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.
445 Pairs of C<isl_union_set> and/or C<isl_union_map> arguments may
446 have different parameters (as long as they are named), in which case
447 the result will have as parameters the union of the parameters of
450 The names of entire spaces may be set or read off
451 using the following functions.
454 __isl_give isl_dim *isl_dim_set_tuple_name(
455 __isl_take isl_dim *dim,
456 enum isl_dim_type type, const char *s);
457 const char *isl_dim_get_tuple_name(__isl_keep isl_dim *dim,
458 enum isl_dim_type type);
460 The C<dim> argument needs to be one of C<isl_dim_in>, C<isl_dim_out>
461 or C<isl_dim_set>. As with C<isl_dim_get_name>,
462 the C<isl_dim_get_tuple_name> function returns a pointer to some internal
464 Binary operations require the corresponding spaces of their arguments
465 to have the same name.
467 Spaces can be nested. In particular, the domain of a set or
468 the domain or range of a relation can be a nested relation.
469 The following functions can be used to construct and deconstruct
470 such nested dimension specifications.
473 int isl_dim_is_wrapping(__isl_keep isl_dim *dim);
474 __isl_give isl_dim *isl_dim_wrap(__isl_take isl_dim *dim);
475 __isl_give isl_dim *isl_dim_unwrap(__isl_take isl_dim *dim);
477 The input to C<isl_dim_is_wrapping> and C<isl_dim_unwrap> should
478 be the dimension specification of a set, while that of
479 C<isl_dim_wrap> should be the dimension specification of a relation.
480 Conversely, the output of C<isl_dim_unwrap> is the dimension specification
481 of a relation, while that of C<isl_dim_wrap> is the dimension specification
484 Dimension specifications can be created from other dimension
485 specifications using the following functions.
487 __isl_give isl_dim *isl_dim_domain(__isl_take isl_dim *dim);
488 __isl_give isl_dim *isl_dim_from_domain(__isl_take isl_dim *dim);
489 __isl_give isl_dim *isl_dim_range(__isl_take isl_dim *dim);
490 __isl_give isl_dim *isl_dim_from_range(__isl_take isl_dim *dim);
491 __isl_give isl_dim *isl_dim_reverse(__isl_take isl_dim *dim);
492 __isl_give isl_dim *isl_dim_join(__isl_take isl_dim *left,
493 __isl_take isl_dim *right);
494 __isl_give isl_dim *isl_dim_insert(__isl_take isl_dim *dim,
495 enum isl_dim_type type, unsigned pos, unsigned n);
496 __isl_give isl_dim *isl_dim_add(__isl_take isl_dim *dim,
497 enum isl_dim_type type, unsigned n);
498 __isl_give isl_dim *isl_dim_drop(__isl_take isl_dim *dim,
499 enum isl_dim_type type, unsigned first, unsigned n);
501 Note that if dimensions are added or removed from a space, then
502 the name and the internal structure are lost.
504 =head2 Input and Output
506 C<isl> supports its own input/output format, which is similar
507 to the C<Omega> format, but also supports the C<PolyLib> format
512 The C<isl> format is similar to that of C<Omega>, but has a different
513 syntax for describing the parameters and allows for the definition
514 of an existentially quantified variable as the integer division
515 of an affine expression.
516 For example, the set of integers C<i> between C<0> and C<n>
517 such that C<i % 10 <= 6> can be described as
519 [n] -> { [i] : exists (a = [i/10] : 0 <= i and i <= n and
522 A set or relation can have several disjuncts, separated
523 by the keyword C<or>. Each disjunct is either a conjunction
524 of constraints or a projection (C<exists>) of a conjunction
525 of constraints. The constraints are separated by the keyword
528 =head3 C<PolyLib> format
530 If the represented set is a union, then the first line
531 contains a single number representing the number of disjuncts.
532 Otherwise, a line containing the number C<1> is optional.
534 Each disjunct is represented by a matrix of constraints.
535 The first line contains two numbers representing
536 the number of rows and columns,
537 where the number of rows is equal to the number of constraints
538 and the number of columns is equal to two plus the number of variables.
539 The following lines contain the actual rows of the constraint matrix.
540 In each row, the first column indicates whether the constraint
541 is an equality (C<0>) or inequality (C<1>). The final column
542 corresponds to the constant term.
544 If the set is parametric, then the coefficients of the parameters
545 appear in the last columns before the constant column.
546 The coefficients of any existentially quantified variables appear
547 between those of the set variables and those of the parameters.
552 __isl_give isl_basic_set *isl_basic_set_read_from_file(
553 isl_ctx *ctx, FILE *input, int nparam);
554 __isl_give isl_basic_set *isl_basic_set_read_from_str(
555 isl_ctx *ctx, const char *str, int nparam);
556 __isl_give isl_set *isl_set_read_from_file(isl_ctx *ctx,
557 FILE *input, int nparam);
558 __isl_give isl_set *isl_set_read_from_str(isl_ctx *ctx,
559 const char *str, int nparam);
562 __isl_give isl_basic_map *isl_basic_map_read_from_file(
563 isl_ctx *ctx, FILE *input, int nparam);
564 __isl_give isl_basic_map *isl_basic_map_read_from_str(
565 isl_ctx *ctx, const char *str, int nparam);
566 __isl_give isl_map *isl_map_read_from_file(
567 struct isl_ctx *ctx, FILE *input, int nparam);
568 __isl_give isl_map *isl_map_read_from_str(isl_ctx *ctx,
569 const char *str, int nparam);
571 The input format is autodetected and may be either the C<PolyLib> format
572 or the C<isl> format.
573 C<nparam> specifies how many of the final columns in
574 the C<PolyLib> format correspond to parameters.
575 If input is given in the C<isl> format, then the number
576 of parameters needs to be equal to C<nparam>.
577 If C<nparam> is negative, then any number of parameters
578 is accepted in the C<isl> format and zero parameters
579 are assumed in the C<PolyLib> format.
583 Before anything can be printed, an C<isl_printer> needs to
586 __isl_give isl_printer *isl_printer_to_file(isl_ctx *ctx,
588 __isl_give isl_printer *isl_printer_to_str(isl_ctx *ctx);
589 void isl_printer_free(__isl_take isl_printer *printer);
590 __isl_give char *isl_printer_get_str(
591 __isl_keep isl_printer *printer);
593 The behavior of the printer can be modified in various ways
595 __isl_give isl_printer *isl_printer_set_output_format(
596 __isl_take isl_printer *p, int output_format);
597 __isl_give isl_printer *isl_printer_set_indent(
598 __isl_take isl_printer *p, int indent);
599 __isl_give isl_printer *isl_printer_set_prefix(
600 __isl_take isl_printer *p, const char *prefix);
601 __isl_give isl_printer *isl_printer_set_suffix(
602 __isl_take isl_printer *p, const char *suffix);
604 The C<output_format> may be either C<ISL_FORMAT_ISL>, C<ISL_FORMAT_OMEGA>
605 or C<ISL_FORMAT_POLYLIB> and defaults to C<ISL_FORMAT_ISL>.
606 Each line in the output is indented by C<indent> spaces
607 (default: 0), prefixed by C<prefix> and suffixed by C<suffix>.
608 In the C<PolyLib> format output,
609 the coefficients of the existentially quantified variables
610 appear between those of the set variables and those
613 To actually print something, use
616 __isl_give isl_printer *isl_printer_print_basic_set(
617 __isl_take isl_printer *printer,
618 __isl_keep isl_basic_set *bset);
619 __isl_give isl_printer *isl_printer_print_set(
620 __isl_take isl_printer *printer,
621 __isl_keep isl_set *set);
624 __isl_give isl_printer *isl_printer_print_basic_map(
625 __isl_take isl_printer *printer,
626 __isl_keep isl_basic_map *bmap);
627 __isl_give isl_printer *isl_printer_print_map(
628 __isl_take isl_printer *printer,
629 __isl_keep isl_map *map);
631 #include <isl_union_set.h>
632 __isl_give isl_printer *isl_printer_print_union_set(
633 __isl_take isl_printer *p,
634 __isl_keep isl_union_set *uset);
636 #include <isl_union_map.h>
637 __isl_give isl_printer *isl_printer_print_union_map(
638 __isl_take isl_printer *p,
639 __isl_keep isl_union_map *umap);
641 When called on a file printer, the following function flushes
642 the file. When called on a string printer, the buffer is cleared.
644 __isl_give isl_printer *isl_printer_flush(
645 __isl_take isl_printer *p);
647 =head2 Creating New Sets and Relations
649 C<isl> has functions for creating some standard sets and relations.
653 =item * Empty sets and relations
655 __isl_give isl_basic_set *isl_basic_set_empty(
656 __isl_take isl_dim *dim);
657 __isl_give isl_basic_map *isl_basic_map_empty(
658 __isl_take isl_dim *dim);
659 __isl_give isl_set *isl_set_empty(
660 __isl_take isl_dim *dim);
661 __isl_give isl_map *isl_map_empty(
662 __isl_take isl_dim *dim);
663 __isl_give isl_union_set *isl_union_set_empty(
664 __isl_take isl_dim *dim);
665 __isl_give isl_union_map *isl_union_map_empty(
666 __isl_take isl_dim *dim);
668 For C<isl_union_set>s and C<isl_union_map>s, the dimensions specification
669 is only used to specify the parameters.
671 =item * Universe sets and relations
673 __isl_give isl_basic_set *isl_basic_set_universe(
674 __isl_take isl_dim *dim);
675 __isl_give isl_basic_map *isl_basic_map_universe(
676 __isl_take isl_dim *dim);
677 __isl_give isl_set *isl_set_universe(
678 __isl_take isl_dim *dim);
679 __isl_give isl_map *isl_map_universe(
680 __isl_take isl_dim *dim);
682 =item * Identity relations
684 __isl_give isl_basic_map *isl_basic_map_identity(
685 __isl_take isl_dim *set_dim);
686 __isl_give isl_map *isl_map_identity(
687 __isl_take isl_dim *set_dim);
689 These functions take a dimension specification for a B<set>
690 and return an identity relation between two such sets.
692 =item * Lexicographic order
694 __isl_give isl_map *isl_map_lex_lt(
695 __isl_take isl_dim *set_dim);
696 __isl_give isl_map *isl_map_lex_le(
697 __isl_take isl_dim *set_dim);
698 __isl_give isl_map *isl_map_lex_gt(
699 __isl_take isl_dim *set_dim);
700 __isl_give isl_map *isl_map_lex_ge(
701 __isl_take isl_dim *set_dim);
702 __isl_give isl_map *isl_map_lex_lt_first(
703 __isl_take isl_dim *dim, unsigned n);
704 __isl_give isl_map *isl_map_lex_le_first(
705 __isl_take isl_dim *dim, unsigned n);
706 __isl_give isl_map *isl_map_lex_gt_first(
707 __isl_take isl_dim *dim, unsigned n);
708 __isl_give isl_map *isl_map_lex_ge_first(
709 __isl_take isl_dim *dim, unsigned n);
711 The first four functions take a dimension specification for a B<set>
712 and return relations that express that the elements in the domain
713 are lexicographically less
714 (C<isl_map_lex_lt>), less or equal (C<isl_map_lex_le>),
715 greater (C<isl_map_lex_gt>) or greater or equal (C<isl_map_lex_ge>)
716 than the elements in the range.
717 The last four functions take a dimension specification for a map
718 and return relations that express that the first C<n> dimensions
719 in the domain are lexicographically less
720 (C<isl_map_lex_lt_first>), less or equal (C<isl_map_lex_le_first>),
721 greater (C<isl_map_lex_gt_first>) or greater or equal (C<isl_map_lex_ge_first>)
722 than the first C<n> dimensions in the range.
726 A basic set or relation can be converted to a set or relation
727 using the following functions.
729 __isl_give isl_set *isl_set_from_basic_set(
730 __isl_take isl_basic_set *bset);
731 __isl_give isl_map *isl_map_from_basic_map(
732 __isl_take isl_basic_map *bmap);
734 Sets and relations can be converted to union sets and relations
735 using the following functions.
737 __isl_give isl_union_map *isl_union_map_from_map(
738 __isl_take isl_map *map);
739 __isl_give isl_union_set *isl_union_set_from_set(
740 __isl_take isl_set *set);
742 Sets and relations can be copied and freed again using the following
745 __isl_give isl_basic_set *isl_basic_set_copy(
746 __isl_keep isl_basic_set *bset);
747 __isl_give isl_set *isl_set_copy(__isl_keep isl_set *set);
748 __isl_give isl_union_set *isl_union_set_copy(
749 __isl_keep isl_union_set *uset);
750 __isl_give isl_basic_map *isl_basic_map_copy(
751 __isl_keep isl_basic_map *bmap);
752 __isl_give isl_map *isl_map_copy(__isl_keep isl_map *map);
753 __isl_give isl_union_map *isl_union_map_copy(
754 __isl_keep isl_union_map *umap);
755 void isl_basic_set_free(__isl_take isl_basic_set *bset);
756 void isl_set_free(__isl_take isl_set *set);
757 void isl_union_set_free(__isl_take isl_union_set *uset);
758 void isl_basic_map_free(__isl_take isl_basic_map *bmap);
759 void isl_map_free(__isl_take isl_map *map);
760 void isl_union_map_free(__isl_take isl_union_map *umap);
762 Other sets and relations can be constructed by starting
763 from a universe set or relation, adding equality and/or
764 inequality constraints and then projecting out the
765 existentially quantified variables, if any.
766 Constraints can be constructed, manipulated and
767 added to basic sets and relations using the following functions.
769 #include <isl_constraint.h>
770 __isl_give isl_constraint *isl_equality_alloc(
771 __isl_take isl_dim *dim);
772 __isl_give isl_constraint *isl_inequality_alloc(
773 __isl_take isl_dim *dim);
774 void isl_constraint_set_constant(
775 __isl_keep isl_constraint *constraint, isl_int v);
776 void isl_constraint_set_coefficient(
777 __isl_keep isl_constraint *constraint,
778 enum isl_dim_type type, int pos, isl_int v);
779 __isl_give isl_basic_map *isl_basic_map_add_constraint(
780 __isl_take isl_basic_map *bmap,
781 __isl_take isl_constraint *constraint);
782 __isl_give isl_basic_set *isl_basic_set_add_constraint(
783 __isl_take isl_basic_set *bset,
784 __isl_take isl_constraint *constraint);
786 For example, to create a set containing the even integers
787 between 10 and 42, you would use the following code.
791 struct isl_constraint *c;
792 struct isl_basic_set *bset;
795 dim = isl_dim_set_alloc(ctx, 0, 2);
796 bset = isl_basic_set_universe(isl_dim_copy(dim));
798 c = isl_equality_alloc(isl_dim_copy(dim));
799 isl_int_set_si(v, -1);
800 isl_constraint_set_coefficient(c, isl_dim_set, 0, v);
801 isl_int_set_si(v, 2);
802 isl_constraint_set_coefficient(c, isl_dim_set, 1, v);
803 bset = isl_basic_set_add_constraint(bset, c);
805 c = isl_inequality_alloc(isl_dim_copy(dim));
806 isl_int_set_si(v, -10);
807 isl_constraint_set_constant(c, v);
808 isl_int_set_si(v, 1);
809 isl_constraint_set_coefficient(c, isl_dim_set, 0, v);
810 bset = isl_basic_set_add_constraint(bset, c);
812 c = isl_inequality_alloc(dim);
813 isl_int_set_si(v, 42);
814 isl_constraint_set_constant(c, v);
815 isl_int_set_si(v, -1);
816 isl_constraint_set_coefficient(c, isl_dim_set, 0, v);
817 bset = isl_basic_set_add_constraint(bset, c);
819 bset = isl_basic_set_project_out(bset, isl_dim_set, 1, 1);
825 struct isl_basic_set *bset;
826 bset = isl_basic_set_read_from_str(ctx,
827 "{[i] : exists (a : i = 2a and i >= 10 and i <= 42)}", -1);
829 A basic set or relation can also be constructed from two matrices
830 describing the equalities and the inequalities.
832 __isl_give isl_basic_set *isl_basic_set_from_constraint_matrices(
833 __isl_take isl_dim *dim,
834 __isl_take isl_mat *eq, __isl_take isl_mat *ineq,
835 enum isl_dim_type c1,
836 enum isl_dim_type c2, enum isl_dim_type c3,
837 enum isl_dim_type c4);
838 __isl_give isl_basic_map *isl_basic_map_from_constraint_matrices(
839 __isl_take isl_dim *dim,
840 __isl_take isl_mat *eq, __isl_take isl_mat *ineq,
841 enum isl_dim_type c1,
842 enum isl_dim_type c2, enum isl_dim_type c3,
843 enum isl_dim_type c4, enum isl_dim_type c5);
845 The C<isl_dim_type> arguments indicate the order in which
846 different kinds of variables appear in the input matrices
847 and should be a permutation of C<isl_dim_cst>, C<isl_dim_param>,
848 C<isl_dim_set> and C<isl_dim_div> for sets and
849 of C<isl_dim_cst>, C<isl_dim_param>,
850 C<isl_dim_in>, C<isl_dim_out> and C<isl_dim_div> for relations.
852 =head2 Inspecting Sets and Relations
854 Usually, the user should not have to care about the actual constraints
855 of the sets and maps, but should instead apply the abstract operations
856 explained in the following sections.
857 Occasionally, however, it may be required to inspect the individual
858 coefficients of the constraints. This section explains how to do so.
859 In these cases, it may also be useful to have C<isl> compute
860 an explicit representation of the existentially quantified variables.
862 __isl_give isl_set *isl_set_compute_divs(
863 __isl_take isl_set *set);
864 __isl_give isl_map *isl_map_compute_divs(
865 __isl_take isl_map *map);
866 __isl_give isl_union_set *isl_union_set_compute_divs(
867 __isl_take isl_union_set *uset);
868 __isl_give isl_union_map *isl_union_map_compute_divs(
869 __isl_take isl_union_map *umap);
871 This explicit representation defines the existentially quantified
872 variables as integer divisions of the other variables, possibly
873 including earlier existentially quantified variables.
874 An explicitly represented existentially quantified variable therefore
875 has a unique value when the values of the other variables are known.
876 If, furthermore, the same existentials, i.e., existentials
877 with the same explicit representations, should appear in the
878 same order in each of the disjuncts of a set or map, then the user should call
879 either of the following functions.
881 __isl_give isl_set *isl_set_align_divs(
882 __isl_take isl_set *set);
883 __isl_give isl_map *isl_map_align_divs(
884 __isl_take isl_map *map);
886 Alternatively, the existentially quantified variables can be removed
887 using the following functions, which compute an overapproximation.
889 __isl_give isl_basic_set *isl_basic_set_remove_divs(
890 __isl_take isl_basic_set *bset);
891 __isl_give isl_basic_map *isl_basic_map_remove_divs(
892 __isl_take isl_basic_map *bmap);
893 __isl_give isl_set *isl_set_remove_divs(
894 __isl_take isl_set *set);
896 To iterate over all the sets or maps in a union set or map, use
898 int isl_union_set_foreach_set(__isl_keep isl_union_set *uset,
899 int (*fn)(__isl_take isl_set *set, void *user),
901 int isl_union_map_foreach_map(__isl_keep isl_union_map *umap,
902 int (*fn)(__isl_take isl_map *map, void *user),
905 To iterate over all the basic sets or maps in a set or map, use
907 int isl_set_foreach_basic_set(__isl_keep isl_set *set,
908 int (*fn)(__isl_take isl_basic_set *bset, void *user),
910 int isl_map_foreach_basic_map(__isl_keep isl_map *map,
911 int (*fn)(__isl_take isl_basic_map *bmap, void *user),
914 The callback function C<fn> should return 0 if successful and
915 -1 if an error occurs. In the latter case, or if any other error
916 occurs, the above functions will return -1.
918 It should be noted that C<isl> does not guarantee that
919 the basic sets or maps passed to C<fn> are disjoint.
920 If this is required, then the user should call one of
921 the following functions first.
923 __isl_give isl_set *isl_set_make_disjoint(
924 __isl_take isl_set *set);
925 __isl_give isl_map *isl_map_make_disjoint(
926 __isl_take isl_map *map);
928 To iterate over the constraints of a basic set or map, use
930 #include <isl_constraint.h>
932 int isl_basic_map_foreach_constraint(
933 __isl_keep isl_basic_map *bmap,
934 int (*fn)(__isl_take isl_constraint *c, void *user),
936 void isl_constraint_free(struct isl_constraint *c);
938 Again, the callback function C<fn> should return 0 if successful and
939 -1 if an error occurs. In the latter case, or if any other error
940 occurs, the above functions will return -1.
941 The constraint C<c> represents either an equality or an inequality.
942 Use the following function to find out whether a constraint
943 represents an equality. If not, it represents an inequality.
945 int isl_constraint_is_equality(
946 __isl_keep isl_constraint *constraint);
948 The coefficients of the constraints can be inspected using
949 the following functions.
951 void isl_constraint_get_constant(
952 __isl_keep isl_constraint *constraint, isl_int *v);
953 void isl_constraint_get_coefficient(
954 __isl_keep isl_constraint *constraint,
955 enum isl_dim_type type, int pos, isl_int *v);
957 The explicit representations of the existentially quantified
958 variables can be inspected using the following functions.
959 Note that the user is only allowed to use these functions
960 if the inspected set or map is the result of a call
961 to C<isl_set_compute_divs> or C<isl_map_compute_divs>.
963 __isl_give isl_div *isl_constraint_div(
964 __isl_keep isl_constraint *constraint, int pos);
965 void isl_div_get_constant(__isl_keep isl_div *div,
967 void isl_div_get_denominator(__isl_keep isl_div *div,
969 void isl_div_get_coefficient(__isl_keep isl_div *div,
970 enum isl_dim_type type, int pos, isl_int *v);
972 To obtain the constraints of a basic map in matrix
973 form, use the following functions.
975 __isl_give isl_mat *isl_basic_map_equalities_matrix(
976 __isl_keep isl_basic_map *bmap,
977 enum isl_dim_type c1,
978 enum isl_dim_type c2, enum isl_dim_type c3,
979 enum isl_dim_type c4, enum isl_dim_type c5);
980 __isl_give isl_mat *isl_basic_map_inequalities_matrix(
981 __isl_keep isl_basic_map *bmap,
982 enum isl_dim_type c1,
983 enum isl_dim_type c2, enum isl_dim_type c3,
984 enum isl_dim_type c4, enum isl_dim_type c5);
986 The C<isl_dim_type> arguments dictate the order in which
987 different kinds of variables appear in the resulting matrix
988 and should be a permutation of C<isl_dim_cst>, C<isl_dim_param>,
989 C<isl_dim_in>, C<isl_dim_out> and C<isl_dim_div>.
991 The names of the domain and range spaces of a relation can be
992 read off using the following function.
994 const char *isl_basic_map_get_tuple_name(
995 __isl_keep isl_basic_map *bmap,
996 enum isl_dim_type type);
998 As with C<isl_dim_get_tuple_name>, the value returned points to
999 an internal data structure.
1003 =head3 Unary Properties
1009 The following functions test whether the given set or relation
1010 contains any integer points. The ``fast'' variants do not perform
1011 any computations, but simply check if the given set or relation
1012 is already known to be empty.
1014 int isl_basic_set_fast_is_empty(__isl_keep isl_basic_set *bset);
1015 int isl_basic_set_is_empty(__isl_keep isl_basic_set *bset);
1016 int isl_set_is_empty(__isl_keep isl_set *set);
1017 int isl_union_set_is_empty(__isl_keep isl_union_set *uset);
1018 int isl_basic_map_fast_is_empty(__isl_keep isl_basic_map *bmap);
1019 int isl_basic_map_is_empty(__isl_keep isl_basic_map *bmap);
1020 int isl_map_fast_is_empty(__isl_keep isl_map *map);
1021 int isl_map_is_empty(__isl_keep isl_map *map);
1022 int isl_union_map_is_empty(__isl_keep isl_union_map *umap);
1024 =item * Universality
1026 int isl_basic_set_is_universe(__isl_keep isl_basic_set *bset);
1027 int isl_basic_map_is_universe(__isl_keep isl_basic_map *bmap);
1028 int isl_set_fast_is_universe(__isl_keep isl_set *set);
1030 =item * Single-valuedness
1032 int isl_map_is_single_valued(__isl_keep isl_map *map);
1036 int isl_map_is_bijective(__isl_keep isl_map *map);
1040 The followning functions check whether the domain of the given
1041 (basic) set is a wrapped relation.
1043 int isl_basic_set_is_wrapping(
1044 __isl_keep isl_basic_set *bset);
1045 int isl_set_is_wrapping(__isl_keep isl_set *set);
1049 =head3 Binary Properties
1055 int isl_set_fast_is_equal(__isl_keep isl_set *set1,
1056 __isl_keep isl_set *set2);
1057 int isl_set_is_equal(__isl_keep isl_set *set1,
1058 __isl_keep isl_set *set2);
1059 int isl_basic_map_is_equal(
1060 __isl_keep isl_basic_map *bmap1,
1061 __isl_keep isl_basic_map *bmap2);
1062 int isl_map_is_equal(__isl_keep isl_map *map1,
1063 __isl_keep isl_map *map2);
1064 int isl_map_fast_is_equal(__isl_keep isl_map *map1,
1065 __isl_keep isl_map *map2);
1066 int isl_union_map_is_equal(
1067 __isl_keep isl_union_map *umap1,
1068 __isl_keep isl_union_map *umap2);
1070 =item * Disjointness
1072 int isl_set_fast_is_disjoint(__isl_keep isl_set *set1,
1073 __isl_keep isl_set *set2);
1077 int isl_set_is_subset(__isl_keep isl_set *set1,
1078 __isl_keep isl_set *set2);
1079 int isl_set_is_strict_subset(
1080 __isl_keep isl_set *set1,
1081 __isl_keep isl_set *set2);
1082 int isl_basic_map_is_subset(
1083 __isl_keep isl_basic_map *bmap1,
1084 __isl_keep isl_basic_map *bmap2);
1085 int isl_basic_map_is_strict_subset(
1086 __isl_keep isl_basic_map *bmap1,
1087 __isl_keep isl_basic_map *bmap2);
1088 int isl_map_is_subset(
1089 __isl_keep isl_map *map1,
1090 __isl_keep isl_map *map2);
1091 int isl_map_is_strict_subset(
1092 __isl_keep isl_map *map1,
1093 __isl_keep isl_map *map2);
1094 int isl_union_map_is_subset(
1095 __isl_keep isl_union_map *umap1,
1096 __isl_keep isl_union_map *umap2);
1097 int isl_union_map_is_strict_subset(
1098 __isl_keep isl_union_map *umap1,
1099 __isl_keep isl_union_map *umap2);
1103 =head2 Unary Operations
1109 __isl_give isl_set *isl_set_complement(
1110 __isl_take isl_set *set);
1114 __isl_give isl_basic_map *isl_basic_map_reverse(
1115 __isl_take isl_basic_map *bmap);
1116 __isl_give isl_map *isl_map_reverse(
1117 __isl_take isl_map *map);
1118 __isl_give isl_union_map *isl_union_map_reverse(
1119 __isl_take isl_union_map *umap);
1123 __isl_give isl_basic_set *isl_basic_set_project_out(
1124 __isl_take isl_basic_set *bset,
1125 enum isl_dim_type type, unsigned first, unsigned n);
1126 __isl_give isl_basic_map *isl_basic_map_project_out(
1127 __isl_take isl_basic_map *bmap,
1128 enum isl_dim_type type, unsigned first, unsigned n);
1129 __isl_give isl_set *isl_set_project_out(__isl_take isl_set *set,
1130 enum isl_dim_type type, unsigned first, unsigned n);
1131 __isl_give isl_map *isl_map_project_out(__isl_take isl_map *map,
1132 enum isl_dim_type type, unsigned first, unsigned n);
1133 __isl_give isl_basic_set *isl_basic_map_domain(
1134 __isl_take isl_basic_map *bmap);
1135 __isl_give isl_basic_set *isl_basic_map_range(
1136 __isl_take isl_basic_map *bmap);
1137 __isl_give isl_set *isl_map_domain(
1138 __isl_take isl_map *bmap);
1139 __isl_give isl_set *isl_map_range(
1140 __isl_take isl_map *map);
1141 __isl_give isl_union_set *isl_union_map_domain(
1142 __isl_take isl_union_map *umap);
1143 __isl_give isl_union_set *isl_union_map_range(
1144 __isl_take isl_union_map *umap);
1146 __isl_give isl_basic_map *isl_basic_map_domain_map(
1147 __isl_take isl_basic_map *bmap);
1148 __isl_give isl_basic_map *isl_basic_map_range_map(
1149 __isl_take isl_basic_map *bmap);
1150 __isl_give isl_map *isl_map_domain_map(__isl_take isl_map *map);
1151 __isl_give isl_map *isl_map_range_map(__isl_take isl_map *map);
1152 __isl_give isl_union_map *isl_union_map_domain_map(
1153 __isl_take isl_union_map *umap);
1154 __isl_give isl_union_map *isl_union_map_range_map(
1155 __isl_take isl_union_map *umap);
1157 The functions above construct a (basic, regular or union) relation
1158 that maps (a wrapped version of) the input relation to its domain or range.
1162 __isl_give isl_basic_set *isl_basic_map_deltas(
1163 __isl_take isl_basic_map *bmap);
1164 __isl_give isl_set *isl_map_deltas(__isl_take isl_map *map);
1165 __isl_give isl_union_set *isl_union_map_deltas(
1166 __isl_take isl_union_map *umap);
1168 These functions return a (basic) set containing the differences
1169 between image elements and corresponding domain elements in the input.
1173 Simplify the representation of a set or relation by trying
1174 to combine pairs of basic sets or relations into a single
1175 basic set or relation.
1177 __isl_give isl_set *isl_set_coalesce(__isl_take isl_set *set);
1178 __isl_give isl_map *isl_map_coalesce(__isl_take isl_map *map);
1179 __isl_give isl_union_set *isl_union_set_coalesce(
1180 __isl_take isl_union_set *uset);
1181 __isl_give isl_union_map *isl_union_map_coalesce(
1182 __isl_take isl_union_map *umap);
1186 __isl_give isl_basic_set *isl_set_convex_hull(
1187 __isl_take isl_set *set);
1188 __isl_give isl_basic_map *isl_map_convex_hull(
1189 __isl_take isl_map *map);
1191 If the input set or relation has any existentially quantified
1192 variables, then the result of these operations is currently undefined.
1196 __isl_give isl_basic_set *isl_set_simple_hull(
1197 __isl_take isl_set *set);
1198 __isl_give isl_basic_map *isl_map_simple_hull(
1199 __isl_take isl_map *map);
1201 These functions compute a single basic set or relation
1202 that contains the whole input set or relation.
1203 In particular, the output is described by translates
1204 of the constraints describing the basic sets or relations in the input.
1208 (See \autoref{s:simple hull}.)
1214 __isl_give isl_basic_set *isl_basic_set_affine_hull(
1215 __isl_take isl_basic_set *bset);
1216 __isl_give isl_basic_set *isl_set_affine_hull(
1217 __isl_take isl_set *set);
1218 __isl_give isl_union_set *isl_union_set_affine_hull(
1219 __isl_take isl_union_set *uset);
1220 __isl_give isl_basic_map *isl_basic_map_affine_hull(
1221 __isl_take isl_basic_map *bmap);
1222 __isl_give isl_basic_map *isl_map_affine_hull(
1223 __isl_take isl_map *map);
1224 __isl_give isl_union_map *isl_union_map_affine_hull(
1225 __isl_take isl_union_map *umap);
1227 In case of union sets and relations, the affine hull is computed
1232 __isl_give isl_map *isl_map_power(__isl_take isl_map *map,
1233 unsigned param, int *exact);
1235 Compute a parametric representation for all positive powers I<k> of C<map>.
1236 The power I<k> is equated to the parameter at position C<param>.
1237 The result may be an overapproximation. If the result is exact,
1238 then C<*exact> is set to C<1>.
1239 The current implementation only produces exact results for particular
1240 cases of piecewise translations (i.e., piecewise uniform dependences).
1242 =item * Transitive closure
1244 __isl_give isl_map *isl_map_transitive_closure(
1245 __isl_take isl_map *map, int *exact);
1246 __isl_give isl_union_map *isl_union_map_transitive_closure(
1247 __isl_take isl_union_map *umap, int *exact);
1249 Compute the transitive closure of C<map>.
1250 The result may be an overapproximation. If the result is known to be exact,
1251 then C<*exact> is set to C<1>.
1252 The current implementation only produces exact results for particular
1253 cases of piecewise translations (i.e., piecewise uniform dependences).
1255 =item * Reaching path lengths
1257 __isl_give isl_map *isl_map_reaching_path_lengths(
1258 __isl_take isl_map *map, int *exact);
1260 Compute a relation that maps each element in the range of C<map>
1261 to the lengths of all paths composed of edges in C<map> that
1262 end up in the given element.
1263 The result may be an overapproximation. If the result is known to be exact,
1264 then C<*exact> is set to C<1>.
1265 To compute the I<maximal> path length, the resulting relation
1266 should be postprocessed by C<isl_map_lexmax>.
1267 In particular, if the input relation is a dependence relation
1268 (mapping sources to sinks), then the maximal path length corresponds
1269 to the free schedule.
1270 Note, however, that C<isl_map_lexmax> expects the maximum to be
1271 finite, so if the path lengths are unbounded (possibly due to
1272 the overapproximation), then you will get an error message.
1276 __isl_give isl_basic_set *isl_basic_map_wrap(
1277 __isl_take isl_basic_map *bmap);
1278 __isl_give isl_set *isl_map_wrap(
1279 __isl_take isl_map *map);
1280 __isl_give isl_union_set *isl_union_map_wrap(
1281 __isl_take isl_union_map *umap);
1282 __isl_give isl_basic_map *isl_basic_set_unwrap(
1283 __isl_take isl_basic_set *bset);
1284 __isl_give isl_map *isl_set_unwrap(
1285 __isl_take isl_set *set);
1286 __isl_give isl_union_map *isl_union_set_unwrap(
1287 __isl_take isl_union_set *uset);
1289 =item * Dimension manipulation
1291 __isl_give isl_set *isl_set_add_dims(
1292 __isl_take isl_set *set,
1293 enum isl_dim_type type, unsigned n);
1294 __isl_give isl_map *isl_map_add_dims(
1295 __isl_take isl_map *map,
1296 enum isl_dim_type type, unsigned n);
1298 It is usually not advisable to directly change the (input or output)
1299 space of a set or a relation as this removes the name and the internal
1300 structure of the space. However, the above functions can be useful
1301 to add new parameters.
1305 =head2 Binary Operations
1307 The two arguments of a binary operation not only need to live
1308 in the same C<isl_ctx>, they currently also need to have
1309 the same (number of) parameters.
1311 =head3 Basic Operations
1315 =item * Intersection
1317 __isl_give isl_basic_set *isl_basic_set_intersect(
1318 __isl_take isl_basic_set *bset1,
1319 __isl_take isl_basic_set *bset2);
1320 __isl_give isl_set *isl_set_intersect(
1321 __isl_take isl_set *set1,
1322 __isl_take isl_set *set2);
1323 __isl_give isl_union_set *isl_union_set_intersect(
1324 __isl_take isl_union_set *uset1,
1325 __isl_take isl_union_set *uset2);
1326 __isl_give isl_basic_map *isl_basic_map_intersect_domain(
1327 __isl_take isl_basic_map *bmap,
1328 __isl_take isl_basic_set *bset);
1329 __isl_give isl_basic_map *isl_basic_map_intersect_range(
1330 __isl_take isl_basic_map *bmap,
1331 __isl_take isl_basic_set *bset);
1332 __isl_give isl_basic_map *isl_basic_map_intersect(
1333 __isl_take isl_basic_map *bmap1,
1334 __isl_take isl_basic_map *bmap2);
1335 __isl_give isl_map *isl_map_intersect_domain(
1336 __isl_take isl_map *map,
1337 __isl_take isl_set *set);
1338 __isl_give isl_map *isl_map_intersect_range(
1339 __isl_take isl_map *map,
1340 __isl_take isl_set *set);
1341 __isl_give isl_map *isl_map_intersect(
1342 __isl_take isl_map *map1,
1343 __isl_take isl_map *map2);
1344 __isl_give isl_union_map *isl_union_map_intersect_domain(
1345 __isl_take isl_union_map *umap,
1346 __isl_take isl_union_set *uset);
1347 __isl_give isl_union_map *isl_union_map_intersect(
1348 __isl_take isl_union_map *umap1,
1349 __isl_take isl_union_map *umap2);
1353 __isl_give isl_set *isl_basic_set_union(
1354 __isl_take isl_basic_set *bset1,
1355 __isl_take isl_basic_set *bset2);
1356 __isl_give isl_map *isl_basic_map_union(
1357 __isl_take isl_basic_map *bmap1,
1358 __isl_take isl_basic_map *bmap2);
1359 __isl_give isl_set *isl_set_union(
1360 __isl_take isl_set *set1,
1361 __isl_take isl_set *set2);
1362 __isl_give isl_map *isl_map_union(
1363 __isl_take isl_map *map1,
1364 __isl_take isl_map *map2);
1365 __isl_give isl_union_set *isl_union_set_union(
1366 __isl_take isl_union_set *uset1,
1367 __isl_take isl_union_set *uset2);
1368 __isl_give isl_union_map *isl_union_map_union(
1369 __isl_take isl_union_map *umap1,
1370 __isl_take isl_union_map *umap2);
1372 =item * Set difference
1374 __isl_give isl_set *isl_set_subtract(
1375 __isl_take isl_set *set1,
1376 __isl_take isl_set *set2);
1377 __isl_give isl_map *isl_map_subtract(
1378 __isl_take isl_map *map1,
1379 __isl_take isl_map *map2);
1380 __isl_give isl_union_set *isl_union_set_subtract(
1381 __isl_take isl_union_set *uset1,
1382 __isl_take isl_union_set *uset2);
1383 __isl_give isl_union_map *isl_union_map_subtract(
1384 __isl_take isl_union_map *umap1,
1385 __isl_take isl_union_map *umap2);
1389 __isl_give isl_basic_set *isl_basic_set_apply(
1390 __isl_take isl_basic_set *bset,
1391 __isl_take isl_basic_map *bmap);
1392 __isl_give isl_set *isl_set_apply(
1393 __isl_take isl_set *set,
1394 __isl_take isl_map *map);
1395 __isl_give isl_union_set *isl_union_set_apply(
1396 __isl_take isl_union_set *uset,
1397 __isl_take isl_union_map *umap);
1398 __isl_give isl_basic_map *isl_basic_map_apply_domain(
1399 __isl_take isl_basic_map *bmap1,
1400 __isl_take isl_basic_map *bmap2);
1401 __isl_give isl_basic_map *isl_basic_map_apply_range(
1402 __isl_take isl_basic_map *bmap1,
1403 __isl_take isl_basic_map *bmap2);
1404 __isl_give isl_map *isl_map_apply_domain(
1405 __isl_take isl_map *map1,
1406 __isl_take isl_map *map2);
1407 __isl_give isl_union_map *isl_union_map_apply_domain(
1408 __isl_take isl_union_map *umap1,
1409 __isl_take isl_union_map *umap2);
1410 __isl_give isl_map *isl_map_apply_range(
1411 __isl_take isl_map *map1,
1412 __isl_take isl_map *map2);
1413 __isl_give isl_union_map *isl_union_map_apply_range(
1414 __isl_take isl_union_map *umap1,
1415 __isl_take isl_union_map *umap2);
1417 =item * Simplification
1419 __isl_give isl_basic_set *isl_basic_set_gist(
1420 __isl_take isl_basic_set *bset,
1421 __isl_take isl_basic_set *context);
1422 __isl_give isl_set *isl_set_gist(__isl_take isl_set *set,
1423 __isl_take isl_set *context);
1424 __isl_give isl_union_set *isl_union_set_gist(
1425 __isl_take isl_union_set *uset,
1426 __isl_take isl_union_set *context);
1427 __isl_give isl_basic_map *isl_basic_map_gist(
1428 __isl_take isl_basic_map *bmap,
1429 __isl_take isl_basic_map *context);
1430 __isl_give isl_map *isl_map_gist(__isl_take isl_map *map,
1431 __isl_take isl_map *context);
1432 __isl_give isl_union_map *isl_union_map_gist(
1433 __isl_take isl_union_map *umap,
1434 __isl_take isl_union_map *context);
1436 The gist operation returns a set or relation that has the
1437 same intersection with the context as the input set or relation.
1438 Any implicit equality in the intersection is made explicit in the result,
1439 while all inequalities that are redundant with respect to the intersection
1441 In case of union sets and relations, the gist operation is performed
1446 =head3 Lexicographic Optimization
1448 Given a (basic) set C<set> (or C<bset>) and a zero-dimensional domain C<dom>,
1449 the following functions
1450 compute a set that contains the lexicographic minimum or maximum
1451 of the elements in C<set> (or C<bset>) for those values of the parameters
1452 that satisfy C<dom>.
1453 If C<empty> is not C<NULL>, then C<*empty> is assigned a set
1454 that contains the parameter values in C<dom> for which C<set> (or C<bset>)
1456 In other words, the union of the parameter values
1457 for which the result is non-empty and of C<*empty>
1460 __isl_give isl_set *isl_basic_set_partial_lexmin(
1461 __isl_take isl_basic_set *bset,
1462 __isl_take isl_basic_set *dom,
1463 __isl_give isl_set **empty);
1464 __isl_give isl_set *isl_basic_set_partial_lexmax(
1465 __isl_take isl_basic_set *bset,
1466 __isl_take isl_basic_set *dom,
1467 __isl_give isl_set **empty);
1468 __isl_give isl_set *isl_set_partial_lexmin(
1469 __isl_take isl_set *set, __isl_take isl_set *dom,
1470 __isl_give isl_set **empty);
1471 __isl_give isl_set *isl_set_partial_lexmax(
1472 __isl_take isl_set *set, __isl_take isl_set *dom,
1473 __isl_give isl_set **empty);
1475 Given a (basic) set C<set> (or C<bset>), the following functions simply
1476 return a set containing the lexicographic minimum or maximum
1477 of the elements in C<set> (or C<bset>).
1478 In case of union sets, the optimum is computed per space.
1480 __isl_give isl_set *isl_basic_set_lexmin(
1481 __isl_take isl_basic_set *bset);
1482 __isl_give isl_set *isl_basic_set_lexmax(
1483 __isl_take isl_basic_set *bset);
1484 __isl_give isl_set *isl_set_lexmin(
1485 __isl_take isl_set *set);
1486 __isl_give isl_set *isl_set_lexmax(
1487 __isl_take isl_set *set);
1488 __isl_give isl_union_set *isl_union_set_lexmin(
1489 __isl_take isl_union_set *uset);
1490 __isl_give isl_union_set *isl_union_set_lexmax(
1491 __isl_take isl_union_set *uset);
1493 Given a (basic) relation C<map> (or C<bmap>) and a domain C<dom>,
1494 the following functions
1495 compute a relation that maps each element of C<dom>
1496 to the single lexicographic minimum or maximum
1497 of the elements that are associated to that same
1498 element in C<map> (or C<bmap>).
1499 If C<empty> is not C<NULL>, then C<*empty> is assigned a set
1500 that contains the elements in C<dom> that do not map
1501 to any elements in C<map> (or C<bmap>).
1502 In other words, the union of the domain of the result and of C<*empty>
1505 __isl_give isl_map *isl_basic_map_partial_lexmax(
1506 __isl_take isl_basic_map *bmap,
1507 __isl_take isl_basic_set *dom,
1508 __isl_give isl_set **empty);
1509 __isl_give isl_map *isl_basic_map_partial_lexmin(
1510 __isl_take isl_basic_map *bmap,
1511 __isl_take isl_basic_set *dom,
1512 __isl_give isl_set **empty);
1513 __isl_give isl_map *isl_map_partial_lexmax(
1514 __isl_take isl_map *map, __isl_take isl_set *dom,
1515 __isl_give isl_set **empty);
1516 __isl_give isl_map *isl_map_partial_lexmin(
1517 __isl_take isl_map *map, __isl_take isl_set *dom,
1518 __isl_give isl_set **empty);
1520 Given a (basic) map C<map> (or C<bmap>), the following functions simply
1521 return a map mapping each element in the domain of
1522 C<map> (or C<bmap>) to the lexicographic minimum or maximum
1523 of all elements associated to that element.
1524 In case of union relations, the optimum is computed per space.
1526 __isl_give isl_map *isl_basic_map_lexmin(
1527 __isl_take isl_basic_map *bmap);
1528 __isl_give isl_map *isl_basic_map_lexmax(
1529 __isl_take isl_basic_map *bmap);
1530 __isl_give isl_map *isl_map_lexmin(
1531 __isl_take isl_map *map);
1532 __isl_give isl_map *isl_map_lexmax(
1533 __isl_take isl_map *map);
1534 __isl_give isl_union_map *isl_union_map_lexmin(
1535 __isl_take isl_union_map *umap);
1536 __isl_give isl_union_map *isl_union_map_lexmax(
1537 __isl_take isl_union_map *umap);
1541 Matrices can be created, copied and freed using the following functions.
1543 #include <isl_mat.h>
1544 __isl_give isl_mat *isl_mat_alloc(struct isl_ctx *ctx,
1545 unsigned n_row, unsigned n_col);
1546 __isl_give isl_mat *isl_mat_copy(__isl_keep isl_mat *mat);
1547 void isl_mat_free(__isl_take isl_mat *mat);
1549 Note that the elements of a newly created matrix may have arbitrary values.
1550 The elements can be changed and inspected using the following functions.
1552 int isl_mat_rows(__isl_keep isl_mat *mat);
1553 int isl_mat_cols(__isl_keep isl_mat *mat);
1554 int isl_mat_get_element(__isl_keep isl_mat *mat,
1555 int row, int col, isl_int *v);
1556 __isl_give isl_mat *isl_mat_set_element(__isl_take isl_mat *mat,
1557 int row, int col, isl_int v);
1559 C<isl_mat_get_element> will return a negative value if anything went wrong.
1560 In that case, the value of C<*v> is undefined.
1562 The following function can be used to compute the (right) inverse
1563 of a matrix, i.e., a matrix such that the product of the original
1564 and the inverse (in that order) is a multiple of the identity matrix.
1565 The input matrix is assumed to be of full row-rank.
1567 __isl_give isl_mat *isl_mat_right_inverse(__isl_take isl_mat *mat);
1569 The following function can be used to compute the (right) kernel
1570 (or null space) of a matrix, i.e., a matrix such that the product of
1571 the original and the kernel (in that order) is the zero matrix.
1573 __isl_give isl_mat *isl_mat_right_kernel(__isl_take isl_mat *mat);
1577 Points are elements of a set. They can be used to construct
1578 simple sets (boxes) or they can be used to represent the
1579 individual elements of a set.
1580 The zero point (the origin) can be created using
1582 __isl_give isl_point *isl_point_zero(__isl_take isl_dim *dim);
1584 The coordinates of a point can be inspected, set and changed
1587 void isl_point_get_coordinate(__isl_keep isl_point *pnt,
1588 enum isl_dim_type type, int pos, isl_int *v);
1589 __isl_give isl_point *isl_point_set_coordinate(
1590 __isl_take isl_point *pnt,
1591 enum isl_dim_type type, int pos, isl_int v);
1593 __isl_give isl_point *isl_point_add_ui(
1594 __isl_take isl_point *pnt,
1595 enum isl_dim_type type, int pos, unsigned val);
1596 __isl_give isl_point *isl_point_sub_ui(
1597 __isl_take isl_point *pnt,
1598 enum isl_dim_type type, int pos, unsigned val);
1600 Points can be copied or freed using
1602 __isl_give isl_point *isl_point_copy(
1603 __isl_keep isl_point *pnt);
1604 void isl_point_free(__isl_take isl_point *pnt);
1606 A singleton set can be created from a point using
1608 __isl_give isl_set *isl_set_from_point(
1609 __isl_take isl_point *pnt);
1611 and a box can be created from two opposite extremal points using
1613 __isl_give isl_set *isl_set_box_from_points(
1614 __isl_take isl_point *pnt1,
1615 __isl_take isl_point *pnt2);
1617 All elements of a B<bounded> (union) set can be enumerated using
1618 the following functions.
1620 int isl_set_foreach_point(__isl_keep isl_set *set,
1621 int (*fn)(__isl_take isl_point *pnt, void *user),
1623 int isl_union_set_foreach_point(__isl_keep isl_union_set *uset,
1624 int (*fn)(__isl_take isl_point *pnt, void *user),
1627 The function C<fn> is called for each integer point in
1628 C<set> with as second argument the last argument of
1629 the C<isl_set_foreach_point> call. The function C<fn>
1630 should return C<0> on success and C<-1> on failure.
1631 In the latter case, C<isl_set_foreach_point> will stop
1632 enumerating and return C<-1> as well.
1633 If the enumeration is performed successfully and to completion,
1634 then C<isl_set_foreach_point> returns C<0>.
1636 To obtain a single point of a set, use
1638 __isl_give isl_point *isl_set_sample_point(
1639 __isl_take isl_set *set);
1641 If C<set> does not contain any (integer) points, then the
1642 resulting point will be ``void'', a property that can be
1645 int isl_point_is_void(__isl_keep isl_point *pnt);
1647 =head2 Piecewise Quasipolynomials
1649 A piecewise quasipolynomial is a particular kind of function that maps
1650 a parametric point to a rational value.
1651 More specifically, a quasipolynomial is a polynomial expression in greatest
1652 integer parts of affine expressions of parameters and variables.
1653 A piecewise quasipolynomial is a subdivision of a given parametric
1654 domain into disjoint cells with a quasipolynomial associated to
1655 each cell. The value of the piecewise quasipolynomial at a given
1656 point is the value of the quasipolynomial associated to the cell
1657 that contains the point. Outside of the union of cells,
1658 the value is assumed to be zero.
1659 For example, the piecewise quasipolynomial
1661 [n] -> { [x] -> ((1 + n) - x) : x <= n and x >= 0 }
1663 maps C<x> to C<1 + n - x> for values of C<x> between C<0> and C<n>.
1664 A given piecewise quasipolynomial has a fixed domain dimension.
1665 Union piecewise quasipolynomials are used to contain piecewise quasipolynomials
1666 defined over different domains.
1667 Piecewise quasipolynomials are mainly used by the C<barvinok>
1668 library for representing the number of elements in a parametric set or map.
1669 For example, the piecewise quasipolynomial above represents
1670 the number of points in the map
1672 [n] -> { [x] -> [y] : x,y >= 0 and 0 <= x + y <= n }
1674 =head3 Printing (Piecewise) Quasipolynomials
1676 Quasipolynomials and piecewise quasipolynomials can be printed
1677 using the following functions.
1679 __isl_give isl_printer *isl_printer_print_qpolynomial(
1680 __isl_take isl_printer *p,
1681 __isl_keep isl_qpolynomial *qp);
1683 __isl_give isl_printer *isl_printer_print_pw_qpolynomial(
1684 __isl_take isl_printer *p,
1685 __isl_keep isl_pw_qpolynomial *pwqp);
1687 __isl_give isl_printer *isl_printer_print_union_pw_qpolynomial(
1688 __isl_take isl_printer *p,
1689 __isl_keep isl_union_pw_qpolynomial *upwqp);
1691 The output format of the printer
1692 needs to be set to either C<ISL_FORMAT_ISL> or C<ISL_FORMAT_C>.
1693 For C<isl_printer_print_union_pw_qpolynomial>, only C<ISL_FORMAT_ISL>
1696 =head3 Creating New (Piecewise) Quasipolynomials
1698 Some simple quasipolynomials can be created using the following functions.
1699 More complicated quasipolynomials can be created by applying
1700 operations such as addition and multiplication
1701 on the resulting quasipolynomials
1703 __isl_give isl_qpolynomial *isl_qpolynomial_zero(
1704 __isl_take isl_dim *dim);
1705 __isl_give isl_qpolynomial *isl_qpolynomial_one(
1706 __isl_take isl_dim *dim);
1707 __isl_give isl_qpolynomial *isl_qpolynomial_infty(
1708 __isl_take isl_dim *dim);
1709 __isl_give isl_qpolynomial *isl_qpolynomial_neginfty(
1710 __isl_take isl_dim *dim);
1711 __isl_give isl_qpolynomial *isl_qpolynomial_nan(
1712 __isl_take isl_dim *dim);
1713 __isl_give isl_qpolynomial *isl_qpolynomial_rat_cst(
1714 __isl_take isl_dim *dim,
1715 const isl_int n, const isl_int d);
1716 __isl_give isl_qpolynomial *isl_qpolynomial_div(
1717 __isl_take isl_div *div);
1718 __isl_give isl_qpolynomial *isl_qpolynomial_var(
1719 __isl_take isl_dim *dim,
1720 enum isl_dim_type type, unsigned pos);
1722 The zero piecewise quasipolynomial or a piecewise quasipolynomial
1723 with a single cell can be created using the following functions.
1724 Multiple of these single cell piecewise quasipolynomials can
1725 be combined to create more complicated piecewise quasipolynomials.
1727 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_zero(
1728 __isl_take isl_dim *dim);
1729 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_alloc(
1730 __isl_take isl_set *set,
1731 __isl_take isl_qpolynomial *qp);
1733 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_zero(
1734 __isl_take isl_dim *dim);
1735 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_from_pw_qpolynomial(
1736 __isl_take isl_pw_qpolynomial *pwqp);
1737 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_add_pw_qpolynomial(
1738 __isl_take isl_union_pw_qpolynomial *upwqp,
1739 __isl_take isl_pw_qpolynomial *pwqp);
1741 Quasipolynomials can be copied and freed again using the following
1744 __isl_give isl_qpolynomial *isl_qpolynomial_copy(
1745 __isl_keep isl_qpolynomial *qp);
1746 void isl_qpolynomial_free(__isl_take isl_qpolynomial *qp);
1748 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_copy(
1749 __isl_keep isl_pw_qpolynomial *pwqp);
1750 void isl_pw_qpolynomial_free(
1751 __isl_take isl_pw_qpolynomial *pwqp);
1753 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_copy(
1754 __isl_keep isl_union_pw_qpolynomial *upwqp);
1755 void isl_union_pw_qpolynomial_free(
1756 __isl_take isl_union_pw_qpolynomial *upwqp);
1758 =head3 Inspecting (Piecewise) Quasipolynomials
1760 To iterate over all piecewise quasipolynomials in a union
1761 piecewise quasipolynomial, use the following function
1763 int isl_union_pw_qpolynomial_foreach_pw_qpolynomial(
1764 __isl_keep isl_union_pw_qpolynomial *upwqp,
1765 int (*fn)(__isl_take isl_pw_qpolynomial *pwqp, void *user),
1768 To iterate over the cells in a piecewise quasipolynomial,
1769 use either of the following two functions
1771 int isl_pw_qpolynomial_foreach_piece(
1772 __isl_keep isl_pw_qpolynomial *pwqp,
1773 int (*fn)(__isl_take isl_set *set,
1774 __isl_take isl_qpolynomial *qp,
1775 void *user), void *user);
1776 int isl_pw_qpolynomial_foreach_lifted_piece(
1777 __isl_keep isl_pw_qpolynomial *pwqp,
1778 int (*fn)(__isl_take isl_set *set,
1779 __isl_take isl_qpolynomial *qp,
1780 void *user), void *user);
1782 As usual, the function C<fn> should return C<0> on success
1783 and C<-1> on failure. The difference between
1784 C<isl_pw_qpolynomial_foreach_piece> and
1785 C<isl_pw_qpolynomial_foreach_lifted_piece> is that
1786 C<isl_pw_qpolynomial_foreach_lifted_piece> will first
1787 compute unique representations for all existentially quantified
1788 variables and then turn these existentially quantified variables
1789 into extra set variables, adapting the associated quasipolynomial
1790 accordingly. This means that the C<set> passed to C<fn>
1791 will not have any existentially quantified variables, but that
1792 the dimensions of the sets may be different for different
1793 invocations of C<fn>.
1795 To iterate over all terms in a quasipolynomial,
1798 int isl_qpolynomial_foreach_term(
1799 __isl_keep isl_qpolynomial *qp,
1800 int (*fn)(__isl_take isl_term *term,
1801 void *user), void *user);
1803 The terms themselves can be inspected and freed using
1806 unsigned isl_term_dim(__isl_keep isl_term *term,
1807 enum isl_dim_type type);
1808 void isl_term_get_num(__isl_keep isl_term *term,
1810 void isl_term_get_den(__isl_keep isl_term *term,
1812 int isl_term_get_exp(__isl_keep isl_term *term,
1813 enum isl_dim_type type, unsigned pos);
1814 __isl_give isl_div *isl_term_get_div(
1815 __isl_keep isl_term *term, unsigned pos);
1816 void isl_term_free(__isl_take isl_term *term);
1818 Each term is a product of parameters, set variables and
1819 integer divisions. The function C<isl_term_get_exp>
1820 returns the exponent of a given dimensions in the given term.
1821 The C<isl_int>s in the arguments of C<isl_term_get_num>
1822 and C<isl_term_get_den> need to have been initialized
1823 using C<isl_int_init> before calling these functions.
1825 =head3 Properties of (Piecewise) Quasipolynomials
1827 To check whether a quasipolynomial is actually a constant,
1828 use the following function.
1830 int isl_qpolynomial_is_cst(__isl_keep isl_qpolynomial *qp,
1831 isl_int *n, isl_int *d);
1833 If C<qp> is a constant and if C<n> and C<d> are not C<NULL>
1834 then the numerator and denominator of the constant
1835 are returned in C<*n> and C<*d>, respectively.
1837 =head3 Operations on (Piecewise) Quasipolynomials
1839 __isl_give isl_qpolynomial *isl_qpolynomial_neg(
1840 __isl_take isl_qpolynomial *qp);
1841 __isl_give isl_qpolynomial *isl_qpolynomial_add(
1842 __isl_take isl_qpolynomial *qp1,
1843 __isl_take isl_qpolynomial *qp2);
1844 __isl_give isl_qpolynomial *isl_qpolynomial_sub(
1845 __isl_take isl_qpolynomial *qp1,
1846 __isl_take isl_qpolynomial *qp2);
1847 __isl_give isl_qpolynomial *isl_qpolynomial_mul(
1848 __isl_take isl_qpolynomial *qp1,
1849 __isl_take isl_qpolynomial *qp2);
1851 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_add(
1852 __isl_take isl_pw_qpolynomial *pwqp1,
1853 __isl_take isl_pw_qpolynomial *pwqp2);
1854 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_sub(
1855 __isl_take isl_pw_qpolynomial *pwqp1,
1856 __isl_take isl_pw_qpolynomial *pwqp2);
1857 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_add_disjoint(
1858 __isl_take isl_pw_qpolynomial *pwqp1,
1859 __isl_take isl_pw_qpolynomial *pwqp2);
1860 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_neg(
1861 __isl_take isl_pw_qpolynomial *pwqp);
1862 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_mul(
1863 __isl_take isl_pw_qpolynomial *pwqp1,
1864 __isl_take isl_pw_qpolynomial *pwqp2);
1866 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_add(
1867 __isl_take isl_union_pw_qpolynomial *upwqp1,
1868 __isl_take isl_union_pw_qpolynomial *upwqp2);
1869 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_sub(
1870 __isl_take isl_union_pw_qpolynomial *upwqp1,
1871 __isl_take isl_union_pw_qpolynomial *upwqp2);
1872 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_mul(
1873 __isl_take isl_union_pw_qpolynomial *upwqp1,
1874 __isl_take isl_union_pw_qpolynomial *upwqp2);
1876 __isl_give isl_qpolynomial *isl_pw_qpolynomial_eval(
1877 __isl_take isl_pw_qpolynomial *pwqp,
1878 __isl_take isl_point *pnt);
1880 __isl_give isl_qpolynomial *isl_union_pw_qpolynomial_eval(
1881 __isl_take isl_union_pw_qpolynomial *upwqp,
1882 __isl_take isl_point *pnt);
1884 __isl_give isl_set *isl_pw_qpolynomial_domain(
1885 __isl_take isl_pw_qpolynomial *pwqp);
1886 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_intersect_domain(
1887 __isl_take isl_pw_qpolynomial *pwpq,
1888 __isl_take isl_set *set);
1890 __isl_give isl_union_set *isl_union_pw_qpolynomial_domain(
1891 __isl_take isl_union_pw_qpolynomial *upwqp);
1892 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_intersect_domain(
1893 __isl_take isl_union_pw_qpolynomial *upwpq,
1894 __isl_take isl_union_set *uset);
1896 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_coalesce(
1897 __isl_take isl_union_pw_qpolynomial *upwqp);
1899 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_gist(
1900 __isl_take isl_pw_qpolynomial *pwqp,
1901 __isl_take isl_set *context);
1903 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_gist(
1904 __isl_take isl_union_pw_qpolynomial *upwqp,
1905 __isl_take isl_union_set *context);
1907 The gist operation applies the gist operation to each of
1908 the cells in the domain of the input piecewise quasipolynomial.
1909 In future, the operation will also exploit the context
1910 to simplify the quasipolynomials associated to each cell.
1912 =head2 Bounds on Piecewise Quasipolynomials and Piecewise Quasipolynomial Reductions
1914 A piecewise quasipolynomial reduction is a piecewise
1915 reduction (or fold) of quasipolynomials.
1916 In particular, the reduction can be maximum or a minimum.
1917 The objects are mainly used to represent the result of
1918 an upper or lower bound on a quasipolynomial over its domain,
1919 i.e., as the result of the following function.
1921 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_bound(
1922 __isl_take isl_pw_qpolynomial *pwqp,
1923 enum isl_fold type, int *tight);
1925 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_bound(
1926 __isl_take isl_union_pw_qpolynomial *upwqp,
1927 enum isl_fold type, int *tight);
1929 The C<type> argument may be either C<isl_fold_min> or C<isl_fold_max>.
1930 If C<tight> is not C<NULL>, then C<*tight> is set to C<1>
1931 is the returned bound is known be tight, i.e., for each value
1932 of the parameters there is at least
1933 one element in the domain that reaches the bound.
1934 If the domain of C<pwqp> is not wrapping, then the bound is computed
1935 over all elements in that domain and the result has a purely parametric
1936 domain. If the domain of C<pwqp> is wrapping, then the bound is
1937 computed over the range of the wrapped relation. The domain of the
1938 wrapped relation becomes the domain of the result.
1940 A (piecewise) quasipolynomial reduction can be copied or freed using the
1941 following functions.
1943 __isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_copy(
1944 __isl_keep isl_qpolynomial_fold *fold);
1945 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_copy(
1946 __isl_keep isl_pw_qpolynomial_fold *pwf);
1947 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_copy(
1948 __isl_keep isl_union_pw_qpolynomial_fold *upwf);
1949 void isl_qpolynomial_fold_free(
1950 __isl_take isl_qpolynomial_fold *fold);
1951 void isl_pw_qpolynomial_fold_free(
1952 __isl_take isl_pw_qpolynomial_fold *pwf);
1953 void isl_union_pw_qpolynomial_fold_free(
1954 __isl_take isl_union_pw_qpolynomial_fold *upwf);
1956 =head3 Printing Piecewise Quasipolynomial Reductions
1958 Piecewise quasipolynomial reductions can be printed
1959 using the following function.
1961 __isl_give isl_printer *isl_printer_print_pw_qpolynomial_fold(
1962 __isl_take isl_printer *p,
1963 __isl_keep isl_pw_qpolynomial_fold *pwf);
1964 __isl_give isl_printer *isl_printer_print_union_pw_qpolynomial_fold(
1965 __isl_take isl_printer *p,
1966 __isl_keep isl_union_pw_qpolynomial_fold *upwf);
1968 For C<isl_printer_print_pw_qpolynomial_fold>,
1969 output format of the printer
1970 needs to be set to either C<ISL_FORMAT_ISL> or C<ISL_FORMAT_C>.
1971 For C<isl_printer_print_union_pw_qpolynomial_fold>,
1972 output format of the printer
1973 needs to be set to either C<ISL_FORMAT_ISL>.
1975 =head3 Inspecting (Piecewise) Quasipolynomial Reductions
1977 To iterate over all piecewise quasipolynomial reductions in a union
1978 piecewise quasipolynomial reduction, use the following function
1980 int isl_union_pw_qpolynomial_fold_foreach_pw_qpolynomial_fold(
1981 __isl_keep isl_union_pw_qpolynomial_fold *upwf,
1982 int (*fn)(__isl_take isl_pw_qpolynomial_fold *pwf,
1983 void *user), void *user);
1985 To iterate over the cells in a piecewise quasipolynomial reduction,
1986 use either of the following two functions
1988 int isl_pw_qpolynomial_fold_foreach_piece(
1989 __isl_keep isl_pw_qpolynomial_fold *pwf,
1990 int (*fn)(__isl_take isl_set *set,
1991 __isl_take isl_qpolynomial_fold *fold,
1992 void *user), void *user);
1993 int isl_pw_qpolynomial_fold_foreach_lifted_piece(
1994 __isl_keep isl_pw_qpolynomial_fold *pwf,
1995 int (*fn)(__isl_take isl_set *set,
1996 __isl_take isl_qpolynomial_fold *fold,
1997 void *user), void *user);
1999 See L<Inspecting (Piecewise) Quasipolynomials> for an explanation
2000 of the difference between these two functions.
2002 To iterate over all quasipolynomials in a reduction, use
2004 int isl_qpolynomial_fold_foreach_qpolynomial(
2005 __isl_keep isl_qpolynomial_fold *fold,
2006 int (*fn)(__isl_take isl_qpolynomial *qp,
2007 void *user), void *user);
2009 =head3 Operations on Piecewise Quasipolynomial Reductions
2011 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_fold(
2012 __isl_take isl_pw_qpolynomial_fold *pwf1,
2013 __isl_take isl_pw_qpolynomial_fold *pwf2);
2015 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_fold(
2016 __isl_take isl_union_pw_qpolynomial_fold *upwf1,
2017 __isl_take isl_union_pw_qpolynomial_fold *upwf2);
2019 __isl_give isl_qpolynomial *isl_pw_qpolynomial_fold_eval(
2020 __isl_take isl_pw_qpolynomial_fold *pwf,
2021 __isl_take isl_point *pnt);
2023 __isl_give isl_qpolynomial *isl_union_pw_qpolynomial_fold_eval(
2024 __isl_take isl_union_pw_qpolynomial_fold *upwf,
2025 __isl_take isl_point *pnt);
2027 __isl_give isl_union_set *isl_union_pw_qpolynomial_fold_domain(
2028 __isl_take isl_union_pw_qpolynomial_fold *upwf);
2029 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_intersect_domain(
2030 __isl_take isl_union_pw_qpolynomial_fold *upwf,
2031 __isl_take isl_union_set *uset);
2033 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_coalesce(
2034 __isl_take isl_pw_qpolynomial_fold *pwf);
2036 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_coalesce(
2037 __isl_take isl_union_pw_qpolynomial_fold *upwf);
2039 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_gist(
2040 __isl_take isl_pw_qpolynomial_fold *pwf,
2041 __isl_take isl_set *context);
2043 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_gist(
2044 __isl_take isl_union_pw_qpolynomial_fold *upwf,
2045 __isl_take isl_union_set *context);
2047 The gist operation applies the gist operation to each of
2048 the cells in the domain of the input piecewise quasipolynomial reduction.
2049 In future, the operation will also exploit the context
2050 to simplify the quasipolynomial reductions associated to each cell.
2052 __isl_give isl_pw_qpolynomial_fold *
2053 isl_map_apply_pw_qpolynomial_fold(
2054 __isl_take isl_map *map,
2055 __isl_take isl_pw_qpolynomial_fold *pwf,
2057 __isl_give isl_union_pw_qpolynomial_fold *
2058 isl_union_map_apply_union_pw_qpolynomial_fold(
2059 __isl_take isl_union_map *umap,
2060 __isl_take isl_union_pw_qpolynomial_fold *upwf,
2064 compose the given map with the given piecewise quasipolynomial reduction.
2065 That is, compute a bound (of the same type as C<pwf> or C<upwf> itself)
2066 over all elements in the intersection of the range of the map
2067 and the domain of the piecewise quasipolynomial reduction
2068 as a function of an element in the domain of the map.
2070 =head2 Dependence Analysis
2072 C<isl> contains specialized functionality for performing
2073 array dataflow analysis. That is, given a I<sink> access relation
2074 and a collection of possible I<source> access relations,
2075 C<isl> can compute relations that describe
2076 for each iteration of the sink access, which iteration
2077 of which of the source access relations was the last
2078 to access the same data element before the given iteration
2080 To compute standard flow dependences, the sink should be
2081 a read, while the sources should be writes.
2082 If any of the source accesses are marked as being I<may>
2083 accesses, then there will be a dependence to the last
2084 I<must> access B<and> to any I<may> access that follows
2085 this last I<must> access.
2086 In particular, if I<all> sources are I<may> accesses,
2087 then memory based dependence analysis is performed.
2088 If, on the other hand, all sources are I<must> accesses,
2089 then value based dependence analysis is performed.
2091 #include <isl_flow.h>
2093 typedef int (*isl_access_level_before)(void *first, void *second);
2095 __isl_give isl_access_info *isl_access_info_alloc(
2096 __isl_take isl_map *sink,
2097 void *sink_user, isl_access_level_before fn,
2099 __isl_give isl_access_info *isl_access_info_add_source(
2100 __isl_take isl_access_info *acc,
2101 __isl_take isl_map *source, int must,
2103 void isl_access_info_free(__isl_take isl_access_info *acc);
2105 __isl_give isl_flow *isl_access_info_compute_flow(
2106 __isl_take isl_access_info *acc);
2108 int isl_flow_foreach(__isl_keep isl_flow *deps,
2109 int (*fn)(__isl_take isl_map *dep, int must,
2110 void *dep_user, void *user),
2112 __isl_give isl_set *isl_flow_get_no_source(
2113 __isl_keep isl_flow *deps, int must);
2114 void isl_flow_free(__isl_take isl_flow *deps);
2116 The function C<isl_access_info_compute_flow> performs the actual
2117 dependence analysis. The other functions are used to construct
2118 the input for this function or to read off the output.
2120 The input is collected in an C<isl_access_info>, which can
2121 be created through a call to C<isl_access_info_alloc>.
2122 The arguments to this functions are the sink access relation
2123 C<sink>, a token C<sink_user> used to identify the sink
2124 access to the user, a callback function for specifying the
2125 relative order of source and sink accesses, and the number
2126 of source access relations that will be added.
2127 The callback function has type C<int (*)(void *first, void *second)>.
2128 The function is called with two user supplied tokens identifying
2129 either a source or the sink and it should return the shared nesting
2130 level and the relative order of the two accesses.
2131 In particular, let I<n> be the number of loops shared by
2132 the two accesses. If C<first> precedes C<second> textually,
2133 then the function should return I<2 * n + 1>; otherwise,
2134 it should return I<2 * n>.
2135 The sources can be added to the C<isl_access_info> by performing
2136 (at most) C<max_source> calls to C<isl_access_info_add_source>.
2137 C<must> indicates whether the source is a I<must> access
2138 or a I<may> access. Note that a multi-valued access relation
2139 should only be marked I<must> if every iteration in the domain
2140 of the relation accesses I<all> elements in its image.
2141 The C<source_user> token is again used to identify
2142 the source access. The range of the source access relation
2143 C<source> should have the same dimension as the range
2144 of the sink access relation.
2145 The C<isl_access_info_free> function should usually not be
2146 called explicitly, because it is called implicitly by
2147 C<isl_access_info_compute_flow>.
2149 The result of the dependence analysis is collected in an
2150 C<isl_flow>. There may be elements in the domain of
2151 the sink access for which no preceding source access could be
2152 found or for which all preceding sources are I<may> accesses.
2153 The sets of these elements can be obtained through
2154 calls to C<isl_flow_get_no_source>, the first with C<must> set
2155 and the second with C<must> unset.
2156 In the case of standard flow dependence analysis,
2157 with the sink a read and the sources I<must> writes,
2158 the first set corresponds to the reads from uninitialized
2159 array elements and the second set is empty.
2160 The actual flow dependences can be extracted using
2161 C<isl_flow_foreach>. This function will call the user-specified
2162 callback function C<fn> for each B<non-empty> dependence between
2163 a source and the sink. The callback function is called
2164 with four arguments, the actual flow dependence relation
2165 mapping source iterations to sink iterations, a boolean that
2166 indicates whether it is a I<must> or I<may> dependence, a token
2167 identifying the source and an additional C<void *> with value
2168 equal to the third argument of the C<isl_flow_foreach> call.
2169 A dependence is marked I<must> if it originates from a I<must>
2170 source and if it is not followed by any I<may> sources.
2172 After finishing with an C<isl_flow>, the user should call
2173 C<isl_flow_free> to free all associated memory.
2175 A higher-level interface to dependence analysis is provided
2176 by the following function.
2178 #include <isl_flow.h>
2180 int isl_union_map_compute_flow(__isl_take isl_union_map *sink,
2181 __isl_take isl_union_map *must_source,
2182 __isl_take isl_union_map *may_source,
2183 __isl_take isl_union_map *schedule,
2184 __isl_give isl_union_map **must_dep,
2185 __isl_give isl_union_map **may_dep,
2186 __isl_give isl_union_set **must_no_source,
2187 __isl_give isl_union_set **may_no_source);
2189 The arrays are identified by the tuple names of the ranges
2190 of the accesses. The iteration domains by the tuple names
2191 of the domains of the accesses and of the schedule.
2192 The relative order of the iteration domains is given by the
2193 schedule. Any of C<must_dep>, C<may_dep>, C<must_no_source>
2194 or C<may_no_source> may be C<NULL>, but a C<NULL> value for
2195 any of the other arguments is treated as an error.
2197 =head2 Parametric Vertex Enumeration
2199 The parametric vertex enumeration described in this section
2200 is mainly intended to be used internally and by the C<barvinok>
2203 #include <isl_vertices.h>
2204 __isl_give isl_vertices *isl_basic_set_compute_vertices(
2205 __isl_keep isl_basic_set *bset);
2207 The function C<isl_basic_set_compute_vertices> performs the
2208 actual computation of the parametric vertices and the chamber
2209 decomposition and store the result in an C<isl_vertices> object.
2210 This information can be queried by either iterating over all
2211 the vertices or iterating over all the chambers or cells
2212 and then iterating over all vertices that are active on the chamber.
2214 int isl_vertices_foreach_vertex(
2215 __isl_keep isl_vertices *vertices,
2216 int (*fn)(__isl_take isl_vertex *vertex, void *user),
2219 int isl_vertices_foreach_cell(
2220 __isl_keep isl_vertices *vertices,
2221 int (*fn)(__isl_take isl_cell *cell, void *user),
2223 int isl_cell_foreach_vertex(__isl_keep isl_cell *cell,
2224 int (*fn)(__isl_take isl_vertex *vertex, void *user),
2227 Other operations that can be performed on an C<isl_vertices> object are
2230 isl_ctx *isl_vertices_get_ctx(
2231 __isl_keep isl_vertices *vertices);
2232 int isl_vertices_get_n_vertices(
2233 __isl_keep isl_vertices *vertices);
2234 void isl_vertices_free(__isl_take isl_vertices *vertices);
2236 Vertices can be inspected and destroyed using the following functions.
2238 isl_ctx *isl_vertex_get_ctx(__isl_keep isl_vertex *vertex);
2239 int isl_vertex_get_id(__isl_keep isl_vertex *vertex);
2240 __isl_give isl_basic_set *isl_vertex_get_domain(
2241 __isl_keep isl_vertex *vertex);
2242 __isl_give isl_basic_set *isl_vertex_get_expr(
2243 __isl_keep isl_vertex *vertex);
2244 void isl_vertex_free(__isl_take isl_vertex *vertex);
2246 C<isl_vertex_get_expr> returns a singleton parametric set describing
2247 the vertex, while C<isl_vertex_get_domain> returns the activity domain
2249 Note that C<isl_vertex_get_domain> and C<isl_vertex_get_expr> return
2250 B<rational> basic sets, so they should mainly be used for inspection
2251 and should not be mixed with integer sets.
2253 Chambers can be inspected and destroyed using the following functions.
2255 isl_ctx *isl_cell_get_ctx(__isl_keep isl_cell *cell);
2256 __isl_give isl_basic_set *isl_cell_get_domain(
2257 __isl_keep isl_cell *cell);
2258 void isl_cell_free(__isl_take isl_cell *cell);
2262 Although C<isl> is mainly meant to be used as a library,
2263 it also contains some basic applications that use some
2264 of the functionality of C<isl>.
2265 The input may be specified in either the L<isl format>
2266 or the L<PolyLib format>.
2268 =head2 C<isl_polyhedron_sample>
2270 C<isl_polyhedron_sample> takes a polyhedron as input and prints
2271 an integer element of the polyhedron, if there is any.
2272 The first column in the output is the denominator and is always
2273 equal to 1. If the polyhedron contains no integer points,
2274 then a vector of length zero is printed.
2278 C<isl_pip> takes the same input as the C<example> program
2279 from the C<piplib> distribution, i.e., a set of constraints
2280 on the parameters, a line containing only -1 and finally a set
2281 of constraints on a parametric polyhedron.
2282 The coefficients of the parameters appear in the last columns
2283 (but before the final constant column).
2284 The output is the lexicographic minimum of the parametric polyhedron.
2285 As C<isl> currently does not have its own output format, the output
2286 is just a dump of the internal state.
2288 =head2 C<isl_polyhedron_minimize>
2290 C<isl_polyhedron_minimize> computes the minimum of some linear
2291 or affine objective function over the integer points in a polyhedron.
2292 If an affine objective function
2293 is given, then the constant should appear in the last column.
2295 =head2 C<isl_polytope_scan>
2297 Given a polytope, C<isl_polytope_scan> prints
2298 all integer points in the polytope.
2300 =head1 C<isl-polylib>
2302 The C<isl-polylib> library provides the following functions for converting
2303 between C<isl> objects and C<PolyLib> objects.
2304 The library is distributed separately for licensing reasons.
2306 #include <isl_set_polylib.h>
2307 __isl_give isl_basic_set *isl_basic_set_new_from_polylib(
2308 Polyhedron *P, __isl_take isl_dim *dim);
2309 Polyhedron *isl_basic_set_to_polylib(
2310 __isl_keep isl_basic_set *bset);
2311 __isl_give isl_set *isl_set_new_from_polylib(Polyhedron *D,
2312 __isl_take isl_dim *dim);
2313 Polyhedron *isl_set_to_polylib(__isl_keep isl_set *set);
2315 #include <isl_map_polylib.h>
2316 __isl_give isl_basic_map *isl_basic_map_new_from_polylib(
2317 Polyhedron *P, __isl_take isl_dim *dim);
2318 __isl_give isl_map *isl_map_new_from_polylib(Polyhedron *D,
2319 __isl_take isl_dim *dim);
2320 Polyhedron *isl_basic_map_to_polylib(
2321 __isl_keep isl_basic_map *bmap);
2322 Polyhedron *isl_map_to_polylib(__isl_keep isl_map *map);