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 To iterate over all the sets or maps in a union set or map, use
888 int isl_union_set_foreach_set(__isl_keep isl_union_set *uset,
889 int (*fn)(__isl_take isl_set *set, void *user),
891 int isl_union_map_foreach_map(__isl_keep isl_union_map *umap,
892 int (*fn)(__isl_take isl_map *map, void *user),
895 To iterate over all the basic sets or maps in a set or map, use
897 int isl_set_foreach_basic_set(__isl_keep isl_set *set,
898 int (*fn)(__isl_take isl_basic_set *bset, void *user),
900 int isl_map_foreach_basic_map(__isl_keep isl_map *map,
901 int (*fn)(__isl_take isl_basic_map *bmap, void *user),
904 The callback function C<fn> should return 0 if successful and
905 -1 if an error occurs. In the latter case, or if any other error
906 occurs, the above functions will return -1.
908 It should be noted that C<isl> does not guarantee that
909 the basic sets or maps passed to C<fn> are disjoint.
910 If this is required, then the user should call one of
911 the following functions first.
913 __isl_give isl_set *isl_set_make_disjoint(
914 __isl_take isl_set *set);
915 __isl_give isl_map *isl_map_make_disjoint(
916 __isl_take isl_map *map);
918 To iterate over the constraints of a basic set or map, use
920 #include <isl_constraint.h>
922 int isl_basic_map_foreach_constraint(
923 __isl_keep isl_basic_map *bmap,
924 int (*fn)(__isl_take isl_constraint *c, void *user),
926 void isl_constraint_free(struct isl_constraint *c);
928 Again, the callback function C<fn> should return 0 if successful and
929 -1 if an error occurs. In the latter case, or if any other error
930 occurs, the above functions will return -1.
931 The constraint C<c> represents either an equality or an inequality.
932 Use the following function to find out whether a constraint
933 represents an equality. If not, it represents an inequality.
935 int isl_constraint_is_equality(
936 __isl_keep isl_constraint *constraint);
938 The coefficients of the constraints can be inspected using
939 the following functions.
941 void isl_constraint_get_constant(
942 __isl_keep isl_constraint *constraint, isl_int *v);
943 void isl_constraint_get_coefficient(
944 __isl_keep isl_constraint *constraint,
945 enum isl_dim_type type, int pos, isl_int *v);
947 The explicit representations of the existentially quantified
948 variables can be inspected using the following functions.
949 Note that the user is only allowed to use these functions
950 if the inspected set or map is the result of a call
951 to C<isl_set_compute_divs> or C<isl_map_compute_divs>.
953 __isl_give isl_div *isl_constraint_div(
954 __isl_keep isl_constraint *constraint, int pos);
955 void isl_div_get_constant(__isl_keep isl_div *div,
957 void isl_div_get_denominator(__isl_keep isl_div *div,
959 void isl_div_get_coefficient(__isl_keep isl_div *div,
960 enum isl_dim_type type, int pos, isl_int *v);
962 To obtain the constraints of a basic map in matrix
963 form, use the following functions.
965 __isl_give isl_mat *isl_basic_map_equalities_matrix(
966 __isl_keep isl_basic_map *bmap,
967 enum isl_dim_type c1,
968 enum isl_dim_type c2, enum isl_dim_type c3,
969 enum isl_dim_type c4, enum isl_dim_type c5);
970 __isl_give isl_mat *isl_basic_map_inequalities_matrix(
971 __isl_keep isl_basic_map *bmap,
972 enum isl_dim_type c1,
973 enum isl_dim_type c2, enum isl_dim_type c3,
974 enum isl_dim_type c4, enum isl_dim_type c5);
976 The C<isl_dim_type> arguments dictate the order in which
977 different kinds of variables appear in the resulting matrix
978 and should be a permutation of C<isl_dim_cst>, C<isl_dim_param>,
979 C<isl_dim_in>, C<isl_dim_out> and C<isl_dim_div>.
983 =head3 Unary Properties
989 The following functions test whether the given set or relation
990 contains any integer points. The ``fast'' variants do not perform
991 any computations, but simply check if the given set or relation
992 is already known to be empty.
994 int isl_basic_set_fast_is_empty(__isl_keep isl_basic_set *bset);
995 int isl_basic_set_is_empty(__isl_keep isl_basic_set *bset);
996 int isl_set_is_empty(__isl_keep isl_set *set);
997 int isl_union_set_is_empty(__isl_keep isl_union_set *uset);
998 int isl_basic_map_fast_is_empty(__isl_keep isl_basic_map *bmap);
999 int isl_basic_map_is_empty(__isl_keep isl_basic_map *bmap);
1000 int isl_map_fast_is_empty(__isl_keep isl_map *map);
1001 int isl_map_is_empty(__isl_keep isl_map *map);
1002 int isl_union_map_is_empty(__isl_keep isl_union_map *umap);
1004 =item * Universality
1006 int isl_basic_set_is_universe(__isl_keep isl_basic_set *bset);
1007 int isl_basic_map_is_universe(__isl_keep isl_basic_map *bmap);
1008 int isl_set_fast_is_universe(__isl_keep isl_set *set);
1010 =item * Single-valuedness
1012 int isl_map_is_single_valued(__isl_keep isl_map *map);
1016 int isl_map_is_bijective(__isl_keep isl_map *map);
1020 The followning functions check whether the domain of the given
1021 (basic) set is a wrapped relation.
1023 int isl_basic_set_is_wrapping(
1024 __isl_keep isl_basic_set *bset);
1025 int isl_set_is_wrapping(__isl_keep isl_set *set);
1029 =head3 Binary Properties
1035 int isl_set_fast_is_equal(__isl_keep isl_set *set1,
1036 __isl_keep isl_set *set2);
1037 int isl_set_is_equal(__isl_keep isl_set *set1,
1038 __isl_keep isl_set *set2);
1039 int isl_basic_map_is_equal(
1040 __isl_keep isl_basic_map *bmap1,
1041 __isl_keep isl_basic_map *bmap2);
1042 int isl_map_is_equal(__isl_keep isl_map *map1,
1043 __isl_keep isl_map *map2);
1044 int isl_map_fast_is_equal(__isl_keep isl_map *map1,
1045 __isl_keep isl_map *map2);
1046 int isl_union_map_is_equal(
1047 __isl_keep isl_union_map *umap1,
1048 __isl_keep isl_union_map *umap2);
1050 =item * Disjointness
1052 int isl_set_fast_is_disjoint(__isl_keep isl_set *set1,
1053 __isl_keep isl_set *set2);
1057 int isl_set_is_subset(__isl_keep isl_set *set1,
1058 __isl_keep isl_set *set2);
1059 int isl_set_is_strict_subset(
1060 __isl_keep isl_set *set1,
1061 __isl_keep isl_set *set2);
1062 int isl_basic_map_is_subset(
1063 __isl_keep isl_basic_map *bmap1,
1064 __isl_keep isl_basic_map *bmap2);
1065 int isl_basic_map_is_strict_subset(
1066 __isl_keep isl_basic_map *bmap1,
1067 __isl_keep isl_basic_map *bmap2);
1068 int isl_map_is_subset(
1069 __isl_keep isl_map *map1,
1070 __isl_keep isl_map *map2);
1071 int isl_map_is_strict_subset(
1072 __isl_keep isl_map *map1,
1073 __isl_keep isl_map *map2);
1074 int isl_union_map_is_subset(
1075 __isl_keep isl_union_map *umap1,
1076 __isl_keep isl_union_map *umap2);
1077 int isl_union_map_is_strict_subset(
1078 __isl_keep isl_union_map *umap1,
1079 __isl_keep isl_union_map *umap2);
1083 =head2 Unary Operations
1089 __isl_give isl_set *isl_set_complement(
1090 __isl_take isl_set *set);
1094 __isl_give isl_basic_map *isl_basic_map_reverse(
1095 __isl_take isl_basic_map *bmap);
1096 __isl_give isl_map *isl_map_reverse(
1097 __isl_take isl_map *map);
1098 __isl_give isl_union_map *isl_union_map_reverse(
1099 __isl_take isl_union_map *umap);
1103 __isl_give isl_basic_set *isl_basic_set_project_out(
1104 __isl_take isl_basic_set *bset,
1105 enum isl_dim_type type, unsigned first, unsigned n);
1106 __isl_give isl_basic_map *isl_basic_map_project_out(
1107 __isl_take isl_basic_map *bmap,
1108 enum isl_dim_type type, unsigned first, unsigned n);
1109 __isl_give isl_set *isl_set_project_out(__isl_take isl_set *set,
1110 enum isl_dim_type type, unsigned first, unsigned n);
1111 __isl_give isl_map *isl_map_project_out(__isl_take isl_map *map,
1112 enum isl_dim_type type, unsigned first, unsigned n);
1113 __isl_give isl_basic_set *isl_basic_map_domain(
1114 __isl_take isl_basic_map *bmap);
1115 __isl_give isl_basic_set *isl_basic_map_range(
1116 __isl_take isl_basic_map *bmap);
1117 __isl_give isl_set *isl_map_domain(
1118 __isl_take isl_map *bmap);
1119 __isl_give isl_set *isl_map_range(
1120 __isl_take isl_map *map);
1121 __isl_give isl_union_set *isl_union_map_domain(
1122 __isl_take isl_union_map *umap);
1123 __isl_give isl_union_set *isl_union_map_range(
1124 __isl_take isl_union_map *umap);
1128 __isl_give isl_basic_set *isl_basic_map_deltas(
1129 __isl_take isl_basic_map *bmap);
1130 __isl_give isl_set *isl_map_deltas(__isl_take isl_map *map);
1131 __isl_give isl_union_set *isl_union_map_deltas(
1132 __isl_take isl_union_map *umap);
1134 These functions return a (basic) set containing the differences
1135 between image elements and corresponding domain elements in the input.
1139 Simplify the representation of a set or relation by trying
1140 to combine pairs of basic sets or relations into a single
1141 basic set or relation.
1143 __isl_give isl_set *isl_set_coalesce(__isl_take isl_set *set);
1144 __isl_give isl_map *isl_map_coalesce(__isl_take isl_map *map);
1145 __isl_give isl_union_set *isl_union_set_coalesce(
1146 __isl_take isl_union_set *uset);
1147 __isl_give isl_union_map *isl_union_map_coalesce(
1148 __isl_take isl_union_map *umap);
1152 __isl_give isl_basic_set *isl_set_convex_hull(
1153 __isl_take isl_set *set);
1154 __isl_give isl_basic_map *isl_map_convex_hull(
1155 __isl_take isl_map *map);
1157 If the input set or relation has any existentially quantified
1158 variables, then the result of these operations is currently undefined.
1162 __isl_give isl_basic_set *isl_set_simple_hull(
1163 __isl_take isl_set *set);
1164 __isl_give isl_basic_map *isl_map_simple_hull(
1165 __isl_take isl_map *map);
1167 These functions compute a single basic set or relation
1168 that contains the whole input set or relation.
1169 In particular, the output is described by translates
1170 of the constraints describing the basic sets or relations in the input.
1174 (See \autoref{s:simple hull}.)
1180 __isl_give isl_basic_set *isl_basic_set_affine_hull(
1181 __isl_take isl_basic_set *bset);
1182 __isl_give isl_basic_set *isl_set_affine_hull(
1183 __isl_take isl_set *set);
1184 __isl_give isl_union_set *isl_union_set_affine_hull(
1185 __isl_take isl_union_set *uset);
1186 __isl_give isl_basic_map *isl_basic_map_affine_hull(
1187 __isl_take isl_basic_map *bmap);
1188 __isl_give isl_basic_map *isl_map_affine_hull(
1189 __isl_take isl_map *map);
1190 __isl_give isl_union_map *isl_union_map_affine_hull(
1191 __isl_take isl_union_map *umap);
1193 In case of union sets and relations, the affine hull is computed
1198 __isl_give isl_map *isl_map_power(__isl_take isl_map *map,
1199 unsigned param, int *exact);
1201 Compute a parametric representation for all positive powers I<k> of C<map>.
1202 The power I<k> is equated to the parameter at position C<param>.
1203 The result may be an overapproximation. If the result is exact,
1204 then C<*exact> is set to C<1>.
1205 The current implementation only produces exact results for particular
1206 cases of piecewise translations (i.e., piecewise uniform dependences).
1208 =item * Transitive closure
1210 __isl_give isl_map *isl_map_transitive_closure(
1211 __isl_take isl_map *map, int *exact);
1212 __isl_give isl_union_map *isl_union_map_transitive_closure(
1213 __isl_take isl_union_map *umap, int *exact);
1215 Compute the transitive closure of C<map>.
1216 The result may be an overapproximation. If the result is known to be exact,
1217 then C<*exact> is set to C<1>.
1218 The current implementation only produces exact results for particular
1219 cases of piecewise translations (i.e., piecewise uniform dependences).
1221 =item * Reaching path lengths
1223 __isl_give isl_map *isl_map_reaching_path_lengths(
1224 __isl_take isl_map *map, int *exact);
1226 Compute a relation that maps each element in the range of C<map>
1227 to the lengths of all paths composed of edges in C<map> that
1228 end up in the given element.
1229 The result may be an overapproximation. If the result is known to be exact,
1230 then C<*exact> is set to C<1>.
1231 To compute the I<maximal> path length, the resulting relation
1232 should be postprocessed by C<isl_map_lexmax>.
1233 In particular, if the input relation is a dependence relation
1234 (mapping sources to sinks), then the maximal path length corresponds
1235 to the free schedule.
1236 Note, however, that C<isl_map_lexmax> expects the maximum to be
1237 finite, so if the path lengths are unbounded (possibly due to
1238 the overapproximation), then you will get an error message.
1242 __isl_give isl_basic_set *isl_basic_map_wrap(
1243 __isl_take isl_basic_map *bmap);
1244 __isl_give isl_set *isl_map_wrap(
1245 __isl_take isl_map *map);
1246 __isl_give isl_union_set *isl_union_map_wrap(
1247 __isl_take isl_union_map *umap);
1248 __isl_give isl_basic_map *isl_basic_set_unwrap(
1249 __isl_take isl_basic_set *bset);
1250 __isl_give isl_map *isl_set_unwrap(
1251 __isl_take isl_set *set);
1252 __isl_give isl_union_map *isl_union_set_unwrap(
1253 __isl_take isl_union_set *uset);
1257 =head2 Binary Operations
1259 The two arguments of a binary operation not only need to live
1260 in the same C<isl_ctx>, they currently also need to have
1261 the same (number of) parameters.
1263 =head3 Basic Operations
1267 =item * Intersection
1269 __isl_give isl_basic_set *isl_basic_set_intersect(
1270 __isl_take isl_basic_set *bset1,
1271 __isl_take isl_basic_set *bset2);
1272 __isl_give isl_set *isl_set_intersect(
1273 __isl_take isl_set *set1,
1274 __isl_take isl_set *set2);
1275 __isl_give isl_union_set *isl_union_set_intersect(
1276 __isl_take isl_union_set *uset1,
1277 __isl_take isl_union_set *uset2);
1278 __isl_give isl_basic_map *isl_basic_map_intersect_domain(
1279 __isl_take isl_basic_map *bmap,
1280 __isl_take isl_basic_set *bset);
1281 __isl_give isl_basic_map *isl_basic_map_intersect_range(
1282 __isl_take isl_basic_map *bmap,
1283 __isl_take isl_basic_set *bset);
1284 __isl_give isl_basic_map *isl_basic_map_intersect(
1285 __isl_take isl_basic_map *bmap1,
1286 __isl_take isl_basic_map *bmap2);
1287 __isl_give isl_map *isl_map_intersect_domain(
1288 __isl_take isl_map *map,
1289 __isl_take isl_set *set);
1290 __isl_give isl_map *isl_map_intersect_range(
1291 __isl_take isl_map *map,
1292 __isl_take isl_set *set);
1293 __isl_give isl_map *isl_map_intersect(
1294 __isl_take isl_map *map1,
1295 __isl_take isl_map *map2);
1296 __isl_give isl_union_map *isl_union_map_intersect_domain(
1297 __isl_take isl_union_map *umap,
1298 __isl_take isl_union_set *uset);
1299 __isl_give isl_union_map *isl_union_map_intersect(
1300 __isl_take isl_union_map *umap1,
1301 __isl_take isl_union_map *umap2);
1305 __isl_give isl_set *isl_basic_set_union(
1306 __isl_take isl_basic_set *bset1,
1307 __isl_take isl_basic_set *bset2);
1308 __isl_give isl_map *isl_basic_map_union(
1309 __isl_take isl_basic_map *bmap1,
1310 __isl_take isl_basic_map *bmap2);
1311 __isl_give isl_set *isl_set_union(
1312 __isl_take isl_set *set1,
1313 __isl_take isl_set *set2);
1314 __isl_give isl_map *isl_map_union(
1315 __isl_take isl_map *map1,
1316 __isl_take isl_map *map2);
1317 __isl_give isl_union_set *isl_union_set_union(
1318 __isl_take isl_union_set *uset1,
1319 __isl_take isl_union_set *uset2);
1320 __isl_give isl_union_map *isl_union_map_union(
1321 __isl_take isl_union_map *umap1,
1322 __isl_take isl_union_map *umap2);
1324 =item * Set difference
1326 __isl_give isl_set *isl_set_subtract(
1327 __isl_take isl_set *set1,
1328 __isl_take isl_set *set2);
1329 __isl_give isl_map *isl_map_subtract(
1330 __isl_take isl_map *map1,
1331 __isl_take isl_map *map2);
1332 __isl_give isl_union_set *isl_union_set_subtract(
1333 __isl_take isl_union_set *uset1,
1334 __isl_take isl_union_set *uset2);
1335 __isl_give isl_union_map *isl_union_map_subtract(
1336 __isl_take isl_union_map *umap1,
1337 __isl_take isl_union_map *umap2);
1341 __isl_give isl_basic_set *isl_basic_set_apply(
1342 __isl_take isl_basic_set *bset,
1343 __isl_take isl_basic_map *bmap);
1344 __isl_give isl_set *isl_set_apply(
1345 __isl_take isl_set *set,
1346 __isl_take isl_map *map);
1347 __isl_give isl_union_set *isl_union_set_apply(
1348 __isl_take isl_union_set *uset,
1349 __isl_take isl_union_map *umap);
1350 __isl_give isl_basic_map *isl_basic_map_apply_domain(
1351 __isl_take isl_basic_map *bmap1,
1352 __isl_take isl_basic_map *bmap2);
1353 __isl_give isl_basic_map *isl_basic_map_apply_range(
1354 __isl_take isl_basic_map *bmap1,
1355 __isl_take isl_basic_map *bmap2);
1356 __isl_give isl_map *isl_map_apply_domain(
1357 __isl_take isl_map *map1,
1358 __isl_take isl_map *map2);
1359 __isl_give isl_map *isl_map_apply_range(
1360 __isl_take isl_map *map1,
1361 __isl_take isl_map *map2);
1362 __isl_give isl_union_map *isl_union_map_apply_range(
1363 __isl_take isl_union_map *umap1,
1364 __isl_take isl_union_map *umap2);
1366 =item * Simplification
1368 __isl_give isl_basic_set *isl_basic_set_gist(
1369 __isl_take isl_basic_set *bset,
1370 __isl_take isl_basic_set *context);
1371 __isl_give isl_set *isl_set_gist(__isl_take isl_set *set,
1372 __isl_take isl_set *context);
1373 __isl_give isl_union_set *isl_union_set_gist(
1374 __isl_take isl_union_set *uset,
1375 __isl_take isl_union_set *context);
1376 __isl_give isl_basic_map *isl_basic_map_gist(
1377 __isl_take isl_basic_map *bmap,
1378 __isl_take isl_basic_map *context);
1379 __isl_give isl_map *isl_map_gist(__isl_take isl_map *map,
1380 __isl_take isl_map *context);
1381 __isl_give isl_union_map *isl_union_map_gist(
1382 __isl_take isl_union_map *umap,
1383 __isl_take isl_union_map *context);
1385 The gist operation returns a set or relation that has the
1386 same intersection with the context as the input set or relation.
1387 Any implicit equality in the intersection is made explicit in the result,
1388 while all inequalities that are redundant with respect to the intersection
1390 In case of union sets and relations, the gist operation is performed
1395 =head3 Lexicographic Optimization
1397 Given a (basic) set C<set> (or C<bset>) and a zero-dimensional domain C<dom>,
1398 the following functions
1399 compute a set that contains the lexicographic minimum or maximum
1400 of the elements in C<set> (or C<bset>) for those values of the parameters
1401 that satisfy C<dom>.
1402 If C<empty> is not C<NULL>, then C<*empty> is assigned a set
1403 that contains the parameter values in C<dom> for which C<set> (or C<bset>)
1405 In other words, the union of the parameter values
1406 for which the result is non-empty and of C<*empty>
1409 __isl_give isl_set *isl_basic_set_partial_lexmin(
1410 __isl_take isl_basic_set *bset,
1411 __isl_take isl_basic_set *dom,
1412 __isl_give isl_set **empty);
1413 __isl_give isl_set *isl_basic_set_partial_lexmax(
1414 __isl_take isl_basic_set *bset,
1415 __isl_take isl_basic_set *dom,
1416 __isl_give isl_set **empty);
1417 __isl_give isl_set *isl_set_partial_lexmin(
1418 __isl_take isl_set *set, __isl_take isl_set *dom,
1419 __isl_give isl_set **empty);
1420 __isl_give isl_set *isl_set_partial_lexmax(
1421 __isl_take isl_set *set, __isl_take isl_set *dom,
1422 __isl_give isl_set **empty);
1424 Given a (basic) set C<set> (or C<bset>), the following functions simply
1425 return a set containing the lexicographic minimum or maximum
1426 of the elements in C<set> (or C<bset>).
1427 In case of union sets, the optimum is computed per space.
1429 __isl_give isl_set *isl_basic_set_lexmin(
1430 __isl_take isl_basic_set *bset);
1431 __isl_give isl_set *isl_basic_set_lexmax(
1432 __isl_take isl_basic_set *bset);
1433 __isl_give isl_set *isl_set_lexmin(
1434 __isl_take isl_set *set);
1435 __isl_give isl_set *isl_set_lexmax(
1436 __isl_take isl_set *set);
1437 __isl_give isl_union_set *isl_union_set_lexmin(
1438 __isl_take isl_union_set *uset);
1439 __isl_give isl_union_set *isl_union_set_lexmax(
1440 __isl_take isl_union_set *uset);
1442 Given a (basic) relation C<map> (or C<bmap>) and a domain C<dom>,
1443 the following functions
1444 compute a relation that maps each element of C<dom>
1445 to the single lexicographic minimum or maximum
1446 of the elements that are associated to that same
1447 element in C<map> (or C<bmap>).
1448 If C<empty> is not C<NULL>, then C<*empty> is assigned a set
1449 that contains the elements in C<dom> that do not map
1450 to any elements in C<map> (or C<bmap>).
1451 In other words, the union of the domain of the result and of C<*empty>
1454 __isl_give isl_map *isl_basic_map_partial_lexmax(
1455 __isl_take isl_basic_map *bmap,
1456 __isl_take isl_basic_set *dom,
1457 __isl_give isl_set **empty);
1458 __isl_give isl_map *isl_basic_map_partial_lexmin(
1459 __isl_take isl_basic_map *bmap,
1460 __isl_take isl_basic_set *dom,
1461 __isl_give isl_set **empty);
1462 __isl_give isl_map *isl_map_partial_lexmax(
1463 __isl_take isl_map *map, __isl_take isl_set *dom,
1464 __isl_give isl_set **empty);
1465 __isl_give isl_map *isl_map_partial_lexmin(
1466 __isl_take isl_map *map, __isl_take isl_set *dom,
1467 __isl_give isl_set **empty);
1469 Given a (basic) map C<map> (or C<bmap>), the following functions simply
1470 return a map mapping each element in the domain of
1471 C<map> (or C<bmap>) to the lexicographic minimum or maximum
1472 of all elements associated to that element.
1473 In case of union relations, the optimum is computed per space.
1475 __isl_give isl_map *isl_basic_map_lexmin(
1476 __isl_take isl_basic_map *bmap);
1477 __isl_give isl_map *isl_basic_map_lexmax(
1478 __isl_take isl_basic_map *bmap);
1479 __isl_give isl_map *isl_map_lexmin(
1480 __isl_take isl_map *map);
1481 __isl_give isl_map *isl_map_lexmax(
1482 __isl_take isl_map *map);
1483 __isl_give isl_union_map *isl_union_map_lexmin(
1484 __isl_take isl_union_map *umap);
1485 __isl_give isl_union_map *isl_union_map_lexmax(
1486 __isl_take isl_union_map *umap);
1490 Matrices can be created, copied and freed using the following functions.
1492 #include <isl_mat.h>
1493 __isl_give isl_mat *isl_mat_alloc(struct isl_ctx *ctx,
1494 unsigned n_row, unsigned n_col);
1495 __isl_give isl_mat *isl_mat_copy(__isl_keep isl_mat *mat);
1496 void isl_mat_free(__isl_take isl_mat *mat);
1498 Note that the elements of a newly created matrix may have arbitrary values.
1499 The elements can be changed and inspected using the following functions.
1501 int isl_mat_rows(__isl_keep isl_mat *mat);
1502 int isl_mat_cols(__isl_keep isl_mat *mat);
1503 int isl_mat_get_element(__isl_keep isl_mat *mat,
1504 int row, int col, isl_int *v);
1505 __isl_give isl_mat *isl_mat_set_element(__isl_take isl_mat *mat,
1506 int row, int col, isl_int v);
1508 C<isl_mat_get_element> will return a negative value if anything went wrong.
1509 In that case, the value of C<*v> is undefined.
1511 The following function can be used to compute the (right) inverse
1512 of a matrix, i.e., a matrix such that the product of the original
1513 and the inverse (in that order) is a multiple of the identity matrix.
1514 The input matrix is assumed to be of full row-rank.
1516 __isl_give isl_mat *isl_mat_right_inverse(__isl_take isl_mat *mat);
1518 The following function can be used to compute the (right) kernel
1519 (or null space) of a matrix, i.e., a matrix such that the product of
1520 the original and the kernel (in that order) is the zero matrix.
1522 __isl_give isl_mat *isl_mat_right_kernel(__isl_take isl_mat *mat);
1526 Points are elements of a set. They can be used to construct
1527 simple sets (boxes) or they can be used to represent the
1528 individual elements of a set.
1529 The zero point (the origin) can be created using
1531 __isl_give isl_point *isl_point_zero(__isl_take isl_dim *dim);
1533 The coordinates of a point can be inspected, set and changed
1536 void isl_point_get_coordinate(__isl_keep isl_point *pnt,
1537 enum isl_dim_type type, int pos, isl_int *v);
1538 __isl_give isl_point *isl_point_set_coordinate(
1539 __isl_take isl_point *pnt,
1540 enum isl_dim_type type, int pos, isl_int v);
1542 __isl_give isl_point *isl_point_add_ui(
1543 __isl_take isl_point *pnt,
1544 enum isl_dim_type type, int pos, unsigned val);
1545 __isl_give isl_point *isl_point_sub_ui(
1546 __isl_take isl_point *pnt,
1547 enum isl_dim_type type, int pos, unsigned val);
1549 Points can be copied or freed using
1551 __isl_give isl_point *isl_point_copy(
1552 __isl_keep isl_point *pnt);
1553 void isl_point_free(__isl_take isl_point *pnt);
1555 A singleton set can be created from a point using
1557 __isl_give isl_set *isl_set_from_point(
1558 __isl_take isl_point *pnt);
1560 and a box can be created from two opposite extremal points using
1562 __isl_give isl_set *isl_set_box_from_points(
1563 __isl_take isl_point *pnt1,
1564 __isl_take isl_point *pnt2);
1566 All elements of a B<bounded> (union) set can be enumerated using
1567 the following functions.
1569 int isl_set_foreach_point(__isl_keep isl_set *set,
1570 int (*fn)(__isl_take isl_point *pnt, void *user),
1572 int isl_union_set_foreach_point(__isl_keep isl_union_set *uset,
1573 int (*fn)(__isl_take isl_point *pnt, void *user),
1576 The function C<fn> is called for each integer point in
1577 C<set> with as second argument the last argument of
1578 the C<isl_set_foreach_point> call. The function C<fn>
1579 should return C<0> on success and C<-1> on failure.
1580 In the latter case, C<isl_set_foreach_point> will stop
1581 enumerating and return C<-1> as well.
1582 If the enumeration is performed successfully and to completion,
1583 then C<isl_set_foreach_point> returns C<0>.
1585 To obtain a single point of a set, use
1587 __isl_give isl_point *isl_set_sample_point(
1588 __isl_take isl_set *set);
1590 If C<set> does not contain any (integer) points, then the
1591 resulting point will be ``void'', a property that can be
1594 int isl_point_is_void(__isl_keep isl_point *pnt);
1596 =head2 Piecewise Quasipolynomials
1598 A piecewise quasipolynomial is a particular kind of function that maps
1599 a parametric point to a rational value.
1600 More specifically, a quasipolynomial is a polynomial expression in greatest
1601 integer parts of affine expressions of parameters and variables.
1602 A piecewise quasipolynomial is a subdivision of a given parametric
1603 domain into disjoint cells with a quasipolynomial associated to
1604 each cell. The value of the piecewise quasipolynomial at a given
1605 point is the value of the quasipolynomial associated to the cell
1606 that contains the point. Outside of the union of cells,
1607 the value is assumed to be zero.
1608 For example, the piecewise quasipolynomial
1610 [n] -> { [x] -> ((1 + n) - x) : x <= n and x >= 0 }
1612 maps C<x> to C<1 + n - x> for values of C<x> between C<0> and C<n>.
1613 A given piecewise quasipolynomial has a fixed domain dimension.
1614 Union piecewise quasipolynomials are used to contain piecewise quasipolynomials
1615 defined over different domains.
1616 Piecewise quasipolynomials are mainly used by the C<barvinok>
1617 library for representing the number of elements in a parametric set or map.
1618 For example, the piecewise quasipolynomial above represents
1619 the number of points in the map
1621 [n] -> { [x] -> [y] : x,y >= 0 and 0 <= x + y <= n }
1623 =head3 Printing (Piecewise) Quasipolynomials
1625 Quasipolynomials and piecewise quasipolynomials can be printed
1626 using the following functions.
1628 __isl_give isl_printer *isl_printer_print_qpolynomial(
1629 __isl_take isl_printer *p,
1630 __isl_keep isl_qpolynomial *qp);
1632 __isl_give isl_printer *isl_printer_print_pw_qpolynomial(
1633 __isl_take isl_printer *p,
1634 __isl_keep isl_pw_qpolynomial *pwqp);
1636 __isl_give isl_printer *isl_printer_print_union_pw_qpolynomial(
1637 __isl_take isl_printer *p,
1638 __isl_keep isl_union_pw_qpolynomial *upwqp);
1640 The output format of the printer
1641 needs to be set to either C<ISL_FORMAT_ISL> or C<ISL_FORMAT_C>.
1642 For C<isl_printer_print_union_pw_qpolynomial>, only C<ISL_FORMAT_ISL>
1645 =head3 Creating New (Piecewise) Quasipolynomials
1647 Some simple quasipolynomials can be created using the following functions.
1648 More complicated quasipolynomials can be created by applying
1649 operations such as addition and multiplication
1650 on the resulting quasipolynomials
1652 __isl_give isl_qpolynomial *isl_qpolynomial_zero(
1653 __isl_take isl_dim *dim);
1654 __isl_give isl_qpolynomial *isl_qpolynomial_one(
1655 __isl_take isl_dim *dim);
1656 __isl_give isl_qpolynomial *isl_qpolynomial_infty(
1657 __isl_take isl_dim *dim);
1658 __isl_give isl_qpolynomial *isl_qpolynomial_neginfty(
1659 __isl_take isl_dim *dim);
1660 __isl_give isl_qpolynomial *isl_qpolynomial_nan(
1661 __isl_take isl_dim *dim);
1662 __isl_give isl_qpolynomial *isl_qpolynomial_rat_cst(
1663 __isl_take isl_dim *dim,
1664 const isl_int n, const isl_int d);
1665 __isl_give isl_qpolynomial *isl_qpolynomial_div(
1666 __isl_take isl_div *div);
1667 __isl_give isl_qpolynomial *isl_qpolynomial_var(
1668 __isl_take isl_dim *dim,
1669 enum isl_dim_type type, unsigned pos);
1671 The zero piecewise quasipolynomial or a piecewise quasipolynomial
1672 with a single cell can be created using the following functions.
1673 Multiple of these single cell piecewise quasipolynomials can
1674 be combined to create more complicated piecewise quasipolynomials.
1676 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_zero(
1677 __isl_take isl_dim *dim);
1678 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_alloc(
1679 __isl_take isl_set *set,
1680 __isl_take isl_qpolynomial *qp);
1682 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_zero(
1683 __isl_take isl_dim *dim);
1684 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_from_pw_qpolynomial(
1685 __isl_take isl_pw_qpolynomial *pwqp);
1686 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_add_pw_qpolynomial(
1687 __isl_take isl_union_pw_qpolynomial *upwqp,
1688 __isl_take isl_pw_qpolynomial *pwqp);
1690 Quasipolynomials can be copied and freed again using the following
1693 __isl_give isl_qpolynomial *isl_qpolynomial_copy(
1694 __isl_keep isl_qpolynomial *qp);
1695 void isl_qpolynomial_free(__isl_take isl_qpolynomial *qp);
1697 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_copy(
1698 __isl_keep isl_pw_qpolynomial *pwqp);
1699 void isl_pw_qpolynomial_free(
1700 __isl_take isl_pw_qpolynomial *pwqp);
1702 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_copy(
1703 __isl_keep isl_union_pw_qpolynomial *upwqp);
1704 void isl_union_pw_qpolynomial_free(
1705 __isl_take isl_union_pw_qpolynomial *upwqp);
1707 =head3 Inspecting (Piecewise) Quasipolynomials
1709 To iterate over all piecewise quasipolynomials in a union
1710 piecewise quasipolynomial, use the following function
1712 int isl_union_pw_qpolynomial_foreach_pw_qpolynomial(
1713 __isl_keep isl_union_pw_qpolynomial *upwqp,
1714 int (*fn)(__isl_take isl_pw_qpolynomial *pwqp, void *user),
1717 To iterate over the cells in a piecewise quasipolynomial,
1718 use either of the following two functions
1720 int isl_pw_qpolynomial_foreach_piece(
1721 __isl_keep isl_pw_qpolynomial *pwqp,
1722 int (*fn)(__isl_take isl_set *set,
1723 __isl_take isl_qpolynomial *qp,
1724 void *user), void *user);
1725 int isl_pw_qpolynomial_foreach_lifted_piece(
1726 __isl_keep isl_pw_qpolynomial *pwqp,
1727 int (*fn)(__isl_take isl_set *set,
1728 __isl_take isl_qpolynomial *qp,
1729 void *user), void *user);
1731 As usual, the function C<fn> should return C<0> on success
1732 and C<-1> on failure. The difference between
1733 C<isl_pw_qpolynomial_foreach_piece> and
1734 C<isl_pw_qpolynomial_foreach_lifted_piece> is that
1735 C<isl_pw_qpolynomial_foreach_lifted_piece> will first
1736 compute unique representations for all existentially quantified
1737 variables and then turn these existentially quantified variables
1738 into extra set variables, adapting the associated quasipolynomial
1739 accordingly. This means that the C<set> passed to C<fn>
1740 will not have any existentially quantified variables, but that
1741 the dimensions of the sets may be different for different
1742 invocations of C<fn>.
1744 To iterate over all terms in a quasipolynomial,
1747 int isl_qpolynomial_foreach_term(
1748 __isl_keep isl_qpolynomial *qp,
1749 int (*fn)(__isl_take isl_term *term,
1750 void *user), void *user);
1752 The terms themselves can be inspected and freed using
1755 unsigned isl_term_dim(__isl_keep isl_term *term,
1756 enum isl_dim_type type);
1757 void isl_term_get_num(__isl_keep isl_term *term,
1759 void isl_term_get_den(__isl_keep isl_term *term,
1761 int isl_term_get_exp(__isl_keep isl_term *term,
1762 enum isl_dim_type type, unsigned pos);
1763 __isl_give isl_div *isl_term_get_div(
1764 __isl_keep isl_term *term, unsigned pos);
1765 void isl_term_free(__isl_take isl_term *term);
1767 Each term is a product of parameters, set variables and
1768 integer divisions. The function C<isl_term_get_exp>
1769 returns the exponent of a given dimensions in the given term.
1770 The C<isl_int>s in the arguments of C<isl_term_get_num>
1771 and C<isl_term_get_den> need to have been initialized
1772 using C<isl_int_init> before calling these functions.
1774 =head3 Properties of (Piecewise) Quasipolynomials
1776 To check whether a quasipolynomial is actually a constant,
1777 use the following function.
1779 int isl_qpolynomial_is_cst(__isl_keep isl_qpolynomial *qp,
1780 isl_int *n, isl_int *d);
1782 If C<qp> is a constant and if C<n> and C<d> are not C<NULL>
1783 then the numerator and denominator of the constant
1784 are returned in C<*n> and C<*d>, respectively.
1786 =head3 Operations on (Piecewise) Quasipolynomials
1788 __isl_give isl_qpolynomial *isl_qpolynomial_neg(
1789 __isl_take isl_qpolynomial *qp);
1790 __isl_give isl_qpolynomial *isl_qpolynomial_add(
1791 __isl_take isl_qpolynomial *qp1,
1792 __isl_take isl_qpolynomial *qp2);
1793 __isl_give isl_qpolynomial *isl_qpolynomial_sub(
1794 __isl_take isl_qpolynomial *qp1,
1795 __isl_take isl_qpolynomial *qp2);
1796 __isl_give isl_qpolynomial *isl_qpolynomial_mul(
1797 __isl_take isl_qpolynomial *qp1,
1798 __isl_take isl_qpolynomial *qp2);
1800 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_add(
1801 __isl_take isl_pw_qpolynomial *pwqp1,
1802 __isl_take isl_pw_qpolynomial *pwqp2);
1803 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_sub(
1804 __isl_take isl_pw_qpolynomial *pwqp1,
1805 __isl_take isl_pw_qpolynomial *pwqp2);
1806 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_add_disjoint(
1807 __isl_take isl_pw_qpolynomial *pwqp1,
1808 __isl_take isl_pw_qpolynomial *pwqp2);
1809 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_neg(
1810 __isl_take isl_pw_qpolynomial *pwqp);
1811 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_mul(
1812 __isl_take isl_pw_qpolynomial *pwqp1,
1813 __isl_take isl_pw_qpolynomial *pwqp2);
1815 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_add(
1816 __isl_take isl_union_pw_qpolynomial *upwqp1,
1817 __isl_take isl_union_pw_qpolynomial *upwqp2);
1818 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_sub(
1819 __isl_take isl_union_pw_qpolynomial *upwqp1,
1820 __isl_take isl_union_pw_qpolynomial *upwqp2);
1821 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_mul(
1822 __isl_take isl_union_pw_qpolynomial *upwqp1,
1823 __isl_take isl_union_pw_qpolynomial *upwqp2);
1825 __isl_give isl_qpolynomial *isl_pw_qpolynomial_eval(
1826 __isl_take isl_pw_qpolynomial *pwqp,
1827 __isl_take isl_point *pnt);
1829 __isl_give isl_qpolynomial *isl_union_pw_qpolynomial_eval(
1830 __isl_take isl_union_pw_qpolynomial *upwqp,
1831 __isl_take isl_point *pnt);
1833 __isl_give isl_set *isl_pw_qpolynomial_domain(
1834 __isl_take isl_pw_qpolynomial *pwqp);
1835 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_intersect_domain(
1836 __isl_take isl_pw_qpolynomial *pwpq,
1837 __isl_take isl_set *set);
1839 __isl_give isl_union_set *isl_union_pw_qpolynomial_domain(
1840 __isl_take isl_union_pw_qpolynomial *upwqp);
1841 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_intersect_domain(
1842 __isl_take isl_union_pw_qpolynomial *upwpq,
1843 __isl_take isl_union_set *uset);
1845 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_coalesce(
1846 __isl_take isl_union_pw_qpolynomial *upwqp);
1848 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_gist(
1849 __isl_take isl_pw_qpolynomial *pwqp,
1850 __isl_take isl_set *context);
1852 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_gist(
1853 __isl_take isl_union_pw_qpolynomial *upwqp,
1854 __isl_take isl_union_set *context);
1856 The gist operation applies the gist operation to each of
1857 the cells in the domain of the input piecewise quasipolynomial.
1858 In future, the operation will also exploit the context
1859 to simplify the quasipolynomials associated to each cell.
1861 =head2 Bounds on Piecewise Quasipolynomials and Piecewise Quasipolynomial Reductions
1863 A piecewise quasipolynomial reduction is a piecewise
1864 reduction (or fold) of quasipolynomials.
1865 In particular, the reduction can be maximum or a minimum.
1866 The objects are mainly used to represent the result of
1867 an upper or lower bound on a quasipolynomial over its domain,
1868 i.e., as the result of the following function.
1870 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_bound(
1871 __isl_take isl_pw_qpolynomial *pwqp,
1872 enum isl_fold type, int *tight);
1874 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_bound(
1875 __isl_take isl_union_pw_qpolynomial *upwqp,
1876 enum isl_fold type, int *tight);
1878 The C<type> argument may be either C<isl_fold_min> or C<isl_fold_max>.
1879 If C<tight> is not C<NULL>, then C<*tight> is set to C<1>
1880 is the returned bound is known be tight, i.e., for each value
1881 of the parameters there is at least
1882 one element in the domain that reaches the bound.
1883 If the domain of C<pwqp> is not wrapping, then the bound is computed
1884 over all elements in that domain and the result has a purely parametric
1885 domain. If the domain of C<pwqp> is wrapping, then the bound is
1886 computed over the range of the wrapped relation. The domain of the
1887 wrapped relation becomes the domain of the result.
1889 A (piecewise) quasipolynomial reduction can be copied or freed using the
1890 following functions.
1892 __isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_copy(
1893 __isl_keep isl_qpolynomial_fold *fold);
1894 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_copy(
1895 __isl_keep isl_pw_qpolynomial_fold *pwf);
1896 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_copy(
1897 __isl_keep isl_union_pw_qpolynomial_fold *upwf);
1898 void isl_qpolynomial_fold_free(
1899 __isl_take isl_qpolynomial_fold *fold);
1900 void isl_pw_qpolynomial_fold_free(
1901 __isl_take isl_pw_qpolynomial_fold *pwf);
1902 void isl_union_pw_qpolynomial_fold_free(
1903 __isl_take isl_union_pw_qpolynomial_fold *upwf);
1905 =head3 Printing Piecewise Quasipolynomial Reductions
1907 Piecewise quasipolynomial reductions can be printed
1908 using the following function.
1910 __isl_give isl_printer *isl_printer_print_pw_qpolynomial_fold(
1911 __isl_take isl_printer *p,
1912 __isl_keep isl_pw_qpolynomial_fold *pwf);
1913 __isl_give isl_printer *isl_printer_print_union_pw_qpolynomial_fold(
1914 __isl_take isl_printer *p,
1915 __isl_keep isl_union_pw_qpolynomial_fold *upwf);
1917 For C<isl_printer_print_pw_qpolynomial_fold>,
1918 output format of the printer
1919 needs to be set to either C<ISL_FORMAT_ISL> or C<ISL_FORMAT_C>.
1920 For C<isl_printer_print_union_pw_qpolynomial_fold>,
1921 output format of the printer
1922 needs to be set to either C<ISL_FORMAT_ISL>.
1924 =head3 Inspecting (Piecewise) Quasipolynomial Reductions
1926 To iterate over all piecewise quasipolynomial reductions in a union
1927 piecewise quasipolynomial reduction, use the following function
1929 int isl_union_pw_qpolynomial_fold_foreach_pw_qpolynomial_fold(
1930 __isl_keep isl_union_pw_qpolynomial_fold *upwf,
1931 int (*fn)(__isl_take isl_pw_qpolynomial_fold *pwf,
1932 void *user), void *user);
1934 To iterate over the cells in a piecewise quasipolynomial reduction,
1935 use either of the following two functions
1937 int isl_pw_qpolynomial_fold_foreach_piece(
1938 __isl_keep isl_pw_qpolynomial_fold *pwf,
1939 int (*fn)(__isl_take isl_set *set,
1940 __isl_take isl_qpolynomial_fold *fold,
1941 void *user), void *user);
1942 int isl_pw_qpolynomial_fold_foreach_lifted_piece(
1943 __isl_keep isl_pw_qpolynomial_fold *pwf,
1944 int (*fn)(__isl_take isl_set *set,
1945 __isl_take isl_qpolynomial_fold *fold,
1946 void *user), void *user);
1948 See L<Inspecting (Piecewise) Quasipolynomials> for an explanation
1949 of the difference between these two functions.
1951 To iterate over all quasipolynomials in a reduction, use
1953 int isl_qpolynomial_fold_foreach_qpolynomial(
1954 __isl_keep isl_qpolynomial_fold *fold,
1955 int (*fn)(__isl_take isl_qpolynomial *qp,
1956 void *user), void *user);
1958 =head3 Operations on Piecewise Quasipolynomial Reductions
1960 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_fold(
1961 __isl_take isl_pw_qpolynomial_fold *pwf1,
1962 __isl_take isl_pw_qpolynomial_fold *pwf2);
1964 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_fold(
1965 __isl_take isl_union_pw_qpolynomial_fold *upwf1,
1966 __isl_take isl_union_pw_qpolynomial_fold *upwf2);
1968 __isl_give isl_qpolynomial *isl_pw_qpolynomial_fold_eval(
1969 __isl_take isl_pw_qpolynomial_fold *pwf,
1970 __isl_take isl_point *pnt);
1972 __isl_give isl_qpolynomial *isl_union_pw_qpolynomial_fold_eval(
1973 __isl_take isl_union_pw_qpolynomial_fold *upwf,
1974 __isl_take isl_point *pnt);
1976 __isl_give isl_union_set *isl_union_pw_qpolynomial_fold_domain(
1977 __isl_take isl_union_pw_qpolynomial_fold *upwf);
1978 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_intersect_domain(
1979 __isl_take isl_union_pw_qpolynomial_fold *upwf,
1980 __isl_take isl_union_set *uset);
1982 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_coalesce(
1983 __isl_take isl_pw_qpolynomial_fold *pwf);
1985 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_coalesce(
1986 __isl_take isl_union_pw_qpolynomial_fold *upwf);
1988 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_gist(
1989 __isl_take isl_pw_qpolynomial_fold *pwf,
1990 __isl_take isl_set *context);
1992 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_gist(
1993 __isl_take isl_union_pw_qpolynomial_fold *upwf,
1994 __isl_take isl_union_set *context);
1996 The gist operation applies the gist operation to each of
1997 the cells in the domain of the input piecewise quasipolynomial reduction.
1998 In future, the operation will also exploit the context
1999 to simplify the quasipolynomial reductions associated to each cell.
2001 __isl_give isl_pw_qpolynomial_fold *
2002 isl_map_apply_pw_qpolynomial_fold(
2003 __isl_take isl_map *map,
2004 __isl_take isl_pw_qpolynomial_fold *pwf,
2006 __isl_give isl_union_pw_qpolynomial_fold *
2007 isl_union_map_apply_union_pw_qpolynomial_fold(
2008 __isl_take isl_union_map *umap,
2009 __isl_take isl_union_pw_qpolynomial_fold *upwf,
2013 compose the given map with the given piecewise quasipolynomial reduction.
2014 That is, compute a bound (of the same type as C<pwf> or C<upwf> itself)
2015 over all elements in the intersection of the range of the map
2016 and the domain of the piecewise quasipolynomial reduction
2017 as a function of an element in the domain of the map.
2019 =head2 Dependence Analysis
2021 C<isl> contains specialized functionality for performing
2022 array dataflow analysis. That is, given a I<sink> access relation
2023 and a collection of possible I<source> access relations,
2024 C<isl> can compute relations that describe
2025 for each iteration of the sink access, which iteration
2026 of which of the source access relations was the last
2027 to access the same data element before the given iteration
2029 To compute standard flow dependences, the sink should be
2030 a read, while the sources should be writes.
2031 If any of the source accesses are marked as being I<may>
2032 accesses, then there will be a dependence to the last
2033 I<must> access B<and> to any I<may> access that follows
2034 this last I<must> access.
2035 In particular, if I<all> sources are I<may> accesses,
2036 then memory based dependence analysis is performed.
2037 If, on the other hand, all sources are I<must> accesses,
2038 then value based dependence analysis is performed.
2040 #include <isl_flow.h>
2042 __isl_give isl_access_info *isl_access_info_alloc(
2043 __isl_take isl_map *sink,
2044 void *sink_user, isl_access_level_before fn,
2046 __isl_give isl_access_info *isl_access_info_add_source(
2047 __isl_take isl_access_info *acc,
2048 __isl_take isl_map *source, int must,
2051 __isl_give isl_flow *isl_access_info_compute_flow(
2052 __isl_take isl_access_info *acc);
2054 int isl_flow_foreach(__isl_keep isl_flow *deps,
2055 int (*fn)(__isl_take isl_map *dep, int must,
2056 void *dep_user, void *user),
2058 __isl_give isl_set *isl_flow_get_no_source(
2059 __isl_keep isl_flow *deps, int must);
2060 void isl_flow_free(__isl_take isl_flow *deps);
2062 The function C<isl_access_info_compute_flow> performs the actual
2063 dependence analysis. The other functions are used to construct
2064 the input for this function or to read off the output.
2066 The input is collected in an C<isl_access_info>, which can
2067 be created through a call to C<isl_access_info_alloc>.
2068 The arguments to this functions are the sink access relation
2069 C<sink>, a token C<sink_user> used to identify the sink
2070 access to the user, a callback function for specifying the
2071 relative order of source and sink accesses, and the number
2072 of source access relations that will be added.
2073 The callback function has type C<int (*)(void *first, void *second)>.
2074 The function is called with two user supplied tokens identifying
2075 either a source or the sink and it should return the shared nesting
2076 level and the relative order of the two accesses.
2077 In particular, let I<n> be the number of loops shared by
2078 the two accesses. If C<first> precedes C<second> textually,
2079 then the function should return I<2 * n + 1>; otherwise,
2080 it should return I<2 * n>.
2081 The sources can be added to the C<isl_access_info> by performing
2082 (at most) C<max_source> calls to C<isl_access_info_add_source>.
2083 C<must> indicates whether the source is a I<must> access
2084 or a I<may> access. Note that a multi-valued access relation
2085 should only be marked I<must> if every iteration in the domain
2086 of the relation accesses I<all> elements in its image.
2087 The C<source_user> token is again used to identify
2088 the source access. The range of the source access relation
2089 C<source> should have the same dimension as the range
2090 of the sink access relation.
2092 The result of the dependence analysis is collected in an
2093 C<isl_flow>. There may be elements in the domain of
2094 the sink access for which no preceding source access could be
2095 found or for which all preceding sources are I<may> accesses.
2096 The sets of these elements can be obtained through
2097 calls to C<isl_flow_get_no_source>, the first with C<must> set
2098 and the second with C<must> unset.
2099 In the case of standard flow dependence analysis,
2100 with the sink a read and the sources I<must> writes,
2101 the first set corresponds to the reads from uninitialized
2102 array elements and the second set is empty.
2103 The actual flow dependences can be extracted using
2104 C<isl_flow_foreach>. This function will call the user-specified
2105 callback function C<fn> for each B<non-empty> dependence between
2106 a source and the sink. The callback function is called
2107 with four arguments, the actual flow dependence relation
2108 mapping source iterations to sink iterations, a boolean that
2109 indicates whether it is a I<must> or I<may> dependence, a token
2110 identifying the source and an additional C<void *> with value
2111 equal to the third argument of the C<isl_flow_foreach> call.
2112 A dependence is marked I<must> if it originates from a I<must>
2113 source and if it is not followed by any I<may> sources.
2115 After finishing with an C<isl_flow>, the user should call
2116 C<isl_flow_free> to free all associated memory.
2118 =head2 Parametric Vertex Enumeration
2120 The parametric vertex enumeration described in this section
2121 is mainly intended to be used internally and by the C<barvinok>
2124 #include <isl_vertices.h>
2125 __isl_give isl_vertices *isl_basic_set_compute_vertices(
2126 __isl_keep isl_basic_set *bset);
2128 The function C<isl_basic_set_compute_vertices> performs the
2129 actual computation of the parametric vertices and the chamber
2130 decomposition and store the result in an C<isl_vertices> object.
2131 This information can be queried by either iterating over all
2132 the vertices or iterating over all the chambers or cells
2133 and then iterating over all vertices that are active on the chamber.
2135 int isl_vertices_foreach_vertex(
2136 __isl_keep isl_vertices *vertices,
2137 int (*fn)(__isl_take isl_vertex *vertex, void *user),
2140 int isl_vertices_foreach_cell(
2141 __isl_keep isl_vertices *vertices,
2142 int (*fn)(__isl_take isl_cell *cell, void *user),
2144 int isl_cell_foreach_vertex(__isl_keep isl_cell *cell,
2145 int (*fn)(__isl_take isl_vertex *vertex, void *user),
2148 Other operations that can be performed on an C<isl_vertices> object are
2151 isl_ctx *isl_vertices_get_ctx(
2152 __isl_keep isl_vertices *vertices);
2153 int isl_vertices_get_n_vertices(
2154 __isl_keep isl_vertices *vertices);
2155 void isl_vertices_free(__isl_take isl_vertices *vertices);
2157 Vertices can be inspected and destroyed using the following functions.
2159 isl_ctx *isl_vertex_get_ctx(__isl_keep isl_vertex *vertex);
2160 int isl_vertex_get_id(__isl_keep isl_vertex *vertex);
2161 __isl_give isl_basic_set *isl_vertex_get_domain(
2162 __isl_keep isl_vertex *vertex);
2163 __isl_give isl_basic_set *isl_vertex_get_expr(
2164 __isl_keep isl_vertex *vertex);
2165 void isl_vertex_free(__isl_take isl_vertex *vertex);
2167 C<isl_vertex_get_expr> returns a singleton parametric set describing
2168 the vertex, while C<isl_vertex_get_domain> returns the activity domain
2170 Note that C<isl_vertex_get_domain> and C<isl_vertex_get_expr> return
2171 B<rational> basic sets, so they should mainly be used for inspection
2172 and should not be mixed with integer sets.
2174 Chambers can be inspected and destroyed using the following functions.
2176 isl_ctx *isl_cell_get_ctx(__isl_keep isl_cell *cell);
2177 __isl_give isl_basic_set *isl_cell_get_domain(
2178 __isl_keep isl_cell *cell);
2179 void isl_cell_free(__isl_take isl_cell *cell);
2183 Although C<isl> is mainly meant to be used as a library,
2184 it also contains some basic applications that use some
2185 of the functionality of C<isl>.
2186 The input may be specified in either the L<isl format>
2187 or the L<PolyLib format>.
2189 =head2 C<isl_polyhedron_sample>
2191 C<isl_polyhedron_sample> takes a polyhedron as input and prints
2192 an integer element of the polyhedron, if there is any.
2193 The first column in the output is the denominator and is always
2194 equal to 1. If the polyhedron contains no integer points,
2195 then a vector of length zero is printed.
2199 C<isl_pip> takes the same input as the C<example> program
2200 from the C<piplib> distribution, i.e., a set of constraints
2201 on the parameters, a line containing only -1 and finally a set
2202 of constraints on a parametric polyhedron.
2203 The coefficients of the parameters appear in the last columns
2204 (but before the final constant column).
2205 The output is the lexicographic minimum of the parametric polyhedron.
2206 As C<isl> currently does not have its own output format, the output
2207 is just a dump of the internal state.
2209 =head2 C<isl_polyhedron_minimize>
2211 C<isl_polyhedron_minimize> computes the minimum of some linear
2212 or affine objective function over the integer points in a polyhedron.
2213 If an affine objective function
2214 is given, then the constant should appear in the last column.
2216 =head2 C<isl_polytope_scan>
2218 Given a polytope, C<isl_polytope_scan> prints
2219 all integer points in the polytope.
2221 =head1 C<isl-polylib>
2223 The C<isl-polylib> library provides the following functions for converting
2224 between C<isl> objects and C<PolyLib> objects.
2225 The library is distributed separately for licensing reasons.
2227 #include <isl_set_polylib.h>
2228 __isl_give isl_basic_set *isl_basic_set_new_from_polylib(
2229 Polyhedron *P, __isl_take isl_dim *dim);
2230 Polyhedron *isl_basic_set_to_polylib(
2231 __isl_keep isl_basic_set *bset);
2232 __isl_give isl_set *isl_set_new_from_polylib(Polyhedron *D,
2233 __isl_take isl_dim *dim);
2234 Polyhedron *isl_set_to_polylib(__isl_keep isl_set *set);
2236 #include <isl_map_polylib.h>
2237 __isl_give isl_basic_map *isl_basic_map_new_from_polylib(
2238 Polyhedron *P, __isl_take isl_dim *dim);
2239 __isl_give isl_map *isl_map_new_from_polylib(Polyhedron *D,
2240 __isl_take isl_dim *dim);
2241 Polyhedron *isl_basic_map_to_polylib(
2242 __isl_keep isl_basic_map *bmap);
2243 Polyhedron *isl_map_to_polylib(__isl_keep isl_map *map);