3 C<isl> is a thread-safe C library for manipulating
4 sets and relations of integer points bounded by affine constraints.
5 The descriptions of the sets and relations may involve
6 both parameters and existentially quantified variables.
7 All computations are performed in exact integer arithmetic
9 The C<isl> library offers functionality that is similar
10 to that offered by the C<Omega> and C<Omega+> libraries,
11 but the underlying algorithms are in most cases completely different.
13 The library is by no means complete and some fairly basic
14 functionality is still missing.
15 Still, even in its current form, the library has been successfully
16 used as a backend polyhedral library for the polyhedral
17 scanner C<CLooG> and as part of an equivalence checker of
18 static affine programs.
19 For bug reports, feature requests and questions,
20 visit the the discussion group at
21 L<http://groups.google.com/group/isl-development>.
23 =head2 Backward Incompatible Changes
25 =head3 Changes since isl-0.02
29 =item * The old printing functions have been deprecated
30 and replaced by C<isl_printer> functions, see L<Input and Output>.
32 =item * Most functions related to dependence analysis have acquired
33 an extra C<must> argument. To obtain the old behavior, this argument
34 should be given the value 1. See L<Dependence Analysis>.
38 =head3 Changes since isl-0.03
42 =item * The function C<isl_pw_qpolynomial_fold_add> has been
43 renamed to C<isl_pw_qpolynomial_fold_fold>.
44 Similarly, C<isl_union_pw_qpolynomial_fold_add> has been
45 renamed to C<isl_union_pw_qpolynomial_fold_fold>.
49 =head3 Changes since isl-0.04
53 =item * All header files have been renamed from C<isl_header.h>
58 =head3 Changes since isl-0.05
62 =item * The functions C<isl_printer_print_basic_set> and
63 C<isl_printer_print_basic_map> no longer print a newline.
65 =item * The functions C<isl_flow_get_no_source>
66 and C<isl_union_map_compute_flow> now return
67 the accesses for which no source could be found instead of
68 the iterations where those accesses occur.
70 =item * The functions C<isl_basic_map_identity> and
71 C<isl_map_identity> now take a B<map> space as input. An old call
72 C<isl_map_identity(space)> can be rewritten to
73 C<isl_map_identity(isl_space_map_from_set(space))>.
75 =item * The function C<isl_map_power> no longer takes
76 a parameter position as input. Instead, the exponent
77 is now expressed as the domain of the resulting relation.
81 =head3 Changes since isl-0.06
85 =item * The format of C<isl_printer_print_qpolynomial>'s
86 C<ISL_FORMAT_ISL> output has changed.
87 Use C<ISL_FORMAT_C> to obtain the old output.
89 =item * The C<*_fast_*> functions have been renamed to C<*_plain_*>.
90 Some of the old names have been kept for backward compatibility,
91 but they will be removed in the future.
95 =head3 Changes since isl-0.07
99 =item * The function C<isl_pw_aff_max> has been renamed to
100 C<isl_pw_aff_union_max>.
101 Similarly, the function C<isl_pw_aff_add> has been renamed to
102 C<isl_pw_aff_union_add>.
104 =item * The C<isl_dim> type has been renamed to C<isl_space>
105 along with the associated functions.
106 Some of the old names have been kept for backward compatibility,
107 but they will be removed in the future.
109 =item * Spaces of maps, sets and parameter domains are now
110 treated differently. The distinction between map spaces and set spaces
111 has always been made on a conceptual level, but proper use of such spaces
112 was never checked. Furthermore, up until isl-0.07 there was no way
113 of explicitly creating a parameter space. These can now be created
114 directly using C<isl_space_params_alloc> or from other spaces using
117 =item * The space in which C<isl_aff>, C<isl_pw_aff>, C<isl_qpolynomial>,
118 C<isl_pw_qpolynomial>, C<isl_qpolynomial_fold> and C<isl_pw_qpolynomial_fold>
119 objects live is now a map space
120 instead of a set space. This means, for example, that the dimensions
121 of the domain of an C<isl_aff> are now considered to be of type
122 C<isl_dim_in> instead of C<isl_dim_set>. Extra functions have been
123 added to obtain the domain space. Some of the constructors still
124 take a domain space and have therefore been renamed.
126 =item * The functions C<isl_equality_alloc> and C<isl_inequality_alloc>
127 now take an C<isl_local_space> instead of an C<isl_space>.
128 An C<isl_local_space> can be created from an C<isl_space>
129 using C<isl_local_space_from_space>.
131 =item * The C<isl_div> type has been removed. Functions that used
132 to return an C<isl_div> now return an C<isl_aff>.
133 Note that the space of an C<isl_aff> is that of relation.
134 When replacing a call to C<isl_div_get_coefficient> by a call to
135 C<isl_aff_get_coefficient> any C<isl_dim_set> argument needs
136 to be replaced by C<isl_dim_in>.
137 A call to C<isl_aff_from_div> can be replaced by a call
139 A call to C<isl_qpolynomial_div(div)> call be replaced by
142 isl_qpolynomial_from_aff(isl_aff_floor(div))
144 The function C<isl_constraint_div> has also been renamed
145 to C<isl_constraint_get_div>.
147 =item * The C<nparam> argument has been removed from
148 C<isl_map_read_from_str> and similar functions.
149 When reading input in the original PolyLib format,
150 the result will have no parameters.
151 If parameters are expected, the caller may want to perform
152 dimension manipulation on the result.
156 =head3 Changes since isl-0.09
160 =item * The C<schedule_split_parallel> option has been replaced
161 by the C<schedule_split_scaled> option.
163 =item * The first argument of C<isl_pw_aff_cond> is now
164 an C<isl_pw_aff> instead of an C<isl_set>.
165 A call C<isl_pw_aff_cond(a, b, c)> can be replaced by
167 isl_pw_aff_cond(isl_set_indicator_function(a), b, c)
171 =head3 Changes since isl-0.10
175 =item * The functions C<isl_set_dim_has_lower_bound> and
176 C<isl_set_dim_has_upper_bound> have been renamed to
177 C<isl_set_dim_has_any_lower_bound> and
178 C<isl_set_dim_has_any_upper_bound>.
179 The new C<isl_set_dim_has_lower_bound> and
180 C<isl_set_dim_has_upper_bound> have slightly different meanings.
186 C<isl> is released under the MIT license.
190 Permission is hereby granted, free of charge, to any person obtaining a copy of
191 this software and associated documentation files (the "Software"), to deal in
192 the Software without restriction, including without limitation the rights to
193 use, copy, modify, merge, publish, distribute, sublicense, and/or sell copies
194 of the Software, and to permit persons to whom the Software is furnished to do
195 so, subject to the following conditions:
197 The above copyright notice and this permission notice shall be included in all
198 copies or substantial portions of the Software.
200 THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
201 IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
202 FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
203 AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
204 LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
205 OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
210 Note that C<isl> currently requires C<GMP>, which is released
211 under the GNU Lesser General Public License (LGPL). This means
212 that code linked against C<isl> is also linked against LGPL code.
216 The source of C<isl> can be obtained either as a tarball
217 or from the git repository. Both are available from
218 L<http://freshmeat.net/projects/isl/>.
219 The installation process depends on how you obtained
222 =head2 Installation from the git repository
226 =item 1 Clone or update the repository
228 The first time the source is obtained, you need to clone
231 git clone git://repo.or.cz/isl.git
233 To obtain updates, you need to pull in the latest changes
237 =item 2 Generate C<configure>
243 After performing the above steps, continue
244 with the L<Common installation instructions>.
246 =head2 Common installation instructions
250 =item 1 Obtain C<GMP>
252 Building C<isl> requires C<GMP>, including its headers files.
253 Your distribution may not provide these header files by default
254 and you may need to install a package called C<gmp-devel> or something
255 similar. Alternatively, C<GMP> can be built from
256 source, available from L<http://gmplib.org/>.
260 C<isl> uses the standard C<autoconf> C<configure> script.
265 optionally followed by some configure options.
266 A complete list of options can be obtained by running
270 Below we discuss some of the more common options.
272 C<isl> can optionally use C<piplib>, but no
273 C<piplib> functionality is currently used by default.
274 The C<--with-piplib> option can
275 be used to specify which C<piplib>
276 library to use, either an installed version (C<system>),
277 an externally built version (C<build>)
278 or no version (C<no>). The option C<build> is mostly useful
279 in C<configure> scripts of larger projects that bundle both C<isl>
286 Installation prefix for C<isl>
288 =item C<--with-gmp-prefix>
290 Installation prefix for C<GMP> (architecture-independent files).
292 =item C<--with-gmp-exec-prefix>
294 Installation prefix for C<GMP> (architecture-dependent files).
296 =item C<--with-piplib>
298 Which copy of C<piplib> to use, either C<no> (default), C<system> or C<build>.
300 =item C<--with-piplib-prefix>
302 Installation prefix for C<system> C<piplib> (architecture-independent files).
304 =item C<--with-piplib-exec-prefix>
306 Installation prefix for C<system> C<piplib> (architecture-dependent files).
308 =item C<--with-piplib-builddir>
310 Location where C<build> C<piplib> was built.
318 =item 4 Install (optional)
324 =head1 Integer Set Library
326 =head2 Initialization
328 All manipulations of integer sets and relations occur within
329 the context of an C<isl_ctx>.
330 A given C<isl_ctx> can only be used within a single thread.
331 All arguments of a function are required to have been allocated
332 within the same context.
333 There are currently no functions available for moving an object
334 from one C<isl_ctx> to another C<isl_ctx>. This means that
335 there is currently no way of safely moving an object from one
336 thread to another, unless the whole C<isl_ctx> is moved.
338 An C<isl_ctx> can be allocated using C<isl_ctx_alloc> and
339 freed using C<isl_ctx_free>.
340 All objects allocated within an C<isl_ctx> should be freed
341 before the C<isl_ctx> itself is freed.
343 isl_ctx *isl_ctx_alloc();
344 void isl_ctx_free(isl_ctx *ctx);
348 An C<isl_val> represents an integer value, a rational value
349 or one of three special values, infinity, negative infinity and NaN.
350 Some predefined values can be created using the following functions.
353 __isl_give isl_val *isl_val_zero(isl_ctx *ctx);
354 __isl_give isl_val *isl_val_one(isl_ctx *ctx);
355 __isl_give isl_val *isl_val_nan(isl_ctx *ctx);
356 __isl_give isl_val *isl_val_infty(isl_ctx *ctx);
357 __isl_give isl_val *isl_val_neginfty(isl_ctx *ctx);
359 Specific integer values can be created using the following functions.
362 __isl_give isl_val *isl_val_int_from_si(isl_ctx *ctx,
364 __isl_give isl_val *isl_val_int_from_ui(isl_ctx *ctx,
367 They can be copied and freed using the following functions.
370 __isl_give isl_val *isl_val_copy(__isl_keep isl_val *v);
371 void *isl_val_free(__isl_take isl_val *v);
373 They can be inspected using the following functions.
376 isl_ctx *isl_val_get_ctx(__isl_keep isl_val *val);
377 long isl_val_get_num_si(__isl_keep isl_val *v);
378 long isl_val_get_den_si(__isl_keep isl_val *v);
379 double isl_val_get_d(__isl_keep isl_val *v);
381 Note that C<isl_val_get_num_si>, C<isl_val_get_den_si> and
382 C<isl_val_get_d> can only be applied to rational values.
384 An C<isl_val> can be modified using the following function.
387 __isl_give isl_val *isl_val_set_si(__isl_take isl_val *v,
390 The following unary properties are defined on C<isl_val>s.
393 int isl_val_sgn(__isl_keep isl_val *v);
394 int isl_val_is_zero(__isl_keep isl_val *v);
395 int isl_val_is_one(__isl_keep isl_val *v);
396 int isl_val_is_negone(__isl_keep isl_val *v);
397 int isl_val_is_nonneg(__isl_keep isl_val *v);
398 int isl_val_is_nonpos(__isl_keep isl_val *v);
399 int isl_val_is_pos(__isl_keep isl_val *v);
400 int isl_val_is_neg(__isl_keep isl_val *v);
401 int isl_val_is_int(__isl_keep isl_val *v);
402 int isl_val_is_rat(__isl_keep isl_val *v);
403 int isl_val_is_nan(__isl_keep isl_val *v);
404 int isl_val_is_infty(__isl_keep isl_val *v);
405 int isl_val_is_neginfty(__isl_keep isl_val *v);
407 Note that the sign of NaN is undefined.
409 The following binary properties are defined on pairs of C<isl_val>s.
412 int isl_val_lt(__isl_keep isl_val *v1,
413 __isl_keep isl_val *v2);
414 int isl_val_le(__isl_keep isl_val *v1,
415 __isl_keep isl_val *v2);
416 int isl_val_gt(__isl_keep isl_val *v1,
417 __isl_keep isl_val *v2);
418 int isl_val_ge(__isl_keep isl_val *v1,
419 __isl_keep isl_val *v2);
420 int isl_val_eq(__isl_keep isl_val *v1,
421 __isl_keep isl_val *v2);
422 int isl_val_ne(__isl_keep isl_val *v1,
423 __isl_keep isl_val *v2);
425 For integer C<isl_val>s we additionally have the following binary property.
428 int isl_val_is_divisible_by(__isl_keep isl_val *v1,
429 __isl_keep isl_val *v2);
431 An C<isl_val> can also be compared to an integer using the following
432 function. The result is undefined for NaN.
435 int isl_val_cmp_si(__isl_keep isl_val *v, long i);
437 The following unary operations are available on C<isl_val>s.
440 __isl_give isl_val *isl_val_abs(__isl_take isl_val *v);
441 __isl_give isl_val *isl_val_neg(__isl_take isl_val *v);
442 __isl_give isl_val *isl_val_floor(__isl_take isl_val *v);
443 __isl_give isl_val *isl_val_ceil(__isl_take isl_val *v);
444 __isl_give isl_val *isl_val_trunc(__isl_take isl_val *v);
446 The following binary operations are available on C<isl_val>s.
449 __isl_give isl_val *isl_val_abs(__isl_take isl_val *v);
450 __isl_give isl_val *isl_val_neg(__isl_take isl_val *v);
451 __isl_give isl_val *isl_val_floor(__isl_take isl_val *v);
452 __isl_give isl_val *isl_val_ceil(__isl_take isl_val *v);
453 __isl_give isl_val *isl_val_trunc(__isl_take isl_val *v);
454 __isl_give isl_val *isl_val_2exp(__isl_take isl_val *v);
455 __isl_give isl_val *isl_val_min(__isl_take isl_val *v1,
456 __isl_take isl_val *v2);
457 __isl_give isl_val *isl_val_max(__isl_take isl_val *v1,
458 __isl_take isl_val *v2);
459 __isl_give isl_val *isl_val_add(__isl_take isl_val *v1,
460 __isl_take isl_val *v2);
461 __isl_give isl_val *isl_val_add_ui(__isl_take isl_val *v1,
463 __isl_give isl_val *isl_val_sub(__isl_take isl_val *v1,
464 __isl_take isl_val *v2);
465 __isl_give isl_val *isl_val_sub_ui(__isl_take isl_val *v1,
467 __isl_give isl_val *isl_val_mul(__isl_take isl_val *v1,
468 __isl_take isl_val *v2);
469 __isl_give isl_val *isl_val_mul_ui(__isl_take isl_val *v1,
471 __isl_give isl_val *isl_val_div(__isl_take isl_val *v1,
472 __isl_take isl_val *v2);
474 On integer values, we additionally have the following operations.
477 __isl_give isl_val *isl_val_2exp(__isl_take isl_val *v);
478 __isl_give isl_val *isl_val_mod(__isl_take isl_val *v1,
479 __isl_take isl_val *v2);
480 __isl_give isl_val *isl_val_gcd(__isl_take isl_val *v1,
481 __isl_take isl_val *v2);
482 __isl_give isl_val *isl_val_gcdext(__isl_take isl_val *v1,
483 __isl_take isl_val *v2, __isl_give isl_val **x,
484 __isl_give isl_val **y);
486 The function C<isl_val_gcdext> returns the greatest common divisor g
487 of C<v1> and C<v2> as well as two integers C<*x> and C<*y> such
488 that C<*x> * C<v1> + C<*y> * C<v2> = g.
490 A value can be read from input using
493 __isl_give isl_val *isl_val_read_from_str(isl_ctx *ctx,
496 A value can be printed using
499 __isl_give isl_printer *isl_printer_print_val(
500 __isl_take isl_printer *p, __isl_keep isl_val *v);
502 =head3 GMP specific functions
504 These functions are only available if C<isl> has been compiled with C<GMP>
507 Specific integer and rational values can be created from C<GMP> values using
508 the following functions.
510 #include <isl/val_gmp.h>
511 __isl_give isl_val *isl_val_int_from_gmp(isl_ctx *ctx,
513 __isl_give isl_val *isl_val_from_gmp(isl_ctx *ctx,
514 const mpz_t n, const mpz_t d);
516 The numerator and denominator of a rational value can be extracted as
517 C<GMP> values using the following functions.
519 #include <isl/val_gmp.h>
520 int isl_val_get_num_gmp(__isl_keep isl_val *v, mpz_t z);
521 int isl_val_get_den_gmp(__isl_keep isl_val *v, mpz_t z);
523 =head2 Integers (obsolescent)
525 All operations on integers, mainly the coefficients
526 of the constraints describing the sets and relations,
527 are performed in exact integer arithmetic using C<GMP>.
528 However, to allow future versions of C<isl> to optionally
529 support fixed integer arithmetic, all calls to C<GMP>
530 are wrapped inside C<isl> specific macros.
531 The basic type is C<isl_int> and the operations below
532 are available on this type.
533 The meanings of these operations are essentially the same
534 as their C<GMP> C<mpz_> counterparts.
535 As always with C<GMP> types, C<isl_int>s need to be
536 initialized with C<isl_int_init> before they can be used
537 and they need to be released with C<isl_int_clear>
539 The user should not assume that an C<isl_int> is represented
540 as a C<mpz_t>, but should instead explicitly convert between
541 C<mpz_t>s and C<isl_int>s using C<isl_int_set_gmp> and
542 C<isl_int_get_gmp> whenever a C<mpz_t> is required.
546 =item isl_int_init(i)
548 =item isl_int_clear(i)
550 =item isl_int_set(r,i)
552 =item isl_int_set_si(r,i)
554 =item isl_int_set_gmp(r,g)
556 =item isl_int_get_gmp(i,g)
558 =item isl_int_abs(r,i)
560 =item isl_int_neg(r,i)
562 =item isl_int_swap(i,j)
564 =item isl_int_swap_or_set(i,j)
566 =item isl_int_add_ui(r,i,j)
568 =item isl_int_sub_ui(r,i,j)
570 =item isl_int_add(r,i,j)
572 =item isl_int_sub(r,i,j)
574 =item isl_int_mul(r,i,j)
576 =item isl_int_mul_ui(r,i,j)
578 =item isl_int_addmul(r,i,j)
580 =item isl_int_submul(r,i,j)
582 =item isl_int_gcd(r,i,j)
584 =item isl_int_lcm(r,i,j)
586 =item isl_int_divexact(r,i,j)
588 =item isl_int_cdiv_q(r,i,j)
590 =item isl_int_fdiv_q(r,i,j)
592 =item isl_int_fdiv_r(r,i,j)
594 =item isl_int_fdiv_q_ui(r,i,j)
596 =item isl_int_read(r,s)
598 =item isl_int_print(out,i,width)
602 =item isl_int_cmp(i,j)
604 =item isl_int_cmp_si(i,si)
606 =item isl_int_eq(i,j)
608 =item isl_int_ne(i,j)
610 =item isl_int_lt(i,j)
612 =item isl_int_le(i,j)
614 =item isl_int_gt(i,j)
616 =item isl_int_ge(i,j)
618 =item isl_int_abs_eq(i,j)
620 =item isl_int_abs_ne(i,j)
622 =item isl_int_abs_lt(i,j)
624 =item isl_int_abs_gt(i,j)
626 =item isl_int_abs_ge(i,j)
628 =item isl_int_is_zero(i)
630 =item isl_int_is_one(i)
632 =item isl_int_is_negone(i)
634 =item isl_int_is_pos(i)
636 =item isl_int_is_neg(i)
638 =item isl_int_is_nonpos(i)
640 =item isl_int_is_nonneg(i)
642 =item isl_int_is_divisible_by(i,j)
646 =head2 Sets and Relations
648 C<isl> uses six types of objects for representing sets and relations,
649 C<isl_basic_set>, C<isl_basic_map>, C<isl_set>, C<isl_map>,
650 C<isl_union_set> and C<isl_union_map>.
651 C<isl_basic_set> and C<isl_basic_map> represent sets and relations that
652 can be described as a conjunction of affine constraints, while
653 C<isl_set> and C<isl_map> represent unions of
654 C<isl_basic_set>s and C<isl_basic_map>s, respectively.
655 However, all C<isl_basic_set>s or C<isl_basic_map>s in the union need
656 to live in the same space. C<isl_union_set>s and C<isl_union_map>s
657 represent unions of C<isl_set>s or C<isl_map>s in I<different> spaces,
658 where spaces are considered different if they have a different number
659 of dimensions and/or different names (see L<"Spaces">).
660 The difference between sets and relations (maps) is that sets have
661 one set of variables, while relations have two sets of variables,
662 input variables and output variables.
664 =head2 Memory Management
666 Since a high-level operation on sets and/or relations usually involves
667 several substeps and since the user is usually not interested in
668 the intermediate results, most functions that return a new object
669 will also release all the objects passed as arguments.
670 If the user still wants to use one or more of these arguments
671 after the function call, she should pass along a copy of the
672 object rather than the object itself.
673 The user is then responsible for making sure that the original
674 object gets used somewhere else or is explicitly freed.
676 The arguments and return values of all documented functions are
677 annotated to make clear which arguments are released and which
678 arguments are preserved. In particular, the following annotations
685 C<__isl_give> means that a new object is returned.
686 The user should make sure that the returned pointer is
687 used exactly once as a value for an C<__isl_take> argument.
688 In between, it can be used as a value for as many
689 C<__isl_keep> arguments as the user likes.
690 There is one exception, and that is the case where the
691 pointer returned is C<NULL>. Is this case, the user
692 is free to use it as an C<__isl_take> argument or not.
696 C<__isl_take> means that the object the argument points to
697 is taken over by the function and may no longer be used
698 by the user as an argument to any other function.
699 The pointer value must be one returned by a function
700 returning an C<__isl_give> pointer.
701 If the user passes in a C<NULL> value, then this will
702 be treated as an error in the sense that the function will
703 not perform its usual operation. However, it will still
704 make sure that all the other C<__isl_take> arguments
709 C<__isl_keep> means that the function will only use the object
710 temporarily. After the function has finished, the user
711 can still use it as an argument to other functions.
712 A C<NULL> value will be treated in the same way as
713 a C<NULL> value for an C<__isl_take> argument.
717 =head2 Error Handling
719 C<isl> supports different ways to react in case a runtime error is triggered.
720 Runtime errors arise, e.g., if a function such as C<isl_map_intersect> is called
721 with two maps that have incompatible spaces. There are three possible ways
722 to react on error: to warn, to continue or to abort.
724 The default behavior is to warn. In this mode, C<isl> prints a warning, stores
725 the last error in the corresponding C<isl_ctx> and the function in which the
726 error was triggered returns C<NULL>. An error does not corrupt internal state,
727 such that isl can continue to be used. C<isl> also provides functions to
728 read the last error and to reset the memory that stores the last error. The
729 last error is only stored for information purposes. Its presence does not
730 change the behavior of C<isl>. Hence, resetting an error is not required to
731 continue to use isl, but only to observe new errors.
734 enum isl_error isl_ctx_last_error(isl_ctx *ctx);
735 void isl_ctx_reset_error(isl_ctx *ctx);
737 Another option is to continue on error. This is similar to warn on error mode,
738 except that C<isl> does not print any warning. This allows a program to
739 implement its own error reporting.
741 The last option is to directly abort the execution of the program from within
742 the isl library. This makes it obviously impossible to recover from an error,
743 but it allows to directly spot the error location. By aborting on error,
744 debuggers break at the location the error occurred and can provide a stack
745 trace. Other tools that automatically provide stack traces on abort or that do
746 not want to continue execution after an error was triggered may also prefer to
749 The on error behavior of isl can be specified by calling
750 C<isl_options_set_on_error> or by setting the command line option
751 C<--isl-on-error>. Valid arguments for the function call are
752 C<ISL_ON_ERROR_WARN>, C<ISL_ON_ERROR_CONTINUE> and C<ISL_ON_ERROR_ABORT>. The
753 choices for the command line option are C<warn>, C<continue> and C<abort>.
754 It is also possible to query the current error mode.
756 #include <isl/options.h>
757 int isl_options_set_on_error(isl_ctx *ctx, int val);
758 int isl_options_get_on_error(isl_ctx *ctx);
762 Identifiers are used to identify both individual dimensions
763 and tuples of dimensions. They consist of an optional name and an optional
764 user pointer. The name and the user pointer cannot both be C<NULL>, however.
765 Identifiers with the same name but different pointer values
766 are considered to be distinct.
767 Similarly, identifiers with different names but the same pointer value
768 are also considered to be distinct.
769 Equal identifiers are represented using the same object.
770 Pairs of identifiers can therefore be tested for equality using the
772 Identifiers can be constructed, copied, freed, inspected and printed
773 using the following functions.
776 __isl_give isl_id *isl_id_alloc(isl_ctx *ctx,
777 __isl_keep const char *name, void *user);
778 __isl_give isl_id *isl_id_set_free_user(
779 __isl_take isl_id *id,
780 __isl_give void (*free_user)(void *user));
781 __isl_give isl_id *isl_id_copy(isl_id *id);
782 void *isl_id_free(__isl_take isl_id *id);
784 isl_ctx *isl_id_get_ctx(__isl_keep isl_id *id);
785 void *isl_id_get_user(__isl_keep isl_id *id);
786 __isl_keep const char *isl_id_get_name(__isl_keep isl_id *id);
788 __isl_give isl_printer *isl_printer_print_id(
789 __isl_take isl_printer *p, __isl_keep isl_id *id);
791 The callback set by C<isl_id_set_free_user> is called on the user
792 pointer when the last reference to the C<isl_id> is freed.
793 Note that C<isl_id_get_name> returns a pointer to some internal
794 data structure, so the result can only be used while the
795 corresponding C<isl_id> is alive.
799 Whenever a new set, relation or similiar object is created from scratch,
800 the space in which it lives needs to be specified using an C<isl_space>.
801 Each space involves zero or more parameters and zero, one or two
802 tuples of set or input/output dimensions. The parameters and dimensions
803 are identified by an C<isl_dim_type> and a position.
804 The type C<isl_dim_param> refers to parameters,
805 the type C<isl_dim_set> refers to set dimensions (for spaces
806 with a single tuple of dimensions) and the types C<isl_dim_in>
807 and C<isl_dim_out> refer to input and output dimensions
808 (for spaces with two tuples of dimensions).
809 Local spaces (see L</"Local Spaces">) also contain dimensions
810 of type C<isl_dim_div>.
811 Note that parameters are only identified by their position within
812 a given object. Across different objects, parameters are (usually)
813 identified by their names or identifiers. Only unnamed parameters
814 are identified by their positions across objects. The use of unnamed
815 parameters is discouraged.
817 #include <isl/space.h>
818 __isl_give isl_space *isl_space_alloc(isl_ctx *ctx,
819 unsigned nparam, unsigned n_in, unsigned n_out);
820 __isl_give isl_space *isl_space_params_alloc(isl_ctx *ctx,
822 __isl_give isl_space *isl_space_set_alloc(isl_ctx *ctx,
823 unsigned nparam, unsigned dim);
824 __isl_give isl_space *isl_space_copy(__isl_keep isl_space *space);
825 void *isl_space_free(__isl_take isl_space *space);
826 unsigned isl_space_dim(__isl_keep isl_space *space,
827 enum isl_dim_type type);
829 The space used for creating a parameter domain
830 needs to be created using C<isl_space_params_alloc>.
831 For other sets, the space
832 needs to be created using C<isl_space_set_alloc>, while
833 for a relation, the space
834 needs to be created using C<isl_space_alloc>.
835 C<isl_space_dim> can be used
836 to find out the number of dimensions of each type in
837 a space, where type may be
838 C<isl_dim_param>, C<isl_dim_in> (only for relations),
839 C<isl_dim_out> (only for relations), C<isl_dim_set>
840 (only for sets) or C<isl_dim_all>.
842 To check whether a given space is that of a set or a map
843 or whether it is a parameter space, use these functions:
845 #include <isl/space.h>
846 int isl_space_is_params(__isl_keep isl_space *space);
847 int isl_space_is_set(__isl_keep isl_space *space);
848 int isl_space_is_map(__isl_keep isl_space *space);
850 Spaces can be compared using the following functions:
852 #include <isl/space.h>
853 int isl_space_is_equal(__isl_keep isl_space *space1,
854 __isl_keep isl_space *space2);
855 int isl_space_is_domain(__isl_keep isl_space *space1,
856 __isl_keep isl_space *space2);
857 int isl_space_is_range(__isl_keep isl_space *space1,
858 __isl_keep isl_space *space2);
860 C<isl_space_is_domain> checks whether the first argument is equal
861 to the domain of the second argument. This requires in particular that
862 the first argument is a set space and that the second argument
865 It is often useful to create objects that live in the
866 same space as some other object. This can be accomplished
867 by creating the new objects
868 (see L<Creating New Sets and Relations> or
869 L<Creating New (Piecewise) Quasipolynomials>) based on the space
870 of the original object.
873 __isl_give isl_space *isl_basic_set_get_space(
874 __isl_keep isl_basic_set *bset);
875 __isl_give isl_space *isl_set_get_space(__isl_keep isl_set *set);
877 #include <isl/union_set.h>
878 __isl_give isl_space *isl_union_set_get_space(
879 __isl_keep isl_union_set *uset);
882 __isl_give isl_space *isl_basic_map_get_space(
883 __isl_keep isl_basic_map *bmap);
884 __isl_give isl_space *isl_map_get_space(__isl_keep isl_map *map);
886 #include <isl/union_map.h>
887 __isl_give isl_space *isl_union_map_get_space(
888 __isl_keep isl_union_map *umap);
890 #include <isl/constraint.h>
891 __isl_give isl_space *isl_constraint_get_space(
892 __isl_keep isl_constraint *constraint);
894 #include <isl/polynomial.h>
895 __isl_give isl_space *isl_qpolynomial_get_domain_space(
896 __isl_keep isl_qpolynomial *qp);
897 __isl_give isl_space *isl_qpolynomial_get_space(
898 __isl_keep isl_qpolynomial *qp);
899 __isl_give isl_space *isl_qpolynomial_fold_get_space(
900 __isl_keep isl_qpolynomial_fold *fold);
901 __isl_give isl_space *isl_pw_qpolynomial_get_domain_space(
902 __isl_keep isl_pw_qpolynomial *pwqp);
903 __isl_give isl_space *isl_pw_qpolynomial_get_space(
904 __isl_keep isl_pw_qpolynomial *pwqp);
905 __isl_give isl_space *isl_pw_qpolynomial_fold_get_domain_space(
906 __isl_keep isl_pw_qpolynomial_fold *pwf);
907 __isl_give isl_space *isl_pw_qpolynomial_fold_get_space(
908 __isl_keep isl_pw_qpolynomial_fold *pwf);
909 __isl_give isl_space *isl_union_pw_qpolynomial_get_space(
910 __isl_keep isl_union_pw_qpolynomial *upwqp);
911 __isl_give isl_space *isl_union_pw_qpolynomial_fold_get_space(
912 __isl_keep isl_union_pw_qpolynomial_fold *upwf);
915 __isl_give isl_space *isl_multi_val_get_space(
916 __isl_keep isl_multi_val *mv);
919 __isl_give isl_space *isl_aff_get_domain_space(
920 __isl_keep isl_aff *aff);
921 __isl_give isl_space *isl_aff_get_space(
922 __isl_keep isl_aff *aff);
923 __isl_give isl_space *isl_pw_aff_get_domain_space(
924 __isl_keep isl_pw_aff *pwaff);
925 __isl_give isl_space *isl_pw_aff_get_space(
926 __isl_keep isl_pw_aff *pwaff);
927 __isl_give isl_space *isl_multi_aff_get_domain_space(
928 __isl_keep isl_multi_aff *maff);
929 __isl_give isl_space *isl_multi_aff_get_space(
930 __isl_keep isl_multi_aff *maff);
931 __isl_give isl_space *isl_pw_multi_aff_get_domain_space(
932 __isl_keep isl_pw_multi_aff *pma);
933 __isl_give isl_space *isl_pw_multi_aff_get_space(
934 __isl_keep isl_pw_multi_aff *pma);
935 __isl_give isl_space *isl_union_pw_multi_aff_get_space(
936 __isl_keep isl_union_pw_multi_aff *upma);
937 __isl_give isl_space *isl_multi_pw_aff_get_domain_space(
938 __isl_keep isl_multi_pw_aff *mpa);
939 __isl_give isl_space *isl_multi_pw_aff_get_space(
940 __isl_keep isl_multi_pw_aff *mpa);
942 #include <isl/point.h>
943 __isl_give isl_space *isl_point_get_space(
944 __isl_keep isl_point *pnt);
946 The identifiers or names of the individual dimensions may be set or read off
947 using the following functions.
949 #include <isl/space.h>
950 __isl_give isl_space *isl_space_set_dim_id(
951 __isl_take isl_space *space,
952 enum isl_dim_type type, unsigned pos,
953 __isl_take isl_id *id);
954 int isl_space_has_dim_id(__isl_keep isl_space *space,
955 enum isl_dim_type type, unsigned pos);
956 __isl_give isl_id *isl_space_get_dim_id(
957 __isl_keep isl_space *space,
958 enum isl_dim_type type, unsigned pos);
959 __isl_give isl_space *isl_space_set_dim_name(
960 __isl_take isl_space *space,
961 enum isl_dim_type type, unsigned pos,
962 __isl_keep const char *name);
963 int isl_space_has_dim_name(__isl_keep isl_space *space,
964 enum isl_dim_type type, unsigned pos);
965 __isl_keep const char *isl_space_get_dim_name(
966 __isl_keep isl_space *space,
967 enum isl_dim_type type, unsigned pos);
969 Note that C<isl_space_get_name> returns a pointer to some internal
970 data structure, so the result can only be used while the
971 corresponding C<isl_space> is alive.
972 Also note that every function that operates on two sets or relations
973 requires that both arguments have the same parameters. This also
974 means that if one of the arguments has named parameters, then the
975 other needs to have named parameters too and the names need to match.
976 Pairs of C<isl_set>, C<isl_map>, C<isl_union_set> and/or C<isl_union_map>
977 arguments may have different parameters (as long as they are named),
978 in which case the result will have as parameters the union of the parameters of
981 Given the identifier or name of a dimension (typically a parameter),
982 its position can be obtained from the following function.
984 #include <isl/space.h>
985 int isl_space_find_dim_by_id(__isl_keep isl_space *space,
986 enum isl_dim_type type, __isl_keep isl_id *id);
987 int isl_space_find_dim_by_name(__isl_keep isl_space *space,
988 enum isl_dim_type type, const char *name);
990 The identifiers or names of entire spaces may be set or read off
991 using the following functions.
993 #include <isl/space.h>
994 __isl_give isl_space *isl_space_set_tuple_id(
995 __isl_take isl_space *space,
996 enum isl_dim_type type, __isl_take isl_id *id);
997 __isl_give isl_space *isl_space_reset_tuple_id(
998 __isl_take isl_space *space, enum isl_dim_type type);
999 int isl_space_has_tuple_id(__isl_keep isl_space *space,
1000 enum isl_dim_type type);
1001 __isl_give isl_id *isl_space_get_tuple_id(
1002 __isl_keep isl_space *space, enum isl_dim_type type);
1003 __isl_give isl_space *isl_space_set_tuple_name(
1004 __isl_take isl_space *space,
1005 enum isl_dim_type type, const char *s);
1006 int isl_space_has_tuple_name(__isl_keep isl_space *space,
1007 enum isl_dim_type type);
1008 const char *isl_space_get_tuple_name(__isl_keep isl_space *space,
1009 enum isl_dim_type type);
1011 The C<type> argument needs to be one of C<isl_dim_in>, C<isl_dim_out>
1012 or C<isl_dim_set>. As with C<isl_space_get_name>,
1013 the C<isl_space_get_tuple_name> function returns a pointer to some internal
1015 Binary operations require the corresponding spaces of their arguments
1016 to have the same name.
1018 Spaces can be nested. In particular, the domain of a set or
1019 the domain or range of a relation can be a nested relation.
1020 The following functions can be used to construct and deconstruct
1023 #include <isl/space.h>
1024 int isl_space_is_wrapping(__isl_keep isl_space *space);
1025 __isl_give isl_space *isl_space_wrap(__isl_take isl_space *space);
1026 __isl_give isl_space *isl_space_unwrap(__isl_take isl_space *space);
1028 The input to C<isl_space_is_wrapping> and C<isl_space_unwrap> should
1029 be the space of a set, while that of
1030 C<isl_space_wrap> should be the space of a relation.
1031 Conversely, the output of C<isl_space_unwrap> is the space
1032 of a relation, while that of C<isl_space_wrap> is the space of a set.
1034 Spaces can be created from other spaces
1035 using the following functions.
1037 __isl_give isl_space *isl_space_domain(__isl_take isl_space *space);
1038 __isl_give isl_space *isl_space_from_domain(__isl_take isl_space *space);
1039 __isl_give isl_space *isl_space_range(__isl_take isl_space *space);
1040 __isl_give isl_space *isl_space_from_range(__isl_take isl_space *space);
1041 __isl_give isl_space *isl_space_params(
1042 __isl_take isl_space *space);
1043 __isl_give isl_space *isl_space_set_from_params(
1044 __isl_take isl_space *space);
1045 __isl_give isl_space *isl_space_reverse(__isl_take isl_space *space);
1046 __isl_give isl_space *isl_space_join(__isl_take isl_space *left,
1047 __isl_take isl_space *right);
1048 __isl_give isl_space *isl_space_align_params(
1049 __isl_take isl_space *space1, __isl_take isl_space *space2)
1050 __isl_give isl_space *isl_space_insert_dims(__isl_take isl_space *space,
1051 enum isl_dim_type type, unsigned pos, unsigned n);
1052 __isl_give isl_space *isl_space_add_dims(__isl_take isl_space *space,
1053 enum isl_dim_type type, unsigned n);
1054 __isl_give isl_space *isl_space_drop_dims(__isl_take isl_space *space,
1055 enum isl_dim_type type, unsigned first, unsigned n);
1056 __isl_give isl_space *isl_space_move_dims(__isl_take isl_space *space,
1057 enum isl_dim_type dst_type, unsigned dst_pos,
1058 enum isl_dim_type src_type, unsigned src_pos,
1060 __isl_give isl_space *isl_space_map_from_set(
1061 __isl_take isl_space *space);
1062 __isl_give isl_space *isl_space_map_from_domain_and_range(
1063 __isl_take isl_space *domain,
1064 __isl_take isl_space *range);
1065 __isl_give isl_space *isl_space_zip(__isl_take isl_space *space);
1066 __isl_give isl_space *isl_space_curry(
1067 __isl_take isl_space *space);
1068 __isl_give isl_space *isl_space_uncurry(
1069 __isl_take isl_space *space);
1071 Note that if dimensions are added or removed from a space, then
1072 the name and the internal structure are lost.
1076 A local space is essentially a space with
1077 zero or more existentially quantified variables.
1078 The local space of a (constraint of a) basic set or relation can be obtained
1079 using the following functions.
1081 #include <isl/constraint.h>
1082 __isl_give isl_local_space *isl_constraint_get_local_space(
1083 __isl_keep isl_constraint *constraint);
1085 #include <isl/set.h>
1086 __isl_give isl_local_space *isl_basic_set_get_local_space(
1087 __isl_keep isl_basic_set *bset);
1089 #include <isl/map.h>
1090 __isl_give isl_local_space *isl_basic_map_get_local_space(
1091 __isl_keep isl_basic_map *bmap);
1093 A new local space can be created from a space using
1095 #include <isl/local_space.h>
1096 __isl_give isl_local_space *isl_local_space_from_space(
1097 __isl_take isl_space *space);
1099 They can be inspected, modified, copied and freed using the following functions.
1101 #include <isl/local_space.h>
1102 isl_ctx *isl_local_space_get_ctx(
1103 __isl_keep isl_local_space *ls);
1104 int isl_local_space_is_set(__isl_keep isl_local_space *ls);
1105 int isl_local_space_dim(__isl_keep isl_local_space *ls,
1106 enum isl_dim_type type);
1107 int isl_local_space_has_dim_id(
1108 __isl_keep isl_local_space *ls,
1109 enum isl_dim_type type, unsigned pos);
1110 __isl_give isl_id *isl_local_space_get_dim_id(
1111 __isl_keep isl_local_space *ls,
1112 enum isl_dim_type type, unsigned pos);
1113 int isl_local_space_has_dim_name(
1114 __isl_keep isl_local_space *ls,
1115 enum isl_dim_type type, unsigned pos)
1116 const char *isl_local_space_get_dim_name(
1117 __isl_keep isl_local_space *ls,
1118 enum isl_dim_type type, unsigned pos);
1119 __isl_give isl_local_space *isl_local_space_set_dim_name(
1120 __isl_take isl_local_space *ls,
1121 enum isl_dim_type type, unsigned pos, const char *s);
1122 __isl_give isl_local_space *isl_local_space_set_dim_id(
1123 __isl_take isl_local_space *ls,
1124 enum isl_dim_type type, unsigned pos,
1125 __isl_take isl_id *id);
1126 __isl_give isl_space *isl_local_space_get_space(
1127 __isl_keep isl_local_space *ls);
1128 __isl_give isl_aff *isl_local_space_get_div(
1129 __isl_keep isl_local_space *ls, int pos);
1130 __isl_give isl_local_space *isl_local_space_copy(
1131 __isl_keep isl_local_space *ls);
1132 void *isl_local_space_free(__isl_take isl_local_space *ls);
1134 Note that C<isl_local_space_get_div> can only be used on local spaces
1137 Two local spaces can be compared using
1139 int isl_local_space_is_equal(__isl_keep isl_local_space *ls1,
1140 __isl_keep isl_local_space *ls2);
1142 Local spaces can be created from other local spaces
1143 using the following functions.
1145 __isl_give isl_local_space *isl_local_space_domain(
1146 __isl_take isl_local_space *ls);
1147 __isl_give isl_local_space *isl_local_space_range(
1148 __isl_take isl_local_space *ls);
1149 __isl_give isl_local_space *isl_local_space_from_domain(
1150 __isl_take isl_local_space *ls);
1151 __isl_give isl_local_space *isl_local_space_intersect(
1152 __isl_take isl_local_space *ls1,
1153 __isl_take isl_local_space *ls2);
1154 __isl_give isl_local_space *isl_local_space_add_dims(
1155 __isl_take isl_local_space *ls,
1156 enum isl_dim_type type, unsigned n);
1157 __isl_give isl_local_space *isl_local_space_insert_dims(
1158 __isl_take isl_local_space *ls,
1159 enum isl_dim_type type, unsigned first, unsigned n);
1160 __isl_give isl_local_space *isl_local_space_drop_dims(
1161 __isl_take isl_local_space *ls,
1162 enum isl_dim_type type, unsigned first, unsigned n);
1164 =head2 Input and Output
1166 C<isl> supports its own input/output format, which is similar
1167 to the C<Omega> format, but also supports the C<PolyLib> format
1170 =head3 C<isl> format
1172 The C<isl> format is similar to that of C<Omega>, but has a different
1173 syntax for describing the parameters and allows for the definition
1174 of an existentially quantified variable as the integer division
1175 of an affine expression.
1176 For example, the set of integers C<i> between C<0> and C<n>
1177 such that C<i % 10 <= 6> can be described as
1179 [n] -> { [i] : exists (a = [i/10] : 0 <= i and i <= n and
1182 A set or relation can have several disjuncts, separated
1183 by the keyword C<or>. Each disjunct is either a conjunction
1184 of constraints or a projection (C<exists>) of a conjunction
1185 of constraints. The constraints are separated by the keyword
1188 =head3 C<PolyLib> format
1190 If the represented set is a union, then the first line
1191 contains a single number representing the number of disjuncts.
1192 Otherwise, a line containing the number C<1> is optional.
1194 Each disjunct is represented by a matrix of constraints.
1195 The first line contains two numbers representing
1196 the number of rows and columns,
1197 where the number of rows is equal to the number of constraints
1198 and the number of columns is equal to two plus the number of variables.
1199 The following lines contain the actual rows of the constraint matrix.
1200 In each row, the first column indicates whether the constraint
1201 is an equality (C<0>) or inequality (C<1>). The final column
1202 corresponds to the constant term.
1204 If the set is parametric, then the coefficients of the parameters
1205 appear in the last columns before the constant column.
1206 The coefficients of any existentially quantified variables appear
1207 between those of the set variables and those of the parameters.
1209 =head3 Extended C<PolyLib> format
1211 The extended C<PolyLib> format is nearly identical to the
1212 C<PolyLib> format. The only difference is that the line
1213 containing the number of rows and columns of a constraint matrix
1214 also contains four additional numbers:
1215 the number of output dimensions, the number of input dimensions,
1216 the number of local dimensions (i.e., the number of existentially
1217 quantified variables) and the number of parameters.
1218 For sets, the number of ``output'' dimensions is equal
1219 to the number of set dimensions, while the number of ``input''
1224 #include <isl/set.h>
1225 __isl_give isl_basic_set *isl_basic_set_read_from_file(
1226 isl_ctx *ctx, FILE *input);
1227 __isl_give isl_basic_set *isl_basic_set_read_from_str(
1228 isl_ctx *ctx, const char *str);
1229 __isl_give isl_set *isl_set_read_from_file(isl_ctx *ctx,
1231 __isl_give isl_set *isl_set_read_from_str(isl_ctx *ctx,
1234 #include <isl/map.h>
1235 __isl_give isl_basic_map *isl_basic_map_read_from_file(
1236 isl_ctx *ctx, FILE *input);
1237 __isl_give isl_basic_map *isl_basic_map_read_from_str(
1238 isl_ctx *ctx, const char *str);
1239 __isl_give isl_map *isl_map_read_from_file(
1240 isl_ctx *ctx, FILE *input);
1241 __isl_give isl_map *isl_map_read_from_str(isl_ctx *ctx,
1244 #include <isl/union_set.h>
1245 __isl_give isl_union_set *isl_union_set_read_from_file(
1246 isl_ctx *ctx, FILE *input);
1247 __isl_give isl_union_set *isl_union_set_read_from_str(
1248 isl_ctx *ctx, const char *str);
1250 #include <isl/union_map.h>
1251 __isl_give isl_union_map *isl_union_map_read_from_file(
1252 isl_ctx *ctx, FILE *input);
1253 __isl_give isl_union_map *isl_union_map_read_from_str(
1254 isl_ctx *ctx, const char *str);
1256 The input format is autodetected and may be either the C<PolyLib> format
1257 or the C<isl> format.
1261 Before anything can be printed, an C<isl_printer> needs to
1264 __isl_give isl_printer *isl_printer_to_file(isl_ctx *ctx,
1266 __isl_give isl_printer *isl_printer_to_str(isl_ctx *ctx);
1267 void *isl_printer_free(__isl_take isl_printer *printer);
1268 __isl_give char *isl_printer_get_str(
1269 __isl_keep isl_printer *printer);
1271 The printer can be inspected using the following functions.
1273 FILE *isl_printer_get_file(
1274 __isl_keep isl_printer *printer);
1275 int isl_printer_get_output_format(
1276 __isl_keep isl_printer *p);
1278 The behavior of the printer can be modified in various ways
1280 __isl_give isl_printer *isl_printer_set_output_format(
1281 __isl_take isl_printer *p, int output_format);
1282 __isl_give isl_printer *isl_printer_set_indent(
1283 __isl_take isl_printer *p, int indent);
1284 __isl_give isl_printer *isl_printer_indent(
1285 __isl_take isl_printer *p, int indent);
1286 __isl_give isl_printer *isl_printer_set_prefix(
1287 __isl_take isl_printer *p, const char *prefix);
1288 __isl_give isl_printer *isl_printer_set_suffix(
1289 __isl_take isl_printer *p, const char *suffix);
1291 The C<output_format> may be either C<ISL_FORMAT_ISL>, C<ISL_FORMAT_OMEGA>,
1292 C<ISL_FORMAT_POLYLIB>, C<ISL_FORMAT_EXT_POLYLIB> or C<ISL_FORMAT_LATEX>
1293 and defaults to C<ISL_FORMAT_ISL>.
1294 Each line in the output is indented by C<indent> (set by
1295 C<isl_printer_set_indent>) spaces
1296 (default: 0), prefixed by C<prefix> and suffixed by C<suffix>.
1297 In the C<PolyLib> format output,
1298 the coefficients of the existentially quantified variables
1299 appear between those of the set variables and those
1301 The function C<isl_printer_indent> increases the indentation
1302 by the specified amount (which may be negative).
1304 To actually print something, use
1306 #include <isl/printer.h>
1307 __isl_give isl_printer *isl_printer_print_double(
1308 __isl_take isl_printer *p, double d);
1310 #include <isl/set.h>
1311 __isl_give isl_printer *isl_printer_print_basic_set(
1312 __isl_take isl_printer *printer,
1313 __isl_keep isl_basic_set *bset);
1314 __isl_give isl_printer *isl_printer_print_set(
1315 __isl_take isl_printer *printer,
1316 __isl_keep isl_set *set);
1318 #include <isl/map.h>
1319 __isl_give isl_printer *isl_printer_print_basic_map(
1320 __isl_take isl_printer *printer,
1321 __isl_keep isl_basic_map *bmap);
1322 __isl_give isl_printer *isl_printer_print_map(
1323 __isl_take isl_printer *printer,
1324 __isl_keep isl_map *map);
1326 #include <isl/union_set.h>
1327 __isl_give isl_printer *isl_printer_print_union_set(
1328 __isl_take isl_printer *p,
1329 __isl_keep isl_union_set *uset);
1331 #include <isl/union_map.h>
1332 __isl_give isl_printer *isl_printer_print_union_map(
1333 __isl_take isl_printer *p,
1334 __isl_keep isl_union_map *umap);
1336 When called on a file printer, the following function flushes
1337 the file. When called on a string printer, the buffer is cleared.
1339 __isl_give isl_printer *isl_printer_flush(
1340 __isl_take isl_printer *p);
1342 =head2 Creating New Sets and Relations
1344 C<isl> has functions for creating some standard sets and relations.
1348 =item * Empty sets and relations
1350 __isl_give isl_basic_set *isl_basic_set_empty(
1351 __isl_take isl_space *space);
1352 __isl_give isl_basic_map *isl_basic_map_empty(
1353 __isl_take isl_space *space);
1354 __isl_give isl_set *isl_set_empty(
1355 __isl_take isl_space *space);
1356 __isl_give isl_map *isl_map_empty(
1357 __isl_take isl_space *space);
1358 __isl_give isl_union_set *isl_union_set_empty(
1359 __isl_take isl_space *space);
1360 __isl_give isl_union_map *isl_union_map_empty(
1361 __isl_take isl_space *space);
1363 For C<isl_union_set>s and C<isl_union_map>s, the space
1364 is only used to specify the parameters.
1366 =item * Universe sets and relations
1368 __isl_give isl_basic_set *isl_basic_set_universe(
1369 __isl_take isl_space *space);
1370 __isl_give isl_basic_map *isl_basic_map_universe(
1371 __isl_take isl_space *space);
1372 __isl_give isl_set *isl_set_universe(
1373 __isl_take isl_space *space);
1374 __isl_give isl_map *isl_map_universe(
1375 __isl_take isl_space *space);
1376 __isl_give isl_union_set *isl_union_set_universe(
1377 __isl_take isl_union_set *uset);
1378 __isl_give isl_union_map *isl_union_map_universe(
1379 __isl_take isl_union_map *umap);
1381 The sets and relations constructed by the functions above
1382 contain all integer values, while those constructed by the
1383 functions below only contain non-negative values.
1385 __isl_give isl_basic_set *isl_basic_set_nat_universe(
1386 __isl_take isl_space *space);
1387 __isl_give isl_basic_map *isl_basic_map_nat_universe(
1388 __isl_take isl_space *space);
1389 __isl_give isl_set *isl_set_nat_universe(
1390 __isl_take isl_space *space);
1391 __isl_give isl_map *isl_map_nat_universe(
1392 __isl_take isl_space *space);
1394 =item * Identity relations
1396 __isl_give isl_basic_map *isl_basic_map_identity(
1397 __isl_take isl_space *space);
1398 __isl_give isl_map *isl_map_identity(
1399 __isl_take isl_space *space);
1401 The number of input and output dimensions in C<space> needs
1404 =item * Lexicographic order
1406 __isl_give isl_map *isl_map_lex_lt(
1407 __isl_take isl_space *set_space);
1408 __isl_give isl_map *isl_map_lex_le(
1409 __isl_take isl_space *set_space);
1410 __isl_give isl_map *isl_map_lex_gt(
1411 __isl_take isl_space *set_space);
1412 __isl_give isl_map *isl_map_lex_ge(
1413 __isl_take isl_space *set_space);
1414 __isl_give isl_map *isl_map_lex_lt_first(
1415 __isl_take isl_space *space, unsigned n);
1416 __isl_give isl_map *isl_map_lex_le_first(
1417 __isl_take isl_space *space, unsigned n);
1418 __isl_give isl_map *isl_map_lex_gt_first(
1419 __isl_take isl_space *space, unsigned n);
1420 __isl_give isl_map *isl_map_lex_ge_first(
1421 __isl_take isl_space *space, unsigned n);
1423 The first four functions take a space for a B<set>
1424 and return relations that express that the elements in the domain
1425 are lexicographically less
1426 (C<isl_map_lex_lt>), less or equal (C<isl_map_lex_le>),
1427 greater (C<isl_map_lex_gt>) or greater or equal (C<isl_map_lex_ge>)
1428 than the elements in the range.
1429 The last four functions take a space for a map
1430 and return relations that express that the first C<n> dimensions
1431 in the domain are lexicographically less
1432 (C<isl_map_lex_lt_first>), less or equal (C<isl_map_lex_le_first>),
1433 greater (C<isl_map_lex_gt_first>) or greater or equal (C<isl_map_lex_ge_first>)
1434 than the first C<n> dimensions in the range.
1438 A basic set or relation can be converted to a set or relation
1439 using the following functions.
1441 __isl_give isl_set *isl_set_from_basic_set(
1442 __isl_take isl_basic_set *bset);
1443 __isl_give isl_map *isl_map_from_basic_map(
1444 __isl_take isl_basic_map *bmap);
1446 Sets and relations can be converted to union sets and relations
1447 using the following functions.
1449 __isl_give isl_union_set *isl_union_set_from_basic_set(
1450 __isl_take isl_basic_set *bset);
1451 __isl_give isl_union_map *isl_union_map_from_basic_map(
1452 __isl_take isl_basic_map *bmap);
1453 __isl_give isl_union_set *isl_union_set_from_set(
1454 __isl_take isl_set *set);
1455 __isl_give isl_union_map *isl_union_map_from_map(
1456 __isl_take isl_map *map);
1458 The inverse conversions below can only be used if the input
1459 union set or relation is known to contain elements in exactly one
1462 __isl_give isl_set *isl_set_from_union_set(
1463 __isl_take isl_union_set *uset);
1464 __isl_give isl_map *isl_map_from_union_map(
1465 __isl_take isl_union_map *umap);
1467 A zero-dimensional (basic) set can be constructed on a given parameter domain
1468 using the following function.
1470 __isl_give isl_basic_set *isl_basic_set_from_params(
1471 __isl_take isl_basic_set *bset);
1472 __isl_give isl_set *isl_set_from_params(
1473 __isl_take isl_set *set);
1475 Sets and relations can be copied and freed again using the following
1478 __isl_give isl_basic_set *isl_basic_set_copy(
1479 __isl_keep isl_basic_set *bset);
1480 __isl_give isl_set *isl_set_copy(__isl_keep isl_set *set);
1481 __isl_give isl_union_set *isl_union_set_copy(
1482 __isl_keep isl_union_set *uset);
1483 __isl_give isl_basic_map *isl_basic_map_copy(
1484 __isl_keep isl_basic_map *bmap);
1485 __isl_give isl_map *isl_map_copy(__isl_keep isl_map *map);
1486 __isl_give isl_union_map *isl_union_map_copy(
1487 __isl_keep isl_union_map *umap);
1488 void *isl_basic_set_free(__isl_take isl_basic_set *bset);
1489 void *isl_set_free(__isl_take isl_set *set);
1490 void *isl_union_set_free(__isl_take isl_union_set *uset);
1491 void *isl_basic_map_free(__isl_take isl_basic_map *bmap);
1492 void *isl_map_free(__isl_take isl_map *map);
1493 void *isl_union_map_free(__isl_take isl_union_map *umap);
1495 Other sets and relations can be constructed by starting
1496 from a universe set or relation, adding equality and/or
1497 inequality constraints and then projecting out the
1498 existentially quantified variables, if any.
1499 Constraints can be constructed, manipulated and
1500 added to (or removed from) (basic) sets and relations
1501 using the following functions.
1503 #include <isl/constraint.h>
1504 __isl_give isl_constraint *isl_equality_alloc(
1505 __isl_take isl_local_space *ls);
1506 __isl_give isl_constraint *isl_inequality_alloc(
1507 __isl_take isl_local_space *ls);
1508 __isl_give isl_constraint *isl_constraint_set_constant(
1509 __isl_take isl_constraint *constraint, isl_int v);
1510 __isl_give isl_constraint *isl_constraint_set_constant_si(
1511 __isl_take isl_constraint *constraint, int v);
1512 __isl_give isl_constraint *isl_constraint_set_constant_val(
1513 __isl_take isl_constraint *constraint,
1514 __isl_take isl_val *v);
1515 __isl_give isl_constraint *isl_constraint_set_coefficient(
1516 __isl_take isl_constraint *constraint,
1517 enum isl_dim_type type, int pos, isl_int v);
1518 __isl_give isl_constraint *isl_constraint_set_coefficient_si(
1519 __isl_take isl_constraint *constraint,
1520 enum isl_dim_type type, int pos, int v);
1521 __isl_give isl_constraint *
1522 isl_constraint_set_coefficient_val(
1523 __isl_take isl_constraint *constraint,
1524 enum isl_dim_type type, int pos, isl_val *v);
1525 __isl_give isl_basic_map *isl_basic_map_add_constraint(
1526 __isl_take isl_basic_map *bmap,
1527 __isl_take isl_constraint *constraint);
1528 __isl_give isl_basic_set *isl_basic_set_add_constraint(
1529 __isl_take isl_basic_set *bset,
1530 __isl_take isl_constraint *constraint);
1531 __isl_give isl_map *isl_map_add_constraint(
1532 __isl_take isl_map *map,
1533 __isl_take isl_constraint *constraint);
1534 __isl_give isl_set *isl_set_add_constraint(
1535 __isl_take isl_set *set,
1536 __isl_take isl_constraint *constraint);
1537 __isl_give isl_basic_set *isl_basic_set_drop_constraint(
1538 __isl_take isl_basic_set *bset,
1539 __isl_take isl_constraint *constraint);
1541 For example, to create a set containing the even integers
1542 between 10 and 42, you would use the following code.
1545 isl_local_space *ls;
1547 isl_basic_set *bset;
1549 space = isl_space_set_alloc(ctx, 0, 2);
1550 bset = isl_basic_set_universe(isl_space_copy(space));
1551 ls = isl_local_space_from_space(space);
1553 c = isl_equality_alloc(isl_local_space_copy(ls));
1554 c = isl_constraint_set_coefficient_si(c, isl_dim_set, 0, -1);
1555 c = isl_constraint_set_coefficient_si(c, isl_dim_set, 1, 2);
1556 bset = isl_basic_set_add_constraint(bset, c);
1558 c = isl_inequality_alloc(isl_local_space_copy(ls));
1559 c = isl_constraint_set_constant_si(c, -10);
1560 c = isl_constraint_set_coefficient_si(c, isl_dim_set, 0, 1);
1561 bset = isl_basic_set_add_constraint(bset, c);
1563 c = isl_inequality_alloc(ls);
1564 c = isl_constraint_set_constant_si(c, 42);
1565 c = isl_constraint_set_coefficient_si(c, isl_dim_set, 0, -1);
1566 bset = isl_basic_set_add_constraint(bset, c);
1568 bset = isl_basic_set_project_out(bset, isl_dim_set, 1, 1);
1572 isl_basic_set *bset;
1573 bset = isl_basic_set_read_from_str(ctx,
1574 "{[i] : exists (a : i = 2a and i >= 10 and i <= 42)}");
1576 A basic set or relation can also be constructed from two matrices
1577 describing the equalities and the inequalities.
1579 __isl_give isl_basic_set *isl_basic_set_from_constraint_matrices(
1580 __isl_take isl_space *space,
1581 __isl_take isl_mat *eq, __isl_take isl_mat *ineq,
1582 enum isl_dim_type c1,
1583 enum isl_dim_type c2, enum isl_dim_type c3,
1584 enum isl_dim_type c4);
1585 __isl_give isl_basic_map *isl_basic_map_from_constraint_matrices(
1586 __isl_take isl_space *space,
1587 __isl_take isl_mat *eq, __isl_take isl_mat *ineq,
1588 enum isl_dim_type c1,
1589 enum isl_dim_type c2, enum isl_dim_type c3,
1590 enum isl_dim_type c4, enum isl_dim_type c5);
1592 The C<isl_dim_type> arguments indicate the order in which
1593 different kinds of variables appear in the input matrices
1594 and should be a permutation of C<isl_dim_cst>, C<isl_dim_param>,
1595 C<isl_dim_set> and C<isl_dim_div> for sets and
1596 of C<isl_dim_cst>, C<isl_dim_param>,
1597 C<isl_dim_in>, C<isl_dim_out> and C<isl_dim_div> for relations.
1599 A (basic or union) set or relation can also be constructed from a
1600 (union) (piecewise) (multiple) affine expression
1601 or a list of affine expressions
1602 (See L<"Piecewise Quasi Affine Expressions"> and
1603 L<"Piecewise Multiple Quasi Affine Expressions">).
1605 __isl_give isl_basic_map *isl_basic_map_from_aff(
1606 __isl_take isl_aff *aff);
1607 __isl_give isl_map *isl_map_from_aff(
1608 __isl_take isl_aff *aff);
1609 __isl_give isl_set *isl_set_from_pw_aff(
1610 __isl_take isl_pw_aff *pwaff);
1611 __isl_give isl_map *isl_map_from_pw_aff(
1612 __isl_take isl_pw_aff *pwaff);
1613 __isl_give isl_basic_map *isl_basic_map_from_aff_list(
1614 __isl_take isl_space *domain_space,
1615 __isl_take isl_aff_list *list);
1616 __isl_give isl_basic_map *isl_basic_map_from_multi_aff(
1617 __isl_take isl_multi_aff *maff)
1618 __isl_give isl_map *isl_map_from_multi_aff(
1619 __isl_take isl_multi_aff *maff)
1620 __isl_give isl_set *isl_set_from_pw_multi_aff(
1621 __isl_take isl_pw_multi_aff *pma);
1622 __isl_give isl_map *isl_map_from_pw_multi_aff(
1623 __isl_take isl_pw_multi_aff *pma);
1624 __isl_give isl_union_map *
1625 isl_union_map_from_union_pw_multi_aff(
1626 __isl_take isl_union_pw_multi_aff *upma);
1628 The C<domain_dim> argument describes the domain of the resulting
1629 basic relation. It is required because the C<list> may consist
1630 of zero affine expressions.
1632 =head2 Inspecting Sets and Relations
1634 Usually, the user should not have to care about the actual constraints
1635 of the sets and maps, but should instead apply the abstract operations
1636 explained in the following sections.
1637 Occasionally, however, it may be required to inspect the individual
1638 coefficients of the constraints. This section explains how to do so.
1639 In these cases, it may also be useful to have C<isl> compute
1640 an explicit representation of the existentially quantified variables.
1642 __isl_give isl_set *isl_set_compute_divs(
1643 __isl_take isl_set *set);
1644 __isl_give isl_map *isl_map_compute_divs(
1645 __isl_take isl_map *map);
1646 __isl_give isl_union_set *isl_union_set_compute_divs(
1647 __isl_take isl_union_set *uset);
1648 __isl_give isl_union_map *isl_union_map_compute_divs(
1649 __isl_take isl_union_map *umap);
1651 This explicit representation defines the existentially quantified
1652 variables as integer divisions of the other variables, possibly
1653 including earlier existentially quantified variables.
1654 An explicitly represented existentially quantified variable therefore
1655 has a unique value when the values of the other variables are known.
1656 If, furthermore, the same existentials, i.e., existentials
1657 with the same explicit representations, should appear in the
1658 same order in each of the disjuncts of a set or map, then the user should call
1659 either of the following functions.
1661 __isl_give isl_set *isl_set_align_divs(
1662 __isl_take isl_set *set);
1663 __isl_give isl_map *isl_map_align_divs(
1664 __isl_take isl_map *map);
1666 Alternatively, the existentially quantified variables can be removed
1667 using the following functions, which compute an overapproximation.
1669 __isl_give isl_basic_set *isl_basic_set_remove_divs(
1670 __isl_take isl_basic_set *bset);
1671 __isl_give isl_basic_map *isl_basic_map_remove_divs(
1672 __isl_take isl_basic_map *bmap);
1673 __isl_give isl_set *isl_set_remove_divs(
1674 __isl_take isl_set *set);
1675 __isl_give isl_map *isl_map_remove_divs(
1676 __isl_take isl_map *map);
1678 It is also possible to only remove those divs that are defined
1679 in terms of a given range of dimensions or only those for which
1680 no explicit representation is known.
1682 __isl_give isl_basic_set *
1683 isl_basic_set_remove_divs_involving_dims(
1684 __isl_take isl_basic_set *bset,
1685 enum isl_dim_type type,
1686 unsigned first, unsigned n);
1687 __isl_give isl_basic_map *
1688 isl_basic_map_remove_divs_involving_dims(
1689 __isl_take isl_basic_map *bmap,
1690 enum isl_dim_type type,
1691 unsigned first, unsigned n);
1692 __isl_give isl_set *isl_set_remove_divs_involving_dims(
1693 __isl_take isl_set *set, enum isl_dim_type type,
1694 unsigned first, unsigned n);
1695 __isl_give isl_map *isl_map_remove_divs_involving_dims(
1696 __isl_take isl_map *map, enum isl_dim_type type,
1697 unsigned first, unsigned n);
1699 __isl_give isl_basic_set *
1700 isl_basic_set_remove_unknown_divs(
1701 __isl_take isl_basic_set *bset);
1702 __isl_give isl_set *isl_set_remove_unknown_divs(
1703 __isl_take isl_set *set);
1704 __isl_give isl_map *isl_map_remove_unknown_divs(
1705 __isl_take isl_map *map);
1707 To iterate over all the sets or maps in a union set or map, use
1709 int isl_union_set_foreach_set(__isl_keep isl_union_set *uset,
1710 int (*fn)(__isl_take isl_set *set, void *user),
1712 int isl_union_map_foreach_map(__isl_keep isl_union_map *umap,
1713 int (*fn)(__isl_take isl_map *map, void *user),
1716 The number of sets or maps in a union set or map can be obtained
1719 int isl_union_set_n_set(__isl_keep isl_union_set *uset);
1720 int isl_union_map_n_map(__isl_keep isl_union_map *umap);
1722 To extract the set or map in a given space from a union, use
1724 __isl_give isl_set *isl_union_set_extract_set(
1725 __isl_keep isl_union_set *uset,
1726 __isl_take isl_space *space);
1727 __isl_give isl_map *isl_union_map_extract_map(
1728 __isl_keep isl_union_map *umap,
1729 __isl_take isl_space *space);
1731 To iterate over all the basic sets or maps in a set or map, use
1733 int isl_set_foreach_basic_set(__isl_keep isl_set *set,
1734 int (*fn)(__isl_take isl_basic_set *bset, void *user),
1736 int isl_map_foreach_basic_map(__isl_keep isl_map *map,
1737 int (*fn)(__isl_take isl_basic_map *bmap, void *user),
1740 The callback function C<fn> should return 0 if successful and
1741 -1 if an error occurs. In the latter case, or if any other error
1742 occurs, the above functions will return -1.
1744 It should be noted that C<isl> does not guarantee that
1745 the basic sets or maps passed to C<fn> are disjoint.
1746 If this is required, then the user should call one of
1747 the following functions first.
1749 __isl_give isl_set *isl_set_make_disjoint(
1750 __isl_take isl_set *set);
1751 __isl_give isl_map *isl_map_make_disjoint(
1752 __isl_take isl_map *map);
1754 The number of basic sets in a set can be obtained
1757 int isl_set_n_basic_set(__isl_keep isl_set *set);
1759 To iterate over the constraints of a basic set or map, use
1761 #include <isl/constraint.h>
1763 int isl_basic_set_n_constraint(
1764 __isl_keep isl_basic_set *bset);
1765 int isl_basic_set_foreach_constraint(
1766 __isl_keep isl_basic_set *bset,
1767 int (*fn)(__isl_take isl_constraint *c, void *user),
1769 int isl_basic_map_foreach_constraint(
1770 __isl_keep isl_basic_map *bmap,
1771 int (*fn)(__isl_take isl_constraint *c, void *user),
1773 void *isl_constraint_free(__isl_take isl_constraint *c);
1775 Again, the callback function C<fn> should return 0 if successful and
1776 -1 if an error occurs. In the latter case, or if any other error
1777 occurs, the above functions will return -1.
1778 The constraint C<c> represents either an equality or an inequality.
1779 Use the following function to find out whether a constraint
1780 represents an equality. If not, it represents an inequality.
1782 int isl_constraint_is_equality(
1783 __isl_keep isl_constraint *constraint);
1785 The coefficients of the constraints can be inspected using
1786 the following functions.
1788 int isl_constraint_is_lower_bound(
1789 __isl_keep isl_constraint *constraint,
1790 enum isl_dim_type type, unsigned pos);
1791 int isl_constraint_is_upper_bound(
1792 __isl_keep isl_constraint *constraint,
1793 enum isl_dim_type type, unsigned pos);
1794 void isl_constraint_get_constant(
1795 __isl_keep isl_constraint *constraint, isl_int *v);
1796 __isl_give isl_val *isl_constraint_get_constant_val(
1797 __isl_keep isl_constraint *constraint);
1798 void isl_constraint_get_coefficient(
1799 __isl_keep isl_constraint *constraint,
1800 enum isl_dim_type type, int pos, isl_int *v);
1801 __isl_give isl_val *isl_constraint_get_coefficient_val(
1802 __isl_keep isl_constraint *constraint,
1803 enum isl_dim_type type, int pos);
1804 int isl_constraint_involves_dims(
1805 __isl_keep isl_constraint *constraint,
1806 enum isl_dim_type type, unsigned first, unsigned n);
1808 The explicit representations of the existentially quantified
1809 variables can be inspected using the following function.
1810 Note that the user is only allowed to use this function
1811 if the inspected set or map is the result of a call
1812 to C<isl_set_compute_divs> or C<isl_map_compute_divs>.
1813 The existentially quantified variable is equal to the floor
1814 of the returned affine expression. The affine expression
1815 itself can be inspected using the functions in
1816 L<"Piecewise Quasi Affine Expressions">.
1818 __isl_give isl_aff *isl_constraint_get_div(
1819 __isl_keep isl_constraint *constraint, int pos);
1821 To obtain the constraints of a basic set or map in matrix
1822 form, use the following functions.
1824 __isl_give isl_mat *isl_basic_set_equalities_matrix(
1825 __isl_keep isl_basic_set *bset,
1826 enum isl_dim_type c1, enum isl_dim_type c2,
1827 enum isl_dim_type c3, enum isl_dim_type c4);
1828 __isl_give isl_mat *isl_basic_set_inequalities_matrix(
1829 __isl_keep isl_basic_set *bset,
1830 enum isl_dim_type c1, enum isl_dim_type c2,
1831 enum isl_dim_type c3, enum isl_dim_type c4);
1832 __isl_give isl_mat *isl_basic_map_equalities_matrix(
1833 __isl_keep isl_basic_map *bmap,
1834 enum isl_dim_type c1,
1835 enum isl_dim_type c2, enum isl_dim_type c3,
1836 enum isl_dim_type c4, enum isl_dim_type c5);
1837 __isl_give isl_mat *isl_basic_map_inequalities_matrix(
1838 __isl_keep isl_basic_map *bmap,
1839 enum isl_dim_type c1,
1840 enum isl_dim_type c2, enum isl_dim_type c3,
1841 enum isl_dim_type c4, enum isl_dim_type c5);
1843 The C<isl_dim_type> arguments dictate the order in which
1844 different kinds of variables appear in the resulting matrix
1845 and should be a permutation of C<isl_dim_cst>, C<isl_dim_param>,
1846 C<isl_dim_in>, C<isl_dim_out> and C<isl_dim_div>.
1848 The number of parameters, input, output or set dimensions can
1849 be obtained using the following functions.
1851 unsigned isl_basic_set_dim(__isl_keep isl_basic_set *bset,
1852 enum isl_dim_type type);
1853 unsigned isl_basic_map_dim(__isl_keep isl_basic_map *bmap,
1854 enum isl_dim_type type);
1855 unsigned isl_set_dim(__isl_keep isl_set *set,
1856 enum isl_dim_type type);
1857 unsigned isl_map_dim(__isl_keep isl_map *map,
1858 enum isl_dim_type type);
1860 To check whether the description of a set or relation depends
1861 on one or more given dimensions, it is not necessary to iterate over all
1862 constraints. Instead the following functions can be used.
1864 int isl_basic_set_involves_dims(
1865 __isl_keep isl_basic_set *bset,
1866 enum isl_dim_type type, unsigned first, unsigned n);
1867 int isl_set_involves_dims(__isl_keep isl_set *set,
1868 enum isl_dim_type type, unsigned first, unsigned n);
1869 int isl_basic_map_involves_dims(
1870 __isl_keep isl_basic_map *bmap,
1871 enum isl_dim_type type, unsigned first, unsigned n);
1872 int isl_map_involves_dims(__isl_keep isl_map *map,
1873 enum isl_dim_type type, unsigned first, unsigned n);
1875 Similarly, the following functions can be used to check whether
1876 a given dimension is involved in any lower or upper bound.
1878 int isl_set_dim_has_any_lower_bound(__isl_keep isl_set *set,
1879 enum isl_dim_type type, unsigned pos);
1880 int isl_set_dim_has_any_upper_bound(__isl_keep isl_set *set,
1881 enum isl_dim_type type, unsigned pos);
1883 Note that these functions return true even if there is a bound on
1884 the dimension on only some of the basic sets of C<set>.
1885 To check if they have a bound for all of the basic sets in C<set>,
1886 use the following functions instead.
1888 int isl_set_dim_has_lower_bound(__isl_keep isl_set *set,
1889 enum isl_dim_type type, unsigned pos);
1890 int isl_set_dim_has_upper_bound(__isl_keep isl_set *set,
1891 enum isl_dim_type type, unsigned pos);
1893 The identifiers or names of the domain and range spaces of a set
1894 or relation can be read off or set using the following functions.
1896 __isl_give isl_set *isl_set_set_tuple_id(
1897 __isl_take isl_set *set, __isl_take isl_id *id);
1898 __isl_give isl_set *isl_set_reset_tuple_id(
1899 __isl_take isl_set *set);
1900 int isl_set_has_tuple_id(__isl_keep isl_set *set);
1901 __isl_give isl_id *isl_set_get_tuple_id(
1902 __isl_keep isl_set *set);
1903 __isl_give isl_map *isl_map_set_tuple_id(
1904 __isl_take isl_map *map, enum isl_dim_type type,
1905 __isl_take isl_id *id);
1906 __isl_give isl_map *isl_map_reset_tuple_id(
1907 __isl_take isl_map *map, enum isl_dim_type type);
1908 int isl_map_has_tuple_id(__isl_keep isl_map *map,
1909 enum isl_dim_type type);
1910 __isl_give isl_id *isl_map_get_tuple_id(
1911 __isl_keep isl_map *map, enum isl_dim_type type);
1913 const char *isl_basic_set_get_tuple_name(
1914 __isl_keep isl_basic_set *bset);
1915 __isl_give isl_basic_set *isl_basic_set_set_tuple_name(
1916 __isl_take isl_basic_set *set, const char *s);
1917 int isl_set_has_tuple_name(__isl_keep isl_set *set);
1918 const char *isl_set_get_tuple_name(
1919 __isl_keep isl_set *set);
1920 const char *isl_basic_map_get_tuple_name(
1921 __isl_keep isl_basic_map *bmap,
1922 enum isl_dim_type type);
1923 __isl_give isl_basic_map *isl_basic_map_set_tuple_name(
1924 __isl_take isl_basic_map *bmap,
1925 enum isl_dim_type type, const char *s);
1926 int isl_map_has_tuple_name(__isl_keep isl_map *map,
1927 enum isl_dim_type type);
1928 const char *isl_map_get_tuple_name(
1929 __isl_keep isl_map *map,
1930 enum isl_dim_type type);
1932 As with C<isl_space_get_tuple_name>, the value returned points to
1933 an internal data structure.
1934 The identifiers, positions or names of individual dimensions can be
1935 read off using the following functions.
1937 __isl_give isl_id *isl_basic_set_get_dim_id(
1938 __isl_keep isl_basic_set *bset,
1939 enum isl_dim_type type, unsigned pos);
1940 __isl_give isl_set *isl_set_set_dim_id(
1941 __isl_take isl_set *set, enum isl_dim_type type,
1942 unsigned pos, __isl_take isl_id *id);
1943 int isl_set_has_dim_id(__isl_keep isl_set *set,
1944 enum isl_dim_type type, unsigned pos);
1945 __isl_give isl_id *isl_set_get_dim_id(
1946 __isl_keep isl_set *set, enum isl_dim_type type,
1948 int isl_basic_map_has_dim_id(
1949 __isl_keep isl_basic_map *bmap,
1950 enum isl_dim_type type, unsigned pos);
1951 __isl_give isl_map *isl_map_set_dim_id(
1952 __isl_take isl_map *map, enum isl_dim_type type,
1953 unsigned pos, __isl_take isl_id *id);
1954 int isl_map_has_dim_id(__isl_keep isl_map *map,
1955 enum isl_dim_type type, unsigned pos);
1956 __isl_give isl_id *isl_map_get_dim_id(
1957 __isl_keep isl_map *map, enum isl_dim_type type,
1960 int isl_set_find_dim_by_id(__isl_keep isl_set *set,
1961 enum isl_dim_type type, __isl_keep isl_id *id);
1962 int isl_map_find_dim_by_id(__isl_keep isl_map *map,
1963 enum isl_dim_type type, __isl_keep isl_id *id);
1964 int isl_set_find_dim_by_name(__isl_keep isl_set *set,
1965 enum isl_dim_type type, const char *name);
1966 int isl_map_find_dim_by_name(__isl_keep isl_map *map,
1967 enum isl_dim_type type, const char *name);
1969 const char *isl_constraint_get_dim_name(
1970 __isl_keep isl_constraint *constraint,
1971 enum isl_dim_type type, unsigned pos);
1972 const char *isl_basic_set_get_dim_name(
1973 __isl_keep isl_basic_set *bset,
1974 enum isl_dim_type type, unsigned pos);
1975 int isl_set_has_dim_name(__isl_keep isl_set *set,
1976 enum isl_dim_type type, unsigned pos);
1977 const char *isl_set_get_dim_name(
1978 __isl_keep isl_set *set,
1979 enum isl_dim_type type, unsigned pos);
1980 const char *isl_basic_map_get_dim_name(
1981 __isl_keep isl_basic_map *bmap,
1982 enum isl_dim_type type, unsigned pos);
1983 int isl_map_has_dim_name(__isl_keep isl_map *map,
1984 enum isl_dim_type type, unsigned pos);
1985 const char *isl_map_get_dim_name(
1986 __isl_keep isl_map *map,
1987 enum isl_dim_type type, unsigned pos);
1989 These functions are mostly useful to obtain the identifiers, positions
1990 or names of the parameters. Identifiers of individual dimensions are
1991 essentially only useful for printing. They are ignored by all other
1992 operations and may not be preserved across those operations.
1996 =head3 Unary Properties
2002 The following functions test whether the given set or relation
2003 contains any integer points. The ``plain'' variants do not perform
2004 any computations, but simply check if the given set or relation
2005 is already known to be empty.
2007 int isl_basic_set_plain_is_empty(__isl_keep isl_basic_set *bset);
2008 int isl_basic_set_is_empty(__isl_keep isl_basic_set *bset);
2009 int isl_set_plain_is_empty(__isl_keep isl_set *set);
2010 int isl_set_is_empty(__isl_keep isl_set *set);
2011 int isl_union_set_is_empty(__isl_keep isl_union_set *uset);
2012 int isl_basic_map_plain_is_empty(__isl_keep isl_basic_map *bmap);
2013 int isl_basic_map_is_empty(__isl_keep isl_basic_map *bmap);
2014 int isl_map_plain_is_empty(__isl_keep isl_map *map);
2015 int isl_map_is_empty(__isl_keep isl_map *map);
2016 int isl_union_map_is_empty(__isl_keep isl_union_map *umap);
2018 =item * Universality
2020 int isl_basic_set_is_universe(__isl_keep isl_basic_set *bset);
2021 int isl_basic_map_is_universe(__isl_keep isl_basic_map *bmap);
2022 int isl_set_plain_is_universe(__isl_keep isl_set *set);
2024 =item * Single-valuedness
2026 int isl_basic_map_is_single_valued(
2027 __isl_keep isl_basic_map *bmap);
2028 int isl_map_plain_is_single_valued(
2029 __isl_keep isl_map *map);
2030 int isl_map_is_single_valued(__isl_keep isl_map *map);
2031 int isl_union_map_is_single_valued(__isl_keep isl_union_map *umap);
2035 int isl_map_plain_is_injective(__isl_keep isl_map *map);
2036 int isl_map_is_injective(__isl_keep isl_map *map);
2037 int isl_union_map_plain_is_injective(
2038 __isl_keep isl_union_map *umap);
2039 int isl_union_map_is_injective(
2040 __isl_keep isl_union_map *umap);
2044 int isl_map_is_bijective(__isl_keep isl_map *map);
2045 int isl_union_map_is_bijective(__isl_keep isl_union_map *umap);
2049 int isl_basic_map_plain_is_fixed(
2050 __isl_keep isl_basic_map *bmap,
2051 enum isl_dim_type type, unsigned pos,
2053 int isl_set_plain_is_fixed(__isl_keep isl_set *set,
2054 enum isl_dim_type type, unsigned pos,
2056 int isl_map_plain_is_fixed(__isl_keep isl_map *map,
2057 enum isl_dim_type type, unsigned pos,
2060 Check if the relation obviously lies on a hyperplane where the given dimension
2061 has a fixed value and if so, return that value in C<*val>.
2065 To check whether a set is a parameter domain, use this function:
2067 int isl_set_is_params(__isl_keep isl_set *set);
2068 int isl_union_set_is_params(
2069 __isl_keep isl_union_set *uset);
2073 The following functions check whether the domain of the given
2074 (basic) set is a wrapped relation.
2076 int isl_basic_set_is_wrapping(
2077 __isl_keep isl_basic_set *bset);
2078 int isl_set_is_wrapping(__isl_keep isl_set *set);
2080 =item * Internal Product
2082 int isl_basic_map_can_zip(
2083 __isl_keep isl_basic_map *bmap);
2084 int isl_map_can_zip(__isl_keep isl_map *map);
2086 Check whether the product of domain and range of the given relation
2088 i.e., whether both domain and range are nested relations.
2092 int isl_basic_map_can_curry(
2093 __isl_keep isl_basic_map *bmap);
2094 int isl_map_can_curry(__isl_keep isl_map *map);
2096 Check whether the domain of the (basic) relation is a wrapped relation.
2098 int isl_basic_map_can_uncurry(
2099 __isl_keep isl_basic_map *bmap);
2100 int isl_map_can_uncurry(__isl_keep isl_map *map);
2102 Check whether the range of the (basic) relation is a wrapped relation.
2106 =head3 Binary Properties
2112 int isl_set_plain_is_equal(__isl_keep isl_set *set1,
2113 __isl_keep isl_set *set2);
2114 int isl_set_is_equal(__isl_keep isl_set *set1,
2115 __isl_keep isl_set *set2);
2116 int isl_union_set_is_equal(
2117 __isl_keep isl_union_set *uset1,
2118 __isl_keep isl_union_set *uset2);
2119 int isl_basic_map_is_equal(
2120 __isl_keep isl_basic_map *bmap1,
2121 __isl_keep isl_basic_map *bmap2);
2122 int isl_map_is_equal(__isl_keep isl_map *map1,
2123 __isl_keep isl_map *map2);
2124 int isl_map_plain_is_equal(__isl_keep isl_map *map1,
2125 __isl_keep isl_map *map2);
2126 int isl_union_map_is_equal(
2127 __isl_keep isl_union_map *umap1,
2128 __isl_keep isl_union_map *umap2);
2130 =item * Disjointness
2132 int isl_set_plain_is_disjoint(__isl_keep isl_set *set1,
2133 __isl_keep isl_set *set2);
2134 int isl_set_is_disjoint(__isl_keep isl_set *set1,
2135 __isl_keep isl_set *set2);
2136 int isl_map_is_disjoint(__isl_keep isl_map *map1,
2137 __isl_keep isl_map *map2);
2141 int isl_basic_set_is_subset(
2142 __isl_keep isl_basic_set *bset1,
2143 __isl_keep isl_basic_set *bset2);
2144 int isl_set_is_subset(__isl_keep isl_set *set1,
2145 __isl_keep isl_set *set2);
2146 int isl_set_is_strict_subset(
2147 __isl_keep isl_set *set1,
2148 __isl_keep isl_set *set2);
2149 int isl_union_set_is_subset(
2150 __isl_keep isl_union_set *uset1,
2151 __isl_keep isl_union_set *uset2);
2152 int isl_union_set_is_strict_subset(
2153 __isl_keep isl_union_set *uset1,
2154 __isl_keep isl_union_set *uset2);
2155 int isl_basic_map_is_subset(
2156 __isl_keep isl_basic_map *bmap1,
2157 __isl_keep isl_basic_map *bmap2);
2158 int isl_basic_map_is_strict_subset(
2159 __isl_keep isl_basic_map *bmap1,
2160 __isl_keep isl_basic_map *bmap2);
2161 int isl_map_is_subset(
2162 __isl_keep isl_map *map1,
2163 __isl_keep isl_map *map2);
2164 int isl_map_is_strict_subset(
2165 __isl_keep isl_map *map1,
2166 __isl_keep isl_map *map2);
2167 int isl_union_map_is_subset(
2168 __isl_keep isl_union_map *umap1,
2169 __isl_keep isl_union_map *umap2);
2170 int isl_union_map_is_strict_subset(
2171 __isl_keep isl_union_map *umap1,
2172 __isl_keep isl_union_map *umap2);
2174 Check whether the first argument is a (strict) subset of the
2179 int isl_set_plain_cmp(__isl_keep isl_set *set1,
2180 __isl_keep isl_set *set2);
2182 This function is useful for sorting C<isl_set>s.
2183 The order depends on the internal representation of the inputs.
2184 The order is fixed over different calls to the function (assuming
2185 the internal representation of the inputs has not changed), but may
2186 change over different versions of C<isl>.
2190 =head2 Unary Operations
2196 __isl_give isl_set *isl_set_complement(
2197 __isl_take isl_set *set);
2198 __isl_give isl_map *isl_map_complement(
2199 __isl_take isl_map *map);
2203 __isl_give isl_basic_map *isl_basic_map_reverse(
2204 __isl_take isl_basic_map *bmap);
2205 __isl_give isl_map *isl_map_reverse(
2206 __isl_take isl_map *map);
2207 __isl_give isl_union_map *isl_union_map_reverse(
2208 __isl_take isl_union_map *umap);
2212 __isl_give isl_basic_set *isl_basic_set_project_out(
2213 __isl_take isl_basic_set *bset,
2214 enum isl_dim_type type, unsigned first, unsigned n);
2215 __isl_give isl_basic_map *isl_basic_map_project_out(
2216 __isl_take isl_basic_map *bmap,
2217 enum isl_dim_type type, unsigned first, unsigned n);
2218 __isl_give isl_set *isl_set_project_out(__isl_take isl_set *set,
2219 enum isl_dim_type type, unsigned first, unsigned n);
2220 __isl_give isl_map *isl_map_project_out(__isl_take isl_map *map,
2221 enum isl_dim_type type, unsigned first, unsigned n);
2222 __isl_give isl_basic_set *isl_basic_set_params(
2223 __isl_take isl_basic_set *bset);
2224 __isl_give isl_basic_set *isl_basic_map_domain(
2225 __isl_take isl_basic_map *bmap);
2226 __isl_give isl_basic_set *isl_basic_map_range(
2227 __isl_take isl_basic_map *bmap);
2228 __isl_give isl_set *isl_set_params(__isl_take isl_set *set);
2229 __isl_give isl_set *isl_map_params(__isl_take isl_map *map);
2230 __isl_give isl_set *isl_map_domain(
2231 __isl_take isl_map *bmap);
2232 __isl_give isl_set *isl_map_range(
2233 __isl_take isl_map *map);
2234 __isl_give isl_set *isl_union_set_params(
2235 __isl_take isl_union_set *uset);
2236 __isl_give isl_set *isl_union_map_params(
2237 __isl_take isl_union_map *umap);
2238 __isl_give isl_union_set *isl_union_map_domain(
2239 __isl_take isl_union_map *umap);
2240 __isl_give isl_union_set *isl_union_map_range(
2241 __isl_take isl_union_map *umap);
2243 __isl_give isl_basic_map *isl_basic_map_domain_map(
2244 __isl_take isl_basic_map *bmap);
2245 __isl_give isl_basic_map *isl_basic_map_range_map(
2246 __isl_take isl_basic_map *bmap);
2247 __isl_give isl_map *isl_map_domain_map(__isl_take isl_map *map);
2248 __isl_give isl_map *isl_map_range_map(__isl_take isl_map *map);
2249 __isl_give isl_union_map *isl_union_map_domain_map(
2250 __isl_take isl_union_map *umap);
2251 __isl_give isl_union_map *isl_union_map_range_map(
2252 __isl_take isl_union_map *umap);
2254 The functions above construct a (basic, regular or union) relation
2255 that maps (a wrapped version of) the input relation to its domain or range.
2259 __isl_give isl_basic_set *isl_basic_set_eliminate(
2260 __isl_take isl_basic_set *bset,
2261 enum isl_dim_type type,
2262 unsigned first, unsigned n);
2263 __isl_give isl_set *isl_set_eliminate(
2264 __isl_take isl_set *set, enum isl_dim_type type,
2265 unsigned first, unsigned n);
2266 __isl_give isl_basic_map *isl_basic_map_eliminate(
2267 __isl_take isl_basic_map *bmap,
2268 enum isl_dim_type type,
2269 unsigned first, unsigned n);
2270 __isl_give isl_map *isl_map_eliminate(
2271 __isl_take isl_map *map, enum isl_dim_type type,
2272 unsigned first, unsigned n);
2274 Eliminate the coefficients for the given dimensions from the constraints,
2275 without removing the dimensions.
2279 __isl_give isl_basic_set *isl_basic_set_fix(
2280 __isl_take isl_basic_set *bset,
2281 enum isl_dim_type type, unsigned pos,
2283 __isl_give isl_basic_set *isl_basic_set_fix_si(
2284 __isl_take isl_basic_set *bset,
2285 enum isl_dim_type type, unsigned pos, int value);
2286 __isl_give isl_set *isl_set_fix(__isl_take isl_set *set,
2287 enum isl_dim_type type, unsigned pos,
2289 __isl_give isl_set *isl_set_fix_si(__isl_take isl_set *set,
2290 enum isl_dim_type type, unsigned pos, int value);
2291 __isl_give isl_basic_map *isl_basic_map_fix_si(
2292 __isl_take isl_basic_map *bmap,
2293 enum isl_dim_type type, unsigned pos, int value);
2294 __isl_give isl_map *isl_map_fix(__isl_take isl_map *map,
2295 enum isl_dim_type type, unsigned pos,
2297 __isl_give isl_map *isl_map_fix_si(__isl_take isl_map *map,
2298 enum isl_dim_type type, unsigned pos, int value);
2300 Intersect the set or relation with the hyperplane where the given
2301 dimension has the fixed given value.
2303 __isl_give isl_basic_map *isl_basic_map_lower_bound_si(
2304 __isl_take isl_basic_map *bmap,
2305 enum isl_dim_type type, unsigned pos, int value);
2306 __isl_give isl_basic_map *isl_basic_map_upper_bound_si(
2307 __isl_take isl_basic_map *bmap,
2308 enum isl_dim_type type, unsigned pos, int value);
2309 __isl_give isl_set *isl_set_lower_bound(
2310 __isl_take isl_set *set,
2311 enum isl_dim_type type, unsigned pos,
2313 __isl_give isl_set *isl_set_lower_bound_si(
2314 __isl_take isl_set *set,
2315 enum isl_dim_type type, unsigned pos, int value);
2316 __isl_give isl_map *isl_map_lower_bound_si(
2317 __isl_take isl_map *map,
2318 enum isl_dim_type type, unsigned pos, int value);
2319 __isl_give isl_set *isl_set_upper_bound(
2320 __isl_take isl_set *set,
2321 enum isl_dim_type type, unsigned pos,
2323 __isl_give isl_set *isl_set_upper_bound_si(
2324 __isl_take isl_set *set,
2325 enum isl_dim_type type, unsigned pos, int value);
2326 __isl_give isl_map *isl_map_upper_bound_si(
2327 __isl_take isl_map *map,
2328 enum isl_dim_type type, unsigned pos, int value);
2330 Intersect the set or relation with the half-space where the given
2331 dimension has a value bounded by the fixed given value.
2333 __isl_give isl_set *isl_set_equate(__isl_take isl_set *set,
2334 enum isl_dim_type type1, int pos1,
2335 enum isl_dim_type type2, int pos2);
2336 __isl_give isl_basic_map *isl_basic_map_equate(
2337 __isl_take isl_basic_map *bmap,
2338 enum isl_dim_type type1, int pos1,
2339 enum isl_dim_type type2, int pos2);
2340 __isl_give isl_map *isl_map_equate(__isl_take isl_map *map,
2341 enum isl_dim_type type1, int pos1,
2342 enum isl_dim_type type2, int pos2);
2344 Intersect the set or relation with the hyperplane where the given
2345 dimensions are equal to each other.
2347 __isl_give isl_map *isl_map_oppose(__isl_take isl_map *map,
2348 enum isl_dim_type type1, int pos1,
2349 enum isl_dim_type type2, int pos2);
2351 Intersect the relation with the hyperplane where the given
2352 dimensions have opposite values.
2354 __isl_give isl_basic_map *isl_basic_map_order_ge(
2355 __isl_take isl_basic_map *bmap,
2356 enum isl_dim_type type1, int pos1,
2357 enum isl_dim_type type2, int pos2);
2358 __isl_give isl_map *isl_map_order_lt(__isl_take isl_map *map,
2359 enum isl_dim_type type1, int pos1,
2360 enum isl_dim_type type2, int pos2);
2361 __isl_give isl_basic_map *isl_basic_map_order_gt(
2362 __isl_take isl_basic_map *bmap,
2363 enum isl_dim_type type1, int pos1,
2364 enum isl_dim_type type2, int pos2);
2365 __isl_give isl_map *isl_map_order_gt(__isl_take isl_map *map,
2366 enum isl_dim_type type1, int pos1,
2367 enum isl_dim_type type2, int pos2);
2369 Intersect the relation with the half-space where the given
2370 dimensions satisfy the given ordering.
2374 __isl_give isl_map *isl_set_identity(
2375 __isl_take isl_set *set);
2376 __isl_give isl_union_map *isl_union_set_identity(
2377 __isl_take isl_union_set *uset);
2379 Construct an identity relation on the given (union) set.
2383 __isl_give isl_basic_set *isl_basic_map_deltas(
2384 __isl_take isl_basic_map *bmap);
2385 __isl_give isl_set *isl_map_deltas(__isl_take isl_map *map);
2386 __isl_give isl_union_set *isl_union_map_deltas(
2387 __isl_take isl_union_map *umap);
2389 These functions return a (basic) set containing the differences
2390 between image elements and corresponding domain elements in the input.
2392 __isl_give isl_basic_map *isl_basic_map_deltas_map(
2393 __isl_take isl_basic_map *bmap);
2394 __isl_give isl_map *isl_map_deltas_map(
2395 __isl_take isl_map *map);
2396 __isl_give isl_union_map *isl_union_map_deltas_map(
2397 __isl_take isl_union_map *umap);
2399 The functions above construct a (basic, regular or union) relation
2400 that maps (a wrapped version of) the input relation to its delta set.
2404 Simplify the representation of a set or relation by trying
2405 to combine pairs of basic sets or relations into a single
2406 basic set or relation.
2408 __isl_give isl_set *isl_set_coalesce(__isl_take isl_set *set);
2409 __isl_give isl_map *isl_map_coalesce(__isl_take isl_map *map);
2410 __isl_give isl_union_set *isl_union_set_coalesce(
2411 __isl_take isl_union_set *uset);
2412 __isl_give isl_union_map *isl_union_map_coalesce(
2413 __isl_take isl_union_map *umap);
2415 One of the methods for combining pairs of basic sets or relations
2416 can result in coefficients that are much larger than those that appear
2417 in the constraints of the input. By default, the coefficients are
2418 not allowed to grow larger, but this can be changed by unsetting
2419 the following option.
2421 int isl_options_set_coalesce_bounded_wrapping(
2422 isl_ctx *ctx, int val);
2423 int isl_options_get_coalesce_bounded_wrapping(
2426 =item * Detecting equalities
2428 __isl_give isl_basic_set *isl_basic_set_detect_equalities(
2429 __isl_take isl_basic_set *bset);
2430 __isl_give isl_basic_map *isl_basic_map_detect_equalities(
2431 __isl_take isl_basic_map *bmap);
2432 __isl_give isl_set *isl_set_detect_equalities(
2433 __isl_take isl_set *set);
2434 __isl_give isl_map *isl_map_detect_equalities(
2435 __isl_take isl_map *map);
2436 __isl_give isl_union_set *isl_union_set_detect_equalities(
2437 __isl_take isl_union_set *uset);
2438 __isl_give isl_union_map *isl_union_map_detect_equalities(
2439 __isl_take isl_union_map *umap);
2441 Simplify the representation of a set or relation by detecting implicit
2444 =item * Removing redundant constraints
2446 __isl_give isl_basic_set *isl_basic_set_remove_redundancies(
2447 __isl_take isl_basic_set *bset);
2448 __isl_give isl_set *isl_set_remove_redundancies(
2449 __isl_take isl_set *set);
2450 __isl_give isl_basic_map *isl_basic_map_remove_redundancies(
2451 __isl_take isl_basic_map *bmap);
2452 __isl_give isl_map *isl_map_remove_redundancies(
2453 __isl_take isl_map *map);
2457 __isl_give isl_basic_set *isl_set_convex_hull(
2458 __isl_take isl_set *set);
2459 __isl_give isl_basic_map *isl_map_convex_hull(
2460 __isl_take isl_map *map);
2462 If the input set or relation has any existentially quantified
2463 variables, then the result of these operations is currently undefined.
2467 __isl_give isl_basic_set *
2468 isl_set_unshifted_simple_hull(
2469 __isl_take isl_set *set);
2470 __isl_give isl_basic_map *
2471 isl_map_unshifted_simple_hull(
2472 __isl_take isl_map *map);
2473 __isl_give isl_basic_set *isl_set_simple_hull(
2474 __isl_take isl_set *set);
2475 __isl_give isl_basic_map *isl_map_simple_hull(
2476 __isl_take isl_map *map);
2477 __isl_give isl_union_map *isl_union_map_simple_hull(
2478 __isl_take isl_union_map *umap);
2480 These functions compute a single basic set or relation
2481 that contains the whole input set or relation.
2482 In particular, the output is described by translates
2483 of the constraints describing the basic sets or relations in the input.
2484 In case of C<isl_set_unshifted_simple_hull>, only the original
2485 constraints are used, without any translation.
2489 (See \autoref{s:simple hull}.)
2495 __isl_give isl_basic_set *isl_basic_set_affine_hull(
2496 __isl_take isl_basic_set *bset);
2497 __isl_give isl_basic_set *isl_set_affine_hull(
2498 __isl_take isl_set *set);
2499 __isl_give isl_union_set *isl_union_set_affine_hull(
2500 __isl_take isl_union_set *uset);
2501 __isl_give isl_basic_map *isl_basic_map_affine_hull(
2502 __isl_take isl_basic_map *bmap);
2503 __isl_give isl_basic_map *isl_map_affine_hull(
2504 __isl_take isl_map *map);
2505 __isl_give isl_union_map *isl_union_map_affine_hull(
2506 __isl_take isl_union_map *umap);
2508 In case of union sets and relations, the affine hull is computed
2511 =item * Polyhedral hull
2513 __isl_give isl_basic_set *isl_set_polyhedral_hull(
2514 __isl_take isl_set *set);
2515 __isl_give isl_basic_map *isl_map_polyhedral_hull(
2516 __isl_take isl_map *map);
2517 __isl_give isl_union_set *isl_union_set_polyhedral_hull(
2518 __isl_take isl_union_set *uset);
2519 __isl_give isl_union_map *isl_union_map_polyhedral_hull(
2520 __isl_take isl_union_map *umap);
2522 These functions compute a single basic set or relation
2523 not involving any existentially quantified variables
2524 that contains the whole input set or relation.
2525 In case of union sets and relations, the polyhedral hull is computed
2528 =item * Other approximations
2530 __isl_give isl_basic_set *
2531 isl_basic_set_drop_constraints_involving_dims(
2532 __isl_take isl_basic_set *bset,
2533 enum isl_dim_type type,
2534 unsigned first, unsigned n);
2535 __isl_give isl_basic_map *
2536 isl_basic_map_drop_constraints_involving_dims(
2537 __isl_take isl_basic_map *bmap,
2538 enum isl_dim_type type,
2539 unsigned first, unsigned n);
2540 __isl_give isl_basic_set *
2541 isl_basic_set_drop_constraints_not_involving_dims(
2542 __isl_take isl_basic_set *bset,
2543 enum isl_dim_type type,
2544 unsigned first, unsigned n);
2545 __isl_give isl_set *
2546 isl_set_drop_constraints_involving_dims(
2547 __isl_take isl_set *set,
2548 enum isl_dim_type type,
2549 unsigned first, unsigned n);
2550 __isl_give isl_map *
2551 isl_map_drop_constraints_involving_dims(
2552 __isl_take isl_map *map,
2553 enum isl_dim_type type,
2554 unsigned first, unsigned n);
2556 These functions drop any constraints (not) involving the specified dimensions.
2557 Note that the result depends on the representation of the input.
2561 __isl_give isl_basic_set *isl_basic_set_sample(
2562 __isl_take isl_basic_set *bset);
2563 __isl_give isl_basic_set *isl_set_sample(
2564 __isl_take isl_set *set);
2565 __isl_give isl_basic_map *isl_basic_map_sample(
2566 __isl_take isl_basic_map *bmap);
2567 __isl_give isl_basic_map *isl_map_sample(
2568 __isl_take isl_map *map);
2570 If the input (basic) set or relation is non-empty, then return
2571 a singleton subset of the input. Otherwise, return an empty set.
2573 =item * Optimization
2575 #include <isl/ilp.h>
2576 enum isl_lp_result isl_basic_set_max(
2577 __isl_keep isl_basic_set *bset,
2578 __isl_keep isl_aff *obj, isl_int *opt)
2579 enum isl_lp_result isl_set_min(__isl_keep isl_set *set,
2580 __isl_keep isl_aff *obj, isl_int *opt);
2581 enum isl_lp_result isl_set_max(__isl_keep isl_set *set,
2582 __isl_keep isl_aff *obj, isl_int *opt);
2584 Compute the minimum or maximum of the integer affine expression C<obj>
2585 over the points in C<set>, returning the result in C<opt>.
2586 The return value may be one of C<isl_lp_error>,
2587 C<isl_lp_ok>, C<isl_lp_unbounded> or C<isl_lp_empty>.
2589 =item * Parametric optimization
2591 __isl_give isl_pw_aff *isl_set_dim_min(
2592 __isl_take isl_set *set, int pos);
2593 __isl_give isl_pw_aff *isl_set_dim_max(
2594 __isl_take isl_set *set, int pos);
2595 __isl_give isl_pw_aff *isl_map_dim_max(
2596 __isl_take isl_map *map, int pos);
2598 Compute the minimum or maximum of the given set or output dimension
2599 as a function of the parameters (and input dimensions), but independently
2600 of the other set or output dimensions.
2601 For lexicographic optimization, see L<"Lexicographic Optimization">.
2605 The following functions compute either the set of (rational) coefficient
2606 values of valid constraints for the given set or the set of (rational)
2607 values satisfying the constraints with coefficients from the given set.
2608 Internally, these two sets of functions perform essentially the
2609 same operations, except that the set of coefficients is assumed to
2610 be a cone, while the set of values may be any polyhedron.
2611 The current implementation is based on the Farkas lemma and
2612 Fourier-Motzkin elimination, but this may change or be made optional
2613 in future. In particular, future implementations may use different
2614 dualization algorithms or skip the elimination step.
2616 __isl_give isl_basic_set *isl_basic_set_coefficients(
2617 __isl_take isl_basic_set *bset);
2618 __isl_give isl_basic_set *isl_set_coefficients(
2619 __isl_take isl_set *set);
2620 __isl_give isl_union_set *isl_union_set_coefficients(
2621 __isl_take isl_union_set *bset);
2622 __isl_give isl_basic_set *isl_basic_set_solutions(
2623 __isl_take isl_basic_set *bset);
2624 __isl_give isl_basic_set *isl_set_solutions(
2625 __isl_take isl_set *set);
2626 __isl_give isl_union_set *isl_union_set_solutions(
2627 __isl_take isl_union_set *bset);
2631 __isl_give isl_map *isl_map_fixed_power(
2632 __isl_take isl_map *map, isl_int exp);
2633 __isl_give isl_union_map *isl_union_map_fixed_power(
2634 __isl_take isl_union_map *umap, isl_int exp);
2636 Compute the given power of C<map>, where C<exp> is assumed to be non-zero.
2637 If the exponent C<exp> is negative, then the -C<exp> th power of the inverse
2638 of C<map> is computed.
2640 __isl_give isl_map *isl_map_power(__isl_take isl_map *map,
2642 __isl_give isl_union_map *isl_union_map_power(
2643 __isl_take isl_union_map *umap, int *exact);
2645 Compute a parametric representation for all positive powers I<k> of C<map>.
2646 The result maps I<k> to a nested relation corresponding to the
2647 I<k>th power of C<map>.
2648 The result may be an overapproximation. If the result is known to be exact,
2649 then C<*exact> is set to C<1>.
2651 =item * Transitive closure
2653 __isl_give isl_map *isl_map_transitive_closure(
2654 __isl_take isl_map *map, int *exact);
2655 __isl_give isl_union_map *isl_union_map_transitive_closure(
2656 __isl_take isl_union_map *umap, int *exact);
2658 Compute the transitive closure of C<map>.
2659 The result may be an overapproximation. If the result is known to be exact,
2660 then C<*exact> is set to C<1>.
2662 =item * Reaching path lengths
2664 __isl_give isl_map *isl_map_reaching_path_lengths(
2665 __isl_take isl_map *map, int *exact);
2667 Compute a relation that maps each element in the range of C<map>
2668 to the lengths of all paths composed of edges in C<map> that
2669 end up in the given element.
2670 The result may be an overapproximation. If the result is known to be exact,
2671 then C<*exact> is set to C<1>.
2672 To compute the I<maximal> path length, the resulting relation
2673 should be postprocessed by C<isl_map_lexmax>.
2674 In particular, if the input relation is a dependence relation
2675 (mapping sources to sinks), then the maximal path length corresponds
2676 to the free schedule.
2677 Note, however, that C<isl_map_lexmax> expects the maximum to be
2678 finite, so if the path lengths are unbounded (possibly due to
2679 the overapproximation), then you will get an error message.
2683 __isl_give isl_basic_set *isl_basic_map_wrap(
2684 __isl_take isl_basic_map *bmap);
2685 __isl_give isl_set *isl_map_wrap(
2686 __isl_take isl_map *map);
2687 __isl_give isl_union_set *isl_union_map_wrap(
2688 __isl_take isl_union_map *umap);
2689 __isl_give isl_basic_map *isl_basic_set_unwrap(
2690 __isl_take isl_basic_set *bset);
2691 __isl_give isl_map *isl_set_unwrap(
2692 __isl_take isl_set *set);
2693 __isl_give isl_union_map *isl_union_set_unwrap(
2694 __isl_take isl_union_set *uset);
2698 Remove any internal structure of domain (and range) of the given
2699 set or relation. If there is any such internal structure in the input,
2700 then the name of the space is also removed.
2702 __isl_give isl_basic_set *isl_basic_set_flatten(
2703 __isl_take isl_basic_set *bset);
2704 __isl_give isl_set *isl_set_flatten(
2705 __isl_take isl_set *set);
2706 __isl_give isl_basic_map *isl_basic_map_flatten_domain(
2707 __isl_take isl_basic_map *bmap);
2708 __isl_give isl_basic_map *isl_basic_map_flatten_range(
2709 __isl_take isl_basic_map *bmap);
2710 __isl_give isl_map *isl_map_flatten_range(
2711 __isl_take isl_map *map);
2712 __isl_give isl_map *isl_map_flatten_domain(
2713 __isl_take isl_map *map);
2714 __isl_give isl_basic_map *isl_basic_map_flatten(
2715 __isl_take isl_basic_map *bmap);
2716 __isl_give isl_map *isl_map_flatten(
2717 __isl_take isl_map *map);
2719 __isl_give isl_map *isl_set_flatten_map(
2720 __isl_take isl_set *set);
2722 The function above constructs a relation
2723 that maps the input set to a flattened version of the set.
2727 Lift the input set to a space with extra dimensions corresponding
2728 to the existentially quantified variables in the input.
2729 In particular, the result lives in a wrapped map where the domain
2730 is the original space and the range corresponds to the original
2731 existentially quantified variables.
2733 __isl_give isl_basic_set *isl_basic_set_lift(
2734 __isl_take isl_basic_set *bset);
2735 __isl_give isl_set *isl_set_lift(
2736 __isl_take isl_set *set);
2737 __isl_give isl_union_set *isl_union_set_lift(
2738 __isl_take isl_union_set *uset);
2740 Given a local space that contains the existentially quantified
2741 variables of a set, a basic relation that, when applied to
2742 a basic set, has essentially the same effect as C<isl_basic_set_lift>,
2743 can be constructed using the following function.
2745 #include <isl/local_space.h>
2746 __isl_give isl_basic_map *isl_local_space_lifting(
2747 __isl_take isl_local_space *ls);
2749 =item * Internal Product
2751 __isl_give isl_basic_map *isl_basic_map_zip(
2752 __isl_take isl_basic_map *bmap);
2753 __isl_give isl_map *isl_map_zip(
2754 __isl_take isl_map *map);
2755 __isl_give isl_union_map *isl_union_map_zip(
2756 __isl_take isl_union_map *umap);
2758 Given a relation with nested relations for domain and range,
2759 interchange the range of the domain with the domain of the range.
2763 __isl_give isl_basic_map *isl_basic_map_curry(
2764 __isl_take isl_basic_map *bmap);
2765 __isl_give isl_basic_map *isl_basic_map_uncurry(
2766 __isl_take isl_basic_map *bmap);
2767 __isl_give isl_map *isl_map_curry(
2768 __isl_take isl_map *map);
2769 __isl_give isl_map *isl_map_uncurry(
2770 __isl_take isl_map *map);
2771 __isl_give isl_union_map *isl_union_map_curry(
2772 __isl_take isl_union_map *umap);
2773 __isl_give isl_union_map *isl_union_map_uncurry(
2774 __isl_take isl_union_map *umap);
2776 Given a relation with a nested relation for domain,
2777 the C<curry> functions
2778 move the range of the nested relation out of the domain
2779 and use it as the domain of a nested relation in the range,
2780 with the original range as range of this nested relation.
2781 The C<uncurry> functions perform the inverse operation.
2783 =item * Aligning parameters
2785 __isl_give isl_basic_set *isl_basic_set_align_params(
2786 __isl_take isl_basic_set *bset,
2787 __isl_take isl_space *model);
2788 __isl_give isl_set *isl_set_align_params(
2789 __isl_take isl_set *set,
2790 __isl_take isl_space *model);
2791 __isl_give isl_basic_map *isl_basic_map_align_params(
2792 __isl_take isl_basic_map *bmap,
2793 __isl_take isl_space *model);
2794 __isl_give isl_map *isl_map_align_params(
2795 __isl_take isl_map *map,
2796 __isl_take isl_space *model);
2798 Change the order of the parameters of the given set or relation
2799 such that the first parameters match those of C<model>.
2800 This may involve the introduction of extra parameters.
2801 All parameters need to be named.
2803 =item * Dimension manipulation
2805 __isl_give isl_basic_set *isl_basic_set_add_dims(
2806 __isl_take isl_basic_set *bset,
2807 enum isl_dim_type type, unsigned n);
2808 __isl_give isl_set *isl_set_add_dims(
2809 __isl_take isl_set *set,
2810 enum isl_dim_type type, unsigned n);
2811 __isl_give isl_map *isl_map_add_dims(
2812 __isl_take isl_map *map,
2813 enum isl_dim_type type, unsigned n);
2814 __isl_give isl_basic_set *isl_basic_set_insert_dims(
2815 __isl_take isl_basic_set *bset,
2816 enum isl_dim_type type, unsigned pos,
2818 __isl_give isl_basic_map *isl_basic_map_insert_dims(
2819 __isl_take isl_basic_map *bmap,
2820 enum isl_dim_type type, unsigned pos,
2822 __isl_give isl_set *isl_set_insert_dims(
2823 __isl_take isl_set *set,
2824 enum isl_dim_type type, unsigned pos, unsigned n);
2825 __isl_give isl_map *isl_map_insert_dims(
2826 __isl_take isl_map *map,
2827 enum isl_dim_type type, unsigned pos, unsigned n);
2828 __isl_give isl_basic_set *isl_basic_set_move_dims(
2829 __isl_take isl_basic_set *bset,
2830 enum isl_dim_type dst_type, unsigned dst_pos,
2831 enum isl_dim_type src_type, unsigned src_pos,
2833 __isl_give isl_basic_map *isl_basic_map_move_dims(
2834 __isl_take isl_basic_map *bmap,
2835 enum isl_dim_type dst_type, unsigned dst_pos,
2836 enum isl_dim_type src_type, unsigned src_pos,
2838 __isl_give isl_set *isl_set_move_dims(
2839 __isl_take isl_set *set,
2840 enum isl_dim_type dst_type, unsigned dst_pos,
2841 enum isl_dim_type src_type, unsigned src_pos,
2843 __isl_give isl_map *isl_map_move_dims(
2844 __isl_take isl_map *map,
2845 enum isl_dim_type dst_type, unsigned dst_pos,
2846 enum isl_dim_type src_type, unsigned src_pos,
2849 It is usually not advisable to directly change the (input or output)
2850 space of a set or a relation as this removes the name and the internal
2851 structure of the space. However, the above functions can be useful
2852 to add new parameters, assuming
2853 C<isl_set_align_params> and C<isl_map_align_params>
2858 =head2 Binary Operations
2860 The two arguments of a binary operation not only need to live
2861 in the same C<isl_ctx>, they currently also need to have
2862 the same (number of) parameters.
2864 =head3 Basic Operations
2868 =item * Intersection
2870 __isl_give isl_basic_set *isl_basic_set_intersect_params(
2871 __isl_take isl_basic_set *bset1,
2872 __isl_take isl_basic_set *bset2);
2873 __isl_give isl_basic_set *isl_basic_set_intersect(
2874 __isl_take isl_basic_set *bset1,
2875 __isl_take isl_basic_set *bset2);
2876 __isl_give isl_set *isl_set_intersect_params(
2877 __isl_take isl_set *set,
2878 __isl_take isl_set *params);
2879 __isl_give isl_set *isl_set_intersect(
2880 __isl_take isl_set *set1,
2881 __isl_take isl_set *set2);
2882 __isl_give isl_union_set *isl_union_set_intersect_params(
2883 __isl_take isl_union_set *uset,
2884 __isl_take isl_set *set);
2885 __isl_give isl_union_map *isl_union_map_intersect_params(
2886 __isl_take isl_union_map *umap,
2887 __isl_take isl_set *set);
2888 __isl_give isl_union_set *isl_union_set_intersect(
2889 __isl_take isl_union_set *uset1,
2890 __isl_take isl_union_set *uset2);
2891 __isl_give isl_basic_map *isl_basic_map_intersect_domain(
2892 __isl_take isl_basic_map *bmap,
2893 __isl_take isl_basic_set *bset);
2894 __isl_give isl_basic_map *isl_basic_map_intersect_range(
2895 __isl_take isl_basic_map *bmap,
2896 __isl_take isl_basic_set *bset);
2897 __isl_give isl_basic_map *isl_basic_map_intersect(
2898 __isl_take isl_basic_map *bmap1,
2899 __isl_take isl_basic_map *bmap2);
2900 __isl_give isl_map *isl_map_intersect_params(
2901 __isl_take isl_map *map,
2902 __isl_take isl_set *params);
2903 __isl_give isl_map *isl_map_intersect_domain(
2904 __isl_take isl_map *map,
2905 __isl_take isl_set *set);
2906 __isl_give isl_map *isl_map_intersect_range(
2907 __isl_take isl_map *map,
2908 __isl_take isl_set *set);
2909 __isl_give isl_map *isl_map_intersect(
2910 __isl_take isl_map *map1,
2911 __isl_take isl_map *map2);
2912 __isl_give isl_union_map *isl_union_map_intersect_domain(
2913 __isl_take isl_union_map *umap,
2914 __isl_take isl_union_set *uset);
2915 __isl_give isl_union_map *isl_union_map_intersect_range(
2916 __isl_take isl_union_map *umap,
2917 __isl_take isl_union_set *uset);
2918 __isl_give isl_union_map *isl_union_map_intersect(
2919 __isl_take isl_union_map *umap1,
2920 __isl_take isl_union_map *umap2);
2922 The second argument to the C<_params> functions needs to be
2923 a parametric (basic) set. For the other functions, a parametric set
2924 for either argument is only allowed if the other argument is
2925 a parametric set as well.
2929 __isl_give isl_set *isl_basic_set_union(
2930 __isl_take isl_basic_set *bset1,
2931 __isl_take isl_basic_set *bset2);
2932 __isl_give isl_map *isl_basic_map_union(
2933 __isl_take isl_basic_map *bmap1,
2934 __isl_take isl_basic_map *bmap2);
2935 __isl_give isl_set *isl_set_union(
2936 __isl_take isl_set *set1,
2937 __isl_take isl_set *set2);
2938 __isl_give isl_map *isl_map_union(
2939 __isl_take isl_map *map1,
2940 __isl_take isl_map *map2);
2941 __isl_give isl_union_set *isl_union_set_union(
2942 __isl_take isl_union_set *uset1,
2943 __isl_take isl_union_set *uset2);
2944 __isl_give isl_union_map *isl_union_map_union(
2945 __isl_take isl_union_map *umap1,
2946 __isl_take isl_union_map *umap2);
2948 =item * Set difference
2950 __isl_give isl_set *isl_set_subtract(
2951 __isl_take isl_set *set1,
2952 __isl_take isl_set *set2);
2953 __isl_give isl_map *isl_map_subtract(
2954 __isl_take isl_map *map1,
2955 __isl_take isl_map *map2);
2956 __isl_give isl_map *isl_map_subtract_domain(
2957 __isl_take isl_map *map,
2958 __isl_take isl_set *dom);
2959 __isl_give isl_map *isl_map_subtract_range(
2960 __isl_take isl_map *map,
2961 __isl_take isl_set *dom);
2962 __isl_give isl_union_set *isl_union_set_subtract(
2963 __isl_take isl_union_set *uset1,
2964 __isl_take isl_union_set *uset2);
2965 __isl_give isl_union_map *isl_union_map_subtract(
2966 __isl_take isl_union_map *umap1,
2967 __isl_take isl_union_map *umap2);
2968 __isl_give isl_union_map *isl_union_map_subtract_domain(
2969 __isl_take isl_union_map *umap,
2970 __isl_take isl_union_set *dom);
2971 __isl_give isl_union_map *isl_union_map_subtract_range(
2972 __isl_take isl_union_map *umap,
2973 __isl_take isl_union_set *dom);
2977 __isl_give isl_basic_set *isl_basic_set_apply(
2978 __isl_take isl_basic_set *bset,
2979 __isl_take isl_basic_map *bmap);
2980 __isl_give isl_set *isl_set_apply(
2981 __isl_take isl_set *set,
2982 __isl_take isl_map *map);
2983 __isl_give isl_union_set *isl_union_set_apply(
2984 __isl_take isl_union_set *uset,
2985 __isl_take isl_union_map *umap);
2986 __isl_give isl_basic_map *isl_basic_map_apply_domain(
2987 __isl_take isl_basic_map *bmap1,
2988 __isl_take isl_basic_map *bmap2);
2989 __isl_give isl_basic_map *isl_basic_map_apply_range(
2990 __isl_take isl_basic_map *bmap1,
2991 __isl_take isl_basic_map *bmap2);
2992 __isl_give isl_map *isl_map_apply_domain(
2993 __isl_take isl_map *map1,
2994 __isl_take isl_map *map2);
2995 __isl_give isl_union_map *isl_union_map_apply_domain(
2996 __isl_take isl_union_map *umap1,
2997 __isl_take isl_union_map *umap2);
2998 __isl_give isl_map *isl_map_apply_range(
2999 __isl_take isl_map *map1,
3000 __isl_take isl_map *map2);
3001 __isl_give isl_union_map *isl_union_map_apply_range(
3002 __isl_take isl_union_map *umap1,
3003 __isl_take isl_union_map *umap2);
3007 __isl_give isl_basic_set *
3008 isl_basic_set_preimage_multi_aff(
3009 __isl_take isl_basic_set *bset,
3010 __isl_take isl_multi_aff *ma);
3011 __isl_give isl_set *isl_set_preimage_multi_aff(
3012 __isl_take isl_set *set,
3013 __isl_take isl_multi_aff *ma);
3014 __isl_give isl_set *isl_set_preimage_pw_multi_aff(
3015 __isl_take isl_set *set,
3016 __isl_take isl_pw_multi_aff *pma);
3017 __isl_give isl_map *isl_map_preimage_domain_multi_aff(
3018 __isl_take isl_map *map,
3019 __isl_take isl_multi_aff *ma);
3020 __isl_give isl_union_map *
3021 isl_union_map_preimage_domain_multi_aff(
3022 __isl_take isl_union_map *umap,
3023 __isl_take isl_multi_aff *ma);
3025 These functions compute the preimage of the given set or map domain under
3026 the given function. In other words, the expression is plugged
3027 into the set description or into the domain of the map.
3028 Objects of types C<isl_multi_aff> and C<isl_pw_multi_aff> are described in
3029 L</"Piecewise Multiple Quasi Affine Expressions">.
3031 =item * Cartesian Product
3033 __isl_give isl_set *isl_set_product(
3034 __isl_take isl_set *set1,
3035 __isl_take isl_set *set2);
3036 __isl_give isl_union_set *isl_union_set_product(
3037 __isl_take isl_union_set *uset1,
3038 __isl_take isl_union_set *uset2);
3039 __isl_give isl_basic_map *isl_basic_map_domain_product(
3040 __isl_take isl_basic_map *bmap1,
3041 __isl_take isl_basic_map *bmap2);
3042 __isl_give isl_basic_map *isl_basic_map_range_product(
3043 __isl_take isl_basic_map *bmap1,
3044 __isl_take isl_basic_map *bmap2);
3045 __isl_give isl_basic_map *isl_basic_map_product(
3046 __isl_take isl_basic_map *bmap1,
3047 __isl_take isl_basic_map *bmap2);
3048 __isl_give isl_map *isl_map_domain_product(
3049 __isl_take isl_map *map1,
3050 __isl_take isl_map *map2);
3051 __isl_give isl_map *isl_map_range_product(
3052 __isl_take isl_map *map1,
3053 __isl_take isl_map *map2);
3054 __isl_give isl_union_map *isl_union_map_domain_product(
3055 __isl_take isl_union_map *umap1,
3056 __isl_take isl_union_map *umap2);
3057 __isl_give isl_union_map *isl_union_map_range_product(
3058 __isl_take isl_union_map *umap1,
3059 __isl_take isl_union_map *umap2);
3060 __isl_give isl_map *isl_map_product(
3061 __isl_take isl_map *map1,
3062 __isl_take isl_map *map2);
3063 __isl_give isl_union_map *isl_union_map_product(
3064 __isl_take isl_union_map *umap1,
3065 __isl_take isl_union_map *umap2);
3067 The above functions compute the cross product of the given
3068 sets or relations. The domains and ranges of the results
3069 are wrapped maps between domains and ranges of the inputs.
3070 To obtain a ``flat'' product, use the following functions
3073 __isl_give isl_basic_set *isl_basic_set_flat_product(
3074 __isl_take isl_basic_set *bset1,
3075 __isl_take isl_basic_set *bset2);
3076 __isl_give isl_set *isl_set_flat_product(
3077 __isl_take isl_set *set1,
3078 __isl_take isl_set *set2);
3079 __isl_give isl_basic_map *isl_basic_map_flat_range_product(
3080 __isl_take isl_basic_map *bmap1,
3081 __isl_take isl_basic_map *bmap2);
3082 __isl_give isl_map *isl_map_flat_domain_product(
3083 __isl_take isl_map *map1,
3084 __isl_take isl_map *map2);
3085 __isl_give isl_map *isl_map_flat_range_product(
3086 __isl_take isl_map *map1,
3087 __isl_take isl_map *map2);
3088 __isl_give isl_union_map *isl_union_map_flat_range_product(
3089 __isl_take isl_union_map *umap1,
3090 __isl_take isl_union_map *umap2);
3091 __isl_give isl_basic_map *isl_basic_map_flat_product(
3092 __isl_take isl_basic_map *bmap1,
3093 __isl_take isl_basic_map *bmap2);
3094 __isl_give isl_map *isl_map_flat_product(
3095 __isl_take isl_map *map1,
3096 __isl_take isl_map *map2);
3098 =item * Simplification
3100 __isl_give isl_basic_set *isl_basic_set_gist(
3101 __isl_take isl_basic_set *bset,
3102 __isl_take isl_basic_set *context);
3103 __isl_give isl_set *isl_set_gist(__isl_take isl_set *set,
3104 __isl_take isl_set *context);
3105 __isl_give isl_set *isl_set_gist_params(
3106 __isl_take isl_set *set,
3107 __isl_take isl_set *context);
3108 __isl_give isl_union_set *isl_union_set_gist(
3109 __isl_take isl_union_set *uset,
3110 __isl_take isl_union_set *context);
3111 __isl_give isl_union_set *isl_union_set_gist_params(
3112 __isl_take isl_union_set *uset,
3113 __isl_take isl_set *set);
3114 __isl_give isl_basic_map *isl_basic_map_gist(
3115 __isl_take isl_basic_map *bmap,
3116 __isl_take isl_basic_map *context);
3117 __isl_give isl_map *isl_map_gist(__isl_take isl_map *map,
3118 __isl_take isl_map *context);
3119 __isl_give isl_map *isl_map_gist_params(
3120 __isl_take isl_map *map,
3121 __isl_take isl_set *context);
3122 __isl_give isl_map *isl_map_gist_domain(
3123 __isl_take isl_map *map,
3124 __isl_take isl_set *context);
3125 __isl_give isl_map *isl_map_gist_range(
3126 __isl_take isl_map *map,
3127 __isl_take isl_set *context);
3128 __isl_give isl_union_map *isl_union_map_gist(
3129 __isl_take isl_union_map *umap,
3130 __isl_take isl_union_map *context);
3131 __isl_give isl_union_map *isl_union_map_gist_params(
3132 __isl_take isl_union_map *umap,
3133 __isl_take isl_set *set);
3134 __isl_give isl_union_map *isl_union_map_gist_domain(
3135 __isl_take isl_union_map *umap,
3136 __isl_take isl_union_set *uset);
3137 __isl_give isl_union_map *isl_union_map_gist_range(
3138 __isl_take isl_union_map *umap,
3139 __isl_take isl_union_set *uset);
3141 The gist operation returns a set or relation that has the
3142 same intersection with the context as the input set or relation.
3143 Any implicit equality in the intersection is made explicit in the result,
3144 while all inequalities that are redundant with respect to the intersection
3146 In case of union sets and relations, the gist operation is performed
3151 =head3 Lexicographic Optimization
3153 Given a (basic) set C<set> (or C<bset>) and a zero-dimensional domain C<dom>,
3154 the following functions
3155 compute a set that contains the lexicographic minimum or maximum
3156 of the elements in C<set> (or C<bset>) for those values of the parameters
3157 that satisfy C<dom>.
3158 If C<empty> is not C<NULL>, then C<*empty> is assigned a set
3159 that contains the parameter values in C<dom> for which C<set> (or C<bset>)
3161 In other words, the union of the parameter values
3162 for which the result is non-empty and of C<*empty>
3165 __isl_give isl_set *isl_basic_set_partial_lexmin(
3166 __isl_take isl_basic_set *bset,
3167 __isl_take isl_basic_set *dom,
3168 __isl_give isl_set **empty);
3169 __isl_give isl_set *isl_basic_set_partial_lexmax(
3170 __isl_take isl_basic_set *bset,
3171 __isl_take isl_basic_set *dom,
3172 __isl_give isl_set **empty);
3173 __isl_give isl_set *isl_set_partial_lexmin(
3174 __isl_take isl_set *set, __isl_take isl_set *dom,
3175 __isl_give isl_set **empty);
3176 __isl_give isl_set *isl_set_partial_lexmax(
3177 __isl_take isl_set *set, __isl_take isl_set *dom,
3178 __isl_give isl_set **empty);
3180 Given a (basic) set C<set> (or C<bset>), the following functions simply
3181 return a set containing the lexicographic minimum or maximum
3182 of the elements in C<set> (or C<bset>).
3183 In case of union sets, the optimum is computed per space.
3185 __isl_give isl_set *isl_basic_set_lexmin(
3186 __isl_take isl_basic_set *bset);
3187 __isl_give isl_set *isl_basic_set_lexmax(
3188 __isl_take isl_basic_set *bset);
3189 __isl_give isl_set *isl_set_lexmin(
3190 __isl_take isl_set *set);
3191 __isl_give isl_set *isl_set_lexmax(
3192 __isl_take isl_set *set);
3193 __isl_give isl_union_set *isl_union_set_lexmin(
3194 __isl_take isl_union_set *uset);
3195 __isl_give isl_union_set *isl_union_set_lexmax(
3196 __isl_take isl_union_set *uset);
3198 Given a (basic) relation C<map> (or C<bmap>) and a domain C<dom>,
3199 the following functions
3200 compute a relation that maps each element of C<dom>
3201 to the single lexicographic minimum or maximum
3202 of the elements that are associated to that same
3203 element in C<map> (or C<bmap>).
3204 If C<empty> is not C<NULL>, then C<*empty> is assigned a set
3205 that contains the elements in C<dom> that do not map
3206 to any elements in C<map> (or C<bmap>).
3207 In other words, the union of the domain of the result and of C<*empty>
3210 __isl_give isl_map *isl_basic_map_partial_lexmax(
3211 __isl_take isl_basic_map *bmap,
3212 __isl_take isl_basic_set *dom,
3213 __isl_give isl_set **empty);
3214 __isl_give isl_map *isl_basic_map_partial_lexmin(
3215 __isl_take isl_basic_map *bmap,
3216 __isl_take isl_basic_set *dom,
3217 __isl_give isl_set **empty);
3218 __isl_give isl_map *isl_map_partial_lexmax(
3219 __isl_take isl_map *map, __isl_take isl_set *dom,
3220 __isl_give isl_set **empty);
3221 __isl_give isl_map *isl_map_partial_lexmin(
3222 __isl_take isl_map *map, __isl_take isl_set *dom,
3223 __isl_give isl_set **empty);
3225 Given a (basic) map C<map> (or C<bmap>), the following functions simply
3226 return a map mapping each element in the domain of
3227 C<map> (or C<bmap>) to the lexicographic minimum or maximum
3228 of all elements associated to that element.
3229 In case of union relations, the optimum is computed per space.
3231 __isl_give isl_map *isl_basic_map_lexmin(
3232 __isl_take isl_basic_map *bmap);
3233 __isl_give isl_map *isl_basic_map_lexmax(
3234 __isl_take isl_basic_map *bmap);
3235 __isl_give isl_map *isl_map_lexmin(
3236 __isl_take isl_map *map);
3237 __isl_give isl_map *isl_map_lexmax(
3238 __isl_take isl_map *map);
3239 __isl_give isl_union_map *isl_union_map_lexmin(
3240 __isl_take isl_union_map *umap);
3241 __isl_give isl_union_map *isl_union_map_lexmax(
3242 __isl_take isl_union_map *umap);
3244 The following functions return their result in the form of
3245 a piecewise multi-affine expression
3246 (See L<"Piecewise Multiple Quasi Affine Expressions">),
3247 but are otherwise equivalent to the corresponding functions
3248 returning a basic set or relation.
3250 __isl_give isl_pw_multi_aff *
3251 isl_basic_map_lexmin_pw_multi_aff(
3252 __isl_take isl_basic_map *bmap);
3253 __isl_give isl_pw_multi_aff *
3254 isl_basic_set_partial_lexmin_pw_multi_aff(
3255 __isl_take isl_basic_set *bset,
3256 __isl_take isl_basic_set *dom,
3257 __isl_give isl_set **empty);
3258 __isl_give isl_pw_multi_aff *
3259 isl_basic_set_partial_lexmax_pw_multi_aff(
3260 __isl_take isl_basic_set *bset,
3261 __isl_take isl_basic_set *dom,
3262 __isl_give isl_set **empty);
3263 __isl_give isl_pw_multi_aff *
3264 isl_basic_map_partial_lexmin_pw_multi_aff(
3265 __isl_take isl_basic_map *bmap,
3266 __isl_take isl_basic_set *dom,
3267 __isl_give isl_set **empty);
3268 __isl_give isl_pw_multi_aff *
3269 isl_basic_map_partial_lexmax_pw_multi_aff(
3270 __isl_take isl_basic_map *bmap,
3271 __isl_take isl_basic_set *dom,
3272 __isl_give isl_set **empty);
3273 __isl_give isl_pw_multi_aff *isl_set_lexmin_pw_multi_aff(
3274 __isl_take isl_set *set);
3275 __isl_give isl_pw_multi_aff *isl_set_lexmax_pw_multi_aff(
3276 __isl_take isl_set *set);
3277 __isl_give isl_pw_multi_aff *isl_map_lexmin_pw_multi_aff(
3278 __isl_take isl_map *map);
3279 __isl_give isl_pw_multi_aff *isl_map_lexmax_pw_multi_aff(
3280 __isl_take isl_map *map);
3284 Lists are defined over several element types, including
3285 C<isl_val>, C<isl_id>, C<isl_aff>, C<isl_pw_aff>, C<isl_constraint>,
3286 C<isl_basic_set>, C<isl_set>, C<isl_ast_expr> and C<isl_ast_node>.
3287 Here we take lists of C<isl_set>s as an example.
3288 Lists can be created, copied, modified and freed using the following functions.
3290 #include <isl/list.h>
3291 __isl_give isl_set_list *isl_set_list_from_set(
3292 __isl_take isl_set *el);
3293 __isl_give isl_set_list *isl_set_list_alloc(
3294 isl_ctx *ctx, int n);
3295 __isl_give isl_set_list *isl_set_list_copy(
3296 __isl_keep isl_set_list *list);
3297 __isl_give isl_set_list *isl_set_list_insert(
3298 __isl_take isl_set_list *list, unsigned pos,
3299 __isl_take isl_set *el);
3300 __isl_give isl_set_list *isl_set_list_add(
3301 __isl_take isl_set_list *list,
3302 __isl_take isl_set *el);
3303 __isl_give isl_set_list *isl_set_list_drop(
3304 __isl_take isl_set_list *list,
3305 unsigned first, unsigned n);
3306 __isl_give isl_set_list *isl_set_list_set_set(
3307 __isl_take isl_set_list *list, int index,
3308 __isl_take isl_set *set);
3309 __isl_give isl_set_list *isl_set_list_concat(
3310 __isl_take isl_set_list *list1,
3311 __isl_take isl_set_list *list2);
3312 __isl_give isl_set_list *isl_set_list_sort(
3313 __isl_take isl_set_list *list,
3314 int (*cmp)(__isl_keep isl_set *a,
3315 __isl_keep isl_set *b, void *user),
3317 void *isl_set_list_free(__isl_take isl_set_list *list);
3319 C<isl_set_list_alloc> creates an empty list with a capacity for
3320 C<n> elements. C<isl_set_list_from_set> creates a list with a single
3323 Lists can be inspected using the following functions.
3325 #include <isl/list.h>
3326 isl_ctx *isl_set_list_get_ctx(__isl_keep isl_set_list *list);
3327 int isl_set_list_n_set(__isl_keep isl_set_list *list);
3328 __isl_give isl_set *isl_set_list_get_set(
3329 __isl_keep isl_set_list *list, int index);
3330 int isl_set_list_foreach(__isl_keep isl_set_list *list,
3331 int (*fn)(__isl_take isl_set *el, void *user),
3333 int isl_set_list_foreach_scc(__isl_keep isl_set_list *list,
3334 int (*follows)(__isl_keep isl_set *a,
3335 __isl_keep isl_set *b, void *user),
3337 int (*fn)(__isl_take isl_set *el, void *user),
3340 The function C<isl_set_list_foreach_scc> calls C<fn> on each of the
3341 strongly connected components of the graph with as vertices the elements
3342 of C<list> and a directed edge from vertex C<b> to vertex C<a>
3343 iff C<follows(a, b)> returns C<1>. The callbacks C<follows> and C<fn>
3344 should return C<-1> on error.
3346 Lists can be printed using
3348 #include <isl/list.h>
3349 __isl_give isl_printer *isl_printer_print_set_list(
3350 __isl_take isl_printer *p,
3351 __isl_keep isl_set_list *list);
3353 =head2 Multiple Values
3355 An C<isl_multi_val> object represents a sequence of zero or more values,
3356 living in a set space.
3358 An C<isl_multi_val> can be constructed from an C<isl_val_list>
3359 using the following function
3361 #include <isl/val.h>
3362 __isl_give isl_multi_val *isl_multi_val_from_val_list(
3363 __isl_take isl_space *space,
3364 __isl_take isl_val_list *list);
3366 The zero multiple value (with value zero for each set dimension)
3367 can be created using the following function.
3369 #include <isl/val.h>
3370 __isl_give isl_multi_val *isl_multi_val_zero(
3371 __isl_take isl_space *space);
3373 Multiple values can be copied and freed using
3375 #include <isl/val.h>
3376 __isl_give isl_multi_val *isl_multi_val_copy(
3377 __isl_keep isl_multi_val *mv);
3378 void *isl_multi_val_free(__isl_take isl_multi_val *mv);
3380 They can be inspected using
3382 #include <isl/val.h>
3383 isl_ctx *isl_multi_val_get_ctx(
3384 __isl_keep isl_multi_val *mv);
3385 unsigned isl_multi_val_dim(__isl_keep isl_multi_val *mv,
3386 enum isl_dim_type type);
3387 __isl_give isl_val *isl_multi_val_get_val(
3388 __isl_keep isl_multi_val *mv, int pos);
3389 const char *isl_multi_val_get_tuple_name(
3390 __isl_keep isl_multi_val *mv,
3391 enum isl_dim_type type);
3393 They can be modified using
3395 #include <isl/val.h>
3396 __isl_give isl_multi_val *isl_multi_val_set_val(
3397 __isl_take isl_multi_val *mv, int pos,
3398 __isl_take isl_val *val);
3399 __isl_give isl_multi_val *isl_multi_val_set_dim_name(
3400 __isl_take isl_multi_val *mv,
3401 enum isl_dim_type type, unsigned pos, const char *s);
3402 __isl_give isl_multi_val *isl_multi_val_set_tuple_name(
3403 __isl_take isl_multi_val *mv,
3404 enum isl_dim_type type, const char *s);
3405 __isl_give isl_multi_val *isl_multi_val_set_tuple_id(
3406 __isl_take isl_multi_val *mv,
3407 enum isl_dim_type type, __isl_take isl_id *id);
3409 __isl_give isl_multi_val *isl_multi_val_insert_dims(
3410 __isl_take isl_multi_val *mv,
3411 enum isl_dim_type type, unsigned first, unsigned n);
3412 __isl_give isl_multi_val *isl_multi_val_add_dims(
3413 __isl_take isl_multi_val *mv,
3414 enum isl_dim_type type, unsigned n);
3415 __isl_give isl_multi_val *isl_multi_val_drop_dims(
3416 __isl_take isl_multi_val *mv,
3417 enum isl_dim_type type, unsigned first, unsigned n);
3421 #include <isl/val.h>
3422 __isl_give isl_multi_val *isl_multi_val_align_params(
3423 __isl_take isl_multi_val *mv,
3424 __isl_take isl_space *model);
3425 __isl_give isl_multi_val *isl_multi_val_range_splice(
3426 __isl_take isl_multi_val *mv1, unsigned pos,
3427 __isl_take isl_multi_val *mv2);
3428 __isl_give isl_multi_val *isl_multi_val_range_product(
3429 __isl_take isl_multi_val *mv1,
3430 __isl_take isl_multi_val *mv2);
3431 __isl_give isl_multi_val *isl_multi_val_flat_range_product(
3432 __isl_take isl_multi_val *mv1,
3433 __isl_take isl_multi_aff *mv2);
3434 __isl_give isl_multi_val *isl_multi_val_add_val(
3435 __isl_take isl_multi_val *mv,
3436 __isl_take isl_val *v);
3437 __isl_give isl_multi_val *isl_multi_val_mod_val(
3438 __isl_take isl_multi_val *mv,
3439 __isl_take isl_val *v);
3443 Vectors can be created, copied and freed using the following functions.
3445 #include <isl/vec.h>
3446 __isl_give isl_vec *isl_vec_alloc(isl_ctx *ctx,
3448 __isl_give isl_vec *isl_vec_copy(__isl_keep isl_vec *vec);
3449 void *isl_vec_free(__isl_take isl_vec *vec);
3451 Note that the elements of a newly created vector may have arbitrary values.
3452 The elements can be changed and inspected using the following functions.
3454 isl_ctx *isl_vec_get_ctx(__isl_keep isl_vec *vec);
3455 int isl_vec_size(__isl_keep isl_vec *vec);
3456 int isl_vec_get_element(__isl_keep isl_vec *vec,
3457 int pos, isl_int *v);
3458 __isl_give isl_val *isl_vec_get_element_val(
3459 __isl_keep isl_vec *vec, int pos);
3460 __isl_give isl_vec *isl_vec_set_element(
3461 __isl_take isl_vec *vec, int pos, isl_int v);
3462 __isl_give isl_vec *isl_vec_set_element_si(
3463 __isl_take isl_vec *vec, int pos, int v);
3464 __isl_give isl_vec *isl_vec_set_element_val(
3465 __isl_take isl_vec *vec, int pos,
3466 __isl_take isl_val *v);
3467 __isl_give isl_vec *isl_vec_set(__isl_take isl_vec *vec,
3469 __isl_give isl_vec *isl_vec_set_si(__isl_take isl_vec *vec,
3471 __isl_give isl_vec *isl_vec_set_val(
3472 __isl_take isl_vec *vec, __isl_take isl_val *v);
3473 __isl_give isl_vec *isl_vec_fdiv_r(__isl_take isl_vec *vec,
3476 C<isl_vec_get_element> will return a negative value if anything went wrong.
3477 In that case, the value of C<*v> is undefined.
3479 The following function can be used to concatenate two vectors.
3481 __isl_give isl_vec *isl_vec_concat(__isl_take isl_vec *vec1,
3482 __isl_take isl_vec *vec2);
3486 Matrices can be created, copied and freed using the following functions.
3488 #include <isl/mat.h>
3489 __isl_give isl_mat *isl_mat_alloc(isl_ctx *ctx,
3490 unsigned n_row, unsigned n_col);
3491 __isl_give isl_mat *isl_mat_copy(__isl_keep isl_mat *mat);
3492 void *isl_mat_free(__isl_take isl_mat *mat);
3494 Note that the elements of a newly created matrix may have arbitrary values.
3495 The elements can be changed and inspected using the following functions.
3497 isl_ctx *isl_mat_get_ctx(__isl_keep isl_mat *mat);
3498 int isl_mat_rows(__isl_keep isl_mat *mat);
3499 int isl_mat_cols(__isl_keep isl_mat *mat);
3500 int isl_mat_get_element(__isl_keep isl_mat *mat,
3501 int row, int col, isl_int *v);
3502 __isl_give isl_val *isl_mat_get_element_val(
3503 __isl_keep isl_mat *mat, int row, int col);
3504 __isl_give isl_mat *isl_mat_set_element(__isl_take isl_mat *mat,
3505 int row, int col, isl_int v);
3506 __isl_give isl_mat *isl_mat_set_element_si(__isl_take isl_mat *mat,
3507 int row, int col, int v);
3508 __isl_give isl_mat *isl_mat_set_element_val(
3509 __isl_take isl_mat *mat, int row, int col,
3510 __isl_take isl_val *v);
3512 C<isl_mat_get_element> will return a negative value if anything went wrong.
3513 In that case, the value of C<*v> is undefined.
3515 The following function can be used to compute the (right) inverse
3516 of a matrix, i.e., a matrix such that the product of the original
3517 and the inverse (in that order) is a multiple of the identity matrix.
3518 The input matrix is assumed to be of full row-rank.
3520 __isl_give isl_mat *isl_mat_right_inverse(__isl_take isl_mat *mat);
3522 The following function can be used to compute the (right) kernel
3523 (or null space) of a matrix, i.e., a matrix such that the product of
3524 the original and the kernel (in that order) is the zero matrix.
3526 __isl_give isl_mat *isl_mat_right_kernel(__isl_take isl_mat *mat);
3528 =head2 Piecewise Quasi Affine Expressions
3530 The zero quasi affine expression or the quasi affine expression
3531 that is equal to a specified dimension on a given domain can be created using
3533 __isl_give isl_aff *isl_aff_zero_on_domain(
3534 __isl_take isl_local_space *ls);
3535 __isl_give isl_pw_aff *isl_pw_aff_zero_on_domain(
3536 __isl_take isl_local_space *ls);
3537 __isl_give isl_aff *isl_aff_var_on_domain(
3538 __isl_take isl_local_space *ls,
3539 enum isl_dim_type type, unsigned pos);
3540 __isl_give isl_pw_aff *isl_pw_aff_var_on_domain(
3541 __isl_take isl_local_space *ls,
3542 enum isl_dim_type type, unsigned pos);
3544 Note that the space in which the resulting objects live is a map space
3545 with the given space as domain and a one-dimensional range.
3547 An empty piecewise quasi affine expression (one with no cells)
3548 or a piecewise quasi affine expression with a single cell can
3549 be created using the following functions.
3551 #include <isl/aff.h>
3552 __isl_give isl_pw_aff *isl_pw_aff_empty(
3553 __isl_take isl_space *space);
3554 __isl_give isl_pw_aff *isl_pw_aff_alloc(
3555 __isl_take isl_set *set, __isl_take isl_aff *aff);
3556 __isl_give isl_pw_aff *isl_pw_aff_from_aff(
3557 __isl_take isl_aff *aff);
3559 A piecewise quasi affine expression that is equal to 1 on a set
3560 and 0 outside the set can be created using the following function.
3562 #include <isl/aff.h>
3563 __isl_give isl_pw_aff *isl_set_indicator_function(
3564 __isl_take isl_set *set);
3566 Quasi affine expressions can be copied and freed using
3568 #include <isl/aff.h>
3569 __isl_give isl_aff *isl_aff_copy(__isl_keep isl_aff *aff);
3570 void *isl_aff_free(__isl_take isl_aff *aff);
3572 __isl_give isl_pw_aff *isl_pw_aff_copy(
3573 __isl_keep isl_pw_aff *pwaff);
3574 void *isl_pw_aff_free(__isl_take isl_pw_aff *pwaff);
3576 A (rational) bound on a dimension can be extracted from an C<isl_constraint>
3577 using the following function. The constraint is required to have
3578 a non-zero coefficient for the specified dimension.
3580 #include <isl/constraint.h>
3581 __isl_give isl_aff *isl_constraint_get_bound(
3582 __isl_keep isl_constraint *constraint,
3583 enum isl_dim_type type, int pos);
3585 The entire affine expression of the constraint can also be extracted
3586 using the following function.
3588 #include <isl/constraint.h>
3589 __isl_give isl_aff *isl_constraint_get_aff(
3590 __isl_keep isl_constraint *constraint);
3592 Conversely, an equality constraint equating
3593 the affine expression to zero or an inequality constraint enforcing
3594 the affine expression to be non-negative, can be constructed using
3596 __isl_give isl_constraint *isl_equality_from_aff(
3597 __isl_take isl_aff *aff);
3598 __isl_give isl_constraint *isl_inequality_from_aff(
3599 __isl_take isl_aff *aff);
3601 The expression can be inspected using
3603 #include <isl/aff.h>
3604 isl_ctx *isl_aff_get_ctx(__isl_keep isl_aff *aff);
3605 int isl_aff_dim(__isl_keep isl_aff *aff,
3606 enum isl_dim_type type);
3607 __isl_give isl_local_space *isl_aff_get_domain_local_space(
3608 __isl_keep isl_aff *aff);
3609 __isl_give isl_local_space *isl_aff_get_local_space(
3610 __isl_keep isl_aff *aff);
3611 const char *isl_aff_get_dim_name(__isl_keep isl_aff *aff,
3612 enum isl_dim_type type, unsigned pos);
3613 const char *isl_pw_aff_get_dim_name(
3614 __isl_keep isl_pw_aff *pa,
3615 enum isl_dim_type type, unsigned pos);
3616 int isl_pw_aff_has_dim_id(__isl_keep isl_pw_aff *pa,
3617 enum isl_dim_type type, unsigned pos);
3618 __isl_give isl_id *isl_pw_aff_get_dim_id(
3619 __isl_keep isl_pw_aff *pa,
3620 enum isl_dim_type type, unsigned pos);
3621 __isl_give isl_id *isl_pw_aff_get_tuple_id(
3622 __isl_keep isl_pw_aff *pa,
3623 enum isl_dim_type type);
3624 int isl_aff_get_constant(__isl_keep isl_aff *aff,
3626 __isl_give isl_val *isl_aff_get_constant_val(
3627 __isl_keep isl_aff *aff);
3628 int isl_aff_get_coefficient(__isl_keep isl_aff *aff,
3629 enum isl_dim_type type, int pos, isl_int *v);
3630 __isl_give isl_val *isl_aff_get_coefficient_val(
3631 __isl_keep isl_aff *aff,
3632 enum isl_dim_type type, int pos);
3633 int isl_aff_get_denominator(__isl_keep isl_aff *aff,
3635 __isl_give isl_aff *isl_aff_get_div(
3636 __isl_keep isl_aff *aff, int pos);
3638 int isl_pw_aff_n_piece(__isl_keep isl_pw_aff *pwaff);
3639 int isl_pw_aff_foreach_piece(__isl_keep isl_pw_aff *pwaff,
3640 int (*fn)(__isl_take isl_set *set,
3641 __isl_take isl_aff *aff,
3642 void *user), void *user);
3644 int isl_aff_is_cst(__isl_keep isl_aff *aff);
3645 int isl_pw_aff_is_cst(__isl_keep isl_pw_aff *pwaff);
3647 int isl_aff_involves_dims(__isl_keep isl_aff *aff,
3648 enum isl_dim_type type, unsigned first, unsigned n);
3649 int isl_pw_aff_involves_dims(__isl_keep isl_pw_aff *pwaff,
3650 enum isl_dim_type type, unsigned first, unsigned n);
3652 isl_ctx *isl_pw_aff_get_ctx(__isl_keep isl_pw_aff *pwaff);
3653 unsigned isl_pw_aff_dim(__isl_keep isl_pw_aff *pwaff,
3654 enum isl_dim_type type);
3655 int isl_pw_aff_is_empty(__isl_keep isl_pw_aff *pwaff);
3657 It can be modified using
3659 #include <isl/aff.h>
3660 __isl_give isl_pw_aff *isl_pw_aff_set_tuple_id(
3661 __isl_take isl_pw_aff *pwaff,
3662 enum isl_dim_type type, __isl_take isl_id *id);
3663 __isl_give isl_aff *isl_aff_set_dim_name(
3664 __isl_take isl_aff *aff, enum isl_dim_type type,
3665 unsigned pos, const char *s);
3666 __isl_give isl_aff *isl_aff_set_dim_id(
3667 __isl_take isl_aff *aff, enum isl_dim_type type,
3668 unsigned pos, __isl_take isl_id *id);
3669 __isl_give isl_pw_aff *isl_pw_aff_set_dim_id(
3670 __isl_take isl_pw_aff *pma,
3671 enum isl_dim_type type, unsigned pos,
3672 __isl_take isl_id *id);
3673 __isl_give isl_aff *isl_aff_set_constant(
3674 __isl_take isl_aff *aff, isl_int v);
3675 __isl_give isl_aff *isl_aff_set_constant_si(
3676 __isl_take isl_aff *aff, int v);
3677 __isl_give isl_aff *isl_aff_set_constant_val(
3678 __isl_take isl_aff *aff, __isl_take isl_val *v);
3679 __isl_give isl_aff *isl_aff_set_coefficient(
3680 __isl_take isl_aff *aff,
3681 enum isl_dim_type type, int pos, isl_int v);
3682 __isl_give isl_aff *isl_aff_set_coefficient_si(
3683 __isl_take isl_aff *aff,
3684 enum isl_dim_type type, int pos, int v);
3685 __isl_give isl_aff *isl_aff_set_coefficient_val(
3686 __isl_take isl_aff *aff,
3687 enum isl_dim_type type, int pos,
3688 __isl_take isl_val *v);
3689 __isl_give isl_aff *isl_aff_set_denominator(
3690 __isl_take isl_aff *aff, isl_int v);
3692 __isl_give isl_aff *isl_aff_add_constant(
3693 __isl_take isl_aff *aff, isl_int v);
3694 __isl_give isl_aff *isl_aff_add_constant_si(
3695 __isl_take isl_aff *aff, int v);
3696 __isl_give isl_aff *isl_aff_add_constant_val(
3697 __isl_take isl_aff *aff, __isl_take isl_val *v);
3698 __isl_give isl_aff *isl_aff_add_constant_num(
3699 __isl_take isl_aff *aff, isl_int v);
3700 __isl_give isl_aff *isl_aff_add_constant_num_si(
3701 __isl_take isl_aff *aff, int v);
3702 __isl_give isl_aff *isl_aff_add_coefficient(
3703 __isl_take isl_aff *aff,
3704 enum isl_dim_type type, int pos, isl_int v);
3705 __isl_give isl_aff *isl_aff_add_coefficient_si(
3706 __isl_take isl_aff *aff,
3707 enum isl_dim_type type, int pos, int v);
3708 __isl_give isl_aff *isl_aff_add_coefficient_val(
3709 __isl_take isl_aff *aff,
3710 enum isl_dim_type type, int pos,
3711 __isl_take isl_val *v);
3713 __isl_give isl_aff *isl_aff_insert_dims(
3714 __isl_take isl_aff *aff,
3715 enum isl_dim_type type, unsigned first, unsigned n);
3716 __isl_give isl_pw_aff *isl_pw_aff_insert_dims(
3717 __isl_take isl_pw_aff *pwaff,
3718 enum isl_dim_type type, unsigned first, unsigned n);
3719 __isl_give isl_aff *isl_aff_add_dims(
3720 __isl_take isl_aff *aff,
3721 enum isl_dim_type type, unsigned n);
3722 __isl_give isl_pw_aff *isl_pw_aff_add_dims(
3723 __isl_take isl_pw_aff *pwaff,
3724 enum isl_dim_type type, unsigned n);
3725 __isl_give isl_aff *isl_aff_drop_dims(
3726 __isl_take isl_aff *aff,
3727 enum isl_dim_type type, unsigned first, unsigned n);
3728 __isl_give isl_pw_aff *isl_pw_aff_drop_dims(
3729 __isl_take isl_pw_aff *pwaff,
3730 enum isl_dim_type type, unsigned first, unsigned n);
3732 Note that C<isl_aff_set_constant>, C<isl_aff_set_constant_si>,
3733 C<isl_aff_set_coefficient> and C<isl_aff_set_coefficient_si>
3734 set the I<numerator> of the constant or coefficient, while
3735 C<isl_aff_set_constant_val> and C<isl_aff_set_coefficient_val> set
3736 the constant or coefficient as a whole.
3737 The C<add_constant> and C<add_coefficient> functions add an integer
3738 or rational value to
3739 the possibly rational constant or coefficient.
3740 The C<add_constant_num> functions add an integer value to
3743 To check whether an affine expressions is obviously zero
3744 or obviously equal to some other affine expression, use
3746 #include <isl/aff.h>
3747 int isl_aff_plain_is_zero(__isl_keep isl_aff *aff);
3748 int isl_aff_plain_is_equal(__isl_keep isl_aff *aff1,
3749 __isl_keep isl_aff *aff2);
3750 int isl_pw_aff_plain_is_equal(
3751 __isl_keep isl_pw_aff *pwaff1,
3752 __isl_keep isl_pw_aff *pwaff2);
3756 #include <isl/aff.h>
3757 __isl_give isl_aff *isl_aff_add(__isl_take isl_aff *aff1,
3758 __isl_take isl_aff *aff2);
3759 __isl_give isl_pw_aff *isl_pw_aff_add(
3760 __isl_take isl_pw_aff *pwaff1,
3761 __isl_take isl_pw_aff *pwaff2);
3762 __isl_give isl_pw_aff *isl_pw_aff_min(
3763 __isl_take isl_pw_aff *pwaff1,
3764 __isl_take isl_pw_aff *pwaff2);
3765 __isl_give isl_pw_aff *isl_pw_aff_max(
3766 __isl_take isl_pw_aff *pwaff1,
3767 __isl_take isl_pw_aff *pwaff2);
3768 __isl_give isl_aff *isl_aff_sub(__isl_take isl_aff *aff1,
3769 __isl_take isl_aff *aff2);
3770 __isl_give isl_pw_aff *isl_pw_aff_sub(
3771 __isl_take isl_pw_aff *pwaff1,
3772 __isl_take isl_pw_aff *pwaff2);
3773 __isl_give isl_aff *isl_aff_neg(__isl_take isl_aff *aff);
3774 __isl_give isl_pw_aff *isl_pw_aff_neg(
3775 __isl_take isl_pw_aff *pwaff);
3776 __isl_give isl_aff *isl_aff_ceil(__isl_take isl_aff *aff);
3777 __isl_give isl_pw_aff *isl_pw_aff_ceil(
3778 __isl_take isl_pw_aff *pwaff);
3779 __isl_give isl_aff *isl_aff_floor(__isl_take isl_aff *aff);
3780 __isl_give isl_pw_aff *isl_pw_aff_floor(
3781 __isl_take isl_pw_aff *pwaff);
3782 __isl_give isl_aff *isl_aff_mod(__isl_take isl_aff *aff,
3784 __isl_give isl_pw_aff *isl_pw_aff_mod(
3785 __isl_take isl_pw_aff *pwaff, isl_int mod);
3786 __isl_give isl_aff *isl_aff_scale(__isl_take isl_aff *aff,
3788 __isl_give isl_pw_aff *isl_pw_aff_scale(
3789 __isl_take isl_pw_aff *pwaff, isl_int f);
3790 __isl_give isl_aff *isl_aff_scale_down(__isl_take isl_aff *aff,
3792 __isl_give isl_aff *isl_aff_scale_down_ui(
3793 __isl_take isl_aff *aff, unsigned f);
3794 __isl_give isl_pw_aff *isl_pw_aff_scale_down(
3795 __isl_take isl_pw_aff *pwaff, isl_int f);
3797 __isl_give isl_pw_aff *isl_pw_aff_list_min(
3798 __isl_take isl_pw_aff_list *list);
3799 __isl_give isl_pw_aff *isl_pw_aff_list_max(
3800 __isl_take isl_pw_aff_list *list);
3802 __isl_give isl_pw_aff *isl_pw_aff_coalesce(
3803 __isl_take isl_pw_aff *pwqp);
3805 __isl_give isl_aff *isl_aff_align_params(
3806 __isl_take isl_aff *aff,
3807 __isl_take isl_space *model);
3808 __isl_give isl_pw_aff *isl_pw_aff_align_params(
3809 __isl_take isl_pw_aff *pwaff,
3810 __isl_take isl_space *model);
3812 __isl_give isl_aff *isl_aff_project_domain_on_params(
3813 __isl_take isl_aff *aff);
3815 __isl_give isl_aff *isl_aff_gist_params(
3816 __isl_take isl_aff *aff,
3817 __isl_take isl_set *context);
3818 __isl_give isl_aff *isl_aff_gist(__isl_take isl_aff *aff,
3819 __isl_take isl_set *context);
3820 __isl_give isl_pw_aff *isl_pw_aff_gist_params(
3821 __isl_take isl_pw_aff *pwaff,
3822 __isl_take isl_set *context);
3823 __isl_give isl_pw_aff *isl_pw_aff_gist(
3824 __isl_take isl_pw_aff *pwaff,
3825 __isl_take isl_set *context);
3827 __isl_give isl_set *isl_pw_aff_domain(
3828 __isl_take isl_pw_aff *pwaff);
3829 __isl_give isl_pw_aff *isl_pw_aff_intersect_domain(
3830 __isl_take isl_pw_aff *pa,
3831 __isl_take isl_set *set);
3832 __isl_give isl_pw_aff *isl_pw_aff_intersect_params(
3833 __isl_take isl_pw_aff *pa,
3834 __isl_take isl_set *set);
3836 __isl_give isl_aff *isl_aff_mul(__isl_take isl_aff *aff1,
3837 __isl_take isl_aff *aff2);
3838 __isl_give isl_aff *isl_aff_div(__isl_take isl_aff *aff1,
3839 __isl_take isl_aff *aff2);
3840 __isl_give isl_pw_aff *isl_pw_aff_mul(
3841 __isl_take isl_pw_aff *pwaff1,
3842 __isl_take isl_pw_aff *pwaff2);
3843 __isl_give isl_pw_aff *isl_pw_aff_div(
3844 __isl_take isl_pw_aff *pa1,
3845 __isl_take isl_pw_aff *pa2);
3846 __isl_give isl_pw_aff *isl_pw_aff_tdiv_q(
3847 __isl_take isl_pw_aff *pa1,
3848 __isl_take isl_pw_aff *pa2);
3849 __isl_give isl_pw_aff *isl_pw_aff_tdiv_r(
3850 __isl_take isl_pw_aff *pa1,
3851 __isl_take isl_pw_aff *pa2);
3853 When multiplying two affine expressions, at least one of the two needs
3854 to be a constant. Similarly, when dividing an affine expression by another,
3855 the second expression needs to be a constant.
3856 C<isl_pw_aff_tdiv_q> computes the quotient of an integer division with
3857 rounding towards zero. C<isl_pw_aff_tdiv_r> computes the corresponding
3860 #include <isl/aff.h>
3861 __isl_give isl_aff *isl_aff_pullback_multi_aff(
3862 __isl_take isl_aff *aff,
3863 __isl_take isl_multi_aff *ma);
3864 __isl_give isl_pw_aff *isl_pw_aff_pullback_multi_aff(
3865 __isl_take isl_pw_aff *pa,
3866 __isl_take isl_multi_aff *ma);
3867 __isl_give isl_pw_aff *isl_pw_aff_pullback_pw_multi_aff(
3868 __isl_take isl_pw_aff *pa,
3869 __isl_take isl_pw_multi_aff *pma);
3871 These functions precompose the input expression by the given
3872 C<isl_multi_aff> or C<isl_pw_multi_aff>. In other words,
3873 the C<isl_multi_aff> or C<isl_pw_multi_aff> is plugged
3874 into the (piecewise) affine expression.
3875 Objects of type C<isl_multi_aff> are described in
3876 L</"Piecewise Multiple Quasi Affine Expressions">.
3878 #include <isl/aff.h>
3879 __isl_give isl_basic_set *isl_aff_zero_basic_set(
3880 __isl_take isl_aff *aff);
3881 __isl_give isl_basic_set *isl_aff_neg_basic_set(
3882 __isl_take isl_aff *aff);
3883 __isl_give isl_basic_set *isl_aff_le_basic_set(
3884 __isl_take isl_aff *aff1, __isl_take isl_aff *aff2);
3885 __isl_give isl_basic_set *isl_aff_ge_basic_set(
3886 __isl_take isl_aff *aff1, __isl_take isl_aff *aff2);
3887 __isl_give isl_set *isl_pw_aff_eq_set(
3888 __isl_take isl_pw_aff *pwaff1,
3889 __isl_take isl_pw_aff *pwaff2);
3890 __isl_give isl_set *isl_pw_aff_ne_set(
3891 __isl_take isl_pw_aff *pwaff1,
3892 __isl_take isl_pw_aff *pwaff2);
3893 __isl_give isl_set *isl_pw_aff_le_set(
3894 __isl_take isl_pw_aff *pwaff1,
3895 __isl_take isl_pw_aff *pwaff2);
3896 __isl_give isl_set *isl_pw_aff_lt_set(
3897 __isl_take isl_pw_aff *pwaff1,
3898 __isl_take isl_pw_aff *pwaff2);
3899 __isl_give isl_set *isl_pw_aff_ge_set(
3900 __isl_take isl_pw_aff *pwaff1,
3901 __isl_take isl_pw_aff *pwaff2);
3902 __isl_give isl_set *isl_pw_aff_gt_set(
3903 __isl_take isl_pw_aff *pwaff1,
3904 __isl_take isl_pw_aff *pwaff2);
3906 __isl_give isl_set *isl_pw_aff_list_eq_set(
3907 __isl_take isl_pw_aff_list *list1,
3908 __isl_take isl_pw_aff_list *list2);
3909 __isl_give isl_set *isl_pw_aff_list_ne_set(
3910 __isl_take isl_pw_aff_list *list1,
3911 __isl_take isl_pw_aff_list *list2);
3912 __isl_give isl_set *isl_pw_aff_list_le_set(
3913 __isl_take isl_pw_aff_list *list1,
3914 __isl_take isl_pw_aff_list *list2);
3915 __isl_give isl_set *isl_pw_aff_list_lt_set(
3916 __isl_take isl_pw_aff_list *list1,
3917 __isl_take isl_pw_aff_list *list2);
3918 __isl_give isl_set *isl_pw_aff_list_ge_set(
3919 __isl_take isl_pw_aff_list *list1,
3920 __isl_take isl_pw_aff_list *list2);
3921 __isl_give isl_set *isl_pw_aff_list_gt_set(
3922 __isl_take isl_pw_aff_list *list1,
3923 __isl_take isl_pw_aff_list *list2);
3925 The function C<isl_aff_neg_basic_set> returns a basic set
3926 containing those elements in the domain space
3927 of C<aff> where C<aff> is negative.
3928 The function C<isl_aff_ge_basic_set> returns a basic set
3929 containing those elements in the shared space
3930 of C<aff1> and C<aff2> where C<aff1> is greater than or equal to C<aff2>.
3931 The function C<isl_pw_aff_ge_set> returns a set
3932 containing those elements in the shared domain
3933 of C<pwaff1> and C<pwaff2> where C<pwaff1> is greater than or equal to C<pwaff2>.
3934 The functions operating on C<isl_pw_aff_list> apply the corresponding
3935 C<isl_pw_aff> function to each pair of elements in the two lists.
3937 #include <isl/aff.h>
3938 __isl_give isl_set *isl_pw_aff_nonneg_set(
3939 __isl_take isl_pw_aff *pwaff);
3940 __isl_give isl_set *isl_pw_aff_zero_set(
3941 __isl_take isl_pw_aff *pwaff);
3942 __isl_give isl_set *isl_pw_aff_non_zero_set(
3943 __isl_take isl_pw_aff *pwaff);
3945 The function C<isl_pw_aff_nonneg_set> returns a set
3946 containing those elements in the domain
3947 of C<pwaff> where C<pwaff> is non-negative.
3949 #include <isl/aff.h>
3950 __isl_give isl_pw_aff *isl_pw_aff_cond(
3951 __isl_take isl_pw_aff *cond,
3952 __isl_take isl_pw_aff *pwaff_true,
3953 __isl_take isl_pw_aff *pwaff_false);
3955 The function C<isl_pw_aff_cond> performs a conditional operator
3956 and returns an expression that is equal to C<pwaff_true>
3957 for elements where C<cond> is non-zero and equal to C<pwaff_false> for elements
3958 where C<cond> is zero.
3960 #include <isl/aff.h>
3961 __isl_give isl_pw_aff *isl_pw_aff_union_min(
3962 __isl_take isl_pw_aff *pwaff1,
3963 __isl_take isl_pw_aff *pwaff2);
3964 __isl_give isl_pw_aff *isl_pw_aff_union_max(
3965 __isl_take isl_pw_aff *pwaff1,
3966 __isl_take isl_pw_aff *pwaff2);
3967 __isl_give isl_pw_aff *isl_pw_aff_union_add(
3968 __isl_take isl_pw_aff *pwaff1,
3969 __isl_take isl_pw_aff *pwaff2);
3971 The function C<isl_pw_aff_union_max> computes a piecewise quasi-affine
3972 expression with a domain that is the union of those of C<pwaff1> and
3973 C<pwaff2> and such that on each cell, the quasi-affine expression is
3974 the maximum of those of C<pwaff1> and C<pwaff2>. If only one of
3975 C<pwaff1> or C<pwaff2> is defined on a given cell, then the
3976 associated expression is the defined one.
3978 An expression can be read from input using
3980 #include <isl/aff.h>
3981 __isl_give isl_aff *isl_aff_read_from_str(
3982 isl_ctx *ctx, const char *str);
3983 __isl_give isl_pw_aff *isl_pw_aff_read_from_str(
3984 isl_ctx *ctx, const char *str);
3986 An expression can be printed using
3988 #include <isl/aff.h>
3989 __isl_give isl_printer *isl_printer_print_aff(
3990 __isl_take isl_printer *p, __isl_keep isl_aff *aff);
3992 __isl_give isl_printer *isl_printer_print_pw_aff(
3993 __isl_take isl_printer *p,
3994 __isl_keep isl_pw_aff *pwaff);
3996 =head2 Piecewise Multiple Quasi Affine Expressions
3998 An C<isl_multi_aff> object represents a sequence of
3999 zero or more affine expressions, all defined on the same domain space.
4000 Similarly, an C<isl_multi_pw_aff> object represents a sequence of
4001 zero or more piecewise affine expressions.
4003 An C<isl_multi_aff> can be constructed from a single
4004 C<isl_aff> or an C<isl_aff_list> using the
4005 following functions. Similarly for C<isl_multi_pw_aff>.
4007 #include <isl/aff.h>
4008 __isl_give isl_multi_aff *isl_multi_aff_from_aff(
4009 __isl_take isl_aff *aff);
4010 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_from_pw_aff(
4011 __isl_take isl_pw_aff *pa);
4012 __isl_give isl_multi_aff *isl_multi_aff_from_aff_list(
4013 __isl_take isl_space *space,
4014 __isl_take isl_aff_list *list);
4016 An empty piecewise multiple quasi affine expression (one with no cells),
4017 the zero piecewise multiple quasi affine expression (with value zero
4018 for each output dimension),
4019 a piecewise multiple quasi affine expression with a single cell (with
4020 either a universe or a specified domain) or
4021 a zero-dimensional piecewise multiple quasi affine expression
4023 can be created using the following functions.
4025 #include <isl/aff.h>
4026 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_empty(
4027 __isl_take isl_space *space);
4028 __isl_give isl_multi_aff *isl_multi_aff_zero(
4029 __isl_take isl_space *space);
4030 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_zero(
4031 __isl_take isl_space *space);
4032 __isl_give isl_multi_aff *isl_multi_aff_identity(
4033 __isl_take isl_space *space);
4034 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_identity(
4035 __isl_take isl_space *space);
4036 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_identity(
4037 __isl_take isl_space *space);
4038 __isl_give isl_pw_multi_aff *
4039 isl_pw_multi_aff_from_multi_aff(
4040 __isl_take isl_multi_aff *ma);
4041 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_alloc(
4042 __isl_take isl_set *set,
4043 __isl_take isl_multi_aff *maff);
4044 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_from_domain(
4045 __isl_take isl_set *set);
4047 __isl_give isl_union_pw_multi_aff *
4048 isl_union_pw_multi_aff_empty(
4049 __isl_take isl_space *space);
4050 __isl_give isl_union_pw_multi_aff *
4051 isl_union_pw_multi_aff_add_pw_multi_aff(
4052 __isl_take isl_union_pw_multi_aff *upma,
4053 __isl_take isl_pw_multi_aff *pma);
4054 __isl_give isl_union_pw_multi_aff *
4055 isl_union_pw_multi_aff_from_domain(
4056 __isl_take isl_union_set *uset);
4058 A piecewise multiple quasi affine expression can also be initialized
4059 from an C<isl_set> or C<isl_map>, provided the C<isl_set> is a singleton
4060 and the C<isl_map> is single-valued.
4061 In case of a conversion from an C<isl_union_set> or an C<isl_union_map>
4062 to an C<isl_union_pw_multi_aff>, these properties need to hold in each space.
4064 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_from_set(
4065 __isl_take isl_set *set);
4066 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_from_map(
4067 __isl_take isl_map *map);
4069 __isl_give isl_union_pw_multi_aff *
4070 isl_union_pw_multi_aff_from_union_set(
4071 __isl_take isl_union_set *uset);
4072 __isl_give isl_union_pw_multi_aff *
4073 isl_union_pw_multi_aff_from_union_map(
4074 __isl_take isl_union_map *umap);
4076 Multiple quasi affine expressions can be copied and freed using
4078 #include <isl/aff.h>
4079 __isl_give isl_multi_aff *isl_multi_aff_copy(
4080 __isl_keep isl_multi_aff *maff);
4081 void *isl_multi_aff_free(__isl_take isl_multi_aff *maff);
4083 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_copy(
4084 __isl_keep isl_pw_multi_aff *pma);
4085 void *isl_pw_multi_aff_free(
4086 __isl_take isl_pw_multi_aff *pma);
4088 __isl_give isl_union_pw_multi_aff *
4089 isl_union_pw_multi_aff_copy(
4090 __isl_keep isl_union_pw_multi_aff *upma);
4091 void *isl_union_pw_multi_aff_free(
4092 __isl_take isl_union_pw_multi_aff *upma);
4094 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_copy(
4095 __isl_keep isl_multi_pw_aff *mpa);
4096 void *isl_multi_pw_aff_free(
4097 __isl_take isl_multi_pw_aff *mpa);
4099 The expression can be inspected using
4101 #include <isl/aff.h>
4102 isl_ctx *isl_multi_aff_get_ctx(
4103 __isl_keep isl_multi_aff *maff);
4104 isl_ctx *isl_pw_multi_aff_get_ctx(
4105 __isl_keep isl_pw_multi_aff *pma);
4106 isl_ctx *isl_union_pw_multi_aff_get_ctx(
4107 __isl_keep isl_union_pw_multi_aff *upma);
4108 isl_ctx *isl_multi_pw_aff_get_ctx(
4109 __isl_keep isl_multi_pw_aff *mpa);
4110 unsigned isl_multi_aff_dim(__isl_keep isl_multi_aff *maff,
4111 enum isl_dim_type type);
4112 unsigned isl_pw_multi_aff_dim(
4113 __isl_keep isl_pw_multi_aff *pma,
4114 enum isl_dim_type type);
4115 unsigned isl_multi_pw_aff_dim(
4116 __isl_keep isl_multi_pw_aff *mpa,
4117 enum isl_dim_type type);
4118 __isl_give isl_aff *isl_multi_aff_get_aff(
4119 __isl_keep isl_multi_aff *multi, int pos);
4120 __isl_give isl_pw_aff *isl_pw_multi_aff_get_pw_aff(
4121 __isl_keep isl_pw_multi_aff *pma, int pos);
4122 __isl_give isl_pw_aff *isl_multi_pw_aff_get_pw_aff(
4123 __isl_keep isl_multi_pw_aff *mpa, int pos);
4124 const char *isl_pw_multi_aff_get_dim_name(
4125 __isl_keep isl_pw_multi_aff *pma,
4126 enum isl_dim_type type, unsigned pos);
4127 __isl_give isl_id *isl_pw_multi_aff_get_dim_id(
4128 __isl_keep isl_pw_multi_aff *pma,
4129 enum isl_dim_type type, unsigned pos);
4130 const char *isl_multi_aff_get_tuple_name(
4131 __isl_keep isl_multi_aff *multi,
4132 enum isl_dim_type type);
4133 int isl_pw_multi_aff_has_tuple_name(
4134 __isl_keep isl_pw_multi_aff *pma,
4135 enum isl_dim_type type);
4136 const char *isl_pw_multi_aff_get_tuple_name(
4137 __isl_keep isl_pw_multi_aff *pma,
4138 enum isl_dim_type type);
4139 int isl_pw_multi_aff_has_tuple_id(
4140 __isl_keep isl_pw_multi_aff *pma,
4141 enum isl_dim_type type);
4142 __isl_give isl_id *isl_pw_multi_aff_get_tuple_id(
4143 __isl_keep isl_pw_multi_aff *pma,
4144 enum isl_dim_type type);
4146 int isl_pw_multi_aff_foreach_piece(
4147 __isl_keep isl_pw_multi_aff *pma,
4148 int (*fn)(__isl_take isl_set *set,
4149 __isl_take isl_multi_aff *maff,
4150 void *user), void *user);
4152 int isl_union_pw_multi_aff_foreach_pw_multi_aff(
4153 __isl_keep isl_union_pw_multi_aff *upma,
4154 int (*fn)(__isl_take isl_pw_multi_aff *pma,
4155 void *user), void *user);
4157 It can be modified using
4159 #include <isl/aff.h>
4160 __isl_give isl_multi_aff *isl_multi_aff_set_aff(
4161 __isl_take isl_multi_aff *multi, int pos,
4162 __isl_take isl_aff *aff);
4163 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_set_pw_aff(
4164 __isl_take isl_pw_multi_aff *pma, unsigned pos,
4165 __isl_take isl_pw_aff *pa);
4166 __isl_give isl_multi_aff *isl_multi_aff_set_dim_name(
4167 __isl_take isl_multi_aff *maff,
4168 enum isl_dim_type type, unsigned pos, const char *s);
4169 __isl_give isl_multi_aff *isl_multi_aff_set_tuple_name(
4170 __isl_take isl_multi_aff *maff,
4171 enum isl_dim_type type, const char *s);
4172 __isl_give isl_multi_aff *isl_multi_aff_set_tuple_id(
4173 __isl_take isl_multi_aff *maff,
4174 enum isl_dim_type type, __isl_take isl_id *id);
4175 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_set_tuple_id(
4176 __isl_take isl_pw_multi_aff *pma,
4177 enum isl_dim_type type, __isl_take isl_id *id);
4179 __isl_give isl_multi_pw_aff *
4180 isl_multi_pw_aff_set_dim_name(
4181 __isl_take isl_multi_pw_aff *mpa,
4182 enum isl_dim_type type, unsigned pos, const char *s);
4183 __isl_give isl_multi_pw_aff *
4184 isl_multi_pw_aff_set_tuple_name(
4185 __isl_take isl_multi_pw_aff *mpa,
4186 enum isl_dim_type type, const char *s);
4188 __isl_give isl_multi_aff *isl_multi_aff_insert_dims(
4189 __isl_take isl_multi_aff *ma,
4190 enum isl_dim_type type, unsigned first, unsigned n);
4191 __isl_give isl_multi_aff *isl_multi_aff_add_dims(
4192 __isl_take isl_multi_aff *ma,
4193 enum isl_dim_type type, unsigned n);
4194 __isl_give isl_multi_aff *isl_multi_aff_drop_dims(
4195 __isl_take isl_multi_aff *maff,
4196 enum isl_dim_type type, unsigned first, unsigned n);
4197 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_drop_dims(
4198 __isl_take isl_pw_multi_aff *pma,
4199 enum isl_dim_type type, unsigned first, unsigned n);
4201 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_insert_dims(
4202 __isl_take isl_multi_pw_aff *mpa,
4203 enum isl_dim_type type, unsigned first, unsigned n);
4204 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_add_dims(
4205 __isl_take isl_multi_pw_aff *mpa,
4206 enum isl_dim_type type, unsigned n);
4208 To check whether two multiple affine expressions are
4209 obviously equal to each other, use
4211 int isl_multi_aff_plain_is_equal(__isl_keep isl_multi_aff *maff1,
4212 __isl_keep isl_multi_aff *maff2);
4213 int isl_pw_multi_aff_plain_is_equal(
4214 __isl_keep isl_pw_multi_aff *pma1,
4215 __isl_keep isl_pw_multi_aff *pma2);
4219 #include <isl/aff.h>
4220 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_union_lexmin(
4221 __isl_take isl_pw_multi_aff *pma1,
4222 __isl_take isl_pw_multi_aff *pma2);
4223 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_union_lexmax(
4224 __isl_take isl_pw_multi_aff *pma1,
4225 __isl_take isl_pw_multi_aff *pma2);
4226 __isl_give isl_multi_aff *isl_multi_aff_add(
4227 __isl_take isl_multi_aff *maff1,
4228 __isl_take isl_multi_aff *maff2);
4229 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_add(
4230 __isl_take isl_pw_multi_aff *pma1,
4231 __isl_take isl_pw_multi_aff *pma2);
4232 __isl_give isl_union_pw_multi_aff *isl_union_pw_multi_aff_add(
4233 __isl_take isl_union_pw_multi_aff *upma1,
4234 __isl_take isl_union_pw_multi_aff *upma2);
4235 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_union_add(
4236 __isl_take isl_pw_multi_aff *pma1,
4237 __isl_take isl_pw_multi_aff *pma2);
4238 __isl_give isl_multi_aff *isl_multi_aff_sub(
4239 __isl_take isl_multi_aff *ma1,
4240 __isl_take isl_multi_aff *ma2);
4241 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_sub(
4242 __isl_take isl_pw_multi_aff *pma1,
4243 __isl_take isl_pw_multi_aff *pma2);
4244 __isl_give isl_union_pw_multi_aff *isl_union_pw_multi_aff_sub(
4245 __isl_take isl_union_pw_multi_aff *upma1,
4246 __isl_take isl_union_pw_multi_aff *upma2);
4248 C<isl_multi_aff_sub> subtracts the second argument from the first.
4250 __isl_give isl_multi_aff *isl_multi_aff_scale(
4251 __isl_take isl_multi_aff *maff,
4253 __isl_give isl_multi_aff *isl_multi_aff_scale_vec(
4254 __isl_take isl_multi_aff *ma,
4255 __isl_take isl_vec *v);
4256 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_scale_vec(
4257 __isl_take isl_pw_multi_aff *pma,
4258 __isl_take isl_vec *v);
4259 __isl_give isl_union_pw_multi_aff *isl_union_pw_multi_aff_scale_vec(
4260 __isl_take isl_union_pw_multi_aff *upma,
4261 __isl_take isl_vec *v);
4263 C<isl_multi_aff_scale_vec> scales the first elements of C<ma>
4264 by the corresponding elements of C<v>.
4266 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_intersect_params(
4267 __isl_take isl_pw_multi_aff *pma,
4268 __isl_take isl_set *set);
4269 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_intersect_domain(
4270 __isl_take isl_pw_multi_aff *pma,
4271 __isl_take isl_set *set);
4272 __isl_give isl_union_pw_multi_aff *
4273 isl_union_pw_multi_aff_intersect_domain(
4274 __isl_take isl_union_pw_multi_aff *upma,
4275 __isl_take isl_union_set *uset);
4276 __isl_give isl_multi_aff *isl_multi_aff_lift(
4277 __isl_take isl_multi_aff *maff,
4278 __isl_give isl_local_space **ls);
4279 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_coalesce(
4280 __isl_take isl_pw_multi_aff *pma);
4281 __isl_give isl_multi_aff *isl_multi_aff_align_params(
4282 __isl_take isl_multi_aff *multi,
4283 __isl_take isl_space *model);
4284 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_align_params(
4285 __isl_take isl_pw_multi_aff *pma,
4286 __isl_take isl_space *model);
4287 __isl_give isl_pw_multi_aff *
4288 isl_pw_multi_aff_project_domain_on_params(
4289 __isl_take isl_pw_multi_aff *pma);
4290 __isl_give isl_multi_aff *isl_multi_aff_gist_params(
4291 __isl_take isl_multi_aff *maff,
4292 __isl_take isl_set *context);
4293 __isl_give isl_multi_aff *isl_multi_aff_gist(
4294 __isl_take isl_multi_aff *maff,
4295 __isl_take isl_set *context);
4296 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_gist_params(
4297 __isl_take isl_pw_multi_aff *pma,
4298 __isl_take isl_set *set);
4299 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_gist(
4300 __isl_take isl_pw_multi_aff *pma,
4301 __isl_take isl_set *set);
4302 __isl_give isl_set *isl_pw_multi_aff_domain(
4303 __isl_take isl_pw_multi_aff *pma);
4304 __isl_give isl_union_set *isl_union_pw_multi_aff_domain(
4305 __isl_take isl_union_pw_multi_aff *upma);
4306 __isl_give isl_multi_aff *isl_multi_aff_range_splice(
4307 __isl_take isl_multi_aff *ma1, unsigned pos,
4308 __isl_take isl_multi_aff *ma2);
4309 __isl_give isl_multi_aff *isl_multi_aff_splice(
4310 __isl_take isl_multi_aff *ma1,
4311 unsigned in_pos, unsigned out_pos,
4312 __isl_take isl_multi_aff *ma2);
4313 __isl_give isl_multi_aff *isl_multi_aff_range_product(
4314 __isl_take isl_multi_aff *ma1,
4315 __isl_take isl_multi_aff *ma2);
4316 __isl_give isl_multi_aff *isl_multi_aff_flat_range_product(
4317 __isl_take isl_multi_aff *ma1,
4318 __isl_take isl_multi_aff *ma2);
4319 __isl_give isl_multi_aff *isl_multi_aff_product(
4320 __isl_take isl_multi_aff *ma1,
4321 __isl_take isl_multi_aff *ma2);
4322 __isl_give isl_pw_multi_aff *
4323 isl_pw_multi_aff_range_product(
4324 __isl_take isl_pw_multi_aff *pma1,
4325 __isl_take isl_pw_multi_aff *pma2);
4326 __isl_give isl_pw_multi_aff *
4327 isl_pw_multi_aff_flat_range_product(
4328 __isl_take isl_pw_multi_aff *pma1,
4329 __isl_take isl_pw_multi_aff *pma2);
4330 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_product(
4331 __isl_take isl_pw_multi_aff *pma1,
4332 __isl_take isl_pw_multi_aff *pma2);
4333 __isl_give isl_union_pw_multi_aff *
4334 isl_union_pw_multi_aff_flat_range_product(
4335 __isl_take isl_union_pw_multi_aff *upma1,
4336 __isl_take isl_union_pw_multi_aff *upma2);
4337 __isl_give isl_multi_pw_aff *
4338 isl_multi_pw_aff_range_splice(
4339 __isl_take isl_multi_pw_aff *mpa1, unsigned pos,
4340 __isl_take isl_multi_pw_aff *mpa2);
4341 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_splice(
4342 __isl_take isl_multi_pw_aff *mpa1,
4343 unsigned in_pos, unsigned out_pos,
4344 __isl_take isl_multi_pw_aff *mpa2);
4345 __isl_give isl_multi_pw_aff *
4346 isl_multi_pw_aff_range_product(
4347 __isl_take isl_multi_pw_aff *mpa1,
4348 __isl_take isl_multi_pw_aff *mpa2);
4349 __isl_give isl_multi_pw_aff *
4350 isl_multi_pw_aff_flat_range_product(
4351 __isl_take isl_multi_pw_aff *mpa1,
4352 __isl_take isl_multi_pw_aff *mpa2);
4354 If the C<ls> argument of C<isl_multi_aff_lift> is not C<NULL>,
4355 then it is assigned the local space that lies at the basis of
4356 the lifting applied.
4358 #include <isl/aff.h>
4359 __isl_give isl_multi_aff *isl_multi_aff_pullback_multi_aff(
4360 __isl_take isl_multi_aff *ma1,
4361 __isl_take isl_multi_aff *ma2);
4362 __isl_give isl_pw_multi_aff *
4363 isl_pw_multi_aff_pullback_multi_aff(
4364 __isl_take isl_pw_multi_aff *pma,
4365 __isl_take isl_multi_aff *ma);
4366 __isl_give isl_pw_multi_aff *
4367 isl_pw_multi_aff_pullback_pw_multi_aff(
4368 __isl_take isl_pw_multi_aff *pma1,
4369 __isl_take isl_pw_multi_aff *pma2);
4371 The function C<isl_multi_aff_pullback_multi_aff> precomposes C<ma1> by C<ma2>.
4372 In other words, C<ma2> is plugged
4375 __isl_give isl_set *isl_multi_aff_lex_le_set(
4376 __isl_take isl_multi_aff *ma1,
4377 __isl_take isl_multi_aff *ma2);
4378 __isl_give isl_set *isl_multi_aff_lex_ge_set(
4379 __isl_take isl_multi_aff *ma1,
4380 __isl_take isl_multi_aff *ma2);
4382 The function C<isl_multi_aff_lex_le_set> returns a set
4383 containing those elements in the shared domain space
4384 where C<ma1> is lexicographically smaller than or
4387 An expression can be read from input using
4389 #include <isl/aff.h>
4390 __isl_give isl_multi_aff *isl_multi_aff_read_from_str(
4391 isl_ctx *ctx, const char *str);
4392 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_read_from_str(
4393 isl_ctx *ctx, const char *str);
4394 __isl_give isl_union_pw_multi_aff *
4395 isl_union_pw_multi_aff_read_from_str(
4396 isl_ctx *ctx, const char *str);
4398 An expression can be printed using
4400 #include <isl/aff.h>
4401 __isl_give isl_printer *isl_printer_print_multi_aff(
4402 __isl_take isl_printer *p,
4403 __isl_keep isl_multi_aff *maff);
4404 __isl_give isl_printer *isl_printer_print_pw_multi_aff(
4405 __isl_take isl_printer *p,
4406 __isl_keep isl_pw_multi_aff *pma);
4407 __isl_give isl_printer *isl_printer_print_union_pw_multi_aff(
4408 __isl_take isl_printer *p,
4409 __isl_keep isl_union_pw_multi_aff *upma);
4410 __isl_give isl_printer *isl_printer_print_multi_pw_aff(
4411 __isl_take isl_printer *p,
4412 __isl_keep isl_multi_pw_aff *mpa);
4416 Points are elements of a set. They can be used to construct
4417 simple sets (boxes) or they can be used to represent the
4418 individual elements of a set.
4419 The zero point (the origin) can be created using
4421 __isl_give isl_point *isl_point_zero(__isl_take isl_space *space);
4423 The coordinates of a point can be inspected, set and changed
4426 int isl_point_get_coordinate(__isl_keep isl_point *pnt,
4427 enum isl_dim_type type, int pos, isl_int *v);
4428 __isl_give isl_val *isl_point_get_coordinate_val(
4429 __isl_keep isl_point *pnt,
4430 enum isl_dim_type type, int pos);
4431 __isl_give isl_point *isl_point_set_coordinate(
4432 __isl_take isl_point *pnt,
4433 enum isl_dim_type type, int pos, isl_int v);
4434 __isl_give isl_point *isl_point_set_coordinate_val(
4435 __isl_take isl_point *pnt,
4436 enum isl_dim_type type, int pos,
4437 __isl_take isl_val *v);
4439 __isl_give isl_point *isl_point_add_ui(
4440 __isl_take isl_point *pnt,
4441 enum isl_dim_type type, int pos, unsigned val);
4442 __isl_give isl_point *isl_point_sub_ui(
4443 __isl_take isl_point *pnt,
4444 enum isl_dim_type type, int pos, unsigned val);
4446 Other properties can be obtained using
4448 isl_ctx *isl_point_get_ctx(__isl_keep isl_point *pnt);
4450 Points can be copied or freed using
4452 __isl_give isl_point *isl_point_copy(
4453 __isl_keep isl_point *pnt);
4454 void isl_point_free(__isl_take isl_point *pnt);
4456 A singleton set can be created from a point using
4458 __isl_give isl_basic_set *isl_basic_set_from_point(
4459 __isl_take isl_point *pnt);
4460 __isl_give isl_set *isl_set_from_point(
4461 __isl_take isl_point *pnt);
4463 and a box can be created from two opposite extremal points using
4465 __isl_give isl_basic_set *isl_basic_set_box_from_points(
4466 __isl_take isl_point *pnt1,
4467 __isl_take isl_point *pnt2);
4468 __isl_give isl_set *isl_set_box_from_points(
4469 __isl_take isl_point *pnt1,
4470 __isl_take isl_point *pnt2);
4472 All elements of a B<bounded> (union) set can be enumerated using
4473 the following functions.
4475 int isl_set_foreach_point(__isl_keep isl_set *set,
4476 int (*fn)(__isl_take isl_point *pnt, void *user),
4478 int isl_union_set_foreach_point(__isl_keep isl_union_set *uset,
4479 int (*fn)(__isl_take isl_point *pnt, void *user),
4482 The function C<fn> is called for each integer point in
4483 C<set> with as second argument the last argument of
4484 the C<isl_set_foreach_point> call. The function C<fn>
4485 should return C<0> on success and C<-1> on failure.
4486 In the latter case, C<isl_set_foreach_point> will stop
4487 enumerating and return C<-1> as well.
4488 If the enumeration is performed successfully and to completion,
4489 then C<isl_set_foreach_point> returns C<0>.
4491 To obtain a single point of a (basic) set, use
4493 __isl_give isl_point *isl_basic_set_sample_point(
4494 __isl_take isl_basic_set *bset);
4495 __isl_give isl_point *isl_set_sample_point(
4496 __isl_take isl_set *set);
4498 If C<set> does not contain any (integer) points, then the
4499 resulting point will be ``void'', a property that can be
4502 int isl_point_is_void(__isl_keep isl_point *pnt);
4504 =head2 Piecewise Quasipolynomials
4506 A piecewise quasipolynomial is a particular kind of function that maps
4507 a parametric point to a rational value.
4508 More specifically, a quasipolynomial is a polynomial expression in greatest
4509 integer parts of affine expressions of parameters and variables.
4510 A piecewise quasipolynomial is a subdivision of a given parametric
4511 domain into disjoint cells with a quasipolynomial associated to
4512 each cell. The value of the piecewise quasipolynomial at a given
4513 point is the value of the quasipolynomial associated to the cell
4514 that contains the point. Outside of the union of cells,
4515 the value is assumed to be zero.
4516 For example, the piecewise quasipolynomial
4518 [n] -> { [x] -> ((1 + n) - x) : x <= n and x >= 0 }
4520 maps C<x> to C<1 + n - x> for values of C<x> between C<0> and C<n>.
4521 A given piecewise quasipolynomial has a fixed domain dimension.
4522 Union piecewise quasipolynomials are used to contain piecewise quasipolynomials
4523 defined over different domains.
4524 Piecewise quasipolynomials are mainly used by the C<barvinok>
4525 library for representing the number of elements in a parametric set or map.
4526 For example, the piecewise quasipolynomial above represents
4527 the number of points in the map
4529 [n] -> { [x] -> [y] : x,y >= 0 and 0 <= x + y <= n }
4531 =head3 Input and Output
4533 Piecewise quasipolynomials can be read from input using
4535 __isl_give isl_union_pw_qpolynomial *
4536 isl_union_pw_qpolynomial_read_from_str(
4537 isl_ctx *ctx, const char *str);
4539 Quasipolynomials and piecewise quasipolynomials can be printed
4540 using the following functions.
4542 __isl_give isl_printer *isl_printer_print_qpolynomial(
4543 __isl_take isl_printer *p,
4544 __isl_keep isl_qpolynomial *qp);
4546 __isl_give isl_printer *isl_printer_print_pw_qpolynomial(
4547 __isl_take isl_printer *p,
4548 __isl_keep isl_pw_qpolynomial *pwqp);
4550 __isl_give isl_printer *isl_printer_print_union_pw_qpolynomial(
4551 __isl_take isl_printer *p,
4552 __isl_keep isl_union_pw_qpolynomial *upwqp);
4554 The output format of the printer
4555 needs to be set to either C<ISL_FORMAT_ISL> or C<ISL_FORMAT_C>.
4556 For C<isl_printer_print_union_pw_qpolynomial>, only C<ISL_FORMAT_ISL>
4558 In case of printing in C<ISL_FORMAT_C>, the user may want
4559 to set the names of all dimensions
4561 __isl_give isl_qpolynomial *isl_qpolynomial_set_dim_name(
4562 __isl_take isl_qpolynomial *qp,
4563 enum isl_dim_type type, unsigned pos,
4565 __isl_give isl_pw_qpolynomial *
4566 isl_pw_qpolynomial_set_dim_name(
4567 __isl_take isl_pw_qpolynomial *pwqp,
4568 enum isl_dim_type type, unsigned pos,
4571 =head3 Creating New (Piecewise) Quasipolynomials
4573 Some simple quasipolynomials can be created using the following functions.
4574 More complicated quasipolynomials can be created by applying
4575 operations such as addition and multiplication
4576 on the resulting quasipolynomials
4578 __isl_give isl_qpolynomial *isl_qpolynomial_zero_on_domain(
4579 __isl_take isl_space *domain);
4580 __isl_give isl_qpolynomial *isl_qpolynomial_one_on_domain(
4581 __isl_take isl_space *domain);
4582 __isl_give isl_qpolynomial *isl_qpolynomial_infty_on_domain(
4583 __isl_take isl_space *domain);
4584 __isl_give isl_qpolynomial *isl_qpolynomial_neginfty_on_domain(
4585 __isl_take isl_space *domain);
4586 __isl_give isl_qpolynomial *isl_qpolynomial_nan_on_domain(
4587 __isl_take isl_space *domain);
4588 __isl_give isl_qpolynomial *isl_qpolynomial_rat_cst_on_domain(
4589 __isl_take isl_space *domain,
4590 const isl_int n, const isl_int d);
4591 __isl_give isl_qpolynomial *isl_qpolynomial_var_on_domain(
4592 __isl_take isl_space *domain,
4593 enum isl_dim_type type, unsigned pos);
4594 __isl_give isl_qpolynomial *isl_qpolynomial_from_aff(
4595 __isl_take isl_aff *aff);
4597 Note that the space in which a quasipolynomial lives is a map space
4598 with a one-dimensional range. The C<domain> argument in some of
4599 the functions above corresponds to the domain of this map space.
4601 The zero piecewise quasipolynomial or a piecewise quasipolynomial
4602 with a single cell can be created using the following functions.
4603 Multiple of these single cell piecewise quasipolynomials can
4604 be combined to create more complicated piecewise quasipolynomials.
4606 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_zero(
4607 __isl_take isl_space *space);
4608 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_alloc(
4609 __isl_take isl_set *set,
4610 __isl_take isl_qpolynomial *qp);
4611 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_from_qpolynomial(
4612 __isl_take isl_qpolynomial *qp);
4613 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_from_pw_aff(
4614 __isl_take isl_pw_aff *pwaff);
4616 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_zero(
4617 __isl_take isl_space *space);
4618 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_from_pw_qpolynomial(
4619 __isl_take isl_pw_qpolynomial *pwqp);
4620 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_add_pw_qpolynomial(
4621 __isl_take isl_union_pw_qpolynomial *upwqp,
4622 __isl_take isl_pw_qpolynomial *pwqp);
4624 Quasipolynomials can be copied and freed again using the following
4627 __isl_give isl_qpolynomial *isl_qpolynomial_copy(
4628 __isl_keep isl_qpolynomial *qp);
4629 void *isl_qpolynomial_free(__isl_take isl_qpolynomial *qp);
4631 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_copy(
4632 __isl_keep isl_pw_qpolynomial *pwqp);
4633 void *isl_pw_qpolynomial_free(
4634 __isl_take isl_pw_qpolynomial *pwqp);
4636 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_copy(
4637 __isl_keep isl_union_pw_qpolynomial *upwqp);
4638 void *isl_union_pw_qpolynomial_free(
4639 __isl_take isl_union_pw_qpolynomial *upwqp);
4641 =head3 Inspecting (Piecewise) Quasipolynomials
4643 To iterate over all piecewise quasipolynomials in a union
4644 piecewise quasipolynomial, use the following function
4646 int isl_union_pw_qpolynomial_foreach_pw_qpolynomial(
4647 __isl_keep isl_union_pw_qpolynomial *upwqp,
4648 int (*fn)(__isl_take isl_pw_qpolynomial *pwqp, void *user),
4651 To extract the piecewise quasipolynomial in a given space from a union, use
4653 __isl_give isl_pw_qpolynomial *
4654 isl_union_pw_qpolynomial_extract_pw_qpolynomial(
4655 __isl_keep isl_union_pw_qpolynomial *upwqp,
4656 __isl_take isl_space *space);
4658 To iterate over the cells in a piecewise quasipolynomial,
4659 use either of the following two functions
4661 int isl_pw_qpolynomial_foreach_piece(
4662 __isl_keep isl_pw_qpolynomial *pwqp,
4663 int (*fn)(__isl_take isl_set *set,
4664 __isl_take isl_qpolynomial *qp,
4665 void *user), void *user);
4666 int isl_pw_qpolynomial_foreach_lifted_piece(
4667 __isl_keep isl_pw_qpolynomial *pwqp,
4668 int (*fn)(__isl_take isl_set *set,
4669 __isl_take isl_qpolynomial *qp,
4670 void *user), void *user);
4672 As usual, the function C<fn> should return C<0> on success
4673 and C<-1> on failure. The difference between
4674 C<isl_pw_qpolynomial_foreach_piece> and
4675 C<isl_pw_qpolynomial_foreach_lifted_piece> is that
4676 C<isl_pw_qpolynomial_foreach_lifted_piece> will first
4677 compute unique representations for all existentially quantified
4678 variables and then turn these existentially quantified variables
4679 into extra set variables, adapting the associated quasipolynomial
4680 accordingly. This means that the C<set> passed to C<fn>
4681 will not have any existentially quantified variables, but that
4682 the dimensions of the sets may be different for different
4683 invocations of C<fn>.
4685 To iterate over all terms in a quasipolynomial,
4688 int isl_qpolynomial_foreach_term(
4689 __isl_keep isl_qpolynomial *qp,
4690 int (*fn)(__isl_take isl_term *term,
4691 void *user), void *user);
4693 The terms themselves can be inspected and freed using
4696 unsigned isl_term_dim(__isl_keep isl_term *term,
4697 enum isl_dim_type type);
4698 void isl_term_get_num(__isl_keep isl_term *term,
4700 void isl_term_get_den(__isl_keep isl_term *term,
4702 int isl_term_get_exp(__isl_keep isl_term *term,
4703 enum isl_dim_type type, unsigned pos);
4704 __isl_give isl_aff *isl_term_get_div(
4705 __isl_keep isl_term *term, unsigned pos);
4706 void isl_term_free(__isl_take isl_term *term);
4708 Each term is a product of parameters, set variables and
4709 integer divisions. The function C<isl_term_get_exp>
4710 returns the exponent of a given dimensions in the given term.
4711 The C<isl_int>s in the arguments of C<isl_term_get_num>
4712 and C<isl_term_get_den> need to have been initialized
4713 using C<isl_int_init> before calling these functions.
4715 =head3 Properties of (Piecewise) Quasipolynomials
4717 To check whether a quasipolynomial is actually a constant,
4718 use the following function.
4720 int isl_qpolynomial_is_cst(__isl_keep isl_qpolynomial *qp,
4721 isl_int *n, isl_int *d);
4723 If C<qp> is a constant and if C<n> and C<d> are not C<NULL>
4724 then the numerator and denominator of the constant
4725 are returned in C<*n> and C<*d>, respectively.
4727 To check whether two union piecewise quasipolynomials are
4728 obviously equal, use
4730 int isl_union_pw_qpolynomial_plain_is_equal(
4731 __isl_keep isl_union_pw_qpolynomial *upwqp1,
4732 __isl_keep isl_union_pw_qpolynomial *upwqp2);
4734 =head3 Operations on (Piecewise) Quasipolynomials
4736 __isl_give isl_qpolynomial *isl_qpolynomial_scale(
4737 __isl_take isl_qpolynomial *qp, isl_int v);
4738 __isl_give isl_qpolynomial *isl_qpolynomial_neg(
4739 __isl_take isl_qpolynomial *qp);
4740 __isl_give isl_qpolynomial *isl_qpolynomial_add(
4741 __isl_take isl_qpolynomial *qp1,
4742 __isl_take isl_qpolynomial *qp2);
4743 __isl_give isl_qpolynomial *isl_qpolynomial_sub(
4744 __isl_take isl_qpolynomial *qp1,
4745 __isl_take isl_qpolynomial *qp2);
4746 __isl_give isl_qpolynomial *isl_qpolynomial_mul(
4747 __isl_take isl_qpolynomial *qp1,
4748 __isl_take isl_qpolynomial *qp2);
4749 __isl_give isl_qpolynomial *isl_qpolynomial_pow(
4750 __isl_take isl_qpolynomial *qp, unsigned exponent);
4752 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_add(
4753 __isl_take isl_pw_qpolynomial *pwqp1,
4754 __isl_take isl_pw_qpolynomial *pwqp2);
4755 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_sub(
4756 __isl_take isl_pw_qpolynomial *pwqp1,
4757 __isl_take isl_pw_qpolynomial *pwqp2);
4758 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_add_disjoint(
4759 __isl_take isl_pw_qpolynomial *pwqp1,
4760 __isl_take isl_pw_qpolynomial *pwqp2);
4761 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_neg(
4762 __isl_take isl_pw_qpolynomial *pwqp);
4763 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_mul(
4764 __isl_take isl_pw_qpolynomial *pwqp1,
4765 __isl_take isl_pw_qpolynomial *pwqp2);
4766 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_pow(
4767 __isl_take isl_pw_qpolynomial *pwqp, unsigned exponent);
4769 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_add(
4770 __isl_take isl_union_pw_qpolynomial *upwqp1,
4771 __isl_take isl_union_pw_qpolynomial *upwqp2);
4772 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_sub(
4773 __isl_take isl_union_pw_qpolynomial *upwqp1,
4774 __isl_take isl_union_pw_qpolynomial *upwqp2);
4775 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_mul(
4776 __isl_take isl_union_pw_qpolynomial *upwqp1,
4777 __isl_take isl_union_pw_qpolynomial *upwqp2);
4779 __isl_give isl_qpolynomial *isl_pw_qpolynomial_eval(
4780 __isl_take isl_pw_qpolynomial *pwqp,
4781 __isl_take isl_point *pnt);
4783 __isl_give isl_qpolynomial *isl_union_pw_qpolynomial_eval(
4784 __isl_take isl_union_pw_qpolynomial *upwqp,
4785 __isl_take isl_point *pnt);
4787 __isl_give isl_set *isl_pw_qpolynomial_domain(
4788 __isl_take isl_pw_qpolynomial *pwqp);
4789 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_intersect_domain(
4790 __isl_take isl_pw_qpolynomial *pwpq,
4791 __isl_take isl_set *set);
4792 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_intersect_params(
4793 __isl_take isl_pw_qpolynomial *pwpq,
4794 __isl_take isl_set *set);
4796 __isl_give isl_union_set *isl_union_pw_qpolynomial_domain(
4797 __isl_take isl_union_pw_qpolynomial *upwqp);
4798 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_intersect_domain(
4799 __isl_take isl_union_pw_qpolynomial *upwpq,
4800 __isl_take isl_union_set *uset);
4801 __isl_give isl_union_pw_qpolynomial *
4802 isl_union_pw_qpolynomial_intersect_params(
4803 __isl_take isl_union_pw_qpolynomial *upwpq,
4804 __isl_take isl_set *set);
4806 __isl_give isl_qpolynomial *isl_qpolynomial_align_params(
4807 __isl_take isl_qpolynomial *qp,
4808 __isl_take isl_space *model);
4810 __isl_give isl_qpolynomial *isl_qpolynomial_project_domain_on_params(
4811 __isl_take isl_qpolynomial *qp);
4812 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_project_domain_on_params(
4813 __isl_take isl_pw_qpolynomial *pwqp);
4815 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_coalesce(
4816 __isl_take isl_union_pw_qpolynomial *upwqp);
4818 __isl_give isl_qpolynomial *isl_qpolynomial_gist_params(
4819 __isl_take isl_qpolynomial *qp,
4820 __isl_take isl_set *context);
4821 __isl_give isl_qpolynomial *isl_qpolynomial_gist(
4822 __isl_take isl_qpolynomial *qp,
4823 __isl_take isl_set *context);
4825 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_gist_params(
4826 __isl_take isl_pw_qpolynomial *pwqp,
4827 __isl_take isl_set *context);
4828 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_gist(
4829 __isl_take isl_pw_qpolynomial *pwqp,
4830 __isl_take isl_set *context);
4832 __isl_give isl_union_pw_qpolynomial *
4833 isl_union_pw_qpolynomial_gist_params(
4834 __isl_take isl_union_pw_qpolynomial *upwqp,
4835 __isl_take isl_set *context);
4836 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_gist(
4837 __isl_take isl_union_pw_qpolynomial *upwqp,
4838 __isl_take isl_union_set *context);
4840 The gist operation applies the gist operation to each of
4841 the cells in the domain of the input piecewise quasipolynomial.
4842 The context is also exploited
4843 to simplify the quasipolynomials associated to each cell.
4845 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_to_polynomial(
4846 __isl_take isl_pw_qpolynomial *pwqp, int sign);
4847 __isl_give isl_union_pw_qpolynomial *
4848 isl_union_pw_qpolynomial_to_polynomial(
4849 __isl_take isl_union_pw_qpolynomial *upwqp, int sign);
4851 Approximate each quasipolynomial by a polynomial. If C<sign> is positive,
4852 the polynomial will be an overapproximation. If C<sign> is negative,
4853 it will be an underapproximation. If C<sign> is zero, the approximation
4854 will lie somewhere in between.
4856 =head2 Bounds on Piecewise Quasipolynomials and Piecewise Quasipolynomial Reductions
4858 A piecewise quasipolynomial reduction is a piecewise
4859 reduction (or fold) of quasipolynomials.
4860 In particular, the reduction can be maximum or a minimum.
4861 The objects are mainly used to represent the result of
4862 an upper or lower bound on a quasipolynomial over its domain,
4863 i.e., as the result of the following function.
4865 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_bound(
4866 __isl_take isl_pw_qpolynomial *pwqp,
4867 enum isl_fold type, int *tight);
4869 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_bound(
4870 __isl_take isl_union_pw_qpolynomial *upwqp,
4871 enum isl_fold type, int *tight);
4873 The C<type> argument may be either C<isl_fold_min> or C<isl_fold_max>.
4874 If C<tight> is not C<NULL>, then C<*tight> is set to C<1>
4875 is the returned bound is known be tight, i.e., for each value
4876 of the parameters there is at least
4877 one element in the domain that reaches the bound.
4878 If the domain of C<pwqp> is not wrapping, then the bound is computed
4879 over all elements in that domain and the result has a purely parametric
4880 domain. If the domain of C<pwqp> is wrapping, then the bound is
4881 computed over the range of the wrapped relation. The domain of the
4882 wrapped relation becomes the domain of the result.
4884 A (piecewise) quasipolynomial reduction can be copied or freed using the
4885 following functions.
4887 __isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_copy(
4888 __isl_keep isl_qpolynomial_fold *fold);
4889 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_copy(
4890 __isl_keep isl_pw_qpolynomial_fold *pwf);
4891 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_copy(
4892 __isl_keep isl_union_pw_qpolynomial_fold *upwf);
4893 void isl_qpolynomial_fold_free(
4894 __isl_take isl_qpolynomial_fold *fold);
4895 void *isl_pw_qpolynomial_fold_free(
4896 __isl_take isl_pw_qpolynomial_fold *pwf);
4897 void *isl_union_pw_qpolynomial_fold_free(
4898 __isl_take isl_union_pw_qpolynomial_fold *upwf);
4900 =head3 Printing Piecewise Quasipolynomial Reductions
4902 Piecewise quasipolynomial reductions can be printed
4903 using the following function.
4905 __isl_give isl_printer *isl_printer_print_pw_qpolynomial_fold(
4906 __isl_take isl_printer *p,
4907 __isl_keep isl_pw_qpolynomial_fold *pwf);
4908 __isl_give isl_printer *isl_printer_print_union_pw_qpolynomial_fold(
4909 __isl_take isl_printer *p,
4910 __isl_keep isl_union_pw_qpolynomial_fold *upwf);
4912 For C<isl_printer_print_pw_qpolynomial_fold>,
4913 output format of the printer
4914 needs to be set to either C<ISL_FORMAT_ISL> or C<ISL_FORMAT_C>.
4915 For C<isl_printer_print_union_pw_qpolynomial_fold>,
4916 output format of the printer
4917 needs to be set to C<ISL_FORMAT_ISL>.
4918 In case of printing in C<ISL_FORMAT_C>, the user may want
4919 to set the names of all dimensions
4921 __isl_give isl_pw_qpolynomial_fold *
4922 isl_pw_qpolynomial_fold_set_dim_name(
4923 __isl_take isl_pw_qpolynomial_fold *pwf,
4924 enum isl_dim_type type, unsigned pos,
4927 =head3 Inspecting (Piecewise) Quasipolynomial Reductions
4929 To iterate over all piecewise quasipolynomial reductions in a union
4930 piecewise quasipolynomial reduction, use the following function
4932 int isl_union_pw_qpolynomial_fold_foreach_pw_qpolynomial_fold(
4933 __isl_keep isl_union_pw_qpolynomial_fold *upwf,
4934 int (*fn)(__isl_take isl_pw_qpolynomial_fold *pwf,
4935 void *user), void *user);
4937 To iterate over the cells in a piecewise quasipolynomial reduction,
4938 use either of the following two functions
4940 int isl_pw_qpolynomial_fold_foreach_piece(
4941 __isl_keep isl_pw_qpolynomial_fold *pwf,
4942 int (*fn)(__isl_take isl_set *set,
4943 __isl_take isl_qpolynomial_fold *fold,
4944 void *user), void *user);
4945 int isl_pw_qpolynomial_fold_foreach_lifted_piece(
4946 __isl_keep isl_pw_qpolynomial_fold *pwf,
4947 int (*fn)(__isl_take isl_set *set,
4948 __isl_take isl_qpolynomial_fold *fold,
4949 void *user), void *user);
4951 See L<Inspecting (Piecewise) Quasipolynomials> for an explanation
4952 of the difference between these two functions.
4954 To iterate over all quasipolynomials in a reduction, use
4956 int isl_qpolynomial_fold_foreach_qpolynomial(
4957 __isl_keep isl_qpolynomial_fold *fold,
4958 int (*fn)(__isl_take isl_qpolynomial *qp,
4959 void *user), void *user);
4961 =head3 Properties of Piecewise Quasipolynomial Reductions
4963 To check whether two union piecewise quasipolynomial reductions are
4964 obviously equal, use
4966 int isl_union_pw_qpolynomial_fold_plain_is_equal(
4967 __isl_keep isl_union_pw_qpolynomial_fold *upwf1,
4968 __isl_keep isl_union_pw_qpolynomial_fold *upwf2);
4970 =head3 Operations on Piecewise Quasipolynomial Reductions
4972 __isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_scale(
4973 __isl_take isl_qpolynomial_fold *fold, isl_int v);
4975 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_add(
4976 __isl_take isl_pw_qpolynomial_fold *pwf1,
4977 __isl_take isl_pw_qpolynomial_fold *pwf2);
4979 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_fold(
4980 __isl_take isl_pw_qpolynomial_fold *pwf1,
4981 __isl_take isl_pw_qpolynomial_fold *pwf2);
4983 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_fold(
4984 __isl_take isl_union_pw_qpolynomial_fold *upwf1,
4985 __isl_take isl_union_pw_qpolynomial_fold *upwf2);
4987 __isl_give isl_qpolynomial *isl_pw_qpolynomial_fold_eval(
4988 __isl_take isl_pw_qpolynomial_fold *pwf,
4989 __isl_take isl_point *pnt);
4991 __isl_give isl_qpolynomial *isl_union_pw_qpolynomial_fold_eval(
4992 __isl_take isl_union_pw_qpolynomial_fold *upwf,
4993 __isl_take isl_point *pnt);
4995 __isl_give isl_pw_qpolynomial_fold *
4996 isl_pw_qpolynomial_fold_intersect_params(
4997 __isl_take isl_pw_qpolynomial_fold *pwf,
4998 __isl_take isl_set *set);
5000 __isl_give isl_union_set *isl_union_pw_qpolynomial_fold_domain(
5001 __isl_take isl_union_pw_qpolynomial_fold *upwf);
5002 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_intersect_domain(
5003 __isl_take isl_union_pw_qpolynomial_fold *upwf,
5004 __isl_take isl_union_set *uset);
5005 __isl_give isl_union_pw_qpolynomial_fold *
5006 isl_union_pw_qpolynomial_fold_intersect_params(
5007 __isl_take isl_union_pw_qpolynomial_fold *upwf,
5008 __isl_take isl_set *set);
5010 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_project_domain_on_params(
5011 __isl_take isl_pw_qpolynomial_fold *pwf);
5013 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_coalesce(
5014 __isl_take isl_pw_qpolynomial_fold *pwf);
5016 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_coalesce(
5017 __isl_take isl_union_pw_qpolynomial_fold *upwf);
5019 __isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_gist_params(
5020 __isl_take isl_qpolynomial_fold *fold,
5021 __isl_take isl_set *context);
5022 __isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_gist(
5023 __isl_take isl_qpolynomial_fold *fold,
5024 __isl_take isl_set *context);
5026 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_gist(
5027 __isl_take isl_pw_qpolynomial_fold *pwf,
5028 __isl_take isl_set *context);
5029 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_gist_params(
5030 __isl_take isl_pw_qpolynomial_fold *pwf,
5031 __isl_take isl_set *context);
5033 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_gist(
5034 __isl_take isl_union_pw_qpolynomial_fold *upwf,
5035 __isl_take isl_union_set *context);
5036 __isl_give isl_union_pw_qpolynomial_fold *
5037 isl_union_pw_qpolynomial_fold_gist_params(
5038 __isl_take isl_union_pw_qpolynomial_fold *upwf,
5039 __isl_take isl_set *context);
5041 The gist operation applies the gist operation to each of
5042 the cells in the domain of the input piecewise quasipolynomial reduction.
5043 In future, the operation will also exploit the context
5044 to simplify the quasipolynomial reductions associated to each cell.
5046 __isl_give isl_pw_qpolynomial_fold *
5047 isl_set_apply_pw_qpolynomial_fold(
5048 __isl_take isl_set *set,
5049 __isl_take isl_pw_qpolynomial_fold *pwf,
5051 __isl_give isl_pw_qpolynomial_fold *
5052 isl_map_apply_pw_qpolynomial_fold(
5053 __isl_take isl_map *map,
5054 __isl_take isl_pw_qpolynomial_fold *pwf,
5056 __isl_give isl_union_pw_qpolynomial_fold *
5057 isl_union_set_apply_union_pw_qpolynomial_fold(
5058 __isl_take isl_union_set *uset,
5059 __isl_take isl_union_pw_qpolynomial_fold *upwf,
5061 __isl_give isl_union_pw_qpolynomial_fold *
5062 isl_union_map_apply_union_pw_qpolynomial_fold(
5063 __isl_take isl_union_map *umap,
5064 __isl_take isl_union_pw_qpolynomial_fold *upwf,
5067 The functions taking a map
5068 compose the given map with the given piecewise quasipolynomial reduction.
5069 That is, compute a bound (of the same type as C<pwf> or C<upwf> itself)
5070 over all elements in the intersection of the range of the map
5071 and the domain of the piecewise quasipolynomial reduction
5072 as a function of an element in the domain of the map.
5073 The functions taking a set compute a bound over all elements in the
5074 intersection of the set and the domain of the
5075 piecewise quasipolynomial reduction.
5077 =head2 Parametric Vertex Enumeration
5079 The parametric vertex enumeration described in this section
5080 is mainly intended to be used internally and by the C<barvinok>
5083 #include <isl/vertices.h>
5084 __isl_give isl_vertices *isl_basic_set_compute_vertices(
5085 __isl_keep isl_basic_set *bset);
5087 The function C<isl_basic_set_compute_vertices> performs the
5088 actual computation of the parametric vertices and the chamber
5089 decomposition and store the result in an C<isl_vertices> object.
5090 This information can be queried by either iterating over all
5091 the vertices or iterating over all the chambers or cells
5092 and then iterating over all vertices that are active on the chamber.
5094 int isl_vertices_foreach_vertex(
5095 __isl_keep isl_vertices *vertices,
5096 int (*fn)(__isl_take isl_vertex *vertex, void *user),
5099 int isl_vertices_foreach_cell(
5100 __isl_keep isl_vertices *vertices,
5101 int (*fn)(__isl_take isl_cell *cell, void *user),
5103 int isl_cell_foreach_vertex(__isl_keep isl_cell *cell,
5104 int (*fn)(__isl_take isl_vertex *vertex, void *user),
5107 Other operations that can be performed on an C<isl_vertices> object are
5110 isl_ctx *isl_vertices_get_ctx(
5111 __isl_keep isl_vertices *vertices);
5112 int isl_vertices_get_n_vertices(
5113 __isl_keep isl_vertices *vertices);
5114 void isl_vertices_free(__isl_take isl_vertices *vertices);
5116 Vertices can be inspected and destroyed using the following functions.
5118 isl_ctx *isl_vertex_get_ctx(__isl_keep isl_vertex *vertex);
5119 int isl_vertex_get_id(__isl_keep isl_vertex *vertex);
5120 __isl_give isl_basic_set *isl_vertex_get_domain(
5121 __isl_keep isl_vertex *vertex);
5122 __isl_give isl_basic_set *isl_vertex_get_expr(
5123 __isl_keep isl_vertex *vertex);
5124 void isl_vertex_free(__isl_take isl_vertex *vertex);
5126 C<isl_vertex_get_expr> returns a singleton parametric set describing
5127 the vertex, while C<isl_vertex_get_domain> returns the activity domain
5129 Note that C<isl_vertex_get_domain> and C<isl_vertex_get_expr> return
5130 B<rational> basic sets, so they should mainly be used for inspection
5131 and should not be mixed with integer sets.
5133 Chambers can be inspected and destroyed using the following functions.
5135 isl_ctx *isl_cell_get_ctx(__isl_keep isl_cell *cell);
5136 __isl_give isl_basic_set *isl_cell_get_domain(
5137 __isl_keep isl_cell *cell);
5138 void isl_cell_free(__isl_take isl_cell *cell);
5140 =head1 Polyhedral Compilation Library
5142 This section collects functionality in C<isl> that has been specifically
5143 designed for use during polyhedral compilation.
5145 =head2 Dependence Analysis
5147 C<isl> contains specialized functionality for performing
5148 array dataflow analysis. That is, given a I<sink> access relation
5149 and a collection of possible I<source> access relations,
5150 C<isl> can compute relations that describe
5151 for each iteration of the sink access, which iteration
5152 of which of the source access relations was the last
5153 to access the same data element before the given iteration
5155 The resulting dependence relations map source iterations
5156 to the corresponding sink iterations.
5157 To compute standard flow dependences, the sink should be
5158 a read, while the sources should be writes.
5159 If any of the source accesses are marked as being I<may>
5160 accesses, then there will be a dependence from the last
5161 I<must> access B<and> from any I<may> access that follows
5162 this last I<must> access.
5163 In particular, if I<all> sources are I<may> accesses,
5164 then memory based dependence analysis is performed.
5165 If, on the other hand, all sources are I<must> accesses,
5166 then value based dependence analysis is performed.
5168 #include <isl/flow.h>
5170 typedef int (*isl_access_level_before)(void *first, void *second);
5172 __isl_give isl_access_info *isl_access_info_alloc(
5173 __isl_take isl_map *sink,
5174 void *sink_user, isl_access_level_before fn,
5176 __isl_give isl_access_info *isl_access_info_add_source(
5177 __isl_take isl_access_info *acc,
5178 __isl_take isl_map *source, int must,
5180 void *isl_access_info_free(__isl_take isl_access_info *acc);
5182 __isl_give isl_flow *isl_access_info_compute_flow(
5183 __isl_take isl_access_info *acc);
5185 int isl_flow_foreach(__isl_keep isl_flow *deps,
5186 int (*fn)(__isl_take isl_map *dep, int must,
5187 void *dep_user, void *user),
5189 __isl_give isl_map *isl_flow_get_no_source(
5190 __isl_keep isl_flow *deps, int must);
5191 void isl_flow_free(__isl_take isl_flow *deps);
5193 The function C<isl_access_info_compute_flow> performs the actual
5194 dependence analysis. The other functions are used to construct
5195 the input for this function or to read off the output.
5197 The input is collected in an C<isl_access_info>, which can
5198 be created through a call to C<isl_access_info_alloc>.
5199 The arguments to this functions are the sink access relation
5200 C<sink>, a token C<sink_user> used to identify the sink
5201 access to the user, a callback function for specifying the
5202 relative order of source and sink accesses, and the number
5203 of source access relations that will be added.
5204 The callback function has type C<int (*)(void *first, void *second)>.
5205 The function is called with two user supplied tokens identifying
5206 either a source or the sink and it should return the shared nesting
5207 level and the relative order of the two accesses.
5208 In particular, let I<n> be the number of loops shared by
5209 the two accesses. If C<first> precedes C<second> textually,
5210 then the function should return I<2 * n + 1>; otherwise,
5211 it should return I<2 * n>.
5212 The sources can be added to the C<isl_access_info> by performing
5213 (at most) C<max_source> calls to C<isl_access_info_add_source>.
5214 C<must> indicates whether the source is a I<must> access
5215 or a I<may> access. Note that a multi-valued access relation
5216 should only be marked I<must> if every iteration in the domain
5217 of the relation accesses I<all> elements in its image.
5218 The C<source_user> token is again used to identify
5219 the source access. The range of the source access relation
5220 C<source> should have the same dimension as the range
5221 of the sink access relation.
5222 The C<isl_access_info_free> function should usually not be
5223 called explicitly, because it is called implicitly by
5224 C<isl_access_info_compute_flow>.
5226 The result of the dependence analysis is collected in an
5227 C<isl_flow>. There may be elements of
5228 the sink access for which no preceding source access could be
5229 found or for which all preceding sources are I<may> accesses.
5230 The relations containing these elements can be obtained through
5231 calls to C<isl_flow_get_no_source>, the first with C<must> set
5232 and the second with C<must> unset.
5233 In the case of standard flow dependence analysis,
5234 with the sink a read and the sources I<must> writes,
5235 the first relation corresponds to the reads from uninitialized
5236 array elements and the second relation is empty.
5237 The actual flow dependences can be extracted using
5238 C<isl_flow_foreach>. This function will call the user-specified
5239 callback function C<fn> for each B<non-empty> dependence between
5240 a source and the sink. The callback function is called
5241 with four arguments, the actual flow dependence relation
5242 mapping source iterations to sink iterations, a boolean that
5243 indicates whether it is a I<must> or I<may> dependence, a token
5244 identifying the source and an additional C<void *> with value
5245 equal to the third argument of the C<isl_flow_foreach> call.
5246 A dependence is marked I<must> if it originates from a I<must>
5247 source and if it is not followed by any I<may> sources.
5249 After finishing with an C<isl_flow>, the user should call
5250 C<isl_flow_free> to free all associated memory.
5252 A higher-level interface to dependence analysis is provided
5253 by the following function.
5255 #include <isl/flow.h>
5257 int isl_union_map_compute_flow(__isl_take isl_union_map *sink,
5258 __isl_take isl_union_map *must_source,
5259 __isl_take isl_union_map *may_source,
5260 __isl_take isl_union_map *schedule,
5261 __isl_give isl_union_map **must_dep,
5262 __isl_give isl_union_map **may_dep,
5263 __isl_give isl_union_map **must_no_source,
5264 __isl_give isl_union_map **may_no_source);
5266 The arrays are identified by the tuple names of the ranges
5267 of the accesses. The iteration domains by the tuple names
5268 of the domains of the accesses and of the schedule.
5269 The relative order of the iteration domains is given by the
5270 schedule. The relations returned through C<must_no_source>
5271 and C<may_no_source> are subsets of C<sink>.
5272 Any of C<must_dep>, C<may_dep>, C<must_no_source>
5273 or C<may_no_source> may be C<NULL>, but a C<NULL> value for
5274 any of the other arguments is treated as an error.
5276 =head3 Interaction with Dependence Analysis
5278 During the dependence analysis, we frequently need to perform
5279 the following operation. Given a relation between sink iterations
5280 and potential source iterations from a particular source domain,
5281 what is the last potential source iteration corresponding to each
5282 sink iteration. It can sometimes be convenient to adjust
5283 the set of potential source iterations before or after each such operation.
5284 The prototypical example is fuzzy array dataflow analysis,
5285 where we need to analyze if, based on data-dependent constraints,
5286 the sink iteration can ever be executed without one or more of
5287 the corresponding potential source iterations being executed.
5288 If so, we can introduce extra parameters and select an unknown
5289 but fixed source iteration from the potential source iterations.
5290 To be able to perform such manipulations, C<isl> provides the following
5293 #include <isl/flow.h>
5295 typedef __isl_give isl_restriction *(*isl_access_restrict)(
5296 __isl_keep isl_map *source_map,
5297 __isl_keep isl_set *sink, void *source_user,
5299 __isl_give isl_access_info *isl_access_info_set_restrict(
5300 __isl_take isl_access_info *acc,
5301 isl_access_restrict fn, void *user);
5303 The function C<isl_access_info_set_restrict> should be called
5304 before calling C<isl_access_info_compute_flow> and registers a callback function
5305 that will be called any time C<isl> is about to compute the last
5306 potential source. The first argument is the (reverse) proto-dependence,
5307 mapping sink iterations to potential source iterations.
5308 The second argument represents the sink iterations for which
5309 we want to compute the last source iteration.
5310 The third argument is the token corresponding to the source
5311 and the final argument is the token passed to C<isl_access_info_set_restrict>.
5312 The callback is expected to return a restriction on either the input or
5313 the output of the operation computing the last potential source.
5314 If the input needs to be restricted then restrictions are needed
5315 for both the source and the sink iterations. The sink iterations
5316 and the potential source iterations will be intersected with these sets.
5317 If the output needs to be restricted then only a restriction on the source
5318 iterations is required.
5319 If any error occurs, the callback should return C<NULL>.
5320 An C<isl_restriction> object can be created, freed and inspected
5321 using the following functions.
5323 #include <isl/flow.h>
5325 __isl_give isl_restriction *isl_restriction_input(
5326 __isl_take isl_set *source_restr,
5327 __isl_take isl_set *sink_restr);
5328 __isl_give isl_restriction *isl_restriction_output(
5329 __isl_take isl_set *source_restr);
5330 __isl_give isl_restriction *isl_restriction_none(
5331 __isl_take isl_map *source_map);
5332 __isl_give isl_restriction *isl_restriction_empty(
5333 __isl_take isl_map *source_map);
5334 void *isl_restriction_free(
5335 __isl_take isl_restriction *restr);
5336 isl_ctx *isl_restriction_get_ctx(
5337 __isl_keep isl_restriction *restr);
5339 C<isl_restriction_none> and C<isl_restriction_empty> are special
5340 cases of C<isl_restriction_input>. C<isl_restriction_none>
5341 is essentially equivalent to
5343 isl_restriction_input(isl_set_universe(
5344 isl_space_range(isl_map_get_space(source_map))),
5346 isl_space_domain(isl_map_get_space(source_map))));
5348 whereas C<isl_restriction_empty> is essentially equivalent to
5350 isl_restriction_input(isl_set_empty(
5351 isl_space_range(isl_map_get_space(source_map))),
5353 isl_space_domain(isl_map_get_space(source_map))));
5357 B<The functionality described in this section is fairly new
5358 and may be subject to change.>
5360 The following function can be used to compute a schedule
5361 for a union of domains.
5362 By default, the algorithm used to construct the schedule is similar
5363 to that of C<Pluto>.
5364 Alternatively, Feautrier's multi-dimensional scheduling algorithm can
5366 The generated schedule respects all C<validity> dependences.
5367 That is, all dependence distances over these dependences in the
5368 scheduled space are lexicographically positive.
5369 The default algorithm tries to minimize the dependence distances over
5370 C<proximity> dependences.
5371 Moreover, it tries to obtain sequences (bands) of schedule dimensions
5372 for groups of domains where the dependence distances have only
5373 non-negative values.
5374 When using Feautrier's algorithm, the C<proximity> dependence
5375 distances are only minimized during the extension to a
5376 full-dimensional schedule.
5378 #include <isl/schedule.h>
5379 __isl_give isl_schedule *isl_union_set_compute_schedule(
5380 __isl_take isl_union_set *domain,
5381 __isl_take isl_union_map *validity,
5382 __isl_take isl_union_map *proximity);
5383 void *isl_schedule_free(__isl_take isl_schedule *sched);
5385 A mapping from the domains to the scheduled space can be obtained
5386 from an C<isl_schedule> using the following function.
5388 __isl_give isl_union_map *isl_schedule_get_map(
5389 __isl_keep isl_schedule *sched);
5391 A representation of the schedule can be printed using
5393 __isl_give isl_printer *isl_printer_print_schedule(
5394 __isl_take isl_printer *p,
5395 __isl_keep isl_schedule *schedule);
5397 A representation of the schedule as a forest of bands can be obtained
5398 using the following function.
5400 __isl_give isl_band_list *isl_schedule_get_band_forest(
5401 __isl_keep isl_schedule *schedule);
5403 The individual bands can be visited in depth-first post-order
5404 using the following function.
5406 #include <isl/schedule.h>
5407 int isl_schedule_foreach_band(
5408 __isl_keep isl_schedule *sched,
5409 int (*fn)(__isl_keep isl_band *band, void *user),
5412 The list can be manipulated as explained in L<"Lists">.
5413 The bands inside the list can be copied and freed using the following
5416 #include <isl/band.h>
5417 __isl_give isl_band *isl_band_copy(
5418 __isl_keep isl_band *band);
5419 void *isl_band_free(__isl_take isl_band *band);
5421 Each band contains zero or more scheduling dimensions.
5422 These are referred to as the members of the band.
5423 The section of the schedule that corresponds to the band is
5424 referred to as the partial schedule of the band.
5425 For those nodes that participate in a band, the outer scheduling
5426 dimensions form the prefix schedule, while the inner scheduling
5427 dimensions form the suffix schedule.
5428 That is, if we take a cut of the band forest, then the union of
5429 the concatenations of the prefix, partial and suffix schedules of
5430 each band in the cut is equal to the entire schedule (modulo
5431 some possible padding at the end with zero scheduling dimensions).
5432 The properties of a band can be inspected using the following functions.
5434 #include <isl/band.h>
5435 isl_ctx *isl_band_get_ctx(__isl_keep isl_band *band);
5437 int isl_band_has_children(__isl_keep isl_band *band);
5438 __isl_give isl_band_list *isl_band_get_children(
5439 __isl_keep isl_band *band);
5441 __isl_give isl_union_map *isl_band_get_prefix_schedule(
5442 __isl_keep isl_band *band);
5443 __isl_give isl_union_map *isl_band_get_partial_schedule(
5444 __isl_keep isl_band *band);
5445 __isl_give isl_union_map *isl_band_get_suffix_schedule(
5446 __isl_keep isl_band *band);
5448 int isl_band_n_member(__isl_keep isl_band *band);
5449 int isl_band_member_is_zero_distance(
5450 __isl_keep isl_band *band, int pos);
5452 int isl_band_list_foreach_band(
5453 __isl_keep isl_band_list *list,
5454 int (*fn)(__isl_keep isl_band *band, void *user),
5457 Note that a scheduling dimension is considered to be ``zero
5458 distance'' if it does not carry any proximity dependences
5460 That is, if the dependence distances of the proximity
5461 dependences are all zero in that direction (for fixed
5462 iterations of outer bands).
5463 Like C<isl_schedule_foreach_band>,
5464 the function C<isl_band_list_foreach_band> calls C<fn> on the bands
5465 in depth-first post-order.
5467 A band can be tiled using the following function.
5469 #include <isl/band.h>
5470 int isl_band_tile(__isl_keep isl_band *band,
5471 __isl_take isl_vec *sizes);
5473 int isl_options_set_tile_scale_tile_loops(isl_ctx *ctx,
5475 int isl_options_get_tile_scale_tile_loops(isl_ctx *ctx);
5476 int isl_options_set_tile_shift_point_loops(isl_ctx *ctx,
5478 int isl_options_get_tile_shift_point_loops(isl_ctx *ctx);
5480 The C<isl_band_tile> function tiles the band using the given tile sizes
5481 inside its schedule.
5482 A new child band is created to represent the point loops and it is
5483 inserted between the modified band and its children.
5484 The C<tile_scale_tile_loops> option specifies whether the tile
5485 loops iterators should be scaled by the tile sizes.
5486 If the C<tile_shift_point_loops> option is set, then the point loops
5487 are shifted to start at zero.
5489 A band can be split into two nested bands using the following function.
5491 int isl_band_split(__isl_keep isl_band *band, int pos);
5493 The resulting outer band contains the first C<pos> dimensions of C<band>
5494 while the inner band contains the remaining dimensions.
5496 A representation of the band can be printed using
5498 #include <isl/band.h>
5499 __isl_give isl_printer *isl_printer_print_band(
5500 __isl_take isl_printer *p,
5501 __isl_keep isl_band *band);
5505 #include <isl/schedule.h>
5506 int isl_options_set_schedule_max_coefficient(
5507 isl_ctx *ctx, int val);
5508 int isl_options_get_schedule_max_coefficient(
5510 int isl_options_set_schedule_max_constant_term(
5511 isl_ctx *ctx, int val);
5512 int isl_options_get_schedule_max_constant_term(
5514 int isl_options_set_schedule_fuse(isl_ctx *ctx, int val);
5515 int isl_options_get_schedule_fuse(isl_ctx *ctx);
5516 int isl_options_set_schedule_maximize_band_depth(
5517 isl_ctx *ctx, int val);
5518 int isl_options_get_schedule_maximize_band_depth(
5520 int isl_options_set_schedule_outer_zero_distance(
5521 isl_ctx *ctx, int val);
5522 int isl_options_get_schedule_outer_zero_distance(
5524 int isl_options_set_schedule_split_scaled(
5525 isl_ctx *ctx, int val);
5526 int isl_options_get_schedule_split_scaled(
5528 int isl_options_set_schedule_algorithm(
5529 isl_ctx *ctx, int val);
5530 int isl_options_get_schedule_algorithm(
5532 int isl_options_set_schedule_separate_components(
5533 isl_ctx *ctx, int val);
5534 int isl_options_get_schedule_separate_components(
5539 =item * schedule_max_coefficient
5541 This option enforces that the coefficients for variable and parameter
5542 dimensions in the calculated schedule are not larger than the specified value.
5543 This option can significantly increase the speed of the scheduling calculation
5544 and may also prevent fusing of unrelated dimensions. A value of -1 means that
5545 this option does not introduce bounds on the variable or parameter
5548 =item * schedule_max_constant_term
5550 This option enforces that the constant coefficients in the calculated schedule
5551 are not larger than the maximal constant term. This option can significantly
5552 increase the speed of the scheduling calculation and may also prevent fusing of
5553 unrelated dimensions. A value of -1 means that this option does not introduce
5554 bounds on the constant coefficients.
5556 =item * schedule_fuse
5558 This option controls the level of fusion.
5559 If this option is set to C<ISL_SCHEDULE_FUSE_MIN>, then loops in the
5560 resulting schedule will be distributed as much as possible.
5561 If this option is set to C<ISL_SCHEDULE_FUSE_MAX>, then C<isl> will
5562 try to fuse loops in the resulting schedule.
5564 =item * schedule_maximize_band_depth
5566 If this option is set, we do not split bands at the point
5567 where we detect splitting is necessary. Instead, we
5568 backtrack and split bands as early as possible. This
5569 reduces the number of splits and maximizes the width of
5570 the bands. Wider bands give more possibilities for tiling.
5571 Note that if the C<schedule_fuse> option is set to C<ISL_SCHEDULE_FUSE_MIN>,
5572 then bands will be split as early as possible, even if there is no need.
5573 The C<schedule_maximize_band_depth> option therefore has no effect in this case.
5575 =item * schedule_outer_zero_distance
5577 If this option is set, then we try to construct schedules
5578 where the outermost scheduling dimension in each band
5579 results in a zero dependence distance over the proximity
5582 =item * schedule_split_scaled
5584 If this option is set, then we try to construct schedules in which the
5585 constant term is split off from the linear part if the linear parts of
5586 the scheduling rows for all nodes in the graphs have a common non-trivial
5588 The constant term is then placed in a separate band and the linear
5591 =item * schedule_algorithm
5593 Selects the scheduling algorithm to be used.
5594 Available scheduling algorithms are C<ISL_SCHEDULE_ALGORITHM_ISL>
5595 and C<ISL_SCHEDULE_ALGORITHM_FEAUTRIER>.
5597 =item * schedule_separate_components
5599 If at any point the dependence graph contains any (weakly connected) components,
5600 then these components are scheduled separately.
5601 If this option is not set, then some iterations of the domains
5602 in these components may be scheduled together.
5603 If this option is set, then the components are given consecutive
5608 =head2 AST Generation
5610 This section describes the C<isl> functionality for generating
5611 ASTs that visit all the elements
5612 in a domain in an order specified by a schedule.
5613 In particular, given a C<isl_union_map>, an AST is generated
5614 that visits all the elements in the domain of the C<isl_union_map>
5615 according to the lexicographic order of the corresponding image
5616 element(s). If the range of the C<isl_union_map> consists of
5617 elements in more than one space, then each of these spaces is handled
5618 separately in an arbitrary order.
5619 It should be noted that the image elements only specify the I<order>
5620 in which the corresponding domain elements should be visited.
5621 No direct relation between the image elements and the loop iterators
5622 in the generated AST should be assumed.
5624 Each AST is generated within a build. The initial build
5625 simply specifies the constraints on the parameters (if any)
5626 and can be created, inspected, copied and freed using the following functions.
5628 #include <isl/ast_build.h>
5629 __isl_give isl_ast_build *isl_ast_build_from_context(
5630 __isl_take isl_set *set);
5631 isl_ctx *isl_ast_build_get_ctx(
5632 __isl_keep isl_ast_build *build);
5633 __isl_give isl_ast_build *isl_ast_build_copy(
5634 __isl_keep isl_ast_build *build);
5635 void *isl_ast_build_free(
5636 __isl_take isl_ast_build *build);
5638 The C<set> argument is usually a parameter set with zero or more parameters.
5639 More C<isl_ast_build> functions are described in L</"Nested AST Generation">
5640 and L</"Fine-grained Control over AST Generation">.
5641 Finally, the AST itself can be constructed using the following
5644 #include <isl/ast_build.h>
5645 __isl_give isl_ast_node *isl_ast_build_ast_from_schedule(
5646 __isl_keep isl_ast_build *build,
5647 __isl_take isl_union_map *schedule);
5649 =head3 Inspecting the AST
5651 The basic properties of an AST node can be obtained as follows.
5653 #include <isl/ast.h>
5654 isl_ctx *isl_ast_node_get_ctx(
5655 __isl_keep isl_ast_node *node);
5656 enum isl_ast_node_type isl_ast_node_get_type(
5657 __isl_keep isl_ast_node *node);
5659 The type of an AST node is one of
5660 C<isl_ast_node_for>,
5662 C<isl_ast_node_block> or
5663 C<isl_ast_node_user>.
5664 An C<isl_ast_node_for> represents a for node.
5665 An C<isl_ast_node_if> represents an if node.
5666 An C<isl_ast_node_block> represents a compound node.
5667 An C<isl_ast_node_user> represents an expression statement.
5668 An expression statement typically corresponds to a domain element, i.e.,
5669 one of the elements that is visited by the AST.
5671 Each type of node has its own additional properties.
5673 #include <isl/ast.h>
5674 __isl_give isl_ast_expr *isl_ast_node_for_get_iterator(
5675 __isl_keep isl_ast_node *node);
5676 __isl_give isl_ast_expr *isl_ast_node_for_get_init(
5677 __isl_keep isl_ast_node *node);
5678 __isl_give isl_ast_expr *isl_ast_node_for_get_cond(
5679 __isl_keep isl_ast_node *node);
5680 __isl_give isl_ast_expr *isl_ast_node_for_get_inc(
5681 __isl_keep isl_ast_node *node);
5682 __isl_give isl_ast_node *isl_ast_node_for_get_body(
5683 __isl_keep isl_ast_node *node);
5684 int isl_ast_node_for_is_degenerate(
5685 __isl_keep isl_ast_node *node);
5687 An C<isl_ast_for> is considered degenerate if it is known to execute
5690 #include <isl/ast.h>
5691 __isl_give isl_ast_expr *isl_ast_node_if_get_cond(
5692 __isl_keep isl_ast_node *node);
5693 __isl_give isl_ast_node *isl_ast_node_if_get_then(
5694 __isl_keep isl_ast_node *node);
5695 int isl_ast_node_if_has_else(
5696 __isl_keep isl_ast_node *node);
5697 __isl_give isl_ast_node *isl_ast_node_if_get_else(
5698 __isl_keep isl_ast_node *node);
5700 __isl_give isl_ast_node_list *
5701 isl_ast_node_block_get_children(
5702 __isl_keep isl_ast_node *node);
5704 __isl_give isl_ast_expr *isl_ast_node_user_get_expr(
5705 __isl_keep isl_ast_node *node);
5707 Each of the returned C<isl_ast_expr>s can in turn be inspected using
5708 the following functions.
5710 #include <isl/ast.h>
5711 isl_ctx *isl_ast_expr_get_ctx(
5712 __isl_keep isl_ast_expr *expr);
5713 enum isl_ast_expr_type isl_ast_expr_get_type(
5714 __isl_keep isl_ast_expr *expr);
5716 The type of an AST expression is one of
5718 C<isl_ast_expr_id> or
5719 C<isl_ast_expr_int>.
5720 An C<isl_ast_expr_op> represents the result of an operation.
5721 An C<isl_ast_expr_id> represents an identifier.
5722 An C<isl_ast_expr_int> represents an integer value.
5724 Each type of expression has its own additional properties.
5726 #include <isl/ast.h>
5727 enum isl_ast_op_type isl_ast_expr_get_op_type(
5728 __isl_keep isl_ast_expr *expr);
5729 int isl_ast_expr_get_op_n_arg(__isl_keep isl_ast_expr *expr);
5730 __isl_give isl_ast_expr *isl_ast_expr_get_op_arg(
5731 __isl_keep isl_ast_expr *expr, int pos);
5732 int isl_ast_node_foreach_ast_op_type(
5733 __isl_keep isl_ast_node *node,
5734 int (*fn)(enum isl_ast_op_type type, void *user),
5737 C<isl_ast_expr_get_op_type> returns the type of the operation
5738 performed. C<isl_ast_expr_get_op_n_arg> returns the number of
5739 arguments. C<isl_ast_expr_get_op_arg> returns the specified
5741 C<isl_ast_node_foreach_ast_op_type> calls C<fn> for each distinct
5742 C<isl_ast_op_type> that appears in C<node>.
5743 The operation type is one of the following.
5747 =item C<isl_ast_op_and>
5749 Logical I<and> of two arguments.
5750 Both arguments can be evaluated.
5752 =item C<isl_ast_op_and_then>
5754 Logical I<and> of two arguments.
5755 The second argument can only be evaluated if the first evaluates to true.
5757 =item C<isl_ast_op_or>
5759 Logical I<or> of two arguments.
5760 Both arguments can be evaluated.
5762 =item C<isl_ast_op_or_else>
5764 Logical I<or> of two arguments.
5765 The second argument can only be evaluated if the first evaluates to false.
5767 =item C<isl_ast_op_max>
5769 Maximum of two or more arguments.
5771 =item C<isl_ast_op_min>
5773 Minimum of two or more arguments.
5775 =item C<isl_ast_op_minus>
5779 =item C<isl_ast_op_add>
5781 Sum of two arguments.
5783 =item C<isl_ast_op_sub>
5785 Difference of two arguments.
5787 =item C<isl_ast_op_mul>
5789 Product of two arguments.
5791 =item C<isl_ast_op_div>
5793 Exact division. That is, the result is known to be an integer.
5795 =item C<isl_ast_op_fdiv_q>
5797 Result of integer division, rounded towards negative
5800 =item C<isl_ast_op_pdiv_q>
5802 Result of integer division, where dividend is known to be non-negative.
5804 =item C<isl_ast_op_pdiv_r>
5806 Remainder of integer division, where dividend is known to be non-negative.
5808 =item C<isl_ast_op_cond>
5810 Conditional operator defined on three arguments.
5811 If the first argument evaluates to true, then the result
5812 is equal to the second argument. Otherwise, the result
5813 is equal to the third argument.
5814 The second and third argument may only be evaluated if
5815 the first argument evaluates to true and false, respectively.
5816 Corresponds to C<a ? b : c> in C.
5818 =item C<isl_ast_op_select>
5820 Conditional operator defined on three arguments.
5821 If the first argument evaluates to true, then the result
5822 is equal to the second argument. Otherwise, the result
5823 is equal to the third argument.
5824 The second and third argument may be evaluated independently
5825 of the value of the first argument.
5826 Corresponds to C<a * b + (1 - a) * c> in C.
5828 =item C<isl_ast_op_eq>
5832 =item C<isl_ast_op_le>
5834 Less than or equal relation.
5836 =item C<isl_ast_op_lt>
5840 =item C<isl_ast_op_ge>
5842 Greater than or equal relation.
5844 =item C<isl_ast_op_gt>
5846 Greater than relation.
5848 =item C<isl_ast_op_call>
5851 The number of arguments of the C<isl_ast_expr> is one more than
5852 the number of arguments in the function call, the first argument
5853 representing the function being called.
5857 #include <isl/ast.h>
5858 __isl_give isl_id *isl_ast_expr_get_id(
5859 __isl_keep isl_ast_expr *expr);
5861 Return the identifier represented by the AST expression.
5863 #include <isl/ast.h>
5864 int isl_ast_expr_get_int(__isl_keep isl_ast_expr *expr,
5867 Return the integer represented by the AST expression.
5868 Note that the integer is returned through the C<v> argument.
5869 The return value of the function itself indicates whether the
5870 operation was performed successfully.
5872 =head3 Manipulating and printing the AST
5874 AST nodes can be copied and freed using the following functions.
5876 #include <isl/ast.h>
5877 __isl_give isl_ast_node *isl_ast_node_copy(
5878 __isl_keep isl_ast_node *node);
5879 void *isl_ast_node_free(__isl_take isl_ast_node *node);
5881 AST expressions can be copied and freed using the following functions.
5883 #include <isl/ast.h>
5884 __isl_give isl_ast_expr *isl_ast_expr_copy(
5885 __isl_keep isl_ast_expr *expr);
5886 void *isl_ast_expr_free(__isl_take isl_ast_expr *expr);
5888 New AST expressions can be created either directly or within
5889 the context of an C<isl_ast_build>.
5891 #include <isl/ast.h>
5892 __isl_give isl_ast_expr *isl_ast_expr_from_id(
5893 __isl_take isl_id *id);
5894 __isl_give isl_ast_expr *isl_ast_expr_neg(
5895 __isl_take isl_ast_expr *expr);
5896 __isl_give isl_ast_expr *isl_ast_expr_add(
5897 __isl_take isl_ast_expr *expr1,
5898 __isl_take isl_ast_expr *expr2);
5899 __isl_give isl_ast_expr *isl_ast_expr_sub(
5900 __isl_take isl_ast_expr *expr1,
5901 __isl_take isl_ast_expr *expr2);
5902 __isl_give isl_ast_expr *isl_ast_expr_mul(
5903 __isl_take isl_ast_expr *expr1,
5904 __isl_take isl_ast_expr *expr2);
5905 __isl_give isl_ast_expr *isl_ast_expr_div(
5906 __isl_take isl_ast_expr *expr1,
5907 __isl_take isl_ast_expr *expr2);
5908 __isl_give isl_ast_expr *isl_ast_expr_and(
5909 __isl_take isl_ast_expr *expr1,
5910 __isl_take isl_ast_expr *expr2)
5911 __isl_give isl_ast_expr *isl_ast_expr_or(
5912 __isl_take isl_ast_expr *expr1,
5913 __isl_take isl_ast_expr *expr2)
5915 #include <isl/ast_build.h>
5916 __isl_give isl_ast_expr *isl_ast_build_expr_from_pw_aff(
5917 __isl_keep isl_ast_build *build,
5918 __isl_take isl_pw_aff *pa);
5919 __isl_give isl_ast_expr *
5920 isl_ast_build_call_from_pw_multi_aff(
5921 __isl_keep isl_ast_build *build,
5922 __isl_take isl_pw_multi_aff *pma);
5924 The domains of C<pa> and C<pma> should correspond
5925 to the schedule space of C<build>.
5926 The tuple id of C<pma> is used as the function being called.
5928 User specified data can be attached to an C<isl_ast_node> and obtained
5929 from the same C<isl_ast_node> using the following functions.
5931 #include <isl/ast.h>
5932 __isl_give isl_ast_node *isl_ast_node_set_annotation(
5933 __isl_take isl_ast_node *node,
5934 __isl_take isl_id *annotation);
5935 __isl_give isl_id *isl_ast_node_get_annotation(
5936 __isl_keep isl_ast_node *node);
5938 Basic printing can be performed using the following functions.
5940 #include <isl/ast.h>
5941 __isl_give isl_printer *isl_printer_print_ast_expr(
5942 __isl_take isl_printer *p,
5943 __isl_keep isl_ast_expr *expr);
5944 __isl_give isl_printer *isl_printer_print_ast_node(
5945 __isl_take isl_printer *p,
5946 __isl_keep isl_ast_node *node);
5948 More advanced printing can be performed using the following functions.
5950 #include <isl/ast.h>
5951 __isl_give isl_printer *isl_ast_op_type_print_macro(
5952 enum isl_ast_op_type type,
5953 __isl_take isl_printer *p);
5954 __isl_give isl_printer *isl_ast_node_print_macros(
5955 __isl_keep isl_ast_node *node,
5956 __isl_take isl_printer *p);
5957 __isl_give isl_printer *isl_ast_node_print(
5958 __isl_keep isl_ast_node *node,
5959 __isl_take isl_printer *p,
5960 __isl_take isl_ast_print_options *options);
5961 __isl_give isl_printer *isl_ast_node_for_print(
5962 __isl_keep isl_ast_node *node,
5963 __isl_take isl_printer *p,
5964 __isl_take isl_ast_print_options *options);
5965 __isl_give isl_printer *isl_ast_node_if_print(
5966 __isl_keep isl_ast_node *node,
5967 __isl_take isl_printer *p,
5968 __isl_take isl_ast_print_options *options);
5970 While printing an C<isl_ast_node> in C<ISL_FORMAT_C>,
5971 C<isl> may print out an AST that makes use of macros such
5972 as C<floord>, C<min> and C<max>.
5973 C<isl_ast_op_type_print_macro> prints out the macro
5974 corresponding to a specific C<isl_ast_op_type>.
5975 C<isl_ast_node_print_macros> scans the C<isl_ast_node>
5976 for expressions where these macros would be used and prints
5977 out the required macro definitions.
5978 Essentially, C<isl_ast_node_print_macros> calls
5979 C<isl_ast_node_foreach_ast_op_type> with C<isl_ast_op_type_print_macro>
5980 as function argument.
5981 C<isl_ast_node_print>, C<isl_ast_node_for_print> and
5982 C<isl_ast_node_if_print> print an C<isl_ast_node>
5983 in C<ISL_FORMAT_C>, but allow for some extra control
5984 through an C<isl_ast_print_options> object.
5985 This object can be created using the following functions.
5987 #include <isl/ast.h>
5988 __isl_give isl_ast_print_options *
5989 isl_ast_print_options_alloc(isl_ctx *ctx);
5990 __isl_give isl_ast_print_options *
5991 isl_ast_print_options_copy(
5992 __isl_keep isl_ast_print_options *options);
5993 void *isl_ast_print_options_free(
5994 __isl_take isl_ast_print_options *options);
5996 __isl_give isl_ast_print_options *
5997 isl_ast_print_options_set_print_user(
5998 __isl_take isl_ast_print_options *options,
5999 __isl_give isl_printer *(*print_user)(
6000 __isl_take isl_printer *p,
6001 __isl_take isl_ast_print_options *options,
6002 __isl_keep isl_ast_node *node, void *user),
6004 __isl_give isl_ast_print_options *
6005 isl_ast_print_options_set_print_for(
6006 __isl_take isl_ast_print_options *options,
6007 __isl_give isl_printer *(*print_for)(
6008 __isl_take isl_printer *p,
6009 __isl_take isl_ast_print_options *options,
6010 __isl_keep isl_ast_node *node, void *user),
6013 The callback set by C<isl_ast_print_options_set_print_user>
6014 is called whenever a node of type C<isl_ast_node_user> needs to
6016 The callback set by C<isl_ast_print_options_set_print_for>
6017 is called whenever a node of type C<isl_ast_node_for> needs to
6019 Note that C<isl_ast_node_for_print> will I<not> call the
6020 callback set by C<isl_ast_print_options_set_print_for> on the node
6021 on which C<isl_ast_node_for_print> is called, but only on nested
6022 nodes of type C<isl_ast_node_for>. It is therefore safe to
6023 call C<isl_ast_node_for_print> from within the callback set by
6024 C<isl_ast_print_options_set_print_for>.
6026 The following option determines the type to be used for iterators
6027 while printing the AST.
6029 int isl_options_set_ast_iterator_type(
6030 isl_ctx *ctx, const char *val);
6031 const char *isl_options_get_ast_iterator_type(
6036 #include <isl/ast_build.h>
6037 int isl_options_set_ast_build_atomic_upper_bound(
6038 isl_ctx *ctx, int val);
6039 int isl_options_get_ast_build_atomic_upper_bound(
6041 int isl_options_set_ast_build_prefer_pdiv(isl_ctx *ctx,
6043 int isl_options_get_ast_build_prefer_pdiv(isl_ctx *ctx);
6044 int isl_options_set_ast_build_exploit_nested_bounds(
6045 isl_ctx *ctx, int val);
6046 int isl_options_get_ast_build_exploit_nested_bounds(
6048 int isl_options_set_ast_build_group_coscheduled(
6049 isl_ctx *ctx, int val);
6050 int isl_options_get_ast_build_group_coscheduled(
6052 int isl_options_set_ast_build_scale_strides(
6053 isl_ctx *ctx, int val);
6054 int isl_options_get_ast_build_scale_strides(
6056 int isl_options_set_ast_build_allow_else(isl_ctx *ctx,
6058 int isl_options_get_ast_build_allow_else(isl_ctx *ctx);
6059 int isl_options_set_ast_build_allow_or(isl_ctx *ctx,
6061 int isl_options_get_ast_build_allow_or(isl_ctx *ctx);
6065 =item * ast_build_atomic_upper_bound
6067 Generate loop upper bounds that consist of the current loop iterator,
6068 an operator and an expression not involving the iterator.
6069 If this option is not set, then the current loop iterator may appear
6070 several times in the upper bound.
6071 For example, when this option is turned off, AST generation
6074 [n] -> { A[i] -> [i] : 0 <= i <= 100, n }
6078 for (int c0 = 0; c0 <= 100 && n >= c0; c0 += 1)
6081 When the option is turned on, the following AST is generated
6083 for (int c0 = 0; c0 <= min(100, n); c0 += 1)
6086 =item * ast_build_prefer_pdiv
6088 If this option is turned off, then the AST generation will
6089 produce ASTs that may only contain C<isl_ast_op_fdiv_q>
6090 operators, but no C<isl_ast_op_pdiv_q> or
6091 C<isl_ast_op_pdiv_r> operators.
6092 If this options is turned on, then C<isl> will try to convert
6093 some of the C<isl_ast_op_fdiv_q> operators to (expressions containing)
6094 C<isl_ast_op_pdiv_q> or C<isl_ast_op_pdiv_r> operators.
6096 =item * ast_build_exploit_nested_bounds
6098 Simplify conditions based on bounds of nested for loops.
6099 In particular, remove conditions that are implied by the fact
6100 that one or more nested loops have at least one iteration,
6101 meaning that the upper bound is at least as large as the lower bound.
6102 For example, when this option is turned off, AST generation
6105 [N,M] -> { A[i,j] -> [i,j] : 0 <= i <= N and
6111 for (int c0 = 0; c0 <= N; c0 += 1)
6112 for (int c1 = 0; c1 <= M; c1 += 1)
6115 When the option is turned on, the following AST is generated
6117 for (int c0 = 0; c0 <= N; c0 += 1)
6118 for (int c1 = 0; c1 <= M; c1 += 1)
6121 =item * ast_build_group_coscheduled
6123 If two domain elements are assigned the same schedule point, then
6124 they may be executed in any order and they may even appear in different
6125 loops. If this options is set, then the AST generator will make
6126 sure that coscheduled domain elements do not appear in separate parts
6127 of the AST. This is useful in case of nested AST generation
6128 if the outer AST generation is given only part of a schedule
6129 and the inner AST generation should handle the domains that are
6130 coscheduled by this initial part of the schedule together.
6131 For example if an AST is generated for a schedule
6133 { A[i] -> [0]; B[i] -> [0] }
6135 then the C<isl_ast_build_set_create_leaf> callback described
6136 below may get called twice, once for each domain.
6137 Setting this option ensures that the callback is only called once
6138 on both domains together.
6140 =item * ast_build_separation_bounds
6142 This option specifies which bounds to use during separation.
6143 If this option is set to C<ISL_AST_BUILD_SEPARATION_BOUNDS_IMPLICIT>
6144 then all (possibly implicit) bounds on the current dimension will
6145 be used during separation.
6146 If this option is set to C<ISL_AST_BUILD_SEPARATION_BOUNDS_EXPLICIT>
6147 then only those bounds that are explicitly available will
6148 be used during separation.
6150 =item * ast_build_scale_strides
6152 This option specifies whether the AST generator is allowed
6153 to scale down iterators of strided loops.
6155 =item * ast_build_allow_else
6157 This option specifies whether the AST generator is allowed
6158 to construct if statements with else branches.
6160 =item * ast_build_allow_or
6162 This option specifies whether the AST generator is allowed
6163 to construct if conditions with disjunctions.
6167 =head3 Fine-grained Control over AST Generation
6169 Besides specifying the constraints on the parameters,
6170 an C<isl_ast_build> object can be used to control
6171 various aspects of the AST generation process.
6172 The most prominent way of control is through ``options'',
6173 which can be set using the following function.
6175 #include <isl/ast_build.h>
6176 __isl_give isl_ast_build *
6177 isl_ast_build_set_options(
6178 __isl_take isl_ast_build *control,
6179 __isl_take isl_union_map *options);
6181 The options are encoded in an <isl_union_map>.
6182 The domain of this union relation refers to the schedule domain,
6183 i.e., the range of the schedule passed to C<isl_ast_build_ast_from_schedule>.
6184 In the case of nested AST generation (see L</"Nested AST Generation">),
6185 the domain of C<options> should refer to the extra piece of the schedule.
6186 That is, it should be equal to the range of the wrapped relation in the
6187 range of the schedule.
6188 The range of the options can consist of elements in one or more spaces,
6189 the names of which determine the effect of the option.
6190 The values of the range typically also refer to the schedule dimension
6191 to which the option applies. In case of nested AST generation
6192 (see L</"Nested AST Generation">), these values refer to the position
6193 of the schedule dimension within the innermost AST generation.
6194 The constraints on the domain elements of
6195 the option should only refer to this dimension and earlier dimensions.
6196 We consider the following spaces.
6200 =item C<separation_class>
6202 This space is a wrapped relation between two one dimensional spaces.
6203 The input space represents the schedule dimension to which the option
6204 applies and the output space represents the separation class.
6205 While constructing a loop corresponding to the specified schedule
6206 dimension(s), the AST generator will try to generate separate loops
6207 for domain elements that are assigned different classes.
6208 If only some of the elements are assigned a class, then those elements
6209 that are not assigned any class will be treated as belonging to a class
6210 that is separate from the explicitly assigned classes.
6211 The typical use case for this option is to separate full tiles from
6213 The other options, described below, are applied after the separation
6216 As an example, consider the separation into full and partial tiles
6217 of a tiling of a triangular domain.
6218 Take, for example, the domain
6220 { A[i,j] : 0 <= i,j and i + j <= 100 }
6222 and a tiling into tiles of 10 by 10. The input to the AST generator
6223 is then the schedule
6225 { A[i,j] -> [([i/10]),[j/10],i,j] : 0 <= i,j and
6228 Without any options, the following AST is generated
6230 for (int c0 = 0; c0 <= 10; c0 += 1)
6231 for (int c1 = 0; c1 <= -c0 + 10; c1 += 1)
6232 for (int c2 = 10 * c0;
6233 c2 <= min(-10 * c1 + 100, 10 * c0 + 9);
6235 for (int c3 = 10 * c1;
6236 c3 <= min(10 * c1 + 9, -c2 + 100);
6240 Separation into full and partial tiles can be obtained by assigning
6241 a class, say C<0>, to the full tiles. The full tiles are represented by those
6242 values of the first and second schedule dimensions for which there are
6243 values of the third and fourth dimensions to cover an entire tile.
6244 That is, we need to specify the following option
6246 { [a,b,c,d] -> separation_class[[0]->[0]] :
6247 exists b': 0 <= 10a,10b' and
6248 10a+9+10b'+9 <= 100;
6249 [a,b,c,d] -> separation_class[[1]->[0]] :
6250 0 <= 10a,10b and 10a+9+10b+9 <= 100 }
6254 { [a, b, c, d] -> separation_class[[1] -> [0]] :
6255 a >= 0 and b >= 0 and b <= 8 - a;
6256 [a, b, c, d] -> separation_class[[0] -> [0]] :
6259 With this option, the generated AST is as follows
6262 for (int c0 = 0; c0 <= 8; c0 += 1) {
6263 for (int c1 = 0; c1 <= -c0 + 8; c1 += 1)
6264 for (int c2 = 10 * c0;
6265 c2 <= 10 * c0 + 9; c2 += 1)
6266 for (int c3 = 10 * c1;
6267 c3 <= 10 * c1 + 9; c3 += 1)
6269 for (int c1 = -c0 + 9; c1 <= -c0 + 10; c1 += 1)
6270 for (int c2 = 10 * c0;
6271 c2 <= min(-10 * c1 + 100, 10 * c0 + 9);
6273 for (int c3 = 10 * c1;
6274 c3 <= min(-c2 + 100, 10 * c1 + 9);
6278 for (int c0 = 9; c0 <= 10; c0 += 1)
6279 for (int c1 = 0; c1 <= -c0 + 10; c1 += 1)
6280 for (int c2 = 10 * c0;
6281 c2 <= min(-10 * c1 + 100, 10 * c0 + 9);
6283 for (int c3 = 10 * c1;
6284 c3 <= min(10 * c1 + 9, -c2 + 100);
6291 This is a single-dimensional space representing the schedule dimension(s)
6292 to which ``separation'' should be applied. Separation tries to split
6293 a loop into several pieces if this can avoid the generation of guards
6295 See also the C<atomic> option.
6299 This is a single-dimensional space representing the schedule dimension(s)
6300 for which the domains should be considered ``atomic''. That is, the
6301 AST generator will make sure that any given domain space will only appear
6302 in a single loop at the specified level.
6304 Consider the following schedule
6306 { a[i] -> [i] : 0 <= i < 10;
6307 b[i] -> [i+1] : 0 <= i < 10 }
6309 If the following option is specified
6311 { [i] -> separate[x] }
6313 then the following AST will be generated
6317 for (int c0 = 1; c0 <= 9; c0 += 1) {
6324 If, on the other hand, the following option is specified
6326 { [i] -> atomic[x] }
6328 then the following AST will be generated
6330 for (int c0 = 0; c0 <= 10; c0 += 1) {
6337 If neither C<atomic> nor C<separate> is specified, then the AST generator
6338 may produce either of these two results or some intermediate form.
6342 This is a single-dimensional space representing the schedule dimension(s)
6343 that should be I<completely> unrolled.
6344 To obtain a partial unrolling, the user should apply an additional
6345 strip-mining to the schedule and fully unroll the inner loop.
6349 Additional control is available through the following functions.
6351 #include <isl/ast_build.h>
6352 __isl_give isl_ast_build *
6353 isl_ast_build_set_iterators(
6354 __isl_take isl_ast_build *control,
6355 __isl_take isl_id_list *iterators);
6357 The function C<isl_ast_build_set_iterators> allows the user to
6358 specify a list of iterator C<isl_id>s to be used as iterators.
6359 If the input schedule is injective, then
6360 the number of elements in this list should be as large as the dimension
6361 of the schedule space, but no direct correspondence should be assumed
6362 between dimensions and elements.
6363 If the input schedule is not injective, then an additional number
6364 of C<isl_id>s equal to the largest dimension of the input domains
6366 If the number of provided C<isl_id>s is insufficient, then additional
6367 names are automatically generated.
6369 #include <isl/ast_build.h>
6370 __isl_give isl_ast_build *
6371 isl_ast_build_set_create_leaf(
6372 __isl_take isl_ast_build *control,
6373 __isl_give isl_ast_node *(*fn)(
6374 __isl_take isl_ast_build *build,
6375 void *user), void *user);
6378 C<isl_ast_build_set_create_leaf> function allows for the
6379 specification of a callback that should be called whenever the AST
6380 generator arrives at an element of the schedule domain.
6381 The callback should return an AST node that should be inserted
6382 at the corresponding position of the AST. The default action (when
6383 the callback is not set) is to continue generating parts of the AST to scan
6384 all the domain elements associated to the schedule domain element
6385 and to insert user nodes, ``calling'' the domain element, for each of them.
6386 The C<build> argument contains the current state of the C<isl_ast_build>.
6387 To ease nested AST generation (see L</"Nested AST Generation">),
6388 all control information that is
6389 specific to the current AST generation such as the options and
6390 the callbacks has been removed from this C<isl_ast_build>.
6391 The callback would typically return the result of a nested
6393 user defined node created using the following function.
6395 #include <isl/ast.h>
6396 __isl_give isl_ast_node *isl_ast_node_alloc_user(
6397 __isl_take isl_ast_expr *expr);
6399 #include <isl/ast_build.h>
6400 __isl_give isl_ast_build *
6401 isl_ast_build_set_at_each_domain(
6402 __isl_take isl_ast_build *build,
6403 __isl_give isl_ast_node *(*fn)(
6404 __isl_take isl_ast_node *node,
6405 __isl_keep isl_ast_build *build,
6406 void *user), void *user);
6407 __isl_give isl_ast_build *
6408 isl_ast_build_set_before_each_for(
6409 __isl_take isl_ast_build *build,
6410 __isl_give isl_id *(*fn)(
6411 __isl_keep isl_ast_build *build,
6412 void *user), void *user);
6413 __isl_give isl_ast_build *
6414 isl_ast_build_set_after_each_for(
6415 __isl_take isl_ast_build *build,
6416 __isl_give isl_ast_node *(*fn)(
6417 __isl_take isl_ast_node *node,
6418 __isl_keep isl_ast_build *build,
6419 void *user), void *user);
6421 The callback set by C<isl_ast_build_set_at_each_domain> will
6422 be called for each domain AST node.
6423 The callbacks set by C<isl_ast_build_set_before_each_for>
6424 and C<isl_ast_build_set_after_each_for> will be called
6425 for each for AST node. The first will be called in depth-first
6426 pre-order, while the second will be called in depth-first post-order.
6427 Since C<isl_ast_build_set_before_each_for> is called before the for
6428 node is actually constructed, it is only passed an C<isl_ast_build>.
6429 The returned C<isl_id> will be added as an annotation (using
6430 C<isl_ast_node_set_annotation>) to the constructed for node.
6431 In particular, if the user has also specified an C<after_each_for>
6432 callback, then the annotation can be retrieved from the node passed to
6433 that callback using C<isl_ast_node_get_annotation>.
6434 All callbacks should C<NULL> on failure.
6435 The given C<isl_ast_build> can be used to create new
6436 C<isl_ast_expr> objects using C<isl_ast_build_expr_from_pw_aff>
6437 or C<isl_ast_build_call_from_pw_multi_aff>.
6439 =head3 Nested AST Generation
6441 C<isl> allows the user to create an AST within the context
6442 of another AST. These nested ASTs are created using the
6443 same C<isl_ast_build_ast_from_schedule> function that is used to create the
6444 outer AST. The C<build> argument should be an C<isl_ast_build>
6445 passed to a callback set by
6446 C<isl_ast_build_set_create_leaf>.
6447 The space of the range of the C<schedule> argument should refer
6448 to this build. In particular, the space should be a wrapped
6449 relation and the domain of this wrapped relation should be the
6450 same as that of the range of the schedule returned by
6451 C<isl_ast_build_get_schedule> below.
6452 In practice, the new schedule is typically
6453 created by calling C<isl_union_map_range_product> on the old schedule
6454 and some extra piece of the schedule.
6455 The space of the schedule domain is also available from
6456 the C<isl_ast_build>.
6458 #include <isl/ast_build.h>
6459 __isl_give isl_union_map *isl_ast_build_get_schedule(
6460 __isl_keep isl_ast_build *build);
6461 __isl_give isl_space *isl_ast_build_get_schedule_space(
6462 __isl_keep isl_ast_build *build);
6463 __isl_give isl_ast_build *isl_ast_build_restrict(
6464 __isl_take isl_ast_build *build,
6465 __isl_take isl_set *set);
6467 The C<isl_ast_build_get_schedule> function returns a (partial)
6468 schedule for the domains elements for which part of the AST still needs to
6469 be generated in the current build.
6470 In particular, the domain elements are mapped to those iterations of the loops
6471 enclosing the current point of the AST generation inside which
6472 the domain elements are executed.
6473 No direct correspondence between
6474 the input schedule and this schedule should be assumed.
6475 The space obtained from C<isl_ast_build_get_schedule_space> can be used
6476 to create a set for C<isl_ast_build_restrict> to intersect
6477 with the current build. In particular, the set passed to
6478 C<isl_ast_build_restrict> can have additional parameters.
6479 The ids of the set dimensions in the space returned by
6480 C<isl_ast_build_get_schedule_space> correspond to the
6481 iterators of the already generated loops.
6482 The user should not rely on the ids of the output dimensions
6483 of the relations in the union relation returned by
6484 C<isl_ast_build_get_schedule> having any particular value.
6488 Although C<isl> is mainly meant to be used as a library,
6489 it also contains some basic applications that use some
6490 of the functionality of C<isl>.
6491 The input may be specified in either the L<isl format>
6492 or the L<PolyLib format>.
6494 =head2 C<isl_polyhedron_sample>
6496 C<isl_polyhedron_sample> takes a polyhedron as input and prints
6497 an integer element of the polyhedron, if there is any.
6498 The first column in the output is the denominator and is always
6499 equal to 1. If the polyhedron contains no integer points,
6500 then a vector of length zero is printed.
6504 C<isl_pip> takes the same input as the C<example> program
6505 from the C<piplib> distribution, i.e., a set of constraints
6506 on the parameters, a line containing only -1 and finally a set
6507 of constraints on a parametric polyhedron.
6508 The coefficients of the parameters appear in the last columns
6509 (but before the final constant column).
6510 The output is the lexicographic minimum of the parametric polyhedron.
6511 As C<isl> currently does not have its own output format, the output
6512 is just a dump of the internal state.
6514 =head2 C<isl_polyhedron_minimize>
6516 C<isl_polyhedron_minimize> computes the minimum of some linear
6517 or affine objective function over the integer points in a polyhedron.
6518 If an affine objective function
6519 is given, then the constant should appear in the last column.
6521 =head2 C<isl_polytope_scan>
6523 Given a polytope, C<isl_polytope_scan> prints
6524 all integer points in the polytope.
6526 =head2 C<isl_codegen>
6528 Given a schedule, a context set and an options relation,
6529 C<isl_codegen> prints out an AST that scans the domain elements
6530 of the schedule in the order of their image(s) taking into account
6531 the constraints in the context set.