3 C<isl> is a thread-safe C library for manipulating
4 sets and relations of integer points bounded by affine constraints.
5 The descriptions of the sets and relations may involve
6 both parameters and existentially quantified variables.
7 All computations are performed in exact integer arithmetic
9 The C<isl> library offers functionality that is similar
10 to that offered by the C<Omega> and C<Omega+> libraries,
11 but the underlying algorithms are in most cases completely different.
13 The library is by no means complete and some fairly basic
14 functionality is still missing.
15 Still, even in its current form, the library has been successfully
16 used as a backend polyhedral library for the polyhedral
17 scanner C<CLooG> and as part of an equivalence checker of
18 static affine programs.
19 For bug reports, feature requests and questions,
20 visit the the discussion group at
21 L<http://groups.google.com/group/isl-development>.
23 =head2 Backward Incompatible Changes
25 =head3 Changes since isl-0.02
29 =item * The old printing functions have been deprecated
30 and replaced by C<isl_printer> functions, see L<Input and Output>.
32 =item * Most functions related to dependence analysis have acquired
33 an extra C<must> argument. To obtain the old behavior, this argument
34 should be given the value 1. See L<Dependence Analysis>.
38 =head3 Changes since isl-0.03
42 =item * The function C<isl_pw_qpolynomial_fold_add> has been
43 renamed to C<isl_pw_qpolynomial_fold_fold>.
44 Similarly, C<isl_union_pw_qpolynomial_fold_add> has been
45 renamed to C<isl_union_pw_qpolynomial_fold_fold>.
51 The source of C<isl> can be obtained either as a tarball
52 or from the git repository. Both are available from
53 L<http://freshmeat.net/projects/isl/>.
54 The installation process depends on how you obtained
57 =head2 Installation from the git repository
61 =item 1 Clone or update the repository
63 The first time the source is obtained, you need to clone
66 git clone git://repo.or.cz/isl.git
68 To obtain updates, you need to pull in the latest changes
72 =item 2 Generate C<configure>
78 After performing the above steps, continue
79 with the L<Common installation instructions>.
81 =head2 Common installation instructions
87 Building C<isl> requires C<GMP>, including its headers files.
88 Your distribution may not provide these header files by default
89 and you may need to install a package called C<gmp-devel> or something
90 similar. Alternatively, C<GMP> can be built from
91 source, available from L<http://gmplib.org/>.
95 C<isl> uses the standard C<autoconf> C<configure> script.
100 optionally followed by some configure options.
101 A complete list of options can be obtained by running
105 Below we discuss some of the more common options.
107 C<isl> can optionally use C<piplib>, but no
108 C<piplib> functionality is currently used by default.
109 The C<--with-piplib> option can
110 be used to specify which C<piplib>
111 library to use, either an installed version (C<system>),
112 an externally built version (C<build>)
113 or no version (C<no>). The option C<build> is mostly useful
114 in C<configure> scripts of larger projects that bundle both C<isl>
121 Installation prefix for C<isl>
123 =item C<--with-gmp-prefix>
125 Installation prefix for C<GMP> (architecture-independent files).
127 =item C<--with-gmp-exec-prefix>
129 Installation prefix for C<GMP> (architecture-dependent files).
131 =item C<--with-piplib>
133 Which copy of C<piplib> to use, either C<no> (default), C<system> or C<build>.
135 =item C<--with-piplib-prefix>
137 Installation prefix for C<system> C<piplib> (architecture-independent files).
139 =item C<--with-piplib-exec-prefix>
141 Installation prefix for C<system> C<piplib> (architecture-dependent files).
143 =item C<--with-piplib-builddir>
145 Location where C<build> C<piplib> was built.
153 =item 4 Install (optional)
161 =head2 Initialization
163 All manipulations of integer sets and relations occur within
164 the context of an C<isl_ctx>.
165 A given C<isl_ctx> can only be used within a single thread.
166 All arguments of a function are required to have been allocated
167 within the same context.
168 There are currently no functions available for moving an object
169 from one C<isl_ctx> to another C<isl_ctx>. This means that
170 there is currently no way of safely moving an object from one
171 thread to another, unless the whole C<isl_ctx> is moved.
173 An C<isl_ctx> can be allocated using C<isl_ctx_alloc> and
174 freed using C<isl_ctx_free>.
175 All objects allocated within an C<isl_ctx> should be freed
176 before the C<isl_ctx> itself is freed.
178 isl_ctx *isl_ctx_alloc();
179 void isl_ctx_free(isl_ctx *ctx);
183 All operations on integers, mainly the coefficients
184 of the constraints describing the sets and relations,
185 are performed in exact integer arithmetic using C<GMP>.
186 However, to allow future versions of C<isl> to optionally
187 support fixed integer arithmetic, all calls to C<GMP>
188 are wrapped inside C<isl> specific macros.
189 The basic type is C<isl_int> and the following operations
190 are available on this type.
191 The meanings of these operations are essentially the same
192 as their C<GMP> C<mpz_> counterparts.
193 As always with C<GMP> types, C<isl_int>s need to be
194 initialized with C<isl_int_init> before they can be used
195 and they need to be released with C<isl_int_clear>
200 =item isl_int_init(i)
202 =item isl_int_clear(i)
204 =item isl_int_set(r,i)
206 =item isl_int_set_si(r,i)
208 =item isl_int_abs(r,i)
210 =item isl_int_neg(r,i)
212 =item isl_int_swap(i,j)
214 =item isl_int_swap_or_set(i,j)
216 =item isl_int_add_ui(r,i,j)
218 =item isl_int_sub_ui(r,i,j)
220 =item isl_int_add(r,i,j)
222 =item isl_int_sub(r,i,j)
224 =item isl_int_mul(r,i,j)
226 =item isl_int_mul_ui(r,i,j)
228 =item isl_int_addmul(r,i,j)
230 =item isl_int_submul(r,i,j)
232 =item isl_int_gcd(r,i,j)
234 =item isl_int_lcm(r,i,j)
236 =item isl_int_divexact(r,i,j)
238 =item isl_int_cdiv_q(r,i,j)
240 =item isl_int_fdiv_q(r,i,j)
242 =item isl_int_fdiv_r(r,i,j)
244 =item isl_int_fdiv_q_ui(r,i,j)
246 =item isl_int_read(r,s)
248 =item isl_int_print(out,i,width)
252 =item isl_int_cmp(i,j)
254 =item isl_int_cmp_si(i,si)
256 =item isl_int_eq(i,j)
258 =item isl_int_ne(i,j)
260 =item isl_int_lt(i,j)
262 =item isl_int_le(i,j)
264 =item isl_int_gt(i,j)
266 =item isl_int_ge(i,j)
268 =item isl_int_abs_eq(i,j)
270 =item isl_int_abs_ne(i,j)
272 =item isl_int_abs_lt(i,j)
274 =item isl_int_abs_gt(i,j)
276 =item isl_int_abs_ge(i,j)
278 =item isl_int_is_zero(i)
280 =item isl_int_is_one(i)
282 =item isl_int_is_negone(i)
284 =item isl_int_is_pos(i)
286 =item isl_int_is_neg(i)
288 =item isl_int_is_nonpos(i)
290 =item isl_int_is_nonneg(i)
292 =item isl_int_is_divisible_by(i,j)
296 =head2 Sets and Relations
298 C<isl> uses six types of objects for representing sets and relations,
299 C<isl_basic_set>, C<isl_basic_map>, C<isl_set>, C<isl_map>,
300 C<isl_union_set> and C<isl_union_map>.
301 C<isl_basic_set> and C<isl_basic_map> represent sets and relations that
302 can be described as a conjunction of affine constraints, while
303 C<isl_set> and C<isl_map> represent unions of
304 C<isl_basic_set>s and C<isl_basic_map>s, respectively.
305 However, all C<isl_basic_set>s or C<isl_basic_map>s in the union need
306 to have the same dimension. C<isl_union_set>s and C<isl_union_map>s
307 represent unions of C<isl_set>s or C<isl_map>s of I<different> dimensions,
308 where dimensions with different space names
309 (see L<Dimension Specifications>) are considered different as well.
310 The difference between sets and relations (maps) is that sets have
311 one set of variables, while relations have two sets of variables,
312 input variables and output variables.
314 =head2 Memory Management
316 Since a high-level operation on sets and/or relations usually involves
317 several substeps and since the user is usually not interested in
318 the intermediate results, most functions that return a new object
319 will also release all the objects passed as arguments.
320 If the user still wants to use one or more of these arguments
321 after the function call, she should pass along a copy of the
322 object rather than the object itself.
323 The user is then responsible for make sure that the original
324 object gets used somewhere else or is explicitly freed.
326 The arguments and return values of all documents functions are
327 annotated to make clear which arguments are released and which
328 arguments are preserved. In particular, the following annotations
335 C<__isl_give> means that a new object is returned.
336 The user should make sure that the returned pointer is
337 used exactly once as a value for an C<__isl_take> argument.
338 In between, it can be used as a value for as many
339 C<__isl_keep> arguments as the user likes.
340 There is one exception, and that is the case where the
341 pointer returned is C<NULL>. Is this case, the user
342 is free to use it as an C<__isl_take> argument or not.
346 C<__isl_take> means that the object the argument points to
347 is taken over by the function and may no longer be used
348 by the user as an argument to any other function.
349 The pointer value must be one returned by a function
350 returning an C<__isl_give> pointer.
351 If the user passes in a C<NULL> value, then this will
352 be treated as an error in the sense that the function will
353 not perform its usual operation. However, it will still
354 make sure that all the the other C<__isl_take> arguments
359 C<__isl_keep> means that the function will only use the object
360 temporarily. After the function has finished, the user
361 can still use it as an argument to other functions.
362 A C<NULL> value will be treated in the same way as
363 a C<NULL> value for an C<__isl_take> argument.
367 =head2 Dimension Specifications
369 Whenever a new set or relation is created from scratch,
370 its dimension needs to be specified using an C<isl_dim>.
373 __isl_give isl_dim *isl_dim_alloc(isl_ctx *ctx,
374 unsigned nparam, unsigned n_in, unsigned n_out);
375 __isl_give isl_dim *isl_dim_set_alloc(isl_ctx *ctx,
376 unsigned nparam, unsigned dim);
377 __isl_give isl_dim *isl_dim_copy(__isl_keep isl_dim *dim);
378 void isl_dim_free(__isl_take isl_dim *dim);
379 unsigned isl_dim_size(__isl_keep isl_dim *dim,
380 enum isl_dim_type type);
382 The dimension specification used for creating a set
383 needs to be created using C<isl_dim_set_alloc>, while
384 that for creating a relation
385 needs to be created using C<isl_dim_alloc>.
386 C<isl_dim_size> can be used
387 to find out the number of dimensions of each type in
388 a dimension specification, where type may be
389 C<isl_dim_param>, C<isl_dim_in> (only for relations),
390 C<isl_dim_out> (only for relations), C<isl_dim_set>
391 (only for sets) or C<isl_dim_all>.
393 It is often useful to create objects that live in the
394 same space as some other object. This can be accomplished
395 by creating the new objects
396 (see L<Creating New Sets and Relations> or
397 L<Creating New (Piecewise) Quasipolynomials>) based on the dimension
398 specification of the original object.
401 __isl_give isl_dim *isl_basic_set_get_dim(
402 __isl_keep isl_basic_set *bset);
403 __isl_give isl_dim *isl_set_get_dim(__isl_keep isl_set *set);
405 #include <isl_union_set.h>
406 __isl_give isl_dim *isl_union_set_get_dim(
407 __isl_keep isl_union_set *uset);
410 __isl_give isl_dim *isl_basic_map_get_dim(
411 __isl_keep isl_basic_map *bmap);
412 __isl_give isl_dim *isl_map_get_dim(__isl_keep isl_map *map);
414 #include <isl_union_map.h>
415 __isl_give isl_dim *isl_union_map_get_dim(
416 __isl_keep isl_union_map *umap);
418 #include <isl_polynomial.h>
419 __isl_give isl_dim *isl_qpolynomial_get_dim(
420 __isl_keep isl_qpolynomial *qp);
421 __isl_give isl_dim *isl_pw_qpolynomial_get_dim(
422 __isl_keep isl_pw_qpolynomial *pwqp);
423 __isl_give isl_dim *isl_union_pw_qpolynomial_get_dim(
424 __isl_keep isl_union_pw_qpolynomial *upwqp);
425 __isl_give isl_dim *isl_union_pw_qpolynomial_fold_get_dim(
426 __isl_keep isl_union_pw_qpolynomial_fold *upwf);
428 The names of the individual dimensions may be set or read off
429 using the following functions.
432 __isl_give isl_dim *isl_dim_set_name(__isl_take isl_dim *dim,
433 enum isl_dim_type type, unsigned pos,
434 __isl_keep const char *name);
435 __isl_keep const char *isl_dim_get_name(__isl_keep isl_dim *dim,
436 enum isl_dim_type type, unsigned pos);
438 Note that C<isl_dim_get_name> returns a pointer to some internal
439 data structure, so the result can only be used while the
440 corresponding C<isl_dim> is alive.
441 Also note that every function that operates on two sets or relations
442 requires that both arguments have the same parameters. This also
443 means that if one of the arguments has named parameters, then the
444 other needs to have named parameters too and the names need to match.
445 Pairs of C<isl_union_set> and/or C<isl_union_map> arguments may
446 have different parameters (as long as they are named), in which case
447 the result will have as parameters the union of the parameters of
450 The names of entire spaces may be set or read off
451 using the following functions.
454 __isl_give isl_dim *isl_dim_set_tuple_name(
455 __isl_take isl_dim *dim,
456 enum isl_dim_type type, const char *s);
457 const char *isl_dim_get_tuple_name(__isl_keep isl_dim *dim,
458 enum isl_dim_type type);
460 The C<dim> argument needs to be one of C<isl_dim_in>, C<isl_dim_out>
461 or C<isl_dim_set>. As with C<isl_dim_get_name>,
462 the C<isl_dim_get_tuple_name> function returns a pointer to some internal
464 Binary operations require the corresponding spaces of their arguments
465 to have the same name.
467 Spaces can be nested. In particular, the domain of a set or
468 the domain or range of a relation can be a nested relation.
469 The following functions can be used to construct and deconstruct
470 such nested dimension specifications.
473 int isl_dim_is_wrapping(__isl_keep isl_dim *dim);
474 __isl_give isl_dim *isl_dim_wrap(__isl_take isl_dim *dim);
475 __isl_give isl_dim *isl_dim_unwrap(__isl_take isl_dim *dim);
477 The input to C<isl_dim_is_wrapping> and C<isl_dim_unwrap> should
478 be the dimension specification of a set, while that of
479 C<isl_dim_wrap> should be the dimension specification of a relation.
480 Conversely, the output of C<isl_dim_unwrap> is the dimension specification
481 of a relation, while that of C<isl_dim_wrap> is the dimension specification
484 =head2 Input and Output
486 C<isl> supports its own input/output format, which is similar
487 to the C<Omega> format, but also supports the C<PolyLib> format
492 The C<isl> format is similar to that of C<Omega>, but has a different
493 syntax for describing the parameters and allows for the definition
494 of an existentially quantified variable as the integer division
495 of an affine expression.
496 For example, the set of integers C<i> between C<0> and C<n>
497 such that C<i % 10 <= 6> can be described as
499 [n] -> { [i] : exists (a = [i/10] : 0 <= i and i <= n and
502 A set or relation can have several disjuncts, separated
503 by the keyword C<or>. Each disjunct is either a conjunction
504 of constraints or a projection (C<exists>) of a conjunction
505 of constraints. The constraints are separated by the keyword
508 =head3 C<PolyLib> format
510 If the represented set is a union, then the first line
511 contains a single number representing the number of disjuncts.
512 Otherwise, a line containing the number C<1> is optional.
514 Each disjunct is represented by a matrix of constraints.
515 The first line contains two numbers representing
516 the number of rows and columns,
517 where the number of rows is equal to the number of constraints
518 and the number of columns is equal to two plus the number of variables.
519 The following lines contain the actual rows of the constraint matrix.
520 In each row, the first column indicates whether the constraint
521 is an equality (C<0>) or inequality (C<1>). The final column
522 corresponds to the constant term.
524 If the set is parametric, then the coefficients of the parameters
525 appear in the last columns before the constant column.
526 The coefficients of any existentially quantified variables appear
527 between those of the set variables and those of the parameters.
532 __isl_give isl_basic_set *isl_basic_set_read_from_file(
533 isl_ctx *ctx, FILE *input, int nparam);
534 __isl_give isl_basic_set *isl_basic_set_read_from_str(
535 isl_ctx *ctx, const char *str, int nparam);
536 __isl_give isl_set *isl_set_read_from_file(isl_ctx *ctx,
537 FILE *input, int nparam);
538 __isl_give isl_set *isl_set_read_from_str(isl_ctx *ctx,
539 const char *str, int nparam);
542 __isl_give isl_basic_map *isl_basic_map_read_from_file(
543 isl_ctx *ctx, FILE *input, int nparam);
544 __isl_give isl_basic_map *isl_basic_map_read_from_str(
545 isl_ctx *ctx, const char *str, int nparam);
546 __isl_give isl_map *isl_map_read_from_file(
547 struct isl_ctx *ctx, FILE *input, int nparam);
548 __isl_give isl_map *isl_map_read_from_str(isl_ctx *ctx,
549 const char *str, int nparam);
551 The input format is autodetected and may be either the C<PolyLib> format
552 or the C<isl> format.
553 C<nparam> specifies how many of the final columns in
554 the C<PolyLib> format correspond to parameters.
555 If input is given in the C<isl> format, then the number
556 of parameters needs to be equal to C<nparam>.
557 If C<nparam> is negative, then any number of parameters
558 is accepted in the C<isl> format and zero parameters
559 are assumed in the C<PolyLib> format.
563 Before anything can be printed, an C<isl_printer> needs to
566 __isl_give isl_printer *isl_printer_to_file(isl_ctx *ctx,
568 __isl_give isl_printer *isl_printer_to_str(isl_ctx *ctx);
569 void isl_printer_free(__isl_take isl_printer *printer);
570 __isl_give char *isl_printer_get_str(
571 __isl_keep isl_printer *printer);
573 The behavior of the printer can be modified in various ways
575 __isl_give isl_printer *isl_printer_set_output_format(
576 __isl_take isl_printer *p, int output_format);
577 __isl_give isl_printer *isl_printer_set_indent(
578 __isl_take isl_printer *p, int indent);
579 __isl_give isl_printer *isl_printer_set_prefix(
580 __isl_take isl_printer *p, const char *prefix);
581 __isl_give isl_printer *isl_printer_set_suffix(
582 __isl_take isl_printer *p, const char *suffix);
584 The C<output_format> may be either C<ISL_FORMAT_ISL>, C<ISL_FORMAT_OMEGA>
585 or C<ISL_FORMAT_POLYLIB> and defaults to C<ISL_FORMAT_ISL>.
586 Each line in the output is indented by C<indent> spaces
587 (default: 0), prefixed by C<prefix> and suffixed by C<suffix>.
588 In the C<PolyLib> format output,
589 the coefficients of the existentially quantified variables
590 appear between those of the set variables and those
593 To actually print something, use
596 __isl_give isl_printer *isl_printer_print_basic_set(
597 __isl_take isl_printer *printer,
598 __isl_keep isl_basic_set *bset);
599 __isl_give isl_printer *isl_printer_print_set(
600 __isl_take isl_printer *printer,
601 __isl_keep isl_set *set);
604 __isl_give isl_printer *isl_printer_print_basic_map(
605 __isl_take isl_printer *printer,
606 __isl_keep isl_basic_map *bmap);
607 __isl_give isl_printer *isl_printer_print_map(
608 __isl_take isl_printer *printer,
609 __isl_keep isl_map *map);
611 #include <isl_union_set.h>
612 __isl_give isl_printer *isl_printer_print_union_set(
613 __isl_take isl_printer *p,
614 __isl_keep isl_union_set *uset);
616 #include <isl_union_map.h>
617 __isl_give isl_printer *isl_printer_print_union_map(
618 __isl_take isl_printer *p,
619 __isl_keep isl_union_map *umap);
621 When called on a file printer, the following function flushes
622 the file. When called on a string printer, the buffer is cleared.
624 __isl_give isl_printer *isl_printer_flush(
625 __isl_take isl_printer *p);
627 =head2 Creating New Sets and Relations
629 C<isl> has functions for creating some standard sets and relations.
633 =item * Empty sets and relations
635 __isl_give isl_basic_set *isl_basic_set_empty(
636 __isl_take isl_dim *dim);
637 __isl_give isl_basic_map *isl_basic_map_empty(
638 __isl_take isl_dim *dim);
639 __isl_give isl_set *isl_set_empty(
640 __isl_take isl_dim *dim);
641 __isl_give isl_map *isl_map_empty(
642 __isl_take isl_dim *dim);
643 __isl_give isl_union_set *isl_union_set_empty(
644 __isl_take isl_dim *dim);
645 __isl_give isl_union_map *isl_union_map_empty(
646 __isl_take isl_dim *dim);
648 For C<isl_union_set>s and C<isl_union_map>s, the dimensions specification
649 is only used to specify the parameters.
651 =item * Universe sets and relations
653 __isl_give isl_basic_set *isl_basic_set_universe(
654 __isl_take isl_dim *dim);
655 __isl_give isl_basic_map *isl_basic_map_universe(
656 __isl_take isl_dim *dim);
657 __isl_give isl_set *isl_set_universe(
658 __isl_take isl_dim *dim);
659 __isl_give isl_map *isl_map_universe(
660 __isl_take isl_dim *dim);
662 =item * Identity relations
664 __isl_give isl_basic_map *isl_basic_map_identity(
665 __isl_take isl_dim *set_dim);
666 __isl_give isl_map *isl_map_identity(
667 __isl_take isl_dim *set_dim);
669 These functions take a dimension specification for a B<set>
670 and return an identity relation between two such sets.
672 =item * Lexicographic order
674 __isl_give isl_map *isl_map_lex_lt(
675 __isl_take isl_dim *set_dim);
676 __isl_give isl_map *isl_map_lex_le(
677 __isl_take isl_dim *set_dim);
678 __isl_give isl_map *isl_map_lex_gt(
679 __isl_take isl_dim *set_dim);
680 __isl_give isl_map *isl_map_lex_ge(
681 __isl_take isl_dim *set_dim);
682 __isl_give isl_map *isl_map_lex_lt_first(
683 __isl_take isl_dim *dim, unsigned n);
684 __isl_give isl_map *isl_map_lex_le_first(
685 __isl_take isl_dim *dim, unsigned n);
686 __isl_give isl_map *isl_map_lex_gt_first(
687 __isl_take isl_dim *dim, unsigned n);
688 __isl_give isl_map *isl_map_lex_ge_first(
689 __isl_take isl_dim *dim, unsigned n);
691 The first four functions take a dimension specification for a B<set>
692 and return relations that express that the elements in the domain
693 are lexicographically less
694 (C<isl_map_lex_lt>), less or equal (C<isl_map_lex_le>),
695 greater (C<isl_map_lex_gt>) or greater or equal (C<isl_map_lex_ge>)
696 than the elements in the range.
697 The last four functions take a dimension specification for a map
698 and return relations that express that the first C<n> dimensions
699 in the domain are lexicographically less
700 (C<isl_map_lex_lt_first>), less or equal (C<isl_map_lex_le_first>),
701 greater (C<isl_map_lex_gt_first>) or greater or equal (C<isl_map_lex_ge_first>)
702 than the first C<n> dimensions in the range.
706 A basic set or relation can be converted to a set or relation
707 using the following functions.
709 __isl_give isl_set *isl_set_from_basic_set(
710 __isl_take isl_basic_set *bset);
711 __isl_give isl_map *isl_map_from_basic_map(
712 __isl_take isl_basic_map *bmap);
714 Sets and relations can be converted to union sets and relations
715 using the following functions.
717 __isl_give isl_union_map *isl_union_map_from_map(
718 __isl_take isl_map *map);
719 __isl_give isl_union_set *isl_union_set_from_set(
720 __isl_take isl_set *set);
722 Sets and relations can be copied and freed again using the following
725 __isl_give isl_basic_set *isl_basic_set_copy(
726 __isl_keep isl_basic_set *bset);
727 __isl_give isl_set *isl_set_copy(__isl_keep isl_set *set);
728 __isl_give isl_union_set *isl_union_set_copy(
729 __isl_keep isl_union_set *uset);
730 __isl_give isl_basic_map *isl_basic_map_copy(
731 __isl_keep isl_basic_map *bmap);
732 __isl_give isl_map *isl_map_copy(__isl_keep isl_map *map);
733 __isl_give isl_union_map *isl_union_map_copy(
734 __isl_keep isl_union_map *umap);
735 void isl_basic_set_free(__isl_take isl_basic_set *bset);
736 void isl_set_free(__isl_take isl_set *set);
737 void isl_union_set_free(__isl_take isl_union_set *uset);
738 void isl_basic_map_free(__isl_take isl_basic_map *bmap);
739 void isl_map_free(__isl_take isl_map *map);
740 void isl_union_map_free(__isl_take isl_union_map *umap);
742 Other sets and relations can be constructed by starting
743 from a universe set or relation, adding equality and/or
744 inequality constraints and then projecting out the
745 existentially quantified variables, if any.
746 Constraints can be constructed, manipulated and
747 added to basic sets and relations using the following functions.
749 #include <isl_constraint.h>
750 __isl_give isl_constraint *isl_equality_alloc(
751 __isl_take isl_dim *dim);
752 __isl_give isl_constraint *isl_inequality_alloc(
753 __isl_take isl_dim *dim);
754 void isl_constraint_set_constant(
755 __isl_keep isl_constraint *constraint, isl_int v);
756 void isl_constraint_set_coefficient(
757 __isl_keep isl_constraint *constraint,
758 enum isl_dim_type type, int pos, isl_int v);
759 __isl_give isl_basic_map *isl_basic_map_add_constraint(
760 __isl_take isl_basic_map *bmap,
761 __isl_take isl_constraint *constraint);
762 __isl_give isl_basic_set *isl_basic_set_add_constraint(
763 __isl_take isl_basic_set *bset,
764 __isl_take isl_constraint *constraint);
766 For example, to create a set containing the even integers
767 between 10 and 42, you would use the following code.
771 struct isl_constraint *c;
772 struct isl_basic_set *bset;
775 dim = isl_dim_set_alloc(ctx, 0, 2);
776 bset = isl_basic_set_universe(isl_dim_copy(dim));
778 c = isl_equality_alloc(isl_dim_copy(dim));
779 isl_int_set_si(v, -1);
780 isl_constraint_set_coefficient(c, isl_dim_set, 0, v);
781 isl_int_set_si(v, 2);
782 isl_constraint_set_coefficient(c, isl_dim_set, 1, v);
783 bset = isl_basic_set_add_constraint(bset, c);
785 c = isl_inequality_alloc(isl_dim_copy(dim));
786 isl_int_set_si(v, -10);
787 isl_constraint_set_constant(c, v);
788 isl_int_set_si(v, 1);
789 isl_constraint_set_coefficient(c, isl_dim_set, 0, v);
790 bset = isl_basic_set_add_constraint(bset, c);
792 c = isl_inequality_alloc(dim);
793 isl_int_set_si(v, 42);
794 isl_constraint_set_constant(c, v);
795 isl_int_set_si(v, -1);
796 isl_constraint_set_coefficient(c, isl_dim_set, 0, v);
797 bset = isl_basic_set_add_constraint(bset, c);
799 bset = isl_basic_set_project_out(bset, isl_dim_set, 1, 1);
805 struct isl_basic_set *bset;
806 bset = isl_basic_set_read_from_str(ctx,
807 "{[i] : exists (a : i = 2a and i >= 10 and i <= 42)}", -1);
809 =head2 Inspecting Sets and Relations
811 Usually, the user should not have to care about the actual constraints
812 of the sets and maps, but should instead apply the abstract operations
813 explained in the following sections.
814 Occasionally, however, it may be required to inspect the individual
815 coefficients of the constraints. This section explains how to do so.
816 In these cases, it may also be useful to have C<isl> compute
817 an explicit representation of the existentially quantified variables.
819 __isl_give isl_set *isl_set_compute_divs(
820 __isl_take isl_set *set);
821 __isl_give isl_map *isl_map_compute_divs(
822 __isl_take isl_map *map);
823 __isl_give isl_union_set *isl_union_set_compute_divs(
824 __isl_take isl_union_set *uset);
825 __isl_give isl_union_map *isl_union_map_compute_divs(
826 __isl_take isl_union_map *umap);
828 This explicit representation defines the existentially quantified
829 variables as integer divisions of the other variables, possibly
830 including earlier existentially quantified variables.
831 An explicitly represented existentially quantified variable therefore
832 has a unique value when the values of the other variables are known.
833 If, furthermore, the same existentials, i.e., existentials
834 with the same explicit representations, should appear in the
835 same order in each of the disjuncts of a set or map, then the user should call
836 either of the following functions.
838 __isl_give isl_set *isl_set_align_divs(
839 __isl_take isl_set *set);
840 __isl_give isl_map *isl_map_align_divs(
841 __isl_take isl_map *map);
843 To iterate over all the sets or maps in a union set or map, use
845 int isl_union_set_foreach_set(__isl_keep isl_union_set *uset,
846 int (*fn)(__isl_take isl_set *set, void *user),
848 int isl_union_map_foreach_map(__isl_keep isl_union_map *umap,
849 int (*fn)(__isl_take isl_map *map, void *user),
852 To iterate over all the basic sets or maps in a set or map, use
854 int isl_set_foreach_basic_set(__isl_keep isl_set *set,
855 int (*fn)(__isl_take isl_basic_set *bset, void *user),
857 int isl_map_foreach_basic_map(__isl_keep isl_map *map,
858 int (*fn)(__isl_take isl_basic_map *bmap, void *user),
861 The callback function C<fn> should return 0 if successful and
862 -1 if an error occurs. In the latter case, or if any other error
863 occurs, the above functions will return -1.
865 It should be noted that C<isl> does not guarantee that
866 the basic sets or maps passed to C<fn> are disjoint.
867 If this is required, then the user should call one of
868 the following functions first.
870 __isl_give isl_set *isl_set_make_disjoint(
871 __isl_take isl_set *set);
872 __isl_give isl_map *isl_map_make_disjoint(
873 __isl_take isl_map *map);
875 To iterate over the constraints of a basic set or map, use
877 #include <isl_constraint.h>
879 int isl_basic_map_foreach_constraint(
880 __isl_keep isl_basic_map *bmap,
881 int (*fn)(__isl_take isl_constraint *c, void *user),
883 void isl_constraint_free(struct isl_constraint *c);
885 Again, the callback function C<fn> should return 0 if successful and
886 -1 if an error occurs. In the latter case, or if any other error
887 occurs, the above functions will return -1.
888 The constraint C<c> represents either an equality or an inequality.
889 Use the following function to find out whether a constraint
890 represents an equality. If not, it represents an inequality.
892 int isl_constraint_is_equality(
893 __isl_keep isl_constraint *constraint);
895 The coefficients of the constraints can be inspected using
896 the following functions.
898 void isl_constraint_get_constant(
899 __isl_keep isl_constraint *constraint, isl_int *v);
900 void isl_constraint_get_coefficient(
901 __isl_keep isl_constraint *constraint,
902 enum isl_dim_type type, int pos, isl_int *v);
904 The explicit representations of the existentially quantified
905 variables can be inspected using the following functions.
906 Note that the user is only allowed to use these functions
907 if the inspected set or map is the result of a call
908 to C<isl_set_compute_divs> or C<isl_map_compute_divs>.
910 __isl_give isl_div *isl_constraint_div(
911 __isl_keep isl_constraint *constraint, int pos);
912 void isl_div_get_constant(__isl_keep isl_div *div,
914 void isl_div_get_denominator(__isl_keep isl_div *div,
916 void isl_div_get_coefficient(__isl_keep isl_div *div,
917 enum isl_dim_type type, int pos, isl_int *v);
919 To obtain the constraints of a basic map in matrix
920 form, use the following functions.
922 __isl_give isl_mat *isl_basic_map_equalities_matrix(
923 __isl_keep isl_basic_map *bmap,
924 enum isl_dim_type c1,
925 enum isl_dim_type c2, enum isl_dim_type c3,
926 enum isl_dim_type c4, enum isl_dim_type c5);
927 __isl_give isl_mat *isl_basic_map_inequalities_matrix(
928 __isl_keep isl_basic_map *bmap,
929 enum isl_dim_type c1,
930 enum isl_dim_type c2, enum isl_dim_type c3,
931 enum isl_dim_type c4, enum isl_dim_type c5);
933 The C<isl_dim_type> arguments dictate the order in which
934 different kinds of variables appear in the resulting matrix
935 and should be a permutation of C<isl_dim_cst>, C<isl_dim_param>,
936 C<isl_dim_in>, C<isl_dim_out> and C<isl_dim_div>.
940 =head3 Unary Properties
946 The following functions test whether the given set or relation
947 contains any integer points. The ``fast'' variants do not perform
948 any computations, but simply check if the given set or relation
949 is already known to be empty.
951 int isl_basic_set_fast_is_empty(__isl_keep isl_basic_set *bset);
952 int isl_basic_set_is_empty(__isl_keep isl_basic_set *bset);
953 int isl_set_is_empty(__isl_keep isl_set *set);
954 int isl_union_set_is_empty(__isl_keep isl_union_set *uset);
955 int isl_basic_map_fast_is_empty(__isl_keep isl_basic_map *bmap);
956 int isl_basic_map_is_empty(__isl_keep isl_basic_map *bmap);
957 int isl_map_fast_is_empty(__isl_keep isl_map *map);
958 int isl_map_is_empty(__isl_keep isl_map *map);
959 int isl_union_map_is_empty(__isl_keep isl_union_map *umap);
963 int isl_basic_set_is_universe(__isl_keep isl_basic_set *bset);
964 int isl_basic_map_is_universe(__isl_keep isl_basic_map *bmap);
965 int isl_set_fast_is_universe(__isl_keep isl_set *set);
967 =item * Single-valuedness
969 int isl_map_is_single_valued(__isl_keep isl_map *map);
973 int isl_map_is_bijective(__isl_keep isl_map *map);
977 The followning functions check whether the domain of the given
978 (basic) set is a wrapped relation.
980 int isl_basic_set_is_wrapping(
981 __isl_keep isl_basic_set *bset);
982 int isl_set_is_wrapping(__isl_keep isl_set *set);
986 =head3 Binary Properties
992 int isl_set_fast_is_equal(__isl_keep isl_set *set1,
993 __isl_keep isl_set *set2);
994 int isl_set_is_equal(__isl_keep isl_set *set1,
995 __isl_keep isl_set *set2);
996 int isl_basic_map_is_equal(
997 __isl_keep isl_basic_map *bmap1,
998 __isl_keep isl_basic_map *bmap2);
999 int isl_map_is_equal(__isl_keep isl_map *map1,
1000 __isl_keep isl_map *map2);
1001 int isl_map_fast_is_equal(__isl_keep isl_map *map1,
1002 __isl_keep isl_map *map2);
1003 int isl_union_map_is_equal(
1004 __isl_keep isl_union_map *umap1,
1005 __isl_keep isl_union_map *umap2);
1007 =item * Disjointness
1009 int isl_set_fast_is_disjoint(__isl_keep isl_set *set1,
1010 __isl_keep isl_set *set2);
1014 int isl_set_is_subset(__isl_keep isl_set *set1,
1015 __isl_keep isl_set *set2);
1016 int isl_set_is_strict_subset(
1017 __isl_keep isl_set *set1,
1018 __isl_keep isl_set *set2);
1019 int isl_basic_map_is_subset(
1020 __isl_keep isl_basic_map *bmap1,
1021 __isl_keep isl_basic_map *bmap2);
1022 int isl_basic_map_is_strict_subset(
1023 __isl_keep isl_basic_map *bmap1,
1024 __isl_keep isl_basic_map *bmap2);
1025 int isl_map_is_subset(
1026 __isl_keep isl_map *map1,
1027 __isl_keep isl_map *map2);
1028 int isl_map_is_strict_subset(
1029 __isl_keep isl_map *map1,
1030 __isl_keep isl_map *map2);
1031 int isl_union_map_is_subset(
1032 __isl_keep isl_union_map *umap1,
1033 __isl_keep isl_union_map *umap2);
1034 int isl_union_map_is_strict_subset(
1035 __isl_keep isl_union_map *umap1,
1036 __isl_keep isl_union_map *umap2);
1040 =head2 Unary Operations
1046 __isl_give isl_set *isl_set_complement(
1047 __isl_take isl_set *set);
1051 __isl_give isl_basic_map *isl_basic_map_reverse(
1052 __isl_take isl_basic_map *bmap);
1053 __isl_give isl_map *isl_map_reverse(
1054 __isl_take isl_map *map);
1055 __isl_give isl_union_map *isl_union_map_reverse(
1056 __isl_take isl_union_map *umap);
1060 __isl_give isl_basic_set *isl_basic_set_project_out(
1061 __isl_take isl_basic_set *bset,
1062 enum isl_dim_type type, unsigned first, unsigned n);
1063 __isl_give isl_basic_map *isl_basic_map_project_out(
1064 __isl_take isl_basic_map *bmap,
1065 enum isl_dim_type type, unsigned first, unsigned n);
1066 __isl_give isl_set *isl_set_project_out(__isl_take isl_set *set,
1067 enum isl_dim_type type, unsigned first, unsigned n);
1068 __isl_give isl_map *isl_map_project_out(__isl_take isl_map *map,
1069 enum isl_dim_type type, unsigned first, unsigned n);
1070 __isl_give isl_basic_set *isl_basic_map_domain(
1071 __isl_take isl_basic_map *bmap);
1072 __isl_give isl_basic_set *isl_basic_map_range(
1073 __isl_take isl_basic_map *bmap);
1074 __isl_give isl_set *isl_map_domain(
1075 __isl_take isl_map *bmap);
1076 __isl_give isl_set *isl_map_range(
1077 __isl_take isl_map *map);
1078 __isl_give isl_union_set *isl_union_map_domain(
1079 __isl_take isl_union_map *umap);
1080 __isl_give isl_union_set *isl_union_map_range(
1081 __isl_take isl_union_map *umap);
1085 __isl_give isl_basic_set *isl_basic_map_deltas(
1086 __isl_take isl_basic_map *bmap);
1087 __isl_give isl_set *isl_map_deltas(__isl_take isl_map *map);
1088 __isl_give isl_union_set *isl_union_map_deltas(
1089 __isl_take isl_union_map *umap);
1091 These functions return a (basic) set containing the differences
1092 between image elements and corresponding domain elements in the input.
1096 Simplify the representation of a set or relation by trying
1097 to combine pairs of basic sets or relations into a single
1098 basic set or relation.
1100 __isl_give isl_set *isl_set_coalesce(__isl_take isl_set *set);
1101 __isl_give isl_map *isl_map_coalesce(__isl_take isl_map *map);
1102 __isl_give isl_union_set *isl_union_set_coalesce(
1103 __isl_take isl_union_set *uset);
1104 __isl_give isl_union_map *isl_union_map_coalesce(
1105 __isl_take isl_union_map *umap);
1109 __isl_give isl_basic_set *isl_set_convex_hull(
1110 __isl_take isl_set *set);
1111 __isl_give isl_basic_map *isl_map_convex_hull(
1112 __isl_take isl_map *map);
1114 If the input set or relation has any existentially quantified
1115 variables, then the result of these operations is currently undefined.
1119 __isl_give isl_basic_set *isl_set_simple_hull(
1120 __isl_take isl_set *set);
1121 __isl_give isl_basic_map *isl_map_simple_hull(
1122 __isl_take isl_map *map);
1124 These functions compute a single basic set or relation
1125 that contains the whole input set or relation.
1126 In particular, the output is described by translates
1127 of the constraints describing the basic sets or relations in the input.
1131 (See \autoref{s:simple hull}.)
1137 __isl_give isl_basic_set *isl_basic_set_affine_hull(
1138 __isl_take isl_basic_set *bset);
1139 __isl_give isl_basic_set *isl_set_affine_hull(
1140 __isl_take isl_set *set);
1141 __isl_give isl_union_set *isl_union_set_affine_hull(
1142 __isl_take isl_union_set *uset);
1143 __isl_give isl_basic_map *isl_basic_map_affine_hull(
1144 __isl_take isl_basic_map *bmap);
1145 __isl_give isl_basic_map *isl_map_affine_hull(
1146 __isl_take isl_map *map);
1147 __isl_give isl_union_map *isl_union_map_affine_hull(
1148 __isl_take isl_union_map *umap);
1150 In case of union sets and relations, the affine hull is computed
1155 __isl_give isl_map *isl_map_power(__isl_take isl_map *map,
1156 unsigned param, int *exact);
1158 Compute a parametric representation for all positive powers I<k> of C<map>.
1159 The power I<k> is equated to the parameter at position C<param>.
1160 The result may be an overapproximation. If the result is exact,
1161 then C<*exact> is set to C<1>.
1162 The current implementation only produces exact results for particular
1163 cases of piecewise translations (i.e., piecewise uniform dependences).
1165 =item * Transitive closure
1167 __isl_give isl_map *isl_map_transitive_closure(
1168 __isl_take isl_map *map, int *exact);
1169 __isl_give isl_union_map *isl_union_map_transitive_closure(
1170 __isl_take isl_union_map *umap, int *exact);
1172 Compute the transitive closure of C<map>.
1173 The result may be an overapproximation. If the result is known to be exact,
1174 then C<*exact> is set to C<1>.
1175 The current implementation only produces exact results for particular
1176 cases of piecewise translations (i.e., piecewise uniform dependences).
1178 =item * Reaching path lengths
1180 __isl_give isl_map *isl_map_reaching_path_lengths(
1181 __isl_take isl_map *map, int *exact);
1183 Compute a relation that maps each element in the range of C<map>
1184 to the lengths of all paths composed of edges in C<map> that
1185 end up in the given element.
1186 The result may be an overapproximation. If the result is known to be exact,
1187 then C<*exact> is set to C<1>.
1188 To compute the I<maximal> path length, the resulting relation
1189 should be postprocessed by C<isl_map_lexmax>.
1190 In particular, if the input relation is a dependence relation
1191 (mapping sources to sinks), then the maximal path length corresponds
1192 to the free schedule.
1193 Note, however, that C<isl_map_lexmax> expects the maximum to be
1194 finite, so if the path lengths are unbounded (possibly due to
1195 the overapproximation), then you will get an error message.
1199 __isl_give isl_basic_set *isl_basic_map_wrap(
1200 __isl_take isl_basic_map *bmap);
1201 __isl_give isl_set *isl_map_wrap(
1202 __isl_take isl_map *map);
1203 __isl_give isl_union_set *isl_union_map_wrap(
1204 __isl_take isl_union_map *umap);
1205 __isl_give isl_basic_map *isl_basic_set_unwrap(
1206 __isl_take isl_basic_set *bset);
1207 __isl_give isl_map *isl_set_unwrap(
1208 __isl_take isl_set *set);
1209 __isl_give isl_union_map *isl_union_set_unwrap(
1210 __isl_take isl_union_set *uset);
1214 =head2 Binary Operations
1216 The two arguments of a binary operation not only need to live
1217 in the same C<isl_ctx>, they currently also need to have
1218 the same (number of) parameters.
1220 =head3 Basic Operations
1224 =item * Intersection
1226 __isl_give isl_basic_set *isl_basic_set_intersect(
1227 __isl_take isl_basic_set *bset1,
1228 __isl_take isl_basic_set *bset2);
1229 __isl_give isl_set *isl_set_intersect(
1230 __isl_take isl_set *set1,
1231 __isl_take isl_set *set2);
1232 __isl_give isl_union_set *isl_union_set_intersect(
1233 __isl_take isl_union_set *uset1,
1234 __isl_take isl_union_set *uset2);
1235 __isl_give isl_basic_map *isl_basic_map_intersect_domain(
1236 __isl_take isl_basic_map *bmap,
1237 __isl_take isl_basic_set *bset);
1238 __isl_give isl_basic_map *isl_basic_map_intersect_range(
1239 __isl_take isl_basic_map *bmap,
1240 __isl_take isl_basic_set *bset);
1241 __isl_give isl_basic_map *isl_basic_map_intersect(
1242 __isl_take isl_basic_map *bmap1,
1243 __isl_take isl_basic_map *bmap2);
1244 __isl_give isl_map *isl_map_intersect_domain(
1245 __isl_take isl_map *map,
1246 __isl_take isl_set *set);
1247 __isl_give isl_map *isl_map_intersect_range(
1248 __isl_take isl_map *map,
1249 __isl_take isl_set *set);
1250 __isl_give isl_map *isl_map_intersect(
1251 __isl_take isl_map *map1,
1252 __isl_take isl_map *map2);
1253 __isl_give isl_union_map *isl_union_map_intersect_domain(
1254 __isl_take isl_union_map *umap,
1255 __isl_take isl_union_set *uset);
1256 __isl_give isl_union_map *isl_union_map_intersect(
1257 __isl_take isl_union_map *umap1,
1258 __isl_take isl_union_map *umap2);
1262 __isl_give isl_set *isl_basic_set_union(
1263 __isl_take isl_basic_set *bset1,
1264 __isl_take isl_basic_set *bset2);
1265 __isl_give isl_map *isl_basic_map_union(
1266 __isl_take isl_basic_map *bmap1,
1267 __isl_take isl_basic_map *bmap2);
1268 __isl_give isl_set *isl_set_union(
1269 __isl_take isl_set *set1,
1270 __isl_take isl_set *set2);
1271 __isl_give isl_map *isl_map_union(
1272 __isl_take isl_map *map1,
1273 __isl_take isl_map *map2);
1274 __isl_give isl_union_set *isl_union_set_union(
1275 __isl_take isl_union_set *uset1,
1276 __isl_take isl_union_set *uset2);
1277 __isl_give isl_union_map *isl_union_map_union(
1278 __isl_take isl_union_map *umap1,
1279 __isl_take isl_union_map *umap2);
1281 =item * Set difference
1283 __isl_give isl_set *isl_set_subtract(
1284 __isl_take isl_set *set1,
1285 __isl_take isl_set *set2);
1286 __isl_give isl_map *isl_map_subtract(
1287 __isl_take isl_map *map1,
1288 __isl_take isl_map *map2);
1289 __isl_give isl_union_set *isl_union_set_subtract(
1290 __isl_take isl_union_set *uset1,
1291 __isl_take isl_union_set *uset2);
1292 __isl_give isl_union_map *isl_union_map_subtract(
1293 __isl_take isl_union_map *umap1,
1294 __isl_take isl_union_map *umap2);
1298 __isl_give isl_basic_set *isl_basic_set_apply(
1299 __isl_take isl_basic_set *bset,
1300 __isl_take isl_basic_map *bmap);
1301 __isl_give isl_set *isl_set_apply(
1302 __isl_take isl_set *set,
1303 __isl_take isl_map *map);
1304 __isl_give isl_union_set *isl_union_set_apply(
1305 __isl_take isl_union_set *uset,
1306 __isl_take isl_union_map *umap);
1307 __isl_give isl_basic_map *isl_basic_map_apply_domain(
1308 __isl_take isl_basic_map *bmap1,
1309 __isl_take isl_basic_map *bmap2);
1310 __isl_give isl_basic_map *isl_basic_map_apply_range(
1311 __isl_take isl_basic_map *bmap1,
1312 __isl_take isl_basic_map *bmap2);
1313 __isl_give isl_map *isl_map_apply_domain(
1314 __isl_take isl_map *map1,
1315 __isl_take isl_map *map2);
1316 __isl_give isl_map *isl_map_apply_range(
1317 __isl_take isl_map *map1,
1318 __isl_take isl_map *map2);
1319 __isl_give isl_union_map *isl_union_map_apply_range(
1320 __isl_take isl_union_map *umap1,
1321 __isl_take isl_union_map *umap2);
1323 =item * Simplification
1325 __isl_give isl_basic_set *isl_basic_set_gist(
1326 __isl_take isl_basic_set *bset,
1327 __isl_take isl_basic_set *context);
1328 __isl_give isl_set *isl_set_gist(__isl_take isl_set *set,
1329 __isl_take isl_set *context);
1330 __isl_give isl_union_set *isl_union_set_gist(
1331 __isl_take isl_union_set *uset,
1332 __isl_take isl_union_set *context);
1333 __isl_give isl_basic_map *isl_basic_map_gist(
1334 __isl_take isl_basic_map *bmap,
1335 __isl_take isl_basic_map *context);
1336 __isl_give isl_map *isl_map_gist(__isl_take isl_map *map,
1337 __isl_take isl_map *context);
1338 __isl_give isl_union_map *isl_union_map_gist(
1339 __isl_take isl_union_map *umap,
1340 __isl_take isl_union_map *context);
1342 The gist operation returns a set or relation that has the
1343 same intersection with the context as the input set or relation.
1344 Any implicit equality in the intersection is made explicit in the result,
1345 while all inequalities that are redundant with respect to the intersection
1347 In case of union sets and relations, the gist operation is performed
1352 =head3 Lexicographic Optimization
1354 Given a (basic) set C<set> (or C<bset>) and a zero-dimensional domain C<dom>,
1355 the following functions
1356 compute a set that contains the lexicographic minimum or maximum
1357 of the elements in C<set> (or C<bset>) for those values of the parameters
1358 that satisfy C<dom>.
1359 If C<empty> is not C<NULL>, then C<*empty> is assigned a set
1360 that contains the parameter values in C<dom> for which C<set> (or C<bset>)
1362 In other words, the union of the parameter values
1363 for which the result is non-empty and of C<*empty>
1366 __isl_give isl_set *isl_basic_set_partial_lexmin(
1367 __isl_take isl_basic_set *bset,
1368 __isl_take isl_basic_set *dom,
1369 __isl_give isl_set **empty);
1370 __isl_give isl_set *isl_basic_set_partial_lexmax(
1371 __isl_take isl_basic_set *bset,
1372 __isl_take isl_basic_set *dom,
1373 __isl_give isl_set **empty);
1374 __isl_give isl_set *isl_set_partial_lexmin(
1375 __isl_take isl_set *set, __isl_take isl_set *dom,
1376 __isl_give isl_set **empty);
1377 __isl_give isl_set *isl_set_partial_lexmax(
1378 __isl_take isl_set *set, __isl_take isl_set *dom,
1379 __isl_give isl_set **empty);
1381 Given a (basic) set C<set> (or C<bset>), the following functions simply
1382 return a set containing the lexicographic minimum or maximum
1383 of the elements in C<set> (or C<bset>).
1384 In case of union sets, the optimum is computed per space.
1386 __isl_give isl_set *isl_basic_set_lexmin(
1387 __isl_take isl_basic_set *bset);
1388 __isl_give isl_set *isl_basic_set_lexmax(
1389 __isl_take isl_basic_set *bset);
1390 __isl_give isl_set *isl_set_lexmin(
1391 __isl_take isl_set *set);
1392 __isl_give isl_set *isl_set_lexmax(
1393 __isl_take isl_set *set);
1394 __isl_give isl_union_set *isl_union_set_lexmin(
1395 __isl_take isl_union_set *uset);
1396 __isl_give isl_union_set *isl_union_set_lexmax(
1397 __isl_take isl_union_set *uset);
1399 Given a (basic) relation C<map> (or C<bmap>) and a domain C<dom>,
1400 the following functions
1401 compute a relation that maps each element of C<dom>
1402 to the single lexicographic minimum or maximum
1403 of the elements that are associated to that same
1404 element in C<map> (or C<bmap>).
1405 If C<empty> is not C<NULL>, then C<*empty> is assigned a set
1406 that contains the elements in C<dom> that do not map
1407 to any elements in C<map> (or C<bmap>).
1408 In other words, the union of the domain of the result and of C<*empty>
1411 __isl_give isl_map *isl_basic_map_partial_lexmax(
1412 __isl_take isl_basic_map *bmap,
1413 __isl_take isl_basic_set *dom,
1414 __isl_give isl_set **empty);
1415 __isl_give isl_map *isl_basic_map_partial_lexmin(
1416 __isl_take isl_basic_map *bmap,
1417 __isl_take isl_basic_set *dom,
1418 __isl_give isl_set **empty);
1419 __isl_give isl_map *isl_map_partial_lexmax(
1420 __isl_take isl_map *map, __isl_take isl_set *dom,
1421 __isl_give isl_set **empty);
1422 __isl_give isl_map *isl_map_partial_lexmin(
1423 __isl_take isl_map *map, __isl_take isl_set *dom,
1424 __isl_give isl_set **empty);
1426 Given a (basic) map C<map> (or C<bmap>), the following functions simply
1427 return a map mapping each element in the domain of
1428 C<map> (or C<bmap>) to the lexicographic minimum or maximum
1429 of all elements associated to that element.
1430 In case of union relations, the optimum is computed per space.
1432 __isl_give isl_map *isl_basic_map_lexmin(
1433 __isl_take isl_basic_map *bmap);
1434 __isl_give isl_map *isl_basic_map_lexmax(
1435 __isl_take isl_basic_map *bmap);
1436 __isl_give isl_map *isl_map_lexmin(
1437 __isl_take isl_map *map);
1438 __isl_give isl_map *isl_map_lexmax(
1439 __isl_take isl_map *map);
1440 __isl_give isl_union_map *isl_union_map_lexmin(
1441 __isl_take isl_union_map *umap);
1442 __isl_give isl_union_map *isl_union_map_lexmax(
1443 __isl_take isl_union_map *umap);
1447 Matrices can be created, copied and freed using the following functions.
1449 #include <isl_mat.h>
1450 __isl_give isl_mat *isl_mat_alloc(struct isl_ctx *ctx,
1451 unsigned n_row, unsigned n_col);
1452 __isl_give isl_mat *isl_mat_copy(__isl_keep isl_mat *mat);
1453 void isl_mat_free(__isl_take isl_mat *mat);
1455 Note that the elements of a newly created matrix may have arbitrary values.
1456 The elements can be changed and inspected using the following functions.
1458 int isl_mat_rows(__isl_keep isl_mat *mat);
1459 int isl_mat_cols(__isl_keep isl_mat *mat);
1460 int isl_mat_get_element(__isl_keep isl_mat *mat,
1461 int row, int col, isl_int *v);
1462 __isl_give isl_mat *isl_mat_set_element(__isl_take isl_mat *mat,
1463 int row, int col, isl_int v);
1465 C<isl_mat_get_element> will return a negative value if anything went wrong.
1466 In that case, the value of C<*v> is undefined.
1468 The following function can be used to compute the (right) inverse
1469 of a matrix, i.e., a matrix such that the product of the original
1470 and the inverse (in that order) is a multiple of the identity matrix.
1471 The input matrix is assumed to be of full row-rank.
1473 __isl_give isl_mat *isl_mat_right_inverse(__isl_take isl_mat *mat);
1475 The following function can be used to compute the (right) kernel
1476 (or null space) of a matrix, i.e., a matrix such that the product of
1477 the original and the kernel (in that order) is the zero matrix.
1479 __isl_give isl_mat *isl_mat_right_kernel(__isl_take isl_mat *mat);
1483 Points are elements of a set. They can be used to construct
1484 simple sets (boxes) or they can be used to represent the
1485 individual elements of a set.
1486 The zero point (the origin) can be created using
1488 __isl_give isl_point *isl_point_zero(__isl_take isl_dim *dim);
1490 The coordinates of a point can be inspected, set and changed
1493 void isl_point_get_coordinate(__isl_keep isl_point *pnt,
1494 enum isl_dim_type type, int pos, isl_int *v);
1495 __isl_give isl_point *isl_point_set_coordinate(
1496 __isl_take isl_point *pnt,
1497 enum isl_dim_type type, int pos, isl_int v);
1499 __isl_give isl_point *isl_point_add_ui(
1500 __isl_take isl_point *pnt,
1501 enum isl_dim_type type, int pos, unsigned val);
1502 __isl_give isl_point *isl_point_sub_ui(
1503 __isl_take isl_point *pnt,
1504 enum isl_dim_type type, int pos, unsigned val);
1506 Points can be copied or freed using
1508 __isl_give isl_point *isl_point_copy(
1509 __isl_keep isl_point *pnt);
1510 void isl_point_free(__isl_take isl_point *pnt);
1512 A singleton set can be created from a point using
1514 __isl_give isl_set *isl_set_from_point(
1515 __isl_take isl_point *pnt);
1517 and a box can be created from two opposite extremal points using
1519 __isl_give isl_set *isl_set_box_from_points(
1520 __isl_take isl_point *pnt1,
1521 __isl_take isl_point *pnt2);
1523 All elements of a B<bounded> (union) set can be enumerated using
1524 the following functions.
1526 int isl_set_foreach_point(__isl_keep isl_set *set,
1527 int (*fn)(__isl_take isl_point *pnt, void *user),
1529 int isl_union_set_foreach_point(__isl_keep isl_union_set *uset,
1530 int (*fn)(__isl_take isl_point *pnt, void *user),
1533 The function C<fn> is called for each integer point in
1534 C<set> with as second argument the last argument of
1535 the C<isl_set_foreach_point> call. The function C<fn>
1536 should return C<0> on success and C<-1> on failure.
1537 In the latter case, C<isl_set_foreach_point> will stop
1538 enumerating and return C<-1> as well.
1539 If the enumeration is performed successfully and to completion,
1540 then C<isl_set_foreach_point> returns C<0>.
1542 To obtain a single point of a set, use
1544 __isl_give isl_point *isl_set_sample_point(
1545 __isl_take isl_set *set);
1547 If C<set> does not contain any (integer) points, then the
1548 resulting point will be ``void'', a property that can be
1551 int isl_point_is_void(__isl_keep isl_point *pnt);
1553 =head2 Piecewise Quasipolynomials
1555 A piecewise quasipolynomial is a particular kind of function that maps
1556 a parametric point to a rational value.
1557 More specifically, a quasipolynomial is a polynomial expression in greatest
1558 integer parts of affine expressions of parameters and variables.
1559 A piecewise quasipolynomial is a subdivision of a given parametric
1560 domain into disjoint cells with a quasipolynomial associated to
1561 each cell. The value of the piecewise quasipolynomial at a given
1562 point is the value of the quasipolynomial associated to the cell
1563 that contains the point. Outside of the union of cells,
1564 the value is assumed to be zero.
1565 For example, the piecewise quasipolynomial
1567 [n] -> { [x] -> ((1 + n) - x) : x <= n and x >= 0 }
1569 maps C<x> to C<1 + n - x> for values of C<x> between C<0> and C<n>.
1570 A given piecewise quasipolynomial has a fixed domain dimension.
1571 Union piecewise quasipolynomials are used to contain piecewise quasipolynomials
1572 defined over different domains.
1573 Piecewise quasipolynomials are mainly used by the C<barvinok>
1574 library for representing the number of elements in a parametric set or map.
1575 For example, the piecewise quasipolynomial above represents
1576 the number of points in the map
1578 [n] -> { [x] -> [y] : x,y >= 0 and 0 <= x + y <= n }
1580 =head3 Printing (Piecewise) Quasipolynomials
1582 Quasipolynomials and piecewise quasipolynomials can be printed
1583 using the following functions.
1585 __isl_give isl_printer *isl_printer_print_qpolynomial(
1586 __isl_take isl_printer *p,
1587 __isl_keep isl_qpolynomial *qp);
1589 __isl_give isl_printer *isl_printer_print_pw_qpolynomial(
1590 __isl_take isl_printer *p,
1591 __isl_keep isl_pw_qpolynomial *pwqp);
1593 __isl_give isl_printer *isl_printer_print_union_pw_qpolynomial(
1594 __isl_take isl_printer *p,
1595 __isl_keep isl_union_pw_qpolynomial *upwqp);
1597 The output format of the printer
1598 needs to be set to either C<ISL_FORMAT_ISL> or C<ISL_FORMAT_C>.
1599 For C<isl_printer_print_union_pw_qpolynomial>, only C<ISL_FORMAT_ISL>
1602 =head3 Creating New (Piecewise) Quasipolynomials
1604 Some simple quasipolynomials can be created using the following functions.
1605 More complicated quasipolynomials can be created by applying
1606 operations such as addition and multiplication
1607 on the resulting quasipolynomials
1609 __isl_give isl_qpolynomial *isl_qpolynomial_zero(
1610 __isl_take isl_dim *dim);
1611 __isl_give isl_qpolynomial *isl_qpolynomial_one(
1612 __isl_take isl_dim *dim);
1613 __isl_give isl_qpolynomial *isl_qpolynomial_infty(
1614 __isl_take isl_dim *dim);
1615 __isl_give isl_qpolynomial *isl_qpolynomial_neginfty(
1616 __isl_take isl_dim *dim);
1617 __isl_give isl_qpolynomial *isl_qpolynomial_nan(
1618 __isl_take isl_dim *dim);
1619 __isl_give isl_qpolynomial *isl_qpolynomial_rat_cst(
1620 __isl_take isl_dim *dim,
1621 const isl_int n, const isl_int d);
1622 __isl_give isl_qpolynomial *isl_qpolynomial_div(
1623 __isl_take isl_div *div);
1624 __isl_give isl_qpolynomial *isl_qpolynomial_var(
1625 __isl_take isl_dim *dim,
1626 enum isl_dim_type type, unsigned pos);
1628 The zero piecewise quasipolynomial or a piecewise quasipolynomial
1629 with a single cell can be created using the following functions.
1630 Multiple of these single cell piecewise quasipolynomials can
1631 be combined to create more complicated piecewise quasipolynomials.
1633 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_zero(
1634 __isl_take isl_dim *dim);
1635 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_alloc(
1636 __isl_take isl_set *set,
1637 __isl_take isl_qpolynomial *qp);
1639 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_zero(
1640 __isl_take isl_dim *dim);
1641 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_from_pw_qpolynomial(
1642 __isl_take isl_pw_qpolynomial *pwqp);
1643 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_add_pw_qpolynomial(
1644 __isl_take isl_union_pw_qpolynomial *upwqp,
1645 __isl_take isl_pw_qpolynomial *pwqp);
1647 Quasipolynomials can be copied and freed again using the following
1650 __isl_give isl_qpolynomial *isl_qpolynomial_copy(
1651 __isl_keep isl_qpolynomial *qp);
1652 void isl_qpolynomial_free(__isl_take isl_qpolynomial *qp);
1654 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_copy(
1655 __isl_keep isl_pw_qpolynomial *pwqp);
1656 void isl_pw_qpolynomial_free(
1657 __isl_take isl_pw_qpolynomial *pwqp);
1659 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_copy(
1660 __isl_keep isl_union_pw_qpolynomial *upwqp);
1661 void isl_union_pw_qpolynomial_free(
1662 __isl_take isl_union_pw_qpolynomial *upwqp);
1664 =head3 Inspecting (Piecewise) Quasipolynomials
1666 To iterate over all piecewise quasipolynomials in a union
1667 piecewise quasipolynomial, use the following function
1669 int isl_union_pw_qpolynomial_foreach_pw_qpolynomial(
1670 __isl_keep isl_union_pw_qpolynomial *upwqp,
1671 int (*fn)(__isl_take isl_pw_qpolynomial *pwqp, void *user),
1674 To iterate over the cells in a piecewise quasipolynomial,
1675 use either of the following two functions
1677 int isl_pw_qpolynomial_foreach_piece(
1678 __isl_keep isl_pw_qpolynomial *pwqp,
1679 int (*fn)(__isl_take isl_set *set,
1680 __isl_take isl_qpolynomial *qp,
1681 void *user), void *user);
1682 int isl_pw_qpolynomial_foreach_lifted_piece(
1683 __isl_keep isl_pw_qpolynomial *pwqp,
1684 int (*fn)(__isl_take isl_set *set,
1685 __isl_take isl_qpolynomial *qp,
1686 void *user), void *user);
1688 As usual, the function C<fn> should return C<0> on success
1689 and C<-1> on failure. The difference between
1690 C<isl_pw_qpolynomial_foreach_piece> and
1691 C<isl_pw_qpolynomial_foreach_lifted_piece> is that
1692 C<isl_pw_qpolynomial_foreach_lifted_piece> will first
1693 compute unique representations for all existentially quantified
1694 variables and then turn these existentially quantified variables
1695 into extra set variables, adapting the associated quasipolynomial
1696 accordingly. This means that the C<set> passed to C<fn>
1697 will not have any existentially quantified variables, but that
1698 the dimensions of the sets may be different for different
1699 invocations of C<fn>.
1701 To iterate over all terms in a quasipolynomial,
1704 int isl_qpolynomial_foreach_term(
1705 __isl_keep isl_qpolynomial *qp,
1706 int (*fn)(__isl_take isl_term *term,
1707 void *user), void *user);
1709 The terms themselves can be inspected and freed using
1712 unsigned isl_term_dim(__isl_keep isl_term *term,
1713 enum isl_dim_type type);
1714 void isl_term_get_num(__isl_keep isl_term *term,
1716 void isl_term_get_den(__isl_keep isl_term *term,
1718 int isl_term_get_exp(__isl_keep isl_term *term,
1719 enum isl_dim_type type, unsigned pos);
1720 __isl_give isl_div *isl_term_get_div(
1721 __isl_keep isl_term *term, unsigned pos);
1722 void isl_term_free(__isl_take isl_term *term);
1724 Each term is a product of parameters, set variables and
1725 integer divisions. The function C<isl_term_get_exp>
1726 returns the exponent of a given dimensions in the given term.
1727 The C<isl_int>s in the arguments of C<isl_term_get_num>
1728 and C<isl_term_get_den> need to have been initialized
1729 using C<isl_int_init> before calling these functions.
1731 =head3 Properties of (Piecewise) Quasipolynomials
1733 To check whether a quasipolynomial is actually a constant,
1734 use the following function.
1736 int isl_qpolynomial_is_cst(__isl_keep isl_qpolynomial *qp,
1737 isl_int *n, isl_int *d);
1739 If C<qp> is a constant and if C<n> and C<d> are not C<NULL>
1740 then the numerator and denominator of the constant
1741 are returned in C<*n> and C<*d>, respectively.
1743 =head3 Operations on (Piecewise) Quasipolynomials
1745 __isl_give isl_qpolynomial *isl_qpolynomial_neg(
1746 __isl_take isl_qpolynomial *qp);
1747 __isl_give isl_qpolynomial *isl_qpolynomial_add(
1748 __isl_take isl_qpolynomial *qp1,
1749 __isl_take isl_qpolynomial *qp2);
1750 __isl_give isl_qpolynomial *isl_qpolynomial_sub(
1751 __isl_take isl_qpolynomial *qp1,
1752 __isl_take isl_qpolynomial *qp2);
1753 __isl_give isl_qpolynomial *isl_qpolynomial_mul(
1754 __isl_take isl_qpolynomial *qp1,
1755 __isl_take isl_qpolynomial *qp2);
1757 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_add(
1758 __isl_take isl_pw_qpolynomial *pwqp1,
1759 __isl_take isl_pw_qpolynomial *pwqp2);
1760 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_sub(
1761 __isl_take isl_pw_qpolynomial *pwqp1,
1762 __isl_take isl_pw_qpolynomial *pwqp2);
1763 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_add_disjoint(
1764 __isl_take isl_pw_qpolynomial *pwqp1,
1765 __isl_take isl_pw_qpolynomial *pwqp2);
1766 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_neg(
1767 __isl_take isl_pw_qpolynomial *pwqp);
1768 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_mul(
1769 __isl_take isl_pw_qpolynomial *pwqp1,
1770 __isl_take isl_pw_qpolynomial *pwqp2);
1772 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_add(
1773 __isl_take isl_union_pw_qpolynomial *upwqp1,
1774 __isl_take isl_union_pw_qpolynomial *upwqp2);
1775 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_sub(
1776 __isl_take isl_union_pw_qpolynomial *upwqp1,
1777 __isl_take isl_union_pw_qpolynomial *upwqp2);
1778 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_mul(
1779 __isl_take isl_union_pw_qpolynomial *upwqp1,
1780 __isl_take isl_union_pw_qpolynomial *upwqp2);
1782 __isl_give isl_qpolynomial *isl_pw_qpolynomial_eval(
1783 __isl_take isl_pw_qpolynomial *pwqp,
1784 __isl_take isl_point *pnt);
1786 __isl_give isl_qpolynomial *isl_union_pw_qpolynomial_eval(
1787 __isl_take isl_union_pw_qpolynomial *upwqp,
1788 __isl_take isl_point *pnt);
1790 __isl_give isl_set *isl_pw_qpolynomial_domain(
1791 __isl_take isl_pw_qpolynomial *pwqp);
1792 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_intersect_domain(
1793 __isl_take isl_pw_qpolynomial *pwpq,
1794 __isl_take isl_set *set);
1796 __isl_give isl_union_set *isl_union_pw_qpolynomial_domain(
1797 __isl_take isl_union_pw_qpolynomial *upwqp);
1798 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_intersect_domain(
1799 __isl_take isl_union_pw_qpolynomial *upwpq,
1800 __isl_take isl_union_set *uset);
1802 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_coalesce(
1803 __isl_take isl_union_pw_qpolynomial *upwqp);
1805 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_gist(
1806 __isl_take isl_pw_qpolynomial *pwqp,
1807 __isl_take isl_set *context);
1809 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_gist(
1810 __isl_take isl_union_pw_qpolynomial *upwqp,
1811 __isl_take isl_union_set *context);
1813 The gist operation applies the gist operation to each of
1814 the cells in the domain of the input piecewise quasipolynomial.
1815 In future, the operation will also exploit the context
1816 to simplify the quasipolynomials associated to each cell.
1818 =head2 Bounds on Piecewise Quasipolynomials and Piecewise Quasipolynomial Reductions
1820 A piecewise quasipolynomial reduction is a piecewise
1821 reduction (or fold) of quasipolynomials.
1822 In particular, the reduction can be maximum or a minimum.
1823 The objects are mainly used to represent the result of
1824 an upper or lower bound on a quasipolynomial over its domain,
1825 i.e., as the result of the following function.
1827 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_bound(
1828 __isl_take isl_pw_qpolynomial *pwqp,
1829 enum isl_fold type, int *tight);
1831 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_bound(
1832 __isl_take isl_union_pw_qpolynomial *upwqp,
1833 enum isl_fold type, int *tight);
1835 The C<type> argument may be either C<isl_fold_min> or C<isl_fold_max>.
1836 If C<tight> is not C<NULL>, then C<*tight> is set to C<1>
1837 is the returned bound is known be tight, i.e., for each value
1838 of the parameters there is at least
1839 one element in the domain that reaches the bound.
1840 If the domain of C<pwqp> is not wrapping, then the bound is computed
1841 over all elements in that domain and the result has a purely parametric
1842 domain. If the domain of C<pwqp> is wrapping, then the bound is
1843 computed over the range of the wrapped relation. The domain of the
1844 wrapped relation becomes the domain of the result.
1846 A (piecewise) quasipolynomial reduction can be copied or freed using the
1847 following functions.
1849 __isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_copy(
1850 __isl_keep isl_qpolynomial_fold *fold);
1851 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_copy(
1852 __isl_keep isl_pw_qpolynomial_fold *pwf);
1853 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_copy(
1854 __isl_keep isl_union_pw_qpolynomial_fold *upwf);
1855 void isl_qpolynomial_fold_free(
1856 __isl_take isl_qpolynomial_fold *fold);
1857 void isl_pw_qpolynomial_fold_free(
1858 __isl_take isl_pw_qpolynomial_fold *pwf);
1859 void isl_union_pw_qpolynomial_fold_free(
1860 __isl_take isl_union_pw_qpolynomial_fold *upwf);
1862 =head3 Printing Piecewise Quasipolynomial Reductions
1864 Piecewise quasipolynomial reductions can be printed
1865 using the following function.
1867 __isl_give isl_printer *isl_printer_print_pw_qpolynomial_fold(
1868 __isl_take isl_printer *p,
1869 __isl_keep isl_pw_qpolynomial_fold *pwf);
1870 __isl_give isl_printer *isl_printer_print_union_pw_qpolynomial_fold(
1871 __isl_take isl_printer *p,
1872 __isl_keep isl_union_pw_qpolynomial_fold *upwf);
1874 For C<isl_printer_print_pw_qpolynomial_fold>,
1875 output format of the printer
1876 needs to be set to either C<ISL_FORMAT_ISL> or C<ISL_FORMAT_C>.
1877 For C<isl_printer_print_union_pw_qpolynomial_fold>,
1878 output format of the printer
1879 needs to be set to either C<ISL_FORMAT_ISL>.
1881 =head3 Inspecting (Piecewise) Quasipolynomial Reductions
1883 To iterate over all piecewise quasipolynomial reductions in a union
1884 piecewise quasipolynomial reduction, use the following function
1886 int isl_union_pw_qpolynomial_fold_foreach_pw_qpolynomial_fold(
1887 __isl_keep isl_union_pw_qpolynomial_fold *upwf,
1888 int (*fn)(__isl_take isl_pw_qpolynomial_fold *pwf,
1889 void *user), void *user);
1891 To iterate over the cells in a piecewise quasipolynomial reduction,
1892 use either of the following two functions
1894 int isl_pw_qpolynomial_fold_foreach_piece(
1895 __isl_keep isl_pw_qpolynomial_fold *pwf,
1896 int (*fn)(__isl_take isl_set *set,
1897 __isl_take isl_qpolynomial_fold *fold,
1898 void *user), void *user);
1899 int isl_pw_qpolynomial_fold_foreach_lifted_piece(
1900 __isl_keep isl_pw_qpolynomial_fold *pwf,
1901 int (*fn)(__isl_take isl_set *set,
1902 __isl_take isl_qpolynomial_fold *fold,
1903 void *user), void *user);
1905 See L<Inspecting (Piecewise) Quasipolynomials> for an explanation
1906 of the difference between these two functions.
1908 To iterate over all quasipolynomials in a reduction, use
1910 int isl_qpolynomial_fold_foreach_qpolynomial(
1911 __isl_keep isl_qpolynomial_fold *fold,
1912 int (*fn)(__isl_take isl_qpolynomial *qp,
1913 void *user), void *user);
1915 =head3 Operations on Piecewise Quasipolynomial Reductions
1917 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_fold(
1918 __isl_take isl_pw_qpolynomial_fold *pwf1,
1919 __isl_take isl_pw_qpolynomial_fold *pwf2);
1921 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_fold(
1922 __isl_take isl_union_pw_qpolynomial_fold *upwf1,
1923 __isl_take isl_union_pw_qpolynomial_fold *upwf2);
1925 __isl_give isl_qpolynomial *isl_pw_qpolynomial_fold_eval(
1926 __isl_take isl_pw_qpolynomial_fold *pwf,
1927 __isl_take isl_point *pnt);
1929 __isl_give isl_qpolynomial *isl_union_pw_qpolynomial_fold_eval(
1930 __isl_take isl_union_pw_qpolynomial_fold *upwf,
1931 __isl_take isl_point *pnt);
1933 __isl_give isl_union_set *isl_union_pw_qpolynomial_fold_domain(
1934 __isl_take isl_union_pw_qpolynomial_fold *upwf);
1935 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_intersect_domain(
1936 __isl_take isl_union_pw_qpolynomial_fold *upwf,
1937 __isl_take isl_union_set *uset);
1939 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_coalesce(
1940 __isl_take isl_pw_qpolynomial_fold *pwf);
1942 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_coalesce(
1943 __isl_take isl_union_pw_qpolynomial_fold *upwf);
1945 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_gist(
1946 __isl_take isl_pw_qpolynomial_fold *pwf,
1947 __isl_take isl_set *context);
1949 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_gist(
1950 __isl_take isl_union_pw_qpolynomial_fold *upwf,
1951 __isl_take isl_union_set *context);
1953 The gist operation applies the gist operation to each of
1954 the cells in the domain of the input piecewise quasipolynomial reduction.
1955 In future, the operation will also exploit the context
1956 to simplify the quasipolynomial reductions associated to each cell.
1958 __isl_give isl_pw_qpolynomial_fold *
1959 isl_map_apply_pw_qpolynomial_fold(
1960 __isl_take isl_map *map,
1961 __isl_take isl_pw_qpolynomial_fold *pwf,
1963 __isl_give isl_union_pw_qpolynomial_fold *
1964 isl_union_map_apply_union_pw_qpolynomial_fold(
1965 __isl_take isl_union_map *umap,
1966 __isl_take isl_union_pw_qpolynomial_fold *upwf,
1970 compose the given map with the given piecewise quasipolynomial reduction.
1971 That is, compute a bound (of the same type as C<pwf> or C<upwf> itself)
1972 over all elements in the intersection of the range of the map
1973 and the domain of the piecewise quasipolynomial reduction
1974 as a function of an element in the domain of the map.
1976 =head2 Dependence Analysis
1978 C<isl> contains specialized functionality for performing
1979 array dataflow analysis. That is, given a I<sink> access relation
1980 and a collection of possible I<source> access relations,
1981 C<isl> can compute relations that describe
1982 for each iteration of the sink access, which iteration
1983 of which of the source access relations was the last
1984 to access the same data element before the given iteration
1986 To compute standard flow dependences, the sink should be
1987 a read, while the sources should be writes.
1988 If any of the source accesses are marked as being I<may>
1989 accesses, then there will be a dependence to the last
1990 I<must> access B<and> to any I<may> access that follows
1991 this last I<must> access.
1992 In particular, if I<all> sources are I<may> accesses,
1993 then memory based dependence analysis is performed.
1994 If, on the other hand, all sources are I<must> accesses,
1995 then value based dependence analysis is performed.
1997 #include <isl_flow.h>
1999 __isl_give isl_access_info *isl_access_info_alloc(
2000 __isl_take isl_map *sink,
2001 void *sink_user, isl_access_level_before fn,
2003 __isl_give isl_access_info *isl_access_info_add_source(
2004 __isl_take isl_access_info *acc,
2005 __isl_take isl_map *source, int must,
2008 __isl_give isl_flow *isl_access_info_compute_flow(
2009 __isl_take isl_access_info *acc);
2011 int isl_flow_foreach(__isl_keep isl_flow *deps,
2012 int (*fn)(__isl_take isl_map *dep, int must,
2013 void *dep_user, void *user),
2015 __isl_give isl_set *isl_flow_get_no_source(
2016 __isl_keep isl_flow *deps, int must);
2017 void isl_flow_free(__isl_take isl_flow *deps);
2019 The function C<isl_access_info_compute_flow> performs the actual
2020 dependence analysis. The other functions are used to construct
2021 the input for this function or to read off the output.
2023 The input is collected in an C<isl_access_info>, which can
2024 be created through a call to C<isl_access_info_alloc>.
2025 The arguments to this functions are the sink access relation
2026 C<sink>, a token C<sink_user> used to identify the sink
2027 access to the user, a callback function for specifying the
2028 relative order of source and sink accesses, and the number
2029 of source access relations that will be added.
2030 The callback function has type C<int (*)(void *first, void *second)>.
2031 The function is called with two user supplied tokens identifying
2032 either a source or the sink and it should return the shared nesting
2033 level and the relative order of the two accesses.
2034 In particular, let I<n> be the number of loops shared by
2035 the two accesses. If C<first> precedes C<second> textually,
2036 then the function should return I<2 * n + 1>; otherwise,
2037 it should return I<2 * n>.
2038 The sources can be added to the C<isl_access_info> by performing
2039 (at most) C<max_source> calls to C<isl_access_info_add_source>.
2040 C<must> indicates whether the source is a I<must> access
2041 or a I<may> access. Note that a multi-valued access relation
2042 should only be marked I<must> if every iteration in the domain
2043 of the relation accesses I<all> elements in its image.
2044 The C<source_user> token is again used to identify
2045 the source access. The range of the source access relation
2046 C<source> should have the same dimension as the range
2047 of the sink access relation.
2049 The result of the dependence analysis is collected in an
2050 C<isl_flow>. There may be elements in the domain of
2051 the sink access for which no preceding source access could be
2052 found or for which all preceding sources are I<may> accesses.
2053 The sets of these elements can be obtained through
2054 calls to C<isl_flow_get_no_source>, the first with C<must> set
2055 and the second with C<must> unset.
2056 In the case of standard flow dependence analysis,
2057 with the sink a read and the sources I<must> writes,
2058 the first set corresponds to the reads from uninitialized
2059 array elements and the second set is empty.
2060 The actual flow dependences can be extracted using
2061 C<isl_flow_foreach>. This function will call the user-specified
2062 callback function C<fn> for each B<non-empty> dependence between
2063 a source and the sink. The callback function is called
2064 with four arguments, the actual flow dependence relation
2065 mapping source iterations to sink iterations, a boolean that
2066 indicates whether it is a I<must> or I<may> dependence, a token
2067 identifying the source and an additional C<void *> with value
2068 equal to the third argument of the C<isl_flow_foreach> call.
2069 A dependence is marked I<must> if it originates from a I<must>
2070 source and if it is not followed by any I<may> sources.
2072 After finishing with an C<isl_flow>, the user should call
2073 C<isl_flow_free> to free all associated memory.
2075 =head2 Parametric Vertex Enumeration
2077 The parametric vertex enumeration described in this section
2078 is mainly intended to be used internally and by the C<barvinok>
2081 #include <isl_vertices.h>
2082 __isl_give isl_vertices *isl_basic_set_compute_vertices(
2083 __isl_keep isl_basic_set *bset);
2085 The function C<isl_basic_set_compute_vertices> performs the
2086 actual computation of the parametric vertices and the chamber
2087 decomposition and store the result in an C<isl_vertices> object.
2088 This information can be queried by either iterating over all
2089 the vertices or iterating over all the chambers or cells
2090 and then iterating over all vertices that are active on the chamber.
2092 int isl_vertices_foreach_vertex(
2093 __isl_keep isl_vertices *vertices,
2094 int (*fn)(__isl_take isl_vertex *vertex, void *user),
2097 int isl_vertices_foreach_cell(
2098 __isl_keep isl_vertices *vertices,
2099 int (*fn)(__isl_take isl_cell *cell, void *user),
2101 int isl_cell_foreach_vertex(__isl_keep isl_cell *cell,
2102 int (*fn)(__isl_take isl_vertex *vertex, void *user),
2105 Other operations that can be performed on an C<isl_vertices> object are
2108 isl_ctx *isl_vertices_get_ctx(
2109 __isl_keep isl_vertices *vertices);
2110 int isl_vertices_get_n_vertices(
2111 __isl_keep isl_vertices *vertices);
2112 void isl_vertices_free(__isl_take isl_vertices *vertices);
2114 Vertices can be inspected and destroyed using the following functions.
2116 isl_ctx *isl_vertex_get_ctx(__isl_keep isl_vertex *vertex);
2117 int isl_vertex_get_id(__isl_keep isl_vertex *vertex);
2118 __isl_give isl_basic_set *isl_vertex_get_domain(
2119 __isl_keep isl_vertex *vertex);
2120 __isl_give isl_basic_set *isl_vertex_get_expr(
2121 __isl_keep isl_vertex *vertex);
2122 void isl_vertex_free(__isl_take isl_vertex *vertex);
2124 C<isl_vertex_get_expr> returns a singleton parametric set describing
2125 the vertex, while C<isl_vertex_get_domain> returns the activity domain
2127 Note that C<isl_vertex_get_domain> and C<isl_vertex_get_expr> return
2128 B<rational> basic sets, so they should mainly be used for inspection
2129 and should not be mixed with integer sets.
2131 Chambers can be inspected and destroyed using the following functions.
2133 isl_ctx *isl_cell_get_ctx(__isl_keep isl_cell *cell);
2134 __isl_give isl_basic_set *isl_cell_get_domain(
2135 __isl_keep isl_cell *cell);
2136 void isl_cell_free(__isl_take isl_cell *cell);
2140 Although C<isl> is mainly meant to be used as a library,
2141 it also contains some basic applications that use some
2142 of the functionality of C<isl>.
2143 The input may be specified in either the L<isl format>
2144 or the L<PolyLib format>.
2146 =head2 C<isl_polyhedron_sample>
2148 C<isl_polyhedron_sample> takes a polyhedron as input and prints
2149 an integer element of the polyhedron, if there is any.
2150 The first column in the output is the denominator and is always
2151 equal to 1. If the polyhedron contains no integer points,
2152 then a vector of length zero is printed.
2156 C<isl_pip> takes the same input as the C<example> program
2157 from the C<piplib> distribution, i.e., a set of constraints
2158 on the parameters, a line containing only -1 and finally a set
2159 of constraints on a parametric polyhedron.
2160 The coefficients of the parameters appear in the last columns
2161 (but before the final constant column).
2162 The output is the lexicographic minimum of the parametric polyhedron.
2163 As C<isl> currently does not have its own output format, the output
2164 is just a dump of the internal state.
2166 =head2 C<isl_polyhedron_minimize>
2168 C<isl_polyhedron_minimize> computes the minimum of some linear
2169 or affine objective function over the integer points in a polyhedron.
2170 If an affine objective function
2171 is given, then the constant should appear in the last column.
2173 =head2 C<isl_polytope_scan>
2175 Given a polytope, C<isl_polytope_scan> prints
2176 all integer points in the polytope.
2178 =head1 C<isl-polylib>
2180 The C<isl-polylib> library provides the following functions for converting
2181 between C<isl> objects and C<PolyLib> objects.
2182 The library is distributed separately for licensing reasons.
2184 #include <isl_set_polylib.h>
2185 __isl_give isl_basic_set *isl_basic_set_new_from_polylib(
2186 Polyhedron *P, __isl_take isl_dim *dim);
2187 Polyhedron *isl_basic_set_to_polylib(
2188 __isl_keep isl_basic_set *bset);
2189 __isl_give isl_set *isl_set_new_from_polylib(Polyhedron *D,
2190 __isl_take isl_dim *dim);
2191 Polyhedron *isl_set_to_polylib(__isl_keep isl_set *set);
2193 #include <isl_map_polylib.h>
2194 __isl_give isl_basic_map *isl_basic_map_new_from_polylib(
2195 Polyhedron *P, __isl_take isl_dim *dim);
2196 __isl_give isl_map *isl_map_new_from_polylib(Polyhedron *D,
2197 __isl_take isl_dim *dim);
2198 Polyhedron *isl_basic_map_to_polylib(
2199 __isl_keep isl_basic_map *bmap);
2200 Polyhedron *isl_map_to_polylib(__isl_keep isl_map *map);