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>.
49 =head3 Changes since isl-0.04
53 =item * All header files have been renamed from C<isl_header.h>
58 =head3 Changes since isl-0.05
62 =item * The functions C<isl_printer_print_basic_set> and
63 C<isl_printer_print_basic_map> no longer print a newline.
65 =item * The functions C<isl_flow_get_no_source>
66 and C<isl_union_map_compute_flow> now return
67 the accesses for which no source could be found instead of
68 the iterations where those accesses occur.
70 =item * The functions C<isl_basic_map_identity> and
71 C<isl_map_identity> now take the dimension specification
72 of a B<map> as input. An old call
73 C<isl_map_identity(dim)> can be rewritten to
74 C<isl_map_identity(isl_dim_map_from_set(dim))>.
76 =item * The function C<isl_map_power> no longer takes
77 a parameter position as input. Instead, the exponent
78 is now expressed as the domain of the resulting relation.
84 The source of C<isl> can be obtained either as a tarball
85 or from the git repository. Both are available from
86 L<http://freshmeat.net/projects/isl/>.
87 The installation process depends on how you obtained
90 =head2 Installation from the git repository
94 =item 1 Clone or update the repository
96 The first time the source is obtained, you need to clone
99 git clone git://repo.or.cz/isl.git
101 To obtain updates, you need to pull in the latest changes
105 =item 2 Generate C<configure>
111 After performing the above steps, continue
112 with the L<Common installation instructions>.
114 =head2 Common installation instructions
118 =item 1 Obtain C<GMP>
120 Building C<isl> requires C<GMP>, including its headers files.
121 Your distribution may not provide these header files by default
122 and you may need to install a package called C<gmp-devel> or something
123 similar. Alternatively, C<GMP> can be built from
124 source, available from L<http://gmplib.org/>.
128 C<isl> uses the standard C<autoconf> C<configure> script.
133 optionally followed by some configure options.
134 A complete list of options can be obtained by running
138 Below we discuss some of the more common options.
140 C<isl> can optionally use C<piplib>, but no
141 C<piplib> functionality is currently used by default.
142 The C<--with-piplib> option can
143 be used to specify which C<piplib>
144 library to use, either an installed version (C<system>),
145 an externally built version (C<build>)
146 or no version (C<no>). The option C<build> is mostly useful
147 in C<configure> scripts of larger projects that bundle both C<isl>
154 Installation prefix for C<isl>
156 =item C<--with-gmp-prefix>
158 Installation prefix for C<GMP> (architecture-independent files).
160 =item C<--with-gmp-exec-prefix>
162 Installation prefix for C<GMP> (architecture-dependent files).
164 =item C<--with-piplib>
166 Which copy of C<piplib> to use, either C<no> (default), C<system> or C<build>.
168 =item C<--with-piplib-prefix>
170 Installation prefix for C<system> C<piplib> (architecture-independent files).
172 =item C<--with-piplib-exec-prefix>
174 Installation prefix for C<system> C<piplib> (architecture-dependent files).
176 =item C<--with-piplib-builddir>
178 Location where C<build> C<piplib> was built.
186 =item 4 Install (optional)
194 =head2 Initialization
196 All manipulations of integer sets and relations occur within
197 the context of an C<isl_ctx>.
198 A given C<isl_ctx> can only be used within a single thread.
199 All arguments of a function are required to have been allocated
200 within the same context.
201 There are currently no functions available for moving an object
202 from one C<isl_ctx> to another C<isl_ctx>. This means that
203 there is currently no way of safely moving an object from one
204 thread to another, unless the whole C<isl_ctx> is moved.
206 An C<isl_ctx> can be allocated using C<isl_ctx_alloc> and
207 freed using C<isl_ctx_free>.
208 All objects allocated within an C<isl_ctx> should be freed
209 before the C<isl_ctx> itself is freed.
211 isl_ctx *isl_ctx_alloc();
212 void isl_ctx_free(isl_ctx *ctx);
216 All operations on integers, mainly the coefficients
217 of the constraints describing the sets and relations,
218 are performed in exact integer arithmetic using C<GMP>.
219 However, to allow future versions of C<isl> to optionally
220 support fixed integer arithmetic, all calls to C<GMP>
221 are wrapped inside C<isl> specific macros.
222 The basic type is C<isl_int> and the operations below
223 are available on this type.
224 The meanings of these operations are essentially the same
225 as their C<GMP> C<mpz_> counterparts.
226 As always with C<GMP> types, C<isl_int>s need to be
227 initialized with C<isl_int_init> before they can be used
228 and they need to be released with C<isl_int_clear>
230 The user should not assume that an C<isl_int> is represented
231 as a C<mpz_t>, but should instead explicitly convert between
232 C<mpz_t>s and C<isl_int>s using C<isl_int_set_gmp> and
233 C<isl_int_get_gmp> whenever a C<mpz_t> is required.
237 =item isl_int_init(i)
239 =item isl_int_clear(i)
241 =item isl_int_set(r,i)
243 =item isl_int_set_si(r,i)
245 =item isl_int_set_gmp(r,g)
247 =item isl_int_get_gmp(i,g)
249 =item isl_int_abs(r,i)
251 =item isl_int_neg(r,i)
253 =item isl_int_swap(i,j)
255 =item isl_int_swap_or_set(i,j)
257 =item isl_int_add_ui(r,i,j)
259 =item isl_int_sub_ui(r,i,j)
261 =item isl_int_add(r,i,j)
263 =item isl_int_sub(r,i,j)
265 =item isl_int_mul(r,i,j)
267 =item isl_int_mul_ui(r,i,j)
269 =item isl_int_addmul(r,i,j)
271 =item isl_int_submul(r,i,j)
273 =item isl_int_gcd(r,i,j)
275 =item isl_int_lcm(r,i,j)
277 =item isl_int_divexact(r,i,j)
279 =item isl_int_cdiv_q(r,i,j)
281 =item isl_int_fdiv_q(r,i,j)
283 =item isl_int_fdiv_r(r,i,j)
285 =item isl_int_fdiv_q_ui(r,i,j)
287 =item isl_int_read(r,s)
289 =item isl_int_print(out,i,width)
293 =item isl_int_cmp(i,j)
295 =item isl_int_cmp_si(i,si)
297 =item isl_int_eq(i,j)
299 =item isl_int_ne(i,j)
301 =item isl_int_lt(i,j)
303 =item isl_int_le(i,j)
305 =item isl_int_gt(i,j)
307 =item isl_int_ge(i,j)
309 =item isl_int_abs_eq(i,j)
311 =item isl_int_abs_ne(i,j)
313 =item isl_int_abs_lt(i,j)
315 =item isl_int_abs_gt(i,j)
317 =item isl_int_abs_ge(i,j)
319 =item isl_int_is_zero(i)
321 =item isl_int_is_one(i)
323 =item isl_int_is_negone(i)
325 =item isl_int_is_pos(i)
327 =item isl_int_is_neg(i)
329 =item isl_int_is_nonpos(i)
331 =item isl_int_is_nonneg(i)
333 =item isl_int_is_divisible_by(i,j)
337 =head2 Sets and Relations
339 C<isl> uses six types of objects for representing sets and relations,
340 C<isl_basic_set>, C<isl_basic_map>, C<isl_set>, C<isl_map>,
341 C<isl_union_set> and C<isl_union_map>.
342 C<isl_basic_set> and C<isl_basic_map> represent sets and relations that
343 can be described as a conjunction of affine constraints, while
344 C<isl_set> and C<isl_map> represent unions of
345 C<isl_basic_set>s and C<isl_basic_map>s, respectively.
346 However, all C<isl_basic_set>s or C<isl_basic_map>s in the union need
347 to have the same dimension. C<isl_union_set>s and C<isl_union_map>s
348 represent unions of C<isl_set>s or C<isl_map>s of I<different> dimensions,
349 where dimensions with different space names
350 (see L<Dimension Specifications>) are considered different as well.
351 The difference between sets and relations (maps) is that sets have
352 one set of variables, while relations have two sets of variables,
353 input variables and output variables.
355 =head2 Memory Management
357 Since a high-level operation on sets and/or relations usually involves
358 several substeps and since the user is usually not interested in
359 the intermediate results, most functions that return a new object
360 will also release all the objects passed as arguments.
361 If the user still wants to use one or more of these arguments
362 after the function call, she should pass along a copy of the
363 object rather than the object itself.
364 The user is then responsible for making sure that the original
365 object gets used somewhere else or is explicitly freed.
367 The arguments and return values of all documents functions are
368 annotated to make clear which arguments are released and which
369 arguments are preserved. In particular, the following annotations
376 C<__isl_give> means that a new object is returned.
377 The user should make sure that the returned pointer is
378 used exactly once as a value for an C<__isl_take> argument.
379 In between, it can be used as a value for as many
380 C<__isl_keep> arguments as the user likes.
381 There is one exception, and that is the case where the
382 pointer returned is C<NULL>. Is this case, the user
383 is free to use it as an C<__isl_take> argument or not.
387 C<__isl_take> means that the object the argument points to
388 is taken over by the function and may no longer be used
389 by the user as an argument to any other function.
390 The pointer value must be one returned by a function
391 returning an C<__isl_give> pointer.
392 If the user passes in a C<NULL> value, then this will
393 be treated as an error in the sense that the function will
394 not perform its usual operation. However, it will still
395 make sure that all the the other C<__isl_take> arguments
400 C<__isl_keep> means that the function will only use the object
401 temporarily. After the function has finished, the user
402 can still use it as an argument to other functions.
403 A C<NULL> value will be treated in the same way as
404 a C<NULL> value for an C<__isl_take> argument.
408 =head2 Dimension Specifications
410 Whenever a new set or relation is created from scratch,
411 its dimension needs to be specified using an C<isl_dim>.
414 __isl_give isl_dim *isl_dim_alloc(isl_ctx *ctx,
415 unsigned nparam, unsigned n_in, unsigned n_out);
416 __isl_give isl_dim *isl_dim_set_alloc(isl_ctx *ctx,
417 unsigned nparam, unsigned dim);
418 __isl_give isl_dim *isl_dim_copy(__isl_keep isl_dim *dim);
419 void isl_dim_free(__isl_take isl_dim *dim);
420 unsigned isl_dim_size(__isl_keep isl_dim *dim,
421 enum isl_dim_type type);
423 The dimension specification used for creating a set
424 needs to be created using C<isl_dim_set_alloc>, while
425 that for creating a relation
426 needs to be created using C<isl_dim_alloc>.
427 C<isl_dim_size> can be used
428 to find out the number of dimensions of each type in
429 a dimension specification, where type may be
430 C<isl_dim_param>, C<isl_dim_in> (only for relations),
431 C<isl_dim_out> (only for relations), C<isl_dim_set>
432 (only for sets) or C<isl_dim_all>.
434 It is often useful to create objects that live in the
435 same space as some other object. This can be accomplished
436 by creating the new objects
437 (see L<Creating New Sets and Relations> or
438 L<Creating New (Piecewise) Quasipolynomials>) based on the dimension
439 specification of the original object.
442 __isl_give isl_dim *isl_basic_set_get_dim(
443 __isl_keep isl_basic_set *bset);
444 __isl_give isl_dim *isl_set_get_dim(__isl_keep isl_set *set);
446 #include <isl/union_set.h>
447 __isl_give isl_dim *isl_union_set_get_dim(
448 __isl_keep isl_union_set *uset);
451 __isl_give isl_dim *isl_basic_map_get_dim(
452 __isl_keep isl_basic_map *bmap);
453 __isl_give isl_dim *isl_map_get_dim(__isl_keep isl_map *map);
455 #include <isl/union_map.h>
456 __isl_give isl_dim *isl_union_map_get_dim(
457 __isl_keep isl_union_map *umap);
459 #include <isl/constraint.h>
460 __isl_give isl_dim *isl_constraint_get_dim(
461 __isl_keep isl_constraint *constraint);
463 #include <isl/polynomial.h>
464 __isl_give isl_dim *isl_qpolynomial_get_dim(
465 __isl_keep isl_qpolynomial *qp);
466 __isl_give isl_dim *isl_pw_qpolynomial_get_dim(
467 __isl_keep isl_pw_qpolynomial *pwqp);
468 __isl_give isl_dim *isl_union_pw_qpolynomial_get_dim(
469 __isl_keep isl_union_pw_qpolynomial *upwqp);
470 __isl_give isl_dim *isl_union_pw_qpolynomial_fold_get_dim(
471 __isl_keep isl_union_pw_qpolynomial_fold *upwf);
473 The names of the individual dimensions may be set or read off
474 using the following functions.
477 __isl_give isl_dim *isl_dim_set_name(__isl_take isl_dim *dim,
478 enum isl_dim_type type, unsigned pos,
479 __isl_keep const char *name);
480 __isl_keep const char *isl_dim_get_name(__isl_keep isl_dim *dim,
481 enum isl_dim_type type, unsigned pos);
483 Note that C<isl_dim_get_name> returns a pointer to some internal
484 data structure, so the result can only be used while the
485 corresponding C<isl_dim> is alive.
486 Also note that every function that operates on two sets or relations
487 requires that both arguments have the same parameters. This also
488 means that if one of the arguments has named parameters, then the
489 other needs to have named parameters too and the names need to match.
490 Pairs of C<isl_union_set> and/or C<isl_union_map> arguments may
491 have different parameters (as long as they are named), in which case
492 the result will have as parameters the union of the parameters of
495 The names of entire spaces may be set or read off
496 using the following functions.
499 __isl_give isl_dim *isl_dim_set_tuple_name(
500 __isl_take isl_dim *dim,
501 enum isl_dim_type type, const char *s);
502 const char *isl_dim_get_tuple_name(__isl_keep isl_dim *dim,
503 enum isl_dim_type type);
505 The C<dim> argument needs to be one of C<isl_dim_in>, C<isl_dim_out>
506 or C<isl_dim_set>. As with C<isl_dim_get_name>,
507 the C<isl_dim_get_tuple_name> function returns a pointer to some internal
509 Binary operations require the corresponding spaces of their arguments
510 to have the same name.
512 Spaces can be nested. In particular, the domain of a set or
513 the domain or range of a relation can be a nested relation.
514 The following functions can be used to construct and deconstruct
515 such nested dimension specifications.
518 int isl_dim_is_wrapping(__isl_keep isl_dim *dim);
519 __isl_give isl_dim *isl_dim_wrap(__isl_take isl_dim *dim);
520 __isl_give isl_dim *isl_dim_unwrap(__isl_take isl_dim *dim);
522 The input to C<isl_dim_is_wrapping> and C<isl_dim_unwrap> should
523 be the dimension specification of a set, while that of
524 C<isl_dim_wrap> should be the dimension specification of a relation.
525 Conversely, the output of C<isl_dim_unwrap> is the dimension specification
526 of a relation, while that of C<isl_dim_wrap> is the dimension specification
529 Dimension specifications can be created from other dimension
530 specifications using the following functions.
532 __isl_give isl_dim *isl_dim_domain(__isl_take isl_dim *dim);
533 __isl_give isl_dim *isl_dim_from_domain(__isl_take isl_dim *dim);
534 __isl_give isl_dim *isl_dim_range(__isl_take isl_dim *dim);
535 __isl_give isl_dim *isl_dim_from_range(__isl_take isl_dim *dim);
536 __isl_give isl_dim *isl_dim_reverse(__isl_take isl_dim *dim);
537 __isl_give isl_dim *isl_dim_join(__isl_take isl_dim *left,
538 __isl_take isl_dim *right);
539 __isl_give isl_dim *isl_dim_insert(__isl_take isl_dim *dim,
540 enum isl_dim_type type, unsigned pos, unsigned n);
541 __isl_give isl_dim *isl_dim_add(__isl_take isl_dim *dim,
542 enum isl_dim_type type, unsigned n);
543 __isl_give isl_dim *isl_dim_drop(__isl_take isl_dim *dim,
544 enum isl_dim_type type, unsigned first, unsigned n);
545 __isl_give isl_dim *isl_dim_map_from_set(
546 __isl_take isl_dim *dim);
547 __isl_give isl_dim *isl_dim_zip(__isl_take isl_dim *dim);
549 Note that if dimensions are added or removed from a space, then
550 the name and the internal structure are lost.
552 =head2 Input and Output
554 C<isl> supports its own input/output format, which is similar
555 to the C<Omega> format, but also supports the C<PolyLib> format
560 The C<isl> format is similar to that of C<Omega>, but has a different
561 syntax for describing the parameters and allows for the definition
562 of an existentially quantified variable as the integer division
563 of an affine expression.
564 For example, the set of integers C<i> between C<0> and C<n>
565 such that C<i % 10 <= 6> can be described as
567 [n] -> { [i] : exists (a = [i/10] : 0 <= i and i <= n and
570 A set or relation can have several disjuncts, separated
571 by the keyword C<or>. Each disjunct is either a conjunction
572 of constraints or a projection (C<exists>) of a conjunction
573 of constraints. The constraints are separated by the keyword
576 =head3 C<PolyLib> format
578 If the represented set is a union, then the first line
579 contains a single number representing the number of disjuncts.
580 Otherwise, a line containing the number C<1> is optional.
582 Each disjunct is represented by a matrix of constraints.
583 The first line contains two numbers representing
584 the number of rows and columns,
585 where the number of rows is equal to the number of constraints
586 and the number of columns is equal to two plus the number of variables.
587 The following lines contain the actual rows of the constraint matrix.
588 In each row, the first column indicates whether the constraint
589 is an equality (C<0>) or inequality (C<1>). The final column
590 corresponds to the constant term.
592 If the set is parametric, then the coefficients of the parameters
593 appear in the last columns before the constant column.
594 The coefficients of any existentially quantified variables appear
595 between those of the set variables and those of the parameters.
597 =head3 Extended C<PolyLib> format
599 The extended C<PolyLib> format is nearly identical to the
600 C<PolyLib> format. The only difference is that the line
601 containing the number of rows and columns of a constraint matrix
602 also contains four additional numbers:
603 the number of output dimensions, the number of input dimensions,
604 the number of local dimensions (i.e., the number of existentially
605 quantified variables) and the number of parameters.
606 For sets, the number of ``output'' dimensions is equal
607 to the number of set dimensions, while the number of ``input''
613 __isl_give isl_basic_set *isl_basic_set_read_from_file(
614 isl_ctx *ctx, FILE *input, int nparam);
615 __isl_give isl_basic_set *isl_basic_set_read_from_str(
616 isl_ctx *ctx, const char *str, int nparam);
617 __isl_give isl_set *isl_set_read_from_file(isl_ctx *ctx,
618 FILE *input, int nparam);
619 __isl_give isl_set *isl_set_read_from_str(isl_ctx *ctx,
620 const char *str, int nparam);
623 __isl_give isl_basic_map *isl_basic_map_read_from_file(
624 isl_ctx *ctx, FILE *input, int nparam);
625 __isl_give isl_basic_map *isl_basic_map_read_from_str(
626 isl_ctx *ctx, const char *str, int nparam);
627 __isl_give isl_map *isl_map_read_from_file(
628 struct isl_ctx *ctx, FILE *input, int nparam);
629 __isl_give isl_map *isl_map_read_from_str(isl_ctx *ctx,
630 const char *str, int nparam);
632 #include <isl/union_set.h>
633 __isl_give isl_union_set *isl_union_set_read_from_file(
634 isl_ctx *ctx, FILE *input);
635 __isl_give isl_union_set *isl_union_set_read_from_str(
636 struct isl_ctx *ctx, const char *str);
638 #include <isl/union_map.h>
639 __isl_give isl_union_map *isl_union_map_read_from_file(
640 isl_ctx *ctx, FILE *input);
641 __isl_give isl_union_map *isl_union_map_read_from_str(
642 struct isl_ctx *ctx, const char *str);
644 The input format is autodetected and may be either the C<PolyLib> format
645 or the C<isl> format.
646 C<nparam> specifies how many of the final columns in
647 the C<PolyLib> format correspond to parameters.
648 If input is given in the C<isl> format, then the number
649 of parameters needs to be equal to C<nparam>.
650 If C<nparam> is negative, then any number of parameters
651 is accepted in the C<isl> format and zero parameters
652 are assumed in the C<PolyLib> format.
656 Before anything can be printed, an C<isl_printer> needs to
659 __isl_give isl_printer *isl_printer_to_file(isl_ctx *ctx,
661 __isl_give isl_printer *isl_printer_to_str(isl_ctx *ctx);
662 void isl_printer_free(__isl_take isl_printer *printer);
663 __isl_give char *isl_printer_get_str(
664 __isl_keep isl_printer *printer);
666 The behavior of the printer can be modified in various ways
668 __isl_give isl_printer *isl_printer_set_output_format(
669 __isl_take isl_printer *p, int output_format);
670 __isl_give isl_printer *isl_printer_set_indent(
671 __isl_take isl_printer *p, int indent);
672 __isl_give isl_printer *isl_printer_set_prefix(
673 __isl_take isl_printer *p, const char *prefix);
674 __isl_give isl_printer *isl_printer_set_suffix(
675 __isl_take isl_printer *p, const char *suffix);
677 The C<output_format> may be either C<ISL_FORMAT_ISL>, C<ISL_FORMAT_OMEGA>,
678 C<ISL_FORMAT_POLYLIB>, C<ISL_FORMAT_EXT_POLYLIB> or C<ISL_FORMAT_LATEX>
679 and defaults to C<ISL_FORMAT_ISL>.
680 Each line in the output is indented by C<indent> spaces
681 (default: 0), prefixed by C<prefix> and suffixed by C<suffix>.
682 In the C<PolyLib> format output,
683 the coefficients of the existentially quantified variables
684 appear between those of the set variables and those
687 To actually print something, use
690 __isl_give isl_printer *isl_printer_print_basic_set(
691 __isl_take isl_printer *printer,
692 __isl_keep isl_basic_set *bset);
693 __isl_give isl_printer *isl_printer_print_set(
694 __isl_take isl_printer *printer,
695 __isl_keep isl_set *set);
698 __isl_give isl_printer *isl_printer_print_basic_map(
699 __isl_take isl_printer *printer,
700 __isl_keep isl_basic_map *bmap);
701 __isl_give isl_printer *isl_printer_print_map(
702 __isl_take isl_printer *printer,
703 __isl_keep isl_map *map);
705 #include <isl/union_set.h>
706 __isl_give isl_printer *isl_printer_print_union_set(
707 __isl_take isl_printer *p,
708 __isl_keep isl_union_set *uset);
710 #include <isl/union_map.h>
711 __isl_give isl_printer *isl_printer_print_union_map(
712 __isl_take isl_printer *p,
713 __isl_keep isl_union_map *umap);
715 When called on a file printer, the following function flushes
716 the file. When called on a string printer, the buffer is cleared.
718 __isl_give isl_printer *isl_printer_flush(
719 __isl_take isl_printer *p);
721 =head2 Creating New Sets and Relations
723 C<isl> has functions for creating some standard sets and relations.
727 =item * Empty sets and relations
729 __isl_give isl_basic_set *isl_basic_set_empty(
730 __isl_take isl_dim *dim);
731 __isl_give isl_basic_map *isl_basic_map_empty(
732 __isl_take isl_dim *dim);
733 __isl_give isl_set *isl_set_empty(
734 __isl_take isl_dim *dim);
735 __isl_give isl_map *isl_map_empty(
736 __isl_take isl_dim *dim);
737 __isl_give isl_union_set *isl_union_set_empty(
738 __isl_take isl_dim *dim);
739 __isl_give isl_union_map *isl_union_map_empty(
740 __isl_take isl_dim *dim);
742 For C<isl_union_set>s and C<isl_union_map>s, the dimensions specification
743 is only used to specify the parameters.
745 =item * Universe sets and relations
747 __isl_give isl_basic_set *isl_basic_set_universe(
748 __isl_take isl_dim *dim);
749 __isl_give isl_basic_map *isl_basic_map_universe(
750 __isl_take isl_dim *dim);
751 __isl_give isl_set *isl_set_universe(
752 __isl_take isl_dim *dim);
753 __isl_give isl_map *isl_map_universe(
754 __isl_take isl_dim *dim);
756 The sets and relations constructed by the functions above
757 contain all integer values, while those constructed by the
758 functions below only contain non-negative values.
760 __isl_give isl_basic_set *isl_basic_set_nat_universe(
761 __isl_take isl_dim *dim);
762 __isl_give isl_basic_map *isl_basic_map_nat_universe(
763 __isl_take isl_dim *dim);
764 __isl_give isl_set *isl_set_nat_universe(
765 __isl_take isl_dim *dim);
766 __isl_give isl_map *isl_map_nat_universe(
767 __isl_take isl_dim *dim);
769 =item * Identity relations
771 __isl_give isl_basic_map *isl_basic_map_identity(
772 __isl_take isl_dim *dim);
773 __isl_give isl_map *isl_map_identity(
774 __isl_take isl_dim *dim);
776 The number of input and output dimensions in C<dim> needs
779 =item * Lexicographic order
781 __isl_give isl_map *isl_map_lex_lt(
782 __isl_take isl_dim *set_dim);
783 __isl_give isl_map *isl_map_lex_le(
784 __isl_take isl_dim *set_dim);
785 __isl_give isl_map *isl_map_lex_gt(
786 __isl_take isl_dim *set_dim);
787 __isl_give isl_map *isl_map_lex_ge(
788 __isl_take isl_dim *set_dim);
789 __isl_give isl_map *isl_map_lex_lt_first(
790 __isl_take isl_dim *dim, unsigned n);
791 __isl_give isl_map *isl_map_lex_le_first(
792 __isl_take isl_dim *dim, unsigned n);
793 __isl_give isl_map *isl_map_lex_gt_first(
794 __isl_take isl_dim *dim, unsigned n);
795 __isl_give isl_map *isl_map_lex_ge_first(
796 __isl_take isl_dim *dim, unsigned n);
798 The first four functions take a dimension specification for a B<set>
799 and return relations that express that the elements in the domain
800 are lexicographically less
801 (C<isl_map_lex_lt>), less or equal (C<isl_map_lex_le>),
802 greater (C<isl_map_lex_gt>) or greater or equal (C<isl_map_lex_ge>)
803 than the elements in the range.
804 The last four functions take a dimension specification for a map
805 and return relations that express that the first C<n> dimensions
806 in the domain are lexicographically less
807 (C<isl_map_lex_lt_first>), less or equal (C<isl_map_lex_le_first>),
808 greater (C<isl_map_lex_gt_first>) or greater or equal (C<isl_map_lex_ge_first>)
809 than the first C<n> dimensions in the range.
813 A basic set or relation can be converted to a set or relation
814 using the following functions.
816 __isl_give isl_set *isl_set_from_basic_set(
817 __isl_take isl_basic_set *bset);
818 __isl_give isl_map *isl_map_from_basic_map(
819 __isl_take isl_basic_map *bmap);
821 Sets and relations can be converted to union sets and relations
822 using the following functions.
824 __isl_give isl_union_map *isl_union_map_from_map(
825 __isl_take isl_map *map);
826 __isl_give isl_union_set *isl_union_set_from_set(
827 __isl_take isl_set *set);
829 Sets and relations can be copied and freed again using the following
832 __isl_give isl_basic_set *isl_basic_set_copy(
833 __isl_keep isl_basic_set *bset);
834 __isl_give isl_set *isl_set_copy(__isl_keep isl_set *set);
835 __isl_give isl_union_set *isl_union_set_copy(
836 __isl_keep isl_union_set *uset);
837 __isl_give isl_basic_map *isl_basic_map_copy(
838 __isl_keep isl_basic_map *bmap);
839 __isl_give isl_map *isl_map_copy(__isl_keep isl_map *map);
840 __isl_give isl_union_map *isl_union_map_copy(
841 __isl_keep isl_union_map *umap);
842 void isl_basic_set_free(__isl_take isl_basic_set *bset);
843 void isl_set_free(__isl_take isl_set *set);
844 void isl_union_set_free(__isl_take isl_union_set *uset);
845 void isl_basic_map_free(__isl_take isl_basic_map *bmap);
846 void isl_map_free(__isl_take isl_map *map);
847 void isl_union_map_free(__isl_take isl_union_map *umap);
849 Other sets and relations can be constructed by starting
850 from a universe set or relation, adding equality and/or
851 inequality constraints and then projecting out the
852 existentially quantified variables, if any.
853 Constraints can be constructed, manipulated and
854 added to basic sets and relations using the following functions.
856 #include <isl/constraint.h>
857 __isl_give isl_constraint *isl_equality_alloc(
858 __isl_take isl_dim *dim);
859 __isl_give isl_constraint *isl_inequality_alloc(
860 __isl_take isl_dim *dim);
861 void isl_constraint_set_constant(
862 __isl_keep isl_constraint *constraint, isl_int v);
863 void isl_constraint_set_coefficient(
864 __isl_keep isl_constraint *constraint,
865 enum isl_dim_type type, int pos, isl_int v);
866 __isl_give isl_basic_map *isl_basic_map_add_constraint(
867 __isl_take isl_basic_map *bmap,
868 __isl_take isl_constraint *constraint);
869 __isl_give isl_basic_set *isl_basic_set_add_constraint(
870 __isl_take isl_basic_set *bset,
871 __isl_take isl_constraint *constraint);
873 For example, to create a set containing the even integers
874 between 10 and 42, you would use the following code.
878 struct isl_constraint *c;
879 struct isl_basic_set *bset;
882 dim = isl_dim_set_alloc(ctx, 0, 2);
883 bset = isl_basic_set_universe(isl_dim_copy(dim));
885 c = isl_equality_alloc(isl_dim_copy(dim));
886 isl_int_set_si(v, -1);
887 isl_constraint_set_coefficient(c, isl_dim_set, 0, v);
888 isl_int_set_si(v, 2);
889 isl_constraint_set_coefficient(c, isl_dim_set, 1, v);
890 bset = isl_basic_set_add_constraint(bset, c);
892 c = isl_inequality_alloc(isl_dim_copy(dim));
893 isl_int_set_si(v, -10);
894 isl_constraint_set_constant(c, v);
895 isl_int_set_si(v, 1);
896 isl_constraint_set_coefficient(c, isl_dim_set, 0, v);
897 bset = isl_basic_set_add_constraint(bset, c);
899 c = isl_inequality_alloc(dim);
900 isl_int_set_si(v, 42);
901 isl_constraint_set_constant(c, v);
902 isl_int_set_si(v, -1);
903 isl_constraint_set_coefficient(c, isl_dim_set, 0, v);
904 bset = isl_basic_set_add_constraint(bset, c);
906 bset = isl_basic_set_project_out(bset, isl_dim_set, 1, 1);
912 struct isl_basic_set *bset;
913 bset = isl_basic_set_read_from_str(ctx,
914 "{[i] : exists (a : i = 2a and i >= 10 and i <= 42)}", -1);
916 A basic set or relation can also be constructed from two matrices
917 describing the equalities and the inequalities.
919 __isl_give isl_basic_set *isl_basic_set_from_constraint_matrices(
920 __isl_take isl_dim *dim,
921 __isl_take isl_mat *eq, __isl_take isl_mat *ineq,
922 enum isl_dim_type c1,
923 enum isl_dim_type c2, enum isl_dim_type c3,
924 enum isl_dim_type c4);
925 __isl_give isl_basic_map *isl_basic_map_from_constraint_matrices(
926 __isl_take isl_dim *dim,
927 __isl_take isl_mat *eq, __isl_take isl_mat *ineq,
928 enum isl_dim_type c1,
929 enum isl_dim_type c2, enum isl_dim_type c3,
930 enum isl_dim_type c4, enum isl_dim_type c5);
932 The C<isl_dim_type> arguments indicate the order in which
933 different kinds of variables appear in the input matrices
934 and should be a permutation of C<isl_dim_cst>, C<isl_dim_param>,
935 C<isl_dim_set> and C<isl_dim_div> for sets and
936 of C<isl_dim_cst>, C<isl_dim_param>,
937 C<isl_dim_in>, C<isl_dim_out> and C<isl_dim_div> for relations.
939 =head2 Inspecting Sets and Relations
941 Usually, the user should not have to care about the actual constraints
942 of the sets and maps, but should instead apply the abstract operations
943 explained in the following sections.
944 Occasionally, however, it may be required to inspect the individual
945 coefficients of the constraints. This section explains how to do so.
946 In these cases, it may also be useful to have C<isl> compute
947 an explicit representation of the existentially quantified variables.
949 __isl_give isl_set *isl_set_compute_divs(
950 __isl_take isl_set *set);
951 __isl_give isl_map *isl_map_compute_divs(
952 __isl_take isl_map *map);
953 __isl_give isl_union_set *isl_union_set_compute_divs(
954 __isl_take isl_union_set *uset);
955 __isl_give isl_union_map *isl_union_map_compute_divs(
956 __isl_take isl_union_map *umap);
958 This explicit representation defines the existentially quantified
959 variables as integer divisions of the other variables, possibly
960 including earlier existentially quantified variables.
961 An explicitly represented existentially quantified variable therefore
962 has a unique value when the values of the other variables are known.
963 If, furthermore, the same existentials, i.e., existentials
964 with the same explicit representations, should appear in the
965 same order in each of the disjuncts of a set or map, then the user should call
966 either of the following functions.
968 __isl_give isl_set *isl_set_align_divs(
969 __isl_take isl_set *set);
970 __isl_give isl_map *isl_map_align_divs(
971 __isl_take isl_map *map);
973 Alternatively, the existentially quantified variables can be removed
974 using the following functions, which compute an overapproximation.
976 __isl_give isl_basic_set *isl_basic_set_remove_divs(
977 __isl_take isl_basic_set *bset);
978 __isl_give isl_basic_map *isl_basic_map_remove_divs(
979 __isl_take isl_basic_map *bmap);
980 __isl_give isl_set *isl_set_remove_divs(
981 __isl_take isl_set *set);
982 __isl_give isl_map *isl_map_remove_divs(
983 __isl_take isl_map *map);
985 To iterate over all the sets or maps in a union set or map, use
987 int isl_union_set_foreach_set(__isl_keep isl_union_set *uset,
988 int (*fn)(__isl_take isl_set *set, void *user),
990 int isl_union_map_foreach_map(__isl_keep isl_union_map *umap,
991 int (*fn)(__isl_take isl_map *map, void *user),
994 The number of sets or maps in a union set or map can be obtained
997 int isl_union_set_n_set(__isl_keep isl_union_set *uset);
998 int isl_union_map_n_map(__isl_keep isl_union_map *umap);
1000 To extract the set or map from a union with a given dimension
1003 __isl_give isl_set *isl_union_set_extract_set(
1004 __isl_keep isl_union_set *uset,
1005 __isl_take isl_dim *dim);
1006 __isl_give isl_map *isl_union_map_extract_map(
1007 __isl_keep isl_union_map *umap,
1008 __isl_take isl_dim *dim);
1010 To iterate over all the basic sets or maps in a set or map, use
1012 int isl_set_foreach_basic_set(__isl_keep isl_set *set,
1013 int (*fn)(__isl_take isl_basic_set *bset, void *user),
1015 int isl_map_foreach_basic_map(__isl_keep isl_map *map,
1016 int (*fn)(__isl_take isl_basic_map *bmap, void *user),
1019 The callback function C<fn> should return 0 if successful and
1020 -1 if an error occurs. In the latter case, or if any other error
1021 occurs, the above functions will return -1.
1023 It should be noted that C<isl> does not guarantee that
1024 the basic sets or maps passed to C<fn> are disjoint.
1025 If this is required, then the user should call one of
1026 the following functions first.
1028 __isl_give isl_set *isl_set_make_disjoint(
1029 __isl_take isl_set *set);
1030 __isl_give isl_map *isl_map_make_disjoint(
1031 __isl_take isl_map *map);
1033 The number of basic sets in a set can be obtained
1036 int isl_set_n_basic_set(__isl_keep isl_set *set);
1038 To iterate over the constraints of a basic set or map, use
1040 #include <isl/constraint.h>
1042 int isl_basic_map_foreach_constraint(
1043 __isl_keep isl_basic_map *bmap,
1044 int (*fn)(__isl_take isl_constraint *c, void *user),
1046 void isl_constraint_free(struct isl_constraint *c);
1048 Again, the callback function C<fn> should return 0 if successful and
1049 -1 if an error occurs. In the latter case, or if any other error
1050 occurs, the above functions will return -1.
1051 The constraint C<c> represents either an equality or an inequality.
1052 Use the following function to find out whether a constraint
1053 represents an equality. If not, it represents an inequality.
1055 int isl_constraint_is_equality(
1056 __isl_keep isl_constraint *constraint);
1058 The coefficients of the constraints can be inspected using
1059 the following functions.
1061 void isl_constraint_get_constant(
1062 __isl_keep isl_constraint *constraint, isl_int *v);
1063 void isl_constraint_get_coefficient(
1064 __isl_keep isl_constraint *constraint,
1065 enum isl_dim_type type, int pos, isl_int *v);
1067 The explicit representations of the existentially quantified
1068 variables can be inspected using the following functions.
1069 Note that the user is only allowed to use these functions
1070 if the inspected set or map is the result of a call
1071 to C<isl_set_compute_divs> or C<isl_map_compute_divs>.
1073 __isl_give isl_div *isl_constraint_div(
1074 __isl_keep isl_constraint *constraint, int pos);
1075 void isl_div_get_constant(__isl_keep isl_div *div,
1077 void isl_div_get_denominator(__isl_keep isl_div *div,
1079 void isl_div_get_coefficient(__isl_keep isl_div *div,
1080 enum isl_dim_type type, int pos, isl_int *v);
1082 To obtain the constraints of a basic set or map in matrix
1083 form, use the following functions.
1085 __isl_give isl_mat *isl_basic_set_equalities_matrix(
1086 __isl_keep isl_basic_set *bset,
1087 enum isl_dim_type c1, enum isl_dim_type c2,
1088 enum isl_dim_type c3, enum isl_dim_type c4);
1089 __isl_give isl_mat *isl_basic_set_inequalities_matrix(
1090 __isl_keep isl_basic_set *bset,
1091 enum isl_dim_type c1, enum isl_dim_type c2,
1092 enum isl_dim_type c3, enum isl_dim_type c4);
1093 __isl_give isl_mat *isl_basic_map_equalities_matrix(
1094 __isl_keep isl_basic_map *bmap,
1095 enum isl_dim_type c1,
1096 enum isl_dim_type c2, enum isl_dim_type c3,
1097 enum isl_dim_type c4, enum isl_dim_type c5);
1098 __isl_give isl_mat *isl_basic_map_inequalities_matrix(
1099 __isl_keep isl_basic_map *bmap,
1100 enum isl_dim_type c1,
1101 enum isl_dim_type c2, enum isl_dim_type c3,
1102 enum isl_dim_type c4, enum isl_dim_type c5);
1104 The C<isl_dim_type> arguments dictate the order in which
1105 different kinds of variables appear in the resulting matrix
1106 and should be a permutation of C<isl_dim_cst>, C<isl_dim_param>,
1107 C<isl_dim_in>, C<isl_dim_out> and C<isl_dim_div>.
1109 The names of the domain and range spaces of a set or relation can be
1110 read off using the following functions.
1112 const char *isl_basic_set_get_tuple_name(
1113 __isl_keep isl_basic_set *bset);
1114 const char *isl_set_get_tuple_name(
1115 __isl_keep isl_set *set);
1116 const char *isl_basic_map_get_tuple_name(
1117 __isl_keep isl_basic_map *bmap,
1118 enum isl_dim_type type);
1119 const char *isl_map_get_tuple_name(
1120 __isl_keep isl_map *map,
1121 enum isl_dim_type type);
1123 As with C<isl_dim_get_tuple_name>, the value returned points to
1124 an internal data structure.
1125 The names of individual dimensions can be read off using
1126 the following functions.
1128 const char *isl_constraint_get_dim_name(
1129 __isl_keep isl_constraint *constraint,
1130 enum isl_dim_type type, unsigned pos);
1131 const char *isl_basic_set_get_dim_name(
1132 __isl_keep isl_basic_set *bset,
1133 enum isl_dim_type type, unsigned pos);
1134 const char *isl_set_get_dim_name(
1135 __isl_keep isl_set *set,
1136 enum isl_dim_type type, unsigned pos);
1137 const char *isl_basic_map_get_dim_name(
1138 __isl_keep isl_basic_map *bmap,
1139 enum isl_dim_type type, unsigned pos);
1140 const char *isl_map_get_dim_name(
1141 __isl_keep isl_map *map,
1142 enum isl_dim_type type, unsigned pos);
1144 These functions are mostly useful to obtain the names
1149 =head3 Unary Properties
1155 The following functions test whether the given set or relation
1156 contains any integer points. The ``fast'' variants do not perform
1157 any computations, but simply check if the given set or relation
1158 is already known to be empty.
1160 int isl_basic_set_fast_is_empty(__isl_keep isl_basic_set *bset);
1161 int isl_basic_set_is_empty(__isl_keep isl_basic_set *bset);
1162 int isl_set_is_empty(__isl_keep isl_set *set);
1163 int isl_union_set_is_empty(__isl_keep isl_union_set *uset);
1164 int isl_basic_map_fast_is_empty(__isl_keep isl_basic_map *bmap);
1165 int isl_basic_map_is_empty(__isl_keep isl_basic_map *bmap);
1166 int isl_map_fast_is_empty(__isl_keep isl_map *map);
1167 int isl_map_is_empty(__isl_keep isl_map *map);
1168 int isl_union_map_is_empty(__isl_keep isl_union_map *umap);
1170 =item * Universality
1172 int isl_basic_set_is_universe(__isl_keep isl_basic_set *bset);
1173 int isl_basic_map_is_universe(__isl_keep isl_basic_map *bmap);
1174 int isl_set_fast_is_universe(__isl_keep isl_set *set);
1176 =item * Single-valuedness
1178 int isl_map_is_single_valued(__isl_keep isl_map *map);
1179 int isl_union_map_is_single_valued(__isl_keep isl_union_map *umap);
1183 int isl_map_is_injective(__isl_keep isl_map *map);
1184 int isl_union_map_is_injective(__isl_keep isl_union_map *umap);
1188 int isl_map_is_bijective(__isl_keep isl_map *map);
1189 int isl_union_map_is_bijective(__isl_keep isl_union_map *umap);
1193 The following functions check whether the domain of the given
1194 (basic) set is a wrapped relation.
1196 int isl_basic_set_is_wrapping(
1197 __isl_keep isl_basic_set *bset);
1198 int isl_set_is_wrapping(__isl_keep isl_set *set);
1200 =item * Internal Product
1202 int isl_basic_map_can_zip(
1203 __isl_keep isl_basic_map *bmap);
1204 int isl_map_can_zip(__isl_keep isl_map *map);
1206 Check whether the product of domain and range of the given relation
1208 i.e., whether both domain and range are nested relations.
1212 =head3 Binary Properties
1218 int isl_set_fast_is_equal(__isl_keep isl_set *set1,
1219 __isl_keep isl_set *set2);
1220 int isl_set_is_equal(__isl_keep isl_set *set1,
1221 __isl_keep isl_set *set2);
1222 int isl_union_set_is_equal(
1223 __isl_keep isl_union_set *uset1,
1224 __isl_keep isl_union_set *uset2);
1225 int isl_basic_map_is_equal(
1226 __isl_keep isl_basic_map *bmap1,
1227 __isl_keep isl_basic_map *bmap2);
1228 int isl_map_is_equal(__isl_keep isl_map *map1,
1229 __isl_keep isl_map *map2);
1230 int isl_map_fast_is_equal(__isl_keep isl_map *map1,
1231 __isl_keep isl_map *map2);
1232 int isl_union_map_is_equal(
1233 __isl_keep isl_union_map *umap1,
1234 __isl_keep isl_union_map *umap2);
1236 =item * Disjointness
1238 int isl_set_fast_is_disjoint(__isl_keep isl_set *set1,
1239 __isl_keep isl_set *set2);
1243 int isl_set_is_subset(__isl_keep isl_set *set1,
1244 __isl_keep isl_set *set2);
1245 int isl_set_is_strict_subset(
1246 __isl_keep isl_set *set1,
1247 __isl_keep isl_set *set2);
1248 int isl_union_set_is_subset(
1249 __isl_keep isl_union_set *uset1,
1250 __isl_keep isl_union_set *uset2);
1251 int isl_union_set_is_strict_subset(
1252 __isl_keep isl_union_set *uset1,
1253 __isl_keep isl_union_set *uset2);
1254 int isl_basic_map_is_subset(
1255 __isl_keep isl_basic_map *bmap1,
1256 __isl_keep isl_basic_map *bmap2);
1257 int isl_basic_map_is_strict_subset(
1258 __isl_keep isl_basic_map *bmap1,
1259 __isl_keep isl_basic_map *bmap2);
1260 int isl_map_is_subset(
1261 __isl_keep isl_map *map1,
1262 __isl_keep isl_map *map2);
1263 int isl_map_is_strict_subset(
1264 __isl_keep isl_map *map1,
1265 __isl_keep isl_map *map2);
1266 int isl_union_map_is_subset(
1267 __isl_keep isl_union_map *umap1,
1268 __isl_keep isl_union_map *umap2);
1269 int isl_union_map_is_strict_subset(
1270 __isl_keep isl_union_map *umap1,
1271 __isl_keep isl_union_map *umap2);
1275 =head2 Unary Operations
1281 __isl_give isl_set *isl_set_complement(
1282 __isl_take isl_set *set);
1286 __isl_give isl_basic_map *isl_basic_map_reverse(
1287 __isl_take isl_basic_map *bmap);
1288 __isl_give isl_map *isl_map_reverse(
1289 __isl_take isl_map *map);
1290 __isl_give isl_union_map *isl_union_map_reverse(
1291 __isl_take isl_union_map *umap);
1295 __isl_give isl_basic_set *isl_basic_set_project_out(
1296 __isl_take isl_basic_set *bset,
1297 enum isl_dim_type type, unsigned first, unsigned n);
1298 __isl_give isl_basic_map *isl_basic_map_project_out(
1299 __isl_take isl_basic_map *bmap,
1300 enum isl_dim_type type, unsigned first, unsigned n);
1301 __isl_give isl_set *isl_set_project_out(__isl_take isl_set *set,
1302 enum isl_dim_type type, unsigned first, unsigned n);
1303 __isl_give isl_map *isl_map_project_out(__isl_take isl_map *map,
1304 enum isl_dim_type type, unsigned first, unsigned n);
1305 __isl_give isl_basic_set *isl_basic_map_domain(
1306 __isl_take isl_basic_map *bmap);
1307 __isl_give isl_basic_set *isl_basic_map_range(
1308 __isl_take isl_basic_map *bmap);
1309 __isl_give isl_set *isl_map_domain(
1310 __isl_take isl_map *bmap);
1311 __isl_give isl_set *isl_map_range(
1312 __isl_take isl_map *map);
1313 __isl_give isl_union_set *isl_union_map_domain(
1314 __isl_take isl_union_map *umap);
1315 __isl_give isl_union_set *isl_union_map_range(
1316 __isl_take isl_union_map *umap);
1318 __isl_give isl_basic_map *isl_basic_map_domain_map(
1319 __isl_take isl_basic_map *bmap);
1320 __isl_give isl_basic_map *isl_basic_map_range_map(
1321 __isl_take isl_basic_map *bmap);
1322 __isl_give isl_map *isl_map_domain_map(__isl_take isl_map *map);
1323 __isl_give isl_map *isl_map_range_map(__isl_take isl_map *map);
1324 __isl_give isl_union_map *isl_union_map_domain_map(
1325 __isl_take isl_union_map *umap);
1326 __isl_give isl_union_map *isl_union_map_range_map(
1327 __isl_take isl_union_map *umap);
1329 The functions above construct a (basic, regular or union) relation
1330 that maps (a wrapped version of) the input relation to its domain or range.
1334 __isl_give isl_map *isl_set_identity(
1335 __isl_take isl_set *set);
1336 __isl_give isl_union_map *isl_union_set_identity(
1337 __isl_take isl_union_set *uset);
1339 Construct an identity relation on the given (union) set.
1343 __isl_give isl_basic_set *isl_basic_map_deltas(
1344 __isl_take isl_basic_map *bmap);
1345 __isl_give isl_set *isl_map_deltas(__isl_take isl_map *map);
1346 __isl_give isl_union_set *isl_union_map_deltas(
1347 __isl_take isl_union_map *umap);
1349 These functions return a (basic) set containing the differences
1350 between image elements and corresponding domain elements in the input.
1352 __isl_give isl_basic_map *isl_basic_map_deltas_map(
1353 __isl_take isl_basic_map *bmap);
1354 __isl_give isl_map *isl_map_deltas_map(
1355 __isl_take isl_map *map);
1356 __isl_give isl_union_map *isl_union_map_deltas_map(
1357 __isl_take isl_union_map *umap);
1359 The functions above construct a (basic, regular or union) relation
1360 that maps (a wrapped version of) the input relation to its delta set.
1364 Simplify the representation of a set or relation by trying
1365 to combine pairs of basic sets or relations into a single
1366 basic set or relation.
1368 __isl_give isl_set *isl_set_coalesce(__isl_take isl_set *set);
1369 __isl_give isl_map *isl_map_coalesce(__isl_take isl_map *map);
1370 __isl_give isl_union_set *isl_union_set_coalesce(
1371 __isl_take isl_union_set *uset);
1372 __isl_give isl_union_map *isl_union_map_coalesce(
1373 __isl_take isl_union_map *umap);
1375 =item * Detecting equalities
1377 __isl_give isl_basic_set *isl_basic_set_detect_equalities(
1378 __isl_take isl_basic_set *bset);
1379 __isl_give isl_basic_map *isl_basic_map_detect_equalities(
1380 __isl_take isl_basic_map *bmap);
1381 __isl_give isl_set *isl_set_detect_equalities(
1382 __isl_take isl_set *set);
1383 __isl_give isl_map *isl_map_detect_equalities(
1384 __isl_take isl_map *map);
1385 __isl_give isl_union_set *isl_union_set_detect_equalities(
1386 __isl_take isl_union_set *uset);
1387 __isl_give isl_union_map *isl_union_map_detect_equalities(
1388 __isl_take isl_union_map *umap);
1390 Simplify the representation of a set or relation by detecting implicit
1395 __isl_give isl_basic_set *isl_set_convex_hull(
1396 __isl_take isl_set *set);
1397 __isl_give isl_basic_map *isl_map_convex_hull(
1398 __isl_take isl_map *map);
1400 If the input set or relation has any existentially quantified
1401 variables, then the result of these operations is currently undefined.
1405 __isl_give isl_basic_set *isl_set_simple_hull(
1406 __isl_take isl_set *set);
1407 __isl_give isl_basic_map *isl_map_simple_hull(
1408 __isl_take isl_map *map);
1409 __isl_give isl_union_map *isl_union_map_simple_hull(
1410 __isl_take isl_union_map *umap);
1412 These functions compute a single basic set or relation
1413 that contains the whole input set or relation.
1414 In particular, the output is described by translates
1415 of the constraints describing the basic sets or relations in the input.
1419 (See \autoref{s:simple hull}.)
1425 __isl_give isl_basic_set *isl_basic_set_affine_hull(
1426 __isl_take isl_basic_set *bset);
1427 __isl_give isl_basic_set *isl_set_affine_hull(
1428 __isl_take isl_set *set);
1429 __isl_give isl_union_set *isl_union_set_affine_hull(
1430 __isl_take isl_union_set *uset);
1431 __isl_give isl_basic_map *isl_basic_map_affine_hull(
1432 __isl_take isl_basic_map *bmap);
1433 __isl_give isl_basic_map *isl_map_affine_hull(
1434 __isl_take isl_map *map);
1435 __isl_give isl_union_map *isl_union_map_affine_hull(
1436 __isl_take isl_union_map *umap);
1438 In case of union sets and relations, the affine hull is computed
1441 =item * Polyhedral hull
1443 __isl_give isl_basic_set *isl_set_polyhedral_hull(
1444 __isl_take isl_set *set);
1445 __isl_give isl_basic_map *isl_map_polyhedral_hull(
1446 __isl_take isl_map *map);
1447 __isl_give isl_union_set *isl_union_set_polyhedral_hull(
1448 __isl_take isl_union_set *uset);
1449 __isl_give isl_union_map *isl_union_map_polyhedral_hull(
1450 __isl_take isl_union_map *umap);
1452 These functions compute a single basic set or relation
1453 not involving any existentially quantified variables
1454 that contains the whole input set or relation.
1455 In case of union sets and relations, the polyhedral hull is computed
1460 The following functions compute either the set of (rational) coefficient
1461 values of valid constraints for the given set or the set of (rational)
1462 values satisfying the constraints with coefficients from the given set.
1463 Internally, these two sets of functions perform essentially the
1464 same operations, except that the set of coefficients is assumed to
1465 be a cone, while the set of values may be any polyhedron.
1466 The current implementation is based on the Farkas lemma and
1467 Fourier-Motzkin elimination, but this may change or be made optional
1468 in future. In particular, future implementations may use different
1469 dualization algorithms or skip the elimination step.
1471 __isl_give isl_basic_set *isl_basic_set_coefficients(
1472 __isl_take isl_basic_set *bset);
1473 __isl_give isl_basic_set *isl_set_coefficients(
1474 __isl_take isl_set *set);
1475 __isl_give isl_union_set *isl_union_set_coefficients(
1476 __isl_take isl_union_set *bset);
1477 __isl_give isl_basic_set *isl_basic_set_solutions(
1478 __isl_take isl_basic_set *bset);
1479 __isl_give isl_basic_set *isl_set_solutions(
1480 __isl_take isl_set *set);
1481 __isl_give isl_union_set *isl_union_set_solutions(
1482 __isl_take isl_union_set *bset);
1486 __isl_give isl_map *isl_map_power(__isl_take isl_map *map,
1488 __isl_give isl_union_map *isl_union_map_power(
1489 __isl_take isl_union_map *umap, int *exact);
1491 Compute a parametric representation for all positive powers I<k> of C<map>.
1492 The result maps I<k> to a nested relation corresponding to the
1493 I<k>th power of C<map>.
1494 The result may be an overapproximation. If the result is known to be exact,
1495 then C<*exact> is set to C<1>.
1497 =item * Transitive closure
1499 __isl_give isl_map *isl_map_transitive_closure(
1500 __isl_take isl_map *map, int *exact);
1501 __isl_give isl_union_map *isl_union_map_transitive_closure(
1502 __isl_take isl_union_map *umap, int *exact);
1504 Compute the transitive closure of C<map>.
1505 The result may be an overapproximation. If the result is known to be exact,
1506 then C<*exact> is set to C<1>.
1508 =item * Reaching path lengths
1510 __isl_give isl_map *isl_map_reaching_path_lengths(
1511 __isl_take isl_map *map, int *exact);
1513 Compute a relation that maps each element in the range of C<map>
1514 to the lengths of all paths composed of edges in C<map> that
1515 end up in the given element.
1516 The result may be an overapproximation. If the result is known to be exact,
1517 then C<*exact> is set to C<1>.
1518 To compute the I<maximal> path length, the resulting relation
1519 should be postprocessed by C<isl_map_lexmax>.
1520 In particular, if the input relation is a dependence relation
1521 (mapping sources to sinks), then the maximal path length corresponds
1522 to the free schedule.
1523 Note, however, that C<isl_map_lexmax> expects the maximum to be
1524 finite, so if the path lengths are unbounded (possibly due to
1525 the overapproximation), then you will get an error message.
1529 __isl_give isl_basic_set *isl_basic_map_wrap(
1530 __isl_take isl_basic_map *bmap);
1531 __isl_give isl_set *isl_map_wrap(
1532 __isl_take isl_map *map);
1533 __isl_give isl_union_set *isl_union_map_wrap(
1534 __isl_take isl_union_map *umap);
1535 __isl_give isl_basic_map *isl_basic_set_unwrap(
1536 __isl_take isl_basic_set *bset);
1537 __isl_give isl_map *isl_set_unwrap(
1538 __isl_take isl_set *set);
1539 __isl_give isl_union_map *isl_union_set_unwrap(
1540 __isl_take isl_union_set *uset);
1544 Remove any internal structure of domain (and range) of the given
1545 set or relation. If there is any such internal structure in the input,
1546 then the name of the space is also removed.
1548 __isl_give isl_basic_set *isl_basic_set_flatten(
1549 __isl_take isl_basic_set *bset);
1550 __isl_give isl_set *isl_set_flatten(
1551 __isl_take isl_set *set);
1552 __isl_give isl_basic_map *isl_basic_map_flatten(
1553 __isl_take isl_basic_map *bmap);
1554 __isl_give isl_map *isl_map_flatten(
1555 __isl_take isl_map *map);
1557 __isl_give isl_map *isl_set_flatten_map(
1558 __isl_take isl_set *set);
1560 The function above constructs a relation
1561 that maps the input set to a flattened version of the set.
1565 Lift the input set to a space with extra dimensions corresponding
1566 to the existentially quantified variables in the input.
1567 In particular, the result lives in a wrapped map where the domain
1568 is the original space and the range corresponds to the original
1569 existentially quantified variables.
1571 __isl_give isl_basic_set *isl_basic_set_lift(
1572 __isl_take isl_basic_set *bset);
1573 __isl_give isl_set *isl_set_lift(
1574 __isl_take isl_set *set);
1575 __isl_give isl_union_set *isl_union_set_lift(
1576 __isl_take isl_union_set *uset);
1578 =item * Internal Product
1580 __isl_give isl_basic_map *isl_basic_map_zip(
1581 __isl_take isl_basic_map *bmap);
1582 __isl_give isl_map *isl_map_zip(
1583 __isl_take isl_map *map);
1584 __isl_give isl_union_map *isl_union_map_zip(
1585 __isl_take isl_union_map *umap);
1587 Given a relation with nested relations for domain and range,
1588 interchange the range of the domain with the domain of the range.
1590 =item * Dimension manipulation
1592 __isl_give isl_set *isl_set_add_dims(
1593 __isl_take isl_set *set,
1594 enum isl_dim_type type, unsigned n);
1595 __isl_give isl_map *isl_map_add_dims(
1596 __isl_take isl_map *map,
1597 enum isl_dim_type type, unsigned n);
1599 It is usually not advisable to directly change the (input or output)
1600 space of a set or a relation as this removes the name and the internal
1601 structure of the space. However, the above functions can be useful
1602 to add new parameters.
1606 =head2 Binary Operations
1608 The two arguments of a binary operation not only need to live
1609 in the same C<isl_ctx>, they currently also need to have
1610 the same (number of) parameters.
1612 =head3 Basic Operations
1616 =item * Intersection
1618 __isl_give isl_basic_set *isl_basic_set_intersect(
1619 __isl_take isl_basic_set *bset1,
1620 __isl_take isl_basic_set *bset2);
1621 __isl_give isl_set *isl_set_intersect(
1622 __isl_take isl_set *set1,
1623 __isl_take isl_set *set2);
1624 __isl_give isl_union_set *isl_union_set_intersect(
1625 __isl_take isl_union_set *uset1,
1626 __isl_take isl_union_set *uset2);
1627 __isl_give isl_basic_map *isl_basic_map_intersect_domain(
1628 __isl_take isl_basic_map *bmap,
1629 __isl_take isl_basic_set *bset);
1630 __isl_give isl_basic_map *isl_basic_map_intersect_range(
1631 __isl_take isl_basic_map *bmap,
1632 __isl_take isl_basic_set *bset);
1633 __isl_give isl_basic_map *isl_basic_map_intersect(
1634 __isl_take isl_basic_map *bmap1,
1635 __isl_take isl_basic_map *bmap2);
1636 __isl_give isl_map *isl_map_intersect_domain(
1637 __isl_take isl_map *map,
1638 __isl_take isl_set *set);
1639 __isl_give isl_map *isl_map_intersect_range(
1640 __isl_take isl_map *map,
1641 __isl_take isl_set *set);
1642 __isl_give isl_map *isl_map_intersect(
1643 __isl_take isl_map *map1,
1644 __isl_take isl_map *map2);
1645 __isl_give isl_union_map *isl_union_map_intersect_domain(
1646 __isl_take isl_union_map *umap,
1647 __isl_take isl_union_set *uset);
1648 __isl_give isl_union_map *isl_union_map_intersect_range(
1649 __isl_take isl_union_map *umap,
1650 __isl_take isl_union_set *uset);
1651 __isl_give isl_union_map *isl_union_map_intersect(
1652 __isl_take isl_union_map *umap1,
1653 __isl_take isl_union_map *umap2);
1657 __isl_give isl_set *isl_basic_set_union(
1658 __isl_take isl_basic_set *bset1,
1659 __isl_take isl_basic_set *bset2);
1660 __isl_give isl_map *isl_basic_map_union(
1661 __isl_take isl_basic_map *bmap1,
1662 __isl_take isl_basic_map *bmap2);
1663 __isl_give isl_set *isl_set_union(
1664 __isl_take isl_set *set1,
1665 __isl_take isl_set *set2);
1666 __isl_give isl_map *isl_map_union(
1667 __isl_take isl_map *map1,
1668 __isl_take isl_map *map2);
1669 __isl_give isl_union_set *isl_union_set_union(
1670 __isl_take isl_union_set *uset1,
1671 __isl_take isl_union_set *uset2);
1672 __isl_give isl_union_map *isl_union_map_union(
1673 __isl_take isl_union_map *umap1,
1674 __isl_take isl_union_map *umap2);
1676 =item * Set difference
1678 __isl_give isl_set *isl_set_subtract(
1679 __isl_take isl_set *set1,
1680 __isl_take isl_set *set2);
1681 __isl_give isl_map *isl_map_subtract(
1682 __isl_take isl_map *map1,
1683 __isl_take isl_map *map2);
1684 __isl_give isl_union_set *isl_union_set_subtract(
1685 __isl_take isl_union_set *uset1,
1686 __isl_take isl_union_set *uset2);
1687 __isl_give isl_union_map *isl_union_map_subtract(
1688 __isl_take isl_union_map *umap1,
1689 __isl_take isl_union_map *umap2);
1693 __isl_give isl_basic_set *isl_basic_set_apply(
1694 __isl_take isl_basic_set *bset,
1695 __isl_take isl_basic_map *bmap);
1696 __isl_give isl_set *isl_set_apply(
1697 __isl_take isl_set *set,
1698 __isl_take isl_map *map);
1699 __isl_give isl_union_set *isl_union_set_apply(
1700 __isl_take isl_union_set *uset,
1701 __isl_take isl_union_map *umap);
1702 __isl_give isl_basic_map *isl_basic_map_apply_domain(
1703 __isl_take isl_basic_map *bmap1,
1704 __isl_take isl_basic_map *bmap2);
1705 __isl_give isl_basic_map *isl_basic_map_apply_range(
1706 __isl_take isl_basic_map *bmap1,
1707 __isl_take isl_basic_map *bmap2);
1708 __isl_give isl_map *isl_map_apply_domain(
1709 __isl_take isl_map *map1,
1710 __isl_take isl_map *map2);
1711 __isl_give isl_union_map *isl_union_map_apply_domain(
1712 __isl_take isl_union_map *umap1,
1713 __isl_take isl_union_map *umap2);
1714 __isl_give isl_map *isl_map_apply_range(
1715 __isl_take isl_map *map1,
1716 __isl_take isl_map *map2);
1717 __isl_give isl_union_map *isl_union_map_apply_range(
1718 __isl_take isl_union_map *umap1,
1719 __isl_take isl_union_map *umap2);
1721 =item * Cartesian Product
1723 __isl_give isl_set *isl_set_product(
1724 __isl_take isl_set *set1,
1725 __isl_take isl_set *set2);
1726 __isl_give isl_union_set *isl_union_set_product(
1727 __isl_take isl_union_set *uset1,
1728 __isl_take isl_union_set *uset2);
1729 __isl_give isl_basic_map *isl_basic_map_range_product(
1730 __isl_take isl_basic_map *bmap1,
1731 __isl_take isl_basic_map *bmap2);
1732 __isl_give isl_map *isl_map_range_product(
1733 __isl_take isl_map *map1,
1734 __isl_take isl_map *map2);
1735 __isl_give isl_union_map *isl_union_map_range_product(
1736 __isl_take isl_union_map *umap1,
1737 __isl_take isl_union_map *umap2);
1738 __isl_give isl_map *isl_map_product(
1739 __isl_take isl_map *map1,
1740 __isl_take isl_map *map2);
1741 __isl_give isl_union_map *isl_union_map_product(
1742 __isl_take isl_union_map *umap1,
1743 __isl_take isl_union_map *umap2);
1745 The above functions compute the cross product of the given
1746 sets or relations. The domains and ranges of the results
1747 are wrapped maps between domains and ranges of the inputs.
1748 To obtain a ``flat'' product, use the following functions
1751 __isl_give isl_basic_set *isl_basic_set_flat_product(
1752 __isl_take isl_basic_set *bset1,
1753 __isl_take isl_basic_set *bset2);
1754 __isl_give isl_set *isl_set_flat_product(
1755 __isl_take isl_set *set1,
1756 __isl_take isl_set *set2);
1757 __isl_give isl_basic_map *isl_basic_map_flat_product(
1758 __isl_take isl_basic_map *bmap1,
1759 __isl_take isl_basic_map *bmap2);
1760 __isl_give isl_map *isl_map_flat_product(
1761 __isl_take isl_map *map1,
1762 __isl_take isl_map *map2);
1764 =item * Simplification
1766 __isl_give isl_basic_set *isl_basic_set_gist(
1767 __isl_take isl_basic_set *bset,
1768 __isl_take isl_basic_set *context);
1769 __isl_give isl_set *isl_set_gist(__isl_take isl_set *set,
1770 __isl_take isl_set *context);
1771 __isl_give isl_union_set *isl_union_set_gist(
1772 __isl_take isl_union_set *uset,
1773 __isl_take isl_union_set *context);
1774 __isl_give isl_basic_map *isl_basic_map_gist(
1775 __isl_take isl_basic_map *bmap,
1776 __isl_take isl_basic_map *context);
1777 __isl_give isl_map *isl_map_gist(__isl_take isl_map *map,
1778 __isl_take isl_map *context);
1779 __isl_give isl_union_map *isl_union_map_gist(
1780 __isl_take isl_union_map *umap,
1781 __isl_take isl_union_map *context);
1783 The gist operation returns a set or relation that has the
1784 same intersection with the context as the input set or relation.
1785 Any implicit equality in the intersection is made explicit in the result,
1786 while all inequalities that are redundant with respect to the intersection
1788 In case of union sets and relations, the gist operation is performed
1793 =head3 Lexicographic Optimization
1795 Given a (basic) set C<set> (or C<bset>) and a zero-dimensional domain C<dom>,
1796 the following functions
1797 compute a set that contains the lexicographic minimum or maximum
1798 of the elements in C<set> (or C<bset>) for those values of the parameters
1799 that satisfy C<dom>.
1800 If C<empty> is not C<NULL>, then C<*empty> is assigned a set
1801 that contains the parameter values in C<dom> for which C<set> (or C<bset>)
1803 In other words, the union of the parameter values
1804 for which the result is non-empty and of C<*empty>
1807 __isl_give isl_set *isl_basic_set_partial_lexmin(
1808 __isl_take isl_basic_set *bset,
1809 __isl_take isl_basic_set *dom,
1810 __isl_give isl_set **empty);
1811 __isl_give isl_set *isl_basic_set_partial_lexmax(
1812 __isl_take isl_basic_set *bset,
1813 __isl_take isl_basic_set *dom,
1814 __isl_give isl_set **empty);
1815 __isl_give isl_set *isl_set_partial_lexmin(
1816 __isl_take isl_set *set, __isl_take isl_set *dom,
1817 __isl_give isl_set **empty);
1818 __isl_give isl_set *isl_set_partial_lexmax(
1819 __isl_take isl_set *set, __isl_take isl_set *dom,
1820 __isl_give isl_set **empty);
1822 Given a (basic) set C<set> (or C<bset>), the following functions simply
1823 return a set containing the lexicographic minimum or maximum
1824 of the elements in C<set> (or C<bset>).
1825 In case of union sets, the optimum is computed per space.
1827 __isl_give isl_set *isl_basic_set_lexmin(
1828 __isl_take isl_basic_set *bset);
1829 __isl_give isl_set *isl_basic_set_lexmax(
1830 __isl_take isl_basic_set *bset);
1831 __isl_give isl_set *isl_set_lexmin(
1832 __isl_take isl_set *set);
1833 __isl_give isl_set *isl_set_lexmax(
1834 __isl_take isl_set *set);
1835 __isl_give isl_union_set *isl_union_set_lexmin(
1836 __isl_take isl_union_set *uset);
1837 __isl_give isl_union_set *isl_union_set_lexmax(
1838 __isl_take isl_union_set *uset);
1840 Given a (basic) relation C<map> (or C<bmap>) and a domain C<dom>,
1841 the following functions
1842 compute a relation that maps each element of C<dom>
1843 to the single lexicographic minimum or maximum
1844 of the elements that are associated to that same
1845 element in C<map> (or C<bmap>).
1846 If C<empty> is not C<NULL>, then C<*empty> is assigned a set
1847 that contains the elements in C<dom> that do not map
1848 to any elements in C<map> (or C<bmap>).
1849 In other words, the union of the domain of the result and of C<*empty>
1852 __isl_give isl_map *isl_basic_map_partial_lexmax(
1853 __isl_take isl_basic_map *bmap,
1854 __isl_take isl_basic_set *dom,
1855 __isl_give isl_set **empty);
1856 __isl_give isl_map *isl_basic_map_partial_lexmin(
1857 __isl_take isl_basic_map *bmap,
1858 __isl_take isl_basic_set *dom,
1859 __isl_give isl_set **empty);
1860 __isl_give isl_map *isl_map_partial_lexmax(
1861 __isl_take isl_map *map, __isl_take isl_set *dom,
1862 __isl_give isl_set **empty);
1863 __isl_give isl_map *isl_map_partial_lexmin(
1864 __isl_take isl_map *map, __isl_take isl_set *dom,
1865 __isl_give isl_set **empty);
1867 Given a (basic) map C<map> (or C<bmap>), the following functions simply
1868 return a map mapping each element in the domain of
1869 C<map> (or C<bmap>) to the lexicographic minimum or maximum
1870 of all elements associated to that element.
1871 In case of union relations, the optimum is computed per space.
1873 __isl_give isl_map *isl_basic_map_lexmin(
1874 __isl_take isl_basic_map *bmap);
1875 __isl_give isl_map *isl_basic_map_lexmax(
1876 __isl_take isl_basic_map *bmap);
1877 __isl_give isl_map *isl_map_lexmin(
1878 __isl_take isl_map *map);
1879 __isl_give isl_map *isl_map_lexmax(
1880 __isl_take isl_map *map);
1881 __isl_give isl_union_map *isl_union_map_lexmin(
1882 __isl_take isl_union_map *umap);
1883 __isl_give isl_union_map *isl_union_map_lexmax(
1884 __isl_take isl_union_map *umap);
1888 Matrices can be created, copied and freed using the following functions.
1890 #include <isl/mat.h>
1891 __isl_give isl_mat *isl_mat_alloc(struct isl_ctx *ctx,
1892 unsigned n_row, unsigned n_col);
1893 __isl_give isl_mat *isl_mat_copy(__isl_keep isl_mat *mat);
1894 void isl_mat_free(__isl_take isl_mat *mat);
1896 Note that the elements of a newly created matrix may have arbitrary values.
1897 The elements can be changed and inspected using the following functions.
1899 int isl_mat_rows(__isl_keep isl_mat *mat);
1900 int isl_mat_cols(__isl_keep isl_mat *mat);
1901 int isl_mat_get_element(__isl_keep isl_mat *mat,
1902 int row, int col, isl_int *v);
1903 __isl_give isl_mat *isl_mat_set_element(__isl_take isl_mat *mat,
1904 int row, int col, isl_int v);
1905 __isl_give isl_mat *isl_mat_set_element_si(__isl_take isl_mat *mat,
1906 int row, int col, int v);
1908 C<isl_mat_get_element> will return a negative value if anything went wrong.
1909 In that case, the value of C<*v> is undefined.
1911 The following function can be used to compute the (right) inverse
1912 of a matrix, i.e., a matrix such that the product of the original
1913 and the inverse (in that order) is a multiple of the identity matrix.
1914 The input matrix is assumed to be of full row-rank.
1916 __isl_give isl_mat *isl_mat_right_inverse(__isl_take isl_mat *mat);
1918 The following function can be used to compute the (right) kernel
1919 (or null space) of a matrix, i.e., a matrix such that the product of
1920 the original and the kernel (in that order) is the zero matrix.
1922 __isl_give isl_mat *isl_mat_right_kernel(__isl_take isl_mat *mat);
1926 Points are elements of a set. They can be used to construct
1927 simple sets (boxes) or they can be used to represent the
1928 individual elements of a set.
1929 The zero point (the origin) can be created using
1931 __isl_give isl_point *isl_point_zero(__isl_take isl_dim *dim);
1933 The coordinates of a point can be inspected, set and changed
1936 void isl_point_get_coordinate(__isl_keep isl_point *pnt,
1937 enum isl_dim_type type, int pos, isl_int *v);
1938 __isl_give isl_point *isl_point_set_coordinate(
1939 __isl_take isl_point *pnt,
1940 enum isl_dim_type type, int pos, isl_int v);
1942 __isl_give isl_point *isl_point_add_ui(
1943 __isl_take isl_point *pnt,
1944 enum isl_dim_type type, int pos, unsigned val);
1945 __isl_give isl_point *isl_point_sub_ui(
1946 __isl_take isl_point *pnt,
1947 enum isl_dim_type type, int pos, unsigned val);
1949 Points can be copied or freed using
1951 __isl_give isl_point *isl_point_copy(
1952 __isl_keep isl_point *pnt);
1953 void isl_point_free(__isl_take isl_point *pnt);
1955 A singleton set can be created from a point using
1957 __isl_give isl_basic_set *isl_basic_set_from_point(
1958 __isl_take isl_point *pnt);
1959 __isl_give isl_set *isl_set_from_point(
1960 __isl_take isl_point *pnt);
1962 and a box can be created from two opposite extremal points using
1964 __isl_give isl_basic_set *isl_basic_set_box_from_points(
1965 __isl_take isl_point *pnt1,
1966 __isl_take isl_point *pnt2);
1967 __isl_give isl_set *isl_set_box_from_points(
1968 __isl_take isl_point *pnt1,
1969 __isl_take isl_point *pnt2);
1971 All elements of a B<bounded> (union) set can be enumerated using
1972 the following functions.
1974 int isl_set_foreach_point(__isl_keep isl_set *set,
1975 int (*fn)(__isl_take isl_point *pnt, void *user),
1977 int isl_union_set_foreach_point(__isl_keep isl_union_set *uset,
1978 int (*fn)(__isl_take isl_point *pnt, void *user),
1981 The function C<fn> is called for each integer point in
1982 C<set> with as second argument the last argument of
1983 the C<isl_set_foreach_point> call. The function C<fn>
1984 should return C<0> on success and C<-1> on failure.
1985 In the latter case, C<isl_set_foreach_point> will stop
1986 enumerating and return C<-1> as well.
1987 If the enumeration is performed successfully and to completion,
1988 then C<isl_set_foreach_point> returns C<0>.
1990 To obtain a single point of a (basic) set, use
1992 __isl_give isl_point *isl_basic_set_sample_point(
1993 __isl_take isl_basic_set *bset);
1994 __isl_give isl_point *isl_set_sample_point(
1995 __isl_take isl_set *set);
1997 If C<set> does not contain any (integer) points, then the
1998 resulting point will be ``void'', a property that can be
2001 int isl_point_is_void(__isl_keep isl_point *pnt);
2003 =head2 Piecewise Quasipolynomials
2005 A piecewise quasipolynomial is a particular kind of function that maps
2006 a parametric point to a rational value.
2007 More specifically, a quasipolynomial is a polynomial expression in greatest
2008 integer parts of affine expressions of parameters and variables.
2009 A piecewise quasipolynomial is a subdivision of a given parametric
2010 domain into disjoint cells with a quasipolynomial associated to
2011 each cell. The value of the piecewise quasipolynomial at a given
2012 point is the value of the quasipolynomial associated to the cell
2013 that contains the point. Outside of the union of cells,
2014 the value is assumed to be zero.
2015 For example, the piecewise quasipolynomial
2017 [n] -> { [x] -> ((1 + n) - x) : x <= n and x >= 0 }
2019 maps C<x> to C<1 + n - x> for values of C<x> between C<0> and C<n>.
2020 A given piecewise quasipolynomial has a fixed domain dimension.
2021 Union piecewise quasipolynomials are used to contain piecewise quasipolynomials
2022 defined over different domains.
2023 Piecewise quasipolynomials are mainly used by the C<barvinok>
2024 library for representing the number of elements in a parametric set or map.
2025 For example, the piecewise quasipolynomial above represents
2026 the number of points in the map
2028 [n] -> { [x] -> [y] : x,y >= 0 and 0 <= x + y <= n }
2030 =head3 Printing (Piecewise) Quasipolynomials
2032 Quasipolynomials and piecewise quasipolynomials can be printed
2033 using the following functions.
2035 __isl_give isl_printer *isl_printer_print_qpolynomial(
2036 __isl_take isl_printer *p,
2037 __isl_keep isl_qpolynomial *qp);
2039 __isl_give isl_printer *isl_printer_print_pw_qpolynomial(
2040 __isl_take isl_printer *p,
2041 __isl_keep isl_pw_qpolynomial *pwqp);
2043 __isl_give isl_printer *isl_printer_print_union_pw_qpolynomial(
2044 __isl_take isl_printer *p,
2045 __isl_keep isl_union_pw_qpolynomial *upwqp);
2047 The output format of the printer
2048 needs to be set to either C<ISL_FORMAT_ISL> or C<ISL_FORMAT_C>.
2049 For C<isl_printer_print_union_pw_qpolynomial>, only C<ISL_FORMAT_ISL>
2051 In case of printing in C<ISL_FORMAT_C>, the user may want
2052 to set the names of all dimensions
2054 __isl_give isl_qpolynomial *isl_qpolynomial_set_dim_name(
2055 __isl_take isl_qpolynomial *qp,
2056 enum isl_dim_type type, unsigned pos,
2058 __isl_give isl_pw_qpolynomial *
2059 isl_pw_qpolynomial_set_dim_name(
2060 __isl_take isl_pw_qpolynomial *pwqp,
2061 enum isl_dim_type type, unsigned pos,
2064 =head3 Creating New (Piecewise) Quasipolynomials
2066 Some simple quasipolynomials can be created using the following functions.
2067 More complicated quasipolynomials can be created by applying
2068 operations such as addition and multiplication
2069 on the resulting quasipolynomials
2071 __isl_give isl_qpolynomial *isl_qpolynomial_zero(
2072 __isl_take isl_dim *dim);
2073 __isl_give isl_qpolynomial *isl_qpolynomial_one(
2074 __isl_take isl_dim *dim);
2075 __isl_give isl_qpolynomial *isl_qpolynomial_infty(
2076 __isl_take isl_dim *dim);
2077 __isl_give isl_qpolynomial *isl_qpolynomial_neginfty(
2078 __isl_take isl_dim *dim);
2079 __isl_give isl_qpolynomial *isl_qpolynomial_nan(
2080 __isl_take isl_dim *dim);
2081 __isl_give isl_qpolynomial *isl_qpolynomial_rat_cst(
2082 __isl_take isl_dim *dim,
2083 const isl_int n, const isl_int d);
2084 __isl_give isl_qpolynomial *isl_qpolynomial_div(
2085 __isl_take isl_div *div);
2086 __isl_give isl_qpolynomial *isl_qpolynomial_var(
2087 __isl_take isl_dim *dim,
2088 enum isl_dim_type type, unsigned pos);
2090 The zero piecewise quasipolynomial or a piecewise quasipolynomial
2091 with a single cell can be created using the following functions.
2092 Multiple of these single cell piecewise quasipolynomials can
2093 be combined to create more complicated piecewise quasipolynomials.
2095 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_zero(
2096 __isl_take isl_dim *dim);
2097 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_alloc(
2098 __isl_take isl_set *set,
2099 __isl_take isl_qpolynomial *qp);
2101 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_zero(
2102 __isl_take isl_dim *dim);
2103 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_from_pw_qpolynomial(
2104 __isl_take isl_pw_qpolynomial *pwqp);
2105 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_add_pw_qpolynomial(
2106 __isl_take isl_union_pw_qpolynomial *upwqp,
2107 __isl_take isl_pw_qpolynomial *pwqp);
2109 Quasipolynomials can be copied and freed again using the following
2112 __isl_give isl_qpolynomial *isl_qpolynomial_copy(
2113 __isl_keep isl_qpolynomial *qp);
2114 void isl_qpolynomial_free(__isl_take isl_qpolynomial *qp);
2116 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_copy(
2117 __isl_keep isl_pw_qpolynomial *pwqp);
2118 void isl_pw_qpolynomial_free(
2119 __isl_take isl_pw_qpolynomial *pwqp);
2121 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_copy(
2122 __isl_keep isl_union_pw_qpolynomial *upwqp);
2123 void isl_union_pw_qpolynomial_free(
2124 __isl_take isl_union_pw_qpolynomial *upwqp);
2126 =head3 Inspecting (Piecewise) Quasipolynomials
2128 To iterate over all piecewise quasipolynomials in a union
2129 piecewise quasipolynomial, use the following function
2131 int isl_union_pw_qpolynomial_foreach_pw_qpolynomial(
2132 __isl_keep isl_union_pw_qpolynomial *upwqp,
2133 int (*fn)(__isl_take isl_pw_qpolynomial *pwqp, void *user),
2136 To extract the piecewise quasipolynomial from a union with a given dimension
2139 __isl_give isl_pw_qpolynomial *
2140 isl_union_pw_qpolynomial_extract_pw_qpolynomial(
2141 __isl_keep isl_union_pw_qpolynomial *upwqp,
2142 __isl_take isl_dim *dim);
2144 To iterate over the cells in a piecewise quasipolynomial,
2145 use either of the following two functions
2147 int isl_pw_qpolynomial_foreach_piece(
2148 __isl_keep isl_pw_qpolynomial *pwqp,
2149 int (*fn)(__isl_take isl_set *set,
2150 __isl_take isl_qpolynomial *qp,
2151 void *user), void *user);
2152 int isl_pw_qpolynomial_foreach_lifted_piece(
2153 __isl_keep isl_pw_qpolynomial *pwqp,
2154 int (*fn)(__isl_take isl_set *set,
2155 __isl_take isl_qpolynomial *qp,
2156 void *user), void *user);
2158 As usual, the function C<fn> should return C<0> on success
2159 and C<-1> on failure. The difference between
2160 C<isl_pw_qpolynomial_foreach_piece> and
2161 C<isl_pw_qpolynomial_foreach_lifted_piece> is that
2162 C<isl_pw_qpolynomial_foreach_lifted_piece> will first
2163 compute unique representations for all existentially quantified
2164 variables and then turn these existentially quantified variables
2165 into extra set variables, adapting the associated quasipolynomial
2166 accordingly. This means that the C<set> passed to C<fn>
2167 will not have any existentially quantified variables, but that
2168 the dimensions of the sets may be different for different
2169 invocations of C<fn>.
2171 To iterate over all terms in a quasipolynomial,
2174 int isl_qpolynomial_foreach_term(
2175 __isl_keep isl_qpolynomial *qp,
2176 int (*fn)(__isl_take isl_term *term,
2177 void *user), void *user);
2179 The terms themselves can be inspected and freed using
2182 unsigned isl_term_dim(__isl_keep isl_term *term,
2183 enum isl_dim_type type);
2184 void isl_term_get_num(__isl_keep isl_term *term,
2186 void isl_term_get_den(__isl_keep isl_term *term,
2188 int isl_term_get_exp(__isl_keep isl_term *term,
2189 enum isl_dim_type type, unsigned pos);
2190 __isl_give isl_div *isl_term_get_div(
2191 __isl_keep isl_term *term, unsigned pos);
2192 void isl_term_free(__isl_take isl_term *term);
2194 Each term is a product of parameters, set variables and
2195 integer divisions. The function C<isl_term_get_exp>
2196 returns the exponent of a given dimensions in the given term.
2197 The C<isl_int>s in the arguments of C<isl_term_get_num>
2198 and C<isl_term_get_den> need to have been initialized
2199 using C<isl_int_init> before calling these functions.
2201 =head3 Properties of (Piecewise) Quasipolynomials
2203 To check whether a quasipolynomial is actually a constant,
2204 use the following function.
2206 int isl_qpolynomial_is_cst(__isl_keep isl_qpolynomial *qp,
2207 isl_int *n, isl_int *d);
2209 If C<qp> is a constant and if C<n> and C<d> are not C<NULL>
2210 then the numerator and denominator of the constant
2211 are returned in C<*n> and C<*d>, respectively.
2213 =head3 Operations on (Piecewise) Quasipolynomials
2215 __isl_give isl_qpolynomial *isl_qpolynomial_neg(
2216 __isl_take isl_qpolynomial *qp);
2217 __isl_give isl_qpolynomial *isl_qpolynomial_add(
2218 __isl_take isl_qpolynomial *qp1,
2219 __isl_take isl_qpolynomial *qp2);
2220 __isl_give isl_qpolynomial *isl_qpolynomial_sub(
2221 __isl_take isl_qpolynomial *qp1,
2222 __isl_take isl_qpolynomial *qp2);
2223 __isl_give isl_qpolynomial *isl_qpolynomial_mul(
2224 __isl_take isl_qpolynomial *qp1,
2225 __isl_take isl_qpolynomial *qp2);
2226 __isl_give isl_qpolynomial *isl_qpolynomial_pow(
2227 __isl_take isl_qpolynomial *qp, unsigned exponent);
2229 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_add(
2230 __isl_take isl_pw_qpolynomial *pwqp1,
2231 __isl_take isl_pw_qpolynomial *pwqp2);
2232 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_sub(
2233 __isl_take isl_pw_qpolynomial *pwqp1,
2234 __isl_take isl_pw_qpolynomial *pwqp2);
2235 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_add_disjoint(
2236 __isl_take isl_pw_qpolynomial *pwqp1,
2237 __isl_take isl_pw_qpolynomial *pwqp2);
2238 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_neg(
2239 __isl_take isl_pw_qpolynomial *pwqp);
2240 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_mul(
2241 __isl_take isl_pw_qpolynomial *pwqp1,
2242 __isl_take isl_pw_qpolynomial *pwqp2);
2244 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_add(
2245 __isl_take isl_union_pw_qpolynomial *upwqp1,
2246 __isl_take isl_union_pw_qpolynomial *upwqp2);
2247 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_sub(
2248 __isl_take isl_union_pw_qpolynomial *upwqp1,
2249 __isl_take isl_union_pw_qpolynomial *upwqp2);
2250 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_mul(
2251 __isl_take isl_union_pw_qpolynomial *upwqp1,
2252 __isl_take isl_union_pw_qpolynomial *upwqp2);
2254 __isl_give isl_qpolynomial *isl_pw_qpolynomial_eval(
2255 __isl_take isl_pw_qpolynomial *pwqp,
2256 __isl_take isl_point *pnt);
2258 __isl_give isl_qpolynomial *isl_union_pw_qpolynomial_eval(
2259 __isl_take isl_union_pw_qpolynomial *upwqp,
2260 __isl_take isl_point *pnt);
2262 __isl_give isl_set *isl_pw_qpolynomial_domain(
2263 __isl_take isl_pw_qpolynomial *pwqp);
2264 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_intersect_domain(
2265 __isl_take isl_pw_qpolynomial *pwpq,
2266 __isl_take isl_set *set);
2268 __isl_give isl_union_set *isl_union_pw_qpolynomial_domain(
2269 __isl_take isl_union_pw_qpolynomial *upwqp);
2270 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_intersect_domain(
2271 __isl_take isl_union_pw_qpolynomial *upwpq,
2272 __isl_take isl_union_set *uset);
2274 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_coalesce(
2275 __isl_take isl_union_pw_qpolynomial *upwqp);
2277 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_gist(
2278 __isl_take isl_pw_qpolynomial *pwqp,
2279 __isl_take isl_set *context);
2281 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_gist(
2282 __isl_take isl_union_pw_qpolynomial *upwqp,
2283 __isl_take isl_union_set *context);
2285 The gist operation applies the gist operation to each of
2286 the cells in the domain of the input piecewise quasipolynomial.
2287 The context is also exploited
2288 to simplify the quasipolynomials associated to each cell.
2290 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_to_polynomial(
2291 __isl_take isl_pw_qpolynomial *pwqp, int sign);
2292 __isl_give isl_union_pw_qpolynomial *
2293 isl_union_pw_qpolynomial_to_polynomial(
2294 __isl_take isl_union_pw_qpolynomial *upwqp, int sign);
2296 Approximate each quasipolynomial by a polynomial. If C<sign> is positive,
2297 the polynomial will be an overapproximation. If C<sign> is negative,
2298 it will be an underapproximation. If C<sign> is zero, the approximation
2299 will lie somewhere in between.
2301 =head2 Bounds on Piecewise Quasipolynomials and Piecewise Quasipolynomial Reductions
2303 A piecewise quasipolynomial reduction is a piecewise
2304 reduction (or fold) of quasipolynomials.
2305 In particular, the reduction can be maximum or a minimum.
2306 The objects are mainly used to represent the result of
2307 an upper or lower bound on a quasipolynomial over its domain,
2308 i.e., as the result of the following function.
2310 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_bound(
2311 __isl_take isl_pw_qpolynomial *pwqp,
2312 enum isl_fold type, int *tight);
2314 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_bound(
2315 __isl_take isl_union_pw_qpolynomial *upwqp,
2316 enum isl_fold type, int *tight);
2318 The C<type> argument may be either C<isl_fold_min> or C<isl_fold_max>.
2319 If C<tight> is not C<NULL>, then C<*tight> is set to C<1>
2320 is the returned bound is known be tight, i.e., for each value
2321 of the parameters there is at least
2322 one element in the domain that reaches the bound.
2323 If the domain of C<pwqp> is not wrapping, then the bound is computed
2324 over all elements in that domain and the result has a purely parametric
2325 domain. If the domain of C<pwqp> is wrapping, then the bound is
2326 computed over the range of the wrapped relation. The domain of the
2327 wrapped relation becomes the domain of the result.
2329 A (piecewise) quasipolynomial reduction can be copied or freed using the
2330 following functions.
2332 __isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_copy(
2333 __isl_keep isl_qpolynomial_fold *fold);
2334 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_copy(
2335 __isl_keep isl_pw_qpolynomial_fold *pwf);
2336 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_copy(
2337 __isl_keep isl_union_pw_qpolynomial_fold *upwf);
2338 void isl_qpolynomial_fold_free(
2339 __isl_take isl_qpolynomial_fold *fold);
2340 void isl_pw_qpolynomial_fold_free(
2341 __isl_take isl_pw_qpolynomial_fold *pwf);
2342 void isl_union_pw_qpolynomial_fold_free(
2343 __isl_take isl_union_pw_qpolynomial_fold *upwf);
2345 =head3 Printing Piecewise Quasipolynomial Reductions
2347 Piecewise quasipolynomial reductions can be printed
2348 using the following function.
2350 __isl_give isl_printer *isl_printer_print_pw_qpolynomial_fold(
2351 __isl_take isl_printer *p,
2352 __isl_keep isl_pw_qpolynomial_fold *pwf);
2353 __isl_give isl_printer *isl_printer_print_union_pw_qpolynomial_fold(
2354 __isl_take isl_printer *p,
2355 __isl_keep isl_union_pw_qpolynomial_fold *upwf);
2357 For C<isl_printer_print_pw_qpolynomial_fold>,
2358 output format of the printer
2359 needs to be set to either C<ISL_FORMAT_ISL> or C<ISL_FORMAT_C>.
2360 For C<isl_printer_print_union_pw_qpolynomial_fold>,
2361 output format of the printer
2362 needs to be set to C<ISL_FORMAT_ISL>.
2363 In case of printing in C<ISL_FORMAT_C>, the user may want
2364 to set the names of all dimensions
2366 __isl_give isl_pw_qpolynomial_fold *
2367 isl_pw_qpolynomial_fold_set_dim_name(
2368 __isl_take isl_pw_qpolynomial_fold *pwf,
2369 enum isl_dim_type type, unsigned pos,
2372 =head3 Inspecting (Piecewise) Quasipolynomial Reductions
2374 To iterate over all piecewise quasipolynomial reductions in a union
2375 piecewise quasipolynomial reduction, use the following function
2377 int isl_union_pw_qpolynomial_fold_foreach_pw_qpolynomial_fold(
2378 __isl_keep isl_union_pw_qpolynomial_fold *upwf,
2379 int (*fn)(__isl_take isl_pw_qpolynomial_fold *pwf,
2380 void *user), void *user);
2382 To iterate over the cells in a piecewise quasipolynomial reduction,
2383 use either of the following two functions
2385 int isl_pw_qpolynomial_fold_foreach_piece(
2386 __isl_keep isl_pw_qpolynomial_fold *pwf,
2387 int (*fn)(__isl_take isl_set *set,
2388 __isl_take isl_qpolynomial_fold *fold,
2389 void *user), void *user);
2390 int isl_pw_qpolynomial_fold_foreach_lifted_piece(
2391 __isl_keep isl_pw_qpolynomial_fold *pwf,
2392 int (*fn)(__isl_take isl_set *set,
2393 __isl_take isl_qpolynomial_fold *fold,
2394 void *user), void *user);
2396 See L<Inspecting (Piecewise) Quasipolynomials> for an explanation
2397 of the difference between these two functions.
2399 To iterate over all quasipolynomials in a reduction, use
2401 int isl_qpolynomial_fold_foreach_qpolynomial(
2402 __isl_keep isl_qpolynomial_fold *fold,
2403 int (*fn)(__isl_take isl_qpolynomial *qp,
2404 void *user), void *user);
2406 =head3 Operations on Piecewise Quasipolynomial Reductions
2408 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_add(
2409 __isl_take isl_pw_qpolynomial_fold *pwf1,
2410 __isl_take isl_pw_qpolynomial_fold *pwf2);
2412 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_fold(
2413 __isl_take isl_pw_qpolynomial_fold *pwf1,
2414 __isl_take isl_pw_qpolynomial_fold *pwf2);
2416 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_fold(
2417 __isl_take isl_union_pw_qpolynomial_fold *upwf1,
2418 __isl_take isl_union_pw_qpolynomial_fold *upwf2);
2420 __isl_give isl_qpolynomial *isl_pw_qpolynomial_fold_eval(
2421 __isl_take isl_pw_qpolynomial_fold *pwf,
2422 __isl_take isl_point *pnt);
2424 __isl_give isl_qpolynomial *isl_union_pw_qpolynomial_fold_eval(
2425 __isl_take isl_union_pw_qpolynomial_fold *upwf,
2426 __isl_take isl_point *pnt);
2428 __isl_give isl_union_set *isl_union_pw_qpolynomial_fold_domain(
2429 __isl_take isl_union_pw_qpolynomial_fold *upwf);
2430 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_intersect_domain(
2431 __isl_take isl_union_pw_qpolynomial_fold *upwf,
2432 __isl_take isl_union_set *uset);
2434 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_coalesce(
2435 __isl_take isl_pw_qpolynomial_fold *pwf);
2437 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_coalesce(
2438 __isl_take isl_union_pw_qpolynomial_fold *upwf);
2440 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_gist(
2441 __isl_take isl_pw_qpolynomial_fold *pwf,
2442 __isl_take isl_set *context);
2444 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_gist(
2445 __isl_take isl_union_pw_qpolynomial_fold *upwf,
2446 __isl_take isl_union_set *context);
2448 The gist operation applies the gist operation to each of
2449 the cells in the domain of the input piecewise quasipolynomial reduction.
2450 In future, the operation will also exploit the context
2451 to simplify the quasipolynomial reductions associated to each cell.
2453 __isl_give isl_pw_qpolynomial_fold *
2454 isl_set_apply_pw_qpolynomial_fold(
2455 __isl_take isl_set *set,
2456 __isl_take isl_pw_qpolynomial_fold *pwf,
2458 __isl_give isl_pw_qpolynomial_fold *
2459 isl_map_apply_pw_qpolynomial_fold(
2460 __isl_take isl_map *map,
2461 __isl_take isl_pw_qpolynomial_fold *pwf,
2463 __isl_give isl_union_pw_qpolynomial_fold *
2464 isl_union_set_apply_union_pw_qpolynomial_fold(
2465 __isl_take isl_union_set *uset,
2466 __isl_take isl_union_pw_qpolynomial_fold *upwf,
2468 __isl_give isl_union_pw_qpolynomial_fold *
2469 isl_union_map_apply_union_pw_qpolynomial_fold(
2470 __isl_take isl_union_map *umap,
2471 __isl_take isl_union_pw_qpolynomial_fold *upwf,
2474 The functions taking a map
2475 compose the given map with the given piecewise quasipolynomial reduction.
2476 That is, compute a bound (of the same type as C<pwf> or C<upwf> itself)
2477 over all elements in the intersection of the range of the map
2478 and the domain of the piecewise quasipolynomial reduction
2479 as a function of an element in the domain of the map.
2480 The functions taking a set compute a bound over all elements in the
2481 intersection of the set and the domain of the
2482 piecewise quasipolynomial reduction.
2484 =head2 Dependence Analysis
2486 C<isl> contains specialized functionality for performing
2487 array dataflow analysis. That is, given a I<sink> access relation
2488 and a collection of possible I<source> access relations,
2489 C<isl> can compute relations that describe
2490 for each iteration of the sink access, which iteration
2491 of which of the source access relations was the last
2492 to access the same data element before the given iteration
2494 To compute standard flow dependences, the sink should be
2495 a read, while the sources should be writes.
2496 If any of the source accesses are marked as being I<may>
2497 accesses, then there will be a dependence to the last
2498 I<must> access B<and> to any I<may> access that follows
2499 this last I<must> access.
2500 In particular, if I<all> sources are I<may> accesses,
2501 then memory based dependence analysis is performed.
2502 If, on the other hand, all sources are I<must> accesses,
2503 then value based dependence analysis is performed.
2505 #include <isl/flow.h>
2507 typedef int (*isl_access_level_before)(void *first, void *second);
2509 __isl_give isl_access_info *isl_access_info_alloc(
2510 __isl_take isl_map *sink,
2511 void *sink_user, isl_access_level_before fn,
2513 __isl_give isl_access_info *isl_access_info_add_source(
2514 __isl_take isl_access_info *acc,
2515 __isl_take isl_map *source, int must,
2517 void isl_access_info_free(__isl_take isl_access_info *acc);
2519 __isl_give isl_flow *isl_access_info_compute_flow(
2520 __isl_take isl_access_info *acc);
2522 int isl_flow_foreach(__isl_keep isl_flow *deps,
2523 int (*fn)(__isl_take isl_map *dep, int must,
2524 void *dep_user, void *user),
2526 __isl_give isl_map *isl_flow_get_no_source(
2527 __isl_keep isl_flow *deps, int must);
2528 void isl_flow_free(__isl_take isl_flow *deps);
2530 The function C<isl_access_info_compute_flow> performs the actual
2531 dependence analysis. The other functions are used to construct
2532 the input for this function or to read off the output.
2534 The input is collected in an C<isl_access_info>, which can
2535 be created through a call to C<isl_access_info_alloc>.
2536 The arguments to this functions are the sink access relation
2537 C<sink>, a token C<sink_user> used to identify the sink
2538 access to the user, a callback function for specifying the
2539 relative order of source and sink accesses, and the number
2540 of source access relations that will be added.
2541 The callback function has type C<int (*)(void *first, void *second)>.
2542 The function is called with two user supplied tokens identifying
2543 either a source or the sink and it should return the shared nesting
2544 level and the relative order of the two accesses.
2545 In particular, let I<n> be the number of loops shared by
2546 the two accesses. If C<first> precedes C<second> textually,
2547 then the function should return I<2 * n + 1>; otherwise,
2548 it should return I<2 * n>.
2549 The sources can be added to the C<isl_access_info> by performing
2550 (at most) C<max_source> calls to C<isl_access_info_add_source>.
2551 C<must> indicates whether the source is a I<must> access
2552 or a I<may> access. Note that a multi-valued access relation
2553 should only be marked I<must> if every iteration in the domain
2554 of the relation accesses I<all> elements in its image.
2555 The C<source_user> token is again used to identify
2556 the source access. The range of the source access relation
2557 C<source> should have the same dimension as the range
2558 of the sink access relation.
2559 The C<isl_access_info_free> function should usually not be
2560 called explicitly, because it is called implicitly by
2561 C<isl_access_info_compute_flow>.
2563 The result of the dependence analysis is collected in an
2564 C<isl_flow>. There may be elements of
2565 the sink access for which no preceding source access could be
2566 found or for which all preceding sources are I<may> accesses.
2567 The relations containing these elements can be obtained through
2568 calls to C<isl_flow_get_no_source>, the first with C<must> set
2569 and the second with C<must> unset.
2570 In the case of standard flow dependence analysis,
2571 with the sink a read and the sources I<must> writes,
2572 the first relation corresponds to the reads from uninitialized
2573 array elements and the second relation is empty.
2574 The actual flow dependences can be extracted using
2575 C<isl_flow_foreach>. This function will call the user-specified
2576 callback function C<fn> for each B<non-empty> dependence between
2577 a source and the sink. The callback function is called
2578 with four arguments, the actual flow dependence relation
2579 mapping source iterations to sink iterations, a boolean that
2580 indicates whether it is a I<must> or I<may> dependence, a token
2581 identifying the source and an additional C<void *> with value
2582 equal to the third argument of the C<isl_flow_foreach> call.
2583 A dependence is marked I<must> if it originates from a I<must>
2584 source and if it is not followed by any I<may> sources.
2586 After finishing with an C<isl_flow>, the user should call
2587 C<isl_flow_free> to free all associated memory.
2589 A higher-level interface to dependence analysis is provided
2590 by the following function.
2592 #include <isl/flow.h>
2594 int isl_union_map_compute_flow(__isl_take isl_union_map *sink,
2595 __isl_take isl_union_map *must_source,
2596 __isl_take isl_union_map *may_source,
2597 __isl_take isl_union_map *schedule,
2598 __isl_give isl_union_map **must_dep,
2599 __isl_give isl_union_map **may_dep,
2600 __isl_give isl_union_map **must_no_source,
2601 __isl_give isl_union_map **may_no_source);
2603 The arrays are identified by the tuple names of the ranges
2604 of the accesses. The iteration domains by the tuple names
2605 of the domains of the accesses and of the schedule.
2606 The relative order of the iteration domains is given by the
2607 schedule. The relations returned through C<must_no_source>
2608 and C<may_no_source> are subsets of C<sink>.
2609 Any of C<must_dep>, C<may_dep>, C<must_no_source>
2610 or C<may_no_source> may be C<NULL>, but a C<NULL> value for
2611 any of the other arguments is treated as an error.
2615 B<The functionality described in this section is fairly new
2616 and may be subject to change.>
2618 The following function can be used to compute a schedule
2619 for a union of domains. The generated schedule respects
2620 all C<validity> dependences. That is, all dependence distances
2621 over these dependences in the scheduled space are lexicographically
2622 positive. The generated schedule schedule also tries to minimize
2623 the dependence distances over C<proximity> dependences.
2624 Moreover, it tries to obtain sequences (bands) of schedule dimensions
2625 for groups of domains where the dependence distances have only
2626 non-negative values.
2627 The algorithm used to construct the schedule is similar to that
2630 #include <isl/schedule.h>
2631 __isl_give isl_schedule *isl_union_set_compute_schedule(
2632 __isl_take isl_union_set *domain,
2633 __isl_take isl_union_map *validity,
2634 __isl_take isl_union_map *proximity);
2635 void *isl_schedule_free(__isl_take isl_schedule *sched);
2637 A mapping from the domains to the scheduled space can be obtained
2638 from an C<isl_schedule> using the following function.
2640 __isl_give isl_union_map *isl_schedule_get_map(
2641 __isl_keep isl_schedule *sched);
2643 This mapping can also be obtained in pieces using the following functions.
2645 int isl_schedule_n_band(__isl_keep isl_schedule *sched);
2646 __isl_give isl_union_map *isl_schedule_get_band(
2647 __isl_keep isl_schedule *sched, unsigned band);
2649 C<isl_schedule_n_band> returns the maximal number of bands.
2650 C<isl_schedule_get_band> returns a union of mappings from a domain to
2651 the band of consecutive schedule dimensions with the given sequence
2652 number for that domain. Bands with the same sequence number but for
2653 different domains may be completely unrelated.
2654 Within a band, the corresponding coordinates of the distance vectors
2655 are all non-negative, assuming that the coordinates for all previous
2658 =head2 Parametric Vertex Enumeration
2660 The parametric vertex enumeration described in this section
2661 is mainly intended to be used internally and by the C<barvinok>
2664 #include <isl/vertices.h>
2665 __isl_give isl_vertices *isl_basic_set_compute_vertices(
2666 __isl_keep isl_basic_set *bset);
2668 The function C<isl_basic_set_compute_vertices> performs the
2669 actual computation of the parametric vertices and the chamber
2670 decomposition and store the result in an C<isl_vertices> object.
2671 This information can be queried by either iterating over all
2672 the vertices or iterating over all the chambers or cells
2673 and then iterating over all vertices that are active on the chamber.
2675 int isl_vertices_foreach_vertex(
2676 __isl_keep isl_vertices *vertices,
2677 int (*fn)(__isl_take isl_vertex *vertex, void *user),
2680 int isl_vertices_foreach_cell(
2681 __isl_keep isl_vertices *vertices,
2682 int (*fn)(__isl_take isl_cell *cell, void *user),
2684 int isl_cell_foreach_vertex(__isl_keep isl_cell *cell,
2685 int (*fn)(__isl_take isl_vertex *vertex, void *user),
2688 Other operations that can be performed on an C<isl_vertices> object are
2691 isl_ctx *isl_vertices_get_ctx(
2692 __isl_keep isl_vertices *vertices);
2693 int isl_vertices_get_n_vertices(
2694 __isl_keep isl_vertices *vertices);
2695 void isl_vertices_free(__isl_take isl_vertices *vertices);
2697 Vertices can be inspected and destroyed using the following functions.
2699 isl_ctx *isl_vertex_get_ctx(__isl_keep isl_vertex *vertex);
2700 int isl_vertex_get_id(__isl_keep isl_vertex *vertex);
2701 __isl_give isl_basic_set *isl_vertex_get_domain(
2702 __isl_keep isl_vertex *vertex);
2703 __isl_give isl_basic_set *isl_vertex_get_expr(
2704 __isl_keep isl_vertex *vertex);
2705 void isl_vertex_free(__isl_take isl_vertex *vertex);
2707 C<isl_vertex_get_expr> returns a singleton parametric set describing
2708 the vertex, while C<isl_vertex_get_domain> returns the activity domain
2710 Note that C<isl_vertex_get_domain> and C<isl_vertex_get_expr> return
2711 B<rational> basic sets, so they should mainly be used for inspection
2712 and should not be mixed with integer sets.
2714 Chambers can be inspected and destroyed using the following functions.
2716 isl_ctx *isl_cell_get_ctx(__isl_keep isl_cell *cell);
2717 __isl_give isl_basic_set *isl_cell_get_domain(
2718 __isl_keep isl_cell *cell);
2719 void isl_cell_free(__isl_take isl_cell *cell);
2723 Although C<isl> is mainly meant to be used as a library,
2724 it also contains some basic applications that use some
2725 of the functionality of C<isl>.
2726 The input may be specified in either the L<isl format>
2727 or the L<PolyLib format>.
2729 =head2 C<isl_polyhedron_sample>
2731 C<isl_polyhedron_sample> takes a polyhedron as input and prints
2732 an integer element of the polyhedron, if there is any.
2733 The first column in the output is the denominator and is always
2734 equal to 1. If the polyhedron contains no integer points,
2735 then a vector of length zero is printed.
2739 C<isl_pip> takes the same input as the C<example> program
2740 from the C<piplib> distribution, i.e., a set of constraints
2741 on the parameters, a line containing only -1 and finally a set
2742 of constraints on a parametric polyhedron.
2743 The coefficients of the parameters appear in the last columns
2744 (but before the final constant column).
2745 The output is the lexicographic minimum of the parametric polyhedron.
2746 As C<isl> currently does not have its own output format, the output
2747 is just a dump of the internal state.
2749 =head2 C<isl_polyhedron_minimize>
2751 C<isl_polyhedron_minimize> computes the minimum of some linear
2752 or affine objective function over the integer points in a polyhedron.
2753 If an affine objective function
2754 is given, then the constant should appear in the last column.
2756 =head2 C<isl_polytope_scan>
2758 Given a polytope, C<isl_polytope_scan> prints
2759 all integer points in the polytope.
2761 =head1 C<isl-polylib>
2763 The C<isl-polylib> library provides the following functions for converting
2764 between C<isl> objects and C<PolyLib> objects.
2765 The library is distributed separately for licensing reasons.
2767 #include <isl_set_polylib.h>
2768 __isl_give isl_basic_set *isl_basic_set_new_from_polylib(
2769 Polyhedron *P, __isl_take isl_dim *dim);
2770 Polyhedron *isl_basic_set_to_polylib(
2771 __isl_keep isl_basic_set *bset);
2772 __isl_give isl_set *isl_set_new_from_polylib(Polyhedron *D,
2773 __isl_take isl_dim *dim);
2774 Polyhedron *isl_set_to_polylib(__isl_keep isl_set *set);
2776 #include <isl_map_polylib.h>
2777 __isl_give isl_basic_map *isl_basic_map_new_from_polylib(
2778 Polyhedron *P, __isl_take isl_dim *dim);
2779 __isl_give isl_map *isl_map_new_from_polylib(Polyhedron *D,
2780 __isl_take isl_dim *dim);
2781 Polyhedron *isl_basic_map_to_polylib(
2782 __isl_keep isl_basic_map *bmap);
2783 Polyhedron *isl_map_to_polylib(__isl_keep isl_map *map);