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>.
51 The source of C<isl> can be obtained either as a tarball
52 or from the git repository. Both are available from
53 L<http://freshmeat.net/projects/isl/>.
54 The installation process depends on how you obtained
57 =head2 Installation from the git repository
61 =item 1 Clone or update the repository
63 The first time the source is obtained, you need to clone
66 git clone git://repo.or.cz/isl.git
68 To obtain updates, you need to pull in the latest changes
72 =item 2 Generate C<configure>
78 After performing the above steps, continue
79 with the L<Common installation instructions>.
81 =head2 Common installation instructions
87 Building C<isl> requires C<GMP>, including its headers files.
88 Your distribution may not provide these header files by default
89 and you may need to install a package called C<gmp-devel> or something
90 similar. Alternatively, C<GMP> can be built from
91 source, available from L<http://gmplib.org/>.
95 C<isl> uses the standard C<autoconf> C<configure> script.
100 optionally followed by some configure options.
101 A complete list of options can be obtained by running
105 Below we discuss some of the more common options.
107 C<isl> can optionally use C<piplib>, but no
108 C<piplib> functionality is currently used by default.
109 The C<--with-piplib> option can
110 be used to specify which C<piplib>
111 library to use, either an installed version (C<system>),
112 an externally built version (C<build>)
113 or no version (C<no>). The option C<build> is mostly useful
114 in C<configure> scripts of larger projects that bundle both C<isl>
121 Installation prefix for C<isl>
123 =item C<--with-gmp-prefix>
125 Installation prefix for C<GMP> (architecture-independent files).
127 =item C<--with-gmp-exec-prefix>
129 Installation prefix for C<GMP> (architecture-dependent files).
131 =item C<--with-piplib>
133 Which copy of C<piplib> to use, either C<no> (default), C<system> or C<build>.
135 =item C<--with-piplib-prefix>
137 Installation prefix for C<system> C<piplib> (architecture-independent files).
139 =item C<--with-piplib-exec-prefix>
141 Installation prefix for C<system> C<piplib> (architecture-dependent files).
143 =item C<--with-piplib-builddir>
145 Location where C<build> C<piplib> was built.
153 =item 4 Install (optional)
161 =head2 Initialization
163 All manipulations of integer sets and relations occur within
164 the context of an C<isl_ctx>.
165 A given C<isl_ctx> can only be used within a single thread.
166 All arguments of a function are required to have been allocated
167 within the same context.
168 There are currently no functions available for moving an object
169 from one C<isl_ctx> to another C<isl_ctx>. This means that
170 there is currently no way of safely moving an object from one
171 thread to another, unless the whole C<isl_ctx> is moved.
173 An C<isl_ctx> can be allocated using C<isl_ctx_alloc> and
174 freed using C<isl_ctx_free>.
175 All objects allocated within an C<isl_ctx> should be freed
176 before the C<isl_ctx> itself is freed.
178 isl_ctx *isl_ctx_alloc();
179 void isl_ctx_free(isl_ctx *ctx);
183 All operations on integers, mainly the coefficients
184 of the constraints describing the sets and relations,
185 are performed in exact integer arithmetic using C<GMP>.
186 However, to allow future versions of C<isl> to optionally
187 support fixed integer arithmetic, all calls to C<GMP>
188 are wrapped inside C<isl> specific macros.
189 The basic type is C<isl_int> and the following operations
190 are available on this type.
191 The meanings of these operations are essentially the same
192 as their C<GMP> C<mpz_> counterparts.
193 As always with C<GMP> types, C<isl_int>s need to be
194 initialized with C<isl_int_init> before they can be used
195 and they need to be released with C<isl_int_clear>
200 =item isl_int_init(i)
202 =item isl_int_clear(i)
204 =item isl_int_set(r,i)
206 =item isl_int_set_si(r,i)
208 =item isl_int_abs(r,i)
210 =item isl_int_neg(r,i)
212 =item isl_int_swap(i,j)
214 =item isl_int_swap_or_set(i,j)
216 =item isl_int_add_ui(r,i,j)
218 =item isl_int_sub_ui(r,i,j)
220 =item isl_int_add(r,i,j)
222 =item isl_int_sub(r,i,j)
224 =item isl_int_mul(r,i,j)
226 =item isl_int_mul_ui(r,i,j)
228 =item isl_int_addmul(r,i,j)
230 =item isl_int_submul(r,i,j)
232 =item isl_int_gcd(r,i,j)
234 =item isl_int_lcm(r,i,j)
236 =item isl_int_divexact(r,i,j)
238 =item isl_int_cdiv_q(r,i,j)
240 =item isl_int_fdiv_q(r,i,j)
242 =item isl_int_fdiv_r(r,i,j)
244 =item isl_int_fdiv_q_ui(r,i,j)
246 =item isl_int_read(r,s)
248 =item isl_int_print(out,i,width)
252 =item isl_int_cmp(i,j)
254 =item isl_int_cmp_si(i,si)
256 =item isl_int_eq(i,j)
258 =item isl_int_ne(i,j)
260 =item isl_int_lt(i,j)
262 =item isl_int_le(i,j)
264 =item isl_int_gt(i,j)
266 =item isl_int_ge(i,j)
268 =item isl_int_abs_eq(i,j)
270 =item isl_int_abs_ne(i,j)
272 =item isl_int_abs_lt(i,j)
274 =item isl_int_abs_gt(i,j)
276 =item isl_int_abs_ge(i,j)
278 =item isl_int_is_zero(i)
280 =item isl_int_is_one(i)
282 =item isl_int_is_negone(i)
284 =item isl_int_is_pos(i)
286 =item isl_int_is_neg(i)
288 =item isl_int_is_nonpos(i)
290 =item isl_int_is_nonneg(i)
292 =item isl_int_is_divisible_by(i,j)
296 =head2 Sets and Relations
298 C<isl> uses six types of objects for representing sets and relations,
299 C<isl_basic_set>, C<isl_basic_map>, C<isl_set>, C<isl_map>,
300 C<isl_union_set> and C<isl_union_map>.
301 C<isl_basic_set> and C<isl_basic_map> represent sets and relations that
302 can be described as a conjunction of affine constraints, while
303 C<isl_set> and C<isl_map> represent unions of
304 C<isl_basic_set>s and C<isl_basic_map>s, respectively.
305 However, all C<isl_basic_set>s or C<isl_basic_map>s in the union need
306 to have the same dimension. C<isl_union_set>s and C<isl_union_map>s
307 represent unions of C<isl_set>s or C<isl_map>s of I<different> dimensions,
308 where dimensions with different space names
309 (see L<Dimension Specifications>) are considered different as well.
310 The difference between sets and relations (maps) is that sets have
311 one set of variables, while relations have two sets of variables,
312 input variables and output variables.
314 =head2 Memory Management
316 Since a high-level operation on sets and/or relations usually involves
317 several substeps and since the user is usually not interested in
318 the intermediate results, most functions that return a new object
319 will also release all the objects passed as arguments.
320 If the user still wants to use one or more of these arguments
321 after the function call, she should pass along a copy of the
322 object rather than the object itself.
323 The user is then responsible for make sure that the original
324 object gets used somewhere else or is explicitly freed.
326 The arguments and return values of all documents functions are
327 annotated to make clear which arguments are released and which
328 arguments are preserved. In particular, the following annotations
335 C<__isl_give> means that a new object is returned.
336 The user should make sure that the returned pointer is
337 used exactly once as a value for an C<__isl_take> argument.
338 In between, it can be used as a value for as many
339 C<__isl_keep> arguments as the user likes.
340 There is one exception, and that is the case where the
341 pointer returned is C<NULL>. Is this case, the user
342 is free to use it as an C<__isl_take> argument or not.
346 C<__isl_take> means that the object the argument points to
347 is taken over by the function and may no longer be used
348 by the user as an argument to any other function.
349 The pointer value must be one returned by a function
350 returning an C<__isl_give> pointer.
351 If the user passes in a C<NULL> value, then this will
352 be treated as an error in the sense that the function will
353 not perform its usual operation. However, it will still
354 make sure that all the the other C<__isl_take> arguments
359 C<__isl_keep> means that the function will only use the object
360 temporarily. After the function has finished, the user
361 can still use it as an argument to other functions.
362 A C<NULL> value will be treated in the same way as
363 a C<NULL> value for an C<__isl_take> argument.
367 =head2 Dimension Specifications
369 Whenever a new set or relation is created from scratch,
370 its dimension needs to be specified using an C<isl_dim>.
373 __isl_give isl_dim *isl_dim_alloc(isl_ctx *ctx,
374 unsigned nparam, unsigned n_in, unsigned n_out);
375 __isl_give isl_dim *isl_dim_set_alloc(isl_ctx *ctx,
376 unsigned nparam, unsigned dim);
377 __isl_give isl_dim *isl_dim_copy(__isl_keep isl_dim *dim);
378 void isl_dim_free(__isl_take isl_dim *dim);
379 unsigned isl_dim_size(__isl_keep isl_dim *dim,
380 enum isl_dim_type type);
382 The dimension specification used for creating a set
383 needs to be created using C<isl_dim_set_alloc>, while
384 that for creating a relation
385 needs to be created using C<isl_dim_alloc>.
386 C<isl_dim_size> can be used
387 to find out the number of dimensions of each type in
388 a dimension specification, where type may be
389 C<isl_dim_param>, C<isl_dim_in> (only for relations),
390 C<isl_dim_out> (only for relations), C<isl_dim_set>
391 (only for sets) or C<isl_dim_all>.
393 It is often useful to create objects that live in the
394 same space as some other object. This can be accomplished
395 by creating the new objects
396 (see L<Creating New Sets and Relations> or
397 L<Creating New (Piecewise) Quasipolynomials>) based on the dimension
398 specification of the original object.
401 __isl_give isl_dim *isl_basic_set_get_dim(
402 __isl_keep isl_basic_set *bset);
403 __isl_give isl_dim *isl_set_get_dim(__isl_keep isl_set *set);
405 #include <isl_union_set.h>
406 __isl_give isl_dim *isl_union_set_get_dim(
407 __isl_keep isl_union_set *uset);
410 __isl_give isl_dim *isl_basic_map_get_dim(
411 __isl_keep isl_basic_map *bmap);
412 __isl_give isl_dim *isl_map_get_dim(__isl_keep isl_map *map);
414 #include <isl_union_map.h>
415 __isl_give isl_dim *isl_union_map_get_dim(
416 __isl_keep isl_union_map *umap);
418 #include <isl_polynomial.h>
419 __isl_give isl_dim *isl_qpolynomial_get_dim(
420 __isl_keep isl_qpolynomial *qp);
421 __isl_give isl_dim *isl_pw_qpolynomial_get_dim(
422 __isl_keep isl_pw_qpolynomial *pwqp);
423 __isl_give isl_dim *isl_union_pw_qpolynomial_get_dim(
424 __isl_keep isl_union_pw_qpolynomial *upwqp);
425 __isl_give isl_dim *isl_union_pw_qpolynomial_fold_get_dim(
426 __isl_keep isl_union_pw_qpolynomial_fold *upwf);
428 The names of the individual dimensions may be set or read off
429 using the following functions.
432 __isl_give isl_dim *isl_dim_set_name(__isl_take isl_dim *dim,
433 enum isl_dim_type type, unsigned pos,
434 __isl_keep const char *name);
435 __isl_keep const char *isl_dim_get_name(__isl_keep isl_dim *dim,
436 enum isl_dim_type type, unsigned pos);
438 Note that C<isl_dim_get_name> returns a pointer to some internal
439 data structure, so the result can only be used while the
440 corresponding C<isl_dim> is alive.
441 Also note that every function that operates on two sets or relations
442 requires that both arguments have the same parameters. This also
443 means that if one of the arguments has named parameters, then the
444 other needs to have named parameters too and the names need to match.
446 The names of entire spaces may be set or read off
447 using the following functions.
450 __isl_give isl_dim *isl_dim_set_tuple_name(
451 __isl_take isl_dim *dim,
452 enum isl_dim_type type, const char *s);
453 const char *isl_dim_get_tuple_name(__isl_keep isl_dim *dim,
454 enum isl_dim_type type);
456 The C<dim> argument needs to be one of C<isl_dim_in>, C<isl_dim_out>
457 or C<isl_dim_set>. As with C<isl_dim_get_name>,
458 the C<isl_dim_get_tuple_name> function returns a pointer to some internal
460 Binary operations require the corresponding spaces of their arguments
461 to have the same name.
463 Spaces can be nested. In particular, the domain of a set or
464 the domain or range of a relation can be a nested relation.
465 The following functions can be used to construct and deconstruct
466 such nested dimension specifications.
469 int isl_dim_is_wrapping(__isl_keep isl_dim *dim);
470 __isl_give isl_dim *isl_dim_wrap(__isl_take isl_dim *dim);
471 __isl_give isl_dim *isl_dim_unwrap(__isl_take isl_dim *dim);
473 The input to C<isl_dim_is_wrapping> and C<isl_dim_unwrap> should
474 be the dimension specification of a set, while that of
475 C<isl_dim_wrap> should be the dimension specification of a relation.
476 Conversely, the output of C<isl_dim_unwrap> is the dimension specification
477 of a relation, while that of C<isl_dim_wrap> is the dimension specification
480 =head2 Input and Output
482 C<isl> supports its own input/output format, which is similar
483 to the C<Omega> format, but also supports the C<PolyLib> format
488 The C<isl> format is similar to that of C<Omega>, but has a different
489 syntax for describing the parameters and allows for the definition
490 of an existentially quantified variable as the integer division
491 of an affine expression.
492 For example, the set of integers C<i> between C<0> and C<n>
493 such that C<i % 10 <= 6> can be described as
495 [n] -> { [i] : exists (a = [i/10] : 0 <= i and i <= n and
498 A set or relation can have several disjuncts, separated
499 by the keyword C<or>. Each disjunct is either a conjunction
500 of constraints or a projection (C<exists>) of a conjunction
501 of constraints. The constraints are separated by the keyword
504 =head3 C<PolyLib> format
506 If the represented set is a union, then the first line
507 contains a single number representing the number of disjuncts.
508 Otherwise, a line containing the number C<1> is optional.
510 Each disjunct is represented by a matrix of constraints.
511 The first line contains two numbers representing
512 the number of rows and columns,
513 where the number of rows is equal to the number of constraints
514 and the number of columns is equal to two plus the number of variables.
515 The following lines contain the actual rows of the constraint matrix.
516 In each row, the first column indicates whether the constraint
517 is an equality (C<0>) or inequality (C<1>). The final column
518 corresponds to the constant term.
520 If the set is parametric, then the coefficients of the parameters
521 appear in the last columns before the constant column.
522 The coefficients of any existentially quantified variables appear
523 between those of the set variables and those of the parameters.
528 __isl_give isl_basic_set *isl_basic_set_read_from_file(
529 isl_ctx *ctx, FILE *input, int nparam);
530 __isl_give isl_basic_set *isl_basic_set_read_from_str(
531 isl_ctx *ctx, const char *str, int nparam);
532 __isl_give isl_set *isl_set_read_from_file(isl_ctx *ctx,
533 FILE *input, int nparam);
534 __isl_give isl_set *isl_set_read_from_str(isl_ctx *ctx,
535 const char *str, int nparam);
538 __isl_give isl_basic_map *isl_basic_map_read_from_file(
539 isl_ctx *ctx, FILE *input, int nparam);
540 __isl_give isl_basic_map *isl_basic_map_read_from_str(
541 isl_ctx *ctx, const char *str, int nparam);
542 __isl_give isl_map *isl_map_read_from_file(
543 struct isl_ctx *ctx, FILE *input, int nparam);
544 __isl_give isl_map *isl_map_read_from_str(isl_ctx *ctx,
545 const char *str, int nparam);
547 The input format is autodetected and may be either the C<PolyLib> format
548 or the C<isl> format.
549 C<nparam> specifies how many of the final columns in
550 the C<PolyLib> format correspond to parameters.
551 If input is given in the C<isl> format, then the number
552 of parameters needs to be equal to C<nparam>.
553 If C<nparam> is negative, then any number of parameters
554 is accepted in the C<isl> format and zero parameters
555 are assumed in the C<PolyLib> format.
559 Before anything can be printed, an C<isl_printer> needs to
562 __isl_give isl_printer *isl_printer_to_file(isl_ctx *ctx,
564 __isl_give isl_printer *isl_printer_to_str(isl_ctx *ctx);
565 void isl_printer_free(__isl_take isl_printer *printer);
566 __isl_give char *isl_printer_get_str(
567 __isl_keep isl_printer *printer);
569 The behavior of the printer can be modified in various ways
571 __isl_give isl_printer *isl_printer_set_output_format(
572 __isl_take isl_printer *p, int output_format);
573 __isl_give isl_printer *isl_printer_set_indent(
574 __isl_take isl_printer *p, int indent);
575 __isl_give isl_printer *isl_printer_set_prefix(
576 __isl_take isl_printer *p, const char *prefix);
577 __isl_give isl_printer *isl_printer_set_suffix(
578 __isl_take isl_printer *p, const char *suffix);
580 The C<output_format> may be either C<ISL_FORMAT_ISL>, C<ISL_FORMAT_OMEGA>
581 or C<ISL_FORMAT_POLYLIB> and defaults to C<ISL_FORMAT_ISL>.
582 Each line in the output is indented by C<indent> spaces
583 (default: 0), prefixed by C<prefix> and suffixed by C<suffix>.
584 In the C<PolyLib> format output,
585 the coefficients of the existentially quantified variables
586 appear between those of the set variables and those
589 To actually print something, use
592 __isl_give isl_printer *isl_printer_print_basic_set(
593 __isl_take isl_printer *printer,
594 __isl_keep isl_basic_set *bset);
595 __isl_give isl_printer *isl_printer_print_set(
596 __isl_take isl_printer *printer,
597 __isl_keep isl_set *set);
600 __isl_give isl_printer *isl_printer_print_basic_map(
601 __isl_take isl_printer *printer,
602 __isl_keep isl_basic_map *bmap);
603 __isl_give isl_printer *isl_printer_print_map(
604 __isl_take isl_printer *printer,
605 __isl_keep isl_map *map);
607 #include <isl_union_set.h>
608 __isl_give isl_printer *isl_printer_print_union_set(
609 __isl_take isl_printer *p,
610 __isl_keep isl_union_set *uset);
612 #include <isl_union_map.h>
613 __isl_give isl_printer *isl_printer_print_union_map(
614 __isl_take isl_printer *p,
615 __isl_keep isl_union_map *umap);
617 When called on a file printer, the following function flushes
618 the file. When called on a string printer, the buffer is cleared.
620 __isl_give isl_printer *isl_printer_flush(
621 __isl_take isl_printer *p);
623 =head2 Creating New Sets and Relations
625 C<isl> has functions for creating some standard sets and relations.
629 =item * Empty sets and relations
631 __isl_give isl_basic_set *isl_basic_set_empty(
632 __isl_take isl_dim *dim);
633 __isl_give isl_basic_map *isl_basic_map_empty(
634 __isl_take isl_dim *dim);
635 __isl_give isl_set *isl_set_empty(
636 __isl_take isl_dim *dim);
637 __isl_give isl_map *isl_map_empty(
638 __isl_take isl_dim *dim);
639 __isl_give isl_union_set *isl_union_set_empty(
640 __isl_take isl_dim *dim);
641 __isl_give isl_union_map *isl_union_map_empty(
642 __isl_take isl_dim *dim);
644 For C<isl_union_set>s and C<isl_union_map>s, the dimensions specification
645 is only used to specify the parameters.
647 =item * Universe sets and relations
649 __isl_give isl_basic_set *isl_basic_set_universe(
650 __isl_take isl_dim *dim);
651 __isl_give isl_basic_map *isl_basic_map_universe(
652 __isl_take isl_dim *dim);
653 __isl_give isl_set *isl_set_universe(
654 __isl_take isl_dim *dim);
655 __isl_give isl_map *isl_map_universe(
656 __isl_take isl_dim *dim);
658 =item * Identity relations
660 __isl_give isl_basic_map *isl_basic_map_identity(
661 __isl_take isl_dim *set_dim);
662 __isl_give isl_map *isl_map_identity(
663 __isl_take isl_dim *set_dim);
665 These functions take a dimension specification for a B<set>
666 and return an identity relation between two such sets.
668 =item * Lexicographic order
670 __isl_give isl_map *isl_map_lex_lt(
671 __isl_take isl_dim *set_dim);
672 __isl_give isl_map *isl_map_lex_le(
673 __isl_take isl_dim *set_dim);
674 __isl_give isl_map *isl_map_lex_gt(
675 __isl_take isl_dim *set_dim);
676 __isl_give isl_map *isl_map_lex_ge(
677 __isl_take isl_dim *set_dim);
678 __isl_give isl_map *isl_map_lex_lt_first(
679 __isl_take isl_dim *dim, unsigned n);
680 __isl_give isl_map *isl_map_lex_le_first(
681 __isl_take isl_dim *dim, unsigned n);
682 __isl_give isl_map *isl_map_lex_gt_first(
683 __isl_take isl_dim *dim, unsigned n);
684 __isl_give isl_map *isl_map_lex_ge_first(
685 __isl_take isl_dim *dim, unsigned n);
687 The first four functions take a dimension specification for a B<set>
688 and return relations that express that the elements in the domain
689 are lexicographically less
690 (C<isl_map_lex_lt>), less or equal (C<isl_map_lex_le>),
691 greater (C<isl_map_lex_gt>) or greater or equal (C<isl_map_lex_ge>)
692 than the elements in the range.
693 The last four functions take a dimension specification for a map
694 and return relations that express that the first C<n> dimensions
695 in the domain are lexicographically less
696 (C<isl_map_lex_lt_first>), less or equal (C<isl_map_lex_le_first>),
697 greater (C<isl_map_lex_gt_first>) or greater or equal (C<isl_map_lex_ge_first>)
698 than the first C<n> dimensions in the range.
702 A basic set or relation can be converted to a set or relation
703 using the following functions.
705 __isl_give isl_set *isl_set_from_basic_set(
706 __isl_take isl_basic_set *bset);
707 __isl_give isl_map *isl_map_from_basic_map(
708 __isl_take isl_basic_map *bmap);
710 Sets and relations can be converted to union sets and relations
711 using the following functions.
713 __isl_give isl_union_map *isl_union_map_from_map(
714 __isl_take isl_map *map);
715 __isl_give isl_union_set *isl_union_set_from_set(
716 __isl_take isl_set *set);
718 Sets and relations can be copied and freed again using the following
721 __isl_give isl_basic_set *isl_basic_set_copy(
722 __isl_keep isl_basic_set *bset);
723 __isl_give isl_set *isl_set_copy(__isl_keep isl_set *set);
724 __isl_give isl_union_set *isl_union_set_copy(
725 __isl_keep isl_union_set *uset);
726 __isl_give isl_basic_map *isl_basic_map_copy(
727 __isl_keep isl_basic_map *bmap);
728 __isl_give isl_map *isl_map_copy(__isl_keep isl_map *map);
729 __isl_give isl_union_map *isl_union_map_copy(
730 __isl_keep isl_union_map *umap);
731 void isl_basic_set_free(__isl_take isl_basic_set *bset);
732 void isl_set_free(__isl_take isl_set *set);
733 void isl_union_set_free(__isl_take isl_union_set *uset);
734 void isl_basic_map_free(__isl_take isl_basic_map *bmap);
735 void isl_map_free(__isl_take isl_map *map);
736 void isl_union_map_free(__isl_take isl_union_map *umap);
738 Other sets and relations can be constructed by starting
739 from a universe set or relation, adding equality and/or
740 inequality constraints and then projecting out the
741 existentially quantified variables, if any.
742 Constraints can be constructed, manipulated and
743 added to basic sets and relations using the following functions.
745 #include <isl_constraint.h>
746 __isl_give isl_constraint *isl_equality_alloc(
747 __isl_take isl_dim *dim);
748 __isl_give isl_constraint *isl_inequality_alloc(
749 __isl_take isl_dim *dim);
750 void isl_constraint_set_constant(
751 __isl_keep isl_constraint *constraint, isl_int v);
752 void isl_constraint_set_coefficient(
753 __isl_keep isl_constraint *constraint,
754 enum isl_dim_type type, int pos, isl_int v);
755 __isl_give isl_basic_map *isl_basic_map_add_constraint(
756 __isl_take isl_basic_map *bmap,
757 __isl_take isl_constraint *constraint);
758 __isl_give isl_basic_set *isl_basic_set_add_constraint(
759 __isl_take isl_basic_set *bset,
760 __isl_take isl_constraint *constraint);
762 For example, to create a set containing the even integers
763 between 10 and 42, you would use the following code.
767 struct isl_constraint *c;
768 struct isl_basic_set *bset;
771 dim = isl_dim_set_alloc(ctx, 0, 2);
772 bset = isl_basic_set_universe(isl_dim_copy(dim));
774 c = isl_equality_alloc(isl_dim_copy(dim));
775 isl_int_set_si(v, -1);
776 isl_constraint_set_coefficient(c, isl_dim_set, 0, v);
777 isl_int_set_si(v, 2);
778 isl_constraint_set_coefficient(c, isl_dim_set, 1, v);
779 bset = isl_basic_set_add_constraint(bset, c);
781 c = isl_inequality_alloc(isl_dim_copy(dim));
782 isl_int_set_si(v, -10);
783 isl_constraint_set_constant(c, v);
784 isl_int_set_si(v, 1);
785 isl_constraint_set_coefficient(c, isl_dim_set, 0, v);
786 bset = isl_basic_set_add_constraint(bset, c);
788 c = isl_inequality_alloc(dim);
789 isl_int_set_si(v, 42);
790 isl_constraint_set_constant(c, v);
791 isl_int_set_si(v, -1);
792 isl_constraint_set_coefficient(c, isl_dim_set, 0, v);
793 bset = isl_basic_set_add_constraint(bset, c);
795 bset = isl_basic_set_project_out(bset, isl_dim_set, 1, 1);
801 struct isl_basic_set *bset;
802 bset = isl_basic_set_read_from_str(ctx,
803 "{[i] : exists (a : i = 2a and i >= 10 and i <= 42)}", -1);
805 =head2 Inspecting Sets and Relations
807 Usually, the user should not have to care about the actual constraints
808 of the sets and maps, but should instead apply the abstract operations
809 explained in the following sections.
810 Occasionally, however, it may be required to inspect the individual
811 coefficients of the constraints. This section explains how to do so.
812 In these cases, it may also be useful to have C<isl> compute
813 an explicit representation of the existentially quantified variables.
815 __isl_give isl_set *isl_set_compute_divs(
816 __isl_take isl_set *set);
817 __isl_give isl_map *isl_map_compute_divs(
818 __isl_take isl_map *map);
819 __isl_give isl_union_set *isl_union_set_compute_divs(
820 __isl_take isl_union_set *uset);
821 __isl_give isl_union_map *isl_union_map_compute_divs(
822 __isl_take isl_union_map *umap);
824 This explicit representation defines the existentially quantified
825 variables as integer divisions of the other variables, possibly
826 including earlier existentially quantified variables.
827 An explicitly represented existentially quantified variable therefore
828 has a unique value when the values of the other variables are known.
829 If, furthermore, the same existentials, i.e., existentials
830 with the same explicit representations, should appear in the
831 same order in each of the disjuncts of a set or map, then the user should call
832 either of the following functions.
834 __isl_give isl_set *isl_set_align_divs(
835 __isl_take isl_set *set);
836 __isl_give isl_map *isl_map_align_divs(
837 __isl_take isl_map *map);
839 To iterate over all the sets or maps in a union set or map, use
841 int isl_union_set_foreach_set(__isl_keep isl_union_set *uset,
842 int (*fn)(__isl_take isl_set *set, void *user),
844 int isl_union_map_foreach_map(__isl_keep isl_union_map *umap,
845 int (*fn)(__isl_take isl_map *map, void *user),
848 To iterate over all the basic sets or maps in a set or map, use
850 int isl_set_foreach_basic_set(__isl_keep isl_set *set,
851 int (*fn)(__isl_take isl_basic_set *bset, void *user),
853 int isl_map_foreach_basic_map(__isl_keep isl_map *map,
854 int (*fn)(__isl_take isl_basic_map *bmap, void *user),
857 The callback function C<fn> should return 0 if successful and
858 -1 if an error occurs. In the latter case, or if any other error
859 occurs, the above functions will return -1.
861 It should be noted that C<isl> does not guarantee that
862 the basic sets or maps passed to C<fn> are disjoint.
863 If this is required, then the user should call one of
864 the following functions first.
866 __isl_give isl_set *isl_set_make_disjoint(
867 __isl_take isl_set *set);
868 __isl_give isl_map *isl_map_make_disjoint(
869 __isl_take isl_map *map);
871 To iterate over the constraints of a basic set or map, use
873 #include <isl_constraint.h>
875 int isl_basic_map_foreach_constraint(
876 __isl_keep isl_basic_map *bmap,
877 int (*fn)(__isl_take isl_constraint *c, void *user),
879 void isl_constraint_free(struct isl_constraint *c);
881 Again, the callback function C<fn> should return 0 if successful and
882 -1 if an error occurs. In the latter case, or if any other error
883 occurs, the above functions will return -1.
884 The constraint C<c> represents either an equality or an inequality.
885 Use the following function to find out whether a constraint
886 represents an equality. If not, it represents an inequality.
888 int isl_constraint_is_equality(
889 __isl_keep isl_constraint *constraint);
891 The coefficients of the constraints can be inspected using
892 the following functions.
894 void isl_constraint_get_constant(
895 __isl_keep isl_constraint *constraint, isl_int *v);
896 void isl_constraint_get_coefficient(
897 __isl_keep isl_constraint *constraint,
898 enum isl_dim_type type, int pos, isl_int *v);
900 The explicit representations of the existentially quantified
901 variables can be inspected using the following functions.
902 Note that the user is only allowed to use these functions
903 if the inspected set or map is the result of a call
904 to C<isl_set_compute_divs> or C<isl_map_compute_divs>.
906 __isl_give isl_div *isl_constraint_div(
907 __isl_keep isl_constraint *constraint, int pos);
908 void isl_div_get_constant(__isl_keep isl_div *div,
910 void isl_div_get_denominator(__isl_keep isl_div *div,
912 void isl_div_get_coefficient(__isl_keep isl_div *div,
913 enum isl_dim_type type, int pos, isl_int *v);
917 =head3 Unary Properties
923 The following functions test whether the given set or relation
924 contains any integer points. The ``fast'' variants do not perform
925 any computations, but simply check if the given set or relation
926 is already known to be empty.
928 int isl_basic_set_fast_is_empty(__isl_keep isl_basic_set *bset);
929 int isl_basic_set_is_empty(__isl_keep isl_basic_set *bset);
930 int isl_set_is_empty(__isl_keep isl_set *set);
931 int isl_union_set_is_empty(__isl_keep isl_union_set *uset);
932 int isl_basic_map_fast_is_empty(__isl_keep isl_basic_map *bmap);
933 int isl_basic_map_is_empty(__isl_keep isl_basic_map *bmap);
934 int isl_map_fast_is_empty(__isl_keep isl_map *map);
935 int isl_map_is_empty(__isl_keep isl_map *map);
936 int isl_union_map_is_empty(__isl_keep isl_union_map *umap);
940 int isl_basic_set_is_universe(__isl_keep isl_basic_set *bset);
941 int isl_basic_map_is_universe(__isl_keep isl_basic_map *bmap);
942 int isl_set_fast_is_universe(__isl_keep isl_set *set);
944 =item * Single-valuedness
946 int isl_map_is_single_valued(__isl_keep isl_map *map);
950 int isl_map_is_bijective(__isl_keep isl_map *map);
954 The followning functions check whether the domain of the given
955 (basic) set is a wrapped relation.
957 int isl_basic_set_is_wrapping(
958 __isl_keep isl_basic_set *bset);
959 int isl_set_is_wrapping(__isl_keep isl_set *set);
963 =head3 Binary Properties
969 int isl_set_fast_is_equal(__isl_keep isl_set *set1,
970 __isl_keep isl_set *set2);
971 int isl_set_is_equal(__isl_keep isl_set *set1,
972 __isl_keep isl_set *set2);
973 int isl_basic_map_is_equal(
974 __isl_keep isl_basic_map *bmap1,
975 __isl_keep isl_basic_map *bmap2);
976 int isl_map_is_equal(__isl_keep isl_map *map1,
977 __isl_keep isl_map *map2);
978 int isl_map_fast_is_equal(__isl_keep isl_map *map1,
979 __isl_keep isl_map *map2);
980 int isl_union_map_is_equal(
981 __isl_keep isl_union_map *umap1,
982 __isl_keep isl_union_map *umap2);
986 int isl_set_fast_is_disjoint(__isl_keep isl_set *set1,
987 __isl_keep isl_set *set2);
991 int isl_set_is_subset(__isl_keep isl_set *set1,
992 __isl_keep isl_set *set2);
993 int isl_set_is_strict_subset(
994 __isl_keep isl_set *set1,
995 __isl_keep isl_set *set2);
996 int isl_basic_map_is_subset(
997 __isl_keep isl_basic_map *bmap1,
998 __isl_keep isl_basic_map *bmap2);
999 int isl_basic_map_is_strict_subset(
1000 __isl_keep isl_basic_map *bmap1,
1001 __isl_keep isl_basic_map *bmap2);
1002 int isl_map_is_subset(
1003 __isl_keep isl_map *map1,
1004 __isl_keep isl_map *map2);
1005 int isl_map_is_strict_subset(
1006 __isl_keep isl_map *map1,
1007 __isl_keep isl_map *map2);
1008 int isl_union_map_is_subset(
1009 __isl_keep isl_union_map *umap1,
1010 __isl_keep isl_union_map *umap2);
1011 int isl_union_map_is_strict_subset(
1012 __isl_keep isl_union_map *umap1,
1013 __isl_keep isl_union_map *umap2);
1017 =head2 Unary Operations
1023 __isl_give isl_set *isl_set_complement(
1024 __isl_take isl_set *set);
1028 __isl_give isl_basic_map *isl_basic_map_reverse(
1029 __isl_take isl_basic_map *bmap);
1030 __isl_give isl_map *isl_map_reverse(
1031 __isl_take isl_map *map);
1032 __isl_give isl_union_map *isl_union_map_reverse(
1033 __isl_take isl_union_map *umap);
1037 __isl_give isl_basic_set *isl_basic_set_project_out(
1038 __isl_take isl_basic_set *bset,
1039 enum isl_dim_type type, unsigned first, unsigned n);
1040 __isl_give isl_basic_map *isl_basic_map_project_out(
1041 __isl_take isl_basic_map *bmap,
1042 enum isl_dim_type type, unsigned first, unsigned n);
1043 __isl_give isl_set *isl_set_project_out(__isl_take isl_set *set,
1044 enum isl_dim_type type, unsigned first, unsigned n);
1045 __isl_give isl_map *isl_map_project_out(__isl_take isl_map *map,
1046 enum isl_dim_type type, unsigned first, unsigned n);
1047 __isl_give isl_basic_set *isl_basic_map_domain(
1048 __isl_take isl_basic_map *bmap);
1049 __isl_give isl_basic_set *isl_basic_map_range(
1050 __isl_take isl_basic_map *bmap);
1051 __isl_give isl_set *isl_map_domain(
1052 __isl_take isl_map *bmap);
1053 __isl_give isl_set *isl_map_range(
1054 __isl_take isl_map *map);
1055 __isl_give isl_union_set *isl_union_map_domain(
1056 __isl_take isl_union_map *umap);
1057 __isl_give isl_union_set *isl_union_map_range(
1058 __isl_take isl_union_map *umap);
1062 __isl_give isl_basic_set *isl_basic_map_deltas(
1063 __isl_take isl_basic_map *bmap);
1064 __isl_give isl_set *isl_map_deltas(__isl_take isl_map *map);
1065 __isl_give isl_union_set *isl_union_map_deltas(
1066 __isl_take isl_union_map *umap);
1068 These functions return a (basic) set containing the differences
1069 between image elements and corresponding domain elements in the input.
1073 Simplify the representation of a set or relation by trying
1074 to combine pairs of basic sets or relations into a single
1075 basic set or relation.
1077 __isl_give isl_set *isl_set_coalesce(__isl_take isl_set *set);
1078 __isl_give isl_map *isl_map_coalesce(__isl_take isl_map *map);
1079 __isl_give isl_union_set *isl_union_set_coalesce(
1080 __isl_take isl_union_set *uset);
1081 __isl_give isl_union_map *isl_union_map_coalesce(
1082 __isl_take isl_union_map *umap);
1086 __isl_give isl_basic_set *isl_set_convex_hull(
1087 __isl_take isl_set *set);
1088 __isl_give isl_basic_map *isl_map_convex_hull(
1089 __isl_take isl_map *map);
1091 If the input set or relation has any existentially quantified
1092 variables, then the result of these operations is currently undefined.
1096 __isl_give isl_basic_set *isl_set_simple_hull(
1097 __isl_take isl_set *set);
1098 __isl_give isl_basic_map *isl_map_simple_hull(
1099 __isl_take isl_map *map);
1101 These functions compute a single basic set or relation
1102 that contains the whole input set or relation.
1103 In particular, the output is described by translates
1104 of the constraints describing the basic sets or relations in the input.
1108 (See \autoref{s:simple hull}.)
1114 __isl_give isl_basic_set *isl_basic_set_affine_hull(
1115 __isl_take isl_basic_set *bset);
1116 __isl_give isl_basic_set *isl_set_affine_hull(
1117 __isl_take isl_set *set);
1118 __isl_give isl_union_set *isl_union_set_affine_hull(
1119 __isl_take isl_union_set *uset);
1120 __isl_give isl_basic_map *isl_basic_map_affine_hull(
1121 __isl_take isl_basic_map *bmap);
1122 __isl_give isl_basic_map *isl_map_affine_hull(
1123 __isl_take isl_map *map);
1124 __isl_give isl_union_map *isl_union_map_affine_hull(
1125 __isl_take isl_union_map *umap);
1127 In case of union sets and relations, the affine hull is computed
1132 __isl_give isl_map *isl_map_power(__isl_take isl_map *map,
1133 unsigned param, int *exact);
1135 Compute a parametric representation for all positive powers I<k> of C<map>.
1136 The power I<k> is equated to the parameter at position C<param>.
1137 The result may be an overapproximation. If the result is exact,
1138 then C<*exact> is set to C<1>.
1139 The current implementation only produces exact results for particular
1140 cases of piecewise translations (i.e., piecewise uniform dependences).
1142 =item * Transitive closure
1144 __isl_give isl_map *isl_map_transitive_closure(
1145 __isl_take isl_map *map, int *exact);
1146 __isl_give isl_union_map *isl_union_map_transitive_closure(
1147 __isl_take isl_union_map *umap, int *exact);
1149 Compute the transitive closure of C<map>.
1150 The result may be an overapproximation. If the result is known to be exact,
1151 then C<*exact> is set to C<1>.
1152 The current implementation only produces exact results for particular
1153 cases of piecewise translations (i.e., piecewise uniform dependences).
1155 =item * Reaching path lengths
1157 __isl_give isl_map *isl_map_reaching_path_lengths(
1158 __isl_take isl_map *map, int *exact);
1160 Compute a relation that maps each element in the range of C<map>
1161 to the lengths of all paths composed of edges in C<map> that
1162 end up in the given element.
1163 The result may be an overapproximation. If the result is known to be exact,
1164 then C<*exact> is set to C<1>.
1165 To compute the I<maximal> path length, the resulting relation
1166 should be postprocessed by C<isl_map_lexmax>.
1167 In particular, if the input relation is a dependence relation
1168 (mapping sources to sinks), then the maximal path length corresponds
1169 to the free schedule.
1170 Note, however, that C<isl_map_lexmax> expects the maximum to be
1171 finite, so if the path lengths are unbounded (possibly due to
1172 the overapproximation), then you will get an error message.
1176 __isl_give isl_basic_set *isl_basic_map_wrap(
1177 __isl_take isl_basic_map *bmap);
1178 __isl_give isl_set *isl_map_wrap(
1179 __isl_take isl_map *map);
1180 __isl_give isl_union_set *isl_union_map_wrap(
1181 __isl_take isl_union_map *umap);
1182 __isl_give isl_basic_map *isl_basic_set_unwrap(
1183 __isl_take isl_basic_set *bset);
1184 __isl_give isl_map *isl_set_unwrap(
1185 __isl_take isl_set *set);
1186 __isl_give isl_union_map *isl_union_set_unwrap(
1187 __isl_take isl_union_set *uset);
1191 =head2 Binary Operations
1193 The two arguments of a binary operation not only need to live
1194 in the same C<isl_ctx>, they currently also need to have
1195 the same (number of) parameters.
1197 =head3 Basic Operations
1201 =item * Intersection
1203 __isl_give isl_basic_set *isl_basic_set_intersect(
1204 __isl_take isl_basic_set *bset1,
1205 __isl_take isl_basic_set *bset2);
1206 __isl_give isl_set *isl_set_intersect(
1207 __isl_take isl_set *set1,
1208 __isl_take isl_set *set2);
1209 __isl_give isl_union_set *isl_union_set_intersect(
1210 __isl_take isl_union_set *uset1,
1211 __isl_take isl_union_set *uset2);
1212 __isl_give isl_basic_map *isl_basic_map_intersect_domain(
1213 __isl_take isl_basic_map *bmap,
1214 __isl_take isl_basic_set *bset);
1215 __isl_give isl_basic_map *isl_basic_map_intersect_range(
1216 __isl_take isl_basic_map *bmap,
1217 __isl_take isl_basic_set *bset);
1218 __isl_give isl_basic_map *isl_basic_map_intersect(
1219 __isl_take isl_basic_map *bmap1,
1220 __isl_take isl_basic_map *bmap2);
1221 __isl_give isl_map *isl_map_intersect_domain(
1222 __isl_take isl_map *map,
1223 __isl_take isl_set *set);
1224 __isl_give isl_map *isl_map_intersect_range(
1225 __isl_take isl_map *map,
1226 __isl_take isl_set *set);
1227 __isl_give isl_map *isl_map_intersect(
1228 __isl_take isl_map *map1,
1229 __isl_take isl_map *map2);
1230 __isl_give isl_union_map *isl_union_map_intersect_domain(
1231 __isl_take isl_union_map *umap,
1232 __isl_take isl_union_set *uset);
1233 __isl_give isl_union_map *isl_union_map_intersect(
1234 __isl_take isl_union_map *umap1,
1235 __isl_take isl_union_map *umap2);
1239 __isl_give isl_set *isl_basic_set_union(
1240 __isl_take isl_basic_set *bset1,
1241 __isl_take isl_basic_set *bset2);
1242 __isl_give isl_map *isl_basic_map_union(
1243 __isl_take isl_basic_map *bmap1,
1244 __isl_take isl_basic_map *bmap2);
1245 __isl_give isl_set *isl_set_union(
1246 __isl_take isl_set *set1,
1247 __isl_take isl_set *set2);
1248 __isl_give isl_map *isl_map_union(
1249 __isl_take isl_map *map1,
1250 __isl_take isl_map *map2);
1251 __isl_give isl_union_set *isl_union_set_union(
1252 __isl_take isl_union_set *uset1,
1253 __isl_take isl_union_set *uset2);
1254 __isl_give isl_union_map *isl_union_map_union(
1255 __isl_take isl_union_map *umap1,
1256 __isl_take isl_union_map *umap2);
1258 =item * Set difference
1260 __isl_give isl_set *isl_set_subtract(
1261 __isl_take isl_set *set1,
1262 __isl_take isl_set *set2);
1263 __isl_give isl_map *isl_map_subtract(
1264 __isl_take isl_map *map1,
1265 __isl_take isl_map *map2);
1266 __isl_give isl_union_set *isl_union_set_subtract(
1267 __isl_take isl_union_set *uset1,
1268 __isl_take isl_union_set *uset2);
1269 __isl_give isl_union_map *isl_union_map_subtract(
1270 __isl_take isl_union_map *umap1,
1271 __isl_take isl_union_map *umap2);
1275 __isl_give isl_basic_set *isl_basic_set_apply(
1276 __isl_take isl_basic_set *bset,
1277 __isl_take isl_basic_map *bmap);
1278 __isl_give isl_set *isl_set_apply(
1279 __isl_take isl_set *set,
1280 __isl_take isl_map *map);
1281 __isl_give isl_union_set *isl_union_set_apply(
1282 __isl_take isl_union_set *uset,
1283 __isl_take isl_union_map *umap);
1284 __isl_give isl_basic_map *isl_basic_map_apply_domain(
1285 __isl_take isl_basic_map *bmap1,
1286 __isl_take isl_basic_map *bmap2);
1287 __isl_give isl_basic_map *isl_basic_map_apply_range(
1288 __isl_take isl_basic_map *bmap1,
1289 __isl_take isl_basic_map *bmap2);
1290 __isl_give isl_map *isl_map_apply_domain(
1291 __isl_take isl_map *map1,
1292 __isl_take isl_map *map2);
1293 __isl_give isl_map *isl_map_apply_range(
1294 __isl_take isl_map *map1,
1295 __isl_take isl_map *map2);
1296 __isl_give isl_union_map *isl_union_map_apply_range(
1297 __isl_take isl_union_map *umap1,
1298 __isl_take isl_union_map *umap2);
1300 =item * Simplification
1302 __isl_give isl_basic_set *isl_basic_set_gist(
1303 __isl_take isl_basic_set *bset,
1304 __isl_take isl_basic_set *context);
1305 __isl_give isl_set *isl_set_gist(__isl_take isl_set *set,
1306 __isl_take isl_set *context);
1307 __isl_give isl_union_set *isl_union_set_gist(
1308 __isl_take isl_union_set *uset,
1309 __isl_take isl_union_set *context);
1310 __isl_give isl_basic_map *isl_basic_map_gist(
1311 __isl_take isl_basic_map *bmap,
1312 __isl_take isl_basic_map *context);
1313 __isl_give isl_map *isl_map_gist(__isl_take isl_map *map,
1314 __isl_take isl_map *context);
1315 __isl_give isl_union_map *isl_union_map_gist(
1316 __isl_take isl_union_map *umap,
1317 __isl_take isl_union_map *context);
1319 The gist operation returns a set or relation that has the
1320 same intersection with the context as the input set or relation.
1321 Any implicit equality in the intersection is made explicit in the result,
1322 while all inequalities that are redundant with respect to the intersection
1324 In case of union sets and relations, the gist operation is performed
1329 =head3 Lexicographic Optimization
1331 Given a (basic) set C<set> (or C<bset>) and a zero-dimensional domain C<dom>,
1332 the following functions
1333 compute a set that contains the lexicographic minimum or maximum
1334 of the elements in C<set> (or C<bset>) for those values of the parameters
1335 that satisfy C<dom>.
1336 If C<empty> is not C<NULL>, then C<*empty> is assigned a set
1337 that contains the parameter values in C<dom> for which C<set> (or C<bset>)
1339 In other words, the union of the parameter values
1340 for which the result is non-empty and of C<*empty>
1343 __isl_give isl_set *isl_basic_set_partial_lexmin(
1344 __isl_take isl_basic_set *bset,
1345 __isl_take isl_basic_set *dom,
1346 __isl_give isl_set **empty);
1347 __isl_give isl_set *isl_basic_set_partial_lexmax(
1348 __isl_take isl_basic_set *bset,
1349 __isl_take isl_basic_set *dom,
1350 __isl_give isl_set **empty);
1351 __isl_give isl_set *isl_set_partial_lexmin(
1352 __isl_take isl_set *set, __isl_take isl_set *dom,
1353 __isl_give isl_set **empty);
1354 __isl_give isl_set *isl_set_partial_lexmax(
1355 __isl_take isl_set *set, __isl_take isl_set *dom,
1356 __isl_give isl_set **empty);
1358 Given a (basic) set C<set> (or C<bset>), the following functions simply
1359 return a set containing the lexicographic minimum or maximum
1360 of the elements in C<set> (or C<bset>).
1361 In case of union sets, the optimum is computed per space.
1363 __isl_give isl_set *isl_basic_set_lexmin(
1364 __isl_take isl_basic_set *bset);
1365 __isl_give isl_set *isl_basic_set_lexmax(
1366 __isl_take isl_basic_set *bset);
1367 __isl_give isl_set *isl_set_lexmin(
1368 __isl_take isl_set *set);
1369 __isl_give isl_set *isl_set_lexmax(
1370 __isl_take isl_set *set);
1371 __isl_give isl_union_set *isl_union_set_lexmin(
1372 __isl_take isl_union_set *uset);
1373 __isl_give isl_union_set *isl_union_set_lexmax(
1374 __isl_take isl_union_set *uset);
1376 Given a (basic) relation C<map> (or C<bmap>) and a domain C<dom>,
1377 the following functions
1378 compute a relation that maps each element of C<dom>
1379 to the single lexicographic minimum or maximum
1380 of the elements that are associated to that same
1381 element in C<map> (or C<bmap>).
1382 If C<empty> is not C<NULL>, then C<*empty> is assigned a set
1383 that contains the elements in C<dom> that do not map
1384 to any elements in C<map> (or C<bmap>).
1385 In other words, the union of the domain of the result and of C<*empty>
1388 __isl_give isl_map *isl_basic_map_partial_lexmax(
1389 __isl_take isl_basic_map *bmap,
1390 __isl_take isl_basic_set *dom,
1391 __isl_give isl_set **empty);
1392 __isl_give isl_map *isl_basic_map_partial_lexmin(
1393 __isl_take isl_basic_map *bmap,
1394 __isl_take isl_basic_set *dom,
1395 __isl_give isl_set **empty);
1396 __isl_give isl_map *isl_map_partial_lexmax(
1397 __isl_take isl_map *map, __isl_take isl_set *dom,
1398 __isl_give isl_set **empty);
1399 __isl_give isl_map *isl_map_partial_lexmin(
1400 __isl_take isl_map *map, __isl_take isl_set *dom,
1401 __isl_give isl_set **empty);
1403 Given a (basic) map C<map> (or C<bmap>), the following functions simply
1404 return a map mapping each element in the domain of
1405 C<map> (or C<bmap>) to the lexicographic minimum or maximum
1406 of all elements associated to that element.
1407 In case of union relations, the optimum is computed per space.
1409 __isl_give isl_map *isl_basic_map_lexmin(
1410 __isl_take isl_basic_map *bmap);
1411 __isl_give isl_map *isl_basic_map_lexmax(
1412 __isl_take isl_basic_map *bmap);
1413 __isl_give isl_map *isl_map_lexmin(
1414 __isl_take isl_map *map);
1415 __isl_give isl_map *isl_map_lexmax(
1416 __isl_take isl_map *map);
1417 __isl_give isl_union_map *isl_union_map_lexmin(
1418 __isl_take isl_union_map *umap);
1419 __isl_give isl_union_map *isl_union_map_lexmax(
1420 __isl_take isl_union_map *umap);
1424 Points are elements of a set. They can be used to construct
1425 simple sets (boxes) or they can be used to represent the
1426 individual elements of a set.
1427 The zero point (the origin) can be created using
1429 __isl_give isl_point *isl_point_zero(__isl_take isl_dim *dim);
1431 The coordinates of a point can be inspected, set and changed
1434 void isl_point_get_coordinate(__isl_keep isl_point *pnt,
1435 enum isl_dim_type type, int pos, isl_int *v);
1436 __isl_give isl_point *isl_point_set_coordinate(
1437 __isl_take isl_point *pnt,
1438 enum isl_dim_type type, int pos, isl_int v);
1440 __isl_give isl_point *isl_point_add_ui(
1441 __isl_take isl_point *pnt,
1442 enum isl_dim_type type, int pos, unsigned val);
1443 __isl_give isl_point *isl_point_sub_ui(
1444 __isl_take isl_point *pnt,
1445 enum isl_dim_type type, int pos, unsigned val);
1447 Points can be copied or freed using
1449 __isl_give isl_point *isl_point_copy(
1450 __isl_keep isl_point *pnt);
1451 void isl_point_free(__isl_take isl_point *pnt);
1453 A singleton set can be created from a point using
1455 __isl_give isl_set *isl_set_from_point(
1456 __isl_take isl_point *pnt);
1458 and a box can be created from two opposite extremal points using
1460 __isl_give isl_set *isl_set_box_from_points(
1461 __isl_take isl_point *pnt1,
1462 __isl_take isl_point *pnt2);
1464 All elements of a B<bounded> (union) set can be enumerated using
1465 the following functions.
1467 int isl_set_foreach_point(__isl_keep isl_set *set,
1468 int (*fn)(__isl_take isl_point *pnt, void *user),
1470 int isl_union_set_foreach_point(__isl_keep isl_union_set *uset,
1471 int (*fn)(__isl_take isl_point *pnt, void *user),
1474 The function C<fn> is called for each integer point in
1475 C<set> with as second argument the last argument of
1476 the C<isl_set_foreach_point> call. The function C<fn>
1477 should return C<0> on success and C<-1> on failure.
1478 In the latter case, C<isl_set_foreach_point> will stop
1479 enumerating and return C<-1> as well.
1480 If the enumeration is performed successfully and to completion,
1481 then C<isl_set_foreach_point> returns C<0>.
1483 To obtain a single point of a set, use
1485 __isl_give isl_point *isl_set_sample_point(
1486 __isl_take isl_set *set);
1488 If C<set> does not contain any (integer) points, then the
1489 resulting point will be ``void'', a property that can be
1492 int isl_point_is_void(__isl_keep isl_point *pnt);
1494 =head2 Piecewise Quasipolynomials
1496 A piecewise quasipolynomial is a particular kind of function that maps
1497 a parametric point to a rational value.
1498 More specifically, a quasipolynomial is a polynomial expression in greatest
1499 integer parts of affine expressions of parameters and variables.
1500 A piecewise quasipolynomial is a subdivision of a given parametric
1501 domain into disjoint cells with a quasipolynomial associated to
1502 each cell. The value of the piecewise quasipolynomial at a given
1503 point is the value of the quasipolynomial associated to the cell
1504 that contains the point. Outside of the union of cells,
1505 the value is assumed to be zero.
1506 For example, the piecewise quasipolynomial
1508 [n] -> { [x] -> ((1 + n) - x) : x <= n and x >= 0 }
1510 maps C<x> to C<1 + n - x> for values of C<x> between C<0> and C<n>.
1511 A given piecewise quasipolynomial has a fixed domain dimension.
1512 Union piecewise quasipolynomials are used to contain piecewise quasipolynomials
1513 defined over different domains.
1514 Piecewise quasipolynomials are mainly used by the C<barvinok>
1515 library for representing the number of elements in a parametric set or map.
1516 For example, the piecewise quasipolynomial above represents
1517 the number of points in the map
1519 [n] -> { [x] -> [y] : x,y >= 0 and 0 <= x + y <= n }
1521 =head3 Printing (Piecewise) Quasipolynomials
1523 Quasipolynomials and piecewise quasipolynomials can be printed
1524 using the following functions.
1526 __isl_give isl_printer *isl_printer_print_qpolynomial(
1527 __isl_take isl_printer *p,
1528 __isl_keep isl_qpolynomial *qp);
1530 __isl_give isl_printer *isl_printer_print_pw_qpolynomial(
1531 __isl_take isl_printer *p,
1532 __isl_keep isl_pw_qpolynomial *pwqp);
1534 __isl_give isl_printer *isl_printer_print_union_pw_qpolynomial(
1535 __isl_take isl_printer *p,
1536 __isl_keep isl_union_pw_qpolynomial *upwqp);
1538 The output format of the printer
1539 needs to be set to either C<ISL_FORMAT_ISL> or C<ISL_FORMAT_C>.
1540 For C<isl_printer_print_union_pw_qpolynomial>, only C<ISL_FORMAT_ISL>
1543 =head3 Creating New (Piecewise) Quasipolynomials
1545 Some simple quasipolynomials can be created using the following functions.
1546 More complicated quasipolynomials can be created by applying
1547 operations such as addition and multiplication
1548 on the resulting quasipolynomials
1550 __isl_give isl_qpolynomial *isl_qpolynomial_zero(
1551 __isl_take isl_dim *dim);
1552 __isl_give isl_qpolynomial *isl_qpolynomial_infty(
1553 __isl_take isl_dim *dim);
1554 __isl_give isl_qpolynomial *isl_qpolynomial_neginfty(
1555 __isl_take isl_dim *dim);
1556 __isl_give isl_qpolynomial *isl_qpolynomial_nan(
1557 __isl_take isl_dim *dim);
1558 __isl_give isl_qpolynomial *isl_qpolynomial_rat_cst(
1559 __isl_take isl_dim *dim,
1560 const isl_int n, const isl_int d);
1561 __isl_give isl_qpolynomial *isl_qpolynomial_div(
1562 __isl_take isl_div *div);
1563 __isl_give isl_qpolynomial *isl_qpolynomial_var(
1564 __isl_take isl_dim *dim,
1565 enum isl_dim_type type, unsigned pos);
1567 The zero piecewise quasipolynomial or a piecewise quasipolynomial
1568 with a single cell can be created using the following functions.
1569 Multiple of these single cell piecewise quasipolynomials can
1570 be combined to create more complicated piecewise quasipolynomials.
1572 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_zero(
1573 __isl_take isl_dim *dim);
1574 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_alloc(
1575 __isl_take isl_set *set,
1576 __isl_take isl_qpolynomial *qp);
1578 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_zero(
1579 __isl_take isl_dim *dim);
1580 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_from_pw_qpolynomial(
1581 __isl_take isl_pw_qpolynomial *pwqp);
1582 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_add_pw_qpolynomial(
1583 __isl_take isl_union_pw_qpolynomial *upwqp,
1584 __isl_take isl_pw_qpolynomial *pwqp);
1586 Quasipolynomials can be copied and freed again using the following
1589 __isl_give isl_qpolynomial *isl_qpolynomial_copy(
1590 __isl_keep isl_qpolynomial *qp);
1591 void isl_qpolynomial_free(__isl_take isl_qpolynomial *qp);
1593 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_copy(
1594 __isl_keep isl_pw_qpolynomial *pwqp);
1595 void isl_pw_qpolynomial_free(
1596 __isl_take isl_pw_qpolynomial *pwqp);
1598 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_copy(
1599 __isl_keep isl_union_pw_qpolynomial *upwqp);
1600 void isl_union_pw_qpolynomial_free(
1601 __isl_take isl_union_pw_qpolynomial *upwqp);
1603 =head3 Inspecting (Piecewise) Quasipolynomials
1605 To iterate over all piecewise quasipolynomials in a union
1606 piecewise quasipolynomial, use the following function
1608 int isl_union_pw_qpolynomial_foreach_pw_qpolynomial(
1609 __isl_keep isl_union_pw_qpolynomial *upwqp,
1610 int (*fn)(__isl_take isl_pw_qpolynomial *pwqp, void *user),
1613 To iterate over the cells in a piecewise quasipolynomial,
1614 use either of the following two functions
1616 int isl_pw_qpolynomial_foreach_piece(
1617 __isl_keep isl_pw_qpolynomial *pwqp,
1618 int (*fn)(__isl_take isl_set *set,
1619 __isl_take isl_qpolynomial *qp,
1620 void *user), void *user);
1621 int isl_pw_qpolynomial_foreach_lifted_piece(
1622 __isl_keep isl_pw_qpolynomial *pwqp,
1623 int (*fn)(__isl_take isl_set *set,
1624 __isl_take isl_qpolynomial *qp,
1625 void *user), void *user);
1627 As usual, the function C<fn> should return C<0> on success
1628 and C<-1> on failure. The difference between
1629 C<isl_pw_qpolynomial_foreach_piece> and
1630 C<isl_pw_qpolynomial_foreach_lifted_piece> is that
1631 C<isl_pw_qpolynomial_foreach_lifted_piece> will first
1632 compute unique representations for all existentially quantified
1633 variables and then turn these existentially quantified variables
1634 into extra set variables, adapting the associated quasipolynomial
1635 accordingly. This means that the C<set> passed to C<fn>
1636 will not have any existentially quantified variables, but that
1637 the dimensions of the sets may be different for different
1638 invocations of C<fn>.
1640 To iterate over all terms in a quasipolynomial,
1643 int isl_qpolynomial_foreach_term(
1644 __isl_keep isl_qpolynomial *qp,
1645 int (*fn)(__isl_take isl_term *term,
1646 void *user), void *user);
1648 The terms themselves can be inspected and freed using
1651 unsigned isl_term_dim(__isl_keep isl_term *term,
1652 enum isl_dim_type type);
1653 void isl_term_get_num(__isl_keep isl_term *term,
1655 void isl_term_get_den(__isl_keep isl_term *term,
1657 int isl_term_get_exp(__isl_keep isl_term *term,
1658 enum isl_dim_type type, unsigned pos);
1659 __isl_give isl_div *isl_term_get_div(
1660 __isl_keep isl_term *term, unsigned pos);
1661 void isl_term_free(__isl_take isl_term *term);
1663 Each term is a product of parameters, set variables and
1664 integer divisions. The function C<isl_term_get_exp>
1665 returns the exponent of a given dimensions in the given term.
1666 The C<isl_int>s in the arguments of C<isl_term_get_num>
1667 and C<isl_term_get_den> need to have been initialized
1668 using C<isl_int_init> before calling these functions.
1670 =head3 Properties of (Piecewise) Quasipolynomials
1672 To check whether a quasipolynomial is actually a constant,
1673 use the following function.
1675 int isl_qpolynomial_is_cst(__isl_keep isl_qpolynomial *qp,
1676 isl_int *n, isl_int *d);
1678 If C<qp> is a constant and if C<n> and C<d> are not C<NULL>
1679 then the numerator and denominator of the constant
1680 are returned in C<*n> and C<*d>, respectively.
1682 =head3 Operations on (Piecewise) Quasipolynomials
1684 __isl_give isl_qpolynomial *isl_qpolynomial_neg(
1685 __isl_take isl_qpolynomial *qp);
1686 __isl_give isl_qpolynomial *isl_qpolynomial_add(
1687 __isl_take isl_qpolynomial *qp1,
1688 __isl_take isl_qpolynomial *qp2);
1689 __isl_give isl_qpolynomial *isl_qpolynomial_sub(
1690 __isl_take isl_qpolynomial *qp1,
1691 __isl_take isl_qpolynomial *qp2);
1692 __isl_give isl_qpolynomial *isl_qpolynomial_mul(
1693 __isl_take isl_qpolynomial *qp1,
1694 __isl_take isl_qpolynomial *qp2);
1696 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_add(
1697 __isl_take isl_pw_qpolynomial *pwqp1,
1698 __isl_take isl_pw_qpolynomial *pwqp2);
1699 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_sub(
1700 __isl_take isl_pw_qpolynomial *pwqp1,
1701 __isl_take isl_pw_qpolynomial *pwqp2);
1702 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_add_disjoint(
1703 __isl_take isl_pw_qpolynomial *pwqp1,
1704 __isl_take isl_pw_qpolynomial *pwqp2);
1705 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_neg(
1706 __isl_take isl_pw_qpolynomial *pwqp);
1707 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_mul(
1708 __isl_take isl_pw_qpolynomial *pwqp1,
1709 __isl_take isl_pw_qpolynomial *pwqp2);
1711 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_add(
1712 __isl_take isl_union_pw_qpolynomial *upwqp1,
1713 __isl_take isl_union_pw_qpolynomial *upwqp2);
1714 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_sub(
1715 __isl_take isl_union_pw_qpolynomial *upwqp1,
1716 __isl_take isl_union_pw_qpolynomial *upwqp2);
1717 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_mul(
1718 __isl_take isl_union_pw_qpolynomial *upwqp1,
1719 __isl_take isl_union_pw_qpolynomial *upwqp2);
1721 __isl_give isl_qpolynomial *isl_pw_qpolynomial_eval(
1722 __isl_take isl_pw_qpolynomial *pwqp,
1723 __isl_take isl_point *pnt);
1725 __isl_give isl_qpolynomial *isl_union_pw_qpolynomial_eval(
1726 __isl_take isl_union_pw_qpolynomial *upwqp,
1727 __isl_take isl_point *pnt);
1729 __isl_give isl_set *isl_pw_qpolynomial_domain(
1730 __isl_take isl_pw_qpolynomial *pwqp);
1731 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_intersect_domain(
1732 __isl_take isl_pw_qpolynomial *pwpq,
1733 __isl_take isl_set *set);
1735 __isl_give isl_union_set *isl_union_pw_qpolynomial_domain(
1736 __isl_take isl_union_pw_qpolynomial *upwqp);
1737 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_intersect_domain(
1738 __isl_take isl_union_pw_qpolynomial *upwpq,
1739 __isl_take isl_union_set *uset);
1741 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_coalesce(
1742 __isl_take isl_union_pw_qpolynomial *upwqp);
1744 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_gist(
1745 __isl_take isl_pw_qpolynomial *pwqp,
1746 __isl_take isl_set *context);
1748 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_gist(
1749 __isl_take isl_union_pw_qpolynomial *upwqp,
1750 __isl_take isl_union_set *context);
1752 The gist operation applies the gist operation to each of
1753 the cells in the domain of the input piecewise quasipolynomial.
1754 In future, the operation will also exploit the context
1755 to simplify the quasipolynomials associated to each cell.
1757 =head2 Bounds on Piecewise Quasipolynomials and Piecewise Quasipolynomial Reductions
1759 A piecewise quasipolynomial reduction is a piecewise
1760 reduction (or fold) of quasipolynomials.
1761 In particular, the reduction can be maximum or a minimum.
1762 The objects are mainly used to represent the result of
1763 an upper or lower bound on a quasipolynomial over its domain,
1764 i.e., as the result of the following function.
1766 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_bound(
1767 __isl_take isl_pw_qpolynomial *pwqp,
1768 enum isl_fold type, int *tight);
1770 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_bound(
1771 __isl_take isl_union_pw_qpolynomial *upwqp,
1772 enum isl_fold type, int *tight);
1774 The C<type> argument may be either C<isl_fold_min> or C<isl_fold_max>.
1775 If C<tight> is not C<NULL>, then C<*tight> is set to C<1>
1776 is the returned bound is known be tight, i.e., for each value
1777 of the parameters there is at least
1778 one element in the domain that reaches the bound.
1779 If the domain of C<pwqp> is not wrapping, then the bound is computed
1780 over all elements in that domain and the result has a purely parametric
1781 domain. If the domain of C<pwqp> is wrapping, then the bound is
1782 computed over the range of the wrapped relation. The domain of the
1783 wrapped relation becomes the domain of the result.
1785 A (piecewise) quasipolynomial reduction can be copied or freed using the
1786 following functions.
1788 __isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_copy(
1789 __isl_keep isl_qpolynomial_fold *fold);
1790 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_copy(
1791 __isl_keep isl_pw_qpolynomial_fold *pwf);
1792 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_copy(
1793 __isl_keep isl_union_pw_qpolynomial_fold *upwf);
1794 void isl_qpolynomial_fold_free(
1795 __isl_take isl_qpolynomial_fold *fold);
1796 void isl_pw_qpolynomial_fold_free(
1797 __isl_take isl_pw_qpolynomial_fold *pwf);
1798 void isl_union_pw_qpolynomial_fold_free(
1799 __isl_take isl_union_pw_qpolynomial_fold *upwf);
1801 =head3 Printing Piecewise Quasipolynomial Reductions
1803 Piecewise quasipolynomial reductions can be printed
1804 using the following function.
1806 __isl_give isl_printer *isl_printer_print_pw_qpolynomial_fold(
1807 __isl_take isl_printer *p,
1808 __isl_keep isl_pw_qpolynomial_fold *pwf);
1809 __isl_give isl_printer *isl_printer_print_union_pw_qpolynomial_fold(
1810 __isl_take isl_printer *p,
1811 __isl_keep isl_union_pw_qpolynomial_fold *upwf);
1813 For C<isl_printer_print_pw_qpolynomial_fold>,
1814 output format of the printer
1815 needs to be set to either C<ISL_FORMAT_ISL> or C<ISL_FORMAT_C>.
1816 For C<isl_printer_print_union_pw_qpolynomial_fold>,
1817 output format of the printer
1818 needs to be set to either C<ISL_FORMAT_ISL>.
1820 =head3 Inspecting (Piecewise) Quasipolynomial Reductions
1822 To iterate over all piecewise quasipolynomial reductions in a union
1823 piecewise quasipolynomial reduction, use the following function
1825 int isl_union_pw_qpolynomial_fold_foreach_pw_qpolynomial_fold(
1826 __isl_keep isl_union_pw_qpolynomial_fold *upwf,
1827 int (*fn)(__isl_take isl_pw_qpolynomial_fold *pwf,
1828 void *user), void *user);
1830 To iterate over the cells in a piecewise quasipolynomial reduction,
1831 use either of the following two functions
1833 int isl_pw_qpolynomial_fold_foreach_piece(
1834 __isl_keep isl_pw_qpolynomial_fold *pwf,
1835 int (*fn)(__isl_take isl_set *set,
1836 __isl_take isl_qpolynomial_fold *fold,
1837 void *user), void *user);
1838 int isl_pw_qpolynomial_fold_foreach_lifted_piece(
1839 __isl_keep isl_pw_qpolynomial_fold *pwf,
1840 int (*fn)(__isl_take isl_set *set,
1841 __isl_take isl_qpolynomial_fold *fold,
1842 void *user), void *user);
1844 See L<Inspecting (Piecewise) Quasipolynomials> for an explanation
1845 of the difference between these two functions.
1847 To iterate over all quasipolynomials in a reduction, use
1849 int isl_qpolynomial_fold_foreach_qpolynomial(
1850 __isl_keep isl_qpolynomial_fold *fold,
1851 int (*fn)(__isl_take isl_qpolynomial *qp,
1852 void *user), void *user);
1854 =head3 Operations on Piecewise Quasipolynomial Reductions
1856 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_fold(
1857 __isl_take isl_pw_qpolynomial_fold *pwf1,
1858 __isl_take isl_pw_qpolynomial_fold *pwf2);
1860 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_fold(
1861 __isl_take isl_union_pw_qpolynomial_fold *upwf1,
1862 __isl_take isl_union_pw_qpolynomial_fold *upwf2);
1864 __isl_give isl_qpolynomial *isl_pw_qpolynomial_fold_eval(
1865 __isl_take isl_pw_qpolynomial_fold *pwf,
1866 __isl_take isl_point *pnt);
1868 __isl_give isl_qpolynomial *isl_union_pw_qpolynomial_fold_eval(
1869 __isl_take isl_union_pw_qpolynomial_fold *upwf,
1870 __isl_take isl_point *pnt);
1872 __isl_give isl_union_set *isl_union_pw_qpolynomial_fold_domain(
1873 __isl_take isl_union_pw_qpolynomial_fold *upwf);
1874 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_intersect_domain(
1875 __isl_take isl_union_pw_qpolynomial_fold *upwf,
1876 __isl_take isl_union_set *uset);
1878 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_coalesce(
1879 __isl_take isl_pw_qpolynomial_fold *pwf);
1881 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_coalesce(
1882 __isl_take isl_union_pw_qpolynomial_fold *upwf);
1884 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_gist(
1885 __isl_take isl_pw_qpolynomial_fold *pwf,
1886 __isl_take isl_set *context);
1888 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_gist(
1889 __isl_take isl_union_pw_qpolynomial_fold *upwf,
1890 __isl_take isl_union_set *context);
1892 The gist operation applies the gist operation to each of
1893 the cells in the domain of the input piecewise quasipolynomial reduction.
1894 In future, the operation will also exploit the context
1895 to simplify the quasipolynomial reductions associated to each cell.
1897 __isl_give isl_pw_qpolynomial_fold *
1898 isl_map_apply_pw_qpolynomial_fold(
1899 __isl_take isl_map *map,
1900 __isl_take isl_pw_qpolynomial_fold *pwf,
1902 __isl_give isl_union_pw_qpolynomial_fold *
1903 isl_union_map_apply_union_pw_qpolynomial_fold(
1904 __isl_take isl_union_map *umap,
1905 __isl_take isl_union_pw_qpolynomial_fold *upwf,
1909 compose the given map with the given piecewise quasipolynomial reduction.
1910 That is, compute a bound (of the same type as C<pwf> or C<upwf> itself)
1911 over all elements in the intersection of the range of the map
1912 and the domain of the piecewise quasipolynomial reduction
1913 as a function of an element in the domain of the map.
1915 =head2 Dependence Analysis
1917 C<isl> contains specialized functionality for performing
1918 array dataflow analysis. That is, given a I<sink> access relation
1919 and a collection of possible I<source> access relations,
1920 C<isl> can compute relations that describe
1921 for each iteration of the sink access, which iteration
1922 of which of the source access relations was the last
1923 to access the same data element before the given iteration
1925 To compute standard flow dependences, the sink should be
1926 a read, while the sources should be writes.
1927 If any of the source accesses are marked as being I<may>
1928 accesses, then there will be a dependence to the last
1929 I<must> access B<and> to any I<may> access that follows
1930 this last I<must> access.
1931 In particular, if I<all> sources are I<may> accesses,
1932 then memory based dependence analysis is performed.
1933 If, on the other hand, all sources are I<must> accesses,
1934 then value based dependence analysis is performed.
1936 #include <isl_flow.h>
1938 __isl_give isl_access_info *isl_access_info_alloc(
1939 __isl_take isl_map *sink,
1940 void *sink_user, isl_access_level_before fn,
1942 __isl_give isl_access_info *isl_access_info_add_source(
1943 __isl_take isl_access_info *acc,
1944 __isl_take isl_map *source, int must,
1947 __isl_give isl_flow *isl_access_info_compute_flow(
1948 __isl_take isl_access_info *acc);
1950 int isl_flow_foreach(__isl_keep isl_flow *deps,
1951 int (*fn)(__isl_take isl_map *dep, int must,
1952 void *dep_user, void *user),
1954 __isl_give isl_set *isl_flow_get_no_source(
1955 __isl_keep isl_flow *deps, int must);
1956 void isl_flow_free(__isl_take isl_flow *deps);
1958 The function C<isl_access_info_compute_flow> performs the actual
1959 dependence analysis. The other functions are used to construct
1960 the input for this function or to read off the output.
1962 The input is collected in an C<isl_access_info>, which can
1963 be created through a call to C<isl_access_info_alloc>.
1964 The arguments to this functions are the sink access relation
1965 C<sink>, a token C<sink_user> used to identify the sink
1966 access to the user, a callback function for specifying the
1967 relative order of source and sink accesses, and the number
1968 of source access relations that will be added.
1969 The callback function has type C<int (*)(void *first, void *second)>.
1970 The function is called with two user supplied tokens identifying
1971 either a source or the sink and it should return the shared nesting
1972 level and the relative order of the two accesses.
1973 In particular, let I<n> be the number of loops shared by
1974 the two accesses. If C<first> precedes C<second> textually,
1975 then the function should return I<2 * n + 1>; otherwise,
1976 it should return I<2 * n>.
1977 The sources can be added to the C<isl_access_info> by performing
1978 (at most) C<max_source> calls to C<isl_access_info_add_source>.
1979 C<must> indicates whether the source is a I<must> access
1980 or a I<may> access. Note that a multi-valued access relation
1981 should only be marked I<must> if every iteration in the domain
1982 of the relation accesses I<all> elements in its image.
1983 The C<source_user> token is again used to identify
1984 the source access. The range of the source access relation
1985 C<source> should have the same dimension as the range
1986 of the sink access relation.
1988 The result of the dependence analysis is collected in an
1989 C<isl_flow>. There may be elements in the domain of
1990 the sink access for which no preceding source access could be
1991 found or for which all preceding sources are I<may> accesses.
1992 The sets of these elements can be obtained through
1993 calls to C<isl_flow_get_no_source>, the first with C<must> set
1994 and the second with C<must> unset.
1995 In the case of standard flow dependence analysis,
1996 with the sink a read and the sources I<must> writes,
1997 the first set corresponds to the reads from uninitialized
1998 array elements and the second set is empty.
1999 The actual flow dependences can be extracted using
2000 C<isl_flow_foreach>. This function will call the user-specified
2001 callback function C<fn> for each B<non-empty> dependence between
2002 a source and the sink. The callback function is called
2003 with four arguments, the actual flow dependence relation
2004 mapping source iterations to sink iterations, a boolean that
2005 indicates whether it is a I<must> or I<may> dependence, a token
2006 identifying the source and an additional C<void *> with value
2007 equal to the third argument of the C<isl_flow_foreach> call.
2008 A dependence is marked I<must> if it originates from a I<must>
2009 source and if it is not followed by any I<may> sources.
2011 After finishing with an C<isl_flow>, the user should call
2012 C<isl_flow_free> to free all associated memory.
2014 =head2 Parametric Vertex Enumeration
2016 The parametric vertex enumeration described in this section
2017 is mainly intended to be used internally and by the C<barvinok>
2020 #include <isl_vertices.h>
2021 __isl_give isl_vertices *isl_basic_set_compute_vertices(
2022 __isl_keep isl_basic_set *bset);
2024 The function C<isl_basic_set_compute_vertices> performs the
2025 actual computation of the parametric vertices and the chamber
2026 decomposition and store the result in an C<isl_vertices> object.
2027 This information can be queried by either iterating over all
2028 the vertices or iterating over all the chambers or cells
2029 and then iterating over all vertices that are active on the chamber.
2031 int isl_vertices_foreach_vertex(
2032 __isl_keep isl_vertices *vertices,
2033 int (*fn)(__isl_take isl_vertex *vertex, void *user),
2036 int isl_vertices_foreach_cell(
2037 __isl_keep isl_vertices *vertices,
2038 int (*fn)(__isl_take isl_cell *cell, void *user),
2040 int isl_cell_foreach_vertex(__isl_keep isl_cell *cell,
2041 int (*fn)(__isl_take isl_vertex *vertex, void *user),
2044 Other operations that can be performed on an C<isl_vertices> object are
2047 isl_ctx *isl_vertices_get_ctx(
2048 __isl_keep isl_vertices *vertices);
2049 int isl_vertices_get_n_vertices(
2050 __isl_keep isl_vertices *vertices);
2051 void isl_vertices_free(__isl_take isl_vertices *vertices);
2053 Vertices can be inspected and destroyed using the following functions.
2055 isl_ctx *isl_vertex_get_ctx(__isl_keep isl_vertex *vertex);
2056 int isl_vertex_get_id(__isl_keep isl_vertex *vertex);
2057 __isl_give isl_basic_set *isl_vertex_get_domain(
2058 __isl_keep isl_vertex *vertex);
2059 __isl_give isl_basic_set *isl_vertex_get_expr(
2060 __isl_keep isl_vertex *vertex);
2061 void isl_vertex_free(__isl_take isl_vertex *vertex);
2063 C<isl_vertex_get_expr> returns a singleton parametric set describing
2064 the vertex, while C<isl_vertex_get_domain> returns the activity domain
2066 Note that C<isl_vertex_get_domain> and C<isl_vertex_get_expr> return
2067 B<rational> basic sets, so they should mainly be used for inspection
2068 and should not be mixed with integer sets.
2070 Chambers can be inspected and destroyed using the following functions.
2072 isl_ctx *isl_cell_get_ctx(__isl_keep isl_cell *cell);
2073 __isl_give isl_basic_set *isl_cell_get_domain(
2074 __isl_keep isl_cell *cell);
2075 void isl_cell_free(__isl_take isl_cell *cell);
2079 Although C<isl> is mainly meant to be used as a library,
2080 it also contains some basic applications that use some
2081 of the functionality of C<isl>.
2082 The input may be specified in either the L<isl format>
2083 or the L<PolyLib format>.
2085 =head2 C<isl_polyhedron_sample>
2087 C<isl_polyhedron_sample> takes a polyhedron as input and prints
2088 an integer element of the polyhedron, if there is any.
2089 The first column in the output is the denominator and is always
2090 equal to 1. If the polyhedron contains no integer points,
2091 then a vector of length zero is printed.
2095 C<isl_pip> takes the same input as the C<example> program
2096 from the C<piplib> distribution, i.e., a set of constraints
2097 on the parameters, a line containing only -1 and finally a set
2098 of constraints on a parametric polyhedron.
2099 The coefficients of the parameters appear in the last columns
2100 (but before the final constant column).
2101 The output is the lexicographic minimum of the parametric polyhedron.
2102 As C<isl> currently does not have its own output format, the output
2103 is just a dump of the internal state.
2105 =head2 C<isl_polyhedron_minimize>
2107 C<isl_polyhedron_minimize> computes the minimum of some linear
2108 or affine objective function over the integer points in a polyhedron.
2109 If an affine objective function
2110 is given, then the constant should appear in the last column.
2112 =head2 C<isl_polytope_scan>
2114 Given a polytope, C<isl_polytope_scan> prints
2115 all integer points in the polytope.
2117 =head1 C<isl-polylib>
2119 The C<isl-polylib> library provides the following functions for converting
2120 between C<isl> objects and C<PolyLib> objects.
2121 The library is distributed separately for licensing reasons.
2123 #include <isl_set_polylib.h>
2124 __isl_give isl_basic_set *isl_basic_set_new_from_polylib(
2125 Polyhedron *P, __isl_take isl_dim *dim);
2126 Polyhedron *isl_basic_set_to_polylib(
2127 __isl_keep isl_basic_set *bset);
2128 __isl_give isl_set *isl_set_new_from_polylib(Polyhedron *D,
2129 __isl_take isl_dim *dim);
2130 Polyhedron *isl_set_to_polylib(__isl_keep isl_set *set);
2132 #include <isl_map_polylib.h>
2133 __isl_give isl_basic_map *isl_basic_map_new_from_polylib(
2134 Polyhedron *P, __isl_take isl_dim *dim);
2135 __isl_give isl_map *isl_map_new_from_polylib(Polyhedron *D,
2136 __isl_take isl_dim *dim);
2137 Polyhedron *isl_basic_map_to_polylib(
2138 __isl_keep isl_basic_map *bmap);
2139 Polyhedron *isl_map_to_polylib(__isl_keep isl_map *map);