3 C<isl> is a thread-safe C library for manipulating
4 sets and relations of integer points bounded by affine constraints.
5 The descriptions of the sets and relations may involve
6 both parameters and existentially quantified variables.
7 All computations are performed in exact integer arithmetic
9 The C<isl> library offers functionality that is similar
10 to that offered by the C<Omega> and C<Omega+> libraries,
11 but the underlying algorithms are in most cases completely different.
13 The library is by no means complete and some fairly basic
14 functionality is still missing.
15 Still, even in its current form, the library has been successfully
16 used as a backend polyhedral library for the polyhedral
17 scanner C<CLooG> and as part of an equivalence checker of
18 static affine programs.
19 For bug reports, feature requests and questions,
20 visit the the discussion group at
21 L<http://groups.google.com/group/isl-development>.
23 =head2 Backward Incompatible Changes
25 =head3 Changes since isl-0.02
29 =item * The old printing functions have been deprecated
30 and replaced by C<isl_printer> functions, see L<Input and Output>.
32 =item * Most functions related to dependence analysis have acquired
33 an extra C<must> argument. To obtain the old behavior, this argument
34 should be given the value 1. See L<Dependence Analysis>.
38 =head3 Changes since isl-0.03
42 =item * The function C<isl_pw_qpolynomial_fold_add> has been
43 renamed to C<isl_pw_qpolynomial_fold_fold>.
44 Similarly, C<isl_union_pw_qpolynomial_fold_add> has been
45 renamed to C<isl_union_pw_qpolynomial_fold_fold>.
49 =head3 Changes since isl-0.04
53 =item * All header files have been renamed from C<isl_header.h>
58 =head3 Changes since isl-0.05
62 =item * The functions C<isl_printer_print_basic_set> and
63 C<isl_printer_print_basic_map> no longer print a newline.
65 =item * The functions C<isl_flow_get_no_source>
66 and C<isl_union_map_compute_flow> now return
67 the accesses for which no source could be found instead of
68 the iterations where those accesses occur.
70 =item * The functions C<isl_basic_map_identity> and
71 C<isl_map_identity> now take a B<map> space as input. An old call
72 C<isl_map_identity(space)> can be rewritten to
73 C<isl_map_identity(isl_space_map_from_set(space))>.
75 =item * The function C<isl_map_power> no longer takes
76 a parameter position as input. Instead, the exponent
77 is now expressed as the domain of the resulting relation.
81 =head3 Changes since isl-0.06
85 =item * The format of C<isl_printer_print_qpolynomial>'s
86 C<ISL_FORMAT_ISL> output has changed.
87 Use C<ISL_FORMAT_C> to obtain the old output.
89 =item * The C<*_fast_*> functions have been renamed to C<*_plain_*>.
90 Some of the old names have been kept for backward compatibility,
91 but they will be removed in the future.
95 =head3 Changes since isl-0.07
99 =item * The function C<isl_pw_aff_max> has been renamed to
100 C<isl_pw_aff_union_max>.
101 Similarly, the function C<isl_pw_aff_add> has been renamed to
102 C<isl_pw_aff_union_add>.
104 =item * The C<isl_dim> type has been renamed to C<isl_space>
105 along with the associated functions.
106 Some of the old names have been kept for backward compatibility,
107 but they will be removed in the future.
109 =item * Spaces of maps, sets and parameter domains are now
110 treated differently. The distinction between map spaces and set spaces
111 has always been made on a conceptual level, but proper use of such spaces
112 was never checked. Furthermore, up until isl-0.07 there was no way
113 of explicitly creating a parameter space. These can now be created
114 directly using C<isl_space_params_alloc> or from other spaces using
117 =item * The space in which C<isl_aff>, C<isl_pw_aff>, C<isl_qpolynomial>,
118 C<isl_pw_qpolynomial>, C<isl_qpolynomial_fold> and C<isl_pw_qpolynomial_fold>
119 objects live is now a map space
120 instead of a set space. This means, for example, that the dimensions
121 of the domain of an C<isl_aff> are now considered to be of type
122 C<isl_dim_in> instead of C<isl_dim_set>. Extra functions have been
123 added to obtain the domain space. Some of the constructors still
124 take a domain space and have therefore been renamed.
126 =item * The functions C<isl_equality_alloc> and C<isl_inequality_alloc>
127 now take an C<isl_local_space> instead of an C<isl_space>.
128 An C<isl_local_space> can be created from an C<isl_space>
129 using C<isl_local_space_from_space>.
131 =item * The C<isl_div> type has been removed. Functions that used
132 to return an C<isl_div> now return an C<isl_aff>.
133 Note that the space of an C<isl_aff> is that of relation.
134 When replacing a call to C<isl_div_get_coefficient> by a call to
135 C<isl_aff_get_coefficient> any C<isl_dim_set> argument needs
136 to be replaced by C<isl_dim_in>.
137 A call to C<isl_aff_from_div> can be replaced by a call
139 A call to C<isl_qpolynomial_div(div)> call be replaced by
142 isl_qpolynomial_from_aff(isl_aff_floor(div))
144 The function C<isl_constraint_div> has also been renamed
145 to C<isl_constraint_get_div>.
147 =item * The C<nparam> argument has been removed from
148 C<isl_map_read_from_str> and similar functions.
149 When reading input in the original PolyLib format,
150 the result will have no parameters.
151 If parameters are expected, the caller may want to perform
152 dimension manipulation on the result.
156 =head3 Changes since isl-0.09
160 =item * The C<schedule_split_parallel> option has been replaced
161 by the C<schedule_split_scaled> option.
163 =item * The first argument of C<isl_pw_aff_cond> is now
164 an C<isl_pw_aff> instead of an C<isl_set>.
165 A call C<isl_pw_aff_cond(a, b, c)> can be replaced by
167 isl_pw_aff_cond(isl_set_indicator_function(a), b, c)
171 =head3 Changes since isl-0.10
175 =item * The functions C<isl_set_dim_has_lower_bound> and
176 C<isl_set_dim_has_upper_bound> have been renamed to
177 C<isl_set_dim_has_any_lower_bound> and
178 C<isl_set_dim_has_any_upper_bound>.
179 The new C<isl_set_dim_has_lower_bound> and
180 C<isl_set_dim_has_upper_bound> have slightly different meanings.
186 C<isl> is released under the MIT license.
190 Permission is hereby granted, free of charge, to any person obtaining a copy of
191 this software and associated documentation files (the "Software"), to deal in
192 the Software without restriction, including without limitation the rights to
193 use, copy, modify, merge, publish, distribute, sublicense, and/or sell copies
194 of the Software, and to permit persons to whom the Software is furnished to do
195 so, subject to the following conditions:
197 The above copyright notice and this permission notice shall be included in all
198 copies or substantial portions of the Software.
200 THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
201 IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
202 FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
203 AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
204 LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
205 OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
210 Note that C<isl> currently requires C<GMP>, which is released
211 under the GNU Lesser General Public License (LGPL). This means
212 that code linked against C<isl> is also linked against LGPL code.
216 The source of C<isl> can be obtained either as a tarball
217 or from the git repository. Both are available from
218 L<http://freshmeat.net/projects/isl/>.
219 The installation process depends on how you obtained
222 =head2 Installation from the git repository
226 =item 1 Clone or update the repository
228 The first time the source is obtained, you need to clone
231 git clone git://repo.or.cz/isl.git
233 To obtain updates, you need to pull in the latest changes
237 =item 2 Generate C<configure>
243 After performing the above steps, continue
244 with the L<Common installation instructions>.
246 =head2 Common installation instructions
250 =item 1 Obtain C<GMP>
252 Building C<isl> requires C<GMP>, including its headers files.
253 Your distribution may not provide these header files by default
254 and you may need to install a package called C<gmp-devel> or something
255 similar. Alternatively, C<GMP> can be built from
256 source, available from L<http://gmplib.org/>.
260 C<isl> uses the standard C<autoconf> C<configure> script.
265 optionally followed by some configure options.
266 A complete list of options can be obtained by running
270 Below we discuss some of the more common options.
272 C<isl> can optionally use C<piplib>, but no
273 C<piplib> functionality is currently used by default.
274 The C<--with-piplib> option can
275 be used to specify which C<piplib>
276 library to use, either an installed version (C<system>),
277 an externally built version (C<build>)
278 or no version (C<no>). The option C<build> is mostly useful
279 in C<configure> scripts of larger projects that bundle both C<isl>
286 Installation prefix for C<isl>
288 =item C<--with-gmp-prefix>
290 Installation prefix for C<GMP> (architecture-independent files).
292 =item C<--with-gmp-exec-prefix>
294 Installation prefix for C<GMP> (architecture-dependent files).
296 =item C<--with-piplib>
298 Which copy of C<piplib> to use, either C<no> (default), C<system> or C<build>.
300 =item C<--with-piplib-prefix>
302 Installation prefix for C<system> C<piplib> (architecture-independent files).
304 =item C<--with-piplib-exec-prefix>
306 Installation prefix for C<system> C<piplib> (architecture-dependent files).
308 =item C<--with-piplib-builddir>
310 Location where C<build> C<piplib> was built.
318 =item 4 Install (optional)
324 =head1 Integer Set Library
326 =head2 Initialization
328 All manipulations of integer sets and relations occur within
329 the context of an C<isl_ctx>.
330 A given C<isl_ctx> can only be used within a single thread.
331 All arguments of a function are required to have been allocated
332 within the same context.
333 There are currently no functions available for moving an object
334 from one C<isl_ctx> to another C<isl_ctx>. This means that
335 there is currently no way of safely moving an object from one
336 thread to another, unless the whole C<isl_ctx> is moved.
338 An C<isl_ctx> can be allocated using C<isl_ctx_alloc> and
339 freed using C<isl_ctx_free>.
340 All objects allocated within an C<isl_ctx> should be freed
341 before the C<isl_ctx> itself is freed.
343 isl_ctx *isl_ctx_alloc();
344 void isl_ctx_free(isl_ctx *ctx);
348 An C<isl_val> represents an integer value, a rational value
349 or one of three special values, infinity, negative infinity and NaN.
350 Some predefined values can be created using the following functions.
353 __isl_give isl_val *isl_val_zero(isl_ctx *ctx);
354 __isl_give isl_val *isl_val_one(isl_ctx *ctx);
355 __isl_give isl_val *isl_val_nan(isl_ctx *ctx);
356 __isl_give isl_val *isl_val_infty(isl_ctx *ctx);
357 __isl_give isl_val *isl_val_neginfty(isl_ctx *ctx);
359 Specific integer values can be created using the following functions.
362 __isl_give isl_val *isl_val_int_from_si(isl_ctx *ctx,
364 __isl_give isl_val *isl_val_int_from_ui(isl_ctx *ctx,
367 They can be copied and freed using the following functions.
370 __isl_give isl_val *isl_val_copy(__isl_keep isl_val *v);
371 void *isl_val_free(__isl_take isl_val *v);
373 They can be inspected using the following functions.
376 isl_ctx *isl_val_get_ctx(__isl_keep isl_val *val);
377 long isl_val_get_num_si(__isl_keep isl_val *v);
378 long isl_val_get_den_si(__isl_keep isl_val *v);
379 double isl_val_get_d(__isl_keep isl_val *v);
381 Note that C<isl_val_get_num_si>, C<isl_val_get_den_si> and
382 C<isl_val_get_d> can only be applied to rational values.
384 An C<isl_val> can be modified using the following function.
387 __isl_give isl_val *isl_val_set_si(__isl_take isl_val *v,
390 The following unary properties are defined on C<isl_val>s.
393 int isl_val_sgn(__isl_keep isl_val *v);
394 int isl_val_is_zero(__isl_keep isl_val *v);
395 int isl_val_is_one(__isl_keep isl_val *v);
396 int isl_val_is_negone(__isl_keep isl_val *v);
397 int isl_val_is_nonneg(__isl_keep isl_val *v);
398 int isl_val_is_nonpos(__isl_keep isl_val *v);
399 int isl_val_is_pos(__isl_keep isl_val *v);
400 int isl_val_is_neg(__isl_keep isl_val *v);
401 int isl_val_is_int(__isl_keep isl_val *v);
402 int isl_val_is_rat(__isl_keep isl_val *v);
403 int isl_val_is_nan(__isl_keep isl_val *v);
404 int isl_val_is_infty(__isl_keep isl_val *v);
405 int isl_val_is_neginfty(__isl_keep isl_val *v);
407 Note that the sign of NaN is undefined.
409 The following binary properties are defined on pairs of C<isl_val>s.
412 int isl_val_lt(__isl_keep isl_val *v1,
413 __isl_keep isl_val *v2);
414 int isl_val_le(__isl_keep isl_val *v1,
415 __isl_keep isl_val *v2);
416 int isl_val_gt(__isl_keep isl_val *v1,
417 __isl_keep isl_val *v2);
418 int isl_val_ge(__isl_keep isl_val *v1,
419 __isl_keep isl_val *v2);
420 int isl_val_eq(__isl_keep isl_val *v1,
421 __isl_keep isl_val *v2);
422 int isl_val_ne(__isl_keep isl_val *v1,
423 __isl_keep isl_val *v2);
425 For integer C<isl_val>s we additionally have the following binary property.
428 int isl_val_is_divisible_by(__isl_keep isl_val *v1,
429 __isl_keep isl_val *v2);
431 An C<isl_val> can also be compared to an integer using the following
432 function. The result is undefined for NaN.
435 int isl_val_cmp_si(__isl_keep isl_val *v, long i);
437 The following unary operations are available on C<isl_val>s.
440 __isl_give isl_val *isl_val_abs(__isl_take isl_val *v);
441 __isl_give isl_val *isl_val_neg(__isl_take isl_val *v);
442 __isl_give isl_val *isl_val_floor(__isl_take isl_val *v);
443 __isl_give isl_val *isl_val_ceil(__isl_take isl_val *v);
444 __isl_give isl_val *isl_val_trunc(__isl_take isl_val *v);
446 The following binary operations are available on C<isl_val>s.
449 __isl_give isl_val *isl_val_abs(__isl_take isl_val *v);
450 __isl_give isl_val *isl_val_neg(__isl_take isl_val *v);
451 __isl_give isl_val *isl_val_floor(__isl_take isl_val *v);
452 __isl_give isl_val *isl_val_ceil(__isl_take isl_val *v);
453 __isl_give isl_val *isl_val_trunc(__isl_take isl_val *v);
454 __isl_give isl_val *isl_val_2exp(__isl_take isl_val *v);
455 __isl_give isl_val *isl_val_min(__isl_take isl_val *v1,
456 __isl_take isl_val *v2);
457 __isl_give isl_val *isl_val_max(__isl_take isl_val *v1,
458 __isl_take isl_val *v2);
459 __isl_give isl_val *isl_val_add(__isl_take isl_val *v1,
460 __isl_take isl_val *v2);
461 __isl_give isl_val *isl_val_add_ui(__isl_take isl_val *v1,
463 __isl_give isl_val *isl_val_sub(__isl_take isl_val *v1,
464 __isl_take isl_val *v2);
465 __isl_give isl_val *isl_val_sub_ui(__isl_take isl_val *v1,
467 __isl_give isl_val *isl_val_mul(__isl_take isl_val *v1,
468 __isl_take isl_val *v2);
469 __isl_give isl_val *isl_val_mul_ui(__isl_take isl_val *v1,
471 __isl_give isl_val *isl_val_div(__isl_take isl_val *v1,
472 __isl_take isl_val *v2);
474 On integer values, we additionally have the following operations.
477 __isl_give isl_val *isl_val_2exp(__isl_take isl_val *v);
478 __isl_give isl_val *isl_val_mod(__isl_take isl_val *v1,
479 __isl_take isl_val *v2);
480 __isl_give isl_val *isl_val_gcd(__isl_take isl_val *v1,
481 __isl_take isl_val *v2);
482 __isl_give isl_val *isl_val_gcdext(__isl_take isl_val *v1,
483 __isl_take isl_val *v2, __isl_give isl_val **x,
484 __isl_give isl_val **y);
486 The function C<isl_val_gcdext> returns the greatest common divisor g
487 of C<v1> and C<v2> as well as two integers C<*x> and C<*y> such
488 that C<*x> * C<v1> + C<*y> * C<v2> = g.
490 A value can be read from input using
493 __isl_give isl_val *isl_val_read_from_str(isl_ctx *ctx,
496 A value can be printed using
499 __isl_give isl_printer *isl_printer_print_val(
500 __isl_take isl_printer *p, __isl_keep isl_val *v);
502 =head3 GMP specific functions
504 These functions are only available if C<isl> has been compiled with C<GMP>
507 Specific integer and rational values can be created from C<GMP> values using
508 the following functions.
510 #include <isl/val_gmp.h>
511 __isl_give isl_val *isl_val_int_from_gmp(isl_ctx *ctx,
513 __isl_give isl_val *isl_val_from_gmp(isl_ctx *ctx,
514 const mpz_t n, const mpz_t d);
516 The numerator and denominator of a rational value can be extracted as
517 C<GMP> values using the following functions.
519 #include <isl/val_gmp.h>
520 int isl_val_get_num_gmp(__isl_keep isl_val *v, mpz_t z);
521 int isl_val_get_den_gmp(__isl_keep isl_val *v, mpz_t z);
523 =head2 Integers (obsolescent)
525 All operations on integers, mainly the coefficients
526 of the constraints describing the sets and relations,
527 are performed in exact integer arithmetic using C<GMP>.
528 However, to allow future versions of C<isl> to optionally
529 support fixed integer arithmetic, all calls to C<GMP>
530 are wrapped inside C<isl> specific macros.
531 The basic type is C<isl_int> and the operations below
532 are available on this type.
533 The meanings of these operations are essentially the same
534 as their C<GMP> C<mpz_> counterparts.
535 As always with C<GMP> types, C<isl_int>s need to be
536 initialized with C<isl_int_init> before they can be used
537 and they need to be released with C<isl_int_clear>
539 The user should not assume that an C<isl_int> is represented
540 as a C<mpz_t>, but should instead explicitly convert between
541 C<mpz_t>s and C<isl_int>s using C<isl_int_set_gmp> and
542 C<isl_int_get_gmp> whenever a C<mpz_t> is required.
546 =item isl_int_init(i)
548 =item isl_int_clear(i)
550 =item isl_int_set(r,i)
552 =item isl_int_set_si(r,i)
554 =item isl_int_set_gmp(r,g)
556 =item isl_int_get_gmp(i,g)
558 =item isl_int_abs(r,i)
560 =item isl_int_neg(r,i)
562 =item isl_int_swap(i,j)
564 =item isl_int_swap_or_set(i,j)
566 =item isl_int_add_ui(r,i,j)
568 =item isl_int_sub_ui(r,i,j)
570 =item isl_int_add(r,i,j)
572 =item isl_int_sub(r,i,j)
574 =item isl_int_mul(r,i,j)
576 =item isl_int_mul_ui(r,i,j)
578 =item isl_int_addmul(r,i,j)
580 =item isl_int_submul(r,i,j)
582 =item isl_int_gcd(r,i,j)
584 =item isl_int_lcm(r,i,j)
586 =item isl_int_divexact(r,i,j)
588 =item isl_int_cdiv_q(r,i,j)
590 =item isl_int_fdiv_q(r,i,j)
592 =item isl_int_fdiv_r(r,i,j)
594 =item isl_int_fdiv_q_ui(r,i,j)
596 =item isl_int_read(r,s)
598 =item isl_int_print(out,i,width)
602 =item isl_int_cmp(i,j)
604 =item isl_int_cmp_si(i,si)
606 =item isl_int_eq(i,j)
608 =item isl_int_ne(i,j)
610 =item isl_int_lt(i,j)
612 =item isl_int_le(i,j)
614 =item isl_int_gt(i,j)
616 =item isl_int_ge(i,j)
618 =item isl_int_abs_eq(i,j)
620 =item isl_int_abs_ne(i,j)
622 =item isl_int_abs_lt(i,j)
624 =item isl_int_abs_gt(i,j)
626 =item isl_int_abs_ge(i,j)
628 =item isl_int_is_zero(i)
630 =item isl_int_is_one(i)
632 =item isl_int_is_negone(i)
634 =item isl_int_is_pos(i)
636 =item isl_int_is_neg(i)
638 =item isl_int_is_nonpos(i)
640 =item isl_int_is_nonneg(i)
642 =item isl_int_is_divisible_by(i,j)
646 =head2 Sets and Relations
648 C<isl> uses six types of objects for representing sets and relations,
649 C<isl_basic_set>, C<isl_basic_map>, C<isl_set>, C<isl_map>,
650 C<isl_union_set> and C<isl_union_map>.
651 C<isl_basic_set> and C<isl_basic_map> represent sets and relations that
652 can be described as a conjunction of affine constraints, while
653 C<isl_set> and C<isl_map> represent unions of
654 C<isl_basic_set>s and C<isl_basic_map>s, respectively.
655 However, all C<isl_basic_set>s or C<isl_basic_map>s in the union need
656 to live in the same space. C<isl_union_set>s and C<isl_union_map>s
657 represent unions of C<isl_set>s or C<isl_map>s in I<different> spaces,
658 where spaces are considered different if they have a different number
659 of dimensions and/or different names (see L<"Spaces">).
660 The difference between sets and relations (maps) is that sets have
661 one set of variables, while relations have two sets of variables,
662 input variables and output variables.
664 =head2 Memory Management
666 Since a high-level operation on sets and/or relations usually involves
667 several substeps and since the user is usually not interested in
668 the intermediate results, most functions that return a new object
669 will also release all the objects passed as arguments.
670 If the user still wants to use one or more of these arguments
671 after the function call, she should pass along a copy of the
672 object rather than the object itself.
673 The user is then responsible for making sure that the original
674 object gets used somewhere else or is explicitly freed.
676 The arguments and return values of all documented functions are
677 annotated to make clear which arguments are released and which
678 arguments are preserved. In particular, the following annotations
685 C<__isl_give> means that a new object is returned.
686 The user should make sure that the returned pointer is
687 used exactly once as a value for an C<__isl_take> argument.
688 In between, it can be used as a value for as many
689 C<__isl_keep> arguments as the user likes.
690 There is one exception, and that is the case where the
691 pointer returned is C<NULL>. Is this case, the user
692 is free to use it as an C<__isl_take> argument or not.
696 C<__isl_take> means that the object the argument points to
697 is taken over by the function and may no longer be used
698 by the user as an argument to any other function.
699 The pointer value must be one returned by a function
700 returning an C<__isl_give> pointer.
701 If the user passes in a C<NULL> value, then this will
702 be treated as an error in the sense that the function will
703 not perform its usual operation. However, it will still
704 make sure that all the other C<__isl_take> arguments
709 C<__isl_keep> means that the function will only use the object
710 temporarily. After the function has finished, the user
711 can still use it as an argument to other functions.
712 A C<NULL> value will be treated in the same way as
713 a C<NULL> value for an C<__isl_take> argument.
717 =head2 Error Handling
719 C<isl> supports different ways to react in case a runtime error is triggered.
720 Runtime errors arise, e.g., if a function such as C<isl_map_intersect> is called
721 with two maps that have incompatible spaces. There are three possible ways
722 to react on error: to warn, to continue or to abort.
724 The default behavior is to warn. In this mode, C<isl> prints a warning, stores
725 the last error in the corresponding C<isl_ctx> and the function in which the
726 error was triggered returns C<NULL>. An error does not corrupt internal state,
727 such that isl can continue to be used. C<isl> also provides functions to
728 read the last error and to reset the memory that stores the last error. The
729 last error is only stored for information purposes. Its presence does not
730 change the behavior of C<isl>. Hence, resetting an error is not required to
731 continue to use isl, but only to observe new errors.
734 enum isl_error isl_ctx_last_error(isl_ctx *ctx);
735 void isl_ctx_reset_error(isl_ctx *ctx);
737 Another option is to continue on error. This is similar to warn on error mode,
738 except that C<isl> does not print any warning. This allows a program to
739 implement its own error reporting.
741 The last option is to directly abort the execution of the program from within
742 the isl library. This makes it obviously impossible to recover from an error,
743 but it allows to directly spot the error location. By aborting on error,
744 debuggers break at the location the error occurred and can provide a stack
745 trace. Other tools that automatically provide stack traces on abort or that do
746 not want to continue execution after an error was triggered may also prefer to
749 The on error behavior of isl can be specified by calling
750 C<isl_options_set_on_error> or by setting the command line option
751 C<--isl-on-error>. Valid arguments for the function call are
752 C<ISL_ON_ERROR_WARN>, C<ISL_ON_ERROR_CONTINUE> and C<ISL_ON_ERROR_ABORT>. The
753 choices for the command line option are C<warn>, C<continue> and C<abort>.
754 It is also possible to query the current error mode.
756 #include <isl/options.h>
757 int isl_options_set_on_error(isl_ctx *ctx, int val);
758 int isl_options_get_on_error(isl_ctx *ctx);
762 Identifiers are used to identify both individual dimensions
763 and tuples of dimensions. They consist of an optional name and an optional
764 user pointer. The name and the user pointer cannot both be C<NULL>, however.
765 Identifiers with the same name but different pointer values
766 are considered to be distinct.
767 Similarly, identifiers with different names but the same pointer value
768 are also considered to be distinct.
769 Equal identifiers are represented using the same object.
770 Pairs of identifiers can therefore be tested for equality using the
772 Identifiers can be constructed, copied, freed, inspected and printed
773 using the following functions.
776 __isl_give isl_id *isl_id_alloc(isl_ctx *ctx,
777 __isl_keep const char *name, void *user);
778 __isl_give isl_id *isl_id_set_free_user(
779 __isl_take isl_id *id,
780 __isl_give void (*free_user)(void *user));
781 __isl_give isl_id *isl_id_copy(isl_id *id);
782 void *isl_id_free(__isl_take isl_id *id);
784 isl_ctx *isl_id_get_ctx(__isl_keep isl_id *id);
785 void *isl_id_get_user(__isl_keep isl_id *id);
786 __isl_keep const char *isl_id_get_name(__isl_keep isl_id *id);
788 __isl_give isl_printer *isl_printer_print_id(
789 __isl_take isl_printer *p, __isl_keep isl_id *id);
791 The callback set by C<isl_id_set_free_user> is called on the user
792 pointer when the last reference to the C<isl_id> is freed.
793 Note that C<isl_id_get_name> returns a pointer to some internal
794 data structure, so the result can only be used while the
795 corresponding C<isl_id> is alive.
799 Whenever a new set, relation or similiar object is created from scratch,
800 the space in which it lives needs to be specified using an C<isl_space>.
801 Each space involves zero or more parameters and zero, one or two
802 tuples of set or input/output dimensions. The parameters and dimensions
803 are identified by an C<isl_dim_type> and a position.
804 The type C<isl_dim_param> refers to parameters,
805 the type C<isl_dim_set> refers to set dimensions (for spaces
806 with a single tuple of dimensions) and the types C<isl_dim_in>
807 and C<isl_dim_out> refer to input and output dimensions
808 (for spaces with two tuples of dimensions).
809 Local spaces (see L</"Local Spaces">) also contain dimensions
810 of type C<isl_dim_div>.
811 Note that parameters are only identified by their position within
812 a given object. Across different objects, parameters are (usually)
813 identified by their names or identifiers. Only unnamed parameters
814 are identified by their positions across objects. The use of unnamed
815 parameters is discouraged.
817 #include <isl/space.h>
818 __isl_give isl_space *isl_space_alloc(isl_ctx *ctx,
819 unsigned nparam, unsigned n_in, unsigned n_out);
820 __isl_give isl_space *isl_space_params_alloc(isl_ctx *ctx,
822 __isl_give isl_space *isl_space_set_alloc(isl_ctx *ctx,
823 unsigned nparam, unsigned dim);
824 __isl_give isl_space *isl_space_copy(__isl_keep isl_space *space);
825 void *isl_space_free(__isl_take isl_space *space);
826 unsigned isl_space_dim(__isl_keep isl_space *space,
827 enum isl_dim_type type);
829 The space used for creating a parameter domain
830 needs to be created using C<isl_space_params_alloc>.
831 For other sets, the space
832 needs to be created using C<isl_space_set_alloc>, while
833 for a relation, the space
834 needs to be created using C<isl_space_alloc>.
835 C<isl_space_dim> can be used
836 to find out the number of dimensions of each type in
837 a space, where type may be
838 C<isl_dim_param>, C<isl_dim_in> (only for relations),
839 C<isl_dim_out> (only for relations), C<isl_dim_set>
840 (only for sets) or C<isl_dim_all>.
842 To check whether a given space is that of a set or a map
843 or whether it is a parameter space, use these functions:
845 #include <isl/space.h>
846 int isl_space_is_params(__isl_keep isl_space *space);
847 int isl_space_is_set(__isl_keep isl_space *space);
848 int isl_space_is_map(__isl_keep isl_space *space);
850 Spaces can be compared using the following functions:
852 #include <isl/space.h>
853 int isl_space_is_equal(__isl_keep isl_space *space1,
854 __isl_keep isl_space *space2);
855 int isl_space_is_domain(__isl_keep isl_space *space1,
856 __isl_keep isl_space *space2);
857 int isl_space_is_range(__isl_keep isl_space *space1,
858 __isl_keep isl_space *space2);
860 C<isl_space_is_domain> checks whether the first argument is equal
861 to the domain of the second argument. This requires in particular that
862 the first argument is a set space and that the second argument
865 It is often useful to create objects that live in the
866 same space as some other object. This can be accomplished
867 by creating the new objects
868 (see L<Creating New Sets and Relations> or
869 L<Creating New (Piecewise) Quasipolynomials>) based on the space
870 of the original object.
873 __isl_give isl_space *isl_basic_set_get_space(
874 __isl_keep isl_basic_set *bset);
875 __isl_give isl_space *isl_set_get_space(__isl_keep isl_set *set);
877 #include <isl/union_set.h>
878 __isl_give isl_space *isl_union_set_get_space(
879 __isl_keep isl_union_set *uset);
882 __isl_give isl_space *isl_basic_map_get_space(
883 __isl_keep isl_basic_map *bmap);
884 __isl_give isl_space *isl_map_get_space(__isl_keep isl_map *map);
886 #include <isl/union_map.h>
887 __isl_give isl_space *isl_union_map_get_space(
888 __isl_keep isl_union_map *umap);
890 #include <isl/constraint.h>
891 __isl_give isl_space *isl_constraint_get_space(
892 __isl_keep isl_constraint *constraint);
894 #include <isl/polynomial.h>
895 __isl_give isl_space *isl_qpolynomial_get_domain_space(
896 __isl_keep isl_qpolynomial *qp);
897 __isl_give isl_space *isl_qpolynomial_get_space(
898 __isl_keep isl_qpolynomial *qp);
899 __isl_give isl_space *isl_qpolynomial_fold_get_space(
900 __isl_keep isl_qpolynomial_fold *fold);
901 __isl_give isl_space *isl_pw_qpolynomial_get_domain_space(
902 __isl_keep isl_pw_qpolynomial *pwqp);
903 __isl_give isl_space *isl_pw_qpolynomial_get_space(
904 __isl_keep isl_pw_qpolynomial *pwqp);
905 __isl_give isl_space *isl_pw_qpolynomial_fold_get_domain_space(
906 __isl_keep isl_pw_qpolynomial_fold *pwf);
907 __isl_give isl_space *isl_pw_qpolynomial_fold_get_space(
908 __isl_keep isl_pw_qpolynomial_fold *pwf);
909 __isl_give isl_space *isl_union_pw_qpolynomial_get_space(
910 __isl_keep isl_union_pw_qpolynomial *upwqp);
911 __isl_give isl_space *isl_union_pw_qpolynomial_fold_get_space(
912 __isl_keep isl_union_pw_qpolynomial_fold *upwf);
915 __isl_give isl_space *isl_multi_val_get_space(
916 __isl_keep isl_multi_val *mv);
919 __isl_give isl_space *isl_aff_get_domain_space(
920 __isl_keep isl_aff *aff);
921 __isl_give isl_space *isl_aff_get_space(
922 __isl_keep isl_aff *aff);
923 __isl_give isl_space *isl_pw_aff_get_domain_space(
924 __isl_keep isl_pw_aff *pwaff);
925 __isl_give isl_space *isl_pw_aff_get_space(
926 __isl_keep isl_pw_aff *pwaff);
927 __isl_give isl_space *isl_multi_aff_get_domain_space(
928 __isl_keep isl_multi_aff *maff);
929 __isl_give isl_space *isl_multi_aff_get_space(
930 __isl_keep isl_multi_aff *maff);
931 __isl_give isl_space *isl_pw_multi_aff_get_domain_space(
932 __isl_keep isl_pw_multi_aff *pma);
933 __isl_give isl_space *isl_pw_multi_aff_get_space(
934 __isl_keep isl_pw_multi_aff *pma);
935 __isl_give isl_space *isl_union_pw_multi_aff_get_space(
936 __isl_keep isl_union_pw_multi_aff *upma);
937 __isl_give isl_space *isl_multi_pw_aff_get_domain_space(
938 __isl_keep isl_multi_pw_aff *mpa);
939 __isl_give isl_space *isl_multi_pw_aff_get_space(
940 __isl_keep isl_multi_pw_aff *mpa);
942 #include <isl/point.h>
943 __isl_give isl_space *isl_point_get_space(
944 __isl_keep isl_point *pnt);
946 The identifiers or names of the individual dimensions may be set or read off
947 using the following functions.
949 #include <isl/space.h>
950 __isl_give isl_space *isl_space_set_dim_id(
951 __isl_take isl_space *space,
952 enum isl_dim_type type, unsigned pos,
953 __isl_take isl_id *id);
954 int isl_space_has_dim_id(__isl_keep isl_space *space,
955 enum isl_dim_type type, unsigned pos);
956 __isl_give isl_id *isl_space_get_dim_id(
957 __isl_keep isl_space *space,
958 enum isl_dim_type type, unsigned pos);
959 __isl_give isl_space *isl_space_set_dim_name(
960 __isl_take isl_space *space,
961 enum isl_dim_type type, unsigned pos,
962 __isl_keep const char *name);
963 int isl_space_has_dim_name(__isl_keep isl_space *space,
964 enum isl_dim_type type, unsigned pos);
965 __isl_keep const char *isl_space_get_dim_name(
966 __isl_keep isl_space *space,
967 enum isl_dim_type type, unsigned pos);
969 Note that C<isl_space_get_name> returns a pointer to some internal
970 data structure, so the result can only be used while the
971 corresponding C<isl_space> is alive.
972 Also note that every function that operates on two sets or relations
973 requires that both arguments have the same parameters. This also
974 means that if one of the arguments has named parameters, then the
975 other needs to have named parameters too and the names need to match.
976 Pairs of C<isl_set>, C<isl_map>, C<isl_union_set> and/or C<isl_union_map>
977 arguments may have different parameters (as long as they are named),
978 in which case the result will have as parameters the union of the parameters of
981 Given the identifier or name of a dimension (typically a parameter),
982 its position can be obtained from the following function.
984 #include <isl/space.h>
985 int isl_space_find_dim_by_id(__isl_keep isl_space *space,
986 enum isl_dim_type type, __isl_keep isl_id *id);
987 int isl_space_find_dim_by_name(__isl_keep isl_space *space,
988 enum isl_dim_type type, const char *name);
990 The identifiers or names of entire spaces may be set or read off
991 using the following functions.
993 #include <isl/space.h>
994 __isl_give isl_space *isl_space_set_tuple_id(
995 __isl_take isl_space *space,
996 enum isl_dim_type type, __isl_take isl_id *id);
997 __isl_give isl_space *isl_space_reset_tuple_id(
998 __isl_take isl_space *space, enum isl_dim_type type);
999 int isl_space_has_tuple_id(__isl_keep isl_space *space,
1000 enum isl_dim_type type);
1001 __isl_give isl_id *isl_space_get_tuple_id(
1002 __isl_keep isl_space *space, enum isl_dim_type type);
1003 __isl_give isl_space *isl_space_set_tuple_name(
1004 __isl_take isl_space *space,
1005 enum isl_dim_type type, const char *s);
1006 int isl_space_has_tuple_name(__isl_keep isl_space *space,
1007 enum isl_dim_type type);
1008 const char *isl_space_get_tuple_name(__isl_keep isl_space *space,
1009 enum isl_dim_type type);
1011 The C<type> argument needs to be one of C<isl_dim_in>, C<isl_dim_out>
1012 or C<isl_dim_set>. As with C<isl_space_get_name>,
1013 the C<isl_space_get_tuple_name> function returns a pointer to some internal
1015 Binary operations require the corresponding spaces of their arguments
1016 to have the same name.
1018 Spaces can be nested. In particular, the domain of a set or
1019 the domain or range of a relation can be a nested relation.
1020 The following functions can be used to construct and deconstruct
1023 #include <isl/space.h>
1024 int isl_space_is_wrapping(__isl_keep isl_space *space);
1025 __isl_give isl_space *isl_space_wrap(__isl_take isl_space *space);
1026 __isl_give isl_space *isl_space_unwrap(__isl_take isl_space *space);
1028 The input to C<isl_space_is_wrapping> and C<isl_space_unwrap> should
1029 be the space of a set, while that of
1030 C<isl_space_wrap> should be the space of a relation.
1031 Conversely, the output of C<isl_space_unwrap> is the space
1032 of a relation, while that of C<isl_space_wrap> is the space of a set.
1034 Spaces can be created from other spaces
1035 using the following functions.
1037 __isl_give isl_space *isl_space_domain(__isl_take isl_space *space);
1038 __isl_give isl_space *isl_space_from_domain(__isl_take isl_space *space);
1039 __isl_give isl_space *isl_space_range(__isl_take isl_space *space);
1040 __isl_give isl_space *isl_space_from_range(__isl_take isl_space *space);
1041 __isl_give isl_space *isl_space_params(
1042 __isl_take isl_space *space);
1043 __isl_give isl_space *isl_space_set_from_params(
1044 __isl_take isl_space *space);
1045 __isl_give isl_space *isl_space_reverse(__isl_take isl_space *space);
1046 __isl_give isl_space *isl_space_join(__isl_take isl_space *left,
1047 __isl_take isl_space *right);
1048 __isl_give isl_space *isl_space_align_params(
1049 __isl_take isl_space *space1, __isl_take isl_space *space2)
1050 __isl_give isl_space *isl_space_insert_dims(__isl_take isl_space *space,
1051 enum isl_dim_type type, unsigned pos, unsigned n);
1052 __isl_give isl_space *isl_space_add_dims(__isl_take isl_space *space,
1053 enum isl_dim_type type, unsigned n);
1054 __isl_give isl_space *isl_space_drop_dims(__isl_take isl_space *space,
1055 enum isl_dim_type type, unsigned first, unsigned n);
1056 __isl_give isl_space *isl_space_move_dims(__isl_take isl_space *space,
1057 enum isl_dim_type dst_type, unsigned dst_pos,
1058 enum isl_dim_type src_type, unsigned src_pos,
1060 __isl_give isl_space *isl_space_map_from_set(
1061 __isl_take isl_space *space);
1062 __isl_give isl_space *isl_space_map_from_domain_and_range(
1063 __isl_take isl_space *domain,
1064 __isl_take isl_space *range);
1065 __isl_give isl_space *isl_space_zip(__isl_take isl_space *space);
1066 __isl_give isl_space *isl_space_curry(
1067 __isl_take isl_space *space);
1068 __isl_give isl_space *isl_space_uncurry(
1069 __isl_take isl_space *space);
1071 Note that if dimensions are added or removed from a space, then
1072 the name and the internal structure are lost.
1076 A local space is essentially a space with
1077 zero or more existentially quantified variables.
1078 The local space of a (constraint of a) basic set or relation can be obtained
1079 using the following functions.
1081 #include <isl/constraint.h>
1082 __isl_give isl_local_space *isl_constraint_get_local_space(
1083 __isl_keep isl_constraint *constraint);
1085 #include <isl/set.h>
1086 __isl_give isl_local_space *isl_basic_set_get_local_space(
1087 __isl_keep isl_basic_set *bset);
1089 #include <isl/map.h>
1090 __isl_give isl_local_space *isl_basic_map_get_local_space(
1091 __isl_keep isl_basic_map *bmap);
1093 A new local space can be created from a space using
1095 #include <isl/local_space.h>
1096 __isl_give isl_local_space *isl_local_space_from_space(
1097 __isl_take isl_space *space);
1099 They can be inspected, modified, copied and freed using the following functions.
1101 #include <isl/local_space.h>
1102 isl_ctx *isl_local_space_get_ctx(
1103 __isl_keep isl_local_space *ls);
1104 int isl_local_space_is_set(__isl_keep isl_local_space *ls);
1105 int isl_local_space_dim(__isl_keep isl_local_space *ls,
1106 enum isl_dim_type type);
1107 int isl_local_space_has_dim_id(
1108 __isl_keep isl_local_space *ls,
1109 enum isl_dim_type type, unsigned pos);
1110 __isl_give isl_id *isl_local_space_get_dim_id(
1111 __isl_keep isl_local_space *ls,
1112 enum isl_dim_type type, unsigned pos);
1113 int isl_local_space_has_dim_name(
1114 __isl_keep isl_local_space *ls,
1115 enum isl_dim_type type, unsigned pos)
1116 const char *isl_local_space_get_dim_name(
1117 __isl_keep isl_local_space *ls,
1118 enum isl_dim_type type, unsigned pos);
1119 __isl_give isl_local_space *isl_local_space_set_dim_name(
1120 __isl_take isl_local_space *ls,
1121 enum isl_dim_type type, unsigned pos, const char *s);
1122 __isl_give isl_local_space *isl_local_space_set_dim_id(
1123 __isl_take isl_local_space *ls,
1124 enum isl_dim_type type, unsigned pos,
1125 __isl_take isl_id *id);
1126 __isl_give isl_space *isl_local_space_get_space(
1127 __isl_keep isl_local_space *ls);
1128 __isl_give isl_aff *isl_local_space_get_div(
1129 __isl_keep isl_local_space *ls, int pos);
1130 __isl_give isl_local_space *isl_local_space_copy(
1131 __isl_keep isl_local_space *ls);
1132 void *isl_local_space_free(__isl_take isl_local_space *ls);
1134 Note that C<isl_local_space_get_div> can only be used on local spaces
1137 Two local spaces can be compared using
1139 int isl_local_space_is_equal(__isl_keep isl_local_space *ls1,
1140 __isl_keep isl_local_space *ls2);
1142 Local spaces can be created from other local spaces
1143 using the following functions.
1145 __isl_give isl_local_space *isl_local_space_domain(
1146 __isl_take isl_local_space *ls);
1147 __isl_give isl_local_space *isl_local_space_range(
1148 __isl_take isl_local_space *ls);
1149 __isl_give isl_local_space *isl_local_space_from_domain(
1150 __isl_take isl_local_space *ls);
1151 __isl_give isl_local_space *isl_local_space_intersect(
1152 __isl_take isl_local_space *ls1,
1153 __isl_take isl_local_space *ls2);
1154 __isl_give isl_local_space *isl_local_space_add_dims(
1155 __isl_take isl_local_space *ls,
1156 enum isl_dim_type type, unsigned n);
1157 __isl_give isl_local_space *isl_local_space_insert_dims(
1158 __isl_take isl_local_space *ls,
1159 enum isl_dim_type type, unsigned first, unsigned n);
1160 __isl_give isl_local_space *isl_local_space_drop_dims(
1161 __isl_take isl_local_space *ls,
1162 enum isl_dim_type type, unsigned first, unsigned n);
1164 =head2 Input and Output
1166 C<isl> supports its own input/output format, which is similar
1167 to the C<Omega> format, but also supports the C<PolyLib> format
1170 =head3 C<isl> format
1172 The C<isl> format is similar to that of C<Omega>, but has a different
1173 syntax for describing the parameters and allows for the definition
1174 of an existentially quantified variable as the integer division
1175 of an affine expression.
1176 For example, the set of integers C<i> between C<0> and C<n>
1177 such that C<i % 10 <= 6> can be described as
1179 [n] -> { [i] : exists (a = [i/10] : 0 <= i and i <= n and
1182 A set or relation can have several disjuncts, separated
1183 by the keyword C<or>. Each disjunct is either a conjunction
1184 of constraints or a projection (C<exists>) of a conjunction
1185 of constraints. The constraints are separated by the keyword
1188 =head3 C<PolyLib> format
1190 If the represented set is a union, then the first line
1191 contains a single number representing the number of disjuncts.
1192 Otherwise, a line containing the number C<1> is optional.
1194 Each disjunct is represented by a matrix of constraints.
1195 The first line contains two numbers representing
1196 the number of rows and columns,
1197 where the number of rows is equal to the number of constraints
1198 and the number of columns is equal to two plus the number of variables.
1199 The following lines contain the actual rows of the constraint matrix.
1200 In each row, the first column indicates whether the constraint
1201 is an equality (C<0>) or inequality (C<1>). The final column
1202 corresponds to the constant term.
1204 If the set is parametric, then the coefficients of the parameters
1205 appear in the last columns before the constant column.
1206 The coefficients of any existentially quantified variables appear
1207 between those of the set variables and those of the parameters.
1209 =head3 Extended C<PolyLib> format
1211 The extended C<PolyLib> format is nearly identical to the
1212 C<PolyLib> format. The only difference is that the line
1213 containing the number of rows and columns of a constraint matrix
1214 also contains four additional numbers:
1215 the number of output dimensions, the number of input dimensions,
1216 the number of local dimensions (i.e., the number of existentially
1217 quantified variables) and the number of parameters.
1218 For sets, the number of ``output'' dimensions is equal
1219 to the number of set dimensions, while the number of ``input''
1224 #include <isl/set.h>
1225 __isl_give isl_basic_set *isl_basic_set_read_from_file(
1226 isl_ctx *ctx, FILE *input);
1227 __isl_give isl_basic_set *isl_basic_set_read_from_str(
1228 isl_ctx *ctx, const char *str);
1229 __isl_give isl_set *isl_set_read_from_file(isl_ctx *ctx,
1231 __isl_give isl_set *isl_set_read_from_str(isl_ctx *ctx,
1234 #include <isl/map.h>
1235 __isl_give isl_basic_map *isl_basic_map_read_from_file(
1236 isl_ctx *ctx, FILE *input);
1237 __isl_give isl_basic_map *isl_basic_map_read_from_str(
1238 isl_ctx *ctx, const char *str);
1239 __isl_give isl_map *isl_map_read_from_file(
1240 isl_ctx *ctx, FILE *input);
1241 __isl_give isl_map *isl_map_read_from_str(isl_ctx *ctx,
1244 #include <isl/union_set.h>
1245 __isl_give isl_union_set *isl_union_set_read_from_file(
1246 isl_ctx *ctx, FILE *input);
1247 __isl_give isl_union_set *isl_union_set_read_from_str(
1248 isl_ctx *ctx, const char *str);
1250 #include <isl/union_map.h>
1251 __isl_give isl_union_map *isl_union_map_read_from_file(
1252 isl_ctx *ctx, FILE *input);
1253 __isl_give isl_union_map *isl_union_map_read_from_str(
1254 isl_ctx *ctx, const char *str);
1256 The input format is autodetected and may be either the C<PolyLib> format
1257 or the C<isl> format.
1261 Before anything can be printed, an C<isl_printer> needs to
1264 __isl_give isl_printer *isl_printer_to_file(isl_ctx *ctx,
1266 __isl_give isl_printer *isl_printer_to_str(isl_ctx *ctx);
1267 void *isl_printer_free(__isl_take isl_printer *printer);
1268 __isl_give char *isl_printer_get_str(
1269 __isl_keep isl_printer *printer);
1271 The printer can be inspected using the following functions.
1273 FILE *isl_printer_get_file(
1274 __isl_keep isl_printer *printer);
1275 int isl_printer_get_output_format(
1276 __isl_keep isl_printer *p);
1278 The behavior of the printer can be modified in various ways
1280 __isl_give isl_printer *isl_printer_set_output_format(
1281 __isl_take isl_printer *p, int output_format);
1282 __isl_give isl_printer *isl_printer_set_indent(
1283 __isl_take isl_printer *p, int indent);
1284 __isl_give isl_printer *isl_printer_indent(
1285 __isl_take isl_printer *p, int indent);
1286 __isl_give isl_printer *isl_printer_set_prefix(
1287 __isl_take isl_printer *p, const char *prefix);
1288 __isl_give isl_printer *isl_printer_set_suffix(
1289 __isl_take isl_printer *p, const char *suffix);
1291 The C<output_format> may be either C<ISL_FORMAT_ISL>, C<ISL_FORMAT_OMEGA>,
1292 C<ISL_FORMAT_POLYLIB>, C<ISL_FORMAT_EXT_POLYLIB> or C<ISL_FORMAT_LATEX>
1293 and defaults to C<ISL_FORMAT_ISL>.
1294 Each line in the output is indented by C<indent> (set by
1295 C<isl_printer_set_indent>) spaces
1296 (default: 0), prefixed by C<prefix> and suffixed by C<suffix>.
1297 In the C<PolyLib> format output,
1298 the coefficients of the existentially quantified variables
1299 appear between those of the set variables and those
1301 The function C<isl_printer_indent> increases the indentation
1302 by the specified amount (which may be negative).
1304 To actually print something, use
1306 #include <isl/printer.h>
1307 __isl_give isl_printer *isl_printer_print_double(
1308 __isl_take isl_printer *p, double d);
1310 #include <isl/set.h>
1311 __isl_give isl_printer *isl_printer_print_basic_set(
1312 __isl_take isl_printer *printer,
1313 __isl_keep isl_basic_set *bset);
1314 __isl_give isl_printer *isl_printer_print_set(
1315 __isl_take isl_printer *printer,
1316 __isl_keep isl_set *set);
1318 #include <isl/map.h>
1319 __isl_give isl_printer *isl_printer_print_basic_map(
1320 __isl_take isl_printer *printer,
1321 __isl_keep isl_basic_map *bmap);
1322 __isl_give isl_printer *isl_printer_print_map(
1323 __isl_take isl_printer *printer,
1324 __isl_keep isl_map *map);
1326 #include <isl/union_set.h>
1327 __isl_give isl_printer *isl_printer_print_union_set(
1328 __isl_take isl_printer *p,
1329 __isl_keep isl_union_set *uset);
1331 #include <isl/union_map.h>
1332 __isl_give isl_printer *isl_printer_print_union_map(
1333 __isl_take isl_printer *p,
1334 __isl_keep isl_union_map *umap);
1336 When called on a file printer, the following function flushes
1337 the file. When called on a string printer, the buffer is cleared.
1339 __isl_give isl_printer *isl_printer_flush(
1340 __isl_take isl_printer *p);
1342 =head2 Creating New Sets and Relations
1344 C<isl> has functions for creating some standard sets and relations.
1348 =item * Empty sets and relations
1350 __isl_give isl_basic_set *isl_basic_set_empty(
1351 __isl_take isl_space *space);
1352 __isl_give isl_basic_map *isl_basic_map_empty(
1353 __isl_take isl_space *space);
1354 __isl_give isl_set *isl_set_empty(
1355 __isl_take isl_space *space);
1356 __isl_give isl_map *isl_map_empty(
1357 __isl_take isl_space *space);
1358 __isl_give isl_union_set *isl_union_set_empty(
1359 __isl_take isl_space *space);
1360 __isl_give isl_union_map *isl_union_map_empty(
1361 __isl_take isl_space *space);
1363 For C<isl_union_set>s and C<isl_union_map>s, the space
1364 is only used to specify the parameters.
1366 =item * Universe sets and relations
1368 __isl_give isl_basic_set *isl_basic_set_universe(
1369 __isl_take isl_space *space);
1370 __isl_give isl_basic_map *isl_basic_map_universe(
1371 __isl_take isl_space *space);
1372 __isl_give isl_set *isl_set_universe(
1373 __isl_take isl_space *space);
1374 __isl_give isl_map *isl_map_universe(
1375 __isl_take isl_space *space);
1376 __isl_give isl_union_set *isl_union_set_universe(
1377 __isl_take isl_union_set *uset);
1378 __isl_give isl_union_map *isl_union_map_universe(
1379 __isl_take isl_union_map *umap);
1381 The sets and relations constructed by the functions above
1382 contain all integer values, while those constructed by the
1383 functions below only contain non-negative values.
1385 __isl_give isl_basic_set *isl_basic_set_nat_universe(
1386 __isl_take isl_space *space);
1387 __isl_give isl_basic_map *isl_basic_map_nat_universe(
1388 __isl_take isl_space *space);
1389 __isl_give isl_set *isl_set_nat_universe(
1390 __isl_take isl_space *space);
1391 __isl_give isl_map *isl_map_nat_universe(
1392 __isl_take isl_space *space);
1394 =item * Identity relations
1396 __isl_give isl_basic_map *isl_basic_map_identity(
1397 __isl_take isl_space *space);
1398 __isl_give isl_map *isl_map_identity(
1399 __isl_take isl_space *space);
1401 The number of input and output dimensions in C<space> needs
1404 =item * Lexicographic order
1406 __isl_give isl_map *isl_map_lex_lt(
1407 __isl_take isl_space *set_space);
1408 __isl_give isl_map *isl_map_lex_le(
1409 __isl_take isl_space *set_space);
1410 __isl_give isl_map *isl_map_lex_gt(
1411 __isl_take isl_space *set_space);
1412 __isl_give isl_map *isl_map_lex_ge(
1413 __isl_take isl_space *set_space);
1414 __isl_give isl_map *isl_map_lex_lt_first(
1415 __isl_take isl_space *space, unsigned n);
1416 __isl_give isl_map *isl_map_lex_le_first(
1417 __isl_take isl_space *space, unsigned n);
1418 __isl_give isl_map *isl_map_lex_gt_first(
1419 __isl_take isl_space *space, unsigned n);
1420 __isl_give isl_map *isl_map_lex_ge_first(
1421 __isl_take isl_space *space, unsigned n);
1423 The first four functions take a space for a B<set>
1424 and return relations that express that the elements in the domain
1425 are lexicographically less
1426 (C<isl_map_lex_lt>), less or equal (C<isl_map_lex_le>),
1427 greater (C<isl_map_lex_gt>) or greater or equal (C<isl_map_lex_ge>)
1428 than the elements in the range.
1429 The last four functions take a space for a map
1430 and return relations that express that the first C<n> dimensions
1431 in the domain are lexicographically less
1432 (C<isl_map_lex_lt_first>), less or equal (C<isl_map_lex_le_first>),
1433 greater (C<isl_map_lex_gt_first>) or greater or equal (C<isl_map_lex_ge_first>)
1434 than the first C<n> dimensions in the range.
1438 A basic set or relation can be converted to a set or relation
1439 using the following functions.
1441 __isl_give isl_set *isl_set_from_basic_set(
1442 __isl_take isl_basic_set *bset);
1443 __isl_give isl_map *isl_map_from_basic_map(
1444 __isl_take isl_basic_map *bmap);
1446 Sets and relations can be converted to union sets and relations
1447 using the following functions.
1449 __isl_give isl_union_set *isl_union_set_from_basic_set(
1450 __isl_take isl_basic_set *bset);
1451 __isl_give isl_union_map *isl_union_map_from_basic_map(
1452 __isl_take isl_basic_map *bmap);
1453 __isl_give isl_union_set *isl_union_set_from_set(
1454 __isl_take isl_set *set);
1455 __isl_give isl_union_map *isl_union_map_from_map(
1456 __isl_take isl_map *map);
1458 The inverse conversions below can only be used if the input
1459 union set or relation is known to contain elements in exactly one
1462 __isl_give isl_set *isl_set_from_union_set(
1463 __isl_take isl_union_set *uset);
1464 __isl_give isl_map *isl_map_from_union_map(
1465 __isl_take isl_union_map *umap);
1467 A zero-dimensional (basic) set can be constructed on a given parameter domain
1468 using the following function.
1470 __isl_give isl_basic_set *isl_basic_set_from_params(
1471 __isl_take isl_basic_set *bset);
1472 __isl_give isl_set *isl_set_from_params(
1473 __isl_take isl_set *set);
1475 Sets and relations can be copied and freed again using the following
1478 __isl_give isl_basic_set *isl_basic_set_copy(
1479 __isl_keep isl_basic_set *bset);
1480 __isl_give isl_set *isl_set_copy(__isl_keep isl_set *set);
1481 __isl_give isl_union_set *isl_union_set_copy(
1482 __isl_keep isl_union_set *uset);
1483 __isl_give isl_basic_map *isl_basic_map_copy(
1484 __isl_keep isl_basic_map *bmap);
1485 __isl_give isl_map *isl_map_copy(__isl_keep isl_map *map);
1486 __isl_give isl_union_map *isl_union_map_copy(
1487 __isl_keep isl_union_map *umap);
1488 void *isl_basic_set_free(__isl_take isl_basic_set *bset);
1489 void *isl_set_free(__isl_take isl_set *set);
1490 void *isl_union_set_free(__isl_take isl_union_set *uset);
1491 void *isl_basic_map_free(__isl_take isl_basic_map *bmap);
1492 void *isl_map_free(__isl_take isl_map *map);
1493 void *isl_union_map_free(__isl_take isl_union_map *umap);
1495 Other sets and relations can be constructed by starting
1496 from a universe set or relation, adding equality and/or
1497 inequality constraints and then projecting out the
1498 existentially quantified variables, if any.
1499 Constraints can be constructed, manipulated and
1500 added to (or removed from) (basic) sets and relations
1501 using the following functions.
1503 #include <isl/constraint.h>
1504 __isl_give isl_constraint *isl_equality_alloc(
1505 __isl_take isl_local_space *ls);
1506 __isl_give isl_constraint *isl_inequality_alloc(
1507 __isl_take isl_local_space *ls);
1508 __isl_give isl_constraint *isl_constraint_set_constant(
1509 __isl_take isl_constraint *constraint, isl_int v);
1510 __isl_give isl_constraint *isl_constraint_set_constant_si(
1511 __isl_take isl_constraint *constraint, int v);
1512 __isl_give isl_constraint *isl_constraint_set_constant_val(
1513 __isl_take isl_constraint *constraint,
1514 __isl_take isl_val *v);
1515 __isl_give isl_constraint *isl_constraint_set_coefficient(
1516 __isl_take isl_constraint *constraint,
1517 enum isl_dim_type type, int pos, isl_int v);
1518 __isl_give isl_constraint *isl_constraint_set_coefficient_si(
1519 __isl_take isl_constraint *constraint,
1520 enum isl_dim_type type, int pos, int v);
1521 __isl_give isl_constraint *
1522 isl_constraint_set_coefficient_val(
1523 __isl_take isl_constraint *constraint,
1524 enum isl_dim_type type, int pos, isl_val *v);
1525 __isl_give isl_basic_map *isl_basic_map_add_constraint(
1526 __isl_take isl_basic_map *bmap,
1527 __isl_take isl_constraint *constraint);
1528 __isl_give isl_basic_set *isl_basic_set_add_constraint(
1529 __isl_take isl_basic_set *bset,
1530 __isl_take isl_constraint *constraint);
1531 __isl_give isl_map *isl_map_add_constraint(
1532 __isl_take isl_map *map,
1533 __isl_take isl_constraint *constraint);
1534 __isl_give isl_set *isl_set_add_constraint(
1535 __isl_take isl_set *set,
1536 __isl_take isl_constraint *constraint);
1537 __isl_give isl_basic_set *isl_basic_set_drop_constraint(
1538 __isl_take isl_basic_set *bset,
1539 __isl_take isl_constraint *constraint);
1541 For example, to create a set containing the even integers
1542 between 10 and 42, you would use the following code.
1545 isl_local_space *ls;
1547 isl_basic_set *bset;
1549 space = isl_space_set_alloc(ctx, 0, 2);
1550 bset = isl_basic_set_universe(isl_space_copy(space));
1551 ls = isl_local_space_from_space(space);
1553 c = isl_equality_alloc(isl_local_space_copy(ls));
1554 c = isl_constraint_set_coefficient_si(c, isl_dim_set, 0, -1);
1555 c = isl_constraint_set_coefficient_si(c, isl_dim_set, 1, 2);
1556 bset = isl_basic_set_add_constraint(bset, c);
1558 c = isl_inequality_alloc(isl_local_space_copy(ls));
1559 c = isl_constraint_set_constant_si(c, -10);
1560 c = isl_constraint_set_coefficient_si(c, isl_dim_set, 0, 1);
1561 bset = isl_basic_set_add_constraint(bset, c);
1563 c = isl_inequality_alloc(ls);
1564 c = isl_constraint_set_constant_si(c, 42);
1565 c = isl_constraint_set_coefficient_si(c, isl_dim_set, 0, -1);
1566 bset = isl_basic_set_add_constraint(bset, c);
1568 bset = isl_basic_set_project_out(bset, isl_dim_set, 1, 1);
1572 isl_basic_set *bset;
1573 bset = isl_basic_set_read_from_str(ctx,
1574 "{[i] : exists (a : i = 2a and i >= 10 and i <= 42)}");
1576 A basic set or relation can also be constructed from two matrices
1577 describing the equalities and the inequalities.
1579 __isl_give isl_basic_set *isl_basic_set_from_constraint_matrices(
1580 __isl_take isl_space *space,
1581 __isl_take isl_mat *eq, __isl_take isl_mat *ineq,
1582 enum isl_dim_type c1,
1583 enum isl_dim_type c2, enum isl_dim_type c3,
1584 enum isl_dim_type c4);
1585 __isl_give isl_basic_map *isl_basic_map_from_constraint_matrices(
1586 __isl_take isl_space *space,
1587 __isl_take isl_mat *eq, __isl_take isl_mat *ineq,
1588 enum isl_dim_type c1,
1589 enum isl_dim_type c2, enum isl_dim_type c3,
1590 enum isl_dim_type c4, enum isl_dim_type c5);
1592 The C<isl_dim_type> arguments indicate the order in which
1593 different kinds of variables appear in the input matrices
1594 and should be a permutation of C<isl_dim_cst>, C<isl_dim_param>,
1595 C<isl_dim_set> and C<isl_dim_div> for sets and
1596 of C<isl_dim_cst>, C<isl_dim_param>,
1597 C<isl_dim_in>, C<isl_dim_out> and C<isl_dim_div> for relations.
1599 A (basic or union) set or relation can also be constructed from a
1600 (union) (piecewise) (multiple) affine expression
1601 or a list of affine expressions
1602 (See L<"Piecewise Quasi Affine Expressions"> and
1603 L<"Piecewise Multiple Quasi Affine Expressions">).
1605 __isl_give isl_basic_map *isl_basic_map_from_aff(
1606 __isl_take isl_aff *aff);
1607 __isl_give isl_map *isl_map_from_aff(
1608 __isl_take isl_aff *aff);
1609 __isl_give isl_set *isl_set_from_pw_aff(
1610 __isl_take isl_pw_aff *pwaff);
1611 __isl_give isl_map *isl_map_from_pw_aff(
1612 __isl_take isl_pw_aff *pwaff);
1613 __isl_give isl_basic_map *isl_basic_map_from_aff_list(
1614 __isl_take isl_space *domain_space,
1615 __isl_take isl_aff_list *list);
1616 __isl_give isl_basic_map *isl_basic_map_from_multi_aff(
1617 __isl_take isl_multi_aff *maff)
1618 __isl_give isl_map *isl_map_from_multi_aff(
1619 __isl_take isl_multi_aff *maff)
1620 __isl_give isl_set *isl_set_from_pw_multi_aff(
1621 __isl_take isl_pw_multi_aff *pma);
1622 __isl_give isl_map *isl_map_from_pw_multi_aff(
1623 __isl_take isl_pw_multi_aff *pma);
1624 __isl_give isl_union_map *
1625 isl_union_map_from_union_pw_multi_aff(
1626 __isl_take isl_union_pw_multi_aff *upma);
1628 The C<domain_dim> argument describes the domain of the resulting
1629 basic relation. It is required because the C<list> may consist
1630 of zero affine expressions.
1632 =head2 Inspecting Sets and Relations
1634 Usually, the user should not have to care about the actual constraints
1635 of the sets and maps, but should instead apply the abstract operations
1636 explained in the following sections.
1637 Occasionally, however, it may be required to inspect the individual
1638 coefficients of the constraints. This section explains how to do so.
1639 In these cases, it may also be useful to have C<isl> compute
1640 an explicit representation of the existentially quantified variables.
1642 __isl_give isl_set *isl_set_compute_divs(
1643 __isl_take isl_set *set);
1644 __isl_give isl_map *isl_map_compute_divs(
1645 __isl_take isl_map *map);
1646 __isl_give isl_union_set *isl_union_set_compute_divs(
1647 __isl_take isl_union_set *uset);
1648 __isl_give isl_union_map *isl_union_map_compute_divs(
1649 __isl_take isl_union_map *umap);
1651 This explicit representation defines the existentially quantified
1652 variables as integer divisions of the other variables, possibly
1653 including earlier existentially quantified variables.
1654 An explicitly represented existentially quantified variable therefore
1655 has a unique value when the values of the other variables are known.
1656 If, furthermore, the same existentials, i.e., existentials
1657 with the same explicit representations, should appear in the
1658 same order in each of the disjuncts of a set or map, then the user should call
1659 either of the following functions.
1661 __isl_give isl_set *isl_set_align_divs(
1662 __isl_take isl_set *set);
1663 __isl_give isl_map *isl_map_align_divs(
1664 __isl_take isl_map *map);
1666 Alternatively, the existentially quantified variables can be removed
1667 using the following functions, which compute an overapproximation.
1669 __isl_give isl_basic_set *isl_basic_set_remove_divs(
1670 __isl_take isl_basic_set *bset);
1671 __isl_give isl_basic_map *isl_basic_map_remove_divs(
1672 __isl_take isl_basic_map *bmap);
1673 __isl_give isl_set *isl_set_remove_divs(
1674 __isl_take isl_set *set);
1675 __isl_give isl_map *isl_map_remove_divs(
1676 __isl_take isl_map *map);
1678 It is also possible to only remove those divs that are defined
1679 in terms of a given range of dimensions or only those for which
1680 no explicit representation is known.
1682 __isl_give isl_basic_set *
1683 isl_basic_set_remove_divs_involving_dims(
1684 __isl_take isl_basic_set *bset,
1685 enum isl_dim_type type,
1686 unsigned first, unsigned n);
1687 __isl_give isl_basic_map *
1688 isl_basic_map_remove_divs_involving_dims(
1689 __isl_take isl_basic_map *bmap,
1690 enum isl_dim_type type,
1691 unsigned first, unsigned n);
1692 __isl_give isl_set *isl_set_remove_divs_involving_dims(
1693 __isl_take isl_set *set, enum isl_dim_type type,
1694 unsigned first, unsigned n);
1695 __isl_give isl_map *isl_map_remove_divs_involving_dims(
1696 __isl_take isl_map *map, enum isl_dim_type type,
1697 unsigned first, unsigned n);
1699 __isl_give isl_basic_set *
1700 isl_basic_set_remove_unknown_divs(
1701 __isl_take isl_basic_set *bset);
1702 __isl_give isl_set *isl_set_remove_unknown_divs(
1703 __isl_take isl_set *set);
1704 __isl_give isl_map *isl_map_remove_unknown_divs(
1705 __isl_take isl_map *map);
1707 To iterate over all the sets or maps in a union set or map, use
1709 int isl_union_set_foreach_set(__isl_keep isl_union_set *uset,
1710 int (*fn)(__isl_take isl_set *set, void *user),
1712 int isl_union_map_foreach_map(__isl_keep isl_union_map *umap,
1713 int (*fn)(__isl_take isl_map *map, void *user),
1716 The number of sets or maps in a union set or map can be obtained
1719 int isl_union_set_n_set(__isl_keep isl_union_set *uset);
1720 int isl_union_map_n_map(__isl_keep isl_union_map *umap);
1722 To extract the set or map in a given space from a union, use
1724 __isl_give isl_set *isl_union_set_extract_set(
1725 __isl_keep isl_union_set *uset,
1726 __isl_take isl_space *space);
1727 __isl_give isl_map *isl_union_map_extract_map(
1728 __isl_keep isl_union_map *umap,
1729 __isl_take isl_space *space);
1731 To iterate over all the basic sets or maps in a set or map, use
1733 int isl_set_foreach_basic_set(__isl_keep isl_set *set,
1734 int (*fn)(__isl_take isl_basic_set *bset, void *user),
1736 int isl_map_foreach_basic_map(__isl_keep isl_map *map,
1737 int (*fn)(__isl_take isl_basic_map *bmap, void *user),
1740 The callback function C<fn> should return 0 if successful and
1741 -1 if an error occurs. In the latter case, or if any other error
1742 occurs, the above functions will return -1.
1744 It should be noted that C<isl> does not guarantee that
1745 the basic sets or maps passed to C<fn> are disjoint.
1746 If this is required, then the user should call one of
1747 the following functions first.
1749 __isl_give isl_set *isl_set_make_disjoint(
1750 __isl_take isl_set *set);
1751 __isl_give isl_map *isl_map_make_disjoint(
1752 __isl_take isl_map *map);
1754 The number of basic sets in a set can be obtained
1757 int isl_set_n_basic_set(__isl_keep isl_set *set);
1759 To iterate over the constraints of a basic set or map, use
1761 #include <isl/constraint.h>
1763 int isl_basic_set_n_constraint(
1764 __isl_keep isl_basic_set *bset);
1765 int isl_basic_set_foreach_constraint(
1766 __isl_keep isl_basic_set *bset,
1767 int (*fn)(__isl_take isl_constraint *c, void *user),
1769 int isl_basic_map_foreach_constraint(
1770 __isl_keep isl_basic_map *bmap,
1771 int (*fn)(__isl_take isl_constraint *c, void *user),
1773 void *isl_constraint_free(__isl_take isl_constraint *c);
1775 Again, the callback function C<fn> should return 0 if successful and
1776 -1 if an error occurs. In the latter case, or if any other error
1777 occurs, the above functions will return -1.
1778 The constraint C<c> represents either an equality or an inequality.
1779 Use the following function to find out whether a constraint
1780 represents an equality. If not, it represents an inequality.
1782 int isl_constraint_is_equality(
1783 __isl_keep isl_constraint *constraint);
1785 The coefficients of the constraints can be inspected using
1786 the following functions.
1788 int isl_constraint_is_lower_bound(
1789 __isl_keep isl_constraint *constraint,
1790 enum isl_dim_type type, unsigned pos);
1791 int isl_constraint_is_upper_bound(
1792 __isl_keep isl_constraint *constraint,
1793 enum isl_dim_type type, unsigned pos);
1794 void isl_constraint_get_constant(
1795 __isl_keep isl_constraint *constraint, isl_int *v);
1796 __isl_give isl_val *isl_constraint_get_constant_val(
1797 __isl_keep isl_constraint *constraint);
1798 void isl_constraint_get_coefficient(
1799 __isl_keep isl_constraint *constraint,
1800 enum isl_dim_type type, int pos, isl_int *v);
1801 __isl_give isl_val *isl_constraint_get_coefficient_val(
1802 __isl_keep isl_constraint *constraint,
1803 enum isl_dim_type type, int pos);
1804 int isl_constraint_involves_dims(
1805 __isl_keep isl_constraint *constraint,
1806 enum isl_dim_type type, unsigned first, unsigned n);
1808 The explicit representations of the existentially quantified
1809 variables can be inspected using the following function.
1810 Note that the user is only allowed to use this function
1811 if the inspected set or map is the result of a call
1812 to C<isl_set_compute_divs> or C<isl_map_compute_divs>.
1813 The existentially quantified variable is equal to the floor
1814 of the returned affine expression. The affine expression
1815 itself can be inspected using the functions in
1816 L<"Piecewise Quasi Affine Expressions">.
1818 __isl_give isl_aff *isl_constraint_get_div(
1819 __isl_keep isl_constraint *constraint, int pos);
1821 To obtain the constraints of a basic set or map in matrix
1822 form, use the following functions.
1824 __isl_give isl_mat *isl_basic_set_equalities_matrix(
1825 __isl_keep isl_basic_set *bset,
1826 enum isl_dim_type c1, enum isl_dim_type c2,
1827 enum isl_dim_type c3, enum isl_dim_type c4);
1828 __isl_give isl_mat *isl_basic_set_inequalities_matrix(
1829 __isl_keep isl_basic_set *bset,
1830 enum isl_dim_type c1, enum isl_dim_type c2,
1831 enum isl_dim_type c3, enum isl_dim_type c4);
1832 __isl_give isl_mat *isl_basic_map_equalities_matrix(
1833 __isl_keep isl_basic_map *bmap,
1834 enum isl_dim_type c1,
1835 enum isl_dim_type c2, enum isl_dim_type c3,
1836 enum isl_dim_type c4, enum isl_dim_type c5);
1837 __isl_give isl_mat *isl_basic_map_inequalities_matrix(
1838 __isl_keep isl_basic_map *bmap,
1839 enum isl_dim_type c1,
1840 enum isl_dim_type c2, enum isl_dim_type c3,
1841 enum isl_dim_type c4, enum isl_dim_type c5);
1843 The C<isl_dim_type> arguments dictate the order in which
1844 different kinds of variables appear in the resulting matrix
1845 and should be a permutation of C<isl_dim_cst>, C<isl_dim_param>,
1846 C<isl_dim_in>, C<isl_dim_out> and C<isl_dim_div>.
1848 The number of parameters, input, output or set dimensions can
1849 be obtained using the following functions.
1851 unsigned isl_basic_set_dim(__isl_keep isl_basic_set *bset,
1852 enum isl_dim_type type);
1853 unsigned isl_basic_map_dim(__isl_keep isl_basic_map *bmap,
1854 enum isl_dim_type type);
1855 unsigned isl_set_dim(__isl_keep isl_set *set,
1856 enum isl_dim_type type);
1857 unsigned isl_map_dim(__isl_keep isl_map *map,
1858 enum isl_dim_type type);
1860 To check whether the description of a set or relation depends
1861 on one or more given dimensions, it is not necessary to iterate over all
1862 constraints. Instead the following functions can be used.
1864 int isl_basic_set_involves_dims(
1865 __isl_keep isl_basic_set *bset,
1866 enum isl_dim_type type, unsigned first, unsigned n);
1867 int isl_set_involves_dims(__isl_keep isl_set *set,
1868 enum isl_dim_type type, unsigned first, unsigned n);
1869 int isl_basic_map_involves_dims(
1870 __isl_keep isl_basic_map *bmap,
1871 enum isl_dim_type type, unsigned first, unsigned n);
1872 int isl_map_involves_dims(__isl_keep isl_map *map,
1873 enum isl_dim_type type, unsigned first, unsigned n);
1875 Similarly, the following functions can be used to check whether
1876 a given dimension is involved in any lower or upper bound.
1878 int isl_set_dim_has_any_lower_bound(__isl_keep isl_set *set,
1879 enum isl_dim_type type, unsigned pos);
1880 int isl_set_dim_has_any_upper_bound(__isl_keep isl_set *set,
1881 enum isl_dim_type type, unsigned pos);
1883 Note that these functions return true even if there is a bound on
1884 the dimension on only some of the basic sets of C<set>.
1885 To check if they have a bound for all of the basic sets in C<set>,
1886 use the following functions instead.
1888 int isl_set_dim_has_lower_bound(__isl_keep isl_set *set,
1889 enum isl_dim_type type, unsigned pos);
1890 int isl_set_dim_has_upper_bound(__isl_keep isl_set *set,
1891 enum isl_dim_type type, unsigned pos);
1893 The identifiers or names of the domain and range spaces of a set
1894 or relation can be read off or set using the following functions.
1896 __isl_give isl_set *isl_set_set_tuple_id(
1897 __isl_take isl_set *set, __isl_take isl_id *id);
1898 __isl_give isl_set *isl_set_reset_tuple_id(
1899 __isl_take isl_set *set);
1900 int isl_set_has_tuple_id(__isl_keep isl_set *set);
1901 __isl_give isl_id *isl_set_get_tuple_id(
1902 __isl_keep isl_set *set);
1903 __isl_give isl_map *isl_map_set_tuple_id(
1904 __isl_take isl_map *map, enum isl_dim_type type,
1905 __isl_take isl_id *id);
1906 __isl_give isl_map *isl_map_reset_tuple_id(
1907 __isl_take isl_map *map, enum isl_dim_type type);
1908 int isl_map_has_tuple_id(__isl_keep isl_map *map,
1909 enum isl_dim_type type);
1910 __isl_give isl_id *isl_map_get_tuple_id(
1911 __isl_keep isl_map *map, enum isl_dim_type type);
1913 const char *isl_basic_set_get_tuple_name(
1914 __isl_keep isl_basic_set *bset);
1915 __isl_give isl_basic_set *isl_basic_set_set_tuple_name(
1916 __isl_take isl_basic_set *set, const char *s);
1917 int isl_set_has_tuple_name(__isl_keep isl_set *set);
1918 const char *isl_set_get_tuple_name(
1919 __isl_keep isl_set *set);
1920 const char *isl_basic_map_get_tuple_name(
1921 __isl_keep isl_basic_map *bmap,
1922 enum isl_dim_type type);
1923 __isl_give isl_basic_map *isl_basic_map_set_tuple_name(
1924 __isl_take isl_basic_map *bmap,
1925 enum isl_dim_type type, const char *s);
1926 int isl_map_has_tuple_name(__isl_keep isl_map *map,
1927 enum isl_dim_type type);
1928 const char *isl_map_get_tuple_name(
1929 __isl_keep isl_map *map,
1930 enum isl_dim_type type);
1932 As with C<isl_space_get_tuple_name>, the value returned points to
1933 an internal data structure.
1934 The identifiers, positions or names of individual dimensions can be
1935 read off using the following functions.
1937 __isl_give isl_id *isl_basic_set_get_dim_id(
1938 __isl_keep isl_basic_set *bset,
1939 enum isl_dim_type type, unsigned pos);
1940 __isl_give isl_set *isl_set_set_dim_id(
1941 __isl_take isl_set *set, enum isl_dim_type type,
1942 unsigned pos, __isl_take isl_id *id);
1943 int isl_set_has_dim_id(__isl_keep isl_set *set,
1944 enum isl_dim_type type, unsigned pos);
1945 __isl_give isl_id *isl_set_get_dim_id(
1946 __isl_keep isl_set *set, enum isl_dim_type type,
1948 int isl_basic_map_has_dim_id(
1949 __isl_keep isl_basic_map *bmap,
1950 enum isl_dim_type type, unsigned pos);
1951 __isl_give isl_map *isl_map_set_dim_id(
1952 __isl_take isl_map *map, enum isl_dim_type type,
1953 unsigned pos, __isl_take isl_id *id);
1954 int isl_map_has_dim_id(__isl_keep isl_map *map,
1955 enum isl_dim_type type, unsigned pos);
1956 __isl_give isl_id *isl_map_get_dim_id(
1957 __isl_keep isl_map *map, enum isl_dim_type type,
1960 int isl_set_find_dim_by_id(__isl_keep isl_set *set,
1961 enum isl_dim_type type, __isl_keep isl_id *id);
1962 int isl_map_find_dim_by_id(__isl_keep isl_map *map,
1963 enum isl_dim_type type, __isl_keep isl_id *id);
1964 int isl_set_find_dim_by_name(__isl_keep isl_set *set,
1965 enum isl_dim_type type, const char *name);
1966 int isl_map_find_dim_by_name(__isl_keep isl_map *map,
1967 enum isl_dim_type type, const char *name);
1969 const char *isl_constraint_get_dim_name(
1970 __isl_keep isl_constraint *constraint,
1971 enum isl_dim_type type, unsigned pos);
1972 const char *isl_basic_set_get_dim_name(
1973 __isl_keep isl_basic_set *bset,
1974 enum isl_dim_type type, unsigned pos);
1975 int isl_set_has_dim_name(__isl_keep isl_set *set,
1976 enum isl_dim_type type, unsigned pos);
1977 const char *isl_set_get_dim_name(
1978 __isl_keep isl_set *set,
1979 enum isl_dim_type type, unsigned pos);
1980 const char *isl_basic_map_get_dim_name(
1981 __isl_keep isl_basic_map *bmap,
1982 enum isl_dim_type type, unsigned pos);
1983 int isl_map_has_dim_name(__isl_keep isl_map *map,
1984 enum isl_dim_type type, unsigned pos);
1985 const char *isl_map_get_dim_name(
1986 __isl_keep isl_map *map,
1987 enum isl_dim_type type, unsigned pos);
1989 These functions are mostly useful to obtain the identifiers, positions
1990 or names of the parameters. Identifiers of individual dimensions are
1991 essentially only useful for printing. They are ignored by all other
1992 operations and may not be preserved across those operations.
1996 =head3 Unary Properties
2002 The following functions test whether the given set or relation
2003 contains any integer points. The ``plain'' variants do not perform
2004 any computations, but simply check if the given set or relation
2005 is already known to be empty.
2007 int isl_basic_set_plain_is_empty(__isl_keep isl_basic_set *bset);
2008 int isl_basic_set_is_empty(__isl_keep isl_basic_set *bset);
2009 int isl_set_plain_is_empty(__isl_keep isl_set *set);
2010 int isl_set_is_empty(__isl_keep isl_set *set);
2011 int isl_union_set_is_empty(__isl_keep isl_union_set *uset);
2012 int isl_basic_map_plain_is_empty(__isl_keep isl_basic_map *bmap);
2013 int isl_basic_map_is_empty(__isl_keep isl_basic_map *bmap);
2014 int isl_map_plain_is_empty(__isl_keep isl_map *map);
2015 int isl_map_is_empty(__isl_keep isl_map *map);
2016 int isl_union_map_is_empty(__isl_keep isl_union_map *umap);
2018 =item * Universality
2020 int isl_basic_set_is_universe(__isl_keep isl_basic_set *bset);
2021 int isl_basic_map_is_universe(__isl_keep isl_basic_map *bmap);
2022 int isl_set_plain_is_universe(__isl_keep isl_set *set);
2024 =item * Single-valuedness
2026 int isl_basic_map_is_single_valued(
2027 __isl_keep isl_basic_map *bmap);
2028 int isl_map_plain_is_single_valued(
2029 __isl_keep isl_map *map);
2030 int isl_map_is_single_valued(__isl_keep isl_map *map);
2031 int isl_union_map_is_single_valued(__isl_keep isl_union_map *umap);
2035 int isl_map_plain_is_injective(__isl_keep isl_map *map);
2036 int isl_map_is_injective(__isl_keep isl_map *map);
2037 int isl_union_map_plain_is_injective(
2038 __isl_keep isl_union_map *umap);
2039 int isl_union_map_is_injective(
2040 __isl_keep isl_union_map *umap);
2044 int isl_map_is_bijective(__isl_keep isl_map *map);
2045 int isl_union_map_is_bijective(__isl_keep isl_union_map *umap);
2049 int isl_basic_map_plain_is_fixed(
2050 __isl_keep isl_basic_map *bmap,
2051 enum isl_dim_type type, unsigned pos,
2053 int isl_set_plain_is_fixed(__isl_keep isl_set *set,
2054 enum isl_dim_type type, unsigned pos,
2056 int isl_map_plain_is_fixed(__isl_keep isl_map *map,
2057 enum isl_dim_type type, unsigned pos,
2060 Check if the relation obviously lies on a hyperplane where the given dimension
2061 has a fixed value and if so, return that value in C<*val>.
2065 To check whether a set is a parameter domain, use this function:
2067 int isl_set_is_params(__isl_keep isl_set *set);
2068 int isl_union_set_is_params(
2069 __isl_keep isl_union_set *uset);
2073 The following functions check whether the domain of the given
2074 (basic) set is a wrapped relation.
2076 int isl_basic_set_is_wrapping(
2077 __isl_keep isl_basic_set *bset);
2078 int isl_set_is_wrapping(__isl_keep isl_set *set);
2080 =item * Internal Product
2082 int isl_basic_map_can_zip(
2083 __isl_keep isl_basic_map *bmap);
2084 int isl_map_can_zip(__isl_keep isl_map *map);
2086 Check whether the product of domain and range of the given relation
2088 i.e., whether both domain and range are nested relations.
2092 int isl_basic_map_can_curry(
2093 __isl_keep isl_basic_map *bmap);
2094 int isl_map_can_curry(__isl_keep isl_map *map);
2096 Check whether the domain of the (basic) relation is a wrapped relation.
2098 int isl_basic_map_can_uncurry(
2099 __isl_keep isl_basic_map *bmap);
2100 int isl_map_can_uncurry(__isl_keep isl_map *map);
2102 Check whether the range of the (basic) relation is a wrapped relation.
2106 =head3 Binary Properties
2112 int isl_set_plain_is_equal(__isl_keep isl_set *set1,
2113 __isl_keep isl_set *set2);
2114 int isl_set_is_equal(__isl_keep isl_set *set1,
2115 __isl_keep isl_set *set2);
2116 int isl_union_set_is_equal(
2117 __isl_keep isl_union_set *uset1,
2118 __isl_keep isl_union_set *uset2);
2119 int isl_basic_map_is_equal(
2120 __isl_keep isl_basic_map *bmap1,
2121 __isl_keep isl_basic_map *bmap2);
2122 int isl_map_is_equal(__isl_keep isl_map *map1,
2123 __isl_keep isl_map *map2);
2124 int isl_map_plain_is_equal(__isl_keep isl_map *map1,
2125 __isl_keep isl_map *map2);
2126 int isl_union_map_is_equal(
2127 __isl_keep isl_union_map *umap1,
2128 __isl_keep isl_union_map *umap2);
2130 =item * Disjointness
2132 int isl_set_plain_is_disjoint(__isl_keep isl_set *set1,
2133 __isl_keep isl_set *set2);
2134 int isl_set_is_disjoint(__isl_keep isl_set *set1,
2135 __isl_keep isl_set *set2);
2136 int isl_map_is_disjoint(__isl_keep isl_map *map1,
2137 __isl_keep isl_map *map2);
2141 int isl_basic_set_is_subset(
2142 __isl_keep isl_basic_set *bset1,
2143 __isl_keep isl_basic_set *bset2);
2144 int isl_set_is_subset(__isl_keep isl_set *set1,
2145 __isl_keep isl_set *set2);
2146 int isl_set_is_strict_subset(
2147 __isl_keep isl_set *set1,
2148 __isl_keep isl_set *set2);
2149 int isl_union_set_is_subset(
2150 __isl_keep isl_union_set *uset1,
2151 __isl_keep isl_union_set *uset2);
2152 int isl_union_set_is_strict_subset(
2153 __isl_keep isl_union_set *uset1,
2154 __isl_keep isl_union_set *uset2);
2155 int isl_basic_map_is_subset(
2156 __isl_keep isl_basic_map *bmap1,
2157 __isl_keep isl_basic_map *bmap2);
2158 int isl_basic_map_is_strict_subset(
2159 __isl_keep isl_basic_map *bmap1,
2160 __isl_keep isl_basic_map *bmap2);
2161 int isl_map_is_subset(
2162 __isl_keep isl_map *map1,
2163 __isl_keep isl_map *map2);
2164 int isl_map_is_strict_subset(
2165 __isl_keep isl_map *map1,
2166 __isl_keep isl_map *map2);
2167 int isl_union_map_is_subset(
2168 __isl_keep isl_union_map *umap1,
2169 __isl_keep isl_union_map *umap2);
2170 int isl_union_map_is_strict_subset(
2171 __isl_keep isl_union_map *umap1,
2172 __isl_keep isl_union_map *umap2);
2174 Check whether the first argument is a (strict) subset of the
2179 int isl_set_plain_cmp(__isl_keep isl_set *set1,
2180 __isl_keep isl_set *set2);
2182 This function is useful for sorting C<isl_set>s.
2183 The order depends on the internal representation of the inputs.
2184 The order is fixed over different calls to the function (assuming
2185 the internal representation of the inputs has not changed), but may
2186 change over different versions of C<isl>.
2190 =head2 Unary Operations
2196 __isl_give isl_set *isl_set_complement(
2197 __isl_take isl_set *set);
2198 __isl_give isl_map *isl_map_complement(
2199 __isl_take isl_map *map);
2203 __isl_give isl_basic_map *isl_basic_map_reverse(
2204 __isl_take isl_basic_map *bmap);
2205 __isl_give isl_map *isl_map_reverse(
2206 __isl_take isl_map *map);
2207 __isl_give isl_union_map *isl_union_map_reverse(
2208 __isl_take isl_union_map *umap);
2212 __isl_give isl_basic_set *isl_basic_set_project_out(
2213 __isl_take isl_basic_set *bset,
2214 enum isl_dim_type type, unsigned first, unsigned n);
2215 __isl_give isl_basic_map *isl_basic_map_project_out(
2216 __isl_take isl_basic_map *bmap,
2217 enum isl_dim_type type, unsigned first, unsigned n);
2218 __isl_give isl_set *isl_set_project_out(__isl_take isl_set *set,
2219 enum isl_dim_type type, unsigned first, unsigned n);
2220 __isl_give isl_map *isl_map_project_out(__isl_take isl_map *map,
2221 enum isl_dim_type type, unsigned first, unsigned n);
2222 __isl_give isl_basic_set *isl_basic_set_params(
2223 __isl_take isl_basic_set *bset);
2224 __isl_give isl_basic_set *isl_basic_map_domain(
2225 __isl_take isl_basic_map *bmap);
2226 __isl_give isl_basic_set *isl_basic_map_range(
2227 __isl_take isl_basic_map *bmap);
2228 __isl_give isl_set *isl_set_params(__isl_take isl_set *set);
2229 __isl_give isl_set *isl_map_params(__isl_take isl_map *map);
2230 __isl_give isl_set *isl_map_domain(
2231 __isl_take isl_map *bmap);
2232 __isl_give isl_set *isl_map_range(
2233 __isl_take isl_map *map);
2234 __isl_give isl_set *isl_union_set_params(
2235 __isl_take isl_union_set *uset);
2236 __isl_give isl_set *isl_union_map_params(
2237 __isl_take isl_union_map *umap);
2238 __isl_give isl_union_set *isl_union_map_domain(
2239 __isl_take isl_union_map *umap);
2240 __isl_give isl_union_set *isl_union_map_range(
2241 __isl_take isl_union_map *umap);
2243 __isl_give isl_basic_map *isl_basic_map_domain_map(
2244 __isl_take isl_basic_map *bmap);
2245 __isl_give isl_basic_map *isl_basic_map_range_map(
2246 __isl_take isl_basic_map *bmap);
2247 __isl_give isl_map *isl_map_domain_map(__isl_take isl_map *map);
2248 __isl_give isl_map *isl_map_range_map(__isl_take isl_map *map);
2249 __isl_give isl_union_map *isl_union_map_domain_map(
2250 __isl_take isl_union_map *umap);
2251 __isl_give isl_union_map *isl_union_map_range_map(
2252 __isl_take isl_union_map *umap);
2254 The functions above construct a (basic, regular or union) relation
2255 that maps (a wrapped version of) the input relation to its domain or range.
2259 __isl_give isl_basic_set *isl_basic_set_eliminate(
2260 __isl_take isl_basic_set *bset,
2261 enum isl_dim_type type,
2262 unsigned first, unsigned n);
2263 __isl_give isl_set *isl_set_eliminate(
2264 __isl_take isl_set *set, enum isl_dim_type type,
2265 unsigned first, unsigned n);
2266 __isl_give isl_basic_map *isl_basic_map_eliminate(
2267 __isl_take isl_basic_map *bmap,
2268 enum isl_dim_type type,
2269 unsigned first, unsigned n);
2270 __isl_give isl_map *isl_map_eliminate(
2271 __isl_take isl_map *map, enum isl_dim_type type,
2272 unsigned first, unsigned n);
2274 Eliminate the coefficients for the given dimensions from the constraints,
2275 without removing the dimensions.
2279 __isl_give isl_basic_set *isl_basic_set_fix(
2280 __isl_take isl_basic_set *bset,
2281 enum isl_dim_type type, unsigned pos,
2283 __isl_give isl_basic_set *isl_basic_set_fix_si(
2284 __isl_take isl_basic_set *bset,
2285 enum isl_dim_type type, unsigned pos, int value);
2286 __isl_give isl_set *isl_set_fix(__isl_take isl_set *set,
2287 enum isl_dim_type type, unsigned pos,
2289 __isl_give isl_set *isl_set_fix_si(__isl_take isl_set *set,
2290 enum isl_dim_type type, unsigned pos, int value);
2291 __isl_give isl_basic_map *isl_basic_map_fix_si(
2292 __isl_take isl_basic_map *bmap,
2293 enum isl_dim_type type, unsigned pos, int value);
2294 __isl_give isl_map *isl_map_fix(__isl_take isl_map *map,
2295 enum isl_dim_type type, unsigned pos,
2297 __isl_give isl_map *isl_map_fix_si(__isl_take isl_map *map,
2298 enum isl_dim_type type, unsigned pos, int value);
2300 Intersect the set or relation with the hyperplane where the given
2301 dimension has the fixed given value.
2303 __isl_give isl_basic_map *isl_basic_map_lower_bound_si(
2304 __isl_take isl_basic_map *bmap,
2305 enum isl_dim_type type, unsigned pos, int value);
2306 __isl_give isl_basic_map *isl_basic_map_upper_bound_si(
2307 __isl_take isl_basic_map *bmap,
2308 enum isl_dim_type type, unsigned pos, int value);
2309 __isl_give isl_set *isl_set_lower_bound(
2310 __isl_take isl_set *set,
2311 enum isl_dim_type type, unsigned pos,
2313 __isl_give isl_set *isl_set_lower_bound_si(
2314 __isl_take isl_set *set,
2315 enum isl_dim_type type, unsigned pos, int value);
2316 __isl_give isl_map *isl_map_lower_bound_si(
2317 __isl_take isl_map *map,
2318 enum isl_dim_type type, unsigned pos, int value);
2319 __isl_give isl_set *isl_set_upper_bound(
2320 __isl_take isl_set *set,
2321 enum isl_dim_type type, unsigned pos,
2323 __isl_give isl_set *isl_set_upper_bound_si(
2324 __isl_take isl_set *set,
2325 enum isl_dim_type type, unsigned pos, int value);
2326 __isl_give isl_map *isl_map_upper_bound_si(
2327 __isl_take isl_map *map,
2328 enum isl_dim_type type, unsigned pos, int value);
2330 Intersect the set or relation with the half-space where the given
2331 dimension has a value bounded by the fixed given value.
2333 __isl_give isl_set *isl_set_equate(__isl_take isl_set *set,
2334 enum isl_dim_type type1, int pos1,
2335 enum isl_dim_type type2, int pos2);
2336 __isl_give isl_basic_map *isl_basic_map_equate(
2337 __isl_take isl_basic_map *bmap,
2338 enum isl_dim_type type1, int pos1,
2339 enum isl_dim_type type2, int pos2);
2340 __isl_give isl_map *isl_map_equate(__isl_take isl_map *map,
2341 enum isl_dim_type type1, int pos1,
2342 enum isl_dim_type type2, int pos2);
2344 Intersect the set or relation with the hyperplane where the given
2345 dimensions are equal to each other.
2347 __isl_give isl_map *isl_map_oppose(__isl_take isl_map *map,
2348 enum isl_dim_type type1, int pos1,
2349 enum isl_dim_type type2, int pos2);
2351 Intersect the relation with the hyperplane where the given
2352 dimensions have opposite values.
2354 __isl_give isl_basic_map *isl_basic_map_order_ge(
2355 __isl_take isl_basic_map *bmap,
2356 enum isl_dim_type type1, int pos1,
2357 enum isl_dim_type type2, int pos2);
2358 __isl_give isl_map *isl_map_order_lt(__isl_take isl_map *map,
2359 enum isl_dim_type type1, int pos1,
2360 enum isl_dim_type type2, int pos2);
2361 __isl_give isl_basic_map *isl_basic_map_order_gt(
2362 __isl_take isl_basic_map *bmap,
2363 enum isl_dim_type type1, int pos1,
2364 enum isl_dim_type type2, int pos2);
2365 __isl_give isl_map *isl_map_order_gt(__isl_take isl_map *map,
2366 enum isl_dim_type type1, int pos1,
2367 enum isl_dim_type type2, int pos2);
2369 Intersect the relation with the half-space where the given
2370 dimensions satisfy the given ordering.
2374 __isl_give isl_map *isl_set_identity(
2375 __isl_take isl_set *set);
2376 __isl_give isl_union_map *isl_union_set_identity(
2377 __isl_take isl_union_set *uset);
2379 Construct an identity relation on the given (union) set.
2383 __isl_give isl_basic_set *isl_basic_map_deltas(
2384 __isl_take isl_basic_map *bmap);
2385 __isl_give isl_set *isl_map_deltas(__isl_take isl_map *map);
2386 __isl_give isl_union_set *isl_union_map_deltas(
2387 __isl_take isl_union_map *umap);
2389 These functions return a (basic) set containing the differences
2390 between image elements and corresponding domain elements in the input.
2392 __isl_give isl_basic_map *isl_basic_map_deltas_map(
2393 __isl_take isl_basic_map *bmap);
2394 __isl_give isl_map *isl_map_deltas_map(
2395 __isl_take isl_map *map);
2396 __isl_give isl_union_map *isl_union_map_deltas_map(
2397 __isl_take isl_union_map *umap);
2399 The functions above construct a (basic, regular or union) relation
2400 that maps (a wrapped version of) the input relation to its delta set.
2404 Simplify the representation of a set or relation by trying
2405 to combine pairs of basic sets or relations into a single
2406 basic set or relation.
2408 __isl_give isl_set *isl_set_coalesce(__isl_take isl_set *set);
2409 __isl_give isl_map *isl_map_coalesce(__isl_take isl_map *map);
2410 __isl_give isl_union_set *isl_union_set_coalesce(
2411 __isl_take isl_union_set *uset);
2412 __isl_give isl_union_map *isl_union_map_coalesce(
2413 __isl_take isl_union_map *umap);
2415 One of the methods for combining pairs of basic sets or relations
2416 can result in coefficients that are much larger than those that appear
2417 in the constraints of the input. By default, the coefficients are
2418 not allowed to grow larger, but this can be changed by unsetting
2419 the following option.
2421 int isl_options_set_coalesce_bounded_wrapping(
2422 isl_ctx *ctx, int val);
2423 int isl_options_get_coalesce_bounded_wrapping(
2426 =item * Detecting equalities
2428 __isl_give isl_basic_set *isl_basic_set_detect_equalities(
2429 __isl_take isl_basic_set *bset);
2430 __isl_give isl_basic_map *isl_basic_map_detect_equalities(
2431 __isl_take isl_basic_map *bmap);
2432 __isl_give isl_set *isl_set_detect_equalities(
2433 __isl_take isl_set *set);
2434 __isl_give isl_map *isl_map_detect_equalities(
2435 __isl_take isl_map *map);
2436 __isl_give isl_union_set *isl_union_set_detect_equalities(
2437 __isl_take isl_union_set *uset);
2438 __isl_give isl_union_map *isl_union_map_detect_equalities(
2439 __isl_take isl_union_map *umap);
2441 Simplify the representation of a set or relation by detecting implicit
2444 =item * Removing redundant constraints
2446 __isl_give isl_basic_set *isl_basic_set_remove_redundancies(
2447 __isl_take isl_basic_set *bset);
2448 __isl_give isl_set *isl_set_remove_redundancies(
2449 __isl_take isl_set *set);
2450 __isl_give isl_basic_map *isl_basic_map_remove_redundancies(
2451 __isl_take isl_basic_map *bmap);
2452 __isl_give isl_map *isl_map_remove_redundancies(
2453 __isl_take isl_map *map);
2457 __isl_give isl_basic_set *isl_set_convex_hull(
2458 __isl_take isl_set *set);
2459 __isl_give isl_basic_map *isl_map_convex_hull(
2460 __isl_take isl_map *map);
2462 If the input set or relation has any existentially quantified
2463 variables, then the result of these operations is currently undefined.
2467 __isl_give isl_basic_set *
2468 isl_set_unshifted_simple_hull(
2469 __isl_take isl_set *set);
2470 __isl_give isl_basic_map *
2471 isl_map_unshifted_simple_hull(
2472 __isl_take isl_map *map);
2473 __isl_give isl_basic_set *isl_set_simple_hull(
2474 __isl_take isl_set *set);
2475 __isl_give isl_basic_map *isl_map_simple_hull(
2476 __isl_take isl_map *map);
2477 __isl_give isl_union_map *isl_union_map_simple_hull(
2478 __isl_take isl_union_map *umap);
2480 These functions compute a single basic set or relation
2481 that contains the whole input set or relation.
2482 In particular, the output is described by translates
2483 of the constraints describing the basic sets or relations in the input.
2484 In case of C<isl_set_unshifted_simple_hull>, only the original
2485 constraints are used, without any translation.
2489 (See \autoref{s:simple hull}.)
2495 __isl_give isl_basic_set *isl_basic_set_affine_hull(
2496 __isl_take isl_basic_set *bset);
2497 __isl_give isl_basic_set *isl_set_affine_hull(
2498 __isl_take isl_set *set);
2499 __isl_give isl_union_set *isl_union_set_affine_hull(
2500 __isl_take isl_union_set *uset);
2501 __isl_give isl_basic_map *isl_basic_map_affine_hull(
2502 __isl_take isl_basic_map *bmap);
2503 __isl_give isl_basic_map *isl_map_affine_hull(
2504 __isl_take isl_map *map);
2505 __isl_give isl_union_map *isl_union_map_affine_hull(
2506 __isl_take isl_union_map *umap);
2508 In case of union sets and relations, the affine hull is computed
2511 =item * Polyhedral hull
2513 __isl_give isl_basic_set *isl_set_polyhedral_hull(
2514 __isl_take isl_set *set);
2515 __isl_give isl_basic_map *isl_map_polyhedral_hull(
2516 __isl_take isl_map *map);
2517 __isl_give isl_union_set *isl_union_set_polyhedral_hull(
2518 __isl_take isl_union_set *uset);
2519 __isl_give isl_union_map *isl_union_map_polyhedral_hull(
2520 __isl_take isl_union_map *umap);
2522 These functions compute a single basic set or relation
2523 not involving any existentially quantified variables
2524 that contains the whole input set or relation.
2525 In case of union sets and relations, the polyhedral hull is computed
2528 =item * Other approximations
2530 __isl_give isl_basic_set *
2531 isl_basic_set_drop_constraints_involving_dims(
2532 __isl_take isl_basic_set *bset,
2533 enum isl_dim_type type,
2534 unsigned first, unsigned n);
2535 __isl_give isl_basic_map *
2536 isl_basic_map_drop_constraints_involving_dims(
2537 __isl_take isl_basic_map *bmap,
2538 enum isl_dim_type type,
2539 unsigned first, unsigned n);
2540 __isl_give isl_basic_set *
2541 isl_basic_set_drop_constraints_not_involving_dims(
2542 __isl_take isl_basic_set *bset,
2543 enum isl_dim_type type,
2544 unsigned first, unsigned n);
2545 __isl_give isl_set *
2546 isl_set_drop_constraints_involving_dims(
2547 __isl_take isl_set *set,
2548 enum isl_dim_type type,
2549 unsigned first, unsigned n);
2550 __isl_give isl_map *
2551 isl_map_drop_constraints_involving_dims(
2552 __isl_take isl_map *map,
2553 enum isl_dim_type type,
2554 unsigned first, unsigned n);
2556 These functions drop any constraints (not) involving the specified dimensions.
2557 Note that the result depends on the representation of the input.
2561 __isl_give isl_basic_set *isl_basic_set_sample(
2562 __isl_take isl_basic_set *bset);
2563 __isl_give isl_basic_set *isl_set_sample(
2564 __isl_take isl_set *set);
2565 __isl_give isl_basic_map *isl_basic_map_sample(
2566 __isl_take isl_basic_map *bmap);
2567 __isl_give isl_basic_map *isl_map_sample(
2568 __isl_take isl_map *map);
2570 If the input (basic) set or relation is non-empty, then return
2571 a singleton subset of the input. Otherwise, return an empty set.
2573 =item * Optimization
2575 #include <isl/ilp.h>
2576 enum isl_lp_result isl_basic_set_max(
2577 __isl_keep isl_basic_set *bset,
2578 __isl_keep isl_aff *obj, isl_int *opt)
2579 enum isl_lp_result isl_set_min(__isl_keep isl_set *set,
2580 __isl_keep isl_aff *obj, isl_int *opt);
2581 enum isl_lp_result isl_set_max(__isl_keep isl_set *set,
2582 __isl_keep isl_aff *obj, isl_int *opt);
2584 Compute the minimum or maximum of the integer affine expression C<obj>
2585 over the points in C<set>, returning the result in C<opt>.
2586 The return value may be one of C<isl_lp_error>,
2587 C<isl_lp_ok>, C<isl_lp_unbounded> or C<isl_lp_empty>.
2589 =item * Parametric optimization
2591 __isl_give isl_pw_aff *isl_set_dim_min(
2592 __isl_take isl_set *set, int pos);
2593 __isl_give isl_pw_aff *isl_set_dim_max(
2594 __isl_take isl_set *set, int pos);
2595 __isl_give isl_pw_aff *isl_map_dim_max(
2596 __isl_take isl_map *map, int pos);
2598 Compute the minimum or maximum of the given set or output dimension
2599 as a function of the parameters (and input dimensions), but independently
2600 of the other set or output dimensions.
2601 For lexicographic optimization, see L<"Lexicographic Optimization">.
2605 The following functions compute either the set of (rational) coefficient
2606 values of valid constraints for the given set or the set of (rational)
2607 values satisfying the constraints with coefficients from the given set.
2608 Internally, these two sets of functions perform essentially the
2609 same operations, except that the set of coefficients is assumed to
2610 be a cone, while the set of values may be any polyhedron.
2611 The current implementation is based on the Farkas lemma and
2612 Fourier-Motzkin elimination, but this may change or be made optional
2613 in future. In particular, future implementations may use different
2614 dualization algorithms or skip the elimination step.
2616 __isl_give isl_basic_set *isl_basic_set_coefficients(
2617 __isl_take isl_basic_set *bset);
2618 __isl_give isl_basic_set *isl_set_coefficients(
2619 __isl_take isl_set *set);
2620 __isl_give isl_union_set *isl_union_set_coefficients(
2621 __isl_take isl_union_set *bset);
2622 __isl_give isl_basic_set *isl_basic_set_solutions(
2623 __isl_take isl_basic_set *bset);
2624 __isl_give isl_basic_set *isl_set_solutions(
2625 __isl_take isl_set *set);
2626 __isl_give isl_union_set *isl_union_set_solutions(
2627 __isl_take isl_union_set *bset);
2631 __isl_give isl_map *isl_map_fixed_power(
2632 __isl_take isl_map *map, isl_int exp);
2633 __isl_give isl_union_map *isl_union_map_fixed_power(
2634 __isl_take isl_union_map *umap, isl_int exp);
2636 Compute the given power of C<map>, where C<exp> is assumed to be non-zero.
2637 If the exponent C<exp> is negative, then the -C<exp> th power of the inverse
2638 of C<map> is computed.
2640 __isl_give isl_map *isl_map_power(__isl_take isl_map *map,
2642 __isl_give isl_union_map *isl_union_map_power(
2643 __isl_take isl_union_map *umap, int *exact);
2645 Compute a parametric representation for all positive powers I<k> of C<map>.
2646 The result maps I<k> to a nested relation corresponding to the
2647 I<k>th power of C<map>.
2648 The result may be an overapproximation. If the result is known to be exact,
2649 then C<*exact> is set to C<1>.
2651 =item * Transitive closure
2653 __isl_give isl_map *isl_map_transitive_closure(
2654 __isl_take isl_map *map, int *exact);
2655 __isl_give isl_union_map *isl_union_map_transitive_closure(
2656 __isl_take isl_union_map *umap, int *exact);
2658 Compute the transitive closure of C<map>.
2659 The result may be an overapproximation. If the result is known to be exact,
2660 then C<*exact> is set to C<1>.
2662 =item * Reaching path lengths
2664 __isl_give isl_map *isl_map_reaching_path_lengths(
2665 __isl_take isl_map *map, int *exact);
2667 Compute a relation that maps each element in the range of C<map>
2668 to the lengths of all paths composed of edges in C<map> that
2669 end up in the given element.
2670 The result may be an overapproximation. If the result is known to be exact,
2671 then C<*exact> is set to C<1>.
2672 To compute the I<maximal> path length, the resulting relation
2673 should be postprocessed by C<isl_map_lexmax>.
2674 In particular, if the input relation is a dependence relation
2675 (mapping sources to sinks), then the maximal path length corresponds
2676 to the free schedule.
2677 Note, however, that C<isl_map_lexmax> expects the maximum to be
2678 finite, so if the path lengths are unbounded (possibly due to
2679 the overapproximation), then you will get an error message.
2683 __isl_give isl_basic_set *isl_basic_map_wrap(
2684 __isl_take isl_basic_map *bmap);
2685 __isl_give isl_set *isl_map_wrap(
2686 __isl_take isl_map *map);
2687 __isl_give isl_union_set *isl_union_map_wrap(
2688 __isl_take isl_union_map *umap);
2689 __isl_give isl_basic_map *isl_basic_set_unwrap(
2690 __isl_take isl_basic_set *bset);
2691 __isl_give isl_map *isl_set_unwrap(
2692 __isl_take isl_set *set);
2693 __isl_give isl_union_map *isl_union_set_unwrap(
2694 __isl_take isl_union_set *uset);
2698 Remove any internal structure of domain (and range) of the given
2699 set or relation. If there is any such internal structure in the input,
2700 then the name of the space is also removed.
2702 __isl_give isl_basic_set *isl_basic_set_flatten(
2703 __isl_take isl_basic_set *bset);
2704 __isl_give isl_set *isl_set_flatten(
2705 __isl_take isl_set *set);
2706 __isl_give isl_basic_map *isl_basic_map_flatten_domain(
2707 __isl_take isl_basic_map *bmap);
2708 __isl_give isl_basic_map *isl_basic_map_flatten_range(
2709 __isl_take isl_basic_map *bmap);
2710 __isl_give isl_map *isl_map_flatten_range(
2711 __isl_take isl_map *map);
2712 __isl_give isl_map *isl_map_flatten_domain(
2713 __isl_take isl_map *map);
2714 __isl_give isl_basic_map *isl_basic_map_flatten(
2715 __isl_take isl_basic_map *bmap);
2716 __isl_give isl_map *isl_map_flatten(
2717 __isl_take isl_map *map);
2719 __isl_give isl_map *isl_set_flatten_map(
2720 __isl_take isl_set *set);
2722 The function above constructs a relation
2723 that maps the input set to a flattened version of the set.
2727 Lift the input set to a space with extra dimensions corresponding
2728 to the existentially quantified variables in the input.
2729 In particular, the result lives in a wrapped map where the domain
2730 is the original space and the range corresponds to the original
2731 existentially quantified variables.
2733 __isl_give isl_basic_set *isl_basic_set_lift(
2734 __isl_take isl_basic_set *bset);
2735 __isl_give isl_set *isl_set_lift(
2736 __isl_take isl_set *set);
2737 __isl_give isl_union_set *isl_union_set_lift(
2738 __isl_take isl_union_set *uset);
2740 Given a local space that contains the existentially quantified
2741 variables of a set, a basic relation that, when applied to
2742 a basic set, has essentially the same effect as C<isl_basic_set_lift>,
2743 can be constructed using the following function.
2745 #include <isl/local_space.h>
2746 __isl_give isl_basic_map *isl_local_space_lifting(
2747 __isl_take isl_local_space *ls);
2749 =item * Internal Product
2751 __isl_give isl_basic_map *isl_basic_map_zip(
2752 __isl_take isl_basic_map *bmap);
2753 __isl_give isl_map *isl_map_zip(
2754 __isl_take isl_map *map);
2755 __isl_give isl_union_map *isl_union_map_zip(
2756 __isl_take isl_union_map *umap);
2758 Given a relation with nested relations for domain and range,
2759 interchange the range of the domain with the domain of the range.
2763 __isl_give isl_basic_map *isl_basic_map_curry(
2764 __isl_take isl_basic_map *bmap);
2765 __isl_give isl_basic_map *isl_basic_map_uncurry(
2766 __isl_take isl_basic_map *bmap);
2767 __isl_give isl_map *isl_map_curry(
2768 __isl_take isl_map *map);
2769 __isl_give isl_map *isl_map_uncurry(
2770 __isl_take isl_map *map);
2771 __isl_give isl_union_map *isl_union_map_curry(
2772 __isl_take isl_union_map *umap);
2773 __isl_give isl_union_map *isl_union_map_uncurry(
2774 __isl_take isl_union_map *umap);
2776 Given a relation with a nested relation for domain,
2777 the C<curry> functions
2778 move the range of the nested relation out of the domain
2779 and use it as the domain of a nested relation in the range,
2780 with the original range as range of this nested relation.
2781 The C<uncurry> functions perform the inverse operation.
2783 =item * Aligning parameters
2785 __isl_give isl_basic_set *isl_basic_set_align_params(
2786 __isl_take isl_basic_set *bset,
2787 __isl_take isl_space *model);
2788 __isl_give isl_set *isl_set_align_params(
2789 __isl_take isl_set *set,
2790 __isl_take isl_space *model);
2791 __isl_give isl_basic_map *isl_basic_map_align_params(
2792 __isl_take isl_basic_map *bmap,
2793 __isl_take isl_space *model);
2794 __isl_give isl_map *isl_map_align_params(
2795 __isl_take isl_map *map,
2796 __isl_take isl_space *model);
2798 Change the order of the parameters of the given set or relation
2799 such that the first parameters match those of C<model>.
2800 This may involve the introduction of extra parameters.
2801 All parameters need to be named.
2803 =item * Dimension manipulation
2805 __isl_give isl_basic_set *isl_basic_set_add_dims(
2806 __isl_take isl_basic_set *bset,
2807 enum isl_dim_type type, unsigned n);
2808 __isl_give isl_set *isl_set_add_dims(
2809 __isl_take isl_set *set,
2810 enum isl_dim_type type, unsigned n);
2811 __isl_give isl_map *isl_map_add_dims(
2812 __isl_take isl_map *map,
2813 enum isl_dim_type type, unsigned n);
2814 __isl_give isl_basic_set *isl_basic_set_insert_dims(
2815 __isl_take isl_basic_set *bset,
2816 enum isl_dim_type type, unsigned pos,
2818 __isl_give isl_basic_map *isl_basic_map_insert_dims(
2819 __isl_take isl_basic_map *bmap,
2820 enum isl_dim_type type, unsigned pos,
2822 __isl_give isl_set *isl_set_insert_dims(
2823 __isl_take isl_set *set,
2824 enum isl_dim_type type, unsigned pos, unsigned n);
2825 __isl_give isl_map *isl_map_insert_dims(
2826 __isl_take isl_map *map,
2827 enum isl_dim_type type, unsigned pos, unsigned n);
2828 __isl_give isl_basic_set *isl_basic_set_move_dims(
2829 __isl_take isl_basic_set *bset,
2830 enum isl_dim_type dst_type, unsigned dst_pos,
2831 enum isl_dim_type src_type, unsigned src_pos,
2833 __isl_give isl_basic_map *isl_basic_map_move_dims(
2834 __isl_take isl_basic_map *bmap,
2835 enum isl_dim_type dst_type, unsigned dst_pos,
2836 enum isl_dim_type src_type, unsigned src_pos,
2838 __isl_give isl_set *isl_set_move_dims(
2839 __isl_take isl_set *set,
2840 enum isl_dim_type dst_type, unsigned dst_pos,
2841 enum isl_dim_type src_type, unsigned src_pos,
2843 __isl_give isl_map *isl_map_move_dims(
2844 __isl_take isl_map *map,
2845 enum isl_dim_type dst_type, unsigned dst_pos,
2846 enum isl_dim_type src_type, unsigned src_pos,
2849 It is usually not advisable to directly change the (input or output)
2850 space of a set or a relation as this removes the name and the internal
2851 structure of the space. However, the above functions can be useful
2852 to add new parameters, assuming
2853 C<isl_set_align_params> and C<isl_map_align_params>
2858 =head2 Binary Operations
2860 The two arguments of a binary operation not only need to live
2861 in the same C<isl_ctx>, they currently also need to have
2862 the same (number of) parameters.
2864 =head3 Basic Operations
2868 =item * Intersection
2870 __isl_give isl_basic_set *isl_basic_set_intersect_params(
2871 __isl_take isl_basic_set *bset1,
2872 __isl_take isl_basic_set *bset2);
2873 __isl_give isl_basic_set *isl_basic_set_intersect(
2874 __isl_take isl_basic_set *bset1,
2875 __isl_take isl_basic_set *bset2);
2876 __isl_give isl_set *isl_set_intersect_params(
2877 __isl_take isl_set *set,
2878 __isl_take isl_set *params);
2879 __isl_give isl_set *isl_set_intersect(
2880 __isl_take isl_set *set1,
2881 __isl_take isl_set *set2);
2882 __isl_give isl_union_set *isl_union_set_intersect_params(
2883 __isl_take isl_union_set *uset,
2884 __isl_take isl_set *set);
2885 __isl_give isl_union_map *isl_union_map_intersect_params(
2886 __isl_take isl_union_map *umap,
2887 __isl_take isl_set *set);
2888 __isl_give isl_union_set *isl_union_set_intersect(
2889 __isl_take isl_union_set *uset1,
2890 __isl_take isl_union_set *uset2);
2891 __isl_give isl_basic_map *isl_basic_map_intersect_domain(
2892 __isl_take isl_basic_map *bmap,
2893 __isl_take isl_basic_set *bset);
2894 __isl_give isl_basic_map *isl_basic_map_intersect_range(
2895 __isl_take isl_basic_map *bmap,
2896 __isl_take isl_basic_set *bset);
2897 __isl_give isl_basic_map *isl_basic_map_intersect(
2898 __isl_take isl_basic_map *bmap1,
2899 __isl_take isl_basic_map *bmap2);
2900 __isl_give isl_map *isl_map_intersect_params(
2901 __isl_take isl_map *map,
2902 __isl_take isl_set *params);
2903 __isl_give isl_map *isl_map_intersect_domain(
2904 __isl_take isl_map *map,
2905 __isl_take isl_set *set);
2906 __isl_give isl_map *isl_map_intersect_range(
2907 __isl_take isl_map *map,
2908 __isl_take isl_set *set);
2909 __isl_give isl_map *isl_map_intersect(
2910 __isl_take isl_map *map1,
2911 __isl_take isl_map *map2);
2912 __isl_give isl_union_map *isl_union_map_intersect_domain(
2913 __isl_take isl_union_map *umap,
2914 __isl_take isl_union_set *uset);
2915 __isl_give isl_union_map *isl_union_map_intersect_range(
2916 __isl_take isl_union_map *umap,
2917 __isl_take isl_union_set *uset);
2918 __isl_give isl_union_map *isl_union_map_intersect(
2919 __isl_take isl_union_map *umap1,
2920 __isl_take isl_union_map *umap2);
2922 The second argument to the C<_params> functions needs to be
2923 a parametric (basic) set. For the other functions, a parametric set
2924 for either argument is only allowed if the other argument is
2925 a parametric set as well.
2929 __isl_give isl_set *isl_basic_set_union(
2930 __isl_take isl_basic_set *bset1,
2931 __isl_take isl_basic_set *bset2);
2932 __isl_give isl_map *isl_basic_map_union(
2933 __isl_take isl_basic_map *bmap1,
2934 __isl_take isl_basic_map *bmap2);
2935 __isl_give isl_set *isl_set_union(
2936 __isl_take isl_set *set1,
2937 __isl_take isl_set *set2);
2938 __isl_give isl_map *isl_map_union(
2939 __isl_take isl_map *map1,
2940 __isl_take isl_map *map2);
2941 __isl_give isl_union_set *isl_union_set_union(
2942 __isl_take isl_union_set *uset1,
2943 __isl_take isl_union_set *uset2);
2944 __isl_give isl_union_map *isl_union_map_union(
2945 __isl_take isl_union_map *umap1,
2946 __isl_take isl_union_map *umap2);
2948 =item * Set difference
2950 __isl_give isl_set *isl_set_subtract(
2951 __isl_take isl_set *set1,
2952 __isl_take isl_set *set2);
2953 __isl_give isl_map *isl_map_subtract(
2954 __isl_take isl_map *map1,
2955 __isl_take isl_map *map2);
2956 __isl_give isl_map *isl_map_subtract_domain(
2957 __isl_take isl_map *map,
2958 __isl_take isl_set *dom);
2959 __isl_give isl_map *isl_map_subtract_range(
2960 __isl_take isl_map *map,
2961 __isl_take isl_set *dom);
2962 __isl_give isl_union_set *isl_union_set_subtract(
2963 __isl_take isl_union_set *uset1,
2964 __isl_take isl_union_set *uset2);
2965 __isl_give isl_union_map *isl_union_map_subtract(
2966 __isl_take isl_union_map *umap1,
2967 __isl_take isl_union_map *umap2);
2968 __isl_give isl_union_map *isl_union_map_subtract_domain(
2969 __isl_take isl_union_map *umap,
2970 __isl_take isl_union_set *dom);
2971 __isl_give isl_union_map *isl_union_map_subtract_range(
2972 __isl_take isl_union_map *umap,
2973 __isl_take isl_union_set *dom);
2977 __isl_give isl_basic_set *isl_basic_set_apply(
2978 __isl_take isl_basic_set *bset,
2979 __isl_take isl_basic_map *bmap);
2980 __isl_give isl_set *isl_set_apply(
2981 __isl_take isl_set *set,
2982 __isl_take isl_map *map);
2983 __isl_give isl_union_set *isl_union_set_apply(
2984 __isl_take isl_union_set *uset,
2985 __isl_take isl_union_map *umap);
2986 __isl_give isl_basic_map *isl_basic_map_apply_domain(
2987 __isl_take isl_basic_map *bmap1,
2988 __isl_take isl_basic_map *bmap2);
2989 __isl_give isl_basic_map *isl_basic_map_apply_range(
2990 __isl_take isl_basic_map *bmap1,
2991 __isl_take isl_basic_map *bmap2);
2992 __isl_give isl_map *isl_map_apply_domain(
2993 __isl_take isl_map *map1,
2994 __isl_take isl_map *map2);
2995 __isl_give isl_union_map *isl_union_map_apply_domain(
2996 __isl_take isl_union_map *umap1,
2997 __isl_take isl_union_map *umap2);
2998 __isl_give isl_map *isl_map_apply_range(
2999 __isl_take isl_map *map1,
3000 __isl_take isl_map *map2);
3001 __isl_give isl_union_map *isl_union_map_apply_range(
3002 __isl_take isl_union_map *umap1,
3003 __isl_take isl_union_map *umap2);
3007 __isl_give isl_basic_set *
3008 isl_basic_set_preimage_multi_aff(
3009 __isl_take isl_basic_set *bset,
3010 __isl_take isl_multi_aff *ma);
3011 __isl_give isl_set *isl_set_preimage_multi_aff(
3012 __isl_take isl_set *set,
3013 __isl_take isl_multi_aff *ma);
3014 __isl_give isl_set *isl_set_preimage_pw_multi_aff(
3015 __isl_take isl_set *set,
3016 __isl_take isl_pw_multi_aff *pma);
3017 __isl_give isl_map *isl_map_preimage_domain_multi_aff(
3018 __isl_take isl_map *map,
3019 __isl_take isl_multi_aff *ma);
3020 __isl_give isl_union_map *
3021 isl_union_map_preimage_domain_multi_aff(
3022 __isl_take isl_union_map *umap,
3023 __isl_take isl_multi_aff *ma);
3025 These functions compute the preimage of the given set or map domain under
3026 the given function. In other words, the expression is plugged
3027 into the set description or into the domain of the map.
3028 Objects of types C<isl_multi_aff> and C<isl_pw_multi_aff> are described in
3029 L</"Piecewise Multiple Quasi Affine Expressions">.
3031 =item * Cartesian Product
3033 __isl_give isl_set *isl_set_product(
3034 __isl_take isl_set *set1,
3035 __isl_take isl_set *set2);
3036 __isl_give isl_union_set *isl_union_set_product(
3037 __isl_take isl_union_set *uset1,
3038 __isl_take isl_union_set *uset2);
3039 __isl_give isl_basic_map *isl_basic_map_domain_product(
3040 __isl_take isl_basic_map *bmap1,
3041 __isl_take isl_basic_map *bmap2);
3042 __isl_give isl_basic_map *isl_basic_map_range_product(
3043 __isl_take isl_basic_map *bmap1,
3044 __isl_take isl_basic_map *bmap2);
3045 __isl_give isl_basic_map *isl_basic_map_product(
3046 __isl_take isl_basic_map *bmap1,
3047 __isl_take isl_basic_map *bmap2);
3048 __isl_give isl_map *isl_map_domain_product(
3049 __isl_take isl_map *map1,
3050 __isl_take isl_map *map2);
3051 __isl_give isl_map *isl_map_range_product(
3052 __isl_take isl_map *map1,
3053 __isl_take isl_map *map2);
3054 __isl_give isl_union_map *isl_union_map_domain_product(
3055 __isl_take isl_union_map *umap1,
3056 __isl_take isl_union_map *umap2);
3057 __isl_give isl_union_map *isl_union_map_range_product(
3058 __isl_take isl_union_map *umap1,
3059 __isl_take isl_union_map *umap2);
3060 __isl_give isl_map *isl_map_product(
3061 __isl_take isl_map *map1,
3062 __isl_take isl_map *map2);
3063 __isl_give isl_union_map *isl_union_map_product(
3064 __isl_take isl_union_map *umap1,
3065 __isl_take isl_union_map *umap2);
3067 The above functions compute the cross product of the given
3068 sets or relations. The domains and ranges of the results
3069 are wrapped maps between domains and ranges of the inputs.
3070 To obtain a ``flat'' product, use the following functions
3073 __isl_give isl_basic_set *isl_basic_set_flat_product(
3074 __isl_take isl_basic_set *bset1,
3075 __isl_take isl_basic_set *bset2);
3076 __isl_give isl_set *isl_set_flat_product(
3077 __isl_take isl_set *set1,
3078 __isl_take isl_set *set2);
3079 __isl_give isl_basic_map *isl_basic_map_flat_range_product(
3080 __isl_take isl_basic_map *bmap1,
3081 __isl_take isl_basic_map *bmap2);
3082 __isl_give isl_map *isl_map_flat_domain_product(
3083 __isl_take isl_map *map1,
3084 __isl_take isl_map *map2);
3085 __isl_give isl_map *isl_map_flat_range_product(
3086 __isl_take isl_map *map1,
3087 __isl_take isl_map *map2);
3088 __isl_give isl_union_map *isl_union_map_flat_range_product(
3089 __isl_take isl_union_map *umap1,
3090 __isl_take isl_union_map *umap2);
3091 __isl_give isl_basic_map *isl_basic_map_flat_product(
3092 __isl_take isl_basic_map *bmap1,
3093 __isl_take isl_basic_map *bmap2);
3094 __isl_give isl_map *isl_map_flat_product(
3095 __isl_take isl_map *map1,
3096 __isl_take isl_map *map2);
3098 =item * Simplification
3100 __isl_give isl_basic_set *isl_basic_set_gist(
3101 __isl_take isl_basic_set *bset,
3102 __isl_take isl_basic_set *context);
3103 __isl_give isl_set *isl_set_gist(__isl_take isl_set *set,
3104 __isl_take isl_set *context);
3105 __isl_give isl_set *isl_set_gist_params(
3106 __isl_take isl_set *set,
3107 __isl_take isl_set *context);
3108 __isl_give isl_union_set *isl_union_set_gist(
3109 __isl_take isl_union_set *uset,
3110 __isl_take isl_union_set *context);
3111 __isl_give isl_union_set *isl_union_set_gist_params(
3112 __isl_take isl_union_set *uset,
3113 __isl_take isl_set *set);
3114 __isl_give isl_basic_map *isl_basic_map_gist(
3115 __isl_take isl_basic_map *bmap,
3116 __isl_take isl_basic_map *context);
3117 __isl_give isl_map *isl_map_gist(__isl_take isl_map *map,
3118 __isl_take isl_map *context);
3119 __isl_give isl_map *isl_map_gist_params(
3120 __isl_take isl_map *map,
3121 __isl_take isl_set *context);
3122 __isl_give isl_map *isl_map_gist_domain(
3123 __isl_take isl_map *map,
3124 __isl_take isl_set *context);
3125 __isl_give isl_map *isl_map_gist_range(
3126 __isl_take isl_map *map,
3127 __isl_take isl_set *context);
3128 __isl_give isl_union_map *isl_union_map_gist(
3129 __isl_take isl_union_map *umap,
3130 __isl_take isl_union_map *context);
3131 __isl_give isl_union_map *isl_union_map_gist_params(
3132 __isl_take isl_union_map *umap,
3133 __isl_take isl_set *set);
3134 __isl_give isl_union_map *isl_union_map_gist_domain(
3135 __isl_take isl_union_map *umap,
3136 __isl_take isl_union_set *uset);
3137 __isl_give isl_union_map *isl_union_map_gist_range(
3138 __isl_take isl_union_map *umap,
3139 __isl_take isl_union_set *uset);
3141 The gist operation returns a set or relation that has the
3142 same intersection with the context as the input set or relation.
3143 Any implicit equality in the intersection is made explicit in the result,
3144 while all inequalities that are redundant with respect to the intersection
3146 In case of union sets and relations, the gist operation is performed
3151 =head3 Lexicographic Optimization
3153 Given a (basic) set C<set> (or C<bset>) and a zero-dimensional domain C<dom>,
3154 the following functions
3155 compute a set that contains the lexicographic minimum or maximum
3156 of the elements in C<set> (or C<bset>) for those values of the parameters
3157 that satisfy C<dom>.
3158 If C<empty> is not C<NULL>, then C<*empty> is assigned a set
3159 that contains the parameter values in C<dom> for which C<set> (or C<bset>)
3161 In other words, the union of the parameter values
3162 for which the result is non-empty and of C<*empty>
3165 __isl_give isl_set *isl_basic_set_partial_lexmin(
3166 __isl_take isl_basic_set *bset,
3167 __isl_take isl_basic_set *dom,
3168 __isl_give isl_set **empty);
3169 __isl_give isl_set *isl_basic_set_partial_lexmax(
3170 __isl_take isl_basic_set *bset,
3171 __isl_take isl_basic_set *dom,
3172 __isl_give isl_set **empty);
3173 __isl_give isl_set *isl_set_partial_lexmin(
3174 __isl_take isl_set *set, __isl_take isl_set *dom,
3175 __isl_give isl_set **empty);
3176 __isl_give isl_set *isl_set_partial_lexmax(
3177 __isl_take isl_set *set, __isl_take isl_set *dom,
3178 __isl_give isl_set **empty);
3180 Given a (basic) set C<set> (or C<bset>), the following functions simply
3181 return a set containing the lexicographic minimum or maximum
3182 of the elements in C<set> (or C<bset>).
3183 In case of union sets, the optimum is computed per space.
3185 __isl_give isl_set *isl_basic_set_lexmin(
3186 __isl_take isl_basic_set *bset);
3187 __isl_give isl_set *isl_basic_set_lexmax(
3188 __isl_take isl_basic_set *bset);
3189 __isl_give isl_set *isl_set_lexmin(
3190 __isl_take isl_set *set);
3191 __isl_give isl_set *isl_set_lexmax(
3192 __isl_take isl_set *set);
3193 __isl_give isl_union_set *isl_union_set_lexmin(
3194 __isl_take isl_union_set *uset);
3195 __isl_give isl_union_set *isl_union_set_lexmax(
3196 __isl_take isl_union_set *uset);
3198 Given a (basic) relation C<map> (or C<bmap>) and a domain C<dom>,
3199 the following functions
3200 compute a relation that maps each element of C<dom>
3201 to the single lexicographic minimum or maximum
3202 of the elements that are associated to that same
3203 element in C<map> (or C<bmap>).
3204 If C<empty> is not C<NULL>, then C<*empty> is assigned a set
3205 that contains the elements in C<dom> that do not map
3206 to any elements in C<map> (or C<bmap>).
3207 In other words, the union of the domain of the result and of C<*empty>
3210 __isl_give isl_map *isl_basic_map_partial_lexmax(
3211 __isl_take isl_basic_map *bmap,
3212 __isl_take isl_basic_set *dom,
3213 __isl_give isl_set **empty);
3214 __isl_give isl_map *isl_basic_map_partial_lexmin(
3215 __isl_take isl_basic_map *bmap,
3216 __isl_take isl_basic_set *dom,
3217 __isl_give isl_set **empty);
3218 __isl_give isl_map *isl_map_partial_lexmax(
3219 __isl_take isl_map *map, __isl_take isl_set *dom,
3220 __isl_give isl_set **empty);
3221 __isl_give isl_map *isl_map_partial_lexmin(
3222 __isl_take isl_map *map, __isl_take isl_set *dom,
3223 __isl_give isl_set **empty);
3225 Given a (basic) map C<map> (or C<bmap>), the following functions simply
3226 return a map mapping each element in the domain of
3227 C<map> (or C<bmap>) to the lexicographic minimum or maximum
3228 of all elements associated to that element.
3229 In case of union relations, the optimum is computed per space.
3231 __isl_give isl_map *isl_basic_map_lexmin(
3232 __isl_take isl_basic_map *bmap);
3233 __isl_give isl_map *isl_basic_map_lexmax(
3234 __isl_take isl_basic_map *bmap);
3235 __isl_give isl_map *isl_map_lexmin(
3236 __isl_take isl_map *map);
3237 __isl_give isl_map *isl_map_lexmax(
3238 __isl_take isl_map *map);
3239 __isl_give isl_union_map *isl_union_map_lexmin(
3240 __isl_take isl_union_map *umap);
3241 __isl_give isl_union_map *isl_union_map_lexmax(
3242 __isl_take isl_union_map *umap);
3244 The following functions return their result in the form of
3245 a piecewise multi-affine expression
3246 (See L<"Piecewise Multiple Quasi Affine Expressions">),
3247 but are otherwise equivalent to the corresponding functions
3248 returning a basic set or relation.
3250 __isl_give isl_pw_multi_aff *
3251 isl_basic_map_lexmin_pw_multi_aff(
3252 __isl_take isl_basic_map *bmap);
3253 __isl_give isl_pw_multi_aff *
3254 isl_basic_set_partial_lexmin_pw_multi_aff(
3255 __isl_take isl_basic_set *bset,
3256 __isl_take isl_basic_set *dom,
3257 __isl_give isl_set **empty);
3258 __isl_give isl_pw_multi_aff *
3259 isl_basic_set_partial_lexmax_pw_multi_aff(
3260 __isl_take isl_basic_set *bset,
3261 __isl_take isl_basic_set *dom,
3262 __isl_give isl_set **empty);
3263 __isl_give isl_pw_multi_aff *
3264 isl_basic_map_partial_lexmin_pw_multi_aff(
3265 __isl_take isl_basic_map *bmap,
3266 __isl_take isl_basic_set *dom,
3267 __isl_give isl_set **empty);
3268 __isl_give isl_pw_multi_aff *
3269 isl_basic_map_partial_lexmax_pw_multi_aff(
3270 __isl_take isl_basic_map *bmap,
3271 __isl_take isl_basic_set *dom,
3272 __isl_give isl_set **empty);
3273 __isl_give isl_pw_multi_aff *isl_set_lexmin_pw_multi_aff(
3274 __isl_take isl_set *set);
3275 __isl_give isl_pw_multi_aff *isl_set_lexmax_pw_multi_aff(
3276 __isl_take isl_set *set);
3277 __isl_give isl_pw_multi_aff *isl_map_lexmin_pw_multi_aff(
3278 __isl_take isl_map *map);
3279 __isl_give isl_pw_multi_aff *isl_map_lexmax_pw_multi_aff(
3280 __isl_take isl_map *map);
3284 Lists are defined over several element types, including
3285 C<isl_val>, C<isl_id>, C<isl_aff>, C<isl_pw_aff>, C<isl_constraint>,
3286 C<isl_basic_set>, C<isl_set>, C<isl_ast_expr> and C<isl_ast_node>.
3287 Here we take lists of C<isl_set>s as an example.
3288 Lists can be created, copied, modified and freed using the following functions.
3290 #include <isl/list.h>
3291 __isl_give isl_set_list *isl_set_list_from_set(
3292 __isl_take isl_set *el);
3293 __isl_give isl_set_list *isl_set_list_alloc(
3294 isl_ctx *ctx, int n);
3295 __isl_give isl_set_list *isl_set_list_copy(
3296 __isl_keep isl_set_list *list);
3297 __isl_give isl_set_list *isl_set_list_insert(
3298 __isl_take isl_set_list *list, unsigned pos,
3299 __isl_take isl_set *el);
3300 __isl_give isl_set_list *isl_set_list_add(
3301 __isl_take isl_set_list *list,
3302 __isl_take isl_set *el);
3303 __isl_give isl_set_list *isl_set_list_drop(
3304 __isl_take isl_set_list *list,
3305 unsigned first, unsigned n);
3306 __isl_give isl_set_list *isl_set_list_set_set(
3307 __isl_take isl_set_list *list, int index,
3308 __isl_take isl_set *set);
3309 __isl_give isl_set_list *isl_set_list_concat(
3310 __isl_take isl_set_list *list1,
3311 __isl_take isl_set_list *list2);
3312 __isl_give isl_set_list *isl_set_list_sort(
3313 __isl_take isl_set_list *list,
3314 int (*cmp)(__isl_keep isl_set *a,
3315 __isl_keep isl_set *b, void *user),
3317 void *isl_set_list_free(__isl_take isl_set_list *list);
3319 C<isl_set_list_alloc> creates an empty list with a capacity for
3320 C<n> elements. C<isl_set_list_from_set> creates a list with a single
3323 Lists can be inspected using the following functions.
3325 #include <isl/list.h>
3326 isl_ctx *isl_set_list_get_ctx(__isl_keep isl_set_list *list);
3327 int isl_set_list_n_set(__isl_keep isl_set_list *list);
3328 __isl_give isl_set *isl_set_list_get_set(
3329 __isl_keep isl_set_list *list, int index);
3330 int isl_set_list_foreach(__isl_keep isl_set_list *list,
3331 int (*fn)(__isl_take isl_set *el, void *user),
3333 int isl_set_list_foreach_scc(__isl_keep isl_set_list *list,
3334 int (*follows)(__isl_keep isl_set *a,
3335 __isl_keep isl_set *b, void *user),
3337 int (*fn)(__isl_take isl_set *el, void *user),
3340 The function C<isl_set_list_foreach_scc> calls C<fn> on each of the
3341 strongly connected components of the graph with as vertices the elements
3342 of C<list> and a directed edge from vertex C<b> to vertex C<a>
3343 iff C<follows(a, b)> returns C<1>. The callbacks C<follows> and C<fn>
3344 should return C<-1> on error.
3346 Lists can be printed using
3348 #include <isl/list.h>
3349 __isl_give isl_printer *isl_printer_print_set_list(
3350 __isl_take isl_printer *p,
3351 __isl_keep isl_set_list *list);
3353 =head2 Multiple Values
3355 An C<isl_multi_val> object represents a sequence of zero or more values,
3356 living in a set space.
3358 An C<isl_multi_val> can be constructed from an C<isl_val_list>
3359 using the following function
3361 #include <isl/val.h>
3362 __isl_give isl_multi_val *isl_multi_val_from_val_list(
3363 __isl_take isl_space *space,
3364 __isl_take isl_val_list *list);
3366 The zero multiple value (with value zero for each set dimension)
3367 can be created using the following function.
3369 #include <isl/val.h>
3370 __isl_give isl_multi_val *isl_multi_val_zero(
3371 __isl_take isl_space *space);
3373 Multiple values can be copied and freed using
3375 #include <isl/val.h>
3376 __isl_give isl_multi_val *isl_multi_val_copy(
3377 __isl_keep isl_multi_val *mv);
3378 void *isl_multi_val_free(__isl_take isl_multi_val *mv);
3380 They can be inspected using
3382 #include <isl/val.h>
3383 isl_ctx *isl_multi_val_get_ctx(
3384 __isl_keep isl_multi_val *mv);
3385 unsigned isl_multi_val_dim(__isl_keep isl_multi_val *mv,
3386 enum isl_dim_type type);
3387 __isl_give isl_val *isl_multi_val_get_val(
3388 __isl_keep isl_multi_val *mv, int pos);
3389 const char *isl_multi_val_get_tuple_name(
3390 __isl_keep isl_multi_val *mv,
3391 enum isl_dim_type type);
3393 They can be modified using
3395 #include <isl/val.h>
3396 __isl_give isl_multi_val *isl_multi_val_set_val(
3397 __isl_take isl_multi_val *mv, int pos,
3398 __isl_take isl_val *val);
3399 __isl_give isl_multi_val *isl_multi_val_set_dim_name(
3400 __isl_take isl_multi_val *mv,
3401 enum isl_dim_type type, unsigned pos, const char *s);
3402 __isl_give isl_multi_val *isl_multi_val_set_tuple_name(
3403 __isl_take isl_multi_val *mv,
3404 enum isl_dim_type type, const char *s);
3405 __isl_give isl_multi_val *isl_multi_val_set_tuple_id(
3406 __isl_take isl_multi_val *mv,
3407 enum isl_dim_type type, __isl_take isl_id *id);
3409 __isl_give isl_multi_val *isl_multi_val_insert_dims(
3410 __isl_take isl_multi_val *mv,
3411 enum isl_dim_type type, unsigned first, unsigned n);
3412 __isl_give isl_multi_val *isl_multi_val_add_dims(
3413 __isl_take isl_multi_val *mv,
3414 enum isl_dim_type type, unsigned n);
3415 __isl_give isl_multi_val *isl_multi_val_drop_dims(
3416 __isl_take isl_multi_val *mv,
3417 enum isl_dim_type type, unsigned first, unsigned n);
3421 #include <isl/val.h>
3422 __isl_give isl_multi_val *isl_multi_val_align_params(
3423 __isl_take isl_multi_val *mv,
3424 __isl_take isl_space *model);
3425 __isl_give isl_multi_val *isl_multi_val_range_splice(
3426 __isl_take isl_multi_val *mv1, unsigned pos,
3427 __isl_take isl_multi_val *mv2);
3428 __isl_give isl_multi_val *isl_multi_val_range_product(
3429 __isl_take isl_multi_val *mv1,
3430 __isl_take isl_multi_val *mv2);
3431 __isl_give isl_multi_val *isl_multi_val_flat_range_product(
3432 __isl_take isl_multi_val *mv1,
3433 __isl_take isl_multi_aff *mv2);
3434 __isl_give isl_multi_val *isl_multi_val_add_val(
3435 __isl_take isl_multi_val *mv,
3436 __isl_take isl_val *v);
3437 __isl_give isl_multi_val *isl_multi_val_mod_val(
3438 __isl_take isl_multi_val *mv,
3439 __isl_take isl_val *v);
3440 __isl_give isl_multi_val *isl_multi_val_scale_val(
3441 __isl_take isl_multi_val *mv,
3442 __isl_take isl_val *v);
3446 Vectors can be created, copied and freed using the following functions.
3448 #include <isl/vec.h>
3449 __isl_give isl_vec *isl_vec_alloc(isl_ctx *ctx,
3451 __isl_give isl_vec *isl_vec_copy(__isl_keep isl_vec *vec);
3452 void *isl_vec_free(__isl_take isl_vec *vec);
3454 Note that the elements of a newly created vector may have arbitrary values.
3455 The elements can be changed and inspected using the following functions.
3457 isl_ctx *isl_vec_get_ctx(__isl_keep isl_vec *vec);
3458 int isl_vec_size(__isl_keep isl_vec *vec);
3459 int isl_vec_get_element(__isl_keep isl_vec *vec,
3460 int pos, isl_int *v);
3461 __isl_give isl_val *isl_vec_get_element_val(
3462 __isl_keep isl_vec *vec, int pos);
3463 __isl_give isl_vec *isl_vec_set_element(
3464 __isl_take isl_vec *vec, int pos, isl_int v);
3465 __isl_give isl_vec *isl_vec_set_element_si(
3466 __isl_take isl_vec *vec, int pos, int v);
3467 __isl_give isl_vec *isl_vec_set_element_val(
3468 __isl_take isl_vec *vec, int pos,
3469 __isl_take isl_val *v);
3470 __isl_give isl_vec *isl_vec_set(__isl_take isl_vec *vec,
3472 __isl_give isl_vec *isl_vec_set_si(__isl_take isl_vec *vec,
3474 __isl_give isl_vec *isl_vec_set_val(
3475 __isl_take isl_vec *vec, __isl_take isl_val *v);
3476 __isl_give isl_vec *isl_vec_fdiv_r(__isl_take isl_vec *vec,
3479 C<isl_vec_get_element> will return a negative value if anything went wrong.
3480 In that case, the value of C<*v> is undefined.
3482 The following function can be used to concatenate two vectors.
3484 __isl_give isl_vec *isl_vec_concat(__isl_take isl_vec *vec1,
3485 __isl_take isl_vec *vec2);
3489 Matrices can be created, copied and freed using the following functions.
3491 #include <isl/mat.h>
3492 __isl_give isl_mat *isl_mat_alloc(isl_ctx *ctx,
3493 unsigned n_row, unsigned n_col);
3494 __isl_give isl_mat *isl_mat_copy(__isl_keep isl_mat *mat);
3495 void *isl_mat_free(__isl_take isl_mat *mat);
3497 Note that the elements of a newly created matrix may have arbitrary values.
3498 The elements can be changed and inspected using the following functions.
3500 isl_ctx *isl_mat_get_ctx(__isl_keep isl_mat *mat);
3501 int isl_mat_rows(__isl_keep isl_mat *mat);
3502 int isl_mat_cols(__isl_keep isl_mat *mat);
3503 int isl_mat_get_element(__isl_keep isl_mat *mat,
3504 int row, int col, isl_int *v);
3505 __isl_give isl_val *isl_mat_get_element_val(
3506 __isl_keep isl_mat *mat, int row, int col);
3507 __isl_give isl_mat *isl_mat_set_element(__isl_take isl_mat *mat,
3508 int row, int col, isl_int v);
3509 __isl_give isl_mat *isl_mat_set_element_si(__isl_take isl_mat *mat,
3510 int row, int col, int v);
3511 __isl_give isl_mat *isl_mat_set_element_val(
3512 __isl_take isl_mat *mat, int row, int col,
3513 __isl_take isl_val *v);
3515 C<isl_mat_get_element> will return a negative value if anything went wrong.
3516 In that case, the value of C<*v> is undefined.
3518 The following function can be used to compute the (right) inverse
3519 of a matrix, i.e., a matrix such that the product of the original
3520 and the inverse (in that order) is a multiple of the identity matrix.
3521 The input matrix is assumed to be of full row-rank.
3523 __isl_give isl_mat *isl_mat_right_inverse(__isl_take isl_mat *mat);
3525 The following function can be used to compute the (right) kernel
3526 (or null space) of a matrix, i.e., a matrix such that the product of
3527 the original and the kernel (in that order) is the zero matrix.
3529 __isl_give isl_mat *isl_mat_right_kernel(__isl_take isl_mat *mat);
3531 =head2 Piecewise Quasi Affine Expressions
3533 The zero quasi affine expression or the quasi affine expression
3534 that is equal to a specified dimension on a given domain can be created using
3536 __isl_give isl_aff *isl_aff_zero_on_domain(
3537 __isl_take isl_local_space *ls);
3538 __isl_give isl_pw_aff *isl_pw_aff_zero_on_domain(
3539 __isl_take isl_local_space *ls);
3540 __isl_give isl_aff *isl_aff_var_on_domain(
3541 __isl_take isl_local_space *ls,
3542 enum isl_dim_type type, unsigned pos);
3543 __isl_give isl_pw_aff *isl_pw_aff_var_on_domain(
3544 __isl_take isl_local_space *ls,
3545 enum isl_dim_type type, unsigned pos);
3547 Note that the space in which the resulting objects live is a map space
3548 with the given space as domain and a one-dimensional range.
3550 An empty piecewise quasi affine expression (one with no cells)
3551 or a piecewise quasi affine expression with a single cell can
3552 be created using the following functions.
3554 #include <isl/aff.h>
3555 __isl_give isl_pw_aff *isl_pw_aff_empty(
3556 __isl_take isl_space *space);
3557 __isl_give isl_pw_aff *isl_pw_aff_alloc(
3558 __isl_take isl_set *set, __isl_take isl_aff *aff);
3559 __isl_give isl_pw_aff *isl_pw_aff_from_aff(
3560 __isl_take isl_aff *aff);
3562 A piecewise quasi affine expression that is equal to 1 on a set
3563 and 0 outside the set can be created using the following function.
3565 #include <isl/aff.h>
3566 __isl_give isl_pw_aff *isl_set_indicator_function(
3567 __isl_take isl_set *set);
3569 Quasi affine expressions can be copied and freed using
3571 #include <isl/aff.h>
3572 __isl_give isl_aff *isl_aff_copy(__isl_keep isl_aff *aff);
3573 void *isl_aff_free(__isl_take isl_aff *aff);
3575 __isl_give isl_pw_aff *isl_pw_aff_copy(
3576 __isl_keep isl_pw_aff *pwaff);
3577 void *isl_pw_aff_free(__isl_take isl_pw_aff *pwaff);
3579 A (rational) bound on a dimension can be extracted from an C<isl_constraint>
3580 using the following function. The constraint is required to have
3581 a non-zero coefficient for the specified dimension.
3583 #include <isl/constraint.h>
3584 __isl_give isl_aff *isl_constraint_get_bound(
3585 __isl_keep isl_constraint *constraint,
3586 enum isl_dim_type type, int pos);
3588 The entire affine expression of the constraint can also be extracted
3589 using the following function.
3591 #include <isl/constraint.h>
3592 __isl_give isl_aff *isl_constraint_get_aff(
3593 __isl_keep isl_constraint *constraint);
3595 Conversely, an equality constraint equating
3596 the affine expression to zero or an inequality constraint enforcing
3597 the affine expression to be non-negative, can be constructed using
3599 __isl_give isl_constraint *isl_equality_from_aff(
3600 __isl_take isl_aff *aff);
3601 __isl_give isl_constraint *isl_inequality_from_aff(
3602 __isl_take isl_aff *aff);
3604 The expression can be inspected using
3606 #include <isl/aff.h>
3607 isl_ctx *isl_aff_get_ctx(__isl_keep isl_aff *aff);
3608 int isl_aff_dim(__isl_keep isl_aff *aff,
3609 enum isl_dim_type type);
3610 __isl_give isl_local_space *isl_aff_get_domain_local_space(
3611 __isl_keep isl_aff *aff);
3612 __isl_give isl_local_space *isl_aff_get_local_space(
3613 __isl_keep isl_aff *aff);
3614 const char *isl_aff_get_dim_name(__isl_keep isl_aff *aff,
3615 enum isl_dim_type type, unsigned pos);
3616 const char *isl_pw_aff_get_dim_name(
3617 __isl_keep isl_pw_aff *pa,
3618 enum isl_dim_type type, unsigned pos);
3619 int isl_pw_aff_has_dim_id(__isl_keep isl_pw_aff *pa,
3620 enum isl_dim_type type, unsigned pos);
3621 __isl_give isl_id *isl_pw_aff_get_dim_id(
3622 __isl_keep isl_pw_aff *pa,
3623 enum isl_dim_type type, unsigned pos);
3624 __isl_give isl_id *isl_pw_aff_get_tuple_id(
3625 __isl_keep isl_pw_aff *pa,
3626 enum isl_dim_type type);
3627 int isl_aff_get_constant(__isl_keep isl_aff *aff,
3629 __isl_give isl_val *isl_aff_get_constant_val(
3630 __isl_keep isl_aff *aff);
3631 int isl_aff_get_coefficient(__isl_keep isl_aff *aff,
3632 enum isl_dim_type type, int pos, isl_int *v);
3633 __isl_give isl_val *isl_aff_get_coefficient_val(
3634 __isl_keep isl_aff *aff,
3635 enum isl_dim_type type, int pos);
3636 int isl_aff_get_denominator(__isl_keep isl_aff *aff,
3638 __isl_give isl_val *isl_aff_get_denominator_val(
3639 __isl_keep isl_aff *aff);
3640 __isl_give isl_aff *isl_aff_get_div(
3641 __isl_keep isl_aff *aff, int pos);
3643 int isl_pw_aff_n_piece(__isl_keep isl_pw_aff *pwaff);
3644 int isl_pw_aff_foreach_piece(__isl_keep isl_pw_aff *pwaff,
3645 int (*fn)(__isl_take isl_set *set,
3646 __isl_take isl_aff *aff,
3647 void *user), void *user);
3649 int isl_aff_is_cst(__isl_keep isl_aff *aff);
3650 int isl_pw_aff_is_cst(__isl_keep isl_pw_aff *pwaff);
3652 int isl_aff_involves_dims(__isl_keep isl_aff *aff,
3653 enum isl_dim_type type, unsigned first, unsigned n);
3654 int isl_pw_aff_involves_dims(__isl_keep isl_pw_aff *pwaff,
3655 enum isl_dim_type type, unsigned first, unsigned n);
3657 isl_ctx *isl_pw_aff_get_ctx(__isl_keep isl_pw_aff *pwaff);
3658 unsigned isl_pw_aff_dim(__isl_keep isl_pw_aff *pwaff,
3659 enum isl_dim_type type);
3660 int isl_pw_aff_is_empty(__isl_keep isl_pw_aff *pwaff);
3662 It can be modified using
3664 #include <isl/aff.h>
3665 __isl_give isl_pw_aff *isl_pw_aff_set_tuple_id(
3666 __isl_take isl_pw_aff *pwaff,
3667 enum isl_dim_type type, __isl_take isl_id *id);
3668 __isl_give isl_aff *isl_aff_set_dim_name(
3669 __isl_take isl_aff *aff, enum isl_dim_type type,
3670 unsigned pos, const char *s);
3671 __isl_give isl_aff *isl_aff_set_dim_id(
3672 __isl_take isl_aff *aff, enum isl_dim_type type,
3673 unsigned pos, __isl_take isl_id *id);
3674 __isl_give isl_pw_aff *isl_pw_aff_set_dim_id(
3675 __isl_take isl_pw_aff *pma,
3676 enum isl_dim_type type, unsigned pos,
3677 __isl_take isl_id *id);
3678 __isl_give isl_aff *isl_aff_set_constant(
3679 __isl_take isl_aff *aff, isl_int v);
3680 __isl_give isl_aff *isl_aff_set_constant_si(
3681 __isl_take isl_aff *aff, int v);
3682 __isl_give isl_aff *isl_aff_set_constant_val(
3683 __isl_take isl_aff *aff, __isl_take isl_val *v);
3684 __isl_give isl_aff *isl_aff_set_coefficient(
3685 __isl_take isl_aff *aff,
3686 enum isl_dim_type type, int pos, isl_int v);
3687 __isl_give isl_aff *isl_aff_set_coefficient_si(
3688 __isl_take isl_aff *aff,
3689 enum isl_dim_type type, int pos, int v);
3690 __isl_give isl_aff *isl_aff_set_coefficient_val(
3691 __isl_take isl_aff *aff,
3692 enum isl_dim_type type, int pos,
3693 __isl_take isl_val *v);
3694 __isl_give isl_aff *isl_aff_set_denominator(
3695 __isl_take isl_aff *aff, isl_int v);
3697 __isl_give isl_aff *isl_aff_add_constant(
3698 __isl_take isl_aff *aff, isl_int v);
3699 __isl_give isl_aff *isl_aff_add_constant_si(
3700 __isl_take isl_aff *aff, int v);
3701 __isl_give isl_aff *isl_aff_add_constant_val(
3702 __isl_take isl_aff *aff, __isl_take isl_val *v);
3703 __isl_give isl_aff *isl_aff_add_constant_num(
3704 __isl_take isl_aff *aff, isl_int v);
3705 __isl_give isl_aff *isl_aff_add_constant_num_si(
3706 __isl_take isl_aff *aff, int v);
3707 __isl_give isl_aff *isl_aff_add_coefficient(
3708 __isl_take isl_aff *aff,
3709 enum isl_dim_type type, int pos, isl_int v);
3710 __isl_give isl_aff *isl_aff_add_coefficient_si(
3711 __isl_take isl_aff *aff,
3712 enum isl_dim_type type, int pos, int v);
3713 __isl_give isl_aff *isl_aff_add_coefficient_val(
3714 __isl_take isl_aff *aff,
3715 enum isl_dim_type type, int pos,
3716 __isl_take isl_val *v);
3718 __isl_give isl_aff *isl_aff_insert_dims(
3719 __isl_take isl_aff *aff,
3720 enum isl_dim_type type, unsigned first, unsigned n);
3721 __isl_give isl_pw_aff *isl_pw_aff_insert_dims(
3722 __isl_take isl_pw_aff *pwaff,
3723 enum isl_dim_type type, unsigned first, unsigned n);
3724 __isl_give isl_aff *isl_aff_add_dims(
3725 __isl_take isl_aff *aff,
3726 enum isl_dim_type type, unsigned n);
3727 __isl_give isl_pw_aff *isl_pw_aff_add_dims(
3728 __isl_take isl_pw_aff *pwaff,
3729 enum isl_dim_type type, unsigned n);
3730 __isl_give isl_aff *isl_aff_drop_dims(
3731 __isl_take isl_aff *aff,
3732 enum isl_dim_type type, unsigned first, unsigned n);
3733 __isl_give isl_pw_aff *isl_pw_aff_drop_dims(
3734 __isl_take isl_pw_aff *pwaff,
3735 enum isl_dim_type type, unsigned first, unsigned n);
3737 Note that C<isl_aff_set_constant>, C<isl_aff_set_constant_si>,
3738 C<isl_aff_set_coefficient> and C<isl_aff_set_coefficient_si>
3739 set the I<numerator> of the constant or coefficient, while
3740 C<isl_aff_set_constant_val> and C<isl_aff_set_coefficient_val> set
3741 the constant or coefficient as a whole.
3742 The C<add_constant> and C<add_coefficient> functions add an integer
3743 or rational value to
3744 the possibly rational constant or coefficient.
3745 The C<add_constant_num> functions add an integer value to
3748 To check whether an affine expressions is obviously zero
3749 or obviously equal to some other affine expression, use
3751 #include <isl/aff.h>
3752 int isl_aff_plain_is_zero(__isl_keep isl_aff *aff);
3753 int isl_aff_plain_is_equal(__isl_keep isl_aff *aff1,
3754 __isl_keep isl_aff *aff2);
3755 int isl_pw_aff_plain_is_equal(
3756 __isl_keep isl_pw_aff *pwaff1,
3757 __isl_keep isl_pw_aff *pwaff2);
3761 #include <isl/aff.h>
3762 __isl_give isl_aff *isl_aff_add(__isl_take isl_aff *aff1,
3763 __isl_take isl_aff *aff2);
3764 __isl_give isl_pw_aff *isl_pw_aff_add(
3765 __isl_take isl_pw_aff *pwaff1,
3766 __isl_take isl_pw_aff *pwaff2);
3767 __isl_give isl_pw_aff *isl_pw_aff_min(
3768 __isl_take isl_pw_aff *pwaff1,
3769 __isl_take isl_pw_aff *pwaff2);
3770 __isl_give isl_pw_aff *isl_pw_aff_max(
3771 __isl_take isl_pw_aff *pwaff1,
3772 __isl_take isl_pw_aff *pwaff2);
3773 __isl_give isl_aff *isl_aff_sub(__isl_take isl_aff *aff1,
3774 __isl_take isl_aff *aff2);
3775 __isl_give isl_pw_aff *isl_pw_aff_sub(
3776 __isl_take isl_pw_aff *pwaff1,
3777 __isl_take isl_pw_aff *pwaff2);
3778 __isl_give isl_aff *isl_aff_neg(__isl_take isl_aff *aff);
3779 __isl_give isl_pw_aff *isl_pw_aff_neg(
3780 __isl_take isl_pw_aff *pwaff);
3781 __isl_give isl_aff *isl_aff_ceil(__isl_take isl_aff *aff);
3782 __isl_give isl_pw_aff *isl_pw_aff_ceil(
3783 __isl_take isl_pw_aff *pwaff);
3784 __isl_give isl_aff *isl_aff_floor(__isl_take isl_aff *aff);
3785 __isl_give isl_pw_aff *isl_pw_aff_floor(
3786 __isl_take isl_pw_aff *pwaff);
3787 __isl_give isl_aff *isl_aff_mod(__isl_take isl_aff *aff,
3789 __isl_give isl_aff *isl_aff_mod_val(__isl_take isl_aff *aff,
3790 __isl_take isl_val *mod);
3791 __isl_give isl_pw_aff *isl_pw_aff_mod(
3792 __isl_take isl_pw_aff *pwaff, isl_int mod);
3793 __isl_give isl_aff *isl_aff_scale(__isl_take isl_aff *aff,
3795 __isl_give isl_aff *isl_aff_scale_val(__isl_take isl_aff *aff,
3796 __isl_take isl_val *v);
3797 __isl_give isl_pw_aff *isl_pw_aff_scale(
3798 __isl_take isl_pw_aff *pwaff, isl_int f);
3799 __isl_give isl_pw_aff *isl_pw_aff_scale_val(
3800 __isl_take isl_pw_aff *pa, __isl_take isl_val *v);
3801 __isl_give isl_aff *isl_aff_scale_down(__isl_take isl_aff *aff,
3803 __isl_give isl_aff *isl_aff_scale_down_ui(
3804 __isl_take isl_aff *aff, unsigned f);
3805 __isl_give isl_aff *isl_aff_scale_down_val(
3806 __isl_take isl_aff *aff, __isl_take isl_val *v);
3807 __isl_give isl_pw_aff *isl_pw_aff_scale_down(
3808 __isl_take isl_pw_aff *pwaff, isl_int f);
3809 __isl_give isl_pw_aff *isl_pw_aff_scale_down_val(
3810 __isl_take isl_pw_aff *pa,
3811 __isl_take isl_val *f);
3813 __isl_give isl_pw_aff *isl_pw_aff_list_min(
3814 __isl_take isl_pw_aff_list *list);
3815 __isl_give isl_pw_aff *isl_pw_aff_list_max(
3816 __isl_take isl_pw_aff_list *list);
3818 __isl_give isl_pw_aff *isl_pw_aff_coalesce(
3819 __isl_take isl_pw_aff *pwqp);
3821 __isl_give isl_aff *isl_aff_align_params(
3822 __isl_take isl_aff *aff,
3823 __isl_take isl_space *model);
3824 __isl_give isl_pw_aff *isl_pw_aff_align_params(
3825 __isl_take isl_pw_aff *pwaff,
3826 __isl_take isl_space *model);
3828 __isl_give isl_aff *isl_aff_project_domain_on_params(
3829 __isl_take isl_aff *aff);
3831 __isl_give isl_aff *isl_aff_gist_params(
3832 __isl_take isl_aff *aff,
3833 __isl_take isl_set *context);
3834 __isl_give isl_aff *isl_aff_gist(__isl_take isl_aff *aff,
3835 __isl_take isl_set *context);
3836 __isl_give isl_pw_aff *isl_pw_aff_gist_params(
3837 __isl_take isl_pw_aff *pwaff,
3838 __isl_take isl_set *context);
3839 __isl_give isl_pw_aff *isl_pw_aff_gist(
3840 __isl_take isl_pw_aff *pwaff,
3841 __isl_take isl_set *context);
3843 __isl_give isl_set *isl_pw_aff_domain(
3844 __isl_take isl_pw_aff *pwaff);
3845 __isl_give isl_pw_aff *isl_pw_aff_intersect_domain(
3846 __isl_take isl_pw_aff *pa,
3847 __isl_take isl_set *set);
3848 __isl_give isl_pw_aff *isl_pw_aff_intersect_params(
3849 __isl_take isl_pw_aff *pa,
3850 __isl_take isl_set *set);
3852 __isl_give isl_aff *isl_aff_mul(__isl_take isl_aff *aff1,
3853 __isl_take isl_aff *aff2);
3854 __isl_give isl_aff *isl_aff_div(__isl_take isl_aff *aff1,
3855 __isl_take isl_aff *aff2);
3856 __isl_give isl_pw_aff *isl_pw_aff_mul(
3857 __isl_take isl_pw_aff *pwaff1,
3858 __isl_take isl_pw_aff *pwaff2);
3859 __isl_give isl_pw_aff *isl_pw_aff_div(
3860 __isl_take isl_pw_aff *pa1,
3861 __isl_take isl_pw_aff *pa2);
3862 __isl_give isl_pw_aff *isl_pw_aff_tdiv_q(
3863 __isl_take isl_pw_aff *pa1,
3864 __isl_take isl_pw_aff *pa2);
3865 __isl_give isl_pw_aff *isl_pw_aff_tdiv_r(
3866 __isl_take isl_pw_aff *pa1,
3867 __isl_take isl_pw_aff *pa2);
3869 When multiplying two affine expressions, at least one of the two needs
3870 to be a constant. Similarly, when dividing an affine expression by another,
3871 the second expression needs to be a constant.
3872 C<isl_pw_aff_tdiv_q> computes the quotient of an integer division with
3873 rounding towards zero. C<isl_pw_aff_tdiv_r> computes the corresponding
3876 #include <isl/aff.h>
3877 __isl_give isl_aff *isl_aff_pullback_multi_aff(
3878 __isl_take isl_aff *aff,
3879 __isl_take isl_multi_aff *ma);
3880 __isl_give isl_pw_aff *isl_pw_aff_pullback_multi_aff(
3881 __isl_take isl_pw_aff *pa,
3882 __isl_take isl_multi_aff *ma);
3883 __isl_give isl_pw_aff *isl_pw_aff_pullback_pw_multi_aff(
3884 __isl_take isl_pw_aff *pa,
3885 __isl_take isl_pw_multi_aff *pma);
3887 These functions precompose the input expression by the given
3888 C<isl_multi_aff> or C<isl_pw_multi_aff>. In other words,
3889 the C<isl_multi_aff> or C<isl_pw_multi_aff> is plugged
3890 into the (piecewise) affine expression.
3891 Objects of type C<isl_multi_aff> are described in
3892 L</"Piecewise Multiple Quasi Affine Expressions">.
3894 #include <isl/aff.h>
3895 __isl_give isl_basic_set *isl_aff_zero_basic_set(
3896 __isl_take isl_aff *aff);
3897 __isl_give isl_basic_set *isl_aff_neg_basic_set(
3898 __isl_take isl_aff *aff);
3899 __isl_give isl_basic_set *isl_aff_le_basic_set(
3900 __isl_take isl_aff *aff1, __isl_take isl_aff *aff2);
3901 __isl_give isl_basic_set *isl_aff_ge_basic_set(
3902 __isl_take isl_aff *aff1, __isl_take isl_aff *aff2);
3903 __isl_give isl_set *isl_pw_aff_eq_set(
3904 __isl_take isl_pw_aff *pwaff1,
3905 __isl_take isl_pw_aff *pwaff2);
3906 __isl_give isl_set *isl_pw_aff_ne_set(
3907 __isl_take isl_pw_aff *pwaff1,
3908 __isl_take isl_pw_aff *pwaff2);
3909 __isl_give isl_set *isl_pw_aff_le_set(
3910 __isl_take isl_pw_aff *pwaff1,
3911 __isl_take isl_pw_aff *pwaff2);
3912 __isl_give isl_set *isl_pw_aff_lt_set(
3913 __isl_take isl_pw_aff *pwaff1,
3914 __isl_take isl_pw_aff *pwaff2);
3915 __isl_give isl_set *isl_pw_aff_ge_set(
3916 __isl_take isl_pw_aff *pwaff1,
3917 __isl_take isl_pw_aff *pwaff2);
3918 __isl_give isl_set *isl_pw_aff_gt_set(
3919 __isl_take isl_pw_aff *pwaff1,
3920 __isl_take isl_pw_aff *pwaff2);
3922 __isl_give isl_set *isl_pw_aff_list_eq_set(
3923 __isl_take isl_pw_aff_list *list1,
3924 __isl_take isl_pw_aff_list *list2);
3925 __isl_give isl_set *isl_pw_aff_list_ne_set(
3926 __isl_take isl_pw_aff_list *list1,
3927 __isl_take isl_pw_aff_list *list2);
3928 __isl_give isl_set *isl_pw_aff_list_le_set(
3929 __isl_take isl_pw_aff_list *list1,
3930 __isl_take isl_pw_aff_list *list2);
3931 __isl_give isl_set *isl_pw_aff_list_lt_set(
3932 __isl_take isl_pw_aff_list *list1,
3933 __isl_take isl_pw_aff_list *list2);
3934 __isl_give isl_set *isl_pw_aff_list_ge_set(
3935 __isl_take isl_pw_aff_list *list1,
3936 __isl_take isl_pw_aff_list *list2);
3937 __isl_give isl_set *isl_pw_aff_list_gt_set(
3938 __isl_take isl_pw_aff_list *list1,
3939 __isl_take isl_pw_aff_list *list2);
3941 The function C<isl_aff_neg_basic_set> returns a basic set
3942 containing those elements in the domain space
3943 of C<aff> where C<aff> is negative.
3944 The function C<isl_aff_ge_basic_set> returns a basic set
3945 containing those elements in the shared space
3946 of C<aff1> and C<aff2> where C<aff1> is greater than or equal to C<aff2>.
3947 The function C<isl_pw_aff_ge_set> returns a set
3948 containing those elements in the shared domain
3949 of C<pwaff1> and C<pwaff2> where C<pwaff1> is greater than or equal to C<pwaff2>.
3950 The functions operating on C<isl_pw_aff_list> apply the corresponding
3951 C<isl_pw_aff> function to each pair of elements in the two lists.
3953 #include <isl/aff.h>
3954 __isl_give isl_set *isl_pw_aff_nonneg_set(
3955 __isl_take isl_pw_aff *pwaff);
3956 __isl_give isl_set *isl_pw_aff_zero_set(
3957 __isl_take isl_pw_aff *pwaff);
3958 __isl_give isl_set *isl_pw_aff_non_zero_set(
3959 __isl_take isl_pw_aff *pwaff);
3961 The function C<isl_pw_aff_nonneg_set> returns a set
3962 containing those elements in the domain
3963 of C<pwaff> where C<pwaff> is non-negative.
3965 #include <isl/aff.h>
3966 __isl_give isl_pw_aff *isl_pw_aff_cond(
3967 __isl_take isl_pw_aff *cond,
3968 __isl_take isl_pw_aff *pwaff_true,
3969 __isl_take isl_pw_aff *pwaff_false);
3971 The function C<isl_pw_aff_cond> performs a conditional operator
3972 and returns an expression that is equal to C<pwaff_true>
3973 for elements where C<cond> is non-zero and equal to C<pwaff_false> for elements
3974 where C<cond> is zero.
3976 #include <isl/aff.h>
3977 __isl_give isl_pw_aff *isl_pw_aff_union_min(
3978 __isl_take isl_pw_aff *pwaff1,
3979 __isl_take isl_pw_aff *pwaff2);
3980 __isl_give isl_pw_aff *isl_pw_aff_union_max(
3981 __isl_take isl_pw_aff *pwaff1,
3982 __isl_take isl_pw_aff *pwaff2);
3983 __isl_give isl_pw_aff *isl_pw_aff_union_add(
3984 __isl_take isl_pw_aff *pwaff1,
3985 __isl_take isl_pw_aff *pwaff2);
3987 The function C<isl_pw_aff_union_max> computes a piecewise quasi-affine
3988 expression with a domain that is the union of those of C<pwaff1> and
3989 C<pwaff2> and such that on each cell, the quasi-affine expression is
3990 the maximum of those of C<pwaff1> and C<pwaff2>. If only one of
3991 C<pwaff1> or C<pwaff2> is defined on a given cell, then the
3992 associated expression is the defined one.
3994 An expression can be read from input using
3996 #include <isl/aff.h>
3997 __isl_give isl_aff *isl_aff_read_from_str(
3998 isl_ctx *ctx, const char *str);
3999 __isl_give isl_pw_aff *isl_pw_aff_read_from_str(
4000 isl_ctx *ctx, const char *str);
4002 An expression can be printed using
4004 #include <isl/aff.h>
4005 __isl_give isl_printer *isl_printer_print_aff(
4006 __isl_take isl_printer *p, __isl_keep isl_aff *aff);
4008 __isl_give isl_printer *isl_printer_print_pw_aff(
4009 __isl_take isl_printer *p,
4010 __isl_keep isl_pw_aff *pwaff);
4012 =head2 Piecewise Multiple Quasi Affine Expressions
4014 An C<isl_multi_aff> object represents a sequence of
4015 zero or more affine expressions, all defined on the same domain space.
4016 Similarly, an C<isl_multi_pw_aff> object represents a sequence of
4017 zero or more piecewise affine expressions.
4019 An C<isl_multi_aff> can be constructed from a single
4020 C<isl_aff> or an C<isl_aff_list> using the
4021 following functions. Similarly for C<isl_multi_pw_aff>.
4023 #include <isl/aff.h>
4024 __isl_give isl_multi_aff *isl_multi_aff_from_aff(
4025 __isl_take isl_aff *aff);
4026 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_from_pw_aff(
4027 __isl_take isl_pw_aff *pa);
4028 __isl_give isl_multi_aff *isl_multi_aff_from_aff_list(
4029 __isl_take isl_space *space,
4030 __isl_take isl_aff_list *list);
4032 An empty piecewise multiple quasi affine expression (one with no cells),
4033 the zero piecewise multiple quasi affine expression (with value zero
4034 for each output dimension),
4035 a piecewise multiple quasi affine expression with a single cell (with
4036 either a universe or a specified domain) or
4037 a zero-dimensional piecewise multiple quasi affine expression
4039 can be created using the following functions.
4041 #include <isl/aff.h>
4042 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_empty(
4043 __isl_take isl_space *space);
4044 __isl_give isl_multi_aff *isl_multi_aff_zero(
4045 __isl_take isl_space *space);
4046 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_zero(
4047 __isl_take isl_space *space);
4048 __isl_give isl_multi_aff *isl_multi_aff_identity(
4049 __isl_take isl_space *space);
4050 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_identity(
4051 __isl_take isl_space *space);
4052 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_identity(
4053 __isl_take isl_space *space);
4054 __isl_give isl_pw_multi_aff *
4055 isl_pw_multi_aff_from_multi_aff(
4056 __isl_take isl_multi_aff *ma);
4057 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_alloc(
4058 __isl_take isl_set *set,
4059 __isl_take isl_multi_aff *maff);
4060 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_from_domain(
4061 __isl_take isl_set *set);
4063 __isl_give isl_union_pw_multi_aff *
4064 isl_union_pw_multi_aff_empty(
4065 __isl_take isl_space *space);
4066 __isl_give isl_union_pw_multi_aff *
4067 isl_union_pw_multi_aff_add_pw_multi_aff(
4068 __isl_take isl_union_pw_multi_aff *upma,
4069 __isl_take isl_pw_multi_aff *pma);
4070 __isl_give isl_union_pw_multi_aff *
4071 isl_union_pw_multi_aff_from_domain(
4072 __isl_take isl_union_set *uset);
4074 A piecewise multiple quasi affine expression can also be initialized
4075 from an C<isl_set> or C<isl_map>, provided the C<isl_set> is a singleton
4076 and the C<isl_map> is single-valued.
4077 In case of a conversion from an C<isl_union_set> or an C<isl_union_map>
4078 to an C<isl_union_pw_multi_aff>, these properties need to hold in each space.
4080 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_from_set(
4081 __isl_take isl_set *set);
4082 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_from_map(
4083 __isl_take isl_map *map);
4085 __isl_give isl_union_pw_multi_aff *
4086 isl_union_pw_multi_aff_from_union_set(
4087 __isl_take isl_union_set *uset);
4088 __isl_give isl_union_pw_multi_aff *
4089 isl_union_pw_multi_aff_from_union_map(
4090 __isl_take isl_union_map *umap);
4092 Multiple quasi affine expressions can be copied and freed using
4094 #include <isl/aff.h>
4095 __isl_give isl_multi_aff *isl_multi_aff_copy(
4096 __isl_keep isl_multi_aff *maff);
4097 void *isl_multi_aff_free(__isl_take isl_multi_aff *maff);
4099 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_copy(
4100 __isl_keep isl_pw_multi_aff *pma);
4101 void *isl_pw_multi_aff_free(
4102 __isl_take isl_pw_multi_aff *pma);
4104 __isl_give isl_union_pw_multi_aff *
4105 isl_union_pw_multi_aff_copy(
4106 __isl_keep isl_union_pw_multi_aff *upma);
4107 void *isl_union_pw_multi_aff_free(
4108 __isl_take isl_union_pw_multi_aff *upma);
4110 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_copy(
4111 __isl_keep isl_multi_pw_aff *mpa);
4112 void *isl_multi_pw_aff_free(
4113 __isl_take isl_multi_pw_aff *mpa);
4115 The expression can be inspected using
4117 #include <isl/aff.h>
4118 isl_ctx *isl_multi_aff_get_ctx(
4119 __isl_keep isl_multi_aff *maff);
4120 isl_ctx *isl_pw_multi_aff_get_ctx(
4121 __isl_keep isl_pw_multi_aff *pma);
4122 isl_ctx *isl_union_pw_multi_aff_get_ctx(
4123 __isl_keep isl_union_pw_multi_aff *upma);
4124 isl_ctx *isl_multi_pw_aff_get_ctx(
4125 __isl_keep isl_multi_pw_aff *mpa);
4126 unsigned isl_multi_aff_dim(__isl_keep isl_multi_aff *maff,
4127 enum isl_dim_type type);
4128 unsigned isl_pw_multi_aff_dim(
4129 __isl_keep isl_pw_multi_aff *pma,
4130 enum isl_dim_type type);
4131 unsigned isl_multi_pw_aff_dim(
4132 __isl_keep isl_multi_pw_aff *mpa,
4133 enum isl_dim_type type);
4134 __isl_give isl_aff *isl_multi_aff_get_aff(
4135 __isl_keep isl_multi_aff *multi, int pos);
4136 __isl_give isl_pw_aff *isl_pw_multi_aff_get_pw_aff(
4137 __isl_keep isl_pw_multi_aff *pma, int pos);
4138 __isl_give isl_pw_aff *isl_multi_pw_aff_get_pw_aff(
4139 __isl_keep isl_multi_pw_aff *mpa, int pos);
4140 const char *isl_pw_multi_aff_get_dim_name(
4141 __isl_keep isl_pw_multi_aff *pma,
4142 enum isl_dim_type type, unsigned pos);
4143 __isl_give isl_id *isl_pw_multi_aff_get_dim_id(
4144 __isl_keep isl_pw_multi_aff *pma,
4145 enum isl_dim_type type, unsigned pos);
4146 const char *isl_multi_aff_get_tuple_name(
4147 __isl_keep isl_multi_aff *multi,
4148 enum isl_dim_type type);
4149 int isl_pw_multi_aff_has_tuple_name(
4150 __isl_keep isl_pw_multi_aff *pma,
4151 enum isl_dim_type type);
4152 const char *isl_pw_multi_aff_get_tuple_name(
4153 __isl_keep isl_pw_multi_aff *pma,
4154 enum isl_dim_type type);
4155 int isl_pw_multi_aff_has_tuple_id(
4156 __isl_keep isl_pw_multi_aff *pma,
4157 enum isl_dim_type type);
4158 __isl_give isl_id *isl_pw_multi_aff_get_tuple_id(
4159 __isl_keep isl_pw_multi_aff *pma,
4160 enum isl_dim_type type);
4162 int isl_pw_multi_aff_foreach_piece(
4163 __isl_keep isl_pw_multi_aff *pma,
4164 int (*fn)(__isl_take isl_set *set,
4165 __isl_take isl_multi_aff *maff,
4166 void *user), void *user);
4168 int isl_union_pw_multi_aff_foreach_pw_multi_aff(
4169 __isl_keep isl_union_pw_multi_aff *upma,
4170 int (*fn)(__isl_take isl_pw_multi_aff *pma,
4171 void *user), void *user);
4173 It can be modified using
4175 #include <isl/aff.h>
4176 __isl_give isl_multi_aff *isl_multi_aff_set_aff(
4177 __isl_take isl_multi_aff *multi, int pos,
4178 __isl_take isl_aff *aff);
4179 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_set_pw_aff(
4180 __isl_take isl_pw_multi_aff *pma, unsigned pos,
4181 __isl_take isl_pw_aff *pa);
4182 __isl_give isl_multi_aff *isl_multi_aff_set_dim_name(
4183 __isl_take isl_multi_aff *maff,
4184 enum isl_dim_type type, unsigned pos, const char *s);
4185 __isl_give isl_multi_aff *isl_multi_aff_set_tuple_name(
4186 __isl_take isl_multi_aff *maff,
4187 enum isl_dim_type type, const char *s);
4188 __isl_give isl_multi_aff *isl_multi_aff_set_tuple_id(
4189 __isl_take isl_multi_aff *maff,
4190 enum isl_dim_type type, __isl_take isl_id *id);
4191 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_set_tuple_id(
4192 __isl_take isl_pw_multi_aff *pma,
4193 enum isl_dim_type type, __isl_take isl_id *id);
4195 __isl_give isl_multi_pw_aff *
4196 isl_multi_pw_aff_set_dim_name(
4197 __isl_take isl_multi_pw_aff *mpa,
4198 enum isl_dim_type type, unsigned pos, const char *s);
4199 __isl_give isl_multi_pw_aff *
4200 isl_multi_pw_aff_set_tuple_name(
4201 __isl_take isl_multi_pw_aff *mpa,
4202 enum isl_dim_type type, const char *s);
4204 __isl_give isl_multi_aff *isl_multi_aff_insert_dims(
4205 __isl_take isl_multi_aff *ma,
4206 enum isl_dim_type type, unsigned first, unsigned n);
4207 __isl_give isl_multi_aff *isl_multi_aff_add_dims(
4208 __isl_take isl_multi_aff *ma,
4209 enum isl_dim_type type, unsigned n);
4210 __isl_give isl_multi_aff *isl_multi_aff_drop_dims(
4211 __isl_take isl_multi_aff *maff,
4212 enum isl_dim_type type, unsigned first, unsigned n);
4213 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_drop_dims(
4214 __isl_take isl_pw_multi_aff *pma,
4215 enum isl_dim_type type, unsigned first, unsigned n);
4217 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_insert_dims(
4218 __isl_take isl_multi_pw_aff *mpa,
4219 enum isl_dim_type type, unsigned first, unsigned n);
4220 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_add_dims(
4221 __isl_take isl_multi_pw_aff *mpa,
4222 enum isl_dim_type type, unsigned n);
4224 To check whether two multiple affine expressions are
4225 obviously equal to each other, use
4227 int isl_multi_aff_plain_is_equal(__isl_keep isl_multi_aff *maff1,
4228 __isl_keep isl_multi_aff *maff2);
4229 int isl_pw_multi_aff_plain_is_equal(
4230 __isl_keep isl_pw_multi_aff *pma1,
4231 __isl_keep isl_pw_multi_aff *pma2);
4235 #include <isl/aff.h>
4236 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_union_lexmin(
4237 __isl_take isl_pw_multi_aff *pma1,
4238 __isl_take isl_pw_multi_aff *pma2);
4239 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_union_lexmax(
4240 __isl_take isl_pw_multi_aff *pma1,
4241 __isl_take isl_pw_multi_aff *pma2);
4242 __isl_give isl_multi_aff *isl_multi_aff_add(
4243 __isl_take isl_multi_aff *maff1,
4244 __isl_take isl_multi_aff *maff2);
4245 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_add(
4246 __isl_take isl_pw_multi_aff *pma1,
4247 __isl_take isl_pw_multi_aff *pma2);
4248 __isl_give isl_union_pw_multi_aff *isl_union_pw_multi_aff_add(
4249 __isl_take isl_union_pw_multi_aff *upma1,
4250 __isl_take isl_union_pw_multi_aff *upma2);
4251 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_union_add(
4252 __isl_take isl_pw_multi_aff *pma1,
4253 __isl_take isl_pw_multi_aff *pma2);
4254 __isl_give isl_multi_aff *isl_multi_aff_sub(
4255 __isl_take isl_multi_aff *ma1,
4256 __isl_take isl_multi_aff *ma2);
4257 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_sub(
4258 __isl_take isl_pw_multi_aff *pma1,
4259 __isl_take isl_pw_multi_aff *pma2);
4260 __isl_give isl_union_pw_multi_aff *isl_union_pw_multi_aff_sub(
4261 __isl_take isl_union_pw_multi_aff *upma1,
4262 __isl_take isl_union_pw_multi_aff *upma2);
4264 C<isl_multi_aff_sub> subtracts the second argument from the first.
4266 __isl_give isl_multi_aff *isl_multi_aff_scale(
4267 __isl_take isl_multi_aff *maff,
4269 __isl_give isl_multi_aff *isl_multi_aff_scale_val(
4270 __isl_take isl_multi_aff *ma,
4271 __isl_take isl_val *v);
4272 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_scale_val(
4273 __isl_take isl_pw_multi_aff *pma,
4274 __isl_take isl_val *v);
4275 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_scale_val(
4276 __isl_take isl_multi_pw_aff *mpa,
4277 __isl_take isl_val *v);
4278 __isl_give isl_multi_aff *isl_multi_aff_scale_vec(
4279 __isl_take isl_multi_aff *ma,
4280 __isl_take isl_vec *v);
4281 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_scale_vec(
4282 __isl_take isl_pw_multi_aff *pma,
4283 __isl_take isl_vec *v);
4284 __isl_give isl_union_pw_multi_aff *isl_union_pw_multi_aff_scale_vec(
4285 __isl_take isl_union_pw_multi_aff *upma,
4286 __isl_take isl_vec *v);
4288 C<isl_multi_aff_scale_vec> scales the first elements of C<ma>
4289 by the corresponding elements of C<v>.
4291 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_intersect_params(
4292 __isl_take isl_pw_multi_aff *pma,
4293 __isl_take isl_set *set);
4294 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_intersect_domain(
4295 __isl_take isl_pw_multi_aff *pma,
4296 __isl_take isl_set *set);
4297 __isl_give isl_union_pw_multi_aff *
4298 isl_union_pw_multi_aff_intersect_domain(
4299 __isl_take isl_union_pw_multi_aff *upma,
4300 __isl_take isl_union_set *uset);
4301 __isl_give isl_multi_aff *isl_multi_aff_lift(
4302 __isl_take isl_multi_aff *maff,
4303 __isl_give isl_local_space **ls);
4304 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_coalesce(
4305 __isl_take isl_pw_multi_aff *pma);
4306 __isl_give isl_multi_aff *isl_multi_aff_align_params(
4307 __isl_take isl_multi_aff *multi,
4308 __isl_take isl_space *model);
4309 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_align_params(
4310 __isl_take isl_pw_multi_aff *pma,
4311 __isl_take isl_space *model);
4312 __isl_give isl_pw_multi_aff *
4313 isl_pw_multi_aff_project_domain_on_params(
4314 __isl_take isl_pw_multi_aff *pma);
4315 __isl_give isl_multi_aff *isl_multi_aff_gist_params(
4316 __isl_take isl_multi_aff *maff,
4317 __isl_take isl_set *context);
4318 __isl_give isl_multi_aff *isl_multi_aff_gist(
4319 __isl_take isl_multi_aff *maff,
4320 __isl_take isl_set *context);
4321 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_gist_params(
4322 __isl_take isl_pw_multi_aff *pma,
4323 __isl_take isl_set *set);
4324 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_gist(
4325 __isl_take isl_pw_multi_aff *pma,
4326 __isl_take isl_set *set);
4327 __isl_give isl_set *isl_pw_multi_aff_domain(
4328 __isl_take isl_pw_multi_aff *pma);
4329 __isl_give isl_union_set *isl_union_pw_multi_aff_domain(
4330 __isl_take isl_union_pw_multi_aff *upma);
4331 __isl_give isl_multi_aff *isl_multi_aff_range_splice(
4332 __isl_take isl_multi_aff *ma1, unsigned pos,
4333 __isl_take isl_multi_aff *ma2);
4334 __isl_give isl_multi_aff *isl_multi_aff_splice(
4335 __isl_take isl_multi_aff *ma1,
4336 unsigned in_pos, unsigned out_pos,
4337 __isl_take isl_multi_aff *ma2);
4338 __isl_give isl_multi_aff *isl_multi_aff_range_product(
4339 __isl_take isl_multi_aff *ma1,
4340 __isl_take isl_multi_aff *ma2);
4341 __isl_give isl_multi_aff *isl_multi_aff_flat_range_product(
4342 __isl_take isl_multi_aff *ma1,
4343 __isl_take isl_multi_aff *ma2);
4344 __isl_give isl_multi_aff *isl_multi_aff_product(
4345 __isl_take isl_multi_aff *ma1,
4346 __isl_take isl_multi_aff *ma2);
4347 __isl_give isl_pw_multi_aff *
4348 isl_pw_multi_aff_range_product(
4349 __isl_take isl_pw_multi_aff *pma1,
4350 __isl_take isl_pw_multi_aff *pma2);
4351 __isl_give isl_pw_multi_aff *
4352 isl_pw_multi_aff_flat_range_product(
4353 __isl_take isl_pw_multi_aff *pma1,
4354 __isl_take isl_pw_multi_aff *pma2);
4355 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_product(
4356 __isl_take isl_pw_multi_aff *pma1,
4357 __isl_take isl_pw_multi_aff *pma2);
4358 __isl_give isl_union_pw_multi_aff *
4359 isl_union_pw_multi_aff_flat_range_product(
4360 __isl_take isl_union_pw_multi_aff *upma1,
4361 __isl_take isl_union_pw_multi_aff *upma2);
4362 __isl_give isl_multi_pw_aff *
4363 isl_multi_pw_aff_range_splice(
4364 __isl_take isl_multi_pw_aff *mpa1, unsigned pos,
4365 __isl_take isl_multi_pw_aff *mpa2);
4366 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_splice(
4367 __isl_take isl_multi_pw_aff *mpa1,
4368 unsigned in_pos, unsigned out_pos,
4369 __isl_take isl_multi_pw_aff *mpa2);
4370 __isl_give isl_multi_pw_aff *
4371 isl_multi_pw_aff_range_product(
4372 __isl_take isl_multi_pw_aff *mpa1,
4373 __isl_take isl_multi_pw_aff *mpa2);
4374 __isl_give isl_multi_pw_aff *
4375 isl_multi_pw_aff_flat_range_product(
4376 __isl_take isl_multi_pw_aff *mpa1,
4377 __isl_take isl_multi_pw_aff *mpa2);
4379 If the C<ls> argument of C<isl_multi_aff_lift> is not C<NULL>,
4380 then it is assigned the local space that lies at the basis of
4381 the lifting applied.
4383 #include <isl/aff.h>
4384 __isl_give isl_multi_aff *isl_multi_aff_pullback_multi_aff(
4385 __isl_take isl_multi_aff *ma1,
4386 __isl_take isl_multi_aff *ma2);
4387 __isl_give isl_pw_multi_aff *
4388 isl_pw_multi_aff_pullback_multi_aff(
4389 __isl_take isl_pw_multi_aff *pma,
4390 __isl_take isl_multi_aff *ma);
4391 __isl_give isl_pw_multi_aff *
4392 isl_pw_multi_aff_pullback_pw_multi_aff(
4393 __isl_take isl_pw_multi_aff *pma1,
4394 __isl_take isl_pw_multi_aff *pma2);
4396 The function C<isl_multi_aff_pullback_multi_aff> precomposes C<ma1> by C<ma2>.
4397 In other words, C<ma2> is plugged
4400 __isl_give isl_set *isl_multi_aff_lex_le_set(
4401 __isl_take isl_multi_aff *ma1,
4402 __isl_take isl_multi_aff *ma2);
4403 __isl_give isl_set *isl_multi_aff_lex_ge_set(
4404 __isl_take isl_multi_aff *ma1,
4405 __isl_take isl_multi_aff *ma2);
4407 The function C<isl_multi_aff_lex_le_set> returns a set
4408 containing those elements in the shared domain space
4409 where C<ma1> is lexicographically smaller than or
4412 An expression can be read from input using
4414 #include <isl/aff.h>
4415 __isl_give isl_multi_aff *isl_multi_aff_read_from_str(
4416 isl_ctx *ctx, const char *str);
4417 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_read_from_str(
4418 isl_ctx *ctx, const char *str);
4419 __isl_give isl_union_pw_multi_aff *
4420 isl_union_pw_multi_aff_read_from_str(
4421 isl_ctx *ctx, const char *str);
4423 An expression can be printed using
4425 #include <isl/aff.h>
4426 __isl_give isl_printer *isl_printer_print_multi_aff(
4427 __isl_take isl_printer *p,
4428 __isl_keep isl_multi_aff *maff);
4429 __isl_give isl_printer *isl_printer_print_pw_multi_aff(
4430 __isl_take isl_printer *p,
4431 __isl_keep isl_pw_multi_aff *pma);
4432 __isl_give isl_printer *isl_printer_print_union_pw_multi_aff(
4433 __isl_take isl_printer *p,
4434 __isl_keep isl_union_pw_multi_aff *upma);
4435 __isl_give isl_printer *isl_printer_print_multi_pw_aff(
4436 __isl_take isl_printer *p,
4437 __isl_keep isl_multi_pw_aff *mpa);
4441 Points are elements of a set. They can be used to construct
4442 simple sets (boxes) or they can be used to represent the
4443 individual elements of a set.
4444 The zero point (the origin) can be created using
4446 __isl_give isl_point *isl_point_zero(__isl_take isl_space *space);
4448 The coordinates of a point can be inspected, set and changed
4451 int isl_point_get_coordinate(__isl_keep isl_point *pnt,
4452 enum isl_dim_type type, int pos, isl_int *v);
4453 __isl_give isl_val *isl_point_get_coordinate_val(
4454 __isl_keep isl_point *pnt,
4455 enum isl_dim_type type, int pos);
4456 __isl_give isl_point *isl_point_set_coordinate(
4457 __isl_take isl_point *pnt,
4458 enum isl_dim_type type, int pos, isl_int v);
4459 __isl_give isl_point *isl_point_set_coordinate_val(
4460 __isl_take isl_point *pnt,
4461 enum isl_dim_type type, int pos,
4462 __isl_take isl_val *v);
4464 __isl_give isl_point *isl_point_add_ui(
4465 __isl_take isl_point *pnt,
4466 enum isl_dim_type type, int pos, unsigned val);
4467 __isl_give isl_point *isl_point_sub_ui(
4468 __isl_take isl_point *pnt,
4469 enum isl_dim_type type, int pos, unsigned val);
4471 Other properties can be obtained using
4473 isl_ctx *isl_point_get_ctx(__isl_keep isl_point *pnt);
4475 Points can be copied or freed using
4477 __isl_give isl_point *isl_point_copy(
4478 __isl_keep isl_point *pnt);
4479 void isl_point_free(__isl_take isl_point *pnt);
4481 A singleton set can be created from a point using
4483 __isl_give isl_basic_set *isl_basic_set_from_point(
4484 __isl_take isl_point *pnt);
4485 __isl_give isl_set *isl_set_from_point(
4486 __isl_take isl_point *pnt);
4488 and a box can be created from two opposite extremal points using
4490 __isl_give isl_basic_set *isl_basic_set_box_from_points(
4491 __isl_take isl_point *pnt1,
4492 __isl_take isl_point *pnt2);
4493 __isl_give isl_set *isl_set_box_from_points(
4494 __isl_take isl_point *pnt1,
4495 __isl_take isl_point *pnt2);
4497 All elements of a B<bounded> (union) set can be enumerated using
4498 the following functions.
4500 int isl_set_foreach_point(__isl_keep isl_set *set,
4501 int (*fn)(__isl_take isl_point *pnt, void *user),
4503 int isl_union_set_foreach_point(__isl_keep isl_union_set *uset,
4504 int (*fn)(__isl_take isl_point *pnt, void *user),
4507 The function C<fn> is called for each integer point in
4508 C<set> with as second argument the last argument of
4509 the C<isl_set_foreach_point> call. The function C<fn>
4510 should return C<0> on success and C<-1> on failure.
4511 In the latter case, C<isl_set_foreach_point> will stop
4512 enumerating and return C<-1> as well.
4513 If the enumeration is performed successfully and to completion,
4514 then C<isl_set_foreach_point> returns C<0>.
4516 To obtain a single point of a (basic) set, use
4518 __isl_give isl_point *isl_basic_set_sample_point(
4519 __isl_take isl_basic_set *bset);
4520 __isl_give isl_point *isl_set_sample_point(
4521 __isl_take isl_set *set);
4523 If C<set> does not contain any (integer) points, then the
4524 resulting point will be ``void'', a property that can be
4527 int isl_point_is_void(__isl_keep isl_point *pnt);
4529 =head2 Piecewise Quasipolynomials
4531 A piecewise quasipolynomial is a particular kind of function that maps
4532 a parametric point to a rational value.
4533 More specifically, a quasipolynomial is a polynomial expression in greatest
4534 integer parts of affine expressions of parameters and variables.
4535 A piecewise quasipolynomial is a subdivision of a given parametric
4536 domain into disjoint cells with a quasipolynomial associated to
4537 each cell. The value of the piecewise quasipolynomial at a given
4538 point is the value of the quasipolynomial associated to the cell
4539 that contains the point. Outside of the union of cells,
4540 the value is assumed to be zero.
4541 For example, the piecewise quasipolynomial
4543 [n] -> { [x] -> ((1 + n) - x) : x <= n and x >= 0 }
4545 maps C<x> to C<1 + n - x> for values of C<x> between C<0> and C<n>.
4546 A given piecewise quasipolynomial has a fixed domain dimension.
4547 Union piecewise quasipolynomials are used to contain piecewise quasipolynomials
4548 defined over different domains.
4549 Piecewise quasipolynomials are mainly used by the C<barvinok>
4550 library for representing the number of elements in a parametric set or map.
4551 For example, the piecewise quasipolynomial above represents
4552 the number of points in the map
4554 [n] -> { [x] -> [y] : x,y >= 0 and 0 <= x + y <= n }
4556 =head3 Input and Output
4558 Piecewise quasipolynomials can be read from input using
4560 __isl_give isl_union_pw_qpolynomial *
4561 isl_union_pw_qpolynomial_read_from_str(
4562 isl_ctx *ctx, const char *str);
4564 Quasipolynomials and piecewise quasipolynomials can be printed
4565 using the following functions.
4567 __isl_give isl_printer *isl_printer_print_qpolynomial(
4568 __isl_take isl_printer *p,
4569 __isl_keep isl_qpolynomial *qp);
4571 __isl_give isl_printer *isl_printer_print_pw_qpolynomial(
4572 __isl_take isl_printer *p,
4573 __isl_keep isl_pw_qpolynomial *pwqp);
4575 __isl_give isl_printer *isl_printer_print_union_pw_qpolynomial(
4576 __isl_take isl_printer *p,
4577 __isl_keep isl_union_pw_qpolynomial *upwqp);
4579 The output format of the printer
4580 needs to be set to either C<ISL_FORMAT_ISL> or C<ISL_FORMAT_C>.
4581 For C<isl_printer_print_union_pw_qpolynomial>, only C<ISL_FORMAT_ISL>
4583 In case of printing in C<ISL_FORMAT_C>, the user may want
4584 to set the names of all dimensions
4586 __isl_give isl_qpolynomial *isl_qpolynomial_set_dim_name(
4587 __isl_take isl_qpolynomial *qp,
4588 enum isl_dim_type type, unsigned pos,
4590 __isl_give isl_pw_qpolynomial *
4591 isl_pw_qpolynomial_set_dim_name(
4592 __isl_take isl_pw_qpolynomial *pwqp,
4593 enum isl_dim_type type, unsigned pos,
4596 =head3 Creating New (Piecewise) Quasipolynomials
4598 Some simple quasipolynomials can be created using the following functions.
4599 More complicated quasipolynomials can be created by applying
4600 operations such as addition and multiplication
4601 on the resulting quasipolynomials
4603 __isl_give isl_qpolynomial *isl_qpolynomial_zero_on_domain(
4604 __isl_take isl_space *domain);
4605 __isl_give isl_qpolynomial *isl_qpolynomial_one_on_domain(
4606 __isl_take isl_space *domain);
4607 __isl_give isl_qpolynomial *isl_qpolynomial_infty_on_domain(
4608 __isl_take isl_space *domain);
4609 __isl_give isl_qpolynomial *isl_qpolynomial_neginfty_on_domain(
4610 __isl_take isl_space *domain);
4611 __isl_give isl_qpolynomial *isl_qpolynomial_nan_on_domain(
4612 __isl_take isl_space *domain);
4613 __isl_give isl_qpolynomial *isl_qpolynomial_rat_cst_on_domain(
4614 __isl_take isl_space *domain,
4615 const isl_int n, const isl_int d);
4616 __isl_give isl_qpolynomial *isl_qpolynomial_val_on_domain(
4617 __isl_take isl_space *domain,
4618 __isl_take isl_val *val);
4619 __isl_give isl_qpolynomial *isl_qpolynomial_var_on_domain(
4620 __isl_take isl_space *domain,
4621 enum isl_dim_type type, unsigned pos);
4622 __isl_give isl_qpolynomial *isl_qpolynomial_from_aff(
4623 __isl_take isl_aff *aff);
4625 Note that the space in which a quasipolynomial lives is a map space
4626 with a one-dimensional range. The C<domain> argument in some of
4627 the functions above corresponds to the domain of this map space.
4629 The zero piecewise quasipolynomial or a piecewise quasipolynomial
4630 with a single cell can be created using the following functions.
4631 Multiple of these single cell piecewise quasipolynomials can
4632 be combined to create more complicated piecewise quasipolynomials.
4634 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_zero(
4635 __isl_take isl_space *space);
4636 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_alloc(
4637 __isl_take isl_set *set,
4638 __isl_take isl_qpolynomial *qp);
4639 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_from_qpolynomial(
4640 __isl_take isl_qpolynomial *qp);
4641 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_from_pw_aff(
4642 __isl_take isl_pw_aff *pwaff);
4644 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_zero(
4645 __isl_take isl_space *space);
4646 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_from_pw_qpolynomial(
4647 __isl_take isl_pw_qpolynomial *pwqp);
4648 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_add_pw_qpolynomial(
4649 __isl_take isl_union_pw_qpolynomial *upwqp,
4650 __isl_take isl_pw_qpolynomial *pwqp);
4652 Quasipolynomials can be copied and freed again using the following
4655 __isl_give isl_qpolynomial *isl_qpolynomial_copy(
4656 __isl_keep isl_qpolynomial *qp);
4657 void *isl_qpolynomial_free(__isl_take isl_qpolynomial *qp);
4659 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_copy(
4660 __isl_keep isl_pw_qpolynomial *pwqp);
4661 void *isl_pw_qpolynomial_free(
4662 __isl_take isl_pw_qpolynomial *pwqp);
4664 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_copy(
4665 __isl_keep isl_union_pw_qpolynomial *upwqp);
4666 void *isl_union_pw_qpolynomial_free(
4667 __isl_take isl_union_pw_qpolynomial *upwqp);
4669 =head3 Inspecting (Piecewise) Quasipolynomials
4671 To iterate over all piecewise quasipolynomials in a union
4672 piecewise quasipolynomial, use the following function
4674 int isl_union_pw_qpolynomial_foreach_pw_qpolynomial(
4675 __isl_keep isl_union_pw_qpolynomial *upwqp,
4676 int (*fn)(__isl_take isl_pw_qpolynomial *pwqp, void *user),
4679 To extract the piecewise quasipolynomial in a given space from a union, use
4681 __isl_give isl_pw_qpolynomial *
4682 isl_union_pw_qpolynomial_extract_pw_qpolynomial(
4683 __isl_keep isl_union_pw_qpolynomial *upwqp,
4684 __isl_take isl_space *space);
4686 To iterate over the cells in a piecewise quasipolynomial,
4687 use either of the following two functions
4689 int isl_pw_qpolynomial_foreach_piece(
4690 __isl_keep isl_pw_qpolynomial *pwqp,
4691 int (*fn)(__isl_take isl_set *set,
4692 __isl_take isl_qpolynomial *qp,
4693 void *user), void *user);
4694 int isl_pw_qpolynomial_foreach_lifted_piece(
4695 __isl_keep isl_pw_qpolynomial *pwqp,
4696 int (*fn)(__isl_take isl_set *set,
4697 __isl_take isl_qpolynomial *qp,
4698 void *user), void *user);
4700 As usual, the function C<fn> should return C<0> on success
4701 and C<-1> on failure. The difference between
4702 C<isl_pw_qpolynomial_foreach_piece> and
4703 C<isl_pw_qpolynomial_foreach_lifted_piece> is that
4704 C<isl_pw_qpolynomial_foreach_lifted_piece> will first
4705 compute unique representations for all existentially quantified
4706 variables and then turn these existentially quantified variables
4707 into extra set variables, adapting the associated quasipolynomial
4708 accordingly. This means that the C<set> passed to C<fn>
4709 will not have any existentially quantified variables, but that
4710 the dimensions of the sets may be different for different
4711 invocations of C<fn>.
4713 The constant term of a quasipolynomial can be extracted using
4715 __isl_give isl_val *isl_qpolynomial_get_constant_val(
4716 __isl_keep isl_qpolynomial *qp);
4718 To iterate over all terms in a quasipolynomial,
4721 int isl_qpolynomial_foreach_term(
4722 __isl_keep isl_qpolynomial *qp,
4723 int (*fn)(__isl_take isl_term *term,
4724 void *user), void *user);
4726 The terms themselves can be inspected and freed using
4729 unsigned isl_term_dim(__isl_keep isl_term *term,
4730 enum isl_dim_type type);
4731 void isl_term_get_num(__isl_keep isl_term *term,
4733 void isl_term_get_den(__isl_keep isl_term *term,
4735 __isl_give isl_val *isl_term_get_coefficient_val(
4736 __isl_keep isl_term *term);
4737 int isl_term_get_exp(__isl_keep isl_term *term,
4738 enum isl_dim_type type, unsigned pos);
4739 __isl_give isl_aff *isl_term_get_div(
4740 __isl_keep isl_term *term, unsigned pos);
4741 void isl_term_free(__isl_take isl_term *term);
4743 Each term is a product of parameters, set variables and
4744 integer divisions. The function C<isl_term_get_exp>
4745 returns the exponent of a given dimensions in the given term.
4746 The C<isl_int>s in the arguments of C<isl_term_get_num>
4747 and C<isl_term_get_den> need to have been initialized
4748 using C<isl_int_init> before calling these functions.
4750 =head3 Properties of (Piecewise) Quasipolynomials
4752 To check whether a quasipolynomial is actually a constant,
4753 use the following function.
4755 int isl_qpolynomial_is_cst(__isl_keep isl_qpolynomial *qp,
4756 isl_int *n, isl_int *d);
4758 If C<qp> is a constant and if C<n> and C<d> are not C<NULL>
4759 then the numerator and denominator of the constant
4760 are returned in C<*n> and C<*d>, respectively.
4762 To check whether two union piecewise quasipolynomials are
4763 obviously equal, use
4765 int isl_union_pw_qpolynomial_plain_is_equal(
4766 __isl_keep isl_union_pw_qpolynomial *upwqp1,
4767 __isl_keep isl_union_pw_qpolynomial *upwqp2);
4769 =head3 Operations on (Piecewise) Quasipolynomials
4771 __isl_give isl_qpolynomial *isl_qpolynomial_scale(
4772 __isl_take isl_qpolynomial *qp, isl_int v);
4773 __isl_give isl_qpolynomial *isl_qpolynomial_scale_val(
4774 __isl_take isl_qpolynomial *qp,
4775 __isl_take isl_val *v);
4776 __isl_give isl_qpolynomial *isl_qpolynomial_neg(
4777 __isl_take isl_qpolynomial *qp);
4778 __isl_give isl_qpolynomial *isl_qpolynomial_add(
4779 __isl_take isl_qpolynomial *qp1,
4780 __isl_take isl_qpolynomial *qp2);
4781 __isl_give isl_qpolynomial *isl_qpolynomial_sub(
4782 __isl_take isl_qpolynomial *qp1,
4783 __isl_take isl_qpolynomial *qp2);
4784 __isl_give isl_qpolynomial *isl_qpolynomial_mul(
4785 __isl_take isl_qpolynomial *qp1,
4786 __isl_take isl_qpolynomial *qp2);
4787 __isl_give isl_qpolynomial *isl_qpolynomial_pow(
4788 __isl_take isl_qpolynomial *qp, unsigned exponent);
4790 __isl_give isl_pw_qpolynomial *
4791 isl_pw_qpolynomial_scale_val(
4792 __isl_take isl_pw_qpolynomial *pwqp,
4793 __isl_take isl_val *v);
4794 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_add(
4795 __isl_take isl_pw_qpolynomial *pwqp1,
4796 __isl_take isl_pw_qpolynomial *pwqp2);
4797 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_sub(
4798 __isl_take isl_pw_qpolynomial *pwqp1,
4799 __isl_take isl_pw_qpolynomial *pwqp2);
4800 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_add_disjoint(
4801 __isl_take isl_pw_qpolynomial *pwqp1,
4802 __isl_take isl_pw_qpolynomial *pwqp2);
4803 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_neg(
4804 __isl_take isl_pw_qpolynomial *pwqp);
4805 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_mul(
4806 __isl_take isl_pw_qpolynomial *pwqp1,
4807 __isl_take isl_pw_qpolynomial *pwqp2);
4808 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_pow(
4809 __isl_take isl_pw_qpolynomial *pwqp, unsigned exponent);
4811 __isl_give isl_union_pw_qpolynomial *
4812 isl_union_pw_qpolynomial_scale_val(
4813 __isl_take isl_union_pw_qpolynomial *upwqp,
4814 __isl_take isl_val *v);
4815 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_add(
4816 __isl_take isl_union_pw_qpolynomial *upwqp1,
4817 __isl_take isl_union_pw_qpolynomial *upwqp2);
4818 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_sub(
4819 __isl_take isl_union_pw_qpolynomial *upwqp1,
4820 __isl_take isl_union_pw_qpolynomial *upwqp2);
4821 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_mul(
4822 __isl_take isl_union_pw_qpolynomial *upwqp1,
4823 __isl_take isl_union_pw_qpolynomial *upwqp2);
4825 __isl_give isl_qpolynomial *isl_pw_qpolynomial_eval(
4826 __isl_take isl_pw_qpolynomial *pwqp,
4827 __isl_take isl_point *pnt);
4829 __isl_give isl_qpolynomial *isl_union_pw_qpolynomial_eval(
4830 __isl_take isl_union_pw_qpolynomial *upwqp,
4831 __isl_take isl_point *pnt);
4833 __isl_give isl_set *isl_pw_qpolynomial_domain(
4834 __isl_take isl_pw_qpolynomial *pwqp);
4835 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_intersect_domain(
4836 __isl_take isl_pw_qpolynomial *pwpq,
4837 __isl_take isl_set *set);
4838 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_intersect_params(
4839 __isl_take isl_pw_qpolynomial *pwpq,
4840 __isl_take isl_set *set);
4842 __isl_give isl_union_set *isl_union_pw_qpolynomial_domain(
4843 __isl_take isl_union_pw_qpolynomial *upwqp);
4844 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_intersect_domain(
4845 __isl_take isl_union_pw_qpolynomial *upwpq,
4846 __isl_take isl_union_set *uset);
4847 __isl_give isl_union_pw_qpolynomial *
4848 isl_union_pw_qpolynomial_intersect_params(
4849 __isl_take isl_union_pw_qpolynomial *upwpq,
4850 __isl_take isl_set *set);
4852 __isl_give isl_qpolynomial *isl_qpolynomial_align_params(
4853 __isl_take isl_qpolynomial *qp,
4854 __isl_take isl_space *model);
4856 __isl_give isl_qpolynomial *isl_qpolynomial_project_domain_on_params(
4857 __isl_take isl_qpolynomial *qp);
4858 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_project_domain_on_params(
4859 __isl_take isl_pw_qpolynomial *pwqp);
4861 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_coalesce(
4862 __isl_take isl_union_pw_qpolynomial *upwqp);
4864 __isl_give isl_qpolynomial *isl_qpolynomial_gist_params(
4865 __isl_take isl_qpolynomial *qp,
4866 __isl_take isl_set *context);
4867 __isl_give isl_qpolynomial *isl_qpolynomial_gist(
4868 __isl_take isl_qpolynomial *qp,
4869 __isl_take isl_set *context);
4871 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_gist_params(
4872 __isl_take isl_pw_qpolynomial *pwqp,
4873 __isl_take isl_set *context);
4874 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_gist(
4875 __isl_take isl_pw_qpolynomial *pwqp,
4876 __isl_take isl_set *context);
4878 __isl_give isl_union_pw_qpolynomial *
4879 isl_union_pw_qpolynomial_gist_params(
4880 __isl_take isl_union_pw_qpolynomial *upwqp,
4881 __isl_take isl_set *context);
4882 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_gist(
4883 __isl_take isl_union_pw_qpolynomial *upwqp,
4884 __isl_take isl_union_set *context);
4886 The gist operation applies the gist operation to each of
4887 the cells in the domain of the input piecewise quasipolynomial.
4888 The context is also exploited
4889 to simplify the quasipolynomials associated to each cell.
4891 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_to_polynomial(
4892 __isl_take isl_pw_qpolynomial *pwqp, int sign);
4893 __isl_give isl_union_pw_qpolynomial *
4894 isl_union_pw_qpolynomial_to_polynomial(
4895 __isl_take isl_union_pw_qpolynomial *upwqp, int sign);
4897 Approximate each quasipolynomial by a polynomial. If C<sign> is positive,
4898 the polynomial will be an overapproximation. If C<sign> is negative,
4899 it will be an underapproximation. If C<sign> is zero, the approximation
4900 will lie somewhere in between.
4902 =head2 Bounds on Piecewise Quasipolynomials and Piecewise Quasipolynomial Reductions
4904 A piecewise quasipolynomial reduction is a piecewise
4905 reduction (or fold) of quasipolynomials.
4906 In particular, the reduction can be maximum or a minimum.
4907 The objects are mainly used to represent the result of
4908 an upper or lower bound on a quasipolynomial over its domain,
4909 i.e., as the result of the following function.
4911 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_bound(
4912 __isl_take isl_pw_qpolynomial *pwqp,
4913 enum isl_fold type, int *tight);
4915 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_bound(
4916 __isl_take isl_union_pw_qpolynomial *upwqp,
4917 enum isl_fold type, int *tight);
4919 The C<type> argument may be either C<isl_fold_min> or C<isl_fold_max>.
4920 If C<tight> is not C<NULL>, then C<*tight> is set to C<1>
4921 is the returned bound is known be tight, i.e., for each value
4922 of the parameters there is at least
4923 one element in the domain that reaches the bound.
4924 If the domain of C<pwqp> is not wrapping, then the bound is computed
4925 over all elements in that domain and the result has a purely parametric
4926 domain. If the domain of C<pwqp> is wrapping, then the bound is
4927 computed over the range of the wrapped relation. The domain of the
4928 wrapped relation becomes the domain of the result.
4930 A (piecewise) quasipolynomial reduction can be copied or freed using the
4931 following functions.
4933 __isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_copy(
4934 __isl_keep isl_qpolynomial_fold *fold);
4935 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_copy(
4936 __isl_keep isl_pw_qpolynomial_fold *pwf);
4937 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_copy(
4938 __isl_keep isl_union_pw_qpolynomial_fold *upwf);
4939 void isl_qpolynomial_fold_free(
4940 __isl_take isl_qpolynomial_fold *fold);
4941 void *isl_pw_qpolynomial_fold_free(
4942 __isl_take isl_pw_qpolynomial_fold *pwf);
4943 void *isl_union_pw_qpolynomial_fold_free(
4944 __isl_take isl_union_pw_qpolynomial_fold *upwf);
4946 =head3 Printing Piecewise Quasipolynomial Reductions
4948 Piecewise quasipolynomial reductions can be printed
4949 using the following function.
4951 __isl_give isl_printer *isl_printer_print_pw_qpolynomial_fold(
4952 __isl_take isl_printer *p,
4953 __isl_keep isl_pw_qpolynomial_fold *pwf);
4954 __isl_give isl_printer *isl_printer_print_union_pw_qpolynomial_fold(
4955 __isl_take isl_printer *p,
4956 __isl_keep isl_union_pw_qpolynomial_fold *upwf);
4958 For C<isl_printer_print_pw_qpolynomial_fold>,
4959 output format of the printer
4960 needs to be set to either C<ISL_FORMAT_ISL> or C<ISL_FORMAT_C>.
4961 For C<isl_printer_print_union_pw_qpolynomial_fold>,
4962 output format of the printer
4963 needs to be set to C<ISL_FORMAT_ISL>.
4964 In case of printing in C<ISL_FORMAT_C>, the user may want
4965 to set the names of all dimensions
4967 __isl_give isl_pw_qpolynomial_fold *
4968 isl_pw_qpolynomial_fold_set_dim_name(
4969 __isl_take isl_pw_qpolynomial_fold *pwf,
4970 enum isl_dim_type type, unsigned pos,
4973 =head3 Inspecting (Piecewise) Quasipolynomial Reductions
4975 To iterate over all piecewise quasipolynomial reductions in a union
4976 piecewise quasipolynomial reduction, use the following function
4978 int isl_union_pw_qpolynomial_fold_foreach_pw_qpolynomial_fold(
4979 __isl_keep isl_union_pw_qpolynomial_fold *upwf,
4980 int (*fn)(__isl_take isl_pw_qpolynomial_fold *pwf,
4981 void *user), void *user);
4983 To iterate over the cells in a piecewise quasipolynomial reduction,
4984 use either of the following two functions
4986 int isl_pw_qpolynomial_fold_foreach_piece(
4987 __isl_keep isl_pw_qpolynomial_fold *pwf,
4988 int (*fn)(__isl_take isl_set *set,
4989 __isl_take isl_qpolynomial_fold *fold,
4990 void *user), void *user);
4991 int isl_pw_qpolynomial_fold_foreach_lifted_piece(
4992 __isl_keep isl_pw_qpolynomial_fold *pwf,
4993 int (*fn)(__isl_take isl_set *set,
4994 __isl_take isl_qpolynomial_fold *fold,
4995 void *user), void *user);
4997 See L<Inspecting (Piecewise) Quasipolynomials> for an explanation
4998 of the difference between these two functions.
5000 To iterate over all quasipolynomials in a reduction, use
5002 int isl_qpolynomial_fold_foreach_qpolynomial(
5003 __isl_keep isl_qpolynomial_fold *fold,
5004 int (*fn)(__isl_take isl_qpolynomial *qp,
5005 void *user), void *user);
5007 =head3 Properties of Piecewise Quasipolynomial Reductions
5009 To check whether two union piecewise quasipolynomial reductions are
5010 obviously equal, use
5012 int isl_union_pw_qpolynomial_fold_plain_is_equal(
5013 __isl_keep isl_union_pw_qpolynomial_fold *upwf1,
5014 __isl_keep isl_union_pw_qpolynomial_fold *upwf2);
5016 =head3 Operations on Piecewise Quasipolynomial Reductions
5018 __isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_scale(
5019 __isl_take isl_qpolynomial_fold *fold, isl_int v);
5020 __isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_scale_val(
5021 __isl_take isl_qpolynomial_fold *fold,
5022 __isl_take isl_val *v);
5023 __isl_give isl_pw_qpolynomial_fold *
5024 isl_pw_qpolynomial_fold_scale_val(
5025 __isl_take isl_pw_qpolynomial_fold *pwf,
5026 __isl_take isl_val *v);
5027 __isl_give isl_union_pw_qpolynomial_fold *
5028 isl_union_pw_qpolynomial_fold_scale_val(
5029 __isl_take isl_union_pw_qpolynomial_fold *upwf,
5030 __isl_take isl_val *v);
5032 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_add(
5033 __isl_take isl_pw_qpolynomial_fold *pwf1,
5034 __isl_take isl_pw_qpolynomial_fold *pwf2);
5036 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_fold(
5037 __isl_take isl_pw_qpolynomial_fold *pwf1,
5038 __isl_take isl_pw_qpolynomial_fold *pwf2);
5040 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_fold(
5041 __isl_take isl_union_pw_qpolynomial_fold *upwf1,
5042 __isl_take isl_union_pw_qpolynomial_fold *upwf2);
5044 __isl_give isl_qpolynomial *isl_pw_qpolynomial_fold_eval(
5045 __isl_take isl_pw_qpolynomial_fold *pwf,
5046 __isl_take isl_point *pnt);
5048 __isl_give isl_qpolynomial *isl_union_pw_qpolynomial_fold_eval(
5049 __isl_take isl_union_pw_qpolynomial_fold *upwf,
5050 __isl_take isl_point *pnt);
5052 __isl_give isl_pw_qpolynomial_fold *
5053 isl_pw_qpolynomial_fold_intersect_params(
5054 __isl_take isl_pw_qpolynomial_fold *pwf,
5055 __isl_take isl_set *set);
5057 __isl_give isl_union_set *isl_union_pw_qpolynomial_fold_domain(
5058 __isl_take isl_union_pw_qpolynomial_fold *upwf);
5059 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_intersect_domain(
5060 __isl_take isl_union_pw_qpolynomial_fold *upwf,
5061 __isl_take isl_union_set *uset);
5062 __isl_give isl_union_pw_qpolynomial_fold *
5063 isl_union_pw_qpolynomial_fold_intersect_params(
5064 __isl_take isl_union_pw_qpolynomial_fold *upwf,
5065 __isl_take isl_set *set);
5067 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_project_domain_on_params(
5068 __isl_take isl_pw_qpolynomial_fold *pwf);
5070 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_coalesce(
5071 __isl_take isl_pw_qpolynomial_fold *pwf);
5073 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_coalesce(
5074 __isl_take isl_union_pw_qpolynomial_fold *upwf);
5076 __isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_gist_params(
5077 __isl_take isl_qpolynomial_fold *fold,
5078 __isl_take isl_set *context);
5079 __isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_gist(
5080 __isl_take isl_qpolynomial_fold *fold,
5081 __isl_take isl_set *context);
5083 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_gist(
5084 __isl_take isl_pw_qpolynomial_fold *pwf,
5085 __isl_take isl_set *context);
5086 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_gist_params(
5087 __isl_take isl_pw_qpolynomial_fold *pwf,
5088 __isl_take isl_set *context);
5090 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_gist(
5091 __isl_take isl_union_pw_qpolynomial_fold *upwf,
5092 __isl_take isl_union_set *context);
5093 __isl_give isl_union_pw_qpolynomial_fold *
5094 isl_union_pw_qpolynomial_fold_gist_params(
5095 __isl_take isl_union_pw_qpolynomial_fold *upwf,
5096 __isl_take isl_set *context);
5098 The gist operation applies the gist operation to each of
5099 the cells in the domain of the input piecewise quasipolynomial reduction.
5100 In future, the operation will also exploit the context
5101 to simplify the quasipolynomial reductions associated to each cell.
5103 __isl_give isl_pw_qpolynomial_fold *
5104 isl_set_apply_pw_qpolynomial_fold(
5105 __isl_take isl_set *set,
5106 __isl_take isl_pw_qpolynomial_fold *pwf,
5108 __isl_give isl_pw_qpolynomial_fold *
5109 isl_map_apply_pw_qpolynomial_fold(
5110 __isl_take isl_map *map,
5111 __isl_take isl_pw_qpolynomial_fold *pwf,
5113 __isl_give isl_union_pw_qpolynomial_fold *
5114 isl_union_set_apply_union_pw_qpolynomial_fold(
5115 __isl_take isl_union_set *uset,
5116 __isl_take isl_union_pw_qpolynomial_fold *upwf,
5118 __isl_give isl_union_pw_qpolynomial_fold *
5119 isl_union_map_apply_union_pw_qpolynomial_fold(
5120 __isl_take isl_union_map *umap,
5121 __isl_take isl_union_pw_qpolynomial_fold *upwf,
5124 The functions taking a map
5125 compose the given map with the given piecewise quasipolynomial reduction.
5126 That is, compute a bound (of the same type as C<pwf> or C<upwf> itself)
5127 over all elements in the intersection of the range of the map
5128 and the domain of the piecewise quasipolynomial reduction
5129 as a function of an element in the domain of the map.
5130 The functions taking a set compute a bound over all elements in the
5131 intersection of the set and the domain of the
5132 piecewise quasipolynomial reduction.
5134 =head2 Parametric Vertex Enumeration
5136 The parametric vertex enumeration described in this section
5137 is mainly intended to be used internally and by the C<barvinok>
5140 #include <isl/vertices.h>
5141 __isl_give isl_vertices *isl_basic_set_compute_vertices(
5142 __isl_keep isl_basic_set *bset);
5144 The function C<isl_basic_set_compute_vertices> performs the
5145 actual computation of the parametric vertices and the chamber
5146 decomposition and store the result in an C<isl_vertices> object.
5147 This information can be queried by either iterating over all
5148 the vertices or iterating over all the chambers or cells
5149 and then iterating over all vertices that are active on the chamber.
5151 int isl_vertices_foreach_vertex(
5152 __isl_keep isl_vertices *vertices,
5153 int (*fn)(__isl_take isl_vertex *vertex, void *user),
5156 int isl_vertices_foreach_cell(
5157 __isl_keep isl_vertices *vertices,
5158 int (*fn)(__isl_take isl_cell *cell, void *user),
5160 int isl_cell_foreach_vertex(__isl_keep isl_cell *cell,
5161 int (*fn)(__isl_take isl_vertex *vertex, void *user),
5164 Other operations that can be performed on an C<isl_vertices> object are
5167 isl_ctx *isl_vertices_get_ctx(
5168 __isl_keep isl_vertices *vertices);
5169 int isl_vertices_get_n_vertices(
5170 __isl_keep isl_vertices *vertices);
5171 void isl_vertices_free(__isl_take isl_vertices *vertices);
5173 Vertices can be inspected and destroyed using the following functions.
5175 isl_ctx *isl_vertex_get_ctx(__isl_keep isl_vertex *vertex);
5176 int isl_vertex_get_id(__isl_keep isl_vertex *vertex);
5177 __isl_give isl_basic_set *isl_vertex_get_domain(
5178 __isl_keep isl_vertex *vertex);
5179 __isl_give isl_basic_set *isl_vertex_get_expr(
5180 __isl_keep isl_vertex *vertex);
5181 void isl_vertex_free(__isl_take isl_vertex *vertex);
5183 C<isl_vertex_get_expr> returns a singleton parametric set describing
5184 the vertex, while C<isl_vertex_get_domain> returns the activity domain
5186 Note that C<isl_vertex_get_domain> and C<isl_vertex_get_expr> return
5187 B<rational> basic sets, so they should mainly be used for inspection
5188 and should not be mixed with integer sets.
5190 Chambers can be inspected and destroyed using the following functions.
5192 isl_ctx *isl_cell_get_ctx(__isl_keep isl_cell *cell);
5193 __isl_give isl_basic_set *isl_cell_get_domain(
5194 __isl_keep isl_cell *cell);
5195 void isl_cell_free(__isl_take isl_cell *cell);
5197 =head1 Polyhedral Compilation Library
5199 This section collects functionality in C<isl> that has been specifically
5200 designed for use during polyhedral compilation.
5202 =head2 Dependence Analysis
5204 C<isl> contains specialized functionality for performing
5205 array dataflow analysis. That is, given a I<sink> access relation
5206 and a collection of possible I<source> access relations,
5207 C<isl> can compute relations that describe
5208 for each iteration of the sink access, which iteration
5209 of which of the source access relations was the last
5210 to access the same data element before the given iteration
5212 The resulting dependence relations map source iterations
5213 to the corresponding sink iterations.
5214 To compute standard flow dependences, the sink should be
5215 a read, while the sources should be writes.
5216 If any of the source accesses are marked as being I<may>
5217 accesses, then there will be a dependence from the last
5218 I<must> access B<and> from any I<may> access that follows
5219 this last I<must> access.
5220 In particular, if I<all> sources are I<may> accesses,
5221 then memory based dependence analysis is performed.
5222 If, on the other hand, all sources are I<must> accesses,
5223 then value based dependence analysis is performed.
5225 #include <isl/flow.h>
5227 typedef int (*isl_access_level_before)(void *first, void *second);
5229 __isl_give isl_access_info *isl_access_info_alloc(
5230 __isl_take isl_map *sink,
5231 void *sink_user, isl_access_level_before fn,
5233 __isl_give isl_access_info *isl_access_info_add_source(
5234 __isl_take isl_access_info *acc,
5235 __isl_take isl_map *source, int must,
5237 void *isl_access_info_free(__isl_take isl_access_info *acc);
5239 __isl_give isl_flow *isl_access_info_compute_flow(
5240 __isl_take isl_access_info *acc);
5242 int isl_flow_foreach(__isl_keep isl_flow *deps,
5243 int (*fn)(__isl_take isl_map *dep, int must,
5244 void *dep_user, void *user),
5246 __isl_give isl_map *isl_flow_get_no_source(
5247 __isl_keep isl_flow *deps, int must);
5248 void isl_flow_free(__isl_take isl_flow *deps);
5250 The function C<isl_access_info_compute_flow> performs the actual
5251 dependence analysis. The other functions are used to construct
5252 the input for this function or to read off the output.
5254 The input is collected in an C<isl_access_info>, which can
5255 be created through a call to C<isl_access_info_alloc>.
5256 The arguments to this functions are the sink access relation
5257 C<sink>, a token C<sink_user> used to identify the sink
5258 access to the user, a callback function for specifying the
5259 relative order of source and sink accesses, and the number
5260 of source access relations that will be added.
5261 The callback function has type C<int (*)(void *first, void *second)>.
5262 The function is called with two user supplied tokens identifying
5263 either a source or the sink and it should return the shared nesting
5264 level and the relative order of the two accesses.
5265 In particular, let I<n> be the number of loops shared by
5266 the two accesses. If C<first> precedes C<second> textually,
5267 then the function should return I<2 * n + 1>; otherwise,
5268 it should return I<2 * n>.
5269 The sources can be added to the C<isl_access_info> by performing
5270 (at most) C<max_source> calls to C<isl_access_info_add_source>.
5271 C<must> indicates whether the source is a I<must> access
5272 or a I<may> access. Note that a multi-valued access relation
5273 should only be marked I<must> if every iteration in the domain
5274 of the relation accesses I<all> elements in its image.
5275 The C<source_user> token is again used to identify
5276 the source access. The range of the source access relation
5277 C<source> should have the same dimension as the range
5278 of the sink access relation.
5279 The C<isl_access_info_free> function should usually not be
5280 called explicitly, because it is called implicitly by
5281 C<isl_access_info_compute_flow>.
5283 The result of the dependence analysis is collected in an
5284 C<isl_flow>. There may be elements of
5285 the sink access for which no preceding source access could be
5286 found or for which all preceding sources are I<may> accesses.
5287 The relations containing these elements can be obtained through
5288 calls to C<isl_flow_get_no_source>, the first with C<must> set
5289 and the second with C<must> unset.
5290 In the case of standard flow dependence analysis,
5291 with the sink a read and the sources I<must> writes,
5292 the first relation corresponds to the reads from uninitialized
5293 array elements and the second relation is empty.
5294 The actual flow dependences can be extracted using
5295 C<isl_flow_foreach>. This function will call the user-specified
5296 callback function C<fn> for each B<non-empty> dependence between
5297 a source and the sink. The callback function is called
5298 with four arguments, the actual flow dependence relation
5299 mapping source iterations to sink iterations, a boolean that
5300 indicates whether it is a I<must> or I<may> dependence, a token
5301 identifying the source and an additional C<void *> with value
5302 equal to the third argument of the C<isl_flow_foreach> call.
5303 A dependence is marked I<must> if it originates from a I<must>
5304 source and if it is not followed by any I<may> sources.
5306 After finishing with an C<isl_flow>, the user should call
5307 C<isl_flow_free> to free all associated memory.
5309 A higher-level interface to dependence analysis is provided
5310 by the following function.
5312 #include <isl/flow.h>
5314 int isl_union_map_compute_flow(__isl_take isl_union_map *sink,
5315 __isl_take isl_union_map *must_source,
5316 __isl_take isl_union_map *may_source,
5317 __isl_take isl_union_map *schedule,
5318 __isl_give isl_union_map **must_dep,
5319 __isl_give isl_union_map **may_dep,
5320 __isl_give isl_union_map **must_no_source,
5321 __isl_give isl_union_map **may_no_source);
5323 The arrays are identified by the tuple names of the ranges
5324 of the accesses. The iteration domains by the tuple names
5325 of the domains of the accesses and of the schedule.
5326 The relative order of the iteration domains is given by the
5327 schedule. The relations returned through C<must_no_source>
5328 and C<may_no_source> are subsets of C<sink>.
5329 Any of C<must_dep>, C<may_dep>, C<must_no_source>
5330 or C<may_no_source> may be C<NULL>, but a C<NULL> value for
5331 any of the other arguments is treated as an error.
5333 =head3 Interaction with Dependence Analysis
5335 During the dependence analysis, we frequently need to perform
5336 the following operation. Given a relation between sink iterations
5337 and potential source iterations from a particular source domain,
5338 what is the last potential source iteration corresponding to each
5339 sink iteration. It can sometimes be convenient to adjust
5340 the set of potential source iterations before or after each such operation.
5341 The prototypical example is fuzzy array dataflow analysis,
5342 where we need to analyze if, based on data-dependent constraints,
5343 the sink iteration can ever be executed without one or more of
5344 the corresponding potential source iterations being executed.
5345 If so, we can introduce extra parameters and select an unknown
5346 but fixed source iteration from the potential source iterations.
5347 To be able to perform such manipulations, C<isl> provides the following
5350 #include <isl/flow.h>
5352 typedef __isl_give isl_restriction *(*isl_access_restrict)(
5353 __isl_keep isl_map *source_map,
5354 __isl_keep isl_set *sink, void *source_user,
5356 __isl_give isl_access_info *isl_access_info_set_restrict(
5357 __isl_take isl_access_info *acc,
5358 isl_access_restrict fn, void *user);
5360 The function C<isl_access_info_set_restrict> should be called
5361 before calling C<isl_access_info_compute_flow> and registers a callback function
5362 that will be called any time C<isl> is about to compute the last
5363 potential source. The first argument is the (reverse) proto-dependence,
5364 mapping sink iterations to potential source iterations.
5365 The second argument represents the sink iterations for which
5366 we want to compute the last source iteration.
5367 The third argument is the token corresponding to the source
5368 and the final argument is the token passed to C<isl_access_info_set_restrict>.
5369 The callback is expected to return a restriction on either the input or
5370 the output of the operation computing the last potential source.
5371 If the input needs to be restricted then restrictions are needed
5372 for both the source and the sink iterations. The sink iterations
5373 and the potential source iterations will be intersected with these sets.
5374 If the output needs to be restricted then only a restriction on the source
5375 iterations is required.
5376 If any error occurs, the callback should return C<NULL>.
5377 An C<isl_restriction> object can be created, freed and inspected
5378 using the following functions.
5380 #include <isl/flow.h>
5382 __isl_give isl_restriction *isl_restriction_input(
5383 __isl_take isl_set *source_restr,
5384 __isl_take isl_set *sink_restr);
5385 __isl_give isl_restriction *isl_restriction_output(
5386 __isl_take isl_set *source_restr);
5387 __isl_give isl_restriction *isl_restriction_none(
5388 __isl_take isl_map *source_map);
5389 __isl_give isl_restriction *isl_restriction_empty(
5390 __isl_take isl_map *source_map);
5391 void *isl_restriction_free(
5392 __isl_take isl_restriction *restr);
5393 isl_ctx *isl_restriction_get_ctx(
5394 __isl_keep isl_restriction *restr);
5396 C<isl_restriction_none> and C<isl_restriction_empty> are special
5397 cases of C<isl_restriction_input>. C<isl_restriction_none>
5398 is essentially equivalent to
5400 isl_restriction_input(isl_set_universe(
5401 isl_space_range(isl_map_get_space(source_map))),
5403 isl_space_domain(isl_map_get_space(source_map))));
5405 whereas C<isl_restriction_empty> is essentially equivalent to
5407 isl_restriction_input(isl_set_empty(
5408 isl_space_range(isl_map_get_space(source_map))),
5410 isl_space_domain(isl_map_get_space(source_map))));
5414 B<The functionality described in this section is fairly new
5415 and may be subject to change.>
5417 The following function can be used to compute a schedule
5418 for a union of domains.
5419 By default, the algorithm used to construct the schedule is similar
5420 to that of C<Pluto>.
5421 Alternatively, Feautrier's multi-dimensional scheduling algorithm can
5423 The generated schedule respects all C<validity> dependences.
5424 That is, all dependence distances over these dependences in the
5425 scheduled space are lexicographically positive.
5426 The default algorithm tries to minimize the dependence distances over
5427 C<proximity> dependences.
5428 Moreover, it tries to obtain sequences (bands) of schedule dimensions
5429 for groups of domains where the dependence distances have only
5430 non-negative values.
5431 When using Feautrier's algorithm, the C<proximity> dependence
5432 distances are only minimized during the extension to a
5433 full-dimensional schedule.
5435 #include <isl/schedule.h>
5436 __isl_give isl_schedule *isl_union_set_compute_schedule(
5437 __isl_take isl_union_set *domain,
5438 __isl_take isl_union_map *validity,
5439 __isl_take isl_union_map *proximity);
5440 void *isl_schedule_free(__isl_take isl_schedule *sched);
5442 A mapping from the domains to the scheduled space can be obtained
5443 from an C<isl_schedule> using the following function.
5445 __isl_give isl_union_map *isl_schedule_get_map(
5446 __isl_keep isl_schedule *sched);
5448 A representation of the schedule can be printed using
5450 __isl_give isl_printer *isl_printer_print_schedule(
5451 __isl_take isl_printer *p,
5452 __isl_keep isl_schedule *schedule);
5454 A representation of the schedule as a forest of bands can be obtained
5455 using the following function.
5457 __isl_give isl_band_list *isl_schedule_get_band_forest(
5458 __isl_keep isl_schedule *schedule);
5460 The individual bands can be visited in depth-first post-order
5461 using the following function.
5463 #include <isl/schedule.h>
5464 int isl_schedule_foreach_band(
5465 __isl_keep isl_schedule *sched,
5466 int (*fn)(__isl_keep isl_band *band, void *user),
5469 The list can be manipulated as explained in L<"Lists">.
5470 The bands inside the list can be copied and freed using the following
5473 #include <isl/band.h>
5474 __isl_give isl_band *isl_band_copy(
5475 __isl_keep isl_band *band);
5476 void *isl_band_free(__isl_take isl_band *band);
5478 Each band contains zero or more scheduling dimensions.
5479 These are referred to as the members of the band.
5480 The section of the schedule that corresponds to the band is
5481 referred to as the partial schedule of the band.
5482 For those nodes that participate in a band, the outer scheduling
5483 dimensions form the prefix schedule, while the inner scheduling
5484 dimensions form the suffix schedule.
5485 That is, if we take a cut of the band forest, then the union of
5486 the concatenations of the prefix, partial and suffix schedules of
5487 each band in the cut is equal to the entire schedule (modulo
5488 some possible padding at the end with zero scheduling dimensions).
5489 The properties of a band can be inspected using the following functions.
5491 #include <isl/band.h>
5492 isl_ctx *isl_band_get_ctx(__isl_keep isl_band *band);
5494 int isl_band_has_children(__isl_keep isl_band *band);
5495 __isl_give isl_band_list *isl_band_get_children(
5496 __isl_keep isl_band *band);
5498 __isl_give isl_union_map *isl_band_get_prefix_schedule(
5499 __isl_keep isl_band *band);
5500 __isl_give isl_union_map *isl_band_get_partial_schedule(
5501 __isl_keep isl_band *band);
5502 __isl_give isl_union_map *isl_band_get_suffix_schedule(
5503 __isl_keep isl_band *band);
5505 int isl_band_n_member(__isl_keep isl_band *band);
5506 int isl_band_member_is_zero_distance(
5507 __isl_keep isl_band *band, int pos);
5509 int isl_band_list_foreach_band(
5510 __isl_keep isl_band_list *list,
5511 int (*fn)(__isl_keep isl_band *band, void *user),
5514 Note that a scheduling dimension is considered to be ``zero
5515 distance'' if it does not carry any proximity dependences
5517 That is, if the dependence distances of the proximity
5518 dependences are all zero in that direction (for fixed
5519 iterations of outer bands).
5520 Like C<isl_schedule_foreach_band>,
5521 the function C<isl_band_list_foreach_band> calls C<fn> on the bands
5522 in depth-first post-order.
5524 A band can be tiled using the following function.
5526 #include <isl/band.h>
5527 int isl_band_tile(__isl_keep isl_band *band,
5528 __isl_take isl_vec *sizes);
5530 int isl_options_set_tile_scale_tile_loops(isl_ctx *ctx,
5532 int isl_options_get_tile_scale_tile_loops(isl_ctx *ctx);
5533 int isl_options_set_tile_shift_point_loops(isl_ctx *ctx,
5535 int isl_options_get_tile_shift_point_loops(isl_ctx *ctx);
5537 The C<isl_band_tile> function tiles the band using the given tile sizes
5538 inside its schedule.
5539 A new child band is created to represent the point loops and it is
5540 inserted between the modified band and its children.
5541 The C<tile_scale_tile_loops> option specifies whether the tile
5542 loops iterators should be scaled by the tile sizes.
5543 If the C<tile_shift_point_loops> option is set, then the point loops
5544 are shifted to start at zero.
5546 A band can be split into two nested bands using the following function.
5548 int isl_band_split(__isl_keep isl_band *band, int pos);
5550 The resulting outer band contains the first C<pos> dimensions of C<band>
5551 while the inner band contains the remaining dimensions.
5553 A representation of the band can be printed using
5555 #include <isl/band.h>
5556 __isl_give isl_printer *isl_printer_print_band(
5557 __isl_take isl_printer *p,
5558 __isl_keep isl_band *band);
5562 #include <isl/schedule.h>
5563 int isl_options_set_schedule_max_coefficient(
5564 isl_ctx *ctx, int val);
5565 int isl_options_get_schedule_max_coefficient(
5567 int isl_options_set_schedule_max_constant_term(
5568 isl_ctx *ctx, int val);
5569 int isl_options_get_schedule_max_constant_term(
5571 int isl_options_set_schedule_fuse(isl_ctx *ctx, int val);
5572 int isl_options_get_schedule_fuse(isl_ctx *ctx);
5573 int isl_options_set_schedule_maximize_band_depth(
5574 isl_ctx *ctx, int val);
5575 int isl_options_get_schedule_maximize_band_depth(
5577 int isl_options_set_schedule_outer_zero_distance(
5578 isl_ctx *ctx, int val);
5579 int isl_options_get_schedule_outer_zero_distance(
5581 int isl_options_set_schedule_split_scaled(
5582 isl_ctx *ctx, int val);
5583 int isl_options_get_schedule_split_scaled(
5585 int isl_options_set_schedule_algorithm(
5586 isl_ctx *ctx, int val);
5587 int isl_options_get_schedule_algorithm(
5589 int isl_options_set_schedule_separate_components(
5590 isl_ctx *ctx, int val);
5591 int isl_options_get_schedule_separate_components(
5596 =item * schedule_max_coefficient
5598 This option enforces that the coefficients for variable and parameter
5599 dimensions in the calculated schedule are not larger than the specified value.
5600 This option can significantly increase the speed of the scheduling calculation
5601 and may also prevent fusing of unrelated dimensions. A value of -1 means that
5602 this option does not introduce bounds on the variable or parameter
5605 =item * schedule_max_constant_term
5607 This option enforces that the constant coefficients in the calculated schedule
5608 are not larger than the maximal constant term. This option can significantly
5609 increase the speed of the scheduling calculation and may also prevent fusing of
5610 unrelated dimensions. A value of -1 means that this option does not introduce
5611 bounds on the constant coefficients.
5613 =item * schedule_fuse
5615 This option controls the level of fusion.
5616 If this option is set to C<ISL_SCHEDULE_FUSE_MIN>, then loops in the
5617 resulting schedule will be distributed as much as possible.
5618 If this option is set to C<ISL_SCHEDULE_FUSE_MAX>, then C<isl> will
5619 try to fuse loops in the resulting schedule.
5621 =item * schedule_maximize_band_depth
5623 If this option is set, we do not split bands at the point
5624 where we detect splitting is necessary. Instead, we
5625 backtrack and split bands as early as possible. This
5626 reduces the number of splits and maximizes the width of
5627 the bands. Wider bands give more possibilities for tiling.
5628 Note that if the C<schedule_fuse> option is set to C<ISL_SCHEDULE_FUSE_MIN>,
5629 then bands will be split as early as possible, even if there is no need.
5630 The C<schedule_maximize_band_depth> option therefore has no effect in this case.
5632 =item * schedule_outer_zero_distance
5634 If this option is set, then we try to construct schedules
5635 where the outermost scheduling dimension in each band
5636 results in a zero dependence distance over the proximity
5639 =item * schedule_split_scaled
5641 If this option is set, then we try to construct schedules in which the
5642 constant term is split off from the linear part if the linear parts of
5643 the scheduling rows for all nodes in the graphs have a common non-trivial
5645 The constant term is then placed in a separate band and the linear
5648 =item * schedule_algorithm
5650 Selects the scheduling algorithm to be used.
5651 Available scheduling algorithms are C<ISL_SCHEDULE_ALGORITHM_ISL>
5652 and C<ISL_SCHEDULE_ALGORITHM_FEAUTRIER>.
5654 =item * schedule_separate_components
5656 If at any point the dependence graph contains any (weakly connected) components,
5657 then these components are scheduled separately.
5658 If this option is not set, then some iterations of the domains
5659 in these components may be scheduled together.
5660 If this option is set, then the components are given consecutive
5665 =head2 AST Generation
5667 This section describes the C<isl> functionality for generating
5668 ASTs that visit all the elements
5669 in a domain in an order specified by a schedule.
5670 In particular, given a C<isl_union_map>, an AST is generated
5671 that visits all the elements in the domain of the C<isl_union_map>
5672 according to the lexicographic order of the corresponding image
5673 element(s). If the range of the C<isl_union_map> consists of
5674 elements in more than one space, then each of these spaces is handled
5675 separately in an arbitrary order.
5676 It should be noted that the image elements only specify the I<order>
5677 in which the corresponding domain elements should be visited.
5678 No direct relation between the image elements and the loop iterators
5679 in the generated AST should be assumed.
5681 Each AST is generated within a build. The initial build
5682 simply specifies the constraints on the parameters (if any)
5683 and can be created, inspected, copied and freed using the following functions.
5685 #include <isl/ast_build.h>
5686 __isl_give isl_ast_build *isl_ast_build_from_context(
5687 __isl_take isl_set *set);
5688 isl_ctx *isl_ast_build_get_ctx(
5689 __isl_keep isl_ast_build *build);
5690 __isl_give isl_ast_build *isl_ast_build_copy(
5691 __isl_keep isl_ast_build *build);
5692 void *isl_ast_build_free(
5693 __isl_take isl_ast_build *build);
5695 The C<set> argument is usually a parameter set with zero or more parameters.
5696 More C<isl_ast_build> functions are described in L</"Nested AST Generation">
5697 and L</"Fine-grained Control over AST Generation">.
5698 Finally, the AST itself can be constructed using the following
5701 #include <isl/ast_build.h>
5702 __isl_give isl_ast_node *isl_ast_build_ast_from_schedule(
5703 __isl_keep isl_ast_build *build,
5704 __isl_take isl_union_map *schedule);
5706 =head3 Inspecting the AST
5708 The basic properties of an AST node can be obtained as follows.
5710 #include <isl/ast.h>
5711 isl_ctx *isl_ast_node_get_ctx(
5712 __isl_keep isl_ast_node *node);
5713 enum isl_ast_node_type isl_ast_node_get_type(
5714 __isl_keep isl_ast_node *node);
5716 The type of an AST node is one of
5717 C<isl_ast_node_for>,
5719 C<isl_ast_node_block> or
5720 C<isl_ast_node_user>.
5721 An C<isl_ast_node_for> represents a for node.
5722 An C<isl_ast_node_if> represents an if node.
5723 An C<isl_ast_node_block> represents a compound node.
5724 An C<isl_ast_node_user> represents an expression statement.
5725 An expression statement typically corresponds to a domain element, i.e.,
5726 one of the elements that is visited by the AST.
5728 Each type of node has its own additional properties.
5730 #include <isl/ast.h>
5731 __isl_give isl_ast_expr *isl_ast_node_for_get_iterator(
5732 __isl_keep isl_ast_node *node);
5733 __isl_give isl_ast_expr *isl_ast_node_for_get_init(
5734 __isl_keep isl_ast_node *node);
5735 __isl_give isl_ast_expr *isl_ast_node_for_get_cond(
5736 __isl_keep isl_ast_node *node);
5737 __isl_give isl_ast_expr *isl_ast_node_for_get_inc(
5738 __isl_keep isl_ast_node *node);
5739 __isl_give isl_ast_node *isl_ast_node_for_get_body(
5740 __isl_keep isl_ast_node *node);
5741 int isl_ast_node_for_is_degenerate(
5742 __isl_keep isl_ast_node *node);
5744 An C<isl_ast_for> is considered degenerate if it is known to execute
5747 #include <isl/ast.h>
5748 __isl_give isl_ast_expr *isl_ast_node_if_get_cond(
5749 __isl_keep isl_ast_node *node);
5750 __isl_give isl_ast_node *isl_ast_node_if_get_then(
5751 __isl_keep isl_ast_node *node);
5752 int isl_ast_node_if_has_else(
5753 __isl_keep isl_ast_node *node);
5754 __isl_give isl_ast_node *isl_ast_node_if_get_else(
5755 __isl_keep isl_ast_node *node);
5757 __isl_give isl_ast_node_list *
5758 isl_ast_node_block_get_children(
5759 __isl_keep isl_ast_node *node);
5761 __isl_give isl_ast_expr *isl_ast_node_user_get_expr(
5762 __isl_keep isl_ast_node *node);
5764 Each of the returned C<isl_ast_expr>s can in turn be inspected using
5765 the following functions.
5767 #include <isl/ast.h>
5768 isl_ctx *isl_ast_expr_get_ctx(
5769 __isl_keep isl_ast_expr *expr);
5770 enum isl_ast_expr_type isl_ast_expr_get_type(
5771 __isl_keep isl_ast_expr *expr);
5773 The type of an AST expression is one of
5775 C<isl_ast_expr_id> or
5776 C<isl_ast_expr_int>.
5777 An C<isl_ast_expr_op> represents the result of an operation.
5778 An C<isl_ast_expr_id> represents an identifier.
5779 An C<isl_ast_expr_int> represents an integer value.
5781 Each type of expression has its own additional properties.
5783 #include <isl/ast.h>
5784 enum isl_ast_op_type isl_ast_expr_get_op_type(
5785 __isl_keep isl_ast_expr *expr);
5786 int isl_ast_expr_get_op_n_arg(__isl_keep isl_ast_expr *expr);
5787 __isl_give isl_ast_expr *isl_ast_expr_get_op_arg(
5788 __isl_keep isl_ast_expr *expr, int pos);
5789 int isl_ast_node_foreach_ast_op_type(
5790 __isl_keep isl_ast_node *node,
5791 int (*fn)(enum isl_ast_op_type type, void *user),
5794 C<isl_ast_expr_get_op_type> returns the type of the operation
5795 performed. C<isl_ast_expr_get_op_n_arg> returns the number of
5796 arguments. C<isl_ast_expr_get_op_arg> returns the specified
5798 C<isl_ast_node_foreach_ast_op_type> calls C<fn> for each distinct
5799 C<isl_ast_op_type> that appears in C<node>.
5800 The operation type is one of the following.
5804 =item C<isl_ast_op_and>
5806 Logical I<and> of two arguments.
5807 Both arguments can be evaluated.
5809 =item C<isl_ast_op_and_then>
5811 Logical I<and> of two arguments.
5812 The second argument can only be evaluated if the first evaluates to true.
5814 =item C<isl_ast_op_or>
5816 Logical I<or> of two arguments.
5817 Both arguments can be evaluated.
5819 =item C<isl_ast_op_or_else>
5821 Logical I<or> of two arguments.
5822 The second argument can only be evaluated if the first evaluates to false.
5824 =item C<isl_ast_op_max>
5826 Maximum of two or more arguments.
5828 =item C<isl_ast_op_min>
5830 Minimum of two or more arguments.
5832 =item C<isl_ast_op_minus>
5836 =item C<isl_ast_op_add>
5838 Sum of two arguments.
5840 =item C<isl_ast_op_sub>
5842 Difference of two arguments.
5844 =item C<isl_ast_op_mul>
5846 Product of two arguments.
5848 =item C<isl_ast_op_div>
5850 Exact division. That is, the result is known to be an integer.
5852 =item C<isl_ast_op_fdiv_q>
5854 Result of integer division, rounded towards negative
5857 =item C<isl_ast_op_pdiv_q>
5859 Result of integer division, where dividend is known to be non-negative.
5861 =item C<isl_ast_op_pdiv_r>
5863 Remainder of integer division, where dividend is known to be non-negative.
5865 =item C<isl_ast_op_cond>
5867 Conditional operator defined on three arguments.
5868 If the first argument evaluates to true, then the result
5869 is equal to the second argument. Otherwise, the result
5870 is equal to the third argument.
5871 The second and third argument may only be evaluated if
5872 the first argument evaluates to true and false, respectively.
5873 Corresponds to C<a ? b : c> in C.
5875 =item C<isl_ast_op_select>
5877 Conditional operator defined on three arguments.
5878 If the first argument evaluates to true, then the result
5879 is equal to the second argument. Otherwise, the result
5880 is equal to the third argument.
5881 The second and third argument may be evaluated independently
5882 of the value of the first argument.
5883 Corresponds to C<a * b + (1 - a) * c> in C.
5885 =item C<isl_ast_op_eq>
5889 =item C<isl_ast_op_le>
5891 Less than or equal relation.
5893 =item C<isl_ast_op_lt>
5897 =item C<isl_ast_op_ge>
5899 Greater than or equal relation.
5901 =item C<isl_ast_op_gt>
5903 Greater than relation.
5905 =item C<isl_ast_op_call>
5908 The number of arguments of the C<isl_ast_expr> is one more than
5909 the number of arguments in the function call, the first argument
5910 representing the function being called.
5914 #include <isl/ast.h>
5915 __isl_give isl_id *isl_ast_expr_get_id(
5916 __isl_keep isl_ast_expr *expr);
5918 Return the identifier represented by the AST expression.
5920 #include <isl/ast.h>
5921 int isl_ast_expr_get_int(__isl_keep isl_ast_expr *expr,
5924 Return the integer represented by the AST expression.
5925 Note that the integer is returned through the C<v> argument.
5926 The return value of the function itself indicates whether the
5927 operation was performed successfully.
5929 =head3 Manipulating and printing the AST
5931 AST nodes can be copied and freed using the following functions.
5933 #include <isl/ast.h>
5934 __isl_give isl_ast_node *isl_ast_node_copy(
5935 __isl_keep isl_ast_node *node);
5936 void *isl_ast_node_free(__isl_take isl_ast_node *node);
5938 AST expressions can be copied and freed using the following functions.
5940 #include <isl/ast.h>
5941 __isl_give isl_ast_expr *isl_ast_expr_copy(
5942 __isl_keep isl_ast_expr *expr);
5943 void *isl_ast_expr_free(__isl_take isl_ast_expr *expr);
5945 New AST expressions can be created either directly or within
5946 the context of an C<isl_ast_build>.
5948 #include <isl/ast.h>
5949 __isl_give isl_ast_expr *isl_ast_expr_from_id(
5950 __isl_take isl_id *id);
5951 __isl_give isl_ast_expr *isl_ast_expr_neg(
5952 __isl_take isl_ast_expr *expr);
5953 __isl_give isl_ast_expr *isl_ast_expr_add(
5954 __isl_take isl_ast_expr *expr1,
5955 __isl_take isl_ast_expr *expr2);
5956 __isl_give isl_ast_expr *isl_ast_expr_sub(
5957 __isl_take isl_ast_expr *expr1,
5958 __isl_take isl_ast_expr *expr2);
5959 __isl_give isl_ast_expr *isl_ast_expr_mul(
5960 __isl_take isl_ast_expr *expr1,
5961 __isl_take isl_ast_expr *expr2);
5962 __isl_give isl_ast_expr *isl_ast_expr_div(
5963 __isl_take isl_ast_expr *expr1,
5964 __isl_take isl_ast_expr *expr2);
5965 __isl_give isl_ast_expr *isl_ast_expr_and(
5966 __isl_take isl_ast_expr *expr1,
5967 __isl_take isl_ast_expr *expr2)
5968 __isl_give isl_ast_expr *isl_ast_expr_or(
5969 __isl_take isl_ast_expr *expr1,
5970 __isl_take isl_ast_expr *expr2)
5972 #include <isl/ast_build.h>
5973 __isl_give isl_ast_expr *isl_ast_build_expr_from_pw_aff(
5974 __isl_keep isl_ast_build *build,
5975 __isl_take isl_pw_aff *pa);
5976 __isl_give isl_ast_expr *
5977 isl_ast_build_call_from_pw_multi_aff(
5978 __isl_keep isl_ast_build *build,
5979 __isl_take isl_pw_multi_aff *pma);
5981 The domains of C<pa> and C<pma> should correspond
5982 to the schedule space of C<build>.
5983 The tuple id of C<pma> is used as the function being called.
5985 User specified data can be attached to an C<isl_ast_node> and obtained
5986 from the same C<isl_ast_node> using the following functions.
5988 #include <isl/ast.h>
5989 __isl_give isl_ast_node *isl_ast_node_set_annotation(
5990 __isl_take isl_ast_node *node,
5991 __isl_take isl_id *annotation);
5992 __isl_give isl_id *isl_ast_node_get_annotation(
5993 __isl_keep isl_ast_node *node);
5995 Basic printing can be performed using the following functions.
5997 #include <isl/ast.h>
5998 __isl_give isl_printer *isl_printer_print_ast_expr(
5999 __isl_take isl_printer *p,
6000 __isl_keep isl_ast_expr *expr);
6001 __isl_give isl_printer *isl_printer_print_ast_node(
6002 __isl_take isl_printer *p,
6003 __isl_keep isl_ast_node *node);
6005 More advanced printing can be performed using the following functions.
6007 #include <isl/ast.h>
6008 __isl_give isl_printer *isl_ast_op_type_print_macro(
6009 enum isl_ast_op_type type,
6010 __isl_take isl_printer *p);
6011 __isl_give isl_printer *isl_ast_node_print_macros(
6012 __isl_keep isl_ast_node *node,
6013 __isl_take isl_printer *p);
6014 __isl_give isl_printer *isl_ast_node_print(
6015 __isl_keep isl_ast_node *node,
6016 __isl_take isl_printer *p,
6017 __isl_take isl_ast_print_options *options);
6018 __isl_give isl_printer *isl_ast_node_for_print(
6019 __isl_keep isl_ast_node *node,
6020 __isl_take isl_printer *p,
6021 __isl_take isl_ast_print_options *options);
6022 __isl_give isl_printer *isl_ast_node_if_print(
6023 __isl_keep isl_ast_node *node,
6024 __isl_take isl_printer *p,
6025 __isl_take isl_ast_print_options *options);
6027 While printing an C<isl_ast_node> in C<ISL_FORMAT_C>,
6028 C<isl> may print out an AST that makes use of macros such
6029 as C<floord>, C<min> and C<max>.
6030 C<isl_ast_op_type_print_macro> prints out the macro
6031 corresponding to a specific C<isl_ast_op_type>.
6032 C<isl_ast_node_print_macros> scans the C<isl_ast_node>
6033 for expressions where these macros would be used and prints
6034 out the required macro definitions.
6035 Essentially, C<isl_ast_node_print_macros> calls
6036 C<isl_ast_node_foreach_ast_op_type> with C<isl_ast_op_type_print_macro>
6037 as function argument.
6038 C<isl_ast_node_print>, C<isl_ast_node_for_print> and
6039 C<isl_ast_node_if_print> print an C<isl_ast_node>
6040 in C<ISL_FORMAT_C>, but allow for some extra control
6041 through an C<isl_ast_print_options> object.
6042 This object can be created using the following functions.
6044 #include <isl/ast.h>
6045 __isl_give isl_ast_print_options *
6046 isl_ast_print_options_alloc(isl_ctx *ctx);
6047 __isl_give isl_ast_print_options *
6048 isl_ast_print_options_copy(
6049 __isl_keep isl_ast_print_options *options);
6050 void *isl_ast_print_options_free(
6051 __isl_take isl_ast_print_options *options);
6053 __isl_give isl_ast_print_options *
6054 isl_ast_print_options_set_print_user(
6055 __isl_take isl_ast_print_options *options,
6056 __isl_give isl_printer *(*print_user)(
6057 __isl_take isl_printer *p,
6058 __isl_take isl_ast_print_options *options,
6059 __isl_keep isl_ast_node *node, void *user),
6061 __isl_give isl_ast_print_options *
6062 isl_ast_print_options_set_print_for(
6063 __isl_take isl_ast_print_options *options,
6064 __isl_give isl_printer *(*print_for)(
6065 __isl_take isl_printer *p,
6066 __isl_take isl_ast_print_options *options,
6067 __isl_keep isl_ast_node *node, void *user),
6070 The callback set by C<isl_ast_print_options_set_print_user>
6071 is called whenever a node of type C<isl_ast_node_user> needs to
6073 The callback set by C<isl_ast_print_options_set_print_for>
6074 is called whenever a node of type C<isl_ast_node_for> needs to
6076 Note that C<isl_ast_node_for_print> will I<not> call the
6077 callback set by C<isl_ast_print_options_set_print_for> on the node
6078 on which C<isl_ast_node_for_print> is called, but only on nested
6079 nodes of type C<isl_ast_node_for>. It is therefore safe to
6080 call C<isl_ast_node_for_print> from within the callback set by
6081 C<isl_ast_print_options_set_print_for>.
6083 The following option determines the type to be used for iterators
6084 while printing the AST.
6086 int isl_options_set_ast_iterator_type(
6087 isl_ctx *ctx, const char *val);
6088 const char *isl_options_get_ast_iterator_type(
6093 #include <isl/ast_build.h>
6094 int isl_options_set_ast_build_atomic_upper_bound(
6095 isl_ctx *ctx, int val);
6096 int isl_options_get_ast_build_atomic_upper_bound(
6098 int isl_options_set_ast_build_prefer_pdiv(isl_ctx *ctx,
6100 int isl_options_get_ast_build_prefer_pdiv(isl_ctx *ctx);
6101 int isl_options_set_ast_build_exploit_nested_bounds(
6102 isl_ctx *ctx, int val);
6103 int isl_options_get_ast_build_exploit_nested_bounds(
6105 int isl_options_set_ast_build_group_coscheduled(
6106 isl_ctx *ctx, int val);
6107 int isl_options_get_ast_build_group_coscheduled(
6109 int isl_options_set_ast_build_scale_strides(
6110 isl_ctx *ctx, int val);
6111 int isl_options_get_ast_build_scale_strides(
6113 int isl_options_set_ast_build_allow_else(isl_ctx *ctx,
6115 int isl_options_get_ast_build_allow_else(isl_ctx *ctx);
6116 int isl_options_set_ast_build_allow_or(isl_ctx *ctx,
6118 int isl_options_get_ast_build_allow_or(isl_ctx *ctx);
6122 =item * ast_build_atomic_upper_bound
6124 Generate loop upper bounds that consist of the current loop iterator,
6125 an operator and an expression not involving the iterator.
6126 If this option is not set, then the current loop iterator may appear
6127 several times in the upper bound.
6128 For example, when this option is turned off, AST generation
6131 [n] -> { A[i] -> [i] : 0 <= i <= 100, n }
6135 for (int c0 = 0; c0 <= 100 && n >= c0; c0 += 1)
6138 When the option is turned on, the following AST is generated
6140 for (int c0 = 0; c0 <= min(100, n); c0 += 1)
6143 =item * ast_build_prefer_pdiv
6145 If this option is turned off, then the AST generation will
6146 produce ASTs that may only contain C<isl_ast_op_fdiv_q>
6147 operators, but no C<isl_ast_op_pdiv_q> or
6148 C<isl_ast_op_pdiv_r> operators.
6149 If this options is turned on, then C<isl> will try to convert
6150 some of the C<isl_ast_op_fdiv_q> operators to (expressions containing)
6151 C<isl_ast_op_pdiv_q> or C<isl_ast_op_pdiv_r> operators.
6153 =item * ast_build_exploit_nested_bounds
6155 Simplify conditions based on bounds of nested for loops.
6156 In particular, remove conditions that are implied by the fact
6157 that one or more nested loops have at least one iteration,
6158 meaning that the upper bound is at least as large as the lower bound.
6159 For example, when this option is turned off, AST generation
6162 [N,M] -> { A[i,j] -> [i,j] : 0 <= i <= N and
6168 for (int c0 = 0; c0 <= N; c0 += 1)
6169 for (int c1 = 0; c1 <= M; c1 += 1)
6172 When the option is turned on, the following AST is generated
6174 for (int c0 = 0; c0 <= N; c0 += 1)
6175 for (int c1 = 0; c1 <= M; c1 += 1)
6178 =item * ast_build_group_coscheduled
6180 If two domain elements are assigned the same schedule point, then
6181 they may be executed in any order and they may even appear in different
6182 loops. If this options is set, then the AST generator will make
6183 sure that coscheduled domain elements do not appear in separate parts
6184 of the AST. This is useful in case of nested AST generation
6185 if the outer AST generation is given only part of a schedule
6186 and the inner AST generation should handle the domains that are
6187 coscheduled by this initial part of the schedule together.
6188 For example if an AST is generated for a schedule
6190 { A[i] -> [0]; B[i] -> [0] }
6192 then the C<isl_ast_build_set_create_leaf> callback described
6193 below may get called twice, once for each domain.
6194 Setting this option ensures that the callback is only called once
6195 on both domains together.
6197 =item * ast_build_separation_bounds
6199 This option specifies which bounds to use during separation.
6200 If this option is set to C<ISL_AST_BUILD_SEPARATION_BOUNDS_IMPLICIT>
6201 then all (possibly implicit) bounds on the current dimension will
6202 be used during separation.
6203 If this option is set to C<ISL_AST_BUILD_SEPARATION_BOUNDS_EXPLICIT>
6204 then only those bounds that are explicitly available will
6205 be used during separation.
6207 =item * ast_build_scale_strides
6209 This option specifies whether the AST generator is allowed
6210 to scale down iterators of strided loops.
6212 =item * ast_build_allow_else
6214 This option specifies whether the AST generator is allowed
6215 to construct if statements with else branches.
6217 =item * ast_build_allow_or
6219 This option specifies whether the AST generator is allowed
6220 to construct if conditions with disjunctions.
6224 =head3 Fine-grained Control over AST Generation
6226 Besides specifying the constraints on the parameters,
6227 an C<isl_ast_build> object can be used to control
6228 various aspects of the AST generation process.
6229 The most prominent way of control is through ``options'',
6230 which can be set using the following function.
6232 #include <isl/ast_build.h>
6233 __isl_give isl_ast_build *
6234 isl_ast_build_set_options(
6235 __isl_take isl_ast_build *control,
6236 __isl_take isl_union_map *options);
6238 The options are encoded in an <isl_union_map>.
6239 The domain of this union relation refers to the schedule domain,
6240 i.e., the range of the schedule passed to C<isl_ast_build_ast_from_schedule>.
6241 In the case of nested AST generation (see L</"Nested AST Generation">),
6242 the domain of C<options> should refer to the extra piece of the schedule.
6243 That is, it should be equal to the range of the wrapped relation in the
6244 range of the schedule.
6245 The range of the options can consist of elements in one or more spaces,
6246 the names of which determine the effect of the option.
6247 The values of the range typically also refer to the schedule dimension
6248 to which the option applies. In case of nested AST generation
6249 (see L</"Nested AST Generation">), these values refer to the position
6250 of the schedule dimension within the innermost AST generation.
6251 The constraints on the domain elements of
6252 the option should only refer to this dimension and earlier dimensions.
6253 We consider the following spaces.
6257 =item C<separation_class>
6259 This space is a wrapped relation between two one dimensional spaces.
6260 The input space represents the schedule dimension to which the option
6261 applies and the output space represents the separation class.
6262 While constructing a loop corresponding to the specified schedule
6263 dimension(s), the AST generator will try to generate separate loops
6264 for domain elements that are assigned different classes.
6265 If only some of the elements are assigned a class, then those elements
6266 that are not assigned any class will be treated as belonging to a class
6267 that is separate from the explicitly assigned classes.
6268 The typical use case for this option is to separate full tiles from
6270 The other options, described below, are applied after the separation
6273 As an example, consider the separation into full and partial tiles
6274 of a tiling of a triangular domain.
6275 Take, for example, the domain
6277 { A[i,j] : 0 <= i,j and i + j <= 100 }
6279 and a tiling into tiles of 10 by 10. The input to the AST generator
6280 is then the schedule
6282 { A[i,j] -> [([i/10]),[j/10],i,j] : 0 <= i,j and
6285 Without any options, the following AST is generated
6287 for (int c0 = 0; c0 <= 10; c0 += 1)
6288 for (int c1 = 0; c1 <= -c0 + 10; c1 += 1)
6289 for (int c2 = 10 * c0;
6290 c2 <= min(-10 * c1 + 100, 10 * c0 + 9);
6292 for (int c3 = 10 * c1;
6293 c3 <= min(10 * c1 + 9, -c2 + 100);
6297 Separation into full and partial tiles can be obtained by assigning
6298 a class, say C<0>, to the full tiles. The full tiles are represented by those
6299 values of the first and second schedule dimensions for which there are
6300 values of the third and fourth dimensions to cover an entire tile.
6301 That is, we need to specify the following option
6303 { [a,b,c,d] -> separation_class[[0]->[0]] :
6304 exists b': 0 <= 10a,10b' and
6305 10a+9+10b'+9 <= 100;
6306 [a,b,c,d] -> separation_class[[1]->[0]] :
6307 0 <= 10a,10b and 10a+9+10b+9 <= 100 }
6311 { [a, b, c, d] -> separation_class[[1] -> [0]] :
6312 a >= 0 and b >= 0 and b <= 8 - a;
6313 [a, b, c, d] -> separation_class[[0] -> [0]] :
6316 With this option, the generated AST is as follows
6319 for (int c0 = 0; c0 <= 8; c0 += 1) {
6320 for (int c1 = 0; c1 <= -c0 + 8; c1 += 1)
6321 for (int c2 = 10 * c0;
6322 c2 <= 10 * c0 + 9; c2 += 1)
6323 for (int c3 = 10 * c1;
6324 c3 <= 10 * c1 + 9; c3 += 1)
6326 for (int c1 = -c0 + 9; c1 <= -c0 + 10; c1 += 1)
6327 for (int c2 = 10 * c0;
6328 c2 <= min(-10 * c1 + 100, 10 * c0 + 9);
6330 for (int c3 = 10 * c1;
6331 c3 <= min(-c2 + 100, 10 * c1 + 9);
6335 for (int c0 = 9; c0 <= 10; c0 += 1)
6336 for (int c1 = 0; c1 <= -c0 + 10; c1 += 1)
6337 for (int c2 = 10 * c0;
6338 c2 <= min(-10 * c1 + 100, 10 * c0 + 9);
6340 for (int c3 = 10 * c1;
6341 c3 <= min(10 * c1 + 9, -c2 + 100);
6348 This is a single-dimensional space representing the schedule dimension(s)
6349 to which ``separation'' should be applied. Separation tries to split
6350 a loop into several pieces if this can avoid the generation of guards
6352 See also the C<atomic> option.
6356 This is a single-dimensional space representing the schedule dimension(s)
6357 for which the domains should be considered ``atomic''. That is, the
6358 AST generator will make sure that any given domain space will only appear
6359 in a single loop at the specified level.
6361 Consider the following schedule
6363 { a[i] -> [i] : 0 <= i < 10;
6364 b[i] -> [i+1] : 0 <= i < 10 }
6366 If the following option is specified
6368 { [i] -> separate[x] }
6370 then the following AST will be generated
6374 for (int c0 = 1; c0 <= 9; c0 += 1) {
6381 If, on the other hand, the following option is specified
6383 { [i] -> atomic[x] }
6385 then the following AST will be generated
6387 for (int c0 = 0; c0 <= 10; c0 += 1) {
6394 If neither C<atomic> nor C<separate> is specified, then the AST generator
6395 may produce either of these two results or some intermediate form.
6399 This is a single-dimensional space representing the schedule dimension(s)
6400 that should be I<completely> unrolled.
6401 To obtain a partial unrolling, the user should apply an additional
6402 strip-mining to the schedule and fully unroll the inner loop.
6406 Additional control is available through the following functions.
6408 #include <isl/ast_build.h>
6409 __isl_give isl_ast_build *
6410 isl_ast_build_set_iterators(
6411 __isl_take isl_ast_build *control,
6412 __isl_take isl_id_list *iterators);
6414 The function C<isl_ast_build_set_iterators> allows the user to
6415 specify a list of iterator C<isl_id>s to be used as iterators.
6416 If the input schedule is injective, then
6417 the number of elements in this list should be as large as the dimension
6418 of the schedule space, but no direct correspondence should be assumed
6419 between dimensions and elements.
6420 If the input schedule is not injective, then an additional number
6421 of C<isl_id>s equal to the largest dimension of the input domains
6423 If the number of provided C<isl_id>s is insufficient, then additional
6424 names are automatically generated.
6426 #include <isl/ast_build.h>
6427 __isl_give isl_ast_build *
6428 isl_ast_build_set_create_leaf(
6429 __isl_take isl_ast_build *control,
6430 __isl_give isl_ast_node *(*fn)(
6431 __isl_take isl_ast_build *build,
6432 void *user), void *user);
6435 C<isl_ast_build_set_create_leaf> function allows for the
6436 specification of a callback that should be called whenever the AST
6437 generator arrives at an element of the schedule domain.
6438 The callback should return an AST node that should be inserted
6439 at the corresponding position of the AST. The default action (when
6440 the callback is not set) is to continue generating parts of the AST to scan
6441 all the domain elements associated to the schedule domain element
6442 and to insert user nodes, ``calling'' the domain element, for each of them.
6443 The C<build> argument contains the current state of the C<isl_ast_build>.
6444 To ease nested AST generation (see L</"Nested AST Generation">),
6445 all control information that is
6446 specific to the current AST generation such as the options and
6447 the callbacks has been removed from this C<isl_ast_build>.
6448 The callback would typically return the result of a nested
6450 user defined node created using the following function.
6452 #include <isl/ast.h>
6453 __isl_give isl_ast_node *isl_ast_node_alloc_user(
6454 __isl_take isl_ast_expr *expr);
6456 #include <isl/ast_build.h>
6457 __isl_give isl_ast_build *
6458 isl_ast_build_set_at_each_domain(
6459 __isl_take isl_ast_build *build,
6460 __isl_give isl_ast_node *(*fn)(
6461 __isl_take isl_ast_node *node,
6462 __isl_keep isl_ast_build *build,
6463 void *user), void *user);
6464 __isl_give isl_ast_build *
6465 isl_ast_build_set_before_each_for(
6466 __isl_take isl_ast_build *build,
6467 __isl_give isl_id *(*fn)(
6468 __isl_keep isl_ast_build *build,
6469 void *user), void *user);
6470 __isl_give isl_ast_build *
6471 isl_ast_build_set_after_each_for(
6472 __isl_take isl_ast_build *build,
6473 __isl_give isl_ast_node *(*fn)(
6474 __isl_take isl_ast_node *node,
6475 __isl_keep isl_ast_build *build,
6476 void *user), void *user);
6478 The callback set by C<isl_ast_build_set_at_each_domain> will
6479 be called for each domain AST node.
6480 The callbacks set by C<isl_ast_build_set_before_each_for>
6481 and C<isl_ast_build_set_after_each_for> will be called
6482 for each for AST node. The first will be called in depth-first
6483 pre-order, while the second will be called in depth-first post-order.
6484 Since C<isl_ast_build_set_before_each_for> is called before the for
6485 node is actually constructed, it is only passed an C<isl_ast_build>.
6486 The returned C<isl_id> will be added as an annotation (using
6487 C<isl_ast_node_set_annotation>) to the constructed for node.
6488 In particular, if the user has also specified an C<after_each_for>
6489 callback, then the annotation can be retrieved from the node passed to
6490 that callback using C<isl_ast_node_get_annotation>.
6491 All callbacks should C<NULL> on failure.
6492 The given C<isl_ast_build> can be used to create new
6493 C<isl_ast_expr> objects using C<isl_ast_build_expr_from_pw_aff>
6494 or C<isl_ast_build_call_from_pw_multi_aff>.
6496 =head3 Nested AST Generation
6498 C<isl> allows the user to create an AST within the context
6499 of another AST. These nested ASTs are created using the
6500 same C<isl_ast_build_ast_from_schedule> function that is used to create the
6501 outer AST. The C<build> argument should be an C<isl_ast_build>
6502 passed to a callback set by
6503 C<isl_ast_build_set_create_leaf>.
6504 The space of the range of the C<schedule> argument should refer
6505 to this build. In particular, the space should be a wrapped
6506 relation and the domain of this wrapped relation should be the
6507 same as that of the range of the schedule returned by
6508 C<isl_ast_build_get_schedule> below.
6509 In practice, the new schedule is typically
6510 created by calling C<isl_union_map_range_product> on the old schedule
6511 and some extra piece of the schedule.
6512 The space of the schedule domain is also available from
6513 the C<isl_ast_build>.
6515 #include <isl/ast_build.h>
6516 __isl_give isl_union_map *isl_ast_build_get_schedule(
6517 __isl_keep isl_ast_build *build);
6518 __isl_give isl_space *isl_ast_build_get_schedule_space(
6519 __isl_keep isl_ast_build *build);
6520 __isl_give isl_ast_build *isl_ast_build_restrict(
6521 __isl_take isl_ast_build *build,
6522 __isl_take isl_set *set);
6524 The C<isl_ast_build_get_schedule> function returns a (partial)
6525 schedule for the domains elements for which part of the AST still needs to
6526 be generated in the current build.
6527 In particular, the domain elements are mapped to those iterations of the loops
6528 enclosing the current point of the AST generation inside which
6529 the domain elements are executed.
6530 No direct correspondence between
6531 the input schedule and this schedule should be assumed.
6532 The space obtained from C<isl_ast_build_get_schedule_space> can be used
6533 to create a set for C<isl_ast_build_restrict> to intersect
6534 with the current build. In particular, the set passed to
6535 C<isl_ast_build_restrict> can have additional parameters.
6536 The ids of the set dimensions in the space returned by
6537 C<isl_ast_build_get_schedule_space> correspond to the
6538 iterators of the already generated loops.
6539 The user should not rely on the ids of the output dimensions
6540 of the relations in the union relation returned by
6541 C<isl_ast_build_get_schedule> having any particular value.
6545 Although C<isl> is mainly meant to be used as a library,
6546 it also contains some basic applications that use some
6547 of the functionality of C<isl>.
6548 The input may be specified in either the L<isl format>
6549 or the L<PolyLib format>.
6551 =head2 C<isl_polyhedron_sample>
6553 C<isl_polyhedron_sample> takes a polyhedron as input and prints
6554 an integer element of the polyhedron, if there is any.
6555 The first column in the output is the denominator and is always
6556 equal to 1. If the polyhedron contains no integer points,
6557 then a vector of length zero is printed.
6561 C<isl_pip> takes the same input as the C<example> program
6562 from the C<piplib> distribution, i.e., a set of constraints
6563 on the parameters, a line containing only -1 and finally a set
6564 of constraints on a parametric polyhedron.
6565 The coefficients of the parameters appear in the last columns
6566 (but before the final constant column).
6567 The output is the lexicographic minimum of the parametric polyhedron.
6568 As C<isl> currently does not have its own output format, the output
6569 is just a dump of the internal state.
6571 =head2 C<isl_polyhedron_minimize>
6573 C<isl_polyhedron_minimize> computes the minimum of some linear
6574 or affine objective function over the integer points in a polyhedron.
6575 If an affine objective function
6576 is given, then the constant should appear in the last column.
6578 =head2 C<isl_polytope_scan>
6580 Given a polytope, C<isl_polytope_scan> prints
6581 all integer points in the polytope.
6583 =head2 C<isl_codegen>
6585 Given a schedule, a context set and an options relation,
6586 C<isl_codegen> prints out an AST that scans the domain elements
6587 of the schedule in the order of their image(s) taking into account
6588 the constraints in the context set.