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 =item * Identity relations
732 __isl_give isl_basic_map *isl_basic_map_identity(
733 __isl_take isl_dim *set_dim);
734 __isl_give isl_map *isl_map_identity(
735 __isl_take isl_dim *set_dim);
737 These functions take a dimension specification for a B<set>
738 and return an identity relation between two such sets.
740 =item * Lexicographic order
742 __isl_give isl_map *isl_map_lex_lt(
743 __isl_take isl_dim *set_dim);
744 __isl_give isl_map *isl_map_lex_le(
745 __isl_take isl_dim *set_dim);
746 __isl_give isl_map *isl_map_lex_gt(
747 __isl_take isl_dim *set_dim);
748 __isl_give isl_map *isl_map_lex_ge(
749 __isl_take isl_dim *set_dim);
750 __isl_give isl_map *isl_map_lex_lt_first(
751 __isl_take isl_dim *dim, unsigned n);
752 __isl_give isl_map *isl_map_lex_le_first(
753 __isl_take isl_dim *dim, unsigned n);
754 __isl_give isl_map *isl_map_lex_gt_first(
755 __isl_take isl_dim *dim, unsigned n);
756 __isl_give isl_map *isl_map_lex_ge_first(
757 __isl_take isl_dim *dim, unsigned n);
759 The first four functions take a dimension specification for a B<set>
760 and return relations that express that the elements in the domain
761 are lexicographically less
762 (C<isl_map_lex_lt>), less or equal (C<isl_map_lex_le>),
763 greater (C<isl_map_lex_gt>) or greater or equal (C<isl_map_lex_ge>)
764 than the elements in the range.
765 The last four functions take a dimension specification for a map
766 and return relations that express that the first C<n> dimensions
767 in the domain are lexicographically less
768 (C<isl_map_lex_lt_first>), less or equal (C<isl_map_lex_le_first>),
769 greater (C<isl_map_lex_gt_first>) or greater or equal (C<isl_map_lex_ge_first>)
770 than the first C<n> dimensions in the range.
774 A basic set or relation can be converted to a set or relation
775 using the following functions.
777 __isl_give isl_set *isl_set_from_basic_set(
778 __isl_take isl_basic_set *bset);
779 __isl_give isl_map *isl_map_from_basic_map(
780 __isl_take isl_basic_map *bmap);
782 Sets and relations can be converted to union sets and relations
783 using the following functions.
785 __isl_give isl_union_map *isl_union_map_from_map(
786 __isl_take isl_map *map);
787 __isl_give isl_union_set *isl_union_set_from_set(
788 __isl_take isl_set *set);
790 Sets and relations can be copied and freed again using the following
793 __isl_give isl_basic_set *isl_basic_set_copy(
794 __isl_keep isl_basic_set *bset);
795 __isl_give isl_set *isl_set_copy(__isl_keep isl_set *set);
796 __isl_give isl_union_set *isl_union_set_copy(
797 __isl_keep isl_union_set *uset);
798 __isl_give isl_basic_map *isl_basic_map_copy(
799 __isl_keep isl_basic_map *bmap);
800 __isl_give isl_map *isl_map_copy(__isl_keep isl_map *map);
801 __isl_give isl_union_map *isl_union_map_copy(
802 __isl_keep isl_union_map *umap);
803 void isl_basic_set_free(__isl_take isl_basic_set *bset);
804 void isl_set_free(__isl_take isl_set *set);
805 void isl_union_set_free(__isl_take isl_union_set *uset);
806 void isl_basic_map_free(__isl_take isl_basic_map *bmap);
807 void isl_map_free(__isl_take isl_map *map);
808 void isl_union_map_free(__isl_take isl_union_map *umap);
810 Other sets and relations can be constructed by starting
811 from a universe set or relation, adding equality and/or
812 inequality constraints and then projecting out the
813 existentially quantified variables, if any.
814 Constraints can be constructed, manipulated and
815 added to basic sets and relations using the following functions.
817 #include <isl/constraint.h>
818 __isl_give isl_constraint *isl_equality_alloc(
819 __isl_take isl_dim *dim);
820 __isl_give isl_constraint *isl_inequality_alloc(
821 __isl_take isl_dim *dim);
822 void isl_constraint_set_constant(
823 __isl_keep isl_constraint *constraint, isl_int v);
824 void isl_constraint_set_coefficient(
825 __isl_keep isl_constraint *constraint,
826 enum isl_dim_type type, int pos, isl_int v);
827 __isl_give isl_basic_map *isl_basic_map_add_constraint(
828 __isl_take isl_basic_map *bmap,
829 __isl_take isl_constraint *constraint);
830 __isl_give isl_basic_set *isl_basic_set_add_constraint(
831 __isl_take isl_basic_set *bset,
832 __isl_take isl_constraint *constraint);
834 For example, to create a set containing the even integers
835 between 10 and 42, you would use the following code.
839 struct isl_constraint *c;
840 struct isl_basic_set *bset;
843 dim = isl_dim_set_alloc(ctx, 0, 2);
844 bset = isl_basic_set_universe(isl_dim_copy(dim));
846 c = isl_equality_alloc(isl_dim_copy(dim));
847 isl_int_set_si(v, -1);
848 isl_constraint_set_coefficient(c, isl_dim_set, 0, v);
849 isl_int_set_si(v, 2);
850 isl_constraint_set_coefficient(c, isl_dim_set, 1, v);
851 bset = isl_basic_set_add_constraint(bset, c);
853 c = isl_inequality_alloc(isl_dim_copy(dim));
854 isl_int_set_si(v, -10);
855 isl_constraint_set_constant(c, v);
856 isl_int_set_si(v, 1);
857 isl_constraint_set_coefficient(c, isl_dim_set, 0, v);
858 bset = isl_basic_set_add_constraint(bset, c);
860 c = isl_inequality_alloc(dim);
861 isl_int_set_si(v, 42);
862 isl_constraint_set_constant(c, v);
863 isl_int_set_si(v, -1);
864 isl_constraint_set_coefficient(c, isl_dim_set, 0, v);
865 bset = isl_basic_set_add_constraint(bset, c);
867 bset = isl_basic_set_project_out(bset, isl_dim_set, 1, 1);
873 struct isl_basic_set *bset;
874 bset = isl_basic_set_read_from_str(ctx,
875 "{[i] : exists (a : i = 2a and i >= 10 and i <= 42)}", -1);
877 A basic set or relation can also be constructed from two matrices
878 describing the equalities and the inequalities.
880 __isl_give isl_basic_set *isl_basic_set_from_constraint_matrices(
881 __isl_take isl_dim *dim,
882 __isl_take isl_mat *eq, __isl_take isl_mat *ineq,
883 enum isl_dim_type c1,
884 enum isl_dim_type c2, enum isl_dim_type c3,
885 enum isl_dim_type c4);
886 __isl_give isl_basic_map *isl_basic_map_from_constraint_matrices(
887 __isl_take isl_dim *dim,
888 __isl_take isl_mat *eq, __isl_take isl_mat *ineq,
889 enum isl_dim_type c1,
890 enum isl_dim_type c2, enum isl_dim_type c3,
891 enum isl_dim_type c4, enum isl_dim_type c5);
893 The C<isl_dim_type> arguments indicate the order in which
894 different kinds of variables appear in the input matrices
895 and should be a permutation of C<isl_dim_cst>, C<isl_dim_param>,
896 C<isl_dim_set> and C<isl_dim_div> for sets and
897 of C<isl_dim_cst>, C<isl_dim_param>,
898 C<isl_dim_in>, C<isl_dim_out> and C<isl_dim_div> for relations.
900 =head2 Inspecting Sets and Relations
902 Usually, the user should not have to care about the actual constraints
903 of the sets and maps, but should instead apply the abstract operations
904 explained in the following sections.
905 Occasionally, however, it may be required to inspect the individual
906 coefficients of the constraints. This section explains how to do so.
907 In these cases, it may also be useful to have C<isl> compute
908 an explicit representation of the existentially quantified variables.
910 __isl_give isl_set *isl_set_compute_divs(
911 __isl_take isl_set *set);
912 __isl_give isl_map *isl_map_compute_divs(
913 __isl_take isl_map *map);
914 __isl_give isl_union_set *isl_union_set_compute_divs(
915 __isl_take isl_union_set *uset);
916 __isl_give isl_union_map *isl_union_map_compute_divs(
917 __isl_take isl_union_map *umap);
919 This explicit representation defines the existentially quantified
920 variables as integer divisions of the other variables, possibly
921 including earlier existentially quantified variables.
922 An explicitly represented existentially quantified variable therefore
923 has a unique value when the values of the other variables are known.
924 If, furthermore, the same existentials, i.e., existentials
925 with the same explicit representations, should appear in the
926 same order in each of the disjuncts of a set or map, then the user should call
927 either of the following functions.
929 __isl_give isl_set *isl_set_align_divs(
930 __isl_take isl_set *set);
931 __isl_give isl_map *isl_map_align_divs(
932 __isl_take isl_map *map);
934 Alternatively, the existentially quantified variables can be removed
935 using the following functions, which compute an overapproximation.
937 __isl_give isl_basic_set *isl_basic_set_remove_divs(
938 __isl_take isl_basic_set *bset);
939 __isl_give isl_basic_map *isl_basic_map_remove_divs(
940 __isl_take isl_basic_map *bmap);
941 __isl_give isl_set *isl_set_remove_divs(
942 __isl_take isl_set *set);
944 To iterate over all the sets or maps in a union set or map, use
946 int isl_union_set_foreach_set(__isl_keep isl_union_set *uset,
947 int (*fn)(__isl_take isl_set *set, void *user),
949 int isl_union_map_foreach_map(__isl_keep isl_union_map *umap,
950 int (*fn)(__isl_take isl_map *map, void *user),
953 The number of sets or maps in a union set or map can be obtained
956 int isl_union_set_n_set(__isl_keep isl_union_set *uset);
957 int isl_union_map_n_map(__isl_keep isl_union_map *umap);
959 To extract the set or map from a union with a given dimension
962 __isl_give isl_set *isl_union_set_extract_set(
963 __isl_keep isl_union_set *uset,
964 __isl_take isl_dim *dim);
965 __isl_give isl_map *isl_union_map_extract_map(
966 __isl_keep isl_union_map *umap,
967 __isl_take isl_dim *dim);
969 To iterate over all the basic sets or maps in a set or map, use
971 int isl_set_foreach_basic_set(__isl_keep isl_set *set,
972 int (*fn)(__isl_take isl_basic_set *bset, void *user),
974 int isl_map_foreach_basic_map(__isl_keep isl_map *map,
975 int (*fn)(__isl_take isl_basic_map *bmap, void *user),
978 The callback function C<fn> should return 0 if successful and
979 -1 if an error occurs. In the latter case, or if any other error
980 occurs, the above functions will return -1.
982 It should be noted that C<isl> does not guarantee that
983 the basic sets or maps passed to C<fn> are disjoint.
984 If this is required, then the user should call one of
985 the following functions first.
987 __isl_give isl_set *isl_set_make_disjoint(
988 __isl_take isl_set *set);
989 __isl_give isl_map *isl_map_make_disjoint(
990 __isl_take isl_map *map);
992 The number of basic sets in a set can be obtained
995 int isl_set_n_basic_set(__isl_keep isl_set *set);
997 To iterate over the constraints of a basic set or map, use
999 #include <isl/constraint.h>
1001 int isl_basic_map_foreach_constraint(
1002 __isl_keep isl_basic_map *bmap,
1003 int (*fn)(__isl_take isl_constraint *c, void *user),
1005 void isl_constraint_free(struct isl_constraint *c);
1007 Again, the callback function C<fn> should return 0 if successful and
1008 -1 if an error occurs. In the latter case, or if any other error
1009 occurs, the above functions will return -1.
1010 The constraint C<c> represents either an equality or an inequality.
1011 Use the following function to find out whether a constraint
1012 represents an equality. If not, it represents an inequality.
1014 int isl_constraint_is_equality(
1015 __isl_keep isl_constraint *constraint);
1017 The coefficients of the constraints can be inspected using
1018 the following functions.
1020 void isl_constraint_get_constant(
1021 __isl_keep isl_constraint *constraint, isl_int *v);
1022 void isl_constraint_get_coefficient(
1023 __isl_keep isl_constraint *constraint,
1024 enum isl_dim_type type, int pos, isl_int *v);
1026 The explicit representations of the existentially quantified
1027 variables can be inspected using the following functions.
1028 Note that the user is only allowed to use these functions
1029 if the inspected set or map is the result of a call
1030 to C<isl_set_compute_divs> or C<isl_map_compute_divs>.
1032 __isl_give isl_div *isl_constraint_div(
1033 __isl_keep isl_constraint *constraint, int pos);
1034 void isl_div_get_constant(__isl_keep isl_div *div,
1036 void isl_div_get_denominator(__isl_keep isl_div *div,
1038 void isl_div_get_coefficient(__isl_keep isl_div *div,
1039 enum isl_dim_type type, int pos, isl_int *v);
1041 To obtain the constraints of a basic set or map in matrix
1042 form, use the following functions.
1044 __isl_give isl_mat *isl_basic_set_equalities_matrix(
1045 __isl_keep isl_basic_set *bset,
1046 enum isl_dim_type c1, enum isl_dim_type c2,
1047 enum isl_dim_type c3, enum isl_dim_type c4);
1048 __isl_give isl_mat *isl_basic_set_inequalities_matrix(
1049 __isl_keep isl_basic_set *bset,
1050 enum isl_dim_type c1, enum isl_dim_type c2,
1051 enum isl_dim_type c3, enum isl_dim_type c4);
1052 __isl_give isl_mat *isl_basic_map_equalities_matrix(
1053 __isl_keep isl_basic_map *bmap,
1054 enum isl_dim_type c1,
1055 enum isl_dim_type c2, enum isl_dim_type c3,
1056 enum isl_dim_type c4, enum isl_dim_type c5);
1057 __isl_give isl_mat *isl_basic_map_inequalities_matrix(
1058 __isl_keep isl_basic_map *bmap,
1059 enum isl_dim_type c1,
1060 enum isl_dim_type c2, enum isl_dim_type c3,
1061 enum isl_dim_type c4, enum isl_dim_type c5);
1063 The C<isl_dim_type> arguments dictate the order in which
1064 different kinds of variables appear in the resulting matrix
1065 and should be a permutation of C<isl_dim_cst>, C<isl_dim_param>,
1066 C<isl_dim_in>, C<isl_dim_out> and C<isl_dim_div>.
1068 The names of the domain and range spaces of a set or relation can be
1069 read off using the following functions.
1071 const char *isl_basic_set_get_tuple_name(
1072 __isl_keep isl_basic_set *bset);
1073 const char *isl_set_get_tuple_name(
1074 __isl_keep isl_set *set);
1075 const char *isl_basic_map_get_tuple_name(
1076 __isl_keep isl_basic_map *bmap,
1077 enum isl_dim_type type);
1078 const char *isl_map_get_tuple_name(
1079 __isl_keep isl_map *map,
1080 enum isl_dim_type type);
1082 As with C<isl_dim_get_tuple_name>, the value returned points to
1083 an internal data structure.
1084 The names of individual dimensions can be read off using
1085 the following functions.
1087 const char *isl_constraint_get_dim_name(
1088 __isl_keep isl_constraint *constraint,
1089 enum isl_dim_type type, unsigned pos);
1090 const char *isl_set_get_dim_name(
1091 __isl_keep isl_set *set,
1092 enum isl_dim_type type, unsigned pos);
1093 const char *isl_basic_map_get_dim_name(
1094 __isl_keep isl_basic_map *bmap,
1095 enum isl_dim_type type, unsigned pos);
1096 const char *isl_map_get_dim_name(
1097 __isl_keep isl_map *map,
1098 enum isl_dim_type type, unsigned pos);
1100 These functions are mostly useful to obtain the names
1105 =head3 Unary Properties
1111 The following functions test whether the given set or relation
1112 contains any integer points. The ``fast'' variants do not perform
1113 any computations, but simply check if the given set or relation
1114 is already known to be empty.
1116 int isl_basic_set_fast_is_empty(__isl_keep isl_basic_set *bset);
1117 int isl_basic_set_is_empty(__isl_keep isl_basic_set *bset);
1118 int isl_set_is_empty(__isl_keep isl_set *set);
1119 int isl_union_set_is_empty(__isl_keep isl_union_set *uset);
1120 int isl_basic_map_fast_is_empty(__isl_keep isl_basic_map *bmap);
1121 int isl_basic_map_is_empty(__isl_keep isl_basic_map *bmap);
1122 int isl_map_fast_is_empty(__isl_keep isl_map *map);
1123 int isl_map_is_empty(__isl_keep isl_map *map);
1124 int isl_union_map_is_empty(__isl_keep isl_union_map *umap);
1126 =item * Universality
1128 int isl_basic_set_is_universe(__isl_keep isl_basic_set *bset);
1129 int isl_basic_map_is_universe(__isl_keep isl_basic_map *bmap);
1130 int isl_set_fast_is_universe(__isl_keep isl_set *set);
1132 =item * Single-valuedness
1134 int isl_map_is_single_valued(__isl_keep isl_map *map);
1138 int isl_map_is_bijective(__isl_keep isl_map *map);
1142 The followning functions check whether the domain of the given
1143 (basic) set is a wrapped relation.
1145 int isl_basic_set_is_wrapping(
1146 __isl_keep isl_basic_set *bset);
1147 int isl_set_is_wrapping(__isl_keep isl_set *set);
1151 =head3 Binary Properties
1157 int isl_set_fast_is_equal(__isl_keep isl_set *set1,
1158 __isl_keep isl_set *set2);
1159 int isl_set_is_equal(__isl_keep isl_set *set1,
1160 __isl_keep isl_set *set2);
1161 int isl_union_set_is_equal(
1162 __isl_keep isl_union_set *uset1,
1163 __isl_keep isl_union_set *uset2);
1164 int isl_basic_map_is_equal(
1165 __isl_keep isl_basic_map *bmap1,
1166 __isl_keep isl_basic_map *bmap2);
1167 int isl_map_is_equal(__isl_keep isl_map *map1,
1168 __isl_keep isl_map *map2);
1169 int isl_map_fast_is_equal(__isl_keep isl_map *map1,
1170 __isl_keep isl_map *map2);
1171 int isl_union_map_is_equal(
1172 __isl_keep isl_union_map *umap1,
1173 __isl_keep isl_union_map *umap2);
1175 =item * Disjointness
1177 int isl_set_fast_is_disjoint(__isl_keep isl_set *set1,
1178 __isl_keep isl_set *set2);
1182 int isl_set_is_subset(__isl_keep isl_set *set1,
1183 __isl_keep isl_set *set2);
1184 int isl_set_is_strict_subset(
1185 __isl_keep isl_set *set1,
1186 __isl_keep isl_set *set2);
1187 int isl_union_set_is_subset(
1188 __isl_keep isl_union_set *uset1,
1189 __isl_keep isl_union_set *uset2);
1190 int isl_union_set_is_strict_subset(
1191 __isl_keep isl_union_set *uset1,
1192 __isl_keep isl_union_set *uset2);
1193 int isl_basic_map_is_subset(
1194 __isl_keep isl_basic_map *bmap1,
1195 __isl_keep isl_basic_map *bmap2);
1196 int isl_basic_map_is_strict_subset(
1197 __isl_keep isl_basic_map *bmap1,
1198 __isl_keep isl_basic_map *bmap2);
1199 int isl_map_is_subset(
1200 __isl_keep isl_map *map1,
1201 __isl_keep isl_map *map2);
1202 int isl_map_is_strict_subset(
1203 __isl_keep isl_map *map1,
1204 __isl_keep isl_map *map2);
1205 int isl_union_map_is_subset(
1206 __isl_keep isl_union_map *umap1,
1207 __isl_keep isl_union_map *umap2);
1208 int isl_union_map_is_strict_subset(
1209 __isl_keep isl_union_map *umap1,
1210 __isl_keep isl_union_map *umap2);
1214 =head2 Unary Operations
1220 __isl_give isl_set *isl_set_complement(
1221 __isl_take isl_set *set);
1225 __isl_give isl_basic_map *isl_basic_map_reverse(
1226 __isl_take isl_basic_map *bmap);
1227 __isl_give isl_map *isl_map_reverse(
1228 __isl_take isl_map *map);
1229 __isl_give isl_union_map *isl_union_map_reverse(
1230 __isl_take isl_union_map *umap);
1234 __isl_give isl_basic_set *isl_basic_set_project_out(
1235 __isl_take isl_basic_set *bset,
1236 enum isl_dim_type type, unsigned first, unsigned n);
1237 __isl_give isl_basic_map *isl_basic_map_project_out(
1238 __isl_take isl_basic_map *bmap,
1239 enum isl_dim_type type, unsigned first, unsigned n);
1240 __isl_give isl_set *isl_set_project_out(__isl_take isl_set *set,
1241 enum isl_dim_type type, unsigned first, unsigned n);
1242 __isl_give isl_map *isl_map_project_out(__isl_take isl_map *map,
1243 enum isl_dim_type type, unsigned first, unsigned n);
1244 __isl_give isl_basic_set *isl_basic_map_domain(
1245 __isl_take isl_basic_map *bmap);
1246 __isl_give isl_basic_set *isl_basic_map_range(
1247 __isl_take isl_basic_map *bmap);
1248 __isl_give isl_set *isl_map_domain(
1249 __isl_take isl_map *bmap);
1250 __isl_give isl_set *isl_map_range(
1251 __isl_take isl_map *map);
1252 __isl_give isl_union_set *isl_union_map_domain(
1253 __isl_take isl_union_map *umap);
1254 __isl_give isl_union_set *isl_union_map_range(
1255 __isl_take isl_union_map *umap);
1257 __isl_give isl_basic_map *isl_basic_map_domain_map(
1258 __isl_take isl_basic_map *bmap);
1259 __isl_give isl_basic_map *isl_basic_map_range_map(
1260 __isl_take isl_basic_map *bmap);
1261 __isl_give isl_map *isl_map_domain_map(__isl_take isl_map *map);
1262 __isl_give isl_map *isl_map_range_map(__isl_take isl_map *map);
1263 __isl_give isl_union_map *isl_union_map_domain_map(
1264 __isl_take isl_union_map *umap);
1265 __isl_give isl_union_map *isl_union_map_range_map(
1266 __isl_take isl_union_map *umap);
1268 The functions above construct a (basic, regular or union) relation
1269 that maps (a wrapped version of) the input relation to its domain or range.
1273 __isl_give isl_map *isl_set_identity(
1274 __isl_take isl_set *set);
1275 __isl_give isl_union_map *isl_union_set_identity(
1276 __isl_take isl_union_set *uset);
1278 Construct an identity relation on the given (union) set.
1282 __isl_give isl_basic_set *isl_basic_map_deltas(
1283 __isl_take isl_basic_map *bmap);
1284 __isl_give isl_set *isl_map_deltas(__isl_take isl_map *map);
1285 __isl_give isl_union_set *isl_union_map_deltas(
1286 __isl_take isl_union_map *umap);
1288 These functions return a (basic) set containing the differences
1289 between image elements and corresponding domain elements in the input.
1293 Simplify the representation of a set or relation by trying
1294 to combine pairs of basic sets or relations into a single
1295 basic set or relation.
1297 __isl_give isl_set *isl_set_coalesce(__isl_take isl_set *set);
1298 __isl_give isl_map *isl_map_coalesce(__isl_take isl_map *map);
1299 __isl_give isl_union_set *isl_union_set_coalesce(
1300 __isl_take isl_union_set *uset);
1301 __isl_give isl_union_map *isl_union_map_coalesce(
1302 __isl_take isl_union_map *umap);
1304 =item * Detecting equalities
1306 __isl_give isl_basic_set *isl_basic_set_detect_equalities(
1307 __isl_take isl_basic_set *bset);
1308 __isl_give isl_basic_map *isl_basic_map_detect_equalities(
1309 __isl_take isl_basic_map *bmap);
1310 __isl_give isl_set *isl_set_detect_equalities(
1311 __isl_take isl_set *set);
1312 __isl_give isl_map *isl_map_detect_equalities(
1313 __isl_take isl_map *map);
1314 __isl_give isl_union_set *isl_union_set_detect_equalities(
1315 __isl_take isl_union_set *uset);
1316 __isl_give isl_union_map *isl_union_map_detect_equalities(
1317 __isl_take isl_union_map *umap);
1319 Simplify the representation of a set or relation by detecting implicit
1324 __isl_give isl_basic_set *isl_set_convex_hull(
1325 __isl_take isl_set *set);
1326 __isl_give isl_basic_map *isl_map_convex_hull(
1327 __isl_take isl_map *map);
1329 If the input set or relation has any existentially quantified
1330 variables, then the result of these operations is currently undefined.
1334 __isl_give isl_basic_set *isl_set_simple_hull(
1335 __isl_take isl_set *set);
1336 __isl_give isl_basic_map *isl_map_simple_hull(
1337 __isl_take isl_map *map);
1338 __isl_give isl_union_map *isl_union_map_simple_hull(
1339 __isl_take isl_union_map *umap);
1341 These functions compute a single basic set or relation
1342 that contains the whole input set or relation.
1343 In particular, the output is described by translates
1344 of the constraints describing the basic sets or relations in the input.
1348 (See \autoref{s:simple hull}.)
1354 __isl_give isl_basic_set *isl_basic_set_affine_hull(
1355 __isl_take isl_basic_set *bset);
1356 __isl_give isl_basic_set *isl_set_affine_hull(
1357 __isl_take isl_set *set);
1358 __isl_give isl_union_set *isl_union_set_affine_hull(
1359 __isl_take isl_union_set *uset);
1360 __isl_give isl_basic_map *isl_basic_map_affine_hull(
1361 __isl_take isl_basic_map *bmap);
1362 __isl_give isl_basic_map *isl_map_affine_hull(
1363 __isl_take isl_map *map);
1364 __isl_give isl_union_map *isl_union_map_affine_hull(
1365 __isl_take isl_union_map *umap);
1367 In case of union sets and relations, the affine hull is computed
1370 =item * Polyhedral hull
1372 __isl_give isl_basic_set *isl_set_polyhedral_hull(
1373 __isl_take isl_set *set);
1374 __isl_give isl_basic_map *isl_map_polyhedral_hull(
1375 __isl_take isl_map *map);
1376 __isl_give isl_union_set *isl_union_set_polyhedral_hull(
1377 __isl_take isl_union_set *uset);
1378 __isl_give isl_union_map *isl_union_map_polyhedral_hull(
1379 __isl_take isl_union_map *umap);
1381 These functions compute a single basic set or relation
1382 not involving any existentially quantified variables
1383 that contains the whole input set or relation.
1384 In case of union sets and relations, the polyhedral hull is computed
1389 __isl_give isl_map *isl_map_power(__isl_take isl_map *map,
1390 unsigned param, int *exact);
1392 Compute a parametric representation for all positive powers I<k> of C<map>.
1393 The power I<k> is equated to the parameter at position C<param>.
1394 The result may be an overapproximation. If the result is exact,
1395 then C<*exact> is set to C<1>.
1396 The current implementation only produces exact results for particular
1397 cases of piecewise translations (i.e., piecewise uniform dependences).
1399 =item * Transitive closure
1401 __isl_give isl_map *isl_map_transitive_closure(
1402 __isl_take isl_map *map, int *exact);
1403 __isl_give isl_union_map *isl_union_map_transitive_closure(
1404 __isl_take isl_union_map *umap, int *exact);
1406 Compute the transitive closure of C<map>.
1407 The result may be an overapproximation. If the result is known to be 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 * Reaching path lengths
1414 __isl_give isl_map *isl_map_reaching_path_lengths(
1415 __isl_take isl_map *map, int *exact);
1417 Compute a relation that maps each element in the range of C<map>
1418 to the lengths of all paths composed of edges in C<map> that
1419 end up in the given element.
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 To compute the I<maximal> path length, the resulting relation
1423 should be postprocessed by C<isl_map_lexmax>.
1424 In particular, if the input relation is a dependence relation
1425 (mapping sources to sinks), then the maximal path length corresponds
1426 to the free schedule.
1427 Note, however, that C<isl_map_lexmax> expects the maximum to be
1428 finite, so if the path lengths are unbounded (possibly due to
1429 the overapproximation), then you will get an error message.
1433 __isl_give isl_basic_set *isl_basic_map_wrap(
1434 __isl_take isl_basic_map *bmap);
1435 __isl_give isl_set *isl_map_wrap(
1436 __isl_take isl_map *map);
1437 __isl_give isl_union_set *isl_union_map_wrap(
1438 __isl_take isl_union_map *umap);
1439 __isl_give isl_basic_map *isl_basic_set_unwrap(
1440 __isl_take isl_basic_set *bset);
1441 __isl_give isl_map *isl_set_unwrap(
1442 __isl_take isl_set *set);
1443 __isl_give isl_union_map *isl_union_set_unwrap(
1444 __isl_take isl_union_set *uset);
1448 Remove any internal structure of domain (and range) of the given
1449 set or relation. If there is any such internal structure in the input,
1450 then the name of the space is also removed.
1452 __isl_give isl_basic_set *isl_basic_set_flatten(
1453 __isl_take isl_basic_set *bset);
1454 __isl_give isl_set *isl_set_flatten(
1455 __isl_take isl_set *set);
1456 __isl_give isl_map *isl_map_flatten(
1457 __isl_take isl_map *map);
1459 __isl_give isl_map *isl_set_flatten_map(
1460 __isl_take isl_set *set);
1462 The function above constructs a relation
1463 that maps the input set to a flattened version of the set.
1465 =item * Dimension manipulation
1467 __isl_give isl_set *isl_set_add_dims(
1468 __isl_take isl_set *set,
1469 enum isl_dim_type type, unsigned n);
1470 __isl_give isl_map *isl_map_add_dims(
1471 __isl_take isl_map *map,
1472 enum isl_dim_type type, unsigned n);
1474 It is usually not advisable to directly change the (input or output)
1475 space of a set or a relation as this removes the name and the internal
1476 structure of the space. However, the above functions can be useful
1477 to add new parameters.
1481 =head2 Binary Operations
1483 The two arguments of a binary operation not only need to live
1484 in the same C<isl_ctx>, they currently also need to have
1485 the same (number of) parameters.
1487 =head3 Basic Operations
1491 =item * Intersection
1493 __isl_give isl_basic_set *isl_basic_set_intersect(
1494 __isl_take isl_basic_set *bset1,
1495 __isl_take isl_basic_set *bset2);
1496 __isl_give isl_set *isl_set_intersect(
1497 __isl_take isl_set *set1,
1498 __isl_take isl_set *set2);
1499 __isl_give isl_union_set *isl_union_set_intersect(
1500 __isl_take isl_union_set *uset1,
1501 __isl_take isl_union_set *uset2);
1502 __isl_give isl_basic_map *isl_basic_map_intersect_domain(
1503 __isl_take isl_basic_map *bmap,
1504 __isl_take isl_basic_set *bset);
1505 __isl_give isl_basic_map *isl_basic_map_intersect_range(
1506 __isl_take isl_basic_map *bmap,
1507 __isl_take isl_basic_set *bset);
1508 __isl_give isl_basic_map *isl_basic_map_intersect(
1509 __isl_take isl_basic_map *bmap1,
1510 __isl_take isl_basic_map *bmap2);
1511 __isl_give isl_map *isl_map_intersect_domain(
1512 __isl_take isl_map *map,
1513 __isl_take isl_set *set);
1514 __isl_give isl_map *isl_map_intersect_range(
1515 __isl_take isl_map *map,
1516 __isl_take isl_set *set);
1517 __isl_give isl_map *isl_map_intersect(
1518 __isl_take isl_map *map1,
1519 __isl_take isl_map *map2);
1520 __isl_give isl_union_map *isl_union_map_intersect_domain(
1521 __isl_take isl_union_map *umap,
1522 __isl_take isl_union_set *uset);
1523 __isl_give isl_union_map *isl_union_map_intersect_range(
1524 __isl_take isl_union_map *umap,
1525 __isl_take isl_union_set *uset);
1526 __isl_give isl_union_map *isl_union_map_intersect(
1527 __isl_take isl_union_map *umap1,
1528 __isl_take isl_union_map *umap2);
1532 __isl_give isl_set *isl_basic_set_union(
1533 __isl_take isl_basic_set *bset1,
1534 __isl_take isl_basic_set *bset2);
1535 __isl_give isl_map *isl_basic_map_union(
1536 __isl_take isl_basic_map *bmap1,
1537 __isl_take isl_basic_map *bmap2);
1538 __isl_give isl_set *isl_set_union(
1539 __isl_take isl_set *set1,
1540 __isl_take isl_set *set2);
1541 __isl_give isl_map *isl_map_union(
1542 __isl_take isl_map *map1,
1543 __isl_take isl_map *map2);
1544 __isl_give isl_union_set *isl_union_set_union(
1545 __isl_take isl_union_set *uset1,
1546 __isl_take isl_union_set *uset2);
1547 __isl_give isl_union_map *isl_union_map_union(
1548 __isl_take isl_union_map *umap1,
1549 __isl_take isl_union_map *umap2);
1551 =item * Set difference
1553 __isl_give isl_set *isl_set_subtract(
1554 __isl_take isl_set *set1,
1555 __isl_take isl_set *set2);
1556 __isl_give isl_map *isl_map_subtract(
1557 __isl_take isl_map *map1,
1558 __isl_take isl_map *map2);
1559 __isl_give isl_union_set *isl_union_set_subtract(
1560 __isl_take isl_union_set *uset1,
1561 __isl_take isl_union_set *uset2);
1562 __isl_give isl_union_map *isl_union_map_subtract(
1563 __isl_take isl_union_map *umap1,
1564 __isl_take isl_union_map *umap2);
1568 __isl_give isl_basic_set *isl_basic_set_apply(
1569 __isl_take isl_basic_set *bset,
1570 __isl_take isl_basic_map *bmap);
1571 __isl_give isl_set *isl_set_apply(
1572 __isl_take isl_set *set,
1573 __isl_take isl_map *map);
1574 __isl_give isl_union_set *isl_union_set_apply(
1575 __isl_take isl_union_set *uset,
1576 __isl_take isl_union_map *umap);
1577 __isl_give isl_basic_map *isl_basic_map_apply_domain(
1578 __isl_take isl_basic_map *bmap1,
1579 __isl_take isl_basic_map *bmap2);
1580 __isl_give isl_basic_map *isl_basic_map_apply_range(
1581 __isl_take isl_basic_map *bmap1,
1582 __isl_take isl_basic_map *bmap2);
1583 __isl_give isl_map *isl_map_apply_domain(
1584 __isl_take isl_map *map1,
1585 __isl_take isl_map *map2);
1586 __isl_give isl_union_map *isl_union_map_apply_domain(
1587 __isl_take isl_union_map *umap1,
1588 __isl_take isl_union_map *umap2);
1589 __isl_give isl_map *isl_map_apply_range(
1590 __isl_take isl_map *map1,
1591 __isl_take isl_map *map2);
1592 __isl_give isl_union_map *isl_union_map_apply_range(
1593 __isl_take isl_union_map *umap1,
1594 __isl_take isl_union_map *umap2);
1596 =item * Cartesian Product
1598 __isl_give isl_set *isl_set_product(
1599 __isl_take isl_set *set1,
1600 __isl_take isl_set *set2);
1601 __isl_give isl_union_set *isl_union_set_product(
1602 __isl_take isl_union_set *uset1,
1603 __isl_take isl_union_set *uset2);
1604 __isl_give isl_basic_map *isl_basic_map_range_product(
1605 __isl_take isl_basic_map *bmap1,
1606 __isl_take isl_basic_map *bmap2);
1607 __isl_give isl_map *isl_map_range_product(
1608 __isl_take isl_map *map1,
1609 __isl_take isl_map *map2);
1610 __isl_give isl_union_map *isl_union_map_range_product(
1611 __isl_take isl_union_map *umap1,
1612 __isl_take isl_union_map *umap2);
1613 __isl_give isl_map *isl_map_product(
1614 __isl_take isl_map *map1,
1615 __isl_take isl_map *map2);
1616 __isl_give isl_union_map *isl_union_map_product(
1617 __isl_take isl_union_map *umap1,
1618 __isl_take isl_union_map *umap2);
1620 The above functions compute the cross product of the given
1621 sets or relations. The domains and ranges of the results
1622 are wrapped maps between domains and ranges of the inputs.
1623 To obtain a ``flat'' product, use the following functions
1626 __isl_give isl_set *isl_set_flat_product(
1627 __isl_take isl_set *set1,
1628 __isl_take isl_set *set2);
1629 __isl_give isl_map *isl_map_flat_product(
1630 __isl_take isl_map *map1,
1631 __isl_take isl_map *map2);
1633 =item * Simplification
1635 __isl_give isl_basic_set *isl_basic_set_gist(
1636 __isl_take isl_basic_set *bset,
1637 __isl_take isl_basic_set *context);
1638 __isl_give isl_set *isl_set_gist(__isl_take isl_set *set,
1639 __isl_take isl_set *context);
1640 __isl_give isl_union_set *isl_union_set_gist(
1641 __isl_take isl_union_set *uset,
1642 __isl_take isl_union_set *context);
1643 __isl_give isl_basic_map *isl_basic_map_gist(
1644 __isl_take isl_basic_map *bmap,
1645 __isl_take isl_basic_map *context);
1646 __isl_give isl_map *isl_map_gist(__isl_take isl_map *map,
1647 __isl_take isl_map *context);
1648 __isl_give isl_union_map *isl_union_map_gist(
1649 __isl_take isl_union_map *umap,
1650 __isl_take isl_union_map *context);
1652 The gist operation returns a set or relation that has the
1653 same intersection with the context as the input set or relation.
1654 Any implicit equality in the intersection is made explicit in the result,
1655 while all inequalities that are redundant with respect to the intersection
1657 In case of union sets and relations, the gist operation is performed
1662 =head3 Lexicographic Optimization
1664 Given a (basic) set C<set> (or C<bset>) and a zero-dimensional domain C<dom>,
1665 the following functions
1666 compute a set that contains the lexicographic minimum or maximum
1667 of the elements in C<set> (or C<bset>) for those values of the parameters
1668 that satisfy C<dom>.
1669 If C<empty> is not C<NULL>, then C<*empty> is assigned a set
1670 that contains the parameter values in C<dom> for which C<set> (or C<bset>)
1672 In other words, the union of the parameter values
1673 for which the result is non-empty and of C<*empty>
1676 __isl_give isl_set *isl_basic_set_partial_lexmin(
1677 __isl_take isl_basic_set *bset,
1678 __isl_take isl_basic_set *dom,
1679 __isl_give isl_set **empty);
1680 __isl_give isl_set *isl_basic_set_partial_lexmax(
1681 __isl_take isl_basic_set *bset,
1682 __isl_take isl_basic_set *dom,
1683 __isl_give isl_set **empty);
1684 __isl_give isl_set *isl_set_partial_lexmin(
1685 __isl_take isl_set *set, __isl_take isl_set *dom,
1686 __isl_give isl_set **empty);
1687 __isl_give isl_set *isl_set_partial_lexmax(
1688 __isl_take isl_set *set, __isl_take isl_set *dom,
1689 __isl_give isl_set **empty);
1691 Given a (basic) set C<set> (or C<bset>), the following functions simply
1692 return a set containing the lexicographic minimum or maximum
1693 of the elements in C<set> (or C<bset>).
1694 In case of union sets, the optimum is computed per space.
1696 __isl_give isl_set *isl_basic_set_lexmin(
1697 __isl_take isl_basic_set *bset);
1698 __isl_give isl_set *isl_basic_set_lexmax(
1699 __isl_take isl_basic_set *bset);
1700 __isl_give isl_set *isl_set_lexmin(
1701 __isl_take isl_set *set);
1702 __isl_give isl_set *isl_set_lexmax(
1703 __isl_take isl_set *set);
1704 __isl_give isl_union_set *isl_union_set_lexmin(
1705 __isl_take isl_union_set *uset);
1706 __isl_give isl_union_set *isl_union_set_lexmax(
1707 __isl_take isl_union_set *uset);
1709 Given a (basic) relation C<map> (or C<bmap>) and a domain C<dom>,
1710 the following functions
1711 compute a relation that maps each element of C<dom>
1712 to the single lexicographic minimum or maximum
1713 of the elements that are associated to that same
1714 element in C<map> (or C<bmap>).
1715 If C<empty> is not C<NULL>, then C<*empty> is assigned a set
1716 that contains the elements in C<dom> that do not map
1717 to any elements in C<map> (or C<bmap>).
1718 In other words, the union of the domain of the result and of C<*empty>
1721 __isl_give isl_map *isl_basic_map_partial_lexmax(
1722 __isl_take isl_basic_map *bmap,
1723 __isl_take isl_basic_set *dom,
1724 __isl_give isl_set **empty);
1725 __isl_give isl_map *isl_basic_map_partial_lexmin(
1726 __isl_take isl_basic_map *bmap,
1727 __isl_take isl_basic_set *dom,
1728 __isl_give isl_set **empty);
1729 __isl_give isl_map *isl_map_partial_lexmax(
1730 __isl_take isl_map *map, __isl_take isl_set *dom,
1731 __isl_give isl_set **empty);
1732 __isl_give isl_map *isl_map_partial_lexmin(
1733 __isl_take isl_map *map, __isl_take isl_set *dom,
1734 __isl_give isl_set **empty);
1736 Given a (basic) map C<map> (or C<bmap>), the following functions simply
1737 return a map mapping each element in the domain of
1738 C<map> (or C<bmap>) to the lexicographic minimum or maximum
1739 of all elements associated to that element.
1740 In case of union relations, the optimum is computed per space.
1742 __isl_give isl_map *isl_basic_map_lexmin(
1743 __isl_take isl_basic_map *bmap);
1744 __isl_give isl_map *isl_basic_map_lexmax(
1745 __isl_take isl_basic_map *bmap);
1746 __isl_give isl_map *isl_map_lexmin(
1747 __isl_take isl_map *map);
1748 __isl_give isl_map *isl_map_lexmax(
1749 __isl_take isl_map *map);
1750 __isl_give isl_union_map *isl_union_map_lexmin(
1751 __isl_take isl_union_map *umap);
1752 __isl_give isl_union_map *isl_union_map_lexmax(
1753 __isl_take isl_union_map *umap);
1757 Matrices can be created, copied and freed using the following functions.
1759 #include <isl/mat.h>
1760 __isl_give isl_mat *isl_mat_alloc(struct isl_ctx *ctx,
1761 unsigned n_row, unsigned n_col);
1762 __isl_give isl_mat *isl_mat_copy(__isl_keep isl_mat *mat);
1763 void isl_mat_free(__isl_take isl_mat *mat);
1765 Note that the elements of a newly created matrix may have arbitrary values.
1766 The elements can be changed and inspected using the following functions.
1768 int isl_mat_rows(__isl_keep isl_mat *mat);
1769 int isl_mat_cols(__isl_keep isl_mat *mat);
1770 int isl_mat_get_element(__isl_keep isl_mat *mat,
1771 int row, int col, isl_int *v);
1772 __isl_give isl_mat *isl_mat_set_element(__isl_take isl_mat *mat,
1773 int row, int col, isl_int v);
1775 C<isl_mat_get_element> will return a negative value if anything went wrong.
1776 In that case, the value of C<*v> is undefined.
1778 The following function can be used to compute the (right) inverse
1779 of a matrix, i.e., a matrix such that the product of the original
1780 and the inverse (in that order) is a multiple of the identity matrix.
1781 The input matrix is assumed to be of full row-rank.
1783 __isl_give isl_mat *isl_mat_right_inverse(__isl_take isl_mat *mat);
1785 The following function can be used to compute the (right) kernel
1786 (or null space) of a matrix, i.e., a matrix such that the product of
1787 the original and the kernel (in that order) is the zero matrix.
1789 __isl_give isl_mat *isl_mat_right_kernel(__isl_take isl_mat *mat);
1793 Points are elements of a set. They can be used to construct
1794 simple sets (boxes) or they can be used to represent the
1795 individual elements of a set.
1796 The zero point (the origin) can be created using
1798 __isl_give isl_point *isl_point_zero(__isl_take isl_dim *dim);
1800 The coordinates of a point can be inspected, set and changed
1803 void isl_point_get_coordinate(__isl_keep isl_point *pnt,
1804 enum isl_dim_type type, int pos, isl_int *v);
1805 __isl_give isl_point *isl_point_set_coordinate(
1806 __isl_take isl_point *pnt,
1807 enum isl_dim_type type, int pos, isl_int v);
1809 __isl_give isl_point *isl_point_add_ui(
1810 __isl_take isl_point *pnt,
1811 enum isl_dim_type type, int pos, unsigned val);
1812 __isl_give isl_point *isl_point_sub_ui(
1813 __isl_take isl_point *pnt,
1814 enum isl_dim_type type, int pos, unsigned val);
1816 Points can be copied or freed using
1818 __isl_give isl_point *isl_point_copy(
1819 __isl_keep isl_point *pnt);
1820 void isl_point_free(__isl_take isl_point *pnt);
1822 A singleton set can be created from a point using
1824 __isl_give isl_basic_set *isl_basic_set_from_point(
1825 __isl_take isl_point *pnt);
1826 __isl_give isl_set *isl_set_from_point(
1827 __isl_take isl_point *pnt);
1829 and a box can be created from two opposite extremal points using
1831 __isl_give isl_basic_set *isl_basic_set_box_from_points(
1832 __isl_take isl_point *pnt1,
1833 __isl_take isl_point *pnt2);
1834 __isl_give isl_set *isl_set_box_from_points(
1835 __isl_take isl_point *pnt1,
1836 __isl_take isl_point *pnt2);
1838 All elements of a B<bounded> (union) set can be enumerated using
1839 the following functions.
1841 int isl_set_foreach_point(__isl_keep isl_set *set,
1842 int (*fn)(__isl_take isl_point *pnt, void *user),
1844 int isl_union_set_foreach_point(__isl_keep isl_union_set *uset,
1845 int (*fn)(__isl_take isl_point *pnt, void *user),
1848 The function C<fn> is called for each integer point in
1849 C<set> with as second argument the last argument of
1850 the C<isl_set_foreach_point> call. The function C<fn>
1851 should return C<0> on success and C<-1> on failure.
1852 In the latter case, C<isl_set_foreach_point> will stop
1853 enumerating and return C<-1> as well.
1854 If the enumeration is performed successfully and to completion,
1855 then C<isl_set_foreach_point> returns C<0>.
1857 To obtain a single point of a (basic) set, use
1859 __isl_give isl_point *isl_basic_set_sample_point(
1860 __isl_take isl_basic_set *bset);
1861 __isl_give isl_point *isl_set_sample_point(
1862 __isl_take isl_set *set);
1864 If C<set> does not contain any (integer) points, then the
1865 resulting point will be ``void'', a property that can be
1868 int isl_point_is_void(__isl_keep isl_point *pnt);
1870 =head2 Piecewise Quasipolynomials
1872 A piecewise quasipolynomial is a particular kind of function that maps
1873 a parametric point to a rational value.
1874 More specifically, a quasipolynomial is a polynomial expression in greatest
1875 integer parts of affine expressions of parameters and variables.
1876 A piecewise quasipolynomial is a subdivision of a given parametric
1877 domain into disjoint cells with a quasipolynomial associated to
1878 each cell. The value of the piecewise quasipolynomial at a given
1879 point is the value of the quasipolynomial associated to the cell
1880 that contains the point. Outside of the union of cells,
1881 the value is assumed to be zero.
1882 For example, the piecewise quasipolynomial
1884 [n] -> { [x] -> ((1 + n) - x) : x <= n and x >= 0 }
1886 maps C<x> to C<1 + n - x> for values of C<x> between C<0> and C<n>.
1887 A given piecewise quasipolynomial has a fixed domain dimension.
1888 Union piecewise quasipolynomials are used to contain piecewise quasipolynomials
1889 defined over different domains.
1890 Piecewise quasipolynomials are mainly used by the C<barvinok>
1891 library for representing the number of elements in a parametric set or map.
1892 For example, the piecewise quasipolynomial above represents
1893 the number of points in the map
1895 [n] -> { [x] -> [y] : x,y >= 0 and 0 <= x + y <= n }
1897 =head3 Printing (Piecewise) Quasipolynomials
1899 Quasipolynomials and piecewise quasipolynomials can be printed
1900 using the following functions.
1902 __isl_give isl_printer *isl_printer_print_qpolynomial(
1903 __isl_take isl_printer *p,
1904 __isl_keep isl_qpolynomial *qp);
1906 __isl_give isl_printer *isl_printer_print_pw_qpolynomial(
1907 __isl_take isl_printer *p,
1908 __isl_keep isl_pw_qpolynomial *pwqp);
1910 __isl_give isl_printer *isl_printer_print_union_pw_qpolynomial(
1911 __isl_take isl_printer *p,
1912 __isl_keep isl_union_pw_qpolynomial *upwqp);
1914 The output format of the printer
1915 needs to be set to either C<ISL_FORMAT_ISL> or C<ISL_FORMAT_C>.
1916 For C<isl_printer_print_union_pw_qpolynomial>, only C<ISL_FORMAT_ISL>
1918 In case of printing in C<ISL_FORMAT_C>, the user may want
1919 to set the names of all dimensions
1921 __isl_give isl_qpolynomial *isl_qpolynomial_set_dim_name(
1922 __isl_take isl_qpolynomial *qp,
1923 enum isl_dim_type type, unsigned pos,
1925 __isl_give isl_pw_qpolynomial *
1926 isl_pw_qpolynomial_set_dim_name(
1927 __isl_take isl_pw_qpolynomial *pwqp,
1928 enum isl_dim_type type, unsigned pos,
1931 =head3 Creating New (Piecewise) Quasipolynomials
1933 Some simple quasipolynomials can be created using the following functions.
1934 More complicated quasipolynomials can be created by applying
1935 operations such as addition and multiplication
1936 on the resulting quasipolynomials
1938 __isl_give isl_qpolynomial *isl_qpolynomial_zero(
1939 __isl_take isl_dim *dim);
1940 __isl_give isl_qpolynomial *isl_qpolynomial_one(
1941 __isl_take isl_dim *dim);
1942 __isl_give isl_qpolynomial *isl_qpolynomial_infty(
1943 __isl_take isl_dim *dim);
1944 __isl_give isl_qpolynomial *isl_qpolynomial_neginfty(
1945 __isl_take isl_dim *dim);
1946 __isl_give isl_qpolynomial *isl_qpolynomial_nan(
1947 __isl_take isl_dim *dim);
1948 __isl_give isl_qpolynomial *isl_qpolynomial_rat_cst(
1949 __isl_take isl_dim *dim,
1950 const isl_int n, const isl_int d);
1951 __isl_give isl_qpolynomial *isl_qpolynomial_div(
1952 __isl_take isl_div *div);
1953 __isl_give isl_qpolynomial *isl_qpolynomial_var(
1954 __isl_take isl_dim *dim,
1955 enum isl_dim_type type, unsigned pos);
1957 The zero piecewise quasipolynomial or a piecewise quasipolynomial
1958 with a single cell can be created using the following functions.
1959 Multiple of these single cell piecewise quasipolynomials can
1960 be combined to create more complicated piecewise quasipolynomials.
1962 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_zero(
1963 __isl_take isl_dim *dim);
1964 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_alloc(
1965 __isl_take isl_set *set,
1966 __isl_take isl_qpolynomial *qp);
1968 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_zero(
1969 __isl_take isl_dim *dim);
1970 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_from_pw_qpolynomial(
1971 __isl_take isl_pw_qpolynomial *pwqp);
1972 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_add_pw_qpolynomial(
1973 __isl_take isl_union_pw_qpolynomial *upwqp,
1974 __isl_take isl_pw_qpolynomial *pwqp);
1976 Quasipolynomials can be copied and freed again using the following
1979 __isl_give isl_qpolynomial *isl_qpolynomial_copy(
1980 __isl_keep isl_qpolynomial *qp);
1981 void isl_qpolynomial_free(__isl_take isl_qpolynomial *qp);
1983 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_copy(
1984 __isl_keep isl_pw_qpolynomial *pwqp);
1985 void isl_pw_qpolynomial_free(
1986 __isl_take isl_pw_qpolynomial *pwqp);
1988 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_copy(
1989 __isl_keep isl_union_pw_qpolynomial *upwqp);
1990 void isl_union_pw_qpolynomial_free(
1991 __isl_take isl_union_pw_qpolynomial *upwqp);
1993 =head3 Inspecting (Piecewise) Quasipolynomials
1995 To iterate over all piecewise quasipolynomials in a union
1996 piecewise quasipolynomial, use the following function
1998 int isl_union_pw_qpolynomial_foreach_pw_qpolynomial(
1999 __isl_keep isl_union_pw_qpolynomial *upwqp,
2000 int (*fn)(__isl_take isl_pw_qpolynomial *pwqp, void *user),
2003 To extract the piecewise quasipolynomial from a union with a given dimension
2006 __isl_give isl_pw_qpolynomial *
2007 isl_union_pw_qpolynomial_extract_pw_qpolynomial(
2008 __isl_keep isl_union_pw_qpolynomial *upwqp,
2009 __isl_take isl_dim *dim);
2011 To iterate over the cells in a piecewise quasipolynomial,
2012 use either of the following two functions
2014 int isl_pw_qpolynomial_foreach_piece(
2015 __isl_keep isl_pw_qpolynomial *pwqp,
2016 int (*fn)(__isl_take isl_set *set,
2017 __isl_take isl_qpolynomial *qp,
2018 void *user), void *user);
2019 int isl_pw_qpolynomial_foreach_lifted_piece(
2020 __isl_keep isl_pw_qpolynomial *pwqp,
2021 int (*fn)(__isl_take isl_set *set,
2022 __isl_take isl_qpolynomial *qp,
2023 void *user), void *user);
2025 As usual, the function C<fn> should return C<0> on success
2026 and C<-1> on failure. The difference between
2027 C<isl_pw_qpolynomial_foreach_piece> and
2028 C<isl_pw_qpolynomial_foreach_lifted_piece> is that
2029 C<isl_pw_qpolynomial_foreach_lifted_piece> will first
2030 compute unique representations for all existentially quantified
2031 variables and then turn these existentially quantified variables
2032 into extra set variables, adapting the associated quasipolynomial
2033 accordingly. This means that the C<set> passed to C<fn>
2034 will not have any existentially quantified variables, but that
2035 the dimensions of the sets may be different for different
2036 invocations of C<fn>.
2038 To iterate over all terms in a quasipolynomial,
2041 int isl_qpolynomial_foreach_term(
2042 __isl_keep isl_qpolynomial *qp,
2043 int (*fn)(__isl_take isl_term *term,
2044 void *user), void *user);
2046 The terms themselves can be inspected and freed using
2049 unsigned isl_term_dim(__isl_keep isl_term *term,
2050 enum isl_dim_type type);
2051 void isl_term_get_num(__isl_keep isl_term *term,
2053 void isl_term_get_den(__isl_keep isl_term *term,
2055 int isl_term_get_exp(__isl_keep isl_term *term,
2056 enum isl_dim_type type, unsigned pos);
2057 __isl_give isl_div *isl_term_get_div(
2058 __isl_keep isl_term *term, unsigned pos);
2059 void isl_term_free(__isl_take isl_term *term);
2061 Each term is a product of parameters, set variables and
2062 integer divisions. The function C<isl_term_get_exp>
2063 returns the exponent of a given dimensions in the given term.
2064 The C<isl_int>s in the arguments of C<isl_term_get_num>
2065 and C<isl_term_get_den> need to have been initialized
2066 using C<isl_int_init> before calling these functions.
2068 =head3 Properties of (Piecewise) Quasipolynomials
2070 To check whether a quasipolynomial is actually a constant,
2071 use the following function.
2073 int isl_qpolynomial_is_cst(__isl_keep isl_qpolynomial *qp,
2074 isl_int *n, isl_int *d);
2076 If C<qp> is a constant and if C<n> and C<d> are not C<NULL>
2077 then the numerator and denominator of the constant
2078 are returned in C<*n> and C<*d>, respectively.
2080 =head3 Operations on (Piecewise) Quasipolynomials
2082 __isl_give isl_qpolynomial *isl_qpolynomial_neg(
2083 __isl_take isl_qpolynomial *qp);
2084 __isl_give isl_qpolynomial *isl_qpolynomial_add(
2085 __isl_take isl_qpolynomial *qp1,
2086 __isl_take isl_qpolynomial *qp2);
2087 __isl_give isl_qpolynomial *isl_qpolynomial_sub(
2088 __isl_take isl_qpolynomial *qp1,
2089 __isl_take isl_qpolynomial *qp2);
2090 __isl_give isl_qpolynomial *isl_qpolynomial_mul(
2091 __isl_take isl_qpolynomial *qp1,
2092 __isl_take isl_qpolynomial *qp2);
2093 __isl_give isl_qpolynomial *isl_qpolynomial_pow(
2094 __isl_take isl_qpolynomial *qp, unsigned exponent);
2096 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_add(
2097 __isl_take isl_pw_qpolynomial *pwqp1,
2098 __isl_take isl_pw_qpolynomial *pwqp2);
2099 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_sub(
2100 __isl_take isl_pw_qpolynomial *pwqp1,
2101 __isl_take isl_pw_qpolynomial *pwqp2);
2102 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_add_disjoint(
2103 __isl_take isl_pw_qpolynomial *pwqp1,
2104 __isl_take isl_pw_qpolynomial *pwqp2);
2105 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_neg(
2106 __isl_take isl_pw_qpolynomial *pwqp);
2107 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_mul(
2108 __isl_take isl_pw_qpolynomial *pwqp1,
2109 __isl_take isl_pw_qpolynomial *pwqp2);
2111 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_add(
2112 __isl_take isl_union_pw_qpolynomial *upwqp1,
2113 __isl_take isl_union_pw_qpolynomial *upwqp2);
2114 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_sub(
2115 __isl_take isl_union_pw_qpolynomial *upwqp1,
2116 __isl_take isl_union_pw_qpolynomial *upwqp2);
2117 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_mul(
2118 __isl_take isl_union_pw_qpolynomial *upwqp1,
2119 __isl_take isl_union_pw_qpolynomial *upwqp2);
2121 __isl_give isl_qpolynomial *isl_pw_qpolynomial_eval(
2122 __isl_take isl_pw_qpolynomial *pwqp,
2123 __isl_take isl_point *pnt);
2125 __isl_give isl_qpolynomial *isl_union_pw_qpolynomial_eval(
2126 __isl_take isl_union_pw_qpolynomial *upwqp,
2127 __isl_take isl_point *pnt);
2129 __isl_give isl_set *isl_pw_qpolynomial_domain(
2130 __isl_take isl_pw_qpolynomial *pwqp);
2131 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_intersect_domain(
2132 __isl_take isl_pw_qpolynomial *pwpq,
2133 __isl_take isl_set *set);
2135 __isl_give isl_union_set *isl_union_pw_qpolynomial_domain(
2136 __isl_take isl_union_pw_qpolynomial *upwqp);
2137 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_intersect_domain(
2138 __isl_take isl_union_pw_qpolynomial *upwpq,
2139 __isl_take isl_union_set *uset);
2141 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_coalesce(
2142 __isl_take isl_union_pw_qpolynomial *upwqp);
2144 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_gist(
2145 __isl_take isl_pw_qpolynomial *pwqp,
2146 __isl_take isl_set *context);
2148 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_gist(
2149 __isl_take isl_union_pw_qpolynomial *upwqp,
2150 __isl_take isl_union_set *context);
2152 The gist operation applies the gist operation to each of
2153 the cells in the domain of the input piecewise quasipolynomial.
2154 The context is also exploited
2155 to simplify the quasipolynomials associated to each cell.
2157 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_to_polynomial(
2158 __isl_take isl_pw_qpolynomial *pwqp, int sign);
2159 __isl_give isl_union_pw_qpolynomial *
2160 isl_union_pw_qpolynomial_to_polynomial(
2161 __isl_take isl_union_pw_qpolynomial *upwqp, int sign);
2163 Approximate each quasipolynomial by a polynomial. If C<sign> is positive,
2164 the polynomial will be an overapproximation. If C<sign> is negative,
2165 it will be an underapproximation. If C<sign> is zero, the approximation
2166 will lie somewhere in between.
2168 =head2 Bounds on Piecewise Quasipolynomials and Piecewise Quasipolynomial Reductions
2170 A piecewise quasipolynomial reduction is a piecewise
2171 reduction (or fold) of quasipolynomials.
2172 In particular, the reduction can be maximum or a minimum.
2173 The objects are mainly used to represent the result of
2174 an upper or lower bound on a quasipolynomial over its domain,
2175 i.e., as the result of the following function.
2177 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_bound(
2178 __isl_take isl_pw_qpolynomial *pwqp,
2179 enum isl_fold type, int *tight);
2181 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_bound(
2182 __isl_take isl_union_pw_qpolynomial *upwqp,
2183 enum isl_fold type, int *tight);
2185 The C<type> argument may be either C<isl_fold_min> or C<isl_fold_max>.
2186 If C<tight> is not C<NULL>, then C<*tight> is set to C<1>
2187 is the returned bound is known be tight, i.e., for each value
2188 of the parameters there is at least
2189 one element in the domain that reaches the bound.
2190 If the domain of C<pwqp> is not wrapping, then the bound is computed
2191 over all elements in that domain and the result has a purely parametric
2192 domain. If the domain of C<pwqp> is wrapping, then the bound is
2193 computed over the range of the wrapped relation. The domain of the
2194 wrapped relation becomes the domain of the result.
2196 A (piecewise) quasipolynomial reduction can be copied or freed using the
2197 following functions.
2199 __isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_copy(
2200 __isl_keep isl_qpolynomial_fold *fold);
2201 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_copy(
2202 __isl_keep isl_pw_qpolynomial_fold *pwf);
2203 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_copy(
2204 __isl_keep isl_union_pw_qpolynomial_fold *upwf);
2205 void isl_qpolynomial_fold_free(
2206 __isl_take isl_qpolynomial_fold *fold);
2207 void isl_pw_qpolynomial_fold_free(
2208 __isl_take isl_pw_qpolynomial_fold *pwf);
2209 void isl_union_pw_qpolynomial_fold_free(
2210 __isl_take isl_union_pw_qpolynomial_fold *upwf);
2212 =head3 Printing Piecewise Quasipolynomial Reductions
2214 Piecewise quasipolynomial reductions can be printed
2215 using the following function.
2217 __isl_give isl_printer *isl_printer_print_pw_qpolynomial_fold(
2218 __isl_take isl_printer *p,
2219 __isl_keep isl_pw_qpolynomial_fold *pwf);
2220 __isl_give isl_printer *isl_printer_print_union_pw_qpolynomial_fold(
2221 __isl_take isl_printer *p,
2222 __isl_keep isl_union_pw_qpolynomial_fold *upwf);
2224 For C<isl_printer_print_pw_qpolynomial_fold>,
2225 output format of the printer
2226 needs to be set to either C<ISL_FORMAT_ISL> or C<ISL_FORMAT_C>.
2227 For C<isl_printer_print_union_pw_qpolynomial_fold>,
2228 output format of the printer
2229 needs to be set to C<ISL_FORMAT_ISL>.
2230 In case of printing in C<ISL_FORMAT_C>, the user may want
2231 to set the names of all dimensions
2233 __isl_give isl_pw_qpolynomial_fold *
2234 isl_pw_qpolynomial_fold_set_dim_name(
2235 __isl_take isl_pw_qpolynomial_fold *pwf,
2236 enum isl_dim_type type, unsigned pos,
2239 =head3 Inspecting (Piecewise) Quasipolynomial Reductions
2241 To iterate over all piecewise quasipolynomial reductions in a union
2242 piecewise quasipolynomial reduction, use the following function
2244 int isl_union_pw_qpolynomial_fold_foreach_pw_qpolynomial_fold(
2245 __isl_keep isl_union_pw_qpolynomial_fold *upwf,
2246 int (*fn)(__isl_take isl_pw_qpolynomial_fold *pwf,
2247 void *user), void *user);
2249 To iterate over the cells in a piecewise quasipolynomial reduction,
2250 use either of the following two functions
2252 int isl_pw_qpolynomial_fold_foreach_piece(
2253 __isl_keep isl_pw_qpolynomial_fold *pwf,
2254 int (*fn)(__isl_take isl_set *set,
2255 __isl_take isl_qpolynomial_fold *fold,
2256 void *user), void *user);
2257 int isl_pw_qpolynomial_fold_foreach_lifted_piece(
2258 __isl_keep isl_pw_qpolynomial_fold *pwf,
2259 int (*fn)(__isl_take isl_set *set,
2260 __isl_take isl_qpolynomial_fold *fold,
2261 void *user), void *user);
2263 See L<Inspecting (Piecewise) Quasipolynomials> for an explanation
2264 of the difference between these two functions.
2266 To iterate over all quasipolynomials in a reduction, use
2268 int isl_qpolynomial_fold_foreach_qpolynomial(
2269 __isl_keep isl_qpolynomial_fold *fold,
2270 int (*fn)(__isl_take isl_qpolynomial *qp,
2271 void *user), void *user);
2273 =head3 Operations on Piecewise Quasipolynomial Reductions
2275 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_add(
2276 __isl_take isl_pw_qpolynomial_fold *pwf1,
2277 __isl_take isl_pw_qpolynomial_fold *pwf2);
2279 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_fold(
2280 __isl_take isl_pw_qpolynomial_fold *pwf1,
2281 __isl_take isl_pw_qpolynomial_fold *pwf2);
2283 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_fold(
2284 __isl_take isl_union_pw_qpolynomial_fold *upwf1,
2285 __isl_take isl_union_pw_qpolynomial_fold *upwf2);
2287 __isl_give isl_qpolynomial *isl_pw_qpolynomial_fold_eval(
2288 __isl_take isl_pw_qpolynomial_fold *pwf,
2289 __isl_take isl_point *pnt);
2291 __isl_give isl_qpolynomial *isl_union_pw_qpolynomial_fold_eval(
2292 __isl_take isl_union_pw_qpolynomial_fold *upwf,
2293 __isl_take isl_point *pnt);
2295 __isl_give isl_union_set *isl_union_pw_qpolynomial_fold_domain(
2296 __isl_take isl_union_pw_qpolynomial_fold *upwf);
2297 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_intersect_domain(
2298 __isl_take isl_union_pw_qpolynomial_fold *upwf,
2299 __isl_take isl_union_set *uset);
2301 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_coalesce(
2302 __isl_take isl_pw_qpolynomial_fold *pwf);
2304 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_coalesce(
2305 __isl_take isl_union_pw_qpolynomial_fold *upwf);
2307 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_gist(
2308 __isl_take isl_pw_qpolynomial_fold *pwf,
2309 __isl_take isl_set *context);
2311 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_gist(
2312 __isl_take isl_union_pw_qpolynomial_fold *upwf,
2313 __isl_take isl_union_set *context);
2315 The gist operation applies the gist operation to each of
2316 the cells in the domain of the input piecewise quasipolynomial reduction.
2317 In future, the operation will also exploit the context
2318 to simplify the quasipolynomial reductions associated to each cell.
2320 __isl_give isl_pw_qpolynomial_fold *
2321 isl_set_apply_pw_qpolynomial_fold(
2322 __isl_take isl_set *set,
2323 __isl_take isl_pw_qpolynomial_fold *pwf,
2325 __isl_give isl_pw_qpolynomial_fold *
2326 isl_map_apply_pw_qpolynomial_fold(
2327 __isl_take isl_map *map,
2328 __isl_take isl_pw_qpolynomial_fold *pwf,
2330 __isl_give isl_union_pw_qpolynomial_fold *
2331 isl_union_set_apply_union_pw_qpolynomial_fold(
2332 __isl_take isl_union_set *uset,
2333 __isl_take isl_union_pw_qpolynomial_fold *upwf,
2335 __isl_give isl_union_pw_qpolynomial_fold *
2336 isl_union_map_apply_union_pw_qpolynomial_fold(
2337 __isl_take isl_union_map *umap,
2338 __isl_take isl_union_pw_qpolynomial_fold *upwf,
2341 The functions taking a map
2342 compose the given map with the given piecewise quasipolynomial reduction.
2343 That is, compute a bound (of the same type as C<pwf> or C<upwf> itself)
2344 over all elements in the intersection of the range of the map
2345 and the domain of the piecewise quasipolynomial reduction
2346 as a function of an element in the domain of the map.
2347 The functions taking a set compute a bound over all elements in the
2348 intersection of the set and the domain of the
2349 piecewise quasipolynomial reduction.
2351 =head2 Dependence Analysis
2353 C<isl> contains specialized functionality for performing
2354 array dataflow analysis. That is, given a I<sink> access relation
2355 and a collection of possible I<source> access relations,
2356 C<isl> can compute relations that describe
2357 for each iteration of the sink access, which iteration
2358 of which of the source access relations was the last
2359 to access the same data element before the given iteration
2361 To compute standard flow dependences, the sink should be
2362 a read, while the sources should be writes.
2363 If any of the source accesses are marked as being I<may>
2364 accesses, then there will be a dependence to the last
2365 I<must> access B<and> to any I<may> access that follows
2366 this last I<must> access.
2367 In particular, if I<all> sources are I<may> accesses,
2368 then memory based dependence analysis is performed.
2369 If, on the other hand, all sources are I<must> accesses,
2370 then value based dependence analysis is performed.
2372 #include <isl/flow.h>
2374 typedef int (*isl_access_level_before)(void *first, void *second);
2376 __isl_give isl_access_info *isl_access_info_alloc(
2377 __isl_take isl_map *sink,
2378 void *sink_user, isl_access_level_before fn,
2380 __isl_give isl_access_info *isl_access_info_add_source(
2381 __isl_take isl_access_info *acc,
2382 __isl_take isl_map *source, int must,
2384 void isl_access_info_free(__isl_take isl_access_info *acc);
2386 __isl_give isl_flow *isl_access_info_compute_flow(
2387 __isl_take isl_access_info *acc);
2389 int isl_flow_foreach(__isl_keep isl_flow *deps,
2390 int (*fn)(__isl_take isl_map *dep, int must,
2391 void *dep_user, void *user),
2393 __isl_give isl_set *isl_flow_get_no_source(
2394 __isl_keep isl_flow *deps, int must);
2395 void isl_flow_free(__isl_take isl_flow *deps);
2397 The function C<isl_access_info_compute_flow> performs the actual
2398 dependence analysis. The other functions are used to construct
2399 the input for this function or to read off the output.
2401 The input is collected in an C<isl_access_info>, which can
2402 be created through a call to C<isl_access_info_alloc>.
2403 The arguments to this functions are the sink access relation
2404 C<sink>, a token C<sink_user> used to identify the sink
2405 access to the user, a callback function for specifying the
2406 relative order of source and sink accesses, and the number
2407 of source access relations that will be added.
2408 The callback function has type C<int (*)(void *first, void *second)>.
2409 The function is called with two user supplied tokens identifying
2410 either a source or the sink and it should return the shared nesting
2411 level and the relative order of the two accesses.
2412 In particular, let I<n> be the number of loops shared by
2413 the two accesses. If C<first> precedes C<second> textually,
2414 then the function should return I<2 * n + 1>; otherwise,
2415 it should return I<2 * n>.
2416 The sources can be added to the C<isl_access_info> by performing
2417 (at most) C<max_source> calls to C<isl_access_info_add_source>.
2418 C<must> indicates whether the source is a I<must> access
2419 or a I<may> access. Note that a multi-valued access relation
2420 should only be marked I<must> if every iteration in the domain
2421 of the relation accesses I<all> elements in its image.
2422 The C<source_user> token is again used to identify
2423 the source access. The range of the source access relation
2424 C<source> should have the same dimension as the range
2425 of the sink access relation.
2426 The C<isl_access_info_free> function should usually not be
2427 called explicitly, because it is called implicitly by
2428 C<isl_access_info_compute_flow>.
2430 The result of the dependence analysis is collected in an
2431 C<isl_flow>. There may be elements in the domain of
2432 the sink access for which no preceding source access could be
2433 found or for which all preceding sources are I<may> accesses.
2434 The sets of these elements can be obtained through
2435 calls to C<isl_flow_get_no_source>, the first with C<must> set
2436 and the second with C<must> unset.
2437 In the case of standard flow dependence analysis,
2438 with the sink a read and the sources I<must> writes,
2439 the first set corresponds to the reads from uninitialized
2440 array elements and the second set is empty.
2441 The actual flow dependences can be extracted using
2442 C<isl_flow_foreach>. This function will call the user-specified
2443 callback function C<fn> for each B<non-empty> dependence between
2444 a source and the sink. The callback function is called
2445 with four arguments, the actual flow dependence relation
2446 mapping source iterations to sink iterations, a boolean that
2447 indicates whether it is a I<must> or I<may> dependence, a token
2448 identifying the source and an additional C<void *> with value
2449 equal to the third argument of the C<isl_flow_foreach> call.
2450 A dependence is marked I<must> if it originates from a I<must>
2451 source and if it is not followed by any I<may> sources.
2453 After finishing with an C<isl_flow>, the user should call
2454 C<isl_flow_free> to free all associated memory.
2456 A higher-level interface to dependence analysis is provided
2457 by the following function.
2459 #include <isl/flow.h>
2461 int isl_union_map_compute_flow(__isl_take isl_union_map *sink,
2462 __isl_take isl_union_map *must_source,
2463 __isl_take isl_union_map *may_source,
2464 __isl_take isl_union_map *schedule,
2465 __isl_give isl_union_map **must_dep,
2466 __isl_give isl_union_map **may_dep,
2467 __isl_give isl_union_set **must_no_source,
2468 __isl_give isl_union_set **may_no_source);
2470 The arrays are identified by the tuple names of the ranges
2471 of the accesses. The iteration domains by the tuple names
2472 of the domains of the accesses and of the schedule.
2473 The relative order of the iteration domains is given by the
2474 schedule. Any of C<must_dep>, C<may_dep>, C<must_no_source>
2475 or C<may_no_source> may be C<NULL>, but a C<NULL> value for
2476 any of the other arguments is treated as an error.
2478 =head2 Parametric Vertex Enumeration
2480 The parametric vertex enumeration described in this section
2481 is mainly intended to be used internally and by the C<barvinok>
2484 #include <isl/vertices.h>
2485 __isl_give isl_vertices *isl_basic_set_compute_vertices(
2486 __isl_keep isl_basic_set *bset);
2488 The function C<isl_basic_set_compute_vertices> performs the
2489 actual computation of the parametric vertices and the chamber
2490 decomposition and store the result in an C<isl_vertices> object.
2491 This information can be queried by either iterating over all
2492 the vertices or iterating over all the chambers or cells
2493 and then iterating over all vertices that are active on the chamber.
2495 int isl_vertices_foreach_vertex(
2496 __isl_keep isl_vertices *vertices,
2497 int (*fn)(__isl_take isl_vertex *vertex, void *user),
2500 int isl_vertices_foreach_cell(
2501 __isl_keep isl_vertices *vertices,
2502 int (*fn)(__isl_take isl_cell *cell, void *user),
2504 int isl_cell_foreach_vertex(__isl_keep isl_cell *cell,
2505 int (*fn)(__isl_take isl_vertex *vertex, void *user),
2508 Other operations that can be performed on an C<isl_vertices> object are
2511 isl_ctx *isl_vertices_get_ctx(
2512 __isl_keep isl_vertices *vertices);
2513 int isl_vertices_get_n_vertices(
2514 __isl_keep isl_vertices *vertices);
2515 void isl_vertices_free(__isl_take isl_vertices *vertices);
2517 Vertices can be inspected and destroyed using the following functions.
2519 isl_ctx *isl_vertex_get_ctx(__isl_keep isl_vertex *vertex);
2520 int isl_vertex_get_id(__isl_keep isl_vertex *vertex);
2521 __isl_give isl_basic_set *isl_vertex_get_domain(
2522 __isl_keep isl_vertex *vertex);
2523 __isl_give isl_basic_set *isl_vertex_get_expr(
2524 __isl_keep isl_vertex *vertex);
2525 void isl_vertex_free(__isl_take isl_vertex *vertex);
2527 C<isl_vertex_get_expr> returns a singleton parametric set describing
2528 the vertex, while C<isl_vertex_get_domain> returns the activity domain
2530 Note that C<isl_vertex_get_domain> and C<isl_vertex_get_expr> return
2531 B<rational> basic sets, so they should mainly be used for inspection
2532 and should not be mixed with integer sets.
2534 Chambers can be inspected and destroyed using the following functions.
2536 isl_ctx *isl_cell_get_ctx(__isl_keep isl_cell *cell);
2537 __isl_give isl_basic_set *isl_cell_get_domain(
2538 __isl_keep isl_cell *cell);
2539 void isl_cell_free(__isl_take isl_cell *cell);
2543 Although C<isl> is mainly meant to be used as a library,
2544 it also contains some basic applications that use some
2545 of the functionality of C<isl>.
2546 The input may be specified in either the L<isl format>
2547 or the L<PolyLib format>.
2549 =head2 C<isl_polyhedron_sample>
2551 C<isl_polyhedron_sample> takes a polyhedron as input and prints
2552 an integer element of the polyhedron, if there is any.
2553 The first column in the output is the denominator and is always
2554 equal to 1. If the polyhedron contains no integer points,
2555 then a vector of length zero is printed.
2559 C<isl_pip> takes the same input as the C<example> program
2560 from the C<piplib> distribution, i.e., a set of constraints
2561 on the parameters, a line containing only -1 and finally a set
2562 of constraints on a parametric polyhedron.
2563 The coefficients of the parameters appear in the last columns
2564 (but before the final constant column).
2565 The output is the lexicographic minimum of the parametric polyhedron.
2566 As C<isl> currently does not have its own output format, the output
2567 is just a dump of the internal state.
2569 =head2 C<isl_polyhedron_minimize>
2571 C<isl_polyhedron_minimize> computes the minimum of some linear
2572 or affine objective function over the integer points in a polyhedron.
2573 If an affine objective function
2574 is given, then the constant should appear in the last column.
2576 =head2 C<isl_polytope_scan>
2578 Given a polytope, C<isl_polytope_scan> prints
2579 all integer points in the polytope.
2581 =head1 C<isl-polylib>
2583 The C<isl-polylib> library provides the following functions for converting
2584 between C<isl> objects and C<PolyLib> objects.
2585 The library is distributed separately for licensing reasons.
2587 #include <isl_set_polylib.h>
2588 __isl_give isl_basic_set *isl_basic_set_new_from_polylib(
2589 Polyhedron *P, __isl_take isl_dim *dim);
2590 Polyhedron *isl_basic_set_to_polylib(
2591 __isl_keep isl_basic_set *bset);
2592 __isl_give isl_set *isl_set_new_from_polylib(Polyhedron *D,
2593 __isl_take isl_dim *dim);
2594 Polyhedron *isl_set_to_polylib(__isl_keep isl_set *set);
2596 #include <isl_map_polylib.h>
2597 __isl_give isl_basic_map *isl_basic_map_new_from_polylib(
2598 Polyhedron *P, __isl_take isl_dim *dim);
2599 __isl_give isl_map *isl_map_new_from_polylib(Polyhedron *D,
2600 __isl_take isl_dim *dim);
2601 Polyhedron *isl_basic_map_to_polylib(
2602 __isl_keep isl_basic_map *bmap);
2603 Polyhedron *isl_map_to_polylib(__isl_keep isl_map *map);