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.
22 The source of C<isl> can be obtained either as a tarball
23 or from the git repository. Both are available from
24 L<http://freshmeat.net/projects/isl/>.
25 The installation process depends on how you obtained
28 =head2 Installation from the git repository
32 =item 1 Clone or update the repository
34 The first time the source is obtained, you need to clone
37 git clone git://repo.or.cz/isl.git
39 To obtain updates, you need to pull in the latest changes
43 =item 2 Get submodule (optional)
45 C<isl> can optionally use the C<piplib> library and provides
46 this library as a submodule. If you want to use it, then
47 after you have cloned C<isl>, you need to grab the submodules
52 To obtain updates, you only need
56 Note that C<isl> currently does not use any C<piplib>
57 functionality by default.
59 =item 3 Generate C<configure>
65 After performing the above steps, continue
66 with the L<Common installation instructions>.
68 =head2 Common installation instructions
74 Building C<isl> requires C<GMP>, including its headers files.
75 Your distribution may not provide these header files by default
76 and you may need to install a package called C<gmp-devel> or something
77 similar. Alternatively, C<GMP> can be built from
78 source, available from L<http://gmplib.org/>.
82 C<isl> uses the standard C<autoconf> C<configure> script.
87 optionally followed by some configure options.
88 A complete list of options can be obtained by running
92 Below we discuss some of the more common options.
94 C<isl> can optionally use C<piplib>, but no
95 C<piplib> functionality is currently used by default.
96 The C<--with-piplib> option can
97 be used to specify which C<piplib>
98 library to use, either an installed version (C<system>),
99 an externally built version (C<build>), a bundled version (C<bundled>)
100 or no version (C<no>). The option C<build> is mostly useful
101 in C<configure> scripts of larger projects that bundle both C<isl>
108 Installation prefix for C<isl>
110 =item C<--with-gmp-prefix>
112 Installation prefix for C<GMP> (architecture-independent files).
114 =item C<--with-gmp-exec-prefix>
116 Installation prefix for C<GMP> (architecture-dependent files).
118 =item C<--with-piplib>
120 Which copy of C<piplib> to use, either C<no> (default), C<system>, C<build>
121 or C<bundled>. Note that C<bundled> only works if you have obtained
122 C<isl> and its submodules from the git repository.
124 =item C<--with-piplib-prefix>
126 Installation prefix for C<system> C<piplib> (architecture-independent files).
128 =item C<--with-piplib-exec-prefix>
130 Installation prefix for C<system> C<piplib> (architecture-dependent files).
132 =item C<--with-piplib-builddir>
134 Location where C<build> C<piplib> was built.
142 =item 4 Install (optional)
150 =head2 Initialization
152 All manipulations of integer sets and relations occur within
153 the context of an C<isl_ctx>.
154 A given C<isl_ctx> can only be used within a single thread.
155 All arguments of a function are required to have been allocated
156 within the same context.
157 There are currently no functions available for moving an object
158 from one C<isl_ctx> to another C<isl_ctx>. This means that
159 there is currently no way of safely moving an object from one
160 thread to another, unless the whole C<isl_ctx> is moved.
162 An C<isl_ctx> can be allocated using C<isl_ctx_alloc> and
163 freed using C<isl_ctx_free>.
164 All objects allocated within an C<isl_ctx> should be freed
165 before the C<isl_ctx> itself is freed.
167 isl_ctx *isl_ctx_alloc();
168 void isl_ctx_free(isl_ctx *ctx);
172 All operations on integers, mainly the coefficients
173 of the constraints describing the sets and relations,
174 are performed in exact integer arithmetic using C<GMP>.
175 However, to allow future versions of C<isl> to optionally
176 support fixed integer arithmetic, all calls to C<GMP>
177 are wrapped inside C<isl> specific macros.
178 The basic type is C<isl_int> and the following operations
179 are available on this type.
180 The meanings of these operations are essentially the same
181 as their C<GMP> C<mpz_> counterparts.
182 As always with C<GMP> types, C<isl_int>s need to be
183 initialized with C<isl_int_init> before they can be used
184 and they need to be released with C<isl_int_clear>
189 =item isl_int_init(i)
191 =item isl_int_clear(i)
193 =item isl_int_set(r,i)
195 =item isl_int_set_si(r,i)
197 =item isl_int_abs(r,i)
199 =item isl_int_neg(r,i)
201 =item isl_int_swap(i,j)
203 =item isl_int_swap_or_set(i,j)
205 =item isl_int_add_ui(r,i,j)
207 =item isl_int_sub_ui(r,i,j)
209 =item isl_int_add(r,i,j)
211 =item isl_int_sub(r,i,j)
213 =item isl_int_mul(r,i,j)
215 =item isl_int_mul_ui(r,i,j)
217 =item isl_int_addmul(r,i,j)
219 =item isl_int_submul(r,i,j)
221 =item isl_int_gcd(r,i,j)
223 =item isl_int_lcm(r,i,j)
225 =item isl_int_divexact(r,i,j)
227 =item isl_int_cdiv_q(r,i,j)
229 =item isl_int_fdiv_q(r,i,j)
231 =item isl_int_fdiv_r(r,i,j)
233 =item isl_int_fdiv_q_ui(r,i,j)
235 =item isl_int_read(r,s)
237 =item isl_int_print(out,i,width)
241 =item isl_int_cmp(i,j)
243 =item isl_int_cmp_si(i,si)
245 =item isl_int_eq(i,j)
247 =item isl_int_ne(i,j)
249 =item isl_int_lt(i,j)
251 =item isl_int_le(i,j)
253 =item isl_int_gt(i,j)
255 =item isl_int_ge(i,j)
257 =item isl_int_abs_eq(i,j)
259 =item isl_int_abs_ne(i,j)
261 =item isl_int_abs_lt(i,j)
263 =item isl_int_abs_gt(i,j)
265 =item isl_int_abs_ge(i,j)
267 =item isl_int_is_zero(i)
269 =item isl_int_is_one(i)
271 =item isl_int_is_negone(i)
273 =item isl_int_is_pos(i)
275 =item isl_int_is_neg(i)
277 =item isl_int_is_nonpos(i)
279 =item isl_int_is_nonneg(i)
281 =item isl_int_is_divisible_by(i,j)
285 =head2 Sets and Relations
287 C<isl> uses four types of objects for representing sets and relations,
288 C<isl_basic_set>, C<isl_basic_map>, C<isl_set> and C<isl_map>.
289 C<isl_basic_set> and C<isl_basic_map> represent sets and relations that
290 can be described as a conjunction of affine constraints, while
291 C<isl_set> and C<isl_map> represent unions of
292 C<isl_basic_set>s and C<isl_basic_map>s, respectively.
293 The difference between sets and relations (maps) is that sets have
294 one set of variables, while relations have two sets of variables,
295 input variables and output variables.
297 =head2 Memory Management
299 Since a high-level operation on sets and/or relations usually involves
300 several substeps and since the user is usually not interested in
301 the intermediate results, most functions that return a new object
302 will also release all the objects passed as arguments.
303 If the user still wants to use one or more of these arguments
304 after the function call, she should pass along a copy of the
305 object rather than the object itself.
306 The user is then responsible for make sure that the original
307 object gets used somewhere else or is explicitly freed.
309 The arguments and return values of all documents functions are
310 annotated to make clear which arguments are released and which
311 arguments are preserved. In particular, the following annotations
318 C<__isl_give> means that a new object is returned.
319 The user should make sure that the returned pointer is
320 used exactly once as a value for an C<__isl_take> argument.
321 In between, it can be used as a value for as many
322 C<__isl_keep> arguments as the user likes.
323 There is one exception, and that is the case where the
324 pointer returned is C<NULL>. Is this case, the user
325 is free to use it as an C<__isl_take> argument or not.
329 C<__isl_take> means that the object the argument points to
330 is taken over by the function and may no longer be used
331 by the user as an argument to any other function.
332 The pointer value must be one returned by a function
333 returning an C<__isl_give> pointer.
334 If the user passes in a C<NULL> value, then this will
335 be treated as an error in the sense that the function will
336 not perform its usual operation. However, it will still
337 make sure that all the the other C<__isl_take> arguments
342 C<__isl_keep> means that the function will only use the object
343 temporarily. After the function has finished, the user
344 can still use it as an argument to other functions.
345 A C<NULL> value will be treated in the same way as
346 a C<NULL> value for an C<__isl_take> argument.
350 =head2 Dimension Specifications
352 Whenever a new set or relation is created from scratch,
353 its dimension needs to be specified using an C<isl_dim>.
356 __isl_give isl_dim *isl_dim_alloc(isl_ctx *ctx,
357 unsigned nparam, unsigned n_in, unsigned n_out);
358 __isl_give isl_dim *isl_dim_set_alloc(isl_ctx *ctx,
359 unsigned nparam, unsigned dim);
360 __isl_give isl_dim *isl_dim_copy(__isl_keep isl_dim *dim);
361 void isl_dim_free(__isl_take isl_dim *dim);
362 unsigned isl_dim_size(__isl_keep isl_dim *dim,
363 enum isl_dim_type type);
365 The dimension specification used for creating a set
366 needs to be created using C<isl_dim_set_alloc>, while
367 that for creating a relation
368 needs to be created using C<isl_dim_alloc>.
369 C<isl_dim_size> can be used
370 to find out the number of dimensions of each type in
371 a dimension specification, where type may be
372 C<isl_dim_param>, C<isl_dim_in> (only for relations),
373 C<isl_dim_out> (only for relations), C<isl_dim_set>
374 (only for sets) or C<isl_dim_all>.
376 =head2 Input and Output
378 C<isl> supports its own input/output format, which is similar
379 to the C<Omega> format, but also supports the C<PolyLib> format
384 The C<isl> format is similar to that of C<Omega>, but has a different
385 syntax for describing the parameters and allows for the definition
386 of an existentially quantified variable as the integer division
387 of an affine expression.
388 For example, the set of integers C<i> between C<0> and C<n>
389 such that C<i % 10 <= 6> can be described as
391 [n] -> { [i] : exists (a = [i/10] : 0 <= i and i <= n and
394 A set or relation can have several disjuncts, separated
395 by the keyword C<or>. Each disjunct is either a conjunction
396 of constraints or a projection (C<exists>) of a conjunction
397 of constraints. The constraints are separated by the keyword
400 =head3 C<PolyLib> format
402 If the represented set is a union, then the first line
403 contains a single number representing the number of disjuncts.
404 Otherwise, a line containing the number C<1> is optional.
406 Each disjunct is represented by a matrix of constraints.
407 The first line contains two numbers representing
408 the number of rows and columns,
409 where the number of rows is equal to the number of constraints
410 and the number of columns is equal to two plus the number of variables.
411 The following lines contain the actual rows of the constraint matrix.
412 In each row, the first column indicates whether the constraint
413 is an equality (C<0>) or inequality (C<1>). The final column
414 corresponds to the constant term.
416 If the set is parametric, then the coefficients of the parameters
417 appear in the last columns before the constant column.
418 The coefficients of any existentially quantified variables appear
419 between those of the set variables and those of the parameters.
424 __isl_give isl_basic_set *isl_basic_set_read_from_file(
425 isl_ctx *ctx, FILE *input, int nparam);
426 __isl_give isl_basic_set *isl_basic_set_read_from_str(
427 isl_ctx *ctx, const char *str, int nparam);
428 __isl_give isl_set *isl_set_read_from_file(isl_ctx *ctx,
429 FILE *input, int nparam);
430 __isl_give isl_set *isl_set_read_from_str(isl_ctx *ctx,
431 const char *str, int nparam);
434 __isl_give isl_basic_map *isl_basic_map_read_from_file(
435 isl_ctx *ctx, FILE *input, int nparam);
436 __isl_give isl_basic_map *isl_basic_map_read_from_str(
437 isl_ctx *ctx, const char *str, int nparam);
438 __isl_give isl_map *isl_map_read_from_file(
439 struct isl_ctx *ctx, FILE *input, int nparam);
440 __isl_give isl_map *isl_map_read_from_str(isl_ctx *ctx,
441 const char *str, int nparam);
443 The input format is autodetected and may be either the C<PolyLib> format
444 or the C<isl> format.
445 C<nparam> specifies how many of the final columns in
446 the C<PolyLib> format correspond to parameters.
447 If input is given in the C<isl> format, then the number
448 of parameters needs to be equal to C<nparam>.
449 If C<nparam> is negative, then any number of parameters
450 is accepted in the C<isl> format and zero parameters
451 are assumed in the C<PolyLib> format.
456 void isl_basic_set_print(__isl_keep isl_basic_set *bset,
457 FILE *out, int indent,
458 const char *prefix, const char *suffix,
459 unsigned output_format);
460 void isl_set_print(__isl_keep struct isl_set *set,
461 FILE *out, int indent, unsigned output_format);
464 void isl_basic_map_print(__isl_keep isl_basic_map *bmap,
465 FILE *out, int indent,
466 const char *prefix, const char *suffix,
467 unsigned output_format);
468 void isl_map_print(__isl_keep struct isl_map *map,
469 FILE *out, int indent, unsigned output_format);
471 The C<output_format> may be either C<ISL_FORMAT_ISL>, C<ISL_FORMAT_OMEGA>
472 or C<ISL_FORMAT_POLYLIB>.
473 Each line in the output is indented by C<indent> spaces,
474 prefixed by C<prefix> and suffixed by C<suffix>.
475 In the C<PolyLib> format output,
476 the coefficients of the existentially quantified variables
477 appear between those of the set variables and those
480 =head3 Dumping the internal state
482 For lack of proper output functions, the following functions
483 can be used to dump the internal state of a set or relation.
484 The user should not depend on the output format of these functions.
486 void isl_basic_set_dump(__isl_keep isl_basic_set *bset,
487 FILE *out, int indent);
488 void isl_basic_map_dump(__isl_keep isl_basic_map *bmap,
489 FILE *out, int indent);
490 void isl_set_dump(__isl_keep isl_set *set,
491 FILE *out, int indent);
492 void isl_map_dump(__isl_keep isl_map *map,
493 FILE *out, int indent);
495 =head2 Creating New Sets and Relations
497 C<isl> has functions for creating some standard sets and relations.
501 =item * Empty sets and relations
503 __isl_give isl_basic_set *isl_basic_set_empty(
504 __isl_take isl_dim *dim);
505 __isl_give isl_basic_map *isl_basic_map_empty(
506 __isl_take isl_dim *dim);
507 __isl_give isl_set *isl_set_empty(
508 __isl_take isl_dim *dim);
509 __isl_give isl_map *isl_map_empty(
510 __isl_take isl_dim *dim);
512 =item * Universe sets and relations
514 __isl_give isl_basic_set *isl_basic_set_universe(
515 __isl_take isl_dim *dim);
516 __isl_give isl_basic_map *isl_basic_map_universe(
517 __isl_take isl_dim *dim);
518 __isl_give isl_set *isl_set_universe(
519 __isl_take isl_dim *dim);
520 __isl_give isl_map *isl_map_universe(
521 __isl_take isl_dim *dim);
523 =item * Identity relations
525 __isl_give isl_basic_map *isl_basic_map_identity(
526 __isl_take isl_dim *set_dim);
527 __isl_give isl_map *isl_map_identity(
528 __isl_take isl_dim *set_dim);
530 These functions take a dimension specification for a B<set>
531 and return an identity relation between two such sets.
533 =item * Lexicographic order
535 __isl_give isl_map *isl_map_lex_lt(
536 __isl_take isl_dim *set_dim);
537 __isl_give isl_map *isl_map_lex_le(
538 __isl_take isl_dim *set_dim);
539 __isl_give isl_map *isl_map_lex_gt(
540 __isl_take isl_dim *set_dim);
541 __isl_give isl_map *isl_map_lex_ge(
542 __isl_take isl_dim *set_dim);
544 These functions take a dimension specification for a B<set>
545 and return relations that express that the elements in the domain
546 are lexicographically less
547 (C<isl_map_lex_lt>), less or equal (C<isl_map_lex_le>),
548 greater (C<isl_map_lex_gt>) or greater or equal (C<isl_map_lex_ge>)
549 than the elements in the range.
553 A basic set or relation can be converted to a set or relation
554 using the following functions.
556 __isl_give isl_set *isl_set_from_basic_set(
557 __isl_take isl_basic_set *bset);
558 __isl_give isl_map *isl_map_from_basic_map(
559 __isl_take isl_basic_map *bmap);
561 Sets and relations can be copied and freed again using the following
564 __isl_give isl_basic_set *isl_basic_set_copy(
565 __isl_keep isl_basic_set *bset);
566 __isl_give isl_set *isl_set_copy(__isl_keep isl_set *set);
567 __isl_give isl_basic_map *isl_basic_map_copy(
568 __isl_keep isl_basic_map *bmap);
569 __isl_give isl_map *isl_map_copy(__isl_keep isl_map *map);
570 void isl_basic_set_free(__isl_take isl_basic_set *bset);
571 void isl_set_free(__isl_take isl_set *set);
572 void isl_basic_map_free(__isl_take isl_basic_map *bmap);
573 void isl_map_free(__isl_take isl_map *map);
575 Other sets and relations can be constructed by starting
576 from a universe set or relation, adding equality and/or
577 inequality constraints and then projecting out the
578 existentially quantified variables, if any.
579 Constraints can be constructed, manipulated and
580 added to basic sets and relations using the following functions.
582 #include <isl_constraint.h>
583 __isl_give isl_constraint *isl_equality_alloc(
584 __isl_take isl_dim *dim);
585 __isl_give isl_constraint *isl_inequality_alloc(
586 __isl_take isl_dim *dim);
587 void isl_constraint_set_constant(
588 __isl_keep isl_constraint *constraint, isl_int v);
589 void isl_constraint_set_coefficient(
590 __isl_keep isl_constraint *constraint,
591 enum isl_dim_type type, int pos, isl_int v);
592 __isl_give isl_basic_map *isl_basic_map_add_constraint(
593 __isl_take isl_basic_map *bmap,
594 __isl_take isl_constraint *constraint);
595 __isl_give isl_basic_set *isl_basic_set_add_constraint(
596 __isl_take isl_basic_set *bset,
597 __isl_take isl_constraint *constraint);
599 For example, to create a set containing the even integers
600 between 10 and 42, you would use the following code.
604 struct isl_constraint *c;
605 struct isl_basic_set *bset;
608 dim = isl_dim_set_alloc(ctx, 0, 2);
609 bset = isl_basic_set_universe(isl_dim_copy(dim));
611 c = isl_equality_alloc(isl_dim_copy(dim));
612 isl_int_set_si(v, -1);
613 isl_constraint_set_coefficient(c, isl_dim_set, 0, v);
614 isl_int_set_si(v, 2);
615 isl_constraint_set_coefficient(c, isl_dim_set, 1, v);
616 bset = isl_basic_set_add_constraint(bset, c);
618 c = isl_inequality_alloc(isl_dim_copy(dim));
619 isl_int_set_si(v, -10);
620 isl_constraint_set_constant(c, v);
621 isl_int_set_si(v, 1);
622 isl_constraint_set_coefficient(c, isl_dim_set, 0, v);
623 bset = isl_basic_set_add_constraint(bset, c);
625 c = isl_inequality_alloc(dim);
626 isl_int_set_si(v, 42);
627 isl_constraint_set_constant(c, v);
628 isl_int_set_si(v, -1);
629 isl_constraint_set_coefficient(c, isl_dim_set, 0, v);
630 bset = isl_basic_set_add_constraint(bset, c);
632 bset = isl_basic_set_project_out(bset, isl_dim_set, 1, 1);
638 struct isl_basic_set *bset;
639 bset = isl_basic_set_read_from_str(ctx,
640 "{[i] : exists (a : i = 2a and i >= 10 and i <= 42)}", -1);
644 =head3 Unary Properties
650 The following functions test whether the given set or relation
651 contains any integer points. The ``fast'' variants do not perform
652 any computations, but simply check if the given set or relation
653 is already known to be empty.
655 int isl_basic_set_fast_is_empty(__isl_keep isl_basic_set *bset);
656 int isl_basic_set_is_empty(__isl_keep isl_basic_set *bset);
657 int isl_set_is_empty(__isl_keep isl_set *set);
658 int isl_basic_map_fast_is_empty(__isl_keep isl_basic_map *bmap);
659 int isl_basic_map_is_empty(__isl_keep isl_basic_map *bmap);
660 int isl_map_fast_is_empty(__isl_keep isl_map *map);
661 int isl_map_is_empty(__isl_keep isl_map *map);
665 int isl_basic_set_is_universe(__isl_keep isl_basic_set *bset);
666 int isl_basic_map_is_universe(__isl_keep isl_basic_map *bmap);
670 =head3 Binary Properties
676 int isl_set_fast_is_equal(__isl_keep isl_set *set1,
677 __isl_keep isl_set *set2);
678 int isl_set_is_equal(__isl_keep isl_set *set1,
679 __isl_keep isl_set *set2);
680 int isl_map_is_equal(__isl_keep isl_map *map1,
681 __isl_keep isl_map *map2);
682 int isl_map_fast_is_equal(__isl_keep isl_map *map1,
683 __isl_keep isl_map *map2);
684 int isl_basic_map_is_equal(
685 __isl_keep isl_basic_map *bmap1,
686 __isl_keep isl_basic_map *bmap2);
690 int isl_set_fast_is_disjoint(__isl_keep isl_set *set1,
691 __isl_keep isl_set *set2);
695 int isl_set_is_subset(__isl_keep isl_set *set1,
696 __isl_keep isl_set *set2);
697 int isl_set_is_strict_subset(
698 __isl_keep isl_set *set1,
699 __isl_keep isl_set *set2);
700 int isl_basic_map_is_subset(
701 __isl_keep isl_basic_map *bmap1,
702 __isl_keep isl_basic_map *bmap2);
703 int isl_basic_map_is_strict_subset(
704 __isl_keep isl_basic_map *bmap1,
705 __isl_keep isl_basic_map *bmap2);
706 int isl_map_is_subset(
707 __isl_keep isl_map *map1,
708 __isl_keep isl_map *map2);
709 int isl_map_is_strict_subset(
710 __isl_keep isl_map *map1,
711 __isl_keep isl_map *map2);
715 =head2 Unary Operations
721 __isl_give isl_basic_set *isl_basic_set_project_out(
722 __isl_take isl_basic_set *bset,
723 enum isl_dim_type type, unsigned first, unsigned n);
724 __isl_give isl_basic_map *isl_basic_map_project_out(
725 __isl_take isl_basic_map *bmap,
726 enum isl_dim_type type, unsigned first, unsigned n);
727 __isl_give isl_set *isl_set_project_out(__isl_take isl_set *set,
728 enum isl_dim_type type, unsigned first, unsigned n);
729 __isl_give isl_map *isl_map_project_out(__isl_take isl_map *map,
730 enum isl_dim_type type, unsigned first, unsigned n);
731 __isl_give isl_basic_set *isl_basic_map_domain(
732 __isl_take isl_basic_map *bmap);
733 __isl_give isl_basic_set *isl_basic_map_range(
734 __isl_take isl_basic_map *bmap);
735 __isl_give isl_set *isl_map_domain(
736 __isl_take isl_map *bmap);
737 __isl_give isl_set *isl_map_range(
738 __isl_take isl_map *map);
742 Simplify the representation of a set or relation by trying
743 to combine pairs of basic sets or relations into a single
744 basic set or relation.
746 __isl_give isl_set *isl_set_coalesce(__isl_take isl_set *set);
747 __isl_give isl_map *isl_map_coalesce(__isl_take isl_map *map);
751 __isl_give isl_basic_set *isl_set_convex_hull(
752 __isl_take isl_set *set);
753 __isl_give isl_basic_map *isl_map_convex_hull(
754 __isl_take isl_map *map);
756 If the input set or relation has any existentially quantified
757 variables, then the result of these operations is currently undefined.
761 __isl_give isl_basic_set *isl_basic_set_affine_hull(
762 __isl_take isl_basic_set *bset);
763 __isl_give isl_basic_set *isl_set_affine_hull(
764 __isl_take isl_set *set);
765 __isl_give isl_basic_map *isl_basic_map_affine_hull(
766 __isl_take isl_basic_map *bmap);
767 __isl_give isl_basic_map *isl_map_affine_hull(
768 __isl_take isl_map *map);
772 __isl_give isl_map *isl_map_power(__isl_take isl_map *map,
773 unsigned param, int *exact);
775 Compute a parametric representation for all positive powers I<k> of C<map>.
776 The power I<k> is equated to the parameter at position C<param>.
777 The result may be an overapproximation. If the result is exact,
778 then C<*exact> is set to C<1>.
779 The current implementation only produces exact results for particular
780 cases of piecewise translations (i.e., piecewise uniform dependences).
782 =item * Transitive closure
784 __isl_give isl_map *isl_map_transitive_closure(
785 __isl_take isl_map *map, int *exact);
787 Compute the transitive closure of C<map>.
788 The result may be an overapproximation. If the result is exact,
789 then C<*exact> is set to C<1>.
790 The current implementation only produces exact results for particular
791 cases of piecewise translations (i.e., piecewise uniform dependences).
795 =head2 Binary Operations
797 The two arguments of a binary operation not only need to live
798 in the same C<isl_ctx>, they currently also need to have
799 the same (number of) parameters.
801 =head3 Basic Operations
807 __isl_give isl_basic_set *isl_basic_set_intersect(
808 __isl_take isl_basic_set *bset1,
809 __isl_take isl_basic_set *bset2);
810 __isl_give isl_set *isl_set_intersect(
811 __isl_take isl_set *set1,
812 __isl_take isl_set *set2);
813 __isl_give isl_basic_map *isl_basic_map_intersect_domain(
814 __isl_take isl_basic_map *bmap,
815 __isl_take isl_basic_set *bset);
816 __isl_give isl_basic_map *isl_basic_map_intersect_range(
817 __isl_take isl_basic_map *bmap,
818 __isl_take isl_basic_set *bset);
819 __isl_give isl_basic_map *isl_basic_map_intersect(
820 __isl_take isl_basic_map *bmap1,
821 __isl_take isl_basic_map *bmap2);
822 __isl_give isl_map *isl_map_intersect_domain(
823 __isl_take isl_map *map,
824 __isl_take isl_set *set);
825 __isl_give isl_map *isl_map_intersect_range(
826 __isl_take isl_map *map,
827 __isl_take isl_set *set);
828 __isl_give isl_map *isl_map_intersect(
829 __isl_take isl_map *map1,
830 __isl_take isl_map *map2);
834 __isl_give isl_set *isl_basic_set_union(
835 __isl_take isl_basic_set *bset1,
836 __isl_take isl_basic_set *bset2);
837 __isl_give isl_map *isl_basic_map_union(
838 __isl_take isl_basic_map *bmap1,
839 __isl_take isl_basic_map *bmap2);
840 __isl_give isl_set *isl_set_union(
841 __isl_take isl_set *set1,
842 __isl_take isl_set *set2);
843 __isl_give isl_map *isl_map_union(
844 __isl_take isl_map *map1,
845 __isl_take isl_map *map2);
847 =item * Set difference
849 __isl_give isl_set *isl_set_subtract(
850 __isl_take isl_set *set1,
851 __isl_take isl_set *set2);
852 __isl_give isl_map *isl_map_subtract(
853 __isl_take isl_map *map1,
854 __isl_take isl_map *map2);
858 __isl_give isl_basic_set *isl_basic_set_apply(
859 __isl_take isl_basic_set *bset,
860 __isl_take isl_basic_map *bmap);
861 __isl_give isl_set *isl_set_apply(
862 __isl_take isl_set *set,
863 __isl_take isl_map *map);
864 __isl_give isl_basic_map *isl_basic_map_apply_domain(
865 __isl_take isl_basic_map *bmap1,
866 __isl_take isl_basic_map *bmap2);
867 __isl_give isl_basic_map *isl_basic_map_apply_range(
868 __isl_take isl_basic_map *bmap1,
869 __isl_take isl_basic_map *bmap2);
870 __isl_give isl_map *isl_map_apply_domain(
871 __isl_take isl_map *map1,
872 __isl_take isl_map *map2);
873 __isl_give isl_map *isl_map_apply_range(
874 __isl_take isl_map *map1,
875 __isl_take isl_map *map2);
879 =head3 Lexicographic Optimization
881 Given a (basic) set C<set> (or C<bset>) and a zero-dimensional domain C<dom>,
882 the following functions
883 compute a set that contains the lexicographic minimum or maximum
884 of the elements in C<set> (or C<bset>) for those values of the parameters
886 If C<empty> is not C<NULL>, then C<*empty> is assigned a set
887 that contains the parameter values in C<dom> for which C<set> (or C<bset>)
889 In other words, the union of the parameter values
890 for which the result is non-empty and of C<*empty>
893 __isl_give isl_set *isl_basic_set_partial_lexmin(
894 __isl_take isl_basic_set *bset,
895 __isl_take isl_basic_set *dom,
896 __isl_give isl_set **empty);
897 __isl_give isl_set *isl_basic_set_partial_lexmax(
898 __isl_take isl_basic_set *bset,
899 __isl_take isl_basic_set *dom,
900 __isl_give isl_set **empty);
901 __isl_give isl_set *isl_set_partial_lexmin(
902 __isl_take isl_set *set, __isl_take isl_set *dom,
903 __isl_give isl_set **empty);
904 __isl_give isl_set *isl_set_partial_lexmax(
905 __isl_take isl_set *set, __isl_take isl_set *dom,
906 __isl_give isl_set **empty);
908 Given a (basic) set C<set> (or C<bset>), the following functions simply
909 return a set containing the lexicographic minimum or maximum
910 of the elements in C<set> (or C<bset>).
912 __isl_give isl_set *isl_basic_set_lexmin(
913 __isl_take isl_basic_set *bset);
914 __isl_give isl_set *isl_basic_set_lexmax(
915 __isl_take isl_basic_set *bset);
916 __isl_give isl_set *isl_set_lexmin(
917 __isl_take isl_set *set);
918 __isl_give isl_set *isl_set_lexmax(
919 __isl_take isl_set *set);
921 Given a (basic) relation C<map> (or C<bmap>) and a domain C<dom>,
922 the following functions
923 compute a relation that maps each element of C<dom>
924 to the single lexicographic minimum or maximum
925 of the elements that are associated to that same
926 element in C<map> (or C<bmap>).
927 If C<empty> is not C<NULL>, then C<*empty> is assigned a set
928 that contains the elements in C<dom> that do not map
929 to any elements in C<map> (or C<bmap>).
930 In other words, the union of the domain of the result and of C<*empty>
933 __isl_give isl_map *isl_basic_map_partial_lexmax(
934 __isl_take isl_basic_map *bmap,
935 __isl_take isl_basic_set *dom,
936 __isl_give isl_set **empty);
937 __isl_give isl_map *isl_basic_map_partial_lexmin(
938 __isl_take isl_basic_map *bmap,
939 __isl_take isl_basic_set *dom,
940 __isl_give isl_set **empty);
941 __isl_give isl_map *isl_map_partial_lexmax(
942 __isl_take isl_map *map, __isl_take isl_set *dom,
943 __isl_give isl_set **empty);
944 __isl_give isl_map *isl_map_partial_lexmin(
945 __isl_take isl_map *map, __isl_take isl_set *dom,
946 __isl_give isl_set **empty);
948 Given a (basic) map C<map> (or C<bmap>), the following functions simply
949 return a map mapping each element in the domain of
950 C<map> (or C<bmap>) to the lexicographic minimum or maximum
951 of all elements associated to that element.
953 __isl_give isl_map *isl_basic_map_lexmin(
954 __isl_take isl_basic_map *bmap);
955 __isl_give isl_map *isl_basic_map_lexmax(
956 __isl_take isl_basic_map *bmap);
957 __isl_give isl_map *isl_map_lexmin(
958 __isl_take isl_map *map);
959 __isl_give isl_map *isl_map_lexmax(
960 __isl_take isl_map *map);
962 =head2 Dependence Analysis
964 C<isl> contains specialized functionality for performing
965 array dataflow analysis. That is, given a I<sink> access relation
966 and a collection of possible I<source> access relations,
967 C<isl> can compute relations that describe
968 for each iteration of the sink access, which iteration
969 of which of the source access relations was the last
970 to access the same data element before the given iteration
972 To compute standard flow dependences, the sink should be
973 a read, while the sources should be writes.
975 #include <isl_flow.h>
977 __isl_give isl_access_info *isl_access_info_alloc(
978 __isl_take isl_map *sink,
979 void *sink_user, isl_access_level_before fn,
981 __isl_give isl_access_info *isl_access_info_add_source(
982 __isl_take isl_access_info *acc,
983 __isl_take isl_map *source, void *source_user);
985 __isl_give isl_flow *isl_access_info_compute_flow(
986 __isl_take isl_access_info *acc);
988 int isl_flow_foreach(__isl_keep isl_flow *deps,
989 int (*fn)(__isl_take isl_map *dep, void *dep_user,
992 __isl_give isl_set *isl_flow_get_no_source(
993 __isl_keep isl_flow *deps);
994 void isl_flow_free(__isl_take isl_flow *deps);
996 The function C<isl_access_info_compute_flow> performs the actual
997 dependence analysis. The other functions are used to construct
998 the input for this function or to read off the output.
1000 The input is collected in an C<isl_access_info>, which can
1001 be created through a call to C<isl_access_info_alloc>.
1002 The arguments to this functions are the sink access relation
1003 C<sink>, a token C<sink_user> used to identify the sink
1004 access to the user, a callback function for specifying the
1005 relative order of source and sink accesses, and the number
1006 of source access relations that will be added.
1007 The callback function has type C<int (*)(void *first, void *second)>.
1008 The function is called with two user supplied tokens identifying
1009 either a source or the sink and it should return the shared nesting
1010 level and the relative order of the two accesses.
1011 In particular, let I<n> be the number of loops shared by
1012 the two accesses. If C<first> precedes C<second> textually,
1013 then the function should return I<2 * n + 1>; otherwise,
1014 it should return I<2 * n>.
1015 The sources can be added to the C<isl_access_info> by performing
1016 (at most) C<max_source> calls to C<isl_access_info_add_source>.
1017 The C<source_user> token is again used to identify
1018 the source access. The range of the source access relation
1019 C<source> should have the same dimension as the range
1020 of the sink access relation.
1022 The result of the dependence analysis is collected in an
1023 C<isl_flow>. There may be elements in the domain of
1024 the sink access for which no preceding source access could be
1025 find. The set of these elements can be obtained through
1026 a call to C<isl_flow_get_no_source>.
1027 In the case of standard flow dependence analysis,
1028 this set corresponds to the reads from uninitialized
1030 The actual flow dependences can be extracted using
1031 C<isl_flow_foreach>. This function will call the user-specified
1032 callback function C<fn> for each B<non-empty> dependence between
1033 a source and the sink. The callback function is called
1034 with three arguments, the actual flow dependence relation
1035 mapping source iterations to sink iterations, a token
1036 identifying the source and an additional C<void *> with value
1037 equal to the third argument of the C<isl_flow_foreach> call.
1039 After finishing with an C<isl_flow>, the user should call
1040 C<isl_flow_free> to free all associated memory.
1044 Although C<isl> is mainly meant to be used as a library,
1045 it also contains some basic applications that use some
1046 of the functionality of C<isl>.
1047 The input may specified either in the L<isl format>
1048 or the L<PolyLib format>.
1050 =head2 C<isl_polyhedron_sample>
1052 C<isl_polyhedron_sample> takes a polyhedron as input and prints
1053 an integer element of the polyhedron, if there is any.
1054 The first column in the output is the denominator and is always
1055 equal to 1. If the polyhedron contains no integer points,
1056 then a vector of length zero is printed.
1060 C<isl_pip> takes the same input as the C<example> program
1061 from the C<piplib> distribution, i.e., a set of constraints
1062 on the parameters, a line contains only -1 and finally a set
1063 of constraints on a parametric polyhedron.
1064 The coefficients of the parameters appear in the last columns
1065 (but before the final constant column).
1066 The output is the lexicographic minimum of the parametric polyhedron.
1067 As C<isl> currently does not have its own output format, the output
1068 is just a dump of the internal state.
1070 =head2 C<isl_polyhedron_minimize>
1072 C<isl_polyhedron_minimize> computes the minimum of some linear
1073 or affine objective function over the integer points in a polyhedron.
1074 If an affine objective function
1075 is given, then the constant should appear in the last column.
1077 =head2 C<isl_polytope_scan>
1079 Given a polytope, C<isl_polytope_scan> prints
1080 all integer points in the polytope.
1082 =head1 C<isl-polylib>
1084 The C<isl-polylib> library provides the following functions for converting
1085 between C<isl> objects and C<PolyLib> objects.
1086 The library is distributed separately for licensing reasons.
1088 #include <isl_set_polylib.h>
1089 __isl_give isl_basic_set *isl_basic_set_new_from_polylib(
1090 Polyhedron *P, __isl_take isl_dim *dim);
1091 Polyhedron *isl_basic_set_to_polylib(
1092 __isl_keep isl_basic_set *bset);
1093 __isl_give isl_set *isl_set_new_from_polylib(Polyhedron *D,
1094 __isl_take isl_dim *dim);
1095 Polyhedron *isl_set_to_polylib(__isl_keep isl_set *set);
1097 #include <isl_map_polylib.h>
1098 __isl_give isl_basic_map *isl_basic_map_new_from_polylib(
1099 Polyhedron *P, __isl_take isl_dim *dim);
1100 __isl_give isl_map *isl_map_new_from_polylib(Polyhedron *D,
1101 __isl_take isl_dim *dim);
1102 Polyhedron *isl_basic_map_to_polylib(
1103 __isl_keep isl_basic_map *bmap);
1104 Polyhedron *isl_map_to_polylib(__isl_keep isl_map *map);