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>.
2063 __isl_give isl_val *
2064 isl_basic_map_plain_get_val_if_fixed(
2065 __isl_keep isl_basic_map *bmap,
2066 enum isl_dim_type type, unsigned pos);
2067 __isl_give isl_val *isl_map_plain_get_val_if_fixed(
2068 __isl_keep isl_map *map,
2069 enum isl_dim_type type, unsigned pos);
2071 If the relation obviously lies on a hyperplane where the given dimension
2072 has a fixed value, then return that value.
2073 Otherwise return NaN.
2077 To check whether a set is a parameter domain, use this function:
2079 int isl_set_is_params(__isl_keep isl_set *set);
2080 int isl_union_set_is_params(
2081 __isl_keep isl_union_set *uset);
2085 The following functions check whether the domain of the given
2086 (basic) set is a wrapped relation.
2088 int isl_basic_set_is_wrapping(
2089 __isl_keep isl_basic_set *bset);
2090 int isl_set_is_wrapping(__isl_keep isl_set *set);
2092 =item * Internal Product
2094 int isl_basic_map_can_zip(
2095 __isl_keep isl_basic_map *bmap);
2096 int isl_map_can_zip(__isl_keep isl_map *map);
2098 Check whether the product of domain and range of the given relation
2100 i.e., whether both domain and range are nested relations.
2104 int isl_basic_map_can_curry(
2105 __isl_keep isl_basic_map *bmap);
2106 int isl_map_can_curry(__isl_keep isl_map *map);
2108 Check whether the domain of the (basic) relation is a wrapped relation.
2110 int isl_basic_map_can_uncurry(
2111 __isl_keep isl_basic_map *bmap);
2112 int isl_map_can_uncurry(__isl_keep isl_map *map);
2114 Check whether the range of the (basic) relation is a wrapped relation.
2118 =head3 Binary Properties
2124 int isl_set_plain_is_equal(__isl_keep isl_set *set1,
2125 __isl_keep isl_set *set2);
2126 int isl_set_is_equal(__isl_keep isl_set *set1,
2127 __isl_keep isl_set *set2);
2128 int isl_union_set_is_equal(
2129 __isl_keep isl_union_set *uset1,
2130 __isl_keep isl_union_set *uset2);
2131 int isl_basic_map_is_equal(
2132 __isl_keep isl_basic_map *bmap1,
2133 __isl_keep isl_basic_map *bmap2);
2134 int isl_map_is_equal(__isl_keep isl_map *map1,
2135 __isl_keep isl_map *map2);
2136 int isl_map_plain_is_equal(__isl_keep isl_map *map1,
2137 __isl_keep isl_map *map2);
2138 int isl_union_map_is_equal(
2139 __isl_keep isl_union_map *umap1,
2140 __isl_keep isl_union_map *umap2);
2142 =item * Disjointness
2144 int isl_set_plain_is_disjoint(__isl_keep isl_set *set1,
2145 __isl_keep isl_set *set2);
2146 int isl_set_is_disjoint(__isl_keep isl_set *set1,
2147 __isl_keep isl_set *set2);
2148 int isl_map_is_disjoint(__isl_keep isl_map *map1,
2149 __isl_keep isl_map *map2);
2153 int isl_basic_set_is_subset(
2154 __isl_keep isl_basic_set *bset1,
2155 __isl_keep isl_basic_set *bset2);
2156 int isl_set_is_subset(__isl_keep isl_set *set1,
2157 __isl_keep isl_set *set2);
2158 int isl_set_is_strict_subset(
2159 __isl_keep isl_set *set1,
2160 __isl_keep isl_set *set2);
2161 int isl_union_set_is_subset(
2162 __isl_keep isl_union_set *uset1,
2163 __isl_keep isl_union_set *uset2);
2164 int isl_union_set_is_strict_subset(
2165 __isl_keep isl_union_set *uset1,
2166 __isl_keep isl_union_set *uset2);
2167 int isl_basic_map_is_subset(
2168 __isl_keep isl_basic_map *bmap1,
2169 __isl_keep isl_basic_map *bmap2);
2170 int isl_basic_map_is_strict_subset(
2171 __isl_keep isl_basic_map *bmap1,
2172 __isl_keep isl_basic_map *bmap2);
2173 int isl_map_is_subset(
2174 __isl_keep isl_map *map1,
2175 __isl_keep isl_map *map2);
2176 int isl_map_is_strict_subset(
2177 __isl_keep isl_map *map1,
2178 __isl_keep isl_map *map2);
2179 int isl_union_map_is_subset(
2180 __isl_keep isl_union_map *umap1,
2181 __isl_keep isl_union_map *umap2);
2182 int isl_union_map_is_strict_subset(
2183 __isl_keep isl_union_map *umap1,
2184 __isl_keep isl_union_map *umap2);
2186 Check whether the first argument is a (strict) subset of the
2191 int isl_set_plain_cmp(__isl_keep isl_set *set1,
2192 __isl_keep isl_set *set2);
2194 This function is useful for sorting C<isl_set>s.
2195 The order depends on the internal representation of the inputs.
2196 The order is fixed over different calls to the function (assuming
2197 the internal representation of the inputs has not changed), but may
2198 change over different versions of C<isl>.
2202 =head2 Unary Operations
2208 __isl_give isl_set *isl_set_complement(
2209 __isl_take isl_set *set);
2210 __isl_give isl_map *isl_map_complement(
2211 __isl_take isl_map *map);
2215 __isl_give isl_basic_map *isl_basic_map_reverse(
2216 __isl_take isl_basic_map *bmap);
2217 __isl_give isl_map *isl_map_reverse(
2218 __isl_take isl_map *map);
2219 __isl_give isl_union_map *isl_union_map_reverse(
2220 __isl_take isl_union_map *umap);
2224 __isl_give isl_basic_set *isl_basic_set_project_out(
2225 __isl_take isl_basic_set *bset,
2226 enum isl_dim_type type, unsigned first, unsigned n);
2227 __isl_give isl_basic_map *isl_basic_map_project_out(
2228 __isl_take isl_basic_map *bmap,
2229 enum isl_dim_type type, unsigned first, unsigned n);
2230 __isl_give isl_set *isl_set_project_out(__isl_take isl_set *set,
2231 enum isl_dim_type type, unsigned first, unsigned n);
2232 __isl_give isl_map *isl_map_project_out(__isl_take isl_map *map,
2233 enum isl_dim_type type, unsigned first, unsigned n);
2234 __isl_give isl_basic_set *isl_basic_set_params(
2235 __isl_take isl_basic_set *bset);
2236 __isl_give isl_basic_set *isl_basic_map_domain(
2237 __isl_take isl_basic_map *bmap);
2238 __isl_give isl_basic_set *isl_basic_map_range(
2239 __isl_take isl_basic_map *bmap);
2240 __isl_give isl_set *isl_set_params(__isl_take isl_set *set);
2241 __isl_give isl_set *isl_map_params(__isl_take isl_map *map);
2242 __isl_give isl_set *isl_map_domain(
2243 __isl_take isl_map *bmap);
2244 __isl_give isl_set *isl_map_range(
2245 __isl_take isl_map *map);
2246 __isl_give isl_set *isl_union_set_params(
2247 __isl_take isl_union_set *uset);
2248 __isl_give isl_set *isl_union_map_params(
2249 __isl_take isl_union_map *umap);
2250 __isl_give isl_union_set *isl_union_map_domain(
2251 __isl_take isl_union_map *umap);
2252 __isl_give isl_union_set *isl_union_map_range(
2253 __isl_take isl_union_map *umap);
2255 __isl_give isl_basic_map *isl_basic_map_domain_map(
2256 __isl_take isl_basic_map *bmap);
2257 __isl_give isl_basic_map *isl_basic_map_range_map(
2258 __isl_take isl_basic_map *bmap);
2259 __isl_give isl_map *isl_map_domain_map(__isl_take isl_map *map);
2260 __isl_give isl_map *isl_map_range_map(__isl_take isl_map *map);
2261 __isl_give isl_union_map *isl_union_map_domain_map(
2262 __isl_take isl_union_map *umap);
2263 __isl_give isl_union_map *isl_union_map_range_map(
2264 __isl_take isl_union_map *umap);
2266 The functions above construct a (basic, regular or union) relation
2267 that maps (a wrapped version of) the input relation to its domain or range.
2271 __isl_give isl_basic_set *isl_basic_set_eliminate(
2272 __isl_take isl_basic_set *bset,
2273 enum isl_dim_type type,
2274 unsigned first, unsigned n);
2275 __isl_give isl_set *isl_set_eliminate(
2276 __isl_take isl_set *set, enum isl_dim_type type,
2277 unsigned first, unsigned n);
2278 __isl_give isl_basic_map *isl_basic_map_eliminate(
2279 __isl_take isl_basic_map *bmap,
2280 enum isl_dim_type type,
2281 unsigned first, unsigned n);
2282 __isl_give isl_map *isl_map_eliminate(
2283 __isl_take isl_map *map, enum isl_dim_type type,
2284 unsigned first, unsigned n);
2286 Eliminate the coefficients for the given dimensions from the constraints,
2287 without removing the dimensions.
2291 __isl_give isl_basic_set *isl_basic_set_fix(
2292 __isl_take isl_basic_set *bset,
2293 enum isl_dim_type type, unsigned pos,
2295 __isl_give isl_basic_set *isl_basic_set_fix_si(
2296 __isl_take isl_basic_set *bset,
2297 enum isl_dim_type type, unsigned pos, int value);
2298 __isl_give isl_basic_set *isl_basic_set_fix_val(
2299 __isl_take isl_basic_set *bset,
2300 enum isl_dim_type type, unsigned pos,
2301 __isl_take isl_val *v);
2302 __isl_give isl_set *isl_set_fix(__isl_take isl_set *set,
2303 enum isl_dim_type type, unsigned pos,
2305 __isl_give isl_set *isl_set_fix_si(__isl_take isl_set *set,
2306 enum isl_dim_type type, unsigned pos, int value);
2307 __isl_give isl_set *isl_set_fix_val(
2308 __isl_take isl_set *set,
2309 enum isl_dim_type type, unsigned pos,
2310 __isl_take isl_val *v);
2311 __isl_give isl_basic_map *isl_basic_map_fix_si(
2312 __isl_take isl_basic_map *bmap,
2313 enum isl_dim_type type, unsigned pos, int value);
2314 __isl_give isl_basic_map *isl_basic_map_fix_val(
2315 __isl_take isl_basic_map *bmap,
2316 enum isl_dim_type type, unsigned pos,
2317 __isl_take isl_val *v);
2318 __isl_give isl_map *isl_map_fix(__isl_take isl_map *map,
2319 enum isl_dim_type type, unsigned pos,
2321 __isl_give isl_map *isl_map_fix_si(__isl_take isl_map *map,
2322 enum isl_dim_type type, unsigned pos, int value);
2323 __isl_give isl_map *isl_map_fix_val(
2324 __isl_take isl_map *map,
2325 enum isl_dim_type type, unsigned pos,
2326 __isl_take isl_val *v);
2328 Intersect the set or relation with the hyperplane where the given
2329 dimension has the fixed given value.
2331 __isl_give isl_basic_map *isl_basic_map_lower_bound_si(
2332 __isl_take isl_basic_map *bmap,
2333 enum isl_dim_type type, unsigned pos, int value);
2334 __isl_give isl_basic_map *isl_basic_map_upper_bound_si(
2335 __isl_take isl_basic_map *bmap,
2336 enum isl_dim_type type, unsigned pos, int value);
2337 __isl_give isl_set *isl_set_lower_bound(
2338 __isl_take isl_set *set,
2339 enum isl_dim_type type, unsigned pos,
2341 __isl_give isl_set *isl_set_lower_bound_si(
2342 __isl_take isl_set *set,
2343 enum isl_dim_type type, unsigned pos, int value);
2344 __isl_give isl_set *isl_set_lower_bound_val(
2345 __isl_take isl_set *set,
2346 enum isl_dim_type type, unsigned pos,
2347 __isl_take isl_val *value);
2348 __isl_give isl_map *isl_map_lower_bound_si(
2349 __isl_take isl_map *map,
2350 enum isl_dim_type type, unsigned pos, int value);
2351 __isl_give isl_set *isl_set_upper_bound(
2352 __isl_take isl_set *set,
2353 enum isl_dim_type type, unsigned pos,
2355 __isl_give isl_set *isl_set_upper_bound_si(
2356 __isl_take isl_set *set,
2357 enum isl_dim_type type, unsigned pos, int value);
2358 __isl_give isl_set *isl_set_upper_bound_val(
2359 __isl_take isl_set *set,
2360 enum isl_dim_type type, unsigned pos,
2361 __isl_take isl_val *value);
2362 __isl_give isl_map *isl_map_upper_bound_si(
2363 __isl_take isl_map *map,
2364 enum isl_dim_type type, unsigned pos, int value);
2366 Intersect the set or relation with the half-space where the given
2367 dimension has a value bounded by the fixed given integer value.
2369 __isl_give isl_set *isl_set_equate(__isl_take isl_set *set,
2370 enum isl_dim_type type1, int pos1,
2371 enum isl_dim_type type2, int pos2);
2372 __isl_give isl_basic_map *isl_basic_map_equate(
2373 __isl_take isl_basic_map *bmap,
2374 enum isl_dim_type type1, int pos1,
2375 enum isl_dim_type type2, int pos2);
2376 __isl_give isl_map *isl_map_equate(__isl_take isl_map *map,
2377 enum isl_dim_type type1, int pos1,
2378 enum isl_dim_type type2, int pos2);
2380 Intersect the set or relation with the hyperplane where the given
2381 dimensions are equal to each other.
2383 __isl_give isl_map *isl_map_oppose(__isl_take isl_map *map,
2384 enum isl_dim_type type1, int pos1,
2385 enum isl_dim_type type2, int pos2);
2387 Intersect the relation with the hyperplane where the given
2388 dimensions have opposite values.
2390 __isl_give isl_basic_map *isl_basic_map_order_ge(
2391 __isl_take isl_basic_map *bmap,
2392 enum isl_dim_type type1, int pos1,
2393 enum isl_dim_type type2, int pos2);
2394 __isl_give isl_map *isl_map_order_lt(__isl_take isl_map *map,
2395 enum isl_dim_type type1, int pos1,
2396 enum isl_dim_type type2, int pos2);
2397 __isl_give isl_basic_map *isl_basic_map_order_gt(
2398 __isl_take isl_basic_map *bmap,
2399 enum isl_dim_type type1, int pos1,
2400 enum isl_dim_type type2, int pos2);
2401 __isl_give isl_map *isl_map_order_gt(__isl_take isl_map *map,
2402 enum isl_dim_type type1, int pos1,
2403 enum isl_dim_type type2, int pos2);
2405 Intersect the relation with the half-space where the given
2406 dimensions satisfy the given ordering.
2410 __isl_give isl_map *isl_set_identity(
2411 __isl_take isl_set *set);
2412 __isl_give isl_union_map *isl_union_set_identity(
2413 __isl_take isl_union_set *uset);
2415 Construct an identity relation on the given (union) set.
2419 __isl_give isl_basic_set *isl_basic_map_deltas(
2420 __isl_take isl_basic_map *bmap);
2421 __isl_give isl_set *isl_map_deltas(__isl_take isl_map *map);
2422 __isl_give isl_union_set *isl_union_map_deltas(
2423 __isl_take isl_union_map *umap);
2425 These functions return a (basic) set containing the differences
2426 between image elements and corresponding domain elements in the input.
2428 __isl_give isl_basic_map *isl_basic_map_deltas_map(
2429 __isl_take isl_basic_map *bmap);
2430 __isl_give isl_map *isl_map_deltas_map(
2431 __isl_take isl_map *map);
2432 __isl_give isl_union_map *isl_union_map_deltas_map(
2433 __isl_take isl_union_map *umap);
2435 The functions above construct a (basic, regular or union) relation
2436 that maps (a wrapped version of) the input relation to its delta set.
2440 Simplify the representation of a set or relation by trying
2441 to combine pairs of basic sets or relations into a single
2442 basic set or relation.
2444 __isl_give isl_set *isl_set_coalesce(__isl_take isl_set *set);
2445 __isl_give isl_map *isl_map_coalesce(__isl_take isl_map *map);
2446 __isl_give isl_union_set *isl_union_set_coalesce(
2447 __isl_take isl_union_set *uset);
2448 __isl_give isl_union_map *isl_union_map_coalesce(
2449 __isl_take isl_union_map *umap);
2451 One of the methods for combining pairs of basic sets or relations
2452 can result in coefficients that are much larger than those that appear
2453 in the constraints of the input. By default, the coefficients are
2454 not allowed to grow larger, but this can be changed by unsetting
2455 the following option.
2457 int isl_options_set_coalesce_bounded_wrapping(
2458 isl_ctx *ctx, int val);
2459 int isl_options_get_coalesce_bounded_wrapping(
2462 =item * Detecting equalities
2464 __isl_give isl_basic_set *isl_basic_set_detect_equalities(
2465 __isl_take isl_basic_set *bset);
2466 __isl_give isl_basic_map *isl_basic_map_detect_equalities(
2467 __isl_take isl_basic_map *bmap);
2468 __isl_give isl_set *isl_set_detect_equalities(
2469 __isl_take isl_set *set);
2470 __isl_give isl_map *isl_map_detect_equalities(
2471 __isl_take isl_map *map);
2472 __isl_give isl_union_set *isl_union_set_detect_equalities(
2473 __isl_take isl_union_set *uset);
2474 __isl_give isl_union_map *isl_union_map_detect_equalities(
2475 __isl_take isl_union_map *umap);
2477 Simplify the representation of a set or relation by detecting implicit
2480 =item * Removing redundant constraints
2482 __isl_give isl_basic_set *isl_basic_set_remove_redundancies(
2483 __isl_take isl_basic_set *bset);
2484 __isl_give isl_set *isl_set_remove_redundancies(
2485 __isl_take isl_set *set);
2486 __isl_give isl_basic_map *isl_basic_map_remove_redundancies(
2487 __isl_take isl_basic_map *bmap);
2488 __isl_give isl_map *isl_map_remove_redundancies(
2489 __isl_take isl_map *map);
2493 __isl_give isl_basic_set *isl_set_convex_hull(
2494 __isl_take isl_set *set);
2495 __isl_give isl_basic_map *isl_map_convex_hull(
2496 __isl_take isl_map *map);
2498 If the input set or relation has any existentially quantified
2499 variables, then the result of these operations is currently undefined.
2503 __isl_give isl_basic_set *
2504 isl_set_unshifted_simple_hull(
2505 __isl_take isl_set *set);
2506 __isl_give isl_basic_map *
2507 isl_map_unshifted_simple_hull(
2508 __isl_take isl_map *map);
2509 __isl_give isl_basic_set *isl_set_simple_hull(
2510 __isl_take isl_set *set);
2511 __isl_give isl_basic_map *isl_map_simple_hull(
2512 __isl_take isl_map *map);
2513 __isl_give isl_union_map *isl_union_map_simple_hull(
2514 __isl_take isl_union_map *umap);
2516 These functions compute a single basic set or relation
2517 that contains the whole input set or relation.
2518 In particular, the output is described by translates
2519 of the constraints describing the basic sets or relations in the input.
2520 In case of C<isl_set_unshifted_simple_hull>, only the original
2521 constraints are used, without any translation.
2525 (See \autoref{s:simple hull}.)
2531 __isl_give isl_basic_set *isl_basic_set_affine_hull(
2532 __isl_take isl_basic_set *bset);
2533 __isl_give isl_basic_set *isl_set_affine_hull(
2534 __isl_take isl_set *set);
2535 __isl_give isl_union_set *isl_union_set_affine_hull(
2536 __isl_take isl_union_set *uset);
2537 __isl_give isl_basic_map *isl_basic_map_affine_hull(
2538 __isl_take isl_basic_map *bmap);
2539 __isl_give isl_basic_map *isl_map_affine_hull(
2540 __isl_take isl_map *map);
2541 __isl_give isl_union_map *isl_union_map_affine_hull(
2542 __isl_take isl_union_map *umap);
2544 In case of union sets and relations, the affine hull is computed
2547 =item * Polyhedral hull
2549 __isl_give isl_basic_set *isl_set_polyhedral_hull(
2550 __isl_take isl_set *set);
2551 __isl_give isl_basic_map *isl_map_polyhedral_hull(
2552 __isl_take isl_map *map);
2553 __isl_give isl_union_set *isl_union_set_polyhedral_hull(
2554 __isl_take isl_union_set *uset);
2555 __isl_give isl_union_map *isl_union_map_polyhedral_hull(
2556 __isl_take isl_union_map *umap);
2558 These functions compute a single basic set or relation
2559 not involving any existentially quantified variables
2560 that contains the whole input set or relation.
2561 In case of union sets and relations, the polyhedral hull is computed
2564 =item * Other approximations
2566 __isl_give isl_basic_set *
2567 isl_basic_set_drop_constraints_involving_dims(
2568 __isl_take isl_basic_set *bset,
2569 enum isl_dim_type type,
2570 unsigned first, unsigned n);
2571 __isl_give isl_basic_map *
2572 isl_basic_map_drop_constraints_involving_dims(
2573 __isl_take isl_basic_map *bmap,
2574 enum isl_dim_type type,
2575 unsigned first, unsigned n);
2576 __isl_give isl_basic_set *
2577 isl_basic_set_drop_constraints_not_involving_dims(
2578 __isl_take isl_basic_set *bset,
2579 enum isl_dim_type type,
2580 unsigned first, unsigned n);
2581 __isl_give isl_set *
2582 isl_set_drop_constraints_involving_dims(
2583 __isl_take isl_set *set,
2584 enum isl_dim_type type,
2585 unsigned first, unsigned n);
2586 __isl_give isl_map *
2587 isl_map_drop_constraints_involving_dims(
2588 __isl_take isl_map *map,
2589 enum isl_dim_type type,
2590 unsigned first, unsigned n);
2592 These functions drop any constraints (not) involving the specified dimensions.
2593 Note that the result depends on the representation of the input.
2597 __isl_give isl_basic_set *isl_basic_set_sample(
2598 __isl_take isl_basic_set *bset);
2599 __isl_give isl_basic_set *isl_set_sample(
2600 __isl_take isl_set *set);
2601 __isl_give isl_basic_map *isl_basic_map_sample(
2602 __isl_take isl_basic_map *bmap);
2603 __isl_give isl_basic_map *isl_map_sample(
2604 __isl_take isl_map *map);
2606 If the input (basic) set or relation is non-empty, then return
2607 a singleton subset of the input. Otherwise, return an empty set.
2609 =item * Optimization
2611 #include <isl/ilp.h>
2612 enum isl_lp_result isl_basic_set_max(
2613 __isl_keep isl_basic_set *bset,
2614 __isl_keep isl_aff *obj, isl_int *opt)
2615 __isl_give isl_val *isl_basic_set_max_val(
2616 __isl_keep isl_basic_set *bset,
2617 __isl_keep isl_aff *obj);
2618 enum isl_lp_result isl_set_min(__isl_keep isl_set *set,
2619 __isl_keep isl_aff *obj, isl_int *opt);
2620 __isl_give isl_val *isl_set_min_val(
2621 __isl_keep isl_set *set,
2622 __isl_keep isl_aff *obj);
2623 enum isl_lp_result isl_set_max(__isl_keep isl_set *set,
2624 __isl_keep isl_aff *obj, isl_int *opt);
2625 __isl_give isl_val *isl_set_max_val(
2626 __isl_keep isl_set *set,
2627 __isl_keep isl_aff *obj);
2629 Compute the minimum or maximum of the integer affine expression C<obj>
2630 over the points in C<set>, returning the result in C<opt>.
2631 The return value may be one of C<isl_lp_error>,
2632 C<isl_lp_ok>, C<isl_lp_unbounded> or C<isl_lp_empty>, in case of
2633 an C<isl_lp_result>. If the result is an C<isl_val> then
2634 the result is C<NULL> in case of an error, the optimal value in case
2635 there is one, negative infinity or infinity if the problem is unbounded and
2636 NaN if the problem is empty.
2638 =item * Parametric optimization
2640 __isl_give isl_pw_aff *isl_set_dim_min(
2641 __isl_take isl_set *set, int pos);
2642 __isl_give isl_pw_aff *isl_set_dim_max(
2643 __isl_take isl_set *set, int pos);
2644 __isl_give isl_pw_aff *isl_map_dim_max(
2645 __isl_take isl_map *map, int pos);
2647 Compute the minimum or maximum of the given set or output dimension
2648 as a function of the parameters (and input dimensions), but independently
2649 of the other set or output dimensions.
2650 For lexicographic optimization, see L<"Lexicographic Optimization">.
2654 The following functions compute either the set of (rational) coefficient
2655 values of valid constraints for the given set or the set of (rational)
2656 values satisfying the constraints with coefficients from the given set.
2657 Internally, these two sets of functions perform essentially the
2658 same operations, except that the set of coefficients is assumed to
2659 be a cone, while the set of values may be any polyhedron.
2660 The current implementation is based on the Farkas lemma and
2661 Fourier-Motzkin elimination, but this may change or be made optional
2662 in future. In particular, future implementations may use different
2663 dualization algorithms or skip the elimination step.
2665 __isl_give isl_basic_set *isl_basic_set_coefficients(
2666 __isl_take isl_basic_set *bset);
2667 __isl_give isl_basic_set *isl_set_coefficients(
2668 __isl_take isl_set *set);
2669 __isl_give isl_union_set *isl_union_set_coefficients(
2670 __isl_take isl_union_set *bset);
2671 __isl_give isl_basic_set *isl_basic_set_solutions(
2672 __isl_take isl_basic_set *bset);
2673 __isl_give isl_basic_set *isl_set_solutions(
2674 __isl_take isl_set *set);
2675 __isl_give isl_union_set *isl_union_set_solutions(
2676 __isl_take isl_union_set *bset);
2680 __isl_give isl_map *isl_map_fixed_power(
2681 __isl_take isl_map *map, isl_int exp);
2682 __isl_give isl_union_map *isl_union_map_fixed_power(
2683 __isl_take isl_union_map *umap, isl_int exp);
2685 Compute the given power of C<map>, where C<exp> is assumed to be non-zero.
2686 If the exponent C<exp> is negative, then the -C<exp> th power of the inverse
2687 of C<map> is computed.
2689 __isl_give isl_map *isl_map_power(__isl_take isl_map *map,
2691 __isl_give isl_union_map *isl_union_map_power(
2692 __isl_take isl_union_map *umap, int *exact);
2694 Compute a parametric representation for all positive powers I<k> of C<map>.
2695 The result maps I<k> to a nested relation corresponding to the
2696 I<k>th power of C<map>.
2697 The result may be an overapproximation. If the result is known to be exact,
2698 then C<*exact> is set to C<1>.
2700 =item * Transitive closure
2702 __isl_give isl_map *isl_map_transitive_closure(
2703 __isl_take isl_map *map, int *exact);
2704 __isl_give isl_union_map *isl_union_map_transitive_closure(
2705 __isl_take isl_union_map *umap, int *exact);
2707 Compute the transitive closure of C<map>.
2708 The result may be an overapproximation. If the result is known to be exact,
2709 then C<*exact> is set to C<1>.
2711 =item * Reaching path lengths
2713 __isl_give isl_map *isl_map_reaching_path_lengths(
2714 __isl_take isl_map *map, int *exact);
2716 Compute a relation that maps each element in the range of C<map>
2717 to the lengths of all paths composed of edges in C<map> that
2718 end up in the given element.
2719 The result may be an overapproximation. If the result is known to be exact,
2720 then C<*exact> is set to C<1>.
2721 To compute the I<maximal> path length, the resulting relation
2722 should be postprocessed by C<isl_map_lexmax>.
2723 In particular, if the input relation is a dependence relation
2724 (mapping sources to sinks), then the maximal path length corresponds
2725 to the free schedule.
2726 Note, however, that C<isl_map_lexmax> expects the maximum to be
2727 finite, so if the path lengths are unbounded (possibly due to
2728 the overapproximation), then you will get an error message.
2732 __isl_give isl_basic_set *isl_basic_map_wrap(
2733 __isl_take isl_basic_map *bmap);
2734 __isl_give isl_set *isl_map_wrap(
2735 __isl_take isl_map *map);
2736 __isl_give isl_union_set *isl_union_map_wrap(
2737 __isl_take isl_union_map *umap);
2738 __isl_give isl_basic_map *isl_basic_set_unwrap(
2739 __isl_take isl_basic_set *bset);
2740 __isl_give isl_map *isl_set_unwrap(
2741 __isl_take isl_set *set);
2742 __isl_give isl_union_map *isl_union_set_unwrap(
2743 __isl_take isl_union_set *uset);
2747 Remove any internal structure of domain (and range) of the given
2748 set or relation. If there is any such internal structure in the input,
2749 then the name of the space is also removed.
2751 __isl_give isl_basic_set *isl_basic_set_flatten(
2752 __isl_take isl_basic_set *bset);
2753 __isl_give isl_set *isl_set_flatten(
2754 __isl_take isl_set *set);
2755 __isl_give isl_basic_map *isl_basic_map_flatten_domain(
2756 __isl_take isl_basic_map *bmap);
2757 __isl_give isl_basic_map *isl_basic_map_flatten_range(
2758 __isl_take isl_basic_map *bmap);
2759 __isl_give isl_map *isl_map_flatten_range(
2760 __isl_take isl_map *map);
2761 __isl_give isl_map *isl_map_flatten_domain(
2762 __isl_take isl_map *map);
2763 __isl_give isl_basic_map *isl_basic_map_flatten(
2764 __isl_take isl_basic_map *bmap);
2765 __isl_give isl_map *isl_map_flatten(
2766 __isl_take isl_map *map);
2768 __isl_give isl_map *isl_set_flatten_map(
2769 __isl_take isl_set *set);
2771 The function above constructs a relation
2772 that maps the input set to a flattened version of the set.
2776 Lift the input set to a space with extra dimensions corresponding
2777 to the existentially quantified variables in the input.
2778 In particular, the result lives in a wrapped map where the domain
2779 is the original space and the range corresponds to the original
2780 existentially quantified variables.
2782 __isl_give isl_basic_set *isl_basic_set_lift(
2783 __isl_take isl_basic_set *bset);
2784 __isl_give isl_set *isl_set_lift(
2785 __isl_take isl_set *set);
2786 __isl_give isl_union_set *isl_union_set_lift(
2787 __isl_take isl_union_set *uset);
2789 Given a local space that contains the existentially quantified
2790 variables of a set, a basic relation that, when applied to
2791 a basic set, has essentially the same effect as C<isl_basic_set_lift>,
2792 can be constructed using the following function.
2794 #include <isl/local_space.h>
2795 __isl_give isl_basic_map *isl_local_space_lifting(
2796 __isl_take isl_local_space *ls);
2798 =item * Internal Product
2800 __isl_give isl_basic_map *isl_basic_map_zip(
2801 __isl_take isl_basic_map *bmap);
2802 __isl_give isl_map *isl_map_zip(
2803 __isl_take isl_map *map);
2804 __isl_give isl_union_map *isl_union_map_zip(
2805 __isl_take isl_union_map *umap);
2807 Given a relation with nested relations for domain and range,
2808 interchange the range of the domain with the domain of the range.
2812 __isl_give isl_basic_map *isl_basic_map_curry(
2813 __isl_take isl_basic_map *bmap);
2814 __isl_give isl_basic_map *isl_basic_map_uncurry(
2815 __isl_take isl_basic_map *bmap);
2816 __isl_give isl_map *isl_map_curry(
2817 __isl_take isl_map *map);
2818 __isl_give isl_map *isl_map_uncurry(
2819 __isl_take isl_map *map);
2820 __isl_give isl_union_map *isl_union_map_curry(
2821 __isl_take isl_union_map *umap);
2822 __isl_give isl_union_map *isl_union_map_uncurry(
2823 __isl_take isl_union_map *umap);
2825 Given a relation with a nested relation for domain,
2826 the C<curry> functions
2827 move the range of the nested relation out of the domain
2828 and use it as the domain of a nested relation in the range,
2829 with the original range as range of this nested relation.
2830 The C<uncurry> functions perform the inverse operation.
2832 =item * Aligning parameters
2834 __isl_give isl_basic_set *isl_basic_set_align_params(
2835 __isl_take isl_basic_set *bset,
2836 __isl_take isl_space *model);
2837 __isl_give isl_set *isl_set_align_params(
2838 __isl_take isl_set *set,
2839 __isl_take isl_space *model);
2840 __isl_give isl_basic_map *isl_basic_map_align_params(
2841 __isl_take isl_basic_map *bmap,
2842 __isl_take isl_space *model);
2843 __isl_give isl_map *isl_map_align_params(
2844 __isl_take isl_map *map,
2845 __isl_take isl_space *model);
2847 Change the order of the parameters of the given set or relation
2848 such that the first parameters match those of C<model>.
2849 This may involve the introduction of extra parameters.
2850 All parameters need to be named.
2852 =item * Dimension manipulation
2854 __isl_give isl_basic_set *isl_basic_set_add_dims(
2855 __isl_take isl_basic_set *bset,
2856 enum isl_dim_type type, unsigned n);
2857 __isl_give isl_set *isl_set_add_dims(
2858 __isl_take isl_set *set,
2859 enum isl_dim_type type, unsigned n);
2860 __isl_give isl_map *isl_map_add_dims(
2861 __isl_take isl_map *map,
2862 enum isl_dim_type type, unsigned n);
2863 __isl_give isl_basic_set *isl_basic_set_insert_dims(
2864 __isl_take isl_basic_set *bset,
2865 enum isl_dim_type type, unsigned pos,
2867 __isl_give isl_basic_map *isl_basic_map_insert_dims(
2868 __isl_take isl_basic_map *bmap,
2869 enum isl_dim_type type, unsigned pos,
2871 __isl_give isl_set *isl_set_insert_dims(
2872 __isl_take isl_set *set,
2873 enum isl_dim_type type, unsigned pos, unsigned n);
2874 __isl_give isl_map *isl_map_insert_dims(
2875 __isl_take isl_map *map,
2876 enum isl_dim_type type, unsigned pos, unsigned n);
2877 __isl_give isl_basic_set *isl_basic_set_move_dims(
2878 __isl_take isl_basic_set *bset,
2879 enum isl_dim_type dst_type, unsigned dst_pos,
2880 enum isl_dim_type src_type, unsigned src_pos,
2882 __isl_give isl_basic_map *isl_basic_map_move_dims(
2883 __isl_take isl_basic_map *bmap,
2884 enum isl_dim_type dst_type, unsigned dst_pos,
2885 enum isl_dim_type src_type, unsigned src_pos,
2887 __isl_give isl_set *isl_set_move_dims(
2888 __isl_take isl_set *set,
2889 enum isl_dim_type dst_type, unsigned dst_pos,
2890 enum isl_dim_type src_type, unsigned src_pos,
2892 __isl_give isl_map *isl_map_move_dims(
2893 __isl_take isl_map *map,
2894 enum isl_dim_type dst_type, unsigned dst_pos,
2895 enum isl_dim_type src_type, unsigned src_pos,
2898 It is usually not advisable to directly change the (input or output)
2899 space of a set or a relation as this removes the name and the internal
2900 structure of the space. However, the above functions can be useful
2901 to add new parameters, assuming
2902 C<isl_set_align_params> and C<isl_map_align_params>
2907 =head2 Binary Operations
2909 The two arguments of a binary operation not only need to live
2910 in the same C<isl_ctx>, they currently also need to have
2911 the same (number of) parameters.
2913 =head3 Basic Operations
2917 =item * Intersection
2919 __isl_give isl_basic_set *isl_basic_set_intersect_params(
2920 __isl_take isl_basic_set *bset1,
2921 __isl_take isl_basic_set *bset2);
2922 __isl_give isl_basic_set *isl_basic_set_intersect(
2923 __isl_take isl_basic_set *bset1,
2924 __isl_take isl_basic_set *bset2);
2925 __isl_give isl_set *isl_set_intersect_params(
2926 __isl_take isl_set *set,
2927 __isl_take isl_set *params);
2928 __isl_give isl_set *isl_set_intersect(
2929 __isl_take isl_set *set1,
2930 __isl_take isl_set *set2);
2931 __isl_give isl_union_set *isl_union_set_intersect_params(
2932 __isl_take isl_union_set *uset,
2933 __isl_take isl_set *set);
2934 __isl_give isl_union_map *isl_union_map_intersect_params(
2935 __isl_take isl_union_map *umap,
2936 __isl_take isl_set *set);
2937 __isl_give isl_union_set *isl_union_set_intersect(
2938 __isl_take isl_union_set *uset1,
2939 __isl_take isl_union_set *uset2);
2940 __isl_give isl_basic_map *isl_basic_map_intersect_domain(
2941 __isl_take isl_basic_map *bmap,
2942 __isl_take isl_basic_set *bset);
2943 __isl_give isl_basic_map *isl_basic_map_intersect_range(
2944 __isl_take isl_basic_map *bmap,
2945 __isl_take isl_basic_set *bset);
2946 __isl_give isl_basic_map *isl_basic_map_intersect(
2947 __isl_take isl_basic_map *bmap1,
2948 __isl_take isl_basic_map *bmap2);
2949 __isl_give isl_map *isl_map_intersect_params(
2950 __isl_take isl_map *map,
2951 __isl_take isl_set *params);
2952 __isl_give isl_map *isl_map_intersect_domain(
2953 __isl_take isl_map *map,
2954 __isl_take isl_set *set);
2955 __isl_give isl_map *isl_map_intersect_range(
2956 __isl_take isl_map *map,
2957 __isl_take isl_set *set);
2958 __isl_give isl_map *isl_map_intersect(
2959 __isl_take isl_map *map1,
2960 __isl_take isl_map *map2);
2961 __isl_give isl_union_map *isl_union_map_intersect_domain(
2962 __isl_take isl_union_map *umap,
2963 __isl_take isl_union_set *uset);
2964 __isl_give isl_union_map *isl_union_map_intersect_range(
2965 __isl_take isl_union_map *umap,
2966 __isl_take isl_union_set *uset);
2967 __isl_give isl_union_map *isl_union_map_intersect(
2968 __isl_take isl_union_map *umap1,
2969 __isl_take isl_union_map *umap2);
2971 The second argument to the C<_params> functions needs to be
2972 a parametric (basic) set. For the other functions, a parametric set
2973 for either argument is only allowed if the other argument is
2974 a parametric set as well.
2978 __isl_give isl_set *isl_basic_set_union(
2979 __isl_take isl_basic_set *bset1,
2980 __isl_take isl_basic_set *bset2);
2981 __isl_give isl_map *isl_basic_map_union(
2982 __isl_take isl_basic_map *bmap1,
2983 __isl_take isl_basic_map *bmap2);
2984 __isl_give isl_set *isl_set_union(
2985 __isl_take isl_set *set1,
2986 __isl_take isl_set *set2);
2987 __isl_give isl_map *isl_map_union(
2988 __isl_take isl_map *map1,
2989 __isl_take isl_map *map2);
2990 __isl_give isl_union_set *isl_union_set_union(
2991 __isl_take isl_union_set *uset1,
2992 __isl_take isl_union_set *uset2);
2993 __isl_give isl_union_map *isl_union_map_union(
2994 __isl_take isl_union_map *umap1,
2995 __isl_take isl_union_map *umap2);
2997 =item * Set difference
2999 __isl_give isl_set *isl_set_subtract(
3000 __isl_take isl_set *set1,
3001 __isl_take isl_set *set2);
3002 __isl_give isl_map *isl_map_subtract(
3003 __isl_take isl_map *map1,
3004 __isl_take isl_map *map2);
3005 __isl_give isl_map *isl_map_subtract_domain(
3006 __isl_take isl_map *map,
3007 __isl_take isl_set *dom);
3008 __isl_give isl_map *isl_map_subtract_range(
3009 __isl_take isl_map *map,
3010 __isl_take isl_set *dom);
3011 __isl_give isl_union_set *isl_union_set_subtract(
3012 __isl_take isl_union_set *uset1,
3013 __isl_take isl_union_set *uset2);
3014 __isl_give isl_union_map *isl_union_map_subtract(
3015 __isl_take isl_union_map *umap1,
3016 __isl_take isl_union_map *umap2);
3017 __isl_give isl_union_map *isl_union_map_subtract_domain(
3018 __isl_take isl_union_map *umap,
3019 __isl_take isl_union_set *dom);
3020 __isl_give isl_union_map *isl_union_map_subtract_range(
3021 __isl_take isl_union_map *umap,
3022 __isl_take isl_union_set *dom);
3026 __isl_give isl_basic_set *isl_basic_set_apply(
3027 __isl_take isl_basic_set *bset,
3028 __isl_take isl_basic_map *bmap);
3029 __isl_give isl_set *isl_set_apply(
3030 __isl_take isl_set *set,
3031 __isl_take isl_map *map);
3032 __isl_give isl_union_set *isl_union_set_apply(
3033 __isl_take isl_union_set *uset,
3034 __isl_take isl_union_map *umap);
3035 __isl_give isl_basic_map *isl_basic_map_apply_domain(
3036 __isl_take isl_basic_map *bmap1,
3037 __isl_take isl_basic_map *bmap2);
3038 __isl_give isl_basic_map *isl_basic_map_apply_range(
3039 __isl_take isl_basic_map *bmap1,
3040 __isl_take isl_basic_map *bmap2);
3041 __isl_give isl_map *isl_map_apply_domain(
3042 __isl_take isl_map *map1,
3043 __isl_take isl_map *map2);
3044 __isl_give isl_union_map *isl_union_map_apply_domain(
3045 __isl_take isl_union_map *umap1,
3046 __isl_take isl_union_map *umap2);
3047 __isl_give isl_map *isl_map_apply_range(
3048 __isl_take isl_map *map1,
3049 __isl_take isl_map *map2);
3050 __isl_give isl_union_map *isl_union_map_apply_range(
3051 __isl_take isl_union_map *umap1,
3052 __isl_take isl_union_map *umap2);
3056 __isl_give isl_basic_set *
3057 isl_basic_set_preimage_multi_aff(
3058 __isl_take isl_basic_set *bset,
3059 __isl_take isl_multi_aff *ma);
3060 __isl_give isl_set *isl_set_preimage_multi_aff(
3061 __isl_take isl_set *set,
3062 __isl_take isl_multi_aff *ma);
3063 __isl_give isl_set *isl_set_preimage_pw_multi_aff(
3064 __isl_take isl_set *set,
3065 __isl_take isl_pw_multi_aff *pma);
3066 __isl_give isl_map *isl_map_preimage_domain_multi_aff(
3067 __isl_take isl_map *map,
3068 __isl_take isl_multi_aff *ma);
3069 __isl_give isl_union_map *
3070 isl_union_map_preimage_domain_multi_aff(
3071 __isl_take isl_union_map *umap,
3072 __isl_take isl_multi_aff *ma);
3074 These functions compute the preimage of the given set or map domain under
3075 the given function. In other words, the expression is plugged
3076 into the set description or into the domain of the map.
3077 Objects of types C<isl_multi_aff> and C<isl_pw_multi_aff> are described in
3078 L</"Piecewise Multiple Quasi Affine Expressions">.
3080 =item * Cartesian Product
3082 __isl_give isl_set *isl_set_product(
3083 __isl_take isl_set *set1,
3084 __isl_take isl_set *set2);
3085 __isl_give isl_union_set *isl_union_set_product(
3086 __isl_take isl_union_set *uset1,
3087 __isl_take isl_union_set *uset2);
3088 __isl_give isl_basic_map *isl_basic_map_domain_product(
3089 __isl_take isl_basic_map *bmap1,
3090 __isl_take isl_basic_map *bmap2);
3091 __isl_give isl_basic_map *isl_basic_map_range_product(
3092 __isl_take isl_basic_map *bmap1,
3093 __isl_take isl_basic_map *bmap2);
3094 __isl_give isl_basic_map *isl_basic_map_product(
3095 __isl_take isl_basic_map *bmap1,
3096 __isl_take isl_basic_map *bmap2);
3097 __isl_give isl_map *isl_map_domain_product(
3098 __isl_take isl_map *map1,
3099 __isl_take isl_map *map2);
3100 __isl_give isl_map *isl_map_range_product(
3101 __isl_take isl_map *map1,
3102 __isl_take isl_map *map2);
3103 __isl_give isl_union_map *isl_union_map_domain_product(
3104 __isl_take isl_union_map *umap1,
3105 __isl_take isl_union_map *umap2);
3106 __isl_give isl_union_map *isl_union_map_range_product(
3107 __isl_take isl_union_map *umap1,
3108 __isl_take isl_union_map *umap2);
3109 __isl_give isl_map *isl_map_product(
3110 __isl_take isl_map *map1,
3111 __isl_take isl_map *map2);
3112 __isl_give isl_union_map *isl_union_map_product(
3113 __isl_take isl_union_map *umap1,
3114 __isl_take isl_union_map *umap2);
3116 The above functions compute the cross product of the given
3117 sets or relations. The domains and ranges of the results
3118 are wrapped maps between domains and ranges of the inputs.
3119 To obtain a ``flat'' product, use the following functions
3122 __isl_give isl_basic_set *isl_basic_set_flat_product(
3123 __isl_take isl_basic_set *bset1,
3124 __isl_take isl_basic_set *bset2);
3125 __isl_give isl_set *isl_set_flat_product(
3126 __isl_take isl_set *set1,
3127 __isl_take isl_set *set2);
3128 __isl_give isl_basic_map *isl_basic_map_flat_range_product(
3129 __isl_take isl_basic_map *bmap1,
3130 __isl_take isl_basic_map *bmap2);
3131 __isl_give isl_map *isl_map_flat_domain_product(
3132 __isl_take isl_map *map1,
3133 __isl_take isl_map *map2);
3134 __isl_give isl_map *isl_map_flat_range_product(
3135 __isl_take isl_map *map1,
3136 __isl_take isl_map *map2);
3137 __isl_give isl_union_map *isl_union_map_flat_range_product(
3138 __isl_take isl_union_map *umap1,
3139 __isl_take isl_union_map *umap2);
3140 __isl_give isl_basic_map *isl_basic_map_flat_product(
3141 __isl_take isl_basic_map *bmap1,
3142 __isl_take isl_basic_map *bmap2);
3143 __isl_give isl_map *isl_map_flat_product(
3144 __isl_take isl_map *map1,
3145 __isl_take isl_map *map2);
3147 =item * Simplification
3149 __isl_give isl_basic_set *isl_basic_set_gist(
3150 __isl_take isl_basic_set *bset,
3151 __isl_take isl_basic_set *context);
3152 __isl_give isl_set *isl_set_gist(__isl_take isl_set *set,
3153 __isl_take isl_set *context);
3154 __isl_give isl_set *isl_set_gist_params(
3155 __isl_take isl_set *set,
3156 __isl_take isl_set *context);
3157 __isl_give isl_union_set *isl_union_set_gist(
3158 __isl_take isl_union_set *uset,
3159 __isl_take isl_union_set *context);
3160 __isl_give isl_union_set *isl_union_set_gist_params(
3161 __isl_take isl_union_set *uset,
3162 __isl_take isl_set *set);
3163 __isl_give isl_basic_map *isl_basic_map_gist(
3164 __isl_take isl_basic_map *bmap,
3165 __isl_take isl_basic_map *context);
3166 __isl_give isl_map *isl_map_gist(__isl_take isl_map *map,
3167 __isl_take isl_map *context);
3168 __isl_give isl_map *isl_map_gist_params(
3169 __isl_take isl_map *map,
3170 __isl_take isl_set *context);
3171 __isl_give isl_map *isl_map_gist_domain(
3172 __isl_take isl_map *map,
3173 __isl_take isl_set *context);
3174 __isl_give isl_map *isl_map_gist_range(
3175 __isl_take isl_map *map,
3176 __isl_take isl_set *context);
3177 __isl_give isl_union_map *isl_union_map_gist(
3178 __isl_take isl_union_map *umap,
3179 __isl_take isl_union_map *context);
3180 __isl_give isl_union_map *isl_union_map_gist_params(
3181 __isl_take isl_union_map *umap,
3182 __isl_take isl_set *set);
3183 __isl_give isl_union_map *isl_union_map_gist_domain(
3184 __isl_take isl_union_map *umap,
3185 __isl_take isl_union_set *uset);
3186 __isl_give isl_union_map *isl_union_map_gist_range(
3187 __isl_take isl_union_map *umap,
3188 __isl_take isl_union_set *uset);
3190 The gist operation returns a set or relation that has the
3191 same intersection with the context as the input set or relation.
3192 Any implicit equality in the intersection is made explicit in the result,
3193 while all inequalities that are redundant with respect to the intersection
3195 In case of union sets and relations, the gist operation is performed
3200 =head3 Lexicographic Optimization
3202 Given a (basic) set C<set> (or C<bset>) and a zero-dimensional domain C<dom>,
3203 the following functions
3204 compute a set that contains the lexicographic minimum or maximum
3205 of the elements in C<set> (or C<bset>) for those values of the parameters
3206 that satisfy C<dom>.
3207 If C<empty> is not C<NULL>, then C<*empty> is assigned a set
3208 that contains the parameter values in C<dom> for which C<set> (or C<bset>)
3210 In other words, the union of the parameter values
3211 for which the result is non-empty and of C<*empty>
3214 __isl_give isl_set *isl_basic_set_partial_lexmin(
3215 __isl_take isl_basic_set *bset,
3216 __isl_take isl_basic_set *dom,
3217 __isl_give isl_set **empty);
3218 __isl_give isl_set *isl_basic_set_partial_lexmax(
3219 __isl_take isl_basic_set *bset,
3220 __isl_take isl_basic_set *dom,
3221 __isl_give isl_set **empty);
3222 __isl_give isl_set *isl_set_partial_lexmin(
3223 __isl_take isl_set *set, __isl_take isl_set *dom,
3224 __isl_give isl_set **empty);
3225 __isl_give isl_set *isl_set_partial_lexmax(
3226 __isl_take isl_set *set, __isl_take isl_set *dom,
3227 __isl_give isl_set **empty);
3229 Given a (basic) set C<set> (or C<bset>), the following functions simply
3230 return a set containing the lexicographic minimum or maximum
3231 of the elements in C<set> (or C<bset>).
3232 In case of union sets, the optimum is computed per space.
3234 __isl_give isl_set *isl_basic_set_lexmin(
3235 __isl_take isl_basic_set *bset);
3236 __isl_give isl_set *isl_basic_set_lexmax(
3237 __isl_take isl_basic_set *bset);
3238 __isl_give isl_set *isl_set_lexmin(
3239 __isl_take isl_set *set);
3240 __isl_give isl_set *isl_set_lexmax(
3241 __isl_take isl_set *set);
3242 __isl_give isl_union_set *isl_union_set_lexmin(
3243 __isl_take isl_union_set *uset);
3244 __isl_give isl_union_set *isl_union_set_lexmax(
3245 __isl_take isl_union_set *uset);
3247 Given a (basic) relation C<map> (or C<bmap>) and a domain C<dom>,
3248 the following functions
3249 compute a relation that maps each element of C<dom>
3250 to the single lexicographic minimum or maximum
3251 of the elements that are associated to that same
3252 element in C<map> (or C<bmap>).
3253 If C<empty> is not C<NULL>, then C<*empty> is assigned a set
3254 that contains the elements in C<dom> that do not map
3255 to any elements in C<map> (or C<bmap>).
3256 In other words, the union of the domain of the result and of C<*empty>
3259 __isl_give isl_map *isl_basic_map_partial_lexmax(
3260 __isl_take isl_basic_map *bmap,
3261 __isl_take isl_basic_set *dom,
3262 __isl_give isl_set **empty);
3263 __isl_give isl_map *isl_basic_map_partial_lexmin(
3264 __isl_take isl_basic_map *bmap,
3265 __isl_take isl_basic_set *dom,
3266 __isl_give isl_set **empty);
3267 __isl_give isl_map *isl_map_partial_lexmax(
3268 __isl_take isl_map *map, __isl_take isl_set *dom,
3269 __isl_give isl_set **empty);
3270 __isl_give isl_map *isl_map_partial_lexmin(
3271 __isl_take isl_map *map, __isl_take isl_set *dom,
3272 __isl_give isl_set **empty);
3274 Given a (basic) map C<map> (or C<bmap>), the following functions simply
3275 return a map mapping each element in the domain of
3276 C<map> (or C<bmap>) to the lexicographic minimum or maximum
3277 of all elements associated to that element.
3278 In case of union relations, the optimum is computed per space.
3280 __isl_give isl_map *isl_basic_map_lexmin(
3281 __isl_take isl_basic_map *bmap);
3282 __isl_give isl_map *isl_basic_map_lexmax(
3283 __isl_take isl_basic_map *bmap);
3284 __isl_give isl_map *isl_map_lexmin(
3285 __isl_take isl_map *map);
3286 __isl_give isl_map *isl_map_lexmax(
3287 __isl_take isl_map *map);
3288 __isl_give isl_union_map *isl_union_map_lexmin(
3289 __isl_take isl_union_map *umap);
3290 __isl_give isl_union_map *isl_union_map_lexmax(
3291 __isl_take isl_union_map *umap);
3293 The following functions return their result in the form of
3294 a piecewise multi-affine expression
3295 (See L<"Piecewise Multiple Quasi Affine Expressions">),
3296 but are otherwise equivalent to the corresponding functions
3297 returning a basic set or relation.
3299 __isl_give isl_pw_multi_aff *
3300 isl_basic_map_lexmin_pw_multi_aff(
3301 __isl_take isl_basic_map *bmap);
3302 __isl_give isl_pw_multi_aff *
3303 isl_basic_set_partial_lexmin_pw_multi_aff(
3304 __isl_take isl_basic_set *bset,
3305 __isl_take isl_basic_set *dom,
3306 __isl_give isl_set **empty);
3307 __isl_give isl_pw_multi_aff *
3308 isl_basic_set_partial_lexmax_pw_multi_aff(
3309 __isl_take isl_basic_set *bset,
3310 __isl_take isl_basic_set *dom,
3311 __isl_give isl_set **empty);
3312 __isl_give isl_pw_multi_aff *
3313 isl_basic_map_partial_lexmin_pw_multi_aff(
3314 __isl_take isl_basic_map *bmap,
3315 __isl_take isl_basic_set *dom,
3316 __isl_give isl_set **empty);
3317 __isl_give isl_pw_multi_aff *
3318 isl_basic_map_partial_lexmax_pw_multi_aff(
3319 __isl_take isl_basic_map *bmap,
3320 __isl_take isl_basic_set *dom,
3321 __isl_give isl_set **empty);
3322 __isl_give isl_pw_multi_aff *isl_set_lexmin_pw_multi_aff(
3323 __isl_take isl_set *set);
3324 __isl_give isl_pw_multi_aff *isl_set_lexmax_pw_multi_aff(
3325 __isl_take isl_set *set);
3326 __isl_give isl_pw_multi_aff *isl_map_lexmin_pw_multi_aff(
3327 __isl_take isl_map *map);
3328 __isl_give isl_pw_multi_aff *isl_map_lexmax_pw_multi_aff(
3329 __isl_take isl_map *map);
3333 Lists are defined over several element types, including
3334 C<isl_val>, C<isl_id>, C<isl_aff>, C<isl_pw_aff>, C<isl_constraint>,
3335 C<isl_basic_set>, C<isl_set>, C<isl_ast_expr> and C<isl_ast_node>.
3336 Here we take lists of C<isl_set>s as an example.
3337 Lists can be created, copied, modified and freed using the following functions.
3339 #include <isl/list.h>
3340 __isl_give isl_set_list *isl_set_list_from_set(
3341 __isl_take isl_set *el);
3342 __isl_give isl_set_list *isl_set_list_alloc(
3343 isl_ctx *ctx, int n);
3344 __isl_give isl_set_list *isl_set_list_copy(
3345 __isl_keep isl_set_list *list);
3346 __isl_give isl_set_list *isl_set_list_insert(
3347 __isl_take isl_set_list *list, unsigned pos,
3348 __isl_take isl_set *el);
3349 __isl_give isl_set_list *isl_set_list_add(
3350 __isl_take isl_set_list *list,
3351 __isl_take isl_set *el);
3352 __isl_give isl_set_list *isl_set_list_drop(
3353 __isl_take isl_set_list *list,
3354 unsigned first, unsigned n);
3355 __isl_give isl_set_list *isl_set_list_set_set(
3356 __isl_take isl_set_list *list, int index,
3357 __isl_take isl_set *set);
3358 __isl_give isl_set_list *isl_set_list_concat(
3359 __isl_take isl_set_list *list1,
3360 __isl_take isl_set_list *list2);
3361 __isl_give isl_set_list *isl_set_list_sort(
3362 __isl_take isl_set_list *list,
3363 int (*cmp)(__isl_keep isl_set *a,
3364 __isl_keep isl_set *b, void *user),
3366 void *isl_set_list_free(__isl_take isl_set_list *list);
3368 C<isl_set_list_alloc> creates an empty list with a capacity for
3369 C<n> elements. C<isl_set_list_from_set> creates a list with a single
3372 Lists can be inspected using the following functions.
3374 #include <isl/list.h>
3375 isl_ctx *isl_set_list_get_ctx(__isl_keep isl_set_list *list);
3376 int isl_set_list_n_set(__isl_keep isl_set_list *list);
3377 __isl_give isl_set *isl_set_list_get_set(
3378 __isl_keep isl_set_list *list, int index);
3379 int isl_set_list_foreach(__isl_keep isl_set_list *list,
3380 int (*fn)(__isl_take isl_set *el, void *user),
3382 int isl_set_list_foreach_scc(__isl_keep isl_set_list *list,
3383 int (*follows)(__isl_keep isl_set *a,
3384 __isl_keep isl_set *b, void *user),
3386 int (*fn)(__isl_take isl_set *el, void *user),
3389 The function C<isl_set_list_foreach_scc> calls C<fn> on each of the
3390 strongly connected components of the graph with as vertices the elements
3391 of C<list> and a directed edge from vertex C<b> to vertex C<a>
3392 iff C<follows(a, b)> returns C<1>. The callbacks C<follows> and C<fn>
3393 should return C<-1> on error.
3395 Lists can be printed using
3397 #include <isl/list.h>
3398 __isl_give isl_printer *isl_printer_print_set_list(
3399 __isl_take isl_printer *p,
3400 __isl_keep isl_set_list *list);
3402 =head2 Multiple Values
3404 An C<isl_multi_val> object represents a sequence of zero or more values,
3405 living in a set space.
3407 An C<isl_multi_val> can be constructed from an C<isl_val_list>
3408 using the following function
3410 #include <isl/val.h>
3411 __isl_give isl_multi_val *isl_multi_val_from_val_list(
3412 __isl_take isl_space *space,
3413 __isl_take isl_val_list *list);
3415 The zero multiple value (with value zero for each set dimension)
3416 can be created using the following function.
3418 #include <isl/val.h>
3419 __isl_give isl_multi_val *isl_multi_val_zero(
3420 __isl_take isl_space *space);
3422 Multiple values can be copied and freed using
3424 #include <isl/val.h>
3425 __isl_give isl_multi_val *isl_multi_val_copy(
3426 __isl_keep isl_multi_val *mv);
3427 void *isl_multi_val_free(__isl_take isl_multi_val *mv);
3429 They can be inspected using
3431 #include <isl/val.h>
3432 isl_ctx *isl_multi_val_get_ctx(
3433 __isl_keep isl_multi_val *mv);
3434 unsigned isl_multi_val_dim(__isl_keep isl_multi_val *mv,
3435 enum isl_dim_type type);
3436 __isl_give isl_val *isl_multi_val_get_val(
3437 __isl_keep isl_multi_val *mv, int pos);
3438 const char *isl_multi_val_get_tuple_name(
3439 __isl_keep isl_multi_val *mv,
3440 enum isl_dim_type type);
3442 They can be modified using
3444 #include <isl/val.h>
3445 __isl_give isl_multi_val *isl_multi_val_set_val(
3446 __isl_take isl_multi_val *mv, int pos,
3447 __isl_take isl_val *val);
3448 __isl_give isl_multi_val *isl_multi_val_set_dim_name(
3449 __isl_take isl_multi_val *mv,
3450 enum isl_dim_type type, unsigned pos, const char *s);
3451 __isl_give isl_multi_val *isl_multi_val_set_tuple_name(
3452 __isl_take isl_multi_val *mv,
3453 enum isl_dim_type type, const char *s);
3454 __isl_give isl_multi_val *isl_multi_val_set_tuple_id(
3455 __isl_take isl_multi_val *mv,
3456 enum isl_dim_type type, __isl_take isl_id *id);
3458 __isl_give isl_multi_val *isl_multi_val_insert_dims(
3459 __isl_take isl_multi_val *mv,
3460 enum isl_dim_type type, unsigned first, unsigned n);
3461 __isl_give isl_multi_val *isl_multi_val_add_dims(
3462 __isl_take isl_multi_val *mv,
3463 enum isl_dim_type type, unsigned n);
3464 __isl_give isl_multi_val *isl_multi_val_drop_dims(
3465 __isl_take isl_multi_val *mv,
3466 enum isl_dim_type type, unsigned first, unsigned n);
3470 #include <isl/val.h>
3471 __isl_give isl_multi_val *isl_multi_val_align_params(
3472 __isl_take isl_multi_val *mv,
3473 __isl_take isl_space *model);
3474 __isl_give isl_multi_val *isl_multi_val_range_splice(
3475 __isl_take isl_multi_val *mv1, unsigned pos,
3476 __isl_take isl_multi_val *mv2);
3477 __isl_give isl_multi_val *isl_multi_val_range_product(
3478 __isl_take isl_multi_val *mv1,
3479 __isl_take isl_multi_val *mv2);
3480 __isl_give isl_multi_val *isl_multi_val_flat_range_product(
3481 __isl_take isl_multi_val *mv1,
3482 __isl_take isl_multi_aff *mv2);
3483 __isl_give isl_multi_val *isl_multi_val_add_val(
3484 __isl_take isl_multi_val *mv,
3485 __isl_take isl_val *v);
3486 __isl_give isl_multi_val *isl_multi_val_mod_val(
3487 __isl_take isl_multi_val *mv,
3488 __isl_take isl_val *v);
3489 __isl_give isl_multi_val *isl_multi_val_scale_val(
3490 __isl_take isl_multi_val *mv,
3491 __isl_take isl_val *v);
3495 Vectors can be created, copied and freed using the following functions.
3497 #include <isl/vec.h>
3498 __isl_give isl_vec *isl_vec_alloc(isl_ctx *ctx,
3500 __isl_give isl_vec *isl_vec_copy(__isl_keep isl_vec *vec);
3501 void *isl_vec_free(__isl_take isl_vec *vec);
3503 Note that the elements of a newly created vector may have arbitrary values.
3504 The elements can be changed and inspected using the following functions.
3506 isl_ctx *isl_vec_get_ctx(__isl_keep isl_vec *vec);
3507 int isl_vec_size(__isl_keep isl_vec *vec);
3508 int isl_vec_get_element(__isl_keep isl_vec *vec,
3509 int pos, isl_int *v);
3510 __isl_give isl_val *isl_vec_get_element_val(
3511 __isl_keep isl_vec *vec, int pos);
3512 __isl_give isl_vec *isl_vec_set_element(
3513 __isl_take isl_vec *vec, int pos, isl_int v);
3514 __isl_give isl_vec *isl_vec_set_element_si(
3515 __isl_take isl_vec *vec, int pos, int v);
3516 __isl_give isl_vec *isl_vec_set_element_val(
3517 __isl_take isl_vec *vec, int pos,
3518 __isl_take isl_val *v);
3519 __isl_give isl_vec *isl_vec_set(__isl_take isl_vec *vec,
3521 __isl_give isl_vec *isl_vec_set_si(__isl_take isl_vec *vec,
3523 __isl_give isl_vec *isl_vec_set_val(
3524 __isl_take isl_vec *vec, __isl_take isl_val *v);
3525 __isl_give isl_vec *isl_vec_fdiv_r(__isl_take isl_vec *vec,
3528 C<isl_vec_get_element> will return a negative value if anything went wrong.
3529 In that case, the value of C<*v> is undefined.
3531 The following function can be used to concatenate two vectors.
3533 __isl_give isl_vec *isl_vec_concat(__isl_take isl_vec *vec1,
3534 __isl_take isl_vec *vec2);
3538 Matrices can be created, copied and freed using the following functions.
3540 #include <isl/mat.h>
3541 __isl_give isl_mat *isl_mat_alloc(isl_ctx *ctx,
3542 unsigned n_row, unsigned n_col);
3543 __isl_give isl_mat *isl_mat_copy(__isl_keep isl_mat *mat);
3544 void *isl_mat_free(__isl_take isl_mat *mat);
3546 Note that the elements of a newly created matrix may have arbitrary values.
3547 The elements can be changed and inspected using the following functions.
3549 isl_ctx *isl_mat_get_ctx(__isl_keep isl_mat *mat);
3550 int isl_mat_rows(__isl_keep isl_mat *mat);
3551 int isl_mat_cols(__isl_keep isl_mat *mat);
3552 int isl_mat_get_element(__isl_keep isl_mat *mat,
3553 int row, int col, isl_int *v);
3554 __isl_give isl_val *isl_mat_get_element_val(
3555 __isl_keep isl_mat *mat, int row, int col);
3556 __isl_give isl_mat *isl_mat_set_element(__isl_take isl_mat *mat,
3557 int row, int col, isl_int v);
3558 __isl_give isl_mat *isl_mat_set_element_si(__isl_take isl_mat *mat,
3559 int row, int col, int v);
3560 __isl_give isl_mat *isl_mat_set_element_val(
3561 __isl_take isl_mat *mat, int row, int col,
3562 __isl_take isl_val *v);
3564 C<isl_mat_get_element> will return a negative value if anything went wrong.
3565 In that case, the value of C<*v> is undefined.
3567 The following function can be used to compute the (right) inverse
3568 of a matrix, i.e., a matrix such that the product of the original
3569 and the inverse (in that order) is a multiple of the identity matrix.
3570 The input matrix is assumed to be of full row-rank.
3572 __isl_give isl_mat *isl_mat_right_inverse(__isl_take isl_mat *mat);
3574 The following function can be used to compute the (right) kernel
3575 (or null space) of a matrix, i.e., a matrix such that the product of
3576 the original and the kernel (in that order) is the zero matrix.
3578 __isl_give isl_mat *isl_mat_right_kernel(__isl_take isl_mat *mat);
3580 =head2 Piecewise Quasi Affine Expressions
3582 The zero quasi affine expression or the quasi affine expression
3583 that is equal to a specified dimension on a given domain can be created using
3585 __isl_give isl_aff *isl_aff_zero_on_domain(
3586 __isl_take isl_local_space *ls);
3587 __isl_give isl_pw_aff *isl_pw_aff_zero_on_domain(
3588 __isl_take isl_local_space *ls);
3589 __isl_give isl_aff *isl_aff_var_on_domain(
3590 __isl_take isl_local_space *ls,
3591 enum isl_dim_type type, unsigned pos);
3592 __isl_give isl_pw_aff *isl_pw_aff_var_on_domain(
3593 __isl_take isl_local_space *ls,
3594 enum isl_dim_type type, unsigned pos);
3596 Note that the space in which the resulting objects live is a map space
3597 with the given space as domain and a one-dimensional range.
3599 An empty piecewise quasi affine expression (one with no cells)
3600 or a piecewise quasi affine expression with a single cell can
3601 be created using the following functions.
3603 #include <isl/aff.h>
3604 __isl_give isl_pw_aff *isl_pw_aff_empty(
3605 __isl_take isl_space *space);
3606 __isl_give isl_pw_aff *isl_pw_aff_alloc(
3607 __isl_take isl_set *set, __isl_take isl_aff *aff);
3608 __isl_give isl_pw_aff *isl_pw_aff_from_aff(
3609 __isl_take isl_aff *aff);
3611 A piecewise quasi affine expression that is equal to 1 on a set
3612 and 0 outside the set can be created using the following function.
3614 #include <isl/aff.h>
3615 __isl_give isl_pw_aff *isl_set_indicator_function(
3616 __isl_take isl_set *set);
3618 Quasi affine expressions can be copied and freed using
3620 #include <isl/aff.h>
3621 __isl_give isl_aff *isl_aff_copy(__isl_keep isl_aff *aff);
3622 void *isl_aff_free(__isl_take isl_aff *aff);
3624 __isl_give isl_pw_aff *isl_pw_aff_copy(
3625 __isl_keep isl_pw_aff *pwaff);
3626 void *isl_pw_aff_free(__isl_take isl_pw_aff *pwaff);
3628 A (rational) bound on a dimension can be extracted from an C<isl_constraint>
3629 using the following function. The constraint is required to have
3630 a non-zero coefficient for the specified dimension.
3632 #include <isl/constraint.h>
3633 __isl_give isl_aff *isl_constraint_get_bound(
3634 __isl_keep isl_constraint *constraint,
3635 enum isl_dim_type type, int pos);
3637 The entire affine expression of the constraint can also be extracted
3638 using the following function.
3640 #include <isl/constraint.h>
3641 __isl_give isl_aff *isl_constraint_get_aff(
3642 __isl_keep isl_constraint *constraint);
3644 Conversely, an equality constraint equating
3645 the affine expression to zero or an inequality constraint enforcing
3646 the affine expression to be non-negative, can be constructed using
3648 __isl_give isl_constraint *isl_equality_from_aff(
3649 __isl_take isl_aff *aff);
3650 __isl_give isl_constraint *isl_inequality_from_aff(
3651 __isl_take isl_aff *aff);
3653 The expression can be inspected using
3655 #include <isl/aff.h>
3656 isl_ctx *isl_aff_get_ctx(__isl_keep isl_aff *aff);
3657 int isl_aff_dim(__isl_keep isl_aff *aff,
3658 enum isl_dim_type type);
3659 __isl_give isl_local_space *isl_aff_get_domain_local_space(
3660 __isl_keep isl_aff *aff);
3661 __isl_give isl_local_space *isl_aff_get_local_space(
3662 __isl_keep isl_aff *aff);
3663 const char *isl_aff_get_dim_name(__isl_keep isl_aff *aff,
3664 enum isl_dim_type type, unsigned pos);
3665 const char *isl_pw_aff_get_dim_name(
3666 __isl_keep isl_pw_aff *pa,
3667 enum isl_dim_type type, unsigned pos);
3668 int isl_pw_aff_has_dim_id(__isl_keep isl_pw_aff *pa,
3669 enum isl_dim_type type, unsigned pos);
3670 __isl_give isl_id *isl_pw_aff_get_dim_id(
3671 __isl_keep isl_pw_aff *pa,
3672 enum isl_dim_type type, unsigned pos);
3673 __isl_give isl_id *isl_pw_aff_get_tuple_id(
3674 __isl_keep isl_pw_aff *pa,
3675 enum isl_dim_type type);
3676 int isl_aff_get_constant(__isl_keep isl_aff *aff,
3678 __isl_give isl_val *isl_aff_get_constant_val(
3679 __isl_keep isl_aff *aff);
3680 int isl_aff_get_coefficient(__isl_keep isl_aff *aff,
3681 enum isl_dim_type type, int pos, isl_int *v);
3682 __isl_give isl_val *isl_aff_get_coefficient_val(
3683 __isl_keep isl_aff *aff,
3684 enum isl_dim_type type, int pos);
3685 int isl_aff_get_denominator(__isl_keep isl_aff *aff,
3687 __isl_give isl_val *isl_aff_get_denominator_val(
3688 __isl_keep isl_aff *aff);
3689 __isl_give isl_aff *isl_aff_get_div(
3690 __isl_keep isl_aff *aff, int pos);
3692 int isl_pw_aff_n_piece(__isl_keep isl_pw_aff *pwaff);
3693 int isl_pw_aff_foreach_piece(__isl_keep isl_pw_aff *pwaff,
3694 int (*fn)(__isl_take isl_set *set,
3695 __isl_take isl_aff *aff,
3696 void *user), void *user);
3698 int isl_aff_is_cst(__isl_keep isl_aff *aff);
3699 int isl_pw_aff_is_cst(__isl_keep isl_pw_aff *pwaff);
3701 int isl_aff_involves_dims(__isl_keep isl_aff *aff,
3702 enum isl_dim_type type, unsigned first, unsigned n);
3703 int isl_pw_aff_involves_dims(__isl_keep isl_pw_aff *pwaff,
3704 enum isl_dim_type type, unsigned first, unsigned n);
3706 isl_ctx *isl_pw_aff_get_ctx(__isl_keep isl_pw_aff *pwaff);
3707 unsigned isl_pw_aff_dim(__isl_keep isl_pw_aff *pwaff,
3708 enum isl_dim_type type);
3709 int isl_pw_aff_is_empty(__isl_keep isl_pw_aff *pwaff);
3711 It can be modified using
3713 #include <isl/aff.h>
3714 __isl_give isl_pw_aff *isl_pw_aff_set_tuple_id(
3715 __isl_take isl_pw_aff *pwaff,
3716 enum isl_dim_type type, __isl_take isl_id *id);
3717 __isl_give isl_aff *isl_aff_set_dim_name(
3718 __isl_take isl_aff *aff, enum isl_dim_type type,
3719 unsigned pos, const char *s);
3720 __isl_give isl_aff *isl_aff_set_dim_id(
3721 __isl_take isl_aff *aff, enum isl_dim_type type,
3722 unsigned pos, __isl_take isl_id *id);
3723 __isl_give isl_pw_aff *isl_pw_aff_set_dim_id(
3724 __isl_take isl_pw_aff *pma,
3725 enum isl_dim_type type, unsigned pos,
3726 __isl_take isl_id *id);
3727 __isl_give isl_aff *isl_aff_set_constant(
3728 __isl_take isl_aff *aff, isl_int v);
3729 __isl_give isl_aff *isl_aff_set_constant_si(
3730 __isl_take isl_aff *aff, int v);
3731 __isl_give isl_aff *isl_aff_set_constant_val(
3732 __isl_take isl_aff *aff, __isl_take isl_val *v);
3733 __isl_give isl_aff *isl_aff_set_coefficient(
3734 __isl_take isl_aff *aff,
3735 enum isl_dim_type type, int pos, isl_int v);
3736 __isl_give isl_aff *isl_aff_set_coefficient_si(
3737 __isl_take isl_aff *aff,
3738 enum isl_dim_type type, int pos, int v);
3739 __isl_give isl_aff *isl_aff_set_coefficient_val(
3740 __isl_take isl_aff *aff,
3741 enum isl_dim_type type, int pos,
3742 __isl_take isl_val *v);
3743 __isl_give isl_aff *isl_aff_set_denominator(
3744 __isl_take isl_aff *aff, isl_int v);
3746 __isl_give isl_aff *isl_aff_add_constant(
3747 __isl_take isl_aff *aff, isl_int v);
3748 __isl_give isl_aff *isl_aff_add_constant_si(
3749 __isl_take isl_aff *aff, int v);
3750 __isl_give isl_aff *isl_aff_add_constant_val(
3751 __isl_take isl_aff *aff, __isl_take isl_val *v);
3752 __isl_give isl_aff *isl_aff_add_constant_num(
3753 __isl_take isl_aff *aff, isl_int v);
3754 __isl_give isl_aff *isl_aff_add_constant_num_si(
3755 __isl_take isl_aff *aff, int v);
3756 __isl_give isl_aff *isl_aff_add_coefficient(
3757 __isl_take isl_aff *aff,
3758 enum isl_dim_type type, int pos, isl_int v);
3759 __isl_give isl_aff *isl_aff_add_coefficient_si(
3760 __isl_take isl_aff *aff,
3761 enum isl_dim_type type, int pos, int v);
3762 __isl_give isl_aff *isl_aff_add_coefficient_val(
3763 __isl_take isl_aff *aff,
3764 enum isl_dim_type type, int pos,
3765 __isl_take isl_val *v);
3767 __isl_give isl_aff *isl_aff_insert_dims(
3768 __isl_take isl_aff *aff,
3769 enum isl_dim_type type, unsigned first, unsigned n);
3770 __isl_give isl_pw_aff *isl_pw_aff_insert_dims(
3771 __isl_take isl_pw_aff *pwaff,
3772 enum isl_dim_type type, unsigned first, unsigned n);
3773 __isl_give isl_aff *isl_aff_add_dims(
3774 __isl_take isl_aff *aff,
3775 enum isl_dim_type type, unsigned n);
3776 __isl_give isl_pw_aff *isl_pw_aff_add_dims(
3777 __isl_take isl_pw_aff *pwaff,
3778 enum isl_dim_type type, unsigned n);
3779 __isl_give isl_aff *isl_aff_drop_dims(
3780 __isl_take isl_aff *aff,
3781 enum isl_dim_type type, unsigned first, unsigned n);
3782 __isl_give isl_pw_aff *isl_pw_aff_drop_dims(
3783 __isl_take isl_pw_aff *pwaff,
3784 enum isl_dim_type type, unsigned first, unsigned n);
3786 Note that C<isl_aff_set_constant>, C<isl_aff_set_constant_si>,
3787 C<isl_aff_set_coefficient> and C<isl_aff_set_coefficient_si>
3788 set the I<numerator> of the constant or coefficient, while
3789 C<isl_aff_set_constant_val> and C<isl_aff_set_coefficient_val> set
3790 the constant or coefficient as a whole.
3791 The C<add_constant> and C<add_coefficient> functions add an integer
3792 or rational value to
3793 the possibly rational constant or coefficient.
3794 The C<add_constant_num> functions add an integer value to
3797 To check whether an affine expressions is obviously zero
3798 or obviously equal to some other affine expression, use
3800 #include <isl/aff.h>
3801 int isl_aff_plain_is_zero(__isl_keep isl_aff *aff);
3802 int isl_aff_plain_is_equal(__isl_keep isl_aff *aff1,
3803 __isl_keep isl_aff *aff2);
3804 int isl_pw_aff_plain_is_equal(
3805 __isl_keep isl_pw_aff *pwaff1,
3806 __isl_keep isl_pw_aff *pwaff2);
3810 #include <isl/aff.h>
3811 __isl_give isl_aff *isl_aff_add(__isl_take isl_aff *aff1,
3812 __isl_take isl_aff *aff2);
3813 __isl_give isl_pw_aff *isl_pw_aff_add(
3814 __isl_take isl_pw_aff *pwaff1,
3815 __isl_take isl_pw_aff *pwaff2);
3816 __isl_give isl_pw_aff *isl_pw_aff_min(
3817 __isl_take isl_pw_aff *pwaff1,
3818 __isl_take isl_pw_aff *pwaff2);
3819 __isl_give isl_pw_aff *isl_pw_aff_max(
3820 __isl_take isl_pw_aff *pwaff1,
3821 __isl_take isl_pw_aff *pwaff2);
3822 __isl_give isl_aff *isl_aff_sub(__isl_take isl_aff *aff1,
3823 __isl_take isl_aff *aff2);
3824 __isl_give isl_pw_aff *isl_pw_aff_sub(
3825 __isl_take isl_pw_aff *pwaff1,
3826 __isl_take isl_pw_aff *pwaff2);
3827 __isl_give isl_aff *isl_aff_neg(__isl_take isl_aff *aff);
3828 __isl_give isl_pw_aff *isl_pw_aff_neg(
3829 __isl_take isl_pw_aff *pwaff);
3830 __isl_give isl_aff *isl_aff_ceil(__isl_take isl_aff *aff);
3831 __isl_give isl_pw_aff *isl_pw_aff_ceil(
3832 __isl_take isl_pw_aff *pwaff);
3833 __isl_give isl_aff *isl_aff_floor(__isl_take isl_aff *aff);
3834 __isl_give isl_pw_aff *isl_pw_aff_floor(
3835 __isl_take isl_pw_aff *pwaff);
3836 __isl_give isl_aff *isl_aff_mod(__isl_take isl_aff *aff,
3838 __isl_give isl_aff *isl_aff_mod_val(__isl_take isl_aff *aff,
3839 __isl_take isl_val *mod);
3840 __isl_give isl_pw_aff *isl_pw_aff_mod(
3841 __isl_take isl_pw_aff *pwaff, isl_int mod);
3842 __isl_give isl_pw_aff *isl_pw_aff_mod_val(
3843 __isl_take isl_pw_aff *pa,
3844 __isl_take isl_val *mod);
3845 __isl_give isl_aff *isl_aff_scale(__isl_take isl_aff *aff,
3847 __isl_give isl_aff *isl_aff_scale_val(__isl_take isl_aff *aff,
3848 __isl_take isl_val *v);
3849 __isl_give isl_pw_aff *isl_pw_aff_scale(
3850 __isl_take isl_pw_aff *pwaff, isl_int f);
3851 __isl_give isl_pw_aff *isl_pw_aff_scale_val(
3852 __isl_take isl_pw_aff *pa, __isl_take isl_val *v);
3853 __isl_give isl_aff *isl_aff_scale_down(__isl_take isl_aff *aff,
3855 __isl_give isl_aff *isl_aff_scale_down_ui(
3856 __isl_take isl_aff *aff, unsigned f);
3857 __isl_give isl_aff *isl_aff_scale_down_val(
3858 __isl_take isl_aff *aff, __isl_take isl_val *v);
3859 __isl_give isl_pw_aff *isl_pw_aff_scale_down(
3860 __isl_take isl_pw_aff *pwaff, isl_int f);
3861 __isl_give isl_pw_aff *isl_pw_aff_scale_down_val(
3862 __isl_take isl_pw_aff *pa,
3863 __isl_take isl_val *f);
3865 __isl_give isl_pw_aff *isl_pw_aff_list_min(
3866 __isl_take isl_pw_aff_list *list);
3867 __isl_give isl_pw_aff *isl_pw_aff_list_max(
3868 __isl_take isl_pw_aff_list *list);
3870 __isl_give isl_pw_aff *isl_pw_aff_coalesce(
3871 __isl_take isl_pw_aff *pwqp);
3873 __isl_give isl_aff *isl_aff_align_params(
3874 __isl_take isl_aff *aff,
3875 __isl_take isl_space *model);
3876 __isl_give isl_pw_aff *isl_pw_aff_align_params(
3877 __isl_take isl_pw_aff *pwaff,
3878 __isl_take isl_space *model);
3880 __isl_give isl_aff *isl_aff_project_domain_on_params(
3881 __isl_take isl_aff *aff);
3883 __isl_give isl_aff *isl_aff_gist_params(
3884 __isl_take isl_aff *aff,
3885 __isl_take isl_set *context);
3886 __isl_give isl_aff *isl_aff_gist(__isl_take isl_aff *aff,
3887 __isl_take isl_set *context);
3888 __isl_give isl_pw_aff *isl_pw_aff_gist_params(
3889 __isl_take isl_pw_aff *pwaff,
3890 __isl_take isl_set *context);
3891 __isl_give isl_pw_aff *isl_pw_aff_gist(
3892 __isl_take isl_pw_aff *pwaff,
3893 __isl_take isl_set *context);
3895 __isl_give isl_set *isl_pw_aff_domain(
3896 __isl_take isl_pw_aff *pwaff);
3897 __isl_give isl_pw_aff *isl_pw_aff_intersect_domain(
3898 __isl_take isl_pw_aff *pa,
3899 __isl_take isl_set *set);
3900 __isl_give isl_pw_aff *isl_pw_aff_intersect_params(
3901 __isl_take isl_pw_aff *pa,
3902 __isl_take isl_set *set);
3904 __isl_give isl_aff *isl_aff_mul(__isl_take isl_aff *aff1,
3905 __isl_take isl_aff *aff2);
3906 __isl_give isl_aff *isl_aff_div(__isl_take isl_aff *aff1,
3907 __isl_take isl_aff *aff2);
3908 __isl_give isl_pw_aff *isl_pw_aff_mul(
3909 __isl_take isl_pw_aff *pwaff1,
3910 __isl_take isl_pw_aff *pwaff2);
3911 __isl_give isl_pw_aff *isl_pw_aff_div(
3912 __isl_take isl_pw_aff *pa1,
3913 __isl_take isl_pw_aff *pa2);
3914 __isl_give isl_pw_aff *isl_pw_aff_tdiv_q(
3915 __isl_take isl_pw_aff *pa1,
3916 __isl_take isl_pw_aff *pa2);
3917 __isl_give isl_pw_aff *isl_pw_aff_tdiv_r(
3918 __isl_take isl_pw_aff *pa1,
3919 __isl_take isl_pw_aff *pa2);
3921 When multiplying two affine expressions, at least one of the two needs
3922 to be a constant. Similarly, when dividing an affine expression by another,
3923 the second expression needs to be a constant.
3924 C<isl_pw_aff_tdiv_q> computes the quotient of an integer division with
3925 rounding towards zero. C<isl_pw_aff_tdiv_r> computes the corresponding
3928 #include <isl/aff.h>
3929 __isl_give isl_aff *isl_aff_pullback_multi_aff(
3930 __isl_take isl_aff *aff,
3931 __isl_take isl_multi_aff *ma);
3932 __isl_give isl_pw_aff *isl_pw_aff_pullback_multi_aff(
3933 __isl_take isl_pw_aff *pa,
3934 __isl_take isl_multi_aff *ma);
3935 __isl_give isl_pw_aff *isl_pw_aff_pullback_pw_multi_aff(
3936 __isl_take isl_pw_aff *pa,
3937 __isl_take isl_pw_multi_aff *pma);
3939 These functions precompose the input expression by the given
3940 C<isl_multi_aff> or C<isl_pw_multi_aff>. In other words,
3941 the C<isl_multi_aff> or C<isl_pw_multi_aff> is plugged
3942 into the (piecewise) affine expression.
3943 Objects of type C<isl_multi_aff> are described in
3944 L</"Piecewise Multiple Quasi Affine Expressions">.
3946 #include <isl/aff.h>
3947 __isl_give isl_basic_set *isl_aff_zero_basic_set(
3948 __isl_take isl_aff *aff);
3949 __isl_give isl_basic_set *isl_aff_neg_basic_set(
3950 __isl_take isl_aff *aff);
3951 __isl_give isl_basic_set *isl_aff_le_basic_set(
3952 __isl_take isl_aff *aff1, __isl_take isl_aff *aff2);
3953 __isl_give isl_basic_set *isl_aff_ge_basic_set(
3954 __isl_take isl_aff *aff1, __isl_take isl_aff *aff2);
3955 __isl_give isl_set *isl_pw_aff_eq_set(
3956 __isl_take isl_pw_aff *pwaff1,
3957 __isl_take isl_pw_aff *pwaff2);
3958 __isl_give isl_set *isl_pw_aff_ne_set(
3959 __isl_take isl_pw_aff *pwaff1,
3960 __isl_take isl_pw_aff *pwaff2);
3961 __isl_give isl_set *isl_pw_aff_le_set(
3962 __isl_take isl_pw_aff *pwaff1,
3963 __isl_take isl_pw_aff *pwaff2);
3964 __isl_give isl_set *isl_pw_aff_lt_set(
3965 __isl_take isl_pw_aff *pwaff1,
3966 __isl_take isl_pw_aff *pwaff2);
3967 __isl_give isl_set *isl_pw_aff_ge_set(
3968 __isl_take isl_pw_aff *pwaff1,
3969 __isl_take isl_pw_aff *pwaff2);
3970 __isl_give isl_set *isl_pw_aff_gt_set(
3971 __isl_take isl_pw_aff *pwaff1,
3972 __isl_take isl_pw_aff *pwaff2);
3974 __isl_give isl_set *isl_pw_aff_list_eq_set(
3975 __isl_take isl_pw_aff_list *list1,
3976 __isl_take isl_pw_aff_list *list2);
3977 __isl_give isl_set *isl_pw_aff_list_ne_set(
3978 __isl_take isl_pw_aff_list *list1,
3979 __isl_take isl_pw_aff_list *list2);
3980 __isl_give isl_set *isl_pw_aff_list_le_set(
3981 __isl_take isl_pw_aff_list *list1,
3982 __isl_take isl_pw_aff_list *list2);
3983 __isl_give isl_set *isl_pw_aff_list_lt_set(
3984 __isl_take isl_pw_aff_list *list1,
3985 __isl_take isl_pw_aff_list *list2);
3986 __isl_give isl_set *isl_pw_aff_list_ge_set(
3987 __isl_take isl_pw_aff_list *list1,
3988 __isl_take isl_pw_aff_list *list2);
3989 __isl_give isl_set *isl_pw_aff_list_gt_set(
3990 __isl_take isl_pw_aff_list *list1,
3991 __isl_take isl_pw_aff_list *list2);
3993 The function C<isl_aff_neg_basic_set> returns a basic set
3994 containing those elements in the domain space
3995 of C<aff> where C<aff> is negative.
3996 The function C<isl_aff_ge_basic_set> returns a basic set
3997 containing those elements in the shared space
3998 of C<aff1> and C<aff2> where C<aff1> is greater than or equal to C<aff2>.
3999 The function C<isl_pw_aff_ge_set> returns a set
4000 containing those elements in the shared domain
4001 of C<pwaff1> and C<pwaff2> where C<pwaff1> is greater than or equal to C<pwaff2>.
4002 The functions operating on C<isl_pw_aff_list> apply the corresponding
4003 C<isl_pw_aff> function to each pair of elements in the two lists.
4005 #include <isl/aff.h>
4006 __isl_give isl_set *isl_pw_aff_nonneg_set(
4007 __isl_take isl_pw_aff *pwaff);
4008 __isl_give isl_set *isl_pw_aff_zero_set(
4009 __isl_take isl_pw_aff *pwaff);
4010 __isl_give isl_set *isl_pw_aff_non_zero_set(
4011 __isl_take isl_pw_aff *pwaff);
4013 The function C<isl_pw_aff_nonneg_set> returns a set
4014 containing those elements in the domain
4015 of C<pwaff> where C<pwaff> is non-negative.
4017 #include <isl/aff.h>
4018 __isl_give isl_pw_aff *isl_pw_aff_cond(
4019 __isl_take isl_pw_aff *cond,
4020 __isl_take isl_pw_aff *pwaff_true,
4021 __isl_take isl_pw_aff *pwaff_false);
4023 The function C<isl_pw_aff_cond> performs a conditional operator
4024 and returns an expression that is equal to C<pwaff_true>
4025 for elements where C<cond> is non-zero and equal to C<pwaff_false> for elements
4026 where C<cond> is zero.
4028 #include <isl/aff.h>
4029 __isl_give isl_pw_aff *isl_pw_aff_union_min(
4030 __isl_take isl_pw_aff *pwaff1,
4031 __isl_take isl_pw_aff *pwaff2);
4032 __isl_give isl_pw_aff *isl_pw_aff_union_max(
4033 __isl_take isl_pw_aff *pwaff1,
4034 __isl_take isl_pw_aff *pwaff2);
4035 __isl_give isl_pw_aff *isl_pw_aff_union_add(
4036 __isl_take isl_pw_aff *pwaff1,
4037 __isl_take isl_pw_aff *pwaff2);
4039 The function C<isl_pw_aff_union_max> computes a piecewise quasi-affine
4040 expression with a domain that is the union of those of C<pwaff1> and
4041 C<pwaff2> and such that on each cell, the quasi-affine expression is
4042 the maximum of those of C<pwaff1> and C<pwaff2>. If only one of
4043 C<pwaff1> or C<pwaff2> is defined on a given cell, then the
4044 associated expression is the defined one.
4046 An expression can be read from input using
4048 #include <isl/aff.h>
4049 __isl_give isl_aff *isl_aff_read_from_str(
4050 isl_ctx *ctx, const char *str);
4051 __isl_give isl_pw_aff *isl_pw_aff_read_from_str(
4052 isl_ctx *ctx, const char *str);
4054 An expression can be printed using
4056 #include <isl/aff.h>
4057 __isl_give isl_printer *isl_printer_print_aff(
4058 __isl_take isl_printer *p, __isl_keep isl_aff *aff);
4060 __isl_give isl_printer *isl_printer_print_pw_aff(
4061 __isl_take isl_printer *p,
4062 __isl_keep isl_pw_aff *pwaff);
4064 =head2 Piecewise Multiple Quasi Affine Expressions
4066 An C<isl_multi_aff> object represents a sequence of
4067 zero or more affine expressions, all defined on the same domain space.
4068 Similarly, an C<isl_multi_pw_aff> object represents a sequence of
4069 zero or more piecewise affine expressions.
4071 An C<isl_multi_aff> can be constructed from a single
4072 C<isl_aff> or an C<isl_aff_list> using the
4073 following functions. Similarly for C<isl_multi_pw_aff>.
4075 #include <isl/aff.h>
4076 __isl_give isl_multi_aff *isl_multi_aff_from_aff(
4077 __isl_take isl_aff *aff);
4078 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_from_pw_aff(
4079 __isl_take isl_pw_aff *pa);
4080 __isl_give isl_multi_aff *isl_multi_aff_from_aff_list(
4081 __isl_take isl_space *space,
4082 __isl_take isl_aff_list *list);
4084 An empty piecewise multiple quasi affine expression (one with no cells),
4085 the zero piecewise multiple quasi affine expression (with value zero
4086 for each output dimension),
4087 a piecewise multiple quasi affine expression with a single cell (with
4088 either a universe or a specified domain) or
4089 a zero-dimensional piecewise multiple quasi affine expression
4091 can be created using the following functions.
4093 #include <isl/aff.h>
4094 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_empty(
4095 __isl_take isl_space *space);
4096 __isl_give isl_multi_aff *isl_multi_aff_zero(
4097 __isl_take isl_space *space);
4098 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_zero(
4099 __isl_take isl_space *space);
4100 __isl_give isl_multi_aff *isl_multi_aff_identity(
4101 __isl_take isl_space *space);
4102 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_identity(
4103 __isl_take isl_space *space);
4104 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_identity(
4105 __isl_take isl_space *space);
4106 __isl_give isl_pw_multi_aff *
4107 isl_pw_multi_aff_from_multi_aff(
4108 __isl_take isl_multi_aff *ma);
4109 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_alloc(
4110 __isl_take isl_set *set,
4111 __isl_take isl_multi_aff *maff);
4112 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_from_domain(
4113 __isl_take isl_set *set);
4115 __isl_give isl_union_pw_multi_aff *
4116 isl_union_pw_multi_aff_empty(
4117 __isl_take isl_space *space);
4118 __isl_give isl_union_pw_multi_aff *
4119 isl_union_pw_multi_aff_add_pw_multi_aff(
4120 __isl_take isl_union_pw_multi_aff *upma,
4121 __isl_take isl_pw_multi_aff *pma);
4122 __isl_give isl_union_pw_multi_aff *
4123 isl_union_pw_multi_aff_from_domain(
4124 __isl_take isl_union_set *uset);
4126 A piecewise multiple quasi affine expression can also be initialized
4127 from an C<isl_set> or C<isl_map>, provided the C<isl_set> is a singleton
4128 and the C<isl_map> is single-valued.
4129 In case of a conversion from an C<isl_union_set> or an C<isl_union_map>
4130 to an C<isl_union_pw_multi_aff>, these properties need to hold in each space.
4132 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_from_set(
4133 __isl_take isl_set *set);
4134 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_from_map(
4135 __isl_take isl_map *map);
4137 __isl_give isl_union_pw_multi_aff *
4138 isl_union_pw_multi_aff_from_union_set(
4139 __isl_take isl_union_set *uset);
4140 __isl_give isl_union_pw_multi_aff *
4141 isl_union_pw_multi_aff_from_union_map(
4142 __isl_take isl_union_map *umap);
4144 Multiple quasi affine expressions can be copied and freed using
4146 #include <isl/aff.h>
4147 __isl_give isl_multi_aff *isl_multi_aff_copy(
4148 __isl_keep isl_multi_aff *maff);
4149 void *isl_multi_aff_free(__isl_take isl_multi_aff *maff);
4151 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_copy(
4152 __isl_keep isl_pw_multi_aff *pma);
4153 void *isl_pw_multi_aff_free(
4154 __isl_take isl_pw_multi_aff *pma);
4156 __isl_give isl_union_pw_multi_aff *
4157 isl_union_pw_multi_aff_copy(
4158 __isl_keep isl_union_pw_multi_aff *upma);
4159 void *isl_union_pw_multi_aff_free(
4160 __isl_take isl_union_pw_multi_aff *upma);
4162 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_copy(
4163 __isl_keep isl_multi_pw_aff *mpa);
4164 void *isl_multi_pw_aff_free(
4165 __isl_take isl_multi_pw_aff *mpa);
4167 The expression can be inspected using
4169 #include <isl/aff.h>
4170 isl_ctx *isl_multi_aff_get_ctx(
4171 __isl_keep isl_multi_aff *maff);
4172 isl_ctx *isl_pw_multi_aff_get_ctx(
4173 __isl_keep isl_pw_multi_aff *pma);
4174 isl_ctx *isl_union_pw_multi_aff_get_ctx(
4175 __isl_keep isl_union_pw_multi_aff *upma);
4176 isl_ctx *isl_multi_pw_aff_get_ctx(
4177 __isl_keep isl_multi_pw_aff *mpa);
4178 unsigned isl_multi_aff_dim(__isl_keep isl_multi_aff *maff,
4179 enum isl_dim_type type);
4180 unsigned isl_pw_multi_aff_dim(
4181 __isl_keep isl_pw_multi_aff *pma,
4182 enum isl_dim_type type);
4183 unsigned isl_multi_pw_aff_dim(
4184 __isl_keep isl_multi_pw_aff *mpa,
4185 enum isl_dim_type type);
4186 __isl_give isl_aff *isl_multi_aff_get_aff(
4187 __isl_keep isl_multi_aff *multi, int pos);
4188 __isl_give isl_pw_aff *isl_pw_multi_aff_get_pw_aff(
4189 __isl_keep isl_pw_multi_aff *pma, int pos);
4190 __isl_give isl_pw_aff *isl_multi_pw_aff_get_pw_aff(
4191 __isl_keep isl_multi_pw_aff *mpa, int pos);
4192 const char *isl_pw_multi_aff_get_dim_name(
4193 __isl_keep isl_pw_multi_aff *pma,
4194 enum isl_dim_type type, unsigned pos);
4195 __isl_give isl_id *isl_pw_multi_aff_get_dim_id(
4196 __isl_keep isl_pw_multi_aff *pma,
4197 enum isl_dim_type type, unsigned pos);
4198 const char *isl_multi_aff_get_tuple_name(
4199 __isl_keep isl_multi_aff *multi,
4200 enum isl_dim_type type);
4201 int isl_pw_multi_aff_has_tuple_name(
4202 __isl_keep isl_pw_multi_aff *pma,
4203 enum isl_dim_type type);
4204 const char *isl_pw_multi_aff_get_tuple_name(
4205 __isl_keep isl_pw_multi_aff *pma,
4206 enum isl_dim_type type);
4207 int isl_pw_multi_aff_has_tuple_id(
4208 __isl_keep isl_pw_multi_aff *pma,
4209 enum isl_dim_type type);
4210 __isl_give isl_id *isl_pw_multi_aff_get_tuple_id(
4211 __isl_keep isl_pw_multi_aff *pma,
4212 enum isl_dim_type type);
4214 int isl_pw_multi_aff_foreach_piece(
4215 __isl_keep isl_pw_multi_aff *pma,
4216 int (*fn)(__isl_take isl_set *set,
4217 __isl_take isl_multi_aff *maff,
4218 void *user), void *user);
4220 int isl_union_pw_multi_aff_foreach_pw_multi_aff(
4221 __isl_keep isl_union_pw_multi_aff *upma,
4222 int (*fn)(__isl_take isl_pw_multi_aff *pma,
4223 void *user), void *user);
4225 It can be modified using
4227 #include <isl/aff.h>
4228 __isl_give isl_multi_aff *isl_multi_aff_set_aff(
4229 __isl_take isl_multi_aff *multi, int pos,
4230 __isl_take isl_aff *aff);
4231 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_set_pw_aff(
4232 __isl_take isl_pw_multi_aff *pma, unsigned pos,
4233 __isl_take isl_pw_aff *pa);
4234 __isl_give isl_multi_aff *isl_multi_aff_set_dim_name(
4235 __isl_take isl_multi_aff *maff,
4236 enum isl_dim_type type, unsigned pos, const char *s);
4237 __isl_give isl_multi_aff *isl_multi_aff_set_tuple_name(
4238 __isl_take isl_multi_aff *maff,
4239 enum isl_dim_type type, const char *s);
4240 __isl_give isl_multi_aff *isl_multi_aff_set_tuple_id(
4241 __isl_take isl_multi_aff *maff,
4242 enum isl_dim_type type, __isl_take isl_id *id);
4243 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_set_tuple_id(
4244 __isl_take isl_pw_multi_aff *pma,
4245 enum isl_dim_type type, __isl_take isl_id *id);
4247 __isl_give isl_multi_pw_aff *
4248 isl_multi_pw_aff_set_dim_name(
4249 __isl_take isl_multi_pw_aff *mpa,
4250 enum isl_dim_type type, unsigned pos, const char *s);
4251 __isl_give isl_multi_pw_aff *
4252 isl_multi_pw_aff_set_tuple_name(
4253 __isl_take isl_multi_pw_aff *mpa,
4254 enum isl_dim_type type, const char *s);
4256 __isl_give isl_multi_aff *isl_multi_aff_insert_dims(
4257 __isl_take isl_multi_aff *ma,
4258 enum isl_dim_type type, unsigned first, unsigned n);
4259 __isl_give isl_multi_aff *isl_multi_aff_add_dims(
4260 __isl_take isl_multi_aff *ma,
4261 enum isl_dim_type type, unsigned n);
4262 __isl_give isl_multi_aff *isl_multi_aff_drop_dims(
4263 __isl_take isl_multi_aff *maff,
4264 enum isl_dim_type type, unsigned first, unsigned n);
4265 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_drop_dims(
4266 __isl_take isl_pw_multi_aff *pma,
4267 enum isl_dim_type type, unsigned first, unsigned n);
4269 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_insert_dims(
4270 __isl_take isl_multi_pw_aff *mpa,
4271 enum isl_dim_type type, unsigned first, unsigned n);
4272 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_add_dims(
4273 __isl_take isl_multi_pw_aff *mpa,
4274 enum isl_dim_type type, unsigned n);
4276 To check whether two multiple affine expressions are
4277 obviously equal to each other, use
4279 int isl_multi_aff_plain_is_equal(__isl_keep isl_multi_aff *maff1,
4280 __isl_keep isl_multi_aff *maff2);
4281 int isl_pw_multi_aff_plain_is_equal(
4282 __isl_keep isl_pw_multi_aff *pma1,
4283 __isl_keep isl_pw_multi_aff *pma2);
4287 #include <isl/aff.h>
4288 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_union_lexmin(
4289 __isl_take isl_pw_multi_aff *pma1,
4290 __isl_take isl_pw_multi_aff *pma2);
4291 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_union_lexmax(
4292 __isl_take isl_pw_multi_aff *pma1,
4293 __isl_take isl_pw_multi_aff *pma2);
4294 __isl_give isl_multi_aff *isl_multi_aff_add(
4295 __isl_take isl_multi_aff *maff1,
4296 __isl_take isl_multi_aff *maff2);
4297 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_add(
4298 __isl_take isl_pw_multi_aff *pma1,
4299 __isl_take isl_pw_multi_aff *pma2);
4300 __isl_give isl_union_pw_multi_aff *isl_union_pw_multi_aff_add(
4301 __isl_take isl_union_pw_multi_aff *upma1,
4302 __isl_take isl_union_pw_multi_aff *upma2);
4303 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_union_add(
4304 __isl_take isl_pw_multi_aff *pma1,
4305 __isl_take isl_pw_multi_aff *pma2);
4306 __isl_give isl_multi_aff *isl_multi_aff_sub(
4307 __isl_take isl_multi_aff *ma1,
4308 __isl_take isl_multi_aff *ma2);
4309 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_sub(
4310 __isl_take isl_pw_multi_aff *pma1,
4311 __isl_take isl_pw_multi_aff *pma2);
4312 __isl_give isl_union_pw_multi_aff *isl_union_pw_multi_aff_sub(
4313 __isl_take isl_union_pw_multi_aff *upma1,
4314 __isl_take isl_union_pw_multi_aff *upma2);
4316 C<isl_multi_aff_sub> subtracts the second argument from the first.
4318 __isl_give isl_multi_aff *isl_multi_aff_scale(
4319 __isl_take isl_multi_aff *maff,
4321 __isl_give isl_multi_aff *isl_multi_aff_scale_val(
4322 __isl_take isl_multi_aff *ma,
4323 __isl_take isl_val *v);
4324 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_scale_val(
4325 __isl_take isl_pw_multi_aff *pma,
4326 __isl_take isl_val *v);
4327 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_scale_val(
4328 __isl_take isl_multi_pw_aff *mpa,
4329 __isl_take isl_val *v);
4330 __isl_give isl_multi_aff *isl_multi_aff_scale_vec(
4331 __isl_take isl_multi_aff *ma,
4332 __isl_take isl_vec *v);
4333 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_scale_vec(
4334 __isl_take isl_pw_multi_aff *pma,
4335 __isl_take isl_vec *v);
4336 __isl_give isl_union_pw_multi_aff *isl_union_pw_multi_aff_scale_vec(
4337 __isl_take isl_union_pw_multi_aff *upma,
4338 __isl_take isl_vec *v);
4340 C<isl_multi_aff_scale_vec> scales the first elements of C<ma>
4341 by the corresponding elements of C<v>.
4343 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_intersect_params(
4344 __isl_take isl_pw_multi_aff *pma,
4345 __isl_take isl_set *set);
4346 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_intersect_domain(
4347 __isl_take isl_pw_multi_aff *pma,
4348 __isl_take isl_set *set);
4349 __isl_give isl_union_pw_multi_aff *
4350 isl_union_pw_multi_aff_intersect_domain(
4351 __isl_take isl_union_pw_multi_aff *upma,
4352 __isl_take isl_union_set *uset);
4353 __isl_give isl_multi_aff *isl_multi_aff_lift(
4354 __isl_take isl_multi_aff *maff,
4355 __isl_give isl_local_space **ls);
4356 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_coalesce(
4357 __isl_take isl_pw_multi_aff *pma);
4358 __isl_give isl_multi_aff *isl_multi_aff_align_params(
4359 __isl_take isl_multi_aff *multi,
4360 __isl_take isl_space *model);
4361 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_align_params(
4362 __isl_take isl_pw_multi_aff *pma,
4363 __isl_take isl_space *model);
4364 __isl_give isl_pw_multi_aff *
4365 isl_pw_multi_aff_project_domain_on_params(
4366 __isl_take isl_pw_multi_aff *pma);
4367 __isl_give isl_multi_aff *isl_multi_aff_gist_params(
4368 __isl_take isl_multi_aff *maff,
4369 __isl_take isl_set *context);
4370 __isl_give isl_multi_aff *isl_multi_aff_gist(
4371 __isl_take isl_multi_aff *maff,
4372 __isl_take isl_set *context);
4373 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_gist_params(
4374 __isl_take isl_pw_multi_aff *pma,
4375 __isl_take isl_set *set);
4376 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_gist(
4377 __isl_take isl_pw_multi_aff *pma,
4378 __isl_take isl_set *set);
4379 __isl_give isl_set *isl_pw_multi_aff_domain(
4380 __isl_take isl_pw_multi_aff *pma);
4381 __isl_give isl_union_set *isl_union_pw_multi_aff_domain(
4382 __isl_take isl_union_pw_multi_aff *upma);
4383 __isl_give isl_multi_aff *isl_multi_aff_range_splice(
4384 __isl_take isl_multi_aff *ma1, unsigned pos,
4385 __isl_take isl_multi_aff *ma2);
4386 __isl_give isl_multi_aff *isl_multi_aff_splice(
4387 __isl_take isl_multi_aff *ma1,
4388 unsigned in_pos, unsigned out_pos,
4389 __isl_take isl_multi_aff *ma2);
4390 __isl_give isl_multi_aff *isl_multi_aff_range_product(
4391 __isl_take isl_multi_aff *ma1,
4392 __isl_take isl_multi_aff *ma2);
4393 __isl_give isl_multi_aff *isl_multi_aff_flat_range_product(
4394 __isl_take isl_multi_aff *ma1,
4395 __isl_take isl_multi_aff *ma2);
4396 __isl_give isl_multi_aff *isl_multi_aff_product(
4397 __isl_take isl_multi_aff *ma1,
4398 __isl_take isl_multi_aff *ma2);
4399 __isl_give isl_pw_multi_aff *
4400 isl_pw_multi_aff_range_product(
4401 __isl_take isl_pw_multi_aff *pma1,
4402 __isl_take isl_pw_multi_aff *pma2);
4403 __isl_give isl_pw_multi_aff *
4404 isl_pw_multi_aff_flat_range_product(
4405 __isl_take isl_pw_multi_aff *pma1,
4406 __isl_take isl_pw_multi_aff *pma2);
4407 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_product(
4408 __isl_take isl_pw_multi_aff *pma1,
4409 __isl_take isl_pw_multi_aff *pma2);
4410 __isl_give isl_union_pw_multi_aff *
4411 isl_union_pw_multi_aff_flat_range_product(
4412 __isl_take isl_union_pw_multi_aff *upma1,
4413 __isl_take isl_union_pw_multi_aff *upma2);
4414 __isl_give isl_multi_pw_aff *
4415 isl_multi_pw_aff_range_splice(
4416 __isl_take isl_multi_pw_aff *mpa1, unsigned pos,
4417 __isl_take isl_multi_pw_aff *mpa2);
4418 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_splice(
4419 __isl_take isl_multi_pw_aff *mpa1,
4420 unsigned in_pos, unsigned out_pos,
4421 __isl_take isl_multi_pw_aff *mpa2);
4422 __isl_give isl_multi_pw_aff *
4423 isl_multi_pw_aff_range_product(
4424 __isl_take isl_multi_pw_aff *mpa1,
4425 __isl_take isl_multi_pw_aff *mpa2);
4426 __isl_give isl_multi_pw_aff *
4427 isl_multi_pw_aff_flat_range_product(
4428 __isl_take isl_multi_pw_aff *mpa1,
4429 __isl_take isl_multi_pw_aff *mpa2);
4431 If the C<ls> argument of C<isl_multi_aff_lift> is not C<NULL>,
4432 then it is assigned the local space that lies at the basis of
4433 the lifting applied.
4435 #include <isl/aff.h>
4436 __isl_give isl_multi_aff *isl_multi_aff_pullback_multi_aff(
4437 __isl_take isl_multi_aff *ma1,
4438 __isl_take isl_multi_aff *ma2);
4439 __isl_give isl_pw_multi_aff *
4440 isl_pw_multi_aff_pullback_multi_aff(
4441 __isl_take isl_pw_multi_aff *pma,
4442 __isl_take isl_multi_aff *ma);
4443 __isl_give isl_pw_multi_aff *
4444 isl_pw_multi_aff_pullback_pw_multi_aff(
4445 __isl_take isl_pw_multi_aff *pma1,
4446 __isl_take isl_pw_multi_aff *pma2);
4448 The function C<isl_multi_aff_pullback_multi_aff> precomposes C<ma1> by C<ma2>.
4449 In other words, C<ma2> is plugged
4452 __isl_give isl_set *isl_multi_aff_lex_le_set(
4453 __isl_take isl_multi_aff *ma1,
4454 __isl_take isl_multi_aff *ma2);
4455 __isl_give isl_set *isl_multi_aff_lex_ge_set(
4456 __isl_take isl_multi_aff *ma1,
4457 __isl_take isl_multi_aff *ma2);
4459 The function C<isl_multi_aff_lex_le_set> returns a set
4460 containing those elements in the shared domain space
4461 where C<ma1> is lexicographically smaller than or
4464 An expression can be read from input using
4466 #include <isl/aff.h>
4467 __isl_give isl_multi_aff *isl_multi_aff_read_from_str(
4468 isl_ctx *ctx, const char *str);
4469 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_read_from_str(
4470 isl_ctx *ctx, const char *str);
4471 __isl_give isl_union_pw_multi_aff *
4472 isl_union_pw_multi_aff_read_from_str(
4473 isl_ctx *ctx, const char *str);
4475 An expression can be printed using
4477 #include <isl/aff.h>
4478 __isl_give isl_printer *isl_printer_print_multi_aff(
4479 __isl_take isl_printer *p,
4480 __isl_keep isl_multi_aff *maff);
4481 __isl_give isl_printer *isl_printer_print_pw_multi_aff(
4482 __isl_take isl_printer *p,
4483 __isl_keep isl_pw_multi_aff *pma);
4484 __isl_give isl_printer *isl_printer_print_union_pw_multi_aff(
4485 __isl_take isl_printer *p,
4486 __isl_keep isl_union_pw_multi_aff *upma);
4487 __isl_give isl_printer *isl_printer_print_multi_pw_aff(
4488 __isl_take isl_printer *p,
4489 __isl_keep isl_multi_pw_aff *mpa);
4493 Points are elements of a set. They can be used to construct
4494 simple sets (boxes) or they can be used to represent the
4495 individual elements of a set.
4496 The zero point (the origin) can be created using
4498 __isl_give isl_point *isl_point_zero(__isl_take isl_space *space);
4500 The coordinates of a point can be inspected, set and changed
4503 int isl_point_get_coordinate(__isl_keep isl_point *pnt,
4504 enum isl_dim_type type, int pos, isl_int *v);
4505 __isl_give isl_val *isl_point_get_coordinate_val(
4506 __isl_keep isl_point *pnt,
4507 enum isl_dim_type type, int pos);
4508 __isl_give isl_point *isl_point_set_coordinate(
4509 __isl_take isl_point *pnt,
4510 enum isl_dim_type type, int pos, isl_int v);
4511 __isl_give isl_point *isl_point_set_coordinate_val(
4512 __isl_take isl_point *pnt,
4513 enum isl_dim_type type, int pos,
4514 __isl_take isl_val *v);
4516 __isl_give isl_point *isl_point_add_ui(
4517 __isl_take isl_point *pnt,
4518 enum isl_dim_type type, int pos, unsigned val);
4519 __isl_give isl_point *isl_point_sub_ui(
4520 __isl_take isl_point *pnt,
4521 enum isl_dim_type type, int pos, unsigned val);
4523 Other properties can be obtained using
4525 isl_ctx *isl_point_get_ctx(__isl_keep isl_point *pnt);
4527 Points can be copied or freed using
4529 __isl_give isl_point *isl_point_copy(
4530 __isl_keep isl_point *pnt);
4531 void isl_point_free(__isl_take isl_point *pnt);
4533 A singleton set can be created from a point using
4535 __isl_give isl_basic_set *isl_basic_set_from_point(
4536 __isl_take isl_point *pnt);
4537 __isl_give isl_set *isl_set_from_point(
4538 __isl_take isl_point *pnt);
4540 and a box can be created from two opposite extremal points using
4542 __isl_give isl_basic_set *isl_basic_set_box_from_points(
4543 __isl_take isl_point *pnt1,
4544 __isl_take isl_point *pnt2);
4545 __isl_give isl_set *isl_set_box_from_points(
4546 __isl_take isl_point *pnt1,
4547 __isl_take isl_point *pnt2);
4549 All elements of a B<bounded> (union) set can be enumerated using
4550 the following functions.
4552 int isl_set_foreach_point(__isl_keep isl_set *set,
4553 int (*fn)(__isl_take isl_point *pnt, void *user),
4555 int isl_union_set_foreach_point(__isl_keep isl_union_set *uset,
4556 int (*fn)(__isl_take isl_point *pnt, void *user),
4559 The function C<fn> is called for each integer point in
4560 C<set> with as second argument the last argument of
4561 the C<isl_set_foreach_point> call. The function C<fn>
4562 should return C<0> on success and C<-1> on failure.
4563 In the latter case, C<isl_set_foreach_point> will stop
4564 enumerating and return C<-1> as well.
4565 If the enumeration is performed successfully and to completion,
4566 then C<isl_set_foreach_point> returns C<0>.
4568 To obtain a single point of a (basic) set, use
4570 __isl_give isl_point *isl_basic_set_sample_point(
4571 __isl_take isl_basic_set *bset);
4572 __isl_give isl_point *isl_set_sample_point(
4573 __isl_take isl_set *set);
4575 If C<set> does not contain any (integer) points, then the
4576 resulting point will be ``void'', a property that can be
4579 int isl_point_is_void(__isl_keep isl_point *pnt);
4581 =head2 Piecewise Quasipolynomials
4583 A piecewise quasipolynomial is a particular kind of function that maps
4584 a parametric point to a rational value.
4585 More specifically, a quasipolynomial is a polynomial expression in greatest
4586 integer parts of affine expressions of parameters and variables.
4587 A piecewise quasipolynomial is a subdivision of a given parametric
4588 domain into disjoint cells with a quasipolynomial associated to
4589 each cell. The value of the piecewise quasipolynomial at a given
4590 point is the value of the quasipolynomial associated to the cell
4591 that contains the point. Outside of the union of cells,
4592 the value is assumed to be zero.
4593 For example, the piecewise quasipolynomial
4595 [n] -> { [x] -> ((1 + n) - x) : x <= n and x >= 0 }
4597 maps C<x> to C<1 + n - x> for values of C<x> between C<0> and C<n>.
4598 A given piecewise quasipolynomial has a fixed domain dimension.
4599 Union piecewise quasipolynomials are used to contain piecewise quasipolynomials
4600 defined over different domains.
4601 Piecewise quasipolynomials are mainly used by the C<barvinok>
4602 library for representing the number of elements in a parametric set or map.
4603 For example, the piecewise quasipolynomial above represents
4604 the number of points in the map
4606 [n] -> { [x] -> [y] : x,y >= 0 and 0 <= x + y <= n }
4608 =head3 Input and Output
4610 Piecewise quasipolynomials can be read from input using
4612 __isl_give isl_union_pw_qpolynomial *
4613 isl_union_pw_qpolynomial_read_from_str(
4614 isl_ctx *ctx, const char *str);
4616 Quasipolynomials and piecewise quasipolynomials can be printed
4617 using the following functions.
4619 __isl_give isl_printer *isl_printer_print_qpolynomial(
4620 __isl_take isl_printer *p,
4621 __isl_keep isl_qpolynomial *qp);
4623 __isl_give isl_printer *isl_printer_print_pw_qpolynomial(
4624 __isl_take isl_printer *p,
4625 __isl_keep isl_pw_qpolynomial *pwqp);
4627 __isl_give isl_printer *isl_printer_print_union_pw_qpolynomial(
4628 __isl_take isl_printer *p,
4629 __isl_keep isl_union_pw_qpolynomial *upwqp);
4631 The output format of the printer
4632 needs to be set to either C<ISL_FORMAT_ISL> or C<ISL_FORMAT_C>.
4633 For C<isl_printer_print_union_pw_qpolynomial>, only C<ISL_FORMAT_ISL>
4635 In case of printing in C<ISL_FORMAT_C>, the user may want
4636 to set the names of all dimensions
4638 __isl_give isl_qpolynomial *isl_qpolynomial_set_dim_name(
4639 __isl_take isl_qpolynomial *qp,
4640 enum isl_dim_type type, unsigned pos,
4642 __isl_give isl_pw_qpolynomial *
4643 isl_pw_qpolynomial_set_dim_name(
4644 __isl_take isl_pw_qpolynomial *pwqp,
4645 enum isl_dim_type type, unsigned pos,
4648 =head3 Creating New (Piecewise) Quasipolynomials
4650 Some simple quasipolynomials can be created using the following functions.
4651 More complicated quasipolynomials can be created by applying
4652 operations such as addition and multiplication
4653 on the resulting quasipolynomials
4655 __isl_give isl_qpolynomial *isl_qpolynomial_zero_on_domain(
4656 __isl_take isl_space *domain);
4657 __isl_give isl_qpolynomial *isl_qpolynomial_one_on_domain(
4658 __isl_take isl_space *domain);
4659 __isl_give isl_qpolynomial *isl_qpolynomial_infty_on_domain(
4660 __isl_take isl_space *domain);
4661 __isl_give isl_qpolynomial *isl_qpolynomial_neginfty_on_domain(
4662 __isl_take isl_space *domain);
4663 __isl_give isl_qpolynomial *isl_qpolynomial_nan_on_domain(
4664 __isl_take isl_space *domain);
4665 __isl_give isl_qpolynomial *isl_qpolynomial_rat_cst_on_domain(
4666 __isl_take isl_space *domain,
4667 const isl_int n, const isl_int d);
4668 __isl_give isl_qpolynomial *isl_qpolynomial_val_on_domain(
4669 __isl_take isl_space *domain,
4670 __isl_take isl_val *val);
4671 __isl_give isl_qpolynomial *isl_qpolynomial_var_on_domain(
4672 __isl_take isl_space *domain,
4673 enum isl_dim_type type, unsigned pos);
4674 __isl_give isl_qpolynomial *isl_qpolynomial_from_aff(
4675 __isl_take isl_aff *aff);
4677 Note that the space in which a quasipolynomial lives is a map space
4678 with a one-dimensional range. The C<domain> argument in some of
4679 the functions above corresponds to the domain of this map space.
4681 The zero piecewise quasipolynomial or a piecewise quasipolynomial
4682 with a single cell can be created using the following functions.
4683 Multiple of these single cell piecewise quasipolynomials can
4684 be combined to create more complicated piecewise quasipolynomials.
4686 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_zero(
4687 __isl_take isl_space *space);
4688 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_alloc(
4689 __isl_take isl_set *set,
4690 __isl_take isl_qpolynomial *qp);
4691 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_from_qpolynomial(
4692 __isl_take isl_qpolynomial *qp);
4693 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_from_pw_aff(
4694 __isl_take isl_pw_aff *pwaff);
4696 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_zero(
4697 __isl_take isl_space *space);
4698 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_from_pw_qpolynomial(
4699 __isl_take isl_pw_qpolynomial *pwqp);
4700 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_add_pw_qpolynomial(
4701 __isl_take isl_union_pw_qpolynomial *upwqp,
4702 __isl_take isl_pw_qpolynomial *pwqp);
4704 Quasipolynomials can be copied and freed again using the following
4707 __isl_give isl_qpolynomial *isl_qpolynomial_copy(
4708 __isl_keep isl_qpolynomial *qp);
4709 void *isl_qpolynomial_free(__isl_take isl_qpolynomial *qp);
4711 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_copy(
4712 __isl_keep isl_pw_qpolynomial *pwqp);
4713 void *isl_pw_qpolynomial_free(
4714 __isl_take isl_pw_qpolynomial *pwqp);
4716 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_copy(
4717 __isl_keep isl_union_pw_qpolynomial *upwqp);
4718 void *isl_union_pw_qpolynomial_free(
4719 __isl_take isl_union_pw_qpolynomial *upwqp);
4721 =head3 Inspecting (Piecewise) Quasipolynomials
4723 To iterate over all piecewise quasipolynomials in a union
4724 piecewise quasipolynomial, use the following function
4726 int isl_union_pw_qpolynomial_foreach_pw_qpolynomial(
4727 __isl_keep isl_union_pw_qpolynomial *upwqp,
4728 int (*fn)(__isl_take isl_pw_qpolynomial *pwqp, void *user),
4731 To extract the piecewise quasipolynomial in a given space from a union, use
4733 __isl_give isl_pw_qpolynomial *
4734 isl_union_pw_qpolynomial_extract_pw_qpolynomial(
4735 __isl_keep isl_union_pw_qpolynomial *upwqp,
4736 __isl_take isl_space *space);
4738 To iterate over the cells in a piecewise quasipolynomial,
4739 use either of the following two functions
4741 int isl_pw_qpolynomial_foreach_piece(
4742 __isl_keep isl_pw_qpolynomial *pwqp,
4743 int (*fn)(__isl_take isl_set *set,
4744 __isl_take isl_qpolynomial *qp,
4745 void *user), void *user);
4746 int isl_pw_qpolynomial_foreach_lifted_piece(
4747 __isl_keep isl_pw_qpolynomial *pwqp,
4748 int (*fn)(__isl_take isl_set *set,
4749 __isl_take isl_qpolynomial *qp,
4750 void *user), void *user);
4752 As usual, the function C<fn> should return C<0> on success
4753 and C<-1> on failure. The difference between
4754 C<isl_pw_qpolynomial_foreach_piece> and
4755 C<isl_pw_qpolynomial_foreach_lifted_piece> is that
4756 C<isl_pw_qpolynomial_foreach_lifted_piece> will first
4757 compute unique representations for all existentially quantified
4758 variables and then turn these existentially quantified variables
4759 into extra set variables, adapting the associated quasipolynomial
4760 accordingly. This means that the C<set> passed to C<fn>
4761 will not have any existentially quantified variables, but that
4762 the dimensions of the sets may be different for different
4763 invocations of C<fn>.
4765 The constant term of a quasipolynomial can be extracted using
4767 __isl_give isl_val *isl_qpolynomial_get_constant_val(
4768 __isl_keep isl_qpolynomial *qp);
4770 To iterate over all terms in a quasipolynomial,
4773 int isl_qpolynomial_foreach_term(
4774 __isl_keep isl_qpolynomial *qp,
4775 int (*fn)(__isl_take isl_term *term,
4776 void *user), void *user);
4778 The terms themselves can be inspected and freed using
4781 unsigned isl_term_dim(__isl_keep isl_term *term,
4782 enum isl_dim_type type);
4783 void isl_term_get_num(__isl_keep isl_term *term,
4785 void isl_term_get_den(__isl_keep isl_term *term,
4787 __isl_give isl_val *isl_term_get_coefficient_val(
4788 __isl_keep isl_term *term);
4789 int isl_term_get_exp(__isl_keep isl_term *term,
4790 enum isl_dim_type type, unsigned pos);
4791 __isl_give isl_aff *isl_term_get_div(
4792 __isl_keep isl_term *term, unsigned pos);
4793 void isl_term_free(__isl_take isl_term *term);
4795 Each term is a product of parameters, set variables and
4796 integer divisions. The function C<isl_term_get_exp>
4797 returns the exponent of a given dimensions in the given term.
4798 The C<isl_int>s in the arguments of C<isl_term_get_num>
4799 and C<isl_term_get_den> need to have been initialized
4800 using C<isl_int_init> before calling these functions.
4802 =head3 Properties of (Piecewise) Quasipolynomials
4804 To check whether a quasipolynomial is actually a constant,
4805 use the following function.
4807 int isl_qpolynomial_is_cst(__isl_keep isl_qpolynomial *qp,
4808 isl_int *n, isl_int *d);
4810 If C<qp> is a constant and if C<n> and C<d> are not C<NULL>
4811 then the numerator and denominator of the constant
4812 are returned in C<*n> and C<*d>, respectively.
4814 To check whether two union piecewise quasipolynomials are
4815 obviously equal, use
4817 int isl_union_pw_qpolynomial_plain_is_equal(
4818 __isl_keep isl_union_pw_qpolynomial *upwqp1,
4819 __isl_keep isl_union_pw_qpolynomial *upwqp2);
4821 =head3 Operations on (Piecewise) Quasipolynomials
4823 __isl_give isl_qpolynomial *isl_qpolynomial_scale(
4824 __isl_take isl_qpolynomial *qp, isl_int v);
4825 __isl_give isl_qpolynomial *isl_qpolynomial_scale_val(
4826 __isl_take isl_qpolynomial *qp,
4827 __isl_take isl_val *v);
4828 __isl_give isl_qpolynomial *isl_qpolynomial_neg(
4829 __isl_take isl_qpolynomial *qp);
4830 __isl_give isl_qpolynomial *isl_qpolynomial_add(
4831 __isl_take isl_qpolynomial *qp1,
4832 __isl_take isl_qpolynomial *qp2);
4833 __isl_give isl_qpolynomial *isl_qpolynomial_sub(
4834 __isl_take isl_qpolynomial *qp1,
4835 __isl_take isl_qpolynomial *qp2);
4836 __isl_give isl_qpolynomial *isl_qpolynomial_mul(
4837 __isl_take isl_qpolynomial *qp1,
4838 __isl_take isl_qpolynomial *qp2);
4839 __isl_give isl_qpolynomial *isl_qpolynomial_pow(
4840 __isl_take isl_qpolynomial *qp, unsigned exponent);
4842 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_fix_val(
4843 __isl_take isl_pw_qpolynomial *pwqp,
4844 enum isl_dim_type type, unsigned n,
4845 __isl_take isl_val *v);
4846 __isl_give isl_pw_qpolynomial *
4847 isl_pw_qpolynomial_scale_val(
4848 __isl_take isl_pw_qpolynomial *pwqp,
4849 __isl_take isl_val *v);
4850 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_add(
4851 __isl_take isl_pw_qpolynomial *pwqp1,
4852 __isl_take isl_pw_qpolynomial *pwqp2);
4853 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_sub(
4854 __isl_take isl_pw_qpolynomial *pwqp1,
4855 __isl_take isl_pw_qpolynomial *pwqp2);
4856 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_add_disjoint(
4857 __isl_take isl_pw_qpolynomial *pwqp1,
4858 __isl_take isl_pw_qpolynomial *pwqp2);
4859 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_neg(
4860 __isl_take isl_pw_qpolynomial *pwqp);
4861 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_mul(
4862 __isl_take isl_pw_qpolynomial *pwqp1,
4863 __isl_take isl_pw_qpolynomial *pwqp2);
4864 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_pow(
4865 __isl_take isl_pw_qpolynomial *pwqp, unsigned exponent);
4867 __isl_give isl_union_pw_qpolynomial *
4868 isl_union_pw_qpolynomial_scale_val(
4869 __isl_take isl_union_pw_qpolynomial *upwqp,
4870 __isl_take isl_val *v);
4871 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_add(
4872 __isl_take isl_union_pw_qpolynomial *upwqp1,
4873 __isl_take isl_union_pw_qpolynomial *upwqp2);
4874 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_sub(
4875 __isl_take isl_union_pw_qpolynomial *upwqp1,
4876 __isl_take isl_union_pw_qpolynomial *upwqp2);
4877 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_mul(
4878 __isl_take isl_union_pw_qpolynomial *upwqp1,
4879 __isl_take isl_union_pw_qpolynomial *upwqp2);
4881 __isl_give isl_qpolynomial *isl_pw_qpolynomial_eval(
4882 __isl_take isl_pw_qpolynomial *pwqp,
4883 __isl_take isl_point *pnt);
4885 __isl_give isl_qpolynomial *isl_union_pw_qpolynomial_eval(
4886 __isl_take isl_union_pw_qpolynomial *upwqp,
4887 __isl_take isl_point *pnt);
4889 __isl_give isl_set *isl_pw_qpolynomial_domain(
4890 __isl_take isl_pw_qpolynomial *pwqp);
4891 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_intersect_domain(
4892 __isl_take isl_pw_qpolynomial *pwpq,
4893 __isl_take isl_set *set);
4894 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_intersect_params(
4895 __isl_take isl_pw_qpolynomial *pwpq,
4896 __isl_take isl_set *set);
4898 __isl_give isl_union_set *isl_union_pw_qpolynomial_domain(
4899 __isl_take isl_union_pw_qpolynomial *upwqp);
4900 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_intersect_domain(
4901 __isl_take isl_union_pw_qpolynomial *upwpq,
4902 __isl_take isl_union_set *uset);
4903 __isl_give isl_union_pw_qpolynomial *
4904 isl_union_pw_qpolynomial_intersect_params(
4905 __isl_take isl_union_pw_qpolynomial *upwpq,
4906 __isl_take isl_set *set);
4908 __isl_give isl_qpolynomial *isl_qpolynomial_align_params(
4909 __isl_take isl_qpolynomial *qp,
4910 __isl_take isl_space *model);
4912 __isl_give isl_qpolynomial *isl_qpolynomial_project_domain_on_params(
4913 __isl_take isl_qpolynomial *qp);
4914 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_project_domain_on_params(
4915 __isl_take isl_pw_qpolynomial *pwqp);
4917 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_coalesce(
4918 __isl_take isl_union_pw_qpolynomial *upwqp);
4920 __isl_give isl_qpolynomial *isl_qpolynomial_gist_params(
4921 __isl_take isl_qpolynomial *qp,
4922 __isl_take isl_set *context);
4923 __isl_give isl_qpolynomial *isl_qpolynomial_gist(
4924 __isl_take isl_qpolynomial *qp,
4925 __isl_take isl_set *context);
4927 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_gist_params(
4928 __isl_take isl_pw_qpolynomial *pwqp,
4929 __isl_take isl_set *context);
4930 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_gist(
4931 __isl_take isl_pw_qpolynomial *pwqp,
4932 __isl_take isl_set *context);
4934 __isl_give isl_union_pw_qpolynomial *
4935 isl_union_pw_qpolynomial_gist_params(
4936 __isl_take isl_union_pw_qpolynomial *upwqp,
4937 __isl_take isl_set *context);
4938 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_gist(
4939 __isl_take isl_union_pw_qpolynomial *upwqp,
4940 __isl_take isl_union_set *context);
4942 The gist operation applies the gist operation to each of
4943 the cells in the domain of the input piecewise quasipolynomial.
4944 The context is also exploited
4945 to simplify the quasipolynomials associated to each cell.
4947 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_to_polynomial(
4948 __isl_take isl_pw_qpolynomial *pwqp, int sign);
4949 __isl_give isl_union_pw_qpolynomial *
4950 isl_union_pw_qpolynomial_to_polynomial(
4951 __isl_take isl_union_pw_qpolynomial *upwqp, int sign);
4953 Approximate each quasipolynomial by a polynomial. If C<sign> is positive,
4954 the polynomial will be an overapproximation. If C<sign> is negative,
4955 it will be an underapproximation. If C<sign> is zero, the approximation
4956 will lie somewhere in between.
4958 =head2 Bounds on Piecewise Quasipolynomials and Piecewise Quasipolynomial Reductions
4960 A piecewise quasipolynomial reduction is a piecewise
4961 reduction (or fold) of quasipolynomials.
4962 In particular, the reduction can be maximum or a minimum.
4963 The objects are mainly used to represent the result of
4964 an upper or lower bound on a quasipolynomial over its domain,
4965 i.e., as the result of the following function.
4967 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_bound(
4968 __isl_take isl_pw_qpolynomial *pwqp,
4969 enum isl_fold type, int *tight);
4971 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_bound(
4972 __isl_take isl_union_pw_qpolynomial *upwqp,
4973 enum isl_fold type, int *tight);
4975 The C<type> argument may be either C<isl_fold_min> or C<isl_fold_max>.
4976 If C<tight> is not C<NULL>, then C<*tight> is set to C<1>
4977 is the returned bound is known be tight, i.e., for each value
4978 of the parameters there is at least
4979 one element in the domain that reaches the bound.
4980 If the domain of C<pwqp> is not wrapping, then the bound is computed
4981 over all elements in that domain and the result has a purely parametric
4982 domain. If the domain of C<pwqp> is wrapping, then the bound is
4983 computed over the range of the wrapped relation. The domain of the
4984 wrapped relation becomes the domain of the result.
4986 A (piecewise) quasipolynomial reduction can be copied or freed using the
4987 following functions.
4989 __isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_copy(
4990 __isl_keep isl_qpolynomial_fold *fold);
4991 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_copy(
4992 __isl_keep isl_pw_qpolynomial_fold *pwf);
4993 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_copy(
4994 __isl_keep isl_union_pw_qpolynomial_fold *upwf);
4995 void isl_qpolynomial_fold_free(
4996 __isl_take isl_qpolynomial_fold *fold);
4997 void *isl_pw_qpolynomial_fold_free(
4998 __isl_take isl_pw_qpolynomial_fold *pwf);
4999 void *isl_union_pw_qpolynomial_fold_free(
5000 __isl_take isl_union_pw_qpolynomial_fold *upwf);
5002 =head3 Printing Piecewise Quasipolynomial Reductions
5004 Piecewise quasipolynomial reductions can be printed
5005 using the following function.
5007 __isl_give isl_printer *isl_printer_print_pw_qpolynomial_fold(
5008 __isl_take isl_printer *p,
5009 __isl_keep isl_pw_qpolynomial_fold *pwf);
5010 __isl_give isl_printer *isl_printer_print_union_pw_qpolynomial_fold(
5011 __isl_take isl_printer *p,
5012 __isl_keep isl_union_pw_qpolynomial_fold *upwf);
5014 For C<isl_printer_print_pw_qpolynomial_fold>,
5015 output format of the printer
5016 needs to be set to either C<ISL_FORMAT_ISL> or C<ISL_FORMAT_C>.
5017 For C<isl_printer_print_union_pw_qpolynomial_fold>,
5018 output format of the printer
5019 needs to be set to C<ISL_FORMAT_ISL>.
5020 In case of printing in C<ISL_FORMAT_C>, the user may want
5021 to set the names of all dimensions
5023 __isl_give isl_pw_qpolynomial_fold *
5024 isl_pw_qpolynomial_fold_set_dim_name(
5025 __isl_take isl_pw_qpolynomial_fold *pwf,
5026 enum isl_dim_type type, unsigned pos,
5029 =head3 Inspecting (Piecewise) Quasipolynomial Reductions
5031 To iterate over all piecewise quasipolynomial reductions in a union
5032 piecewise quasipolynomial reduction, use the following function
5034 int isl_union_pw_qpolynomial_fold_foreach_pw_qpolynomial_fold(
5035 __isl_keep isl_union_pw_qpolynomial_fold *upwf,
5036 int (*fn)(__isl_take isl_pw_qpolynomial_fold *pwf,
5037 void *user), void *user);
5039 To iterate over the cells in a piecewise quasipolynomial reduction,
5040 use either of the following two functions
5042 int isl_pw_qpolynomial_fold_foreach_piece(
5043 __isl_keep isl_pw_qpolynomial_fold *pwf,
5044 int (*fn)(__isl_take isl_set *set,
5045 __isl_take isl_qpolynomial_fold *fold,
5046 void *user), void *user);
5047 int isl_pw_qpolynomial_fold_foreach_lifted_piece(
5048 __isl_keep isl_pw_qpolynomial_fold *pwf,
5049 int (*fn)(__isl_take isl_set *set,
5050 __isl_take isl_qpolynomial_fold *fold,
5051 void *user), void *user);
5053 See L<Inspecting (Piecewise) Quasipolynomials> for an explanation
5054 of the difference between these two functions.
5056 To iterate over all quasipolynomials in a reduction, use
5058 int isl_qpolynomial_fold_foreach_qpolynomial(
5059 __isl_keep isl_qpolynomial_fold *fold,
5060 int (*fn)(__isl_take isl_qpolynomial *qp,
5061 void *user), void *user);
5063 =head3 Properties of Piecewise Quasipolynomial Reductions
5065 To check whether two union piecewise quasipolynomial reductions are
5066 obviously equal, use
5068 int isl_union_pw_qpolynomial_fold_plain_is_equal(
5069 __isl_keep isl_union_pw_qpolynomial_fold *upwf1,
5070 __isl_keep isl_union_pw_qpolynomial_fold *upwf2);
5072 =head3 Operations on Piecewise Quasipolynomial Reductions
5074 __isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_scale(
5075 __isl_take isl_qpolynomial_fold *fold, isl_int v);
5076 __isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_scale_val(
5077 __isl_take isl_qpolynomial_fold *fold,
5078 __isl_take isl_val *v);
5079 __isl_give isl_pw_qpolynomial_fold *
5080 isl_pw_qpolynomial_fold_scale_val(
5081 __isl_take isl_pw_qpolynomial_fold *pwf,
5082 __isl_take isl_val *v);
5083 __isl_give isl_union_pw_qpolynomial_fold *
5084 isl_union_pw_qpolynomial_fold_scale_val(
5085 __isl_take isl_union_pw_qpolynomial_fold *upwf,
5086 __isl_take isl_val *v);
5088 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_add(
5089 __isl_take isl_pw_qpolynomial_fold *pwf1,
5090 __isl_take isl_pw_qpolynomial_fold *pwf2);
5092 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_fold(
5093 __isl_take isl_pw_qpolynomial_fold *pwf1,
5094 __isl_take isl_pw_qpolynomial_fold *pwf2);
5096 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_fold(
5097 __isl_take isl_union_pw_qpolynomial_fold *upwf1,
5098 __isl_take isl_union_pw_qpolynomial_fold *upwf2);
5100 __isl_give isl_qpolynomial *isl_pw_qpolynomial_fold_eval(
5101 __isl_take isl_pw_qpolynomial_fold *pwf,
5102 __isl_take isl_point *pnt);
5104 __isl_give isl_qpolynomial *isl_union_pw_qpolynomial_fold_eval(
5105 __isl_take isl_union_pw_qpolynomial_fold *upwf,
5106 __isl_take isl_point *pnt);
5108 __isl_give isl_pw_qpolynomial_fold *
5109 isl_pw_qpolynomial_fold_intersect_params(
5110 __isl_take isl_pw_qpolynomial_fold *pwf,
5111 __isl_take isl_set *set);
5113 __isl_give isl_union_set *isl_union_pw_qpolynomial_fold_domain(
5114 __isl_take isl_union_pw_qpolynomial_fold *upwf);
5115 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_intersect_domain(
5116 __isl_take isl_union_pw_qpolynomial_fold *upwf,
5117 __isl_take isl_union_set *uset);
5118 __isl_give isl_union_pw_qpolynomial_fold *
5119 isl_union_pw_qpolynomial_fold_intersect_params(
5120 __isl_take isl_union_pw_qpolynomial_fold *upwf,
5121 __isl_take isl_set *set);
5123 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_project_domain_on_params(
5124 __isl_take isl_pw_qpolynomial_fold *pwf);
5126 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_coalesce(
5127 __isl_take isl_pw_qpolynomial_fold *pwf);
5129 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_coalesce(
5130 __isl_take isl_union_pw_qpolynomial_fold *upwf);
5132 __isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_gist_params(
5133 __isl_take isl_qpolynomial_fold *fold,
5134 __isl_take isl_set *context);
5135 __isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_gist(
5136 __isl_take isl_qpolynomial_fold *fold,
5137 __isl_take isl_set *context);
5139 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_gist(
5140 __isl_take isl_pw_qpolynomial_fold *pwf,
5141 __isl_take isl_set *context);
5142 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_gist_params(
5143 __isl_take isl_pw_qpolynomial_fold *pwf,
5144 __isl_take isl_set *context);
5146 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_gist(
5147 __isl_take isl_union_pw_qpolynomial_fold *upwf,
5148 __isl_take isl_union_set *context);
5149 __isl_give isl_union_pw_qpolynomial_fold *
5150 isl_union_pw_qpolynomial_fold_gist_params(
5151 __isl_take isl_union_pw_qpolynomial_fold *upwf,
5152 __isl_take isl_set *context);
5154 The gist operation applies the gist operation to each of
5155 the cells in the domain of the input piecewise quasipolynomial reduction.
5156 In future, the operation will also exploit the context
5157 to simplify the quasipolynomial reductions associated to each cell.
5159 __isl_give isl_pw_qpolynomial_fold *
5160 isl_set_apply_pw_qpolynomial_fold(
5161 __isl_take isl_set *set,
5162 __isl_take isl_pw_qpolynomial_fold *pwf,
5164 __isl_give isl_pw_qpolynomial_fold *
5165 isl_map_apply_pw_qpolynomial_fold(
5166 __isl_take isl_map *map,
5167 __isl_take isl_pw_qpolynomial_fold *pwf,
5169 __isl_give isl_union_pw_qpolynomial_fold *
5170 isl_union_set_apply_union_pw_qpolynomial_fold(
5171 __isl_take isl_union_set *uset,
5172 __isl_take isl_union_pw_qpolynomial_fold *upwf,
5174 __isl_give isl_union_pw_qpolynomial_fold *
5175 isl_union_map_apply_union_pw_qpolynomial_fold(
5176 __isl_take isl_union_map *umap,
5177 __isl_take isl_union_pw_qpolynomial_fold *upwf,
5180 The functions taking a map
5181 compose the given map with the given piecewise quasipolynomial reduction.
5182 That is, compute a bound (of the same type as C<pwf> or C<upwf> itself)
5183 over all elements in the intersection of the range of the map
5184 and the domain of the piecewise quasipolynomial reduction
5185 as a function of an element in the domain of the map.
5186 The functions taking a set compute a bound over all elements in the
5187 intersection of the set and the domain of the
5188 piecewise quasipolynomial reduction.
5190 =head2 Parametric Vertex Enumeration
5192 The parametric vertex enumeration described in this section
5193 is mainly intended to be used internally and by the C<barvinok>
5196 #include <isl/vertices.h>
5197 __isl_give isl_vertices *isl_basic_set_compute_vertices(
5198 __isl_keep isl_basic_set *bset);
5200 The function C<isl_basic_set_compute_vertices> performs the
5201 actual computation of the parametric vertices and the chamber
5202 decomposition and store the result in an C<isl_vertices> object.
5203 This information can be queried by either iterating over all
5204 the vertices or iterating over all the chambers or cells
5205 and then iterating over all vertices that are active on the chamber.
5207 int isl_vertices_foreach_vertex(
5208 __isl_keep isl_vertices *vertices,
5209 int (*fn)(__isl_take isl_vertex *vertex, void *user),
5212 int isl_vertices_foreach_cell(
5213 __isl_keep isl_vertices *vertices,
5214 int (*fn)(__isl_take isl_cell *cell, void *user),
5216 int isl_cell_foreach_vertex(__isl_keep isl_cell *cell,
5217 int (*fn)(__isl_take isl_vertex *vertex, void *user),
5220 Other operations that can be performed on an C<isl_vertices> object are
5223 isl_ctx *isl_vertices_get_ctx(
5224 __isl_keep isl_vertices *vertices);
5225 int isl_vertices_get_n_vertices(
5226 __isl_keep isl_vertices *vertices);
5227 void isl_vertices_free(__isl_take isl_vertices *vertices);
5229 Vertices can be inspected and destroyed using the following functions.
5231 isl_ctx *isl_vertex_get_ctx(__isl_keep isl_vertex *vertex);
5232 int isl_vertex_get_id(__isl_keep isl_vertex *vertex);
5233 __isl_give isl_basic_set *isl_vertex_get_domain(
5234 __isl_keep isl_vertex *vertex);
5235 __isl_give isl_basic_set *isl_vertex_get_expr(
5236 __isl_keep isl_vertex *vertex);
5237 void isl_vertex_free(__isl_take isl_vertex *vertex);
5239 C<isl_vertex_get_expr> returns a singleton parametric set describing
5240 the vertex, while C<isl_vertex_get_domain> returns the activity domain
5242 Note that C<isl_vertex_get_domain> and C<isl_vertex_get_expr> return
5243 B<rational> basic sets, so they should mainly be used for inspection
5244 and should not be mixed with integer sets.
5246 Chambers can be inspected and destroyed using the following functions.
5248 isl_ctx *isl_cell_get_ctx(__isl_keep isl_cell *cell);
5249 __isl_give isl_basic_set *isl_cell_get_domain(
5250 __isl_keep isl_cell *cell);
5251 void isl_cell_free(__isl_take isl_cell *cell);
5253 =head1 Polyhedral Compilation Library
5255 This section collects functionality in C<isl> that has been specifically
5256 designed for use during polyhedral compilation.
5258 =head2 Dependence Analysis
5260 C<isl> contains specialized functionality for performing
5261 array dataflow analysis. That is, given a I<sink> access relation
5262 and a collection of possible I<source> access relations,
5263 C<isl> can compute relations that describe
5264 for each iteration of the sink access, which iteration
5265 of which of the source access relations was the last
5266 to access the same data element before the given iteration
5268 The resulting dependence relations map source iterations
5269 to the corresponding sink iterations.
5270 To compute standard flow dependences, the sink should be
5271 a read, while the sources should be writes.
5272 If any of the source accesses are marked as being I<may>
5273 accesses, then there will be a dependence from the last
5274 I<must> access B<and> from any I<may> access that follows
5275 this last I<must> access.
5276 In particular, if I<all> sources are I<may> accesses,
5277 then memory based dependence analysis is performed.
5278 If, on the other hand, all sources are I<must> accesses,
5279 then value based dependence analysis is performed.
5281 #include <isl/flow.h>
5283 typedef int (*isl_access_level_before)(void *first, void *second);
5285 __isl_give isl_access_info *isl_access_info_alloc(
5286 __isl_take isl_map *sink,
5287 void *sink_user, isl_access_level_before fn,
5289 __isl_give isl_access_info *isl_access_info_add_source(
5290 __isl_take isl_access_info *acc,
5291 __isl_take isl_map *source, int must,
5293 void *isl_access_info_free(__isl_take isl_access_info *acc);
5295 __isl_give isl_flow *isl_access_info_compute_flow(
5296 __isl_take isl_access_info *acc);
5298 int isl_flow_foreach(__isl_keep isl_flow *deps,
5299 int (*fn)(__isl_take isl_map *dep, int must,
5300 void *dep_user, void *user),
5302 __isl_give isl_map *isl_flow_get_no_source(
5303 __isl_keep isl_flow *deps, int must);
5304 void isl_flow_free(__isl_take isl_flow *deps);
5306 The function C<isl_access_info_compute_flow> performs the actual
5307 dependence analysis. The other functions are used to construct
5308 the input for this function or to read off the output.
5310 The input is collected in an C<isl_access_info>, which can
5311 be created through a call to C<isl_access_info_alloc>.
5312 The arguments to this functions are the sink access relation
5313 C<sink>, a token C<sink_user> used to identify the sink
5314 access to the user, a callback function for specifying the
5315 relative order of source and sink accesses, and the number
5316 of source access relations that will be added.
5317 The callback function has type C<int (*)(void *first, void *second)>.
5318 The function is called with two user supplied tokens identifying
5319 either a source or the sink and it should return the shared nesting
5320 level and the relative order of the two accesses.
5321 In particular, let I<n> be the number of loops shared by
5322 the two accesses. If C<first> precedes C<second> textually,
5323 then the function should return I<2 * n + 1>; otherwise,
5324 it should return I<2 * n>.
5325 The sources can be added to the C<isl_access_info> by performing
5326 (at most) C<max_source> calls to C<isl_access_info_add_source>.
5327 C<must> indicates whether the source is a I<must> access
5328 or a I<may> access. Note that a multi-valued access relation
5329 should only be marked I<must> if every iteration in the domain
5330 of the relation accesses I<all> elements in its image.
5331 The C<source_user> token is again used to identify
5332 the source access. The range of the source access relation
5333 C<source> should have the same dimension as the range
5334 of the sink access relation.
5335 The C<isl_access_info_free> function should usually not be
5336 called explicitly, because it is called implicitly by
5337 C<isl_access_info_compute_flow>.
5339 The result of the dependence analysis is collected in an
5340 C<isl_flow>. There may be elements of
5341 the sink access for which no preceding source access could be
5342 found or for which all preceding sources are I<may> accesses.
5343 The relations containing these elements can be obtained through
5344 calls to C<isl_flow_get_no_source>, the first with C<must> set
5345 and the second with C<must> unset.
5346 In the case of standard flow dependence analysis,
5347 with the sink a read and the sources I<must> writes,
5348 the first relation corresponds to the reads from uninitialized
5349 array elements and the second relation is empty.
5350 The actual flow dependences can be extracted using
5351 C<isl_flow_foreach>. This function will call the user-specified
5352 callback function C<fn> for each B<non-empty> dependence between
5353 a source and the sink. The callback function is called
5354 with four arguments, the actual flow dependence relation
5355 mapping source iterations to sink iterations, a boolean that
5356 indicates whether it is a I<must> or I<may> dependence, a token
5357 identifying the source and an additional C<void *> with value
5358 equal to the third argument of the C<isl_flow_foreach> call.
5359 A dependence is marked I<must> if it originates from a I<must>
5360 source and if it is not followed by any I<may> sources.
5362 After finishing with an C<isl_flow>, the user should call
5363 C<isl_flow_free> to free all associated memory.
5365 A higher-level interface to dependence analysis is provided
5366 by the following function.
5368 #include <isl/flow.h>
5370 int isl_union_map_compute_flow(__isl_take isl_union_map *sink,
5371 __isl_take isl_union_map *must_source,
5372 __isl_take isl_union_map *may_source,
5373 __isl_take isl_union_map *schedule,
5374 __isl_give isl_union_map **must_dep,
5375 __isl_give isl_union_map **may_dep,
5376 __isl_give isl_union_map **must_no_source,
5377 __isl_give isl_union_map **may_no_source);
5379 The arrays are identified by the tuple names of the ranges
5380 of the accesses. The iteration domains by the tuple names
5381 of the domains of the accesses and of the schedule.
5382 The relative order of the iteration domains is given by the
5383 schedule. The relations returned through C<must_no_source>
5384 and C<may_no_source> are subsets of C<sink>.
5385 Any of C<must_dep>, C<may_dep>, C<must_no_source>
5386 or C<may_no_source> may be C<NULL>, but a C<NULL> value for
5387 any of the other arguments is treated as an error.
5389 =head3 Interaction with Dependence Analysis
5391 During the dependence analysis, we frequently need to perform
5392 the following operation. Given a relation between sink iterations
5393 and potential source iterations from a particular source domain,
5394 what is the last potential source iteration corresponding to each
5395 sink iteration. It can sometimes be convenient to adjust
5396 the set of potential source iterations before or after each such operation.
5397 The prototypical example is fuzzy array dataflow analysis,
5398 where we need to analyze if, based on data-dependent constraints,
5399 the sink iteration can ever be executed without one or more of
5400 the corresponding potential source iterations being executed.
5401 If so, we can introduce extra parameters and select an unknown
5402 but fixed source iteration from the potential source iterations.
5403 To be able to perform such manipulations, C<isl> provides the following
5406 #include <isl/flow.h>
5408 typedef __isl_give isl_restriction *(*isl_access_restrict)(
5409 __isl_keep isl_map *source_map,
5410 __isl_keep isl_set *sink, void *source_user,
5412 __isl_give isl_access_info *isl_access_info_set_restrict(
5413 __isl_take isl_access_info *acc,
5414 isl_access_restrict fn, void *user);
5416 The function C<isl_access_info_set_restrict> should be called
5417 before calling C<isl_access_info_compute_flow> and registers a callback function
5418 that will be called any time C<isl> is about to compute the last
5419 potential source. The first argument is the (reverse) proto-dependence,
5420 mapping sink iterations to potential source iterations.
5421 The second argument represents the sink iterations for which
5422 we want to compute the last source iteration.
5423 The third argument is the token corresponding to the source
5424 and the final argument is the token passed to C<isl_access_info_set_restrict>.
5425 The callback is expected to return a restriction on either the input or
5426 the output of the operation computing the last potential source.
5427 If the input needs to be restricted then restrictions are needed
5428 for both the source and the sink iterations. The sink iterations
5429 and the potential source iterations will be intersected with these sets.
5430 If the output needs to be restricted then only a restriction on the source
5431 iterations is required.
5432 If any error occurs, the callback should return C<NULL>.
5433 An C<isl_restriction> object can be created, freed and inspected
5434 using the following functions.
5436 #include <isl/flow.h>
5438 __isl_give isl_restriction *isl_restriction_input(
5439 __isl_take isl_set *source_restr,
5440 __isl_take isl_set *sink_restr);
5441 __isl_give isl_restriction *isl_restriction_output(
5442 __isl_take isl_set *source_restr);
5443 __isl_give isl_restriction *isl_restriction_none(
5444 __isl_take isl_map *source_map);
5445 __isl_give isl_restriction *isl_restriction_empty(
5446 __isl_take isl_map *source_map);
5447 void *isl_restriction_free(
5448 __isl_take isl_restriction *restr);
5449 isl_ctx *isl_restriction_get_ctx(
5450 __isl_keep isl_restriction *restr);
5452 C<isl_restriction_none> and C<isl_restriction_empty> are special
5453 cases of C<isl_restriction_input>. C<isl_restriction_none>
5454 is essentially equivalent to
5456 isl_restriction_input(isl_set_universe(
5457 isl_space_range(isl_map_get_space(source_map))),
5459 isl_space_domain(isl_map_get_space(source_map))));
5461 whereas C<isl_restriction_empty> is essentially equivalent to
5463 isl_restriction_input(isl_set_empty(
5464 isl_space_range(isl_map_get_space(source_map))),
5466 isl_space_domain(isl_map_get_space(source_map))));
5470 B<The functionality described in this section is fairly new
5471 and may be subject to change.>
5473 The following function can be used to compute a schedule
5474 for a union of domains.
5475 By default, the algorithm used to construct the schedule is similar
5476 to that of C<Pluto>.
5477 Alternatively, Feautrier's multi-dimensional scheduling algorithm can
5479 The generated schedule respects all C<validity> dependences.
5480 That is, all dependence distances over these dependences in the
5481 scheduled space are lexicographically positive.
5482 The default algorithm tries to minimize the dependence distances over
5483 C<proximity> dependences.
5484 Moreover, it tries to obtain sequences (bands) of schedule dimensions
5485 for groups of domains where the dependence distances have only
5486 non-negative values.
5487 When using Feautrier's algorithm, the C<proximity> dependence
5488 distances are only minimized during the extension to a
5489 full-dimensional schedule.
5491 #include <isl/schedule.h>
5492 __isl_give isl_schedule *isl_union_set_compute_schedule(
5493 __isl_take isl_union_set *domain,
5494 __isl_take isl_union_map *validity,
5495 __isl_take isl_union_map *proximity);
5496 void *isl_schedule_free(__isl_take isl_schedule *sched);
5498 A mapping from the domains to the scheduled space can be obtained
5499 from an C<isl_schedule> using the following function.
5501 __isl_give isl_union_map *isl_schedule_get_map(
5502 __isl_keep isl_schedule *sched);
5504 A representation of the schedule can be printed using
5506 __isl_give isl_printer *isl_printer_print_schedule(
5507 __isl_take isl_printer *p,
5508 __isl_keep isl_schedule *schedule);
5510 A representation of the schedule as a forest of bands can be obtained
5511 using the following function.
5513 __isl_give isl_band_list *isl_schedule_get_band_forest(
5514 __isl_keep isl_schedule *schedule);
5516 The individual bands can be visited in depth-first post-order
5517 using the following function.
5519 #include <isl/schedule.h>
5520 int isl_schedule_foreach_band(
5521 __isl_keep isl_schedule *sched,
5522 int (*fn)(__isl_keep isl_band *band, void *user),
5525 The list can be manipulated as explained in L<"Lists">.
5526 The bands inside the list can be copied and freed using the following
5529 #include <isl/band.h>
5530 __isl_give isl_band *isl_band_copy(
5531 __isl_keep isl_band *band);
5532 void *isl_band_free(__isl_take isl_band *band);
5534 Each band contains zero or more scheduling dimensions.
5535 These are referred to as the members of the band.
5536 The section of the schedule that corresponds to the band is
5537 referred to as the partial schedule of the band.
5538 For those nodes that participate in a band, the outer scheduling
5539 dimensions form the prefix schedule, while the inner scheduling
5540 dimensions form the suffix schedule.
5541 That is, if we take a cut of the band forest, then the union of
5542 the concatenations of the prefix, partial and suffix schedules of
5543 each band in the cut is equal to the entire schedule (modulo
5544 some possible padding at the end with zero scheduling dimensions).
5545 The properties of a band can be inspected using the following functions.
5547 #include <isl/band.h>
5548 isl_ctx *isl_band_get_ctx(__isl_keep isl_band *band);
5550 int isl_band_has_children(__isl_keep isl_band *band);
5551 __isl_give isl_band_list *isl_band_get_children(
5552 __isl_keep isl_band *band);
5554 __isl_give isl_union_map *isl_band_get_prefix_schedule(
5555 __isl_keep isl_band *band);
5556 __isl_give isl_union_map *isl_band_get_partial_schedule(
5557 __isl_keep isl_band *band);
5558 __isl_give isl_union_map *isl_band_get_suffix_schedule(
5559 __isl_keep isl_band *band);
5561 int isl_band_n_member(__isl_keep isl_band *band);
5562 int isl_band_member_is_zero_distance(
5563 __isl_keep isl_band *band, int pos);
5565 int isl_band_list_foreach_band(
5566 __isl_keep isl_band_list *list,
5567 int (*fn)(__isl_keep isl_band *band, void *user),
5570 Note that a scheduling dimension is considered to be ``zero
5571 distance'' if it does not carry any proximity dependences
5573 That is, if the dependence distances of the proximity
5574 dependences are all zero in that direction (for fixed
5575 iterations of outer bands).
5576 Like C<isl_schedule_foreach_band>,
5577 the function C<isl_band_list_foreach_band> calls C<fn> on the bands
5578 in depth-first post-order.
5580 A band can be tiled using the following function.
5582 #include <isl/band.h>
5583 int isl_band_tile(__isl_keep isl_band *band,
5584 __isl_take isl_vec *sizes);
5586 int isl_options_set_tile_scale_tile_loops(isl_ctx *ctx,
5588 int isl_options_get_tile_scale_tile_loops(isl_ctx *ctx);
5589 int isl_options_set_tile_shift_point_loops(isl_ctx *ctx,
5591 int isl_options_get_tile_shift_point_loops(isl_ctx *ctx);
5593 The C<isl_band_tile> function tiles the band using the given tile sizes
5594 inside its schedule.
5595 A new child band is created to represent the point loops and it is
5596 inserted between the modified band and its children.
5597 The C<tile_scale_tile_loops> option specifies whether the tile
5598 loops iterators should be scaled by the tile sizes.
5599 If the C<tile_shift_point_loops> option is set, then the point loops
5600 are shifted to start at zero.
5602 A band can be split into two nested bands using the following function.
5604 int isl_band_split(__isl_keep isl_band *band, int pos);
5606 The resulting outer band contains the first C<pos> dimensions of C<band>
5607 while the inner band contains the remaining dimensions.
5609 A representation of the band can be printed using
5611 #include <isl/band.h>
5612 __isl_give isl_printer *isl_printer_print_band(
5613 __isl_take isl_printer *p,
5614 __isl_keep isl_band *band);
5618 #include <isl/schedule.h>
5619 int isl_options_set_schedule_max_coefficient(
5620 isl_ctx *ctx, int val);
5621 int isl_options_get_schedule_max_coefficient(
5623 int isl_options_set_schedule_max_constant_term(
5624 isl_ctx *ctx, int val);
5625 int isl_options_get_schedule_max_constant_term(
5627 int isl_options_set_schedule_fuse(isl_ctx *ctx, int val);
5628 int isl_options_get_schedule_fuse(isl_ctx *ctx);
5629 int isl_options_set_schedule_maximize_band_depth(
5630 isl_ctx *ctx, int val);
5631 int isl_options_get_schedule_maximize_band_depth(
5633 int isl_options_set_schedule_outer_zero_distance(
5634 isl_ctx *ctx, int val);
5635 int isl_options_get_schedule_outer_zero_distance(
5637 int isl_options_set_schedule_split_scaled(
5638 isl_ctx *ctx, int val);
5639 int isl_options_get_schedule_split_scaled(
5641 int isl_options_set_schedule_algorithm(
5642 isl_ctx *ctx, int val);
5643 int isl_options_get_schedule_algorithm(
5645 int isl_options_set_schedule_separate_components(
5646 isl_ctx *ctx, int val);
5647 int isl_options_get_schedule_separate_components(
5652 =item * schedule_max_coefficient
5654 This option enforces that the coefficients for variable and parameter
5655 dimensions in the calculated schedule are not larger than the specified value.
5656 This option can significantly increase the speed of the scheduling calculation
5657 and may also prevent fusing of unrelated dimensions. A value of -1 means that
5658 this option does not introduce bounds on the variable or parameter
5661 =item * schedule_max_constant_term
5663 This option enforces that the constant coefficients in the calculated schedule
5664 are not larger than the maximal constant term. This option can significantly
5665 increase the speed of the scheduling calculation and may also prevent fusing of
5666 unrelated dimensions. A value of -1 means that this option does not introduce
5667 bounds on the constant coefficients.
5669 =item * schedule_fuse
5671 This option controls the level of fusion.
5672 If this option is set to C<ISL_SCHEDULE_FUSE_MIN>, then loops in the
5673 resulting schedule will be distributed as much as possible.
5674 If this option is set to C<ISL_SCHEDULE_FUSE_MAX>, then C<isl> will
5675 try to fuse loops in the resulting schedule.
5677 =item * schedule_maximize_band_depth
5679 If this option is set, we do not split bands at the point
5680 where we detect splitting is necessary. Instead, we
5681 backtrack and split bands as early as possible. This
5682 reduces the number of splits and maximizes the width of
5683 the bands. Wider bands give more possibilities for tiling.
5684 Note that if the C<schedule_fuse> option is set to C<ISL_SCHEDULE_FUSE_MIN>,
5685 then bands will be split as early as possible, even if there is no need.
5686 The C<schedule_maximize_band_depth> option therefore has no effect in this case.
5688 =item * schedule_outer_zero_distance
5690 If this option is set, then we try to construct schedules
5691 where the outermost scheduling dimension in each band
5692 results in a zero dependence distance over the proximity
5695 =item * schedule_split_scaled
5697 If this option is set, then we try to construct schedules in which the
5698 constant term is split off from the linear part if the linear parts of
5699 the scheduling rows for all nodes in the graphs have a common non-trivial
5701 The constant term is then placed in a separate band and the linear
5704 =item * schedule_algorithm
5706 Selects the scheduling algorithm to be used.
5707 Available scheduling algorithms are C<ISL_SCHEDULE_ALGORITHM_ISL>
5708 and C<ISL_SCHEDULE_ALGORITHM_FEAUTRIER>.
5710 =item * schedule_separate_components
5712 If at any point the dependence graph contains any (weakly connected) components,
5713 then these components are scheduled separately.
5714 If this option is not set, then some iterations of the domains
5715 in these components may be scheduled together.
5716 If this option is set, then the components are given consecutive
5721 =head2 AST Generation
5723 This section describes the C<isl> functionality for generating
5724 ASTs that visit all the elements
5725 in a domain in an order specified by a schedule.
5726 In particular, given a C<isl_union_map>, an AST is generated
5727 that visits all the elements in the domain of the C<isl_union_map>
5728 according to the lexicographic order of the corresponding image
5729 element(s). If the range of the C<isl_union_map> consists of
5730 elements in more than one space, then each of these spaces is handled
5731 separately in an arbitrary order.
5732 It should be noted that the image elements only specify the I<order>
5733 in which the corresponding domain elements should be visited.
5734 No direct relation between the image elements and the loop iterators
5735 in the generated AST should be assumed.
5737 Each AST is generated within a build. The initial build
5738 simply specifies the constraints on the parameters (if any)
5739 and can be created, inspected, copied and freed using the following functions.
5741 #include <isl/ast_build.h>
5742 __isl_give isl_ast_build *isl_ast_build_from_context(
5743 __isl_take isl_set *set);
5744 isl_ctx *isl_ast_build_get_ctx(
5745 __isl_keep isl_ast_build *build);
5746 __isl_give isl_ast_build *isl_ast_build_copy(
5747 __isl_keep isl_ast_build *build);
5748 void *isl_ast_build_free(
5749 __isl_take isl_ast_build *build);
5751 The C<set> argument is usually a parameter set with zero or more parameters.
5752 More C<isl_ast_build> functions are described in L</"Nested AST Generation">
5753 and L</"Fine-grained Control over AST Generation">.
5754 Finally, the AST itself can be constructed using the following
5757 #include <isl/ast_build.h>
5758 __isl_give isl_ast_node *isl_ast_build_ast_from_schedule(
5759 __isl_keep isl_ast_build *build,
5760 __isl_take isl_union_map *schedule);
5762 =head3 Inspecting the AST
5764 The basic properties of an AST node can be obtained as follows.
5766 #include <isl/ast.h>
5767 isl_ctx *isl_ast_node_get_ctx(
5768 __isl_keep isl_ast_node *node);
5769 enum isl_ast_node_type isl_ast_node_get_type(
5770 __isl_keep isl_ast_node *node);
5772 The type of an AST node is one of
5773 C<isl_ast_node_for>,
5775 C<isl_ast_node_block> or
5776 C<isl_ast_node_user>.
5777 An C<isl_ast_node_for> represents a for node.
5778 An C<isl_ast_node_if> represents an if node.
5779 An C<isl_ast_node_block> represents a compound node.
5780 An C<isl_ast_node_user> represents an expression statement.
5781 An expression statement typically corresponds to a domain element, i.e.,
5782 one of the elements that is visited by the AST.
5784 Each type of node has its own additional properties.
5786 #include <isl/ast.h>
5787 __isl_give isl_ast_expr *isl_ast_node_for_get_iterator(
5788 __isl_keep isl_ast_node *node);
5789 __isl_give isl_ast_expr *isl_ast_node_for_get_init(
5790 __isl_keep isl_ast_node *node);
5791 __isl_give isl_ast_expr *isl_ast_node_for_get_cond(
5792 __isl_keep isl_ast_node *node);
5793 __isl_give isl_ast_expr *isl_ast_node_for_get_inc(
5794 __isl_keep isl_ast_node *node);
5795 __isl_give isl_ast_node *isl_ast_node_for_get_body(
5796 __isl_keep isl_ast_node *node);
5797 int isl_ast_node_for_is_degenerate(
5798 __isl_keep isl_ast_node *node);
5800 An C<isl_ast_for> is considered degenerate if it is known to execute
5803 #include <isl/ast.h>
5804 __isl_give isl_ast_expr *isl_ast_node_if_get_cond(
5805 __isl_keep isl_ast_node *node);
5806 __isl_give isl_ast_node *isl_ast_node_if_get_then(
5807 __isl_keep isl_ast_node *node);
5808 int isl_ast_node_if_has_else(
5809 __isl_keep isl_ast_node *node);
5810 __isl_give isl_ast_node *isl_ast_node_if_get_else(
5811 __isl_keep isl_ast_node *node);
5813 __isl_give isl_ast_node_list *
5814 isl_ast_node_block_get_children(
5815 __isl_keep isl_ast_node *node);
5817 __isl_give isl_ast_expr *isl_ast_node_user_get_expr(
5818 __isl_keep isl_ast_node *node);
5820 Each of the returned C<isl_ast_expr>s can in turn be inspected using
5821 the following functions.
5823 #include <isl/ast.h>
5824 isl_ctx *isl_ast_expr_get_ctx(
5825 __isl_keep isl_ast_expr *expr);
5826 enum isl_ast_expr_type isl_ast_expr_get_type(
5827 __isl_keep isl_ast_expr *expr);
5829 The type of an AST expression is one of
5831 C<isl_ast_expr_id> or
5832 C<isl_ast_expr_int>.
5833 An C<isl_ast_expr_op> represents the result of an operation.
5834 An C<isl_ast_expr_id> represents an identifier.
5835 An C<isl_ast_expr_int> represents an integer value.
5837 Each type of expression has its own additional properties.
5839 #include <isl/ast.h>
5840 enum isl_ast_op_type isl_ast_expr_get_op_type(
5841 __isl_keep isl_ast_expr *expr);
5842 int isl_ast_expr_get_op_n_arg(__isl_keep isl_ast_expr *expr);
5843 __isl_give isl_ast_expr *isl_ast_expr_get_op_arg(
5844 __isl_keep isl_ast_expr *expr, int pos);
5845 int isl_ast_node_foreach_ast_op_type(
5846 __isl_keep isl_ast_node *node,
5847 int (*fn)(enum isl_ast_op_type type, void *user),
5850 C<isl_ast_expr_get_op_type> returns the type of the operation
5851 performed. C<isl_ast_expr_get_op_n_arg> returns the number of
5852 arguments. C<isl_ast_expr_get_op_arg> returns the specified
5854 C<isl_ast_node_foreach_ast_op_type> calls C<fn> for each distinct
5855 C<isl_ast_op_type> that appears in C<node>.
5856 The operation type is one of the following.
5860 =item C<isl_ast_op_and>
5862 Logical I<and> of two arguments.
5863 Both arguments can be evaluated.
5865 =item C<isl_ast_op_and_then>
5867 Logical I<and> of two arguments.
5868 The second argument can only be evaluated if the first evaluates to true.
5870 =item C<isl_ast_op_or>
5872 Logical I<or> of two arguments.
5873 Both arguments can be evaluated.
5875 =item C<isl_ast_op_or_else>
5877 Logical I<or> of two arguments.
5878 The second argument can only be evaluated if the first evaluates to false.
5880 =item C<isl_ast_op_max>
5882 Maximum of two or more arguments.
5884 =item C<isl_ast_op_min>
5886 Minimum of two or more arguments.
5888 =item C<isl_ast_op_minus>
5892 =item C<isl_ast_op_add>
5894 Sum of two arguments.
5896 =item C<isl_ast_op_sub>
5898 Difference of two arguments.
5900 =item C<isl_ast_op_mul>
5902 Product of two arguments.
5904 =item C<isl_ast_op_div>
5906 Exact division. That is, the result is known to be an integer.
5908 =item C<isl_ast_op_fdiv_q>
5910 Result of integer division, rounded towards negative
5913 =item C<isl_ast_op_pdiv_q>
5915 Result of integer division, where dividend is known to be non-negative.
5917 =item C<isl_ast_op_pdiv_r>
5919 Remainder of integer division, where dividend is known to be non-negative.
5921 =item C<isl_ast_op_cond>
5923 Conditional operator defined on three arguments.
5924 If the first argument evaluates to true, then the result
5925 is equal to the second argument. Otherwise, the result
5926 is equal to the third argument.
5927 The second and third argument may only be evaluated if
5928 the first argument evaluates to true and false, respectively.
5929 Corresponds to C<a ? b : c> in C.
5931 =item C<isl_ast_op_select>
5933 Conditional operator defined on three arguments.
5934 If the first argument evaluates to true, then the result
5935 is equal to the second argument. Otherwise, the result
5936 is equal to the third argument.
5937 The second and third argument may be evaluated independently
5938 of the value of the first argument.
5939 Corresponds to C<a * b + (1 - a) * c> in C.
5941 =item C<isl_ast_op_eq>
5945 =item C<isl_ast_op_le>
5947 Less than or equal relation.
5949 =item C<isl_ast_op_lt>
5953 =item C<isl_ast_op_ge>
5955 Greater than or equal relation.
5957 =item C<isl_ast_op_gt>
5959 Greater than relation.
5961 =item C<isl_ast_op_call>
5964 The number of arguments of the C<isl_ast_expr> is one more than
5965 the number of arguments in the function call, the first argument
5966 representing the function being called.
5970 #include <isl/ast.h>
5971 __isl_give isl_id *isl_ast_expr_get_id(
5972 __isl_keep isl_ast_expr *expr);
5974 Return the identifier represented by the AST expression.
5976 #include <isl/ast.h>
5977 int isl_ast_expr_get_int(__isl_keep isl_ast_expr *expr,
5980 Return the integer represented by the AST expression.
5981 Note that the integer is returned through the C<v> argument.
5982 The return value of the function itself indicates whether the
5983 operation was performed successfully.
5985 =head3 Manipulating and printing the AST
5987 AST nodes can be copied and freed using the following functions.
5989 #include <isl/ast.h>
5990 __isl_give isl_ast_node *isl_ast_node_copy(
5991 __isl_keep isl_ast_node *node);
5992 void *isl_ast_node_free(__isl_take isl_ast_node *node);
5994 AST expressions can be copied and freed using the following functions.
5996 #include <isl/ast.h>
5997 __isl_give isl_ast_expr *isl_ast_expr_copy(
5998 __isl_keep isl_ast_expr *expr);
5999 void *isl_ast_expr_free(__isl_take isl_ast_expr *expr);
6001 New AST expressions can be created either directly or within
6002 the context of an C<isl_ast_build>.
6004 #include <isl/ast.h>
6005 __isl_give isl_ast_expr *isl_ast_expr_from_id(
6006 __isl_take isl_id *id);
6007 __isl_give isl_ast_expr *isl_ast_expr_neg(
6008 __isl_take isl_ast_expr *expr);
6009 __isl_give isl_ast_expr *isl_ast_expr_add(
6010 __isl_take isl_ast_expr *expr1,
6011 __isl_take isl_ast_expr *expr2);
6012 __isl_give isl_ast_expr *isl_ast_expr_sub(
6013 __isl_take isl_ast_expr *expr1,
6014 __isl_take isl_ast_expr *expr2);
6015 __isl_give isl_ast_expr *isl_ast_expr_mul(
6016 __isl_take isl_ast_expr *expr1,
6017 __isl_take isl_ast_expr *expr2);
6018 __isl_give isl_ast_expr *isl_ast_expr_div(
6019 __isl_take isl_ast_expr *expr1,
6020 __isl_take isl_ast_expr *expr2);
6021 __isl_give isl_ast_expr *isl_ast_expr_and(
6022 __isl_take isl_ast_expr *expr1,
6023 __isl_take isl_ast_expr *expr2)
6024 __isl_give isl_ast_expr *isl_ast_expr_or(
6025 __isl_take isl_ast_expr *expr1,
6026 __isl_take isl_ast_expr *expr2)
6028 #include <isl/ast_build.h>
6029 __isl_give isl_ast_expr *isl_ast_build_expr_from_pw_aff(
6030 __isl_keep isl_ast_build *build,
6031 __isl_take isl_pw_aff *pa);
6032 __isl_give isl_ast_expr *
6033 isl_ast_build_call_from_pw_multi_aff(
6034 __isl_keep isl_ast_build *build,
6035 __isl_take isl_pw_multi_aff *pma);
6037 The domains of C<pa> and C<pma> should correspond
6038 to the schedule space of C<build>.
6039 The tuple id of C<pma> is used as the function being called.
6041 User specified data can be attached to an C<isl_ast_node> and obtained
6042 from the same C<isl_ast_node> using the following functions.
6044 #include <isl/ast.h>
6045 __isl_give isl_ast_node *isl_ast_node_set_annotation(
6046 __isl_take isl_ast_node *node,
6047 __isl_take isl_id *annotation);
6048 __isl_give isl_id *isl_ast_node_get_annotation(
6049 __isl_keep isl_ast_node *node);
6051 Basic printing can be performed using the following functions.
6053 #include <isl/ast.h>
6054 __isl_give isl_printer *isl_printer_print_ast_expr(
6055 __isl_take isl_printer *p,
6056 __isl_keep isl_ast_expr *expr);
6057 __isl_give isl_printer *isl_printer_print_ast_node(
6058 __isl_take isl_printer *p,
6059 __isl_keep isl_ast_node *node);
6061 More advanced printing can be performed using the following functions.
6063 #include <isl/ast.h>
6064 __isl_give isl_printer *isl_ast_op_type_print_macro(
6065 enum isl_ast_op_type type,
6066 __isl_take isl_printer *p);
6067 __isl_give isl_printer *isl_ast_node_print_macros(
6068 __isl_keep isl_ast_node *node,
6069 __isl_take isl_printer *p);
6070 __isl_give isl_printer *isl_ast_node_print(
6071 __isl_keep isl_ast_node *node,
6072 __isl_take isl_printer *p,
6073 __isl_take isl_ast_print_options *options);
6074 __isl_give isl_printer *isl_ast_node_for_print(
6075 __isl_keep isl_ast_node *node,
6076 __isl_take isl_printer *p,
6077 __isl_take isl_ast_print_options *options);
6078 __isl_give isl_printer *isl_ast_node_if_print(
6079 __isl_keep isl_ast_node *node,
6080 __isl_take isl_printer *p,
6081 __isl_take isl_ast_print_options *options);
6083 While printing an C<isl_ast_node> in C<ISL_FORMAT_C>,
6084 C<isl> may print out an AST that makes use of macros such
6085 as C<floord>, C<min> and C<max>.
6086 C<isl_ast_op_type_print_macro> prints out the macro
6087 corresponding to a specific C<isl_ast_op_type>.
6088 C<isl_ast_node_print_macros> scans the C<isl_ast_node>
6089 for expressions where these macros would be used and prints
6090 out the required macro definitions.
6091 Essentially, C<isl_ast_node_print_macros> calls
6092 C<isl_ast_node_foreach_ast_op_type> with C<isl_ast_op_type_print_macro>
6093 as function argument.
6094 C<isl_ast_node_print>, C<isl_ast_node_for_print> and
6095 C<isl_ast_node_if_print> print an C<isl_ast_node>
6096 in C<ISL_FORMAT_C>, but allow for some extra control
6097 through an C<isl_ast_print_options> object.
6098 This object can be created using the following functions.
6100 #include <isl/ast.h>
6101 __isl_give isl_ast_print_options *
6102 isl_ast_print_options_alloc(isl_ctx *ctx);
6103 __isl_give isl_ast_print_options *
6104 isl_ast_print_options_copy(
6105 __isl_keep isl_ast_print_options *options);
6106 void *isl_ast_print_options_free(
6107 __isl_take isl_ast_print_options *options);
6109 __isl_give isl_ast_print_options *
6110 isl_ast_print_options_set_print_user(
6111 __isl_take isl_ast_print_options *options,
6112 __isl_give isl_printer *(*print_user)(
6113 __isl_take isl_printer *p,
6114 __isl_take isl_ast_print_options *options,
6115 __isl_keep isl_ast_node *node, void *user),
6117 __isl_give isl_ast_print_options *
6118 isl_ast_print_options_set_print_for(
6119 __isl_take isl_ast_print_options *options,
6120 __isl_give isl_printer *(*print_for)(
6121 __isl_take isl_printer *p,
6122 __isl_take isl_ast_print_options *options,
6123 __isl_keep isl_ast_node *node, void *user),
6126 The callback set by C<isl_ast_print_options_set_print_user>
6127 is called whenever a node of type C<isl_ast_node_user> needs to
6129 The callback set by C<isl_ast_print_options_set_print_for>
6130 is called whenever a node of type C<isl_ast_node_for> needs to
6132 Note that C<isl_ast_node_for_print> will I<not> call the
6133 callback set by C<isl_ast_print_options_set_print_for> on the node
6134 on which C<isl_ast_node_for_print> is called, but only on nested
6135 nodes of type C<isl_ast_node_for>. It is therefore safe to
6136 call C<isl_ast_node_for_print> from within the callback set by
6137 C<isl_ast_print_options_set_print_for>.
6139 The following option determines the type to be used for iterators
6140 while printing the AST.
6142 int isl_options_set_ast_iterator_type(
6143 isl_ctx *ctx, const char *val);
6144 const char *isl_options_get_ast_iterator_type(
6149 #include <isl/ast_build.h>
6150 int isl_options_set_ast_build_atomic_upper_bound(
6151 isl_ctx *ctx, int val);
6152 int isl_options_get_ast_build_atomic_upper_bound(
6154 int isl_options_set_ast_build_prefer_pdiv(isl_ctx *ctx,
6156 int isl_options_get_ast_build_prefer_pdiv(isl_ctx *ctx);
6157 int isl_options_set_ast_build_exploit_nested_bounds(
6158 isl_ctx *ctx, int val);
6159 int isl_options_get_ast_build_exploit_nested_bounds(
6161 int isl_options_set_ast_build_group_coscheduled(
6162 isl_ctx *ctx, int val);
6163 int isl_options_get_ast_build_group_coscheduled(
6165 int isl_options_set_ast_build_scale_strides(
6166 isl_ctx *ctx, int val);
6167 int isl_options_get_ast_build_scale_strides(
6169 int isl_options_set_ast_build_allow_else(isl_ctx *ctx,
6171 int isl_options_get_ast_build_allow_else(isl_ctx *ctx);
6172 int isl_options_set_ast_build_allow_or(isl_ctx *ctx,
6174 int isl_options_get_ast_build_allow_or(isl_ctx *ctx);
6178 =item * ast_build_atomic_upper_bound
6180 Generate loop upper bounds that consist of the current loop iterator,
6181 an operator and an expression not involving the iterator.
6182 If this option is not set, then the current loop iterator may appear
6183 several times in the upper bound.
6184 For example, when this option is turned off, AST generation
6187 [n] -> { A[i] -> [i] : 0 <= i <= 100, n }
6191 for (int c0 = 0; c0 <= 100 && n >= c0; c0 += 1)
6194 When the option is turned on, the following AST is generated
6196 for (int c0 = 0; c0 <= min(100, n); c0 += 1)
6199 =item * ast_build_prefer_pdiv
6201 If this option is turned off, then the AST generation will
6202 produce ASTs that may only contain C<isl_ast_op_fdiv_q>
6203 operators, but no C<isl_ast_op_pdiv_q> or
6204 C<isl_ast_op_pdiv_r> operators.
6205 If this options is turned on, then C<isl> will try to convert
6206 some of the C<isl_ast_op_fdiv_q> operators to (expressions containing)
6207 C<isl_ast_op_pdiv_q> or C<isl_ast_op_pdiv_r> operators.
6209 =item * ast_build_exploit_nested_bounds
6211 Simplify conditions based on bounds of nested for loops.
6212 In particular, remove conditions that are implied by the fact
6213 that one or more nested loops have at least one iteration,
6214 meaning that the upper bound is at least as large as the lower bound.
6215 For example, when this option is turned off, AST generation
6218 [N,M] -> { A[i,j] -> [i,j] : 0 <= i <= N and
6224 for (int c0 = 0; c0 <= N; c0 += 1)
6225 for (int c1 = 0; c1 <= M; c1 += 1)
6228 When the option is turned on, the following AST is generated
6230 for (int c0 = 0; c0 <= N; c0 += 1)
6231 for (int c1 = 0; c1 <= M; c1 += 1)
6234 =item * ast_build_group_coscheduled
6236 If two domain elements are assigned the same schedule point, then
6237 they may be executed in any order and they may even appear in different
6238 loops. If this options is set, then the AST generator will make
6239 sure that coscheduled domain elements do not appear in separate parts
6240 of the AST. This is useful in case of nested AST generation
6241 if the outer AST generation is given only part of a schedule
6242 and the inner AST generation should handle the domains that are
6243 coscheduled by this initial part of the schedule together.
6244 For example if an AST is generated for a schedule
6246 { A[i] -> [0]; B[i] -> [0] }
6248 then the C<isl_ast_build_set_create_leaf> callback described
6249 below may get called twice, once for each domain.
6250 Setting this option ensures that the callback is only called once
6251 on both domains together.
6253 =item * ast_build_separation_bounds
6255 This option specifies which bounds to use during separation.
6256 If this option is set to C<ISL_AST_BUILD_SEPARATION_BOUNDS_IMPLICIT>
6257 then all (possibly implicit) bounds on the current dimension will
6258 be used during separation.
6259 If this option is set to C<ISL_AST_BUILD_SEPARATION_BOUNDS_EXPLICIT>
6260 then only those bounds that are explicitly available will
6261 be used during separation.
6263 =item * ast_build_scale_strides
6265 This option specifies whether the AST generator is allowed
6266 to scale down iterators of strided loops.
6268 =item * ast_build_allow_else
6270 This option specifies whether the AST generator is allowed
6271 to construct if statements with else branches.
6273 =item * ast_build_allow_or
6275 This option specifies whether the AST generator is allowed
6276 to construct if conditions with disjunctions.
6280 =head3 Fine-grained Control over AST Generation
6282 Besides specifying the constraints on the parameters,
6283 an C<isl_ast_build> object can be used to control
6284 various aspects of the AST generation process.
6285 The most prominent way of control is through ``options'',
6286 which can be set using the following function.
6288 #include <isl/ast_build.h>
6289 __isl_give isl_ast_build *
6290 isl_ast_build_set_options(
6291 __isl_take isl_ast_build *control,
6292 __isl_take isl_union_map *options);
6294 The options are encoded in an <isl_union_map>.
6295 The domain of this union relation refers to the schedule domain,
6296 i.e., the range of the schedule passed to C<isl_ast_build_ast_from_schedule>.
6297 In the case of nested AST generation (see L</"Nested AST Generation">),
6298 the domain of C<options> should refer to the extra piece of the schedule.
6299 That is, it should be equal to the range of the wrapped relation in the
6300 range of the schedule.
6301 The range of the options can consist of elements in one or more spaces,
6302 the names of which determine the effect of the option.
6303 The values of the range typically also refer to the schedule dimension
6304 to which the option applies. In case of nested AST generation
6305 (see L</"Nested AST Generation">), these values refer to the position
6306 of the schedule dimension within the innermost AST generation.
6307 The constraints on the domain elements of
6308 the option should only refer to this dimension and earlier dimensions.
6309 We consider the following spaces.
6313 =item C<separation_class>
6315 This space is a wrapped relation between two one dimensional spaces.
6316 The input space represents the schedule dimension to which the option
6317 applies and the output space represents the separation class.
6318 While constructing a loop corresponding to the specified schedule
6319 dimension(s), the AST generator will try to generate separate loops
6320 for domain elements that are assigned different classes.
6321 If only some of the elements are assigned a class, then those elements
6322 that are not assigned any class will be treated as belonging to a class
6323 that is separate from the explicitly assigned classes.
6324 The typical use case for this option is to separate full tiles from
6326 The other options, described below, are applied after the separation
6329 As an example, consider the separation into full and partial tiles
6330 of a tiling of a triangular domain.
6331 Take, for example, the domain
6333 { A[i,j] : 0 <= i,j and i + j <= 100 }
6335 and a tiling into tiles of 10 by 10. The input to the AST generator
6336 is then the schedule
6338 { A[i,j] -> [([i/10]),[j/10],i,j] : 0 <= i,j and
6341 Without any options, the following AST is generated
6343 for (int c0 = 0; c0 <= 10; c0 += 1)
6344 for (int c1 = 0; c1 <= -c0 + 10; c1 += 1)
6345 for (int c2 = 10 * c0;
6346 c2 <= min(-10 * c1 + 100, 10 * c0 + 9);
6348 for (int c3 = 10 * c1;
6349 c3 <= min(10 * c1 + 9, -c2 + 100);
6353 Separation into full and partial tiles can be obtained by assigning
6354 a class, say C<0>, to the full tiles. The full tiles are represented by those
6355 values of the first and second schedule dimensions for which there are
6356 values of the third and fourth dimensions to cover an entire tile.
6357 That is, we need to specify the following option
6359 { [a,b,c,d] -> separation_class[[0]->[0]] :
6360 exists b': 0 <= 10a,10b' and
6361 10a+9+10b'+9 <= 100;
6362 [a,b,c,d] -> separation_class[[1]->[0]] :
6363 0 <= 10a,10b and 10a+9+10b+9 <= 100 }
6367 { [a, b, c, d] -> separation_class[[1] -> [0]] :
6368 a >= 0 and b >= 0 and b <= 8 - a;
6369 [a, b, c, d] -> separation_class[[0] -> [0]] :
6372 With this option, the generated AST is as follows
6375 for (int c0 = 0; c0 <= 8; c0 += 1) {
6376 for (int c1 = 0; c1 <= -c0 + 8; c1 += 1)
6377 for (int c2 = 10 * c0;
6378 c2 <= 10 * c0 + 9; c2 += 1)
6379 for (int c3 = 10 * c1;
6380 c3 <= 10 * c1 + 9; c3 += 1)
6382 for (int c1 = -c0 + 9; c1 <= -c0 + 10; c1 += 1)
6383 for (int c2 = 10 * c0;
6384 c2 <= min(-10 * c1 + 100, 10 * c0 + 9);
6386 for (int c3 = 10 * c1;
6387 c3 <= min(-c2 + 100, 10 * c1 + 9);
6391 for (int c0 = 9; c0 <= 10; c0 += 1)
6392 for (int c1 = 0; c1 <= -c0 + 10; c1 += 1)
6393 for (int c2 = 10 * c0;
6394 c2 <= min(-10 * c1 + 100, 10 * c0 + 9);
6396 for (int c3 = 10 * c1;
6397 c3 <= min(10 * c1 + 9, -c2 + 100);
6404 This is a single-dimensional space representing the schedule dimension(s)
6405 to which ``separation'' should be applied. Separation tries to split
6406 a loop into several pieces if this can avoid the generation of guards
6408 See also the C<atomic> option.
6412 This is a single-dimensional space representing the schedule dimension(s)
6413 for which the domains should be considered ``atomic''. That is, the
6414 AST generator will make sure that any given domain space will only appear
6415 in a single loop at the specified level.
6417 Consider the following schedule
6419 { a[i] -> [i] : 0 <= i < 10;
6420 b[i] -> [i+1] : 0 <= i < 10 }
6422 If the following option is specified
6424 { [i] -> separate[x] }
6426 then the following AST will be generated
6430 for (int c0 = 1; c0 <= 9; c0 += 1) {
6437 If, on the other hand, the following option is specified
6439 { [i] -> atomic[x] }
6441 then the following AST will be generated
6443 for (int c0 = 0; c0 <= 10; c0 += 1) {
6450 If neither C<atomic> nor C<separate> is specified, then the AST generator
6451 may produce either of these two results or some intermediate form.
6455 This is a single-dimensional space representing the schedule dimension(s)
6456 that should be I<completely> unrolled.
6457 To obtain a partial unrolling, the user should apply an additional
6458 strip-mining to the schedule and fully unroll the inner loop.
6462 Additional control is available through the following functions.
6464 #include <isl/ast_build.h>
6465 __isl_give isl_ast_build *
6466 isl_ast_build_set_iterators(
6467 __isl_take isl_ast_build *control,
6468 __isl_take isl_id_list *iterators);
6470 The function C<isl_ast_build_set_iterators> allows the user to
6471 specify a list of iterator C<isl_id>s to be used as iterators.
6472 If the input schedule is injective, then
6473 the number of elements in this list should be as large as the dimension
6474 of the schedule space, but no direct correspondence should be assumed
6475 between dimensions and elements.
6476 If the input schedule is not injective, then an additional number
6477 of C<isl_id>s equal to the largest dimension of the input domains
6479 If the number of provided C<isl_id>s is insufficient, then additional
6480 names are automatically generated.
6482 #include <isl/ast_build.h>
6483 __isl_give isl_ast_build *
6484 isl_ast_build_set_create_leaf(
6485 __isl_take isl_ast_build *control,
6486 __isl_give isl_ast_node *(*fn)(
6487 __isl_take isl_ast_build *build,
6488 void *user), void *user);
6491 C<isl_ast_build_set_create_leaf> function allows for the
6492 specification of a callback that should be called whenever the AST
6493 generator arrives at an element of the schedule domain.
6494 The callback should return an AST node that should be inserted
6495 at the corresponding position of the AST. The default action (when
6496 the callback is not set) is to continue generating parts of the AST to scan
6497 all the domain elements associated to the schedule domain element
6498 and to insert user nodes, ``calling'' the domain element, for each of them.
6499 The C<build> argument contains the current state of the C<isl_ast_build>.
6500 To ease nested AST generation (see L</"Nested AST Generation">),
6501 all control information that is
6502 specific to the current AST generation such as the options and
6503 the callbacks has been removed from this C<isl_ast_build>.
6504 The callback would typically return the result of a nested
6506 user defined node created using the following function.
6508 #include <isl/ast.h>
6509 __isl_give isl_ast_node *isl_ast_node_alloc_user(
6510 __isl_take isl_ast_expr *expr);
6512 #include <isl/ast_build.h>
6513 __isl_give isl_ast_build *
6514 isl_ast_build_set_at_each_domain(
6515 __isl_take isl_ast_build *build,
6516 __isl_give isl_ast_node *(*fn)(
6517 __isl_take isl_ast_node *node,
6518 __isl_keep isl_ast_build *build,
6519 void *user), void *user);
6520 __isl_give isl_ast_build *
6521 isl_ast_build_set_before_each_for(
6522 __isl_take isl_ast_build *build,
6523 __isl_give isl_id *(*fn)(
6524 __isl_keep isl_ast_build *build,
6525 void *user), void *user);
6526 __isl_give isl_ast_build *
6527 isl_ast_build_set_after_each_for(
6528 __isl_take isl_ast_build *build,
6529 __isl_give isl_ast_node *(*fn)(
6530 __isl_take isl_ast_node *node,
6531 __isl_keep isl_ast_build *build,
6532 void *user), void *user);
6534 The callback set by C<isl_ast_build_set_at_each_domain> will
6535 be called for each domain AST node.
6536 The callbacks set by C<isl_ast_build_set_before_each_for>
6537 and C<isl_ast_build_set_after_each_for> will be called
6538 for each for AST node. The first will be called in depth-first
6539 pre-order, while the second will be called in depth-first post-order.
6540 Since C<isl_ast_build_set_before_each_for> is called before the for
6541 node is actually constructed, it is only passed an C<isl_ast_build>.
6542 The returned C<isl_id> will be added as an annotation (using
6543 C<isl_ast_node_set_annotation>) to the constructed for node.
6544 In particular, if the user has also specified an C<after_each_for>
6545 callback, then the annotation can be retrieved from the node passed to
6546 that callback using C<isl_ast_node_get_annotation>.
6547 All callbacks should C<NULL> on failure.
6548 The given C<isl_ast_build> can be used to create new
6549 C<isl_ast_expr> objects using C<isl_ast_build_expr_from_pw_aff>
6550 or C<isl_ast_build_call_from_pw_multi_aff>.
6552 =head3 Nested AST Generation
6554 C<isl> allows the user to create an AST within the context
6555 of another AST. These nested ASTs are created using the
6556 same C<isl_ast_build_ast_from_schedule> function that is used to create the
6557 outer AST. The C<build> argument should be an C<isl_ast_build>
6558 passed to a callback set by
6559 C<isl_ast_build_set_create_leaf>.
6560 The space of the range of the C<schedule> argument should refer
6561 to this build. In particular, the space should be a wrapped
6562 relation and the domain of this wrapped relation should be the
6563 same as that of the range of the schedule returned by
6564 C<isl_ast_build_get_schedule> below.
6565 In practice, the new schedule is typically
6566 created by calling C<isl_union_map_range_product> on the old schedule
6567 and some extra piece of the schedule.
6568 The space of the schedule domain is also available from
6569 the C<isl_ast_build>.
6571 #include <isl/ast_build.h>
6572 __isl_give isl_union_map *isl_ast_build_get_schedule(
6573 __isl_keep isl_ast_build *build);
6574 __isl_give isl_space *isl_ast_build_get_schedule_space(
6575 __isl_keep isl_ast_build *build);
6576 __isl_give isl_ast_build *isl_ast_build_restrict(
6577 __isl_take isl_ast_build *build,
6578 __isl_take isl_set *set);
6580 The C<isl_ast_build_get_schedule> function returns a (partial)
6581 schedule for the domains elements for which part of the AST still needs to
6582 be generated in the current build.
6583 In particular, the domain elements are mapped to those iterations of the loops
6584 enclosing the current point of the AST generation inside which
6585 the domain elements are executed.
6586 No direct correspondence between
6587 the input schedule and this schedule should be assumed.
6588 The space obtained from C<isl_ast_build_get_schedule_space> can be used
6589 to create a set for C<isl_ast_build_restrict> to intersect
6590 with the current build. In particular, the set passed to
6591 C<isl_ast_build_restrict> can have additional parameters.
6592 The ids of the set dimensions in the space returned by
6593 C<isl_ast_build_get_schedule_space> correspond to the
6594 iterators of the already generated loops.
6595 The user should not rely on the ids of the output dimensions
6596 of the relations in the union relation returned by
6597 C<isl_ast_build_get_schedule> having any particular value.
6601 Although C<isl> is mainly meant to be used as a library,
6602 it also contains some basic applications that use some
6603 of the functionality of C<isl>.
6604 The input may be specified in either the L<isl format>
6605 or the L<PolyLib format>.
6607 =head2 C<isl_polyhedron_sample>
6609 C<isl_polyhedron_sample> takes a polyhedron as input and prints
6610 an integer element of the polyhedron, if there is any.
6611 The first column in the output is the denominator and is always
6612 equal to 1. If the polyhedron contains no integer points,
6613 then a vector of length zero is printed.
6617 C<isl_pip> takes the same input as the C<example> program
6618 from the C<piplib> distribution, i.e., a set of constraints
6619 on the parameters, a line containing only -1 and finally a set
6620 of constraints on a parametric polyhedron.
6621 The coefficients of the parameters appear in the last columns
6622 (but before the final constant column).
6623 The output is the lexicographic minimum of the parametric polyhedron.
6624 As C<isl> currently does not have its own output format, the output
6625 is just a dump of the internal state.
6627 =head2 C<isl_polyhedron_minimize>
6629 C<isl_polyhedron_minimize> computes the minimum of some linear
6630 or affine objective function over the integer points in a polyhedron.
6631 If an affine objective function
6632 is given, then the constant should appear in the last column.
6634 =head2 C<isl_polytope_scan>
6636 Given a polytope, C<isl_polytope_scan> prints
6637 all integer points in the polytope.
6639 =head2 C<isl_codegen>
6641 Given a schedule, a context set and an options relation,
6642 C<isl_codegen> prints out an AST that scans the domain elements
6643 of the schedule in the order of their image(s) taking into account
6644 the constraints in the context set.