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);
755 __isl_give isl_union_set *isl_union_set_universe(
756 __isl_take isl_union_set *uset);
757 __isl_give isl_union_map *isl_union_map_universe(
758 __isl_take isl_union_map *umap);
760 The sets and relations constructed by the functions above
761 contain all integer values, while those constructed by the
762 functions below only contain non-negative values.
764 __isl_give isl_basic_set *isl_basic_set_nat_universe(
765 __isl_take isl_dim *dim);
766 __isl_give isl_basic_map *isl_basic_map_nat_universe(
767 __isl_take isl_dim *dim);
768 __isl_give isl_set *isl_set_nat_universe(
769 __isl_take isl_dim *dim);
770 __isl_give isl_map *isl_map_nat_universe(
771 __isl_take isl_dim *dim);
773 =item * Identity relations
775 __isl_give isl_basic_map *isl_basic_map_identity(
776 __isl_take isl_dim *dim);
777 __isl_give isl_map *isl_map_identity(
778 __isl_take isl_dim *dim);
780 The number of input and output dimensions in C<dim> needs
783 =item * Lexicographic order
785 __isl_give isl_map *isl_map_lex_lt(
786 __isl_take isl_dim *set_dim);
787 __isl_give isl_map *isl_map_lex_le(
788 __isl_take isl_dim *set_dim);
789 __isl_give isl_map *isl_map_lex_gt(
790 __isl_take isl_dim *set_dim);
791 __isl_give isl_map *isl_map_lex_ge(
792 __isl_take isl_dim *set_dim);
793 __isl_give isl_map *isl_map_lex_lt_first(
794 __isl_take isl_dim *dim, unsigned n);
795 __isl_give isl_map *isl_map_lex_le_first(
796 __isl_take isl_dim *dim, unsigned n);
797 __isl_give isl_map *isl_map_lex_gt_first(
798 __isl_take isl_dim *dim, unsigned n);
799 __isl_give isl_map *isl_map_lex_ge_first(
800 __isl_take isl_dim *dim, unsigned n);
802 The first four functions take a dimension specification for a B<set>
803 and return relations that express that the elements in the domain
804 are lexicographically less
805 (C<isl_map_lex_lt>), less or equal (C<isl_map_lex_le>),
806 greater (C<isl_map_lex_gt>) or greater or equal (C<isl_map_lex_ge>)
807 than the elements in the range.
808 The last four functions take a dimension specification for a map
809 and return relations that express that the first C<n> dimensions
810 in the domain are lexicographically less
811 (C<isl_map_lex_lt_first>), less or equal (C<isl_map_lex_le_first>),
812 greater (C<isl_map_lex_gt_first>) or greater or equal (C<isl_map_lex_ge_first>)
813 than the first C<n> dimensions in the range.
817 A basic set or relation can be converted to a set or relation
818 using the following functions.
820 __isl_give isl_set *isl_set_from_basic_set(
821 __isl_take isl_basic_set *bset);
822 __isl_give isl_map *isl_map_from_basic_map(
823 __isl_take isl_basic_map *bmap);
825 Sets and relations can be converted to union sets and relations
826 using the following functions.
828 __isl_give isl_union_map *isl_union_map_from_map(
829 __isl_take isl_map *map);
830 __isl_give isl_union_set *isl_union_set_from_set(
831 __isl_take isl_set *set);
833 Sets and relations can be copied and freed again using the following
836 __isl_give isl_basic_set *isl_basic_set_copy(
837 __isl_keep isl_basic_set *bset);
838 __isl_give isl_set *isl_set_copy(__isl_keep isl_set *set);
839 __isl_give isl_union_set *isl_union_set_copy(
840 __isl_keep isl_union_set *uset);
841 __isl_give isl_basic_map *isl_basic_map_copy(
842 __isl_keep isl_basic_map *bmap);
843 __isl_give isl_map *isl_map_copy(__isl_keep isl_map *map);
844 __isl_give isl_union_map *isl_union_map_copy(
845 __isl_keep isl_union_map *umap);
846 void isl_basic_set_free(__isl_take isl_basic_set *bset);
847 void isl_set_free(__isl_take isl_set *set);
848 void isl_union_set_free(__isl_take isl_union_set *uset);
849 void isl_basic_map_free(__isl_take isl_basic_map *bmap);
850 void isl_map_free(__isl_take isl_map *map);
851 void isl_union_map_free(__isl_take isl_union_map *umap);
853 Other sets and relations can be constructed by starting
854 from a universe set or relation, adding equality and/or
855 inequality constraints and then projecting out the
856 existentially quantified variables, if any.
857 Constraints can be constructed, manipulated and
858 added to basic sets and relations using the following functions.
860 #include <isl/constraint.h>
861 __isl_give isl_constraint *isl_equality_alloc(
862 __isl_take isl_dim *dim);
863 __isl_give isl_constraint *isl_inequality_alloc(
864 __isl_take isl_dim *dim);
865 void isl_constraint_set_constant(
866 __isl_keep isl_constraint *constraint, isl_int v);
867 void isl_constraint_set_coefficient(
868 __isl_keep isl_constraint *constraint,
869 enum isl_dim_type type, int pos, isl_int v);
870 __isl_give isl_basic_map *isl_basic_map_add_constraint(
871 __isl_take isl_basic_map *bmap,
872 __isl_take isl_constraint *constraint);
873 __isl_give isl_basic_set *isl_basic_set_add_constraint(
874 __isl_take isl_basic_set *bset,
875 __isl_take isl_constraint *constraint);
877 For example, to create a set containing the even integers
878 between 10 and 42, you would use the following code.
882 struct isl_constraint *c;
883 struct isl_basic_set *bset;
886 dim = isl_dim_set_alloc(ctx, 0, 2);
887 bset = isl_basic_set_universe(isl_dim_copy(dim));
889 c = isl_equality_alloc(isl_dim_copy(dim));
890 isl_int_set_si(v, -1);
891 isl_constraint_set_coefficient(c, isl_dim_set, 0, v);
892 isl_int_set_si(v, 2);
893 isl_constraint_set_coefficient(c, isl_dim_set, 1, v);
894 bset = isl_basic_set_add_constraint(bset, c);
896 c = isl_inequality_alloc(isl_dim_copy(dim));
897 isl_int_set_si(v, -10);
898 isl_constraint_set_constant(c, v);
899 isl_int_set_si(v, 1);
900 isl_constraint_set_coefficient(c, isl_dim_set, 0, v);
901 bset = isl_basic_set_add_constraint(bset, c);
903 c = isl_inequality_alloc(dim);
904 isl_int_set_si(v, 42);
905 isl_constraint_set_constant(c, v);
906 isl_int_set_si(v, -1);
907 isl_constraint_set_coefficient(c, isl_dim_set, 0, v);
908 bset = isl_basic_set_add_constraint(bset, c);
910 bset = isl_basic_set_project_out(bset, isl_dim_set, 1, 1);
916 struct isl_basic_set *bset;
917 bset = isl_basic_set_read_from_str(ctx,
918 "{[i] : exists (a : i = 2a and i >= 10 and i <= 42)}", -1);
920 A basic set or relation can also be constructed from two matrices
921 describing the equalities and the inequalities.
923 __isl_give isl_basic_set *isl_basic_set_from_constraint_matrices(
924 __isl_take isl_dim *dim,
925 __isl_take isl_mat *eq, __isl_take isl_mat *ineq,
926 enum isl_dim_type c1,
927 enum isl_dim_type c2, enum isl_dim_type c3,
928 enum isl_dim_type c4);
929 __isl_give isl_basic_map *isl_basic_map_from_constraint_matrices(
930 __isl_take isl_dim *dim,
931 __isl_take isl_mat *eq, __isl_take isl_mat *ineq,
932 enum isl_dim_type c1,
933 enum isl_dim_type c2, enum isl_dim_type c3,
934 enum isl_dim_type c4, enum isl_dim_type c5);
936 The C<isl_dim_type> arguments indicate the order in which
937 different kinds of variables appear in the input matrices
938 and should be a permutation of C<isl_dim_cst>, C<isl_dim_param>,
939 C<isl_dim_set> and C<isl_dim_div> for sets and
940 of C<isl_dim_cst>, C<isl_dim_param>,
941 C<isl_dim_in>, C<isl_dim_out> and C<isl_dim_div> for relations.
943 =head2 Inspecting Sets and Relations
945 Usually, the user should not have to care about the actual constraints
946 of the sets and maps, but should instead apply the abstract operations
947 explained in the following sections.
948 Occasionally, however, it may be required to inspect the individual
949 coefficients of the constraints. This section explains how to do so.
950 In these cases, it may also be useful to have C<isl> compute
951 an explicit representation of the existentially quantified variables.
953 __isl_give isl_set *isl_set_compute_divs(
954 __isl_take isl_set *set);
955 __isl_give isl_map *isl_map_compute_divs(
956 __isl_take isl_map *map);
957 __isl_give isl_union_set *isl_union_set_compute_divs(
958 __isl_take isl_union_set *uset);
959 __isl_give isl_union_map *isl_union_map_compute_divs(
960 __isl_take isl_union_map *umap);
962 This explicit representation defines the existentially quantified
963 variables as integer divisions of the other variables, possibly
964 including earlier existentially quantified variables.
965 An explicitly represented existentially quantified variable therefore
966 has a unique value when the values of the other variables are known.
967 If, furthermore, the same existentials, i.e., existentials
968 with the same explicit representations, should appear in the
969 same order in each of the disjuncts of a set or map, then the user should call
970 either of the following functions.
972 __isl_give isl_set *isl_set_align_divs(
973 __isl_take isl_set *set);
974 __isl_give isl_map *isl_map_align_divs(
975 __isl_take isl_map *map);
977 Alternatively, the existentially quantified variables can be removed
978 using the following functions, which compute an overapproximation.
980 __isl_give isl_basic_set *isl_basic_set_remove_divs(
981 __isl_take isl_basic_set *bset);
982 __isl_give isl_basic_map *isl_basic_map_remove_divs(
983 __isl_take isl_basic_map *bmap);
984 __isl_give isl_set *isl_set_remove_divs(
985 __isl_take isl_set *set);
986 __isl_give isl_map *isl_map_remove_divs(
987 __isl_take isl_map *map);
989 To iterate over all the sets or maps in a union set or map, use
991 int isl_union_set_foreach_set(__isl_keep isl_union_set *uset,
992 int (*fn)(__isl_take isl_set *set, void *user),
994 int isl_union_map_foreach_map(__isl_keep isl_union_map *umap,
995 int (*fn)(__isl_take isl_map *map, void *user),
998 The number of sets or maps in a union set or map can be obtained
1001 int isl_union_set_n_set(__isl_keep isl_union_set *uset);
1002 int isl_union_map_n_map(__isl_keep isl_union_map *umap);
1004 To extract the set or map from a union with a given dimension
1007 __isl_give isl_set *isl_union_set_extract_set(
1008 __isl_keep isl_union_set *uset,
1009 __isl_take isl_dim *dim);
1010 __isl_give isl_map *isl_union_map_extract_map(
1011 __isl_keep isl_union_map *umap,
1012 __isl_take isl_dim *dim);
1014 To iterate over all the basic sets or maps in a set or map, use
1016 int isl_set_foreach_basic_set(__isl_keep isl_set *set,
1017 int (*fn)(__isl_take isl_basic_set *bset, void *user),
1019 int isl_map_foreach_basic_map(__isl_keep isl_map *map,
1020 int (*fn)(__isl_take isl_basic_map *bmap, void *user),
1023 The callback function C<fn> should return 0 if successful and
1024 -1 if an error occurs. In the latter case, or if any other error
1025 occurs, the above functions will return -1.
1027 It should be noted that C<isl> does not guarantee that
1028 the basic sets or maps passed to C<fn> are disjoint.
1029 If this is required, then the user should call one of
1030 the following functions first.
1032 __isl_give isl_set *isl_set_make_disjoint(
1033 __isl_take isl_set *set);
1034 __isl_give isl_map *isl_map_make_disjoint(
1035 __isl_take isl_map *map);
1037 The number of basic sets in a set can be obtained
1040 int isl_set_n_basic_set(__isl_keep isl_set *set);
1042 To iterate over the constraints of a basic set or map, use
1044 #include <isl/constraint.h>
1046 int isl_basic_map_foreach_constraint(
1047 __isl_keep isl_basic_map *bmap,
1048 int (*fn)(__isl_take isl_constraint *c, void *user),
1050 void isl_constraint_free(struct isl_constraint *c);
1052 Again, the callback function C<fn> should return 0 if successful and
1053 -1 if an error occurs. In the latter case, or if any other error
1054 occurs, the above functions will return -1.
1055 The constraint C<c> represents either an equality or an inequality.
1056 Use the following function to find out whether a constraint
1057 represents an equality. If not, it represents an inequality.
1059 int isl_constraint_is_equality(
1060 __isl_keep isl_constraint *constraint);
1062 The coefficients of the constraints can be inspected using
1063 the following functions.
1065 void isl_constraint_get_constant(
1066 __isl_keep isl_constraint *constraint, isl_int *v);
1067 void isl_constraint_get_coefficient(
1068 __isl_keep isl_constraint *constraint,
1069 enum isl_dim_type type, int pos, isl_int *v);
1071 The explicit representations of the existentially quantified
1072 variables can be inspected using the following functions.
1073 Note that the user is only allowed to use these functions
1074 if the inspected set or map is the result of a call
1075 to C<isl_set_compute_divs> or C<isl_map_compute_divs>.
1077 __isl_give isl_div *isl_constraint_div(
1078 __isl_keep isl_constraint *constraint, int pos);
1079 isl_ctx *isl_div_get_ctx(__isl_keep isl_div *div);
1080 void isl_div_get_constant(__isl_keep isl_div *div,
1082 void isl_div_get_denominator(__isl_keep isl_div *div,
1084 void isl_div_get_coefficient(__isl_keep isl_div *div,
1085 enum isl_dim_type type, int pos, isl_int *v);
1087 To obtain the constraints of a basic set or map in matrix
1088 form, use the following functions.
1090 __isl_give isl_mat *isl_basic_set_equalities_matrix(
1091 __isl_keep isl_basic_set *bset,
1092 enum isl_dim_type c1, enum isl_dim_type c2,
1093 enum isl_dim_type c3, enum isl_dim_type c4);
1094 __isl_give isl_mat *isl_basic_set_inequalities_matrix(
1095 __isl_keep isl_basic_set *bset,
1096 enum isl_dim_type c1, enum isl_dim_type c2,
1097 enum isl_dim_type c3, enum isl_dim_type c4);
1098 __isl_give isl_mat *isl_basic_map_equalities_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);
1103 __isl_give isl_mat *isl_basic_map_inequalities_matrix(
1104 __isl_keep isl_basic_map *bmap,
1105 enum isl_dim_type c1,
1106 enum isl_dim_type c2, enum isl_dim_type c3,
1107 enum isl_dim_type c4, enum isl_dim_type c5);
1109 The C<isl_dim_type> arguments dictate the order in which
1110 different kinds of variables appear in the resulting matrix
1111 and should be a permutation of C<isl_dim_cst>, C<isl_dim_param>,
1112 C<isl_dim_in>, C<isl_dim_out> and C<isl_dim_div>.
1114 The names of the domain and range spaces of a set or relation can be
1115 read off using the following functions.
1117 const char *isl_basic_set_get_tuple_name(
1118 __isl_keep isl_basic_set *bset);
1119 const char *isl_set_get_tuple_name(
1120 __isl_keep isl_set *set);
1121 const char *isl_basic_map_get_tuple_name(
1122 __isl_keep isl_basic_map *bmap,
1123 enum isl_dim_type type);
1124 const char *isl_map_get_tuple_name(
1125 __isl_keep isl_map *map,
1126 enum isl_dim_type type);
1128 As with C<isl_dim_get_tuple_name>, the value returned points to
1129 an internal data structure.
1130 The names of individual dimensions can be read off using
1131 the following functions.
1133 const char *isl_constraint_get_dim_name(
1134 __isl_keep isl_constraint *constraint,
1135 enum isl_dim_type type, unsigned pos);
1136 const char *isl_basic_set_get_dim_name(
1137 __isl_keep isl_basic_set *bset,
1138 enum isl_dim_type type, unsigned pos);
1139 const char *isl_set_get_dim_name(
1140 __isl_keep isl_set *set,
1141 enum isl_dim_type type, unsigned pos);
1142 const char *isl_basic_map_get_dim_name(
1143 __isl_keep isl_basic_map *bmap,
1144 enum isl_dim_type type, unsigned pos);
1145 const char *isl_map_get_dim_name(
1146 __isl_keep isl_map *map,
1147 enum isl_dim_type type, unsigned pos);
1149 These functions are mostly useful to obtain the names
1154 =head3 Unary Properties
1160 The following functions test whether the given set or relation
1161 contains any integer points. The ``plain'' variants do not perform
1162 any computations, but simply check if the given set or relation
1163 is already known to be empty.
1165 int isl_basic_set_plain_is_empty(__isl_keep isl_basic_set *bset);
1166 int isl_basic_set_is_empty(__isl_keep isl_basic_set *bset);
1167 int isl_set_plain_is_empty(__isl_keep isl_set *set);
1168 int isl_set_is_empty(__isl_keep isl_set *set);
1169 int isl_union_set_is_empty(__isl_keep isl_union_set *uset);
1170 int isl_basic_map_plain_is_empty(__isl_keep isl_basic_map *bmap);
1171 int isl_basic_map_is_empty(__isl_keep isl_basic_map *bmap);
1172 int isl_map_plain_is_empty(__isl_keep isl_map *map);
1173 int isl_map_is_empty(__isl_keep isl_map *map);
1174 int isl_union_map_is_empty(__isl_keep isl_union_map *umap);
1176 =item * Universality
1178 int isl_basic_set_is_universe(__isl_keep isl_basic_set *bset);
1179 int isl_basic_map_is_universe(__isl_keep isl_basic_map *bmap);
1180 int isl_set_plain_is_universe(__isl_keep isl_set *set);
1182 =item * Single-valuedness
1184 int isl_map_is_single_valued(__isl_keep isl_map *map);
1185 int isl_union_map_is_single_valued(__isl_keep isl_union_map *umap);
1189 int isl_map_plain_is_injective(__isl_keep isl_map *map);
1190 int isl_map_is_injective(__isl_keep isl_map *map);
1191 int isl_union_map_plain_is_injective(
1192 __isl_keep isl_union_map *umap);
1193 int isl_union_map_is_injective(
1194 __isl_keep isl_union_map *umap);
1198 int isl_map_is_bijective(__isl_keep isl_map *map);
1199 int isl_union_map_is_bijective(__isl_keep isl_union_map *umap);
1203 The following functions check whether the domain of the given
1204 (basic) set is a wrapped relation.
1206 int isl_basic_set_is_wrapping(
1207 __isl_keep isl_basic_set *bset);
1208 int isl_set_is_wrapping(__isl_keep isl_set *set);
1210 =item * Internal Product
1212 int isl_basic_map_can_zip(
1213 __isl_keep isl_basic_map *bmap);
1214 int isl_map_can_zip(__isl_keep isl_map *map);
1216 Check whether the product of domain and range of the given relation
1218 i.e., whether both domain and range are nested relations.
1222 =head3 Binary Properties
1228 int isl_set_plain_is_equal(__isl_keep isl_set *set1,
1229 __isl_keep isl_set *set2);
1230 int isl_set_is_equal(__isl_keep isl_set *set1,
1231 __isl_keep isl_set *set2);
1232 int isl_union_set_is_equal(
1233 __isl_keep isl_union_set *uset1,
1234 __isl_keep isl_union_set *uset2);
1235 int isl_basic_map_is_equal(
1236 __isl_keep isl_basic_map *bmap1,
1237 __isl_keep isl_basic_map *bmap2);
1238 int isl_map_is_equal(__isl_keep isl_map *map1,
1239 __isl_keep isl_map *map2);
1240 int isl_map_plain_is_equal(__isl_keep isl_map *map1,
1241 __isl_keep isl_map *map2);
1242 int isl_union_map_is_equal(
1243 __isl_keep isl_union_map *umap1,
1244 __isl_keep isl_union_map *umap2);
1246 =item * Disjointness
1248 int isl_set_plain_is_disjoint(__isl_keep isl_set *set1,
1249 __isl_keep isl_set *set2);
1253 int isl_set_is_subset(__isl_keep isl_set *set1,
1254 __isl_keep isl_set *set2);
1255 int isl_set_is_strict_subset(
1256 __isl_keep isl_set *set1,
1257 __isl_keep isl_set *set2);
1258 int isl_union_set_is_subset(
1259 __isl_keep isl_union_set *uset1,
1260 __isl_keep isl_union_set *uset2);
1261 int isl_union_set_is_strict_subset(
1262 __isl_keep isl_union_set *uset1,
1263 __isl_keep isl_union_set *uset2);
1264 int isl_basic_map_is_subset(
1265 __isl_keep isl_basic_map *bmap1,
1266 __isl_keep isl_basic_map *bmap2);
1267 int isl_basic_map_is_strict_subset(
1268 __isl_keep isl_basic_map *bmap1,
1269 __isl_keep isl_basic_map *bmap2);
1270 int isl_map_is_subset(
1271 __isl_keep isl_map *map1,
1272 __isl_keep isl_map *map2);
1273 int isl_map_is_strict_subset(
1274 __isl_keep isl_map *map1,
1275 __isl_keep isl_map *map2);
1276 int isl_union_map_is_subset(
1277 __isl_keep isl_union_map *umap1,
1278 __isl_keep isl_union_map *umap2);
1279 int isl_union_map_is_strict_subset(
1280 __isl_keep isl_union_map *umap1,
1281 __isl_keep isl_union_map *umap2);
1285 =head2 Unary Operations
1291 __isl_give isl_set *isl_set_complement(
1292 __isl_take isl_set *set);
1296 __isl_give isl_basic_map *isl_basic_map_reverse(
1297 __isl_take isl_basic_map *bmap);
1298 __isl_give isl_map *isl_map_reverse(
1299 __isl_take isl_map *map);
1300 __isl_give isl_union_map *isl_union_map_reverse(
1301 __isl_take isl_union_map *umap);
1305 __isl_give isl_basic_set *isl_basic_set_project_out(
1306 __isl_take isl_basic_set *bset,
1307 enum isl_dim_type type, unsigned first, unsigned n);
1308 __isl_give isl_basic_map *isl_basic_map_project_out(
1309 __isl_take isl_basic_map *bmap,
1310 enum isl_dim_type type, unsigned first, unsigned n);
1311 __isl_give isl_set *isl_set_project_out(__isl_take isl_set *set,
1312 enum isl_dim_type type, unsigned first, unsigned n);
1313 __isl_give isl_map *isl_map_project_out(__isl_take isl_map *map,
1314 enum isl_dim_type type, unsigned first, unsigned n);
1315 __isl_give isl_basic_set *isl_basic_map_domain(
1316 __isl_take isl_basic_map *bmap);
1317 __isl_give isl_basic_set *isl_basic_map_range(
1318 __isl_take isl_basic_map *bmap);
1319 __isl_give isl_set *isl_map_domain(
1320 __isl_take isl_map *bmap);
1321 __isl_give isl_set *isl_map_range(
1322 __isl_take isl_map *map);
1323 __isl_give isl_union_set *isl_union_map_domain(
1324 __isl_take isl_union_map *umap);
1325 __isl_give isl_union_set *isl_union_map_range(
1326 __isl_take isl_union_map *umap);
1328 __isl_give isl_basic_map *isl_basic_map_domain_map(
1329 __isl_take isl_basic_map *bmap);
1330 __isl_give isl_basic_map *isl_basic_map_range_map(
1331 __isl_take isl_basic_map *bmap);
1332 __isl_give isl_map *isl_map_domain_map(__isl_take isl_map *map);
1333 __isl_give isl_map *isl_map_range_map(__isl_take isl_map *map);
1334 __isl_give isl_union_map *isl_union_map_domain_map(
1335 __isl_take isl_union_map *umap);
1336 __isl_give isl_union_map *isl_union_map_range_map(
1337 __isl_take isl_union_map *umap);
1339 The functions above construct a (basic, regular or union) relation
1340 that maps (a wrapped version of) the input relation to its domain or range.
1344 __isl_give isl_set *isl_set_eliminate(
1345 __isl_take isl_set *set, enum isl_dim_type type,
1346 unsigned first, unsigned n);
1348 Eliminate the coefficients for the given dimensions from the constraints,
1349 without removing the dimensions.
1353 __isl_give isl_map *isl_set_identity(
1354 __isl_take isl_set *set);
1355 __isl_give isl_union_map *isl_union_set_identity(
1356 __isl_take isl_union_set *uset);
1358 Construct an identity relation on the given (union) set.
1362 __isl_give isl_basic_set *isl_basic_map_deltas(
1363 __isl_take isl_basic_map *bmap);
1364 __isl_give isl_set *isl_map_deltas(__isl_take isl_map *map);
1365 __isl_give isl_union_set *isl_union_map_deltas(
1366 __isl_take isl_union_map *umap);
1368 These functions return a (basic) set containing the differences
1369 between image elements and corresponding domain elements in the input.
1371 __isl_give isl_basic_map *isl_basic_map_deltas_map(
1372 __isl_take isl_basic_map *bmap);
1373 __isl_give isl_map *isl_map_deltas_map(
1374 __isl_take isl_map *map);
1375 __isl_give isl_union_map *isl_union_map_deltas_map(
1376 __isl_take isl_union_map *umap);
1378 The functions above construct a (basic, regular or union) relation
1379 that maps (a wrapped version of) the input relation to its delta set.
1383 Simplify the representation of a set or relation by trying
1384 to combine pairs of basic sets or relations into a single
1385 basic set or relation.
1387 __isl_give isl_set *isl_set_coalesce(__isl_take isl_set *set);
1388 __isl_give isl_map *isl_map_coalesce(__isl_take isl_map *map);
1389 __isl_give isl_union_set *isl_union_set_coalesce(
1390 __isl_take isl_union_set *uset);
1391 __isl_give isl_union_map *isl_union_map_coalesce(
1392 __isl_take isl_union_map *umap);
1394 =item * Detecting equalities
1396 __isl_give isl_basic_set *isl_basic_set_detect_equalities(
1397 __isl_take isl_basic_set *bset);
1398 __isl_give isl_basic_map *isl_basic_map_detect_equalities(
1399 __isl_take isl_basic_map *bmap);
1400 __isl_give isl_set *isl_set_detect_equalities(
1401 __isl_take isl_set *set);
1402 __isl_give isl_map *isl_map_detect_equalities(
1403 __isl_take isl_map *map);
1404 __isl_give isl_union_set *isl_union_set_detect_equalities(
1405 __isl_take isl_union_set *uset);
1406 __isl_give isl_union_map *isl_union_map_detect_equalities(
1407 __isl_take isl_union_map *umap);
1409 Simplify the representation of a set or relation by detecting implicit
1414 __isl_give isl_basic_set *isl_set_convex_hull(
1415 __isl_take isl_set *set);
1416 __isl_give isl_basic_map *isl_map_convex_hull(
1417 __isl_take isl_map *map);
1419 If the input set or relation has any existentially quantified
1420 variables, then the result of these operations is currently undefined.
1424 __isl_give isl_basic_set *isl_set_simple_hull(
1425 __isl_take isl_set *set);
1426 __isl_give isl_basic_map *isl_map_simple_hull(
1427 __isl_take isl_map *map);
1428 __isl_give isl_union_map *isl_union_map_simple_hull(
1429 __isl_take isl_union_map *umap);
1431 These functions compute a single basic set or relation
1432 that contains the whole input set or relation.
1433 In particular, the output is described by translates
1434 of the constraints describing the basic sets or relations in the input.
1438 (See \autoref{s:simple hull}.)
1444 __isl_give isl_basic_set *isl_basic_set_affine_hull(
1445 __isl_take isl_basic_set *bset);
1446 __isl_give isl_basic_set *isl_set_affine_hull(
1447 __isl_take isl_set *set);
1448 __isl_give isl_union_set *isl_union_set_affine_hull(
1449 __isl_take isl_union_set *uset);
1450 __isl_give isl_basic_map *isl_basic_map_affine_hull(
1451 __isl_take isl_basic_map *bmap);
1452 __isl_give isl_basic_map *isl_map_affine_hull(
1453 __isl_take isl_map *map);
1454 __isl_give isl_union_map *isl_union_map_affine_hull(
1455 __isl_take isl_union_map *umap);
1457 In case of union sets and relations, the affine hull is computed
1460 =item * Polyhedral hull
1462 __isl_give isl_basic_set *isl_set_polyhedral_hull(
1463 __isl_take isl_set *set);
1464 __isl_give isl_basic_map *isl_map_polyhedral_hull(
1465 __isl_take isl_map *map);
1466 __isl_give isl_union_set *isl_union_set_polyhedral_hull(
1467 __isl_take isl_union_set *uset);
1468 __isl_give isl_union_map *isl_union_map_polyhedral_hull(
1469 __isl_take isl_union_map *umap);
1471 These functions compute a single basic set or relation
1472 not involving any existentially quantified variables
1473 that contains the whole input set or relation.
1474 In case of union sets and relations, the polyhedral hull is computed
1479 The following functions compute either the set of (rational) coefficient
1480 values of valid constraints for the given set or the set of (rational)
1481 values satisfying the constraints with coefficients from the given set.
1482 Internally, these two sets of functions perform essentially the
1483 same operations, except that the set of coefficients is assumed to
1484 be a cone, while the set of values may be any polyhedron.
1485 The current implementation is based on the Farkas lemma and
1486 Fourier-Motzkin elimination, but this may change or be made optional
1487 in future. In particular, future implementations may use different
1488 dualization algorithms or skip the elimination step.
1490 __isl_give isl_basic_set *isl_basic_set_coefficients(
1491 __isl_take isl_basic_set *bset);
1492 __isl_give isl_basic_set *isl_set_coefficients(
1493 __isl_take isl_set *set);
1494 __isl_give isl_union_set *isl_union_set_coefficients(
1495 __isl_take isl_union_set *bset);
1496 __isl_give isl_basic_set *isl_basic_set_solutions(
1497 __isl_take isl_basic_set *bset);
1498 __isl_give isl_basic_set *isl_set_solutions(
1499 __isl_take isl_set *set);
1500 __isl_give isl_union_set *isl_union_set_solutions(
1501 __isl_take isl_union_set *bset);
1505 __isl_give isl_map *isl_map_power(__isl_take isl_map *map,
1507 __isl_give isl_union_map *isl_union_map_power(
1508 __isl_take isl_union_map *umap, int *exact);
1510 Compute a parametric representation for all positive powers I<k> of C<map>.
1511 The result maps I<k> to a nested relation corresponding to the
1512 I<k>th power of C<map>.
1513 The result may be an overapproximation. If the result is known to be exact,
1514 then C<*exact> is set to C<1>.
1516 =item * Transitive closure
1518 __isl_give isl_map *isl_map_transitive_closure(
1519 __isl_take isl_map *map, int *exact);
1520 __isl_give isl_union_map *isl_union_map_transitive_closure(
1521 __isl_take isl_union_map *umap, int *exact);
1523 Compute the transitive closure of C<map>.
1524 The result may be an overapproximation. If the result is known to be exact,
1525 then C<*exact> is set to C<1>.
1527 =item * Reaching path lengths
1529 __isl_give isl_map *isl_map_reaching_path_lengths(
1530 __isl_take isl_map *map, int *exact);
1532 Compute a relation that maps each element in the range of C<map>
1533 to the lengths of all paths composed of edges in C<map> that
1534 end up in the given element.
1535 The result may be an overapproximation. If the result is known to be exact,
1536 then C<*exact> is set to C<1>.
1537 To compute the I<maximal> path length, the resulting relation
1538 should be postprocessed by C<isl_map_lexmax>.
1539 In particular, if the input relation is a dependence relation
1540 (mapping sources to sinks), then the maximal path length corresponds
1541 to the free schedule.
1542 Note, however, that C<isl_map_lexmax> expects the maximum to be
1543 finite, so if the path lengths are unbounded (possibly due to
1544 the overapproximation), then you will get an error message.
1548 __isl_give isl_basic_set *isl_basic_map_wrap(
1549 __isl_take isl_basic_map *bmap);
1550 __isl_give isl_set *isl_map_wrap(
1551 __isl_take isl_map *map);
1552 __isl_give isl_union_set *isl_union_map_wrap(
1553 __isl_take isl_union_map *umap);
1554 __isl_give isl_basic_map *isl_basic_set_unwrap(
1555 __isl_take isl_basic_set *bset);
1556 __isl_give isl_map *isl_set_unwrap(
1557 __isl_take isl_set *set);
1558 __isl_give isl_union_map *isl_union_set_unwrap(
1559 __isl_take isl_union_set *uset);
1563 Remove any internal structure of domain (and range) of the given
1564 set or relation. If there is any such internal structure in the input,
1565 then the name of the space is also removed.
1567 __isl_give isl_basic_set *isl_basic_set_flatten(
1568 __isl_take isl_basic_set *bset);
1569 __isl_give isl_set *isl_set_flatten(
1570 __isl_take isl_set *set);
1571 __isl_give isl_basic_map *isl_basic_map_flatten(
1572 __isl_take isl_basic_map *bmap);
1573 __isl_give isl_map *isl_map_flatten(
1574 __isl_take isl_map *map);
1576 __isl_give isl_map *isl_set_flatten_map(
1577 __isl_take isl_set *set);
1579 The function above constructs a relation
1580 that maps the input set to a flattened version of the set.
1584 Lift the input set to a space with extra dimensions corresponding
1585 to the existentially quantified variables in the input.
1586 In particular, the result lives in a wrapped map where the domain
1587 is the original space and the range corresponds to the original
1588 existentially quantified variables.
1590 __isl_give isl_basic_set *isl_basic_set_lift(
1591 __isl_take isl_basic_set *bset);
1592 __isl_give isl_set *isl_set_lift(
1593 __isl_take isl_set *set);
1594 __isl_give isl_union_set *isl_union_set_lift(
1595 __isl_take isl_union_set *uset);
1597 =item * Internal Product
1599 __isl_give isl_basic_map *isl_basic_map_zip(
1600 __isl_take isl_basic_map *bmap);
1601 __isl_give isl_map *isl_map_zip(
1602 __isl_take isl_map *map);
1603 __isl_give isl_union_map *isl_union_map_zip(
1604 __isl_take isl_union_map *umap);
1606 Given a relation with nested relations for domain and range,
1607 interchange the range of the domain with the domain of the range.
1609 =item * Dimension manipulation
1611 __isl_give isl_set *isl_set_add_dims(
1612 __isl_take isl_set *set,
1613 enum isl_dim_type type, unsigned n);
1614 __isl_give isl_map *isl_map_add_dims(
1615 __isl_take isl_map *map,
1616 enum isl_dim_type type, unsigned n);
1618 It is usually not advisable to directly change the (input or output)
1619 space of a set or a relation as this removes the name and the internal
1620 structure of the space. However, the above functions can be useful
1621 to add new parameters.
1625 =head2 Binary Operations
1627 The two arguments of a binary operation not only need to live
1628 in the same C<isl_ctx>, they currently also need to have
1629 the same (number of) parameters.
1631 =head3 Basic Operations
1635 =item * Intersection
1637 __isl_give isl_basic_set *isl_basic_set_intersect(
1638 __isl_take isl_basic_set *bset1,
1639 __isl_take isl_basic_set *bset2);
1640 __isl_give isl_set *isl_set_intersect(
1641 __isl_take isl_set *set1,
1642 __isl_take isl_set *set2);
1643 __isl_give isl_union_set *isl_union_set_intersect(
1644 __isl_take isl_union_set *uset1,
1645 __isl_take isl_union_set *uset2);
1646 __isl_give isl_basic_map *isl_basic_map_intersect_domain(
1647 __isl_take isl_basic_map *bmap,
1648 __isl_take isl_basic_set *bset);
1649 __isl_give isl_basic_map *isl_basic_map_intersect_range(
1650 __isl_take isl_basic_map *bmap,
1651 __isl_take isl_basic_set *bset);
1652 __isl_give isl_basic_map *isl_basic_map_intersect(
1653 __isl_take isl_basic_map *bmap1,
1654 __isl_take isl_basic_map *bmap2);
1655 __isl_give isl_map *isl_map_intersect_domain(
1656 __isl_take isl_map *map,
1657 __isl_take isl_set *set);
1658 __isl_give isl_map *isl_map_intersect_range(
1659 __isl_take isl_map *map,
1660 __isl_take isl_set *set);
1661 __isl_give isl_map *isl_map_intersect(
1662 __isl_take isl_map *map1,
1663 __isl_take isl_map *map2);
1664 __isl_give isl_union_map *isl_union_map_intersect_domain(
1665 __isl_take isl_union_map *umap,
1666 __isl_take isl_union_set *uset);
1667 __isl_give isl_union_map *isl_union_map_intersect_range(
1668 __isl_take isl_union_map *umap,
1669 __isl_take isl_union_set *uset);
1670 __isl_give isl_union_map *isl_union_map_intersect(
1671 __isl_take isl_union_map *umap1,
1672 __isl_take isl_union_map *umap2);
1676 __isl_give isl_set *isl_basic_set_union(
1677 __isl_take isl_basic_set *bset1,
1678 __isl_take isl_basic_set *bset2);
1679 __isl_give isl_map *isl_basic_map_union(
1680 __isl_take isl_basic_map *bmap1,
1681 __isl_take isl_basic_map *bmap2);
1682 __isl_give isl_set *isl_set_union(
1683 __isl_take isl_set *set1,
1684 __isl_take isl_set *set2);
1685 __isl_give isl_map *isl_map_union(
1686 __isl_take isl_map *map1,
1687 __isl_take isl_map *map2);
1688 __isl_give isl_union_set *isl_union_set_union(
1689 __isl_take isl_union_set *uset1,
1690 __isl_take isl_union_set *uset2);
1691 __isl_give isl_union_map *isl_union_map_union(
1692 __isl_take isl_union_map *umap1,
1693 __isl_take isl_union_map *umap2);
1695 =item * Set difference
1697 __isl_give isl_set *isl_set_subtract(
1698 __isl_take isl_set *set1,
1699 __isl_take isl_set *set2);
1700 __isl_give isl_map *isl_map_subtract(
1701 __isl_take isl_map *map1,
1702 __isl_take isl_map *map2);
1703 __isl_give isl_union_set *isl_union_set_subtract(
1704 __isl_take isl_union_set *uset1,
1705 __isl_take isl_union_set *uset2);
1706 __isl_give isl_union_map *isl_union_map_subtract(
1707 __isl_take isl_union_map *umap1,
1708 __isl_take isl_union_map *umap2);
1712 __isl_give isl_basic_set *isl_basic_set_apply(
1713 __isl_take isl_basic_set *bset,
1714 __isl_take isl_basic_map *bmap);
1715 __isl_give isl_set *isl_set_apply(
1716 __isl_take isl_set *set,
1717 __isl_take isl_map *map);
1718 __isl_give isl_union_set *isl_union_set_apply(
1719 __isl_take isl_union_set *uset,
1720 __isl_take isl_union_map *umap);
1721 __isl_give isl_basic_map *isl_basic_map_apply_domain(
1722 __isl_take isl_basic_map *bmap1,
1723 __isl_take isl_basic_map *bmap2);
1724 __isl_give isl_basic_map *isl_basic_map_apply_range(
1725 __isl_take isl_basic_map *bmap1,
1726 __isl_take isl_basic_map *bmap2);
1727 __isl_give isl_map *isl_map_apply_domain(
1728 __isl_take isl_map *map1,
1729 __isl_take isl_map *map2);
1730 __isl_give isl_union_map *isl_union_map_apply_domain(
1731 __isl_take isl_union_map *umap1,
1732 __isl_take isl_union_map *umap2);
1733 __isl_give isl_map *isl_map_apply_range(
1734 __isl_take isl_map *map1,
1735 __isl_take isl_map *map2);
1736 __isl_give isl_union_map *isl_union_map_apply_range(
1737 __isl_take isl_union_map *umap1,
1738 __isl_take isl_union_map *umap2);
1740 =item * Cartesian Product
1742 __isl_give isl_set *isl_set_product(
1743 __isl_take isl_set *set1,
1744 __isl_take isl_set *set2);
1745 __isl_give isl_union_set *isl_union_set_product(
1746 __isl_take isl_union_set *uset1,
1747 __isl_take isl_union_set *uset2);
1748 __isl_give isl_basic_map *isl_basic_map_range_product(
1749 __isl_take isl_basic_map *bmap1,
1750 __isl_take isl_basic_map *bmap2);
1751 __isl_give isl_map *isl_map_range_product(
1752 __isl_take isl_map *map1,
1753 __isl_take isl_map *map2);
1754 __isl_give isl_union_map *isl_union_map_range_product(
1755 __isl_take isl_union_map *umap1,
1756 __isl_take isl_union_map *umap2);
1757 __isl_give isl_map *isl_map_product(
1758 __isl_take isl_map *map1,
1759 __isl_take isl_map *map2);
1760 __isl_give isl_union_map *isl_union_map_product(
1761 __isl_take isl_union_map *umap1,
1762 __isl_take isl_union_map *umap2);
1764 The above functions compute the cross product of the given
1765 sets or relations. The domains and ranges of the results
1766 are wrapped maps between domains and ranges of the inputs.
1767 To obtain a ``flat'' product, use the following functions
1770 __isl_give isl_basic_set *isl_basic_set_flat_product(
1771 __isl_take isl_basic_set *bset1,
1772 __isl_take isl_basic_set *bset2);
1773 __isl_give isl_set *isl_set_flat_product(
1774 __isl_take isl_set *set1,
1775 __isl_take isl_set *set2);
1776 __isl_give isl_basic_map *isl_basic_map_flat_product(
1777 __isl_take isl_basic_map *bmap1,
1778 __isl_take isl_basic_map *bmap2);
1779 __isl_give isl_map *isl_map_flat_product(
1780 __isl_take isl_map *map1,
1781 __isl_take isl_map *map2);
1783 =item * Simplification
1785 __isl_give isl_basic_set *isl_basic_set_gist(
1786 __isl_take isl_basic_set *bset,
1787 __isl_take isl_basic_set *context);
1788 __isl_give isl_set *isl_set_gist(__isl_take isl_set *set,
1789 __isl_take isl_set *context);
1790 __isl_give isl_union_set *isl_union_set_gist(
1791 __isl_take isl_union_set *uset,
1792 __isl_take isl_union_set *context);
1793 __isl_give isl_basic_map *isl_basic_map_gist(
1794 __isl_take isl_basic_map *bmap,
1795 __isl_take isl_basic_map *context);
1796 __isl_give isl_map *isl_map_gist(__isl_take isl_map *map,
1797 __isl_take isl_map *context);
1798 __isl_give isl_union_map *isl_union_map_gist(
1799 __isl_take isl_union_map *umap,
1800 __isl_take isl_union_map *context);
1802 The gist operation returns a set or relation that has the
1803 same intersection with the context as the input set or relation.
1804 Any implicit equality in the intersection is made explicit in the result,
1805 while all inequalities that are redundant with respect to the intersection
1807 In case of union sets and relations, the gist operation is performed
1812 =head3 Lexicographic Optimization
1814 Given a (basic) set C<set> (or C<bset>) and a zero-dimensional domain C<dom>,
1815 the following functions
1816 compute a set that contains the lexicographic minimum or maximum
1817 of the elements in C<set> (or C<bset>) for those values of the parameters
1818 that satisfy C<dom>.
1819 If C<empty> is not C<NULL>, then C<*empty> is assigned a set
1820 that contains the parameter values in C<dom> for which C<set> (or C<bset>)
1822 In other words, the union of the parameter values
1823 for which the result is non-empty and of C<*empty>
1826 __isl_give isl_set *isl_basic_set_partial_lexmin(
1827 __isl_take isl_basic_set *bset,
1828 __isl_take isl_basic_set *dom,
1829 __isl_give isl_set **empty);
1830 __isl_give isl_set *isl_basic_set_partial_lexmax(
1831 __isl_take isl_basic_set *bset,
1832 __isl_take isl_basic_set *dom,
1833 __isl_give isl_set **empty);
1834 __isl_give isl_set *isl_set_partial_lexmin(
1835 __isl_take isl_set *set, __isl_take isl_set *dom,
1836 __isl_give isl_set **empty);
1837 __isl_give isl_set *isl_set_partial_lexmax(
1838 __isl_take isl_set *set, __isl_take isl_set *dom,
1839 __isl_give isl_set **empty);
1841 Given a (basic) set C<set> (or C<bset>), the following functions simply
1842 return a set containing the lexicographic minimum or maximum
1843 of the elements in C<set> (or C<bset>).
1844 In case of union sets, the optimum is computed per space.
1846 __isl_give isl_set *isl_basic_set_lexmin(
1847 __isl_take isl_basic_set *bset);
1848 __isl_give isl_set *isl_basic_set_lexmax(
1849 __isl_take isl_basic_set *bset);
1850 __isl_give isl_set *isl_set_lexmin(
1851 __isl_take isl_set *set);
1852 __isl_give isl_set *isl_set_lexmax(
1853 __isl_take isl_set *set);
1854 __isl_give isl_union_set *isl_union_set_lexmin(
1855 __isl_take isl_union_set *uset);
1856 __isl_give isl_union_set *isl_union_set_lexmax(
1857 __isl_take isl_union_set *uset);
1859 Given a (basic) relation C<map> (or C<bmap>) and a domain C<dom>,
1860 the following functions
1861 compute a relation that maps each element of C<dom>
1862 to the single lexicographic minimum or maximum
1863 of the elements that are associated to that same
1864 element in C<map> (or C<bmap>).
1865 If C<empty> is not C<NULL>, then C<*empty> is assigned a set
1866 that contains the elements in C<dom> that do not map
1867 to any elements in C<map> (or C<bmap>).
1868 In other words, the union of the domain of the result and of C<*empty>
1871 __isl_give isl_map *isl_basic_map_partial_lexmax(
1872 __isl_take isl_basic_map *bmap,
1873 __isl_take isl_basic_set *dom,
1874 __isl_give isl_set **empty);
1875 __isl_give isl_map *isl_basic_map_partial_lexmin(
1876 __isl_take isl_basic_map *bmap,
1877 __isl_take isl_basic_set *dom,
1878 __isl_give isl_set **empty);
1879 __isl_give isl_map *isl_map_partial_lexmax(
1880 __isl_take isl_map *map, __isl_take isl_set *dom,
1881 __isl_give isl_set **empty);
1882 __isl_give isl_map *isl_map_partial_lexmin(
1883 __isl_take isl_map *map, __isl_take isl_set *dom,
1884 __isl_give isl_set **empty);
1886 Given a (basic) map C<map> (or C<bmap>), the following functions simply
1887 return a map mapping each element in the domain of
1888 C<map> (or C<bmap>) to the lexicographic minimum or maximum
1889 of all elements associated to that element.
1890 In case of union relations, the optimum is computed per space.
1892 __isl_give isl_map *isl_basic_map_lexmin(
1893 __isl_take isl_basic_map *bmap);
1894 __isl_give isl_map *isl_basic_map_lexmax(
1895 __isl_take isl_basic_map *bmap);
1896 __isl_give isl_map *isl_map_lexmin(
1897 __isl_take isl_map *map);
1898 __isl_give isl_map *isl_map_lexmax(
1899 __isl_take isl_map *map);
1900 __isl_give isl_union_map *isl_union_map_lexmin(
1901 __isl_take isl_union_map *umap);
1902 __isl_give isl_union_map *isl_union_map_lexmax(
1903 __isl_take isl_union_map *umap);
1907 Matrices can be created, copied and freed using the following functions.
1909 #include <isl/mat.h>
1910 __isl_give isl_mat *isl_mat_alloc(struct isl_ctx *ctx,
1911 unsigned n_row, unsigned n_col);
1912 __isl_give isl_mat *isl_mat_copy(__isl_keep isl_mat *mat);
1913 void isl_mat_free(__isl_take isl_mat *mat);
1915 Note that the elements of a newly created matrix may have arbitrary values.
1916 The elements can be changed and inspected using the following functions.
1918 isl_ctx *isl_mat_get_ctx(__isl_keep isl_mat *mat);
1919 int isl_mat_rows(__isl_keep isl_mat *mat);
1920 int isl_mat_cols(__isl_keep isl_mat *mat);
1921 int isl_mat_get_element(__isl_keep isl_mat *mat,
1922 int row, int col, isl_int *v);
1923 __isl_give isl_mat *isl_mat_set_element(__isl_take isl_mat *mat,
1924 int row, int col, isl_int v);
1925 __isl_give isl_mat *isl_mat_set_element_si(__isl_take isl_mat *mat,
1926 int row, int col, int v);
1928 C<isl_mat_get_element> will return a negative value if anything went wrong.
1929 In that case, the value of C<*v> is undefined.
1931 The following function can be used to compute the (right) inverse
1932 of a matrix, i.e., a matrix such that the product of the original
1933 and the inverse (in that order) is a multiple of the identity matrix.
1934 The input matrix is assumed to be of full row-rank.
1936 __isl_give isl_mat *isl_mat_right_inverse(__isl_take isl_mat *mat);
1938 The following function can be used to compute the (right) kernel
1939 (or null space) of a matrix, i.e., a matrix such that the product of
1940 the original and the kernel (in that order) is the zero matrix.
1942 __isl_give isl_mat *isl_mat_right_kernel(__isl_take isl_mat *mat);
1946 Points are elements of a set. They can be used to construct
1947 simple sets (boxes) or they can be used to represent the
1948 individual elements of a set.
1949 The zero point (the origin) can be created using
1951 __isl_give isl_point *isl_point_zero(__isl_take isl_dim *dim);
1953 The coordinates of a point can be inspected, set and changed
1956 void isl_point_get_coordinate(__isl_keep isl_point *pnt,
1957 enum isl_dim_type type, int pos, isl_int *v);
1958 __isl_give isl_point *isl_point_set_coordinate(
1959 __isl_take isl_point *pnt,
1960 enum isl_dim_type type, int pos, isl_int v);
1962 __isl_give isl_point *isl_point_add_ui(
1963 __isl_take isl_point *pnt,
1964 enum isl_dim_type type, int pos, unsigned val);
1965 __isl_give isl_point *isl_point_sub_ui(
1966 __isl_take isl_point *pnt,
1967 enum isl_dim_type type, int pos, unsigned val);
1969 Points can be copied or freed using
1971 __isl_give isl_point *isl_point_copy(
1972 __isl_keep isl_point *pnt);
1973 void isl_point_free(__isl_take isl_point *pnt);
1975 A singleton set can be created from a point using
1977 __isl_give isl_basic_set *isl_basic_set_from_point(
1978 __isl_take isl_point *pnt);
1979 __isl_give isl_set *isl_set_from_point(
1980 __isl_take isl_point *pnt);
1982 and a box can be created from two opposite extremal points using
1984 __isl_give isl_basic_set *isl_basic_set_box_from_points(
1985 __isl_take isl_point *pnt1,
1986 __isl_take isl_point *pnt2);
1987 __isl_give isl_set *isl_set_box_from_points(
1988 __isl_take isl_point *pnt1,
1989 __isl_take isl_point *pnt2);
1991 All elements of a B<bounded> (union) set can be enumerated using
1992 the following functions.
1994 int isl_set_foreach_point(__isl_keep isl_set *set,
1995 int (*fn)(__isl_take isl_point *pnt, void *user),
1997 int isl_union_set_foreach_point(__isl_keep isl_union_set *uset,
1998 int (*fn)(__isl_take isl_point *pnt, void *user),
2001 The function C<fn> is called for each integer point in
2002 C<set> with as second argument the last argument of
2003 the C<isl_set_foreach_point> call. The function C<fn>
2004 should return C<0> on success and C<-1> on failure.
2005 In the latter case, C<isl_set_foreach_point> will stop
2006 enumerating and return C<-1> as well.
2007 If the enumeration is performed successfully and to completion,
2008 then C<isl_set_foreach_point> returns C<0>.
2010 To obtain a single point of a (basic) set, use
2012 __isl_give isl_point *isl_basic_set_sample_point(
2013 __isl_take isl_basic_set *bset);
2014 __isl_give isl_point *isl_set_sample_point(
2015 __isl_take isl_set *set);
2017 If C<set> does not contain any (integer) points, then the
2018 resulting point will be ``void'', a property that can be
2021 int isl_point_is_void(__isl_keep isl_point *pnt);
2023 =head2 Piecewise Quasipolynomials
2025 A piecewise quasipolynomial is a particular kind of function that maps
2026 a parametric point to a rational value.
2027 More specifically, a quasipolynomial is a polynomial expression in greatest
2028 integer parts of affine expressions of parameters and variables.
2029 A piecewise quasipolynomial is a subdivision of a given parametric
2030 domain into disjoint cells with a quasipolynomial associated to
2031 each cell. The value of the piecewise quasipolynomial at a given
2032 point is the value of the quasipolynomial associated to the cell
2033 that contains the point. Outside of the union of cells,
2034 the value is assumed to be zero.
2035 For example, the piecewise quasipolynomial
2037 [n] -> { [x] -> ((1 + n) - x) : x <= n and x >= 0 }
2039 maps C<x> to C<1 + n - x> for values of C<x> between C<0> and C<n>.
2040 A given piecewise quasipolynomial has a fixed domain dimension.
2041 Union piecewise quasipolynomials are used to contain piecewise quasipolynomials
2042 defined over different domains.
2043 Piecewise quasipolynomials are mainly used by the C<barvinok>
2044 library for representing the number of elements in a parametric set or map.
2045 For example, the piecewise quasipolynomial above represents
2046 the number of points in the map
2048 [n] -> { [x] -> [y] : x,y >= 0 and 0 <= x + y <= n }
2050 =head3 Printing (Piecewise) Quasipolynomials
2052 Quasipolynomials and piecewise quasipolynomials can be printed
2053 using the following functions.
2055 __isl_give isl_printer *isl_printer_print_qpolynomial(
2056 __isl_take isl_printer *p,
2057 __isl_keep isl_qpolynomial *qp);
2059 __isl_give isl_printer *isl_printer_print_pw_qpolynomial(
2060 __isl_take isl_printer *p,
2061 __isl_keep isl_pw_qpolynomial *pwqp);
2063 __isl_give isl_printer *isl_printer_print_union_pw_qpolynomial(
2064 __isl_take isl_printer *p,
2065 __isl_keep isl_union_pw_qpolynomial *upwqp);
2067 The output format of the printer
2068 needs to be set to either C<ISL_FORMAT_ISL> or C<ISL_FORMAT_C>.
2069 For C<isl_printer_print_union_pw_qpolynomial>, only C<ISL_FORMAT_ISL>
2071 In case of printing in C<ISL_FORMAT_C>, the user may want
2072 to set the names of all dimensions
2074 __isl_give isl_qpolynomial *isl_qpolynomial_set_dim_name(
2075 __isl_take isl_qpolynomial *qp,
2076 enum isl_dim_type type, unsigned pos,
2078 __isl_give isl_pw_qpolynomial *
2079 isl_pw_qpolynomial_set_dim_name(
2080 __isl_take isl_pw_qpolynomial *pwqp,
2081 enum isl_dim_type type, unsigned pos,
2084 =head3 Creating New (Piecewise) Quasipolynomials
2086 Some simple quasipolynomials can be created using the following functions.
2087 More complicated quasipolynomials can be created by applying
2088 operations such as addition and multiplication
2089 on the resulting quasipolynomials
2091 __isl_give isl_qpolynomial *isl_qpolynomial_zero(
2092 __isl_take isl_dim *dim);
2093 __isl_give isl_qpolynomial *isl_qpolynomial_one(
2094 __isl_take isl_dim *dim);
2095 __isl_give isl_qpolynomial *isl_qpolynomial_infty(
2096 __isl_take isl_dim *dim);
2097 __isl_give isl_qpolynomial *isl_qpolynomial_neginfty(
2098 __isl_take isl_dim *dim);
2099 __isl_give isl_qpolynomial *isl_qpolynomial_nan(
2100 __isl_take isl_dim *dim);
2101 __isl_give isl_qpolynomial *isl_qpolynomial_rat_cst(
2102 __isl_take isl_dim *dim,
2103 const isl_int n, const isl_int d);
2104 __isl_give isl_qpolynomial *isl_qpolynomial_div(
2105 __isl_take isl_div *div);
2106 __isl_give isl_qpolynomial *isl_qpolynomial_var(
2107 __isl_take isl_dim *dim,
2108 enum isl_dim_type type, unsigned pos);
2110 The zero piecewise quasipolynomial or a piecewise quasipolynomial
2111 with a single cell can be created using the following functions.
2112 Multiple of these single cell piecewise quasipolynomials can
2113 be combined to create more complicated piecewise quasipolynomials.
2115 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_zero(
2116 __isl_take isl_dim *dim);
2117 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_alloc(
2118 __isl_take isl_set *set,
2119 __isl_take isl_qpolynomial *qp);
2121 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_zero(
2122 __isl_take isl_dim *dim);
2123 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_from_pw_qpolynomial(
2124 __isl_take isl_pw_qpolynomial *pwqp);
2125 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_add_pw_qpolynomial(
2126 __isl_take isl_union_pw_qpolynomial *upwqp,
2127 __isl_take isl_pw_qpolynomial *pwqp);
2129 Quasipolynomials can be copied and freed again using the following
2132 __isl_give isl_qpolynomial *isl_qpolynomial_copy(
2133 __isl_keep isl_qpolynomial *qp);
2134 void isl_qpolynomial_free(__isl_take isl_qpolynomial *qp);
2136 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_copy(
2137 __isl_keep isl_pw_qpolynomial *pwqp);
2138 void isl_pw_qpolynomial_free(
2139 __isl_take isl_pw_qpolynomial *pwqp);
2141 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_copy(
2142 __isl_keep isl_union_pw_qpolynomial *upwqp);
2143 void isl_union_pw_qpolynomial_free(
2144 __isl_take isl_union_pw_qpolynomial *upwqp);
2146 =head3 Inspecting (Piecewise) Quasipolynomials
2148 To iterate over all piecewise quasipolynomials in a union
2149 piecewise quasipolynomial, use the following function
2151 int isl_union_pw_qpolynomial_foreach_pw_qpolynomial(
2152 __isl_keep isl_union_pw_qpolynomial *upwqp,
2153 int (*fn)(__isl_take isl_pw_qpolynomial *pwqp, void *user),
2156 To extract the piecewise quasipolynomial from a union with a given dimension
2159 __isl_give isl_pw_qpolynomial *
2160 isl_union_pw_qpolynomial_extract_pw_qpolynomial(
2161 __isl_keep isl_union_pw_qpolynomial *upwqp,
2162 __isl_take isl_dim *dim);
2164 To iterate over the cells in a piecewise quasipolynomial,
2165 use either of the following two functions
2167 int isl_pw_qpolynomial_foreach_piece(
2168 __isl_keep isl_pw_qpolynomial *pwqp,
2169 int (*fn)(__isl_take isl_set *set,
2170 __isl_take isl_qpolynomial *qp,
2171 void *user), void *user);
2172 int isl_pw_qpolynomial_foreach_lifted_piece(
2173 __isl_keep isl_pw_qpolynomial *pwqp,
2174 int (*fn)(__isl_take isl_set *set,
2175 __isl_take isl_qpolynomial *qp,
2176 void *user), void *user);
2178 As usual, the function C<fn> should return C<0> on success
2179 and C<-1> on failure. The difference between
2180 C<isl_pw_qpolynomial_foreach_piece> and
2181 C<isl_pw_qpolynomial_foreach_lifted_piece> is that
2182 C<isl_pw_qpolynomial_foreach_lifted_piece> will first
2183 compute unique representations for all existentially quantified
2184 variables and then turn these existentially quantified variables
2185 into extra set variables, adapting the associated quasipolynomial
2186 accordingly. This means that the C<set> passed to C<fn>
2187 will not have any existentially quantified variables, but that
2188 the dimensions of the sets may be different for different
2189 invocations of C<fn>.
2191 To iterate over all terms in a quasipolynomial,
2194 int isl_qpolynomial_foreach_term(
2195 __isl_keep isl_qpolynomial *qp,
2196 int (*fn)(__isl_take isl_term *term,
2197 void *user), void *user);
2199 The terms themselves can be inspected and freed using
2202 unsigned isl_term_dim(__isl_keep isl_term *term,
2203 enum isl_dim_type type);
2204 void isl_term_get_num(__isl_keep isl_term *term,
2206 void isl_term_get_den(__isl_keep isl_term *term,
2208 int isl_term_get_exp(__isl_keep isl_term *term,
2209 enum isl_dim_type type, unsigned pos);
2210 __isl_give isl_div *isl_term_get_div(
2211 __isl_keep isl_term *term, unsigned pos);
2212 void isl_term_free(__isl_take isl_term *term);
2214 Each term is a product of parameters, set variables and
2215 integer divisions. The function C<isl_term_get_exp>
2216 returns the exponent of a given dimensions in the given term.
2217 The C<isl_int>s in the arguments of C<isl_term_get_num>
2218 and C<isl_term_get_den> need to have been initialized
2219 using C<isl_int_init> before calling these functions.
2221 =head3 Properties of (Piecewise) Quasipolynomials
2223 To check whether a quasipolynomial is actually a constant,
2224 use the following function.
2226 int isl_qpolynomial_is_cst(__isl_keep isl_qpolynomial *qp,
2227 isl_int *n, isl_int *d);
2229 If C<qp> is a constant and if C<n> and C<d> are not C<NULL>
2230 then the numerator and denominator of the constant
2231 are returned in C<*n> and C<*d>, respectively.
2233 =head3 Operations on (Piecewise) Quasipolynomials
2235 __isl_give isl_qpolynomial *isl_qpolynomial_neg(
2236 __isl_take isl_qpolynomial *qp);
2237 __isl_give isl_qpolynomial *isl_qpolynomial_add(
2238 __isl_take isl_qpolynomial *qp1,
2239 __isl_take isl_qpolynomial *qp2);
2240 __isl_give isl_qpolynomial *isl_qpolynomial_sub(
2241 __isl_take isl_qpolynomial *qp1,
2242 __isl_take isl_qpolynomial *qp2);
2243 __isl_give isl_qpolynomial *isl_qpolynomial_mul(
2244 __isl_take isl_qpolynomial *qp1,
2245 __isl_take isl_qpolynomial *qp2);
2246 __isl_give isl_qpolynomial *isl_qpolynomial_pow(
2247 __isl_take isl_qpolynomial *qp, unsigned exponent);
2249 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_add(
2250 __isl_take isl_pw_qpolynomial *pwqp1,
2251 __isl_take isl_pw_qpolynomial *pwqp2);
2252 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_sub(
2253 __isl_take isl_pw_qpolynomial *pwqp1,
2254 __isl_take isl_pw_qpolynomial *pwqp2);
2255 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_add_disjoint(
2256 __isl_take isl_pw_qpolynomial *pwqp1,
2257 __isl_take isl_pw_qpolynomial *pwqp2);
2258 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_neg(
2259 __isl_take isl_pw_qpolynomial *pwqp);
2260 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_mul(
2261 __isl_take isl_pw_qpolynomial *pwqp1,
2262 __isl_take isl_pw_qpolynomial *pwqp2);
2264 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_add(
2265 __isl_take isl_union_pw_qpolynomial *upwqp1,
2266 __isl_take isl_union_pw_qpolynomial *upwqp2);
2267 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_sub(
2268 __isl_take isl_union_pw_qpolynomial *upwqp1,
2269 __isl_take isl_union_pw_qpolynomial *upwqp2);
2270 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_mul(
2271 __isl_take isl_union_pw_qpolynomial *upwqp1,
2272 __isl_take isl_union_pw_qpolynomial *upwqp2);
2274 __isl_give isl_qpolynomial *isl_pw_qpolynomial_eval(
2275 __isl_take isl_pw_qpolynomial *pwqp,
2276 __isl_take isl_point *pnt);
2278 __isl_give isl_qpolynomial *isl_union_pw_qpolynomial_eval(
2279 __isl_take isl_union_pw_qpolynomial *upwqp,
2280 __isl_take isl_point *pnt);
2282 __isl_give isl_set *isl_pw_qpolynomial_domain(
2283 __isl_take isl_pw_qpolynomial *pwqp);
2284 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_intersect_domain(
2285 __isl_take isl_pw_qpolynomial *pwpq,
2286 __isl_take isl_set *set);
2288 __isl_give isl_union_set *isl_union_pw_qpolynomial_domain(
2289 __isl_take isl_union_pw_qpolynomial *upwqp);
2290 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_intersect_domain(
2291 __isl_take isl_union_pw_qpolynomial *upwpq,
2292 __isl_take isl_union_set *uset);
2294 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_coalesce(
2295 __isl_take isl_union_pw_qpolynomial *upwqp);
2297 __isl_give isl_qpolynomial *isl_qpolynomial_gist(
2298 __isl_take isl_qpolynomial *qp,
2299 __isl_take isl_set *context);
2301 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_gist(
2302 __isl_take isl_pw_qpolynomial *pwqp,
2303 __isl_take isl_set *context);
2305 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_gist(
2306 __isl_take isl_union_pw_qpolynomial *upwqp,
2307 __isl_take isl_union_set *context);
2309 The gist operation applies the gist operation to each of
2310 the cells in the domain of the input piecewise quasipolynomial.
2311 The context is also exploited
2312 to simplify the quasipolynomials associated to each cell.
2314 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_to_polynomial(
2315 __isl_take isl_pw_qpolynomial *pwqp, int sign);
2316 __isl_give isl_union_pw_qpolynomial *
2317 isl_union_pw_qpolynomial_to_polynomial(
2318 __isl_take isl_union_pw_qpolynomial *upwqp, int sign);
2320 Approximate each quasipolynomial by a polynomial. If C<sign> is positive,
2321 the polynomial will be an overapproximation. If C<sign> is negative,
2322 it will be an underapproximation. If C<sign> is zero, the approximation
2323 will lie somewhere in between.
2325 =head2 Bounds on Piecewise Quasipolynomials and Piecewise Quasipolynomial Reductions
2327 A piecewise quasipolynomial reduction is a piecewise
2328 reduction (or fold) of quasipolynomials.
2329 In particular, the reduction can be maximum or a minimum.
2330 The objects are mainly used to represent the result of
2331 an upper or lower bound on a quasipolynomial over its domain,
2332 i.e., as the result of the following function.
2334 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_bound(
2335 __isl_take isl_pw_qpolynomial *pwqp,
2336 enum isl_fold type, int *tight);
2338 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_bound(
2339 __isl_take isl_union_pw_qpolynomial *upwqp,
2340 enum isl_fold type, int *tight);
2342 The C<type> argument may be either C<isl_fold_min> or C<isl_fold_max>.
2343 If C<tight> is not C<NULL>, then C<*tight> is set to C<1>
2344 is the returned bound is known be tight, i.e., for each value
2345 of the parameters there is at least
2346 one element in the domain that reaches the bound.
2347 If the domain of C<pwqp> is not wrapping, then the bound is computed
2348 over all elements in that domain and the result has a purely parametric
2349 domain. If the domain of C<pwqp> is wrapping, then the bound is
2350 computed over the range of the wrapped relation. The domain of the
2351 wrapped relation becomes the domain of the result.
2353 A (piecewise) quasipolynomial reduction can be copied or freed using the
2354 following functions.
2356 __isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_copy(
2357 __isl_keep isl_qpolynomial_fold *fold);
2358 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_copy(
2359 __isl_keep isl_pw_qpolynomial_fold *pwf);
2360 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_copy(
2361 __isl_keep isl_union_pw_qpolynomial_fold *upwf);
2362 void isl_qpolynomial_fold_free(
2363 __isl_take isl_qpolynomial_fold *fold);
2364 void isl_pw_qpolynomial_fold_free(
2365 __isl_take isl_pw_qpolynomial_fold *pwf);
2366 void isl_union_pw_qpolynomial_fold_free(
2367 __isl_take isl_union_pw_qpolynomial_fold *upwf);
2369 =head3 Printing Piecewise Quasipolynomial Reductions
2371 Piecewise quasipolynomial reductions can be printed
2372 using the following function.
2374 __isl_give isl_printer *isl_printer_print_pw_qpolynomial_fold(
2375 __isl_take isl_printer *p,
2376 __isl_keep isl_pw_qpolynomial_fold *pwf);
2377 __isl_give isl_printer *isl_printer_print_union_pw_qpolynomial_fold(
2378 __isl_take isl_printer *p,
2379 __isl_keep isl_union_pw_qpolynomial_fold *upwf);
2381 For C<isl_printer_print_pw_qpolynomial_fold>,
2382 output format of the printer
2383 needs to be set to either C<ISL_FORMAT_ISL> or C<ISL_FORMAT_C>.
2384 For C<isl_printer_print_union_pw_qpolynomial_fold>,
2385 output format of the printer
2386 needs to be set to C<ISL_FORMAT_ISL>.
2387 In case of printing in C<ISL_FORMAT_C>, the user may want
2388 to set the names of all dimensions
2390 __isl_give isl_pw_qpolynomial_fold *
2391 isl_pw_qpolynomial_fold_set_dim_name(
2392 __isl_take isl_pw_qpolynomial_fold *pwf,
2393 enum isl_dim_type type, unsigned pos,
2396 =head3 Inspecting (Piecewise) Quasipolynomial Reductions
2398 To iterate over all piecewise quasipolynomial reductions in a union
2399 piecewise quasipolynomial reduction, use the following function
2401 int isl_union_pw_qpolynomial_fold_foreach_pw_qpolynomial_fold(
2402 __isl_keep isl_union_pw_qpolynomial_fold *upwf,
2403 int (*fn)(__isl_take isl_pw_qpolynomial_fold *pwf,
2404 void *user), void *user);
2406 To iterate over the cells in a piecewise quasipolynomial reduction,
2407 use either of the following two functions
2409 int isl_pw_qpolynomial_fold_foreach_piece(
2410 __isl_keep isl_pw_qpolynomial_fold *pwf,
2411 int (*fn)(__isl_take isl_set *set,
2412 __isl_take isl_qpolynomial_fold *fold,
2413 void *user), void *user);
2414 int isl_pw_qpolynomial_fold_foreach_lifted_piece(
2415 __isl_keep isl_pw_qpolynomial_fold *pwf,
2416 int (*fn)(__isl_take isl_set *set,
2417 __isl_take isl_qpolynomial_fold *fold,
2418 void *user), void *user);
2420 See L<Inspecting (Piecewise) Quasipolynomials> for an explanation
2421 of the difference between these two functions.
2423 To iterate over all quasipolynomials in a reduction, use
2425 int isl_qpolynomial_fold_foreach_qpolynomial(
2426 __isl_keep isl_qpolynomial_fold *fold,
2427 int (*fn)(__isl_take isl_qpolynomial *qp,
2428 void *user), void *user);
2430 =head3 Operations on Piecewise Quasipolynomial Reductions
2432 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_add(
2433 __isl_take isl_pw_qpolynomial_fold *pwf1,
2434 __isl_take isl_pw_qpolynomial_fold *pwf2);
2436 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_fold(
2437 __isl_take isl_pw_qpolynomial_fold *pwf1,
2438 __isl_take isl_pw_qpolynomial_fold *pwf2);
2440 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_fold(
2441 __isl_take isl_union_pw_qpolynomial_fold *upwf1,
2442 __isl_take isl_union_pw_qpolynomial_fold *upwf2);
2444 __isl_give isl_qpolynomial *isl_pw_qpolynomial_fold_eval(
2445 __isl_take isl_pw_qpolynomial_fold *pwf,
2446 __isl_take isl_point *pnt);
2448 __isl_give isl_qpolynomial *isl_union_pw_qpolynomial_fold_eval(
2449 __isl_take isl_union_pw_qpolynomial_fold *upwf,
2450 __isl_take isl_point *pnt);
2452 __isl_give isl_union_set *isl_union_pw_qpolynomial_fold_domain(
2453 __isl_take isl_union_pw_qpolynomial_fold *upwf);
2454 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_intersect_domain(
2455 __isl_take isl_union_pw_qpolynomial_fold *upwf,
2456 __isl_take isl_union_set *uset);
2458 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_coalesce(
2459 __isl_take isl_pw_qpolynomial_fold *pwf);
2461 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_coalesce(
2462 __isl_take isl_union_pw_qpolynomial_fold *upwf);
2464 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_gist(
2465 __isl_take isl_pw_qpolynomial_fold *pwf,
2466 __isl_take isl_set *context);
2468 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_gist(
2469 __isl_take isl_union_pw_qpolynomial_fold *upwf,
2470 __isl_take isl_union_set *context);
2472 The gist operation applies the gist operation to each of
2473 the cells in the domain of the input piecewise quasipolynomial reduction.
2474 In future, the operation will also exploit the context
2475 to simplify the quasipolynomial reductions associated to each cell.
2477 __isl_give isl_pw_qpolynomial_fold *
2478 isl_set_apply_pw_qpolynomial_fold(
2479 __isl_take isl_set *set,
2480 __isl_take isl_pw_qpolynomial_fold *pwf,
2482 __isl_give isl_pw_qpolynomial_fold *
2483 isl_map_apply_pw_qpolynomial_fold(
2484 __isl_take isl_map *map,
2485 __isl_take isl_pw_qpolynomial_fold *pwf,
2487 __isl_give isl_union_pw_qpolynomial_fold *
2488 isl_union_set_apply_union_pw_qpolynomial_fold(
2489 __isl_take isl_union_set *uset,
2490 __isl_take isl_union_pw_qpolynomial_fold *upwf,
2492 __isl_give isl_union_pw_qpolynomial_fold *
2493 isl_union_map_apply_union_pw_qpolynomial_fold(
2494 __isl_take isl_union_map *umap,
2495 __isl_take isl_union_pw_qpolynomial_fold *upwf,
2498 The functions taking a map
2499 compose the given map with the given piecewise quasipolynomial reduction.
2500 That is, compute a bound (of the same type as C<pwf> or C<upwf> itself)
2501 over all elements in the intersection of the range of the map
2502 and the domain of the piecewise quasipolynomial reduction
2503 as a function of an element in the domain of the map.
2504 The functions taking a set compute a bound over all elements in the
2505 intersection of the set and the domain of the
2506 piecewise quasipolynomial reduction.
2508 =head2 Dependence Analysis
2510 C<isl> contains specialized functionality for performing
2511 array dataflow analysis. That is, given a I<sink> access relation
2512 and a collection of possible I<source> access relations,
2513 C<isl> can compute relations that describe
2514 for each iteration of the sink access, which iteration
2515 of which of the source access relations was the last
2516 to access the same data element before the given iteration
2518 To compute standard flow dependences, the sink should be
2519 a read, while the sources should be writes.
2520 If any of the source accesses are marked as being I<may>
2521 accesses, then there will be a dependence to the last
2522 I<must> access B<and> to any I<may> access that follows
2523 this last I<must> access.
2524 In particular, if I<all> sources are I<may> accesses,
2525 then memory based dependence analysis is performed.
2526 If, on the other hand, all sources are I<must> accesses,
2527 then value based dependence analysis is performed.
2529 #include <isl/flow.h>
2531 typedef int (*isl_access_level_before)(void *first, void *second);
2533 __isl_give isl_access_info *isl_access_info_alloc(
2534 __isl_take isl_map *sink,
2535 void *sink_user, isl_access_level_before fn,
2537 __isl_give isl_access_info *isl_access_info_add_source(
2538 __isl_take isl_access_info *acc,
2539 __isl_take isl_map *source, int must,
2541 void isl_access_info_free(__isl_take isl_access_info *acc);
2543 __isl_give isl_flow *isl_access_info_compute_flow(
2544 __isl_take isl_access_info *acc);
2546 int isl_flow_foreach(__isl_keep isl_flow *deps,
2547 int (*fn)(__isl_take isl_map *dep, int must,
2548 void *dep_user, void *user),
2550 __isl_give isl_map *isl_flow_get_no_source(
2551 __isl_keep isl_flow *deps, int must);
2552 void isl_flow_free(__isl_take isl_flow *deps);
2554 The function C<isl_access_info_compute_flow> performs the actual
2555 dependence analysis. The other functions are used to construct
2556 the input for this function or to read off the output.
2558 The input is collected in an C<isl_access_info>, which can
2559 be created through a call to C<isl_access_info_alloc>.
2560 The arguments to this functions are the sink access relation
2561 C<sink>, a token C<sink_user> used to identify the sink
2562 access to the user, a callback function for specifying the
2563 relative order of source and sink accesses, and the number
2564 of source access relations that will be added.
2565 The callback function has type C<int (*)(void *first, void *second)>.
2566 The function is called with two user supplied tokens identifying
2567 either a source or the sink and it should return the shared nesting
2568 level and the relative order of the two accesses.
2569 In particular, let I<n> be the number of loops shared by
2570 the two accesses. If C<first> precedes C<second> textually,
2571 then the function should return I<2 * n + 1>; otherwise,
2572 it should return I<2 * n>.
2573 The sources can be added to the C<isl_access_info> by performing
2574 (at most) C<max_source> calls to C<isl_access_info_add_source>.
2575 C<must> indicates whether the source is a I<must> access
2576 or a I<may> access. Note that a multi-valued access relation
2577 should only be marked I<must> if every iteration in the domain
2578 of the relation accesses I<all> elements in its image.
2579 The C<source_user> token is again used to identify
2580 the source access. The range of the source access relation
2581 C<source> should have the same dimension as the range
2582 of the sink access relation.
2583 The C<isl_access_info_free> function should usually not be
2584 called explicitly, because it is called implicitly by
2585 C<isl_access_info_compute_flow>.
2587 The result of the dependence analysis is collected in an
2588 C<isl_flow>. There may be elements of
2589 the sink access for which no preceding source access could be
2590 found or for which all preceding sources are I<may> accesses.
2591 The relations containing these elements can be obtained through
2592 calls to C<isl_flow_get_no_source>, the first with C<must> set
2593 and the second with C<must> unset.
2594 In the case of standard flow dependence analysis,
2595 with the sink a read and the sources I<must> writes,
2596 the first relation corresponds to the reads from uninitialized
2597 array elements and the second relation is empty.
2598 The actual flow dependences can be extracted using
2599 C<isl_flow_foreach>. This function will call the user-specified
2600 callback function C<fn> for each B<non-empty> dependence between
2601 a source and the sink. The callback function is called
2602 with four arguments, the actual flow dependence relation
2603 mapping source iterations to sink iterations, a boolean that
2604 indicates whether it is a I<must> or I<may> dependence, a token
2605 identifying the source and an additional C<void *> with value
2606 equal to the third argument of the C<isl_flow_foreach> call.
2607 A dependence is marked I<must> if it originates from a I<must>
2608 source and if it is not followed by any I<may> sources.
2610 After finishing with an C<isl_flow>, the user should call
2611 C<isl_flow_free> to free all associated memory.
2613 A higher-level interface to dependence analysis is provided
2614 by the following function.
2616 #include <isl/flow.h>
2618 int isl_union_map_compute_flow(__isl_take isl_union_map *sink,
2619 __isl_take isl_union_map *must_source,
2620 __isl_take isl_union_map *may_source,
2621 __isl_take isl_union_map *schedule,
2622 __isl_give isl_union_map **must_dep,
2623 __isl_give isl_union_map **may_dep,
2624 __isl_give isl_union_map **must_no_source,
2625 __isl_give isl_union_map **may_no_source);
2627 The arrays are identified by the tuple names of the ranges
2628 of the accesses. The iteration domains by the tuple names
2629 of the domains of the accesses and of the schedule.
2630 The relative order of the iteration domains is given by the
2631 schedule. The relations returned through C<must_no_source>
2632 and C<may_no_source> are subsets of C<sink>.
2633 Any of C<must_dep>, C<may_dep>, C<must_no_source>
2634 or C<may_no_source> may be C<NULL>, but a C<NULL> value for
2635 any of the other arguments is treated as an error.
2639 B<The functionality described in this section is fairly new
2640 and may be subject to change.>
2642 The following function can be used to compute a schedule
2643 for a union of domains. The generated schedule respects
2644 all C<validity> dependences. That is, all dependence distances
2645 over these dependences in the scheduled space are lexicographically
2646 positive. The generated schedule schedule also tries to minimize
2647 the dependence distances over C<proximity> dependences.
2648 Moreover, it tries to obtain sequences (bands) of schedule dimensions
2649 for groups of domains where the dependence distances have only
2650 non-negative values.
2651 The algorithm used to construct the schedule is similar to that
2654 #include <isl/schedule.h>
2655 __isl_give isl_schedule *isl_union_set_compute_schedule(
2656 __isl_take isl_union_set *domain,
2657 __isl_take isl_union_map *validity,
2658 __isl_take isl_union_map *proximity);
2659 void *isl_schedule_free(__isl_take isl_schedule *sched);
2661 A mapping from the domains to the scheduled space can be obtained
2662 from an C<isl_schedule> using the following function.
2664 __isl_give isl_union_map *isl_schedule_get_map(
2665 __isl_keep isl_schedule *sched);
2667 This mapping can also be obtained in pieces using the following functions.
2669 int isl_schedule_n_band(__isl_keep isl_schedule *sched);
2670 __isl_give isl_union_map *isl_schedule_get_band(
2671 __isl_keep isl_schedule *sched, unsigned band);
2673 C<isl_schedule_n_band> returns the maximal number of bands.
2674 C<isl_schedule_get_band> returns a union of mappings from a domain to
2675 the band of consecutive schedule dimensions with the given sequence
2676 number for that domain. Bands with the same sequence number but for
2677 different domains may be completely unrelated.
2678 Within a band, the corresponding coordinates of the distance vectors
2679 are all non-negative, assuming that the coordinates for all previous
2682 =head2 Parametric Vertex Enumeration
2684 The parametric vertex enumeration described in this section
2685 is mainly intended to be used internally and by the C<barvinok>
2688 #include <isl/vertices.h>
2689 __isl_give isl_vertices *isl_basic_set_compute_vertices(
2690 __isl_keep isl_basic_set *bset);
2692 The function C<isl_basic_set_compute_vertices> performs the
2693 actual computation of the parametric vertices and the chamber
2694 decomposition and store the result in an C<isl_vertices> object.
2695 This information can be queried by either iterating over all
2696 the vertices or iterating over all the chambers or cells
2697 and then iterating over all vertices that are active on the chamber.
2699 int isl_vertices_foreach_vertex(
2700 __isl_keep isl_vertices *vertices,
2701 int (*fn)(__isl_take isl_vertex *vertex, void *user),
2704 int isl_vertices_foreach_cell(
2705 __isl_keep isl_vertices *vertices,
2706 int (*fn)(__isl_take isl_cell *cell, void *user),
2708 int isl_cell_foreach_vertex(__isl_keep isl_cell *cell,
2709 int (*fn)(__isl_take isl_vertex *vertex, void *user),
2712 Other operations that can be performed on an C<isl_vertices> object are
2715 isl_ctx *isl_vertices_get_ctx(
2716 __isl_keep isl_vertices *vertices);
2717 int isl_vertices_get_n_vertices(
2718 __isl_keep isl_vertices *vertices);
2719 void isl_vertices_free(__isl_take isl_vertices *vertices);
2721 Vertices can be inspected and destroyed using the following functions.
2723 isl_ctx *isl_vertex_get_ctx(__isl_keep isl_vertex *vertex);
2724 int isl_vertex_get_id(__isl_keep isl_vertex *vertex);
2725 __isl_give isl_basic_set *isl_vertex_get_domain(
2726 __isl_keep isl_vertex *vertex);
2727 __isl_give isl_basic_set *isl_vertex_get_expr(
2728 __isl_keep isl_vertex *vertex);
2729 void isl_vertex_free(__isl_take isl_vertex *vertex);
2731 C<isl_vertex_get_expr> returns a singleton parametric set describing
2732 the vertex, while C<isl_vertex_get_domain> returns the activity domain
2734 Note that C<isl_vertex_get_domain> and C<isl_vertex_get_expr> return
2735 B<rational> basic sets, so they should mainly be used for inspection
2736 and should not be mixed with integer sets.
2738 Chambers can be inspected and destroyed using the following functions.
2740 isl_ctx *isl_cell_get_ctx(__isl_keep isl_cell *cell);
2741 __isl_give isl_basic_set *isl_cell_get_domain(
2742 __isl_keep isl_cell *cell);
2743 void isl_cell_free(__isl_take isl_cell *cell);
2747 Although C<isl> is mainly meant to be used as a library,
2748 it also contains some basic applications that use some
2749 of the functionality of C<isl>.
2750 The input may be specified in either the L<isl format>
2751 or the L<PolyLib format>.
2753 =head2 C<isl_polyhedron_sample>
2755 C<isl_polyhedron_sample> takes a polyhedron as input and prints
2756 an integer element of the polyhedron, if there is any.
2757 The first column in the output is the denominator and is always
2758 equal to 1. If the polyhedron contains no integer points,
2759 then a vector of length zero is printed.
2763 C<isl_pip> takes the same input as the C<example> program
2764 from the C<piplib> distribution, i.e., a set of constraints
2765 on the parameters, a line containing only -1 and finally a set
2766 of constraints on a parametric polyhedron.
2767 The coefficients of the parameters appear in the last columns
2768 (but before the final constant column).
2769 The output is the lexicographic minimum of the parametric polyhedron.
2770 As C<isl> currently does not have its own output format, the output
2771 is just a dump of the internal state.
2773 =head2 C<isl_polyhedron_minimize>
2775 C<isl_polyhedron_minimize> computes the minimum of some linear
2776 or affine objective function over the integer points in a polyhedron.
2777 If an affine objective function
2778 is given, then the constant should appear in the last column.
2780 =head2 C<isl_polytope_scan>
2782 Given a polytope, C<isl_polytope_scan> prints
2783 all integer points in the polytope.