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_map *isl_set_identity(
1345 __isl_take isl_set *set);
1346 __isl_give isl_union_map *isl_union_set_identity(
1347 __isl_take isl_union_set *uset);
1349 Construct an identity relation on the given (union) set.
1353 __isl_give isl_basic_set *isl_basic_map_deltas(
1354 __isl_take isl_basic_map *bmap);
1355 __isl_give isl_set *isl_map_deltas(__isl_take isl_map *map);
1356 __isl_give isl_union_set *isl_union_map_deltas(
1357 __isl_take isl_union_map *umap);
1359 These functions return a (basic) set containing the differences
1360 between image elements and corresponding domain elements in the input.
1362 __isl_give isl_basic_map *isl_basic_map_deltas_map(
1363 __isl_take isl_basic_map *bmap);
1364 __isl_give isl_map *isl_map_deltas_map(
1365 __isl_take isl_map *map);
1366 __isl_give isl_union_map *isl_union_map_deltas_map(
1367 __isl_take isl_union_map *umap);
1369 The functions above construct a (basic, regular or union) relation
1370 that maps (a wrapped version of) the input relation to its delta set.
1374 Simplify the representation of a set or relation by trying
1375 to combine pairs of basic sets or relations into a single
1376 basic set or relation.
1378 __isl_give isl_set *isl_set_coalesce(__isl_take isl_set *set);
1379 __isl_give isl_map *isl_map_coalesce(__isl_take isl_map *map);
1380 __isl_give isl_union_set *isl_union_set_coalesce(
1381 __isl_take isl_union_set *uset);
1382 __isl_give isl_union_map *isl_union_map_coalesce(
1383 __isl_take isl_union_map *umap);
1385 =item * Detecting equalities
1387 __isl_give isl_basic_set *isl_basic_set_detect_equalities(
1388 __isl_take isl_basic_set *bset);
1389 __isl_give isl_basic_map *isl_basic_map_detect_equalities(
1390 __isl_take isl_basic_map *bmap);
1391 __isl_give isl_set *isl_set_detect_equalities(
1392 __isl_take isl_set *set);
1393 __isl_give isl_map *isl_map_detect_equalities(
1394 __isl_take isl_map *map);
1395 __isl_give isl_union_set *isl_union_set_detect_equalities(
1396 __isl_take isl_union_set *uset);
1397 __isl_give isl_union_map *isl_union_map_detect_equalities(
1398 __isl_take isl_union_map *umap);
1400 Simplify the representation of a set or relation by detecting implicit
1405 __isl_give isl_basic_set *isl_set_convex_hull(
1406 __isl_take isl_set *set);
1407 __isl_give isl_basic_map *isl_map_convex_hull(
1408 __isl_take isl_map *map);
1410 If the input set or relation has any existentially quantified
1411 variables, then the result of these operations is currently undefined.
1415 __isl_give isl_basic_set *isl_set_simple_hull(
1416 __isl_take isl_set *set);
1417 __isl_give isl_basic_map *isl_map_simple_hull(
1418 __isl_take isl_map *map);
1419 __isl_give isl_union_map *isl_union_map_simple_hull(
1420 __isl_take isl_union_map *umap);
1422 These functions compute a single basic set or relation
1423 that contains the whole input set or relation.
1424 In particular, the output is described by translates
1425 of the constraints describing the basic sets or relations in the input.
1429 (See \autoref{s:simple hull}.)
1435 __isl_give isl_basic_set *isl_basic_set_affine_hull(
1436 __isl_take isl_basic_set *bset);
1437 __isl_give isl_basic_set *isl_set_affine_hull(
1438 __isl_take isl_set *set);
1439 __isl_give isl_union_set *isl_union_set_affine_hull(
1440 __isl_take isl_union_set *uset);
1441 __isl_give isl_basic_map *isl_basic_map_affine_hull(
1442 __isl_take isl_basic_map *bmap);
1443 __isl_give isl_basic_map *isl_map_affine_hull(
1444 __isl_take isl_map *map);
1445 __isl_give isl_union_map *isl_union_map_affine_hull(
1446 __isl_take isl_union_map *umap);
1448 In case of union sets and relations, the affine hull is computed
1451 =item * Polyhedral hull
1453 __isl_give isl_basic_set *isl_set_polyhedral_hull(
1454 __isl_take isl_set *set);
1455 __isl_give isl_basic_map *isl_map_polyhedral_hull(
1456 __isl_take isl_map *map);
1457 __isl_give isl_union_set *isl_union_set_polyhedral_hull(
1458 __isl_take isl_union_set *uset);
1459 __isl_give isl_union_map *isl_union_map_polyhedral_hull(
1460 __isl_take isl_union_map *umap);
1462 These functions compute a single basic set or relation
1463 not involving any existentially quantified variables
1464 that contains the whole input set or relation.
1465 In case of union sets and relations, the polyhedral hull is computed
1470 The following functions compute either the set of (rational) coefficient
1471 values of valid constraints for the given set or the set of (rational)
1472 values satisfying the constraints with coefficients from the given set.
1473 Internally, these two sets of functions perform essentially the
1474 same operations, except that the set of coefficients is assumed to
1475 be a cone, while the set of values may be any polyhedron.
1476 The current implementation is based on the Farkas lemma and
1477 Fourier-Motzkin elimination, but this may change or be made optional
1478 in future. In particular, future implementations may use different
1479 dualization algorithms or skip the elimination step.
1481 __isl_give isl_basic_set *isl_basic_set_coefficients(
1482 __isl_take isl_basic_set *bset);
1483 __isl_give isl_basic_set *isl_set_coefficients(
1484 __isl_take isl_set *set);
1485 __isl_give isl_union_set *isl_union_set_coefficients(
1486 __isl_take isl_union_set *bset);
1487 __isl_give isl_basic_set *isl_basic_set_solutions(
1488 __isl_take isl_basic_set *bset);
1489 __isl_give isl_basic_set *isl_set_solutions(
1490 __isl_take isl_set *set);
1491 __isl_give isl_union_set *isl_union_set_solutions(
1492 __isl_take isl_union_set *bset);
1496 __isl_give isl_map *isl_map_power(__isl_take isl_map *map,
1498 __isl_give isl_union_map *isl_union_map_power(
1499 __isl_take isl_union_map *umap, int *exact);
1501 Compute a parametric representation for all positive powers I<k> of C<map>.
1502 The result maps I<k> to a nested relation corresponding to the
1503 I<k>th power of C<map>.
1504 The result may be an overapproximation. If the result is known to be exact,
1505 then C<*exact> is set to C<1>.
1507 =item * Transitive closure
1509 __isl_give isl_map *isl_map_transitive_closure(
1510 __isl_take isl_map *map, int *exact);
1511 __isl_give isl_union_map *isl_union_map_transitive_closure(
1512 __isl_take isl_union_map *umap, int *exact);
1514 Compute the transitive closure of C<map>.
1515 The result may be an overapproximation. If the result is known to be exact,
1516 then C<*exact> is set to C<1>.
1518 =item * Reaching path lengths
1520 __isl_give isl_map *isl_map_reaching_path_lengths(
1521 __isl_take isl_map *map, int *exact);
1523 Compute a relation that maps each element in the range of C<map>
1524 to the lengths of all paths composed of edges in C<map> that
1525 end up in the given element.
1526 The result may be an overapproximation. If the result is known to be exact,
1527 then C<*exact> is set to C<1>.
1528 To compute the I<maximal> path length, the resulting relation
1529 should be postprocessed by C<isl_map_lexmax>.
1530 In particular, if the input relation is a dependence relation
1531 (mapping sources to sinks), then the maximal path length corresponds
1532 to the free schedule.
1533 Note, however, that C<isl_map_lexmax> expects the maximum to be
1534 finite, so if the path lengths are unbounded (possibly due to
1535 the overapproximation), then you will get an error message.
1539 __isl_give isl_basic_set *isl_basic_map_wrap(
1540 __isl_take isl_basic_map *bmap);
1541 __isl_give isl_set *isl_map_wrap(
1542 __isl_take isl_map *map);
1543 __isl_give isl_union_set *isl_union_map_wrap(
1544 __isl_take isl_union_map *umap);
1545 __isl_give isl_basic_map *isl_basic_set_unwrap(
1546 __isl_take isl_basic_set *bset);
1547 __isl_give isl_map *isl_set_unwrap(
1548 __isl_take isl_set *set);
1549 __isl_give isl_union_map *isl_union_set_unwrap(
1550 __isl_take isl_union_set *uset);
1554 Remove any internal structure of domain (and range) of the given
1555 set or relation. If there is any such internal structure in the input,
1556 then the name of the space is also removed.
1558 __isl_give isl_basic_set *isl_basic_set_flatten(
1559 __isl_take isl_basic_set *bset);
1560 __isl_give isl_set *isl_set_flatten(
1561 __isl_take isl_set *set);
1562 __isl_give isl_basic_map *isl_basic_map_flatten(
1563 __isl_take isl_basic_map *bmap);
1564 __isl_give isl_map *isl_map_flatten(
1565 __isl_take isl_map *map);
1567 __isl_give isl_map *isl_set_flatten_map(
1568 __isl_take isl_set *set);
1570 The function above constructs a relation
1571 that maps the input set to a flattened version of the set.
1575 Lift the input set to a space with extra dimensions corresponding
1576 to the existentially quantified variables in the input.
1577 In particular, the result lives in a wrapped map where the domain
1578 is the original space and the range corresponds to the original
1579 existentially quantified variables.
1581 __isl_give isl_basic_set *isl_basic_set_lift(
1582 __isl_take isl_basic_set *bset);
1583 __isl_give isl_set *isl_set_lift(
1584 __isl_take isl_set *set);
1585 __isl_give isl_union_set *isl_union_set_lift(
1586 __isl_take isl_union_set *uset);
1588 =item * Internal Product
1590 __isl_give isl_basic_map *isl_basic_map_zip(
1591 __isl_take isl_basic_map *bmap);
1592 __isl_give isl_map *isl_map_zip(
1593 __isl_take isl_map *map);
1594 __isl_give isl_union_map *isl_union_map_zip(
1595 __isl_take isl_union_map *umap);
1597 Given a relation with nested relations for domain and range,
1598 interchange the range of the domain with the domain of the range.
1600 =item * Dimension manipulation
1602 __isl_give isl_set *isl_set_add_dims(
1603 __isl_take isl_set *set,
1604 enum isl_dim_type type, unsigned n);
1605 __isl_give isl_map *isl_map_add_dims(
1606 __isl_take isl_map *map,
1607 enum isl_dim_type type, unsigned n);
1609 It is usually not advisable to directly change the (input or output)
1610 space of a set or a relation as this removes the name and the internal
1611 structure of the space. However, the above functions can be useful
1612 to add new parameters.
1616 =head2 Binary Operations
1618 The two arguments of a binary operation not only need to live
1619 in the same C<isl_ctx>, they currently also need to have
1620 the same (number of) parameters.
1622 =head3 Basic Operations
1626 =item * Intersection
1628 __isl_give isl_basic_set *isl_basic_set_intersect(
1629 __isl_take isl_basic_set *bset1,
1630 __isl_take isl_basic_set *bset2);
1631 __isl_give isl_set *isl_set_intersect(
1632 __isl_take isl_set *set1,
1633 __isl_take isl_set *set2);
1634 __isl_give isl_union_set *isl_union_set_intersect(
1635 __isl_take isl_union_set *uset1,
1636 __isl_take isl_union_set *uset2);
1637 __isl_give isl_basic_map *isl_basic_map_intersect_domain(
1638 __isl_take isl_basic_map *bmap,
1639 __isl_take isl_basic_set *bset);
1640 __isl_give isl_basic_map *isl_basic_map_intersect_range(
1641 __isl_take isl_basic_map *bmap,
1642 __isl_take isl_basic_set *bset);
1643 __isl_give isl_basic_map *isl_basic_map_intersect(
1644 __isl_take isl_basic_map *bmap1,
1645 __isl_take isl_basic_map *bmap2);
1646 __isl_give isl_map *isl_map_intersect_domain(
1647 __isl_take isl_map *map,
1648 __isl_take isl_set *set);
1649 __isl_give isl_map *isl_map_intersect_range(
1650 __isl_take isl_map *map,
1651 __isl_take isl_set *set);
1652 __isl_give isl_map *isl_map_intersect(
1653 __isl_take isl_map *map1,
1654 __isl_take isl_map *map2);
1655 __isl_give isl_union_map *isl_union_map_intersect_domain(
1656 __isl_take isl_union_map *umap,
1657 __isl_take isl_union_set *uset);
1658 __isl_give isl_union_map *isl_union_map_intersect_range(
1659 __isl_take isl_union_map *umap,
1660 __isl_take isl_union_set *uset);
1661 __isl_give isl_union_map *isl_union_map_intersect(
1662 __isl_take isl_union_map *umap1,
1663 __isl_take isl_union_map *umap2);
1667 __isl_give isl_set *isl_basic_set_union(
1668 __isl_take isl_basic_set *bset1,
1669 __isl_take isl_basic_set *bset2);
1670 __isl_give isl_map *isl_basic_map_union(
1671 __isl_take isl_basic_map *bmap1,
1672 __isl_take isl_basic_map *bmap2);
1673 __isl_give isl_set *isl_set_union(
1674 __isl_take isl_set *set1,
1675 __isl_take isl_set *set2);
1676 __isl_give isl_map *isl_map_union(
1677 __isl_take isl_map *map1,
1678 __isl_take isl_map *map2);
1679 __isl_give isl_union_set *isl_union_set_union(
1680 __isl_take isl_union_set *uset1,
1681 __isl_take isl_union_set *uset2);
1682 __isl_give isl_union_map *isl_union_map_union(
1683 __isl_take isl_union_map *umap1,
1684 __isl_take isl_union_map *umap2);
1686 =item * Set difference
1688 __isl_give isl_set *isl_set_subtract(
1689 __isl_take isl_set *set1,
1690 __isl_take isl_set *set2);
1691 __isl_give isl_map *isl_map_subtract(
1692 __isl_take isl_map *map1,
1693 __isl_take isl_map *map2);
1694 __isl_give isl_union_set *isl_union_set_subtract(
1695 __isl_take isl_union_set *uset1,
1696 __isl_take isl_union_set *uset2);
1697 __isl_give isl_union_map *isl_union_map_subtract(
1698 __isl_take isl_union_map *umap1,
1699 __isl_take isl_union_map *umap2);
1703 __isl_give isl_basic_set *isl_basic_set_apply(
1704 __isl_take isl_basic_set *bset,
1705 __isl_take isl_basic_map *bmap);
1706 __isl_give isl_set *isl_set_apply(
1707 __isl_take isl_set *set,
1708 __isl_take isl_map *map);
1709 __isl_give isl_union_set *isl_union_set_apply(
1710 __isl_take isl_union_set *uset,
1711 __isl_take isl_union_map *umap);
1712 __isl_give isl_basic_map *isl_basic_map_apply_domain(
1713 __isl_take isl_basic_map *bmap1,
1714 __isl_take isl_basic_map *bmap2);
1715 __isl_give isl_basic_map *isl_basic_map_apply_range(
1716 __isl_take isl_basic_map *bmap1,
1717 __isl_take isl_basic_map *bmap2);
1718 __isl_give isl_map *isl_map_apply_domain(
1719 __isl_take isl_map *map1,
1720 __isl_take isl_map *map2);
1721 __isl_give isl_union_map *isl_union_map_apply_domain(
1722 __isl_take isl_union_map *umap1,
1723 __isl_take isl_union_map *umap2);
1724 __isl_give isl_map *isl_map_apply_range(
1725 __isl_take isl_map *map1,
1726 __isl_take isl_map *map2);
1727 __isl_give isl_union_map *isl_union_map_apply_range(
1728 __isl_take isl_union_map *umap1,
1729 __isl_take isl_union_map *umap2);
1731 =item * Cartesian Product
1733 __isl_give isl_set *isl_set_product(
1734 __isl_take isl_set *set1,
1735 __isl_take isl_set *set2);
1736 __isl_give isl_union_set *isl_union_set_product(
1737 __isl_take isl_union_set *uset1,
1738 __isl_take isl_union_set *uset2);
1739 __isl_give isl_basic_map *isl_basic_map_range_product(
1740 __isl_take isl_basic_map *bmap1,
1741 __isl_take isl_basic_map *bmap2);
1742 __isl_give isl_map *isl_map_range_product(
1743 __isl_take isl_map *map1,
1744 __isl_take isl_map *map2);
1745 __isl_give isl_union_map *isl_union_map_range_product(
1746 __isl_take isl_union_map *umap1,
1747 __isl_take isl_union_map *umap2);
1748 __isl_give isl_map *isl_map_product(
1749 __isl_take isl_map *map1,
1750 __isl_take isl_map *map2);
1751 __isl_give isl_union_map *isl_union_map_product(
1752 __isl_take isl_union_map *umap1,
1753 __isl_take isl_union_map *umap2);
1755 The above functions compute the cross product of the given
1756 sets or relations. The domains and ranges of the results
1757 are wrapped maps between domains and ranges of the inputs.
1758 To obtain a ``flat'' product, use the following functions
1761 __isl_give isl_basic_set *isl_basic_set_flat_product(
1762 __isl_take isl_basic_set *bset1,
1763 __isl_take isl_basic_set *bset2);
1764 __isl_give isl_set *isl_set_flat_product(
1765 __isl_take isl_set *set1,
1766 __isl_take isl_set *set2);
1767 __isl_give isl_basic_map *isl_basic_map_flat_product(
1768 __isl_take isl_basic_map *bmap1,
1769 __isl_take isl_basic_map *bmap2);
1770 __isl_give isl_map *isl_map_flat_product(
1771 __isl_take isl_map *map1,
1772 __isl_take isl_map *map2);
1774 =item * Simplification
1776 __isl_give isl_basic_set *isl_basic_set_gist(
1777 __isl_take isl_basic_set *bset,
1778 __isl_take isl_basic_set *context);
1779 __isl_give isl_set *isl_set_gist(__isl_take isl_set *set,
1780 __isl_take isl_set *context);
1781 __isl_give isl_union_set *isl_union_set_gist(
1782 __isl_take isl_union_set *uset,
1783 __isl_take isl_union_set *context);
1784 __isl_give isl_basic_map *isl_basic_map_gist(
1785 __isl_take isl_basic_map *bmap,
1786 __isl_take isl_basic_map *context);
1787 __isl_give isl_map *isl_map_gist(__isl_take isl_map *map,
1788 __isl_take isl_map *context);
1789 __isl_give isl_union_map *isl_union_map_gist(
1790 __isl_take isl_union_map *umap,
1791 __isl_take isl_union_map *context);
1793 The gist operation returns a set or relation that has the
1794 same intersection with the context as the input set or relation.
1795 Any implicit equality in the intersection is made explicit in the result,
1796 while all inequalities that are redundant with respect to the intersection
1798 In case of union sets and relations, the gist operation is performed
1803 =head3 Lexicographic Optimization
1805 Given a (basic) set C<set> (or C<bset>) and a zero-dimensional domain C<dom>,
1806 the following functions
1807 compute a set that contains the lexicographic minimum or maximum
1808 of the elements in C<set> (or C<bset>) for those values of the parameters
1809 that satisfy C<dom>.
1810 If C<empty> is not C<NULL>, then C<*empty> is assigned a set
1811 that contains the parameter values in C<dom> for which C<set> (or C<bset>)
1813 In other words, the union of the parameter values
1814 for which the result is non-empty and of C<*empty>
1817 __isl_give isl_set *isl_basic_set_partial_lexmin(
1818 __isl_take isl_basic_set *bset,
1819 __isl_take isl_basic_set *dom,
1820 __isl_give isl_set **empty);
1821 __isl_give isl_set *isl_basic_set_partial_lexmax(
1822 __isl_take isl_basic_set *bset,
1823 __isl_take isl_basic_set *dom,
1824 __isl_give isl_set **empty);
1825 __isl_give isl_set *isl_set_partial_lexmin(
1826 __isl_take isl_set *set, __isl_take isl_set *dom,
1827 __isl_give isl_set **empty);
1828 __isl_give isl_set *isl_set_partial_lexmax(
1829 __isl_take isl_set *set, __isl_take isl_set *dom,
1830 __isl_give isl_set **empty);
1832 Given a (basic) set C<set> (or C<bset>), the following functions simply
1833 return a set containing the lexicographic minimum or maximum
1834 of the elements in C<set> (or C<bset>).
1835 In case of union sets, the optimum is computed per space.
1837 __isl_give isl_set *isl_basic_set_lexmin(
1838 __isl_take isl_basic_set *bset);
1839 __isl_give isl_set *isl_basic_set_lexmax(
1840 __isl_take isl_basic_set *bset);
1841 __isl_give isl_set *isl_set_lexmin(
1842 __isl_take isl_set *set);
1843 __isl_give isl_set *isl_set_lexmax(
1844 __isl_take isl_set *set);
1845 __isl_give isl_union_set *isl_union_set_lexmin(
1846 __isl_take isl_union_set *uset);
1847 __isl_give isl_union_set *isl_union_set_lexmax(
1848 __isl_take isl_union_set *uset);
1850 Given a (basic) relation C<map> (or C<bmap>) and a domain C<dom>,
1851 the following functions
1852 compute a relation that maps each element of C<dom>
1853 to the single lexicographic minimum or maximum
1854 of the elements that are associated to that same
1855 element in C<map> (or C<bmap>).
1856 If C<empty> is not C<NULL>, then C<*empty> is assigned a set
1857 that contains the elements in C<dom> that do not map
1858 to any elements in C<map> (or C<bmap>).
1859 In other words, the union of the domain of the result and of C<*empty>
1862 __isl_give isl_map *isl_basic_map_partial_lexmax(
1863 __isl_take isl_basic_map *bmap,
1864 __isl_take isl_basic_set *dom,
1865 __isl_give isl_set **empty);
1866 __isl_give isl_map *isl_basic_map_partial_lexmin(
1867 __isl_take isl_basic_map *bmap,
1868 __isl_take isl_basic_set *dom,
1869 __isl_give isl_set **empty);
1870 __isl_give isl_map *isl_map_partial_lexmax(
1871 __isl_take isl_map *map, __isl_take isl_set *dom,
1872 __isl_give isl_set **empty);
1873 __isl_give isl_map *isl_map_partial_lexmin(
1874 __isl_take isl_map *map, __isl_take isl_set *dom,
1875 __isl_give isl_set **empty);
1877 Given a (basic) map C<map> (or C<bmap>), the following functions simply
1878 return a map mapping each element in the domain of
1879 C<map> (or C<bmap>) to the lexicographic minimum or maximum
1880 of all elements associated to that element.
1881 In case of union relations, the optimum is computed per space.
1883 __isl_give isl_map *isl_basic_map_lexmin(
1884 __isl_take isl_basic_map *bmap);
1885 __isl_give isl_map *isl_basic_map_lexmax(
1886 __isl_take isl_basic_map *bmap);
1887 __isl_give isl_map *isl_map_lexmin(
1888 __isl_take isl_map *map);
1889 __isl_give isl_map *isl_map_lexmax(
1890 __isl_take isl_map *map);
1891 __isl_give isl_union_map *isl_union_map_lexmin(
1892 __isl_take isl_union_map *umap);
1893 __isl_give isl_union_map *isl_union_map_lexmax(
1894 __isl_take isl_union_map *umap);
1898 Matrices can be created, copied and freed using the following functions.
1900 #include <isl/mat.h>
1901 __isl_give isl_mat *isl_mat_alloc(struct isl_ctx *ctx,
1902 unsigned n_row, unsigned n_col);
1903 __isl_give isl_mat *isl_mat_copy(__isl_keep isl_mat *mat);
1904 void isl_mat_free(__isl_take isl_mat *mat);
1906 Note that the elements of a newly created matrix may have arbitrary values.
1907 The elements can be changed and inspected using the following functions.
1909 isl_ctx *isl_mat_get_ctx(__isl_keep isl_mat *mat);
1910 int isl_mat_rows(__isl_keep isl_mat *mat);
1911 int isl_mat_cols(__isl_keep isl_mat *mat);
1912 int isl_mat_get_element(__isl_keep isl_mat *mat,
1913 int row, int col, isl_int *v);
1914 __isl_give isl_mat *isl_mat_set_element(__isl_take isl_mat *mat,
1915 int row, int col, isl_int v);
1916 __isl_give isl_mat *isl_mat_set_element_si(__isl_take isl_mat *mat,
1917 int row, int col, int v);
1919 C<isl_mat_get_element> will return a negative value if anything went wrong.
1920 In that case, the value of C<*v> is undefined.
1922 The following function can be used to compute the (right) inverse
1923 of a matrix, i.e., a matrix such that the product of the original
1924 and the inverse (in that order) is a multiple of the identity matrix.
1925 The input matrix is assumed to be of full row-rank.
1927 __isl_give isl_mat *isl_mat_right_inverse(__isl_take isl_mat *mat);
1929 The following function can be used to compute the (right) kernel
1930 (or null space) of a matrix, i.e., a matrix such that the product of
1931 the original and the kernel (in that order) is the zero matrix.
1933 __isl_give isl_mat *isl_mat_right_kernel(__isl_take isl_mat *mat);
1937 Points are elements of a set. They can be used to construct
1938 simple sets (boxes) or they can be used to represent the
1939 individual elements of a set.
1940 The zero point (the origin) can be created using
1942 __isl_give isl_point *isl_point_zero(__isl_take isl_dim *dim);
1944 The coordinates of a point can be inspected, set and changed
1947 void isl_point_get_coordinate(__isl_keep isl_point *pnt,
1948 enum isl_dim_type type, int pos, isl_int *v);
1949 __isl_give isl_point *isl_point_set_coordinate(
1950 __isl_take isl_point *pnt,
1951 enum isl_dim_type type, int pos, isl_int v);
1953 __isl_give isl_point *isl_point_add_ui(
1954 __isl_take isl_point *pnt,
1955 enum isl_dim_type type, int pos, unsigned val);
1956 __isl_give isl_point *isl_point_sub_ui(
1957 __isl_take isl_point *pnt,
1958 enum isl_dim_type type, int pos, unsigned val);
1960 Points can be copied or freed using
1962 __isl_give isl_point *isl_point_copy(
1963 __isl_keep isl_point *pnt);
1964 void isl_point_free(__isl_take isl_point *pnt);
1966 A singleton set can be created from a point using
1968 __isl_give isl_basic_set *isl_basic_set_from_point(
1969 __isl_take isl_point *pnt);
1970 __isl_give isl_set *isl_set_from_point(
1971 __isl_take isl_point *pnt);
1973 and a box can be created from two opposite extremal points using
1975 __isl_give isl_basic_set *isl_basic_set_box_from_points(
1976 __isl_take isl_point *pnt1,
1977 __isl_take isl_point *pnt2);
1978 __isl_give isl_set *isl_set_box_from_points(
1979 __isl_take isl_point *pnt1,
1980 __isl_take isl_point *pnt2);
1982 All elements of a B<bounded> (union) set can be enumerated using
1983 the following functions.
1985 int isl_set_foreach_point(__isl_keep isl_set *set,
1986 int (*fn)(__isl_take isl_point *pnt, void *user),
1988 int isl_union_set_foreach_point(__isl_keep isl_union_set *uset,
1989 int (*fn)(__isl_take isl_point *pnt, void *user),
1992 The function C<fn> is called for each integer point in
1993 C<set> with as second argument the last argument of
1994 the C<isl_set_foreach_point> call. The function C<fn>
1995 should return C<0> on success and C<-1> on failure.
1996 In the latter case, C<isl_set_foreach_point> will stop
1997 enumerating and return C<-1> as well.
1998 If the enumeration is performed successfully and to completion,
1999 then C<isl_set_foreach_point> returns C<0>.
2001 To obtain a single point of a (basic) set, use
2003 __isl_give isl_point *isl_basic_set_sample_point(
2004 __isl_take isl_basic_set *bset);
2005 __isl_give isl_point *isl_set_sample_point(
2006 __isl_take isl_set *set);
2008 If C<set> does not contain any (integer) points, then the
2009 resulting point will be ``void'', a property that can be
2012 int isl_point_is_void(__isl_keep isl_point *pnt);
2014 =head2 Piecewise Quasipolynomials
2016 A piecewise quasipolynomial is a particular kind of function that maps
2017 a parametric point to a rational value.
2018 More specifically, a quasipolynomial is a polynomial expression in greatest
2019 integer parts of affine expressions of parameters and variables.
2020 A piecewise quasipolynomial is a subdivision of a given parametric
2021 domain into disjoint cells with a quasipolynomial associated to
2022 each cell. The value of the piecewise quasipolynomial at a given
2023 point is the value of the quasipolynomial associated to the cell
2024 that contains the point. Outside of the union of cells,
2025 the value is assumed to be zero.
2026 For example, the piecewise quasipolynomial
2028 [n] -> { [x] -> ((1 + n) - x) : x <= n and x >= 0 }
2030 maps C<x> to C<1 + n - x> for values of C<x> between C<0> and C<n>.
2031 A given piecewise quasipolynomial has a fixed domain dimension.
2032 Union piecewise quasipolynomials are used to contain piecewise quasipolynomials
2033 defined over different domains.
2034 Piecewise quasipolynomials are mainly used by the C<barvinok>
2035 library for representing the number of elements in a parametric set or map.
2036 For example, the piecewise quasipolynomial above represents
2037 the number of points in the map
2039 [n] -> { [x] -> [y] : x,y >= 0 and 0 <= x + y <= n }
2041 =head3 Printing (Piecewise) Quasipolynomials
2043 Quasipolynomials and piecewise quasipolynomials can be printed
2044 using the following functions.
2046 __isl_give isl_printer *isl_printer_print_qpolynomial(
2047 __isl_take isl_printer *p,
2048 __isl_keep isl_qpolynomial *qp);
2050 __isl_give isl_printer *isl_printer_print_pw_qpolynomial(
2051 __isl_take isl_printer *p,
2052 __isl_keep isl_pw_qpolynomial *pwqp);
2054 __isl_give isl_printer *isl_printer_print_union_pw_qpolynomial(
2055 __isl_take isl_printer *p,
2056 __isl_keep isl_union_pw_qpolynomial *upwqp);
2058 The output format of the printer
2059 needs to be set to either C<ISL_FORMAT_ISL> or C<ISL_FORMAT_C>.
2060 For C<isl_printer_print_union_pw_qpolynomial>, only C<ISL_FORMAT_ISL>
2062 In case of printing in C<ISL_FORMAT_C>, the user may want
2063 to set the names of all dimensions
2065 __isl_give isl_qpolynomial *isl_qpolynomial_set_dim_name(
2066 __isl_take isl_qpolynomial *qp,
2067 enum isl_dim_type type, unsigned pos,
2069 __isl_give isl_pw_qpolynomial *
2070 isl_pw_qpolynomial_set_dim_name(
2071 __isl_take isl_pw_qpolynomial *pwqp,
2072 enum isl_dim_type type, unsigned pos,
2075 =head3 Creating New (Piecewise) Quasipolynomials
2077 Some simple quasipolynomials can be created using the following functions.
2078 More complicated quasipolynomials can be created by applying
2079 operations such as addition and multiplication
2080 on the resulting quasipolynomials
2082 __isl_give isl_qpolynomial *isl_qpolynomial_zero(
2083 __isl_take isl_dim *dim);
2084 __isl_give isl_qpolynomial *isl_qpolynomial_one(
2085 __isl_take isl_dim *dim);
2086 __isl_give isl_qpolynomial *isl_qpolynomial_infty(
2087 __isl_take isl_dim *dim);
2088 __isl_give isl_qpolynomial *isl_qpolynomial_neginfty(
2089 __isl_take isl_dim *dim);
2090 __isl_give isl_qpolynomial *isl_qpolynomial_nan(
2091 __isl_take isl_dim *dim);
2092 __isl_give isl_qpolynomial *isl_qpolynomial_rat_cst(
2093 __isl_take isl_dim *dim,
2094 const isl_int n, const isl_int d);
2095 __isl_give isl_qpolynomial *isl_qpolynomial_div(
2096 __isl_take isl_div *div);
2097 __isl_give isl_qpolynomial *isl_qpolynomial_var(
2098 __isl_take isl_dim *dim,
2099 enum isl_dim_type type, unsigned pos);
2101 The zero piecewise quasipolynomial or a piecewise quasipolynomial
2102 with a single cell can be created using the following functions.
2103 Multiple of these single cell piecewise quasipolynomials can
2104 be combined to create more complicated piecewise quasipolynomials.
2106 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_zero(
2107 __isl_take isl_dim *dim);
2108 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_alloc(
2109 __isl_take isl_set *set,
2110 __isl_take isl_qpolynomial *qp);
2112 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_zero(
2113 __isl_take isl_dim *dim);
2114 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_from_pw_qpolynomial(
2115 __isl_take isl_pw_qpolynomial *pwqp);
2116 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_add_pw_qpolynomial(
2117 __isl_take isl_union_pw_qpolynomial *upwqp,
2118 __isl_take isl_pw_qpolynomial *pwqp);
2120 Quasipolynomials can be copied and freed again using the following
2123 __isl_give isl_qpolynomial *isl_qpolynomial_copy(
2124 __isl_keep isl_qpolynomial *qp);
2125 void isl_qpolynomial_free(__isl_take isl_qpolynomial *qp);
2127 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_copy(
2128 __isl_keep isl_pw_qpolynomial *pwqp);
2129 void isl_pw_qpolynomial_free(
2130 __isl_take isl_pw_qpolynomial *pwqp);
2132 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_copy(
2133 __isl_keep isl_union_pw_qpolynomial *upwqp);
2134 void isl_union_pw_qpolynomial_free(
2135 __isl_take isl_union_pw_qpolynomial *upwqp);
2137 =head3 Inspecting (Piecewise) Quasipolynomials
2139 To iterate over all piecewise quasipolynomials in a union
2140 piecewise quasipolynomial, use the following function
2142 int isl_union_pw_qpolynomial_foreach_pw_qpolynomial(
2143 __isl_keep isl_union_pw_qpolynomial *upwqp,
2144 int (*fn)(__isl_take isl_pw_qpolynomial *pwqp, void *user),
2147 To extract the piecewise quasipolynomial from a union with a given dimension
2150 __isl_give isl_pw_qpolynomial *
2151 isl_union_pw_qpolynomial_extract_pw_qpolynomial(
2152 __isl_keep isl_union_pw_qpolynomial *upwqp,
2153 __isl_take isl_dim *dim);
2155 To iterate over the cells in a piecewise quasipolynomial,
2156 use either of the following two functions
2158 int isl_pw_qpolynomial_foreach_piece(
2159 __isl_keep isl_pw_qpolynomial *pwqp,
2160 int (*fn)(__isl_take isl_set *set,
2161 __isl_take isl_qpolynomial *qp,
2162 void *user), void *user);
2163 int isl_pw_qpolynomial_foreach_lifted_piece(
2164 __isl_keep isl_pw_qpolynomial *pwqp,
2165 int (*fn)(__isl_take isl_set *set,
2166 __isl_take isl_qpolynomial *qp,
2167 void *user), void *user);
2169 As usual, the function C<fn> should return C<0> on success
2170 and C<-1> on failure. The difference between
2171 C<isl_pw_qpolynomial_foreach_piece> and
2172 C<isl_pw_qpolynomial_foreach_lifted_piece> is that
2173 C<isl_pw_qpolynomial_foreach_lifted_piece> will first
2174 compute unique representations for all existentially quantified
2175 variables and then turn these existentially quantified variables
2176 into extra set variables, adapting the associated quasipolynomial
2177 accordingly. This means that the C<set> passed to C<fn>
2178 will not have any existentially quantified variables, but that
2179 the dimensions of the sets may be different for different
2180 invocations of C<fn>.
2182 To iterate over all terms in a quasipolynomial,
2185 int isl_qpolynomial_foreach_term(
2186 __isl_keep isl_qpolynomial *qp,
2187 int (*fn)(__isl_take isl_term *term,
2188 void *user), void *user);
2190 The terms themselves can be inspected and freed using
2193 unsigned isl_term_dim(__isl_keep isl_term *term,
2194 enum isl_dim_type type);
2195 void isl_term_get_num(__isl_keep isl_term *term,
2197 void isl_term_get_den(__isl_keep isl_term *term,
2199 int isl_term_get_exp(__isl_keep isl_term *term,
2200 enum isl_dim_type type, unsigned pos);
2201 __isl_give isl_div *isl_term_get_div(
2202 __isl_keep isl_term *term, unsigned pos);
2203 void isl_term_free(__isl_take isl_term *term);
2205 Each term is a product of parameters, set variables and
2206 integer divisions. The function C<isl_term_get_exp>
2207 returns the exponent of a given dimensions in the given term.
2208 The C<isl_int>s in the arguments of C<isl_term_get_num>
2209 and C<isl_term_get_den> need to have been initialized
2210 using C<isl_int_init> before calling these functions.
2212 =head3 Properties of (Piecewise) Quasipolynomials
2214 To check whether a quasipolynomial is actually a constant,
2215 use the following function.
2217 int isl_qpolynomial_is_cst(__isl_keep isl_qpolynomial *qp,
2218 isl_int *n, isl_int *d);
2220 If C<qp> is a constant and if C<n> and C<d> are not C<NULL>
2221 then the numerator and denominator of the constant
2222 are returned in C<*n> and C<*d>, respectively.
2224 =head3 Operations on (Piecewise) Quasipolynomials
2226 __isl_give isl_qpolynomial *isl_qpolynomial_neg(
2227 __isl_take isl_qpolynomial *qp);
2228 __isl_give isl_qpolynomial *isl_qpolynomial_add(
2229 __isl_take isl_qpolynomial *qp1,
2230 __isl_take isl_qpolynomial *qp2);
2231 __isl_give isl_qpolynomial *isl_qpolynomial_sub(
2232 __isl_take isl_qpolynomial *qp1,
2233 __isl_take isl_qpolynomial *qp2);
2234 __isl_give isl_qpolynomial *isl_qpolynomial_mul(
2235 __isl_take isl_qpolynomial *qp1,
2236 __isl_take isl_qpolynomial *qp2);
2237 __isl_give isl_qpolynomial *isl_qpolynomial_pow(
2238 __isl_take isl_qpolynomial *qp, unsigned exponent);
2240 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_add(
2241 __isl_take isl_pw_qpolynomial *pwqp1,
2242 __isl_take isl_pw_qpolynomial *pwqp2);
2243 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_sub(
2244 __isl_take isl_pw_qpolynomial *pwqp1,
2245 __isl_take isl_pw_qpolynomial *pwqp2);
2246 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_add_disjoint(
2247 __isl_take isl_pw_qpolynomial *pwqp1,
2248 __isl_take isl_pw_qpolynomial *pwqp2);
2249 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_neg(
2250 __isl_take isl_pw_qpolynomial *pwqp);
2251 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_mul(
2252 __isl_take isl_pw_qpolynomial *pwqp1,
2253 __isl_take isl_pw_qpolynomial *pwqp2);
2255 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_add(
2256 __isl_take isl_union_pw_qpolynomial *upwqp1,
2257 __isl_take isl_union_pw_qpolynomial *upwqp2);
2258 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_sub(
2259 __isl_take isl_union_pw_qpolynomial *upwqp1,
2260 __isl_take isl_union_pw_qpolynomial *upwqp2);
2261 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_mul(
2262 __isl_take isl_union_pw_qpolynomial *upwqp1,
2263 __isl_take isl_union_pw_qpolynomial *upwqp2);
2265 __isl_give isl_qpolynomial *isl_pw_qpolynomial_eval(
2266 __isl_take isl_pw_qpolynomial *pwqp,
2267 __isl_take isl_point *pnt);
2269 __isl_give isl_qpolynomial *isl_union_pw_qpolynomial_eval(
2270 __isl_take isl_union_pw_qpolynomial *upwqp,
2271 __isl_take isl_point *pnt);
2273 __isl_give isl_set *isl_pw_qpolynomial_domain(
2274 __isl_take isl_pw_qpolynomial *pwqp);
2275 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_intersect_domain(
2276 __isl_take isl_pw_qpolynomial *pwpq,
2277 __isl_take isl_set *set);
2279 __isl_give isl_union_set *isl_union_pw_qpolynomial_domain(
2280 __isl_take isl_union_pw_qpolynomial *upwqp);
2281 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_intersect_domain(
2282 __isl_take isl_union_pw_qpolynomial *upwpq,
2283 __isl_take isl_union_set *uset);
2285 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_coalesce(
2286 __isl_take isl_union_pw_qpolynomial *upwqp);
2288 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_gist(
2289 __isl_take isl_pw_qpolynomial *pwqp,
2290 __isl_take isl_set *context);
2292 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_gist(
2293 __isl_take isl_union_pw_qpolynomial *upwqp,
2294 __isl_take isl_union_set *context);
2296 The gist operation applies the gist operation to each of
2297 the cells in the domain of the input piecewise quasipolynomial.
2298 The context is also exploited
2299 to simplify the quasipolynomials associated to each cell.
2301 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_to_polynomial(
2302 __isl_take isl_pw_qpolynomial *pwqp, int sign);
2303 __isl_give isl_union_pw_qpolynomial *
2304 isl_union_pw_qpolynomial_to_polynomial(
2305 __isl_take isl_union_pw_qpolynomial *upwqp, int sign);
2307 Approximate each quasipolynomial by a polynomial. If C<sign> is positive,
2308 the polynomial will be an overapproximation. If C<sign> is negative,
2309 it will be an underapproximation. If C<sign> is zero, the approximation
2310 will lie somewhere in between.
2312 =head2 Bounds on Piecewise Quasipolynomials and Piecewise Quasipolynomial Reductions
2314 A piecewise quasipolynomial reduction is a piecewise
2315 reduction (or fold) of quasipolynomials.
2316 In particular, the reduction can be maximum or a minimum.
2317 The objects are mainly used to represent the result of
2318 an upper or lower bound on a quasipolynomial over its domain,
2319 i.e., as the result of the following function.
2321 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_bound(
2322 __isl_take isl_pw_qpolynomial *pwqp,
2323 enum isl_fold type, int *tight);
2325 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_bound(
2326 __isl_take isl_union_pw_qpolynomial *upwqp,
2327 enum isl_fold type, int *tight);
2329 The C<type> argument may be either C<isl_fold_min> or C<isl_fold_max>.
2330 If C<tight> is not C<NULL>, then C<*tight> is set to C<1>
2331 is the returned bound is known be tight, i.e., for each value
2332 of the parameters there is at least
2333 one element in the domain that reaches the bound.
2334 If the domain of C<pwqp> is not wrapping, then the bound is computed
2335 over all elements in that domain and the result has a purely parametric
2336 domain. If the domain of C<pwqp> is wrapping, then the bound is
2337 computed over the range of the wrapped relation. The domain of the
2338 wrapped relation becomes the domain of the result.
2340 A (piecewise) quasipolynomial reduction can be copied or freed using the
2341 following functions.
2343 __isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_copy(
2344 __isl_keep isl_qpolynomial_fold *fold);
2345 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_copy(
2346 __isl_keep isl_pw_qpolynomial_fold *pwf);
2347 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_copy(
2348 __isl_keep isl_union_pw_qpolynomial_fold *upwf);
2349 void isl_qpolynomial_fold_free(
2350 __isl_take isl_qpolynomial_fold *fold);
2351 void isl_pw_qpolynomial_fold_free(
2352 __isl_take isl_pw_qpolynomial_fold *pwf);
2353 void isl_union_pw_qpolynomial_fold_free(
2354 __isl_take isl_union_pw_qpolynomial_fold *upwf);
2356 =head3 Printing Piecewise Quasipolynomial Reductions
2358 Piecewise quasipolynomial reductions can be printed
2359 using the following function.
2361 __isl_give isl_printer *isl_printer_print_pw_qpolynomial_fold(
2362 __isl_take isl_printer *p,
2363 __isl_keep isl_pw_qpolynomial_fold *pwf);
2364 __isl_give isl_printer *isl_printer_print_union_pw_qpolynomial_fold(
2365 __isl_take isl_printer *p,
2366 __isl_keep isl_union_pw_qpolynomial_fold *upwf);
2368 For C<isl_printer_print_pw_qpolynomial_fold>,
2369 output format of the printer
2370 needs to be set to either C<ISL_FORMAT_ISL> or C<ISL_FORMAT_C>.
2371 For C<isl_printer_print_union_pw_qpolynomial_fold>,
2372 output format of the printer
2373 needs to be set to C<ISL_FORMAT_ISL>.
2374 In case of printing in C<ISL_FORMAT_C>, the user may want
2375 to set the names of all dimensions
2377 __isl_give isl_pw_qpolynomial_fold *
2378 isl_pw_qpolynomial_fold_set_dim_name(
2379 __isl_take isl_pw_qpolynomial_fold *pwf,
2380 enum isl_dim_type type, unsigned pos,
2383 =head3 Inspecting (Piecewise) Quasipolynomial Reductions
2385 To iterate over all piecewise quasipolynomial reductions in a union
2386 piecewise quasipolynomial reduction, use the following function
2388 int isl_union_pw_qpolynomial_fold_foreach_pw_qpolynomial_fold(
2389 __isl_keep isl_union_pw_qpolynomial_fold *upwf,
2390 int (*fn)(__isl_take isl_pw_qpolynomial_fold *pwf,
2391 void *user), void *user);
2393 To iterate over the cells in a piecewise quasipolynomial reduction,
2394 use either of the following two functions
2396 int isl_pw_qpolynomial_fold_foreach_piece(
2397 __isl_keep isl_pw_qpolynomial_fold *pwf,
2398 int (*fn)(__isl_take isl_set *set,
2399 __isl_take isl_qpolynomial_fold *fold,
2400 void *user), void *user);
2401 int isl_pw_qpolynomial_fold_foreach_lifted_piece(
2402 __isl_keep isl_pw_qpolynomial_fold *pwf,
2403 int (*fn)(__isl_take isl_set *set,
2404 __isl_take isl_qpolynomial_fold *fold,
2405 void *user), void *user);
2407 See L<Inspecting (Piecewise) Quasipolynomials> for an explanation
2408 of the difference between these two functions.
2410 To iterate over all quasipolynomials in a reduction, use
2412 int isl_qpolynomial_fold_foreach_qpolynomial(
2413 __isl_keep isl_qpolynomial_fold *fold,
2414 int (*fn)(__isl_take isl_qpolynomial *qp,
2415 void *user), void *user);
2417 =head3 Operations on Piecewise Quasipolynomial Reductions
2419 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_add(
2420 __isl_take isl_pw_qpolynomial_fold *pwf1,
2421 __isl_take isl_pw_qpolynomial_fold *pwf2);
2423 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_fold(
2424 __isl_take isl_pw_qpolynomial_fold *pwf1,
2425 __isl_take isl_pw_qpolynomial_fold *pwf2);
2427 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_fold(
2428 __isl_take isl_union_pw_qpolynomial_fold *upwf1,
2429 __isl_take isl_union_pw_qpolynomial_fold *upwf2);
2431 __isl_give isl_qpolynomial *isl_pw_qpolynomial_fold_eval(
2432 __isl_take isl_pw_qpolynomial_fold *pwf,
2433 __isl_take isl_point *pnt);
2435 __isl_give isl_qpolynomial *isl_union_pw_qpolynomial_fold_eval(
2436 __isl_take isl_union_pw_qpolynomial_fold *upwf,
2437 __isl_take isl_point *pnt);
2439 __isl_give isl_union_set *isl_union_pw_qpolynomial_fold_domain(
2440 __isl_take isl_union_pw_qpolynomial_fold *upwf);
2441 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_intersect_domain(
2442 __isl_take isl_union_pw_qpolynomial_fold *upwf,
2443 __isl_take isl_union_set *uset);
2445 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_coalesce(
2446 __isl_take isl_pw_qpolynomial_fold *pwf);
2448 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_coalesce(
2449 __isl_take isl_union_pw_qpolynomial_fold *upwf);
2451 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_gist(
2452 __isl_take isl_pw_qpolynomial_fold *pwf,
2453 __isl_take isl_set *context);
2455 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_gist(
2456 __isl_take isl_union_pw_qpolynomial_fold *upwf,
2457 __isl_take isl_union_set *context);
2459 The gist operation applies the gist operation to each of
2460 the cells in the domain of the input piecewise quasipolynomial reduction.
2461 In future, the operation will also exploit the context
2462 to simplify the quasipolynomial reductions associated to each cell.
2464 __isl_give isl_pw_qpolynomial_fold *
2465 isl_set_apply_pw_qpolynomial_fold(
2466 __isl_take isl_set *set,
2467 __isl_take isl_pw_qpolynomial_fold *pwf,
2469 __isl_give isl_pw_qpolynomial_fold *
2470 isl_map_apply_pw_qpolynomial_fold(
2471 __isl_take isl_map *map,
2472 __isl_take isl_pw_qpolynomial_fold *pwf,
2474 __isl_give isl_union_pw_qpolynomial_fold *
2475 isl_union_set_apply_union_pw_qpolynomial_fold(
2476 __isl_take isl_union_set *uset,
2477 __isl_take isl_union_pw_qpolynomial_fold *upwf,
2479 __isl_give isl_union_pw_qpolynomial_fold *
2480 isl_union_map_apply_union_pw_qpolynomial_fold(
2481 __isl_take isl_union_map *umap,
2482 __isl_take isl_union_pw_qpolynomial_fold *upwf,
2485 The functions taking a map
2486 compose the given map with the given piecewise quasipolynomial reduction.
2487 That is, compute a bound (of the same type as C<pwf> or C<upwf> itself)
2488 over all elements in the intersection of the range of the map
2489 and the domain of the piecewise quasipolynomial reduction
2490 as a function of an element in the domain of the map.
2491 The functions taking a set compute a bound over all elements in the
2492 intersection of the set and the domain of the
2493 piecewise quasipolynomial reduction.
2495 =head2 Dependence Analysis
2497 C<isl> contains specialized functionality for performing
2498 array dataflow analysis. That is, given a I<sink> access relation
2499 and a collection of possible I<source> access relations,
2500 C<isl> can compute relations that describe
2501 for each iteration of the sink access, which iteration
2502 of which of the source access relations was the last
2503 to access the same data element before the given iteration
2505 To compute standard flow dependences, the sink should be
2506 a read, while the sources should be writes.
2507 If any of the source accesses are marked as being I<may>
2508 accesses, then there will be a dependence to the last
2509 I<must> access B<and> to any I<may> access that follows
2510 this last I<must> access.
2511 In particular, if I<all> sources are I<may> accesses,
2512 then memory based dependence analysis is performed.
2513 If, on the other hand, all sources are I<must> accesses,
2514 then value based dependence analysis is performed.
2516 #include <isl/flow.h>
2518 typedef int (*isl_access_level_before)(void *first, void *second);
2520 __isl_give isl_access_info *isl_access_info_alloc(
2521 __isl_take isl_map *sink,
2522 void *sink_user, isl_access_level_before fn,
2524 __isl_give isl_access_info *isl_access_info_add_source(
2525 __isl_take isl_access_info *acc,
2526 __isl_take isl_map *source, int must,
2528 void isl_access_info_free(__isl_take isl_access_info *acc);
2530 __isl_give isl_flow *isl_access_info_compute_flow(
2531 __isl_take isl_access_info *acc);
2533 int isl_flow_foreach(__isl_keep isl_flow *deps,
2534 int (*fn)(__isl_take isl_map *dep, int must,
2535 void *dep_user, void *user),
2537 __isl_give isl_map *isl_flow_get_no_source(
2538 __isl_keep isl_flow *deps, int must);
2539 void isl_flow_free(__isl_take isl_flow *deps);
2541 The function C<isl_access_info_compute_flow> performs the actual
2542 dependence analysis. The other functions are used to construct
2543 the input for this function or to read off the output.
2545 The input is collected in an C<isl_access_info>, which can
2546 be created through a call to C<isl_access_info_alloc>.
2547 The arguments to this functions are the sink access relation
2548 C<sink>, a token C<sink_user> used to identify the sink
2549 access to the user, a callback function for specifying the
2550 relative order of source and sink accesses, and the number
2551 of source access relations that will be added.
2552 The callback function has type C<int (*)(void *first, void *second)>.
2553 The function is called with two user supplied tokens identifying
2554 either a source or the sink and it should return the shared nesting
2555 level and the relative order of the two accesses.
2556 In particular, let I<n> be the number of loops shared by
2557 the two accesses. If C<first> precedes C<second> textually,
2558 then the function should return I<2 * n + 1>; otherwise,
2559 it should return I<2 * n>.
2560 The sources can be added to the C<isl_access_info> by performing
2561 (at most) C<max_source> calls to C<isl_access_info_add_source>.
2562 C<must> indicates whether the source is a I<must> access
2563 or a I<may> access. Note that a multi-valued access relation
2564 should only be marked I<must> if every iteration in the domain
2565 of the relation accesses I<all> elements in its image.
2566 The C<source_user> token is again used to identify
2567 the source access. The range of the source access relation
2568 C<source> should have the same dimension as the range
2569 of the sink access relation.
2570 The C<isl_access_info_free> function should usually not be
2571 called explicitly, because it is called implicitly by
2572 C<isl_access_info_compute_flow>.
2574 The result of the dependence analysis is collected in an
2575 C<isl_flow>. There may be elements of
2576 the sink access for which no preceding source access could be
2577 found or for which all preceding sources are I<may> accesses.
2578 The relations containing these elements can be obtained through
2579 calls to C<isl_flow_get_no_source>, the first with C<must> set
2580 and the second with C<must> unset.
2581 In the case of standard flow dependence analysis,
2582 with the sink a read and the sources I<must> writes,
2583 the first relation corresponds to the reads from uninitialized
2584 array elements and the second relation is empty.
2585 The actual flow dependences can be extracted using
2586 C<isl_flow_foreach>. This function will call the user-specified
2587 callback function C<fn> for each B<non-empty> dependence between
2588 a source and the sink. The callback function is called
2589 with four arguments, the actual flow dependence relation
2590 mapping source iterations to sink iterations, a boolean that
2591 indicates whether it is a I<must> or I<may> dependence, a token
2592 identifying the source and an additional C<void *> with value
2593 equal to the third argument of the C<isl_flow_foreach> call.
2594 A dependence is marked I<must> if it originates from a I<must>
2595 source and if it is not followed by any I<may> sources.
2597 After finishing with an C<isl_flow>, the user should call
2598 C<isl_flow_free> to free all associated memory.
2600 A higher-level interface to dependence analysis is provided
2601 by the following function.
2603 #include <isl/flow.h>
2605 int isl_union_map_compute_flow(__isl_take isl_union_map *sink,
2606 __isl_take isl_union_map *must_source,
2607 __isl_take isl_union_map *may_source,
2608 __isl_take isl_union_map *schedule,
2609 __isl_give isl_union_map **must_dep,
2610 __isl_give isl_union_map **may_dep,
2611 __isl_give isl_union_map **must_no_source,
2612 __isl_give isl_union_map **may_no_source);
2614 The arrays are identified by the tuple names of the ranges
2615 of the accesses. The iteration domains by the tuple names
2616 of the domains of the accesses and of the schedule.
2617 The relative order of the iteration domains is given by the
2618 schedule. The relations returned through C<must_no_source>
2619 and C<may_no_source> are subsets of C<sink>.
2620 Any of C<must_dep>, C<may_dep>, C<must_no_source>
2621 or C<may_no_source> may be C<NULL>, but a C<NULL> value for
2622 any of the other arguments is treated as an error.
2626 B<The functionality described in this section is fairly new
2627 and may be subject to change.>
2629 The following function can be used to compute a schedule
2630 for a union of domains. The generated schedule respects
2631 all C<validity> dependences. That is, all dependence distances
2632 over these dependences in the scheduled space are lexicographically
2633 positive. The generated schedule schedule also tries to minimize
2634 the dependence distances over C<proximity> dependences.
2635 Moreover, it tries to obtain sequences (bands) of schedule dimensions
2636 for groups of domains where the dependence distances have only
2637 non-negative values.
2638 The algorithm used to construct the schedule is similar to that
2641 #include <isl/schedule.h>
2642 __isl_give isl_schedule *isl_union_set_compute_schedule(
2643 __isl_take isl_union_set *domain,
2644 __isl_take isl_union_map *validity,
2645 __isl_take isl_union_map *proximity);
2646 void *isl_schedule_free(__isl_take isl_schedule *sched);
2648 A mapping from the domains to the scheduled space can be obtained
2649 from an C<isl_schedule> using the following function.
2651 __isl_give isl_union_map *isl_schedule_get_map(
2652 __isl_keep isl_schedule *sched);
2654 This mapping can also be obtained in pieces using the following functions.
2656 int isl_schedule_n_band(__isl_keep isl_schedule *sched);
2657 __isl_give isl_union_map *isl_schedule_get_band(
2658 __isl_keep isl_schedule *sched, unsigned band);
2660 C<isl_schedule_n_band> returns the maximal number of bands.
2661 C<isl_schedule_get_band> returns a union of mappings from a domain to
2662 the band of consecutive schedule dimensions with the given sequence
2663 number for that domain. Bands with the same sequence number but for
2664 different domains may be completely unrelated.
2665 Within a band, the corresponding coordinates of the distance vectors
2666 are all non-negative, assuming that the coordinates for all previous
2669 =head2 Parametric Vertex Enumeration
2671 The parametric vertex enumeration described in this section
2672 is mainly intended to be used internally and by the C<barvinok>
2675 #include <isl/vertices.h>
2676 __isl_give isl_vertices *isl_basic_set_compute_vertices(
2677 __isl_keep isl_basic_set *bset);
2679 The function C<isl_basic_set_compute_vertices> performs the
2680 actual computation of the parametric vertices and the chamber
2681 decomposition and store the result in an C<isl_vertices> object.
2682 This information can be queried by either iterating over all
2683 the vertices or iterating over all the chambers or cells
2684 and then iterating over all vertices that are active on the chamber.
2686 int isl_vertices_foreach_vertex(
2687 __isl_keep isl_vertices *vertices,
2688 int (*fn)(__isl_take isl_vertex *vertex, void *user),
2691 int isl_vertices_foreach_cell(
2692 __isl_keep isl_vertices *vertices,
2693 int (*fn)(__isl_take isl_cell *cell, void *user),
2695 int isl_cell_foreach_vertex(__isl_keep isl_cell *cell,
2696 int (*fn)(__isl_take isl_vertex *vertex, void *user),
2699 Other operations that can be performed on an C<isl_vertices> object are
2702 isl_ctx *isl_vertices_get_ctx(
2703 __isl_keep isl_vertices *vertices);
2704 int isl_vertices_get_n_vertices(
2705 __isl_keep isl_vertices *vertices);
2706 void isl_vertices_free(__isl_take isl_vertices *vertices);
2708 Vertices can be inspected and destroyed using the following functions.
2710 isl_ctx *isl_vertex_get_ctx(__isl_keep isl_vertex *vertex);
2711 int isl_vertex_get_id(__isl_keep isl_vertex *vertex);
2712 __isl_give isl_basic_set *isl_vertex_get_domain(
2713 __isl_keep isl_vertex *vertex);
2714 __isl_give isl_basic_set *isl_vertex_get_expr(
2715 __isl_keep isl_vertex *vertex);
2716 void isl_vertex_free(__isl_take isl_vertex *vertex);
2718 C<isl_vertex_get_expr> returns a singleton parametric set describing
2719 the vertex, while C<isl_vertex_get_domain> returns the activity domain
2721 Note that C<isl_vertex_get_domain> and C<isl_vertex_get_expr> return
2722 B<rational> basic sets, so they should mainly be used for inspection
2723 and should not be mixed with integer sets.
2725 Chambers can be inspected and destroyed using the following functions.
2727 isl_ctx *isl_cell_get_ctx(__isl_keep isl_cell *cell);
2728 __isl_give isl_basic_set *isl_cell_get_domain(
2729 __isl_keep isl_cell *cell);
2730 void isl_cell_free(__isl_take isl_cell *cell);
2734 Although C<isl> is mainly meant to be used as a library,
2735 it also contains some basic applications that use some
2736 of the functionality of C<isl>.
2737 The input may be specified in either the L<isl format>
2738 or the L<PolyLib format>.
2740 =head2 C<isl_polyhedron_sample>
2742 C<isl_polyhedron_sample> takes a polyhedron as input and prints
2743 an integer element of the polyhedron, if there is any.
2744 The first column in the output is the denominator and is always
2745 equal to 1. If the polyhedron contains no integer points,
2746 then a vector of length zero is printed.
2750 C<isl_pip> takes the same input as the C<example> program
2751 from the C<piplib> distribution, i.e., a set of constraints
2752 on the parameters, a line containing only -1 and finally a set
2753 of constraints on a parametric polyhedron.
2754 The coefficients of the parameters appear in the last columns
2755 (but before the final constant column).
2756 The output is the lexicographic minimum of the parametric polyhedron.
2757 As C<isl> currently does not have its own output format, the output
2758 is just a dump of the internal state.
2760 =head2 C<isl_polyhedron_minimize>
2762 C<isl_polyhedron_minimize> computes the minimum of some linear
2763 or affine objective function over the integer points in a polyhedron.
2764 If an affine objective function
2765 is given, then the constant should appear in the last column.
2767 =head2 C<isl_polytope_scan>
2769 Given a polytope, C<isl_polytope_scan> prints
2770 all integer points in the polytope.