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.
553 =head3 Extended C<PolyLib> format
555 The extended C<PolyLib> format is nearly identical to the
556 C<PolyLib> format. The only difference is that the line
557 containing the number of rows and columns of a constraint matrix
558 also contains four additional numbers:
559 the number of output dimensions, the number of input dimensions,
560 the number of local dimensions (i.e., the number of existentially
561 quantified variables) and the number of parameters.
562 For sets, the number of ``output'' dimensions is equal
563 to the number of set dimensions, while the number of ``input''
569 __isl_give isl_basic_set *isl_basic_set_read_from_file(
570 isl_ctx *ctx, FILE *input, int nparam);
571 __isl_give isl_basic_set *isl_basic_set_read_from_str(
572 isl_ctx *ctx, const char *str, int nparam);
573 __isl_give isl_set *isl_set_read_from_file(isl_ctx *ctx,
574 FILE *input, int nparam);
575 __isl_give isl_set *isl_set_read_from_str(isl_ctx *ctx,
576 const char *str, int nparam);
579 __isl_give isl_basic_map *isl_basic_map_read_from_file(
580 isl_ctx *ctx, FILE *input, int nparam);
581 __isl_give isl_basic_map *isl_basic_map_read_from_str(
582 isl_ctx *ctx, const char *str, int nparam);
583 __isl_give isl_map *isl_map_read_from_file(
584 struct isl_ctx *ctx, FILE *input, int nparam);
585 __isl_give isl_map *isl_map_read_from_str(isl_ctx *ctx,
586 const char *str, int nparam);
588 The input format is autodetected and may be either the C<PolyLib> format
589 or the C<isl> format.
590 C<nparam> specifies how many of the final columns in
591 the C<PolyLib> format correspond to parameters.
592 If input is given in the C<isl> format, then the number
593 of parameters needs to be equal to C<nparam>.
594 If C<nparam> is negative, then any number of parameters
595 is accepted in the C<isl> format and zero parameters
596 are assumed in the C<PolyLib> format.
600 Before anything can be printed, an C<isl_printer> needs to
603 __isl_give isl_printer *isl_printer_to_file(isl_ctx *ctx,
605 __isl_give isl_printer *isl_printer_to_str(isl_ctx *ctx);
606 void isl_printer_free(__isl_take isl_printer *printer);
607 __isl_give char *isl_printer_get_str(
608 __isl_keep isl_printer *printer);
610 The behavior of the printer can be modified in various ways
612 __isl_give isl_printer *isl_printer_set_output_format(
613 __isl_take isl_printer *p, int output_format);
614 __isl_give isl_printer *isl_printer_set_indent(
615 __isl_take isl_printer *p, int indent);
616 __isl_give isl_printer *isl_printer_set_prefix(
617 __isl_take isl_printer *p, const char *prefix);
618 __isl_give isl_printer *isl_printer_set_suffix(
619 __isl_take isl_printer *p, const char *suffix);
621 The C<output_format> may be either C<ISL_FORMAT_ISL>, C<ISL_FORMAT_OMEGA>,
622 C<ISL_FORMAT_POLYLIB>, C<ISL_FORMAT_EXT_POLYLIB> or C<ISL_FORMAT_LATEX>
623 and defaults to C<ISL_FORMAT_ISL>.
624 Each line in the output is indented by C<indent> spaces
625 (default: 0), prefixed by C<prefix> and suffixed by C<suffix>.
626 In the C<PolyLib> format output,
627 the coefficients of the existentially quantified variables
628 appear between those of the set variables and those
631 To actually print something, use
634 __isl_give isl_printer *isl_printer_print_basic_set(
635 __isl_take isl_printer *printer,
636 __isl_keep isl_basic_set *bset);
637 __isl_give isl_printer *isl_printer_print_set(
638 __isl_take isl_printer *printer,
639 __isl_keep isl_set *set);
642 __isl_give isl_printer *isl_printer_print_basic_map(
643 __isl_take isl_printer *printer,
644 __isl_keep isl_basic_map *bmap);
645 __isl_give isl_printer *isl_printer_print_map(
646 __isl_take isl_printer *printer,
647 __isl_keep isl_map *map);
649 #include <isl_union_set.h>
650 __isl_give isl_printer *isl_printer_print_union_set(
651 __isl_take isl_printer *p,
652 __isl_keep isl_union_set *uset);
654 #include <isl_union_map.h>
655 __isl_give isl_printer *isl_printer_print_union_map(
656 __isl_take isl_printer *p,
657 __isl_keep isl_union_map *umap);
659 When called on a file printer, the following function flushes
660 the file. When called on a string printer, the buffer is cleared.
662 __isl_give isl_printer *isl_printer_flush(
663 __isl_take isl_printer *p);
665 =head2 Creating New Sets and Relations
667 C<isl> has functions for creating some standard sets and relations.
671 =item * Empty sets and relations
673 __isl_give isl_basic_set *isl_basic_set_empty(
674 __isl_take isl_dim *dim);
675 __isl_give isl_basic_map *isl_basic_map_empty(
676 __isl_take isl_dim *dim);
677 __isl_give isl_set *isl_set_empty(
678 __isl_take isl_dim *dim);
679 __isl_give isl_map *isl_map_empty(
680 __isl_take isl_dim *dim);
681 __isl_give isl_union_set *isl_union_set_empty(
682 __isl_take isl_dim *dim);
683 __isl_give isl_union_map *isl_union_map_empty(
684 __isl_take isl_dim *dim);
686 For C<isl_union_set>s and C<isl_union_map>s, the dimensions specification
687 is only used to specify the parameters.
689 =item * Universe sets and relations
691 __isl_give isl_basic_set *isl_basic_set_universe(
692 __isl_take isl_dim *dim);
693 __isl_give isl_basic_map *isl_basic_map_universe(
694 __isl_take isl_dim *dim);
695 __isl_give isl_set *isl_set_universe(
696 __isl_take isl_dim *dim);
697 __isl_give isl_map *isl_map_universe(
698 __isl_take isl_dim *dim);
700 =item * Identity relations
702 __isl_give isl_basic_map *isl_basic_map_identity(
703 __isl_take isl_dim *set_dim);
704 __isl_give isl_map *isl_map_identity(
705 __isl_take isl_dim *set_dim);
707 These functions take a dimension specification for a B<set>
708 and return an identity relation between two such sets.
710 =item * Lexicographic order
712 __isl_give isl_map *isl_map_lex_lt(
713 __isl_take isl_dim *set_dim);
714 __isl_give isl_map *isl_map_lex_le(
715 __isl_take isl_dim *set_dim);
716 __isl_give isl_map *isl_map_lex_gt(
717 __isl_take isl_dim *set_dim);
718 __isl_give isl_map *isl_map_lex_ge(
719 __isl_take isl_dim *set_dim);
720 __isl_give isl_map *isl_map_lex_lt_first(
721 __isl_take isl_dim *dim, unsigned n);
722 __isl_give isl_map *isl_map_lex_le_first(
723 __isl_take isl_dim *dim, unsigned n);
724 __isl_give isl_map *isl_map_lex_gt_first(
725 __isl_take isl_dim *dim, unsigned n);
726 __isl_give isl_map *isl_map_lex_ge_first(
727 __isl_take isl_dim *dim, unsigned n);
729 The first four functions take a dimension specification for a B<set>
730 and return relations that express that the elements in the domain
731 are lexicographically less
732 (C<isl_map_lex_lt>), less or equal (C<isl_map_lex_le>),
733 greater (C<isl_map_lex_gt>) or greater or equal (C<isl_map_lex_ge>)
734 than the elements in the range.
735 The last four functions take a dimension specification for a map
736 and return relations that express that the first C<n> dimensions
737 in the domain are lexicographically less
738 (C<isl_map_lex_lt_first>), less or equal (C<isl_map_lex_le_first>),
739 greater (C<isl_map_lex_gt_first>) or greater or equal (C<isl_map_lex_ge_first>)
740 than the first C<n> dimensions in the range.
744 A basic set or relation can be converted to a set or relation
745 using the following functions.
747 __isl_give isl_set *isl_set_from_basic_set(
748 __isl_take isl_basic_set *bset);
749 __isl_give isl_map *isl_map_from_basic_map(
750 __isl_take isl_basic_map *bmap);
752 Sets and relations can be converted to union sets and relations
753 using the following functions.
755 __isl_give isl_union_map *isl_union_map_from_map(
756 __isl_take isl_map *map);
757 __isl_give isl_union_set *isl_union_set_from_set(
758 __isl_take isl_set *set);
760 Sets and relations can be copied and freed again using the following
763 __isl_give isl_basic_set *isl_basic_set_copy(
764 __isl_keep isl_basic_set *bset);
765 __isl_give isl_set *isl_set_copy(__isl_keep isl_set *set);
766 __isl_give isl_union_set *isl_union_set_copy(
767 __isl_keep isl_union_set *uset);
768 __isl_give isl_basic_map *isl_basic_map_copy(
769 __isl_keep isl_basic_map *bmap);
770 __isl_give isl_map *isl_map_copy(__isl_keep isl_map *map);
771 __isl_give isl_union_map *isl_union_map_copy(
772 __isl_keep isl_union_map *umap);
773 void isl_basic_set_free(__isl_take isl_basic_set *bset);
774 void isl_set_free(__isl_take isl_set *set);
775 void isl_union_set_free(__isl_take isl_union_set *uset);
776 void isl_basic_map_free(__isl_take isl_basic_map *bmap);
777 void isl_map_free(__isl_take isl_map *map);
778 void isl_union_map_free(__isl_take isl_union_map *umap);
780 Other sets and relations can be constructed by starting
781 from a universe set or relation, adding equality and/or
782 inequality constraints and then projecting out the
783 existentially quantified variables, if any.
784 Constraints can be constructed, manipulated and
785 added to basic sets and relations using the following functions.
787 #include <isl_constraint.h>
788 __isl_give isl_constraint *isl_equality_alloc(
789 __isl_take isl_dim *dim);
790 __isl_give isl_constraint *isl_inequality_alloc(
791 __isl_take isl_dim *dim);
792 void isl_constraint_set_constant(
793 __isl_keep isl_constraint *constraint, isl_int v);
794 void isl_constraint_set_coefficient(
795 __isl_keep isl_constraint *constraint,
796 enum isl_dim_type type, int pos, isl_int v);
797 __isl_give isl_basic_map *isl_basic_map_add_constraint(
798 __isl_take isl_basic_map *bmap,
799 __isl_take isl_constraint *constraint);
800 __isl_give isl_basic_set *isl_basic_set_add_constraint(
801 __isl_take isl_basic_set *bset,
802 __isl_take isl_constraint *constraint);
804 For example, to create a set containing the even integers
805 between 10 and 42, you would use the following code.
809 struct isl_constraint *c;
810 struct isl_basic_set *bset;
813 dim = isl_dim_set_alloc(ctx, 0, 2);
814 bset = isl_basic_set_universe(isl_dim_copy(dim));
816 c = isl_equality_alloc(isl_dim_copy(dim));
817 isl_int_set_si(v, -1);
818 isl_constraint_set_coefficient(c, isl_dim_set, 0, v);
819 isl_int_set_si(v, 2);
820 isl_constraint_set_coefficient(c, isl_dim_set, 1, v);
821 bset = isl_basic_set_add_constraint(bset, c);
823 c = isl_inequality_alloc(isl_dim_copy(dim));
824 isl_int_set_si(v, -10);
825 isl_constraint_set_constant(c, v);
826 isl_int_set_si(v, 1);
827 isl_constraint_set_coefficient(c, isl_dim_set, 0, v);
828 bset = isl_basic_set_add_constraint(bset, c);
830 c = isl_inequality_alloc(dim);
831 isl_int_set_si(v, 42);
832 isl_constraint_set_constant(c, v);
833 isl_int_set_si(v, -1);
834 isl_constraint_set_coefficient(c, isl_dim_set, 0, v);
835 bset = isl_basic_set_add_constraint(bset, c);
837 bset = isl_basic_set_project_out(bset, isl_dim_set, 1, 1);
843 struct isl_basic_set *bset;
844 bset = isl_basic_set_read_from_str(ctx,
845 "{[i] : exists (a : i = 2a and i >= 10 and i <= 42)}", -1);
847 A basic set or relation can also be constructed from two matrices
848 describing the equalities and the inequalities.
850 __isl_give isl_basic_set *isl_basic_set_from_constraint_matrices(
851 __isl_take isl_dim *dim,
852 __isl_take isl_mat *eq, __isl_take isl_mat *ineq,
853 enum isl_dim_type c1,
854 enum isl_dim_type c2, enum isl_dim_type c3,
855 enum isl_dim_type c4);
856 __isl_give isl_basic_map *isl_basic_map_from_constraint_matrices(
857 __isl_take isl_dim *dim,
858 __isl_take isl_mat *eq, __isl_take isl_mat *ineq,
859 enum isl_dim_type c1,
860 enum isl_dim_type c2, enum isl_dim_type c3,
861 enum isl_dim_type c4, enum isl_dim_type c5);
863 The C<isl_dim_type> arguments indicate the order in which
864 different kinds of variables appear in the input matrices
865 and should be a permutation of C<isl_dim_cst>, C<isl_dim_param>,
866 C<isl_dim_set> and C<isl_dim_div> for sets and
867 of C<isl_dim_cst>, C<isl_dim_param>,
868 C<isl_dim_in>, C<isl_dim_out> and C<isl_dim_div> for relations.
870 =head2 Inspecting Sets and Relations
872 Usually, the user should not have to care about the actual constraints
873 of the sets and maps, but should instead apply the abstract operations
874 explained in the following sections.
875 Occasionally, however, it may be required to inspect the individual
876 coefficients of the constraints. This section explains how to do so.
877 In these cases, it may also be useful to have C<isl> compute
878 an explicit representation of the existentially quantified variables.
880 __isl_give isl_set *isl_set_compute_divs(
881 __isl_take isl_set *set);
882 __isl_give isl_map *isl_map_compute_divs(
883 __isl_take isl_map *map);
884 __isl_give isl_union_set *isl_union_set_compute_divs(
885 __isl_take isl_union_set *uset);
886 __isl_give isl_union_map *isl_union_map_compute_divs(
887 __isl_take isl_union_map *umap);
889 This explicit representation defines the existentially quantified
890 variables as integer divisions of the other variables, possibly
891 including earlier existentially quantified variables.
892 An explicitly represented existentially quantified variable therefore
893 has a unique value when the values of the other variables are known.
894 If, furthermore, the same existentials, i.e., existentials
895 with the same explicit representations, should appear in the
896 same order in each of the disjuncts of a set or map, then the user should call
897 either of the following functions.
899 __isl_give isl_set *isl_set_align_divs(
900 __isl_take isl_set *set);
901 __isl_give isl_map *isl_map_align_divs(
902 __isl_take isl_map *map);
904 Alternatively, the existentially quantified variables can be removed
905 using the following functions, which compute an overapproximation.
907 __isl_give isl_basic_set *isl_basic_set_remove_divs(
908 __isl_take isl_basic_set *bset);
909 __isl_give isl_basic_map *isl_basic_map_remove_divs(
910 __isl_take isl_basic_map *bmap);
911 __isl_give isl_set *isl_set_remove_divs(
912 __isl_take isl_set *set);
914 To iterate over all the sets or maps in a union set or map, use
916 int isl_union_set_foreach_set(__isl_keep isl_union_set *uset,
917 int (*fn)(__isl_take isl_set *set, void *user),
919 int isl_union_map_foreach_map(__isl_keep isl_union_map *umap,
920 int (*fn)(__isl_take isl_map *map, void *user),
923 The number of sets or maps in a union set or map can be obtained
926 int isl_union_set_n_set(__isl_keep isl_union_set *uset);
927 int isl_union_map_n_map(__isl_keep isl_union_map *umap);
929 To extract the set or map from a union with a given dimension
932 __isl_give isl_set *isl_union_set_extract_set(
933 __isl_keep isl_union_set *uset,
934 __isl_take isl_dim *dim);
935 __isl_give isl_map *isl_union_map_extract_map(
936 __isl_keep isl_union_map *umap,
937 __isl_take isl_dim *dim);
939 To iterate over all the basic sets or maps in a set or map, use
941 int isl_set_foreach_basic_set(__isl_keep isl_set *set,
942 int (*fn)(__isl_take isl_basic_set *bset, void *user),
944 int isl_map_foreach_basic_map(__isl_keep isl_map *map,
945 int (*fn)(__isl_take isl_basic_map *bmap, void *user),
948 The callback function C<fn> should return 0 if successful and
949 -1 if an error occurs. In the latter case, or if any other error
950 occurs, the above functions will return -1.
952 It should be noted that C<isl> does not guarantee that
953 the basic sets or maps passed to C<fn> are disjoint.
954 If this is required, then the user should call one of
955 the following functions first.
957 __isl_give isl_set *isl_set_make_disjoint(
958 __isl_take isl_set *set);
959 __isl_give isl_map *isl_map_make_disjoint(
960 __isl_take isl_map *map);
962 The number of basic sets in a set can be obtained
965 int isl_set_n_basic_set(__isl_keep isl_set *set);
967 To iterate over the constraints of a basic set or map, use
969 #include <isl_constraint.h>
971 int isl_basic_map_foreach_constraint(
972 __isl_keep isl_basic_map *bmap,
973 int (*fn)(__isl_take isl_constraint *c, void *user),
975 void isl_constraint_free(struct isl_constraint *c);
977 Again, the callback function C<fn> should return 0 if successful and
978 -1 if an error occurs. In the latter case, or if any other error
979 occurs, the above functions will return -1.
980 The constraint C<c> represents either an equality or an inequality.
981 Use the following function to find out whether a constraint
982 represents an equality. If not, it represents an inequality.
984 int isl_constraint_is_equality(
985 __isl_keep isl_constraint *constraint);
987 The coefficients of the constraints can be inspected using
988 the following functions.
990 void isl_constraint_get_constant(
991 __isl_keep isl_constraint *constraint, isl_int *v);
992 void isl_constraint_get_coefficient(
993 __isl_keep isl_constraint *constraint,
994 enum isl_dim_type type, int pos, isl_int *v);
996 The explicit representations of the existentially quantified
997 variables can be inspected using the following functions.
998 Note that the user is only allowed to use these functions
999 if the inspected set or map is the result of a call
1000 to C<isl_set_compute_divs> or C<isl_map_compute_divs>.
1002 __isl_give isl_div *isl_constraint_div(
1003 __isl_keep isl_constraint *constraint, int pos);
1004 void isl_div_get_constant(__isl_keep isl_div *div,
1006 void isl_div_get_denominator(__isl_keep isl_div *div,
1008 void isl_div_get_coefficient(__isl_keep isl_div *div,
1009 enum isl_dim_type type, int pos, isl_int *v);
1011 To obtain the constraints of a basic map in matrix
1012 form, use the following functions.
1014 __isl_give isl_mat *isl_basic_map_equalities_matrix(
1015 __isl_keep isl_basic_map *bmap,
1016 enum isl_dim_type c1,
1017 enum isl_dim_type c2, enum isl_dim_type c3,
1018 enum isl_dim_type c4, enum isl_dim_type c5);
1019 __isl_give isl_mat *isl_basic_map_inequalities_matrix(
1020 __isl_keep isl_basic_map *bmap,
1021 enum isl_dim_type c1,
1022 enum isl_dim_type c2, enum isl_dim_type c3,
1023 enum isl_dim_type c4, enum isl_dim_type c5);
1025 The C<isl_dim_type> arguments dictate the order in which
1026 different kinds of variables appear in the resulting matrix
1027 and should be a permutation of C<isl_dim_cst>, C<isl_dim_param>,
1028 C<isl_dim_in>, C<isl_dim_out> and C<isl_dim_div>.
1030 The names of the domain and range spaces of a set or relation can be
1031 read off using the following functions.
1033 const char *isl_set_get_tuple_name(
1034 __isl_keep isl_set *set);
1035 const char *isl_basic_map_get_tuple_name(
1036 __isl_keep isl_basic_map *bmap,
1037 enum isl_dim_type type);
1038 const char *isl_map_get_tuple_name(
1039 __isl_keep isl_map *map,
1040 enum isl_dim_type type);
1042 As with C<isl_dim_get_tuple_name>, the value returned points to
1043 an internal data structure.
1044 The names of individual dimensions can be read off using
1045 the following functions.
1047 const char *isl_constraint_get_dim_name(
1048 __isl_keep isl_constraint *constraint,
1049 enum isl_dim_type type, unsigned pos);
1050 const char *isl_set_get_dim_name(
1051 __isl_keep isl_set *set,
1052 enum isl_dim_type type, unsigned pos);
1053 const char *isl_basic_map_get_dim_name(
1054 __isl_keep isl_basic_map *bmap,
1055 enum isl_dim_type type, unsigned pos);
1056 const char *isl_map_get_dim_name(
1057 __isl_keep isl_map *map,
1058 enum isl_dim_type type, unsigned pos);
1060 These functions are mostly useful to obtain the names
1065 =head3 Unary Properties
1071 The following functions test whether the given set or relation
1072 contains any integer points. The ``fast'' variants do not perform
1073 any computations, but simply check if the given set or relation
1074 is already known to be empty.
1076 int isl_basic_set_fast_is_empty(__isl_keep isl_basic_set *bset);
1077 int isl_basic_set_is_empty(__isl_keep isl_basic_set *bset);
1078 int isl_set_is_empty(__isl_keep isl_set *set);
1079 int isl_union_set_is_empty(__isl_keep isl_union_set *uset);
1080 int isl_basic_map_fast_is_empty(__isl_keep isl_basic_map *bmap);
1081 int isl_basic_map_is_empty(__isl_keep isl_basic_map *bmap);
1082 int isl_map_fast_is_empty(__isl_keep isl_map *map);
1083 int isl_map_is_empty(__isl_keep isl_map *map);
1084 int isl_union_map_is_empty(__isl_keep isl_union_map *umap);
1086 =item * Universality
1088 int isl_basic_set_is_universe(__isl_keep isl_basic_set *bset);
1089 int isl_basic_map_is_universe(__isl_keep isl_basic_map *bmap);
1090 int isl_set_fast_is_universe(__isl_keep isl_set *set);
1092 =item * Single-valuedness
1094 int isl_map_is_single_valued(__isl_keep isl_map *map);
1098 int isl_map_is_bijective(__isl_keep isl_map *map);
1102 The followning functions check whether the domain of the given
1103 (basic) set is a wrapped relation.
1105 int isl_basic_set_is_wrapping(
1106 __isl_keep isl_basic_set *bset);
1107 int isl_set_is_wrapping(__isl_keep isl_set *set);
1111 =head3 Binary Properties
1117 int isl_set_fast_is_equal(__isl_keep isl_set *set1,
1118 __isl_keep isl_set *set2);
1119 int isl_set_is_equal(__isl_keep isl_set *set1,
1120 __isl_keep isl_set *set2);
1121 int isl_basic_map_is_equal(
1122 __isl_keep isl_basic_map *bmap1,
1123 __isl_keep isl_basic_map *bmap2);
1124 int isl_map_is_equal(__isl_keep isl_map *map1,
1125 __isl_keep isl_map *map2);
1126 int isl_map_fast_is_equal(__isl_keep isl_map *map1,
1127 __isl_keep isl_map *map2);
1128 int isl_union_map_is_equal(
1129 __isl_keep isl_union_map *umap1,
1130 __isl_keep isl_union_map *umap2);
1132 =item * Disjointness
1134 int isl_set_fast_is_disjoint(__isl_keep isl_set *set1,
1135 __isl_keep isl_set *set2);
1139 int isl_set_is_subset(__isl_keep isl_set *set1,
1140 __isl_keep isl_set *set2);
1141 int isl_set_is_strict_subset(
1142 __isl_keep isl_set *set1,
1143 __isl_keep isl_set *set2);
1144 int isl_basic_map_is_subset(
1145 __isl_keep isl_basic_map *bmap1,
1146 __isl_keep isl_basic_map *bmap2);
1147 int isl_basic_map_is_strict_subset(
1148 __isl_keep isl_basic_map *bmap1,
1149 __isl_keep isl_basic_map *bmap2);
1150 int isl_map_is_subset(
1151 __isl_keep isl_map *map1,
1152 __isl_keep isl_map *map2);
1153 int isl_map_is_strict_subset(
1154 __isl_keep isl_map *map1,
1155 __isl_keep isl_map *map2);
1156 int isl_union_map_is_subset(
1157 __isl_keep isl_union_map *umap1,
1158 __isl_keep isl_union_map *umap2);
1159 int isl_union_map_is_strict_subset(
1160 __isl_keep isl_union_map *umap1,
1161 __isl_keep isl_union_map *umap2);
1165 =head2 Unary Operations
1171 __isl_give isl_set *isl_set_complement(
1172 __isl_take isl_set *set);
1176 __isl_give isl_basic_map *isl_basic_map_reverse(
1177 __isl_take isl_basic_map *bmap);
1178 __isl_give isl_map *isl_map_reverse(
1179 __isl_take isl_map *map);
1180 __isl_give isl_union_map *isl_union_map_reverse(
1181 __isl_take isl_union_map *umap);
1185 __isl_give isl_basic_set *isl_basic_set_project_out(
1186 __isl_take isl_basic_set *bset,
1187 enum isl_dim_type type, unsigned first, unsigned n);
1188 __isl_give isl_basic_map *isl_basic_map_project_out(
1189 __isl_take isl_basic_map *bmap,
1190 enum isl_dim_type type, unsigned first, unsigned n);
1191 __isl_give isl_set *isl_set_project_out(__isl_take isl_set *set,
1192 enum isl_dim_type type, unsigned first, unsigned n);
1193 __isl_give isl_map *isl_map_project_out(__isl_take isl_map *map,
1194 enum isl_dim_type type, unsigned first, unsigned n);
1195 __isl_give isl_basic_set *isl_basic_map_domain(
1196 __isl_take isl_basic_map *bmap);
1197 __isl_give isl_basic_set *isl_basic_map_range(
1198 __isl_take isl_basic_map *bmap);
1199 __isl_give isl_set *isl_map_domain(
1200 __isl_take isl_map *bmap);
1201 __isl_give isl_set *isl_map_range(
1202 __isl_take isl_map *map);
1203 __isl_give isl_union_set *isl_union_map_domain(
1204 __isl_take isl_union_map *umap);
1205 __isl_give isl_union_set *isl_union_map_range(
1206 __isl_take isl_union_map *umap);
1208 __isl_give isl_basic_map *isl_basic_map_domain_map(
1209 __isl_take isl_basic_map *bmap);
1210 __isl_give isl_basic_map *isl_basic_map_range_map(
1211 __isl_take isl_basic_map *bmap);
1212 __isl_give isl_map *isl_map_domain_map(__isl_take isl_map *map);
1213 __isl_give isl_map *isl_map_range_map(__isl_take isl_map *map);
1214 __isl_give isl_union_map *isl_union_map_domain_map(
1215 __isl_take isl_union_map *umap);
1216 __isl_give isl_union_map *isl_union_map_range_map(
1217 __isl_take isl_union_map *umap);
1219 The functions above construct a (basic, regular or union) relation
1220 that maps (a wrapped version of) the input relation to its domain or range.
1224 __isl_give isl_map *isl_set_identity(
1225 __isl_take isl_set *set);
1226 __isl_give isl_union_map *isl_union_set_identity(
1227 __isl_take isl_union_set *uset);
1229 Construct an identity relation on the given (union) set.
1233 __isl_give isl_basic_set *isl_basic_map_deltas(
1234 __isl_take isl_basic_map *bmap);
1235 __isl_give isl_set *isl_map_deltas(__isl_take isl_map *map);
1236 __isl_give isl_union_set *isl_union_map_deltas(
1237 __isl_take isl_union_map *umap);
1239 These functions return a (basic) set containing the differences
1240 between image elements and corresponding domain elements in the input.
1244 Simplify the representation of a set or relation by trying
1245 to combine pairs of basic sets or relations into a single
1246 basic set or relation.
1248 __isl_give isl_set *isl_set_coalesce(__isl_take isl_set *set);
1249 __isl_give isl_map *isl_map_coalesce(__isl_take isl_map *map);
1250 __isl_give isl_union_set *isl_union_set_coalesce(
1251 __isl_take isl_union_set *uset);
1252 __isl_give isl_union_map *isl_union_map_coalesce(
1253 __isl_take isl_union_map *umap);
1257 __isl_give isl_basic_set *isl_set_convex_hull(
1258 __isl_take isl_set *set);
1259 __isl_give isl_basic_map *isl_map_convex_hull(
1260 __isl_take isl_map *map);
1262 If the input set or relation has any existentially quantified
1263 variables, then the result of these operations is currently undefined.
1267 __isl_give isl_basic_set *isl_set_simple_hull(
1268 __isl_take isl_set *set);
1269 __isl_give isl_basic_map *isl_map_simple_hull(
1270 __isl_take isl_map *map);
1272 These functions compute a single basic set or relation
1273 that contains the whole input set or relation.
1274 In particular, the output is described by translates
1275 of the constraints describing the basic sets or relations in the input.
1279 (See \autoref{s:simple hull}.)
1285 __isl_give isl_basic_set *isl_basic_set_affine_hull(
1286 __isl_take isl_basic_set *bset);
1287 __isl_give isl_basic_set *isl_set_affine_hull(
1288 __isl_take isl_set *set);
1289 __isl_give isl_union_set *isl_union_set_affine_hull(
1290 __isl_take isl_union_set *uset);
1291 __isl_give isl_basic_map *isl_basic_map_affine_hull(
1292 __isl_take isl_basic_map *bmap);
1293 __isl_give isl_basic_map *isl_map_affine_hull(
1294 __isl_take isl_map *map);
1295 __isl_give isl_union_map *isl_union_map_affine_hull(
1296 __isl_take isl_union_map *umap);
1298 In case of union sets and relations, the affine hull is computed
1303 __isl_give isl_map *isl_map_power(__isl_take isl_map *map,
1304 unsigned param, int *exact);
1306 Compute a parametric representation for all positive powers I<k> of C<map>.
1307 The power I<k> is equated to the parameter at position C<param>.
1308 The result may be an overapproximation. If the result is exact,
1309 then C<*exact> is set to C<1>.
1310 The current implementation only produces exact results for particular
1311 cases of piecewise translations (i.e., piecewise uniform dependences).
1313 =item * Transitive closure
1315 __isl_give isl_map *isl_map_transitive_closure(
1316 __isl_take isl_map *map, int *exact);
1317 __isl_give isl_union_map *isl_union_map_transitive_closure(
1318 __isl_take isl_union_map *umap, int *exact);
1320 Compute the transitive closure of C<map>.
1321 The result may be an overapproximation. If the result is known to be exact,
1322 then C<*exact> is set to C<1>.
1323 The current implementation only produces exact results for particular
1324 cases of piecewise translations (i.e., piecewise uniform dependences).
1326 =item * Reaching path lengths
1328 __isl_give isl_map *isl_map_reaching_path_lengths(
1329 __isl_take isl_map *map, int *exact);
1331 Compute a relation that maps each element in the range of C<map>
1332 to the lengths of all paths composed of edges in C<map> that
1333 end up in the given element.
1334 The result may be an overapproximation. If the result is known to be exact,
1335 then C<*exact> is set to C<1>.
1336 To compute the I<maximal> path length, the resulting relation
1337 should be postprocessed by C<isl_map_lexmax>.
1338 In particular, if the input relation is a dependence relation
1339 (mapping sources to sinks), then the maximal path length corresponds
1340 to the free schedule.
1341 Note, however, that C<isl_map_lexmax> expects the maximum to be
1342 finite, so if the path lengths are unbounded (possibly due to
1343 the overapproximation), then you will get an error message.
1347 __isl_give isl_basic_set *isl_basic_map_wrap(
1348 __isl_take isl_basic_map *bmap);
1349 __isl_give isl_set *isl_map_wrap(
1350 __isl_take isl_map *map);
1351 __isl_give isl_union_set *isl_union_map_wrap(
1352 __isl_take isl_union_map *umap);
1353 __isl_give isl_basic_map *isl_basic_set_unwrap(
1354 __isl_take isl_basic_set *bset);
1355 __isl_give isl_map *isl_set_unwrap(
1356 __isl_take isl_set *set);
1357 __isl_give isl_union_map *isl_union_set_unwrap(
1358 __isl_take isl_union_set *uset);
1362 Remove any internal structure of domain (and range) of the given
1363 set or relation. If there is any such internal structure in the input,
1364 then the name of the space is also removed.
1366 __isl_give isl_set *isl_set_flatten(
1367 __isl_take isl_set *set);
1368 __isl_give isl_map *isl_map_flatten(
1369 __isl_take isl_map *map);
1371 =item * Dimension manipulation
1373 __isl_give isl_set *isl_set_add_dims(
1374 __isl_take isl_set *set,
1375 enum isl_dim_type type, unsigned n);
1376 __isl_give isl_map *isl_map_add_dims(
1377 __isl_take isl_map *map,
1378 enum isl_dim_type type, unsigned n);
1380 It is usually not advisable to directly change the (input or output)
1381 space of a set or a relation as this removes the name and the internal
1382 structure of the space. However, the above functions can be useful
1383 to add new parameters.
1387 =head2 Binary Operations
1389 The two arguments of a binary operation not only need to live
1390 in the same C<isl_ctx>, they currently also need to have
1391 the same (number of) parameters.
1393 =head3 Basic Operations
1397 =item * Intersection
1399 __isl_give isl_basic_set *isl_basic_set_intersect(
1400 __isl_take isl_basic_set *bset1,
1401 __isl_take isl_basic_set *bset2);
1402 __isl_give isl_set *isl_set_intersect(
1403 __isl_take isl_set *set1,
1404 __isl_take isl_set *set2);
1405 __isl_give isl_union_set *isl_union_set_intersect(
1406 __isl_take isl_union_set *uset1,
1407 __isl_take isl_union_set *uset2);
1408 __isl_give isl_basic_map *isl_basic_map_intersect_domain(
1409 __isl_take isl_basic_map *bmap,
1410 __isl_take isl_basic_set *bset);
1411 __isl_give isl_basic_map *isl_basic_map_intersect_range(
1412 __isl_take isl_basic_map *bmap,
1413 __isl_take isl_basic_set *bset);
1414 __isl_give isl_basic_map *isl_basic_map_intersect(
1415 __isl_take isl_basic_map *bmap1,
1416 __isl_take isl_basic_map *bmap2);
1417 __isl_give isl_map *isl_map_intersect_domain(
1418 __isl_take isl_map *map,
1419 __isl_take isl_set *set);
1420 __isl_give isl_map *isl_map_intersect_range(
1421 __isl_take isl_map *map,
1422 __isl_take isl_set *set);
1423 __isl_give isl_map *isl_map_intersect(
1424 __isl_take isl_map *map1,
1425 __isl_take isl_map *map2);
1426 __isl_give isl_union_map *isl_union_map_intersect_domain(
1427 __isl_take isl_union_map *umap,
1428 __isl_take isl_union_set *uset);
1429 __isl_give isl_union_map *isl_union_map_intersect_range(
1430 __isl_take isl_union_map *umap,
1431 __isl_take isl_union_set *uset);
1432 __isl_give isl_union_map *isl_union_map_intersect(
1433 __isl_take isl_union_map *umap1,
1434 __isl_take isl_union_map *umap2);
1438 __isl_give isl_set *isl_basic_set_union(
1439 __isl_take isl_basic_set *bset1,
1440 __isl_take isl_basic_set *bset2);
1441 __isl_give isl_map *isl_basic_map_union(
1442 __isl_take isl_basic_map *bmap1,
1443 __isl_take isl_basic_map *bmap2);
1444 __isl_give isl_set *isl_set_union(
1445 __isl_take isl_set *set1,
1446 __isl_take isl_set *set2);
1447 __isl_give isl_map *isl_map_union(
1448 __isl_take isl_map *map1,
1449 __isl_take isl_map *map2);
1450 __isl_give isl_union_set *isl_union_set_union(
1451 __isl_take isl_union_set *uset1,
1452 __isl_take isl_union_set *uset2);
1453 __isl_give isl_union_map *isl_union_map_union(
1454 __isl_take isl_union_map *umap1,
1455 __isl_take isl_union_map *umap2);
1457 =item * Set difference
1459 __isl_give isl_set *isl_set_subtract(
1460 __isl_take isl_set *set1,
1461 __isl_take isl_set *set2);
1462 __isl_give isl_map *isl_map_subtract(
1463 __isl_take isl_map *map1,
1464 __isl_take isl_map *map2);
1465 __isl_give isl_union_set *isl_union_set_subtract(
1466 __isl_take isl_union_set *uset1,
1467 __isl_take isl_union_set *uset2);
1468 __isl_give isl_union_map *isl_union_map_subtract(
1469 __isl_take isl_union_map *umap1,
1470 __isl_take isl_union_map *umap2);
1474 __isl_give isl_basic_set *isl_basic_set_apply(
1475 __isl_take isl_basic_set *bset,
1476 __isl_take isl_basic_map *bmap);
1477 __isl_give isl_set *isl_set_apply(
1478 __isl_take isl_set *set,
1479 __isl_take isl_map *map);
1480 __isl_give isl_union_set *isl_union_set_apply(
1481 __isl_take isl_union_set *uset,
1482 __isl_take isl_union_map *umap);
1483 __isl_give isl_basic_map *isl_basic_map_apply_domain(
1484 __isl_take isl_basic_map *bmap1,
1485 __isl_take isl_basic_map *bmap2);
1486 __isl_give isl_basic_map *isl_basic_map_apply_range(
1487 __isl_take isl_basic_map *bmap1,
1488 __isl_take isl_basic_map *bmap2);
1489 __isl_give isl_map *isl_map_apply_domain(
1490 __isl_take isl_map *map1,
1491 __isl_take isl_map *map2);
1492 __isl_give isl_union_map *isl_union_map_apply_domain(
1493 __isl_take isl_union_map *umap1,
1494 __isl_take isl_union_map *umap2);
1495 __isl_give isl_map *isl_map_apply_range(
1496 __isl_take isl_map *map1,
1497 __isl_take isl_map *map2);
1498 __isl_give isl_union_map *isl_union_map_apply_range(
1499 __isl_take isl_union_map *umap1,
1500 __isl_take isl_union_map *umap2);
1502 =item * Simplification
1504 __isl_give isl_basic_set *isl_basic_set_gist(
1505 __isl_take isl_basic_set *bset,
1506 __isl_take isl_basic_set *context);
1507 __isl_give isl_set *isl_set_gist(__isl_take isl_set *set,
1508 __isl_take isl_set *context);
1509 __isl_give isl_union_set *isl_union_set_gist(
1510 __isl_take isl_union_set *uset,
1511 __isl_take isl_union_set *context);
1512 __isl_give isl_basic_map *isl_basic_map_gist(
1513 __isl_take isl_basic_map *bmap,
1514 __isl_take isl_basic_map *context);
1515 __isl_give isl_map *isl_map_gist(__isl_take isl_map *map,
1516 __isl_take isl_map *context);
1517 __isl_give isl_union_map *isl_union_map_gist(
1518 __isl_take isl_union_map *umap,
1519 __isl_take isl_union_map *context);
1521 The gist operation returns a set or relation that has the
1522 same intersection with the context as the input set or relation.
1523 Any implicit equality in the intersection is made explicit in the result,
1524 while all inequalities that are redundant with respect to the intersection
1526 In case of union sets and relations, the gist operation is performed
1531 =head3 Lexicographic Optimization
1533 Given a (basic) set C<set> (or C<bset>) and a zero-dimensional domain C<dom>,
1534 the following functions
1535 compute a set that contains the lexicographic minimum or maximum
1536 of the elements in C<set> (or C<bset>) for those values of the parameters
1537 that satisfy C<dom>.
1538 If C<empty> is not C<NULL>, then C<*empty> is assigned a set
1539 that contains the parameter values in C<dom> for which C<set> (or C<bset>)
1541 In other words, the union of the parameter values
1542 for which the result is non-empty and of C<*empty>
1545 __isl_give isl_set *isl_basic_set_partial_lexmin(
1546 __isl_take isl_basic_set *bset,
1547 __isl_take isl_basic_set *dom,
1548 __isl_give isl_set **empty);
1549 __isl_give isl_set *isl_basic_set_partial_lexmax(
1550 __isl_take isl_basic_set *bset,
1551 __isl_take isl_basic_set *dom,
1552 __isl_give isl_set **empty);
1553 __isl_give isl_set *isl_set_partial_lexmin(
1554 __isl_take isl_set *set, __isl_take isl_set *dom,
1555 __isl_give isl_set **empty);
1556 __isl_give isl_set *isl_set_partial_lexmax(
1557 __isl_take isl_set *set, __isl_take isl_set *dom,
1558 __isl_give isl_set **empty);
1560 Given a (basic) set C<set> (or C<bset>), the following functions simply
1561 return a set containing the lexicographic minimum or maximum
1562 of the elements in C<set> (or C<bset>).
1563 In case of union sets, the optimum is computed per space.
1565 __isl_give isl_set *isl_basic_set_lexmin(
1566 __isl_take isl_basic_set *bset);
1567 __isl_give isl_set *isl_basic_set_lexmax(
1568 __isl_take isl_basic_set *bset);
1569 __isl_give isl_set *isl_set_lexmin(
1570 __isl_take isl_set *set);
1571 __isl_give isl_set *isl_set_lexmax(
1572 __isl_take isl_set *set);
1573 __isl_give isl_union_set *isl_union_set_lexmin(
1574 __isl_take isl_union_set *uset);
1575 __isl_give isl_union_set *isl_union_set_lexmax(
1576 __isl_take isl_union_set *uset);
1578 Given a (basic) relation C<map> (or C<bmap>) and a domain C<dom>,
1579 the following functions
1580 compute a relation that maps each element of C<dom>
1581 to the single lexicographic minimum or maximum
1582 of the elements that are associated to that same
1583 element in C<map> (or C<bmap>).
1584 If C<empty> is not C<NULL>, then C<*empty> is assigned a set
1585 that contains the elements in C<dom> that do not map
1586 to any elements in C<map> (or C<bmap>).
1587 In other words, the union of the domain of the result and of C<*empty>
1590 __isl_give isl_map *isl_basic_map_partial_lexmax(
1591 __isl_take isl_basic_map *bmap,
1592 __isl_take isl_basic_set *dom,
1593 __isl_give isl_set **empty);
1594 __isl_give isl_map *isl_basic_map_partial_lexmin(
1595 __isl_take isl_basic_map *bmap,
1596 __isl_take isl_basic_set *dom,
1597 __isl_give isl_set **empty);
1598 __isl_give isl_map *isl_map_partial_lexmax(
1599 __isl_take isl_map *map, __isl_take isl_set *dom,
1600 __isl_give isl_set **empty);
1601 __isl_give isl_map *isl_map_partial_lexmin(
1602 __isl_take isl_map *map, __isl_take isl_set *dom,
1603 __isl_give isl_set **empty);
1605 Given a (basic) map C<map> (or C<bmap>), the following functions simply
1606 return a map mapping each element in the domain of
1607 C<map> (or C<bmap>) to the lexicographic minimum or maximum
1608 of all elements associated to that element.
1609 In case of union relations, the optimum is computed per space.
1611 __isl_give isl_map *isl_basic_map_lexmin(
1612 __isl_take isl_basic_map *bmap);
1613 __isl_give isl_map *isl_basic_map_lexmax(
1614 __isl_take isl_basic_map *bmap);
1615 __isl_give isl_map *isl_map_lexmin(
1616 __isl_take isl_map *map);
1617 __isl_give isl_map *isl_map_lexmax(
1618 __isl_take isl_map *map);
1619 __isl_give isl_union_map *isl_union_map_lexmin(
1620 __isl_take isl_union_map *umap);
1621 __isl_give isl_union_map *isl_union_map_lexmax(
1622 __isl_take isl_union_map *umap);
1626 Matrices can be created, copied and freed using the following functions.
1628 #include <isl_mat.h>
1629 __isl_give isl_mat *isl_mat_alloc(struct isl_ctx *ctx,
1630 unsigned n_row, unsigned n_col);
1631 __isl_give isl_mat *isl_mat_copy(__isl_keep isl_mat *mat);
1632 void isl_mat_free(__isl_take isl_mat *mat);
1634 Note that the elements of a newly created matrix may have arbitrary values.
1635 The elements can be changed and inspected using the following functions.
1637 int isl_mat_rows(__isl_keep isl_mat *mat);
1638 int isl_mat_cols(__isl_keep isl_mat *mat);
1639 int isl_mat_get_element(__isl_keep isl_mat *mat,
1640 int row, int col, isl_int *v);
1641 __isl_give isl_mat *isl_mat_set_element(__isl_take isl_mat *mat,
1642 int row, int col, isl_int v);
1644 C<isl_mat_get_element> will return a negative value if anything went wrong.
1645 In that case, the value of C<*v> is undefined.
1647 The following function can be used to compute the (right) inverse
1648 of a matrix, i.e., a matrix such that the product of the original
1649 and the inverse (in that order) is a multiple of the identity matrix.
1650 The input matrix is assumed to be of full row-rank.
1652 __isl_give isl_mat *isl_mat_right_inverse(__isl_take isl_mat *mat);
1654 The following function can be used to compute the (right) kernel
1655 (or null space) of a matrix, i.e., a matrix such that the product of
1656 the original and the kernel (in that order) is the zero matrix.
1658 __isl_give isl_mat *isl_mat_right_kernel(__isl_take isl_mat *mat);
1662 Points are elements of a set. They can be used to construct
1663 simple sets (boxes) or they can be used to represent the
1664 individual elements of a set.
1665 The zero point (the origin) can be created using
1667 __isl_give isl_point *isl_point_zero(__isl_take isl_dim *dim);
1669 The coordinates of a point can be inspected, set and changed
1672 void isl_point_get_coordinate(__isl_keep isl_point *pnt,
1673 enum isl_dim_type type, int pos, isl_int *v);
1674 __isl_give isl_point *isl_point_set_coordinate(
1675 __isl_take isl_point *pnt,
1676 enum isl_dim_type type, int pos, isl_int v);
1678 __isl_give isl_point *isl_point_add_ui(
1679 __isl_take isl_point *pnt,
1680 enum isl_dim_type type, int pos, unsigned val);
1681 __isl_give isl_point *isl_point_sub_ui(
1682 __isl_take isl_point *pnt,
1683 enum isl_dim_type type, int pos, unsigned val);
1685 Points can be copied or freed using
1687 __isl_give isl_point *isl_point_copy(
1688 __isl_keep isl_point *pnt);
1689 void isl_point_free(__isl_take isl_point *pnt);
1691 A singleton set can be created from a point using
1693 __isl_give isl_set *isl_set_from_point(
1694 __isl_take isl_point *pnt);
1696 and a box can be created from two opposite extremal points using
1698 __isl_give isl_set *isl_set_box_from_points(
1699 __isl_take isl_point *pnt1,
1700 __isl_take isl_point *pnt2);
1702 All elements of a B<bounded> (union) set can be enumerated using
1703 the following functions.
1705 int isl_set_foreach_point(__isl_keep isl_set *set,
1706 int (*fn)(__isl_take isl_point *pnt, void *user),
1708 int isl_union_set_foreach_point(__isl_keep isl_union_set *uset,
1709 int (*fn)(__isl_take isl_point *pnt, void *user),
1712 The function C<fn> is called for each integer point in
1713 C<set> with as second argument the last argument of
1714 the C<isl_set_foreach_point> call. The function C<fn>
1715 should return C<0> on success and C<-1> on failure.
1716 In the latter case, C<isl_set_foreach_point> will stop
1717 enumerating and return C<-1> as well.
1718 If the enumeration is performed successfully and to completion,
1719 then C<isl_set_foreach_point> returns C<0>.
1721 To obtain a single point of a (basic) set, use
1723 __isl_give isl_point *isl_basic_set_sample_point(
1724 __isl_take isl_basic_set *bset);
1725 __isl_give isl_point *isl_set_sample_point(
1726 __isl_take isl_set *set);
1728 If C<set> does not contain any (integer) points, then the
1729 resulting point will be ``void'', a property that can be
1732 int isl_point_is_void(__isl_keep isl_point *pnt);
1734 =head2 Piecewise Quasipolynomials
1736 A piecewise quasipolynomial is a particular kind of function that maps
1737 a parametric point to a rational value.
1738 More specifically, a quasipolynomial is a polynomial expression in greatest
1739 integer parts of affine expressions of parameters and variables.
1740 A piecewise quasipolynomial is a subdivision of a given parametric
1741 domain into disjoint cells with a quasipolynomial associated to
1742 each cell. The value of the piecewise quasipolynomial at a given
1743 point is the value of the quasipolynomial associated to the cell
1744 that contains the point. Outside of the union of cells,
1745 the value is assumed to be zero.
1746 For example, the piecewise quasipolynomial
1748 [n] -> { [x] -> ((1 + n) - x) : x <= n and x >= 0 }
1750 maps C<x> to C<1 + n - x> for values of C<x> between C<0> and C<n>.
1751 A given piecewise quasipolynomial has a fixed domain dimension.
1752 Union piecewise quasipolynomials are used to contain piecewise quasipolynomials
1753 defined over different domains.
1754 Piecewise quasipolynomials are mainly used by the C<barvinok>
1755 library for representing the number of elements in a parametric set or map.
1756 For example, the piecewise quasipolynomial above represents
1757 the number of points in the map
1759 [n] -> { [x] -> [y] : x,y >= 0 and 0 <= x + y <= n }
1761 =head3 Printing (Piecewise) Quasipolynomials
1763 Quasipolynomials and piecewise quasipolynomials can be printed
1764 using the following functions.
1766 __isl_give isl_printer *isl_printer_print_qpolynomial(
1767 __isl_take isl_printer *p,
1768 __isl_keep isl_qpolynomial *qp);
1770 __isl_give isl_printer *isl_printer_print_pw_qpolynomial(
1771 __isl_take isl_printer *p,
1772 __isl_keep isl_pw_qpolynomial *pwqp);
1774 __isl_give isl_printer *isl_printer_print_union_pw_qpolynomial(
1775 __isl_take isl_printer *p,
1776 __isl_keep isl_union_pw_qpolynomial *upwqp);
1778 The output format of the printer
1779 needs to be set to either C<ISL_FORMAT_ISL> or C<ISL_FORMAT_C>.
1780 For C<isl_printer_print_union_pw_qpolynomial>, only C<ISL_FORMAT_ISL>
1782 In case of printing in C<ISL_FORMAT_C>, the user may want
1783 to set the names of all dimensions
1785 __isl_give isl_qpolynomial *isl_qpolynomial_set_dim_name(
1786 __isl_take isl_qpolynomial *qp,
1787 enum isl_dim_type type, unsigned pos,
1789 __isl_give isl_pw_qpolynomial *
1790 isl_pw_qpolynomial_set_dim_name(
1791 __isl_take isl_pw_qpolynomial *pwqp,
1792 enum isl_dim_type type, unsigned pos,
1795 =head3 Creating New (Piecewise) Quasipolynomials
1797 Some simple quasipolynomials can be created using the following functions.
1798 More complicated quasipolynomials can be created by applying
1799 operations such as addition and multiplication
1800 on the resulting quasipolynomials
1802 __isl_give isl_qpolynomial *isl_qpolynomial_zero(
1803 __isl_take isl_dim *dim);
1804 __isl_give isl_qpolynomial *isl_qpolynomial_one(
1805 __isl_take isl_dim *dim);
1806 __isl_give isl_qpolynomial *isl_qpolynomial_infty(
1807 __isl_take isl_dim *dim);
1808 __isl_give isl_qpolynomial *isl_qpolynomial_neginfty(
1809 __isl_take isl_dim *dim);
1810 __isl_give isl_qpolynomial *isl_qpolynomial_nan(
1811 __isl_take isl_dim *dim);
1812 __isl_give isl_qpolynomial *isl_qpolynomial_rat_cst(
1813 __isl_take isl_dim *dim,
1814 const isl_int n, const isl_int d);
1815 __isl_give isl_qpolynomial *isl_qpolynomial_div(
1816 __isl_take isl_div *div);
1817 __isl_give isl_qpolynomial *isl_qpolynomial_var(
1818 __isl_take isl_dim *dim,
1819 enum isl_dim_type type, unsigned pos);
1821 The zero piecewise quasipolynomial or a piecewise quasipolynomial
1822 with a single cell can be created using the following functions.
1823 Multiple of these single cell piecewise quasipolynomials can
1824 be combined to create more complicated piecewise quasipolynomials.
1826 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_zero(
1827 __isl_take isl_dim *dim);
1828 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_alloc(
1829 __isl_take isl_set *set,
1830 __isl_take isl_qpolynomial *qp);
1832 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_zero(
1833 __isl_take isl_dim *dim);
1834 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_from_pw_qpolynomial(
1835 __isl_take isl_pw_qpolynomial *pwqp);
1836 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_add_pw_qpolynomial(
1837 __isl_take isl_union_pw_qpolynomial *upwqp,
1838 __isl_take isl_pw_qpolynomial *pwqp);
1840 Quasipolynomials can be copied and freed again using the following
1843 __isl_give isl_qpolynomial *isl_qpolynomial_copy(
1844 __isl_keep isl_qpolynomial *qp);
1845 void isl_qpolynomial_free(__isl_take isl_qpolynomial *qp);
1847 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_copy(
1848 __isl_keep isl_pw_qpolynomial *pwqp);
1849 void isl_pw_qpolynomial_free(
1850 __isl_take isl_pw_qpolynomial *pwqp);
1852 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_copy(
1853 __isl_keep isl_union_pw_qpolynomial *upwqp);
1854 void isl_union_pw_qpolynomial_free(
1855 __isl_take isl_union_pw_qpolynomial *upwqp);
1857 =head3 Inspecting (Piecewise) Quasipolynomials
1859 To iterate over all piecewise quasipolynomials in a union
1860 piecewise quasipolynomial, use the following function
1862 int isl_union_pw_qpolynomial_foreach_pw_qpolynomial(
1863 __isl_keep isl_union_pw_qpolynomial *upwqp,
1864 int (*fn)(__isl_take isl_pw_qpolynomial *pwqp, void *user),
1867 To extract the piecewise quasipolynomial from a union with a given dimension
1870 __isl_give isl_pw_qpolynomial *
1871 isl_union_pw_qpolynomial_extract_pw_qpolynomial(
1872 __isl_keep isl_union_pw_qpolynomial *upwqp,
1873 __isl_take isl_dim *dim);
1875 To iterate over the cells in a piecewise quasipolynomial,
1876 use either of the following two functions
1878 int isl_pw_qpolynomial_foreach_piece(
1879 __isl_keep isl_pw_qpolynomial *pwqp,
1880 int (*fn)(__isl_take isl_set *set,
1881 __isl_take isl_qpolynomial *qp,
1882 void *user), void *user);
1883 int isl_pw_qpolynomial_foreach_lifted_piece(
1884 __isl_keep isl_pw_qpolynomial *pwqp,
1885 int (*fn)(__isl_take isl_set *set,
1886 __isl_take isl_qpolynomial *qp,
1887 void *user), void *user);
1889 As usual, the function C<fn> should return C<0> on success
1890 and C<-1> on failure. The difference between
1891 C<isl_pw_qpolynomial_foreach_piece> and
1892 C<isl_pw_qpolynomial_foreach_lifted_piece> is that
1893 C<isl_pw_qpolynomial_foreach_lifted_piece> will first
1894 compute unique representations for all existentially quantified
1895 variables and then turn these existentially quantified variables
1896 into extra set variables, adapting the associated quasipolynomial
1897 accordingly. This means that the C<set> passed to C<fn>
1898 will not have any existentially quantified variables, but that
1899 the dimensions of the sets may be different for different
1900 invocations of C<fn>.
1902 To iterate over all terms in a quasipolynomial,
1905 int isl_qpolynomial_foreach_term(
1906 __isl_keep isl_qpolynomial *qp,
1907 int (*fn)(__isl_take isl_term *term,
1908 void *user), void *user);
1910 The terms themselves can be inspected and freed using
1913 unsigned isl_term_dim(__isl_keep isl_term *term,
1914 enum isl_dim_type type);
1915 void isl_term_get_num(__isl_keep isl_term *term,
1917 void isl_term_get_den(__isl_keep isl_term *term,
1919 int isl_term_get_exp(__isl_keep isl_term *term,
1920 enum isl_dim_type type, unsigned pos);
1921 __isl_give isl_div *isl_term_get_div(
1922 __isl_keep isl_term *term, unsigned pos);
1923 void isl_term_free(__isl_take isl_term *term);
1925 Each term is a product of parameters, set variables and
1926 integer divisions. The function C<isl_term_get_exp>
1927 returns the exponent of a given dimensions in the given term.
1928 The C<isl_int>s in the arguments of C<isl_term_get_num>
1929 and C<isl_term_get_den> need to have been initialized
1930 using C<isl_int_init> before calling these functions.
1932 =head3 Properties of (Piecewise) Quasipolynomials
1934 To check whether a quasipolynomial is actually a constant,
1935 use the following function.
1937 int isl_qpolynomial_is_cst(__isl_keep isl_qpolynomial *qp,
1938 isl_int *n, isl_int *d);
1940 If C<qp> is a constant and if C<n> and C<d> are not C<NULL>
1941 then the numerator and denominator of the constant
1942 are returned in C<*n> and C<*d>, respectively.
1944 =head3 Operations on (Piecewise) Quasipolynomials
1946 __isl_give isl_qpolynomial *isl_qpolynomial_neg(
1947 __isl_take isl_qpolynomial *qp);
1948 __isl_give isl_qpolynomial *isl_qpolynomial_add(
1949 __isl_take isl_qpolynomial *qp1,
1950 __isl_take isl_qpolynomial *qp2);
1951 __isl_give isl_qpolynomial *isl_qpolynomial_sub(
1952 __isl_take isl_qpolynomial *qp1,
1953 __isl_take isl_qpolynomial *qp2);
1954 __isl_give isl_qpolynomial *isl_qpolynomial_mul(
1955 __isl_take isl_qpolynomial *qp1,
1956 __isl_take isl_qpolynomial *qp2);
1958 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_add(
1959 __isl_take isl_pw_qpolynomial *pwqp1,
1960 __isl_take isl_pw_qpolynomial *pwqp2);
1961 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_sub(
1962 __isl_take isl_pw_qpolynomial *pwqp1,
1963 __isl_take isl_pw_qpolynomial *pwqp2);
1964 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_add_disjoint(
1965 __isl_take isl_pw_qpolynomial *pwqp1,
1966 __isl_take isl_pw_qpolynomial *pwqp2);
1967 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_neg(
1968 __isl_take isl_pw_qpolynomial *pwqp);
1969 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_mul(
1970 __isl_take isl_pw_qpolynomial *pwqp1,
1971 __isl_take isl_pw_qpolynomial *pwqp2);
1973 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_add(
1974 __isl_take isl_union_pw_qpolynomial *upwqp1,
1975 __isl_take isl_union_pw_qpolynomial *upwqp2);
1976 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_sub(
1977 __isl_take isl_union_pw_qpolynomial *upwqp1,
1978 __isl_take isl_union_pw_qpolynomial *upwqp2);
1979 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_mul(
1980 __isl_take isl_union_pw_qpolynomial *upwqp1,
1981 __isl_take isl_union_pw_qpolynomial *upwqp2);
1983 __isl_give isl_qpolynomial *isl_pw_qpolynomial_eval(
1984 __isl_take isl_pw_qpolynomial *pwqp,
1985 __isl_take isl_point *pnt);
1987 __isl_give isl_qpolynomial *isl_union_pw_qpolynomial_eval(
1988 __isl_take isl_union_pw_qpolynomial *upwqp,
1989 __isl_take isl_point *pnt);
1991 __isl_give isl_set *isl_pw_qpolynomial_domain(
1992 __isl_take isl_pw_qpolynomial *pwqp);
1993 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_intersect_domain(
1994 __isl_take isl_pw_qpolynomial *pwpq,
1995 __isl_take isl_set *set);
1997 __isl_give isl_union_set *isl_union_pw_qpolynomial_domain(
1998 __isl_take isl_union_pw_qpolynomial *upwqp);
1999 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_intersect_domain(
2000 __isl_take isl_union_pw_qpolynomial *upwpq,
2001 __isl_take isl_union_set *uset);
2003 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_coalesce(
2004 __isl_take isl_union_pw_qpolynomial *upwqp);
2006 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_gist(
2007 __isl_take isl_pw_qpolynomial *pwqp,
2008 __isl_take isl_set *context);
2010 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_gist(
2011 __isl_take isl_union_pw_qpolynomial *upwqp,
2012 __isl_take isl_union_set *context);
2014 The gist operation applies the gist operation to each of
2015 the cells in the domain of the input piecewise quasipolynomial.
2016 In future, the operation will also exploit the context
2017 to simplify the quasipolynomials associated to each cell.
2019 =head2 Bounds on Piecewise Quasipolynomials and Piecewise Quasipolynomial Reductions
2021 A piecewise quasipolynomial reduction is a piecewise
2022 reduction (or fold) of quasipolynomials.
2023 In particular, the reduction can be maximum or a minimum.
2024 The objects are mainly used to represent the result of
2025 an upper or lower bound on a quasipolynomial over its domain,
2026 i.e., as the result of the following function.
2028 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_bound(
2029 __isl_take isl_pw_qpolynomial *pwqp,
2030 enum isl_fold type, int *tight);
2032 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_bound(
2033 __isl_take isl_union_pw_qpolynomial *upwqp,
2034 enum isl_fold type, int *tight);
2036 The C<type> argument may be either C<isl_fold_min> or C<isl_fold_max>.
2037 If C<tight> is not C<NULL>, then C<*tight> is set to C<1>
2038 is the returned bound is known be tight, i.e., for each value
2039 of the parameters there is at least
2040 one element in the domain that reaches the bound.
2041 If the domain of C<pwqp> is not wrapping, then the bound is computed
2042 over all elements in that domain and the result has a purely parametric
2043 domain. If the domain of C<pwqp> is wrapping, then the bound is
2044 computed over the range of the wrapped relation. The domain of the
2045 wrapped relation becomes the domain of the result.
2047 A (piecewise) quasipolynomial reduction can be copied or freed using the
2048 following functions.
2050 __isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_copy(
2051 __isl_keep isl_qpolynomial_fold *fold);
2052 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_copy(
2053 __isl_keep isl_pw_qpolynomial_fold *pwf);
2054 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_copy(
2055 __isl_keep isl_union_pw_qpolynomial_fold *upwf);
2056 void isl_qpolynomial_fold_free(
2057 __isl_take isl_qpolynomial_fold *fold);
2058 void isl_pw_qpolynomial_fold_free(
2059 __isl_take isl_pw_qpolynomial_fold *pwf);
2060 void isl_union_pw_qpolynomial_fold_free(
2061 __isl_take isl_union_pw_qpolynomial_fold *upwf);
2063 =head3 Printing Piecewise Quasipolynomial Reductions
2065 Piecewise quasipolynomial reductions can be printed
2066 using the following function.
2068 __isl_give isl_printer *isl_printer_print_pw_qpolynomial_fold(
2069 __isl_take isl_printer *p,
2070 __isl_keep isl_pw_qpolynomial_fold *pwf);
2071 __isl_give isl_printer *isl_printer_print_union_pw_qpolynomial_fold(
2072 __isl_take isl_printer *p,
2073 __isl_keep isl_union_pw_qpolynomial_fold *upwf);
2075 For C<isl_printer_print_pw_qpolynomial_fold>,
2076 output format of the printer
2077 needs to be set to either C<ISL_FORMAT_ISL> or C<ISL_FORMAT_C>.
2078 For C<isl_printer_print_union_pw_qpolynomial_fold>,
2079 output format of the printer
2080 needs to be set to either C<ISL_FORMAT_ISL>.
2082 =head3 Inspecting (Piecewise) Quasipolynomial Reductions
2084 To iterate over all piecewise quasipolynomial reductions in a union
2085 piecewise quasipolynomial reduction, use the following function
2087 int isl_union_pw_qpolynomial_fold_foreach_pw_qpolynomial_fold(
2088 __isl_keep isl_union_pw_qpolynomial_fold *upwf,
2089 int (*fn)(__isl_take isl_pw_qpolynomial_fold *pwf,
2090 void *user), void *user);
2092 To iterate over the cells in a piecewise quasipolynomial reduction,
2093 use either of the following two functions
2095 int isl_pw_qpolynomial_fold_foreach_piece(
2096 __isl_keep isl_pw_qpolynomial_fold *pwf,
2097 int (*fn)(__isl_take isl_set *set,
2098 __isl_take isl_qpolynomial_fold *fold,
2099 void *user), void *user);
2100 int isl_pw_qpolynomial_fold_foreach_lifted_piece(
2101 __isl_keep isl_pw_qpolynomial_fold *pwf,
2102 int (*fn)(__isl_take isl_set *set,
2103 __isl_take isl_qpolynomial_fold *fold,
2104 void *user), void *user);
2106 See L<Inspecting (Piecewise) Quasipolynomials> for an explanation
2107 of the difference between these two functions.
2109 To iterate over all quasipolynomials in a reduction, use
2111 int isl_qpolynomial_fold_foreach_qpolynomial(
2112 __isl_keep isl_qpolynomial_fold *fold,
2113 int (*fn)(__isl_take isl_qpolynomial *qp,
2114 void *user), void *user);
2116 =head3 Operations on Piecewise Quasipolynomial Reductions
2118 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_fold(
2119 __isl_take isl_pw_qpolynomial_fold *pwf1,
2120 __isl_take isl_pw_qpolynomial_fold *pwf2);
2122 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_fold(
2123 __isl_take isl_union_pw_qpolynomial_fold *upwf1,
2124 __isl_take isl_union_pw_qpolynomial_fold *upwf2);
2126 __isl_give isl_qpolynomial *isl_pw_qpolynomial_fold_eval(
2127 __isl_take isl_pw_qpolynomial_fold *pwf,
2128 __isl_take isl_point *pnt);
2130 __isl_give isl_qpolynomial *isl_union_pw_qpolynomial_fold_eval(
2131 __isl_take isl_union_pw_qpolynomial_fold *upwf,
2132 __isl_take isl_point *pnt);
2134 __isl_give isl_union_set *isl_union_pw_qpolynomial_fold_domain(
2135 __isl_take isl_union_pw_qpolynomial_fold *upwf);
2136 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_intersect_domain(
2137 __isl_take isl_union_pw_qpolynomial_fold *upwf,
2138 __isl_take isl_union_set *uset);
2140 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_coalesce(
2141 __isl_take isl_pw_qpolynomial_fold *pwf);
2143 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_coalesce(
2144 __isl_take isl_union_pw_qpolynomial_fold *upwf);
2146 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_gist(
2147 __isl_take isl_pw_qpolynomial_fold *pwf,
2148 __isl_take isl_set *context);
2150 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_gist(
2151 __isl_take isl_union_pw_qpolynomial_fold *upwf,
2152 __isl_take isl_union_set *context);
2154 The gist operation applies the gist operation to each of
2155 the cells in the domain of the input piecewise quasipolynomial reduction.
2156 In future, the operation will also exploit the context
2157 to simplify the quasipolynomial reductions associated to each cell.
2159 __isl_give isl_pw_qpolynomial_fold *
2160 isl_map_apply_pw_qpolynomial_fold(
2161 __isl_take isl_map *map,
2162 __isl_take isl_pw_qpolynomial_fold *pwf,
2164 __isl_give isl_union_pw_qpolynomial_fold *
2165 isl_union_map_apply_union_pw_qpolynomial_fold(
2166 __isl_take isl_union_map *umap,
2167 __isl_take isl_union_pw_qpolynomial_fold *upwf,
2171 compose the given map with the given piecewise quasipolynomial reduction.
2172 That is, compute a bound (of the same type as C<pwf> or C<upwf> itself)
2173 over all elements in the intersection of the range of the map
2174 and the domain of the piecewise quasipolynomial reduction
2175 as a function of an element in the domain of the map.
2177 =head2 Dependence Analysis
2179 C<isl> contains specialized functionality for performing
2180 array dataflow analysis. That is, given a I<sink> access relation
2181 and a collection of possible I<source> access relations,
2182 C<isl> can compute relations that describe
2183 for each iteration of the sink access, which iteration
2184 of which of the source access relations was the last
2185 to access the same data element before the given iteration
2187 To compute standard flow dependences, the sink should be
2188 a read, while the sources should be writes.
2189 If any of the source accesses are marked as being I<may>
2190 accesses, then there will be a dependence to the last
2191 I<must> access B<and> to any I<may> access that follows
2192 this last I<must> access.
2193 In particular, if I<all> sources are I<may> accesses,
2194 then memory based dependence analysis is performed.
2195 If, on the other hand, all sources are I<must> accesses,
2196 then value based dependence analysis is performed.
2198 #include <isl_flow.h>
2200 typedef int (*isl_access_level_before)(void *first, void *second);
2202 __isl_give isl_access_info *isl_access_info_alloc(
2203 __isl_take isl_map *sink,
2204 void *sink_user, isl_access_level_before fn,
2206 __isl_give isl_access_info *isl_access_info_add_source(
2207 __isl_take isl_access_info *acc,
2208 __isl_take isl_map *source, int must,
2210 void isl_access_info_free(__isl_take isl_access_info *acc);
2212 __isl_give isl_flow *isl_access_info_compute_flow(
2213 __isl_take isl_access_info *acc);
2215 int isl_flow_foreach(__isl_keep isl_flow *deps,
2216 int (*fn)(__isl_take isl_map *dep, int must,
2217 void *dep_user, void *user),
2219 __isl_give isl_set *isl_flow_get_no_source(
2220 __isl_keep isl_flow *deps, int must);
2221 void isl_flow_free(__isl_take isl_flow *deps);
2223 The function C<isl_access_info_compute_flow> performs the actual
2224 dependence analysis. The other functions are used to construct
2225 the input for this function or to read off the output.
2227 The input is collected in an C<isl_access_info>, which can
2228 be created through a call to C<isl_access_info_alloc>.
2229 The arguments to this functions are the sink access relation
2230 C<sink>, a token C<sink_user> used to identify the sink
2231 access to the user, a callback function for specifying the
2232 relative order of source and sink accesses, and the number
2233 of source access relations that will be added.
2234 The callback function has type C<int (*)(void *first, void *second)>.
2235 The function is called with two user supplied tokens identifying
2236 either a source or the sink and it should return the shared nesting
2237 level and the relative order of the two accesses.
2238 In particular, let I<n> be the number of loops shared by
2239 the two accesses. If C<first> precedes C<second> textually,
2240 then the function should return I<2 * n + 1>; otherwise,
2241 it should return I<2 * n>.
2242 The sources can be added to the C<isl_access_info> by performing
2243 (at most) C<max_source> calls to C<isl_access_info_add_source>.
2244 C<must> indicates whether the source is a I<must> access
2245 or a I<may> access. Note that a multi-valued access relation
2246 should only be marked I<must> if every iteration in the domain
2247 of the relation accesses I<all> elements in its image.
2248 The C<source_user> token is again used to identify
2249 the source access. The range of the source access relation
2250 C<source> should have the same dimension as the range
2251 of the sink access relation.
2252 The C<isl_access_info_free> function should usually not be
2253 called explicitly, because it is called implicitly by
2254 C<isl_access_info_compute_flow>.
2256 The result of the dependence analysis is collected in an
2257 C<isl_flow>. There may be elements in the domain of
2258 the sink access for which no preceding source access could be
2259 found or for which all preceding sources are I<may> accesses.
2260 The sets of these elements can be obtained through
2261 calls to C<isl_flow_get_no_source>, the first with C<must> set
2262 and the second with C<must> unset.
2263 In the case of standard flow dependence analysis,
2264 with the sink a read and the sources I<must> writes,
2265 the first set corresponds to the reads from uninitialized
2266 array elements and the second set is empty.
2267 The actual flow dependences can be extracted using
2268 C<isl_flow_foreach>. This function will call the user-specified
2269 callback function C<fn> for each B<non-empty> dependence between
2270 a source and the sink. The callback function is called
2271 with four arguments, the actual flow dependence relation
2272 mapping source iterations to sink iterations, a boolean that
2273 indicates whether it is a I<must> or I<may> dependence, a token
2274 identifying the source and an additional C<void *> with value
2275 equal to the third argument of the C<isl_flow_foreach> call.
2276 A dependence is marked I<must> if it originates from a I<must>
2277 source and if it is not followed by any I<may> sources.
2279 After finishing with an C<isl_flow>, the user should call
2280 C<isl_flow_free> to free all associated memory.
2282 A higher-level interface to dependence analysis is provided
2283 by the following function.
2285 #include <isl_flow.h>
2287 int isl_union_map_compute_flow(__isl_take isl_union_map *sink,
2288 __isl_take isl_union_map *must_source,
2289 __isl_take isl_union_map *may_source,
2290 __isl_take isl_union_map *schedule,
2291 __isl_give isl_union_map **must_dep,
2292 __isl_give isl_union_map **may_dep,
2293 __isl_give isl_union_set **must_no_source,
2294 __isl_give isl_union_set **may_no_source);
2296 The arrays are identified by the tuple names of the ranges
2297 of the accesses. The iteration domains by the tuple names
2298 of the domains of the accesses and of the schedule.
2299 The relative order of the iteration domains is given by the
2300 schedule. Any of C<must_dep>, C<may_dep>, C<must_no_source>
2301 or C<may_no_source> may be C<NULL>, but a C<NULL> value for
2302 any of the other arguments is treated as an error.
2304 =head2 Parametric Vertex Enumeration
2306 The parametric vertex enumeration described in this section
2307 is mainly intended to be used internally and by the C<barvinok>
2310 #include <isl_vertices.h>
2311 __isl_give isl_vertices *isl_basic_set_compute_vertices(
2312 __isl_keep isl_basic_set *bset);
2314 The function C<isl_basic_set_compute_vertices> performs the
2315 actual computation of the parametric vertices and the chamber
2316 decomposition and store the result in an C<isl_vertices> object.
2317 This information can be queried by either iterating over all
2318 the vertices or iterating over all the chambers or cells
2319 and then iterating over all vertices that are active on the chamber.
2321 int isl_vertices_foreach_vertex(
2322 __isl_keep isl_vertices *vertices,
2323 int (*fn)(__isl_take isl_vertex *vertex, void *user),
2326 int isl_vertices_foreach_cell(
2327 __isl_keep isl_vertices *vertices,
2328 int (*fn)(__isl_take isl_cell *cell, void *user),
2330 int isl_cell_foreach_vertex(__isl_keep isl_cell *cell,
2331 int (*fn)(__isl_take isl_vertex *vertex, void *user),
2334 Other operations that can be performed on an C<isl_vertices> object are
2337 isl_ctx *isl_vertices_get_ctx(
2338 __isl_keep isl_vertices *vertices);
2339 int isl_vertices_get_n_vertices(
2340 __isl_keep isl_vertices *vertices);
2341 void isl_vertices_free(__isl_take isl_vertices *vertices);
2343 Vertices can be inspected and destroyed using the following functions.
2345 isl_ctx *isl_vertex_get_ctx(__isl_keep isl_vertex *vertex);
2346 int isl_vertex_get_id(__isl_keep isl_vertex *vertex);
2347 __isl_give isl_basic_set *isl_vertex_get_domain(
2348 __isl_keep isl_vertex *vertex);
2349 __isl_give isl_basic_set *isl_vertex_get_expr(
2350 __isl_keep isl_vertex *vertex);
2351 void isl_vertex_free(__isl_take isl_vertex *vertex);
2353 C<isl_vertex_get_expr> returns a singleton parametric set describing
2354 the vertex, while C<isl_vertex_get_domain> returns the activity domain
2356 Note that C<isl_vertex_get_domain> and C<isl_vertex_get_expr> return
2357 B<rational> basic sets, so they should mainly be used for inspection
2358 and should not be mixed with integer sets.
2360 Chambers can be inspected and destroyed using the following functions.
2362 isl_ctx *isl_cell_get_ctx(__isl_keep isl_cell *cell);
2363 __isl_give isl_basic_set *isl_cell_get_domain(
2364 __isl_keep isl_cell *cell);
2365 void isl_cell_free(__isl_take isl_cell *cell);
2369 Although C<isl> is mainly meant to be used as a library,
2370 it also contains some basic applications that use some
2371 of the functionality of C<isl>.
2372 The input may be specified in either the L<isl format>
2373 or the L<PolyLib format>.
2375 =head2 C<isl_polyhedron_sample>
2377 C<isl_polyhedron_sample> takes a polyhedron as input and prints
2378 an integer element of the polyhedron, if there is any.
2379 The first column in the output is the denominator and is always
2380 equal to 1. If the polyhedron contains no integer points,
2381 then a vector of length zero is printed.
2385 C<isl_pip> takes the same input as the C<example> program
2386 from the C<piplib> distribution, i.e., a set of constraints
2387 on the parameters, a line containing only -1 and finally a set
2388 of constraints on a parametric polyhedron.
2389 The coefficients of the parameters appear in the last columns
2390 (but before the final constant column).
2391 The output is the lexicographic minimum of the parametric polyhedron.
2392 As C<isl> currently does not have its own output format, the output
2393 is just a dump of the internal state.
2395 =head2 C<isl_polyhedron_minimize>
2397 C<isl_polyhedron_minimize> computes the minimum of some linear
2398 or affine objective function over the integer points in a polyhedron.
2399 If an affine objective function
2400 is given, then the constant should appear in the last column.
2402 =head2 C<isl_polytope_scan>
2404 Given a polytope, C<isl_polytope_scan> prints
2405 all integer points in the polytope.
2407 =head1 C<isl-polylib>
2409 The C<isl-polylib> library provides the following functions for converting
2410 between C<isl> objects and C<PolyLib> objects.
2411 The library is distributed separately for licensing reasons.
2413 #include <isl_set_polylib.h>
2414 __isl_give isl_basic_set *isl_basic_set_new_from_polylib(
2415 Polyhedron *P, __isl_take isl_dim *dim);
2416 Polyhedron *isl_basic_set_to_polylib(
2417 __isl_keep isl_basic_set *bset);
2418 __isl_give isl_set *isl_set_new_from_polylib(Polyhedron *D,
2419 __isl_take isl_dim *dim);
2420 Polyhedron *isl_set_to_polylib(__isl_keep isl_set *set);
2422 #include <isl_map_polylib.h>
2423 __isl_give isl_basic_map *isl_basic_map_new_from_polylib(
2424 Polyhedron *P, __isl_take isl_dim *dim);
2425 __isl_give isl_map *isl_map_new_from_polylib(Polyhedron *D,
2426 __isl_take isl_dim *dim);
2427 Polyhedron *isl_basic_map_to_polylib(
2428 __isl_keep isl_basic_map *bmap);
2429 Polyhedron *isl_map_to_polylib(__isl_keep isl_map *map);