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 *isl_map_plain_get_val_if_fixed(
2064 __isl_keep isl_map *map,
2065 enum isl_dim_type type, unsigned pos);
2067 If the relation obviously lies on a hyperplane where the given dimension
2068 has a fixed value, then return that value.
2069 Otherwise return NaN.
2073 To check whether a set is a parameter domain, use this function:
2075 int isl_set_is_params(__isl_keep isl_set *set);
2076 int isl_union_set_is_params(
2077 __isl_keep isl_union_set *uset);
2081 The following functions check whether the domain of the given
2082 (basic) set is a wrapped relation.
2084 int isl_basic_set_is_wrapping(
2085 __isl_keep isl_basic_set *bset);
2086 int isl_set_is_wrapping(__isl_keep isl_set *set);
2088 =item * Internal Product
2090 int isl_basic_map_can_zip(
2091 __isl_keep isl_basic_map *bmap);
2092 int isl_map_can_zip(__isl_keep isl_map *map);
2094 Check whether the product of domain and range of the given relation
2096 i.e., whether both domain and range are nested relations.
2100 int isl_basic_map_can_curry(
2101 __isl_keep isl_basic_map *bmap);
2102 int isl_map_can_curry(__isl_keep isl_map *map);
2104 Check whether the domain of the (basic) relation is a wrapped relation.
2106 int isl_basic_map_can_uncurry(
2107 __isl_keep isl_basic_map *bmap);
2108 int isl_map_can_uncurry(__isl_keep isl_map *map);
2110 Check whether the range of the (basic) relation is a wrapped relation.
2114 =head3 Binary Properties
2120 int isl_set_plain_is_equal(__isl_keep isl_set *set1,
2121 __isl_keep isl_set *set2);
2122 int isl_set_is_equal(__isl_keep isl_set *set1,
2123 __isl_keep isl_set *set2);
2124 int isl_union_set_is_equal(
2125 __isl_keep isl_union_set *uset1,
2126 __isl_keep isl_union_set *uset2);
2127 int isl_basic_map_is_equal(
2128 __isl_keep isl_basic_map *bmap1,
2129 __isl_keep isl_basic_map *bmap2);
2130 int isl_map_is_equal(__isl_keep isl_map *map1,
2131 __isl_keep isl_map *map2);
2132 int isl_map_plain_is_equal(__isl_keep isl_map *map1,
2133 __isl_keep isl_map *map2);
2134 int isl_union_map_is_equal(
2135 __isl_keep isl_union_map *umap1,
2136 __isl_keep isl_union_map *umap2);
2138 =item * Disjointness
2140 int isl_set_plain_is_disjoint(__isl_keep isl_set *set1,
2141 __isl_keep isl_set *set2);
2142 int isl_set_is_disjoint(__isl_keep isl_set *set1,
2143 __isl_keep isl_set *set2);
2144 int isl_map_is_disjoint(__isl_keep isl_map *map1,
2145 __isl_keep isl_map *map2);
2149 int isl_basic_set_is_subset(
2150 __isl_keep isl_basic_set *bset1,
2151 __isl_keep isl_basic_set *bset2);
2152 int isl_set_is_subset(__isl_keep isl_set *set1,
2153 __isl_keep isl_set *set2);
2154 int isl_set_is_strict_subset(
2155 __isl_keep isl_set *set1,
2156 __isl_keep isl_set *set2);
2157 int isl_union_set_is_subset(
2158 __isl_keep isl_union_set *uset1,
2159 __isl_keep isl_union_set *uset2);
2160 int isl_union_set_is_strict_subset(
2161 __isl_keep isl_union_set *uset1,
2162 __isl_keep isl_union_set *uset2);
2163 int isl_basic_map_is_subset(
2164 __isl_keep isl_basic_map *bmap1,
2165 __isl_keep isl_basic_map *bmap2);
2166 int isl_basic_map_is_strict_subset(
2167 __isl_keep isl_basic_map *bmap1,
2168 __isl_keep isl_basic_map *bmap2);
2169 int isl_map_is_subset(
2170 __isl_keep isl_map *map1,
2171 __isl_keep isl_map *map2);
2172 int isl_map_is_strict_subset(
2173 __isl_keep isl_map *map1,
2174 __isl_keep isl_map *map2);
2175 int isl_union_map_is_subset(
2176 __isl_keep isl_union_map *umap1,
2177 __isl_keep isl_union_map *umap2);
2178 int isl_union_map_is_strict_subset(
2179 __isl_keep isl_union_map *umap1,
2180 __isl_keep isl_union_map *umap2);
2182 Check whether the first argument is a (strict) subset of the
2187 int isl_set_plain_cmp(__isl_keep isl_set *set1,
2188 __isl_keep isl_set *set2);
2190 This function is useful for sorting C<isl_set>s.
2191 The order depends on the internal representation of the inputs.
2192 The order is fixed over different calls to the function (assuming
2193 the internal representation of the inputs has not changed), but may
2194 change over different versions of C<isl>.
2198 =head2 Unary Operations
2204 __isl_give isl_set *isl_set_complement(
2205 __isl_take isl_set *set);
2206 __isl_give isl_map *isl_map_complement(
2207 __isl_take isl_map *map);
2211 __isl_give isl_basic_map *isl_basic_map_reverse(
2212 __isl_take isl_basic_map *bmap);
2213 __isl_give isl_map *isl_map_reverse(
2214 __isl_take isl_map *map);
2215 __isl_give isl_union_map *isl_union_map_reverse(
2216 __isl_take isl_union_map *umap);
2220 __isl_give isl_basic_set *isl_basic_set_project_out(
2221 __isl_take isl_basic_set *bset,
2222 enum isl_dim_type type, unsigned first, unsigned n);
2223 __isl_give isl_basic_map *isl_basic_map_project_out(
2224 __isl_take isl_basic_map *bmap,
2225 enum isl_dim_type type, unsigned first, unsigned n);
2226 __isl_give isl_set *isl_set_project_out(__isl_take isl_set *set,
2227 enum isl_dim_type type, unsigned first, unsigned n);
2228 __isl_give isl_map *isl_map_project_out(__isl_take isl_map *map,
2229 enum isl_dim_type type, unsigned first, unsigned n);
2230 __isl_give isl_basic_set *isl_basic_set_params(
2231 __isl_take isl_basic_set *bset);
2232 __isl_give isl_basic_set *isl_basic_map_domain(
2233 __isl_take isl_basic_map *bmap);
2234 __isl_give isl_basic_set *isl_basic_map_range(
2235 __isl_take isl_basic_map *bmap);
2236 __isl_give isl_set *isl_set_params(__isl_take isl_set *set);
2237 __isl_give isl_set *isl_map_params(__isl_take isl_map *map);
2238 __isl_give isl_set *isl_map_domain(
2239 __isl_take isl_map *bmap);
2240 __isl_give isl_set *isl_map_range(
2241 __isl_take isl_map *map);
2242 __isl_give isl_set *isl_union_set_params(
2243 __isl_take isl_union_set *uset);
2244 __isl_give isl_set *isl_union_map_params(
2245 __isl_take isl_union_map *umap);
2246 __isl_give isl_union_set *isl_union_map_domain(
2247 __isl_take isl_union_map *umap);
2248 __isl_give isl_union_set *isl_union_map_range(
2249 __isl_take isl_union_map *umap);
2251 __isl_give isl_basic_map *isl_basic_map_domain_map(
2252 __isl_take isl_basic_map *bmap);
2253 __isl_give isl_basic_map *isl_basic_map_range_map(
2254 __isl_take isl_basic_map *bmap);
2255 __isl_give isl_map *isl_map_domain_map(__isl_take isl_map *map);
2256 __isl_give isl_map *isl_map_range_map(__isl_take isl_map *map);
2257 __isl_give isl_union_map *isl_union_map_domain_map(
2258 __isl_take isl_union_map *umap);
2259 __isl_give isl_union_map *isl_union_map_range_map(
2260 __isl_take isl_union_map *umap);
2262 The functions above construct a (basic, regular or union) relation
2263 that maps (a wrapped version of) the input relation to its domain or range.
2267 __isl_give isl_basic_set *isl_basic_set_eliminate(
2268 __isl_take isl_basic_set *bset,
2269 enum isl_dim_type type,
2270 unsigned first, unsigned n);
2271 __isl_give isl_set *isl_set_eliminate(
2272 __isl_take isl_set *set, enum isl_dim_type type,
2273 unsigned first, unsigned n);
2274 __isl_give isl_basic_map *isl_basic_map_eliminate(
2275 __isl_take isl_basic_map *bmap,
2276 enum isl_dim_type type,
2277 unsigned first, unsigned n);
2278 __isl_give isl_map *isl_map_eliminate(
2279 __isl_take isl_map *map, enum isl_dim_type type,
2280 unsigned first, unsigned n);
2282 Eliminate the coefficients for the given dimensions from the constraints,
2283 without removing the dimensions.
2287 __isl_give isl_basic_set *isl_basic_set_fix(
2288 __isl_take isl_basic_set *bset,
2289 enum isl_dim_type type, unsigned pos,
2291 __isl_give isl_basic_set *isl_basic_set_fix_si(
2292 __isl_take isl_basic_set *bset,
2293 enum isl_dim_type type, unsigned pos, int value);
2294 __isl_give isl_basic_set *isl_basic_set_fix_val(
2295 __isl_take isl_basic_set *bset,
2296 enum isl_dim_type type, unsigned pos,
2297 __isl_take isl_val *v);
2298 __isl_give isl_set *isl_set_fix(__isl_take isl_set *set,
2299 enum isl_dim_type type, unsigned pos,
2301 __isl_give isl_set *isl_set_fix_si(__isl_take isl_set *set,
2302 enum isl_dim_type type, unsigned pos, int value);
2303 __isl_give isl_set *isl_set_fix_val(
2304 __isl_take isl_set *set,
2305 enum isl_dim_type type, unsigned pos,
2306 __isl_take isl_val *v);
2307 __isl_give isl_basic_map *isl_basic_map_fix_si(
2308 __isl_take isl_basic_map *bmap,
2309 enum isl_dim_type type, unsigned pos, int value);
2310 __isl_give isl_basic_map *isl_basic_map_fix_val(
2311 __isl_take isl_basic_map *bmap,
2312 enum isl_dim_type type, unsigned pos,
2313 __isl_take isl_val *v);
2314 __isl_give isl_map *isl_map_fix(__isl_take isl_map *map,
2315 enum isl_dim_type type, unsigned pos,
2317 __isl_give isl_map *isl_map_fix_si(__isl_take isl_map *map,
2318 enum isl_dim_type type, unsigned pos, int value);
2319 __isl_give isl_map *isl_map_fix_val(
2320 __isl_take isl_map *map,
2321 enum isl_dim_type type, unsigned pos,
2322 __isl_take isl_val *v);
2324 Intersect the set or relation with the hyperplane where the given
2325 dimension has the fixed given value.
2327 __isl_give isl_basic_map *isl_basic_map_lower_bound_si(
2328 __isl_take isl_basic_map *bmap,
2329 enum isl_dim_type type, unsigned pos, int value);
2330 __isl_give isl_basic_map *isl_basic_map_upper_bound_si(
2331 __isl_take isl_basic_map *bmap,
2332 enum isl_dim_type type, unsigned pos, int value);
2333 __isl_give isl_set *isl_set_lower_bound(
2334 __isl_take isl_set *set,
2335 enum isl_dim_type type, unsigned pos,
2337 __isl_give isl_set *isl_set_lower_bound_si(
2338 __isl_take isl_set *set,
2339 enum isl_dim_type type, unsigned pos, int value);
2340 __isl_give isl_set *isl_set_lower_bound_val(
2341 __isl_take isl_set *set,
2342 enum isl_dim_type type, unsigned pos,
2343 __isl_take isl_val *value);
2344 __isl_give isl_map *isl_map_lower_bound_si(
2345 __isl_take isl_map *map,
2346 enum isl_dim_type type, unsigned pos, int value);
2347 __isl_give isl_set *isl_set_upper_bound(
2348 __isl_take isl_set *set,
2349 enum isl_dim_type type, unsigned pos,
2351 __isl_give isl_set *isl_set_upper_bound_si(
2352 __isl_take isl_set *set,
2353 enum isl_dim_type type, unsigned pos, int value);
2354 __isl_give isl_set *isl_set_upper_bound_val(
2355 __isl_take isl_set *set,
2356 enum isl_dim_type type, unsigned pos,
2357 __isl_take isl_val *value);
2358 __isl_give isl_map *isl_map_upper_bound_si(
2359 __isl_take isl_map *map,
2360 enum isl_dim_type type, unsigned pos, int value);
2362 Intersect the set or relation with the half-space where the given
2363 dimension has a value bounded by the fixed given integer value.
2365 __isl_give isl_set *isl_set_equate(__isl_take isl_set *set,
2366 enum isl_dim_type type1, int pos1,
2367 enum isl_dim_type type2, int pos2);
2368 __isl_give isl_basic_map *isl_basic_map_equate(
2369 __isl_take isl_basic_map *bmap,
2370 enum isl_dim_type type1, int pos1,
2371 enum isl_dim_type type2, int pos2);
2372 __isl_give isl_map *isl_map_equate(__isl_take isl_map *map,
2373 enum isl_dim_type type1, int pos1,
2374 enum isl_dim_type type2, int pos2);
2376 Intersect the set or relation with the hyperplane where the given
2377 dimensions are equal to each other.
2379 __isl_give isl_map *isl_map_oppose(__isl_take isl_map *map,
2380 enum isl_dim_type type1, int pos1,
2381 enum isl_dim_type type2, int pos2);
2383 Intersect the relation with the hyperplane where the given
2384 dimensions have opposite values.
2386 __isl_give isl_basic_map *isl_basic_map_order_ge(
2387 __isl_take isl_basic_map *bmap,
2388 enum isl_dim_type type1, int pos1,
2389 enum isl_dim_type type2, int pos2);
2390 __isl_give isl_map *isl_map_order_lt(__isl_take isl_map *map,
2391 enum isl_dim_type type1, int pos1,
2392 enum isl_dim_type type2, int pos2);
2393 __isl_give isl_basic_map *isl_basic_map_order_gt(
2394 __isl_take isl_basic_map *bmap,
2395 enum isl_dim_type type1, int pos1,
2396 enum isl_dim_type type2, int pos2);
2397 __isl_give isl_map *isl_map_order_gt(__isl_take isl_map *map,
2398 enum isl_dim_type type1, int pos1,
2399 enum isl_dim_type type2, int pos2);
2401 Intersect the relation with the half-space where the given
2402 dimensions satisfy the given ordering.
2406 __isl_give isl_map *isl_set_identity(
2407 __isl_take isl_set *set);
2408 __isl_give isl_union_map *isl_union_set_identity(
2409 __isl_take isl_union_set *uset);
2411 Construct an identity relation on the given (union) set.
2415 __isl_give isl_basic_set *isl_basic_map_deltas(
2416 __isl_take isl_basic_map *bmap);
2417 __isl_give isl_set *isl_map_deltas(__isl_take isl_map *map);
2418 __isl_give isl_union_set *isl_union_map_deltas(
2419 __isl_take isl_union_map *umap);
2421 These functions return a (basic) set containing the differences
2422 between image elements and corresponding domain elements in the input.
2424 __isl_give isl_basic_map *isl_basic_map_deltas_map(
2425 __isl_take isl_basic_map *bmap);
2426 __isl_give isl_map *isl_map_deltas_map(
2427 __isl_take isl_map *map);
2428 __isl_give isl_union_map *isl_union_map_deltas_map(
2429 __isl_take isl_union_map *umap);
2431 The functions above construct a (basic, regular or union) relation
2432 that maps (a wrapped version of) the input relation to its delta set.
2436 Simplify the representation of a set or relation by trying
2437 to combine pairs of basic sets or relations into a single
2438 basic set or relation.
2440 __isl_give isl_set *isl_set_coalesce(__isl_take isl_set *set);
2441 __isl_give isl_map *isl_map_coalesce(__isl_take isl_map *map);
2442 __isl_give isl_union_set *isl_union_set_coalesce(
2443 __isl_take isl_union_set *uset);
2444 __isl_give isl_union_map *isl_union_map_coalesce(
2445 __isl_take isl_union_map *umap);
2447 One of the methods for combining pairs of basic sets or relations
2448 can result in coefficients that are much larger than those that appear
2449 in the constraints of the input. By default, the coefficients are
2450 not allowed to grow larger, but this can be changed by unsetting
2451 the following option.
2453 int isl_options_set_coalesce_bounded_wrapping(
2454 isl_ctx *ctx, int val);
2455 int isl_options_get_coalesce_bounded_wrapping(
2458 =item * Detecting equalities
2460 __isl_give isl_basic_set *isl_basic_set_detect_equalities(
2461 __isl_take isl_basic_set *bset);
2462 __isl_give isl_basic_map *isl_basic_map_detect_equalities(
2463 __isl_take isl_basic_map *bmap);
2464 __isl_give isl_set *isl_set_detect_equalities(
2465 __isl_take isl_set *set);
2466 __isl_give isl_map *isl_map_detect_equalities(
2467 __isl_take isl_map *map);
2468 __isl_give isl_union_set *isl_union_set_detect_equalities(
2469 __isl_take isl_union_set *uset);
2470 __isl_give isl_union_map *isl_union_map_detect_equalities(
2471 __isl_take isl_union_map *umap);
2473 Simplify the representation of a set or relation by detecting implicit
2476 =item * Removing redundant constraints
2478 __isl_give isl_basic_set *isl_basic_set_remove_redundancies(
2479 __isl_take isl_basic_set *bset);
2480 __isl_give isl_set *isl_set_remove_redundancies(
2481 __isl_take isl_set *set);
2482 __isl_give isl_basic_map *isl_basic_map_remove_redundancies(
2483 __isl_take isl_basic_map *bmap);
2484 __isl_give isl_map *isl_map_remove_redundancies(
2485 __isl_take isl_map *map);
2489 __isl_give isl_basic_set *isl_set_convex_hull(
2490 __isl_take isl_set *set);
2491 __isl_give isl_basic_map *isl_map_convex_hull(
2492 __isl_take isl_map *map);
2494 If the input set or relation has any existentially quantified
2495 variables, then the result of these operations is currently undefined.
2499 __isl_give isl_basic_set *
2500 isl_set_unshifted_simple_hull(
2501 __isl_take isl_set *set);
2502 __isl_give isl_basic_map *
2503 isl_map_unshifted_simple_hull(
2504 __isl_take isl_map *map);
2505 __isl_give isl_basic_set *isl_set_simple_hull(
2506 __isl_take isl_set *set);
2507 __isl_give isl_basic_map *isl_map_simple_hull(
2508 __isl_take isl_map *map);
2509 __isl_give isl_union_map *isl_union_map_simple_hull(
2510 __isl_take isl_union_map *umap);
2512 These functions compute a single basic set or relation
2513 that contains the whole input set or relation.
2514 In particular, the output is described by translates
2515 of the constraints describing the basic sets or relations in the input.
2516 In case of C<isl_set_unshifted_simple_hull>, only the original
2517 constraints are used, without any translation.
2521 (See \autoref{s:simple hull}.)
2527 __isl_give isl_basic_set *isl_basic_set_affine_hull(
2528 __isl_take isl_basic_set *bset);
2529 __isl_give isl_basic_set *isl_set_affine_hull(
2530 __isl_take isl_set *set);
2531 __isl_give isl_union_set *isl_union_set_affine_hull(
2532 __isl_take isl_union_set *uset);
2533 __isl_give isl_basic_map *isl_basic_map_affine_hull(
2534 __isl_take isl_basic_map *bmap);
2535 __isl_give isl_basic_map *isl_map_affine_hull(
2536 __isl_take isl_map *map);
2537 __isl_give isl_union_map *isl_union_map_affine_hull(
2538 __isl_take isl_union_map *umap);
2540 In case of union sets and relations, the affine hull is computed
2543 =item * Polyhedral hull
2545 __isl_give isl_basic_set *isl_set_polyhedral_hull(
2546 __isl_take isl_set *set);
2547 __isl_give isl_basic_map *isl_map_polyhedral_hull(
2548 __isl_take isl_map *map);
2549 __isl_give isl_union_set *isl_union_set_polyhedral_hull(
2550 __isl_take isl_union_set *uset);
2551 __isl_give isl_union_map *isl_union_map_polyhedral_hull(
2552 __isl_take isl_union_map *umap);
2554 These functions compute a single basic set or relation
2555 not involving any existentially quantified variables
2556 that contains the whole input set or relation.
2557 In case of union sets and relations, the polyhedral hull is computed
2560 =item * Other approximations
2562 __isl_give isl_basic_set *
2563 isl_basic_set_drop_constraints_involving_dims(
2564 __isl_take isl_basic_set *bset,
2565 enum isl_dim_type type,
2566 unsigned first, unsigned n);
2567 __isl_give isl_basic_map *
2568 isl_basic_map_drop_constraints_involving_dims(
2569 __isl_take isl_basic_map *bmap,
2570 enum isl_dim_type type,
2571 unsigned first, unsigned n);
2572 __isl_give isl_basic_set *
2573 isl_basic_set_drop_constraints_not_involving_dims(
2574 __isl_take isl_basic_set *bset,
2575 enum isl_dim_type type,
2576 unsigned first, unsigned n);
2577 __isl_give isl_set *
2578 isl_set_drop_constraints_involving_dims(
2579 __isl_take isl_set *set,
2580 enum isl_dim_type type,
2581 unsigned first, unsigned n);
2582 __isl_give isl_map *
2583 isl_map_drop_constraints_involving_dims(
2584 __isl_take isl_map *map,
2585 enum isl_dim_type type,
2586 unsigned first, unsigned n);
2588 These functions drop any constraints (not) involving the specified dimensions.
2589 Note that the result depends on the representation of the input.
2593 __isl_give isl_basic_set *isl_basic_set_sample(
2594 __isl_take isl_basic_set *bset);
2595 __isl_give isl_basic_set *isl_set_sample(
2596 __isl_take isl_set *set);
2597 __isl_give isl_basic_map *isl_basic_map_sample(
2598 __isl_take isl_basic_map *bmap);
2599 __isl_give isl_basic_map *isl_map_sample(
2600 __isl_take isl_map *map);
2602 If the input (basic) set or relation is non-empty, then return
2603 a singleton subset of the input. Otherwise, return an empty set.
2605 =item * Optimization
2607 #include <isl/ilp.h>
2608 enum isl_lp_result isl_basic_set_max(
2609 __isl_keep isl_basic_set *bset,
2610 __isl_keep isl_aff *obj, isl_int *opt)
2611 __isl_give isl_val *isl_basic_set_max_val(
2612 __isl_keep isl_basic_set *bset,
2613 __isl_keep isl_aff *obj);
2614 enum isl_lp_result isl_set_min(__isl_keep isl_set *set,
2615 __isl_keep isl_aff *obj, isl_int *opt);
2616 __isl_give isl_val *isl_set_min_val(
2617 __isl_keep isl_set *set,
2618 __isl_keep isl_aff *obj);
2619 enum isl_lp_result isl_set_max(__isl_keep isl_set *set,
2620 __isl_keep isl_aff *obj, isl_int *opt);
2621 __isl_give isl_val *isl_set_max_val(
2622 __isl_keep isl_set *set,
2623 __isl_keep isl_aff *obj);
2625 Compute the minimum or maximum of the integer affine expression C<obj>
2626 over the points in C<set>, returning the result in C<opt>.
2627 The return value may be one of C<isl_lp_error>,
2628 C<isl_lp_ok>, C<isl_lp_unbounded> or C<isl_lp_empty>, in case of
2629 an C<isl_lp_result>. If the result is an C<isl_val> then
2630 the result is C<NULL> in case of an error, the optimal value in case
2631 there is one, negative infinity or infinity if the problem is unbounded and
2632 NaN if the problem is empty.
2634 =item * Parametric optimization
2636 __isl_give isl_pw_aff *isl_set_dim_min(
2637 __isl_take isl_set *set, int pos);
2638 __isl_give isl_pw_aff *isl_set_dim_max(
2639 __isl_take isl_set *set, int pos);
2640 __isl_give isl_pw_aff *isl_map_dim_max(
2641 __isl_take isl_map *map, int pos);
2643 Compute the minimum or maximum of the given set or output dimension
2644 as a function of the parameters (and input dimensions), but independently
2645 of the other set or output dimensions.
2646 For lexicographic optimization, see L<"Lexicographic Optimization">.
2650 The following functions compute either the set of (rational) coefficient
2651 values of valid constraints for the given set or the set of (rational)
2652 values satisfying the constraints with coefficients from the given set.
2653 Internally, these two sets of functions perform essentially the
2654 same operations, except that the set of coefficients is assumed to
2655 be a cone, while the set of values may be any polyhedron.
2656 The current implementation is based on the Farkas lemma and
2657 Fourier-Motzkin elimination, but this may change or be made optional
2658 in future. In particular, future implementations may use different
2659 dualization algorithms or skip the elimination step.
2661 __isl_give isl_basic_set *isl_basic_set_coefficients(
2662 __isl_take isl_basic_set *bset);
2663 __isl_give isl_basic_set *isl_set_coefficients(
2664 __isl_take isl_set *set);
2665 __isl_give isl_union_set *isl_union_set_coefficients(
2666 __isl_take isl_union_set *bset);
2667 __isl_give isl_basic_set *isl_basic_set_solutions(
2668 __isl_take isl_basic_set *bset);
2669 __isl_give isl_basic_set *isl_set_solutions(
2670 __isl_take isl_set *set);
2671 __isl_give isl_union_set *isl_union_set_solutions(
2672 __isl_take isl_union_set *bset);
2676 __isl_give isl_map *isl_map_fixed_power(
2677 __isl_take isl_map *map, isl_int exp);
2678 __isl_give isl_union_map *isl_union_map_fixed_power(
2679 __isl_take isl_union_map *umap, isl_int exp);
2681 Compute the given power of C<map>, where C<exp> is assumed to be non-zero.
2682 If the exponent C<exp> is negative, then the -C<exp> th power of the inverse
2683 of C<map> is computed.
2685 __isl_give isl_map *isl_map_power(__isl_take isl_map *map,
2687 __isl_give isl_union_map *isl_union_map_power(
2688 __isl_take isl_union_map *umap, int *exact);
2690 Compute a parametric representation for all positive powers I<k> of C<map>.
2691 The result maps I<k> to a nested relation corresponding to the
2692 I<k>th power of C<map>.
2693 The result may be an overapproximation. If the result is known to be exact,
2694 then C<*exact> is set to C<1>.
2696 =item * Transitive closure
2698 __isl_give isl_map *isl_map_transitive_closure(
2699 __isl_take isl_map *map, int *exact);
2700 __isl_give isl_union_map *isl_union_map_transitive_closure(
2701 __isl_take isl_union_map *umap, int *exact);
2703 Compute the transitive closure of C<map>.
2704 The result may be an overapproximation. If the result is known to be exact,
2705 then C<*exact> is set to C<1>.
2707 =item * Reaching path lengths
2709 __isl_give isl_map *isl_map_reaching_path_lengths(
2710 __isl_take isl_map *map, int *exact);
2712 Compute a relation that maps each element in the range of C<map>
2713 to the lengths of all paths composed of edges in C<map> that
2714 end up in the given element.
2715 The result may be an overapproximation. If the result is known to be exact,
2716 then C<*exact> is set to C<1>.
2717 To compute the I<maximal> path length, the resulting relation
2718 should be postprocessed by C<isl_map_lexmax>.
2719 In particular, if the input relation is a dependence relation
2720 (mapping sources to sinks), then the maximal path length corresponds
2721 to the free schedule.
2722 Note, however, that C<isl_map_lexmax> expects the maximum to be
2723 finite, so if the path lengths are unbounded (possibly due to
2724 the overapproximation), then you will get an error message.
2728 __isl_give isl_basic_set *isl_basic_map_wrap(
2729 __isl_take isl_basic_map *bmap);
2730 __isl_give isl_set *isl_map_wrap(
2731 __isl_take isl_map *map);
2732 __isl_give isl_union_set *isl_union_map_wrap(
2733 __isl_take isl_union_map *umap);
2734 __isl_give isl_basic_map *isl_basic_set_unwrap(
2735 __isl_take isl_basic_set *bset);
2736 __isl_give isl_map *isl_set_unwrap(
2737 __isl_take isl_set *set);
2738 __isl_give isl_union_map *isl_union_set_unwrap(
2739 __isl_take isl_union_set *uset);
2743 Remove any internal structure of domain (and range) of the given
2744 set or relation. If there is any such internal structure in the input,
2745 then the name of the space is also removed.
2747 __isl_give isl_basic_set *isl_basic_set_flatten(
2748 __isl_take isl_basic_set *bset);
2749 __isl_give isl_set *isl_set_flatten(
2750 __isl_take isl_set *set);
2751 __isl_give isl_basic_map *isl_basic_map_flatten_domain(
2752 __isl_take isl_basic_map *bmap);
2753 __isl_give isl_basic_map *isl_basic_map_flatten_range(
2754 __isl_take isl_basic_map *bmap);
2755 __isl_give isl_map *isl_map_flatten_range(
2756 __isl_take isl_map *map);
2757 __isl_give isl_map *isl_map_flatten_domain(
2758 __isl_take isl_map *map);
2759 __isl_give isl_basic_map *isl_basic_map_flatten(
2760 __isl_take isl_basic_map *bmap);
2761 __isl_give isl_map *isl_map_flatten(
2762 __isl_take isl_map *map);
2764 __isl_give isl_map *isl_set_flatten_map(
2765 __isl_take isl_set *set);
2767 The function above constructs a relation
2768 that maps the input set to a flattened version of the set.
2772 Lift the input set to a space with extra dimensions corresponding
2773 to the existentially quantified variables in the input.
2774 In particular, the result lives in a wrapped map where the domain
2775 is the original space and the range corresponds to the original
2776 existentially quantified variables.
2778 __isl_give isl_basic_set *isl_basic_set_lift(
2779 __isl_take isl_basic_set *bset);
2780 __isl_give isl_set *isl_set_lift(
2781 __isl_take isl_set *set);
2782 __isl_give isl_union_set *isl_union_set_lift(
2783 __isl_take isl_union_set *uset);
2785 Given a local space that contains the existentially quantified
2786 variables of a set, a basic relation that, when applied to
2787 a basic set, has essentially the same effect as C<isl_basic_set_lift>,
2788 can be constructed using the following function.
2790 #include <isl/local_space.h>
2791 __isl_give isl_basic_map *isl_local_space_lifting(
2792 __isl_take isl_local_space *ls);
2794 =item * Internal Product
2796 __isl_give isl_basic_map *isl_basic_map_zip(
2797 __isl_take isl_basic_map *bmap);
2798 __isl_give isl_map *isl_map_zip(
2799 __isl_take isl_map *map);
2800 __isl_give isl_union_map *isl_union_map_zip(
2801 __isl_take isl_union_map *umap);
2803 Given a relation with nested relations for domain and range,
2804 interchange the range of the domain with the domain of the range.
2808 __isl_give isl_basic_map *isl_basic_map_curry(
2809 __isl_take isl_basic_map *bmap);
2810 __isl_give isl_basic_map *isl_basic_map_uncurry(
2811 __isl_take isl_basic_map *bmap);
2812 __isl_give isl_map *isl_map_curry(
2813 __isl_take isl_map *map);
2814 __isl_give isl_map *isl_map_uncurry(
2815 __isl_take isl_map *map);
2816 __isl_give isl_union_map *isl_union_map_curry(
2817 __isl_take isl_union_map *umap);
2818 __isl_give isl_union_map *isl_union_map_uncurry(
2819 __isl_take isl_union_map *umap);
2821 Given a relation with a nested relation for domain,
2822 the C<curry> functions
2823 move the range of the nested relation out of the domain
2824 and use it as the domain of a nested relation in the range,
2825 with the original range as range of this nested relation.
2826 The C<uncurry> functions perform the inverse operation.
2828 =item * Aligning parameters
2830 __isl_give isl_basic_set *isl_basic_set_align_params(
2831 __isl_take isl_basic_set *bset,
2832 __isl_take isl_space *model);
2833 __isl_give isl_set *isl_set_align_params(
2834 __isl_take isl_set *set,
2835 __isl_take isl_space *model);
2836 __isl_give isl_basic_map *isl_basic_map_align_params(
2837 __isl_take isl_basic_map *bmap,
2838 __isl_take isl_space *model);
2839 __isl_give isl_map *isl_map_align_params(
2840 __isl_take isl_map *map,
2841 __isl_take isl_space *model);
2843 Change the order of the parameters of the given set or relation
2844 such that the first parameters match those of C<model>.
2845 This may involve the introduction of extra parameters.
2846 All parameters need to be named.
2848 =item * Dimension manipulation
2850 __isl_give isl_basic_set *isl_basic_set_add_dims(
2851 __isl_take isl_basic_set *bset,
2852 enum isl_dim_type type, unsigned n);
2853 __isl_give isl_set *isl_set_add_dims(
2854 __isl_take isl_set *set,
2855 enum isl_dim_type type, unsigned n);
2856 __isl_give isl_map *isl_map_add_dims(
2857 __isl_take isl_map *map,
2858 enum isl_dim_type type, unsigned n);
2859 __isl_give isl_basic_set *isl_basic_set_insert_dims(
2860 __isl_take isl_basic_set *bset,
2861 enum isl_dim_type type, unsigned pos,
2863 __isl_give isl_basic_map *isl_basic_map_insert_dims(
2864 __isl_take isl_basic_map *bmap,
2865 enum isl_dim_type type, unsigned pos,
2867 __isl_give isl_set *isl_set_insert_dims(
2868 __isl_take isl_set *set,
2869 enum isl_dim_type type, unsigned pos, unsigned n);
2870 __isl_give isl_map *isl_map_insert_dims(
2871 __isl_take isl_map *map,
2872 enum isl_dim_type type, unsigned pos, unsigned n);
2873 __isl_give isl_basic_set *isl_basic_set_move_dims(
2874 __isl_take isl_basic_set *bset,
2875 enum isl_dim_type dst_type, unsigned dst_pos,
2876 enum isl_dim_type src_type, unsigned src_pos,
2878 __isl_give isl_basic_map *isl_basic_map_move_dims(
2879 __isl_take isl_basic_map *bmap,
2880 enum isl_dim_type dst_type, unsigned dst_pos,
2881 enum isl_dim_type src_type, unsigned src_pos,
2883 __isl_give isl_set *isl_set_move_dims(
2884 __isl_take isl_set *set,
2885 enum isl_dim_type dst_type, unsigned dst_pos,
2886 enum isl_dim_type src_type, unsigned src_pos,
2888 __isl_give isl_map *isl_map_move_dims(
2889 __isl_take isl_map *map,
2890 enum isl_dim_type dst_type, unsigned dst_pos,
2891 enum isl_dim_type src_type, unsigned src_pos,
2894 It is usually not advisable to directly change the (input or output)
2895 space of a set or a relation as this removes the name and the internal
2896 structure of the space. However, the above functions can be useful
2897 to add new parameters, assuming
2898 C<isl_set_align_params> and C<isl_map_align_params>
2903 =head2 Binary Operations
2905 The two arguments of a binary operation not only need to live
2906 in the same C<isl_ctx>, they currently also need to have
2907 the same (number of) parameters.
2909 =head3 Basic Operations
2913 =item * Intersection
2915 __isl_give isl_basic_set *isl_basic_set_intersect_params(
2916 __isl_take isl_basic_set *bset1,
2917 __isl_take isl_basic_set *bset2);
2918 __isl_give isl_basic_set *isl_basic_set_intersect(
2919 __isl_take isl_basic_set *bset1,
2920 __isl_take isl_basic_set *bset2);
2921 __isl_give isl_set *isl_set_intersect_params(
2922 __isl_take isl_set *set,
2923 __isl_take isl_set *params);
2924 __isl_give isl_set *isl_set_intersect(
2925 __isl_take isl_set *set1,
2926 __isl_take isl_set *set2);
2927 __isl_give isl_union_set *isl_union_set_intersect_params(
2928 __isl_take isl_union_set *uset,
2929 __isl_take isl_set *set);
2930 __isl_give isl_union_map *isl_union_map_intersect_params(
2931 __isl_take isl_union_map *umap,
2932 __isl_take isl_set *set);
2933 __isl_give isl_union_set *isl_union_set_intersect(
2934 __isl_take isl_union_set *uset1,
2935 __isl_take isl_union_set *uset2);
2936 __isl_give isl_basic_map *isl_basic_map_intersect_domain(
2937 __isl_take isl_basic_map *bmap,
2938 __isl_take isl_basic_set *bset);
2939 __isl_give isl_basic_map *isl_basic_map_intersect_range(
2940 __isl_take isl_basic_map *bmap,
2941 __isl_take isl_basic_set *bset);
2942 __isl_give isl_basic_map *isl_basic_map_intersect(
2943 __isl_take isl_basic_map *bmap1,
2944 __isl_take isl_basic_map *bmap2);
2945 __isl_give isl_map *isl_map_intersect_params(
2946 __isl_take isl_map *map,
2947 __isl_take isl_set *params);
2948 __isl_give isl_map *isl_map_intersect_domain(
2949 __isl_take isl_map *map,
2950 __isl_take isl_set *set);
2951 __isl_give isl_map *isl_map_intersect_range(
2952 __isl_take isl_map *map,
2953 __isl_take isl_set *set);
2954 __isl_give isl_map *isl_map_intersect(
2955 __isl_take isl_map *map1,
2956 __isl_take isl_map *map2);
2957 __isl_give isl_union_map *isl_union_map_intersect_domain(
2958 __isl_take isl_union_map *umap,
2959 __isl_take isl_union_set *uset);
2960 __isl_give isl_union_map *isl_union_map_intersect_range(
2961 __isl_take isl_union_map *umap,
2962 __isl_take isl_union_set *uset);
2963 __isl_give isl_union_map *isl_union_map_intersect(
2964 __isl_take isl_union_map *umap1,
2965 __isl_take isl_union_map *umap2);
2967 The second argument to the C<_params> functions needs to be
2968 a parametric (basic) set. For the other functions, a parametric set
2969 for either argument is only allowed if the other argument is
2970 a parametric set as well.
2974 __isl_give isl_set *isl_basic_set_union(
2975 __isl_take isl_basic_set *bset1,
2976 __isl_take isl_basic_set *bset2);
2977 __isl_give isl_map *isl_basic_map_union(
2978 __isl_take isl_basic_map *bmap1,
2979 __isl_take isl_basic_map *bmap2);
2980 __isl_give isl_set *isl_set_union(
2981 __isl_take isl_set *set1,
2982 __isl_take isl_set *set2);
2983 __isl_give isl_map *isl_map_union(
2984 __isl_take isl_map *map1,
2985 __isl_take isl_map *map2);
2986 __isl_give isl_union_set *isl_union_set_union(
2987 __isl_take isl_union_set *uset1,
2988 __isl_take isl_union_set *uset2);
2989 __isl_give isl_union_map *isl_union_map_union(
2990 __isl_take isl_union_map *umap1,
2991 __isl_take isl_union_map *umap2);
2993 =item * Set difference
2995 __isl_give isl_set *isl_set_subtract(
2996 __isl_take isl_set *set1,
2997 __isl_take isl_set *set2);
2998 __isl_give isl_map *isl_map_subtract(
2999 __isl_take isl_map *map1,
3000 __isl_take isl_map *map2);
3001 __isl_give isl_map *isl_map_subtract_domain(
3002 __isl_take isl_map *map,
3003 __isl_take isl_set *dom);
3004 __isl_give isl_map *isl_map_subtract_range(
3005 __isl_take isl_map *map,
3006 __isl_take isl_set *dom);
3007 __isl_give isl_union_set *isl_union_set_subtract(
3008 __isl_take isl_union_set *uset1,
3009 __isl_take isl_union_set *uset2);
3010 __isl_give isl_union_map *isl_union_map_subtract(
3011 __isl_take isl_union_map *umap1,
3012 __isl_take isl_union_map *umap2);
3013 __isl_give isl_union_map *isl_union_map_subtract_domain(
3014 __isl_take isl_union_map *umap,
3015 __isl_take isl_union_set *dom);
3016 __isl_give isl_union_map *isl_union_map_subtract_range(
3017 __isl_take isl_union_map *umap,
3018 __isl_take isl_union_set *dom);
3022 __isl_give isl_basic_set *isl_basic_set_apply(
3023 __isl_take isl_basic_set *bset,
3024 __isl_take isl_basic_map *bmap);
3025 __isl_give isl_set *isl_set_apply(
3026 __isl_take isl_set *set,
3027 __isl_take isl_map *map);
3028 __isl_give isl_union_set *isl_union_set_apply(
3029 __isl_take isl_union_set *uset,
3030 __isl_take isl_union_map *umap);
3031 __isl_give isl_basic_map *isl_basic_map_apply_domain(
3032 __isl_take isl_basic_map *bmap1,
3033 __isl_take isl_basic_map *bmap2);
3034 __isl_give isl_basic_map *isl_basic_map_apply_range(
3035 __isl_take isl_basic_map *bmap1,
3036 __isl_take isl_basic_map *bmap2);
3037 __isl_give isl_map *isl_map_apply_domain(
3038 __isl_take isl_map *map1,
3039 __isl_take isl_map *map2);
3040 __isl_give isl_union_map *isl_union_map_apply_domain(
3041 __isl_take isl_union_map *umap1,
3042 __isl_take isl_union_map *umap2);
3043 __isl_give isl_map *isl_map_apply_range(
3044 __isl_take isl_map *map1,
3045 __isl_take isl_map *map2);
3046 __isl_give isl_union_map *isl_union_map_apply_range(
3047 __isl_take isl_union_map *umap1,
3048 __isl_take isl_union_map *umap2);
3052 __isl_give isl_basic_set *
3053 isl_basic_set_preimage_multi_aff(
3054 __isl_take isl_basic_set *bset,
3055 __isl_take isl_multi_aff *ma);
3056 __isl_give isl_set *isl_set_preimage_multi_aff(
3057 __isl_take isl_set *set,
3058 __isl_take isl_multi_aff *ma);
3059 __isl_give isl_set *isl_set_preimage_pw_multi_aff(
3060 __isl_take isl_set *set,
3061 __isl_take isl_pw_multi_aff *pma);
3062 __isl_give isl_map *isl_map_preimage_domain_multi_aff(
3063 __isl_take isl_map *map,
3064 __isl_take isl_multi_aff *ma);
3065 __isl_give isl_union_map *
3066 isl_union_map_preimage_domain_multi_aff(
3067 __isl_take isl_union_map *umap,
3068 __isl_take isl_multi_aff *ma);
3070 These functions compute the preimage of the given set or map domain under
3071 the given function. In other words, the expression is plugged
3072 into the set description or into the domain of the map.
3073 Objects of types C<isl_multi_aff> and C<isl_pw_multi_aff> are described in
3074 L</"Piecewise Multiple Quasi Affine Expressions">.
3076 =item * Cartesian Product
3078 __isl_give isl_set *isl_set_product(
3079 __isl_take isl_set *set1,
3080 __isl_take isl_set *set2);
3081 __isl_give isl_union_set *isl_union_set_product(
3082 __isl_take isl_union_set *uset1,
3083 __isl_take isl_union_set *uset2);
3084 __isl_give isl_basic_map *isl_basic_map_domain_product(
3085 __isl_take isl_basic_map *bmap1,
3086 __isl_take isl_basic_map *bmap2);
3087 __isl_give isl_basic_map *isl_basic_map_range_product(
3088 __isl_take isl_basic_map *bmap1,
3089 __isl_take isl_basic_map *bmap2);
3090 __isl_give isl_basic_map *isl_basic_map_product(
3091 __isl_take isl_basic_map *bmap1,
3092 __isl_take isl_basic_map *bmap2);
3093 __isl_give isl_map *isl_map_domain_product(
3094 __isl_take isl_map *map1,
3095 __isl_take isl_map *map2);
3096 __isl_give isl_map *isl_map_range_product(
3097 __isl_take isl_map *map1,
3098 __isl_take isl_map *map2);
3099 __isl_give isl_union_map *isl_union_map_domain_product(
3100 __isl_take isl_union_map *umap1,
3101 __isl_take isl_union_map *umap2);
3102 __isl_give isl_union_map *isl_union_map_range_product(
3103 __isl_take isl_union_map *umap1,
3104 __isl_take isl_union_map *umap2);
3105 __isl_give isl_map *isl_map_product(
3106 __isl_take isl_map *map1,
3107 __isl_take isl_map *map2);
3108 __isl_give isl_union_map *isl_union_map_product(
3109 __isl_take isl_union_map *umap1,
3110 __isl_take isl_union_map *umap2);
3112 The above functions compute the cross product of the given
3113 sets or relations. The domains and ranges of the results
3114 are wrapped maps between domains and ranges of the inputs.
3115 To obtain a ``flat'' product, use the following functions
3118 __isl_give isl_basic_set *isl_basic_set_flat_product(
3119 __isl_take isl_basic_set *bset1,
3120 __isl_take isl_basic_set *bset2);
3121 __isl_give isl_set *isl_set_flat_product(
3122 __isl_take isl_set *set1,
3123 __isl_take isl_set *set2);
3124 __isl_give isl_basic_map *isl_basic_map_flat_range_product(
3125 __isl_take isl_basic_map *bmap1,
3126 __isl_take isl_basic_map *bmap2);
3127 __isl_give isl_map *isl_map_flat_domain_product(
3128 __isl_take isl_map *map1,
3129 __isl_take isl_map *map2);
3130 __isl_give isl_map *isl_map_flat_range_product(
3131 __isl_take isl_map *map1,
3132 __isl_take isl_map *map2);
3133 __isl_give isl_union_map *isl_union_map_flat_range_product(
3134 __isl_take isl_union_map *umap1,
3135 __isl_take isl_union_map *umap2);
3136 __isl_give isl_basic_map *isl_basic_map_flat_product(
3137 __isl_take isl_basic_map *bmap1,
3138 __isl_take isl_basic_map *bmap2);
3139 __isl_give isl_map *isl_map_flat_product(
3140 __isl_take isl_map *map1,
3141 __isl_take isl_map *map2);
3143 =item * Simplification
3145 __isl_give isl_basic_set *isl_basic_set_gist(
3146 __isl_take isl_basic_set *bset,
3147 __isl_take isl_basic_set *context);
3148 __isl_give isl_set *isl_set_gist(__isl_take isl_set *set,
3149 __isl_take isl_set *context);
3150 __isl_give isl_set *isl_set_gist_params(
3151 __isl_take isl_set *set,
3152 __isl_take isl_set *context);
3153 __isl_give isl_union_set *isl_union_set_gist(
3154 __isl_take isl_union_set *uset,
3155 __isl_take isl_union_set *context);
3156 __isl_give isl_union_set *isl_union_set_gist_params(
3157 __isl_take isl_union_set *uset,
3158 __isl_take isl_set *set);
3159 __isl_give isl_basic_map *isl_basic_map_gist(
3160 __isl_take isl_basic_map *bmap,
3161 __isl_take isl_basic_map *context);
3162 __isl_give isl_map *isl_map_gist(__isl_take isl_map *map,
3163 __isl_take isl_map *context);
3164 __isl_give isl_map *isl_map_gist_params(
3165 __isl_take isl_map *map,
3166 __isl_take isl_set *context);
3167 __isl_give isl_map *isl_map_gist_domain(
3168 __isl_take isl_map *map,
3169 __isl_take isl_set *context);
3170 __isl_give isl_map *isl_map_gist_range(
3171 __isl_take isl_map *map,
3172 __isl_take isl_set *context);
3173 __isl_give isl_union_map *isl_union_map_gist(
3174 __isl_take isl_union_map *umap,
3175 __isl_take isl_union_map *context);
3176 __isl_give isl_union_map *isl_union_map_gist_params(
3177 __isl_take isl_union_map *umap,
3178 __isl_take isl_set *set);
3179 __isl_give isl_union_map *isl_union_map_gist_domain(
3180 __isl_take isl_union_map *umap,
3181 __isl_take isl_union_set *uset);
3182 __isl_give isl_union_map *isl_union_map_gist_range(
3183 __isl_take isl_union_map *umap,
3184 __isl_take isl_union_set *uset);
3186 The gist operation returns a set or relation that has the
3187 same intersection with the context as the input set or relation.
3188 Any implicit equality in the intersection is made explicit in the result,
3189 while all inequalities that are redundant with respect to the intersection
3191 In case of union sets and relations, the gist operation is performed
3196 =head3 Lexicographic Optimization
3198 Given a (basic) set C<set> (or C<bset>) and a zero-dimensional domain C<dom>,
3199 the following functions
3200 compute a set that contains the lexicographic minimum or maximum
3201 of the elements in C<set> (or C<bset>) for those values of the parameters
3202 that satisfy C<dom>.
3203 If C<empty> is not C<NULL>, then C<*empty> is assigned a set
3204 that contains the parameter values in C<dom> for which C<set> (or C<bset>)
3206 In other words, the union of the parameter values
3207 for which the result is non-empty and of C<*empty>
3210 __isl_give isl_set *isl_basic_set_partial_lexmin(
3211 __isl_take isl_basic_set *bset,
3212 __isl_take isl_basic_set *dom,
3213 __isl_give isl_set **empty);
3214 __isl_give isl_set *isl_basic_set_partial_lexmax(
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_set_partial_lexmin(
3219 __isl_take isl_set *set, __isl_take isl_set *dom,
3220 __isl_give isl_set **empty);
3221 __isl_give isl_set *isl_set_partial_lexmax(
3222 __isl_take isl_set *set, __isl_take isl_set *dom,
3223 __isl_give isl_set **empty);
3225 Given a (basic) set C<set> (or C<bset>), the following functions simply
3226 return a set containing the lexicographic minimum or maximum
3227 of the elements in C<set> (or C<bset>).
3228 In case of union sets, the optimum is computed per space.
3230 __isl_give isl_set *isl_basic_set_lexmin(
3231 __isl_take isl_basic_set *bset);
3232 __isl_give isl_set *isl_basic_set_lexmax(
3233 __isl_take isl_basic_set *bset);
3234 __isl_give isl_set *isl_set_lexmin(
3235 __isl_take isl_set *set);
3236 __isl_give isl_set *isl_set_lexmax(
3237 __isl_take isl_set *set);
3238 __isl_give isl_union_set *isl_union_set_lexmin(
3239 __isl_take isl_union_set *uset);
3240 __isl_give isl_union_set *isl_union_set_lexmax(
3241 __isl_take isl_union_set *uset);
3243 Given a (basic) relation C<map> (or C<bmap>) and a domain C<dom>,
3244 the following functions
3245 compute a relation that maps each element of C<dom>
3246 to the single lexicographic minimum or maximum
3247 of the elements that are associated to that same
3248 element in C<map> (or C<bmap>).
3249 If C<empty> is not C<NULL>, then C<*empty> is assigned a set
3250 that contains the elements in C<dom> that do not map
3251 to any elements in C<map> (or C<bmap>).
3252 In other words, the union of the domain of the result and of C<*empty>
3255 __isl_give isl_map *isl_basic_map_partial_lexmax(
3256 __isl_take isl_basic_map *bmap,
3257 __isl_take isl_basic_set *dom,
3258 __isl_give isl_set **empty);
3259 __isl_give isl_map *isl_basic_map_partial_lexmin(
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_map_partial_lexmax(
3264 __isl_take isl_map *map, __isl_take isl_set *dom,
3265 __isl_give isl_set **empty);
3266 __isl_give isl_map *isl_map_partial_lexmin(
3267 __isl_take isl_map *map, __isl_take isl_set *dom,
3268 __isl_give isl_set **empty);
3270 Given a (basic) map C<map> (or C<bmap>), the following functions simply
3271 return a map mapping each element in the domain of
3272 C<map> (or C<bmap>) to the lexicographic minimum or maximum
3273 of all elements associated to that element.
3274 In case of union relations, the optimum is computed per space.
3276 __isl_give isl_map *isl_basic_map_lexmin(
3277 __isl_take isl_basic_map *bmap);
3278 __isl_give isl_map *isl_basic_map_lexmax(
3279 __isl_take isl_basic_map *bmap);
3280 __isl_give isl_map *isl_map_lexmin(
3281 __isl_take isl_map *map);
3282 __isl_give isl_map *isl_map_lexmax(
3283 __isl_take isl_map *map);
3284 __isl_give isl_union_map *isl_union_map_lexmin(
3285 __isl_take isl_union_map *umap);
3286 __isl_give isl_union_map *isl_union_map_lexmax(
3287 __isl_take isl_union_map *umap);
3289 The following functions return their result in the form of
3290 a piecewise multi-affine expression
3291 (See L<"Piecewise Multiple Quasi Affine Expressions">),
3292 but are otherwise equivalent to the corresponding functions
3293 returning a basic set or relation.
3295 __isl_give isl_pw_multi_aff *
3296 isl_basic_map_lexmin_pw_multi_aff(
3297 __isl_take isl_basic_map *bmap);
3298 __isl_give isl_pw_multi_aff *
3299 isl_basic_set_partial_lexmin_pw_multi_aff(
3300 __isl_take isl_basic_set *bset,
3301 __isl_take isl_basic_set *dom,
3302 __isl_give isl_set **empty);
3303 __isl_give isl_pw_multi_aff *
3304 isl_basic_set_partial_lexmax_pw_multi_aff(
3305 __isl_take isl_basic_set *bset,
3306 __isl_take isl_basic_set *dom,
3307 __isl_give isl_set **empty);
3308 __isl_give isl_pw_multi_aff *
3309 isl_basic_map_partial_lexmin_pw_multi_aff(
3310 __isl_take isl_basic_map *bmap,
3311 __isl_take isl_basic_set *dom,
3312 __isl_give isl_set **empty);
3313 __isl_give isl_pw_multi_aff *
3314 isl_basic_map_partial_lexmax_pw_multi_aff(
3315 __isl_take isl_basic_map *bmap,
3316 __isl_take isl_basic_set *dom,
3317 __isl_give isl_set **empty);
3318 __isl_give isl_pw_multi_aff *isl_set_lexmin_pw_multi_aff(
3319 __isl_take isl_set *set);
3320 __isl_give isl_pw_multi_aff *isl_set_lexmax_pw_multi_aff(
3321 __isl_take isl_set *set);
3322 __isl_give isl_pw_multi_aff *isl_map_lexmin_pw_multi_aff(
3323 __isl_take isl_map *map);
3324 __isl_give isl_pw_multi_aff *isl_map_lexmax_pw_multi_aff(
3325 __isl_take isl_map *map);
3329 Lists are defined over several element types, including
3330 C<isl_val>, C<isl_id>, C<isl_aff>, C<isl_pw_aff>, C<isl_constraint>,
3331 C<isl_basic_set>, C<isl_set>, C<isl_ast_expr> and C<isl_ast_node>.
3332 Here we take lists of C<isl_set>s as an example.
3333 Lists can be created, copied, modified and freed using the following functions.
3335 #include <isl/list.h>
3336 __isl_give isl_set_list *isl_set_list_from_set(
3337 __isl_take isl_set *el);
3338 __isl_give isl_set_list *isl_set_list_alloc(
3339 isl_ctx *ctx, int n);
3340 __isl_give isl_set_list *isl_set_list_copy(
3341 __isl_keep isl_set_list *list);
3342 __isl_give isl_set_list *isl_set_list_insert(
3343 __isl_take isl_set_list *list, unsigned pos,
3344 __isl_take isl_set *el);
3345 __isl_give isl_set_list *isl_set_list_add(
3346 __isl_take isl_set_list *list,
3347 __isl_take isl_set *el);
3348 __isl_give isl_set_list *isl_set_list_drop(
3349 __isl_take isl_set_list *list,
3350 unsigned first, unsigned n);
3351 __isl_give isl_set_list *isl_set_list_set_set(
3352 __isl_take isl_set_list *list, int index,
3353 __isl_take isl_set *set);
3354 __isl_give isl_set_list *isl_set_list_concat(
3355 __isl_take isl_set_list *list1,
3356 __isl_take isl_set_list *list2);
3357 __isl_give isl_set_list *isl_set_list_sort(
3358 __isl_take isl_set_list *list,
3359 int (*cmp)(__isl_keep isl_set *a,
3360 __isl_keep isl_set *b, void *user),
3362 void *isl_set_list_free(__isl_take isl_set_list *list);
3364 C<isl_set_list_alloc> creates an empty list with a capacity for
3365 C<n> elements. C<isl_set_list_from_set> creates a list with a single
3368 Lists can be inspected using the following functions.
3370 #include <isl/list.h>
3371 isl_ctx *isl_set_list_get_ctx(__isl_keep isl_set_list *list);
3372 int isl_set_list_n_set(__isl_keep isl_set_list *list);
3373 __isl_give isl_set *isl_set_list_get_set(
3374 __isl_keep isl_set_list *list, int index);
3375 int isl_set_list_foreach(__isl_keep isl_set_list *list,
3376 int (*fn)(__isl_take isl_set *el, void *user),
3378 int isl_set_list_foreach_scc(__isl_keep isl_set_list *list,
3379 int (*follows)(__isl_keep isl_set *a,
3380 __isl_keep isl_set *b, void *user),
3382 int (*fn)(__isl_take isl_set *el, void *user),
3385 The function C<isl_set_list_foreach_scc> calls C<fn> on each of the
3386 strongly connected components of the graph with as vertices the elements
3387 of C<list> and a directed edge from vertex C<b> to vertex C<a>
3388 iff C<follows(a, b)> returns C<1>. The callbacks C<follows> and C<fn>
3389 should return C<-1> on error.
3391 Lists can be printed using
3393 #include <isl/list.h>
3394 __isl_give isl_printer *isl_printer_print_set_list(
3395 __isl_take isl_printer *p,
3396 __isl_keep isl_set_list *list);
3398 =head2 Multiple Values
3400 An C<isl_multi_val> object represents a sequence of zero or more values,
3401 living in a set space.
3403 An C<isl_multi_val> can be constructed from an C<isl_val_list>
3404 using the following function
3406 #include <isl/val.h>
3407 __isl_give isl_multi_val *isl_multi_val_from_val_list(
3408 __isl_take isl_space *space,
3409 __isl_take isl_val_list *list);
3411 The zero multiple value (with value zero for each set dimension)
3412 can be created using the following function.
3414 #include <isl/val.h>
3415 __isl_give isl_multi_val *isl_multi_val_zero(
3416 __isl_take isl_space *space);
3418 Multiple values can be copied and freed using
3420 #include <isl/val.h>
3421 __isl_give isl_multi_val *isl_multi_val_copy(
3422 __isl_keep isl_multi_val *mv);
3423 void *isl_multi_val_free(__isl_take isl_multi_val *mv);
3425 They can be inspected using
3427 #include <isl/val.h>
3428 isl_ctx *isl_multi_val_get_ctx(
3429 __isl_keep isl_multi_val *mv);
3430 unsigned isl_multi_val_dim(__isl_keep isl_multi_val *mv,
3431 enum isl_dim_type type);
3432 __isl_give isl_val *isl_multi_val_get_val(
3433 __isl_keep isl_multi_val *mv, int pos);
3434 const char *isl_multi_val_get_tuple_name(
3435 __isl_keep isl_multi_val *mv,
3436 enum isl_dim_type type);
3438 They can be modified using
3440 #include <isl/val.h>
3441 __isl_give isl_multi_val *isl_multi_val_set_val(
3442 __isl_take isl_multi_val *mv, int pos,
3443 __isl_take isl_val *val);
3444 __isl_give isl_multi_val *isl_multi_val_set_dim_name(
3445 __isl_take isl_multi_val *mv,
3446 enum isl_dim_type type, unsigned pos, const char *s);
3447 __isl_give isl_multi_val *isl_multi_val_set_tuple_name(
3448 __isl_take isl_multi_val *mv,
3449 enum isl_dim_type type, const char *s);
3450 __isl_give isl_multi_val *isl_multi_val_set_tuple_id(
3451 __isl_take isl_multi_val *mv,
3452 enum isl_dim_type type, __isl_take isl_id *id);
3454 __isl_give isl_multi_val *isl_multi_val_insert_dims(
3455 __isl_take isl_multi_val *mv,
3456 enum isl_dim_type type, unsigned first, unsigned n);
3457 __isl_give isl_multi_val *isl_multi_val_add_dims(
3458 __isl_take isl_multi_val *mv,
3459 enum isl_dim_type type, unsigned n);
3460 __isl_give isl_multi_val *isl_multi_val_drop_dims(
3461 __isl_take isl_multi_val *mv,
3462 enum isl_dim_type type, unsigned first, unsigned n);
3466 #include <isl/val.h>
3467 __isl_give isl_multi_val *isl_multi_val_align_params(
3468 __isl_take isl_multi_val *mv,
3469 __isl_take isl_space *model);
3470 __isl_give isl_multi_val *isl_multi_val_range_splice(
3471 __isl_take isl_multi_val *mv1, unsigned pos,
3472 __isl_take isl_multi_val *mv2);
3473 __isl_give isl_multi_val *isl_multi_val_range_product(
3474 __isl_take isl_multi_val *mv1,
3475 __isl_take isl_multi_val *mv2);
3476 __isl_give isl_multi_val *isl_multi_val_flat_range_product(
3477 __isl_take isl_multi_val *mv1,
3478 __isl_take isl_multi_aff *mv2);
3479 __isl_give isl_multi_val *isl_multi_val_add_val(
3480 __isl_take isl_multi_val *mv,
3481 __isl_take isl_val *v);
3482 __isl_give isl_multi_val *isl_multi_val_mod_val(
3483 __isl_take isl_multi_val *mv,
3484 __isl_take isl_val *v);
3485 __isl_give isl_multi_val *isl_multi_val_scale_val(
3486 __isl_take isl_multi_val *mv,
3487 __isl_take isl_val *v);
3491 Vectors can be created, copied and freed using the following functions.
3493 #include <isl/vec.h>
3494 __isl_give isl_vec *isl_vec_alloc(isl_ctx *ctx,
3496 __isl_give isl_vec *isl_vec_copy(__isl_keep isl_vec *vec);
3497 void *isl_vec_free(__isl_take isl_vec *vec);
3499 Note that the elements of a newly created vector may have arbitrary values.
3500 The elements can be changed and inspected using the following functions.
3502 isl_ctx *isl_vec_get_ctx(__isl_keep isl_vec *vec);
3503 int isl_vec_size(__isl_keep isl_vec *vec);
3504 int isl_vec_get_element(__isl_keep isl_vec *vec,
3505 int pos, isl_int *v);
3506 __isl_give isl_val *isl_vec_get_element_val(
3507 __isl_keep isl_vec *vec, int pos);
3508 __isl_give isl_vec *isl_vec_set_element(
3509 __isl_take isl_vec *vec, int pos, isl_int v);
3510 __isl_give isl_vec *isl_vec_set_element_si(
3511 __isl_take isl_vec *vec, int pos, int v);
3512 __isl_give isl_vec *isl_vec_set_element_val(
3513 __isl_take isl_vec *vec, int pos,
3514 __isl_take isl_val *v);
3515 __isl_give isl_vec *isl_vec_set(__isl_take isl_vec *vec,
3517 __isl_give isl_vec *isl_vec_set_si(__isl_take isl_vec *vec,
3519 __isl_give isl_vec *isl_vec_set_val(
3520 __isl_take isl_vec *vec, __isl_take isl_val *v);
3521 __isl_give isl_vec *isl_vec_fdiv_r(__isl_take isl_vec *vec,
3524 C<isl_vec_get_element> will return a negative value if anything went wrong.
3525 In that case, the value of C<*v> is undefined.
3527 The following function can be used to concatenate two vectors.
3529 __isl_give isl_vec *isl_vec_concat(__isl_take isl_vec *vec1,
3530 __isl_take isl_vec *vec2);
3534 Matrices can be created, copied and freed using the following functions.
3536 #include <isl/mat.h>
3537 __isl_give isl_mat *isl_mat_alloc(isl_ctx *ctx,
3538 unsigned n_row, unsigned n_col);
3539 __isl_give isl_mat *isl_mat_copy(__isl_keep isl_mat *mat);
3540 void *isl_mat_free(__isl_take isl_mat *mat);
3542 Note that the elements of a newly created matrix may have arbitrary values.
3543 The elements can be changed and inspected using the following functions.
3545 isl_ctx *isl_mat_get_ctx(__isl_keep isl_mat *mat);
3546 int isl_mat_rows(__isl_keep isl_mat *mat);
3547 int isl_mat_cols(__isl_keep isl_mat *mat);
3548 int isl_mat_get_element(__isl_keep isl_mat *mat,
3549 int row, int col, isl_int *v);
3550 __isl_give isl_val *isl_mat_get_element_val(
3551 __isl_keep isl_mat *mat, int row, int col);
3552 __isl_give isl_mat *isl_mat_set_element(__isl_take isl_mat *mat,
3553 int row, int col, isl_int v);
3554 __isl_give isl_mat *isl_mat_set_element_si(__isl_take isl_mat *mat,
3555 int row, int col, int v);
3556 __isl_give isl_mat *isl_mat_set_element_val(
3557 __isl_take isl_mat *mat, int row, int col,
3558 __isl_take isl_val *v);
3560 C<isl_mat_get_element> will return a negative value if anything went wrong.
3561 In that case, the value of C<*v> is undefined.
3563 The following function can be used to compute the (right) inverse
3564 of a matrix, i.e., a matrix such that the product of the original
3565 and the inverse (in that order) is a multiple of the identity matrix.
3566 The input matrix is assumed to be of full row-rank.
3568 __isl_give isl_mat *isl_mat_right_inverse(__isl_take isl_mat *mat);
3570 The following function can be used to compute the (right) kernel
3571 (or null space) of a matrix, i.e., a matrix such that the product of
3572 the original and the kernel (in that order) is the zero matrix.
3574 __isl_give isl_mat *isl_mat_right_kernel(__isl_take isl_mat *mat);
3576 =head2 Piecewise Quasi Affine Expressions
3578 The zero quasi affine expression or the quasi affine expression
3579 that is equal to a specified dimension on a given domain can be created using
3581 __isl_give isl_aff *isl_aff_zero_on_domain(
3582 __isl_take isl_local_space *ls);
3583 __isl_give isl_pw_aff *isl_pw_aff_zero_on_domain(
3584 __isl_take isl_local_space *ls);
3585 __isl_give isl_aff *isl_aff_var_on_domain(
3586 __isl_take isl_local_space *ls,
3587 enum isl_dim_type type, unsigned pos);
3588 __isl_give isl_pw_aff *isl_pw_aff_var_on_domain(
3589 __isl_take isl_local_space *ls,
3590 enum isl_dim_type type, unsigned pos);
3592 Note that the space in which the resulting objects live is a map space
3593 with the given space as domain and a one-dimensional range.
3595 An empty piecewise quasi affine expression (one with no cells)
3596 or a piecewise quasi affine expression with a single cell can
3597 be created using the following functions.
3599 #include <isl/aff.h>
3600 __isl_give isl_pw_aff *isl_pw_aff_empty(
3601 __isl_take isl_space *space);
3602 __isl_give isl_pw_aff *isl_pw_aff_alloc(
3603 __isl_take isl_set *set, __isl_take isl_aff *aff);
3604 __isl_give isl_pw_aff *isl_pw_aff_from_aff(
3605 __isl_take isl_aff *aff);
3607 A piecewise quasi affine expression that is equal to 1 on a set
3608 and 0 outside the set can be created using the following function.
3610 #include <isl/aff.h>
3611 __isl_give isl_pw_aff *isl_set_indicator_function(
3612 __isl_take isl_set *set);
3614 Quasi affine expressions can be copied and freed using
3616 #include <isl/aff.h>
3617 __isl_give isl_aff *isl_aff_copy(__isl_keep isl_aff *aff);
3618 void *isl_aff_free(__isl_take isl_aff *aff);
3620 __isl_give isl_pw_aff *isl_pw_aff_copy(
3621 __isl_keep isl_pw_aff *pwaff);
3622 void *isl_pw_aff_free(__isl_take isl_pw_aff *pwaff);
3624 A (rational) bound on a dimension can be extracted from an C<isl_constraint>
3625 using the following function. The constraint is required to have
3626 a non-zero coefficient for the specified dimension.
3628 #include <isl/constraint.h>
3629 __isl_give isl_aff *isl_constraint_get_bound(
3630 __isl_keep isl_constraint *constraint,
3631 enum isl_dim_type type, int pos);
3633 The entire affine expression of the constraint can also be extracted
3634 using the following function.
3636 #include <isl/constraint.h>
3637 __isl_give isl_aff *isl_constraint_get_aff(
3638 __isl_keep isl_constraint *constraint);
3640 Conversely, an equality constraint equating
3641 the affine expression to zero or an inequality constraint enforcing
3642 the affine expression to be non-negative, can be constructed using
3644 __isl_give isl_constraint *isl_equality_from_aff(
3645 __isl_take isl_aff *aff);
3646 __isl_give isl_constraint *isl_inequality_from_aff(
3647 __isl_take isl_aff *aff);
3649 The expression can be inspected using
3651 #include <isl/aff.h>
3652 isl_ctx *isl_aff_get_ctx(__isl_keep isl_aff *aff);
3653 int isl_aff_dim(__isl_keep isl_aff *aff,
3654 enum isl_dim_type type);
3655 __isl_give isl_local_space *isl_aff_get_domain_local_space(
3656 __isl_keep isl_aff *aff);
3657 __isl_give isl_local_space *isl_aff_get_local_space(
3658 __isl_keep isl_aff *aff);
3659 const char *isl_aff_get_dim_name(__isl_keep isl_aff *aff,
3660 enum isl_dim_type type, unsigned pos);
3661 const char *isl_pw_aff_get_dim_name(
3662 __isl_keep isl_pw_aff *pa,
3663 enum isl_dim_type type, unsigned pos);
3664 int isl_pw_aff_has_dim_id(__isl_keep isl_pw_aff *pa,
3665 enum isl_dim_type type, unsigned pos);
3666 __isl_give isl_id *isl_pw_aff_get_dim_id(
3667 __isl_keep isl_pw_aff *pa,
3668 enum isl_dim_type type, unsigned pos);
3669 __isl_give isl_id *isl_pw_aff_get_tuple_id(
3670 __isl_keep isl_pw_aff *pa,
3671 enum isl_dim_type type);
3672 int isl_aff_get_constant(__isl_keep isl_aff *aff,
3674 __isl_give isl_val *isl_aff_get_constant_val(
3675 __isl_keep isl_aff *aff);
3676 int isl_aff_get_coefficient(__isl_keep isl_aff *aff,
3677 enum isl_dim_type type, int pos, isl_int *v);
3678 __isl_give isl_val *isl_aff_get_coefficient_val(
3679 __isl_keep isl_aff *aff,
3680 enum isl_dim_type type, int pos);
3681 int isl_aff_get_denominator(__isl_keep isl_aff *aff,
3683 __isl_give isl_val *isl_aff_get_denominator_val(
3684 __isl_keep isl_aff *aff);
3685 __isl_give isl_aff *isl_aff_get_div(
3686 __isl_keep isl_aff *aff, int pos);
3688 int isl_pw_aff_n_piece(__isl_keep isl_pw_aff *pwaff);
3689 int isl_pw_aff_foreach_piece(__isl_keep isl_pw_aff *pwaff,
3690 int (*fn)(__isl_take isl_set *set,
3691 __isl_take isl_aff *aff,
3692 void *user), void *user);
3694 int isl_aff_is_cst(__isl_keep isl_aff *aff);
3695 int isl_pw_aff_is_cst(__isl_keep isl_pw_aff *pwaff);
3697 int isl_aff_involves_dims(__isl_keep isl_aff *aff,
3698 enum isl_dim_type type, unsigned first, unsigned n);
3699 int isl_pw_aff_involves_dims(__isl_keep isl_pw_aff *pwaff,
3700 enum isl_dim_type type, unsigned first, unsigned n);
3702 isl_ctx *isl_pw_aff_get_ctx(__isl_keep isl_pw_aff *pwaff);
3703 unsigned isl_pw_aff_dim(__isl_keep isl_pw_aff *pwaff,
3704 enum isl_dim_type type);
3705 int isl_pw_aff_is_empty(__isl_keep isl_pw_aff *pwaff);
3707 It can be modified using
3709 #include <isl/aff.h>
3710 __isl_give isl_pw_aff *isl_pw_aff_set_tuple_id(
3711 __isl_take isl_pw_aff *pwaff,
3712 enum isl_dim_type type, __isl_take isl_id *id);
3713 __isl_give isl_aff *isl_aff_set_dim_name(
3714 __isl_take isl_aff *aff, enum isl_dim_type type,
3715 unsigned pos, const char *s);
3716 __isl_give isl_aff *isl_aff_set_dim_id(
3717 __isl_take isl_aff *aff, enum isl_dim_type type,
3718 unsigned pos, __isl_take isl_id *id);
3719 __isl_give isl_pw_aff *isl_pw_aff_set_dim_id(
3720 __isl_take isl_pw_aff *pma,
3721 enum isl_dim_type type, unsigned pos,
3722 __isl_take isl_id *id);
3723 __isl_give isl_aff *isl_aff_set_constant(
3724 __isl_take isl_aff *aff, isl_int v);
3725 __isl_give isl_aff *isl_aff_set_constant_si(
3726 __isl_take isl_aff *aff, int v);
3727 __isl_give isl_aff *isl_aff_set_constant_val(
3728 __isl_take isl_aff *aff, __isl_take isl_val *v);
3729 __isl_give isl_aff *isl_aff_set_coefficient(
3730 __isl_take isl_aff *aff,
3731 enum isl_dim_type type, int pos, isl_int v);
3732 __isl_give isl_aff *isl_aff_set_coefficient_si(
3733 __isl_take isl_aff *aff,
3734 enum isl_dim_type type, int pos, int v);
3735 __isl_give isl_aff *isl_aff_set_coefficient_val(
3736 __isl_take isl_aff *aff,
3737 enum isl_dim_type type, int pos,
3738 __isl_take isl_val *v);
3739 __isl_give isl_aff *isl_aff_set_denominator(
3740 __isl_take isl_aff *aff, isl_int v);
3742 __isl_give isl_aff *isl_aff_add_constant(
3743 __isl_take isl_aff *aff, isl_int v);
3744 __isl_give isl_aff *isl_aff_add_constant_si(
3745 __isl_take isl_aff *aff, int v);
3746 __isl_give isl_aff *isl_aff_add_constant_val(
3747 __isl_take isl_aff *aff, __isl_take isl_val *v);
3748 __isl_give isl_aff *isl_aff_add_constant_num(
3749 __isl_take isl_aff *aff, isl_int v);
3750 __isl_give isl_aff *isl_aff_add_constant_num_si(
3751 __isl_take isl_aff *aff, int v);
3752 __isl_give isl_aff *isl_aff_add_coefficient(
3753 __isl_take isl_aff *aff,
3754 enum isl_dim_type type, int pos, isl_int v);
3755 __isl_give isl_aff *isl_aff_add_coefficient_si(
3756 __isl_take isl_aff *aff,
3757 enum isl_dim_type type, int pos, int v);
3758 __isl_give isl_aff *isl_aff_add_coefficient_val(
3759 __isl_take isl_aff *aff,
3760 enum isl_dim_type type, int pos,
3761 __isl_take isl_val *v);
3763 __isl_give isl_aff *isl_aff_insert_dims(
3764 __isl_take isl_aff *aff,
3765 enum isl_dim_type type, unsigned first, unsigned n);
3766 __isl_give isl_pw_aff *isl_pw_aff_insert_dims(
3767 __isl_take isl_pw_aff *pwaff,
3768 enum isl_dim_type type, unsigned first, unsigned n);
3769 __isl_give isl_aff *isl_aff_add_dims(
3770 __isl_take isl_aff *aff,
3771 enum isl_dim_type type, unsigned n);
3772 __isl_give isl_pw_aff *isl_pw_aff_add_dims(
3773 __isl_take isl_pw_aff *pwaff,
3774 enum isl_dim_type type, unsigned n);
3775 __isl_give isl_aff *isl_aff_drop_dims(
3776 __isl_take isl_aff *aff,
3777 enum isl_dim_type type, unsigned first, unsigned n);
3778 __isl_give isl_pw_aff *isl_pw_aff_drop_dims(
3779 __isl_take isl_pw_aff *pwaff,
3780 enum isl_dim_type type, unsigned first, unsigned n);
3782 Note that C<isl_aff_set_constant>, C<isl_aff_set_constant_si>,
3783 C<isl_aff_set_coefficient> and C<isl_aff_set_coefficient_si>
3784 set the I<numerator> of the constant or coefficient, while
3785 C<isl_aff_set_constant_val> and C<isl_aff_set_coefficient_val> set
3786 the constant or coefficient as a whole.
3787 The C<add_constant> and C<add_coefficient> functions add an integer
3788 or rational value to
3789 the possibly rational constant or coefficient.
3790 The C<add_constant_num> functions add an integer value to
3793 To check whether an affine expressions is obviously zero
3794 or obviously equal to some other affine expression, use
3796 #include <isl/aff.h>
3797 int isl_aff_plain_is_zero(__isl_keep isl_aff *aff);
3798 int isl_aff_plain_is_equal(__isl_keep isl_aff *aff1,
3799 __isl_keep isl_aff *aff2);
3800 int isl_pw_aff_plain_is_equal(
3801 __isl_keep isl_pw_aff *pwaff1,
3802 __isl_keep isl_pw_aff *pwaff2);
3806 #include <isl/aff.h>
3807 __isl_give isl_aff *isl_aff_add(__isl_take isl_aff *aff1,
3808 __isl_take isl_aff *aff2);
3809 __isl_give isl_pw_aff *isl_pw_aff_add(
3810 __isl_take isl_pw_aff *pwaff1,
3811 __isl_take isl_pw_aff *pwaff2);
3812 __isl_give isl_pw_aff *isl_pw_aff_min(
3813 __isl_take isl_pw_aff *pwaff1,
3814 __isl_take isl_pw_aff *pwaff2);
3815 __isl_give isl_pw_aff *isl_pw_aff_max(
3816 __isl_take isl_pw_aff *pwaff1,
3817 __isl_take isl_pw_aff *pwaff2);
3818 __isl_give isl_aff *isl_aff_sub(__isl_take isl_aff *aff1,
3819 __isl_take isl_aff *aff2);
3820 __isl_give isl_pw_aff *isl_pw_aff_sub(
3821 __isl_take isl_pw_aff *pwaff1,
3822 __isl_take isl_pw_aff *pwaff2);
3823 __isl_give isl_aff *isl_aff_neg(__isl_take isl_aff *aff);
3824 __isl_give isl_pw_aff *isl_pw_aff_neg(
3825 __isl_take isl_pw_aff *pwaff);
3826 __isl_give isl_aff *isl_aff_ceil(__isl_take isl_aff *aff);
3827 __isl_give isl_pw_aff *isl_pw_aff_ceil(
3828 __isl_take isl_pw_aff *pwaff);
3829 __isl_give isl_aff *isl_aff_floor(__isl_take isl_aff *aff);
3830 __isl_give isl_pw_aff *isl_pw_aff_floor(
3831 __isl_take isl_pw_aff *pwaff);
3832 __isl_give isl_aff *isl_aff_mod(__isl_take isl_aff *aff,
3834 __isl_give isl_aff *isl_aff_mod_val(__isl_take isl_aff *aff,
3835 __isl_take isl_val *mod);
3836 __isl_give isl_pw_aff *isl_pw_aff_mod(
3837 __isl_take isl_pw_aff *pwaff, isl_int mod);
3838 __isl_give isl_pw_aff *isl_pw_aff_mod_val(
3839 __isl_take isl_pw_aff *pa,
3840 __isl_take isl_val *mod);
3841 __isl_give isl_aff *isl_aff_scale(__isl_take isl_aff *aff,
3843 __isl_give isl_aff *isl_aff_scale_val(__isl_take isl_aff *aff,
3844 __isl_take isl_val *v);
3845 __isl_give isl_pw_aff *isl_pw_aff_scale(
3846 __isl_take isl_pw_aff *pwaff, isl_int f);
3847 __isl_give isl_pw_aff *isl_pw_aff_scale_val(
3848 __isl_take isl_pw_aff *pa, __isl_take isl_val *v);
3849 __isl_give isl_aff *isl_aff_scale_down(__isl_take isl_aff *aff,
3851 __isl_give isl_aff *isl_aff_scale_down_ui(
3852 __isl_take isl_aff *aff, unsigned f);
3853 __isl_give isl_aff *isl_aff_scale_down_val(
3854 __isl_take isl_aff *aff, __isl_take isl_val *v);
3855 __isl_give isl_pw_aff *isl_pw_aff_scale_down(
3856 __isl_take isl_pw_aff *pwaff, isl_int f);
3857 __isl_give isl_pw_aff *isl_pw_aff_scale_down_val(
3858 __isl_take isl_pw_aff *pa,
3859 __isl_take isl_val *f);
3861 __isl_give isl_pw_aff *isl_pw_aff_list_min(
3862 __isl_take isl_pw_aff_list *list);
3863 __isl_give isl_pw_aff *isl_pw_aff_list_max(
3864 __isl_take isl_pw_aff_list *list);
3866 __isl_give isl_pw_aff *isl_pw_aff_coalesce(
3867 __isl_take isl_pw_aff *pwqp);
3869 __isl_give isl_aff *isl_aff_align_params(
3870 __isl_take isl_aff *aff,
3871 __isl_take isl_space *model);
3872 __isl_give isl_pw_aff *isl_pw_aff_align_params(
3873 __isl_take isl_pw_aff *pwaff,
3874 __isl_take isl_space *model);
3876 __isl_give isl_aff *isl_aff_project_domain_on_params(
3877 __isl_take isl_aff *aff);
3879 __isl_give isl_aff *isl_aff_gist_params(
3880 __isl_take isl_aff *aff,
3881 __isl_take isl_set *context);
3882 __isl_give isl_aff *isl_aff_gist(__isl_take isl_aff *aff,
3883 __isl_take isl_set *context);
3884 __isl_give isl_pw_aff *isl_pw_aff_gist_params(
3885 __isl_take isl_pw_aff *pwaff,
3886 __isl_take isl_set *context);
3887 __isl_give isl_pw_aff *isl_pw_aff_gist(
3888 __isl_take isl_pw_aff *pwaff,
3889 __isl_take isl_set *context);
3891 __isl_give isl_set *isl_pw_aff_domain(
3892 __isl_take isl_pw_aff *pwaff);
3893 __isl_give isl_pw_aff *isl_pw_aff_intersect_domain(
3894 __isl_take isl_pw_aff *pa,
3895 __isl_take isl_set *set);
3896 __isl_give isl_pw_aff *isl_pw_aff_intersect_params(
3897 __isl_take isl_pw_aff *pa,
3898 __isl_take isl_set *set);
3900 __isl_give isl_aff *isl_aff_mul(__isl_take isl_aff *aff1,
3901 __isl_take isl_aff *aff2);
3902 __isl_give isl_aff *isl_aff_div(__isl_take isl_aff *aff1,
3903 __isl_take isl_aff *aff2);
3904 __isl_give isl_pw_aff *isl_pw_aff_mul(
3905 __isl_take isl_pw_aff *pwaff1,
3906 __isl_take isl_pw_aff *pwaff2);
3907 __isl_give isl_pw_aff *isl_pw_aff_div(
3908 __isl_take isl_pw_aff *pa1,
3909 __isl_take isl_pw_aff *pa2);
3910 __isl_give isl_pw_aff *isl_pw_aff_tdiv_q(
3911 __isl_take isl_pw_aff *pa1,
3912 __isl_take isl_pw_aff *pa2);
3913 __isl_give isl_pw_aff *isl_pw_aff_tdiv_r(
3914 __isl_take isl_pw_aff *pa1,
3915 __isl_take isl_pw_aff *pa2);
3917 When multiplying two affine expressions, at least one of the two needs
3918 to be a constant. Similarly, when dividing an affine expression by another,
3919 the second expression needs to be a constant.
3920 C<isl_pw_aff_tdiv_q> computes the quotient of an integer division with
3921 rounding towards zero. C<isl_pw_aff_tdiv_r> computes the corresponding
3924 #include <isl/aff.h>
3925 __isl_give isl_aff *isl_aff_pullback_multi_aff(
3926 __isl_take isl_aff *aff,
3927 __isl_take isl_multi_aff *ma);
3928 __isl_give isl_pw_aff *isl_pw_aff_pullback_multi_aff(
3929 __isl_take isl_pw_aff *pa,
3930 __isl_take isl_multi_aff *ma);
3931 __isl_give isl_pw_aff *isl_pw_aff_pullback_pw_multi_aff(
3932 __isl_take isl_pw_aff *pa,
3933 __isl_take isl_pw_multi_aff *pma);
3935 These functions precompose the input expression by the given
3936 C<isl_multi_aff> or C<isl_pw_multi_aff>. In other words,
3937 the C<isl_multi_aff> or C<isl_pw_multi_aff> is plugged
3938 into the (piecewise) affine expression.
3939 Objects of type C<isl_multi_aff> are described in
3940 L</"Piecewise Multiple Quasi Affine Expressions">.
3942 #include <isl/aff.h>
3943 __isl_give isl_basic_set *isl_aff_zero_basic_set(
3944 __isl_take isl_aff *aff);
3945 __isl_give isl_basic_set *isl_aff_neg_basic_set(
3946 __isl_take isl_aff *aff);
3947 __isl_give isl_basic_set *isl_aff_le_basic_set(
3948 __isl_take isl_aff *aff1, __isl_take isl_aff *aff2);
3949 __isl_give isl_basic_set *isl_aff_ge_basic_set(
3950 __isl_take isl_aff *aff1, __isl_take isl_aff *aff2);
3951 __isl_give isl_set *isl_pw_aff_eq_set(
3952 __isl_take isl_pw_aff *pwaff1,
3953 __isl_take isl_pw_aff *pwaff2);
3954 __isl_give isl_set *isl_pw_aff_ne_set(
3955 __isl_take isl_pw_aff *pwaff1,
3956 __isl_take isl_pw_aff *pwaff2);
3957 __isl_give isl_set *isl_pw_aff_le_set(
3958 __isl_take isl_pw_aff *pwaff1,
3959 __isl_take isl_pw_aff *pwaff2);
3960 __isl_give isl_set *isl_pw_aff_lt_set(
3961 __isl_take isl_pw_aff *pwaff1,
3962 __isl_take isl_pw_aff *pwaff2);
3963 __isl_give isl_set *isl_pw_aff_ge_set(
3964 __isl_take isl_pw_aff *pwaff1,
3965 __isl_take isl_pw_aff *pwaff2);
3966 __isl_give isl_set *isl_pw_aff_gt_set(
3967 __isl_take isl_pw_aff *pwaff1,
3968 __isl_take isl_pw_aff *pwaff2);
3970 __isl_give isl_set *isl_pw_aff_list_eq_set(
3971 __isl_take isl_pw_aff_list *list1,
3972 __isl_take isl_pw_aff_list *list2);
3973 __isl_give isl_set *isl_pw_aff_list_ne_set(
3974 __isl_take isl_pw_aff_list *list1,
3975 __isl_take isl_pw_aff_list *list2);
3976 __isl_give isl_set *isl_pw_aff_list_le_set(
3977 __isl_take isl_pw_aff_list *list1,
3978 __isl_take isl_pw_aff_list *list2);
3979 __isl_give isl_set *isl_pw_aff_list_lt_set(
3980 __isl_take isl_pw_aff_list *list1,
3981 __isl_take isl_pw_aff_list *list2);
3982 __isl_give isl_set *isl_pw_aff_list_ge_set(
3983 __isl_take isl_pw_aff_list *list1,
3984 __isl_take isl_pw_aff_list *list2);
3985 __isl_give isl_set *isl_pw_aff_list_gt_set(
3986 __isl_take isl_pw_aff_list *list1,
3987 __isl_take isl_pw_aff_list *list2);
3989 The function C<isl_aff_neg_basic_set> returns a basic set
3990 containing those elements in the domain space
3991 of C<aff> where C<aff> is negative.
3992 The function C<isl_aff_ge_basic_set> returns a basic set
3993 containing those elements in the shared space
3994 of C<aff1> and C<aff2> where C<aff1> is greater than or equal to C<aff2>.
3995 The function C<isl_pw_aff_ge_set> returns a set
3996 containing those elements in the shared domain
3997 of C<pwaff1> and C<pwaff2> where C<pwaff1> is greater than or equal to C<pwaff2>.
3998 The functions operating on C<isl_pw_aff_list> apply the corresponding
3999 C<isl_pw_aff> function to each pair of elements in the two lists.
4001 #include <isl/aff.h>
4002 __isl_give isl_set *isl_pw_aff_nonneg_set(
4003 __isl_take isl_pw_aff *pwaff);
4004 __isl_give isl_set *isl_pw_aff_zero_set(
4005 __isl_take isl_pw_aff *pwaff);
4006 __isl_give isl_set *isl_pw_aff_non_zero_set(
4007 __isl_take isl_pw_aff *pwaff);
4009 The function C<isl_pw_aff_nonneg_set> returns a set
4010 containing those elements in the domain
4011 of C<pwaff> where C<pwaff> is non-negative.
4013 #include <isl/aff.h>
4014 __isl_give isl_pw_aff *isl_pw_aff_cond(
4015 __isl_take isl_pw_aff *cond,
4016 __isl_take isl_pw_aff *pwaff_true,
4017 __isl_take isl_pw_aff *pwaff_false);
4019 The function C<isl_pw_aff_cond> performs a conditional operator
4020 and returns an expression that is equal to C<pwaff_true>
4021 for elements where C<cond> is non-zero and equal to C<pwaff_false> for elements
4022 where C<cond> is zero.
4024 #include <isl/aff.h>
4025 __isl_give isl_pw_aff *isl_pw_aff_union_min(
4026 __isl_take isl_pw_aff *pwaff1,
4027 __isl_take isl_pw_aff *pwaff2);
4028 __isl_give isl_pw_aff *isl_pw_aff_union_max(
4029 __isl_take isl_pw_aff *pwaff1,
4030 __isl_take isl_pw_aff *pwaff2);
4031 __isl_give isl_pw_aff *isl_pw_aff_union_add(
4032 __isl_take isl_pw_aff *pwaff1,
4033 __isl_take isl_pw_aff *pwaff2);
4035 The function C<isl_pw_aff_union_max> computes a piecewise quasi-affine
4036 expression with a domain that is the union of those of C<pwaff1> and
4037 C<pwaff2> and such that on each cell, the quasi-affine expression is
4038 the maximum of those of C<pwaff1> and C<pwaff2>. If only one of
4039 C<pwaff1> or C<pwaff2> is defined on a given cell, then the
4040 associated expression is the defined one.
4042 An expression can be read from input using
4044 #include <isl/aff.h>
4045 __isl_give isl_aff *isl_aff_read_from_str(
4046 isl_ctx *ctx, const char *str);
4047 __isl_give isl_pw_aff *isl_pw_aff_read_from_str(
4048 isl_ctx *ctx, const char *str);
4050 An expression can be printed using
4052 #include <isl/aff.h>
4053 __isl_give isl_printer *isl_printer_print_aff(
4054 __isl_take isl_printer *p, __isl_keep isl_aff *aff);
4056 __isl_give isl_printer *isl_printer_print_pw_aff(
4057 __isl_take isl_printer *p,
4058 __isl_keep isl_pw_aff *pwaff);
4060 =head2 Piecewise Multiple Quasi Affine Expressions
4062 An C<isl_multi_aff> object represents a sequence of
4063 zero or more affine expressions, all defined on the same domain space.
4064 Similarly, an C<isl_multi_pw_aff> object represents a sequence of
4065 zero or more piecewise affine expressions.
4067 An C<isl_multi_aff> can be constructed from a single
4068 C<isl_aff> or an C<isl_aff_list> using the
4069 following functions. Similarly for C<isl_multi_pw_aff>.
4071 #include <isl/aff.h>
4072 __isl_give isl_multi_aff *isl_multi_aff_from_aff(
4073 __isl_take isl_aff *aff);
4074 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_from_pw_aff(
4075 __isl_take isl_pw_aff *pa);
4076 __isl_give isl_multi_aff *isl_multi_aff_from_aff_list(
4077 __isl_take isl_space *space,
4078 __isl_take isl_aff_list *list);
4080 An empty piecewise multiple quasi affine expression (one with no cells),
4081 the zero piecewise multiple quasi affine expression (with value zero
4082 for each output dimension),
4083 a piecewise multiple quasi affine expression with a single cell (with
4084 either a universe or a specified domain) or
4085 a zero-dimensional piecewise multiple quasi affine expression
4087 can be created using the following functions.
4089 #include <isl/aff.h>
4090 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_empty(
4091 __isl_take isl_space *space);
4092 __isl_give isl_multi_aff *isl_multi_aff_zero(
4093 __isl_take isl_space *space);
4094 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_zero(
4095 __isl_take isl_space *space);
4096 __isl_give isl_multi_aff *isl_multi_aff_identity(
4097 __isl_take isl_space *space);
4098 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_identity(
4099 __isl_take isl_space *space);
4100 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_identity(
4101 __isl_take isl_space *space);
4102 __isl_give isl_pw_multi_aff *
4103 isl_pw_multi_aff_from_multi_aff(
4104 __isl_take isl_multi_aff *ma);
4105 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_alloc(
4106 __isl_take isl_set *set,
4107 __isl_take isl_multi_aff *maff);
4108 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_from_domain(
4109 __isl_take isl_set *set);
4111 __isl_give isl_union_pw_multi_aff *
4112 isl_union_pw_multi_aff_empty(
4113 __isl_take isl_space *space);
4114 __isl_give isl_union_pw_multi_aff *
4115 isl_union_pw_multi_aff_add_pw_multi_aff(
4116 __isl_take isl_union_pw_multi_aff *upma,
4117 __isl_take isl_pw_multi_aff *pma);
4118 __isl_give isl_union_pw_multi_aff *
4119 isl_union_pw_multi_aff_from_domain(
4120 __isl_take isl_union_set *uset);
4122 A piecewise multiple quasi affine expression can also be initialized
4123 from an C<isl_set> or C<isl_map>, provided the C<isl_set> is a singleton
4124 and the C<isl_map> is single-valued.
4125 In case of a conversion from an C<isl_union_set> or an C<isl_union_map>
4126 to an C<isl_union_pw_multi_aff>, these properties need to hold in each space.
4128 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_from_set(
4129 __isl_take isl_set *set);
4130 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_from_map(
4131 __isl_take isl_map *map);
4133 __isl_give isl_union_pw_multi_aff *
4134 isl_union_pw_multi_aff_from_union_set(
4135 __isl_take isl_union_set *uset);
4136 __isl_give isl_union_pw_multi_aff *
4137 isl_union_pw_multi_aff_from_union_map(
4138 __isl_take isl_union_map *umap);
4140 Multiple quasi affine expressions can be copied and freed using
4142 #include <isl/aff.h>
4143 __isl_give isl_multi_aff *isl_multi_aff_copy(
4144 __isl_keep isl_multi_aff *maff);
4145 void *isl_multi_aff_free(__isl_take isl_multi_aff *maff);
4147 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_copy(
4148 __isl_keep isl_pw_multi_aff *pma);
4149 void *isl_pw_multi_aff_free(
4150 __isl_take isl_pw_multi_aff *pma);
4152 __isl_give isl_union_pw_multi_aff *
4153 isl_union_pw_multi_aff_copy(
4154 __isl_keep isl_union_pw_multi_aff *upma);
4155 void *isl_union_pw_multi_aff_free(
4156 __isl_take isl_union_pw_multi_aff *upma);
4158 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_copy(
4159 __isl_keep isl_multi_pw_aff *mpa);
4160 void *isl_multi_pw_aff_free(
4161 __isl_take isl_multi_pw_aff *mpa);
4163 The expression can be inspected using
4165 #include <isl/aff.h>
4166 isl_ctx *isl_multi_aff_get_ctx(
4167 __isl_keep isl_multi_aff *maff);
4168 isl_ctx *isl_pw_multi_aff_get_ctx(
4169 __isl_keep isl_pw_multi_aff *pma);
4170 isl_ctx *isl_union_pw_multi_aff_get_ctx(
4171 __isl_keep isl_union_pw_multi_aff *upma);
4172 isl_ctx *isl_multi_pw_aff_get_ctx(
4173 __isl_keep isl_multi_pw_aff *mpa);
4174 unsigned isl_multi_aff_dim(__isl_keep isl_multi_aff *maff,
4175 enum isl_dim_type type);
4176 unsigned isl_pw_multi_aff_dim(
4177 __isl_keep isl_pw_multi_aff *pma,
4178 enum isl_dim_type type);
4179 unsigned isl_multi_pw_aff_dim(
4180 __isl_keep isl_multi_pw_aff *mpa,
4181 enum isl_dim_type type);
4182 __isl_give isl_aff *isl_multi_aff_get_aff(
4183 __isl_keep isl_multi_aff *multi, int pos);
4184 __isl_give isl_pw_aff *isl_pw_multi_aff_get_pw_aff(
4185 __isl_keep isl_pw_multi_aff *pma, int pos);
4186 __isl_give isl_pw_aff *isl_multi_pw_aff_get_pw_aff(
4187 __isl_keep isl_multi_pw_aff *mpa, int pos);
4188 const char *isl_pw_multi_aff_get_dim_name(
4189 __isl_keep isl_pw_multi_aff *pma,
4190 enum isl_dim_type type, unsigned pos);
4191 __isl_give isl_id *isl_pw_multi_aff_get_dim_id(
4192 __isl_keep isl_pw_multi_aff *pma,
4193 enum isl_dim_type type, unsigned pos);
4194 const char *isl_multi_aff_get_tuple_name(
4195 __isl_keep isl_multi_aff *multi,
4196 enum isl_dim_type type);
4197 int isl_pw_multi_aff_has_tuple_name(
4198 __isl_keep isl_pw_multi_aff *pma,
4199 enum isl_dim_type type);
4200 const char *isl_pw_multi_aff_get_tuple_name(
4201 __isl_keep isl_pw_multi_aff *pma,
4202 enum isl_dim_type type);
4203 int isl_pw_multi_aff_has_tuple_id(
4204 __isl_keep isl_pw_multi_aff *pma,
4205 enum isl_dim_type type);
4206 __isl_give isl_id *isl_pw_multi_aff_get_tuple_id(
4207 __isl_keep isl_pw_multi_aff *pma,
4208 enum isl_dim_type type);
4210 int isl_pw_multi_aff_foreach_piece(
4211 __isl_keep isl_pw_multi_aff *pma,
4212 int (*fn)(__isl_take isl_set *set,
4213 __isl_take isl_multi_aff *maff,
4214 void *user), void *user);
4216 int isl_union_pw_multi_aff_foreach_pw_multi_aff(
4217 __isl_keep isl_union_pw_multi_aff *upma,
4218 int (*fn)(__isl_take isl_pw_multi_aff *pma,
4219 void *user), void *user);
4221 It can be modified using
4223 #include <isl/aff.h>
4224 __isl_give isl_multi_aff *isl_multi_aff_set_aff(
4225 __isl_take isl_multi_aff *multi, int pos,
4226 __isl_take isl_aff *aff);
4227 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_set_pw_aff(
4228 __isl_take isl_pw_multi_aff *pma, unsigned pos,
4229 __isl_take isl_pw_aff *pa);
4230 __isl_give isl_multi_aff *isl_multi_aff_set_dim_name(
4231 __isl_take isl_multi_aff *maff,
4232 enum isl_dim_type type, unsigned pos, const char *s);
4233 __isl_give isl_multi_aff *isl_multi_aff_set_tuple_name(
4234 __isl_take isl_multi_aff *maff,
4235 enum isl_dim_type type, const char *s);
4236 __isl_give isl_multi_aff *isl_multi_aff_set_tuple_id(
4237 __isl_take isl_multi_aff *maff,
4238 enum isl_dim_type type, __isl_take isl_id *id);
4239 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_set_tuple_id(
4240 __isl_take isl_pw_multi_aff *pma,
4241 enum isl_dim_type type, __isl_take isl_id *id);
4243 __isl_give isl_multi_pw_aff *
4244 isl_multi_pw_aff_set_dim_name(
4245 __isl_take isl_multi_pw_aff *mpa,
4246 enum isl_dim_type type, unsigned pos, const char *s);
4247 __isl_give isl_multi_pw_aff *
4248 isl_multi_pw_aff_set_tuple_name(
4249 __isl_take isl_multi_pw_aff *mpa,
4250 enum isl_dim_type type, const char *s);
4252 __isl_give isl_multi_aff *isl_multi_aff_insert_dims(
4253 __isl_take isl_multi_aff *ma,
4254 enum isl_dim_type type, unsigned first, unsigned n);
4255 __isl_give isl_multi_aff *isl_multi_aff_add_dims(
4256 __isl_take isl_multi_aff *ma,
4257 enum isl_dim_type type, unsigned n);
4258 __isl_give isl_multi_aff *isl_multi_aff_drop_dims(
4259 __isl_take isl_multi_aff *maff,
4260 enum isl_dim_type type, unsigned first, unsigned n);
4261 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_drop_dims(
4262 __isl_take isl_pw_multi_aff *pma,
4263 enum isl_dim_type type, unsigned first, unsigned n);
4265 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_insert_dims(
4266 __isl_take isl_multi_pw_aff *mpa,
4267 enum isl_dim_type type, unsigned first, unsigned n);
4268 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_add_dims(
4269 __isl_take isl_multi_pw_aff *mpa,
4270 enum isl_dim_type type, unsigned n);
4272 To check whether two multiple affine expressions are
4273 obviously equal to each other, use
4275 int isl_multi_aff_plain_is_equal(__isl_keep isl_multi_aff *maff1,
4276 __isl_keep isl_multi_aff *maff2);
4277 int isl_pw_multi_aff_plain_is_equal(
4278 __isl_keep isl_pw_multi_aff *pma1,
4279 __isl_keep isl_pw_multi_aff *pma2);
4283 #include <isl/aff.h>
4284 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_union_lexmin(
4285 __isl_take isl_pw_multi_aff *pma1,
4286 __isl_take isl_pw_multi_aff *pma2);
4287 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_union_lexmax(
4288 __isl_take isl_pw_multi_aff *pma1,
4289 __isl_take isl_pw_multi_aff *pma2);
4290 __isl_give isl_multi_aff *isl_multi_aff_add(
4291 __isl_take isl_multi_aff *maff1,
4292 __isl_take isl_multi_aff *maff2);
4293 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_add(
4294 __isl_take isl_pw_multi_aff *pma1,
4295 __isl_take isl_pw_multi_aff *pma2);
4296 __isl_give isl_union_pw_multi_aff *isl_union_pw_multi_aff_add(
4297 __isl_take isl_union_pw_multi_aff *upma1,
4298 __isl_take isl_union_pw_multi_aff *upma2);
4299 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_union_add(
4300 __isl_take isl_pw_multi_aff *pma1,
4301 __isl_take isl_pw_multi_aff *pma2);
4302 __isl_give isl_multi_aff *isl_multi_aff_sub(
4303 __isl_take isl_multi_aff *ma1,
4304 __isl_take isl_multi_aff *ma2);
4305 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_sub(
4306 __isl_take isl_pw_multi_aff *pma1,
4307 __isl_take isl_pw_multi_aff *pma2);
4308 __isl_give isl_union_pw_multi_aff *isl_union_pw_multi_aff_sub(
4309 __isl_take isl_union_pw_multi_aff *upma1,
4310 __isl_take isl_union_pw_multi_aff *upma2);
4312 C<isl_multi_aff_sub> subtracts the second argument from the first.
4314 __isl_give isl_multi_aff *isl_multi_aff_scale(
4315 __isl_take isl_multi_aff *maff,
4317 __isl_give isl_multi_aff *isl_multi_aff_scale_val(
4318 __isl_take isl_multi_aff *ma,
4319 __isl_take isl_val *v);
4320 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_scale_val(
4321 __isl_take isl_pw_multi_aff *pma,
4322 __isl_take isl_val *v);
4323 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_scale_val(
4324 __isl_take isl_multi_pw_aff *mpa,
4325 __isl_take isl_val *v);
4326 __isl_give isl_multi_aff *isl_multi_aff_scale_vec(
4327 __isl_take isl_multi_aff *ma,
4328 __isl_take isl_vec *v);
4329 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_scale_vec(
4330 __isl_take isl_pw_multi_aff *pma,
4331 __isl_take isl_vec *v);
4332 __isl_give isl_union_pw_multi_aff *isl_union_pw_multi_aff_scale_vec(
4333 __isl_take isl_union_pw_multi_aff *upma,
4334 __isl_take isl_vec *v);
4336 C<isl_multi_aff_scale_vec> scales the first elements of C<ma>
4337 by the corresponding elements of C<v>.
4339 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_intersect_params(
4340 __isl_take isl_pw_multi_aff *pma,
4341 __isl_take isl_set *set);
4342 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_intersect_domain(
4343 __isl_take isl_pw_multi_aff *pma,
4344 __isl_take isl_set *set);
4345 __isl_give isl_union_pw_multi_aff *
4346 isl_union_pw_multi_aff_intersect_domain(
4347 __isl_take isl_union_pw_multi_aff *upma,
4348 __isl_take isl_union_set *uset);
4349 __isl_give isl_multi_aff *isl_multi_aff_lift(
4350 __isl_take isl_multi_aff *maff,
4351 __isl_give isl_local_space **ls);
4352 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_coalesce(
4353 __isl_take isl_pw_multi_aff *pma);
4354 __isl_give isl_multi_aff *isl_multi_aff_align_params(
4355 __isl_take isl_multi_aff *multi,
4356 __isl_take isl_space *model);
4357 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_align_params(
4358 __isl_take isl_pw_multi_aff *pma,
4359 __isl_take isl_space *model);
4360 __isl_give isl_pw_multi_aff *
4361 isl_pw_multi_aff_project_domain_on_params(
4362 __isl_take isl_pw_multi_aff *pma);
4363 __isl_give isl_multi_aff *isl_multi_aff_gist_params(
4364 __isl_take isl_multi_aff *maff,
4365 __isl_take isl_set *context);
4366 __isl_give isl_multi_aff *isl_multi_aff_gist(
4367 __isl_take isl_multi_aff *maff,
4368 __isl_take isl_set *context);
4369 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_gist_params(
4370 __isl_take isl_pw_multi_aff *pma,
4371 __isl_take isl_set *set);
4372 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_gist(
4373 __isl_take isl_pw_multi_aff *pma,
4374 __isl_take isl_set *set);
4375 __isl_give isl_set *isl_pw_multi_aff_domain(
4376 __isl_take isl_pw_multi_aff *pma);
4377 __isl_give isl_union_set *isl_union_pw_multi_aff_domain(
4378 __isl_take isl_union_pw_multi_aff *upma);
4379 __isl_give isl_multi_aff *isl_multi_aff_range_splice(
4380 __isl_take isl_multi_aff *ma1, unsigned pos,
4381 __isl_take isl_multi_aff *ma2);
4382 __isl_give isl_multi_aff *isl_multi_aff_splice(
4383 __isl_take isl_multi_aff *ma1,
4384 unsigned in_pos, unsigned out_pos,
4385 __isl_take isl_multi_aff *ma2);
4386 __isl_give isl_multi_aff *isl_multi_aff_range_product(
4387 __isl_take isl_multi_aff *ma1,
4388 __isl_take isl_multi_aff *ma2);
4389 __isl_give isl_multi_aff *isl_multi_aff_flat_range_product(
4390 __isl_take isl_multi_aff *ma1,
4391 __isl_take isl_multi_aff *ma2);
4392 __isl_give isl_multi_aff *isl_multi_aff_product(
4393 __isl_take isl_multi_aff *ma1,
4394 __isl_take isl_multi_aff *ma2);
4395 __isl_give isl_pw_multi_aff *
4396 isl_pw_multi_aff_range_product(
4397 __isl_take isl_pw_multi_aff *pma1,
4398 __isl_take isl_pw_multi_aff *pma2);
4399 __isl_give isl_pw_multi_aff *
4400 isl_pw_multi_aff_flat_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 *isl_pw_multi_aff_product(
4404 __isl_take isl_pw_multi_aff *pma1,
4405 __isl_take isl_pw_multi_aff *pma2);
4406 __isl_give isl_union_pw_multi_aff *
4407 isl_union_pw_multi_aff_flat_range_product(
4408 __isl_take isl_union_pw_multi_aff *upma1,
4409 __isl_take isl_union_pw_multi_aff *upma2);
4410 __isl_give isl_multi_pw_aff *
4411 isl_multi_pw_aff_range_splice(
4412 __isl_take isl_multi_pw_aff *mpa1, unsigned pos,
4413 __isl_take isl_multi_pw_aff *mpa2);
4414 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_splice(
4415 __isl_take isl_multi_pw_aff *mpa1,
4416 unsigned in_pos, unsigned out_pos,
4417 __isl_take isl_multi_pw_aff *mpa2);
4418 __isl_give isl_multi_pw_aff *
4419 isl_multi_pw_aff_range_product(
4420 __isl_take isl_multi_pw_aff *mpa1,
4421 __isl_take isl_multi_pw_aff *mpa2);
4422 __isl_give isl_multi_pw_aff *
4423 isl_multi_pw_aff_flat_range_product(
4424 __isl_take isl_multi_pw_aff *mpa1,
4425 __isl_take isl_multi_pw_aff *mpa2);
4427 If the C<ls> argument of C<isl_multi_aff_lift> is not C<NULL>,
4428 then it is assigned the local space that lies at the basis of
4429 the lifting applied.
4431 #include <isl/aff.h>
4432 __isl_give isl_multi_aff *isl_multi_aff_pullback_multi_aff(
4433 __isl_take isl_multi_aff *ma1,
4434 __isl_take isl_multi_aff *ma2);
4435 __isl_give isl_pw_multi_aff *
4436 isl_pw_multi_aff_pullback_multi_aff(
4437 __isl_take isl_pw_multi_aff *pma,
4438 __isl_take isl_multi_aff *ma);
4439 __isl_give isl_pw_multi_aff *
4440 isl_pw_multi_aff_pullback_pw_multi_aff(
4441 __isl_take isl_pw_multi_aff *pma1,
4442 __isl_take isl_pw_multi_aff *pma2);
4444 The function C<isl_multi_aff_pullback_multi_aff> precomposes C<ma1> by C<ma2>.
4445 In other words, C<ma2> is plugged
4448 __isl_give isl_set *isl_multi_aff_lex_le_set(
4449 __isl_take isl_multi_aff *ma1,
4450 __isl_take isl_multi_aff *ma2);
4451 __isl_give isl_set *isl_multi_aff_lex_ge_set(
4452 __isl_take isl_multi_aff *ma1,
4453 __isl_take isl_multi_aff *ma2);
4455 The function C<isl_multi_aff_lex_le_set> returns a set
4456 containing those elements in the shared domain space
4457 where C<ma1> is lexicographically smaller than or
4460 An expression can be read from input using
4462 #include <isl/aff.h>
4463 __isl_give isl_multi_aff *isl_multi_aff_read_from_str(
4464 isl_ctx *ctx, const char *str);
4465 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_read_from_str(
4466 isl_ctx *ctx, const char *str);
4467 __isl_give isl_union_pw_multi_aff *
4468 isl_union_pw_multi_aff_read_from_str(
4469 isl_ctx *ctx, const char *str);
4471 An expression can be printed using
4473 #include <isl/aff.h>
4474 __isl_give isl_printer *isl_printer_print_multi_aff(
4475 __isl_take isl_printer *p,
4476 __isl_keep isl_multi_aff *maff);
4477 __isl_give isl_printer *isl_printer_print_pw_multi_aff(
4478 __isl_take isl_printer *p,
4479 __isl_keep isl_pw_multi_aff *pma);
4480 __isl_give isl_printer *isl_printer_print_union_pw_multi_aff(
4481 __isl_take isl_printer *p,
4482 __isl_keep isl_union_pw_multi_aff *upma);
4483 __isl_give isl_printer *isl_printer_print_multi_pw_aff(
4484 __isl_take isl_printer *p,
4485 __isl_keep isl_multi_pw_aff *mpa);
4489 Points are elements of a set. They can be used to construct
4490 simple sets (boxes) or they can be used to represent the
4491 individual elements of a set.
4492 The zero point (the origin) can be created using
4494 __isl_give isl_point *isl_point_zero(__isl_take isl_space *space);
4496 The coordinates of a point can be inspected, set and changed
4499 int isl_point_get_coordinate(__isl_keep isl_point *pnt,
4500 enum isl_dim_type type, int pos, isl_int *v);
4501 __isl_give isl_val *isl_point_get_coordinate_val(
4502 __isl_keep isl_point *pnt,
4503 enum isl_dim_type type, int pos);
4504 __isl_give isl_point *isl_point_set_coordinate(
4505 __isl_take isl_point *pnt,
4506 enum isl_dim_type type, int pos, isl_int v);
4507 __isl_give isl_point *isl_point_set_coordinate_val(
4508 __isl_take isl_point *pnt,
4509 enum isl_dim_type type, int pos,
4510 __isl_take isl_val *v);
4512 __isl_give isl_point *isl_point_add_ui(
4513 __isl_take isl_point *pnt,
4514 enum isl_dim_type type, int pos, unsigned val);
4515 __isl_give isl_point *isl_point_sub_ui(
4516 __isl_take isl_point *pnt,
4517 enum isl_dim_type type, int pos, unsigned val);
4519 Other properties can be obtained using
4521 isl_ctx *isl_point_get_ctx(__isl_keep isl_point *pnt);
4523 Points can be copied or freed using
4525 __isl_give isl_point *isl_point_copy(
4526 __isl_keep isl_point *pnt);
4527 void isl_point_free(__isl_take isl_point *pnt);
4529 A singleton set can be created from a point using
4531 __isl_give isl_basic_set *isl_basic_set_from_point(
4532 __isl_take isl_point *pnt);
4533 __isl_give isl_set *isl_set_from_point(
4534 __isl_take isl_point *pnt);
4536 and a box can be created from two opposite extremal points using
4538 __isl_give isl_basic_set *isl_basic_set_box_from_points(
4539 __isl_take isl_point *pnt1,
4540 __isl_take isl_point *pnt2);
4541 __isl_give isl_set *isl_set_box_from_points(
4542 __isl_take isl_point *pnt1,
4543 __isl_take isl_point *pnt2);
4545 All elements of a B<bounded> (union) set can be enumerated using
4546 the following functions.
4548 int isl_set_foreach_point(__isl_keep isl_set *set,
4549 int (*fn)(__isl_take isl_point *pnt, void *user),
4551 int isl_union_set_foreach_point(__isl_keep isl_union_set *uset,
4552 int (*fn)(__isl_take isl_point *pnt, void *user),
4555 The function C<fn> is called for each integer point in
4556 C<set> with as second argument the last argument of
4557 the C<isl_set_foreach_point> call. The function C<fn>
4558 should return C<0> on success and C<-1> on failure.
4559 In the latter case, C<isl_set_foreach_point> will stop
4560 enumerating and return C<-1> as well.
4561 If the enumeration is performed successfully and to completion,
4562 then C<isl_set_foreach_point> returns C<0>.
4564 To obtain a single point of a (basic) set, use
4566 __isl_give isl_point *isl_basic_set_sample_point(
4567 __isl_take isl_basic_set *bset);
4568 __isl_give isl_point *isl_set_sample_point(
4569 __isl_take isl_set *set);
4571 If C<set> does not contain any (integer) points, then the
4572 resulting point will be ``void'', a property that can be
4575 int isl_point_is_void(__isl_keep isl_point *pnt);
4577 =head2 Piecewise Quasipolynomials
4579 A piecewise quasipolynomial is a particular kind of function that maps
4580 a parametric point to a rational value.
4581 More specifically, a quasipolynomial is a polynomial expression in greatest
4582 integer parts of affine expressions of parameters and variables.
4583 A piecewise quasipolynomial is a subdivision of a given parametric
4584 domain into disjoint cells with a quasipolynomial associated to
4585 each cell. The value of the piecewise quasipolynomial at a given
4586 point is the value of the quasipolynomial associated to the cell
4587 that contains the point. Outside of the union of cells,
4588 the value is assumed to be zero.
4589 For example, the piecewise quasipolynomial
4591 [n] -> { [x] -> ((1 + n) - x) : x <= n and x >= 0 }
4593 maps C<x> to C<1 + n - x> for values of C<x> between C<0> and C<n>.
4594 A given piecewise quasipolynomial has a fixed domain dimension.
4595 Union piecewise quasipolynomials are used to contain piecewise quasipolynomials
4596 defined over different domains.
4597 Piecewise quasipolynomials are mainly used by the C<barvinok>
4598 library for representing the number of elements in a parametric set or map.
4599 For example, the piecewise quasipolynomial above represents
4600 the number of points in the map
4602 [n] -> { [x] -> [y] : x,y >= 0 and 0 <= x + y <= n }
4604 =head3 Input and Output
4606 Piecewise quasipolynomials can be read from input using
4608 __isl_give isl_union_pw_qpolynomial *
4609 isl_union_pw_qpolynomial_read_from_str(
4610 isl_ctx *ctx, const char *str);
4612 Quasipolynomials and piecewise quasipolynomials can be printed
4613 using the following functions.
4615 __isl_give isl_printer *isl_printer_print_qpolynomial(
4616 __isl_take isl_printer *p,
4617 __isl_keep isl_qpolynomial *qp);
4619 __isl_give isl_printer *isl_printer_print_pw_qpolynomial(
4620 __isl_take isl_printer *p,
4621 __isl_keep isl_pw_qpolynomial *pwqp);
4623 __isl_give isl_printer *isl_printer_print_union_pw_qpolynomial(
4624 __isl_take isl_printer *p,
4625 __isl_keep isl_union_pw_qpolynomial *upwqp);
4627 The output format of the printer
4628 needs to be set to either C<ISL_FORMAT_ISL> or C<ISL_FORMAT_C>.
4629 For C<isl_printer_print_union_pw_qpolynomial>, only C<ISL_FORMAT_ISL>
4631 In case of printing in C<ISL_FORMAT_C>, the user may want
4632 to set the names of all dimensions
4634 __isl_give isl_qpolynomial *isl_qpolynomial_set_dim_name(
4635 __isl_take isl_qpolynomial *qp,
4636 enum isl_dim_type type, unsigned pos,
4638 __isl_give isl_pw_qpolynomial *
4639 isl_pw_qpolynomial_set_dim_name(
4640 __isl_take isl_pw_qpolynomial *pwqp,
4641 enum isl_dim_type type, unsigned pos,
4644 =head3 Creating New (Piecewise) Quasipolynomials
4646 Some simple quasipolynomials can be created using the following functions.
4647 More complicated quasipolynomials can be created by applying
4648 operations such as addition and multiplication
4649 on the resulting quasipolynomials
4651 __isl_give isl_qpolynomial *isl_qpolynomial_zero_on_domain(
4652 __isl_take isl_space *domain);
4653 __isl_give isl_qpolynomial *isl_qpolynomial_one_on_domain(
4654 __isl_take isl_space *domain);
4655 __isl_give isl_qpolynomial *isl_qpolynomial_infty_on_domain(
4656 __isl_take isl_space *domain);
4657 __isl_give isl_qpolynomial *isl_qpolynomial_neginfty_on_domain(
4658 __isl_take isl_space *domain);
4659 __isl_give isl_qpolynomial *isl_qpolynomial_nan_on_domain(
4660 __isl_take isl_space *domain);
4661 __isl_give isl_qpolynomial *isl_qpolynomial_rat_cst_on_domain(
4662 __isl_take isl_space *domain,
4663 const isl_int n, const isl_int d);
4664 __isl_give isl_qpolynomial *isl_qpolynomial_val_on_domain(
4665 __isl_take isl_space *domain,
4666 __isl_take isl_val *val);
4667 __isl_give isl_qpolynomial *isl_qpolynomial_var_on_domain(
4668 __isl_take isl_space *domain,
4669 enum isl_dim_type type, unsigned pos);
4670 __isl_give isl_qpolynomial *isl_qpolynomial_from_aff(
4671 __isl_take isl_aff *aff);
4673 Note that the space in which a quasipolynomial lives is a map space
4674 with a one-dimensional range. The C<domain> argument in some of
4675 the functions above corresponds to the domain of this map space.
4677 The zero piecewise quasipolynomial or a piecewise quasipolynomial
4678 with a single cell can be created using the following functions.
4679 Multiple of these single cell piecewise quasipolynomials can
4680 be combined to create more complicated piecewise quasipolynomials.
4682 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_zero(
4683 __isl_take isl_space *space);
4684 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_alloc(
4685 __isl_take isl_set *set,
4686 __isl_take isl_qpolynomial *qp);
4687 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_from_qpolynomial(
4688 __isl_take isl_qpolynomial *qp);
4689 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_from_pw_aff(
4690 __isl_take isl_pw_aff *pwaff);
4692 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_zero(
4693 __isl_take isl_space *space);
4694 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_from_pw_qpolynomial(
4695 __isl_take isl_pw_qpolynomial *pwqp);
4696 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_add_pw_qpolynomial(
4697 __isl_take isl_union_pw_qpolynomial *upwqp,
4698 __isl_take isl_pw_qpolynomial *pwqp);
4700 Quasipolynomials can be copied and freed again using the following
4703 __isl_give isl_qpolynomial *isl_qpolynomial_copy(
4704 __isl_keep isl_qpolynomial *qp);
4705 void *isl_qpolynomial_free(__isl_take isl_qpolynomial *qp);
4707 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_copy(
4708 __isl_keep isl_pw_qpolynomial *pwqp);
4709 void *isl_pw_qpolynomial_free(
4710 __isl_take isl_pw_qpolynomial *pwqp);
4712 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_copy(
4713 __isl_keep isl_union_pw_qpolynomial *upwqp);
4714 void *isl_union_pw_qpolynomial_free(
4715 __isl_take isl_union_pw_qpolynomial *upwqp);
4717 =head3 Inspecting (Piecewise) Quasipolynomials
4719 To iterate over all piecewise quasipolynomials in a union
4720 piecewise quasipolynomial, use the following function
4722 int isl_union_pw_qpolynomial_foreach_pw_qpolynomial(
4723 __isl_keep isl_union_pw_qpolynomial *upwqp,
4724 int (*fn)(__isl_take isl_pw_qpolynomial *pwqp, void *user),
4727 To extract the piecewise quasipolynomial in a given space from a union, use
4729 __isl_give isl_pw_qpolynomial *
4730 isl_union_pw_qpolynomial_extract_pw_qpolynomial(
4731 __isl_keep isl_union_pw_qpolynomial *upwqp,
4732 __isl_take isl_space *space);
4734 To iterate over the cells in a piecewise quasipolynomial,
4735 use either of the following two functions
4737 int isl_pw_qpolynomial_foreach_piece(
4738 __isl_keep isl_pw_qpolynomial *pwqp,
4739 int (*fn)(__isl_take isl_set *set,
4740 __isl_take isl_qpolynomial *qp,
4741 void *user), void *user);
4742 int isl_pw_qpolynomial_foreach_lifted_piece(
4743 __isl_keep isl_pw_qpolynomial *pwqp,
4744 int (*fn)(__isl_take isl_set *set,
4745 __isl_take isl_qpolynomial *qp,
4746 void *user), void *user);
4748 As usual, the function C<fn> should return C<0> on success
4749 and C<-1> on failure. The difference between
4750 C<isl_pw_qpolynomial_foreach_piece> and
4751 C<isl_pw_qpolynomial_foreach_lifted_piece> is that
4752 C<isl_pw_qpolynomial_foreach_lifted_piece> will first
4753 compute unique representations for all existentially quantified
4754 variables and then turn these existentially quantified variables
4755 into extra set variables, adapting the associated quasipolynomial
4756 accordingly. This means that the C<set> passed to C<fn>
4757 will not have any existentially quantified variables, but that
4758 the dimensions of the sets may be different for different
4759 invocations of C<fn>.
4761 The constant term of a quasipolynomial can be extracted using
4763 __isl_give isl_val *isl_qpolynomial_get_constant_val(
4764 __isl_keep isl_qpolynomial *qp);
4766 To iterate over all terms in a quasipolynomial,
4769 int isl_qpolynomial_foreach_term(
4770 __isl_keep isl_qpolynomial *qp,
4771 int (*fn)(__isl_take isl_term *term,
4772 void *user), void *user);
4774 The terms themselves can be inspected and freed using
4777 unsigned isl_term_dim(__isl_keep isl_term *term,
4778 enum isl_dim_type type);
4779 void isl_term_get_num(__isl_keep isl_term *term,
4781 void isl_term_get_den(__isl_keep isl_term *term,
4783 __isl_give isl_val *isl_term_get_coefficient_val(
4784 __isl_keep isl_term *term);
4785 int isl_term_get_exp(__isl_keep isl_term *term,
4786 enum isl_dim_type type, unsigned pos);
4787 __isl_give isl_aff *isl_term_get_div(
4788 __isl_keep isl_term *term, unsigned pos);
4789 void isl_term_free(__isl_take isl_term *term);
4791 Each term is a product of parameters, set variables and
4792 integer divisions. The function C<isl_term_get_exp>
4793 returns the exponent of a given dimensions in the given term.
4794 The C<isl_int>s in the arguments of C<isl_term_get_num>
4795 and C<isl_term_get_den> need to have been initialized
4796 using C<isl_int_init> before calling these functions.
4798 =head3 Properties of (Piecewise) Quasipolynomials
4800 To check whether a quasipolynomial is actually a constant,
4801 use the following function.
4803 int isl_qpolynomial_is_cst(__isl_keep isl_qpolynomial *qp,
4804 isl_int *n, isl_int *d);
4806 If C<qp> is a constant and if C<n> and C<d> are not C<NULL>
4807 then the numerator and denominator of the constant
4808 are returned in C<*n> and C<*d>, respectively.
4810 To check whether two union piecewise quasipolynomials are
4811 obviously equal, use
4813 int isl_union_pw_qpolynomial_plain_is_equal(
4814 __isl_keep isl_union_pw_qpolynomial *upwqp1,
4815 __isl_keep isl_union_pw_qpolynomial *upwqp2);
4817 =head3 Operations on (Piecewise) Quasipolynomials
4819 __isl_give isl_qpolynomial *isl_qpolynomial_scale(
4820 __isl_take isl_qpolynomial *qp, isl_int v);
4821 __isl_give isl_qpolynomial *isl_qpolynomial_scale_val(
4822 __isl_take isl_qpolynomial *qp,
4823 __isl_take isl_val *v);
4824 __isl_give isl_qpolynomial *isl_qpolynomial_neg(
4825 __isl_take isl_qpolynomial *qp);
4826 __isl_give isl_qpolynomial *isl_qpolynomial_add(
4827 __isl_take isl_qpolynomial *qp1,
4828 __isl_take isl_qpolynomial *qp2);
4829 __isl_give isl_qpolynomial *isl_qpolynomial_sub(
4830 __isl_take isl_qpolynomial *qp1,
4831 __isl_take isl_qpolynomial *qp2);
4832 __isl_give isl_qpolynomial *isl_qpolynomial_mul(
4833 __isl_take isl_qpolynomial *qp1,
4834 __isl_take isl_qpolynomial *qp2);
4835 __isl_give isl_qpolynomial *isl_qpolynomial_pow(
4836 __isl_take isl_qpolynomial *qp, unsigned exponent);
4838 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_fix_val(
4839 __isl_take isl_pw_qpolynomial *pwqp,
4840 enum isl_dim_type type, unsigned n,
4841 __isl_take isl_val *v);
4842 __isl_give isl_pw_qpolynomial *
4843 isl_pw_qpolynomial_scale_val(
4844 __isl_take isl_pw_qpolynomial *pwqp,
4845 __isl_take isl_val *v);
4846 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_add(
4847 __isl_take isl_pw_qpolynomial *pwqp1,
4848 __isl_take isl_pw_qpolynomial *pwqp2);
4849 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_sub(
4850 __isl_take isl_pw_qpolynomial *pwqp1,
4851 __isl_take isl_pw_qpolynomial *pwqp2);
4852 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_add_disjoint(
4853 __isl_take isl_pw_qpolynomial *pwqp1,
4854 __isl_take isl_pw_qpolynomial *pwqp2);
4855 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_neg(
4856 __isl_take isl_pw_qpolynomial *pwqp);
4857 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_mul(
4858 __isl_take isl_pw_qpolynomial *pwqp1,
4859 __isl_take isl_pw_qpolynomial *pwqp2);
4860 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_pow(
4861 __isl_take isl_pw_qpolynomial *pwqp, unsigned exponent);
4863 __isl_give isl_union_pw_qpolynomial *
4864 isl_union_pw_qpolynomial_scale_val(
4865 __isl_take isl_union_pw_qpolynomial *upwqp,
4866 __isl_take isl_val *v);
4867 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_add(
4868 __isl_take isl_union_pw_qpolynomial *upwqp1,
4869 __isl_take isl_union_pw_qpolynomial *upwqp2);
4870 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_sub(
4871 __isl_take isl_union_pw_qpolynomial *upwqp1,
4872 __isl_take isl_union_pw_qpolynomial *upwqp2);
4873 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_mul(
4874 __isl_take isl_union_pw_qpolynomial *upwqp1,
4875 __isl_take isl_union_pw_qpolynomial *upwqp2);
4877 __isl_give isl_qpolynomial *isl_pw_qpolynomial_eval(
4878 __isl_take isl_pw_qpolynomial *pwqp,
4879 __isl_take isl_point *pnt);
4881 __isl_give isl_qpolynomial *isl_union_pw_qpolynomial_eval(
4882 __isl_take isl_union_pw_qpolynomial *upwqp,
4883 __isl_take isl_point *pnt);
4885 __isl_give isl_set *isl_pw_qpolynomial_domain(
4886 __isl_take isl_pw_qpolynomial *pwqp);
4887 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_intersect_domain(
4888 __isl_take isl_pw_qpolynomial *pwpq,
4889 __isl_take isl_set *set);
4890 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_intersect_params(
4891 __isl_take isl_pw_qpolynomial *pwpq,
4892 __isl_take isl_set *set);
4894 __isl_give isl_union_set *isl_union_pw_qpolynomial_domain(
4895 __isl_take isl_union_pw_qpolynomial *upwqp);
4896 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_intersect_domain(
4897 __isl_take isl_union_pw_qpolynomial *upwpq,
4898 __isl_take isl_union_set *uset);
4899 __isl_give isl_union_pw_qpolynomial *
4900 isl_union_pw_qpolynomial_intersect_params(
4901 __isl_take isl_union_pw_qpolynomial *upwpq,
4902 __isl_take isl_set *set);
4904 __isl_give isl_qpolynomial *isl_qpolynomial_align_params(
4905 __isl_take isl_qpolynomial *qp,
4906 __isl_take isl_space *model);
4908 __isl_give isl_qpolynomial *isl_qpolynomial_project_domain_on_params(
4909 __isl_take isl_qpolynomial *qp);
4910 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_project_domain_on_params(
4911 __isl_take isl_pw_qpolynomial *pwqp);
4913 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_coalesce(
4914 __isl_take isl_union_pw_qpolynomial *upwqp);
4916 __isl_give isl_qpolynomial *isl_qpolynomial_gist_params(
4917 __isl_take isl_qpolynomial *qp,
4918 __isl_take isl_set *context);
4919 __isl_give isl_qpolynomial *isl_qpolynomial_gist(
4920 __isl_take isl_qpolynomial *qp,
4921 __isl_take isl_set *context);
4923 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_gist_params(
4924 __isl_take isl_pw_qpolynomial *pwqp,
4925 __isl_take isl_set *context);
4926 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_gist(
4927 __isl_take isl_pw_qpolynomial *pwqp,
4928 __isl_take isl_set *context);
4930 __isl_give isl_union_pw_qpolynomial *
4931 isl_union_pw_qpolynomial_gist_params(
4932 __isl_take isl_union_pw_qpolynomial *upwqp,
4933 __isl_take isl_set *context);
4934 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_gist(
4935 __isl_take isl_union_pw_qpolynomial *upwqp,
4936 __isl_take isl_union_set *context);
4938 The gist operation applies the gist operation to each of
4939 the cells in the domain of the input piecewise quasipolynomial.
4940 The context is also exploited
4941 to simplify the quasipolynomials associated to each cell.
4943 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_to_polynomial(
4944 __isl_take isl_pw_qpolynomial *pwqp, int sign);
4945 __isl_give isl_union_pw_qpolynomial *
4946 isl_union_pw_qpolynomial_to_polynomial(
4947 __isl_take isl_union_pw_qpolynomial *upwqp, int sign);
4949 Approximate each quasipolynomial by a polynomial. If C<sign> is positive,
4950 the polynomial will be an overapproximation. If C<sign> is negative,
4951 it will be an underapproximation. If C<sign> is zero, the approximation
4952 will lie somewhere in between.
4954 =head2 Bounds on Piecewise Quasipolynomials and Piecewise Quasipolynomial Reductions
4956 A piecewise quasipolynomial reduction is a piecewise
4957 reduction (or fold) of quasipolynomials.
4958 In particular, the reduction can be maximum or a minimum.
4959 The objects are mainly used to represent the result of
4960 an upper or lower bound on a quasipolynomial over its domain,
4961 i.e., as the result of the following function.
4963 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_bound(
4964 __isl_take isl_pw_qpolynomial *pwqp,
4965 enum isl_fold type, int *tight);
4967 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_bound(
4968 __isl_take isl_union_pw_qpolynomial *upwqp,
4969 enum isl_fold type, int *tight);
4971 The C<type> argument may be either C<isl_fold_min> or C<isl_fold_max>.
4972 If C<tight> is not C<NULL>, then C<*tight> is set to C<1>
4973 is the returned bound is known be tight, i.e., for each value
4974 of the parameters there is at least
4975 one element in the domain that reaches the bound.
4976 If the domain of C<pwqp> is not wrapping, then the bound is computed
4977 over all elements in that domain and the result has a purely parametric
4978 domain. If the domain of C<pwqp> is wrapping, then the bound is
4979 computed over the range of the wrapped relation. The domain of the
4980 wrapped relation becomes the domain of the result.
4982 A (piecewise) quasipolynomial reduction can be copied or freed using the
4983 following functions.
4985 __isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_copy(
4986 __isl_keep isl_qpolynomial_fold *fold);
4987 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_copy(
4988 __isl_keep isl_pw_qpolynomial_fold *pwf);
4989 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_copy(
4990 __isl_keep isl_union_pw_qpolynomial_fold *upwf);
4991 void isl_qpolynomial_fold_free(
4992 __isl_take isl_qpolynomial_fold *fold);
4993 void *isl_pw_qpolynomial_fold_free(
4994 __isl_take isl_pw_qpolynomial_fold *pwf);
4995 void *isl_union_pw_qpolynomial_fold_free(
4996 __isl_take isl_union_pw_qpolynomial_fold *upwf);
4998 =head3 Printing Piecewise Quasipolynomial Reductions
5000 Piecewise quasipolynomial reductions can be printed
5001 using the following function.
5003 __isl_give isl_printer *isl_printer_print_pw_qpolynomial_fold(
5004 __isl_take isl_printer *p,
5005 __isl_keep isl_pw_qpolynomial_fold *pwf);
5006 __isl_give isl_printer *isl_printer_print_union_pw_qpolynomial_fold(
5007 __isl_take isl_printer *p,
5008 __isl_keep isl_union_pw_qpolynomial_fold *upwf);
5010 For C<isl_printer_print_pw_qpolynomial_fold>,
5011 output format of the printer
5012 needs to be set to either C<ISL_FORMAT_ISL> or C<ISL_FORMAT_C>.
5013 For C<isl_printer_print_union_pw_qpolynomial_fold>,
5014 output format of the printer
5015 needs to be set to C<ISL_FORMAT_ISL>.
5016 In case of printing in C<ISL_FORMAT_C>, the user may want
5017 to set the names of all dimensions
5019 __isl_give isl_pw_qpolynomial_fold *
5020 isl_pw_qpolynomial_fold_set_dim_name(
5021 __isl_take isl_pw_qpolynomial_fold *pwf,
5022 enum isl_dim_type type, unsigned pos,
5025 =head3 Inspecting (Piecewise) Quasipolynomial Reductions
5027 To iterate over all piecewise quasipolynomial reductions in a union
5028 piecewise quasipolynomial reduction, use the following function
5030 int isl_union_pw_qpolynomial_fold_foreach_pw_qpolynomial_fold(
5031 __isl_keep isl_union_pw_qpolynomial_fold *upwf,
5032 int (*fn)(__isl_take isl_pw_qpolynomial_fold *pwf,
5033 void *user), void *user);
5035 To iterate over the cells in a piecewise quasipolynomial reduction,
5036 use either of the following two functions
5038 int isl_pw_qpolynomial_fold_foreach_piece(
5039 __isl_keep isl_pw_qpolynomial_fold *pwf,
5040 int (*fn)(__isl_take isl_set *set,
5041 __isl_take isl_qpolynomial_fold *fold,
5042 void *user), void *user);
5043 int isl_pw_qpolynomial_fold_foreach_lifted_piece(
5044 __isl_keep isl_pw_qpolynomial_fold *pwf,
5045 int (*fn)(__isl_take isl_set *set,
5046 __isl_take isl_qpolynomial_fold *fold,
5047 void *user), void *user);
5049 See L<Inspecting (Piecewise) Quasipolynomials> for an explanation
5050 of the difference between these two functions.
5052 To iterate over all quasipolynomials in a reduction, use
5054 int isl_qpolynomial_fold_foreach_qpolynomial(
5055 __isl_keep isl_qpolynomial_fold *fold,
5056 int (*fn)(__isl_take isl_qpolynomial *qp,
5057 void *user), void *user);
5059 =head3 Properties of Piecewise Quasipolynomial Reductions
5061 To check whether two union piecewise quasipolynomial reductions are
5062 obviously equal, use
5064 int isl_union_pw_qpolynomial_fold_plain_is_equal(
5065 __isl_keep isl_union_pw_qpolynomial_fold *upwf1,
5066 __isl_keep isl_union_pw_qpolynomial_fold *upwf2);
5068 =head3 Operations on Piecewise Quasipolynomial Reductions
5070 __isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_scale(
5071 __isl_take isl_qpolynomial_fold *fold, isl_int v);
5072 __isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_scale_val(
5073 __isl_take isl_qpolynomial_fold *fold,
5074 __isl_take isl_val *v);
5075 __isl_give isl_pw_qpolynomial_fold *
5076 isl_pw_qpolynomial_fold_scale_val(
5077 __isl_take isl_pw_qpolynomial_fold *pwf,
5078 __isl_take isl_val *v);
5079 __isl_give isl_union_pw_qpolynomial_fold *
5080 isl_union_pw_qpolynomial_fold_scale_val(
5081 __isl_take isl_union_pw_qpolynomial_fold *upwf,
5082 __isl_take isl_val *v);
5084 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_add(
5085 __isl_take isl_pw_qpolynomial_fold *pwf1,
5086 __isl_take isl_pw_qpolynomial_fold *pwf2);
5088 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_fold(
5089 __isl_take isl_pw_qpolynomial_fold *pwf1,
5090 __isl_take isl_pw_qpolynomial_fold *pwf2);
5092 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_fold(
5093 __isl_take isl_union_pw_qpolynomial_fold *upwf1,
5094 __isl_take isl_union_pw_qpolynomial_fold *upwf2);
5096 __isl_give isl_qpolynomial *isl_pw_qpolynomial_fold_eval(
5097 __isl_take isl_pw_qpolynomial_fold *pwf,
5098 __isl_take isl_point *pnt);
5100 __isl_give isl_qpolynomial *isl_union_pw_qpolynomial_fold_eval(
5101 __isl_take isl_union_pw_qpolynomial_fold *upwf,
5102 __isl_take isl_point *pnt);
5104 __isl_give isl_pw_qpolynomial_fold *
5105 isl_pw_qpolynomial_fold_intersect_params(
5106 __isl_take isl_pw_qpolynomial_fold *pwf,
5107 __isl_take isl_set *set);
5109 __isl_give isl_union_set *isl_union_pw_qpolynomial_fold_domain(
5110 __isl_take isl_union_pw_qpolynomial_fold *upwf);
5111 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_intersect_domain(
5112 __isl_take isl_union_pw_qpolynomial_fold *upwf,
5113 __isl_take isl_union_set *uset);
5114 __isl_give isl_union_pw_qpolynomial_fold *
5115 isl_union_pw_qpolynomial_fold_intersect_params(
5116 __isl_take isl_union_pw_qpolynomial_fold *upwf,
5117 __isl_take isl_set *set);
5119 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_project_domain_on_params(
5120 __isl_take isl_pw_qpolynomial_fold *pwf);
5122 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_coalesce(
5123 __isl_take isl_pw_qpolynomial_fold *pwf);
5125 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_coalesce(
5126 __isl_take isl_union_pw_qpolynomial_fold *upwf);
5128 __isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_gist_params(
5129 __isl_take isl_qpolynomial_fold *fold,
5130 __isl_take isl_set *context);
5131 __isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_gist(
5132 __isl_take isl_qpolynomial_fold *fold,
5133 __isl_take isl_set *context);
5135 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_gist(
5136 __isl_take isl_pw_qpolynomial_fold *pwf,
5137 __isl_take isl_set *context);
5138 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_gist_params(
5139 __isl_take isl_pw_qpolynomial_fold *pwf,
5140 __isl_take isl_set *context);
5142 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_gist(
5143 __isl_take isl_union_pw_qpolynomial_fold *upwf,
5144 __isl_take isl_union_set *context);
5145 __isl_give isl_union_pw_qpolynomial_fold *
5146 isl_union_pw_qpolynomial_fold_gist_params(
5147 __isl_take isl_union_pw_qpolynomial_fold *upwf,
5148 __isl_take isl_set *context);
5150 The gist operation applies the gist operation to each of
5151 the cells in the domain of the input piecewise quasipolynomial reduction.
5152 In future, the operation will also exploit the context
5153 to simplify the quasipolynomial reductions associated to each cell.
5155 __isl_give isl_pw_qpolynomial_fold *
5156 isl_set_apply_pw_qpolynomial_fold(
5157 __isl_take isl_set *set,
5158 __isl_take isl_pw_qpolynomial_fold *pwf,
5160 __isl_give isl_pw_qpolynomial_fold *
5161 isl_map_apply_pw_qpolynomial_fold(
5162 __isl_take isl_map *map,
5163 __isl_take isl_pw_qpolynomial_fold *pwf,
5165 __isl_give isl_union_pw_qpolynomial_fold *
5166 isl_union_set_apply_union_pw_qpolynomial_fold(
5167 __isl_take isl_union_set *uset,
5168 __isl_take isl_union_pw_qpolynomial_fold *upwf,
5170 __isl_give isl_union_pw_qpolynomial_fold *
5171 isl_union_map_apply_union_pw_qpolynomial_fold(
5172 __isl_take isl_union_map *umap,
5173 __isl_take isl_union_pw_qpolynomial_fold *upwf,
5176 The functions taking a map
5177 compose the given map with the given piecewise quasipolynomial reduction.
5178 That is, compute a bound (of the same type as C<pwf> or C<upwf> itself)
5179 over all elements in the intersection of the range of the map
5180 and the domain of the piecewise quasipolynomial reduction
5181 as a function of an element in the domain of the map.
5182 The functions taking a set compute a bound over all elements in the
5183 intersection of the set and the domain of the
5184 piecewise quasipolynomial reduction.
5186 =head2 Parametric Vertex Enumeration
5188 The parametric vertex enumeration described in this section
5189 is mainly intended to be used internally and by the C<barvinok>
5192 #include <isl/vertices.h>
5193 __isl_give isl_vertices *isl_basic_set_compute_vertices(
5194 __isl_keep isl_basic_set *bset);
5196 The function C<isl_basic_set_compute_vertices> performs the
5197 actual computation of the parametric vertices and the chamber
5198 decomposition and store the result in an C<isl_vertices> object.
5199 This information can be queried by either iterating over all
5200 the vertices or iterating over all the chambers or cells
5201 and then iterating over all vertices that are active on the chamber.
5203 int isl_vertices_foreach_vertex(
5204 __isl_keep isl_vertices *vertices,
5205 int (*fn)(__isl_take isl_vertex *vertex, void *user),
5208 int isl_vertices_foreach_cell(
5209 __isl_keep isl_vertices *vertices,
5210 int (*fn)(__isl_take isl_cell *cell, void *user),
5212 int isl_cell_foreach_vertex(__isl_keep isl_cell *cell,
5213 int (*fn)(__isl_take isl_vertex *vertex, void *user),
5216 Other operations that can be performed on an C<isl_vertices> object are
5219 isl_ctx *isl_vertices_get_ctx(
5220 __isl_keep isl_vertices *vertices);
5221 int isl_vertices_get_n_vertices(
5222 __isl_keep isl_vertices *vertices);
5223 void isl_vertices_free(__isl_take isl_vertices *vertices);
5225 Vertices can be inspected and destroyed using the following functions.
5227 isl_ctx *isl_vertex_get_ctx(__isl_keep isl_vertex *vertex);
5228 int isl_vertex_get_id(__isl_keep isl_vertex *vertex);
5229 __isl_give isl_basic_set *isl_vertex_get_domain(
5230 __isl_keep isl_vertex *vertex);
5231 __isl_give isl_basic_set *isl_vertex_get_expr(
5232 __isl_keep isl_vertex *vertex);
5233 void isl_vertex_free(__isl_take isl_vertex *vertex);
5235 C<isl_vertex_get_expr> returns a singleton parametric set describing
5236 the vertex, while C<isl_vertex_get_domain> returns the activity domain
5238 Note that C<isl_vertex_get_domain> and C<isl_vertex_get_expr> return
5239 B<rational> basic sets, so they should mainly be used for inspection
5240 and should not be mixed with integer sets.
5242 Chambers can be inspected and destroyed using the following functions.
5244 isl_ctx *isl_cell_get_ctx(__isl_keep isl_cell *cell);
5245 __isl_give isl_basic_set *isl_cell_get_domain(
5246 __isl_keep isl_cell *cell);
5247 void isl_cell_free(__isl_take isl_cell *cell);
5249 =head1 Polyhedral Compilation Library
5251 This section collects functionality in C<isl> that has been specifically
5252 designed for use during polyhedral compilation.
5254 =head2 Dependence Analysis
5256 C<isl> contains specialized functionality for performing
5257 array dataflow analysis. That is, given a I<sink> access relation
5258 and a collection of possible I<source> access relations,
5259 C<isl> can compute relations that describe
5260 for each iteration of the sink access, which iteration
5261 of which of the source access relations was the last
5262 to access the same data element before the given iteration
5264 The resulting dependence relations map source iterations
5265 to the corresponding sink iterations.
5266 To compute standard flow dependences, the sink should be
5267 a read, while the sources should be writes.
5268 If any of the source accesses are marked as being I<may>
5269 accesses, then there will be a dependence from the last
5270 I<must> access B<and> from any I<may> access that follows
5271 this last I<must> access.
5272 In particular, if I<all> sources are I<may> accesses,
5273 then memory based dependence analysis is performed.
5274 If, on the other hand, all sources are I<must> accesses,
5275 then value based dependence analysis is performed.
5277 #include <isl/flow.h>
5279 typedef int (*isl_access_level_before)(void *first, void *second);
5281 __isl_give isl_access_info *isl_access_info_alloc(
5282 __isl_take isl_map *sink,
5283 void *sink_user, isl_access_level_before fn,
5285 __isl_give isl_access_info *isl_access_info_add_source(
5286 __isl_take isl_access_info *acc,
5287 __isl_take isl_map *source, int must,
5289 void *isl_access_info_free(__isl_take isl_access_info *acc);
5291 __isl_give isl_flow *isl_access_info_compute_flow(
5292 __isl_take isl_access_info *acc);
5294 int isl_flow_foreach(__isl_keep isl_flow *deps,
5295 int (*fn)(__isl_take isl_map *dep, int must,
5296 void *dep_user, void *user),
5298 __isl_give isl_map *isl_flow_get_no_source(
5299 __isl_keep isl_flow *deps, int must);
5300 void isl_flow_free(__isl_take isl_flow *deps);
5302 The function C<isl_access_info_compute_flow> performs the actual
5303 dependence analysis. The other functions are used to construct
5304 the input for this function or to read off the output.
5306 The input is collected in an C<isl_access_info>, which can
5307 be created through a call to C<isl_access_info_alloc>.
5308 The arguments to this functions are the sink access relation
5309 C<sink>, a token C<sink_user> used to identify the sink
5310 access to the user, a callback function for specifying the
5311 relative order of source and sink accesses, and the number
5312 of source access relations that will be added.
5313 The callback function has type C<int (*)(void *first, void *second)>.
5314 The function is called with two user supplied tokens identifying
5315 either a source or the sink and it should return the shared nesting
5316 level and the relative order of the two accesses.
5317 In particular, let I<n> be the number of loops shared by
5318 the two accesses. If C<first> precedes C<second> textually,
5319 then the function should return I<2 * n + 1>; otherwise,
5320 it should return I<2 * n>.
5321 The sources can be added to the C<isl_access_info> by performing
5322 (at most) C<max_source> calls to C<isl_access_info_add_source>.
5323 C<must> indicates whether the source is a I<must> access
5324 or a I<may> access. Note that a multi-valued access relation
5325 should only be marked I<must> if every iteration in the domain
5326 of the relation accesses I<all> elements in its image.
5327 The C<source_user> token is again used to identify
5328 the source access. The range of the source access relation
5329 C<source> should have the same dimension as the range
5330 of the sink access relation.
5331 The C<isl_access_info_free> function should usually not be
5332 called explicitly, because it is called implicitly by
5333 C<isl_access_info_compute_flow>.
5335 The result of the dependence analysis is collected in an
5336 C<isl_flow>. There may be elements of
5337 the sink access for which no preceding source access could be
5338 found or for which all preceding sources are I<may> accesses.
5339 The relations containing these elements can be obtained through
5340 calls to C<isl_flow_get_no_source>, the first with C<must> set
5341 and the second with C<must> unset.
5342 In the case of standard flow dependence analysis,
5343 with the sink a read and the sources I<must> writes,
5344 the first relation corresponds to the reads from uninitialized
5345 array elements and the second relation is empty.
5346 The actual flow dependences can be extracted using
5347 C<isl_flow_foreach>. This function will call the user-specified
5348 callback function C<fn> for each B<non-empty> dependence between
5349 a source and the sink. The callback function is called
5350 with four arguments, the actual flow dependence relation
5351 mapping source iterations to sink iterations, a boolean that
5352 indicates whether it is a I<must> or I<may> dependence, a token
5353 identifying the source and an additional C<void *> with value
5354 equal to the third argument of the C<isl_flow_foreach> call.
5355 A dependence is marked I<must> if it originates from a I<must>
5356 source and if it is not followed by any I<may> sources.
5358 After finishing with an C<isl_flow>, the user should call
5359 C<isl_flow_free> to free all associated memory.
5361 A higher-level interface to dependence analysis is provided
5362 by the following function.
5364 #include <isl/flow.h>
5366 int isl_union_map_compute_flow(__isl_take isl_union_map *sink,
5367 __isl_take isl_union_map *must_source,
5368 __isl_take isl_union_map *may_source,
5369 __isl_take isl_union_map *schedule,
5370 __isl_give isl_union_map **must_dep,
5371 __isl_give isl_union_map **may_dep,
5372 __isl_give isl_union_map **must_no_source,
5373 __isl_give isl_union_map **may_no_source);
5375 The arrays are identified by the tuple names of the ranges
5376 of the accesses. The iteration domains by the tuple names
5377 of the domains of the accesses and of the schedule.
5378 The relative order of the iteration domains is given by the
5379 schedule. The relations returned through C<must_no_source>
5380 and C<may_no_source> are subsets of C<sink>.
5381 Any of C<must_dep>, C<may_dep>, C<must_no_source>
5382 or C<may_no_source> may be C<NULL>, but a C<NULL> value for
5383 any of the other arguments is treated as an error.
5385 =head3 Interaction with Dependence Analysis
5387 During the dependence analysis, we frequently need to perform
5388 the following operation. Given a relation between sink iterations
5389 and potential source iterations from a particular source domain,
5390 what is the last potential source iteration corresponding to each
5391 sink iteration. It can sometimes be convenient to adjust
5392 the set of potential source iterations before or after each such operation.
5393 The prototypical example is fuzzy array dataflow analysis,
5394 where we need to analyze if, based on data-dependent constraints,
5395 the sink iteration can ever be executed without one or more of
5396 the corresponding potential source iterations being executed.
5397 If so, we can introduce extra parameters and select an unknown
5398 but fixed source iteration from the potential source iterations.
5399 To be able to perform such manipulations, C<isl> provides the following
5402 #include <isl/flow.h>
5404 typedef __isl_give isl_restriction *(*isl_access_restrict)(
5405 __isl_keep isl_map *source_map,
5406 __isl_keep isl_set *sink, void *source_user,
5408 __isl_give isl_access_info *isl_access_info_set_restrict(
5409 __isl_take isl_access_info *acc,
5410 isl_access_restrict fn, void *user);
5412 The function C<isl_access_info_set_restrict> should be called
5413 before calling C<isl_access_info_compute_flow> and registers a callback function
5414 that will be called any time C<isl> is about to compute the last
5415 potential source. The first argument is the (reverse) proto-dependence,
5416 mapping sink iterations to potential source iterations.
5417 The second argument represents the sink iterations for which
5418 we want to compute the last source iteration.
5419 The third argument is the token corresponding to the source
5420 and the final argument is the token passed to C<isl_access_info_set_restrict>.
5421 The callback is expected to return a restriction on either the input or
5422 the output of the operation computing the last potential source.
5423 If the input needs to be restricted then restrictions are needed
5424 for both the source and the sink iterations. The sink iterations
5425 and the potential source iterations will be intersected with these sets.
5426 If the output needs to be restricted then only a restriction on the source
5427 iterations is required.
5428 If any error occurs, the callback should return C<NULL>.
5429 An C<isl_restriction> object can be created, freed and inspected
5430 using the following functions.
5432 #include <isl/flow.h>
5434 __isl_give isl_restriction *isl_restriction_input(
5435 __isl_take isl_set *source_restr,
5436 __isl_take isl_set *sink_restr);
5437 __isl_give isl_restriction *isl_restriction_output(
5438 __isl_take isl_set *source_restr);
5439 __isl_give isl_restriction *isl_restriction_none(
5440 __isl_take isl_map *source_map);
5441 __isl_give isl_restriction *isl_restriction_empty(
5442 __isl_take isl_map *source_map);
5443 void *isl_restriction_free(
5444 __isl_take isl_restriction *restr);
5445 isl_ctx *isl_restriction_get_ctx(
5446 __isl_keep isl_restriction *restr);
5448 C<isl_restriction_none> and C<isl_restriction_empty> are special
5449 cases of C<isl_restriction_input>. C<isl_restriction_none>
5450 is essentially equivalent to
5452 isl_restriction_input(isl_set_universe(
5453 isl_space_range(isl_map_get_space(source_map))),
5455 isl_space_domain(isl_map_get_space(source_map))));
5457 whereas C<isl_restriction_empty> is essentially equivalent to
5459 isl_restriction_input(isl_set_empty(
5460 isl_space_range(isl_map_get_space(source_map))),
5462 isl_space_domain(isl_map_get_space(source_map))));
5466 B<The functionality described in this section is fairly new
5467 and may be subject to change.>
5469 The following function can be used to compute a schedule
5470 for a union of domains.
5471 By default, the algorithm used to construct the schedule is similar
5472 to that of C<Pluto>.
5473 Alternatively, Feautrier's multi-dimensional scheduling algorithm can
5475 The generated schedule respects all C<validity> dependences.
5476 That is, all dependence distances over these dependences in the
5477 scheduled space are lexicographically positive.
5478 The default algorithm tries to minimize the dependence distances over
5479 C<proximity> dependences.
5480 Moreover, it tries to obtain sequences (bands) of schedule dimensions
5481 for groups of domains where the dependence distances have only
5482 non-negative values.
5483 When using Feautrier's algorithm, the C<proximity> dependence
5484 distances are only minimized during the extension to a
5485 full-dimensional schedule.
5487 #include <isl/schedule.h>
5488 __isl_give isl_schedule *isl_union_set_compute_schedule(
5489 __isl_take isl_union_set *domain,
5490 __isl_take isl_union_map *validity,
5491 __isl_take isl_union_map *proximity);
5492 void *isl_schedule_free(__isl_take isl_schedule *sched);
5494 A mapping from the domains to the scheduled space can be obtained
5495 from an C<isl_schedule> using the following function.
5497 __isl_give isl_union_map *isl_schedule_get_map(
5498 __isl_keep isl_schedule *sched);
5500 A representation of the schedule can be printed using
5502 __isl_give isl_printer *isl_printer_print_schedule(
5503 __isl_take isl_printer *p,
5504 __isl_keep isl_schedule *schedule);
5506 A representation of the schedule as a forest of bands can be obtained
5507 using the following function.
5509 __isl_give isl_band_list *isl_schedule_get_band_forest(
5510 __isl_keep isl_schedule *schedule);
5512 The individual bands can be visited in depth-first post-order
5513 using the following function.
5515 #include <isl/schedule.h>
5516 int isl_schedule_foreach_band(
5517 __isl_keep isl_schedule *sched,
5518 int (*fn)(__isl_keep isl_band *band, void *user),
5521 The list can be manipulated as explained in L<"Lists">.
5522 The bands inside the list can be copied and freed using the following
5525 #include <isl/band.h>
5526 __isl_give isl_band *isl_band_copy(
5527 __isl_keep isl_band *band);
5528 void *isl_band_free(__isl_take isl_band *band);
5530 Each band contains zero or more scheduling dimensions.
5531 These are referred to as the members of the band.
5532 The section of the schedule that corresponds to the band is
5533 referred to as the partial schedule of the band.
5534 For those nodes that participate in a band, the outer scheduling
5535 dimensions form the prefix schedule, while the inner scheduling
5536 dimensions form the suffix schedule.
5537 That is, if we take a cut of the band forest, then the union of
5538 the concatenations of the prefix, partial and suffix schedules of
5539 each band in the cut is equal to the entire schedule (modulo
5540 some possible padding at the end with zero scheduling dimensions).
5541 The properties of a band can be inspected using the following functions.
5543 #include <isl/band.h>
5544 isl_ctx *isl_band_get_ctx(__isl_keep isl_band *band);
5546 int isl_band_has_children(__isl_keep isl_band *band);
5547 __isl_give isl_band_list *isl_band_get_children(
5548 __isl_keep isl_band *band);
5550 __isl_give isl_union_map *isl_band_get_prefix_schedule(
5551 __isl_keep isl_band *band);
5552 __isl_give isl_union_map *isl_band_get_partial_schedule(
5553 __isl_keep isl_band *band);
5554 __isl_give isl_union_map *isl_band_get_suffix_schedule(
5555 __isl_keep isl_band *band);
5557 int isl_band_n_member(__isl_keep isl_band *band);
5558 int isl_band_member_is_zero_distance(
5559 __isl_keep isl_band *band, int pos);
5561 int isl_band_list_foreach_band(
5562 __isl_keep isl_band_list *list,
5563 int (*fn)(__isl_keep isl_band *band, void *user),
5566 Note that a scheduling dimension is considered to be ``zero
5567 distance'' if it does not carry any proximity dependences
5569 That is, if the dependence distances of the proximity
5570 dependences are all zero in that direction (for fixed
5571 iterations of outer bands).
5572 Like C<isl_schedule_foreach_band>,
5573 the function C<isl_band_list_foreach_band> calls C<fn> on the bands
5574 in depth-first post-order.
5576 A band can be tiled using the following function.
5578 #include <isl/band.h>
5579 int isl_band_tile(__isl_keep isl_band *band,
5580 __isl_take isl_vec *sizes);
5582 int isl_options_set_tile_scale_tile_loops(isl_ctx *ctx,
5584 int isl_options_get_tile_scale_tile_loops(isl_ctx *ctx);
5585 int isl_options_set_tile_shift_point_loops(isl_ctx *ctx,
5587 int isl_options_get_tile_shift_point_loops(isl_ctx *ctx);
5589 The C<isl_band_tile> function tiles the band using the given tile sizes
5590 inside its schedule.
5591 A new child band is created to represent the point loops and it is
5592 inserted between the modified band and its children.
5593 The C<tile_scale_tile_loops> option specifies whether the tile
5594 loops iterators should be scaled by the tile sizes.
5595 If the C<tile_shift_point_loops> option is set, then the point loops
5596 are shifted to start at zero.
5598 A band can be split into two nested bands using the following function.
5600 int isl_band_split(__isl_keep isl_band *band, int pos);
5602 The resulting outer band contains the first C<pos> dimensions of C<band>
5603 while the inner band contains the remaining dimensions.
5605 A representation of the band can be printed using
5607 #include <isl/band.h>
5608 __isl_give isl_printer *isl_printer_print_band(
5609 __isl_take isl_printer *p,
5610 __isl_keep isl_band *band);
5614 #include <isl/schedule.h>
5615 int isl_options_set_schedule_max_coefficient(
5616 isl_ctx *ctx, int val);
5617 int isl_options_get_schedule_max_coefficient(
5619 int isl_options_set_schedule_max_constant_term(
5620 isl_ctx *ctx, int val);
5621 int isl_options_get_schedule_max_constant_term(
5623 int isl_options_set_schedule_fuse(isl_ctx *ctx, int val);
5624 int isl_options_get_schedule_fuse(isl_ctx *ctx);
5625 int isl_options_set_schedule_maximize_band_depth(
5626 isl_ctx *ctx, int val);
5627 int isl_options_get_schedule_maximize_band_depth(
5629 int isl_options_set_schedule_outer_zero_distance(
5630 isl_ctx *ctx, int val);
5631 int isl_options_get_schedule_outer_zero_distance(
5633 int isl_options_set_schedule_split_scaled(
5634 isl_ctx *ctx, int val);
5635 int isl_options_get_schedule_split_scaled(
5637 int isl_options_set_schedule_algorithm(
5638 isl_ctx *ctx, int val);
5639 int isl_options_get_schedule_algorithm(
5641 int isl_options_set_schedule_separate_components(
5642 isl_ctx *ctx, int val);
5643 int isl_options_get_schedule_separate_components(
5648 =item * schedule_max_coefficient
5650 This option enforces that the coefficients for variable and parameter
5651 dimensions in the calculated schedule are not larger than the specified value.
5652 This option can significantly increase the speed of the scheduling calculation
5653 and may also prevent fusing of unrelated dimensions. A value of -1 means that
5654 this option does not introduce bounds on the variable or parameter
5657 =item * schedule_max_constant_term
5659 This option enforces that the constant coefficients in the calculated schedule
5660 are not larger than the maximal constant term. This option can significantly
5661 increase the speed of the scheduling calculation and may also prevent fusing of
5662 unrelated dimensions. A value of -1 means that this option does not introduce
5663 bounds on the constant coefficients.
5665 =item * schedule_fuse
5667 This option controls the level of fusion.
5668 If this option is set to C<ISL_SCHEDULE_FUSE_MIN>, then loops in the
5669 resulting schedule will be distributed as much as possible.
5670 If this option is set to C<ISL_SCHEDULE_FUSE_MAX>, then C<isl> will
5671 try to fuse loops in the resulting schedule.
5673 =item * schedule_maximize_band_depth
5675 If this option is set, we do not split bands at the point
5676 where we detect splitting is necessary. Instead, we
5677 backtrack and split bands as early as possible. This
5678 reduces the number of splits and maximizes the width of
5679 the bands. Wider bands give more possibilities for tiling.
5680 Note that if the C<schedule_fuse> option is set to C<ISL_SCHEDULE_FUSE_MIN>,
5681 then bands will be split as early as possible, even if there is no need.
5682 The C<schedule_maximize_band_depth> option therefore has no effect in this case.
5684 =item * schedule_outer_zero_distance
5686 If this option is set, then we try to construct schedules
5687 where the outermost scheduling dimension in each band
5688 results in a zero dependence distance over the proximity
5691 =item * schedule_split_scaled
5693 If this option is set, then we try to construct schedules in which the
5694 constant term is split off from the linear part if the linear parts of
5695 the scheduling rows for all nodes in the graphs have a common non-trivial
5697 The constant term is then placed in a separate band and the linear
5700 =item * schedule_algorithm
5702 Selects the scheduling algorithm to be used.
5703 Available scheduling algorithms are C<ISL_SCHEDULE_ALGORITHM_ISL>
5704 and C<ISL_SCHEDULE_ALGORITHM_FEAUTRIER>.
5706 =item * schedule_separate_components
5708 If at any point the dependence graph contains any (weakly connected) components,
5709 then these components are scheduled separately.
5710 If this option is not set, then some iterations of the domains
5711 in these components may be scheduled together.
5712 If this option is set, then the components are given consecutive
5717 =head2 AST Generation
5719 This section describes the C<isl> functionality for generating
5720 ASTs that visit all the elements
5721 in a domain in an order specified by a schedule.
5722 In particular, given a C<isl_union_map>, an AST is generated
5723 that visits all the elements in the domain of the C<isl_union_map>
5724 according to the lexicographic order of the corresponding image
5725 element(s). If the range of the C<isl_union_map> consists of
5726 elements in more than one space, then each of these spaces is handled
5727 separately in an arbitrary order.
5728 It should be noted that the image elements only specify the I<order>
5729 in which the corresponding domain elements should be visited.
5730 No direct relation between the image elements and the loop iterators
5731 in the generated AST should be assumed.
5733 Each AST is generated within a build. The initial build
5734 simply specifies the constraints on the parameters (if any)
5735 and can be created, inspected, copied and freed using the following functions.
5737 #include <isl/ast_build.h>
5738 __isl_give isl_ast_build *isl_ast_build_from_context(
5739 __isl_take isl_set *set);
5740 isl_ctx *isl_ast_build_get_ctx(
5741 __isl_keep isl_ast_build *build);
5742 __isl_give isl_ast_build *isl_ast_build_copy(
5743 __isl_keep isl_ast_build *build);
5744 void *isl_ast_build_free(
5745 __isl_take isl_ast_build *build);
5747 The C<set> argument is usually a parameter set with zero or more parameters.
5748 More C<isl_ast_build> functions are described in L</"Nested AST Generation">
5749 and L</"Fine-grained Control over AST Generation">.
5750 Finally, the AST itself can be constructed using the following
5753 #include <isl/ast_build.h>
5754 __isl_give isl_ast_node *isl_ast_build_ast_from_schedule(
5755 __isl_keep isl_ast_build *build,
5756 __isl_take isl_union_map *schedule);
5758 =head3 Inspecting the AST
5760 The basic properties of an AST node can be obtained as follows.
5762 #include <isl/ast.h>
5763 isl_ctx *isl_ast_node_get_ctx(
5764 __isl_keep isl_ast_node *node);
5765 enum isl_ast_node_type isl_ast_node_get_type(
5766 __isl_keep isl_ast_node *node);
5768 The type of an AST node is one of
5769 C<isl_ast_node_for>,
5771 C<isl_ast_node_block> or
5772 C<isl_ast_node_user>.
5773 An C<isl_ast_node_for> represents a for node.
5774 An C<isl_ast_node_if> represents an if node.
5775 An C<isl_ast_node_block> represents a compound node.
5776 An C<isl_ast_node_user> represents an expression statement.
5777 An expression statement typically corresponds to a domain element, i.e.,
5778 one of the elements that is visited by the AST.
5780 Each type of node has its own additional properties.
5782 #include <isl/ast.h>
5783 __isl_give isl_ast_expr *isl_ast_node_for_get_iterator(
5784 __isl_keep isl_ast_node *node);
5785 __isl_give isl_ast_expr *isl_ast_node_for_get_init(
5786 __isl_keep isl_ast_node *node);
5787 __isl_give isl_ast_expr *isl_ast_node_for_get_cond(
5788 __isl_keep isl_ast_node *node);
5789 __isl_give isl_ast_expr *isl_ast_node_for_get_inc(
5790 __isl_keep isl_ast_node *node);
5791 __isl_give isl_ast_node *isl_ast_node_for_get_body(
5792 __isl_keep isl_ast_node *node);
5793 int isl_ast_node_for_is_degenerate(
5794 __isl_keep isl_ast_node *node);
5796 An C<isl_ast_for> is considered degenerate if it is known to execute
5799 #include <isl/ast.h>
5800 __isl_give isl_ast_expr *isl_ast_node_if_get_cond(
5801 __isl_keep isl_ast_node *node);
5802 __isl_give isl_ast_node *isl_ast_node_if_get_then(
5803 __isl_keep isl_ast_node *node);
5804 int isl_ast_node_if_has_else(
5805 __isl_keep isl_ast_node *node);
5806 __isl_give isl_ast_node *isl_ast_node_if_get_else(
5807 __isl_keep isl_ast_node *node);
5809 __isl_give isl_ast_node_list *
5810 isl_ast_node_block_get_children(
5811 __isl_keep isl_ast_node *node);
5813 __isl_give isl_ast_expr *isl_ast_node_user_get_expr(
5814 __isl_keep isl_ast_node *node);
5816 Each of the returned C<isl_ast_expr>s can in turn be inspected using
5817 the following functions.
5819 #include <isl/ast.h>
5820 isl_ctx *isl_ast_expr_get_ctx(
5821 __isl_keep isl_ast_expr *expr);
5822 enum isl_ast_expr_type isl_ast_expr_get_type(
5823 __isl_keep isl_ast_expr *expr);
5825 The type of an AST expression is one of
5827 C<isl_ast_expr_id> or
5828 C<isl_ast_expr_int>.
5829 An C<isl_ast_expr_op> represents the result of an operation.
5830 An C<isl_ast_expr_id> represents an identifier.
5831 An C<isl_ast_expr_int> represents an integer value.
5833 Each type of expression has its own additional properties.
5835 #include <isl/ast.h>
5836 enum isl_ast_op_type isl_ast_expr_get_op_type(
5837 __isl_keep isl_ast_expr *expr);
5838 int isl_ast_expr_get_op_n_arg(__isl_keep isl_ast_expr *expr);
5839 __isl_give isl_ast_expr *isl_ast_expr_get_op_arg(
5840 __isl_keep isl_ast_expr *expr, int pos);
5841 int isl_ast_node_foreach_ast_op_type(
5842 __isl_keep isl_ast_node *node,
5843 int (*fn)(enum isl_ast_op_type type, void *user),
5846 C<isl_ast_expr_get_op_type> returns the type of the operation
5847 performed. C<isl_ast_expr_get_op_n_arg> returns the number of
5848 arguments. C<isl_ast_expr_get_op_arg> returns the specified
5850 C<isl_ast_node_foreach_ast_op_type> calls C<fn> for each distinct
5851 C<isl_ast_op_type> that appears in C<node>.
5852 The operation type is one of the following.
5856 =item C<isl_ast_op_and>
5858 Logical I<and> of two arguments.
5859 Both arguments can be evaluated.
5861 =item C<isl_ast_op_and_then>
5863 Logical I<and> of two arguments.
5864 The second argument can only be evaluated if the first evaluates to true.
5866 =item C<isl_ast_op_or>
5868 Logical I<or> of two arguments.
5869 Both arguments can be evaluated.
5871 =item C<isl_ast_op_or_else>
5873 Logical I<or> of two arguments.
5874 The second argument can only be evaluated if the first evaluates to false.
5876 =item C<isl_ast_op_max>
5878 Maximum of two or more arguments.
5880 =item C<isl_ast_op_min>
5882 Minimum of two or more arguments.
5884 =item C<isl_ast_op_minus>
5888 =item C<isl_ast_op_add>
5890 Sum of two arguments.
5892 =item C<isl_ast_op_sub>
5894 Difference of two arguments.
5896 =item C<isl_ast_op_mul>
5898 Product of two arguments.
5900 =item C<isl_ast_op_div>
5902 Exact division. That is, the result is known to be an integer.
5904 =item C<isl_ast_op_fdiv_q>
5906 Result of integer division, rounded towards negative
5909 =item C<isl_ast_op_pdiv_q>
5911 Result of integer division, where dividend is known to be non-negative.
5913 =item C<isl_ast_op_pdiv_r>
5915 Remainder of integer division, where dividend is known to be non-negative.
5917 =item C<isl_ast_op_cond>
5919 Conditional operator defined on three arguments.
5920 If the first argument evaluates to true, then the result
5921 is equal to the second argument. Otherwise, the result
5922 is equal to the third argument.
5923 The second and third argument may only be evaluated if
5924 the first argument evaluates to true and false, respectively.
5925 Corresponds to C<a ? b : c> in C.
5927 =item C<isl_ast_op_select>
5929 Conditional operator defined on three arguments.
5930 If the first argument evaluates to true, then the result
5931 is equal to the second argument. Otherwise, the result
5932 is equal to the third argument.
5933 The second and third argument may be evaluated independently
5934 of the value of the first argument.
5935 Corresponds to C<a * b + (1 - a) * c> in C.
5937 =item C<isl_ast_op_eq>
5941 =item C<isl_ast_op_le>
5943 Less than or equal relation.
5945 =item C<isl_ast_op_lt>
5949 =item C<isl_ast_op_ge>
5951 Greater than or equal relation.
5953 =item C<isl_ast_op_gt>
5955 Greater than relation.
5957 =item C<isl_ast_op_call>
5960 The number of arguments of the C<isl_ast_expr> is one more than
5961 the number of arguments in the function call, the first argument
5962 representing the function being called.
5966 #include <isl/ast.h>
5967 __isl_give isl_id *isl_ast_expr_get_id(
5968 __isl_keep isl_ast_expr *expr);
5970 Return the identifier represented by the AST expression.
5972 #include <isl/ast.h>
5973 int isl_ast_expr_get_int(__isl_keep isl_ast_expr *expr,
5976 Return the integer represented by the AST expression.
5977 Note that the integer is returned through the C<v> argument.
5978 The return value of the function itself indicates whether the
5979 operation was performed successfully.
5981 =head3 Manipulating and printing the AST
5983 AST nodes can be copied and freed using the following functions.
5985 #include <isl/ast.h>
5986 __isl_give isl_ast_node *isl_ast_node_copy(
5987 __isl_keep isl_ast_node *node);
5988 void *isl_ast_node_free(__isl_take isl_ast_node *node);
5990 AST expressions can be copied and freed using the following functions.
5992 #include <isl/ast.h>
5993 __isl_give isl_ast_expr *isl_ast_expr_copy(
5994 __isl_keep isl_ast_expr *expr);
5995 void *isl_ast_expr_free(__isl_take isl_ast_expr *expr);
5997 New AST expressions can be created either directly or within
5998 the context of an C<isl_ast_build>.
6000 #include <isl/ast.h>
6001 __isl_give isl_ast_expr *isl_ast_expr_from_id(
6002 __isl_take isl_id *id);
6003 __isl_give isl_ast_expr *isl_ast_expr_neg(
6004 __isl_take isl_ast_expr *expr);
6005 __isl_give isl_ast_expr *isl_ast_expr_add(
6006 __isl_take isl_ast_expr *expr1,
6007 __isl_take isl_ast_expr *expr2);
6008 __isl_give isl_ast_expr *isl_ast_expr_sub(
6009 __isl_take isl_ast_expr *expr1,
6010 __isl_take isl_ast_expr *expr2);
6011 __isl_give isl_ast_expr *isl_ast_expr_mul(
6012 __isl_take isl_ast_expr *expr1,
6013 __isl_take isl_ast_expr *expr2);
6014 __isl_give isl_ast_expr *isl_ast_expr_div(
6015 __isl_take isl_ast_expr *expr1,
6016 __isl_take isl_ast_expr *expr2);
6017 __isl_give isl_ast_expr *isl_ast_expr_and(
6018 __isl_take isl_ast_expr *expr1,
6019 __isl_take isl_ast_expr *expr2)
6020 __isl_give isl_ast_expr *isl_ast_expr_or(
6021 __isl_take isl_ast_expr *expr1,
6022 __isl_take isl_ast_expr *expr2)
6024 #include <isl/ast_build.h>
6025 __isl_give isl_ast_expr *isl_ast_build_expr_from_pw_aff(
6026 __isl_keep isl_ast_build *build,
6027 __isl_take isl_pw_aff *pa);
6028 __isl_give isl_ast_expr *
6029 isl_ast_build_call_from_pw_multi_aff(
6030 __isl_keep isl_ast_build *build,
6031 __isl_take isl_pw_multi_aff *pma);
6033 The domains of C<pa> and C<pma> should correspond
6034 to the schedule space of C<build>.
6035 The tuple id of C<pma> is used as the function being called.
6037 User specified data can be attached to an C<isl_ast_node> and obtained
6038 from the same C<isl_ast_node> using the following functions.
6040 #include <isl/ast.h>
6041 __isl_give isl_ast_node *isl_ast_node_set_annotation(
6042 __isl_take isl_ast_node *node,
6043 __isl_take isl_id *annotation);
6044 __isl_give isl_id *isl_ast_node_get_annotation(
6045 __isl_keep isl_ast_node *node);
6047 Basic printing can be performed using the following functions.
6049 #include <isl/ast.h>
6050 __isl_give isl_printer *isl_printer_print_ast_expr(
6051 __isl_take isl_printer *p,
6052 __isl_keep isl_ast_expr *expr);
6053 __isl_give isl_printer *isl_printer_print_ast_node(
6054 __isl_take isl_printer *p,
6055 __isl_keep isl_ast_node *node);
6057 More advanced printing can be performed using the following functions.
6059 #include <isl/ast.h>
6060 __isl_give isl_printer *isl_ast_op_type_print_macro(
6061 enum isl_ast_op_type type,
6062 __isl_take isl_printer *p);
6063 __isl_give isl_printer *isl_ast_node_print_macros(
6064 __isl_keep isl_ast_node *node,
6065 __isl_take isl_printer *p);
6066 __isl_give isl_printer *isl_ast_node_print(
6067 __isl_keep isl_ast_node *node,
6068 __isl_take isl_printer *p,
6069 __isl_take isl_ast_print_options *options);
6070 __isl_give isl_printer *isl_ast_node_for_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_if_print(
6075 __isl_keep isl_ast_node *node,
6076 __isl_take isl_printer *p,
6077 __isl_take isl_ast_print_options *options);
6079 While printing an C<isl_ast_node> in C<ISL_FORMAT_C>,
6080 C<isl> may print out an AST that makes use of macros such
6081 as C<floord>, C<min> and C<max>.
6082 C<isl_ast_op_type_print_macro> prints out the macro
6083 corresponding to a specific C<isl_ast_op_type>.
6084 C<isl_ast_node_print_macros> scans the C<isl_ast_node>
6085 for expressions where these macros would be used and prints
6086 out the required macro definitions.
6087 Essentially, C<isl_ast_node_print_macros> calls
6088 C<isl_ast_node_foreach_ast_op_type> with C<isl_ast_op_type_print_macro>
6089 as function argument.
6090 C<isl_ast_node_print>, C<isl_ast_node_for_print> and
6091 C<isl_ast_node_if_print> print an C<isl_ast_node>
6092 in C<ISL_FORMAT_C>, but allow for some extra control
6093 through an C<isl_ast_print_options> object.
6094 This object can be created using the following functions.
6096 #include <isl/ast.h>
6097 __isl_give isl_ast_print_options *
6098 isl_ast_print_options_alloc(isl_ctx *ctx);
6099 __isl_give isl_ast_print_options *
6100 isl_ast_print_options_copy(
6101 __isl_keep isl_ast_print_options *options);
6102 void *isl_ast_print_options_free(
6103 __isl_take isl_ast_print_options *options);
6105 __isl_give isl_ast_print_options *
6106 isl_ast_print_options_set_print_user(
6107 __isl_take isl_ast_print_options *options,
6108 __isl_give isl_printer *(*print_user)(
6109 __isl_take isl_printer *p,
6110 __isl_take isl_ast_print_options *options,
6111 __isl_keep isl_ast_node *node, void *user),
6113 __isl_give isl_ast_print_options *
6114 isl_ast_print_options_set_print_for(
6115 __isl_take isl_ast_print_options *options,
6116 __isl_give isl_printer *(*print_for)(
6117 __isl_take isl_printer *p,
6118 __isl_take isl_ast_print_options *options,
6119 __isl_keep isl_ast_node *node, void *user),
6122 The callback set by C<isl_ast_print_options_set_print_user>
6123 is called whenever a node of type C<isl_ast_node_user> needs to
6125 The callback set by C<isl_ast_print_options_set_print_for>
6126 is called whenever a node of type C<isl_ast_node_for> needs to
6128 Note that C<isl_ast_node_for_print> will I<not> call the
6129 callback set by C<isl_ast_print_options_set_print_for> on the node
6130 on which C<isl_ast_node_for_print> is called, but only on nested
6131 nodes of type C<isl_ast_node_for>. It is therefore safe to
6132 call C<isl_ast_node_for_print> from within the callback set by
6133 C<isl_ast_print_options_set_print_for>.
6135 The following option determines the type to be used for iterators
6136 while printing the AST.
6138 int isl_options_set_ast_iterator_type(
6139 isl_ctx *ctx, const char *val);
6140 const char *isl_options_get_ast_iterator_type(
6145 #include <isl/ast_build.h>
6146 int isl_options_set_ast_build_atomic_upper_bound(
6147 isl_ctx *ctx, int val);
6148 int isl_options_get_ast_build_atomic_upper_bound(
6150 int isl_options_set_ast_build_prefer_pdiv(isl_ctx *ctx,
6152 int isl_options_get_ast_build_prefer_pdiv(isl_ctx *ctx);
6153 int isl_options_set_ast_build_exploit_nested_bounds(
6154 isl_ctx *ctx, int val);
6155 int isl_options_get_ast_build_exploit_nested_bounds(
6157 int isl_options_set_ast_build_group_coscheduled(
6158 isl_ctx *ctx, int val);
6159 int isl_options_get_ast_build_group_coscheduled(
6161 int isl_options_set_ast_build_scale_strides(
6162 isl_ctx *ctx, int val);
6163 int isl_options_get_ast_build_scale_strides(
6165 int isl_options_set_ast_build_allow_else(isl_ctx *ctx,
6167 int isl_options_get_ast_build_allow_else(isl_ctx *ctx);
6168 int isl_options_set_ast_build_allow_or(isl_ctx *ctx,
6170 int isl_options_get_ast_build_allow_or(isl_ctx *ctx);
6174 =item * ast_build_atomic_upper_bound
6176 Generate loop upper bounds that consist of the current loop iterator,
6177 an operator and an expression not involving the iterator.
6178 If this option is not set, then the current loop iterator may appear
6179 several times in the upper bound.
6180 For example, when this option is turned off, AST generation
6183 [n] -> { A[i] -> [i] : 0 <= i <= 100, n }
6187 for (int c0 = 0; c0 <= 100 && n >= c0; c0 += 1)
6190 When the option is turned on, the following AST is generated
6192 for (int c0 = 0; c0 <= min(100, n); c0 += 1)
6195 =item * ast_build_prefer_pdiv
6197 If this option is turned off, then the AST generation will
6198 produce ASTs that may only contain C<isl_ast_op_fdiv_q>
6199 operators, but no C<isl_ast_op_pdiv_q> or
6200 C<isl_ast_op_pdiv_r> operators.
6201 If this options is turned on, then C<isl> will try to convert
6202 some of the C<isl_ast_op_fdiv_q> operators to (expressions containing)
6203 C<isl_ast_op_pdiv_q> or C<isl_ast_op_pdiv_r> operators.
6205 =item * ast_build_exploit_nested_bounds
6207 Simplify conditions based on bounds of nested for loops.
6208 In particular, remove conditions that are implied by the fact
6209 that one or more nested loops have at least one iteration,
6210 meaning that the upper bound is at least as large as the lower bound.
6211 For example, when this option is turned off, AST generation
6214 [N,M] -> { A[i,j] -> [i,j] : 0 <= i <= N and
6220 for (int c0 = 0; c0 <= N; c0 += 1)
6221 for (int c1 = 0; c1 <= M; c1 += 1)
6224 When the option is turned on, the following AST is generated
6226 for (int c0 = 0; c0 <= N; c0 += 1)
6227 for (int c1 = 0; c1 <= M; c1 += 1)
6230 =item * ast_build_group_coscheduled
6232 If two domain elements are assigned the same schedule point, then
6233 they may be executed in any order and they may even appear in different
6234 loops. If this options is set, then the AST generator will make
6235 sure that coscheduled domain elements do not appear in separate parts
6236 of the AST. This is useful in case of nested AST generation
6237 if the outer AST generation is given only part of a schedule
6238 and the inner AST generation should handle the domains that are
6239 coscheduled by this initial part of the schedule together.
6240 For example if an AST is generated for a schedule
6242 { A[i] -> [0]; B[i] -> [0] }
6244 then the C<isl_ast_build_set_create_leaf> callback described
6245 below may get called twice, once for each domain.
6246 Setting this option ensures that the callback is only called once
6247 on both domains together.
6249 =item * ast_build_separation_bounds
6251 This option specifies which bounds to use during separation.
6252 If this option is set to C<ISL_AST_BUILD_SEPARATION_BOUNDS_IMPLICIT>
6253 then all (possibly implicit) bounds on the current dimension will
6254 be used during separation.
6255 If this option is set to C<ISL_AST_BUILD_SEPARATION_BOUNDS_EXPLICIT>
6256 then only those bounds that are explicitly available will
6257 be used during separation.
6259 =item * ast_build_scale_strides
6261 This option specifies whether the AST generator is allowed
6262 to scale down iterators of strided loops.
6264 =item * ast_build_allow_else
6266 This option specifies whether the AST generator is allowed
6267 to construct if statements with else branches.
6269 =item * ast_build_allow_or
6271 This option specifies whether the AST generator is allowed
6272 to construct if conditions with disjunctions.
6276 =head3 Fine-grained Control over AST Generation
6278 Besides specifying the constraints on the parameters,
6279 an C<isl_ast_build> object can be used to control
6280 various aspects of the AST generation process.
6281 The most prominent way of control is through ``options'',
6282 which can be set using the following function.
6284 #include <isl/ast_build.h>
6285 __isl_give isl_ast_build *
6286 isl_ast_build_set_options(
6287 __isl_take isl_ast_build *control,
6288 __isl_take isl_union_map *options);
6290 The options are encoded in an <isl_union_map>.
6291 The domain of this union relation refers to the schedule domain,
6292 i.e., the range of the schedule passed to C<isl_ast_build_ast_from_schedule>.
6293 In the case of nested AST generation (see L</"Nested AST Generation">),
6294 the domain of C<options> should refer to the extra piece of the schedule.
6295 That is, it should be equal to the range of the wrapped relation in the
6296 range of the schedule.
6297 The range of the options can consist of elements in one or more spaces,
6298 the names of which determine the effect of the option.
6299 The values of the range typically also refer to the schedule dimension
6300 to which the option applies. In case of nested AST generation
6301 (see L</"Nested AST Generation">), these values refer to the position
6302 of the schedule dimension within the innermost AST generation.
6303 The constraints on the domain elements of
6304 the option should only refer to this dimension and earlier dimensions.
6305 We consider the following spaces.
6309 =item C<separation_class>
6311 This space is a wrapped relation between two one dimensional spaces.
6312 The input space represents the schedule dimension to which the option
6313 applies and the output space represents the separation class.
6314 While constructing a loop corresponding to the specified schedule
6315 dimension(s), the AST generator will try to generate separate loops
6316 for domain elements that are assigned different classes.
6317 If only some of the elements are assigned a class, then those elements
6318 that are not assigned any class will be treated as belonging to a class
6319 that is separate from the explicitly assigned classes.
6320 The typical use case for this option is to separate full tiles from
6322 The other options, described below, are applied after the separation
6325 As an example, consider the separation into full and partial tiles
6326 of a tiling of a triangular domain.
6327 Take, for example, the domain
6329 { A[i,j] : 0 <= i,j and i + j <= 100 }
6331 and a tiling into tiles of 10 by 10. The input to the AST generator
6332 is then the schedule
6334 { A[i,j] -> [([i/10]),[j/10],i,j] : 0 <= i,j and
6337 Without any options, the following AST is generated
6339 for (int c0 = 0; c0 <= 10; c0 += 1)
6340 for (int c1 = 0; c1 <= -c0 + 10; c1 += 1)
6341 for (int c2 = 10 * c0;
6342 c2 <= min(-10 * c1 + 100, 10 * c0 + 9);
6344 for (int c3 = 10 * c1;
6345 c3 <= min(10 * c1 + 9, -c2 + 100);
6349 Separation into full and partial tiles can be obtained by assigning
6350 a class, say C<0>, to the full tiles. The full tiles are represented by those
6351 values of the first and second schedule dimensions for which there are
6352 values of the third and fourth dimensions to cover an entire tile.
6353 That is, we need to specify the following option
6355 { [a,b,c,d] -> separation_class[[0]->[0]] :
6356 exists b': 0 <= 10a,10b' and
6357 10a+9+10b'+9 <= 100;
6358 [a,b,c,d] -> separation_class[[1]->[0]] :
6359 0 <= 10a,10b and 10a+9+10b+9 <= 100 }
6363 { [a, b, c, d] -> separation_class[[1] -> [0]] :
6364 a >= 0 and b >= 0 and b <= 8 - a;
6365 [a, b, c, d] -> separation_class[[0] -> [0]] :
6368 With this option, the generated AST is as follows
6371 for (int c0 = 0; c0 <= 8; c0 += 1) {
6372 for (int c1 = 0; c1 <= -c0 + 8; c1 += 1)
6373 for (int c2 = 10 * c0;
6374 c2 <= 10 * c0 + 9; c2 += 1)
6375 for (int c3 = 10 * c1;
6376 c3 <= 10 * c1 + 9; c3 += 1)
6378 for (int c1 = -c0 + 9; c1 <= -c0 + 10; c1 += 1)
6379 for (int c2 = 10 * c0;
6380 c2 <= min(-10 * c1 + 100, 10 * c0 + 9);
6382 for (int c3 = 10 * c1;
6383 c3 <= min(-c2 + 100, 10 * c1 + 9);
6387 for (int c0 = 9; c0 <= 10; c0 += 1)
6388 for (int c1 = 0; c1 <= -c0 + 10; c1 += 1)
6389 for (int c2 = 10 * c0;
6390 c2 <= min(-10 * c1 + 100, 10 * c0 + 9);
6392 for (int c3 = 10 * c1;
6393 c3 <= min(10 * c1 + 9, -c2 + 100);
6400 This is a single-dimensional space representing the schedule dimension(s)
6401 to which ``separation'' should be applied. Separation tries to split
6402 a loop into several pieces if this can avoid the generation of guards
6404 See also the C<atomic> option.
6408 This is a single-dimensional space representing the schedule dimension(s)
6409 for which the domains should be considered ``atomic''. That is, the
6410 AST generator will make sure that any given domain space will only appear
6411 in a single loop at the specified level.
6413 Consider the following schedule
6415 { a[i] -> [i] : 0 <= i < 10;
6416 b[i] -> [i+1] : 0 <= i < 10 }
6418 If the following option is specified
6420 { [i] -> separate[x] }
6422 then the following AST will be generated
6426 for (int c0 = 1; c0 <= 9; c0 += 1) {
6433 If, on the other hand, the following option is specified
6435 { [i] -> atomic[x] }
6437 then the following AST will be generated
6439 for (int c0 = 0; c0 <= 10; c0 += 1) {
6446 If neither C<atomic> nor C<separate> is specified, then the AST generator
6447 may produce either of these two results or some intermediate form.
6451 This is a single-dimensional space representing the schedule dimension(s)
6452 that should be I<completely> unrolled.
6453 To obtain a partial unrolling, the user should apply an additional
6454 strip-mining to the schedule and fully unroll the inner loop.
6458 Additional control is available through the following functions.
6460 #include <isl/ast_build.h>
6461 __isl_give isl_ast_build *
6462 isl_ast_build_set_iterators(
6463 __isl_take isl_ast_build *control,
6464 __isl_take isl_id_list *iterators);
6466 The function C<isl_ast_build_set_iterators> allows the user to
6467 specify a list of iterator C<isl_id>s to be used as iterators.
6468 If the input schedule is injective, then
6469 the number of elements in this list should be as large as the dimension
6470 of the schedule space, but no direct correspondence should be assumed
6471 between dimensions and elements.
6472 If the input schedule is not injective, then an additional number
6473 of C<isl_id>s equal to the largest dimension of the input domains
6475 If the number of provided C<isl_id>s is insufficient, then additional
6476 names are automatically generated.
6478 #include <isl/ast_build.h>
6479 __isl_give isl_ast_build *
6480 isl_ast_build_set_create_leaf(
6481 __isl_take isl_ast_build *control,
6482 __isl_give isl_ast_node *(*fn)(
6483 __isl_take isl_ast_build *build,
6484 void *user), void *user);
6487 C<isl_ast_build_set_create_leaf> function allows for the
6488 specification of a callback that should be called whenever the AST
6489 generator arrives at an element of the schedule domain.
6490 The callback should return an AST node that should be inserted
6491 at the corresponding position of the AST. The default action (when
6492 the callback is not set) is to continue generating parts of the AST to scan
6493 all the domain elements associated to the schedule domain element
6494 and to insert user nodes, ``calling'' the domain element, for each of them.
6495 The C<build> argument contains the current state of the C<isl_ast_build>.
6496 To ease nested AST generation (see L</"Nested AST Generation">),
6497 all control information that is
6498 specific to the current AST generation such as the options and
6499 the callbacks has been removed from this C<isl_ast_build>.
6500 The callback would typically return the result of a nested
6502 user defined node created using the following function.
6504 #include <isl/ast.h>
6505 __isl_give isl_ast_node *isl_ast_node_alloc_user(
6506 __isl_take isl_ast_expr *expr);
6508 #include <isl/ast_build.h>
6509 __isl_give isl_ast_build *
6510 isl_ast_build_set_at_each_domain(
6511 __isl_take isl_ast_build *build,
6512 __isl_give isl_ast_node *(*fn)(
6513 __isl_take isl_ast_node *node,
6514 __isl_keep isl_ast_build *build,
6515 void *user), void *user);
6516 __isl_give isl_ast_build *
6517 isl_ast_build_set_before_each_for(
6518 __isl_take isl_ast_build *build,
6519 __isl_give isl_id *(*fn)(
6520 __isl_keep isl_ast_build *build,
6521 void *user), void *user);
6522 __isl_give isl_ast_build *
6523 isl_ast_build_set_after_each_for(
6524 __isl_take isl_ast_build *build,
6525 __isl_give isl_ast_node *(*fn)(
6526 __isl_take isl_ast_node *node,
6527 __isl_keep isl_ast_build *build,
6528 void *user), void *user);
6530 The callback set by C<isl_ast_build_set_at_each_domain> will
6531 be called for each domain AST node.
6532 The callbacks set by C<isl_ast_build_set_before_each_for>
6533 and C<isl_ast_build_set_after_each_for> will be called
6534 for each for AST node. The first will be called in depth-first
6535 pre-order, while the second will be called in depth-first post-order.
6536 Since C<isl_ast_build_set_before_each_for> is called before the for
6537 node is actually constructed, it is only passed an C<isl_ast_build>.
6538 The returned C<isl_id> will be added as an annotation (using
6539 C<isl_ast_node_set_annotation>) to the constructed for node.
6540 In particular, if the user has also specified an C<after_each_for>
6541 callback, then the annotation can be retrieved from the node passed to
6542 that callback using C<isl_ast_node_get_annotation>.
6543 All callbacks should C<NULL> on failure.
6544 The given C<isl_ast_build> can be used to create new
6545 C<isl_ast_expr> objects using C<isl_ast_build_expr_from_pw_aff>
6546 or C<isl_ast_build_call_from_pw_multi_aff>.
6548 =head3 Nested AST Generation
6550 C<isl> allows the user to create an AST within the context
6551 of another AST. These nested ASTs are created using the
6552 same C<isl_ast_build_ast_from_schedule> function that is used to create the
6553 outer AST. The C<build> argument should be an C<isl_ast_build>
6554 passed to a callback set by
6555 C<isl_ast_build_set_create_leaf>.
6556 The space of the range of the C<schedule> argument should refer
6557 to this build. In particular, the space should be a wrapped
6558 relation and the domain of this wrapped relation should be the
6559 same as that of the range of the schedule returned by
6560 C<isl_ast_build_get_schedule> below.
6561 In practice, the new schedule is typically
6562 created by calling C<isl_union_map_range_product> on the old schedule
6563 and some extra piece of the schedule.
6564 The space of the schedule domain is also available from
6565 the C<isl_ast_build>.
6567 #include <isl/ast_build.h>
6568 __isl_give isl_union_map *isl_ast_build_get_schedule(
6569 __isl_keep isl_ast_build *build);
6570 __isl_give isl_space *isl_ast_build_get_schedule_space(
6571 __isl_keep isl_ast_build *build);
6572 __isl_give isl_ast_build *isl_ast_build_restrict(
6573 __isl_take isl_ast_build *build,
6574 __isl_take isl_set *set);
6576 The C<isl_ast_build_get_schedule> function returns a (partial)
6577 schedule for the domains elements for which part of the AST still needs to
6578 be generated in the current build.
6579 In particular, the domain elements are mapped to those iterations of the loops
6580 enclosing the current point of the AST generation inside which
6581 the domain elements are executed.
6582 No direct correspondence between
6583 the input schedule and this schedule should be assumed.
6584 The space obtained from C<isl_ast_build_get_schedule_space> can be used
6585 to create a set for C<isl_ast_build_restrict> to intersect
6586 with the current build. In particular, the set passed to
6587 C<isl_ast_build_restrict> can have additional parameters.
6588 The ids of the set dimensions in the space returned by
6589 C<isl_ast_build_get_schedule_space> correspond to the
6590 iterators of the already generated loops.
6591 The user should not rely on the ids of the output dimensions
6592 of the relations in the union relation returned by
6593 C<isl_ast_build_get_schedule> having any particular value.
6597 Although C<isl> is mainly meant to be used as a library,
6598 it also contains some basic applications that use some
6599 of the functionality of C<isl>.
6600 The input may be specified in either the L<isl format>
6601 or the L<PolyLib format>.
6603 =head2 C<isl_polyhedron_sample>
6605 C<isl_polyhedron_sample> takes a polyhedron as input and prints
6606 an integer element of the polyhedron, if there is any.
6607 The first column in the output is the denominator and is always
6608 equal to 1. If the polyhedron contains no integer points,
6609 then a vector of length zero is printed.
6613 C<isl_pip> takes the same input as the C<example> program
6614 from the C<piplib> distribution, i.e., a set of constraints
6615 on the parameters, a line containing only -1 and finally a set
6616 of constraints on a parametric polyhedron.
6617 The coefficients of the parameters appear in the last columns
6618 (but before the final constant column).
6619 The output is the lexicographic minimum of the parametric polyhedron.
6620 As C<isl> currently does not have its own output format, the output
6621 is just a dump of the internal state.
6623 =head2 C<isl_polyhedron_minimize>
6625 C<isl_polyhedron_minimize> computes the minimum of some linear
6626 or affine objective function over the integer points in a polyhedron.
6627 If an affine objective function
6628 is given, then the constant should appear in the last column.
6630 =head2 C<isl_polytope_scan>
6632 Given a polytope, C<isl_polytope_scan> prints
6633 all integer points in the polytope.
6635 =head2 C<isl_codegen>
6637 Given a schedule, a context set and an options relation,
6638 C<isl_codegen> prints out an AST that scans the domain elements
6639 of the schedule in the order of their image(s) taking into account
6640 the constraints in the context set.