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_multi_val_get_space(
895 __isl_keep isl_multi_val *mv);
898 __isl_give isl_space *isl_aff_get_domain_space(
899 __isl_keep isl_aff *aff);
900 __isl_give isl_space *isl_aff_get_space(
901 __isl_keep isl_aff *aff);
902 __isl_give isl_space *isl_pw_aff_get_domain_space(
903 __isl_keep isl_pw_aff *pwaff);
904 __isl_give isl_space *isl_pw_aff_get_space(
905 __isl_keep isl_pw_aff *pwaff);
906 __isl_give isl_space *isl_multi_aff_get_domain_space(
907 __isl_keep isl_multi_aff *maff);
908 __isl_give isl_space *isl_multi_aff_get_space(
909 __isl_keep isl_multi_aff *maff);
910 __isl_give isl_space *isl_pw_multi_aff_get_domain_space(
911 __isl_keep isl_pw_multi_aff *pma);
912 __isl_give isl_space *isl_pw_multi_aff_get_space(
913 __isl_keep isl_pw_multi_aff *pma);
914 __isl_give isl_space *isl_union_pw_multi_aff_get_space(
915 __isl_keep isl_union_pw_multi_aff *upma);
916 __isl_give isl_space *isl_multi_pw_aff_get_domain_space(
917 __isl_keep isl_multi_pw_aff *mpa);
918 __isl_give isl_space *isl_multi_pw_aff_get_space(
919 __isl_keep isl_multi_pw_aff *mpa);
921 #include <isl/point.h>
922 __isl_give isl_space *isl_point_get_space(
923 __isl_keep isl_point *pnt);
925 The identifiers or names of the individual dimensions may be set or read off
926 using the following functions.
928 #include <isl/space.h>
929 __isl_give isl_space *isl_space_set_dim_id(
930 __isl_take isl_space *space,
931 enum isl_dim_type type, unsigned pos,
932 __isl_take isl_id *id);
933 int isl_space_has_dim_id(__isl_keep isl_space *space,
934 enum isl_dim_type type, unsigned pos);
935 __isl_give isl_id *isl_space_get_dim_id(
936 __isl_keep isl_space *space,
937 enum isl_dim_type type, unsigned pos);
938 __isl_give isl_space *isl_space_set_dim_name(
939 __isl_take isl_space *space,
940 enum isl_dim_type type, unsigned pos,
941 __isl_keep const char *name);
942 int isl_space_has_dim_name(__isl_keep isl_space *space,
943 enum isl_dim_type type, unsigned pos);
944 __isl_keep const char *isl_space_get_dim_name(
945 __isl_keep isl_space *space,
946 enum isl_dim_type type, unsigned pos);
948 Note that C<isl_space_get_name> returns a pointer to some internal
949 data structure, so the result can only be used while the
950 corresponding C<isl_space> is alive.
951 Also note that every function that operates on two sets or relations
952 requires that both arguments have the same parameters. This also
953 means that if one of the arguments has named parameters, then the
954 other needs to have named parameters too and the names need to match.
955 Pairs of C<isl_set>, C<isl_map>, C<isl_union_set> and/or C<isl_union_map>
956 arguments may have different parameters (as long as they are named),
957 in which case the result will have as parameters the union of the parameters of
960 Given the identifier or name of a dimension (typically a parameter),
961 its position can be obtained from the following function.
963 #include <isl/space.h>
964 int isl_space_find_dim_by_id(__isl_keep isl_space *space,
965 enum isl_dim_type type, __isl_keep isl_id *id);
966 int isl_space_find_dim_by_name(__isl_keep isl_space *space,
967 enum isl_dim_type type, const char *name);
969 The identifiers or names of entire spaces may be set or read off
970 using the following functions.
972 #include <isl/space.h>
973 __isl_give isl_space *isl_space_set_tuple_id(
974 __isl_take isl_space *space,
975 enum isl_dim_type type, __isl_take isl_id *id);
976 __isl_give isl_space *isl_space_reset_tuple_id(
977 __isl_take isl_space *space, enum isl_dim_type type);
978 int isl_space_has_tuple_id(__isl_keep isl_space *space,
979 enum isl_dim_type type);
980 __isl_give isl_id *isl_space_get_tuple_id(
981 __isl_keep isl_space *space, enum isl_dim_type type);
982 __isl_give isl_space *isl_space_set_tuple_name(
983 __isl_take isl_space *space,
984 enum isl_dim_type type, const char *s);
985 int isl_space_has_tuple_name(__isl_keep isl_space *space,
986 enum isl_dim_type type);
987 const char *isl_space_get_tuple_name(__isl_keep isl_space *space,
988 enum isl_dim_type type);
990 The C<type> argument needs to be one of C<isl_dim_in>, C<isl_dim_out>
991 or C<isl_dim_set>. As with C<isl_space_get_name>,
992 the C<isl_space_get_tuple_name> function returns a pointer to some internal
994 Binary operations require the corresponding spaces of their arguments
995 to have the same name.
997 Spaces can be nested. In particular, the domain of a set or
998 the domain or range of a relation can be a nested relation.
999 The following functions can be used to construct and deconstruct
1002 #include <isl/space.h>
1003 int isl_space_is_wrapping(__isl_keep isl_space *space);
1004 __isl_give isl_space *isl_space_wrap(__isl_take isl_space *space);
1005 __isl_give isl_space *isl_space_unwrap(__isl_take isl_space *space);
1007 The input to C<isl_space_is_wrapping> and C<isl_space_unwrap> should
1008 be the space of a set, while that of
1009 C<isl_space_wrap> should be the space of a relation.
1010 Conversely, the output of C<isl_space_unwrap> is the space
1011 of a relation, while that of C<isl_space_wrap> is the space of a set.
1013 Spaces can be created from other spaces
1014 using the following functions.
1016 __isl_give isl_space *isl_space_domain(__isl_take isl_space *space);
1017 __isl_give isl_space *isl_space_from_domain(__isl_take isl_space *space);
1018 __isl_give isl_space *isl_space_range(__isl_take isl_space *space);
1019 __isl_give isl_space *isl_space_from_range(__isl_take isl_space *space);
1020 __isl_give isl_space *isl_space_params(
1021 __isl_take isl_space *space);
1022 __isl_give isl_space *isl_space_set_from_params(
1023 __isl_take isl_space *space);
1024 __isl_give isl_space *isl_space_reverse(__isl_take isl_space *space);
1025 __isl_give isl_space *isl_space_join(__isl_take isl_space *left,
1026 __isl_take isl_space *right);
1027 __isl_give isl_space *isl_space_align_params(
1028 __isl_take isl_space *space1, __isl_take isl_space *space2)
1029 __isl_give isl_space *isl_space_insert_dims(__isl_take isl_space *space,
1030 enum isl_dim_type type, unsigned pos, unsigned n);
1031 __isl_give isl_space *isl_space_add_dims(__isl_take isl_space *space,
1032 enum isl_dim_type type, unsigned n);
1033 __isl_give isl_space *isl_space_drop_dims(__isl_take isl_space *space,
1034 enum isl_dim_type type, unsigned first, unsigned n);
1035 __isl_give isl_space *isl_space_move_dims(__isl_take isl_space *space,
1036 enum isl_dim_type dst_type, unsigned dst_pos,
1037 enum isl_dim_type src_type, unsigned src_pos,
1039 __isl_give isl_space *isl_space_map_from_set(
1040 __isl_take isl_space *space);
1041 __isl_give isl_space *isl_space_map_from_domain_and_range(
1042 __isl_take isl_space *domain,
1043 __isl_take isl_space *range);
1044 __isl_give isl_space *isl_space_zip(__isl_take isl_space *space);
1045 __isl_give isl_space *isl_space_curry(
1046 __isl_take isl_space *space);
1047 __isl_give isl_space *isl_space_uncurry(
1048 __isl_take isl_space *space);
1050 Note that if dimensions are added or removed from a space, then
1051 the name and the internal structure are lost.
1055 A local space is essentially a space with
1056 zero or more existentially quantified variables.
1057 The local space of a (constraint of a) basic set or relation can be obtained
1058 using the following functions.
1060 #include <isl/constraint.h>
1061 __isl_give isl_local_space *isl_constraint_get_local_space(
1062 __isl_keep isl_constraint *constraint);
1064 #include <isl/set.h>
1065 __isl_give isl_local_space *isl_basic_set_get_local_space(
1066 __isl_keep isl_basic_set *bset);
1068 #include <isl/map.h>
1069 __isl_give isl_local_space *isl_basic_map_get_local_space(
1070 __isl_keep isl_basic_map *bmap);
1072 A new local space can be created from a space using
1074 #include <isl/local_space.h>
1075 __isl_give isl_local_space *isl_local_space_from_space(
1076 __isl_take isl_space *space);
1078 They can be inspected, modified, copied and freed using the following functions.
1080 #include <isl/local_space.h>
1081 isl_ctx *isl_local_space_get_ctx(
1082 __isl_keep isl_local_space *ls);
1083 int isl_local_space_is_set(__isl_keep isl_local_space *ls);
1084 int isl_local_space_dim(__isl_keep isl_local_space *ls,
1085 enum isl_dim_type type);
1086 int isl_local_space_has_dim_id(
1087 __isl_keep isl_local_space *ls,
1088 enum isl_dim_type type, unsigned pos);
1089 __isl_give isl_id *isl_local_space_get_dim_id(
1090 __isl_keep isl_local_space *ls,
1091 enum isl_dim_type type, unsigned pos);
1092 int isl_local_space_has_dim_name(
1093 __isl_keep isl_local_space *ls,
1094 enum isl_dim_type type, unsigned pos)
1095 const char *isl_local_space_get_dim_name(
1096 __isl_keep isl_local_space *ls,
1097 enum isl_dim_type type, unsigned pos);
1098 __isl_give isl_local_space *isl_local_space_set_dim_name(
1099 __isl_take isl_local_space *ls,
1100 enum isl_dim_type type, unsigned pos, const char *s);
1101 __isl_give isl_local_space *isl_local_space_set_dim_id(
1102 __isl_take isl_local_space *ls,
1103 enum isl_dim_type type, unsigned pos,
1104 __isl_take isl_id *id);
1105 __isl_give isl_space *isl_local_space_get_space(
1106 __isl_keep isl_local_space *ls);
1107 __isl_give isl_aff *isl_local_space_get_div(
1108 __isl_keep isl_local_space *ls, int pos);
1109 __isl_give isl_local_space *isl_local_space_copy(
1110 __isl_keep isl_local_space *ls);
1111 void *isl_local_space_free(__isl_take isl_local_space *ls);
1113 Note that C<isl_local_space_get_div> can only be used on local spaces
1116 Two local spaces can be compared using
1118 int isl_local_space_is_equal(__isl_keep isl_local_space *ls1,
1119 __isl_keep isl_local_space *ls2);
1121 Local spaces can be created from other local spaces
1122 using the following functions.
1124 __isl_give isl_local_space *isl_local_space_domain(
1125 __isl_take isl_local_space *ls);
1126 __isl_give isl_local_space *isl_local_space_range(
1127 __isl_take isl_local_space *ls);
1128 __isl_give isl_local_space *isl_local_space_from_domain(
1129 __isl_take isl_local_space *ls);
1130 __isl_give isl_local_space *isl_local_space_intersect(
1131 __isl_take isl_local_space *ls1,
1132 __isl_take isl_local_space *ls2);
1133 __isl_give isl_local_space *isl_local_space_add_dims(
1134 __isl_take isl_local_space *ls,
1135 enum isl_dim_type type, unsigned n);
1136 __isl_give isl_local_space *isl_local_space_insert_dims(
1137 __isl_take isl_local_space *ls,
1138 enum isl_dim_type type, unsigned first, unsigned n);
1139 __isl_give isl_local_space *isl_local_space_drop_dims(
1140 __isl_take isl_local_space *ls,
1141 enum isl_dim_type type, unsigned first, unsigned n);
1143 =head2 Input and Output
1145 C<isl> supports its own input/output format, which is similar
1146 to the C<Omega> format, but also supports the C<PolyLib> format
1149 =head3 C<isl> format
1151 The C<isl> format is similar to that of C<Omega>, but has a different
1152 syntax for describing the parameters and allows for the definition
1153 of an existentially quantified variable as the integer division
1154 of an affine expression.
1155 For example, the set of integers C<i> between C<0> and C<n>
1156 such that C<i % 10 <= 6> can be described as
1158 [n] -> { [i] : exists (a = [i/10] : 0 <= i and i <= n and
1161 A set or relation can have several disjuncts, separated
1162 by the keyword C<or>. Each disjunct is either a conjunction
1163 of constraints or a projection (C<exists>) of a conjunction
1164 of constraints. The constraints are separated by the keyword
1167 =head3 C<PolyLib> format
1169 If the represented set is a union, then the first line
1170 contains a single number representing the number of disjuncts.
1171 Otherwise, a line containing the number C<1> is optional.
1173 Each disjunct is represented by a matrix of constraints.
1174 The first line contains two numbers representing
1175 the number of rows and columns,
1176 where the number of rows is equal to the number of constraints
1177 and the number of columns is equal to two plus the number of variables.
1178 The following lines contain the actual rows of the constraint matrix.
1179 In each row, the first column indicates whether the constraint
1180 is an equality (C<0>) or inequality (C<1>). The final column
1181 corresponds to the constant term.
1183 If the set is parametric, then the coefficients of the parameters
1184 appear in the last columns before the constant column.
1185 The coefficients of any existentially quantified variables appear
1186 between those of the set variables and those of the parameters.
1188 =head3 Extended C<PolyLib> format
1190 The extended C<PolyLib> format is nearly identical to the
1191 C<PolyLib> format. The only difference is that the line
1192 containing the number of rows and columns of a constraint matrix
1193 also contains four additional numbers:
1194 the number of output dimensions, the number of input dimensions,
1195 the number of local dimensions (i.e., the number of existentially
1196 quantified variables) and the number of parameters.
1197 For sets, the number of ``output'' dimensions is equal
1198 to the number of set dimensions, while the number of ``input''
1203 #include <isl/set.h>
1204 __isl_give isl_basic_set *isl_basic_set_read_from_file(
1205 isl_ctx *ctx, FILE *input);
1206 __isl_give isl_basic_set *isl_basic_set_read_from_str(
1207 isl_ctx *ctx, const char *str);
1208 __isl_give isl_set *isl_set_read_from_file(isl_ctx *ctx,
1210 __isl_give isl_set *isl_set_read_from_str(isl_ctx *ctx,
1213 #include <isl/map.h>
1214 __isl_give isl_basic_map *isl_basic_map_read_from_file(
1215 isl_ctx *ctx, FILE *input);
1216 __isl_give isl_basic_map *isl_basic_map_read_from_str(
1217 isl_ctx *ctx, const char *str);
1218 __isl_give isl_map *isl_map_read_from_file(
1219 isl_ctx *ctx, FILE *input);
1220 __isl_give isl_map *isl_map_read_from_str(isl_ctx *ctx,
1223 #include <isl/union_set.h>
1224 __isl_give isl_union_set *isl_union_set_read_from_file(
1225 isl_ctx *ctx, FILE *input);
1226 __isl_give isl_union_set *isl_union_set_read_from_str(
1227 isl_ctx *ctx, const char *str);
1229 #include <isl/union_map.h>
1230 __isl_give isl_union_map *isl_union_map_read_from_file(
1231 isl_ctx *ctx, FILE *input);
1232 __isl_give isl_union_map *isl_union_map_read_from_str(
1233 isl_ctx *ctx, const char *str);
1235 The input format is autodetected and may be either the C<PolyLib> format
1236 or the C<isl> format.
1240 Before anything can be printed, an C<isl_printer> needs to
1243 __isl_give isl_printer *isl_printer_to_file(isl_ctx *ctx,
1245 __isl_give isl_printer *isl_printer_to_str(isl_ctx *ctx);
1246 void *isl_printer_free(__isl_take isl_printer *printer);
1247 __isl_give char *isl_printer_get_str(
1248 __isl_keep isl_printer *printer);
1250 The printer can be inspected using the following functions.
1252 FILE *isl_printer_get_file(
1253 __isl_keep isl_printer *printer);
1254 int isl_printer_get_output_format(
1255 __isl_keep isl_printer *p);
1257 The behavior of the printer can be modified in various ways
1259 __isl_give isl_printer *isl_printer_set_output_format(
1260 __isl_take isl_printer *p, int output_format);
1261 __isl_give isl_printer *isl_printer_set_indent(
1262 __isl_take isl_printer *p, int indent);
1263 __isl_give isl_printer *isl_printer_indent(
1264 __isl_take isl_printer *p, int indent);
1265 __isl_give isl_printer *isl_printer_set_prefix(
1266 __isl_take isl_printer *p, const char *prefix);
1267 __isl_give isl_printer *isl_printer_set_suffix(
1268 __isl_take isl_printer *p, const char *suffix);
1270 The C<output_format> may be either C<ISL_FORMAT_ISL>, C<ISL_FORMAT_OMEGA>,
1271 C<ISL_FORMAT_POLYLIB>, C<ISL_FORMAT_EXT_POLYLIB> or C<ISL_FORMAT_LATEX>
1272 and defaults to C<ISL_FORMAT_ISL>.
1273 Each line in the output is indented by C<indent> (set by
1274 C<isl_printer_set_indent>) spaces
1275 (default: 0), prefixed by C<prefix> and suffixed by C<suffix>.
1276 In the C<PolyLib> format output,
1277 the coefficients of the existentially quantified variables
1278 appear between those of the set variables and those
1280 The function C<isl_printer_indent> increases the indentation
1281 by the specified amount (which may be negative).
1283 To actually print something, use
1285 #include <isl/printer.h>
1286 __isl_give isl_printer *isl_printer_print_double(
1287 __isl_take isl_printer *p, double d);
1289 #include <isl/set.h>
1290 __isl_give isl_printer *isl_printer_print_basic_set(
1291 __isl_take isl_printer *printer,
1292 __isl_keep isl_basic_set *bset);
1293 __isl_give isl_printer *isl_printer_print_set(
1294 __isl_take isl_printer *printer,
1295 __isl_keep isl_set *set);
1297 #include <isl/map.h>
1298 __isl_give isl_printer *isl_printer_print_basic_map(
1299 __isl_take isl_printer *printer,
1300 __isl_keep isl_basic_map *bmap);
1301 __isl_give isl_printer *isl_printer_print_map(
1302 __isl_take isl_printer *printer,
1303 __isl_keep isl_map *map);
1305 #include <isl/union_set.h>
1306 __isl_give isl_printer *isl_printer_print_union_set(
1307 __isl_take isl_printer *p,
1308 __isl_keep isl_union_set *uset);
1310 #include <isl/union_map.h>
1311 __isl_give isl_printer *isl_printer_print_union_map(
1312 __isl_take isl_printer *p,
1313 __isl_keep isl_union_map *umap);
1315 When called on a file printer, the following function flushes
1316 the file. When called on a string printer, the buffer is cleared.
1318 __isl_give isl_printer *isl_printer_flush(
1319 __isl_take isl_printer *p);
1321 =head2 Creating New Sets and Relations
1323 C<isl> has functions for creating some standard sets and relations.
1327 =item * Empty sets and relations
1329 __isl_give isl_basic_set *isl_basic_set_empty(
1330 __isl_take isl_space *space);
1331 __isl_give isl_basic_map *isl_basic_map_empty(
1332 __isl_take isl_space *space);
1333 __isl_give isl_set *isl_set_empty(
1334 __isl_take isl_space *space);
1335 __isl_give isl_map *isl_map_empty(
1336 __isl_take isl_space *space);
1337 __isl_give isl_union_set *isl_union_set_empty(
1338 __isl_take isl_space *space);
1339 __isl_give isl_union_map *isl_union_map_empty(
1340 __isl_take isl_space *space);
1342 For C<isl_union_set>s and C<isl_union_map>s, the space
1343 is only used to specify the parameters.
1345 =item * Universe sets and relations
1347 __isl_give isl_basic_set *isl_basic_set_universe(
1348 __isl_take isl_space *space);
1349 __isl_give isl_basic_map *isl_basic_map_universe(
1350 __isl_take isl_space *space);
1351 __isl_give isl_set *isl_set_universe(
1352 __isl_take isl_space *space);
1353 __isl_give isl_map *isl_map_universe(
1354 __isl_take isl_space *space);
1355 __isl_give isl_union_set *isl_union_set_universe(
1356 __isl_take isl_union_set *uset);
1357 __isl_give isl_union_map *isl_union_map_universe(
1358 __isl_take isl_union_map *umap);
1360 The sets and relations constructed by the functions above
1361 contain all integer values, while those constructed by the
1362 functions below only contain non-negative values.
1364 __isl_give isl_basic_set *isl_basic_set_nat_universe(
1365 __isl_take isl_space *space);
1366 __isl_give isl_basic_map *isl_basic_map_nat_universe(
1367 __isl_take isl_space *space);
1368 __isl_give isl_set *isl_set_nat_universe(
1369 __isl_take isl_space *space);
1370 __isl_give isl_map *isl_map_nat_universe(
1371 __isl_take isl_space *space);
1373 =item * Identity relations
1375 __isl_give isl_basic_map *isl_basic_map_identity(
1376 __isl_take isl_space *space);
1377 __isl_give isl_map *isl_map_identity(
1378 __isl_take isl_space *space);
1380 The number of input and output dimensions in C<space> needs
1383 =item * Lexicographic order
1385 __isl_give isl_map *isl_map_lex_lt(
1386 __isl_take isl_space *set_space);
1387 __isl_give isl_map *isl_map_lex_le(
1388 __isl_take isl_space *set_space);
1389 __isl_give isl_map *isl_map_lex_gt(
1390 __isl_take isl_space *set_space);
1391 __isl_give isl_map *isl_map_lex_ge(
1392 __isl_take isl_space *set_space);
1393 __isl_give isl_map *isl_map_lex_lt_first(
1394 __isl_take isl_space *space, unsigned n);
1395 __isl_give isl_map *isl_map_lex_le_first(
1396 __isl_take isl_space *space, unsigned n);
1397 __isl_give isl_map *isl_map_lex_gt_first(
1398 __isl_take isl_space *space, unsigned n);
1399 __isl_give isl_map *isl_map_lex_ge_first(
1400 __isl_take isl_space *space, unsigned n);
1402 The first four functions take a space for a B<set>
1403 and return relations that express that the elements in the domain
1404 are lexicographically less
1405 (C<isl_map_lex_lt>), less or equal (C<isl_map_lex_le>),
1406 greater (C<isl_map_lex_gt>) or greater or equal (C<isl_map_lex_ge>)
1407 than the elements in the range.
1408 The last four functions take a space for a map
1409 and return relations that express that the first C<n> dimensions
1410 in the domain are lexicographically less
1411 (C<isl_map_lex_lt_first>), less or equal (C<isl_map_lex_le_first>),
1412 greater (C<isl_map_lex_gt_first>) or greater or equal (C<isl_map_lex_ge_first>)
1413 than the first C<n> dimensions in the range.
1417 A basic set or relation can be converted to a set or relation
1418 using the following functions.
1420 __isl_give isl_set *isl_set_from_basic_set(
1421 __isl_take isl_basic_set *bset);
1422 __isl_give isl_map *isl_map_from_basic_map(
1423 __isl_take isl_basic_map *bmap);
1425 Sets and relations can be converted to union sets and relations
1426 using the following functions.
1428 __isl_give isl_union_set *isl_union_set_from_basic_set(
1429 __isl_take isl_basic_set *bset);
1430 __isl_give isl_union_map *isl_union_map_from_basic_map(
1431 __isl_take isl_basic_map *bmap);
1432 __isl_give isl_union_set *isl_union_set_from_set(
1433 __isl_take isl_set *set);
1434 __isl_give isl_union_map *isl_union_map_from_map(
1435 __isl_take isl_map *map);
1437 The inverse conversions below can only be used if the input
1438 union set or relation is known to contain elements in exactly one
1441 __isl_give isl_set *isl_set_from_union_set(
1442 __isl_take isl_union_set *uset);
1443 __isl_give isl_map *isl_map_from_union_map(
1444 __isl_take isl_union_map *umap);
1446 A zero-dimensional (basic) set can be constructed on a given parameter domain
1447 using the following function.
1449 __isl_give isl_basic_set *isl_basic_set_from_params(
1450 __isl_take isl_basic_set *bset);
1451 __isl_give isl_set *isl_set_from_params(
1452 __isl_take isl_set *set);
1454 Sets and relations can be copied and freed again using the following
1457 __isl_give isl_basic_set *isl_basic_set_copy(
1458 __isl_keep isl_basic_set *bset);
1459 __isl_give isl_set *isl_set_copy(__isl_keep isl_set *set);
1460 __isl_give isl_union_set *isl_union_set_copy(
1461 __isl_keep isl_union_set *uset);
1462 __isl_give isl_basic_map *isl_basic_map_copy(
1463 __isl_keep isl_basic_map *bmap);
1464 __isl_give isl_map *isl_map_copy(__isl_keep isl_map *map);
1465 __isl_give isl_union_map *isl_union_map_copy(
1466 __isl_keep isl_union_map *umap);
1467 void *isl_basic_set_free(__isl_take isl_basic_set *bset);
1468 void *isl_set_free(__isl_take isl_set *set);
1469 void *isl_union_set_free(__isl_take isl_union_set *uset);
1470 void *isl_basic_map_free(__isl_take isl_basic_map *bmap);
1471 void *isl_map_free(__isl_take isl_map *map);
1472 void *isl_union_map_free(__isl_take isl_union_map *umap);
1474 Other sets and relations can be constructed by starting
1475 from a universe set or relation, adding equality and/or
1476 inequality constraints and then projecting out the
1477 existentially quantified variables, if any.
1478 Constraints can be constructed, manipulated and
1479 added to (or removed from) (basic) sets and relations
1480 using the following functions.
1482 #include <isl/constraint.h>
1483 __isl_give isl_constraint *isl_equality_alloc(
1484 __isl_take isl_local_space *ls);
1485 __isl_give isl_constraint *isl_inequality_alloc(
1486 __isl_take isl_local_space *ls);
1487 __isl_give isl_constraint *isl_constraint_set_constant(
1488 __isl_take isl_constraint *constraint, isl_int v);
1489 __isl_give isl_constraint *isl_constraint_set_constant_si(
1490 __isl_take isl_constraint *constraint, int v);
1491 __isl_give isl_constraint *isl_constraint_set_coefficient(
1492 __isl_take isl_constraint *constraint,
1493 enum isl_dim_type type, int pos, isl_int v);
1494 __isl_give isl_constraint *isl_constraint_set_coefficient_si(
1495 __isl_take isl_constraint *constraint,
1496 enum isl_dim_type type, int pos, int v);
1497 __isl_give isl_basic_map *isl_basic_map_add_constraint(
1498 __isl_take isl_basic_map *bmap,
1499 __isl_take isl_constraint *constraint);
1500 __isl_give isl_basic_set *isl_basic_set_add_constraint(
1501 __isl_take isl_basic_set *bset,
1502 __isl_take isl_constraint *constraint);
1503 __isl_give isl_map *isl_map_add_constraint(
1504 __isl_take isl_map *map,
1505 __isl_take isl_constraint *constraint);
1506 __isl_give isl_set *isl_set_add_constraint(
1507 __isl_take isl_set *set,
1508 __isl_take isl_constraint *constraint);
1509 __isl_give isl_basic_set *isl_basic_set_drop_constraint(
1510 __isl_take isl_basic_set *bset,
1511 __isl_take isl_constraint *constraint);
1513 For example, to create a set containing the even integers
1514 between 10 and 42, you would use the following code.
1517 isl_local_space *ls;
1519 isl_basic_set *bset;
1521 space = isl_space_set_alloc(ctx, 0, 2);
1522 bset = isl_basic_set_universe(isl_space_copy(space));
1523 ls = isl_local_space_from_space(space);
1525 c = isl_equality_alloc(isl_local_space_copy(ls));
1526 c = isl_constraint_set_coefficient_si(c, isl_dim_set, 0, -1);
1527 c = isl_constraint_set_coefficient_si(c, isl_dim_set, 1, 2);
1528 bset = isl_basic_set_add_constraint(bset, c);
1530 c = isl_inequality_alloc(isl_local_space_copy(ls));
1531 c = isl_constraint_set_constant_si(c, -10);
1532 c = isl_constraint_set_coefficient_si(c, isl_dim_set, 0, 1);
1533 bset = isl_basic_set_add_constraint(bset, c);
1535 c = isl_inequality_alloc(ls);
1536 c = isl_constraint_set_constant_si(c, 42);
1537 c = isl_constraint_set_coefficient_si(c, isl_dim_set, 0, -1);
1538 bset = isl_basic_set_add_constraint(bset, c);
1540 bset = isl_basic_set_project_out(bset, isl_dim_set, 1, 1);
1544 isl_basic_set *bset;
1545 bset = isl_basic_set_read_from_str(ctx,
1546 "{[i] : exists (a : i = 2a and i >= 10 and i <= 42)}");
1548 A basic set or relation can also be constructed from two matrices
1549 describing the equalities and the inequalities.
1551 __isl_give isl_basic_set *isl_basic_set_from_constraint_matrices(
1552 __isl_take isl_space *space,
1553 __isl_take isl_mat *eq, __isl_take isl_mat *ineq,
1554 enum isl_dim_type c1,
1555 enum isl_dim_type c2, enum isl_dim_type c3,
1556 enum isl_dim_type c4);
1557 __isl_give isl_basic_map *isl_basic_map_from_constraint_matrices(
1558 __isl_take isl_space *space,
1559 __isl_take isl_mat *eq, __isl_take isl_mat *ineq,
1560 enum isl_dim_type c1,
1561 enum isl_dim_type c2, enum isl_dim_type c3,
1562 enum isl_dim_type c4, enum isl_dim_type c5);
1564 The C<isl_dim_type> arguments indicate the order in which
1565 different kinds of variables appear in the input matrices
1566 and should be a permutation of C<isl_dim_cst>, C<isl_dim_param>,
1567 C<isl_dim_set> and C<isl_dim_div> for sets and
1568 of C<isl_dim_cst>, C<isl_dim_param>,
1569 C<isl_dim_in>, C<isl_dim_out> and C<isl_dim_div> for relations.
1571 A (basic or union) set or relation can also be constructed from a
1572 (union) (piecewise) (multiple) affine expression
1573 or a list of affine expressions
1574 (See L<"Piecewise Quasi Affine Expressions"> and
1575 L<"Piecewise Multiple Quasi Affine Expressions">).
1577 __isl_give isl_basic_map *isl_basic_map_from_aff(
1578 __isl_take isl_aff *aff);
1579 __isl_give isl_map *isl_map_from_aff(
1580 __isl_take isl_aff *aff);
1581 __isl_give isl_set *isl_set_from_pw_aff(
1582 __isl_take isl_pw_aff *pwaff);
1583 __isl_give isl_map *isl_map_from_pw_aff(
1584 __isl_take isl_pw_aff *pwaff);
1585 __isl_give isl_basic_map *isl_basic_map_from_aff_list(
1586 __isl_take isl_space *domain_space,
1587 __isl_take isl_aff_list *list);
1588 __isl_give isl_basic_map *isl_basic_map_from_multi_aff(
1589 __isl_take isl_multi_aff *maff)
1590 __isl_give isl_map *isl_map_from_multi_aff(
1591 __isl_take isl_multi_aff *maff)
1592 __isl_give isl_set *isl_set_from_pw_multi_aff(
1593 __isl_take isl_pw_multi_aff *pma);
1594 __isl_give isl_map *isl_map_from_pw_multi_aff(
1595 __isl_take isl_pw_multi_aff *pma);
1596 __isl_give isl_union_map *
1597 isl_union_map_from_union_pw_multi_aff(
1598 __isl_take isl_union_pw_multi_aff *upma);
1600 The C<domain_dim> argument describes the domain of the resulting
1601 basic relation. It is required because the C<list> may consist
1602 of zero affine expressions.
1604 =head2 Inspecting Sets and Relations
1606 Usually, the user should not have to care about the actual constraints
1607 of the sets and maps, but should instead apply the abstract operations
1608 explained in the following sections.
1609 Occasionally, however, it may be required to inspect the individual
1610 coefficients of the constraints. This section explains how to do so.
1611 In these cases, it may also be useful to have C<isl> compute
1612 an explicit representation of the existentially quantified variables.
1614 __isl_give isl_set *isl_set_compute_divs(
1615 __isl_take isl_set *set);
1616 __isl_give isl_map *isl_map_compute_divs(
1617 __isl_take isl_map *map);
1618 __isl_give isl_union_set *isl_union_set_compute_divs(
1619 __isl_take isl_union_set *uset);
1620 __isl_give isl_union_map *isl_union_map_compute_divs(
1621 __isl_take isl_union_map *umap);
1623 This explicit representation defines the existentially quantified
1624 variables as integer divisions of the other variables, possibly
1625 including earlier existentially quantified variables.
1626 An explicitly represented existentially quantified variable therefore
1627 has a unique value when the values of the other variables are known.
1628 If, furthermore, the same existentials, i.e., existentials
1629 with the same explicit representations, should appear in the
1630 same order in each of the disjuncts of a set or map, then the user should call
1631 either of the following functions.
1633 __isl_give isl_set *isl_set_align_divs(
1634 __isl_take isl_set *set);
1635 __isl_give isl_map *isl_map_align_divs(
1636 __isl_take isl_map *map);
1638 Alternatively, the existentially quantified variables can be removed
1639 using the following functions, which compute an overapproximation.
1641 __isl_give isl_basic_set *isl_basic_set_remove_divs(
1642 __isl_take isl_basic_set *bset);
1643 __isl_give isl_basic_map *isl_basic_map_remove_divs(
1644 __isl_take isl_basic_map *bmap);
1645 __isl_give isl_set *isl_set_remove_divs(
1646 __isl_take isl_set *set);
1647 __isl_give isl_map *isl_map_remove_divs(
1648 __isl_take isl_map *map);
1650 It is also possible to only remove those divs that are defined
1651 in terms of a given range of dimensions or only those for which
1652 no explicit representation is known.
1654 __isl_give isl_basic_set *
1655 isl_basic_set_remove_divs_involving_dims(
1656 __isl_take isl_basic_set *bset,
1657 enum isl_dim_type type,
1658 unsigned first, unsigned n);
1659 __isl_give isl_basic_map *
1660 isl_basic_map_remove_divs_involving_dims(
1661 __isl_take isl_basic_map *bmap,
1662 enum isl_dim_type type,
1663 unsigned first, unsigned n);
1664 __isl_give isl_set *isl_set_remove_divs_involving_dims(
1665 __isl_take isl_set *set, enum isl_dim_type type,
1666 unsigned first, unsigned n);
1667 __isl_give isl_map *isl_map_remove_divs_involving_dims(
1668 __isl_take isl_map *map, enum isl_dim_type type,
1669 unsigned first, unsigned n);
1671 __isl_give isl_basic_set *
1672 isl_basic_set_remove_unknown_divs(
1673 __isl_take isl_basic_set *bset);
1674 __isl_give isl_set *isl_set_remove_unknown_divs(
1675 __isl_take isl_set *set);
1676 __isl_give isl_map *isl_map_remove_unknown_divs(
1677 __isl_take isl_map *map);
1679 To iterate over all the sets or maps in a union set or map, use
1681 int isl_union_set_foreach_set(__isl_keep isl_union_set *uset,
1682 int (*fn)(__isl_take isl_set *set, void *user),
1684 int isl_union_map_foreach_map(__isl_keep isl_union_map *umap,
1685 int (*fn)(__isl_take isl_map *map, void *user),
1688 The number of sets or maps in a union set or map can be obtained
1691 int isl_union_set_n_set(__isl_keep isl_union_set *uset);
1692 int isl_union_map_n_map(__isl_keep isl_union_map *umap);
1694 To extract the set or map in a given space from a union, use
1696 __isl_give isl_set *isl_union_set_extract_set(
1697 __isl_keep isl_union_set *uset,
1698 __isl_take isl_space *space);
1699 __isl_give isl_map *isl_union_map_extract_map(
1700 __isl_keep isl_union_map *umap,
1701 __isl_take isl_space *space);
1703 To iterate over all the basic sets or maps in a set or map, use
1705 int isl_set_foreach_basic_set(__isl_keep isl_set *set,
1706 int (*fn)(__isl_take isl_basic_set *bset, void *user),
1708 int isl_map_foreach_basic_map(__isl_keep isl_map *map,
1709 int (*fn)(__isl_take isl_basic_map *bmap, void *user),
1712 The callback function C<fn> should return 0 if successful and
1713 -1 if an error occurs. In the latter case, or if any other error
1714 occurs, the above functions will return -1.
1716 It should be noted that C<isl> does not guarantee that
1717 the basic sets or maps passed to C<fn> are disjoint.
1718 If this is required, then the user should call one of
1719 the following functions first.
1721 __isl_give isl_set *isl_set_make_disjoint(
1722 __isl_take isl_set *set);
1723 __isl_give isl_map *isl_map_make_disjoint(
1724 __isl_take isl_map *map);
1726 The number of basic sets in a set can be obtained
1729 int isl_set_n_basic_set(__isl_keep isl_set *set);
1731 To iterate over the constraints of a basic set or map, use
1733 #include <isl/constraint.h>
1735 int isl_basic_set_n_constraint(
1736 __isl_keep isl_basic_set *bset);
1737 int isl_basic_set_foreach_constraint(
1738 __isl_keep isl_basic_set *bset,
1739 int (*fn)(__isl_take isl_constraint *c, void *user),
1741 int isl_basic_map_foreach_constraint(
1742 __isl_keep isl_basic_map *bmap,
1743 int (*fn)(__isl_take isl_constraint *c, void *user),
1745 void *isl_constraint_free(__isl_take isl_constraint *c);
1747 Again, the callback function C<fn> should return 0 if successful and
1748 -1 if an error occurs. In the latter case, or if any other error
1749 occurs, the above functions will return -1.
1750 The constraint C<c> represents either an equality or an inequality.
1751 Use the following function to find out whether a constraint
1752 represents an equality. If not, it represents an inequality.
1754 int isl_constraint_is_equality(
1755 __isl_keep isl_constraint *constraint);
1757 The coefficients of the constraints can be inspected using
1758 the following functions.
1760 int isl_constraint_is_lower_bound(
1761 __isl_keep isl_constraint *constraint,
1762 enum isl_dim_type type, unsigned pos);
1763 int isl_constraint_is_upper_bound(
1764 __isl_keep isl_constraint *constraint,
1765 enum isl_dim_type type, unsigned pos);
1766 void isl_constraint_get_constant(
1767 __isl_keep isl_constraint *constraint, isl_int *v);
1768 void isl_constraint_get_coefficient(
1769 __isl_keep isl_constraint *constraint,
1770 enum isl_dim_type type, int pos, isl_int *v);
1771 int isl_constraint_involves_dims(
1772 __isl_keep isl_constraint *constraint,
1773 enum isl_dim_type type, unsigned first, unsigned n);
1775 The explicit representations of the existentially quantified
1776 variables can be inspected using the following function.
1777 Note that the user is only allowed to use this function
1778 if the inspected set or map is the result of a call
1779 to C<isl_set_compute_divs> or C<isl_map_compute_divs>.
1780 The existentially quantified variable is equal to the floor
1781 of the returned affine expression. The affine expression
1782 itself can be inspected using the functions in
1783 L<"Piecewise Quasi Affine Expressions">.
1785 __isl_give isl_aff *isl_constraint_get_div(
1786 __isl_keep isl_constraint *constraint, int pos);
1788 To obtain the constraints of a basic set or map in matrix
1789 form, use the following functions.
1791 __isl_give isl_mat *isl_basic_set_equalities_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_set_inequalities_matrix(
1796 __isl_keep isl_basic_set *bset,
1797 enum isl_dim_type c1, enum isl_dim_type c2,
1798 enum isl_dim_type c3, enum isl_dim_type c4);
1799 __isl_give isl_mat *isl_basic_map_equalities_matrix(
1800 __isl_keep isl_basic_map *bmap,
1801 enum isl_dim_type c1,
1802 enum isl_dim_type c2, enum isl_dim_type c3,
1803 enum isl_dim_type c4, enum isl_dim_type c5);
1804 __isl_give isl_mat *isl_basic_map_inequalities_matrix(
1805 __isl_keep isl_basic_map *bmap,
1806 enum isl_dim_type c1,
1807 enum isl_dim_type c2, enum isl_dim_type c3,
1808 enum isl_dim_type c4, enum isl_dim_type c5);
1810 The C<isl_dim_type> arguments dictate the order in which
1811 different kinds of variables appear in the resulting matrix
1812 and should be a permutation of C<isl_dim_cst>, C<isl_dim_param>,
1813 C<isl_dim_in>, C<isl_dim_out> and C<isl_dim_div>.
1815 The number of parameters, input, output or set dimensions can
1816 be obtained using the following functions.
1818 unsigned isl_basic_set_dim(__isl_keep isl_basic_set *bset,
1819 enum isl_dim_type type);
1820 unsigned isl_basic_map_dim(__isl_keep isl_basic_map *bmap,
1821 enum isl_dim_type type);
1822 unsigned isl_set_dim(__isl_keep isl_set *set,
1823 enum isl_dim_type type);
1824 unsigned isl_map_dim(__isl_keep isl_map *map,
1825 enum isl_dim_type type);
1827 To check whether the description of a set or relation depends
1828 on one or more given dimensions, it is not necessary to iterate over all
1829 constraints. Instead the following functions can be used.
1831 int isl_basic_set_involves_dims(
1832 __isl_keep isl_basic_set *bset,
1833 enum isl_dim_type type, unsigned first, unsigned n);
1834 int isl_set_involves_dims(__isl_keep isl_set *set,
1835 enum isl_dim_type type, unsigned first, unsigned n);
1836 int isl_basic_map_involves_dims(
1837 __isl_keep isl_basic_map *bmap,
1838 enum isl_dim_type type, unsigned first, unsigned n);
1839 int isl_map_involves_dims(__isl_keep isl_map *map,
1840 enum isl_dim_type type, unsigned first, unsigned n);
1842 Similarly, the following functions can be used to check whether
1843 a given dimension is involved in any lower or upper bound.
1845 int isl_set_dim_has_any_lower_bound(__isl_keep isl_set *set,
1846 enum isl_dim_type type, unsigned pos);
1847 int isl_set_dim_has_any_upper_bound(__isl_keep isl_set *set,
1848 enum isl_dim_type type, unsigned pos);
1850 Note that these functions return true even if there is a bound on
1851 the dimension on only some of the basic sets of C<set>.
1852 To check if they have a bound for all of the basic sets in C<set>,
1853 use the following functions instead.
1855 int isl_set_dim_has_lower_bound(__isl_keep isl_set *set,
1856 enum isl_dim_type type, unsigned pos);
1857 int isl_set_dim_has_upper_bound(__isl_keep isl_set *set,
1858 enum isl_dim_type type, unsigned pos);
1860 The identifiers or names of the domain and range spaces of a set
1861 or relation can be read off or set using the following functions.
1863 __isl_give isl_set *isl_set_set_tuple_id(
1864 __isl_take isl_set *set, __isl_take isl_id *id);
1865 __isl_give isl_set *isl_set_reset_tuple_id(
1866 __isl_take isl_set *set);
1867 int isl_set_has_tuple_id(__isl_keep isl_set *set);
1868 __isl_give isl_id *isl_set_get_tuple_id(
1869 __isl_keep isl_set *set);
1870 __isl_give isl_map *isl_map_set_tuple_id(
1871 __isl_take isl_map *map, enum isl_dim_type type,
1872 __isl_take isl_id *id);
1873 __isl_give isl_map *isl_map_reset_tuple_id(
1874 __isl_take isl_map *map, enum isl_dim_type type);
1875 int isl_map_has_tuple_id(__isl_keep isl_map *map,
1876 enum isl_dim_type type);
1877 __isl_give isl_id *isl_map_get_tuple_id(
1878 __isl_keep isl_map *map, enum isl_dim_type type);
1880 const char *isl_basic_set_get_tuple_name(
1881 __isl_keep isl_basic_set *bset);
1882 __isl_give isl_basic_set *isl_basic_set_set_tuple_name(
1883 __isl_take isl_basic_set *set, const char *s);
1884 int isl_set_has_tuple_name(__isl_keep isl_set *set);
1885 const char *isl_set_get_tuple_name(
1886 __isl_keep isl_set *set);
1887 const char *isl_basic_map_get_tuple_name(
1888 __isl_keep isl_basic_map *bmap,
1889 enum isl_dim_type type);
1890 __isl_give isl_basic_map *isl_basic_map_set_tuple_name(
1891 __isl_take isl_basic_map *bmap,
1892 enum isl_dim_type type, const char *s);
1893 int isl_map_has_tuple_name(__isl_keep isl_map *map,
1894 enum isl_dim_type type);
1895 const char *isl_map_get_tuple_name(
1896 __isl_keep isl_map *map,
1897 enum isl_dim_type type);
1899 As with C<isl_space_get_tuple_name>, the value returned points to
1900 an internal data structure.
1901 The identifiers, positions or names of individual dimensions can be
1902 read off using the following functions.
1904 __isl_give isl_id *isl_basic_set_get_dim_id(
1905 __isl_keep isl_basic_set *bset,
1906 enum isl_dim_type type, unsigned pos);
1907 __isl_give isl_set *isl_set_set_dim_id(
1908 __isl_take isl_set *set, enum isl_dim_type type,
1909 unsigned pos, __isl_take isl_id *id);
1910 int isl_set_has_dim_id(__isl_keep isl_set *set,
1911 enum isl_dim_type type, unsigned pos);
1912 __isl_give isl_id *isl_set_get_dim_id(
1913 __isl_keep isl_set *set, enum isl_dim_type type,
1915 int isl_basic_map_has_dim_id(
1916 __isl_keep isl_basic_map *bmap,
1917 enum isl_dim_type type, unsigned pos);
1918 __isl_give isl_map *isl_map_set_dim_id(
1919 __isl_take isl_map *map, enum isl_dim_type type,
1920 unsigned pos, __isl_take isl_id *id);
1921 int isl_map_has_dim_id(__isl_keep isl_map *map,
1922 enum isl_dim_type type, unsigned pos);
1923 __isl_give isl_id *isl_map_get_dim_id(
1924 __isl_keep isl_map *map, enum isl_dim_type type,
1927 int isl_set_find_dim_by_id(__isl_keep isl_set *set,
1928 enum isl_dim_type type, __isl_keep isl_id *id);
1929 int isl_map_find_dim_by_id(__isl_keep isl_map *map,
1930 enum isl_dim_type type, __isl_keep isl_id *id);
1931 int isl_set_find_dim_by_name(__isl_keep isl_set *set,
1932 enum isl_dim_type type, const char *name);
1933 int isl_map_find_dim_by_name(__isl_keep isl_map *map,
1934 enum isl_dim_type type, const char *name);
1936 const char *isl_constraint_get_dim_name(
1937 __isl_keep isl_constraint *constraint,
1938 enum isl_dim_type type, unsigned pos);
1939 const char *isl_basic_set_get_dim_name(
1940 __isl_keep isl_basic_set *bset,
1941 enum isl_dim_type type, unsigned pos);
1942 int isl_set_has_dim_name(__isl_keep isl_set *set,
1943 enum isl_dim_type type, unsigned pos);
1944 const char *isl_set_get_dim_name(
1945 __isl_keep isl_set *set,
1946 enum isl_dim_type type, unsigned pos);
1947 const char *isl_basic_map_get_dim_name(
1948 __isl_keep isl_basic_map *bmap,
1949 enum isl_dim_type type, unsigned pos);
1950 int isl_map_has_dim_name(__isl_keep isl_map *map,
1951 enum isl_dim_type type, unsigned pos);
1952 const char *isl_map_get_dim_name(
1953 __isl_keep isl_map *map,
1954 enum isl_dim_type type, unsigned pos);
1956 These functions are mostly useful to obtain the identifiers, positions
1957 or names of the parameters. Identifiers of individual dimensions are
1958 essentially only useful for printing. They are ignored by all other
1959 operations and may not be preserved across those operations.
1963 =head3 Unary Properties
1969 The following functions test whether the given set or relation
1970 contains any integer points. The ``plain'' variants do not perform
1971 any computations, but simply check if the given set or relation
1972 is already known to be empty.
1974 int isl_basic_set_plain_is_empty(__isl_keep isl_basic_set *bset);
1975 int isl_basic_set_is_empty(__isl_keep isl_basic_set *bset);
1976 int isl_set_plain_is_empty(__isl_keep isl_set *set);
1977 int isl_set_is_empty(__isl_keep isl_set *set);
1978 int isl_union_set_is_empty(__isl_keep isl_union_set *uset);
1979 int isl_basic_map_plain_is_empty(__isl_keep isl_basic_map *bmap);
1980 int isl_basic_map_is_empty(__isl_keep isl_basic_map *bmap);
1981 int isl_map_plain_is_empty(__isl_keep isl_map *map);
1982 int isl_map_is_empty(__isl_keep isl_map *map);
1983 int isl_union_map_is_empty(__isl_keep isl_union_map *umap);
1985 =item * Universality
1987 int isl_basic_set_is_universe(__isl_keep isl_basic_set *bset);
1988 int isl_basic_map_is_universe(__isl_keep isl_basic_map *bmap);
1989 int isl_set_plain_is_universe(__isl_keep isl_set *set);
1991 =item * Single-valuedness
1993 int isl_basic_map_is_single_valued(
1994 __isl_keep isl_basic_map *bmap);
1995 int isl_map_plain_is_single_valued(
1996 __isl_keep isl_map *map);
1997 int isl_map_is_single_valued(__isl_keep isl_map *map);
1998 int isl_union_map_is_single_valued(__isl_keep isl_union_map *umap);
2002 int isl_map_plain_is_injective(__isl_keep isl_map *map);
2003 int isl_map_is_injective(__isl_keep isl_map *map);
2004 int isl_union_map_plain_is_injective(
2005 __isl_keep isl_union_map *umap);
2006 int isl_union_map_is_injective(
2007 __isl_keep isl_union_map *umap);
2011 int isl_map_is_bijective(__isl_keep isl_map *map);
2012 int isl_union_map_is_bijective(__isl_keep isl_union_map *umap);
2016 int isl_basic_map_plain_is_fixed(
2017 __isl_keep isl_basic_map *bmap,
2018 enum isl_dim_type type, unsigned pos,
2020 int isl_set_plain_is_fixed(__isl_keep isl_set *set,
2021 enum isl_dim_type type, unsigned pos,
2023 int isl_map_plain_is_fixed(__isl_keep isl_map *map,
2024 enum isl_dim_type type, unsigned pos,
2027 Check if the relation obviously lies on a hyperplane where the given dimension
2028 has a fixed value and if so, return that value in C<*val>.
2032 To check whether a set is a parameter domain, use this function:
2034 int isl_set_is_params(__isl_keep isl_set *set);
2035 int isl_union_set_is_params(
2036 __isl_keep isl_union_set *uset);
2040 The following functions check whether the domain of the given
2041 (basic) set is a wrapped relation.
2043 int isl_basic_set_is_wrapping(
2044 __isl_keep isl_basic_set *bset);
2045 int isl_set_is_wrapping(__isl_keep isl_set *set);
2047 =item * Internal Product
2049 int isl_basic_map_can_zip(
2050 __isl_keep isl_basic_map *bmap);
2051 int isl_map_can_zip(__isl_keep isl_map *map);
2053 Check whether the product of domain and range of the given relation
2055 i.e., whether both domain and range are nested relations.
2059 int isl_basic_map_can_curry(
2060 __isl_keep isl_basic_map *bmap);
2061 int isl_map_can_curry(__isl_keep isl_map *map);
2063 Check whether the domain of the (basic) relation is a wrapped relation.
2065 int isl_basic_map_can_uncurry(
2066 __isl_keep isl_basic_map *bmap);
2067 int isl_map_can_uncurry(__isl_keep isl_map *map);
2069 Check whether the range of the (basic) relation is a wrapped relation.
2073 =head3 Binary Properties
2079 int isl_set_plain_is_equal(__isl_keep isl_set *set1,
2080 __isl_keep isl_set *set2);
2081 int isl_set_is_equal(__isl_keep isl_set *set1,
2082 __isl_keep isl_set *set2);
2083 int isl_union_set_is_equal(
2084 __isl_keep isl_union_set *uset1,
2085 __isl_keep isl_union_set *uset2);
2086 int isl_basic_map_is_equal(
2087 __isl_keep isl_basic_map *bmap1,
2088 __isl_keep isl_basic_map *bmap2);
2089 int isl_map_is_equal(__isl_keep isl_map *map1,
2090 __isl_keep isl_map *map2);
2091 int isl_map_plain_is_equal(__isl_keep isl_map *map1,
2092 __isl_keep isl_map *map2);
2093 int isl_union_map_is_equal(
2094 __isl_keep isl_union_map *umap1,
2095 __isl_keep isl_union_map *umap2);
2097 =item * Disjointness
2099 int isl_set_plain_is_disjoint(__isl_keep isl_set *set1,
2100 __isl_keep isl_set *set2);
2101 int isl_set_is_disjoint(__isl_keep isl_set *set1,
2102 __isl_keep isl_set *set2);
2103 int isl_map_is_disjoint(__isl_keep isl_map *map1,
2104 __isl_keep isl_map *map2);
2108 int isl_basic_set_is_subset(
2109 __isl_keep isl_basic_set *bset1,
2110 __isl_keep isl_basic_set *bset2);
2111 int isl_set_is_subset(__isl_keep isl_set *set1,
2112 __isl_keep isl_set *set2);
2113 int isl_set_is_strict_subset(
2114 __isl_keep isl_set *set1,
2115 __isl_keep isl_set *set2);
2116 int isl_union_set_is_subset(
2117 __isl_keep isl_union_set *uset1,
2118 __isl_keep isl_union_set *uset2);
2119 int isl_union_set_is_strict_subset(
2120 __isl_keep isl_union_set *uset1,
2121 __isl_keep isl_union_set *uset2);
2122 int isl_basic_map_is_subset(
2123 __isl_keep isl_basic_map *bmap1,
2124 __isl_keep isl_basic_map *bmap2);
2125 int isl_basic_map_is_strict_subset(
2126 __isl_keep isl_basic_map *bmap1,
2127 __isl_keep isl_basic_map *bmap2);
2128 int isl_map_is_subset(
2129 __isl_keep isl_map *map1,
2130 __isl_keep isl_map *map2);
2131 int isl_map_is_strict_subset(
2132 __isl_keep isl_map *map1,
2133 __isl_keep isl_map *map2);
2134 int isl_union_map_is_subset(
2135 __isl_keep isl_union_map *umap1,
2136 __isl_keep isl_union_map *umap2);
2137 int isl_union_map_is_strict_subset(
2138 __isl_keep isl_union_map *umap1,
2139 __isl_keep isl_union_map *umap2);
2141 Check whether the first argument is a (strict) subset of the
2146 int isl_set_plain_cmp(__isl_keep isl_set *set1,
2147 __isl_keep isl_set *set2);
2149 This function is useful for sorting C<isl_set>s.
2150 The order depends on the internal representation of the inputs.
2151 The order is fixed over different calls to the function (assuming
2152 the internal representation of the inputs has not changed), but may
2153 change over different versions of C<isl>.
2157 =head2 Unary Operations
2163 __isl_give isl_set *isl_set_complement(
2164 __isl_take isl_set *set);
2165 __isl_give isl_map *isl_map_complement(
2166 __isl_take isl_map *map);
2170 __isl_give isl_basic_map *isl_basic_map_reverse(
2171 __isl_take isl_basic_map *bmap);
2172 __isl_give isl_map *isl_map_reverse(
2173 __isl_take isl_map *map);
2174 __isl_give isl_union_map *isl_union_map_reverse(
2175 __isl_take isl_union_map *umap);
2179 __isl_give isl_basic_set *isl_basic_set_project_out(
2180 __isl_take isl_basic_set *bset,
2181 enum isl_dim_type type, unsigned first, unsigned n);
2182 __isl_give isl_basic_map *isl_basic_map_project_out(
2183 __isl_take isl_basic_map *bmap,
2184 enum isl_dim_type type, unsigned first, unsigned n);
2185 __isl_give isl_set *isl_set_project_out(__isl_take isl_set *set,
2186 enum isl_dim_type type, unsigned first, unsigned n);
2187 __isl_give isl_map *isl_map_project_out(__isl_take isl_map *map,
2188 enum isl_dim_type type, unsigned first, unsigned n);
2189 __isl_give isl_basic_set *isl_basic_set_params(
2190 __isl_take isl_basic_set *bset);
2191 __isl_give isl_basic_set *isl_basic_map_domain(
2192 __isl_take isl_basic_map *bmap);
2193 __isl_give isl_basic_set *isl_basic_map_range(
2194 __isl_take isl_basic_map *bmap);
2195 __isl_give isl_set *isl_set_params(__isl_take isl_set *set);
2196 __isl_give isl_set *isl_map_params(__isl_take isl_map *map);
2197 __isl_give isl_set *isl_map_domain(
2198 __isl_take isl_map *bmap);
2199 __isl_give isl_set *isl_map_range(
2200 __isl_take isl_map *map);
2201 __isl_give isl_set *isl_union_set_params(
2202 __isl_take isl_union_set *uset);
2203 __isl_give isl_set *isl_union_map_params(
2204 __isl_take isl_union_map *umap);
2205 __isl_give isl_union_set *isl_union_map_domain(
2206 __isl_take isl_union_map *umap);
2207 __isl_give isl_union_set *isl_union_map_range(
2208 __isl_take isl_union_map *umap);
2210 __isl_give isl_basic_map *isl_basic_map_domain_map(
2211 __isl_take isl_basic_map *bmap);
2212 __isl_give isl_basic_map *isl_basic_map_range_map(
2213 __isl_take isl_basic_map *bmap);
2214 __isl_give isl_map *isl_map_domain_map(__isl_take isl_map *map);
2215 __isl_give isl_map *isl_map_range_map(__isl_take isl_map *map);
2216 __isl_give isl_union_map *isl_union_map_domain_map(
2217 __isl_take isl_union_map *umap);
2218 __isl_give isl_union_map *isl_union_map_range_map(
2219 __isl_take isl_union_map *umap);
2221 The functions above construct a (basic, regular or union) relation
2222 that maps (a wrapped version of) the input relation to its domain or range.
2226 __isl_give isl_basic_set *isl_basic_set_eliminate(
2227 __isl_take isl_basic_set *bset,
2228 enum isl_dim_type type,
2229 unsigned first, unsigned n);
2230 __isl_give isl_set *isl_set_eliminate(
2231 __isl_take isl_set *set, enum isl_dim_type type,
2232 unsigned first, unsigned n);
2233 __isl_give isl_basic_map *isl_basic_map_eliminate(
2234 __isl_take isl_basic_map *bmap,
2235 enum isl_dim_type type,
2236 unsigned first, unsigned n);
2237 __isl_give isl_map *isl_map_eliminate(
2238 __isl_take isl_map *map, enum isl_dim_type type,
2239 unsigned first, unsigned n);
2241 Eliminate the coefficients for the given dimensions from the constraints,
2242 without removing the dimensions.
2246 __isl_give isl_basic_set *isl_basic_set_fix(
2247 __isl_take isl_basic_set *bset,
2248 enum isl_dim_type type, unsigned pos,
2250 __isl_give isl_basic_set *isl_basic_set_fix_si(
2251 __isl_take isl_basic_set *bset,
2252 enum isl_dim_type type, unsigned pos, int value);
2253 __isl_give isl_set *isl_set_fix(__isl_take isl_set *set,
2254 enum isl_dim_type type, unsigned pos,
2256 __isl_give isl_set *isl_set_fix_si(__isl_take isl_set *set,
2257 enum isl_dim_type type, unsigned pos, int value);
2258 __isl_give isl_basic_map *isl_basic_map_fix_si(
2259 __isl_take isl_basic_map *bmap,
2260 enum isl_dim_type type, unsigned pos, int value);
2261 __isl_give isl_map *isl_map_fix(__isl_take isl_map *map,
2262 enum isl_dim_type type, unsigned pos,
2264 __isl_give isl_map *isl_map_fix_si(__isl_take isl_map *map,
2265 enum isl_dim_type type, unsigned pos, int value);
2267 Intersect the set or relation with the hyperplane where the given
2268 dimension has the fixed given value.
2270 __isl_give isl_basic_map *isl_basic_map_lower_bound_si(
2271 __isl_take isl_basic_map *bmap,
2272 enum isl_dim_type type, unsigned pos, int value);
2273 __isl_give isl_basic_map *isl_basic_map_upper_bound_si(
2274 __isl_take isl_basic_map *bmap,
2275 enum isl_dim_type type, unsigned pos, int value);
2276 __isl_give isl_set *isl_set_lower_bound(
2277 __isl_take isl_set *set,
2278 enum isl_dim_type type, unsigned pos,
2280 __isl_give isl_set *isl_set_lower_bound_si(
2281 __isl_take isl_set *set,
2282 enum isl_dim_type type, unsigned pos, int value);
2283 __isl_give isl_map *isl_map_lower_bound_si(
2284 __isl_take isl_map *map,
2285 enum isl_dim_type type, unsigned pos, int value);
2286 __isl_give isl_set *isl_set_upper_bound(
2287 __isl_take isl_set *set,
2288 enum isl_dim_type type, unsigned pos,
2290 __isl_give isl_set *isl_set_upper_bound_si(
2291 __isl_take isl_set *set,
2292 enum isl_dim_type type, unsigned pos, int value);
2293 __isl_give isl_map *isl_map_upper_bound_si(
2294 __isl_take isl_map *map,
2295 enum isl_dim_type type, unsigned pos, int value);
2297 Intersect the set or relation with the half-space where the given
2298 dimension has a value bounded by the fixed given value.
2300 __isl_give isl_set *isl_set_equate(__isl_take isl_set *set,
2301 enum isl_dim_type type1, int pos1,
2302 enum isl_dim_type type2, int pos2);
2303 __isl_give isl_basic_map *isl_basic_map_equate(
2304 __isl_take isl_basic_map *bmap,
2305 enum isl_dim_type type1, int pos1,
2306 enum isl_dim_type type2, int pos2);
2307 __isl_give isl_map *isl_map_equate(__isl_take isl_map *map,
2308 enum isl_dim_type type1, int pos1,
2309 enum isl_dim_type type2, int pos2);
2311 Intersect the set or relation with the hyperplane where the given
2312 dimensions are equal to each other.
2314 __isl_give isl_map *isl_map_oppose(__isl_take isl_map *map,
2315 enum isl_dim_type type1, int pos1,
2316 enum isl_dim_type type2, int pos2);
2318 Intersect the relation with the hyperplane where the given
2319 dimensions have opposite values.
2321 __isl_give isl_basic_map *isl_basic_map_order_ge(
2322 __isl_take isl_basic_map *bmap,
2323 enum isl_dim_type type1, int pos1,
2324 enum isl_dim_type type2, int pos2);
2325 __isl_give isl_map *isl_map_order_lt(__isl_take isl_map *map,
2326 enum isl_dim_type type1, int pos1,
2327 enum isl_dim_type type2, int pos2);
2328 __isl_give isl_basic_map *isl_basic_map_order_gt(
2329 __isl_take isl_basic_map *bmap,
2330 enum isl_dim_type type1, int pos1,
2331 enum isl_dim_type type2, int pos2);
2332 __isl_give isl_map *isl_map_order_gt(__isl_take isl_map *map,
2333 enum isl_dim_type type1, int pos1,
2334 enum isl_dim_type type2, int pos2);
2336 Intersect the relation with the half-space where the given
2337 dimensions satisfy the given ordering.
2341 __isl_give isl_map *isl_set_identity(
2342 __isl_take isl_set *set);
2343 __isl_give isl_union_map *isl_union_set_identity(
2344 __isl_take isl_union_set *uset);
2346 Construct an identity relation on the given (union) set.
2350 __isl_give isl_basic_set *isl_basic_map_deltas(
2351 __isl_take isl_basic_map *bmap);
2352 __isl_give isl_set *isl_map_deltas(__isl_take isl_map *map);
2353 __isl_give isl_union_set *isl_union_map_deltas(
2354 __isl_take isl_union_map *umap);
2356 These functions return a (basic) set containing the differences
2357 between image elements and corresponding domain elements in the input.
2359 __isl_give isl_basic_map *isl_basic_map_deltas_map(
2360 __isl_take isl_basic_map *bmap);
2361 __isl_give isl_map *isl_map_deltas_map(
2362 __isl_take isl_map *map);
2363 __isl_give isl_union_map *isl_union_map_deltas_map(
2364 __isl_take isl_union_map *umap);
2366 The functions above construct a (basic, regular or union) relation
2367 that maps (a wrapped version of) the input relation to its delta set.
2371 Simplify the representation of a set or relation by trying
2372 to combine pairs of basic sets or relations into a single
2373 basic set or relation.
2375 __isl_give isl_set *isl_set_coalesce(__isl_take isl_set *set);
2376 __isl_give isl_map *isl_map_coalesce(__isl_take isl_map *map);
2377 __isl_give isl_union_set *isl_union_set_coalesce(
2378 __isl_take isl_union_set *uset);
2379 __isl_give isl_union_map *isl_union_map_coalesce(
2380 __isl_take isl_union_map *umap);
2382 One of the methods for combining pairs of basic sets or relations
2383 can result in coefficients that are much larger than those that appear
2384 in the constraints of the input. By default, the coefficients are
2385 not allowed to grow larger, but this can be changed by unsetting
2386 the following option.
2388 int isl_options_set_coalesce_bounded_wrapping(
2389 isl_ctx *ctx, int val);
2390 int isl_options_get_coalesce_bounded_wrapping(
2393 =item * Detecting equalities
2395 __isl_give isl_basic_set *isl_basic_set_detect_equalities(
2396 __isl_take isl_basic_set *bset);
2397 __isl_give isl_basic_map *isl_basic_map_detect_equalities(
2398 __isl_take isl_basic_map *bmap);
2399 __isl_give isl_set *isl_set_detect_equalities(
2400 __isl_take isl_set *set);
2401 __isl_give isl_map *isl_map_detect_equalities(
2402 __isl_take isl_map *map);
2403 __isl_give isl_union_set *isl_union_set_detect_equalities(
2404 __isl_take isl_union_set *uset);
2405 __isl_give isl_union_map *isl_union_map_detect_equalities(
2406 __isl_take isl_union_map *umap);
2408 Simplify the representation of a set or relation by detecting implicit
2411 =item * Removing redundant constraints
2413 __isl_give isl_basic_set *isl_basic_set_remove_redundancies(
2414 __isl_take isl_basic_set *bset);
2415 __isl_give isl_set *isl_set_remove_redundancies(
2416 __isl_take isl_set *set);
2417 __isl_give isl_basic_map *isl_basic_map_remove_redundancies(
2418 __isl_take isl_basic_map *bmap);
2419 __isl_give isl_map *isl_map_remove_redundancies(
2420 __isl_take isl_map *map);
2424 __isl_give isl_basic_set *isl_set_convex_hull(
2425 __isl_take isl_set *set);
2426 __isl_give isl_basic_map *isl_map_convex_hull(
2427 __isl_take isl_map *map);
2429 If the input set or relation has any existentially quantified
2430 variables, then the result of these operations is currently undefined.
2434 __isl_give isl_basic_set *
2435 isl_set_unshifted_simple_hull(
2436 __isl_take isl_set *set);
2437 __isl_give isl_basic_map *
2438 isl_map_unshifted_simple_hull(
2439 __isl_take isl_map *map);
2440 __isl_give isl_basic_set *isl_set_simple_hull(
2441 __isl_take isl_set *set);
2442 __isl_give isl_basic_map *isl_map_simple_hull(
2443 __isl_take isl_map *map);
2444 __isl_give isl_union_map *isl_union_map_simple_hull(
2445 __isl_take isl_union_map *umap);
2447 These functions compute a single basic set or relation
2448 that contains the whole input set or relation.
2449 In particular, the output is described by translates
2450 of the constraints describing the basic sets or relations in the input.
2451 In case of C<isl_set_unshifted_simple_hull>, only the original
2452 constraints are used, without any translation.
2456 (See \autoref{s:simple hull}.)
2462 __isl_give isl_basic_set *isl_basic_set_affine_hull(
2463 __isl_take isl_basic_set *bset);
2464 __isl_give isl_basic_set *isl_set_affine_hull(
2465 __isl_take isl_set *set);
2466 __isl_give isl_union_set *isl_union_set_affine_hull(
2467 __isl_take isl_union_set *uset);
2468 __isl_give isl_basic_map *isl_basic_map_affine_hull(
2469 __isl_take isl_basic_map *bmap);
2470 __isl_give isl_basic_map *isl_map_affine_hull(
2471 __isl_take isl_map *map);
2472 __isl_give isl_union_map *isl_union_map_affine_hull(
2473 __isl_take isl_union_map *umap);
2475 In case of union sets and relations, the affine hull is computed
2478 =item * Polyhedral hull
2480 __isl_give isl_basic_set *isl_set_polyhedral_hull(
2481 __isl_take isl_set *set);
2482 __isl_give isl_basic_map *isl_map_polyhedral_hull(
2483 __isl_take isl_map *map);
2484 __isl_give isl_union_set *isl_union_set_polyhedral_hull(
2485 __isl_take isl_union_set *uset);
2486 __isl_give isl_union_map *isl_union_map_polyhedral_hull(
2487 __isl_take isl_union_map *umap);
2489 These functions compute a single basic set or relation
2490 not involving any existentially quantified variables
2491 that contains the whole input set or relation.
2492 In case of union sets and relations, the polyhedral hull is computed
2495 =item * Other approximations
2497 __isl_give isl_basic_set *
2498 isl_basic_set_drop_constraints_involving_dims(
2499 __isl_take isl_basic_set *bset,
2500 enum isl_dim_type type,
2501 unsigned first, unsigned n);
2502 __isl_give isl_basic_map *
2503 isl_basic_map_drop_constraints_involving_dims(
2504 __isl_take isl_basic_map *bmap,
2505 enum isl_dim_type type,
2506 unsigned first, unsigned n);
2507 __isl_give isl_basic_set *
2508 isl_basic_set_drop_constraints_not_involving_dims(
2509 __isl_take isl_basic_set *bset,
2510 enum isl_dim_type type,
2511 unsigned first, unsigned n);
2512 __isl_give isl_set *
2513 isl_set_drop_constraints_involving_dims(
2514 __isl_take isl_set *set,
2515 enum isl_dim_type type,
2516 unsigned first, unsigned n);
2517 __isl_give isl_map *
2518 isl_map_drop_constraints_involving_dims(
2519 __isl_take isl_map *map,
2520 enum isl_dim_type type,
2521 unsigned first, unsigned n);
2523 These functions drop any constraints (not) involving the specified dimensions.
2524 Note that the result depends on the representation of the input.
2528 __isl_give isl_basic_set *isl_basic_set_sample(
2529 __isl_take isl_basic_set *bset);
2530 __isl_give isl_basic_set *isl_set_sample(
2531 __isl_take isl_set *set);
2532 __isl_give isl_basic_map *isl_basic_map_sample(
2533 __isl_take isl_basic_map *bmap);
2534 __isl_give isl_basic_map *isl_map_sample(
2535 __isl_take isl_map *map);
2537 If the input (basic) set or relation is non-empty, then return
2538 a singleton subset of the input. Otherwise, return an empty set.
2540 =item * Optimization
2542 #include <isl/ilp.h>
2543 enum isl_lp_result isl_basic_set_max(
2544 __isl_keep isl_basic_set *bset,
2545 __isl_keep isl_aff *obj, isl_int *opt)
2546 enum isl_lp_result isl_set_min(__isl_keep isl_set *set,
2547 __isl_keep isl_aff *obj, isl_int *opt);
2548 enum isl_lp_result isl_set_max(__isl_keep isl_set *set,
2549 __isl_keep isl_aff *obj, isl_int *opt);
2551 Compute the minimum or maximum of the integer affine expression C<obj>
2552 over the points in C<set>, returning the result in C<opt>.
2553 The return value may be one of C<isl_lp_error>,
2554 C<isl_lp_ok>, C<isl_lp_unbounded> or C<isl_lp_empty>.
2556 =item * Parametric optimization
2558 __isl_give isl_pw_aff *isl_set_dim_min(
2559 __isl_take isl_set *set, int pos);
2560 __isl_give isl_pw_aff *isl_set_dim_max(
2561 __isl_take isl_set *set, int pos);
2562 __isl_give isl_pw_aff *isl_map_dim_max(
2563 __isl_take isl_map *map, int pos);
2565 Compute the minimum or maximum of the given set or output dimension
2566 as a function of the parameters (and input dimensions), but independently
2567 of the other set or output dimensions.
2568 For lexicographic optimization, see L<"Lexicographic Optimization">.
2572 The following functions compute either the set of (rational) coefficient
2573 values of valid constraints for the given set or the set of (rational)
2574 values satisfying the constraints with coefficients from the given set.
2575 Internally, these two sets of functions perform essentially the
2576 same operations, except that the set of coefficients is assumed to
2577 be a cone, while the set of values may be any polyhedron.
2578 The current implementation is based on the Farkas lemma and
2579 Fourier-Motzkin elimination, but this may change or be made optional
2580 in future. In particular, future implementations may use different
2581 dualization algorithms or skip the elimination step.
2583 __isl_give isl_basic_set *isl_basic_set_coefficients(
2584 __isl_take isl_basic_set *bset);
2585 __isl_give isl_basic_set *isl_set_coefficients(
2586 __isl_take isl_set *set);
2587 __isl_give isl_union_set *isl_union_set_coefficients(
2588 __isl_take isl_union_set *bset);
2589 __isl_give isl_basic_set *isl_basic_set_solutions(
2590 __isl_take isl_basic_set *bset);
2591 __isl_give isl_basic_set *isl_set_solutions(
2592 __isl_take isl_set *set);
2593 __isl_give isl_union_set *isl_union_set_solutions(
2594 __isl_take isl_union_set *bset);
2598 __isl_give isl_map *isl_map_fixed_power(
2599 __isl_take isl_map *map, isl_int exp);
2600 __isl_give isl_union_map *isl_union_map_fixed_power(
2601 __isl_take isl_union_map *umap, isl_int exp);
2603 Compute the given power of C<map>, where C<exp> is assumed to be non-zero.
2604 If the exponent C<exp> is negative, then the -C<exp> th power of the inverse
2605 of C<map> is computed.
2607 __isl_give isl_map *isl_map_power(__isl_take isl_map *map,
2609 __isl_give isl_union_map *isl_union_map_power(
2610 __isl_take isl_union_map *umap, int *exact);
2612 Compute a parametric representation for all positive powers I<k> of C<map>.
2613 The result maps I<k> to a nested relation corresponding to the
2614 I<k>th power of C<map>.
2615 The result may be an overapproximation. If the result is known to be exact,
2616 then C<*exact> is set to C<1>.
2618 =item * Transitive closure
2620 __isl_give isl_map *isl_map_transitive_closure(
2621 __isl_take isl_map *map, int *exact);
2622 __isl_give isl_union_map *isl_union_map_transitive_closure(
2623 __isl_take isl_union_map *umap, int *exact);
2625 Compute the transitive closure of C<map>.
2626 The result may be an overapproximation. If the result is known to be exact,
2627 then C<*exact> is set to C<1>.
2629 =item * Reaching path lengths
2631 __isl_give isl_map *isl_map_reaching_path_lengths(
2632 __isl_take isl_map *map, int *exact);
2634 Compute a relation that maps each element in the range of C<map>
2635 to the lengths of all paths composed of edges in C<map> that
2636 end up in the given element.
2637 The result may be an overapproximation. If the result is known to be exact,
2638 then C<*exact> is set to C<1>.
2639 To compute the I<maximal> path length, the resulting relation
2640 should be postprocessed by C<isl_map_lexmax>.
2641 In particular, if the input relation is a dependence relation
2642 (mapping sources to sinks), then the maximal path length corresponds
2643 to the free schedule.
2644 Note, however, that C<isl_map_lexmax> expects the maximum to be
2645 finite, so if the path lengths are unbounded (possibly due to
2646 the overapproximation), then you will get an error message.
2650 __isl_give isl_basic_set *isl_basic_map_wrap(
2651 __isl_take isl_basic_map *bmap);
2652 __isl_give isl_set *isl_map_wrap(
2653 __isl_take isl_map *map);
2654 __isl_give isl_union_set *isl_union_map_wrap(
2655 __isl_take isl_union_map *umap);
2656 __isl_give isl_basic_map *isl_basic_set_unwrap(
2657 __isl_take isl_basic_set *bset);
2658 __isl_give isl_map *isl_set_unwrap(
2659 __isl_take isl_set *set);
2660 __isl_give isl_union_map *isl_union_set_unwrap(
2661 __isl_take isl_union_set *uset);
2665 Remove any internal structure of domain (and range) of the given
2666 set or relation. If there is any such internal structure in the input,
2667 then the name of the space is also removed.
2669 __isl_give isl_basic_set *isl_basic_set_flatten(
2670 __isl_take isl_basic_set *bset);
2671 __isl_give isl_set *isl_set_flatten(
2672 __isl_take isl_set *set);
2673 __isl_give isl_basic_map *isl_basic_map_flatten_domain(
2674 __isl_take isl_basic_map *bmap);
2675 __isl_give isl_basic_map *isl_basic_map_flatten_range(
2676 __isl_take isl_basic_map *bmap);
2677 __isl_give isl_map *isl_map_flatten_range(
2678 __isl_take isl_map *map);
2679 __isl_give isl_map *isl_map_flatten_domain(
2680 __isl_take isl_map *map);
2681 __isl_give isl_basic_map *isl_basic_map_flatten(
2682 __isl_take isl_basic_map *bmap);
2683 __isl_give isl_map *isl_map_flatten(
2684 __isl_take isl_map *map);
2686 __isl_give isl_map *isl_set_flatten_map(
2687 __isl_take isl_set *set);
2689 The function above constructs a relation
2690 that maps the input set to a flattened version of the set.
2694 Lift the input set to a space with extra dimensions corresponding
2695 to the existentially quantified variables in the input.
2696 In particular, the result lives in a wrapped map where the domain
2697 is the original space and the range corresponds to the original
2698 existentially quantified variables.
2700 __isl_give isl_basic_set *isl_basic_set_lift(
2701 __isl_take isl_basic_set *bset);
2702 __isl_give isl_set *isl_set_lift(
2703 __isl_take isl_set *set);
2704 __isl_give isl_union_set *isl_union_set_lift(
2705 __isl_take isl_union_set *uset);
2707 Given a local space that contains the existentially quantified
2708 variables of a set, a basic relation that, when applied to
2709 a basic set, has essentially the same effect as C<isl_basic_set_lift>,
2710 can be constructed using the following function.
2712 #include <isl/local_space.h>
2713 __isl_give isl_basic_map *isl_local_space_lifting(
2714 __isl_take isl_local_space *ls);
2716 =item * Internal Product
2718 __isl_give isl_basic_map *isl_basic_map_zip(
2719 __isl_take isl_basic_map *bmap);
2720 __isl_give isl_map *isl_map_zip(
2721 __isl_take isl_map *map);
2722 __isl_give isl_union_map *isl_union_map_zip(
2723 __isl_take isl_union_map *umap);
2725 Given a relation with nested relations for domain and range,
2726 interchange the range of the domain with the domain of the range.
2730 __isl_give isl_basic_map *isl_basic_map_curry(
2731 __isl_take isl_basic_map *bmap);
2732 __isl_give isl_basic_map *isl_basic_map_uncurry(
2733 __isl_take isl_basic_map *bmap);
2734 __isl_give isl_map *isl_map_curry(
2735 __isl_take isl_map *map);
2736 __isl_give isl_map *isl_map_uncurry(
2737 __isl_take isl_map *map);
2738 __isl_give isl_union_map *isl_union_map_curry(
2739 __isl_take isl_union_map *umap);
2740 __isl_give isl_union_map *isl_union_map_uncurry(
2741 __isl_take isl_union_map *umap);
2743 Given a relation with a nested relation for domain,
2744 the C<curry> functions
2745 move the range of the nested relation out of the domain
2746 and use it as the domain of a nested relation in the range,
2747 with the original range as range of this nested relation.
2748 The C<uncurry> functions perform the inverse operation.
2750 =item * Aligning parameters
2752 __isl_give isl_basic_set *isl_basic_set_align_params(
2753 __isl_take isl_basic_set *bset,
2754 __isl_take isl_space *model);
2755 __isl_give isl_set *isl_set_align_params(
2756 __isl_take isl_set *set,
2757 __isl_take isl_space *model);
2758 __isl_give isl_basic_map *isl_basic_map_align_params(
2759 __isl_take isl_basic_map *bmap,
2760 __isl_take isl_space *model);
2761 __isl_give isl_map *isl_map_align_params(
2762 __isl_take isl_map *map,
2763 __isl_take isl_space *model);
2765 Change the order of the parameters of the given set or relation
2766 such that the first parameters match those of C<model>.
2767 This may involve the introduction of extra parameters.
2768 All parameters need to be named.
2770 =item * Dimension manipulation
2772 __isl_give isl_basic_set *isl_basic_set_add_dims(
2773 __isl_take isl_basic_set *bset,
2774 enum isl_dim_type type, unsigned n);
2775 __isl_give isl_set *isl_set_add_dims(
2776 __isl_take isl_set *set,
2777 enum isl_dim_type type, unsigned n);
2778 __isl_give isl_map *isl_map_add_dims(
2779 __isl_take isl_map *map,
2780 enum isl_dim_type type, unsigned n);
2781 __isl_give isl_basic_set *isl_basic_set_insert_dims(
2782 __isl_take isl_basic_set *bset,
2783 enum isl_dim_type type, unsigned pos,
2785 __isl_give isl_basic_map *isl_basic_map_insert_dims(
2786 __isl_take isl_basic_map *bmap,
2787 enum isl_dim_type type, unsigned pos,
2789 __isl_give isl_set *isl_set_insert_dims(
2790 __isl_take isl_set *set,
2791 enum isl_dim_type type, unsigned pos, unsigned n);
2792 __isl_give isl_map *isl_map_insert_dims(
2793 __isl_take isl_map *map,
2794 enum isl_dim_type type, unsigned pos, unsigned n);
2795 __isl_give isl_basic_set *isl_basic_set_move_dims(
2796 __isl_take isl_basic_set *bset,
2797 enum isl_dim_type dst_type, unsigned dst_pos,
2798 enum isl_dim_type src_type, unsigned src_pos,
2800 __isl_give isl_basic_map *isl_basic_map_move_dims(
2801 __isl_take isl_basic_map *bmap,
2802 enum isl_dim_type dst_type, unsigned dst_pos,
2803 enum isl_dim_type src_type, unsigned src_pos,
2805 __isl_give isl_set *isl_set_move_dims(
2806 __isl_take isl_set *set,
2807 enum isl_dim_type dst_type, unsigned dst_pos,
2808 enum isl_dim_type src_type, unsigned src_pos,
2810 __isl_give isl_map *isl_map_move_dims(
2811 __isl_take isl_map *map,
2812 enum isl_dim_type dst_type, unsigned dst_pos,
2813 enum isl_dim_type src_type, unsigned src_pos,
2816 It is usually not advisable to directly change the (input or output)
2817 space of a set or a relation as this removes the name and the internal
2818 structure of the space. However, the above functions can be useful
2819 to add new parameters, assuming
2820 C<isl_set_align_params> and C<isl_map_align_params>
2825 =head2 Binary Operations
2827 The two arguments of a binary operation not only need to live
2828 in the same C<isl_ctx>, they currently also need to have
2829 the same (number of) parameters.
2831 =head3 Basic Operations
2835 =item * Intersection
2837 __isl_give isl_basic_set *isl_basic_set_intersect_params(
2838 __isl_take isl_basic_set *bset1,
2839 __isl_take isl_basic_set *bset2);
2840 __isl_give isl_basic_set *isl_basic_set_intersect(
2841 __isl_take isl_basic_set *bset1,
2842 __isl_take isl_basic_set *bset2);
2843 __isl_give isl_set *isl_set_intersect_params(
2844 __isl_take isl_set *set,
2845 __isl_take isl_set *params);
2846 __isl_give isl_set *isl_set_intersect(
2847 __isl_take isl_set *set1,
2848 __isl_take isl_set *set2);
2849 __isl_give isl_union_set *isl_union_set_intersect_params(
2850 __isl_take isl_union_set *uset,
2851 __isl_take isl_set *set);
2852 __isl_give isl_union_map *isl_union_map_intersect_params(
2853 __isl_take isl_union_map *umap,
2854 __isl_take isl_set *set);
2855 __isl_give isl_union_set *isl_union_set_intersect(
2856 __isl_take isl_union_set *uset1,
2857 __isl_take isl_union_set *uset2);
2858 __isl_give isl_basic_map *isl_basic_map_intersect_domain(
2859 __isl_take isl_basic_map *bmap,
2860 __isl_take isl_basic_set *bset);
2861 __isl_give isl_basic_map *isl_basic_map_intersect_range(
2862 __isl_take isl_basic_map *bmap,
2863 __isl_take isl_basic_set *bset);
2864 __isl_give isl_basic_map *isl_basic_map_intersect(
2865 __isl_take isl_basic_map *bmap1,
2866 __isl_take isl_basic_map *bmap2);
2867 __isl_give isl_map *isl_map_intersect_params(
2868 __isl_take isl_map *map,
2869 __isl_take isl_set *params);
2870 __isl_give isl_map *isl_map_intersect_domain(
2871 __isl_take isl_map *map,
2872 __isl_take isl_set *set);
2873 __isl_give isl_map *isl_map_intersect_range(
2874 __isl_take isl_map *map,
2875 __isl_take isl_set *set);
2876 __isl_give isl_map *isl_map_intersect(
2877 __isl_take isl_map *map1,
2878 __isl_take isl_map *map2);
2879 __isl_give isl_union_map *isl_union_map_intersect_domain(
2880 __isl_take isl_union_map *umap,
2881 __isl_take isl_union_set *uset);
2882 __isl_give isl_union_map *isl_union_map_intersect_range(
2883 __isl_take isl_union_map *umap,
2884 __isl_take isl_union_set *uset);
2885 __isl_give isl_union_map *isl_union_map_intersect(
2886 __isl_take isl_union_map *umap1,
2887 __isl_take isl_union_map *umap2);
2889 The second argument to the C<_params> functions needs to be
2890 a parametric (basic) set. For the other functions, a parametric set
2891 for either argument is only allowed if the other argument is
2892 a parametric set as well.
2896 __isl_give isl_set *isl_basic_set_union(
2897 __isl_take isl_basic_set *bset1,
2898 __isl_take isl_basic_set *bset2);
2899 __isl_give isl_map *isl_basic_map_union(
2900 __isl_take isl_basic_map *bmap1,
2901 __isl_take isl_basic_map *bmap2);
2902 __isl_give isl_set *isl_set_union(
2903 __isl_take isl_set *set1,
2904 __isl_take isl_set *set2);
2905 __isl_give isl_map *isl_map_union(
2906 __isl_take isl_map *map1,
2907 __isl_take isl_map *map2);
2908 __isl_give isl_union_set *isl_union_set_union(
2909 __isl_take isl_union_set *uset1,
2910 __isl_take isl_union_set *uset2);
2911 __isl_give isl_union_map *isl_union_map_union(
2912 __isl_take isl_union_map *umap1,
2913 __isl_take isl_union_map *umap2);
2915 =item * Set difference
2917 __isl_give isl_set *isl_set_subtract(
2918 __isl_take isl_set *set1,
2919 __isl_take isl_set *set2);
2920 __isl_give isl_map *isl_map_subtract(
2921 __isl_take isl_map *map1,
2922 __isl_take isl_map *map2);
2923 __isl_give isl_map *isl_map_subtract_domain(
2924 __isl_take isl_map *map,
2925 __isl_take isl_set *dom);
2926 __isl_give isl_map *isl_map_subtract_range(
2927 __isl_take isl_map *map,
2928 __isl_take isl_set *dom);
2929 __isl_give isl_union_set *isl_union_set_subtract(
2930 __isl_take isl_union_set *uset1,
2931 __isl_take isl_union_set *uset2);
2932 __isl_give isl_union_map *isl_union_map_subtract(
2933 __isl_take isl_union_map *umap1,
2934 __isl_take isl_union_map *umap2);
2935 __isl_give isl_union_map *isl_union_map_subtract_domain(
2936 __isl_take isl_union_map *umap,
2937 __isl_take isl_union_set *dom);
2938 __isl_give isl_union_map *isl_union_map_subtract_range(
2939 __isl_take isl_union_map *umap,
2940 __isl_take isl_union_set *dom);
2944 __isl_give isl_basic_set *isl_basic_set_apply(
2945 __isl_take isl_basic_set *bset,
2946 __isl_take isl_basic_map *bmap);
2947 __isl_give isl_set *isl_set_apply(
2948 __isl_take isl_set *set,
2949 __isl_take isl_map *map);
2950 __isl_give isl_union_set *isl_union_set_apply(
2951 __isl_take isl_union_set *uset,
2952 __isl_take isl_union_map *umap);
2953 __isl_give isl_basic_map *isl_basic_map_apply_domain(
2954 __isl_take isl_basic_map *bmap1,
2955 __isl_take isl_basic_map *bmap2);
2956 __isl_give isl_basic_map *isl_basic_map_apply_range(
2957 __isl_take isl_basic_map *bmap1,
2958 __isl_take isl_basic_map *bmap2);
2959 __isl_give isl_map *isl_map_apply_domain(
2960 __isl_take isl_map *map1,
2961 __isl_take isl_map *map2);
2962 __isl_give isl_union_map *isl_union_map_apply_domain(
2963 __isl_take isl_union_map *umap1,
2964 __isl_take isl_union_map *umap2);
2965 __isl_give isl_map *isl_map_apply_range(
2966 __isl_take isl_map *map1,
2967 __isl_take isl_map *map2);
2968 __isl_give isl_union_map *isl_union_map_apply_range(
2969 __isl_take isl_union_map *umap1,
2970 __isl_take isl_union_map *umap2);
2974 __isl_give isl_basic_set *
2975 isl_basic_set_preimage_multi_aff(
2976 __isl_take isl_basic_set *bset,
2977 __isl_take isl_multi_aff *ma);
2978 __isl_give isl_set *isl_set_preimage_multi_aff(
2979 __isl_take isl_set *set,
2980 __isl_take isl_multi_aff *ma);
2981 __isl_give isl_set *isl_set_preimage_pw_multi_aff(
2982 __isl_take isl_set *set,
2983 __isl_take isl_pw_multi_aff *pma);
2984 __isl_give isl_map *isl_map_preimage_domain_multi_aff(
2985 __isl_take isl_map *map,
2986 __isl_take isl_multi_aff *ma);
2987 __isl_give isl_union_map *
2988 isl_union_map_preimage_domain_multi_aff(
2989 __isl_take isl_union_map *umap,
2990 __isl_take isl_multi_aff *ma);
2992 These functions compute the preimage of the given set or map domain under
2993 the given function. In other words, the expression is plugged
2994 into the set description or into the domain of the map.
2995 Objects of types C<isl_multi_aff> and C<isl_pw_multi_aff> are described in
2996 L</"Piecewise Multiple Quasi Affine Expressions">.
2998 =item * Cartesian Product
3000 __isl_give isl_set *isl_set_product(
3001 __isl_take isl_set *set1,
3002 __isl_take isl_set *set2);
3003 __isl_give isl_union_set *isl_union_set_product(
3004 __isl_take isl_union_set *uset1,
3005 __isl_take isl_union_set *uset2);
3006 __isl_give isl_basic_map *isl_basic_map_domain_product(
3007 __isl_take isl_basic_map *bmap1,
3008 __isl_take isl_basic_map *bmap2);
3009 __isl_give isl_basic_map *isl_basic_map_range_product(
3010 __isl_take isl_basic_map *bmap1,
3011 __isl_take isl_basic_map *bmap2);
3012 __isl_give isl_basic_map *isl_basic_map_product(
3013 __isl_take isl_basic_map *bmap1,
3014 __isl_take isl_basic_map *bmap2);
3015 __isl_give isl_map *isl_map_domain_product(
3016 __isl_take isl_map *map1,
3017 __isl_take isl_map *map2);
3018 __isl_give isl_map *isl_map_range_product(
3019 __isl_take isl_map *map1,
3020 __isl_take isl_map *map2);
3021 __isl_give isl_union_map *isl_union_map_domain_product(
3022 __isl_take isl_union_map *umap1,
3023 __isl_take isl_union_map *umap2);
3024 __isl_give isl_union_map *isl_union_map_range_product(
3025 __isl_take isl_union_map *umap1,
3026 __isl_take isl_union_map *umap2);
3027 __isl_give isl_map *isl_map_product(
3028 __isl_take isl_map *map1,
3029 __isl_take isl_map *map2);
3030 __isl_give isl_union_map *isl_union_map_product(
3031 __isl_take isl_union_map *umap1,
3032 __isl_take isl_union_map *umap2);
3034 The above functions compute the cross product of the given
3035 sets or relations. The domains and ranges of the results
3036 are wrapped maps between domains and ranges of the inputs.
3037 To obtain a ``flat'' product, use the following functions
3040 __isl_give isl_basic_set *isl_basic_set_flat_product(
3041 __isl_take isl_basic_set *bset1,
3042 __isl_take isl_basic_set *bset2);
3043 __isl_give isl_set *isl_set_flat_product(
3044 __isl_take isl_set *set1,
3045 __isl_take isl_set *set2);
3046 __isl_give isl_basic_map *isl_basic_map_flat_range_product(
3047 __isl_take isl_basic_map *bmap1,
3048 __isl_take isl_basic_map *bmap2);
3049 __isl_give isl_map *isl_map_flat_domain_product(
3050 __isl_take isl_map *map1,
3051 __isl_take isl_map *map2);
3052 __isl_give isl_map *isl_map_flat_range_product(
3053 __isl_take isl_map *map1,
3054 __isl_take isl_map *map2);
3055 __isl_give isl_union_map *isl_union_map_flat_range_product(
3056 __isl_take isl_union_map *umap1,
3057 __isl_take isl_union_map *umap2);
3058 __isl_give isl_basic_map *isl_basic_map_flat_product(
3059 __isl_take isl_basic_map *bmap1,
3060 __isl_take isl_basic_map *bmap2);
3061 __isl_give isl_map *isl_map_flat_product(
3062 __isl_take isl_map *map1,
3063 __isl_take isl_map *map2);
3065 =item * Simplification
3067 __isl_give isl_basic_set *isl_basic_set_gist(
3068 __isl_take isl_basic_set *bset,
3069 __isl_take isl_basic_set *context);
3070 __isl_give isl_set *isl_set_gist(__isl_take isl_set *set,
3071 __isl_take isl_set *context);
3072 __isl_give isl_set *isl_set_gist_params(
3073 __isl_take isl_set *set,
3074 __isl_take isl_set *context);
3075 __isl_give isl_union_set *isl_union_set_gist(
3076 __isl_take isl_union_set *uset,
3077 __isl_take isl_union_set *context);
3078 __isl_give isl_union_set *isl_union_set_gist_params(
3079 __isl_take isl_union_set *uset,
3080 __isl_take isl_set *set);
3081 __isl_give isl_basic_map *isl_basic_map_gist(
3082 __isl_take isl_basic_map *bmap,
3083 __isl_take isl_basic_map *context);
3084 __isl_give isl_map *isl_map_gist(__isl_take isl_map *map,
3085 __isl_take isl_map *context);
3086 __isl_give isl_map *isl_map_gist_params(
3087 __isl_take isl_map *map,
3088 __isl_take isl_set *context);
3089 __isl_give isl_map *isl_map_gist_domain(
3090 __isl_take isl_map *map,
3091 __isl_take isl_set *context);
3092 __isl_give isl_map *isl_map_gist_range(
3093 __isl_take isl_map *map,
3094 __isl_take isl_set *context);
3095 __isl_give isl_union_map *isl_union_map_gist(
3096 __isl_take isl_union_map *umap,
3097 __isl_take isl_union_map *context);
3098 __isl_give isl_union_map *isl_union_map_gist_params(
3099 __isl_take isl_union_map *umap,
3100 __isl_take isl_set *set);
3101 __isl_give isl_union_map *isl_union_map_gist_domain(
3102 __isl_take isl_union_map *umap,
3103 __isl_take isl_union_set *uset);
3104 __isl_give isl_union_map *isl_union_map_gist_range(
3105 __isl_take isl_union_map *umap,
3106 __isl_take isl_union_set *uset);
3108 The gist operation returns a set or relation that has the
3109 same intersection with the context as the input set or relation.
3110 Any implicit equality in the intersection is made explicit in the result,
3111 while all inequalities that are redundant with respect to the intersection
3113 In case of union sets and relations, the gist operation is performed
3118 =head3 Lexicographic Optimization
3120 Given a (basic) set C<set> (or C<bset>) and a zero-dimensional domain C<dom>,
3121 the following functions
3122 compute a set that contains the lexicographic minimum or maximum
3123 of the elements in C<set> (or C<bset>) for those values of the parameters
3124 that satisfy C<dom>.
3125 If C<empty> is not C<NULL>, then C<*empty> is assigned a set
3126 that contains the parameter values in C<dom> for which C<set> (or C<bset>)
3128 In other words, the union of the parameter values
3129 for which the result is non-empty and of C<*empty>
3132 __isl_give isl_set *isl_basic_set_partial_lexmin(
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_basic_set_partial_lexmax(
3137 __isl_take isl_basic_set *bset,
3138 __isl_take isl_basic_set *dom,
3139 __isl_give isl_set **empty);
3140 __isl_give isl_set *isl_set_partial_lexmin(
3141 __isl_take isl_set *set, __isl_take isl_set *dom,
3142 __isl_give isl_set **empty);
3143 __isl_give isl_set *isl_set_partial_lexmax(
3144 __isl_take isl_set *set, __isl_take isl_set *dom,
3145 __isl_give isl_set **empty);
3147 Given a (basic) set C<set> (or C<bset>), the following functions simply
3148 return a set containing the lexicographic minimum or maximum
3149 of the elements in C<set> (or C<bset>).
3150 In case of union sets, the optimum is computed per space.
3152 __isl_give isl_set *isl_basic_set_lexmin(
3153 __isl_take isl_basic_set *bset);
3154 __isl_give isl_set *isl_basic_set_lexmax(
3155 __isl_take isl_basic_set *bset);
3156 __isl_give isl_set *isl_set_lexmin(
3157 __isl_take isl_set *set);
3158 __isl_give isl_set *isl_set_lexmax(
3159 __isl_take isl_set *set);
3160 __isl_give isl_union_set *isl_union_set_lexmin(
3161 __isl_take isl_union_set *uset);
3162 __isl_give isl_union_set *isl_union_set_lexmax(
3163 __isl_take isl_union_set *uset);
3165 Given a (basic) relation C<map> (or C<bmap>) and a domain C<dom>,
3166 the following functions
3167 compute a relation that maps each element of C<dom>
3168 to the single lexicographic minimum or maximum
3169 of the elements that are associated to that same
3170 element in C<map> (or C<bmap>).
3171 If C<empty> is not C<NULL>, then C<*empty> is assigned a set
3172 that contains the elements in C<dom> that do not map
3173 to any elements in C<map> (or C<bmap>).
3174 In other words, the union of the domain of the result and of C<*empty>
3177 __isl_give isl_map *isl_basic_map_partial_lexmax(
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_basic_map_partial_lexmin(
3182 __isl_take isl_basic_map *bmap,
3183 __isl_take isl_basic_set *dom,
3184 __isl_give isl_set **empty);
3185 __isl_give isl_map *isl_map_partial_lexmax(
3186 __isl_take isl_map *map, __isl_take isl_set *dom,
3187 __isl_give isl_set **empty);
3188 __isl_give isl_map *isl_map_partial_lexmin(
3189 __isl_take isl_map *map, __isl_take isl_set *dom,
3190 __isl_give isl_set **empty);
3192 Given a (basic) map C<map> (or C<bmap>), the following functions simply
3193 return a map mapping each element in the domain of
3194 C<map> (or C<bmap>) to the lexicographic minimum or maximum
3195 of all elements associated to that element.
3196 In case of union relations, the optimum is computed per space.
3198 __isl_give isl_map *isl_basic_map_lexmin(
3199 __isl_take isl_basic_map *bmap);
3200 __isl_give isl_map *isl_basic_map_lexmax(
3201 __isl_take isl_basic_map *bmap);
3202 __isl_give isl_map *isl_map_lexmin(
3203 __isl_take isl_map *map);
3204 __isl_give isl_map *isl_map_lexmax(
3205 __isl_take isl_map *map);
3206 __isl_give isl_union_map *isl_union_map_lexmin(
3207 __isl_take isl_union_map *umap);
3208 __isl_give isl_union_map *isl_union_map_lexmax(
3209 __isl_take isl_union_map *umap);
3211 The following functions return their result in the form of
3212 a piecewise multi-affine expression
3213 (See L<"Piecewise Multiple Quasi Affine Expressions">),
3214 but are otherwise equivalent to the corresponding functions
3215 returning a basic set or relation.
3217 __isl_give isl_pw_multi_aff *
3218 isl_basic_map_lexmin_pw_multi_aff(
3219 __isl_take isl_basic_map *bmap);
3220 __isl_give isl_pw_multi_aff *
3221 isl_basic_set_partial_lexmin_pw_multi_aff(
3222 __isl_take isl_basic_set *bset,
3223 __isl_take isl_basic_set *dom,
3224 __isl_give isl_set **empty);
3225 __isl_give isl_pw_multi_aff *
3226 isl_basic_set_partial_lexmax_pw_multi_aff(
3227 __isl_take isl_basic_set *bset,
3228 __isl_take isl_basic_set *dom,
3229 __isl_give isl_set **empty);
3230 __isl_give isl_pw_multi_aff *
3231 isl_basic_map_partial_lexmin_pw_multi_aff(
3232 __isl_take isl_basic_map *bmap,
3233 __isl_take isl_basic_set *dom,
3234 __isl_give isl_set **empty);
3235 __isl_give isl_pw_multi_aff *
3236 isl_basic_map_partial_lexmax_pw_multi_aff(
3237 __isl_take isl_basic_map *bmap,
3238 __isl_take isl_basic_set *dom,
3239 __isl_give isl_set **empty);
3240 __isl_give isl_pw_multi_aff *isl_set_lexmin_pw_multi_aff(
3241 __isl_take isl_set *set);
3242 __isl_give isl_pw_multi_aff *isl_set_lexmax_pw_multi_aff(
3243 __isl_take isl_set *set);
3244 __isl_give isl_pw_multi_aff *isl_map_lexmin_pw_multi_aff(
3245 __isl_take isl_map *map);
3246 __isl_give isl_pw_multi_aff *isl_map_lexmax_pw_multi_aff(
3247 __isl_take isl_map *map);
3251 Lists are defined over several element types, including
3252 C<isl_val>, C<isl_id>, C<isl_aff>, C<isl_pw_aff>, C<isl_constraint>,
3253 C<isl_basic_set>, C<isl_set>, C<isl_ast_expr> and C<isl_ast_node>.
3254 Here we take lists of C<isl_set>s as an example.
3255 Lists can be created, copied, modified and freed using the following functions.
3257 #include <isl/list.h>
3258 __isl_give isl_set_list *isl_set_list_from_set(
3259 __isl_take isl_set *el);
3260 __isl_give isl_set_list *isl_set_list_alloc(
3261 isl_ctx *ctx, int n);
3262 __isl_give isl_set_list *isl_set_list_copy(
3263 __isl_keep isl_set_list *list);
3264 __isl_give isl_set_list *isl_set_list_insert(
3265 __isl_take isl_set_list *list, unsigned pos,
3266 __isl_take isl_set *el);
3267 __isl_give isl_set_list *isl_set_list_add(
3268 __isl_take isl_set_list *list,
3269 __isl_take isl_set *el);
3270 __isl_give isl_set_list *isl_set_list_drop(
3271 __isl_take isl_set_list *list,
3272 unsigned first, unsigned n);
3273 __isl_give isl_set_list *isl_set_list_set_set(
3274 __isl_take isl_set_list *list, int index,
3275 __isl_take isl_set *set);
3276 __isl_give isl_set_list *isl_set_list_concat(
3277 __isl_take isl_set_list *list1,
3278 __isl_take isl_set_list *list2);
3279 __isl_give isl_set_list *isl_set_list_sort(
3280 __isl_take isl_set_list *list,
3281 int (*cmp)(__isl_keep isl_set *a,
3282 __isl_keep isl_set *b, void *user),
3284 void *isl_set_list_free(__isl_take isl_set_list *list);
3286 C<isl_set_list_alloc> creates an empty list with a capacity for
3287 C<n> elements. C<isl_set_list_from_set> creates a list with a single
3290 Lists can be inspected using the following functions.
3292 #include <isl/list.h>
3293 isl_ctx *isl_set_list_get_ctx(__isl_keep isl_set_list *list);
3294 int isl_set_list_n_set(__isl_keep isl_set_list *list);
3295 __isl_give isl_set *isl_set_list_get_set(
3296 __isl_keep isl_set_list *list, int index);
3297 int isl_set_list_foreach(__isl_keep isl_set_list *list,
3298 int (*fn)(__isl_take isl_set *el, void *user),
3300 int isl_set_list_foreach_scc(__isl_keep isl_set_list *list,
3301 int (*follows)(__isl_keep isl_set *a,
3302 __isl_keep isl_set *b, void *user),
3304 int (*fn)(__isl_take isl_set *el, void *user),
3307 The function C<isl_set_list_foreach_scc> calls C<fn> on each of the
3308 strongly connected components of the graph with as vertices the elements
3309 of C<list> and a directed edge from vertex C<b> to vertex C<a>
3310 iff C<follows(a, b)> returns C<1>. The callbacks C<follows> and C<fn>
3311 should return C<-1> on error.
3313 Lists can be printed using
3315 #include <isl/list.h>
3316 __isl_give isl_printer *isl_printer_print_set_list(
3317 __isl_take isl_printer *p,
3318 __isl_keep isl_set_list *list);
3320 =head2 Multiple Values
3322 An C<isl_multi_val> object represents a sequence of zero or more values,
3323 living in a set space.
3325 An C<isl_multi_val> can be constructed from an C<isl_val_list>
3326 using the following function
3328 #include <isl/val.h>
3329 __isl_give isl_multi_val *isl_multi_val_from_val_list(
3330 __isl_take isl_space *space,
3331 __isl_take isl_val_list *list);
3333 The zero multiple value (with value zero for each set dimension)
3334 can be created using the following function.
3336 #include <isl/val.h>
3337 __isl_give isl_multi_val *isl_multi_val_zero(
3338 __isl_take isl_space *space);
3340 Multiple values can be copied and freed using
3342 #include <isl/val.h>
3343 __isl_give isl_multi_val *isl_multi_val_copy(
3344 __isl_keep isl_multi_val *mv);
3345 void *isl_multi_val_free(__isl_take isl_multi_val *mv);
3347 They can be inspected using
3349 #include <isl/val.h>
3350 isl_ctx *isl_multi_val_get_ctx(
3351 __isl_keep isl_multi_val *mv);
3352 unsigned isl_multi_val_dim(__isl_keep isl_multi_val *mv,
3353 enum isl_dim_type type);
3354 __isl_give isl_val *isl_multi_val_get_val(
3355 __isl_keep isl_multi_val *mv, int pos);
3356 const char *isl_multi_val_get_tuple_name(
3357 __isl_keep isl_multi_val *mv,
3358 enum isl_dim_type type);
3360 They can be modified using
3362 #include <isl/val.h>
3363 __isl_give isl_multi_val *isl_multi_val_set_val(
3364 __isl_take isl_multi_val *mv, int pos,
3365 __isl_take isl_val *val);
3366 __isl_give isl_multi_val *isl_multi_val_set_dim_name(
3367 __isl_take isl_multi_val *mv,
3368 enum isl_dim_type type, unsigned pos, const char *s);
3369 __isl_give isl_multi_val *isl_multi_val_set_tuple_name(
3370 __isl_take isl_multi_val *mv,
3371 enum isl_dim_type type, const char *s);
3372 __isl_give isl_multi_val *isl_multi_val_set_tuple_id(
3373 __isl_take isl_multi_val *mv,
3374 enum isl_dim_type type, __isl_take isl_id *id);
3376 __isl_give isl_multi_val *isl_multi_val_insert_dims(
3377 __isl_take isl_multi_val *mv,
3378 enum isl_dim_type type, unsigned first, unsigned n);
3379 __isl_give isl_multi_val *isl_multi_val_add_dims(
3380 __isl_take isl_multi_val *mv,
3381 enum isl_dim_type type, unsigned n);
3382 __isl_give isl_multi_val *isl_multi_val_drop_dims(
3383 __isl_take isl_multi_val *mv,
3384 enum isl_dim_type type, unsigned first, unsigned n);
3388 #include <isl/val.h>
3389 __isl_give isl_multi_val *isl_multi_val_align_params(
3390 __isl_take isl_multi_val *mv,
3391 __isl_take isl_space *model);
3392 __isl_give isl_multi_val *isl_multi_val_range_splice(
3393 __isl_take isl_multi_val *mv1, unsigned pos,
3394 __isl_take isl_multi_val *mv2);
3395 __isl_give isl_multi_val *isl_multi_val_range_product(
3396 __isl_take isl_multi_val *mv1,
3397 __isl_take isl_multi_val *mv2);
3398 __isl_give isl_multi_val *isl_multi_val_flat_range_product(
3399 __isl_take isl_multi_val *mv1,
3400 __isl_take isl_multi_aff *mv2);
3401 __isl_give isl_multi_val *isl_multi_val_add_val(
3402 __isl_take isl_multi_val *mv,
3403 __isl_take isl_val *v);
3407 Vectors can be created, copied and freed using the following functions.
3409 #include <isl/vec.h>
3410 __isl_give isl_vec *isl_vec_alloc(isl_ctx *ctx,
3412 __isl_give isl_vec *isl_vec_copy(__isl_keep isl_vec *vec);
3413 void *isl_vec_free(__isl_take isl_vec *vec);
3415 Note that the elements of a newly created vector may have arbitrary values.
3416 The elements can be changed and inspected using the following functions.
3418 isl_ctx *isl_vec_get_ctx(__isl_keep isl_vec *vec);
3419 int isl_vec_size(__isl_keep isl_vec *vec);
3420 int isl_vec_get_element(__isl_keep isl_vec *vec,
3421 int pos, isl_int *v);
3422 __isl_give isl_vec *isl_vec_set_element(
3423 __isl_take isl_vec *vec, int pos, isl_int v);
3424 __isl_give isl_vec *isl_vec_set_element_si(
3425 __isl_take isl_vec *vec, int pos, int v);
3426 __isl_give isl_vec *isl_vec_set(__isl_take isl_vec *vec,
3428 __isl_give isl_vec *isl_vec_set_si(__isl_take isl_vec *vec,
3430 __isl_give isl_vec *isl_vec_fdiv_r(__isl_take isl_vec *vec,
3433 C<isl_vec_get_element> will return a negative value if anything went wrong.
3434 In that case, the value of C<*v> is undefined.
3436 The following function can be used to concatenate two vectors.
3438 __isl_give isl_vec *isl_vec_concat(__isl_take isl_vec *vec1,
3439 __isl_take isl_vec *vec2);
3443 Matrices can be created, copied and freed using the following functions.
3445 #include <isl/mat.h>
3446 __isl_give isl_mat *isl_mat_alloc(isl_ctx *ctx,
3447 unsigned n_row, unsigned n_col);
3448 __isl_give isl_mat *isl_mat_copy(__isl_keep isl_mat *mat);
3449 void *isl_mat_free(__isl_take isl_mat *mat);
3451 Note that the elements of a newly created matrix may have arbitrary values.
3452 The elements can be changed and inspected using the following functions.
3454 isl_ctx *isl_mat_get_ctx(__isl_keep isl_mat *mat);
3455 int isl_mat_rows(__isl_keep isl_mat *mat);
3456 int isl_mat_cols(__isl_keep isl_mat *mat);
3457 int isl_mat_get_element(__isl_keep isl_mat *mat,
3458 int row, int col, isl_int *v);
3459 __isl_give isl_mat *isl_mat_set_element(__isl_take isl_mat *mat,
3460 int row, int col, isl_int v);
3461 __isl_give isl_mat *isl_mat_set_element_si(__isl_take isl_mat *mat,
3462 int row, int col, int v);
3464 C<isl_mat_get_element> will return a negative value if anything went wrong.
3465 In that case, the value of C<*v> is undefined.
3467 The following function can be used to compute the (right) inverse
3468 of a matrix, i.e., a matrix such that the product of the original
3469 and the inverse (in that order) is a multiple of the identity matrix.
3470 The input matrix is assumed to be of full row-rank.
3472 __isl_give isl_mat *isl_mat_right_inverse(__isl_take isl_mat *mat);
3474 The following function can be used to compute the (right) kernel
3475 (or null space) of a matrix, i.e., a matrix such that the product of
3476 the original and the kernel (in that order) is the zero matrix.
3478 __isl_give isl_mat *isl_mat_right_kernel(__isl_take isl_mat *mat);
3480 =head2 Piecewise Quasi Affine Expressions
3482 The zero quasi affine expression or the quasi affine expression
3483 that is equal to a specified dimension on a given domain can be created using
3485 __isl_give isl_aff *isl_aff_zero_on_domain(
3486 __isl_take isl_local_space *ls);
3487 __isl_give isl_pw_aff *isl_pw_aff_zero_on_domain(
3488 __isl_take isl_local_space *ls);
3489 __isl_give isl_aff *isl_aff_var_on_domain(
3490 __isl_take isl_local_space *ls,
3491 enum isl_dim_type type, unsigned pos);
3492 __isl_give isl_pw_aff *isl_pw_aff_var_on_domain(
3493 __isl_take isl_local_space *ls,
3494 enum isl_dim_type type, unsigned pos);
3496 Note that the space in which the resulting objects live is a map space
3497 with the given space as domain and a one-dimensional range.
3499 An empty piecewise quasi affine expression (one with no cells)
3500 or a piecewise quasi affine expression with a single cell can
3501 be created using the following functions.
3503 #include <isl/aff.h>
3504 __isl_give isl_pw_aff *isl_pw_aff_empty(
3505 __isl_take isl_space *space);
3506 __isl_give isl_pw_aff *isl_pw_aff_alloc(
3507 __isl_take isl_set *set, __isl_take isl_aff *aff);
3508 __isl_give isl_pw_aff *isl_pw_aff_from_aff(
3509 __isl_take isl_aff *aff);
3511 A piecewise quasi affine expression that is equal to 1 on a set
3512 and 0 outside the set can be created using the following function.
3514 #include <isl/aff.h>
3515 __isl_give isl_pw_aff *isl_set_indicator_function(
3516 __isl_take isl_set *set);
3518 Quasi affine expressions can be copied and freed using
3520 #include <isl/aff.h>
3521 __isl_give isl_aff *isl_aff_copy(__isl_keep isl_aff *aff);
3522 void *isl_aff_free(__isl_take isl_aff *aff);
3524 __isl_give isl_pw_aff *isl_pw_aff_copy(
3525 __isl_keep isl_pw_aff *pwaff);
3526 void *isl_pw_aff_free(__isl_take isl_pw_aff *pwaff);
3528 A (rational) bound on a dimension can be extracted from an C<isl_constraint>
3529 using the following function. The constraint is required to have
3530 a non-zero coefficient for the specified dimension.
3532 #include <isl/constraint.h>
3533 __isl_give isl_aff *isl_constraint_get_bound(
3534 __isl_keep isl_constraint *constraint,
3535 enum isl_dim_type type, int pos);
3537 The entire affine expression of the constraint can also be extracted
3538 using the following function.
3540 #include <isl/constraint.h>
3541 __isl_give isl_aff *isl_constraint_get_aff(
3542 __isl_keep isl_constraint *constraint);
3544 Conversely, an equality constraint equating
3545 the affine expression to zero or an inequality constraint enforcing
3546 the affine expression to be non-negative, can be constructed using
3548 __isl_give isl_constraint *isl_equality_from_aff(
3549 __isl_take isl_aff *aff);
3550 __isl_give isl_constraint *isl_inequality_from_aff(
3551 __isl_take isl_aff *aff);
3553 The expression can be inspected using
3555 #include <isl/aff.h>
3556 isl_ctx *isl_aff_get_ctx(__isl_keep isl_aff *aff);
3557 int isl_aff_dim(__isl_keep isl_aff *aff,
3558 enum isl_dim_type type);
3559 __isl_give isl_local_space *isl_aff_get_domain_local_space(
3560 __isl_keep isl_aff *aff);
3561 __isl_give isl_local_space *isl_aff_get_local_space(
3562 __isl_keep isl_aff *aff);
3563 const char *isl_aff_get_dim_name(__isl_keep isl_aff *aff,
3564 enum isl_dim_type type, unsigned pos);
3565 const char *isl_pw_aff_get_dim_name(
3566 __isl_keep isl_pw_aff *pa,
3567 enum isl_dim_type type, unsigned pos);
3568 int isl_pw_aff_has_dim_id(__isl_keep isl_pw_aff *pa,
3569 enum isl_dim_type type, unsigned pos);
3570 __isl_give isl_id *isl_pw_aff_get_dim_id(
3571 __isl_keep isl_pw_aff *pa,
3572 enum isl_dim_type type, unsigned pos);
3573 __isl_give isl_id *isl_pw_aff_get_tuple_id(
3574 __isl_keep isl_pw_aff *pa,
3575 enum isl_dim_type type);
3576 int isl_aff_get_constant(__isl_keep isl_aff *aff,
3578 int isl_aff_get_coefficient(__isl_keep isl_aff *aff,
3579 enum isl_dim_type type, int pos, isl_int *v);
3580 int isl_aff_get_denominator(__isl_keep isl_aff *aff,
3582 __isl_give isl_aff *isl_aff_get_div(
3583 __isl_keep isl_aff *aff, int pos);
3585 int isl_pw_aff_n_piece(__isl_keep isl_pw_aff *pwaff);
3586 int isl_pw_aff_foreach_piece(__isl_keep isl_pw_aff *pwaff,
3587 int (*fn)(__isl_take isl_set *set,
3588 __isl_take isl_aff *aff,
3589 void *user), void *user);
3591 int isl_aff_is_cst(__isl_keep isl_aff *aff);
3592 int isl_pw_aff_is_cst(__isl_keep isl_pw_aff *pwaff);
3594 int isl_aff_involves_dims(__isl_keep isl_aff *aff,
3595 enum isl_dim_type type, unsigned first, unsigned n);
3596 int isl_pw_aff_involves_dims(__isl_keep isl_pw_aff *pwaff,
3597 enum isl_dim_type type, unsigned first, unsigned n);
3599 isl_ctx *isl_pw_aff_get_ctx(__isl_keep isl_pw_aff *pwaff);
3600 unsigned isl_pw_aff_dim(__isl_keep isl_pw_aff *pwaff,
3601 enum isl_dim_type type);
3602 int isl_pw_aff_is_empty(__isl_keep isl_pw_aff *pwaff);
3604 It can be modified using
3606 #include <isl/aff.h>
3607 __isl_give isl_pw_aff *isl_pw_aff_set_tuple_id(
3608 __isl_take isl_pw_aff *pwaff,
3609 enum isl_dim_type type, __isl_take isl_id *id);
3610 __isl_give isl_aff *isl_aff_set_dim_name(
3611 __isl_take isl_aff *aff, enum isl_dim_type type,
3612 unsigned pos, const char *s);
3613 __isl_give isl_aff *isl_aff_set_dim_id(
3614 __isl_take isl_aff *aff, enum isl_dim_type type,
3615 unsigned pos, __isl_take isl_id *id);
3616 __isl_give isl_pw_aff *isl_pw_aff_set_dim_id(
3617 __isl_take isl_pw_aff *pma,
3618 enum isl_dim_type type, unsigned pos,
3619 __isl_take isl_id *id);
3620 __isl_give isl_aff *isl_aff_set_constant(
3621 __isl_take isl_aff *aff, isl_int v);
3622 __isl_give isl_aff *isl_aff_set_constant_si(
3623 __isl_take isl_aff *aff, int v);
3624 __isl_give isl_aff *isl_aff_set_coefficient(
3625 __isl_take isl_aff *aff,
3626 enum isl_dim_type type, int pos, isl_int v);
3627 __isl_give isl_aff *isl_aff_set_coefficient_si(
3628 __isl_take isl_aff *aff,
3629 enum isl_dim_type type, int pos, int v);
3630 __isl_give isl_aff *isl_aff_set_denominator(
3631 __isl_take isl_aff *aff, isl_int v);
3633 __isl_give isl_aff *isl_aff_add_constant(
3634 __isl_take isl_aff *aff, isl_int v);
3635 __isl_give isl_aff *isl_aff_add_constant_si(
3636 __isl_take isl_aff *aff, int v);
3637 __isl_give isl_aff *isl_aff_add_constant_num(
3638 __isl_take isl_aff *aff, isl_int v);
3639 __isl_give isl_aff *isl_aff_add_constant_num_si(
3640 __isl_take isl_aff *aff, int v);
3641 __isl_give isl_aff *isl_aff_add_coefficient(
3642 __isl_take isl_aff *aff,
3643 enum isl_dim_type type, int pos, isl_int v);
3644 __isl_give isl_aff *isl_aff_add_coefficient_si(
3645 __isl_take isl_aff *aff,
3646 enum isl_dim_type type, int pos, int v);
3648 __isl_give isl_aff *isl_aff_insert_dims(
3649 __isl_take isl_aff *aff,
3650 enum isl_dim_type type, unsigned first, unsigned n);
3651 __isl_give isl_pw_aff *isl_pw_aff_insert_dims(
3652 __isl_take isl_pw_aff *pwaff,
3653 enum isl_dim_type type, unsigned first, unsigned n);
3654 __isl_give isl_aff *isl_aff_add_dims(
3655 __isl_take isl_aff *aff,
3656 enum isl_dim_type type, unsigned n);
3657 __isl_give isl_pw_aff *isl_pw_aff_add_dims(
3658 __isl_take isl_pw_aff *pwaff,
3659 enum isl_dim_type type, unsigned n);
3660 __isl_give isl_aff *isl_aff_drop_dims(
3661 __isl_take isl_aff *aff,
3662 enum isl_dim_type type, unsigned first, unsigned n);
3663 __isl_give isl_pw_aff *isl_pw_aff_drop_dims(
3664 __isl_take isl_pw_aff *pwaff,
3665 enum isl_dim_type type, unsigned first, unsigned n);
3667 Note that the C<set_constant> and C<set_coefficient> functions
3668 set the I<numerator> of the constant or coefficient, while
3669 C<add_constant> and C<add_coefficient> add an integer value to
3670 the possibly rational constant or coefficient.
3671 The C<add_constant_num> functions add an integer value to
3674 To check whether an affine expressions is obviously zero
3675 or obviously equal to some other affine expression, use
3677 #include <isl/aff.h>
3678 int isl_aff_plain_is_zero(__isl_keep isl_aff *aff);
3679 int isl_aff_plain_is_equal(__isl_keep isl_aff *aff1,
3680 __isl_keep isl_aff *aff2);
3681 int isl_pw_aff_plain_is_equal(
3682 __isl_keep isl_pw_aff *pwaff1,
3683 __isl_keep isl_pw_aff *pwaff2);
3687 #include <isl/aff.h>
3688 __isl_give isl_aff *isl_aff_add(__isl_take isl_aff *aff1,
3689 __isl_take isl_aff *aff2);
3690 __isl_give isl_pw_aff *isl_pw_aff_add(
3691 __isl_take isl_pw_aff *pwaff1,
3692 __isl_take isl_pw_aff *pwaff2);
3693 __isl_give isl_pw_aff *isl_pw_aff_min(
3694 __isl_take isl_pw_aff *pwaff1,
3695 __isl_take isl_pw_aff *pwaff2);
3696 __isl_give isl_pw_aff *isl_pw_aff_max(
3697 __isl_take isl_pw_aff *pwaff1,
3698 __isl_take isl_pw_aff *pwaff2);
3699 __isl_give isl_aff *isl_aff_sub(__isl_take isl_aff *aff1,
3700 __isl_take isl_aff *aff2);
3701 __isl_give isl_pw_aff *isl_pw_aff_sub(
3702 __isl_take isl_pw_aff *pwaff1,
3703 __isl_take isl_pw_aff *pwaff2);
3704 __isl_give isl_aff *isl_aff_neg(__isl_take isl_aff *aff);
3705 __isl_give isl_pw_aff *isl_pw_aff_neg(
3706 __isl_take isl_pw_aff *pwaff);
3707 __isl_give isl_aff *isl_aff_ceil(__isl_take isl_aff *aff);
3708 __isl_give isl_pw_aff *isl_pw_aff_ceil(
3709 __isl_take isl_pw_aff *pwaff);
3710 __isl_give isl_aff *isl_aff_floor(__isl_take isl_aff *aff);
3711 __isl_give isl_pw_aff *isl_pw_aff_floor(
3712 __isl_take isl_pw_aff *pwaff);
3713 __isl_give isl_aff *isl_aff_mod(__isl_take isl_aff *aff,
3715 __isl_give isl_pw_aff *isl_pw_aff_mod(
3716 __isl_take isl_pw_aff *pwaff, isl_int mod);
3717 __isl_give isl_aff *isl_aff_scale(__isl_take isl_aff *aff,
3719 __isl_give isl_pw_aff *isl_pw_aff_scale(
3720 __isl_take isl_pw_aff *pwaff, isl_int f);
3721 __isl_give isl_aff *isl_aff_scale_down(__isl_take isl_aff *aff,
3723 __isl_give isl_aff *isl_aff_scale_down_ui(
3724 __isl_take isl_aff *aff, unsigned f);
3725 __isl_give isl_pw_aff *isl_pw_aff_scale_down(
3726 __isl_take isl_pw_aff *pwaff, isl_int f);
3728 __isl_give isl_pw_aff *isl_pw_aff_list_min(
3729 __isl_take isl_pw_aff_list *list);
3730 __isl_give isl_pw_aff *isl_pw_aff_list_max(
3731 __isl_take isl_pw_aff_list *list);
3733 __isl_give isl_pw_aff *isl_pw_aff_coalesce(
3734 __isl_take isl_pw_aff *pwqp);
3736 __isl_give isl_aff *isl_aff_align_params(
3737 __isl_take isl_aff *aff,
3738 __isl_take isl_space *model);
3739 __isl_give isl_pw_aff *isl_pw_aff_align_params(
3740 __isl_take isl_pw_aff *pwaff,
3741 __isl_take isl_space *model);
3743 __isl_give isl_aff *isl_aff_project_domain_on_params(
3744 __isl_take isl_aff *aff);
3746 __isl_give isl_aff *isl_aff_gist_params(
3747 __isl_take isl_aff *aff,
3748 __isl_take isl_set *context);
3749 __isl_give isl_aff *isl_aff_gist(__isl_take isl_aff *aff,
3750 __isl_take isl_set *context);
3751 __isl_give isl_pw_aff *isl_pw_aff_gist_params(
3752 __isl_take isl_pw_aff *pwaff,
3753 __isl_take isl_set *context);
3754 __isl_give isl_pw_aff *isl_pw_aff_gist(
3755 __isl_take isl_pw_aff *pwaff,
3756 __isl_take isl_set *context);
3758 __isl_give isl_set *isl_pw_aff_domain(
3759 __isl_take isl_pw_aff *pwaff);
3760 __isl_give isl_pw_aff *isl_pw_aff_intersect_domain(
3761 __isl_take isl_pw_aff *pa,
3762 __isl_take isl_set *set);
3763 __isl_give isl_pw_aff *isl_pw_aff_intersect_params(
3764 __isl_take isl_pw_aff *pa,
3765 __isl_take isl_set *set);
3767 __isl_give isl_aff *isl_aff_mul(__isl_take isl_aff *aff1,
3768 __isl_take isl_aff *aff2);
3769 __isl_give isl_aff *isl_aff_div(__isl_take isl_aff *aff1,
3770 __isl_take isl_aff *aff2);
3771 __isl_give isl_pw_aff *isl_pw_aff_mul(
3772 __isl_take isl_pw_aff *pwaff1,
3773 __isl_take isl_pw_aff *pwaff2);
3774 __isl_give isl_pw_aff *isl_pw_aff_div(
3775 __isl_take isl_pw_aff *pa1,
3776 __isl_take isl_pw_aff *pa2);
3777 __isl_give isl_pw_aff *isl_pw_aff_tdiv_q(
3778 __isl_take isl_pw_aff *pa1,
3779 __isl_take isl_pw_aff *pa2);
3780 __isl_give isl_pw_aff *isl_pw_aff_tdiv_r(
3781 __isl_take isl_pw_aff *pa1,
3782 __isl_take isl_pw_aff *pa2);
3784 When multiplying two affine expressions, at least one of the two needs
3785 to be a constant. Similarly, when dividing an affine expression by another,
3786 the second expression needs to be a constant.
3787 C<isl_pw_aff_tdiv_q> computes the quotient of an integer division with
3788 rounding towards zero. C<isl_pw_aff_tdiv_r> computes the corresponding
3791 #include <isl/aff.h>
3792 __isl_give isl_aff *isl_aff_pullback_multi_aff(
3793 __isl_take isl_aff *aff,
3794 __isl_take isl_multi_aff *ma);
3795 __isl_give isl_pw_aff *isl_pw_aff_pullback_multi_aff(
3796 __isl_take isl_pw_aff *pa,
3797 __isl_take isl_multi_aff *ma);
3798 __isl_give isl_pw_aff *isl_pw_aff_pullback_pw_multi_aff(
3799 __isl_take isl_pw_aff *pa,
3800 __isl_take isl_pw_multi_aff *pma);
3802 These functions precompose the input expression by the given
3803 C<isl_multi_aff> or C<isl_pw_multi_aff>. In other words,
3804 the C<isl_multi_aff> or C<isl_pw_multi_aff> is plugged
3805 into the (piecewise) affine expression.
3806 Objects of type C<isl_multi_aff> are described in
3807 L</"Piecewise Multiple Quasi Affine Expressions">.
3809 #include <isl/aff.h>
3810 __isl_give isl_basic_set *isl_aff_zero_basic_set(
3811 __isl_take isl_aff *aff);
3812 __isl_give isl_basic_set *isl_aff_neg_basic_set(
3813 __isl_take isl_aff *aff);
3814 __isl_give isl_basic_set *isl_aff_le_basic_set(
3815 __isl_take isl_aff *aff1, __isl_take isl_aff *aff2);
3816 __isl_give isl_basic_set *isl_aff_ge_basic_set(
3817 __isl_take isl_aff *aff1, __isl_take isl_aff *aff2);
3818 __isl_give isl_set *isl_pw_aff_eq_set(
3819 __isl_take isl_pw_aff *pwaff1,
3820 __isl_take isl_pw_aff *pwaff2);
3821 __isl_give isl_set *isl_pw_aff_ne_set(
3822 __isl_take isl_pw_aff *pwaff1,
3823 __isl_take isl_pw_aff *pwaff2);
3824 __isl_give isl_set *isl_pw_aff_le_set(
3825 __isl_take isl_pw_aff *pwaff1,
3826 __isl_take isl_pw_aff *pwaff2);
3827 __isl_give isl_set *isl_pw_aff_lt_set(
3828 __isl_take isl_pw_aff *pwaff1,
3829 __isl_take isl_pw_aff *pwaff2);
3830 __isl_give isl_set *isl_pw_aff_ge_set(
3831 __isl_take isl_pw_aff *pwaff1,
3832 __isl_take isl_pw_aff *pwaff2);
3833 __isl_give isl_set *isl_pw_aff_gt_set(
3834 __isl_take isl_pw_aff *pwaff1,
3835 __isl_take isl_pw_aff *pwaff2);
3837 __isl_give isl_set *isl_pw_aff_list_eq_set(
3838 __isl_take isl_pw_aff_list *list1,
3839 __isl_take isl_pw_aff_list *list2);
3840 __isl_give isl_set *isl_pw_aff_list_ne_set(
3841 __isl_take isl_pw_aff_list *list1,
3842 __isl_take isl_pw_aff_list *list2);
3843 __isl_give isl_set *isl_pw_aff_list_le_set(
3844 __isl_take isl_pw_aff_list *list1,
3845 __isl_take isl_pw_aff_list *list2);
3846 __isl_give isl_set *isl_pw_aff_list_lt_set(
3847 __isl_take isl_pw_aff_list *list1,
3848 __isl_take isl_pw_aff_list *list2);
3849 __isl_give isl_set *isl_pw_aff_list_ge_set(
3850 __isl_take isl_pw_aff_list *list1,
3851 __isl_take isl_pw_aff_list *list2);
3852 __isl_give isl_set *isl_pw_aff_list_gt_set(
3853 __isl_take isl_pw_aff_list *list1,
3854 __isl_take isl_pw_aff_list *list2);
3856 The function C<isl_aff_neg_basic_set> returns a basic set
3857 containing those elements in the domain space
3858 of C<aff> where C<aff> is negative.
3859 The function C<isl_aff_ge_basic_set> returns a basic set
3860 containing those elements in the shared space
3861 of C<aff1> and C<aff2> where C<aff1> is greater than or equal to C<aff2>.
3862 The function C<isl_pw_aff_ge_set> returns a set
3863 containing those elements in the shared domain
3864 of C<pwaff1> and C<pwaff2> where C<pwaff1> is greater than or equal to C<pwaff2>.
3865 The functions operating on C<isl_pw_aff_list> apply the corresponding
3866 C<isl_pw_aff> function to each pair of elements in the two lists.
3868 #include <isl/aff.h>
3869 __isl_give isl_set *isl_pw_aff_nonneg_set(
3870 __isl_take isl_pw_aff *pwaff);
3871 __isl_give isl_set *isl_pw_aff_zero_set(
3872 __isl_take isl_pw_aff *pwaff);
3873 __isl_give isl_set *isl_pw_aff_non_zero_set(
3874 __isl_take isl_pw_aff *pwaff);
3876 The function C<isl_pw_aff_nonneg_set> returns a set
3877 containing those elements in the domain
3878 of C<pwaff> where C<pwaff> is non-negative.
3880 #include <isl/aff.h>
3881 __isl_give isl_pw_aff *isl_pw_aff_cond(
3882 __isl_take isl_pw_aff *cond,
3883 __isl_take isl_pw_aff *pwaff_true,
3884 __isl_take isl_pw_aff *pwaff_false);
3886 The function C<isl_pw_aff_cond> performs a conditional operator
3887 and returns an expression that is equal to C<pwaff_true>
3888 for elements where C<cond> is non-zero and equal to C<pwaff_false> for elements
3889 where C<cond> is zero.
3891 #include <isl/aff.h>
3892 __isl_give isl_pw_aff *isl_pw_aff_union_min(
3893 __isl_take isl_pw_aff *pwaff1,
3894 __isl_take isl_pw_aff *pwaff2);
3895 __isl_give isl_pw_aff *isl_pw_aff_union_max(
3896 __isl_take isl_pw_aff *pwaff1,
3897 __isl_take isl_pw_aff *pwaff2);
3898 __isl_give isl_pw_aff *isl_pw_aff_union_add(
3899 __isl_take isl_pw_aff *pwaff1,
3900 __isl_take isl_pw_aff *pwaff2);
3902 The function C<isl_pw_aff_union_max> computes a piecewise quasi-affine
3903 expression with a domain that is the union of those of C<pwaff1> and
3904 C<pwaff2> and such that on each cell, the quasi-affine expression is
3905 the maximum of those of C<pwaff1> and C<pwaff2>. If only one of
3906 C<pwaff1> or C<pwaff2> is defined on a given cell, then the
3907 associated expression is the defined one.
3909 An expression can be read from input using
3911 #include <isl/aff.h>
3912 __isl_give isl_aff *isl_aff_read_from_str(
3913 isl_ctx *ctx, const char *str);
3914 __isl_give isl_pw_aff *isl_pw_aff_read_from_str(
3915 isl_ctx *ctx, const char *str);
3917 An expression can be printed using
3919 #include <isl/aff.h>
3920 __isl_give isl_printer *isl_printer_print_aff(
3921 __isl_take isl_printer *p, __isl_keep isl_aff *aff);
3923 __isl_give isl_printer *isl_printer_print_pw_aff(
3924 __isl_take isl_printer *p,
3925 __isl_keep isl_pw_aff *pwaff);
3927 =head2 Piecewise Multiple Quasi Affine Expressions
3929 An C<isl_multi_aff> object represents a sequence of
3930 zero or more affine expressions, all defined on the same domain space.
3931 Similarly, an C<isl_multi_pw_aff> object represents a sequence of
3932 zero or more piecewise affine expressions.
3934 An C<isl_multi_aff> can be constructed from a single
3935 C<isl_aff> or an C<isl_aff_list> using the
3936 following functions. Similarly for C<isl_multi_pw_aff>.
3938 #include <isl/aff.h>
3939 __isl_give isl_multi_aff *isl_multi_aff_from_aff(
3940 __isl_take isl_aff *aff);
3941 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_from_pw_aff(
3942 __isl_take isl_pw_aff *pa);
3943 __isl_give isl_multi_aff *isl_multi_aff_from_aff_list(
3944 __isl_take isl_space *space,
3945 __isl_take isl_aff_list *list);
3947 An empty piecewise multiple quasi affine expression (one with no cells),
3948 the zero piecewise multiple quasi affine expression (with value zero
3949 for each output dimension),
3950 a piecewise multiple quasi affine expression with a single cell (with
3951 either a universe or a specified domain) or
3952 a zero-dimensional piecewise multiple quasi affine expression
3954 can be created using the following functions.
3956 #include <isl/aff.h>
3957 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_empty(
3958 __isl_take isl_space *space);
3959 __isl_give isl_multi_aff *isl_multi_aff_zero(
3960 __isl_take isl_space *space);
3961 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_zero(
3962 __isl_take isl_space *space);
3963 __isl_give isl_multi_aff *isl_multi_aff_identity(
3964 __isl_take isl_space *space);
3965 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_identity(
3966 __isl_take isl_space *space);
3967 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_identity(
3968 __isl_take isl_space *space);
3969 __isl_give isl_pw_multi_aff *
3970 isl_pw_multi_aff_from_multi_aff(
3971 __isl_take isl_multi_aff *ma);
3972 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_alloc(
3973 __isl_take isl_set *set,
3974 __isl_take isl_multi_aff *maff);
3975 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_from_domain(
3976 __isl_take isl_set *set);
3978 __isl_give isl_union_pw_multi_aff *
3979 isl_union_pw_multi_aff_empty(
3980 __isl_take isl_space *space);
3981 __isl_give isl_union_pw_multi_aff *
3982 isl_union_pw_multi_aff_add_pw_multi_aff(
3983 __isl_take isl_union_pw_multi_aff *upma,
3984 __isl_take isl_pw_multi_aff *pma);
3985 __isl_give isl_union_pw_multi_aff *
3986 isl_union_pw_multi_aff_from_domain(
3987 __isl_take isl_union_set *uset);
3989 A piecewise multiple quasi affine expression can also be initialized
3990 from an C<isl_set> or C<isl_map>, provided the C<isl_set> is a singleton
3991 and the C<isl_map> is single-valued.
3992 In case of a conversion from an C<isl_union_set> or an C<isl_union_map>
3993 to an C<isl_union_pw_multi_aff>, these properties need to hold in each space.
3995 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_from_set(
3996 __isl_take isl_set *set);
3997 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_from_map(
3998 __isl_take isl_map *map);
4000 __isl_give isl_union_pw_multi_aff *
4001 isl_union_pw_multi_aff_from_union_set(
4002 __isl_take isl_union_set *uset);
4003 __isl_give isl_union_pw_multi_aff *
4004 isl_union_pw_multi_aff_from_union_map(
4005 __isl_take isl_union_map *umap);
4007 Multiple quasi affine expressions can be copied and freed using
4009 #include <isl/aff.h>
4010 __isl_give isl_multi_aff *isl_multi_aff_copy(
4011 __isl_keep isl_multi_aff *maff);
4012 void *isl_multi_aff_free(__isl_take isl_multi_aff *maff);
4014 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_copy(
4015 __isl_keep isl_pw_multi_aff *pma);
4016 void *isl_pw_multi_aff_free(
4017 __isl_take isl_pw_multi_aff *pma);
4019 __isl_give isl_union_pw_multi_aff *
4020 isl_union_pw_multi_aff_copy(
4021 __isl_keep isl_union_pw_multi_aff *upma);
4022 void *isl_union_pw_multi_aff_free(
4023 __isl_take isl_union_pw_multi_aff *upma);
4025 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_copy(
4026 __isl_keep isl_multi_pw_aff *mpa);
4027 void *isl_multi_pw_aff_free(
4028 __isl_take isl_multi_pw_aff *mpa);
4030 The expression can be inspected using
4032 #include <isl/aff.h>
4033 isl_ctx *isl_multi_aff_get_ctx(
4034 __isl_keep isl_multi_aff *maff);
4035 isl_ctx *isl_pw_multi_aff_get_ctx(
4036 __isl_keep isl_pw_multi_aff *pma);
4037 isl_ctx *isl_union_pw_multi_aff_get_ctx(
4038 __isl_keep isl_union_pw_multi_aff *upma);
4039 isl_ctx *isl_multi_pw_aff_get_ctx(
4040 __isl_keep isl_multi_pw_aff *mpa);
4041 unsigned isl_multi_aff_dim(__isl_keep isl_multi_aff *maff,
4042 enum isl_dim_type type);
4043 unsigned isl_pw_multi_aff_dim(
4044 __isl_keep isl_pw_multi_aff *pma,
4045 enum isl_dim_type type);
4046 unsigned isl_multi_pw_aff_dim(
4047 __isl_keep isl_multi_pw_aff *mpa,
4048 enum isl_dim_type type);
4049 __isl_give isl_aff *isl_multi_aff_get_aff(
4050 __isl_keep isl_multi_aff *multi, int pos);
4051 __isl_give isl_pw_aff *isl_pw_multi_aff_get_pw_aff(
4052 __isl_keep isl_pw_multi_aff *pma, int pos);
4053 __isl_give isl_pw_aff *isl_multi_pw_aff_get_pw_aff(
4054 __isl_keep isl_multi_pw_aff *mpa, int pos);
4055 const char *isl_pw_multi_aff_get_dim_name(
4056 __isl_keep isl_pw_multi_aff *pma,
4057 enum isl_dim_type type, unsigned pos);
4058 __isl_give isl_id *isl_pw_multi_aff_get_dim_id(
4059 __isl_keep isl_pw_multi_aff *pma,
4060 enum isl_dim_type type, unsigned pos);
4061 const char *isl_multi_aff_get_tuple_name(
4062 __isl_keep isl_multi_aff *multi,
4063 enum isl_dim_type type);
4064 int isl_pw_multi_aff_has_tuple_name(
4065 __isl_keep isl_pw_multi_aff *pma,
4066 enum isl_dim_type type);
4067 const char *isl_pw_multi_aff_get_tuple_name(
4068 __isl_keep isl_pw_multi_aff *pma,
4069 enum isl_dim_type type);
4070 int isl_pw_multi_aff_has_tuple_id(
4071 __isl_keep isl_pw_multi_aff *pma,
4072 enum isl_dim_type type);
4073 __isl_give isl_id *isl_pw_multi_aff_get_tuple_id(
4074 __isl_keep isl_pw_multi_aff *pma,
4075 enum isl_dim_type type);
4077 int isl_pw_multi_aff_foreach_piece(
4078 __isl_keep isl_pw_multi_aff *pma,
4079 int (*fn)(__isl_take isl_set *set,
4080 __isl_take isl_multi_aff *maff,
4081 void *user), void *user);
4083 int isl_union_pw_multi_aff_foreach_pw_multi_aff(
4084 __isl_keep isl_union_pw_multi_aff *upma,
4085 int (*fn)(__isl_take isl_pw_multi_aff *pma,
4086 void *user), void *user);
4088 It can be modified using
4090 #include <isl/aff.h>
4091 __isl_give isl_multi_aff *isl_multi_aff_set_aff(
4092 __isl_take isl_multi_aff *multi, int pos,
4093 __isl_take isl_aff *aff);
4094 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_set_pw_aff(
4095 __isl_take isl_pw_multi_aff *pma, unsigned pos,
4096 __isl_take isl_pw_aff *pa);
4097 __isl_give isl_multi_aff *isl_multi_aff_set_dim_name(
4098 __isl_take isl_multi_aff *maff,
4099 enum isl_dim_type type, unsigned pos, const char *s);
4100 __isl_give isl_multi_aff *isl_multi_aff_set_tuple_name(
4101 __isl_take isl_multi_aff *maff,
4102 enum isl_dim_type type, const char *s);
4103 __isl_give isl_multi_aff *isl_multi_aff_set_tuple_id(
4104 __isl_take isl_multi_aff *maff,
4105 enum isl_dim_type type, __isl_take isl_id *id);
4106 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_set_tuple_id(
4107 __isl_take isl_pw_multi_aff *pma,
4108 enum isl_dim_type type, __isl_take isl_id *id);
4110 __isl_give isl_multi_pw_aff *
4111 isl_multi_pw_aff_set_dim_name(
4112 __isl_take isl_multi_pw_aff *mpa,
4113 enum isl_dim_type type, unsigned pos, const char *s);
4114 __isl_give isl_multi_pw_aff *
4115 isl_multi_pw_aff_set_tuple_name(
4116 __isl_take isl_multi_pw_aff *mpa,
4117 enum isl_dim_type type, const char *s);
4119 __isl_give isl_multi_aff *isl_multi_aff_insert_dims(
4120 __isl_take isl_multi_aff *ma,
4121 enum isl_dim_type type, unsigned first, unsigned n);
4122 __isl_give isl_multi_aff *isl_multi_aff_add_dims(
4123 __isl_take isl_multi_aff *ma,
4124 enum isl_dim_type type, unsigned n);
4125 __isl_give isl_multi_aff *isl_multi_aff_drop_dims(
4126 __isl_take isl_multi_aff *maff,
4127 enum isl_dim_type type, unsigned first, unsigned n);
4128 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_drop_dims(
4129 __isl_take isl_pw_multi_aff *pma,
4130 enum isl_dim_type type, unsigned first, unsigned n);
4132 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_insert_dims(
4133 __isl_take isl_multi_pw_aff *mpa,
4134 enum isl_dim_type type, unsigned first, unsigned n);
4135 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_add_dims(
4136 __isl_take isl_multi_pw_aff *mpa,
4137 enum isl_dim_type type, unsigned n);
4139 To check whether two multiple affine expressions are
4140 obviously equal to each other, use
4142 int isl_multi_aff_plain_is_equal(__isl_keep isl_multi_aff *maff1,
4143 __isl_keep isl_multi_aff *maff2);
4144 int isl_pw_multi_aff_plain_is_equal(
4145 __isl_keep isl_pw_multi_aff *pma1,
4146 __isl_keep isl_pw_multi_aff *pma2);
4150 #include <isl/aff.h>
4151 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_union_lexmin(
4152 __isl_take isl_pw_multi_aff *pma1,
4153 __isl_take isl_pw_multi_aff *pma2);
4154 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_union_lexmax(
4155 __isl_take isl_pw_multi_aff *pma1,
4156 __isl_take isl_pw_multi_aff *pma2);
4157 __isl_give isl_multi_aff *isl_multi_aff_add(
4158 __isl_take isl_multi_aff *maff1,
4159 __isl_take isl_multi_aff *maff2);
4160 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_add(
4161 __isl_take isl_pw_multi_aff *pma1,
4162 __isl_take isl_pw_multi_aff *pma2);
4163 __isl_give isl_union_pw_multi_aff *isl_union_pw_multi_aff_add(
4164 __isl_take isl_union_pw_multi_aff *upma1,
4165 __isl_take isl_union_pw_multi_aff *upma2);
4166 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_union_add(
4167 __isl_take isl_pw_multi_aff *pma1,
4168 __isl_take isl_pw_multi_aff *pma2);
4169 __isl_give isl_multi_aff *isl_multi_aff_sub(
4170 __isl_take isl_multi_aff *ma1,
4171 __isl_take isl_multi_aff *ma2);
4172 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_sub(
4173 __isl_take isl_pw_multi_aff *pma1,
4174 __isl_take isl_pw_multi_aff *pma2);
4175 __isl_give isl_union_pw_multi_aff *isl_union_pw_multi_aff_sub(
4176 __isl_take isl_union_pw_multi_aff *upma1,
4177 __isl_take isl_union_pw_multi_aff *upma2);
4179 C<isl_multi_aff_sub> subtracts the second argument from the first.
4181 __isl_give isl_multi_aff *isl_multi_aff_scale(
4182 __isl_take isl_multi_aff *maff,
4184 __isl_give isl_multi_aff *isl_multi_aff_scale_vec(
4185 __isl_take isl_multi_aff *ma,
4186 __isl_take isl_vec *v);
4187 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_scale_vec(
4188 __isl_take isl_pw_multi_aff *pma,
4189 __isl_take isl_vec *v);
4190 __isl_give isl_union_pw_multi_aff *isl_union_pw_multi_aff_scale_vec(
4191 __isl_take isl_union_pw_multi_aff *upma,
4192 __isl_take isl_vec *v);
4194 C<isl_multi_aff_scale_vec> scales the first elements of C<ma>
4195 by the corresponding elements of C<v>.
4197 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_intersect_params(
4198 __isl_take isl_pw_multi_aff *pma,
4199 __isl_take isl_set *set);
4200 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_intersect_domain(
4201 __isl_take isl_pw_multi_aff *pma,
4202 __isl_take isl_set *set);
4203 __isl_give isl_union_pw_multi_aff *
4204 isl_union_pw_multi_aff_intersect_domain(
4205 __isl_take isl_union_pw_multi_aff *upma,
4206 __isl_take isl_union_set *uset);
4207 __isl_give isl_multi_aff *isl_multi_aff_lift(
4208 __isl_take isl_multi_aff *maff,
4209 __isl_give isl_local_space **ls);
4210 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_coalesce(
4211 __isl_take isl_pw_multi_aff *pma);
4212 __isl_give isl_multi_aff *isl_multi_aff_align_params(
4213 __isl_take isl_multi_aff *multi,
4214 __isl_take isl_space *model);
4215 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_align_params(
4216 __isl_take isl_pw_multi_aff *pma,
4217 __isl_take isl_space *model);
4218 __isl_give isl_pw_multi_aff *
4219 isl_pw_multi_aff_project_domain_on_params(
4220 __isl_take isl_pw_multi_aff *pma);
4221 __isl_give isl_multi_aff *isl_multi_aff_gist_params(
4222 __isl_take isl_multi_aff *maff,
4223 __isl_take isl_set *context);
4224 __isl_give isl_multi_aff *isl_multi_aff_gist(
4225 __isl_take isl_multi_aff *maff,
4226 __isl_take isl_set *context);
4227 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_gist_params(
4228 __isl_take isl_pw_multi_aff *pma,
4229 __isl_take isl_set *set);
4230 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_gist(
4231 __isl_take isl_pw_multi_aff *pma,
4232 __isl_take isl_set *set);
4233 __isl_give isl_set *isl_pw_multi_aff_domain(
4234 __isl_take isl_pw_multi_aff *pma);
4235 __isl_give isl_union_set *isl_union_pw_multi_aff_domain(
4236 __isl_take isl_union_pw_multi_aff *upma);
4237 __isl_give isl_multi_aff *isl_multi_aff_range_splice(
4238 __isl_take isl_multi_aff *ma1, unsigned pos,
4239 __isl_take isl_multi_aff *ma2);
4240 __isl_give isl_multi_aff *isl_multi_aff_splice(
4241 __isl_take isl_multi_aff *ma1,
4242 unsigned in_pos, unsigned out_pos,
4243 __isl_take isl_multi_aff *ma2);
4244 __isl_give isl_multi_aff *isl_multi_aff_range_product(
4245 __isl_take isl_multi_aff *ma1,
4246 __isl_take isl_multi_aff *ma2);
4247 __isl_give isl_multi_aff *isl_multi_aff_flat_range_product(
4248 __isl_take isl_multi_aff *ma1,
4249 __isl_take isl_multi_aff *ma2);
4250 __isl_give isl_multi_aff *isl_multi_aff_product(
4251 __isl_take isl_multi_aff *ma1,
4252 __isl_take isl_multi_aff *ma2);
4253 __isl_give isl_pw_multi_aff *
4254 isl_pw_multi_aff_range_product(
4255 __isl_take isl_pw_multi_aff *pma1,
4256 __isl_take isl_pw_multi_aff *pma2);
4257 __isl_give isl_pw_multi_aff *
4258 isl_pw_multi_aff_flat_range_product(
4259 __isl_take isl_pw_multi_aff *pma1,
4260 __isl_take isl_pw_multi_aff *pma2);
4261 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_product(
4262 __isl_take isl_pw_multi_aff *pma1,
4263 __isl_take isl_pw_multi_aff *pma2);
4264 __isl_give isl_union_pw_multi_aff *
4265 isl_union_pw_multi_aff_flat_range_product(
4266 __isl_take isl_union_pw_multi_aff *upma1,
4267 __isl_take isl_union_pw_multi_aff *upma2);
4268 __isl_give isl_multi_pw_aff *
4269 isl_multi_pw_aff_range_splice(
4270 __isl_take isl_multi_pw_aff *mpa1, unsigned pos,
4271 __isl_take isl_multi_pw_aff *mpa2);
4272 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_splice(
4273 __isl_take isl_multi_pw_aff *mpa1,
4274 unsigned in_pos, unsigned out_pos,
4275 __isl_take isl_multi_pw_aff *mpa2);
4276 __isl_give isl_multi_pw_aff *
4277 isl_multi_pw_aff_range_product(
4278 __isl_take isl_multi_pw_aff *mpa1,
4279 __isl_take isl_multi_pw_aff *mpa2);
4280 __isl_give isl_multi_pw_aff *
4281 isl_multi_pw_aff_flat_range_product(
4282 __isl_take isl_multi_pw_aff *mpa1,
4283 __isl_take isl_multi_pw_aff *mpa2);
4285 If the C<ls> argument of C<isl_multi_aff_lift> is not C<NULL>,
4286 then it is assigned the local space that lies at the basis of
4287 the lifting applied.
4289 #include <isl/aff.h>
4290 __isl_give isl_multi_aff *isl_multi_aff_pullback_multi_aff(
4291 __isl_take isl_multi_aff *ma1,
4292 __isl_take isl_multi_aff *ma2);
4293 __isl_give isl_pw_multi_aff *
4294 isl_pw_multi_aff_pullback_multi_aff(
4295 __isl_take isl_pw_multi_aff *pma,
4296 __isl_take isl_multi_aff *ma);
4297 __isl_give isl_pw_multi_aff *
4298 isl_pw_multi_aff_pullback_pw_multi_aff(
4299 __isl_take isl_pw_multi_aff *pma1,
4300 __isl_take isl_pw_multi_aff *pma2);
4302 The function C<isl_multi_aff_pullback_multi_aff> precomposes C<ma1> by C<ma2>.
4303 In other words, C<ma2> is plugged
4306 __isl_give isl_set *isl_multi_aff_lex_le_set(
4307 __isl_take isl_multi_aff *ma1,
4308 __isl_take isl_multi_aff *ma2);
4309 __isl_give isl_set *isl_multi_aff_lex_ge_set(
4310 __isl_take isl_multi_aff *ma1,
4311 __isl_take isl_multi_aff *ma2);
4313 The function C<isl_multi_aff_lex_le_set> returns a set
4314 containing those elements in the shared domain space
4315 where C<ma1> is lexicographically smaller than or
4318 An expression can be read from input using
4320 #include <isl/aff.h>
4321 __isl_give isl_multi_aff *isl_multi_aff_read_from_str(
4322 isl_ctx *ctx, const char *str);
4323 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_read_from_str(
4324 isl_ctx *ctx, const char *str);
4325 __isl_give isl_union_pw_multi_aff *
4326 isl_union_pw_multi_aff_read_from_str(
4327 isl_ctx *ctx, const char *str);
4329 An expression can be printed using
4331 #include <isl/aff.h>
4332 __isl_give isl_printer *isl_printer_print_multi_aff(
4333 __isl_take isl_printer *p,
4334 __isl_keep isl_multi_aff *maff);
4335 __isl_give isl_printer *isl_printer_print_pw_multi_aff(
4336 __isl_take isl_printer *p,
4337 __isl_keep isl_pw_multi_aff *pma);
4338 __isl_give isl_printer *isl_printer_print_union_pw_multi_aff(
4339 __isl_take isl_printer *p,
4340 __isl_keep isl_union_pw_multi_aff *upma);
4341 __isl_give isl_printer *isl_printer_print_multi_pw_aff(
4342 __isl_take isl_printer *p,
4343 __isl_keep isl_multi_pw_aff *mpa);
4347 Points are elements of a set. They can be used to construct
4348 simple sets (boxes) or they can be used to represent the
4349 individual elements of a set.
4350 The zero point (the origin) can be created using
4352 __isl_give isl_point *isl_point_zero(__isl_take isl_space *space);
4354 The coordinates of a point can be inspected, set and changed
4357 int isl_point_get_coordinate(__isl_keep isl_point *pnt,
4358 enum isl_dim_type type, int pos, isl_int *v);
4359 __isl_give isl_point *isl_point_set_coordinate(
4360 __isl_take isl_point *pnt,
4361 enum isl_dim_type type, int pos, isl_int v);
4363 __isl_give isl_point *isl_point_add_ui(
4364 __isl_take isl_point *pnt,
4365 enum isl_dim_type type, int pos, unsigned val);
4366 __isl_give isl_point *isl_point_sub_ui(
4367 __isl_take isl_point *pnt,
4368 enum isl_dim_type type, int pos, unsigned val);
4370 Other properties can be obtained using
4372 isl_ctx *isl_point_get_ctx(__isl_keep isl_point *pnt);
4374 Points can be copied or freed using
4376 __isl_give isl_point *isl_point_copy(
4377 __isl_keep isl_point *pnt);
4378 void isl_point_free(__isl_take isl_point *pnt);
4380 A singleton set can be created from a point using
4382 __isl_give isl_basic_set *isl_basic_set_from_point(
4383 __isl_take isl_point *pnt);
4384 __isl_give isl_set *isl_set_from_point(
4385 __isl_take isl_point *pnt);
4387 and a box can be created from two opposite extremal points using
4389 __isl_give isl_basic_set *isl_basic_set_box_from_points(
4390 __isl_take isl_point *pnt1,
4391 __isl_take isl_point *pnt2);
4392 __isl_give isl_set *isl_set_box_from_points(
4393 __isl_take isl_point *pnt1,
4394 __isl_take isl_point *pnt2);
4396 All elements of a B<bounded> (union) set can be enumerated using
4397 the following functions.
4399 int isl_set_foreach_point(__isl_keep isl_set *set,
4400 int (*fn)(__isl_take isl_point *pnt, void *user),
4402 int isl_union_set_foreach_point(__isl_keep isl_union_set *uset,
4403 int (*fn)(__isl_take isl_point *pnt, void *user),
4406 The function C<fn> is called for each integer point in
4407 C<set> with as second argument the last argument of
4408 the C<isl_set_foreach_point> call. The function C<fn>
4409 should return C<0> on success and C<-1> on failure.
4410 In the latter case, C<isl_set_foreach_point> will stop
4411 enumerating and return C<-1> as well.
4412 If the enumeration is performed successfully and to completion,
4413 then C<isl_set_foreach_point> returns C<0>.
4415 To obtain a single point of a (basic) set, use
4417 __isl_give isl_point *isl_basic_set_sample_point(
4418 __isl_take isl_basic_set *bset);
4419 __isl_give isl_point *isl_set_sample_point(
4420 __isl_take isl_set *set);
4422 If C<set> does not contain any (integer) points, then the
4423 resulting point will be ``void'', a property that can be
4426 int isl_point_is_void(__isl_keep isl_point *pnt);
4428 =head2 Piecewise Quasipolynomials
4430 A piecewise quasipolynomial is a particular kind of function that maps
4431 a parametric point to a rational value.
4432 More specifically, a quasipolynomial is a polynomial expression in greatest
4433 integer parts of affine expressions of parameters and variables.
4434 A piecewise quasipolynomial is a subdivision of a given parametric
4435 domain into disjoint cells with a quasipolynomial associated to
4436 each cell. The value of the piecewise quasipolynomial at a given
4437 point is the value of the quasipolynomial associated to the cell
4438 that contains the point. Outside of the union of cells,
4439 the value is assumed to be zero.
4440 For example, the piecewise quasipolynomial
4442 [n] -> { [x] -> ((1 + n) - x) : x <= n and x >= 0 }
4444 maps C<x> to C<1 + n - x> for values of C<x> between C<0> and C<n>.
4445 A given piecewise quasipolynomial has a fixed domain dimension.
4446 Union piecewise quasipolynomials are used to contain piecewise quasipolynomials
4447 defined over different domains.
4448 Piecewise quasipolynomials are mainly used by the C<barvinok>
4449 library for representing the number of elements in a parametric set or map.
4450 For example, the piecewise quasipolynomial above represents
4451 the number of points in the map
4453 [n] -> { [x] -> [y] : x,y >= 0 and 0 <= x + y <= n }
4455 =head3 Input and Output
4457 Piecewise quasipolynomials can be read from input using
4459 __isl_give isl_union_pw_qpolynomial *
4460 isl_union_pw_qpolynomial_read_from_str(
4461 isl_ctx *ctx, const char *str);
4463 Quasipolynomials and piecewise quasipolynomials can be printed
4464 using the following functions.
4466 __isl_give isl_printer *isl_printer_print_qpolynomial(
4467 __isl_take isl_printer *p,
4468 __isl_keep isl_qpolynomial *qp);
4470 __isl_give isl_printer *isl_printer_print_pw_qpolynomial(
4471 __isl_take isl_printer *p,
4472 __isl_keep isl_pw_qpolynomial *pwqp);
4474 __isl_give isl_printer *isl_printer_print_union_pw_qpolynomial(
4475 __isl_take isl_printer *p,
4476 __isl_keep isl_union_pw_qpolynomial *upwqp);
4478 The output format of the printer
4479 needs to be set to either C<ISL_FORMAT_ISL> or C<ISL_FORMAT_C>.
4480 For C<isl_printer_print_union_pw_qpolynomial>, only C<ISL_FORMAT_ISL>
4482 In case of printing in C<ISL_FORMAT_C>, the user may want
4483 to set the names of all dimensions
4485 __isl_give isl_qpolynomial *isl_qpolynomial_set_dim_name(
4486 __isl_take isl_qpolynomial *qp,
4487 enum isl_dim_type type, unsigned pos,
4489 __isl_give isl_pw_qpolynomial *
4490 isl_pw_qpolynomial_set_dim_name(
4491 __isl_take isl_pw_qpolynomial *pwqp,
4492 enum isl_dim_type type, unsigned pos,
4495 =head3 Creating New (Piecewise) Quasipolynomials
4497 Some simple quasipolynomials can be created using the following functions.
4498 More complicated quasipolynomials can be created by applying
4499 operations such as addition and multiplication
4500 on the resulting quasipolynomials
4502 __isl_give isl_qpolynomial *isl_qpolynomial_zero_on_domain(
4503 __isl_take isl_space *domain);
4504 __isl_give isl_qpolynomial *isl_qpolynomial_one_on_domain(
4505 __isl_take isl_space *domain);
4506 __isl_give isl_qpolynomial *isl_qpolynomial_infty_on_domain(
4507 __isl_take isl_space *domain);
4508 __isl_give isl_qpolynomial *isl_qpolynomial_neginfty_on_domain(
4509 __isl_take isl_space *domain);
4510 __isl_give isl_qpolynomial *isl_qpolynomial_nan_on_domain(
4511 __isl_take isl_space *domain);
4512 __isl_give isl_qpolynomial *isl_qpolynomial_rat_cst_on_domain(
4513 __isl_take isl_space *domain,
4514 const isl_int n, const isl_int d);
4515 __isl_give isl_qpolynomial *isl_qpolynomial_var_on_domain(
4516 __isl_take isl_space *domain,
4517 enum isl_dim_type type, unsigned pos);
4518 __isl_give isl_qpolynomial *isl_qpolynomial_from_aff(
4519 __isl_take isl_aff *aff);
4521 Note that the space in which a quasipolynomial lives is a map space
4522 with a one-dimensional range. The C<domain> argument in some of
4523 the functions above corresponds to the domain of this map space.
4525 The zero piecewise quasipolynomial or a piecewise quasipolynomial
4526 with a single cell can be created using the following functions.
4527 Multiple of these single cell piecewise quasipolynomials can
4528 be combined to create more complicated piecewise quasipolynomials.
4530 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_zero(
4531 __isl_take isl_space *space);
4532 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_alloc(
4533 __isl_take isl_set *set,
4534 __isl_take isl_qpolynomial *qp);
4535 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_from_qpolynomial(
4536 __isl_take isl_qpolynomial *qp);
4537 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_from_pw_aff(
4538 __isl_take isl_pw_aff *pwaff);
4540 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_zero(
4541 __isl_take isl_space *space);
4542 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_from_pw_qpolynomial(
4543 __isl_take isl_pw_qpolynomial *pwqp);
4544 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_add_pw_qpolynomial(
4545 __isl_take isl_union_pw_qpolynomial *upwqp,
4546 __isl_take isl_pw_qpolynomial *pwqp);
4548 Quasipolynomials can be copied and freed again using the following
4551 __isl_give isl_qpolynomial *isl_qpolynomial_copy(
4552 __isl_keep isl_qpolynomial *qp);
4553 void *isl_qpolynomial_free(__isl_take isl_qpolynomial *qp);
4555 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_copy(
4556 __isl_keep isl_pw_qpolynomial *pwqp);
4557 void *isl_pw_qpolynomial_free(
4558 __isl_take isl_pw_qpolynomial *pwqp);
4560 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_copy(
4561 __isl_keep isl_union_pw_qpolynomial *upwqp);
4562 void *isl_union_pw_qpolynomial_free(
4563 __isl_take isl_union_pw_qpolynomial *upwqp);
4565 =head3 Inspecting (Piecewise) Quasipolynomials
4567 To iterate over all piecewise quasipolynomials in a union
4568 piecewise quasipolynomial, use the following function
4570 int isl_union_pw_qpolynomial_foreach_pw_qpolynomial(
4571 __isl_keep isl_union_pw_qpolynomial *upwqp,
4572 int (*fn)(__isl_take isl_pw_qpolynomial *pwqp, void *user),
4575 To extract the piecewise quasipolynomial in a given space from a union, use
4577 __isl_give isl_pw_qpolynomial *
4578 isl_union_pw_qpolynomial_extract_pw_qpolynomial(
4579 __isl_keep isl_union_pw_qpolynomial *upwqp,
4580 __isl_take isl_space *space);
4582 To iterate over the cells in a piecewise quasipolynomial,
4583 use either of the following two functions
4585 int isl_pw_qpolynomial_foreach_piece(
4586 __isl_keep isl_pw_qpolynomial *pwqp,
4587 int (*fn)(__isl_take isl_set *set,
4588 __isl_take isl_qpolynomial *qp,
4589 void *user), void *user);
4590 int isl_pw_qpolynomial_foreach_lifted_piece(
4591 __isl_keep isl_pw_qpolynomial *pwqp,
4592 int (*fn)(__isl_take isl_set *set,
4593 __isl_take isl_qpolynomial *qp,
4594 void *user), void *user);
4596 As usual, the function C<fn> should return C<0> on success
4597 and C<-1> on failure. The difference between
4598 C<isl_pw_qpolynomial_foreach_piece> and
4599 C<isl_pw_qpolynomial_foreach_lifted_piece> is that
4600 C<isl_pw_qpolynomial_foreach_lifted_piece> will first
4601 compute unique representations for all existentially quantified
4602 variables and then turn these existentially quantified variables
4603 into extra set variables, adapting the associated quasipolynomial
4604 accordingly. This means that the C<set> passed to C<fn>
4605 will not have any existentially quantified variables, but that
4606 the dimensions of the sets may be different for different
4607 invocations of C<fn>.
4609 To iterate over all terms in a quasipolynomial,
4612 int isl_qpolynomial_foreach_term(
4613 __isl_keep isl_qpolynomial *qp,
4614 int (*fn)(__isl_take isl_term *term,
4615 void *user), void *user);
4617 The terms themselves can be inspected and freed using
4620 unsigned isl_term_dim(__isl_keep isl_term *term,
4621 enum isl_dim_type type);
4622 void isl_term_get_num(__isl_keep isl_term *term,
4624 void isl_term_get_den(__isl_keep isl_term *term,
4626 int isl_term_get_exp(__isl_keep isl_term *term,
4627 enum isl_dim_type type, unsigned pos);
4628 __isl_give isl_aff *isl_term_get_div(
4629 __isl_keep isl_term *term, unsigned pos);
4630 void isl_term_free(__isl_take isl_term *term);
4632 Each term is a product of parameters, set variables and
4633 integer divisions. The function C<isl_term_get_exp>
4634 returns the exponent of a given dimensions in the given term.
4635 The C<isl_int>s in the arguments of C<isl_term_get_num>
4636 and C<isl_term_get_den> need to have been initialized
4637 using C<isl_int_init> before calling these functions.
4639 =head3 Properties of (Piecewise) Quasipolynomials
4641 To check whether a quasipolynomial is actually a constant,
4642 use the following function.
4644 int isl_qpolynomial_is_cst(__isl_keep isl_qpolynomial *qp,
4645 isl_int *n, isl_int *d);
4647 If C<qp> is a constant and if C<n> and C<d> are not C<NULL>
4648 then the numerator and denominator of the constant
4649 are returned in C<*n> and C<*d>, respectively.
4651 To check whether two union piecewise quasipolynomials are
4652 obviously equal, use
4654 int isl_union_pw_qpolynomial_plain_is_equal(
4655 __isl_keep isl_union_pw_qpolynomial *upwqp1,
4656 __isl_keep isl_union_pw_qpolynomial *upwqp2);
4658 =head3 Operations on (Piecewise) Quasipolynomials
4660 __isl_give isl_qpolynomial *isl_qpolynomial_scale(
4661 __isl_take isl_qpolynomial *qp, isl_int v);
4662 __isl_give isl_qpolynomial *isl_qpolynomial_neg(
4663 __isl_take isl_qpolynomial *qp);
4664 __isl_give isl_qpolynomial *isl_qpolynomial_add(
4665 __isl_take isl_qpolynomial *qp1,
4666 __isl_take isl_qpolynomial *qp2);
4667 __isl_give isl_qpolynomial *isl_qpolynomial_sub(
4668 __isl_take isl_qpolynomial *qp1,
4669 __isl_take isl_qpolynomial *qp2);
4670 __isl_give isl_qpolynomial *isl_qpolynomial_mul(
4671 __isl_take isl_qpolynomial *qp1,
4672 __isl_take isl_qpolynomial *qp2);
4673 __isl_give isl_qpolynomial *isl_qpolynomial_pow(
4674 __isl_take isl_qpolynomial *qp, unsigned exponent);
4676 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_add(
4677 __isl_take isl_pw_qpolynomial *pwqp1,
4678 __isl_take isl_pw_qpolynomial *pwqp2);
4679 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_sub(
4680 __isl_take isl_pw_qpolynomial *pwqp1,
4681 __isl_take isl_pw_qpolynomial *pwqp2);
4682 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_add_disjoint(
4683 __isl_take isl_pw_qpolynomial *pwqp1,
4684 __isl_take isl_pw_qpolynomial *pwqp2);
4685 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_neg(
4686 __isl_take isl_pw_qpolynomial *pwqp);
4687 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_mul(
4688 __isl_take isl_pw_qpolynomial *pwqp1,
4689 __isl_take isl_pw_qpolynomial *pwqp2);
4690 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_pow(
4691 __isl_take isl_pw_qpolynomial *pwqp, unsigned exponent);
4693 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_add(
4694 __isl_take isl_union_pw_qpolynomial *upwqp1,
4695 __isl_take isl_union_pw_qpolynomial *upwqp2);
4696 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_sub(
4697 __isl_take isl_union_pw_qpolynomial *upwqp1,
4698 __isl_take isl_union_pw_qpolynomial *upwqp2);
4699 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_mul(
4700 __isl_take isl_union_pw_qpolynomial *upwqp1,
4701 __isl_take isl_union_pw_qpolynomial *upwqp2);
4703 __isl_give isl_qpolynomial *isl_pw_qpolynomial_eval(
4704 __isl_take isl_pw_qpolynomial *pwqp,
4705 __isl_take isl_point *pnt);
4707 __isl_give isl_qpolynomial *isl_union_pw_qpolynomial_eval(
4708 __isl_take isl_union_pw_qpolynomial *upwqp,
4709 __isl_take isl_point *pnt);
4711 __isl_give isl_set *isl_pw_qpolynomial_domain(
4712 __isl_take isl_pw_qpolynomial *pwqp);
4713 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_intersect_domain(
4714 __isl_take isl_pw_qpolynomial *pwpq,
4715 __isl_take isl_set *set);
4716 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_intersect_params(
4717 __isl_take isl_pw_qpolynomial *pwpq,
4718 __isl_take isl_set *set);
4720 __isl_give isl_union_set *isl_union_pw_qpolynomial_domain(
4721 __isl_take isl_union_pw_qpolynomial *upwqp);
4722 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_intersect_domain(
4723 __isl_take isl_union_pw_qpolynomial *upwpq,
4724 __isl_take isl_union_set *uset);
4725 __isl_give isl_union_pw_qpolynomial *
4726 isl_union_pw_qpolynomial_intersect_params(
4727 __isl_take isl_union_pw_qpolynomial *upwpq,
4728 __isl_take isl_set *set);
4730 __isl_give isl_qpolynomial *isl_qpolynomial_align_params(
4731 __isl_take isl_qpolynomial *qp,
4732 __isl_take isl_space *model);
4734 __isl_give isl_qpolynomial *isl_qpolynomial_project_domain_on_params(
4735 __isl_take isl_qpolynomial *qp);
4736 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_project_domain_on_params(
4737 __isl_take isl_pw_qpolynomial *pwqp);
4739 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_coalesce(
4740 __isl_take isl_union_pw_qpolynomial *upwqp);
4742 __isl_give isl_qpolynomial *isl_qpolynomial_gist_params(
4743 __isl_take isl_qpolynomial *qp,
4744 __isl_take isl_set *context);
4745 __isl_give isl_qpolynomial *isl_qpolynomial_gist(
4746 __isl_take isl_qpolynomial *qp,
4747 __isl_take isl_set *context);
4749 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_gist_params(
4750 __isl_take isl_pw_qpolynomial *pwqp,
4751 __isl_take isl_set *context);
4752 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_gist(
4753 __isl_take isl_pw_qpolynomial *pwqp,
4754 __isl_take isl_set *context);
4756 __isl_give isl_union_pw_qpolynomial *
4757 isl_union_pw_qpolynomial_gist_params(
4758 __isl_take isl_union_pw_qpolynomial *upwqp,
4759 __isl_take isl_set *context);
4760 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_gist(
4761 __isl_take isl_union_pw_qpolynomial *upwqp,
4762 __isl_take isl_union_set *context);
4764 The gist operation applies the gist operation to each of
4765 the cells in the domain of the input piecewise quasipolynomial.
4766 The context is also exploited
4767 to simplify the quasipolynomials associated to each cell.
4769 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_to_polynomial(
4770 __isl_take isl_pw_qpolynomial *pwqp, int sign);
4771 __isl_give isl_union_pw_qpolynomial *
4772 isl_union_pw_qpolynomial_to_polynomial(
4773 __isl_take isl_union_pw_qpolynomial *upwqp, int sign);
4775 Approximate each quasipolynomial by a polynomial. If C<sign> is positive,
4776 the polynomial will be an overapproximation. If C<sign> is negative,
4777 it will be an underapproximation. If C<sign> is zero, the approximation
4778 will lie somewhere in between.
4780 =head2 Bounds on Piecewise Quasipolynomials and Piecewise Quasipolynomial Reductions
4782 A piecewise quasipolynomial reduction is a piecewise
4783 reduction (or fold) of quasipolynomials.
4784 In particular, the reduction can be maximum or a minimum.
4785 The objects are mainly used to represent the result of
4786 an upper or lower bound on a quasipolynomial over its domain,
4787 i.e., as the result of the following function.
4789 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_bound(
4790 __isl_take isl_pw_qpolynomial *pwqp,
4791 enum isl_fold type, int *tight);
4793 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_bound(
4794 __isl_take isl_union_pw_qpolynomial *upwqp,
4795 enum isl_fold type, int *tight);
4797 The C<type> argument may be either C<isl_fold_min> or C<isl_fold_max>.
4798 If C<tight> is not C<NULL>, then C<*tight> is set to C<1>
4799 is the returned bound is known be tight, i.e., for each value
4800 of the parameters there is at least
4801 one element in the domain that reaches the bound.
4802 If the domain of C<pwqp> is not wrapping, then the bound is computed
4803 over all elements in that domain and the result has a purely parametric
4804 domain. If the domain of C<pwqp> is wrapping, then the bound is
4805 computed over the range of the wrapped relation. The domain of the
4806 wrapped relation becomes the domain of the result.
4808 A (piecewise) quasipolynomial reduction can be copied or freed using the
4809 following functions.
4811 __isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_copy(
4812 __isl_keep isl_qpolynomial_fold *fold);
4813 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_copy(
4814 __isl_keep isl_pw_qpolynomial_fold *pwf);
4815 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_copy(
4816 __isl_keep isl_union_pw_qpolynomial_fold *upwf);
4817 void isl_qpolynomial_fold_free(
4818 __isl_take isl_qpolynomial_fold *fold);
4819 void *isl_pw_qpolynomial_fold_free(
4820 __isl_take isl_pw_qpolynomial_fold *pwf);
4821 void *isl_union_pw_qpolynomial_fold_free(
4822 __isl_take isl_union_pw_qpolynomial_fold *upwf);
4824 =head3 Printing Piecewise Quasipolynomial Reductions
4826 Piecewise quasipolynomial reductions can be printed
4827 using the following function.
4829 __isl_give isl_printer *isl_printer_print_pw_qpolynomial_fold(
4830 __isl_take isl_printer *p,
4831 __isl_keep isl_pw_qpolynomial_fold *pwf);
4832 __isl_give isl_printer *isl_printer_print_union_pw_qpolynomial_fold(
4833 __isl_take isl_printer *p,
4834 __isl_keep isl_union_pw_qpolynomial_fold *upwf);
4836 For C<isl_printer_print_pw_qpolynomial_fold>,
4837 output format of the printer
4838 needs to be set to either C<ISL_FORMAT_ISL> or C<ISL_FORMAT_C>.
4839 For C<isl_printer_print_union_pw_qpolynomial_fold>,
4840 output format of the printer
4841 needs to be set to C<ISL_FORMAT_ISL>.
4842 In case of printing in C<ISL_FORMAT_C>, the user may want
4843 to set the names of all dimensions
4845 __isl_give isl_pw_qpolynomial_fold *
4846 isl_pw_qpolynomial_fold_set_dim_name(
4847 __isl_take isl_pw_qpolynomial_fold *pwf,
4848 enum isl_dim_type type, unsigned pos,
4851 =head3 Inspecting (Piecewise) Quasipolynomial Reductions
4853 To iterate over all piecewise quasipolynomial reductions in a union
4854 piecewise quasipolynomial reduction, use the following function
4856 int isl_union_pw_qpolynomial_fold_foreach_pw_qpolynomial_fold(
4857 __isl_keep isl_union_pw_qpolynomial_fold *upwf,
4858 int (*fn)(__isl_take isl_pw_qpolynomial_fold *pwf,
4859 void *user), void *user);
4861 To iterate over the cells in a piecewise quasipolynomial reduction,
4862 use either of the following two functions
4864 int isl_pw_qpolynomial_fold_foreach_piece(
4865 __isl_keep isl_pw_qpolynomial_fold *pwf,
4866 int (*fn)(__isl_take isl_set *set,
4867 __isl_take isl_qpolynomial_fold *fold,
4868 void *user), void *user);
4869 int isl_pw_qpolynomial_fold_foreach_lifted_piece(
4870 __isl_keep isl_pw_qpolynomial_fold *pwf,
4871 int (*fn)(__isl_take isl_set *set,
4872 __isl_take isl_qpolynomial_fold *fold,
4873 void *user), void *user);
4875 See L<Inspecting (Piecewise) Quasipolynomials> for an explanation
4876 of the difference between these two functions.
4878 To iterate over all quasipolynomials in a reduction, use
4880 int isl_qpolynomial_fold_foreach_qpolynomial(
4881 __isl_keep isl_qpolynomial_fold *fold,
4882 int (*fn)(__isl_take isl_qpolynomial *qp,
4883 void *user), void *user);
4885 =head3 Properties of Piecewise Quasipolynomial Reductions
4887 To check whether two union piecewise quasipolynomial reductions are
4888 obviously equal, use
4890 int isl_union_pw_qpolynomial_fold_plain_is_equal(
4891 __isl_keep isl_union_pw_qpolynomial_fold *upwf1,
4892 __isl_keep isl_union_pw_qpolynomial_fold *upwf2);
4894 =head3 Operations on Piecewise Quasipolynomial Reductions
4896 __isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_scale(
4897 __isl_take isl_qpolynomial_fold *fold, isl_int v);
4899 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_add(
4900 __isl_take isl_pw_qpolynomial_fold *pwf1,
4901 __isl_take isl_pw_qpolynomial_fold *pwf2);
4903 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_fold(
4904 __isl_take isl_pw_qpolynomial_fold *pwf1,
4905 __isl_take isl_pw_qpolynomial_fold *pwf2);
4907 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_fold(
4908 __isl_take isl_union_pw_qpolynomial_fold *upwf1,
4909 __isl_take isl_union_pw_qpolynomial_fold *upwf2);
4911 __isl_give isl_qpolynomial *isl_pw_qpolynomial_fold_eval(
4912 __isl_take isl_pw_qpolynomial_fold *pwf,
4913 __isl_take isl_point *pnt);
4915 __isl_give isl_qpolynomial *isl_union_pw_qpolynomial_fold_eval(
4916 __isl_take isl_union_pw_qpolynomial_fold *upwf,
4917 __isl_take isl_point *pnt);
4919 __isl_give isl_pw_qpolynomial_fold *
4920 isl_pw_qpolynomial_fold_intersect_params(
4921 __isl_take isl_pw_qpolynomial_fold *pwf,
4922 __isl_take isl_set *set);
4924 __isl_give isl_union_set *isl_union_pw_qpolynomial_fold_domain(
4925 __isl_take isl_union_pw_qpolynomial_fold *upwf);
4926 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_intersect_domain(
4927 __isl_take isl_union_pw_qpolynomial_fold *upwf,
4928 __isl_take isl_union_set *uset);
4929 __isl_give isl_union_pw_qpolynomial_fold *
4930 isl_union_pw_qpolynomial_fold_intersect_params(
4931 __isl_take isl_union_pw_qpolynomial_fold *upwf,
4932 __isl_take isl_set *set);
4934 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_project_domain_on_params(
4935 __isl_take isl_pw_qpolynomial_fold *pwf);
4937 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_coalesce(
4938 __isl_take isl_pw_qpolynomial_fold *pwf);
4940 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_coalesce(
4941 __isl_take isl_union_pw_qpolynomial_fold *upwf);
4943 __isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_gist_params(
4944 __isl_take isl_qpolynomial_fold *fold,
4945 __isl_take isl_set *context);
4946 __isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_gist(
4947 __isl_take isl_qpolynomial_fold *fold,
4948 __isl_take isl_set *context);
4950 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_gist(
4951 __isl_take isl_pw_qpolynomial_fold *pwf,
4952 __isl_take isl_set *context);
4953 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_gist_params(
4954 __isl_take isl_pw_qpolynomial_fold *pwf,
4955 __isl_take isl_set *context);
4957 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_gist(
4958 __isl_take isl_union_pw_qpolynomial_fold *upwf,
4959 __isl_take isl_union_set *context);
4960 __isl_give isl_union_pw_qpolynomial_fold *
4961 isl_union_pw_qpolynomial_fold_gist_params(
4962 __isl_take isl_union_pw_qpolynomial_fold *upwf,
4963 __isl_take isl_set *context);
4965 The gist operation applies the gist operation to each of
4966 the cells in the domain of the input piecewise quasipolynomial reduction.
4967 In future, the operation will also exploit the context
4968 to simplify the quasipolynomial reductions associated to each cell.
4970 __isl_give isl_pw_qpolynomial_fold *
4971 isl_set_apply_pw_qpolynomial_fold(
4972 __isl_take isl_set *set,
4973 __isl_take isl_pw_qpolynomial_fold *pwf,
4975 __isl_give isl_pw_qpolynomial_fold *
4976 isl_map_apply_pw_qpolynomial_fold(
4977 __isl_take isl_map *map,
4978 __isl_take isl_pw_qpolynomial_fold *pwf,
4980 __isl_give isl_union_pw_qpolynomial_fold *
4981 isl_union_set_apply_union_pw_qpolynomial_fold(
4982 __isl_take isl_union_set *uset,
4983 __isl_take isl_union_pw_qpolynomial_fold *upwf,
4985 __isl_give isl_union_pw_qpolynomial_fold *
4986 isl_union_map_apply_union_pw_qpolynomial_fold(
4987 __isl_take isl_union_map *umap,
4988 __isl_take isl_union_pw_qpolynomial_fold *upwf,
4991 The functions taking a map
4992 compose the given map with the given piecewise quasipolynomial reduction.
4993 That is, compute a bound (of the same type as C<pwf> or C<upwf> itself)
4994 over all elements in the intersection of the range of the map
4995 and the domain of the piecewise quasipolynomial reduction
4996 as a function of an element in the domain of the map.
4997 The functions taking a set compute a bound over all elements in the
4998 intersection of the set and the domain of the
4999 piecewise quasipolynomial reduction.
5001 =head2 Parametric Vertex Enumeration
5003 The parametric vertex enumeration described in this section
5004 is mainly intended to be used internally and by the C<barvinok>
5007 #include <isl/vertices.h>
5008 __isl_give isl_vertices *isl_basic_set_compute_vertices(
5009 __isl_keep isl_basic_set *bset);
5011 The function C<isl_basic_set_compute_vertices> performs the
5012 actual computation of the parametric vertices and the chamber
5013 decomposition and store the result in an C<isl_vertices> object.
5014 This information can be queried by either iterating over all
5015 the vertices or iterating over all the chambers or cells
5016 and then iterating over all vertices that are active on the chamber.
5018 int isl_vertices_foreach_vertex(
5019 __isl_keep isl_vertices *vertices,
5020 int (*fn)(__isl_take isl_vertex *vertex, void *user),
5023 int isl_vertices_foreach_cell(
5024 __isl_keep isl_vertices *vertices,
5025 int (*fn)(__isl_take isl_cell *cell, void *user),
5027 int isl_cell_foreach_vertex(__isl_keep isl_cell *cell,
5028 int (*fn)(__isl_take isl_vertex *vertex, void *user),
5031 Other operations that can be performed on an C<isl_vertices> object are
5034 isl_ctx *isl_vertices_get_ctx(
5035 __isl_keep isl_vertices *vertices);
5036 int isl_vertices_get_n_vertices(
5037 __isl_keep isl_vertices *vertices);
5038 void isl_vertices_free(__isl_take isl_vertices *vertices);
5040 Vertices can be inspected and destroyed using the following functions.
5042 isl_ctx *isl_vertex_get_ctx(__isl_keep isl_vertex *vertex);
5043 int isl_vertex_get_id(__isl_keep isl_vertex *vertex);
5044 __isl_give isl_basic_set *isl_vertex_get_domain(
5045 __isl_keep isl_vertex *vertex);
5046 __isl_give isl_basic_set *isl_vertex_get_expr(
5047 __isl_keep isl_vertex *vertex);
5048 void isl_vertex_free(__isl_take isl_vertex *vertex);
5050 C<isl_vertex_get_expr> returns a singleton parametric set describing
5051 the vertex, while C<isl_vertex_get_domain> returns the activity domain
5053 Note that C<isl_vertex_get_domain> and C<isl_vertex_get_expr> return
5054 B<rational> basic sets, so they should mainly be used for inspection
5055 and should not be mixed with integer sets.
5057 Chambers can be inspected and destroyed using the following functions.
5059 isl_ctx *isl_cell_get_ctx(__isl_keep isl_cell *cell);
5060 __isl_give isl_basic_set *isl_cell_get_domain(
5061 __isl_keep isl_cell *cell);
5062 void isl_cell_free(__isl_take isl_cell *cell);
5064 =head1 Polyhedral Compilation Library
5066 This section collects functionality in C<isl> that has been specifically
5067 designed for use during polyhedral compilation.
5069 =head2 Dependence Analysis
5071 C<isl> contains specialized functionality for performing
5072 array dataflow analysis. That is, given a I<sink> access relation
5073 and a collection of possible I<source> access relations,
5074 C<isl> can compute relations that describe
5075 for each iteration of the sink access, which iteration
5076 of which of the source access relations was the last
5077 to access the same data element before the given iteration
5079 The resulting dependence relations map source iterations
5080 to the corresponding sink iterations.
5081 To compute standard flow dependences, the sink should be
5082 a read, while the sources should be writes.
5083 If any of the source accesses are marked as being I<may>
5084 accesses, then there will be a dependence from the last
5085 I<must> access B<and> from any I<may> access that follows
5086 this last I<must> access.
5087 In particular, if I<all> sources are I<may> accesses,
5088 then memory based dependence analysis is performed.
5089 If, on the other hand, all sources are I<must> accesses,
5090 then value based dependence analysis is performed.
5092 #include <isl/flow.h>
5094 typedef int (*isl_access_level_before)(void *first, void *second);
5096 __isl_give isl_access_info *isl_access_info_alloc(
5097 __isl_take isl_map *sink,
5098 void *sink_user, isl_access_level_before fn,
5100 __isl_give isl_access_info *isl_access_info_add_source(
5101 __isl_take isl_access_info *acc,
5102 __isl_take isl_map *source, int must,
5104 void *isl_access_info_free(__isl_take isl_access_info *acc);
5106 __isl_give isl_flow *isl_access_info_compute_flow(
5107 __isl_take isl_access_info *acc);
5109 int isl_flow_foreach(__isl_keep isl_flow *deps,
5110 int (*fn)(__isl_take isl_map *dep, int must,
5111 void *dep_user, void *user),
5113 __isl_give isl_map *isl_flow_get_no_source(
5114 __isl_keep isl_flow *deps, int must);
5115 void isl_flow_free(__isl_take isl_flow *deps);
5117 The function C<isl_access_info_compute_flow> performs the actual
5118 dependence analysis. The other functions are used to construct
5119 the input for this function or to read off the output.
5121 The input is collected in an C<isl_access_info>, which can
5122 be created through a call to C<isl_access_info_alloc>.
5123 The arguments to this functions are the sink access relation
5124 C<sink>, a token C<sink_user> used to identify the sink
5125 access to the user, a callback function for specifying the
5126 relative order of source and sink accesses, and the number
5127 of source access relations that will be added.
5128 The callback function has type C<int (*)(void *first, void *second)>.
5129 The function is called with two user supplied tokens identifying
5130 either a source or the sink and it should return the shared nesting
5131 level and the relative order of the two accesses.
5132 In particular, let I<n> be the number of loops shared by
5133 the two accesses. If C<first> precedes C<second> textually,
5134 then the function should return I<2 * n + 1>; otherwise,
5135 it should return I<2 * n>.
5136 The sources can be added to the C<isl_access_info> by performing
5137 (at most) C<max_source> calls to C<isl_access_info_add_source>.
5138 C<must> indicates whether the source is a I<must> access
5139 or a I<may> access. Note that a multi-valued access relation
5140 should only be marked I<must> if every iteration in the domain
5141 of the relation accesses I<all> elements in its image.
5142 The C<source_user> token is again used to identify
5143 the source access. The range of the source access relation
5144 C<source> should have the same dimension as the range
5145 of the sink access relation.
5146 The C<isl_access_info_free> function should usually not be
5147 called explicitly, because it is called implicitly by
5148 C<isl_access_info_compute_flow>.
5150 The result of the dependence analysis is collected in an
5151 C<isl_flow>. There may be elements of
5152 the sink access for which no preceding source access could be
5153 found or for which all preceding sources are I<may> accesses.
5154 The relations containing these elements can be obtained through
5155 calls to C<isl_flow_get_no_source>, the first with C<must> set
5156 and the second with C<must> unset.
5157 In the case of standard flow dependence analysis,
5158 with the sink a read and the sources I<must> writes,
5159 the first relation corresponds to the reads from uninitialized
5160 array elements and the second relation is empty.
5161 The actual flow dependences can be extracted using
5162 C<isl_flow_foreach>. This function will call the user-specified
5163 callback function C<fn> for each B<non-empty> dependence between
5164 a source and the sink. The callback function is called
5165 with four arguments, the actual flow dependence relation
5166 mapping source iterations to sink iterations, a boolean that
5167 indicates whether it is a I<must> or I<may> dependence, a token
5168 identifying the source and an additional C<void *> with value
5169 equal to the third argument of the C<isl_flow_foreach> call.
5170 A dependence is marked I<must> if it originates from a I<must>
5171 source and if it is not followed by any I<may> sources.
5173 After finishing with an C<isl_flow>, the user should call
5174 C<isl_flow_free> to free all associated memory.
5176 A higher-level interface to dependence analysis is provided
5177 by the following function.
5179 #include <isl/flow.h>
5181 int isl_union_map_compute_flow(__isl_take isl_union_map *sink,
5182 __isl_take isl_union_map *must_source,
5183 __isl_take isl_union_map *may_source,
5184 __isl_take isl_union_map *schedule,
5185 __isl_give isl_union_map **must_dep,
5186 __isl_give isl_union_map **may_dep,
5187 __isl_give isl_union_map **must_no_source,
5188 __isl_give isl_union_map **may_no_source);
5190 The arrays are identified by the tuple names of the ranges
5191 of the accesses. The iteration domains by the tuple names
5192 of the domains of the accesses and of the schedule.
5193 The relative order of the iteration domains is given by the
5194 schedule. The relations returned through C<must_no_source>
5195 and C<may_no_source> are subsets of C<sink>.
5196 Any of C<must_dep>, C<may_dep>, C<must_no_source>
5197 or C<may_no_source> may be C<NULL>, but a C<NULL> value for
5198 any of the other arguments is treated as an error.
5200 =head3 Interaction with Dependence Analysis
5202 During the dependence analysis, we frequently need to perform
5203 the following operation. Given a relation between sink iterations
5204 and potential source iterations from a particular source domain,
5205 what is the last potential source iteration corresponding to each
5206 sink iteration. It can sometimes be convenient to adjust
5207 the set of potential source iterations before or after each such operation.
5208 The prototypical example is fuzzy array dataflow analysis,
5209 where we need to analyze if, based on data-dependent constraints,
5210 the sink iteration can ever be executed without one or more of
5211 the corresponding potential source iterations being executed.
5212 If so, we can introduce extra parameters and select an unknown
5213 but fixed source iteration from the potential source iterations.
5214 To be able to perform such manipulations, C<isl> provides the following
5217 #include <isl/flow.h>
5219 typedef __isl_give isl_restriction *(*isl_access_restrict)(
5220 __isl_keep isl_map *source_map,
5221 __isl_keep isl_set *sink, void *source_user,
5223 __isl_give isl_access_info *isl_access_info_set_restrict(
5224 __isl_take isl_access_info *acc,
5225 isl_access_restrict fn, void *user);
5227 The function C<isl_access_info_set_restrict> should be called
5228 before calling C<isl_access_info_compute_flow> and registers a callback function
5229 that will be called any time C<isl> is about to compute the last
5230 potential source. The first argument is the (reverse) proto-dependence,
5231 mapping sink iterations to potential source iterations.
5232 The second argument represents the sink iterations for which
5233 we want to compute the last source iteration.
5234 The third argument is the token corresponding to the source
5235 and the final argument is the token passed to C<isl_access_info_set_restrict>.
5236 The callback is expected to return a restriction on either the input or
5237 the output of the operation computing the last potential source.
5238 If the input needs to be restricted then restrictions are needed
5239 for both the source and the sink iterations. The sink iterations
5240 and the potential source iterations will be intersected with these sets.
5241 If the output needs to be restricted then only a restriction on the source
5242 iterations is required.
5243 If any error occurs, the callback should return C<NULL>.
5244 An C<isl_restriction> object can be created, freed and inspected
5245 using the following functions.
5247 #include <isl/flow.h>
5249 __isl_give isl_restriction *isl_restriction_input(
5250 __isl_take isl_set *source_restr,
5251 __isl_take isl_set *sink_restr);
5252 __isl_give isl_restriction *isl_restriction_output(
5253 __isl_take isl_set *source_restr);
5254 __isl_give isl_restriction *isl_restriction_none(
5255 __isl_take isl_map *source_map);
5256 __isl_give isl_restriction *isl_restriction_empty(
5257 __isl_take isl_map *source_map);
5258 void *isl_restriction_free(
5259 __isl_take isl_restriction *restr);
5260 isl_ctx *isl_restriction_get_ctx(
5261 __isl_keep isl_restriction *restr);
5263 C<isl_restriction_none> and C<isl_restriction_empty> are special
5264 cases of C<isl_restriction_input>. C<isl_restriction_none>
5265 is essentially equivalent to
5267 isl_restriction_input(isl_set_universe(
5268 isl_space_range(isl_map_get_space(source_map))),
5270 isl_space_domain(isl_map_get_space(source_map))));
5272 whereas C<isl_restriction_empty> is essentially equivalent to
5274 isl_restriction_input(isl_set_empty(
5275 isl_space_range(isl_map_get_space(source_map))),
5277 isl_space_domain(isl_map_get_space(source_map))));
5281 B<The functionality described in this section is fairly new
5282 and may be subject to change.>
5284 The following function can be used to compute a schedule
5285 for a union of domains.
5286 By default, the algorithm used to construct the schedule is similar
5287 to that of C<Pluto>.
5288 Alternatively, Feautrier's multi-dimensional scheduling algorithm can
5290 The generated schedule respects all C<validity> dependences.
5291 That is, all dependence distances over these dependences in the
5292 scheduled space are lexicographically positive.
5293 The default algorithm tries to minimize the dependence distances over
5294 C<proximity> dependences.
5295 Moreover, it tries to obtain sequences (bands) of schedule dimensions
5296 for groups of domains where the dependence distances have only
5297 non-negative values.
5298 When using Feautrier's algorithm, the C<proximity> dependence
5299 distances are only minimized during the extension to a
5300 full-dimensional schedule.
5302 #include <isl/schedule.h>
5303 __isl_give isl_schedule *isl_union_set_compute_schedule(
5304 __isl_take isl_union_set *domain,
5305 __isl_take isl_union_map *validity,
5306 __isl_take isl_union_map *proximity);
5307 void *isl_schedule_free(__isl_take isl_schedule *sched);
5309 A mapping from the domains to the scheduled space can be obtained
5310 from an C<isl_schedule> using the following function.
5312 __isl_give isl_union_map *isl_schedule_get_map(
5313 __isl_keep isl_schedule *sched);
5315 A representation of the schedule can be printed using
5317 __isl_give isl_printer *isl_printer_print_schedule(
5318 __isl_take isl_printer *p,
5319 __isl_keep isl_schedule *schedule);
5321 A representation of the schedule as a forest of bands can be obtained
5322 using the following function.
5324 __isl_give isl_band_list *isl_schedule_get_band_forest(
5325 __isl_keep isl_schedule *schedule);
5327 The individual bands can be visited in depth-first post-order
5328 using the following function.
5330 #include <isl/schedule.h>
5331 int isl_schedule_foreach_band(
5332 __isl_keep isl_schedule *sched,
5333 int (*fn)(__isl_keep isl_band *band, void *user),
5336 The list can be manipulated as explained in L<"Lists">.
5337 The bands inside the list can be copied and freed using the following
5340 #include <isl/band.h>
5341 __isl_give isl_band *isl_band_copy(
5342 __isl_keep isl_band *band);
5343 void *isl_band_free(__isl_take isl_band *band);
5345 Each band contains zero or more scheduling dimensions.
5346 These are referred to as the members of the band.
5347 The section of the schedule that corresponds to the band is
5348 referred to as the partial schedule of the band.
5349 For those nodes that participate in a band, the outer scheduling
5350 dimensions form the prefix schedule, while the inner scheduling
5351 dimensions form the suffix schedule.
5352 That is, if we take a cut of the band forest, then the union of
5353 the concatenations of the prefix, partial and suffix schedules of
5354 each band in the cut is equal to the entire schedule (modulo
5355 some possible padding at the end with zero scheduling dimensions).
5356 The properties of a band can be inspected using the following functions.
5358 #include <isl/band.h>
5359 isl_ctx *isl_band_get_ctx(__isl_keep isl_band *band);
5361 int isl_band_has_children(__isl_keep isl_band *band);
5362 __isl_give isl_band_list *isl_band_get_children(
5363 __isl_keep isl_band *band);
5365 __isl_give isl_union_map *isl_band_get_prefix_schedule(
5366 __isl_keep isl_band *band);
5367 __isl_give isl_union_map *isl_band_get_partial_schedule(
5368 __isl_keep isl_band *band);
5369 __isl_give isl_union_map *isl_band_get_suffix_schedule(
5370 __isl_keep isl_band *band);
5372 int isl_band_n_member(__isl_keep isl_band *band);
5373 int isl_band_member_is_zero_distance(
5374 __isl_keep isl_band *band, int pos);
5376 int isl_band_list_foreach_band(
5377 __isl_keep isl_band_list *list,
5378 int (*fn)(__isl_keep isl_band *band, void *user),
5381 Note that a scheduling dimension is considered to be ``zero
5382 distance'' if it does not carry any proximity dependences
5384 That is, if the dependence distances of the proximity
5385 dependences are all zero in that direction (for fixed
5386 iterations of outer bands).
5387 Like C<isl_schedule_foreach_band>,
5388 the function C<isl_band_list_foreach_band> calls C<fn> on the bands
5389 in depth-first post-order.
5391 A band can be tiled using the following function.
5393 #include <isl/band.h>
5394 int isl_band_tile(__isl_keep isl_band *band,
5395 __isl_take isl_vec *sizes);
5397 int isl_options_set_tile_scale_tile_loops(isl_ctx *ctx,
5399 int isl_options_get_tile_scale_tile_loops(isl_ctx *ctx);
5400 int isl_options_set_tile_shift_point_loops(isl_ctx *ctx,
5402 int isl_options_get_tile_shift_point_loops(isl_ctx *ctx);
5404 The C<isl_band_tile> function tiles the band using the given tile sizes
5405 inside its schedule.
5406 A new child band is created to represent the point loops and it is
5407 inserted between the modified band and its children.
5408 The C<tile_scale_tile_loops> option specifies whether the tile
5409 loops iterators should be scaled by the tile sizes.
5410 If the C<tile_shift_point_loops> option is set, then the point loops
5411 are shifted to start at zero.
5413 A band can be split into two nested bands using the following function.
5415 int isl_band_split(__isl_keep isl_band *band, int pos);
5417 The resulting outer band contains the first C<pos> dimensions of C<band>
5418 while the inner band contains the remaining dimensions.
5420 A representation of the band can be printed using
5422 #include <isl/band.h>
5423 __isl_give isl_printer *isl_printer_print_band(
5424 __isl_take isl_printer *p,
5425 __isl_keep isl_band *band);
5429 #include <isl/schedule.h>
5430 int isl_options_set_schedule_max_coefficient(
5431 isl_ctx *ctx, int val);
5432 int isl_options_get_schedule_max_coefficient(
5434 int isl_options_set_schedule_max_constant_term(
5435 isl_ctx *ctx, int val);
5436 int isl_options_get_schedule_max_constant_term(
5438 int isl_options_set_schedule_fuse(isl_ctx *ctx, int val);
5439 int isl_options_get_schedule_fuse(isl_ctx *ctx);
5440 int isl_options_set_schedule_maximize_band_depth(
5441 isl_ctx *ctx, int val);
5442 int isl_options_get_schedule_maximize_band_depth(
5444 int isl_options_set_schedule_outer_zero_distance(
5445 isl_ctx *ctx, int val);
5446 int isl_options_get_schedule_outer_zero_distance(
5448 int isl_options_set_schedule_split_scaled(
5449 isl_ctx *ctx, int val);
5450 int isl_options_get_schedule_split_scaled(
5452 int isl_options_set_schedule_algorithm(
5453 isl_ctx *ctx, int val);
5454 int isl_options_get_schedule_algorithm(
5456 int isl_options_set_schedule_separate_components(
5457 isl_ctx *ctx, int val);
5458 int isl_options_get_schedule_separate_components(
5463 =item * schedule_max_coefficient
5465 This option enforces that the coefficients for variable and parameter
5466 dimensions in the calculated schedule are not larger than the specified value.
5467 This option can significantly increase the speed of the scheduling calculation
5468 and may also prevent fusing of unrelated dimensions. A value of -1 means that
5469 this option does not introduce bounds on the variable or parameter
5472 =item * schedule_max_constant_term
5474 This option enforces that the constant coefficients in the calculated schedule
5475 are not larger than the maximal constant term. This option can significantly
5476 increase the speed of the scheduling calculation and may also prevent fusing of
5477 unrelated dimensions. A value of -1 means that this option does not introduce
5478 bounds on the constant coefficients.
5480 =item * schedule_fuse
5482 This option controls the level of fusion.
5483 If this option is set to C<ISL_SCHEDULE_FUSE_MIN>, then loops in the
5484 resulting schedule will be distributed as much as possible.
5485 If this option is set to C<ISL_SCHEDULE_FUSE_MAX>, then C<isl> will
5486 try to fuse loops in the resulting schedule.
5488 =item * schedule_maximize_band_depth
5490 If this option is set, we do not split bands at the point
5491 where we detect splitting is necessary. Instead, we
5492 backtrack and split bands as early as possible. This
5493 reduces the number of splits and maximizes the width of
5494 the bands. Wider bands give more possibilities for tiling.
5495 Note that if the C<schedule_fuse> option is set to C<ISL_SCHEDULE_FUSE_MIN>,
5496 then bands will be split as early as possible, even if there is no need.
5497 The C<schedule_maximize_band_depth> option therefore has no effect in this case.
5499 =item * schedule_outer_zero_distance
5501 If this option is set, then we try to construct schedules
5502 where the outermost scheduling dimension in each band
5503 results in a zero dependence distance over the proximity
5506 =item * schedule_split_scaled
5508 If this option is set, then we try to construct schedules in which the
5509 constant term is split off from the linear part if the linear parts of
5510 the scheduling rows for all nodes in the graphs have a common non-trivial
5512 The constant term is then placed in a separate band and the linear
5515 =item * schedule_algorithm
5517 Selects the scheduling algorithm to be used.
5518 Available scheduling algorithms are C<ISL_SCHEDULE_ALGORITHM_ISL>
5519 and C<ISL_SCHEDULE_ALGORITHM_FEAUTRIER>.
5521 =item * schedule_separate_components
5523 If at any point the dependence graph contains any (weakly connected) components,
5524 then these components are scheduled separately.
5525 If this option is not set, then some iterations of the domains
5526 in these components may be scheduled together.
5527 If this option is set, then the components are given consecutive
5532 =head2 AST Generation
5534 This section describes the C<isl> functionality for generating
5535 ASTs that visit all the elements
5536 in a domain in an order specified by a schedule.
5537 In particular, given a C<isl_union_map>, an AST is generated
5538 that visits all the elements in the domain of the C<isl_union_map>
5539 according to the lexicographic order of the corresponding image
5540 element(s). If the range of the C<isl_union_map> consists of
5541 elements in more than one space, then each of these spaces is handled
5542 separately in an arbitrary order.
5543 It should be noted that the image elements only specify the I<order>
5544 in which the corresponding domain elements should be visited.
5545 No direct relation between the image elements and the loop iterators
5546 in the generated AST should be assumed.
5548 Each AST is generated within a build. The initial build
5549 simply specifies the constraints on the parameters (if any)
5550 and can be created, inspected, copied and freed using the following functions.
5552 #include <isl/ast_build.h>
5553 __isl_give isl_ast_build *isl_ast_build_from_context(
5554 __isl_take isl_set *set);
5555 isl_ctx *isl_ast_build_get_ctx(
5556 __isl_keep isl_ast_build *build);
5557 __isl_give isl_ast_build *isl_ast_build_copy(
5558 __isl_keep isl_ast_build *build);
5559 void *isl_ast_build_free(
5560 __isl_take isl_ast_build *build);
5562 The C<set> argument is usually a parameter set with zero or more parameters.
5563 More C<isl_ast_build> functions are described in L</"Nested AST Generation">
5564 and L</"Fine-grained Control over AST Generation">.
5565 Finally, the AST itself can be constructed using the following
5568 #include <isl/ast_build.h>
5569 __isl_give isl_ast_node *isl_ast_build_ast_from_schedule(
5570 __isl_keep isl_ast_build *build,
5571 __isl_take isl_union_map *schedule);
5573 =head3 Inspecting the AST
5575 The basic properties of an AST node can be obtained as follows.
5577 #include <isl/ast.h>
5578 isl_ctx *isl_ast_node_get_ctx(
5579 __isl_keep isl_ast_node *node);
5580 enum isl_ast_node_type isl_ast_node_get_type(
5581 __isl_keep isl_ast_node *node);
5583 The type of an AST node is one of
5584 C<isl_ast_node_for>,
5586 C<isl_ast_node_block> or
5587 C<isl_ast_node_user>.
5588 An C<isl_ast_node_for> represents a for node.
5589 An C<isl_ast_node_if> represents an if node.
5590 An C<isl_ast_node_block> represents a compound node.
5591 An C<isl_ast_node_user> represents an expression statement.
5592 An expression statement typically corresponds to a domain element, i.e.,
5593 one of the elements that is visited by the AST.
5595 Each type of node has its own additional properties.
5597 #include <isl/ast.h>
5598 __isl_give isl_ast_expr *isl_ast_node_for_get_iterator(
5599 __isl_keep isl_ast_node *node);
5600 __isl_give isl_ast_expr *isl_ast_node_for_get_init(
5601 __isl_keep isl_ast_node *node);
5602 __isl_give isl_ast_expr *isl_ast_node_for_get_cond(
5603 __isl_keep isl_ast_node *node);
5604 __isl_give isl_ast_expr *isl_ast_node_for_get_inc(
5605 __isl_keep isl_ast_node *node);
5606 __isl_give isl_ast_node *isl_ast_node_for_get_body(
5607 __isl_keep isl_ast_node *node);
5608 int isl_ast_node_for_is_degenerate(
5609 __isl_keep isl_ast_node *node);
5611 An C<isl_ast_for> is considered degenerate if it is known to execute
5614 #include <isl/ast.h>
5615 __isl_give isl_ast_expr *isl_ast_node_if_get_cond(
5616 __isl_keep isl_ast_node *node);
5617 __isl_give isl_ast_node *isl_ast_node_if_get_then(
5618 __isl_keep isl_ast_node *node);
5619 int isl_ast_node_if_has_else(
5620 __isl_keep isl_ast_node *node);
5621 __isl_give isl_ast_node *isl_ast_node_if_get_else(
5622 __isl_keep isl_ast_node *node);
5624 __isl_give isl_ast_node_list *
5625 isl_ast_node_block_get_children(
5626 __isl_keep isl_ast_node *node);
5628 __isl_give isl_ast_expr *isl_ast_node_user_get_expr(
5629 __isl_keep isl_ast_node *node);
5631 Each of the returned C<isl_ast_expr>s can in turn be inspected using
5632 the following functions.
5634 #include <isl/ast.h>
5635 isl_ctx *isl_ast_expr_get_ctx(
5636 __isl_keep isl_ast_expr *expr);
5637 enum isl_ast_expr_type isl_ast_expr_get_type(
5638 __isl_keep isl_ast_expr *expr);
5640 The type of an AST expression is one of
5642 C<isl_ast_expr_id> or
5643 C<isl_ast_expr_int>.
5644 An C<isl_ast_expr_op> represents the result of an operation.
5645 An C<isl_ast_expr_id> represents an identifier.
5646 An C<isl_ast_expr_int> represents an integer value.
5648 Each type of expression has its own additional properties.
5650 #include <isl/ast.h>
5651 enum isl_ast_op_type isl_ast_expr_get_op_type(
5652 __isl_keep isl_ast_expr *expr);
5653 int isl_ast_expr_get_op_n_arg(__isl_keep isl_ast_expr *expr);
5654 __isl_give isl_ast_expr *isl_ast_expr_get_op_arg(
5655 __isl_keep isl_ast_expr *expr, int pos);
5656 int isl_ast_node_foreach_ast_op_type(
5657 __isl_keep isl_ast_node *node,
5658 int (*fn)(enum isl_ast_op_type type, void *user),
5661 C<isl_ast_expr_get_op_type> returns the type of the operation
5662 performed. C<isl_ast_expr_get_op_n_arg> returns the number of
5663 arguments. C<isl_ast_expr_get_op_arg> returns the specified
5665 C<isl_ast_node_foreach_ast_op_type> calls C<fn> for each distinct
5666 C<isl_ast_op_type> that appears in C<node>.
5667 The operation type is one of the following.
5671 =item C<isl_ast_op_and>
5673 Logical I<and> of two arguments.
5674 Both arguments can be evaluated.
5676 =item C<isl_ast_op_and_then>
5678 Logical I<and> of two arguments.
5679 The second argument can only be evaluated if the first evaluates to true.
5681 =item C<isl_ast_op_or>
5683 Logical I<or> of two arguments.
5684 Both arguments can be evaluated.
5686 =item C<isl_ast_op_or_else>
5688 Logical I<or> of two arguments.
5689 The second argument can only be evaluated if the first evaluates to false.
5691 =item C<isl_ast_op_max>
5693 Maximum of two or more arguments.
5695 =item C<isl_ast_op_min>
5697 Minimum of two or more arguments.
5699 =item C<isl_ast_op_minus>
5703 =item C<isl_ast_op_add>
5705 Sum of two arguments.
5707 =item C<isl_ast_op_sub>
5709 Difference of two arguments.
5711 =item C<isl_ast_op_mul>
5713 Product of two arguments.
5715 =item C<isl_ast_op_div>
5717 Exact division. That is, the result is known to be an integer.
5719 =item C<isl_ast_op_fdiv_q>
5721 Result of integer division, rounded towards negative
5724 =item C<isl_ast_op_pdiv_q>
5726 Result of integer division, where dividend is known to be non-negative.
5728 =item C<isl_ast_op_pdiv_r>
5730 Remainder of integer division, where dividend is known to be non-negative.
5732 =item C<isl_ast_op_cond>
5734 Conditional operator defined on three arguments.
5735 If the first argument evaluates to true, then the result
5736 is equal to the second argument. Otherwise, the result
5737 is equal to the third argument.
5738 The second and third argument may only be evaluated if
5739 the first argument evaluates to true and false, respectively.
5740 Corresponds to C<a ? b : c> in C.
5742 =item C<isl_ast_op_select>
5744 Conditional operator defined on three arguments.
5745 If the first argument evaluates to true, then the result
5746 is equal to the second argument. Otherwise, the result
5747 is equal to the third argument.
5748 The second and third argument may be evaluated independently
5749 of the value of the first argument.
5750 Corresponds to C<a * b + (1 - a) * c> in C.
5752 =item C<isl_ast_op_eq>
5756 =item C<isl_ast_op_le>
5758 Less than or equal relation.
5760 =item C<isl_ast_op_lt>
5764 =item C<isl_ast_op_ge>
5766 Greater than or equal relation.
5768 =item C<isl_ast_op_gt>
5770 Greater than relation.
5772 =item C<isl_ast_op_call>
5775 The number of arguments of the C<isl_ast_expr> is one more than
5776 the number of arguments in the function call, the first argument
5777 representing the function being called.
5781 #include <isl/ast.h>
5782 __isl_give isl_id *isl_ast_expr_get_id(
5783 __isl_keep isl_ast_expr *expr);
5785 Return the identifier represented by the AST expression.
5787 #include <isl/ast.h>
5788 int isl_ast_expr_get_int(__isl_keep isl_ast_expr *expr,
5791 Return the integer represented by the AST expression.
5792 Note that the integer is returned through the C<v> argument.
5793 The return value of the function itself indicates whether the
5794 operation was performed successfully.
5796 =head3 Manipulating and printing the AST
5798 AST nodes can be copied and freed using the following functions.
5800 #include <isl/ast.h>
5801 __isl_give isl_ast_node *isl_ast_node_copy(
5802 __isl_keep isl_ast_node *node);
5803 void *isl_ast_node_free(__isl_take isl_ast_node *node);
5805 AST expressions can be copied and freed using the following functions.
5807 #include <isl/ast.h>
5808 __isl_give isl_ast_expr *isl_ast_expr_copy(
5809 __isl_keep isl_ast_expr *expr);
5810 void *isl_ast_expr_free(__isl_take isl_ast_expr *expr);
5812 New AST expressions can be created either directly or within
5813 the context of an C<isl_ast_build>.
5815 #include <isl/ast.h>
5816 __isl_give isl_ast_expr *isl_ast_expr_from_id(
5817 __isl_take isl_id *id);
5818 __isl_give isl_ast_expr *isl_ast_expr_neg(
5819 __isl_take isl_ast_expr *expr);
5820 __isl_give isl_ast_expr *isl_ast_expr_add(
5821 __isl_take isl_ast_expr *expr1,
5822 __isl_take isl_ast_expr *expr2);
5823 __isl_give isl_ast_expr *isl_ast_expr_sub(
5824 __isl_take isl_ast_expr *expr1,
5825 __isl_take isl_ast_expr *expr2);
5826 __isl_give isl_ast_expr *isl_ast_expr_mul(
5827 __isl_take isl_ast_expr *expr1,
5828 __isl_take isl_ast_expr *expr2);
5829 __isl_give isl_ast_expr *isl_ast_expr_div(
5830 __isl_take isl_ast_expr *expr1,
5831 __isl_take isl_ast_expr *expr2);
5832 __isl_give isl_ast_expr *isl_ast_expr_and(
5833 __isl_take isl_ast_expr *expr1,
5834 __isl_take isl_ast_expr *expr2)
5835 __isl_give isl_ast_expr *isl_ast_expr_or(
5836 __isl_take isl_ast_expr *expr1,
5837 __isl_take isl_ast_expr *expr2)
5839 #include <isl/ast_build.h>
5840 __isl_give isl_ast_expr *isl_ast_build_expr_from_pw_aff(
5841 __isl_keep isl_ast_build *build,
5842 __isl_take isl_pw_aff *pa);
5843 __isl_give isl_ast_expr *
5844 isl_ast_build_call_from_pw_multi_aff(
5845 __isl_keep isl_ast_build *build,
5846 __isl_take isl_pw_multi_aff *pma);
5848 The domains of C<pa> and C<pma> should correspond
5849 to the schedule space of C<build>.
5850 The tuple id of C<pma> is used as the function being called.
5852 User specified data can be attached to an C<isl_ast_node> and obtained
5853 from the same C<isl_ast_node> using the following functions.
5855 #include <isl/ast.h>
5856 __isl_give isl_ast_node *isl_ast_node_set_annotation(
5857 __isl_take isl_ast_node *node,
5858 __isl_take isl_id *annotation);
5859 __isl_give isl_id *isl_ast_node_get_annotation(
5860 __isl_keep isl_ast_node *node);
5862 Basic printing can be performed using the following functions.
5864 #include <isl/ast.h>
5865 __isl_give isl_printer *isl_printer_print_ast_expr(
5866 __isl_take isl_printer *p,
5867 __isl_keep isl_ast_expr *expr);
5868 __isl_give isl_printer *isl_printer_print_ast_node(
5869 __isl_take isl_printer *p,
5870 __isl_keep isl_ast_node *node);
5872 More advanced printing can be performed using the following functions.
5874 #include <isl/ast.h>
5875 __isl_give isl_printer *isl_ast_op_type_print_macro(
5876 enum isl_ast_op_type type,
5877 __isl_take isl_printer *p);
5878 __isl_give isl_printer *isl_ast_node_print_macros(
5879 __isl_keep isl_ast_node *node,
5880 __isl_take isl_printer *p);
5881 __isl_give isl_printer *isl_ast_node_print(
5882 __isl_keep isl_ast_node *node,
5883 __isl_take isl_printer *p,
5884 __isl_take isl_ast_print_options *options);
5885 __isl_give isl_printer *isl_ast_node_for_print(
5886 __isl_keep isl_ast_node *node,
5887 __isl_take isl_printer *p,
5888 __isl_take isl_ast_print_options *options);
5889 __isl_give isl_printer *isl_ast_node_if_print(
5890 __isl_keep isl_ast_node *node,
5891 __isl_take isl_printer *p,
5892 __isl_take isl_ast_print_options *options);
5894 While printing an C<isl_ast_node> in C<ISL_FORMAT_C>,
5895 C<isl> may print out an AST that makes use of macros such
5896 as C<floord>, C<min> and C<max>.
5897 C<isl_ast_op_type_print_macro> prints out the macro
5898 corresponding to a specific C<isl_ast_op_type>.
5899 C<isl_ast_node_print_macros> scans the C<isl_ast_node>
5900 for expressions where these macros would be used and prints
5901 out the required macro definitions.
5902 Essentially, C<isl_ast_node_print_macros> calls
5903 C<isl_ast_node_foreach_ast_op_type> with C<isl_ast_op_type_print_macro>
5904 as function argument.
5905 C<isl_ast_node_print>, C<isl_ast_node_for_print> and
5906 C<isl_ast_node_if_print> print an C<isl_ast_node>
5907 in C<ISL_FORMAT_C>, but allow for some extra control
5908 through an C<isl_ast_print_options> object.
5909 This object can be created using the following functions.
5911 #include <isl/ast.h>
5912 __isl_give isl_ast_print_options *
5913 isl_ast_print_options_alloc(isl_ctx *ctx);
5914 __isl_give isl_ast_print_options *
5915 isl_ast_print_options_copy(
5916 __isl_keep isl_ast_print_options *options);
5917 void *isl_ast_print_options_free(
5918 __isl_take isl_ast_print_options *options);
5920 __isl_give isl_ast_print_options *
5921 isl_ast_print_options_set_print_user(
5922 __isl_take isl_ast_print_options *options,
5923 __isl_give isl_printer *(*print_user)(
5924 __isl_take isl_printer *p,
5925 __isl_take isl_ast_print_options *options,
5926 __isl_keep isl_ast_node *node, void *user),
5928 __isl_give isl_ast_print_options *
5929 isl_ast_print_options_set_print_for(
5930 __isl_take isl_ast_print_options *options,
5931 __isl_give isl_printer *(*print_for)(
5932 __isl_take isl_printer *p,
5933 __isl_take isl_ast_print_options *options,
5934 __isl_keep isl_ast_node *node, void *user),
5937 The callback set by C<isl_ast_print_options_set_print_user>
5938 is called whenever a node of type C<isl_ast_node_user> needs to
5940 The callback set by C<isl_ast_print_options_set_print_for>
5941 is called whenever a node of type C<isl_ast_node_for> needs to
5943 Note that C<isl_ast_node_for_print> will I<not> call the
5944 callback set by C<isl_ast_print_options_set_print_for> on the node
5945 on which C<isl_ast_node_for_print> is called, but only on nested
5946 nodes of type C<isl_ast_node_for>. It is therefore safe to
5947 call C<isl_ast_node_for_print> from within the callback set by
5948 C<isl_ast_print_options_set_print_for>.
5950 The following option determines the type to be used for iterators
5951 while printing the AST.
5953 int isl_options_set_ast_iterator_type(
5954 isl_ctx *ctx, const char *val);
5955 const char *isl_options_get_ast_iterator_type(
5960 #include <isl/ast_build.h>
5961 int isl_options_set_ast_build_atomic_upper_bound(
5962 isl_ctx *ctx, int val);
5963 int isl_options_get_ast_build_atomic_upper_bound(
5965 int isl_options_set_ast_build_prefer_pdiv(isl_ctx *ctx,
5967 int isl_options_get_ast_build_prefer_pdiv(isl_ctx *ctx);
5968 int isl_options_set_ast_build_exploit_nested_bounds(
5969 isl_ctx *ctx, int val);
5970 int isl_options_get_ast_build_exploit_nested_bounds(
5972 int isl_options_set_ast_build_group_coscheduled(
5973 isl_ctx *ctx, int val);
5974 int isl_options_get_ast_build_group_coscheduled(
5976 int isl_options_set_ast_build_scale_strides(
5977 isl_ctx *ctx, int val);
5978 int isl_options_get_ast_build_scale_strides(
5980 int isl_options_set_ast_build_allow_else(isl_ctx *ctx,
5982 int isl_options_get_ast_build_allow_else(isl_ctx *ctx);
5983 int isl_options_set_ast_build_allow_or(isl_ctx *ctx,
5985 int isl_options_get_ast_build_allow_or(isl_ctx *ctx);
5989 =item * ast_build_atomic_upper_bound
5991 Generate loop upper bounds that consist of the current loop iterator,
5992 an operator and an expression not involving the iterator.
5993 If this option is not set, then the current loop iterator may appear
5994 several times in the upper bound.
5995 For example, when this option is turned off, AST generation
5998 [n] -> { A[i] -> [i] : 0 <= i <= 100, n }
6002 for (int c0 = 0; c0 <= 100 && n >= c0; c0 += 1)
6005 When the option is turned on, the following AST is generated
6007 for (int c0 = 0; c0 <= min(100, n); c0 += 1)
6010 =item * ast_build_prefer_pdiv
6012 If this option is turned off, then the AST generation will
6013 produce ASTs that may only contain C<isl_ast_op_fdiv_q>
6014 operators, but no C<isl_ast_op_pdiv_q> or
6015 C<isl_ast_op_pdiv_r> operators.
6016 If this options is turned on, then C<isl> will try to convert
6017 some of the C<isl_ast_op_fdiv_q> operators to (expressions containing)
6018 C<isl_ast_op_pdiv_q> or C<isl_ast_op_pdiv_r> operators.
6020 =item * ast_build_exploit_nested_bounds
6022 Simplify conditions based on bounds of nested for loops.
6023 In particular, remove conditions that are implied by the fact
6024 that one or more nested loops have at least one iteration,
6025 meaning that the upper bound is at least as large as the lower bound.
6026 For example, when this option is turned off, AST generation
6029 [N,M] -> { A[i,j] -> [i,j] : 0 <= i <= N and
6035 for (int c0 = 0; c0 <= N; c0 += 1)
6036 for (int c1 = 0; c1 <= M; c1 += 1)
6039 When the option is turned on, the following AST is generated
6041 for (int c0 = 0; c0 <= N; c0 += 1)
6042 for (int c1 = 0; c1 <= M; c1 += 1)
6045 =item * ast_build_group_coscheduled
6047 If two domain elements are assigned the same schedule point, then
6048 they may be executed in any order and they may even appear in different
6049 loops. If this options is set, then the AST generator will make
6050 sure that coscheduled domain elements do not appear in separate parts
6051 of the AST. This is useful in case of nested AST generation
6052 if the outer AST generation is given only part of a schedule
6053 and the inner AST generation should handle the domains that are
6054 coscheduled by this initial part of the schedule together.
6055 For example if an AST is generated for a schedule
6057 { A[i] -> [0]; B[i] -> [0] }
6059 then the C<isl_ast_build_set_create_leaf> callback described
6060 below may get called twice, once for each domain.
6061 Setting this option ensures that the callback is only called once
6062 on both domains together.
6064 =item * ast_build_separation_bounds
6066 This option specifies which bounds to use during separation.
6067 If this option is set to C<ISL_AST_BUILD_SEPARATION_BOUNDS_IMPLICIT>
6068 then all (possibly implicit) bounds on the current dimension will
6069 be used during separation.
6070 If this option is set to C<ISL_AST_BUILD_SEPARATION_BOUNDS_EXPLICIT>
6071 then only those bounds that are explicitly available will
6072 be used during separation.
6074 =item * ast_build_scale_strides
6076 This option specifies whether the AST generator is allowed
6077 to scale down iterators of strided loops.
6079 =item * ast_build_allow_else
6081 This option specifies whether the AST generator is allowed
6082 to construct if statements with else branches.
6084 =item * ast_build_allow_or
6086 This option specifies whether the AST generator is allowed
6087 to construct if conditions with disjunctions.
6091 =head3 Fine-grained Control over AST Generation
6093 Besides specifying the constraints on the parameters,
6094 an C<isl_ast_build> object can be used to control
6095 various aspects of the AST generation process.
6096 The most prominent way of control is through ``options'',
6097 which can be set using the following function.
6099 #include <isl/ast_build.h>
6100 __isl_give isl_ast_build *
6101 isl_ast_build_set_options(
6102 __isl_take isl_ast_build *control,
6103 __isl_take isl_union_map *options);
6105 The options are encoded in an <isl_union_map>.
6106 The domain of this union relation refers to the schedule domain,
6107 i.e., the range of the schedule passed to C<isl_ast_build_ast_from_schedule>.
6108 In the case of nested AST generation (see L</"Nested AST Generation">),
6109 the domain of C<options> should refer to the extra piece of the schedule.
6110 That is, it should be equal to the range of the wrapped relation in the
6111 range of the schedule.
6112 The range of the options can consist of elements in one or more spaces,
6113 the names of which determine the effect of the option.
6114 The values of the range typically also refer to the schedule dimension
6115 to which the option applies. In case of nested AST generation
6116 (see L</"Nested AST Generation">), these values refer to the position
6117 of the schedule dimension within the innermost AST generation.
6118 The constraints on the domain elements of
6119 the option should only refer to this dimension and earlier dimensions.
6120 We consider the following spaces.
6124 =item C<separation_class>
6126 This space is a wrapped relation between two one dimensional spaces.
6127 The input space represents the schedule dimension to which the option
6128 applies and the output space represents the separation class.
6129 While constructing a loop corresponding to the specified schedule
6130 dimension(s), the AST generator will try to generate separate loops
6131 for domain elements that are assigned different classes.
6132 If only some of the elements are assigned a class, then those elements
6133 that are not assigned any class will be treated as belonging to a class
6134 that is separate from the explicitly assigned classes.
6135 The typical use case for this option is to separate full tiles from
6137 The other options, described below, are applied after the separation
6140 As an example, consider the separation into full and partial tiles
6141 of a tiling of a triangular domain.
6142 Take, for example, the domain
6144 { A[i,j] : 0 <= i,j and i + j <= 100 }
6146 and a tiling into tiles of 10 by 10. The input to the AST generator
6147 is then the schedule
6149 { A[i,j] -> [([i/10]),[j/10],i,j] : 0 <= i,j and
6152 Without any options, the following AST is generated
6154 for (int c0 = 0; c0 <= 10; c0 += 1)
6155 for (int c1 = 0; c1 <= -c0 + 10; c1 += 1)
6156 for (int c2 = 10 * c0;
6157 c2 <= min(-10 * c1 + 100, 10 * c0 + 9);
6159 for (int c3 = 10 * c1;
6160 c3 <= min(10 * c1 + 9, -c2 + 100);
6164 Separation into full and partial tiles can be obtained by assigning
6165 a class, say C<0>, to the full tiles. The full tiles are represented by those
6166 values of the first and second schedule dimensions for which there are
6167 values of the third and fourth dimensions to cover an entire tile.
6168 That is, we need to specify the following option
6170 { [a,b,c,d] -> separation_class[[0]->[0]] :
6171 exists b': 0 <= 10a,10b' and
6172 10a+9+10b'+9 <= 100;
6173 [a,b,c,d] -> separation_class[[1]->[0]] :
6174 0 <= 10a,10b and 10a+9+10b+9 <= 100 }
6178 { [a, b, c, d] -> separation_class[[1] -> [0]] :
6179 a >= 0 and b >= 0 and b <= 8 - a;
6180 [a, b, c, d] -> separation_class[[0] -> [0]] :
6183 With this option, the generated AST is as follows
6186 for (int c0 = 0; c0 <= 8; c0 += 1) {
6187 for (int c1 = 0; c1 <= -c0 + 8; c1 += 1)
6188 for (int c2 = 10 * c0;
6189 c2 <= 10 * c0 + 9; c2 += 1)
6190 for (int c3 = 10 * c1;
6191 c3 <= 10 * c1 + 9; c3 += 1)
6193 for (int c1 = -c0 + 9; c1 <= -c0 + 10; c1 += 1)
6194 for (int c2 = 10 * c0;
6195 c2 <= min(-10 * c1 + 100, 10 * c0 + 9);
6197 for (int c3 = 10 * c1;
6198 c3 <= min(-c2 + 100, 10 * c1 + 9);
6202 for (int c0 = 9; c0 <= 10; c0 += 1)
6203 for (int c1 = 0; c1 <= -c0 + 10; c1 += 1)
6204 for (int c2 = 10 * c0;
6205 c2 <= min(-10 * c1 + 100, 10 * c0 + 9);
6207 for (int c3 = 10 * c1;
6208 c3 <= min(10 * c1 + 9, -c2 + 100);
6215 This is a single-dimensional space representing the schedule dimension(s)
6216 to which ``separation'' should be applied. Separation tries to split
6217 a loop into several pieces if this can avoid the generation of guards
6219 See also the C<atomic> option.
6223 This is a single-dimensional space representing the schedule dimension(s)
6224 for which the domains should be considered ``atomic''. That is, the
6225 AST generator will make sure that any given domain space will only appear
6226 in a single loop at the specified level.
6228 Consider the following schedule
6230 { a[i] -> [i] : 0 <= i < 10;
6231 b[i] -> [i+1] : 0 <= i < 10 }
6233 If the following option is specified
6235 { [i] -> separate[x] }
6237 then the following AST will be generated
6241 for (int c0 = 1; c0 <= 9; c0 += 1) {
6248 If, on the other hand, the following option is specified
6250 { [i] -> atomic[x] }
6252 then the following AST will be generated
6254 for (int c0 = 0; c0 <= 10; c0 += 1) {
6261 If neither C<atomic> nor C<separate> is specified, then the AST generator
6262 may produce either of these two results or some intermediate form.
6266 This is a single-dimensional space representing the schedule dimension(s)
6267 that should be I<completely> unrolled.
6268 To obtain a partial unrolling, the user should apply an additional
6269 strip-mining to the schedule and fully unroll the inner loop.
6273 Additional control is available through the following functions.
6275 #include <isl/ast_build.h>
6276 __isl_give isl_ast_build *
6277 isl_ast_build_set_iterators(
6278 __isl_take isl_ast_build *control,
6279 __isl_take isl_id_list *iterators);
6281 The function C<isl_ast_build_set_iterators> allows the user to
6282 specify a list of iterator C<isl_id>s to be used as iterators.
6283 If the input schedule is injective, then
6284 the number of elements in this list should be as large as the dimension
6285 of the schedule space, but no direct correspondence should be assumed
6286 between dimensions and elements.
6287 If the input schedule is not injective, then an additional number
6288 of C<isl_id>s equal to the largest dimension of the input domains
6290 If the number of provided C<isl_id>s is insufficient, then additional
6291 names are automatically generated.
6293 #include <isl/ast_build.h>
6294 __isl_give isl_ast_build *
6295 isl_ast_build_set_create_leaf(
6296 __isl_take isl_ast_build *control,
6297 __isl_give isl_ast_node *(*fn)(
6298 __isl_take isl_ast_build *build,
6299 void *user), void *user);
6302 C<isl_ast_build_set_create_leaf> function allows for the
6303 specification of a callback that should be called whenever the AST
6304 generator arrives at an element of the schedule domain.
6305 The callback should return an AST node that should be inserted
6306 at the corresponding position of the AST. The default action (when
6307 the callback is not set) is to continue generating parts of the AST to scan
6308 all the domain elements associated to the schedule domain element
6309 and to insert user nodes, ``calling'' the domain element, for each of them.
6310 The C<build> argument contains the current state of the C<isl_ast_build>.
6311 To ease nested AST generation (see L</"Nested AST Generation">),
6312 all control information that is
6313 specific to the current AST generation such as the options and
6314 the callbacks has been removed from this C<isl_ast_build>.
6315 The callback would typically return the result of a nested
6317 user defined node created using the following function.
6319 #include <isl/ast.h>
6320 __isl_give isl_ast_node *isl_ast_node_alloc_user(
6321 __isl_take isl_ast_expr *expr);
6323 #include <isl/ast_build.h>
6324 __isl_give isl_ast_build *
6325 isl_ast_build_set_at_each_domain(
6326 __isl_take isl_ast_build *build,
6327 __isl_give isl_ast_node *(*fn)(
6328 __isl_take isl_ast_node *node,
6329 __isl_keep isl_ast_build *build,
6330 void *user), void *user);
6331 __isl_give isl_ast_build *
6332 isl_ast_build_set_before_each_for(
6333 __isl_take isl_ast_build *build,
6334 __isl_give isl_id *(*fn)(
6335 __isl_keep isl_ast_build *build,
6336 void *user), void *user);
6337 __isl_give isl_ast_build *
6338 isl_ast_build_set_after_each_for(
6339 __isl_take isl_ast_build *build,
6340 __isl_give isl_ast_node *(*fn)(
6341 __isl_take isl_ast_node *node,
6342 __isl_keep isl_ast_build *build,
6343 void *user), void *user);
6345 The callback set by C<isl_ast_build_set_at_each_domain> will
6346 be called for each domain AST node.
6347 The callbacks set by C<isl_ast_build_set_before_each_for>
6348 and C<isl_ast_build_set_after_each_for> will be called
6349 for each for AST node. The first will be called in depth-first
6350 pre-order, while the second will be called in depth-first post-order.
6351 Since C<isl_ast_build_set_before_each_for> is called before the for
6352 node is actually constructed, it is only passed an C<isl_ast_build>.
6353 The returned C<isl_id> will be added as an annotation (using
6354 C<isl_ast_node_set_annotation>) to the constructed for node.
6355 In particular, if the user has also specified an C<after_each_for>
6356 callback, then the annotation can be retrieved from the node passed to
6357 that callback using C<isl_ast_node_get_annotation>.
6358 All callbacks should C<NULL> on failure.
6359 The given C<isl_ast_build> can be used to create new
6360 C<isl_ast_expr> objects using C<isl_ast_build_expr_from_pw_aff>
6361 or C<isl_ast_build_call_from_pw_multi_aff>.
6363 =head3 Nested AST Generation
6365 C<isl> allows the user to create an AST within the context
6366 of another AST. These nested ASTs are created using the
6367 same C<isl_ast_build_ast_from_schedule> function that is used to create the
6368 outer AST. The C<build> argument should be an C<isl_ast_build>
6369 passed to a callback set by
6370 C<isl_ast_build_set_create_leaf>.
6371 The space of the range of the C<schedule> argument should refer
6372 to this build. In particular, the space should be a wrapped
6373 relation and the domain of this wrapped relation should be the
6374 same as that of the range of the schedule returned by
6375 C<isl_ast_build_get_schedule> below.
6376 In practice, the new schedule is typically
6377 created by calling C<isl_union_map_range_product> on the old schedule
6378 and some extra piece of the schedule.
6379 The space of the schedule domain is also available from
6380 the C<isl_ast_build>.
6382 #include <isl/ast_build.h>
6383 __isl_give isl_union_map *isl_ast_build_get_schedule(
6384 __isl_keep isl_ast_build *build);
6385 __isl_give isl_space *isl_ast_build_get_schedule_space(
6386 __isl_keep isl_ast_build *build);
6387 __isl_give isl_ast_build *isl_ast_build_restrict(
6388 __isl_take isl_ast_build *build,
6389 __isl_take isl_set *set);
6391 The C<isl_ast_build_get_schedule> function returns a (partial)
6392 schedule for the domains elements for which part of the AST still needs to
6393 be generated in the current build.
6394 In particular, the domain elements are mapped to those iterations of the loops
6395 enclosing the current point of the AST generation inside which
6396 the domain elements are executed.
6397 No direct correspondence between
6398 the input schedule and this schedule should be assumed.
6399 The space obtained from C<isl_ast_build_get_schedule_space> can be used
6400 to create a set for C<isl_ast_build_restrict> to intersect
6401 with the current build. In particular, the set passed to
6402 C<isl_ast_build_restrict> can have additional parameters.
6403 The ids of the set dimensions in the space returned by
6404 C<isl_ast_build_get_schedule_space> correspond to the
6405 iterators of the already generated loops.
6406 The user should not rely on the ids of the output dimensions
6407 of the relations in the union relation returned by
6408 C<isl_ast_build_get_schedule> having any particular value.
6412 Although C<isl> is mainly meant to be used as a library,
6413 it also contains some basic applications that use some
6414 of the functionality of C<isl>.
6415 The input may be specified in either the L<isl format>
6416 or the L<PolyLib format>.
6418 =head2 C<isl_polyhedron_sample>
6420 C<isl_polyhedron_sample> takes a polyhedron as input and prints
6421 an integer element of the polyhedron, if there is any.
6422 The first column in the output is the denominator and is always
6423 equal to 1. If the polyhedron contains no integer points,
6424 then a vector of length zero is printed.
6428 C<isl_pip> takes the same input as the C<example> program
6429 from the C<piplib> distribution, i.e., a set of constraints
6430 on the parameters, a line containing only -1 and finally a set
6431 of constraints on a parametric polyhedron.
6432 The coefficients of the parameters appear in the last columns
6433 (but before the final constant column).
6434 The output is the lexicographic minimum of the parametric polyhedron.
6435 As C<isl> currently does not have its own output format, the output
6436 is just a dump of the internal state.
6438 =head2 C<isl_polyhedron_minimize>
6440 C<isl_polyhedron_minimize> computes the minimum of some linear
6441 or affine objective function over the integer points in a polyhedron.
6442 If an affine objective function
6443 is given, then the constant should appear in the last column.
6445 =head2 C<isl_polytope_scan>
6447 Given a polytope, C<isl_polytope_scan> prints
6448 all integer points in the polytope.
6450 =head2 C<isl_codegen>
6452 Given a schedule, a context set and an options relation,
6453 C<isl_codegen> prints out an AST that scans the domain elements
6454 of the schedule in the order of their image(s) taking into account
6455 the constraints in the context set.