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_basic_set *isl_basic_map_deltas(
1211 __isl_take isl_basic_map *bmap);
1212 __isl_give isl_set *isl_map_deltas(__isl_take isl_map *map);
1213 __isl_give isl_union_set *isl_union_map_deltas(
1214 __isl_take isl_union_map *umap);
1216 These functions return a (basic) set containing the differences
1217 between image elements and corresponding domain elements in the input.
1221 Simplify the representation of a set or relation by trying
1222 to combine pairs of basic sets or relations into a single
1223 basic set or relation.
1225 __isl_give isl_set *isl_set_coalesce(__isl_take isl_set *set);
1226 __isl_give isl_map *isl_map_coalesce(__isl_take isl_map *map);
1227 __isl_give isl_union_set *isl_union_set_coalesce(
1228 __isl_take isl_union_set *uset);
1229 __isl_give isl_union_map *isl_union_map_coalesce(
1230 __isl_take isl_union_map *umap);
1234 __isl_give isl_basic_set *isl_set_convex_hull(
1235 __isl_take isl_set *set);
1236 __isl_give isl_basic_map *isl_map_convex_hull(
1237 __isl_take isl_map *map);
1239 If the input set or relation has any existentially quantified
1240 variables, then the result of these operations is currently undefined.
1244 __isl_give isl_basic_set *isl_set_simple_hull(
1245 __isl_take isl_set *set);
1246 __isl_give isl_basic_map *isl_map_simple_hull(
1247 __isl_take isl_map *map);
1249 These functions compute a single basic set or relation
1250 that contains the whole input set or relation.
1251 In particular, the output is described by translates
1252 of the constraints describing the basic sets or relations in the input.
1256 (See \autoref{s:simple hull}.)
1262 __isl_give isl_basic_set *isl_basic_set_affine_hull(
1263 __isl_take isl_basic_set *bset);
1264 __isl_give isl_basic_set *isl_set_affine_hull(
1265 __isl_take isl_set *set);
1266 __isl_give isl_union_set *isl_union_set_affine_hull(
1267 __isl_take isl_union_set *uset);
1268 __isl_give isl_basic_map *isl_basic_map_affine_hull(
1269 __isl_take isl_basic_map *bmap);
1270 __isl_give isl_basic_map *isl_map_affine_hull(
1271 __isl_take isl_map *map);
1272 __isl_give isl_union_map *isl_union_map_affine_hull(
1273 __isl_take isl_union_map *umap);
1275 In case of union sets and relations, the affine hull is computed
1280 __isl_give isl_map *isl_map_power(__isl_take isl_map *map,
1281 unsigned param, int *exact);
1283 Compute a parametric representation for all positive powers I<k> of C<map>.
1284 The power I<k> is equated to the parameter at position C<param>.
1285 The result may be an overapproximation. If the result is exact,
1286 then C<*exact> is set to C<1>.
1287 The current implementation only produces exact results for particular
1288 cases of piecewise translations (i.e., piecewise uniform dependences).
1290 =item * Transitive closure
1292 __isl_give isl_map *isl_map_transitive_closure(
1293 __isl_take isl_map *map, int *exact);
1294 __isl_give isl_union_map *isl_union_map_transitive_closure(
1295 __isl_take isl_union_map *umap, int *exact);
1297 Compute the transitive closure of C<map>.
1298 The result may be an overapproximation. If the result is known to be exact,
1299 then C<*exact> is set to C<1>.
1300 The current implementation only produces exact results for particular
1301 cases of piecewise translations (i.e., piecewise uniform dependences).
1303 =item * Reaching path lengths
1305 __isl_give isl_map *isl_map_reaching_path_lengths(
1306 __isl_take isl_map *map, int *exact);
1308 Compute a relation that maps each element in the range of C<map>
1309 to the lengths of all paths composed of edges in C<map> that
1310 end up in the given element.
1311 The result may be an overapproximation. If the result is known to be exact,
1312 then C<*exact> is set to C<1>.
1313 To compute the I<maximal> path length, the resulting relation
1314 should be postprocessed by C<isl_map_lexmax>.
1315 In particular, if the input relation is a dependence relation
1316 (mapping sources to sinks), then the maximal path length corresponds
1317 to the free schedule.
1318 Note, however, that C<isl_map_lexmax> expects the maximum to be
1319 finite, so if the path lengths are unbounded (possibly due to
1320 the overapproximation), then you will get an error message.
1324 __isl_give isl_basic_set *isl_basic_map_wrap(
1325 __isl_take isl_basic_map *bmap);
1326 __isl_give isl_set *isl_map_wrap(
1327 __isl_take isl_map *map);
1328 __isl_give isl_union_set *isl_union_map_wrap(
1329 __isl_take isl_union_map *umap);
1330 __isl_give isl_basic_map *isl_basic_set_unwrap(
1331 __isl_take isl_basic_set *bset);
1332 __isl_give isl_map *isl_set_unwrap(
1333 __isl_take isl_set *set);
1334 __isl_give isl_union_map *isl_union_set_unwrap(
1335 __isl_take isl_union_set *uset);
1339 Remove any internal structure of domain (and range) of the given
1340 set or relation. If there is any such internal structure in the input,
1341 then the name of the space is also removed.
1343 __isl_give isl_set *isl_set_flatten(
1344 __isl_take isl_set *set);
1345 __isl_give isl_map *isl_map_flatten(
1346 __isl_take isl_map *map);
1348 =item * Dimension manipulation
1350 __isl_give isl_set *isl_set_add_dims(
1351 __isl_take isl_set *set,
1352 enum isl_dim_type type, unsigned n);
1353 __isl_give isl_map *isl_map_add_dims(
1354 __isl_take isl_map *map,
1355 enum isl_dim_type type, unsigned n);
1357 It is usually not advisable to directly change the (input or output)
1358 space of a set or a relation as this removes the name and the internal
1359 structure of the space. However, the above functions can be useful
1360 to add new parameters.
1364 =head2 Binary Operations
1366 The two arguments of a binary operation not only need to live
1367 in the same C<isl_ctx>, they currently also need to have
1368 the same (number of) parameters.
1370 =head3 Basic Operations
1374 =item * Intersection
1376 __isl_give isl_basic_set *isl_basic_set_intersect(
1377 __isl_take isl_basic_set *bset1,
1378 __isl_take isl_basic_set *bset2);
1379 __isl_give isl_set *isl_set_intersect(
1380 __isl_take isl_set *set1,
1381 __isl_take isl_set *set2);
1382 __isl_give isl_union_set *isl_union_set_intersect(
1383 __isl_take isl_union_set *uset1,
1384 __isl_take isl_union_set *uset2);
1385 __isl_give isl_basic_map *isl_basic_map_intersect_domain(
1386 __isl_take isl_basic_map *bmap,
1387 __isl_take isl_basic_set *bset);
1388 __isl_give isl_basic_map *isl_basic_map_intersect_range(
1389 __isl_take isl_basic_map *bmap,
1390 __isl_take isl_basic_set *bset);
1391 __isl_give isl_basic_map *isl_basic_map_intersect(
1392 __isl_take isl_basic_map *bmap1,
1393 __isl_take isl_basic_map *bmap2);
1394 __isl_give isl_map *isl_map_intersect_domain(
1395 __isl_take isl_map *map,
1396 __isl_take isl_set *set);
1397 __isl_give isl_map *isl_map_intersect_range(
1398 __isl_take isl_map *map,
1399 __isl_take isl_set *set);
1400 __isl_give isl_map *isl_map_intersect(
1401 __isl_take isl_map *map1,
1402 __isl_take isl_map *map2);
1403 __isl_give isl_union_map *isl_union_map_intersect_domain(
1404 __isl_take isl_union_map *umap,
1405 __isl_take isl_union_set *uset);
1406 __isl_give isl_union_map *isl_union_map_intersect_range(
1407 __isl_take isl_union_map *umap,
1408 __isl_take isl_union_set *uset);
1409 __isl_give isl_union_map *isl_union_map_intersect(
1410 __isl_take isl_union_map *umap1,
1411 __isl_take isl_union_map *umap2);
1415 __isl_give isl_set *isl_basic_set_union(
1416 __isl_take isl_basic_set *bset1,
1417 __isl_take isl_basic_set *bset2);
1418 __isl_give isl_map *isl_basic_map_union(
1419 __isl_take isl_basic_map *bmap1,
1420 __isl_take isl_basic_map *bmap2);
1421 __isl_give isl_set *isl_set_union(
1422 __isl_take isl_set *set1,
1423 __isl_take isl_set *set2);
1424 __isl_give isl_map *isl_map_union(
1425 __isl_take isl_map *map1,
1426 __isl_take isl_map *map2);
1427 __isl_give isl_union_set *isl_union_set_union(
1428 __isl_take isl_union_set *uset1,
1429 __isl_take isl_union_set *uset2);
1430 __isl_give isl_union_map *isl_union_map_union(
1431 __isl_take isl_union_map *umap1,
1432 __isl_take isl_union_map *umap2);
1434 =item * Set difference
1436 __isl_give isl_set *isl_set_subtract(
1437 __isl_take isl_set *set1,
1438 __isl_take isl_set *set2);
1439 __isl_give isl_map *isl_map_subtract(
1440 __isl_take isl_map *map1,
1441 __isl_take isl_map *map2);
1442 __isl_give isl_union_set *isl_union_set_subtract(
1443 __isl_take isl_union_set *uset1,
1444 __isl_take isl_union_set *uset2);
1445 __isl_give isl_union_map *isl_union_map_subtract(
1446 __isl_take isl_union_map *umap1,
1447 __isl_take isl_union_map *umap2);
1451 __isl_give isl_basic_set *isl_basic_set_apply(
1452 __isl_take isl_basic_set *bset,
1453 __isl_take isl_basic_map *bmap);
1454 __isl_give isl_set *isl_set_apply(
1455 __isl_take isl_set *set,
1456 __isl_take isl_map *map);
1457 __isl_give isl_union_set *isl_union_set_apply(
1458 __isl_take isl_union_set *uset,
1459 __isl_take isl_union_map *umap);
1460 __isl_give isl_basic_map *isl_basic_map_apply_domain(
1461 __isl_take isl_basic_map *bmap1,
1462 __isl_take isl_basic_map *bmap2);
1463 __isl_give isl_basic_map *isl_basic_map_apply_range(
1464 __isl_take isl_basic_map *bmap1,
1465 __isl_take isl_basic_map *bmap2);
1466 __isl_give isl_map *isl_map_apply_domain(
1467 __isl_take isl_map *map1,
1468 __isl_take isl_map *map2);
1469 __isl_give isl_union_map *isl_union_map_apply_domain(
1470 __isl_take isl_union_map *umap1,
1471 __isl_take isl_union_map *umap2);
1472 __isl_give isl_map *isl_map_apply_range(
1473 __isl_take isl_map *map1,
1474 __isl_take isl_map *map2);
1475 __isl_give isl_union_map *isl_union_map_apply_range(
1476 __isl_take isl_union_map *umap1,
1477 __isl_take isl_union_map *umap2);
1479 =item * Simplification
1481 __isl_give isl_basic_set *isl_basic_set_gist(
1482 __isl_take isl_basic_set *bset,
1483 __isl_take isl_basic_set *context);
1484 __isl_give isl_set *isl_set_gist(__isl_take isl_set *set,
1485 __isl_take isl_set *context);
1486 __isl_give isl_union_set *isl_union_set_gist(
1487 __isl_take isl_union_set *uset,
1488 __isl_take isl_union_set *context);
1489 __isl_give isl_basic_map *isl_basic_map_gist(
1490 __isl_take isl_basic_map *bmap,
1491 __isl_take isl_basic_map *context);
1492 __isl_give isl_map *isl_map_gist(__isl_take isl_map *map,
1493 __isl_take isl_map *context);
1494 __isl_give isl_union_map *isl_union_map_gist(
1495 __isl_take isl_union_map *umap,
1496 __isl_take isl_union_map *context);
1498 The gist operation returns a set or relation that has the
1499 same intersection with the context as the input set or relation.
1500 Any implicit equality in the intersection is made explicit in the result,
1501 while all inequalities that are redundant with respect to the intersection
1503 In case of union sets and relations, the gist operation is performed
1508 =head3 Lexicographic Optimization
1510 Given a (basic) set C<set> (or C<bset>) and a zero-dimensional domain C<dom>,
1511 the following functions
1512 compute a set that contains the lexicographic minimum or maximum
1513 of the elements in C<set> (or C<bset>) for those values of the parameters
1514 that satisfy C<dom>.
1515 If C<empty> is not C<NULL>, then C<*empty> is assigned a set
1516 that contains the parameter values in C<dom> for which C<set> (or C<bset>)
1518 In other words, the union of the parameter values
1519 for which the result is non-empty and of C<*empty>
1522 __isl_give isl_set *isl_basic_set_partial_lexmin(
1523 __isl_take isl_basic_set *bset,
1524 __isl_take isl_basic_set *dom,
1525 __isl_give isl_set **empty);
1526 __isl_give isl_set *isl_basic_set_partial_lexmax(
1527 __isl_take isl_basic_set *bset,
1528 __isl_take isl_basic_set *dom,
1529 __isl_give isl_set **empty);
1530 __isl_give isl_set *isl_set_partial_lexmin(
1531 __isl_take isl_set *set, __isl_take isl_set *dom,
1532 __isl_give isl_set **empty);
1533 __isl_give isl_set *isl_set_partial_lexmax(
1534 __isl_take isl_set *set, __isl_take isl_set *dom,
1535 __isl_give isl_set **empty);
1537 Given a (basic) set C<set> (or C<bset>), the following functions simply
1538 return a set containing the lexicographic minimum or maximum
1539 of the elements in C<set> (or C<bset>).
1540 In case of union sets, the optimum is computed per space.
1542 __isl_give isl_set *isl_basic_set_lexmin(
1543 __isl_take isl_basic_set *bset);
1544 __isl_give isl_set *isl_basic_set_lexmax(
1545 __isl_take isl_basic_set *bset);
1546 __isl_give isl_set *isl_set_lexmin(
1547 __isl_take isl_set *set);
1548 __isl_give isl_set *isl_set_lexmax(
1549 __isl_take isl_set *set);
1550 __isl_give isl_union_set *isl_union_set_lexmin(
1551 __isl_take isl_union_set *uset);
1552 __isl_give isl_union_set *isl_union_set_lexmax(
1553 __isl_take isl_union_set *uset);
1555 Given a (basic) relation C<map> (or C<bmap>) and a domain C<dom>,
1556 the following functions
1557 compute a relation that maps each element of C<dom>
1558 to the single lexicographic minimum or maximum
1559 of the elements that are associated to that same
1560 element in C<map> (or C<bmap>).
1561 If C<empty> is not C<NULL>, then C<*empty> is assigned a set
1562 that contains the elements in C<dom> that do not map
1563 to any elements in C<map> (or C<bmap>).
1564 In other words, the union of the domain of the result and of C<*empty>
1567 __isl_give isl_map *isl_basic_map_partial_lexmax(
1568 __isl_take isl_basic_map *bmap,
1569 __isl_take isl_basic_set *dom,
1570 __isl_give isl_set **empty);
1571 __isl_give isl_map *isl_basic_map_partial_lexmin(
1572 __isl_take isl_basic_map *bmap,
1573 __isl_take isl_basic_set *dom,
1574 __isl_give isl_set **empty);
1575 __isl_give isl_map *isl_map_partial_lexmax(
1576 __isl_take isl_map *map, __isl_take isl_set *dom,
1577 __isl_give isl_set **empty);
1578 __isl_give isl_map *isl_map_partial_lexmin(
1579 __isl_take isl_map *map, __isl_take isl_set *dom,
1580 __isl_give isl_set **empty);
1582 Given a (basic) map C<map> (or C<bmap>), the following functions simply
1583 return a map mapping each element in the domain of
1584 C<map> (or C<bmap>) to the lexicographic minimum or maximum
1585 of all elements associated to that element.
1586 In case of union relations, the optimum is computed per space.
1588 __isl_give isl_map *isl_basic_map_lexmin(
1589 __isl_take isl_basic_map *bmap);
1590 __isl_give isl_map *isl_basic_map_lexmax(
1591 __isl_take isl_basic_map *bmap);
1592 __isl_give isl_map *isl_map_lexmin(
1593 __isl_take isl_map *map);
1594 __isl_give isl_map *isl_map_lexmax(
1595 __isl_take isl_map *map);
1596 __isl_give isl_union_map *isl_union_map_lexmin(
1597 __isl_take isl_union_map *umap);
1598 __isl_give isl_union_map *isl_union_map_lexmax(
1599 __isl_take isl_union_map *umap);
1603 Matrices can be created, copied and freed using the following functions.
1605 #include <isl_mat.h>
1606 __isl_give isl_mat *isl_mat_alloc(struct isl_ctx *ctx,
1607 unsigned n_row, unsigned n_col);
1608 __isl_give isl_mat *isl_mat_copy(__isl_keep isl_mat *mat);
1609 void isl_mat_free(__isl_take isl_mat *mat);
1611 Note that the elements of a newly created matrix may have arbitrary values.
1612 The elements can be changed and inspected using the following functions.
1614 int isl_mat_rows(__isl_keep isl_mat *mat);
1615 int isl_mat_cols(__isl_keep isl_mat *mat);
1616 int isl_mat_get_element(__isl_keep isl_mat *mat,
1617 int row, int col, isl_int *v);
1618 __isl_give isl_mat *isl_mat_set_element(__isl_take isl_mat *mat,
1619 int row, int col, isl_int v);
1621 C<isl_mat_get_element> will return a negative value if anything went wrong.
1622 In that case, the value of C<*v> is undefined.
1624 The following function can be used to compute the (right) inverse
1625 of a matrix, i.e., a matrix such that the product of the original
1626 and the inverse (in that order) is a multiple of the identity matrix.
1627 The input matrix is assumed to be of full row-rank.
1629 __isl_give isl_mat *isl_mat_right_inverse(__isl_take isl_mat *mat);
1631 The following function can be used to compute the (right) kernel
1632 (or null space) of a matrix, i.e., a matrix such that the product of
1633 the original and the kernel (in that order) is the zero matrix.
1635 __isl_give isl_mat *isl_mat_right_kernel(__isl_take isl_mat *mat);
1639 Points are elements of a set. They can be used to construct
1640 simple sets (boxes) or they can be used to represent the
1641 individual elements of a set.
1642 The zero point (the origin) can be created using
1644 __isl_give isl_point *isl_point_zero(__isl_take isl_dim *dim);
1646 The coordinates of a point can be inspected, set and changed
1649 void isl_point_get_coordinate(__isl_keep isl_point *pnt,
1650 enum isl_dim_type type, int pos, isl_int *v);
1651 __isl_give isl_point *isl_point_set_coordinate(
1652 __isl_take isl_point *pnt,
1653 enum isl_dim_type type, int pos, isl_int v);
1655 __isl_give isl_point *isl_point_add_ui(
1656 __isl_take isl_point *pnt,
1657 enum isl_dim_type type, int pos, unsigned val);
1658 __isl_give isl_point *isl_point_sub_ui(
1659 __isl_take isl_point *pnt,
1660 enum isl_dim_type type, int pos, unsigned val);
1662 Points can be copied or freed using
1664 __isl_give isl_point *isl_point_copy(
1665 __isl_keep isl_point *pnt);
1666 void isl_point_free(__isl_take isl_point *pnt);
1668 A singleton set can be created from a point using
1670 __isl_give isl_set *isl_set_from_point(
1671 __isl_take isl_point *pnt);
1673 and a box can be created from two opposite extremal points using
1675 __isl_give isl_set *isl_set_box_from_points(
1676 __isl_take isl_point *pnt1,
1677 __isl_take isl_point *pnt2);
1679 All elements of a B<bounded> (union) set can be enumerated using
1680 the following functions.
1682 int isl_set_foreach_point(__isl_keep isl_set *set,
1683 int (*fn)(__isl_take isl_point *pnt, void *user),
1685 int isl_union_set_foreach_point(__isl_keep isl_union_set *uset,
1686 int (*fn)(__isl_take isl_point *pnt, void *user),
1689 The function C<fn> is called for each integer point in
1690 C<set> with as second argument the last argument of
1691 the C<isl_set_foreach_point> call. The function C<fn>
1692 should return C<0> on success and C<-1> on failure.
1693 In the latter case, C<isl_set_foreach_point> will stop
1694 enumerating and return C<-1> as well.
1695 If the enumeration is performed successfully and to completion,
1696 then C<isl_set_foreach_point> returns C<0>.
1698 To obtain a single point of a (basic) set, use
1700 __isl_give isl_point *isl_basic_set_sample_point(
1701 __isl_take isl_basic_set *bset);
1702 __isl_give isl_point *isl_set_sample_point(
1703 __isl_take isl_set *set);
1705 If C<set> does not contain any (integer) points, then the
1706 resulting point will be ``void'', a property that can be
1709 int isl_point_is_void(__isl_keep isl_point *pnt);
1711 =head2 Piecewise Quasipolynomials
1713 A piecewise quasipolynomial is a particular kind of function that maps
1714 a parametric point to a rational value.
1715 More specifically, a quasipolynomial is a polynomial expression in greatest
1716 integer parts of affine expressions of parameters and variables.
1717 A piecewise quasipolynomial is a subdivision of a given parametric
1718 domain into disjoint cells with a quasipolynomial associated to
1719 each cell. The value of the piecewise quasipolynomial at a given
1720 point is the value of the quasipolynomial associated to the cell
1721 that contains the point. Outside of the union of cells,
1722 the value is assumed to be zero.
1723 For example, the piecewise quasipolynomial
1725 [n] -> { [x] -> ((1 + n) - x) : x <= n and x >= 0 }
1727 maps C<x> to C<1 + n - x> for values of C<x> between C<0> and C<n>.
1728 A given piecewise quasipolynomial has a fixed domain dimension.
1729 Union piecewise quasipolynomials are used to contain piecewise quasipolynomials
1730 defined over different domains.
1731 Piecewise quasipolynomials are mainly used by the C<barvinok>
1732 library for representing the number of elements in a parametric set or map.
1733 For example, the piecewise quasipolynomial above represents
1734 the number of points in the map
1736 [n] -> { [x] -> [y] : x,y >= 0 and 0 <= x + y <= n }
1738 =head3 Printing (Piecewise) Quasipolynomials
1740 Quasipolynomials and piecewise quasipolynomials can be printed
1741 using the following functions.
1743 __isl_give isl_printer *isl_printer_print_qpolynomial(
1744 __isl_take isl_printer *p,
1745 __isl_keep isl_qpolynomial *qp);
1747 __isl_give isl_printer *isl_printer_print_pw_qpolynomial(
1748 __isl_take isl_printer *p,
1749 __isl_keep isl_pw_qpolynomial *pwqp);
1751 __isl_give isl_printer *isl_printer_print_union_pw_qpolynomial(
1752 __isl_take isl_printer *p,
1753 __isl_keep isl_union_pw_qpolynomial *upwqp);
1755 The output format of the printer
1756 needs to be set to either C<ISL_FORMAT_ISL> or C<ISL_FORMAT_C>.
1757 For C<isl_printer_print_union_pw_qpolynomial>, only C<ISL_FORMAT_ISL>
1759 In case of printing in C<ISL_FORMAT_C>, the user may want
1760 to set the names of all dimensions
1762 __isl_give isl_qpolynomial *isl_qpolynomial_set_dim_name(
1763 __isl_take isl_qpolynomial *qp,
1764 enum isl_dim_type type, unsigned pos,
1766 __isl_give isl_pw_qpolynomial *
1767 isl_pw_qpolynomial_set_dim_name(
1768 __isl_take isl_pw_qpolynomial *pwqp,
1769 enum isl_dim_type type, unsigned pos,
1772 =head3 Creating New (Piecewise) Quasipolynomials
1774 Some simple quasipolynomials can be created using the following functions.
1775 More complicated quasipolynomials can be created by applying
1776 operations such as addition and multiplication
1777 on the resulting quasipolynomials
1779 __isl_give isl_qpolynomial *isl_qpolynomial_zero(
1780 __isl_take isl_dim *dim);
1781 __isl_give isl_qpolynomial *isl_qpolynomial_one(
1782 __isl_take isl_dim *dim);
1783 __isl_give isl_qpolynomial *isl_qpolynomial_infty(
1784 __isl_take isl_dim *dim);
1785 __isl_give isl_qpolynomial *isl_qpolynomial_neginfty(
1786 __isl_take isl_dim *dim);
1787 __isl_give isl_qpolynomial *isl_qpolynomial_nan(
1788 __isl_take isl_dim *dim);
1789 __isl_give isl_qpolynomial *isl_qpolynomial_rat_cst(
1790 __isl_take isl_dim *dim,
1791 const isl_int n, const isl_int d);
1792 __isl_give isl_qpolynomial *isl_qpolynomial_div(
1793 __isl_take isl_div *div);
1794 __isl_give isl_qpolynomial *isl_qpolynomial_var(
1795 __isl_take isl_dim *dim,
1796 enum isl_dim_type type, unsigned pos);
1798 The zero piecewise quasipolynomial or a piecewise quasipolynomial
1799 with a single cell can be created using the following functions.
1800 Multiple of these single cell piecewise quasipolynomials can
1801 be combined to create more complicated piecewise quasipolynomials.
1803 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_zero(
1804 __isl_take isl_dim *dim);
1805 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_alloc(
1806 __isl_take isl_set *set,
1807 __isl_take isl_qpolynomial *qp);
1809 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_zero(
1810 __isl_take isl_dim *dim);
1811 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_from_pw_qpolynomial(
1812 __isl_take isl_pw_qpolynomial *pwqp);
1813 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_add_pw_qpolynomial(
1814 __isl_take isl_union_pw_qpolynomial *upwqp,
1815 __isl_take isl_pw_qpolynomial *pwqp);
1817 Quasipolynomials can be copied and freed again using the following
1820 __isl_give isl_qpolynomial *isl_qpolynomial_copy(
1821 __isl_keep isl_qpolynomial *qp);
1822 void isl_qpolynomial_free(__isl_take isl_qpolynomial *qp);
1824 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_copy(
1825 __isl_keep isl_pw_qpolynomial *pwqp);
1826 void isl_pw_qpolynomial_free(
1827 __isl_take isl_pw_qpolynomial *pwqp);
1829 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_copy(
1830 __isl_keep isl_union_pw_qpolynomial *upwqp);
1831 void isl_union_pw_qpolynomial_free(
1832 __isl_take isl_union_pw_qpolynomial *upwqp);
1834 =head3 Inspecting (Piecewise) Quasipolynomials
1836 To iterate over all piecewise quasipolynomials in a union
1837 piecewise quasipolynomial, use the following function
1839 int isl_union_pw_qpolynomial_foreach_pw_qpolynomial(
1840 __isl_keep isl_union_pw_qpolynomial *upwqp,
1841 int (*fn)(__isl_take isl_pw_qpolynomial *pwqp, void *user),
1844 To extract the piecewise quasipolynomial from a union with a given dimension
1847 __isl_give isl_pw_qpolynomial *
1848 isl_union_pw_qpolynomial_extract_pw_qpolynomial(
1849 __isl_keep isl_union_pw_qpolynomial *upwqp,
1850 __isl_take isl_dim *dim);
1852 To iterate over the cells in a piecewise quasipolynomial,
1853 use either of the following two functions
1855 int isl_pw_qpolynomial_foreach_piece(
1856 __isl_keep isl_pw_qpolynomial *pwqp,
1857 int (*fn)(__isl_take isl_set *set,
1858 __isl_take isl_qpolynomial *qp,
1859 void *user), void *user);
1860 int isl_pw_qpolynomial_foreach_lifted_piece(
1861 __isl_keep isl_pw_qpolynomial *pwqp,
1862 int (*fn)(__isl_take isl_set *set,
1863 __isl_take isl_qpolynomial *qp,
1864 void *user), void *user);
1866 As usual, the function C<fn> should return C<0> on success
1867 and C<-1> on failure. The difference between
1868 C<isl_pw_qpolynomial_foreach_piece> and
1869 C<isl_pw_qpolynomial_foreach_lifted_piece> is that
1870 C<isl_pw_qpolynomial_foreach_lifted_piece> will first
1871 compute unique representations for all existentially quantified
1872 variables and then turn these existentially quantified variables
1873 into extra set variables, adapting the associated quasipolynomial
1874 accordingly. This means that the C<set> passed to C<fn>
1875 will not have any existentially quantified variables, but that
1876 the dimensions of the sets may be different for different
1877 invocations of C<fn>.
1879 To iterate over all terms in a quasipolynomial,
1882 int isl_qpolynomial_foreach_term(
1883 __isl_keep isl_qpolynomial *qp,
1884 int (*fn)(__isl_take isl_term *term,
1885 void *user), void *user);
1887 The terms themselves can be inspected and freed using
1890 unsigned isl_term_dim(__isl_keep isl_term *term,
1891 enum isl_dim_type type);
1892 void isl_term_get_num(__isl_keep isl_term *term,
1894 void isl_term_get_den(__isl_keep isl_term *term,
1896 int isl_term_get_exp(__isl_keep isl_term *term,
1897 enum isl_dim_type type, unsigned pos);
1898 __isl_give isl_div *isl_term_get_div(
1899 __isl_keep isl_term *term, unsigned pos);
1900 void isl_term_free(__isl_take isl_term *term);
1902 Each term is a product of parameters, set variables and
1903 integer divisions. The function C<isl_term_get_exp>
1904 returns the exponent of a given dimensions in the given term.
1905 The C<isl_int>s in the arguments of C<isl_term_get_num>
1906 and C<isl_term_get_den> need to have been initialized
1907 using C<isl_int_init> before calling these functions.
1909 =head3 Properties of (Piecewise) Quasipolynomials
1911 To check whether a quasipolynomial is actually a constant,
1912 use the following function.
1914 int isl_qpolynomial_is_cst(__isl_keep isl_qpolynomial *qp,
1915 isl_int *n, isl_int *d);
1917 If C<qp> is a constant and if C<n> and C<d> are not C<NULL>
1918 then the numerator and denominator of the constant
1919 are returned in C<*n> and C<*d>, respectively.
1921 =head3 Operations on (Piecewise) Quasipolynomials
1923 __isl_give isl_qpolynomial *isl_qpolynomial_neg(
1924 __isl_take isl_qpolynomial *qp);
1925 __isl_give isl_qpolynomial *isl_qpolynomial_add(
1926 __isl_take isl_qpolynomial *qp1,
1927 __isl_take isl_qpolynomial *qp2);
1928 __isl_give isl_qpolynomial *isl_qpolynomial_sub(
1929 __isl_take isl_qpolynomial *qp1,
1930 __isl_take isl_qpolynomial *qp2);
1931 __isl_give isl_qpolynomial *isl_qpolynomial_mul(
1932 __isl_take isl_qpolynomial *qp1,
1933 __isl_take isl_qpolynomial *qp2);
1935 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_add(
1936 __isl_take isl_pw_qpolynomial *pwqp1,
1937 __isl_take isl_pw_qpolynomial *pwqp2);
1938 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_sub(
1939 __isl_take isl_pw_qpolynomial *pwqp1,
1940 __isl_take isl_pw_qpolynomial *pwqp2);
1941 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_add_disjoint(
1942 __isl_take isl_pw_qpolynomial *pwqp1,
1943 __isl_take isl_pw_qpolynomial *pwqp2);
1944 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_neg(
1945 __isl_take isl_pw_qpolynomial *pwqp);
1946 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_mul(
1947 __isl_take isl_pw_qpolynomial *pwqp1,
1948 __isl_take isl_pw_qpolynomial *pwqp2);
1950 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_add(
1951 __isl_take isl_union_pw_qpolynomial *upwqp1,
1952 __isl_take isl_union_pw_qpolynomial *upwqp2);
1953 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_sub(
1954 __isl_take isl_union_pw_qpolynomial *upwqp1,
1955 __isl_take isl_union_pw_qpolynomial *upwqp2);
1956 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_mul(
1957 __isl_take isl_union_pw_qpolynomial *upwqp1,
1958 __isl_take isl_union_pw_qpolynomial *upwqp2);
1960 __isl_give isl_qpolynomial *isl_pw_qpolynomial_eval(
1961 __isl_take isl_pw_qpolynomial *pwqp,
1962 __isl_take isl_point *pnt);
1964 __isl_give isl_qpolynomial *isl_union_pw_qpolynomial_eval(
1965 __isl_take isl_union_pw_qpolynomial *upwqp,
1966 __isl_take isl_point *pnt);
1968 __isl_give isl_set *isl_pw_qpolynomial_domain(
1969 __isl_take isl_pw_qpolynomial *pwqp);
1970 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_intersect_domain(
1971 __isl_take isl_pw_qpolynomial *pwpq,
1972 __isl_take isl_set *set);
1974 __isl_give isl_union_set *isl_union_pw_qpolynomial_domain(
1975 __isl_take isl_union_pw_qpolynomial *upwqp);
1976 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_intersect_domain(
1977 __isl_take isl_union_pw_qpolynomial *upwpq,
1978 __isl_take isl_union_set *uset);
1980 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_coalesce(
1981 __isl_take isl_union_pw_qpolynomial *upwqp);
1983 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_gist(
1984 __isl_take isl_pw_qpolynomial *pwqp,
1985 __isl_take isl_set *context);
1987 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_gist(
1988 __isl_take isl_union_pw_qpolynomial *upwqp,
1989 __isl_take isl_union_set *context);
1991 The gist operation applies the gist operation to each of
1992 the cells in the domain of the input piecewise quasipolynomial.
1993 In future, the operation will also exploit the context
1994 to simplify the quasipolynomials associated to each cell.
1996 =head2 Bounds on Piecewise Quasipolynomials and Piecewise Quasipolynomial Reductions
1998 A piecewise quasipolynomial reduction is a piecewise
1999 reduction (or fold) of quasipolynomials.
2000 In particular, the reduction can be maximum or a minimum.
2001 The objects are mainly used to represent the result of
2002 an upper or lower bound on a quasipolynomial over its domain,
2003 i.e., as the result of the following function.
2005 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_bound(
2006 __isl_take isl_pw_qpolynomial *pwqp,
2007 enum isl_fold type, int *tight);
2009 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_bound(
2010 __isl_take isl_union_pw_qpolynomial *upwqp,
2011 enum isl_fold type, int *tight);
2013 The C<type> argument may be either C<isl_fold_min> or C<isl_fold_max>.
2014 If C<tight> is not C<NULL>, then C<*tight> is set to C<1>
2015 is the returned bound is known be tight, i.e., for each value
2016 of the parameters there is at least
2017 one element in the domain that reaches the bound.
2018 If the domain of C<pwqp> is not wrapping, then the bound is computed
2019 over all elements in that domain and the result has a purely parametric
2020 domain. If the domain of C<pwqp> is wrapping, then the bound is
2021 computed over the range of the wrapped relation. The domain of the
2022 wrapped relation becomes the domain of the result.
2024 A (piecewise) quasipolynomial reduction can be copied or freed using the
2025 following functions.
2027 __isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_copy(
2028 __isl_keep isl_qpolynomial_fold *fold);
2029 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_copy(
2030 __isl_keep isl_pw_qpolynomial_fold *pwf);
2031 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_copy(
2032 __isl_keep isl_union_pw_qpolynomial_fold *upwf);
2033 void isl_qpolynomial_fold_free(
2034 __isl_take isl_qpolynomial_fold *fold);
2035 void isl_pw_qpolynomial_fold_free(
2036 __isl_take isl_pw_qpolynomial_fold *pwf);
2037 void isl_union_pw_qpolynomial_fold_free(
2038 __isl_take isl_union_pw_qpolynomial_fold *upwf);
2040 =head3 Printing Piecewise Quasipolynomial Reductions
2042 Piecewise quasipolynomial reductions can be printed
2043 using the following function.
2045 __isl_give isl_printer *isl_printer_print_pw_qpolynomial_fold(
2046 __isl_take isl_printer *p,
2047 __isl_keep isl_pw_qpolynomial_fold *pwf);
2048 __isl_give isl_printer *isl_printer_print_union_pw_qpolynomial_fold(
2049 __isl_take isl_printer *p,
2050 __isl_keep isl_union_pw_qpolynomial_fold *upwf);
2052 For C<isl_printer_print_pw_qpolynomial_fold>,
2053 output format of the printer
2054 needs to be set to either C<ISL_FORMAT_ISL> or C<ISL_FORMAT_C>.
2055 For C<isl_printer_print_union_pw_qpolynomial_fold>,
2056 output format of the printer
2057 needs to be set to either C<ISL_FORMAT_ISL>.
2059 =head3 Inspecting (Piecewise) Quasipolynomial Reductions
2061 To iterate over all piecewise quasipolynomial reductions in a union
2062 piecewise quasipolynomial reduction, use the following function
2064 int isl_union_pw_qpolynomial_fold_foreach_pw_qpolynomial_fold(
2065 __isl_keep isl_union_pw_qpolynomial_fold *upwf,
2066 int (*fn)(__isl_take isl_pw_qpolynomial_fold *pwf,
2067 void *user), void *user);
2069 To iterate over the cells in a piecewise quasipolynomial reduction,
2070 use either of the following two functions
2072 int isl_pw_qpolynomial_fold_foreach_piece(
2073 __isl_keep isl_pw_qpolynomial_fold *pwf,
2074 int (*fn)(__isl_take isl_set *set,
2075 __isl_take isl_qpolynomial_fold *fold,
2076 void *user), void *user);
2077 int isl_pw_qpolynomial_fold_foreach_lifted_piece(
2078 __isl_keep isl_pw_qpolynomial_fold *pwf,
2079 int (*fn)(__isl_take isl_set *set,
2080 __isl_take isl_qpolynomial_fold *fold,
2081 void *user), void *user);
2083 See L<Inspecting (Piecewise) Quasipolynomials> for an explanation
2084 of the difference between these two functions.
2086 To iterate over all quasipolynomials in a reduction, use
2088 int isl_qpolynomial_fold_foreach_qpolynomial(
2089 __isl_keep isl_qpolynomial_fold *fold,
2090 int (*fn)(__isl_take isl_qpolynomial *qp,
2091 void *user), void *user);
2093 =head3 Operations on Piecewise Quasipolynomial Reductions
2095 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_fold(
2096 __isl_take isl_pw_qpolynomial_fold *pwf1,
2097 __isl_take isl_pw_qpolynomial_fold *pwf2);
2099 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_fold(
2100 __isl_take isl_union_pw_qpolynomial_fold *upwf1,
2101 __isl_take isl_union_pw_qpolynomial_fold *upwf2);
2103 __isl_give isl_qpolynomial *isl_pw_qpolynomial_fold_eval(
2104 __isl_take isl_pw_qpolynomial_fold *pwf,
2105 __isl_take isl_point *pnt);
2107 __isl_give isl_qpolynomial *isl_union_pw_qpolynomial_fold_eval(
2108 __isl_take isl_union_pw_qpolynomial_fold *upwf,
2109 __isl_take isl_point *pnt);
2111 __isl_give isl_union_set *isl_union_pw_qpolynomial_fold_domain(
2112 __isl_take isl_union_pw_qpolynomial_fold *upwf);
2113 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_intersect_domain(
2114 __isl_take isl_union_pw_qpolynomial_fold *upwf,
2115 __isl_take isl_union_set *uset);
2117 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_coalesce(
2118 __isl_take isl_pw_qpolynomial_fold *pwf);
2120 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_coalesce(
2121 __isl_take isl_union_pw_qpolynomial_fold *upwf);
2123 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_gist(
2124 __isl_take isl_pw_qpolynomial_fold *pwf,
2125 __isl_take isl_set *context);
2127 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_gist(
2128 __isl_take isl_union_pw_qpolynomial_fold *upwf,
2129 __isl_take isl_union_set *context);
2131 The gist operation applies the gist operation to each of
2132 the cells in the domain of the input piecewise quasipolynomial reduction.
2133 In future, the operation will also exploit the context
2134 to simplify the quasipolynomial reductions associated to each cell.
2136 __isl_give isl_pw_qpolynomial_fold *
2137 isl_map_apply_pw_qpolynomial_fold(
2138 __isl_take isl_map *map,
2139 __isl_take isl_pw_qpolynomial_fold *pwf,
2141 __isl_give isl_union_pw_qpolynomial_fold *
2142 isl_union_map_apply_union_pw_qpolynomial_fold(
2143 __isl_take isl_union_map *umap,
2144 __isl_take isl_union_pw_qpolynomial_fold *upwf,
2148 compose the given map with the given piecewise quasipolynomial reduction.
2149 That is, compute a bound (of the same type as C<pwf> or C<upwf> itself)
2150 over all elements in the intersection of the range of the map
2151 and the domain of the piecewise quasipolynomial reduction
2152 as a function of an element in the domain of the map.
2154 =head2 Dependence Analysis
2156 C<isl> contains specialized functionality for performing
2157 array dataflow analysis. That is, given a I<sink> access relation
2158 and a collection of possible I<source> access relations,
2159 C<isl> can compute relations that describe
2160 for each iteration of the sink access, which iteration
2161 of which of the source access relations was the last
2162 to access the same data element before the given iteration
2164 To compute standard flow dependences, the sink should be
2165 a read, while the sources should be writes.
2166 If any of the source accesses are marked as being I<may>
2167 accesses, then there will be a dependence to the last
2168 I<must> access B<and> to any I<may> access that follows
2169 this last I<must> access.
2170 In particular, if I<all> sources are I<may> accesses,
2171 then memory based dependence analysis is performed.
2172 If, on the other hand, all sources are I<must> accesses,
2173 then value based dependence analysis is performed.
2175 #include <isl_flow.h>
2177 typedef int (*isl_access_level_before)(void *first, void *second);
2179 __isl_give isl_access_info *isl_access_info_alloc(
2180 __isl_take isl_map *sink,
2181 void *sink_user, isl_access_level_before fn,
2183 __isl_give isl_access_info *isl_access_info_add_source(
2184 __isl_take isl_access_info *acc,
2185 __isl_take isl_map *source, int must,
2187 void isl_access_info_free(__isl_take isl_access_info *acc);
2189 __isl_give isl_flow *isl_access_info_compute_flow(
2190 __isl_take isl_access_info *acc);
2192 int isl_flow_foreach(__isl_keep isl_flow *deps,
2193 int (*fn)(__isl_take isl_map *dep, int must,
2194 void *dep_user, void *user),
2196 __isl_give isl_set *isl_flow_get_no_source(
2197 __isl_keep isl_flow *deps, int must);
2198 void isl_flow_free(__isl_take isl_flow *deps);
2200 The function C<isl_access_info_compute_flow> performs the actual
2201 dependence analysis. The other functions are used to construct
2202 the input for this function or to read off the output.
2204 The input is collected in an C<isl_access_info>, which can
2205 be created through a call to C<isl_access_info_alloc>.
2206 The arguments to this functions are the sink access relation
2207 C<sink>, a token C<sink_user> used to identify the sink
2208 access to the user, a callback function for specifying the
2209 relative order of source and sink accesses, and the number
2210 of source access relations that will be added.
2211 The callback function has type C<int (*)(void *first, void *second)>.
2212 The function is called with two user supplied tokens identifying
2213 either a source or the sink and it should return the shared nesting
2214 level and the relative order of the two accesses.
2215 In particular, let I<n> be the number of loops shared by
2216 the two accesses. If C<first> precedes C<second> textually,
2217 then the function should return I<2 * n + 1>; otherwise,
2218 it should return I<2 * n>.
2219 The sources can be added to the C<isl_access_info> by performing
2220 (at most) C<max_source> calls to C<isl_access_info_add_source>.
2221 C<must> indicates whether the source is a I<must> access
2222 or a I<may> access. Note that a multi-valued access relation
2223 should only be marked I<must> if every iteration in the domain
2224 of the relation accesses I<all> elements in its image.
2225 The C<source_user> token is again used to identify
2226 the source access. The range of the source access relation
2227 C<source> should have the same dimension as the range
2228 of the sink access relation.
2229 The C<isl_access_info_free> function should usually not be
2230 called explicitly, because it is called implicitly by
2231 C<isl_access_info_compute_flow>.
2233 The result of the dependence analysis is collected in an
2234 C<isl_flow>. There may be elements in the domain of
2235 the sink access for which no preceding source access could be
2236 found or for which all preceding sources are I<may> accesses.
2237 The sets of these elements can be obtained through
2238 calls to C<isl_flow_get_no_source>, the first with C<must> set
2239 and the second with C<must> unset.
2240 In the case of standard flow dependence analysis,
2241 with the sink a read and the sources I<must> writes,
2242 the first set corresponds to the reads from uninitialized
2243 array elements and the second set is empty.
2244 The actual flow dependences can be extracted using
2245 C<isl_flow_foreach>. This function will call the user-specified
2246 callback function C<fn> for each B<non-empty> dependence between
2247 a source and the sink. The callback function is called
2248 with four arguments, the actual flow dependence relation
2249 mapping source iterations to sink iterations, a boolean that
2250 indicates whether it is a I<must> or I<may> dependence, a token
2251 identifying the source and an additional C<void *> with value
2252 equal to the third argument of the C<isl_flow_foreach> call.
2253 A dependence is marked I<must> if it originates from a I<must>
2254 source and if it is not followed by any I<may> sources.
2256 After finishing with an C<isl_flow>, the user should call
2257 C<isl_flow_free> to free all associated memory.
2259 A higher-level interface to dependence analysis is provided
2260 by the following function.
2262 #include <isl_flow.h>
2264 int isl_union_map_compute_flow(__isl_take isl_union_map *sink,
2265 __isl_take isl_union_map *must_source,
2266 __isl_take isl_union_map *may_source,
2267 __isl_take isl_union_map *schedule,
2268 __isl_give isl_union_map **must_dep,
2269 __isl_give isl_union_map **may_dep,
2270 __isl_give isl_union_set **must_no_source,
2271 __isl_give isl_union_set **may_no_source);
2273 The arrays are identified by the tuple names of the ranges
2274 of the accesses. The iteration domains by the tuple names
2275 of the domains of the accesses and of the schedule.
2276 The relative order of the iteration domains is given by the
2277 schedule. Any of C<must_dep>, C<may_dep>, C<must_no_source>
2278 or C<may_no_source> may be C<NULL>, but a C<NULL> value for
2279 any of the other arguments is treated as an error.
2281 =head2 Parametric Vertex Enumeration
2283 The parametric vertex enumeration described in this section
2284 is mainly intended to be used internally and by the C<barvinok>
2287 #include <isl_vertices.h>
2288 __isl_give isl_vertices *isl_basic_set_compute_vertices(
2289 __isl_keep isl_basic_set *bset);
2291 The function C<isl_basic_set_compute_vertices> performs the
2292 actual computation of the parametric vertices and the chamber
2293 decomposition and store the result in an C<isl_vertices> object.
2294 This information can be queried by either iterating over all
2295 the vertices or iterating over all the chambers or cells
2296 and then iterating over all vertices that are active on the chamber.
2298 int isl_vertices_foreach_vertex(
2299 __isl_keep isl_vertices *vertices,
2300 int (*fn)(__isl_take isl_vertex *vertex, void *user),
2303 int isl_vertices_foreach_cell(
2304 __isl_keep isl_vertices *vertices,
2305 int (*fn)(__isl_take isl_cell *cell, void *user),
2307 int isl_cell_foreach_vertex(__isl_keep isl_cell *cell,
2308 int (*fn)(__isl_take isl_vertex *vertex, void *user),
2311 Other operations that can be performed on an C<isl_vertices> object are
2314 isl_ctx *isl_vertices_get_ctx(
2315 __isl_keep isl_vertices *vertices);
2316 int isl_vertices_get_n_vertices(
2317 __isl_keep isl_vertices *vertices);
2318 void isl_vertices_free(__isl_take isl_vertices *vertices);
2320 Vertices can be inspected and destroyed using the following functions.
2322 isl_ctx *isl_vertex_get_ctx(__isl_keep isl_vertex *vertex);
2323 int isl_vertex_get_id(__isl_keep isl_vertex *vertex);
2324 __isl_give isl_basic_set *isl_vertex_get_domain(
2325 __isl_keep isl_vertex *vertex);
2326 __isl_give isl_basic_set *isl_vertex_get_expr(
2327 __isl_keep isl_vertex *vertex);
2328 void isl_vertex_free(__isl_take isl_vertex *vertex);
2330 C<isl_vertex_get_expr> returns a singleton parametric set describing
2331 the vertex, while C<isl_vertex_get_domain> returns the activity domain
2333 Note that C<isl_vertex_get_domain> and C<isl_vertex_get_expr> return
2334 B<rational> basic sets, so they should mainly be used for inspection
2335 and should not be mixed with integer sets.
2337 Chambers can be inspected and destroyed using the following functions.
2339 isl_ctx *isl_cell_get_ctx(__isl_keep isl_cell *cell);
2340 __isl_give isl_basic_set *isl_cell_get_domain(
2341 __isl_keep isl_cell *cell);
2342 void isl_cell_free(__isl_take isl_cell *cell);
2346 Although C<isl> is mainly meant to be used as a library,
2347 it also contains some basic applications that use some
2348 of the functionality of C<isl>.
2349 The input may be specified in either the L<isl format>
2350 or the L<PolyLib format>.
2352 =head2 C<isl_polyhedron_sample>
2354 C<isl_polyhedron_sample> takes a polyhedron as input and prints
2355 an integer element of the polyhedron, if there is any.
2356 The first column in the output is the denominator and is always
2357 equal to 1. If the polyhedron contains no integer points,
2358 then a vector of length zero is printed.
2362 C<isl_pip> takes the same input as the C<example> program
2363 from the C<piplib> distribution, i.e., a set of constraints
2364 on the parameters, a line containing only -1 and finally a set
2365 of constraints on a parametric polyhedron.
2366 The coefficients of the parameters appear in the last columns
2367 (but before the final constant column).
2368 The output is the lexicographic minimum of the parametric polyhedron.
2369 As C<isl> currently does not have its own output format, the output
2370 is just a dump of the internal state.
2372 =head2 C<isl_polyhedron_minimize>
2374 C<isl_polyhedron_minimize> computes the minimum of some linear
2375 or affine objective function over the integer points in a polyhedron.
2376 If an affine objective function
2377 is given, then the constant should appear in the last column.
2379 =head2 C<isl_polytope_scan>
2381 Given a polytope, C<isl_polytope_scan> prints
2382 all integer points in the polytope.
2384 =head1 C<isl-polylib>
2386 The C<isl-polylib> library provides the following functions for converting
2387 between C<isl> objects and C<PolyLib> objects.
2388 The library is distributed separately for licensing reasons.
2390 #include <isl_set_polylib.h>
2391 __isl_give isl_basic_set *isl_basic_set_new_from_polylib(
2392 Polyhedron *P, __isl_take isl_dim *dim);
2393 Polyhedron *isl_basic_set_to_polylib(
2394 __isl_keep isl_basic_set *bset);
2395 __isl_give isl_set *isl_set_new_from_polylib(Polyhedron *D,
2396 __isl_take isl_dim *dim);
2397 Polyhedron *isl_set_to_polylib(__isl_keep isl_set *set);
2399 #include <isl_map_polylib.h>
2400 __isl_give isl_basic_map *isl_basic_map_new_from_polylib(
2401 Polyhedron *P, __isl_take isl_dim *dim);
2402 __isl_give isl_map *isl_map_new_from_polylib(Polyhedron *D,
2403 __isl_take isl_dim *dim);
2404 Polyhedron *isl_basic_map_to_polylib(
2405 __isl_keep isl_basic_map *bmap);
2406 Polyhedron *isl_map_to_polylib(__isl_keep isl_map *map);