap1,
2132 __isl_keep isl_union_map *umap2);
2133 int isl_union_map_is_strict_subset(
2134 __isl_keep isl_union_map *umap1,
2135 __isl_keep isl_union_map *umap2);
2137 Check whether the first argument is a (strict) subset of the
2142 int isl_set_plain_cmp(__isl_keep isl_set *set1,
2143 __isl_keep isl_set *set2);
2145 This function is useful for sorting C<isl_set>s.
2146 The order depends on the internal representation of the inputs.
2147 The order is fixed over different calls to the function (assuming
2148 the internal representation of the inputs has not changed), but may
2149 change over different versions of C<isl>.
2153 =head2 Unary Operations
2159 __isl_give isl_set *isl_set_complement(
2160 __isl_take isl_set *set);
2161 __isl_give isl_map *isl_map_complement(
2162 __isl_take isl_map *map);
2166 __isl_give isl_basic_map *isl_basic_map_reverse(
2167 __isl_take isl_basic_map *bmap);
2168 __isl_give isl_map *isl_map_reverse(
2169 __isl_take isl_map *map);
2170 __isl_give isl_union_map *isl_union_map_reverse(
2171 __isl_take isl_union_map *umap);
2175 __isl_give isl_basic_set *isl_basic_set_project_out(
2176 __isl_take isl_basic_set *bset,
2177 enum isl_dim_type type, unsigned first, unsigned n);
2178 __isl_give isl_basic_map *isl_basic_map_project_out(
2179 __isl_take isl_basic_map *bmap,
2180 enum isl_dim_type type, unsigned first, unsigned n);
2181 __isl_give isl_set *isl_set_project_out(__isl_take isl_set *set,
2182 enum isl_dim_type type, unsigned first, unsigned n);
2183 __isl_give isl_map *isl_map_project_out(__isl_take isl_map *map,
2184 enum isl_dim_type type, unsigned first, unsigned n);
2185 __isl_give isl_basic_set *isl_basic_set_params(
2186 __isl_take isl_basic_set *bset);
2187 __isl_give isl_basic_set *isl_basic_map_domain(
2188 __isl_take isl_basic_map *bmap);
2189 __isl_give isl_basic_set *isl_basic_map_range(
2190 __isl_take isl_basic_map *bmap);
2191 __isl_give isl_set *isl_set_params(__isl_take isl_set *set);
2192 __isl_give isl_set *isl_map_params(__isl_take isl_map *map);
2193 __isl_give isl_set *isl_map_domain(
2194 __isl_take isl_map *bmap);
2195 __isl_give isl_set *isl_map_range(
2196 __isl_take isl_map *map);
2197 __isl_give isl_set *isl_union_set_params(
2198 __isl_take isl_union_set *uset);
2199 __isl_give isl_set *isl_union_map_params(
2200 __isl_take isl_union_map *umap);
2201 __isl_give isl_union_set *isl_union_map_domain(
2202 __isl_take isl_union_map *umap);
2203 __isl_give isl_union_set *isl_union_map_range(
2204 __isl_take isl_union_map *umap);
2206 __isl_give isl_basic_map *isl_basic_map_domain_map(
2207 __isl_take isl_basic_map *bmap);
2208 __isl_give isl_basic_map *isl_basic_map_range_map(
2209 __isl_take isl_basic_map *bmap);
2210 __isl_give isl_map *isl_map_domain_map(__isl_take isl_map *map);
2211 __isl_give isl_map *isl_map_range_map(__isl_take isl_map *map);
2212 __isl_give isl_union_map *isl_union_map_domain_map(
2213 __isl_take isl_union_map *umap);
2214 __isl_give isl_union_map *isl_union_map_range_map(
2215 __isl_take isl_union_map *umap);
2217 The functions above construct a (basic, regular or union) relation
2218 that maps (a wrapped version of) the input relation to its domain or range.
2222 __isl_give isl_basic_set *isl_basic_set_eliminate(
2223 __isl_take isl_basic_set *bset,
2224 enum isl_dim_type type,
2225 unsigned first, unsigned n);
2226 __isl_give isl_set *isl_set_eliminate(
2227 __isl_take isl_set *set, enum isl_dim_type type,
2228 unsigned first, unsigned n);
2229 __isl_give isl_basic_map *isl_basic_map_eliminate(
2230 __isl_take isl_basic_map *bmap,
2231 enum isl_dim_type type,
2232 unsigned first, unsigned n);
2233 __isl_give isl_map *isl_map_eliminate(
2234 __isl_take isl_map *map, enum isl_dim_type type,
2235 unsigned first, unsigned n);
2237 Eliminate the coefficients for the given dimensions from the constraints,
2238 without removing the dimensions.
2242 __isl_give isl_basic_set *isl_basic_set_fix(
2243 __isl_take isl_basic_set *bset,
2244 enum isl_dim_type type, unsigned pos,
2246 __isl_give isl_basic_set *isl_basic_set_fix_si(
2247 __isl_take isl_basic_set *bset,
2248 enum isl_dim_type type, unsigned pos, int value);
2249 __isl_give isl_set *isl_set_fix(__isl_take isl_set *set,
2250 enum isl_dim_type type, unsigned pos,
2252 __isl_give isl_set *isl_set_fix_si(__isl_take isl_set *set,
2253 enum isl_dim_type type, unsigned pos, int value);
2254 __isl_give isl_basic_map *isl_basic_map_fix_si(
2255 __isl_take isl_basic_map *bmap,
2256 enum isl_dim_type type, unsigned pos, int value);
2257 __isl_give isl_map *isl_map_fix(__isl_take isl_map *map,
2258 enum isl_dim_type type, unsigned pos,
2260 __isl_give isl_map *isl_map_fix_si(__isl_take isl_map *map,
2261 enum isl_dim_type type, unsigned pos, int value);
2263 Intersect the set or relation with the hyperplane where the given
2264 dimension has the fixed given value.
2266 __isl_give isl_basic_map *isl_basic_map_lower_bound_si(
2267 __isl_take isl_basic_map *bmap,
2268 enum isl_dim_type type, unsigned pos, int value);
2269 __isl_give isl_basic_map *isl_basic_map_upper_bound_si(
2270 __isl_take isl_basic_map *bmap,
2271 enum isl_dim_type type, unsigned pos, int value);
2272 __isl_give isl_set *isl_set_lower_bound(
2273 __isl_take isl_set *set,
2274 enum isl_dim_type type, unsigned pos,
2276 __isl_give isl_set *isl_set_lower_bound_si(
2277 __isl_take isl_set *set,
2278 enum isl_dim_type type, unsigned pos, int value);
2279 __isl_give isl_map *isl_map_lower_bound_si(
2280 __isl_take isl_map *map,
2281 enum isl_dim_type type, unsigned pos, int value);
2282 __isl_give isl_set *isl_set_upper_bound(
2283 __isl_take isl_set *set,
2284 enum isl_dim_type type, unsigned pos,
2286 __isl_give isl_set *isl_set_upper_bound_si(
2287 __isl_take isl_set *set,
2288 enum isl_dim_type type, unsigned pos, int value);
2289 __isl_give isl_map *isl_map_upper_bound_si(
2290 __isl_take isl_map *map,
2291 enum isl_dim_type type, unsigned pos, int value);
2293 Intersect the set or relation with the half-space where the given
2294 dimension has a value bounded by the fixed given value.
2296 __isl_give isl_set *isl_set_equate(__isl_take isl_set *set,
2297 enum isl_dim_type type1, int pos1,
2298 enum isl_dim_type type2, int pos2);
2299 __isl_give isl_basic_map *isl_basic_map_equate(
2300 __isl_take isl_basic_map *bmap,
2301 enum isl_dim_type type1, int pos1,
2302 enum isl_dim_type type2, int pos2);
2303 __isl_give isl_map *isl_map_equate(__isl_take isl_map *map,
2304 enum isl_dim_type type1, int pos1,
2305 enum isl_dim_type type2, int pos2);
2307 Intersect the set or relation with the hyperplane where the given
2308 dimensions are equal to each other.
2310 __isl_give isl_map *isl_map_oppose(__isl_take isl_map *map,
2311 enum isl_dim_type type1, int pos1,
2312 enum isl_dim_type type2, int pos2);
2314 Intersect the relation with the hyperplane where the given
2315 dimensions have opposite values.
2317 __isl_give isl_basic_map *isl_basic_map_order_ge(
2318 __isl_take isl_basic_map *bmap,
2319 enum isl_dim_type type1, int pos1,
2320 enum isl_dim_type type2, int pos2);
2321 __isl_give isl_map *isl_map_order_lt(__isl_take isl_map *map,
2322 enum isl_dim_type type1, int pos1,
2323 enum isl_dim_type type2, int pos2);
2324 __isl_give isl_basic_map *isl_basic_map_order_gt(
2325 __isl_take isl_basic_map *bmap,
2326 enum isl_dim_type type1, int pos1,
2327 enum isl_dim_type type2, int pos2);
2328 __isl_give isl_map *isl_map_order_gt(__isl_take isl_map *map,
2329 enum isl_dim_type type1, int pos1,
2330 enum isl_dim_type type2, int pos2);
2332 Intersect the relation with the half-space where the given
2333 dimensions satisfy the given ordering.
2337 __isl_give isl_map *isl_set_identity(
2338 __isl_take isl_set *set);
2339 __isl_give isl_union_map *isl_union_set_identity(
2340 __isl_take isl_union_set *uset);
2342 Construct an identity relation on the given (union) set.
2346 __isl_give isl_basic_set *isl_basic_map_deltas(
2347 __isl_take isl_basic_map *bmap);
2348 __isl_give isl_set *isl_map_deltas(__isl_take isl_map *map);
2349 __isl_give isl_union_set *isl_union_map_deltas(
2350 __isl_take isl_union_map *umap);
2352 These functions return a (basic) set containing the differences
2353 between image elements and corresponding domain elements in the input.
2355 __isl_give isl_basic_map *isl_basic_map_deltas_map(
2356 __isl_take isl_basic_map *bmap);
2357 __isl_give isl_map *isl_map_deltas_map(
2358 __isl_take isl_map *map);
2359 __isl_give isl_union_map *isl_union_map_deltas_map(
2360 __isl_take isl_union_map *umap);
2362 The functions above construct a (basic, regular or union) relation
2363 that maps (a wrapped version of) the input relation to its delta set.
2367 Simplify the representation of a set or relation by trying
2368 to combine pairs of basic sets or relations into a single
2369 basic set or relation.
2371 __isl_give isl_set *isl_set_coalesce(__isl_take isl_set *set);
2372 __isl_give isl_map *isl_map_coalesce(__isl_take isl_map *map);
2373 __isl_give isl_union_set *isl_union_set_coalesce(
2374 __isl_take isl_union_set *uset);
2375 __isl_give isl_union_map *isl_union_map_coalesce(
2376 __isl_take isl_union_map *umap);
2378 One of the methods for combining pairs of basic sets or relations
2379 can result in coefficients that are much larger than those that appear
2380 in the constraints of the input. By default, the coefficients are
2381 not allowed to grow larger, but this can be changed by unsetting
2382 the following option.
2384 int isl_options_set_coalesce_bounded_wrapping(
2385 isl_ctx *ctx, int val);
2386 int isl_options_get_coalesce_bounded_wrapping(
2389 =item * Detecting equalities
2391 __isl_give isl_basic_set *isl_basic_set_detect_equalities(
2392 __isl_take isl_basic_set *bset);
2393 __isl_give isl_basic_map *isl_basic_map_detect_equalities(
2394 __isl_take isl_basic_map *bmap);
2395 __isl_give isl_set *isl_set_detect_equalities(
2396 __isl_take isl_set *set);
2397 __isl_give isl_map *isl_map_detect_equalities(
2398 __isl_take isl_map *map);
2399 __isl_give isl_union_set *isl_union_set_detect_equalities(
2400 __isl_take isl_union_set *uset);
2401 __isl_give isl_union_map *isl_union_map_detect_equalities(
2402 __isl_take isl_union_map *umap);
2404 Simplify the representation of a set or relation by detecting implicit
2407 =item * Removing redundant constraints
2409 __isl_give isl_basic_set *isl_basic_set_remove_redundancies(
2410 __isl_take isl_basic_set *bset);
2411 __isl_give isl_set *isl_set_remove_redundancies(
2412 __isl_take isl_set *set);
2413 __isl_give isl_basic_map *isl_basic_map_remove_redundancies(
2414 __isl_take isl_basic_map *bmap);
2415 __isl_give isl_map *isl_map_remove_redundancies(
2416 __isl_take isl_map *map);
2420 __isl_give isl_basic_set *isl_set_convex_hull(
2421 __isl_take isl_set *set);
2422 __isl_give isl_basic_map *isl_map_convex_hull(
2423 __isl_take isl_map *map);
2425 If the input set or relation has any existentially quantified
2426 variables, then the result of these operations is currently undefined.
2430 __isl_give isl_basic_set *
2431 isl_set_unshifted_simple_hull(
2432 __isl_take isl_set *set);
2433 __isl_give isl_basic_map *
2434 isl_map_unshifted_simple_hull(
2435 __isl_take isl_map *map);
2436 __isl_give isl_basic_set *isl_set_simple_hull(
2437 __isl_take isl_set *set);
2438 __isl_give isl_basic_map *isl_map_simple_hull(
2439 __isl_take isl_map *map);
2440 __isl_give isl_union_map *isl_union_map_simple_hull(
2441 __isl_take isl_union_map *umap);
2443 These functions compute a single basic set or relation
2444 that contains the whole input set or relation.
2445 In particular, the output is described by translates
2446 of the constraints describing the basic sets or relations in the input.
2447 In case of C<isl_set_unshifted_simple_hull>, only the original
2448 constraints are used, without any translation.
2452 (See \autoref{s:simple hull}.)
2458 __isl_give isl_basic_set *isl_basic_set_affine_hull(
2459 __isl_take isl_basic_set *bset);
2460 __isl_give isl_basic_set *isl_set_affine_hull(
2461 __isl_take isl_set *set);
2462 __isl_give isl_union_set *isl_union_set_affine_hull(
2463 __isl_take isl_union_set *uset);
2464 __isl_give isl_basic_map *isl_basic_map_affine_hull(
2465 __isl_take isl_basic_map *bmap);
2466 __isl_give isl_basic_map *isl_map_affine_hull(
2467 __isl_take isl_map *map);
2468 __isl_give isl_union_map *isl_union_map_affine_hull(
2469 __isl_take isl_union_map *umap);
2471 In case of union sets and relations, the affine hull is computed
2474 =item * Polyhedral hull
2476 __isl_give isl_basic_set *isl_set_polyhedral_hull(
2477 __isl_take isl_set *set);
2478 __isl_give isl_basic_map *isl_map_polyhedral_hull(
2479 __isl_take isl_map *map);
2480 __isl_give isl_union_set *isl_union_set_polyhedral_hull(
2481 __isl_take isl_union_set *uset);
2482 __isl_give isl_union_map *isl_union_map_polyhedral_hull(
2483 __isl_take isl_union_map *umap);
2485 These functions compute a single basic set or relation
2486 not involving any existentially quantified variables
2487 that contains the whole input set or relation.
2488 In case of union sets and relations, the polyhedral hull is computed
2491 =item * Other approximations
2493 __isl_give isl_basic_set *
2494 isl_basic_set_drop_constraints_involving_dims(
2495 __isl_take isl_basic_set *bset,
2496 enum isl_dim_type type,
2497 unsigned first, unsigned n);
2498 __isl_give isl_basic_map *
2499 isl_basic_map_drop_constraints_involving_dims(
2500 __isl_take isl_basic_map *bmap,
2501 enum isl_dim_type type,
2502 unsigned first, unsigned n);
2503 __isl_give isl_basic_set *
2504 isl_basic_set_drop_constraints_not_involving_dims(
2505 __isl_take isl_basic_set *bset,
2506 enum isl_dim_type type,
2507 unsigned first, unsigned n);
2508 __isl_give isl_set *
2509 isl_set_drop_constraints_involving_dims(
2510 __isl_take isl_set *set,
2511 enum isl_dim_type type,
2512 unsigned first, unsigned n);
2513 __isl_give isl_map *
2514 isl_map_drop_constraints_involving_dims(
2515 __isl_take isl_map *map,
2516 enum isl_dim_type type,
2517 unsigned first, unsigned n);
2519 These functions drop any constraints (not) involving the specified dimensions.
2520 Note that the result depends on the representation of the input.
2524 __isl_give isl_basic_set *isl_basic_set_sample(
2525 __isl_take isl_basic_set *bset);
2526 __isl_give isl_basic_set *isl_set_sample(
2527 __isl_take isl_set *set);
2528 __isl_give isl_basic_map *isl_basic_map_sample(
2529 __isl_take isl_basic_map *bmap);
2530 __isl_give isl_basic_map *isl_map_sample(
2531 __isl_take isl_map *map);
2533 If the input (basic) set or relation is non-empty, then return
2534 a singleton subset of the input. Otherwise, return an empty set.
2536 =item * Optimization
2538 #include <isl/ilp.h>
2539 enum isl_lp_result isl_basic_set_max(
2540 __isl_keep isl_basic_set *bset,
2541 __isl_keep isl_aff *obj, isl_int *opt)
2542 enum isl_lp_result isl_set_min(__isl_keep isl_set *set,
2543 __isl_keep isl_aff *obj, isl_int *opt);
2544 enum isl_lp_result isl_set_max(__isl_keep isl_set *set,
2545 __isl_keep isl_aff *obj, isl_int *opt);
2547 Compute the minimum or maximum of the integer affine expression C<obj>
2548 over the points in C<set>, returning the result in C<opt>.
2549 The return value may be one of C<isl_lp_error>,
2550 C<isl_lp_ok>, C<isl_lp_unbounded> or C<isl_lp_empty>.
2552 =item * Parametric optimization
2554 __isl_give isl_pw_aff *isl_set_dim_min(
2555 __isl_take isl_set *set, int pos);
2556 __isl_give isl_pw_aff *isl_set_dim_max(
2557 __isl_take isl_set *set, int pos);
2558 __isl_give isl_pw_aff *isl_map_dim_max(
2559 __isl_take isl_map *map, int pos);
2561 Compute the minimum or maximum of the given set or output dimension
2562 as a function of the parameters (and input dimensions), but independently
2563 of the other set or output dimensions.
2564 For lexicographic optimization, see L<"Lexicographic Optimization">.
2568 The following functions compute either the set of (rational) coefficient
2569 values of valid constraints for the given set or the set of (rational)
2570 values satisfying the constraints with coefficients from the given set.
2571 Internally, these two sets of functions perform essentially the
2572 same operations, except that the set of coefficients is assumed to
2573 be a cone, while the set of values may be any polyhedron.
2574 The current implementation is based on the Farkas lemma and
2575 Fourier-Motzkin elimination, but this may change or be made optional
2576 in future. In particular, future implementations may use different
2577 dualization algorithms or skip the elimination step.
2579 __isl_give isl_basic_set *isl_basic_set_coefficients(
2580 __isl_take isl_basic_set *bset);
2581 __isl_give isl_basic_set *isl_set_coefficients(
2582 __isl_take isl_set *set);
2583 __isl_give isl_union_set *isl_union_set_coefficients(
2584 __isl_take isl_union_set *bset);
2585 __isl_give isl_basic_set *isl_basic_set_solutions(
2586 __isl_take isl_basic_set *bset);
2587 __isl_give isl_basic_set *isl_set_solutions(
2588 __isl_take isl_set *set);
2589 __isl_give isl_union_set *isl_union_set_solutions(
2590 __isl_take isl_union_set *bset);
2594 __isl_give isl_map *isl_map_fixed_power(
2595 __isl_take isl_map *map, isl_int exp);
2596 __isl_give isl_union_map *isl_union_map_fixed_power(
2597 __isl_take isl_union_map *umap, isl_int exp);
2599 Compute the given power of C<map>, where C<exp> is assumed to be non-zero.
2600 If the exponent C<exp> is negative, then the -C<exp> th power of the inverse
2601 of C<map> is computed.
2603 __isl_give isl_map *isl_map_power(__isl_take isl_map *map,
2605 __isl_give isl_union_map *isl_union_map_power(
2606 __isl_take isl_union_map *umap, int *exact);
2608 Compute a parametric representation for all positive powers I<k> of C<map>.
2609 The result maps I<k> to a nested relation corresponding to the
2610 I<k>th power of C<map>.
2611 The result may be an overapproximation. If the result is known to be exact,
2612 then C<*exact> is set to C<1>.
2614 =item * Transitive closure
2616 __isl_give isl_map *isl_map_transitive_closure(
2617 __isl_take isl_map *map, int *exact);
2618 __isl_give isl_union_map *isl_union_map_transitive_closure(
2619 __isl_take isl_union_map *umap, int *exact);
2621 Compute the transitive closure of C<map>.
2622 The result may be an overapproximation. If the result is known to be exact,
2623 then C<*exact> is set to C<1>.
2625 =item * Reaching path lengths
2627 __isl_give isl_map *isl_map_reaching_path_lengths(
2628 __isl_take isl_map *map, int *exact);
2630 Compute a relation that maps each element in the range of C<map>
2631 to the lengths of all paths composed of edges in C<map> that
2632 end up in the given element.
2633 The result may be an overapproximation. If the result is known to be exact,
2634 then C<*exact> is set to C<1>.
2635 To compute the I<maximal> path length, the resulting relation
2636 should be postprocessed by C<isl_map_lexmax>.
2637 In particular, if the input relation is a dependence relation
2638 (mapping sources to sinks), then the maximal path length corresponds
2639 to the free schedule.
2640 Note, however, that C<isl_map_lexmax> expects the maximum to be
2641 finite, so if the path lengths are unbounded (possibly due to
2642 the overapproximation), then you will get an error message.
2646 __isl_give isl_basic_set *isl_basic_map_wrap(
2647 __isl_take isl_basic_map *bmap);
2648 __isl_give isl_set *isl_map_wrap(
2649 __isl_take isl_map *map);
2650 __isl_give isl_union_set *isl_union_map_wrap(
2651 __isl_take isl_union_map *umap);
2652 __isl_give isl_basic_map *isl_basic_set_unwrap(
2653 __isl_take isl_basic_set *bset);
2654 __isl_give isl_map *isl_set_unwrap(
2655 __isl_take isl_set *set);
2656 __isl_give isl_union_map *isl_union_set_unwrap(
2657 __isl_take isl_union_set *uset);
2661 Remove any internal structure of domain (and range) of the given
2662 set or relation. If there is any such internal structure in the input,
2663 then the name of the space is also removed.
2665 __isl_give isl_basic_set *isl_basic_set_flatten(
2666 __isl_take isl_basic_set *bset);
2667 __isl_give isl_set *isl_set_flatten(
2668 __isl_take isl_set *set);
2669 __isl_give isl_basic_map *isl_basic_map_flatten_domain(
2670 __isl_take isl_basic_map *bmap);
2671 __isl_give isl_basic_map *isl_basic_map_flatten_range(
2672 __isl_take isl_basic_map *bmap);
2673 __isl_give isl_map *isl_map_flatten_range(
2674 __isl_take isl_map *map);
2675 __isl_give isl_map *isl_map_flatten_domain(
2676 __isl_take isl_map *map);
2677 __isl_give isl_basic_map *isl_basic_map_flatten(
2678 __isl_take isl_basic_map *bmap);
2679 __isl_give isl_map *isl_map_flatten(
2680 __isl_take isl_map *map);
2682 __isl_give isl_map *isl_set_flatten_map(
2683 __isl_take isl_set *set);
2685 The function above constructs a relation
2686 that maps the input set to a flattened version of the set.
2690 Lift the input set to a space with extra dimensions corresponding
2691 to the existentially quantified variables in the input.
2692 In particular, the result lives in a wrapped map where the domain
2693 is the original space and the range corresponds to the original
2694 existentially quantified variables.
2696 __isl_give isl_basic_set *isl_basic_set_lift(
2697 __isl_take isl_basic_set *bset);
2698 __isl_give isl_set *isl_set_lift(
2699 __isl_take isl_set *set);
2700 __isl_give isl_union_set *isl_union_set_lift(
2701 __isl_take isl_union_set *uset);
2703 Given a local space that contains the existentially quantified
2704 variables of a set, a basic relation that, when applied to
2705 a basic set, has essentially the same effect as C<isl_basic_set_lift>,
2706 can be constructed using the following function.
2708 #include <isl/local_space.h>
2709 __isl_give isl_basic_map *isl_local_space_lifting(
2710 __isl_take isl_local_space *ls);
2712 =item * Internal Product
2714 __isl_give isl_basic_map *isl_basic_map_zip(
2715 __isl_take isl_basic_map *bmap);
2716 __isl_give isl_map *isl_map_zip(
2717 __isl_take isl_map *map);
2718 __isl_give isl_union_map *isl_union_map_zip(
2719 __isl_take isl_union_map *umap);
2721 Given a relation with nested relations for domain and range,
2722 interchange the range of the domain with the domain of the range.
2726 __isl_give isl_basic_map *isl_basic_map_curry(
2727 __isl_take isl_basic_map *bmap);
2728 __isl_give isl_basic_map *isl_basic_map_uncurry(
2729 __isl_take isl_basic_map *bmap);
2730 __isl_give isl_map *isl_map_curry(
2731 __isl_take isl_map *map);
2732 __isl_give isl_map *isl_map_uncurry(
2733 __isl_take isl_map *map);
2734 __isl_give isl_union_map *isl_union_map_curry(
2735 __isl_take isl_union_map *umap);
2736 __isl_give isl_union_map *isl_union_map_uncurry(
2737 __isl_take isl_union_map *umap);
2739 Given a relation with a nested relation for domain,
2740 the C<curry> functions
2741 move the range of the nested relation out of the domain
2742 and use it as the domain of a nested relation in the range,
2743 with the original range as range of this nested relation.
2744 The C<uncurry> functions perform the inverse operation.
2746 =item * Aligning parameters
2748 __isl_give isl_basic_set *isl_basic_set_align_params(
2749 __isl_take isl_basic_set *bset,
2750 __isl_take isl_space *model);
2751 __isl_give isl_set *isl_set_align_params(
2752 __isl_take isl_set *set,
2753 __isl_take isl_space *model);
2754 __isl_give isl_basic_map *isl_basic_map_align_params(
2755 __isl_take isl_basic_map *bmap,
2756 __isl_take isl_space *model);
2757 __isl_give isl_map *isl_map_align_params(
2758 __isl_take isl_map *map,
2759 __isl_take isl_space *model);
2761 Change the order of the parameters of the given set or relation
2762 such that the first parameters match those of C<model>.
2763 This may involve the introduction of extra parameters.
2764 All parameters need to be named.
2766 =item * Dimension manipulation
2768 __isl_give isl_basic_set *isl_basic_set_add_dims(
2769 __isl_take isl_basic_set *bset,
2770 enum isl_dim_type type, unsigned n);
2771 __isl_give isl_set *isl_set_add_dims(
2772 __isl_take isl_set *set,
2773 enum isl_dim_type type, unsigned n);
2774 __isl_give isl_map *isl_map_add_dims(
2775 __isl_take isl_map *map,
2776 enum isl_dim_type type, unsigned n);
2777 __isl_give isl_basic_set *isl_basic_set_insert_dims(
2778 __isl_take isl_basic_set *bset,
2779 enum isl_dim_type type, unsigned pos,
2781 __isl_give isl_basic_map *isl_basic_map_insert_dims(
2782 __isl_take isl_basic_map *bmap,
2783 enum isl_dim_type type, unsigned pos,
2785 __isl_give isl_set *isl_set_insert_dims(
2786 __isl_take isl_set *set,
2787 enum isl_dim_type type, unsigned pos, unsigned n);
2788 __isl_give isl_map *isl_map_insert_dims(
2789 __isl_take isl_map *map,
2790 enum isl_dim_type type, unsigned pos, unsigned n);
2791 __isl_give isl_basic_set *isl_basic_set_move_dims(
2792 __isl_take isl_basic_set *bset,
2793 enum isl_dim_type dst_type, unsigned dst_pos,
2794 enum isl_dim_type src_type, unsigned src_pos,
2796 __isl_give isl_basic_map *isl_basic_map_move_dims(
2797 __isl_take isl_basic_map *bmap,
2798 enum isl_dim_type dst_type, unsigned dst_pos,
2799 enum isl_dim_type src_type, unsigned src_pos,
2801 __isl_give isl_set *isl_set_move_dims(
2802 __isl_take isl_set *set,
2803 enum isl_dim_type dst_type, unsigned dst_pos,
2804 enum isl_dim_type src_type, unsigned src_pos,
2806 __isl_give isl_map *isl_map_move_dims(
2807 __isl_take isl_map *map,
2808 enum isl_dim_type dst_type, unsigned dst_pos,
2809 enum isl_dim_type src_type, unsigned src_pos,
2812 It is usually not advisable to directly change the (input or output)
2813 space of a set or a relation as this removes the name and the internal
2814 structure of the space. However, the above functions can be useful
2815 to add new parameters, assuming
2816 C<isl_set_align_params> and C<isl_map_align_params>
2821 =head2 Binary Operations
2823 The two arguments of a binary operation not only need to live
2824 in the same C<isl_ctx>, they currently also need to have
2825 the same (number of) parameters.
2827 =head3 Basic Operations
2831 =item * Intersection
2833 __isl_give isl_basic_set *isl_basic_set_intersect_params(
2834 __isl_take isl_basic_set *bset1,
2835 __isl_take isl_basic_set *bset2);
2836 __isl_give isl_basic_set *isl_basic_set_intersect(
2837 __isl_take isl_basic_set *bset1,
2838 __isl_take isl_basic_set *bset2);
2839 __isl_give isl_set *isl_set_intersect_params(
2840 __isl_take isl_set *set,
2841 __isl_take isl_set *params);
2842 __isl_give isl_set *isl_set_intersect(
2843 __isl_take isl_set *set1,
2844 __isl_take isl_set *set2);
2845 __isl_give isl_union_set *isl_union_set_intersect_params(
2846 __isl_take isl_union_set *uset,
2847 __isl_take isl_set *set);
2848 __isl_give isl_union_map *isl_union_map_intersect_params(
2849 __isl_take isl_union_map *umap,
2850 __isl_take isl_set *set);
2851 __isl_give isl_union_set *isl_union_set_intersect(
2852 __isl_take isl_union_set *uset1,
2853 __isl_take isl_union_set *uset2);
2854 __isl_give isl_basic_map *isl_basic_map_intersect_domain(
2855 __isl_take isl_basic_map *bmap,
2856 __isl_take isl_basic_set *bset);
2857 __isl_give isl_basic_map *isl_basic_map_intersect_range(
2858 __isl_take isl_basic_map *bmap,
2859 __isl_take isl_basic_set *bset);
2860 __isl_give isl_basic_map *isl_basic_map_intersect(
2861 __isl_take isl_basic_map *bmap1,
2862 __isl_take isl_basic_map *bmap2);
2863 __isl_give isl_map *isl_map_intersect_params(
2864 __isl_take isl_map *map,
2865 __isl_take isl_set *params);
2866 __isl_give isl_map *isl_map_intersect_domain(
2867 __isl_take isl_map *map,
2868 __isl_take isl_set *set);
2869 __isl_give isl_map *isl_map_intersect_range(
2870 __isl_take isl_map *map,
2871 __isl_take isl_set *set);
2872 __isl_give isl_map *isl_map_intersect(
2873 __isl_take isl_map *map1,
2874 __isl_take isl_map *map2);
2875 __isl_give isl_union_map *isl_union_map_intersect_domain(
2876 __isl_take isl_union_map *umap,
2877 __isl_take isl_union_set *uset);
2878 __isl_give isl_union_map *isl_union_map_intersect_range(
2879 __isl_take isl_union_map *umap,
2880 __isl_take isl_union_set *uset);
2881 __isl_give isl_union_map *isl_union_map_intersect(
2882 __isl_take isl_union_map *umap1,
2883 __isl_take isl_union_map *umap2);
2885 The second argument to the C<_params> functions needs to be
2886 a parametric (basic) set. For the other functions, a parametric set
2887 for either argument is only allowed if the other argument is
2888 a parametric set as well.
2892 __isl_give isl_set *isl_basic_set_union(
2893 __isl_take isl_basic_set *bset1,
2894 __isl_take isl_basic_set *bset2);
2895 __isl_give isl_map *isl_basic_map_union(
2896 __isl_take isl_basic_map *bmap1,
2897 __isl_take isl_basic_map *bmap2);
2898 __isl_give isl_set *isl_set_union(
2899 __isl_take isl_set *set1,
2900 __isl_take isl_set *set2);
2901 __isl_give isl_map *isl_map_union(
2902 __isl_take isl_map *map1,
2903 __isl_take isl_map *map2);
2904 __isl_give isl_union_set *isl_union_set_union(
2905 __isl_take isl_union_set *uset1,
2906 __isl_take isl_union_set *uset2);
2907 __isl_give isl_union_map *isl_union_map_union(
2908 __isl_take isl_union_map *umap1,
2909 __isl_take isl_union_map *umap2);
2911 =item * Set difference
2913 __isl_give isl_set *isl_set_subtract(
2914 __isl_take isl_set *set1,
2915 __isl_take isl_set *set2);
2916 __isl_give isl_map *isl_map_subtract(
2917 __isl_take isl_map *map1,
2918 __isl_take isl_map *map2);
2919 __isl_give isl_map *isl_map_subtract_domain(
2920 __isl_take isl_map *map,
2921 __isl_take isl_set *dom);
2922 __isl_give isl_map *isl_map_subtract_range(
2923 __isl_take isl_map *map,
2924 __isl_take isl_set *dom);
2925 __isl_give isl_union_set *isl_union_set_subtract(
2926 __isl_take isl_union_set *uset1,
2927 __isl_take isl_union_set *uset2);
2928 __isl_give isl_union_map *isl_union_map_subtract(
2929 __isl_take isl_union_map *umap1,
2930 __isl_take isl_union_map *umap2);
2931 __isl_give isl_union_map *isl_union_map_subtract_domain(
2932 __isl_take isl_union_map *umap,
2933 __isl_take isl_union_set *dom);
2934 __isl_give isl_union_map *isl_union_map_subtract_range(
2935 __isl_take isl_union_map *umap,
2936 __isl_take isl_union_set *dom);
2940 __isl_give isl_basic_set *isl_basic_set_apply(
2941 __isl_take isl_basic_set *bset,
2942 __isl_take isl_basic_map *bmap);
2943 __isl_give isl_set *isl_set_apply(
2944 __isl_take isl_set *set,
2945 __isl_take isl_map *map);
2946 __isl_give isl_union_set *isl_union_set_apply(
2947 __isl_take isl_union_set *uset,
2948 __isl_take isl_union_map *umap);
2949 __isl_give isl_basic_map *isl_basic_map_apply_domain(
2950 __isl_take isl_basic_map *bmap1,
2951 __isl_take isl_basic_map *bmap2);
2952 __isl_give isl_basic_map *isl_basic_map_apply_range(
2953 __isl_take isl_basic_map *bmap1,
2954 __isl_take isl_basic_map *bmap2);
2955 __isl_give isl_map *isl_map_apply_domain(
2956 __isl_take isl_map *map1,
2957 __isl_take isl_map *map2);
2958 __isl_give isl_union_map *isl_union_map_apply_domain(
2959 __isl_take isl_union_map *umap1,
2960 __isl_take isl_union_map *umap2);
2961 __isl_give isl_map *isl_map_apply_range(
2962 __isl_take isl_map *map1,
2963 __isl_take isl_map *map2);
2964 __isl_give isl_union_map *isl_union_map_apply_range(
2965 __isl_take isl_union_map *umap1,
2966 __isl_take isl_union_map *umap2);
2970 __isl_give isl_basic_set *
2971 isl_basic_set_preimage_multi_aff(
2972 __isl_take isl_basic_set *bset,
2973 __isl_take isl_multi_aff *ma);
2974 __isl_give isl_set *isl_set_preimage_multi_aff(
2975 __isl_take isl_set *set,
2976 __isl_take isl_multi_aff *ma);
2977 __isl_give isl_set *isl_set_preimage_pw_multi_aff(
2978 __isl_take isl_set *set,
2979 __isl_take isl_pw_multi_aff *pma);
2980 __isl_give isl_map *isl_map_preimage_domain_multi_aff(
2981 __isl_take isl_map *map,
2982 __isl_take isl_multi_aff *ma);
2983 __isl_give isl_union_map *
2984 isl_union_map_preimage_domain_multi_aff(
2985 __isl_take isl_union_map *umap,
2986 __isl_take isl_multi_aff *ma);
2988 These functions compute the preimage of the given set or map domain under
2989 the given function. In other words, the expression is plugged
2990 into the set description or into the domain of the map.
2991 Objects of types C<isl_multi_aff> and C<isl_pw_multi_aff> are described in
2992 L</"Piecewise Multiple Quasi Affine Expressions">.
2994 =item * Cartesian Product
2996 __isl_give isl_set *isl_set_product(
2997 __isl_take isl_set *set1,
2998 __isl_take isl_set *set2);
2999 __isl_give isl_union_set *isl_union_set_product(
3000 __isl_take isl_union_set *uset1,
3001 __isl_take isl_union_set *uset2);
3002 __isl_give isl_basic_map *isl_basic_map_domain_product(
3003 __isl_take isl_basic_map *bmap1,
3004 __isl_take isl_basic_map *bmap2);
3005 __isl_give isl_basic_map *isl_basic_map_range_product(
3006 __isl_take isl_basic_map *bmap1,
3007 __isl_take isl_basic_map *bmap2);
3008 __isl_give isl_basic_map *isl_basic_map_product(
3009 __isl_take isl_basic_map *bmap1,
3010 __isl_take isl_basic_map *bmap2);
3011 __isl_give isl_map *isl_map_domain_product(
3012 __isl_take isl_map *map1,
3013 __isl_take isl_map *map2);
3014 __isl_give isl_map *isl_map_range_product(
3015 __isl_take isl_map *map1,
3016 __isl_take isl_map *map2);
3017 __isl_give isl_union_map *isl_union_map_domain_product(
3018 __isl_take isl_union_map *umap1,
3019 __isl_take isl_union_map *umap2);
3020 __isl_give isl_union_map *isl_union_map_range_product(
3021 __isl_take isl_union_map *umap1,
3022 __isl_take isl_union_map *umap2);
3023 __isl_give isl_map *isl_map_product(
3024 __isl_take isl_map *map1,
3025 __isl_take isl_map *map2);
3026 __isl_give isl_union_map *isl_union_map_product(
3027 __isl_take isl_union_map *umap1,
3028 __isl_take isl_union_map *umap2);
3030 The above functions compute the cross product of the given
3031 sets or relations. The domains and ranges of the results
3032 are wrapped maps between domains and ranges of the inputs.
3033 To obtain a ``flat'' product, use the following functions
3036 __isl_give isl_basic_set *isl_basic_set_flat_product(
3037 __isl_take isl_basic_set *bset1,
3038 __isl_take isl_basic_set *bset2);
3039 __isl_give isl_set *isl_set_flat_product(
3040 __isl_take isl_set *set1,
3041 __isl_take isl_set *set2);
3042 __isl_give isl_basic_map *isl_basic_map_flat_range_product(
3043 __isl_take isl_basic_map *bmap1,
3044 __isl_take isl_basic_map *bmap2);
3045 __isl_give isl_map *isl_map_flat_domain_product(
3046 __isl_take isl_map *map1,
3047 __isl_take isl_map *map2);
3048 __isl_give isl_map *isl_map_flat_range_product(
3049 __isl_take isl_map *map1,
3050 __isl_take isl_map *map2);
3051 __isl_give isl_union_map *isl_union_map_flat_range_product(
3052 __isl_take isl_union_map *umap1,
3053 __isl_take isl_union_map *umap2);
3054 __isl_give isl_basic_map *isl_basic_map_flat_product(
3055 __isl_take isl_basic_map *bmap1,
3056 __isl_take isl_basic_map *bmap2);
3057 __isl_give isl_map *isl_map_flat_product(
3058 __isl_take isl_map *map1,
3059 __isl_take isl_map *map2);
3061 =item * Simplification
3063 __isl_give isl_basic_set *isl_basic_set_gist(
3064 __isl_take isl_basic_set *bset,
3065 __isl_take isl_basic_set *context);
3066 __isl_give isl_set *isl_set_gist(__isl_take isl_set *set,
3067 __isl_take isl_set *context);
3068 __isl_give isl_set *isl_set_gist_params(
3069 __isl_take isl_set *set,
3070 __isl_take isl_set *context);
3071 __isl_give isl_union_set *isl_union_set_gist(
3072 __isl_take isl_union_set *uset,
3073 __isl_take isl_union_set *context);
3074 __isl_give isl_union_set *isl_union_set_gist_params(
3075 __isl_take isl_union_set *uset,
3076 __isl_take isl_set *set);
3077 __isl_give isl_basic_map *isl_basic_map_gist(
3078 __isl_take isl_basic_map *bmap,
3079 __isl_take isl_basic_map *context);
3080 __isl_give isl_map *isl_map_gist(__isl_take isl_map *map,
3081 __isl_take isl_map *context);
3082 __isl_give isl_map *isl_map_gist_params(
3083 __isl_take isl_map *map,
3084 __isl_take isl_set *context);
3085 __isl_give isl_map *isl_map_gist_domain(
3086 __isl_take isl_map *map,
3087 __isl_take isl_set *context);
3088 __isl_give isl_map *isl_map_gist_range(
3089 __isl_take isl_map *map,
3090 __isl_take isl_set *context);
3091 __isl_give isl_union_map *isl_union_map_gist(
3092 __isl_take isl_union_map *umap,
3093 __isl_take isl_union_map *context);
3094 __isl_give isl_union_map *isl_union_map_gist_params(
3095 __isl_take isl_union_map *umap,
3096 __isl_take isl_set *set);
3097 __isl_give isl_union_map *isl_union_map_gist_domain(
3098 __isl_take isl_union_map *umap,
3099 __isl_take isl_union_set *uset);
3100 __isl_give isl_union_map *isl_union_map_gist_range(
3101 __isl_take isl_union_map *umap,
3102 __isl_take isl_union_set *uset);
3104 The gist operation returns a set or relation that has the
3105 same intersection with the context as the input set or relation.
3106 Any implicit equality in the intersection is made explicit in the result,
3107 while all inequalities that are redundant with respect to the intersection
3109 In case of union sets and relations, the gist operation is performed
3114 =head3 Lexicographic Optimization
3116 Given a (basic) set C<set> (or C<bset>) and a zero-dimensional domain C<dom>,
3117 the following functions
3118 compute a set that contains the lexicographic minimum or maximum
3119 of the elements in C<set> (or C<bset>) for those values of the parameters
3120 that satisfy C<dom>.
3121 If C<empty> is not C<NULL>, then C<*empty> is assigned a set
3122 that contains the parameter values in C<dom> for which C<set> (or C<bset>)
3124 In other words, the union of the parameter values
3125 for which the result is non-empty and of C<*empty>
3128 __isl_give isl_set *isl_basic_set_partial_lexmin(
3129 __isl_take isl_basic_set *bset,
3130 __isl_take isl_basic_set *dom,
3131 __isl_give isl_set **empty);
3132 __isl_give isl_set *isl_basic_set_partial_lexmax(
3133 __isl_take isl_basic_set *bset,
3134 __isl_take isl_basic_set *dom,
3135 __isl_give isl_set **empty);
3136 __isl_give isl_set *isl_set_partial_lexmin(
3137 __isl_take isl_set *set, __isl_take isl_set *dom,
3138 __isl_give isl_set **empty);
3139 __isl_give isl_set *isl_set_partial_lexmax(
3140 __isl_take isl_set *set, __isl_take isl_set *dom,
3141 __isl_give isl_set **empty);
3143 Given a (basic) set C<set> (or C<bset>), the following functions simply
3144 return a set containing the lexicographic minimum or maximum
3145 of the elements in C<set> (or C<bset>).
3146 In case of union sets, the optimum is computed per space.
3148 __isl_give isl_set *isl_basic_set_lexmin(
3149 __isl_take isl_basic_set *bset);
3150 __isl_give isl_set *isl_basic_set_lexmax(
3151 __isl_take isl_basic_set *bset);
3152 __isl_give isl_set *isl_set_lexmin(
3153 __isl_take isl_set *set);
3154 __isl_give isl_set *isl_set_lexmax(
3155 __isl_take isl_set *set);
3156 __isl_give isl_union_set *isl_union_set_lexmin(
3157 __isl_take isl_union_set *uset);
3158 __isl_give isl_union_set *isl_union_set_lexmax(
3159 __isl_take isl_union_set *uset);
3161 Given a (basic) relation C<map> (or C<bmap>) and a domain C<dom>,
3162 the following functions
3163 compute a relation that maps each element of C<dom>
3164 to the single lexicographic minimum or maximum
3165 of the elements that are associated to that same
3166 element in C<map> (or C<bmap>).
3167 If C<empty> is not C<NULL>, then C<*empty> is assigned a set
3168 that contains the elements in C<dom> that do not map
3169 to any elements in C<map> (or C<bmap>).
3170 In other words, the union of the domain of the result and of C<*empty>
3173 __isl_give isl_map *isl_basic_map_partial_lexmax(
3174 __isl_take isl_basic_map *bmap,
3175 __isl_take isl_basic_set *dom,
3176 __isl_give isl_set **empty);
3177 __isl_give isl_map *isl_basic_map_partial_lexmin(
3178 __isl_take isl_basic_map *bmap,
3179 __isl_take isl_basic_set *dom,
3180 __isl_give isl_set **empty);
3181 __isl_give isl_map *isl_map_partial_lexmax(
3182 __isl_take isl_map *map, __isl_take isl_set *dom,
3183 __isl_give isl_set **empty);
3184 __isl_give isl_map *isl_map_partial_lexmin(
3185 __isl_take isl_map *map, __isl_take isl_set *dom,
3186 __isl_give isl_set **empty);
3188 Given a (basic) map C<map> (or C<bmap>), the following functions simply
3189 return a map mapping each element in the domain of
3190 C<map> (or C<bmap>) to the lexicographic minimum or maximum
3191 of all elements associated to that element.
3192 In case of union relations, the optimum is computed per space.
3194 __isl_give isl_map *isl_basic_map_lexmin(
3195 __isl_take isl_basic_map *bmap);
3196 __isl_give isl_map *isl_basic_map_lexmax(
3197 __isl_take isl_basic_map *bmap);
3198 __isl_give isl_map *isl_map_lexmin(
3199 __isl_take isl_map *map);
3200 __isl_give isl_map *isl_map_lexmax(
3201 __isl_take isl_map *map);
3202 __isl_give isl_union_map *isl_union_map_lexmin(
3203 __isl_take isl_union_map *umap);
3204 __isl_give isl_union_map *isl_union_map_lexmax(
3205 __isl_take isl_union_map *umap);
3207 The following functions return their result in the form of
3208 a piecewise multi-affine expression
3209 (See L<"Piecewise Multiple Quasi Affine Expressions">),
3210 but are otherwise equivalent to the corresponding functions
3211 returning a basic set or relation.
3213 __isl_give isl_pw_multi_aff *
3214 isl_basic_map_lexmin_pw_multi_aff(
3215 __isl_take isl_basic_map *bmap);
3216 __isl_give isl_pw_multi_aff *
3217 isl_basic_set_partial_lexmin_pw_multi_aff(
3218 __isl_take isl_basic_set *bset,
3219 __isl_take isl_basic_set *dom,
3220 __isl_give isl_set **empty);
3221 __isl_give isl_pw_multi_aff *
3222 isl_basic_set_partial_lexmax_pw_multi_aff(
3223 __isl_take isl_basic_set *bset,
3224 __isl_take isl_basic_set *dom,
3225 __isl_give isl_set **empty);
3226 __isl_give isl_pw_multi_aff *
3227 isl_basic_map_partial_lexmin_pw_multi_aff(
3228 __isl_take isl_basic_map *bmap,
3229 __isl_take isl_basic_set *dom,
3230 __isl_give isl_set **empty);
3231 __isl_give isl_pw_multi_aff *
3232 isl_basic_map_partial_lexmax_pw_multi_aff(
3233 __isl_take isl_basic_map *bmap,
3234 __isl_take isl_basic_set *dom,
3235 __isl_give isl_set **empty);
3236 __isl_give isl_pw_multi_aff *isl_set_lexmin_pw_multi_aff(
3237 __isl_take isl_set *set);
3238 __isl_give isl_pw_multi_aff *isl_set_lexmax_pw_multi_aff(
3239 __isl_take isl_set *set);
3240 __isl_give isl_pw_multi_aff *isl_map_lexmin_pw_multi_aff(
3241 __isl_take isl_map *map);
3242 __isl_give isl_pw_multi_aff *isl_map_lexmax_pw_multi_aff(
3243 __isl_take isl_map *map);
3247 Lists are defined over several element types, including
3248 C<isl_val>, C<isl_id>, C<isl_aff>, C<isl_pw_aff>, C<isl_constraint>,
3249 C<isl_basic_set>, C<isl_set>, C<isl_ast_expr> and C<isl_ast_node>.
3250 Here we take lists of C<isl_set>s as an example.
3251 Lists can be created, copied, modified and freed using the following functions.
3253 #include <isl/list.h>
3254 __isl_give isl_set_list *isl_set_list_from_set(
3255 __isl_take isl_set *el);
3256 __isl_give isl_set_list *isl_set_list_alloc(
3257 isl_ctx *ctx, int n);
3258 __isl_give isl_set_list *isl_set_list_copy(
3259 __isl_keep isl_set_list *list);
3260 __isl_give isl_set_list *isl_set_list_insert(
3261 __isl_take isl_set_list *list, unsigned pos,
3262 __isl_take isl_set *el);
3263 __isl_give isl_set_list *isl_set_list_add(
3264 __isl_take isl_set_list *list,
3265 __isl_take isl_set *el);
3266 __isl_give isl_set_list *isl_set_list_drop(
3267 __isl_take isl_set_list *list,
3268 unsigned first, unsigned n);
3269 __isl_give isl_set_list *isl_set_list_set_set(
3270 __isl_take isl_set_list *list, int index,
3271 __isl_take isl_set *set);
3272 __isl_give isl_set_list *isl_set_list_concat(
3273 __isl_take isl_set_list *list1,
3274 __isl_take isl_set_list *list2);
3275 __isl_give isl_set_list *isl_set_list_sort(
3276 __isl_take isl_set_list *list,
3277 int (*cmp)(__isl_keep isl_set *a,
3278 __isl_keep isl_set *b, void *user),
3280 void *isl_set_list_free(__isl_take isl_set_list *list);
3282 C<isl_set_list_alloc> creates an empty list with a capacity for
3283 C<n> elements. C<isl_set_list_from_set> creates a list with a single
3286 Lists can be inspected using the following functions.
3288 #include <isl/list.h>
3289 isl_ctx *isl_set_list_get_ctx(__isl_keep isl_set_list *list);
3290 int isl_set_list_n_set(__isl_keep isl_set_list *list);
3291 __isl_give isl_set *isl_set_list_get_set(
3292 __isl_keep isl_set_list *list, int index);
3293 int isl_set_list_foreach(__isl_keep isl_set_list *list,
3294 int (*fn)(__isl_take isl_set *el, void *user),
3296 int isl_set_list_foreach_scc(__isl_keep isl_set_list *list,
3297 int (*follows)(__isl_keep isl_set *a,
3298 __isl_keep isl_set *b, void *user),
3300 int (*fn)(__isl_take isl_set *el, void *user),
3303 The function C<isl_set_list_foreach_scc> calls C<fn> on each of the
3304 strongly connected components of the graph with as vertices the elements
3305 of C<list> and a directed edge from vertex C<b> to vertex C<a>
3306 iff C<follows(a, b)> returns C<1>. The callbacks C<follows> and C<fn>
3307 should return C<-1> on error.
3309 Lists can be printed using
3311 #include <isl/list.h>
3312 __isl_give isl_printer *isl_printer_print_set_list(
3313 __isl_take isl_printer *p,
3314 __isl_keep isl_set_list *list);
3318 Vectors can be created, copied and freed using the following functions.
3320 #include <isl/vec.h>
3321 __isl_give isl_vec *isl_vec_alloc(isl_ctx *ctx,
3323 __isl_give isl_vec *isl_vec_copy(__isl_keep isl_vec *vec);
3324 void *isl_vec_free(__isl_take isl_vec *vec);
3326 Note that the elements of a newly created vector may have arbitrary values.
3327 The elements can be changed and inspected using the following functions.
3329 isl_ctx *isl_vec_get_ctx(__isl_keep isl_vec *vec);
3330 int isl_vec_size(__isl_keep isl_vec *vec);
3331 int isl_vec_get_element(__isl_keep isl_vec *vec,
3332 int pos, isl_int *v);
3333 __isl_give isl_vec *isl_vec_set_element(
3334 __isl_take isl_vec *vec, int pos, isl_int v);
3335 __isl_give isl_vec *isl_vec_set_element_si(
3336 __isl_take isl_vec *vec, int pos, int v);
3337 __isl_give isl_vec *isl_vec_set(__isl_take isl_vec *vec,
3339 __isl_give isl_vec *isl_vec_set_si(__isl_take isl_vec *vec,
3341 __isl_give isl_vec *isl_vec_fdiv_r(__isl_take isl_vec *vec,
3344 C<isl_vec_get_element> will return a negative value if anything went wrong.
3345 In that case, the value of C<*v> is undefined.
3347 The following function can be used to concatenate two vectors.
3349 __isl_give isl_vec *isl_vec_concat(__isl_take isl_vec *vec1,
3350 __isl_take isl_vec *vec2);
3354 Matrices can be created, copied and freed using the following functions.
3356 #include <isl/mat.h>
3357 __isl_give isl_mat *isl_mat_alloc(isl_ctx *ctx,
3358 unsigned n_row, unsigned n_col);
3359 __isl_give isl_mat *isl_mat_copy(__isl_keep isl_mat *mat);
3360 void *isl_mat_free(__isl_take isl_mat *mat);
3362 Note that the elements of a newly created matrix may have arbitrary values.
3363 The elements can be changed and inspected using the following functions.
3365 isl_ctx *isl_mat_get_ctx(__isl_keep isl_mat *mat);
3366 int isl_mat_rows(__isl_keep isl_mat *mat);
3367 int isl_mat_cols(__isl_keep isl_mat *mat);
3368 int isl_mat_get_element(__isl_keep isl_mat *mat,
3369 int row, int col, isl_int *v);
3370 __isl_give isl_mat *isl_mat_set_element(__isl_take isl_mat *mat,
3371 int row, int col, isl_int v);
3372 __isl_give isl_mat *isl_mat_set_element_si(__isl_take isl_mat *mat,
3373 int row, int col, int v);
3375 C<isl_mat_get_element> will return a negative value if anything went wrong.
3376 In that case, the value of C<*v> is undefined.
3378 The following function can be used to compute the (right) inverse
3379 of a matrix, i.e., a matrix such that the product of the original
3380 and the inverse (in that order) is a multiple of the identity matrix.
3381 The input matrix is assumed to be of full row-rank.
3383 __isl_give isl_mat *isl_mat_right_inverse(__isl_take isl_mat *mat);
3385 The following function can be used to compute the (right) kernel
3386 (or null space) of a matrix, i.e., a matrix such that the product of
3387 the original and the kernel (in that order) is the zero matrix.
3389 __isl_give isl_mat *isl_mat_right_kernel(__isl_take isl_mat *mat);
3391 =head2 Piecewise Quasi Affine Expressions
3393 The zero quasi affine expression or the quasi affine expression
3394 that is equal to a specified dimension on a given domain can be created using
3396 __isl_give isl_aff *isl_aff_zero_on_domain(
3397 __isl_take isl_local_space *ls);
3398 __isl_give isl_pw_aff *isl_pw_aff_zero_on_domain(
3399 __isl_take isl_local_space *ls);
3400 __isl_give isl_aff *isl_aff_var_on_domain(
3401 __isl_take isl_local_space *ls,
3402 enum isl_dim_type type, unsigned pos);
3403 __isl_give isl_pw_aff *isl_pw_aff_var_on_domain(
3404 __isl_take isl_local_space *ls,
3405 enum isl_dim_type type, unsigned pos);
3407 Note that the space in which the resulting objects live is a map space
3408 with the given space as domain and a one-dimensional range.
3410 An empty piecewise quasi affine expression (one with no cells)
3411 or a piecewise quasi affine expression with a single cell can
3412 be created using the following functions.
3414 #include <isl/aff.h>
3415 __isl_give isl_pw_aff *isl_pw_aff_empty(
3416 __isl_take isl_space *space);
3417 __isl_give isl_pw_aff *isl_pw_aff_alloc(
3418 __isl_take isl_set *set, __isl_take isl_aff *aff);
3419 __isl_give isl_pw_aff *isl_pw_aff_from_aff(
3420 __isl_take isl_aff *aff);
3422 A piecewise quasi affine expression that is equal to 1 on a set
3423 and 0 outside the set can be created using the following function.
3425 #include <isl/aff.h>
3426 __isl_give isl_pw_aff *isl_set_indicator_function(
3427 __isl_take isl_set *set);
3429 Quasi affine expressions can be copied and freed using
3431 #include <isl/aff.h>
3432 __isl_give isl_aff *isl_aff_copy(__isl_keep isl_aff *aff);
3433 void *isl_aff_free(__isl_take isl_aff *aff);
3435 __isl_give isl_pw_aff *isl_pw_aff_copy(
3436 __isl_keep isl_pw_aff *pwaff);
3437 void *isl_pw_aff_free(__isl_take isl_pw_aff *pwaff);
3439 A (rational) bound on a dimension can be extracted from an C<isl_constraint>
3440 using the following function. The constraint is required to have
3441 a non-zero coefficient for the specified dimension.
3443 #include <isl/constraint.h>
3444 __isl_give isl_aff *isl_constraint_get_bound(
3445 __isl_keep isl_constraint *constraint,
3446 enum isl_dim_type type, int pos);
3448 The entire affine expression of the constraint can also be extracted
3449 using the following function.
3451 #include <isl/constraint.h>
3452 __isl_give isl_aff *isl_constraint_get_aff(
3453 __isl_keep isl_constraint *constraint);
3455 Conversely, an equality constraint equating
3456 the affine expression to zero or an inequality constraint enforcing
3457 the affine expression to be non-negative, can be constructed using
3459 __isl_give isl_constraint *isl_equality_from_aff(
3460 __isl_take isl_aff *aff);
3461 __isl_give isl_constraint *isl_inequality_from_aff(
3462 __isl_take isl_aff *aff);
3464 The expression can be inspected using
3466 #include <isl/aff.h>
3467 isl_ctx *isl_aff_get_ctx(__isl_keep isl_aff *aff);
3468 int isl_aff_dim(__isl_keep isl_aff *aff,
3469 enum isl_dim_type type);
3470 __isl_give isl_local_space *isl_aff_get_domain_local_space(
3471 __isl_keep isl_aff *aff);
3472 __isl_give isl_local_space *isl_aff_get_local_space(
3473 __isl_keep isl_aff *aff);
3474 const char *isl_aff_get_dim_name(__isl_keep isl_aff *aff,
3475 enum isl_dim_type type, unsigned pos);
3476 const char *isl_pw_aff_get_dim_name(
3477 __isl_keep isl_pw_aff *pa,
3478 enum isl_dim_type type, unsigned pos);
3479 int isl_pw_aff_has_dim_id(__isl_keep isl_pw_aff *pa,
3480 enum isl_dim_type type, unsigned pos);
3481 __isl_give isl_id *isl_pw_aff_get_dim_id(
3482 __isl_keep isl_pw_aff *pa,
3483 enum isl_dim_type type, unsigned pos);
3484 __isl_give isl_id *isl_pw_aff_get_tuple_id(
3485 __isl_keep isl_pw_aff *pa,
3486 enum isl_dim_type type);
3487 int isl_aff_get_constant(__isl_keep isl_aff *aff,
3489 int isl_aff_get_coefficient(__isl_keep isl_aff *aff,
3490 enum isl_dim_type type, int pos, isl_int *v);
3491 int isl_aff_get_denominator(__isl_keep isl_aff *aff,
3493 __isl_give isl_aff *isl_aff_get_div(
3494 __isl_keep isl_aff *aff, int pos);
3496 int isl_pw_aff_n_piece(__isl_keep isl_pw_aff *pwaff);
3497 int isl_pw_aff_foreach_piece(__isl_keep isl_pw_aff *pwaff,
3498 int (*fn)(__isl_take isl_set *set,
3499 __isl_take isl_aff *aff,
3500 void *user), void *user);
3502 int isl_aff_is_cst(__isl_keep isl_aff *aff);
3503 int isl_pw_aff_is_cst(__isl_keep isl_pw_aff *pwaff);
3505 int isl_aff_involves_dims(__isl_keep isl_aff *aff,
3506 enum isl_dim_type type, unsigned first, unsigned n);
3507 int isl_pw_aff_involves_dims(__isl_keep isl_pw_aff *pwaff,
3508 enum isl_dim_type type, unsigned first, unsigned n);
3510 isl_ctx *isl_pw_aff_get_ctx(__isl_keep isl_pw_aff *pwaff);
3511 unsigned isl_pw_aff_dim(__isl_keep isl_pw_aff *pwaff,
3512 enum isl_dim_type type);
3513 int isl_pw_aff_is_empty(__isl_keep isl_pw_aff *pwaff);
3515 It can be modified using
3517 #include <isl/aff.h>
3518 __isl_give isl_pw_aff *isl_pw_aff_set_tuple_id(
3519 __isl_take isl_pw_aff *pwaff,
3520 enum isl_dim_type type, __isl_take isl_id *id);
3521 __isl_give isl_aff *isl_aff_set_dim_name(
3522 __isl_take isl_aff *aff, enum isl_dim_type type,
3523 unsigned pos, const char *s);
3524 __isl_give isl_aff *isl_aff_set_dim_id(
3525 __isl_take isl_aff *aff, enum isl_dim_type type,
3526 unsigned pos, __isl_take isl_id *id);
3527 __isl_give isl_pw_aff *isl_pw_aff_set_dim_id(
3528 __isl_take isl_pw_aff *pma,
3529 enum isl_dim_type type, unsigned pos,
3530 __isl_take isl_id *id);
3531 __isl_give isl_aff *isl_aff_set_constant(
3532 __isl_take isl_aff *aff, isl_int v);
3533 __isl_give isl_aff *isl_aff_set_constant_si(
3534 __isl_take isl_aff *aff, int v);
3535 __isl_give isl_aff *isl_aff_set_coefficient(
3536 __isl_take isl_aff *aff,
3537 enum isl_dim_type type, int pos, isl_int v);
3538 __isl_give isl_aff *isl_aff_set_coefficient_si(
3539 __isl_take isl_aff *aff,
3540 enum isl_dim_type type, int pos, int v);
3541 __isl_give isl_aff *isl_aff_set_denominator(
3542 __isl_take isl_aff *aff, isl_int v);
3544 __isl_give isl_aff *isl_aff_add_constant(
3545 __isl_take isl_aff *aff, isl_int v);
3546 __isl_give isl_aff *isl_aff_add_constant_si(
3547 __isl_take isl_aff *aff, int v);
3548 __isl_give isl_aff *isl_aff_add_constant_num(
3549 __isl_take isl_aff *aff, isl_int v);
3550 __isl_give isl_aff *isl_aff_add_constant_num_si(
3551 __isl_take isl_aff *aff, int v);
3552 __isl_give isl_aff *isl_aff_add_coefficient(
3553 __isl_take isl_aff *aff,
3554 enum isl_dim_type type, int pos, isl_int v);
3555 __isl_give isl_aff *isl_aff_add_coefficient_si(
3556 __isl_take isl_aff *aff,
3557 enum isl_dim_type type, int pos, int v);
3559 __isl_give isl_aff *isl_aff_insert_dims(
3560 __isl_take isl_aff *aff,
3561 enum isl_dim_type type, unsigned first, unsigned n);
3562 __isl_give isl_pw_aff *isl_pw_aff_insert_dims(
3563 __isl_take isl_pw_aff *pwaff,
3564 enum isl_dim_type type, unsigned first, unsigned n);
3565 __isl_give isl_aff *isl_aff_add_dims(
3566 __isl_take isl_aff *aff,
3567 enum isl_dim_type type, unsigned n);
3568 __isl_give isl_pw_aff *isl_pw_aff_add_dims(
3569 __isl_take isl_pw_aff *pwaff,
3570 enum isl_dim_type type, unsigned n);
3571 __isl_give isl_aff *isl_aff_drop_dims(
3572 __isl_take isl_aff *aff,
3573 enum isl_dim_type type, unsigned first, unsigned n);
3574 __isl_give isl_pw_aff *isl_pw_aff_drop_dims(
3575 __isl_take isl_pw_aff *pwaff,
3576 enum isl_dim_type type, unsigned first, unsigned n);
3578 Note that the C<set_constant> and C<set_coefficient> functions
3579 set the I<numerator> of the constant or coefficient, while
3580 C<add_constant> and C<add_coefficient> add an integer value to
3581 the possibly rational constant or coefficient.
3582 The C<add_constant_num> functions add an integer value to
3585 To check whether an affine expressions is obviously zero
3586 or obviously equal to some other affine expression, use
3588 #include <isl/aff.h>
3589 int isl_aff_plain_is_zero(__isl_keep isl_aff *aff);
3590 int isl_aff_plain_is_equal(__isl_keep isl_aff *aff1,
3591 __isl_keep isl_aff *aff2);
3592 int isl_pw_aff_plain_is_equal(
3593 __isl_keep isl_pw_aff *pwaff1,
3594 __isl_keep isl_pw_aff *pwaff2);
3598 #include <isl/aff.h>
3599 __isl_give isl_aff *isl_aff_add(__isl_take isl_aff *aff1,
3600 __isl_take isl_aff *aff2);
3601 __isl_give isl_pw_aff *isl_pw_aff_add(
3602 __isl_take isl_pw_aff *pwaff1,
3603 __isl_take isl_pw_aff *pwaff2);
3604 __isl_give isl_pw_aff *isl_pw_aff_min(
3605 __isl_take isl_pw_aff *pwaff1,
3606 __isl_take isl_pw_aff *pwaff2);
3607 __isl_give isl_pw_aff *isl_pw_aff_max(
3608 __isl_take isl_pw_aff *pwaff1,
3609 __isl_take isl_pw_aff *pwaff2);
3610 __isl_give isl_aff *isl_aff_sub(__isl_take isl_aff *aff1,
3611 __isl_take isl_aff *aff2);
3612 __isl_give isl_pw_aff *isl_pw_aff_sub(
3613 __isl_take isl_pw_aff *pwaff1,
3614 __isl_take isl_pw_aff *pwaff2);
3615 __isl_give isl_aff *isl_aff_neg(__isl_take isl_aff *aff);
3616 __isl_give isl_pw_aff *isl_pw_aff_neg(
3617 __isl_take isl_pw_aff *pwaff);
3618 __isl_give isl_aff *isl_aff_ceil(__isl_take isl_aff *aff);
3619 __isl_give isl_pw_aff *isl_pw_aff_ceil(
3620 __isl_take isl_pw_aff *pwaff);
3621 __isl_give isl_aff *isl_aff_floor(__isl_take isl_aff *aff);
3622 __isl_give isl_pw_aff *isl_pw_aff_floor(
3623 __isl_take isl_pw_aff *pwaff);
3624 __isl_give isl_aff *isl_aff_mod(__isl_take isl_aff *aff,
3626 __isl_give isl_pw_aff *isl_pw_aff_mod(
3627 __isl_take isl_pw_aff *pwaff, isl_int mod);
3628 __isl_give isl_aff *isl_aff_scale(__isl_take isl_aff *aff,
3630 __isl_give isl_pw_aff *isl_pw_aff_scale(
3631 __isl_take isl_pw_aff *pwaff, isl_int f);
3632 __isl_give isl_aff *isl_aff_scale_down(__isl_take isl_aff *aff,
3634 __isl_give isl_aff *isl_aff_scale_down_ui(
3635 __isl_take isl_aff *aff, unsigned f);
3636 __isl_give isl_pw_aff *isl_pw_aff_scale_down(
3637 __isl_take isl_pw_aff *pwaff, isl_int f);
3639 __isl_give isl_pw_aff *isl_pw_aff_list_min(
3640 __isl_take isl_pw_aff_list *list);
3641 __isl_give isl_pw_aff *isl_pw_aff_list_max(
3642 __isl_take isl_pw_aff_list *list);
3644 __isl_give isl_pw_aff *isl_pw_aff_coalesce(
3645 __isl_take isl_pw_aff *pwqp);
3647 __isl_give isl_aff *isl_aff_align_params(
3648 __isl_take isl_aff *aff,
3649 __isl_take isl_space *model);
3650 __isl_give isl_pw_aff *isl_pw_aff_align_params(
3651 __isl_take isl_pw_aff *pwaff,
3652 __isl_take isl_space *model);
3654 __isl_give isl_aff *isl_aff_project_domain_on_params(
3655 __isl_take isl_aff *aff);
3657 __isl_give isl_aff *isl_aff_gist_params(
3658 __isl_take isl_aff *aff,
3659 __isl_take isl_set *context);
3660 __isl_give isl_aff *isl_aff_gist(__isl_take isl_aff *aff,
3661 __isl_take isl_set *context);
3662 __isl_give isl_pw_aff *isl_pw_aff_gist_params(
3663 __isl_take isl_pw_aff *pwaff,
3664 __isl_take isl_set *context);
3665 __isl_give isl_pw_aff *isl_pw_aff_gist(
3666 __isl_take isl_pw_aff *pwaff,
3667 __isl_take isl_set *context);
3669 __isl_give isl_set *isl_pw_aff_domain(
3670 __isl_take isl_pw_aff *pwaff);
3671 __isl_give isl_pw_aff *isl_pw_aff_intersect_domain(
3672 __isl_take isl_pw_aff *pa,
3673 __isl_take isl_set *set);
3674 __isl_give isl_pw_aff *isl_pw_aff_intersect_params(
3675 __isl_take isl_pw_aff *pa,
3676 __isl_take isl_set *set);
3678 __isl_give isl_aff *isl_aff_mul(__isl_take isl_aff *aff1,
3679 __isl_take isl_aff *aff2);
3680 __isl_give isl_aff *isl_aff_div(__isl_take isl_aff *aff1,
3681 __isl_take isl_aff *aff2);
3682 __isl_give isl_pw_aff *isl_pw_aff_mul(
3683 __isl_take isl_pw_aff *pwaff1,
3684 __isl_take isl_pw_aff *pwaff2);
3685 __isl_give isl_pw_aff *isl_pw_aff_div(
3686 __isl_take isl_pw_aff *pa1,
3687 __isl_take isl_pw_aff *pa2);
3688 __isl_give isl_pw_aff *isl_pw_aff_tdiv_q(
3689 __isl_take isl_pw_aff *pa1,
3690 __isl_take isl_pw_aff *pa2);
3691 __isl_give isl_pw_aff *isl_pw_aff_tdiv_r(
3692 __isl_take isl_pw_aff *pa1,
3693 __isl_take isl_pw_aff *pa2);
3695 When multiplying two affine expressions, at least one of the two needs
3696 to be a constant. Similarly, when dividing an affine expression by another,
3697 the second expression needs to be a constant.
3698 C<isl_pw_aff_tdiv_q> computes the quotient of an integer division with
3699 rounding towards zero. C<isl_pw_aff_tdiv_r> computes the corresponding
3702 #include <isl/aff.h>
3703 __isl_give isl_aff *isl_aff_pullback_multi_aff(
3704 __isl_take isl_aff *aff,
3705 __isl_take isl_multi_aff *ma);
3706 __isl_give isl_pw_aff *isl_pw_aff_pullback_multi_aff(
3707 __isl_take isl_pw_aff *pa,
3708 __isl_take isl_multi_aff *ma);
3709 __isl_give isl_pw_aff *isl_pw_aff_pullback_pw_multi_aff(
3710 __isl_take isl_pw_aff *pa,
3711 __isl_take isl_pw_multi_aff *pma);
3713 These functions precompose the input expression by the given
3714 C<isl_multi_aff> or C<isl_pw_multi_aff>. In other words,
3715 the C<isl_multi_aff> or C<isl_pw_multi_aff> is plugged
3716 into the (piecewise) affine expression.
3717 Objects of type C<isl_multi_aff> are described in
3718 L</"Piecewise Multiple Quasi Affine Expressions">.
3720 #include <isl/aff.h>
3721 __isl_give isl_basic_set *isl_aff_zero_basic_set(
3722 __isl_take isl_aff *aff);
3723 __isl_give isl_basic_set *isl_aff_neg_basic_set(
3724 __isl_take isl_aff *aff);
3725 __isl_give isl_basic_set *isl_aff_le_basic_set(
3726 __isl_take isl_aff *aff1, __isl_take isl_aff *aff2);
3727 __isl_give isl_basic_set *isl_aff_ge_basic_set(
3728 __isl_take isl_aff *aff1, __isl_take isl_aff *aff2);
3729 __isl_give isl_set *isl_pw_aff_eq_set(
3730 __isl_take isl_pw_aff *pwaff1,
3731 __isl_take isl_pw_aff *pwaff2);
3732 __isl_give isl_set *isl_pw_aff_ne_set(
3733 __isl_take isl_pw_aff *pwaff1,
3734 __isl_take isl_pw_aff *pwaff2);
3735 __isl_give isl_set *isl_pw_aff_le_set(
3736 __isl_take isl_pw_aff *pwaff1,
3737 __isl_take isl_pw_aff *pwaff2);
3738 __isl_give isl_set *isl_pw_aff_lt_set(
3739 __isl_take isl_pw_aff *pwaff1,
3740 __isl_take isl_pw_aff *pwaff2);
3741 __isl_give isl_set *isl_pw_aff_ge_set(
3742 __isl_take isl_pw_aff *pwaff1,
3743 __isl_take isl_pw_aff *pwaff2);
3744 __isl_give isl_set *isl_pw_aff_gt_set(
3745 __isl_take isl_pw_aff *pwaff1,
3746 __isl_take isl_pw_aff *pwaff2);
3748 __isl_give isl_set *isl_pw_aff_list_eq_set(
3749 __isl_take isl_pw_aff_list *list1,
3750 __isl_take isl_pw_aff_list *list2);
3751 __isl_give isl_set *isl_pw_aff_list_ne_set(
3752 __isl_take isl_pw_aff_list *list1,
3753 __isl_take isl_pw_aff_list *list2);
3754 __isl_give isl_set *isl_pw_aff_list_le_set(
3755 __isl_take isl_pw_aff_list *list1,
3756 __isl_take isl_pw_aff_list *list2);
3757 __isl_give isl_set *isl_pw_aff_list_lt_set(
3758 __isl_take isl_pw_aff_list *list1,
3759 __isl_take isl_pw_aff_list *list2);
3760 __isl_give isl_set *isl_pw_aff_list_ge_set(
3761 __isl_take isl_pw_aff_list *list1,
3762 __isl_take isl_pw_aff_list *list2);
3763 __isl_give isl_set *isl_pw_aff_list_gt_set(
3764 __isl_take isl_pw_aff_list *list1,
3765 __isl_take isl_pw_aff_list *list2);
3767 The function C<isl_aff_neg_basic_set> returns a basic set
3768 containing those elements in the domain space
3769 of C<aff> where C<aff> is negative.
3770 The function C<isl_aff_ge_basic_set> returns a basic set
3771 containing those elements in the shared space
3772 of C<aff1> and C<aff2> where C<aff1> is greater than or equal to C<aff2>.
3773 The function C<isl_pw_aff_ge_set> returns a set
3774 containing those elements in the shared domain
3775 of C<pwaff1> and C<pwaff2> where C<pwaff1> is greater than or equal to C<pwaff2>.
3776 The functions operating on C<isl_pw_aff_list> apply the corresponding
3777 C<isl_pw_aff> function to each pair of elements in the two lists.
3779 #include <isl/aff.h>
3780 __isl_give isl_set *isl_pw_aff_nonneg_set(
3781 __isl_take isl_pw_aff *pwaff);
3782 __isl_give isl_set *isl_pw_aff_zero_set(
3783 __isl_take isl_pw_aff *pwaff);
3784 __isl_give isl_set *isl_pw_aff_non_zero_set(
3785 __isl_take isl_pw_aff *pwaff);
3787 The function C<isl_pw_aff_nonneg_set> returns a set
3788 containing those elements in the domain
3789 of C<pwaff> where C<pwaff> is non-negative.
3791 #include <isl/aff.h>
3792 __isl_give isl_pw_aff *isl_pw_aff_cond(
3793 __isl_take isl_pw_aff *cond,
3794 __isl_take isl_pw_aff *pwaff_true,
3795 __isl_take isl_pw_aff *pwaff_false);
3797 The function C<isl_pw_aff_cond> performs a conditional operator
3798 and returns an expression that is equal to C<pwaff_true>
3799 for elements where C<cond> is non-zero and equal to C<pwaff_false> for elements
3800 where C<cond> is zero.
3802 #include <isl/aff.h>
3803 __isl_give isl_pw_aff *isl_pw_aff_union_min(
3804 __isl_take isl_pw_aff *pwaff1,
3805 __isl_take isl_pw_aff *pwaff2);
3806 __isl_give isl_pw_aff *isl_pw_aff_union_max(
3807 __isl_take isl_pw_aff *pwaff1,
3808 __isl_take isl_pw_aff *pwaff2);
3809 __isl_give isl_pw_aff *isl_pw_aff_union_add(
3810 __isl_take isl_pw_aff *pwaff1,
3811 __isl_take isl_pw_aff *pwaff2);
3813 The function C<isl_pw_aff_union_max> computes a piecewise quasi-affine
3814 expression with a domain that is the union of those of C<pwaff1> and
3815 C<pwaff2> and such that on each cell, the quasi-affine expression is
3816 the maximum of those of C<pwaff1> and C<pwaff2>. If only one of
3817 C<pwaff1> or C<pwaff2> is defined on a given cell, then the
3818 associated expression is the defined one.
3820 An expression can be read from input using
3822 #include <isl/aff.h>
3823 __isl_give isl_aff *isl_aff_read_from_str(
3824 isl_ctx *ctx, const char *str);
3825 __isl_give isl_pw_aff *isl_pw_aff_read_from_str(
3826 isl_ctx *ctx, const char *str);
3828 An expression can be printed using
3830 #include <isl/aff.h>
3831 __isl_give isl_printer *isl_printer_print_aff(
3832 __isl_take isl_printer *p, __isl_keep isl_aff *aff);
3834 __isl_give isl_printer *isl_printer_print_pw_aff(
3835 __isl_take isl_printer *p,
3836 __isl_keep isl_pw_aff *pwaff);
3838 =head2 Piecewise Multiple Quasi Affine Expressions
3840 An C<isl_multi_aff> object represents a sequence of
3841 zero or more affine expressions, all defined on the same domain space.
3842 Similarly, an C<isl_multi_pw_aff> object represents a sequence of
3843 zero or more piecewise affine expressions.
3845 An C<isl_multi_aff> can be constructed from a single
3846 C<isl_aff> or an C<isl_aff_list> using the
3847 following functions. Similarly for C<isl_multi_pw_aff>.
3849 #include <isl/aff.h>
3850 __isl_give isl_multi_aff *isl_multi_aff_from_aff(
3851 __isl_take isl_aff *aff);
3852 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_from_pw_aff(
3853 __isl_take isl_pw_aff *pa);
3854 __isl_give isl_multi_aff *isl_multi_aff_from_aff_list(
3855 __isl_take isl_space *space,
3856 __isl_take isl_aff_list *list);
3858 An empty piecewise multiple quasi affine expression (one with no cells),
3859 the zero piecewise multiple quasi affine expression (with value zero
3860 for each output dimension),
3861 a piecewise multiple quasi affine expression with a single cell (with
3862 either a universe or a specified domain) or
3863 a zero-dimensional piecewise multiple quasi affine expression
3865 can be created using the following functions.
3867 #include <isl/aff.h>
3868 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_empty(
3869 __isl_take isl_space *space);
3870 __isl_give isl_multi_aff *isl_multi_aff_zero(
3871 __isl_take isl_space *space);
3872 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_zero(
3873 __isl_take isl_space *space);
3874 __isl_give isl_multi_aff *isl_multi_aff_identity(
3875 __isl_take isl_space *space);
3876 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_identity(
3877 __isl_take isl_space *space);
3878 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_identity(
3879 __isl_take isl_space *space);
3880 __isl_give isl_pw_multi_aff *
3881 isl_pw_multi_aff_from_multi_aff(
3882 __isl_take isl_multi_aff *ma);
3883 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_alloc(
3884 __isl_take isl_set *set,
3885 __isl_take isl_multi_aff *maff);
3886 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_from_domain(
3887 __isl_take isl_set *set);
3889 __isl_give isl_union_pw_multi_aff *
3890 isl_union_pw_multi_aff_empty(
3891 __isl_take isl_space *space);
3892 __isl_give isl_union_pw_multi_aff *
3893 isl_union_pw_multi_aff_add_pw_multi_aff(
3894 __isl_take isl_union_pw_multi_aff *upma,
3895 __isl_take isl_pw_multi_aff *pma);
3896 __isl_give isl_union_pw_multi_aff *
3897 isl_union_pw_multi_aff_from_domain(
3898 __isl_take isl_union_set *uset);
3900 A piecewise multiple quasi affine expression can also be initialized
3901 from an C<isl_set> or C<isl_map>, provided the C<isl_set> is a singleton
3902 and the C<isl_map> is single-valued.
3903 In case of a conversion from an C<isl_union_set> or an C<isl_union_map>
3904 to an C<isl_union_pw_multi_aff>, these properties need to hold in each space.
3906 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_from_set(
3907 __isl_take isl_set *set);
3908 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_from_map(
3909 __isl_take isl_map *map);
3911 __isl_give isl_union_pw_multi_aff *
3912 isl_union_pw_multi_aff_from_union_set(
3913 __isl_take isl_union_set *uset);
3914 __isl_give isl_union_pw_multi_aff *
3915 isl_union_pw_multi_aff_from_union_map(
3916 __isl_take isl_union_map *umap);
3918 Multiple quasi affine expressions can be copied and freed using
3920 #include <isl/aff.h>
3921 __isl_give isl_multi_aff *isl_multi_aff_copy(
3922 __isl_keep isl_multi_aff *maff);
3923 void *isl_multi_aff_free(__isl_take isl_multi_aff *maff);
3925 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_copy(
3926 __isl_keep isl_pw_multi_aff *pma);
3927 void *isl_pw_multi_aff_free(
3928 __isl_take isl_pw_multi_aff *pma);
3930 __isl_give isl_union_pw_multi_aff *
3931 isl_union_pw_multi_aff_copy(
3932 __isl_keep isl_union_pw_multi_aff *upma);
3933 void *isl_union_pw_multi_aff_free(
3934 __isl_take isl_union_pw_multi_aff *upma);
3936 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_copy(
3937 __isl_keep isl_multi_pw_aff *mpa);
3938 void *isl_multi_pw_aff_free(
3939 __isl_take isl_multi_pw_aff *mpa);
3941 The expression can be inspected using
3943 #include <isl/aff.h>
3944 isl_ctx *isl_multi_aff_get_ctx(
3945 __isl_keep isl_multi_aff *maff);
3946 isl_ctx *isl_pw_multi_aff_get_ctx(
3947 __isl_keep isl_pw_multi_aff *pma);
3948 isl_ctx *isl_union_pw_multi_aff_get_ctx(
3949 __isl_keep isl_union_pw_multi_aff *upma);
3950 isl_ctx *isl_multi_pw_aff_get_ctx(
3951 __isl_keep isl_multi_pw_aff *mpa);
3952 unsigned isl_multi_aff_dim(__isl_keep isl_multi_aff *maff,
3953 enum isl_dim_type type);
3954 unsigned isl_pw_multi_aff_dim(
3955 __isl_keep isl_pw_multi_aff *pma,
3956 enum isl_dim_type type);
3957 unsigned isl_multi_pw_aff_dim(
3958 __isl_keep isl_multi_pw_aff *mpa,
3959 enum isl_dim_type type);
3960 __isl_give isl_aff *isl_multi_aff_get_aff(
3961 __isl_keep isl_multi_aff *multi, int pos);
3962 __isl_give isl_pw_aff *isl_pw_multi_aff_get_pw_aff(
3963 __isl_keep isl_pw_multi_aff *pma, int pos);
3964 __isl_give isl_pw_aff *isl_multi_pw_aff_get_pw_aff(
3965 __isl_keep isl_multi_pw_aff *mpa, int pos);
3966 const char *isl_pw_multi_aff_get_dim_name(
3967 __isl_keep isl_pw_multi_aff *pma,
3968 enum isl_dim_type type, unsigned pos);
3969 __isl_give isl_id *isl_pw_multi_aff_get_dim_id(
3970 __isl_keep isl_pw_multi_aff *pma,
3971 enum isl_dim_type type, unsigned pos);
3972 const char *isl_multi_aff_get_tuple_name(
3973 __isl_keep isl_multi_aff *multi,
3974 enum isl_dim_type type);
3975 int isl_pw_multi_aff_has_tuple_name(
3976 __isl_keep isl_pw_multi_aff *pma,
3977 enum isl_dim_type type);
3978 const char *isl_pw_multi_aff_get_tuple_name(
3979 __isl_keep isl_pw_multi_aff *pma,
3980 enum isl_dim_type type);
3981 int isl_pw_multi_aff_has_tuple_id(
3982 __isl_keep isl_pw_multi_aff *pma,
3983 enum isl_dim_type type);
3984 __isl_give isl_id *isl_pw_multi_aff_get_tuple_id(
3985 __isl_keep isl_pw_multi_aff *pma,
3986 enum isl_dim_type type);
3988 int isl_pw_multi_aff_foreach_piece(
3989 __isl_keep isl_pw_multi_aff *pma,
3990 int (*fn)(__isl_take isl_set *set,
3991 __isl_take isl_multi_aff *maff,
3992 void *user), void *user);
3994 int isl_union_pw_multi_aff_foreach_pw_multi_aff(
3995 __isl_keep isl_union_pw_multi_aff *upma,
3996 int (*fn)(__isl_take isl_pw_multi_aff *pma,
3997 void *user), void *user);
3999 It can be modified using
4001 #include <isl/aff.h>
4002 __isl_give isl_multi_aff *isl_multi_aff_set_aff(
4003 __isl_take isl_multi_aff *multi, int pos,
4004 __isl_take isl_aff *aff);
4005 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_set_pw_aff(
4006 __isl_take isl_pw_multi_aff *pma, unsigned pos,
4007 __isl_take isl_pw_aff *pa);
4008 __isl_give isl_multi_aff *isl_multi_aff_set_dim_name(
4009 __isl_take isl_multi_aff *maff,
4010 enum isl_dim_type type, unsigned pos, const char *s);
4011 __isl_give isl_multi_aff *isl_multi_aff_set_tuple_name(
4012 __isl_take isl_multi_aff *maff,
4013 enum isl_dim_type type, const char *s);
4014 __isl_give isl_multi_aff *isl_multi_aff_set_tuple_id(
4015 __isl_take isl_multi_aff *maff,
4016 enum isl_dim_type type, __isl_take isl_id *id);
4017 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_set_tuple_id(
4018 __isl_take isl_pw_multi_aff *pma,
4019 enum isl_dim_type type, __isl_take isl_id *id);
4021 __isl_give isl_multi_pw_aff *
4022 isl_multi_pw_aff_set_dim_name(
4023 __isl_take isl_multi_pw_aff *mpa,
4024 enum isl_dim_type type, unsigned pos, const char *s);
4025 __isl_give isl_multi_pw_aff *
4026 isl_multi_pw_aff_set_tuple_name(
4027 __isl_take isl_multi_pw_aff *mpa,
4028 enum isl_dim_type type, const char *s);
4030 __isl_give isl_multi_aff *isl_multi_aff_insert_dims(
4031 __isl_take isl_multi_aff *ma,
4032 enum isl_dim_type type, unsigned first, unsigned n);
4033 __isl_give isl_multi_aff *isl_multi_aff_add_dims(
4034 __isl_take isl_multi_aff *ma,
4035 enum isl_dim_type type, unsigned n);
4036 __isl_give isl_multi_aff *isl_multi_aff_drop_dims(
4037 __isl_take isl_multi_aff *maff,
4038 enum isl_dim_type type, unsigned first, unsigned n);
4039 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_drop_dims(
4040 __isl_take isl_pw_multi_aff *pma,
4041 enum isl_dim_type type, unsigned first, unsigned n);
4043 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_insert_dims(
4044 __isl_take isl_multi_pw_aff *mpa,
4045 enum isl_dim_type type, unsigned first, unsigned n);
4046 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_add_dims(
4047 __isl_take isl_multi_pw_aff *mpa,
4048 enum isl_dim_type type, unsigned n);
4050 To check whether two multiple affine expressions are
4051 obviously equal to each other, use
4053 int isl_multi_aff_plain_is_equal(__isl_keep isl_multi_aff *maff1,
4054 __isl_keep isl_multi_aff *maff2);
4055 int isl_pw_multi_aff_plain_is_equal(
4056 __isl_keep isl_pw_multi_aff *pma1,
4057 __isl_keep isl_pw_multi_aff *pma2);
4061 #include <isl/aff.h>
4062 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_union_lexmin(
4063 __isl_take isl_pw_multi_aff *pma1,
4064 __isl_take isl_pw_multi_aff *pma2);
4065 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_union_lexmax(
4066 __isl_take isl_pw_multi_aff *pma1,
4067 __isl_take isl_pw_multi_aff *pma2);
4068 __isl_give isl_multi_aff *isl_multi_aff_add(
4069 __isl_take isl_multi_aff *maff1,
4070 __isl_take isl_multi_aff *maff2);
4071 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_add(
4072 __isl_take isl_pw_multi_aff *pma1,
4073 __isl_take isl_pw_multi_aff *pma2);
4074 __isl_give isl_union_pw_multi_aff *isl_union_pw_multi_aff_add(
4075 __isl_take isl_union_pw_multi_aff *upma1,
4076 __isl_take isl_union_pw_multi_aff *upma2);
4077 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_union_add(
4078 __isl_take isl_pw_multi_aff *pma1,
4079 __isl_take isl_pw_multi_aff *pma2);
4080 __isl_give isl_multi_aff *isl_multi_aff_sub(
4081 __isl_take isl_multi_aff *ma1,
4082 __isl_take isl_multi_aff *ma2);
4083 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_sub(
4084 __isl_take isl_pw_multi_aff *pma1,
4085 __isl_take isl_pw_multi_aff *pma2);
4086 __isl_give isl_union_pw_multi_aff *isl_union_pw_multi_aff_sub(
4087 __isl_take isl_union_pw_multi_aff *upma1,
4088 __isl_take isl_union_pw_multi_aff *upma2);
4090 C<isl_multi_aff_sub> subtracts the second argument from the first.
4092 __isl_give isl_multi_aff *isl_multi_aff_scale(
4093 __isl_take isl_multi_aff *maff,
4095 __isl_give isl_multi_aff *isl_multi_aff_scale_vec(
4096 __isl_take isl_multi_aff *ma,
4097 __isl_take isl_vec *v);
4098 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_scale_vec(
4099 __isl_take isl_pw_multi_aff *pma,
4100 __isl_take isl_vec *v);
4101 __isl_give isl_union_pw_multi_aff *isl_union_pw_multi_aff_scale_vec(
4102 __isl_take isl_union_pw_multi_aff *upma,
4103 __isl_take isl_vec *v);
4105 C<isl_multi_aff_scale_vec> scales the first elements of C<ma>
4106 by the corresponding elements of C<v>.
4108 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_intersect_params(
4109 __isl_take isl_pw_multi_aff *pma,
4110 __isl_take isl_set *set);
4111 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_intersect_domain(
4112 __isl_take isl_pw_multi_aff *pma,
4113 __isl_take isl_set *set);
4114 __isl_give isl_union_pw_multi_aff *
4115 isl_union_pw_multi_aff_intersect_domain(
4116 __isl_take isl_union_pw_multi_aff *upma,
4117 __isl_take isl_union_set *uset);
4118 __isl_give isl_multi_aff *isl_multi_aff_lift(
4119 __isl_take isl_multi_aff *maff,
4120 __isl_give isl_local_space **ls);
4121 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_coalesce(
4122 __isl_take isl_pw_multi_aff *pma);
4123 __isl_give isl_multi_aff *isl_multi_aff_align_params(
4124 __isl_take isl_multi_aff *multi,
4125 __isl_take isl_space *model);
4126 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_align_params(
4127 __isl_take isl_pw_multi_aff *pma,
4128 __isl_take isl_space *model);
4129 __isl_give isl_pw_multi_aff *
4130 isl_pw_multi_aff_project_domain_on_params(
4131 __isl_take isl_pw_multi_aff *pma);
4132 __isl_give isl_multi_aff *isl_multi_aff_gist_params(
4133 __isl_take isl_multi_aff *maff,
4134 __isl_take isl_set *context);
4135 __isl_give isl_multi_aff *isl_multi_aff_gist(
4136 __isl_take isl_multi_aff *maff,
4137 __isl_take isl_set *context);
4138 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_gist_params(
4139 __isl_take isl_pw_multi_aff *pma,
4140 __isl_take isl_set *set);
4141 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_gist(
4142 __isl_take isl_pw_multi_aff *pma,
4143 __isl_take isl_set *set);
4144 __isl_give isl_set *isl_pw_multi_aff_domain(
4145 __isl_take isl_pw_multi_aff *pma);
4146 __isl_give isl_union_set *isl_union_pw_multi_aff_domain(
4147 __isl_take isl_union_pw_multi_aff *upma);
4148 __isl_give isl_multi_aff *isl_multi_aff_range_splice(
4149 __isl_take isl_multi_aff *ma1, unsigned pos,
4150 __isl_take isl_multi_aff *ma2);
4151 __isl_give isl_multi_aff *isl_multi_aff_splice(
4152 __isl_take isl_multi_aff *ma1,
4153 unsigned in_pos, unsigned out_pos,
4154 __isl_take isl_multi_aff *ma2);
4155 __isl_give isl_multi_aff *isl_multi_aff_range_product(
4156 __isl_take isl_multi_aff *ma1,
4157 __isl_take isl_multi_aff *ma2);
4158 __isl_give isl_multi_aff *isl_multi_aff_flat_range_product(
4159 __isl_take isl_multi_aff *ma1,
4160 __isl_take isl_multi_aff *ma2);
4161 __isl_give isl_multi_aff *isl_multi_aff_product(
4162 __isl_take isl_multi_aff *ma1,
4163 __isl_take isl_multi_aff *ma2);
4164 __isl_give isl_pw_multi_aff *
4165 isl_pw_multi_aff_range_product(
4166 __isl_take isl_pw_multi_aff *pma1,
4167 __isl_take isl_pw_multi_aff *pma2);
4168 __isl_give isl_pw_multi_aff *
4169 isl_pw_multi_aff_flat_range_product(
4170 __isl_take isl_pw_multi_aff *pma1,
4171 __isl_take isl_pw_multi_aff *pma2);
4172 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_product(
4173 __isl_take isl_pw_multi_aff *pma1,
4174 __isl_take isl_pw_multi_aff *pma2);
4175 __isl_give isl_union_pw_multi_aff *
4176 isl_union_pw_multi_aff_flat_range_product(
4177 __isl_take isl_union_pw_multi_aff *upma1,
4178 __isl_take isl_union_pw_multi_aff *upma2);
4179 __isl_give isl_multi_pw_aff *
4180 isl_multi_pw_aff_range_splice(
4181 __isl_take isl_multi_pw_aff *mpa1, unsigned pos,
4182 __isl_take isl_multi_pw_aff *mpa2);
4183 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_splice(
4184 __isl_take isl_multi_pw_aff *mpa1,
4185 unsigned in_pos, unsigned out_pos,
4186 __isl_take isl_multi_pw_aff *mpa2);
4187 __isl_give isl_multi_pw_aff *
4188 isl_multi_pw_aff_range_product(
4189 __isl_take isl_multi_pw_aff *mpa1,
4190 __isl_take isl_multi_pw_aff *mpa2);
4191 __isl_give isl_multi_pw_aff *
4192 isl_multi_pw_aff_flat_range_product(
4193 __isl_take isl_multi_pw_aff *mpa1,
4194 __isl_take isl_multi_pw_aff *mpa2);
4196 If the C<ls> argument of C<isl_multi_aff_lift> is not C<NULL>,
4197 then it is assigned the local space that lies at the basis of
4198 the lifting applied.
4200 #include <isl/aff.h>
4201 __isl_give isl_multi_aff *isl_multi_aff_pullback_multi_aff(
4202 __isl_take isl_multi_aff *ma1,
4203 __isl_take isl_multi_aff *ma2);
4204 __isl_give isl_pw_multi_aff *
4205 isl_pw_multi_aff_pullback_multi_aff(
4206 __isl_take isl_pw_multi_aff *pma,
4207 __isl_take isl_multi_aff *ma);
4208 __isl_give isl_pw_multi_aff *
4209 isl_pw_multi_aff_pullback_pw_multi_aff(
4210 __isl_take isl_pw_multi_aff *pma1,
4211 __isl_take isl_pw_multi_aff *pma2);
4213 The function C<isl_multi_aff_pullback_multi_aff> precomposes C<ma1> by C<ma2>.
4214 In other words, C<ma2> is plugged
4217 __isl_give isl_set *isl_multi_aff_lex_le_set(
4218 __isl_take isl_multi_aff *ma1,
4219 __isl_take isl_multi_aff *ma2);
4220 __isl_give isl_set *isl_multi_aff_lex_ge_set(
4221 __isl_take isl_multi_aff *ma1,
4222 __isl_take isl_multi_aff *ma2);
4224 The function C<isl_multi_aff_lex_le_set> returns a set
4225 containing those elements in the shared domain space
4226 where C<ma1> is lexicographically smaller than or
4229 An expression can be read from input using
4231 #include <isl/aff.h>
4232 __isl_give isl_multi_aff *isl_multi_aff_read_from_str(
4233 isl_ctx *ctx, const char *str);
4234 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_read_from_str(
4235 isl_ctx *ctx, const char *str);
4236 __isl_give isl_union_pw_multi_aff *
4237 isl_union_pw_multi_aff_read_from_str(
4238 isl_ctx *ctx, const char *str);
4240 An expression can be printed using
4242 #include <isl/aff.h>
4243 __isl_give isl_printer *isl_printer_print_multi_aff(
4244 __isl_take isl_printer *p,
4245 __isl_keep isl_multi_aff *maff);
4246 __isl_give isl_printer *isl_printer_print_pw_multi_aff(
4247 __isl_take isl_printer *p,
4248 __isl_keep isl_pw_multi_aff *pma);
4249 __isl_give isl_printer *isl_printer_print_union_pw_multi_aff(
4250 __isl_take isl_printer *p,
4251 __isl_keep isl_union_pw_multi_aff *upma);
4252 __isl_give isl_printer *isl_printer_print_multi_pw_aff(
4253 __isl_take isl_printer *p,
4254 __isl_keep isl_multi_pw_aff *mpa);
4258 Points are elements of a set. They can be used to construct
4259 simple sets (boxes) or they can be used to represent the
4260 individual elements of a set.
4261 The zero point (the origin) can be created using
4263 __isl_give isl_point *isl_point_zero(__isl_take isl_space *space);
4265 The coordinates of a point can be inspected, set and changed
4268 int isl_point_get_coordinate(__isl_keep isl_point *pnt,
4269 enum isl_dim_type type, int pos, isl_int *v);
4270 __isl_give isl_point *isl_point_set_coordinate(
4271 __isl_take isl_point *pnt,
4272 enum isl_dim_type type, int pos, isl_int v);
4274 __isl_give isl_point *isl_point_add_ui(
4275 __isl_take isl_point *pnt,
4276 enum isl_dim_type type, int pos, unsigned val);
4277 __isl_give isl_point *isl_point_sub_ui(
4278 __isl_take isl_point *pnt,
4279 enum isl_dim_type type, int pos, unsigned val);
4281 Other properties can be obtained using
4283 isl_ctx *isl_point_get_ctx(__isl_keep isl_point *pnt);
4285 Points can be copied or freed using
4287 __isl_give isl_point *isl_point_copy(
4288 __isl_keep isl_point *pnt);
4289 void isl_point_free(__isl_take isl_point *pnt);
4291 A singleton set can be created from a point using
4293 __isl_give isl_basic_set *isl_basic_set_from_point(
4294 __isl_take isl_point *pnt);
4295 __isl_give isl_set *isl_set_from_point(
4296 __isl_take isl_point *pnt);
4298 and a box can be created from two opposite extremal points using
4300 __isl_give isl_basic_set *isl_basic_set_box_from_points(
4301 __isl_take isl_point *pnt1,
4302 __isl_take isl_point *pnt2);
4303 __isl_give isl_set *isl_set_box_from_points(
4304 __isl_take isl_point *pnt1,
4305 __isl_take isl_point *pnt2);
4307 All elements of a B<bounded> (union) set can be enumerated using
4308 the following functions.
4310 int isl_set_foreach_point(__isl_keep isl_set *set,
4311 int (*fn)(__isl_take isl_point *pnt, void *user),
4313 int isl_union_set_foreach_point(__isl_keep isl_union_set *uset,
4314 int (*fn)(__isl_take isl_point *pnt, void *user),
4317 The function C<fn> is called for each integer point in
4318 C<set> with as second argument the last argument of
4319 the C<isl_set_foreach_point> call. The function C<fn>
4320 should return C<0> on success and C<-1> on failure.
4321 In the latter case, C<isl_set_foreach_point> will stop
4322 enumerating and return C<-1> as well.
4323 If the enumeration is performed successfully and to completion,
4324 then C<isl_set_foreach_point> returns C<0>.
4326 To obtain a single point of a (basic) set, use
4328 __isl_give isl_point *isl_basic_set_sample_point(
4329 __isl_take isl_basic_set *bset);
4330 __isl_give isl_point *isl_set_sample_point(
4331 __isl_take isl_set *set);
4333 If C<set> does not contain any (integer) points, then the
4334 resulting point will be ``void'', a property that can be
4337 int isl_point_is_void(__isl_keep isl_point *pnt);
4339 =head2 Piecewise Quasipolynomials
4341 A piecewise quasipolynomial is a particular kind of function that maps
4342 a parametric point to a rational value.
4343 More specifically, a quasipolynomial is a polynomial expression in greatest
4344 integer parts of affine expressions of parameters and variables.
4345 A piecewise quasipolynomial is a subdivision of a given parametric
4346 domain into disjoint cells with a quasipolynomial associated to
4347 each cell. The value of the piecewise quasipolynomial at a given
4348 point is the value of the quasipolynomial associated to the cell
4349 that contains the point. Outside of the union of cells,
4350 the value is assumed to be zero.
4351 For example, the piecewise quasipolynomial
4353 [n] -> { [x] -> ((1 + n) - x) : x <= n and x >= 0 }
4355 maps C<x> to C<1 + n - x> for values of C<x> between C<0> and C<n>.
4356 A given piecewise quasipolynomial has a fixed domain dimension.
4357 Union piecewise quasipolynomials are used to contain piecewise quasipolynomials
4358 defined over different domains.
4359 Piecewise quasipolynomials are mainly used by the C<barvinok>
4360 library for representing the number of elements in a parametric set or map.
4361 For example, the piecewise quasipolynomial above represents
4362 the number of points in the map
4364 [n] -> { [x] -> [y] : x,y >= 0 and 0 <= x + y <= n }
4366 =head3 Input and Output
4368 Piecewise quasipolynomials can be read from input using
4370 __isl_give isl_union_pw_qpolynomial *
4371 isl_union_pw_qpolynomial_read_from_str(
4372 isl_ctx *ctx, const char *str);
4374 Quasipolynomials and piecewise quasipolynomials can be printed
4375 using the following functions.
4377 __isl_give isl_printer *isl_printer_print_qpolynomial(
4378 __isl_take isl_printer *p,
4379 __isl_keep isl_qpolynomial *qp);
4381 __isl_give isl_printer *isl_printer_print_pw_qpolynomial(
4382 __isl_take isl_printer *p,
4383 __isl_keep isl_pw_qpolynomial *pwqp);
4385 __isl_give isl_printer *isl_printer_print_union_pw_qpolynomial(
4386 __isl_take isl_printer *p,
4387 __isl_keep isl_union_pw_qpolynomial *upwqp);
4389 The output format of the printer
4390 needs to be set to either C<ISL_FORMAT_ISL> or C<ISL_FORMAT_C>.
4391 For C<isl_printer_print_union_pw_qpolynomial>, only C<ISL_FORMAT_ISL>
4393 In case of printing in C<ISL_FORMAT_C>, the user may want
4394 to set the names of all dimensions
4396 __isl_give isl_qpolynomial *isl_qpolynomial_set_dim_name(
4397 __isl_take isl_qpolynomial *qp,
4398 enum isl_dim_type type, unsigned pos,
4400 __isl_give isl_pw_qpolynomial *
4401 isl_pw_qpolynomial_set_dim_name(
4402 __isl_take isl_pw_qpolynomial *pwqp,
4403 enum isl_dim_type type, unsigned pos,
4406 =head3 Creating New (Piecewise) Quasipolynomials
4408 Some simple quasipolynomials can be created using the following functions.
4409 More complicated quasipolynomials can be created by applying
4410 operations such as addition and multiplication
4411 on the resulting quasipolynomials
4413 __isl_give isl_qpolynomial *isl_qpolynomial_zero_on_domain(
4414 __isl_take isl_space *domain);
4415 __isl_give isl_qpolynomial *isl_qpolynomial_one_on_domain(
4416 __isl_take isl_space *domain);
4417 __isl_give isl_qpolynomial *isl_qpolynomial_infty_on_domain(
4418 __isl_take isl_space *domain);
4419 __isl_give isl_qpolynomial *isl_qpolynomial_neginfty_on_domain(
4420 __isl_take isl_space *domain);
4421 __isl_give isl_qpolynomial *isl_qpolynomial_nan_on_domain(
4422 __isl_take isl_space *domain);
4423 __isl_give isl_qpolynomial *isl_qpolynomial_rat_cst_on_domain(
4424 __isl_take isl_space *domain,
4425 const isl_int n, const isl_int d);
4426 __isl_give isl_qpolynomial *isl_qpolynomial_var_on_domain(
4427 __isl_take isl_space *domain,
4428 enum isl_dim_type type, unsigned pos);
4429 __isl_give isl_qpolynomial *isl_qpolynomial_from_aff(
4430 __isl_take isl_aff *aff);
4432 Note that the space in which a quasipolynomial lives is a map space
4433 with a one-dimensional range. The C<domain> argument in some of
4434 the functions above corresponds to the domain of this map space.
4436 The zero piecewise quasipolynomial or a piecewise quasipolynomial
4437 with a single cell can be created using the following functions.
4438 Multiple of these single cell piecewise quasipolynomials can
4439 be combined to create more complicated piecewise quasipolynomials.
4441 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_zero(
4442 __isl_take isl_space *space);
4443 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_alloc(
4444 __isl_take isl_set *set,
4445 __isl_take isl_qpolynomial *qp);
4446 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_from_qpolynomial(
4447 __isl_take isl_qpolynomial *qp);
4448 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_from_pw_aff(
4449 __isl_take isl_pw_aff *pwaff);
4451 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_zero(
4452 __isl_take isl_space *space);
4453 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_from_pw_qpolynomial(
4454 __isl_take isl_pw_qpolynomial *pwqp);
4455 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_add_pw_qpolynomial(
4456 __isl_take isl_union_pw_qpolynomial *upwqp,
4457 __isl_take isl_pw_qpolynomial *pwqp);
4459 Quasipolynomials can be copied and freed again using the following
4462 __isl_give isl_qpolynomial *isl_qpolynomial_copy(
4463 __isl_keep isl_qpolynomial *qp);
4464 void *isl_qpolynomial_free(__isl_take isl_qpolynomial *qp);
4466 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_copy(
4467 __isl_keep isl_pw_qpolynomial *pwqp);
4468 void *isl_pw_qpolynomial_free(
4469 __isl_take isl_pw_qpolynomial *pwqp);
4471 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_copy(
4472 __isl_keep isl_union_pw_qpolynomial *upwqp);
4473 void *isl_union_pw_qpolynomial_free(
4474 __isl_take isl_union_pw_qpolynomial *upwqp);
4476 =head3 Inspecting (Piecewise) Quasipolynomials
4478 To iterate over all piecewise quasipolynomials in a union
4479 piecewise quasipolynomial, use the following function
4481 int isl_union_pw_qpolynomial_foreach_pw_qpolynomial(
4482 __isl_keep isl_union_pw_qpolynomial *upwqp,
4483 int (*fn)(__isl_take isl_pw_qpolynomial *pwqp, void *user),
4486 To extract the piecewise quasipolynomial in a given space from a union, use
4488 __isl_give isl_pw_qpolynomial *
4489 isl_union_pw_qpolynomial_extract_pw_qpolynomial(
4490 __isl_keep isl_union_pw_qpolynomial *upwqp,
4491 __isl_take isl_space *space);
4493 To iterate over the cells in a piecewise quasipolynomial,
4494 use either of the following two functions
4496 int isl_pw_qpolynomial_foreach_piece(
4497 __isl_keep isl_pw_qpolynomial *pwqp,
4498 int (*fn)(__isl_take isl_set *set,
4499 __isl_take isl_qpolynomial *qp,
4500 void *user), void *user);
4501 int isl_pw_qpolynomial_foreach_lifted_piece(
4502 __isl_keep isl_pw_qpolynomial *pwqp,
4503 int (*fn)(__isl_take isl_set *set,
4504 __isl_take isl_qpolynomial *qp,
4505 void *user), void *user);
4507 As usual, the function C<fn> should return C<0> on success
4508 and C<-1> on failure. The difference between
4509 C<isl_pw_qpolynomial_foreach_piece> and
4510 C<isl_pw_qpolynomial_foreach_lifted_piece> is that
4511 C<isl_pw_qpolynomial_foreach_lifted_piece> will first
4512 compute unique representations for all existentially quantified
4513 variables and then turn these existentially quantified variables
4514 into extra set variables, adapting the associated quasipolynomial
4515 accordingly. This means that the C<set> passed to C<fn>
4516 will not have any existentially quantified variables, but that
4517 the dimensions of the sets may be different for different
4518 invocations of C<fn>.
4520 To iterate over all terms in a quasipolynomial,
4523 int isl_qpolynomial_foreach_term(
4524 __isl_keep isl_qpolynomial *qp,
4525 int (*fn)(__isl_take isl_term *term,
4526 void *user), void *user);
4528 The terms themselves can be inspected and freed using
4531 unsigned isl_term_dim(__isl_keep isl_term *term,
4532 enum isl_dim_type type);
4533 void isl_term_get_num(__isl_keep isl_term *term,
4535 void isl_term_get_den(__isl_keep isl_term *term,
4537 int isl_term_get_exp(__isl_keep isl_term *term,
4538 enum isl_dim_type type, unsigned pos);
4539 __isl_give isl_aff *isl_term_get_div(
4540 __isl_keep isl_term *term, unsigned pos);
4541 void isl_term_free(__isl_take isl_term *term);
4543 Each term is a product of parameters, set variables and
4544 integer divisions. The function C<isl_term_get_exp>
4545 returns the exponent of a given dimensions in the given term.
4546 The C<isl_int>s in the arguments of C<isl_term_get_num>
4547 and C<isl_term_get_den> need to have been initialized
4548 using C<isl_int_init> before calling these functions.
4550 =head3 Properties of (Piecewise) Quasipolynomials
4552 To check whether a quasipolynomial is actually a constant,
4553 use the following function.
4555 int isl_qpolynomial_is_cst(__isl_keep isl_qpolynomial *qp,
4556 isl_int *n, isl_int *d);
4558 If C<qp> is a constant and if C<n> and C<d> are not C<NULL>
4559 then the numerator and denominator of the constant
4560 are returned in C<*n> and C<*d>, respectively.
4562 To check whether two union piecewise quasipolynomials are
4563 obviously equal, use
4565 int isl_union_pw_qpolynomial_plain_is_equal(
4566 __isl_keep isl_union_pw_qpolynomial *upwqp1,
4567 __isl_keep isl_union_pw_qpolynomial *upwqp2);
4569 =head3 Operations on (Piecewise) Quasipolynomials
4571 __isl_give isl_qpolynomial *isl_qpolynomial_scale(
4572 __isl_take isl_qpolynomial *qp, isl_int v);
4573 __isl_give isl_qpolynomial *isl_qpolynomial_neg(
4574 __isl_take isl_qpolynomial *qp);
4575 __isl_give isl_qpolynomial *isl_qpolynomial_add(
4576 __isl_take isl_qpolynomial *qp1,
4577 __isl_take isl_qpolynomial *qp2);
4578 __isl_give isl_qpolynomial *isl_qpolynomial_sub(
4579 __isl_take isl_qpolynomial *qp1,
4580 __isl_take isl_qpolynomial *qp2);
4581 __isl_give isl_qpolynomial *isl_qpolynomial_mul(
4582 __isl_take isl_qpolynomial *qp1,
4583 __isl_take isl_qpolynomial *qp2);
4584 __isl_give isl_qpolynomial *isl_qpolynomial_pow(
4585 __isl_take isl_qpolynomial *qp, unsigned exponent);
4587 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_add(
4588 __isl_take isl_pw_qpolynomial *pwqp1,
4589 __isl_take isl_pw_qpolynomial *pwqp2);
4590 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_sub(
4591 __isl_take isl_pw_qpolynomial *pwqp1,
4592 __isl_take isl_pw_qpolynomial *pwqp2);
4593 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_add_disjoint(
4594 __isl_take isl_pw_qpolynomial *pwqp1,
4595 __isl_take isl_pw_qpolynomial *pwqp2);
4596 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_neg(
4597 __isl_take isl_pw_qpolynomial *pwqp);
4598 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_mul(
4599 __isl_take isl_pw_qpolynomial *pwqp1,
4600 __isl_take isl_pw_qpolynomial *pwqp2);
4601 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_pow(
4602 __isl_take isl_pw_qpolynomial *pwqp, unsigned exponent);
4604 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_add(
4605 __isl_take isl_union_pw_qpolynomial *upwqp1,
4606 __isl_take isl_union_pw_qpolynomial *upwqp2);
4607 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_sub(
4608 __isl_take isl_union_pw_qpolynomial *upwqp1,
4609 __isl_take isl_union_pw_qpolynomial *upwqp2);
4610 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_mul(
4611 __isl_take isl_union_pw_qpolynomial *upwqp1,
4612 __isl_take isl_union_pw_qpolynomial *upwqp2);
4614 __isl_give isl_qpolynomial *isl_pw_qpolynomial_eval(
4615 __isl_take isl_pw_qpolynomial *pwqp,
4616 __isl_take isl_point *pnt);
4618 __isl_give isl_qpolynomial *isl_union_pw_qpolynomial_eval(
4619 __isl_take isl_union_pw_qpolynomial *upwqp,
4620 __isl_take isl_point *pnt);
4622 __isl_give isl_set *isl_pw_qpolynomial_domain(
4623 __isl_take isl_pw_qpolynomial *pwqp);
4624 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_intersect_domain(
4625 __isl_take isl_pw_qpolynomial *pwpq,
4626 __isl_take isl_set *set);
4627 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_intersect_params(
4628 __isl_take isl_pw_qpolynomial *pwpq,
4629 __isl_take isl_set *set);
4631 __isl_give isl_union_set *isl_union_pw_qpolynomial_domain(
4632 __isl_take isl_union_pw_qpolynomial *upwqp);
4633 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_intersect_domain(
4634 __isl_take isl_union_pw_qpolynomial *upwpq,
4635 __isl_take isl_union_set *uset);
4636 __isl_give isl_union_pw_qpolynomial *
4637 isl_union_pw_qpolynomial_intersect_params(
4638 __isl_take isl_union_pw_qpolynomial *upwpq,
4639 __isl_take isl_set *set);
4641 __isl_give isl_qpolynomial *isl_qpolynomial_align_params(
4642 __isl_take isl_qpolynomial *qp,
4643 __isl_take isl_space *model);
4645 __isl_give isl_qpolynomial *isl_qpolynomial_project_domain_on_params(
4646 __isl_take isl_qpolynomial *qp);
4647 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_project_domain_on_params(
4648 __isl_take isl_pw_qpolynomial *pwqp);
4650 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_coalesce(
4651 __isl_take isl_union_pw_qpolynomial *upwqp);
4653 __isl_give isl_qpolynomial *isl_qpolynomial_gist_params(
4654 __isl_take isl_qpolynomial *qp,
4655 __isl_take isl_set *context);
4656 __isl_give isl_qpolynomial *isl_qpolynomial_gist(
4657 __isl_take isl_qpolynomial *qp,
4658 __isl_take isl_set *context);
4660 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_gist_params(
4661 __isl_take isl_pw_qpolynomial *pwqp,
4662 __isl_take isl_set *context);
4663 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_gist(
4664 __isl_take isl_pw_qpolynomial *pwqp,
4665 __isl_take isl_set *context);
4667 __isl_give isl_union_pw_qpolynomial *
4668 isl_union_pw_qpolynomial_gist_params(
4669 __isl_take isl_union_pw_qpolynomial *upwqp,
4670 __isl_take isl_set *context);
4671 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_gist(
4672 __isl_take isl_union_pw_qpolynomial *upwqp,
4673 __isl_take isl_union_set *context);
4675 The gist operation applies the gist operation to each of
4676 the cells in the domain of the input piecewise quasipolynomial.
4677 The context is also exploited
4678 to simplify the quasipolynomials associated to each cell.
4680 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_to_polynomial(
4681 __isl_take isl_pw_qpolynomial *pwqp, int sign);
4682 __isl_give isl_union_pw_qpolynomial *
4683 isl_union_pw_qpolynomial_to_polynomial(
4684 __isl_take isl_union_pw_qpolynomial *upwqp, int sign);
4686 Approximate each quasipolynomial by a polynomial. If C<sign> is positive,
4687 the polynomial will be an overapproximation. If C<sign> is negative,
4688 it will be an underapproximation. If C<sign> is zero, the approximation
4689 will lie somewhere in between.
4691 =head2 Bounds on Piecewise Quasipolynomials and Piecewise Quasipolynomial Reductions
4693 A piecewise quasipolynomial reduction is a piecewise
4694 reduction (or fold) of quasipolynomials.
4695 In particular, the reduction can be maximum or a minimum.
4696 The objects are mainly used to represent the result of
4697 an upper or lower bound on a quasipolynomial over its domain,
4698 i.e., as the result of the following function.
4700 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_bound(
4701 __isl_take isl_pw_qpolynomial *pwqp,
4702 enum isl_fold type, int *tight);
4704 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_bound(
4705 __isl_take isl_union_pw_qpolynomial *upwqp,
4706 enum isl_fold type, int *tight);
4708 The C<type> argument may be either C<isl_fold_min> or C<isl_fold_max>.
4709 If C<tight> is not C<NULL>, then C<*tight> is set to C<1>
4710 is the returned bound is known be tight, i.e., for each value
4711 of the parameters there is at least
4712 one element in the domain that reaches the bound.
4713 If the domain of C<pwqp> is not wrapping, then the bound is computed
4714 over all elements in that domain and the result has a purely parametric
4715 domain. If the domain of C<pwqp> is wrapping, then the bound is
4716 computed over the range of the wrapped relation. The domain of the
4717 wrapped relation becomes the domain of the result.
4719 A (piecewise) quasipolynomial reduction can be copied or freed using the
4720 following functions.
4722 __isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_copy(
4723 __isl_keep isl_qpolynomial_fold *fold);
4724 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_copy(
4725 __isl_keep isl_pw_qpolynomial_fold *pwf);
4726 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_copy(
4727 __isl_keep isl_union_pw_qpolynomial_fold *upwf);
4728 void isl_qpolynomial_fold_free(
4729 __isl_take isl_qpolynomial_fold *fold);
4730 void *isl_pw_qpolynomial_fold_free(
4731 __isl_take isl_pw_qpolynomial_fold *pwf);
4732 void *isl_union_pw_qpolynomial_fold_free(
4733 __isl_take isl_union_pw_qpolynomial_fold *upwf);
4735 =head3 Printing Piecewise Quasipolynomial Reductions
4737 Piecewise quasipolynomial reductions can be printed
4738 using the following function.
4740 __isl_give isl_printer *isl_printer_print_pw_qpolynomial_fold(
4741 __isl_take isl_printer *p,
4742 __isl_keep isl_pw_qpolynomial_fold *pwf);
4743 __isl_give isl_printer *isl_printer_print_union_pw_qpolynomial_fold(
4744 __isl_take isl_printer *p,
4745 __isl_keep isl_union_pw_qpolynomial_fold *upwf);
4747 For C<isl_printer_print_pw_qpolynomial_fold>,
4748 output format of the printer
4749 needs to be set to either C<ISL_FORMAT_ISL> or C<ISL_FORMAT_C>.
4750 For C<isl_printer_print_union_pw_qpolynomial_fold>,
4751 output format of the printer
4752 needs to be set to C<ISL_FORMAT_ISL>.
4753 In case of printing in C<ISL_FORMAT_C>, the user may want
4754 to set the names of all dimensions
4756 __isl_give isl_pw_qpolynomial_fold *
4757 isl_pw_qpolynomial_fold_set_dim_name(
4758 __isl_take isl_pw_qpolynomial_fold *pwf,
4759 enum isl_dim_type type, unsigned pos,
4762 =head3 Inspecting (Piecewise) Quasipolynomial Reductions
4764 To iterate over all piecewise quasipolynomial reductions in a union
4765 piecewise quasipolynomial reduction, use the following function
4767 int isl_union_pw_qpolynomial_fold_foreach_pw_qpolynomial_fold(
4768 __isl_keep isl_union_pw_qpolynomial_fold *upwf,
4769 int (*fn)(__isl_take isl_pw_qpolynomial_fold *pwf,
4770 void *user), void *user);
4772 To iterate over the cells in a piecewise quasipolynomial reduction,
4773 use either of the following two functions
4775 int isl_pw_qpolynomial_fold_foreach_piece(
4776 __isl_keep isl_pw_qpolynomial_fold *pwf,
4777 int (*fn)(__isl_take isl_set *set,
4778 __isl_take isl_qpolynomial_fold *fold,
4779 void *user), void *user);
4780 int isl_pw_qpolynomial_fold_foreach_lifted_piece(
4781 __isl_keep isl_pw_qpolynomial_fold *pwf,
4782 int (*fn)(__isl_take isl_set *set,
4783 __isl_take isl_qpolynomial_fold *fold,
4784 void *user), void *user);
4786 See L<Inspecting (Piecewise) Quasipolynomials> for an explanation
4787 of the difference between these two functions.
4789 To iterate over all quasipolynomials in a reduction, use
4791 int isl_qpolynomial_fold_foreach_qpolynomial(
4792 __isl_keep isl_qpolynomial_fold *fold,
4793 int (*fn)(__isl_take isl_qpolynomial *qp,
4794 void *user), void *user);
4796 =head3 Properties of Piecewise Quasipolynomial Reductions
4798 To check whether two union piecewise quasipolynomial reductions are
4799 obviously equal, use
4801 int isl_union_pw_qpolynomial_fold_plain_is_equal(
4802 __isl_keep isl_union_pw_qpolynomial_fold *upwf1,
4803 __isl_keep isl_union_pw_qpolynomial_fold *upwf2);
4805 =head3 Operations on Piecewise Quasipolynomial Reductions
4807 __isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_scale(
4808 __isl_take isl_qpolynomial_fold *fold, isl_int v);
4810 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_add(
4811 __isl_take isl_pw_qpolynomial_fold *pwf1,
4812 __isl_take isl_pw_qpolynomial_fold *pwf2);
4814 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_fold(
4815 __isl_take isl_pw_qpolynomial_fold *pwf1,
4816 __isl_take isl_pw_qpolynomial_fold *pwf2);
4818 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_fold(
4819 __isl_take isl_union_pw_qpolynomial_fold *upwf1,
4820 __isl_take isl_union_pw_qpolynomial_fold *upwf2);
4822 __isl_give isl_qpolynomial *isl_pw_qpolynomial_fold_eval(
4823 __isl_take isl_pw_qpolynomial_fold *pwf,
4824 __isl_take isl_point *pnt);
4826 __isl_give isl_qpolynomial *isl_union_pw_qpolynomial_fold_eval(
4827 __isl_take isl_union_pw_qpolynomial_fold *upwf,
4828 __isl_take isl_point *pnt);
4830 __isl_give isl_pw_qpolynomial_fold *
4831 isl_pw_qpolynomial_fold_intersect_params(
4832 __isl_take isl_pw_qpolynomial_fold *pwf,
4833 __isl_take isl_set *set);
4835 __isl_give isl_union_set *isl_union_pw_qpolynomial_fold_domain(
4836 __isl_take isl_union_pw_qpolynomial_fold *upwf);
4837 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_intersect_domain(
4838 __isl_take isl_union_pw_qpolynomial_fold *upwf,
4839 __isl_take isl_union_set *uset);
4840 __isl_give isl_union_pw_qpolynomial_fold *
4841 isl_union_pw_qpolynomial_fold_intersect_params(
4842 __isl_take isl_union_pw_qpolynomial_fold *upwf,
4843 __isl_take isl_set *set);
4845 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_project_domain_on_params(
4846 __isl_take isl_pw_qpolynomial_fold *pwf);
4848 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_coalesce(
4849 __isl_take isl_pw_qpolynomial_fold *pwf);
4851 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_coalesce(
4852 __isl_take isl_union_pw_qpolynomial_fold *upwf);
4854 __isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_gist_params(
4855 __isl_take isl_qpolynomial_fold *fold,
4856 __isl_take isl_set *context);
4857 __isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_gist(
4858 __isl_take isl_qpolynomial_fold *fold,
4859 __isl_take isl_set *context);
4861 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_gist(
4862 __isl_take isl_pw_qpolynomial_fold *pwf,
4863 __isl_take isl_set *context);
4864 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_gist_params(
4865 __isl_take isl_pw_qpolynomial_fold *pwf,
4866 __isl_take isl_set *context);
4868 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_gist(
4869 __isl_take isl_union_pw_qpolynomial_fold *upwf,
4870 __isl_take isl_union_set *context);
4871 __isl_give isl_union_pw_qpolynomial_fold *
4872 isl_union_pw_qpolynomial_fold_gist_params(
4873 __isl_take isl_union_pw_qpolynomial_fold *upwf,
4874 __isl_take isl_set *context);
4876 The gist operation applies the gist operation to each of
4877 the cells in the domain of the input piecewise quasipolynomial reduction.
4878 In future, the operation will also exploit the context
4879 to simplify the quasipolynomial reductions associated to each cell.
4881 __isl_give isl_pw_qpolynomial_fold *
4882 isl_set_apply_pw_qpolynomial_fold(
4883 __isl_take isl_set *set,
4884 __isl_take isl_pw_qpolynomial_fold *pwf,
4886 __isl_give isl_pw_qpolynomial_fold *
4887 isl_map_apply_pw_qpolynomial_fold(
4888 __isl_take isl_map *map,
4889 __isl_take isl_pw_qpolynomial_fold *pwf,
4891 __isl_give isl_union_pw_qpolynomial_fold *
4892 isl_union_set_apply_union_pw_qpolynomial_fold(
4893 __isl_take isl_union_set *uset,
4894 __isl_take isl_union_pw_qpolynomial_fold *upwf,
4896 __isl_give isl_union_pw_qpolynomial_fold *
4897 isl_union_map_apply_union_pw_qpolynomial_fold(
4898 __isl_take isl_union_map *umap,
4899 __isl_take isl_union_pw_qpolynomial_fold *upwf,
4902 The functions taking a map
4903 compose the given map with the given piecewise quasipolynomial reduction.
4904 That is, compute a bound (of the same type as C<pwf> or C<upwf> itself)
4905 over all elements in the intersection of the range of the map
4906 and the domain of the piecewise quasipolynomial reduction
4907 as a function of an element in the domain of the map.
4908 The functions taking a set compute a bound over all elements in the
4909 intersection of the set and the domain of the
4910 piecewise quasipolynomial reduction.
4912 =head2 Parametric Vertex Enumeration
4914 The parametric vertex enumeration described in this section
4915 is mainly intended to be used internally and by the C<barvinok>
4918 #include <isl/vertices.h>
4919 __isl_give isl_vertices *isl_basic_set_compute_vertices(
4920 __isl_keep isl_basic_set *bset);
4922 The function C<isl_basic_set_compute_vertices> performs the
4923 actual computation of the parametric vertices and the chamber
4924 decomposition and store the result in an C<isl_vertices> object.
4925 This information can be queried by either iterating over all
4926 the vertices or iterating over all the chambers or cells
4927 and then iterating over all vertices that are active on the chamber.
4929 int isl_vertices_foreach_vertex(
4930 __isl_keep isl_vertices *vertices,
4931 int (*fn)(__isl_take isl_vertex *vertex, void *user),
4934 int isl_vertices_foreach_cell(
4935 __isl_keep isl_vertices *vertices,
4936 int (*fn)(__isl_take isl_cell *cell, void *user),
4938 int isl_cell_foreach_vertex(__isl_keep isl_cell *cell,
4939 int (*fn)(__isl_take isl_vertex *vertex, void *user),
4942 Other operations that can be performed on an C<isl_vertices> object are
4945 isl_ctx *isl_vertices_get_ctx(
4946 __isl_keep isl_vertices *vertices);
4947 int isl_vertices_get_n_vertices(
4948 __isl_keep isl_vertices *vertices);
4949 void isl_vertices_free(__isl_take isl_vertices *vertices);
4951 Vertices can be inspected and destroyed using the following functions.
4953 isl_ctx *isl_vertex_get_ctx(__isl_keep isl_vertex *vertex);
4954 int isl_vertex_get_id(__isl_keep isl_vertex *vertex);
4955 __isl_give isl_basic_set *isl_vertex_get_domain(
4956 __isl_keep isl_vertex *vertex);
4957 __isl_give isl_basic_set *isl_vertex_get_expr(
4958 __isl_keep isl_vertex *vertex);
4959 void isl_vertex_free(__isl_take isl_vertex *vertex);
4961 C<isl_vertex_get_expr> returns a singleton parametric set describing
4962 the vertex, while C<isl_vertex_get_domain> returns the activity domain
4964 Note that C<isl_vertex_get_domain> and C<isl_vertex_get_expr> return
4965 B<rational> basic sets, so they should mainly be used for inspection
4966 and should not be mixed with integer sets.
4968 Chambers can be inspected and destroyed using the following functions.
4970 isl_ctx *isl_cell_get_ctx(__isl_keep isl_cell *cell);
4971 __isl_give isl_basic_set *isl_cell_get_domain(
4972 __isl_keep isl_cell *cell);
4973 void isl_cell_free(__isl_take isl_cell *cell);
4975 =head1 Polyhedral Compilation Library
4977 This section collects functionality in C<isl> that has been specifically
4978 designed for use during polyhedral compilation.
4980 =head2 Dependence Analysis
4982 C<isl> contains specialized functionality for performing
4983 array dataflow analysis. That is, given a I<sink> access relation
4984 and a collection of possible I<source> access relations,
4985 C<isl> can compute relations that describe
4986 for each iteration of the sink access, which iteration
4987 of which of the source access relations was the last
4988 to access the same data element before the given iteration
4990 The resulting dependence relations map source iterations
4991 to the corresponding sink iterations.
4992 To compute standard flow dependences, the sink should be
4993 a read, while the sources should be writes.
4994 If any of the source accesses are marked as being I<may>
4995 accesses, then there will be a dependence from the last
4996 I<must> access B<and> from any I<may> access that follows
4997 this last I<must> access.
4998 In particular, if I<all> sources are I<may> accesses,
4999 then memory based dependence analysis is performed.
5000 If, on the other hand, all sources are I<must> accesses,
5001 then value based dependence analysis is performed.
5003 #include <isl/flow.h>
5005 typedef int (*isl_access_level_before)(void *first, void *second);
5007 __isl_give isl_access_info *isl_access_info_alloc(
5008 __isl_take isl_map *sink,
5009 void *sink_user, isl_access_level_before fn,
5011 __isl_give isl_access_info *isl_access_info_add_source(
5012 __isl_take isl_access_info *acc,
5013 __isl_take isl_map *source, int must,
5015 void *isl_access_info_free(__isl_take isl_access_info *acc);
5017 __isl_give isl_flow *isl_access_info_compute_flow(
5018 __isl_take isl_access_info *acc);
5020 int isl_flow_foreach(__isl_keep isl_flow *deps,
5021 int (*fn)(__isl_take isl_map *dep, int must,
5022 void *dep_user, void *user),
5024 __isl_give isl_map *isl_flow_get_no_source(
5025 __isl_keep isl_flow *deps, int must);
5026 void isl_flow_free(__isl_take isl_flow *deps);
5028 The function C<isl_access_info_compute_flow> performs the actual
5029 dependence analysis. The other functions are used to construct
5030 the input for this function or to read off the output.
5032 The input is collected in an C<isl_access_info>, which can
5033 be created through a call to C<isl_access_info_alloc>.
5034 The arguments to this functions are the sink access relation
5035 C<sink>, a token C<sink_user> used to identify the sink
5036 access to the user, a callback function for specifying the
5037 relative order of source and sink accesses, and the number
5038 of source access relations that will be added.
5039 The callback function has type C<int (*)(void *first, void *second)>.
5040 The function is called with two user supplied tokens identifying
5041 either a source or the sink and it should return the shared nesting
5042 level and the relative order of the two accesses.
5043 In particular, let I<n> be the number of loops shared by
5044 the two accesses. If C<first> precedes C<second> textually,
5045 then the function should return I<2 * n + 1>; otherwise,
5046 it should return I<2 * n>.
5047 The sources can be added to the C<isl_access_info> by performing
5048 (at most) C<max_source> calls to C<isl_access_info_add_source>.
5049 C<must> indicates whether the source is a I<must> access
5050 or a I<may> access. Note that a multi-valued access relation
5051 should only be marked I<must> if every iteration in the domain
5052 of the relation accesses I<all> elements in its image.
5053 The C<source_user> token is again used to identify
5054 the source access. The range of the source access relation
5055 C<source> should have the same dimension as the range
5056 of the sink access relation.
5057 The C<isl_access_info_free> function should usually not be
5058 called explicitly, because it is called implicitly by
5059 C<isl_access_info_compute_flow>.
5061 The result of the dependence analysis is collected in an
5062 C<isl_flow>. There may be elements of
5063 the sink access for which no preceding source access could be
5064 found or for which all preceding sources are I<may> accesses.
5065 The relations containing these elements can be obtained through
5066 calls to C<isl_flow_get_no_source>, the first with C<must> set
5067 and the second with C<must> unset.
5068 In the case of standard flow dependence analysis,
5069 with the sink a read and the sources I<must> writes,
5070 the first relation corresponds to the reads from uninitialized
5071 array elements and the second relation is empty.
5072 The actual flow dependences can be extracted using
5073 C<isl_flow_foreach>. This function will call the user-specified
5074 callback function C<fn> for each B<non-empty> dependence between
5075 a source and the sink. The callback function is called
5076 with four arguments, the actual flow dependence relation
5077 mapping source iterations to sink iterations, a boolean that
5078 indicates whether it is a I<must> or I<may> dependence, a token
5079 identifying the source and an additional C<void *> with value
5080 equal to the third argument of the C<isl_flow_foreach> call.
5081 A dependence is marked I<must> if it originates from a I<must>
5082 source and if it is not followed by any I<may> sources.
5084 After finishing with an C<isl_flow>, the user should call
5085 C<isl_flow_free> to free all associated memory.
5087 A higher-level interface to dependence analysis is provided
5088 by the following function.
5090 #include <isl/flow.h>
5092 int isl_union_map_compute_flow(__isl_take isl_union_map *sink,
5093 __isl_take isl_union_map *must_source,
5094 __isl_take isl_union_map *may_source,
5095 __isl_take isl_union_map *schedule,
5096 __isl_give isl_union_map **must_dep,
5097 __isl_give isl_union_map **may_dep,
5098 __isl_give isl_union_map **must_no_source,
5099 __isl_give isl_union_map **may_no_source);
5101 The arrays are identified by the tuple names of the ranges
5102 of the accesses. The iteration domains by the tuple names
5103 of the domains of the accesses and of the schedule.
5104 The relative order of the iteration domains is given by the
5105 schedule. The relations returned through C<must_no_source>
5106 and C<may_no_source> are subsets of C<sink>.
5107 Any of C<must_dep>, C<may_dep>, C<must_no_source>
5108 or C<may_no_source> may be C<NULL>, but a C<NULL> value for
5109 any of the other arguments is treated as an error.
5111 =head3 Interaction with Dependence Analysis
5113 During the dependence analysis, we frequently need to perform
5114 the following operation. Given a relation between sink iterations
5115 and potential source iterations from a particular source domain,
5116 what is the last potential source iteration corresponding to each
5117 sink iteration. It can sometimes be convenient to adjust
5118 the set of potential source iterations before or after each such operation.
5119 The prototypical example is fuzzy array dataflow analysis,
5120 where we need to analyze if, based on data-dependent constraints,
5121 the sink iteration can ever be executed without one or more of
5122 the corresponding potential source iterations being executed.
5123 If so, we can introduce extra parameters and select an unknown
5124 but fixed source iteration from the potential source iterations.
5125 To be able to perform such manipulations, C<isl> provides the following
5128 #include <isl/flow.h>
5130 typedef __isl_give isl_restriction *(*isl_access_restrict)(
5131 __isl_keep isl_map *source_map,
5132 __isl_keep isl_set *sink, void *source_user,
5134 __isl_give isl_access_info *isl_access_info_set_restrict(
5135 __isl_take isl_access_info *acc,
5136 isl_access_restrict fn, void *user);
5138 The function C<isl_access_info_set_restrict> should be called
5139 before calling C<isl_access_info_compute_flow> and registers a callback function
5140 that will be called any time C<isl> is about to compute the last
5141 potential source. The first argument is the (reverse) proto-dependence,
5142 mapping sink iterations to potential source iterations.
5143 The second argument represents the sink iterations for which
5144 we want to compute the last source iteration.
5145 The third argument is the token corresponding to the source
5146 and the final argument is the token passed to C<isl_access_info_set_restrict>.
5147 The callback is expected to return a restriction on either the input or
5148 the output of the operation computing the last potential source.
5149 If the input needs to be restricted then restrictions are needed
5150 for both the source and the sink iterations. The sink iterations
5151 and the potential source iterations will be intersected with these sets.
5152 If the output needs to be restricted then only a restriction on the source
5153 iterations is required.
5154 If any error occurs, the callback should return C<NULL>.
5155 An C<isl_restriction> object can be created, freed and inspected
5156 using the following functions.
5158 #include <isl/flow.h>
5160 __isl_give isl_restriction *isl_restriction_input(
5161 __isl_take isl_set *source_restr,
5162 __isl_take isl_set *sink_restr);
5163 __isl_give isl_restriction *isl_restriction_output(
5164 __isl_take isl_set *source_restr);
5165 __isl_give isl_restriction *isl_restriction_none(
5166 __isl_take isl_map *source_map);
5167 __isl_give isl_restriction *isl_restriction_empty(
5168 __isl_take isl_map *source_map);
5169 void *isl_restriction_free(
5170 __isl_take isl_restriction *restr);
5171 isl_ctx *isl_restriction_get_ctx(
5172 __isl_keep isl_restriction *restr);
5174 C<isl_restriction_none> and C<isl_restriction_empty> are special
5175 cases of C<isl_restriction_input>. C<isl_restriction_none>
5176 is essentially equivalent to
5178 isl_restriction_input(isl_set_universe(
5179 isl_space_range(isl_map_get_space(source_map))),
5181 isl_space_domain(isl_map_get_space(source_map))));
5183 whereas C<isl_restriction_empty> is essentially equivalent to
5185 isl_restriction_input(isl_set_empty(
5186 isl_space_range(isl_map_get_space(source_map))),
5188 isl_space_domain(isl_map_get_space(source_map))));
5192 B<The functionality described in this section is fairly new
5193 and may be subject to change.>
5195 The following function can be used to compute a schedule
5196 for a union of domains.
5197 By default, the algorithm used to construct the schedule is similar
5198 to that of C<Pluto>.
5199 Alternatively, Feautrier's multi-dimensional scheduling algorithm can
5201 The generated schedule respects all C<validity> dependences.
5202 That is, all dependence distances over these dependences in the
5203 scheduled space are lexicographically positive.
5204 The default algorithm tries to minimize the dependence distances over
5205 C<proximity> dependences.
5206 Moreover, it tries to obtain sequences (bands) of schedule dimensions
5207 for groups of domains where the dependence distances have only
5208 non-negative values.
5209 When using Feautrier's algorithm, the C<proximity> dependence
5210 distances are only minimized during the extension to a
5211 full-dimensional schedule.
5213 #include <isl/schedule.h>
5214 __isl_give isl_schedule *isl_union_set_compute_schedule(
5215 __isl_take isl_union_set *domain,
5216 __isl_take isl_union_map *validity,
5217 __isl_take isl_union_map *proximity);
5218 void *isl_schedule_free(__isl_take isl_schedule *sched);
5220 A mapping from the domains to the scheduled space can be obtained
5221 from an C<isl_schedule> using the following function.
5223 __isl_give isl_union_map *isl_schedule_get_map(
5224 __isl_keep isl_schedule *sched);
5226 A representation of the schedule can be printed using
5228 __isl_give isl_printer *isl_printer_print_schedule(
5229 __isl_take isl_printer *p,
5230 __isl_keep isl_schedule *schedule);
5232 A representation of the schedule as a forest of bands can be obtained
5233 using the following function.
5235 __isl_give isl_band_list *isl_schedule_get_band_forest(
5236 __isl_keep isl_schedule *schedule);
5238 The individual bands can be visited in depth-first post-order
5239 using the following function.
5241 #include <isl/schedule.h>
5242 int isl_schedule_foreach_band(
5243 __isl_keep isl_schedule *sched,
5244 int (*fn)(__isl_keep isl_band *band, void *user),
5247 The list can be manipulated as explained in L<"Lists">.
5248 The bands inside the list can be copied and freed using the following
5251 #include <isl/band.h>
5252 __isl_give isl_band *isl_band_copy(
5253 __isl_keep isl_band *band);
5254 void *isl_band_free(__isl_take isl_band *band);
5256 Each band contains zero or more scheduling dimensions.
5257 These are referred to as the members of the band.
5258 The section of the schedule that corresponds to the band is
5259 referred to as the partial schedule of the band.
5260 For those nodes that participate in a band, the outer scheduling
5261 dimensions form the prefix schedule, while the inner scheduling
5262 dimensions form the suffix schedule.
5263 That is, if we take a cut of the band forest, then the union of
5264 the concatenations of the prefix, partial and suffix schedules of
5265 each band in the cut is equal to the entire schedule (modulo
5266 some possible padding at the end with zero scheduling dimensions).
5267 The properties of a band can be inspected using the following functions.
5269 #include <isl/band.h>
5270 isl_ctx *isl_band_get_ctx(__isl_keep isl_band *band);
5272 int isl_band_has_children(__isl_keep isl_band *band);
5273 __isl_give isl_band_list *isl_band_get_children(
5274 __isl_keep isl_band *band);
5276 __isl_give isl_union_map *isl_band_get_prefix_schedule(
5277 __isl_keep isl_band *band);
5278 __isl_give isl_union_map *isl_band_get_partial_schedule(
5279 __isl_keep isl_band *band);
5280 __isl_give isl_union_map *isl_band_get_suffix_schedule(
5281 __isl_keep isl_band *band);
5283 int isl_band_n_member(__isl_keep isl_band *band);
5284 int isl_band_member_is_zero_distance(
5285 __isl_keep isl_band *band, int pos);
5287 int isl_band_list_foreach_band(
5288 __isl_keep isl_band_list *list,
5289 int (*fn)(__isl_keep isl_band *band, void *user),
5292 Note that a scheduling dimension is considered to be ``zero
5293 distance'' if it does not carry any proximity dependences
5295 That is, if the dependence distances of the proximity
5296 dependences are all zero in that direction (for fixed
5297 iterations of outer bands).
5298 Like C<isl_schedule_foreach_band>,
5299 the function C<isl_band_list_foreach_band> calls C<fn> on the bands
5300 in depth-first post-order.
5302 A band can be tiled using the following function.
5304 #include <isl/band.h>
5305 int isl_band_tile(__isl_keep isl_band *band,
5306 __isl_take isl_vec *sizes);
5308 int isl_options_set_tile_scale_tile_loops(isl_ctx *ctx,
5310 int isl_options_get_tile_scale_tile_loops(isl_ctx *ctx);
5311 int isl_options_set_tile_shift_point_loops(isl_ctx *ctx,
5313 int isl_options_get_tile_shift_point_loops(isl_ctx *ctx);
5315 The C<isl_band_tile> function tiles the band using the given tile sizes
5316 inside its schedule.
5317 A new child band is created to represent the point loops and it is
5318 inserted between the modified band and its children.
5319 The C<tile_scale_tile_loops> option specifies whether the tile
5320 loops iterators should be scaled by the tile sizes.
5321 If the C<tile_shift_point_loops> option is set, then the point loops
5322 are shifted to start at zero.
5324 A band can be split into two nested bands using the following function.
5326 int isl_band_split(__isl_keep isl_band *band, int pos);
5328 The resulting outer band contains the first C<pos> dimensions of C<band>
5329 while the inner band contains the remaining dimensions.
5331 A representation of the band can be printed using
5333 #include <isl/band.h>
5334 __isl_give isl_printer *isl_printer_print_band(
5335 __isl_take isl_printer *p,
5336 __isl_keep isl_band *band);
5340 #include <isl/schedule.h>
5341 int isl_options_set_schedule_max_coefficient(
5342 isl_ctx *ctx, int val);
5343 int isl_options_get_schedule_max_coefficient(
5345 int isl_options_set_schedule_max_constant_term(
5346 isl_ctx *ctx, int val);
5347 int isl_options_get_schedule_max_constant_term(
5349 int isl_options_set_schedule_fuse(isl_ctx *ctx, int val);
5350 int isl_options_get_schedule_fuse(isl_ctx *ctx);
5351 int isl_options_set_schedule_maximize_band_depth(
5352 isl_ctx *ctx, int val);
5353 int isl_options_get_schedule_maximize_band_depth(
5355 int isl_options_set_schedule_outer_zero_distance(
5356 isl_ctx *ctx, int val);
5357 int isl_options_get_schedule_outer_zero_distance(
5359 int isl_options_set_schedule_split_scaled(
5360 isl_ctx *ctx, int val);
5361 int isl_options_get_schedule_split_scaled(
5363 int isl_options_set_schedule_algorithm(
5364 isl_ctx *ctx, int val);
5365 int isl_options_get_schedule_algorithm(
5367 int isl_options_set_schedule_separate_components(
5368 isl_ctx *ctx, int val);
5369 int isl_options_get_schedule_separate_components(
5374 =item * schedule_max_coefficient
5376 This option enforces that the coefficients for variable and parameter
5377 dimensions in the calculated schedule are not larger than the specified value.
5378 This option can significantly increase the speed of the scheduling calculation
5379 and may also prevent fusing of unrelated dimensions. A value of -1 means that
5380 this option does not introduce bounds on the variable or parameter
5383 =item * schedule_max_constant_term
5385 This option enforces that the constant coefficients in the calculated schedule
5386 are not larger than the maximal constant term. This option can significantly
5387 increase the speed of the scheduling calculation and may also prevent fusing of
5388 unrelated dimensions. A value of -1 means that this option does not introduce
5389 bounds on the constant coefficients.
5391 =item * schedule_fuse
5393 This option controls the level of fusion.
5394 If this option is set to C<ISL_SCHEDULE_FUSE_MIN>, then loops in the
5395 resulting schedule will be distributed as much as possible.
5396 If this option is set to C<ISL_SCHEDULE_FUSE_MAX>, then C<isl> will
5397 try to fuse loops in the resulting schedule.
5399 =item * schedule_maximize_band_depth
5401 If this option is set, we do not split bands at the point
5402 where we detect splitting is necessary. Instead, we
5403 backtrack and split bands as early as possible. This
5404 reduces the number of splits and maximizes the width of
5405 the bands. Wider bands give more possibilities for tiling.
5406 Note that if the C<schedule_fuse> option is set to C<ISL_SCHEDULE_FUSE_MIN>,
5407 then bands will be split as early as possible, even if there is no need.
5408 The C<schedule_maximize_band_depth> option therefore has no effect in this case.
5410 =item * schedule_outer_zero_distance
5412 If this option is set, then we try to construct schedules
5413 where the outermost scheduling dimension in each band
5414 results in a zero dependence distance over the proximity
5417 =item * schedule_split_scaled
5419 If this option is set, then we try to construct schedules in which the
5420 constant term is split off from the linear part if the linear parts of
5421 the scheduling rows for all nodes in the graphs have a common non-trivial
5423 The constant term is then placed in a separate band and the linear
5426 =item * schedule_algorithm
5428 Selects the scheduling algorithm to be used.
5429 Available scheduling algorithms are C<ISL_SCHEDULE_ALGORITHM_ISL>
5430 and C<ISL_SCHEDULE_ALGORITHM_FEAUTRIER>.
5432 =item * schedule_separate_components
5434 If at any point the dependence graph contains any (weakly connected) components,
5435 then these components are scheduled separately.
5436 If this option is not set, then some iterations of the domains
5437 in these components may be scheduled together.
5438 If this option is set, then the components are given consecutive
5443 =head2 AST Generation
5445 This section describes the C<isl> functionality for generating
5446 ASTs that visit all the elements
5447 in a domain in an order specified by a schedule.
5448 In particular, given a C<isl_union_map>, an AST is generated
5449 that visits all the elements in the domain of the C<isl_union_map>
5450 according to the lexicographic order of the corresponding image
5451 element(s). If the range of the C<isl_union_map> consists of
5452 elements in more than one space, then each of these spaces is handled
5453 separately in an arbitrary order.
5454 It should be noted that the image elements only specify the I<order>
5455 in which the corresponding domain elements should be visited.
5456 No direct relation between the image elements and the loop iterators
5457 in the generated AST should be assumed.
5459 Each AST is generated within a build. The initial build
5460 simply specifies the constraints on the parameters (if any)
5461 and can be created, inspected, copied and freed using the following functions.
5463 #include <isl/ast_build.h>
5464 __isl_give isl_ast_build *isl_ast_build_from_context(
5465 __isl_take isl_set *set);
5466 isl_ctx *isl_ast_build_get_ctx(
5467 __isl_keep isl_ast_build *build);
5468 __isl_give isl_ast_build *isl_ast_build_copy(
5469 __isl_keep isl_ast_build *build);
5470 void *isl_ast_build_free(
5471 __isl_take isl_ast_build *build);
5473 The C<set> argument is usually a parameter set with zero or more parameters.
5474 More C<isl_ast_build> functions are described in L</"Nested AST Generation">
5475 and L</"Fine-grained Control over AST Generation">.
5476 Finally, the AST itself can be constructed using the following
5479 #include <isl/ast_build.h>
5480 __isl_give isl_ast_node *isl_ast_build_ast_from_schedule(
5481 __isl_keep isl_ast_build *build,
5482 __isl_take isl_union_map *schedule);
5484 =head3 Inspecting the AST
5486 The basic properties of an AST node can be obtained as follows.
5488 #include <isl/ast.h>
5489 isl_ctx *isl_ast_node_get_ctx(
5490 __isl_keep isl_ast_node *node);
5491 enum isl_ast_node_type isl_ast_node_get_type(
5492 __isl_keep isl_ast_node *node);
5494 The type of an AST node is one of
5495 C<isl_ast_node_for>,
5497 C<isl_ast_node_block> or
5498 C<isl_ast_node_user>.
5499 An C<isl_ast_node_for> represents a for node.
5500 An C<isl_ast_node_if> represents an if node.
5501 An C<isl_ast_node_block> represents a compound node.
5502 An C<isl_ast_node_user> represents an expression statement.
5503 An expression statement typically corresponds to a domain element, i.e.,
5504 one of the elements that is visited by the AST.
5506 Each type of node has its own additional properties.
5508 #include <isl/ast.h>
5509 __isl_give isl_ast_expr *isl_ast_node_for_get_iterator(
5510 __isl_keep isl_ast_node *node);
5511 __isl_give isl_ast_expr *isl_ast_node_for_get_init(
5512 __isl_keep isl_ast_node *node);
5513 __isl_give isl_ast_expr *isl_ast_node_for_get_cond(
5514 __isl_keep isl_ast_node *node);
5515 __isl_give isl_ast_expr *isl_ast_node_for_get_inc(
5516 __isl_keep isl_ast_node *node);
5517 __isl_give isl_ast_node *isl_ast_node_for_get_body(
5518 __isl_keep isl_ast_node *node);
5519 int isl_ast_node_for_is_degenerate(
5520 __isl_keep isl_ast_node *node);
5522 An C<isl_ast_for> is considered degenerate if it is known to execute
5525 #include <isl/ast.h>
5526 __isl_give isl_ast_expr *isl_ast_node_if_get_cond(
5527 __isl_keep isl_ast_node *node);
5528 __isl_give isl_ast_node *isl_ast_node_if_get_then(
5529 __isl_keep isl_ast_node *node);
5530 int isl_ast_node_if_has_else(
5531 __isl_keep isl_ast_node *node);
5532 __isl_give isl_ast_node *isl_ast_node_if_get_else(
5533 __isl_keep isl_ast_node *node);
5535 __isl_give isl_ast_node_list *
5536 isl_ast_node_block_get_children(
5537 __isl_keep isl_ast_node *node);
5539 __isl_give isl_ast_expr *isl_ast_node_user_get_expr(
5540 __isl_keep isl_ast_node *node);
5542 Each of the returned C<isl_ast_expr>s can in turn be inspected using
5543 the following functions.
5545 #include <isl/ast.h>
5546 isl_ctx *isl_ast_expr_get_ctx(
5547 __isl_keep isl_ast_expr *expr);
5548 enum isl_ast_expr_type isl_ast_expr_get_type(
5549 __isl_keep isl_ast_expr *expr);
5551 The type of an AST expression is one of
5553 C<isl_ast_expr_id> or
5554 C<isl_ast_expr_int>.
5555 An C<isl_ast_expr_op> represents the result of an operation.
5556 An C<isl_ast_expr_id> represents an identifier.
5557 An C<isl_ast_expr_int> represents an integer value.
5559 Each type of expression has its own additional properties.
5561 #include <isl/ast.h>
5562 enum isl_ast_op_type isl_ast_expr_get_op_type(
5563 __isl_keep isl_ast_expr *expr);
5564 int isl_ast_expr_get_op_n_arg(__isl_keep isl_ast_expr *expr);
5565 __isl_give isl_ast_expr *isl_ast_expr_get_op_arg(
5566 __isl_keep isl_ast_expr *expr, int pos);
5567 int isl_ast_node_foreach_ast_op_type(
5568 __isl_keep isl_ast_node *node,
5569 int (*fn)(enum isl_ast_op_type type, void *user),
5572 C<isl_ast_expr_get_op_type> returns the type of the operation
5573 performed. C<isl_ast_expr_get_op_n_arg> returns the number of
5574 arguments. C<isl_ast_expr_get_op_arg> returns the specified
5576 C<isl_ast_node_foreach_ast_op_type> calls C<fn> for each distinct
5577 C<isl_ast_op_type> that appears in C<node>.
5578 The operation type is one of the following.
5582 =item C<isl_ast_op_and>
5584 Logical I<and> of two arguments.
5585 Both arguments can be evaluated.
5587 =item C<isl_ast_op_and_then>
5589 Logical I<and> of two arguments.
5590 The second argument can only be evaluated if the first evaluates to true.
5592 =item C<isl_ast_op_or>
5594 Logical I<or> of two arguments.
5595 Both arguments can be evaluated.
5597 =item C<isl_ast_op_or_else>
5599 Logical I<or> of two arguments.
5600 The second argument can only be evaluated if the first evaluates to false.
5602 =item C<isl_ast_op_max>
5604 Maximum of two or more arguments.
5606 =item C<isl_ast_op_min>
5608 Minimum of two or more arguments.
5610 =item C<isl_ast_op_minus>
5614 =item C<isl_ast_op_add>
5616 Sum of two arguments.
5618 =item C<isl_ast_op_sub>
5620 Difference of two arguments.
5622 =item C<isl_ast_op_mul>
5624 Product of two arguments.
5626 =item C<isl_ast_op_div>
5628 Exact division. That is, the result is known to be an integer.
5630 =item C<isl_ast_op_fdiv_q>
5632 Result of integer division, rounded towards negative
5635 =item C<isl_ast_op_pdiv_q>
5637 Result of integer division, where dividend is known to be non-negative.
5639 =item C<isl_ast_op_pdiv_r>
5641 Remainder of integer division, where dividend is known to be non-negative.
5643 =item C<isl_ast_op_cond>
5645 Conditional operator defined on three arguments.
5646 If the first argument evaluates to true, then the result
5647 is equal to the second argument. Otherwise, the result
5648 is equal to the third argument.
5649 The second and third argument may only be evaluated if
5650 the first argument evaluates to true and false, respectively.
5651 Corresponds to C<a ? b : c> in C.
5653 =item C<isl_ast_op_select>
5655 Conditional operator defined on three arguments.
5656 If the first argument evaluates to true, then the result
5657 is equal to the second argument. Otherwise, the result
5658 is equal to the third argument.
5659 The second and third argument may be evaluated independently
5660 of the value of the first argument.
5661 Corresponds to C<a * b + (1 - a) * c> in C.
5663 =item C<isl_ast_op_eq>
5667 =item C<isl_ast_op_le>
5669 Less than or equal relation.
5671 =item C<isl_ast_op_lt>
5675 =item C<isl_ast_op_ge>
5677 Greater than or equal relation.
5679 =item C<isl_ast_op_gt>
5681 Greater than relation.
5683 =item C<isl_ast_op_call>
5686 The number of arguments of the C<isl_ast_expr> is one more than
5687 the number of arguments in the function call, the first argument
5688 representing the function being called.
5692 #include <isl/ast.h>
5693 __isl_give isl_id *isl_ast_expr_get_id(
5694 __isl_keep isl_ast_expr *expr);
5696 Return the identifier represented by the AST expression.
5698 #include <isl/ast.h>
5699 int isl_ast_expr_get_int(__isl_keep isl_ast_expr *expr,
5702 Return the integer represented by the AST expression.
5703 Note that the integer is returned through the C<v> argument.
5704 The return value of the function itself indicates whether the
5705 operation was performed successfully.
5707 =head3 Manipulating and printing the AST
5709 AST nodes can be copied and freed using the following functions.
5711 #include <isl/ast.h>
5712 __isl_give isl_ast_node *isl_ast_node_copy(
5713 __isl_keep isl_ast_node *node);
5714 void *isl_ast_node_free(__isl_take isl_ast_node *node);
5716 AST expressions can be copied and freed using the following functions.
5718 #include <isl/ast.h>
5719 __isl_give isl_ast_expr *isl_ast_expr_copy(
5720 __isl_keep isl_ast_expr *expr);
5721 void *isl_ast_expr_free(__isl_take isl_ast_expr *expr);
5723 New AST expressions can be created either directly or within
5724 the context of an C<isl_ast_build>.
5726 #include <isl/ast.h>
5727 __isl_give isl_ast_expr *isl_ast_expr_from_id(
5728 __isl_take isl_id *id);
5729 __isl_give isl_ast_expr *isl_ast_expr_neg(
5730 __isl_take isl_ast_expr *expr);
5731 __isl_give isl_ast_expr *isl_ast_expr_add(
5732 __isl_take isl_ast_expr *expr1,
5733 __isl_take isl_ast_expr *expr2);
5734 __isl_give isl_ast_expr *isl_ast_expr_sub(
5735 __isl_take isl_ast_expr *expr1,
5736 __isl_take isl_ast_expr *expr2);
5737 __isl_give isl_ast_expr *isl_ast_expr_mul(
5738 __isl_take isl_ast_expr *expr1,
5739 __isl_take isl_ast_expr *expr2);
5740 __isl_give isl_ast_expr *isl_ast_expr_div(
5741 __isl_take isl_ast_expr *expr1,
5742 __isl_take isl_ast_expr *expr2);
5743 __isl_give isl_ast_expr *isl_ast_expr_and(
5744 __isl_take isl_ast_expr *expr1,
5745 __isl_take isl_ast_expr *expr2)
5746 __isl_give isl_ast_expr *isl_ast_expr_or(
5747 __isl_take isl_ast_expr *expr1,
5748 __isl_take isl_ast_expr *expr2)
5750 #include <isl/ast_build.h>
5751 __isl_give isl_ast_expr *isl_ast_build_expr_from_pw_aff(
5752 __isl_keep isl_ast_build *build,
5753 __isl_take isl_pw_aff *pa);
5754 __isl_give isl_ast_expr *
5755 isl_ast_build_call_from_pw_multi_aff(
5756 __isl_keep isl_ast_build *build,
5757 __isl_take isl_pw_multi_aff *pma);
5759 The domains of C<pa> and C<pma> should correspond
5760 to the schedule space of C<build>.
5761 The tuple id of C<pma> is used as the function being called.
5763 User specified data can be attached to an C<isl_ast_node> and obtained
5764 from the same C<isl_ast_node> using the following functions.
5766 #include <isl/ast.h>
5767 __isl_give isl_ast_node *isl_ast_node_set_annotation(
5768 __isl_take isl_ast_node *node,
5769 __isl_take isl_id *annotation);
5770 __isl_give isl_id *isl_ast_node_get_annotation(
5771 __isl_keep isl_ast_node *node);
5773 Basic printing can be performed using the following functions.
5775 #include <isl/ast.h>
5776 __isl_give isl_printer *isl_printer_print_ast_expr(
5777 __isl_take isl_printer *p,
5778 __isl_keep isl_ast_expr *expr);
5779 __isl_give isl_printer *isl_printer_print_ast_node(
5780 __isl_take isl_printer *p,
5781 __isl_keep isl_ast_node *node);
5783 More advanced printing can be performed using the following functions.
5785 #include <isl/ast.h>
5786 __isl_give isl_printer *isl_ast_op_type_print_macro(
5787 enum isl_ast_op_type type,
5788 __isl_take isl_printer *p);
5789 __isl_give isl_printer *isl_ast_node_print_macros(
5790 __isl_keep isl_ast_node *node,
5791 __isl_take isl_printer *p);
5792 __isl_give isl_printer *isl_ast_node_print(
5793 __isl_keep isl_ast_node *node,
5794 __isl_take isl_printer *p,
5795 __isl_take isl_ast_print_options *options);
5796 __isl_give isl_printer *isl_ast_node_for_print(
5797 __isl_keep isl_ast_node *node,
5798 __isl_take isl_printer *p,
5799 __isl_take isl_ast_print_options *options);
5800 __isl_give isl_printer *isl_ast_node_if_print(
5801 __isl_keep isl_ast_node *node,
5802 __isl_take isl_printer *p,
5803 __isl_take isl_ast_print_options *options);
5805 While printing an C<isl_ast_node> in C<ISL_FORMAT_C>,
5806 C<isl> may print out an AST that makes use of macros such
5807 as C<floord>, C<min> and C<max>.
5808 C<isl_ast_op_type_print_macro> prints out the macro
5809 corresponding to a specific C<isl_ast_op_type>.
5810 C<isl_ast_node_print_macros> scans the C<isl_ast_node>
5811 for expressions where these macros would be used and prints
5812 out the required macro definitions.
5813 Essentially, C<isl_ast_node_print_macros> calls
5814 C<isl_ast_node_foreach_ast_op_type> with C<isl_ast_op_type_print_macro>
5815 as function argument.
5816 C<isl_ast_node_print>, C<isl_ast_node_for_print> and
5817 C<isl_ast_node_if_print> print an C<isl_ast_node>
5818 in C<ISL_FORMAT_C>, but allow for some extra control
5819 through an C<isl_ast_print_options> object.
5820 This object can be created using the following functions.
5822 #include <isl/ast.h>
5823 __isl_give isl_ast_print_options *
5824 isl_ast_print_options_alloc(isl_ctx *ctx);
5825 __isl_give isl_ast_print_options *
5826 isl_ast_print_options_copy(
5827 __isl_keep isl_ast_print_options *options);
5828 void *isl_ast_print_options_free(
5829 __isl_take isl_ast_print_options *options);
5831 __isl_give isl_ast_print_options *
5832 isl_ast_print_options_set_print_user(
5833 __isl_take isl_ast_print_options *options,
5834 __isl_give isl_printer *(*print_user)(
5835 __isl_take isl_printer *p,
5836 __isl_take isl_ast_print_options *options,
5837 __isl_keep isl_ast_node *node, void *user),
5839 __isl_give isl_ast_print_options *
5840 isl_ast_print_options_set_print_for(
5841 __isl_take isl_ast_print_options *options,
5842 __isl_give isl_printer *(*print_for)(
5843 __isl_take isl_printer *p,
5844 __isl_take isl_ast_print_options *options,
5845 __isl_keep isl_ast_node *node, void *user),
5848 The callback set by C<isl_ast_print_options_set_print_user>
5849 is called whenever a node of type C<isl_ast_node_user> needs to
5851 The callback set by C<isl_ast_print_options_set_print_for>
5852 is called whenever a node of type C<isl_ast_node_for> needs to
5854 Note that C<isl_ast_node_for_print> will I<not> call the
5855 callback set by C<isl_ast_print_options_set_print_for> on the node
5856 on which C<isl_ast_node_for_print> is called, but only on nested
5857 nodes of type C<isl_ast_node_for>. It is therefore safe to
5858 call C<isl_ast_node_for_print> from within the callback set by
5859 C<isl_ast_print_options_set_print_for>.
5861 The following option determines the type to be used for iterators
5862 while printing the AST.
5864 int isl_options_set_ast_iterator_type(
5865 isl_ctx *ctx, const char *val);
5866 const char *isl_options_get_ast_iterator_type(
5871 #include <isl/ast_build.h>
5872 int isl_options_set_ast_build_atomic_upper_bound(
5873 isl_ctx *ctx, int val);
5874 int isl_options_get_ast_build_atomic_upper_bound(
5876 int isl_options_set_ast_build_prefer_pdiv(isl_ctx *ctx,
5878 int isl_options_get_ast_build_prefer_pdiv(isl_ctx *ctx);
5879 int isl_options_set_ast_build_exploit_nested_bounds(
5880 isl_ctx *ctx, int val);
5881 int isl_options_get_ast_build_exploit_nested_bounds(
5883 int isl_options_set_ast_build_group_coscheduled(
5884 isl_ctx *ctx, int val);
5885 int isl_options_get_ast_build_group_coscheduled(
5887 int isl_options_set_ast_build_scale_strides(
5888 isl_ctx *ctx, int val);
5889 int isl_options_get_ast_build_scale_strides(
5891 int isl_options_set_ast_build_allow_else(isl_ctx *ctx,
5893 int isl_options_get_ast_build_allow_else(isl_ctx *ctx);
5894 int isl_options_set_ast_build_allow_or(isl_ctx *ctx,
5896 int isl_options_get_ast_build_allow_or(isl_ctx *ctx);
5900 =item * ast_build_atomic_upper_bound
5902 Generate loop upper bounds that consist of the current loop iterator,
5903 an operator and an expression not involving the iterator.
5904 If this option is not set, then the current loop iterator may appear
5905 several times in the upper bound.
5906 For example, when this option is turned off, AST generation
5909 [n] -> { A[i] -> [i] : 0 <= i <= 100, n }
5913 for (int c0 = 0; c0 <= 100 && n >= c0; c0 += 1)
5916 When the option is turned on, the following AST is generated
5918 for (int c0 = 0; c0 <= min(100, n); c0 += 1)
5921 =item * ast_build_prefer_pdiv
5923 If this option is turned off, then the AST generation will
5924 produce ASTs that may only contain C<isl_ast_op_fdiv_q>
5925 operators, but no C<isl_ast_op_pdiv_q> or
5926 C<isl_ast_op_pdiv_r> operators.
5927 If this options is turned on, then C<isl> will try to convert
5928 some of the C<isl_ast_op_fdiv_q> operators to (expressions containing)
5929 C<isl_ast_op_pdiv_q> or C<isl_ast_op_pdiv_r> operators.
5931 =item * ast_build_exploit_nested_bounds
5933 Simplify conditions based on bounds of nested for loops.
5934 In particular, remove conditions that are implied by the fact
5935 that one or more nested loops have at least one iteration,
5936 meaning that the upper bound is at least as large as the lower bound.
5937 For example, when this option is turned off, AST generation
5940 [N,M] -> { A[i,j] -> [i,j] : 0 <= i <= N and
5946 for (int c0 = 0; c0 <= N; c0 += 1)
5947 for (int c1 = 0; c1 <= M; c1 += 1)
5950 When the option is turned on, the following AST is generated
5952 for (int c0 = 0; c0 <= N; c0 += 1)
5953 for (int c1 = 0; c1 <= M; c1 += 1)
5956 =item * ast_build_group_coscheduled
5958 If two domain elements are assigned the same schedule point, then
5959 they may be executed in any order and they may even appear in different
5960 loops. If this options is set, then the AST generator will make
5961 sure that coscheduled domain elements do not appear in separate parts
5962 of the AST. This is useful in case of nested AST generation
5963 if the outer AST generation is given only part of a schedule
5964 and the inner AST generation should handle the domains that are
5965 coscheduled by this initial part of the schedule together.
5966 For example if an AST is generated for a schedule
5968 { A[i] -> [0]; B[i] -> [0] }
5970 then the C<isl_ast_build_set_create_leaf> callback described
5971 below may get called twice, once for each domain.
5972 Setting this option ensures that the callback is only called once
5973 on both domains together.
5975 =item * ast_build_separation_bounds
5977 This option specifies which bounds to use during separation.
5978 If this option is set to C<ISL_AST_BUILD_SEPARATION_BOUNDS_IMPLICIT>
5979 then all (possibly implicit) bounds on the current dimension will
5980 be used during separation.
5981 If this option is set to C<ISL_AST_BUILD_SEPARATION_BOUNDS_EXPLICIT>
5982 then only those bounds that are explicitly available will
5983 be used during separation.
5985 =item * ast_build_scale_strides
5987 This option specifies whether the AST generator is allowed
5988 to scale down iterators of strided loops.
5990 =item * ast_build_allow_else
5992 This option specifies whether the AST generator is allowed
5993 to construct if statements with else branches.
5995 =item * ast_build_allow_or
5997 This option specifies whether the AST generator is allowed
5998 to construct if conditions with disjunctions.
6002 =head3 Fine-grained Control over AST Generation
6004 Besides specifying the constraints on the parameters,
6005 an C<isl_ast_build> object can be used to control
6006 various aspects of the AST generation process.
6007 The most prominent way of control is through ``options'',
6008 which can be set using the following function.
6010 #include <isl/ast_build.h>
6011 __isl_give isl_ast_build *
6012 isl_ast_build_set_options(
6013 __isl_take isl_ast_build *control,
6014 __isl_take isl_union_map *options);
6016 The options are encoded in an <isl_union_map>.
6017 The domain of this union relation refers to the schedule domain,
6018 i.e., the range of the schedule passed to C<isl_ast_build_ast_from_schedule>.
6019 In the case of nested AST generation (see L</"Nested AST Generation">),
6020 the domain of C<options> should refer to the extra piece of the schedule.
6021 That is, it should be equal to the range of the wrapped relation in the
6022 range of the schedule.
6023 The range of the options can consist of elements in one or more spaces,
6024 the names of which determine the effect of the option.
6025 The values of the range typically also refer to the schedule dimension
6026 to which the option applies. In case of nested AST generation
6027 (see L</"Nested AST Generation">), these values refer to the position
6028 of the schedule dimension within the innermost AST generation.
6029 The constraints on the domain elements of
6030 the option should only refer to this dimension and earlier dimensions.
6031 We consider the following spaces.
6035 =item C<separation_class>
6037 This space is a wrapped relation between two one dimensional spaces.
6038 The input space represents the schedule dimension to which the option
6039 applies and the output space represents the separation class.
6040 While constructing a loop corresponding to the specified schedule
6041 dimension(s), the AST generator will try to generate separate loops
6042 for domain elements that are assigned different classes.
6043 If only some of the elements are assigned a class, then those elements
6044 that are not assigned any class will be treated as belonging to a class
6045 that is separate from the explicitly assigned classes.
6046 The typical use case for this option is to separate full tiles from
6048 The other options, described below, are applied after the separation
6051 As an example, consider the separation into full and partial tiles
6052 of a tiling of a triangular domain.
6053 Take, for example, the domain
6055 { A[i,j] : 0 <= i,j and i + j <= 100 }
6057 and a tiling into tiles of 10 by 10. The input to the AST generator
6058 is then the schedule
6060 { A[i,j] -> [([i/10]),[j/10],i,j] : 0 <= i,j and
6063 Without any options, the following AST is generated
6065 for (int c0 = 0; c0 <= 10; c0 += 1)
6066 for (int c1 = 0; c1 <= -c0 + 10; c1 += 1)
6067 for (int c2 = 10 * c0;
6068 c2 <= min(-10 * c1 + 100, 10 * c0 + 9);
6070 for (int c3 = 10 * c1;
6071 c3 <= min(10 * c1 + 9, -c2 + 100);
6075 Separation into full and partial tiles can be obtained by assigning
6076 a class, say C<0>, to the full tiles. The full tiles are represented by those
6077 values of the first and second schedule dimensions for which there are
6078 values of the third and fourth dimensions to cover an entire tile.
6079 That is, we need to specify the following option
6081 { [a,b,c,d] -> separation_class[[0]->[0]] :
6082 exists b': 0 <= 10a,10b' and
6083 10a+9+10b'+9 <= 100;
6084 [a,b,c,d] -> separation_class[[1]->[0]] :
6085 0 <= 10a,10b and 10a+9+10b+9 <= 100 }
6089 { [a, b, c, d] -> separation_class[[1] -> [0]] :
6090 a >= 0 and b >= 0 and b <= 8 - a;
6091 [a, b, c, d] -> separation_class[[0] -> [0]] :
6094 With this option, the generated AST is as follows
6097 for (int c0 = 0; c0 <= 8; c0 += 1) {
6098 for (int c1 = 0; c1 <= -c0 + 8; c1 += 1)
6099 for (int c2 = 10 * c0;
6100 c2 <= 10 * c0 + 9; c2 += 1)
6101 for (int c3 = 10 * c1;
6102 c3 <= 10 * c1 + 9; c3 += 1)
6104 for (int c1 = -c0 + 9; c1 <= -c0 + 10; c1 += 1)
6105 for (int c2 = 10 * c0;
6106 c2 <= min(-10 * c1 + 100, 10 * c0 + 9);
6108 for (int c3 = 10 * c1;
6109 c3 <= min(-c2 + 100, 10 * c1 + 9);
6113 for (int c0 = 9; c0 <= 10; c0 += 1)
6114 for (int c1 = 0; c1 <= -c0 + 10; c1 += 1)
6115 for (int c2 = 10 * c0;
6116 c2 <= min(-10 * c1 + 100, 10 * c0 + 9);
6118 for (int c3 = 10 * c1;
6119 c3 <= min(10 * c1 + 9, -c2 + 100);
6126 This is a single-dimensional space representing the schedule dimension(s)
6127 to which ``separation'' should be applied. Separation tries to split
6128 a loop into several pieces if this can avoid the generation of guards
6130 See also the C<atomic> option.
6134 This is a single-dimensional space representing the schedule dimension(s)
6135 for which the domains should be considered ``atomic''. That is, the
6136 AST generator will make sure that any given domain space will only appear
6137 in a single loop at the specified level.
6139 Consider the following schedule
6141 { a[i] -> [i] : 0 <= i < 10;
6142 b[i] -> [i+1] : 0 <= i < 10 }
6144 If the following option is specified
6146 { [i] -> separate[x] }
6148 then the following AST will be generated
6152 for (int c0 = 1; c0 <= 9; c0 += 1) {
6159 If, on the other hand, the following option is specified
6161 { [i] -> atomic[x] }
6163 then the following AST will be generated
6165 for (int c0 = 0; c0 <= 10; c0 += 1) {
6172 If neither C<atomic> nor C<separate> is specified, then the AST generator
6173 may produce either of these two results or some intermediate form.
6177 This is a single-dimensional space representing the schedule dimension(s)
6178 that should be I<completely> unrolled.
6179 To obtain a partial unrolling, the user should apply an additional
6180 strip-mining to the schedule and fully unroll the inner loop.
6184 Additional control is available through the following functions.
6186 #include <isl/ast_build.h>
6187 __isl_give isl_ast_build *
6188 isl_ast_build_set_iterators(
6189 __isl_take isl_ast_build *control,
6190 __isl_take isl_id_list *iterators);
6192 The function C<isl_ast_build_set_iterators> allows the user to
6193 specify a list of iterator C<isl_id>s to be used as iterators.
6194 If the input schedule is injective, then
6195 the number of elements in this list should be as large as the dimension
6196 of the schedule space, but no direct correspondence should be assumed
6197 between dimensions and elements.
6198 If the input schedule is not injective, then an additional number
6199 of C<isl_id>s equal to the largest dimension of the input domains
6201 If the number of provided C<isl_id>s is insufficient, then additional
6202 names are automatically generated.
6204 #include <isl/ast_build.h>
6205 __isl_give isl_ast_build *
6206 isl_ast_build_set_create_leaf(
6207 __isl_take isl_ast_build *control,
6208 __isl_give isl_ast_node *(*fn)(
6209 __isl_take isl_ast_build *build,
6210 void *user), void *user);
6213 C<isl_ast_build_set_create_leaf> function allows for the
6214 specification of a callback that should be called whenever the AST
6215 generator arrives at an element of the schedule domain.
6216 The callback should return an AST node that should be inserted
6217 at the corresponding position of the AST. The default action (when
6218 the callback is not set) is to continue generating parts of the AST to scan
6219 all the domain elements associated to the schedule domain element
6220 and to insert user nodes, ``calling'' the domain element, for each of them.
6221 The C<build> argument contains the current state of the C<isl_ast_build>.
6222 To ease nested AST generation (see L</"Nested AST Generation">),
6223 all control information that is
6224 specific to the current AST generation such as the options and
6225 the callbacks has been removed from this C<isl_ast_build>.
6226 The callback would typically return the result of a nested
6228 user defined node created using the following function.
6230 #include <isl/ast.h>
6231 __isl_give isl_ast_node *isl_ast_node_alloc_user(
6232 __isl_take isl_ast_expr *expr);
6234 #include <isl/ast_build.h>
6235 __isl_give isl_ast_build *
6236 isl_ast_build_set_at_each_domain(
6237 __isl_take isl_ast_build *build,
6238 __isl_give isl_ast_node *(*fn)(
6239 __isl_take isl_ast_node *node,
6240 __isl_keep isl_ast_build *build,
6241 void *user), void *user);
6242 __isl_give isl_ast_build *
6243 isl_ast_build_set_before_each_for(
6244 __isl_take isl_ast_build *build,
6245 __isl_give isl_id *(*fn)(
6246 __isl_keep isl_ast_build *build,
6247 void *user), void *user);
6248 __isl_give isl_ast_build *
6249 isl_ast_build_set_after_each_for(
6250 __isl_take isl_ast_build *build,
6251 __isl_give isl_ast_node *(*fn)(
6252 __isl_take isl_ast_node *node,
6253 __isl_keep isl_ast_build *build,
6254 void *user), void *user);
6256 The callback set by C<isl_ast_build_set_at_each_domain> will
6257 be called for each domain AST node.
6258 The callbacks set by C<isl_ast_build_set_before_each_for>
6259 and C<isl_ast_build_set_after_each_for> will be called
6260 for each for AST node. The first will be called in depth-first
6261 pre-order, while the second will be called in depth-first post-order.
6262 Since C<isl_ast_build_set_before_each_for> is called before the for
6263 node is actually constructed, it is only passed an C<isl_ast_build>.
6264 The returned C<isl_id> will be added as an annotation (using
6265 C<isl_ast_node_set_annotation>) to the constructed for node.
6266 In particular, if the user has also specified an C<after_each_for>
6267 callback, then the annotation can be retrieved from the node passed to
6268 that callback using C<isl_ast_node_get_annotation>.
6269 All callbacks should C<NULL> on failure.
6270 The given C<isl_ast_build> can be used to create new
6271 C<isl_ast_expr> objects using C<isl_ast_build_expr_from_pw_aff>
6272 or C<isl_ast_build_call_from_pw_multi_aff>.
6274 =head3 Nested AST Generation
6276 C<isl> allows the user to create an AST within the context
6277 of another AST. These nested ASTs are created using the
6278 same C<isl_ast_build_ast_from_schedule> function that is used to create the
6279 outer AST. The C<build> argument should be an C<isl_ast_build>
6280 passed to a callback set by
6281 C<isl_ast_build_set_create_leaf>.
6282 The space of the range of the C<schedule> argument should refer
6283 to this build. In particular, the space should be a wrapped
6284 relation and the domain of this wrapped relation should be the
6285 same as that of the range of the schedule returned by
6286 C<isl_ast_build_get_schedule> below.
6287 In practice, the new schedule is typically
6288 created by calling C<isl_union_map_range_product> on the old schedule
6289 and some extra piece of the schedule.
6290 The space of the schedule domain is also available from
6291 the C<isl_ast_build>.
6293 #include <isl/ast_build.h>
6294 __isl_give isl_union_map *isl_ast_build_get_schedule(
6295 __isl_keep isl_ast_build *build);
6296 __isl_give isl_space *isl_ast_build_get_schedule_space(
6297 __isl_keep isl_ast_build *build);
6298 __isl_give isl_ast_build *isl_ast_build_restrict(
6299 __isl_take isl_ast_build *build,
6300 __isl_take isl_set *set);
6302 The C<isl_ast_build_get_schedule> function returns a (partial)
6303 schedule for the domains elements for which part of the AST still needs to
6304 be generated in the current build.
6305 In particular, the domain elements are mapped to those iterations of the loops
6306 enclosing the current point of the AST generation inside which
6307 the domain elements are executed.
6308 No direct correspondence between
6309 the input schedule and this schedule should be assumed.
6310 The space obtained from C<isl_ast_build_get_schedule_space> can be used
6311 to create a set for C<isl_ast_build_restrict> to intersect
6312 with the current build. In particular, the set passed to
6313 C<isl_ast_build_restrict> can have additional parameters.
6314 The ids of the set dimensions in the space returned by
6315 C<isl_ast_build_get_schedule_space> correspond to the
6316 iterators of the already generated loops.
6317 The user should not rely on the ids of the output dimensions
6318 of the relations in the union relation returned by
6319 C<isl_ast_build_get_schedule> having any particular value.
6323 Although C<isl> is mainly meant to be used as a library,
6324 it also contains some basic applications that use some
6325 of the functionality of C<isl>.
6326 The input may be specified in either the L<isl format>
6327 or the L<PolyLib format>.
6329 =head2 C<isl_polyhedron_sample>
6331 C<isl_polyhedron_sample> takes a polyhedron as input and prints
6332 an integer element of the polyhedron, if there is any.
6333 The first column in the output is the denominator and is always
6334 equal to 1. If the polyhedron contains no integer points,
6335 then a vector of length zero is printed.
6339 C<isl_pip> takes the same input as the C<example> program
6340 from the C<piplib> distribution, i.e., a set of constraints
6341 on the parameters, a line containing only -1 and finally a set
6342 of constraints on a parametric polyhedron.
6343 The coefficients of the parameters appear in the last columns
6344 (but before the final constant column).
6345 The output is the lexicographic minimum of the parametric polyhedron.
6346 As C<isl> currently does not have its own output format, the output
6347 is just a dump of the internal state.
6349 =head2 C<isl_polyhedron_minimize>
6351 C<isl_polyhedron_minimize> computes the minimum of some linear
6352 or affine objective function over the integer points in a polyhedron.
6353 If an affine objective function
6354 is given, then the constant should appear in the last column.
6356 =head2 C<isl_polytope_scan>
6358 Given a polytope, C<isl_polytope_scan> prints
6359 all integer points in the polytope.
6361 =head2 C<isl_codegen>
6363 Given a schedule, a context set and an options relation,
6364 C<isl_codegen> prints out an AST that scans the domain elements
6365 of the schedule in the order of their image(s) taking into account
6366 the constraints in the context set.