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_set_gmp(r,g)
210 =item isl_int_get_gmp(i,g)
212 =item isl_int_abs(r,i)
214 =item isl_int_neg(r,i)
216 =item isl_int_swap(i,j)
218 =item isl_int_swap_or_set(i,j)
220 =item isl_int_add_ui(r,i,j)
222 =item isl_int_sub_ui(r,i,j)
224 =item isl_int_add(r,i,j)
226 =item isl_int_sub(r,i,j)
228 =item isl_int_mul(r,i,j)
230 =item isl_int_mul_ui(r,i,j)
232 =item isl_int_addmul(r,i,j)
234 =item isl_int_submul(r,i,j)
236 =item isl_int_gcd(r,i,j)
238 =item isl_int_lcm(r,i,j)
240 =item isl_int_divexact(r,i,j)
242 =item isl_int_cdiv_q(r,i,j)
244 =item isl_int_fdiv_q(r,i,j)
246 =item isl_int_fdiv_r(r,i,j)
248 =item isl_int_fdiv_q_ui(r,i,j)
250 =item isl_int_read(r,s)
252 =item isl_int_print(out,i,width)
256 =item isl_int_cmp(i,j)
258 =item isl_int_cmp_si(i,si)
260 =item isl_int_eq(i,j)
262 =item isl_int_ne(i,j)
264 =item isl_int_lt(i,j)
266 =item isl_int_le(i,j)
268 =item isl_int_gt(i,j)
270 =item isl_int_ge(i,j)
272 =item isl_int_abs_eq(i,j)
274 =item isl_int_abs_ne(i,j)
276 =item isl_int_abs_lt(i,j)
278 =item isl_int_abs_gt(i,j)
280 =item isl_int_abs_ge(i,j)
282 =item isl_int_is_zero(i)
284 =item isl_int_is_one(i)
286 =item isl_int_is_negone(i)
288 =item isl_int_is_pos(i)
290 =item isl_int_is_neg(i)
292 =item isl_int_is_nonpos(i)
294 =item isl_int_is_nonneg(i)
296 =item isl_int_is_divisible_by(i,j)
300 =head2 Sets and Relations
302 C<isl> uses six types of objects for representing sets and relations,
303 C<isl_basic_set>, C<isl_basic_map>, C<isl_set>, C<isl_map>,
304 C<isl_union_set> and C<isl_union_map>.
305 C<isl_basic_set> and C<isl_basic_map> represent sets and relations that
306 can be described as a conjunction of affine constraints, while
307 C<isl_set> and C<isl_map> represent unions of
308 C<isl_basic_set>s and C<isl_basic_map>s, respectively.
309 However, all C<isl_basic_set>s or C<isl_basic_map>s in the union need
310 to have the same dimension. C<isl_union_set>s and C<isl_union_map>s
311 represent unions of C<isl_set>s or C<isl_map>s of I<different> dimensions,
312 where dimensions with different space names
313 (see L<Dimension Specifications>) are considered different as well.
314 The difference between sets and relations (maps) is that sets have
315 one set of variables, while relations have two sets of variables,
316 input variables and output variables.
318 =head2 Memory Management
320 Since a high-level operation on sets and/or relations usually involves
321 several substeps and since the user is usually not interested in
322 the intermediate results, most functions that return a new object
323 will also release all the objects passed as arguments.
324 If the user still wants to use one or more of these arguments
325 after the function call, she should pass along a copy of the
326 object rather than the object itself.
327 The user is then responsible for make sure that the original
328 object gets used somewhere else or is explicitly freed.
330 The arguments and return values of all documents functions are
331 annotated to make clear which arguments are released and which
332 arguments are preserved. In particular, the following annotations
339 C<__isl_give> means that a new object is returned.
340 The user should make sure that the returned pointer is
341 used exactly once as a value for an C<__isl_take> argument.
342 In between, it can be used as a value for as many
343 C<__isl_keep> arguments as the user likes.
344 There is one exception, and that is the case where the
345 pointer returned is C<NULL>. Is this case, the user
346 is free to use it as an C<__isl_take> argument or not.
350 C<__isl_take> means that the object the argument points to
351 is taken over by the function and may no longer be used
352 by the user as an argument to any other function.
353 The pointer value must be one returned by a function
354 returning an C<__isl_give> pointer.
355 If the user passes in a C<NULL> value, then this will
356 be treated as an error in the sense that the function will
357 not perform its usual operation. However, it will still
358 make sure that all the the other C<__isl_take> arguments
363 C<__isl_keep> means that the function will only use the object
364 temporarily. After the function has finished, the user
365 can still use it as an argument to other functions.
366 A C<NULL> value will be treated in the same way as
367 a C<NULL> value for an C<__isl_take> argument.
371 =head2 Dimension Specifications
373 Whenever a new set or relation is created from scratch,
374 its dimension needs to be specified using an C<isl_dim>.
377 __isl_give isl_dim *isl_dim_alloc(isl_ctx *ctx,
378 unsigned nparam, unsigned n_in, unsigned n_out);
379 __isl_give isl_dim *isl_dim_set_alloc(isl_ctx *ctx,
380 unsigned nparam, unsigned dim);
381 __isl_give isl_dim *isl_dim_copy(__isl_keep isl_dim *dim);
382 void isl_dim_free(__isl_take isl_dim *dim);
383 unsigned isl_dim_size(__isl_keep isl_dim *dim,
384 enum isl_dim_type type);
386 The dimension specification used for creating a set
387 needs to be created using C<isl_dim_set_alloc>, while
388 that for creating a relation
389 needs to be created using C<isl_dim_alloc>.
390 C<isl_dim_size> can be used
391 to find out the number of dimensions of each type in
392 a dimension specification, where type may be
393 C<isl_dim_param>, C<isl_dim_in> (only for relations),
394 C<isl_dim_out> (only for relations), C<isl_dim_set>
395 (only for sets) or C<isl_dim_all>.
397 It is often useful to create objects that live in the
398 same space as some other object. This can be accomplished
399 by creating the new objects
400 (see L<Creating New Sets and Relations> or
401 L<Creating New (Piecewise) Quasipolynomials>) based on the dimension
402 specification of the original object.
405 __isl_give isl_dim *isl_basic_set_get_dim(
406 __isl_keep isl_basic_set *bset);
407 __isl_give isl_dim *isl_set_get_dim(__isl_keep isl_set *set);
409 #include <isl_union_set.h>
410 __isl_give isl_dim *isl_union_set_get_dim(
411 __isl_keep isl_union_set *uset);
414 __isl_give isl_dim *isl_basic_map_get_dim(
415 __isl_keep isl_basic_map *bmap);
416 __isl_give isl_dim *isl_map_get_dim(__isl_keep isl_map *map);
418 #include <isl_union_map.h>
419 __isl_give isl_dim *isl_union_map_get_dim(
420 __isl_keep isl_union_map *umap);
422 #include <isl_polynomial.h>
423 __isl_give isl_dim *isl_qpolynomial_get_dim(
424 __isl_keep isl_qpolynomial *qp);
425 __isl_give isl_dim *isl_pw_qpolynomial_get_dim(
426 __isl_keep isl_pw_qpolynomial *pwqp);
427 __isl_give isl_dim *isl_union_pw_qpolynomial_get_dim(
428 __isl_keep isl_union_pw_qpolynomial *upwqp);
429 __isl_give isl_dim *isl_union_pw_qpolynomial_fold_get_dim(
430 __isl_keep isl_union_pw_qpolynomial_fold *upwf);
432 The names of the individual dimensions may be set or read off
433 using the following functions.
436 __isl_give isl_dim *isl_dim_set_name(__isl_take isl_dim *dim,
437 enum isl_dim_type type, unsigned pos,
438 __isl_keep const char *name);
439 __isl_keep const char *isl_dim_get_name(__isl_keep isl_dim *dim,
440 enum isl_dim_type type, unsigned pos);
442 Note that C<isl_dim_get_name> returns a pointer to some internal
443 data structure, so the result can only be used while the
444 corresponding C<isl_dim> is alive.
445 Also note that every function that operates on two sets or relations
446 requires that both arguments have the same parameters. This also
447 means that if one of the arguments has named parameters, then the
448 other needs to have named parameters too and the names need to match.
449 Pairs of C<isl_union_set> and/or C<isl_union_map> arguments may
450 have different parameters (as long as they are named), in which case
451 the result will have as parameters the union of the parameters of
454 The names of entire spaces may be set or read off
455 using the following functions.
458 __isl_give isl_dim *isl_dim_set_tuple_name(
459 __isl_take isl_dim *dim,
460 enum isl_dim_type type, const char *s);
461 const char *isl_dim_get_tuple_name(__isl_keep isl_dim *dim,
462 enum isl_dim_type type);
464 The C<dim> argument needs to be one of C<isl_dim_in>, C<isl_dim_out>
465 or C<isl_dim_set>. As with C<isl_dim_get_name>,
466 the C<isl_dim_get_tuple_name> function returns a pointer to some internal
468 Binary operations require the corresponding spaces of their arguments
469 to have the same name.
471 Spaces can be nested. In particular, the domain of a set or
472 the domain or range of a relation can be a nested relation.
473 The following functions can be used to construct and deconstruct
474 such nested dimension specifications.
477 int isl_dim_is_wrapping(__isl_keep isl_dim *dim);
478 __isl_give isl_dim *isl_dim_wrap(__isl_take isl_dim *dim);
479 __isl_give isl_dim *isl_dim_unwrap(__isl_take isl_dim *dim);
481 The input to C<isl_dim_is_wrapping> and C<isl_dim_unwrap> should
482 be the dimension specification of a set, while that of
483 C<isl_dim_wrap> should be the dimension specification of a relation.
484 Conversely, the output of C<isl_dim_unwrap> is the dimension specification
485 of a relation, while that of C<isl_dim_wrap> is the dimension specification
488 Dimension specifications can be created from other dimension
489 specifications using the following functions.
491 __isl_give isl_dim *isl_dim_domain(__isl_take isl_dim *dim);
492 __isl_give isl_dim *isl_dim_from_domain(__isl_take isl_dim *dim);
493 __isl_give isl_dim *isl_dim_range(__isl_take isl_dim *dim);
494 __isl_give isl_dim *isl_dim_from_range(__isl_take isl_dim *dim);
495 __isl_give isl_dim *isl_dim_reverse(__isl_take isl_dim *dim);
496 __isl_give isl_dim *isl_dim_join(__isl_take isl_dim *left,
497 __isl_take isl_dim *right);
498 __isl_give isl_dim *isl_dim_insert(__isl_take isl_dim *dim,
499 enum isl_dim_type type, unsigned pos, unsigned n);
500 __isl_give isl_dim *isl_dim_add(__isl_take isl_dim *dim,
501 enum isl_dim_type type, unsigned n);
502 __isl_give isl_dim *isl_dim_drop(__isl_take isl_dim *dim,
503 enum isl_dim_type type, unsigned first, unsigned n);
505 Note that if dimensions are added or removed from a space, then
506 the name and the internal structure are lost.
508 =head2 Input and Output
510 C<isl> supports its own input/output format, which is similar
511 to the C<Omega> format, but also supports the C<PolyLib> format
516 The C<isl> format is similar to that of C<Omega>, but has a different
517 syntax for describing the parameters and allows for the definition
518 of an existentially quantified variable as the integer division
519 of an affine expression.
520 For example, the set of integers C<i> between C<0> and C<n>
521 such that C<i % 10 <= 6> can be described as
523 [n] -> { [i] : exists (a = [i/10] : 0 <= i and i <= n and
526 A set or relation can have several disjuncts, separated
527 by the keyword C<or>. Each disjunct is either a conjunction
528 of constraints or a projection (C<exists>) of a conjunction
529 of constraints. The constraints are separated by the keyword
532 =head3 C<PolyLib> format
534 If the represented set is a union, then the first line
535 contains a single number representing the number of disjuncts.
536 Otherwise, a line containing the number C<1> is optional.
538 Each disjunct is represented by a matrix of constraints.
539 The first line contains two numbers representing
540 the number of rows and columns,
541 where the number of rows is equal to the number of constraints
542 and the number of columns is equal to two plus the number of variables.
543 The following lines contain the actual rows of the constraint matrix.
544 In each row, the first column indicates whether the constraint
545 is an equality (C<0>) or inequality (C<1>). The final column
546 corresponds to the constant term.
548 If the set is parametric, then the coefficients of the parameters
549 appear in the last columns before the constant column.
550 The coefficients of any existentially quantified variables appear
551 between those of the set variables and those of the parameters.
556 __isl_give isl_basic_set *isl_basic_set_read_from_file(
557 isl_ctx *ctx, FILE *input, int nparam);
558 __isl_give isl_basic_set *isl_basic_set_read_from_str(
559 isl_ctx *ctx, const char *str, int nparam);
560 __isl_give isl_set *isl_set_read_from_file(isl_ctx *ctx,
561 FILE *input, int nparam);
562 __isl_give isl_set *isl_set_read_from_str(isl_ctx *ctx,
563 const char *str, int nparam);
566 __isl_give isl_basic_map *isl_basic_map_read_from_file(
567 isl_ctx *ctx, FILE *input, int nparam);
568 __isl_give isl_basic_map *isl_basic_map_read_from_str(
569 isl_ctx *ctx, const char *str, int nparam);
570 __isl_give isl_map *isl_map_read_from_file(
571 struct isl_ctx *ctx, FILE *input, int nparam);
572 __isl_give isl_map *isl_map_read_from_str(isl_ctx *ctx,
573 const char *str, int nparam);
575 The input format is autodetected and may be either the C<PolyLib> format
576 or the C<isl> format.
577 C<nparam> specifies how many of the final columns in
578 the C<PolyLib> format correspond to parameters.
579 If input is given in the C<isl> format, then the number
580 of parameters needs to be equal to C<nparam>.
581 If C<nparam> is negative, then any number of parameters
582 is accepted in the C<isl> format and zero parameters
583 are assumed in the C<PolyLib> format.
587 Before anything can be printed, an C<isl_printer> needs to
590 __isl_give isl_printer *isl_printer_to_file(isl_ctx *ctx,
592 __isl_give isl_printer *isl_printer_to_str(isl_ctx *ctx);
593 void isl_printer_free(__isl_take isl_printer *printer);
594 __isl_give char *isl_printer_get_str(
595 __isl_keep isl_printer *printer);
597 The behavior of the printer can be modified in various ways
599 __isl_give isl_printer *isl_printer_set_output_format(
600 __isl_take isl_printer *p, int output_format);
601 __isl_give isl_printer *isl_printer_set_indent(
602 __isl_take isl_printer *p, int indent);
603 __isl_give isl_printer *isl_printer_set_prefix(
604 __isl_take isl_printer *p, const char *prefix);
605 __isl_give isl_printer *isl_printer_set_suffix(
606 __isl_take isl_printer *p, const char *suffix);
608 The C<output_format> may be either C<ISL_FORMAT_ISL>, C<ISL_FORMAT_OMEGA>
609 or C<ISL_FORMAT_POLYLIB> and defaults to C<ISL_FORMAT_ISL>.
610 Each line in the output is indented by C<indent> spaces
611 (default: 0), prefixed by C<prefix> and suffixed by C<suffix>.
612 In the C<PolyLib> format output,
613 the coefficients of the existentially quantified variables
614 appear between those of the set variables and those
617 To actually print something, use
620 __isl_give isl_printer *isl_printer_print_basic_set(
621 __isl_take isl_printer *printer,
622 __isl_keep isl_basic_set *bset);
623 __isl_give isl_printer *isl_printer_print_set(
624 __isl_take isl_printer *printer,
625 __isl_keep isl_set *set);
628 __isl_give isl_printer *isl_printer_print_basic_map(
629 __isl_take isl_printer *printer,
630 __isl_keep isl_basic_map *bmap);
631 __isl_give isl_printer *isl_printer_print_map(
632 __isl_take isl_printer *printer,
633 __isl_keep isl_map *map);
635 #include <isl_union_set.h>
636 __isl_give isl_printer *isl_printer_print_union_set(
637 __isl_take isl_printer *p,
638 __isl_keep isl_union_set *uset);
640 #include <isl_union_map.h>
641 __isl_give isl_printer *isl_printer_print_union_map(
642 __isl_take isl_printer *p,
643 __isl_keep isl_union_map *umap);
645 When called on a file printer, the following function flushes
646 the file. When called on a string printer, the buffer is cleared.
648 __isl_give isl_printer *isl_printer_flush(
649 __isl_take isl_printer *p);
651 =head2 Creating New Sets and Relations
653 C<isl> has functions for creating some standard sets and relations.
657 =item * Empty sets and relations
659 __isl_give isl_basic_set *isl_basic_set_empty(
660 __isl_take isl_dim *dim);
661 __isl_give isl_basic_map *isl_basic_map_empty(
662 __isl_take isl_dim *dim);
663 __isl_give isl_set *isl_set_empty(
664 __isl_take isl_dim *dim);
665 __isl_give isl_map *isl_map_empty(
666 __isl_take isl_dim *dim);
667 __isl_give isl_union_set *isl_union_set_empty(
668 __isl_take isl_dim *dim);
669 __isl_give isl_union_map *isl_union_map_empty(
670 __isl_take isl_dim *dim);
672 For C<isl_union_set>s and C<isl_union_map>s, the dimensions specification
673 is only used to specify the parameters.
675 =item * Universe sets and relations
677 __isl_give isl_basic_set *isl_basic_set_universe(
678 __isl_take isl_dim *dim);
679 __isl_give isl_basic_map *isl_basic_map_universe(
680 __isl_take isl_dim *dim);
681 __isl_give isl_set *isl_set_universe(
682 __isl_take isl_dim *dim);
683 __isl_give isl_map *isl_map_universe(
684 __isl_take isl_dim *dim);
686 =item * Identity relations
688 __isl_give isl_basic_map *isl_basic_map_identity(
689 __isl_take isl_dim *set_dim);
690 __isl_give isl_map *isl_map_identity(
691 __isl_take isl_dim *set_dim);
693 These functions take a dimension specification for a B<set>
694 and return an identity relation between two such sets.
696 =item * Lexicographic order
698 __isl_give isl_map *isl_map_lex_lt(
699 __isl_take isl_dim *set_dim);
700 __isl_give isl_map *isl_map_lex_le(
701 __isl_take isl_dim *set_dim);
702 __isl_give isl_map *isl_map_lex_gt(
703 __isl_take isl_dim *set_dim);
704 __isl_give isl_map *isl_map_lex_ge(
705 __isl_take isl_dim *set_dim);
706 __isl_give isl_map *isl_map_lex_lt_first(
707 __isl_take isl_dim *dim, unsigned n);
708 __isl_give isl_map *isl_map_lex_le_first(
709 __isl_take isl_dim *dim, unsigned n);
710 __isl_give isl_map *isl_map_lex_gt_first(
711 __isl_take isl_dim *dim, unsigned n);
712 __isl_give isl_map *isl_map_lex_ge_first(
713 __isl_take isl_dim *dim, unsigned n);
715 The first four functions take a dimension specification for a B<set>
716 and return relations that express that the elements in the domain
717 are lexicographically less
718 (C<isl_map_lex_lt>), less or equal (C<isl_map_lex_le>),
719 greater (C<isl_map_lex_gt>) or greater or equal (C<isl_map_lex_ge>)
720 than the elements in the range.
721 The last four functions take a dimension specification for a map
722 and return relations that express that the first C<n> dimensions
723 in the domain are lexicographically less
724 (C<isl_map_lex_lt_first>), less or equal (C<isl_map_lex_le_first>),
725 greater (C<isl_map_lex_gt_first>) or greater or equal (C<isl_map_lex_ge_first>)
726 than the first C<n> dimensions in the range.
730 A basic set or relation can be converted to a set or relation
731 using the following functions.
733 __isl_give isl_set *isl_set_from_basic_set(
734 __isl_take isl_basic_set *bset);
735 __isl_give isl_map *isl_map_from_basic_map(
736 __isl_take isl_basic_map *bmap);
738 Sets and relations can be converted to union sets and relations
739 using the following functions.
741 __isl_give isl_union_map *isl_union_map_from_map(
742 __isl_take isl_map *map);
743 __isl_give isl_union_set *isl_union_set_from_set(
744 __isl_take isl_set *set);
746 Sets and relations can be copied and freed again using the following
749 __isl_give isl_basic_set *isl_basic_set_copy(
750 __isl_keep isl_basic_set *bset);
751 __isl_give isl_set *isl_set_copy(__isl_keep isl_set *set);
752 __isl_give isl_union_set *isl_union_set_copy(
753 __isl_keep isl_union_set *uset);
754 __isl_give isl_basic_map *isl_basic_map_copy(
755 __isl_keep isl_basic_map *bmap);
756 __isl_give isl_map *isl_map_copy(__isl_keep isl_map *map);
757 __isl_give isl_union_map *isl_union_map_copy(
758 __isl_keep isl_union_map *umap);
759 void isl_basic_set_free(__isl_take isl_basic_set *bset);
760 void isl_set_free(__isl_take isl_set *set);
761 void isl_union_set_free(__isl_take isl_union_set *uset);
762 void isl_basic_map_free(__isl_take isl_basic_map *bmap);
763 void isl_map_free(__isl_take isl_map *map);
764 void isl_union_map_free(__isl_take isl_union_map *umap);
766 Other sets and relations can be constructed by starting
767 from a universe set or relation, adding equality and/or
768 inequality constraints and then projecting out the
769 existentially quantified variables, if any.
770 Constraints can be constructed, manipulated and
771 added to basic sets and relations using the following functions.
773 #include <isl_constraint.h>
774 __isl_give isl_constraint *isl_equality_alloc(
775 __isl_take isl_dim *dim);
776 __isl_give isl_constraint *isl_inequality_alloc(
777 __isl_take isl_dim *dim);
778 void isl_constraint_set_constant(
779 __isl_keep isl_constraint *constraint, isl_int v);
780 void isl_constraint_set_coefficient(
781 __isl_keep isl_constraint *constraint,
782 enum isl_dim_type type, int pos, isl_int v);
783 __isl_give isl_basic_map *isl_basic_map_add_constraint(
784 __isl_take isl_basic_map *bmap,
785 __isl_take isl_constraint *constraint);
786 __isl_give isl_basic_set *isl_basic_set_add_constraint(
787 __isl_take isl_basic_set *bset,
788 __isl_take isl_constraint *constraint);
790 For example, to create a set containing the even integers
791 between 10 and 42, you would use the following code.
795 struct isl_constraint *c;
796 struct isl_basic_set *bset;
799 dim = isl_dim_set_alloc(ctx, 0, 2);
800 bset = isl_basic_set_universe(isl_dim_copy(dim));
802 c = isl_equality_alloc(isl_dim_copy(dim));
803 isl_int_set_si(v, -1);
804 isl_constraint_set_coefficient(c, isl_dim_set, 0, v);
805 isl_int_set_si(v, 2);
806 isl_constraint_set_coefficient(c, isl_dim_set, 1, v);
807 bset = isl_basic_set_add_constraint(bset, c);
809 c = isl_inequality_alloc(isl_dim_copy(dim));
810 isl_int_set_si(v, -10);
811 isl_constraint_set_constant(c, v);
812 isl_int_set_si(v, 1);
813 isl_constraint_set_coefficient(c, isl_dim_set, 0, v);
814 bset = isl_basic_set_add_constraint(bset, c);
816 c = isl_inequality_alloc(dim);
817 isl_int_set_si(v, 42);
818 isl_constraint_set_constant(c, v);
819 isl_int_set_si(v, -1);
820 isl_constraint_set_coefficient(c, isl_dim_set, 0, v);
821 bset = isl_basic_set_add_constraint(bset, c);
823 bset = isl_basic_set_project_out(bset, isl_dim_set, 1, 1);
829 struct isl_basic_set *bset;
830 bset = isl_basic_set_read_from_str(ctx,
831 "{[i] : exists (a : i = 2a and i >= 10 and i <= 42)}", -1);
833 A basic set or relation can also be constructed from two matrices
834 describing the equalities and the inequalities.
836 __isl_give isl_basic_set *isl_basic_set_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);
842 __isl_give isl_basic_map *isl_basic_map_from_constraint_matrices(
843 __isl_take isl_dim *dim,
844 __isl_take isl_mat *eq, __isl_take isl_mat *ineq,
845 enum isl_dim_type c1,
846 enum isl_dim_type c2, enum isl_dim_type c3,
847 enum isl_dim_type c4, enum isl_dim_type c5);
849 The C<isl_dim_type> arguments indicate the order in which
850 different kinds of variables appear in the input matrices
851 and should be a permutation of C<isl_dim_cst>, C<isl_dim_param>,
852 C<isl_dim_set> and C<isl_dim_div> for sets and
853 of C<isl_dim_cst>, C<isl_dim_param>,
854 C<isl_dim_in>, C<isl_dim_out> and C<isl_dim_div> for relations.
856 =head2 Inspecting Sets and Relations
858 Usually, the user should not have to care about the actual constraints
859 of the sets and maps, but should instead apply the abstract operations
860 explained in the following sections.
861 Occasionally, however, it may be required to inspect the individual
862 coefficients of the constraints. This section explains how to do so.
863 In these cases, it may also be useful to have C<isl> compute
864 an explicit representation of the existentially quantified variables.
866 __isl_give isl_set *isl_set_compute_divs(
867 __isl_take isl_set *set);
868 __isl_give isl_map *isl_map_compute_divs(
869 __isl_take isl_map *map);
870 __isl_give isl_union_set *isl_union_set_compute_divs(
871 __isl_take isl_union_set *uset);
872 __isl_give isl_union_map *isl_union_map_compute_divs(
873 __isl_take isl_union_map *umap);
875 This explicit representation defines the existentially quantified
876 variables as integer divisions of the other variables, possibly
877 including earlier existentially quantified variables.
878 An explicitly represented existentially quantified variable therefore
879 has a unique value when the values of the other variables are known.
880 If, furthermore, the same existentials, i.e., existentials
881 with the same explicit representations, should appear in the
882 same order in each of the disjuncts of a set or map, then the user should call
883 either of the following functions.
885 __isl_give isl_set *isl_set_align_divs(
886 __isl_take isl_set *set);
887 __isl_give isl_map *isl_map_align_divs(
888 __isl_take isl_map *map);
890 Alternatively, the existentially quantified variables can be removed
891 using the following functions, which compute an overapproximation.
893 __isl_give isl_basic_set *isl_basic_set_remove_divs(
894 __isl_take isl_basic_set *bset);
895 __isl_give isl_basic_map *isl_basic_map_remove_divs(
896 __isl_take isl_basic_map *bmap);
897 __isl_give isl_set *isl_set_remove_divs(
898 __isl_take isl_set *set);
900 To iterate over all the sets or maps in a union set or map, use
902 int isl_union_set_foreach_set(__isl_keep isl_union_set *uset,
903 int (*fn)(__isl_take isl_set *set, void *user),
905 int isl_union_map_foreach_map(__isl_keep isl_union_map *umap,
906 int (*fn)(__isl_take isl_map *map, void *user),
909 The number of sets or maps in a union set or map can be obtained
912 int isl_union_set_n_set(__isl_keep isl_union_set *uset);
913 int isl_union_map_n_map(__isl_keep isl_union_map *umap);
915 To extract the set or map from a union with a given dimension
918 __isl_give isl_set *isl_union_set_extract_set(
919 __isl_keep isl_union_set *uset,
920 __isl_take isl_dim *dim);
921 __isl_give isl_map *isl_union_map_extract_map(
922 __isl_keep isl_union_map *umap,
923 __isl_take isl_dim *dim);
925 To iterate over all the basic sets or maps in a set or map, use
927 int isl_set_foreach_basic_set(__isl_keep isl_set *set,
928 int (*fn)(__isl_take isl_basic_set *bset, void *user),
930 int isl_map_foreach_basic_map(__isl_keep isl_map *map,
931 int (*fn)(__isl_take isl_basic_map *bmap, void *user),
934 The callback function C<fn> should return 0 if successful and
935 -1 if an error occurs. In the latter case, or if any other error
936 occurs, the above functions will return -1.
938 It should be noted that C<isl> does not guarantee that
939 the basic sets or maps passed to C<fn> are disjoint.
940 If this is required, then the user should call one of
941 the following functions first.
943 __isl_give isl_set *isl_set_make_disjoint(
944 __isl_take isl_set *set);
945 __isl_give isl_map *isl_map_make_disjoint(
946 __isl_take isl_map *map);
948 The number of basic sets in a set can be obtained
951 int isl_set_n_basic_set(__isl_keep isl_set *set);
953 To iterate over the constraints of a basic set or map, use
955 #include <isl_constraint.h>
957 int isl_basic_map_foreach_constraint(
958 __isl_keep isl_basic_map *bmap,
959 int (*fn)(__isl_take isl_constraint *c, void *user),
961 void isl_constraint_free(struct isl_constraint *c);
963 Again, the callback function C<fn> should return 0 if successful and
964 -1 if an error occurs. In the latter case, or if any other error
965 occurs, the above functions will return -1.
966 The constraint C<c> represents either an equality or an inequality.
967 Use the following function to find out whether a constraint
968 represents an equality. If not, it represents an inequality.
970 int isl_constraint_is_equality(
971 __isl_keep isl_constraint *constraint);
973 The coefficients of the constraints can be inspected using
974 the following functions.
976 void isl_constraint_get_constant(
977 __isl_keep isl_constraint *constraint, isl_int *v);
978 void isl_constraint_get_coefficient(
979 __isl_keep isl_constraint *constraint,
980 enum isl_dim_type type, int pos, isl_int *v);
982 The explicit representations of the existentially quantified
983 variables can be inspected using the following functions.
984 Note that the user is only allowed to use these functions
985 if the inspected set or map is the result of a call
986 to C<isl_set_compute_divs> or C<isl_map_compute_divs>.
988 __isl_give isl_div *isl_constraint_div(
989 __isl_keep isl_constraint *constraint, int pos);
990 void isl_div_get_constant(__isl_keep isl_div *div,
992 void isl_div_get_denominator(__isl_keep isl_div *div,
994 void isl_div_get_coefficient(__isl_keep isl_div *div,
995 enum isl_dim_type type, int pos, isl_int *v);
997 To obtain the constraints of a basic map in matrix
998 form, use the following functions.
1000 __isl_give isl_mat *isl_basic_map_equalities_matrix(
1001 __isl_keep isl_basic_map *bmap,
1002 enum isl_dim_type c1,
1003 enum isl_dim_type c2, enum isl_dim_type c3,
1004 enum isl_dim_type c4, enum isl_dim_type c5);
1005 __isl_give isl_mat *isl_basic_map_inequalities_matrix(
1006 __isl_keep isl_basic_map *bmap,
1007 enum isl_dim_type c1,
1008 enum isl_dim_type c2, enum isl_dim_type c3,
1009 enum isl_dim_type c4, enum isl_dim_type c5);
1011 The C<isl_dim_type> arguments dictate the order in which
1012 different kinds of variables appear in the resulting matrix
1013 and should be a permutation of C<isl_dim_cst>, C<isl_dim_param>,
1014 C<isl_dim_in>, C<isl_dim_out> and C<isl_dim_div>.
1016 The names of the domain and range spaces of a set or relation can be
1017 read off using the following functions.
1019 const char *isl_set_get_tuple_name(
1020 __isl_keep isl_set *set);
1021 const char *isl_basic_map_get_tuple_name(
1022 __isl_keep isl_basic_map *bmap,
1023 enum isl_dim_type type);
1024 const char *isl_map_get_tuple_name(
1025 __isl_keep isl_map *map,
1026 enum isl_dim_type type);
1028 As with C<isl_dim_get_tuple_name>, the value returned points to
1029 an internal data structure.
1030 The names of individual dimensions can be read off using
1031 the following functions.
1033 const char *isl_constraint_get_dim_name(
1034 __isl_keep isl_constraint *constraint,
1035 enum isl_dim_type type, unsigned pos);
1036 const char *isl_set_get_dim_name(
1037 __isl_keep isl_set *set,
1038 enum isl_dim_type type, unsigned pos);
1039 const char *isl_basic_map_get_dim_name(
1040 __isl_keep isl_basic_map *bmap,
1041 enum isl_dim_type type, unsigned pos);
1042 const char *isl_map_get_dim_name(
1043 __isl_keep isl_map *map,
1044 enum isl_dim_type type, unsigned pos);
1046 These functions are mostly useful to obtain the names
1051 =head3 Unary Properties
1057 The following functions test whether the given set or relation
1058 contains any integer points. The ``fast'' variants do not perform
1059 any computations, but simply check if the given set or relation
1060 is already known to be empty.
1062 int isl_basic_set_fast_is_empty(__isl_keep isl_basic_set *bset);
1063 int isl_basic_set_is_empty(__isl_keep isl_basic_set *bset);
1064 int isl_set_is_empty(__isl_keep isl_set *set);
1065 int isl_union_set_is_empty(__isl_keep isl_union_set *uset);
1066 int isl_basic_map_fast_is_empty(__isl_keep isl_basic_map *bmap);
1067 int isl_basic_map_is_empty(__isl_keep isl_basic_map *bmap);
1068 int isl_map_fast_is_empty(__isl_keep isl_map *map);
1069 int isl_map_is_empty(__isl_keep isl_map *map);
1070 int isl_union_map_is_empty(__isl_keep isl_union_map *umap);
1072 =item * Universality
1074 int isl_basic_set_is_universe(__isl_keep isl_basic_set *bset);
1075 int isl_basic_map_is_universe(__isl_keep isl_basic_map *bmap);
1076 int isl_set_fast_is_universe(__isl_keep isl_set *set);
1078 =item * Single-valuedness
1080 int isl_map_is_single_valued(__isl_keep isl_map *map);
1084 int isl_map_is_bijective(__isl_keep isl_map *map);
1088 The followning functions check whether the domain of the given
1089 (basic) set is a wrapped relation.
1091 int isl_basic_set_is_wrapping(
1092 __isl_keep isl_basic_set *bset);
1093 int isl_set_is_wrapping(__isl_keep isl_set *set);
1097 =head3 Binary Properties
1103 int isl_set_fast_is_equal(__isl_keep isl_set *set1,
1104 __isl_keep isl_set *set2);
1105 int isl_set_is_equal(__isl_keep isl_set *set1,
1106 __isl_keep isl_set *set2);
1107 int isl_basic_map_is_equal(
1108 __isl_keep isl_basic_map *bmap1,
1109 __isl_keep isl_basic_map *bmap2);
1110 int isl_map_is_equal(__isl_keep isl_map *map1,
1111 __isl_keep isl_map *map2);
1112 int isl_map_fast_is_equal(__isl_keep isl_map *map1,
1113 __isl_keep isl_map *map2);
1114 int isl_union_map_is_equal(
1115 __isl_keep isl_union_map *umap1,
1116 __isl_keep isl_union_map *umap2);
1118 =item * Disjointness
1120 int isl_set_fast_is_disjoint(__isl_keep isl_set *set1,
1121 __isl_keep isl_set *set2);
1125 int isl_set_is_subset(__isl_keep isl_set *set1,
1126 __isl_keep isl_set *set2);
1127 int isl_set_is_strict_subset(
1128 __isl_keep isl_set *set1,
1129 __isl_keep isl_set *set2);
1130 int isl_basic_map_is_subset(
1131 __isl_keep isl_basic_map *bmap1,
1132 __isl_keep isl_basic_map *bmap2);
1133 int isl_basic_map_is_strict_subset(
1134 __isl_keep isl_basic_map *bmap1,
1135 __isl_keep isl_basic_map *bmap2);
1136 int isl_map_is_subset(
1137 __isl_keep isl_map *map1,
1138 __isl_keep isl_map *map2);
1139 int isl_map_is_strict_subset(
1140 __isl_keep isl_map *map1,
1141 __isl_keep isl_map *map2);
1142 int isl_union_map_is_subset(
1143 __isl_keep isl_union_map *umap1,
1144 __isl_keep isl_union_map *umap2);
1145 int isl_union_map_is_strict_subset(
1146 __isl_keep isl_union_map *umap1,
1147 __isl_keep isl_union_map *umap2);
1151 =head2 Unary Operations
1157 __isl_give isl_set *isl_set_complement(
1158 __isl_take isl_set *set);
1162 __isl_give isl_basic_map *isl_basic_map_reverse(
1163 __isl_take isl_basic_map *bmap);
1164 __isl_give isl_map *isl_map_reverse(
1165 __isl_take isl_map *map);
1166 __isl_give isl_union_map *isl_union_map_reverse(
1167 __isl_take isl_union_map *umap);
1171 __isl_give isl_basic_set *isl_basic_set_project_out(
1172 __isl_take isl_basic_set *bset,
1173 enum isl_dim_type type, unsigned first, unsigned n);
1174 __isl_give isl_basic_map *isl_basic_map_project_out(
1175 __isl_take isl_basic_map *bmap,
1176 enum isl_dim_type type, unsigned first, unsigned n);
1177 __isl_give isl_set *isl_set_project_out(__isl_take isl_set *set,
1178 enum isl_dim_type type, unsigned first, unsigned n);
1179 __isl_give isl_map *isl_map_project_out(__isl_take isl_map *map,
1180 enum isl_dim_type type, unsigned first, unsigned n);
1181 __isl_give isl_basic_set *isl_basic_map_domain(
1182 __isl_take isl_basic_map *bmap);
1183 __isl_give isl_basic_set *isl_basic_map_range(
1184 __isl_take isl_basic_map *bmap);
1185 __isl_give isl_set *isl_map_domain(
1186 __isl_take isl_map *bmap);
1187 __isl_give isl_set *isl_map_range(
1188 __isl_take isl_map *map);
1189 __isl_give isl_union_set *isl_union_map_domain(
1190 __isl_take isl_union_map *umap);
1191 __isl_give isl_union_set *isl_union_map_range(
1192 __isl_take isl_union_map *umap);
1194 __isl_give isl_basic_map *isl_basic_map_domain_map(
1195 __isl_take isl_basic_map *bmap);
1196 __isl_give isl_basic_map *isl_basic_map_range_map(
1197 __isl_take isl_basic_map *bmap);
1198 __isl_give isl_map *isl_map_domain_map(__isl_take isl_map *map);
1199 __isl_give isl_map *isl_map_range_map(__isl_take isl_map *map);
1200 __isl_give isl_union_map *isl_union_map_domain_map(
1201 __isl_take isl_union_map *umap);
1202 __isl_give isl_union_map *isl_union_map_range_map(
1203 __isl_take isl_union_map *umap);
1205 The functions above construct a (basic, regular or union) relation
1206 that maps (a wrapped version of) the input relation to its domain or range.
1210 __isl_give isl_map *isl_set_identity(
1211 __isl_take isl_set *set);
1212 __isl_give isl_union_map *isl_union_set_identity(
1213 __isl_take isl_union_set *uset);
1215 Construct an identity relation on the given (union) set.
1219 __isl_give isl_basic_set *isl_basic_map_deltas(
1220 __isl_take isl_basic_map *bmap);
1221 __isl_give isl_set *isl_map_deltas(__isl_take isl_map *map);
1222 __isl_give isl_union_set *isl_union_map_deltas(
1223 __isl_take isl_union_map *umap);
1225 These functions return a (basic) set containing the differences
1226 between image elements and corresponding domain elements in the input.
1230 Simplify the representation of a set or relation by trying
1231 to combine pairs of basic sets or relations into a single
1232 basic set or relation.
1234 __isl_give isl_set *isl_set_coalesce(__isl_take isl_set *set);
1235 __isl_give isl_map *isl_map_coalesce(__isl_take isl_map *map);
1236 __isl_give isl_union_set *isl_union_set_coalesce(
1237 __isl_take isl_union_set *uset);
1238 __isl_give isl_union_map *isl_union_map_coalesce(
1239 __isl_take isl_union_map *umap);
1243 __isl_give isl_basic_set *isl_set_convex_hull(
1244 __isl_take isl_set *set);
1245 __isl_give isl_basic_map *isl_map_convex_hull(
1246 __isl_take isl_map *map);
1248 If the input set or relation has any existentially quantified
1249 variables, then the result of these operations is currently undefined.
1253 __isl_give isl_basic_set *isl_set_simple_hull(
1254 __isl_take isl_set *set);
1255 __isl_give isl_basic_map *isl_map_simple_hull(
1256 __isl_take isl_map *map);
1258 These functions compute a single basic set or relation
1259 that contains the whole input set or relation.
1260 In particular, the output is described by translates
1261 of the constraints describing the basic sets or relations in the input.
1265 (See \autoref{s:simple hull}.)
1271 __isl_give isl_basic_set *isl_basic_set_affine_hull(
1272 __isl_take isl_basic_set *bset);
1273 __isl_give isl_basic_set *isl_set_affine_hull(
1274 __isl_take isl_set *set);
1275 __isl_give isl_union_set *isl_union_set_affine_hull(
1276 __isl_take isl_union_set *uset);
1277 __isl_give isl_basic_map *isl_basic_map_affine_hull(
1278 __isl_take isl_basic_map *bmap);
1279 __isl_give isl_basic_map *isl_map_affine_hull(
1280 __isl_take isl_map *map);
1281 __isl_give isl_union_map *isl_union_map_affine_hull(
1282 __isl_take isl_union_map *umap);
1284 In case of union sets and relations, the affine hull is computed
1289 __isl_give isl_map *isl_map_power(__isl_take isl_map *map,
1290 unsigned param, int *exact);
1292 Compute a parametric representation for all positive powers I<k> of C<map>.
1293 The power I<k> is equated to the parameter at position C<param>.
1294 The result may be an overapproximation. If the result is exact,
1295 then C<*exact> is set to C<1>.
1296 The current implementation only produces exact results for particular
1297 cases of piecewise translations (i.e., piecewise uniform dependences).
1299 =item * Transitive closure
1301 __isl_give isl_map *isl_map_transitive_closure(
1302 __isl_take isl_map *map, int *exact);
1303 __isl_give isl_union_map *isl_union_map_transitive_closure(
1304 __isl_take isl_union_map *umap, int *exact);
1306 Compute the transitive closure of C<map>.
1307 The result may be an overapproximation. If the result is known to be exact,
1308 then C<*exact> is set to C<1>.
1309 The current implementation only produces exact results for particular
1310 cases of piecewise translations (i.e., piecewise uniform dependences).
1312 =item * Reaching path lengths
1314 __isl_give isl_map *isl_map_reaching_path_lengths(
1315 __isl_take isl_map *map, int *exact);
1317 Compute a relation that maps each element in the range of C<map>
1318 to the lengths of all paths composed of edges in C<map> that
1319 end up in the given element.
1320 The result may be an overapproximation. If the result is known to be exact,
1321 then C<*exact> is set to C<1>.
1322 To compute the I<maximal> path length, the resulting relation
1323 should be postprocessed by C<isl_map_lexmax>.
1324 In particular, if the input relation is a dependence relation
1325 (mapping sources to sinks), then the maximal path length corresponds
1326 to the free schedule.
1327 Note, however, that C<isl_map_lexmax> expects the maximum to be
1328 finite, so if the path lengths are unbounded (possibly due to
1329 the overapproximation), then you will get an error message.
1333 __isl_give isl_basic_set *isl_basic_map_wrap(
1334 __isl_take isl_basic_map *bmap);
1335 __isl_give isl_set *isl_map_wrap(
1336 __isl_take isl_map *map);
1337 __isl_give isl_union_set *isl_union_map_wrap(
1338 __isl_take isl_union_map *umap);
1339 __isl_give isl_basic_map *isl_basic_set_unwrap(
1340 __isl_take isl_basic_set *bset);
1341 __isl_give isl_map *isl_set_unwrap(
1342 __isl_take isl_set *set);
1343 __isl_give isl_union_map *isl_union_set_unwrap(
1344 __isl_take isl_union_set *uset);
1348 Remove any internal structure of domain (and range) of the given
1349 set or relation. If there is any such internal structure in the input,
1350 then the name of the space is also removed.
1352 __isl_give isl_set *isl_set_flatten(
1353 __isl_take isl_set *set);
1354 __isl_give isl_map *isl_map_flatten(
1355 __isl_take isl_map *map);
1357 =item * Dimension manipulation
1359 __isl_give isl_set *isl_set_add_dims(
1360 __isl_take isl_set *set,
1361 enum isl_dim_type type, unsigned n);
1362 __isl_give isl_map *isl_map_add_dims(
1363 __isl_take isl_map *map,
1364 enum isl_dim_type type, unsigned n);
1366 It is usually not advisable to directly change the (input or output)
1367 space of a set or a relation as this removes the name and the internal
1368 structure of the space. However, the above functions can be useful
1369 to add new parameters.
1373 =head2 Binary Operations
1375 The two arguments of a binary operation not only need to live
1376 in the same C<isl_ctx>, they currently also need to have
1377 the same (number of) parameters.
1379 =head3 Basic Operations
1383 =item * Intersection
1385 __isl_give isl_basic_set *isl_basic_set_intersect(
1386 __isl_take isl_basic_set *bset1,
1387 __isl_take isl_basic_set *bset2);
1388 __isl_give isl_set *isl_set_intersect(
1389 __isl_take isl_set *set1,
1390 __isl_take isl_set *set2);
1391 __isl_give isl_union_set *isl_union_set_intersect(
1392 __isl_take isl_union_set *uset1,
1393 __isl_take isl_union_set *uset2);
1394 __isl_give isl_basic_map *isl_basic_map_intersect_domain(
1395 __isl_take isl_basic_map *bmap,
1396 __isl_take isl_basic_set *bset);
1397 __isl_give isl_basic_map *isl_basic_map_intersect_range(
1398 __isl_take isl_basic_map *bmap,
1399 __isl_take isl_basic_set *bset);
1400 __isl_give isl_basic_map *isl_basic_map_intersect(
1401 __isl_take isl_basic_map *bmap1,
1402 __isl_take isl_basic_map *bmap2);
1403 __isl_give isl_map *isl_map_intersect_domain(
1404 __isl_take isl_map *map,
1405 __isl_take isl_set *set);
1406 __isl_give isl_map *isl_map_intersect_range(
1407 __isl_take isl_map *map,
1408 __isl_take isl_set *set);
1409 __isl_give isl_map *isl_map_intersect(
1410 __isl_take isl_map *map1,
1411 __isl_take isl_map *map2);
1412 __isl_give isl_union_map *isl_union_map_intersect_domain(
1413 __isl_take isl_union_map *umap,
1414 __isl_take isl_union_set *uset);
1415 __isl_give isl_union_map *isl_union_map_intersect_range(
1416 __isl_take isl_union_map *umap,
1417 __isl_take isl_union_set *uset);
1418 __isl_give isl_union_map *isl_union_map_intersect(
1419 __isl_take isl_union_map *umap1,
1420 __isl_take isl_union_map *umap2);
1424 __isl_give isl_set *isl_basic_set_union(
1425 __isl_take isl_basic_set *bset1,
1426 __isl_take isl_basic_set *bset2);
1427 __isl_give isl_map *isl_basic_map_union(
1428 __isl_take isl_basic_map *bmap1,
1429 __isl_take isl_basic_map *bmap2);
1430 __isl_give isl_set *isl_set_union(
1431 __isl_take isl_set *set1,
1432 __isl_take isl_set *set2);
1433 __isl_give isl_map *isl_map_union(
1434 __isl_take isl_map *map1,
1435 __isl_take isl_map *map2);
1436 __isl_give isl_union_set *isl_union_set_union(
1437 __isl_take isl_union_set *uset1,
1438 __isl_take isl_union_set *uset2);
1439 __isl_give isl_union_map *isl_union_map_union(
1440 __isl_take isl_union_map *umap1,
1441 __isl_take isl_union_map *umap2);
1443 =item * Set difference
1445 __isl_give isl_set *isl_set_subtract(
1446 __isl_take isl_set *set1,
1447 __isl_take isl_set *set2);
1448 __isl_give isl_map *isl_map_subtract(
1449 __isl_take isl_map *map1,
1450 __isl_take isl_map *map2);
1451 __isl_give isl_union_set *isl_union_set_subtract(
1452 __isl_take isl_union_set *uset1,
1453 __isl_take isl_union_set *uset2);
1454 __isl_give isl_union_map *isl_union_map_subtract(
1455 __isl_take isl_union_map *umap1,
1456 __isl_take isl_union_map *umap2);
1460 __isl_give isl_basic_set *isl_basic_set_apply(
1461 __isl_take isl_basic_set *bset,
1462 __isl_take isl_basic_map *bmap);
1463 __isl_give isl_set *isl_set_apply(
1464 __isl_take isl_set *set,
1465 __isl_take isl_map *map);
1466 __isl_give isl_union_set *isl_union_set_apply(
1467 __isl_take isl_union_set *uset,
1468 __isl_take isl_union_map *umap);
1469 __isl_give isl_basic_map *isl_basic_map_apply_domain(
1470 __isl_take isl_basic_map *bmap1,
1471 __isl_take isl_basic_map *bmap2);
1472 __isl_give isl_basic_map *isl_basic_map_apply_range(
1473 __isl_take isl_basic_map *bmap1,
1474 __isl_take isl_basic_map *bmap2);
1475 __isl_give isl_map *isl_map_apply_domain(
1476 __isl_take isl_map *map1,
1477 __isl_take isl_map *map2);
1478 __isl_give isl_union_map *isl_union_map_apply_domain(
1479 __isl_take isl_union_map *umap1,
1480 __isl_take isl_union_map *umap2);
1481 __isl_give isl_map *isl_map_apply_range(
1482 __isl_take isl_map *map1,
1483 __isl_take isl_map *map2);
1484 __isl_give isl_union_map *isl_union_map_apply_range(
1485 __isl_take isl_union_map *umap1,
1486 __isl_take isl_union_map *umap2);
1488 =item * Simplification
1490 __isl_give isl_basic_set *isl_basic_set_gist(
1491 __isl_take isl_basic_set *bset,
1492 __isl_take isl_basic_set *context);
1493 __isl_give isl_set *isl_set_gist(__isl_take isl_set *set,
1494 __isl_take isl_set *context);
1495 __isl_give isl_union_set *isl_union_set_gist(
1496 __isl_take isl_union_set *uset,
1497 __isl_take isl_union_set *context);
1498 __isl_give isl_basic_map *isl_basic_map_gist(
1499 __isl_take isl_basic_map *bmap,
1500 __isl_take isl_basic_map *context);
1501 __isl_give isl_map *isl_map_gist(__isl_take isl_map *map,
1502 __isl_take isl_map *context);
1503 __isl_give isl_union_map *isl_union_map_gist(
1504 __isl_take isl_union_map *umap,
1505 __isl_take isl_union_map *context);
1507 The gist operation returns a set or relation that has the
1508 same intersection with the context as the input set or relation.
1509 Any implicit equality in the intersection is made explicit in the result,
1510 while all inequalities that are redundant with respect to the intersection
1512 In case of union sets and relations, the gist operation is performed
1517 =head3 Lexicographic Optimization
1519 Given a (basic) set C<set> (or C<bset>) and a zero-dimensional domain C<dom>,
1520 the following functions
1521 compute a set that contains the lexicographic minimum or maximum
1522 of the elements in C<set> (or C<bset>) for those values of the parameters
1523 that satisfy C<dom>.
1524 If C<empty> is not C<NULL>, then C<*empty> is assigned a set
1525 that contains the parameter values in C<dom> for which C<set> (or C<bset>)
1527 In other words, the union of the parameter values
1528 for which the result is non-empty and of C<*empty>
1531 __isl_give isl_set *isl_basic_set_partial_lexmin(
1532 __isl_take isl_basic_set *bset,
1533 __isl_take isl_basic_set *dom,
1534 __isl_give isl_set **empty);
1535 __isl_give isl_set *isl_basic_set_partial_lexmax(
1536 __isl_take isl_basic_set *bset,
1537 __isl_take isl_basic_set *dom,
1538 __isl_give isl_set **empty);
1539 __isl_give isl_set *isl_set_partial_lexmin(
1540 __isl_take isl_set *set, __isl_take isl_set *dom,
1541 __isl_give isl_set **empty);
1542 __isl_give isl_set *isl_set_partial_lexmax(
1543 __isl_take isl_set *set, __isl_take isl_set *dom,
1544 __isl_give isl_set **empty);
1546 Given a (basic) set C<set> (or C<bset>), the following functions simply
1547 return a set containing the lexicographic minimum or maximum
1548 of the elements in C<set> (or C<bset>).
1549 In case of union sets, the optimum is computed per space.
1551 __isl_give isl_set *isl_basic_set_lexmin(
1552 __isl_take isl_basic_set *bset);
1553 __isl_give isl_set *isl_basic_set_lexmax(
1554 __isl_take isl_basic_set *bset);
1555 __isl_give isl_set *isl_set_lexmin(
1556 __isl_take isl_set *set);
1557 __isl_give isl_set *isl_set_lexmax(
1558 __isl_take isl_set *set);
1559 __isl_give isl_union_set *isl_union_set_lexmin(
1560 __isl_take isl_union_set *uset);
1561 __isl_give isl_union_set *isl_union_set_lexmax(
1562 __isl_take isl_union_set *uset);
1564 Given a (basic) relation C<map> (or C<bmap>) and a domain C<dom>,
1565 the following functions
1566 compute a relation that maps each element of C<dom>
1567 to the single lexicographic minimum or maximum
1568 of the elements that are associated to that same
1569 element in C<map> (or C<bmap>).
1570 If C<empty> is not C<NULL>, then C<*empty> is assigned a set
1571 that contains the elements in C<dom> that do not map
1572 to any elements in C<map> (or C<bmap>).
1573 In other words, the union of the domain of the result and of C<*empty>
1576 __isl_give isl_map *isl_basic_map_partial_lexmax(
1577 __isl_take isl_basic_map *bmap,
1578 __isl_take isl_basic_set *dom,
1579 __isl_give isl_set **empty);
1580 __isl_give isl_map *isl_basic_map_partial_lexmin(
1581 __isl_take isl_basic_map *bmap,
1582 __isl_take isl_basic_set *dom,
1583 __isl_give isl_set **empty);
1584 __isl_give isl_map *isl_map_partial_lexmax(
1585 __isl_take isl_map *map, __isl_take isl_set *dom,
1586 __isl_give isl_set **empty);
1587 __isl_give isl_map *isl_map_partial_lexmin(
1588 __isl_take isl_map *map, __isl_take isl_set *dom,
1589 __isl_give isl_set **empty);
1591 Given a (basic) map C<map> (or C<bmap>), the following functions simply
1592 return a map mapping each element in the domain of
1593 C<map> (or C<bmap>) to the lexicographic minimum or maximum
1594 of all elements associated to that element.
1595 In case of union relations, the optimum is computed per space.
1597 __isl_give isl_map *isl_basic_map_lexmin(
1598 __isl_take isl_basic_map *bmap);
1599 __isl_give isl_map *isl_basic_map_lexmax(
1600 __isl_take isl_basic_map *bmap);
1601 __isl_give isl_map *isl_map_lexmin(
1602 __isl_take isl_map *map);
1603 __isl_give isl_map *isl_map_lexmax(
1604 __isl_take isl_map *map);
1605 __isl_give isl_union_map *isl_union_map_lexmin(
1606 __isl_take isl_union_map *umap);
1607 __isl_give isl_union_map *isl_union_map_lexmax(
1608 __isl_take isl_union_map *umap);
1612 Matrices can be created, copied and freed using the following functions.
1614 #include <isl_mat.h>
1615 __isl_give isl_mat *isl_mat_alloc(struct isl_ctx *ctx,
1616 unsigned n_row, unsigned n_col);
1617 __isl_give isl_mat *isl_mat_copy(__isl_keep isl_mat *mat);
1618 void isl_mat_free(__isl_take isl_mat *mat);
1620 Note that the elements of a newly created matrix may have arbitrary values.
1621 The elements can be changed and inspected using the following functions.
1623 int isl_mat_rows(__isl_keep isl_mat *mat);
1624 int isl_mat_cols(__isl_keep isl_mat *mat);
1625 int isl_mat_get_element(__isl_keep isl_mat *mat,
1626 int row, int col, isl_int *v);
1627 __isl_give isl_mat *isl_mat_set_element(__isl_take isl_mat *mat,
1628 int row, int col, isl_int v);
1630 C<isl_mat_get_element> will return a negative value if anything went wrong.
1631 In that case, the value of C<*v> is undefined.
1633 The following function can be used to compute the (right) inverse
1634 of a matrix, i.e., a matrix such that the product of the original
1635 and the inverse (in that order) is a multiple of the identity matrix.
1636 The input matrix is assumed to be of full row-rank.
1638 __isl_give isl_mat *isl_mat_right_inverse(__isl_take isl_mat *mat);
1640 The following function can be used to compute the (right) kernel
1641 (or null space) of a matrix, i.e., a matrix such that the product of
1642 the original and the kernel (in that order) is the zero matrix.
1644 __isl_give isl_mat *isl_mat_right_kernel(__isl_take isl_mat *mat);
1648 Points are elements of a set. They can be used to construct
1649 simple sets (boxes) or they can be used to represent the
1650 individual elements of a set.
1651 The zero point (the origin) can be created using
1653 __isl_give isl_point *isl_point_zero(__isl_take isl_dim *dim);
1655 The coordinates of a point can be inspected, set and changed
1658 void isl_point_get_coordinate(__isl_keep isl_point *pnt,
1659 enum isl_dim_type type, int pos, isl_int *v);
1660 __isl_give isl_point *isl_point_set_coordinate(
1661 __isl_take isl_point *pnt,
1662 enum isl_dim_type type, int pos, isl_int v);
1664 __isl_give isl_point *isl_point_add_ui(
1665 __isl_take isl_point *pnt,
1666 enum isl_dim_type type, int pos, unsigned val);
1667 __isl_give isl_point *isl_point_sub_ui(
1668 __isl_take isl_point *pnt,
1669 enum isl_dim_type type, int pos, unsigned val);
1671 Points can be copied or freed using
1673 __isl_give isl_point *isl_point_copy(
1674 __isl_keep isl_point *pnt);
1675 void isl_point_free(__isl_take isl_point *pnt);
1677 A singleton set can be created from a point using
1679 __isl_give isl_set *isl_set_from_point(
1680 __isl_take isl_point *pnt);
1682 and a box can be created from two opposite extremal points using
1684 __isl_give isl_set *isl_set_box_from_points(
1685 __isl_take isl_point *pnt1,
1686 __isl_take isl_point *pnt2);
1688 All elements of a B<bounded> (union) set can be enumerated using
1689 the following functions.
1691 int isl_set_foreach_point(__isl_keep isl_set *set,
1692 int (*fn)(__isl_take isl_point *pnt, void *user),
1694 int isl_union_set_foreach_point(__isl_keep isl_union_set *uset,
1695 int (*fn)(__isl_take isl_point *pnt, void *user),
1698 The function C<fn> is called for each integer point in
1699 C<set> with as second argument the last argument of
1700 the C<isl_set_foreach_point> call. The function C<fn>
1701 should return C<0> on success and C<-1> on failure.
1702 In the latter case, C<isl_set_foreach_point> will stop
1703 enumerating and return C<-1> as well.
1704 If the enumeration is performed successfully and to completion,
1705 then C<isl_set_foreach_point> returns C<0>.
1707 To obtain a single point of a (basic) set, use
1709 __isl_give isl_point *isl_basic_set_sample_point(
1710 __isl_take isl_basic_set *bset);
1711 __isl_give isl_point *isl_set_sample_point(
1712 __isl_take isl_set *set);
1714 If C<set> does not contain any (integer) points, then the
1715 resulting point will be ``void'', a property that can be
1718 int isl_point_is_void(__isl_keep isl_point *pnt);
1720 =head2 Piecewise Quasipolynomials
1722 A piecewise quasipolynomial is a particular kind of function that maps
1723 a parametric point to a rational value.
1724 More specifically, a quasipolynomial is a polynomial expression in greatest
1725 integer parts of affine expressions of parameters and variables.
1726 A piecewise quasipolynomial is a subdivision of a given parametric
1727 domain into disjoint cells with a quasipolynomial associated to
1728 each cell. The value of the piecewise quasipolynomial at a given
1729 point is the value of the quasipolynomial associated to the cell
1730 that contains the point. Outside of the union of cells,
1731 the value is assumed to be zero.
1732 For example, the piecewise quasipolynomial
1734 [n] -> { [x] -> ((1 + n) - x) : x <= n and x >= 0 }
1736 maps C<x> to C<1 + n - x> for values of C<x> between C<0> and C<n>.
1737 A given piecewise quasipolynomial has a fixed domain dimension.
1738 Union piecewise quasipolynomials are used to contain piecewise quasipolynomials
1739 defined over different domains.
1740 Piecewise quasipolynomials are mainly used by the C<barvinok>
1741 library for representing the number of elements in a parametric set or map.
1742 For example, the piecewise quasipolynomial above represents
1743 the number of points in the map
1745 [n] -> { [x] -> [y] : x,y >= 0 and 0 <= x + y <= n }
1747 =head3 Printing (Piecewise) Quasipolynomials
1749 Quasipolynomials and piecewise quasipolynomials can be printed
1750 using the following functions.
1752 __isl_give isl_printer *isl_printer_print_qpolynomial(
1753 __isl_take isl_printer *p,
1754 __isl_keep isl_qpolynomial *qp);
1756 __isl_give isl_printer *isl_printer_print_pw_qpolynomial(
1757 __isl_take isl_printer *p,
1758 __isl_keep isl_pw_qpolynomial *pwqp);
1760 __isl_give isl_printer *isl_printer_print_union_pw_qpolynomial(
1761 __isl_take isl_printer *p,
1762 __isl_keep isl_union_pw_qpolynomial *upwqp);
1764 The output format of the printer
1765 needs to be set to either C<ISL_FORMAT_ISL> or C<ISL_FORMAT_C>.
1766 For C<isl_printer_print_union_pw_qpolynomial>, only C<ISL_FORMAT_ISL>
1768 In case of printing in C<ISL_FORMAT_C>, the user may want
1769 to set the names of all dimensions
1771 __isl_give isl_qpolynomial *isl_qpolynomial_set_dim_name(
1772 __isl_take isl_qpolynomial *qp,
1773 enum isl_dim_type type, unsigned pos,
1775 __isl_give isl_pw_qpolynomial *
1776 isl_pw_qpolynomial_set_dim_name(
1777 __isl_take isl_pw_qpolynomial *pwqp,
1778 enum isl_dim_type type, unsigned pos,
1781 =head3 Creating New (Piecewise) Quasipolynomials
1783 Some simple quasipolynomials can be created using the following functions.
1784 More complicated quasipolynomials can be created by applying
1785 operations such as addition and multiplication
1786 on the resulting quasipolynomials
1788 __isl_give isl_qpolynomial *isl_qpolynomial_zero(
1789 __isl_take isl_dim *dim);
1790 __isl_give isl_qpolynomial *isl_qpolynomial_one(
1791 __isl_take isl_dim *dim);
1792 __isl_give isl_qpolynomial *isl_qpolynomial_infty(
1793 __isl_take isl_dim *dim);
1794 __isl_give isl_qpolynomial *isl_qpolynomial_neginfty(
1795 __isl_take isl_dim *dim);
1796 __isl_give isl_qpolynomial *isl_qpolynomial_nan(
1797 __isl_take isl_dim *dim);
1798 __isl_give isl_qpolynomial *isl_qpolynomial_rat_cst(
1799 __isl_take isl_dim *dim,
1800 const isl_int n, const isl_int d);
1801 __isl_give isl_qpolynomial *isl_qpolynomial_div(
1802 __isl_take isl_div *div);
1803 __isl_give isl_qpolynomial *isl_qpolynomial_var(
1804 __isl_take isl_dim *dim,
1805 enum isl_dim_type type, unsigned pos);
1807 The zero piecewise quasipolynomial or a piecewise quasipolynomial
1808 with a single cell can be created using the following functions.
1809 Multiple of these single cell piecewise quasipolynomials can
1810 be combined to create more complicated piecewise quasipolynomials.
1812 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_zero(
1813 __isl_take isl_dim *dim);
1814 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_alloc(
1815 __isl_take isl_set *set,
1816 __isl_take isl_qpolynomial *qp);
1818 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_zero(
1819 __isl_take isl_dim *dim);
1820 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_from_pw_qpolynomial(
1821 __isl_take isl_pw_qpolynomial *pwqp);
1822 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_add_pw_qpolynomial(
1823 __isl_take isl_union_pw_qpolynomial *upwqp,
1824 __isl_take isl_pw_qpolynomial *pwqp);
1826 Quasipolynomials can be copied and freed again using the following
1829 __isl_give isl_qpolynomial *isl_qpolynomial_copy(
1830 __isl_keep isl_qpolynomial *qp);
1831 void isl_qpolynomial_free(__isl_take isl_qpolynomial *qp);
1833 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_copy(
1834 __isl_keep isl_pw_qpolynomial *pwqp);
1835 void isl_pw_qpolynomial_free(
1836 __isl_take isl_pw_qpolynomial *pwqp);
1838 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_copy(
1839 __isl_keep isl_union_pw_qpolynomial *upwqp);
1840 void isl_union_pw_qpolynomial_free(
1841 __isl_take isl_union_pw_qpolynomial *upwqp);
1843 =head3 Inspecting (Piecewise) Quasipolynomials
1845 To iterate over all piecewise quasipolynomials in a union
1846 piecewise quasipolynomial, use the following function
1848 int isl_union_pw_qpolynomial_foreach_pw_qpolynomial(
1849 __isl_keep isl_union_pw_qpolynomial *upwqp,
1850 int (*fn)(__isl_take isl_pw_qpolynomial *pwqp, void *user),
1853 To extract the piecewise quasipolynomial from a union with a given dimension
1856 __isl_give isl_pw_qpolynomial *
1857 isl_union_pw_qpolynomial_extract_pw_qpolynomial(
1858 __isl_keep isl_union_pw_qpolynomial *upwqp,
1859 __isl_take isl_dim *dim);
1861 To iterate over the cells in a piecewise quasipolynomial,
1862 use either of the following two functions
1864 int isl_pw_qpolynomial_foreach_piece(
1865 __isl_keep isl_pw_qpolynomial *pwqp,
1866 int (*fn)(__isl_take isl_set *set,
1867 __isl_take isl_qpolynomial *qp,
1868 void *user), void *user);
1869 int isl_pw_qpolynomial_foreach_lifted_piece(
1870 __isl_keep isl_pw_qpolynomial *pwqp,
1871 int (*fn)(__isl_take isl_set *set,
1872 __isl_take isl_qpolynomial *qp,
1873 void *user), void *user);
1875 As usual, the function C<fn> should return C<0> on success
1876 and C<-1> on failure. The difference between
1877 C<isl_pw_qpolynomial_foreach_piece> and
1878 C<isl_pw_qpolynomial_foreach_lifted_piece> is that
1879 C<isl_pw_qpolynomial_foreach_lifted_piece> will first
1880 compute unique representations for all existentially quantified
1881 variables and then turn these existentially quantified variables
1882 into extra set variables, adapting the associated quasipolynomial
1883 accordingly. This means that the C<set> passed to C<fn>
1884 will not have any existentially quantified variables, but that
1885 the dimensions of the sets may be different for different
1886 invocations of C<fn>.
1888 To iterate over all terms in a quasipolynomial,
1891 int isl_qpolynomial_foreach_term(
1892 __isl_keep isl_qpolynomial *qp,
1893 int (*fn)(__isl_take isl_term *term,
1894 void *user), void *user);
1896 The terms themselves can be inspected and freed using
1899 unsigned isl_term_dim(__isl_keep isl_term *term,
1900 enum isl_dim_type type);
1901 void isl_term_get_num(__isl_keep isl_term *term,
1903 void isl_term_get_den(__isl_keep isl_term *term,
1905 int isl_term_get_exp(__isl_keep isl_term *term,
1906 enum isl_dim_type type, unsigned pos);
1907 __isl_give isl_div *isl_term_get_div(
1908 __isl_keep isl_term *term, unsigned pos);
1909 void isl_term_free(__isl_take isl_term *term);
1911 Each term is a product of parameters, set variables and
1912 integer divisions. The function C<isl_term_get_exp>
1913 returns the exponent of a given dimensions in the given term.
1914 The C<isl_int>s in the arguments of C<isl_term_get_num>
1915 and C<isl_term_get_den> need to have been initialized
1916 using C<isl_int_init> before calling these functions.
1918 =head3 Properties of (Piecewise) Quasipolynomials
1920 To check whether a quasipolynomial is actually a constant,
1921 use the following function.
1923 int isl_qpolynomial_is_cst(__isl_keep isl_qpolynomial *qp,
1924 isl_int *n, isl_int *d);
1926 If C<qp> is a constant and if C<n> and C<d> are not C<NULL>
1927 then the numerator and denominator of the constant
1928 are returned in C<*n> and C<*d>, respectively.
1930 =head3 Operations on (Piecewise) Quasipolynomials
1932 __isl_give isl_qpolynomial *isl_qpolynomial_neg(
1933 __isl_take isl_qpolynomial *qp);
1934 __isl_give isl_qpolynomial *isl_qpolynomial_add(
1935 __isl_take isl_qpolynomial *qp1,
1936 __isl_take isl_qpolynomial *qp2);
1937 __isl_give isl_qpolynomial *isl_qpolynomial_sub(
1938 __isl_take isl_qpolynomial *qp1,
1939 __isl_take isl_qpolynomial *qp2);
1940 __isl_give isl_qpolynomial *isl_qpolynomial_mul(
1941 __isl_take isl_qpolynomial *qp1,
1942 __isl_take isl_qpolynomial *qp2);
1944 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_add(
1945 __isl_take isl_pw_qpolynomial *pwqp1,
1946 __isl_take isl_pw_qpolynomial *pwqp2);
1947 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_sub(
1948 __isl_take isl_pw_qpolynomial *pwqp1,
1949 __isl_take isl_pw_qpolynomial *pwqp2);
1950 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_add_disjoint(
1951 __isl_take isl_pw_qpolynomial *pwqp1,
1952 __isl_take isl_pw_qpolynomial *pwqp2);
1953 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_neg(
1954 __isl_take isl_pw_qpolynomial *pwqp);
1955 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_mul(
1956 __isl_take isl_pw_qpolynomial *pwqp1,
1957 __isl_take isl_pw_qpolynomial *pwqp2);
1959 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_add(
1960 __isl_take isl_union_pw_qpolynomial *upwqp1,
1961 __isl_take isl_union_pw_qpolynomial *upwqp2);
1962 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_sub(
1963 __isl_take isl_union_pw_qpolynomial *upwqp1,
1964 __isl_take isl_union_pw_qpolynomial *upwqp2);
1965 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_mul(
1966 __isl_take isl_union_pw_qpolynomial *upwqp1,
1967 __isl_take isl_union_pw_qpolynomial *upwqp2);
1969 __isl_give isl_qpolynomial *isl_pw_qpolynomial_eval(
1970 __isl_take isl_pw_qpolynomial *pwqp,
1971 __isl_take isl_point *pnt);
1973 __isl_give isl_qpolynomial *isl_union_pw_qpolynomial_eval(
1974 __isl_take isl_union_pw_qpolynomial *upwqp,
1975 __isl_take isl_point *pnt);
1977 __isl_give isl_set *isl_pw_qpolynomial_domain(
1978 __isl_take isl_pw_qpolynomial *pwqp);
1979 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_intersect_domain(
1980 __isl_take isl_pw_qpolynomial *pwpq,
1981 __isl_take isl_set *set);
1983 __isl_give isl_union_set *isl_union_pw_qpolynomial_domain(
1984 __isl_take isl_union_pw_qpolynomial *upwqp);
1985 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_intersect_domain(
1986 __isl_take isl_union_pw_qpolynomial *upwpq,
1987 __isl_take isl_union_set *uset);
1989 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_coalesce(
1990 __isl_take isl_union_pw_qpolynomial *upwqp);
1992 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_gist(
1993 __isl_take isl_pw_qpolynomial *pwqp,
1994 __isl_take isl_set *context);
1996 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_gist(
1997 __isl_take isl_union_pw_qpolynomial *upwqp,
1998 __isl_take isl_union_set *context);
2000 The gist operation applies the gist operation to each of
2001 the cells in the domain of the input piecewise quasipolynomial.
2002 In future, the operation will also exploit the context
2003 to simplify the quasipolynomials associated to each cell.
2005 =head2 Bounds on Piecewise Quasipolynomials and Piecewise Quasipolynomial Reductions
2007 A piecewise quasipolynomial reduction is a piecewise
2008 reduction (or fold) of quasipolynomials.
2009 In particular, the reduction can be maximum or a minimum.
2010 The objects are mainly used to represent the result of
2011 an upper or lower bound on a quasipolynomial over its domain,
2012 i.e., as the result of the following function.
2014 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_bound(
2015 __isl_take isl_pw_qpolynomial *pwqp,
2016 enum isl_fold type, int *tight);
2018 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_bound(
2019 __isl_take isl_union_pw_qpolynomial *upwqp,
2020 enum isl_fold type, int *tight);
2022 The C<type> argument may be either C<isl_fold_min> or C<isl_fold_max>.
2023 If C<tight> is not C<NULL>, then C<*tight> is set to C<1>
2024 is the returned bound is known be tight, i.e., for each value
2025 of the parameters there is at least
2026 one element in the domain that reaches the bound.
2027 If the domain of C<pwqp> is not wrapping, then the bound is computed
2028 over all elements in that domain and the result has a purely parametric
2029 domain. If the domain of C<pwqp> is wrapping, then the bound is
2030 computed over the range of the wrapped relation. The domain of the
2031 wrapped relation becomes the domain of the result.
2033 A (piecewise) quasipolynomial reduction can be copied or freed using the
2034 following functions.
2036 __isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_copy(
2037 __isl_keep isl_qpolynomial_fold *fold);
2038 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_copy(
2039 __isl_keep isl_pw_qpolynomial_fold *pwf);
2040 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_copy(
2041 __isl_keep isl_union_pw_qpolynomial_fold *upwf);
2042 void isl_qpolynomial_fold_free(
2043 __isl_take isl_qpolynomial_fold *fold);
2044 void isl_pw_qpolynomial_fold_free(
2045 __isl_take isl_pw_qpolynomial_fold *pwf);
2046 void isl_union_pw_qpolynomial_fold_free(
2047 __isl_take isl_union_pw_qpolynomial_fold *upwf);
2049 =head3 Printing Piecewise Quasipolynomial Reductions
2051 Piecewise quasipolynomial reductions can be printed
2052 using the following function.
2054 __isl_give isl_printer *isl_printer_print_pw_qpolynomial_fold(
2055 __isl_take isl_printer *p,
2056 __isl_keep isl_pw_qpolynomial_fold *pwf);
2057 __isl_give isl_printer *isl_printer_print_union_pw_qpolynomial_fold(
2058 __isl_take isl_printer *p,
2059 __isl_keep isl_union_pw_qpolynomial_fold *upwf);
2061 For C<isl_printer_print_pw_qpolynomial_fold>,
2062 output format of the printer
2063 needs to be set to either C<ISL_FORMAT_ISL> or C<ISL_FORMAT_C>.
2064 For C<isl_printer_print_union_pw_qpolynomial_fold>,
2065 output format of the printer
2066 needs to be set to either C<ISL_FORMAT_ISL>.
2068 =head3 Inspecting (Piecewise) Quasipolynomial Reductions
2070 To iterate over all piecewise quasipolynomial reductions in a union
2071 piecewise quasipolynomial reduction, use the following function
2073 int isl_union_pw_qpolynomial_fold_foreach_pw_qpolynomial_fold(
2074 __isl_keep isl_union_pw_qpolynomial_fold *upwf,
2075 int (*fn)(__isl_take isl_pw_qpolynomial_fold *pwf,
2076 void *user), void *user);
2078 To iterate over the cells in a piecewise quasipolynomial reduction,
2079 use either of the following two functions
2081 int isl_pw_qpolynomial_fold_foreach_piece(
2082 __isl_keep isl_pw_qpolynomial_fold *pwf,
2083 int (*fn)(__isl_take isl_set *set,
2084 __isl_take isl_qpolynomial_fold *fold,
2085 void *user), void *user);
2086 int isl_pw_qpolynomial_fold_foreach_lifted_piece(
2087 __isl_keep isl_pw_qpolynomial_fold *pwf,
2088 int (*fn)(__isl_take isl_set *set,
2089 __isl_take isl_qpolynomial_fold *fold,
2090 void *user), void *user);
2092 See L<Inspecting (Piecewise) Quasipolynomials> for an explanation
2093 of the difference between these two functions.
2095 To iterate over all quasipolynomials in a reduction, use
2097 int isl_qpolynomial_fold_foreach_qpolynomial(
2098 __isl_keep isl_qpolynomial_fold *fold,
2099 int (*fn)(__isl_take isl_qpolynomial *qp,
2100 void *user), void *user);
2102 =head3 Operations on Piecewise Quasipolynomial Reductions
2104 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_fold(
2105 __isl_take isl_pw_qpolynomial_fold *pwf1,
2106 __isl_take isl_pw_qpolynomial_fold *pwf2);
2108 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_fold(
2109 __isl_take isl_union_pw_qpolynomial_fold *upwf1,
2110 __isl_take isl_union_pw_qpolynomial_fold *upwf2);
2112 __isl_give isl_qpolynomial *isl_pw_qpolynomial_fold_eval(
2113 __isl_take isl_pw_qpolynomial_fold *pwf,
2114 __isl_take isl_point *pnt);
2116 __isl_give isl_qpolynomial *isl_union_pw_qpolynomial_fold_eval(
2117 __isl_take isl_union_pw_qpolynomial_fold *upwf,
2118 __isl_take isl_point *pnt);
2120 __isl_give isl_union_set *isl_union_pw_qpolynomial_fold_domain(
2121 __isl_take isl_union_pw_qpolynomial_fold *upwf);
2122 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_intersect_domain(
2123 __isl_take isl_union_pw_qpolynomial_fold *upwf,
2124 __isl_take isl_union_set *uset);
2126 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_coalesce(
2127 __isl_take isl_pw_qpolynomial_fold *pwf);
2129 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_coalesce(
2130 __isl_take isl_union_pw_qpolynomial_fold *upwf);
2132 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_gist(
2133 __isl_take isl_pw_qpolynomial_fold *pwf,
2134 __isl_take isl_set *context);
2136 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_gist(
2137 __isl_take isl_union_pw_qpolynomial_fold *upwf,
2138 __isl_take isl_union_set *context);
2140 The gist operation applies the gist operation to each of
2141 the cells in the domain of the input piecewise quasipolynomial reduction.
2142 In future, the operation will also exploit the context
2143 to simplify the quasipolynomial reductions associated to each cell.
2145 __isl_give isl_pw_qpolynomial_fold *
2146 isl_map_apply_pw_qpolynomial_fold(
2147 __isl_take isl_map *map,
2148 __isl_take isl_pw_qpolynomial_fold *pwf,
2150 __isl_give isl_union_pw_qpolynomial_fold *
2151 isl_union_map_apply_union_pw_qpolynomial_fold(
2152 __isl_take isl_union_map *umap,
2153 __isl_take isl_union_pw_qpolynomial_fold *upwf,
2157 compose the given map with the given piecewise quasipolynomial reduction.
2158 That is, compute a bound (of the same type as C<pwf> or C<upwf> itself)
2159 over all elements in the intersection of the range of the map
2160 and the domain of the piecewise quasipolynomial reduction
2161 as a function of an element in the domain of the map.
2163 =head2 Dependence Analysis
2165 C<isl> contains specialized functionality for performing
2166 array dataflow analysis. That is, given a I<sink> access relation
2167 and a collection of possible I<source> access relations,
2168 C<isl> can compute relations that describe
2169 for each iteration of the sink access, which iteration
2170 of which of the source access relations was the last
2171 to access the same data element before the given iteration
2173 To compute standard flow dependences, the sink should be
2174 a read, while the sources should be writes.
2175 If any of the source accesses are marked as being I<may>
2176 accesses, then there will be a dependence to the last
2177 I<must> access B<and> to any I<may> access that follows
2178 this last I<must> access.
2179 In particular, if I<all> sources are I<may> accesses,
2180 then memory based dependence analysis is performed.
2181 If, on the other hand, all sources are I<must> accesses,
2182 then value based dependence analysis is performed.
2184 #include <isl_flow.h>
2186 typedef int (*isl_access_level_before)(void *first, void *second);
2188 __isl_give isl_access_info *isl_access_info_alloc(
2189 __isl_take isl_map *sink,
2190 void *sink_user, isl_access_level_before fn,
2192 __isl_give isl_access_info *isl_access_info_add_source(
2193 __isl_take isl_access_info *acc,
2194 __isl_take isl_map *source, int must,
2196 void isl_access_info_free(__isl_take isl_access_info *acc);
2198 __isl_give isl_flow *isl_access_info_compute_flow(
2199 __isl_take isl_access_info *acc);
2201 int isl_flow_foreach(__isl_keep isl_flow *deps,
2202 int (*fn)(__isl_take isl_map *dep, int must,
2203 void *dep_user, void *user),
2205 __isl_give isl_set *isl_flow_get_no_source(
2206 __isl_keep isl_flow *deps, int must);
2207 void isl_flow_free(__isl_take isl_flow *deps);
2209 The function C<isl_access_info_compute_flow> performs the actual
2210 dependence analysis. The other functions are used to construct
2211 the input for this function or to read off the output.
2213 The input is collected in an C<isl_access_info>, which can
2214 be created through a call to C<isl_access_info_alloc>.
2215 The arguments to this functions are the sink access relation
2216 C<sink>, a token C<sink_user> used to identify the sink
2217 access to the user, a callback function for specifying the
2218 relative order of source and sink accesses, and the number
2219 of source access relations that will be added.
2220 The callback function has type C<int (*)(void *first, void *second)>.
2221 The function is called with two user supplied tokens identifying
2222 either a source or the sink and it should return the shared nesting
2223 level and the relative order of the two accesses.
2224 In particular, let I<n> be the number of loops shared by
2225 the two accesses. If C<first> precedes C<second> textually,
2226 then the function should return I<2 * n + 1>; otherwise,
2227 it should return I<2 * n>.
2228 The sources can be added to the C<isl_access_info> by performing
2229 (at most) C<max_source> calls to C<isl_access_info_add_source>.
2230 C<must> indicates whether the source is a I<must> access
2231 or a I<may> access. Note that a multi-valued access relation
2232 should only be marked I<must> if every iteration in the domain
2233 of the relation accesses I<all> elements in its image.
2234 The C<source_user> token is again used to identify
2235 the source access. The range of the source access relation
2236 C<source> should have the same dimension as the range
2237 of the sink access relation.
2238 The C<isl_access_info_free> function should usually not be
2239 called explicitly, because it is called implicitly by
2240 C<isl_access_info_compute_flow>.
2242 The result of the dependence analysis is collected in an
2243 C<isl_flow>. There may be elements in the domain of
2244 the sink access for which no preceding source access could be
2245 found or for which all preceding sources are I<may> accesses.
2246 The sets of these elements can be obtained through
2247 calls to C<isl_flow_get_no_source>, the first with C<must> set
2248 and the second with C<must> unset.
2249 In the case of standard flow dependence analysis,
2250 with the sink a read and the sources I<must> writes,
2251 the first set corresponds to the reads from uninitialized
2252 array elements and the second set is empty.
2253 The actual flow dependences can be extracted using
2254 C<isl_flow_foreach>. This function will call the user-specified
2255 callback function C<fn> for each B<non-empty> dependence between
2256 a source and the sink. The callback function is called
2257 with four arguments, the actual flow dependence relation
2258 mapping source iterations to sink iterations, a boolean that
2259 indicates whether it is a I<must> or I<may> dependence, a token
2260 identifying the source and an additional C<void *> with value
2261 equal to the third argument of the C<isl_flow_foreach> call.
2262 A dependence is marked I<must> if it originates from a I<must>
2263 source and if it is not followed by any I<may> sources.
2265 After finishing with an C<isl_flow>, the user should call
2266 C<isl_flow_free> to free all associated memory.
2268 A higher-level interface to dependence analysis is provided
2269 by the following function.
2271 #include <isl_flow.h>
2273 int isl_union_map_compute_flow(__isl_take isl_union_map *sink,
2274 __isl_take isl_union_map *must_source,
2275 __isl_take isl_union_map *may_source,
2276 __isl_take isl_union_map *schedule,
2277 __isl_give isl_union_map **must_dep,
2278 __isl_give isl_union_map **may_dep,
2279 __isl_give isl_union_set **must_no_source,
2280 __isl_give isl_union_set **may_no_source);
2282 The arrays are identified by the tuple names of the ranges
2283 of the accesses. The iteration domains by the tuple names
2284 of the domains of the accesses and of the schedule.
2285 The relative order of the iteration domains is given by the
2286 schedule. Any of C<must_dep>, C<may_dep>, C<must_no_source>
2287 or C<may_no_source> may be C<NULL>, but a C<NULL> value for
2288 any of the other arguments is treated as an error.
2290 =head2 Parametric Vertex Enumeration
2292 The parametric vertex enumeration described in this section
2293 is mainly intended to be used internally and by the C<barvinok>
2296 #include <isl_vertices.h>
2297 __isl_give isl_vertices *isl_basic_set_compute_vertices(
2298 __isl_keep isl_basic_set *bset);
2300 The function C<isl_basic_set_compute_vertices> performs the
2301 actual computation of the parametric vertices and the chamber
2302 decomposition and store the result in an C<isl_vertices> object.
2303 This information can be queried by either iterating over all
2304 the vertices or iterating over all the chambers or cells
2305 and then iterating over all vertices that are active on the chamber.
2307 int isl_vertices_foreach_vertex(
2308 __isl_keep isl_vertices *vertices,
2309 int (*fn)(__isl_take isl_vertex *vertex, void *user),
2312 int isl_vertices_foreach_cell(
2313 __isl_keep isl_vertices *vertices,
2314 int (*fn)(__isl_take isl_cell *cell, void *user),
2316 int isl_cell_foreach_vertex(__isl_keep isl_cell *cell,
2317 int (*fn)(__isl_take isl_vertex *vertex, void *user),
2320 Other operations that can be performed on an C<isl_vertices> object are
2323 isl_ctx *isl_vertices_get_ctx(
2324 __isl_keep isl_vertices *vertices);
2325 int isl_vertices_get_n_vertices(
2326 __isl_keep isl_vertices *vertices);
2327 void isl_vertices_free(__isl_take isl_vertices *vertices);
2329 Vertices can be inspected and destroyed using the following functions.
2331 isl_ctx *isl_vertex_get_ctx(__isl_keep isl_vertex *vertex);
2332 int isl_vertex_get_id(__isl_keep isl_vertex *vertex);
2333 __isl_give isl_basic_set *isl_vertex_get_domain(
2334 __isl_keep isl_vertex *vertex);
2335 __isl_give isl_basic_set *isl_vertex_get_expr(
2336 __isl_keep isl_vertex *vertex);
2337 void isl_vertex_free(__isl_take isl_vertex *vertex);
2339 C<isl_vertex_get_expr> returns a singleton parametric set describing
2340 the vertex, while C<isl_vertex_get_domain> returns the activity domain
2342 Note that C<isl_vertex_get_domain> and C<isl_vertex_get_expr> return
2343 B<rational> basic sets, so they should mainly be used for inspection
2344 and should not be mixed with integer sets.
2346 Chambers can be inspected and destroyed using the following functions.
2348 isl_ctx *isl_cell_get_ctx(__isl_keep isl_cell *cell);
2349 __isl_give isl_basic_set *isl_cell_get_domain(
2350 __isl_keep isl_cell *cell);
2351 void isl_cell_free(__isl_take isl_cell *cell);
2355 Although C<isl> is mainly meant to be used as a library,
2356 it also contains some basic applications that use some
2357 of the functionality of C<isl>.
2358 The input may be specified in either the L<isl format>
2359 or the L<PolyLib format>.
2361 =head2 C<isl_polyhedron_sample>
2363 C<isl_polyhedron_sample> takes a polyhedron as input and prints
2364 an integer element of the polyhedron, if there is any.
2365 The first column in the output is the denominator and is always
2366 equal to 1. If the polyhedron contains no integer points,
2367 then a vector of length zero is printed.
2371 C<isl_pip> takes the same input as the C<example> program
2372 from the C<piplib> distribution, i.e., a set of constraints
2373 on the parameters, a line containing only -1 and finally a set
2374 of constraints on a parametric polyhedron.
2375 The coefficients of the parameters appear in the last columns
2376 (but before the final constant column).
2377 The output is the lexicographic minimum of the parametric polyhedron.
2378 As C<isl> currently does not have its own output format, the output
2379 is just a dump of the internal state.
2381 =head2 C<isl_polyhedron_minimize>
2383 C<isl_polyhedron_minimize> computes the minimum of some linear
2384 or affine objective function over the integer points in a polyhedron.
2385 If an affine objective function
2386 is given, then the constant should appear in the last column.
2388 =head2 C<isl_polytope_scan>
2390 Given a polytope, C<isl_polytope_scan> prints
2391 all integer points in the polytope.
2393 =head1 C<isl-polylib>
2395 The C<isl-polylib> library provides the following functions for converting
2396 between C<isl> objects and C<PolyLib> objects.
2397 The library is distributed separately for licensing reasons.
2399 #include <isl_set_polylib.h>
2400 __isl_give isl_basic_set *isl_basic_set_new_from_polylib(
2401 Polyhedron *P, __isl_take isl_dim *dim);
2402 Polyhedron *isl_basic_set_to_polylib(
2403 __isl_keep isl_basic_set *bset);
2404 __isl_give isl_set *isl_set_new_from_polylib(Polyhedron *D,
2405 __isl_take isl_dim *dim);
2406 Polyhedron *isl_set_to_polylib(__isl_keep isl_set *set);
2408 #include <isl_map_polylib.h>
2409 __isl_give isl_basic_map *isl_basic_map_new_from_polylib(
2410 Polyhedron *P, __isl_take isl_dim *dim);
2411 __isl_give isl_map *isl_map_new_from_polylib(Polyhedron *D,
2412 __isl_take isl_dim *dim);
2413 Polyhedron *isl_basic_map_to_polylib(
2414 __isl_keep isl_basic_map *bmap);
2415 Polyhedron *isl_map_to_polylib(__isl_keep isl_map *map);