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>.
51 The source of C<isl> can be obtained either as a tarball
52 or from the git repository. Both are available from
53 L<http://freshmeat.net/projects/isl/>.
54 The installation process depends on how you obtained
57 =head2 Installation from the git repository
61 =item 1 Clone or update the repository
63 The first time the source is obtained, you need to clone
66 git clone git://repo.or.cz/isl.git
68 To obtain updates, you need to pull in the latest changes
72 =item 2 Generate C<configure>
78 After performing the above steps, continue
79 with the L<Common installation instructions>.
81 =head2 Common installation instructions
87 Building C<isl> requires C<GMP>, including its headers files.
88 Your distribution may not provide these header files by default
89 and you may need to install a package called C<gmp-devel> or something
90 similar. Alternatively, C<GMP> can be built from
91 source, available from L<http://gmplib.org/>.
95 C<isl> uses the standard C<autoconf> C<configure> script.
100 optionally followed by some configure options.
101 A complete list of options can be obtained by running
105 Below we discuss some of the more common options.
107 C<isl> can optionally use C<piplib>, but no
108 C<piplib> functionality is currently used by default.
109 The C<--with-piplib> option can
110 be used to specify which C<piplib>
111 library to use, either an installed version (C<system>),
112 an externally built version (C<build>)
113 or no version (C<no>). The option C<build> is mostly useful
114 in C<configure> scripts of larger projects that bundle both C<isl>
121 Installation prefix for C<isl>
123 =item C<--with-gmp-prefix>
125 Installation prefix for C<GMP> (architecture-independent files).
127 =item C<--with-gmp-exec-prefix>
129 Installation prefix for C<GMP> (architecture-dependent files).
131 =item C<--with-piplib>
133 Which copy of C<piplib> to use, either C<no> (default), C<system> or C<build>.
135 =item C<--with-piplib-prefix>
137 Installation prefix for C<system> C<piplib> (architecture-independent files).
139 =item C<--with-piplib-exec-prefix>
141 Installation prefix for C<system> C<piplib> (architecture-dependent files).
143 =item C<--with-piplib-builddir>
145 Location where C<build> C<piplib> was built.
153 =item 4 Install (optional)
161 =head2 Initialization
163 All manipulations of integer sets and relations occur within
164 the context of an C<isl_ctx>.
165 A given C<isl_ctx> can only be used within a single thread.
166 All arguments of a function are required to have been allocated
167 within the same context.
168 There are currently no functions available for moving an object
169 from one C<isl_ctx> to another C<isl_ctx>. This means that
170 there is currently no way of safely moving an object from one
171 thread to another, unless the whole C<isl_ctx> is moved.
173 An C<isl_ctx> can be allocated using C<isl_ctx_alloc> and
174 freed using C<isl_ctx_free>.
175 All objects allocated within an C<isl_ctx> should be freed
176 before the C<isl_ctx> itself is freed.
178 isl_ctx *isl_ctx_alloc();
179 void isl_ctx_free(isl_ctx *ctx);
183 All operations on integers, mainly the coefficients
184 of the constraints describing the sets and relations,
185 are performed in exact integer arithmetic using C<GMP>.
186 However, to allow future versions of C<isl> to optionally
187 support fixed integer arithmetic, all calls to C<GMP>
188 are wrapped inside C<isl> specific macros.
189 The basic type is C<isl_int> and the following operations
190 are available on this type.
191 The meanings of these operations are essentially the same
192 as their C<GMP> C<mpz_> counterparts.
193 As always with C<GMP> types, C<isl_int>s need to be
194 initialized with C<isl_int_init> before they can be used
195 and they need to be released with C<isl_int_clear>
200 =item isl_int_init(i)
202 =item isl_int_clear(i)
204 =item isl_int_set(r,i)
206 =item isl_int_set_si(r,i)
208 =item isl_int_abs(r,i)
210 =item isl_int_neg(r,i)
212 =item isl_int_swap(i,j)
214 =item isl_int_swap_or_set(i,j)
216 =item isl_int_add_ui(r,i,j)
218 =item isl_int_sub_ui(r,i,j)
220 =item isl_int_add(r,i,j)
222 =item isl_int_sub(r,i,j)
224 =item isl_int_mul(r,i,j)
226 =item isl_int_mul_ui(r,i,j)
228 =item isl_int_addmul(r,i,j)
230 =item isl_int_submul(r,i,j)
232 =item isl_int_gcd(r,i,j)
234 =item isl_int_lcm(r,i,j)
236 =item isl_int_divexact(r,i,j)
238 =item isl_int_cdiv_q(r,i,j)
240 =item isl_int_fdiv_q(r,i,j)
242 =item isl_int_fdiv_r(r,i,j)
244 =item isl_int_fdiv_q_ui(r,i,j)
246 =item isl_int_read(r,s)
248 =item isl_int_print(out,i,width)
252 =item isl_int_cmp(i,j)
254 =item isl_int_cmp_si(i,si)
256 =item isl_int_eq(i,j)
258 =item isl_int_ne(i,j)
260 =item isl_int_lt(i,j)
262 =item isl_int_le(i,j)
264 =item isl_int_gt(i,j)
266 =item isl_int_ge(i,j)
268 =item isl_int_abs_eq(i,j)
270 =item isl_int_abs_ne(i,j)
272 =item isl_int_abs_lt(i,j)
274 =item isl_int_abs_gt(i,j)
276 =item isl_int_abs_ge(i,j)
278 =item isl_int_is_zero(i)
280 =item isl_int_is_one(i)
282 =item isl_int_is_negone(i)
284 =item isl_int_is_pos(i)
286 =item isl_int_is_neg(i)
288 =item isl_int_is_nonpos(i)
290 =item isl_int_is_nonneg(i)
292 =item isl_int_is_divisible_by(i,j)
296 =head2 Sets and Relations
298 C<isl> uses six types of objects for representing sets and relations,
299 C<isl_basic_set>, C<isl_basic_map>, C<isl_set>, C<isl_map>,
300 C<isl_union_set> and C<isl_union_map>.
301 C<isl_basic_set> and C<isl_basic_map> represent sets and relations that
302 can be described as a conjunction of affine constraints, while
303 C<isl_set> and C<isl_map> represent unions of
304 C<isl_basic_set>s and C<isl_basic_map>s, respectively.
305 However, all C<isl_basic_set>s or C<isl_basic_map>s in the union need
306 to have the same dimension. C<isl_union_set>s and C<isl_union_map>s
307 represent unions of C<isl_set>s or C<isl_map>s of I<different> dimensions,
308 where dimensions with different space names
309 (see L<Dimension Specifications>) are considered different as well.
310 The difference between sets and relations (maps) is that sets have
311 one set of variables, while relations have two sets of variables,
312 input variables and output variables.
314 =head2 Memory Management
316 Since a high-level operation on sets and/or relations usually involves
317 several substeps and since the user is usually not interested in
318 the intermediate results, most functions that return a new object
319 will also release all the objects passed as arguments.
320 If the user still wants to use one or more of these arguments
321 after the function call, she should pass along a copy of the
322 object rather than the object itself.
323 The user is then responsible for make sure that the original
324 object gets used somewhere else or is explicitly freed.
326 The arguments and return values of all documents functions are
327 annotated to make clear which arguments are released and which
328 arguments are preserved. In particular, the following annotations
335 C<__isl_give> means that a new object is returned.
336 The user should make sure that the returned pointer is
337 used exactly once as a value for an C<__isl_take> argument.
338 In between, it can be used as a value for as many
339 C<__isl_keep> arguments as the user likes.
340 There is one exception, and that is the case where the
341 pointer returned is C<NULL>. Is this case, the user
342 is free to use it as an C<__isl_take> argument or not.
346 C<__isl_take> means that the object the argument points to
347 is taken over by the function and may no longer be used
348 by the user as an argument to any other function.
349 The pointer value must be one returned by a function
350 returning an C<__isl_give> pointer.
351 If the user passes in a C<NULL> value, then this will
352 be treated as an error in the sense that the function will
353 not perform its usual operation. However, it will still
354 make sure that all the the other C<__isl_take> arguments
359 C<__isl_keep> means that the function will only use the object
360 temporarily. After the function has finished, the user
361 can still use it as an argument to other functions.
362 A C<NULL> value will be treated in the same way as
363 a C<NULL> value for an C<__isl_take> argument.
367 =head2 Dimension Specifications
369 Whenever a new set or relation is created from scratch,
370 its dimension needs to be specified using an C<isl_dim>.
373 __isl_give isl_dim *isl_dim_alloc(isl_ctx *ctx,
374 unsigned nparam, unsigned n_in, unsigned n_out);
375 __isl_give isl_dim *isl_dim_set_alloc(isl_ctx *ctx,
376 unsigned nparam, unsigned dim);
377 __isl_give isl_dim *isl_dim_copy(__isl_keep isl_dim *dim);
378 void isl_dim_free(__isl_take isl_dim *dim);
379 unsigned isl_dim_size(__isl_keep isl_dim *dim,
380 enum isl_dim_type type);
382 The dimension specification used for creating a set
383 needs to be created using C<isl_dim_set_alloc>, while
384 that for creating a relation
385 needs to be created using C<isl_dim_alloc>.
386 C<isl_dim_size> can be used
387 to find out the number of dimensions of each type in
388 a dimension specification, where type may be
389 C<isl_dim_param>, C<isl_dim_in> (only for relations),
390 C<isl_dim_out> (only for relations), C<isl_dim_set>
391 (only for sets) or C<isl_dim_all>.
393 It is often useful to create objects that live in the
394 same space as some other object. This can be accomplished
395 by creating the new objects
396 (see L<Creating New Sets and Relations> or
397 L<Creating New (Piecewise) Quasipolynomials>) based on the dimension
398 specification of the original object.
401 __isl_give isl_dim *isl_basic_set_get_dim(
402 __isl_keep isl_basic_set *bset);
403 __isl_give isl_dim *isl_set_get_dim(__isl_keep isl_set *set);
405 #include <isl_union_set.h>
406 __isl_give isl_dim *isl_union_set_get_dim(
407 __isl_keep isl_union_set *uset);
410 __isl_give isl_dim *isl_basic_map_get_dim(
411 __isl_keep isl_basic_map *bmap);
412 __isl_give isl_dim *isl_map_get_dim(__isl_keep isl_map *map);
414 #include <isl_union_map.h>
415 __isl_give isl_dim *isl_union_map_get_dim(
416 __isl_keep isl_union_map *umap);
418 #include <isl_polynomial.h>
419 __isl_give isl_dim *isl_qpolynomial_get_dim(
420 __isl_keep isl_qpolynomial *qp);
421 __isl_give isl_dim *isl_pw_qpolynomial_get_dim(
422 __isl_keep isl_pw_qpolynomial *pwqp);
423 __isl_give isl_dim *isl_union_pw_qpolynomial_get_dim(
424 __isl_keep isl_union_pw_qpolynomial *upwqp);
425 __isl_give isl_dim *isl_union_pw_qpolynomial_fold_get_dim(
426 __isl_keep isl_union_pw_qpolynomial_fold *upwf);
428 The names of the individual dimensions may be set or read off
429 using the following functions.
432 __isl_give isl_dim *isl_dim_set_name(__isl_take isl_dim *dim,
433 enum isl_dim_type type, unsigned pos,
434 __isl_keep const char *name);
435 __isl_keep const char *isl_dim_get_name(__isl_keep isl_dim *dim,
436 enum isl_dim_type type, unsigned pos);
438 Note that C<isl_dim_get_name> returns a pointer to some internal
439 data structure, so the result can only be used while the
440 corresponding C<isl_dim> is alive.
441 Also note that every function that operates on two sets or relations
442 requires that both arguments have the same parameters. This also
443 means that if one of the arguments has named parameters, then the
444 other needs to have named parameters too and the names need to match.
445 Pairs of C<isl_union_set> and/or C<isl_union_map> arguments may
446 have different parameters (as long as they are named), in which case
447 the result will have as parameters the union of the parameters of
450 The names of entire spaces may be set or read off
451 using the following functions.
454 __isl_give isl_dim *isl_dim_set_tuple_name(
455 __isl_take isl_dim *dim,
456 enum isl_dim_type type, const char *s);
457 const char *isl_dim_get_tuple_name(__isl_keep isl_dim *dim,
458 enum isl_dim_type type);
460 The C<dim> argument needs to be one of C<isl_dim_in>, C<isl_dim_out>
461 or C<isl_dim_set>. As with C<isl_dim_get_name>,
462 the C<isl_dim_get_tuple_name> function returns a pointer to some internal
464 Binary operations require the corresponding spaces of their arguments
465 to have the same name.
467 Spaces can be nested. In particular, the domain of a set or
468 the domain or range of a relation can be a nested relation.
469 The following functions can be used to construct and deconstruct
470 such nested dimension specifications.
473 int isl_dim_is_wrapping(__isl_keep isl_dim *dim);
474 __isl_give isl_dim *isl_dim_wrap(__isl_take isl_dim *dim);
475 __isl_give isl_dim *isl_dim_unwrap(__isl_take isl_dim *dim);
477 The input to C<isl_dim_is_wrapping> and C<isl_dim_unwrap> should
478 be the dimension specification of a set, while that of
479 C<isl_dim_wrap> should be the dimension specification of a relation.
480 Conversely, the output of C<isl_dim_unwrap> is the dimension specification
481 of a relation, while that of C<isl_dim_wrap> is the dimension specification
484 Dimension specifications can be created from other dimension
485 specifications using the following functions.
487 __isl_give isl_dim *isl_dim_domain(__isl_take isl_dim *dim);
488 __isl_give isl_dim *isl_dim_range(__isl_take isl_dim *dim);
489 __isl_give isl_dim *isl_dim_reverse(__isl_take isl_dim *dim);
490 __isl_give isl_dim *isl_dim_join(__isl_take isl_dim *left,
491 __isl_take isl_dim *right);
492 __isl_give isl_dim *isl_dim_insert(__isl_take isl_dim *dim,
493 enum isl_dim_type type, unsigned pos, unsigned n);
494 __isl_give isl_dim *isl_dim_add(__isl_take isl_dim *dim,
495 enum isl_dim_type type, unsigned n);
496 __isl_give isl_dim *isl_dim_drop(__isl_take isl_dim *dim,
497 enum isl_dim_type type, unsigned first, unsigned n);
499 Note that if dimensions are added or removed from a space, then
500 the name and the internal structure are lost.
502 =head2 Input and Output
504 C<isl> supports its own input/output format, which is similar
505 to the C<Omega> format, but also supports the C<PolyLib> format
510 The C<isl> format is similar to that of C<Omega>, but has a different
511 syntax for describing the parameters and allows for the definition
512 of an existentially quantified variable as the integer division
513 of an affine expression.
514 For example, the set of integers C<i> between C<0> and C<n>
515 such that C<i % 10 <= 6> can be described as
517 [n] -> { [i] : exists (a = [i/10] : 0 <= i and i <= n and
520 A set or relation can have several disjuncts, separated
521 by the keyword C<or>. Each disjunct is either a conjunction
522 of constraints or a projection (C<exists>) of a conjunction
523 of constraints. The constraints are separated by the keyword
526 =head3 C<PolyLib> format
528 If the represented set is a union, then the first line
529 contains a single number representing the number of disjuncts.
530 Otherwise, a line containing the number C<1> is optional.
532 Each disjunct is represented by a matrix of constraints.
533 The first line contains two numbers representing
534 the number of rows and columns,
535 where the number of rows is equal to the number of constraints
536 and the number of columns is equal to two plus the number of variables.
537 The following lines contain the actual rows of the constraint matrix.
538 In each row, the first column indicates whether the constraint
539 is an equality (C<0>) or inequality (C<1>). The final column
540 corresponds to the constant term.
542 If the set is parametric, then the coefficients of the parameters
543 appear in the last columns before the constant column.
544 The coefficients of any existentially quantified variables appear
545 between those of the set variables and those of the parameters.
550 __isl_give isl_basic_set *isl_basic_set_read_from_file(
551 isl_ctx *ctx, FILE *input, int nparam);
552 __isl_give isl_basic_set *isl_basic_set_read_from_str(
553 isl_ctx *ctx, const char *str, int nparam);
554 __isl_give isl_set *isl_set_read_from_file(isl_ctx *ctx,
555 FILE *input, int nparam);
556 __isl_give isl_set *isl_set_read_from_str(isl_ctx *ctx,
557 const char *str, int nparam);
560 __isl_give isl_basic_map *isl_basic_map_read_from_file(
561 isl_ctx *ctx, FILE *input, int nparam);
562 __isl_give isl_basic_map *isl_basic_map_read_from_str(
563 isl_ctx *ctx, const char *str, int nparam);
564 __isl_give isl_map *isl_map_read_from_file(
565 struct isl_ctx *ctx, FILE *input, int nparam);
566 __isl_give isl_map *isl_map_read_from_str(isl_ctx *ctx,
567 const char *str, int nparam);
569 The input format is autodetected and may be either the C<PolyLib> format
570 or the C<isl> format.
571 C<nparam> specifies how many of the final columns in
572 the C<PolyLib> format correspond to parameters.
573 If input is given in the C<isl> format, then the number
574 of parameters needs to be equal to C<nparam>.
575 If C<nparam> is negative, then any number of parameters
576 is accepted in the C<isl> format and zero parameters
577 are assumed in the C<PolyLib> format.
581 Before anything can be printed, an C<isl_printer> needs to
584 __isl_give isl_printer *isl_printer_to_file(isl_ctx *ctx,
586 __isl_give isl_printer *isl_printer_to_str(isl_ctx *ctx);
587 void isl_printer_free(__isl_take isl_printer *printer);
588 __isl_give char *isl_printer_get_str(
589 __isl_keep isl_printer *printer);
591 The behavior of the printer can be modified in various ways
593 __isl_give isl_printer *isl_printer_set_output_format(
594 __isl_take isl_printer *p, int output_format);
595 __isl_give isl_printer *isl_printer_set_indent(
596 __isl_take isl_printer *p, int indent);
597 __isl_give isl_printer *isl_printer_set_prefix(
598 __isl_take isl_printer *p, const char *prefix);
599 __isl_give isl_printer *isl_printer_set_suffix(
600 __isl_take isl_printer *p, const char *suffix);
602 The C<output_format> may be either C<ISL_FORMAT_ISL>, C<ISL_FORMAT_OMEGA>
603 or C<ISL_FORMAT_POLYLIB> and defaults to C<ISL_FORMAT_ISL>.
604 Each line in the output is indented by C<indent> spaces
605 (default: 0), prefixed by C<prefix> and suffixed by C<suffix>.
606 In the C<PolyLib> format output,
607 the coefficients of the existentially quantified variables
608 appear between those of the set variables and those
611 To actually print something, use
614 __isl_give isl_printer *isl_printer_print_basic_set(
615 __isl_take isl_printer *printer,
616 __isl_keep isl_basic_set *bset);
617 __isl_give isl_printer *isl_printer_print_set(
618 __isl_take isl_printer *printer,
619 __isl_keep isl_set *set);
622 __isl_give isl_printer *isl_printer_print_basic_map(
623 __isl_take isl_printer *printer,
624 __isl_keep isl_basic_map *bmap);
625 __isl_give isl_printer *isl_printer_print_map(
626 __isl_take isl_printer *printer,
627 __isl_keep isl_map *map);
629 #include <isl_union_set.h>
630 __isl_give isl_printer *isl_printer_print_union_set(
631 __isl_take isl_printer *p,
632 __isl_keep isl_union_set *uset);
634 #include <isl_union_map.h>
635 __isl_give isl_printer *isl_printer_print_union_map(
636 __isl_take isl_printer *p,
637 __isl_keep isl_union_map *umap);
639 When called on a file printer, the following function flushes
640 the file. When called on a string printer, the buffer is cleared.
642 __isl_give isl_printer *isl_printer_flush(
643 __isl_take isl_printer *p);
645 =head2 Creating New Sets and Relations
647 C<isl> has functions for creating some standard sets and relations.
651 =item * Empty sets and relations
653 __isl_give isl_basic_set *isl_basic_set_empty(
654 __isl_take isl_dim *dim);
655 __isl_give isl_basic_map *isl_basic_map_empty(
656 __isl_take isl_dim *dim);
657 __isl_give isl_set *isl_set_empty(
658 __isl_take isl_dim *dim);
659 __isl_give isl_map *isl_map_empty(
660 __isl_take isl_dim *dim);
661 __isl_give isl_union_set *isl_union_set_empty(
662 __isl_take isl_dim *dim);
663 __isl_give isl_union_map *isl_union_map_empty(
664 __isl_take isl_dim *dim);
666 For C<isl_union_set>s and C<isl_union_map>s, the dimensions specification
667 is only used to specify the parameters.
669 =item * Universe sets and relations
671 __isl_give isl_basic_set *isl_basic_set_universe(
672 __isl_take isl_dim *dim);
673 __isl_give isl_basic_map *isl_basic_map_universe(
674 __isl_take isl_dim *dim);
675 __isl_give isl_set *isl_set_universe(
676 __isl_take isl_dim *dim);
677 __isl_give isl_map *isl_map_universe(
678 __isl_take isl_dim *dim);
680 =item * Identity relations
682 __isl_give isl_basic_map *isl_basic_map_identity(
683 __isl_take isl_dim *set_dim);
684 __isl_give isl_map *isl_map_identity(
685 __isl_take isl_dim *set_dim);
687 These functions take a dimension specification for a B<set>
688 and return an identity relation between two such sets.
690 =item * Lexicographic order
692 __isl_give isl_map *isl_map_lex_lt(
693 __isl_take isl_dim *set_dim);
694 __isl_give isl_map *isl_map_lex_le(
695 __isl_take isl_dim *set_dim);
696 __isl_give isl_map *isl_map_lex_gt(
697 __isl_take isl_dim *set_dim);
698 __isl_give isl_map *isl_map_lex_ge(
699 __isl_take isl_dim *set_dim);
700 __isl_give isl_map *isl_map_lex_lt_first(
701 __isl_take isl_dim *dim, unsigned n);
702 __isl_give isl_map *isl_map_lex_le_first(
703 __isl_take isl_dim *dim, unsigned n);
704 __isl_give isl_map *isl_map_lex_gt_first(
705 __isl_take isl_dim *dim, unsigned n);
706 __isl_give isl_map *isl_map_lex_ge_first(
707 __isl_take isl_dim *dim, unsigned n);
709 The first four functions take a dimension specification for a B<set>
710 and return relations that express that the elements in the domain
711 are lexicographically less
712 (C<isl_map_lex_lt>), less or equal (C<isl_map_lex_le>),
713 greater (C<isl_map_lex_gt>) or greater or equal (C<isl_map_lex_ge>)
714 than the elements in the range.
715 The last four functions take a dimension specification for a map
716 and return relations that express that the first C<n> dimensions
717 in the domain are lexicographically less
718 (C<isl_map_lex_lt_first>), less or equal (C<isl_map_lex_le_first>),
719 greater (C<isl_map_lex_gt_first>) or greater or equal (C<isl_map_lex_ge_first>)
720 than the first C<n> dimensions in the range.
724 A basic set or relation can be converted to a set or relation
725 using the following functions.
727 __isl_give isl_set *isl_set_from_basic_set(
728 __isl_take isl_basic_set *bset);
729 __isl_give isl_map *isl_map_from_basic_map(
730 __isl_take isl_basic_map *bmap);
732 Sets and relations can be converted to union sets and relations
733 using the following functions.
735 __isl_give isl_union_map *isl_union_map_from_map(
736 __isl_take isl_map *map);
737 __isl_give isl_union_set *isl_union_set_from_set(
738 __isl_take isl_set *set);
740 Sets and relations can be copied and freed again using the following
743 __isl_give isl_basic_set *isl_basic_set_copy(
744 __isl_keep isl_basic_set *bset);
745 __isl_give isl_set *isl_set_copy(__isl_keep isl_set *set);
746 __isl_give isl_union_set *isl_union_set_copy(
747 __isl_keep isl_union_set *uset);
748 __isl_give isl_basic_map *isl_basic_map_copy(
749 __isl_keep isl_basic_map *bmap);
750 __isl_give isl_map *isl_map_copy(__isl_keep isl_map *map);
751 __isl_give isl_union_map *isl_union_map_copy(
752 __isl_keep isl_union_map *umap);
753 void isl_basic_set_free(__isl_take isl_basic_set *bset);
754 void isl_set_free(__isl_take isl_set *set);
755 void isl_union_set_free(__isl_take isl_union_set *uset);
756 void isl_basic_map_free(__isl_take isl_basic_map *bmap);
757 void isl_map_free(__isl_take isl_map *map);
758 void isl_union_map_free(__isl_take isl_union_map *umap);
760 Other sets and relations can be constructed by starting
761 from a universe set or relation, adding equality and/or
762 inequality constraints and then projecting out the
763 existentially quantified variables, if any.
764 Constraints can be constructed, manipulated and
765 added to basic sets and relations using the following functions.
767 #include <isl_constraint.h>
768 __isl_give isl_constraint *isl_equality_alloc(
769 __isl_take isl_dim *dim);
770 __isl_give isl_constraint *isl_inequality_alloc(
771 __isl_take isl_dim *dim);
772 void isl_constraint_set_constant(
773 __isl_keep isl_constraint *constraint, isl_int v);
774 void isl_constraint_set_coefficient(
775 __isl_keep isl_constraint *constraint,
776 enum isl_dim_type type, int pos, isl_int v);
777 __isl_give isl_basic_map *isl_basic_map_add_constraint(
778 __isl_take isl_basic_map *bmap,
779 __isl_take isl_constraint *constraint);
780 __isl_give isl_basic_set *isl_basic_set_add_constraint(
781 __isl_take isl_basic_set *bset,
782 __isl_take isl_constraint *constraint);
784 For example, to create a set containing the even integers
785 between 10 and 42, you would use the following code.
789 struct isl_constraint *c;
790 struct isl_basic_set *bset;
793 dim = isl_dim_set_alloc(ctx, 0, 2);
794 bset = isl_basic_set_universe(isl_dim_copy(dim));
796 c = isl_equality_alloc(isl_dim_copy(dim));
797 isl_int_set_si(v, -1);
798 isl_constraint_set_coefficient(c, isl_dim_set, 0, v);
799 isl_int_set_si(v, 2);
800 isl_constraint_set_coefficient(c, isl_dim_set, 1, v);
801 bset = isl_basic_set_add_constraint(bset, c);
803 c = isl_inequality_alloc(isl_dim_copy(dim));
804 isl_int_set_si(v, -10);
805 isl_constraint_set_constant(c, v);
806 isl_int_set_si(v, 1);
807 isl_constraint_set_coefficient(c, isl_dim_set, 0, v);
808 bset = isl_basic_set_add_constraint(bset, c);
810 c = isl_inequality_alloc(dim);
811 isl_int_set_si(v, 42);
812 isl_constraint_set_constant(c, v);
813 isl_int_set_si(v, -1);
814 isl_constraint_set_coefficient(c, isl_dim_set, 0, v);
815 bset = isl_basic_set_add_constraint(bset, c);
817 bset = isl_basic_set_project_out(bset, isl_dim_set, 1, 1);
823 struct isl_basic_set *bset;
824 bset = isl_basic_set_read_from_str(ctx,
825 "{[i] : exists (a : i = 2a and i >= 10 and i <= 42)}", -1);
827 A basic set or relation can also be constructed from two matrices
828 describing the equalities and the inequalities.
830 __isl_give isl_basic_set *isl_basic_set_from_constraint_matrices(
831 __isl_take isl_dim *dim,
832 __isl_take isl_mat *eq, __isl_take isl_mat *ineq,
833 enum isl_dim_type c1,
834 enum isl_dim_type c2, enum isl_dim_type c3,
835 enum isl_dim_type c4);
836 __isl_give isl_basic_map *isl_basic_map_from_constraint_matrices(
837 __isl_take isl_dim *dim,
838 __isl_take isl_mat *eq, __isl_take isl_mat *ineq,
839 enum isl_dim_type c1,
840 enum isl_dim_type c2, enum isl_dim_type c3,
841 enum isl_dim_type c4, enum isl_dim_type c5);
843 The C<isl_dim_type> arguments indicate the order in which
844 different kinds of variables appear in the input matrices
845 and should be a permutation of C<isl_dim_cst>, C<isl_dim_param>,
846 C<isl_dim_set> and C<isl_dim_div> for sets and
847 of C<isl_dim_cst>, C<isl_dim_param>,
848 C<isl_dim_in>, C<isl_dim_out> and C<isl_dim_div> for relations.
850 =head2 Inspecting Sets and Relations
852 Usually, the user should not have to care about the actual constraints
853 of the sets and maps, but should instead apply the abstract operations
854 explained in the following sections.
855 Occasionally, however, it may be required to inspect the individual
856 coefficients of the constraints. This section explains how to do so.
857 In these cases, it may also be useful to have C<isl> compute
858 an explicit representation of the existentially quantified variables.
860 __isl_give isl_set *isl_set_compute_divs(
861 __isl_take isl_set *set);
862 __isl_give isl_map *isl_map_compute_divs(
863 __isl_take isl_map *map);
864 __isl_give isl_union_set *isl_union_set_compute_divs(
865 __isl_take isl_union_set *uset);
866 __isl_give isl_union_map *isl_union_map_compute_divs(
867 __isl_take isl_union_map *umap);
869 This explicit representation defines the existentially quantified
870 variables as integer divisions of the other variables, possibly
871 including earlier existentially quantified variables.
872 An explicitly represented existentially quantified variable therefore
873 has a unique value when the values of the other variables are known.
874 If, furthermore, the same existentials, i.e., existentials
875 with the same explicit representations, should appear in the
876 same order in each of the disjuncts of a set or map, then the user should call
877 either of the following functions.
879 __isl_give isl_set *isl_set_align_divs(
880 __isl_take isl_set *set);
881 __isl_give isl_map *isl_map_align_divs(
882 __isl_take isl_map *map);
884 To iterate over all the sets or maps in a union set or map, use
886 int isl_union_set_foreach_set(__isl_keep isl_union_set *uset,
887 int (*fn)(__isl_take isl_set *set, void *user),
889 int isl_union_map_foreach_map(__isl_keep isl_union_map *umap,
890 int (*fn)(__isl_take isl_map *map, void *user),
893 To iterate over all the basic sets or maps in a set or map, use
895 int isl_set_foreach_basic_set(__isl_keep isl_set *set,
896 int (*fn)(__isl_take isl_basic_set *bset, void *user),
898 int isl_map_foreach_basic_map(__isl_keep isl_map *map,
899 int (*fn)(__isl_take isl_basic_map *bmap, void *user),
902 The callback function C<fn> should return 0 if successful and
903 -1 if an error occurs. In the latter case, or if any other error
904 occurs, the above functions will return -1.
906 It should be noted that C<isl> does not guarantee that
907 the basic sets or maps passed to C<fn> are disjoint.
908 If this is required, then the user should call one of
909 the following functions first.
911 __isl_give isl_set *isl_set_make_disjoint(
912 __isl_take isl_set *set);
913 __isl_give isl_map *isl_map_make_disjoint(
914 __isl_take isl_map *map);
916 To iterate over the constraints of a basic set or map, use
918 #include <isl_constraint.h>
920 int isl_basic_map_foreach_constraint(
921 __isl_keep isl_basic_map *bmap,
922 int (*fn)(__isl_take isl_constraint *c, void *user),
924 void isl_constraint_free(struct isl_constraint *c);
926 Again, the callback function C<fn> should return 0 if successful and
927 -1 if an error occurs. In the latter case, or if any other error
928 occurs, the above functions will return -1.
929 The constraint C<c> represents either an equality or an inequality.
930 Use the following function to find out whether a constraint
931 represents an equality. If not, it represents an inequality.
933 int isl_constraint_is_equality(
934 __isl_keep isl_constraint *constraint);
936 The coefficients of the constraints can be inspected using
937 the following functions.
939 void isl_constraint_get_constant(
940 __isl_keep isl_constraint *constraint, isl_int *v);
941 void isl_constraint_get_coefficient(
942 __isl_keep isl_constraint *constraint,
943 enum isl_dim_type type, int pos, isl_int *v);
945 The explicit representations of the existentially quantified
946 variables can be inspected using the following functions.
947 Note that the user is only allowed to use these functions
948 if the inspected set or map is the result of a call
949 to C<isl_set_compute_divs> or C<isl_map_compute_divs>.
951 __isl_give isl_div *isl_constraint_div(
952 __isl_keep isl_constraint *constraint, int pos);
953 void isl_div_get_constant(__isl_keep isl_div *div,
955 void isl_div_get_denominator(__isl_keep isl_div *div,
957 void isl_div_get_coefficient(__isl_keep isl_div *div,
958 enum isl_dim_type type, int pos, isl_int *v);
960 To obtain the constraints of a basic map in matrix
961 form, use the following functions.
963 __isl_give isl_mat *isl_basic_map_equalities_matrix(
964 __isl_keep isl_basic_map *bmap,
965 enum isl_dim_type c1,
966 enum isl_dim_type c2, enum isl_dim_type c3,
967 enum isl_dim_type c4, enum isl_dim_type c5);
968 __isl_give isl_mat *isl_basic_map_inequalities_matrix(
969 __isl_keep isl_basic_map *bmap,
970 enum isl_dim_type c1,
971 enum isl_dim_type c2, enum isl_dim_type c3,
972 enum isl_dim_type c4, enum isl_dim_type c5);
974 The C<isl_dim_type> arguments dictate the order in which
975 different kinds of variables appear in the resulting matrix
976 and should be a permutation of C<isl_dim_cst>, C<isl_dim_param>,
977 C<isl_dim_in>, C<isl_dim_out> and C<isl_dim_div>.
981 =head3 Unary Properties
987 The following functions test whether the given set or relation
988 contains any integer points. The ``fast'' variants do not perform
989 any computations, but simply check if the given set or relation
990 is already known to be empty.
992 int isl_basic_set_fast_is_empty(__isl_keep isl_basic_set *bset);
993 int isl_basic_set_is_empty(__isl_keep isl_basic_set *bset);
994 int isl_set_is_empty(__isl_keep isl_set *set);
995 int isl_union_set_is_empty(__isl_keep isl_union_set *uset);
996 int isl_basic_map_fast_is_empty(__isl_keep isl_basic_map *bmap);
997 int isl_basic_map_is_empty(__isl_keep isl_basic_map *bmap);
998 int isl_map_fast_is_empty(__isl_keep isl_map *map);
999 int isl_map_is_empty(__isl_keep isl_map *map);
1000 int isl_union_map_is_empty(__isl_keep isl_union_map *umap);
1002 =item * Universality
1004 int isl_basic_set_is_universe(__isl_keep isl_basic_set *bset);
1005 int isl_basic_map_is_universe(__isl_keep isl_basic_map *bmap);
1006 int isl_set_fast_is_universe(__isl_keep isl_set *set);
1008 =item * Single-valuedness
1010 int isl_map_is_single_valued(__isl_keep isl_map *map);
1014 int isl_map_is_bijective(__isl_keep isl_map *map);
1018 The followning functions check whether the domain of the given
1019 (basic) set is a wrapped relation.
1021 int isl_basic_set_is_wrapping(
1022 __isl_keep isl_basic_set *bset);
1023 int isl_set_is_wrapping(__isl_keep isl_set *set);
1027 =head3 Binary Properties
1033 int isl_set_fast_is_equal(__isl_keep isl_set *set1,
1034 __isl_keep isl_set *set2);
1035 int isl_set_is_equal(__isl_keep isl_set *set1,
1036 __isl_keep isl_set *set2);
1037 int isl_basic_map_is_equal(
1038 __isl_keep isl_basic_map *bmap1,
1039 __isl_keep isl_basic_map *bmap2);
1040 int isl_map_is_equal(__isl_keep isl_map *map1,
1041 __isl_keep isl_map *map2);
1042 int isl_map_fast_is_equal(__isl_keep isl_map *map1,
1043 __isl_keep isl_map *map2);
1044 int isl_union_map_is_equal(
1045 __isl_keep isl_union_map *umap1,
1046 __isl_keep isl_union_map *umap2);
1048 =item * Disjointness
1050 int isl_set_fast_is_disjoint(__isl_keep isl_set *set1,
1051 __isl_keep isl_set *set2);
1055 int isl_set_is_subset(__isl_keep isl_set *set1,
1056 __isl_keep isl_set *set2);
1057 int isl_set_is_strict_subset(
1058 __isl_keep isl_set *set1,
1059 __isl_keep isl_set *set2);
1060 int isl_basic_map_is_subset(
1061 __isl_keep isl_basic_map *bmap1,
1062 __isl_keep isl_basic_map *bmap2);
1063 int isl_basic_map_is_strict_subset(
1064 __isl_keep isl_basic_map *bmap1,
1065 __isl_keep isl_basic_map *bmap2);
1066 int isl_map_is_subset(
1067 __isl_keep isl_map *map1,
1068 __isl_keep isl_map *map2);
1069 int isl_map_is_strict_subset(
1070 __isl_keep isl_map *map1,
1071 __isl_keep isl_map *map2);
1072 int isl_union_map_is_subset(
1073 __isl_keep isl_union_map *umap1,
1074 __isl_keep isl_union_map *umap2);
1075 int isl_union_map_is_strict_subset(
1076 __isl_keep isl_union_map *umap1,
1077 __isl_keep isl_union_map *umap2);
1081 =head2 Unary Operations
1087 __isl_give isl_set *isl_set_complement(
1088 __isl_take isl_set *set);
1092 __isl_give isl_basic_map *isl_basic_map_reverse(
1093 __isl_take isl_basic_map *bmap);
1094 __isl_give isl_map *isl_map_reverse(
1095 __isl_take isl_map *map);
1096 __isl_give isl_union_map *isl_union_map_reverse(
1097 __isl_take isl_union_map *umap);
1101 __isl_give isl_basic_set *isl_basic_set_project_out(
1102 __isl_take isl_basic_set *bset,
1103 enum isl_dim_type type, unsigned first, unsigned n);
1104 __isl_give isl_basic_map *isl_basic_map_project_out(
1105 __isl_take isl_basic_map *bmap,
1106 enum isl_dim_type type, unsigned first, unsigned n);
1107 __isl_give isl_set *isl_set_project_out(__isl_take isl_set *set,
1108 enum isl_dim_type type, unsigned first, unsigned n);
1109 __isl_give isl_map *isl_map_project_out(__isl_take isl_map *map,
1110 enum isl_dim_type type, unsigned first, unsigned n);
1111 __isl_give isl_basic_set *isl_basic_map_domain(
1112 __isl_take isl_basic_map *bmap);
1113 __isl_give isl_basic_set *isl_basic_map_range(
1114 __isl_take isl_basic_map *bmap);
1115 __isl_give isl_set *isl_map_domain(
1116 __isl_take isl_map *bmap);
1117 __isl_give isl_set *isl_map_range(
1118 __isl_take isl_map *map);
1119 __isl_give isl_union_set *isl_union_map_domain(
1120 __isl_take isl_union_map *umap);
1121 __isl_give isl_union_set *isl_union_map_range(
1122 __isl_take isl_union_map *umap);
1126 __isl_give isl_basic_set *isl_basic_map_deltas(
1127 __isl_take isl_basic_map *bmap);
1128 __isl_give isl_set *isl_map_deltas(__isl_take isl_map *map);
1129 __isl_give isl_union_set *isl_union_map_deltas(
1130 __isl_take isl_union_map *umap);
1132 These functions return a (basic) set containing the differences
1133 between image elements and corresponding domain elements in the input.
1137 Simplify the representation of a set or relation by trying
1138 to combine pairs of basic sets or relations into a single
1139 basic set or relation.
1141 __isl_give isl_set *isl_set_coalesce(__isl_take isl_set *set);
1142 __isl_give isl_map *isl_map_coalesce(__isl_take isl_map *map);
1143 __isl_give isl_union_set *isl_union_set_coalesce(
1144 __isl_take isl_union_set *uset);
1145 __isl_give isl_union_map *isl_union_map_coalesce(
1146 __isl_take isl_union_map *umap);
1150 __isl_give isl_basic_set *isl_set_convex_hull(
1151 __isl_take isl_set *set);
1152 __isl_give isl_basic_map *isl_map_convex_hull(
1153 __isl_take isl_map *map);
1155 If the input set or relation has any existentially quantified
1156 variables, then the result of these operations is currently undefined.
1160 __isl_give isl_basic_set *isl_set_simple_hull(
1161 __isl_take isl_set *set);
1162 __isl_give isl_basic_map *isl_map_simple_hull(
1163 __isl_take isl_map *map);
1165 These functions compute a single basic set or relation
1166 that contains the whole input set or relation.
1167 In particular, the output is described by translates
1168 of the constraints describing the basic sets or relations in the input.
1172 (See \autoref{s:simple hull}.)
1178 __isl_give isl_basic_set *isl_basic_set_affine_hull(
1179 __isl_take isl_basic_set *bset);
1180 __isl_give isl_basic_set *isl_set_affine_hull(
1181 __isl_take isl_set *set);
1182 __isl_give isl_union_set *isl_union_set_affine_hull(
1183 __isl_take isl_union_set *uset);
1184 __isl_give isl_basic_map *isl_basic_map_affine_hull(
1185 __isl_take isl_basic_map *bmap);
1186 __isl_give isl_basic_map *isl_map_affine_hull(
1187 __isl_take isl_map *map);
1188 __isl_give isl_union_map *isl_union_map_affine_hull(
1189 __isl_take isl_union_map *umap);
1191 In case of union sets and relations, the affine hull is computed
1196 __isl_give isl_map *isl_map_power(__isl_take isl_map *map,
1197 unsigned param, int *exact);
1199 Compute a parametric representation for all positive powers I<k> of C<map>.
1200 The power I<k> is equated to the parameter at position C<param>.
1201 The result may be an overapproximation. If the result is exact,
1202 then C<*exact> is set to C<1>.
1203 The current implementation only produces exact results for particular
1204 cases of piecewise translations (i.e., piecewise uniform dependences).
1206 =item * Transitive closure
1208 __isl_give isl_map *isl_map_transitive_closure(
1209 __isl_take isl_map *map, int *exact);
1210 __isl_give isl_union_map *isl_union_map_transitive_closure(
1211 __isl_take isl_union_map *umap, int *exact);
1213 Compute the transitive closure of C<map>.
1214 The result may be an overapproximation. If the result is known to be exact,
1215 then C<*exact> is set to C<1>.
1216 The current implementation only produces exact results for particular
1217 cases of piecewise translations (i.e., piecewise uniform dependences).
1219 =item * Reaching path lengths
1221 __isl_give isl_map *isl_map_reaching_path_lengths(
1222 __isl_take isl_map *map, int *exact);
1224 Compute a relation that maps each element in the range of C<map>
1225 to the lengths of all paths composed of edges in C<map> that
1226 end up in the given element.
1227 The result may be an overapproximation. If the result is known to be exact,
1228 then C<*exact> is set to C<1>.
1229 To compute the I<maximal> path length, the resulting relation
1230 should be postprocessed by C<isl_map_lexmax>.
1231 In particular, if the input relation is a dependence relation
1232 (mapping sources to sinks), then the maximal path length corresponds
1233 to the free schedule.
1234 Note, however, that C<isl_map_lexmax> expects the maximum to be
1235 finite, so if the path lengths are unbounded (possibly due to
1236 the overapproximation), then you will get an error message.
1240 __isl_give isl_basic_set *isl_basic_map_wrap(
1241 __isl_take isl_basic_map *bmap);
1242 __isl_give isl_set *isl_map_wrap(
1243 __isl_take isl_map *map);
1244 __isl_give isl_union_set *isl_union_map_wrap(
1245 __isl_take isl_union_map *umap);
1246 __isl_give isl_basic_map *isl_basic_set_unwrap(
1247 __isl_take isl_basic_set *bset);
1248 __isl_give isl_map *isl_set_unwrap(
1249 __isl_take isl_set *set);
1250 __isl_give isl_union_map *isl_union_set_unwrap(
1251 __isl_take isl_union_set *uset);
1255 =head2 Binary Operations
1257 The two arguments of a binary operation not only need to live
1258 in the same C<isl_ctx>, they currently also need to have
1259 the same (number of) parameters.
1261 =head3 Basic Operations
1265 =item * Intersection
1267 __isl_give isl_basic_set *isl_basic_set_intersect(
1268 __isl_take isl_basic_set *bset1,
1269 __isl_take isl_basic_set *bset2);
1270 __isl_give isl_set *isl_set_intersect(
1271 __isl_take isl_set *set1,
1272 __isl_take isl_set *set2);
1273 __isl_give isl_union_set *isl_union_set_intersect(
1274 __isl_take isl_union_set *uset1,
1275 __isl_take isl_union_set *uset2);
1276 __isl_give isl_basic_map *isl_basic_map_intersect_domain(
1277 __isl_take isl_basic_map *bmap,
1278 __isl_take isl_basic_set *bset);
1279 __isl_give isl_basic_map *isl_basic_map_intersect_range(
1280 __isl_take isl_basic_map *bmap,
1281 __isl_take isl_basic_set *bset);
1282 __isl_give isl_basic_map *isl_basic_map_intersect(
1283 __isl_take isl_basic_map *bmap1,
1284 __isl_take isl_basic_map *bmap2);
1285 __isl_give isl_map *isl_map_intersect_domain(
1286 __isl_take isl_map *map,
1287 __isl_take isl_set *set);
1288 __isl_give isl_map *isl_map_intersect_range(
1289 __isl_take isl_map *map,
1290 __isl_take isl_set *set);
1291 __isl_give isl_map *isl_map_intersect(
1292 __isl_take isl_map *map1,
1293 __isl_take isl_map *map2);
1294 __isl_give isl_union_map *isl_union_map_intersect_domain(
1295 __isl_take isl_union_map *umap,
1296 __isl_take isl_union_set *uset);
1297 __isl_give isl_union_map *isl_union_map_intersect(
1298 __isl_take isl_union_map *umap1,
1299 __isl_take isl_union_map *umap2);
1303 __isl_give isl_set *isl_basic_set_union(
1304 __isl_take isl_basic_set *bset1,
1305 __isl_take isl_basic_set *bset2);
1306 __isl_give isl_map *isl_basic_map_union(
1307 __isl_take isl_basic_map *bmap1,
1308 __isl_take isl_basic_map *bmap2);
1309 __isl_give isl_set *isl_set_union(
1310 __isl_take isl_set *set1,
1311 __isl_take isl_set *set2);
1312 __isl_give isl_map *isl_map_union(
1313 __isl_take isl_map *map1,
1314 __isl_take isl_map *map2);
1315 __isl_give isl_union_set *isl_union_set_union(
1316 __isl_take isl_union_set *uset1,
1317 __isl_take isl_union_set *uset2);
1318 __isl_give isl_union_map *isl_union_map_union(
1319 __isl_take isl_union_map *umap1,
1320 __isl_take isl_union_map *umap2);
1322 =item * Set difference
1324 __isl_give isl_set *isl_set_subtract(
1325 __isl_take isl_set *set1,
1326 __isl_take isl_set *set2);
1327 __isl_give isl_map *isl_map_subtract(
1328 __isl_take isl_map *map1,
1329 __isl_take isl_map *map2);
1330 __isl_give isl_union_set *isl_union_set_subtract(
1331 __isl_take isl_union_set *uset1,
1332 __isl_take isl_union_set *uset2);
1333 __isl_give isl_union_map *isl_union_map_subtract(
1334 __isl_take isl_union_map *umap1,
1335 __isl_take isl_union_map *umap2);
1339 __isl_give isl_basic_set *isl_basic_set_apply(
1340 __isl_take isl_basic_set *bset,
1341 __isl_take isl_basic_map *bmap);
1342 __isl_give isl_set *isl_set_apply(
1343 __isl_take isl_set *set,
1344 __isl_take isl_map *map);
1345 __isl_give isl_union_set *isl_union_set_apply(
1346 __isl_take isl_union_set *uset,
1347 __isl_take isl_union_map *umap);
1348 __isl_give isl_basic_map *isl_basic_map_apply_domain(
1349 __isl_take isl_basic_map *bmap1,
1350 __isl_take isl_basic_map *bmap2);
1351 __isl_give isl_basic_map *isl_basic_map_apply_range(
1352 __isl_take isl_basic_map *bmap1,
1353 __isl_take isl_basic_map *bmap2);
1354 __isl_give isl_map *isl_map_apply_domain(
1355 __isl_take isl_map *map1,
1356 __isl_take isl_map *map2);
1357 __isl_give isl_map *isl_map_apply_range(
1358 __isl_take isl_map *map1,
1359 __isl_take isl_map *map2);
1360 __isl_give isl_union_map *isl_union_map_apply_range(
1361 __isl_take isl_union_map *umap1,
1362 __isl_take isl_union_map *umap2);
1364 =item * Simplification
1366 __isl_give isl_basic_set *isl_basic_set_gist(
1367 __isl_take isl_basic_set *bset,
1368 __isl_take isl_basic_set *context);
1369 __isl_give isl_set *isl_set_gist(__isl_take isl_set *set,
1370 __isl_take isl_set *context);
1371 __isl_give isl_union_set *isl_union_set_gist(
1372 __isl_take isl_union_set *uset,
1373 __isl_take isl_union_set *context);
1374 __isl_give isl_basic_map *isl_basic_map_gist(
1375 __isl_take isl_basic_map *bmap,
1376 __isl_take isl_basic_map *context);
1377 __isl_give isl_map *isl_map_gist(__isl_take isl_map *map,
1378 __isl_take isl_map *context);
1379 __isl_give isl_union_map *isl_union_map_gist(
1380 __isl_take isl_union_map *umap,
1381 __isl_take isl_union_map *context);
1383 The gist operation returns a set or relation that has the
1384 same intersection with the context as the input set or relation.
1385 Any implicit equality in the intersection is made explicit in the result,
1386 while all inequalities that are redundant with respect to the intersection
1388 In case of union sets and relations, the gist operation is performed
1393 =head3 Lexicographic Optimization
1395 Given a (basic) set C<set> (or C<bset>) and a zero-dimensional domain C<dom>,
1396 the following functions
1397 compute a set that contains the lexicographic minimum or maximum
1398 of the elements in C<set> (or C<bset>) for those values of the parameters
1399 that satisfy C<dom>.
1400 If C<empty> is not C<NULL>, then C<*empty> is assigned a set
1401 that contains the parameter values in C<dom> for which C<set> (or C<bset>)
1403 In other words, the union of the parameter values
1404 for which the result is non-empty and of C<*empty>
1407 __isl_give isl_set *isl_basic_set_partial_lexmin(
1408 __isl_take isl_basic_set *bset,
1409 __isl_take isl_basic_set *dom,
1410 __isl_give isl_set **empty);
1411 __isl_give isl_set *isl_basic_set_partial_lexmax(
1412 __isl_take isl_basic_set *bset,
1413 __isl_take isl_basic_set *dom,
1414 __isl_give isl_set **empty);
1415 __isl_give isl_set *isl_set_partial_lexmin(
1416 __isl_take isl_set *set, __isl_take isl_set *dom,
1417 __isl_give isl_set **empty);
1418 __isl_give isl_set *isl_set_partial_lexmax(
1419 __isl_take isl_set *set, __isl_take isl_set *dom,
1420 __isl_give isl_set **empty);
1422 Given a (basic) set C<set> (or C<bset>), the following functions simply
1423 return a set containing the lexicographic minimum or maximum
1424 of the elements in C<set> (or C<bset>).
1425 In case of union sets, the optimum is computed per space.
1427 __isl_give isl_set *isl_basic_set_lexmin(
1428 __isl_take isl_basic_set *bset);
1429 __isl_give isl_set *isl_basic_set_lexmax(
1430 __isl_take isl_basic_set *bset);
1431 __isl_give isl_set *isl_set_lexmin(
1432 __isl_take isl_set *set);
1433 __isl_give isl_set *isl_set_lexmax(
1434 __isl_take isl_set *set);
1435 __isl_give isl_union_set *isl_union_set_lexmin(
1436 __isl_take isl_union_set *uset);
1437 __isl_give isl_union_set *isl_union_set_lexmax(
1438 __isl_take isl_union_set *uset);
1440 Given a (basic) relation C<map> (or C<bmap>) and a domain C<dom>,
1441 the following functions
1442 compute a relation that maps each element of C<dom>
1443 to the single lexicographic minimum or maximum
1444 of the elements that are associated to that same
1445 element in C<map> (or C<bmap>).
1446 If C<empty> is not C<NULL>, then C<*empty> is assigned a set
1447 that contains the elements in C<dom> that do not map
1448 to any elements in C<map> (or C<bmap>).
1449 In other words, the union of the domain of the result and of C<*empty>
1452 __isl_give isl_map *isl_basic_map_partial_lexmax(
1453 __isl_take isl_basic_map *bmap,
1454 __isl_take isl_basic_set *dom,
1455 __isl_give isl_set **empty);
1456 __isl_give isl_map *isl_basic_map_partial_lexmin(
1457 __isl_take isl_basic_map *bmap,
1458 __isl_take isl_basic_set *dom,
1459 __isl_give isl_set **empty);
1460 __isl_give isl_map *isl_map_partial_lexmax(
1461 __isl_take isl_map *map, __isl_take isl_set *dom,
1462 __isl_give isl_set **empty);
1463 __isl_give isl_map *isl_map_partial_lexmin(
1464 __isl_take isl_map *map, __isl_take isl_set *dom,
1465 __isl_give isl_set **empty);
1467 Given a (basic) map C<map> (or C<bmap>), the following functions simply
1468 return a map mapping each element in the domain of
1469 C<map> (or C<bmap>) to the lexicographic minimum or maximum
1470 of all elements associated to that element.
1471 In case of union relations, the optimum is computed per space.
1473 __isl_give isl_map *isl_basic_map_lexmin(
1474 __isl_take isl_basic_map *bmap);
1475 __isl_give isl_map *isl_basic_map_lexmax(
1476 __isl_take isl_basic_map *bmap);
1477 __isl_give isl_map *isl_map_lexmin(
1478 __isl_take isl_map *map);
1479 __isl_give isl_map *isl_map_lexmax(
1480 __isl_take isl_map *map);
1481 __isl_give isl_union_map *isl_union_map_lexmin(
1482 __isl_take isl_union_map *umap);
1483 __isl_give isl_union_map *isl_union_map_lexmax(
1484 __isl_take isl_union_map *umap);
1488 Matrices can be created, copied and freed using the following functions.
1490 #include <isl_mat.h>
1491 __isl_give isl_mat *isl_mat_alloc(struct isl_ctx *ctx,
1492 unsigned n_row, unsigned n_col);
1493 __isl_give isl_mat *isl_mat_copy(__isl_keep isl_mat *mat);
1494 void isl_mat_free(__isl_take isl_mat *mat);
1496 Note that the elements of a newly created matrix may have arbitrary values.
1497 The elements can be changed and inspected using the following functions.
1499 int isl_mat_rows(__isl_keep isl_mat *mat);
1500 int isl_mat_cols(__isl_keep isl_mat *mat);
1501 int isl_mat_get_element(__isl_keep isl_mat *mat,
1502 int row, int col, isl_int *v);
1503 __isl_give isl_mat *isl_mat_set_element(__isl_take isl_mat *mat,
1504 int row, int col, isl_int v);
1506 C<isl_mat_get_element> will return a negative value if anything went wrong.
1507 In that case, the value of C<*v> is undefined.
1509 The following function can be used to compute the (right) inverse
1510 of a matrix, i.e., a matrix such that the product of the original
1511 and the inverse (in that order) is a multiple of the identity matrix.
1512 The input matrix is assumed to be of full row-rank.
1514 __isl_give isl_mat *isl_mat_right_inverse(__isl_take isl_mat *mat);
1516 The following function can be used to compute the (right) kernel
1517 (or null space) of a matrix, i.e., a matrix such that the product of
1518 the original and the kernel (in that order) is the zero matrix.
1520 __isl_give isl_mat *isl_mat_right_kernel(__isl_take isl_mat *mat);
1524 Points are elements of a set. They can be used to construct
1525 simple sets (boxes) or they can be used to represent the
1526 individual elements of a set.
1527 The zero point (the origin) can be created using
1529 __isl_give isl_point *isl_point_zero(__isl_take isl_dim *dim);
1531 The coordinates of a point can be inspected, set and changed
1534 void isl_point_get_coordinate(__isl_keep isl_point *pnt,
1535 enum isl_dim_type type, int pos, isl_int *v);
1536 __isl_give isl_point *isl_point_set_coordinate(
1537 __isl_take isl_point *pnt,
1538 enum isl_dim_type type, int pos, isl_int v);
1540 __isl_give isl_point *isl_point_add_ui(
1541 __isl_take isl_point *pnt,
1542 enum isl_dim_type type, int pos, unsigned val);
1543 __isl_give isl_point *isl_point_sub_ui(
1544 __isl_take isl_point *pnt,
1545 enum isl_dim_type type, int pos, unsigned val);
1547 Points can be copied or freed using
1549 __isl_give isl_point *isl_point_copy(
1550 __isl_keep isl_point *pnt);
1551 void isl_point_free(__isl_take isl_point *pnt);
1553 A singleton set can be created from a point using
1555 __isl_give isl_set *isl_set_from_point(
1556 __isl_take isl_point *pnt);
1558 and a box can be created from two opposite extremal points using
1560 __isl_give isl_set *isl_set_box_from_points(
1561 __isl_take isl_point *pnt1,
1562 __isl_take isl_point *pnt2);
1564 All elements of a B<bounded> (union) set can be enumerated using
1565 the following functions.
1567 int isl_set_foreach_point(__isl_keep isl_set *set,
1568 int (*fn)(__isl_take isl_point *pnt, void *user),
1570 int isl_union_set_foreach_point(__isl_keep isl_union_set *uset,
1571 int (*fn)(__isl_take isl_point *pnt, void *user),
1574 The function C<fn> is called for each integer point in
1575 C<set> with as second argument the last argument of
1576 the C<isl_set_foreach_point> call. The function C<fn>
1577 should return C<0> on success and C<-1> on failure.
1578 In the latter case, C<isl_set_foreach_point> will stop
1579 enumerating and return C<-1> as well.
1580 If the enumeration is performed successfully and to completion,
1581 then C<isl_set_foreach_point> returns C<0>.
1583 To obtain a single point of a set, use
1585 __isl_give isl_point *isl_set_sample_point(
1586 __isl_take isl_set *set);
1588 If C<set> does not contain any (integer) points, then the
1589 resulting point will be ``void'', a property that can be
1592 int isl_point_is_void(__isl_keep isl_point *pnt);
1594 =head2 Piecewise Quasipolynomials
1596 A piecewise quasipolynomial is a particular kind of function that maps
1597 a parametric point to a rational value.
1598 More specifically, a quasipolynomial is a polynomial expression in greatest
1599 integer parts of affine expressions of parameters and variables.
1600 A piecewise quasipolynomial is a subdivision of a given parametric
1601 domain into disjoint cells with a quasipolynomial associated to
1602 each cell. The value of the piecewise quasipolynomial at a given
1603 point is the value of the quasipolynomial associated to the cell
1604 that contains the point. Outside of the union of cells,
1605 the value is assumed to be zero.
1606 For example, the piecewise quasipolynomial
1608 [n] -> { [x] -> ((1 + n) - x) : x <= n and x >= 0 }
1610 maps C<x> to C<1 + n - x> for values of C<x> between C<0> and C<n>.
1611 A given piecewise quasipolynomial has a fixed domain dimension.
1612 Union piecewise quasipolynomials are used to contain piecewise quasipolynomials
1613 defined over different domains.
1614 Piecewise quasipolynomials are mainly used by the C<barvinok>
1615 library for representing the number of elements in a parametric set or map.
1616 For example, the piecewise quasipolynomial above represents
1617 the number of points in the map
1619 [n] -> { [x] -> [y] : x,y >= 0 and 0 <= x + y <= n }
1621 =head3 Printing (Piecewise) Quasipolynomials
1623 Quasipolynomials and piecewise quasipolynomials can be printed
1624 using the following functions.
1626 __isl_give isl_printer *isl_printer_print_qpolynomial(
1627 __isl_take isl_printer *p,
1628 __isl_keep isl_qpolynomial *qp);
1630 __isl_give isl_printer *isl_printer_print_pw_qpolynomial(
1631 __isl_take isl_printer *p,
1632 __isl_keep isl_pw_qpolynomial *pwqp);
1634 __isl_give isl_printer *isl_printer_print_union_pw_qpolynomial(
1635 __isl_take isl_printer *p,
1636 __isl_keep isl_union_pw_qpolynomial *upwqp);
1638 The output format of the printer
1639 needs to be set to either C<ISL_FORMAT_ISL> or C<ISL_FORMAT_C>.
1640 For C<isl_printer_print_union_pw_qpolynomial>, only C<ISL_FORMAT_ISL>
1643 =head3 Creating New (Piecewise) Quasipolynomials
1645 Some simple quasipolynomials can be created using the following functions.
1646 More complicated quasipolynomials can be created by applying
1647 operations such as addition and multiplication
1648 on the resulting quasipolynomials
1650 __isl_give isl_qpolynomial *isl_qpolynomial_zero(
1651 __isl_take isl_dim *dim);
1652 __isl_give isl_qpolynomial *isl_qpolynomial_one(
1653 __isl_take isl_dim *dim);
1654 __isl_give isl_qpolynomial *isl_qpolynomial_infty(
1655 __isl_take isl_dim *dim);
1656 __isl_give isl_qpolynomial *isl_qpolynomial_neginfty(
1657 __isl_take isl_dim *dim);
1658 __isl_give isl_qpolynomial *isl_qpolynomial_nan(
1659 __isl_take isl_dim *dim);
1660 __isl_give isl_qpolynomial *isl_qpolynomial_rat_cst(
1661 __isl_take isl_dim *dim,
1662 const isl_int n, const isl_int d);
1663 __isl_give isl_qpolynomial *isl_qpolynomial_div(
1664 __isl_take isl_div *div);
1665 __isl_give isl_qpolynomial *isl_qpolynomial_var(
1666 __isl_take isl_dim *dim,
1667 enum isl_dim_type type, unsigned pos);
1669 The zero piecewise quasipolynomial or a piecewise quasipolynomial
1670 with a single cell can be created using the following functions.
1671 Multiple of these single cell piecewise quasipolynomials can
1672 be combined to create more complicated piecewise quasipolynomials.
1674 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_zero(
1675 __isl_take isl_dim *dim);
1676 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_alloc(
1677 __isl_take isl_set *set,
1678 __isl_take isl_qpolynomial *qp);
1680 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_zero(
1681 __isl_take isl_dim *dim);
1682 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_from_pw_qpolynomial(
1683 __isl_take isl_pw_qpolynomial *pwqp);
1684 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_add_pw_qpolynomial(
1685 __isl_take isl_union_pw_qpolynomial *upwqp,
1686 __isl_take isl_pw_qpolynomial *pwqp);
1688 Quasipolynomials can be copied and freed again using the following
1691 __isl_give isl_qpolynomial *isl_qpolynomial_copy(
1692 __isl_keep isl_qpolynomial *qp);
1693 void isl_qpolynomial_free(__isl_take isl_qpolynomial *qp);
1695 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_copy(
1696 __isl_keep isl_pw_qpolynomial *pwqp);
1697 void isl_pw_qpolynomial_free(
1698 __isl_take isl_pw_qpolynomial *pwqp);
1700 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_copy(
1701 __isl_keep isl_union_pw_qpolynomial *upwqp);
1702 void isl_union_pw_qpolynomial_free(
1703 __isl_take isl_union_pw_qpolynomial *upwqp);
1705 =head3 Inspecting (Piecewise) Quasipolynomials
1707 To iterate over all piecewise quasipolynomials in a union
1708 piecewise quasipolynomial, use the following function
1710 int isl_union_pw_qpolynomial_foreach_pw_qpolynomial(
1711 __isl_keep isl_union_pw_qpolynomial *upwqp,
1712 int (*fn)(__isl_take isl_pw_qpolynomial *pwqp, void *user),
1715 To iterate over the cells in a piecewise quasipolynomial,
1716 use either of the following two functions
1718 int isl_pw_qpolynomial_foreach_piece(
1719 __isl_keep isl_pw_qpolynomial *pwqp,
1720 int (*fn)(__isl_take isl_set *set,
1721 __isl_take isl_qpolynomial *qp,
1722 void *user), void *user);
1723 int isl_pw_qpolynomial_foreach_lifted_piece(
1724 __isl_keep isl_pw_qpolynomial *pwqp,
1725 int (*fn)(__isl_take isl_set *set,
1726 __isl_take isl_qpolynomial *qp,
1727 void *user), void *user);
1729 As usual, the function C<fn> should return C<0> on success
1730 and C<-1> on failure. The difference between
1731 C<isl_pw_qpolynomial_foreach_piece> and
1732 C<isl_pw_qpolynomial_foreach_lifted_piece> is that
1733 C<isl_pw_qpolynomial_foreach_lifted_piece> will first
1734 compute unique representations for all existentially quantified
1735 variables and then turn these existentially quantified variables
1736 into extra set variables, adapting the associated quasipolynomial
1737 accordingly. This means that the C<set> passed to C<fn>
1738 will not have any existentially quantified variables, but that
1739 the dimensions of the sets may be different for different
1740 invocations of C<fn>.
1742 To iterate over all terms in a quasipolynomial,
1745 int isl_qpolynomial_foreach_term(
1746 __isl_keep isl_qpolynomial *qp,
1747 int (*fn)(__isl_take isl_term *term,
1748 void *user), void *user);
1750 The terms themselves can be inspected and freed using
1753 unsigned isl_term_dim(__isl_keep isl_term *term,
1754 enum isl_dim_type type);
1755 void isl_term_get_num(__isl_keep isl_term *term,
1757 void isl_term_get_den(__isl_keep isl_term *term,
1759 int isl_term_get_exp(__isl_keep isl_term *term,
1760 enum isl_dim_type type, unsigned pos);
1761 __isl_give isl_div *isl_term_get_div(
1762 __isl_keep isl_term *term, unsigned pos);
1763 void isl_term_free(__isl_take isl_term *term);
1765 Each term is a product of parameters, set variables and
1766 integer divisions. The function C<isl_term_get_exp>
1767 returns the exponent of a given dimensions in the given term.
1768 The C<isl_int>s in the arguments of C<isl_term_get_num>
1769 and C<isl_term_get_den> need to have been initialized
1770 using C<isl_int_init> before calling these functions.
1772 =head3 Properties of (Piecewise) Quasipolynomials
1774 To check whether a quasipolynomial is actually a constant,
1775 use the following function.
1777 int isl_qpolynomial_is_cst(__isl_keep isl_qpolynomial *qp,
1778 isl_int *n, isl_int *d);
1780 If C<qp> is a constant and if C<n> and C<d> are not C<NULL>
1781 then the numerator and denominator of the constant
1782 are returned in C<*n> and C<*d>, respectively.
1784 =head3 Operations on (Piecewise) Quasipolynomials
1786 __isl_give isl_qpolynomial *isl_qpolynomial_neg(
1787 __isl_take isl_qpolynomial *qp);
1788 __isl_give isl_qpolynomial *isl_qpolynomial_add(
1789 __isl_take isl_qpolynomial *qp1,
1790 __isl_take isl_qpolynomial *qp2);
1791 __isl_give isl_qpolynomial *isl_qpolynomial_sub(
1792 __isl_take isl_qpolynomial *qp1,
1793 __isl_take isl_qpolynomial *qp2);
1794 __isl_give isl_qpolynomial *isl_qpolynomial_mul(
1795 __isl_take isl_qpolynomial *qp1,
1796 __isl_take isl_qpolynomial *qp2);
1798 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_add(
1799 __isl_take isl_pw_qpolynomial *pwqp1,
1800 __isl_take isl_pw_qpolynomial *pwqp2);
1801 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_sub(
1802 __isl_take isl_pw_qpolynomial *pwqp1,
1803 __isl_take isl_pw_qpolynomial *pwqp2);
1804 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_add_disjoint(
1805 __isl_take isl_pw_qpolynomial *pwqp1,
1806 __isl_take isl_pw_qpolynomial *pwqp2);
1807 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_neg(
1808 __isl_take isl_pw_qpolynomial *pwqp);
1809 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_mul(
1810 __isl_take isl_pw_qpolynomial *pwqp1,
1811 __isl_take isl_pw_qpolynomial *pwqp2);
1813 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_add(
1814 __isl_take isl_union_pw_qpolynomial *upwqp1,
1815 __isl_take isl_union_pw_qpolynomial *upwqp2);
1816 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_sub(
1817 __isl_take isl_union_pw_qpolynomial *upwqp1,
1818 __isl_take isl_union_pw_qpolynomial *upwqp2);
1819 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_mul(
1820 __isl_take isl_union_pw_qpolynomial *upwqp1,
1821 __isl_take isl_union_pw_qpolynomial *upwqp2);
1823 __isl_give isl_qpolynomial *isl_pw_qpolynomial_eval(
1824 __isl_take isl_pw_qpolynomial *pwqp,
1825 __isl_take isl_point *pnt);
1827 __isl_give isl_qpolynomial *isl_union_pw_qpolynomial_eval(
1828 __isl_take isl_union_pw_qpolynomial *upwqp,
1829 __isl_take isl_point *pnt);
1831 __isl_give isl_set *isl_pw_qpolynomial_domain(
1832 __isl_take isl_pw_qpolynomial *pwqp);
1833 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_intersect_domain(
1834 __isl_take isl_pw_qpolynomial *pwpq,
1835 __isl_take isl_set *set);
1837 __isl_give isl_union_set *isl_union_pw_qpolynomial_domain(
1838 __isl_take isl_union_pw_qpolynomial *upwqp);
1839 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_intersect_domain(
1840 __isl_take isl_union_pw_qpolynomial *upwpq,
1841 __isl_take isl_union_set *uset);
1843 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_coalesce(
1844 __isl_take isl_union_pw_qpolynomial *upwqp);
1846 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_gist(
1847 __isl_take isl_pw_qpolynomial *pwqp,
1848 __isl_take isl_set *context);
1850 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_gist(
1851 __isl_take isl_union_pw_qpolynomial *upwqp,
1852 __isl_take isl_union_set *context);
1854 The gist operation applies the gist operation to each of
1855 the cells in the domain of the input piecewise quasipolynomial.
1856 In future, the operation will also exploit the context
1857 to simplify the quasipolynomials associated to each cell.
1859 =head2 Bounds on Piecewise Quasipolynomials and Piecewise Quasipolynomial Reductions
1861 A piecewise quasipolynomial reduction is a piecewise
1862 reduction (or fold) of quasipolynomials.
1863 In particular, the reduction can be maximum or a minimum.
1864 The objects are mainly used to represent the result of
1865 an upper or lower bound on a quasipolynomial over its domain,
1866 i.e., as the result of the following function.
1868 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_bound(
1869 __isl_take isl_pw_qpolynomial *pwqp,
1870 enum isl_fold type, int *tight);
1872 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_bound(
1873 __isl_take isl_union_pw_qpolynomial *upwqp,
1874 enum isl_fold type, int *tight);
1876 The C<type> argument may be either C<isl_fold_min> or C<isl_fold_max>.
1877 If C<tight> is not C<NULL>, then C<*tight> is set to C<1>
1878 is the returned bound is known be tight, i.e., for each value
1879 of the parameters there is at least
1880 one element in the domain that reaches the bound.
1881 If the domain of C<pwqp> is not wrapping, then the bound is computed
1882 over all elements in that domain and the result has a purely parametric
1883 domain. If the domain of C<pwqp> is wrapping, then the bound is
1884 computed over the range of the wrapped relation. The domain of the
1885 wrapped relation becomes the domain of the result.
1887 A (piecewise) quasipolynomial reduction can be copied or freed using the
1888 following functions.
1890 __isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_copy(
1891 __isl_keep isl_qpolynomial_fold *fold);
1892 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_copy(
1893 __isl_keep isl_pw_qpolynomial_fold *pwf);
1894 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_copy(
1895 __isl_keep isl_union_pw_qpolynomial_fold *upwf);
1896 void isl_qpolynomial_fold_free(
1897 __isl_take isl_qpolynomial_fold *fold);
1898 void isl_pw_qpolynomial_fold_free(
1899 __isl_take isl_pw_qpolynomial_fold *pwf);
1900 void isl_union_pw_qpolynomial_fold_free(
1901 __isl_take isl_union_pw_qpolynomial_fold *upwf);
1903 =head3 Printing Piecewise Quasipolynomial Reductions
1905 Piecewise quasipolynomial reductions can be printed
1906 using the following function.
1908 __isl_give isl_printer *isl_printer_print_pw_qpolynomial_fold(
1909 __isl_take isl_printer *p,
1910 __isl_keep isl_pw_qpolynomial_fold *pwf);
1911 __isl_give isl_printer *isl_printer_print_union_pw_qpolynomial_fold(
1912 __isl_take isl_printer *p,
1913 __isl_keep isl_union_pw_qpolynomial_fold *upwf);
1915 For C<isl_printer_print_pw_qpolynomial_fold>,
1916 output format of the printer
1917 needs to be set to either C<ISL_FORMAT_ISL> or C<ISL_FORMAT_C>.
1918 For C<isl_printer_print_union_pw_qpolynomial_fold>,
1919 output format of the printer
1920 needs to be set to either C<ISL_FORMAT_ISL>.
1922 =head3 Inspecting (Piecewise) Quasipolynomial Reductions
1924 To iterate over all piecewise quasipolynomial reductions in a union
1925 piecewise quasipolynomial reduction, use the following function
1927 int isl_union_pw_qpolynomial_fold_foreach_pw_qpolynomial_fold(
1928 __isl_keep isl_union_pw_qpolynomial_fold *upwf,
1929 int (*fn)(__isl_take isl_pw_qpolynomial_fold *pwf,
1930 void *user), void *user);
1932 To iterate over the cells in a piecewise quasipolynomial reduction,
1933 use either of the following two functions
1935 int isl_pw_qpolynomial_fold_foreach_piece(
1936 __isl_keep isl_pw_qpolynomial_fold *pwf,
1937 int (*fn)(__isl_take isl_set *set,
1938 __isl_take isl_qpolynomial_fold *fold,
1939 void *user), void *user);
1940 int isl_pw_qpolynomial_fold_foreach_lifted_piece(
1941 __isl_keep isl_pw_qpolynomial_fold *pwf,
1942 int (*fn)(__isl_take isl_set *set,
1943 __isl_take isl_qpolynomial_fold *fold,
1944 void *user), void *user);
1946 See L<Inspecting (Piecewise) Quasipolynomials> for an explanation
1947 of the difference between these two functions.
1949 To iterate over all quasipolynomials in a reduction, use
1951 int isl_qpolynomial_fold_foreach_qpolynomial(
1952 __isl_keep isl_qpolynomial_fold *fold,
1953 int (*fn)(__isl_take isl_qpolynomial *qp,
1954 void *user), void *user);
1956 =head3 Operations on Piecewise Quasipolynomial Reductions
1958 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_fold(
1959 __isl_take isl_pw_qpolynomial_fold *pwf1,
1960 __isl_take isl_pw_qpolynomial_fold *pwf2);
1962 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_fold(
1963 __isl_take isl_union_pw_qpolynomial_fold *upwf1,
1964 __isl_take isl_union_pw_qpolynomial_fold *upwf2);
1966 __isl_give isl_qpolynomial *isl_pw_qpolynomial_fold_eval(
1967 __isl_take isl_pw_qpolynomial_fold *pwf,
1968 __isl_take isl_point *pnt);
1970 __isl_give isl_qpolynomial *isl_union_pw_qpolynomial_fold_eval(
1971 __isl_take isl_union_pw_qpolynomial_fold *upwf,
1972 __isl_take isl_point *pnt);
1974 __isl_give isl_union_set *isl_union_pw_qpolynomial_fold_domain(
1975 __isl_take isl_union_pw_qpolynomial_fold *upwf);
1976 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_intersect_domain(
1977 __isl_take isl_union_pw_qpolynomial_fold *upwf,
1978 __isl_take isl_union_set *uset);
1980 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_coalesce(
1981 __isl_take isl_pw_qpolynomial_fold *pwf);
1983 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_coalesce(
1984 __isl_take isl_union_pw_qpolynomial_fold *upwf);
1986 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_gist(
1987 __isl_take isl_pw_qpolynomial_fold *pwf,
1988 __isl_take isl_set *context);
1990 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_gist(
1991 __isl_take isl_union_pw_qpolynomial_fold *upwf,
1992 __isl_take isl_union_set *context);
1994 The gist operation applies the gist operation to each of
1995 the cells in the domain of the input piecewise quasipolynomial reduction.
1996 In future, the operation will also exploit the context
1997 to simplify the quasipolynomial reductions associated to each cell.
1999 __isl_give isl_pw_qpolynomial_fold *
2000 isl_map_apply_pw_qpolynomial_fold(
2001 __isl_take isl_map *map,
2002 __isl_take isl_pw_qpolynomial_fold *pwf,
2004 __isl_give isl_union_pw_qpolynomial_fold *
2005 isl_union_map_apply_union_pw_qpolynomial_fold(
2006 __isl_take isl_union_map *umap,
2007 __isl_take isl_union_pw_qpolynomial_fold *upwf,
2011 compose the given map with the given piecewise quasipolynomial reduction.
2012 That is, compute a bound (of the same type as C<pwf> or C<upwf> itself)
2013 over all elements in the intersection of the range of the map
2014 and the domain of the piecewise quasipolynomial reduction
2015 as a function of an element in the domain of the map.
2017 =head2 Dependence Analysis
2019 C<isl> contains specialized functionality for performing
2020 array dataflow analysis. That is, given a I<sink> access relation
2021 and a collection of possible I<source> access relations,
2022 C<isl> can compute relations that describe
2023 for each iteration of the sink access, which iteration
2024 of which of the source access relations was the last
2025 to access the same data element before the given iteration
2027 To compute standard flow dependences, the sink should be
2028 a read, while the sources should be writes.
2029 If any of the source accesses are marked as being I<may>
2030 accesses, then there will be a dependence to the last
2031 I<must> access B<and> to any I<may> access that follows
2032 this last I<must> access.
2033 In particular, if I<all> sources are I<may> accesses,
2034 then memory based dependence analysis is performed.
2035 If, on the other hand, all sources are I<must> accesses,
2036 then value based dependence analysis is performed.
2038 #include <isl_flow.h>
2040 __isl_give isl_access_info *isl_access_info_alloc(
2041 __isl_take isl_map *sink,
2042 void *sink_user, isl_access_level_before fn,
2044 __isl_give isl_access_info *isl_access_info_add_source(
2045 __isl_take isl_access_info *acc,
2046 __isl_take isl_map *source, int must,
2049 __isl_give isl_flow *isl_access_info_compute_flow(
2050 __isl_take isl_access_info *acc);
2052 int isl_flow_foreach(__isl_keep isl_flow *deps,
2053 int (*fn)(__isl_take isl_map *dep, int must,
2054 void *dep_user, void *user),
2056 __isl_give isl_set *isl_flow_get_no_source(
2057 __isl_keep isl_flow *deps, int must);
2058 void isl_flow_free(__isl_take isl_flow *deps);
2060 The function C<isl_access_info_compute_flow> performs the actual
2061 dependence analysis. The other functions are used to construct
2062 the input for this function or to read off the output.
2064 The input is collected in an C<isl_access_info>, which can
2065 be created through a call to C<isl_access_info_alloc>.
2066 The arguments to this functions are the sink access relation
2067 C<sink>, a token C<sink_user> used to identify the sink
2068 access to the user, a callback function for specifying the
2069 relative order of source and sink accesses, and the number
2070 of source access relations that will be added.
2071 The callback function has type C<int (*)(void *first, void *second)>.
2072 The function is called with two user supplied tokens identifying
2073 either a source or the sink and it should return the shared nesting
2074 level and the relative order of the two accesses.
2075 In particular, let I<n> be the number of loops shared by
2076 the two accesses. If C<first> precedes C<second> textually,
2077 then the function should return I<2 * n + 1>; otherwise,
2078 it should return I<2 * n>.
2079 The sources can be added to the C<isl_access_info> by performing
2080 (at most) C<max_source> calls to C<isl_access_info_add_source>.
2081 C<must> indicates whether the source is a I<must> access
2082 or a I<may> access. Note that a multi-valued access relation
2083 should only be marked I<must> if every iteration in the domain
2084 of the relation accesses I<all> elements in its image.
2085 The C<source_user> token is again used to identify
2086 the source access. The range of the source access relation
2087 C<source> should have the same dimension as the range
2088 of the sink access relation.
2090 The result of the dependence analysis is collected in an
2091 C<isl_flow>. There may be elements in the domain of
2092 the sink access for which no preceding source access could be
2093 found or for which all preceding sources are I<may> accesses.
2094 The sets of these elements can be obtained through
2095 calls to C<isl_flow_get_no_source>, the first with C<must> set
2096 and the second with C<must> unset.
2097 In the case of standard flow dependence analysis,
2098 with the sink a read and the sources I<must> writes,
2099 the first set corresponds to the reads from uninitialized
2100 array elements and the second set is empty.
2101 The actual flow dependences can be extracted using
2102 C<isl_flow_foreach>. This function will call the user-specified
2103 callback function C<fn> for each B<non-empty> dependence between
2104 a source and the sink. The callback function is called
2105 with four arguments, the actual flow dependence relation
2106 mapping source iterations to sink iterations, a boolean that
2107 indicates whether it is a I<must> or I<may> dependence, a token
2108 identifying the source and an additional C<void *> with value
2109 equal to the third argument of the C<isl_flow_foreach> call.
2110 A dependence is marked I<must> if it originates from a I<must>
2111 source and if it is not followed by any I<may> sources.
2113 After finishing with an C<isl_flow>, the user should call
2114 C<isl_flow_free> to free all associated memory.
2116 =head2 Parametric Vertex Enumeration
2118 The parametric vertex enumeration described in this section
2119 is mainly intended to be used internally and by the C<barvinok>
2122 #include <isl_vertices.h>
2123 __isl_give isl_vertices *isl_basic_set_compute_vertices(
2124 __isl_keep isl_basic_set *bset);
2126 The function C<isl_basic_set_compute_vertices> performs the
2127 actual computation of the parametric vertices and the chamber
2128 decomposition and store the result in an C<isl_vertices> object.
2129 This information can be queried by either iterating over all
2130 the vertices or iterating over all the chambers or cells
2131 and then iterating over all vertices that are active on the chamber.
2133 int isl_vertices_foreach_vertex(
2134 __isl_keep isl_vertices *vertices,
2135 int (*fn)(__isl_take isl_vertex *vertex, void *user),
2138 int isl_vertices_foreach_cell(
2139 __isl_keep isl_vertices *vertices,
2140 int (*fn)(__isl_take isl_cell *cell, void *user),
2142 int isl_cell_foreach_vertex(__isl_keep isl_cell *cell,
2143 int (*fn)(__isl_take isl_vertex *vertex, void *user),
2146 Other operations that can be performed on an C<isl_vertices> object are
2149 isl_ctx *isl_vertices_get_ctx(
2150 __isl_keep isl_vertices *vertices);
2151 int isl_vertices_get_n_vertices(
2152 __isl_keep isl_vertices *vertices);
2153 void isl_vertices_free(__isl_take isl_vertices *vertices);
2155 Vertices can be inspected and destroyed using the following functions.
2157 isl_ctx *isl_vertex_get_ctx(__isl_keep isl_vertex *vertex);
2158 int isl_vertex_get_id(__isl_keep isl_vertex *vertex);
2159 __isl_give isl_basic_set *isl_vertex_get_domain(
2160 __isl_keep isl_vertex *vertex);
2161 __isl_give isl_basic_set *isl_vertex_get_expr(
2162 __isl_keep isl_vertex *vertex);
2163 void isl_vertex_free(__isl_take isl_vertex *vertex);
2165 C<isl_vertex_get_expr> returns a singleton parametric set describing
2166 the vertex, while C<isl_vertex_get_domain> returns the activity domain
2168 Note that C<isl_vertex_get_domain> and C<isl_vertex_get_expr> return
2169 B<rational> basic sets, so they should mainly be used for inspection
2170 and should not be mixed with integer sets.
2172 Chambers can be inspected and destroyed using the following functions.
2174 isl_ctx *isl_cell_get_ctx(__isl_keep isl_cell *cell);
2175 __isl_give isl_basic_set *isl_cell_get_domain(
2176 __isl_keep isl_cell *cell);
2177 void isl_cell_free(__isl_take isl_cell *cell);
2181 Although C<isl> is mainly meant to be used as a library,
2182 it also contains some basic applications that use some
2183 of the functionality of C<isl>.
2184 The input may be specified in either the L<isl format>
2185 or the L<PolyLib format>.
2187 =head2 C<isl_polyhedron_sample>
2189 C<isl_polyhedron_sample> takes a polyhedron as input and prints
2190 an integer element of the polyhedron, if there is any.
2191 The first column in the output is the denominator and is always
2192 equal to 1. If the polyhedron contains no integer points,
2193 then a vector of length zero is printed.
2197 C<isl_pip> takes the same input as the C<example> program
2198 from the C<piplib> distribution, i.e., a set of constraints
2199 on the parameters, a line containing only -1 and finally a set
2200 of constraints on a parametric polyhedron.
2201 The coefficients of the parameters appear in the last columns
2202 (but before the final constant column).
2203 The output is the lexicographic minimum of the parametric polyhedron.
2204 As C<isl> currently does not have its own output format, the output
2205 is just a dump of the internal state.
2207 =head2 C<isl_polyhedron_minimize>
2209 C<isl_polyhedron_minimize> computes the minimum of some linear
2210 or affine objective function over the integer points in a polyhedron.
2211 If an affine objective function
2212 is given, then the constant should appear in the last column.
2214 =head2 C<isl_polytope_scan>
2216 Given a polytope, C<isl_polytope_scan> prints
2217 all integer points in the polytope.
2219 =head1 C<isl-polylib>
2221 The C<isl-polylib> library provides the following functions for converting
2222 between C<isl> objects and C<PolyLib> objects.
2223 The library is distributed separately for licensing reasons.
2225 #include <isl_set_polylib.h>
2226 __isl_give isl_basic_set *isl_basic_set_new_from_polylib(
2227 Polyhedron *P, __isl_take isl_dim *dim);
2228 Polyhedron *isl_basic_set_to_polylib(
2229 __isl_keep isl_basic_set *bset);
2230 __isl_give isl_set *isl_set_new_from_polylib(Polyhedron *D,
2231 __isl_take isl_dim *dim);
2232 Polyhedron *isl_set_to_polylib(__isl_keep isl_set *set);
2234 #include <isl_map_polylib.h>
2235 __isl_give isl_basic_map *isl_basic_map_new_from_polylib(
2236 Polyhedron *P, __isl_take isl_dim *dim);
2237 __isl_give isl_map *isl_map_new_from_polylib(Polyhedron *D,
2238 __isl_take isl_dim *dim);
2239 Polyhedron *isl_basic_map_to_polylib(
2240 __isl_keep isl_basic_map *bmap);
2241 Polyhedron *isl_map_to_polylib(__isl_keep isl_map *map);
projects / platform / upstream / isl.git / blob