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.
69 The source of C<isl> can be obtained either as a tarball
70 or from the git repository. Both are available from
71 L<http://freshmeat.net/projects/isl/>.
72 The installation process depends on how you obtained
75 =head2 Installation from the git repository
79 =item 1 Clone or update the repository
81 The first time the source is obtained, you need to clone
84 git clone git://repo.or.cz/isl.git
86 To obtain updates, you need to pull in the latest changes
90 =item 2 Generate C<configure>
96 After performing the above steps, continue
97 with the L<Common installation instructions>.
99 =head2 Common installation instructions
103 =item 1 Obtain C<GMP>
105 Building C<isl> requires C<GMP>, including its headers files.
106 Your distribution may not provide these header files by default
107 and you may need to install a package called C<gmp-devel> or something
108 similar. Alternatively, C<GMP> can be built from
109 source, available from L<http://gmplib.org/>.
113 C<isl> uses the standard C<autoconf> C<configure> script.
118 optionally followed by some configure options.
119 A complete list of options can be obtained by running
123 Below we discuss some of the more common options.
125 C<isl> can optionally use C<piplib>, but no
126 C<piplib> functionality is currently used by default.
127 The C<--with-piplib> option can
128 be used to specify which C<piplib>
129 library to use, either an installed version (C<system>),
130 an externally built version (C<build>)
131 or no version (C<no>). The option C<build> is mostly useful
132 in C<configure> scripts of larger projects that bundle both C<isl>
139 Installation prefix for C<isl>
141 =item C<--with-gmp-prefix>
143 Installation prefix for C<GMP> (architecture-independent files).
145 =item C<--with-gmp-exec-prefix>
147 Installation prefix for C<GMP> (architecture-dependent files).
149 =item C<--with-piplib>
151 Which copy of C<piplib> to use, either C<no> (default), C<system> or C<build>.
153 =item C<--with-piplib-prefix>
155 Installation prefix for C<system> C<piplib> (architecture-independent files).
157 =item C<--with-piplib-exec-prefix>
159 Installation prefix for C<system> C<piplib> (architecture-dependent files).
161 =item C<--with-piplib-builddir>
163 Location where C<build> C<piplib> was built.
171 =item 4 Install (optional)
179 =head2 Initialization
181 All manipulations of integer sets and relations occur within
182 the context of an C<isl_ctx>.
183 A given C<isl_ctx> can only be used within a single thread.
184 All arguments of a function are required to have been allocated
185 within the same context.
186 There are currently no functions available for moving an object
187 from one C<isl_ctx> to another C<isl_ctx>. This means that
188 there is currently no way of safely moving an object from one
189 thread to another, unless the whole C<isl_ctx> is moved.
191 An C<isl_ctx> can be allocated using C<isl_ctx_alloc> and
192 freed using C<isl_ctx_free>.
193 All objects allocated within an C<isl_ctx> should be freed
194 before the C<isl_ctx> itself is freed.
196 isl_ctx *isl_ctx_alloc();
197 void isl_ctx_free(isl_ctx *ctx);
201 All operations on integers, mainly the coefficients
202 of the constraints describing the sets and relations,
203 are performed in exact integer arithmetic using C<GMP>.
204 However, to allow future versions of C<isl> to optionally
205 support fixed integer arithmetic, all calls to C<GMP>
206 are wrapped inside C<isl> specific macros.
207 The basic type is C<isl_int> and the operations below
208 are available on this type.
209 The meanings of these operations are essentially the same
210 as their C<GMP> C<mpz_> counterparts.
211 As always with C<GMP> types, C<isl_int>s need to be
212 initialized with C<isl_int_init> before they can be used
213 and they need to be released with C<isl_int_clear>
215 The user should not assume that an C<isl_int> is represented
216 as a C<mpz_t>, but should instead explicitly convert between
217 C<mpz_t>s and C<isl_int>s using C<isl_int_set_gmp> and
218 C<isl_int_get_gmp> whenever a C<mpz_t> is required.
222 =item isl_int_init(i)
224 =item isl_int_clear(i)
226 =item isl_int_set(r,i)
228 =item isl_int_set_si(r,i)
230 =item isl_int_set_gmp(r,g)
232 =item isl_int_get_gmp(i,g)
234 =item isl_int_abs(r,i)
236 =item isl_int_neg(r,i)
238 =item isl_int_swap(i,j)
240 =item isl_int_swap_or_set(i,j)
242 =item isl_int_add_ui(r,i,j)
244 =item isl_int_sub_ui(r,i,j)
246 =item isl_int_add(r,i,j)
248 =item isl_int_sub(r,i,j)
250 =item isl_int_mul(r,i,j)
252 =item isl_int_mul_ui(r,i,j)
254 =item isl_int_addmul(r,i,j)
256 =item isl_int_submul(r,i,j)
258 =item isl_int_gcd(r,i,j)
260 =item isl_int_lcm(r,i,j)
262 =item isl_int_divexact(r,i,j)
264 =item isl_int_cdiv_q(r,i,j)
266 =item isl_int_fdiv_q(r,i,j)
268 =item isl_int_fdiv_r(r,i,j)
270 =item isl_int_fdiv_q_ui(r,i,j)
272 =item isl_int_read(r,s)
274 =item isl_int_print(out,i,width)
278 =item isl_int_cmp(i,j)
280 =item isl_int_cmp_si(i,si)
282 =item isl_int_eq(i,j)
284 =item isl_int_ne(i,j)
286 =item isl_int_lt(i,j)
288 =item isl_int_le(i,j)
290 =item isl_int_gt(i,j)
292 =item isl_int_ge(i,j)
294 =item isl_int_abs_eq(i,j)
296 =item isl_int_abs_ne(i,j)
298 =item isl_int_abs_lt(i,j)
300 =item isl_int_abs_gt(i,j)
302 =item isl_int_abs_ge(i,j)
304 =item isl_int_is_zero(i)
306 =item isl_int_is_one(i)
308 =item isl_int_is_negone(i)
310 =item isl_int_is_pos(i)
312 =item isl_int_is_neg(i)
314 =item isl_int_is_nonpos(i)
316 =item isl_int_is_nonneg(i)
318 =item isl_int_is_divisible_by(i,j)
322 =head2 Sets and Relations
324 C<isl> uses six types of objects for representing sets and relations,
325 C<isl_basic_set>, C<isl_basic_map>, C<isl_set>, C<isl_map>,
326 C<isl_union_set> and C<isl_union_map>.
327 C<isl_basic_set> and C<isl_basic_map> represent sets and relations that
328 can be described as a conjunction of affine constraints, while
329 C<isl_set> and C<isl_map> represent unions of
330 C<isl_basic_set>s and C<isl_basic_map>s, respectively.
331 However, all C<isl_basic_set>s or C<isl_basic_map>s in the union need
332 to have the same dimension. C<isl_union_set>s and C<isl_union_map>s
333 represent unions of C<isl_set>s or C<isl_map>s of I<different> dimensions,
334 where dimensions with different space names
335 (see L<Dimension Specifications>) are considered different as well.
336 The difference between sets and relations (maps) is that sets have
337 one set of variables, while relations have two sets of variables,
338 input variables and output variables.
340 =head2 Memory Management
342 Since a high-level operation on sets and/or relations usually involves
343 several substeps and since the user is usually not interested in
344 the intermediate results, most functions that return a new object
345 will also release all the objects passed as arguments.
346 If the user still wants to use one or more of these arguments
347 after the function call, she should pass along a copy of the
348 object rather than the object itself.
349 The user is then responsible for make sure that the original
350 object gets used somewhere else or is explicitly freed.
352 The arguments and return values of all documents functions are
353 annotated to make clear which arguments are released and which
354 arguments are preserved. In particular, the following annotations
361 C<__isl_give> means that a new object is returned.
362 The user should make sure that the returned pointer is
363 used exactly once as a value for an C<__isl_take> argument.
364 In between, it can be used as a value for as many
365 C<__isl_keep> arguments as the user likes.
366 There is one exception, and that is the case where the
367 pointer returned is C<NULL>. Is this case, the user
368 is free to use it as an C<__isl_take> argument or not.
372 C<__isl_take> means that the object the argument points to
373 is taken over by the function and may no longer be used
374 by the user as an argument to any other function.
375 The pointer value must be one returned by a function
376 returning an C<__isl_give> pointer.
377 If the user passes in a C<NULL> value, then this will
378 be treated as an error in the sense that the function will
379 not perform its usual operation. However, it will still
380 make sure that all the the other C<__isl_take> arguments
385 C<__isl_keep> means that the function will only use the object
386 temporarily. After the function has finished, the user
387 can still use it as an argument to other functions.
388 A C<NULL> value will be treated in the same way as
389 a C<NULL> value for an C<__isl_take> argument.
393 =head2 Dimension Specifications
395 Whenever a new set or relation is created from scratch,
396 its dimension needs to be specified using an C<isl_dim>.
399 __isl_give isl_dim *isl_dim_alloc(isl_ctx *ctx,
400 unsigned nparam, unsigned n_in, unsigned n_out);
401 __isl_give isl_dim *isl_dim_set_alloc(isl_ctx *ctx,
402 unsigned nparam, unsigned dim);
403 __isl_give isl_dim *isl_dim_copy(__isl_keep isl_dim *dim);
404 void isl_dim_free(__isl_take isl_dim *dim);
405 unsigned isl_dim_size(__isl_keep isl_dim *dim,
406 enum isl_dim_type type);
408 The dimension specification used for creating a set
409 needs to be created using C<isl_dim_set_alloc>, while
410 that for creating a relation
411 needs to be created using C<isl_dim_alloc>.
412 C<isl_dim_size> can be used
413 to find out the number of dimensions of each type in
414 a dimension specification, where type may be
415 C<isl_dim_param>, C<isl_dim_in> (only for relations),
416 C<isl_dim_out> (only for relations), C<isl_dim_set>
417 (only for sets) or C<isl_dim_all>.
419 It is often useful to create objects that live in the
420 same space as some other object. This can be accomplished
421 by creating the new objects
422 (see L<Creating New Sets and Relations> or
423 L<Creating New (Piecewise) Quasipolynomials>) based on the dimension
424 specification of the original object.
427 __isl_give isl_dim *isl_basic_set_get_dim(
428 __isl_keep isl_basic_set *bset);
429 __isl_give isl_dim *isl_set_get_dim(__isl_keep isl_set *set);
431 #include <isl/union_set.h>
432 __isl_give isl_dim *isl_union_set_get_dim(
433 __isl_keep isl_union_set *uset);
436 __isl_give isl_dim *isl_basic_map_get_dim(
437 __isl_keep isl_basic_map *bmap);
438 __isl_give isl_dim *isl_map_get_dim(__isl_keep isl_map *map);
440 #include <isl/union_map.h>
441 __isl_give isl_dim *isl_union_map_get_dim(
442 __isl_keep isl_union_map *umap);
444 #include <isl/polynomial.h>
445 __isl_give isl_dim *isl_qpolynomial_get_dim(
446 __isl_keep isl_qpolynomial *qp);
447 __isl_give isl_dim *isl_pw_qpolynomial_get_dim(
448 __isl_keep isl_pw_qpolynomial *pwqp);
449 __isl_give isl_dim *isl_union_pw_qpolynomial_get_dim(
450 __isl_keep isl_union_pw_qpolynomial *upwqp);
451 __isl_give isl_dim *isl_union_pw_qpolynomial_fold_get_dim(
452 __isl_keep isl_union_pw_qpolynomial_fold *upwf);
454 The names of the individual dimensions may be set or read off
455 using the following functions.
458 __isl_give isl_dim *isl_dim_set_name(__isl_take isl_dim *dim,
459 enum isl_dim_type type, unsigned pos,
460 __isl_keep const char *name);
461 __isl_keep const char *isl_dim_get_name(__isl_keep isl_dim *dim,
462 enum isl_dim_type type, unsigned pos);
464 Note that C<isl_dim_get_name> returns a pointer to some internal
465 data structure, so the result can only be used while the
466 corresponding C<isl_dim> is alive.
467 Also note that every function that operates on two sets or relations
468 requires that both arguments have the same parameters. This also
469 means that if one of the arguments has named parameters, then the
470 other needs to have named parameters too and the names need to match.
471 Pairs of C<isl_union_set> and/or C<isl_union_map> arguments may
472 have different parameters (as long as they are named), in which case
473 the result will have as parameters the union of the parameters of
476 The names of entire spaces may be set or read off
477 using the following functions.
480 __isl_give isl_dim *isl_dim_set_tuple_name(
481 __isl_take isl_dim *dim,
482 enum isl_dim_type type, const char *s);
483 const char *isl_dim_get_tuple_name(__isl_keep isl_dim *dim,
484 enum isl_dim_type type);
486 The C<dim> argument needs to be one of C<isl_dim_in>, C<isl_dim_out>
487 or C<isl_dim_set>. As with C<isl_dim_get_name>,
488 the C<isl_dim_get_tuple_name> function returns a pointer to some internal
490 Binary operations require the corresponding spaces of their arguments
491 to have the same name.
493 Spaces can be nested. In particular, the domain of a set or
494 the domain or range of a relation can be a nested relation.
495 The following functions can be used to construct and deconstruct
496 such nested dimension specifications.
499 int isl_dim_is_wrapping(__isl_keep isl_dim *dim);
500 __isl_give isl_dim *isl_dim_wrap(__isl_take isl_dim *dim);
501 __isl_give isl_dim *isl_dim_unwrap(__isl_take isl_dim *dim);
503 The input to C<isl_dim_is_wrapping> and C<isl_dim_unwrap> should
504 be the dimension specification of a set, while that of
505 C<isl_dim_wrap> should be the dimension specification of a relation.
506 Conversely, the output of C<isl_dim_unwrap> is the dimension specification
507 of a relation, while that of C<isl_dim_wrap> is the dimension specification
510 Dimension specifications can be created from other dimension
511 specifications using the following functions.
513 __isl_give isl_dim *isl_dim_domain(__isl_take isl_dim *dim);
514 __isl_give isl_dim *isl_dim_from_domain(__isl_take isl_dim *dim);
515 __isl_give isl_dim *isl_dim_range(__isl_take isl_dim *dim);
516 __isl_give isl_dim *isl_dim_from_range(__isl_take isl_dim *dim);
517 __isl_give isl_dim *isl_dim_reverse(__isl_take isl_dim *dim);
518 __isl_give isl_dim *isl_dim_join(__isl_take isl_dim *left,
519 __isl_take isl_dim *right);
520 __isl_give isl_dim *isl_dim_insert(__isl_take isl_dim *dim,
521 enum isl_dim_type type, unsigned pos, unsigned n);
522 __isl_give isl_dim *isl_dim_add(__isl_take isl_dim *dim,
523 enum isl_dim_type type, unsigned n);
524 __isl_give isl_dim *isl_dim_drop(__isl_take isl_dim *dim,
525 enum isl_dim_type type, unsigned first, unsigned n);
527 Note that if dimensions are added or removed from a space, then
528 the name and the internal structure are lost.
530 =head2 Input and Output
532 C<isl> supports its own input/output format, which is similar
533 to the C<Omega> format, but also supports the C<PolyLib> format
538 The C<isl> format is similar to that of C<Omega>, but has a different
539 syntax for describing the parameters and allows for the definition
540 of an existentially quantified variable as the integer division
541 of an affine expression.
542 For example, the set of integers C<i> between C<0> and C<n>
543 such that C<i % 10 <= 6> can be described as
545 [n] -> { [i] : exists (a = [i/10] : 0 <= i and i <= n and
548 A set or relation can have several disjuncts, separated
549 by the keyword C<or>. Each disjunct is either a conjunction
550 of constraints or a projection (C<exists>) of a conjunction
551 of constraints. The constraints are separated by the keyword
554 =head3 C<PolyLib> format
556 If the represented set is a union, then the first line
557 contains a single number representing the number of disjuncts.
558 Otherwise, a line containing the number C<1> is optional.
560 Each disjunct is represented by a matrix of constraints.
561 The first line contains two numbers representing
562 the number of rows and columns,
563 where the number of rows is equal to the number of constraints
564 and the number of columns is equal to two plus the number of variables.
565 The following lines contain the actual rows of the constraint matrix.
566 In each row, the first column indicates whether the constraint
567 is an equality (C<0>) or inequality (C<1>). The final column
568 corresponds to the constant term.
570 If the set is parametric, then the coefficients of the parameters
571 appear in the last columns before the constant column.
572 The coefficients of any existentially quantified variables appear
573 between those of the set variables and those of the parameters.
575 =head3 Extended C<PolyLib> format
577 The extended C<PolyLib> format is nearly identical to the
578 C<PolyLib> format. The only difference is that the line
579 containing the number of rows and columns of a constraint matrix
580 also contains four additional numbers:
581 the number of output dimensions, the number of input dimensions,
582 the number of local dimensions (i.e., the number of existentially
583 quantified variables) and the number of parameters.
584 For sets, the number of ``output'' dimensions is equal
585 to the number of set dimensions, while the number of ``input''
591 __isl_give isl_basic_set *isl_basic_set_read_from_file(
592 isl_ctx *ctx, FILE *input, int nparam);
593 __isl_give isl_basic_set *isl_basic_set_read_from_str(
594 isl_ctx *ctx, const char *str, int nparam);
595 __isl_give isl_set *isl_set_read_from_file(isl_ctx *ctx,
596 FILE *input, int nparam);
597 __isl_give isl_set *isl_set_read_from_str(isl_ctx *ctx,
598 const char *str, int nparam);
601 __isl_give isl_basic_map *isl_basic_map_read_from_file(
602 isl_ctx *ctx, FILE *input, int nparam);
603 __isl_give isl_basic_map *isl_basic_map_read_from_str(
604 isl_ctx *ctx, const char *str, int nparam);
605 __isl_give isl_map *isl_map_read_from_file(
606 struct isl_ctx *ctx, FILE *input, int nparam);
607 __isl_give isl_map *isl_map_read_from_str(isl_ctx *ctx,
608 const char *str, int nparam);
610 #include <isl/union_set.h>
611 __isl_give isl_union_set *isl_union_set_read_from_str(
612 struct isl_ctx *ctx, const char *str);
614 #include <isl/union_map.h>
615 __isl_give isl_union_map *isl_union_map_read_from_str(
616 struct isl_ctx *ctx, const char *str);
618 The input format is autodetected and may be either the C<PolyLib> format
619 or the C<isl> format.
620 C<nparam> specifies how many of the final columns in
621 the C<PolyLib> format correspond to parameters.
622 If input is given in the C<isl> format, then the number
623 of parameters needs to be equal to C<nparam>.
624 If C<nparam> is negative, then any number of parameters
625 is accepted in the C<isl> format and zero parameters
626 are assumed in the C<PolyLib> format.
630 Before anything can be printed, an C<isl_printer> needs to
633 __isl_give isl_printer *isl_printer_to_file(isl_ctx *ctx,
635 __isl_give isl_printer *isl_printer_to_str(isl_ctx *ctx);
636 void isl_printer_free(__isl_take isl_printer *printer);
637 __isl_give char *isl_printer_get_str(
638 __isl_keep isl_printer *printer);
640 The behavior of the printer can be modified in various ways
642 __isl_give isl_printer *isl_printer_set_output_format(
643 __isl_take isl_printer *p, int output_format);
644 __isl_give isl_printer *isl_printer_set_indent(
645 __isl_take isl_printer *p, int indent);
646 __isl_give isl_printer *isl_printer_set_prefix(
647 __isl_take isl_printer *p, const char *prefix);
648 __isl_give isl_printer *isl_printer_set_suffix(
649 __isl_take isl_printer *p, const char *suffix);
651 The C<output_format> may be either C<ISL_FORMAT_ISL>, C<ISL_FORMAT_OMEGA>,
652 C<ISL_FORMAT_POLYLIB>, C<ISL_FORMAT_EXT_POLYLIB> or C<ISL_FORMAT_LATEX>
653 and defaults to C<ISL_FORMAT_ISL>.
654 Each line in the output is indented by C<indent> spaces
655 (default: 0), prefixed by C<prefix> and suffixed by C<suffix>.
656 In the C<PolyLib> format output,
657 the coefficients of the existentially quantified variables
658 appear between those of the set variables and those
661 To actually print something, use
664 __isl_give isl_printer *isl_printer_print_basic_set(
665 __isl_take isl_printer *printer,
666 __isl_keep isl_basic_set *bset);
667 __isl_give isl_printer *isl_printer_print_set(
668 __isl_take isl_printer *printer,
669 __isl_keep isl_set *set);
672 __isl_give isl_printer *isl_printer_print_basic_map(
673 __isl_take isl_printer *printer,
674 __isl_keep isl_basic_map *bmap);
675 __isl_give isl_printer *isl_printer_print_map(
676 __isl_take isl_printer *printer,
677 __isl_keep isl_map *map);
679 #include <isl/union_set.h>
680 __isl_give isl_printer *isl_printer_print_union_set(
681 __isl_take isl_printer *p,
682 __isl_keep isl_union_set *uset);
684 #include <isl/union_map.h>
685 __isl_give isl_printer *isl_printer_print_union_map(
686 __isl_take isl_printer *p,
687 __isl_keep isl_union_map *umap);
689 When called on a file printer, the following function flushes
690 the file. When called on a string printer, the buffer is cleared.
692 __isl_give isl_printer *isl_printer_flush(
693 __isl_take isl_printer *p);
695 =head2 Creating New Sets and Relations
697 C<isl> has functions for creating some standard sets and relations.
701 =item * Empty sets and relations
703 __isl_give isl_basic_set *isl_basic_set_empty(
704 __isl_take isl_dim *dim);
705 __isl_give isl_basic_map *isl_basic_map_empty(
706 __isl_take isl_dim *dim);
707 __isl_give isl_set *isl_set_empty(
708 __isl_take isl_dim *dim);
709 __isl_give isl_map *isl_map_empty(
710 __isl_take isl_dim *dim);
711 __isl_give isl_union_set *isl_union_set_empty(
712 __isl_take isl_dim *dim);
713 __isl_give isl_union_map *isl_union_map_empty(
714 __isl_take isl_dim *dim);
716 For C<isl_union_set>s and C<isl_union_map>s, the dimensions specification
717 is only used to specify the parameters.
719 =item * Universe sets and relations
721 __isl_give isl_basic_set *isl_basic_set_universe(
722 __isl_take isl_dim *dim);
723 __isl_give isl_basic_map *isl_basic_map_universe(
724 __isl_take isl_dim *dim);
725 __isl_give isl_set *isl_set_universe(
726 __isl_take isl_dim *dim);
727 __isl_give isl_map *isl_map_universe(
728 __isl_take isl_dim *dim);
730 The sets and relations constructed by the functions above
731 contain all integer values, while those constructed by the
732 functions below only contain non-negative values.
734 __isl_give isl_basic_set *isl_basic_set_nat_universe(
735 __isl_take isl_dim *dim);
736 __isl_give isl_basic_map *isl_basic_map_nat_universe(
737 __isl_take isl_dim *dim);
738 __isl_give isl_set *isl_set_nat_universe(
739 __isl_take isl_dim *dim);
740 __isl_give isl_map *isl_map_nat_universe(
741 __isl_take isl_dim *dim);
743 =item * Identity relations
745 __isl_give isl_basic_map *isl_basic_map_identity(
746 __isl_take isl_dim *set_dim);
747 __isl_give isl_map *isl_map_identity(
748 __isl_take isl_dim *set_dim);
750 These functions take a dimension specification for a B<set>
751 and return an identity relation between two such sets.
753 =item * Lexicographic order
755 __isl_give isl_map *isl_map_lex_lt(
756 __isl_take isl_dim *set_dim);
757 __isl_give isl_map *isl_map_lex_le(
758 __isl_take isl_dim *set_dim);
759 __isl_give isl_map *isl_map_lex_gt(
760 __isl_take isl_dim *set_dim);
761 __isl_give isl_map *isl_map_lex_ge(
762 __isl_take isl_dim *set_dim);
763 __isl_give isl_map *isl_map_lex_lt_first(
764 __isl_take isl_dim *dim, unsigned n);
765 __isl_give isl_map *isl_map_lex_le_first(
766 __isl_take isl_dim *dim, unsigned n);
767 __isl_give isl_map *isl_map_lex_gt_first(
768 __isl_take isl_dim *dim, unsigned n);
769 __isl_give isl_map *isl_map_lex_ge_first(
770 __isl_take isl_dim *dim, unsigned n);
772 The first four functions take a dimension specification for a B<set>
773 and return relations that express that the elements in the domain
774 are lexicographically less
775 (C<isl_map_lex_lt>), less or equal (C<isl_map_lex_le>),
776 greater (C<isl_map_lex_gt>) or greater or equal (C<isl_map_lex_ge>)
777 than the elements in the range.
778 The last four functions take a dimension specification for a map
779 and return relations that express that the first C<n> dimensions
780 in the domain are lexicographically less
781 (C<isl_map_lex_lt_first>), less or equal (C<isl_map_lex_le_first>),
782 greater (C<isl_map_lex_gt_first>) or greater or equal (C<isl_map_lex_ge_first>)
783 than the first C<n> dimensions in the range.
787 A basic set or relation can be converted to a set or relation
788 using the following functions.
790 __isl_give isl_set *isl_set_from_basic_set(
791 __isl_take isl_basic_set *bset);
792 __isl_give isl_map *isl_map_from_basic_map(
793 __isl_take isl_basic_map *bmap);
795 Sets and relations can be converted to union sets and relations
796 using the following functions.
798 __isl_give isl_union_map *isl_union_map_from_map(
799 __isl_take isl_map *map);
800 __isl_give isl_union_set *isl_union_set_from_set(
801 __isl_take isl_set *set);
803 Sets and relations can be copied and freed again using the following
806 __isl_give isl_basic_set *isl_basic_set_copy(
807 __isl_keep isl_basic_set *bset);
808 __isl_give isl_set *isl_set_copy(__isl_keep isl_set *set);
809 __isl_give isl_union_set *isl_union_set_copy(
810 __isl_keep isl_union_set *uset);
811 __isl_give isl_basic_map *isl_basic_map_copy(
812 __isl_keep isl_basic_map *bmap);
813 __isl_give isl_map *isl_map_copy(__isl_keep isl_map *map);
814 __isl_give isl_union_map *isl_union_map_copy(
815 __isl_keep isl_union_map *umap);
816 void isl_basic_set_free(__isl_take isl_basic_set *bset);
817 void isl_set_free(__isl_take isl_set *set);
818 void isl_union_set_free(__isl_take isl_union_set *uset);
819 void isl_basic_map_free(__isl_take isl_basic_map *bmap);
820 void isl_map_free(__isl_take isl_map *map);
821 void isl_union_map_free(__isl_take isl_union_map *umap);
823 Other sets and relations can be constructed by starting
824 from a universe set or relation, adding equality and/or
825 inequality constraints and then projecting out the
826 existentially quantified variables, if any.
827 Constraints can be constructed, manipulated and
828 added to basic sets and relations using the following functions.
830 #include <isl/constraint.h>
831 __isl_give isl_constraint *isl_equality_alloc(
832 __isl_take isl_dim *dim);
833 __isl_give isl_constraint *isl_inequality_alloc(
834 __isl_take isl_dim *dim);
835 void isl_constraint_set_constant(
836 __isl_keep isl_constraint *constraint, isl_int v);
837 void isl_constraint_set_coefficient(
838 __isl_keep isl_constraint *constraint,
839 enum isl_dim_type type, int pos, isl_int v);
840 __isl_give isl_basic_map *isl_basic_map_add_constraint(
841 __isl_take isl_basic_map *bmap,
842 __isl_take isl_constraint *constraint);
843 __isl_give isl_basic_set *isl_basic_set_add_constraint(
844 __isl_take isl_basic_set *bset,
845 __isl_take isl_constraint *constraint);
847 For example, to create a set containing the even integers
848 between 10 and 42, you would use the following code.
852 struct isl_constraint *c;
853 struct isl_basic_set *bset;
856 dim = isl_dim_set_alloc(ctx, 0, 2);
857 bset = isl_basic_set_universe(isl_dim_copy(dim));
859 c = isl_equality_alloc(isl_dim_copy(dim));
860 isl_int_set_si(v, -1);
861 isl_constraint_set_coefficient(c, isl_dim_set, 0, v);
862 isl_int_set_si(v, 2);
863 isl_constraint_set_coefficient(c, isl_dim_set, 1, v);
864 bset = isl_basic_set_add_constraint(bset, c);
866 c = isl_inequality_alloc(isl_dim_copy(dim));
867 isl_int_set_si(v, -10);
868 isl_constraint_set_constant(c, v);
869 isl_int_set_si(v, 1);
870 isl_constraint_set_coefficient(c, isl_dim_set, 0, v);
871 bset = isl_basic_set_add_constraint(bset, c);
873 c = isl_inequality_alloc(dim);
874 isl_int_set_si(v, 42);
875 isl_constraint_set_constant(c, v);
876 isl_int_set_si(v, -1);
877 isl_constraint_set_coefficient(c, isl_dim_set, 0, v);
878 bset = isl_basic_set_add_constraint(bset, c);
880 bset = isl_basic_set_project_out(bset, isl_dim_set, 1, 1);
886 struct isl_basic_set *bset;
887 bset = isl_basic_set_read_from_str(ctx,
888 "{[i] : exists (a : i = 2a and i >= 10 and i <= 42)}", -1);
890 A basic set or relation can also be constructed from two matrices
891 describing the equalities and the inequalities.
893 __isl_give isl_basic_set *isl_basic_set_from_constraint_matrices(
894 __isl_take isl_dim *dim,
895 __isl_take isl_mat *eq, __isl_take isl_mat *ineq,
896 enum isl_dim_type c1,
897 enum isl_dim_type c2, enum isl_dim_type c3,
898 enum isl_dim_type c4);
899 __isl_give isl_basic_map *isl_basic_map_from_constraint_matrices(
900 __isl_take isl_dim *dim,
901 __isl_take isl_mat *eq, __isl_take isl_mat *ineq,
902 enum isl_dim_type c1,
903 enum isl_dim_type c2, enum isl_dim_type c3,
904 enum isl_dim_type c4, enum isl_dim_type c5);
906 The C<isl_dim_type> arguments indicate the order in which
907 different kinds of variables appear in the input matrices
908 and should be a permutation of C<isl_dim_cst>, C<isl_dim_param>,
909 C<isl_dim_set> and C<isl_dim_div> for sets and
910 of C<isl_dim_cst>, C<isl_dim_param>,
911 C<isl_dim_in>, C<isl_dim_out> and C<isl_dim_div> for relations.
913 =head2 Inspecting Sets and Relations
915 Usually, the user should not have to care about the actual constraints
916 of the sets and maps, but should instead apply the abstract operations
917 explained in the following sections.
918 Occasionally, however, it may be required to inspect the individual
919 coefficients of the constraints. This section explains how to do so.
920 In these cases, it may also be useful to have C<isl> compute
921 an explicit representation of the existentially quantified variables.
923 __isl_give isl_set *isl_set_compute_divs(
924 __isl_take isl_set *set);
925 __isl_give isl_map *isl_map_compute_divs(
926 __isl_take isl_map *map);
927 __isl_give isl_union_set *isl_union_set_compute_divs(
928 __isl_take isl_union_set *uset);
929 __isl_give isl_union_map *isl_union_map_compute_divs(
930 __isl_take isl_union_map *umap);
932 This explicit representation defines the existentially quantified
933 variables as integer divisions of the other variables, possibly
934 including earlier existentially quantified variables.
935 An explicitly represented existentially quantified variable therefore
936 has a unique value when the values of the other variables are known.
937 If, furthermore, the same existentials, i.e., existentials
938 with the same explicit representations, should appear in the
939 same order in each of the disjuncts of a set or map, then the user should call
940 either of the following functions.
942 __isl_give isl_set *isl_set_align_divs(
943 __isl_take isl_set *set);
944 __isl_give isl_map *isl_map_align_divs(
945 __isl_take isl_map *map);
947 Alternatively, the existentially quantified variables can be removed
948 using the following functions, which compute an overapproximation.
950 __isl_give isl_basic_set *isl_basic_set_remove_divs(
951 __isl_take isl_basic_set *bset);
952 __isl_give isl_basic_map *isl_basic_map_remove_divs(
953 __isl_take isl_basic_map *bmap);
954 __isl_give isl_set *isl_set_remove_divs(
955 __isl_take isl_set *set);
957 To iterate over all the sets or maps in a union set or map, use
959 int isl_union_set_foreach_set(__isl_keep isl_union_set *uset,
960 int (*fn)(__isl_take isl_set *set, void *user),
962 int isl_union_map_foreach_map(__isl_keep isl_union_map *umap,
963 int (*fn)(__isl_take isl_map *map, void *user),
966 The number of sets or maps in a union set or map can be obtained
969 int isl_union_set_n_set(__isl_keep isl_union_set *uset);
970 int isl_union_map_n_map(__isl_keep isl_union_map *umap);
972 To extract the set or map from a union with a given dimension
975 __isl_give isl_set *isl_union_set_extract_set(
976 __isl_keep isl_union_set *uset,
977 __isl_take isl_dim *dim);
978 __isl_give isl_map *isl_union_map_extract_map(
979 __isl_keep isl_union_map *umap,
980 __isl_take isl_dim *dim);
982 To iterate over all the basic sets or maps in a set or map, use
984 int isl_set_foreach_basic_set(__isl_keep isl_set *set,
985 int (*fn)(__isl_take isl_basic_set *bset, void *user),
987 int isl_map_foreach_basic_map(__isl_keep isl_map *map,
988 int (*fn)(__isl_take isl_basic_map *bmap, void *user),
991 The callback function C<fn> should return 0 if successful and
992 -1 if an error occurs. In the latter case, or if any other error
993 occurs, the above functions will return -1.
995 It should be noted that C<isl> does not guarantee that
996 the basic sets or maps passed to C<fn> are disjoint.
997 If this is required, then the user should call one of
998 the following functions first.
1000 __isl_give isl_set *isl_set_make_disjoint(
1001 __isl_take isl_set *set);
1002 __isl_give isl_map *isl_map_make_disjoint(
1003 __isl_take isl_map *map);
1005 The number of basic sets in a set can be obtained
1008 int isl_set_n_basic_set(__isl_keep isl_set *set);
1010 To iterate over the constraints of a basic set or map, use
1012 #include <isl/constraint.h>
1014 int isl_basic_map_foreach_constraint(
1015 __isl_keep isl_basic_map *bmap,
1016 int (*fn)(__isl_take isl_constraint *c, void *user),
1018 void isl_constraint_free(struct isl_constraint *c);
1020 Again, the callback function C<fn> should return 0 if successful and
1021 -1 if an error occurs. In the latter case, or if any other error
1022 occurs, the above functions will return -1.
1023 The constraint C<c> represents either an equality or an inequality.
1024 Use the following function to find out whether a constraint
1025 represents an equality. If not, it represents an inequality.
1027 int isl_constraint_is_equality(
1028 __isl_keep isl_constraint *constraint);
1030 The coefficients of the constraints can be inspected using
1031 the following functions.
1033 void isl_constraint_get_constant(
1034 __isl_keep isl_constraint *constraint, isl_int *v);
1035 void isl_constraint_get_coefficient(
1036 __isl_keep isl_constraint *constraint,
1037 enum isl_dim_type type, int pos, isl_int *v);
1039 The explicit representations of the existentially quantified
1040 variables can be inspected using the following functions.
1041 Note that the user is only allowed to use these functions
1042 if the inspected set or map is the result of a call
1043 to C<isl_set_compute_divs> or C<isl_map_compute_divs>.
1045 __isl_give isl_div *isl_constraint_div(
1046 __isl_keep isl_constraint *constraint, int pos);
1047 void isl_div_get_constant(__isl_keep isl_div *div,
1049 void isl_div_get_denominator(__isl_keep isl_div *div,
1051 void isl_div_get_coefficient(__isl_keep isl_div *div,
1052 enum isl_dim_type type, int pos, isl_int *v);
1054 To obtain the constraints of a basic set or map in matrix
1055 form, use the following functions.
1057 __isl_give isl_mat *isl_basic_set_equalities_matrix(
1058 __isl_keep isl_basic_set *bset,
1059 enum isl_dim_type c1, enum isl_dim_type c2,
1060 enum isl_dim_type c3, enum isl_dim_type c4);
1061 __isl_give isl_mat *isl_basic_set_inequalities_matrix(
1062 __isl_keep isl_basic_set *bset,
1063 enum isl_dim_type c1, enum isl_dim_type c2,
1064 enum isl_dim_type c3, enum isl_dim_type c4);
1065 __isl_give isl_mat *isl_basic_map_equalities_matrix(
1066 __isl_keep isl_basic_map *bmap,
1067 enum isl_dim_type c1,
1068 enum isl_dim_type c2, enum isl_dim_type c3,
1069 enum isl_dim_type c4, enum isl_dim_type c5);
1070 __isl_give isl_mat *isl_basic_map_inequalities_matrix(
1071 __isl_keep isl_basic_map *bmap,
1072 enum isl_dim_type c1,
1073 enum isl_dim_type c2, enum isl_dim_type c3,
1074 enum isl_dim_type c4, enum isl_dim_type c5);
1076 The C<isl_dim_type> arguments dictate the order in which
1077 different kinds of variables appear in the resulting matrix
1078 and should be a permutation of C<isl_dim_cst>, C<isl_dim_param>,
1079 C<isl_dim_in>, C<isl_dim_out> and C<isl_dim_div>.
1081 The names of the domain and range spaces of a set or relation can be
1082 read off using the following functions.
1084 const char *isl_basic_set_get_tuple_name(
1085 __isl_keep isl_basic_set *bset);
1086 const char *isl_set_get_tuple_name(
1087 __isl_keep isl_set *set);
1088 const char *isl_basic_map_get_tuple_name(
1089 __isl_keep isl_basic_map *bmap,
1090 enum isl_dim_type type);
1091 const char *isl_map_get_tuple_name(
1092 __isl_keep isl_map *map,
1093 enum isl_dim_type type);
1095 As with C<isl_dim_get_tuple_name>, the value returned points to
1096 an internal data structure.
1097 The names of individual dimensions can be read off using
1098 the following functions.
1100 const char *isl_constraint_get_dim_name(
1101 __isl_keep isl_constraint *constraint,
1102 enum isl_dim_type type, unsigned pos);
1103 const char *isl_set_get_dim_name(
1104 __isl_keep isl_set *set,
1105 enum isl_dim_type type, unsigned pos);
1106 const char *isl_basic_map_get_dim_name(
1107 __isl_keep isl_basic_map *bmap,
1108 enum isl_dim_type type, unsigned pos);
1109 const char *isl_map_get_dim_name(
1110 __isl_keep isl_map *map,
1111 enum isl_dim_type type, unsigned pos);
1113 These functions are mostly useful to obtain the names
1118 =head3 Unary Properties
1124 The following functions test whether the given set or relation
1125 contains any integer points. The ``fast'' variants do not perform
1126 any computations, but simply check if the given set or relation
1127 is already known to be empty.
1129 int isl_basic_set_fast_is_empty(__isl_keep isl_basic_set *bset);
1130 int isl_basic_set_is_empty(__isl_keep isl_basic_set *bset);
1131 int isl_set_is_empty(__isl_keep isl_set *set);
1132 int isl_union_set_is_empty(__isl_keep isl_union_set *uset);
1133 int isl_basic_map_fast_is_empty(__isl_keep isl_basic_map *bmap);
1134 int isl_basic_map_is_empty(__isl_keep isl_basic_map *bmap);
1135 int isl_map_fast_is_empty(__isl_keep isl_map *map);
1136 int isl_map_is_empty(__isl_keep isl_map *map);
1137 int isl_union_map_is_empty(__isl_keep isl_union_map *umap);
1139 =item * Universality
1141 int isl_basic_set_is_universe(__isl_keep isl_basic_set *bset);
1142 int isl_basic_map_is_universe(__isl_keep isl_basic_map *bmap);
1143 int isl_set_fast_is_universe(__isl_keep isl_set *set);
1145 =item * Single-valuedness
1147 int isl_map_is_single_valued(__isl_keep isl_map *map);
1151 int isl_map_is_bijective(__isl_keep isl_map *map);
1155 The followning functions check whether the domain of the given
1156 (basic) set is a wrapped relation.
1158 int isl_basic_set_is_wrapping(
1159 __isl_keep isl_basic_set *bset);
1160 int isl_set_is_wrapping(__isl_keep isl_set *set);
1164 =head3 Binary Properties
1170 int isl_set_fast_is_equal(__isl_keep isl_set *set1,
1171 __isl_keep isl_set *set2);
1172 int isl_set_is_equal(__isl_keep isl_set *set1,
1173 __isl_keep isl_set *set2);
1174 int isl_union_set_is_equal(
1175 __isl_keep isl_union_set *uset1,
1176 __isl_keep isl_union_set *uset2);
1177 int isl_basic_map_is_equal(
1178 __isl_keep isl_basic_map *bmap1,
1179 __isl_keep isl_basic_map *bmap2);
1180 int isl_map_is_equal(__isl_keep isl_map *map1,
1181 __isl_keep isl_map *map2);
1182 int isl_map_fast_is_equal(__isl_keep isl_map *map1,
1183 __isl_keep isl_map *map2);
1184 int isl_union_map_is_equal(
1185 __isl_keep isl_union_map *umap1,
1186 __isl_keep isl_union_map *umap2);
1188 =item * Disjointness
1190 int isl_set_fast_is_disjoint(__isl_keep isl_set *set1,
1191 __isl_keep isl_set *set2);
1195 int isl_set_is_subset(__isl_keep isl_set *set1,
1196 __isl_keep isl_set *set2);
1197 int isl_set_is_strict_subset(
1198 __isl_keep isl_set *set1,
1199 __isl_keep isl_set *set2);
1200 int isl_union_set_is_subset(
1201 __isl_keep isl_union_set *uset1,
1202 __isl_keep isl_union_set *uset2);
1203 int isl_union_set_is_strict_subset(
1204 __isl_keep isl_union_set *uset1,
1205 __isl_keep isl_union_set *uset2);
1206 int isl_basic_map_is_subset(
1207 __isl_keep isl_basic_map *bmap1,
1208 __isl_keep isl_basic_map *bmap2);
1209 int isl_basic_map_is_strict_subset(
1210 __isl_keep isl_basic_map *bmap1,
1211 __isl_keep isl_basic_map *bmap2);
1212 int isl_map_is_subset(
1213 __isl_keep isl_map *map1,
1214 __isl_keep isl_map *map2);
1215 int isl_map_is_strict_subset(
1216 __isl_keep isl_map *map1,
1217 __isl_keep isl_map *map2);
1218 int isl_union_map_is_subset(
1219 __isl_keep isl_union_map *umap1,
1220 __isl_keep isl_union_map *umap2);
1221 int isl_union_map_is_strict_subset(
1222 __isl_keep isl_union_map *umap1,
1223 __isl_keep isl_union_map *umap2);
1227 =head2 Unary Operations
1233 __isl_give isl_set *isl_set_complement(
1234 __isl_take isl_set *set);
1238 __isl_give isl_basic_map *isl_basic_map_reverse(
1239 __isl_take isl_basic_map *bmap);
1240 __isl_give isl_map *isl_map_reverse(
1241 __isl_take isl_map *map);
1242 __isl_give isl_union_map *isl_union_map_reverse(
1243 __isl_take isl_union_map *umap);
1247 __isl_give isl_basic_set *isl_basic_set_project_out(
1248 __isl_take isl_basic_set *bset,
1249 enum isl_dim_type type, unsigned first, unsigned n);
1250 __isl_give isl_basic_map *isl_basic_map_project_out(
1251 __isl_take isl_basic_map *bmap,
1252 enum isl_dim_type type, unsigned first, unsigned n);
1253 __isl_give isl_set *isl_set_project_out(__isl_take isl_set *set,
1254 enum isl_dim_type type, unsigned first, unsigned n);
1255 __isl_give isl_map *isl_map_project_out(__isl_take isl_map *map,
1256 enum isl_dim_type type, unsigned first, unsigned n);
1257 __isl_give isl_basic_set *isl_basic_map_domain(
1258 __isl_take isl_basic_map *bmap);
1259 __isl_give isl_basic_set *isl_basic_map_range(
1260 __isl_take isl_basic_map *bmap);
1261 __isl_give isl_set *isl_map_domain(
1262 __isl_take isl_map *bmap);
1263 __isl_give isl_set *isl_map_range(
1264 __isl_take isl_map *map);
1265 __isl_give isl_union_set *isl_union_map_domain(
1266 __isl_take isl_union_map *umap);
1267 __isl_give isl_union_set *isl_union_map_range(
1268 __isl_take isl_union_map *umap);
1270 __isl_give isl_basic_map *isl_basic_map_domain_map(
1271 __isl_take isl_basic_map *bmap);
1272 __isl_give isl_basic_map *isl_basic_map_range_map(
1273 __isl_take isl_basic_map *bmap);
1274 __isl_give isl_map *isl_map_domain_map(__isl_take isl_map *map);
1275 __isl_give isl_map *isl_map_range_map(__isl_take isl_map *map);
1276 __isl_give isl_union_map *isl_union_map_domain_map(
1277 __isl_take isl_union_map *umap);
1278 __isl_give isl_union_map *isl_union_map_range_map(
1279 __isl_take isl_union_map *umap);
1281 The functions above construct a (basic, regular or union) relation
1282 that maps (a wrapped version of) the input relation to its domain or range.
1286 __isl_give isl_map *isl_set_identity(
1287 __isl_take isl_set *set);
1288 __isl_give isl_union_map *isl_union_set_identity(
1289 __isl_take isl_union_set *uset);
1291 Construct an identity relation on the given (union) set.
1295 __isl_give isl_basic_set *isl_basic_map_deltas(
1296 __isl_take isl_basic_map *bmap);
1297 __isl_give isl_set *isl_map_deltas(__isl_take isl_map *map);
1298 __isl_give isl_union_set *isl_union_map_deltas(
1299 __isl_take isl_union_map *umap);
1301 These functions return a (basic) set containing the differences
1302 between image elements and corresponding domain elements in the input.
1306 Simplify the representation of a set or relation by trying
1307 to combine pairs of basic sets or relations into a single
1308 basic set or relation.
1310 __isl_give isl_set *isl_set_coalesce(__isl_take isl_set *set);
1311 __isl_give isl_map *isl_map_coalesce(__isl_take isl_map *map);
1312 __isl_give isl_union_set *isl_union_set_coalesce(
1313 __isl_take isl_union_set *uset);
1314 __isl_give isl_union_map *isl_union_map_coalesce(
1315 __isl_take isl_union_map *umap);
1317 =item * Detecting equalities
1319 __isl_give isl_basic_set *isl_basic_set_detect_equalities(
1320 __isl_take isl_basic_set *bset);
1321 __isl_give isl_basic_map *isl_basic_map_detect_equalities(
1322 __isl_take isl_basic_map *bmap);
1323 __isl_give isl_set *isl_set_detect_equalities(
1324 __isl_take isl_set *set);
1325 __isl_give isl_map *isl_map_detect_equalities(
1326 __isl_take isl_map *map);
1327 __isl_give isl_union_set *isl_union_set_detect_equalities(
1328 __isl_take isl_union_set *uset);
1329 __isl_give isl_union_map *isl_union_map_detect_equalities(
1330 __isl_take isl_union_map *umap);
1332 Simplify the representation of a set or relation by detecting implicit
1337 __isl_give isl_basic_set *isl_set_convex_hull(
1338 __isl_take isl_set *set);
1339 __isl_give isl_basic_map *isl_map_convex_hull(
1340 __isl_take isl_map *map);
1342 If the input set or relation has any existentially quantified
1343 variables, then the result of these operations is currently undefined.
1347 __isl_give isl_basic_set *isl_set_simple_hull(
1348 __isl_take isl_set *set);
1349 __isl_give isl_basic_map *isl_map_simple_hull(
1350 __isl_take isl_map *map);
1351 __isl_give isl_union_map *isl_union_map_simple_hull(
1352 __isl_take isl_union_map *umap);
1354 These functions compute a single basic set or relation
1355 that contains the whole input set or relation.
1356 In particular, the output is described by translates
1357 of the constraints describing the basic sets or relations in the input.
1361 (See \autoref{s:simple hull}.)
1367 __isl_give isl_basic_set *isl_basic_set_affine_hull(
1368 __isl_take isl_basic_set *bset);
1369 __isl_give isl_basic_set *isl_set_affine_hull(
1370 __isl_take isl_set *set);
1371 __isl_give isl_union_set *isl_union_set_affine_hull(
1372 __isl_take isl_union_set *uset);
1373 __isl_give isl_basic_map *isl_basic_map_affine_hull(
1374 __isl_take isl_basic_map *bmap);
1375 __isl_give isl_basic_map *isl_map_affine_hull(
1376 __isl_take isl_map *map);
1377 __isl_give isl_union_map *isl_union_map_affine_hull(
1378 __isl_take isl_union_map *umap);
1380 In case of union sets and relations, the affine hull is computed
1383 =item * Polyhedral hull
1385 __isl_give isl_basic_set *isl_set_polyhedral_hull(
1386 __isl_take isl_set *set);
1387 __isl_give isl_basic_map *isl_map_polyhedral_hull(
1388 __isl_take isl_map *map);
1389 __isl_give isl_union_set *isl_union_set_polyhedral_hull(
1390 __isl_take isl_union_set *uset);
1391 __isl_give isl_union_map *isl_union_map_polyhedral_hull(
1392 __isl_take isl_union_map *umap);
1394 These functions compute a single basic set or relation
1395 not involving any existentially quantified variables
1396 that contains the whole input set or relation.
1397 In case of union sets and relations, the polyhedral hull is computed
1402 __isl_give isl_map *isl_map_power(__isl_take isl_map *map,
1403 unsigned param, int *exact);
1405 Compute a parametric representation for all positive powers I<k> of C<map>.
1406 The power I<k> is equated to the parameter at position C<param>.
1407 The result may be an overapproximation. If the result is exact,
1408 then C<*exact> is set to C<1>.
1409 The current implementation only produces exact results for particular
1410 cases of piecewise translations (i.e., piecewise uniform dependences).
1412 =item * Transitive closure
1414 __isl_give isl_map *isl_map_transitive_closure(
1415 __isl_take isl_map *map, int *exact);
1416 __isl_give isl_union_map *isl_union_map_transitive_closure(
1417 __isl_take isl_union_map *umap, int *exact);
1419 Compute the transitive closure of C<map>.
1420 The result may be an overapproximation. If the result is known to be exact,
1421 then C<*exact> is set to C<1>.
1422 The current implementation only produces exact results for particular
1423 cases of piecewise translations (i.e., piecewise uniform dependences).
1425 =item * Reaching path lengths
1427 __isl_give isl_map *isl_map_reaching_path_lengths(
1428 __isl_take isl_map *map, int *exact);
1430 Compute a relation that maps each element in the range of C<map>
1431 to the lengths of all paths composed of edges in C<map> that
1432 end up in the given element.
1433 The result may be an overapproximation. If the result is known to be exact,
1434 then C<*exact> is set to C<1>.
1435 To compute the I<maximal> path length, the resulting relation
1436 should be postprocessed by C<isl_map_lexmax>.
1437 In particular, if the input relation is a dependence relation
1438 (mapping sources to sinks), then the maximal path length corresponds
1439 to the free schedule.
1440 Note, however, that C<isl_map_lexmax> expects the maximum to be
1441 finite, so if the path lengths are unbounded (possibly due to
1442 the overapproximation), then you will get an error message.
1446 __isl_give isl_basic_set *isl_basic_map_wrap(
1447 __isl_take isl_basic_map *bmap);
1448 __isl_give isl_set *isl_map_wrap(
1449 __isl_take isl_map *map);
1450 __isl_give isl_union_set *isl_union_map_wrap(
1451 __isl_take isl_union_map *umap);
1452 __isl_give isl_basic_map *isl_basic_set_unwrap(
1453 __isl_take isl_basic_set *bset);
1454 __isl_give isl_map *isl_set_unwrap(
1455 __isl_take isl_set *set);
1456 __isl_give isl_union_map *isl_union_set_unwrap(
1457 __isl_take isl_union_set *uset);
1461 Remove any internal structure of domain (and range) of the given
1462 set or relation. If there is any such internal structure in the input,
1463 then the name of the space is also removed.
1465 __isl_give isl_basic_set *isl_basic_set_flatten(
1466 __isl_take isl_basic_set *bset);
1467 __isl_give isl_set *isl_set_flatten(
1468 __isl_take isl_set *set);
1469 __isl_give isl_map *isl_map_flatten(
1470 __isl_take isl_map *map);
1472 __isl_give isl_map *isl_set_flatten_map(
1473 __isl_take isl_set *set);
1475 The function above constructs a relation
1476 that maps the input set to a flattened version of the set.
1478 =item * Dimension manipulation
1480 __isl_give isl_set *isl_set_add_dims(
1481 __isl_take isl_set *set,
1482 enum isl_dim_type type, unsigned n);
1483 __isl_give isl_map *isl_map_add_dims(
1484 __isl_take isl_map *map,
1485 enum isl_dim_type type, unsigned n);
1487 It is usually not advisable to directly change the (input or output)
1488 space of a set or a relation as this removes the name and the internal
1489 structure of the space. However, the above functions can be useful
1490 to add new parameters.
1494 =head2 Binary Operations
1496 The two arguments of a binary operation not only need to live
1497 in the same C<isl_ctx>, they currently also need to have
1498 the same (number of) parameters.
1500 =head3 Basic Operations
1504 =item * Intersection
1506 __isl_give isl_basic_set *isl_basic_set_intersect(
1507 __isl_take isl_basic_set *bset1,
1508 __isl_take isl_basic_set *bset2);
1509 __isl_give isl_set *isl_set_intersect(
1510 __isl_take isl_set *set1,
1511 __isl_take isl_set *set2);
1512 __isl_give isl_union_set *isl_union_set_intersect(
1513 __isl_take isl_union_set *uset1,
1514 __isl_take isl_union_set *uset2);
1515 __isl_give isl_basic_map *isl_basic_map_intersect_domain(
1516 __isl_take isl_basic_map *bmap,
1517 __isl_take isl_basic_set *bset);
1518 __isl_give isl_basic_map *isl_basic_map_intersect_range(
1519 __isl_take isl_basic_map *bmap,
1520 __isl_take isl_basic_set *bset);
1521 __isl_give isl_basic_map *isl_basic_map_intersect(
1522 __isl_take isl_basic_map *bmap1,
1523 __isl_take isl_basic_map *bmap2);
1524 __isl_give isl_map *isl_map_intersect_domain(
1525 __isl_take isl_map *map,
1526 __isl_take isl_set *set);
1527 __isl_give isl_map *isl_map_intersect_range(
1528 __isl_take isl_map *map,
1529 __isl_take isl_set *set);
1530 __isl_give isl_map *isl_map_intersect(
1531 __isl_take isl_map *map1,
1532 __isl_take isl_map *map2);
1533 __isl_give isl_union_map *isl_union_map_intersect_domain(
1534 __isl_take isl_union_map *umap,
1535 __isl_take isl_union_set *uset);
1536 __isl_give isl_union_map *isl_union_map_intersect_range(
1537 __isl_take isl_union_map *umap,
1538 __isl_take isl_union_set *uset);
1539 __isl_give isl_union_map *isl_union_map_intersect(
1540 __isl_take isl_union_map *umap1,
1541 __isl_take isl_union_map *umap2);
1545 __isl_give isl_set *isl_basic_set_union(
1546 __isl_take isl_basic_set *bset1,
1547 __isl_take isl_basic_set *bset2);
1548 __isl_give isl_map *isl_basic_map_union(
1549 __isl_take isl_basic_map *bmap1,
1550 __isl_take isl_basic_map *bmap2);
1551 __isl_give isl_set *isl_set_union(
1552 __isl_take isl_set *set1,
1553 __isl_take isl_set *set2);
1554 __isl_give isl_map *isl_map_union(
1555 __isl_take isl_map *map1,
1556 __isl_take isl_map *map2);
1557 __isl_give isl_union_set *isl_union_set_union(
1558 __isl_take isl_union_set *uset1,
1559 __isl_take isl_union_set *uset2);
1560 __isl_give isl_union_map *isl_union_map_union(
1561 __isl_take isl_union_map *umap1,
1562 __isl_take isl_union_map *umap2);
1564 =item * Set difference
1566 __isl_give isl_set *isl_set_subtract(
1567 __isl_take isl_set *set1,
1568 __isl_take isl_set *set2);
1569 __isl_give isl_map *isl_map_subtract(
1570 __isl_take isl_map *map1,
1571 __isl_take isl_map *map2);
1572 __isl_give isl_union_set *isl_union_set_subtract(
1573 __isl_take isl_union_set *uset1,
1574 __isl_take isl_union_set *uset2);
1575 __isl_give isl_union_map *isl_union_map_subtract(
1576 __isl_take isl_union_map *umap1,
1577 __isl_take isl_union_map *umap2);
1581 __isl_give isl_basic_set *isl_basic_set_apply(
1582 __isl_take isl_basic_set *bset,
1583 __isl_take isl_basic_map *bmap);
1584 __isl_give isl_set *isl_set_apply(
1585 __isl_take isl_set *set,
1586 __isl_take isl_map *map);
1587 __isl_give isl_union_set *isl_union_set_apply(
1588 __isl_take isl_union_set *uset,
1589 __isl_take isl_union_map *umap);
1590 __isl_give isl_basic_map *isl_basic_map_apply_domain(
1591 __isl_take isl_basic_map *bmap1,
1592 __isl_take isl_basic_map *bmap2);
1593 __isl_give isl_basic_map *isl_basic_map_apply_range(
1594 __isl_take isl_basic_map *bmap1,
1595 __isl_take isl_basic_map *bmap2);
1596 __isl_give isl_map *isl_map_apply_domain(
1597 __isl_take isl_map *map1,
1598 __isl_take isl_map *map2);
1599 __isl_give isl_union_map *isl_union_map_apply_domain(
1600 __isl_take isl_union_map *umap1,
1601 __isl_take isl_union_map *umap2);
1602 __isl_give isl_map *isl_map_apply_range(
1603 __isl_take isl_map *map1,
1604 __isl_take isl_map *map2);
1605 __isl_give isl_union_map *isl_union_map_apply_range(
1606 __isl_take isl_union_map *umap1,
1607 __isl_take isl_union_map *umap2);
1609 =item * Cartesian Product
1611 __isl_give isl_set *isl_set_product(
1612 __isl_take isl_set *set1,
1613 __isl_take isl_set *set2);
1614 __isl_give isl_union_set *isl_union_set_product(
1615 __isl_take isl_union_set *uset1,
1616 __isl_take isl_union_set *uset2);
1617 __isl_give isl_basic_map *isl_basic_map_range_product(
1618 __isl_take isl_basic_map *bmap1,
1619 __isl_take isl_basic_map *bmap2);
1620 __isl_give isl_map *isl_map_range_product(
1621 __isl_take isl_map *map1,
1622 __isl_take isl_map *map2);
1623 __isl_give isl_union_map *isl_union_map_range_product(
1624 __isl_take isl_union_map *umap1,
1625 __isl_take isl_union_map *umap2);
1626 __isl_give isl_map *isl_map_product(
1627 __isl_take isl_map *map1,
1628 __isl_take isl_map *map2);
1629 __isl_give isl_union_map *isl_union_map_product(
1630 __isl_take isl_union_map *umap1,
1631 __isl_take isl_union_map *umap2);
1633 The above functions compute the cross product of the given
1634 sets or relations. The domains and ranges of the results
1635 are wrapped maps between domains and ranges of the inputs.
1636 To obtain a ``flat'' product, use the following functions
1639 __isl_give isl_set *isl_set_flat_product(
1640 __isl_take isl_set *set1,
1641 __isl_take isl_set *set2);
1642 __isl_give isl_map *isl_map_flat_product(
1643 __isl_take isl_map *map1,
1644 __isl_take isl_map *map2);
1646 =item * Simplification
1648 __isl_give isl_basic_set *isl_basic_set_gist(
1649 __isl_take isl_basic_set *bset,
1650 __isl_take isl_basic_set *context);
1651 __isl_give isl_set *isl_set_gist(__isl_take isl_set *set,
1652 __isl_take isl_set *context);
1653 __isl_give isl_union_set *isl_union_set_gist(
1654 __isl_take isl_union_set *uset,
1655 __isl_take isl_union_set *context);
1656 __isl_give isl_basic_map *isl_basic_map_gist(
1657 __isl_take isl_basic_map *bmap,
1658 __isl_take isl_basic_map *context);
1659 __isl_give isl_map *isl_map_gist(__isl_take isl_map *map,
1660 __isl_take isl_map *context);
1661 __isl_give isl_union_map *isl_union_map_gist(
1662 __isl_take isl_union_map *umap,
1663 __isl_take isl_union_map *context);
1665 The gist operation returns a set or relation that has the
1666 same intersection with the context as the input set or relation.
1667 Any implicit equality in the intersection is made explicit in the result,
1668 while all inequalities that are redundant with respect to the intersection
1670 In case of union sets and relations, the gist operation is performed
1675 =head3 Lexicographic Optimization
1677 Given a (basic) set C<set> (or C<bset>) and a zero-dimensional domain C<dom>,
1678 the following functions
1679 compute a set that contains the lexicographic minimum or maximum
1680 of the elements in C<set> (or C<bset>) for those values of the parameters
1681 that satisfy C<dom>.
1682 If C<empty> is not C<NULL>, then C<*empty> is assigned a set
1683 that contains the parameter values in C<dom> for which C<set> (or C<bset>)
1685 In other words, the union of the parameter values
1686 for which the result is non-empty and of C<*empty>
1689 __isl_give isl_set *isl_basic_set_partial_lexmin(
1690 __isl_take isl_basic_set *bset,
1691 __isl_take isl_basic_set *dom,
1692 __isl_give isl_set **empty);
1693 __isl_give isl_set *isl_basic_set_partial_lexmax(
1694 __isl_take isl_basic_set *bset,
1695 __isl_take isl_basic_set *dom,
1696 __isl_give isl_set **empty);
1697 __isl_give isl_set *isl_set_partial_lexmin(
1698 __isl_take isl_set *set, __isl_take isl_set *dom,
1699 __isl_give isl_set **empty);
1700 __isl_give isl_set *isl_set_partial_lexmax(
1701 __isl_take isl_set *set, __isl_take isl_set *dom,
1702 __isl_give isl_set **empty);
1704 Given a (basic) set C<set> (or C<bset>), the following functions simply
1705 return a set containing the lexicographic minimum or maximum
1706 of the elements in C<set> (or C<bset>).
1707 In case of union sets, the optimum is computed per space.
1709 __isl_give isl_set *isl_basic_set_lexmin(
1710 __isl_take isl_basic_set *bset);
1711 __isl_give isl_set *isl_basic_set_lexmax(
1712 __isl_take isl_basic_set *bset);
1713 __isl_give isl_set *isl_set_lexmin(
1714 __isl_take isl_set *set);
1715 __isl_give isl_set *isl_set_lexmax(
1716 __isl_take isl_set *set);
1717 __isl_give isl_union_set *isl_union_set_lexmin(
1718 __isl_take isl_union_set *uset);
1719 __isl_give isl_union_set *isl_union_set_lexmax(
1720 __isl_take isl_union_set *uset);
1722 Given a (basic) relation C<map> (or C<bmap>) and a domain C<dom>,
1723 the following functions
1724 compute a relation that maps each element of C<dom>
1725 to the single lexicographic minimum or maximum
1726 of the elements that are associated to that same
1727 element in C<map> (or C<bmap>).
1728 If C<empty> is not C<NULL>, then C<*empty> is assigned a set
1729 that contains the elements in C<dom> that do not map
1730 to any elements in C<map> (or C<bmap>).
1731 In other words, the union of the domain of the result and of C<*empty>
1734 __isl_give isl_map *isl_basic_map_partial_lexmax(
1735 __isl_take isl_basic_map *bmap,
1736 __isl_take isl_basic_set *dom,
1737 __isl_give isl_set **empty);
1738 __isl_give isl_map *isl_basic_map_partial_lexmin(
1739 __isl_take isl_basic_map *bmap,
1740 __isl_take isl_basic_set *dom,
1741 __isl_give isl_set **empty);
1742 __isl_give isl_map *isl_map_partial_lexmax(
1743 __isl_take isl_map *map, __isl_take isl_set *dom,
1744 __isl_give isl_set **empty);
1745 __isl_give isl_map *isl_map_partial_lexmin(
1746 __isl_take isl_map *map, __isl_take isl_set *dom,
1747 __isl_give isl_set **empty);
1749 Given a (basic) map C<map> (or C<bmap>), the following functions simply
1750 return a map mapping each element in the domain of
1751 C<map> (or C<bmap>) to the lexicographic minimum or maximum
1752 of all elements associated to that element.
1753 In case of union relations, the optimum is computed per space.
1755 __isl_give isl_map *isl_basic_map_lexmin(
1756 __isl_take isl_basic_map *bmap);
1757 __isl_give isl_map *isl_basic_map_lexmax(
1758 __isl_take isl_basic_map *bmap);
1759 __isl_give isl_map *isl_map_lexmin(
1760 __isl_take isl_map *map);
1761 __isl_give isl_map *isl_map_lexmax(
1762 __isl_take isl_map *map);
1763 __isl_give isl_union_map *isl_union_map_lexmin(
1764 __isl_take isl_union_map *umap);
1765 __isl_give isl_union_map *isl_union_map_lexmax(
1766 __isl_take isl_union_map *umap);
1770 Matrices can be created, copied and freed using the following functions.
1772 #include <isl/mat.h>
1773 __isl_give isl_mat *isl_mat_alloc(struct isl_ctx *ctx,
1774 unsigned n_row, unsigned n_col);
1775 __isl_give isl_mat *isl_mat_copy(__isl_keep isl_mat *mat);
1776 void isl_mat_free(__isl_take isl_mat *mat);
1778 Note that the elements of a newly created matrix may have arbitrary values.
1779 The elements can be changed and inspected using the following functions.
1781 int isl_mat_rows(__isl_keep isl_mat *mat);
1782 int isl_mat_cols(__isl_keep isl_mat *mat);
1783 int isl_mat_get_element(__isl_keep isl_mat *mat,
1784 int row, int col, isl_int *v);
1785 __isl_give isl_mat *isl_mat_set_element(__isl_take isl_mat *mat,
1786 int row, int col, isl_int v);
1788 C<isl_mat_get_element> will return a negative value if anything went wrong.
1789 In that case, the value of C<*v> is undefined.
1791 The following function can be used to compute the (right) inverse
1792 of a matrix, i.e., a matrix such that the product of the original
1793 and the inverse (in that order) is a multiple of the identity matrix.
1794 The input matrix is assumed to be of full row-rank.
1796 __isl_give isl_mat *isl_mat_right_inverse(__isl_take isl_mat *mat);
1798 The following function can be used to compute the (right) kernel
1799 (or null space) of a matrix, i.e., a matrix such that the product of
1800 the original and the kernel (in that order) is the zero matrix.
1802 __isl_give isl_mat *isl_mat_right_kernel(__isl_take isl_mat *mat);
1806 Points are elements of a set. They can be used to construct
1807 simple sets (boxes) or they can be used to represent the
1808 individual elements of a set.
1809 The zero point (the origin) can be created using
1811 __isl_give isl_point *isl_point_zero(__isl_take isl_dim *dim);
1813 The coordinates of a point can be inspected, set and changed
1816 void isl_point_get_coordinate(__isl_keep isl_point *pnt,
1817 enum isl_dim_type type, int pos, isl_int *v);
1818 __isl_give isl_point *isl_point_set_coordinate(
1819 __isl_take isl_point *pnt,
1820 enum isl_dim_type type, int pos, isl_int v);
1822 __isl_give isl_point *isl_point_add_ui(
1823 __isl_take isl_point *pnt,
1824 enum isl_dim_type type, int pos, unsigned val);
1825 __isl_give isl_point *isl_point_sub_ui(
1826 __isl_take isl_point *pnt,
1827 enum isl_dim_type type, int pos, unsigned val);
1829 Points can be copied or freed using
1831 __isl_give isl_point *isl_point_copy(
1832 __isl_keep isl_point *pnt);
1833 void isl_point_free(__isl_take isl_point *pnt);
1835 A singleton set can be created from a point using
1837 __isl_give isl_basic_set *isl_basic_set_from_point(
1838 __isl_take isl_point *pnt);
1839 __isl_give isl_set *isl_set_from_point(
1840 __isl_take isl_point *pnt);
1842 and a box can be created from two opposite extremal points using
1844 __isl_give isl_basic_set *isl_basic_set_box_from_points(
1845 __isl_take isl_point *pnt1,
1846 __isl_take isl_point *pnt2);
1847 __isl_give isl_set *isl_set_box_from_points(
1848 __isl_take isl_point *pnt1,
1849 __isl_take isl_point *pnt2);
1851 All elements of a B<bounded> (union) set can be enumerated using
1852 the following functions.
1854 int isl_set_foreach_point(__isl_keep isl_set *set,
1855 int (*fn)(__isl_take isl_point *pnt, void *user),
1857 int isl_union_set_foreach_point(__isl_keep isl_union_set *uset,
1858 int (*fn)(__isl_take isl_point *pnt, void *user),
1861 The function C<fn> is called for each integer point in
1862 C<set> with as second argument the last argument of
1863 the C<isl_set_foreach_point> call. The function C<fn>
1864 should return C<0> on success and C<-1> on failure.
1865 In the latter case, C<isl_set_foreach_point> will stop
1866 enumerating and return C<-1> as well.
1867 If the enumeration is performed successfully and to completion,
1868 then C<isl_set_foreach_point> returns C<0>.
1870 To obtain a single point of a (basic) set, use
1872 __isl_give isl_point *isl_basic_set_sample_point(
1873 __isl_take isl_basic_set *bset);
1874 __isl_give isl_point *isl_set_sample_point(
1875 __isl_take isl_set *set);
1877 If C<set> does not contain any (integer) points, then the
1878 resulting point will be ``void'', a property that can be
1881 int isl_point_is_void(__isl_keep isl_point *pnt);
1883 =head2 Piecewise Quasipolynomials
1885 A piecewise quasipolynomial is a particular kind of function that maps
1886 a parametric point to a rational value.
1887 More specifically, a quasipolynomial is a polynomial expression in greatest
1888 integer parts of affine expressions of parameters and variables.
1889 A piecewise quasipolynomial is a subdivision of a given parametric
1890 domain into disjoint cells with a quasipolynomial associated to
1891 each cell. The value of the piecewise quasipolynomial at a given
1892 point is the value of the quasipolynomial associated to the cell
1893 that contains the point. Outside of the union of cells,
1894 the value is assumed to be zero.
1895 For example, the piecewise quasipolynomial
1897 [n] -> { [x] -> ((1 + n) - x) : x <= n and x >= 0 }
1899 maps C<x> to C<1 + n - x> for values of C<x> between C<0> and C<n>.
1900 A given piecewise quasipolynomial has a fixed domain dimension.
1901 Union piecewise quasipolynomials are used to contain piecewise quasipolynomials
1902 defined over different domains.
1903 Piecewise quasipolynomials are mainly used by the C<barvinok>
1904 library for representing the number of elements in a parametric set or map.
1905 For example, the piecewise quasipolynomial above represents
1906 the number of points in the map
1908 [n] -> { [x] -> [y] : x,y >= 0 and 0 <= x + y <= n }
1910 =head3 Printing (Piecewise) Quasipolynomials
1912 Quasipolynomials and piecewise quasipolynomials can be printed
1913 using the following functions.
1915 __isl_give isl_printer *isl_printer_print_qpolynomial(
1916 __isl_take isl_printer *p,
1917 __isl_keep isl_qpolynomial *qp);
1919 __isl_give isl_printer *isl_printer_print_pw_qpolynomial(
1920 __isl_take isl_printer *p,
1921 __isl_keep isl_pw_qpolynomial *pwqp);
1923 __isl_give isl_printer *isl_printer_print_union_pw_qpolynomial(
1924 __isl_take isl_printer *p,
1925 __isl_keep isl_union_pw_qpolynomial *upwqp);
1927 The output format of the printer
1928 needs to be set to either C<ISL_FORMAT_ISL> or C<ISL_FORMAT_C>.
1929 For C<isl_printer_print_union_pw_qpolynomial>, only C<ISL_FORMAT_ISL>
1931 In case of printing in C<ISL_FORMAT_C>, the user may want
1932 to set the names of all dimensions
1934 __isl_give isl_qpolynomial *isl_qpolynomial_set_dim_name(
1935 __isl_take isl_qpolynomial *qp,
1936 enum isl_dim_type type, unsigned pos,
1938 __isl_give isl_pw_qpolynomial *
1939 isl_pw_qpolynomial_set_dim_name(
1940 __isl_take isl_pw_qpolynomial *pwqp,
1941 enum isl_dim_type type, unsigned pos,
1944 =head3 Creating New (Piecewise) Quasipolynomials
1946 Some simple quasipolynomials can be created using the following functions.
1947 More complicated quasipolynomials can be created by applying
1948 operations such as addition and multiplication
1949 on the resulting quasipolynomials
1951 __isl_give isl_qpolynomial *isl_qpolynomial_zero(
1952 __isl_take isl_dim *dim);
1953 __isl_give isl_qpolynomial *isl_qpolynomial_one(
1954 __isl_take isl_dim *dim);
1955 __isl_give isl_qpolynomial *isl_qpolynomial_infty(
1956 __isl_take isl_dim *dim);
1957 __isl_give isl_qpolynomial *isl_qpolynomial_neginfty(
1958 __isl_take isl_dim *dim);
1959 __isl_give isl_qpolynomial *isl_qpolynomial_nan(
1960 __isl_take isl_dim *dim);
1961 __isl_give isl_qpolynomial *isl_qpolynomial_rat_cst(
1962 __isl_take isl_dim *dim,
1963 const isl_int n, const isl_int d);
1964 __isl_give isl_qpolynomial *isl_qpolynomial_div(
1965 __isl_take isl_div *div);
1966 __isl_give isl_qpolynomial *isl_qpolynomial_var(
1967 __isl_take isl_dim *dim,
1968 enum isl_dim_type type, unsigned pos);
1970 The zero piecewise quasipolynomial or a piecewise quasipolynomial
1971 with a single cell can be created using the following functions.
1972 Multiple of these single cell piecewise quasipolynomials can
1973 be combined to create more complicated piecewise quasipolynomials.
1975 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_zero(
1976 __isl_take isl_dim *dim);
1977 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_alloc(
1978 __isl_take isl_set *set,
1979 __isl_take isl_qpolynomial *qp);
1981 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_zero(
1982 __isl_take isl_dim *dim);
1983 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_from_pw_qpolynomial(
1984 __isl_take isl_pw_qpolynomial *pwqp);
1985 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_add_pw_qpolynomial(
1986 __isl_take isl_union_pw_qpolynomial *upwqp,
1987 __isl_take isl_pw_qpolynomial *pwqp);
1989 Quasipolynomials can be copied and freed again using the following
1992 __isl_give isl_qpolynomial *isl_qpolynomial_copy(
1993 __isl_keep isl_qpolynomial *qp);
1994 void isl_qpolynomial_free(__isl_take isl_qpolynomial *qp);
1996 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_copy(
1997 __isl_keep isl_pw_qpolynomial *pwqp);
1998 void isl_pw_qpolynomial_free(
1999 __isl_take isl_pw_qpolynomial *pwqp);
2001 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_copy(
2002 __isl_keep isl_union_pw_qpolynomial *upwqp);
2003 void isl_union_pw_qpolynomial_free(
2004 __isl_take isl_union_pw_qpolynomial *upwqp);
2006 =head3 Inspecting (Piecewise) Quasipolynomials
2008 To iterate over all piecewise quasipolynomials in a union
2009 piecewise quasipolynomial, use the following function
2011 int isl_union_pw_qpolynomial_foreach_pw_qpolynomial(
2012 __isl_keep isl_union_pw_qpolynomial *upwqp,
2013 int (*fn)(__isl_take isl_pw_qpolynomial *pwqp, void *user),
2016 To extract the piecewise quasipolynomial from a union with a given dimension
2019 __isl_give isl_pw_qpolynomial *
2020 isl_union_pw_qpolynomial_extract_pw_qpolynomial(
2021 __isl_keep isl_union_pw_qpolynomial *upwqp,
2022 __isl_take isl_dim *dim);
2024 To iterate over the cells in a piecewise quasipolynomial,
2025 use either of the following two functions
2027 int isl_pw_qpolynomial_foreach_piece(
2028 __isl_keep isl_pw_qpolynomial *pwqp,
2029 int (*fn)(__isl_take isl_set *set,
2030 __isl_take isl_qpolynomial *qp,
2031 void *user), void *user);
2032 int isl_pw_qpolynomial_foreach_lifted_piece(
2033 __isl_keep isl_pw_qpolynomial *pwqp,
2034 int (*fn)(__isl_take isl_set *set,
2035 __isl_take isl_qpolynomial *qp,
2036 void *user), void *user);
2038 As usual, the function C<fn> should return C<0> on success
2039 and C<-1> on failure. The difference between
2040 C<isl_pw_qpolynomial_foreach_piece> and
2041 C<isl_pw_qpolynomial_foreach_lifted_piece> is that
2042 C<isl_pw_qpolynomial_foreach_lifted_piece> will first
2043 compute unique representations for all existentially quantified
2044 variables and then turn these existentially quantified variables
2045 into extra set variables, adapting the associated quasipolynomial
2046 accordingly. This means that the C<set> passed to C<fn>
2047 will not have any existentially quantified variables, but that
2048 the dimensions of the sets may be different for different
2049 invocations of C<fn>.
2051 To iterate over all terms in a quasipolynomial,
2054 int isl_qpolynomial_foreach_term(
2055 __isl_keep isl_qpolynomial *qp,
2056 int (*fn)(__isl_take isl_term *term,
2057 void *user), void *user);
2059 The terms themselves can be inspected and freed using
2062 unsigned isl_term_dim(__isl_keep isl_term *term,
2063 enum isl_dim_type type);
2064 void isl_term_get_num(__isl_keep isl_term *term,
2066 void isl_term_get_den(__isl_keep isl_term *term,
2068 int isl_term_get_exp(__isl_keep isl_term *term,
2069 enum isl_dim_type type, unsigned pos);
2070 __isl_give isl_div *isl_term_get_div(
2071 __isl_keep isl_term *term, unsigned pos);
2072 void isl_term_free(__isl_take isl_term *term);
2074 Each term is a product of parameters, set variables and
2075 integer divisions. The function C<isl_term_get_exp>
2076 returns the exponent of a given dimensions in the given term.
2077 The C<isl_int>s in the arguments of C<isl_term_get_num>
2078 and C<isl_term_get_den> need to have been initialized
2079 using C<isl_int_init> before calling these functions.
2081 =head3 Properties of (Piecewise) Quasipolynomials
2083 To check whether a quasipolynomial is actually a constant,
2084 use the following function.
2086 int isl_qpolynomial_is_cst(__isl_keep isl_qpolynomial *qp,
2087 isl_int *n, isl_int *d);
2089 If C<qp> is a constant and if C<n> and C<d> are not C<NULL>
2090 then the numerator and denominator of the constant
2091 are returned in C<*n> and C<*d>, respectively.
2093 =head3 Operations on (Piecewise) Quasipolynomials
2095 __isl_give isl_qpolynomial *isl_qpolynomial_neg(
2096 __isl_take isl_qpolynomial *qp);
2097 __isl_give isl_qpolynomial *isl_qpolynomial_add(
2098 __isl_take isl_qpolynomial *qp1,
2099 __isl_take isl_qpolynomial *qp2);
2100 __isl_give isl_qpolynomial *isl_qpolynomial_sub(
2101 __isl_take isl_qpolynomial *qp1,
2102 __isl_take isl_qpolynomial *qp2);
2103 __isl_give isl_qpolynomial *isl_qpolynomial_mul(
2104 __isl_take isl_qpolynomial *qp1,
2105 __isl_take isl_qpolynomial *qp2);
2106 __isl_give isl_qpolynomial *isl_qpolynomial_pow(
2107 __isl_take isl_qpolynomial *qp, unsigned exponent);
2109 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_add(
2110 __isl_take isl_pw_qpolynomial *pwqp1,
2111 __isl_take isl_pw_qpolynomial *pwqp2);
2112 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_sub(
2113 __isl_take isl_pw_qpolynomial *pwqp1,
2114 __isl_take isl_pw_qpolynomial *pwqp2);
2115 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_add_disjoint(
2116 __isl_take isl_pw_qpolynomial *pwqp1,
2117 __isl_take isl_pw_qpolynomial *pwqp2);
2118 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_neg(
2119 __isl_take isl_pw_qpolynomial *pwqp);
2120 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_mul(
2121 __isl_take isl_pw_qpolynomial *pwqp1,
2122 __isl_take isl_pw_qpolynomial *pwqp2);
2124 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_add(
2125 __isl_take isl_union_pw_qpolynomial *upwqp1,
2126 __isl_take isl_union_pw_qpolynomial *upwqp2);
2127 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_sub(
2128 __isl_take isl_union_pw_qpolynomial *upwqp1,
2129 __isl_take isl_union_pw_qpolynomial *upwqp2);
2130 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_mul(
2131 __isl_take isl_union_pw_qpolynomial *upwqp1,
2132 __isl_take isl_union_pw_qpolynomial *upwqp2);
2134 __isl_give isl_qpolynomial *isl_pw_qpolynomial_eval(
2135 __isl_take isl_pw_qpolynomial *pwqp,
2136 __isl_take isl_point *pnt);
2138 __isl_give isl_qpolynomial *isl_union_pw_qpolynomial_eval(
2139 __isl_take isl_union_pw_qpolynomial *upwqp,
2140 __isl_take isl_point *pnt);
2142 __isl_give isl_set *isl_pw_qpolynomial_domain(
2143 __isl_take isl_pw_qpolynomial *pwqp);
2144 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_intersect_domain(
2145 __isl_take isl_pw_qpolynomial *pwpq,
2146 __isl_take isl_set *set);
2148 __isl_give isl_union_set *isl_union_pw_qpolynomial_domain(
2149 __isl_take isl_union_pw_qpolynomial *upwqp);
2150 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_intersect_domain(
2151 __isl_take isl_union_pw_qpolynomial *upwpq,
2152 __isl_take isl_union_set *uset);
2154 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_coalesce(
2155 __isl_take isl_union_pw_qpolynomial *upwqp);
2157 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_gist(
2158 __isl_take isl_pw_qpolynomial *pwqp,
2159 __isl_take isl_set *context);
2161 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_gist(
2162 __isl_take isl_union_pw_qpolynomial *upwqp,
2163 __isl_take isl_union_set *context);
2165 The gist operation applies the gist operation to each of
2166 the cells in the domain of the input piecewise quasipolynomial.
2167 The context is also exploited
2168 to simplify the quasipolynomials associated to each cell.
2170 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_to_polynomial(
2171 __isl_take isl_pw_qpolynomial *pwqp, int sign);
2172 __isl_give isl_union_pw_qpolynomial *
2173 isl_union_pw_qpolynomial_to_polynomial(
2174 __isl_take isl_union_pw_qpolynomial *upwqp, int sign);
2176 Approximate each quasipolynomial by a polynomial. If C<sign> is positive,
2177 the polynomial will be an overapproximation. If C<sign> is negative,
2178 it will be an underapproximation. If C<sign> is zero, the approximation
2179 will lie somewhere in between.
2181 =head2 Bounds on Piecewise Quasipolynomials and Piecewise Quasipolynomial Reductions
2183 A piecewise quasipolynomial reduction is a piecewise
2184 reduction (or fold) of quasipolynomials.
2185 In particular, the reduction can be maximum or a minimum.
2186 The objects are mainly used to represent the result of
2187 an upper or lower bound on a quasipolynomial over its domain,
2188 i.e., as the result of the following function.
2190 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_bound(
2191 __isl_take isl_pw_qpolynomial *pwqp,
2192 enum isl_fold type, int *tight);
2194 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_bound(
2195 __isl_take isl_union_pw_qpolynomial *upwqp,
2196 enum isl_fold type, int *tight);
2198 The C<type> argument may be either C<isl_fold_min> or C<isl_fold_max>.
2199 If C<tight> is not C<NULL>, then C<*tight> is set to C<1>
2200 is the returned bound is known be tight, i.e., for each value
2201 of the parameters there is at least
2202 one element in the domain that reaches the bound.
2203 If the domain of C<pwqp> is not wrapping, then the bound is computed
2204 over all elements in that domain and the result has a purely parametric
2205 domain. If the domain of C<pwqp> is wrapping, then the bound is
2206 computed over the range of the wrapped relation. The domain of the
2207 wrapped relation becomes the domain of the result.
2209 A (piecewise) quasipolynomial reduction can be copied or freed using the
2210 following functions.
2212 __isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_copy(
2213 __isl_keep isl_qpolynomial_fold *fold);
2214 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_copy(
2215 __isl_keep isl_pw_qpolynomial_fold *pwf);
2216 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_copy(
2217 __isl_keep isl_union_pw_qpolynomial_fold *upwf);
2218 void isl_qpolynomial_fold_free(
2219 __isl_take isl_qpolynomial_fold *fold);
2220 void isl_pw_qpolynomial_fold_free(
2221 __isl_take isl_pw_qpolynomial_fold *pwf);
2222 void isl_union_pw_qpolynomial_fold_free(
2223 __isl_take isl_union_pw_qpolynomial_fold *upwf);
2225 =head3 Printing Piecewise Quasipolynomial Reductions
2227 Piecewise quasipolynomial reductions can be printed
2228 using the following function.
2230 __isl_give isl_printer *isl_printer_print_pw_qpolynomial_fold(
2231 __isl_take isl_printer *p,
2232 __isl_keep isl_pw_qpolynomial_fold *pwf);
2233 __isl_give isl_printer *isl_printer_print_union_pw_qpolynomial_fold(
2234 __isl_take isl_printer *p,
2235 __isl_keep isl_union_pw_qpolynomial_fold *upwf);
2237 For C<isl_printer_print_pw_qpolynomial_fold>,
2238 output format of the printer
2239 needs to be set to either C<ISL_FORMAT_ISL> or C<ISL_FORMAT_C>.
2240 For C<isl_printer_print_union_pw_qpolynomial_fold>,
2241 output format of the printer
2242 needs to be set to C<ISL_FORMAT_ISL>.
2243 In case of printing in C<ISL_FORMAT_C>, the user may want
2244 to set the names of all dimensions
2246 __isl_give isl_pw_qpolynomial_fold *
2247 isl_pw_qpolynomial_fold_set_dim_name(
2248 __isl_take isl_pw_qpolynomial_fold *pwf,
2249 enum isl_dim_type type, unsigned pos,
2252 =head3 Inspecting (Piecewise) Quasipolynomial Reductions
2254 To iterate over all piecewise quasipolynomial reductions in a union
2255 piecewise quasipolynomial reduction, use the following function
2257 int isl_union_pw_qpolynomial_fold_foreach_pw_qpolynomial_fold(
2258 __isl_keep isl_union_pw_qpolynomial_fold *upwf,
2259 int (*fn)(__isl_take isl_pw_qpolynomial_fold *pwf,
2260 void *user), void *user);
2262 To iterate over the cells in a piecewise quasipolynomial reduction,
2263 use either of the following two functions
2265 int isl_pw_qpolynomial_fold_foreach_piece(
2266 __isl_keep isl_pw_qpolynomial_fold *pwf,
2267 int (*fn)(__isl_take isl_set *set,
2268 __isl_take isl_qpolynomial_fold *fold,
2269 void *user), void *user);
2270 int isl_pw_qpolynomial_fold_foreach_lifted_piece(
2271 __isl_keep isl_pw_qpolynomial_fold *pwf,
2272 int (*fn)(__isl_take isl_set *set,
2273 __isl_take isl_qpolynomial_fold *fold,
2274 void *user), void *user);
2276 See L<Inspecting (Piecewise) Quasipolynomials> for an explanation
2277 of the difference between these two functions.
2279 To iterate over all quasipolynomials in a reduction, use
2281 int isl_qpolynomial_fold_foreach_qpolynomial(
2282 __isl_keep isl_qpolynomial_fold *fold,
2283 int (*fn)(__isl_take isl_qpolynomial *qp,
2284 void *user), void *user);
2286 =head3 Operations on Piecewise Quasipolynomial Reductions
2288 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_add(
2289 __isl_take isl_pw_qpolynomial_fold *pwf1,
2290 __isl_take isl_pw_qpolynomial_fold *pwf2);
2292 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_fold(
2293 __isl_take isl_pw_qpolynomial_fold *pwf1,
2294 __isl_take isl_pw_qpolynomial_fold *pwf2);
2296 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_fold(
2297 __isl_take isl_union_pw_qpolynomial_fold *upwf1,
2298 __isl_take isl_union_pw_qpolynomial_fold *upwf2);
2300 __isl_give isl_qpolynomial *isl_pw_qpolynomial_fold_eval(
2301 __isl_take isl_pw_qpolynomial_fold *pwf,
2302 __isl_take isl_point *pnt);
2304 __isl_give isl_qpolynomial *isl_union_pw_qpolynomial_fold_eval(
2305 __isl_take isl_union_pw_qpolynomial_fold *upwf,
2306 __isl_take isl_point *pnt);
2308 __isl_give isl_union_set *isl_union_pw_qpolynomial_fold_domain(
2309 __isl_take isl_union_pw_qpolynomial_fold *upwf);
2310 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_intersect_domain(
2311 __isl_take isl_union_pw_qpolynomial_fold *upwf,
2312 __isl_take isl_union_set *uset);
2314 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_coalesce(
2315 __isl_take isl_pw_qpolynomial_fold *pwf);
2317 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_coalesce(
2318 __isl_take isl_union_pw_qpolynomial_fold *upwf);
2320 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_gist(
2321 __isl_take isl_pw_qpolynomial_fold *pwf,
2322 __isl_take isl_set *context);
2324 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_gist(
2325 __isl_take isl_union_pw_qpolynomial_fold *upwf,
2326 __isl_take isl_union_set *context);
2328 The gist operation applies the gist operation to each of
2329 the cells in the domain of the input piecewise quasipolynomial reduction.
2330 In future, the operation will also exploit the context
2331 to simplify the quasipolynomial reductions associated to each cell.
2333 __isl_give isl_pw_qpolynomial_fold *
2334 isl_set_apply_pw_qpolynomial_fold(
2335 __isl_take isl_set *set,
2336 __isl_take isl_pw_qpolynomial_fold *pwf,
2338 __isl_give isl_pw_qpolynomial_fold *
2339 isl_map_apply_pw_qpolynomial_fold(
2340 __isl_take isl_map *map,
2341 __isl_take isl_pw_qpolynomial_fold *pwf,
2343 __isl_give isl_union_pw_qpolynomial_fold *
2344 isl_union_set_apply_union_pw_qpolynomial_fold(
2345 __isl_take isl_union_set *uset,
2346 __isl_take isl_union_pw_qpolynomial_fold *upwf,
2348 __isl_give isl_union_pw_qpolynomial_fold *
2349 isl_union_map_apply_union_pw_qpolynomial_fold(
2350 __isl_take isl_union_map *umap,
2351 __isl_take isl_union_pw_qpolynomial_fold *upwf,
2354 The functions taking a map
2355 compose the given map with the given piecewise quasipolynomial reduction.
2356 That is, compute a bound (of the same type as C<pwf> or C<upwf> itself)
2357 over all elements in the intersection of the range of the map
2358 and the domain of the piecewise quasipolynomial reduction
2359 as a function of an element in the domain of the map.
2360 The functions taking a set compute a bound over all elements in the
2361 intersection of the set and the domain of the
2362 piecewise quasipolynomial reduction.
2364 =head2 Dependence Analysis
2366 C<isl> contains specialized functionality for performing
2367 array dataflow analysis. That is, given a I<sink> access relation
2368 and a collection of possible I<source> access relations,
2369 C<isl> can compute relations that describe
2370 for each iteration of the sink access, which iteration
2371 of which of the source access relations was the last
2372 to access the same data element before the given iteration
2374 To compute standard flow dependences, the sink should be
2375 a read, while the sources should be writes.
2376 If any of the source accesses are marked as being I<may>
2377 accesses, then there will be a dependence to the last
2378 I<must> access B<and> to any I<may> access that follows
2379 this last I<must> access.
2380 In particular, if I<all> sources are I<may> accesses,
2381 then memory based dependence analysis is performed.
2382 If, on the other hand, all sources are I<must> accesses,
2383 then value based dependence analysis is performed.
2385 #include <isl/flow.h>
2387 typedef int (*isl_access_level_before)(void *first, void *second);
2389 __isl_give isl_access_info *isl_access_info_alloc(
2390 __isl_take isl_map *sink,
2391 void *sink_user, isl_access_level_before fn,
2393 __isl_give isl_access_info *isl_access_info_add_source(
2394 __isl_take isl_access_info *acc,
2395 __isl_take isl_map *source, int must,
2397 void isl_access_info_free(__isl_take isl_access_info *acc);
2399 __isl_give isl_flow *isl_access_info_compute_flow(
2400 __isl_take isl_access_info *acc);
2402 int isl_flow_foreach(__isl_keep isl_flow *deps,
2403 int (*fn)(__isl_take isl_map *dep, int must,
2404 void *dep_user, void *user),
2406 __isl_give isl_set *isl_flow_get_no_source(
2407 __isl_keep isl_flow *deps, int must);
2408 void isl_flow_free(__isl_take isl_flow *deps);
2410 The function C<isl_access_info_compute_flow> performs the actual
2411 dependence analysis. The other functions are used to construct
2412 the input for this function or to read off the output.
2414 The input is collected in an C<isl_access_info>, which can
2415 be created through a call to C<isl_access_info_alloc>.
2416 The arguments to this functions are the sink access relation
2417 C<sink>, a token C<sink_user> used to identify the sink
2418 access to the user, a callback function for specifying the
2419 relative order of source and sink accesses, and the number
2420 of source access relations that will be added.
2421 The callback function has type C<int (*)(void *first, void *second)>.
2422 The function is called with two user supplied tokens identifying
2423 either a source or the sink and it should return the shared nesting
2424 level and the relative order of the two accesses.
2425 In particular, let I<n> be the number of loops shared by
2426 the two accesses. If C<first> precedes C<second> textually,
2427 then the function should return I<2 * n + 1>; otherwise,
2428 it should return I<2 * n>.
2429 The sources can be added to the C<isl_access_info> by performing
2430 (at most) C<max_source> calls to C<isl_access_info_add_source>.
2431 C<must> indicates whether the source is a I<must> access
2432 or a I<may> access. Note that a multi-valued access relation
2433 should only be marked I<must> if every iteration in the domain
2434 of the relation accesses I<all> elements in its image.
2435 The C<source_user> token is again used to identify
2436 the source access. The range of the source access relation
2437 C<source> should have the same dimension as the range
2438 of the sink access relation.
2439 The C<isl_access_info_free> function should usually not be
2440 called explicitly, because it is called implicitly by
2441 C<isl_access_info_compute_flow>.
2443 The result of the dependence analysis is collected in an
2444 C<isl_flow>. There may be elements in the domain of
2445 the sink access for which no preceding source access could be
2446 found or for which all preceding sources are I<may> accesses.
2447 The sets of these elements can be obtained through
2448 calls to C<isl_flow_get_no_source>, the first with C<must> set
2449 and the second with C<must> unset.
2450 In the case of standard flow dependence analysis,
2451 with the sink a read and the sources I<must> writes,
2452 the first set corresponds to the reads from uninitialized
2453 array elements and the second set is empty.
2454 The actual flow dependences can be extracted using
2455 C<isl_flow_foreach>. This function will call the user-specified
2456 callback function C<fn> for each B<non-empty> dependence between
2457 a source and the sink. The callback function is called
2458 with four arguments, the actual flow dependence relation
2459 mapping source iterations to sink iterations, a boolean that
2460 indicates whether it is a I<must> or I<may> dependence, a token
2461 identifying the source and an additional C<void *> with value
2462 equal to the third argument of the C<isl_flow_foreach> call.
2463 A dependence is marked I<must> if it originates from a I<must>
2464 source and if it is not followed by any I<may> sources.
2466 After finishing with an C<isl_flow>, the user should call
2467 C<isl_flow_free> to free all associated memory.
2469 A higher-level interface to dependence analysis is provided
2470 by the following function.
2472 #include <isl/flow.h>
2474 int isl_union_map_compute_flow(__isl_take isl_union_map *sink,
2475 __isl_take isl_union_map *must_source,
2476 __isl_take isl_union_map *may_source,
2477 __isl_take isl_union_map *schedule,
2478 __isl_give isl_union_map **must_dep,
2479 __isl_give isl_union_map **may_dep,
2480 __isl_give isl_union_set **must_no_source,
2481 __isl_give isl_union_set **may_no_source);
2483 The arrays are identified by the tuple names of the ranges
2484 of the accesses. The iteration domains by the tuple names
2485 of the domains of the accesses and of the schedule.
2486 The relative order of the iteration domains is given by the
2487 schedule. Any of C<must_dep>, C<may_dep>, C<must_no_source>
2488 or C<may_no_source> may be C<NULL>, but a C<NULL> value for
2489 any of the other arguments is treated as an error.
2491 =head2 Parametric Vertex Enumeration
2493 The parametric vertex enumeration described in this section
2494 is mainly intended to be used internally and by the C<barvinok>
2497 #include <isl/vertices.h>
2498 __isl_give isl_vertices *isl_basic_set_compute_vertices(
2499 __isl_keep isl_basic_set *bset);
2501 The function C<isl_basic_set_compute_vertices> performs the
2502 actual computation of the parametric vertices and the chamber
2503 decomposition and store the result in an C<isl_vertices> object.
2504 This information can be queried by either iterating over all
2505 the vertices or iterating over all the chambers or cells
2506 and then iterating over all vertices that are active on the chamber.
2508 int isl_vertices_foreach_vertex(
2509 __isl_keep isl_vertices *vertices,
2510 int (*fn)(__isl_take isl_vertex *vertex, void *user),
2513 int isl_vertices_foreach_cell(
2514 __isl_keep isl_vertices *vertices,
2515 int (*fn)(__isl_take isl_cell *cell, void *user),
2517 int isl_cell_foreach_vertex(__isl_keep isl_cell *cell,
2518 int (*fn)(__isl_take isl_vertex *vertex, void *user),
2521 Other operations that can be performed on an C<isl_vertices> object are
2524 isl_ctx *isl_vertices_get_ctx(
2525 __isl_keep isl_vertices *vertices);
2526 int isl_vertices_get_n_vertices(
2527 __isl_keep isl_vertices *vertices);
2528 void isl_vertices_free(__isl_take isl_vertices *vertices);
2530 Vertices can be inspected and destroyed using the following functions.
2532 isl_ctx *isl_vertex_get_ctx(__isl_keep isl_vertex *vertex);
2533 int isl_vertex_get_id(__isl_keep isl_vertex *vertex);
2534 __isl_give isl_basic_set *isl_vertex_get_domain(
2535 __isl_keep isl_vertex *vertex);
2536 __isl_give isl_basic_set *isl_vertex_get_expr(
2537 __isl_keep isl_vertex *vertex);
2538 void isl_vertex_free(__isl_take isl_vertex *vertex);
2540 C<isl_vertex_get_expr> returns a singleton parametric set describing
2541 the vertex, while C<isl_vertex_get_domain> returns the activity domain
2543 Note that C<isl_vertex_get_domain> and C<isl_vertex_get_expr> return
2544 B<rational> basic sets, so they should mainly be used for inspection
2545 and should not be mixed with integer sets.
2547 Chambers can be inspected and destroyed using the following functions.
2549 isl_ctx *isl_cell_get_ctx(__isl_keep isl_cell *cell);
2550 __isl_give isl_basic_set *isl_cell_get_domain(
2551 __isl_keep isl_cell *cell);
2552 void isl_cell_free(__isl_take isl_cell *cell);
2556 Although C<isl> is mainly meant to be used as a library,
2557 it also contains some basic applications that use some
2558 of the functionality of C<isl>.
2559 The input may be specified in either the L<isl format>
2560 or the L<PolyLib format>.
2562 =head2 C<isl_polyhedron_sample>
2564 C<isl_polyhedron_sample> takes a polyhedron as input and prints
2565 an integer element of the polyhedron, if there is any.
2566 The first column in the output is the denominator and is always
2567 equal to 1. If the polyhedron contains no integer points,
2568 then a vector of length zero is printed.
2572 C<isl_pip> takes the same input as the C<example> program
2573 from the C<piplib> distribution, i.e., a set of constraints
2574 on the parameters, a line containing only -1 and finally a set
2575 of constraints on a parametric polyhedron.
2576 The coefficients of the parameters appear in the last columns
2577 (but before the final constant column).
2578 The output is the lexicographic minimum of the parametric polyhedron.
2579 As C<isl> currently does not have its own output format, the output
2580 is just a dump of the internal state.
2582 =head2 C<isl_polyhedron_minimize>
2584 C<isl_polyhedron_minimize> computes the minimum of some linear
2585 or affine objective function over the integer points in a polyhedron.
2586 If an affine objective function
2587 is given, then the constant should appear in the last column.
2589 =head2 C<isl_polytope_scan>
2591 Given a polytope, C<isl_polytope_scan> prints
2592 all integer points in the polytope.
2594 =head1 C<isl-polylib>
2596 The C<isl-polylib> library provides the following functions for converting
2597 between C<isl> objects and C<PolyLib> objects.
2598 The library is distributed separately for licensing reasons.
2600 #include <isl_set_polylib.h>
2601 __isl_give isl_basic_set *isl_basic_set_new_from_polylib(
2602 Polyhedron *P, __isl_take isl_dim *dim);
2603 Polyhedron *isl_basic_set_to_polylib(
2604 __isl_keep isl_basic_set *bset);
2605 __isl_give isl_set *isl_set_new_from_polylib(Polyhedron *D,
2606 __isl_take isl_dim *dim);
2607 Polyhedron *isl_set_to_polylib(__isl_keep isl_set *set);
2609 #include <isl_map_polylib.h>
2610 __isl_give isl_basic_map *isl_basic_map_new_from_polylib(
2611 Polyhedron *P, __isl_take isl_dim *dim);
2612 __isl_give isl_map *isl_map_new_from_polylib(Polyhedron *D,
2613 __isl_take isl_dim *dim);
2614 Polyhedron *isl_basic_map_to_polylib(
2615 __isl_keep isl_basic_map *bmap);
2616 Polyhedron *isl_map_to_polylib(__isl_keep isl_map *map);