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 In previous versions of C<isl>, integers were represented
555 in the external interface using the C<isl_int> type.
556 This type has now been superseded by C<isl_val>.
557 The C<isl_int> type will be removed from the external interface
558 in future releases. New code should not use C<isl_int>.
560 The operations below are currently available on C<isl_int>s.
561 The meanings of these operations are essentially the same
562 as their C<GMP> C<mpz_> counterparts.
563 As always with C<GMP> types, C<isl_int>s need to be
564 initialized with C<isl_int_init> before they can be used
565 and they need to be released with C<isl_int_clear>
567 The user should not assume that an C<isl_int> is represented
568 as a C<mpz_t>, but should instead explicitly convert between
569 C<mpz_t>s and C<isl_int>s using C<isl_int_set_gmp> and
570 C<isl_int_get_gmp> whenever a C<mpz_t> is required.
574 =item isl_int_init(i)
576 =item isl_int_clear(i)
578 =item isl_int_set(r,i)
580 =item isl_int_set_si(r,i)
582 =item isl_int_set_gmp(r,g)
584 =item isl_int_get_gmp(i,g)
586 =item isl_int_abs(r,i)
588 =item isl_int_neg(r,i)
590 =item isl_int_swap(i,j)
592 =item isl_int_swap_or_set(i,j)
594 =item isl_int_add_ui(r,i,j)
596 =item isl_int_sub_ui(r,i,j)
598 =item isl_int_add(r,i,j)
600 =item isl_int_sub(r,i,j)
602 =item isl_int_mul(r,i,j)
604 =item isl_int_mul_ui(r,i,j)
606 =item isl_int_addmul(r,i,j)
608 =item isl_int_submul(r,i,j)
610 =item isl_int_gcd(r,i,j)
612 =item isl_int_lcm(r,i,j)
614 =item isl_int_divexact(r,i,j)
616 =item isl_int_cdiv_q(r,i,j)
618 =item isl_int_fdiv_q(r,i,j)
620 =item isl_int_fdiv_r(r,i,j)
622 =item isl_int_fdiv_q_ui(r,i,j)
624 =item isl_int_read(r,s)
626 =item isl_int_print(out,i,width)
630 =item isl_int_cmp(i,j)
632 =item isl_int_cmp_si(i,si)
634 =item isl_int_eq(i,j)
636 =item isl_int_ne(i,j)
638 =item isl_int_lt(i,j)
640 =item isl_int_le(i,j)
642 =item isl_int_gt(i,j)
644 =item isl_int_ge(i,j)
646 =item isl_int_abs_eq(i,j)
648 =item isl_int_abs_ne(i,j)
650 =item isl_int_abs_lt(i,j)
652 =item isl_int_abs_gt(i,j)
654 =item isl_int_abs_ge(i,j)
656 =item isl_int_is_zero(i)
658 =item isl_int_is_one(i)
660 =item isl_int_is_negone(i)
662 =item isl_int_is_pos(i)
664 =item isl_int_is_neg(i)
666 =item isl_int_is_nonpos(i)
668 =item isl_int_is_nonneg(i)
670 =item isl_int_is_divisible_by(i,j)
674 =head2 Sets and Relations
676 C<isl> uses six types of objects for representing sets and relations,
677 C<isl_basic_set>, C<isl_basic_map>, C<isl_set>, C<isl_map>,
678 C<isl_union_set> and C<isl_union_map>.
679 C<isl_basic_set> and C<isl_basic_map> represent sets and relations that
680 can be described as a conjunction of affine constraints, while
681 C<isl_set> and C<isl_map> represent unions of
682 C<isl_basic_set>s and C<isl_basic_map>s, respectively.
683 However, all C<isl_basic_set>s or C<isl_basic_map>s in the union need
684 to live in the same space. C<isl_union_set>s and C<isl_union_map>s
685 represent unions of C<isl_set>s or C<isl_map>s in I<different> spaces,
686 where spaces are considered different if they have a different number
687 of dimensions and/or different names (see L<"Spaces">).
688 The difference between sets and relations (maps) is that sets have
689 one set of variables, while relations have two sets of variables,
690 input variables and output variables.
692 =head2 Memory Management
694 Since a high-level operation on sets and/or relations usually involves
695 several substeps and since the user is usually not interested in
696 the intermediate results, most functions that return a new object
697 will also release all the objects passed as arguments.
698 If the user still wants to use one or more of these arguments
699 after the function call, she should pass along a copy of the
700 object rather than the object itself.
701 The user is then responsible for making sure that the original
702 object gets used somewhere else or is explicitly freed.
704 The arguments and return values of all documented functions are
705 annotated to make clear which arguments are released and which
706 arguments are preserved. In particular, the following annotations
713 C<__isl_give> means that a new object is returned.
714 The user should make sure that the returned pointer is
715 used exactly once as a value for an C<__isl_take> argument.
716 In between, it can be used as a value for as many
717 C<__isl_keep> arguments as the user likes.
718 There is one exception, and that is the case where the
719 pointer returned is C<NULL>. Is this case, the user
720 is free to use it as an C<__isl_take> argument or not.
724 C<__isl_take> means that the object the argument points to
725 is taken over by the function and may no longer be used
726 by the user as an argument to any other function.
727 The pointer value must be one returned by a function
728 returning an C<__isl_give> pointer.
729 If the user passes in a C<NULL> value, then this will
730 be treated as an error in the sense that the function will
731 not perform its usual operation. However, it will still
732 make sure that all the other C<__isl_take> arguments
737 C<__isl_keep> means that the function will only use the object
738 temporarily. After the function has finished, the user
739 can still use it as an argument to other functions.
740 A C<NULL> value will be treated in the same way as
741 a C<NULL> value for an C<__isl_take> argument.
745 =head2 Error Handling
747 C<isl> supports different ways to react in case a runtime error is triggered.
748 Runtime errors arise, e.g., if a function such as C<isl_map_intersect> is called
749 with two maps that have incompatible spaces. There are three possible ways
750 to react on error: to warn, to continue or to abort.
752 The default behavior is to warn. In this mode, C<isl> prints a warning, stores
753 the last error in the corresponding C<isl_ctx> and the function in which the
754 error was triggered returns C<NULL>. An error does not corrupt internal state,
755 such that isl can continue to be used. C<isl> also provides functions to
756 read the last error and to reset the memory that stores the last error. The
757 last error is only stored for information purposes. Its presence does not
758 change the behavior of C<isl>. Hence, resetting an error is not required to
759 continue to use isl, but only to observe new errors.
762 enum isl_error isl_ctx_last_error(isl_ctx *ctx);
763 void isl_ctx_reset_error(isl_ctx *ctx);
765 Another option is to continue on error. This is similar to warn on error mode,
766 except that C<isl> does not print any warning. This allows a program to
767 implement its own error reporting.
769 The last option is to directly abort the execution of the program from within
770 the isl library. This makes it obviously impossible to recover from an error,
771 but it allows to directly spot the error location. By aborting on error,
772 debuggers break at the location the error occurred and can provide a stack
773 trace. Other tools that automatically provide stack traces on abort or that do
774 not want to continue execution after an error was triggered may also prefer to
777 The on error behavior of isl can be specified by calling
778 C<isl_options_set_on_error> or by setting the command line option
779 C<--isl-on-error>. Valid arguments for the function call are
780 C<ISL_ON_ERROR_WARN>, C<ISL_ON_ERROR_CONTINUE> and C<ISL_ON_ERROR_ABORT>. The
781 choices for the command line option are C<warn>, C<continue> and C<abort>.
782 It is also possible to query the current error mode.
784 #include <isl/options.h>
785 int isl_options_set_on_error(isl_ctx *ctx, int val);
786 int isl_options_get_on_error(isl_ctx *ctx);
790 Identifiers are used to identify both individual dimensions
791 and tuples of dimensions. They consist of an optional name and an optional
792 user pointer. The name and the user pointer cannot both be C<NULL>, however.
793 Identifiers with the same name but different pointer values
794 are considered to be distinct.
795 Similarly, identifiers with different names but the same pointer value
796 are also considered to be distinct.
797 Equal identifiers are represented using the same object.
798 Pairs of identifiers can therefore be tested for equality using the
800 Identifiers can be constructed, copied, freed, inspected and printed
801 using the following functions.
804 __isl_give isl_id *isl_id_alloc(isl_ctx *ctx,
805 __isl_keep const char *name, void *user);
806 __isl_give isl_id *isl_id_set_free_user(
807 __isl_take isl_id *id,
808 __isl_give void (*free_user)(void *user));
809 __isl_give isl_id *isl_id_copy(isl_id *id);
810 void *isl_id_free(__isl_take isl_id *id);
812 isl_ctx *isl_id_get_ctx(__isl_keep isl_id *id);
813 void *isl_id_get_user(__isl_keep isl_id *id);
814 __isl_keep const char *isl_id_get_name(__isl_keep isl_id *id);
816 __isl_give isl_printer *isl_printer_print_id(
817 __isl_take isl_printer *p, __isl_keep isl_id *id);
819 The callback set by C<isl_id_set_free_user> is called on the user
820 pointer when the last reference to the C<isl_id> is freed.
821 Note that C<isl_id_get_name> returns a pointer to some internal
822 data structure, so the result can only be used while the
823 corresponding C<isl_id> is alive.
827 Whenever a new set, relation or similiar object is created from scratch,
828 the space in which it lives needs to be specified using an C<isl_space>.
829 Each space involves zero or more parameters and zero, one or two
830 tuples of set or input/output dimensions. The parameters and dimensions
831 are identified by an C<isl_dim_type> and a position.
832 The type C<isl_dim_param> refers to parameters,
833 the type C<isl_dim_set> refers to set dimensions (for spaces
834 with a single tuple of dimensions) and the types C<isl_dim_in>
835 and C<isl_dim_out> refer to input and output dimensions
836 (for spaces with two tuples of dimensions).
837 Local spaces (see L</"Local Spaces">) also contain dimensions
838 of type C<isl_dim_div>.
839 Note that parameters are only identified by their position within
840 a given object. Across different objects, parameters are (usually)
841 identified by their names or identifiers. Only unnamed parameters
842 are identified by their positions across objects. The use of unnamed
843 parameters is discouraged.
845 #include <isl/space.h>
846 __isl_give isl_space *isl_space_alloc(isl_ctx *ctx,
847 unsigned nparam, unsigned n_in, unsigned n_out);
848 __isl_give isl_space *isl_space_params_alloc(isl_ctx *ctx,
850 __isl_give isl_space *isl_space_set_alloc(isl_ctx *ctx,
851 unsigned nparam, unsigned dim);
852 __isl_give isl_space *isl_space_copy(__isl_keep isl_space *space);
853 void *isl_space_free(__isl_take isl_space *space);
854 unsigned isl_space_dim(__isl_keep isl_space *space,
855 enum isl_dim_type type);
857 The space used for creating a parameter domain
858 needs to be created using C<isl_space_params_alloc>.
859 For other sets, the space
860 needs to be created using C<isl_space_set_alloc>, while
861 for a relation, the space
862 needs to be created using C<isl_space_alloc>.
863 C<isl_space_dim> can be used
864 to find out the number of dimensions of each type in
865 a space, where type may be
866 C<isl_dim_param>, C<isl_dim_in> (only for relations),
867 C<isl_dim_out> (only for relations), C<isl_dim_set>
868 (only for sets) or C<isl_dim_all>.
870 To check whether a given space is that of a set or a map
871 or whether it is a parameter space, use these functions:
873 #include <isl/space.h>
874 int isl_space_is_params(__isl_keep isl_space *space);
875 int isl_space_is_set(__isl_keep isl_space *space);
876 int isl_space_is_map(__isl_keep isl_space *space);
878 Spaces can be compared using the following functions:
880 #include <isl/space.h>
881 int isl_space_is_equal(__isl_keep isl_space *space1,
882 __isl_keep isl_space *space2);
883 int isl_space_is_domain(__isl_keep isl_space *space1,
884 __isl_keep isl_space *space2);
885 int isl_space_is_range(__isl_keep isl_space *space1,
886 __isl_keep isl_space *space2);
888 C<isl_space_is_domain> checks whether the first argument is equal
889 to the domain of the second argument. This requires in particular that
890 the first argument is a set space and that the second argument
893 It is often useful to create objects that live in the
894 same space as some other object. This can be accomplished
895 by creating the new objects
896 (see L<Creating New Sets and Relations> or
897 L<Creating New (Piecewise) Quasipolynomials>) based on the space
898 of the original object.
901 __isl_give isl_space *isl_basic_set_get_space(
902 __isl_keep isl_basic_set *bset);
903 __isl_give isl_space *isl_set_get_space(__isl_keep isl_set *set);
905 #include <isl/union_set.h>
906 __isl_give isl_space *isl_union_set_get_space(
907 __isl_keep isl_union_set *uset);
910 __isl_give isl_space *isl_basic_map_get_space(
911 __isl_keep isl_basic_map *bmap);
912 __isl_give isl_space *isl_map_get_space(__isl_keep isl_map *map);
914 #include <isl/union_map.h>
915 __isl_give isl_space *isl_union_map_get_space(
916 __isl_keep isl_union_map *umap);
918 #include <isl/constraint.h>
919 __isl_give isl_space *isl_constraint_get_space(
920 __isl_keep isl_constraint *constraint);
922 #include <isl/polynomial.h>
923 __isl_give isl_space *isl_qpolynomial_get_domain_space(
924 __isl_keep isl_qpolynomial *qp);
925 __isl_give isl_space *isl_qpolynomial_get_space(
926 __isl_keep isl_qpolynomial *qp);
927 __isl_give isl_space *isl_qpolynomial_fold_get_space(
928 __isl_keep isl_qpolynomial_fold *fold);
929 __isl_give isl_space *isl_pw_qpolynomial_get_domain_space(
930 __isl_keep isl_pw_qpolynomial *pwqp);
931 __isl_give isl_space *isl_pw_qpolynomial_get_space(
932 __isl_keep isl_pw_qpolynomial *pwqp);
933 __isl_give isl_space *isl_pw_qpolynomial_fold_get_domain_space(
934 __isl_keep isl_pw_qpolynomial_fold *pwf);
935 __isl_give isl_space *isl_pw_qpolynomial_fold_get_space(
936 __isl_keep isl_pw_qpolynomial_fold *pwf);
937 __isl_give isl_space *isl_union_pw_qpolynomial_get_space(
938 __isl_keep isl_union_pw_qpolynomial *upwqp);
939 __isl_give isl_space *isl_union_pw_qpolynomial_fold_get_space(
940 __isl_keep isl_union_pw_qpolynomial_fold *upwf);
943 __isl_give isl_space *isl_multi_val_get_space(
944 __isl_keep isl_multi_val *mv);
947 __isl_give isl_space *isl_aff_get_domain_space(
948 __isl_keep isl_aff *aff);
949 __isl_give isl_space *isl_aff_get_space(
950 __isl_keep isl_aff *aff);
951 __isl_give isl_space *isl_pw_aff_get_domain_space(
952 __isl_keep isl_pw_aff *pwaff);
953 __isl_give isl_space *isl_pw_aff_get_space(
954 __isl_keep isl_pw_aff *pwaff);
955 __isl_give isl_space *isl_multi_aff_get_domain_space(
956 __isl_keep isl_multi_aff *maff);
957 __isl_give isl_space *isl_multi_aff_get_space(
958 __isl_keep isl_multi_aff *maff);
959 __isl_give isl_space *isl_pw_multi_aff_get_domain_space(
960 __isl_keep isl_pw_multi_aff *pma);
961 __isl_give isl_space *isl_pw_multi_aff_get_space(
962 __isl_keep isl_pw_multi_aff *pma);
963 __isl_give isl_space *isl_union_pw_multi_aff_get_space(
964 __isl_keep isl_union_pw_multi_aff *upma);
965 __isl_give isl_space *isl_multi_pw_aff_get_domain_space(
966 __isl_keep isl_multi_pw_aff *mpa);
967 __isl_give isl_space *isl_multi_pw_aff_get_space(
968 __isl_keep isl_multi_pw_aff *mpa);
970 #include <isl/point.h>
971 __isl_give isl_space *isl_point_get_space(
972 __isl_keep isl_point *pnt);
974 The identifiers or names of the individual dimensions may be set or read off
975 using the following functions.
977 #include <isl/space.h>
978 __isl_give isl_space *isl_space_set_dim_id(
979 __isl_take isl_space *space,
980 enum isl_dim_type type, unsigned pos,
981 __isl_take isl_id *id);
982 int isl_space_has_dim_id(__isl_keep isl_space *space,
983 enum isl_dim_type type, unsigned pos);
984 __isl_give isl_id *isl_space_get_dim_id(
985 __isl_keep isl_space *space,
986 enum isl_dim_type type, unsigned pos);
987 __isl_give isl_space *isl_space_set_dim_name(
988 __isl_take isl_space *space,
989 enum isl_dim_type type, unsigned pos,
990 __isl_keep const char *name);
991 int isl_space_has_dim_name(__isl_keep isl_space *space,
992 enum isl_dim_type type, unsigned pos);
993 __isl_keep const char *isl_space_get_dim_name(
994 __isl_keep isl_space *space,
995 enum isl_dim_type type, unsigned pos);
997 Note that C<isl_space_get_name> returns a pointer to some internal
998 data structure, so the result can only be used while the
999 corresponding C<isl_space> is alive.
1000 Also note that every function that operates on two sets or relations
1001 requires that both arguments have the same parameters. This also
1002 means that if one of the arguments has named parameters, then the
1003 other needs to have named parameters too and the names need to match.
1004 Pairs of C<isl_set>, C<isl_map>, C<isl_union_set> and/or C<isl_union_map>
1005 arguments may have different parameters (as long as they are named),
1006 in which case the result will have as parameters the union of the parameters of
1009 Given the identifier or name of a dimension (typically a parameter),
1010 its position can be obtained from the following function.
1012 #include <isl/space.h>
1013 int isl_space_find_dim_by_id(__isl_keep isl_space *space,
1014 enum isl_dim_type type, __isl_keep isl_id *id);
1015 int isl_space_find_dim_by_name(__isl_keep isl_space *space,
1016 enum isl_dim_type type, const char *name);
1018 The identifiers or names of entire spaces may be set or read off
1019 using the following functions.
1021 #include <isl/space.h>
1022 __isl_give isl_space *isl_space_set_tuple_id(
1023 __isl_take isl_space *space,
1024 enum isl_dim_type type, __isl_take isl_id *id);
1025 __isl_give isl_space *isl_space_reset_tuple_id(
1026 __isl_take isl_space *space, enum isl_dim_type type);
1027 int isl_space_has_tuple_id(__isl_keep isl_space *space,
1028 enum isl_dim_type type);
1029 __isl_give isl_id *isl_space_get_tuple_id(
1030 __isl_keep isl_space *space, enum isl_dim_type type);
1031 __isl_give isl_space *isl_space_set_tuple_name(
1032 __isl_take isl_space *space,
1033 enum isl_dim_type type, const char *s);
1034 int isl_space_has_tuple_name(__isl_keep isl_space *space,
1035 enum isl_dim_type type);
1036 const char *isl_space_get_tuple_name(__isl_keep isl_space *space,
1037 enum isl_dim_type type);
1039 The C<type> argument needs to be one of C<isl_dim_in>, C<isl_dim_out>
1040 or C<isl_dim_set>. As with C<isl_space_get_name>,
1041 the C<isl_space_get_tuple_name> function returns a pointer to some internal
1043 Binary operations require the corresponding spaces of their arguments
1044 to have the same name.
1046 Spaces can be nested. In particular, the domain of a set or
1047 the domain or range of a relation can be a nested relation.
1048 The following functions can be used to construct and deconstruct
1051 #include <isl/space.h>
1052 int isl_space_is_wrapping(__isl_keep isl_space *space);
1053 __isl_give isl_space *isl_space_wrap(__isl_take isl_space *space);
1054 __isl_give isl_space *isl_space_unwrap(__isl_take isl_space *space);
1056 The input to C<isl_space_is_wrapping> and C<isl_space_unwrap> should
1057 be the space of a set, while that of
1058 C<isl_space_wrap> should be the space of a relation.
1059 Conversely, the output of C<isl_space_unwrap> is the space
1060 of a relation, while that of C<isl_space_wrap> is the space of a set.
1062 Spaces can be created from other spaces
1063 using the following functions.
1065 __isl_give isl_space *isl_space_domain(__isl_take isl_space *space);
1066 __isl_give isl_space *isl_space_from_domain(__isl_take isl_space *space);
1067 __isl_give isl_space *isl_space_range(__isl_take isl_space *space);
1068 __isl_give isl_space *isl_space_from_range(__isl_take isl_space *space);
1069 __isl_give isl_space *isl_space_params(
1070 __isl_take isl_space *space);
1071 __isl_give isl_space *isl_space_set_from_params(
1072 __isl_take isl_space *space);
1073 __isl_give isl_space *isl_space_reverse(__isl_take isl_space *space);
1074 __isl_give isl_space *isl_space_join(__isl_take isl_space *left,
1075 __isl_take isl_space *right);
1076 __isl_give isl_space *isl_space_align_params(
1077 __isl_take isl_space *space1, __isl_take isl_space *space2)
1078 __isl_give isl_space *isl_space_insert_dims(__isl_take isl_space *space,
1079 enum isl_dim_type type, unsigned pos, unsigned n);
1080 __isl_give isl_space *isl_space_add_dims(__isl_take isl_space *space,
1081 enum isl_dim_type type, unsigned n);
1082 __isl_give isl_space *isl_space_drop_dims(__isl_take isl_space *space,
1083 enum isl_dim_type type, unsigned first, unsigned n);
1084 __isl_give isl_space *isl_space_move_dims(__isl_take isl_space *space,
1085 enum isl_dim_type dst_type, unsigned dst_pos,
1086 enum isl_dim_type src_type, unsigned src_pos,
1088 __isl_give isl_space *isl_space_map_from_set(
1089 __isl_take isl_space *space);
1090 __isl_give isl_space *isl_space_map_from_domain_and_range(
1091 __isl_take isl_space *domain,
1092 __isl_take isl_space *range);
1093 __isl_give isl_space *isl_space_zip(__isl_take isl_space *space);
1094 __isl_give isl_space *isl_space_curry(
1095 __isl_take isl_space *space);
1096 __isl_give isl_space *isl_space_uncurry(
1097 __isl_take isl_space *space);
1099 Note that if dimensions are added or removed from a space, then
1100 the name and the internal structure are lost.
1104 A local space is essentially a space with
1105 zero or more existentially quantified variables.
1106 The local space of a (constraint of a) basic set or relation can be obtained
1107 using the following functions.
1109 #include <isl/constraint.h>
1110 __isl_give isl_local_space *isl_constraint_get_local_space(
1111 __isl_keep isl_constraint *constraint);
1113 #include <isl/set.h>
1114 __isl_give isl_local_space *isl_basic_set_get_local_space(
1115 __isl_keep isl_basic_set *bset);
1117 #include <isl/map.h>
1118 __isl_give isl_local_space *isl_basic_map_get_local_space(
1119 __isl_keep isl_basic_map *bmap);
1121 A new local space can be created from a space using
1123 #include <isl/local_space.h>
1124 __isl_give isl_local_space *isl_local_space_from_space(
1125 __isl_take isl_space *space);
1127 They can be inspected, modified, copied and freed using the following functions.
1129 #include <isl/local_space.h>
1130 isl_ctx *isl_local_space_get_ctx(
1131 __isl_keep isl_local_space *ls);
1132 int isl_local_space_is_set(__isl_keep isl_local_space *ls);
1133 int isl_local_space_dim(__isl_keep isl_local_space *ls,
1134 enum isl_dim_type type);
1135 int isl_local_space_has_dim_id(
1136 __isl_keep isl_local_space *ls,
1137 enum isl_dim_type type, unsigned pos);
1138 __isl_give isl_id *isl_local_space_get_dim_id(
1139 __isl_keep isl_local_space *ls,
1140 enum isl_dim_type type, unsigned pos);
1141 int isl_local_space_has_dim_name(
1142 __isl_keep isl_local_space *ls,
1143 enum isl_dim_type type, unsigned pos)
1144 const char *isl_local_space_get_dim_name(
1145 __isl_keep isl_local_space *ls,
1146 enum isl_dim_type type, unsigned pos);
1147 __isl_give isl_local_space *isl_local_space_set_dim_name(
1148 __isl_take isl_local_space *ls,
1149 enum isl_dim_type type, unsigned pos, const char *s);
1150 __isl_give isl_local_space *isl_local_space_set_dim_id(
1151 __isl_take isl_local_space *ls,
1152 enum isl_dim_type type, unsigned pos,
1153 __isl_take isl_id *id);
1154 __isl_give isl_space *isl_local_space_get_space(
1155 __isl_keep isl_local_space *ls);
1156 __isl_give isl_aff *isl_local_space_get_div(
1157 __isl_keep isl_local_space *ls, int pos);
1158 __isl_give isl_local_space *isl_local_space_copy(
1159 __isl_keep isl_local_space *ls);
1160 void *isl_local_space_free(__isl_take isl_local_space *ls);
1162 Note that C<isl_local_space_get_div> can only be used on local spaces
1165 Two local spaces can be compared using
1167 int isl_local_space_is_equal(__isl_keep isl_local_space *ls1,
1168 __isl_keep isl_local_space *ls2);
1170 Local spaces can be created from other local spaces
1171 using the following functions.
1173 __isl_give isl_local_space *isl_local_space_domain(
1174 __isl_take isl_local_space *ls);
1175 __isl_give isl_local_space *isl_local_space_range(
1176 __isl_take isl_local_space *ls);
1177 __isl_give isl_local_space *isl_local_space_from_domain(
1178 __isl_take isl_local_space *ls);
1179 __isl_give isl_local_space *isl_local_space_intersect(
1180 __isl_take isl_local_space *ls1,
1181 __isl_take isl_local_space *ls2);
1182 __isl_give isl_local_space *isl_local_space_add_dims(
1183 __isl_take isl_local_space *ls,
1184 enum isl_dim_type type, unsigned n);
1185 __isl_give isl_local_space *isl_local_space_insert_dims(
1186 __isl_take isl_local_space *ls,
1187 enum isl_dim_type type, unsigned first, unsigned n);
1188 __isl_give isl_local_space *isl_local_space_drop_dims(
1189 __isl_take isl_local_space *ls,
1190 enum isl_dim_type type, unsigned first, unsigned n);
1192 =head2 Input and Output
1194 C<isl> supports its own input/output format, which is similar
1195 to the C<Omega> format, but also supports the C<PolyLib> format
1198 =head3 C<isl> format
1200 The C<isl> format is similar to that of C<Omega>, but has a different
1201 syntax for describing the parameters and allows for the definition
1202 of an existentially quantified variable as the integer division
1203 of an affine expression.
1204 For example, the set of integers C<i> between C<0> and C<n>
1205 such that C<i % 10 <= 6> can be described as
1207 [n] -> { [i] : exists (a = [i/10] : 0 <= i and i <= n and
1210 A set or relation can have several disjuncts, separated
1211 by the keyword C<or>. Each disjunct is either a conjunction
1212 of constraints or a projection (C<exists>) of a conjunction
1213 of constraints. The constraints are separated by the keyword
1216 =head3 C<PolyLib> format
1218 If the represented set is a union, then the first line
1219 contains a single number representing the number of disjuncts.
1220 Otherwise, a line containing the number C<1> is optional.
1222 Each disjunct is represented by a matrix of constraints.
1223 The first line contains two numbers representing
1224 the number of rows and columns,
1225 where the number of rows is equal to the number of constraints
1226 and the number of columns is equal to two plus the number of variables.
1227 The following lines contain the actual rows of the constraint matrix.
1228 In each row, the first column indicates whether the constraint
1229 is an equality (C<0>) or inequality (C<1>). The final column
1230 corresponds to the constant term.
1232 If the set is parametric, then the coefficients of the parameters
1233 appear in the last columns before the constant column.
1234 The coefficients of any existentially quantified variables appear
1235 between those of the set variables and those of the parameters.
1237 =head3 Extended C<PolyLib> format
1239 The extended C<PolyLib> format is nearly identical to the
1240 C<PolyLib> format. The only difference is that the line
1241 containing the number of rows and columns of a constraint matrix
1242 also contains four additional numbers:
1243 the number of output dimensions, the number of input dimensions,
1244 the number of local dimensions (i.e., the number of existentially
1245 quantified variables) and the number of parameters.
1246 For sets, the number of ``output'' dimensions is equal
1247 to the number of set dimensions, while the number of ``input''
1252 #include <isl/set.h>
1253 __isl_give isl_basic_set *isl_basic_set_read_from_file(
1254 isl_ctx *ctx, FILE *input);
1255 __isl_give isl_basic_set *isl_basic_set_read_from_str(
1256 isl_ctx *ctx, const char *str);
1257 __isl_give isl_set *isl_set_read_from_file(isl_ctx *ctx,
1259 __isl_give isl_set *isl_set_read_from_str(isl_ctx *ctx,
1262 #include <isl/map.h>
1263 __isl_give isl_basic_map *isl_basic_map_read_from_file(
1264 isl_ctx *ctx, FILE *input);
1265 __isl_give isl_basic_map *isl_basic_map_read_from_str(
1266 isl_ctx *ctx, const char *str);
1267 __isl_give isl_map *isl_map_read_from_file(
1268 isl_ctx *ctx, FILE *input);
1269 __isl_give isl_map *isl_map_read_from_str(isl_ctx *ctx,
1272 #include <isl/union_set.h>
1273 __isl_give isl_union_set *isl_union_set_read_from_file(
1274 isl_ctx *ctx, FILE *input);
1275 __isl_give isl_union_set *isl_union_set_read_from_str(
1276 isl_ctx *ctx, const char *str);
1278 #include <isl/union_map.h>
1279 __isl_give isl_union_map *isl_union_map_read_from_file(
1280 isl_ctx *ctx, FILE *input);
1281 __isl_give isl_union_map *isl_union_map_read_from_str(
1282 isl_ctx *ctx, const char *str);
1284 The input format is autodetected and may be either the C<PolyLib> format
1285 or the C<isl> format.
1289 Before anything can be printed, an C<isl_printer> needs to
1292 __isl_give isl_printer *isl_printer_to_file(isl_ctx *ctx,
1294 __isl_give isl_printer *isl_printer_to_str(isl_ctx *ctx);
1295 void *isl_printer_free(__isl_take isl_printer *printer);
1296 __isl_give char *isl_printer_get_str(
1297 __isl_keep isl_printer *printer);
1299 The printer can be inspected using the following functions.
1301 FILE *isl_printer_get_file(
1302 __isl_keep isl_printer *printer);
1303 int isl_printer_get_output_format(
1304 __isl_keep isl_printer *p);
1306 The behavior of the printer can be modified in various ways
1308 __isl_give isl_printer *isl_printer_set_output_format(
1309 __isl_take isl_printer *p, int output_format);
1310 __isl_give isl_printer *isl_printer_set_indent(
1311 __isl_take isl_printer *p, int indent);
1312 __isl_give isl_printer *isl_printer_indent(
1313 __isl_take isl_printer *p, int indent);
1314 __isl_give isl_printer *isl_printer_set_prefix(
1315 __isl_take isl_printer *p, const char *prefix);
1316 __isl_give isl_printer *isl_printer_set_suffix(
1317 __isl_take isl_printer *p, const char *suffix);
1319 The C<output_format> may be either C<ISL_FORMAT_ISL>, C<ISL_FORMAT_OMEGA>,
1320 C<ISL_FORMAT_POLYLIB>, C<ISL_FORMAT_EXT_POLYLIB> or C<ISL_FORMAT_LATEX>
1321 and defaults to C<ISL_FORMAT_ISL>.
1322 Each line in the output is indented by C<indent> (set by
1323 C<isl_printer_set_indent>) spaces
1324 (default: 0), prefixed by C<prefix> and suffixed by C<suffix>.
1325 In the C<PolyLib> format output,
1326 the coefficients of the existentially quantified variables
1327 appear between those of the set variables and those
1329 The function C<isl_printer_indent> increases the indentation
1330 by the specified amount (which may be negative).
1332 To actually print something, use
1334 #include <isl/printer.h>
1335 __isl_give isl_printer *isl_printer_print_double(
1336 __isl_take isl_printer *p, double d);
1338 #include <isl/set.h>
1339 __isl_give isl_printer *isl_printer_print_basic_set(
1340 __isl_take isl_printer *printer,
1341 __isl_keep isl_basic_set *bset);
1342 __isl_give isl_printer *isl_printer_print_set(
1343 __isl_take isl_printer *printer,
1344 __isl_keep isl_set *set);
1346 #include <isl/map.h>
1347 __isl_give isl_printer *isl_printer_print_basic_map(
1348 __isl_take isl_printer *printer,
1349 __isl_keep isl_basic_map *bmap);
1350 __isl_give isl_printer *isl_printer_print_map(
1351 __isl_take isl_printer *printer,
1352 __isl_keep isl_map *map);
1354 #include <isl/union_set.h>
1355 __isl_give isl_printer *isl_printer_print_union_set(
1356 __isl_take isl_printer *p,
1357 __isl_keep isl_union_set *uset);
1359 #include <isl/union_map.h>
1360 __isl_give isl_printer *isl_printer_print_union_map(
1361 __isl_take isl_printer *p,
1362 __isl_keep isl_union_map *umap);
1364 When called on a file printer, the following function flushes
1365 the file. When called on a string printer, the buffer is cleared.
1367 __isl_give isl_printer *isl_printer_flush(
1368 __isl_take isl_printer *p);
1370 =head2 Creating New Sets and Relations
1372 C<isl> has functions for creating some standard sets and relations.
1376 =item * Empty sets and relations
1378 __isl_give isl_basic_set *isl_basic_set_empty(
1379 __isl_take isl_space *space);
1380 __isl_give isl_basic_map *isl_basic_map_empty(
1381 __isl_take isl_space *space);
1382 __isl_give isl_set *isl_set_empty(
1383 __isl_take isl_space *space);
1384 __isl_give isl_map *isl_map_empty(
1385 __isl_take isl_space *space);
1386 __isl_give isl_union_set *isl_union_set_empty(
1387 __isl_take isl_space *space);
1388 __isl_give isl_union_map *isl_union_map_empty(
1389 __isl_take isl_space *space);
1391 For C<isl_union_set>s and C<isl_union_map>s, the space
1392 is only used to specify the parameters.
1394 =item * Universe sets and relations
1396 __isl_give isl_basic_set *isl_basic_set_universe(
1397 __isl_take isl_space *space);
1398 __isl_give isl_basic_map *isl_basic_map_universe(
1399 __isl_take isl_space *space);
1400 __isl_give isl_set *isl_set_universe(
1401 __isl_take isl_space *space);
1402 __isl_give isl_map *isl_map_universe(
1403 __isl_take isl_space *space);
1404 __isl_give isl_union_set *isl_union_set_universe(
1405 __isl_take isl_union_set *uset);
1406 __isl_give isl_union_map *isl_union_map_universe(
1407 __isl_take isl_union_map *umap);
1409 The sets and relations constructed by the functions above
1410 contain all integer values, while those constructed by the
1411 functions below only contain non-negative values.
1413 __isl_give isl_basic_set *isl_basic_set_nat_universe(
1414 __isl_take isl_space *space);
1415 __isl_give isl_basic_map *isl_basic_map_nat_universe(
1416 __isl_take isl_space *space);
1417 __isl_give isl_set *isl_set_nat_universe(
1418 __isl_take isl_space *space);
1419 __isl_give isl_map *isl_map_nat_universe(
1420 __isl_take isl_space *space);
1422 =item * Identity relations
1424 __isl_give isl_basic_map *isl_basic_map_identity(
1425 __isl_take isl_space *space);
1426 __isl_give isl_map *isl_map_identity(
1427 __isl_take isl_space *space);
1429 The number of input and output dimensions in C<space> needs
1432 =item * Lexicographic order
1434 __isl_give isl_map *isl_map_lex_lt(
1435 __isl_take isl_space *set_space);
1436 __isl_give isl_map *isl_map_lex_le(
1437 __isl_take isl_space *set_space);
1438 __isl_give isl_map *isl_map_lex_gt(
1439 __isl_take isl_space *set_space);
1440 __isl_give isl_map *isl_map_lex_ge(
1441 __isl_take isl_space *set_space);
1442 __isl_give isl_map *isl_map_lex_lt_first(
1443 __isl_take isl_space *space, unsigned n);
1444 __isl_give isl_map *isl_map_lex_le_first(
1445 __isl_take isl_space *space, unsigned n);
1446 __isl_give isl_map *isl_map_lex_gt_first(
1447 __isl_take isl_space *space, unsigned n);
1448 __isl_give isl_map *isl_map_lex_ge_first(
1449 __isl_take isl_space *space, unsigned n);
1451 The first four functions take a space for a B<set>
1452 and return relations that express that the elements in the domain
1453 are lexicographically less
1454 (C<isl_map_lex_lt>), less or equal (C<isl_map_lex_le>),
1455 greater (C<isl_map_lex_gt>) or greater or equal (C<isl_map_lex_ge>)
1456 than the elements in the range.
1457 The last four functions take a space for a map
1458 and return relations that express that the first C<n> dimensions
1459 in the domain are lexicographically less
1460 (C<isl_map_lex_lt_first>), less or equal (C<isl_map_lex_le_first>),
1461 greater (C<isl_map_lex_gt_first>) or greater or equal (C<isl_map_lex_ge_first>)
1462 than the first C<n> dimensions in the range.
1466 A basic set or relation can be converted to a set or relation
1467 using the following functions.
1469 __isl_give isl_set *isl_set_from_basic_set(
1470 __isl_take isl_basic_set *bset);
1471 __isl_give isl_map *isl_map_from_basic_map(
1472 __isl_take isl_basic_map *bmap);
1474 Sets and relations can be converted to union sets and relations
1475 using the following functions.
1477 __isl_give isl_union_set *isl_union_set_from_basic_set(
1478 __isl_take isl_basic_set *bset);
1479 __isl_give isl_union_map *isl_union_map_from_basic_map(
1480 __isl_take isl_basic_map *bmap);
1481 __isl_give isl_union_set *isl_union_set_from_set(
1482 __isl_take isl_set *set);
1483 __isl_give isl_union_map *isl_union_map_from_map(
1484 __isl_take isl_map *map);
1486 The inverse conversions below can only be used if the input
1487 union set or relation is known to contain elements in exactly one
1490 __isl_give isl_set *isl_set_from_union_set(
1491 __isl_take isl_union_set *uset);
1492 __isl_give isl_map *isl_map_from_union_map(
1493 __isl_take isl_union_map *umap);
1495 A zero-dimensional (basic) set can be constructed on a given parameter domain
1496 using the following function.
1498 __isl_give isl_basic_set *isl_basic_set_from_params(
1499 __isl_take isl_basic_set *bset);
1500 __isl_give isl_set *isl_set_from_params(
1501 __isl_take isl_set *set);
1503 Sets and relations can be copied and freed again using the following
1506 __isl_give isl_basic_set *isl_basic_set_copy(
1507 __isl_keep isl_basic_set *bset);
1508 __isl_give isl_set *isl_set_copy(__isl_keep isl_set *set);
1509 __isl_give isl_union_set *isl_union_set_copy(
1510 __isl_keep isl_union_set *uset);
1511 __isl_give isl_basic_map *isl_basic_map_copy(
1512 __isl_keep isl_basic_map *bmap);
1513 __isl_give isl_map *isl_map_copy(__isl_keep isl_map *map);
1514 __isl_give isl_union_map *isl_union_map_copy(
1515 __isl_keep isl_union_map *umap);
1516 void *isl_basic_set_free(__isl_take isl_basic_set *bset);
1517 void *isl_set_free(__isl_take isl_set *set);
1518 void *isl_union_set_free(__isl_take isl_union_set *uset);
1519 void *isl_basic_map_free(__isl_take isl_basic_map *bmap);
1520 void *isl_map_free(__isl_take isl_map *map);
1521 void *isl_union_map_free(__isl_take isl_union_map *umap);
1523 Other sets and relations can be constructed by starting
1524 from a universe set or relation, adding equality and/or
1525 inequality constraints and then projecting out the
1526 existentially quantified variables, if any.
1527 Constraints can be constructed, manipulated and
1528 added to (or removed from) (basic) sets and relations
1529 using the following functions.
1531 #include <isl/constraint.h>
1532 __isl_give isl_constraint *isl_equality_alloc(
1533 __isl_take isl_local_space *ls);
1534 __isl_give isl_constraint *isl_inequality_alloc(
1535 __isl_take isl_local_space *ls);
1536 __isl_give isl_constraint *isl_constraint_set_constant(
1537 __isl_take isl_constraint *constraint, isl_int v);
1538 __isl_give isl_constraint *isl_constraint_set_constant_si(
1539 __isl_take isl_constraint *constraint, int v);
1540 __isl_give isl_constraint *isl_constraint_set_constant_val(
1541 __isl_take isl_constraint *constraint,
1542 __isl_take isl_val *v);
1543 __isl_give isl_constraint *isl_constraint_set_coefficient(
1544 __isl_take isl_constraint *constraint,
1545 enum isl_dim_type type, int pos, isl_int v);
1546 __isl_give isl_constraint *isl_constraint_set_coefficient_si(
1547 __isl_take isl_constraint *constraint,
1548 enum isl_dim_type type, int pos, int v);
1549 __isl_give isl_constraint *
1550 isl_constraint_set_coefficient_val(
1551 __isl_take isl_constraint *constraint,
1552 enum isl_dim_type type, int pos, isl_val *v);
1553 __isl_give isl_basic_map *isl_basic_map_add_constraint(
1554 __isl_take isl_basic_map *bmap,
1555 __isl_take isl_constraint *constraint);
1556 __isl_give isl_basic_set *isl_basic_set_add_constraint(
1557 __isl_take isl_basic_set *bset,
1558 __isl_take isl_constraint *constraint);
1559 __isl_give isl_map *isl_map_add_constraint(
1560 __isl_take isl_map *map,
1561 __isl_take isl_constraint *constraint);
1562 __isl_give isl_set *isl_set_add_constraint(
1563 __isl_take isl_set *set,
1564 __isl_take isl_constraint *constraint);
1565 __isl_give isl_basic_set *isl_basic_set_drop_constraint(
1566 __isl_take isl_basic_set *bset,
1567 __isl_take isl_constraint *constraint);
1569 For example, to create a set containing the even integers
1570 between 10 and 42, you would use the following code.
1573 isl_local_space *ls;
1575 isl_basic_set *bset;
1577 space = isl_space_set_alloc(ctx, 0, 2);
1578 bset = isl_basic_set_universe(isl_space_copy(space));
1579 ls = isl_local_space_from_space(space);
1581 c = isl_equality_alloc(isl_local_space_copy(ls));
1582 c = isl_constraint_set_coefficient_si(c, isl_dim_set, 0, -1);
1583 c = isl_constraint_set_coefficient_si(c, isl_dim_set, 1, 2);
1584 bset = isl_basic_set_add_constraint(bset, c);
1586 c = isl_inequality_alloc(isl_local_space_copy(ls));
1587 c = isl_constraint_set_constant_si(c, -10);
1588 c = isl_constraint_set_coefficient_si(c, isl_dim_set, 0, 1);
1589 bset = isl_basic_set_add_constraint(bset, c);
1591 c = isl_inequality_alloc(ls);
1592 c = isl_constraint_set_constant_si(c, 42);
1593 c = isl_constraint_set_coefficient_si(c, isl_dim_set, 0, -1);
1594 bset = isl_basic_set_add_constraint(bset, c);
1596 bset = isl_basic_set_project_out(bset, isl_dim_set, 1, 1);
1600 isl_basic_set *bset;
1601 bset = isl_basic_set_read_from_str(ctx,
1602 "{[i] : exists (a : i = 2a and i >= 10 and i <= 42)}");
1604 A basic set or relation can also be constructed from two matrices
1605 describing the equalities and the inequalities.
1607 __isl_give isl_basic_set *isl_basic_set_from_constraint_matrices(
1608 __isl_take isl_space *space,
1609 __isl_take isl_mat *eq, __isl_take isl_mat *ineq,
1610 enum isl_dim_type c1,
1611 enum isl_dim_type c2, enum isl_dim_type c3,
1612 enum isl_dim_type c4);
1613 __isl_give isl_basic_map *isl_basic_map_from_constraint_matrices(
1614 __isl_take isl_space *space,
1615 __isl_take isl_mat *eq, __isl_take isl_mat *ineq,
1616 enum isl_dim_type c1,
1617 enum isl_dim_type c2, enum isl_dim_type c3,
1618 enum isl_dim_type c4, enum isl_dim_type c5);
1620 The C<isl_dim_type> arguments indicate the order in which
1621 different kinds of variables appear in the input matrices
1622 and should be a permutation of C<isl_dim_cst>, C<isl_dim_param>,
1623 C<isl_dim_set> and C<isl_dim_div> for sets and
1624 of C<isl_dim_cst>, C<isl_dim_param>,
1625 C<isl_dim_in>, C<isl_dim_out> and C<isl_dim_div> for relations.
1627 A (basic or union) set or relation can also be constructed from a
1628 (union) (piecewise) (multiple) affine expression
1629 or a list of affine expressions
1630 (See L<"Piecewise Quasi Affine Expressions"> and
1631 L<"Piecewise Multiple Quasi Affine Expressions">).
1633 __isl_give isl_basic_map *isl_basic_map_from_aff(
1634 __isl_take isl_aff *aff);
1635 __isl_give isl_map *isl_map_from_aff(
1636 __isl_take isl_aff *aff);
1637 __isl_give isl_set *isl_set_from_pw_aff(
1638 __isl_take isl_pw_aff *pwaff);
1639 __isl_give isl_map *isl_map_from_pw_aff(
1640 __isl_take isl_pw_aff *pwaff);
1641 __isl_give isl_basic_map *isl_basic_map_from_aff_list(
1642 __isl_take isl_space *domain_space,
1643 __isl_take isl_aff_list *list);
1644 __isl_give isl_basic_map *isl_basic_map_from_multi_aff(
1645 __isl_take isl_multi_aff *maff)
1646 __isl_give isl_map *isl_map_from_multi_aff(
1647 __isl_take isl_multi_aff *maff)
1648 __isl_give isl_set *isl_set_from_pw_multi_aff(
1649 __isl_take isl_pw_multi_aff *pma);
1650 __isl_give isl_map *isl_map_from_pw_multi_aff(
1651 __isl_take isl_pw_multi_aff *pma);
1652 __isl_give isl_union_map *
1653 isl_union_map_from_union_pw_multi_aff(
1654 __isl_take isl_union_pw_multi_aff *upma);
1656 The C<domain_dim> argument describes the domain of the resulting
1657 basic relation. It is required because the C<list> may consist
1658 of zero affine expressions.
1660 =head2 Inspecting Sets and Relations
1662 Usually, the user should not have to care about the actual constraints
1663 of the sets and maps, but should instead apply the abstract operations
1664 explained in the following sections.
1665 Occasionally, however, it may be required to inspect the individual
1666 coefficients of the constraints. This section explains how to do so.
1667 In these cases, it may also be useful to have C<isl> compute
1668 an explicit representation of the existentially quantified variables.
1670 __isl_give isl_set *isl_set_compute_divs(
1671 __isl_take isl_set *set);
1672 __isl_give isl_map *isl_map_compute_divs(
1673 __isl_take isl_map *map);
1674 __isl_give isl_union_set *isl_union_set_compute_divs(
1675 __isl_take isl_union_set *uset);
1676 __isl_give isl_union_map *isl_union_map_compute_divs(
1677 __isl_take isl_union_map *umap);
1679 This explicit representation defines the existentially quantified
1680 variables as integer divisions of the other variables, possibly
1681 including earlier existentially quantified variables.
1682 An explicitly represented existentially quantified variable therefore
1683 has a unique value when the values of the other variables are known.
1684 If, furthermore, the same existentials, i.e., existentials
1685 with the same explicit representations, should appear in the
1686 same order in each of the disjuncts of a set or map, then the user should call
1687 either of the following functions.
1689 __isl_give isl_set *isl_set_align_divs(
1690 __isl_take isl_set *set);
1691 __isl_give isl_map *isl_map_align_divs(
1692 __isl_take isl_map *map);
1694 Alternatively, the existentially quantified variables can be removed
1695 using the following functions, which compute an overapproximation.
1697 __isl_give isl_basic_set *isl_basic_set_remove_divs(
1698 __isl_take isl_basic_set *bset);
1699 __isl_give isl_basic_map *isl_basic_map_remove_divs(
1700 __isl_take isl_basic_map *bmap);
1701 __isl_give isl_set *isl_set_remove_divs(
1702 __isl_take isl_set *set);
1703 __isl_give isl_map *isl_map_remove_divs(
1704 __isl_take isl_map *map);
1706 It is also possible to only remove those divs that are defined
1707 in terms of a given range of dimensions or only those for which
1708 no explicit representation is known.
1710 __isl_give isl_basic_set *
1711 isl_basic_set_remove_divs_involving_dims(
1712 __isl_take isl_basic_set *bset,
1713 enum isl_dim_type type,
1714 unsigned first, unsigned n);
1715 __isl_give isl_basic_map *
1716 isl_basic_map_remove_divs_involving_dims(
1717 __isl_take isl_basic_map *bmap,
1718 enum isl_dim_type type,
1719 unsigned first, unsigned n);
1720 __isl_give isl_set *isl_set_remove_divs_involving_dims(
1721 __isl_take isl_set *set, enum isl_dim_type type,
1722 unsigned first, unsigned n);
1723 __isl_give isl_map *isl_map_remove_divs_involving_dims(
1724 __isl_take isl_map *map, enum isl_dim_type type,
1725 unsigned first, unsigned n);
1727 __isl_give isl_basic_set *
1728 isl_basic_set_remove_unknown_divs(
1729 __isl_take isl_basic_set *bset);
1730 __isl_give isl_set *isl_set_remove_unknown_divs(
1731 __isl_take isl_set *set);
1732 __isl_give isl_map *isl_map_remove_unknown_divs(
1733 __isl_take isl_map *map);
1735 To iterate over all the sets or maps in a union set or map, use
1737 int isl_union_set_foreach_set(__isl_keep isl_union_set *uset,
1738 int (*fn)(__isl_take isl_set *set, void *user),
1740 int isl_union_map_foreach_map(__isl_keep isl_union_map *umap,
1741 int (*fn)(__isl_take isl_map *map, void *user),
1744 The number of sets or maps in a union set or map can be obtained
1747 int isl_union_set_n_set(__isl_keep isl_union_set *uset);
1748 int isl_union_map_n_map(__isl_keep isl_union_map *umap);
1750 To extract the set or map in a given space from a union, use
1752 __isl_give isl_set *isl_union_set_extract_set(
1753 __isl_keep isl_union_set *uset,
1754 __isl_take isl_space *space);
1755 __isl_give isl_map *isl_union_map_extract_map(
1756 __isl_keep isl_union_map *umap,
1757 __isl_take isl_space *space);
1759 To iterate over all the basic sets or maps in a set or map, use
1761 int isl_set_foreach_basic_set(__isl_keep isl_set *set,
1762 int (*fn)(__isl_take isl_basic_set *bset, void *user),
1764 int isl_map_foreach_basic_map(__isl_keep isl_map *map,
1765 int (*fn)(__isl_take isl_basic_map *bmap, void *user),
1768 The callback function C<fn> should return 0 if successful and
1769 -1 if an error occurs. In the latter case, or if any other error
1770 occurs, the above functions will return -1.
1772 It should be noted that C<isl> does not guarantee that
1773 the basic sets or maps passed to C<fn> are disjoint.
1774 If this is required, then the user should call one of
1775 the following functions first.
1777 __isl_give isl_set *isl_set_make_disjoint(
1778 __isl_take isl_set *set);
1779 __isl_give isl_map *isl_map_make_disjoint(
1780 __isl_take isl_map *map);
1782 The number of basic sets in a set can be obtained
1785 int isl_set_n_basic_set(__isl_keep isl_set *set);
1787 To iterate over the constraints of a basic set or map, use
1789 #include <isl/constraint.h>
1791 int isl_basic_set_n_constraint(
1792 __isl_keep isl_basic_set *bset);
1793 int isl_basic_set_foreach_constraint(
1794 __isl_keep isl_basic_set *bset,
1795 int (*fn)(__isl_take isl_constraint *c, void *user),
1797 int isl_basic_map_foreach_constraint(
1798 __isl_keep isl_basic_map *bmap,
1799 int (*fn)(__isl_take isl_constraint *c, void *user),
1801 void *isl_constraint_free(__isl_take isl_constraint *c);
1803 Again, the callback function C<fn> should return 0 if successful and
1804 -1 if an error occurs. In the latter case, or if any other error
1805 occurs, the above functions will return -1.
1806 The constraint C<c> represents either an equality or an inequality.
1807 Use the following function to find out whether a constraint
1808 represents an equality. If not, it represents an inequality.
1810 int isl_constraint_is_equality(
1811 __isl_keep isl_constraint *constraint);
1813 The coefficients of the constraints can be inspected using
1814 the following functions.
1816 int isl_constraint_is_lower_bound(
1817 __isl_keep isl_constraint *constraint,
1818 enum isl_dim_type type, unsigned pos);
1819 int isl_constraint_is_upper_bound(
1820 __isl_keep isl_constraint *constraint,
1821 enum isl_dim_type type, unsigned pos);
1822 void isl_constraint_get_constant(
1823 __isl_keep isl_constraint *constraint, isl_int *v);
1824 __isl_give isl_val *isl_constraint_get_constant_val(
1825 __isl_keep isl_constraint *constraint);
1826 void isl_constraint_get_coefficient(
1827 __isl_keep isl_constraint *constraint,
1828 enum isl_dim_type type, int pos, isl_int *v);
1829 __isl_give isl_val *isl_constraint_get_coefficient_val(
1830 __isl_keep isl_constraint *constraint,
1831 enum isl_dim_type type, int pos);
1832 int isl_constraint_involves_dims(
1833 __isl_keep isl_constraint *constraint,
1834 enum isl_dim_type type, unsigned first, unsigned n);
1836 The explicit representations of the existentially quantified
1837 variables can be inspected using the following function.
1838 Note that the user is only allowed to use this function
1839 if the inspected set or map is the result of a call
1840 to C<isl_set_compute_divs> or C<isl_map_compute_divs>.
1841 The existentially quantified variable is equal to the floor
1842 of the returned affine expression. The affine expression
1843 itself can be inspected using the functions in
1844 L<"Piecewise Quasi Affine Expressions">.
1846 __isl_give isl_aff *isl_constraint_get_div(
1847 __isl_keep isl_constraint *constraint, int pos);
1849 To obtain the constraints of a basic set or map in matrix
1850 form, use the following functions.
1852 __isl_give isl_mat *isl_basic_set_equalities_matrix(
1853 __isl_keep isl_basic_set *bset,
1854 enum isl_dim_type c1, enum isl_dim_type c2,
1855 enum isl_dim_type c3, enum isl_dim_type c4);
1856 __isl_give isl_mat *isl_basic_set_inequalities_matrix(
1857 __isl_keep isl_basic_set *bset,
1858 enum isl_dim_type c1, enum isl_dim_type c2,
1859 enum isl_dim_type c3, enum isl_dim_type c4);
1860 __isl_give isl_mat *isl_basic_map_equalities_matrix(
1861 __isl_keep isl_basic_map *bmap,
1862 enum isl_dim_type c1,
1863 enum isl_dim_type c2, enum isl_dim_type c3,
1864 enum isl_dim_type c4, enum isl_dim_type c5);
1865 __isl_give isl_mat *isl_basic_map_inequalities_matrix(
1866 __isl_keep isl_basic_map *bmap,
1867 enum isl_dim_type c1,
1868 enum isl_dim_type c2, enum isl_dim_type c3,
1869 enum isl_dim_type c4, enum isl_dim_type c5);
1871 The C<isl_dim_type> arguments dictate the order in which
1872 different kinds of variables appear in the resulting matrix
1873 and should be a permutation of C<isl_dim_cst>, C<isl_dim_param>,
1874 C<isl_dim_in>, C<isl_dim_out> and C<isl_dim_div>.
1876 The number of parameters, input, output or set dimensions can
1877 be obtained using the following functions.
1879 unsigned isl_basic_set_dim(__isl_keep isl_basic_set *bset,
1880 enum isl_dim_type type);
1881 unsigned isl_basic_map_dim(__isl_keep isl_basic_map *bmap,
1882 enum isl_dim_type type);
1883 unsigned isl_set_dim(__isl_keep isl_set *set,
1884 enum isl_dim_type type);
1885 unsigned isl_map_dim(__isl_keep isl_map *map,
1886 enum isl_dim_type type);
1888 To check whether the description of a set or relation depends
1889 on one or more given dimensions, it is not necessary to iterate over all
1890 constraints. Instead the following functions can be used.
1892 int isl_basic_set_involves_dims(
1893 __isl_keep isl_basic_set *bset,
1894 enum isl_dim_type type, unsigned first, unsigned n);
1895 int isl_set_involves_dims(__isl_keep isl_set *set,
1896 enum isl_dim_type type, unsigned first, unsigned n);
1897 int isl_basic_map_involves_dims(
1898 __isl_keep isl_basic_map *bmap,
1899 enum isl_dim_type type, unsigned first, unsigned n);
1900 int isl_map_involves_dims(__isl_keep isl_map *map,
1901 enum isl_dim_type type, unsigned first, unsigned n);
1903 Similarly, the following functions can be used to check whether
1904 a given dimension is involved in any lower or upper bound.
1906 int isl_set_dim_has_any_lower_bound(__isl_keep isl_set *set,
1907 enum isl_dim_type type, unsigned pos);
1908 int isl_set_dim_has_any_upper_bound(__isl_keep isl_set *set,
1909 enum isl_dim_type type, unsigned pos);
1911 Note that these functions return true even if there is a bound on
1912 the dimension on only some of the basic sets of C<set>.
1913 To check if they have a bound for all of the basic sets in C<set>,
1914 use the following functions instead.
1916 int isl_set_dim_has_lower_bound(__isl_keep isl_set *set,
1917 enum isl_dim_type type, unsigned pos);
1918 int isl_set_dim_has_upper_bound(__isl_keep isl_set *set,
1919 enum isl_dim_type type, unsigned pos);
1921 The identifiers or names of the domain and range spaces of a set
1922 or relation can be read off or set using the following functions.
1924 __isl_give isl_set *isl_set_set_tuple_id(
1925 __isl_take isl_set *set, __isl_take isl_id *id);
1926 __isl_give isl_set *isl_set_reset_tuple_id(
1927 __isl_take isl_set *set);
1928 int isl_set_has_tuple_id(__isl_keep isl_set *set);
1929 __isl_give isl_id *isl_set_get_tuple_id(
1930 __isl_keep isl_set *set);
1931 __isl_give isl_map *isl_map_set_tuple_id(
1932 __isl_take isl_map *map, enum isl_dim_type type,
1933 __isl_take isl_id *id);
1934 __isl_give isl_map *isl_map_reset_tuple_id(
1935 __isl_take isl_map *map, enum isl_dim_type type);
1936 int isl_map_has_tuple_id(__isl_keep isl_map *map,
1937 enum isl_dim_type type);
1938 __isl_give isl_id *isl_map_get_tuple_id(
1939 __isl_keep isl_map *map, enum isl_dim_type type);
1941 const char *isl_basic_set_get_tuple_name(
1942 __isl_keep isl_basic_set *bset);
1943 __isl_give isl_basic_set *isl_basic_set_set_tuple_name(
1944 __isl_take isl_basic_set *set, const char *s);
1945 int isl_set_has_tuple_name(__isl_keep isl_set *set);
1946 const char *isl_set_get_tuple_name(
1947 __isl_keep isl_set *set);
1948 const char *isl_basic_map_get_tuple_name(
1949 __isl_keep isl_basic_map *bmap,
1950 enum isl_dim_type type);
1951 __isl_give isl_basic_map *isl_basic_map_set_tuple_name(
1952 __isl_take isl_basic_map *bmap,
1953 enum isl_dim_type type, const char *s);
1954 int isl_map_has_tuple_name(__isl_keep isl_map *map,
1955 enum isl_dim_type type);
1956 const char *isl_map_get_tuple_name(
1957 __isl_keep isl_map *map,
1958 enum isl_dim_type type);
1960 As with C<isl_space_get_tuple_name>, the value returned points to
1961 an internal data structure.
1962 The identifiers, positions or names of individual dimensions can be
1963 read off using the following functions.
1965 __isl_give isl_id *isl_basic_set_get_dim_id(
1966 __isl_keep isl_basic_set *bset,
1967 enum isl_dim_type type, unsigned pos);
1968 __isl_give isl_set *isl_set_set_dim_id(
1969 __isl_take isl_set *set, enum isl_dim_type type,
1970 unsigned pos, __isl_take isl_id *id);
1971 int isl_set_has_dim_id(__isl_keep isl_set *set,
1972 enum isl_dim_type type, unsigned pos);
1973 __isl_give isl_id *isl_set_get_dim_id(
1974 __isl_keep isl_set *set, enum isl_dim_type type,
1976 int isl_basic_map_has_dim_id(
1977 __isl_keep isl_basic_map *bmap,
1978 enum isl_dim_type type, unsigned pos);
1979 __isl_give isl_map *isl_map_set_dim_id(
1980 __isl_take isl_map *map, enum isl_dim_type type,
1981 unsigned pos, __isl_take isl_id *id);
1982 int isl_map_has_dim_id(__isl_keep isl_map *map,
1983 enum isl_dim_type type, unsigned pos);
1984 __isl_give isl_id *isl_map_get_dim_id(
1985 __isl_keep isl_map *map, enum isl_dim_type type,
1988 int isl_set_find_dim_by_id(__isl_keep isl_set *set,
1989 enum isl_dim_type type, __isl_keep isl_id *id);
1990 int isl_map_find_dim_by_id(__isl_keep isl_map *map,
1991 enum isl_dim_type type, __isl_keep isl_id *id);
1992 int isl_set_find_dim_by_name(__isl_keep isl_set *set,
1993 enum isl_dim_type type, const char *name);
1994 int isl_map_find_dim_by_name(__isl_keep isl_map *map,
1995 enum isl_dim_type type, const char *name);
1997 const char *isl_constraint_get_dim_name(
1998 __isl_keep isl_constraint *constraint,
1999 enum isl_dim_type type, unsigned pos);
2000 const char *isl_basic_set_get_dim_name(
2001 __isl_keep isl_basic_set *bset,
2002 enum isl_dim_type type, unsigned pos);
2003 int isl_set_has_dim_name(__isl_keep isl_set *set,
2004 enum isl_dim_type type, unsigned pos);
2005 const char *isl_set_get_dim_name(
2006 __isl_keep isl_set *set,
2007 enum isl_dim_type type, unsigned pos);
2008 const char *isl_basic_map_get_dim_name(
2009 __isl_keep isl_basic_map *bmap,
2010 enum isl_dim_type type, unsigned pos);
2011 int isl_map_has_dim_name(__isl_keep isl_map *map,
2012 enum isl_dim_type type, unsigned pos);
2013 const char *isl_map_get_dim_name(
2014 __isl_keep isl_map *map,
2015 enum isl_dim_type type, unsigned pos);
2017 These functions are mostly useful to obtain the identifiers, positions
2018 or names of the parameters. Identifiers of individual dimensions are
2019 essentially only useful for printing. They are ignored by all other
2020 operations and may not be preserved across those operations.
2024 =head3 Unary Properties
2030 The following functions test whether the given set or relation
2031 contains any integer points. The ``plain'' variants do not perform
2032 any computations, but simply check if the given set or relation
2033 is already known to be empty.
2035 int isl_basic_set_plain_is_empty(__isl_keep isl_basic_set *bset);
2036 int isl_basic_set_is_empty(__isl_keep isl_basic_set *bset);
2037 int isl_set_plain_is_empty(__isl_keep isl_set *set);
2038 int isl_set_is_empty(__isl_keep isl_set *set);
2039 int isl_union_set_is_empty(__isl_keep isl_union_set *uset);
2040 int isl_basic_map_plain_is_empty(__isl_keep isl_basic_map *bmap);
2041 int isl_basic_map_is_empty(__isl_keep isl_basic_map *bmap);
2042 int isl_map_plain_is_empty(__isl_keep isl_map *map);
2043 int isl_map_is_empty(__isl_keep isl_map *map);
2044 int isl_union_map_is_empty(__isl_keep isl_union_map *umap);
2046 =item * Universality
2048 int isl_basic_set_is_universe(__isl_keep isl_basic_set *bset);
2049 int isl_basic_map_is_universe(__isl_keep isl_basic_map *bmap);
2050 int isl_set_plain_is_universe(__isl_keep isl_set *set);
2052 =item * Single-valuedness
2054 int isl_basic_map_is_single_valued(
2055 __isl_keep isl_basic_map *bmap);
2056 int isl_map_plain_is_single_valued(
2057 __isl_keep isl_map *map);
2058 int isl_map_is_single_valued(__isl_keep isl_map *map);
2059 int isl_union_map_is_single_valued(__isl_keep isl_union_map *umap);
2063 int isl_map_plain_is_injective(__isl_keep isl_map *map);
2064 int isl_map_is_injective(__isl_keep isl_map *map);
2065 int isl_union_map_plain_is_injective(
2066 __isl_keep isl_union_map *umap);
2067 int isl_union_map_is_injective(
2068 __isl_keep isl_union_map *umap);
2072 int isl_map_is_bijective(__isl_keep isl_map *map);
2073 int isl_union_map_is_bijective(__isl_keep isl_union_map *umap);
2077 int isl_basic_map_plain_is_fixed(
2078 __isl_keep isl_basic_map *bmap,
2079 enum isl_dim_type type, unsigned pos,
2081 int isl_set_plain_is_fixed(__isl_keep isl_set *set,
2082 enum isl_dim_type type, unsigned pos,
2084 int isl_map_plain_is_fixed(__isl_keep isl_map *map,
2085 enum isl_dim_type type, unsigned pos,
2088 Check if the relation obviously lies on a hyperplane where the given dimension
2089 has a fixed value and if so, return that value in C<*val>.
2091 __isl_give isl_val *
2092 isl_basic_map_plain_get_val_if_fixed(
2093 __isl_keep isl_basic_map *bmap,
2094 enum isl_dim_type type, unsigned pos);
2095 __isl_give isl_val *isl_set_plain_get_val_if_fixed(
2096 __isl_keep isl_set *set,
2097 enum isl_dim_type type, unsigned pos);
2098 __isl_give isl_val *isl_map_plain_get_val_if_fixed(
2099 __isl_keep isl_map *map,
2100 enum isl_dim_type type, unsigned pos);
2102 If the set or relation obviously lies on a hyperplane where the given dimension
2103 has a fixed value, then return that value.
2104 Otherwise return NaN.
2108 int isl_set_dim_residue_class_val(
2109 __isl_keep isl_set *set,
2110 int pos, __isl_give isl_val **modulo,
2111 __isl_give isl_val **residue);
2113 Check if the values of the given set dimension are equal to a fixed
2114 value modulo some integer value. If so, assign the modulo to C<*modulo>
2115 and the fixed value to C<*residue>. If the given dimension attains only
2116 a single value, then assign C<0> to C<*modulo> and the fixed value to
2118 If the dimension does not attain only a single value and if no modulo
2119 can be found then assign C<1> to C<*modulo> and C<1> to C<*residue>.
2123 To check whether a set is a parameter domain, use this function:
2125 int isl_set_is_params(__isl_keep isl_set *set);
2126 int isl_union_set_is_params(
2127 __isl_keep isl_union_set *uset);
2131 The following functions check whether the domain of the given
2132 (basic) set is a wrapped relation.
2134 int isl_basic_set_is_wrapping(
2135 __isl_keep isl_basic_set *bset);
2136 int isl_set_is_wrapping(__isl_keep isl_set *set);
2138 =item * Internal Product
2140 int isl_basic_map_can_zip(
2141 __isl_keep isl_basic_map *bmap);
2142 int isl_map_can_zip(__isl_keep isl_map *map);
2144 Check whether the product of domain and range of the given relation
2146 i.e., whether both domain and range are nested relations.
2150 int isl_basic_map_can_curry(
2151 __isl_keep isl_basic_map *bmap);
2152 int isl_map_can_curry(__isl_keep isl_map *map);
2154 Check whether the domain of the (basic) relation is a wrapped relation.
2156 int isl_basic_map_can_uncurry(
2157 __isl_keep isl_basic_map *bmap);
2158 int isl_map_can_uncurry(__isl_keep isl_map *map);
2160 Check whether the range of the (basic) relation is a wrapped relation.
2164 =head3 Binary Properties
2170 int isl_set_plain_is_equal(__isl_keep isl_set *set1,
2171 __isl_keep isl_set *set2);
2172 int isl_set_is_equal(__isl_keep isl_set *set1,
2173 __isl_keep isl_set *set2);
2174 int isl_union_set_is_equal(
2175 __isl_keep isl_union_set *uset1,
2176 __isl_keep isl_union_set *uset2);
2177 int isl_basic_map_is_equal(
2178 __isl_keep isl_basic_map *bmap1,
2179 __isl_keep isl_basic_map *bmap2);
2180 int isl_map_is_equal(__isl_keep isl_map *map1,
2181 __isl_keep isl_map *map2);
2182 int isl_map_plain_is_equal(__isl_keep isl_map *map1,
2183 __isl_keep isl_map *map2);
2184 int isl_union_map_is_equal(
2185 __isl_keep isl_union_map *umap1,
2186 __isl_keep isl_union_map *umap2);
2188 =item * Disjointness
2190 int isl_set_plain_is_disjoint(__isl_keep isl_set *set1,
2191 __isl_keep isl_set *set2);
2192 int isl_set_is_disjoint(__isl_keep isl_set *set1,
2193 __isl_keep isl_set *set2);
2194 int isl_map_is_disjoint(__isl_keep isl_map *map1,
2195 __isl_keep isl_map *map2);
2199 int isl_basic_set_is_subset(
2200 __isl_keep isl_basic_set *bset1,
2201 __isl_keep isl_basic_set *bset2);
2202 int isl_set_is_subset(__isl_keep isl_set *set1,
2203 __isl_keep isl_set *set2);
2204 int isl_set_is_strict_subset(
2205 __isl_keep isl_set *set1,
2206 __isl_keep isl_set *set2);
2207 int isl_union_set_is_subset(
2208 __isl_keep isl_union_set *uset1,
2209 __isl_keep isl_union_set *uset2);
2210 int isl_union_set_is_strict_subset(
2211 __isl_keep isl_union_set *uset1,
2212 __isl_keep isl_union_set *uset2);
2213 int isl_basic_map_is_subset(
2214 __isl_keep isl_basic_map *bmap1,
2215 __isl_keep isl_basic_map *bmap2);
2216 int isl_basic_map_is_strict_subset(
2217 __isl_keep isl_basic_map *bmap1,
2218 __isl_keep isl_basic_map *bmap2);
2219 int isl_map_is_subset(
2220 __isl_keep isl_map *map1,
2221 __isl_keep isl_map *map2);
2222 int isl_map_is_strict_subset(
2223 __isl_keep isl_map *map1,
2224 __isl_keep isl_map *map2);
2225 int isl_union_map_is_subset(
2226 __isl_keep isl_union_map *umap1,
2227 __isl_keep isl_union_map *umap2);
2228 int isl_union_map_is_strict_subset(
2229 __isl_keep isl_union_map *umap1,
2230 __isl_keep isl_union_map *umap2);
2232 Check whether the first argument is a (strict) subset of the
2237 int isl_set_plain_cmp(__isl_keep isl_set *set1,
2238 __isl_keep isl_set *set2);
2240 This function is useful for sorting C<isl_set>s.
2241 The order depends on the internal representation of the inputs.
2242 The order is fixed over different calls to the function (assuming
2243 the internal representation of the inputs has not changed), but may
2244 change over different versions of C<isl>.
2248 =head2 Unary Operations
2254 __isl_give isl_set *isl_set_complement(
2255 __isl_take isl_set *set);
2256 __isl_give isl_map *isl_map_complement(
2257 __isl_take isl_map *map);
2261 __isl_give isl_basic_map *isl_basic_map_reverse(
2262 __isl_take isl_basic_map *bmap);
2263 __isl_give isl_map *isl_map_reverse(
2264 __isl_take isl_map *map);
2265 __isl_give isl_union_map *isl_union_map_reverse(
2266 __isl_take isl_union_map *umap);
2270 __isl_give isl_basic_set *isl_basic_set_project_out(
2271 __isl_take isl_basic_set *bset,
2272 enum isl_dim_type type, unsigned first, unsigned n);
2273 __isl_give isl_basic_map *isl_basic_map_project_out(
2274 __isl_take isl_basic_map *bmap,
2275 enum isl_dim_type type, unsigned first, unsigned n);
2276 __isl_give isl_set *isl_set_project_out(__isl_take isl_set *set,
2277 enum isl_dim_type type, unsigned first, unsigned n);
2278 __isl_give isl_map *isl_map_project_out(__isl_take isl_map *map,
2279 enum isl_dim_type type, unsigned first, unsigned n);
2280 __isl_give isl_basic_set *isl_basic_set_params(
2281 __isl_take isl_basic_set *bset);
2282 __isl_give isl_basic_set *isl_basic_map_domain(
2283 __isl_take isl_basic_map *bmap);
2284 __isl_give isl_basic_set *isl_basic_map_range(
2285 __isl_take isl_basic_map *bmap);
2286 __isl_give isl_set *isl_set_params(__isl_take isl_set *set);
2287 __isl_give isl_set *isl_map_params(__isl_take isl_map *map);
2288 __isl_give isl_set *isl_map_domain(
2289 __isl_take isl_map *bmap);
2290 __isl_give isl_set *isl_map_range(
2291 __isl_take isl_map *map);
2292 __isl_give isl_set *isl_union_set_params(
2293 __isl_take isl_union_set *uset);
2294 __isl_give isl_set *isl_union_map_params(
2295 __isl_take isl_union_map *umap);
2296 __isl_give isl_union_set *isl_union_map_domain(
2297 __isl_take isl_union_map *umap);
2298 __isl_give isl_union_set *isl_union_map_range(
2299 __isl_take isl_union_map *umap);
2301 __isl_give isl_basic_map *isl_basic_map_domain_map(
2302 __isl_take isl_basic_map *bmap);
2303 __isl_give isl_basic_map *isl_basic_map_range_map(
2304 __isl_take isl_basic_map *bmap);
2305 __isl_give isl_map *isl_map_domain_map(__isl_take isl_map *map);
2306 __isl_give isl_map *isl_map_range_map(__isl_take isl_map *map);
2307 __isl_give isl_union_map *isl_union_map_domain_map(
2308 __isl_take isl_union_map *umap);
2309 __isl_give isl_union_map *isl_union_map_range_map(
2310 __isl_take isl_union_map *umap);
2312 The functions above construct a (basic, regular or union) relation
2313 that maps (a wrapped version of) the input relation to its domain or range.
2317 __isl_give isl_basic_set *isl_basic_set_eliminate(
2318 __isl_take isl_basic_set *bset,
2319 enum isl_dim_type type,
2320 unsigned first, unsigned n);
2321 __isl_give isl_set *isl_set_eliminate(
2322 __isl_take isl_set *set, enum isl_dim_type type,
2323 unsigned first, unsigned n);
2324 __isl_give isl_basic_map *isl_basic_map_eliminate(
2325 __isl_take isl_basic_map *bmap,
2326 enum isl_dim_type type,
2327 unsigned first, unsigned n);
2328 __isl_give isl_map *isl_map_eliminate(
2329 __isl_take isl_map *map, enum isl_dim_type type,
2330 unsigned first, unsigned n);
2332 Eliminate the coefficients for the given dimensions from the constraints,
2333 without removing the dimensions.
2337 __isl_give isl_basic_set *isl_basic_set_fix(
2338 __isl_take isl_basic_set *bset,
2339 enum isl_dim_type type, unsigned pos,
2341 __isl_give isl_basic_set *isl_basic_set_fix_si(
2342 __isl_take isl_basic_set *bset,
2343 enum isl_dim_type type, unsigned pos, int value);
2344 __isl_give isl_basic_set *isl_basic_set_fix_val(
2345 __isl_take isl_basic_set *bset,
2346 enum isl_dim_type type, unsigned pos,
2347 __isl_take isl_val *v);
2348 __isl_give isl_set *isl_set_fix(__isl_take isl_set *set,
2349 enum isl_dim_type type, unsigned pos,
2351 __isl_give isl_set *isl_set_fix_si(__isl_take isl_set *set,
2352 enum isl_dim_type type, unsigned pos, int value);
2353 __isl_give isl_set *isl_set_fix_val(
2354 __isl_take isl_set *set,
2355 enum isl_dim_type type, unsigned pos,
2356 __isl_take isl_val *v);
2357 __isl_give isl_basic_map *isl_basic_map_fix_si(
2358 __isl_take isl_basic_map *bmap,
2359 enum isl_dim_type type, unsigned pos, int value);
2360 __isl_give isl_basic_map *isl_basic_map_fix_val(
2361 __isl_take isl_basic_map *bmap,
2362 enum isl_dim_type type, unsigned pos,
2363 __isl_take isl_val *v);
2364 __isl_give isl_map *isl_map_fix(__isl_take isl_map *map,
2365 enum isl_dim_type type, unsigned pos,
2367 __isl_give isl_map *isl_map_fix_si(__isl_take isl_map *map,
2368 enum isl_dim_type type, unsigned pos, int value);
2369 __isl_give isl_map *isl_map_fix_val(
2370 __isl_take isl_map *map,
2371 enum isl_dim_type type, unsigned pos,
2372 __isl_take isl_val *v);
2374 Intersect the set or relation with the hyperplane where the given
2375 dimension has the fixed given value.
2377 __isl_give isl_basic_map *isl_basic_map_lower_bound_si(
2378 __isl_take isl_basic_map *bmap,
2379 enum isl_dim_type type, unsigned pos, int value);
2380 __isl_give isl_basic_map *isl_basic_map_upper_bound_si(
2381 __isl_take isl_basic_map *bmap,
2382 enum isl_dim_type type, unsigned pos, int value);
2383 __isl_give isl_set *isl_set_lower_bound(
2384 __isl_take isl_set *set,
2385 enum isl_dim_type type, unsigned pos,
2387 __isl_give isl_set *isl_set_lower_bound_si(
2388 __isl_take isl_set *set,
2389 enum isl_dim_type type, unsigned pos, int value);
2390 __isl_give isl_set *isl_set_lower_bound_val(
2391 __isl_take isl_set *set,
2392 enum isl_dim_type type, unsigned pos,
2393 __isl_take isl_val *value);
2394 __isl_give isl_map *isl_map_lower_bound_si(
2395 __isl_take isl_map *map,
2396 enum isl_dim_type type, unsigned pos, int value);
2397 __isl_give isl_set *isl_set_upper_bound(
2398 __isl_take isl_set *set,
2399 enum isl_dim_type type, unsigned pos,
2401 __isl_give isl_set *isl_set_upper_bound_si(
2402 __isl_take isl_set *set,
2403 enum isl_dim_type type, unsigned pos, int value);
2404 __isl_give isl_set *isl_set_upper_bound_val(
2405 __isl_take isl_set *set,
2406 enum isl_dim_type type, unsigned pos,
2407 __isl_take isl_val *value);
2408 __isl_give isl_map *isl_map_upper_bound_si(
2409 __isl_take isl_map *map,
2410 enum isl_dim_type type, unsigned pos, int value);
2412 Intersect the set or relation with the half-space where the given
2413 dimension has a value bounded by the fixed given integer value.
2415 __isl_give isl_set *isl_set_equate(__isl_take isl_set *set,
2416 enum isl_dim_type type1, int pos1,
2417 enum isl_dim_type type2, int pos2);
2418 __isl_give isl_basic_map *isl_basic_map_equate(
2419 __isl_take isl_basic_map *bmap,
2420 enum isl_dim_type type1, int pos1,
2421 enum isl_dim_type type2, int pos2);
2422 __isl_give isl_map *isl_map_equate(__isl_take isl_map *map,
2423 enum isl_dim_type type1, int pos1,
2424 enum isl_dim_type type2, int pos2);
2426 Intersect the set or relation with the hyperplane where the given
2427 dimensions are equal to each other.
2429 __isl_give isl_map *isl_map_oppose(__isl_take isl_map *map,
2430 enum isl_dim_type type1, int pos1,
2431 enum isl_dim_type type2, int pos2);
2433 Intersect the relation with the hyperplane where the given
2434 dimensions have opposite values.
2436 __isl_give isl_basic_map *isl_basic_map_order_ge(
2437 __isl_take isl_basic_map *bmap,
2438 enum isl_dim_type type1, int pos1,
2439 enum isl_dim_type type2, int pos2);
2440 __isl_give isl_map *isl_map_order_lt(__isl_take isl_map *map,
2441 enum isl_dim_type type1, int pos1,
2442 enum isl_dim_type type2, int pos2);
2443 __isl_give isl_basic_map *isl_basic_map_order_gt(
2444 __isl_take isl_basic_map *bmap,
2445 enum isl_dim_type type1, int pos1,
2446 enum isl_dim_type type2, int pos2);
2447 __isl_give isl_map *isl_map_order_gt(__isl_take isl_map *map,
2448 enum isl_dim_type type1, int pos1,
2449 enum isl_dim_type type2, int pos2);
2451 Intersect the relation with the half-space where the given
2452 dimensions satisfy the given ordering.
2456 __isl_give isl_map *isl_set_identity(
2457 __isl_take isl_set *set);
2458 __isl_give isl_union_map *isl_union_set_identity(
2459 __isl_take isl_union_set *uset);
2461 Construct an identity relation on the given (union) set.
2465 __isl_give isl_basic_set *isl_basic_map_deltas(
2466 __isl_take isl_basic_map *bmap);
2467 __isl_give isl_set *isl_map_deltas(__isl_take isl_map *map);
2468 __isl_give isl_union_set *isl_union_map_deltas(
2469 __isl_take isl_union_map *umap);
2471 These functions return a (basic) set containing the differences
2472 between image elements and corresponding domain elements in the input.
2474 __isl_give isl_basic_map *isl_basic_map_deltas_map(
2475 __isl_take isl_basic_map *bmap);
2476 __isl_give isl_map *isl_map_deltas_map(
2477 __isl_take isl_map *map);
2478 __isl_give isl_union_map *isl_union_map_deltas_map(
2479 __isl_take isl_union_map *umap);
2481 The functions above construct a (basic, regular or union) relation
2482 that maps (a wrapped version of) the input relation to its delta set.
2486 Simplify the representation of a set or relation by trying
2487 to combine pairs of basic sets or relations into a single
2488 basic set or relation.
2490 __isl_give isl_set *isl_set_coalesce(__isl_take isl_set *set);
2491 __isl_give isl_map *isl_map_coalesce(__isl_take isl_map *map);
2492 __isl_give isl_union_set *isl_union_set_coalesce(
2493 __isl_take isl_union_set *uset);
2494 __isl_give isl_union_map *isl_union_map_coalesce(
2495 __isl_take isl_union_map *umap);
2497 One of the methods for combining pairs of basic sets or relations
2498 can result in coefficients that are much larger than those that appear
2499 in the constraints of the input. By default, the coefficients are
2500 not allowed to grow larger, but this can be changed by unsetting
2501 the following option.
2503 int isl_options_set_coalesce_bounded_wrapping(
2504 isl_ctx *ctx, int val);
2505 int isl_options_get_coalesce_bounded_wrapping(
2508 =item * Detecting equalities
2510 __isl_give isl_basic_set *isl_basic_set_detect_equalities(
2511 __isl_take isl_basic_set *bset);
2512 __isl_give isl_basic_map *isl_basic_map_detect_equalities(
2513 __isl_take isl_basic_map *bmap);
2514 __isl_give isl_set *isl_set_detect_equalities(
2515 __isl_take isl_set *set);
2516 __isl_give isl_map *isl_map_detect_equalities(
2517 __isl_take isl_map *map);
2518 __isl_give isl_union_set *isl_union_set_detect_equalities(
2519 __isl_take isl_union_set *uset);
2520 __isl_give isl_union_map *isl_union_map_detect_equalities(
2521 __isl_take isl_union_map *umap);
2523 Simplify the representation of a set or relation by detecting implicit
2526 =item * Removing redundant constraints
2528 __isl_give isl_basic_set *isl_basic_set_remove_redundancies(
2529 __isl_take isl_basic_set *bset);
2530 __isl_give isl_set *isl_set_remove_redundancies(
2531 __isl_take isl_set *set);
2532 __isl_give isl_basic_map *isl_basic_map_remove_redundancies(
2533 __isl_take isl_basic_map *bmap);
2534 __isl_give isl_map *isl_map_remove_redundancies(
2535 __isl_take isl_map *map);
2539 __isl_give isl_basic_set *isl_set_convex_hull(
2540 __isl_take isl_set *set);
2541 __isl_give isl_basic_map *isl_map_convex_hull(
2542 __isl_take isl_map *map);
2544 If the input set or relation has any existentially quantified
2545 variables, then the result of these operations is currently undefined.
2549 __isl_give isl_basic_set *
2550 isl_set_unshifted_simple_hull(
2551 __isl_take isl_set *set);
2552 __isl_give isl_basic_map *
2553 isl_map_unshifted_simple_hull(
2554 __isl_take isl_map *map);
2555 __isl_give isl_basic_set *isl_set_simple_hull(
2556 __isl_take isl_set *set);
2557 __isl_give isl_basic_map *isl_map_simple_hull(
2558 __isl_take isl_map *map);
2559 __isl_give isl_union_map *isl_union_map_simple_hull(
2560 __isl_take isl_union_map *umap);
2562 These functions compute a single basic set or relation
2563 that contains the whole input set or relation.
2564 In particular, the output is described by translates
2565 of the constraints describing the basic sets or relations in the input.
2566 In case of C<isl_set_unshifted_simple_hull>, only the original
2567 constraints are used, without any translation.
2571 (See \autoref{s:simple hull}.)
2577 __isl_give isl_basic_set *isl_basic_set_affine_hull(
2578 __isl_take isl_basic_set *bset);
2579 __isl_give isl_basic_set *isl_set_affine_hull(
2580 __isl_take isl_set *set);
2581 __isl_give isl_union_set *isl_union_set_affine_hull(
2582 __isl_take isl_union_set *uset);
2583 __isl_give isl_basic_map *isl_basic_map_affine_hull(
2584 __isl_take isl_basic_map *bmap);
2585 __isl_give isl_basic_map *isl_map_affine_hull(
2586 __isl_take isl_map *map);
2587 __isl_give isl_union_map *isl_union_map_affine_hull(
2588 __isl_take isl_union_map *umap);
2590 In case of union sets and relations, the affine hull is computed
2593 =item * Polyhedral hull
2595 __isl_give isl_basic_set *isl_set_polyhedral_hull(
2596 __isl_take isl_set *set);
2597 __isl_give isl_basic_map *isl_map_polyhedral_hull(
2598 __isl_take isl_map *map);
2599 __isl_give isl_union_set *isl_union_set_polyhedral_hull(
2600 __isl_take isl_union_set *uset);
2601 __isl_give isl_union_map *isl_union_map_polyhedral_hull(
2602 __isl_take isl_union_map *umap);
2604 These functions compute a single basic set or relation
2605 not involving any existentially quantified variables
2606 that contains the whole input set or relation.
2607 In case of union sets and relations, the polyhedral hull is computed
2610 =item * Other approximations
2612 __isl_give isl_basic_set *
2613 isl_basic_set_drop_constraints_involving_dims(
2614 __isl_take isl_basic_set *bset,
2615 enum isl_dim_type type,
2616 unsigned first, unsigned n);
2617 __isl_give isl_basic_map *
2618 isl_basic_map_drop_constraints_involving_dims(
2619 __isl_take isl_basic_map *bmap,
2620 enum isl_dim_type type,
2621 unsigned first, unsigned n);
2622 __isl_give isl_basic_set *
2623 isl_basic_set_drop_constraints_not_involving_dims(
2624 __isl_take isl_basic_set *bset,
2625 enum isl_dim_type type,
2626 unsigned first, unsigned n);
2627 __isl_give isl_set *
2628 isl_set_drop_constraints_involving_dims(
2629 __isl_take isl_set *set,
2630 enum isl_dim_type type,
2631 unsigned first, unsigned n);
2632 __isl_give isl_map *
2633 isl_map_drop_constraints_involving_dims(
2634 __isl_take isl_map *map,
2635 enum isl_dim_type type,
2636 unsigned first, unsigned n);
2638 These functions drop any constraints (not) involving the specified dimensions.
2639 Note that the result depends on the representation of the input.
2643 __isl_give isl_basic_set *isl_basic_set_sample(
2644 __isl_take isl_basic_set *bset);
2645 __isl_give isl_basic_set *isl_set_sample(
2646 __isl_take isl_set *set);
2647 __isl_give isl_basic_map *isl_basic_map_sample(
2648 __isl_take isl_basic_map *bmap);
2649 __isl_give isl_basic_map *isl_map_sample(
2650 __isl_take isl_map *map);
2652 If the input (basic) set or relation is non-empty, then return
2653 a singleton subset of the input. Otherwise, return an empty set.
2655 =item * Optimization
2657 #include <isl/ilp.h>
2658 enum isl_lp_result isl_basic_set_max(
2659 __isl_keep isl_basic_set *bset,
2660 __isl_keep isl_aff *obj, isl_int *opt)
2661 __isl_give isl_val *isl_basic_set_max_val(
2662 __isl_keep isl_basic_set *bset,
2663 __isl_keep isl_aff *obj);
2664 enum isl_lp_result isl_set_min(__isl_keep isl_set *set,
2665 __isl_keep isl_aff *obj, isl_int *opt);
2666 __isl_give isl_val *isl_set_min_val(
2667 __isl_keep isl_set *set,
2668 __isl_keep isl_aff *obj);
2669 enum isl_lp_result isl_set_max(__isl_keep isl_set *set,
2670 __isl_keep isl_aff *obj, isl_int *opt);
2671 __isl_give isl_val *isl_set_max_val(
2672 __isl_keep isl_set *set,
2673 __isl_keep isl_aff *obj);
2675 Compute the minimum or maximum of the integer affine expression C<obj>
2676 over the points in C<set>, returning the result in C<opt>.
2677 The return value may be one of C<isl_lp_error>,
2678 C<isl_lp_ok>, C<isl_lp_unbounded> or C<isl_lp_empty>, in case of
2679 an C<isl_lp_result>. If the result is an C<isl_val> then
2680 the result is C<NULL> in case of an error, the optimal value in case
2681 there is one, negative infinity or infinity if the problem is unbounded and
2682 NaN if the problem is empty.
2684 =item * Parametric optimization
2686 __isl_give isl_pw_aff *isl_set_dim_min(
2687 __isl_take isl_set *set, int pos);
2688 __isl_give isl_pw_aff *isl_set_dim_max(
2689 __isl_take isl_set *set, int pos);
2690 __isl_give isl_pw_aff *isl_map_dim_max(
2691 __isl_take isl_map *map, int pos);
2693 Compute the minimum or maximum of the given set or output dimension
2694 as a function of the parameters (and input dimensions), but independently
2695 of the other set or output dimensions.
2696 For lexicographic optimization, see L<"Lexicographic Optimization">.
2700 The following functions compute either the set of (rational) coefficient
2701 values of valid constraints for the given set or the set of (rational)
2702 values satisfying the constraints with coefficients from the given set.
2703 Internally, these two sets of functions perform essentially the
2704 same operations, except that the set of coefficients is assumed to
2705 be a cone, while the set of values may be any polyhedron.
2706 The current implementation is based on the Farkas lemma and
2707 Fourier-Motzkin elimination, but this may change or be made optional
2708 in future. In particular, future implementations may use different
2709 dualization algorithms or skip the elimination step.
2711 __isl_give isl_basic_set *isl_basic_set_coefficients(
2712 __isl_take isl_basic_set *bset);
2713 __isl_give isl_basic_set *isl_set_coefficients(
2714 __isl_take isl_set *set);
2715 __isl_give isl_union_set *isl_union_set_coefficients(
2716 __isl_take isl_union_set *bset);
2717 __isl_give isl_basic_set *isl_basic_set_solutions(
2718 __isl_take isl_basic_set *bset);
2719 __isl_give isl_basic_set *isl_set_solutions(
2720 __isl_take isl_set *set);
2721 __isl_give isl_union_set *isl_union_set_solutions(
2722 __isl_take isl_union_set *bset);
2726 __isl_give isl_map *isl_map_fixed_power(
2727 __isl_take isl_map *map, isl_int exp);
2728 __isl_give isl_map *isl_map_fixed_power_val(
2729 __isl_take isl_map *map,
2730 __isl_take isl_val *exp);
2731 __isl_give isl_union_map *isl_union_map_fixed_power(
2732 __isl_take isl_union_map *umap, isl_int exp);
2733 __isl_give isl_union_map *
2734 isl_union_map_fixed_power_val(
2735 __isl_take isl_union_map *umap,
2736 __isl_take isl_val *exp);
2738 Compute the given power of C<map>, where C<exp> is assumed to be non-zero.
2739 If the exponent C<exp> is negative, then the -C<exp> th power of the inverse
2740 of C<map> is computed.
2742 __isl_give isl_map *isl_map_power(__isl_take isl_map *map,
2744 __isl_give isl_union_map *isl_union_map_power(
2745 __isl_take isl_union_map *umap, int *exact);
2747 Compute a parametric representation for all positive powers I<k> of C<map>.
2748 The result maps I<k> to a nested relation corresponding to the
2749 I<k>th power of C<map>.
2750 The result may be an overapproximation. If the result is known to be exact,
2751 then C<*exact> is set to C<1>.
2753 =item * Transitive closure
2755 __isl_give isl_map *isl_map_transitive_closure(
2756 __isl_take isl_map *map, int *exact);
2757 __isl_give isl_union_map *isl_union_map_transitive_closure(
2758 __isl_take isl_union_map *umap, int *exact);
2760 Compute the transitive closure of C<map>.
2761 The result may be an overapproximation. If the result is known to be exact,
2762 then C<*exact> is set to C<1>.
2764 =item * Reaching path lengths
2766 __isl_give isl_map *isl_map_reaching_path_lengths(
2767 __isl_take isl_map *map, int *exact);
2769 Compute a relation that maps each element in the range of C<map>
2770 to the lengths of all paths composed of edges in C<map> that
2771 end up in the given element.
2772 The result may be an overapproximation. If the result is known to be exact,
2773 then C<*exact> is set to C<1>.
2774 To compute the I<maximal> path length, the resulting relation
2775 should be postprocessed by C<isl_map_lexmax>.
2776 In particular, if the input relation is a dependence relation
2777 (mapping sources to sinks), then the maximal path length corresponds
2778 to the free schedule.
2779 Note, however, that C<isl_map_lexmax> expects the maximum to be
2780 finite, so if the path lengths are unbounded (possibly due to
2781 the overapproximation), then you will get an error message.
2785 __isl_give isl_basic_set *isl_basic_map_wrap(
2786 __isl_take isl_basic_map *bmap);
2787 __isl_give isl_set *isl_map_wrap(
2788 __isl_take isl_map *map);
2789 __isl_give isl_union_set *isl_union_map_wrap(
2790 __isl_take isl_union_map *umap);
2791 __isl_give isl_basic_map *isl_basic_set_unwrap(
2792 __isl_take isl_basic_set *bset);
2793 __isl_give isl_map *isl_set_unwrap(
2794 __isl_take isl_set *set);
2795 __isl_give isl_union_map *isl_union_set_unwrap(
2796 __isl_take isl_union_set *uset);
2800 Remove any internal structure of domain (and range) of the given
2801 set or relation. If there is any such internal structure in the input,
2802 then the name of the space is also removed.
2804 __isl_give isl_basic_set *isl_basic_set_flatten(
2805 __isl_take isl_basic_set *bset);
2806 __isl_give isl_set *isl_set_flatten(
2807 __isl_take isl_set *set);
2808 __isl_give isl_basic_map *isl_basic_map_flatten_domain(
2809 __isl_take isl_basic_map *bmap);
2810 __isl_give isl_basic_map *isl_basic_map_flatten_range(
2811 __isl_take isl_basic_map *bmap);
2812 __isl_give isl_map *isl_map_flatten_range(
2813 __isl_take isl_map *map);
2814 __isl_give isl_map *isl_map_flatten_domain(
2815 __isl_take isl_map *map);
2816 __isl_give isl_basic_map *isl_basic_map_flatten(
2817 __isl_take isl_basic_map *bmap);
2818 __isl_give isl_map *isl_map_flatten(
2819 __isl_take isl_map *map);
2821 __isl_give isl_map *isl_set_flatten_map(
2822 __isl_take isl_set *set);
2824 The function above constructs a relation
2825 that maps the input set to a flattened version of the set.
2829 Lift the input set to a space with extra dimensions corresponding
2830 to the existentially quantified variables in the input.
2831 In particular, the result lives in a wrapped map where the domain
2832 is the original space and the range corresponds to the original
2833 existentially quantified variables.
2835 __isl_give isl_basic_set *isl_basic_set_lift(
2836 __isl_take isl_basic_set *bset);
2837 __isl_give isl_set *isl_set_lift(
2838 __isl_take isl_set *set);
2839 __isl_give isl_union_set *isl_union_set_lift(
2840 __isl_take isl_union_set *uset);
2842 Given a local space that contains the existentially quantified
2843 variables of a set, a basic relation that, when applied to
2844 a basic set, has essentially the same effect as C<isl_basic_set_lift>,
2845 can be constructed using the following function.
2847 #include <isl/local_space.h>
2848 __isl_give isl_basic_map *isl_local_space_lifting(
2849 __isl_take isl_local_space *ls);
2851 =item * Internal Product
2853 __isl_give isl_basic_map *isl_basic_map_zip(
2854 __isl_take isl_basic_map *bmap);
2855 __isl_give isl_map *isl_map_zip(
2856 __isl_take isl_map *map);
2857 __isl_give isl_union_map *isl_union_map_zip(
2858 __isl_take isl_union_map *umap);
2860 Given a relation with nested relations for domain and range,
2861 interchange the range of the domain with the domain of the range.
2865 __isl_give isl_basic_map *isl_basic_map_curry(
2866 __isl_take isl_basic_map *bmap);
2867 __isl_give isl_basic_map *isl_basic_map_uncurry(
2868 __isl_take isl_basic_map *bmap);
2869 __isl_give isl_map *isl_map_curry(
2870 __isl_take isl_map *map);
2871 __isl_give isl_map *isl_map_uncurry(
2872 __isl_take isl_map *map);
2873 __isl_give isl_union_map *isl_union_map_curry(
2874 __isl_take isl_union_map *umap);
2875 __isl_give isl_union_map *isl_union_map_uncurry(
2876 __isl_take isl_union_map *umap);
2878 Given a relation with a nested relation for domain,
2879 the C<curry> functions
2880 move the range of the nested relation out of the domain
2881 and use it as the domain of a nested relation in the range,
2882 with the original range as range of this nested relation.
2883 The C<uncurry> functions perform the inverse operation.
2885 =item * Aligning parameters
2887 __isl_give isl_basic_set *isl_basic_set_align_params(
2888 __isl_take isl_basic_set *bset,
2889 __isl_take isl_space *model);
2890 __isl_give isl_set *isl_set_align_params(
2891 __isl_take isl_set *set,
2892 __isl_take isl_space *model);
2893 __isl_give isl_basic_map *isl_basic_map_align_params(
2894 __isl_take isl_basic_map *bmap,
2895 __isl_take isl_space *model);
2896 __isl_give isl_map *isl_map_align_params(
2897 __isl_take isl_map *map,
2898 __isl_take isl_space *model);
2900 Change the order of the parameters of the given set or relation
2901 such that the first parameters match those of C<model>.
2902 This may involve the introduction of extra parameters.
2903 All parameters need to be named.
2905 =item * Dimension manipulation
2907 __isl_give isl_basic_set *isl_basic_set_add_dims(
2908 __isl_take isl_basic_set *bset,
2909 enum isl_dim_type type, unsigned n);
2910 __isl_give isl_set *isl_set_add_dims(
2911 __isl_take isl_set *set,
2912 enum isl_dim_type type, unsigned n);
2913 __isl_give isl_map *isl_map_add_dims(
2914 __isl_take isl_map *map,
2915 enum isl_dim_type type, unsigned n);
2916 __isl_give isl_basic_set *isl_basic_set_insert_dims(
2917 __isl_take isl_basic_set *bset,
2918 enum isl_dim_type type, unsigned pos,
2920 __isl_give isl_basic_map *isl_basic_map_insert_dims(
2921 __isl_take isl_basic_map *bmap,
2922 enum isl_dim_type type, unsigned pos,
2924 __isl_give isl_set *isl_set_insert_dims(
2925 __isl_take isl_set *set,
2926 enum isl_dim_type type, unsigned pos, unsigned n);
2927 __isl_give isl_map *isl_map_insert_dims(
2928 __isl_take isl_map *map,
2929 enum isl_dim_type type, unsigned pos, unsigned n);
2930 __isl_give isl_basic_set *isl_basic_set_move_dims(
2931 __isl_take isl_basic_set *bset,
2932 enum isl_dim_type dst_type, unsigned dst_pos,
2933 enum isl_dim_type src_type, unsigned src_pos,
2935 __isl_give isl_basic_map *isl_basic_map_move_dims(
2936 __isl_take isl_basic_map *bmap,
2937 enum isl_dim_type dst_type, unsigned dst_pos,
2938 enum isl_dim_type src_type, unsigned src_pos,
2940 __isl_give isl_set *isl_set_move_dims(
2941 __isl_take isl_set *set,
2942 enum isl_dim_type dst_type, unsigned dst_pos,
2943 enum isl_dim_type src_type, unsigned src_pos,
2945 __isl_give isl_map *isl_map_move_dims(
2946 __isl_take isl_map *map,
2947 enum isl_dim_type dst_type, unsigned dst_pos,
2948 enum isl_dim_type src_type, unsigned src_pos,
2951 It is usually not advisable to directly change the (input or output)
2952 space of a set or a relation as this removes the name and the internal
2953 structure of the space. However, the above functions can be useful
2954 to add new parameters, assuming
2955 C<isl_set_align_params> and C<isl_map_align_params>
2960 =head2 Binary Operations
2962 The two arguments of a binary operation not only need to live
2963 in the same C<isl_ctx>, they currently also need to have
2964 the same (number of) parameters.
2966 =head3 Basic Operations
2970 =item * Intersection
2972 __isl_give isl_basic_set *isl_basic_set_intersect_params(
2973 __isl_take isl_basic_set *bset1,
2974 __isl_take isl_basic_set *bset2);
2975 __isl_give isl_basic_set *isl_basic_set_intersect(
2976 __isl_take isl_basic_set *bset1,
2977 __isl_take isl_basic_set *bset2);
2978 __isl_give isl_set *isl_set_intersect_params(
2979 __isl_take isl_set *set,
2980 __isl_take isl_set *params);
2981 __isl_give isl_set *isl_set_intersect(
2982 __isl_take isl_set *set1,
2983 __isl_take isl_set *set2);
2984 __isl_give isl_union_set *isl_union_set_intersect_params(
2985 __isl_take isl_union_set *uset,
2986 __isl_take isl_set *set);
2987 __isl_give isl_union_map *isl_union_map_intersect_params(
2988 __isl_take isl_union_map *umap,
2989 __isl_take isl_set *set);
2990 __isl_give isl_union_set *isl_union_set_intersect(
2991 __isl_take isl_union_set *uset1,
2992 __isl_take isl_union_set *uset2);
2993 __isl_give isl_basic_map *isl_basic_map_intersect_domain(
2994 __isl_take isl_basic_map *bmap,
2995 __isl_take isl_basic_set *bset);
2996 __isl_give isl_basic_map *isl_basic_map_intersect_range(
2997 __isl_take isl_basic_map *bmap,
2998 __isl_take isl_basic_set *bset);
2999 __isl_give isl_basic_map *isl_basic_map_intersect(
3000 __isl_take isl_basic_map *bmap1,
3001 __isl_take isl_basic_map *bmap2);
3002 __isl_give isl_map *isl_map_intersect_params(
3003 __isl_take isl_map *map,
3004 __isl_take isl_set *params);
3005 __isl_give isl_map *isl_map_intersect_domain(
3006 __isl_take isl_map *map,
3007 __isl_take isl_set *set);
3008 __isl_give isl_map *isl_map_intersect_range(
3009 __isl_take isl_map *map,
3010 __isl_take isl_set *set);
3011 __isl_give isl_map *isl_map_intersect(
3012 __isl_take isl_map *map1,
3013 __isl_take isl_map *map2);
3014 __isl_give isl_union_map *isl_union_map_intersect_domain(
3015 __isl_take isl_union_map *umap,
3016 __isl_take isl_union_set *uset);
3017 __isl_give isl_union_map *isl_union_map_intersect_range(
3018 __isl_take isl_union_map *umap,
3019 __isl_take isl_union_set *uset);
3020 __isl_give isl_union_map *isl_union_map_intersect(
3021 __isl_take isl_union_map *umap1,
3022 __isl_take isl_union_map *umap2);
3024 The second argument to the C<_params> functions needs to be
3025 a parametric (basic) set. For the other functions, a parametric set
3026 for either argument is only allowed if the other argument is
3027 a parametric set as well.
3031 __isl_give isl_set *isl_basic_set_union(
3032 __isl_take isl_basic_set *bset1,
3033 __isl_take isl_basic_set *bset2);
3034 __isl_give isl_map *isl_basic_map_union(
3035 __isl_take isl_basic_map *bmap1,
3036 __isl_take isl_basic_map *bmap2);
3037 __isl_give isl_set *isl_set_union(
3038 __isl_take isl_set *set1,
3039 __isl_take isl_set *set2);
3040 __isl_give isl_map *isl_map_union(
3041 __isl_take isl_map *map1,
3042 __isl_take isl_map *map2);
3043 __isl_give isl_union_set *isl_union_set_union(
3044 __isl_take isl_union_set *uset1,
3045 __isl_take isl_union_set *uset2);
3046 __isl_give isl_union_map *isl_union_map_union(
3047 __isl_take isl_union_map *umap1,
3048 __isl_take isl_union_map *umap2);
3050 =item * Set difference
3052 __isl_give isl_set *isl_set_subtract(
3053 __isl_take isl_set *set1,
3054 __isl_take isl_set *set2);
3055 __isl_give isl_map *isl_map_subtract(
3056 __isl_take isl_map *map1,
3057 __isl_take isl_map *map2);
3058 __isl_give isl_map *isl_map_subtract_domain(
3059 __isl_take isl_map *map,
3060 __isl_take isl_set *dom);
3061 __isl_give isl_map *isl_map_subtract_range(
3062 __isl_take isl_map *map,
3063 __isl_take isl_set *dom);
3064 __isl_give isl_union_set *isl_union_set_subtract(
3065 __isl_take isl_union_set *uset1,
3066 __isl_take isl_union_set *uset2);
3067 __isl_give isl_union_map *isl_union_map_subtract(
3068 __isl_take isl_union_map *umap1,
3069 __isl_take isl_union_map *umap2);
3070 __isl_give isl_union_map *isl_union_map_subtract_domain(
3071 __isl_take isl_union_map *umap,
3072 __isl_take isl_union_set *dom);
3073 __isl_give isl_union_map *isl_union_map_subtract_range(
3074 __isl_take isl_union_map *umap,
3075 __isl_take isl_union_set *dom);
3079 __isl_give isl_basic_set *isl_basic_set_apply(
3080 __isl_take isl_basic_set *bset,
3081 __isl_take isl_basic_map *bmap);
3082 __isl_give isl_set *isl_set_apply(
3083 __isl_take isl_set *set,
3084 __isl_take isl_map *map);
3085 __isl_give isl_union_set *isl_union_set_apply(
3086 __isl_take isl_union_set *uset,
3087 __isl_take isl_union_map *umap);
3088 __isl_give isl_basic_map *isl_basic_map_apply_domain(
3089 __isl_take isl_basic_map *bmap1,
3090 __isl_take isl_basic_map *bmap2);
3091 __isl_give isl_basic_map *isl_basic_map_apply_range(
3092 __isl_take isl_basic_map *bmap1,
3093 __isl_take isl_basic_map *bmap2);
3094 __isl_give isl_map *isl_map_apply_domain(
3095 __isl_take isl_map *map1,
3096 __isl_take isl_map *map2);
3097 __isl_give isl_union_map *isl_union_map_apply_domain(
3098 __isl_take isl_union_map *umap1,
3099 __isl_take isl_union_map *umap2);
3100 __isl_give isl_map *isl_map_apply_range(
3101 __isl_take isl_map *map1,
3102 __isl_take isl_map *map2);
3103 __isl_give isl_union_map *isl_union_map_apply_range(
3104 __isl_take isl_union_map *umap1,
3105 __isl_take isl_union_map *umap2);
3109 __isl_give isl_basic_set *
3110 isl_basic_set_preimage_multi_aff(
3111 __isl_take isl_basic_set *bset,
3112 __isl_take isl_multi_aff *ma);
3113 __isl_give isl_set *isl_set_preimage_multi_aff(
3114 __isl_take isl_set *set,
3115 __isl_take isl_multi_aff *ma);
3116 __isl_give isl_set *isl_set_preimage_pw_multi_aff(
3117 __isl_take isl_set *set,
3118 __isl_take isl_pw_multi_aff *pma);
3119 __isl_give isl_map *isl_map_preimage_domain_multi_aff(
3120 __isl_take isl_map *map,
3121 __isl_take isl_multi_aff *ma);
3122 __isl_give isl_union_map *
3123 isl_union_map_preimage_domain_multi_aff(
3124 __isl_take isl_union_map *umap,
3125 __isl_take isl_multi_aff *ma);
3127 These functions compute the preimage of the given set or map domain under
3128 the given function. In other words, the expression is plugged
3129 into the set description or into the domain of the map.
3130 Objects of types C<isl_multi_aff> and C<isl_pw_multi_aff> are described in
3131 L</"Piecewise Multiple Quasi Affine Expressions">.
3133 =item * Cartesian Product
3135 __isl_give isl_set *isl_set_product(
3136 __isl_take isl_set *set1,
3137 __isl_take isl_set *set2);
3138 __isl_give isl_union_set *isl_union_set_product(
3139 __isl_take isl_union_set *uset1,
3140 __isl_take isl_union_set *uset2);
3141 __isl_give isl_basic_map *isl_basic_map_domain_product(
3142 __isl_take isl_basic_map *bmap1,
3143 __isl_take isl_basic_map *bmap2);
3144 __isl_give isl_basic_map *isl_basic_map_range_product(
3145 __isl_take isl_basic_map *bmap1,
3146 __isl_take isl_basic_map *bmap2);
3147 __isl_give isl_basic_map *isl_basic_map_product(
3148 __isl_take isl_basic_map *bmap1,
3149 __isl_take isl_basic_map *bmap2);
3150 __isl_give isl_map *isl_map_domain_product(
3151 __isl_take isl_map *map1,
3152 __isl_take isl_map *map2);
3153 __isl_give isl_map *isl_map_range_product(
3154 __isl_take isl_map *map1,
3155 __isl_take isl_map *map2);
3156 __isl_give isl_union_map *isl_union_map_domain_product(
3157 __isl_take isl_union_map *umap1,
3158 __isl_take isl_union_map *umap2);
3159 __isl_give isl_union_map *isl_union_map_range_product(
3160 __isl_take isl_union_map *umap1,
3161 __isl_take isl_union_map *umap2);
3162 __isl_give isl_map *isl_map_product(
3163 __isl_take isl_map *map1,
3164 __isl_take isl_map *map2);
3165 __isl_give isl_union_map *isl_union_map_product(
3166 __isl_take isl_union_map *umap1,
3167 __isl_take isl_union_map *umap2);
3169 The above functions compute the cross product of the given
3170 sets or relations. The domains and ranges of the results
3171 are wrapped maps between domains and ranges of the inputs.
3172 To obtain a ``flat'' product, use the following functions
3175 __isl_give isl_basic_set *isl_basic_set_flat_product(
3176 __isl_take isl_basic_set *bset1,
3177 __isl_take isl_basic_set *bset2);
3178 __isl_give isl_set *isl_set_flat_product(
3179 __isl_take isl_set *set1,
3180 __isl_take isl_set *set2);
3181 __isl_give isl_basic_map *isl_basic_map_flat_range_product(
3182 __isl_take isl_basic_map *bmap1,
3183 __isl_take isl_basic_map *bmap2);
3184 __isl_give isl_map *isl_map_flat_domain_product(
3185 __isl_take isl_map *map1,
3186 __isl_take isl_map *map2);
3187 __isl_give isl_map *isl_map_flat_range_product(
3188 __isl_take isl_map *map1,
3189 __isl_take isl_map *map2);
3190 __isl_give isl_union_map *isl_union_map_flat_range_product(
3191 __isl_take isl_union_map *umap1,
3192 __isl_take isl_union_map *umap2);
3193 __isl_give isl_basic_map *isl_basic_map_flat_product(
3194 __isl_take isl_basic_map *bmap1,
3195 __isl_take isl_basic_map *bmap2);
3196 __isl_give isl_map *isl_map_flat_product(
3197 __isl_take isl_map *map1,
3198 __isl_take isl_map *map2);
3200 =item * Simplification
3202 __isl_give isl_basic_set *isl_basic_set_gist(
3203 __isl_take isl_basic_set *bset,
3204 __isl_take isl_basic_set *context);
3205 __isl_give isl_set *isl_set_gist(__isl_take isl_set *set,
3206 __isl_take isl_set *context);
3207 __isl_give isl_set *isl_set_gist_params(
3208 __isl_take isl_set *set,
3209 __isl_take isl_set *context);
3210 __isl_give isl_union_set *isl_union_set_gist(
3211 __isl_take isl_union_set *uset,
3212 __isl_take isl_union_set *context);
3213 __isl_give isl_union_set *isl_union_set_gist_params(
3214 __isl_take isl_union_set *uset,
3215 __isl_take isl_set *set);
3216 __isl_give isl_basic_map *isl_basic_map_gist(
3217 __isl_take isl_basic_map *bmap,
3218 __isl_take isl_basic_map *context);
3219 __isl_give isl_map *isl_map_gist(__isl_take isl_map *map,
3220 __isl_take isl_map *context);
3221 __isl_give isl_map *isl_map_gist_params(
3222 __isl_take isl_map *map,
3223 __isl_take isl_set *context);
3224 __isl_give isl_map *isl_map_gist_domain(
3225 __isl_take isl_map *map,
3226 __isl_take isl_set *context);
3227 __isl_give isl_map *isl_map_gist_range(
3228 __isl_take isl_map *map,
3229 __isl_take isl_set *context);
3230 __isl_give isl_union_map *isl_union_map_gist(
3231 __isl_take isl_union_map *umap,
3232 __isl_take isl_union_map *context);
3233 __isl_give isl_union_map *isl_union_map_gist_params(
3234 __isl_take isl_union_map *umap,
3235 __isl_take isl_set *set);
3236 __isl_give isl_union_map *isl_union_map_gist_domain(
3237 __isl_take isl_union_map *umap,
3238 __isl_take isl_union_set *uset);
3239 __isl_give isl_union_map *isl_union_map_gist_range(
3240 __isl_take isl_union_map *umap,
3241 __isl_take isl_union_set *uset);
3243 The gist operation returns a set or relation that has the
3244 same intersection with the context as the input set or relation.
3245 Any implicit equality in the intersection is made explicit in the result,
3246 while all inequalities that are redundant with respect to the intersection
3248 In case of union sets and relations, the gist operation is performed
3253 =head3 Lexicographic Optimization
3255 Given a (basic) set C<set> (or C<bset>) and a zero-dimensional domain C<dom>,
3256 the following functions
3257 compute a set that contains the lexicographic minimum or maximum
3258 of the elements in C<set> (or C<bset>) for those values of the parameters
3259 that satisfy C<dom>.
3260 If C<empty> is not C<NULL>, then C<*empty> is assigned a set
3261 that contains the parameter values in C<dom> for which C<set> (or C<bset>)
3263 In other words, the union of the parameter values
3264 for which the result is non-empty and of C<*empty>
3267 __isl_give isl_set *isl_basic_set_partial_lexmin(
3268 __isl_take isl_basic_set *bset,
3269 __isl_take isl_basic_set *dom,
3270 __isl_give isl_set **empty);
3271 __isl_give isl_set *isl_basic_set_partial_lexmax(
3272 __isl_take isl_basic_set *bset,
3273 __isl_take isl_basic_set *dom,
3274 __isl_give isl_set **empty);
3275 __isl_give isl_set *isl_set_partial_lexmin(
3276 __isl_take isl_set *set, __isl_take isl_set *dom,
3277 __isl_give isl_set **empty);
3278 __isl_give isl_set *isl_set_partial_lexmax(
3279 __isl_take isl_set *set, __isl_take isl_set *dom,
3280 __isl_give isl_set **empty);
3282 Given a (basic) set C<set> (or C<bset>), the following functions simply
3283 return a set containing the lexicographic minimum or maximum
3284 of the elements in C<set> (or C<bset>).
3285 In case of union sets, the optimum is computed per space.
3287 __isl_give isl_set *isl_basic_set_lexmin(
3288 __isl_take isl_basic_set *bset);
3289 __isl_give isl_set *isl_basic_set_lexmax(
3290 __isl_take isl_basic_set *bset);
3291 __isl_give isl_set *isl_set_lexmin(
3292 __isl_take isl_set *set);
3293 __isl_give isl_set *isl_set_lexmax(
3294 __isl_take isl_set *set);
3295 __isl_give isl_union_set *isl_union_set_lexmin(
3296 __isl_take isl_union_set *uset);
3297 __isl_give isl_union_set *isl_union_set_lexmax(
3298 __isl_take isl_union_set *uset);
3300 Given a (basic) relation C<map> (or C<bmap>) and a domain C<dom>,
3301 the following functions
3302 compute a relation that maps each element of C<dom>
3303 to the single lexicographic minimum or maximum
3304 of the elements that are associated to that same
3305 element in C<map> (or C<bmap>).
3306 If C<empty> is not C<NULL>, then C<*empty> is assigned a set
3307 that contains the elements in C<dom> that do not map
3308 to any elements in C<map> (or C<bmap>).
3309 In other words, the union of the domain of the result and of C<*empty>
3312 __isl_give isl_map *isl_basic_map_partial_lexmax(
3313 __isl_take isl_basic_map *bmap,
3314 __isl_take isl_basic_set *dom,
3315 __isl_give isl_set **empty);
3316 __isl_give isl_map *isl_basic_map_partial_lexmin(
3317 __isl_take isl_basic_map *bmap,
3318 __isl_take isl_basic_set *dom,
3319 __isl_give isl_set **empty);
3320 __isl_give isl_map *isl_map_partial_lexmax(
3321 __isl_take isl_map *map, __isl_take isl_set *dom,
3322 __isl_give isl_set **empty);
3323 __isl_give isl_map *isl_map_partial_lexmin(
3324 __isl_take isl_map *map, __isl_take isl_set *dom,
3325 __isl_give isl_set **empty);
3327 Given a (basic) map C<map> (or C<bmap>), the following functions simply
3328 return a map mapping each element in the domain of
3329 C<map> (or C<bmap>) to the lexicographic minimum or maximum
3330 of all elements associated to that element.
3331 In case of union relations, the optimum is computed per space.
3333 __isl_give isl_map *isl_basic_map_lexmin(
3334 __isl_take isl_basic_map *bmap);
3335 __isl_give isl_map *isl_basic_map_lexmax(
3336 __isl_take isl_basic_map *bmap);
3337 __isl_give isl_map *isl_map_lexmin(
3338 __isl_take isl_map *map);
3339 __isl_give isl_map *isl_map_lexmax(
3340 __isl_take isl_map *map);
3341 __isl_give isl_union_map *isl_union_map_lexmin(
3342 __isl_take isl_union_map *umap);
3343 __isl_give isl_union_map *isl_union_map_lexmax(
3344 __isl_take isl_union_map *umap);
3346 The following functions return their result in the form of
3347 a piecewise multi-affine expression
3348 (See L<"Piecewise Multiple Quasi Affine Expressions">),
3349 but are otherwise equivalent to the corresponding functions
3350 returning a basic set or relation.
3352 __isl_give isl_pw_multi_aff *
3353 isl_basic_map_lexmin_pw_multi_aff(
3354 __isl_take isl_basic_map *bmap);
3355 __isl_give isl_pw_multi_aff *
3356 isl_basic_set_partial_lexmin_pw_multi_aff(
3357 __isl_take isl_basic_set *bset,
3358 __isl_take isl_basic_set *dom,
3359 __isl_give isl_set **empty);
3360 __isl_give isl_pw_multi_aff *
3361 isl_basic_set_partial_lexmax_pw_multi_aff(
3362 __isl_take isl_basic_set *bset,
3363 __isl_take isl_basic_set *dom,
3364 __isl_give isl_set **empty);
3365 __isl_give isl_pw_multi_aff *
3366 isl_basic_map_partial_lexmin_pw_multi_aff(
3367 __isl_take isl_basic_map *bmap,
3368 __isl_take isl_basic_set *dom,
3369 __isl_give isl_set **empty);
3370 __isl_give isl_pw_multi_aff *
3371 isl_basic_map_partial_lexmax_pw_multi_aff(
3372 __isl_take isl_basic_map *bmap,
3373 __isl_take isl_basic_set *dom,
3374 __isl_give isl_set **empty);
3375 __isl_give isl_pw_multi_aff *isl_set_lexmin_pw_multi_aff(
3376 __isl_take isl_set *set);
3377 __isl_give isl_pw_multi_aff *isl_set_lexmax_pw_multi_aff(
3378 __isl_take isl_set *set);
3379 __isl_give isl_pw_multi_aff *isl_map_lexmin_pw_multi_aff(
3380 __isl_take isl_map *map);
3381 __isl_give isl_pw_multi_aff *isl_map_lexmax_pw_multi_aff(
3382 __isl_take isl_map *map);
3386 Lists are defined over several element types, including
3387 C<isl_val>, C<isl_id>, C<isl_aff>, C<isl_pw_aff>, C<isl_constraint>,
3388 C<isl_basic_set>, C<isl_set>, C<isl_ast_expr> and C<isl_ast_node>.
3389 Here we take lists of C<isl_set>s as an example.
3390 Lists can be created, copied, modified and freed using the following functions.
3392 #include <isl/list.h>
3393 __isl_give isl_set_list *isl_set_list_from_set(
3394 __isl_take isl_set *el);
3395 __isl_give isl_set_list *isl_set_list_alloc(
3396 isl_ctx *ctx, int n);
3397 __isl_give isl_set_list *isl_set_list_copy(
3398 __isl_keep isl_set_list *list);
3399 __isl_give isl_set_list *isl_set_list_insert(
3400 __isl_take isl_set_list *list, unsigned pos,
3401 __isl_take isl_set *el);
3402 __isl_give isl_set_list *isl_set_list_add(
3403 __isl_take isl_set_list *list,
3404 __isl_take isl_set *el);
3405 __isl_give isl_set_list *isl_set_list_drop(
3406 __isl_take isl_set_list *list,
3407 unsigned first, unsigned n);
3408 __isl_give isl_set_list *isl_set_list_set_set(
3409 __isl_take isl_set_list *list, int index,
3410 __isl_take isl_set *set);
3411 __isl_give isl_set_list *isl_set_list_concat(
3412 __isl_take isl_set_list *list1,
3413 __isl_take isl_set_list *list2);
3414 __isl_give isl_set_list *isl_set_list_sort(
3415 __isl_take isl_set_list *list,
3416 int (*cmp)(__isl_keep isl_set *a,
3417 __isl_keep isl_set *b, void *user),
3419 void *isl_set_list_free(__isl_take isl_set_list *list);
3421 C<isl_set_list_alloc> creates an empty list with a capacity for
3422 C<n> elements. C<isl_set_list_from_set> creates a list with a single
3425 Lists can be inspected using the following functions.
3427 #include <isl/list.h>
3428 isl_ctx *isl_set_list_get_ctx(__isl_keep isl_set_list *list);
3429 int isl_set_list_n_set(__isl_keep isl_set_list *list);
3430 __isl_give isl_set *isl_set_list_get_set(
3431 __isl_keep isl_set_list *list, int index);
3432 int isl_set_list_foreach(__isl_keep isl_set_list *list,
3433 int (*fn)(__isl_take isl_set *el, void *user),
3435 int isl_set_list_foreach_scc(__isl_keep isl_set_list *list,
3436 int (*follows)(__isl_keep isl_set *a,
3437 __isl_keep isl_set *b, void *user),
3439 int (*fn)(__isl_take isl_set *el, void *user),
3442 The function C<isl_set_list_foreach_scc> calls C<fn> on each of the
3443 strongly connected components of the graph with as vertices the elements
3444 of C<list> and a directed edge from vertex C<b> to vertex C<a>
3445 iff C<follows(a, b)> returns C<1>. The callbacks C<follows> and C<fn>
3446 should return C<-1> on error.
3448 Lists can be printed using
3450 #include <isl/list.h>
3451 __isl_give isl_printer *isl_printer_print_set_list(
3452 __isl_take isl_printer *p,
3453 __isl_keep isl_set_list *list);
3455 =head2 Multiple Values
3457 An C<isl_multi_val> object represents a sequence of zero or more values,
3458 living in a set space.
3460 An C<isl_multi_val> can be constructed from an C<isl_val_list>
3461 using the following function
3463 #include <isl/val.h>
3464 __isl_give isl_multi_val *isl_multi_val_from_val_list(
3465 __isl_take isl_space *space,
3466 __isl_take isl_val_list *list);
3468 The zero multiple value (with value zero for each set dimension)
3469 can be created using the following function.
3471 #include <isl/val.h>
3472 __isl_give isl_multi_val *isl_multi_val_zero(
3473 __isl_take isl_space *space);
3475 Multiple values can be copied and freed using
3477 #include <isl/val.h>
3478 __isl_give isl_multi_val *isl_multi_val_copy(
3479 __isl_keep isl_multi_val *mv);
3480 void *isl_multi_val_free(__isl_take isl_multi_val *mv);
3482 They can be inspected using
3484 #include <isl/val.h>
3485 isl_ctx *isl_multi_val_get_ctx(
3486 __isl_keep isl_multi_val *mv);
3487 unsigned isl_multi_val_dim(__isl_keep isl_multi_val *mv,
3488 enum isl_dim_type type);
3489 __isl_give isl_val *isl_multi_val_get_val(
3490 __isl_keep isl_multi_val *mv, int pos);
3491 const char *isl_multi_val_get_tuple_name(
3492 __isl_keep isl_multi_val *mv,
3493 enum isl_dim_type type);
3495 They can be modified using
3497 #include <isl/val.h>
3498 __isl_give isl_multi_val *isl_multi_val_set_val(
3499 __isl_take isl_multi_val *mv, int pos,
3500 __isl_take isl_val *val);
3501 __isl_give isl_multi_val *isl_multi_val_set_dim_name(
3502 __isl_take isl_multi_val *mv,
3503 enum isl_dim_type type, unsigned pos, const char *s);
3504 __isl_give isl_multi_val *isl_multi_val_set_tuple_name(
3505 __isl_take isl_multi_val *mv,
3506 enum isl_dim_type type, const char *s);
3507 __isl_give isl_multi_val *isl_multi_val_set_tuple_id(
3508 __isl_take isl_multi_val *mv,
3509 enum isl_dim_type type, __isl_take isl_id *id);
3511 __isl_give isl_multi_val *isl_multi_val_insert_dims(
3512 __isl_take isl_multi_val *mv,
3513 enum isl_dim_type type, unsigned first, unsigned n);
3514 __isl_give isl_multi_val *isl_multi_val_add_dims(
3515 __isl_take isl_multi_val *mv,
3516 enum isl_dim_type type, unsigned n);
3517 __isl_give isl_multi_val *isl_multi_val_drop_dims(
3518 __isl_take isl_multi_val *mv,
3519 enum isl_dim_type type, unsigned first, unsigned n);
3523 #include <isl/val.h>
3524 __isl_give isl_multi_val *isl_multi_val_align_params(
3525 __isl_take isl_multi_val *mv,
3526 __isl_take isl_space *model);
3527 __isl_give isl_multi_val *isl_multi_val_range_splice(
3528 __isl_take isl_multi_val *mv1, unsigned pos,
3529 __isl_take isl_multi_val *mv2);
3530 __isl_give isl_multi_val *isl_multi_val_range_product(
3531 __isl_take isl_multi_val *mv1,
3532 __isl_take isl_multi_val *mv2);
3533 __isl_give isl_multi_val *isl_multi_val_flat_range_product(
3534 __isl_take isl_multi_val *mv1,
3535 __isl_take isl_multi_aff *mv2);
3536 __isl_give isl_multi_val *isl_multi_val_add_val(
3537 __isl_take isl_multi_val *mv,
3538 __isl_take isl_val *v);
3539 __isl_give isl_multi_val *isl_multi_val_mod_val(
3540 __isl_take isl_multi_val *mv,
3541 __isl_take isl_val *v);
3542 __isl_give isl_multi_val *isl_multi_val_scale_val(
3543 __isl_take isl_multi_val *mv,
3544 __isl_take isl_val *v);
3545 __isl_give isl_multi_val *isl_multi_val_scale_multi_val(
3546 __isl_take isl_multi_val *mv1,
3547 __isl_take isl_multi_val *mv2);
3551 Vectors can be created, copied and freed using the following functions.
3553 #include <isl/vec.h>
3554 __isl_give isl_vec *isl_vec_alloc(isl_ctx *ctx,
3556 __isl_give isl_vec *isl_vec_copy(__isl_keep isl_vec *vec);
3557 void *isl_vec_free(__isl_take isl_vec *vec);
3559 Note that the elements of a newly created vector may have arbitrary values.
3560 The elements can be changed and inspected using the following functions.
3562 isl_ctx *isl_vec_get_ctx(__isl_keep isl_vec *vec);
3563 int isl_vec_size(__isl_keep isl_vec *vec);
3564 int isl_vec_get_element(__isl_keep isl_vec *vec,
3565 int pos, isl_int *v);
3566 __isl_give isl_val *isl_vec_get_element_val(
3567 __isl_keep isl_vec *vec, int pos);
3568 __isl_give isl_vec *isl_vec_set_element(
3569 __isl_take isl_vec *vec, int pos, isl_int v);
3570 __isl_give isl_vec *isl_vec_set_element_si(
3571 __isl_take isl_vec *vec, int pos, int v);
3572 __isl_give isl_vec *isl_vec_set_element_val(
3573 __isl_take isl_vec *vec, int pos,
3574 __isl_take isl_val *v);
3575 __isl_give isl_vec *isl_vec_set(__isl_take isl_vec *vec,
3577 __isl_give isl_vec *isl_vec_set_si(__isl_take isl_vec *vec,
3579 __isl_give isl_vec *isl_vec_set_val(
3580 __isl_take isl_vec *vec, __isl_take isl_val *v);
3581 int isl_vec_cmp_element(__isl_keep isl_vec *vec1,
3582 __isl_keep isl_vec *vec2, int pos);
3583 __isl_give isl_vec *isl_vec_fdiv_r(__isl_take isl_vec *vec,
3586 C<isl_vec_get_element> will return a negative value if anything went wrong.
3587 In that case, the value of C<*v> is undefined.
3589 The following function can be used to concatenate two vectors.
3591 __isl_give isl_vec *isl_vec_concat(__isl_take isl_vec *vec1,
3592 __isl_take isl_vec *vec2);
3596 Matrices can be created, copied and freed using the following functions.
3598 #include <isl/mat.h>
3599 __isl_give isl_mat *isl_mat_alloc(isl_ctx *ctx,
3600 unsigned n_row, unsigned n_col);
3601 __isl_give isl_mat *isl_mat_copy(__isl_keep isl_mat *mat);
3602 void *isl_mat_free(__isl_take isl_mat *mat);
3604 Note that the elements of a newly created matrix may have arbitrary values.
3605 The elements can be changed and inspected using the following functions.
3607 isl_ctx *isl_mat_get_ctx(__isl_keep isl_mat *mat);
3608 int isl_mat_rows(__isl_keep isl_mat *mat);
3609 int isl_mat_cols(__isl_keep isl_mat *mat);
3610 int isl_mat_get_element(__isl_keep isl_mat *mat,
3611 int row, int col, isl_int *v);
3612 __isl_give isl_val *isl_mat_get_element_val(
3613 __isl_keep isl_mat *mat, int row, int col);
3614 __isl_give isl_mat *isl_mat_set_element(__isl_take isl_mat *mat,
3615 int row, int col, isl_int v);
3616 __isl_give isl_mat *isl_mat_set_element_si(__isl_take isl_mat *mat,
3617 int row, int col, int v);
3618 __isl_give isl_mat *isl_mat_set_element_val(
3619 __isl_take isl_mat *mat, int row, int col,
3620 __isl_take isl_val *v);
3622 C<isl_mat_get_element> will return a negative value if anything went wrong.
3623 In that case, the value of C<*v> is undefined.
3625 The following function can be used to compute the (right) inverse
3626 of a matrix, i.e., a matrix such that the product of the original
3627 and the inverse (in that order) is a multiple of the identity matrix.
3628 The input matrix is assumed to be of full row-rank.
3630 __isl_give isl_mat *isl_mat_right_inverse(__isl_take isl_mat *mat);
3632 The following function can be used to compute the (right) kernel
3633 (or null space) of a matrix, i.e., a matrix such that the product of
3634 the original and the kernel (in that order) is the zero matrix.
3636 __isl_give isl_mat *isl_mat_right_kernel(__isl_take isl_mat *mat);
3638 =head2 Piecewise Quasi Affine Expressions
3640 The zero quasi affine expression or the quasi affine expression
3641 that is equal to a specified dimension on a given domain can be created using
3643 __isl_give isl_aff *isl_aff_zero_on_domain(
3644 __isl_take isl_local_space *ls);
3645 __isl_give isl_pw_aff *isl_pw_aff_zero_on_domain(
3646 __isl_take isl_local_space *ls);
3647 __isl_give isl_aff *isl_aff_var_on_domain(
3648 __isl_take isl_local_space *ls,
3649 enum isl_dim_type type, unsigned pos);
3650 __isl_give isl_pw_aff *isl_pw_aff_var_on_domain(
3651 __isl_take isl_local_space *ls,
3652 enum isl_dim_type type, unsigned pos);
3654 Note that the space in which the resulting objects live is a map space
3655 with the given space as domain and a one-dimensional range.
3657 An empty piecewise quasi affine expression (one with no cells)
3658 or a piecewise quasi affine expression with a single cell can
3659 be created using the following functions.
3661 #include <isl/aff.h>
3662 __isl_give isl_pw_aff *isl_pw_aff_empty(
3663 __isl_take isl_space *space);
3664 __isl_give isl_pw_aff *isl_pw_aff_alloc(
3665 __isl_take isl_set *set, __isl_take isl_aff *aff);
3666 __isl_give isl_pw_aff *isl_pw_aff_from_aff(
3667 __isl_take isl_aff *aff);
3669 A piecewise quasi affine expression that is equal to 1 on a set
3670 and 0 outside the set can be created using the following function.
3672 #include <isl/aff.h>
3673 __isl_give isl_pw_aff *isl_set_indicator_function(
3674 __isl_take isl_set *set);
3676 Quasi affine expressions can be copied and freed using
3678 #include <isl/aff.h>
3679 __isl_give isl_aff *isl_aff_copy(__isl_keep isl_aff *aff);
3680 void *isl_aff_free(__isl_take isl_aff *aff);
3682 __isl_give isl_pw_aff *isl_pw_aff_copy(
3683 __isl_keep isl_pw_aff *pwaff);
3684 void *isl_pw_aff_free(__isl_take isl_pw_aff *pwaff);
3686 A (rational) bound on a dimension can be extracted from an C<isl_constraint>
3687 using the following function. The constraint is required to have
3688 a non-zero coefficient for the specified dimension.
3690 #include <isl/constraint.h>
3691 __isl_give isl_aff *isl_constraint_get_bound(
3692 __isl_keep isl_constraint *constraint,
3693 enum isl_dim_type type, int pos);
3695 The entire affine expression of the constraint can also be extracted
3696 using the following function.
3698 #include <isl/constraint.h>
3699 __isl_give isl_aff *isl_constraint_get_aff(
3700 __isl_keep isl_constraint *constraint);
3702 Conversely, an equality constraint equating
3703 the affine expression to zero or an inequality constraint enforcing
3704 the affine expression to be non-negative, can be constructed using
3706 __isl_give isl_constraint *isl_equality_from_aff(
3707 __isl_take isl_aff *aff);
3708 __isl_give isl_constraint *isl_inequality_from_aff(
3709 __isl_take isl_aff *aff);
3711 The expression can be inspected using
3713 #include <isl/aff.h>
3714 isl_ctx *isl_aff_get_ctx(__isl_keep isl_aff *aff);
3715 int isl_aff_dim(__isl_keep isl_aff *aff,
3716 enum isl_dim_type type);
3717 __isl_give isl_local_space *isl_aff_get_domain_local_space(
3718 __isl_keep isl_aff *aff);
3719 __isl_give isl_local_space *isl_aff_get_local_space(
3720 __isl_keep isl_aff *aff);
3721 const char *isl_aff_get_dim_name(__isl_keep isl_aff *aff,
3722 enum isl_dim_type type, unsigned pos);
3723 const char *isl_pw_aff_get_dim_name(
3724 __isl_keep isl_pw_aff *pa,
3725 enum isl_dim_type type, unsigned pos);
3726 int isl_pw_aff_has_dim_id(__isl_keep isl_pw_aff *pa,
3727 enum isl_dim_type type, unsigned pos);
3728 __isl_give isl_id *isl_pw_aff_get_dim_id(
3729 __isl_keep isl_pw_aff *pa,
3730 enum isl_dim_type type, unsigned pos);
3731 __isl_give isl_id *isl_pw_aff_get_tuple_id(
3732 __isl_keep isl_pw_aff *pa,
3733 enum isl_dim_type type);
3734 int isl_aff_get_constant(__isl_keep isl_aff *aff,
3736 __isl_give isl_val *isl_aff_get_constant_val(
3737 __isl_keep isl_aff *aff);
3738 int isl_aff_get_coefficient(__isl_keep isl_aff *aff,
3739 enum isl_dim_type type, int pos, isl_int *v);
3740 __isl_give isl_val *isl_aff_get_coefficient_val(
3741 __isl_keep isl_aff *aff,
3742 enum isl_dim_type type, int pos);
3743 int isl_aff_get_denominator(__isl_keep isl_aff *aff,
3745 __isl_give isl_val *isl_aff_get_denominator_val(
3746 __isl_keep isl_aff *aff);
3747 __isl_give isl_aff *isl_aff_get_div(
3748 __isl_keep isl_aff *aff, int pos);
3750 int isl_pw_aff_n_piece(__isl_keep isl_pw_aff *pwaff);
3751 int isl_pw_aff_foreach_piece(__isl_keep isl_pw_aff *pwaff,
3752 int (*fn)(__isl_take isl_set *set,
3753 __isl_take isl_aff *aff,
3754 void *user), void *user);
3756 int isl_aff_is_cst(__isl_keep isl_aff *aff);
3757 int isl_pw_aff_is_cst(__isl_keep isl_pw_aff *pwaff);
3759 int isl_aff_involves_dims(__isl_keep isl_aff *aff,
3760 enum isl_dim_type type, unsigned first, unsigned n);
3761 int isl_pw_aff_involves_dims(__isl_keep isl_pw_aff *pwaff,
3762 enum isl_dim_type type, unsigned first, unsigned n);
3764 isl_ctx *isl_pw_aff_get_ctx(__isl_keep isl_pw_aff *pwaff);
3765 unsigned isl_pw_aff_dim(__isl_keep isl_pw_aff *pwaff,
3766 enum isl_dim_type type);
3767 int isl_pw_aff_is_empty(__isl_keep isl_pw_aff *pwaff);
3769 It can be modified using
3771 #include <isl/aff.h>
3772 __isl_give isl_pw_aff *isl_pw_aff_set_tuple_id(
3773 __isl_take isl_pw_aff *pwaff,
3774 enum isl_dim_type type, __isl_take isl_id *id);
3775 __isl_give isl_aff *isl_aff_set_dim_name(
3776 __isl_take isl_aff *aff, enum isl_dim_type type,
3777 unsigned pos, const char *s);
3778 __isl_give isl_aff *isl_aff_set_dim_id(
3779 __isl_take isl_aff *aff, enum isl_dim_type type,
3780 unsigned pos, __isl_take isl_id *id);
3781 __isl_give isl_pw_aff *isl_pw_aff_set_dim_id(
3782 __isl_take isl_pw_aff *pma,
3783 enum isl_dim_type type, unsigned pos,
3784 __isl_take isl_id *id);
3785 __isl_give isl_aff *isl_aff_set_constant(
3786 __isl_take isl_aff *aff, isl_int v);
3787 __isl_give isl_aff *isl_aff_set_constant_si(
3788 __isl_take isl_aff *aff, int v);
3789 __isl_give isl_aff *isl_aff_set_constant_val(
3790 __isl_take isl_aff *aff, __isl_take isl_val *v);
3791 __isl_give isl_aff *isl_aff_set_coefficient(
3792 __isl_take isl_aff *aff,
3793 enum isl_dim_type type, int pos, isl_int v);
3794 __isl_give isl_aff *isl_aff_set_coefficient_si(
3795 __isl_take isl_aff *aff,
3796 enum isl_dim_type type, int pos, int v);
3797 __isl_give isl_aff *isl_aff_set_coefficient_val(
3798 __isl_take isl_aff *aff,
3799 enum isl_dim_type type, int pos,
3800 __isl_take isl_val *v);
3801 __isl_give isl_aff *isl_aff_set_denominator(
3802 __isl_take isl_aff *aff, isl_int v);
3804 __isl_give isl_aff *isl_aff_add_constant(
3805 __isl_take isl_aff *aff, isl_int v);
3806 __isl_give isl_aff *isl_aff_add_constant_si(
3807 __isl_take isl_aff *aff, int v);
3808 __isl_give isl_aff *isl_aff_add_constant_val(
3809 __isl_take isl_aff *aff, __isl_take isl_val *v);
3810 __isl_give isl_aff *isl_aff_add_constant_num(
3811 __isl_take isl_aff *aff, isl_int v);
3812 __isl_give isl_aff *isl_aff_add_constant_num_si(
3813 __isl_take isl_aff *aff, int v);
3814 __isl_give isl_aff *isl_aff_add_coefficient(
3815 __isl_take isl_aff *aff,
3816 enum isl_dim_type type, int pos, isl_int v);
3817 __isl_give isl_aff *isl_aff_add_coefficient_si(
3818 __isl_take isl_aff *aff,
3819 enum isl_dim_type type, int pos, int v);
3820 __isl_give isl_aff *isl_aff_add_coefficient_val(
3821 __isl_take isl_aff *aff,
3822 enum isl_dim_type type, int pos,
3823 __isl_take isl_val *v);
3825 __isl_give isl_aff *isl_aff_insert_dims(
3826 __isl_take isl_aff *aff,
3827 enum isl_dim_type type, unsigned first, unsigned n);
3828 __isl_give isl_pw_aff *isl_pw_aff_insert_dims(
3829 __isl_take isl_pw_aff *pwaff,
3830 enum isl_dim_type type, unsigned first, unsigned n);
3831 __isl_give isl_aff *isl_aff_add_dims(
3832 __isl_take isl_aff *aff,
3833 enum isl_dim_type type, unsigned n);
3834 __isl_give isl_pw_aff *isl_pw_aff_add_dims(
3835 __isl_take isl_pw_aff *pwaff,
3836 enum isl_dim_type type, unsigned n);
3837 __isl_give isl_aff *isl_aff_drop_dims(
3838 __isl_take isl_aff *aff,
3839 enum isl_dim_type type, unsigned first, unsigned n);
3840 __isl_give isl_pw_aff *isl_pw_aff_drop_dims(
3841 __isl_take isl_pw_aff *pwaff,
3842 enum isl_dim_type type, unsigned first, unsigned n);
3844 Note that C<isl_aff_set_constant>, C<isl_aff_set_constant_si>,
3845 C<isl_aff_set_coefficient> and C<isl_aff_set_coefficient_si>
3846 set the I<numerator> of the constant or coefficient, while
3847 C<isl_aff_set_constant_val> and C<isl_aff_set_coefficient_val> set
3848 the constant or coefficient as a whole.
3849 The C<add_constant> and C<add_coefficient> functions add an integer
3850 or rational value to
3851 the possibly rational constant or coefficient.
3852 The C<add_constant_num> functions add an integer value to
3855 To check whether an affine expressions is obviously zero
3856 or obviously equal to some other affine expression, use
3858 #include <isl/aff.h>
3859 int isl_aff_plain_is_zero(__isl_keep isl_aff *aff);
3860 int isl_aff_plain_is_equal(__isl_keep isl_aff *aff1,
3861 __isl_keep isl_aff *aff2);
3862 int isl_pw_aff_plain_is_equal(
3863 __isl_keep isl_pw_aff *pwaff1,
3864 __isl_keep isl_pw_aff *pwaff2);
3868 #include <isl/aff.h>
3869 __isl_give isl_aff *isl_aff_add(__isl_take isl_aff *aff1,
3870 __isl_take isl_aff *aff2);
3871 __isl_give isl_pw_aff *isl_pw_aff_add(
3872 __isl_take isl_pw_aff *pwaff1,
3873 __isl_take isl_pw_aff *pwaff2);
3874 __isl_give isl_pw_aff *isl_pw_aff_min(
3875 __isl_take isl_pw_aff *pwaff1,
3876 __isl_take isl_pw_aff *pwaff2);
3877 __isl_give isl_pw_aff *isl_pw_aff_max(
3878 __isl_take isl_pw_aff *pwaff1,
3879 __isl_take isl_pw_aff *pwaff2);
3880 __isl_give isl_aff *isl_aff_sub(__isl_take isl_aff *aff1,
3881 __isl_take isl_aff *aff2);
3882 __isl_give isl_pw_aff *isl_pw_aff_sub(
3883 __isl_take isl_pw_aff *pwaff1,
3884 __isl_take isl_pw_aff *pwaff2);
3885 __isl_give isl_aff *isl_aff_neg(__isl_take isl_aff *aff);
3886 __isl_give isl_pw_aff *isl_pw_aff_neg(
3887 __isl_take isl_pw_aff *pwaff);
3888 __isl_give isl_aff *isl_aff_ceil(__isl_take isl_aff *aff);
3889 __isl_give isl_pw_aff *isl_pw_aff_ceil(
3890 __isl_take isl_pw_aff *pwaff);
3891 __isl_give isl_aff *isl_aff_floor(__isl_take isl_aff *aff);
3892 __isl_give isl_pw_aff *isl_pw_aff_floor(
3893 __isl_take isl_pw_aff *pwaff);
3894 __isl_give isl_aff *isl_aff_mod(__isl_take isl_aff *aff,
3896 __isl_give isl_aff *isl_aff_mod_val(__isl_take isl_aff *aff,
3897 __isl_take isl_val *mod);
3898 __isl_give isl_pw_aff *isl_pw_aff_mod(
3899 __isl_take isl_pw_aff *pwaff, isl_int mod);
3900 __isl_give isl_pw_aff *isl_pw_aff_mod_val(
3901 __isl_take isl_pw_aff *pa,
3902 __isl_take isl_val *mod);
3903 __isl_give isl_aff *isl_aff_scale(__isl_take isl_aff *aff,
3905 __isl_give isl_aff *isl_aff_scale_val(__isl_take isl_aff *aff,
3906 __isl_take isl_val *v);
3907 __isl_give isl_pw_aff *isl_pw_aff_scale(
3908 __isl_take isl_pw_aff *pwaff, isl_int f);
3909 __isl_give isl_pw_aff *isl_pw_aff_scale_val(
3910 __isl_take isl_pw_aff *pa, __isl_take isl_val *v);
3911 __isl_give isl_aff *isl_aff_scale_down(__isl_take isl_aff *aff,
3913 __isl_give isl_aff *isl_aff_scale_down_ui(
3914 __isl_take isl_aff *aff, unsigned f);
3915 __isl_give isl_aff *isl_aff_scale_down_val(
3916 __isl_take isl_aff *aff, __isl_take isl_val *v);
3917 __isl_give isl_pw_aff *isl_pw_aff_scale_down(
3918 __isl_take isl_pw_aff *pwaff, isl_int f);
3919 __isl_give isl_pw_aff *isl_pw_aff_scale_down_val(
3920 __isl_take isl_pw_aff *pa,
3921 __isl_take isl_val *f);
3923 __isl_give isl_pw_aff *isl_pw_aff_list_min(
3924 __isl_take isl_pw_aff_list *list);
3925 __isl_give isl_pw_aff *isl_pw_aff_list_max(
3926 __isl_take isl_pw_aff_list *list);
3928 __isl_give isl_pw_aff *isl_pw_aff_coalesce(
3929 __isl_take isl_pw_aff *pwqp);
3931 __isl_give isl_aff *isl_aff_align_params(
3932 __isl_take isl_aff *aff,
3933 __isl_take isl_space *model);
3934 __isl_give isl_pw_aff *isl_pw_aff_align_params(
3935 __isl_take isl_pw_aff *pwaff,
3936 __isl_take isl_space *model);
3938 __isl_give isl_aff *isl_aff_project_domain_on_params(
3939 __isl_take isl_aff *aff);
3941 __isl_give isl_aff *isl_aff_gist_params(
3942 __isl_take isl_aff *aff,
3943 __isl_take isl_set *context);
3944 __isl_give isl_aff *isl_aff_gist(__isl_take isl_aff *aff,
3945 __isl_take isl_set *context);
3946 __isl_give isl_pw_aff *isl_pw_aff_gist_params(
3947 __isl_take isl_pw_aff *pwaff,
3948 __isl_take isl_set *context);
3949 __isl_give isl_pw_aff *isl_pw_aff_gist(
3950 __isl_take isl_pw_aff *pwaff,
3951 __isl_take isl_set *context);
3953 __isl_give isl_set *isl_pw_aff_domain(
3954 __isl_take isl_pw_aff *pwaff);
3955 __isl_give isl_pw_aff *isl_pw_aff_intersect_domain(
3956 __isl_take isl_pw_aff *pa,
3957 __isl_take isl_set *set);
3958 __isl_give isl_pw_aff *isl_pw_aff_intersect_params(
3959 __isl_take isl_pw_aff *pa,
3960 __isl_take isl_set *set);
3962 __isl_give isl_aff *isl_aff_mul(__isl_take isl_aff *aff1,
3963 __isl_take isl_aff *aff2);
3964 __isl_give isl_aff *isl_aff_div(__isl_take isl_aff *aff1,
3965 __isl_take isl_aff *aff2);
3966 __isl_give isl_pw_aff *isl_pw_aff_mul(
3967 __isl_take isl_pw_aff *pwaff1,
3968 __isl_take isl_pw_aff *pwaff2);
3969 __isl_give isl_pw_aff *isl_pw_aff_div(
3970 __isl_take isl_pw_aff *pa1,
3971 __isl_take isl_pw_aff *pa2);
3972 __isl_give isl_pw_aff *isl_pw_aff_tdiv_q(
3973 __isl_take isl_pw_aff *pa1,
3974 __isl_take isl_pw_aff *pa2);
3975 __isl_give isl_pw_aff *isl_pw_aff_tdiv_r(
3976 __isl_take isl_pw_aff *pa1,
3977 __isl_take isl_pw_aff *pa2);
3979 When multiplying two affine expressions, at least one of the two needs
3980 to be a constant. Similarly, when dividing an affine expression by another,
3981 the second expression needs to be a constant.
3982 C<isl_pw_aff_tdiv_q> computes the quotient of an integer division with
3983 rounding towards zero. C<isl_pw_aff_tdiv_r> computes the corresponding
3986 #include <isl/aff.h>
3987 __isl_give isl_aff *isl_aff_pullback_multi_aff(
3988 __isl_take isl_aff *aff,
3989 __isl_take isl_multi_aff *ma);
3990 __isl_give isl_pw_aff *isl_pw_aff_pullback_multi_aff(
3991 __isl_take isl_pw_aff *pa,
3992 __isl_take isl_multi_aff *ma);
3993 __isl_give isl_pw_aff *isl_pw_aff_pullback_pw_multi_aff(
3994 __isl_take isl_pw_aff *pa,
3995 __isl_take isl_pw_multi_aff *pma);
3997 These functions precompose the input expression by the given
3998 C<isl_multi_aff> or C<isl_pw_multi_aff>. In other words,
3999 the C<isl_multi_aff> or C<isl_pw_multi_aff> is plugged
4000 into the (piecewise) affine expression.
4001 Objects of type C<isl_multi_aff> are described in
4002 L</"Piecewise Multiple Quasi Affine Expressions">.
4004 #include <isl/aff.h>
4005 __isl_give isl_basic_set *isl_aff_zero_basic_set(
4006 __isl_take isl_aff *aff);
4007 __isl_give isl_basic_set *isl_aff_neg_basic_set(
4008 __isl_take isl_aff *aff);
4009 __isl_give isl_basic_set *isl_aff_le_basic_set(
4010 __isl_take isl_aff *aff1, __isl_take isl_aff *aff2);
4011 __isl_give isl_basic_set *isl_aff_ge_basic_set(
4012 __isl_take isl_aff *aff1, __isl_take isl_aff *aff2);
4013 __isl_give isl_set *isl_pw_aff_eq_set(
4014 __isl_take isl_pw_aff *pwaff1,
4015 __isl_take isl_pw_aff *pwaff2);
4016 __isl_give isl_set *isl_pw_aff_ne_set(
4017 __isl_take isl_pw_aff *pwaff1,
4018 __isl_take isl_pw_aff *pwaff2);
4019 __isl_give isl_set *isl_pw_aff_le_set(
4020 __isl_take isl_pw_aff *pwaff1,
4021 __isl_take isl_pw_aff *pwaff2);
4022 __isl_give isl_set *isl_pw_aff_lt_set(
4023 __isl_take isl_pw_aff *pwaff1,
4024 __isl_take isl_pw_aff *pwaff2);
4025 __isl_give isl_set *isl_pw_aff_ge_set(
4026 __isl_take isl_pw_aff *pwaff1,
4027 __isl_take isl_pw_aff *pwaff2);
4028 __isl_give isl_set *isl_pw_aff_gt_set(
4029 __isl_take isl_pw_aff *pwaff1,
4030 __isl_take isl_pw_aff *pwaff2);
4032 __isl_give isl_set *isl_pw_aff_list_eq_set(
4033 __isl_take isl_pw_aff_list *list1,
4034 __isl_take isl_pw_aff_list *list2);
4035 __isl_give isl_set *isl_pw_aff_list_ne_set(
4036 __isl_take isl_pw_aff_list *list1,
4037 __isl_take isl_pw_aff_list *list2);
4038 __isl_give isl_set *isl_pw_aff_list_le_set(
4039 __isl_take isl_pw_aff_list *list1,
4040 __isl_take isl_pw_aff_list *list2);
4041 __isl_give isl_set *isl_pw_aff_list_lt_set(
4042 __isl_take isl_pw_aff_list *list1,
4043 __isl_take isl_pw_aff_list *list2);
4044 __isl_give isl_set *isl_pw_aff_list_ge_set(
4045 __isl_take isl_pw_aff_list *list1,
4046 __isl_take isl_pw_aff_list *list2);
4047 __isl_give isl_set *isl_pw_aff_list_gt_set(
4048 __isl_take isl_pw_aff_list *list1,
4049 __isl_take isl_pw_aff_list *list2);
4051 The function C<isl_aff_neg_basic_set> returns a basic set
4052 containing those elements in the domain space
4053 of C<aff> where C<aff> is negative.
4054 The function C<isl_aff_ge_basic_set> returns a basic set
4055 containing those elements in the shared space
4056 of C<aff1> and C<aff2> where C<aff1> is greater than or equal to C<aff2>.
4057 The function C<isl_pw_aff_ge_set> returns a set
4058 containing those elements in the shared domain
4059 of C<pwaff1> and C<pwaff2> where C<pwaff1> is greater than or equal to C<pwaff2>.
4060 The functions operating on C<isl_pw_aff_list> apply the corresponding
4061 C<isl_pw_aff> function to each pair of elements in the two lists.
4063 #include <isl/aff.h>
4064 __isl_give isl_set *isl_pw_aff_nonneg_set(
4065 __isl_take isl_pw_aff *pwaff);
4066 __isl_give isl_set *isl_pw_aff_zero_set(
4067 __isl_take isl_pw_aff *pwaff);
4068 __isl_give isl_set *isl_pw_aff_non_zero_set(
4069 __isl_take isl_pw_aff *pwaff);
4071 The function C<isl_pw_aff_nonneg_set> returns a set
4072 containing those elements in the domain
4073 of C<pwaff> where C<pwaff> is non-negative.
4075 #include <isl/aff.h>
4076 __isl_give isl_pw_aff *isl_pw_aff_cond(
4077 __isl_take isl_pw_aff *cond,
4078 __isl_take isl_pw_aff *pwaff_true,
4079 __isl_take isl_pw_aff *pwaff_false);
4081 The function C<isl_pw_aff_cond> performs a conditional operator
4082 and returns an expression that is equal to C<pwaff_true>
4083 for elements where C<cond> is non-zero and equal to C<pwaff_false> for elements
4084 where C<cond> is zero.
4086 #include <isl/aff.h>
4087 __isl_give isl_pw_aff *isl_pw_aff_union_min(
4088 __isl_take isl_pw_aff *pwaff1,
4089 __isl_take isl_pw_aff *pwaff2);
4090 __isl_give isl_pw_aff *isl_pw_aff_union_max(
4091 __isl_take isl_pw_aff *pwaff1,
4092 __isl_take isl_pw_aff *pwaff2);
4093 __isl_give isl_pw_aff *isl_pw_aff_union_add(
4094 __isl_take isl_pw_aff *pwaff1,
4095 __isl_take isl_pw_aff *pwaff2);
4097 The function C<isl_pw_aff_union_max> computes a piecewise quasi-affine
4098 expression with a domain that is the union of those of C<pwaff1> and
4099 C<pwaff2> and such that on each cell, the quasi-affine expression is
4100 the maximum of those of C<pwaff1> and C<pwaff2>. If only one of
4101 C<pwaff1> or C<pwaff2> is defined on a given cell, then the
4102 associated expression is the defined one.
4104 An expression can be read from input using
4106 #include <isl/aff.h>
4107 __isl_give isl_aff *isl_aff_read_from_str(
4108 isl_ctx *ctx, const char *str);
4109 __isl_give isl_pw_aff *isl_pw_aff_read_from_str(
4110 isl_ctx *ctx, const char *str);
4112 An expression can be printed using
4114 #include <isl/aff.h>
4115 __isl_give isl_printer *isl_printer_print_aff(
4116 __isl_take isl_printer *p, __isl_keep isl_aff *aff);
4118 __isl_give isl_printer *isl_printer_print_pw_aff(
4119 __isl_take isl_printer *p,
4120 __isl_keep isl_pw_aff *pwaff);
4122 =head2 Piecewise Multiple Quasi Affine Expressions
4124 An C<isl_multi_aff> object represents a sequence of
4125 zero or more affine expressions, all defined on the same domain space.
4126 Similarly, an C<isl_multi_pw_aff> object represents a sequence of
4127 zero or more piecewise affine expressions.
4129 An C<isl_multi_aff> can be constructed from a single
4130 C<isl_aff> or an C<isl_aff_list> using the
4131 following functions. Similarly for C<isl_multi_pw_aff>.
4133 #include <isl/aff.h>
4134 __isl_give isl_multi_aff *isl_multi_aff_from_aff(
4135 __isl_take isl_aff *aff);
4136 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_from_pw_aff(
4137 __isl_take isl_pw_aff *pa);
4138 __isl_give isl_multi_aff *isl_multi_aff_from_aff_list(
4139 __isl_take isl_space *space,
4140 __isl_take isl_aff_list *list);
4142 An empty piecewise multiple quasi affine expression (one with no cells),
4143 the zero piecewise multiple quasi affine expression (with value zero
4144 for each output dimension),
4145 a piecewise multiple quasi affine expression with a single cell (with
4146 either a universe or a specified domain) or
4147 a zero-dimensional piecewise multiple quasi affine expression
4149 can be created using the following functions.
4151 #include <isl/aff.h>
4152 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_empty(
4153 __isl_take isl_space *space);
4154 __isl_give isl_multi_aff *isl_multi_aff_zero(
4155 __isl_take isl_space *space);
4156 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_zero(
4157 __isl_take isl_space *space);
4158 __isl_give isl_multi_aff *isl_multi_aff_identity(
4159 __isl_take isl_space *space);
4160 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_identity(
4161 __isl_take isl_space *space);
4162 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_identity(
4163 __isl_take isl_space *space);
4164 __isl_give isl_pw_multi_aff *
4165 isl_pw_multi_aff_from_multi_aff(
4166 __isl_take isl_multi_aff *ma);
4167 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_alloc(
4168 __isl_take isl_set *set,
4169 __isl_take isl_multi_aff *maff);
4170 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_from_domain(
4171 __isl_take isl_set *set);
4173 __isl_give isl_union_pw_multi_aff *
4174 isl_union_pw_multi_aff_empty(
4175 __isl_take isl_space *space);
4176 __isl_give isl_union_pw_multi_aff *
4177 isl_union_pw_multi_aff_add_pw_multi_aff(
4178 __isl_take isl_union_pw_multi_aff *upma,
4179 __isl_take isl_pw_multi_aff *pma);
4180 __isl_give isl_union_pw_multi_aff *
4181 isl_union_pw_multi_aff_from_domain(
4182 __isl_take isl_union_set *uset);
4184 A piecewise multiple quasi affine expression can also be initialized
4185 from an C<isl_set> or C<isl_map>, provided the C<isl_set> is a singleton
4186 and the C<isl_map> is single-valued.
4187 In case of a conversion from an C<isl_union_set> or an C<isl_union_map>
4188 to an C<isl_union_pw_multi_aff>, these properties need to hold in each space.
4190 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_from_set(
4191 __isl_take isl_set *set);
4192 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_from_map(
4193 __isl_take isl_map *map);
4195 __isl_give isl_union_pw_multi_aff *
4196 isl_union_pw_multi_aff_from_union_set(
4197 __isl_take isl_union_set *uset);
4198 __isl_give isl_union_pw_multi_aff *
4199 isl_union_pw_multi_aff_from_union_map(
4200 __isl_take isl_union_map *umap);
4202 Multiple quasi affine expressions can be copied and freed using
4204 #include <isl/aff.h>
4205 __isl_give isl_multi_aff *isl_multi_aff_copy(
4206 __isl_keep isl_multi_aff *maff);
4207 void *isl_multi_aff_free(__isl_take isl_multi_aff *maff);
4209 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_copy(
4210 __isl_keep isl_pw_multi_aff *pma);
4211 void *isl_pw_multi_aff_free(
4212 __isl_take isl_pw_multi_aff *pma);
4214 __isl_give isl_union_pw_multi_aff *
4215 isl_union_pw_multi_aff_copy(
4216 __isl_keep isl_union_pw_multi_aff *upma);
4217 void *isl_union_pw_multi_aff_free(
4218 __isl_take isl_union_pw_multi_aff *upma);
4220 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_copy(
4221 __isl_keep isl_multi_pw_aff *mpa);
4222 void *isl_multi_pw_aff_free(
4223 __isl_take isl_multi_pw_aff *mpa);
4225 The expression can be inspected using
4227 #include <isl/aff.h>
4228 isl_ctx *isl_multi_aff_get_ctx(
4229 __isl_keep isl_multi_aff *maff);
4230 isl_ctx *isl_pw_multi_aff_get_ctx(
4231 __isl_keep isl_pw_multi_aff *pma);
4232 isl_ctx *isl_union_pw_multi_aff_get_ctx(
4233 __isl_keep isl_union_pw_multi_aff *upma);
4234 isl_ctx *isl_multi_pw_aff_get_ctx(
4235 __isl_keep isl_multi_pw_aff *mpa);
4236 unsigned isl_multi_aff_dim(__isl_keep isl_multi_aff *maff,
4237 enum isl_dim_type type);
4238 unsigned isl_pw_multi_aff_dim(
4239 __isl_keep isl_pw_multi_aff *pma,
4240 enum isl_dim_type type);
4241 unsigned isl_multi_pw_aff_dim(
4242 __isl_keep isl_multi_pw_aff *mpa,
4243 enum isl_dim_type type);
4244 __isl_give isl_aff *isl_multi_aff_get_aff(
4245 __isl_keep isl_multi_aff *multi, int pos);
4246 __isl_give isl_pw_aff *isl_pw_multi_aff_get_pw_aff(
4247 __isl_keep isl_pw_multi_aff *pma, int pos);
4248 __isl_give isl_pw_aff *isl_multi_pw_aff_get_pw_aff(
4249 __isl_keep isl_multi_pw_aff *mpa, int pos);
4250 const char *isl_pw_multi_aff_get_dim_name(
4251 __isl_keep isl_pw_multi_aff *pma,
4252 enum isl_dim_type type, unsigned pos);
4253 __isl_give isl_id *isl_pw_multi_aff_get_dim_id(
4254 __isl_keep isl_pw_multi_aff *pma,
4255 enum isl_dim_type type, unsigned pos);
4256 const char *isl_multi_aff_get_tuple_name(
4257 __isl_keep isl_multi_aff *multi,
4258 enum isl_dim_type type);
4259 int isl_pw_multi_aff_has_tuple_name(
4260 __isl_keep isl_pw_multi_aff *pma,
4261 enum isl_dim_type type);
4262 const char *isl_pw_multi_aff_get_tuple_name(
4263 __isl_keep isl_pw_multi_aff *pma,
4264 enum isl_dim_type type);
4265 int isl_pw_multi_aff_has_tuple_id(
4266 __isl_keep isl_pw_multi_aff *pma,
4267 enum isl_dim_type type);
4268 __isl_give isl_id *isl_pw_multi_aff_get_tuple_id(
4269 __isl_keep isl_pw_multi_aff *pma,
4270 enum isl_dim_type type);
4272 int isl_pw_multi_aff_foreach_piece(
4273 __isl_keep isl_pw_multi_aff *pma,
4274 int (*fn)(__isl_take isl_set *set,
4275 __isl_take isl_multi_aff *maff,
4276 void *user), void *user);
4278 int isl_union_pw_multi_aff_foreach_pw_multi_aff(
4279 __isl_keep isl_union_pw_multi_aff *upma,
4280 int (*fn)(__isl_take isl_pw_multi_aff *pma,
4281 void *user), void *user);
4283 It can be modified using
4285 #include <isl/aff.h>
4286 __isl_give isl_multi_aff *isl_multi_aff_set_aff(
4287 __isl_take isl_multi_aff *multi, int pos,
4288 __isl_take isl_aff *aff);
4289 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_set_pw_aff(
4290 __isl_take isl_pw_multi_aff *pma, unsigned pos,
4291 __isl_take isl_pw_aff *pa);
4292 __isl_give isl_multi_aff *isl_multi_aff_set_dim_name(
4293 __isl_take isl_multi_aff *maff,
4294 enum isl_dim_type type, unsigned pos, const char *s);
4295 __isl_give isl_multi_aff *isl_multi_aff_set_tuple_name(
4296 __isl_take isl_multi_aff *maff,
4297 enum isl_dim_type type, const char *s);
4298 __isl_give isl_multi_aff *isl_multi_aff_set_tuple_id(
4299 __isl_take isl_multi_aff *maff,
4300 enum isl_dim_type type, __isl_take isl_id *id);
4301 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_set_tuple_id(
4302 __isl_take isl_pw_multi_aff *pma,
4303 enum isl_dim_type type, __isl_take isl_id *id);
4305 __isl_give isl_multi_pw_aff *
4306 isl_multi_pw_aff_set_dim_name(
4307 __isl_take isl_multi_pw_aff *mpa,
4308 enum isl_dim_type type, unsigned pos, const char *s);
4309 __isl_give isl_multi_pw_aff *
4310 isl_multi_pw_aff_set_tuple_name(
4311 __isl_take isl_multi_pw_aff *mpa,
4312 enum isl_dim_type type, const char *s);
4314 __isl_give isl_multi_aff *isl_multi_aff_insert_dims(
4315 __isl_take isl_multi_aff *ma,
4316 enum isl_dim_type type, unsigned first, unsigned n);
4317 __isl_give isl_multi_aff *isl_multi_aff_add_dims(
4318 __isl_take isl_multi_aff *ma,
4319 enum isl_dim_type type, unsigned n);
4320 __isl_give isl_multi_aff *isl_multi_aff_drop_dims(
4321 __isl_take isl_multi_aff *maff,
4322 enum isl_dim_type type, unsigned first, unsigned n);
4323 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_drop_dims(
4324 __isl_take isl_pw_multi_aff *pma,
4325 enum isl_dim_type type, unsigned first, unsigned n);
4327 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_insert_dims(
4328 __isl_take isl_multi_pw_aff *mpa,
4329 enum isl_dim_type type, unsigned first, unsigned n);
4330 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_add_dims(
4331 __isl_take isl_multi_pw_aff *mpa,
4332 enum isl_dim_type type, unsigned n);
4334 To check whether two multiple affine expressions are
4335 obviously equal to each other, use
4337 int isl_multi_aff_plain_is_equal(__isl_keep isl_multi_aff *maff1,
4338 __isl_keep isl_multi_aff *maff2);
4339 int isl_pw_multi_aff_plain_is_equal(
4340 __isl_keep isl_pw_multi_aff *pma1,
4341 __isl_keep isl_pw_multi_aff *pma2);
4345 #include <isl/aff.h>
4346 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_union_lexmin(
4347 __isl_take isl_pw_multi_aff *pma1,
4348 __isl_take isl_pw_multi_aff *pma2);
4349 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_union_lexmax(
4350 __isl_take isl_pw_multi_aff *pma1,
4351 __isl_take isl_pw_multi_aff *pma2);
4352 __isl_give isl_multi_aff *isl_multi_aff_add(
4353 __isl_take isl_multi_aff *maff1,
4354 __isl_take isl_multi_aff *maff2);
4355 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_add(
4356 __isl_take isl_pw_multi_aff *pma1,
4357 __isl_take isl_pw_multi_aff *pma2);
4358 __isl_give isl_union_pw_multi_aff *isl_union_pw_multi_aff_add(
4359 __isl_take isl_union_pw_multi_aff *upma1,
4360 __isl_take isl_union_pw_multi_aff *upma2);
4361 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_union_add(
4362 __isl_take isl_pw_multi_aff *pma1,
4363 __isl_take isl_pw_multi_aff *pma2);
4364 __isl_give isl_multi_aff *isl_multi_aff_sub(
4365 __isl_take isl_multi_aff *ma1,
4366 __isl_take isl_multi_aff *ma2);
4367 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_sub(
4368 __isl_take isl_pw_multi_aff *pma1,
4369 __isl_take isl_pw_multi_aff *pma2);
4370 __isl_give isl_union_pw_multi_aff *isl_union_pw_multi_aff_sub(
4371 __isl_take isl_union_pw_multi_aff *upma1,
4372 __isl_take isl_union_pw_multi_aff *upma2);
4374 C<isl_multi_aff_sub> subtracts the second argument from the first.
4376 __isl_give isl_multi_aff *isl_multi_aff_scale(
4377 __isl_take isl_multi_aff *maff,
4379 __isl_give isl_multi_aff *isl_multi_aff_scale_val(
4380 __isl_take isl_multi_aff *ma,
4381 __isl_take isl_val *v);
4382 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_scale_val(
4383 __isl_take isl_pw_multi_aff *pma,
4384 __isl_take isl_val *v);
4385 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_scale_val(
4386 __isl_take isl_multi_pw_aff *mpa,
4387 __isl_take isl_val *v);
4388 __isl_give isl_multi_aff *isl_multi_aff_scale_multi_val(
4389 __isl_take isl_multi_aff *ma,
4390 __isl_take isl_multi_val *mv);
4391 __isl_give isl_pw_multi_aff *
4392 isl_pw_multi_aff_scale_multi_val(
4393 __isl_take isl_pw_multi_aff *pma,
4394 __isl_take isl_multi_val *mv);
4395 __isl_give isl_multi_pw_aff *
4396 isl_multi_pw_aff_scale_multi_val(
4397 __isl_take isl_multi_pw_aff *mpa,
4398 __isl_take isl_multi_val *mv);
4399 __isl_give isl_union_pw_multi_aff *
4400 isl_union_pw_multi_aff_scale_multi_val(
4401 __isl_take isl_union_pw_multi_aff *upma,
4402 __isl_take isl_multi_val *mv);
4404 C<isl_multi_aff_scale_multi_val> scales the elements of C<ma>
4405 by the corresponding elements of C<mv>.
4407 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_intersect_params(
4408 __isl_take isl_pw_multi_aff *pma,
4409 __isl_take isl_set *set);
4410 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_intersect_domain(
4411 __isl_take isl_pw_multi_aff *pma,
4412 __isl_take isl_set *set);
4413 __isl_give isl_union_pw_multi_aff *
4414 isl_union_pw_multi_aff_intersect_domain(
4415 __isl_take isl_union_pw_multi_aff *upma,
4416 __isl_take isl_union_set *uset);
4417 __isl_give isl_multi_aff *isl_multi_aff_lift(
4418 __isl_take isl_multi_aff *maff,
4419 __isl_give isl_local_space **ls);
4420 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_coalesce(
4421 __isl_take isl_pw_multi_aff *pma);
4422 __isl_give isl_multi_aff *isl_multi_aff_align_params(
4423 __isl_take isl_multi_aff *multi,
4424 __isl_take isl_space *model);
4425 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_align_params(
4426 __isl_take isl_pw_multi_aff *pma,
4427 __isl_take isl_space *model);
4428 __isl_give isl_pw_multi_aff *
4429 isl_pw_multi_aff_project_domain_on_params(
4430 __isl_take isl_pw_multi_aff *pma);
4431 __isl_give isl_multi_aff *isl_multi_aff_gist_params(
4432 __isl_take isl_multi_aff *maff,
4433 __isl_take isl_set *context);
4434 __isl_give isl_multi_aff *isl_multi_aff_gist(
4435 __isl_take isl_multi_aff *maff,
4436 __isl_take isl_set *context);
4437 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_gist_params(
4438 __isl_take isl_pw_multi_aff *pma,
4439 __isl_take isl_set *set);
4440 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_gist(
4441 __isl_take isl_pw_multi_aff *pma,
4442 __isl_take isl_set *set);
4443 __isl_give isl_set *isl_pw_multi_aff_domain(
4444 __isl_take isl_pw_multi_aff *pma);
4445 __isl_give isl_union_set *isl_union_pw_multi_aff_domain(
4446 __isl_take isl_union_pw_multi_aff *upma);
4447 __isl_give isl_multi_aff *isl_multi_aff_range_splice(
4448 __isl_take isl_multi_aff *ma1, unsigned pos,
4449 __isl_take isl_multi_aff *ma2);
4450 __isl_give isl_multi_aff *isl_multi_aff_splice(
4451 __isl_take isl_multi_aff *ma1,
4452 unsigned in_pos, unsigned out_pos,
4453 __isl_take isl_multi_aff *ma2);
4454 __isl_give isl_multi_aff *isl_multi_aff_range_product(
4455 __isl_take isl_multi_aff *ma1,
4456 __isl_take isl_multi_aff *ma2);
4457 __isl_give isl_multi_aff *isl_multi_aff_flat_range_product(
4458 __isl_take isl_multi_aff *ma1,
4459 __isl_take isl_multi_aff *ma2);
4460 __isl_give isl_multi_aff *isl_multi_aff_product(
4461 __isl_take isl_multi_aff *ma1,
4462 __isl_take isl_multi_aff *ma2);
4463 __isl_give isl_pw_multi_aff *
4464 isl_pw_multi_aff_range_product(
4465 __isl_take isl_pw_multi_aff *pma1,
4466 __isl_take isl_pw_multi_aff *pma2);
4467 __isl_give isl_pw_multi_aff *
4468 isl_pw_multi_aff_flat_range_product(
4469 __isl_take isl_pw_multi_aff *pma1,
4470 __isl_take isl_pw_multi_aff *pma2);
4471 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_product(
4472 __isl_take isl_pw_multi_aff *pma1,
4473 __isl_take isl_pw_multi_aff *pma2);
4474 __isl_give isl_union_pw_multi_aff *
4475 isl_union_pw_multi_aff_flat_range_product(
4476 __isl_take isl_union_pw_multi_aff *upma1,
4477 __isl_take isl_union_pw_multi_aff *upma2);
4478 __isl_give isl_multi_pw_aff *
4479 isl_multi_pw_aff_range_splice(
4480 __isl_take isl_multi_pw_aff *mpa1, unsigned pos,
4481 __isl_take isl_multi_pw_aff *mpa2);
4482 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_splice(
4483 __isl_take isl_multi_pw_aff *mpa1,
4484 unsigned in_pos, unsigned out_pos,
4485 __isl_take isl_multi_pw_aff *mpa2);
4486 __isl_give isl_multi_pw_aff *
4487 isl_multi_pw_aff_range_product(
4488 __isl_take isl_multi_pw_aff *mpa1,
4489 __isl_take isl_multi_pw_aff *mpa2);
4490 __isl_give isl_multi_pw_aff *
4491 isl_multi_pw_aff_flat_range_product(
4492 __isl_take isl_multi_pw_aff *mpa1,
4493 __isl_take isl_multi_pw_aff *mpa2);
4495 If the C<ls> argument of C<isl_multi_aff_lift> is not C<NULL>,
4496 then it is assigned the local space that lies at the basis of
4497 the lifting applied.
4499 #include <isl/aff.h>
4500 __isl_give isl_multi_aff *isl_multi_aff_pullback_multi_aff(
4501 __isl_take isl_multi_aff *ma1,
4502 __isl_take isl_multi_aff *ma2);
4503 __isl_give isl_pw_multi_aff *
4504 isl_pw_multi_aff_pullback_multi_aff(
4505 __isl_take isl_pw_multi_aff *pma,
4506 __isl_take isl_multi_aff *ma);
4507 __isl_give isl_pw_multi_aff *
4508 isl_pw_multi_aff_pullback_pw_multi_aff(
4509 __isl_take isl_pw_multi_aff *pma1,
4510 __isl_take isl_pw_multi_aff *pma2);
4512 The function C<isl_multi_aff_pullback_multi_aff> precomposes C<ma1> by C<ma2>.
4513 In other words, C<ma2> is plugged
4516 __isl_give isl_set *isl_multi_aff_lex_le_set(
4517 __isl_take isl_multi_aff *ma1,
4518 __isl_take isl_multi_aff *ma2);
4519 __isl_give isl_set *isl_multi_aff_lex_ge_set(
4520 __isl_take isl_multi_aff *ma1,
4521 __isl_take isl_multi_aff *ma2);
4523 The function C<isl_multi_aff_lex_le_set> returns a set
4524 containing those elements in the shared domain space
4525 where C<ma1> is lexicographically smaller than or
4528 An expression can be read from input using
4530 #include <isl/aff.h>
4531 __isl_give isl_multi_aff *isl_multi_aff_read_from_str(
4532 isl_ctx *ctx, const char *str);
4533 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_read_from_str(
4534 isl_ctx *ctx, const char *str);
4535 __isl_give isl_union_pw_multi_aff *
4536 isl_union_pw_multi_aff_read_from_str(
4537 isl_ctx *ctx, const char *str);
4539 An expression can be printed using
4541 #include <isl/aff.h>
4542 __isl_give isl_printer *isl_printer_print_multi_aff(
4543 __isl_take isl_printer *p,
4544 __isl_keep isl_multi_aff *maff);
4545 __isl_give isl_printer *isl_printer_print_pw_multi_aff(
4546 __isl_take isl_printer *p,
4547 __isl_keep isl_pw_multi_aff *pma);
4548 __isl_give isl_printer *isl_printer_print_union_pw_multi_aff(
4549 __isl_take isl_printer *p,
4550 __isl_keep isl_union_pw_multi_aff *upma);
4551 __isl_give isl_printer *isl_printer_print_multi_pw_aff(
4552 __isl_take isl_printer *p,
4553 __isl_keep isl_multi_pw_aff *mpa);
4557 Points are elements of a set. They can be used to construct
4558 simple sets (boxes) or they can be used to represent the
4559 individual elements of a set.
4560 The zero point (the origin) can be created using
4562 __isl_give isl_point *isl_point_zero(__isl_take isl_space *space);
4564 The coordinates of a point can be inspected, set and changed
4567 int isl_point_get_coordinate(__isl_keep isl_point *pnt,
4568 enum isl_dim_type type, int pos, isl_int *v);
4569 __isl_give isl_val *isl_point_get_coordinate_val(
4570 __isl_keep isl_point *pnt,
4571 enum isl_dim_type type, int pos);
4572 __isl_give isl_point *isl_point_set_coordinate(
4573 __isl_take isl_point *pnt,
4574 enum isl_dim_type type, int pos, isl_int v);
4575 __isl_give isl_point *isl_point_set_coordinate_val(
4576 __isl_take isl_point *pnt,
4577 enum isl_dim_type type, int pos,
4578 __isl_take isl_val *v);
4580 __isl_give isl_point *isl_point_add_ui(
4581 __isl_take isl_point *pnt,
4582 enum isl_dim_type type, int pos, unsigned val);
4583 __isl_give isl_point *isl_point_sub_ui(
4584 __isl_take isl_point *pnt,
4585 enum isl_dim_type type, int pos, unsigned val);
4587 Other properties can be obtained using
4589 isl_ctx *isl_point_get_ctx(__isl_keep isl_point *pnt);
4591 Points can be copied or freed using
4593 __isl_give isl_point *isl_point_copy(
4594 __isl_keep isl_point *pnt);
4595 void isl_point_free(__isl_take isl_point *pnt);
4597 A singleton set can be created from a point using
4599 __isl_give isl_basic_set *isl_basic_set_from_point(
4600 __isl_take isl_point *pnt);
4601 __isl_give isl_set *isl_set_from_point(
4602 __isl_take isl_point *pnt);
4604 and a box can be created from two opposite extremal points using
4606 __isl_give isl_basic_set *isl_basic_set_box_from_points(
4607 __isl_take isl_point *pnt1,
4608 __isl_take isl_point *pnt2);
4609 __isl_give isl_set *isl_set_box_from_points(
4610 __isl_take isl_point *pnt1,
4611 __isl_take isl_point *pnt2);
4613 All elements of a B<bounded> (union) set can be enumerated using
4614 the following functions.
4616 int isl_set_foreach_point(__isl_keep isl_set *set,
4617 int (*fn)(__isl_take isl_point *pnt, void *user),
4619 int isl_union_set_foreach_point(__isl_keep isl_union_set *uset,
4620 int (*fn)(__isl_take isl_point *pnt, void *user),
4623 The function C<fn> is called for each integer point in
4624 C<set> with as second argument the last argument of
4625 the C<isl_set_foreach_point> call. The function C<fn>
4626 should return C<0> on success and C<-1> on failure.
4627 In the latter case, C<isl_set_foreach_point> will stop
4628 enumerating and return C<-1> as well.
4629 If the enumeration is performed successfully and to completion,
4630 then C<isl_set_foreach_point> returns C<0>.
4632 To obtain a single point of a (basic) set, use
4634 __isl_give isl_point *isl_basic_set_sample_point(
4635 __isl_take isl_basic_set *bset);
4636 __isl_give isl_point *isl_set_sample_point(
4637 __isl_take isl_set *set);
4639 If C<set> does not contain any (integer) points, then the
4640 resulting point will be ``void'', a property that can be
4643 int isl_point_is_void(__isl_keep isl_point *pnt);
4645 =head2 Piecewise Quasipolynomials
4647 A piecewise quasipolynomial is a particular kind of function that maps
4648 a parametric point to a rational value.
4649 More specifically, a quasipolynomial is a polynomial expression in greatest
4650 integer parts of affine expressions of parameters and variables.
4651 A piecewise quasipolynomial is a subdivision of a given parametric
4652 domain into disjoint cells with a quasipolynomial associated to
4653 each cell. The value of the piecewise quasipolynomial at a given
4654 point is the value of the quasipolynomial associated to the cell
4655 that contains the point. Outside of the union of cells,
4656 the value is assumed to be zero.
4657 For example, the piecewise quasipolynomial
4659 [n] -> { [x] -> ((1 + n) - x) : x <= n and x >= 0 }
4661 maps C<x> to C<1 + n - x> for values of C<x> between C<0> and C<n>.
4662 A given piecewise quasipolynomial has a fixed domain dimension.
4663 Union piecewise quasipolynomials are used to contain piecewise quasipolynomials
4664 defined over different domains.
4665 Piecewise quasipolynomials are mainly used by the C<barvinok>
4666 library for representing the number of elements in a parametric set or map.
4667 For example, the piecewise quasipolynomial above represents
4668 the number of points in the map
4670 [n] -> { [x] -> [y] : x,y >= 0 and 0 <= x + y <= n }
4672 =head3 Input and Output
4674 Piecewise quasipolynomials can be read from input using
4676 __isl_give isl_union_pw_qpolynomial *
4677 isl_union_pw_qpolynomial_read_from_str(
4678 isl_ctx *ctx, const char *str);
4680 Quasipolynomials and piecewise quasipolynomials can be printed
4681 using the following functions.
4683 __isl_give isl_printer *isl_printer_print_qpolynomial(
4684 __isl_take isl_printer *p,
4685 __isl_keep isl_qpolynomial *qp);
4687 __isl_give isl_printer *isl_printer_print_pw_qpolynomial(
4688 __isl_take isl_printer *p,
4689 __isl_keep isl_pw_qpolynomial *pwqp);
4691 __isl_give isl_printer *isl_printer_print_union_pw_qpolynomial(
4692 __isl_take isl_printer *p,
4693 __isl_keep isl_union_pw_qpolynomial *upwqp);
4695 The output format of the printer
4696 needs to be set to either C<ISL_FORMAT_ISL> or C<ISL_FORMAT_C>.
4697 For C<isl_printer_print_union_pw_qpolynomial>, only C<ISL_FORMAT_ISL>
4699 In case of printing in C<ISL_FORMAT_C>, the user may want
4700 to set the names of all dimensions
4702 __isl_give isl_qpolynomial *isl_qpolynomial_set_dim_name(
4703 __isl_take isl_qpolynomial *qp,
4704 enum isl_dim_type type, unsigned pos,
4706 __isl_give isl_pw_qpolynomial *
4707 isl_pw_qpolynomial_set_dim_name(
4708 __isl_take isl_pw_qpolynomial *pwqp,
4709 enum isl_dim_type type, unsigned pos,
4712 =head3 Creating New (Piecewise) Quasipolynomials
4714 Some simple quasipolynomials can be created using the following functions.
4715 More complicated quasipolynomials can be created by applying
4716 operations such as addition and multiplication
4717 on the resulting quasipolynomials
4719 __isl_give isl_qpolynomial *isl_qpolynomial_zero_on_domain(
4720 __isl_take isl_space *domain);
4721 __isl_give isl_qpolynomial *isl_qpolynomial_one_on_domain(
4722 __isl_take isl_space *domain);
4723 __isl_give isl_qpolynomial *isl_qpolynomial_infty_on_domain(
4724 __isl_take isl_space *domain);
4725 __isl_give isl_qpolynomial *isl_qpolynomial_neginfty_on_domain(
4726 __isl_take isl_space *domain);
4727 __isl_give isl_qpolynomial *isl_qpolynomial_nan_on_domain(
4728 __isl_take isl_space *domain);
4729 __isl_give isl_qpolynomial *isl_qpolynomial_rat_cst_on_domain(
4730 __isl_take isl_space *domain,
4731 const isl_int n, const isl_int d);
4732 __isl_give isl_qpolynomial *isl_qpolynomial_val_on_domain(
4733 __isl_take isl_space *domain,
4734 __isl_take isl_val *val);
4735 __isl_give isl_qpolynomial *isl_qpolynomial_var_on_domain(
4736 __isl_take isl_space *domain,
4737 enum isl_dim_type type, unsigned pos);
4738 __isl_give isl_qpolynomial *isl_qpolynomial_from_aff(
4739 __isl_take isl_aff *aff);
4741 Note that the space in which a quasipolynomial lives is a map space
4742 with a one-dimensional range. The C<domain> argument in some of
4743 the functions above corresponds to the domain of this map space.
4745 The zero piecewise quasipolynomial or a piecewise quasipolynomial
4746 with a single cell can be created using the following functions.
4747 Multiple of these single cell piecewise quasipolynomials can
4748 be combined to create more complicated piecewise quasipolynomials.
4750 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_zero(
4751 __isl_take isl_space *space);
4752 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_alloc(
4753 __isl_take isl_set *set,
4754 __isl_take isl_qpolynomial *qp);
4755 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_from_qpolynomial(
4756 __isl_take isl_qpolynomial *qp);
4757 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_from_pw_aff(
4758 __isl_take isl_pw_aff *pwaff);
4760 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_zero(
4761 __isl_take isl_space *space);
4762 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_from_pw_qpolynomial(
4763 __isl_take isl_pw_qpolynomial *pwqp);
4764 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_add_pw_qpolynomial(
4765 __isl_take isl_union_pw_qpolynomial *upwqp,
4766 __isl_take isl_pw_qpolynomial *pwqp);
4768 Quasipolynomials can be copied and freed again using the following
4771 __isl_give isl_qpolynomial *isl_qpolynomial_copy(
4772 __isl_keep isl_qpolynomial *qp);
4773 void *isl_qpolynomial_free(__isl_take isl_qpolynomial *qp);
4775 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_copy(
4776 __isl_keep isl_pw_qpolynomial *pwqp);
4777 void *isl_pw_qpolynomial_free(
4778 __isl_take isl_pw_qpolynomial *pwqp);
4780 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_copy(
4781 __isl_keep isl_union_pw_qpolynomial *upwqp);
4782 void *isl_union_pw_qpolynomial_free(
4783 __isl_take isl_union_pw_qpolynomial *upwqp);
4785 =head3 Inspecting (Piecewise) Quasipolynomials
4787 To iterate over all piecewise quasipolynomials in a union
4788 piecewise quasipolynomial, use the following function
4790 int isl_union_pw_qpolynomial_foreach_pw_qpolynomial(
4791 __isl_keep isl_union_pw_qpolynomial *upwqp,
4792 int (*fn)(__isl_take isl_pw_qpolynomial *pwqp, void *user),
4795 To extract the piecewise quasipolynomial in a given space from a union, use
4797 __isl_give isl_pw_qpolynomial *
4798 isl_union_pw_qpolynomial_extract_pw_qpolynomial(
4799 __isl_keep isl_union_pw_qpolynomial *upwqp,
4800 __isl_take isl_space *space);
4802 To iterate over the cells in a piecewise quasipolynomial,
4803 use either of the following two functions
4805 int isl_pw_qpolynomial_foreach_piece(
4806 __isl_keep isl_pw_qpolynomial *pwqp,
4807 int (*fn)(__isl_take isl_set *set,
4808 __isl_take isl_qpolynomial *qp,
4809 void *user), void *user);
4810 int isl_pw_qpolynomial_foreach_lifted_piece(
4811 __isl_keep isl_pw_qpolynomial *pwqp,
4812 int (*fn)(__isl_take isl_set *set,
4813 __isl_take isl_qpolynomial *qp,
4814 void *user), void *user);
4816 As usual, the function C<fn> should return C<0> on success
4817 and C<-1> on failure. The difference between
4818 C<isl_pw_qpolynomial_foreach_piece> and
4819 C<isl_pw_qpolynomial_foreach_lifted_piece> is that
4820 C<isl_pw_qpolynomial_foreach_lifted_piece> will first
4821 compute unique representations for all existentially quantified
4822 variables and then turn these existentially quantified variables
4823 into extra set variables, adapting the associated quasipolynomial
4824 accordingly. This means that the C<set> passed to C<fn>
4825 will not have any existentially quantified variables, but that
4826 the dimensions of the sets may be different for different
4827 invocations of C<fn>.
4829 The constant term of a quasipolynomial can be extracted using
4831 __isl_give isl_val *isl_qpolynomial_get_constant_val(
4832 __isl_keep isl_qpolynomial *qp);
4834 To iterate over all terms in a quasipolynomial,
4837 int isl_qpolynomial_foreach_term(
4838 __isl_keep isl_qpolynomial *qp,
4839 int (*fn)(__isl_take isl_term *term,
4840 void *user), void *user);
4842 The terms themselves can be inspected and freed using
4845 unsigned isl_term_dim(__isl_keep isl_term *term,
4846 enum isl_dim_type type);
4847 void isl_term_get_num(__isl_keep isl_term *term,
4849 void isl_term_get_den(__isl_keep isl_term *term,
4851 __isl_give isl_val *isl_term_get_coefficient_val(
4852 __isl_keep isl_term *term);
4853 int isl_term_get_exp(__isl_keep isl_term *term,
4854 enum isl_dim_type type, unsigned pos);
4855 __isl_give isl_aff *isl_term_get_div(
4856 __isl_keep isl_term *term, unsigned pos);
4857 void isl_term_free(__isl_take isl_term *term);
4859 Each term is a product of parameters, set variables and
4860 integer divisions. The function C<isl_term_get_exp>
4861 returns the exponent of a given dimensions in the given term.
4862 The C<isl_int>s in the arguments of C<isl_term_get_num>
4863 and C<isl_term_get_den> need to have been initialized
4864 using C<isl_int_init> before calling these functions.
4866 =head3 Properties of (Piecewise) Quasipolynomials
4868 To check whether a quasipolynomial is actually a constant,
4869 use the following function.
4871 int isl_qpolynomial_is_cst(__isl_keep isl_qpolynomial *qp,
4872 isl_int *n, isl_int *d);
4874 If C<qp> is a constant and if C<n> and C<d> are not C<NULL>
4875 then the numerator and denominator of the constant
4876 are returned in C<*n> and C<*d>, respectively.
4878 To check whether two union piecewise quasipolynomials are
4879 obviously equal, use
4881 int isl_union_pw_qpolynomial_plain_is_equal(
4882 __isl_keep isl_union_pw_qpolynomial *upwqp1,
4883 __isl_keep isl_union_pw_qpolynomial *upwqp2);
4885 =head3 Operations on (Piecewise) Quasipolynomials
4887 __isl_give isl_qpolynomial *isl_qpolynomial_scale(
4888 __isl_take isl_qpolynomial *qp, isl_int v);
4889 __isl_give isl_qpolynomial *isl_qpolynomial_scale_val(
4890 __isl_take isl_qpolynomial *qp,
4891 __isl_take isl_val *v);
4892 __isl_give isl_qpolynomial *isl_qpolynomial_neg(
4893 __isl_take isl_qpolynomial *qp);
4894 __isl_give isl_qpolynomial *isl_qpolynomial_add(
4895 __isl_take isl_qpolynomial *qp1,
4896 __isl_take isl_qpolynomial *qp2);
4897 __isl_give isl_qpolynomial *isl_qpolynomial_sub(
4898 __isl_take isl_qpolynomial *qp1,
4899 __isl_take isl_qpolynomial *qp2);
4900 __isl_give isl_qpolynomial *isl_qpolynomial_mul(
4901 __isl_take isl_qpolynomial *qp1,
4902 __isl_take isl_qpolynomial *qp2);
4903 __isl_give isl_qpolynomial *isl_qpolynomial_pow(
4904 __isl_take isl_qpolynomial *qp, unsigned exponent);
4906 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_fix_val(
4907 __isl_take isl_pw_qpolynomial *pwqp,
4908 enum isl_dim_type type, unsigned n,
4909 __isl_take isl_val *v);
4910 __isl_give isl_pw_qpolynomial *
4911 isl_pw_qpolynomial_scale_val(
4912 __isl_take isl_pw_qpolynomial *pwqp,
4913 __isl_take isl_val *v);
4914 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_add(
4915 __isl_take isl_pw_qpolynomial *pwqp1,
4916 __isl_take isl_pw_qpolynomial *pwqp2);
4917 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_sub(
4918 __isl_take isl_pw_qpolynomial *pwqp1,
4919 __isl_take isl_pw_qpolynomial *pwqp2);
4920 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_add_disjoint(
4921 __isl_take isl_pw_qpolynomial *pwqp1,
4922 __isl_take isl_pw_qpolynomial *pwqp2);
4923 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_neg(
4924 __isl_take isl_pw_qpolynomial *pwqp);
4925 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_mul(
4926 __isl_take isl_pw_qpolynomial *pwqp1,
4927 __isl_take isl_pw_qpolynomial *pwqp2);
4928 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_pow(
4929 __isl_take isl_pw_qpolynomial *pwqp, unsigned exponent);
4931 __isl_give isl_union_pw_qpolynomial *
4932 isl_union_pw_qpolynomial_scale_val(
4933 __isl_take isl_union_pw_qpolynomial *upwqp,
4934 __isl_take isl_val *v);
4935 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_add(
4936 __isl_take isl_union_pw_qpolynomial *upwqp1,
4937 __isl_take isl_union_pw_qpolynomial *upwqp2);
4938 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_sub(
4939 __isl_take isl_union_pw_qpolynomial *upwqp1,
4940 __isl_take isl_union_pw_qpolynomial *upwqp2);
4941 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_mul(
4942 __isl_take isl_union_pw_qpolynomial *upwqp1,
4943 __isl_take isl_union_pw_qpolynomial *upwqp2);
4945 __isl_give isl_qpolynomial *isl_pw_qpolynomial_eval(
4946 __isl_take isl_pw_qpolynomial *pwqp,
4947 __isl_take isl_point *pnt);
4949 __isl_give isl_qpolynomial *isl_union_pw_qpolynomial_eval(
4950 __isl_take isl_union_pw_qpolynomial *upwqp,
4951 __isl_take isl_point *pnt);
4953 __isl_give isl_set *isl_pw_qpolynomial_domain(
4954 __isl_take isl_pw_qpolynomial *pwqp);
4955 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_intersect_domain(
4956 __isl_take isl_pw_qpolynomial *pwpq,
4957 __isl_take isl_set *set);
4958 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_intersect_params(
4959 __isl_take isl_pw_qpolynomial *pwpq,
4960 __isl_take isl_set *set);
4962 __isl_give isl_union_set *isl_union_pw_qpolynomial_domain(
4963 __isl_take isl_union_pw_qpolynomial *upwqp);
4964 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_intersect_domain(
4965 __isl_take isl_union_pw_qpolynomial *upwpq,
4966 __isl_take isl_union_set *uset);
4967 __isl_give isl_union_pw_qpolynomial *
4968 isl_union_pw_qpolynomial_intersect_params(
4969 __isl_take isl_union_pw_qpolynomial *upwpq,
4970 __isl_take isl_set *set);
4972 __isl_give isl_qpolynomial *isl_qpolynomial_align_params(
4973 __isl_take isl_qpolynomial *qp,
4974 __isl_take isl_space *model);
4976 __isl_give isl_qpolynomial *isl_qpolynomial_project_domain_on_params(
4977 __isl_take isl_qpolynomial *qp);
4978 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_project_domain_on_params(
4979 __isl_take isl_pw_qpolynomial *pwqp);
4981 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_coalesce(
4982 __isl_take isl_union_pw_qpolynomial *upwqp);
4984 __isl_give isl_qpolynomial *isl_qpolynomial_gist_params(
4985 __isl_take isl_qpolynomial *qp,
4986 __isl_take isl_set *context);
4987 __isl_give isl_qpolynomial *isl_qpolynomial_gist(
4988 __isl_take isl_qpolynomial *qp,
4989 __isl_take isl_set *context);
4991 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_gist_params(
4992 __isl_take isl_pw_qpolynomial *pwqp,
4993 __isl_take isl_set *context);
4994 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_gist(
4995 __isl_take isl_pw_qpolynomial *pwqp,
4996 __isl_take isl_set *context);
4998 __isl_give isl_union_pw_qpolynomial *
4999 isl_union_pw_qpolynomial_gist_params(
5000 __isl_take isl_union_pw_qpolynomial *upwqp,
5001 __isl_take isl_set *context);
5002 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_gist(
5003 __isl_take isl_union_pw_qpolynomial *upwqp,
5004 __isl_take isl_union_set *context);
5006 The gist operation applies the gist operation to each of
5007 the cells in the domain of the input piecewise quasipolynomial.
5008 The context is also exploited
5009 to simplify the quasipolynomials associated to each cell.
5011 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_to_polynomial(
5012 __isl_take isl_pw_qpolynomial *pwqp, int sign);
5013 __isl_give isl_union_pw_qpolynomial *
5014 isl_union_pw_qpolynomial_to_polynomial(
5015 __isl_take isl_union_pw_qpolynomial *upwqp, int sign);
5017 Approximate each quasipolynomial by a polynomial. If C<sign> is positive,
5018 the polynomial will be an overapproximation. If C<sign> is negative,
5019 it will be an underapproximation. If C<sign> is zero, the approximation
5020 will lie somewhere in between.
5022 =head2 Bounds on Piecewise Quasipolynomials and Piecewise Quasipolynomial Reductions
5024 A piecewise quasipolynomial reduction is a piecewise
5025 reduction (or fold) of quasipolynomials.
5026 In particular, the reduction can be maximum or a minimum.
5027 The objects are mainly used to represent the result of
5028 an upper or lower bound on a quasipolynomial over its domain,
5029 i.e., as the result of the following function.
5031 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_bound(
5032 __isl_take isl_pw_qpolynomial *pwqp,
5033 enum isl_fold type, int *tight);
5035 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_bound(
5036 __isl_take isl_union_pw_qpolynomial *upwqp,
5037 enum isl_fold type, int *tight);
5039 The C<type> argument may be either C<isl_fold_min> or C<isl_fold_max>.
5040 If C<tight> is not C<NULL>, then C<*tight> is set to C<1>
5041 is the returned bound is known be tight, i.e., for each value
5042 of the parameters there is at least
5043 one element in the domain that reaches the bound.
5044 If the domain of C<pwqp> is not wrapping, then the bound is computed
5045 over all elements in that domain and the result has a purely parametric
5046 domain. If the domain of C<pwqp> is wrapping, then the bound is
5047 computed over the range of the wrapped relation. The domain of the
5048 wrapped relation becomes the domain of the result.
5050 A (piecewise) quasipolynomial reduction can be copied or freed using the
5051 following functions.
5053 __isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_copy(
5054 __isl_keep isl_qpolynomial_fold *fold);
5055 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_copy(
5056 __isl_keep isl_pw_qpolynomial_fold *pwf);
5057 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_copy(
5058 __isl_keep isl_union_pw_qpolynomial_fold *upwf);
5059 void isl_qpolynomial_fold_free(
5060 __isl_take isl_qpolynomial_fold *fold);
5061 void *isl_pw_qpolynomial_fold_free(
5062 __isl_take isl_pw_qpolynomial_fold *pwf);
5063 void *isl_union_pw_qpolynomial_fold_free(
5064 __isl_take isl_union_pw_qpolynomial_fold *upwf);
5066 =head3 Printing Piecewise Quasipolynomial Reductions
5068 Piecewise quasipolynomial reductions can be printed
5069 using the following function.
5071 __isl_give isl_printer *isl_printer_print_pw_qpolynomial_fold(
5072 __isl_take isl_printer *p,
5073 __isl_keep isl_pw_qpolynomial_fold *pwf);
5074 __isl_give isl_printer *isl_printer_print_union_pw_qpolynomial_fold(
5075 __isl_take isl_printer *p,
5076 __isl_keep isl_union_pw_qpolynomial_fold *upwf);
5078 For C<isl_printer_print_pw_qpolynomial_fold>,
5079 output format of the printer
5080 needs to be set to either C<ISL_FORMAT_ISL> or C<ISL_FORMAT_C>.
5081 For C<isl_printer_print_union_pw_qpolynomial_fold>,
5082 output format of the printer
5083 needs to be set to C<ISL_FORMAT_ISL>.
5084 In case of printing in C<ISL_FORMAT_C>, the user may want
5085 to set the names of all dimensions
5087 __isl_give isl_pw_qpolynomial_fold *
5088 isl_pw_qpolynomial_fold_set_dim_name(
5089 __isl_take isl_pw_qpolynomial_fold *pwf,
5090 enum isl_dim_type type, unsigned pos,
5093 =head3 Inspecting (Piecewise) Quasipolynomial Reductions
5095 To iterate over all piecewise quasipolynomial reductions in a union
5096 piecewise quasipolynomial reduction, use the following function
5098 int isl_union_pw_qpolynomial_fold_foreach_pw_qpolynomial_fold(
5099 __isl_keep isl_union_pw_qpolynomial_fold *upwf,
5100 int (*fn)(__isl_take isl_pw_qpolynomial_fold *pwf,
5101 void *user), void *user);
5103 To iterate over the cells in a piecewise quasipolynomial reduction,
5104 use either of the following two functions
5106 int isl_pw_qpolynomial_fold_foreach_piece(
5107 __isl_keep isl_pw_qpolynomial_fold *pwf,
5108 int (*fn)(__isl_take isl_set *set,
5109 __isl_take isl_qpolynomial_fold *fold,
5110 void *user), void *user);
5111 int isl_pw_qpolynomial_fold_foreach_lifted_piece(
5112 __isl_keep isl_pw_qpolynomial_fold *pwf,
5113 int (*fn)(__isl_take isl_set *set,
5114 __isl_take isl_qpolynomial_fold *fold,
5115 void *user), void *user);
5117 See L<Inspecting (Piecewise) Quasipolynomials> for an explanation
5118 of the difference between these two functions.
5120 To iterate over all quasipolynomials in a reduction, use
5122 int isl_qpolynomial_fold_foreach_qpolynomial(
5123 __isl_keep isl_qpolynomial_fold *fold,
5124 int (*fn)(__isl_take isl_qpolynomial *qp,
5125 void *user), void *user);
5127 =head3 Properties of Piecewise Quasipolynomial Reductions
5129 To check whether two union piecewise quasipolynomial reductions are
5130 obviously equal, use
5132 int isl_union_pw_qpolynomial_fold_plain_is_equal(
5133 __isl_keep isl_union_pw_qpolynomial_fold *upwf1,
5134 __isl_keep isl_union_pw_qpolynomial_fold *upwf2);
5136 =head3 Operations on Piecewise Quasipolynomial Reductions
5138 __isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_scale(
5139 __isl_take isl_qpolynomial_fold *fold, isl_int v);
5140 __isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_scale_val(
5141 __isl_take isl_qpolynomial_fold *fold,
5142 __isl_take isl_val *v);
5143 __isl_give isl_pw_qpolynomial_fold *
5144 isl_pw_qpolynomial_fold_scale_val(
5145 __isl_take isl_pw_qpolynomial_fold *pwf,
5146 __isl_take isl_val *v);
5147 __isl_give isl_union_pw_qpolynomial_fold *
5148 isl_union_pw_qpolynomial_fold_scale_val(
5149 __isl_take isl_union_pw_qpolynomial_fold *upwf,
5150 __isl_take isl_val *v);
5152 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_add(
5153 __isl_take isl_pw_qpolynomial_fold *pwf1,
5154 __isl_take isl_pw_qpolynomial_fold *pwf2);
5156 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_fold(
5157 __isl_take isl_pw_qpolynomial_fold *pwf1,
5158 __isl_take isl_pw_qpolynomial_fold *pwf2);
5160 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_fold(
5161 __isl_take isl_union_pw_qpolynomial_fold *upwf1,
5162 __isl_take isl_union_pw_qpolynomial_fold *upwf2);
5164 __isl_give isl_qpolynomial *isl_pw_qpolynomial_fold_eval(
5165 __isl_take isl_pw_qpolynomial_fold *pwf,
5166 __isl_take isl_point *pnt);
5168 __isl_give isl_qpolynomial *isl_union_pw_qpolynomial_fold_eval(
5169 __isl_take isl_union_pw_qpolynomial_fold *upwf,
5170 __isl_take isl_point *pnt);
5172 __isl_give isl_pw_qpolynomial_fold *
5173 isl_pw_qpolynomial_fold_intersect_params(
5174 __isl_take isl_pw_qpolynomial_fold *pwf,
5175 __isl_take isl_set *set);
5177 __isl_give isl_union_set *isl_union_pw_qpolynomial_fold_domain(
5178 __isl_take isl_union_pw_qpolynomial_fold *upwf);
5179 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_intersect_domain(
5180 __isl_take isl_union_pw_qpolynomial_fold *upwf,
5181 __isl_take isl_union_set *uset);
5182 __isl_give isl_union_pw_qpolynomial_fold *
5183 isl_union_pw_qpolynomial_fold_intersect_params(
5184 __isl_take isl_union_pw_qpolynomial_fold *upwf,
5185 __isl_take isl_set *set);
5187 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_project_domain_on_params(
5188 __isl_take isl_pw_qpolynomial_fold *pwf);
5190 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_coalesce(
5191 __isl_take isl_pw_qpolynomial_fold *pwf);
5193 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_coalesce(
5194 __isl_take isl_union_pw_qpolynomial_fold *upwf);
5196 __isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_gist_params(
5197 __isl_take isl_qpolynomial_fold *fold,
5198 __isl_take isl_set *context);
5199 __isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_gist(
5200 __isl_take isl_qpolynomial_fold *fold,
5201 __isl_take isl_set *context);
5203 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_gist(
5204 __isl_take isl_pw_qpolynomial_fold *pwf,
5205 __isl_take isl_set *context);
5206 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_gist_params(
5207 __isl_take isl_pw_qpolynomial_fold *pwf,
5208 __isl_take isl_set *context);
5210 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_gist(
5211 __isl_take isl_union_pw_qpolynomial_fold *upwf,
5212 __isl_take isl_union_set *context);
5213 __isl_give isl_union_pw_qpolynomial_fold *
5214 isl_union_pw_qpolynomial_fold_gist_params(
5215 __isl_take isl_union_pw_qpolynomial_fold *upwf,
5216 __isl_take isl_set *context);
5218 The gist operation applies the gist operation to each of
5219 the cells in the domain of the input piecewise quasipolynomial reduction.
5220 In future, the operation will also exploit the context
5221 to simplify the quasipolynomial reductions associated to each cell.
5223 __isl_give isl_pw_qpolynomial_fold *
5224 isl_set_apply_pw_qpolynomial_fold(
5225 __isl_take isl_set *set,
5226 __isl_take isl_pw_qpolynomial_fold *pwf,
5228 __isl_give isl_pw_qpolynomial_fold *
5229 isl_map_apply_pw_qpolynomial_fold(
5230 __isl_take isl_map *map,
5231 __isl_take isl_pw_qpolynomial_fold *pwf,
5233 __isl_give isl_union_pw_qpolynomial_fold *
5234 isl_union_set_apply_union_pw_qpolynomial_fold(
5235 __isl_take isl_union_set *uset,
5236 __isl_take isl_union_pw_qpolynomial_fold *upwf,
5238 __isl_give isl_union_pw_qpolynomial_fold *
5239 isl_union_map_apply_union_pw_qpolynomial_fold(
5240 __isl_take isl_union_map *umap,
5241 __isl_take isl_union_pw_qpolynomial_fold *upwf,
5244 The functions taking a map
5245 compose the given map with the given piecewise quasipolynomial reduction.
5246 That is, compute a bound (of the same type as C<pwf> or C<upwf> itself)
5247 over all elements in the intersection of the range of the map
5248 and the domain of the piecewise quasipolynomial reduction
5249 as a function of an element in the domain of the map.
5250 The functions taking a set compute a bound over all elements in the
5251 intersection of the set and the domain of the
5252 piecewise quasipolynomial reduction.
5254 =head2 Parametric Vertex Enumeration
5256 The parametric vertex enumeration described in this section
5257 is mainly intended to be used internally and by the C<barvinok>
5260 #include <isl/vertices.h>
5261 __isl_give isl_vertices *isl_basic_set_compute_vertices(
5262 __isl_keep isl_basic_set *bset);
5264 The function C<isl_basic_set_compute_vertices> performs the
5265 actual computation of the parametric vertices and the chamber
5266 decomposition and store the result in an C<isl_vertices> object.
5267 This information can be queried by either iterating over all
5268 the vertices or iterating over all the chambers or cells
5269 and then iterating over all vertices that are active on the chamber.
5271 int isl_vertices_foreach_vertex(
5272 __isl_keep isl_vertices *vertices,
5273 int (*fn)(__isl_take isl_vertex *vertex, void *user),
5276 int isl_vertices_foreach_cell(
5277 __isl_keep isl_vertices *vertices,
5278 int (*fn)(__isl_take isl_cell *cell, void *user),
5280 int isl_cell_foreach_vertex(__isl_keep isl_cell *cell,
5281 int (*fn)(__isl_take isl_vertex *vertex, void *user),
5284 Other operations that can be performed on an C<isl_vertices> object are
5287 isl_ctx *isl_vertices_get_ctx(
5288 __isl_keep isl_vertices *vertices);
5289 int isl_vertices_get_n_vertices(
5290 __isl_keep isl_vertices *vertices);
5291 void isl_vertices_free(__isl_take isl_vertices *vertices);
5293 Vertices can be inspected and destroyed using the following functions.
5295 isl_ctx *isl_vertex_get_ctx(__isl_keep isl_vertex *vertex);
5296 int isl_vertex_get_id(__isl_keep isl_vertex *vertex);
5297 __isl_give isl_basic_set *isl_vertex_get_domain(
5298 __isl_keep isl_vertex *vertex);
5299 __isl_give isl_basic_set *isl_vertex_get_expr(
5300 __isl_keep isl_vertex *vertex);
5301 void isl_vertex_free(__isl_take isl_vertex *vertex);
5303 C<isl_vertex_get_expr> returns a singleton parametric set describing
5304 the vertex, while C<isl_vertex_get_domain> returns the activity domain
5306 Note that C<isl_vertex_get_domain> and C<isl_vertex_get_expr> return
5307 B<rational> basic sets, so they should mainly be used for inspection
5308 and should not be mixed with integer sets.
5310 Chambers can be inspected and destroyed using the following functions.
5312 isl_ctx *isl_cell_get_ctx(__isl_keep isl_cell *cell);
5313 __isl_give isl_basic_set *isl_cell_get_domain(
5314 __isl_keep isl_cell *cell);
5315 void isl_cell_free(__isl_take isl_cell *cell);
5317 =head1 Polyhedral Compilation Library
5319 This section collects functionality in C<isl> that has been specifically
5320 designed for use during polyhedral compilation.
5322 =head2 Dependence Analysis
5324 C<isl> contains specialized functionality for performing
5325 array dataflow analysis. That is, given a I<sink> access relation
5326 and a collection of possible I<source> access relations,
5327 C<isl> can compute relations that describe
5328 for each iteration of the sink access, which iteration
5329 of which of the source access relations was the last
5330 to access the same data element before the given iteration
5332 The resulting dependence relations map source iterations
5333 to the corresponding sink iterations.
5334 To compute standard flow dependences, the sink should be
5335 a read, while the sources should be writes.
5336 If any of the source accesses are marked as being I<may>
5337 accesses, then there will be a dependence from the last
5338 I<must> access B<and> from any I<may> access that follows
5339 this last I<must> access.
5340 In particular, if I<all> sources are I<may> accesses,
5341 then memory based dependence analysis is performed.
5342 If, on the other hand, all sources are I<must> accesses,
5343 then value based dependence analysis is performed.
5345 #include <isl/flow.h>
5347 typedef int (*isl_access_level_before)(void *first, void *second);
5349 __isl_give isl_access_info *isl_access_info_alloc(
5350 __isl_take isl_map *sink,
5351 void *sink_user, isl_access_level_before fn,
5353 __isl_give isl_access_info *isl_access_info_add_source(
5354 __isl_take isl_access_info *acc,
5355 __isl_take isl_map *source, int must,
5357 void *isl_access_info_free(__isl_take isl_access_info *acc);
5359 __isl_give isl_flow *isl_access_info_compute_flow(
5360 __isl_take isl_access_info *acc);
5362 int isl_flow_foreach(__isl_keep isl_flow *deps,
5363 int (*fn)(__isl_take isl_map *dep, int must,
5364 void *dep_user, void *user),
5366 __isl_give isl_map *isl_flow_get_no_source(
5367 __isl_keep isl_flow *deps, int must);
5368 void isl_flow_free(__isl_take isl_flow *deps);
5370 The function C<isl_access_info_compute_flow> performs the actual
5371 dependence analysis. The other functions are used to construct
5372 the input for this function or to read off the output.
5374 The input is collected in an C<isl_access_info>, which can
5375 be created through a call to C<isl_access_info_alloc>.
5376 The arguments to this functions are the sink access relation
5377 C<sink>, a token C<sink_user> used to identify the sink
5378 access to the user, a callback function for specifying the
5379 relative order of source and sink accesses, and the number
5380 of source access relations that will be added.
5381 The callback function has type C<int (*)(void *first, void *second)>.
5382 The function is called with two user supplied tokens identifying
5383 either a source or the sink and it should return the shared nesting
5384 level and the relative order of the two accesses.
5385 In particular, let I<n> be the number of loops shared by
5386 the two accesses. If C<first> precedes C<second> textually,
5387 then the function should return I<2 * n + 1>; otherwise,
5388 it should return I<2 * n>.
5389 The sources can be added to the C<isl_access_info> by performing
5390 (at most) C<max_source> calls to C<isl_access_info_add_source>.
5391 C<must> indicates whether the source is a I<must> access
5392 or a I<may> access. Note that a multi-valued access relation
5393 should only be marked I<must> if every iteration in the domain
5394 of the relation accesses I<all> elements in its image.
5395 The C<source_user> token is again used to identify
5396 the source access. The range of the source access relation
5397 C<source> should have the same dimension as the range
5398 of the sink access relation.
5399 The C<isl_access_info_free> function should usually not be
5400 called explicitly, because it is called implicitly by
5401 C<isl_access_info_compute_flow>.
5403 The result of the dependence analysis is collected in an
5404 C<isl_flow>. There may be elements of
5405 the sink access for which no preceding source access could be
5406 found or for which all preceding sources are I<may> accesses.
5407 The relations containing these elements can be obtained through
5408 calls to C<isl_flow_get_no_source>, the first with C<must> set
5409 and the second with C<must> unset.
5410 In the case of standard flow dependence analysis,
5411 with the sink a read and the sources I<must> writes,
5412 the first relation corresponds to the reads from uninitialized
5413 array elements and the second relation is empty.
5414 The actual flow dependences can be extracted using
5415 C<isl_flow_foreach>. This function will call the user-specified
5416 callback function C<fn> for each B<non-empty> dependence between
5417 a source and the sink. The callback function is called
5418 with four arguments, the actual flow dependence relation
5419 mapping source iterations to sink iterations, a boolean that
5420 indicates whether it is a I<must> or I<may> dependence, a token
5421 identifying the source and an additional C<void *> with value
5422 equal to the third argument of the C<isl_flow_foreach> call.
5423 A dependence is marked I<must> if it originates from a I<must>
5424 source and if it is not followed by any I<may> sources.
5426 After finishing with an C<isl_flow>, the user should call
5427 C<isl_flow_free> to free all associated memory.
5429 A higher-level interface to dependence analysis is provided
5430 by the following function.
5432 #include <isl/flow.h>
5434 int isl_union_map_compute_flow(__isl_take isl_union_map *sink,
5435 __isl_take isl_union_map *must_source,
5436 __isl_take isl_union_map *may_source,
5437 __isl_take isl_union_map *schedule,
5438 __isl_give isl_union_map **must_dep,
5439 __isl_give isl_union_map **may_dep,
5440 __isl_give isl_union_map **must_no_source,
5441 __isl_give isl_union_map **may_no_source);
5443 The arrays are identified by the tuple names of the ranges
5444 of the accesses. The iteration domains by the tuple names
5445 of the domains of the accesses and of the schedule.
5446 The relative order of the iteration domains is given by the
5447 schedule. The relations returned through C<must_no_source>
5448 and C<may_no_source> are subsets of C<sink>.
5449 Any of C<must_dep>, C<may_dep>, C<must_no_source>
5450 or C<may_no_source> may be C<NULL>, but a C<NULL> value for
5451 any of the other arguments is treated as an error.
5453 =head3 Interaction with Dependence Analysis
5455 During the dependence analysis, we frequently need to perform
5456 the following operation. Given a relation between sink iterations
5457 and potential source iterations from a particular source domain,
5458 what is the last potential source iteration corresponding to each
5459 sink iteration. It can sometimes be convenient to adjust
5460 the set of potential source iterations before or after each such operation.
5461 The prototypical example is fuzzy array dataflow analysis,
5462 where we need to analyze if, based on data-dependent constraints,
5463 the sink iteration can ever be executed without one or more of
5464 the corresponding potential source iterations being executed.
5465 If so, we can introduce extra parameters and select an unknown
5466 but fixed source iteration from the potential source iterations.
5467 To be able to perform such manipulations, C<isl> provides the following
5470 #include <isl/flow.h>
5472 typedef __isl_give isl_restriction *(*isl_access_restrict)(
5473 __isl_keep isl_map *source_map,
5474 __isl_keep isl_set *sink, void *source_user,
5476 __isl_give isl_access_info *isl_access_info_set_restrict(
5477 __isl_take isl_access_info *acc,
5478 isl_access_restrict fn, void *user);
5480 The function C<isl_access_info_set_restrict> should be called
5481 before calling C<isl_access_info_compute_flow> and registers a callback function
5482 that will be called any time C<isl> is about to compute the last
5483 potential source. The first argument is the (reverse) proto-dependence,
5484 mapping sink iterations to potential source iterations.
5485 The second argument represents the sink iterations for which
5486 we want to compute the last source iteration.
5487 The third argument is the token corresponding to the source
5488 and the final argument is the token passed to C<isl_access_info_set_restrict>.
5489 The callback is expected to return a restriction on either the input or
5490 the output of the operation computing the last potential source.
5491 If the input needs to be restricted then restrictions are needed
5492 for both the source and the sink iterations. The sink iterations
5493 and the potential source iterations will be intersected with these sets.
5494 If the output needs to be restricted then only a restriction on the source
5495 iterations is required.
5496 If any error occurs, the callback should return C<NULL>.
5497 An C<isl_restriction> object can be created, freed and inspected
5498 using the following functions.
5500 #include <isl/flow.h>
5502 __isl_give isl_restriction *isl_restriction_input(
5503 __isl_take isl_set *source_restr,
5504 __isl_take isl_set *sink_restr);
5505 __isl_give isl_restriction *isl_restriction_output(
5506 __isl_take isl_set *source_restr);
5507 __isl_give isl_restriction *isl_restriction_none(
5508 __isl_take isl_map *source_map);
5509 __isl_give isl_restriction *isl_restriction_empty(
5510 __isl_take isl_map *source_map);
5511 void *isl_restriction_free(
5512 __isl_take isl_restriction *restr);
5513 isl_ctx *isl_restriction_get_ctx(
5514 __isl_keep isl_restriction *restr);
5516 C<isl_restriction_none> and C<isl_restriction_empty> are special
5517 cases of C<isl_restriction_input>. C<isl_restriction_none>
5518 is essentially equivalent to
5520 isl_restriction_input(isl_set_universe(
5521 isl_space_range(isl_map_get_space(source_map))),
5523 isl_space_domain(isl_map_get_space(source_map))));
5525 whereas C<isl_restriction_empty> is essentially equivalent to
5527 isl_restriction_input(isl_set_empty(
5528 isl_space_range(isl_map_get_space(source_map))),
5530 isl_space_domain(isl_map_get_space(source_map))));
5534 B<The functionality described in this section is fairly new
5535 and may be subject to change.>
5537 The following function can be used to compute a schedule
5538 for a union of domains.
5539 By default, the algorithm used to construct the schedule is similar
5540 to that of C<Pluto>.
5541 Alternatively, Feautrier's multi-dimensional scheduling algorithm can
5543 The generated schedule respects all C<validity> dependences.
5544 That is, all dependence distances over these dependences in the
5545 scheduled space are lexicographically positive.
5546 The default algorithm tries to minimize the dependence distances over
5547 C<proximity> dependences.
5548 Moreover, it tries to obtain sequences (bands) of schedule dimensions
5549 for groups of domains where the dependence distances have only
5550 non-negative values.
5551 When using Feautrier's algorithm, the C<proximity> dependence
5552 distances are only minimized during the extension to a
5553 full-dimensional schedule.
5555 #include <isl/schedule.h>
5556 __isl_give isl_schedule *isl_union_set_compute_schedule(
5557 __isl_take isl_union_set *domain,
5558 __isl_take isl_union_map *validity,
5559 __isl_take isl_union_map *proximity);
5560 void *isl_schedule_free(__isl_take isl_schedule *sched);
5562 A mapping from the domains to the scheduled space can be obtained
5563 from an C<isl_schedule> using the following function.
5565 __isl_give isl_union_map *isl_schedule_get_map(
5566 __isl_keep isl_schedule *sched);
5568 A representation of the schedule can be printed using
5570 __isl_give isl_printer *isl_printer_print_schedule(
5571 __isl_take isl_printer *p,
5572 __isl_keep isl_schedule *schedule);
5574 A representation of the schedule as a forest of bands can be obtained
5575 using the following function.
5577 __isl_give isl_band_list *isl_schedule_get_band_forest(
5578 __isl_keep isl_schedule *schedule);
5580 The individual bands can be visited in depth-first post-order
5581 using the following function.
5583 #include <isl/schedule.h>
5584 int isl_schedule_foreach_band(
5585 __isl_keep isl_schedule *sched,
5586 int (*fn)(__isl_keep isl_band *band, void *user),
5589 The list can be manipulated as explained in L<"Lists">.
5590 The bands inside the list can be copied and freed using the following
5593 #include <isl/band.h>
5594 __isl_give isl_band *isl_band_copy(
5595 __isl_keep isl_band *band);
5596 void *isl_band_free(__isl_take isl_band *band);
5598 Each band contains zero or more scheduling dimensions.
5599 These are referred to as the members of the band.
5600 The section of the schedule that corresponds to the band is
5601 referred to as the partial schedule of the band.
5602 For those nodes that participate in a band, the outer scheduling
5603 dimensions form the prefix schedule, while the inner scheduling
5604 dimensions form the suffix schedule.
5605 That is, if we take a cut of the band forest, then the union of
5606 the concatenations of the prefix, partial and suffix schedules of
5607 each band in the cut is equal to the entire schedule (modulo
5608 some possible padding at the end with zero scheduling dimensions).
5609 The properties of a band can be inspected using the following functions.
5611 #include <isl/band.h>
5612 isl_ctx *isl_band_get_ctx(__isl_keep isl_band *band);
5614 int isl_band_has_children(__isl_keep isl_band *band);
5615 __isl_give isl_band_list *isl_band_get_children(
5616 __isl_keep isl_band *band);
5618 __isl_give isl_union_map *isl_band_get_prefix_schedule(
5619 __isl_keep isl_band *band);
5620 __isl_give isl_union_map *isl_band_get_partial_schedule(
5621 __isl_keep isl_band *band);
5622 __isl_give isl_union_map *isl_band_get_suffix_schedule(
5623 __isl_keep isl_band *band);
5625 int isl_band_n_member(__isl_keep isl_band *band);
5626 int isl_band_member_is_zero_distance(
5627 __isl_keep isl_band *band, int pos);
5629 int isl_band_list_foreach_band(
5630 __isl_keep isl_band_list *list,
5631 int (*fn)(__isl_keep isl_band *band, void *user),
5634 Note that a scheduling dimension is considered to be ``zero
5635 distance'' if it does not carry any proximity dependences
5637 That is, if the dependence distances of the proximity
5638 dependences are all zero in that direction (for fixed
5639 iterations of outer bands).
5640 Like C<isl_schedule_foreach_band>,
5641 the function C<isl_band_list_foreach_band> calls C<fn> on the bands
5642 in depth-first post-order.
5644 A band can be tiled using the following function.
5646 #include <isl/band.h>
5647 int isl_band_tile(__isl_keep isl_band *band,
5648 __isl_take isl_vec *sizes);
5650 int isl_options_set_tile_scale_tile_loops(isl_ctx *ctx,
5652 int isl_options_get_tile_scale_tile_loops(isl_ctx *ctx);
5653 int isl_options_set_tile_shift_point_loops(isl_ctx *ctx,
5655 int isl_options_get_tile_shift_point_loops(isl_ctx *ctx);
5657 The C<isl_band_tile> function tiles the band using the given tile sizes
5658 inside its schedule.
5659 A new child band is created to represent the point loops and it is
5660 inserted between the modified band and its children.
5661 The C<tile_scale_tile_loops> option specifies whether the tile
5662 loops iterators should be scaled by the tile sizes.
5663 If the C<tile_shift_point_loops> option is set, then the point loops
5664 are shifted to start at zero.
5666 A band can be split into two nested bands using the following function.
5668 int isl_band_split(__isl_keep isl_band *band, int pos);
5670 The resulting outer band contains the first C<pos> dimensions of C<band>
5671 while the inner band contains the remaining dimensions.
5673 A representation of the band can be printed using
5675 #include <isl/band.h>
5676 __isl_give isl_printer *isl_printer_print_band(
5677 __isl_take isl_printer *p,
5678 __isl_keep isl_band *band);
5682 #include <isl/schedule.h>
5683 int isl_options_set_schedule_max_coefficient(
5684 isl_ctx *ctx, int val);
5685 int isl_options_get_schedule_max_coefficient(
5687 int isl_options_set_schedule_max_constant_term(
5688 isl_ctx *ctx, int val);
5689 int isl_options_get_schedule_max_constant_term(
5691 int isl_options_set_schedule_fuse(isl_ctx *ctx, int val);
5692 int isl_options_get_schedule_fuse(isl_ctx *ctx);
5693 int isl_options_set_schedule_maximize_band_depth(
5694 isl_ctx *ctx, int val);
5695 int isl_options_get_schedule_maximize_band_depth(
5697 int isl_options_set_schedule_outer_zero_distance(
5698 isl_ctx *ctx, int val);
5699 int isl_options_get_schedule_outer_zero_distance(
5701 int isl_options_set_schedule_split_scaled(
5702 isl_ctx *ctx, int val);
5703 int isl_options_get_schedule_split_scaled(
5705 int isl_options_set_schedule_algorithm(
5706 isl_ctx *ctx, int val);
5707 int isl_options_get_schedule_algorithm(
5709 int isl_options_set_schedule_separate_components(
5710 isl_ctx *ctx, int val);
5711 int isl_options_get_schedule_separate_components(
5716 =item * schedule_max_coefficient
5718 This option enforces that the coefficients for variable and parameter
5719 dimensions in the calculated schedule are not larger than the specified value.
5720 This option can significantly increase the speed of the scheduling calculation
5721 and may also prevent fusing of unrelated dimensions. A value of -1 means that
5722 this option does not introduce bounds on the variable or parameter
5725 =item * schedule_max_constant_term
5727 This option enforces that the constant coefficients in the calculated schedule
5728 are not larger than the maximal constant term. This option can significantly
5729 increase the speed of the scheduling calculation and may also prevent fusing of
5730 unrelated dimensions. A value of -1 means that this option does not introduce
5731 bounds on the constant coefficients.
5733 =item * schedule_fuse
5735 This option controls the level of fusion.
5736 If this option is set to C<ISL_SCHEDULE_FUSE_MIN>, then loops in the
5737 resulting schedule will be distributed as much as possible.
5738 If this option is set to C<ISL_SCHEDULE_FUSE_MAX>, then C<isl> will
5739 try to fuse loops in the resulting schedule.
5741 =item * schedule_maximize_band_depth
5743 If this option is set, we do not split bands at the point
5744 where we detect splitting is necessary. Instead, we
5745 backtrack and split bands as early as possible. This
5746 reduces the number of splits and maximizes the width of
5747 the bands. Wider bands give more possibilities for tiling.
5748 Note that if the C<schedule_fuse> option is set to C<ISL_SCHEDULE_FUSE_MIN>,
5749 then bands will be split as early as possible, even if there is no need.
5750 The C<schedule_maximize_band_depth> option therefore has no effect in this case.
5752 =item * schedule_outer_zero_distance
5754 If this option is set, then we try to construct schedules
5755 where the outermost scheduling dimension in each band
5756 results in a zero dependence distance over the proximity
5759 =item * schedule_split_scaled
5761 If this option is set, then we try to construct schedules in which the
5762 constant term is split off from the linear part if the linear parts of
5763 the scheduling rows for all nodes in the graphs have a common non-trivial
5765 The constant term is then placed in a separate band and the linear
5768 =item * schedule_algorithm
5770 Selects the scheduling algorithm to be used.
5771 Available scheduling algorithms are C<ISL_SCHEDULE_ALGORITHM_ISL>
5772 and C<ISL_SCHEDULE_ALGORITHM_FEAUTRIER>.
5774 =item * schedule_separate_components
5776 If at any point the dependence graph contains any (weakly connected) components,
5777 then these components are scheduled separately.
5778 If this option is not set, then some iterations of the domains
5779 in these components may be scheduled together.
5780 If this option is set, then the components are given consecutive
5785 =head2 AST Generation
5787 This section describes the C<isl> functionality for generating
5788 ASTs that visit all the elements
5789 in a domain in an order specified by a schedule.
5790 In particular, given a C<isl_union_map>, an AST is generated
5791 that visits all the elements in the domain of the C<isl_union_map>
5792 according to the lexicographic order of the corresponding image
5793 element(s). If the range of the C<isl_union_map> consists of
5794 elements in more than one space, then each of these spaces is handled
5795 separately in an arbitrary order.
5796 It should be noted that the image elements only specify the I<order>
5797 in which the corresponding domain elements should be visited.
5798 No direct relation between the image elements and the loop iterators
5799 in the generated AST should be assumed.
5801 Each AST is generated within a build. The initial build
5802 simply specifies the constraints on the parameters (if any)
5803 and can be created, inspected, copied and freed using the following functions.
5805 #include <isl/ast_build.h>
5806 __isl_give isl_ast_build *isl_ast_build_from_context(
5807 __isl_take isl_set *set);
5808 isl_ctx *isl_ast_build_get_ctx(
5809 __isl_keep isl_ast_build *build);
5810 __isl_give isl_ast_build *isl_ast_build_copy(
5811 __isl_keep isl_ast_build *build);
5812 void *isl_ast_build_free(
5813 __isl_take isl_ast_build *build);
5815 The C<set> argument is usually a parameter set with zero or more parameters.
5816 More C<isl_ast_build> functions are described in L</"Nested AST Generation">
5817 and L</"Fine-grained Control over AST Generation">.
5818 Finally, the AST itself can be constructed using the following
5821 #include <isl/ast_build.h>
5822 __isl_give isl_ast_node *isl_ast_build_ast_from_schedule(
5823 __isl_keep isl_ast_build *build,
5824 __isl_take isl_union_map *schedule);
5826 =head3 Inspecting the AST
5828 The basic properties of an AST node can be obtained as follows.
5830 #include <isl/ast.h>
5831 isl_ctx *isl_ast_node_get_ctx(
5832 __isl_keep isl_ast_node *node);
5833 enum isl_ast_node_type isl_ast_node_get_type(
5834 __isl_keep isl_ast_node *node);
5836 The type of an AST node is one of
5837 C<isl_ast_node_for>,
5839 C<isl_ast_node_block> or
5840 C<isl_ast_node_user>.
5841 An C<isl_ast_node_for> represents a for node.
5842 An C<isl_ast_node_if> represents an if node.
5843 An C<isl_ast_node_block> represents a compound node.
5844 An C<isl_ast_node_user> represents an expression statement.
5845 An expression statement typically corresponds to a domain element, i.e.,
5846 one of the elements that is visited by the AST.
5848 Each type of node has its own additional properties.
5850 #include <isl/ast.h>
5851 __isl_give isl_ast_expr *isl_ast_node_for_get_iterator(
5852 __isl_keep isl_ast_node *node);
5853 __isl_give isl_ast_expr *isl_ast_node_for_get_init(
5854 __isl_keep isl_ast_node *node);
5855 __isl_give isl_ast_expr *isl_ast_node_for_get_cond(
5856 __isl_keep isl_ast_node *node);
5857 __isl_give isl_ast_expr *isl_ast_node_for_get_inc(
5858 __isl_keep isl_ast_node *node);
5859 __isl_give isl_ast_node *isl_ast_node_for_get_body(
5860 __isl_keep isl_ast_node *node);
5861 int isl_ast_node_for_is_degenerate(
5862 __isl_keep isl_ast_node *node);
5864 An C<isl_ast_for> is considered degenerate if it is known to execute
5867 #include <isl/ast.h>
5868 __isl_give isl_ast_expr *isl_ast_node_if_get_cond(
5869 __isl_keep isl_ast_node *node);
5870 __isl_give isl_ast_node *isl_ast_node_if_get_then(
5871 __isl_keep isl_ast_node *node);
5872 int isl_ast_node_if_has_else(
5873 __isl_keep isl_ast_node *node);
5874 __isl_give isl_ast_node *isl_ast_node_if_get_else(
5875 __isl_keep isl_ast_node *node);
5877 __isl_give isl_ast_node_list *
5878 isl_ast_node_block_get_children(
5879 __isl_keep isl_ast_node *node);
5881 __isl_give isl_ast_expr *isl_ast_node_user_get_expr(
5882 __isl_keep isl_ast_node *node);
5884 Each of the returned C<isl_ast_expr>s can in turn be inspected using
5885 the following functions.
5887 #include <isl/ast.h>
5888 isl_ctx *isl_ast_expr_get_ctx(
5889 __isl_keep isl_ast_expr *expr);
5890 enum isl_ast_expr_type isl_ast_expr_get_type(
5891 __isl_keep isl_ast_expr *expr);
5893 The type of an AST expression is one of
5895 C<isl_ast_expr_id> or
5896 C<isl_ast_expr_int>.
5897 An C<isl_ast_expr_op> represents the result of an operation.
5898 An C<isl_ast_expr_id> represents an identifier.
5899 An C<isl_ast_expr_int> represents an integer value.
5901 Each type of expression has its own additional properties.
5903 #include <isl/ast.h>
5904 enum isl_ast_op_type isl_ast_expr_get_op_type(
5905 __isl_keep isl_ast_expr *expr);
5906 int isl_ast_expr_get_op_n_arg(__isl_keep isl_ast_expr *expr);
5907 __isl_give isl_ast_expr *isl_ast_expr_get_op_arg(
5908 __isl_keep isl_ast_expr *expr, int pos);
5909 int isl_ast_node_foreach_ast_op_type(
5910 __isl_keep isl_ast_node *node,
5911 int (*fn)(enum isl_ast_op_type type, void *user),
5914 C<isl_ast_expr_get_op_type> returns the type of the operation
5915 performed. C<isl_ast_expr_get_op_n_arg> returns the number of
5916 arguments. C<isl_ast_expr_get_op_arg> returns the specified
5918 C<isl_ast_node_foreach_ast_op_type> calls C<fn> for each distinct
5919 C<isl_ast_op_type> that appears in C<node>.
5920 The operation type is one of the following.
5924 =item C<isl_ast_op_and>
5926 Logical I<and> of two arguments.
5927 Both arguments can be evaluated.
5929 =item C<isl_ast_op_and_then>
5931 Logical I<and> of two arguments.
5932 The second argument can only be evaluated if the first evaluates to true.
5934 =item C<isl_ast_op_or>
5936 Logical I<or> of two arguments.
5937 Both arguments can be evaluated.
5939 =item C<isl_ast_op_or_else>
5941 Logical I<or> of two arguments.
5942 The second argument can only be evaluated if the first evaluates to false.
5944 =item C<isl_ast_op_max>
5946 Maximum of two or more arguments.
5948 =item C<isl_ast_op_min>
5950 Minimum of two or more arguments.
5952 =item C<isl_ast_op_minus>
5956 =item C<isl_ast_op_add>
5958 Sum of two arguments.
5960 =item C<isl_ast_op_sub>
5962 Difference of two arguments.
5964 =item C<isl_ast_op_mul>
5966 Product of two arguments.
5968 =item C<isl_ast_op_div>
5970 Exact division. That is, the result is known to be an integer.
5972 =item C<isl_ast_op_fdiv_q>
5974 Result of integer division, rounded towards negative
5977 =item C<isl_ast_op_pdiv_q>
5979 Result of integer division, where dividend is known to be non-negative.
5981 =item C<isl_ast_op_pdiv_r>
5983 Remainder of integer division, where dividend is known to be non-negative.
5985 =item C<isl_ast_op_cond>
5987 Conditional operator defined on three arguments.
5988 If the first argument evaluates to true, then the result
5989 is equal to the second argument. Otherwise, the result
5990 is equal to the third argument.
5991 The second and third argument may only be evaluated if
5992 the first argument evaluates to true and false, respectively.
5993 Corresponds to C<a ? b : c> in C.
5995 =item C<isl_ast_op_select>
5997 Conditional operator defined on three arguments.
5998 If the first argument evaluates to true, then the result
5999 is equal to the second argument. Otherwise, the result
6000 is equal to the third argument.
6001 The second and third argument may be evaluated independently
6002 of the value of the first argument.
6003 Corresponds to C<a * b + (1 - a) * c> in C.
6005 =item C<isl_ast_op_eq>
6009 =item C<isl_ast_op_le>
6011 Less than or equal relation.
6013 =item C<isl_ast_op_lt>
6017 =item C<isl_ast_op_ge>
6019 Greater than or equal relation.
6021 =item C<isl_ast_op_gt>
6023 Greater than relation.
6025 =item C<isl_ast_op_call>
6028 The number of arguments of the C<isl_ast_expr> is one more than
6029 the number of arguments in the function call, the first argument
6030 representing the function being called.
6034 #include <isl/ast.h>
6035 __isl_give isl_id *isl_ast_expr_get_id(
6036 __isl_keep isl_ast_expr *expr);
6038 Return the identifier represented by the AST expression.
6040 #include <isl/ast.h>
6041 int isl_ast_expr_get_int(__isl_keep isl_ast_expr *expr,
6043 __isl_give isl_val *isl_ast_expr_get_val(
6044 __isl_keep isl_ast_expr *expr);
6046 Return the integer represented by the AST expression.
6047 Note that the integer is returned by C<isl_ast_expr_get_int>
6048 through the C<v> argument.
6049 The return value of this function itself indicates whether the
6050 operation was performed successfully.
6052 =head3 Manipulating and printing the AST
6054 AST nodes can be copied and freed using the following functions.
6056 #include <isl/ast.h>
6057 __isl_give isl_ast_node *isl_ast_node_copy(
6058 __isl_keep isl_ast_node *node);
6059 void *isl_ast_node_free(__isl_take isl_ast_node *node);
6061 AST expressions can be copied and freed using the following functions.
6063 #include <isl/ast.h>
6064 __isl_give isl_ast_expr *isl_ast_expr_copy(
6065 __isl_keep isl_ast_expr *expr);
6066 void *isl_ast_expr_free(__isl_take isl_ast_expr *expr);
6068 New AST expressions can be created either directly or within
6069 the context of an C<isl_ast_build>.
6071 #include <isl/ast.h>
6072 __isl_give isl_ast_expr *isl_ast_expr_from_val(
6073 __isl_take isl_val *v);
6074 __isl_give isl_ast_expr *isl_ast_expr_from_id(
6075 __isl_take isl_id *id);
6076 __isl_give isl_ast_expr *isl_ast_expr_neg(
6077 __isl_take isl_ast_expr *expr);
6078 __isl_give isl_ast_expr *isl_ast_expr_add(
6079 __isl_take isl_ast_expr *expr1,
6080 __isl_take isl_ast_expr *expr2);
6081 __isl_give isl_ast_expr *isl_ast_expr_sub(
6082 __isl_take isl_ast_expr *expr1,
6083 __isl_take isl_ast_expr *expr2);
6084 __isl_give isl_ast_expr *isl_ast_expr_mul(
6085 __isl_take isl_ast_expr *expr1,
6086 __isl_take isl_ast_expr *expr2);
6087 __isl_give isl_ast_expr *isl_ast_expr_div(
6088 __isl_take isl_ast_expr *expr1,
6089 __isl_take isl_ast_expr *expr2);
6090 __isl_give isl_ast_expr *isl_ast_expr_and(
6091 __isl_take isl_ast_expr *expr1,
6092 __isl_take isl_ast_expr *expr2)
6093 __isl_give isl_ast_expr *isl_ast_expr_or(
6094 __isl_take isl_ast_expr *expr1,
6095 __isl_take isl_ast_expr *expr2)
6097 #include <isl/ast_build.h>
6098 __isl_give isl_ast_expr *isl_ast_build_expr_from_pw_aff(
6099 __isl_keep isl_ast_build *build,
6100 __isl_take isl_pw_aff *pa);
6101 __isl_give isl_ast_expr *
6102 isl_ast_build_call_from_pw_multi_aff(
6103 __isl_keep isl_ast_build *build,
6104 __isl_take isl_pw_multi_aff *pma);
6106 The domains of C<pa> and C<pma> should correspond
6107 to the schedule space of C<build>.
6108 The tuple id of C<pma> is used as the function being called.
6110 User specified data can be attached to an C<isl_ast_node> and obtained
6111 from the same C<isl_ast_node> using the following functions.
6113 #include <isl/ast.h>
6114 __isl_give isl_ast_node *isl_ast_node_set_annotation(
6115 __isl_take isl_ast_node *node,
6116 __isl_take isl_id *annotation);
6117 __isl_give isl_id *isl_ast_node_get_annotation(
6118 __isl_keep isl_ast_node *node);
6120 Basic printing can be performed using the following functions.
6122 #include <isl/ast.h>
6123 __isl_give isl_printer *isl_printer_print_ast_expr(
6124 __isl_take isl_printer *p,
6125 __isl_keep isl_ast_expr *expr);
6126 __isl_give isl_printer *isl_printer_print_ast_node(
6127 __isl_take isl_printer *p,
6128 __isl_keep isl_ast_node *node);
6130 More advanced printing can be performed using the following functions.
6132 #include <isl/ast.h>
6133 __isl_give isl_printer *isl_ast_op_type_print_macro(
6134 enum isl_ast_op_type type,
6135 __isl_take isl_printer *p);
6136 __isl_give isl_printer *isl_ast_node_print_macros(
6137 __isl_keep isl_ast_node *node,
6138 __isl_take isl_printer *p);
6139 __isl_give isl_printer *isl_ast_node_print(
6140 __isl_keep isl_ast_node *node,
6141 __isl_take isl_printer *p,
6142 __isl_take isl_ast_print_options *options);
6143 __isl_give isl_printer *isl_ast_node_for_print(
6144 __isl_keep isl_ast_node *node,
6145 __isl_take isl_printer *p,
6146 __isl_take isl_ast_print_options *options);
6147 __isl_give isl_printer *isl_ast_node_if_print(
6148 __isl_keep isl_ast_node *node,
6149 __isl_take isl_printer *p,
6150 __isl_take isl_ast_print_options *options);
6152 While printing an C<isl_ast_node> in C<ISL_FORMAT_C>,
6153 C<isl> may print out an AST that makes use of macros such
6154 as C<floord>, C<min> and C<max>.
6155 C<isl_ast_op_type_print_macro> prints out the macro
6156 corresponding to a specific C<isl_ast_op_type>.
6157 C<isl_ast_node_print_macros> scans the C<isl_ast_node>
6158 for expressions where these macros would be used and prints
6159 out the required macro definitions.
6160 Essentially, C<isl_ast_node_print_macros> calls
6161 C<isl_ast_node_foreach_ast_op_type> with C<isl_ast_op_type_print_macro>
6162 as function argument.
6163 C<isl_ast_node_print>, C<isl_ast_node_for_print> and
6164 C<isl_ast_node_if_print> print an C<isl_ast_node>
6165 in C<ISL_FORMAT_C>, but allow for some extra control
6166 through an C<isl_ast_print_options> object.
6167 This object can be created using the following functions.
6169 #include <isl/ast.h>
6170 __isl_give isl_ast_print_options *
6171 isl_ast_print_options_alloc(isl_ctx *ctx);
6172 __isl_give isl_ast_print_options *
6173 isl_ast_print_options_copy(
6174 __isl_keep isl_ast_print_options *options);
6175 void *isl_ast_print_options_free(
6176 __isl_take isl_ast_print_options *options);
6178 __isl_give isl_ast_print_options *
6179 isl_ast_print_options_set_print_user(
6180 __isl_take isl_ast_print_options *options,
6181 __isl_give isl_printer *(*print_user)(
6182 __isl_take isl_printer *p,
6183 __isl_take isl_ast_print_options *options,
6184 __isl_keep isl_ast_node *node, void *user),
6186 __isl_give isl_ast_print_options *
6187 isl_ast_print_options_set_print_for(
6188 __isl_take isl_ast_print_options *options,
6189 __isl_give isl_printer *(*print_for)(
6190 __isl_take isl_printer *p,
6191 __isl_take isl_ast_print_options *options,
6192 __isl_keep isl_ast_node *node, void *user),
6195 The callback set by C<isl_ast_print_options_set_print_user>
6196 is called whenever a node of type C<isl_ast_node_user> needs to
6198 The callback set by C<isl_ast_print_options_set_print_for>
6199 is called whenever a node of type C<isl_ast_node_for> needs to
6201 Note that C<isl_ast_node_for_print> will I<not> call the
6202 callback set by C<isl_ast_print_options_set_print_for> on the node
6203 on which C<isl_ast_node_for_print> is called, but only on nested
6204 nodes of type C<isl_ast_node_for>. It is therefore safe to
6205 call C<isl_ast_node_for_print> from within the callback set by
6206 C<isl_ast_print_options_set_print_for>.
6208 The following option determines the type to be used for iterators
6209 while printing the AST.
6211 int isl_options_set_ast_iterator_type(
6212 isl_ctx *ctx, const char *val);
6213 const char *isl_options_get_ast_iterator_type(
6218 #include <isl/ast_build.h>
6219 int isl_options_set_ast_build_atomic_upper_bound(
6220 isl_ctx *ctx, int val);
6221 int isl_options_get_ast_build_atomic_upper_bound(
6223 int isl_options_set_ast_build_prefer_pdiv(isl_ctx *ctx,
6225 int isl_options_get_ast_build_prefer_pdiv(isl_ctx *ctx);
6226 int isl_options_set_ast_build_exploit_nested_bounds(
6227 isl_ctx *ctx, int val);
6228 int isl_options_get_ast_build_exploit_nested_bounds(
6230 int isl_options_set_ast_build_group_coscheduled(
6231 isl_ctx *ctx, int val);
6232 int isl_options_get_ast_build_group_coscheduled(
6234 int isl_options_set_ast_build_scale_strides(
6235 isl_ctx *ctx, int val);
6236 int isl_options_get_ast_build_scale_strides(
6238 int isl_options_set_ast_build_allow_else(isl_ctx *ctx,
6240 int isl_options_get_ast_build_allow_else(isl_ctx *ctx);
6241 int isl_options_set_ast_build_allow_or(isl_ctx *ctx,
6243 int isl_options_get_ast_build_allow_or(isl_ctx *ctx);
6247 =item * ast_build_atomic_upper_bound
6249 Generate loop upper bounds that consist of the current loop iterator,
6250 an operator and an expression not involving the iterator.
6251 If this option is not set, then the current loop iterator may appear
6252 several times in the upper bound.
6253 For example, when this option is turned off, AST generation
6256 [n] -> { A[i] -> [i] : 0 <= i <= 100, n }
6260 for (int c0 = 0; c0 <= 100 && n >= c0; c0 += 1)
6263 When the option is turned on, the following AST is generated
6265 for (int c0 = 0; c0 <= min(100, n); c0 += 1)
6268 =item * ast_build_prefer_pdiv
6270 If this option is turned off, then the AST generation will
6271 produce ASTs that may only contain C<isl_ast_op_fdiv_q>
6272 operators, but no C<isl_ast_op_pdiv_q> or
6273 C<isl_ast_op_pdiv_r> operators.
6274 If this options is turned on, then C<isl> will try to convert
6275 some of the C<isl_ast_op_fdiv_q> operators to (expressions containing)
6276 C<isl_ast_op_pdiv_q> or C<isl_ast_op_pdiv_r> operators.
6278 =item * ast_build_exploit_nested_bounds
6280 Simplify conditions based on bounds of nested for loops.
6281 In particular, remove conditions that are implied by the fact
6282 that one or more nested loops have at least one iteration,
6283 meaning that the upper bound is at least as large as the lower bound.
6284 For example, when this option is turned off, AST generation
6287 [N,M] -> { A[i,j] -> [i,j] : 0 <= i <= N and
6293 for (int c0 = 0; c0 <= N; c0 += 1)
6294 for (int c1 = 0; c1 <= M; c1 += 1)
6297 When the option is turned on, the following AST is generated
6299 for (int c0 = 0; c0 <= N; c0 += 1)
6300 for (int c1 = 0; c1 <= M; c1 += 1)
6303 =item * ast_build_group_coscheduled
6305 If two domain elements are assigned the same schedule point, then
6306 they may be executed in any order and they may even appear in different
6307 loops. If this options is set, then the AST generator will make
6308 sure that coscheduled domain elements do not appear in separate parts
6309 of the AST. This is useful in case of nested AST generation
6310 if the outer AST generation is given only part of a schedule
6311 and the inner AST generation should handle the domains that are
6312 coscheduled by this initial part of the schedule together.
6313 For example if an AST is generated for a schedule
6315 { A[i] -> [0]; B[i] -> [0] }
6317 then the C<isl_ast_build_set_create_leaf> callback described
6318 below may get called twice, once for each domain.
6319 Setting this option ensures that the callback is only called once
6320 on both domains together.
6322 =item * ast_build_separation_bounds
6324 This option specifies which bounds to use during separation.
6325 If this option is set to C<ISL_AST_BUILD_SEPARATION_BOUNDS_IMPLICIT>
6326 then all (possibly implicit) bounds on the current dimension will
6327 be used during separation.
6328 If this option is set to C<ISL_AST_BUILD_SEPARATION_BOUNDS_EXPLICIT>
6329 then only those bounds that are explicitly available will
6330 be used during separation.
6332 =item * ast_build_scale_strides
6334 This option specifies whether the AST generator is allowed
6335 to scale down iterators of strided loops.
6337 =item * ast_build_allow_else
6339 This option specifies whether the AST generator is allowed
6340 to construct if statements with else branches.
6342 =item * ast_build_allow_or
6344 This option specifies whether the AST generator is allowed
6345 to construct if conditions with disjunctions.
6349 =head3 Fine-grained Control over AST Generation
6351 Besides specifying the constraints on the parameters,
6352 an C<isl_ast_build> object can be used to control
6353 various aspects of the AST generation process.
6354 The most prominent way of control is through ``options'',
6355 which can be set using the following function.
6357 #include <isl/ast_build.h>
6358 __isl_give isl_ast_build *
6359 isl_ast_build_set_options(
6360 __isl_take isl_ast_build *control,
6361 __isl_take isl_union_map *options);
6363 The options are encoded in an <isl_union_map>.
6364 The domain of this union relation refers to the schedule domain,
6365 i.e., the range of the schedule passed to C<isl_ast_build_ast_from_schedule>.
6366 In the case of nested AST generation (see L</"Nested AST Generation">),
6367 the domain of C<options> should refer to the extra piece of the schedule.
6368 That is, it should be equal to the range of the wrapped relation in the
6369 range of the schedule.
6370 The range of the options can consist of elements in one or more spaces,
6371 the names of which determine the effect of the option.
6372 The values of the range typically also refer to the schedule dimension
6373 to which the option applies. In case of nested AST generation
6374 (see L</"Nested AST Generation">), these values refer to the position
6375 of the schedule dimension within the innermost AST generation.
6376 The constraints on the domain elements of
6377 the option should only refer to this dimension and earlier dimensions.
6378 We consider the following spaces.
6382 =item C<separation_class>
6384 This space is a wrapped relation between two one dimensional spaces.
6385 The input space represents the schedule dimension to which the option
6386 applies and the output space represents the separation class.
6387 While constructing a loop corresponding to the specified schedule
6388 dimension(s), the AST generator will try to generate separate loops
6389 for domain elements that are assigned different classes.
6390 If only some of the elements are assigned a class, then those elements
6391 that are not assigned any class will be treated as belonging to a class
6392 that is separate from the explicitly assigned classes.
6393 The typical use case for this option is to separate full tiles from
6395 The other options, described below, are applied after the separation
6398 As an example, consider the separation into full and partial tiles
6399 of a tiling of a triangular domain.
6400 Take, for example, the domain
6402 { A[i,j] : 0 <= i,j and i + j <= 100 }
6404 and a tiling into tiles of 10 by 10. The input to the AST generator
6405 is then the schedule
6407 { A[i,j] -> [([i/10]),[j/10],i,j] : 0 <= i,j and
6410 Without any options, the following AST is generated
6412 for (int c0 = 0; c0 <= 10; c0 += 1)
6413 for (int c1 = 0; c1 <= -c0 + 10; c1 += 1)
6414 for (int c2 = 10 * c0;
6415 c2 <= min(-10 * c1 + 100, 10 * c0 + 9);
6417 for (int c3 = 10 * c1;
6418 c3 <= min(10 * c1 + 9, -c2 + 100);
6422 Separation into full and partial tiles can be obtained by assigning
6423 a class, say C<0>, to the full tiles. The full tiles are represented by those
6424 values of the first and second schedule dimensions for which there are
6425 values of the third and fourth dimensions to cover an entire tile.
6426 That is, we need to specify the following option
6428 { [a,b,c,d] -> separation_class[[0]->[0]] :
6429 exists b': 0 <= 10a,10b' and
6430 10a+9+10b'+9 <= 100;
6431 [a,b,c,d] -> separation_class[[1]->[0]] :
6432 0 <= 10a,10b and 10a+9+10b+9 <= 100 }
6436 { [a, b, c, d] -> separation_class[[1] -> [0]] :
6437 a >= 0 and b >= 0 and b <= 8 - a;
6438 [a, b, c, d] -> separation_class[[0] -> [0]] :
6441 With this option, the generated AST is as follows
6444 for (int c0 = 0; c0 <= 8; c0 += 1) {
6445 for (int c1 = 0; c1 <= -c0 + 8; c1 += 1)
6446 for (int c2 = 10 * c0;
6447 c2 <= 10 * c0 + 9; c2 += 1)
6448 for (int c3 = 10 * c1;
6449 c3 <= 10 * c1 + 9; c3 += 1)
6451 for (int c1 = -c0 + 9; c1 <= -c0 + 10; c1 += 1)
6452 for (int c2 = 10 * c0;
6453 c2 <= min(-10 * c1 + 100, 10 * c0 + 9);
6455 for (int c3 = 10 * c1;
6456 c3 <= min(-c2 + 100, 10 * c1 + 9);
6460 for (int c0 = 9; c0 <= 10; c0 += 1)
6461 for (int c1 = 0; c1 <= -c0 + 10; c1 += 1)
6462 for (int c2 = 10 * c0;
6463 c2 <= min(-10 * c1 + 100, 10 * c0 + 9);
6465 for (int c3 = 10 * c1;
6466 c3 <= min(10 * c1 + 9, -c2 + 100);
6473 This is a single-dimensional space representing the schedule dimension(s)
6474 to which ``separation'' should be applied. Separation tries to split
6475 a loop into several pieces if this can avoid the generation of guards
6477 See also the C<atomic> option.
6481 This is a single-dimensional space representing the schedule dimension(s)
6482 for which the domains should be considered ``atomic''. That is, the
6483 AST generator will make sure that any given domain space will only appear
6484 in a single loop at the specified level.
6486 Consider the following schedule
6488 { a[i] -> [i] : 0 <= i < 10;
6489 b[i] -> [i+1] : 0 <= i < 10 }
6491 If the following option is specified
6493 { [i] -> separate[x] }
6495 then the following AST will be generated
6499 for (int c0 = 1; c0 <= 9; c0 += 1) {
6506 If, on the other hand, the following option is specified
6508 { [i] -> atomic[x] }
6510 then the following AST will be generated
6512 for (int c0 = 0; c0 <= 10; c0 += 1) {
6519 If neither C<atomic> nor C<separate> is specified, then the AST generator
6520 may produce either of these two results or some intermediate form.
6524 This is a single-dimensional space representing the schedule dimension(s)
6525 that should be I<completely> unrolled.
6526 To obtain a partial unrolling, the user should apply an additional
6527 strip-mining to the schedule and fully unroll the inner loop.
6531 Additional control is available through the following functions.
6533 #include <isl/ast_build.h>
6534 __isl_give isl_ast_build *
6535 isl_ast_build_set_iterators(
6536 __isl_take isl_ast_build *control,
6537 __isl_take isl_id_list *iterators);
6539 The function C<isl_ast_build_set_iterators> allows the user to
6540 specify a list of iterator C<isl_id>s to be used as iterators.
6541 If the input schedule is injective, then
6542 the number of elements in this list should be as large as the dimension
6543 of the schedule space, but no direct correspondence should be assumed
6544 between dimensions and elements.
6545 If the input schedule is not injective, then an additional number
6546 of C<isl_id>s equal to the largest dimension of the input domains
6548 If the number of provided C<isl_id>s is insufficient, then additional
6549 names are automatically generated.
6551 #include <isl/ast_build.h>
6552 __isl_give isl_ast_build *
6553 isl_ast_build_set_create_leaf(
6554 __isl_take isl_ast_build *control,
6555 __isl_give isl_ast_node *(*fn)(
6556 __isl_take isl_ast_build *build,
6557 void *user), void *user);
6560 C<isl_ast_build_set_create_leaf> function allows for the
6561 specification of a callback that should be called whenever the AST
6562 generator arrives at an element of the schedule domain.
6563 The callback should return an AST node that should be inserted
6564 at the corresponding position of the AST. The default action (when
6565 the callback is not set) is to continue generating parts of the AST to scan
6566 all the domain elements associated to the schedule domain element
6567 and to insert user nodes, ``calling'' the domain element, for each of them.
6568 The C<build> argument contains the current state of the C<isl_ast_build>.
6569 To ease nested AST generation (see L</"Nested AST Generation">),
6570 all control information that is
6571 specific to the current AST generation such as the options and
6572 the callbacks has been removed from this C<isl_ast_build>.
6573 The callback would typically return the result of a nested
6575 user defined node created using the following function.
6577 #include <isl/ast.h>
6578 __isl_give isl_ast_node *isl_ast_node_alloc_user(
6579 __isl_take isl_ast_expr *expr);
6581 #include <isl/ast_build.h>
6582 __isl_give isl_ast_build *
6583 isl_ast_build_set_at_each_domain(
6584 __isl_take isl_ast_build *build,
6585 __isl_give isl_ast_node *(*fn)(
6586 __isl_take isl_ast_node *node,
6587 __isl_keep isl_ast_build *build,
6588 void *user), void *user);
6589 __isl_give isl_ast_build *
6590 isl_ast_build_set_before_each_for(
6591 __isl_take isl_ast_build *build,
6592 __isl_give isl_id *(*fn)(
6593 __isl_keep isl_ast_build *build,
6594 void *user), void *user);
6595 __isl_give isl_ast_build *
6596 isl_ast_build_set_after_each_for(
6597 __isl_take isl_ast_build *build,
6598 __isl_give isl_ast_node *(*fn)(
6599 __isl_take isl_ast_node *node,
6600 __isl_keep isl_ast_build *build,
6601 void *user), void *user);
6603 The callback set by C<isl_ast_build_set_at_each_domain> will
6604 be called for each domain AST node.
6605 The callbacks set by C<isl_ast_build_set_before_each_for>
6606 and C<isl_ast_build_set_after_each_for> will be called
6607 for each for AST node. The first will be called in depth-first
6608 pre-order, while the second will be called in depth-first post-order.
6609 Since C<isl_ast_build_set_before_each_for> is called before the for
6610 node is actually constructed, it is only passed an C<isl_ast_build>.
6611 The returned C<isl_id> will be added as an annotation (using
6612 C<isl_ast_node_set_annotation>) to the constructed for node.
6613 In particular, if the user has also specified an C<after_each_for>
6614 callback, then the annotation can be retrieved from the node passed to
6615 that callback using C<isl_ast_node_get_annotation>.
6616 All callbacks should C<NULL> on failure.
6617 The given C<isl_ast_build> can be used to create new
6618 C<isl_ast_expr> objects using C<isl_ast_build_expr_from_pw_aff>
6619 or C<isl_ast_build_call_from_pw_multi_aff>.
6621 =head3 Nested AST Generation
6623 C<isl> allows the user to create an AST within the context
6624 of another AST. These nested ASTs are created using the
6625 same C<isl_ast_build_ast_from_schedule> function that is used to create the
6626 outer AST. The C<build> argument should be an C<isl_ast_build>
6627 passed to a callback set by
6628 C<isl_ast_build_set_create_leaf>.
6629 The space of the range of the C<schedule> argument should refer
6630 to this build. In particular, the space should be a wrapped
6631 relation and the domain of this wrapped relation should be the
6632 same as that of the range of the schedule returned by
6633 C<isl_ast_build_get_schedule> below.
6634 In practice, the new schedule is typically
6635 created by calling C<isl_union_map_range_product> on the old schedule
6636 and some extra piece of the schedule.
6637 The space of the schedule domain is also available from
6638 the C<isl_ast_build>.
6640 #include <isl/ast_build.h>
6641 __isl_give isl_union_map *isl_ast_build_get_schedule(
6642 __isl_keep isl_ast_build *build);
6643 __isl_give isl_space *isl_ast_build_get_schedule_space(
6644 __isl_keep isl_ast_build *build);
6645 __isl_give isl_ast_build *isl_ast_build_restrict(
6646 __isl_take isl_ast_build *build,
6647 __isl_take isl_set *set);
6649 The C<isl_ast_build_get_schedule> function returns a (partial)
6650 schedule for the domains elements for which part of the AST still needs to
6651 be generated in the current build.
6652 In particular, the domain elements are mapped to those iterations of the loops
6653 enclosing the current point of the AST generation inside which
6654 the domain elements are executed.
6655 No direct correspondence between
6656 the input schedule and this schedule should be assumed.
6657 The space obtained from C<isl_ast_build_get_schedule_space> can be used
6658 to create a set for C<isl_ast_build_restrict> to intersect
6659 with the current build. In particular, the set passed to
6660 C<isl_ast_build_restrict> can have additional parameters.
6661 The ids of the set dimensions in the space returned by
6662 C<isl_ast_build_get_schedule_space> correspond to the
6663 iterators of the already generated loops.
6664 The user should not rely on the ids of the output dimensions
6665 of the relations in the union relation returned by
6666 C<isl_ast_build_get_schedule> having any particular value.
6670 Although C<isl> is mainly meant to be used as a library,
6671 it also contains some basic applications that use some
6672 of the functionality of C<isl>.
6673 The input may be specified in either the L<isl format>
6674 or the L<PolyLib format>.
6676 =head2 C<isl_polyhedron_sample>
6678 C<isl_polyhedron_sample> takes a polyhedron as input and prints
6679 an integer element of the polyhedron, if there is any.
6680 The first column in the output is the denominator and is always
6681 equal to 1. If the polyhedron contains no integer points,
6682 then a vector of length zero is printed.
6686 C<isl_pip> takes the same input as the C<example> program
6687 from the C<piplib> distribution, i.e., a set of constraints
6688 on the parameters, a line containing only -1 and finally a set
6689 of constraints on a parametric polyhedron.
6690 The coefficients of the parameters appear in the last columns
6691 (but before the final constant column).
6692 The output is the lexicographic minimum of the parametric polyhedron.
6693 As C<isl> currently does not have its own output format, the output
6694 is just a dump of the internal state.
6696 =head2 C<isl_polyhedron_minimize>
6698 C<isl_polyhedron_minimize> computes the minimum of some linear
6699 or affine objective function over the integer points in a polyhedron.
6700 If an affine objective function
6701 is given, then the constant should appear in the last column.
6703 =head2 C<isl_polytope_scan>
6705 Given a polytope, C<isl_polytope_scan> prints
6706 all integer points in the polytope.
6708 =head2 C<isl_codegen>
6710 Given a schedule, a context set and an options relation,
6711 C<isl_codegen> prints out an AST that scans the domain elements
6712 of the schedule in the order of their image(s) taking into account
6713 the constraints in the context set.