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,
366 __isl_give isl_val *isl_val_int_from_chunks(isl_ctx *ctx,
367 size_t n, size_t size, const void *chunks);
369 The function C<isl_val_int_from_chunks> constructs an C<isl_val>
370 from the C<n> I<digits>, each consisting of C<size> bytes, stored at C<chunks>.
371 The least significant digit is assumed to be stored first.
373 Value objects can be copied and freed using the following functions.
376 __isl_give isl_val *isl_val_copy(__isl_keep isl_val *v);
377 void *isl_val_free(__isl_take isl_val *v);
379 They can be inspected using the following functions.
382 isl_ctx *isl_val_get_ctx(__isl_keep isl_val *val);
383 long isl_val_get_num_si(__isl_keep isl_val *v);
384 long isl_val_get_den_si(__isl_keep isl_val *v);
385 double isl_val_get_d(__isl_keep isl_val *v);
386 size_t isl_val_n_abs_num_chunks(__isl_keep isl_val *v,
388 int isl_val_get_abs_num_chunks(__isl_keep isl_val *v,
389 size_t size, void *chunks);
391 C<isl_val_n_abs_num_chunks> returns the number of I<digits>
392 of C<size> bytes needed to store the absolute value of the
394 C<isl_val_get_abs_num_chunks> stores these digits at C<chunks>,
395 which is assumed to have been preallocated by the caller.
396 The least significant digit is stored first.
397 Note that C<isl_val_get_num_si>, C<isl_val_get_den_si>,
398 C<isl_val_get_d>, C<isl_val_n_abs_num_chunks>
399 and C<isl_val_get_abs_num_chunks> can only be applied to rational values.
401 An C<isl_val> can be modified using the following function.
404 __isl_give isl_val *isl_val_set_si(__isl_take isl_val *v,
407 The following unary properties are defined on C<isl_val>s.
410 int isl_val_sgn(__isl_keep isl_val *v);
411 int isl_val_is_zero(__isl_keep isl_val *v);
412 int isl_val_is_one(__isl_keep isl_val *v);
413 int isl_val_is_negone(__isl_keep isl_val *v);
414 int isl_val_is_nonneg(__isl_keep isl_val *v);
415 int isl_val_is_nonpos(__isl_keep isl_val *v);
416 int isl_val_is_pos(__isl_keep isl_val *v);
417 int isl_val_is_neg(__isl_keep isl_val *v);
418 int isl_val_is_int(__isl_keep isl_val *v);
419 int isl_val_is_rat(__isl_keep isl_val *v);
420 int isl_val_is_nan(__isl_keep isl_val *v);
421 int isl_val_is_infty(__isl_keep isl_val *v);
422 int isl_val_is_neginfty(__isl_keep isl_val *v);
424 Note that the sign of NaN is undefined.
426 The following binary properties are defined on pairs of C<isl_val>s.
429 int isl_val_lt(__isl_keep isl_val *v1,
430 __isl_keep isl_val *v2);
431 int isl_val_le(__isl_keep isl_val *v1,
432 __isl_keep isl_val *v2);
433 int isl_val_gt(__isl_keep isl_val *v1,
434 __isl_keep isl_val *v2);
435 int isl_val_ge(__isl_keep isl_val *v1,
436 __isl_keep isl_val *v2);
437 int isl_val_eq(__isl_keep isl_val *v1,
438 __isl_keep isl_val *v2);
439 int isl_val_ne(__isl_keep isl_val *v1,
440 __isl_keep isl_val *v2);
442 For integer C<isl_val>s we additionally have the following binary property.
445 int isl_val_is_divisible_by(__isl_keep isl_val *v1,
446 __isl_keep isl_val *v2);
448 An C<isl_val> can also be compared to an integer using the following
449 function. The result is undefined for NaN.
452 int isl_val_cmp_si(__isl_keep isl_val *v, long i);
454 The following unary operations are available on C<isl_val>s.
457 __isl_give isl_val *isl_val_abs(__isl_take isl_val *v);
458 __isl_give isl_val *isl_val_neg(__isl_take isl_val *v);
459 __isl_give isl_val *isl_val_floor(__isl_take isl_val *v);
460 __isl_give isl_val *isl_val_ceil(__isl_take isl_val *v);
461 __isl_give isl_val *isl_val_trunc(__isl_take isl_val *v);
463 The following binary operations are available on C<isl_val>s.
466 __isl_give isl_val *isl_val_abs(__isl_take isl_val *v);
467 __isl_give isl_val *isl_val_neg(__isl_take isl_val *v);
468 __isl_give isl_val *isl_val_floor(__isl_take isl_val *v);
469 __isl_give isl_val *isl_val_ceil(__isl_take isl_val *v);
470 __isl_give isl_val *isl_val_trunc(__isl_take isl_val *v);
471 __isl_give isl_val *isl_val_2exp(__isl_take isl_val *v);
472 __isl_give isl_val *isl_val_min(__isl_take isl_val *v1,
473 __isl_take isl_val *v2);
474 __isl_give isl_val *isl_val_max(__isl_take isl_val *v1,
475 __isl_take isl_val *v2);
476 __isl_give isl_val *isl_val_add(__isl_take isl_val *v1,
477 __isl_take isl_val *v2);
478 __isl_give isl_val *isl_val_add_ui(__isl_take isl_val *v1,
480 __isl_give isl_val *isl_val_sub(__isl_take isl_val *v1,
481 __isl_take isl_val *v2);
482 __isl_give isl_val *isl_val_sub_ui(__isl_take isl_val *v1,
484 __isl_give isl_val *isl_val_mul(__isl_take isl_val *v1,
485 __isl_take isl_val *v2);
486 __isl_give isl_val *isl_val_mul_ui(__isl_take isl_val *v1,
488 __isl_give isl_val *isl_val_div(__isl_take isl_val *v1,
489 __isl_take isl_val *v2);
491 On integer values, we additionally have the following operations.
494 __isl_give isl_val *isl_val_2exp(__isl_take isl_val *v);
495 __isl_give isl_val *isl_val_mod(__isl_take isl_val *v1,
496 __isl_take isl_val *v2);
497 __isl_give isl_val *isl_val_gcd(__isl_take isl_val *v1,
498 __isl_take isl_val *v2);
499 __isl_give isl_val *isl_val_gcdext(__isl_take isl_val *v1,
500 __isl_take isl_val *v2, __isl_give isl_val **x,
501 __isl_give isl_val **y);
503 The function C<isl_val_gcdext> returns the greatest common divisor g
504 of C<v1> and C<v2> as well as two integers C<*x> and C<*y> such
505 that C<*x> * C<v1> + C<*y> * C<v2> = g.
507 A value can be read from input using
510 __isl_give isl_val *isl_val_read_from_str(isl_ctx *ctx,
513 A value can be printed using
516 __isl_give isl_printer *isl_printer_print_val(
517 __isl_take isl_printer *p, __isl_keep isl_val *v);
519 =head3 GMP specific functions
521 These functions are only available if C<isl> has been compiled with C<GMP>
524 Specific integer and rational values can be created from C<GMP> values using
525 the following functions.
527 #include <isl/val_gmp.h>
528 __isl_give isl_val *isl_val_int_from_gmp(isl_ctx *ctx,
530 __isl_give isl_val *isl_val_from_gmp(isl_ctx *ctx,
531 const mpz_t n, const mpz_t d);
533 The numerator and denominator of a rational value can be extracted as
534 C<GMP> values using the following functions.
536 #include <isl/val_gmp.h>
537 int isl_val_get_num_gmp(__isl_keep isl_val *v, mpz_t z);
538 int isl_val_get_den_gmp(__isl_keep isl_val *v, mpz_t z);
540 =head3 Conversion from C<isl_int>
542 The following functions are only temporarily available to ease
543 the transition from C<isl_int> to C<isl_val>. They will be removed
546 #include <isl/val_int.h>
547 __isl_give isl_val *isl_val_int_from_isl_int(isl_ctx *ctx,
549 int isl_val_get_num_isl_int(__isl_keep isl_val *v,
552 =head2 Integers (obsolescent)
554 All operations on integers, mainly the coefficients
555 of the constraints describing the sets and relations,
556 are performed in exact integer arithmetic using C<GMP>.
557 However, to allow future versions of C<isl> to optionally
558 support fixed integer arithmetic, all calls to C<GMP>
559 are wrapped inside C<isl> specific macros.
560 The basic type is C<isl_int> and the operations below
561 are available on this type.
562 The meanings of these operations are essentially the same
563 as their C<GMP> C<mpz_> counterparts.
564 As always with C<GMP> types, C<isl_int>s need to be
565 initialized with C<isl_int_init> before they can be used
566 and they need to be released with C<isl_int_clear>
568 The user should not assume that an C<isl_int> is represented
569 as a C<mpz_t>, but should instead explicitly convert between
570 C<mpz_t>s and C<isl_int>s using C<isl_int_set_gmp> and
571 C<isl_int_get_gmp> whenever a C<mpz_t> is required.
575 =item isl_int_init(i)
577 =item isl_int_clear(i)
579 =item isl_int_set(r,i)
581 =item isl_int_set_si(r,i)
583 =item isl_int_set_gmp(r,g)
585 =item isl_int_get_gmp(i,g)
587 =item isl_int_abs(r,i)
589 =item isl_int_neg(r,i)
591 =item isl_int_swap(i,j)
593 =item isl_int_swap_or_set(i,j)
595 =item isl_int_add_ui(r,i,j)
597 =item isl_int_sub_ui(r,i,j)
599 =item isl_int_add(r,i,j)
601 =item isl_int_sub(r,i,j)
603 =item isl_int_mul(r,i,j)
605 =item isl_int_mul_ui(r,i,j)
607 =item isl_int_addmul(r,i,j)
609 =item isl_int_submul(r,i,j)
611 =item isl_int_gcd(r,i,j)
613 =item isl_int_lcm(r,i,j)
615 =item isl_int_divexact(r,i,j)
617 =item isl_int_cdiv_q(r,i,j)
619 =item isl_int_fdiv_q(r,i,j)
621 =item isl_int_fdiv_r(r,i,j)
623 =item isl_int_fdiv_q_ui(r,i,j)
625 =item isl_int_read(r,s)
627 =item isl_int_print(out,i,width)
631 =item isl_int_cmp(i,j)
633 =item isl_int_cmp_si(i,si)
635 =item isl_int_eq(i,j)
637 =item isl_int_ne(i,j)
639 =item isl_int_lt(i,j)
641 =item isl_int_le(i,j)
643 =item isl_int_gt(i,j)
645 =item isl_int_ge(i,j)
647 =item isl_int_abs_eq(i,j)
649 =item isl_int_abs_ne(i,j)
651 =item isl_int_abs_lt(i,j)
653 =item isl_int_abs_gt(i,j)
655 =item isl_int_abs_ge(i,j)
657 =item isl_int_is_zero(i)
659 =item isl_int_is_one(i)
661 =item isl_int_is_negone(i)
663 =item isl_int_is_pos(i)
665 =item isl_int_is_neg(i)
667 =item isl_int_is_nonpos(i)
669 =item isl_int_is_nonneg(i)
671 =item isl_int_is_divisible_by(i,j)
675 =head2 Sets and Relations
677 C<isl> uses six types of objects for representing sets and relations,
678 C<isl_basic_set>, C<isl_basic_map>, C<isl_set>, C<isl_map>,
679 C<isl_union_set> and C<isl_union_map>.
680 C<isl_basic_set> and C<isl_basic_map> represent sets and relations that
681 can be described as a conjunction of affine constraints, while
682 C<isl_set> and C<isl_map> represent unions of
683 C<isl_basic_set>s and C<isl_basic_map>s, respectively.
684 However, all C<isl_basic_set>s or C<isl_basic_map>s in the union need
685 to live in the same space. C<isl_union_set>s and C<isl_union_map>s
686 represent unions of C<isl_set>s or C<isl_map>s in I<different> spaces,
687 where spaces are considered different if they have a different number
688 of dimensions and/or different names (see L<"Spaces">).
689 The difference between sets and relations (maps) is that sets have
690 one set of variables, while relations have two sets of variables,
691 input variables and output variables.
693 =head2 Memory Management
695 Since a high-level operation on sets and/or relations usually involves
696 several substeps and since the user is usually not interested in
697 the intermediate results, most functions that return a new object
698 will also release all the objects passed as arguments.
699 If the user still wants to use one or more of these arguments
700 after the function call, she should pass along a copy of the
701 object rather than the object itself.
702 The user is then responsible for making sure that the original
703 object gets used somewhere else or is explicitly freed.
705 The arguments and return values of all documented functions are
706 annotated to make clear which arguments are released and which
707 arguments are preserved. In particular, the following annotations
714 C<__isl_give> means that a new object is returned.
715 The user should make sure that the returned pointer is
716 used exactly once as a value for an C<__isl_take> argument.
717 In between, it can be used as a value for as many
718 C<__isl_keep> arguments as the user likes.
719 There is one exception, and that is the case where the
720 pointer returned is C<NULL>. Is this case, the user
721 is free to use it as an C<__isl_take> argument or not.
725 C<__isl_take> means that the object the argument points to
726 is taken over by the function and may no longer be used
727 by the user as an argument to any other function.
728 The pointer value must be one returned by a function
729 returning an C<__isl_give> pointer.
730 If the user passes in a C<NULL> value, then this will
731 be treated as an error in the sense that the function will
732 not perform its usual operation. However, it will still
733 make sure that all the other C<__isl_take> arguments
738 C<__isl_keep> means that the function will only use the object
739 temporarily. After the function has finished, the user
740 can still use it as an argument to other functions.
741 A C<NULL> value will be treated in the same way as
742 a C<NULL> value for an C<__isl_take> argument.
746 =head2 Error Handling
748 C<isl> supports different ways to react in case a runtime error is triggered.
749 Runtime errors arise, e.g., if a function such as C<isl_map_intersect> is called
750 with two maps that have incompatible spaces. There are three possible ways
751 to react on error: to warn, to continue or to abort.
753 The default behavior is to warn. In this mode, C<isl> prints a warning, stores
754 the last error in the corresponding C<isl_ctx> and the function in which the
755 error was triggered returns C<NULL>. An error does not corrupt internal state,
756 such that isl can continue to be used. C<isl> also provides functions to
757 read the last error and to reset the memory that stores the last error. The
758 last error is only stored for information purposes. Its presence does not
759 change the behavior of C<isl>. Hence, resetting an error is not required to
760 continue to use isl, but only to observe new errors.
763 enum isl_error isl_ctx_last_error(isl_ctx *ctx);
764 void isl_ctx_reset_error(isl_ctx *ctx);
766 Another option is to continue on error. This is similar to warn on error mode,
767 except that C<isl> does not print any warning. This allows a program to
768 implement its own error reporting.
770 The last option is to directly abort the execution of the program from within
771 the isl library. This makes it obviously impossible to recover from an error,
772 but it allows to directly spot the error location. By aborting on error,
773 debuggers break at the location the error occurred and can provide a stack
774 trace. Other tools that automatically provide stack traces on abort or that do
775 not want to continue execution after an error was triggered may also prefer to
778 The on error behavior of isl can be specified by calling
779 C<isl_options_set_on_error> or by setting the command line option
780 C<--isl-on-error>. Valid arguments for the function call are
781 C<ISL_ON_ERROR_WARN>, C<ISL_ON_ERROR_CONTINUE> and C<ISL_ON_ERROR_ABORT>. The
782 choices for the command line option are C<warn>, C<continue> and C<abort>.
783 It is also possible to query the current error mode.
785 #include <isl/options.h>
786 int isl_options_set_on_error(isl_ctx *ctx, int val);
787 int isl_options_get_on_error(isl_ctx *ctx);
791 Identifiers are used to identify both individual dimensions
792 and tuples of dimensions. They consist of an optional name and an optional
793 user pointer. The name and the user pointer cannot both be C<NULL>, however.
794 Identifiers with the same name but different pointer values
795 are considered to be distinct.
796 Similarly, identifiers with different names but the same pointer value
797 are also considered to be distinct.
798 Equal identifiers are represented using the same object.
799 Pairs of identifiers can therefore be tested for equality using the
801 Identifiers can be constructed, copied, freed, inspected and printed
802 using the following functions.
805 __isl_give isl_id *isl_id_alloc(isl_ctx *ctx,
806 __isl_keep const char *name, void *user);
807 __isl_give isl_id *isl_id_set_free_user(
808 __isl_take isl_id *id,
809 __isl_give void (*free_user)(void *user));
810 __isl_give isl_id *isl_id_copy(isl_id *id);
811 void *isl_id_free(__isl_take isl_id *id);
813 isl_ctx *isl_id_get_ctx(__isl_keep isl_id *id);
814 void *isl_id_get_user(__isl_keep isl_id *id);
815 __isl_keep const char *isl_id_get_name(__isl_keep isl_id *id);
817 __isl_give isl_printer *isl_printer_print_id(
818 __isl_take isl_printer *p, __isl_keep isl_id *id);
820 The callback set by C<isl_id_set_free_user> is called on the user
821 pointer when the last reference to the C<isl_id> is freed.
822 Note that C<isl_id_get_name> returns a pointer to some internal
823 data structure, so the result can only be used while the
824 corresponding C<isl_id> is alive.
828 Whenever a new set, relation or similiar object is created from scratch,
829 the space in which it lives needs to be specified using an C<isl_space>.
830 Each space involves zero or more parameters and zero, one or two
831 tuples of set or input/output dimensions. The parameters and dimensions
832 are identified by an C<isl_dim_type> and a position.
833 The type C<isl_dim_param> refers to parameters,
834 the type C<isl_dim_set> refers to set dimensions (for spaces
835 with a single tuple of dimensions) and the types C<isl_dim_in>
836 and C<isl_dim_out> refer to input and output dimensions
837 (for spaces with two tuples of dimensions).
838 Local spaces (see L</"Local Spaces">) also contain dimensions
839 of type C<isl_dim_div>.
840 Note that parameters are only identified by their position within
841 a given object. Across different objects, parameters are (usually)
842 identified by their names or identifiers. Only unnamed parameters
843 are identified by their positions across objects. The use of unnamed
844 parameters is discouraged.
846 #include <isl/space.h>
847 __isl_give isl_space *isl_space_alloc(isl_ctx *ctx,
848 unsigned nparam, unsigned n_in, unsigned n_out);
849 __isl_give isl_space *isl_space_params_alloc(isl_ctx *ctx,
851 __isl_give isl_space *isl_space_set_alloc(isl_ctx *ctx,
852 unsigned nparam, unsigned dim);
853 __isl_give isl_space *isl_space_copy(__isl_keep isl_space *space);
854 void *isl_space_free(__isl_take isl_space *space);
855 unsigned isl_space_dim(__isl_keep isl_space *space,
856 enum isl_dim_type type);
858 The space used for creating a parameter domain
859 needs to be created using C<isl_space_params_alloc>.
860 For other sets, the space
861 needs to be created using C<isl_space_set_alloc>, while
862 for a relation, the space
863 needs to be created using C<isl_space_alloc>.
864 C<isl_space_dim> can be used
865 to find out the number of dimensions of each type in
866 a space, where type may be
867 C<isl_dim_param>, C<isl_dim_in> (only for relations),
868 C<isl_dim_out> (only for relations), C<isl_dim_set>
869 (only for sets) or C<isl_dim_all>.
871 To check whether a given space is that of a set or a map
872 or whether it is a parameter space, use these functions:
874 #include <isl/space.h>
875 int isl_space_is_params(__isl_keep isl_space *space);
876 int isl_space_is_set(__isl_keep isl_space *space);
877 int isl_space_is_map(__isl_keep isl_space *space);
879 Spaces can be compared using the following functions:
881 #include <isl/space.h>
882 int isl_space_is_equal(__isl_keep isl_space *space1,
883 __isl_keep isl_space *space2);
884 int isl_space_is_domain(__isl_keep isl_space *space1,
885 __isl_keep isl_space *space2);
886 int isl_space_is_range(__isl_keep isl_space *space1,
887 __isl_keep isl_space *space2);
889 C<isl_space_is_domain> checks whether the first argument is equal
890 to the domain of the second argument. This requires in particular that
891 the first argument is a set space and that the second argument
894 It is often useful to create objects that live in the
895 same space as some other object. This can be accomplished
896 by creating the new objects
897 (see L<Creating New Sets and Relations> or
898 L<Creating New (Piecewise) Quasipolynomials>) based on the space
899 of the original object.
902 __isl_give isl_space *isl_basic_set_get_space(
903 __isl_keep isl_basic_set *bset);
904 __isl_give isl_space *isl_set_get_space(__isl_keep isl_set *set);
906 #include <isl/union_set.h>
907 __isl_give isl_space *isl_union_set_get_space(
908 __isl_keep isl_union_set *uset);
911 __isl_give isl_space *isl_basic_map_get_space(
912 __isl_keep isl_basic_map *bmap);
913 __isl_give isl_space *isl_map_get_space(__isl_keep isl_map *map);
915 #include <isl/union_map.h>
916 __isl_give isl_space *isl_union_map_get_space(
917 __isl_keep isl_union_map *umap);
919 #include <isl/constraint.h>
920 __isl_give isl_space *isl_constraint_get_space(
921 __isl_keep isl_constraint *constraint);
923 #include <isl/polynomial.h>
924 __isl_give isl_space *isl_qpolynomial_get_domain_space(
925 __isl_keep isl_qpolynomial *qp);
926 __isl_give isl_space *isl_qpolynomial_get_space(
927 __isl_keep isl_qpolynomial *qp);
928 __isl_give isl_space *isl_qpolynomial_fold_get_space(
929 __isl_keep isl_qpolynomial_fold *fold);
930 __isl_give isl_space *isl_pw_qpolynomial_get_domain_space(
931 __isl_keep isl_pw_qpolynomial *pwqp);
932 __isl_give isl_space *isl_pw_qpolynomial_get_space(
933 __isl_keep isl_pw_qpolynomial *pwqp);
934 __isl_give isl_space *isl_pw_qpolynomial_fold_get_domain_space(
935 __isl_keep isl_pw_qpolynomial_fold *pwf);
936 __isl_give isl_space *isl_pw_qpolynomial_fold_get_space(
937 __isl_keep isl_pw_qpolynomial_fold *pwf);
938 __isl_give isl_space *isl_union_pw_qpolynomial_get_space(
939 __isl_keep isl_union_pw_qpolynomial *upwqp);
940 __isl_give isl_space *isl_union_pw_qpolynomial_fold_get_space(
941 __isl_keep isl_union_pw_qpolynomial_fold *upwf);
944 __isl_give isl_space *isl_multi_val_get_space(
945 __isl_keep isl_multi_val *mv);
948 __isl_give isl_space *isl_aff_get_domain_space(
949 __isl_keep isl_aff *aff);
950 __isl_give isl_space *isl_aff_get_space(
951 __isl_keep isl_aff *aff);
952 __isl_give isl_space *isl_pw_aff_get_domain_space(
953 __isl_keep isl_pw_aff *pwaff);
954 __isl_give isl_space *isl_pw_aff_get_space(
955 __isl_keep isl_pw_aff *pwaff);
956 __isl_give isl_space *isl_multi_aff_get_domain_space(
957 __isl_keep isl_multi_aff *maff);
958 __isl_give isl_space *isl_multi_aff_get_space(
959 __isl_keep isl_multi_aff *maff);
960 __isl_give isl_space *isl_pw_multi_aff_get_domain_space(
961 __isl_keep isl_pw_multi_aff *pma);
962 __isl_give isl_space *isl_pw_multi_aff_get_space(
963 __isl_keep isl_pw_multi_aff *pma);
964 __isl_give isl_space *isl_union_pw_multi_aff_get_space(
965 __isl_keep isl_union_pw_multi_aff *upma);
966 __isl_give isl_space *isl_multi_pw_aff_get_domain_space(
967 __isl_keep isl_multi_pw_aff *mpa);
968 __isl_give isl_space *isl_multi_pw_aff_get_space(
969 __isl_keep isl_multi_pw_aff *mpa);
971 #include <isl/point.h>
972 __isl_give isl_space *isl_point_get_space(
973 __isl_keep isl_point *pnt);
975 The identifiers or names of the individual dimensions may be set or read off
976 using the following functions.
978 #include <isl/space.h>
979 __isl_give isl_space *isl_space_set_dim_id(
980 __isl_take isl_space *space,
981 enum isl_dim_type type, unsigned pos,
982 __isl_take isl_id *id);
983 int isl_space_has_dim_id(__isl_keep isl_space *space,
984 enum isl_dim_type type, unsigned pos);
985 __isl_give isl_id *isl_space_get_dim_id(
986 __isl_keep isl_space *space,
987 enum isl_dim_type type, unsigned pos);
988 __isl_give isl_space *isl_space_set_dim_name(
989 __isl_take isl_space *space,
990 enum isl_dim_type type, unsigned pos,
991 __isl_keep const char *name);
992 int isl_space_has_dim_name(__isl_keep isl_space *space,
993 enum isl_dim_type type, unsigned pos);
994 __isl_keep const char *isl_space_get_dim_name(
995 __isl_keep isl_space *space,
996 enum isl_dim_type type, unsigned pos);
998 Note that C<isl_space_get_name> returns a pointer to some internal
999 data structure, so the result can only be used while the
1000 corresponding C<isl_space> is alive.
1001 Also note that every function that operates on two sets or relations
1002 requires that both arguments have the same parameters. This also
1003 means that if one of the arguments has named parameters, then the
1004 other needs to have named parameters too and the names need to match.
1005 Pairs of C<isl_set>, C<isl_map>, C<isl_union_set> and/or C<isl_union_map>
1006 arguments may have different parameters (as long as they are named),
1007 in which case the result will have as parameters the union of the parameters of
1010 Given the identifier or name of a dimension (typically a parameter),
1011 its position can be obtained from the following function.
1013 #include <isl/space.h>
1014 int isl_space_find_dim_by_id(__isl_keep isl_space *space,
1015 enum isl_dim_type type, __isl_keep isl_id *id);
1016 int isl_space_find_dim_by_name(__isl_keep isl_space *space,
1017 enum isl_dim_type type, const char *name);
1019 The identifiers or names of entire spaces may be set or read off
1020 using the following functions.
1022 #include <isl/space.h>
1023 __isl_give isl_space *isl_space_set_tuple_id(
1024 __isl_take isl_space *space,
1025 enum isl_dim_type type, __isl_take isl_id *id);
1026 __isl_give isl_space *isl_space_reset_tuple_id(
1027 __isl_take isl_space *space, enum isl_dim_type type);
1028 int isl_space_has_tuple_id(__isl_keep isl_space *space,
1029 enum isl_dim_type type);
1030 __isl_give isl_id *isl_space_get_tuple_id(
1031 __isl_keep isl_space *space, enum isl_dim_type type);
1032 __isl_give isl_space *isl_space_set_tuple_name(
1033 __isl_take isl_space *space,
1034 enum isl_dim_type type, const char *s);
1035 int isl_space_has_tuple_name(__isl_keep isl_space *space,
1036 enum isl_dim_type type);
1037 const char *isl_space_get_tuple_name(__isl_keep isl_space *space,
1038 enum isl_dim_type type);
1040 The C<type> argument needs to be one of C<isl_dim_in>, C<isl_dim_out>
1041 or C<isl_dim_set>. As with C<isl_space_get_name>,
1042 the C<isl_space_get_tuple_name> function returns a pointer to some internal
1044 Binary operations require the corresponding spaces of their arguments
1045 to have the same name.
1047 Spaces can be nested. In particular, the domain of a set or
1048 the domain or range of a relation can be a nested relation.
1049 The following functions can be used to construct and deconstruct
1052 #include <isl/space.h>
1053 int isl_space_is_wrapping(__isl_keep isl_space *space);
1054 __isl_give isl_space *isl_space_wrap(__isl_take isl_space *space);
1055 __isl_give isl_space *isl_space_unwrap(__isl_take isl_space *space);
1057 The input to C<isl_space_is_wrapping> and C<isl_space_unwrap> should
1058 be the space of a set, while that of
1059 C<isl_space_wrap> should be the space of a relation.
1060 Conversely, the output of C<isl_space_unwrap> is the space
1061 of a relation, while that of C<isl_space_wrap> is the space of a set.
1063 Spaces can be created from other spaces
1064 using the following functions.
1066 __isl_give isl_space *isl_space_domain(__isl_take isl_space *space);
1067 __isl_give isl_space *isl_space_from_domain(__isl_take isl_space *space);
1068 __isl_give isl_space *isl_space_range(__isl_take isl_space *space);
1069 __isl_give isl_space *isl_space_from_range(__isl_take isl_space *space);
1070 __isl_give isl_space *isl_space_params(
1071 __isl_take isl_space *space);
1072 __isl_give isl_space *isl_space_set_from_params(
1073 __isl_take isl_space *space);
1074 __isl_give isl_space *isl_space_reverse(__isl_take isl_space *space);
1075 __isl_give isl_space *isl_space_join(__isl_take isl_space *left,
1076 __isl_take isl_space *right);
1077 __isl_give isl_space *isl_space_align_params(
1078 __isl_take isl_space *space1, __isl_take isl_space *space2)
1079 __isl_give isl_space *isl_space_insert_dims(__isl_take isl_space *space,
1080 enum isl_dim_type type, unsigned pos, unsigned n);
1081 __isl_give isl_space *isl_space_add_dims(__isl_take isl_space *space,
1082 enum isl_dim_type type, unsigned n);
1083 __isl_give isl_space *isl_space_drop_dims(__isl_take isl_space *space,
1084 enum isl_dim_type type, unsigned first, unsigned n);
1085 __isl_give isl_space *isl_space_move_dims(__isl_take isl_space *space,
1086 enum isl_dim_type dst_type, unsigned dst_pos,
1087 enum isl_dim_type src_type, unsigned src_pos,
1089 __isl_give isl_space *isl_space_map_from_set(
1090 __isl_take isl_space *space);
1091 __isl_give isl_space *isl_space_map_from_domain_and_range(
1092 __isl_take isl_space *domain,
1093 __isl_take isl_space *range);
1094 __isl_give isl_space *isl_space_zip(__isl_take isl_space *space);
1095 __isl_give isl_space *isl_space_curry(
1096 __isl_take isl_space *space);
1097 __isl_give isl_space *isl_space_uncurry(
1098 __isl_take isl_space *space);
1100 Note that if dimensions are added or removed from a space, then
1101 the name and the internal structure are lost.
1105 A local space is essentially a space with
1106 zero or more existentially quantified variables.
1107 The local space of a (constraint of a) basic set or relation can be obtained
1108 using the following functions.
1110 #include <isl/constraint.h>
1111 __isl_give isl_local_space *isl_constraint_get_local_space(
1112 __isl_keep isl_constraint *constraint);
1114 #include <isl/set.h>
1115 __isl_give isl_local_space *isl_basic_set_get_local_space(
1116 __isl_keep isl_basic_set *bset);
1118 #include <isl/map.h>
1119 __isl_give isl_local_space *isl_basic_map_get_local_space(
1120 __isl_keep isl_basic_map *bmap);
1122 A new local space can be created from a space using
1124 #include <isl/local_space.h>
1125 __isl_give isl_local_space *isl_local_space_from_space(
1126 __isl_take isl_space *space);
1128 They can be inspected, modified, copied and freed using the following functions.
1130 #include <isl/local_space.h>
1131 isl_ctx *isl_local_space_get_ctx(
1132 __isl_keep isl_local_space *ls);
1133 int isl_local_space_is_set(__isl_keep isl_local_space *ls);
1134 int isl_local_space_dim(__isl_keep isl_local_space *ls,
1135 enum isl_dim_type type);
1136 int isl_local_space_has_dim_id(
1137 __isl_keep isl_local_space *ls,
1138 enum isl_dim_type type, unsigned pos);
1139 __isl_give isl_id *isl_local_space_get_dim_id(
1140 __isl_keep isl_local_space *ls,
1141 enum isl_dim_type type, unsigned pos);
1142 int isl_local_space_has_dim_name(
1143 __isl_keep isl_local_space *ls,
1144 enum isl_dim_type type, unsigned pos)
1145 const char *isl_local_space_get_dim_name(
1146 __isl_keep isl_local_space *ls,
1147 enum isl_dim_type type, unsigned pos);
1148 __isl_give isl_local_space *isl_local_space_set_dim_name(
1149 __isl_take isl_local_space *ls,
1150 enum isl_dim_type type, unsigned pos, const char *s);
1151 __isl_give isl_local_space *isl_local_space_set_dim_id(
1152 __isl_take isl_local_space *ls,
1153 enum isl_dim_type type, unsigned pos,
1154 __isl_take isl_id *id);
1155 __isl_give isl_space *isl_local_space_get_space(
1156 __isl_keep isl_local_space *ls);
1157 __isl_give isl_aff *isl_local_space_get_div(
1158 __isl_keep isl_local_space *ls, int pos);
1159 __isl_give isl_local_space *isl_local_space_copy(
1160 __isl_keep isl_local_space *ls);
1161 void *isl_local_space_free(__isl_take isl_local_space *ls);
1163 Note that C<isl_local_space_get_div> can only be used on local spaces
1166 Two local spaces can be compared using
1168 int isl_local_space_is_equal(__isl_keep isl_local_space *ls1,
1169 __isl_keep isl_local_space *ls2);
1171 Local spaces can be created from other local spaces
1172 using the following functions.
1174 __isl_give isl_local_space *isl_local_space_domain(
1175 __isl_take isl_local_space *ls);
1176 __isl_give isl_local_space *isl_local_space_range(
1177 __isl_take isl_local_space *ls);
1178 __isl_give isl_local_space *isl_local_space_from_domain(
1179 __isl_take isl_local_space *ls);
1180 __isl_give isl_local_space *isl_local_space_intersect(
1181 __isl_take isl_local_space *ls1,
1182 __isl_take isl_local_space *ls2);
1183 __isl_give isl_local_space *isl_local_space_add_dims(
1184 __isl_take isl_local_space *ls,
1185 enum isl_dim_type type, unsigned n);
1186 __isl_give isl_local_space *isl_local_space_insert_dims(
1187 __isl_take isl_local_space *ls,
1188 enum isl_dim_type type, unsigned first, unsigned n);
1189 __isl_give isl_local_space *isl_local_space_drop_dims(
1190 __isl_take isl_local_space *ls,
1191 enum isl_dim_type type, unsigned first, unsigned n);
1193 =head2 Input and Output
1195 C<isl> supports its own input/output format, which is similar
1196 to the C<Omega> format, but also supports the C<PolyLib> format
1199 =head3 C<isl> format
1201 The C<isl> format is similar to that of C<Omega>, but has a different
1202 syntax for describing the parameters and allows for the definition
1203 of an existentially quantified variable as the integer division
1204 of an affine expression.
1205 For example, the set of integers C<i> between C<0> and C<n>
1206 such that C<i % 10 <= 6> can be described as
1208 [n] -> { [i] : exists (a = [i/10] : 0 <= i and i <= n and
1211 A set or relation can have several disjuncts, separated
1212 by the keyword C<or>. Each disjunct is either a conjunction
1213 of constraints or a projection (C<exists>) of a conjunction
1214 of constraints. The constraints are separated by the keyword
1217 =head3 C<PolyLib> format
1219 If the represented set is a union, then the first line
1220 contains a single number representing the number of disjuncts.
1221 Otherwise, a line containing the number C<1> is optional.
1223 Each disjunct is represented by a matrix of constraints.
1224 The first line contains two numbers representing
1225 the number of rows and columns,
1226 where the number of rows is equal to the number of constraints
1227 and the number of columns is equal to two plus the number of variables.
1228 The following lines contain the actual rows of the constraint matrix.
1229 In each row, the first column indicates whether the constraint
1230 is an equality (C<0>) or inequality (C<1>). The final column
1231 corresponds to the constant term.
1233 If the set is parametric, then the coefficients of the parameters
1234 appear in the last columns before the constant column.
1235 The coefficients of any existentially quantified variables appear
1236 between those of the set variables and those of the parameters.
1238 =head3 Extended C<PolyLib> format
1240 The extended C<PolyLib> format is nearly identical to the
1241 C<PolyLib> format. The only difference is that the line
1242 containing the number of rows and columns of a constraint matrix
1243 also contains four additional numbers:
1244 the number of output dimensions, the number of input dimensions,
1245 the number of local dimensions (i.e., the number of existentially
1246 quantified variables) and the number of parameters.
1247 For sets, the number of ``output'' dimensions is equal
1248 to the number of set dimensions, while the number of ``input''
1253 #include <isl/set.h>
1254 __isl_give isl_basic_set *isl_basic_set_read_from_file(
1255 isl_ctx *ctx, FILE *input);
1256 __isl_give isl_basic_set *isl_basic_set_read_from_str(
1257 isl_ctx *ctx, const char *str);
1258 __isl_give isl_set *isl_set_read_from_file(isl_ctx *ctx,
1260 __isl_give isl_set *isl_set_read_from_str(isl_ctx *ctx,
1263 #include <isl/map.h>
1264 __isl_give isl_basic_map *isl_basic_map_read_from_file(
1265 isl_ctx *ctx, FILE *input);
1266 __isl_give isl_basic_map *isl_basic_map_read_from_str(
1267 isl_ctx *ctx, const char *str);
1268 __isl_give isl_map *isl_map_read_from_file(
1269 isl_ctx *ctx, FILE *input);
1270 __isl_give isl_map *isl_map_read_from_str(isl_ctx *ctx,
1273 #include <isl/union_set.h>
1274 __isl_give isl_union_set *isl_union_set_read_from_file(
1275 isl_ctx *ctx, FILE *input);
1276 __isl_give isl_union_set *isl_union_set_read_from_str(
1277 isl_ctx *ctx, const char *str);
1279 #include <isl/union_map.h>
1280 __isl_give isl_union_map *isl_union_map_read_from_file(
1281 isl_ctx *ctx, FILE *input);
1282 __isl_give isl_union_map *isl_union_map_read_from_str(
1283 isl_ctx *ctx, const char *str);
1285 The input format is autodetected and may be either the C<PolyLib> format
1286 or the C<isl> format.
1290 Before anything can be printed, an C<isl_printer> needs to
1293 __isl_give isl_printer *isl_printer_to_file(isl_ctx *ctx,
1295 __isl_give isl_printer *isl_printer_to_str(isl_ctx *ctx);
1296 void *isl_printer_free(__isl_take isl_printer *printer);
1297 __isl_give char *isl_printer_get_str(
1298 __isl_keep isl_printer *printer);
1300 The printer can be inspected using the following functions.
1302 FILE *isl_printer_get_file(
1303 __isl_keep isl_printer *printer);
1304 int isl_printer_get_output_format(
1305 __isl_keep isl_printer *p);
1307 The behavior of the printer can be modified in various ways
1309 __isl_give isl_printer *isl_printer_set_output_format(
1310 __isl_take isl_printer *p, int output_format);
1311 __isl_give isl_printer *isl_printer_set_indent(
1312 __isl_take isl_printer *p, int indent);
1313 __isl_give isl_printer *isl_printer_indent(
1314 __isl_take isl_printer *p, int indent);
1315 __isl_give isl_printer *isl_printer_set_prefix(
1316 __isl_take isl_printer *p, const char *prefix);
1317 __isl_give isl_printer *isl_printer_set_suffix(
1318 __isl_take isl_printer *p, const char *suffix);
1320 The C<output_format> may be either C<ISL_FORMAT_ISL>, C<ISL_FORMAT_OMEGA>,
1321 C<ISL_FORMAT_POLYLIB>, C<ISL_FORMAT_EXT_POLYLIB> or C<ISL_FORMAT_LATEX>
1322 and defaults to C<ISL_FORMAT_ISL>.
1323 Each line in the output is indented by C<indent> (set by
1324 C<isl_printer_set_indent>) spaces
1325 (default: 0), prefixed by C<prefix> and suffixed by C<suffix>.
1326 In the C<PolyLib> format output,
1327 the coefficients of the existentially quantified variables
1328 appear between those of the set variables and those
1330 The function C<isl_printer_indent> increases the indentation
1331 by the specified amount (which may be negative).
1333 To actually print something, use
1335 #include <isl/printer.h>
1336 __isl_give isl_printer *isl_printer_print_double(
1337 __isl_take isl_printer *p, double d);
1339 #include <isl/set.h>
1340 __isl_give isl_printer *isl_printer_print_basic_set(
1341 __isl_take isl_printer *printer,
1342 __isl_keep isl_basic_set *bset);
1343 __isl_give isl_printer *isl_printer_print_set(
1344 __isl_take isl_printer *printer,
1345 __isl_keep isl_set *set);
1347 #include <isl/map.h>
1348 __isl_give isl_printer *isl_printer_print_basic_map(
1349 __isl_take isl_printer *printer,
1350 __isl_keep isl_basic_map *bmap);
1351 __isl_give isl_printer *isl_printer_print_map(
1352 __isl_take isl_printer *printer,
1353 __isl_keep isl_map *map);
1355 #include <isl/union_set.h>
1356 __isl_give isl_printer *isl_printer_print_union_set(
1357 __isl_take isl_printer *p,
1358 __isl_keep isl_union_set *uset);
1360 #include <isl/union_map.h>
1361 __isl_give isl_printer *isl_printer_print_union_map(
1362 __isl_take isl_printer *p,
1363 __isl_keep isl_union_map *umap);
1365 When called on a file printer, the following function flushes
1366 the file. When called on a string printer, the buffer is cleared.
1368 __isl_give isl_printer *isl_printer_flush(
1369 __isl_take isl_printer *p);
1371 =head2 Creating New Sets and Relations
1373 C<isl> has functions for creating some standard sets and relations.
1377 =item * Empty sets and relations
1379 __isl_give isl_basic_set *isl_basic_set_empty(
1380 __isl_take isl_space *space);
1381 __isl_give isl_basic_map *isl_basic_map_empty(
1382 __isl_take isl_space *space);
1383 __isl_give isl_set *isl_set_empty(
1384 __isl_take isl_space *space);
1385 __isl_give isl_map *isl_map_empty(
1386 __isl_take isl_space *space);
1387 __isl_give isl_union_set *isl_union_set_empty(
1388 __isl_take isl_space *space);
1389 __isl_give isl_union_map *isl_union_map_empty(
1390 __isl_take isl_space *space);
1392 For C<isl_union_set>s and C<isl_union_map>s, the space
1393 is only used to specify the parameters.
1395 =item * Universe sets and relations
1397 __isl_give isl_basic_set *isl_basic_set_universe(
1398 __isl_take isl_space *space);
1399 __isl_give isl_basic_map *isl_basic_map_universe(
1400 __isl_take isl_space *space);
1401 __isl_give isl_set *isl_set_universe(
1402 __isl_take isl_space *space);
1403 __isl_give isl_map *isl_map_universe(
1404 __isl_take isl_space *space);
1405 __isl_give isl_union_set *isl_union_set_universe(
1406 __isl_take isl_union_set *uset);
1407 __isl_give isl_union_map *isl_union_map_universe(
1408 __isl_take isl_union_map *umap);
1410 The sets and relations constructed by the functions above
1411 contain all integer values, while those constructed by the
1412 functions below only contain non-negative values.
1414 __isl_give isl_basic_set *isl_basic_set_nat_universe(
1415 __isl_take isl_space *space);
1416 __isl_give isl_basic_map *isl_basic_map_nat_universe(
1417 __isl_take isl_space *space);
1418 __isl_give isl_set *isl_set_nat_universe(
1419 __isl_take isl_space *space);
1420 __isl_give isl_map *isl_map_nat_universe(
1421 __isl_take isl_space *space);
1423 =item * Identity relations
1425 __isl_give isl_basic_map *isl_basic_map_identity(
1426 __isl_take isl_space *space);
1427 __isl_give isl_map *isl_map_identity(
1428 __isl_take isl_space *space);
1430 The number of input and output dimensions in C<space> needs
1433 =item * Lexicographic order
1435 __isl_give isl_map *isl_map_lex_lt(
1436 __isl_take isl_space *set_space);
1437 __isl_give isl_map *isl_map_lex_le(
1438 __isl_take isl_space *set_space);
1439 __isl_give isl_map *isl_map_lex_gt(
1440 __isl_take isl_space *set_space);
1441 __isl_give isl_map *isl_map_lex_ge(
1442 __isl_take isl_space *set_space);
1443 __isl_give isl_map *isl_map_lex_lt_first(
1444 __isl_take isl_space *space, unsigned n);
1445 __isl_give isl_map *isl_map_lex_le_first(
1446 __isl_take isl_space *space, unsigned n);
1447 __isl_give isl_map *isl_map_lex_gt_first(
1448 __isl_take isl_space *space, unsigned n);
1449 __isl_give isl_map *isl_map_lex_ge_first(
1450 __isl_take isl_space *space, unsigned n);
1452 The first four functions take a space for a B<set>
1453 and return relations that express that the elements in the domain
1454 are lexicographically less
1455 (C<isl_map_lex_lt>), less or equal (C<isl_map_lex_le>),
1456 greater (C<isl_map_lex_gt>) or greater or equal (C<isl_map_lex_ge>)
1457 than the elements in the range.
1458 The last four functions take a space for a map
1459 and return relations that express that the first C<n> dimensions
1460 in the domain are lexicographically less
1461 (C<isl_map_lex_lt_first>), less or equal (C<isl_map_lex_le_first>),
1462 greater (C<isl_map_lex_gt_first>) or greater or equal (C<isl_map_lex_ge_first>)
1463 than the first C<n> dimensions in the range.
1467 A basic set or relation can be converted to a set or relation
1468 using the following functions.
1470 __isl_give isl_set *isl_set_from_basic_set(
1471 __isl_take isl_basic_set *bset);
1472 __isl_give isl_map *isl_map_from_basic_map(
1473 __isl_take isl_basic_map *bmap);
1475 Sets and relations can be converted to union sets and relations
1476 using the following functions.
1478 __isl_give isl_union_set *isl_union_set_from_basic_set(
1479 __isl_take isl_basic_set *bset);
1480 __isl_give isl_union_map *isl_union_map_from_basic_map(
1481 __isl_take isl_basic_map *bmap);
1482 __isl_give isl_union_set *isl_union_set_from_set(
1483 __isl_take isl_set *set);
1484 __isl_give isl_union_map *isl_union_map_from_map(
1485 __isl_take isl_map *map);
1487 The inverse conversions below can only be used if the input
1488 union set or relation is known to contain elements in exactly one
1491 __isl_give isl_set *isl_set_from_union_set(
1492 __isl_take isl_union_set *uset);
1493 __isl_give isl_map *isl_map_from_union_map(
1494 __isl_take isl_union_map *umap);
1496 A zero-dimensional (basic) set can be constructed on a given parameter domain
1497 using the following function.
1499 __isl_give isl_basic_set *isl_basic_set_from_params(
1500 __isl_take isl_basic_set *bset);
1501 __isl_give isl_set *isl_set_from_params(
1502 __isl_take isl_set *set);
1504 Sets and relations can be copied and freed again using the following
1507 __isl_give isl_basic_set *isl_basic_set_copy(
1508 __isl_keep isl_basic_set *bset);
1509 __isl_give isl_set *isl_set_copy(__isl_keep isl_set *set);
1510 __isl_give isl_union_set *isl_union_set_copy(
1511 __isl_keep isl_union_set *uset);
1512 __isl_give isl_basic_map *isl_basic_map_copy(
1513 __isl_keep isl_basic_map *bmap);
1514 __isl_give isl_map *isl_map_copy(__isl_keep isl_map *map);
1515 __isl_give isl_union_map *isl_union_map_copy(
1516 __isl_keep isl_union_map *umap);
1517 void *isl_basic_set_free(__isl_take isl_basic_set *bset);
1518 void *isl_set_free(__isl_take isl_set *set);
1519 void *isl_union_set_free(__isl_take isl_union_set *uset);
1520 void *isl_basic_map_free(__isl_take isl_basic_map *bmap);
1521 void *isl_map_free(__isl_take isl_map *map);
1522 void *isl_union_map_free(__isl_take isl_union_map *umap);
1524 Other sets and relations can be constructed by starting
1525 from a universe set or relation, adding equality and/or
1526 inequality constraints and then projecting out the
1527 existentially quantified variables, if any.
1528 Constraints can be constructed, manipulated and
1529 added to (or removed from) (basic) sets and relations
1530 using the following functions.
1532 #include <isl/constraint.h>
1533 __isl_give isl_constraint *isl_equality_alloc(
1534 __isl_take isl_local_space *ls);
1535 __isl_give isl_constraint *isl_inequality_alloc(
1536 __isl_take isl_local_space *ls);
1537 __isl_give isl_constraint *isl_constraint_set_constant(
1538 __isl_take isl_constraint *constraint, isl_int v);
1539 __isl_give isl_constraint *isl_constraint_set_constant_si(
1540 __isl_take isl_constraint *constraint, int v);
1541 __isl_give isl_constraint *isl_constraint_set_constant_val(
1542 __isl_take isl_constraint *constraint,
1543 __isl_take isl_val *v);
1544 __isl_give isl_constraint *isl_constraint_set_coefficient(
1545 __isl_take isl_constraint *constraint,
1546 enum isl_dim_type type, int pos, isl_int v);
1547 __isl_give isl_constraint *isl_constraint_set_coefficient_si(
1548 __isl_take isl_constraint *constraint,
1549 enum isl_dim_type type, int pos, int v);
1550 __isl_give isl_constraint *
1551 isl_constraint_set_coefficient_val(
1552 __isl_take isl_constraint *constraint,
1553 enum isl_dim_type type, int pos, isl_val *v);
1554 __isl_give isl_basic_map *isl_basic_map_add_constraint(
1555 __isl_take isl_basic_map *bmap,
1556 __isl_take isl_constraint *constraint);
1557 __isl_give isl_basic_set *isl_basic_set_add_constraint(
1558 __isl_take isl_basic_set *bset,
1559 __isl_take isl_constraint *constraint);
1560 __isl_give isl_map *isl_map_add_constraint(
1561 __isl_take isl_map *map,
1562 __isl_take isl_constraint *constraint);
1563 __isl_give isl_set *isl_set_add_constraint(
1564 __isl_take isl_set *set,
1565 __isl_take isl_constraint *constraint);
1566 __isl_give isl_basic_set *isl_basic_set_drop_constraint(
1567 __isl_take isl_basic_set *bset,
1568 __isl_take isl_constraint *constraint);
1570 For example, to create a set containing the even integers
1571 between 10 and 42, you would use the following code.
1574 isl_local_space *ls;
1576 isl_basic_set *bset;
1578 space = isl_space_set_alloc(ctx, 0, 2);
1579 bset = isl_basic_set_universe(isl_space_copy(space));
1580 ls = isl_local_space_from_space(space);
1582 c = isl_equality_alloc(isl_local_space_copy(ls));
1583 c = isl_constraint_set_coefficient_si(c, isl_dim_set, 0, -1);
1584 c = isl_constraint_set_coefficient_si(c, isl_dim_set, 1, 2);
1585 bset = isl_basic_set_add_constraint(bset, c);
1587 c = isl_inequality_alloc(isl_local_space_copy(ls));
1588 c = isl_constraint_set_constant_si(c, -10);
1589 c = isl_constraint_set_coefficient_si(c, isl_dim_set, 0, 1);
1590 bset = isl_basic_set_add_constraint(bset, c);
1592 c = isl_inequality_alloc(ls);
1593 c = isl_constraint_set_constant_si(c, 42);
1594 c = isl_constraint_set_coefficient_si(c, isl_dim_set, 0, -1);
1595 bset = isl_basic_set_add_constraint(bset, c);
1597 bset = isl_basic_set_project_out(bset, isl_dim_set, 1, 1);
1601 isl_basic_set *bset;
1602 bset = isl_basic_set_read_from_str(ctx,
1603 "{[i] : exists (a : i = 2a and i >= 10 and i <= 42)}");
1605 A basic set or relation can also be constructed from two matrices
1606 describing the equalities and the inequalities.
1608 __isl_give isl_basic_set *isl_basic_set_from_constraint_matrices(
1609 __isl_take isl_space *space,
1610 __isl_take isl_mat *eq, __isl_take isl_mat *ineq,
1611 enum isl_dim_type c1,
1612 enum isl_dim_type c2, enum isl_dim_type c3,
1613 enum isl_dim_type c4);
1614 __isl_give isl_basic_map *isl_basic_map_from_constraint_matrices(
1615 __isl_take isl_space *space,
1616 __isl_take isl_mat *eq, __isl_take isl_mat *ineq,
1617 enum isl_dim_type c1,
1618 enum isl_dim_type c2, enum isl_dim_type c3,
1619 enum isl_dim_type c4, enum isl_dim_type c5);
1621 The C<isl_dim_type> arguments indicate the order in which
1622 different kinds of variables appear in the input matrices
1623 and should be a permutation of C<isl_dim_cst>, C<isl_dim_param>,
1624 C<isl_dim_set> and C<isl_dim_div> for sets and
1625 of C<isl_dim_cst>, C<isl_dim_param>,
1626 C<isl_dim_in>, C<isl_dim_out> and C<isl_dim_div> for relations.
1628 A (basic or union) set or relation can also be constructed from a
1629 (union) (piecewise) (multiple) affine expression
1630 or a list of affine expressions
1631 (See L<"Piecewise Quasi Affine Expressions"> and
1632 L<"Piecewise Multiple Quasi Affine Expressions">).
1634 __isl_give isl_basic_map *isl_basic_map_from_aff(
1635 __isl_take isl_aff *aff);
1636 __isl_give isl_map *isl_map_from_aff(
1637 __isl_take isl_aff *aff);
1638 __isl_give isl_set *isl_set_from_pw_aff(
1639 __isl_take isl_pw_aff *pwaff);
1640 __isl_give isl_map *isl_map_from_pw_aff(
1641 __isl_take isl_pw_aff *pwaff);
1642 __isl_give isl_basic_map *isl_basic_map_from_aff_list(
1643 __isl_take isl_space *domain_space,
1644 __isl_take isl_aff_list *list);
1645 __isl_give isl_basic_map *isl_basic_map_from_multi_aff(
1646 __isl_take isl_multi_aff *maff)
1647 __isl_give isl_map *isl_map_from_multi_aff(
1648 __isl_take isl_multi_aff *maff)
1649 __isl_give isl_set *isl_set_from_pw_multi_aff(
1650 __isl_take isl_pw_multi_aff *pma);
1651 __isl_give isl_map *isl_map_from_pw_multi_aff(
1652 __isl_take isl_pw_multi_aff *pma);
1653 __isl_give isl_union_map *
1654 isl_union_map_from_union_pw_multi_aff(
1655 __isl_take isl_union_pw_multi_aff *upma);
1657 The C<domain_dim> argument describes the domain of the resulting
1658 basic relation. It is required because the C<list> may consist
1659 of zero affine expressions.
1661 =head2 Inspecting Sets and Relations
1663 Usually, the user should not have to care about the actual constraints
1664 of the sets and maps, but should instead apply the abstract operations
1665 explained in the following sections.
1666 Occasionally, however, it may be required to inspect the individual
1667 coefficients of the constraints. This section explains how to do so.
1668 In these cases, it may also be useful to have C<isl> compute
1669 an explicit representation of the existentially quantified variables.
1671 __isl_give isl_set *isl_set_compute_divs(
1672 __isl_take isl_set *set);
1673 __isl_give isl_map *isl_map_compute_divs(
1674 __isl_take isl_map *map);
1675 __isl_give isl_union_set *isl_union_set_compute_divs(
1676 __isl_take isl_union_set *uset);
1677 __isl_give isl_union_map *isl_union_map_compute_divs(
1678 __isl_take isl_union_map *umap);
1680 This explicit representation defines the existentially quantified
1681 variables as integer divisions of the other variables, possibly
1682 including earlier existentially quantified variables.
1683 An explicitly represented existentially quantified variable therefore
1684 has a unique value when the values of the other variables are known.
1685 If, furthermore, the same existentials, i.e., existentials
1686 with the same explicit representations, should appear in the
1687 same order in each of the disjuncts of a set or map, then the user should call
1688 either of the following functions.
1690 __isl_give isl_set *isl_set_align_divs(
1691 __isl_take isl_set *set);
1692 __isl_give isl_map *isl_map_align_divs(
1693 __isl_take isl_map *map);
1695 Alternatively, the existentially quantified variables can be removed
1696 using the following functions, which compute an overapproximation.
1698 __isl_give isl_basic_set *isl_basic_set_remove_divs(
1699 __isl_take isl_basic_set *bset);
1700 __isl_give isl_basic_map *isl_basic_map_remove_divs(
1701 __isl_take isl_basic_map *bmap);
1702 __isl_give isl_set *isl_set_remove_divs(
1703 __isl_take isl_set *set);
1704 __isl_give isl_map *isl_map_remove_divs(
1705 __isl_take isl_map *map);
1707 It is also possible to only remove those divs that are defined
1708 in terms of a given range of dimensions or only those for which
1709 no explicit representation is known.
1711 __isl_give isl_basic_set *
1712 isl_basic_set_remove_divs_involving_dims(
1713 __isl_take isl_basic_set *bset,
1714 enum isl_dim_type type,
1715 unsigned first, unsigned n);
1716 __isl_give isl_basic_map *
1717 isl_basic_map_remove_divs_involving_dims(
1718 __isl_take isl_basic_map *bmap,
1719 enum isl_dim_type type,
1720 unsigned first, unsigned n);
1721 __isl_give isl_set *isl_set_remove_divs_involving_dims(
1722 __isl_take isl_set *set, enum isl_dim_type type,
1723 unsigned first, unsigned n);
1724 __isl_give isl_map *isl_map_remove_divs_involving_dims(
1725 __isl_take isl_map *map, enum isl_dim_type type,
1726 unsigned first, unsigned n);
1728 __isl_give isl_basic_set *
1729 isl_basic_set_remove_unknown_divs(
1730 __isl_take isl_basic_set *bset);
1731 __isl_give isl_set *isl_set_remove_unknown_divs(
1732 __isl_take isl_set *set);
1733 __isl_give isl_map *isl_map_remove_unknown_divs(
1734 __isl_take isl_map *map);
1736 To iterate over all the sets or maps in a union set or map, use
1738 int isl_union_set_foreach_set(__isl_keep isl_union_set *uset,
1739 int (*fn)(__isl_take isl_set *set, void *user),
1741 int isl_union_map_foreach_map(__isl_keep isl_union_map *umap,
1742 int (*fn)(__isl_take isl_map *map, void *user),
1745 The number of sets or maps in a union set or map can be obtained
1748 int isl_union_set_n_set(__isl_keep isl_union_set *uset);
1749 int isl_union_map_n_map(__isl_keep isl_union_map *umap);
1751 To extract the set or map in a given space from a union, use
1753 __isl_give isl_set *isl_union_set_extract_set(
1754 __isl_keep isl_union_set *uset,
1755 __isl_take isl_space *space);
1756 __isl_give isl_map *isl_union_map_extract_map(
1757 __isl_keep isl_union_map *umap,
1758 __isl_take isl_space *space);
1760 To iterate over all the basic sets or maps in a set or map, use
1762 int isl_set_foreach_basic_set(__isl_keep isl_set *set,
1763 int (*fn)(__isl_take isl_basic_set *bset, void *user),
1765 int isl_map_foreach_basic_map(__isl_keep isl_map *map,
1766 int (*fn)(__isl_take isl_basic_map *bmap, void *user),
1769 The callback function C<fn> should return 0 if successful and
1770 -1 if an error occurs. In the latter case, or if any other error
1771 occurs, the above functions will return -1.
1773 It should be noted that C<isl> does not guarantee that
1774 the basic sets or maps passed to C<fn> are disjoint.
1775 If this is required, then the user should call one of
1776 the following functions first.
1778 __isl_give isl_set *isl_set_make_disjoint(
1779 __isl_take isl_set *set);
1780 __isl_give isl_map *isl_map_make_disjoint(
1781 __isl_take isl_map *map);
1783 The number of basic sets in a set can be obtained
1786 int isl_set_n_basic_set(__isl_keep isl_set *set);
1788 To iterate over the constraints of a basic set or map, use
1790 #include <isl/constraint.h>
1792 int isl_basic_set_n_constraint(
1793 __isl_keep isl_basic_set *bset);
1794 int isl_basic_set_foreach_constraint(
1795 __isl_keep isl_basic_set *bset,
1796 int (*fn)(__isl_take isl_constraint *c, void *user),
1798 int isl_basic_map_foreach_constraint(
1799 __isl_keep isl_basic_map *bmap,
1800 int (*fn)(__isl_take isl_constraint *c, void *user),
1802 void *isl_constraint_free(__isl_take isl_constraint *c);
1804 Again, the callback function C<fn> should return 0 if successful and
1805 -1 if an error occurs. In the latter case, or if any other error
1806 occurs, the above functions will return -1.
1807 The constraint C<c> represents either an equality or an inequality.
1808 Use the following function to find out whether a constraint
1809 represents an equality. If not, it represents an inequality.
1811 int isl_constraint_is_equality(
1812 __isl_keep isl_constraint *constraint);
1814 The coefficients of the constraints can be inspected using
1815 the following functions.
1817 int isl_constraint_is_lower_bound(
1818 __isl_keep isl_constraint *constraint,
1819 enum isl_dim_type type, unsigned pos);
1820 int isl_constraint_is_upper_bound(
1821 __isl_keep isl_constraint *constraint,
1822 enum isl_dim_type type, unsigned pos);
1823 void isl_constraint_get_constant(
1824 __isl_keep isl_constraint *constraint, isl_int *v);
1825 __isl_give isl_val *isl_constraint_get_constant_val(
1826 __isl_keep isl_constraint *constraint);
1827 void isl_constraint_get_coefficient(
1828 __isl_keep isl_constraint *constraint,
1829 enum isl_dim_type type, int pos, isl_int *v);
1830 __isl_give isl_val *isl_constraint_get_coefficient_val(
1831 __isl_keep isl_constraint *constraint,
1832 enum isl_dim_type type, int pos);
1833 int isl_constraint_involves_dims(
1834 __isl_keep isl_constraint *constraint,
1835 enum isl_dim_type type, unsigned first, unsigned n);
1837 The explicit representations of the existentially quantified
1838 variables can be inspected using the following function.
1839 Note that the user is only allowed to use this function
1840 if the inspected set or map is the result of a call
1841 to C<isl_set_compute_divs> or C<isl_map_compute_divs>.
1842 The existentially quantified variable is equal to the floor
1843 of the returned affine expression. The affine expression
1844 itself can be inspected using the functions in
1845 L<"Piecewise Quasi Affine Expressions">.
1847 __isl_give isl_aff *isl_constraint_get_div(
1848 __isl_keep isl_constraint *constraint, int pos);
1850 To obtain the constraints of a basic set or map in matrix
1851 form, use the following functions.
1853 __isl_give isl_mat *isl_basic_set_equalities_matrix(
1854 __isl_keep isl_basic_set *bset,
1855 enum isl_dim_type c1, enum isl_dim_type c2,
1856 enum isl_dim_type c3, enum isl_dim_type c4);
1857 __isl_give isl_mat *isl_basic_set_inequalities_matrix(
1858 __isl_keep isl_basic_set *bset,
1859 enum isl_dim_type c1, enum isl_dim_type c2,
1860 enum isl_dim_type c3, enum isl_dim_type c4);
1861 __isl_give isl_mat *isl_basic_map_equalities_matrix(
1862 __isl_keep isl_basic_map *bmap,
1863 enum isl_dim_type c1,
1864 enum isl_dim_type c2, enum isl_dim_type c3,
1865 enum isl_dim_type c4, enum isl_dim_type c5);
1866 __isl_give isl_mat *isl_basic_map_inequalities_matrix(
1867 __isl_keep isl_basic_map *bmap,
1868 enum isl_dim_type c1,
1869 enum isl_dim_type c2, enum isl_dim_type c3,
1870 enum isl_dim_type c4, enum isl_dim_type c5);
1872 The C<isl_dim_type> arguments dictate the order in which
1873 different kinds of variables appear in the resulting matrix
1874 and should be a permutation of C<isl_dim_cst>, C<isl_dim_param>,
1875 C<isl_dim_in>, C<isl_dim_out> and C<isl_dim_div>.
1877 The number of parameters, input, output or set dimensions can
1878 be obtained using the following functions.
1880 unsigned isl_basic_set_dim(__isl_keep isl_basic_set *bset,
1881 enum isl_dim_type type);
1882 unsigned isl_basic_map_dim(__isl_keep isl_basic_map *bmap,
1883 enum isl_dim_type type);
1884 unsigned isl_set_dim(__isl_keep isl_set *set,
1885 enum isl_dim_type type);
1886 unsigned isl_map_dim(__isl_keep isl_map *map,
1887 enum isl_dim_type type);
1889 To check whether the description of a set or relation depends
1890 on one or more given dimensions, it is not necessary to iterate over all
1891 constraints. Instead the following functions can be used.
1893 int isl_basic_set_involves_dims(
1894 __isl_keep isl_basic_set *bset,
1895 enum isl_dim_type type, unsigned first, unsigned n);
1896 int isl_set_involves_dims(__isl_keep isl_set *set,
1897 enum isl_dim_type type, unsigned first, unsigned n);
1898 int isl_basic_map_involves_dims(
1899 __isl_keep isl_basic_map *bmap,
1900 enum isl_dim_type type, unsigned first, unsigned n);
1901 int isl_map_involves_dims(__isl_keep isl_map *map,
1902 enum isl_dim_type type, unsigned first, unsigned n);
1904 Similarly, the following functions can be used to check whether
1905 a given dimension is involved in any lower or upper bound.
1907 int isl_set_dim_has_any_lower_bound(__isl_keep isl_set *set,
1908 enum isl_dim_type type, unsigned pos);
1909 int isl_set_dim_has_any_upper_bound(__isl_keep isl_set *set,
1910 enum isl_dim_type type, unsigned pos);
1912 Note that these functions return true even if there is a bound on
1913 the dimension on only some of the basic sets of C<set>.
1914 To check if they have a bound for all of the basic sets in C<set>,
1915 use the following functions instead.
1917 int isl_set_dim_has_lower_bound(__isl_keep isl_set *set,
1918 enum isl_dim_type type, unsigned pos);
1919 int isl_set_dim_has_upper_bound(__isl_keep isl_set *set,
1920 enum isl_dim_type type, unsigned pos);
1922 The identifiers or names of the domain and range spaces of a set
1923 or relation can be read off or set using the following functions.
1925 __isl_give isl_set *isl_set_set_tuple_id(
1926 __isl_take isl_set *set, __isl_take isl_id *id);
1927 __isl_give isl_set *isl_set_reset_tuple_id(
1928 __isl_take isl_set *set);
1929 int isl_set_has_tuple_id(__isl_keep isl_set *set);
1930 __isl_give isl_id *isl_set_get_tuple_id(
1931 __isl_keep isl_set *set);
1932 __isl_give isl_map *isl_map_set_tuple_id(
1933 __isl_take isl_map *map, enum isl_dim_type type,
1934 __isl_take isl_id *id);
1935 __isl_give isl_map *isl_map_reset_tuple_id(
1936 __isl_take isl_map *map, enum isl_dim_type type);
1937 int isl_map_has_tuple_id(__isl_keep isl_map *map,
1938 enum isl_dim_type type);
1939 __isl_give isl_id *isl_map_get_tuple_id(
1940 __isl_keep isl_map *map, enum isl_dim_type type);
1942 const char *isl_basic_set_get_tuple_name(
1943 __isl_keep isl_basic_set *bset);
1944 __isl_give isl_basic_set *isl_basic_set_set_tuple_name(
1945 __isl_take isl_basic_set *set, const char *s);
1946 int isl_set_has_tuple_name(__isl_keep isl_set *set);
1947 const char *isl_set_get_tuple_name(
1948 __isl_keep isl_set *set);
1949 const char *isl_basic_map_get_tuple_name(
1950 __isl_keep isl_basic_map *bmap,
1951 enum isl_dim_type type);
1952 __isl_give isl_basic_map *isl_basic_map_set_tuple_name(
1953 __isl_take isl_basic_map *bmap,
1954 enum isl_dim_type type, const char *s);
1955 int isl_map_has_tuple_name(__isl_keep isl_map *map,
1956 enum isl_dim_type type);
1957 const char *isl_map_get_tuple_name(
1958 __isl_keep isl_map *map,
1959 enum isl_dim_type type);
1961 As with C<isl_space_get_tuple_name>, the value returned points to
1962 an internal data structure.
1963 The identifiers, positions or names of individual dimensions can be
1964 read off using the following functions.
1966 __isl_give isl_id *isl_basic_set_get_dim_id(
1967 __isl_keep isl_basic_set *bset,
1968 enum isl_dim_type type, unsigned pos);
1969 __isl_give isl_set *isl_set_set_dim_id(
1970 __isl_take isl_set *set, enum isl_dim_type type,
1971 unsigned pos, __isl_take isl_id *id);
1972 int isl_set_has_dim_id(__isl_keep isl_set *set,
1973 enum isl_dim_type type, unsigned pos);
1974 __isl_give isl_id *isl_set_get_dim_id(
1975 __isl_keep isl_set *set, enum isl_dim_type type,
1977 int isl_basic_map_has_dim_id(
1978 __isl_keep isl_basic_map *bmap,
1979 enum isl_dim_type type, unsigned pos);
1980 __isl_give isl_map *isl_map_set_dim_id(
1981 __isl_take isl_map *map, enum isl_dim_type type,
1982 unsigned pos, __isl_take isl_id *id);
1983 int isl_map_has_dim_id(__isl_keep isl_map *map,
1984 enum isl_dim_type type, unsigned pos);
1985 __isl_give isl_id *isl_map_get_dim_id(
1986 __isl_keep isl_map *map, enum isl_dim_type type,
1989 int isl_set_find_dim_by_id(__isl_keep isl_set *set,
1990 enum isl_dim_type type, __isl_keep isl_id *id);
1991 int isl_map_find_dim_by_id(__isl_keep isl_map *map,
1992 enum isl_dim_type type, __isl_keep isl_id *id);
1993 int isl_set_find_dim_by_name(__isl_keep isl_set *set,
1994 enum isl_dim_type type, const char *name);
1995 int isl_map_find_dim_by_name(__isl_keep isl_map *map,
1996 enum isl_dim_type type, const char *name);
1998 const char *isl_constraint_get_dim_name(
1999 __isl_keep isl_constraint *constraint,
2000 enum isl_dim_type type, unsigned pos);
2001 const char *isl_basic_set_get_dim_name(
2002 __isl_keep isl_basic_set *bset,
2003 enum isl_dim_type type, unsigned pos);
2004 int isl_set_has_dim_name(__isl_keep isl_set *set,
2005 enum isl_dim_type type, unsigned pos);
2006 const char *isl_set_get_dim_name(
2007 __isl_keep isl_set *set,
2008 enum isl_dim_type type, unsigned pos);
2009 const char *isl_basic_map_get_dim_name(
2010 __isl_keep isl_basic_map *bmap,
2011 enum isl_dim_type type, unsigned pos);
2012 int isl_map_has_dim_name(__isl_keep isl_map *map,
2013 enum isl_dim_type type, unsigned pos);
2014 const char *isl_map_get_dim_name(
2015 __isl_keep isl_map *map,
2016 enum isl_dim_type type, unsigned pos);
2018 These functions are mostly useful to obtain the identifiers, positions
2019 or names of the parameters. Identifiers of individual dimensions are
2020 essentially only useful for printing. They are ignored by all other
2021 operations and may not be preserved across those operations.
2025 =head3 Unary Properties
2031 The following functions test whether the given set or relation
2032 contains any integer points. The ``plain'' variants do not perform
2033 any computations, but simply check if the given set or relation
2034 is already known to be empty.
2036 int isl_basic_set_plain_is_empty(__isl_keep isl_basic_set *bset);
2037 int isl_basic_set_is_empty(__isl_keep isl_basic_set *bset);
2038 int isl_set_plain_is_empty(__isl_keep isl_set *set);
2039 int isl_set_is_empty(__isl_keep isl_set *set);
2040 int isl_union_set_is_empty(__isl_keep isl_union_set *uset);
2041 int isl_basic_map_plain_is_empty(__isl_keep isl_basic_map *bmap);
2042 int isl_basic_map_is_empty(__isl_keep isl_basic_map *bmap);
2043 int isl_map_plain_is_empty(__isl_keep isl_map *map);
2044 int isl_map_is_empty(__isl_keep isl_map *map);
2045 int isl_union_map_is_empty(__isl_keep isl_union_map *umap);
2047 =item * Universality
2049 int isl_basic_set_is_universe(__isl_keep isl_basic_set *bset);
2050 int isl_basic_map_is_universe(__isl_keep isl_basic_map *bmap);
2051 int isl_set_plain_is_universe(__isl_keep isl_set *set);
2053 =item * Single-valuedness
2055 int isl_basic_map_is_single_valued(
2056 __isl_keep isl_basic_map *bmap);
2057 int isl_map_plain_is_single_valued(
2058 __isl_keep isl_map *map);
2059 int isl_map_is_single_valued(__isl_keep isl_map *map);
2060 int isl_union_map_is_single_valued(__isl_keep isl_union_map *umap);
2064 int isl_map_plain_is_injective(__isl_keep isl_map *map);
2065 int isl_map_is_injective(__isl_keep isl_map *map);
2066 int isl_union_map_plain_is_injective(
2067 __isl_keep isl_union_map *umap);
2068 int isl_union_map_is_injective(
2069 __isl_keep isl_union_map *umap);
2073 int isl_map_is_bijective(__isl_keep isl_map *map);
2074 int isl_union_map_is_bijective(__isl_keep isl_union_map *umap);
2078 int isl_basic_map_plain_is_fixed(
2079 __isl_keep isl_basic_map *bmap,
2080 enum isl_dim_type type, unsigned pos,
2082 int isl_set_plain_is_fixed(__isl_keep isl_set *set,
2083 enum isl_dim_type type, unsigned pos,
2085 int isl_map_plain_is_fixed(__isl_keep isl_map *map,
2086 enum isl_dim_type type, unsigned pos,
2089 Check if the relation obviously lies on a hyperplane where the given dimension
2090 has a fixed value and if so, return that value in C<*val>.
2092 __isl_give isl_val *
2093 isl_basic_map_plain_get_val_if_fixed(
2094 __isl_keep isl_basic_map *bmap,
2095 enum isl_dim_type type, unsigned pos);
2096 __isl_give isl_val *isl_set_plain_get_val_if_fixed(
2097 __isl_keep isl_set *set,
2098 enum isl_dim_type type, unsigned pos);
2099 __isl_give isl_val *isl_map_plain_get_val_if_fixed(
2100 __isl_keep isl_map *map,
2101 enum isl_dim_type type, unsigned pos);
2103 If the set or relation obviously lies on a hyperplane where the given dimension
2104 has a fixed value, then return that value.
2105 Otherwise return NaN.
2109 int isl_set_dim_residue_class_val(
2110 __isl_keep isl_set *set,
2111 int pos, __isl_give isl_val **modulo,
2112 __isl_give isl_val **residue);
2114 Check if the values of the given set dimension are equal to a fixed
2115 value modulo some integer value. If so, assign the modulo to C<*modulo>
2116 and the fixed value to C<*residue>. If the given dimension attains only
2117 a single value, then assign C<0> to C<*modulo> and the fixed value to
2119 If the dimension does not attain only a single value and if no modulo
2120 can be found then assign C<1> to C<*modulo> and C<1> to C<*residue>.
2124 To check whether a set is a parameter domain, use this function:
2126 int isl_set_is_params(__isl_keep isl_set *set);
2127 int isl_union_set_is_params(
2128 __isl_keep isl_union_set *uset);
2132 The following functions check whether the domain of the given
2133 (basic) set is a wrapped relation.
2135 int isl_basic_set_is_wrapping(
2136 __isl_keep isl_basic_set *bset);
2137 int isl_set_is_wrapping(__isl_keep isl_set *set);
2139 =item * Internal Product
2141 int isl_basic_map_can_zip(
2142 __isl_keep isl_basic_map *bmap);
2143 int isl_map_can_zip(__isl_keep isl_map *map);
2145 Check whether the product of domain and range of the given relation
2147 i.e., whether both domain and range are nested relations.
2151 int isl_basic_map_can_curry(
2152 __isl_keep isl_basic_map *bmap);
2153 int isl_map_can_curry(__isl_keep isl_map *map);
2155 Check whether the domain of the (basic) relation is a wrapped relation.
2157 int isl_basic_map_can_uncurry(
2158 __isl_keep isl_basic_map *bmap);
2159 int isl_map_can_uncurry(__isl_keep isl_map *map);
2161 Check whether the range of the (basic) relation is a wrapped relation.
2165 =head3 Binary Properties
2171 int isl_set_plain_is_equal(__isl_keep isl_set *set1,
2172 __isl_keep isl_set *set2);
2173 int isl_set_is_equal(__isl_keep isl_set *set1,
2174 __isl_keep isl_set *set2);
2175 int isl_union_set_is_equal(
2176 __isl_keep isl_union_set *uset1,
2177 __isl_keep isl_union_set *uset2);
2178 int isl_basic_map_is_equal(
2179 __isl_keep isl_basic_map *bmap1,
2180 __isl_keep isl_basic_map *bmap2);
2181 int isl_map_is_equal(__isl_keep isl_map *map1,
2182 __isl_keep isl_map *map2);
2183 int isl_map_plain_is_equal(__isl_keep isl_map *map1,
2184 __isl_keep isl_map *map2);
2185 int isl_union_map_is_equal(
2186 __isl_keep isl_union_map *umap1,
2187 __isl_keep isl_union_map *umap2);
2189 =item * Disjointness
2191 int isl_set_plain_is_disjoint(__isl_keep isl_set *set1,
2192 __isl_keep isl_set *set2);
2193 int isl_set_is_disjoint(__isl_keep isl_set *set1,
2194 __isl_keep isl_set *set2);
2195 int isl_map_is_disjoint(__isl_keep isl_map *map1,
2196 __isl_keep isl_map *map2);
2200 int isl_basic_set_is_subset(
2201 __isl_keep isl_basic_set *bset1,
2202 __isl_keep isl_basic_set *bset2);
2203 int isl_set_is_subset(__isl_keep isl_set *set1,
2204 __isl_keep isl_set *set2);
2205 int isl_set_is_strict_subset(
2206 __isl_keep isl_set *set1,
2207 __isl_keep isl_set *set2);
2208 int isl_union_set_is_subset(
2209 __isl_keep isl_union_set *uset1,
2210 __isl_keep isl_union_set *uset2);
2211 int isl_union_set_is_strict_subset(
2212 __isl_keep isl_union_set *uset1,
2213 __isl_keep isl_union_set *uset2);
2214 int isl_basic_map_is_subset(
2215 __isl_keep isl_basic_map *bmap1,
2216 __isl_keep isl_basic_map *bmap2);
2217 int isl_basic_map_is_strict_subset(
2218 __isl_keep isl_basic_map *bmap1,
2219 __isl_keep isl_basic_map *bmap2);
2220 int isl_map_is_subset(
2221 __isl_keep isl_map *map1,
2222 __isl_keep isl_map *map2);
2223 int isl_map_is_strict_subset(
2224 __isl_keep isl_map *map1,
2225 __isl_keep isl_map *map2);
2226 int isl_union_map_is_subset(
2227 __isl_keep isl_union_map *umap1,
2228 __isl_keep isl_union_map *umap2);
2229 int isl_union_map_is_strict_subset(
2230 __isl_keep isl_union_map *umap1,
2231 __isl_keep isl_union_map *umap2);
2233 Check whether the first argument is a (strict) subset of the
2238 int isl_set_plain_cmp(__isl_keep isl_set *set1,
2239 __isl_keep isl_set *set2);
2241 This function is useful for sorting C<isl_set>s.
2242 The order depends on the internal representation of the inputs.
2243 The order is fixed over different calls to the function (assuming
2244 the internal representation of the inputs has not changed), but may
2245 change over different versions of C<isl>.
2249 =head2 Unary Operations
2255 __isl_give isl_set *isl_set_complement(
2256 __isl_take isl_set *set);
2257 __isl_give isl_map *isl_map_complement(
2258 __isl_take isl_map *map);
2262 __isl_give isl_basic_map *isl_basic_map_reverse(
2263 __isl_take isl_basic_map *bmap);
2264 __isl_give isl_map *isl_map_reverse(
2265 __isl_take isl_map *map);
2266 __isl_give isl_union_map *isl_union_map_reverse(
2267 __isl_take isl_union_map *umap);
2271 __isl_give isl_basic_set *isl_basic_set_project_out(
2272 __isl_take isl_basic_set *bset,
2273 enum isl_dim_type type, unsigned first, unsigned n);
2274 __isl_give isl_basic_map *isl_basic_map_project_out(
2275 __isl_take isl_basic_map *bmap,
2276 enum isl_dim_type type, unsigned first, unsigned n);
2277 __isl_give isl_set *isl_set_project_out(__isl_take isl_set *set,
2278 enum isl_dim_type type, unsigned first, unsigned n);
2279 __isl_give isl_map *isl_map_project_out(__isl_take isl_map *map,
2280 enum isl_dim_type type, unsigned first, unsigned n);
2281 __isl_give isl_basic_set *isl_basic_set_params(
2282 __isl_take isl_basic_set *bset);
2283 __isl_give isl_basic_set *isl_basic_map_domain(
2284 __isl_take isl_basic_map *bmap);
2285 __isl_give isl_basic_set *isl_basic_map_range(
2286 __isl_take isl_basic_map *bmap);
2287 __isl_give isl_set *isl_set_params(__isl_take isl_set *set);
2288 __isl_give isl_set *isl_map_params(__isl_take isl_map *map);
2289 __isl_give isl_set *isl_map_domain(
2290 __isl_take isl_map *bmap);
2291 __isl_give isl_set *isl_map_range(
2292 __isl_take isl_map *map);
2293 __isl_give isl_set *isl_union_set_params(
2294 __isl_take isl_union_set *uset);
2295 __isl_give isl_set *isl_union_map_params(
2296 __isl_take isl_union_map *umap);
2297 __isl_give isl_union_set *isl_union_map_domain(
2298 __isl_take isl_union_map *umap);
2299 __isl_give isl_union_set *isl_union_map_range(
2300 __isl_take isl_union_map *umap);
2302 __isl_give isl_basic_map *isl_basic_map_domain_map(
2303 __isl_take isl_basic_map *bmap);
2304 __isl_give isl_basic_map *isl_basic_map_range_map(
2305 __isl_take isl_basic_map *bmap);
2306 __isl_give isl_map *isl_map_domain_map(__isl_take isl_map *map);
2307 __isl_give isl_map *isl_map_range_map(__isl_take isl_map *map);
2308 __isl_give isl_union_map *isl_union_map_domain_map(
2309 __isl_take isl_union_map *umap);
2310 __isl_give isl_union_map *isl_union_map_range_map(
2311 __isl_take isl_union_map *umap);
2313 The functions above construct a (basic, regular or union) relation
2314 that maps (a wrapped version of) the input relation to its domain or range.
2318 __isl_give isl_basic_set *isl_basic_set_eliminate(
2319 __isl_take isl_basic_set *bset,
2320 enum isl_dim_type type,
2321 unsigned first, unsigned n);
2322 __isl_give isl_set *isl_set_eliminate(
2323 __isl_take isl_set *set, enum isl_dim_type type,
2324 unsigned first, unsigned n);
2325 __isl_give isl_basic_map *isl_basic_map_eliminate(
2326 __isl_take isl_basic_map *bmap,
2327 enum isl_dim_type type,
2328 unsigned first, unsigned n);
2329 __isl_give isl_map *isl_map_eliminate(
2330 __isl_take isl_map *map, enum isl_dim_type type,
2331 unsigned first, unsigned n);
2333 Eliminate the coefficients for the given dimensions from the constraints,
2334 without removing the dimensions.
2338 __isl_give isl_basic_set *isl_basic_set_fix(
2339 __isl_take isl_basic_set *bset,
2340 enum isl_dim_type type, unsigned pos,
2342 __isl_give isl_basic_set *isl_basic_set_fix_si(
2343 __isl_take isl_basic_set *bset,
2344 enum isl_dim_type type, unsigned pos, int value);
2345 __isl_give isl_basic_set *isl_basic_set_fix_val(
2346 __isl_take isl_basic_set *bset,
2347 enum isl_dim_type type, unsigned pos,
2348 __isl_take isl_val *v);
2349 __isl_give isl_set *isl_set_fix(__isl_take isl_set *set,
2350 enum isl_dim_type type, unsigned pos,
2352 __isl_give isl_set *isl_set_fix_si(__isl_take isl_set *set,
2353 enum isl_dim_type type, unsigned pos, int value);
2354 __isl_give isl_set *isl_set_fix_val(
2355 __isl_take isl_set *set,
2356 enum isl_dim_type type, unsigned pos,
2357 __isl_take isl_val *v);
2358 __isl_give isl_basic_map *isl_basic_map_fix_si(
2359 __isl_take isl_basic_map *bmap,
2360 enum isl_dim_type type, unsigned pos, int value);
2361 __isl_give isl_basic_map *isl_basic_map_fix_val(
2362 __isl_take isl_basic_map *bmap,
2363 enum isl_dim_type type, unsigned pos,
2364 __isl_take isl_val *v);
2365 __isl_give isl_map *isl_map_fix(__isl_take isl_map *map,
2366 enum isl_dim_type type, unsigned pos,
2368 __isl_give isl_map *isl_map_fix_si(__isl_take isl_map *map,
2369 enum isl_dim_type type, unsigned pos, int value);
2370 __isl_give isl_map *isl_map_fix_val(
2371 __isl_take isl_map *map,
2372 enum isl_dim_type type, unsigned pos,
2373 __isl_take isl_val *v);
2375 Intersect the set or relation with the hyperplane where the given
2376 dimension has the fixed given value.
2378 __isl_give isl_basic_map *isl_basic_map_lower_bound_si(
2379 __isl_take isl_basic_map *bmap,
2380 enum isl_dim_type type, unsigned pos, int value);
2381 __isl_give isl_basic_map *isl_basic_map_upper_bound_si(
2382 __isl_take isl_basic_map *bmap,
2383 enum isl_dim_type type, unsigned pos, int value);
2384 __isl_give isl_set *isl_set_lower_bound(
2385 __isl_take isl_set *set,
2386 enum isl_dim_type type, unsigned pos,
2388 __isl_give isl_set *isl_set_lower_bound_si(
2389 __isl_take isl_set *set,
2390 enum isl_dim_type type, unsigned pos, int value);
2391 __isl_give isl_set *isl_set_lower_bound_val(
2392 __isl_take isl_set *set,
2393 enum isl_dim_type type, unsigned pos,
2394 __isl_take isl_val *value);
2395 __isl_give isl_map *isl_map_lower_bound_si(
2396 __isl_take isl_map *map,
2397 enum isl_dim_type type, unsigned pos, int value);
2398 __isl_give isl_set *isl_set_upper_bound(
2399 __isl_take isl_set *set,
2400 enum isl_dim_type type, unsigned pos,
2402 __isl_give isl_set *isl_set_upper_bound_si(
2403 __isl_take isl_set *set,
2404 enum isl_dim_type type, unsigned pos, int value);
2405 __isl_give isl_set *isl_set_upper_bound_val(
2406 __isl_take isl_set *set,
2407 enum isl_dim_type type, unsigned pos,
2408 __isl_take isl_val *value);
2409 __isl_give isl_map *isl_map_upper_bound_si(
2410 __isl_take isl_map *map,
2411 enum isl_dim_type type, unsigned pos, int value);
2413 Intersect the set or relation with the half-space where the given
2414 dimension has a value bounded by the fixed given integer value.
2416 __isl_give isl_set *isl_set_equate(__isl_take isl_set *set,
2417 enum isl_dim_type type1, int pos1,
2418 enum isl_dim_type type2, int pos2);
2419 __isl_give isl_basic_map *isl_basic_map_equate(
2420 __isl_take isl_basic_map *bmap,
2421 enum isl_dim_type type1, int pos1,
2422 enum isl_dim_type type2, int pos2);
2423 __isl_give isl_map *isl_map_equate(__isl_take isl_map *map,
2424 enum isl_dim_type type1, int pos1,
2425 enum isl_dim_type type2, int pos2);
2427 Intersect the set or relation with the hyperplane where the given
2428 dimensions are equal to each other.
2430 __isl_give isl_map *isl_map_oppose(__isl_take isl_map *map,
2431 enum isl_dim_type type1, int pos1,
2432 enum isl_dim_type type2, int pos2);
2434 Intersect the relation with the hyperplane where the given
2435 dimensions have opposite values.
2437 __isl_give isl_basic_map *isl_basic_map_order_ge(
2438 __isl_take isl_basic_map *bmap,
2439 enum isl_dim_type type1, int pos1,
2440 enum isl_dim_type type2, int pos2);
2441 __isl_give isl_map *isl_map_order_lt(__isl_take isl_map *map,
2442 enum isl_dim_type type1, int pos1,
2443 enum isl_dim_type type2, int pos2);
2444 __isl_give isl_basic_map *isl_basic_map_order_gt(
2445 __isl_take isl_basic_map *bmap,
2446 enum isl_dim_type type1, int pos1,
2447 enum isl_dim_type type2, int pos2);
2448 __isl_give isl_map *isl_map_order_gt(__isl_take isl_map *map,
2449 enum isl_dim_type type1, int pos1,
2450 enum isl_dim_type type2, int pos2);
2452 Intersect the relation with the half-space where the given
2453 dimensions satisfy the given ordering.
2457 __isl_give isl_map *isl_set_identity(
2458 __isl_take isl_set *set);
2459 __isl_give isl_union_map *isl_union_set_identity(
2460 __isl_take isl_union_set *uset);
2462 Construct an identity relation on the given (union) set.
2466 __isl_give isl_basic_set *isl_basic_map_deltas(
2467 __isl_take isl_basic_map *bmap);
2468 __isl_give isl_set *isl_map_deltas(__isl_take isl_map *map);
2469 __isl_give isl_union_set *isl_union_map_deltas(
2470 __isl_take isl_union_map *umap);
2472 These functions return a (basic) set containing the differences
2473 between image elements and corresponding domain elements in the input.
2475 __isl_give isl_basic_map *isl_basic_map_deltas_map(
2476 __isl_take isl_basic_map *bmap);
2477 __isl_give isl_map *isl_map_deltas_map(
2478 __isl_take isl_map *map);
2479 __isl_give isl_union_map *isl_union_map_deltas_map(
2480 __isl_take isl_union_map *umap);
2482 The functions above construct a (basic, regular or union) relation
2483 that maps (a wrapped version of) the input relation to its delta set.
2487 Simplify the representation of a set or relation by trying
2488 to combine pairs of basic sets or relations into a single
2489 basic set or relation.
2491 __isl_give isl_set *isl_set_coalesce(__isl_take isl_set *set);
2492 __isl_give isl_map *isl_map_coalesce(__isl_take isl_map *map);
2493 __isl_give isl_union_set *isl_union_set_coalesce(
2494 __isl_take isl_union_set *uset);
2495 __isl_give isl_union_map *isl_union_map_coalesce(
2496 __isl_take isl_union_map *umap);
2498 One of the methods for combining pairs of basic sets or relations
2499 can result in coefficients that are much larger than those that appear
2500 in the constraints of the input. By default, the coefficients are
2501 not allowed to grow larger, but this can be changed by unsetting
2502 the following option.
2504 int isl_options_set_coalesce_bounded_wrapping(
2505 isl_ctx *ctx, int val);
2506 int isl_options_get_coalesce_bounded_wrapping(
2509 =item * Detecting equalities
2511 __isl_give isl_basic_set *isl_basic_set_detect_equalities(
2512 __isl_take isl_basic_set *bset);
2513 __isl_give isl_basic_map *isl_basic_map_detect_equalities(
2514 __isl_take isl_basic_map *bmap);
2515 __isl_give isl_set *isl_set_detect_equalities(
2516 __isl_take isl_set *set);
2517 __isl_give isl_map *isl_map_detect_equalities(
2518 __isl_take isl_map *map);
2519 __isl_give isl_union_set *isl_union_set_detect_equalities(
2520 __isl_take isl_union_set *uset);
2521 __isl_give isl_union_map *isl_union_map_detect_equalities(
2522 __isl_take isl_union_map *umap);
2524 Simplify the representation of a set or relation by detecting implicit
2527 =item * Removing redundant constraints
2529 __isl_give isl_basic_set *isl_basic_set_remove_redundancies(
2530 __isl_take isl_basic_set *bset);
2531 __isl_give isl_set *isl_set_remove_redundancies(
2532 __isl_take isl_set *set);
2533 __isl_give isl_basic_map *isl_basic_map_remove_redundancies(
2534 __isl_take isl_basic_map *bmap);
2535 __isl_give isl_map *isl_map_remove_redundancies(
2536 __isl_take isl_map *map);
2540 __isl_give isl_basic_set *isl_set_convex_hull(
2541 __isl_take isl_set *set);
2542 __isl_give isl_basic_map *isl_map_convex_hull(
2543 __isl_take isl_map *map);
2545 If the input set or relation has any existentially quantified
2546 variables, then the result of these operations is currently undefined.
2550 __isl_give isl_basic_set *
2551 isl_set_unshifted_simple_hull(
2552 __isl_take isl_set *set);
2553 __isl_give isl_basic_map *
2554 isl_map_unshifted_simple_hull(
2555 __isl_take isl_map *map);
2556 __isl_give isl_basic_set *isl_set_simple_hull(
2557 __isl_take isl_set *set);
2558 __isl_give isl_basic_map *isl_map_simple_hull(
2559 __isl_take isl_map *map);
2560 __isl_give isl_union_map *isl_union_map_simple_hull(
2561 __isl_take isl_union_map *umap);
2563 These functions compute a single basic set or relation
2564 that contains the whole input set or relation.
2565 In particular, the output is described by translates
2566 of the constraints describing the basic sets or relations in the input.
2567 In case of C<isl_set_unshifted_simple_hull>, only the original
2568 constraints are used, without any translation.
2572 (See \autoref{s:simple hull}.)
2578 __isl_give isl_basic_set *isl_basic_set_affine_hull(
2579 __isl_take isl_basic_set *bset);
2580 __isl_give isl_basic_set *isl_set_affine_hull(
2581 __isl_take isl_set *set);
2582 __isl_give isl_union_set *isl_union_set_affine_hull(
2583 __isl_take isl_union_set *uset);
2584 __isl_give isl_basic_map *isl_basic_map_affine_hull(
2585 __isl_take isl_basic_map *bmap);
2586 __isl_give isl_basic_map *isl_map_affine_hull(
2587 __isl_take isl_map *map);
2588 __isl_give isl_union_map *isl_union_map_affine_hull(
2589 __isl_take isl_union_map *umap);
2591 In case of union sets and relations, the affine hull is computed
2594 =item * Polyhedral hull
2596 __isl_give isl_basic_set *isl_set_polyhedral_hull(
2597 __isl_take isl_set *set);
2598 __isl_give isl_basic_map *isl_map_polyhedral_hull(
2599 __isl_take isl_map *map);
2600 __isl_give isl_union_set *isl_union_set_polyhedral_hull(
2601 __isl_take isl_union_set *uset);
2602 __isl_give isl_union_map *isl_union_map_polyhedral_hull(
2603 __isl_take isl_union_map *umap);
2605 These functions compute a single basic set or relation
2606 not involving any existentially quantified variables
2607 that contains the whole input set or relation.
2608 In case of union sets and relations, the polyhedral hull is computed
2611 =item * Other approximations
2613 __isl_give isl_basic_set *
2614 isl_basic_set_drop_constraints_involving_dims(
2615 __isl_take isl_basic_set *bset,
2616 enum isl_dim_type type,
2617 unsigned first, unsigned n);
2618 __isl_give isl_basic_map *
2619 isl_basic_map_drop_constraints_involving_dims(
2620 __isl_take isl_basic_map *bmap,
2621 enum isl_dim_type type,
2622 unsigned first, unsigned n);
2623 __isl_give isl_basic_set *
2624 isl_basic_set_drop_constraints_not_involving_dims(
2625 __isl_take isl_basic_set *bset,
2626 enum isl_dim_type type,
2627 unsigned first, unsigned n);
2628 __isl_give isl_set *
2629 isl_set_drop_constraints_involving_dims(
2630 __isl_take isl_set *set,
2631 enum isl_dim_type type,
2632 unsigned first, unsigned n);
2633 __isl_give isl_map *
2634 isl_map_drop_constraints_involving_dims(
2635 __isl_take isl_map *map,
2636 enum isl_dim_type type,
2637 unsigned first, unsigned n);
2639 These functions drop any constraints (not) involving the specified dimensions.
2640 Note that the result depends on the representation of the input.
2644 __isl_give isl_basic_set *isl_basic_set_sample(
2645 __isl_take isl_basic_set *bset);
2646 __isl_give isl_basic_set *isl_set_sample(
2647 __isl_take isl_set *set);
2648 __isl_give isl_basic_map *isl_basic_map_sample(
2649 __isl_take isl_basic_map *bmap);
2650 __isl_give isl_basic_map *isl_map_sample(
2651 __isl_take isl_map *map);
2653 If the input (basic) set or relation is non-empty, then return
2654 a singleton subset of the input. Otherwise, return an empty set.
2656 =item * Optimization
2658 #include <isl/ilp.h>
2659 enum isl_lp_result isl_basic_set_max(
2660 __isl_keep isl_basic_set *bset,
2661 __isl_keep isl_aff *obj, isl_int *opt)
2662 __isl_give isl_val *isl_basic_set_max_val(
2663 __isl_keep isl_basic_set *bset,
2664 __isl_keep isl_aff *obj);
2665 enum isl_lp_result isl_set_min(__isl_keep isl_set *set,
2666 __isl_keep isl_aff *obj, isl_int *opt);
2667 __isl_give isl_val *isl_set_min_val(
2668 __isl_keep isl_set *set,
2669 __isl_keep isl_aff *obj);
2670 enum isl_lp_result isl_set_max(__isl_keep isl_set *set,
2671 __isl_keep isl_aff *obj, isl_int *opt);
2672 __isl_give isl_val *isl_set_max_val(
2673 __isl_keep isl_set *set,
2674 __isl_keep isl_aff *obj);
2676 Compute the minimum or maximum of the integer affine expression C<obj>
2677 over the points in C<set>, returning the result in C<opt>.
2678 The return value may be one of C<isl_lp_error>,
2679 C<isl_lp_ok>, C<isl_lp_unbounded> or C<isl_lp_empty>, in case of
2680 an C<isl_lp_result>. If the result is an C<isl_val> then
2681 the result is C<NULL> in case of an error, the optimal value in case
2682 there is one, negative infinity or infinity if the problem is unbounded and
2683 NaN if the problem is empty.
2685 =item * Parametric optimization
2687 __isl_give isl_pw_aff *isl_set_dim_min(
2688 __isl_take isl_set *set, int pos);
2689 __isl_give isl_pw_aff *isl_set_dim_max(
2690 __isl_take isl_set *set, int pos);
2691 __isl_give isl_pw_aff *isl_map_dim_max(
2692 __isl_take isl_map *map, int pos);
2694 Compute the minimum or maximum of the given set or output dimension
2695 as a function of the parameters (and input dimensions), but independently
2696 of the other set or output dimensions.
2697 For lexicographic optimization, see L<"Lexicographic Optimization">.
2701 The following functions compute either the set of (rational) coefficient
2702 values of valid constraints for the given set or the set of (rational)
2703 values satisfying the constraints with coefficients from the given set.
2704 Internally, these two sets of functions perform essentially the
2705 same operations, except that the set of coefficients is assumed to
2706 be a cone, while the set of values may be any polyhedron.
2707 The current implementation is based on the Farkas lemma and
2708 Fourier-Motzkin elimination, but this may change or be made optional
2709 in future. In particular, future implementations may use different
2710 dualization algorithms or skip the elimination step.
2712 __isl_give isl_basic_set *isl_basic_set_coefficients(
2713 __isl_take isl_basic_set *bset);
2714 __isl_give isl_basic_set *isl_set_coefficients(
2715 __isl_take isl_set *set);
2716 __isl_give isl_union_set *isl_union_set_coefficients(
2717 __isl_take isl_union_set *bset);
2718 __isl_give isl_basic_set *isl_basic_set_solutions(
2719 __isl_take isl_basic_set *bset);
2720 __isl_give isl_basic_set *isl_set_solutions(
2721 __isl_take isl_set *set);
2722 __isl_give isl_union_set *isl_union_set_solutions(
2723 __isl_take isl_union_set *bset);
2727 __isl_give isl_map *isl_map_fixed_power(
2728 __isl_take isl_map *map, isl_int exp);
2729 __isl_give isl_map *isl_map_fixed_power_val(
2730 __isl_take isl_map *map,
2731 __isl_take isl_val *exp);
2732 __isl_give isl_union_map *isl_union_map_fixed_power(
2733 __isl_take isl_union_map *umap, isl_int exp);
2734 __isl_give isl_union_map *
2735 isl_union_map_fixed_power_val(
2736 __isl_take isl_union_map *umap,
2737 __isl_take isl_val *exp);
2739 Compute the given power of C<map>, where C<exp> is assumed to be non-zero.
2740 If the exponent C<exp> is negative, then the -C<exp> th power of the inverse
2741 of C<map> is computed.
2743 __isl_give isl_map *isl_map_power(__isl_take isl_map *map,
2745 __isl_give isl_union_map *isl_union_map_power(
2746 __isl_take isl_union_map *umap, int *exact);
2748 Compute a parametric representation for all positive powers I<k> of C<map>.
2749 The result maps I<k> to a nested relation corresponding to the
2750 I<k>th power of C<map>.
2751 The result may be an overapproximation. If the result is known to be exact,
2752 then C<*exact> is set to C<1>.
2754 =item * Transitive closure
2756 __isl_give isl_map *isl_map_transitive_closure(
2757 __isl_take isl_map *map, int *exact);
2758 __isl_give isl_union_map *isl_union_map_transitive_closure(
2759 __isl_take isl_union_map *umap, int *exact);
2761 Compute the transitive closure of C<map>.
2762 The result may be an overapproximation. If the result is known to be exact,
2763 then C<*exact> is set to C<1>.
2765 =item * Reaching path lengths
2767 __isl_give isl_map *isl_map_reaching_path_lengths(
2768 __isl_take isl_map *map, int *exact);
2770 Compute a relation that maps each element in the range of C<map>
2771 to the lengths of all paths composed of edges in C<map> that
2772 end up in the given element.
2773 The result may be an overapproximation. If the result is known to be exact,
2774 then C<*exact> is set to C<1>.
2775 To compute the I<maximal> path length, the resulting relation
2776 should be postprocessed by C<isl_map_lexmax>.
2777 In particular, if the input relation is a dependence relation
2778 (mapping sources to sinks), then the maximal path length corresponds
2779 to the free schedule.
2780 Note, however, that C<isl_map_lexmax> expects the maximum to be
2781 finite, so if the path lengths are unbounded (possibly due to
2782 the overapproximation), then you will get an error message.
2786 __isl_give isl_basic_set *isl_basic_map_wrap(
2787 __isl_take isl_basic_map *bmap);
2788 __isl_give isl_set *isl_map_wrap(
2789 __isl_take isl_map *map);
2790 __isl_give isl_union_set *isl_union_map_wrap(
2791 __isl_take isl_union_map *umap);
2792 __isl_give isl_basic_map *isl_basic_set_unwrap(
2793 __isl_take isl_basic_set *bset);
2794 __isl_give isl_map *isl_set_unwrap(
2795 __isl_take isl_set *set);
2796 __isl_give isl_union_map *isl_union_set_unwrap(
2797 __isl_take isl_union_set *uset);
2801 Remove any internal structure of domain (and range) of the given
2802 set or relation. If there is any such internal structure in the input,
2803 then the name of the space is also removed.
2805 __isl_give isl_basic_set *isl_basic_set_flatten(
2806 __isl_take isl_basic_set *bset);
2807 __isl_give isl_set *isl_set_flatten(
2808 __isl_take isl_set *set);
2809 __isl_give isl_basic_map *isl_basic_map_flatten_domain(
2810 __isl_take isl_basic_map *bmap);
2811 __isl_give isl_basic_map *isl_basic_map_flatten_range(
2812 __isl_take isl_basic_map *bmap);
2813 __isl_give isl_map *isl_map_flatten_range(
2814 __isl_take isl_map *map);
2815 __isl_give isl_map *isl_map_flatten_domain(
2816 __isl_take isl_map *map);
2817 __isl_give isl_basic_map *isl_basic_map_flatten(
2818 __isl_take isl_basic_map *bmap);
2819 __isl_give isl_map *isl_map_flatten(
2820 __isl_take isl_map *map);
2822 __isl_give isl_map *isl_set_flatten_map(
2823 __isl_take isl_set *set);
2825 The function above constructs a relation
2826 that maps the input set to a flattened version of the set.
2830 Lift the input set to a space with extra dimensions corresponding
2831 to the existentially quantified variables in the input.
2832 In particular, the result lives in a wrapped map where the domain
2833 is the original space and the range corresponds to the original
2834 existentially quantified variables.
2836 __isl_give isl_basic_set *isl_basic_set_lift(
2837 __isl_take isl_basic_set *bset);
2838 __isl_give isl_set *isl_set_lift(
2839 __isl_take isl_set *set);
2840 __isl_give isl_union_set *isl_union_set_lift(
2841 __isl_take isl_union_set *uset);
2843 Given a local space that contains the existentially quantified
2844 variables of a set, a basic relation that, when applied to
2845 a basic set, has essentially the same effect as C<isl_basic_set_lift>,
2846 can be constructed using the following function.
2848 #include <isl/local_space.h>
2849 __isl_give isl_basic_map *isl_local_space_lifting(
2850 __isl_take isl_local_space *ls);
2852 =item * Internal Product
2854 __isl_give isl_basic_map *isl_basic_map_zip(
2855 __isl_take isl_basic_map *bmap);
2856 __isl_give isl_map *isl_map_zip(
2857 __isl_take isl_map *map);
2858 __isl_give isl_union_map *isl_union_map_zip(
2859 __isl_take isl_union_map *umap);
2861 Given a relation with nested relations for domain and range,
2862 interchange the range of the domain with the domain of the range.
2866 __isl_give isl_basic_map *isl_basic_map_curry(
2867 __isl_take isl_basic_map *bmap);
2868 __isl_give isl_basic_map *isl_basic_map_uncurry(
2869 __isl_take isl_basic_map *bmap);
2870 __isl_give isl_map *isl_map_curry(
2871 __isl_take isl_map *map);
2872 __isl_give isl_map *isl_map_uncurry(
2873 __isl_take isl_map *map);
2874 __isl_give isl_union_map *isl_union_map_curry(
2875 __isl_take isl_union_map *umap);
2876 __isl_give isl_union_map *isl_union_map_uncurry(
2877 __isl_take isl_union_map *umap);
2879 Given a relation with a nested relation for domain,
2880 the C<curry> functions
2881 move the range of the nested relation out of the domain
2882 and use it as the domain of a nested relation in the range,
2883 with the original range as range of this nested relation.
2884 The C<uncurry> functions perform the inverse operation.
2886 =item * Aligning parameters
2888 __isl_give isl_basic_set *isl_basic_set_align_params(
2889 __isl_take isl_basic_set *bset,
2890 __isl_take isl_space *model);
2891 __isl_give isl_set *isl_set_align_params(
2892 __isl_take isl_set *set,
2893 __isl_take isl_space *model);
2894 __isl_give isl_basic_map *isl_basic_map_align_params(
2895 __isl_take isl_basic_map *bmap,
2896 __isl_take isl_space *model);
2897 __isl_give isl_map *isl_map_align_params(
2898 __isl_take isl_map *map,
2899 __isl_take isl_space *model);
2901 Change the order of the parameters of the given set or relation
2902 such that the first parameters match those of C<model>.
2903 This may involve the introduction of extra parameters.
2904 All parameters need to be named.
2906 =item * Dimension manipulation
2908 __isl_give isl_basic_set *isl_basic_set_add_dims(
2909 __isl_take isl_basic_set *bset,
2910 enum isl_dim_type type, unsigned n);
2911 __isl_give isl_set *isl_set_add_dims(
2912 __isl_take isl_set *set,
2913 enum isl_dim_type type, unsigned n);
2914 __isl_give isl_map *isl_map_add_dims(
2915 __isl_take isl_map *map,
2916 enum isl_dim_type type, unsigned n);
2917 __isl_give isl_basic_set *isl_basic_set_insert_dims(
2918 __isl_take isl_basic_set *bset,
2919 enum isl_dim_type type, unsigned pos,
2921 __isl_give isl_basic_map *isl_basic_map_insert_dims(
2922 __isl_take isl_basic_map *bmap,
2923 enum isl_dim_type type, unsigned pos,
2925 __isl_give isl_set *isl_set_insert_dims(
2926 __isl_take isl_set *set,
2927 enum isl_dim_type type, unsigned pos, unsigned n);
2928 __isl_give isl_map *isl_map_insert_dims(
2929 __isl_take isl_map *map,
2930 enum isl_dim_type type, unsigned pos, unsigned n);
2931 __isl_give isl_basic_set *isl_basic_set_move_dims(
2932 __isl_take isl_basic_set *bset,
2933 enum isl_dim_type dst_type, unsigned dst_pos,
2934 enum isl_dim_type src_type, unsigned src_pos,
2936 __isl_give isl_basic_map *isl_basic_map_move_dims(
2937 __isl_take isl_basic_map *bmap,
2938 enum isl_dim_type dst_type, unsigned dst_pos,
2939 enum isl_dim_type src_type, unsigned src_pos,
2941 __isl_give isl_set *isl_set_move_dims(
2942 __isl_take isl_set *set,
2943 enum isl_dim_type dst_type, unsigned dst_pos,
2944 enum isl_dim_type src_type, unsigned src_pos,
2946 __isl_give isl_map *isl_map_move_dims(
2947 __isl_take isl_map *map,
2948 enum isl_dim_type dst_type, unsigned dst_pos,
2949 enum isl_dim_type src_type, unsigned src_pos,
2952 It is usually not advisable to directly change the (input or output)
2953 space of a set or a relation as this removes the name and the internal
2954 structure of the space. However, the above functions can be useful
2955 to add new parameters, assuming
2956 C<isl_set_align_params> and C<isl_map_align_params>
2961 =head2 Binary Operations
2963 The two arguments of a binary operation not only need to live
2964 in the same C<isl_ctx>, they currently also need to have
2965 the same (number of) parameters.
2967 =head3 Basic Operations
2971 =item * Intersection
2973 __isl_give isl_basic_set *isl_basic_set_intersect_params(
2974 __isl_take isl_basic_set *bset1,
2975 __isl_take isl_basic_set *bset2);
2976 __isl_give isl_basic_set *isl_basic_set_intersect(
2977 __isl_take isl_basic_set *bset1,
2978 __isl_take isl_basic_set *bset2);
2979 __isl_give isl_set *isl_set_intersect_params(
2980 __isl_take isl_set *set,
2981 __isl_take isl_set *params);
2982 __isl_give isl_set *isl_set_intersect(
2983 __isl_take isl_set *set1,
2984 __isl_take isl_set *set2);
2985 __isl_give isl_union_set *isl_union_set_intersect_params(
2986 __isl_take isl_union_set *uset,
2987 __isl_take isl_set *set);
2988 __isl_give isl_union_map *isl_union_map_intersect_params(
2989 __isl_take isl_union_map *umap,
2990 __isl_take isl_set *set);
2991 __isl_give isl_union_set *isl_union_set_intersect(
2992 __isl_take isl_union_set *uset1,
2993 __isl_take isl_union_set *uset2);
2994 __isl_give isl_basic_map *isl_basic_map_intersect_domain(
2995 __isl_take isl_basic_map *bmap,
2996 __isl_take isl_basic_set *bset);
2997 __isl_give isl_basic_map *isl_basic_map_intersect_range(
2998 __isl_take isl_basic_map *bmap,
2999 __isl_take isl_basic_set *bset);
3000 __isl_give isl_basic_map *isl_basic_map_intersect(
3001 __isl_take isl_basic_map *bmap1,
3002 __isl_take isl_basic_map *bmap2);
3003 __isl_give isl_map *isl_map_intersect_params(
3004 __isl_take isl_map *map,
3005 __isl_take isl_set *params);
3006 __isl_give isl_map *isl_map_intersect_domain(
3007 __isl_take isl_map *map,
3008 __isl_take isl_set *set);
3009 __isl_give isl_map *isl_map_intersect_range(
3010 __isl_take isl_map *map,
3011 __isl_take isl_set *set);
3012 __isl_give isl_map *isl_map_intersect(
3013 __isl_take isl_map *map1,
3014 __isl_take isl_map *map2);
3015 __isl_give isl_union_map *isl_union_map_intersect_domain(
3016 __isl_take isl_union_map *umap,
3017 __isl_take isl_union_set *uset);
3018 __isl_give isl_union_map *isl_union_map_intersect_range(
3019 __isl_take isl_union_map *umap,
3020 __isl_take isl_union_set *uset);
3021 __isl_give isl_union_map *isl_union_map_intersect(
3022 __isl_take isl_union_map *umap1,
3023 __isl_take isl_union_map *umap2);
3025 The second argument to the C<_params> functions needs to be
3026 a parametric (basic) set. For the other functions, a parametric set
3027 for either argument is only allowed if the other argument is
3028 a parametric set as well.
3032 __isl_give isl_set *isl_basic_set_union(
3033 __isl_take isl_basic_set *bset1,
3034 __isl_take isl_basic_set *bset2);
3035 __isl_give isl_map *isl_basic_map_union(
3036 __isl_take isl_basic_map *bmap1,
3037 __isl_take isl_basic_map *bmap2);
3038 __isl_give isl_set *isl_set_union(
3039 __isl_take isl_set *set1,
3040 __isl_take isl_set *set2);
3041 __isl_give isl_map *isl_map_union(
3042 __isl_take isl_map *map1,
3043 __isl_take isl_map *map2);
3044 __isl_give isl_union_set *isl_union_set_union(
3045 __isl_take isl_union_set *uset1,
3046 __isl_take isl_union_set *uset2);
3047 __isl_give isl_union_map *isl_union_map_union(
3048 __isl_take isl_union_map *umap1,
3049 __isl_take isl_union_map *umap2);
3051 =item * Set difference
3053 __isl_give isl_set *isl_set_subtract(
3054 __isl_take isl_set *set1,
3055 __isl_take isl_set *set2);
3056 __isl_give isl_map *isl_map_subtract(
3057 __isl_take isl_map *map1,
3058 __isl_take isl_map *map2);
3059 __isl_give isl_map *isl_map_subtract_domain(
3060 __isl_take isl_map *map,
3061 __isl_take isl_set *dom);
3062 __isl_give isl_map *isl_map_subtract_range(
3063 __isl_take isl_map *map,
3064 __isl_take isl_set *dom);
3065 __isl_give isl_union_set *isl_union_set_subtract(
3066 __isl_take isl_union_set *uset1,
3067 __isl_take isl_union_set *uset2);
3068 __isl_give isl_union_map *isl_union_map_subtract(
3069 __isl_take isl_union_map *umap1,
3070 __isl_take isl_union_map *umap2);
3071 __isl_give isl_union_map *isl_union_map_subtract_domain(
3072 __isl_take isl_union_map *umap,
3073 __isl_take isl_union_set *dom);
3074 __isl_give isl_union_map *isl_union_map_subtract_range(
3075 __isl_take isl_union_map *umap,
3076 __isl_take isl_union_set *dom);
3080 __isl_give isl_basic_set *isl_basic_set_apply(
3081 __isl_take isl_basic_set *bset,
3082 __isl_take isl_basic_map *bmap);
3083 __isl_give isl_set *isl_set_apply(
3084 __isl_take isl_set *set,
3085 __isl_take isl_map *map);
3086 __isl_give isl_union_set *isl_union_set_apply(
3087 __isl_take isl_union_set *uset,
3088 __isl_take isl_union_map *umap);
3089 __isl_give isl_basic_map *isl_basic_map_apply_domain(
3090 __isl_take isl_basic_map *bmap1,
3091 __isl_take isl_basic_map *bmap2);
3092 __isl_give isl_basic_map *isl_basic_map_apply_range(
3093 __isl_take isl_basic_map *bmap1,
3094 __isl_take isl_basic_map *bmap2);
3095 __isl_give isl_map *isl_map_apply_domain(
3096 __isl_take isl_map *map1,
3097 __isl_take isl_map *map2);
3098 __isl_give isl_union_map *isl_union_map_apply_domain(
3099 __isl_take isl_union_map *umap1,
3100 __isl_take isl_union_map *umap2);
3101 __isl_give isl_map *isl_map_apply_range(
3102 __isl_take isl_map *map1,
3103 __isl_take isl_map *map2);
3104 __isl_give isl_union_map *isl_union_map_apply_range(
3105 __isl_take isl_union_map *umap1,
3106 __isl_take isl_union_map *umap2);
3110 __isl_give isl_basic_set *
3111 isl_basic_set_preimage_multi_aff(
3112 __isl_take isl_basic_set *bset,
3113 __isl_take isl_multi_aff *ma);
3114 __isl_give isl_set *isl_set_preimage_multi_aff(
3115 __isl_take isl_set *set,
3116 __isl_take isl_multi_aff *ma);
3117 __isl_give isl_set *isl_set_preimage_pw_multi_aff(
3118 __isl_take isl_set *set,
3119 __isl_take isl_pw_multi_aff *pma);
3120 __isl_give isl_map *isl_map_preimage_domain_multi_aff(
3121 __isl_take isl_map *map,
3122 __isl_take isl_multi_aff *ma);
3123 __isl_give isl_union_map *
3124 isl_union_map_preimage_domain_multi_aff(
3125 __isl_take isl_union_map *umap,
3126 __isl_take isl_multi_aff *ma);
3128 These functions compute the preimage of the given set or map domain under
3129 the given function. In other words, the expression is plugged
3130 into the set description or into the domain of the map.
3131 Objects of types C<isl_multi_aff> and C<isl_pw_multi_aff> are described in
3132 L</"Piecewise Multiple Quasi Affine Expressions">.
3134 =item * Cartesian Product
3136 __isl_give isl_set *isl_set_product(
3137 __isl_take isl_set *set1,
3138 __isl_take isl_set *set2);
3139 __isl_give isl_union_set *isl_union_set_product(
3140 __isl_take isl_union_set *uset1,
3141 __isl_take isl_union_set *uset2);
3142 __isl_give isl_basic_map *isl_basic_map_domain_product(
3143 __isl_take isl_basic_map *bmap1,
3144 __isl_take isl_basic_map *bmap2);
3145 __isl_give isl_basic_map *isl_basic_map_range_product(
3146 __isl_take isl_basic_map *bmap1,
3147 __isl_take isl_basic_map *bmap2);
3148 __isl_give isl_basic_map *isl_basic_map_product(
3149 __isl_take isl_basic_map *bmap1,
3150 __isl_take isl_basic_map *bmap2);
3151 __isl_give isl_map *isl_map_domain_product(
3152 __isl_take isl_map *map1,
3153 __isl_take isl_map *map2);
3154 __isl_give isl_map *isl_map_range_product(
3155 __isl_take isl_map *map1,
3156 __isl_take isl_map *map2);
3157 __isl_give isl_union_map *isl_union_map_domain_product(
3158 __isl_take isl_union_map *umap1,
3159 __isl_take isl_union_map *umap2);
3160 __isl_give isl_union_map *isl_union_map_range_product(
3161 __isl_take isl_union_map *umap1,
3162 __isl_take isl_union_map *umap2);
3163 __isl_give isl_map *isl_map_product(
3164 __isl_take isl_map *map1,
3165 __isl_take isl_map *map2);
3166 __isl_give isl_union_map *isl_union_map_product(
3167 __isl_take isl_union_map *umap1,
3168 __isl_take isl_union_map *umap2);
3170 The above functions compute the cross product of the given
3171 sets or relations. The domains and ranges of the results
3172 are wrapped maps between domains and ranges of the inputs.
3173 To obtain a ``flat'' product, use the following functions
3176 __isl_give isl_basic_set *isl_basic_set_flat_product(
3177 __isl_take isl_basic_set *bset1,
3178 __isl_take isl_basic_set *bset2);
3179 __isl_give isl_set *isl_set_flat_product(
3180 __isl_take isl_set *set1,
3181 __isl_take isl_set *set2);
3182 __isl_give isl_basic_map *isl_basic_map_flat_range_product(
3183 __isl_take isl_basic_map *bmap1,
3184 __isl_take isl_basic_map *bmap2);
3185 __isl_give isl_map *isl_map_flat_domain_product(
3186 __isl_take isl_map *map1,
3187 __isl_take isl_map *map2);
3188 __isl_give isl_map *isl_map_flat_range_product(
3189 __isl_take isl_map *map1,
3190 __isl_take isl_map *map2);
3191 __isl_give isl_union_map *isl_union_map_flat_range_product(
3192 __isl_take isl_union_map *umap1,
3193 __isl_take isl_union_map *umap2);
3194 __isl_give isl_basic_map *isl_basic_map_flat_product(
3195 __isl_take isl_basic_map *bmap1,
3196 __isl_take isl_basic_map *bmap2);
3197 __isl_give isl_map *isl_map_flat_product(
3198 __isl_take isl_map *map1,
3199 __isl_take isl_map *map2);
3201 =item * Simplification
3203 __isl_give isl_basic_set *isl_basic_set_gist(
3204 __isl_take isl_basic_set *bset,
3205 __isl_take isl_basic_set *context);
3206 __isl_give isl_set *isl_set_gist(__isl_take isl_set *set,
3207 __isl_take isl_set *context);
3208 __isl_give isl_set *isl_set_gist_params(
3209 __isl_take isl_set *set,
3210 __isl_take isl_set *context);
3211 __isl_give isl_union_set *isl_union_set_gist(
3212 __isl_take isl_union_set *uset,
3213 __isl_take isl_union_set *context);
3214 __isl_give isl_union_set *isl_union_set_gist_params(
3215 __isl_take isl_union_set *uset,
3216 __isl_take isl_set *set);
3217 __isl_give isl_basic_map *isl_basic_map_gist(
3218 __isl_take isl_basic_map *bmap,
3219 __isl_take isl_basic_map *context);
3220 __isl_give isl_map *isl_map_gist(__isl_take isl_map *map,
3221 __isl_take isl_map *context);
3222 __isl_give isl_map *isl_map_gist_params(
3223 __isl_take isl_map *map,
3224 __isl_take isl_set *context);
3225 __isl_give isl_map *isl_map_gist_domain(
3226 __isl_take isl_map *map,
3227 __isl_take isl_set *context);
3228 __isl_give isl_map *isl_map_gist_range(
3229 __isl_take isl_map *map,
3230 __isl_take isl_set *context);
3231 __isl_give isl_union_map *isl_union_map_gist(
3232 __isl_take isl_union_map *umap,
3233 __isl_take isl_union_map *context);
3234 __isl_give isl_union_map *isl_union_map_gist_params(
3235 __isl_take isl_union_map *umap,
3236 __isl_take isl_set *set);
3237 __isl_give isl_union_map *isl_union_map_gist_domain(
3238 __isl_take isl_union_map *umap,
3239 __isl_take isl_union_set *uset);
3240 __isl_give isl_union_map *isl_union_map_gist_range(
3241 __isl_take isl_union_map *umap,
3242 __isl_take isl_union_set *uset);
3244 The gist operation returns a set or relation that has the
3245 same intersection with the context as the input set or relation.
3246 Any implicit equality in the intersection is made explicit in the result,
3247 while all inequalities that are redundant with respect to the intersection
3249 In case of union sets and relations, the gist operation is performed
3254 =head3 Lexicographic Optimization
3256 Given a (basic) set C<set> (or C<bset>) and a zero-dimensional domain C<dom>,
3257 the following functions
3258 compute a set that contains the lexicographic minimum or maximum
3259 of the elements in C<set> (or C<bset>) for those values of the parameters
3260 that satisfy C<dom>.
3261 If C<empty> is not C<NULL>, then C<*empty> is assigned a set
3262 that contains the parameter values in C<dom> for which C<set> (or C<bset>)
3264 In other words, the union of the parameter values
3265 for which the result is non-empty and of C<*empty>
3268 __isl_give isl_set *isl_basic_set_partial_lexmin(
3269 __isl_take isl_basic_set *bset,
3270 __isl_take isl_basic_set *dom,
3271 __isl_give isl_set **empty);
3272 __isl_give isl_set *isl_basic_set_partial_lexmax(
3273 __isl_take isl_basic_set *bset,
3274 __isl_take isl_basic_set *dom,
3275 __isl_give isl_set **empty);
3276 __isl_give isl_set *isl_set_partial_lexmin(
3277 __isl_take isl_set *set, __isl_take isl_set *dom,
3278 __isl_give isl_set **empty);
3279 __isl_give isl_set *isl_set_partial_lexmax(
3280 __isl_take isl_set *set, __isl_take isl_set *dom,
3281 __isl_give isl_set **empty);
3283 Given a (basic) set C<set> (or C<bset>), the following functions simply
3284 return a set containing the lexicographic minimum or maximum
3285 of the elements in C<set> (or C<bset>).
3286 In case of union sets, the optimum is computed per space.
3288 __isl_give isl_set *isl_basic_set_lexmin(
3289 __isl_take isl_basic_set *bset);
3290 __isl_give isl_set *isl_basic_set_lexmax(
3291 __isl_take isl_basic_set *bset);
3292 __isl_give isl_set *isl_set_lexmin(
3293 __isl_take isl_set *set);
3294 __isl_give isl_set *isl_set_lexmax(
3295 __isl_take isl_set *set);
3296 __isl_give isl_union_set *isl_union_set_lexmin(
3297 __isl_take isl_union_set *uset);
3298 __isl_give isl_union_set *isl_union_set_lexmax(
3299 __isl_take isl_union_set *uset);
3301 Given a (basic) relation C<map> (or C<bmap>) and a domain C<dom>,
3302 the following functions
3303 compute a relation that maps each element of C<dom>
3304 to the single lexicographic minimum or maximum
3305 of the elements that are associated to that same
3306 element in C<map> (or C<bmap>).
3307 If C<empty> is not C<NULL>, then C<*empty> is assigned a set
3308 that contains the elements in C<dom> that do not map
3309 to any elements in C<map> (or C<bmap>).
3310 In other words, the union of the domain of the result and of C<*empty>
3313 __isl_give isl_map *isl_basic_map_partial_lexmax(
3314 __isl_take isl_basic_map *bmap,
3315 __isl_take isl_basic_set *dom,
3316 __isl_give isl_set **empty);
3317 __isl_give isl_map *isl_basic_map_partial_lexmin(
3318 __isl_take isl_basic_map *bmap,
3319 __isl_take isl_basic_set *dom,
3320 __isl_give isl_set **empty);
3321 __isl_give isl_map *isl_map_partial_lexmax(
3322 __isl_take isl_map *map, __isl_take isl_set *dom,
3323 __isl_give isl_set **empty);
3324 __isl_give isl_map *isl_map_partial_lexmin(
3325 __isl_take isl_map *map, __isl_take isl_set *dom,
3326 __isl_give isl_set **empty);
3328 Given a (basic) map C<map> (or C<bmap>), the following functions simply
3329 return a map mapping each element in the domain of
3330 C<map> (or C<bmap>) to the lexicographic minimum or maximum
3331 of all elements associated to that element.
3332 In case of union relations, the optimum is computed per space.
3334 __isl_give isl_map *isl_basic_map_lexmin(
3335 __isl_take isl_basic_map *bmap);
3336 __isl_give isl_map *isl_basic_map_lexmax(
3337 __isl_take isl_basic_map *bmap);
3338 __isl_give isl_map *isl_map_lexmin(
3339 __isl_take isl_map *map);
3340 __isl_give isl_map *isl_map_lexmax(
3341 __isl_take isl_map *map);
3342 __isl_give isl_union_map *isl_union_map_lexmin(
3343 __isl_take isl_union_map *umap);
3344 __isl_give isl_union_map *isl_union_map_lexmax(
3345 __isl_take isl_union_map *umap);
3347 The following functions return their result in the form of
3348 a piecewise multi-affine expression
3349 (See L<"Piecewise Multiple Quasi Affine Expressions">),
3350 but are otherwise equivalent to the corresponding functions
3351 returning a basic set or relation.
3353 __isl_give isl_pw_multi_aff *
3354 isl_basic_map_lexmin_pw_multi_aff(
3355 __isl_take isl_basic_map *bmap);
3356 __isl_give isl_pw_multi_aff *
3357 isl_basic_set_partial_lexmin_pw_multi_aff(
3358 __isl_take isl_basic_set *bset,
3359 __isl_take isl_basic_set *dom,
3360 __isl_give isl_set **empty);
3361 __isl_give isl_pw_multi_aff *
3362 isl_basic_set_partial_lexmax_pw_multi_aff(
3363 __isl_take isl_basic_set *bset,
3364 __isl_take isl_basic_set *dom,
3365 __isl_give isl_set **empty);
3366 __isl_give isl_pw_multi_aff *
3367 isl_basic_map_partial_lexmin_pw_multi_aff(
3368 __isl_take isl_basic_map *bmap,
3369 __isl_take isl_basic_set *dom,
3370 __isl_give isl_set **empty);
3371 __isl_give isl_pw_multi_aff *
3372 isl_basic_map_partial_lexmax_pw_multi_aff(
3373 __isl_take isl_basic_map *bmap,
3374 __isl_take isl_basic_set *dom,
3375 __isl_give isl_set **empty);
3376 __isl_give isl_pw_multi_aff *isl_set_lexmin_pw_multi_aff(
3377 __isl_take isl_set *set);
3378 __isl_give isl_pw_multi_aff *isl_set_lexmax_pw_multi_aff(
3379 __isl_take isl_set *set);
3380 __isl_give isl_pw_multi_aff *isl_map_lexmin_pw_multi_aff(
3381 __isl_take isl_map *map);
3382 __isl_give isl_pw_multi_aff *isl_map_lexmax_pw_multi_aff(
3383 __isl_take isl_map *map);
3387 Lists are defined over several element types, including
3388 C<isl_val>, C<isl_id>, C<isl_aff>, C<isl_pw_aff>, C<isl_constraint>,
3389 C<isl_basic_set>, C<isl_set>, C<isl_ast_expr> and C<isl_ast_node>.
3390 Here we take lists of C<isl_set>s as an example.
3391 Lists can be created, copied, modified and freed using the following functions.
3393 #include <isl/list.h>
3394 __isl_give isl_set_list *isl_set_list_from_set(
3395 __isl_take isl_set *el);
3396 __isl_give isl_set_list *isl_set_list_alloc(
3397 isl_ctx *ctx, int n);
3398 __isl_give isl_set_list *isl_set_list_copy(
3399 __isl_keep isl_set_list *list);
3400 __isl_give isl_set_list *isl_set_list_insert(
3401 __isl_take isl_set_list *list, unsigned pos,
3402 __isl_take isl_set *el);
3403 __isl_give isl_set_list *isl_set_list_add(
3404 __isl_take isl_set_list *list,
3405 __isl_take isl_set *el);
3406 __isl_give isl_set_list *isl_set_list_drop(
3407 __isl_take isl_set_list *list,
3408 unsigned first, unsigned n);
3409 __isl_give isl_set_list *isl_set_list_set_set(
3410 __isl_take isl_set_list *list, int index,
3411 __isl_take isl_set *set);
3412 __isl_give isl_set_list *isl_set_list_concat(
3413 __isl_take isl_set_list *list1,
3414 __isl_take isl_set_list *list2);
3415 __isl_give isl_set_list *isl_set_list_sort(
3416 __isl_take isl_set_list *list,
3417 int (*cmp)(__isl_keep isl_set *a,
3418 __isl_keep isl_set *b, void *user),
3420 void *isl_set_list_free(__isl_take isl_set_list *list);
3422 C<isl_set_list_alloc> creates an empty list with a capacity for
3423 C<n> elements. C<isl_set_list_from_set> creates a list with a single
3426 Lists can be inspected using the following functions.
3428 #include <isl/list.h>
3429 isl_ctx *isl_set_list_get_ctx(__isl_keep isl_set_list *list);
3430 int isl_set_list_n_set(__isl_keep isl_set_list *list);
3431 __isl_give isl_set *isl_set_list_get_set(
3432 __isl_keep isl_set_list *list, int index);
3433 int isl_set_list_foreach(__isl_keep isl_set_list *list,
3434 int (*fn)(__isl_take isl_set *el, void *user),
3436 int isl_set_list_foreach_scc(__isl_keep isl_set_list *list,
3437 int (*follows)(__isl_keep isl_set *a,
3438 __isl_keep isl_set *b, void *user),
3440 int (*fn)(__isl_take isl_set *el, void *user),
3443 The function C<isl_set_list_foreach_scc> calls C<fn> on each of the
3444 strongly connected components of the graph with as vertices the elements
3445 of C<list> and a directed edge from vertex C<b> to vertex C<a>
3446 iff C<follows(a, b)> returns C<1>. The callbacks C<follows> and C<fn>
3447 should return C<-1> on error.
3449 Lists can be printed using
3451 #include <isl/list.h>
3452 __isl_give isl_printer *isl_printer_print_set_list(
3453 __isl_take isl_printer *p,
3454 __isl_keep isl_set_list *list);
3456 =head2 Multiple Values
3458 An C<isl_multi_val> object represents a sequence of zero or more values,
3459 living in a set space.
3461 An C<isl_multi_val> can be constructed from an C<isl_val_list>
3462 using the following function
3464 #include <isl/val.h>
3465 __isl_give isl_multi_val *isl_multi_val_from_val_list(
3466 __isl_take isl_space *space,
3467 __isl_take isl_val_list *list);
3469 The zero multiple value (with value zero for each set dimension)
3470 can be created using the following function.
3472 #include <isl/val.h>
3473 __isl_give isl_multi_val *isl_multi_val_zero(
3474 __isl_take isl_space *space);
3476 Multiple values can be copied and freed using
3478 #include <isl/val.h>
3479 __isl_give isl_multi_val *isl_multi_val_copy(
3480 __isl_keep isl_multi_val *mv);
3481 void *isl_multi_val_free(__isl_take isl_multi_val *mv);
3483 They can be inspected using
3485 #include <isl/val.h>
3486 isl_ctx *isl_multi_val_get_ctx(
3487 __isl_keep isl_multi_val *mv);
3488 unsigned isl_multi_val_dim(__isl_keep isl_multi_val *mv,
3489 enum isl_dim_type type);
3490 __isl_give isl_val *isl_multi_val_get_val(
3491 __isl_keep isl_multi_val *mv, int pos);
3492 const char *isl_multi_val_get_tuple_name(
3493 __isl_keep isl_multi_val *mv,
3494 enum isl_dim_type type);
3496 They can be modified using
3498 #include <isl/val.h>
3499 __isl_give isl_multi_val *isl_multi_val_set_val(
3500 __isl_take isl_multi_val *mv, int pos,
3501 __isl_take isl_val *val);
3502 __isl_give isl_multi_val *isl_multi_val_set_dim_name(
3503 __isl_take isl_multi_val *mv,
3504 enum isl_dim_type type, unsigned pos, const char *s);
3505 __isl_give isl_multi_val *isl_multi_val_set_tuple_name(
3506 __isl_take isl_multi_val *mv,
3507 enum isl_dim_type type, const char *s);
3508 __isl_give isl_multi_val *isl_multi_val_set_tuple_id(
3509 __isl_take isl_multi_val *mv,
3510 enum isl_dim_type type, __isl_take isl_id *id);
3512 __isl_give isl_multi_val *isl_multi_val_insert_dims(
3513 __isl_take isl_multi_val *mv,
3514 enum isl_dim_type type, unsigned first, unsigned n);
3515 __isl_give isl_multi_val *isl_multi_val_add_dims(
3516 __isl_take isl_multi_val *mv,
3517 enum isl_dim_type type, unsigned n);
3518 __isl_give isl_multi_val *isl_multi_val_drop_dims(
3519 __isl_take isl_multi_val *mv,
3520 enum isl_dim_type type, unsigned first, unsigned n);
3524 #include <isl/val.h>
3525 __isl_give isl_multi_val *isl_multi_val_align_params(
3526 __isl_take isl_multi_val *mv,
3527 __isl_take isl_space *model);
3528 __isl_give isl_multi_val *isl_multi_val_range_splice(
3529 __isl_take isl_multi_val *mv1, unsigned pos,
3530 __isl_take isl_multi_val *mv2);
3531 __isl_give isl_multi_val *isl_multi_val_range_product(
3532 __isl_take isl_multi_val *mv1,
3533 __isl_take isl_multi_val *mv2);
3534 __isl_give isl_multi_val *isl_multi_val_flat_range_product(
3535 __isl_take isl_multi_val *mv1,
3536 __isl_take isl_multi_aff *mv2);
3537 __isl_give isl_multi_val *isl_multi_val_add_val(
3538 __isl_take isl_multi_val *mv,
3539 __isl_take isl_val *v);
3540 __isl_give isl_multi_val *isl_multi_val_mod_val(
3541 __isl_take isl_multi_val *mv,
3542 __isl_take isl_val *v);
3543 __isl_give isl_multi_val *isl_multi_val_scale_val(
3544 __isl_take isl_multi_val *mv,
3545 __isl_take isl_val *v);
3546 __isl_give isl_multi_val *isl_multi_val_scale_multi_val(
3547 __isl_take isl_multi_val *mv1,
3548 __isl_take isl_multi_val *mv2);
3552 Vectors can be created, copied and freed using the following functions.
3554 #include <isl/vec.h>
3555 __isl_give isl_vec *isl_vec_alloc(isl_ctx *ctx,
3557 __isl_give isl_vec *isl_vec_copy(__isl_keep isl_vec *vec);
3558 void *isl_vec_free(__isl_take isl_vec *vec);
3560 Note that the elements of a newly created vector may have arbitrary values.
3561 The elements can be changed and inspected using the following functions.
3563 isl_ctx *isl_vec_get_ctx(__isl_keep isl_vec *vec);
3564 int isl_vec_size(__isl_keep isl_vec *vec);
3565 int isl_vec_get_element(__isl_keep isl_vec *vec,
3566 int pos, isl_int *v);
3567 __isl_give isl_val *isl_vec_get_element_val(
3568 __isl_keep isl_vec *vec, int pos);
3569 __isl_give isl_vec *isl_vec_set_element(
3570 __isl_take isl_vec *vec, int pos, isl_int v);
3571 __isl_give isl_vec *isl_vec_set_element_si(
3572 __isl_take isl_vec *vec, int pos, int v);
3573 __isl_give isl_vec *isl_vec_set_element_val(
3574 __isl_take isl_vec *vec, int pos,
3575 __isl_take isl_val *v);
3576 __isl_give isl_vec *isl_vec_set(__isl_take isl_vec *vec,
3578 __isl_give isl_vec *isl_vec_set_si(__isl_take isl_vec *vec,
3580 __isl_give isl_vec *isl_vec_set_val(
3581 __isl_take isl_vec *vec, __isl_take isl_val *v);
3582 int isl_vec_cmp_element(__isl_keep isl_vec *vec1,
3583 __isl_keep isl_vec *vec2, int pos);
3584 __isl_give isl_vec *isl_vec_fdiv_r(__isl_take isl_vec *vec,
3587 C<isl_vec_get_element> will return a negative value if anything went wrong.
3588 In that case, the value of C<*v> is undefined.
3590 The following function can be used to concatenate two vectors.
3592 __isl_give isl_vec *isl_vec_concat(__isl_take isl_vec *vec1,
3593 __isl_take isl_vec *vec2);
3597 Matrices can be created, copied and freed using the following functions.
3599 #include <isl/mat.h>
3600 __isl_give isl_mat *isl_mat_alloc(isl_ctx *ctx,
3601 unsigned n_row, unsigned n_col);
3602 __isl_give isl_mat *isl_mat_copy(__isl_keep isl_mat *mat);
3603 void *isl_mat_free(__isl_take isl_mat *mat);
3605 Note that the elements of a newly created matrix may have arbitrary values.
3606 The elements can be changed and inspected using the following functions.
3608 isl_ctx *isl_mat_get_ctx(__isl_keep isl_mat *mat);
3609 int isl_mat_rows(__isl_keep isl_mat *mat);
3610 int isl_mat_cols(__isl_keep isl_mat *mat);
3611 int isl_mat_get_element(__isl_keep isl_mat *mat,
3612 int row, int col, isl_int *v);
3613 __isl_give isl_val *isl_mat_get_element_val(
3614 __isl_keep isl_mat *mat, int row, int col);
3615 __isl_give isl_mat *isl_mat_set_element(__isl_take isl_mat *mat,
3616 int row, int col, isl_int v);
3617 __isl_give isl_mat *isl_mat_set_element_si(__isl_take isl_mat *mat,
3618 int row, int col, int v);
3619 __isl_give isl_mat *isl_mat_set_element_val(
3620 __isl_take isl_mat *mat, int row, int col,
3621 __isl_take isl_val *v);
3623 C<isl_mat_get_element> will return a negative value if anything went wrong.
3624 In that case, the value of C<*v> is undefined.
3626 The following function can be used to compute the (right) inverse
3627 of a matrix, i.e., a matrix such that the product of the original
3628 and the inverse (in that order) is a multiple of the identity matrix.
3629 The input matrix is assumed to be of full row-rank.
3631 __isl_give isl_mat *isl_mat_right_inverse(__isl_take isl_mat *mat);
3633 The following function can be used to compute the (right) kernel
3634 (or null space) of a matrix, i.e., a matrix such that the product of
3635 the original and the kernel (in that order) is the zero matrix.
3637 __isl_give isl_mat *isl_mat_right_kernel(__isl_take isl_mat *mat);
3639 =head2 Piecewise Quasi Affine Expressions
3641 The zero quasi affine expression or the quasi affine expression
3642 that is equal to a specified dimension on a given domain can be created using
3644 __isl_give isl_aff *isl_aff_zero_on_domain(
3645 __isl_take isl_local_space *ls);
3646 __isl_give isl_pw_aff *isl_pw_aff_zero_on_domain(
3647 __isl_take isl_local_space *ls);
3648 __isl_give isl_aff *isl_aff_var_on_domain(
3649 __isl_take isl_local_space *ls,
3650 enum isl_dim_type type, unsigned pos);
3651 __isl_give isl_pw_aff *isl_pw_aff_var_on_domain(
3652 __isl_take isl_local_space *ls,
3653 enum isl_dim_type type, unsigned pos);
3655 Note that the space in which the resulting objects live is a map space
3656 with the given space as domain and a one-dimensional range.
3658 An empty piecewise quasi affine expression (one with no cells)
3659 or a piecewise quasi affine expression with a single cell can
3660 be created using the following functions.
3662 #include <isl/aff.h>
3663 __isl_give isl_pw_aff *isl_pw_aff_empty(
3664 __isl_take isl_space *space);
3665 __isl_give isl_pw_aff *isl_pw_aff_alloc(
3666 __isl_take isl_set *set, __isl_take isl_aff *aff);
3667 __isl_give isl_pw_aff *isl_pw_aff_from_aff(
3668 __isl_take isl_aff *aff);
3670 A piecewise quasi affine expression that is equal to 1 on a set
3671 and 0 outside the set can be created using the following function.
3673 #include <isl/aff.h>
3674 __isl_give isl_pw_aff *isl_set_indicator_function(
3675 __isl_take isl_set *set);
3677 Quasi affine expressions can be copied and freed using
3679 #include <isl/aff.h>
3680 __isl_give isl_aff *isl_aff_copy(__isl_keep isl_aff *aff);
3681 void *isl_aff_free(__isl_take isl_aff *aff);
3683 __isl_give isl_pw_aff *isl_pw_aff_copy(
3684 __isl_keep isl_pw_aff *pwaff);
3685 void *isl_pw_aff_free(__isl_take isl_pw_aff *pwaff);
3687 A (rational) bound on a dimension can be extracted from an C<isl_constraint>
3688 using the following function. The constraint is required to have
3689 a non-zero coefficient for the specified dimension.
3691 #include <isl/constraint.h>
3692 __isl_give isl_aff *isl_constraint_get_bound(
3693 __isl_keep isl_constraint *constraint,
3694 enum isl_dim_type type, int pos);
3696 The entire affine expression of the constraint can also be extracted
3697 using the following function.
3699 #include <isl/constraint.h>
3700 __isl_give isl_aff *isl_constraint_get_aff(
3701 __isl_keep isl_constraint *constraint);
3703 Conversely, an equality constraint equating
3704 the affine expression to zero or an inequality constraint enforcing
3705 the affine expression to be non-negative, can be constructed using
3707 __isl_give isl_constraint *isl_equality_from_aff(
3708 __isl_take isl_aff *aff);
3709 __isl_give isl_constraint *isl_inequality_from_aff(
3710 __isl_take isl_aff *aff);
3712 The expression can be inspected using
3714 #include <isl/aff.h>
3715 isl_ctx *isl_aff_get_ctx(__isl_keep isl_aff *aff);
3716 int isl_aff_dim(__isl_keep isl_aff *aff,
3717 enum isl_dim_type type);
3718 __isl_give isl_local_space *isl_aff_get_domain_local_space(
3719 __isl_keep isl_aff *aff);
3720 __isl_give isl_local_space *isl_aff_get_local_space(
3721 __isl_keep isl_aff *aff);
3722 const char *isl_aff_get_dim_name(__isl_keep isl_aff *aff,
3723 enum isl_dim_type type, unsigned pos);
3724 const char *isl_pw_aff_get_dim_name(
3725 __isl_keep isl_pw_aff *pa,
3726 enum isl_dim_type type, unsigned pos);
3727 int isl_pw_aff_has_dim_id(__isl_keep isl_pw_aff *pa,
3728 enum isl_dim_type type, unsigned pos);
3729 __isl_give isl_id *isl_pw_aff_get_dim_id(
3730 __isl_keep isl_pw_aff *pa,
3731 enum isl_dim_type type, unsigned pos);
3732 __isl_give isl_id *isl_pw_aff_get_tuple_id(
3733 __isl_keep isl_pw_aff *pa,
3734 enum isl_dim_type type);
3735 int isl_aff_get_constant(__isl_keep isl_aff *aff,
3737 __isl_give isl_val *isl_aff_get_constant_val(
3738 __isl_keep isl_aff *aff);
3739 int isl_aff_get_coefficient(__isl_keep isl_aff *aff,
3740 enum isl_dim_type type, int pos, isl_int *v);
3741 __isl_give isl_val *isl_aff_get_coefficient_val(
3742 __isl_keep isl_aff *aff,
3743 enum isl_dim_type type, int pos);
3744 int isl_aff_get_denominator(__isl_keep isl_aff *aff,
3746 __isl_give isl_val *isl_aff_get_denominator_val(
3747 __isl_keep isl_aff *aff);
3748 __isl_give isl_aff *isl_aff_get_div(
3749 __isl_keep isl_aff *aff, int pos);
3751 int isl_pw_aff_n_piece(__isl_keep isl_pw_aff *pwaff);
3752 int isl_pw_aff_foreach_piece(__isl_keep isl_pw_aff *pwaff,
3753 int (*fn)(__isl_take isl_set *set,
3754 __isl_take isl_aff *aff,
3755 void *user), void *user);
3757 int isl_aff_is_cst(__isl_keep isl_aff *aff);
3758 int isl_pw_aff_is_cst(__isl_keep isl_pw_aff *pwaff);
3760 int isl_aff_involves_dims(__isl_keep isl_aff *aff,
3761 enum isl_dim_type type, unsigned first, unsigned n);
3762 int isl_pw_aff_involves_dims(__isl_keep isl_pw_aff *pwaff,
3763 enum isl_dim_type type, unsigned first, unsigned n);
3765 isl_ctx *isl_pw_aff_get_ctx(__isl_keep isl_pw_aff *pwaff);
3766 unsigned isl_pw_aff_dim(__isl_keep isl_pw_aff *pwaff,
3767 enum isl_dim_type type);
3768 int isl_pw_aff_is_empty(__isl_keep isl_pw_aff *pwaff);
3770 It can be modified using
3772 #include <isl/aff.h>
3773 __isl_give isl_pw_aff *isl_pw_aff_set_tuple_id(
3774 __isl_take isl_pw_aff *pwaff,
3775 enum isl_dim_type type, __isl_take isl_id *id);
3776 __isl_give isl_aff *isl_aff_set_dim_name(
3777 __isl_take isl_aff *aff, enum isl_dim_type type,
3778 unsigned pos, const char *s);
3779 __isl_give isl_aff *isl_aff_set_dim_id(
3780 __isl_take isl_aff *aff, enum isl_dim_type type,
3781 unsigned pos, __isl_take isl_id *id);
3782 __isl_give isl_pw_aff *isl_pw_aff_set_dim_id(
3783 __isl_take isl_pw_aff *pma,
3784 enum isl_dim_type type, unsigned pos,
3785 __isl_take isl_id *id);
3786 __isl_give isl_aff *isl_aff_set_constant(
3787 __isl_take isl_aff *aff, isl_int v);
3788 __isl_give isl_aff *isl_aff_set_constant_si(
3789 __isl_take isl_aff *aff, int v);
3790 __isl_give isl_aff *isl_aff_set_constant_val(
3791 __isl_take isl_aff *aff, __isl_take isl_val *v);
3792 __isl_give isl_aff *isl_aff_set_coefficient(
3793 __isl_take isl_aff *aff,
3794 enum isl_dim_type type, int pos, isl_int v);
3795 __isl_give isl_aff *isl_aff_set_coefficient_si(
3796 __isl_take isl_aff *aff,
3797 enum isl_dim_type type, int pos, int v);
3798 __isl_give isl_aff *isl_aff_set_coefficient_val(
3799 __isl_take isl_aff *aff,
3800 enum isl_dim_type type, int pos,
3801 __isl_take isl_val *v);
3802 __isl_give isl_aff *isl_aff_set_denominator(
3803 __isl_take isl_aff *aff, isl_int v);
3805 __isl_give isl_aff *isl_aff_add_constant(
3806 __isl_take isl_aff *aff, isl_int v);
3807 __isl_give isl_aff *isl_aff_add_constant_si(
3808 __isl_take isl_aff *aff, int v);
3809 __isl_give isl_aff *isl_aff_add_constant_val(
3810 __isl_take isl_aff *aff, __isl_take isl_val *v);
3811 __isl_give isl_aff *isl_aff_add_constant_num(
3812 __isl_take isl_aff *aff, isl_int v);
3813 __isl_give isl_aff *isl_aff_add_constant_num_si(
3814 __isl_take isl_aff *aff, int v);
3815 __isl_give isl_aff *isl_aff_add_coefficient(
3816 __isl_take isl_aff *aff,
3817 enum isl_dim_type type, int pos, isl_int v);
3818 __isl_give isl_aff *isl_aff_add_coefficient_si(
3819 __isl_take isl_aff *aff,
3820 enum isl_dim_type type, int pos, int v);
3821 __isl_give isl_aff *isl_aff_add_coefficient_val(
3822 __isl_take isl_aff *aff,
3823 enum isl_dim_type type, int pos,
3824 __isl_take isl_val *v);
3826 __isl_give isl_aff *isl_aff_insert_dims(
3827 __isl_take isl_aff *aff,
3828 enum isl_dim_type type, unsigned first, unsigned n);
3829 __isl_give isl_pw_aff *isl_pw_aff_insert_dims(
3830 __isl_take isl_pw_aff *pwaff,
3831 enum isl_dim_type type, unsigned first, unsigned n);
3832 __isl_give isl_aff *isl_aff_add_dims(
3833 __isl_take isl_aff *aff,
3834 enum isl_dim_type type, unsigned n);
3835 __isl_give isl_pw_aff *isl_pw_aff_add_dims(
3836 __isl_take isl_pw_aff *pwaff,
3837 enum isl_dim_type type, unsigned n);
3838 __isl_give isl_aff *isl_aff_drop_dims(
3839 __isl_take isl_aff *aff,
3840 enum isl_dim_type type, unsigned first, unsigned n);
3841 __isl_give isl_pw_aff *isl_pw_aff_drop_dims(
3842 __isl_take isl_pw_aff *pwaff,
3843 enum isl_dim_type type, unsigned first, unsigned n);
3845 Note that C<isl_aff_set_constant>, C<isl_aff_set_constant_si>,
3846 C<isl_aff_set_coefficient> and C<isl_aff_set_coefficient_si>
3847 set the I<numerator> of the constant or coefficient, while
3848 C<isl_aff_set_constant_val> and C<isl_aff_set_coefficient_val> set
3849 the constant or coefficient as a whole.
3850 The C<add_constant> and C<add_coefficient> functions add an integer
3851 or rational value to
3852 the possibly rational constant or coefficient.
3853 The C<add_constant_num> functions add an integer value to
3856 To check whether an affine expressions is obviously zero
3857 or obviously equal to some other affine expression, use
3859 #include <isl/aff.h>
3860 int isl_aff_plain_is_zero(__isl_keep isl_aff *aff);
3861 int isl_aff_plain_is_equal(__isl_keep isl_aff *aff1,
3862 __isl_keep isl_aff *aff2);
3863 int isl_pw_aff_plain_is_equal(
3864 __isl_keep isl_pw_aff *pwaff1,
3865 __isl_keep isl_pw_aff *pwaff2);
3869 #include <isl/aff.h>
3870 __isl_give isl_aff *isl_aff_add(__isl_take isl_aff *aff1,
3871 __isl_take isl_aff *aff2);
3872 __isl_give isl_pw_aff *isl_pw_aff_add(
3873 __isl_take isl_pw_aff *pwaff1,
3874 __isl_take isl_pw_aff *pwaff2);
3875 __isl_give isl_pw_aff *isl_pw_aff_min(
3876 __isl_take isl_pw_aff *pwaff1,
3877 __isl_take isl_pw_aff *pwaff2);
3878 __isl_give isl_pw_aff *isl_pw_aff_max(
3879 __isl_take isl_pw_aff *pwaff1,
3880 __isl_take isl_pw_aff *pwaff2);
3881 __isl_give isl_aff *isl_aff_sub(__isl_take isl_aff *aff1,
3882 __isl_take isl_aff *aff2);
3883 __isl_give isl_pw_aff *isl_pw_aff_sub(
3884 __isl_take isl_pw_aff *pwaff1,
3885 __isl_take isl_pw_aff *pwaff2);
3886 __isl_give isl_aff *isl_aff_neg(__isl_take isl_aff *aff);
3887 __isl_give isl_pw_aff *isl_pw_aff_neg(
3888 __isl_take isl_pw_aff *pwaff);
3889 __isl_give isl_aff *isl_aff_ceil(__isl_take isl_aff *aff);
3890 __isl_give isl_pw_aff *isl_pw_aff_ceil(
3891 __isl_take isl_pw_aff *pwaff);
3892 __isl_give isl_aff *isl_aff_floor(__isl_take isl_aff *aff);
3893 __isl_give isl_pw_aff *isl_pw_aff_floor(
3894 __isl_take isl_pw_aff *pwaff);
3895 __isl_give isl_aff *isl_aff_mod(__isl_take isl_aff *aff,
3897 __isl_give isl_aff *isl_aff_mod_val(__isl_take isl_aff *aff,
3898 __isl_take isl_val *mod);
3899 __isl_give isl_pw_aff *isl_pw_aff_mod(
3900 __isl_take isl_pw_aff *pwaff, isl_int mod);
3901 __isl_give isl_pw_aff *isl_pw_aff_mod_val(
3902 __isl_take isl_pw_aff *pa,
3903 __isl_take isl_val *mod);
3904 __isl_give isl_aff *isl_aff_scale(__isl_take isl_aff *aff,
3906 __isl_give isl_aff *isl_aff_scale_val(__isl_take isl_aff *aff,
3907 __isl_take isl_val *v);
3908 __isl_give isl_pw_aff *isl_pw_aff_scale(
3909 __isl_take isl_pw_aff *pwaff, isl_int f);
3910 __isl_give isl_pw_aff *isl_pw_aff_scale_val(
3911 __isl_take isl_pw_aff *pa, __isl_take isl_val *v);
3912 __isl_give isl_aff *isl_aff_scale_down(__isl_take isl_aff *aff,
3914 __isl_give isl_aff *isl_aff_scale_down_ui(
3915 __isl_take isl_aff *aff, unsigned f);
3916 __isl_give isl_aff *isl_aff_scale_down_val(
3917 __isl_take isl_aff *aff, __isl_take isl_val *v);
3918 __isl_give isl_pw_aff *isl_pw_aff_scale_down(
3919 __isl_take isl_pw_aff *pwaff, isl_int f);
3920 __isl_give isl_pw_aff *isl_pw_aff_scale_down_val(
3921 __isl_take isl_pw_aff *pa,
3922 __isl_take isl_val *f);
3924 __isl_give isl_pw_aff *isl_pw_aff_list_min(
3925 __isl_take isl_pw_aff_list *list);
3926 __isl_give isl_pw_aff *isl_pw_aff_list_max(
3927 __isl_take isl_pw_aff_list *list);
3929 __isl_give isl_pw_aff *isl_pw_aff_coalesce(
3930 __isl_take isl_pw_aff *pwqp);
3932 __isl_give isl_aff *isl_aff_align_params(
3933 __isl_take isl_aff *aff,
3934 __isl_take isl_space *model);
3935 __isl_give isl_pw_aff *isl_pw_aff_align_params(
3936 __isl_take isl_pw_aff *pwaff,
3937 __isl_take isl_space *model);
3939 __isl_give isl_aff *isl_aff_project_domain_on_params(
3940 __isl_take isl_aff *aff);
3942 __isl_give isl_aff *isl_aff_gist_params(
3943 __isl_take isl_aff *aff,
3944 __isl_take isl_set *context);
3945 __isl_give isl_aff *isl_aff_gist(__isl_take isl_aff *aff,
3946 __isl_take isl_set *context);
3947 __isl_give isl_pw_aff *isl_pw_aff_gist_params(
3948 __isl_take isl_pw_aff *pwaff,
3949 __isl_take isl_set *context);
3950 __isl_give isl_pw_aff *isl_pw_aff_gist(
3951 __isl_take isl_pw_aff *pwaff,
3952 __isl_take isl_set *context);
3954 __isl_give isl_set *isl_pw_aff_domain(
3955 __isl_take isl_pw_aff *pwaff);
3956 __isl_give isl_pw_aff *isl_pw_aff_intersect_domain(
3957 __isl_take isl_pw_aff *pa,
3958 __isl_take isl_set *set);
3959 __isl_give isl_pw_aff *isl_pw_aff_intersect_params(
3960 __isl_take isl_pw_aff *pa,
3961 __isl_take isl_set *set);
3963 __isl_give isl_aff *isl_aff_mul(__isl_take isl_aff *aff1,
3964 __isl_take isl_aff *aff2);
3965 __isl_give isl_aff *isl_aff_div(__isl_take isl_aff *aff1,
3966 __isl_take isl_aff *aff2);
3967 __isl_give isl_pw_aff *isl_pw_aff_mul(
3968 __isl_take isl_pw_aff *pwaff1,
3969 __isl_take isl_pw_aff *pwaff2);
3970 __isl_give isl_pw_aff *isl_pw_aff_div(
3971 __isl_take isl_pw_aff *pa1,
3972 __isl_take isl_pw_aff *pa2);
3973 __isl_give isl_pw_aff *isl_pw_aff_tdiv_q(
3974 __isl_take isl_pw_aff *pa1,
3975 __isl_take isl_pw_aff *pa2);
3976 __isl_give isl_pw_aff *isl_pw_aff_tdiv_r(
3977 __isl_take isl_pw_aff *pa1,
3978 __isl_take isl_pw_aff *pa2);
3980 When multiplying two affine expressions, at least one of the two needs
3981 to be a constant. Similarly, when dividing an affine expression by another,
3982 the second expression needs to be a constant.
3983 C<isl_pw_aff_tdiv_q> computes the quotient of an integer division with
3984 rounding towards zero. C<isl_pw_aff_tdiv_r> computes the corresponding
3987 #include <isl/aff.h>
3988 __isl_give isl_aff *isl_aff_pullback_multi_aff(
3989 __isl_take isl_aff *aff,
3990 __isl_take isl_multi_aff *ma);
3991 __isl_give isl_pw_aff *isl_pw_aff_pullback_multi_aff(
3992 __isl_take isl_pw_aff *pa,
3993 __isl_take isl_multi_aff *ma);
3994 __isl_give isl_pw_aff *isl_pw_aff_pullback_pw_multi_aff(
3995 __isl_take isl_pw_aff *pa,
3996 __isl_take isl_pw_multi_aff *pma);
3998 These functions precompose the input expression by the given
3999 C<isl_multi_aff> or C<isl_pw_multi_aff>. In other words,
4000 the C<isl_multi_aff> or C<isl_pw_multi_aff> is plugged
4001 into the (piecewise) affine expression.
4002 Objects of type C<isl_multi_aff> are described in
4003 L</"Piecewise Multiple Quasi Affine Expressions">.
4005 #include <isl/aff.h>
4006 __isl_give isl_basic_set *isl_aff_zero_basic_set(
4007 __isl_take isl_aff *aff);
4008 __isl_give isl_basic_set *isl_aff_neg_basic_set(
4009 __isl_take isl_aff *aff);
4010 __isl_give isl_basic_set *isl_aff_le_basic_set(
4011 __isl_take isl_aff *aff1, __isl_take isl_aff *aff2);
4012 __isl_give isl_basic_set *isl_aff_ge_basic_set(
4013 __isl_take isl_aff *aff1, __isl_take isl_aff *aff2);
4014 __isl_give isl_set *isl_pw_aff_eq_set(
4015 __isl_take isl_pw_aff *pwaff1,
4016 __isl_take isl_pw_aff *pwaff2);
4017 __isl_give isl_set *isl_pw_aff_ne_set(
4018 __isl_take isl_pw_aff *pwaff1,
4019 __isl_take isl_pw_aff *pwaff2);
4020 __isl_give isl_set *isl_pw_aff_le_set(
4021 __isl_take isl_pw_aff *pwaff1,
4022 __isl_take isl_pw_aff *pwaff2);
4023 __isl_give isl_set *isl_pw_aff_lt_set(
4024 __isl_take isl_pw_aff *pwaff1,
4025 __isl_take isl_pw_aff *pwaff2);
4026 __isl_give isl_set *isl_pw_aff_ge_set(
4027 __isl_take isl_pw_aff *pwaff1,
4028 __isl_take isl_pw_aff *pwaff2);
4029 __isl_give isl_set *isl_pw_aff_gt_set(
4030 __isl_take isl_pw_aff *pwaff1,
4031 __isl_take isl_pw_aff *pwaff2);
4033 __isl_give isl_set *isl_pw_aff_list_eq_set(
4034 __isl_take isl_pw_aff_list *list1,
4035 __isl_take isl_pw_aff_list *list2);
4036 __isl_give isl_set *isl_pw_aff_list_ne_set(
4037 __isl_take isl_pw_aff_list *list1,
4038 __isl_take isl_pw_aff_list *list2);
4039 __isl_give isl_set *isl_pw_aff_list_le_set(
4040 __isl_take isl_pw_aff_list *list1,
4041 __isl_take isl_pw_aff_list *list2);
4042 __isl_give isl_set *isl_pw_aff_list_lt_set(
4043 __isl_take isl_pw_aff_list *list1,
4044 __isl_take isl_pw_aff_list *list2);
4045 __isl_give isl_set *isl_pw_aff_list_ge_set(
4046 __isl_take isl_pw_aff_list *list1,
4047 __isl_take isl_pw_aff_list *list2);
4048 __isl_give isl_set *isl_pw_aff_list_gt_set(
4049 __isl_take isl_pw_aff_list *list1,
4050 __isl_take isl_pw_aff_list *list2);
4052 The function C<isl_aff_neg_basic_set> returns a basic set
4053 containing those elements in the domain space
4054 of C<aff> where C<aff> is negative.
4055 The function C<isl_aff_ge_basic_set> returns a basic set
4056 containing those elements in the shared space
4057 of C<aff1> and C<aff2> where C<aff1> is greater than or equal to C<aff2>.
4058 The function C<isl_pw_aff_ge_set> returns a set
4059 containing those elements in the shared domain
4060 of C<pwaff1> and C<pwaff2> where C<pwaff1> is greater than or equal to C<pwaff2>.
4061 The functions operating on C<isl_pw_aff_list> apply the corresponding
4062 C<isl_pw_aff> function to each pair of elements in the two lists.
4064 #include <isl/aff.h>
4065 __isl_give isl_set *isl_pw_aff_nonneg_set(
4066 __isl_take isl_pw_aff *pwaff);
4067 __isl_give isl_set *isl_pw_aff_zero_set(
4068 __isl_take isl_pw_aff *pwaff);
4069 __isl_give isl_set *isl_pw_aff_non_zero_set(
4070 __isl_take isl_pw_aff *pwaff);
4072 The function C<isl_pw_aff_nonneg_set> returns a set
4073 containing those elements in the domain
4074 of C<pwaff> where C<pwaff> is non-negative.
4076 #include <isl/aff.h>
4077 __isl_give isl_pw_aff *isl_pw_aff_cond(
4078 __isl_take isl_pw_aff *cond,
4079 __isl_take isl_pw_aff *pwaff_true,
4080 __isl_take isl_pw_aff *pwaff_false);
4082 The function C<isl_pw_aff_cond> performs a conditional operator
4083 and returns an expression that is equal to C<pwaff_true>
4084 for elements where C<cond> is non-zero and equal to C<pwaff_false> for elements
4085 where C<cond> is zero.
4087 #include <isl/aff.h>
4088 __isl_give isl_pw_aff *isl_pw_aff_union_min(
4089 __isl_take isl_pw_aff *pwaff1,
4090 __isl_take isl_pw_aff *pwaff2);
4091 __isl_give isl_pw_aff *isl_pw_aff_union_max(
4092 __isl_take isl_pw_aff *pwaff1,
4093 __isl_take isl_pw_aff *pwaff2);
4094 __isl_give isl_pw_aff *isl_pw_aff_union_add(
4095 __isl_take isl_pw_aff *pwaff1,
4096 __isl_take isl_pw_aff *pwaff2);
4098 The function C<isl_pw_aff_union_max> computes a piecewise quasi-affine
4099 expression with a domain that is the union of those of C<pwaff1> and
4100 C<pwaff2> and such that on each cell, the quasi-affine expression is
4101 the maximum of those of C<pwaff1> and C<pwaff2>. If only one of
4102 C<pwaff1> or C<pwaff2> is defined on a given cell, then the
4103 associated expression is the defined one.
4105 An expression can be read from input using
4107 #include <isl/aff.h>
4108 __isl_give isl_aff *isl_aff_read_from_str(
4109 isl_ctx *ctx, const char *str);
4110 __isl_give isl_pw_aff *isl_pw_aff_read_from_str(
4111 isl_ctx *ctx, const char *str);
4113 An expression can be printed using
4115 #include <isl/aff.h>
4116 __isl_give isl_printer *isl_printer_print_aff(
4117 __isl_take isl_printer *p, __isl_keep isl_aff *aff);
4119 __isl_give isl_printer *isl_printer_print_pw_aff(
4120 __isl_take isl_printer *p,
4121 __isl_keep isl_pw_aff *pwaff);
4123 =head2 Piecewise Multiple Quasi Affine Expressions
4125 An C<isl_multi_aff> object represents a sequence of
4126 zero or more affine expressions, all defined on the same domain space.
4127 Similarly, an C<isl_multi_pw_aff> object represents a sequence of
4128 zero or more piecewise affine expressions.
4130 An C<isl_multi_aff> can be constructed from a single
4131 C<isl_aff> or an C<isl_aff_list> using the
4132 following functions. Similarly for C<isl_multi_pw_aff>.
4134 #include <isl/aff.h>
4135 __isl_give isl_multi_aff *isl_multi_aff_from_aff(
4136 __isl_take isl_aff *aff);
4137 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_from_pw_aff(
4138 __isl_take isl_pw_aff *pa);
4139 __isl_give isl_multi_aff *isl_multi_aff_from_aff_list(
4140 __isl_take isl_space *space,
4141 __isl_take isl_aff_list *list);
4143 An empty piecewise multiple quasi affine expression (one with no cells),
4144 the zero piecewise multiple quasi affine expression (with value zero
4145 for each output dimension),
4146 a piecewise multiple quasi affine expression with a single cell (with
4147 either a universe or a specified domain) or
4148 a zero-dimensional piecewise multiple quasi affine expression
4150 can be created using the following functions.
4152 #include <isl/aff.h>
4153 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_empty(
4154 __isl_take isl_space *space);
4155 __isl_give isl_multi_aff *isl_multi_aff_zero(
4156 __isl_take isl_space *space);
4157 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_zero(
4158 __isl_take isl_space *space);
4159 __isl_give isl_multi_aff *isl_multi_aff_identity(
4160 __isl_take isl_space *space);
4161 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_identity(
4162 __isl_take isl_space *space);
4163 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_identity(
4164 __isl_take isl_space *space);
4165 __isl_give isl_pw_multi_aff *
4166 isl_pw_multi_aff_from_multi_aff(
4167 __isl_take isl_multi_aff *ma);
4168 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_alloc(
4169 __isl_take isl_set *set,
4170 __isl_take isl_multi_aff *maff);
4171 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_from_domain(
4172 __isl_take isl_set *set);
4174 __isl_give isl_union_pw_multi_aff *
4175 isl_union_pw_multi_aff_empty(
4176 __isl_take isl_space *space);
4177 __isl_give isl_union_pw_multi_aff *
4178 isl_union_pw_multi_aff_add_pw_multi_aff(
4179 __isl_take isl_union_pw_multi_aff *upma,
4180 __isl_take isl_pw_multi_aff *pma);
4181 __isl_give isl_union_pw_multi_aff *
4182 isl_union_pw_multi_aff_from_domain(
4183 __isl_take isl_union_set *uset);
4185 A piecewise multiple quasi affine expression can also be initialized
4186 from an C<isl_set> or C<isl_map>, provided the C<isl_set> is a singleton
4187 and the C<isl_map> is single-valued.
4188 In case of a conversion from an C<isl_union_set> or an C<isl_union_map>
4189 to an C<isl_union_pw_multi_aff>, these properties need to hold in each space.
4191 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_from_set(
4192 __isl_take isl_set *set);
4193 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_from_map(
4194 __isl_take isl_map *map);
4196 __isl_give isl_union_pw_multi_aff *
4197 isl_union_pw_multi_aff_from_union_set(
4198 __isl_take isl_union_set *uset);
4199 __isl_give isl_union_pw_multi_aff *
4200 isl_union_pw_multi_aff_from_union_map(
4201 __isl_take isl_union_map *umap);
4203 Multiple quasi affine expressions can be copied and freed using
4205 #include <isl/aff.h>
4206 __isl_give isl_multi_aff *isl_multi_aff_copy(
4207 __isl_keep isl_multi_aff *maff);
4208 void *isl_multi_aff_free(__isl_take isl_multi_aff *maff);
4210 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_copy(
4211 __isl_keep isl_pw_multi_aff *pma);
4212 void *isl_pw_multi_aff_free(
4213 __isl_take isl_pw_multi_aff *pma);
4215 __isl_give isl_union_pw_multi_aff *
4216 isl_union_pw_multi_aff_copy(
4217 __isl_keep isl_union_pw_multi_aff *upma);
4218 void *isl_union_pw_multi_aff_free(
4219 __isl_take isl_union_pw_multi_aff *upma);
4221 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_copy(
4222 __isl_keep isl_multi_pw_aff *mpa);
4223 void *isl_multi_pw_aff_free(
4224 __isl_take isl_multi_pw_aff *mpa);
4226 The expression can be inspected using
4228 #include <isl/aff.h>
4229 isl_ctx *isl_multi_aff_get_ctx(
4230 __isl_keep isl_multi_aff *maff);
4231 isl_ctx *isl_pw_multi_aff_get_ctx(
4232 __isl_keep isl_pw_multi_aff *pma);
4233 isl_ctx *isl_union_pw_multi_aff_get_ctx(
4234 __isl_keep isl_union_pw_multi_aff *upma);
4235 isl_ctx *isl_multi_pw_aff_get_ctx(
4236 __isl_keep isl_multi_pw_aff *mpa);
4237 unsigned isl_multi_aff_dim(__isl_keep isl_multi_aff *maff,
4238 enum isl_dim_type type);
4239 unsigned isl_pw_multi_aff_dim(
4240 __isl_keep isl_pw_multi_aff *pma,
4241 enum isl_dim_type type);
4242 unsigned isl_multi_pw_aff_dim(
4243 __isl_keep isl_multi_pw_aff *mpa,
4244 enum isl_dim_type type);
4245 __isl_give isl_aff *isl_multi_aff_get_aff(
4246 __isl_keep isl_multi_aff *multi, int pos);
4247 __isl_give isl_pw_aff *isl_pw_multi_aff_get_pw_aff(
4248 __isl_keep isl_pw_multi_aff *pma, int pos);
4249 __isl_give isl_pw_aff *isl_multi_pw_aff_get_pw_aff(
4250 __isl_keep isl_multi_pw_aff *mpa, int pos);
4251 const char *isl_pw_multi_aff_get_dim_name(
4252 __isl_keep isl_pw_multi_aff *pma,
4253 enum isl_dim_type type, unsigned pos);
4254 __isl_give isl_id *isl_pw_multi_aff_get_dim_id(
4255 __isl_keep isl_pw_multi_aff *pma,
4256 enum isl_dim_type type, unsigned pos);
4257 const char *isl_multi_aff_get_tuple_name(
4258 __isl_keep isl_multi_aff *multi,
4259 enum isl_dim_type type);
4260 int isl_pw_multi_aff_has_tuple_name(
4261 __isl_keep isl_pw_multi_aff *pma,
4262 enum isl_dim_type type);
4263 const char *isl_pw_multi_aff_get_tuple_name(
4264 __isl_keep isl_pw_multi_aff *pma,
4265 enum isl_dim_type type);
4266 int isl_pw_multi_aff_has_tuple_id(
4267 __isl_keep isl_pw_multi_aff *pma,
4268 enum isl_dim_type type);
4269 __isl_give isl_id *isl_pw_multi_aff_get_tuple_id(
4270 __isl_keep isl_pw_multi_aff *pma,
4271 enum isl_dim_type type);
4273 int isl_pw_multi_aff_foreach_piece(
4274 __isl_keep isl_pw_multi_aff *pma,
4275 int (*fn)(__isl_take isl_set *set,
4276 __isl_take isl_multi_aff *maff,
4277 void *user), void *user);
4279 int isl_union_pw_multi_aff_foreach_pw_multi_aff(
4280 __isl_keep isl_union_pw_multi_aff *upma,
4281 int (*fn)(__isl_take isl_pw_multi_aff *pma,
4282 void *user), void *user);
4284 It can be modified using
4286 #include <isl/aff.h>
4287 __isl_give isl_multi_aff *isl_multi_aff_set_aff(
4288 __isl_take isl_multi_aff *multi, int pos,
4289 __isl_take isl_aff *aff);
4290 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_set_pw_aff(
4291 __isl_take isl_pw_multi_aff *pma, unsigned pos,
4292 __isl_take isl_pw_aff *pa);
4293 __isl_give isl_multi_aff *isl_multi_aff_set_dim_name(
4294 __isl_take isl_multi_aff *maff,
4295 enum isl_dim_type type, unsigned pos, const char *s);
4296 __isl_give isl_multi_aff *isl_multi_aff_set_tuple_name(
4297 __isl_take isl_multi_aff *maff,
4298 enum isl_dim_type type, const char *s);
4299 __isl_give isl_multi_aff *isl_multi_aff_set_tuple_id(
4300 __isl_take isl_multi_aff *maff,
4301 enum isl_dim_type type, __isl_take isl_id *id);
4302 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_set_tuple_id(
4303 __isl_take isl_pw_multi_aff *pma,
4304 enum isl_dim_type type, __isl_take isl_id *id);
4306 __isl_give isl_multi_pw_aff *
4307 isl_multi_pw_aff_set_dim_name(
4308 __isl_take isl_multi_pw_aff *mpa,
4309 enum isl_dim_type type, unsigned pos, const char *s);
4310 __isl_give isl_multi_pw_aff *
4311 isl_multi_pw_aff_set_tuple_name(
4312 __isl_take isl_multi_pw_aff *mpa,
4313 enum isl_dim_type type, const char *s);
4315 __isl_give isl_multi_aff *isl_multi_aff_insert_dims(
4316 __isl_take isl_multi_aff *ma,
4317 enum isl_dim_type type, unsigned first, unsigned n);
4318 __isl_give isl_multi_aff *isl_multi_aff_add_dims(
4319 __isl_take isl_multi_aff *ma,
4320 enum isl_dim_type type, unsigned n);
4321 __isl_give isl_multi_aff *isl_multi_aff_drop_dims(
4322 __isl_take isl_multi_aff *maff,
4323 enum isl_dim_type type, unsigned first, unsigned n);
4324 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_drop_dims(
4325 __isl_take isl_pw_multi_aff *pma,
4326 enum isl_dim_type type, unsigned first, unsigned n);
4328 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_insert_dims(
4329 __isl_take isl_multi_pw_aff *mpa,
4330 enum isl_dim_type type, unsigned first, unsigned n);
4331 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_add_dims(
4332 __isl_take isl_multi_pw_aff *mpa,
4333 enum isl_dim_type type, unsigned n);
4335 To check whether two multiple affine expressions are
4336 obviously equal to each other, use
4338 int isl_multi_aff_plain_is_equal(__isl_keep isl_multi_aff *maff1,
4339 __isl_keep isl_multi_aff *maff2);
4340 int isl_pw_multi_aff_plain_is_equal(
4341 __isl_keep isl_pw_multi_aff *pma1,
4342 __isl_keep isl_pw_multi_aff *pma2);
4346 #include <isl/aff.h>
4347 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_union_lexmin(
4348 __isl_take isl_pw_multi_aff *pma1,
4349 __isl_take isl_pw_multi_aff *pma2);
4350 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_union_lexmax(
4351 __isl_take isl_pw_multi_aff *pma1,
4352 __isl_take isl_pw_multi_aff *pma2);
4353 __isl_give isl_multi_aff *isl_multi_aff_add(
4354 __isl_take isl_multi_aff *maff1,
4355 __isl_take isl_multi_aff *maff2);
4356 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_add(
4357 __isl_take isl_pw_multi_aff *pma1,
4358 __isl_take isl_pw_multi_aff *pma2);
4359 __isl_give isl_union_pw_multi_aff *isl_union_pw_multi_aff_add(
4360 __isl_take isl_union_pw_multi_aff *upma1,
4361 __isl_take isl_union_pw_multi_aff *upma2);
4362 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_union_add(
4363 __isl_take isl_pw_multi_aff *pma1,
4364 __isl_take isl_pw_multi_aff *pma2);
4365 __isl_give isl_multi_aff *isl_multi_aff_sub(
4366 __isl_take isl_multi_aff *ma1,
4367 __isl_take isl_multi_aff *ma2);
4368 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_sub(
4369 __isl_take isl_pw_multi_aff *pma1,
4370 __isl_take isl_pw_multi_aff *pma2);
4371 __isl_give isl_union_pw_multi_aff *isl_union_pw_multi_aff_sub(
4372 __isl_take isl_union_pw_multi_aff *upma1,
4373 __isl_take isl_union_pw_multi_aff *upma2);
4375 C<isl_multi_aff_sub> subtracts the second argument from the first.
4377 __isl_give isl_multi_aff *isl_multi_aff_scale(
4378 __isl_take isl_multi_aff *maff,
4380 __isl_give isl_multi_aff *isl_multi_aff_scale_val(
4381 __isl_take isl_multi_aff *ma,
4382 __isl_take isl_val *v);
4383 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_scale_val(
4384 __isl_take isl_pw_multi_aff *pma,
4385 __isl_take isl_val *v);
4386 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_scale_val(
4387 __isl_take isl_multi_pw_aff *mpa,
4388 __isl_take isl_val *v);
4389 __isl_give isl_multi_aff *isl_multi_aff_scale_multi_val(
4390 __isl_take isl_multi_aff *ma,
4391 __isl_take isl_multi_val *mv);
4392 __isl_give isl_pw_multi_aff *
4393 isl_pw_multi_aff_scale_multi_val(
4394 __isl_take isl_pw_multi_aff *pma,
4395 __isl_take isl_multi_val *mv);
4396 __isl_give isl_multi_pw_aff *
4397 isl_multi_pw_aff_scale_multi_val(
4398 __isl_take isl_multi_pw_aff *mpa,
4399 __isl_take isl_multi_val *mv);
4400 __isl_give isl_union_pw_multi_aff *
4401 isl_union_pw_multi_aff_scale_multi_val(
4402 __isl_take isl_union_pw_multi_aff *upma,
4403 __isl_take isl_multi_val *mv);
4404 __isl_give isl_multi_aff *isl_multi_aff_scale_vec(
4405 __isl_take isl_multi_aff *ma,
4406 __isl_take isl_vec *v);
4407 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_scale_vec(
4408 __isl_take isl_pw_multi_aff *pma,
4409 __isl_take isl_vec *v);
4410 __isl_give isl_union_pw_multi_aff *isl_union_pw_multi_aff_scale_vec(
4411 __isl_take isl_union_pw_multi_aff *upma,
4412 __isl_take isl_vec *v);
4414 C<isl_multi_aff_scale_multi_val> scales the elements of C<ma>
4415 by the corresponding elements of C<mv>.
4416 C<isl_multi_aff_scale_vec> scales the first elements of C<ma>
4417 by the corresponding elements of C<v>.
4419 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_intersect_params(
4420 __isl_take isl_pw_multi_aff *pma,
4421 __isl_take isl_set *set);
4422 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_intersect_domain(
4423 __isl_take isl_pw_multi_aff *pma,
4424 __isl_take isl_set *set);
4425 __isl_give isl_union_pw_multi_aff *
4426 isl_union_pw_multi_aff_intersect_domain(
4427 __isl_take isl_union_pw_multi_aff *upma,
4428 __isl_take isl_union_set *uset);
4429 __isl_give isl_multi_aff *isl_multi_aff_lift(
4430 __isl_take isl_multi_aff *maff,
4431 __isl_give isl_local_space **ls);
4432 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_coalesce(
4433 __isl_take isl_pw_multi_aff *pma);
4434 __isl_give isl_multi_aff *isl_multi_aff_align_params(
4435 __isl_take isl_multi_aff *multi,
4436 __isl_take isl_space *model);
4437 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_align_params(
4438 __isl_take isl_pw_multi_aff *pma,
4439 __isl_take isl_space *model);
4440 __isl_give isl_pw_multi_aff *
4441 isl_pw_multi_aff_project_domain_on_params(
4442 __isl_take isl_pw_multi_aff *pma);
4443 __isl_give isl_multi_aff *isl_multi_aff_gist_params(
4444 __isl_take isl_multi_aff *maff,
4445 __isl_take isl_set *context);
4446 __isl_give isl_multi_aff *isl_multi_aff_gist(
4447 __isl_take isl_multi_aff *maff,
4448 __isl_take isl_set *context);
4449 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_gist_params(
4450 __isl_take isl_pw_multi_aff *pma,
4451 __isl_take isl_set *set);
4452 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_gist(
4453 __isl_take isl_pw_multi_aff *pma,
4454 __isl_take isl_set *set);
4455 __isl_give isl_set *isl_pw_multi_aff_domain(
4456 __isl_take isl_pw_multi_aff *pma);
4457 __isl_give isl_union_set *isl_union_pw_multi_aff_domain(
4458 __isl_take isl_union_pw_multi_aff *upma);
4459 __isl_give isl_multi_aff *isl_multi_aff_range_splice(
4460 __isl_take isl_multi_aff *ma1, unsigned pos,
4461 __isl_take isl_multi_aff *ma2);
4462 __isl_give isl_multi_aff *isl_multi_aff_splice(
4463 __isl_take isl_multi_aff *ma1,
4464 unsigned in_pos, unsigned out_pos,
4465 __isl_take isl_multi_aff *ma2);
4466 __isl_give isl_multi_aff *isl_multi_aff_range_product(
4467 __isl_take isl_multi_aff *ma1,
4468 __isl_take isl_multi_aff *ma2);
4469 __isl_give isl_multi_aff *isl_multi_aff_flat_range_product(
4470 __isl_take isl_multi_aff *ma1,
4471 __isl_take isl_multi_aff *ma2);
4472 __isl_give isl_multi_aff *isl_multi_aff_product(
4473 __isl_take isl_multi_aff *ma1,
4474 __isl_take isl_multi_aff *ma2);
4475 __isl_give isl_pw_multi_aff *
4476 isl_pw_multi_aff_range_product(
4477 __isl_take isl_pw_multi_aff *pma1,
4478 __isl_take isl_pw_multi_aff *pma2);
4479 __isl_give isl_pw_multi_aff *
4480 isl_pw_multi_aff_flat_range_product(
4481 __isl_take isl_pw_multi_aff *pma1,
4482 __isl_take isl_pw_multi_aff *pma2);
4483 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_product(
4484 __isl_take isl_pw_multi_aff *pma1,
4485 __isl_take isl_pw_multi_aff *pma2);
4486 __isl_give isl_union_pw_multi_aff *
4487 isl_union_pw_multi_aff_flat_range_product(
4488 __isl_take isl_union_pw_multi_aff *upma1,
4489 __isl_take isl_union_pw_multi_aff *upma2);
4490 __isl_give isl_multi_pw_aff *
4491 isl_multi_pw_aff_range_splice(
4492 __isl_take isl_multi_pw_aff *mpa1, unsigned pos,
4493 __isl_take isl_multi_pw_aff *mpa2);
4494 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_splice(
4495 __isl_take isl_multi_pw_aff *mpa1,
4496 unsigned in_pos, unsigned out_pos,
4497 __isl_take isl_multi_pw_aff *mpa2);
4498 __isl_give isl_multi_pw_aff *
4499 isl_multi_pw_aff_range_product(
4500 __isl_take isl_multi_pw_aff *mpa1,
4501 __isl_take isl_multi_pw_aff *mpa2);
4502 __isl_give isl_multi_pw_aff *
4503 isl_multi_pw_aff_flat_range_product(
4504 __isl_take isl_multi_pw_aff *mpa1,
4505 __isl_take isl_multi_pw_aff *mpa2);
4507 If the C<ls> argument of C<isl_multi_aff_lift> is not C<NULL>,
4508 then it is assigned the local space that lies at the basis of
4509 the lifting applied.
4511 #include <isl/aff.h>
4512 __isl_give isl_multi_aff *isl_multi_aff_pullback_multi_aff(
4513 __isl_take isl_multi_aff *ma1,
4514 __isl_take isl_multi_aff *ma2);
4515 __isl_give isl_pw_multi_aff *
4516 isl_pw_multi_aff_pullback_multi_aff(
4517 __isl_take isl_pw_multi_aff *pma,
4518 __isl_take isl_multi_aff *ma);
4519 __isl_give isl_pw_multi_aff *
4520 isl_pw_multi_aff_pullback_pw_multi_aff(
4521 __isl_take isl_pw_multi_aff *pma1,
4522 __isl_take isl_pw_multi_aff *pma2);
4524 The function C<isl_multi_aff_pullback_multi_aff> precomposes C<ma1> by C<ma2>.
4525 In other words, C<ma2> is plugged
4528 __isl_give isl_set *isl_multi_aff_lex_le_set(
4529 __isl_take isl_multi_aff *ma1,
4530 __isl_take isl_multi_aff *ma2);
4531 __isl_give isl_set *isl_multi_aff_lex_ge_set(
4532 __isl_take isl_multi_aff *ma1,
4533 __isl_take isl_multi_aff *ma2);
4535 The function C<isl_multi_aff_lex_le_set> returns a set
4536 containing those elements in the shared domain space
4537 where C<ma1> is lexicographically smaller than or
4540 An expression can be read from input using
4542 #include <isl/aff.h>
4543 __isl_give isl_multi_aff *isl_multi_aff_read_from_str(
4544 isl_ctx *ctx, const char *str);
4545 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_read_from_str(
4546 isl_ctx *ctx, const char *str);
4547 __isl_give isl_union_pw_multi_aff *
4548 isl_union_pw_multi_aff_read_from_str(
4549 isl_ctx *ctx, const char *str);
4551 An expression can be printed using
4553 #include <isl/aff.h>
4554 __isl_give isl_printer *isl_printer_print_multi_aff(
4555 __isl_take isl_printer *p,
4556 __isl_keep isl_multi_aff *maff);
4557 __isl_give isl_printer *isl_printer_print_pw_multi_aff(
4558 __isl_take isl_printer *p,
4559 __isl_keep isl_pw_multi_aff *pma);
4560 __isl_give isl_printer *isl_printer_print_union_pw_multi_aff(
4561 __isl_take isl_printer *p,
4562 __isl_keep isl_union_pw_multi_aff *upma);
4563 __isl_give isl_printer *isl_printer_print_multi_pw_aff(
4564 __isl_take isl_printer *p,
4565 __isl_keep isl_multi_pw_aff *mpa);
4569 Points are elements of a set. They can be used to construct
4570 simple sets (boxes) or they can be used to represent the
4571 individual elements of a set.
4572 The zero point (the origin) can be created using
4574 __isl_give isl_point *isl_point_zero(__isl_take isl_space *space);
4576 The coordinates of a point can be inspected, set and changed
4579 int isl_point_get_coordinate(__isl_keep isl_point *pnt,
4580 enum isl_dim_type type, int pos, isl_int *v);
4581 __isl_give isl_val *isl_point_get_coordinate_val(
4582 __isl_keep isl_point *pnt,
4583 enum isl_dim_type type, int pos);
4584 __isl_give isl_point *isl_point_set_coordinate(
4585 __isl_take isl_point *pnt,
4586 enum isl_dim_type type, int pos, isl_int v);
4587 __isl_give isl_point *isl_point_set_coordinate_val(
4588 __isl_take isl_point *pnt,
4589 enum isl_dim_type type, int pos,
4590 __isl_take isl_val *v);
4592 __isl_give isl_point *isl_point_add_ui(
4593 __isl_take isl_point *pnt,
4594 enum isl_dim_type type, int pos, unsigned val);
4595 __isl_give isl_point *isl_point_sub_ui(
4596 __isl_take isl_point *pnt,
4597 enum isl_dim_type type, int pos, unsigned val);
4599 Other properties can be obtained using
4601 isl_ctx *isl_point_get_ctx(__isl_keep isl_point *pnt);
4603 Points can be copied or freed using
4605 __isl_give isl_point *isl_point_copy(
4606 __isl_keep isl_point *pnt);
4607 void isl_point_free(__isl_take isl_point *pnt);
4609 A singleton set can be created from a point using
4611 __isl_give isl_basic_set *isl_basic_set_from_point(
4612 __isl_take isl_point *pnt);
4613 __isl_give isl_set *isl_set_from_point(
4614 __isl_take isl_point *pnt);
4616 and a box can be created from two opposite extremal points using
4618 __isl_give isl_basic_set *isl_basic_set_box_from_points(
4619 __isl_take isl_point *pnt1,
4620 __isl_take isl_point *pnt2);
4621 __isl_give isl_set *isl_set_box_from_points(
4622 __isl_take isl_point *pnt1,
4623 __isl_take isl_point *pnt2);
4625 All elements of a B<bounded> (union) set can be enumerated using
4626 the following functions.
4628 int isl_set_foreach_point(__isl_keep isl_set *set,
4629 int (*fn)(__isl_take isl_point *pnt, void *user),
4631 int isl_union_set_foreach_point(__isl_keep isl_union_set *uset,
4632 int (*fn)(__isl_take isl_point *pnt, void *user),
4635 The function C<fn> is called for each integer point in
4636 C<set> with as second argument the last argument of
4637 the C<isl_set_foreach_point> call. The function C<fn>
4638 should return C<0> on success and C<-1> on failure.
4639 In the latter case, C<isl_set_foreach_point> will stop
4640 enumerating and return C<-1> as well.
4641 If the enumeration is performed successfully and to completion,
4642 then C<isl_set_foreach_point> returns C<0>.
4644 To obtain a single point of a (basic) set, use
4646 __isl_give isl_point *isl_basic_set_sample_point(
4647 __isl_take isl_basic_set *bset);
4648 __isl_give isl_point *isl_set_sample_point(
4649 __isl_take isl_set *set);
4651 If C<set> does not contain any (integer) points, then the
4652 resulting point will be ``void'', a property that can be
4655 int isl_point_is_void(__isl_keep isl_point *pnt);
4657 =head2 Piecewise Quasipolynomials
4659 A piecewise quasipolynomial is a particular kind of function that maps
4660 a parametric point to a rational value.
4661 More specifically, a quasipolynomial is a polynomial expression in greatest
4662 integer parts of affine expressions of parameters and variables.
4663 A piecewise quasipolynomial is a subdivision of a given parametric
4664 domain into disjoint cells with a quasipolynomial associated to
4665 each cell. The value of the piecewise quasipolynomial at a given
4666 point is the value of the quasipolynomial associated to the cell
4667 that contains the point. Outside of the union of cells,
4668 the value is assumed to be zero.
4669 For example, the piecewise quasipolynomial
4671 [n] -> { [x] -> ((1 + n) - x) : x <= n and x >= 0 }
4673 maps C<x> to C<1 + n - x> for values of C<x> between C<0> and C<n>.
4674 A given piecewise quasipolynomial has a fixed domain dimension.
4675 Union piecewise quasipolynomials are used to contain piecewise quasipolynomials
4676 defined over different domains.
4677 Piecewise quasipolynomials are mainly used by the C<barvinok>
4678 library for representing the number of elements in a parametric set or map.
4679 For example, the piecewise quasipolynomial above represents
4680 the number of points in the map
4682 [n] -> { [x] -> [y] : x,y >= 0 and 0 <= x + y <= n }
4684 =head3 Input and Output
4686 Piecewise quasipolynomials can be read from input using
4688 __isl_give isl_union_pw_qpolynomial *
4689 isl_union_pw_qpolynomial_read_from_str(
4690 isl_ctx *ctx, const char *str);
4692 Quasipolynomials and piecewise quasipolynomials can be printed
4693 using the following functions.
4695 __isl_give isl_printer *isl_printer_print_qpolynomial(
4696 __isl_take isl_printer *p,
4697 __isl_keep isl_qpolynomial *qp);
4699 __isl_give isl_printer *isl_printer_print_pw_qpolynomial(
4700 __isl_take isl_printer *p,
4701 __isl_keep isl_pw_qpolynomial *pwqp);
4703 __isl_give isl_printer *isl_printer_print_union_pw_qpolynomial(
4704 __isl_take isl_printer *p,
4705 __isl_keep isl_union_pw_qpolynomial *upwqp);
4707 The output format of the printer
4708 needs to be set to either C<ISL_FORMAT_ISL> or C<ISL_FORMAT_C>.
4709 For C<isl_printer_print_union_pw_qpolynomial>, only C<ISL_FORMAT_ISL>
4711 In case of printing in C<ISL_FORMAT_C>, the user may want
4712 to set the names of all dimensions
4714 __isl_give isl_qpolynomial *isl_qpolynomial_set_dim_name(
4715 __isl_take isl_qpolynomial *qp,
4716 enum isl_dim_type type, unsigned pos,
4718 __isl_give isl_pw_qpolynomial *
4719 isl_pw_qpolynomial_set_dim_name(
4720 __isl_take isl_pw_qpolynomial *pwqp,
4721 enum isl_dim_type type, unsigned pos,
4724 =head3 Creating New (Piecewise) Quasipolynomials
4726 Some simple quasipolynomials can be created using the following functions.
4727 More complicated quasipolynomials can be created by applying
4728 operations such as addition and multiplication
4729 on the resulting quasipolynomials
4731 __isl_give isl_qpolynomial *isl_qpolynomial_zero_on_domain(
4732 __isl_take isl_space *domain);
4733 __isl_give isl_qpolynomial *isl_qpolynomial_one_on_domain(
4734 __isl_take isl_space *domain);
4735 __isl_give isl_qpolynomial *isl_qpolynomial_infty_on_domain(
4736 __isl_take isl_space *domain);
4737 __isl_give isl_qpolynomial *isl_qpolynomial_neginfty_on_domain(
4738 __isl_take isl_space *domain);
4739 __isl_give isl_qpolynomial *isl_qpolynomial_nan_on_domain(
4740 __isl_take isl_space *domain);
4741 __isl_give isl_qpolynomial *isl_qpolynomial_rat_cst_on_domain(
4742 __isl_take isl_space *domain,
4743 const isl_int n, const isl_int d);
4744 __isl_give isl_qpolynomial *isl_qpolynomial_val_on_domain(
4745 __isl_take isl_space *domain,
4746 __isl_take isl_val *val);
4747 __isl_give isl_qpolynomial *isl_qpolynomial_var_on_domain(
4748 __isl_take isl_space *domain,
4749 enum isl_dim_type type, unsigned pos);
4750 __isl_give isl_qpolynomial *isl_qpolynomial_from_aff(
4751 __isl_take isl_aff *aff);
4753 Note that the space in which a quasipolynomial lives is a map space
4754 with a one-dimensional range. The C<domain> argument in some of
4755 the functions above corresponds to the domain of this map space.
4757 The zero piecewise quasipolynomial or a piecewise quasipolynomial
4758 with a single cell can be created using the following functions.
4759 Multiple of these single cell piecewise quasipolynomials can
4760 be combined to create more complicated piecewise quasipolynomials.
4762 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_zero(
4763 __isl_take isl_space *space);
4764 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_alloc(
4765 __isl_take isl_set *set,
4766 __isl_take isl_qpolynomial *qp);
4767 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_from_qpolynomial(
4768 __isl_take isl_qpolynomial *qp);
4769 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_from_pw_aff(
4770 __isl_take isl_pw_aff *pwaff);
4772 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_zero(
4773 __isl_take isl_space *space);
4774 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_from_pw_qpolynomial(
4775 __isl_take isl_pw_qpolynomial *pwqp);
4776 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_add_pw_qpolynomial(
4777 __isl_take isl_union_pw_qpolynomial *upwqp,
4778 __isl_take isl_pw_qpolynomial *pwqp);
4780 Quasipolynomials can be copied and freed again using the following
4783 __isl_give isl_qpolynomial *isl_qpolynomial_copy(
4784 __isl_keep isl_qpolynomial *qp);
4785 void *isl_qpolynomial_free(__isl_take isl_qpolynomial *qp);
4787 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_copy(
4788 __isl_keep isl_pw_qpolynomial *pwqp);
4789 void *isl_pw_qpolynomial_free(
4790 __isl_take isl_pw_qpolynomial *pwqp);
4792 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_copy(
4793 __isl_keep isl_union_pw_qpolynomial *upwqp);
4794 void *isl_union_pw_qpolynomial_free(
4795 __isl_take isl_union_pw_qpolynomial *upwqp);
4797 =head3 Inspecting (Piecewise) Quasipolynomials
4799 To iterate over all piecewise quasipolynomials in a union
4800 piecewise quasipolynomial, use the following function
4802 int isl_union_pw_qpolynomial_foreach_pw_qpolynomial(
4803 __isl_keep isl_union_pw_qpolynomial *upwqp,
4804 int (*fn)(__isl_take isl_pw_qpolynomial *pwqp, void *user),
4807 To extract the piecewise quasipolynomial in a given space from a union, use
4809 __isl_give isl_pw_qpolynomial *
4810 isl_union_pw_qpolynomial_extract_pw_qpolynomial(
4811 __isl_keep isl_union_pw_qpolynomial *upwqp,
4812 __isl_take isl_space *space);
4814 To iterate over the cells in a piecewise quasipolynomial,
4815 use either of the following two functions
4817 int isl_pw_qpolynomial_foreach_piece(
4818 __isl_keep isl_pw_qpolynomial *pwqp,
4819 int (*fn)(__isl_take isl_set *set,
4820 __isl_take isl_qpolynomial *qp,
4821 void *user), void *user);
4822 int isl_pw_qpolynomial_foreach_lifted_piece(
4823 __isl_keep isl_pw_qpolynomial *pwqp,
4824 int (*fn)(__isl_take isl_set *set,
4825 __isl_take isl_qpolynomial *qp,
4826 void *user), void *user);
4828 As usual, the function C<fn> should return C<0> on success
4829 and C<-1> on failure. The difference between
4830 C<isl_pw_qpolynomial_foreach_piece> and
4831 C<isl_pw_qpolynomial_foreach_lifted_piece> is that
4832 C<isl_pw_qpolynomial_foreach_lifted_piece> will first
4833 compute unique representations for all existentially quantified
4834 variables and then turn these existentially quantified variables
4835 into extra set variables, adapting the associated quasipolynomial
4836 accordingly. This means that the C<set> passed to C<fn>
4837 will not have any existentially quantified variables, but that
4838 the dimensions of the sets may be different for different
4839 invocations of C<fn>.
4841 The constant term of a quasipolynomial can be extracted using
4843 __isl_give isl_val *isl_qpolynomial_get_constant_val(
4844 __isl_keep isl_qpolynomial *qp);
4846 To iterate over all terms in a quasipolynomial,
4849 int isl_qpolynomial_foreach_term(
4850 __isl_keep isl_qpolynomial *qp,
4851 int (*fn)(__isl_take isl_term *term,
4852 void *user), void *user);
4854 The terms themselves can be inspected and freed using
4857 unsigned isl_term_dim(__isl_keep isl_term *term,
4858 enum isl_dim_type type);
4859 void isl_term_get_num(__isl_keep isl_term *term,
4861 void isl_term_get_den(__isl_keep isl_term *term,
4863 __isl_give isl_val *isl_term_get_coefficient_val(
4864 __isl_keep isl_term *term);
4865 int isl_term_get_exp(__isl_keep isl_term *term,
4866 enum isl_dim_type type, unsigned pos);
4867 __isl_give isl_aff *isl_term_get_div(
4868 __isl_keep isl_term *term, unsigned pos);
4869 void isl_term_free(__isl_take isl_term *term);
4871 Each term is a product of parameters, set variables and
4872 integer divisions. The function C<isl_term_get_exp>
4873 returns the exponent of a given dimensions in the given term.
4874 The C<isl_int>s in the arguments of C<isl_term_get_num>
4875 and C<isl_term_get_den> need to have been initialized
4876 using C<isl_int_init> before calling these functions.
4878 =head3 Properties of (Piecewise) Quasipolynomials
4880 To check whether a quasipolynomial is actually a constant,
4881 use the following function.
4883 int isl_qpolynomial_is_cst(__isl_keep isl_qpolynomial *qp,
4884 isl_int *n, isl_int *d);
4886 If C<qp> is a constant and if C<n> and C<d> are not C<NULL>
4887 then the numerator and denominator of the constant
4888 are returned in C<*n> and C<*d>, respectively.
4890 To check whether two union piecewise quasipolynomials are
4891 obviously equal, use
4893 int isl_union_pw_qpolynomial_plain_is_equal(
4894 __isl_keep isl_union_pw_qpolynomial *upwqp1,
4895 __isl_keep isl_union_pw_qpolynomial *upwqp2);
4897 =head3 Operations on (Piecewise) Quasipolynomials
4899 __isl_give isl_qpolynomial *isl_qpolynomial_scale(
4900 __isl_take isl_qpolynomial *qp, isl_int v);
4901 __isl_give isl_qpolynomial *isl_qpolynomial_scale_val(
4902 __isl_take isl_qpolynomial *qp,
4903 __isl_take isl_val *v);
4904 __isl_give isl_qpolynomial *isl_qpolynomial_neg(
4905 __isl_take isl_qpolynomial *qp);
4906 __isl_give isl_qpolynomial *isl_qpolynomial_add(
4907 __isl_take isl_qpolynomial *qp1,
4908 __isl_take isl_qpolynomial *qp2);
4909 __isl_give isl_qpolynomial *isl_qpolynomial_sub(
4910 __isl_take isl_qpolynomial *qp1,
4911 __isl_take isl_qpolynomial *qp2);
4912 __isl_give isl_qpolynomial *isl_qpolynomial_mul(
4913 __isl_take isl_qpolynomial *qp1,
4914 __isl_take isl_qpolynomial *qp2);
4915 __isl_give isl_qpolynomial *isl_qpolynomial_pow(
4916 __isl_take isl_qpolynomial *qp, unsigned exponent);
4918 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_fix_val(
4919 __isl_take isl_pw_qpolynomial *pwqp,
4920 enum isl_dim_type type, unsigned n,
4921 __isl_take isl_val *v);
4922 __isl_give isl_pw_qpolynomial *
4923 isl_pw_qpolynomial_scale_val(
4924 __isl_take isl_pw_qpolynomial *pwqp,
4925 __isl_take isl_val *v);
4926 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_add(
4927 __isl_take isl_pw_qpolynomial *pwqp1,
4928 __isl_take isl_pw_qpolynomial *pwqp2);
4929 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_sub(
4930 __isl_take isl_pw_qpolynomial *pwqp1,
4931 __isl_take isl_pw_qpolynomial *pwqp2);
4932 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_add_disjoint(
4933 __isl_take isl_pw_qpolynomial *pwqp1,
4934 __isl_take isl_pw_qpolynomial *pwqp2);
4935 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_neg(
4936 __isl_take isl_pw_qpolynomial *pwqp);
4937 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_mul(
4938 __isl_take isl_pw_qpolynomial *pwqp1,
4939 __isl_take isl_pw_qpolynomial *pwqp2);
4940 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_pow(
4941 __isl_take isl_pw_qpolynomial *pwqp, unsigned exponent);
4943 __isl_give isl_union_pw_qpolynomial *
4944 isl_union_pw_qpolynomial_scale_val(
4945 __isl_take isl_union_pw_qpolynomial *upwqp,
4946 __isl_take isl_val *v);
4947 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_add(
4948 __isl_take isl_union_pw_qpolynomial *upwqp1,
4949 __isl_take isl_union_pw_qpolynomial *upwqp2);
4950 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_sub(
4951 __isl_take isl_union_pw_qpolynomial *upwqp1,
4952 __isl_take isl_union_pw_qpolynomial *upwqp2);
4953 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_mul(
4954 __isl_take isl_union_pw_qpolynomial *upwqp1,
4955 __isl_take isl_union_pw_qpolynomial *upwqp2);
4957 __isl_give isl_qpolynomial *isl_pw_qpolynomial_eval(
4958 __isl_take isl_pw_qpolynomial *pwqp,
4959 __isl_take isl_point *pnt);
4961 __isl_give isl_qpolynomial *isl_union_pw_qpolynomial_eval(
4962 __isl_take isl_union_pw_qpolynomial *upwqp,
4963 __isl_take isl_point *pnt);
4965 __isl_give isl_set *isl_pw_qpolynomial_domain(
4966 __isl_take isl_pw_qpolynomial *pwqp);
4967 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_intersect_domain(
4968 __isl_take isl_pw_qpolynomial *pwpq,
4969 __isl_take isl_set *set);
4970 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_intersect_params(
4971 __isl_take isl_pw_qpolynomial *pwpq,
4972 __isl_take isl_set *set);
4974 __isl_give isl_union_set *isl_union_pw_qpolynomial_domain(
4975 __isl_take isl_union_pw_qpolynomial *upwqp);
4976 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_intersect_domain(
4977 __isl_take isl_union_pw_qpolynomial *upwpq,
4978 __isl_take isl_union_set *uset);
4979 __isl_give isl_union_pw_qpolynomial *
4980 isl_union_pw_qpolynomial_intersect_params(
4981 __isl_take isl_union_pw_qpolynomial *upwpq,
4982 __isl_take isl_set *set);
4984 __isl_give isl_qpolynomial *isl_qpolynomial_align_params(
4985 __isl_take isl_qpolynomial *qp,
4986 __isl_take isl_space *model);
4988 __isl_give isl_qpolynomial *isl_qpolynomial_project_domain_on_params(
4989 __isl_take isl_qpolynomial *qp);
4990 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_project_domain_on_params(
4991 __isl_take isl_pw_qpolynomial *pwqp);
4993 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_coalesce(
4994 __isl_take isl_union_pw_qpolynomial *upwqp);
4996 __isl_give isl_qpolynomial *isl_qpolynomial_gist_params(
4997 __isl_take isl_qpolynomial *qp,
4998 __isl_take isl_set *context);
4999 __isl_give isl_qpolynomial *isl_qpolynomial_gist(
5000 __isl_take isl_qpolynomial *qp,
5001 __isl_take isl_set *context);
5003 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_gist_params(
5004 __isl_take isl_pw_qpolynomial *pwqp,
5005 __isl_take isl_set *context);
5006 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_gist(
5007 __isl_take isl_pw_qpolynomial *pwqp,
5008 __isl_take isl_set *context);
5010 __isl_give isl_union_pw_qpolynomial *
5011 isl_union_pw_qpolynomial_gist_params(
5012 __isl_take isl_union_pw_qpolynomial *upwqp,
5013 __isl_take isl_set *context);
5014 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_gist(
5015 __isl_take isl_union_pw_qpolynomial *upwqp,
5016 __isl_take isl_union_set *context);
5018 The gist operation applies the gist operation to each of
5019 the cells in the domain of the input piecewise quasipolynomial.
5020 The context is also exploited
5021 to simplify the quasipolynomials associated to each cell.
5023 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_to_polynomial(
5024 __isl_take isl_pw_qpolynomial *pwqp, int sign);
5025 __isl_give isl_union_pw_qpolynomial *
5026 isl_union_pw_qpolynomial_to_polynomial(
5027 __isl_take isl_union_pw_qpolynomial *upwqp, int sign);
5029 Approximate each quasipolynomial by a polynomial. If C<sign> is positive,
5030 the polynomial will be an overapproximation. If C<sign> is negative,
5031 it will be an underapproximation. If C<sign> is zero, the approximation
5032 will lie somewhere in between.
5034 =head2 Bounds on Piecewise Quasipolynomials and Piecewise Quasipolynomial Reductions
5036 A piecewise quasipolynomial reduction is a piecewise
5037 reduction (or fold) of quasipolynomials.
5038 In particular, the reduction can be maximum or a minimum.
5039 The objects are mainly used to represent the result of
5040 an upper or lower bound on a quasipolynomial over its domain,
5041 i.e., as the result of the following function.
5043 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_bound(
5044 __isl_take isl_pw_qpolynomial *pwqp,
5045 enum isl_fold type, int *tight);
5047 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_bound(
5048 __isl_take isl_union_pw_qpolynomial *upwqp,
5049 enum isl_fold type, int *tight);
5051 The C<type> argument may be either C<isl_fold_min> or C<isl_fold_max>.
5052 If C<tight> is not C<NULL>, then C<*tight> is set to C<1>
5053 is the returned bound is known be tight, i.e., for each value
5054 of the parameters there is at least
5055 one element in the domain that reaches the bound.
5056 If the domain of C<pwqp> is not wrapping, then the bound is computed
5057 over all elements in that domain and the result has a purely parametric
5058 domain. If the domain of C<pwqp> is wrapping, then the bound is
5059 computed over the range of the wrapped relation. The domain of the
5060 wrapped relation becomes the domain of the result.
5062 A (piecewise) quasipolynomial reduction can be copied or freed using the
5063 following functions.
5065 __isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_copy(
5066 __isl_keep isl_qpolynomial_fold *fold);
5067 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_copy(
5068 __isl_keep isl_pw_qpolynomial_fold *pwf);
5069 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_copy(
5070 __isl_keep isl_union_pw_qpolynomial_fold *upwf);
5071 void isl_qpolynomial_fold_free(
5072 __isl_take isl_qpolynomial_fold *fold);
5073 void *isl_pw_qpolynomial_fold_free(
5074 __isl_take isl_pw_qpolynomial_fold *pwf);
5075 void *isl_union_pw_qpolynomial_fold_free(
5076 __isl_take isl_union_pw_qpolynomial_fold *upwf);
5078 =head3 Printing Piecewise Quasipolynomial Reductions
5080 Piecewise quasipolynomial reductions can be printed
5081 using the following function.
5083 __isl_give isl_printer *isl_printer_print_pw_qpolynomial_fold(
5084 __isl_take isl_printer *p,
5085 __isl_keep isl_pw_qpolynomial_fold *pwf);
5086 __isl_give isl_printer *isl_printer_print_union_pw_qpolynomial_fold(
5087 __isl_take isl_printer *p,
5088 __isl_keep isl_union_pw_qpolynomial_fold *upwf);
5090 For C<isl_printer_print_pw_qpolynomial_fold>,
5091 output format of the printer
5092 needs to be set to either C<ISL_FORMAT_ISL> or C<ISL_FORMAT_C>.
5093 For C<isl_printer_print_union_pw_qpolynomial_fold>,
5094 output format of the printer
5095 needs to be set to C<ISL_FORMAT_ISL>.
5096 In case of printing in C<ISL_FORMAT_C>, the user may want
5097 to set the names of all dimensions
5099 __isl_give isl_pw_qpolynomial_fold *
5100 isl_pw_qpolynomial_fold_set_dim_name(
5101 __isl_take isl_pw_qpolynomial_fold *pwf,
5102 enum isl_dim_type type, unsigned pos,
5105 =head3 Inspecting (Piecewise) Quasipolynomial Reductions
5107 To iterate over all piecewise quasipolynomial reductions in a union
5108 piecewise quasipolynomial reduction, use the following function
5110 int isl_union_pw_qpolynomial_fold_foreach_pw_qpolynomial_fold(
5111 __isl_keep isl_union_pw_qpolynomial_fold *upwf,
5112 int (*fn)(__isl_take isl_pw_qpolynomial_fold *pwf,
5113 void *user), void *user);
5115 To iterate over the cells in a piecewise quasipolynomial reduction,
5116 use either of the following two functions
5118 int isl_pw_qpolynomial_fold_foreach_piece(
5119 __isl_keep isl_pw_qpolynomial_fold *pwf,
5120 int (*fn)(__isl_take isl_set *set,
5121 __isl_take isl_qpolynomial_fold *fold,
5122 void *user), void *user);
5123 int isl_pw_qpolynomial_fold_foreach_lifted_piece(
5124 __isl_keep isl_pw_qpolynomial_fold *pwf,
5125 int (*fn)(__isl_take isl_set *set,
5126 __isl_take isl_qpolynomial_fold *fold,
5127 void *user), void *user);
5129 See L<Inspecting (Piecewise) Quasipolynomials> for an explanation
5130 of the difference between these two functions.
5132 To iterate over all quasipolynomials in a reduction, use
5134 int isl_qpolynomial_fold_foreach_qpolynomial(
5135 __isl_keep isl_qpolynomial_fold *fold,
5136 int (*fn)(__isl_take isl_qpolynomial *qp,
5137 void *user), void *user);
5139 =head3 Properties of Piecewise Quasipolynomial Reductions
5141 To check whether two union piecewise quasipolynomial reductions are
5142 obviously equal, use
5144 int isl_union_pw_qpolynomial_fold_plain_is_equal(
5145 __isl_keep isl_union_pw_qpolynomial_fold *upwf1,
5146 __isl_keep isl_union_pw_qpolynomial_fold *upwf2);
5148 =head3 Operations on Piecewise Quasipolynomial Reductions
5150 __isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_scale(
5151 __isl_take isl_qpolynomial_fold *fold, isl_int v);
5152 __isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_scale_val(
5153 __isl_take isl_qpolynomial_fold *fold,
5154 __isl_take isl_val *v);
5155 __isl_give isl_pw_qpolynomial_fold *
5156 isl_pw_qpolynomial_fold_scale_val(
5157 __isl_take isl_pw_qpolynomial_fold *pwf,
5158 __isl_take isl_val *v);
5159 __isl_give isl_union_pw_qpolynomial_fold *
5160 isl_union_pw_qpolynomial_fold_scale_val(
5161 __isl_take isl_union_pw_qpolynomial_fold *upwf,
5162 __isl_take isl_val *v);
5164 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_add(
5165 __isl_take isl_pw_qpolynomial_fold *pwf1,
5166 __isl_take isl_pw_qpolynomial_fold *pwf2);
5168 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_fold(
5169 __isl_take isl_pw_qpolynomial_fold *pwf1,
5170 __isl_take isl_pw_qpolynomial_fold *pwf2);
5172 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_fold(
5173 __isl_take isl_union_pw_qpolynomial_fold *upwf1,
5174 __isl_take isl_union_pw_qpolynomial_fold *upwf2);
5176 __isl_give isl_qpolynomial *isl_pw_qpolynomial_fold_eval(
5177 __isl_take isl_pw_qpolynomial_fold *pwf,
5178 __isl_take isl_point *pnt);
5180 __isl_give isl_qpolynomial *isl_union_pw_qpolynomial_fold_eval(
5181 __isl_take isl_union_pw_qpolynomial_fold *upwf,
5182 __isl_take isl_point *pnt);
5184 __isl_give isl_pw_qpolynomial_fold *
5185 isl_pw_qpolynomial_fold_intersect_params(
5186 __isl_take isl_pw_qpolynomial_fold *pwf,
5187 __isl_take isl_set *set);
5189 __isl_give isl_union_set *isl_union_pw_qpolynomial_fold_domain(
5190 __isl_take isl_union_pw_qpolynomial_fold *upwf);
5191 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_intersect_domain(
5192 __isl_take isl_union_pw_qpolynomial_fold *upwf,
5193 __isl_take isl_union_set *uset);
5194 __isl_give isl_union_pw_qpolynomial_fold *
5195 isl_union_pw_qpolynomial_fold_intersect_params(
5196 __isl_take isl_union_pw_qpolynomial_fold *upwf,
5197 __isl_take isl_set *set);
5199 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_project_domain_on_params(
5200 __isl_take isl_pw_qpolynomial_fold *pwf);
5202 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_coalesce(
5203 __isl_take isl_pw_qpolynomial_fold *pwf);
5205 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_coalesce(
5206 __isl_take isl_union_pw_qpolynomial_fold *upwf);
5208 __isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_gist_params(
5209 __isl_take isl_qpolynomial_fold *fold,
5210 __isl_take isl_set *context);
5211 __isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_gist(
5212 __isl_take isl_qpolynomial_fold *fold,
5213 __isl_take isl_set *context);
5215 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_gist(
5216 __isl_take isl_pw_qpolynomial_fold *pwf,
5217 __isl_take isl_set *context);
5218 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_gist_params(
5219 __isl_take isl_pw_qpolynomial_fold *pwf,
5220 __isl_take isl_set *context);
5222 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_gist(
5223 __isl_take isl_union_pw_qpolynomial_fold *upwf,
5224 __isl_take isl_union_set *context);
5225 __isl_give isl_union_pw_qpolynomial_fold *
5226 isl_union_pw_qpolynomial_fold_gist_params(
5227 __isl_take isl_union_pw_qpolynomial_fold *upwf,
5228 __isl_take isl_set *context);
5230 The gist operation applies the gist operation to each of
5231 the cells in the domain of the input piecewise quasipolynomial reduction.
5232 In future, the operation will also exploit the context
5233 to simplify the quasipolynomial reductions associated to each cell.
5235 __isl_give isl_pw_qpolynomial_fold *
5236 isl_set_apply_pw_qpolynomial_fold(
5237 __isl_take isl_set *set,
5238 __isl_take isl_pw_qpolynomial_fold *pwf,
5240 __isl_give isl_pw_qpolynomial_fold *
5241 isl_map_apply_pw_qpolynomial_fold(
5242 __isl_take isl_map *map,
5243 __isl_take isl_pw_qpolynomial_fold *pwf,
5245 __isl_give isl_union_pw_qpolynomial_fold *
5246 isl_union_set_apply_union_pw_qpolynomial_fold(
5247 __isl_take isl_union_set *uset,
5248 __isl_take isl_union_pw_qpolynomial_fold *upwf,
5250 __isl_give isl_union_pw_qpolynomial_fold *
5251 isl_union_map_apply_union_pw_qpolynomial_fold(
5252 __isl_take isl_union_map *umap,
5253 __isl_take isl_union_pw_qpolynomial_fold *upwf,
5256 The functions taking a map
5257 compose the given map with the given piecewise quasipolynomial reduction.
5258 That is, compute a bound (of the same type as C<pwf> or C<upwf> itself)
5259 over all elements in the intersection of the range of the map
5260 and the domain of the piecewise quasipolynomial reduction
5261 as a function of an element in the domain of the map.
5262 The functions taking a set compute a bound over all elements in the
5263 intersection of the set and the domain of the
5264 piecewise quasipolynomial reduction.
5266 =head2 Parametric Vertex Enumeration
5268 The parametric vertex enumeration described in this section
5269 is mainly intended to be used internally and by the C<barvinok>
5272 #include <isl/vertices.h>
5273 __isl_give isl_vertices *isl_basic_set_compute_vertices(
5274 __isl_keep isl_basic_set *bset);
5276 The function C<isl_basic_set_compute_vertices> performs the
5277 actual computation of the parametric vertices and the chamber
5278 decomposition and store the result in an C<isl_vertices> object.
5279 This information can be queried by either iterating over all
5280 the vertices or iterating over all the chambers or cells
5281 and then iterating over all vertices that are active on the chamber.
5283 int isl_vertices_foreach_vertex(
5284 __isl_keep isl_vertices *vertices,
5285 int (*fn)(__isl_take isl_vertex *vertex, void *user),
5288 int isl_vertices_foreach_cell(
5289 __isl_keep isl_vertices *vertices,
5290 int (*fn)(__isl_take isl_cell *cell, void *user),
5292 int isl_cell_foreach_vertex(__isl_keep isl_cell *cell,
5293 int (*fn)(__isl_take isl_vertex *vertex, void *user),
5296 Other operations that can be performed on an C<isl_vertices> object are
5299 isl_ctx *isl_vertices_get_ctx(
5300 __isl_keep isl_vertices *vertices);
5301 int isl_vertices_get_n_vertices(
5302 __isl_keep isl_vertices *vertices);
5303 void isl_vertices_free(__isl_take isl_vertices *vertices);
5305 Vertices can be inspected and destroyed using the following functions.
5307 isl_ctx *isl_vertex_get_ctx(__isl_keep isl_vertex *vertex);
5308 int isl_vertex_get_id(__isl_keep isl_vertex *vertex);
5309 __isl_give isl_basic_set *isl_vertex_get_domain(
5310 __isl_keep isl_vertex *vertex);
5311 __isl_give isl_basic_set *isl_vertex_get_expr(
5312 __isl_keep isl_vertex *vertex);
5313 void isl_vertex_free(__isl_take isl_vertex *vertex);
5315 C<isl_vertex_get_expr> returns a singleton parametric set describing
5316 the vertex, while C<isl_vertex_get_domain> returns the activity domain
5318 Note that C<isl_vertex_get_domain> and C<isl_vertex_get_expr> return
5319 B<rational> basic sets, so they should mainly be used for inspection
5320 and should not be mixed with integer sets.
5322 Chambers can be inspected and destroyed using the following functions.
5324 isl_ctx *isl_cell_get_ctx(__isl_keep isl_cell *cell);
5325 __isl_give isl_basic_set *isl_cell_get_domain(
5326 __isl_keep isl_cell *cell);
5327 void isl_cell_free(__isl_take isl_cell *cell);
5329 =head1 Polyhedral Compilation Library
5331 This section collects functionality in C<isl> that has been specifically
5332 designed for use during polyhedral compilation.
5334 =head2 Dependence Analysis
5336 C<isl> contains specialized functionality for performing
5337 array dataflow analysis. That is, given a I<sink> access relation
5338 and a collection of possible I<source> access relations,
5339 C<isl> can compute relations that describe
5340 for each iteration of the sink access, which iteration
5341 of which of the source access relations was the last
5342 to access the same data element before the given iteration
5344 The resulting dependence relations map source iterations
5345 to the corresponding sink iterations.
5346 To compute standard flow dependences, the sink should be
5347 a read, while the sources should be writes.
5348 If any of the source accesses are marked as being I<may>
5349 accesses, then there will be a dependence from the last
5350 I<must> access B<and> from any I<may> access that follows
5351 this last I<must> access.
5352 In particular, if I<all> sources are I<may> accesses,
5353 then memory based dependence analysis is performed.
5354 If, on the other hand, all sources are I<must> accesses,
5355 then value based dependence analysis is performed.
5357 #include <isl/flow.h>
5359 typedef int (*isl_access_level_before)(void *first, void *second);
5361 __isl_give isl_access_info *isl_access_info_alloc(
5362 __isl_take isl_map *sink,
5363 void *sink_user, isl_access_level_before fn,
5365 __isl_give isl_access_info *isl_access_info_add_source(
5366 __isl_take isl_access_info *acc,
5367 __isl_take isl_map *source, int must,
5369 void *isl_access_info_free(__isl_take isl_access_info *acc);
5371 __isl_give isl_flow *isl_access_info_compute_flow(
5372 __isl_take isl_access_info *acc);
5374 int isl_flow_foreach(__isl_keep isl_flow *deps,
5375 int (*fn)(__isl_take isl_map *dep, int must,
5376 void *dep_user, void *user),
5378 __isl_give isl_map *isl_flow_get_no_source(
5379 __isl_keep isl_flow *deps, int must);
5380 void isl_flow_free(__isl_take isl_flow *deps);
5382 The function C<isl_access_info_compute_flow> performs the actual
5383 dependence analysis. The other functions are used to construct
5384 the input for this function or to read off the output.
5386 The input is collected in an C<isl_access_info>, which can
5387 be created through a call to C<isl_access_info_alloc>.
5388 The arguments to this functions are the sink access relation
5389 C<sink>, a token C<sink_user> used to identify the sink
5390 access to the user, a callback function for specifying the
5391 relative order of source and sink accesses, and the number
5392 of source access relations that will be added.
5393 The callback function has type C<int (*)(void *first, void *second)>.
5394 The function is called with two user supplied tokens identifying
5395 either a source or the sink and it should return the shared nesting
5396 level and the relative order of the two accesses.
5397 In particular, let I<n> be the number of loops shared by
5398 the two accesses. If C<first> precedes C<second> textually,
5399 then the function should return I<2 * n + 1>; otherwise,
5400 it should return I<2 * n>.
5401 The sources can be added to the C<isl_access_info> by performing
5402 (at most) C<max_source> calls to C<isl_access_info_add_source>.
5403 C<must> indicates whether the source is a I<must> access
5404 or a I<may> access. Note that a multi-valued access relation
5405 should only be marked I<must> if every iteration in the domain
5406 of the relation accesses I<all> elements in its image.
5407 The C<source_user> token is again used to identify
5408 the source access. The range of the source access relation
5409 C<source> should have the same dimension as the range
5410 of the sink access relation.
5411 The C<isl_access_info_free> function should usually not be
5412 called explicitly, because it is called implicitly by
5413 C<isl_access_info_compute_flow>.
5415 The result of the dependence analysis is collected in an
5416 C<isl_flow>. There may be elements of
5417 the sink access for which no preceding source access could be
5418 found or for which all preceding sources are I<may> accesses.
5419 The relations containing these elements can be obtained through
5420 calls to C<isl_flow_get_no_source>, the first with C<must> set
5421 and the second with C<must> unset.
5422 In the case of standard flow dependence analysis,
5423 with the sink a read and the sources I<must> writes,
5424 the first relation corresponds to the reads from uninitialized
5425 array elements and the second relation is empty.
5426 The actual flow dependences can be extracted using
5427 C<isl_flow_foreach>. This function will call the user-specified
5428 callback function C<fn> for each B<non-empty> dependence between
5429 a source and the sink. The callback function is called
5430 with four arguments, the actual flow dependence relation
5431 mapping source iterations to sink iterations, a boolean that
5432 indicates whether it is a I<must> or I<may> dependence, a token
5433 identifying the source and an additional C<void *> with value
5434 equal to the third argument of the C<isl_flow_foreach> call.
5435 A dependence is marked I<must> if it originates from a I<must>
5436 source and if it is not followed by any I<may> sources.
5438 After finishing with an C<isl_flow>, the user should call
5439 C<isl_flow_free> to free all associated memory.
5441 A higher-level interface to dependence analysis is provided
5442 by the following function.
5444 #include <isl/flow.h>
5446 int isl_union_map_compute_flow(__isl_take isl_union_map *sink,
5447 __isl_take isl_union_map *must_source,
5448 __isl_take isl_union_map *may_source,
5449 __isl_take isl_union_map *schedule,
5450 __isl_give isl_union_map **must_dep,
5451 __isl_give isl_union_map **may_dep,
5452 __isl_give isl_union_map **must_no_source,
5453 __isl_give isl_union_map **may_no_source);
5455 The arrays are identified by the tuple names of the ranges
5456 of the accesses. The iteration domains by the tuple names
5457 of the domains of the accesses and of the schedule.
5458 The relative order of the iteration domains is given by the
5459 schedule. The relations returned through C<must_no_source>
5460 and C<may_no_source> are subsets of C<sink>.
5461 Any of C<must_dep>, C<may_dep>, C<must_no_source>
5462 or C<may_no_source> may be C<NULL>, but a C<NULL> value for
5463 any of the other arguments is treated as an error.
5465 =head3 Interaction with Dependence Analysis
5467 During the dependence analysis, we frequently need to perform
5468 the following operation. Given a relation between sink iterations
5469 and potential source iterations from a particular source domain,
5470 what is the last potential source iteration corresponding to each
5471 sink iteration. It can sometimes be convenient to adjust
5472 the set of potential source iterations before or after each such operation.
5473 The prototypical example is fuzzy array dataflow analysis,
5474 where we need to analyze if, based on data-dependent constraints,
5475 the sink iteration can ever be executed without one or more of
5476 the corresponding potential source iterations being executed.
5477 If so, we can introduce extra parameters and select an unknown
5478 but fixed source iteration from the potential source iterations.
5479 To be able to perform such manipulations, C<isl> provides the following
5482 #include <isl/flow.h>
5484 typedef __isl_give isl_restriction *(*isl_access_restrict)(
5485 __isl_keep isl_map *source_map,
5486 __isl_keep isl_set *sink, void *source_user,
5488 __isl_give isl_access_info *isl_access_info_set_restrict(
5489 __isl_take isl_access_info *acc,
5490 isl_access_restrict fn, void *user);
5492 The function C<isl_access_info_set_restrict> should be called
5493 before calling C<isl_access_info_compute_flow> and registers a callback function
5494 that will be called any time C<isl> is about to compute the last
5495 potential source. The first argument is the (reverse) proto-dependence,
5496 mapping sink iterations to potential source iterations.
5497 The second argument represents the sink iterations for which
5498 we want to compute the last source iteration.
5499 The third argument is the token corresponding to the source
5500 and the final argument is the token passed to C<isl_access_info_set_restrict>.
5501 The callback is expected to return a restriction on either the input or
5502 the output of the operation computing the last potential source.
5503 If the input needs to be restricted then restrictions are needed
5504 for both the source and the sink iterations. The sink iterations
5505 and the potential source iterations will be intersected with these sets.
5506 If the output needs to be restricted then only a restriction on the source
5507 iterations is required.
5508 If any error occurs, the callback should return C<NULL>.
5509 An C<isl_restriction> object can be created, freed and inspected
5510 using the following functions.
5512 #include <isl/flow.h>
5514 __isl_give isl_restriction *isl_restriction_input(
5515 __isl_take isl_set *source_restr,
5516 __isl_take isl_set *sink_restr);
5517 __isl_give isl_restriction *isl_restriction_output(
5518 __isl_take isl_set *source_restr);
5519 __isl_give isl_restriction *isl_restriction_none(
5520 __isl_take isl_map *source_map);
5521 __isl_give isl_restriction *isl_restriction_empty(
5522 __isl_take isl_map *source_map);
5523 void *isl_restriction_free(
5524 __isl_take isl_restriction *restr);
5525 isl_ctx *isl_restriction_get_ctx(
5526 __isl_keep isl_restriction *restr);
5528 C<isl_restriction_none> and C<isl_restriction_empty> are special
5529 cases of C<isl_restriction_input>. C<isl_restriction_none>
5530 is essentially equivalent to
5532 isl_restriction_input(isl_set_universe(
5533 isl_space_range(isl_map_get_space(source_map))),
5535 isl_space_domain(isl_map_get_space(source_map))));
5537 whereas C<isl_restriction_empty> is essentially equivalent to
5539 isl_restriction_input(isl_set_empty(
5540 isl_space_range(isl_map_get_space(source_map))),
5542 isl_space_domain(isl_map_get_space(source_map))));
5546 B<The functionality described in this section is fairly new
5547 and may be subject to change.>
5549 The following function can be used to compute a schedule
5550 for a union of domains.
5551 By default, the algorithm used to construct the schedule is similar
5552 to that of C<Pluto>.
5553 Alternatively, Feautrier's multi-dimensional scheduling algorithm can
5555 The generated schedule respects all C<validity> dependences.
5556 That is, all dependence distances over these dependences in the
5557 scheduled space are lexicographically positive.
5558 The default algorithm tries to minimize the dependence distances over
5559 C<proximity> dependences.
5560 Moreover, it tries to obtain sequences (bands) of schedule dimensions
5561 for groups of domains where the dependence distances have only
5562 non-negative values.
5563 When using Feautrier's algorithm, the C<proximity> dependence
5564 distances are only minimized during the extension to a
5565 full-dimensional schedule.
5567 #include <isl/schedule.h>
5568 __isl_give isl_schedule *isl_union_set_compute_schedule(
5569 __isl_take isl_union_set *domain,
5570 __isl_take isl_union_map *validity,
5571 __isl_take isl_union_map *proximity);
5572 void *isl_schedule_free(__isl_take isl_schedule *sched);
5574 A mapping from the domains to the scheduled space can be obtained
5575 from an C<isl_schedule> using the following function.
5577 __isl_give isl_union_map *isl_schedule_get_map(
5578 __isl_keep isl_schedule *sched);
5580 A representation of the schedule can be printed using
5582 __isl_give isl_printer *isl_printer_print_schedule(
5583 __isl_take isl_printer *p,
5584 __isl_keep isl_schedule *schedule);
5586 A representation of the schedule as a forest of bands can be obtained
5587 using the following function.
5589 __isl_give isl_band_list *isl_schedule_get_band_forest(
5590 __isl_keep isl_schedule *schedule);
5592 The individual bands can be visited in depth-first post-order
5593 using the following function.
5595 #include <isl/schedule.h>
5596 int isl_schedule_foreach_band(
5597 __isl_keep isl_schedule *sched,
5598 int (*fn)(__isl_keep isl_band *band, void *user),
5601 The list can be manipulated as explained in L<"Lists">.
5602 The bands inside the list can be copied and freed using the following
5605 #include <isl/band.h>
5606 __isl_give isl_band *isl_band_copy(
5607 __isl_keep isl_band *band);
5608 void *isl_band_free(__isl_take isl_band *band);
5610 Each band contains zero or more scheduling dimensions.
5611 These are referred to as the members of the band.
5612 The section of the schedule that corresponds to the band is
5613 referred to as the partial schedule of the band.
5614 For those nodes that participate in a band, the outer scheduling
5615 dimensions form the prefix schedule, while the inner scheduling
5616 dimensions form the suffix schedule.
5617 That is, if we take a cut of the band forest, then the union of
5618 the concatenations of the prefix, partial and suffix schedules of
5619 each band in the cut is equal to the entire schedule (modulo
5620 some possible padding at the end with zero scheduling dimensions).
5621 The properties of a band can be inspected using the following functions.
5623 #include <isl/band.h>
5624 isl_ctx *isl_band_get_ctx(__isl_keep isl_band *band);
5626 int isl_band_has_children(__isl_keep isl_band *band);
5627 __isl_give isl_band_list *isl_band_get_children(
5628 __isl_keep isl_band *band);
5630 __isl_give isl_union_map *isl_band_get_prefix_schedule(
5631 __isl_keep isl_band *band);
5632 __isl_give isl_union_map *isl_band_get_partial_schedule(
5633 __isl_keep isl_band *band);
5634 __isl_give isl_union_map *isl_band_get_suffix_schedule(
5635 __isl_keep isl_band *band);
5637 int isl_band_n_member(__isl_keep isl_band *band);
5638 int isl_band_member_is_zero_distance(
5639 __isl_keep isl_band *band, int pos);
5641 int isl_band_list_foreach_band(
5642 __isl_keep isl_band_list *list,
5643 int (*fn)(__isl_keep isl_band *band, void *user),
5646 Note that a scheduling dimension is considered to be ``zero
5647 distance'' if it does not carry any proximity dependences
5649 That is, if the dependence distances of the proximity
5650 dependences are all zero in that direction (for fixed
5651 iterations of outer bands).
5652 Like C<isl_schedule_foreach_band>,
5653 the function C<isl_band_list_foreach_band> calls C<fn> on the bands
5654 in depth-first post-order.
5656 A band can be tiled using the following function.
5658 #include <isl/band.h>
5659 int isl_band_tile(__isl_keep isl_band *band,
5660 __isl_take isl_vec *sizes);
5662 int isl_options_set_tile_scale_tile_loops(isl_ctx *ctx,
5664 int isl_options_get_tile_scale_tile_loops(isl_ctx *ctx);
5665 int isl_options_set_tile_shift_point_loops(isl_ctx *ctx,
5667 int isl_options_get_tile_shift_point_loops(isl_ctx *ctx);
5669 The C<isl_band_tile> function tiles the band using the given tile sizes
5670 inside its schedule.
5671 A new child band is created to represent the point loops and it is
5672 inserted between the modified band and its children.
5673 The C<tile_scale_tile_loops> option specifies whether the tile
5674 loops iterators should be scaled by the tile sizes.
5675 If the C<tile_shift_point_loops> option is set, then the point loops
5676 are shifted to start at zero.
5678 A band can be split into two nested bands using the following function.
5680 int isl_band_split(__isl_keep isl_band *band, int pos);
5682 The resulting outer band contains the first C<pos> dimensions of C<band>
5683 while the inner band contains the remaining dimensions.
5685 A representation of the band can be printed using
5687 #include <isl/band.h>
5688 __isl_give isl_printer *isl_printer_print_band(
5689 __isl_take isl_printer *p,
5690 __isl_keep isl_band *band);
5694 #include <isl/schedule.h>
5695 int isl_options_set_schedule_max_coefficient(
5696 isl_ctx *ctx, int val);
5697 int isl_options_get_schedule_max_coefficient(
5699 int isl_options_set_schedule_max_constant_term(
5700 isl_ctx *ctx, int val);
5701 int isl_options_get_schedule_max_constant_term(
5703 int isl_options_set_schedule_fuse(isl_ctx *ctx, int val);
5704 int isl_options_get_schedule_fuse(isl_ctx *ctx);
5705 int isl_options_set_schedule_maximize_band_depth(
5706 isl_ctx *ctx, int val);
5707 int isl_options_get_schedule_maximize_band_depth(
5709 int isl_options_set_schedule_outer_zero_distance(
5710 isl_ctx *ctx, int val);
5711 int isl_options_get_schedule_outer_zero_distance(
5713 int isl_options_set_schedule_split_scaled(
5714 isl_ctx *ctx, int val);
5715 int isl_options_get_schedule_split_scaled(
5717 int isl_options_set_schedule_algorithm(
5718 isl_ctx *ctx, int val);
5719 int isl_options_get_schedule_algorithm(
5721 int isl_options_set_schedule_separate_components(
5722 isl_ctx *ctx, int val);
5723 int isl_options_get_schedule_separate_components(
5728 =item * schedule_max_coefficient
5730 This option enforces that the coefficients for variable and parameter
5731 dimensions in the calculated schedule are not larger than the specified value.
5732 This option can significantly increase the speed of the scheduling calculation
5733 and may also prevent fusing of unrelated dimensions. A value of -1 means that
5734 this option does not introduce bounds on the variable or parameter
5737 =item * schedule_max_constant_term
5739 This option enforces that the constant coefficients in the calculated schedule
5740 are not larger than the maximal constant term. This option can significantly
5741 increase the speed of the scheduling calculation and may also prevent fusing of
5742 unrelated dimensions. A value of -1 means that this option does not introduce
5743 bounds on the constant coefficients.
5745 =item * schedule_fuse
5747 This option controls the level of fusion.
5748 If this option is set to C<ISL_SCHEDULE_FUSE_MIN>, then loops in the
5749 resulting schedule will be distributed as much as possible.
5750 If this option is set to C<ISL_SCHEDULE_FUSE_MAX>, then C<isl> will
5751 try to fuse loops in the resulting schedule.
5753 =item * schedule_maximize_band_depth
5755 If this option is set, we do not split bands at the point
5756 where we detect splitting is necessary. Instead, we
5757 backtrack and split bands as early as possible. This
5758 reduces the number of splits and maximizes the width of
5759 the bands. Wider bands give more possibilities for tiling.
5760 Note that if the C<schedule_fuse> option is set to C<ISL_SCHEDULE_FUSE_MIN>,
5761 then bands will be split as early as possible, even if there is no need.
5762 The C<schedule_maximize_band_depth> option therefore has no effect in this case.
5764 =item * schedule_outer_zero_distance
5766 If this option is set, then we try to construct schedules
5767 where the outermost scheduling dimension in each band
5768 results in a zero dependence distance over the proximity
5771 =item * schedule_split_scaled
5773 If this option is set, then we try to construct schedules in which the
5774 constant term is split off from the linear part if the linear parts of
5775 the scheduling rows for all nodes in the graphs have a common non-trivial
5777 The constant term is then placed in a separate band and the linear
5780 =item * schedule_algorithm
5782 Selects the scheduling algorithm to be used.
5783 Available scheduling algorithms are C<ISL_SCHEDULE_ALGORITHM_ISL>
5784 and C<ISL_SCHEDULE_ALGORITHM_FEAUTRIER>.
5786 =item * schedule_separate_components
5788 If at any point the dependence graph contains any (weakly connected) components,
5789 then these components are scheduled separately.
5790 If this option is not set, then some iterations of the domains
5791 in these components may be scheduled together.
5792 If this option is set, then the components are given consecutive
5797 =head2 AST Generation
5799 This section describes the C<isl> functionality for generating
5800 ASTs that visit all the elements
5801 in a domain in an order specified by a schedule.
5802 In particular, given a C<isl_union_map>, an AST is generated
5803 that visits all the elements in the domain of the C<isl_union_map>
5804 according to the lexicographic order of the corresponding image
5805 element(s). If the range of the C<isl_union_map> consists of
5806 elements in more than one space, then each of these spaces is handled
5807 separately in an arbitrary order.
5808 It should be noted that the image elements only specify the I<order>
5809 in which the corresponding domain elements should be visited.
5810 No direct relation between the image elements and the loop iterators
5811 in the generated AST should be assumed.
5813 Each AST is generated within a build. The initial build
5814 simply specifies the constraints on the parameters (if any)
5815 and can be created, inspected, copied and freed using the following functions.
5817 #include <isl/ast_build.h>
5818 __isl_give isl_ast_build *isl_ast_build_from_context(
5819 __isl_take isl_set *set);
5820 isl_ctx *isl_ast_build_get_ctx(
5821 __isl_keep isl_ast_build *build);
5822 __isl_give isl_ast_build *isl_ast_build_copy(
5823 __isl_keep isl_ast_build *build);
5824 void *isl_ast_build_free(
5825 __isl_take isl_ast_build *build);
5827 The C<set> argument is usually a parameter set with zero or more parameters.
5828 More C<isl_ast_build> functions are described in L</"Nested AST Generation">
5829 and L</"Fine-grained Control over AST Generation">.
5830 Finally, the AST itself can be constructed using the following
5833 #include <isl/ast_build.h>
5834 __isl_give isl_ast_node *isl_ast_build_ast_from_schedule(
5835 __isl_keep isl_ast_build *build,
5836 __isl_take isl_union_map *schedule);
5838 =head3 Inspecting the AST
5840 The basic properties of an AST node can be obtained as follows.
5842 #include <isl/ast.h>
5843 isl_ctx *isl_ast_node_get_ctx(
5844 __isl_keep isl_ast_node *node);
5845 enum isl_ast_node_type isl_ast_node_get_type(
5846 __isl_keep isl_ast_node *node);
5848 The type of an AST node is one of
5849 C<isl_ast_node_for>,
5851 C<isl_ast_node_block> or
5852 C<isl_ast_node_user>.
5853 An C<isl_ast_node_for> represents a for node.
5854 An C<isl_ast_node_if> represents an if node.
5855 An C<isl_ast_node_block> represents a compound node.
5856 An C<isl_ast_node_user> represents an expression statement.
5857 An expression statement typically corresponds to a domain element, i.e.,
5858 one of the elements that is visited by the AST.
5860 Each type of node has its own additional properties.
5862 #include <isl/ast.h>
5863 __isl_give isl_ast_expr *isl_ast_node_for_get_iterator(
5864 __isl_keep isl_ast_node *node);
5865 __isl_give isl_ast_expr *isl_ast_node_for_get_init(
5866 __isl_keep isl_ast_node *node);
5867 __isl_give isl_ast_expr *isl_ast_node_for_get_cond(
5868 __isl_keep isl_ast_node *node);
5869 __isl_give isl_ast_expr *isl_ast_node_for_get_inc(
5870 __isl_keep isl_ast_node *node);
5871 __isl_give isl_ast_node *isl_ast_node_for_get_body(
5872 __isl_keep isl_ast_node *node);
5873 int isl_ast_node_for_is_degenerate(
5874 __isl_keep isl_ast_node *node);
5876 An C<isl_ast_for> is considered degenerate if it is known to execute
5879 #include <isl/ast.h>
5880 __isl_give isl_ast_expr *isl_ast_node_if_get_cond(
5881 __isl_keep isl_ast_node *node);
5882 __isl_give isl_ast_node *isl_ast_node_if_get_then(
5883 __isl_keep isl_ast_node *node);
5884 int isl_ast_node_if_has_else(
5885 __isl_keep isl_ast_node *node);
5886 __isl_give isl_ast_node *isl_ast_node_if_get_else(
5887 __isl_keep isl_ast_node *node);
5889 __isl_give isl_ast_node_list *
5890 isl_ast_node_block_get_children(
5891 __isl_keep isl_ast_node *node);
5893 __isl_give isl_ast_expr *isl_ast_node_user_get_expr(
5894 __isl_keep isl_ast_node *node);
5896 Each of the returned C<isl_ast_expr>s can in turn be inspected using
5897 the following functions.
5899 #include <isl/ast.h>
5900 isl_ctx *isl_ast_expr_get_ctx(
5901 __isl_keep isl_ast_expr *expr);
5902 enum isl_ast_expr_type isl_ast_expr_get_type(
5903 __isl_keep isl_ast_expr *expr);
5905 The type of an AST expression is one of
5907 C<isl_ast_expr_id> or
5908 C<isl_ast_expr_int>.
5909 An C<isl_ast_expr_op> represents the result of an operation.
5910 An C<isl_ast_expr_id> represents an identifier.
5911 An C<isl_ast_expr_int> represents an integer value.
5913 Each type of expression has its own additional properties.
5915 #include <isl/ast.h>
5916 enum isl_ast_op_type isl_ast_expr_get_op_type(
5917 __isl_keep isl_ast_expr *expr);
5918 int isl_ast_expr_get_op_n_arg(__isl_keep isl_ast_expr *expr);
5919 __isl_give isl_ast_expr *isl_ast_expr_get_op_arg(
5920 __isl_keep isl_ast_expr *expr, int pos);
5921 int isl_ast_node_foreach_ast_op_type(
5922 __isl_keep isl_ast_node *node,
5923 int (*fn)(enum isl_ast_op_type type, void *user),
5926 C<isl_ast_expr_get_op_type> returns the type of the operation
5927 performed. C<isl_ast_expr_get_op_n_arg> returns the number of
5928 arguments. C<isl_ast_expr_get_op_arg> returns the specified
5930 C<isl_ast_node_foreach_ast_op_type> calls C<fn> for each distinct
5931 C<isl_ast_op_type> that appears in C<node>.
5932 The operation type is one of the following.
5936 =item C<isl_ast_op_and>
5938 Logical I<and> of two arguments.
5939 Both arguments can be evaluated.
5941 =item C<isl_ast_op_and_then>
5943 Logical I<and> of two arguments.
5944 The second argument can only be evaluated if the first evaluates to true.
5946 =item C<isl_ast_op_or>
5948 Logical I<or> of two arguments.
5949 Both arguments can be evaluated.
5951 =item C<isl_ast_op_or_else>
5953 Logical I<or> of two arguments.
5954 The second argument can only be evaluated if the first evaluates to false.
5956 =item C<isl_ast_op_max>
5958 Maximum of two or more arguments.
5960 =item C<isl_ast_op_min>
5962 Minimum of two or more arguments.
5964 =item C<isl_ast_op_minus>
5968 =item C<isl_ast_op_add>
5970 Sum of two arguments.
5972 =item C<isl_ast_op_sub>
5974 Difference of two arguments.
5976 =item C<isl_ast_op_mul>
5978 Product of two arguments.
5980 =item C<isl_ast_op_div>
5982 Exact division. That is, the result is known to be an integer.
5984 =item C<isl_ast_op_fdiv_q>
5986 Result of integer division, rounded towards negative
5989 =item C<isl_ast_op_pdiv_q>
5991 Result of integer division, where dividend is known to be non-negative.
5993 =item C<isl_ast_op_pdiv_r>
5995 Remainder of integer division, where dividend is known to be non-negative.
5997 =item C<isl_ast_op_cond>
5999 Conditional operator defined on three arguments.
6000 If the first argument evaluates to true, then the result
6001 is equal to the second argument. Otherwise, the result
6002 is equal to the third argument.
6003 The second and third argument may only be evaluated if
6004 the first argument evaluates to true and false, respectively.
6005 Corresponds to C<a ? b : c> in C.
6007 =item C<isl_ast_op_select>
6009 Conditional operator defined on three arguments.
6010 If the first argument evaluates to true, then the result
6011 is equal to the second argument. Otherwise, the result
6012 is equal to the third argument.
6013 The second and third argument may be evaluated independently
6014 of the value of the first argument.
6015 Corresponds to C<a * b + (1 - a) * c> in C.
6017 =item C<isl_ast_op_eq>
6021 =item C<isl_ast_op_le>
6023 Less than or equal relation.
6025 =item C<isl_ast_op_lt>
6029 =item C<isl_ast_op_ge>
6031 Greater than or equal relation.
6033 =item C<isl_ast_op_gt>
6035 Greater than relation.
6037 =item C<isl_ast_op_call>
6040 The number of arguments of the C<isl_ast_expr> is one more than
6041 the number of arguments in the function call, the first argument
6042 representing the function being called.
6046 #include <isl/ast.h>
6047 __isl_give isl_id *isl_ast_expr_get_id(
6048 __isl_keep isl_ast_expr *expr);
6050 Return the identifier represented by the AST expression.
6052 #include <isl/ast.h>
6053 int isl_ast_expr_get_int(__isl_keep isl_ast_expr *expr,
6055 __isl_give isl_val *isl_ast_expr_get_val(
6056 __isl_keep isl_ast_expr *expr);
6058 Return the integer represented by the AST expression.
6059 Note that the integer is returned by C<isl_ast_expr_get_int>
6060 through the C<v> argument.
6061 The return value of this function itself indicates whether the
6062 operation was performed successfully.
6064 =head3 Manipulating and printing the AST
6066 AST nodes can be copied and freed using the following functions.
6068 #include <isl/ast.h>
6069 __isl_give isl_ast_node *isl_ast_node_copy(
6070 __isl_keep isl_ast_node *node);
6071 void *isl_ast_node_free(__isl_take isl_ast_node *node);
6073 AST expressions can be copied and freed using the following functions.
6075 #include <isl/ast.h>
6076 __isl_give isl_ast_expr *isl_ast_expr_copy(
6077 __isl_keep isl_ast_expr *expr);
6078 void *isl_ast_expr_free(__isl_take isl_ast_expr *expr);
6080 New AST expressions can be created either directly or within
6081 the context of an C<isl_ast_build>.
6083 #include <isl/ast.h>
6084 __isl_give isl_ast_expr *isl_ast_expr_from_val(
6085 __isl_take isl_val *v);
6086 __isl_give isl_ast_expr *isl_ast_expr_from_id(
6087 __isl_take isl_id *id);
6088 __isl_give isl_ast_expr *isl_ast_expr_neg(
6089 __isl_take isl_ast_expr *expr);
6090 __isl_give isl_ast_expr *isl_ast_expr_add(
6091 __isl_take isl_ast_expr *expr1,
6092 __isl_take isl_ast_expr *expr2);
6093 __isl_give isl_ast_expr *isl_ast_expr_sub(
6094 __isl_take isl_ast_expr *expr1,
6095 __isl_take isl_ast_expr *expr2);
6096 __isl_give isl_ast_expr *isl_ast_expr_mul(
6097 __isl_take isl_ast_expr *expr1,
6098 __isl_take isl_ast_expr *expr2);
6099 __isl_give isl_ast_expr *isl_ast_expr_div(
6100 __isl_take isl_ast_expr *expr1,
6101 __isl_take isl_ast_expr *expr2);
6102 __isl_give isl_ast_expr *isl_ast_expr_and(
6103 __isl_take isl_ast_expr *expr1,
6104 __isl_take isl_ast_expr *expr2)
6105 __isl_give isl_ast_expr *isl_ast_expr_or(
6106 __isl_take isl_ast_expr *expr1,
6107 __isl_take isl_ast_expr *expr2)
6109 #include <isl/ast_build.h>
6110 __isl_give isl_ast_expr *isl_ast_build_expr_from_pw_aff(
6111 __isl_keep isl_ast_build *build,
6112 __isl_take isl_pw_aff *pa);
6113 __isl_give isl_ast_expr *
6114 isl_ast_build_call_from_pw_multi_aff(
6115 __isl_keep isl_ast_build *build,
6116 __isl_take isl_pw_multi_aff *pma);
6118 The domains of C<pa> and C<pma> should correspond
6119 to the schedule space of C<build>.
6120 The tuple id of C<pma> is used as the function being called.
6122 User specified data can be attached to an C<isl_ast_node> and obtained
6123 from the same C<isl_ast_node> using the following functions.
6125 #include <isl/ast.h>
6126 __isl_give isl_ast_node *isl_ast_node_set_annotation(
6127 __isl_take isl_ast_node *node,
6128 __isl_take isl_id *annotation);
6129 __isl_give isl_id *isl_ast_node_get_annotation(
6130 __isl_keep isl_ast_node *node);
6132 Basic printing can be performed using the following functions.
6134 #include <isl/ast.h>
6135 __isl_give isl_printer *isl_printer_print_ast_expr(
6136 __isl_take isl_printer *p,
6137 __isl_keep isl_ast_expr *expr);
6138 __isl_give isl_printer *isl_printer_print_ast_node(
6139 __isl_take isl_printer *p,
6140 __isl_keep isl_ast_node *node);
6142 More advanced printing can be performed using the following functions.
6144 #include <isl/ast.h>
6145 __isl_give isl_printer *isl_ast_op_type_print_macro(
6146 enum isl_ast_op_type type,
6147 __isl_take isl_printer *p);
6148 __isl_give isl_printer *isl_ast_node_print_macros(
6149 __isl_keep isl_ast_node *node,
6150 __isl_take isl_printer *p);
6151 __isl_give isl_printer *isl_ast_node_print(
6152 __isl_keep isl_ast_node *node,
6153 __isl_take isl_printer *p,
6154 __isl_take isl_ast_print_options *options);
6155 __isl_give isl_printer *isl_ast_node_for_print(
6156 __isl_keep isl_ast_node *node,
6157 __isl_take isl_printer *p,
6158 __isl_take isl_ast_print_options *options);
6159 __isl_give isl_printer *isl_ast_node_if_print(
6160 __isl_keep isl_ast_node *node,
6161 __isl_take isl_printer *p,
6162 __isl_take isl_ast_print_options *options);
6164 While printing an C<isl_ast_node> in C<ISL_FORMAT_C>,
6165 C<isl> may print out an AST that makes use of macros such
6166 as C<floord>, C<min> and C<max>.
6167 C<isl_ast_op_type_print_macro> prints out the macro
6168 corresponding to a specific C<isl_ast_op_type>.
6169 C<isl_ast_node_print_macros> scans the C<isl_ast_node>
6170 for expressions where these macros would be used and prints
6171 out the required macro definitions.
6172 Essentially, C<isl_ast_node_print_macros> calls
6173 C<isl_ast_node_foreach_ast_op_type> with C<isl_ast_op_type_print_macro>
6174 as function argument.
6175 C<isl_ast_node_print>, C<isl_ast_node_for_print> and
6176 C<isl_ast_node_if_print> print an C<isl_ast_node>
6177 in C<ISL_FORMAT_C>, but allow for some extra control
6178 through an C<isl_ast_print_options> object.
6179 This object can be created using the following functions.
6181 #include <isl/ast.h>
6182 __isl_give isl_ast_print_options *
6183 isl_ast_print_options_alloc(isl_ctx *ctx);
6184 __isl_give isl_ast_print_options *
6185 isl_ast_print_options_copy(
6186 __isl_keep isl_ast_print_options *options);
6187 void *isl_ast_print_options_free(
6188 __isl_take isl_ast_print_options *options);
6190 __isl_give isl_ast_print_options *
6191 isl_ast_print_options_set_print_user(
6192 __isl_take isl_ast_print_options *options,
6193 __isl_give isl_printer *(*print_user)(
6194 __isl_take isl_printer *p,
6195 __isl_take isl_ast_print_options *options,
6196 __isl_keep isl_ast_node *node, void *user),
6198 __isl_give isl_ast_print_options *
6199 isl_ast_print_options_set_print_for(
6200 __isl_take isl_ast_print_options *options,
6201 __isl_give isl_printer *(*print_for)(
6202 __isl_take isl_printer *p,
6203 __isl_take isl_ast_print_options *options,
6204 __isl_keep isl_ast_node *node, void *user),
6207 The callback set by C<isl_ast_print_options_set_print_user>
6208 is called whenever a node of type C<isl_ast_node_user> needs to
6210 The callback set by C<isl_ast_print_options_set_print_for>
6211 is called whenever a node of type C<isl_ast_node_for> needs to
6213 Note that C<isl_ast_node_for_print> will I<not> call the
6214 callback set by C<isl_ast_print_options_set_print_for> on the node
6215 on which C<isl_ast_node_for_print> is called, but only on nested
6216 nodes of type C<isl_ast_node_for>. It is therefore safe to
6217 call C<isl_ast_node_for_print> from within the callback set by
6218 C<isl_ast_print_options_set_print_for>.
6220 The following option determines the type to be used for iterators
6221 while printing the AST.
6223 int isl_options_set_ast_iterator_type(
6224 isl_ctx *ctx, const char *val);
6225 const char *isl_options_get_ast_iterator_type(
6230 #include <isl/ast_build.h>
6231 int isl_options_set_ast_build_atomic_upper_bound(
6232 isl_ctx *ctx, int val);
6233 int isl_options_get_ast_build_atomic_upper_bound(
6235 int isl_options_set_ast_build_prefer_pdiv(isl_ctx *ctx,
6237 int isl_options_get_ast_build_prefer_pdiv(isl_ctx *ctx);
6238 int isl_options_set_ast_build_exploit_nested_bounds(
6239 isl_ctx *ctx, int val);
6240 int isl_options_get_ast_build_exploit_nested_bounds(
6242 int isl_options_set_ast_build_group_coscheduled(
6243 isl_ctx *ctx, int val);
6244 int isl_options_get_ast_build_group_coscheduled(
6246 int isl_options_set_ast_build_scale_strides(
6247 isl_ctx *ctx, int val);
6248 int isl_options_get_ast_build_scale_strides(
6250 int isl_options_set_ast_build_allow_else(isl_ctx *ctx,
6252 int isl_options_get_ast_build_allow_else(isl_ctx *ctx);
6253 int isl_options_set_ast_build_allow_or(isl_ctx *ctx,
6255 int isl_options_get_ast_build_allow_or(isl_ctx *ctx);
6259 =item * ast_build_atomic_upper_bound
6261 Generate loop upper bounds that consist of the current loop iterator,
6262 an operator and an expression not involving the iterator.
6263 If this option is not set, then the current loop iterator may appear
6264 several times in the upper bound.
6265 For example, when this option is turned off, AST generation
6268 [n] -> { A[i] -> [i] : 0 <= i <= 100, n }
6272 for (int c0 = 0; c0 <= 100 && n >= c0; c0 += 1)
6275 When the option is turned on, the following AST is generated
6277 for (int c0 = 0; c0 <= min(100, n); c0 += 1)
6280 =item * ast_build_prefer_pdiv
6282 If this option is turned off, then the AST generation will
6283 produce ASTs that may only contain C<isl_ast_op_fdiv_q>
6284 operators, but no C<isl_ast_op_pdiv_q> or
6285 C<isl_ast_op_pdiv_r> operators.
6286 If this options is turned on, then C<isl> will try to convert
6287 some of the C<isl_ast_op_fdiv_q> operators to (expressions containing)
6288 C<isl_ast_op_pdiv_q> or C<isl_ast_op_pdiv_r> operators.
6290 =item * ast_build_exploit_nested_bounds
6292 Simplify conditions based on bounds of nested for loops.
6293 In particular, remove conditions that are implied by the fact
6294 that one or more nested loops have at least one iteration,
6295 meaning that the upper bound is at least as large as the lower bound.
6296 For example, when this option is turned off, AST generation
6299 [N,M] -> { A[i,j] -> [i,j] : 0 <= i <= N and
6305 for (int c0 = 0; c0 <= N; c0 += 1)
6306 for (int c1 = 0; c1 <= M; c1 += 1)
6309 When the option is turned on, the following AST is generated
6311 for (int c0 = 0; c0 <= N; c0 += 1)
6312 for (int c1 = 0; c1 <= M; c1 += 1)
6315 =item * ast_build_group_coscheduled
6317 If two domain elements are assigned the same schedule point, then
6318 they may be executed in any order and they may even appear in different
6319 loops. If this options is set, then the AST generator will make
6320 sure that coscheduled domain elements do not appear in separate parts
6321 of the AST. This is useful in case of nested AST generation
6322 if the outer AST generation is given only part of a schedule
6323 and the inner AST generation should handle the domains that are
6324 coscheduled by this initial part of the schedule together.
6325 For example if an AST is generated for a schedule
6327 { A[i] -> [0]; B[i] -> [0] }
6329 then the C<isl_ast_build_set_create_leaf> callback described
6330 below may get called twice, once for each domain.
6331 Setting this option ensures that the callback is only called once
6332 on both domains together.
6334 =item * ast_build_separation_bounds
6336 This option specifies which bounds to use during separation.
6337 If this option is set to C<ISL_AST_BUILD_SEPARATION_BOUNDS_IMPLICIT>
6338 then all (possibly implicit) bounds on the current dimension will
6339 be used during separation.
6340 If this option is set to C<ISL_AST_BUILD_SEPARATION_BOUNDS_EXPLICIT>
6341 then only those bounds that are explicitly available will
6342 be used during separation.
6344 =item * ast_build_scale_strides
6346 This option specifies whether the AST generator is allowed
6347 to scale down iterators of strided loops.
6349 =item * ast_build_allow_else
6351 This option specifies whether the AST generator is allowed
6352 to construct if statements with else branches.
6354 =item * ast_build_allow_or
6356 This option specifies whether the AST generator is allowed
6357 to construct if conditions with disjunctions.
6361 =head3 Fine-grained Control over AST Generation
6363 Besides specifying the constraints on the parameters,
6364 an C<isl_ast_build> object can be used to control
6365 various aspects of the AST generation process.
6366 The most prominent way of control is through ``options'',
6367 which can be set using the following function.
6369 #include <isl/ast_build.h>
6370 __isl_give isl_ast_build *
6371 isl_ast_build_set_options(
6372 __isl_take isl_ast_build *control,
6373 __isl_take isl_union_map *options);
6375 The options are encoded in an <isl_union_map>.
6376 The domain of this union relation refers to the schedule domain,
6377 i.e., the range of the schedule passed to C<isl_ast_build_ast_from_schedule>.
6378 In the case of nested AST generation (see L</"Nested AST Generation">),
6379 the domain of C<options> should refer to the extra piece of the schedule.
6380 That is, it should be equal to the range of the wrapped relation in the
6381 range of the schedule.
6382 The range of the options can consist of elements in one or more spaces,
6383 the names of which determine the effect of the option.
6384 The values of the range typically also refer to the schedule dimension
6385 to which the option applies. In case of nested AST generation
6386 (see L</"Nested AST Generation">), these values refer to the position
6387 of the schedule dimension within the innermost AST generation.
6388 The constraints on the domain elements of
6389 the option should only refer to this dimension and earlier dimensions.
6390 We consider the following spaces.
6394 =item C<separation_class>
6396 This space is a wrapped relation between two one dimensional spaces.
6397 The input space represents the schedule dimension to which the option
6398 applies and the output space represents the separation class.
6399 While constructing a loop corresponding to the specified schedule
6400 dimension(s), the AST generator will try to generate separate loops
6401 for domain elements that are assigned different classes.
6402 If only some of the elements are assigned a class, then those elements
6403 that are not assigned any class will be treated as belonging to a class
6404 that is separate from the explicitly assigned classes.
6405 The typical use case for this option is to separate full tiles from
6407 The other options, described below, are applied after the separation
6410 As an example, consider the separation into full and partial tiles
6411 of a tiling of a triangular domain.
6412 Take, for example, the domain
6414 { A[i,j] : 0 <= i,j and i + j <= 100 }
6416 and a tiling into tiles of 10 by 10. The input to the AST generator
6417 is then the schedule
6419 { A[i,j] -> [([i/10]),[j/10],i,j] : 0 <= i,j and
6422 Without any options, the following AST is generated
6424 for (int c0 = 0; c0 <= 10; c0 += 1)
6425 for (int c1 = 0; c1 <= -c0 + 10; c1 += 1)
6426 for (int c2 = 10 * c0;
6427 c2 <= min(-10 * c1 + 100, 10 * c0 + 9);
6429 for (int c3 = 10 * c1;
6430 c3 <= min(10 * c1 + 9, -c2 + 100);
6434 Separation into full and partial tiles can be obtained by assigning
6435 a class, say C<0>, to the full tiles. The full tiles are represented by those
6436 values of the first and second schedule dimensions for which there are
6437 values of the third and fourth dimensions to cover an entire tile.
6438 That is, we need to specify the following option
6440 { [a,b,c,d] -> separation_class[[0]->[0]] :
6441 exists b': 0 <= 10a,10b' and
6442 10a+9+10b'+9 <= 100;
6443 [a,b,c,d] -> separation_class[[1]->[0]] :
6444 0 <= 10a,10b and 10a+9+10b+9 <= 100 }
6448 { [a, b, c, d] -> separation_class[[1] -> [0]] :
6449 a >= 0 and b >= 0 and b <= 8 - a;
6450 [a, b, c, d] -> separation_class[[0] -> [0]] :
6453 With this option, the generated AST is as follows
6456 for (int c0 = 0; c0 <= 8; c0 += 1) {
6457 for (int c1 = 0; c1 <= -c0 + 8; c1 += 1)
6458 for (int c2 = 10 * c0;
6459 c2 <= 10 * c0 + 9; c2 += 1)
6460 for (int c3 = 10 * c1;
6461 c3 <= 10 * c1 + 9; c3 += 1)
6463 for (int c1 = -c0 + 9; c1 <= -c0 + 10; c1 += 1)
6464 for (int c2 = 10 * c0;
6465 c2 <= min(-10 * c1 + 100, 10 * c0 + 9);
6467 for (int c3 = 10 * c1;
6468 c3 <= min(-c2 + 100, 10 * c1 + 9);
6472 for (int c0 = 9; c0 <= 10; c0 += 1)
6473 for (int c1 = 0; c1 <= -c0 + 10; c1 += 1)
6474 for (int c2 = 10 * c0;
6475 c2 <= min(-10 * c1 + 100, 10 * c0 + 9);
6477 for (int c3 = 10 * c1;
6478 c3 <= min(10 * c1 + 9, -c2 + 100);
6485 This is a single-dimensional space representing the schedule dimension(s)
6486 to which ``separation'' should be applied. Separation tries to split
6487 a loop into several pieces if this can avoid the generation of guards
6489 See also the C<atomic> option.
6493 This is a single-dimensional space representing the schedule dimension(s)
6494 for which the domains should be considered ``atomic''. That is, the
6495 AST generator will make sure that any given domain space will only appear
6496 in a single loop at the specified level.
6498 Consider the following schedule
6500 { a[i] -> [i] : 0 <= i < 10;
6501 b[i] -> [i+1] : 0 <= i < 10 }
6503 If the following option is specified
6505 { [i] -> separate[x] }
6507 then the following AST will be generated
6511 for (int c0 = 1; c0 <= 9; c0 += 1) {
6518 If, on the other hand, the following option is specified
6520 { [i] -> atomic[x] }
6522 then the following AST will be generated
6524 for (int c0 = 0; c0 <= 10; c0 += 1) {
6531 If neither C<atomic> nor C<separate> is specified, then the AST generator
6532 may produce either of these two results or some intermediate form.
6536 This is a single-dimensional space representing the schedule dimension(s)
6537 that should be I<completely> unrolled.
6538 To obtain a partial unrolling, the user should apply an additional
6539 strip-mining to the schedule and fully unroll the inner loop.
6543 Additional control is available through the following functions.
6545 #include <isl/ast_build.h>
6546 __isl_give isl_ast_build *
6547 isl_ast_build_set_iterators(
6548 __isl_take isl_ast_build *control,
6549 __isl_take isl_id_list *iterators);
6551 The function C<isl_ast_build_set_iterators> allows the user to
6552 specify a list of iterator C<isl_id>s to be used as iterators.
6553 If the input schedule is injective, then
6554 the number of elements in this list should be as large as the dimension
6555 of the schedule space, but no direct correspondence should be assumed
6556 between dimensions and elements.
6557 If the input schedule is not injective, then an additional number
6558 of C<isl_id>s equal to the largest dimension of the input domains
6560 If the number of provided C<isl_id>s is insufficient, then additional
6561 names are automatically generated.
6563 #include <isl/ast_build.h>
6564 __isl_give isl_ast_build *
6565 isl_ast_build_set_create_leaf(
6566 __isl_take isl_ast_build *control,
6567 __isl_give isl_ast_node *(*fn)(
6568 __isl_take isl_ast_build *build,
6569 void *user), void *user);
6572 C<isl_ast_build_set_create_leaf> function allows for the
6573 specification of a callback that should be called whenever the AST
6574 generator arrives at an element of the schedule domain.
6575 The callback should return an AST node that should be inserted
6576 at the corresponding position of the AST. The default action (when
6577 the callback is not set) is to continue generating parts of the AST to scan
6578 all the domain elements associated to the schedule domain element
6579 and to insert user nodes, ``calling'' the domain element, for each of them.
6580 The C<build> argument contains the current state of the C<isl_ast_build>.
6581 To ease nested AST generation (see L</"Nested AST Generation">),
6582 all control information that is
6583 specific to the current AST generation such as the options and
6584 the callbacks has been removed from this C<isl_ast_build>.
6585 The callback would typically return the result of a nested
6587 user defined node created using the following function.
6589 #include <isl/ast.h>
6590 __isl_give isl_ast_node *isl_ast_node_alloc_user(
6591 __isl_take isl_ast_expr *expr);
6593 #include <isl/ast_build.h>
6594 __isl_give isl_ast_build *
6595 isl_ast_build_set_at_each_domain(
6596 __isl_take isl_ast_build *build,
6597 __isl_give isl_ast_node *(*fn)(
6598 __isl_take isl_ast_node *node,
6599 __isl_keep isl_ast_build *build,
6600 void *user), void *user);
6601 __isl_give isl_ast_build *
6602 isl_ast_build_set_before_each_for(
6603 __isl_take isl_ast_build *build,
6604 __isl_give isl_id *(*fn)(
6605 __isl_keep isl_ast_build *build,
6606 void *user), void *user);
6607 __isl_give isl_ast_build *
6608 isl_ast_build_set_after_each_for(
6609 __isl_take isl_ast_build *build,
6610 __isl_give isl_ast_node *(*fn)(
6611 __isl_take isl_ast_node *node,
6612 __isl_keep isl_ast_build *build,
6613 void *user), void *user);
6615 The callback set by C<isl_ast_build_set_at_each_domain> will
6616 be called for each domain AST node.
6617 The callbacks set by C<isl_ast_build_set_before_each_for>
6618 and C<isl_ast_build_set_after_each_for> will be called
6619 for each for AST node. The first will be called in depth-first
6620 pre-order, while the second will be called in depth-first post-order.
6621 Since C<isl_ast_build_set_before_each_for> is called before the for
6622 node is actually constructed, it is only passed an C<isl_ast_build>.
6623 The returned C<isl_id> will be added as an annotation (using
6624 C<isl_ast_node_set_annotation>) to the constructed for node.
6625 In particular, if the user has also specified an C<after_each_for>
6626 callback, then the annotation can be retrieved from the node passed to
6627 that callback using C<isl_ast_node_get_annotation>.
6628 All callbacks should C<NULL> on failure.
6629 The given C<isl_ast_build> can be used to create new
6630 C<isl_ast_expr> objects using C<isl_ast_build_expr_from_pw_aff>
6631 or C<isl_ast_build_call_from_pw_multi_aff>.
6633 =head3 Nested AST Generation
6635 C<isl> allows the user to create an AST within the context
6636 of another AST. These nested ASTs are created using the
6637 same C<isl_ast_build_ast_from_schedule> function that is used to create the
6638 outer AST. The C<build> argument should be an C<isl_ast_build>
6639 passed to a callback set by
6640 C<isl_ast_build_set_create_leaf>.
6641 The space of the range of the C<schedule> argument should refer
6642 to this build. In particular, the space should be a wrapped
6643 relation and the domain of this wrapped relation should be the
6644 same as that of the range of the schedule returned by
6645 C<isl_ast_build_get_schedule> below.
6646 In practice, the new schedule is typically
6647 created by calling C<isl_union_map_range_product> on the old schedule
6648 and some extra piece of the schedule.
6649 The space of the schedule domain is also available from
6650 the C<isl_ast_build>.
6652 #include <isl/ast_build.h>
6653 __isl_give isl_union_map *isl_ast_build_get_schedule(
6654 __isl_keep isl_ast_build *build);
6655 __isl_give isl_space *isl_ast_build_get_schedule_space(
6656 __isl_keep isl_ast_build *build);
6657 __isl_give isl_ast_build *isl_ast_build_restrict(
6658 __isl_take isl_ast_build *build,
6659 __isl_take isl_set *set);
6661 The C<isl_ast_build_get_schedule> function returns a (partial)
6662 schedule for the domains elements for which part of the AST still needs to
6663 be generated in the current build.
6664 In particular, the domain elements are mapped to those iterations of the loops
6665 enclosing the current point of the AST generation inside which
6666 the domain elements are executed.
6667 No direct correspondence between
6668 the input schedule and this schedule should be assumed.
6669 The space obtained from C<isl_ast_build_get_schedule_space> can be used
6670 to create a set for C<isl_ast_build_restrict> to intersect
6671 with the current build. In particular, the set passed to
6672 C<isl_ast_build_restrict> can have additional parameters.
6673 The ids of the set dimensions in the space returned by
6674 C<isl_ast_build_get_schedule_space> correspond to the
6675 iterators of the already generated loops.
6676 The user should not rely on the ids of the output dimensions
6677 of the relations in the union relation returned by
6678 C<isl_ast_build_get_schedule> having any particular value.
6682 Although C<isl> is mainly meant to be used as a library,
6683 it also contains some basic applications that use some
6684 of the functionality of C<isl>.
6685 The input may be specified in either the L<isl format>
6686 or the L<PolyLib format>.
6688 =head2 C<isl_polyhedron_sample>
6690 C<isl_polyhedron_sample> takes a polyhedron as input and prints
6691 an integer element of the polyhedron, if there is any.
6692 The first column in the output is the denominator and is always
6693 equal to 1. If the polyhedron contains no integer points,
6694 then a vector of length zero is printed.
6698 C<isl_pip> takes the same input as the C<example> program
6699 from the C<piplib> distribution, i.e., a set of constraints
6700 on the parameters, a line containing only -1 and finally a set
6701 of constraints on a parametric polyhedron.
6702 The coefficients of the parameters appear in the last columns
6703 (but before the final constant column).
6704 The output is the lexicographic minimum of the parametric polyhedron.
6705 As C<isl> currently does not have its own output format, the output
6706 is just a dump of the internal state.
6708 =head2 C<isl_polyhedron_minimize>
6710 C<isl_polyhedron_minimize> computes the minimum of some linear
6711 or affine objective function over the integer points in a polyhedron.
6712 If an affine objective function
6713 is given, then the constant should appear in the last column.
6715 =head2 C<isl_polytope_scan>
6717 Given a polytope, C<isl_polytope_scan> prints
6718 all integer points in the polytope.
6720 =head2 C<isl_codegen>
6722 Given a schedule, a context set and an options relation,
6723 C<isl_codegen> prints out an AST that scans the domain elements
6724 of the schedule in the order of their image(s) taking into account
6725 the constraints in the context set.