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 =head2 Input and Output
486 C<isl> supports its own input/output format, which is similar
487 to the C<Omega> format, but also supports the C<PolyLib> format
492 The C<isl> format is similar to that of C<Omega>, but has a different
493 syntax for describing the parameters and allows for the definition
494 of an existentially quantified variable as the integer division
495 of an affine expression.
496 For example, the set of integers C<i> between C<0> and C<n>
497 such that C<i % 10 <= 6> can be described as
499 [n] -> { [i] : exists (a = [i/10] : 0 <= i and i <= n and
502 A set or relation can have several disjuncts, separated
503 by the keyword C<or>. Each disjunct is either a conjunction
504 of constraints or a projection (C<exists>) of a conjunction
505 of constraints. The constraints are separated by the keyword
508 =head3 C<PolyLib> format
510 If the represented set is a union, then the first line
511 contains a single number representing the number of disjuncts.
512 Otherwise, a line containing the number C<1> is optional.
514 Each disjunct is represented by a matrix of constraints.
515 The first line contains two numbers representing
516 the number of rows and columns,
517 where the number of rows is equal to the number of constraints
518 and the number of columns is equal to two plus the number of variables.
519 The following lines contain the actual rows of the constraint matrix.
520 In each row, the first column indicates whether the constraint
521 is an equality (C<0>) or inequality (C<1>). The final column
522 corresponds to the constant term.
524 If the set is parametric, then the coefficients of the parameters
525 appear in the last columns before the constant column.
526 The coefficients of any existentially quantified variables appear
527 between those of the set variables and those of the parameters.
532 __isl_give isl_basic_set *isl_basic_set_read_from_file(
533 isl_ctx *ctx, FILE *input, int nparam);
534 __isl_give isl_basic_set *isl_basic_set_read_from_str(
535 isl_ctx *ctx, const char *str, int nparam);
536 __isl_give isl_set *isl_set_read_from_file(isl_ctx *ctx,
537 FILE *input, int nparam);
538 __isl_give isl_set *isl_set_read_from_str(isl_ctx *ctx,
539 const char *str, int nparam);
542 __isl_give isl_basic_map *isl_basic_map_read_from_file(
543 isl_ctx *ctx, FILE *input, int nparam);
544 __isl_give isl_basic_map *isl_basic_map_read_from_str(
545 isl_ctx *ctx, const char *str, int nparam);
546 __isl_give isl_map *isl_map_read_from_file(
547 struct isl_ctx *ctx, FILE *input, int nparam);
548 __isl_give isl_map *isl_map_read_from_str(isl_ctx *ctx,
549 const char *str, int nparam);
551 The input format is autodetected and may be either the C<PolyLib> format
552 or the C<isl> format.
553 C<nparam> specifies how many of the final columns in
554 the C<PolyLib> format correspond to parameters.
555 If input is given in the C<isl> format, then the number
556 of parameters needs to be equal to C<nparam>.
557 If C<nparam> is negative, then any number of parameters
558 is accepted in the C<isl> format and zero parameters
559 are assumed in the C<PolyLib> format.
563 Before anything can be printed, an C<isl_printer> needs to
566 __isl_give isl_printer *isl_printer_to_file(isl_ctx *ctx,
568 __isl_give isl_printer *isl_printer_to_str(isl_ctx *ctx);
569 void isl_printer_free(__isl_take isl_printer *printer);
570 __isl_give char *isl_printer_get_str(
571 __isl_keep isl_printer *printer);
573 The behavior of the printer can be modified in various ways
575 __isl_give isl_printer *isl_printer_set_output_format(
576 __isl_take isl_printer *p, int output_format);
577 __isl_give isl_printer *isl_printer_set_indent(
578 __isl_take isl_printer *p, int indent);
579 __isl_give isl_printer *isl_printer_set_prefix(
580 __isl_take isl_printer *p, const char *prefix);
581 __isl_give isl_printer *isl_printer_set_suffix(
582 __isl_take isl_printer *p, const char *suffix);
584 The C<output_format> may be either C<ISL_FORMAT_ISL>, C<ISL_FORMAT_OMEGA>
585 or C<ISL_FORMAT_POLYLIB> and defaults to C<ISL_FORMAT_ISL>.
586 Each line in the output is indented by C<indent> spaces
587 (default: 0), prefixed by C<prefix> and suffixed by C<suffix>.
588 In the C<PolyLib> format output,
589 the coefficients of the existentially quantified variables
590 appear between those of the set variables and those
593 To actually print something, use
596 __isl_give isl_printer *isl_printer_print_basic_set(
597 __isl_take isl_printer *printer,
598 __isl_keep isl_basic_set *bset);
599 __isl_give isl_printer *isl_printer_print_set(
600 __isl_take isl_printer *printer,
601 __isl_keep isl_set *set);
604 __isl_give isl_printer *isl_printer_print_basic_map(
605 __isl_take isl_printer *printer,
606 __isl_keep isl_basic_map *bmap);
607 __isl_give isl_printer *isl_printer_print_map(
608 __isl_take isl_printer *printer,
609 __isl_keep isl_map *map);
611 #include <isl_union_set.h>
612 __isl_give isl_printer *isl_printer_print_union_set(
613 __isl_take isl_printer *p,
614 __isl_keep isl_union_set *uset);
616 #include <isl_union_map.h>
617 __isl_give isl_printer *isl_printer_print_union_map(
618 __isl_take isl_printer *p,
619 __isl_keep isl_union_map *umap);
621 When called on a file printer, the following function flushes
622 the file. When called on a string printer, the buffer is cleared.
624 __isl_give isl_printer *isl_printer_flush(
625 __isl_take isl_printer *p);
627 =head2 Creating New Sets and Relations
629 C<isl> has functions for creating some standard sets and relations.
633 =item * Empty sets and relations
635 __isl_give isl_basic_set *isl_basic_set_empty(
636 __isl_take isl_dim *dim);
637 __isl_give isl_basic_map *isl_basic_map_empty(
638 __isl_take isl_dim *dim);
639 __isl_give isl_set *isl_set_empty(
640 __isl_take isl_dim *dim);
641 __isl_give isl_map *isl_map_empty(
642 __isl_take isl_dim *dim);
643 __isl_give isl_union_set *isl_union_set_empty(
644 __isl_take isl_dim *dim);
645 __isl_give isl_union_map *isl_union_map_empty(
646 __isl_take isl_dim *dim);
648 For C<isl_union_set>s and C<isl_union_map>s, the dimensions specification
649 is only used to specify the parameters.
651 =item * Universe sets and relations
653 __isl_give isl_basic_set *isl_basic_set_universe(
654 __isl_take isl_dim *dim);
655 __isl_give isl_basic_map *isl_basic_map_universe(
656 __isl_take isl_dim *dim);
657 __isl_give isl_set *isl_set_universe(
658 __isl_take isl_dim *dim);
659 __isl_give isl_map *isl_map_universe(
660 __isl_take isl_dim *dim);
662 =item * Identity relations
664 __isl_give isl_basic_map *isl_basic_map_identity(
665 __isl_take isl_dim *set_dim);
666 __isl_give isl_map *isl_map_identity(
667 __isl_take isl_dim *set_dim);
669 These functions take a dimension specification for a B<set>
670 and return an identity relation between two such sets.
672 =item * Lexicographic order
674 __isl_give isl_map *isl_map_lex_lt(
675 __isl_take isl_dim *set_dim);
676 __isl_give isl_map *isl_map_lex_le(
677 __isl_take isl_dim *set_dim);
678 __isl_give isl_map *isl_map_lex_gt(
679 __isl_take isl_dim *set_dim);
680 __isl_give isl_map *isl_map_lex_ge(
681 __isl_take isl_dim *set_dim);
682 __isl_give isl_map *isl_map_lex_lt_first(
683 __isl_take isl_dim *dim, unsigned n);
684 __isl_give isl_map *isl_map_lex_le_first(
685 __isl_take isl_dim *dim, unsigned n);
686 __isl_give isl_map *isl_map_lex_gt_first(
687 __isl_take isl_dim *dim, unsigned n);
688 __isl_give isl_map *isl_map_lex_ge_first(
689 __isl_take isl_dim *dim, unsigned n);
691 The first four functions take a dimension specification for a B<set>
692 and return relations that express that the elements in the domain
693 are lexicographically less
694 (C<isl_map_lex_lt>), less or equal (C<isl_map_lex_le>),
695 greater (C<isl_map_lex_gt>) or greater or equal (C<isl_map_lex_ge>)
696 than the elements in the range.
697 The last four functions take a dimension specification for a map
698 and return relations that express that the first C<n> dimensions
699 in the domain are lexicographically less
700 (C<isl_map_lex_lt_first>), less or equal (C<isl_map_lex_le_first>),
701 greater (C<isl_map_lex_gt_first>) or greater or equal (C<isl_map_lex_ge_first>)
702 than the first C<n> dimensions in the range.
706 A basic set or relation can be converted to a set or relation
707 using the following functions.
709 __isl_give isl_set *isl_set_from_basic_set(
710 __isl_take isl_basic_set *bset);
711 __isl_give isl_map *isl_map_from_basic_map(
712 __isl_take isl_basic_map *bmap);
714 Sets and relations can be converted to union sets and relations
715 using the following functions.
717 __isl_give isl_union_map *isl_union_map_from_map(
718 __isl_take isl_map *map);
719 __isl_give isl_union_set *isl_union_set_from_set(
720 __isl_take isl_set *set);
722 Sets and relations can be copied and freed again using the following
725 __isl_give isl_basic_set *isl_basic_set_copy(
726 __isl_keep isl_basic_set *bset);
727 __isl_give isl_set *isl_set_copy(__isl_keep isl_set *set);
728 __isl_give isl_union_set *isl_union_set_copy(
729 __isl_keep isl_union_set *uset);
730 __isl_give isl_basic_map *isl_basic_map_copy(
731 __isl_keep isl_basic_map *bmap);
732 __isl_give isl_map *isl_map_copy(__isl_keep isl_map *map);
733 __isl_give isl_union_map *isl_union_map_copy(
734 __isl_keep isl_union_map *umap);
735 void isl_basic_set_free(__isl_take isl_basic_set *bset);
736 void isl_set_free(__isl_take isl_set *set);
737 void isl_union_set_free(__isl_take isl_union_set *uset);
738 void isl_basic_map_free(__isl_take isl_basic_map *bmap);
739 void isl_map_free(__isl_take isl_map *map);
740 void isl_union_map_free(__isl_take isl_union_map *umap);
742 Other sets and relations can be constructed by starting
743 from a universe set or relation, adding equality and/or
744 inequality constraints and then projecting out the
745 existentially quantified variables, if any.
746 Constraints can be constructed, manipulated and
747 added to basic sets and relations using the following functions.
749 #include <isl_constraint.h>
750 __isl_give isl_constraint *isl_equality_alloc(
751 __isl_take isl_dim *dim);
752 __isl_give isl_constraint *isl_inequality_alloc(
753 __isl_take isl_dim *dim);
754 void isl_constraint_set_constant(
755 __isl_keep isl_constraint *constraint, isl_int v);
756 void isl_constraint_set_coefficient(
757 __isl_keep isl_constraint *constraint,
758 enum isl_dim_type type, int pos, isl_int v);
759 __isl_give isl_basic_map *isl_basic_map_add_constraint(
760 __isl_take isl_basic_map *bmap,
761 __isl_take isl_constraint *constraint);
762 __isl_give isl_basic_set *isl_basic_set_add_constraint(
763 __isl_take isl_basic_set *bset,
764 __isl_take isl_constraint *constraint);
766 For example, to create a set containing the even integers
767 between 10 and 42, you would use the following code.
771 struct isl_constraint *c;
772 struct isl_basic_set *bset;
775 dim = isl_dim_set_alloc(ctx, 0, 2);
776 bset = isl_basic_set_universe(isl_dim_copy(dim));
778 c = isl_equality_alloc(isl_dim_copy(dim));
779 isl_int_set_si(v, -1);
780 isl_constraint_set_coefficient(c, isl_dim_set, 0, v);
781 isl_int_set_si(v, 2);
782 isl_constraint_set_coefficient(c, isl_dim_set, 1, v);
783 bset = isl_basic_set_add_constraint(bset, c);
785 c = isl_inequality_alloc(isl_dim_copy(dim));
786 isl_int_set_si(v, -10);
787 isl_constraint_set_constant(c, v);
788 isl_int_set_si(v, 1);
789 isl_constraint_set_coefficient(c, isl_dim_set, 0, v);
790 bset = isl_basic_set_add_constraint(bset, c);
792 c = isl_inequality_alloc(dim);
793 isl_int_set_si(v, 42);
794 isl_constraint_set_constant(c, v);
795 isl_int_set_si(v, -1);
796 isl_constraint_set_coefficient(c, isl_dim_set, 0, v);
797 bset = isl_basic_set_add_constraint(bset, c);
799 bset = isl_basic_set_project_out(bset, isl_dim_set, 1, 1);
805 struct isl_basic_set *bset;
806 bset = isl_basic_set_read_from_str(ctx,
807 "{[i] : exists (a : i = 2a and i >= 10 and i <= 42)}", -1);
809 A basic set or relation can also be constructed from two matrices
810 describing the equalities and the inequalities.
812 __isl_give isl_basic_set *isl_basic_set_from_constraint_matrices(
813 __isl_take isl_dim *dim,
814 __isl_take isl_mat *eq, __isl_take isl_mat *ineq,
815 enum isl_dim_type c1,
816 enum isl_dim_type c2, enum isl_dim_type c3,
817 enum isl_dim_type c4);
818 __isl_give isl_basic_map *isl_basic_map_from_constraint_matrices(
819 __isl_take isl_dim *dim,
820 __isl_take isl_mat *eq, __isl_take isl_mat *ineq,
821 enum isl_dim_type c1,
822 enum isl_dim_type c2, enum isl_dim_type c3,
823 enum isl_dim_type c4, enum isl_dim_type c5);
825 The C<isl_dim_type> arguments indicate the order in which
826 different kinds of variables appear in the input matrices
827 and should be a permutation of C<isl_dim_cst>, C<isl_dim_param>,
828 C<isl_dim_set> and C<isl_dim_div> for sets and
829 of C<isl_dim_cst>, C<isl_dim_param>,
830 C<isl_dim_in>, C<isl_dim_out> and C<isl_dim_div> for relations.
832 =head2 Inspecting Sets and Relations
834 Usually, the user should not have to care about the actual constraints
835 of the sets and maps, but should instead apply the abstract operations
836 explained in the following sections.
837 Occasionally, however, it may be required to inspect the individual
838 coefficients of the constraints. This section explains how to do so.
839 In these cases, it may also be useful to have C<isl> compute
840 an explicit representation of the existentially quantified variables.
842 __isl_give isl_set *isl_set_compute_divs(
843 __isl_take isl_set *set);
844 __isl_give isl_map *isl_map_compute_divs(
845 __isl_take isl_map *map);
846 __isl_give isl_union_set *isl_union_set_compute_divs(
847 __isl_take isl_union_set *uset);
848 __isl_give isl_union_map *isl_union_map_compute_divs(
849 __isl_take isl_union_map *umap);
851 This explicit representation defines the existentially quantified
852 variables as integer divisions of the other variables, possibly
853 including earlier existentially quantified variables.
854 An explicitly represented existentially quantified variable therefore
855 has a unique value when the values of the other variables are known.
856 If, furthermore, the same existentials, i.e., existentials
857 with the same explicit representations, should appear in the
858 same order in each of the disjuncts of a set or map, then the user should call
859 either of the following functions.
861 __isl_give isl_set *isl_set_align_divs(
862 __isl_take isl_set *set);
863 __isl_give isl_map *isl_map_align_divs(
864 __isl_take isl_map *map);
866 To iterate over all the sets or maps in a union set or map, use
868 int isl_union_set_foreach_set(__isl_keep isl_union_set *uset,
869 int (*fn)(__isl_take isl_set *set, void *user),
871 int isl_union_map_foreach_map(__isl_keep isl_union_map *umap,
872 int (*fn)(__isl_take isl_map *map, void *user),
875 To iterate over all the basic sets or maps in a set or map, use
877 int isl_set_foreach_basic_set(__isl_keep isl_set *set,
878 int (*fn)(__isl_take isl_basic_set *bset, void *user),
880 int isl_map_foreach_basic_map(__isl_keep isl_map *map,
881 int (*fn)(__isl_take isl_basic_map *bmap, void *user),
884 The callback function C<fn> should return 0 if successful and
885 -1 if an error occurs. In the latter case, or if any other error
886 occurs, the above functions will return -1.
888 It should be noted that C<isl> does not guarantee that
889 the basic sets or maps passed to C<fn> are disjoint.
890 If this is required, then the user should call one of
891 the following functions first.
893 __isl_give isl_set *isl_set_make_disjoint(
894 __isl_take isl_set *set);
895 __isl_give isl_map *isl_map_make_disjoint(
896 __isl_take isl_map *map);
898 To iterate over the constraints of a basic set or map, use
900 #include <isl_constraint.h>
902 int isl_basic_map_foreach_constraint(
903 __isl_keep isl_basic_map *bmap,
904 int (*fn)(__isl_take isl_constraint *c, void *user),
906 void isl_constraint_free(struct isl_constraint *c);
908 Again, the callback function C<fn> should return 0 if successful and
909 -1 if an error occurs. In the latter case, or if any other error
910 occurs, the above functions will return -1.
911 The constraint C<c> represents either an equality or an inequality.
912 Use the following function to find out whether a constraint
913 represents an equality. If not, it represents an inequality.
915 int isl_constraint_is_equality(
916 __isl_keep isl_constraint *constraint);
918 The coefficients of the constraints can be inspected using
919 the following functions.
921 void isl_constraint_get_constant(
922 __isl_keep isl_constraint *constraint, isl_int *v);
923 void isl_constraint_get_coefficient(
924 __isl_keep isl_constraint *constraint,
925 enum isl_dim_type type, int pos, isl_int *v);
927 The explicit representations of the existentially quantified
928 variables can be inspected using the following functions.
929 Note that the user is only allowed to use these functions
930 if the inspected set or map is the result of a call
931 to C<isl_set_compute_divs> or C<isl_map_compute_divs>.
933 __isl_give isl_div *isl_constraint_div(
934 __isl_keep isl_constraint *constraint, int pos);
935 void isl_div_get_constant(__isl_keep isl_div *div,
937 void isl_div_get_denominator(__isl_keep isl_div *div,
939 void isl_div_get_coefficient(__isl_keep isl_div *div,
940 enum isl_dim_type type, int pos, isl_int *v);
942 To obtain the constraints of a basic map in matrix
943 form, use the following functions.
945 __isl_give isl_mat *isl_basic_map_equalities_matrix(
946 __isl_keep isl_basic_map *bmap,
947 enum isl_dim_type c1,
948 enum isl_dim_type c2, enum isl_dim_type c3,
949 enum isl_dim_type c4, enum isl_dim_type c5);
950 __isl_give isl_mat *isl_basic_map_inequalities_matrix(
951 __isl_keep isl_basic_map *bmap,
952 enum isl_dim_type c1,
953 enum isl_dim_type c2, enum isl_dim_type c3,
954 enum isl_dim_type c4, enum isl_dim_type c5);
956 The C<isl_dim_type> arguments dictate the order in which
957 different kinds of variables appear in the resulting matrix
958 and should be a permutation of C<isl_dim_cst>, C<isl_dim_param>,
959 C<isl_dim_in>, C<isl_dim_out> and C<isl_dim_div>.
963 =head3 Unary Properties
969 The following functions test whether the given set or relation
970 contains any integer points. The ``fast'' variants do not perform
971 any computations, but simply check if the given set or relation
972 is already known to be empty.
974 int isl_basic_set_fast_is_empty(__isl_keep isl_basic_set *bset);
975 int isl_basic_set_is_empty(__isl_keep isl_basic_set *bset);
976 int isl_set_is_empty(__isl_keep isl_set *set);
977 int isl_union_set_is_empty(__isl_keep isl_union_set *uset);
978 int isl_basic_map_fast_is_empty(__isl_keep isl_basic_map *bmap);
979 int isl_basic_map_is_empty(__isl_keep isl_basic_map *bmap);
980 int isl_map_fast_is_empty(__isl_keep isl_map *map);
981 int isl_map_is_empty(__isl_keep isl_map *map);
982 int isl_union_map_is_empty(__isl_keep isl_union_map *umap);
986 int isl_basic_set_is_universe(__isl_keep isl_basic_set *bset);
987 int isl_basic_map_is_universe(__isl_keep isl_basic_map *bmap);
988 int isl_set_fast_is_universe(__isl_keep isl_set *set);
990 =item * Single-valuedness
992 int isl_map_is_single_valued(__isl_keep isl_map *map);
996 int isl_map_is_bijective(__isl_keep isl_map *map);
1000 The followning functions check whether the domain of the given
1001 (basic) set is a wrapped relation.
1003 int isl_basic_set_is_wrapping(
1004 __isl_keep isl_basic_set *bset);
1005 int isl_set_is_wrapping(__isl_keep isl_set *set);
1009 =head3 Binary Properties
1015 int isl_set_fast_is_equal(__isl_keep isl_set *set1,
1016 __isl_keep isl_set *set2);
1017 int isl_set_is_equal(__isl_keep isl_set *set1,
1018 __isl_keep isl_set *set2);
1019 int isl_basic_map_is_equal(
1020 __isl_keep isl_basic_map *bmap1,
1021 __isl_keep isl_basic_map *bmap2);
1022 int isl_map_is_equal(__isl_keep isl_map *map1,
1023 __isl_keep isl_map *map2);
1024 int isl_map_fast_is_equal(__isl_keep isl_map *map1,
1025 __isl_keep isl_map *map2);
1026 int isl_union_map_is_equal(
1027 __isl_keep isl_union_map *umap1,
1028 __isl_keep isl_union_map *umap2);
1030 =item * Disjointness
1032 int isl_set_fast_is_disjoint(__isl_keep isl_set *set1,
1033 __isl_keep isl_set *set2);
1037 int isl_set_is_subset(__isl_keep isl_set *set1,
1038 __isl_keep isl_set *set2);
1039 int isl_set_is_strict_subset(
1040 __isl_keep isl_set *set1,
1041 __isl_keep isl_set *set2);
1042 int isl_basic_map_is_subset(
1043 __isl_keep isl_basic_map *bmap1,
1044 __isl_keep isl_basic_map *bmap2);
1045 int isl_basic_map_is_strict_subset(
1046 __isl_keep isl_basic_map *bmap1,
1047 __isl_keep isl_basic_map *bmap2);
1048 int isl_map_is_subset(
1049 __isl_keep isl_map *map1,
1050 __isl_keep isl_map *map2);
1051 int isl_map_is_strict_subset(
1052 __isl_keep isl_map *map1,
1053 __isl_keep isl_map *map2);
1054 int isl_union_map_is_subset(
1055 __isl_keep isl_union_map *umap1,
1056 __isl_keep isl_union_map *umap2);
1057 int isl_union_map_is_strict_subset(
1058 __isl_keep isl_union_map *umap1,
1059 __isl_keep isl_union_map *umap2);
1063 =head2 Unary Operations
1069 __isl_give isl_set *isl_set_complement(
1070 __isl_take isl_set *set);
1074 __isl_give isl_basic_map *isl_basic_map_reverse(
1075 __isl_take isl_basic_map *bmap);
1076 __isl_give isl_map *isl_map_reverse(
1077 __isl_take isl_map *map);
1078 __isl_give isl_union_map *isl_union_map_reverse(
1079 __isl_take isl_union_map *umap);
1083 __isl_give isl_basic_set *isl_basic_set_project_out(
1084 __isl_take isl_basic_set *bset,
1085 enum isl_dim_type type, unsigned first, unsigned n);
1086 __isl_give isl_basic_map *isl_basic_map_project_out(
1087 __isl_take isl_basic_map *bmap,
1088 enum isl_dim_type type, unsigned first, unsigned n);
1089 __isl_give isl_set *isl_set_project_out(__isl_take isl_set *set,
1090 enum isl_dim_type type, unsigned first, unsigned n);
1091 __isl_give isl_map *isl_map_project_out(__isl_take isl_map *map,
1092 enum isl_dim_type type, unsigned first, unsigned n);
1093 __isl_give isl_basic_set *isl_basic_map_domain(
1094 __isl_take isl_basic_map *bmap);
1095 __isl_give isl_basic_set *isl_basic_map_range(
1096 __isl_take isl_basic_map *bmap);
1097 __isl_give isl_set *isl_map_domain(
1098 __isl_take isl_map *bmap);
1099 __isl_give isl_set *isl_map_range(
1100 __isl_take isl_map *map);
1101 __isl_give isl_union_set *isl_union_map_domain(
1102 __isl_take isl_union_map *umap);
1103 __isl_give isl_union_set *isl_union_map_range(
1104 __isl_take isl_union_map *umap);
1108 __isl_give isl_basic_set *isl_basic_map_deltas(
1109 __isl_take isl_basic_map *bmap);
1110 __isl_give isl_set *isl_map_deltas(__isl_take isl_map *map);
1111 __isl_give isl_union_set *isl_union_map_deltas(
1112 __isl_take isl_union_map *umap);
1114 These functions return a (basic) set containing the differences
1115 between image elements and corresponding domain elements in the input.
1119 Simplify the representation of a set or relation by trying
1120 to combine pairs of basic sets or relations into a single
1121 basic set or relation.
1123 __isl_give isl_set *isl_set_coalesce(__isl_take isl_set *set);
1124 __isl_give isl_map *isl_map_coalesce(__isl_take isl_map *map);
1125 __isl_give isl_union_set *isl_union_set_coalesce(
1126 __isl_take isl_union_set *uset);
1127 __isl_give isl_union_map *isl_union_map_coalesce(
1128 __isl_take isl_union_map *umap);
1132 __isl_give isl_basic_set *isl_set_convex_hull(
1133 __isl_take isl_set *set);
1134 __isl_give isl_basic_map *isl_map_convex_hull(
1135 __isl_take isl_map *map);
1137 If the input set or relation has any existentially quantified
1138 variables, then the result of these operations is currently undefined.
1142 __isl_give isl_basic_set *isl_set_simple_hull(
1143 __isl_take isl_set *set);
1144 __isl_give isl_basic_map *isl_map_simple_hull(
1145 __isl_take isl_map *map);
1147 These functions compute a single basic set or relation
1148 that contains the whole input set or relation.
1149 In particular, the output is described by translates
1150 of the constraints describing the basic sets or relations in the input.
1154 (See \autoref{s:simple hull}.)
1160 __isl_give isl_basic_set *isl_basic_set_affine_hull(
1161 __isl_take isl_basic_set *bset);
1162 __isl_give isl_basic_set *isl_set_affine_hull(
1163 __isl_take isl_set *set);
1164 __isl_give isl_union_set *isl_union_set_affine_hull(
1165 __isl_take isl_union_set *uset);
1166 __isl_give isl_basic_map *isl_basic_map_affine_hull(
1167 __isl_take isl_basic_map *bmap);
1168 __isl_give isl_basic_map *isl_map_affine_hull(
1169 __isl_take isl_map *map);
1170 __isl_give isl_union_map *isl_union_map_affine_hull(
1171 __isl_take isl_union_map *umap);
1173 In case of union sets and relations, the affine hull is computed
1178 __isl_give isl_map *isl_map_power(__isl_take isl_map *map,
1179 unsigned param, int *exact);
1181 Compute a parametric representation for all positive powers I<k> of C<map>.
1182 The power I<k> is equated to the parameter at position C<param>.
1183 The result may be an overapproximation. If the result is exact,
1184 then C<*exact> is set to C<1>.
1185 The current implementation only produces exact results for particular
1186 cases of piecewise translations (i.e., piecewise uniform dependences).
1188 =item * Transitive closure
1190 __isl_give isl_map *isl_map_transitive_closure(
1191 __isl_take isl_map *map, int *exact);
1192 __isl_give isl_union_map *isl_union_map_transitive_closure(
1193 __isl_take isl_union_map *umap, int *exact);
1195 Compute the transitive closure of C<map>.
1196 The result may be an overapproximation. If the result is known to be exact,
1197 then C<*exact> is set to C<1>.
1198 The current implementation only produces exact results for particular
1199 cases of piecewise translations (i.e., piecewise uniform dependences).
1201 =item * Reaching path lengths
1203 __isl_give isl_map *isl_map_reaching_path_lengths(
1204 __isl_take isl_map *map, int *exact);
1206 Compute a relation that maps each element in the range of C<map>
1207 to the lengths of all paths composed of edges in C<map> that
1208 end up in the given element.
1209 The result may be an overapproximation. If the result is known to be exact,
1210 then C<*exact> is set to C<1>.
1211 To compute the I<maximal> path length, the resulting relation
1212 should be postprocessed by C<isl_map_lexmax>.
1213 In particular, if the input relation is a dependence relation
1214 (mapping sources to sinks), then the maximal path length corresponds
1215 to the free schedule.
1216 Note, however, that C<isl_map_lexmax> expects the maximum to be
1217 finite, so if the path lengths are unbounded (possibly due to
1218 the overapproximation), then you will get an error message.
1222 __isl_give isl_basic_set *isl_basic_map_wrap(
1223 __isl_take isl_basic_map *bmap);
1224 __isl_give isl_set *isl_map_wrap(
1225 __isl_take isl_map *map);
1226 __isl_give isl_union_set *isl_union_map_wrap(
1227 __isl_take isl_union_map *umap);
1228 __isl_give isl_basic_map *isl_basic_set_unwrap(
1229 __isl_take isl_basic_set *bset);
1230 __isl_give isl_map *isl_set_unwrap(
1231 __isl_take isl_set *set);
1232 __isl_give isl_union_map *isl_union_set_unwrap(
1233 __isl_take isl_union_set *uset);
1237 =head2 Binary Operations
1239 The two arguments of a binary operation not only need to live
1240 in the same C<isl_ctx>, they currently also need to have
1241 the same (number of) parameters.
1243 =head3 Basic Operations
1247 =item * Intersection
1249 __isl_give isl_basic_set *isl_basic_set_intersect(
1250 __isl_take isl_basic_set *bset1,
1251 __isl_take isl_basic_set *bset2);
1252 __isl_give isl_set *isl_set_intersect(
1253 __isl_take isl_set *set1,
1254 __isl_take isl_set *set2);
1255 __isl_give isl_union_set *isl_union_set_intersect(
1256 __isl_take isl_union_set *uset1,
1257 __isl_take isl_union_set *uset2);
1258 __isl_give isl_basic_map *isl_basic_map_intersect_domain(
1259 __isl_take isl_basic_map *bmap,
1260 __isl_take isl_basic_set *bset);
1261 __isl_give isl_basic_map *isl_basic_map_intersect_range(
1262 __isl_take isl_basic_map *bmap,
1263 __isl_take isl_basic_set *bset);
1264 __isl_give isl_basic_map *isl_basic_map_intersect(
1265 __isl_take isl_basic_map *bmap1,
1266 __isl_take isl_basic_map *bmap2);
1267 __isl_give isl_map *isl_map_intersect_domain(
1268 __isl_take isl_map *map,
1269 __isl_take isl_set *set);
1270 __isl_give isl_map *isl_map_intersect_range(
1271 __isl_take isl_map *map,
1272 __isl_take isl_set *set);
1273 __isl_give isl_map *isl_map_intersect(
1274 __isl_take isl_map *map1,
1275 __isl_take isl_map *map2);
1276 __isl_give isl_union_map *isl_union_map_intersect_domain(
1277 __isl_take isl_union_map *umap,
1278 __isl_take isl_union_set *uset);
1279 __isl_give isl_union_map *isl_union_map_intersect(
1280 __isl_take isl_union_map *umap1,
1281 __isl_take isl_union_map *umap2);
1285 __isl_give isl_set *isl_basic_set_union(
1286 __isl_take isl_basic_set *bset1,
1287 __isl_take isl_basic_set *bset2);
1288 __isl_give isl_map *isl_basic_map_union(
1289 __isl_take isl_basic_map *bmap1,
1290 __isl_take isl_basic_map *bmap2);
1291 __isl_give isl_set *isl_set_union(
1292 __isl_take isl_set *set1,
1293 __isl_take isl_set *set2);
1294 __isl_give isl_map *isl_map_union(
1295 __isl_take isl_map *map1,
1296 __isl_take isl_map *map2);
1297 __isl_give isl_union_set *isl_union_set_union(
1298 __isl_take isl_union_set *uset1,
1299 __isl_take isl_union_set *uset2);
1300 __isl_give isl_union_map *isl_union_map_union(
1301 __isl_take isl_union_map *umap1,
1302 __isl_take isl_union_map *umap2);
1304 =item * Set difference
1306 __isl_give isl_set *isl_set_subtract(
1307 __isl_take isl_set *set1,
1308 __isl_take isl_set *set2);
1309 __isl_give isl_map *isl_map_subtract(
1310 __isl_take isl_map *map1,
1311 __isl_take isl_map *map2);
1312 __isl_give isl_union_set *isl_union_set_subtract(
1313 __isl_take isl_union_set *uset1,
1314 __isl_take isl_union_set *uset2);
1315 __isl_give isl_union_map *isl_union_map_subtract(
1316 __isl_take isl_union_map *umap1,
1317 __isl_take isl_union_map *umap2);
1321 __isl_give isl_basic_set *isl_basic_set_apply(
1322 __isl_take isl_basic_set *bset,
1323 __isl_take isl_basic_map *bmap);
1324 __isl_give isl_set *isl_set_apply(
1325 __isl_take isl_set *set,
1326 __isl_take isl_map *map);
1327 __isl_give isl_union_set *isl_union_set_apply(
1328 __isl_take isl_union_set *uset,
1329 __isl_take isl_union_map *umap);
1330 __isl_give isl_basic_map *isl_basic_map_apply_domain(
1331 __isl_take isl_basic_map *bmap1,
1332 __isl_take isl_basic_map *bmap2);
1333 __isl_give isl_basic_map *isl_basic_map_apply_range(
1334 __isl_take isl_basic_map *bmap1,
1335 __isl_take isl_basic_map *bmap2);
1336 __isl_give isl_map *isl_map_apply_domain(
1337 __isl_take isl_map *map1,
1338 __isl_take isl_map *map2);
1339 __isl_give isl_map *isl_map_apply_range(
1340 __isl_take isl_map *map1,
1341 __isl_take isl_map *map2);
1342 __isl_give isl_union_map *isl_union_map_apply_range(
1343 __isl_take isl_union_map *umap1,
1344 __isl_take isl_union_map *umap2);
1346 =item * Simplification
1348 __isl_give isl_basic_set *isl_basic_set_gist(
1349 __isl_take isl_basic_set *bset,
1350 __isl_take isl_basic_set *context);
1351 __isl_give isl_set *isl_set_gist(__isl_take isl_set *set,
1352 __isl_take isl_set *context);
1353 __isl_give isl_union_set *isl_union_set_gist(
1354 __isl_take isl_union_set *uset,
1355 __isl_take isl_union_set *context);
1356 __isl_give isl_basic_map *isl_basic_map_gist(
1357 __isl_take isl_basic_map *bmap,
1358 __isl_take isl_basic_map *context);
1359 __isl_give isl_map *isl_map_gist(__isl_take isl_map *map,
1360 __isl_take isl_map *context);
1361 __isl_give isl_union_map *isl_union_map_gist(
1362 __isl_take isl_union_map *umap,
1363 __isl_take isl_union_map *context);
1365 The gist operation returns a set or relation that has the
1366 same intersection with the context as the input set or relation.
1367 Any implicit equality in the intersection is made explicit in the result,
1368 while all inequalities that are redundant with respect to the intersection
1370 In case of union sets and relations, the gist operation is performed
1375 =head3 Lexicographic Optimization
1377 Given a (basic) set C<set> (or C<bset>) and a zero-dimensional domain C<dom>,
1378 the following functions
1379 compute a set that contains the lexicographic minimum or maximum
1380 of the elements in C<set> (or C<bset>) for those values of the parameters
1381 that satisfy C<dom>.
1382 If C<empty> is not C<NULL>, then C<*empty> is assigned a set
1383 that contains the parameter values in C<dom> for which C<set> (or C<bset>)
1385 In other words, the union of the parameter values
1386 for which the result is non-empty and of C<*empty>
1389 __isl_give isl_set *isl_basic_set_partial_lexmin(
1390 __isl_take isl_basic_set *bset,
1391 __isl_take isl_basic_set *dom,
1392 __isl_give isl_set **empty);
1393 __isl_give isl_set *isl_basic_set_partial_lexmax(
1394 __isl_take isl_basic_set *bset,
1395 __isl_take isl_basic_set *dom,
1396 __isl_give isl_set **empty);
1397 __isl_give isl_set *isl_set_partial_lexmin(
1398 __isl_take isl_set *set, __isl_take isl_set *dom,
1399 __isl_give isl_set **empty);
1400 __isl_give isl_set *isl_set_partial_lexmax(
1401 __isl_take isl_set *set, __isl_take isl_set *dom,
1402 __isl_give isl_set **empty);
1404 Given a (basic) set C<set> (or C<bset>), the following functions simply
1405 return a set containing the lexicographic minimum or maximum
1406 of the elements in C<set> (or C<bset>).
1407 In case of union sets, the optimum is computed per space.
1409 __isl_give isl_set *isl_basic_set_lexmin(
1410 __isl_take isl_basic_set *bset);
1411 __isl_give isl_set *isl_basic_set_lexmax(
1412 __isl_take isl_basic_set *bset);
1413 __isl_give isl_set *isl_set_lexmin(
1414 __isl_take isl_set *set);
1415 __isl_give isl_set *isl_set_lexmax(
1416 __isl_take isl_set *set);
1417 __isl_give isl_union_set *isl_union_set_lexmin(
1418 __isl_take isl_union_set *uset);
1419 __isl_give isl_union_set *isl_union_set_lexmax(
1420 __isl_take isl_union_set *uset);
1422 Given a (basic) relation C<map> (or C<bmap>) and a domain C<dom>,
1423 the following functions
1424 compute a relation that maps each element of C<dom>
1425 to the single lexicographic minimum or maximum
1426 of the elements that are associated to that same
1427 element in C<map> (or C<bmap>).
1428 If C<empty> is not C<NULL>, then C<*empty> is assigned a set
1429 that contains the elements in C<dom> that do not map
1430 to any elements in C<map> (or C<bmap>).
1431 In other words, the union of the domain of the result and of C<*empty>
1434 __isl_give isl_map *isl_basic_map_partial_lexmax(
1435 __isl_take isl_basic_map *bmap,
1436 __isl_take isl_basic_set *dom,
1437 __isl_give isl_set **empty);
1438 __isl_give isl_map *isl_basic_map_partial_lexmin(
1439 __isl_take isl_basic_map *bmap,
1440 __isl_take isl_basic_set *dom,
1441 __isl_give isl_set **empty);
1442 __isl_give isl_map *isl_map_partial_lexmax(
1443 __isl_take isl_map *map, __isl_take isl_set *dom,
1444 __isl_give isl_set **empty);
1445 __isl_give isl_map *isl_map_partial_lexmin(
1446 __isl_take isl_map *map, __isl_take isl_set *dom,
1447 __isl_give isl_set **empty);
1449 Given a (basic) map C<map> (or C<bmap>), the following functions simply
1450 return a map mapping each element in the domain of
1451 C<map> (or C<bmap>) to the lexicographic minimum or maximum
1452 of all elements associated to that element.
1453 In case of union relations, the optimum is computed per space.
1455 __isl_give isl_map *isl_basic_map_lexmin(
1456 __isl_take isl_basic_map *bmap);
1457 __isl_give isl_map *isl_basic_map_lexmax(
1458 __isl_take isl_basic_map *bmap);
1459 __isl_give isl_map *isl_map_lexmin(
1460 __isl_take isl_map *map);
1461 __isl_give isl_map *isl_map_lexmax(
1462 __isl_take isl_map *map);
1463 __isl_give isl_union_map *isl_union_map_lexmin(
1464 __isl_take isl_union_map *umap);
1465 __isl_give isl_union_map *isl_union_map_lexmax(
1466 __isl_take isl_union_map *umap);
1470 Matrices can be created, copied and freed using the following functions.
1472 #include <isl_mat.h>
1473 __isl_give isl_mat *isl_mat_alloc(struct isl_ctx *ctx,
1474 unsigned n_row, unsigned n_col);
1475 __isl_give isl_mat *isl_mat_copy(__isl_keep isl_mat *mat);
1476 void isl_mat_free(__isl_take isl_mat *mat);
1478 Note that the elements of a newly created matrix may have arbitrary values.
1479 The elements can be changed and inspected using the following functions.
1481 int isl_mat_rows(__isl_keep isl_mat *mat);
1482 int isl_mat_cols(__isl_keep isl_mat *mat);
1483 int isl_mat_get_element(__isl_keep isl_mat *mat,
1484 int row, int col, isl_int *v);
1485 __isl_give isl_mat *isl_mat_set_element(__isl_take isl_mat *mat,
1486 int row, int col, isl_int v);
1488 C<isl_mat_get_element> will return a negative value if anything went wrong.
1489 In that case, the value of C<*v> is undefined.
1491 The following function can be used to compute the (right) inverse
1492 of a matrix, i.e., a matrix such that the product of the original
1493 and the inverse (in that order) is a multiple of the identity matrix.
1494 The input matrix is assumed to be of full row-rank.
1496 __isl_give isl_mat *isl_mat_right_inverse(__isl_take isl_mat *mat);
1498 The following function can be used to compute the (right) kernel
1499 (or null space) of a matrix, i.e., a matrix such that the product of
1500 the original and the kernel (in that order) is the zero matrix.
1502 __isl_give isl_mat *isl_mat_right_kernel(__isl_take isl_mat *mat);
1506 Points are elements of a set. They can be used to construct
1507 simple sets (boxes) or they can be used to represent the
1508 individual elements of a set.
1509 The zero point (the origin) can be created using
1511 __isl_give isl_point *isl_point_zero(__isl_take isl_dim *dim);
1513 The coordinates of a point can be inspected, set and changed
1516 void isl_point_get_coordinate(__isl_keep isl_point *pnt,
1517 enum isl_dim_type type, int pos, isl_int *v);
1518 __isl_give isl_point *isl_point_set_coordinate(
1519 __isl_take isl_point *pnt,
1520 enum isl_dim_type type, int pos, isl_int v);
1522 __isl_give isl_point *isl_point_add_ui(
1523 __isl_take isl_point *pnt,
1524 enum isl_dim_type type, int pos, unsigned val);
1525 __isl_give isl_point *isl_point_sub_ui(
1526 __isl_take isl_point *pnt,
1527 enum isl_dim_type type, int pos, unsigned val);
1529 Points can be copied or freed using
1531 __isl_give isl_point *isl_point_copy(
1532 __isl_keep isl_point *pnt);
1533 void isl_point_free(__isl_take isl_point *pnt);
1535 A singleton set can be created from a point using
1537 __isl_give isl_set *isl_set_from_point(
1538 __isl_take isl_point *pnt);
1540 and a box can be created from two opposite extremal points using
1542 __isl_give isl_set *isl_set_box_from_points(
1543 __isl_take isl_point *pnt1,
1544 __isl_take isl_point *pnt2);
1546 All elements of a B<bounded> (union) set can be enumerated using
1547 the following functions.
1549 int isl_set_foreach_point(__isl_keep isl_set *set,
1550 int (*fn)(__isl_take isl_point *pnt, void *user),
1552 int isl_union_set_foreach_point(__isl_keep isl_union_set *uset,
1553 int (*fn)(__isl_take isl_point *pnt, void *user),
1556 The function C<fn> is called for each integer point in
1557 C<set> with as second argument the last argument of
1558 the C<isl_set_foreach_point> call. The function C<fn>
1559 should return C<0> on success and C<-1> on failure.
1560 In the latter case, C<isl_set_foreach_point> will stop
1561 enumerating and return C<-1> as well.
1562 If the enumeration is performed successfully and to completion,
1563 then C<isl_set_foreach_point> returns C<0>.
1565 To obtain a single point of a set, use
1567 __isl_give isl_point *isl_set_sample_point(
1568 __isl_take isl_set *set);
1570 If C<set> does not contain any (integer) points, then the
1571 resulting point will be ``void'', a property that can be
1574 int isl_point_is_void(__isl_keep isl_point *pnt);
1576 =head2 Piecewise Quasipolynomials
1578 A piecewise quasipolynomial is a particular kind of function that maps
1579 a parametric point to a rational value.
1580 More specifically, a quasipolynomial is a polynomial expression in greatest
1581 integer parts of affine expressions of parameters and variables.
1582 A piecewise quasipolynomial is a subdivision of a given parametric
1583 domain into disjoint cells with a quasipolynomial associated to
1584 each cell. The value of the piecewise quasipolynomial at a given
1585 point is the value of the quasipolynomial associated to the cell
1586 that contains the point. Outside of the union of cells,
1587 the value is assumed to be zero.
1588 For example, the piecewise quasipolynomial
1590 [n] -> { [x] -> ((1 + n) - x) : x <= n and x >= 0 }
1592 maps C<x> to C<1 + n - x> for values of C<x> between C<0> and C<n>.
1593 A given piecewise quasipolynomial has a fixed domain dimension.
1594 Union piecewise quasipolynomials are used to contain piecewise quasipolynomials
1595 defined over different domains.
1596 Piecewise quasipolynomials are mainly used by the C<barvinok>
1597 library for representing the number of elements in a parametric set or map.
1598 For example, the piecewise quasipolynomial above represents
1599 the number of points in the map
1601 [n] -> { [x] -> [y] : x,y >= 0 and 0 <= x + y <= n }
1603 =head3 Printing (Piecewise) Quasipolynomials
1605 Quasipolynomials and piecewise quasipolynomials can be printed
1606 using the following functions.
1608 __isl_give isl_printer *isl_printer_print_qpolynomial(
1609 __isl_take isl_printer *p,
1610 __isl_keep isl_qpolynomial *qp);
1612 __isl_give isl_printer *isl_printer_print_pw_qpolynomial(
1613 __isl_take isl_printer *p,
1614 __isl_keep isl_pw_qpolynomial *pwqp);
1616 __isl_give isl_printer *isl_printer_print_union_pw_qpolynomial(
1617 __isl_take isl_printer *p,
1618 __isl_keep isl_union_pw_qpolynomial *upwqp);
1620 The output format of the printer
1621 needs to be set to either C<ISL_FORMAT_ISL> or C<ISL_FORMAT_C>.
1622 For C<isl_printer_print_union_pw_qpolynomial>, only C<ISL_FORMAT_ISL>
1625 =head3 Creating New (Piecewise) Quasipolynomials
1627 Some simple quasipolynomials can be created using the following functions.
1628 More complicated quasipolynomials can be created by applying
1629 operations such as addition and multiplication
1630 on the resulting quasipolynomials
1632 __isl_give isl_qpolynomial *isl_qpolynomial_zero(
1633 __isl_take isl_dim *dim);
1634 __isl_give isl_qpolynomial *isl_qpolynomial_one(
1635 __isl_take isl_dim *dim);
1636 __isl_give isl_qpolynomial *isl_qpolynomial_infty(
1637 __isl_take isl_dim *dim);
1638 __isl_give isl_qpolynomial *isl_qpolynomial_neginfty(
1639 __isl_take isl_dim *dim);
1640 __isl_give isl_qpolynomial *isl_qpolynomial_nan(
1641 __isl_take isl_dim *dim);
1642 __isl_give isl_qpolynomial *isl_qpolynomial_rat_cst(
1643 __isl_take isl_dim *dim,
1644 const isl_int n, const isl_int d);
1645 __isl_give isl_qpolynomial *isl_qpolynomial_div(
1646 __isl_take isl_div *div);
1647 __isl_give isl_qpolynomial *isl_qpolynomial_var(
1648 __isl_take isl_dim *dim,
1649 enum isl_dim_type type, unsigned pos);
1651 The zero piecewise quasipolynomial or a piecewise quasipolynomial
1652 with a single cell can be created using the following functions.
1653 Multiple of these single cell piecewise quasipolynomials can
1654 be combined to create more complicated piecewise quasipolynomials.
1656 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_zero(
1657 __isl_take isl_dim *dim);
1658 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_alloc(
1659 __isl_take isl_set *set,
1660 __isl_take isl_qpolynomial *qp);
1662 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_zero(
1663 __isl_take isl_dim *dim);
1664 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_from_pw_qpolynomial(
1665 __isl_take isl_pw_qpolynomial *pwqp);
1666 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_add_pw_qpolynomial(
1667 __isl_take isl_union_pw_qpolynomial *upwqp,
1668 __isl_take isl_pw_qpolynomial *pwqp);
1670 Quasipolynomials can be copied and freed again using the following
1673 __isl_give isl_qpolynomial *isl_qpolynomial_copy(
1674 __isl_keep isl_qpolynomial *qp);
1675 void isl_qpolynomial_free(__isl_take isl_qpolynomial *qp);
1677 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_copy(
1678 __isl_keep isl_pw_qpolynomial *pwqp);
1679 void isl_pw_qpolynomial_free(
1680 __isl_take isl_pw_qpolynomial *pwqp);
1682 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_copy(
1683 __isl_keep isl_union_pw_qpolynomial *upwqp);
1684 void isl_union_pw_qpolynomial_free(
1685 __isl_take isl_union_pw_qpolynomial *upwqp);
1687 =head3 Inspecting (Piecewise) Quasipolynomials
1689 To iterate over all piecewise quasipolynomials in a union
1690 piecewise quasipolynomial, use the following function
1692 int isl_union_pw_qpolynomial_foreach_pw_qpolynomial(
1693 __isl_keep isl_union_pw_qpolynomial *upwqp,
1694 int (*fn)(__isl_take isl_pw_qpolynomial *pwqp, void *user),
1697 To iterate over the cells in a piecewise quasipolynomial,
1698 use either of the following two functions
1700 int isl_pw_qpolynomial_foreach_piece(
1701 __isl_keep isl_pw_qpolynomial *pwqp,
1702 int (*fn)(__isl_take isl_set *set,
1703 __isl_take isl_qpolynomial *qp,
1704 void *user), void *user);
1705 int isl_pw_qpolynomial_foreach_lifted_piece(
1706 __isl_keep isl_pw_qpolynomial *pwqp,
1707 int (*fn)(__isl_take isl_set *set,
1708 __isl_take isl_qpolynomial *qp,
1709 void *user), void *user);
1711 As usual, the function C<fn> should return C<0> on success
1712 and C<-1> on failure. The difference between
1713 C<isl_pw_qpolynomial_foreach_piece> and
1714 C<isl_pw_qpolynomial_foreach_lifted_piece> is that
1715 C<isl_pw_qpolynomial_foreach_lifted_piece> will first
1716 compute unique representations for all existentially quantified
1717 variables and then turn these existentially quantified variables
1718 into extra set variables, adapting the associated quasipolynomial
1719 accordingly. This means that the C<set> passed to C<fn>
1720 will not have any existentially quantified variables, but that
1721 the dimensions of the sets may be different for different
1722 invocations of C<fn>.
1724 To iterate over all terms in a quasipolynomial,
1727 int isl_qpolynomial_foreach_term(
1728 __isl_keep isl_qpolynomial *qp,
1729 int (*fn)(__isl_take isl_term *term,
1730 void *user), void *user);
1732 The terms themselves can be inspected and freed using
1735 unsigned isl_term_dim(__isl_keep isl_term *term,
1736 enum isl_dim_type type);
1737 void isl_term_get_num(__isl_keep isl_term *term,
1739 void isl_term_get_den(__isl_keep isl_term *term,
1741 int isl_term_get_exp(__isl_keep isl_term *term,
1742 enum isl_dim_type type, unsigned pos);
1743 __isl_give isl_div *isl_term_get_div(
1744 __isl_keep isl_term *term, unsigned pos);
1745 void isl_term_free(__isl_take isl_term *term);
1747 Each term is a product of parameters, set variables and
1748 integer divisions. The function C<isl_term_get_exp>
1749 returns the exponent of a given dimensions in the given term.
1750 The C<isl_int>s in the arguments of C<isl_term_get_num>
1751 and C<isl_term_get_den> need to have been initialized
1752 using C<isl_int_init> before calling these functions.
1754 =head3 Properties of (Piecewise) Quasipolynomials
1756 To check whether a quasipolynomial is actually a constant,
1757 use the following function.
1759 int isl_qpolynomial_is_cst(__isl_keep isl_qpolynomial *qp,
1760 isl_int *n, isl_int *d);
1762 If C<qp> is a constant and if C<n> and C<d> are not C<NULL>
1763 then the numerator and denominator of the constant
1764 are returned in C<*n> and C<*d>, respectively.
1766 =head3 Operations on (Piecewise) Quasipolynomials
1768 __isl_give isl_qpolynomial *isl_qpolynomial_neg(
1769 __isl_take isl_qpolynomial *qp);
1770 __isl_give isl_qpolynomial *isl_qpolynomial_add(
1771 __isl_take isl_qpolynomial *qp1,
1772 __isl_take isl_qpolynomial *qp2);
1773 __isl_give isl_qpolynomial *isl_qpolynomial_sub(
1774 __isl_take isl_qpolynomial *qp1,
1775 __isl_take isl_qpolynomial *qp2);
1776 __isl_give isl_qpolynomial *isl_qpolynomial_mul(
1777 __isl_take isl_qpolynomial *qp1,
1778 __isl_take isl_qpolynomial *qp2);
1780 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_add(
1781 __isl_take isl_pw_qpolynomial *pwqp1,
1782 __isl_take isl_pw_qpolynomial *pwqp2);
1783 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_sub(
1784 __isl_take isl_pw_qpolynomial *pwqp1,
1785 __isl_take isl_pw_qpolynomial *pwqp2);
1786 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_add_disjoint(
1787 __isl_take isl_pw_qpolynomial *pwqp1,
1788 __isl_take isl_pw_qpolynomial *pwqp2);
1789 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_neg(
1790 __isl_take isl_pw_qpolynomial *pwqp);
1791 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_mul(
1792 __isl_take isl_pw_qpolynomial *pwqp1,
1793 __isl_take isl_pw_qpolynomial *pwqp2);
1795 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_add(
1796 __isl_take isl_union_pw_qpolynomial *upwqp1,
1797 __isl_take isl_union_pw_qpolynomial *upwqp2);
1798 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_sub(
1799 __isl_take isl_union_pw_qpolynomial *upwqp1,
1800 __isl_take isl_union_pw_qpolynomial *upwqp2);
1801 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_mul(
1802 __isl_take isl_union_pw_qpolynomial *upwqp1,
1803 __isl_take isl_union_pw_qpolynomial *upwqp2);
1805 __isl_give isl_qpolynomial *isl_pw_qpolynomial_eval(
1806 __isl_take isl_pw_qpolynomial *pwqp,
1807 __isl_take isl_point *pnt);
1809 __isl_give isl_qpolynomial *isl_union_pw_qpolynomial_eval(
1810 __isl_take isl_union_pw_qpolynomial *upwqp,
1811 __isl_take isl_point *pnt);
1813 __isl_give isl_set *isl_pw_qpolynomial_domain(
1814 __isl_take isl_pw_qpolynomial *pwqp);
1815 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_intersect_domain(
1816 __isl_take isl_pw_qpolynomial *pwpq,
1817 __isl_take isl_set *set);
1819 __isl_give isl_union_set *isl_union_pw_qpolynomial_domain(
1820 __isl_take isl_union_pw_qpolynomial *upwqp);
1821 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_intersect_domain(
1822 __isl_take isl_union_pw_qpolynomial *upwpq,
1823 __isl_take isl_union_set *uset);
1825 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_coalesce(
1826 __isl_take isl_union_pw_qpolynomial *upwqp);
1828 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_gist(
1829 __isl_take isl_pw_qpolynomial *pwqp,
1830 __isl_take isl_set *context);
1832 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_gist(
1833 __isl_take isl_union_pw_qpolynomial *upwqp,
1834 __isl_take isl_union_set *context);
1836 The gist operation applies the gist operation to each of
1837 the cells in the domain of the input piecewise quasipolynomial.
1838 In future, the operation will also exploit the context
1839 to simplify the quasipolynomials associated to each cell.
1841 =head2 Bounds on Piecewise Quasipolynomials and Piecewise Quasipolynomial Reductions
1843 A piecewise quasipolynomial reduction is a piecewise
1844 reduction (or fold) of quasipolynomials.
1845 In particular, the reduction can be maximum or a minimum.
1846 The objects are mainly used to represent the result of
1847 an upper or lower bound on a quasipolynomial over its domain,
1848 i.e., as the result of the following function.
1850 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_bound(
1851 __isl_take isl_pw_qpolynomial *pwqp,
1852 enum isl_fold type, int *tight);
1854 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_bound(
1855 __isl_take isl_union_pw_qpolynomial *upwqp,
1856 enum isl_fold type, int *tight);
1858 The C<type> argument may be either C<isl_fold_min> or C<isl_fold_max>.
1859 If C<tight> is not C<NULL>, then C<*tight> is set to C<1>
1860 is the returned bound is known be tight, i.e., for each value
1861 of the parameters there is at least
1862 one element in the domain that reaches the bound.
1863 If the domain of C<pwqp> is not wrapping, then the bound is computed
1864 over all elements in that domain and the result has a purely parametric
1865 domain. If the domain of C<pwqp> is wrapping, then the bound is
1866 computed over the range of the wrapped relation. The domain of the
1867 wrapped relation becomes the domain of the result.
1869 A (piecewise) quasipolynomial reduction can be copied or freed using the
1870 following functions.
1872 __isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_copy(
1873 __isl_keep isl_qpolynomial_fold *fold);
1874 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_copy(
1875 __isl_keep isl_pw_qpolynomial_fold *pwf);
1876 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_copy(
1877 __isl_keep isl_union_pw_qpolynomial_fold *upwf);
1878 void isl_qpolynomial_fold_free(
1879 __isl_take isl_qpolynomial_fold *fold);
1880 void isl_pw_qpolynomial_fold_free(
1881 __isl_take isl_pw_qpolynomial_fold *pwf);
1882 void isl_union_pw_qpolynomial_fold_free(
1883 __isl_take isl_union_pw_qpolynomial_fold *upwf);
1885 =head3 Printing Piecewise Quasipolynomial Reductions
1887 Piecewise quasipolynomial reductions can be printed
1888 using the following function.
1890 __isl_give isl_printer *isl_printer_print_pw_qpolynomial_fold(
1891 __isl_take isl_printer *p,
1892 __isl_keep isl_pw_qpolynomial_fold *pwf);
1893 __isl_give isl_printer *isl_printer_print_union_pw_qpolynomial_fold(
1894 __isl_take isl_printer *p,
1895 __isl_keep isl_union_pw_qpolynomial_fold *upwf);
1897 For C<isl_printer_print_pw_qpolynomial_fold>,
1898 output format of the printer
1899 needs to be set to either C<ISL_FORMAT_ISL> or C<ISL_FORMAT_C>.
1900 For C<isl_printer_print_union_pw_qpolynomial_fold>,
1901 output format of the printer
1902 needs to be set to either C<ISL_FORMAT_ISL>.
1904 =head3 Inspecting (Piecewise) Quasipolynomial Reductions
1906 To iterate over all piecewise quasipolynomial reductions in a union
1907 piecewise quasipolynomial reduction, use the following function
1909 int isl_union_pw_qpolynomial_fold_foreach_pw_qpolynomial_fold(
1910 __isl_keep isl_union_pw_qpolynomial_fold *upwf,
1911 int (*fn)(__isl_take isl_pw_qpolynomial_fold *pwf,
1912 void *user), void *user);
1914 To iterate over the cells in a piecewise quasipolynomial reduction,
1915 use either of the following two functions
1917 int isl_pw_qpolynomial_fold_foreach_piece(
1918 __isl_keep isl_pw_qpolynomial_fold *pwf,
1919 int (*fn)(__isl_take isl_set *set,
1920 __isl_take isl_qpolynomial_fold *fold,
1921 void *user), void *user);
1922 int isl_pw_qpolynomial_fold_foreach_lifted_piece(
1923 __isl_keep isl_pw_qpolynomial_fold *pwf,
1924 int (*fn)(__isl_take isl_set *set,
1925 __isl_take isl_qpolynomial_fold *fold,
1926 void *user), void *user);
1928 See L<Inspecting (Piecewise) Quasipolynomials> for an explanation
1929 of the difference between these two functions.
1931 To iterate over all quasipolynomials in a reduction, use
1933 int isl_qpolynomial_fold_foreach_qpolynomial(
1934 __isl_keep isl_qpolynomial_fold *fold,
1935 int (*fn)(__isl_take isl_qpolynomial *qp,
1936 void *user), void *user);
1938 =head3 Operations on Piecewise Quasipolynomial Reductions
1940 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_fold(
1941 __isl_take isl_pw_qpolynomial_fold *pwf1,
1942 __isl_take isl_pw_qpolynomial_fold *pwf2);
1944 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_fold(
1945 __isl_take isl_union_pw_qpolynomial_fold *upwf1,
1946 __isl_take isl_union_pw_qpolynomial_fold *upwf2);
1948 __isl_give isl_qpolynomial *isl_pw_qpolynomial_fold_eval(
1949 __isl_take isl_pw_qpolynomial_fold *pwf,
1950 __isl_take isl_point *pnt);
1952 __isl_give isl_qpolynomial *isl_union_pw_qpolynomial_fold_eval(
1953 __isl_take isl_union_pw_qpolynomial_fold *upwf,
1954 __isl_take isl_point *pnt);
1956 __isl_give isl_union_set *isl_union_pw_qpolynomial_fold_domain(
1957 __isl_take isl_union_pw_qpolynomial_fold *upwf);
1958 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_intersect_domain(
1959 __isl_take isl_union_pw_qpolynomial_fold *upwf,
1960 __isl_take isl_union_set *uset);
1962 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_coalesce(
1963 __isl_take isl_pw_qpolynomial_fold *pwf);
1965 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_coalesce(
1966 __isl_take isl_union_pw_qpolynomial_fold *upwf);
1968 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_gist(
1969 __isl_take isl_pw_qpolynomial_fold *pwf,
1970 __isl_take isl_set *context);
1972 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_gist(
1973 __isl_take isl_union_pw_qpolynomial_fold *upwf,
1974 __isl_take isl_union_set *context);
1976 The gist operation applies the gist operation to each of
1977 the cells in the domain of the input piecewise quasipolynomial reduction.
1978 In future, the operation will also exploit the context
1979 to simplify the quasipolynomial reductions associated to each cell.
1981 __isl_give isl_pw_qpolynomial_fold *
1982 isl_map_apply_pw_qpolynomial_fold(
1983 __isl_take isl_map *map,
1984 __isl_take isl_pw_qpolynomial_fold *pwf,
1986 __isl_give isl_union_pw_qpolynomial_fold *
1987 isl_union_map_apply_union_pw_qpolynomial_fold(
1988 __isl_take isl_union_map *umap,
1989 __isl_take isl_union_pw_qpolynomial_fold *upwf,
1993 compose the given map with the given piecewise quasipolynomial reduction.
1994 That is, compute a bound (of the same type as C<pwf> or C<upwf> itself)
1995 over all elements in the intersection of the range of the map
1996 and the domain of the piecewise quasipolynomial reduction
1997 as a function of an element in the domain of the map.
1999 =head2 Dependence Analysis
2001 C<isl> contains specialized functionality for performing
2002 array dataflow analysis. That is, given a I<sink> access relation
2003 and a collection of possible I<source> access relations,
2004 C<isl> can compute relations that describe
2005 for each iteration of the sink access, which iteration
2006 of which of the source access relations was the last
2007 to access the same data element before the given iteration
2009 To compute standard flow dependences, the sink should be
2010 a read, while the sources should be writes.
2011 If any of the source accesses are marked as being I<may>
2012 accesses, then there will be a dependence to the last
2013 I<must> access B<and> to any I<may> access that follows
2014 this last I<must> access.
2015 In particular, if I<all> sources are I<may> accesses,
2016 then memory based dependence analysis is performed.
2017 If, on the other hand, all sources are I<must> accesses,
2018 then value based dependence analysis is performed.
2020 #include <isl_flow.h>
2022 __isl_give isl_access_info *isl_access_info_alloc(
2023 __isl_take isl_map *sink,
2024 void *sink_user, isl_access_level_before fn,
2026 __isl_give isl_access_info *isl_access_info_add_source(
2027 __isl_take isl_access_info *acc,
2028 __isl_take isl_map *source, int must,
2031 __isl_give isl_flow *isl_access_info_compute_flow(
2032 __isl_take isl_access_info *acc);
2034 int isl_flow_foreach(__isl_keep isl_flow *deps,
2035 int (*fn)(__isl_take isl_map *dep, int must,
2036 void *dep_user, void *user),
2038 __isl_give isl_set *isl_flow_get_no_source(
2039 __isl_keep isl_flow *deps, int must);
2040 void isl_flow_free(__isl_take isl_flow *deps);
2042 The function C<isl_access_info_compute_flow> performs the actual
2043 dependence analysis. The other functions are used to construct
2044 the input for this function or to read off the output.
2046 The input is collected in an C<isl_access_info>, which can
2047 be created through a call to C<isl_access_info_alloc>.
2048 The arguments to this functions are the sink access relation
2049 C<sink>, a token C<sink_user> used to identify the sink
2050 access to the user, a callback function for specifying the
2051 relative order of source and sink accesses, and the number
2052 of source access relations that will be added.
2053 The callback function has type C<int (*)(void *first, void *second)>.
2054 The function is called with two user supplied tokens identifying
2055 either a source or the sink and it should return the shared nesting
2056 level and the relative order of the two accesses.
2057 In particular, let I<n> be the number of loops shared by
2058 the two accesses. If C<first> precedes C<second> textually,
2059 then the function should return I<2 * n + 1>; otherwise,
2060 it should return I<2 * n>.
2061 The sources can be added to the C<isl_access_info> by performing
2062 (at most) C<max_source> calls to C<isl_access_info_add_source>.
2063 C<must> indicates whether the source is a I<must> access
2064 or a I<may> access. Note that a multi-valued access relation
2065 should only be marked I<must> if every iteration in the domain
2066 of the relation accesses I<all> elements in its image.
2067 The C<source_user> token is again used to identify
2068 the source access. The range of the source access relation
2069 C<source> should have the same dimension as the range
2070 of the sink access relation.
2072 The result of the dependence analysis is collected in an
2073 C<isl_flow>. There may be elements in the domain of
2074 the sink access for which no preceding source access could be
2075 found or for which all preceding sources are I<may> accesses.
2076 The sets of these elements can be obtained through
2077 calls to C<isl_flow_get_no_source>, the first with C<must> set
2078 and the second with C<must> unset.
2079 In the case of standard flow dependence analysis,
2080 with the sink a read and the sources I<must> writes,
2081 the first set corresponds to the reads from uninitialized
2082 array elements and the second set is empty.
2083 The actual flow dependences can be extracted using
2084 C<isl_flow_foreach>. This function will call the user-specified
2085 callback function C<fn> for each B<non-empty> dependence between
2086 a source and the sink. The callback function is called
2087 with four arguments, the actual flow dependence relation
2088 mapping source iterations to sink iterations, a boolean that
2089 indicates whether it is a I<must> or I<may> dependence, a token
2090 identifying the source and an additional C<void *> with value
2091 equal to the third argument of the C<isl_flow_foreach> call.
2092 A dependence is marked I<must> if it originates from a I<must>
2093 source and if it is not followed by any I<may> sources.
2095 After finishing with an C<isl_flow>, the user should call
2096 C<isl_flow_free> to free all associated memory.
2098 =head2 Parametric Vertex Enumeration
2100 The parametric vertex enumeration described in this section
2101 is mainly intended to be used internally and by the C<barvinok>
2104 #include <isl_vertices.h>
2105 __isl_give isl_vertices *isl_basic_set_compute_vertices(
2106 __isl_keep isl_basic_set *bset);
2108 The function C<isl_basic_set_compute_vertices> performs the
2109 actual computation of the parametric vertices and the chamber
2110 decomposition and store the result in an C<isl_vertices> object.
2111 This information can be queried by either iterating over all
2112 the vertices or iterating over all the chambers or cells
2113 and then iterating over all vertices that are active on the chamber.
2115 int isl_vertices_foreach_vertex(
2116 __isl_keep isl_vertices *vertices,
2117 int (*fn)(__isl_take isl_vertex *vertex, void *user),
2120 int isl_vertices_foreach_cell(
2121 __isl_keep isl_vertices *vertices,
2122 int (*fn)(__isl_take isl_cell *cell, void *user),
2124 int isl_cell_foreach_vertex(__isl_keep isl_cell *cell,
2125 int (*fn)(__isl_take isl_vertex *vertex, void *user),
2128 Other operations that can be performed on an C<isl_vertices> object are
2131 isl_ctx *isl_vertices_get_ctx(
2132 __isl_keep isl_vertices *vertices);
2133 int isl_vertices_get_n_vertices(
2134 __isl_keep isl_vertices *vertices);
2135 void isl_vertices_free(__isl_take isl_vertices *vertices);
2137 Vertices can be inspected and destroyed using the following functions.
2139 isl_ctx *isl_vertex_get_ctx(__isl_keep isl_vertex *vertex);
2140 int isl_vertex_get_id(__isl_keep isl_vertex *vertex);
2141 __isl_give isl_basic_set *isl_vertex_get_domain(
2142 __isl_keep isl_vertex *vertex);
2143 __isl_give isl_basic_set *isl_vertex_get_expr(
2144 __isl_keep isl_vertex *vertex);
2145 void isl_vertex_free(__isl_take isl_vertex *vertex);
2147 C<isl_vertex_get_expr> returns a singleton parametric set describing
2148 the vertex, while C<isl_vertex_get_domain> returns the activity domain
2150 Note that C<isl_vertex_get_domain> and C<isl_vertex_get_expr> return
2151 B<rational> basic sets, so they should mainly be used for inspection
2152 and should not be mixed with integer sets.
2154 Chambers can be inspected and destroyed using the following functions.
2156 isl_ctx *isl_cell_get_ctx(__isl_keep isl_cell *cell);
2157 __isl_give isl_basic_set *isl_cell_get_domain(
2158 __isl_keep isl_cell *cell);
2159 void isl_cell_free(__isl_take isl_cell *cell);
2163 Although C<isl> is mainly meant to be used as a library,
2164 it also contains some basic applications that use some
2165 of the functionality of C<isl>.
2166 The input may be specified in either the L<isl format>
2167 or the L<PolyLib format>.
2169 =head2 C<isl_polyhedron_sample>
2171 C<isl_polyhedron_sample> takes a polyhedron as input and prints
2172 an integer element of the polyhedron, if there is any.
2173 The first column in the output is the denominator and is always
2174 equal to 1. If the polyhedron contains no integer points,
2175 then a vector of length zero is printed.
2179 C<isl_pip> takes the same input as the C<example> program
2180 from the C<piplib> distribution, i.e., a set of constraints
2181 on the parameters, a line containing only -1 and finally a set
2182 of constraints on a parametric polyhedron.
2183 The coefficients of the parameters appear in the last columns
2184 (but before the final constant column).
2185 The output is the lexicographic minimum of the parametric polyhedron.
2186 As C<isl> currently does not have its own output format, the output
2187 is just a dump of the internal state.
2189 =head2 C<isl_polyhedron_minimize>
2191 C<isl_polyhedron_minimize> computes the minimum of some linear
2192 or affine objective function over the integer points in a polyhedron.
2193 If an affine objective function
2194 is given, then the constant should appear in the last column.
2196 =head2 C<isl_polytope_scan>
2198 Given a polytope, C<isl_polytope_scan> prints
2199 all integer points in the polytope.
2201 =head1 C<isl-polylib>
2203 The C<isl-polylib> library provides the following functions for converting
2204 between C<isl> objects and C<PolyLib> objects.
2205 The library is distributed separately for licensing reasons.
2207 #include <isl_set_polylib.h>
2208 __isl_give isl_basic_set *isl_basic_set_new_from_polylib(
2209 Polyhedron *P, __isl_take isl_dim *dim);
2210 Polyhedron *isl_basic_set_to_polylib(
2211 __isl_keep isl_basic_set *bset);
2212 __isl_give isl_set *isl_set_new_from_polylib(Polyhedron *D,
2213 __isl_take isl_dim *dim);
2214 Polyhedron *isl_set_to_polylib(__isl_keep isl_set *set);
2216 #include <isl_map_polylib.h>
2217 __isl_give isl_basic_map *isl_basic_map_new_from_polylib(
2218 Polyhedron *P, __isl_take isl_dim *dim);
2219 __isl_give isl_map *isl_map_new_from_polylib(Polyhedron *D,
2220 __isl_take isl_dim *dim);
2221 Polyhedron *isl_basic_map_to_polylib(
2222 __isl_keep isl_basic_map *bmap);
2223 Polyhedron *isl_map_to_polylib(__isl_keep isl_map *map);