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 The number of sets or maps in a union set or map can be obtained
908 int isl_union_set_n_set(__isl_keep isl_union_set *uset);
909 int isl_union_map_n_map(__isl_keep isl_union_map *umap);
911 To extract the set or map from a union with a given dimension
914 __isl_give isl_set *isl_union_set_extract_set(
915 __isl_keep isl_union_set *uset,
916 __isl_take isl_dim *dim);
917 __isl_give isl_map *isl_union_map_extract_map(
918 __isl_keep isl_union_map *umap,
919 __isl_take isl_dim *dim);
921 To iterate over all the basic sets or maps in a set or map, use
923 int isl_set_foreach_basic_set(__isl_keep isl_set *set,
924 int (*fn)(__isl_take isl_basic_set *bset, void *user),
926 int isl_map_foreach_basic_map(__isl_keep isl_map *map,
927 int (*fn)(__isl_take isl_basic_map *bmap, void *user),
930 The callback function C<fn> should return 0 if successful and
931 -1 if an error occurs. In the latter case, or if any other error
932 occurs, the above functions will return -1.
934 It should be noted that C<isl> does not guarantee that
935 the basic sets or maps passed to C<fn> are disjoint.
936 If this is required, then the user should call one of
937 the following functions first.
939 __isl_give isl_set *isl_set_make_disjoint(
940 __isl_take isl_set *set);
941 __isl_give isl_map *isl_map_make_disjoint(
942 __isl_take isl_map *map);
944 The number of basic sets in a set can be obtained
947 int isl_set_n_basic_set(__isl_keep isl_set *set);
949 To iterate over the constraints of a basic set or map, use
951 #include <isl_constraint.h>
953 int isl_basic_map_foreach_constraint(
954 __isl_keep isl_basic_map *bmap,
955 int (*fn)(__isl_take isl_constraint *c, void *user),
957 void isl_constraint_free(struct isl_constraint *c);
959 Again, the callback function C<fn> should return 0 if successful and
960 -1 if an error occurs. In the latter case, or if any other error
961 occurs, the above functions will return -1.
962 The constraint C<c> represents either an equality or an inequality.
963 Use the following function to find out whether a constraint
964 represents an equality. If not, it represents an inequality.
966 int isl_constraint_is_equality(
967 __isl_keep isl_constraint *constraint);
969 The coefficients of the constraints can be inspected using
970 the following functions.
972 void isl_constraint_get_constant(
973 __isl_keep isl_constraint *constraint, isl_int *v);
974 void isl_constraint_get_coefficient(
975 __isl_keep isl_constraint *constraint,
976 enum isl_dim_type type, int pos, isl_int *v);
978 The explicit representations of the existentially quantified
979 variables can be inspected using the following functions.
980 Note that the user is only allowed to use these functions
981 if the inspected set or map is the result of a call
982 to C<isl_set_compute_divs> or C<isl_map_compute_divs>.
984 __isl_give isl_div *isl_constraint_div(
985 __isl_keep isl_constraint *constraint, int pos);
986 void isl_div_get_constant(__isl_keep isl_div *div,
988 void isl_div_get_denominator(__isl_keep isl_div *div,
990 void isl_div_get_coefficient(__isl_keep isl_div *div,
991 enum isl_dim_type type, int pos, isl_int *v);
993 To obtain the constraints of a basic map in matrix
994 form, use the following functions.
996 __isl_give isl_mat *isl_basic_map_equalities_matrix(
997 __isl_keep isl_basic_map *bmap,
998 enum isl_dim_type c1,
999 enum isl_dim_type c2, enum isl_dim_type c3,
1000 enum isl_dim_type c4, enum isl_dim_type c5);
1001 __isl_give isl_mat *isl_basic_map_inequalities_matrix(
1002 __isl_keep isl_basic_map *bmap,
1003 enum isl_dim_type c1,
1004 enum isl_dim_type c2, enum isl_dim_type c3,
1005 enum isl_dim_type c4, enum isl_dim_type c5);
1007 The C<isl_dim_type> arguments dictate the order in which
1008 different kinds of variables appear in the resulting matrix
1009 and should be a permutation of C<isl_dim_cst>, C<isl_dim_param>,
1010 C<isl_dim_in>, C<isl_dim_out> and C<isl_dim_div>.
1012 The names of the domain and range spaces of a set or relation can be
1013 read off using the following functions.
1015 const char *isl_set_get_tuple_name(
1016 __isl_keep isl_set *set);
1017 const char *isl_basic_map_get_tuple_name(
1018 __isl_keep isl_basic_map *bmap,
1019 enum isl_dim_type type);
1020 const char *isl_map_get_tuple_name(
1021 __isl_keep isl_map *map,
1022 enum isl_dim_type type);
1024 As with C<isl_dim_get_tuple_name>, the value returned points to
1025 an internal data structure.
1026 The names of individual dimensions can be read off using
1027 the following functions.
1029 const char *isl_constraint_get_dim_name(
1030 __isl_keep isl_constraint *constraint,
1031 enum isl_dim_type type, unsigned pos);
1032 const char *isl_set_get_dim_name(
1033 __isl_keep isl_set *set,
1034 enum isl_dim_type type, unsigned pos);
1035 const char *isl_basic_map_get_dim_name(
1036 __isl_keep isl_basic_map *bmap,
1037 enum isl_dim_type type, unsigned pos);
1038 const char *isl_map_get_dim_name(
1039 __isl_keep isl_map *map,
1040 enum isl_dim_type type, unsigned pos);
1042 These functions are mostly useful to obtain the names
1047 =head3 Unary Properties
1053 The following functions test whether the given set or relation
1054 contains any integer points. The ``fast'' variants do not perform
1055 any computations, but simply check if the given set or relation
1056 is already known to be empty.
1058 int isl_basic_set_fast_is_empty(__isl_keep isl_basic_set *bset);
1059 int isl_basic_set_is_empty(__isl_keep isl_basic_set *bset);
1060 int isl_set_is_empty(__isl_keep isl_set *set);
1061 int isl_union_set_is_empty(__isl_keep isl_union_set *uset);
1062 int isl_basic_map_fast_is_empty(__isl_keep isl_basic_map *bmap);
1063 int isl_basic_map_is_empty(__isl_keep isl_basic_map *bmap);
1064 int isl_map_fast_is_empty(__isl_keep isl_map *map);
1065 int isl_map_is_empty(__isl_keep isl_map *map);
1066 int isl_union_map_is_empty(__isl_keep isl_union_map *umap);
1068 =item * Universality
1070 int isl_basic_set_is_universe(__isl_keep isl_basic_set *bset);
1071 int isl_basic_map_is_universe(__isl_keep isl_basic_map *bmap);
1072 int isl_set_fast_is_universe(__isl_keep isl_set *set);
1074 =item * Single-valuedness
1076 int isl_map_is_single_valued(__isl_keep isl_map *map);
1080 int isl_map_is_bijective(__isl_keep isl_map *map);
1084 The followning functions check whether the domain of the given
1085 (basic) set is a wrapped relation.
1087 int isl_basic_set_is_wrapping(
1088 __isl_keep isl_basic_set *bset);
1089 int isl_set_is_wrapping(__isl_keep isl_set *set);
1093 =head3 Binary Properties
1099 int isl_set_fast_is_equal(__isl_keep isl_set *set1,
1100 __isl_keep isl_set *set2);
1101 int isl_set_is_equal(__isl_keep isl_set *set1,
1102 __isl_keep isl_set *set2);
1103 int isl_basic_map_is_equal(
1104 __isl_keep isl_basic_map *bmap1,
1105 __isl_keep isl_basic_map *bmap2);
1106 int isl_map_is_equal(__isl_keep isl_map *map1,
1107 __isl_keep isl_map *map2);
1108 int isl_map_fast_is_equal(__isl_keep isl_map *map1,
1109 __isl_keep isl_map *map2);
1110 int isl_union_map_is_equal(
1111 __isl_keep isl_union_map *umap1,
1112 __isl_keep isl_union_map *umap2);
1114 =item * Disjointness
1116 int isl_set_fast_is_disjoint(__isl_keep isl_set *set1,
1117 __isl_keep isl_set *set2);
1121 int isl_set_is_subset(__isl_keep isl_set *set1,
1122 __isl_keep isl_set *set2);
1123 int isl_set_is_strict_subset(
1124 __isl_keep isl_set *set1,
1125 __isl_keep isl_set *set2);
1126 int isl_basic_map_is_subset(
1127 __isl_keep isl_basic_map *bmap1,
1128 __isl_keep isl_basic_map *bmap2);
1129 int isl_basic_map_is_strict_subset(
1130 __isl_keep isl_basic_map *bmap1,
1131 __isl_keep isl_basic_map *bmap2);
1132 int isl_map_is_subset(
1133 __isl_keep isl_map *map1,
1134 __isl_keep isl_map *map2);
1135 int isl_map_is_strict_subset(
1136 __isl_keep isl_map *map1,
1137 __isl_keep isl_map *map2);
1138 int isl_union_map_is_subset(
1139 __isl_keep isl_union_map *umap1,
1140 __isl_keep isl_union_map *umap2);
1141 int isl_union_map_is_strict_subset(
1142 __isl_keep isl_union_map *umap1,
1143 __isl_keep isl_union_map *umap2);
1147 =head2 Unary Operations
1153 __isl_give isl_set *isl_set_complement(
1154 __isl_take isl_set *set);
1158 __isl_give isl_basic_map *isl_basic_map_reverse(
1159 __isl_take isl_basic_map *bmap);
1160 __isl_give isl_map *isl_map_reverse(
1161 __isl_take isl_map *map);
1162 __isl_give isl_union_map *isl_union_map_reverse(
1163 __isl_take isl_union_map *umap);
1167 __isl_give isl_basic_set *isl_basic_set_project_out(
1168 __isl_take isl_basic_set *bset,
1169 enum isl_dim_type type, unsigned first, unsigned n);
1170 __isl_give isl_basic_map *isl_basic_map_project_out(
1171 __isl_take isl_basic_map *bmap,
1172 enum isl_dim_type type, unsigned first, unsigned n);
1173 __isl_give isl_set *isl_set_project_out(__isl_take isl_set *set,
1174 enum isl_dim_type type, unsigned first, unsigned n);
1175 __isl_give isl_map *isl_map_project_out(__isl_take isl_map *map,
1176 enum isl_dim_type type, unsigned first, unsigned n);
1177 __isl_give isl_basic_set *isl_basic_map_domain(
1178 __isl_take isl_basic_map *bmap);
1179 __isl_give isl_basic_set *isl_basic_map_range(
1180 __isl_take isl_basic_map *bmap);
1181 __isl_give isl_set *isl_map_domain(
1182 __isl_take isl_map *bmap);
1183 __isl_give isl_set *isl_map_range(
1184 __isl_take isl_map *map);
1185 __isl_give isl_union_set *isl_union_map_domain(
1186 __isl_take isl_union_map *umap);
1187 __isl_give isl_union_set *isl_union_map_range(
1188 __isl_take isl_union_map *umap);
1190 __isl_give isl_basic_map *isl_basic_map_domain_map(
1191 __isl_take isl_basic_map *bmap);
1192 __isl_give isl_basic_map *isl_basic_map_range_map(
1193 __isl_take isl_basic_map *bmap);
1194 __isl_give isl_map *isl_map_domain_map(__isl_take isl_map *map);
1195 __isl_give isl_map *isl_map_range_map(__isl_take isl_map *map);
1196 __isl_give isl_union_map *isl_union_map_domain_map(
1197 __isl_take isl_union_map *umap);
1198 __isl_give isl_union_map *isl_union_map_range_map(
1199 __isl_take isl_union_map *umap);
1201 The functions above construct a (basic, regular or union) relation
1202 that maps (a wrapped version of) the input relation to its domain or range.
1206 __isl_give isl_basic_set *isl_basic_map_deltas(
1207 __isl_take isl_basic_map *bmap);
1208 __isl_give isl_set *isl_map_deltas(__isl_take isl_map *map);
1209 __isl_give isl_union_set *isl_union_map_deltas(
1210 __isl_take isl_union_map *umap);
1212 These functions return a (basic) set containing the differences
1213 between image elements and corresponding domain elements in the input.
1217 Simplify the representation of a set or relation by trying
1218 to combine pairs of basic sets or relations into a single
1219 basic set or relation.
1221 __isl_give isl_set *isl_set_coalesce(__isl_take isl_set *set);
1222 __isl_give isl_map *isl_map_coalesce(__isl_take isl_map *map);
1223 __isl_give isl_union_set *isl_union_set_coalesce(
1224 __isl_take isl_union_set *uset);
1225 __isl_give isl_union_map *isl_union_map_coalesce(
1226 __isl_take isl_union_map *umap);
1230 __isl_give isl_basic_set *isl_set_convex_hull(
1231 __isl_take isl_set *set);
1232 __isl_give isl_basic_map *isl_map_convex_hull(
1233 __isl_take isl_map *map);
1235 If the input set or relation has any existentially quantified
1236 variables, then the result of these operations is currently undefined.
1240 __isl_give isl_basic_set *isl_set_simple_hull(
1241 __isl_take isl_set *set);
1242 __isl_give isl_basic_map *isl_map_simple_hull(
1243 __isl_take isl_map *map);
1245 These functions compute a single basic set or relation
1246 that contains the whole input set or relation.
1247 In particular, the output is described by translates
1248 of the constraints describing the basic sets or relations in the input.
1252 (See \autoref{s:simple hull}.)
1258 __isl_give isl_basic_set *isl_basic_set_affine_hull(
1259 __isl_take isl_basic_set *bset);
1260 __isl_give isl_basic_set *isl_set_affine_hull(
1261 __isl_take isl_set *set);
1262 __isl_give isl_union_set *isl_union_set_affine_hull(
1263 __isl_take isl_union_set *uset);
1264 __isl_give isl_basic_map *isl_basic_map_affine_hull(
1265 __isl_take isl_basic_map *bmap);
1266 __isl_give isl_basic_map *isl_map_affine_hull(
1267 __isl_take isl_map *map);
1268 __isl_give isl_union_map *isl_union_map_affine_hull(
1269 __isl_take isl_union_map *umap);
1271 In case of union sets and relations, the affine hull is computed
1276 __isl_give isl_map *isl_map_power(__isl_take isl_map *map,
1277 unsigned param, int *exact);
1279 Compute a parametric representation for all positive powers I<k> of C<map>.
1280 The power I<k> is equated to the parameter at position C<param>.
1281 The result may be an overapproximation. If the result is exact,
1282 then C<*exact> is set to C<1>.
1283 The current implementation only produces exact results for particular
1284 cases of piecewise translations (i.e., piecewise uniform dependences).
1286 =item * Transitive closure
1288 __isl_give isl_map *isl_map_transitive_closure(
1289 __isl_take isl_map *map, int *exact);
1290 __isl_give isl_union_map *isl_union_map_transitive_closure(
1291 __isl_take isl_union_map *umap, int *exact);
1293 Compute the transitive closure of C<map>.
1294 The result may be an overapproximation. If the result is known to be exact,
1295 then C<*exact> is set to C<1>.
1296 The current implementation only produces exact results for particular
1297 cases of piecewise translations (i.e., piecewise uniform dependences).
1299 =item * Reaching path lengths
1301 __isl_give isl_map *isl_map_reaching_path_lengths(
1302 __isl_take isl_map *map, int *exact);
1304 Compute a relation that maps each element in the range of C<map>
1305 to the lengths of all paths composed of edges in C<map> that
1306 end up in the given element.
1307 The result may be an overapproximation. If the result is known to be exact,
1308 then C<*exact> is set to C<1>.
1309 To compute the I<maximal> path length, the resulting relation
1310 should be postprocessed by C<isl_map_lexmax>.
1311 In particular, if the input relation is a dependence relation
1312 (mapping sources to sinks), then the maximal path length corresponds
1313 to the free schedule.
1314 Note, however, that C<isl_map_lexmax> expects the maximum to be
1315 finite, so if the path lengths are unbounded (possibly due to
1316 the overapproximation), then you will get an error message.
1320 __isl_give isl_basic_set *isl_basic_map_wrap(
1321 __isl_take isl_basic_map *bmap);
1322 __isl_give isl_set *isl_map_wrap(
1323 __isl_take isl_map *map);
1324 __isl_give isl_union_set *isl_union_map_wrap(
1325 __isl_take isl_union_map *umap);
1326 __isl_give isl_basic_map *isl_basic_set_unwrap(
1327 __isl_take isl_basic_set *bset);
1328 __isl_give isl_map *isl_set_unwrap(
1329 __isl_take isl_set *set);
1330 __isl_give isl_union_map *isl_union_set_unwrap(
1331 __isl_take isl_union_set *uset);
1333 =item * Dimension manipulation
1335 __isl_give isl_set *isl_set_add_dims(
1336 __isl_take isl_set *set,
1337 enum isl_dim_type type, unsigned n);
1338 __isl_give isl_map *isl_map_add_dims(
1339 __isl_take isl_map *map,
1340 enum isl_dim_type type, unsigned n);
1342 It is usually not advisable to directly change the (input or output)
1343 space of a set or a relation as this removes the name and the internal
1344 structure of the space. However, the above functions can be useful
1345 to add new parameters.
1349 =head2 Binary Operations
1351 The two arguments of a binary operation not only need to live
1352 in the same C<isl_ctx>, they currently also need to have
1353 the same (number of) parameters.
1355 =head3 Basic Operations
1359 =item * Intersection
1361 __isl_give isl_basic_set *isl_basic_set_intersect(
1362 __isl_take isl_basic_set *bset1,
1363 __isl_take isl_basic_set *bset2);
1364 __isl_give isl_set *isl_set_intersect(
1365 __isl_take isl_set *set1,
1366 __isl_take isl_set *set2);
1367 __isl_give isl_union_set *isl_union_set_intersect(
1368 __isl_take isl_union_set *uset1,
1369 __isl_take isl_union_set *uset2);
1370 __isl_give isl_basic_map *isl_basic_map_intersect_domain(
1371 __isl_take isl_basic_map *bmap,
1372 __isl_take isl_basic_set *bset);
1373 __isl_give isl_basic_map *isl_basic_map_intersect_range(
1374 __isl_take isl_basic_map *bmap,
1375 __isl_take isl_basic_set *bset);
1376 __isl_give isl_basic_map *isl_basic_map_intersect(
1377 __isl_take isl_basic_map *bmap1,
1378 __isl_take isl_basic_map *bmap2);
1379 __isl_give isl_map *isl_map_intersect_domain(
1380 __isl_take isl_map *map,
1381 __isl_take isl_set *set);
1382 __isl_give isl_map *isl_map_intersect_range(
1383 __isl_take isl_map *map,
1384 __isl_take isl_set *set);
1385 __isl_give isl_map *isl_map_intersect(
1386 __isl_take isl_map *map1,
1387 __isl_take isl_map *map2);
1388 __isl_give isl_union_map *isl_union_map_intersect_domain(
1389 __isl_take isl_union_map *umap,
1390 __isl_take isl_union_set *uset);
1391 __isl_give isl_union_map *isl_union_map_intersect(
1392 __isl_take isl_union_map *umap1,
1393 __isl_take isl_union_map *umap2);
1397 __isl_give isl_set *isl_basic_set_union(
1398 __isl_take isl_basic_set *bset1,
1399 __isl_take isl_basic_set *bset2);
1400 __isl_give isl_map *isl_basic_map_union(
1401 __isl_take isl_basic_map *bmap1,
1402 __isl_take isl_basic_map *bmap2);
1403 __isl_give isl_set *isl_set_union(
1404 __isl_take isl_set *set1,
1405 __isl_take isl_set *set2);
1406 __isl_give isl_map *isl_map_union(
1407 __isl_take isl_map *map1,
1408 __isl_take isl_map *map2);
1409 __isl_give isl_union_set *isl_union_set_union(
1410 __isl_take isl_union_set *uset1,
1411 __isl_take isl_union_set *uset2);
1412 __isl_give isl_union_map *isl_union_map_union(
1413 __isl_take isl_union_map *umap1,
1414 __isl_take isl_union_map *umap2);
1416 =item * Set difference
1418 __isl_give isl_set *isl_set_subtract(
1419 __isl_take isl_set *set1,
1420 __isl_take isl_set *set2);
1421 __isl_give isl_map *isl_map_subtract(
1422 __isl_take isl_map *map1,
1423 __isl_take isl_map *map2);
1424 __isl_give isl_union_set *isl_union_set_subtract(
1425 __isl_take isl_union_set *uset1,
1426 __isl_take isl_union_set *uset2);
1427 __isl_give isl_union_map *isl_union_map_subtract(
1428 __isl_take isl_union_map *umap1,
1429 __isl_take isl_union_map *umap2);
1433 __isl_give isl_basic_set *isl_basic_set_apply(
1434 __isl_take isl_basic_set *bset,
1435 __isl_take isl_basic_map *bmap);
1436 __isl_give isl_set *isl_set_apply(
1437 __isl_take isl_set *set,
1438 __isl_take isl_map *map);
1439 __isl_give isl_union_set *isl_union_set_apply(
1440 __isl_take isl_union_set *uset,
1441 __isl_take isl_union_map *umap);
1442 __isl_give isl_basic_map *isl_basic_map_apply_domain(
1443 __isl_take isl_basic_map *bmap1,
1444 __isl_take isl_basic_map *bmap2);
1445 __isl_give isl_basic_map *isl_basic_map_apply_range(
1446 __isl_take isl_basic_map *bmap1,
1447 __isl_take isl_basic_map *bmap2);
1448 __isl_give isl_map *isl_map_apply_domain(
1449 __isl_take isl_map *map1,
1450 __isl_take isl_map *map2);
1451 __isl_give isl_union_map *isl_union_map_apply_domain(
1452 __isl_take isl_union_map *umap1,
1453 __isl_take isl_union_map *umap2);
1454 __isl_give isl_map *isl_map_apply_range(
1455 __isl_take isl_map *map1,
1456 __isl_take isl_map *map2);
1457 __isl_give isl_union_map *isl_union_map_apply_range(
1458 __isl_take isl_union_map *umap1,
1459 __isl_take isl_union_map *umap2);
1461 =item * Simplification
1463 __isl_give isl_basic_set *isl_basic_set_gist(
1464 __isl_take isl_basic_set *bset,
1465 __isl_take isl_basic_set *context);
1466 __isl_give isl_set *isl_set_gist(__isl_take isl_set *set,
1467 __isl_take isl_set *context);
1468 __isl_give isl_union_set *isl_union_set_gist(
1469 __isl_take isl_union_set *uset,
1470 __isl_take isl_union_set *context);
1471 __isl_give isl_basic_map *isl_basic_map_gist(
1472 __isl_take isl_basic_map *bmap,
1473 __isl_take isl_basic_map *context);
1474 __isl_give isl_map *isl_map_gist(__isl_take isl_map *map,
1475 __isl_take isl_map *context);
1476 __isl_give isl_union_map *isl_union_map_gist(
1477 __isl_take isl_union_map *umap,
1478 __isl_take isl_union_map *context);
1480 The gist operation returns a set or relation that has the
1481 same intersection with the context as the input set or relation.
1482 Any implicit equality in the intersection is made explicit in the result,
1483 while all inequalities that are redundant with respect to the intersection
1485 In case of union sets and relations, the gist operation is performed
1490 =head3 Lexicographic Optimization
1492 Given a (basic) set C<set> (or C<bset>) and a zero-dimensional domain C<dom>,
1493 the following functions
1494 compute a set that contains the lexicographic minimum or maximum
1495 of the elements in C<set> (or C<bset>) for those values of the parameters
1496 that satisfy C<dom>.
1497 If C<empty> is not C<NULL>, then C<*empty> is assigned a set
1498 that contains the parameter values in C<dom> for which C<set> (or C<bset>)
1500 In other words, the union of the parameter values
1501 for which the result is non-empty and of C<*empty>
1504 __isl_give isl_set *isl_basic_set_partial_lexmin(
1505 __isl_take isl_basic_set *bset,
1506 __isl_take isl_basic_set *dom,
1507 __isl_give isl_set **empty);
1508 __isl_give isl_set *isl_basic_set_partial_lexmax(
1509 __isl_take isl_basic_set *bset,
1510 __isl_take isl_basic_set *dom,
1511 __isl_give isl_set **empty);
1512 __isl_give isl_set *isl_set_partial_lexmin(
1513 __isl_take isl_set *set, __isl_take isl_set *dom,
1514 __isl_give isl_set **empty);
1515 __isl_give isl_set *isl_set_partial_lexmax(
1516 __isl_take isl_set *set, __isl_take isl_set *dom,
1517 __isl_give isl_set **empty);
1519 Given a (basic) set C<set> (or C<bset>), the following functions simply
1520 return a set containing the lexicographic minimum or maximum
1521 of the elements in C<set> (or C<bset>).
1522 In case of union sets, the optimum is computed per space.
1524 __isl_give isl_set *isl_basic_set_lexmin(
1525 __isl_take isl_basic_set *bset);
1526 __isl_give isl_set *isl_basic_set_lexmax(
1527 __isl_take isl_basic_set *bset);
1528 __isl_give isl_set *isl_set_lexmin(
1529 __isl_take isl_set *set);
1530 __isl_give isl_set *isl_set_lexmax(
1531 __isl_take isl_set *set);
1532 __isl_give isl_union_set *isl_union_set_lexmin(
1533 __isl_take isl_union_set *uset);
1534 __isl_give isl_union_set *isl_union_set_lexmax(
1535 __isl_take isl_union_set *uset);
1537 Given a (basic) relation C<map> (or C<bmap>) and a domain C<dom>,
1538 the following functions
1539 compute a relation that maps each element of C<dom>
1540 to the single lexicographic minimum or maximum
1541 of the elements that are associated to that same
1542 element in C<map> (or C<bmap>).
1543 If C<empty> is not C<NULL>, then C<*empty> is assigned a set
1544 that contains the elements in C<dom> that do not map
1545 to any elements in C<map> (or C<bmap>).
1546 In other words, the union of the domain of the result and of C<*empty>
1549 __isl_give isl_map *isl_basic_map_partial_lexmax(
1550 __isl_take isl_basic_map *bmap,
1551 __isl_take isl_basic_set *dom,
1552 __isl_give isl_set **empty);
1553 __isl_give isl_map *isl_basic_map_partial_lexmin(
1554 __isl_take isl_basic_map *bmap,
1555 __isl_take isl_basic_set *dom,
1556 __isl_give isl_set **empty);
1557 __isl_give isl_map *isl_map_partial_lexmax(
1558 __isl_take isl_map *map, __isl_take isl_set *dom,
1559 __isl_give isl_set **empty);
1560 __isl_give isl_map *isl_map_partial_lexmin(
1561 __isl_take isl_map *map, __isl_take isl_set *dom,
1562 __isl_give isl_set **empty);
1564 Given a (basic) map C<map> (or C<bmap>), the following functions simply
1565 return a map mapping each element in the domain of
1566 C<map> (or C<bmap>) to the lexicographic minimum or maximum
1567 of all elements associated to that element.
1568 In case of union relations, the optimum is computed per space.
1570 __isl_give isl_map *isl_basic_map_lexmin(
1571 __isl_take isl_basic_map *bmap);
1572 __isl_give isl_map *isl_basic_map_lexmax(
1573 __isl_take isl_basic_map *bmap);
1574 __isl_give isl_map *isl_map_lexmin(
1575 __isl_take isl_map *map);
1576 __isl_give isl_map *isl_map_lexmax(
1577 __isl_take isl_map *map);
1578 __isl_give isl_union_map *isl_union_map_lexmin(
1579 __isl_take isl_union_map *umap);
1580 __isl_give isl_union_map *isl_union_map_lexmax(
1581 __isl_take isl_union_map *umap);
1585 Matrices can be created, copied and freed using the following functions.
1587 #include <isl_mat.h>
1588 __isl_give isl_mat *isl_mat_alloc(struct isl_ctx *ctx,
1589 unsigned n_row, unsigned n_col);
1590 __isl_give isl_mat *isl_mat_copy(__isl_keep isl_mat *mat);
1591 void isl_mat_free(__isl_take isl_mat *mat);
1593 Note that the elements of a newly created matrix may have arbitrary values.
1594 The elements can be changed and inspected using the following functions.
1596 int isl_mat_rows(__isl_keep isl_mat *mat);
1597 int isl_mat_cols(__isl_keep isl_mat *mat);
1598 int isl_mat_get_element(__isl_keep isl_mat *mat,
1599 int row, int col, isl_int *v);
1600 __isl_give isl_mat *isl_mat_set_element(__isl_take isl_mat *mat,
1601 int row, int col, isl_int v);
1603 C<isl_mat_get_element> will return a negative value if anything went wrong.
1604 In that case, the value of C<*v> is undefined.
1606 The following function can be used to compute the (right) inverse
1607 of a matrix, i.e., a matrix such that the product of the original
1608 and the inverse (in that order) is a multiple of the identity matrix.
1609 The input matrix is assumed to be of full row-rank.
1611 __isl_give isl_mat *isl_mat_right_inverse(__isl_take isl_mat *mat);
1613 The following function can be used to compute the (right) kernel
1614 (or null space) of a matrix, i.e., a matrix such that the product of
1615 the original and the kernel (in that order) is the zero matrix.
1617 __isl_give isl_mat *isl_mat_right_kernel(__isl_take isl_mat *mat);
1621 Points are elements of a set. They can be used to construct
1622 simple sets (boxes) or they can be used to represent the
1623 individual elements of a set.
1624 The zero point (the origin) can be created using
1626 __isl_give isl_point *isl_point_zero(__isl_take isl_dim *dim);
1628 The coordinates of a point can be inspected, set and changed
1631 void isl_point_get_coordinate(__isl_keep isl_point *pnt,
1632 enum isl_dim_type type, int pos, isl_int *v);
1633 __isl_give isl_point *isl_point_set_coordinate(
1634 __isl_take isl_point *pnt,
1635 enum isl_dim_type type, int pos, isl_int v);
1637 __isl_give isl_point *isl_point_add_ui(
1638 __isl_take isl_point *pnt,
1639 enum isl_dim_type type, int pos, unsigned val);
1640 __isl_give isl_point *isl_point_sub_ui(
1641 __isl_take isl_point *pnt,
1642 enum isl_dim_type type, int pos, unsigned val);
1644 Points can be copied or freed using
1646 __isl_give isl_point *isl_point_copy(
1647 __isl_keep isl_point *pnt);
1648 void isl_point_free(__isl_take isl_point *pnt);
1650 A singleton set can be created from a point using
1652 __isl_give isl_set *isl_set_from_point(
1653 __isl_take isl_point *pnt);
1655 and a box can be created from two opposite extremal points using
1657 __isl_give isl_set *isl_set_box_from_points(
1658 __isl_take isl_point *pnt1,
1659 __isl_take isl_point *pnt2);
1661 All elements of a B<bounded> (union) set can be enumerated using
1662 the following functions.
1664 int isl_set_foreach_point(__isl_keep isl_set *set,
1665 int (*fn)(__isl_take isl_point *pnt, void *user),
1667 int isl_union_set_foreach_point(__isl_keep isl_union_set *uset,
1668 int (*fn)(__isl_take isl_point *pnt, void *user),
1671 The function C<fn> is called for each integer point in
1672 C<set> with as second argument the last argument of
1673 the C<isl_set_foreach_point> call. The function C<fn>
1674 should return C<0> on success and C<-1> on failure.
1675 In the latter case, C<isl_set_foreach_point> will stop
1676 enumerating and return C<-1> as well.
1677 If the enumeration is performed successfully and to completion,
1678 then C<isl_set_foreach_point> returns C<0>.
1680 To obtain a single point of a set, use
1682 __isl_give isl_point *isl_set_sample_point(
1683 __isl_take isl_set *set);
1685 If C<set> does not contain any (integer) points, then the
1686 resulting point will be ``void'', a property that can be
1689 int isl_point_is_void(__isl_keep isl_point *pnt);
1691 =head2 Piecewise Quasipolynomials
1693 A piecewise quasipolynomial is a particular kind of function that maps
1694 a parametric point to a rational value.
1695 More specifically, a quasipolynomial is a polynomial expression in greatest
1696 integer parts of affine expressions of parameters and variables.
1697 A piecewise quasipolynomial is a subdivision of a given parametric
1698 domain into disjoint cells with a quasipolynomial associated to
1699 each cell. The value of the piecewise quasipolynomial at a given
1700 point is the value of the quasipolynomial associated to the cell
1701 that contains the point. Outside of the union of cells,
1702 the value is assumed to be zero.
1703 For example, the piecewise quasipolynomial
1705 [n] -> { [x] -> ((1 + n) - x) : x <= n and x >= 0 }
1707 maps C<x> to C<1 + n - x> for values of C<x> between C<0> and C<n>.
1708 A given piecewise quasipolynomial has a fixed domain dimension.
1709 Union piecewise quasipolynomials are used to contain piecewise quasipolynomials
1710 defined over different domains.
1711 Piecewise quasipolynomials are mainly used by the C<barvinok>
1712 library for representing the number of elements in a parametric set or map.
1713 For example, the piecewise quasipolynomial above represents
1714 the number of points in the map
1716 [n] -> { [x] -> [y] : x,y >= 0 and 0 <= x + y <= n }
1718 =head3 Printing (Piecewise) Quasipolynomials
1720 Quasipolynomials and piecewise quasipolynomials can be printed
1721 using the following functions.
1723 __isl_give isl_printer *isl_printer_print_qpolynomial(
1724 __isl_take isl_printer *p,
1725 __isl_keep isl_qpolynomial *qp);
1727 __isl_give isl_printer *isl_printer_print_pw_qpolynomial(
1728 __isl_take isl_printer *p,
1729 __isl_keep isl_pw_qpolynomial *pwqp);
1731 __isl_give isl_printer *isl_printer_print_union_pw_qpolynomial(
1732 __isl_take isl_printer *p,
1733 __isl_keep isl_union_pw_qpolynomial *upwqp);
1735 The output format of the printer
1736 needs to be set to either C<ISL_FORMAT_ISL> or C<ISL_FORMAT_C>.
1737 For C<isl_printer_print_union_pw_qpolynomial>, only C<ISL_FORMAT_ISL>
1739 In case of printing in C<ISL_FORMAT_C>, the user may want
1740 to set the names of all dimensions
1742 __isl_give isl_qpolynomial *isl_qpolynomial_set_dim_name(
1743 __isl_take isl_qpolynomial *qp,
1744 enum isl_dim_type type, unsigned pos,
1746 __isl_give isl_pw_qpolynomial *
1747 isl_pw_qpolynomial_set_dim_name(
1748 __isl_take isl_pw_qpolynomial *pwqp,
1749 enum isl_dim_type type, unsigned pos,
1752 =head3 Creating New (Piecewise) Quasipolynomials
1754 Some simple quasipolynomials can be created using the following functions.
1755 More complicated quasipolynomials can be created by applying
1756 operations such as addition and multiplication
1757 on the resulting quasipolynomials
1759 __isl_give isl_qpolynomial *isl_qpolynomial_zero(
1760 __isl_take isl_dim *dim);
1761 __isl_give isl_qpolynomial *isl_qpolynomial_one(
1762 __isl_take isl_dim *dim);
1763 __isl_give isl_qpolynomial *isl_qpolynomial_infty(
1764 __isl_take isl_dim *dim);
1765 __isl_give isl_qpolynomial *isl_qpolynomial_neginfty(
1766 __isl_take isl_dim *dim);
1767 __isl_give isl_qpolynomial *isl_qpolynomial_nan(
1768 __isl_take isl_dim *dim);
1769 __isl_give isl_qpolynomial *isl_qpolynomial_rat_cst(
1770 __isl_take isl_dim *dim,
1771 const isl_int n, const isl_int d);
1772 __isl_give isl_qpolynomial *isl_qpolynomial_div(
1773 __isl_take isl_div *div);
1774 __isl_give isl_qpolynomial *isl_qpolynomial_var(
1775 __isl_take isl_dim *dim,
1776 enum isl_dim_type type, unsigned pos);
1778 The zero piecewise quasipolynomial or a piecewise quasipolynomial
1779 with a single cell can be created using the following functions.
1780 Multiple of these single cell piecewise quasipolynomials can
1781 be combined to create more complicated piecewise quasipolynomials.
1783 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_zero(
1784 __isl_take isl_dim *dim);
1785 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_alloc(
1786 __isl_take isl_set *set,
1787 __isl_take isl_qpolynomial *qp);
1789 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_zero(
1790 __isl_take isl_dim *dim);
1791 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_from_pw_qpolynomial(
1792 __isl_take isl_pw_qpolynomial *pwqp);
1793 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_add_pw_qpolynomial(
1794 __isl_take isl_union_pw_qpolynomial *upwqp,
1795 __isl_take isl_pw_qpolynomial *pwqp);
1797 Quasipolynomials can be copied and freed again using the following
1800 __isl_give isl_qpolynomial *isl_qpolynomial_copy(
1801 __isl_keep isl_qpolynomial *qp);
1802 void isl_qpolynomial_free(__isl_take isl_qpolynomial *qp);
1804 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_copy(
1805 __isl_keep isl_pw_qpolynomial *pwqp);
1806 void isl_pw_qpolynomial_free(
1807 __isl_take isl_pw_qpolynomial *pwqp);
1809 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_copy(
1810 __isl_keep isl_union_pw_qpolynomial *upwqp);
1811 void isl_union_pw_qpolynomial_free(
1812 __isl_take isl_union_pw_qpolynomial *upwqp);
1814 =head3 Inspecting (Piecewise) Quasipolynomials
1816 To iterate over all piecewise quasipolynomials in a union
1817 piecewise quasipolynomial, use the following function
1819 int isl_union_pw_qpolynomial_foreach_pw_qpolynomial(
1820 __isl_keep isl_union_pw_qpolynomial *upwqp,
1821 int (*fn)(__isl_take isl_pw_qpolynomial *pwqp, void *user),
1824 To extract the piecewise quasipolynomial from a union with a given dimension
1827 __isl_give isl_pw_qpolynomial *
1828 isl_union_pw_qpolynomial_extract_pw_qpolynomial(
1829 __isl_keep isl_union_pw_qpolynomial *upwqp,
1830 __isl_take isl_dim *dim);
1832 To iterate over the cells in a piecewise quasipolynomial,
1833 use either of the following two functions
1835 int isl_pw_qpolynomial_foreach_piece(
1836 __isl_keep isl_pw_qpolynomial *pwqp,
1837 int (*fn)(__isl_take isl_set *set,
1838 __isl_take isl_qpolynomial *qp,
1839 void *user), void *user);
1840 int isl_pw_qpolynomial_foreach_lifted_piece(
1841 __isl_keep isl_pw_qpolynomial *pwqp,
1842 int (*fn)(__isl_take isl_set *set,
1843 __isl_take isl_qpolynomial *qp,
1844 void *user), void *user);
1846 As usual, the function C<fn> should return C<0> on success
1847 and C<-1> on failure. The difference between
1848 C<isl_pw_qpolynomial_foreach_piece> and
1849 C<isl_pw_qpolynomial_foreach_lifted_piece> is that
1850 C<isl_pw_qpolynomial_foreach_lifted_piece> will first
1851 compute unique representations for all existentially quantified
1852 variables and then turn these existentially quantified variables
1853 into extra set variables, adapting the associated quasipolynomial
1854 accordingly. This means that the C<set> passed to C<fn>
1855 will not have any existentially quantified variables, but that
1856 the dimensions of the sets may be different for different
1857 invocations of C<fn>.
1859 To iterate over all terms in a quasipolynomial,
1862 int isl_qpolynomial_foreach_term(
1863 __isl_keep isl_qpolynomial *qp,
1864 int (*fn)(__isl_take isl_term *term,
1865 void *user), void *user);
1867 The terms themselves can be inspected and freed using
1870 unsigned isl_term_dim(__isl_keep isl_term *term,
1871 enum isl_dim_type type);
1872 void isl_term_get_num(__isl_keep isl_term *term,
1874 void isl_term_get_den(__isl_keep isl_term *term,
1876 int isl_term_get_exp(__isl_keep isl_term *term,
1877 enum isl_dim_type type, unsigned pos);
1878 __isl_give isl_div *isl_term_get_div(
1879 __isl_keep isl_term *term, unsigned pos);
1880 void isl_term_free(__isl_take isl_term *term);
1882 Each term is a product of parameters, set variables and
1883 integer divisions. The function C<isl_term_get_exp>
1884 returns the exponent of a given dimensions in the given term.
1885 The C<isl_int>s in the arguments of C<isl_term_get_num>
1886 and C<isl_term_get_den> need to have been initialized
1887 using C<isl_int_init> before calling these functions.
1889 =head3 Properties of (Piecewise) Quasipolynomials
1891 To check whether a quasipolynomial is actually a constant,
1892 use the following function.
1894 int isl_qpolynomial_is_cst(__isl_keep isl_qpolynomial *qp,
1895 isl_int *n, isl_int *d);
1897 If C<qp> is a constant and if C<n> and C<d> are not C<NULL>
1898 then the numerator and denominator of the constant
1899 are returned in C<*n> and C<*d>, respectively.
1901 =head3 Operations on (Piecewise) Quasipolynomials
1903 __isl_give isl_qpolynomial *isl_qpolynomial_neg(
1904 __isl_take isl_qpolynomial *qp);
1905 __isl_give isl_qpolynomial *isl_qpolynomial_add(
1906 __isl_take isl_qpolynomial *qp1,
1907 __isl_take isl_qpolynomial *qp2);
1908 __isl_give isl_qpolynomial *isl_qpolynomial_sub(
1909 __isl_take isl_qpolynomial *qp1,
1910 __isl_take isl_qpolynomial *qp2);
1911 __isl_give isl_qpolynomial *isl_qpolynomial_mul(
1912 __isl_take isl_qpolynomial *qp1,
1913 __isl_take isl_qpolynomial *qp2);
1915 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_add(
1916 __isl_take isl_pw_qpolynomial *pwqp1,
1917 __isl_take isl_pw_qpolynomial *pwqp2);
1918 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_sub(
1919 __isl_take isl_pw_qpolynomial *pwqp1,
1920 __isl_take isl_pw_qpolynomial *pwqp2);
1921 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_add_disjoint(
1922 __isl_take isl_pw_qpolynomial *pwqp1,
1923 __isl_take isl_pw_qpolynomial *pwqp2);
1924 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_neg(
1925 __isl_take isl_pw_qpolynomial *pwqp);
1926 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_mul(
1927 __isl_take isl_pw_qpolynomial *pwqp1,
1928 __isl_take isl_pw_qpolynomial *pwqp2);
1930 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_add(
1931 __isl_take isl_union_pw_qpolynomial *upwqp1,
1932 __isl_take isl_union_pw_qpolynomial *upwqp2);
1933 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_sub(
1934 __isl_take isl_union_pw_qpolynomial *upwqp1,
1935 __isl_take isl_union_pw_qpolynomial *upwqp2);
1936 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_mul(
1937 __isl_take isl_union_pw_qpolynomial *upwqp1,
1938 __isl_take isl_union_pw_qpolynomial *upwqp2);
1940 __isl_give isl_qpolynomial *isl_pw_qpolynomial_eval(
1941 __isl_take isl_pw_qpolynomial *pwqp,
1942 __isl_take isl_point *pnt);
1944 __isl_give isl_qpolynomial *isl_union_pw_qpolynomial_eval(
1945 __isl_take isl_union_pw_qpolynomial *upwqp,
1946 __isl_take isl_point *pnt);
1948 __isl_give isl_set *isl_pw_qpolynomial_domain(
1949 __isl_take isl_pw_qpolynomial *pwqp);
1950 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_intersect_domain(
1951 __isl_take isl_pw_qpolynomial *pwpq,
1952 __isl_take isl_set *set);
1954 __isl_give isl_union_set *isl_union_pw_qpolynomial_domain(
1955 __isl_take isl_union_pw_qpolynomial *upwqp);
1956 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_intersect_domain(
1957 __isl_take isl_union_pw_qpolynomial *upwpq,
1958 __isl_take isl_union_set *uset);
1960 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_coalesce(
1961 __isl_take isl_union_pw_qpolynomial *upwqp);
1963 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_gist(
1964 __isl_take isl_pw_qpolynomial *pwqp,
1965 __isl_take isl_set *context);
1967 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_gist(
1968 __isl_take isl_union_pw_qpolynomial *upwqp,
1969 __isl_take isl_union_set *context);
1971 The gist operation applies the gist operation to each of
1972 the cells in the domain of the input piecewise quasipolynomial.
1973 In future, the operation will also exploit the context
1974 to simplify the quasipolynomials associated to each cell.
1976 =head2 Bounds on Piecewise Quasipolynomials and Piecewise Quasipolynomial Reductions
1978 A piecewise quasipolynomial reduction is a piecewise
1979 reduction (or fold) of quasipolynomials.
1980 In particular, the reduction can be maximum or a minimum.
1981 The objects are mainly used to represent the result of
1982 an upper or lower bound on a quasipolynomial over its domain,
1983 i.e., as the result of the following function.
1985 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_bound(
1986 __isl_take isl_pw_qpolynomial *pwqp,
1987 enum isl_fold type, int *tight);
1989 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_bound(
1990 __isl_take isl_union_pw_qpolynomial *upwqp,
1991 enum isl_fold type, int *tight);
1993 The C<type> argument may be either C<isl_fold_min> or C<isl_fold_max>.
1994 If C<tight> is not C<NULL>, then C<*tight> is set to C<1>
1995 is the returned bound is known be tight, i.e., for each value
1996 of the parameters there is at least
1997 one element in the domain that reaches the bound.
1998 If the domain of C<pwqp> is not wrapping, then the bound is computed
1999 over all elements in that domain and the result has a purely parametric
2000 domain. If the domain of C<pwqp> is wrapping, then the bound is
2001 computed over the range of the wrapped relation. The domain of the
2002 wrapped relation becomes the domain of the result.
2004 A (piecewise) quasipolynomial reduction can be copied or freed using the
2005 following functions.
2007 __isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_copy(
2008 __isl_keep isl_qpolynomial_fold *fold);
2009 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_copy(
2010 __isl_keep isl_pw_qpolynomial_fold *pwf);
2011 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_copy(
2012 __isl_keep isl_union_pw_qpolynomial_fold *upwf);
2013 void isl_qpolynomial_fold_free(
2014 __isl_take isl_qpolynomial_fold *fold);
2015 void isl_pw_qpolynomial_fold_free(
2016 __isl_take isl_pw_qpolynomial_fold *pwf);
2017 void isl_union_pw_qpolynomial_fold_free(
2018 __isl_take isl_union_pw_qpolynomial_fold *upwf);
2020 =head3 Printing Piecewise Quasipolynomial Reductions
2022 Piecewise quasipolynomial reductions can be printed
2023 using the following function.
2025 __isl_give isl_printer *isl_printer_print_pw_qpolynomial_fold(
2026 __isl_take isl_printer *p,
2027 __isl_keep isl_pw_qpolynomial_fold *pwf);
2028 __isl_give isl_printer *isl_printer_print_union_pw_qpolynomial_fold(
2029 __isl_take isl_printer *p,
2030 __isl_keep isl_union_pw_qpolynomial_fold *upwf);
2032 For C<isl_printer_print_pw_qpolynomial_fold>,
2033 output format of the printer
2034 needs to be set to either C<ISL_FORMAT_ISL> or C<ISL_FORMAT_C>.
2035 For C<isl_printer_print_union_pw_qpolynomial_fold>,
2036 output format of the printer
2037 needs to be set to either C<ISL_FORMAT_ISL>.
2039 =head3 Inspecting (Piecewise) Quasipolynomial Reductions
2041 To iterate over all piecewise quasipolynomial reductions in a union
2042 piecewise quasipolynomial reduction, use the following function
2044 int isl_union_pw_qpolynomial_fold_foreach_pw_qpolynomial_fold(
2045 __isl_keep isl_union_pw_qpolynomial_fold *upwf,
2046 int (*fn)(__isl_take isl_pw_qpolynomial_fold *pwf,
2047 void *user), void *user);
2049 To iterate over the cells in a piecewise quasipolynomial reduction,
2050 use either of the following two functions
2052 int isl_pw_qpolynomial_fold_foreach_piece(
2053 __isl_keep isl_pw_qpolynomial_fold *pwf,
2054 int (*fn)(__isl_take isl_set *set,
2055 __isl_take isl_qpolynomial_fold *fold,
2056 void *user), void *user);
2057 int isl_pw_qpolynomial_fold_foreach_lifted_piece(
2058 __isl_keep isl_pw_qpolynomial_fold *pwf,
2059 int (*fn)(__isl_take isl_set *set,
2060 __isl_take isl_qpolynomial_fold *fold,
2061 void *user), void *user);
2063 See L<Inspecting (Piecewise) Quasipolynomials> for an explanation
2064 of the difference between these two functions.
2066 To iterate over all quasipolynomials in a reduction, use
2068 int isl_qpolynomial_fold_foreach_qpolynomial(
2069 __isl_keep isl_qpolynomial_fold *fold,
2070 int (*fn)(__isl_take isl_qpolynomial *qp,
2071 void *user), void *user);
2073 =head3 Operations on Piecewise Quasipolynomial Reductions
2075 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_fold(
2076 __isl_take isl_pw_qpolynomial_fold *pwf1,
2077 __isl_take isl_pw_qpolynomial_fold *pwf2);
2079 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_fold(
2080 __isl_take isl_union_pw_qpolynomial_fold *upwf1,
2081 __isl_take isl_union_pw_qpolynomial_fold *upwf2);
2083 __isl_give isl_qpolynomial *isl_pw_qpolynomial_fold_eval(
2084 __isl_take isl_pw_qpolynomial_fold *pwf,
2085 __isl_take isl_point *pnt);
2087 __isl_give isl_qpolynomial *isl_union_pw_qpolynomial_fold_eval(
2088 __isl_take isl_union_pw_qpolynomial_fold *upwf,
2089 __isl_take isl_point *pnt);
2091 __isl_give isl_union_set *isl_union_pw_qpolynomial_fold_domain(
2092 __isl_take isl_union_pw_qpolynomial_fold *upwf);
2093 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_intersect_domain(
2094 __isl_take isl_union_pw_qpolynomial_fold *upwf,
2095 __isl_take isl_union_set *uset);
2097 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_coalesce(
2098 __isl_take isl_pw_qpolynomial_fold *pwf);
2100 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_coalesce(
2101 __isl_take isl_union_pw_qpolynomial_fold *upwf);
2103 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_gist(
2104 __isl_take isl_pw_qpolynomial_fold *pwf,
2105 __isl_take isl_set *context);
2107 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_gist(
2108 __isl_take isl_union_pw_qpolynomial_fold *upwf,
2109 __isl_take isl_union_set *context);
2111 The gist operation applies the gist operation to each of
2112 the cells in the domain of the input piecewise quasipolynomial reduction.
2113 In future, the operation will also exploit the context
2114 to simplify the quasipolynomial reductions associated to each cell.
2116 __isl_give isl_pw_qpolynomial_fold *
2117 isl_map_apply_pw_qpolynomial_fold(
2118 __isl_take isl_map *map,
2119 __isl_take isl_pw_qpolynomial_fold *pwf,
2121 __isl_give isl_union_pw_qpolynomial_fold *
2122 isl_union_map_apply_union_pw_qpolynomial_fold(
2123 __isl_take isl_union_map *umap,
2124 __isl_take isl_union_pw_qpolynomial_fold *upwf,
2128 compose the given map with the given piecewise quasipolynomial reduction.
2129 That is, compute a bound (of the same type as C<pwf> or C<upwf> itself)
2130 over all elements in the intersection of the range of the map
2131 and the domain of the piecewise quasipolynomial reduction
2132 as a function of an element in the domain of the map.
2134 =head2 Dependence Analysis
2136 C<isl> contains specialized functionality for performing
2137 array dataflow analysis. That is, given a I<sink> access relation
2138 and a collection of possible I<source> access relations,
2139 C<isl> can compute relations that describe
2140 for each iteration of the sink access, which iteration
2141 of which of the source access relations was the last
2142 to access the same data element before the given iteration
2144 To compute standard flow dependences, the sink should be
2145 a read, while the sources should be writes.
2146 If any of the source accesses are marked as being I<may>
2147 accesses, then there will be a dependence to the last
2148 I<must> access B<and> to any I<may> access that follows
2149 this last I<must> access.
2150 In particular, if I<all> sources are I<may> accesses,
2151 then memory based dependence analysis is performed.
2152 If, on the other hand, all sources are I<must> accesses,
2153 then value based dependence analysis is performed.
2155 #include <isl_flow.h>
2157 typedef int (*isl_access_level_before)(void *first, void *second);
2159 __isl_give isl_access_info *isl_access_info_alloc(
2160 __isl_take isl_map *sink,
2161 void *sink_user, isl_access_level_before fn,
2163 __isl_give isl_access_info *isl_access_info_add_source(
2164 __isl_take isl_access_info *acc,
2165 __isl_take isl_map *source, int must,
2167 void isl_access_info_free(__isl_take isl_access_info *acc);
2169 __isl_give isl_flow *isl_access_info_compute_flow(
2170 __isl_take isl_access_info *acc);
2172 int isl_flow_foreach(__isl_keep isl_flow *deps,
2173 int (*fn)(__isl_take isl_map *dep, int must,
2174 void *dep_user, void *user),
2176 __isl_give isl_set *isl_flow_get_no_source(
2177 __isl_keep isl_flow *deps, int must);
2178 void isl_flow_free(__isl_take isl_flow *deps);
2180 The function C<isl_access_info_compute_flow> performs the actual
2181 dependence analysis. The other functions are used to construct
2182 the input for this function or to read off the output.
2184 The input is collected in an C<isl_access_info>, which can
2185 be created through a call to C<isl_access_info_alloc>.
2186 The arguments to this functions are the sink access relation
2187 C<sink>, a token C<sink_user> used to identify the sink
2188 access to the user, a callback function for specifying the
2189 relative order of source and sink accesses, and the number
2190 of source access relations that will be added.
2191 The callback function has type C<int (*)(void *first, void *second)>.
2192 The function is called with two user supplied tokens identifying
2193 either a source or the sink and it should return the shared nesting
2194 level and the relative order of the two accesses.
2195 In particular, let I<n> be the number of loops shared by
2196 the two accesses. If C<first> precedes C<second> textually,
2197 then the function should return I<2 * n + 1>; otherwise,
2198 it should return I<2 * n>.
2199 The sources can be added to the C<isl_access_info> by performing
2200 (at most) C<max_source> calls to C<isl_access_info_add_source>.
2201 C<must> indicates whether the source is a I<must> access
2202 or a I<may> access. Note that a multi-valued access relation
2203 should only be marked I<must> if every iteration in the domain
2204 of the relation accesses I<all> elements in its image.
2205 The C<source_user> token is again used to identify
2206 the source access. The range of the source access relation
2207 C<source> should have the same dimension as the range
2208 of the sink access relation.
2209 The C<isl_access_info_free> function should usually not be
2210 called explicitly, because it is called implicitly by
2211 C<isl_access_info_compute_flow>.
2213 The result of the dependence analysis is collected in an
2214 C<isl_flow>. There may be elements in the domain of
2215 the sink access for which no preceding source access could be
2216 found or for which all preceding sources are I<may> accesses.
2217 The sets of these elements can be obtained through
2218 calls to C<isl_flow_get_no_source>, the first with C<must> set
2219 and the second with C<must> unset.
2220 In the case of standard flow dependence analysis,
2221 with the sink a read and the sources I<must> writes,
2222 the first set corresponds to the reads from uninitialized
2223 array elements and the second set is empty.
2224 The actual flow dependences can be extracted using
2225 C<isl_flow_foreach>. This function will call the user-specified
2226 callback function C<fn> for each B<non-empty> dependence between
2227 a source and the sink. The callback function is called
2228 with four arguments, the actual flow dependence relation
2229 mapping source iterations to sink iterations, a boolean that
2230 indicates whether it is a I<must> or I<may> dependence, a token
2231 identifying the source and an additional C<void *> with value
2232 equal to the third argument of the C<isl_flow_foreach> call.
2233 A dependence is marked I<must> if it originates from a I<must>
2234 source and if it is not followed by any I<may> sources.
2236 After finishing with an C<isl_flow>, the user should call
2237 C<isl_flow_free> to free all associated memory.
2239 A higher-level interface to dependence analysis is provided
2240 by the following function.
2242 #include <isl_flow.h>
2244 int isl_union_map_compute_flow(__isl_take isl_union_map *sink,
2245 __isl_take isl_union_map *must_source,
2246 __isl_take isl_union_map *may_source,
2247 __isl_take isl_union_map *schedule,
2248 __isl_give isl_union_map **must_dep,
2249 __isl_give isl_union_map **may_dep,
2250 __isl_give isl_union_set **must_no_source,
2251 __isl_give isl_union_set **may_no_source);
2253 The arrays are identified by the tuple names of the ranges
2254 of the accesses. The iteration domains by the tuple names
2255 of the domains of the accesses and of the schedule.
2256 The relative order of the iteration domains is given by the
2257 schedule. Any of C<must_dep>, C<may_dep>, C<must_no_source>
2258 or C<may_no_source> may be C<NULL>, but a C<NULL> value for
2259 any of the other arguments is treated as an error.
2261 =head2 Parametric Vertex Enumeration
2263 The parametric vertex enumeration described in this section
2264 is mainly intended to be used internally and by the C<barvinok>
2267 #include <isl_vertices.h>
2268 __isl_give isl_vertices *isl_basic_set_compute_vertices(
2269 __isl_keep isl_basic_set *bset);
2271 The function C<isl_basic_set_compute_vertices> performs the
2272 actual computation of the parametric vertices and the chamber
2273 decomposition and store the result in an C<isl_vertices> object.
2274 This information can be queried by either iterating over all
2275 the vertices or iterating over all the chambers or cells
2276 and then iterating over all vertices that are active on the chamber.
2278 int isl_vertices_foreach_vertex(
2279 __isl_keep isl_vertices *vertices,
2280 int (*fn)(__isl_take isl_vertex *vertex, void *user),
2283 int isl_vertices_foreach_cell(
2284 __isl_keep isl_vertices *vertices,
2285 int (*fn)(__isl_take isl_cell *cell, void *user),
2287 int isl_cell_foreach_vertex(__isl_keep isl_cell *cell,
2288 int (*fn)(__isl_take isl_vertex *vertex, void *user),
2291 Other operations that can be performed on an C<isl_vertices> object are
2294 isl_ctx *isl_vertices_get_ctx(
2295 __isl_keep isl_vertices *vertices);
2296 int isl_vertices_get_n_vertices(
2297 __isl_keep isl_vertices *vertices);
2298 void isl_vertices_free(__isl_take isl_vertices *vertices);
2300 Vertices can be inspected and destroyed using the following functions.
2302 isl_ctx *isl_vertex_get_ctx(__isl_keep isl_vertex *vertex);
2303 int isl_vertex_get_id(__isl_keep isl_vertex *vertex);
2304 __isl_give isl_basic_set *isl_vertex_get_domain(
2305 __isl_keep isl_vertex *vertex);
2306 __isl_give isl_basic_set *isl_vertex_get_expr(
2307 __isl_keep isl_vertex *vertex);
2308 void isl_vertex_free(__isl_take isl_vertex *vertex);
2310 C<isl_vertex_get_expr> returns a singleton parametric set describing
2311 the vertex, while C<isl_vertex_get_domain> returns the activity domain
2313 Note that C<isl_vertex_get_domain> and C<isl_vertex_get_expr> return
2314 B<rational> basic sets, so they should mainly be used for inspection
2315 and should not be mixed with integer sets.
2317 Chambers can be inspected and destroyed using the following functions.
2319 isl_ctx *isl_cell_get_ctx(__isl_keep isl_cell *cell);
2320 __isl_give isl_basic_set *isl_cell_get_domain(
2321 __isl_keep isl_cell *cell);
2322 void isl_cell_free(__isl_take isl_cell *cell);
2326 Although C<isl> is mainly meant to be used as a library,
2327 it also contains some basic applications that use some
2328 of the functionality of C<isl>.
2329 The input may be specified in either the L<isl format>
2330 or the L<PolyLib format>.
2332 =head2 C<isl_polyhedron_sample>
2334 C<isl_polyhedron_sample> takes a polyhedron as input and prints
2335 an integer element of the polyhedron, if there is any.
2336 The first column in the output is the denominator and is always
2337 equal to 1. If the polyhedron contains no integer points,
2338 then a vector of length zero is printed.
2342 C<isl_pip> takes the same input as the C<example> program
2343 from the C<piplib> distribution, i.e., a set of constraints
2344 on the parameters, a line containing only -1 and finally a set
2345 of constraints on a parametric polyhedron.
2346 The coefficients of the parameters appear in the last columns
2347 (but before the final constant column).
2348 The output is the lexicographic minimum of the parametric polyhedron.
2349 As C<isl> currently does not have its own output format, the output
2350 is just a dump of the internal state.
2352 =head2 C<isl_polyhedron_minimize>
2354 C<isl_polyhedron_minimize> computes the minimum of some linear
2355 or affine objective function over the integer points in a polyhedron.
2356 If an affine objective function
2357 is given, then the constant should appear in the last column.
2359 =head2 C<isl_polytope_scan>
2361 Given a polytope, C<isl_polytope_scan> prints
2362 all integer points in the polytope.
2364 =head1 C<isl-polylib>
2366 The C<isl-polylib> library provides the following functions for converting
2367 between C<isl> objects and C<PolyLib> objects.
2368 The library is distributed separately for licensing reasons.
2370 #include <isl_set_polylib.h>
2371 __isl_give isl_basic_set *isl_basic_set_new_from_polylib(
2372 Polyhedron *P, __isl_take isl_dim *dim);
2373 Polyhedron *isl_basic_set_to_polylib(
2374 __isl_keep isl_basic_set *bset);
2375 __isl_give isl_set *isl_set_new_from_polylib(Polyhedron *D,
2376 __isl_take isl_dim *dim);
2377 Polyhedron *isl_set_to_polylib(__isl_keep isl_set *set);
2379 #include <isl_map_polylib.h>
2380 __isl_give isl_basic_map *isl_basic_map_new_from_polylib(
2381 Polyhedron *P, __isl_take isl_dim *dim);
2382 __isl_give isl_map *isl_map_new_from_polylib(Polyhedron *D,
2383 __isl_take isl_dim *dim);
2384 Polyhedron *isl_basic_map_to_polylib(
2385 __isl_keep isl_basic_map *bmap);
2386 Polyhedron *isl_map_to_polylib(__isl_keep isl_map *map);