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>.
49 =head3 Changes since isl-0.04
53 =item * All header files have been renamed from C<isl_header.h>
58 =head3 Changes since isl-0.05
62 =item * The functions C<isl_printer_print_basic_set> and
63 C<isl_printer_print_basic_map> no longer print a newline.
65 =item * The functions C<isl_flow_get_no_source>
66 and C<isl_union_map_compute_flow> now return
67 the accesses for which no source could be found instead of
68 the iterations where those accesses occur.
70 =item * The functions C<isl_basic_map_identity> and
71 C<isl_map_identity> now take a B<map> space as input. An old call
72 C<isl_map_identity(space)> can be rewritten to
73 C<isl_map_identity(isl_space_map_from_set(space))>.
75 =item * The function C<isl_map_power> no longer takes
76 a parameter position as input. Instead, the exponent
77 is now expressed as the domain of the resulting relation.
81 =head3 Changes since isl-0.06
85 =item * The format of C<isl_printer_print_qpolynomial>'s
86 C<ISL_FORMAT_ISL> output has changed.
87 Use C<ISL_FORMAT_C> to obtain the old output.
89 =item * The C<*_fast_*> functions have been renamed to C<*_plain_*>.
90 Some of the old names have been kept for backward compatibility,
91 but they will be removed in the future.
95 =head3 Changes since isl-0.07
99 =item * The function C<isl_pw_aff_max> has been renamed to
100 C<isl_pw_aff_union_max>.
101 Similarly, the function C<isl_pw_aff_add> has been renamed to
102 C<isl_pw_aff_union_add>.
104 =item * The C<isl_dim> type has been renamed to C<isl_space>
105 along with the associated functions.
106 Some of the old names have been kept for backward compatibility,
107 but they will be removed in the future.
109 =item * Spaces of maps, sets and parameter domains are now
110 treated differently. The distinction between map spaces and set spaces
111 has always been made on a conceptual level, but proper use of such spaces
112 was never checked. Furthermore, up until isl-0.07 there was no way
113 of explicitly creating a parameter space. These can now be created
114 directly using C<isl_space_params_alloc> or from other spaces using
117 =item * The space in which C<isl_aff>, C<isl_pw_aff>, C<isl_qpolynomial>,
118 C<isl_pw_qpolynomial>, C<isl_qpolynomial_fold> and C<isl_pw_qpolynomial_fold>
119 objects live is now a map space
120 instead of a set space. This means, for example, that the dimensions
121 of the domain of an C<isl_aff> are now considered to be of type
122 C<isl_dim_in> instead of C<isl_dim_set>. Extra functions have been
123 added to obtain the domain space. Some of the constructors still
124 take a domain space and have therefore been renamed.
126 =item * The functions C<isl_equality_alloc> and C<isl_inequality_alloc>
127 now take an C<isl_local_space> instead of an C<isl_space>.
128 An C<isl_local_space> can be created from an C<isl_space>
129 using C<isl_local_space_from_space>.
131 =item * The C<isl_div> type has been removed. Functions that used
132 to return an C<isl_div> now return an C<isl_aff>.
133 Note that the space of an C<isl_aff> is that of relation.
134 When replacing a call to C<isl_div_get_coefficient> by a call to
135 C<isl_aff_get_coefficient> any C<isl_dim_set> argument needs
136 to be replaced by C<isl_dim_in>.
137 A call to C<isl_aff_from_div> can be replaced by a call
139 A call to C<isl_qpolynomial_div(div)> call be replaced by
142 isl_qpolynomial_from_aff(isl_aff_floor(div))
144 The function C<isl_constraint_div> has also been renamed
145 to C<isl_constraint_get_div>.
147 =item * The C<nparam> argument has been removed from
148 C<isl_map_read_from_str> and similar functions.
149 When reading input in the original PolyLib format,
150 the result will have no parameters.
151 If parameters are expected, the caller may want to perform
152 dimension manipulation on the result.
156 =head3 Changes since isl-0.09
160 =item * The C<schedule_split_parallel> option has been replaced
161 by the C<schedule_split_scaled> option.
163 =item * The first argument of C<isl_pw_aff_cond> is now
164 an C<isl_pw_aff> instead of an C<isl_set>.
165 A call C<isl_pw_aff_cond(a, b, c)> can be replaced by
167 isl_pw_aff_cond(isl_set_indicator_function(a), b, c)
171 =head3 Changes since isl-0.10
175 =item * The functions C<isl_set_dim_has_lower_bound> and
176 C<isl_set_dim_has_upper_bound> have been renamed to
177 C<isl_set_dim_has_any_lower_bound> and
178 C<isl_set_dim_has_any_upper_bound>.
179 The new C<isl_set_dim_has_lower_bound> and
180 C<isl_set_dim_has_upper_bound> have slightly different meanings.
186 C<isl> is released under the MIT license.
190 Permission is hereby granted, free of charge, to any person obtaining a copy of
191 this software and associated documentation files (the "Software"), to deal in
192 the Software without restriction, including without limitation the rights to
193 use, copy, modify, merge, publish, distribute, sublicense, and/or sell copies
194 of the Software, and to permit persons to whom the Software is furnished to do
195 so, subject to the following conditions:
197 The above copyright notice and this permission notice shall be included in all
198 copies or substantial portions of the Software.
200 THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
201 IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
202 FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
203 AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
204 LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
205 OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
210 Note that C<isl> currently requires C<GMP>, which is released
211 under the GNU Lesser General Public License (LGPL). This means
212 that code linked against C<isl> is also linked against LGPL code.
216 The source of C<isl> can be obtained either as a tarball
217 or from the git repository. Both are available from
218 L<http://freshmeat.net/projects/isl/>.
219 The installation process depends on how you obtained
222 =head2 Installation from the git repository
226 =item 1 Clone or update the repository
228 The first time the source is obtained, you need to clone
231 git clone git://repo.or.cz/isl.git
233 To obtain updates, you need to pull in the latest changes
237 =item 2 Generate C<configure>
243 After performing the above steps, continue
244 with the L<Common installation instructions>.
246 =head2 Common installation instructions
250 =item 1 Obtain C<GMP>
252 Building C<isl> requires C<GMP>, including its headers files.
253 Your distribution may not provide these header files by default
254 and you may need to install a package called C<gmp-devel> or something
255 similar. Alternatively, C<GMP> can be built from
256 source, available from L<http://gmplib.org/>.
260 C<isl> uses the standard C<autoconf> C<configure> script.
265 optionally followed by some configure options.
266 A complete list of options can be obtained by running
270 Below we discuss some of the more common options.
272 C<isl> can optionally use C<piplib>, but no
273 C<piplib> functionality is currently used by default.
274 The C<--with-piplib> option can
275 be used to specify which C<piplib>
276 library to use, either an installed version (C<system>),
277 an externally built version (C<build>)
278 or no version (C<no>). The option C<build> is mostly useful
279 in C<configure> scripts of larger projects that bundle both C<isl>
286 Installation prefix for C<isl>
288 =item C<--with-gmp-prefix>
290 Installation prefix for C<GMP> (architecture-independent files).
292 =item C<--with-gmp-exec-prefix>
294 Installation prefix for C<GMP> (architecture-dependent files).
296 =item C<--with-piplib>
298 Which copy of C<piplib> to use, either C<no> (default), C<system> or C<build>.
300 =item C<--with-piplib-prefix>
302 Installation prefix for C<system> C<piplib> (architecture-independent files).
304 =item C<--with-piplib-exec-prefix>
306 Installation prefix for C<system> C<piplib> (architecture-dependent files).
308 =item C<--with-piplib-builddir>
310 Location where C<build> C<piplib> was built.
318 =item 4 Install (optional)
324 =head1 Integer Set Library
326 =head2 Initialization
328 All manipulations of integer sets and relations occur within
329 the context of an C<isl_ctx>.
330 A given C<isl_ctx> can only be used within a single thread.
331 All arguments of a function are required to have been allocated
332 within the same context.
333 There are currently no functions available for moving an object
334 from one C<isl_ctx> to another C<isl_ctx>. This means that
335 there is currently no way of safely moving an object from one
336 thread to another, unless the whole C<isl_ctx> is moved.
338 An C<isl_ctx> can be allocated using C<isl_ctx_alloc> and
339 freed using C<isl_ctx_free>.
340 All objects allocated within an C<isl_ctx> should be freed
341 before the C<isl_ctx> itself is freed.
343 isl_ctx *isl_ctx_alloc();
344 void isl_ctx_free(isl_ctx *ctx);
348 An C<isl_val> represents an integer value, a rational value
349 or one of three special values, infinity, negative infinity and NaN.
350 Some predefined values can be created using the following functions.
353 __isl_give isl_val *isl_val_zero(isl_ctx *ctx);
354 __isl_give isl_val *isl_val_one(isl_ctx *ctx);
355 __isl_give isl_val *isl_val_nan(isl_ctx *ctx);
356 __isl_give isl_val *isl_val_infty(isl_ctx *ctx);
357 __isl_give isl_val *isl_val_neginfty(isl_ctx *ctx);
359 Specific integer values can be created using the following functions.
362 __isl_give isl_val *isl_val_int_from_si(isl_ctx *ctx,
364 __isl_give isl_val *isl_val_int_from_ui(isl_ctx *ctx,
367 They can be copied and freed using the following functions.
370 __isl_give isl_val *isl_val_copy(__isl_keep isl_val *v);
371 void *isl_val_free(__isl_take isl_val *v);
373 They can be inspected using the following functions.
376 isl_ctx *isl_val_get_ctx(__isl_keep isl_val *val);
377 long isl_val_get_num_si(__isl_keep isl_val *v);
378 long isl_val_get_den_si(__isl_keep isl_val *v);
379 double isl_val_get_d(__isl_keep isl_val *v);
381 Note that C<isl_val_get_num_si>, C<isl_val_get_den_si> and
382 C<isl_val_get_d> can only be applied to rational values.
384 An C<isl_val> can be modified using the following function.
387 __isl_give isl_val *isl_val_set_si(__isl_take isl_val *v,
390 The following unary properties are defined on C<isl_val>s.
393 int isl_val_sgn(__isl_keep isl_val *v);
394 int isl_val_is_zero(__isl_keep isl_val *v);
395 int isl_val_is_one(__isl_keep isl_val *v);
396 int isl_val_is_negone(__isl_keep isl_val *v);
397 int isl_val_is_nonneg(__isl_keep isl_val *v);
398 int isl_val_is_nonpos(__isl_keep isl_val *v);
399 int isl_val_is_pos(__isl_keep isl_val *v);
400 int isl_val_is_neg(__isl_keep isl_val *v);
401 int isl_val_is_int(__isl_keep isl_val *v);
402 int isl_val_is_rat(__isl_keep isl_val *v);
403 int isl_val_is_nan(__isl_keep isl_val *v);
404 int isl_val_is_infty(__isl_keep isl_val *v);
405 int isl_val_is_neginfty(__isl_keep isl_val *v);
407 Note that the sign of NaN is undefined.
409 The following binary properties are defined on pairs of C<isl_val>s.
412 int isl_val_lt(__isl_keep isl_val *v1,
413 __isl_keep isl_val *v2);
414 int isl_val_le(__isl_keep isl_val *v1,
415 __isl_keep isl_val *v2);
416 int isl_val_gt(__isl_keep isl_val *v1,
417 __isl_keep isl_val *v2);
418 int isl_val_ge(__isl_keep isl_val *v1,
419 __isl_keep isl_val *v2);
420 int isl_val_eq(__isl_keep isl_val *v1,
421 __isl_keep isl_val *v2);
422 int isl_val_ne(__isl_keep isl_val *v1,
423 __isl_keep isl_val *v2);
425 For integer C<isl_val>s we additionally have the following binary property.
428 int isl_val_is_divisible_by(__isl_keep isl_val *v1,
429 __isl_keep isl_val *v2);
431 An C<isl_val> can also be compared to an integer using the following
432 function. The result is undefined for NaN.
435 int isl_val_cmp_si(__isl_keep isl_val *v, long i);
437 The following unary operations are available on C<isl_val>s.
440 __isl_give isl_val *isl_val_abs(__isl_take isl_val *v);
441 __isl_give isl_val *isl_val_neg(__isl_take isl_val *v);
442 __isl_give isl_val *isl_val_floor(__isl_take isl_val *v);
443 __isl_give isl_val *isl_val_ceil(__isl_take isl_val *v);
444 __isl_give isl_val *isl_val_trunc(__isl_take isl_val *v);
446 The following binary operations are available on C<isl_val>s.
449 __isl_give isl_val *isl_val_abs(__isl_take isl_val *v);
450 __isl_give isl_val *isl_val_neg(__isl_take isl_val *v);
451 __isl_give isl_val *isl_val_floor(__isl_take isl_val *v);
452 __isl_give isl_val *isl_val_ceil(__isl_take isl_val *v);
453 __isl_give isl_val *isl_val_trunc(__isl_take isl_val *v);
454 __isl_give isl_val *isl_val_2exp(__isl_take isl_val *v);
455 __isl_give isl_val *isl_val_min(__isl_take isl_val *v1,
456 __isl_take isl_val *v2);
457 __isl_give isl_val *isl_val_max(__isl_take isl_val *v1,
458 __isl_take isl_val *v2);
459 __isl_give isl_val *isl_val_add(__isl_take isl_val *v1,
460 __isl_take isl_val *v2);
461 __isl_give isl_val *isl_val_add_ui(__isl_take isl_val *v1,
463 __isl_give isl_val *isl_val_sub(__isl_take isl_val *v1,
464 __isl_take isl_val *v2);
465 __isl_give isl_val *isl_val_sub_ui(__isl_take isl_val *v1,
467 __isl_give isl_val *isl_val_mul(__isl_take isl_val *v1,
468 __isl_take isl_val *v2);
469 __isl_give isl_val *isl_val_mul_ui(__isl_take isl_val *v1,
471 __isl_give isl_val *isl_val_div(__isl_take isl_val *v1,
472 __isl_take isl_val *v2);
474 On integer values, we additionally have the following operations.
477 __isl_give isl_val *isl_val_2exp(__isl_take isl_val *v);
478 __isl_give isl_val *isl_val_mod(__isl_take isl_val *v1,
479 __isl_take isl_val *v2);
480 __isl_give isl_val *isl_val_gcd(__isl_take isl_val *v1,
481 __isl_take isl_val *v2);
482 __isl_give isl_val *isl_val_gcdext(__isl_take isl_val *v1,
483 __isl_take isl_val *v2, __isl_give isl_val **x,
484 __isl_give isl_val **y);
486 The function C<isl_val_gcdext> returns the greatest common divisor g
487 of C<v1> and C<v2> as well as two integers C<*x> and C<*y> such
488 that C<*x> * C<v1> + C<*y> * C<v2> = g.
490 A value can be read from input using
493 __isl_give isl_val *isl_val_read_from_str(isl_ctx *ctx,
496 A value can be printed using
499 __isl_give isl_printer *isl_printer_print_val(
500 __isl_take isl_printer *p, __isl_keep isl_val *v);
502 =head3 GMP specific functions
504 These functions are only available if C<isl> has been compiled with C<GMP>
507 Specific integer and rational values can be created from C<GMP> values using
508 the following functions.
510 #include <isl/val_gmp.h>
511 __isl_give isl_val *isl_val_int_from_gmp(isl_ctx *ctx,
513 __isl_give isl_val *isl_val_from_gmp(isl_ctx *ctx,
514 const mpz_t n, const mpz_t d);
516 The numerator and denominator of a rational value can be extracted as
517 C<GMP> values using the following functions.
519 #include <isl/val_gmp.h>
520 int isl_val_get_num_gmp(__isl_keep isl_val *v, mpz_t z);
521 int isl_val_get_den_gmp(__isl_keep isl_val *v, mpz_t z);
523 =head2 Integers (obsolescent)
525 All operations on integers, mainly the coefficients
526 of the constraints describing the sets and relations,
527 are performed in exact integer arithmetic using C<GMP>.
528 However, to allow future versions of C<isl> to optionally
529 support fixed integer arithmetic, all calls to C<GMP>
530 are wrapped inside C<isl> specific macros.
531 The basic type is C<isl_int> and the operations below
532 are available on this type.
533 The meanings of these operations are essentially the same
534 as their C<GMP> C<mpz_> counterparts.
535 As always with C<GMP> types, C<isl_int>s need to be
536 initialized with C<isl_int_init> before they can be used
537 and they need to be released with C<isl_int_clear>
539 The user should not assume that an C<isl_int> is represented
540 as a C<mpz_t>, but should instead explicitly convert between
541 C<mpz_t>s and C<isl_int>s using C<isl_int_set_gmp> and
542 C<isl_int_get_gmp> whenever a C<mpz_t> is required.
546 =item isl_int_init(i)
548 =item isl_int_clear(i)
550 =item isl_int_set(r,i)
552 =item isl_int_set_si(r,i)
554 =item isl_int_set_gmp(r,g)
556 =item isl_int_get_gmp(i,g)
558 =item isl_int_abs(r,i)
560 =item isl_int_neg(r,i)
562 =item isl_int_swap(i,j)
564 =item isl_int_swap_or_set(i,j)
566 =item isl_int_add_ui(r,i,j)
568 =item isl_int_sub_ui(r,i,j)
570 =item isl_int_add(r,i,j)
572 =item isl_int_sub(r,i,j)
574 =item isl_int_mul(r,i,j)
576 =item isl_int_mul_ui(r,i,j)
578 =item isl_int_addmul(r,i,j)
580 =item isl_int_submul(r,i,j)
582 =item isl_int_gcd(r,i,j)
584 =item isl_int_lcm(r,i,j)
586 =item isl_int_divexact(r,i,j)
588 =item isl_int_cdiv_q(r,i,j)
590 =item isl_int_fdiv_q(r,i,j)
592 =item isl_int_fdiv_r(r,i,j)
594 =item isl_int_fdiv_q_ui(r,i,j)
596 =item isl_int_read(r,s)
598 =item isl_int_print(out,i,width)
602 =item isl_int_cmp(i,j)
604 =item isl_int_cmp_si(i,si)
606 =item isl_int_eq(i,j)
608 =item isl_int_ne(i,j)
610 =item isl_int_lt(i,j)
612 =item isl_int_le(i,j)
614 =item isl_int_gt(i,j)
616 =item isl_int_ge(i,j)
618 =item isl_int_abs_eq(i,j)
620 =item isl_int_abs_ne(i,j)
622 =item isl_int_abs_lt(i,j)
624 =item isl_int_abs_gt(i,j)
626 =item isl_int_abs_ge(i,j)
628 =item isl_int_is_zero(i)
630 =item isl_int_is_one(i)
632 =item isl_int_is_negone(i)
634 =item isl_int_is_pos(i)
636 =item isl_int_is_neg(i)
638 =item isl_int_is_nonpos(i)
640 =item isl_int_is_nonneg(i)
642 =item isl_int_is_divisible_by(i,j)
646 =head2 Sets and Relations
648 C<isl> uses six types of objects for representing sets and relations,
649 C<isl_basic_set>, C<isl_basic_map>, C<isl_set>, C<isl_map>,
650 C<isl_union_set> and C<isl_union_map>.
651 C<isl_basic_set> and C<isl_basic_map> represent sets and relations that
652 can be described as a conjunction of affine constraints, while
653 C<isl_set> and C<isl_map> represent unions of
654 C<isl_basic_set>s and C<isl_basic_map>s, respectively.
655 However, all C<isl_basic_set>s or C<isl_basic_map>s in the union need
656 to live in the same space. C<isl_union_set>s and C<isl_union_map>s
657 represent unions of C<isl_set>s or C<isl_map>s in I<different> spaces,
658 where spaces are considered different if they have a different number
659 of dimensions and/or different names (see L<"Spaces">).
660 The difference between sets and relations (maps) is that sets have
661 one set of variables, while relations have two sets of variables,
662 input variables and output variables.
664 =head2 Memory Management
666 Since a high-level operation on sets and/or relations usually involves
667 several substeps and since the user is usually not interested in
668 the intermediate results, most functions that return a new object
669 will also release all the objects passed as arguments.
670 If the user still wants to use one or more of these arguments
671 after the function call, she should pass along a copy of the
672 object rather than the object itself.
673 The user is then responsible for making sure that the original
674 object gets used somewhere else or is explicitly freed.
676 The arguments and return values of all documented functions are
677 annotated to make clear which arguments are released and which
678 arguments are preserved. In particular, the following annotations
685 C<__isl_give> means that a new object is returned.
686 The user should make sure that the returned pointer is
687 used exactly once as a value for an C<__isl_take> argument.
688 In between, it can be used as a value for as many
689 C<__isl_keep> arguments as the user likes.
690 There is one exception, and that is the case where the
691 pointer returned is C<NULL>. Is this case, the user
692 is free to use it as an C<__isl_take> argument or not.
696 C<__isl_take> means that the object the argument points to
697 is taken over by the function and may no longer be used
698 by the user as an argument to any other function.
699 The pointer value must be one returned by a function
700 returning an C<__isl_give> pointer.
701 If the user passes in a C<NULL> value, then this will
702 be treated as an error in the sense that the function will
703 not perform its usual operation. However, it will still
704 make sure that all the other C<__isl_take> arguments
709 C<__isl_keep> means that the function will only use the object
710 temporarily. After the function has finished, the user
711 can still use it as an argument to other functions.
712 A C<NULL> value will be treated in the same way as
713 a C<NULL> value for an C<__isl_take> argument.
717 =head2 Error Handling
719 C<isl> supports different ways to react in case a runtime error is triggered.
720 Runtime errors arise, e.g., if a function such as C<isl_map_intersect> is called
721 with two maps that have incompatible spaces. There are three possible ways
722 to react on error: to warn, to continue or to abort.
724 The default behavior is to warn. In this mode, C<isl> prints a warning, stores
725 the last error in the corresponding C<isl_ctx> and the function in which the
726 error was triggered returns C<NULL>. An error does not corrupt internal state,
727 such that isl can continue to be used. C<isl> also provides functions to
728 read the last error and to reset the memory that stores the last error. The
729 last error is only stored for information purposes. Its presence does not
730 change the behavior of C<isl>. Hence, resetting an error is not required to
731 continue to use isl, but only to observe new errors.
734 enum isl_error isl_ctx_last_error(isl_ctx *ctx);
735 void isl_ctx_reset_error(isl_ctx *ctx);
737 Another option is to continue on error. This is similar to warn on error mode,
738 except that C<isl> does not print any warning. This allows a program to
739 implement its own error reporting.
741 The last option is to directly abort the execution of the program from within
742 the isl library. This makes it obviously impossible to recover from an error,
743 but it allows to directly spot the error location. By aborting on error,
744 debuggers break at the location the error occurred and can provide a stack
745 trace. Other tools that automatically provide stack traces on abort or that do
746 not want to continue execution after an error was triggered may also prefer to
749 The on error behavior of isl can be specified by calling
750 C<isl_options_set_on_error> or by setting the command line option
751 C<--isl-on-error>. Valid arguments for the function call are
752 C<ISL_ON_ERROR_WARN>, C<ISL_ON_ERROR_CONTINUE> and C<ISL_ON_ERROR_ABORT>. The
753 choices for the command line option are C<warn>, C<continue> and C<abort>.
754 It is also possible to query the current error mode.
756 #include <isl/options.h>
757 int isl_options_set_on_error(isl_ctx *ctx, int val);
758 int isl_options_get_on_error(isl_ctx *ctx);
762 Identifiers are used to identify both individual dimensions
763 and tuples of dimensions. They consist of an optional name and an optional
764 user pointer. The name and the user pointer cannot both be C<NULL>, however.
765 Identifiers with the same name but different pointer values
766 are considered to be distinct.
767 Similarly, identifiers with different names but the same pointer value
768 are also considered to be distinct.
769 Equal identifiers are represented using the same object.
770 Pairs of identifiers can therefore be tested for equality using the
772 Identifiers can be constructed, copied, freed, inspected and printed
773 using the following functions.
776 __isl_give isl_id *isl_id_alloc(isl_ctx *ctx,
777 __isl_keep const char *name, void *user);
778 __isl_give isl_id *isl_id_set_free_user(
779 __isl_take isl_id *id,
780 __isl_give void (*free_user)(void *user));
781 __isl_give isl_id *isl_id_copy(isl_id *id);
782 void *isl_id_free(__isl_take isl_id *id);
784 isl_ctx *isl_id_get_ctx(__isl_keep isl_id *id);
785 void *isl_id_get_user(__isl_keep isl_id *id);
786 __isl_keep const char *isl_id_get_name(__isl_keep isl_id *id);
788 __isl_give isl_printer *isl_printer_print_id(
789 __isl_take isl_printer *p, __isl_keep isl_id *id);
791 The callback set by C<isl_id_set_free_user> is called on the user
792 pointer when the last reference to the C<isl_id> is freed.
793 Note that C<isl_id_get_name> returns a pointer to some internal
794 data structure, so the result can only be used while the
795 corresponding C<isl_id> is alive.
799 Whenever a new set, relation or similiar object is created from scratch,
800 the space in which it lives needs to be specified using an C<isl_space>.
801 Each space involves zero or more parameters and zero, one or two
802 tuples of set or input/output dimensions. The parameters and dimensions
803 are identified by an C<isl_dim_type> and a position.
804 The type C<isl_dim_param> refers to parameters,
805 the type C<isl_dim_set> refers to set dimensions (for spaces
806 with a single tuple of dimensions) and the types C<isl_dim_in>
807 and C<isl_dim_out> refer to input and output dimensions
808 (for spaces with two tuples of dimensions).
809 Local spaces (see L</"Local Spaces">) also contain dimensions
810 of type C<isl_dim_div>.
811 Note that parameters are only identified by their position within
812 a given object. Across different objects, parameters are (usually)
813 identified by their names or identifiers. Only unnamed parameters
814 are identified by their positions across objects. The use of unnamed
815 parameters is discouraged.
817 #include <isl/space.h>
818 __isl_give isl_space *isl_space_alloc(isl_ctx *ctx,
819 unsigned nparam, unsigned n_in, unsigned n_out);
820 __isl_give isl_space *isl_space_params_alloc(isl_ctx *ctx,
822 __isl_give isl_space *isl_space_set_alloc(isl_ctx *ctx,
823 unsigned nparam, unsigned dim);
824 __isl_give isl_space *isl_space_copy(__isl_keep isl_space *space);
825 void *isl_space_free(__isl_take isl_space *space);
826 unsigned isl_space_dim(__isl_keep isl_space *space,
827 enum isl_dim_type type);
829 The space used for creating a parameter domain
830 needs to be created using C<isl_space_params_alloc>.
831 For other sets, the space
832 needs to be created using C<isl_space_set_alloc>, while
833 for a relation, the space
834 needs to be created using C<isl_space_alloc>.
835 C<isl_space_dim> can be used
836 to find out the number of dimensions of each type in
837 a space, where type may be
838 C<isl_dim_param>, C<isl_dim_in> (only for relations),
839 C<isl_dim_out> (only for relations), C<isl_dim_set>
840 (only for sets) or C<isl_dim_all>.
842 To check whether a given space is that of a set or a map
843 or whether it is a parameter space, use these functions:
845 #include <isl/space.h>
846 int isl_space_is_params(__isl_keep isl_space *space);
847 int isl_space_is_set(__isl_keep isl_space *space);
848 int isl_space_is_map(__isl_keep isl_space *space);
850 Spaces can be compared using the following functions:
852 #include <isl/space.h>
853 int isl_space_is_equal(__isl_keep isl_space *space1,
854 __isl_keep isl_space *space2);
855 int isl_space_is_domain(__isl_keep isl_space *space1,
856 __isl_keep isl_space *space2);
857 int isl_space_is_range(__isl_keep isl_space *space1,
858 __isl_keep isl_space *space2);
860 C<isl_space_is_domain> checks whether the first argument is equal
861 to the domain of the second argument. This requires in particular that
862 the first argument is a set space and that the second argument
865 It is often useful to create objects that live in the
866 same space as some other object. This can be accomplished
867 by creating the new objects
868 (see L<Creating New Sets and Relations> or
869 L<Creating New (Piecewise) Quasipolynomials>) based on the space
870 of the original object.
873 __isl_give isl_space *isl_basic_set_get_space(
874 __isl_keep isl_basic_set *bset);
875 __isl_give isl_space *isl_set_get_space(__isl_keep isl_set *set);
877 #include <isl/union_set.h>
878 __isl_give isl_space *isl_union_set_get_space(
879 __isl_keep isl_union_set *uset);
882 __isl_give isl_space *isl_basic_map_get_space(
883 __isl_keep isl_basic_map *bmap);
884 __isl_give isl_space *isl_map_get_space(__isl_keep isl_map *map);
886 #include <isl/union_map.h>
887 __isl_give isl_space *isl_union_map_get_space(
888 __isl_keep isl_union_map *umap);
890 #include <isl/constraint.h>
891 __isl_give isl_space *isl_constraint_get_space(
892 __isl_keep isl_constraint *constraint);
894 #include <isl/polynomial.h>
895 __isl_give isl_space *isl_qpolynomial_get_domain_space(
896 __isl_keep isl_qpolynomial *qp);
897 __isl_give isl_space *isl_qpolynomial_get_space(
898 __isl_keep isl_qpolynomial *qp);
899 __isl_give isl_space *isl_qpolynomial_fold_get_space(
900 __isl_keep isl_qpolynomial_fold *fold);
901 __isl_give isl_space *isl_pw_qpolynomial_get_domain_space(
902 __isl_keep isl_pw_qpolynomial *pwqp);
903 __isl_give isl_space *isl_pw_qpolynomial_get_space(
904 __isl_keep isl_pw_qpolynomial *pwqp);
905 __isl_give isl_space *isl_pw_qpolynomial_fold_get_domain_space(
906 __isl_keep isl_pw_qpolynomial_fold *pwf);
907 __isl_give isl_space *isl_pw_qpolynomial_fold_get_space(
908 __isl_keep isl_pw_qpolynomial_fold *pwf);
909 __isl_give isl_space *isl_union_pw_qpolynomial_get_space(
910 __isl_keep isl_union_pw_qpolynomial *upwqp);
911 __isl_give isl_space *isl_union_pw_qpolynomial_fold_get_space(
912 __isl_keep isl_union_pw_qpolynomial_fold *upwf);
915 __isl_give isl_space *isl_multi_val_get_space(
916 __isl_keep isl_multi_val *mv);
919 __isl_give isl_space *isl_aff_get_domain_space(
920 __isl_keep isl_aff *aff);
921 __isl_give isl_space *isl_aff_get_space(
922 __isl_keep isl_aff *aff);
923 __isl_give isl_space *isl_pw_aff_get_domain_space(
924 __isl_keep isl_pw_aff *pwaff);
925 __isl_give isl_space *isl_pw_aff_get_space(
926 __isl_keep isl_pw_aff *pwaff);
927 __isl_give isl_space *isl_multi_aff_get_domain_space(
928 __isl_keep isl_multi_aff *maff);
929 __isl_give isl_space *isl_multi_aff_get_space(
930 __isl_keep isl_multi_aff *maff);
931 __isl_give isl_space *isl_pw_multi_aff_get_domain_space(
932 __isl_keep isl_pw_multi_aff *pma);
933 __isl_give isl_space *isl_pw_multi_aff_get_space(
934 __isl_keep isl_pw_multi_aff *pma);
935 __isl_give isl_space *isl_union_pw_multi_aff_get_space(
936 __isl_keep isl_union_pw_multi_aff *upma);
937 __isl_give isl_space *isl_multi_pw_aff_get_domain_space(
938 __isl_keep isl_multi_pw_aff *mpa);
939 __isl_give isl_space *isl_multi_pw_aff_get_space(
940 __isl_keep isl_multi_pw_aff *mpa);
942 #include <isl/point.h>
943 __isl_give isl_space *isl_point_get_space(
944 __isl_keep isl_point *pnt);
946 The identifiers or names of the individual dimensions may be set or read off
947 using the following functions.
949 #include <isl/space.h>
950 __isl_give isl_space *isl_space_set_dim_id(
951 __isl_take isl_space *space,
952 enum isl_dim_type type, unsigned pos,
953 __isl_take isl_id *id);
954 int isl_space_has_dim_id(__isl_keep isl_space *space,
955 enum isl_dim_type type, unsigned pos);
956 __isl_give isl_id *isl_space_get_dim_id(
957 __isl_keep isl_space *space,
958 enum isl_dim_type type, unsigned pos);
959 __isl_give isl_space *isl_space_set_dim_name(
960 __isl_take isl_space *space,
961 enum isl_dim_type type, unsigned pos,
962 __isl_keep const char *name);
963 int isl_space_has_dim_name(__isl_keep isl_space *space,
964 enum isl_dim_type type, unsigned pos);
965 __isl_keep const char *isl_space_get_dim_name(
966 __isl_keep isl_space *space,
967 enum isl_dim_type type, unsigned pos);
969 Note that C<isl_space_get_name> returns a pointer to some internal
970 data structure, so the result can only be used while the
971 corresponding C<isl_space> is alive.
972 Also note that every function that operates on two sets or relations
973 requires that both arguments have the same parameters. This also
974 means that if one of the arguments has named parameters, then the
975 other needs to have named parameters too and the names need to match.
976 Pairs of C<isl_set>, C<isl_map>, C<isl_union_set> and/or C<isl_union_map>
977 arguments may have different parameters (as long as they are named),
978 in which case the result will have as parameters the union of the parameters of
981 Given the identifier or name of a dimension (typically a parameter),
982 its position can be obtained from the following function.
984 #include <isl/space.h>
985 int isl_space_find_dim_by_id(__isl_keep isl_space *space,
986 enum isl_dim_type type, __isl_keep isl_id *id);
987 int isl_space_find_dim_by_name(__isl_keep isl_space *space,
988 enum isl_dim_type type, const char *name);
990 The identifiers or names of entire spaces may be set or read off
991 using the following functions.
993 #include <isl/space.h>
994 __isl_give isl_space *isl_space_set_tuple_id(
995 __isl_take isl_space *space,
996 enum isl_dim_type type, __isl_take isl_id *id);
997 __isl_give isl_space *isl_space_reset_tuple_id(
998 __isl_take isl_space *space, enum isl_dim_type type);
999 int isl_space_has_tuple_id(__isl_keep isl_space *space,
1000 enum isl_dim_type type);
1001 __isl_give isl_id *isl_space_get_tuple_id(
1002 __isl_keep isl_space *space, enum isl_dim_type type);
1003 __isl_give isl_space *isl_space_set_tuple_name(
1004 __isl_take isl_space *space,
1005 enum isl_dim_type type, const char *s);
1006 int isl_space_has_tuple_name(__isl_keep isl_space *space,
1007 enum isl_dim_type type);
1008 const char *isl_space_get_tuple_name(__isl_keep isl_space *space,
1009 enum isl_dim_type type);
1011 The C<type> argument needs to be one of C<isl_dim_in>, C<isl_dim_out>
1012 or C<isl_dim_set>. As with C<isl_space_get_name>,
1013 the C<isl_space_get_tuple_name> function returns a pointer to some internal
1015 Binary operations require the corresponding spaces of their arguments
1016 to have the same name.
1018 Spaces can be nested. In particular, the domain of a set or
1019 the domain or range of a relation can be a nested relation.
1020 The following functions can be used to construct and deconstruct
1023 #include <isl/space.h>
1024 int isl_space_is_wrapping(__isl_keep isl_space *space);
1025 __isl_give isl_space *isl_space_wrap(__isl_take isl_space *space);
1026 __isl_give isl_space *isl_space_unwrap(__isl_take isl_space *space);
1028 The input to C<isl_space_is_wrapping> and C<isl_space_unwrap> should
1029 be the space of a set, while that of
1030 C<isl_space_wrap> should be the space of a relation.
1031 Conversely, the output of C<isl_space_unwrap> is the space
1032 of a relation, while that of C<isl_space_wrap> is the space of a set.
1034 Spaces can be created from other spaces
1035 using the following functions.
1037 __isl_give isl_space *isl_space_domain(__isl_take isl_space *space);
1038 __isl_give isl_space *isl_space_from_domain(__isl_take isl_space *space);
1039 __isl_give isl_space *isl_space_range(__isl_take isl_space *space);
1040 __isl_give isl_space *isl_space_from_range(__isl_take isl_space *space);
1041 __isl_give isl_space *isl_space_params(
1042 __isl_take isl_space *space);
1043 __isl_give isl_space *isl_space_set_from_params(
1044 __isl_take isl_space *space);
1045 __isl_give isl_space *isl_space_reverse(__isl_take isl_space *space);
1046 __isl_give isl_space *isl_space_join(__isl_take isl_space *left,
1047 __isl_take isl_space *right);
1048 __isl_give isl_space *isl_space_align_params(
1049 __isl_take isl_space *space1, __isl_take isl_space *space2)
1050 __isl_give isl_space *isl_space_insert_dims(__isl_take isl_space *space,
1051 enum isl_dim_type type, unsigned pos, unsigned n);
1052 __isl_give isl_space *isl_space_add_dims(__isl_take isl_space *space,
1053 enum isl_dim_type type, unsigned n);
1054 __isl_give isl_space *isl_space_drop_dims(__isl_take isl_space *space,
1055 enum isl_dim_type type, unsigned first, unsigned n);
1056 __isl_give isl_space *isl_space_move_dims(__isl_take isl_space *space,
1057 enum isl_dim_type dst_type, unsigned dst_pos,
1058 enum isl_dim_type src_type, unsigned src_pos,
1060 __isl_give isl_space *isl_space_map_from_set(
1061 __isl_take isl_space *space);
1062 __isl_give isl_space *isl_space_map_from_domain_and_range(
1063 __isl_take isl_space *domain,
1064 __isl_take isl_space *range);
1065 __isl_give isl_space *isl_space_zip(__isl_take isl_space *space);
1066 __isl_give isl_space *isl_space_curry(
1067 __isl_take isl_space *space);
1068 __isl_give isl_space *isl_space_uncurry(
1069 __isl_take isl_space *space);
1071 Note that if dimensions are added or removed from a space, then
1072 the name and the internal structure are lost.
1076 A local space is essentially a space with
1077 zero or more existentially quantified variables.
1078 The local space of a (constraint of a) basic set or relation can be obtained
1079 using the following functions.
1081 #include <isl/constraint.h>
1082 __isl_give isl_local_space *isl_constraint_get_local_space(
1083 __isl_keep isl_constraint *constraint);
1085 #include <isl/set.h>
1086 __isl_give isl_local_space *isl_basic_set_get_local_space(
1087 __isl_keep isl_basic_set *bset);
1089 #include <isl/map.h>
1090 __isl_give isl_local_space *isl_basic_map_get_local_space(
1091 __isl_keep isl_basic_map *bmap);
1093 A new local space can be created from a space using
1095 #include <isl/local_space.h>
1096 __isl_give isl_local_space *isl_local_space_from_space(
1097 __isl_take isl_space *space);
1099 They can be inspected, modified, copied and freed using the following functions.
1101 #include <isl/local_space.h>
1102 isl_ctx *isl_local_space_get_ctx(
1103 __isl_keep isl_local_space *ls);
1104 int isl_local_space_is_set(__isl_keep isl_local_space *ls);
1105 int isl_local_space_dim(__isl_keep isl_local_space *ls,
1106 enum isl_dim_type type);
1107 int isl_local_space_has_dim_id(
1108 __isl_keep isl_local_space *ls,
1109 enum isl_dim_type type, unsigned pos);
1110 __isl_give isl_id *isl_local_space_get_dim_id(
1111 __isl_keep isl_local_space *ls,
1112 enum isl_dim_type type, unsigned pos);
1113 int isl_local_space_has_dim_name(
1114 __isl_keep isl_local_space *ls,
1115 enum isl_dim_type type, unsigned pos)
1116 const char *isl_local_space_get_dim_name(
1117 __isl_keep isl_local_space *ls,
1118 enum isl_dim_type type, unsigned pos);
1119 __isl_give isl_local_space *isl_local_space_set_dim_name(
1120 __isl_take isl_local_space *ls,
1121 enum isl_dim_type type, unsigned pos, const char *s);
1122 __isl_give isl_local_space *isl_local_space_set_dim_id(
1123 __isl_take isl_local_space *ls,
1124 enum isl_dim_type type, unsigned pos,
1125 __isl_take isl_id *id);
1126 __isl_give isl_space *isl_local_space_get_space(
1127 __isl_keep isl_local_space *ls);
1128 __isl_give isl_aff *isl_local_space_get_div(
1129 __isl_keep isl_local_space *ls, int pos);
1130 __isl_give isl_local_space *isl_local_space_copy(
1131 __isl_keep isl_local_space *ls);
1132 void *isl_local_space_free(__isl_take isl_local_space *ls);
1134 Note that C<isl_local_space_get_div> can only be used on local spaces
1137 Two local spaces can be compared using
1139 int isl_local_space_is_equal(__isl_keep isl_local_space *ls1,
1140 __isl_keep isl_local_space *ls2);
1142 Local spaces can be created from other local spaces
1143 using the following functions.
1145 __isl_give isl_local_space *isl_local_space_domain(
1146 __isl_take isl_local_space *ls);
1147 __isl_give isl_local_space *isl_local_space_range(
1148 __isl_take isl_local_space *ls);
1149 __isl_give isl_local_space *isl_local_space_from_domain(
1150 __isl_take isl_local_space *ls);
1151 __isl_give isl_local_space *isl_local_space_intersect(
1152 __isl_take isl_local_space *ls1,
1153 __isl_take isl_local_space *ls2);
1154 __isl_give isl_local_space *isl_local_space_add_dims(
1155 __isl_take isl_local_space *ls,
1156 enum isl_dim_type type, unsigned n);
1157 __isl_give isl_local_space *isl_local_space_insert_dims(
1158 __isl_take isl_local_space *ls,
1159 enum isl_dim_type type, unsigned first, unsigned n);
1160 __isl_give isl_local_space *isl_local_space_drop_dims(
1161 __isl_take isl_local_space *ls,
1162 enum isl_dim_type type, unsigned first, unsigned n);
1164 =head2 Input and Output
1166 C<isl> supports its own input/output format, which is similar
1167 to the C<Omega> format, but also supports the C<PolyLib> format
1170 =head3 C<isl> format
1172 The C<isl> format is similar to that of C<Omega>, but has a different
1173 syntax for describing the parameters and allows for the definition
1174 of an existentially quantified variable as the integer division
1175 of an affine expression.
1176 For example, the set of integers C<i> between C<0> and C<n>
1177 such that C<i % 10 <= 6> can be described as
1179 [n] -> { [i] : exists (a = [i/10] : 0 <= i and i <= n and
1182 A set or relation can have several disjuncts, separated
1183 by the keyword C<or>. Each disjunct is either a conjunction
1184 of constraints or a projection (C<exists>) of a conjunction
1185 of constraints. The constraints are separated by the keyword
1188 =head3 C<PolyLib> format
1190 If the represented set is a union, then the first line
1191 contains a single number representing the number of disjuncts.
1192 Otherwise, a line containing the number C<1> is optional.
1194 Each disjunct is represented by a matrix of constraints.
1195 The first line contains two numbers representing
1196 the number of rows and columns,
1197 where the number of rows is equal to the number of constraints
1198 and the number of columns is equal to two plus the number of variables.
1199 The following lines contain the actual rows of the constraint matrix.
1200 In each row, the first column indicates whether the constraint
1201 is an equality (C<0>) or inequality (C<1>). The final column
1202 corresponds to the constant term.
1204 If the set is parametric, then the coefficients of the parameters
1205 appear in the last columns before the constant column.
1206 The coefficients of any existentially quantified variables appear
1207 between those of the set variables and those of the parameters.
1209 =head3 Extended C<PolyLib> format
1211 The extended C<PolyLib> format is nearly identical to the
1212 C<PolyLib> format. The only difference is that the line
1213 containing the number of rows and columns of a constraint matrix
1214 also contains four additional numbers:
1215 the number of output dimensions, the number of input dimensions,
1216 the number of local dimensions (i.e., the number of existentially
1217 quantified variables) and the number of parameters.
1218 For sets, the number of ``output'' dimensions is equal
1219 to the number of set dimensions, while the number of ``input''
1224 #include <isl/set.h>
1225 __isl_give isl_basic_set *isl_basic_set_read_from_file(
1226 isl_ctx *ctx, FILE *input);
1227 __isl_give isl_basic_set *isl_basic_set_read_from_str(
1228 isl_ctx *ctx, const char *str);
1229 __isl_give isl_set *isl_set_read_from_file(isl_ctx *ctx,
1231 __isl_give isl_set *isl_set_read_from_str(isl_ctx *ctx,
1234 #include <isl/map.h>
1235 __isl_give isl_basic_map *isl_basic_map_read_from_file(
1236 isl_ctx *ctx, FILE *input);
1237 __isl_give isl_basic_map *isl_basic_map_read_from_str(
1238 isl_ctx *ctx, const char *str);
1239 __isl_give isl_map *isl_map_read_from_file(
1240 isl_ctx *ctx, FILE *input);
1241 __isl_give isl_map *isl_map_read_from_str(isl_ctx *ctx,
1244 #include <isl/union_set.h>
1245 __isl_give isl_union_set *isl_union_set_read_from_file(
1246 isl_ctx *ctx, FILE *input);
1247 __isl_give isl_union_set *isl_union_set_read_from_str(
1248 isl_ctx *ctx, const char *str);
1250 #include <isl/union_map.h>
1251 __isl_give isl_union_map *isl_union_map_read_from_file(
1252 isl_ctx *ctx, FILE *input);
1253 __isl_give isl_union_map *isl_union_map_read_from_str(
1254 isl_ctx *ctx, const char *str);
1256 The input format is autodetected and may be either the C<PolyLib> format
1257 or the C<isl> format.
1261 Before anything can be printed, an C<isl_printer> needs to
1264 __isl_give isl_printer *isl_printer_to_file(isl_ctx *ctx,
1266 __isl_give isl_printer *isl_printer_to_str(isl_ctx *ctx);
1267 void *isl_printer_free(__isl_take isl_printer *printer);
1268 __isl_give char *isl_printer_get_str(
1269 __isl_keep isl_printer *printer);
1271 The printer can be inspected using the following functions.
1273 FILE *isl_printer_get_file(
1274 __isl_keep isl_printer *printer);
1275 int isl_printer_get_output_format(
1276 __isl_keep isl_printer *p);
1278 The behavior of the printer can be modified in various ways
1280 __isl_give isl_printer *isl_printer_set_output_format(
1281 __isl_take isl_printer *p, int output_format);
1282 __isl_give isl_printer *isl_printer_set_indent(
1283 __isl_take isl_printer *p, int indent);
1284 __isl_give isl_printer *isl_printer_indent(
1285 __isl_take isl_printer *p, int indent);
1286 __isl_give isl_printer *isl_printer_set_prefix(
1287 __isl_take isl_printer *p, const char *prefix);
1288 __isl_give isl_printer *isl_printer_set_suffix(
1289 __isl_take isl_printer *p, const char *suffix);
1291 The C<output_format> may be either C<ISL_FORMAT_ISL>, C<ISL_FORMAT_OMEGA>,
1292 C<ISL_FORMAT_POLYLIB>, C<ISL_FORMAT_EXT_POLYLIB> or C<ISL_FORMAT_LATEX>
1293 and defaults to C<ISL_FORMAT_ISL>.
1294 Each line in the output is indented by C<indent> (set by
1295 C<isl_printer_set_indent>) spaces
1296 (default: 0), prefixed by C<prefix> and suffixed by C<suffix>.
1297 In the C<PolyLib> format output,
1298 the coefficients of the existentially quantified variables
1299 appear between those of the set variables and those
1301 The function C<isl_printer_indent> increases the indentation
1302 by the specified amount (which may be negative).
1304 To actually print something, use
1306 #include <isl/printer.h>
1307 __isl_give isl_printer *isl_printer_print_double(
1308 __isl_take isl_printer *p, double d);
1310 #include <isl/set.h>
1311 __isl_give isl_printer *isl_printer_print_basic_set(
1312 __isl_take isl_printer *printer,
1313 __isl_keep isl_basic_set *bset);
1314 __isl_give isl_printer *isl_printer_print_set(
1315 __isl_take isl_printer *printer,
1316 __isl_keep isl_set *set);
1318 #include <isl/map.h>
1319 __isl_give isl_printer *isl_printer_print_basic_map(
1320 __isl_take isl_printer *printer,
1321 __isl_keep isl_basic_map *bmap);
1322 __isl_give isl_printer *isl_printer_print_map(
1323 __isl_take isl_printer *printer,
1324 __isl_keep isl_map *map);
1326 #include <isl/union_set.h>
1327 __isl_give isl_printer *isl_printer_print_union_set(
1328 __isl_take isl_printer *p,
1329 __isl_keep isl_union_set *uset);
1331 #include <isl/union_map.h>
1332 __isl_give isl_printer *isl_printer_print_union_map(
1333 __isl_take isl_printer *p,
1334 __isl_keep isl_union_map *umap);
1336 When called on a file printer, the following function flushes
1337 the file. When called on a string printer, the buffer is cleared.
1339 __isl_give isl_printer *isl_printer_flush(
1340 __isl_take isl_printer *p);
1342 =head2 Creating New Sets and Relations
1344 C<isl> has functions for creating some standard sets and relations.
1348 =item * Empty sets and relations
1350 __isl_give isl_basic_set *isl_basic_set_empty(
1351 __isl_take isl_space *space);
1352 __isl_give isl_basic_map *isl_basic_map_empty(
1353 __isl_take isl_space *space);
1354 __isl_give isl_set *isl_set_empty(
1355 __isl_take isl_space *space);
1356 __isl_give isl_map *isl_map_empty(
1357 __isl_take isl_space *space);
1358 __isl_give isl_union_set *isl_union_set_empty(
1359 __isl_take isl_space *space);
1360 __isl_give isl_union_map *isl_union_map_empty(
1361 __isl_take isl_space *space);
1363 For C<isl_union_set>s and C<isl_union_map>s, the space
1364 is only used to specify the parameters.
1366 =item * Universe sets and relations
1368 __isl_give isl_basic_set *isl_basic_set_universe(
1369 __isl_take isl_space *space);
1370 __isl_give isl_basic_map *isl_basic_map_universe(
1371 __isl_take isl_space *space);
1372 __isl_give isl_set *isl_set_universe(
1373 __isl_take isl_space *space);
1374 __isl_give isl_map *isl_map_universe(
1375 __isl_take isl_space *space);
1376 __isl_give isl_union_set *isl_union_set_universe(
1377 __isl_take isl_union_set *uset);
1378 __isl_give isl_union_map *isl_union_map_universe(
1379 __isl_take isl_union_map *umap);
1381 The sets and relations constructed by the functions above
1382 contain all integer values, while those constructed by the
1383 functions below only contain non-negative values.
1385 __isl_give isl_basic_set *isl_basic_set_nat_universe(
1386 __isl_take isl_space *space);
1387 __isl_give isl_basic_map *isl_basic_map_nat_universe(
1388 __isl_take isl_space *space);
1389 __isl_give isl_set *isl_set_nat_universe(
1390 __isl_take isl_space *space);
1391 __isl_give isl_map *isl_map_nat_universe(
1392 __isl_take isl_space *space);
1394 =item * Identity relations
1396 __isl_give isl_basic_map *isl_basic_map_identity(
1397 __isl_take isl_space *space);
1398 __isl_give isl_map *isl_map_identity(
1399 __isl_take isl_space *space);
1401 The number of input and output dimensions in C<space> needs
1404 =item * Lexicographic order
1406 __isl_give isl_map *isl_map_lex_lt(
1407 __isl_take isl_space *set_space);
1408 __isl_give isl_map *isl_map_lex_le(
1409 __isl_take isl_space *set_space);
1410 __isl_give isl_map *isl_map_lex_gt(
1411 __isl_take isl_space *set_space);
1412 __isl_give isl_map *isl_map_lex_ge(
1413 __isl_take isl_space *set_space);
1414 __isl_give isl_map *isl_map_lex_lt_first(
1415 __isl_take isl_space *space, unsigned n);
1416 __isl_give isl_map *isl_map_lex_le_first(
1417 __isl_take isl_space *space, unsigned n);
1418 __isl_give isl_map *isl_map_lex_gt_first(
1419 __isl_take isl_space *space, unsigned n);
1420 __isl_give isl_map *isl_map_lex_ge_first(
1421 __isl_take isl_space *space, unsigned n);
1423 The first four functions take a space for a B<set>
1424 and return relations that express that the elements in the domain
1425 are lexicographically less
1426 (C<isl_map_lex_lt>), less or equal (C<isl_map_lex_le>),
1427 greater (C<isl_map_lex_gt>) or greater or equal (C<isl_map_lex_ge>)
1428 than the elements in the range.
1429 The last four functions take a space for a map
1430 and return relations that express that the first C<n> dimensions
1431 in the domain are lexicographically less
1432 (C<isl_map_lex_lt_first>), less or equal (C<isl_map_lex_le_first>),
1433 greater (C<isl_map_lex_gt_first>) or greater or equal (C<isl_map_lex_ge_first>)
1434 than the first C<n> dimensions in the range.
1438 A basic set or relation can be converted to a set or relation
1439 using the following functions.
1441 __isl_give isl_set *isl_set_from_basic_set(
1442 __isl_take isl_basic_set *bset);
1443 __isl_give isl_map *isl_map_from_basic_map(
1444 __isl_take isl_basic_map *bmap);
1446 Sets and relations can be converted to union sets and relations
1447 using the following functions.
1449 __isl_give isl_union_set *isl_union_set_from_basic_set(
1450 __isl_take isl_basic_set *bset);
1451 __isl_give isl_union_map *isl_union_map_from_basic_map(
1452 __isl_take isl_basic_map *bmap);
1453 __isl_give isl_union_set *isl_union_set_from_set(
1454 __isl_take isl_set *set);
1455 __isl_give isl_union_map *isl_union_map_from_map(
1456 __isl_take isl_map *map);
1458 The inverse conversions below can only be used if the input
1459 union set or relation is known to contain elements in exactly one
1462 __isl_give isl_set *isl_set_from_union_set(
1463 __isl_take isl_union_set *uset);
1464 __isl_give isl_map *isl_map_from_union_map(
1465 __isl_take isl_union_map *umap);
1467 A zero-dimensional (basic) set can be constructed on a given parameter domain
1468 using the following function.
1470 __isl_give isl_basic_set *isl_basic_set_from_params(
1471 __isl_take isl_basic_set *bset);
1472 __isl_give isl_set *isl_set_from_params(
1473 __isl_take isl_set *set);
1475 Sets and relations can be copied and freed again using the following
1478 __isl_give isl_basic_set *isl_basic_set_copy(
1479 __isl_keep isl_basic_set *bset);
1480 __isl_give isl_set *isl_set_copy(__isl_keep isl_set *set);
1481 __isl_give isl_union_set *isl_union_set_copy(
1482 __isl_keep isl_union_set *uset);
1483 __isl_give isl_basic_map *isl_basic_map_copy(
1484 __isl_keep isl_basic_map *bmap);
1485 __isl_give isl_map *isl_map_copy(__isl_keep isl_map *map);
1486 __isl_give isl_union_map *isl_union_map_copy(
1487 __isl_keep isl_union_map *umap);
1488 void *isl_basic_set_free(__isl_take isl_basic_set *bset);
1489 void *isl_set_free(__isl_take isl_set *set);
1490 void *isl_union_set_free(__isl_take isl_union_set *uset);
1491 void *isl_basic_map_free(__isl_take isl_basic_map *bmap);
1492 void *isl_map_free(__isl_take isl_map *map);
1493 void *isl_union_map_free(__isl_take isl_union_map *umap);
1495 Other sets and relations can be constructed by starting
1496 from a universe set or relation, adding equality and/or
1497 inequality constraints and then projecting out the
1498 existentially quantified variables, if any.
1499 Constraints can be constructed, manipulated and
1500 added to (or removed from) (basic) sets and relations
1501 using the following functions.
1503 #include <isl/constraint.h>
1504 __isl_give isl_constraint *isl_equality_alloc(
1505 __isl_take isl_local_space *ls);
1506 __isl_give isl_constraint *isl_inequality_alloc(
1507 __isl_take isl_local_space *ls);
1508 __isl_give isl_constraint *isl_constraint_set_constant(
1509 __isl_take isl_constraint *constraint, isl_int v);
1510 __isl_give isl_constraint *isl_constraint_set_constant_si(
1511 __isl_take isl_constraint *constraint, int v);
1512 __isl_give isl_constraint *isl_constraint_set_constant_val(
1513 __isl_take isl_constraint *constraint,
1514 __isl_take isl_val *v);
1515 __isl_give isl_constraint *isl_constraint_set_coefficient(
1516 __isl_take isl_constraint *constraint,
1517 enum isl_dim_type type, int pos, isl_int v);
1518 __isl_give isl_constraint *isl_constraint_set_coefficient_si(
1519 __isl_take isl_constraint *constraint,
1520 enum isl_dim_type type, int pos, int v);
1521 __isl_give isl_constraint *
1522 isl_constraint_set_coefficient_val(
1523 __isl_take isl_constraint *constraint,
1524 enum isl_dim_type type, int pos, isl_val *v);
1525 __isl_give isl_basic_map *isl_basic_map_add_constraint(
1526 __isl_take isl_basic_map *bmap,
1527 __isl_take isl_constraint *constraint);
1528 __isl_give isl_basic_set *isl_basic_set_add_constraint(
1529 __isl_take isl_basic_set *bset,
1530 __isl_take isl_constraint *constraint);
1531 __isl_give isl_map *isl_map_add_constraint(
1532 __isl_take isl_map *map,
1533 __isl_take isl_constraint *constraint);
1534 __isl_give isl_set *isl_set_add_constraint(
1535 __isl_take isl_set *set,
1536 __isl_take isl_constraint *constraint);
1537 __isl_give isl_basic_set *isl_basic_set_drop_constraint(
1538 __isl_take isl_basic_set *bset,
1539 __isl_take isl_constraint *constraint);
1541 For example, to create a set containing the even integers
1542 between 10 and 42, you would use the following code.
1545 isl_local_space *ls;
1547 isl_basic_set *bset;
1549 space = isl_space_set_alloc(ctx, 0, 2);
1550 bset = isl_basic_set_universe(isl_space_copy(space));
1551 ls = isl_local_space_from_space(space);
1553 c = isl_equality_alloc(isl_local_space_copy(ls));
1554 c = isl_constraint_set_coefficient_si(c, isl_dim_set, 0, -1);
1555 c = isl_constraint_set_coefficient_si(c, isl_dim_set, 1, 2);
1556 bset = isl_basic_set_add_constraint(bset, c);
1558 c = isl_inequality_alloc(isl_local_space_copy(ls));
1559 c = isl_constraint_set_constant_si(c, -10);
1560 c = isl_constraint_set_coefficient_si(c, isl_dim_set, 0, 1);
1561 bset = isl_basic_set_add_constraint(bset, c);
1563 c = isl_inequality_alloc(ls);
1564 c = isl_constraint_set_constant_si(c, 42);
1565 c = isl_constraint_set_coefficient_si(c, isl_dim_set, 0, -1);
1566 bset = isl_basic_set_add_constraint(bset, c);
1568 bset = isl_basic_set_project_out(bset, isl_dim_set, 1, 1);
1572 isl_basic_set *bset;
1573 bset = isl_basic_set_read_from_str(ctx,
1574 "{[i] : exists (a : i = 2a and i >= 10 and i <= 42)}");
1576 A basic set or relation can also be constructed from two matrices
1577 describing the equalities and the inequalities.
1579 __isl_give isl_basic_set *isl_basic_set_from_constraint_matrices(
1580 __isl_take isl_space *space,
1581 __isl_take isl_mat *eq, __isl_take isl_mat *ineq,
1582 enum isl_dim_type c1,
1583 enum isl_dim_type c2, enum isl_dim_type c3,
1584 enum isl_dim_type c4);
1585 __isl_give isl_basic_map *isl_basic_map_from_constraint_matrices(
1586 __isl_take isl_space *space,
1587 __isl_take isl_mat *eq, __isl_take isl_mat *ineq,
1588 enum isl_dim_type c1,
1589 enum isl_dim_type c2, enum isl_dim_type c3,
1590 enum isl_dim_type c4, enum isl_dim_type c5);
1592 The C<isl_dim_type> arguments indicate the order in which
1593 different kinds of variables appear in the input matrices
1594 and should be a permutation of C<isl_dim_cst>, C<isl_dim_param>,
1595 C<isl_dim_set> and C<isl_dim_div> for sets and
1596 of C<isl_dim_cst>, C<isl_dim_param>,
1597 C<isl_dim_in>, C<isl_dim_out> and C<isl_dim_div> for relations.
1599 A (basic or union) set or relation can also be constructed from a
1600 (union) (piecewise) (multiple) affine expression
1601 or a list of affine expressions
1602 (See L<"Piecewise Quasi Affine Expressions"> and
1603 L<"Piecewise Multiple Quasi Affine Expressions">).
1605 __isl_give isl_basic_map *isl_basic_map_from_aff(
1606 __isl_take isl_aff *aff);
1607 __isl_give isl_map *isl_map_from_aff(
1608 __isl_take isl_aff *aff);
1609 __isl_give isl_set *isl_set_from_pw_aff(
1610 __isl_take isl_pw_aff *pwaff);
1611 __isl_give isl_map *isl_map_from_pw_aff(
1612 __isl_take isl_pw_aff *pwaff);
1613 __isl_give isl_basic_map *isl_basic_map_from_aff_list(
1614 __isl_take isl_space *domain_space,
1615 __isl_take isl_aff_list *list);
1616 __isl_give isl_basic_map *isl_basic_map_from_multi_aff(
1617 __isl_take isl_multi_aff *maff)
1618 __isl_give isl_map *isl_map_from_multi_aff(
1619 __isl_take isl_multi_aff *maff)
1620 __isl_give isl_set *isl_set_from_pw_multi_aff(
1621 __isl_take isl_pw_multi_aff *pma);
1622 __isl_give isl_map *isl_map_from_pw_multi_aff(
1623 __isl_take isl_pw_multi_aff *pma);
1624 __isl_give isl_union_map *
1625 isl_union_map_from_union_pw_multi_aff(
1626 __isl_take isl_union_pw_multi_aff *upma);
1628 The C<domain_dim> argument describes the domain of the resulting
1629 basic relation. It is required because the C<list> may consist
1630 of zero affine expressions.
1632 =head2 Inspecting Sets and Relations
1634 Usually, the user should not have to care about the actual constraints
1635 of the sets and maps, but should instead apply the abstract operations
1636 explained in the following sections.
1637 Occasionally, however, it may be required to inspect the individual
1638 coefficients of the constraints. This section explains how to do so.
1639 In these cases, it may also be useful to have C<isl> compute
1640 an explicit representation of the existentially quantified variables.
1642 __isl_give isl_set *isl_set_compute_divs(
1643 __isl_take isl_set *set);
1644 __isl_give isl_map *isl_map_compute_divs(
1645 __isl_take isl_map *map);
1646 __isl_give isl_union_set *isl_union_set_compute_divs(
1647 __isl_take isl_union_set *uset);
1648 __isl_give isl_union_map *isl_union_map_compute_divs(
1649 __isl_take isl_union_map *umap);
1651 This explicit representation defines the existentially quantified
1652 variables as integer divisions of the other variables, possibly
1653 including earlier existentially quantified variables.
1654 An explicitly represented existentially quantified variable therefore
1655 has a unique value when the values of the other variables are known.
1656 If, furthermore, the same existentials, i.e., existentials
1657 with the same explicit representations, should appear in the
1658 same order in each of the disjuncts of a set or map, then the user should call
1659 either of the following functions.
1661 __isl_give isl_set *isl_set_align_divs(
1662 __isl_take isl_set *set);
1663 __isl_give isl_map *isl_map_align_divs(
1664 __isl_take isl_map *map);
1666 Alternatively, the existentially quantified variables can be removed
1667 using the following functions, which compute an overapproximation.
1669 __isl_give isl_basic_set *isl_basic_set_remove_divs(
1670 __isl_take isl_basic_set *bset);
1671 __isl_give isl_basic_map *isl_basic_map_remove_divs(
1672 __isl_take isl_basic_map *bmap);
1673 __isl_give isl_set *isl_set_remove_divs(
1674 __isl_take isl_set *set);
1675 __isl_give isl_map *isl_map_remove_divs(
1676 __isl_take isl_map *map);
1678 It is also possible to only remove those divs that are defined
1679 in terms of a given range of dimensions or only those for which
1680 no explicit representation is known.
1682 __isl_give isl_basic_set *
1683 isl_basic_set_remove_divs_involving_dims(
1684 __isl_take isl_basic_set *bset,
1685 enum isl_dim_type type,
1686 unsigned first, unsigned n);
1687 __isl_give isl_basic_map *
1688 isl_basic_map_remove_divs_involving_dims(
1689 __isl_take isl_basic_map *bmap,
1690 enum isl_dim_type type,
1691 unsigned first, unsigned n);
1692 __isl_give isl_set *isl_set_remove_divs_involving_dims(
1693 __isl_take isl_set *set, enum isl_dim_type type,
1694 unsigned first, unsigned n);
1695 __isl_give isl_map *isl_map_remove_divs_involving_dims(
1696 __isl_take isl_map *map, enum isl_dim_type type,
1697 unsigned first, unsigned n);
1699 __isl_give isl_basic_set *
1700 isl_basic_set_remove_unknown_divs(
1701 __isl_take isl_basic_set *bset);
1702 __isl_give isl_set *isl_set_remove_unknown_divs(
1703 __isl_take isl_set *set);
1704 __isl_give isl_map *isl_map_remove_unknown_divs(
1705 __isl_take isl_map *map);
1707 To iterate over all the sets or maps in a union set or map, use
1709 int isl_union_set_foreach_set(__isl_keep isl_union_set *uset,
1710 int (*fn)(__isl_take isl_set *set, void *user),
1712 int isl_union_map_foreach_map(__isl_keep isl_union_map *umap,
1713 int (*fn)(__isl_take isl_map *map, void *user),
1716 The number of sets or maps in a union set or map can be obtained
1719 int isl_union_set_n_set(__isl_keep isl_union_set *uset);
1720 int isl_union_map_n_map(__isl_keep isl_union_map *umap);
1722 To extract the set or map in a given space from a union, use
1724 __isl_give isl_set *isl_union_set_extract_set(
1725 __isl_keep isl_union_set *uset,
1726 __isl_take isl_space *space);
1727 __isl_give isl_map *isl_union_map_extract_map(
1728 __isl_keep isl_union_map *umap,
1729 __isl_take isl_space *space);
1731 To iterate over all the basic sets or maps in a set or map, use
1733 int isl_set_foreach_basic_set(__isl_keep isl_set *set,
1734 int (*fn)(__isl_take isl_basic_set *bset, void *user),
1736 int isl_map_foreach_basic_map(__isl_keep isl_map *map,
1737 int (*fn)(__isl_take isl_basic_map *bmap, void *user),
1740 The callback function C<fn> should return 0 if successful and
1741 -1 if an error occurs. In the latter case, or if any other error
1742 occurs, the above functions will return -1.
1744 It should be noted that C<isl> does not guarantee that
1745 the basic sets or maps passed to C<fn> are disjoint.
1746 If this is required, then the user should call one of
1747 the following functions first.
1749 __isl_give isl_set *isl_set_make_disjoint(
1750 __isl_take isl_set *set);
1751 __isl_give isl_map *isl_map_make_disjoint(
1752 __isl_take isl_map *map);
1754 The number of basic sets in a set can be obtained
1757 int isl_set_n_basic_set(__isl_keep isl_set *set);
1759 To iterate over the constraints of a basic set or map, use
1761 #include <isl/constraint.h>
1763 int isl_basic_set_n_constraint(
1764 __isl_keep isl_basic_set *bset);
1765 int isl_basic_set_foreach_constraint(
1766 __isl_keep isl_basic_set *bset,
1767 int (*fn)(__isl_take isl_constraint *c, void *user),
1769 int isl_basic_map_foreach_constraint(
1770 __isl_keep isl_basic_map *bmap,
1771 int (*fn)(__isl_take isl_constraint *c, void *user),
1773 void *isl_constraint_free(__isl_take isl_constraint *c);
1775 Again, the callback function C<fn> should return 0 if successful and
1776 -1 if an error occurs. In the latter case, or if any other error
1777 occurs, the above functions will return -1.
1778 The constraint C<c> represents either an equality or an inequality.
1779 Use the following function to find out whether a constraint
1780 represents an equality. If not, it represents an inequality.
1782 int isl_constraint_is_equality(
1783 __isl_keep isl_constraint *constraint);
1785 The coefficients of the constraints can be inspected using
1786 the following functions.
1788 int isl_constraint_is_lower_bound(
1789 __isl_keep isl_constraint *constraint,
1790 enum isl_dim_type type, unsigned pos);
1791 int isl_constraint_is_upper_bound(
1792 __isl_keep isl_constraint *constraint,
1793 enum isl_dim_type type, unsigned pos);
1794 void isl_constraint_get_constant(
1795 __isl_keep isl_constraint *constraint, isl_int *v);
1796 __isl_give isl_val *isl_constraint_get_constant_val(
1797 __isl_keep isl_constraint *constraint);
1798 void isl_constraint_get_coefficient(
1799 __isl_keep isl_constraint *constraint,
1800 enum isl_dim_type type, int pos, isl_int *v);
1801 __isl_give isl_val *isl_constraint_get_coefficient_val(
1802 __isl_keep isl_constraint *constraint,
1803 enum isl_dim_type type, int pos);
1804 int isl_constraint_involves_dims(
1805 __isl_keep isl_constraint *constraint,
1806 enum isl_dim_type type, unsigned first, unsigned n);
1808 The explicit representations of the existentially quantified
1809 variables can be inspected using the following function.
1810 Note that the user is only allowed to use this function
1811 if the inspected set or map is the result of a call
1812 to C<isl_set_compute_divs> or C<isl_map_compute_divs>.
1813 The existentially quantified variable is equal to the floor
1814 of the returned affine expression. The affine expression
1815 itself can be inspected using the functions in
1816 L<"Piecewise Quasi Affine Expressions">.
1818 __isl_give isl_aff *isl_constraint_get_div(
1819 __isl_keep isl_constraint *constraint, int pos);
1821 To obtain the constraints of a basic set or map in matrix
1822 form, use the following functions.
1824 __isl_give isl_mat *isl_basic_set_equalities_matrix(
1825 __isl_keep isl_basic_set *bset,
1826 enum isl_dim_type c1, enum isl_dim_type c2,
1827 enum isl_dim_type c3, enum isl_dim_type c4);
1828 __isl_give isl_mat *isl_basic_set_inequalities_matrix(
1829 __isl_keep isl_basic_set *bset,
1830 enum isl_dim_type c1, enum isl_dim_type c2,
1831 enum isl_dim_type c3, enum isl_dim_type c4);
1832 __isl_give isl_mat *isl_basic_map_equalities_matrix(
1833 __isl_keep isl_basic_map *bmap,
1834 enum isl_dim_type c1,
1835 enum isl_dim_type c2, enum isl_dim_type c3,
1836 enum isl_dim_type c4, enum isl_dim_type c5);
1837 __isl_give isl_mat *isl_basic_map_inequalities_matrix(
1838 __isl_keep isl_basic_map *bmap,
1839 enum isl_dim_type c1,
1840 enum isl_dim_type c2, enum isl_dim_type c3,
1841 enum isl_dim_type c4, enum isl_dim_type c5);
1843 The C<isl_dim_type> arguments dictate the order in which
1844 different kinds of variables appear in the resulting matrix
1845 and should be a permutation of C<isl_dim_cst>, C<isl_dim_param>,
1846 C<isl_dim_in>, C<isl_dim_out> and C<isl_dim_div>.
1848 The number of parameters, input, output or set dimensions can
1849 be obtained using the following functions.
1851 unsigned isl_basic_set_dim(__isl_keep isl_basic_set *bset,
1852 enum isl_dim_type type);
1853 unsigned isl_basic_map_dim(__isl_keep isl_basic_map *bmap,
1854 enum isl_dim_type type);
1855 unsigned isl_set_dim(__isl_keep isl_set *set,
1856 enum isl_dim_type type);
1857 unsigned isl_map_dim(__isl_keep isl_map *map,
1858 enum isl_dim_type type);
1860 To check whether the description of a set or relation depends
1861 on one or more given dimensions, it is not necessary to iterate over all
1862 constraints. Instead the following functions can be used.
1864 int isl_basic_set_involves_dims(
1865 __isl_keep isl_basic_set *bset,
1866 enum isl_dim_type type, unsigned first, unsigned n);
1867 int isl_set_involves_dims(__isl_keep isl_set *set,
1868 enum isl_dim_type type, unsigned first, unsigned n);
1869 int isl_basic_map_involves_dims(
1870 __isl_keep isl_basic_map *bmap,
1871 enum isl_dim_type type, unsigned first, unsigned n);
1872 int isl_map_involves_dims(__isl_keep isl_map *map,
1873 enum isl_dim_type type, unsigned first, unsigned n);
1875 Similarly, the following functions can be used to check whether
1876 a given dimension is involved in any lower or upper bound.
1878 int isl_set_dim_has_any_lower_bound(__isl_keep isl_set *set,
1879 enum isl_dim_type type, unsigned pos);
1880 int isl_set_dim_has_any_upper_bound(__isl_keep isl_set *set,
1881 enum isl_dim_type type, unsigned pos);
1883 Note that these functions return true even if there is a bound on
1884 the dimension on only some of the basic sets of C<set>.
1885 To check if they have a bound for all of the basic sets in C<set>,
1886 use the following functions instead.
1888 int isl_set_dim_has_lower_bound(__isl_keep isl_set *set,
1889 enum isl_dim_type type, unsigned pos);
1890 int isl_set_dim_has_upper_bound(__isl_keep isl_set *set,
1891 enum isl_dim_type type, unsigned pos);
1893 The identifiers or names of the domain and range spaces of a set
1894 or relation can be read off or set using the following functions.
1896 __isl_give isl_set *isl_set_set_tuple_id(
1897 __isl_take isl_set *set, __isl_take isl_id *id);
1898 __isl_give isl_set *isl_set_reset_tuple_id(
1899 __isl_take isl_set *set);
1900 int isl_set_has_tuple_id(__isl_keep isl_set *set);
1901 __isl_give isl_id *isl_set_get_tuple_id(
1902 __isl_keep isl_set *set);
1903 __isl_give isl_map *isl_map_set_tuple_id(
1904 __isl_take isl_map *map, enum isl_dim_type type,
1905 __isl_take isl_id *id);
1906 __isl_give isl_map *isl_map_reset_tuple_id(
1907 __isl_take isl_map *map, enum isl_dim_type type);
1908 int isl_map_has_tuple_id(__isl_keep isl_map *map,
1909 enum isl_dim_type type);
1910 __isl_give isl_id *isl_map_get_tuple_id(
1911 __isl_keep isl_map *map, enum isl_dim_type type);
1913 const char *isl_basic_set_get_tuple_name(
1914 __isl_keep isl_basic_set *bset);
1915 __isl_give isl_basic_set *isl_basic_set_set_tuple_name(
1916 __isl_take isl_basic_set *set, const char *s);
1917 int isl_set_has_tuple_name(__isl_keep isl_set *set);
1918 const char *isl_set_get_tuple_name(
1919 __isl_keep isl_set *set);
1920 const char *isl_basic_map_get_tuple_name(
1921 __isl_keep isl_basic_map *bmap,
1922 enum isl_dim_type type);
1923 __isl_give isl_basic_map *isl_basic_map_set_tuple_name(
1924 __isl_take isl_basic_map *bmap,
1925 enum isl_dim_type type, const char *s);
1926 int isl_map_has_tuple_name(__isl_keep isl_map *map,
1927 enum isl_dim_type type);
1928 const char *isl_map_get_tuple_name(
1929 __isl_keep isl_map *map,
1930 enum isl_dim_type type);
1932 As with C<isl_space_get_tuple_name>, the value returned points to
1933 an internal data structure.
1934 The identifiers, positions or names of individual dimensions can be
1935 read off using the following functions.
1937 __isl_give isl_id *isl_basic_set_get_dim_id(
1938 __isl_keep isl_basic_set *bset,
1939 enum isl_dim_type type, unsigned pos);
1940 __isl_give isl_set *isl_set_set_dim_id(
1941 __isl_take isl_set *set, enum isl_dim_type type,
1942 unsigned pos, __isl_take isl_id *id);
1943 int isl_set_has_dim_id(__isl_keep isl_set *set,
1944 enum isl_dim_type type, unsigned pos);
1945 __isl_give isl_id *isl_set_get_dim_id(
1946 __isl_keep isl_set *set, enum isl_dim_type type,
1948 int isl_basic_map_has_dim_id(
1949 __isl_keep isl_basic_map *bmap,
1950 enum isl_dim_type type, unsigned pos);
1951 __isl_give isl_map *isl_map_set_dim_id(
1952 __isl_take isl_map *map, enum isl_dim_type type,
1953 unsigned pos, __isl_take isl_id *id);
1954 int isl_map_has_dim_id(__isl_keep isl_map *map,
1955 enum isl_dim_type type, unsigned pos);
1956 __isl_give isl_id *isl_map_get_dim_id(
1957 __isl_keep isl_map *map, enum isl_dim_type type,
1960 int isl_set_find_dim_by_id(__isl_keep isl_set *set,
1961 enum isl_dim_type type, __isl_keep isl_id *id);
1962 int isl_map_find_dim_by_id(__isl_keep isl_map *map,
1963 enum isl_dim_type type, __isl_keep isl_id *id);
1964 int isl_set_find_dim_by_name(__isl_keep isl_set *set,
1965 enum isl_dim_type type, const char *name);
1966 int isl_map_find_dim_by_name(__isl_keep isl_map *map,
1967 enum isl_dim_type type, const char *name);
1969 const char *isl_constraint_get_dim_name(
1970 __isl_keep isl_constraint *constraint,
1971 enum isl_dim_type type, unsigned pos);
1972 const char *isl_basic_set_get_dim_name(
1973 __isl_keep isl_basic_set *bset,
1974 enum isl_dim_type type, unsigned pos);
1975 int isl_set_has_dim_name(__isl_keep isl_set *set,
1976 enum isl_dim_type type, unsigned pos);
1977 const char *isl_set_get_dim_name(
1978 __isl_keep isl_set *set,
1979 enum isl_dim_type type, unsigned pos);
1980 const char *isl_basic_map_get_dim_name(
1981 __isl_keep isl_basic_map *bmap,
1982 enum isl_dim_type type, unsigned pos);
1983 int isl_map_has_dim_name(__isl_keep isl_map *map,
1984 enum isl_dim_type type, unsigned pos);
1985 const char *isl_map_get_dim_name(
1986 __isl_keep isl_map *map,
1987 enum isl_dim_type type, unsigned pos);
1989 These functions are mostly useful to obtain the identifiers, positions
1990 or names of the parameters. Identifiers of individual dimensions are
1991 essentially only useful for printing. They are ignored by all other
1992 operations and may not be preserved across those operations.
1996 =head3 Unary Properties
2002 The following functions test whether the given set or relation
2003 contains any integer points. The ``plain'' variants do not perform
2004 any computations, but simply check if the given set or relation
2005 is already known to be empty.
2007 int isl_basic_set_plain_is_empty(__isl_keep isl_basic_set *bset);
2008 int isl_basic_set_is_empty(__isl_keep isl_basic_set *bset);
2009 int isl_set_plain_is_empty(__isl_keep isl_set *set);
2010 int isl_set_is_empty(__isl_keep isl_set *set);
2011 int isl_union_set_is_empty(__isl_keep isl_union_set *uset);
2012 int isl_basic_map_plain_is_empty(__isl_keep isl_basic_map *bmap);
2013 int isl_basic_map_is_empty(__isl_keep isl_basic_map *bmap);
2014 int isl_map_plain_is_empty(__isl_keep isl_map *map);
2015 int isl_map_is_empty(__isl_keep isl_map *map);
2016 int isl_union_map_is_empty(__isl_keep isl_union_map *umap);
2018 =item * Universality
2020 int isl_basic_set_is_universe(__isl_keep isl_basic_set *bset);
2021 int isl_basic_map_is_universe(__isl_keep isl_basic_map *bmap);
2022 int isl_set_plain_is_universe(__isl_keep isl_set *set);
2024 =item * Single-valuedness
2026 int isl_basic_map_is_single_valued(
2027 __isl_keep isl_basic_map *bmap);
2028 int isl_map_plain_is_single_valued(
2029 __isl_keep isl_map *map);
2030 int isl_map_is_single_valued(__isl_keep isl_map *map);
2031 int isl_union_map_is_single_valued(__isl_keep isl_union_map *umap);
2035 int isl_map_plain_is_injective(__isl_keep isl_map *map);
2036 int isl_map_is_injective(__isl_keep isl_map *map);
2037 int isl_union_map_plain_is_injective(
2038 __isl_keep isl_union_map *umap);
2039 int isl_union_map_is_injective(
2040 __isl_keep isl_union_map *umap);
2044 int isl_map_is_bijective(__isl_keep isl_map *map);
2045 int isl_union_map_is_bijective(__isl_keep isl_union_map *umap);
2049 int isl_basic_map_plain_is_fixed(
2050 __isl_keep isl_basic_map *bmap,
2051 enum isl_dim_type type, unsigned pos,
2053 int isl_set_plain_is_fixed(__isl_keep isl_set *set,
2054 enum isl_dim_type type, unsigned pos,
2056 int isl_map_plain_is_fixed(__isl_keep isl_map *map,
2057 enum isl_dim_type type, unsigned pos,
2060 Check if the relation obviously lies on a hyperplane where the given dimension
2061 has a fixed value and if so, return that value in C<*val>.
2063 __isl_give isl_val *
2064 isl_basic_map_plain_get_val_if_fixed(
2065 __isl_keep isl_basic_map *bmap,
2066 enum isl_dim_type type, unsigned pos);
2067 __isl_give isl_val *isl_set_plain_get_val_if_fixed(
2068 __isl_keep isl_set *set,
2069 enum isl_dim_type type, unsigned pos);
2070 __isl_give isl_val *isl_map_plain_get_val_if_fixed(
2071 __isl_keep isl_map *map,
2072 enum isl_dim_type type, unsigned pos);
2074 If the set or relation obviously lies on a hyperplane where the given dimension
2075 has a fixed value, then return that value.
2076 Otherwise return NaN.
2080 int isl_set_dim_residue_class_val(
2081 __isl_keep isl_set *set,
2082 int pos, __isl_give isl_val **modulo,
2083 __isl_give isl_val **residue);
2085 Check if the values of the given set dimension are equal to a fixed
2086 value modulo some integer value. If so, assign the modulo to C<*modulo>
2087 and the fixed value to C<*residue>. If the given dimension attains only
2088 a single value, then assign C<0> to C<*modulo> and the fixed value to
2090 If the dimension does not attain only a single value and if no modulo
2091 can be found then assign C<1> to C<*modulo> and C<1> to C<*residue>.
2095 To check whether a set is a parameter domain, use this function:
2097 int isl_set_is_params(__isl_keep isl_set *set);
2098 int isl_union_set_is_params(
2099 __isl_keep isl_union_set *uset);
2103 The following functions check whether the domain of the given
2104 (basic) set is a wrapped relation.
2106 int isl_basic_set_is_wrapping(
2107 __isl_keep isl_basic_set *bset);
2108 int isl_set_is_wrapping(__isl_keep isl_set *set);
2110 =item * Internal Product
2112 int isl_basic_map_can_zip(
2113 __isl_keep isl_basic_map *bmap);
2114 int isl_map_can_zip(__isl_keep isl_map *map);
2116 Check whether the product of domain and range of the given relation
2118 i.e., whether both domain and range are nested relations.
2122 int isl_basic_map_can_curry(
2123 __isl_keep isl_basic_map *bmap);
2124 int isl_map_can_curry(__isl_keep isl_map *map);
2126 Check whether the domain of the (basic) relation is a wrapped relation.
2128 int isl_basic_map_can_uncurry(
2129 __isl_keep isl_basic_map *bmap);
2130 int isl_map_can_uncurry(__isl_keep isl_map *map);
2132 Check whether the range of the (basic) relation is a wrapped relation.
2136 =head3 Binary Properties
2142 int isl_set_plain_is_equal(__isl_keep isl_set *set1,
2143 __isl_keep isl_set *set2);
2144 int isl_set_is_equal(__isl_keep isl_set *set1,
2145 __isl_keep isl_set *set2);
2146 int isl_union_set_is_equal(
2147 __isl_keep isl_union_set *uset1,
2148 __isl_keep isl_union_set *uset2);
2149 int isl_basic_map_is_equal(
2150 __isl_keep isl_basic_map *bmap1,
2151 __isl_keep isl_basic_map *bmap2);
2152 int isl_map_is_equal(__isl_keep isl_map *map1,
2153 __isl_keep isl_map *map2);
2154 int isl_map_plain_is_equal(__isl_keep isl_map *map1,
2155 __isl_keep isl_map *map2);
2156 int isl_union_map_is_equal(
2157 __isl_keep isl_union_map *umap1,
2158 __isl_keep isl_union_map *umap2);
2160 =item * Disjointness
2162 int isl_set_plain_is_disjoint(__isl_keep isl_set *set1,
2163 __isl_keep isl_set *set2);
2164 int isl_set_is_disjoint(__isl_keep isl_set *set1,
2165 __isl_keep isl_set *set2);
2166 int isl_map_is_disjoint(__isl_keep isl_map *map1,
2167 __isl_keep isl_map *map2);
2171 int isl_basic_set_is_subset(
2172 __isl_keep isl_basic_set *bset1,
2173 __isl_keep isl_basic_set *bset2);
2174 int isl_set_is_subset(__isl_keep isl_set *set1,
2175 __isl_keep isl_set *set2);
2176 int isl_set_is_strict_subset(
2177 __isl_keep isl_set *set1,
2178 __isl_keep isl_set *set2);
2179 int isl_union_set_is_subset(
2180 __isl_keep isl_union_set *uset1,
2181 __isl_keep isl_union_set *uset2);
2182 int isl_union_set_is_strict_subset(
2183 __isl_keep isl_union_set *uset1,
2184 __isl_keep isl_union_set *uset2);
2185 int isl_basic_map_is_subset(
2186 __isl_keep isl_basic_map *bmap1,
2187 __isl_keep isl_basic_map *bmap2);
2188 int isl_basic_map_is_strict_subset(
2189 __isl_keep isl_basic_map *bmap1,
2190 __isl_keep isl_basic_map *bmap2);
2191 int isl_map_is_subset(
2192 __isl_keep isl_map *map1,
2193 __isl_keep isl_map *map2);
2194 int isl_map_is_strict_subset(
2195 __isl_keep isl_map *map1,
2196 __isl_keep isl_map *map2);
2197 int isl_union_map_is_subset(
2198 __isl_keep isl_union_map *umap1,
2199 __isl_keep isl_union_map *umap2);
2200 int isl_union_map_is_strict_subset(
2201 __isl_keep isl_union_map *umap1,
2202 __isl_keep isl_union_map *umap2);
2204 Check whether the first argument is a (strict) subset of the
2209 int isl_set_plain_cmp(__isl_keep isl_set *set1,
2210 __isl_keep isl_set *set2);
2212 This function is useful for sorting C<isl_set>s.
2213 The order depends on the internal representation of the inputs.
2214 The order is fixed over different calls to the function (assuming
2215 the internal representation of the inputs has not changed), but may
2216 change over different versions of C<isl>.
2220 =head2 Unary Operations
2226 __isl_give isl_set *isl_set_complement(
2227 __isl_take isl_set *set);
2228 __isl_give isl_map *isl_map_complement(
2229 __isl_take isl_map *map);
2233 __isl_give isl_basic_map *isl_basic_map_reverse(
2234 __isl_take isl_basic_map *bmap);
2235 __isl_give isl_map *isl_map_reverse(
2236 __isl_take isl_map *map);
2237 __isl_give isl_union_map *isl_union_map_reverse(
2238 __isl_take isl_union_map *umap);
2242 __isl_give isl_basic_set *isl_basic_set_project_out(
2243 __isl_take isl_basic_set *bset,
2244 enum isl_dim_type type, unsigned first, unsigned n);
2245 __isl_give isl_basic_map *isl_basic_map_project_out(
2246 __isl_take isl_basic_map *bmap,
2247 enum isl_dim_type type, unsigned first, unsigned n);
2248 __isl_give isl_set *isl_set_project_out(__isl_take isl_set *set,
2249 enum isl_dim_type type, unsigned first, unsigned n);
2250 __isl_give isl_map *isl_map_project_out(__isl_take isl_map *map,
2251 enum isl_dim_type type, unsigned first, unsigned n);
2252 __isl_give isl_basic_set *isl_basic_set_params(
2253 __isl_take isl_basic_set *bset);
2254 __isl_give isl_basic_set *isl_basic_map_domain(
2255 __isl_take isl_basic_map *bmap);
2256 __isl_give isl_basic_set *isl_basic_map_range(
2257 __isl_take isl_basic_map *bmap);
2258 __isl_give isl_set *isl_set_params(__isl_take isl_set *set);
2259 __isl_give isl_set *isl_map_params(__isl_take isl_map *map);
2260 __isl_give isl_set *isl_map_domain(
2261 __isl_take isl_map *bmap);
2262 __isl_give isl_set *isl_map_range(
2263 __isl_take isl_map *map);
2264 __isl_give isl_set *isl_union_set_params(
2265 __isl_take isl_union_set *uset);
2266 __isl_give isl_set *isl_union_map_params(
2267 __isl_take isl_union_map *umap);
2268 __isl_give isl_union_set *isl_union_map_domain(
2269 __isl_take isl_union_map *umap);
2270 __isl_give isl_union_set *isl_union_map_range(
2271 __isl_take isl_union_map *umap);
2273 __isl_give isl_basic_map *isl_basic_map_domain_map(
2274 __isl_take isl_basic_map *bmap);
2275 __isl_give isl_basic_map *isl_basic_map_range_map(
2276 __isl_take isl_basic_map *bmap);
2277 __isl_give isl_map *isl_map_domain_map(__isl_take isl_map *map);
2278 __isl_give isl_map *isl_map_range_map(__isl_take isl_map *map);
2279 __isl_give isl_union_map *isl_union_map_domain_map(
2280 __isl_take isl_union_map *umap);
2281 __isl_give isl_union_map *isl_union_map_range_map(
2282 __isl_take isl_union_map *umap);
2284 The functions above construct a (basic, regular or union) relation
2285 that maps (a wrapped version of) the input relation to its domain or range.
2289 __isl_give isl_basic_set *isl_basic_set_eliminate(
2290 __isl_take isl_basic_set *bset,
2291 enum isl_dim_type type,
2292 unsigned first, unsigned n);
2293 __isl_give isl_set *isl_set_eliminate(
2294 __isl_take isl_set *set, enum isl_dim_type type,
2295 unsigned first, unsigned n);
2296 __isl_give isl_basic_map *isl_basic_map_eliminate(
2297 __isl_take isl_basic_map *bmap,
2298 enum isl_dim_type type,
2299 unsigned first, unsigned n);
2300 __isl_give isl_map *isl_map_eliminate(
2301 __isl_take isl_map *map, enum isl_dim_type type,
2302 unsigned first, unsigned n);
2304 Eliminate the coefficients for the given dimensions from the constraints,
2305 without removing the dimensions.
2309 __isl_give isl_basic_set *isl_basic_set_fix(
2310 __isl_take isl_basic_set *bset,
2311 enum isl_dim_type type, unsigned pos,
2313 __isl_give isl_basic_set *isl_basic_set_fix_si(
2314 __isl_take isl_basic_set *bset,
2315 enum isl_dim_type type, unsigned pos, int value);
2316 __isl_give isl_basic_set *isl_basic_set_fix_val(
2317 __isl_take isl_basic_set *bset,
2318 enum isl_dim_type type, unsigned pos,
2319 __isl_take isl_val *v);
2320 __isl_give isl_set *isl_set_fix(__isl_take isl_set *set,
2321 enum isl_dim_type type, unsigned pos,
2323 __isl_give isl_set *isl_set_fix_si(__isl_take isl_set *set,
2324 enum isl_dim_type type, unsigned pos, int value);
2325 __isl_give isl_set *isl_set_fix_val(
2326 __isl_take isl_set *set,
2327 enum isl_dim_type type, unsigned pos,
2328 __isl_take isl_val *v);
2329 __isl_give isl_basic_map *isl_basic_map_fix_si(
2330 __isl_take isl_basic_map *bmap,
2331 enum isl_dim_type type, unsigned pos, int value);
2332 __isl_give isl_basic_map *isl_basic_map_fix_val(
2333 __isl_take isl_basic_map *bmap,
2334 enum isl_dim_type type, unsigned pos,
2335 __isl_take isl_val *v);
2336 __isl_give isl_map *isl_map_fix(__isl_take isl_map *map,
2337 enum isl_dim_type type, unsigned pos,
2339 __isl_give isl_map *isl_map_fix_si(__isl_take isl_map *map,
2340 enum isl_dim_type type, unsigned pos, int value);
2341 __isl_give isl_map *isl_map_fix_val(
2342 __isl_take isl_map *map,
2343 enum isl_dim_type type, unsigned pos,
2344 __isl_take isl_val *v);
2346 Intersect the set or relation with the hyperplane where the given
2347 dimension has the fixed given value.
2349 __isl_give isl_basic_map *isl_basic_map_lower_bound_si(
2350 __isl_take isl_basic_map *bmap,
2351 enum isl_dim_type type, unsigned pos, int value);
2352 __isl_give isl_basic_map *isl_basic_map_upper_bound_si(
2353 __isl_take isl_basic_map *bmap,
2354 enum isl_dim_type type, unsigned pos, int value);
2355 __isl_give isl_set *isl_set_lower_bound(
2356 __isl_take isl_set *set,
2357 enum isl_dim_type type, unsigned pos,
2359 __isl_give isl_set *isl_set_lower_bound_si(
2360 __isl_take isl_set *set,
2361 enum isl_dim_type type, unsigned pos, int value);
2362 __isl_give isl_set *isl_set_lower_bound_val(
2363 __isl_take isl_set *set,
2364 enum isl_dim_type type, unsigned pos,
2365 __isl_take isl_val *value);
2366 __isl_give isl_map *isl_map_lower_bound_si(
2367 __isl_take isl_map *map,
2368 enum isl_dim_type type, unsigned pos, int value);
2369 __isl_give isl_set *isl_set_upper_bound(
2370 __isl_take isl_set *set,
2371 enum isl_dim_type type, unsigned pos,
2373 __isl_give isl_set *isl_set_upper_bound_si(
2374 __isl_take isl_set *set,
2375 enum isl_dim_type type, unsigned pos, int value);
2376 __isl_give isl_set *isl_set_upper_bound_val(
2377 __isl_take isl_set *set,
2378 enum isl_dim_type type, unsigned pos,
2379 __isl_take isl_val *value);
2380 __isl_give isl_map *isl_map_upper_bound_si(
2381 __isl_take isl_map *map,
2382 enum isl_dim_type type, unsigned pos, int value);
2384 Intersect the set or relation with the half-space where the given
2385 dimension has a value bounded by the fixed given integer value.
2387 __isl_give isl_set *isl_set_equate(__isl_take isl_set *set,
2388 enum isl_dim_type type1, int pos1,
2389 enum isl_dim_type type2, int pos2);
2390 __isl_give isl_basic_map *isl_basic_map_equate(
2391 __isl_take isl_basic_map *bmap,
2392 enum isl_dim_type type1, int pos1,
2393 enum isl_dim_type type2, int pos2);
2394 __isl_give isl_map *isl_map_equate(__isl_take isl_map *map,
2395 enum isl_dim_type type1, int pos1,
2396 enum isl_dim_type type2, int pos2);
2398 Intersect the set or relation with the hyperplane where the given
2399 dimensions are equal to each other.
2401 __isl_give isl_map *isl_map_oppose(__isl_take isl_map *map,
2402 enum isl_dim_type type1, int pos1,
2403 enum isl_dim_type type2, int pos2);
2405 Intersect the relation with the hyperplane where the given
2406 dimensions have opposite values.
2408 __isl_give isl_basic_map *isl_basic_map_order_ge(
2409 __isl_take isl_basic_map *bmap,
2410 enum isl_dim_type type1, int pos1,
2411 enum isl_dim_type type2, int pos2);
2412 __isl_give isl_map *isl_map_order_lt(__isl_take isl_map *map,
2413 enum isl_dim_type type1, int pos1,
2414 enum isl_dim_type type2, int pos2);
2415 __isl_give isl_basic_map *isl_basic_map_order_gt(
2416 __isl_take isl_basic_map *bmap,
2417 enum isl_dim_type type1, int pos1,
2418 enum isl_dim_type type2, int pos2);
2419 __isl_give isl_map *isl_map_order_gt(__isl_take isl_map *map,
2420 enum isl_dim_type type1, int pos1,
2421 enum isl_dim_type type2, int pos2);
2423 Intersect the relation with the half-space where the given
2424 dimensions satisfy the given ordering.
2428 __isl_give isl_map *isl_set_identity(
2429 __isl_take isl_set *set);
2430 __isl_give isl_union_map *isl_union_set_identity(
2431 __isl_take isl_union_set *uset);
2433 Construct an identity relation on the given (union) set.
2437 __isl_give isl_basic_set *isl_basic_map_deltas(
2438 __isl_take isl_basic_map *bmap);
2439 __isl_give isl_set *isl_map_deltas(__isl_take isl_map *map);
2440 __isl_give isl_union_set *isl_union_map_deltas(
2441 __isl_take isl_union_map *umap);
2443 These functions return a (basic) set containing the differences
2444 between image elements and corresponding domain elements in the input.
2446 __isl_give isl_basic_map *isl_basic_map_deltas_map(
2447 __isl_take isl_basic_map *bmap);
2448 __isl_give isl_map *isl_map_deltas_map(
2449 __isl_take isl_map *map);
2450 __isl_give isl_union_map *isl_union_map_deltas_map(
2451 __isl_take isl_union_map *umap);
2453 The functions above construct a (basic, regular or union) relation
2454 that maps (a wrapped version of) the input relation to its delta set.
2458 Simplify the representation of a set or relation by trying
2459 to combine pairs of basic sets or relations into a single
2460 basic set or relation.
2462 __isl_give isl_set *isl_set_coalesce(__isl_take isl_set *set);
2463 __isl_give isl_map *isl_map_coalesce(__isl_take isl_map *map);
2464 __isl_give isl_union_set *isl_union_set_coalesce(
2465 __isl_take isl_union_set *uset);
2466 __isl_give isl_union_map *isl_union_map_coalesce(
2467 __isl_take isl_union_map *umap);
2469 One of the methods for combining pairs of basic sets or relations
2470 can result in coefficients that are much larger than those that appear
2471 in the constraints of the input. By default, the coefficients are
2472 not allowed to grow larger, but this can be changed by unsetting
2473 the following option.
2475 int isl_options_set_coalesce_bounded_wrapping(
2476 isl_ctx *ctx, int val);
2477 int isl_options_get_coalesce_bounded_wrapping(
2480 =item * Detecting equalities
2482 __isl_give isl_basic_set *isl_basic_set_detect_equalities(
2483 __isl_take isl_basic_set *bset);
2484 __isl_give isl_basic_map *isl_basic_map_detect_equalities(
2485 __isl_take isl_basic_map *bmap);
2486 __isl_give isl_set *isl_set_detect_equalities(
2487 __isl_take isl_set *set);
2488 __isl_give isl_map *isl_map_detect_equalities(
2489 __isl_take isl_map *map);
2490 __isl_give isl_union_set *isl_union_set_detect_equalities(
2491 __isl_take isl_union_set *uset);
2492 __isl_give isl_union_map *isl_union_map_detect_equalities(
2493 __isl_take isl_union_map *umap);
2495 Simplify the representation of a set or relation by detecting implicit
2498 =item * Removing redundant constraints
2500 __isl_give isl_basic_set *isl_basic_set_remove_redundancies(
2501 __isl_take isl_basic_set *bset);
2502 __isl_give isl_set *isl_set_remove_redundancies(
2503 __isl_take isl_set *set);
2504 __isl_give isl_basic_map *isl_basic_map_remove_redundancies(
2505 __isl_take isl_basic_map *bmap);
2506 __isl_give isl_map *isl_map_remove_redundancies(
2507 __isl_take isl_map *map);
2511 __isl_give isl_basic_set *isl_set_convex_hull(
2512 __isl_take isl_set *set);
2513 __isl_give isl_basic_map *isl_map_convex_hull(
2514 __isl_take isl_map *map);
2516 If the input set or relation has any existentially quantified
2517 variables, then the result of these operations is currently undefined.
2521 __isl_give isl_basic_set *
2522 isl_set_unshifted_simple_hull(
2523 __isl_take isl_set *set);
2524 __isl_give isl_basic_map *
2525 isl_map_unshifted_simple_hull(
2526 __isl_take isl_map *map);
2527 __isl_give isl_basic_set *isl_set_simple_hull(
2528 __isl_take isl_set *set);
2529 __isl_give isl_basic_map *isl_map_simple_hull(
2530 __isl_take isl_map *map);
2531 __isl_give isl_union_map *isl_union_map_simple_hull(
2532 __isl_take isl_union_map *umap);
2534 These functions compute a single basic set or relation
2535 that contains the whole input set or relation.
2536 In particular, the output is described by translates
2537 of the constraints describing the basic sets or relations in the input.
2538 In case of C<isl_set_unshifted_simple_hull>, only the original
2539 constraints are used, without any translation.
2543 (See \autoref{s:simple hull}.)
2549 __isl_give isl_basic_set *isl_basic_set_affine_hull(
2550 __isl_take isl_basic_set *bset);
2551 __isl_give isl_basic_set *isl_set_affine_hull(
2552 __isl_take isl_set *set);
2553 __isl_give isl_union_set *isl_union_set_affine_hull(
2554 __isl_take isl_union_set *uset);
2555 __isl_give isl_basic_map *isl_basic_map_affine_hull(
2556 __isl_take isl_basic_map *bmap);
2557 __isl_give isl_basic_map *isl_map_affine_hull(
2558 __isl_take isl_map *map);
2559 __isl_give isl_union_map *isl_union_map_affine_hull(
2560 __isl_take isl_union_map *umap);
2562 In case of union sets and relations, the affine hull is computed
2565 =item * Polyhedral hull
2567 __isl_give isl_basic_set *isl_set_polyhedral_hull(
2568 __isl_take isl_set *set);
2569 __isl_give isl_basic_map *isl_map_polyhedral_hull(
2570 __isl_take isl_map *map);
2571 __isl_give isl_union_set *isl_union_set_polyhedral_hull(
2572 __isl_take isl_union_set *uset);
2573 __isl_give isl_union_map *isl_union_map_polyhedral_hull(
2574 __isl_take isl_union_map *umap);
2576 These functions compute a single basic set or relation
2577 not involving any existentially quantified variables
2578 that contains the whole input set or relation.
2579 In case of union sets and relations, the polyhedral hull is computed
2582 =item * Other approximations
2584 __isl_give isl_basic_set *
2585 isl_basic_set_drop_constraints_involving_dims(
2586 __isl_take isl_basic_set *bset,
2587 enum isl_dim_type type,
2588 unsigned first, unsigned n);
2589 __isl_give isl_basic_map *
2590 isl_basic_map_drop_constraints_involving_dims(
2591 __isl_take isl_basic_map *bmap,
2592 enum isl_dim_type type,
2593 unsigned first, unsigned n);
2594 __isl_give isl_basic_set *
2595 isl_basic_set_drop_constraints_not_involving_dims(
2596 __isl_take isl_basic_set *bset,
2597 enum isl_dim_type type,
2598 unsigned first, unsigned n);
2599 __isl_give isl_set *
2600 isl_set_drop_constraints_involving_dims(
2601 __isl_take isl_set *set,
2602 enum isl_dim_type type,
2603 unsigned first, unsigned n);
2604 __isl_give isl_map *
2605 isl_map_drop_constraints_involving_dims(
2606 __isl_take isl_map *map,
2607 enum isl_dim_type type,
2608 unsigned first, unsigned n);
2610 These functions drop any constraints (not) involving the specified dimensions.
2611 Note that the result depends on the representation of the input.
2615 __isl_give isl_basic_set *isl_basic_set_sample(
2616 __isl_take isl_basic_set *bset);
2617 __isl_give isl_basic_set *isl_set_sample(
2618 __isl_take isl_set *set);
2619 __isl_give isl_basic_map *isl_basic_map_sample(
2620 __isl_take isl_basic_map *bmap);
2621 __isl_give isl_basic_map *isl_map_sample(
2622 __isl_take isl_map *map);
2624 If the input (basic) set or relation is non-empty, then return
2625 a singleton subset of the input. Otherwise, return an empty set.
2627 =item * Optimization
2629 #include <isl/ilp.h>
2630 enum isl_lp_result isl_basic_set_max(
2631 __isl_keep isl_basic_set *bset,
2632 __isl_keep isl_aff *obj, isl_int *opt)
2633 __isl_give isl_val *isl_basic_set_max_val(
2634 __isl_keep isl_basic_set *bset,
2635 __isl_keep isl_aff *obj);
2636 enum isl_lp_result isl_set_min(__isl_keep isl_set *set,
2637 __isl_keep isl_aff *obj, isl_int *opt);
2638 __isl_give isl_val *isl_set_min_val(
2639 __isl_keep isl_set *set,
2640 __isl_keep isl_aff *obj);
2641 enum isl_lp_result isl_set_max(__isl_keep isl_set *set,
2642 __isl_keep isl_aff *obj, isl_int *opt);
2643 __isl_give isl_val *isl_set_max_val(
2644 __isl_keep isl_set *set,
2645 __isl_keep isl_aff *obj);
2647 Compute the minimum or maximum of the integer affine expression C<obj>
2648 over the points in C<set>, returning the result in C<opt>.
2649 The return value may be one of C<isl_lp_error>,
2650 C<isl_lp_ok>, C<isl_lp_unbounded> or C<isl_lp_empty>, in case of
2651 an C<isl_lp_result>. If the result is an C<isl_val> then
2652 the result is C<NULL> in case of an error, the optimal value in case
2653 there is one, negative infinity or infinity if the problem is unbounded and
2654 NaN if the problem is empty.
2656 =item * Parametric optimization
2658 __isl_give isl_pw_aff *isl_set_dim_min(
2659 __isl_take isl_set *set, int pos);
2660 __isl_give isl_pw_aff *isl_set_dim_max(
2661 __isl_take isl_set *set, int pos);
2662 __isl_give isl_pw_aff *isl_map_dim_max(
2663 __isl_take isl_map *map, int pos);
2665 Compute the minimum or maximum of the given set or output dimension
2666 as a function of the parameters (and input dimensions), but independently
2667 of the other set or output dimensions.
2668 For lexicographic optimization, see L<"Lexicographic Optimization">.
2672 The following functions compute either the set of (rational) coefficient
2673 values of valid constraints for the given set or the set of (rational)
2674 values satisfying the constraints with coefficients from the given set.
2675 Internally, these two sets of functions perform essentially the
2676 same operations, except that the set of coefficients is assumed to
2677 be a cone, while the set of values may be any polyhedron.
2678 The current implementation is based on the Farkas lemma and
2679 Fourier-Motzkin elimination, but this may change or be made optional
2680 in future. In particular, future implementations may use different
2681 dualization algorithms or skip the elimination step.
2683 __isl_give isl_basic_set *isl_basic_set_coefficients(
2684 __isl_take isl_basic_set *bset);
2685 __isl_give isl_basic_set *isl_set_coefficients(
2686 __isl_take isl_set *set);
2687 __isl_give isl_union_set *isl_union_set_coefficients(
2688 __isl_take isl_union_set *bset);
2689 __isl_give isl_basic_set *isl_basic_set_solutions(
2690 __isl_take isl_basic_set *bset);
2691 __isl_give isl_basic_set *isl_set_solutions(
2692 __isl_take isl_set *set);
2693 __isl_give isl_union_set *isl_union_set_solutions(
2694 __isl_take isl_union_set *bset);
2698 __isl_give isl_map *isl_map_fixed_power(
2699 __isl_take isl_map *map, isl_int exp);
2700 __isl_give isl_map *isl_map_fixed_power_val(
2701 __isl_take isl_map *map,
2702 __isl_take isl_val *exp);
2703 __isl_give isl_union_map *isl_union_map_fixed_power(
2704 __isl_take isl_union_map *umap, isl_int exp);
2705 __isl_give isl_union_map *
2706 isl_union_map_fixed_power_val(
2707 __isl_take isl_union_map *umap,
2708 __isl_take isl_val *exp);
2710 Compute the given power of C<map>, where C<exp> is assumed to be non-zero.
2711 If the exponent C<exp> is negative, then the -C<exp> th power of the inverse
2712 of C<map> is computed.
2714 __isl_give isl_map *isl_map_power(__isl_take isl_map *map,
2716 __isl_give isl_union_map *isl_union_map_power(
2717 __isl_take isl_union_map *umap, int *exact);
2719 Compute a parametric representation for all positive powers I<k> of C<map>.
2720 The result maps I<k> to a nested relation corresponding to the
2721 I<k>th power of C<map>.
2722 The result may be an overapproximation. If the result is known to be exact,
2723 then C<*exact> is set to C<1>.
2725 =item * Transitive closure
2727 __isl_give isl_map *isl_map_transitive_closure(
2728 __isl_take isl_map *map, int *exact);
2729 __isl_give isl_union_map *isl_union_map_transitive_closure(
2730 __isl_take isl_union_map *umap, int *exact);
2732 Compute the transitive closure of C<map>.
2733 The result may be an overapproximation. If the result is known to be exact,
2734 then C<*exact> is set to C<1>.
2736 =item * Reaching path lengths
2738 __isl_give isl_map *isl_map_reaching_path_lengths(
2739 __isl_take isl_map *map, int *exact);
2741 Compute a relation that maps each element in the range of C<map>
2742 to the lengths of all paths composed of edges in C<map> that
2743 end up in the given element.
2744 The result may be an overapproximation. If the result is known to be exact,
2745 then C<*exact> is set to C<1>.
2746 To compute the I<maximal> path length, the resulting relation
2747 should be postprocessed by C<isl_map_lexmax>.
2748 In particular, if the input relation is a dependence relation
2749 (mapping sources to sinks), then the maximal path length corresponds
2750 to the free schedule.
2751 Note, however, that C<isl_map_lexmax> expects the maximum to be
2752 finite, so if the path lengths are unbounded (possibly due to
2753 the overapproximation), then you will get an error message.
2757 __isl_give isl_basic_set *isl_basic_map_wrap(
2758 __isl_take isl_basic_map *bmap);
2759 __isl_give isl_set *isl_map_wrap(
2760 __isl_take isl_map *map);
2761 __isl_give isl_union_set *isl_union_map_wrap(
2762 __isl_take isl_union_map *umap);
2763 __isl_give isl_basic_map *isl_basic_set_unwrap(
2764 __isl_take isl_basic_set *bset);
2765 __isl_give isl_map *isl_set_unwrap(
2766 __isl_take isl_set *set);
2767 __isl_give isl_union_map *isl_union_set_unwrap(
2768 __isl_take isl_union_set *uset);
2772 Remove any internal structure of domain (and range) of the given
2773 set or relation. If there is any such internal structure in the input,
2774 then the name of the space is also removed.
2776 __isl_give isl_basic_set *isl_basic_set_flatten(
2777 __isl_take isl_basic_set *bset);
2778 __isl_give isl_set *isl_set_flatten(
2779 __isl_take isl_set *set);
2780 __isl_give isl_basic_map *isl_basic_map_flatten_domain(
2781 __isl_take isl_basic_map *bmap);
2782 __isl_give isl_basic_map *isl_basic_map_flatten_range(
2783 __isl_take isl_basic_map *bmap);
2784 __isl_give isl_map *isl_map_flatten_range(
2785 __isl_take isl_map *map);
2786 __isl_give isl_map *isl_map_flatten_domain(
2787 __isl_take isl_map *map);
2788 __isl_give isl_basic_map *isl_basic_map_flatten(
2789 __isl_take isl_basic_map *bmap);
2790 __isl_give isl_map *isl_map_flatten(
2791 __isl_take isl_map *map);
2793 __isl_give isl_map *isl_set_flatten_map(
2794 __isl_take isl_set *set);
2796 The function above constructs a relation
2797 that maps the input set to a flattened version of the set.
2801 Lift the input set to a space with extra dimensions corresponding
2802 to the existentially quantified variables in the input.
2803 In particular, the result lives in a wrapped map where the domain
2804 is the original space and the range corresponds to the original
2805 existentially quantified variables.
2807 __isl_give isl_basic_set *isl_basic_set_lift(
2808 __isl_take isl_basic_set *bset);
2809 __isl_give isl_set *isl_set_lift(
2810 __isl_take isl_set *set);
2811 __isl_give isl_union_set *isl_union_set_lift(
2812 __isl_take isl_union_set *uset);
2814 Given a local space that contains the existentially quantified
2815 variables of a set, a basic relation that, when applied to
2816 a basic set, has essentially the same effect as C<isl_basic_set_lift>,
2817 can be constructed using the following function.
2819 #include <isl/local_space.h>
2820 __isl_give isl_basic_map *isl_local_space_lifting(
2821 __isl_take isl_local_space *ls);
2823 =item * Internal Product
2825 __isl_give isl_basic_map *isl_basic_map_zip(
2826 __isl_take isl_basic_map *bmap);
2827 __isl_give isl_map *isl_map_zip(
2828 __isl_take isl_map *map);
2829 __isl_give isl_union_map *isl_union_map_zip(
2830 __isl_take isl_union_map *umap);
2832 Given a relation with nested relations for domain and range,
2833 interchange the range of the domain with the domain of the range.
2837 __isl_give isl_basic_map *isl_basic_map_curry(
2838 __isl_take isl_basic_map *bmap);
2839 __isl_give isl_basic_map *isl_basic_map_uncurry(
2840 __isl_take isl_basic_map *bmap);
2841 __isl_give isl_map *isl_map_curry(
2842 __isl_take isl_map *map);
2843 __isl_give isl_map *isl_map_uncurry(
2844 __isl_take isl_map *map);
2845 __isl_give isl_union_map *isl_union_map_curry(
2846 __isl_take isl_union_map *umap);
2847 __isl_give isl_union_map *isl_union_map_uncurry(
2848 __isl_take isl_union_map *umap);
2850 Given a relation with a nested relation for domain,
2851 the C<curry> functions
2852 move the range of the nested relation out of the domain
2853 and use it as the domain of a nested relation in the range,
2854 with the original range as range of this nested relation.
2855 The C<uncurry> functions perform the inverse operation.
2857 =item * Aligning parameters
2859 __isl_give isl_basic_set *isl_basic_set_align_params(
2860 __isl_take isl_basic_set *bset,
2861 __isl_take isl_space *model);
2862 __isl_give isl_set *isl_set_align_params(
2863 __isl_take isl_set *set,
2864 __isl_take isl_space *model);
2865 __isl_give isl_basic_map *isl_basic_map_align_params(
2866 __isl_take isl_basic_map *bmap,
2867 __isl_take isl_space *model);
2868 __isl_give isl_map *isl_map_align_params(
2869 __isl_take isl_map *map,
2870 __isl_take isl_space *model);
2872 Change the order of the parameters of the given set or relation
2873 such that the first parameters match those of C<model>.
2874 This may involve the introduction of extra parameters.
2875 All parameters need to be named.
2877 =item * Dimension manipulation
2879 __isl_give isl_basic_set *isl_basic_set_add_dims(
2880 __isl_take isl_basic_set *bset,
2881 enum isl_dim_type type, unsigned n);
2882 __isl_give isl_set *isl_set_add_dims(
2883 __isl_take isl_set *set,
2884 enum isl_dim_type type, unsigned n);
2885 __isl_give isl_map *isl_map_add_dims(
2886 __isl_take isl_map *map,
2887 enum isl_dim_type type, unsigned n);
2888 __isl_give isl_basic_set *isl_basic_set_insert_dims(
2889 __isl_take isl_basic_set *bset,
2890 enum isl_dim_type type, unsigned pos,
2892 __isl_give isl_basic_map *isl_basic_map_insert_dims(
2893 __isl_take isl_basic_map *bmap,
2894 enum isl_dim_type type, unsigned pos,
2896 __isl_give isl_set *isl_set_insert_dims(
2897 __isl_take isl_set *set,
2898 enum isl_dim_type type, unsigned pos, unsigned n);
2899 __isl_give isl_map *isl_map_insert_dims(
2900 __isl_take isl_map *map,
2901 enum isl_dim_type type, unsigned pos, unsigned n);
2902 __isl_give isl_basic_set *isl_basic_set_move_dims(
2903 __isl_take isl_basic_set *bset,
2904 enum isl_dim_type dst_type, unsigned dst_pos,
2905 enum isl_dim_type src_type, unsigned src_pos,
2907 __isl_give isl_basic_map *isl_basic_map_move_dims(
2908 __isl_take isl_basic_map *bmap,
2909 enum isl_dim_type dst_type, unsigned dst_pos,
2910 enum isl_dim_type src_type, unsigned src_pos,
2912 __isl_give isl_set *isl_set_move_dims(
2913 __isl_take isl_set *set,
2914 enum isl_dim_type dst_type, unsigned dst_pos,
2915 enum isl_dim_type src_type, unsigned src_pos,
2917 __isl_give isl_map *isl_map_move_dims(
2918 __isl_take isl_map *map,
2919 enum isl_dim_type dst_type, unsigned dst_pos,
2920 enum isl_dim_type src_type, unsigned src_pos,
2923 It is usually not advisable to directly change the (input or output)
2924 space of a set or a relation as this removes the name and the internal
2925 structure of the space. However, the above functions can be useful
2926 to add new parameters, assuming
2927 C<isl_set_align_params> and C<isl_map_align_params>
2932 =head2 Binary Operations
2934 The two arguments of a binary operation not only need to live
2935 in the same C<isl_ctx>, they currently also need to have
2936 the same (number of) parameters.
2938 =head3 Basic Operations
2942 =item * Intersection
2944 __isl_give isl_basic_set *isl_basic_set_intersect_params(
2945 __isl_take isl_basic_set *bset1,
2946 __isl_take isl_basic_set *bset2);
2947 __isl_give isl_basic_set *isl_basic_set_intersect(
2948 __isl_take isl_basic_set *bset1,
2949 __isl_take isl_basic_set *bset2);
2950 __isl_give isl_set *isl_set_intersect_params(
2951 __isl_take isl_set *set,
2952 __isl_take isl_set *params);
2953 __isl_give isl_set *isl_set_intersect(
2954 __isl_take isl_set *set1,
2955 __isl_take isl_set *set2);
2956 __isl_give isl_union_set *isl_union_set_intersect_params(
2957 __isl_take isl_union_set *uset,
2958 __isl_take isl_set *set);
2959 __isl_give isl_union_map *isl_union_map_intersect_params(
2960 __isl_take isl_union_map *umap,
2961 __isl_take isl_set *set);
2962 __isl_give isl_union_set *isl_union_set_intersect(
2963 __isl_take isl_union_set *uset1,
2964 __isl_take isl_union_set *uset2);
2965 __isl_give isl_basic_map *isl_basic_map_intersect_domain(
2966 __isl_take isl_basic_map *bmap,
2967 __isl_take isl_basic_set *bset);
2968 __isl_give isl_basic_map *isl_basic_map_intersect_range(
2969 __isl_take isl_basic_map *bmap,
2970 __isl_take isl_basic_set *bset);
2971 __isl_give isl_basic_map *isl_basic_map_intersect(
2972 __isl_take isl_basic_map *bmap1,
2973 __isl_take isl_basic_map *bmap2);
2974 __isl_give isl_map *isl_map_intersect_params(
2975 __isl_take isl_map *map,
2976 __isl_take isl_set *params);
2977 __isl_give isl_map *isl_map_intersect_domain(
2978 __isl_take isl_map *map,
2979 __isl_take isl_set *set);
2980 __isl_give isl_map *isl_map_intersect_range(
2981 __isl_take isl_map *map,
2982 __isl_take isl_set *set);
2983 __isl_give isl_map *isl_map_intersect(
2984 __isl_take isl_map *map1,
2985 __isl_take isl_map *map2);
2986 __isl_give isl_union_map *isl_union_map_intersect_domain(
2987 __isl_take isl_union_map *umap,
2988 __isl_take isl_union_set *uset);
2989 __isl_give isl_union_map *isl_union_map_intersect_range(
2990 __isl_take isl_union_map *umap,
2991 __isl_take isl_union_set *uset);
2992 __isl_give isl_union_map *isl_union_map_intersect(
2993 __isl_take isl_union_map *umap1,
2994 __isl_take isl_union_map *umap2);
2996 The second argument to the C<_params> functions needs to be
2997 a parametric (basic) set. For the other functions, a parametric set
2998 for either argument is only allowed if the other argument is
2999 a parametric set as well.
3003 __isl_give isl_set *isl_basic_set_union(
3004 __isl_take isl_basic_set *bset1,
3005 __isl_take isl_basic_set *bset2);
3006 __isl_give isl_map *isl_basic_map_union(
3007 __isl_take isl_basic_map *bmap1,
3008 __isl_take isl_basic_map *bmap2);
3009 __isl_give isl_set *isl_set_union(
3010 __isl_take isl_set *set1,
3011 __isl_take isl_set *set2);
3012 __isl_give isl_map *isl_map_union(
3013 __isl_take isl_map *map1,
3014 __isl_take isl_map *map2);
3015 __isl_give isl_union_set *isl_union_set_union(
3016 __isl_take isl_union_set *uset1,
3017 __isl_take isl_union_set *uset2);
3018 __isl_give isl_union_map *isl_union_map_union(
3019 __isl_take isl_union_map *umap1,
3020 __isl_take isl_union_map *umap2);
3022 =item * Set difference
3024 __isl_give isl_set *isl_set_subtract(
3025 __isl_take isl_set *set1,
3026 __isl_take isl_set *set2);
3027 __isl_give isl_map *isl_map_subtract(
3028 __isl_take isl_map *map1,
3029 __isl_take isl_map *map2);
3030 __isl_give isl_map *isl_map_subtract_domain(
3031 __isl_take isl_map *map,
3032 __isl_take isl_set *dom);
3033 __isl_give isl_map *isl_map_subtract_range(
3034 __isl_take isl_map *map,
3035 __isl_take isl_set *dom);
3036 __isl_give isl_union_set *isl_union_set_subtract(
3037 __isl_take isl_union_set *uset1,
3038 __isl_take isl_union_set *uset2);
3039 __isl_give isl_union_map *isl_union_map_subtract(
3040 __isl_take isl_union_map *umap1,
3041 __isl_take isl_union_map *umap2);
3042 __isl_give isl_union_map *isl_union_map_subtract_domain(
3043 __isl_take isl_union_map *umap,
3044 __isl_take isl_union_set *dom);
3045 __isl_give isl_union_map *isl_union_map_subtract_range(
3046 __isl_take isl_union_map *umap,
3047 __isl_take isl_union_set *dom);
3051 __isl_give isl_basic_set *isl_basic_set_apply(
3052 __isl_take isl_basic_set *bset,
3053 __isl_take isl_basic_map *bmap);
3054 __isl_give isl_set *isl_set_apply(
3055 __isl_take isl_set *set,
3056 __isl_take isl_map *map);
3057 __isl_give isl_union_set *isl_union_set_apply(
3058 __isl_take isl_union_set *uset,
3059 __isl_take isl_union_map *umap);
3060 __isl_give isl_basic_map *isl_basic_map_apply_domain(
3061 __isl_take isl_basic_map *bmap1,
3062 __isl_take isl_basic_map *bmap2);
3063 __isl_give isl_basic_map *isl_basic_map_apply_range(
3064 __isl_take isl_basic_map *bmap1,
3065 __isl_take isl_basic_map *bmap2);
3066 __isl_give isl_map *isl_map_apply_domain(
3067 __isl_take isl_map *map1,
3068 __isl_take isl_map *map2);
3069 __isl_give isl_union_map *isl_union_map_apply_domain(
3070 __isl_take isl_union_map *umap1,
3071 __isl_take isl_union_map *umap2);
3072 __isl_give isl_map *isl_map_apply_range(
3073 __isl_take isl_map *map1,
3074 __isl_take isl_map *map2);
3075 __isl_give isl_union_map *isl_union_map_apply_range(
3076 __isl_take isl_union_map *umap1,
3077 __isl_take isl_union_map *umap2);
3081 __isl_give isl_basic_set *
3082 isl_basic_set_preimage_multi_aff(
3083 __isl_take isl_basic_set *bset,
3084 __isl_take isl_multi_aff *ma);
3085 __isl_give isl_set *isl_set_preimage_multi_aff(
3086 __isl_take isl_set *set,
3087 __isl_take isl_multi_aff *ma);
3088 __isl_give isl_set *isl_set_preimage_pw_multi_aff(
3089 __isl_take isl_set *set,
3090 __isl_take isl_pw_multi_aff *pma);
3091 __isl_give isl_map *isl_map_preimage_domain_multi_aff(
3092 __isl_take isl_map *map,
3093 __isl_take isl_multi_aff *ma);
3094 __isl_give isl_union_map *
3095 isl_union_map_preimage_domain_multi_aff(
3096 __isl_take isl_union_map *umap,
3097 __isl_take isl_multi_aff *ma);
3099 These functions compute the preimage of the given set or map domain under
3100 the given function. In other words, the expression is plugged
3101 into the set description or into the domain of the map.
3102 Objects of types C<isl_multi_aff> and C<isl_pw_multi_aff> are described in
3103 L</"Piecewise Multiple Quasi Affine Expressions">.
3105 =item * Cartesian Product
3107 __isl_give isl_set *isl_set_product(
3108 __isl_take isl_set *set1,
3109 __isl_take isl_set *set2);
3110 __isl_give isl_union_set *isl_union_set_product(
3111 __isl_take isl_union_set *uset1,
3112 __isl_take isl_union_set *uset2);
3113 __isl_give isl_basic_map *isl_basic_map_domain_product(
3114 __isl_take isl_basic_map *bmap1,
3115 __isl_take isl_basic_map *bmap2);
3116 __isl_give isl_basic_map *isl_basic_map_range_product(
3117 __isl_take isl_basic_map *bmap1,
3118 __isl_take isl_basic_map *bmap2);
3119 __isl_give isl_basic_map *isl_basic_map_product(
3120 __isl_take isl_basic_map *bmap1,
3121 __isl_take isl_basic_map *bmap2);
3122 __isl_give isl_map *isl_map_domain_product(
3123 __isl_take isl_map *map1,
3124 __isl_take isl_map *map2);
3125 __isl_give isl_map *isl_map_range_product(
3126 __isl_take isl_map *map1,
3127 __isl_take isl_map *map2);
3128 __isl_give isl_union_map *isl_union_map_domain_product(
3129 __isl_take isl_union_map *umap1,
3130 __isl_take isl_union_map *umap2);
3131 __isl_give isl_union_map *isl_union_map_range_product(
3132 __isl_take isl_union_map *umap1,
3133 __isl_take isl_union_map *umap2);
3134 __isl_give isl_map *isl_map_product(
3135 __isl_take isl_map *map1,
3136 __isl_take isl_map *map2);
3137 __isl_give isl_union_map *isl_union_map_product(
3138 __isl_take isl_union_map *umap1,
3139 __isl_take isl_union_map *umap2);
3141 The above functions compute the cross product of the given
3142 sets or relations. The domains and ranges of the results
3143 are wrapped maps between domains and ranges of the inputs.
3144 To obtain a ``flat'' product, use the following functions
3147 __isl_give isl_basic_set *isl_basic_set_flat_product(
3148 __isl_take isl_basic_set *bset1,
3149 __isl_take isl_basic_set *bset2);
3150 __isl_give isl_set *isl_set_flat_product(
3151 __isl_take isl_set *set1,
3152 __isl_take isl_set *set2);
3153 __isl_give isl_basic_map *isl_basic_map_flat_range_product(
3154 __isl_take isl_basic_map *bmap1,
3155 __isl_take isl_basic_map *bmap2);
3156 __isl_give isl_map *isl_map_flat_domain_product(
3157 __isl_take isl_map *map1,
3158 __isl_take isl_map *map2);
3159 __isl_give isl_map *isl_map_flat_range_product(
3160 __isl_take isl_map *map1,
3161 __isl_take isl_map *map2);
3162 __isl_give isl_union_map *isl_union_map_flat_range_product(
3163 __isl_take isl_union_map *umap1,
3164 __isl_take isl_union_map *umap2);
3165 __isl_give isl_basic_map *isl_basic_map_flat_product(
3166 __isl_take isl_basic_map *bmap1,
3167 __isl_take isl_basic_map *bmap2);
3168 __isl_give isl_map *isl_map_flat_product(
3169 __isl_take isl_map *map1,
3170 __isl_take isl_map *map2);
3172 =item * Simplification
3174 __isl_give isl_basic_set *isl_basic_set_gist(
3175 __isl_take isl_basic_set *bset,
3176 __isl_take isl_basic_set *context);
3177 __isl_give isl_set *isl_set_gist(__isl_take isl_set *set,
3178 __isl_take isl_set *context);
3179 __isl_give isl_set *isl_set_gist_params(
3180 __isl_take isl_set *set,
3181 __isl_take isl_set *context);
3182 __isl_give isl_union_set *isl_union_set_gist(
3183 __isl_take isl_union_set *uset,
3184 __isl_take isl_union_set *context);
3185 __isl_give isl_union_set *isl_union_set_gist_params(
3186 __isl_take isl_union_set *uset,
3187 __isl_take isl_set *set);
3188 __isl_give isl_basic_map *isl_basic_map_gist(
3189 __isl_take isl_basic_map *bmap,
3190 __isl_take isl_basic_map *context);
3191 __isl_give isl_map *isl_map_gist(__isl_take isl_map *map,
3192 __isl_take isl_map *context);
3193 __isl_give isl_map *isl_map_gist_params(
3194 __isl_take isl_map *map,
3195 __isl_take isl_set *context);
3196 __isl_give isl_map *isl_map_gist_domain(
3197 __isl_take isl_map *map,
3198 __isl_take isl_set *context);
3199 __isl_give isl_map *isl_map_gist_range(
3200 __isl_take isl_map *map,
3201 __isl_take isl_set *context);
3202 __isl_give isl_union_map *isl_union_map_gist(
3203 __isl_take isl_union_map *umap,
3204 __isl_take isl_union_map *context);
3205 __isl_give isl_union_map *isl_union_map_gist_params(
3206 __isl_take isl_union_map *umap,
3207 __isl_take isl_set *set);
3208 __isl_give isl_union_map *isl_union_map_gist_domain(
3209 __isl_take isl_union_map *umap,
3210 __isl_take isl_union_set *uset);
3211 __isl_give isl_union_map *isl_union_map_gist_range(
3212 __isl_take isl_union_map *umap,
3213 __isl_take isl_union_set *uset);
3215 The gist operation returns a set or relation that has the
3216 same intersection with the context as the input set or relation.
3217 Any implicit equality in the intersection is made explicit in the result,
3218 while all inequalities that are redundant with respect to the intersection
3220 In case of union sets and relations, the gist operation is performed
3225 =head3 Lexicographic Optimization
3227 Given a (basic) set C<set> (or C<bset>) and a zero-dimensional domain C<dom>,
3228 the following functions
3229 compute a set that contains the lexicographic minimum or maximum
3230 of the elements in C<set> (or C<bset>) for those values of the parameters
3231 that satisfy C<dom>.
3232 If C<empty> is not C<NULL>, then C<*empty> is assigned a set
3233 that contains the parameter values in C<dom> for which C<set> (or C<bset>)
3235 In other words, the union of the parameter values
3236 for which the result is non-empty and of C<*empty>
3239 __isl_give isl_set *isl_basic_set_partial_lexmin(
3240 __isl_take isl_basic_set *bset,
3241 __isl_take isl_basic_set *dom,
3242 __isl_give isl_set **empty);
3243 __isl_give isl_set *isl_basic_set_partial_lexmax(
3244 __isl_take isl_basic_set *bset,
3245 __isl_take isl_basic_set *dom,
3246 __isl_give isl_set **empty);
3247 __isl_give isl_set *isl_set_partial_lexmin(
3248 __isl_take isl_set *set, __isl_take isl_set *dom,
3249 __isl_give isl_set **empty);
3250 __isl_give isl_set *isl_set_partial_lexmax(
3251 __isl_take isl_set *set, __isl_take isl_set *dom,
3252 __isl_give isl_set **empty);
3254 Given a (basic) set C<set> (or C<bset>), the following functions simply
3255 return a set containing the lexicographic minimum or maximum
3256 of the elements in C<set> (or C<bset>).
3257 In case of union sets, the optimum is computed per space.
3259 __isl_give isl_set *isl_basic_set_lexmin(
3260 __isl_take isl_basic_set *bset);
3261 __isl_give isl_set *isl_basic_set_lexmax(
3262 __isl_take isl_basic_set *bset);
3263 __isl_give isl_set *isl_set_lexmin(
3264 __isl_take isl_set *set);
3265 __isl_give isl_set *isl_set_lexmax(
3266 __isl_take isl_set *set);
3267 __isl_give isl_union_set *isl_union_set_lexmin(
3268 __isl_take isl_union_set *uset);
3269 __isl_give isl_union_set *isl_union_set_lexmax(
3270 __isl_take isl_union_set *uset);
3272 Given a (basic) relation C<map> (or C<bmap>) and a domain C<dom>,
3273 the following functions
3274 compute a relation that maps each element of C<dom>
3275 to the single lexicographic minimum or maximum
3276 of the elements that are associated to that same
3277 element in C<map> (or C<bmap>).
3278 If C<empty> is not C<NULL>, then C<*empty> is assigned a set
3279 that contains the elements in C<dom> that do not map
3280 to any elements in C<map> (or C<bmap>).
3281 In other words, the union of the domain of the result and of C<*empty>
3284 __isl_give isl_map *isl_basic_map_partial_lexmax(
3285 __isl_take isl_basic_map *bmap,
3286 __isl_take isl_basic_set *dom,
3287 __isl_give isl_set **empty);
3288 __isl_give isl_map *isl_basic_map_partial_lexmin(
3289 __isl_take isl_basic_map *bmap,
3290 __isl_take isl_basic_set *dom,
3291 __isl_give isl_set **empty);
3292 __isl_give isl_map *isl_map_partial_lexmax(
3293 __isl_take isl_map *map, __isl_take isl_set *dom,
3294 __isl_give isl_set **empty);
3295 __isl_give isl_map *isl_map_partial_lexmin(
3296 __isl_take isl_map *map, __isl_take isl_set *dom,
3297 __isl_give isl_set **empty);
3299 Given a (basic) map C<map> (or C<bmap>), the following functions simply
3300 return a map mapping each element in the domain of
3301 C<map> (or C<bmap>) to the lexicographic minimum or maximum
3302 of all elements associated to that element.
3303 In case of union relations, the optimum is computed per space.
3305 __isl_give isl_map *isl_basic_map_lexmin(
3306 __isl_take isl_basic_map *bmap);
3307 __isl_give isl_map *isl_basic_map_lexmax(
3308 __isl_take isl_basic_map *bmap);
3309 __isl_give isl_map *isl_map_lexmin(
3310 __isl_take isl_map *map);
3311 __isl_give isl_map *isl_map_lexmax(
3312 __isl_take isl_map *map);
3313 __isl_give isl_union_map *isl_union_map_lexmin(
3314 __isl_take isl_union_map *umap);
3315 __isl_give isl_union_map *isl_union_map_lexmax(
3316 __isl_take isl_union_map *umap);
3318 The following functions return their result in the form of
3319 a piecewise multi-affine expression
3320 (See L<"Piecewise Multiple Quasi Affine Expressions">),
3321 but are otherwise equivalent to the corresponding functions
3322 returning a basic set or relation.
3324 __isl_give isl_pw_multi_aff *
3325 isl_basic_map_lexmin_pw_multi_aff(
3326 __isl_take isl_basic_map *bmap);
3327 __isl_give isl_pw_multi_aff *
3328 isl_basic_set_partial_lexmin_pw_multi_aff(
3329 __isl_take isl_basic_set *bset,
3330 __isl_take isl_basic_set *dom,
3331 __isl_give isl_set **empty);
3332 __isl_give isl_pw_multi_aff *
3333 isl_basic_set_partial_lexmax_pw_multi_aff(
3334 __isl_take isl_basic_set *bset,
3335 __isl_take isl_basic_set *dom,
3336 __isl_give isl_set **empty);
3337 __isl_give isl_pw_multi_aff *
3338 isl_basic_map_partial_lexmin_pw_multi_aff(
3339 __isl_take isl_basic_map *bmap,
3340 __isl_take isl_basic_set *dom,
3341 __isl_give isl_set **empty);
3342 __isl_give isl_pw_multi_aff *
3343 isl_basic_map_partial_lexmax_pw_multi_aff(
3344 __isl_take isl_basic_map *bmap,
3345 __isl_take isl_basic_set *dom,
3346 __isl_give isl_set **empty);
3347 __isl_give isl_pw_multi_aff *isl_set_lexmin_pw_multi_aff(
3348 __isl_take isl_set *set);
3349 __isl_give isl_pw_multi_aff *isl_set_lexmax_pw_multi_aff(
3350 __isl_take isl_set *set);
3351 __isl_give isl_pw_multi_aff *isl_map_lexmin_pw_multi_aff(
3352 __isl_take isl_map *map);
3353 __isl_give isl_pw_multi_aff *isl_map_lexmax_pw_multi_aff(
3354 __isl_take isl_map *map);
3358 Lists are defined over several element types, including
3359 C<isl_val>, C<isl_id>, C<isl_aff>, C<isl_pw_aff>, C<isl_constraint>,
3360 C<isl_basic_set>, C<isl_set>, C<isl_ast_expr> and C<isl_ast_node>.
3361 Here we take lists of C<isl_set>s as an example.
3362 Lists can be created, copied, modified and freed using the following functions.
3364 #include <isl/list.h>
3365 __isl_give isl_set_list *isl_set_list_from_set(
3366 __isl_take isl_set *el);
3367 __isl_give isl_set_list *isl_set_list_alloc(
3368 isl_ctx *ctx, int n);
3369 __isl_give isl_set_list *isl_set_list_copy(
3370 __isl_keep isl_set_list *list);
3371 __isl_give isl_set_list *isl_set_list_insert(
3372 __isl_take isl_set_list *list, unsigned pos,
3373 __isl_take isl_set *el);
3374 __isl_give isl_set_list *isl_set_list_add(
3375 __isl_take isl_set_list *list,
3376 __isl_take isl_set *el);
3377 __isl_give isl_set_list *isl_set_list_drop(
3378 __isl_take isl_set_list *list,
3379 unsigned first, unsigned n);
3380 __isl_give isl_set_list *isl_set_list_set_set(
3381 __isl_take isl_set_list *list, int index,
3382 __isl_take isl_set *set);
3383 __isl_give isl_set_list *isl_set_list_concat(
3384 __isl_take isl_set_list *list1,
3385 __isl_take isl_set_list *list2);
3386 __isl_give isl_set_list *isl_set_list_sort(
3387 __isl_take isl_set_list *list,
3388 int (*cmp)(__isl_keep isl_set *a,
3389 __isl_keep isl_set *b, void *user),
3391 void *isl_set_list_free(__isl_take isl_set_list *list);
3393 C<isl_set_list_alloc> creates an empty list with a capacity for
3394 C<n> elements. C<isl_set_list_from_set> creates a list with a single
3397 Lists can be inspected using the following functions.
3399 #include <isl/list.h>
3400 isl_ctx *isl_set_list_get_ctx(__isl_keep isl_set_list *list);
3401 int isl_set_list_n_set(__isl_keep isl_set_list *list);
3402 __isl_give isl_set *isl_set_list_get_set(
3403 __isl_keep isl_set_list *list, int index);
3404 int isl_set_list_foreach(__isl_keep isl_set_list *list,
3405 int (*fn)(__isl_take isl_set *el, void *user),
3407 int isl_set_list_foreach_scc(__isl_keep isl_set_list *list,
3408 int (*follows)(__isl_keep isl_set *a,
3409 __isl_keep isl_set *b, void *user),
3411 int (*fn)(__isl_take isl_set *el, void *user),
3414 The function C<isl_set_list_foreach_scc> calls C<fn> on each of the
3415 strongly connected components of the graph with as vertices the elements
3416 of C<list> and a directed edge from vertex C<b> to vertex C<a>
3417 iff C<follows(a, b)> returns C<1>. The callbacks C<follows> and C<fn>
3418 should return C<-1> on error.
3420 Lists can be printed using
3422 #include <isl/list.h>
3423 __isl_give isl_printer *isl_printer_print_set_list(
3424 __isl_take isl_printer *p,
3425 __isl_keep isl_set_list *list);
3427 =head2 Multiple Values
3429 An C<isl_multi_val> object represents a sequence of zero or more values,
3430 living in a set space.
3432 An C<isl_multi_val> can be constructed from an C<isl_val_list>
3433 using the following function
3435 #include <isl/val.h>
3436 __isl_give isl_multi_val *isl_multi_val_from_val_list(
3437 __isl_take isl_space *space,
3438 __isl_take isl_val_list *list);
3440 The zero multiple value (with value zero for each set dimension)
3441 can be created using the following function.
3443 #include <isl/val.h>
3444 __isl_give isl_multi_val *isl_multi_val_zero(
3445 __isl_take isl_space *space);
3447 Multiple values can be copied and freed using
3449 #include <isl/val.h>
3450 __isl_give isl_multi_val *isl_multi_val_copy(
3451 __isl_keep isl_multi_val *mv);
3452 void *isl_multi_val_free(__isl_take isl_multi_val *mv);
3454 They can be inspected using
3456 #include <isl/val.h>
3457 isl_ctx *isl_multi_val_get_ctx(
3458 __isl_keep isl_multi_val *mv);
3459 unsigned isl_multi_val_dim(__isl_keep isl_multi_val *mv,
3460 enum isl_dim_type type);
3461 __isl_give isl_val *isl_multi_val_get_val(
3462 __isl_keep isl_multi_val *mv, int pos);
3463 const char *isl_multi_val_get_tuple_name(
3464 __isl_keep isl_multi_val *mv,
3465 enum isl_dim_type type);
3467 They can be modified using
3469 #include <isl/val.h>
3470 __isl_give isl_multi_val *isl_multi_val_set_val(
3471 __isl_take isl_multi_val *mv, int pos,
3472 __isl_take isl_val *val);
3473 __isl_give isl_multi_val *isl_multi_val_set_dim_name(
3474 __isl_take isl_multi_val *mv,
3475 enum isl_dim_type type, unsigned pos, const char *s);
3476 __isl_give isl_multi_val *isl_multi_val_set_tuple_name(
3477 __isl_take isl_multi_val *mv,
3478 enum isl_dim_type type, const char *s);
3479 __isl_give isl_multi_val *isl_multi_val_set_tuple_id(
3480 __isl_take isl_multi_val *mv,
3481 enum isl_dim_type type, __isl_take isl_id *id);
3483 __isl_give isl_multi_val *isl_multi_val_insert_dims(
3484 __isl_take isl_multi_val *mv,
3485 enum isl_dim_type type, unsigned first, unsigned n);
3486 __isl_give isl_multi_val *isl_multi_val_add_dims(
3487 __isl_take isl_multi_val *mv,
3488 enum isl_dim_type type, unsigned n);
3489 __isl_give isl_multi_val *isl_multi_val_drop_dims(
3490 __isl_take isl_multi_val *mv,
3491 enum isl_dim_type type, unsigned first, unsigned n);
3495 #include <isl/val.h>
3496 __isl_give isl_multi_val *isl_multi_val_align_params(
3497 __isl_take isl_multi_val *mv,
3498 __isl_take isl_space *model);
3499 __isl_give isl_multi_val *isl_multi_val_range_splice(
3500 __isl_take isl_multi_val *mv1, unsigned pos,
3501 __isl_take isl_multi_val *mv2);
3502 __isl_give isl_multi_val *isl_multi_val_range_product(
3503 __isl_take isl_multi_val *mv1,
3504 __isl_take isl_multi_val *mv2);
3505 __isl_give isl_multi_val *isl_multi_val_flat_range_product(
3506 __isl_take isl_multi_val *mv1,
3507 __isl_take isl_multi_aff *mv2);
3508 __isl_give isl_multi_val *isl_multi_val_add_val(
3509 __isl_take isl_multi_val *mv,
3510 __isl_take isl_val *v);
3511 __isl_give isl_multi_val *isl_multi_val_mod_val(
3512 __isl_take isl_multi_val *mv,
3513 __isl_take isl_val *v);
3514 __isl_give isl_multi_val *isl_multi_val_scale_val(
3515 __isl_take isl_multi_val *mv,
3516 __isl_take isl_val *v);
3520 Vectors can be created, copied and freed using the following functions.
3522 #include <isl/vec.h>
3523 __isl_give isl_vec *isl_vec_alloc(isl_ctx *ctx,
3525 __isl_give isl_vec *isl_vec_copy(__isl_keep isl_vec *vec);
3526 void *isl_vec_free(__isl_take isl_vec *vec);
3528 Note that the elements of a newly created vector may have arbitrary values.
3529 The elements can be changed and inspected using the following functions.
3531 isl_ctx *isl_vec_get_ctx(__isl_keep isl_vec *vec);
3532 int isl_vec_size(__isl_keep isl_vec *vec);
3533 int isl_vec_get_element(__isl_keep isl_vec *vec,
3534 int pos, isl_int *v);
3535 __isl_give isl_val *isl_vec_get_element_val(
3536 __isl_keep isl_vec *vec, int pos);
3537 __isl_give isl_vec *isl_vec_set_element(
3538 __isl_take isl_vec *vec, int pos, isl_int v);
3539 __isl_give isl_vec *isl_vec_set_element_si(
3540 __isl_take isl_vec *vec, int pos, int v);
3541 __isl_give isl_vec *isl_vec_set_element_val(
3542 __isl_take isl_vec *vec, int pos,
3543 __isl_take isl_val *v);
3544 __isl_give isl_vec *isl_vec_set(__isl_take isl_vec *vec,
3546 __isl_give isl_vec *isl_vec_set_si(__isl_take isl_vec *vec,
3548 __isl_give isl_vec *isl_vec_set_val(
3549 __isl_take isl_vec *vec, __isl_take isl_val *v);
3550 int isl_vec_cmp_element(__isl_keep isl_vec *vec1,
3551 __isl_keep isl_vec *vec2, int pos);
3552 __isl_give isl_vec *isl_vec_fdiv_r(__isl_take isl_vec *vec,
3555 C<isl_vec_get_element> will return a negative value if anything went wrong.
3556 In that case, the value of C<*v> is undefined.
3558 The following function can be used to concatenate two vectors.
3560 __isl_give isl_vec *isl_vec_concat(__isl_take isl_vec *vec1,
3561 __isl_take isl_vec *vec2);
3565 Matrices can be created, copied and freed using the following functions.
3567 #include <isl/mat.h>
3568 __isl_give isl_mat *isl_mat_alloc(isl_ctx *ctx,
3569 unsigned n_row, unsigned n_col);
3570 __isl_give isl_mat *isl_mat_copy(__isl_keep isl_mat *mat);
3571 void *isl_mat_free(__isl_take isl_mat *mat);
3573 Note that the elements of a newly created matrix may have arbitrary values.
3574 The elements can be changed and inspected using the following functions.
3576 isl_ctx *isl_mat_get_ctx(__isl_keep isl_mat *mat);
3577 int isl_mat_rows(__isl_keep isl_mat *mat);
3578 int isl_mat_cols(__isl_keep isl_mat *mat);
3579 int isl_mat_get_element(__isl_keep isl_mat *mat,
3580 int row, int col, isl_int *v);
3581 __isl_give isl_val *isl_mat_get_element_val(
3582 __isl_keep isl_mat *mat, int row, int col);
3583 __isl_give isl_mat *isl_mat_set_element(__isl_take isl_mat *mat,
3584 int row, int col, isl_int v);
3585 __isl_give isl_mat *isl_mat_set_element_si(__isl_take isl_mat *mat,
3586 int row, int col, int v);
3587 __isl_give isl_mat *isl_mat_set_element_val(
3588 __isl_take isl_mat *mat, int row, int col,
3589 __isl_take isl_val *v);
3591 C<isl_mat_get_element> will return a negative value if anything went wrong.
3592 In that case, the value of C<*v> is undefined.
3594 The following function can be used to compute the (right) inverse
3595 of a matrix, i.e., a matrix such that the product of the original
3596 and the inverse (in that order) is a multiple of the identity matrix.
3597 The input matrix is assumed to be of full row-rank.
3599 __isl_give isl_mat *isl_mat_right_inverse(__isl_take isl_mat *mat);
3601 The following function can be used to compute the (right) kernel
3602 (or null space) of a matrix, i.e., a matrix such that the product of
3603 the original and the kernel (in that order) is the zero matrix.
3605 __isl_give isl_mat *isl_mat_right_kernel(__isl_take isl_mat *mat);
3607 =head2 Piecewise Quasi Affine Expressions
3609 The zero quasi affine expression or the quasi affine expression
3610 that is equal to a specified dimension on a given domain can be created using
3612 __isl_give isl_aff *isl_aff_zero_on_domain(
3613 __isl_take isl_local_space *ls);
3614 __isl_give isl_pw_aff *isl_pw_aff_zero_on_domain(
3615 __isl_take isl_local_space *ls);
3616 __isl_give isl_aff *isl_aff_var_on_domain(
3617 __isl_take isl_local_space *ls,
3618 enum isl_dim_type type, unsigned pos);
3619 __isl_give isl_pw_aff *isl_pw_aff_var_on_domain(
3620 __isl_take isl_local_space *ls,
3621 enum isl_dim_type type, unsigned pos);
3623 Note that the space in which the resulting objects live is a map space
3624 with the given space as domain and a one-dimensional range.
3626 An empty piecewise quasi affine expression (one with no cells)
3627 or a piecewise quasi affine expression with a single cell can
3628 be created using the following functions.
3630 #include <isl/aff.h>
3631 __isl_give isl_pw_aff *isl_pw_aff_empty(
3632 __isl_take isl_space *space);
3633 __isl_give isl_pw_aff *isl_pw_aff_alloc(
3634 __isl_take isl_set *set, __isl_take isl_aff *aff);
3635 __isl_give isl_pw_aff *isl_pw_aff_from_aff(
3636 __isl_take isl_aff *aff);
3638 A piecewise quasi affine expression that is equal to 1 on a set
3639 and 0 outside the set can be created using the following function.
3641 #include <isl/aff.h>
3642 __isl_give isl_pw_aff *isl_set_indicator_function(
3643 __isl_take isl_set *set);
3645 Quasi affine expressions can be copied and freed using
3647 #include <isl/aff.h>
3648 __isl_give isl_aff *isl_aff_copy(__isl_keep isl_aff *aff);
3649 void *isl_aff_free(__isl_take isl_aff *aff);
3651 __isl_give isl_pw_aff *isl_pw_aff_copy(
3652 __isl_keep isl_pw_aff *pwaff);
3653 void *isl_pw_aff_free(__isl_take isl_pw_aff *pwaff);
3655 A (rational) bound on a dimension can be extracted from an C<isl_constraint>
3656 using the following function. The constraint is required to have
3657 a non-zero coefficient for the specified dimension.
3659 #include <isl/constraint.h>
3660 __isl_give isl_aff *isl_constraint_get_bound(
3661 __isl_keep isl_constraint *constraint,
3662 enum isl_dim_type type, int pos);
3664 The entire affine expression of the constraint can also be extracted
3665 using the following function.
3667 #include <isl/constraint.h>
3668 __isl_give isl_aff *isl_constraint_get_aff(
3669 __isl_keep isl_constraint *constraint);
3671 Conversely, an equality constraint equating
3672 the affine expression to zero or an inequality constraint enforcing
3673 the affine expression to be non-negative, can be constructed using
3675 __isl_give isl_constraint *isl_equality_from_aff(
3676 __isl_take isl_aff *aff);
3677 __isl_give isl_constraint *isl_inequality_from_aff(
3678 __isl_take isl_aff *aff);
3680 The expression can be inspected using
3682 #include <isl/aff.h>
3683 isl_ctx *isl_aff_get_ctx(__isl_keep isl_aff *aff);
3684 int isl_aff_dim(__isl_keep isl_aff *aff,
3685 enum isl_dim_type type);
3686 __isl_give isl_local_space *isl_aff_get_domain_local_space(
3687 __isl_keep isl_aff *aff);
3688 __isl_give isl_local_space *isl_aff_get_local_space(
3689 __isl_keep isl_aff *aff);
3690 const char *isl_aff_get_dim_name(__isl_keep isl_aff *aff,
3691 enum isl_dim_type type, unsigned pos);
3692 const char *isl_pw_aff_get_dim_name(
3693 __isl_keep isl_pw_aff *pa,
3694 enum isl_dim_type type, unsigned pos);
3695 int isl_pw_aff_has_dim_id(__isl_keep isl_pw_aff *pa,
3696 enum isl_dim_type type, unsigned pos);
3697 __isl_give isl_id *isl_pw_aff_get_dim_id(
3698 __isl_keep isl_pw_aff *pa,
3699 enum isl_dim_type type, unsigned pos);
3700 __isl_give isl_id *isl_pw_aff_get_tuple_id(
3701 __isl_keep isl_pw_aff *pa,
3702 enum isl_dim_type type);
3703 int isl_aff_get_constant(__isl_keep isl_aff *aff,
3705 __isl_give isl_val *isl_aff_get_constant_val(
3706 __isl_keep isl_aff *aff);
3707 int isl_aff_get_coefficient(__isl_keep isl_aff *aff,
3708 enum isl_dim_type type, int pos, isl_int *v);
3709 __isl_give isl_val *isl_aff_get_coefficient_val(
3710 __isl_keep isl_aff *aff,
3711 enum isl_dim_type type, int pos);
3712 int isl_aff_get_denominator(__isl_keep isl_aff *aff,
3714 __isl_give isl_val *isl_aff_get_denominator_val(
3715 __isl_keep isl_aff *aff);
3716 __isl_give isl_aff *isl_aff_get_div(
3717 __isl_keep isl_aff *aff, int pos);
3719 int isl_pw_aff_n_piece(__isl_keep isl_pw_aff *pwaff);
3720 int isl_pw_aff_foreach_piece(__isl_keep isl_pw_aff *pwaff,
3721 int (*fn)(__isl_take isl_set *set,
3722 __isl_take isl_aff *aff,
3723 void *user), void *user);
3725 int isl_aff_is_cst(__isl_keep isl_aff *aff);
3726 int isl_pw_aff_is_cst(__isl_keep isl_pw_aff *pwaff);
3728 int isl_aff_involves_dims(__isl_keep isl_aff *aff,
3729 enum isl_dim_type type, unsigned first, unsigned n);
3730 int isl_pw_aff_involves_dims(__isl_keep isl_pw_aff *pwaff,
3731 enum isl_dim_type type, unsigned first, unsigned n);
3733 isl_ctx *isl_pw_aff_get_ctx(__isl_keep isl_pw_aff *pwaff);
3734 unsigned isl_pw_aff_dim(__isl_keep isl_pw_aff *pwaff,
3735 enum isl_dim_type type);
3736 int isl_pw_aff_is_empty(__isl_keep isl_pw_aff *pwaff);
3738 It can be modified using
3740 #include <isl/aff.h>
3741 __isl_give isl_pw_aff *isl_pw_aff_set_tuple_id(
3742 __isl_take isl_pw_aff *pwaff,
3743 enum isl_dim_type type, __isl_take isl_id *id);
3744 __isl_give isl_aff *isl_aff_set_dim_name(
3745 __isl_take isl_aff *aff, enum isl_dim_type type,
3746 unsigned pos, const char *s);
3747 __isl_give isl_aff *isl_aff_set_dim_id(
3748 __isl_take isl_aff *aff, enum isl_dim_type type,
3749 unsigned pos, __isl_take isl_id *id);
3750 __isl_give isl_pw_aff *isl_pw_aff_set_dim_id(
3751 __isl_take isl_pw_aff *pma,
3752 enum isl_dim_type type, unsigned pos,
3753 __isl_take isl_id *id);
3754 __isl_give isl_aff *isl_aff_set_constant(
3755 __isl_take isl_aff *aff, isl_int v);
3756 __isl_give isl_aff *isl_aff_set_constant_si(
3757 __isl_take isl_aff *aff, int v);
3758 __isl_give isl_aff *isl_aff_set_constant_val(
3759 __isl_take isl_aff *aff, __isl_take isl_val *v);
3760 __isl_give isl_aff *isl_aff_set_coefficient(
3761 __isl_take isl_aff *aff,
3762 enum isl_dim_type type, int pos, isl_int v);
3763 __isl_give isl_aff *isl_aff_set_coefficient_si(
3764 __isl_take isl_aff *aff,
3765 enum isl_dim_type type, int pos, int v);
3766 __isl_give isl_aff *isl_aff_set_coefficient_val(
3767 __isl_take isl_aff *aff,
3768 enum isl_dim_type type, int pos,
3769 __isl_take isl_val *v);
3770 __isl_give isl_aff *isl_aff_set_denominator(
3771 __isl_take isl_aff *aff, isl_int v);
3773 __isl_give isl_aff *isl_aff_add_constant(
3774 __isl_take isl_aff *aff, isl_int v);
3775 __isl_give isl_aff *isl_aff_add_constant_si(
3776 __isl_take isl_aff *aff, int v);
3777 __isl_give isl_aff *isl_aff_add_constant_val(
3778 __isl_take isl_aff *aff, __isl_take isl_val *v);
3779 __isl_give isl_aff *isl_aff_add_constant_num(
3780 __isl_take isl_aff *aff, isl_int v);
3781 __isl_give isl_aff *isl_aff_add_constant_num_si(
3782 __isl_take isl_aff *aff, int v);
3783 __isl_give isl_aff *isl_aff_add_coefficient(
3784 __isl_take isl_aff *aff,
3785 enum isl_dim_type type, int pos, isl_int v);
3786 __isl_give isl_aff *isl_aff_add_coefficient_si(
3787 __isl_take isl_aff *aff,
3788 enum isl_dim_type type, int pos, int v);
3789 __isl_give isl_aff *isl_aff_add_coefficient_val(
3790 __isl_take isl_aff *aff,
3791 enum isl_dim_type type, int pos,
3792 __isl_take isl_val *v);
3794 __isl_give isl_aff *isl_aff_insert_dims(
3795 __isl_take isl_aff *aff,
3796 enum isl_dim_type type, unsigned first, unsigned n);
3797 __isl_give isl_pw_aff *isl_pw_aff_insert_dims(
3798 __isl_take isl_pw_aff *pwaff,
3799 enum isl_dim_type type, unsigned first, unsigned n);
3800 __isl_give isl_aff *isl_aff_add_dims(
3801 __isl_take isl_aff *aff,
3802 enum isl_dim_type type, unsigned n);
3803 __isl_give isl_pw_aff *isl_pw_aff_add_dims(
3804 __isl_take isl_pw_aff *pwaff,
3805 enum isl_dim_type type, unsigned n);
3806 __isl_give isl_aff *isl_aff_drop_dims(
3807 __isl_take isl_aff *aff,
3808 enum isl_dim_type type, unsigned first, unsigned n);
3809 __isl_give isl_pw_aff *isl_pw_aff_drop_dims(
3810 __isl_take isl_pw_aff *pwaff,
3811 enum isl_dim_type type, unsigned first, unsigned n);
3813 Note that C<isl_aff_set_constant>, C<isl_aff_set_constant_si>,
3814 C<isl_aff_set_coefficient> and C<isl_aff_set_coefficient_si>
3815 set the I<numerator> of the constant or coefficient, while
3816 C<isl_aff_set_constant_val> and C<isl_aff_set_coefficient_val> set
3817 the constant or coefficient as a whole.
3818 The C<add_constant> and C<add_coefficient> functions add an integer
3819 or rational value to
3820 the possibly rational constant or coefficient.
3821 The C<add_constant_num> functions add an integer value to
3824 To check whether an affine expressions is obviously zero
3825 or obviously equal to some other affine expression, use
3827 #include <isl/aff.h>
3828 int isl_aff_plain_is_zero(__isl_keep isl_aff *aff);
3829 int isl_aff_plain_is_equal(__isl_keep isl_aff *aff1,
3830 __isl_keep isl_aff *aff2);
3831 int isl_pw_aff_plain_is_equal(
3832 __isl_keep isl_pw_aff *pwaff1,
3833 __isl_keep isl_pw_aff *pwaff2);
3837 #include <isl/aff.h>
3838 __isl_give isl_aff *isl_aff_add(__isl_take isl_aff *aff1,
3839 __isl_take isl_aff *aff2);
3840 __isl_give isl_pw_aff *isl_pw_aff_add(
3841 __isl_take isl_pw_aff *pwaff1,
3842 __isl_take isl_pw_aff *pwaff2);
3843 __isl_give isl_pw_aff *isl_pw_aff_min(
3844 __isl_take isl_pw_aff *pwaff1,
3845 __isl_take isl_pw_aff *pwaff2);
3846 __isl_give isl_pw_aff *isl_pw_aff_max(
3847 __isl_take isl_pw_aff *pwaff1,
3848 __isl_take isl_pw_aff *pwaff2);
3849 __isl_give isl_aff *isl_aff_sub(__isl_take isl_aff *aff1,
3850 __isl_take isl_aff *aff2);
3851 __isl_give isl_pw_aff *isl_pw_aff_sub(
3852 __isl_take isl_pw_aff *pwaff1,
3853 __isl_take isl_pw_aff *pwaff2);
3854 __isl_give isl_aff *isl_aff_neg(__isl_take isl_aff *aff);
3855 __isl_give isl_pw_aff *isl_pw_aff_neg(
3856 __isl_take isl_pw_aff *pwaff);
3857 __isl_give isl_aff *isl_aff_ceil(__isl_take isl_aff *aff);
3858 __isl_give isl_pw_aff *isl_pw_aff_ceil(
3859 __isl_take isl_pw_aff *pwaff);
3860 __isl_give isl_aff *isl_aff_floor(__isl_take isl_aff *aff);
3861 __isl_give isl_pw_aff *isl_pw_aff_floor(
3862 __isl_take isl_pw_aff *pwaff);
3863 __isl_give isl_aff *isl_aff_mod(__isl_take isl_aff *aff,
3865 __isl_give isl_aff *isl_aff_mod_val(__isl_take isl_aff *aff,
3866 __isl_take isl_val *mod);
3867 __isl_give isl_pw_aff *isl_pw_aff_mod(
3868 __isl_take isl_pw_aff *pwaff, isl_int mod);
3869 __isl_give isl_pw_aff *isl_pw_aff_mod_val(
3870 __isl_take isl_pw_aff *pa,
3871 __isl_take isl_val *mod);
3872 __isl_give isl_aff *isl_aff_scale(__isl_take isl_aff *aff,
3874 __isl_give isl_aff *isl_aff_scale_val(__isl_take isl_aff *aff,
3875 __isl_take isl_val *v);
3876 __isl_give isl_pw_aff *isl_pw_aff_scale(
3877 __isl_take isl_pw_aff *pwaff, isl_int f);
3878 __isl_give isl_pw_aff *isl_pw_aff_scale_val(
3879 __isl_take isl_pw_aff *pa, __isl_take isl_val *v);
3880 __isl_give isl_aff *isl_aff_scale_down(__isl_take isl_aff *aff,
3882 __isl_give isl_aff *isl_aff_scale_down_ui(
3883 __isl_take isl_aff *aff, unsigned f);
3884 __isl_give isl_aff *isl_aff_scale_down_val(
3885 __isl_take isl_aff *aff, __isl_take isl_val *v);
3886 __isl_give isl_pw_aff *isl_pw_aff_scale_down(
3887 __isl_take isl_pw_aff *pwaff, isl_int f);
3888 __isl_give isl_pw_aff *isl_pw_aff_scale_down_val(
3889 __isl_take isl_pw_aff *pa,
3890 __isl_take isl_val *f);
3892 __isl_give isl_pw_aff *isl_pw_aff_list_min(
3893 __isl_take isl_pw_aff_list *list);
3894 __isl_give isl_pw_aff *isl_pw_aff_list_max(
3895 __isl_take isl_pw_aff_list *list);
3897 __isl_give isl_pw_aff *isl_pw_aff_coalesce(
3898 __isl_take isl_pw_aff *pwqp);
3900 __isl_give isl_aff *isl_aff_align_params(
3901 __isl_take isl_aff *aff,
3902 __isl_take isl_space *model);
3903 __isl_give isl_pw_aff *isl_pw_aff_align_params(
3904 __isl_take isl_pw_aff *pwaff,
3905 __isl_take isl_space *model);
3907 __isl_give isl_aff *isl_aff_project_domain_on_params(
3908 __isl_take isl_aff *aff);
3910 __isl_give isl_aff *isl_aff_gist_params(
3911 __isl_take isl_aff *aff,
3912 __isl_take isl_set *context);
3913 __isl_give isl_aff *isl_aff_gist(__isl_take isl_aff *aff,
3914 __isl_take isl_set *context);
3915 __isl_give isl_pw_aff *isl_pw_aff_gist_params(
3916 __isl_take isl_pw_aff *pwaff,
3917 __isl_take isl_set *context);
3918 __isl_give isl_pw_aff *isl_pw_aff_gist(
3919 __isl_take isl_pw_aff *pwaff,
3920 __isl_take isl_set *context);
3922 __isl_give isl_set *isl_pw_aff_domain(
3923 __isl_take isl_pw_aff *pwaff);
3924 __isl_give isl_pw_aff *isl_pw_aff_intersect_domain(
3925 __isl_take isl_pw_aff *pa,
3926 __isl_take isl_set *set);
3927 __isl_give isl_pw_aff *isl_pw_aff_intersect_params(
3928 __isl_take isl_pw_aff *pa,
3929 __isl_take isl_set *set);
3931 __isl_give isl_aff *isl_aff_mul(__isl_take isl_aff *aff1,
3932 __isl_take isl_aff *aff2);
3933 __isl_give isl_aff *isl_aff_div(__isl_take isl_aff *aff1,
3934 __isl_take isl_aff *aff2);
3935 __isl_give isl_pw_aff *isl_pw_aff_mul(
3936 __isl_take isl_pw_aff *pwaff1,
3937 __isl_take isl_pw_aff *pwaff2);
3938 __isl_give isl_pw_aff *isl_pw_aff_div(
3939 __isl_take isl_pw_aff *pa1,
3940 __isl_take isl_pw_aff *pa2);
3941 __isl_give isl_pw_aff *isl_pw_aff_tdiv_q(
3942 __isl_take isl_pw_aff *pa1,
3943 __isl_take isl_pw_aff *pa2);
3944 __isl_give isl_pw_aff *isl_pw_aff_tdiv_r(
3945 __isl_take isl_pw_aff *pa1,
3946 __isl_take isl_pw_aff *pa2);
3948 When multiplying two affine expressions, at least one of the two needs
3949 to be a constant. Similarly, when dividing an affine expression by another,
3950 the second expression needs to be a constant.
3951 C<isl_pw_aff_tdiv_q> computes the quotient of an integer division with
3952 rounding towards zero. C<isl_pw_aff_tdiv_r> computes the corresponding
3955 #include <isl/aff.h>
3956 __isl_give isl_aff *isl_aff_pullback_multi_aff(
3957 __isl_take isl_aff *aff,
3958 __isl_take isl_multi_aff *ma);
3959 __isl_give isl_pw_aff *isl_pw_aff_pullback_multi_aff(
3960 __isl_take isl_pw_aff *pa,
3961 __isl_take isl_multi_aff *ma);
3962 __isl_give isl_pw_aff *isl_pw_aff_pullback_pw_multi_aff(
3963 __isl_take isl_pw_aff *pa,
3964 __isl_take isl_pw_multi_aff *pma);
3966 These functions precompose the input expression by the given
3967 C<isl_multi_aff> or C<isl_pw_multi_aff>. In other words,
3968 the C<isl_multi_aff> or C<isl_pw_multi_aff> is plugged
3969 into the (piecewise) affine expression.
3970 Objects of type C<isl_multi_aff> are described in
3971 L</"Piecewise Multiple Quasi Affine Expressions">.
3973 #include <isl/aff.h>
3974 __isl_give isl_basic_set *isl_aff_zero_basic_set(
3975 __isl_take isl_aff *aff);
3976 __isl_give isl_basic_set *isl_aff_neg_basic_set(
3977 __isl_take isl_aff *aff);
3978 __isl_give isl_basic_set *isl_aff_le_basic_set(
3979 __isl_take isl_aff *aff1, __isl_take isl_aff *aff2);
3980 __isl_give isl_basic_set *isl_aff_ge_basic_set(
3981 __isl_take isl_aff *aff1, __isl_take isl_aff *aff2);
3982 __isl_give isl_set *isl_pw_aff_eq_set(
3983 __isl_take isl_pw_aff *pwaff1,
3984 __isl_take isl_pw_aff *pwaff2);
3985 __isl_give isl_set *isl_pw_aff_ne_set(
3986 __isl_take isl_pw_aff *pwaff1,
3987 __isl_take isl_pw_aff *pwaff2);
3988 __isl_give isl_set *isl_pw_aff_le_set(
3989 __isl_take isl_pw_aff *pwaff1,
3990 __isl_take isl_pw_aff *pwaff2);
3991 __isl_give isl_set *isl_pw_aff_lt_set(
3992 __isl_take isl_pw_aff *pwaff1,
3993 __isl_take isl_pw_aff *pwaff2);
3994 __isl_give isl_set *isl_pw_aff_ge_set(
3995 __isl_take isl_pw_aff *pwaff1,
3996 __isl_take isl_pw_aff *pwaff2);
3997 __isl_give isl_set *isl_pw_aff_gt_set(
3998 __isl_take isl_pw_aff *pwaff1,
3999 __isl_take isl_pw_aff *pwaff2);
4001 __isl_give isl_set *isl_pw_aff_list_eq_set(
4002 __isl_take isl_pw_aff_list *list1,
4003 __isl_take isl_pw_aff_list *list2);
4004 __isl_give isl_set *isl_pw_aff_list_ne_set(
4005 __isl_take isl_pw_aff_list *list1,
4006 __isl_take isl_pw_aff_list *list2);
4007 __isl_give isl_set *isl_pw_aff_list_le_set(
4008 __isl_take isl_pw_aff_list *list1,
4009 __isl_take isl_pw_aff_list *list2);
4010 __isl_give isl_set *isl_pw_aff_list_lt_set(
4011 __isl_take isl_pw_aff_list *list1,
4012 __isl_take isl_pw_aff_list *list2);
4013 __isl_give isl_set *isl_pw_aff_list_ge_set(
4014 __isl_take isl_pw_aff_list *list1,
4015 __isl_take isl_pw_aff_list *list2);
4016 __isl_give isl_set *isl_pw_aff_list_gt_set(
4017 __isl_take isl_pw_aff_list *list1,
4018 __isl_take isl_pw_aff_list *list2);
4020 The function C<isl_aff_neg_basic_set> returns a basic set
4021 containing those elements in the domain space
4022 of C<aff> where C<aff> is negative.
4023 The function C<isl_aff_ge_basic_set> returns a basic set
4024 containing those elements in the shared space
4025 of C<aff1> and C<aff2> where C<aff1> is greater than or equal to C<aff2>.
4026 The function C<isl_pw_aff_ge_set> returns a set
4027 containing those elements in the shared domain
4028 of C<pwaff1> and C<pwaff2> where C<pwaff1> is greater than or equal to C<pwaff2>.
4029 The functions operating on C<isl_pw_aff_list> apply the corresponding
4030 C<isl_pw_aff> function to each pair of elements in the two lists.
4032 #include <isl/aff.h>
4033 __isl_give isl_set *isl_pw_aff_nonneg_set(
4034 __isl_take isl_pw_aff *pwaff);
4035 __isl_give isl_set *isl_pw_aff_zero_set(
4036 __isl_take isl_pw_aff *pwaff);
4037 __isl_give isl_set *isl_pw_aff_non_zero_set(
4038 __isl_take isl_pw_aff *pwaff);
4040 The function C<isl_pw_aff_nonneg_set> returns a set
4041 containing those elements in the domain
4042 of C<pwaff> where C<pwaff> is non-negative.
4044 #include <isl/aff.h>
4045 __isl_give isl_pw_aff *isl_pw_aff_cond(
4046 __isl_take isl_pw_aff *cond,
4047 __isl_take isl_pw_aff *pwaff_true,
4048 __isl_take isl_pw_aff *pwaff_false);
4050 The function C<isl_pw_aff_cond> performs a conditional operator
4051 and returns an expression that is equal to C<pwaff_true>
4052 for elements where C<cond> is non-zero and equal to C<pwaff_false> for elements
4053 where C<cond> is zero.
4055 #include <isl/aff.h>
4056 __isl_give isl_pw_aff *isl_pw_aff_union_min(
4057 __isl_take isl_pw_aff *pwaff1,
4058 __isl_take isl_pw_aff *pwaff2);
4059 __isl_give isl_pw_aff *isl_pw_aff_union_max(
4060 __isl_take isl_pw_aff *pwaff1,
4061 __isl_take isl_pw_aff *pwaff2);
4062 __isl_give isl_pw_aff *isl_pw_aff_union_add(
4063 __isl_take isl_pw_aff *pwaff1,
4064 __isl_take isl_pw_aff *pwaff2);
4066 The function C<isl_pw_aff_union_max> computes a piecewise quasi-affine
4067 expression with a domain that is the union of those of C<pwaff1> and
4068 C<pwaff2> and such that on each cell, the quasi-affine expression is
4069 the maximum of those of C<pwaff1> and C<pwaff2>. If only one of
4070 C<pwaff1> or C<pwaff2> is defined on a given cell, then the
4071 associated expression is the defined one.
4073 An expression can be read from input using
4075 #include <isl/aff.h>
4076 __isl_give isl_aff *isl_aff_read_from_str(
4077 isl_ctx *ctx, const char *str);
4078 __isl_give isl_pw_aff *isl_pw_aff_read_from_str(
4079 isl_ctx *ctx, const char *str);
4081 An expression can be printed using
4083 #include <isl/aff.h>
4084 __isl_give isl_printer *isl_printer_print_aff(
4085 __isl_take isl_printer *p, __isl_keep isl_aff *aff);
4087 __isl_give isl_printer *isl_printer_print_pw_aff(
4088 __isl_take isl_printer *p,
4089 __isl_keep isl_pw_aff *pwaff);
4091 =head2 Piecewise Multiple Quasi Affine Expressions
4093 An C<isl_multi_aff> object represents a sequence of
4094 zero or more affine expressions, all defined on the same domain space.
4095 Similarly, an C<isl_multi_pw_aff> object represents a sequence of
4096 zero or more piecewise affine expressions.
4098 An C<isl_multi_aff> can be constructed from a single
4099 C<isl_aff> or an C<isl_aff_list> using the
4100 following functions. Similarly for C<isl_multi_pw_aff>.
4102 #include <isl/aff.h>
4103 __isl_give isl_multi_aff *isl_multi_aff_from_aff(
4104 __isl_take isl_aff *aff);
4105 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_from_pw_aff(
4106 __isl_take isl_pw_aff *pa);
4107 __isl_give isl_multi_aff *isl_multi_aff_from_aff_list(
4108 __isl_take isl_space *space,
4109 __isl_take isl_aff_list *list);
4111 An empty piecewise multiple quasi affine expression (one with no cells),
4112 the zero piecewise multiple quasi affine expression (with value zero
4113 for each output dimension),
4114 a piecewise multiple quasi affine expression with a single cell (with
4115 either a universe or a specified domain) or
4116 a zero-dimensional piecewise multiple quasi affine expression
4118 can be created using the following functions.
4120 #include <isl/aff.h>
4121 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_empty(
4122 __isl_take isl_space *space);
4123 __isl_give isl_multi_aff *isl_multi_aff_zero(
4124 __isl_take isl_space *space);
4125 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_zero(
4126 __isl_take isl_space *space);
4127 __isl_give isl_multi_aff *isl_multi_aff_identity(
4128 __isl_take isl_space *space);
4129 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_identity(
4130 __isl_take isl_space *space);
4131 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_identity(
4132 __isl_take isl_space *space);
4133 __isl_give isl_pw_multi_aff *
4134 isl_pw_multi_aff_from_multi_aff(
4135 __isl_take isl_multi_aff *ma);
4136 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_alloc(
4137 __isl_take isl_set *set,
4138 __isl_take isl_multi_aff *maff);
4139 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_from_domain(
4140 __isl_take isl_set *set);
4142 __isl_give isl_union_pw_multi_aff *
4143 isl_union_pw_multi_aff_empty(
4144 __isl_take isl_space *space);
4145 __isl_give isl_union_pw_multi_aff *
4146 isl_union_pw_multi_aff_add_pw_multi_aff(
4147 __isl_take isl_union_pw_multi_aff *upma,
4148 __isl_take isl_pw_multi_aff *pma);
4149 __isl_give isl_union_pw_multi_aff *
4150 isl_union_pw_multi_aff_from_domain(
4151 __isl_take isl_union_set *uset);
4153 A piecewise multiple quasi affine expression can also be initialized
4154 from an C<isl_set> or C<isl_map>, provided the C<isl_set> is a singleton
4155 and the C<isl_map> is single-valued.
4156 In case of a conversion from an C<isl_union_set> or an C<isl_union_map>
4157 to an C<isl_union_pw_multi_aff>, these properties need to hold in each space.
4159 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_from_set(
4160 __isl_take isl_set *set);
4161 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_from_map(
4162 __isl_take isl_map *map);
4164 __isl_give isl_union_pw_multi_aff *
4165 isl_union_pw_multi_aff_from_union_set(
4166 __isl_take isl_union_set *uset);
4167 __isl_give isl_union_pw_multi_aff *
4168 isl_union_pw_multi_aff_from_union_map(
4169 __isl_take isl_union_map *umap);
4171 Multiple quasi affine expressions can be copied and freed using
4173 #include <isl/aff.h>
4174 __isl_give isl_multi_aff *isl_multi_aff_copy(
4175 __isl_keep isl_multi_aff *maff);
4176 void *isl_multi_aff_free(__isl_take isl_multi_aff *maff);
4178 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_copy(
4179 __isl_keep isl_pw_multi_aff *pma);
4180 void *isl_pw_multi_aff_free(
4181 __isl_take isl_pw_multi_aff *pma);
4183 __isl_give isl_union_pw_multi_aff *
4184 isl_union_pw_multi_aff_copy(
4185 __isl_keep isl_union_pw_multi_aff *upma);
4186 void *isl_union_pw_multi_aff_free(
4187 __isl_take isl_union_pw_multi_aff *upma);
4189 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_copy(
4190 __isl_keep isl_multi_pw_aff *mpa);
4191 void *isl_multi_pw_aff_free(
4192 __isl_take isl_multi_pw_aff *mpa);
4194 The expression can be inspected using
4196 #include <isl/aff.h>
4197 isl_ctx *isl_multi_aff_get_ctx(
4198 __isl_keep isl_multi_aff *maff);
4199 isl_ctx *isl_pw_multi_aff_get_ctx(
4200 __isl_keep isl_pw_multi_aff *pma);
4201 isl_ctx *isl_union_pw_multi_aff_get_ctx(
4202 __isl_keep isl_union_pw_multi_aff *upma);
4203 isl_ctx *isl_multi_pw_aff_get_ctx(
4204 __isl_keep isl_multi_pw_aff *mpa);
4205 unsigned isl_multi_aff_dim(__isl_keep isl_multi_aff *maff,
4206 enum isl_dim_type type);
4207 unsigned isl_pw_multi_aff_dim(
4208 __isl_keep isl_pw_multi_aff *pma,
4209 enum isl_dim_type type);
4210 unsigned isl_multi_pw_aff_dim(
4211 __isl_keep isl_multi_pw_aff *mpa,
4212 enum isl_dim_type type);
4213 __isl_give isl_aff *isl_multi_aff_get_aff(
4214 __isl_keep isl_multi_aff *multi, int pos);
4215 __isl_give isl_pw_aff *isl_pw_multi_aff_get_pw_aff(
4216 __isl_keep isl_pw_multi_aff *pma, int pos);
4217 __isl_give isl_pw_aff *isl_multi_pw_aff_get_pw_aff(
4218 __isl_keep isl_multi_pw_aff *mpa, int pos);
4219 const char *isl_pw_multi_aff_get_dim_name(
4220 __isl_keep isl_pw_multi_aff *pma,
4221 enum isl_dim_type type, unsigned pos);
4222 __isl_give isl_id *isl_pw_multi_aff_get_dim_id(
4223 __isl_keep isl_pw_multi_aff *pma,
4224 enum isl_dim_type type, unsigned pos);
4225 const char *isl_multi_aff_get_tuple_name(
4226 __isl_keep isl_multi_aff *multi,
4227 enum isl_dim_type type);
4228 int isl_pw_multi_aff_has_tuple_name(
4229 __isl_keep isl_pw_multi_aff *pma,
4230 enum isl_dim_type type);
4231 const char *isl_pw_multi_aff_get_tuple_name(
4232 __isl_keep isl_pw_multi_aff *pma,
4233 enum isl_dim_type type);
4234 int isl_pw_multi_aff_has_tuple_id(
4235 __isl_keep isl_pw_multi_aff *pma,
4236 enum isl_dim_type type);
4237 __isl_give isl_id *isl_pw_multi_aff_get_tuple_id(
4238 __isl_keep isl_pw_multi_aff *pma,
4239 enum isl_dim_type type);
4241 int isl_pw_multi_aff_foreach_piece(
4242 __isl_keep isl_pw_multi_aff *pma,
4243 int (*fn)(__isl_take isl_set *set,
4244 __isl_take isl_multi_aff *maff,
4245 void *user), void *user);
4247 int isl_union_pw_multi_aff_foreach_pw_multi_aff(
4248 __isl_keep isl_union_pw_multi_aff *upma,
4249 int (*fn)(__isl_take isl_pw_multi_aff *pma,
4250 void *user), void *user);
4252 It can be modified using
4254 #include <isl/aff.h>
4255 __isl_give isl_multi_aff *isl_multi_aff_set_aff(
4256 __isl_take isl_multi_aff *multi, int pos,
4257 __isl_take isl_aff *aff);
4258 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_set_pw_aff(
4259 __isl_take isl_pw_multi_aff *pma, unsigned pos,
4260 __isl_take isl_pw_aff *pa);
4261 __isl_give isl_multi_aff *isl_multi_aff_set_dim_name(
4262 __isl_take isl_multi_aff *maff,
4263 enum isl_dim_type type, unsigned pos, const char *s);
4264 __isl_give isl_multi_aff *isl_multi_aff_set_tuple_name(
4265 __isl_take isl_multi_aff *maff,
4266 enum isl_dim_type type, const char *s);
4267 __isl_give isl_multi_aff *isl_multi_aff_set_tuple_id(
4268 __isl_take isl_multi_aff *maff,
4269 enum isl_dim_type type, __isl_take isl_id *id);
4270 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_set_tuple_id(
4271 __isl_take isl_pw_multi_aff *pma,
4272 enum isl_dim_type type, __isl_take isl_id *id);
4274 __isl_give isl_multi_pw_aff *
4275 isl_multi_pw_aff_set_dim_name(
4276 __isl_take isl_multi_pw_aff *mpa,
4277 enum isl_dim_type type, unsigned pos, const char *s);
4278 __isl_give isl_multi_pw_aff *
4279 isl_multi_pw_aff_set_tuple_name(
4280 __isl_take isl_multi_pw_aff *mpa,
4281 enum isl_dim_type type, const char *s);
4283 __isl_give isl_multi_aff *isl_multi_aff_insert_dims(
4284 __isl_take isl_multi_aff *ma,
4285 enum isl_dim_type type, unsigned first, unsigned n);
4286 __isl_give isl_multi_aff *isl_multi_aff_add_dims(
4287 __isl_take isl_multi_aff *ma,
4288 enum isl_dim_type type, unsigned n);
4289 __isl_give isl_multi_aff *isl_multi_aff_drop_dims(
4290 __isl_take isl_multi_aff *maff,
4291 enum isl_dim_type type, unsigned first, unsigned n);
4292 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_drop_dims(
4293 __isl_take isl_pw_multi_aff *pma,
4294 enum isl_dim_type type, unsigned first, unsigned n);
4296 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_insert_dims(
4297 __isl_take isl_multi_pw_aff *mpa,
4298 enum isl_dim_type type, unsigned first, unsigned n);
4299 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_add_dims(
4300 __isl_take isl_multi_pw_aff *mpa,
4301 enum isl_dim_type type, unsigned n);
4303 To check whether two multiple affine expressions are
4304 obviously equal to each other, use
4306 int isl_multi_aff_plain_is_equal(__isl_keep isl_multi_aff *maff1,
4307 __isl_keep isl_multi_aff *maff2);
4308 int isl_pw_multi_aff_plain_is_equal(
4309 __isl_keep isl_pw_multi_aff *pma1,
4310 __isl_keep isl_pw_multi_aff *pma2);
4314 #include <isl/aff.h>
4315 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_union_lexmin(
4316 __isl_take isl_pw_multi_aff *pma1,
4317 __isl_take isl_pw_multi_aff *pma2);
4318 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_union_lexmax(
4319 __isl_take isl_pw_multi_aff *pma1,
4320 __isl_take isl_pw_multi_aff *pma2);
4321 __isl_give isl_multi_aff *isl_multi_aff_add(
4322 __isl_take isl_multi_aff *maff1,
4323 __isl_take isl_multi_aff *maff2);
4324 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_add(
4325 __isl_take isl_pw_multi_aff *pma1,
4326 __isl_take isl_pw_multi_aff *pma2);
4327 __isl_give isl_union_pw_multi_aff *isl_union_pw_multi_aff_add(
4328 __isl_take isl_union_pw_multi_aff *upma1,
4329 __isl_take isl_union_pw_multi_aff *upma2);
4330 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_union_add(
4331 __isl_take isl_pw_multi_aff *pma1,
4332 __isl_take isl_pw_multi_aff *pma2);
4333 __isl_give isl_multi_aff *isl_multi_aff_sub(
4334 __isl_take isl_multi_aff *ma1,
4335 __isl_take isl_multi_aff *ma2);
4336 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_sub(
4337 __isl_take isl_pw_multi_aff *pma1,
4338 __isl_take isl_pw_multi_aff *pma2);
4339 __isl_give isl_union_pw_multi_aff *isl_union_pw_multi_aff_sub(
4340 __isl_take isl_union_pw_multi_aff *upma1,
4341 __isl_take isl_union_pw_multi_aff *upma2);
4343 C<isl_multi_aff_sub> subtracts the second argument from the first.
4345 __isl_give isl_multi_aff *isl_multi_aff_scale(
4346 __isl_take isl_multi_aff *maff,
4348 __isl_give isl_multi_aff *isl_multi_aff_scale_val(
4349 __isl_take isl_multi_aff *ma,
4350 __isl_take isl_val *v);
4351 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_scale_val(
4352 __isl_take isl_pw_multi_aff *pma,
4353 __isl_take isl_val *v);
4354 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_scale_val(
4355 __isl_take isl_multi_pw_aff *mpa,
4356 __isl_take isl_val *v);
4357 __isl_give isl_multi_aff *isl_multi_aff_scale_vec(
4358 __isl_take isl_multi_aff *ma,
4359 __isl_take isl_vec *v);
4360 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_scale_vec(
4361 __isl_take isl_pw_multi_aff *pma,
4362 __isl_take isl_vec *v);
4363 __isl_give isl_union_pw_multi_aff *isl_union_pw_multi_aff_scale_vec(
4364 __isl_take isl_union_pw_multi_aff *upma,
4365 __isl_take isl_vec *v);
4367 C<isl_multi_aff_scale_vec> scales the first elements of C<ma>
4368 by the corresponding elements of C<v>.
4370 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_intersect_params(
4371 __isl_take isl_pw_multi_aff *pma,
4372 __isl_take isl_set *set);
4373 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_intersect_domain(
4374 __isl_take isl_pw_multi_aff *pma,
4375 __isl_take isl_set *set);
4376 __isl_give isl_union_pw_multi_aff *
4377 isl_union_pw_multi_aff_intersect_domain(
4378 __isl_take isl_union_pw_multi_aff *upma,
4379 __isl_take isl_union_set *uset);
4380 __isl_give isl_multi_aff *isl_multi_aff_lift(
4381 __isl_take isl_multi_aff *maff,
4382 __isl_give isl_local_space **ls);
4383 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_coalesce(
4384 __isl_take isl_pw_multi_aff *pma);
4385 __isl_give isl_multi_aff *isl_multi_aff_align_params(
4386 __isl_take isl_multi_aff *multi,
4387 __isl_take isl_space *model);
4388 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_align_params(
4389 __isl_take isl_pw_multi_aff *pma,
4390 __isl_take isl_space *model);
4391 __isl_give isl_pw_multi_aff *
4392 isl_pw_multi_aff_project_domain_on_params(
4393 __isl_take isl_pw_multi_aff *pma);
4394 __isl_give isl_multi_aff *isl_multi_aff_gist_params(
4395 __isl_take isl_multi_aff *maff,
4396 __isl_take isl_set *context);
4397 __isl_give isl_multi_aff *isl_multi_aff_gist(
4398 __isl_take isl_multi_aff *maff,
4399 __isl_take isl_set *context);
4400 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_gist_params(
4401 __isl_take isl_pw_multi_aff *pma,
4402 __isl_take isl_set *set);
4403 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_gist(
4404 __isl_take isl_pw_multi_aff *pma,
4405 __isl_take isl_set *set);
4406 __isl_give isl_set *isl_pw_multi_aff_domain(
4407 __isl_take isl_pw_multi_aff *pma);
4408 __isl_give isl_union_set *isl_union_pw_multi_aff_domain(
4409 __isl_take isl_union_pw_multi_aff *upma);
4410 __isl_give isl_multi_aff *isl_multi_aff_range_splice(
4411 __isl_take isl_multi_aff *ma1, unsigned pos,
4412 __isl_take isl_multi_aff *ma2);
4413 __isl_give isl_multi_aff *isl_multi_aff_splice(
4414 __isl_take isl_multi_aff *ma1,
4415 unsigned in_pos, unsigned out_pos,
4416 __isl_take isl_multi_aff *ma2);
4417 __isl_give isl_multi_aff *isl_multi_aff_range_product(
4418 __isl_take isl_multi_aff *ma1,
4419 __isl_take isl_multi_aff *ma2);
4420 __isl_give isl_multi_aff *isl_multi_aff_flat_range_product(
4421 __isl_take isl_multi_aff *ma1,
4422 __isl_take isl_multi_aff *ma2);
4423 __isl_give isl_multi_aff *isl_multi_aff_product(
4424 __isl_take isl_multi_aff *ma1,
4425 __isl_take isl_multi_aff *ma2);
4426 __isl_give isl_pw_multi_aff *
4427 isl_pw_multi_aff_range_product(
4428 __isl_take isl_pw_multi_aff *pma1,
4429 __isl_take isl_pw_multi_aff *pma2);
4430 __isl_give isl_pw_multi_aff *
4431 isl_pw_multi_aff_flat_range_product(
4432 __isl_take isl_pw_multi_aff *pma1,
4433 __isl_take isl_pw_multi_aff *pma2);
4434 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_product(
4435 __isl_take isl_pw_multi_aff *pma1,
4436 __isl_take isl_pw_multi_aff *pma2);
4437 __isl_give isl_union_pw_multi_aff *
4438 isl_union_pw_multi_aff_flat_range_product(
4439 __isl_take isl_union_pw_multi_aff *upma1,
4440 __isl_take isl_union_pw_multi_aff *upma2);
4441 __isl_give isl_multi_pw_aff *
4442 isl_multi_pw_aff_range_splice(
4443 __isl_take isl_multi_pw_aff *mpa1, unsigned pos,
4444 __isl_take isl_multi_pw_aff *mpa2);
4445 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_splice(
4446 __isl_take isl_multi_pw_aff *mpa1,
4447 unsigned in_pos, unsigned out_pos,
4448 __isl_take isl_multi_pw_aff *mpa2);
4449 __isl_give isl_multi_pw_aff *
4450 isl_multi_pw_aff_range_product(
4451 __isl_take isl_multi_pw_aff *mpa1,
4452 __isl_take isl_multi_pw_aff *mpa2);
4453 __isl_give isl_multi_pw_aff *
4454 isl_multi_pw_aff_flat_range_product(
4455 __isl_take isl_multi_pw_aff *mpa1,
4456 __isl_take isl_multi_pw_aff *mpa2);
4458 If the C<ls> argument of C<isl_multi_aff_lift> is not C<NULL>,
4459 then it is assigned the local space that lies at the basis of
4460 the lifting applied.
4462 #include <isl/aff.h>
4463 __isl_give isl_multi_aff *isl_multi_aff_pullback_multi_aff(
4464 __isl_take isl_multi_aff *ma1,
4465 __isl_take isl_multi_aff *ma2);
4466 __isl_give isl_pw_multi_aff *
4467 isl_pw_multi_aff_pullback_multi_aff(
4468 __isl_take isl_pw_multi_aff *pma,
4469 __isl_take isl_multi_aff *ma);
4470 __isl_give isl_pw_multi_aff *
4471 isl_pw_multi_aff_pullback_pw_multi_aff(
4472 __isl_take isl_pw_multi_aff *pma1,
4473 __isl_take isl_pw_multi_aff *pma2);
4475 The function C<isl_multi_aff_pullback_multi_aff> precomposes C<ma1> by C<ma2>.
4476 In other words, C<ma2> is plugged
4479 __isl_give isl_set *isl_multi_aff_lex_le_set(
4480 __isl_take isl_multi_aff *ma1,
4481 __isl_take isl_multi_aff *ma2);
4482 __isl_give isl_set *isl_multi_aff_lex_ge_set(
4483 __isl_take isl_multi_aff *ma1,
4484 __isl_take isl_multi_aff *ma2);
4486 The function C<isl_multi_aff_lex_le_set> returns a set
4487 containing those elements in the shared domain space
4488 where C<ma1> is lexicographically smaller than or
4491 An expression can be read from input using
4493 #include <isl/aff.h>
4494 __isl_give isl_multi_aff *isl_multi_aff_read_from_str(
4495 isl_ctx *ctx, const char *str);
4496 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_read_from_str(
4497 isl_ctx *ctx, const char *str);
4498 __isl_give isl_union_pw_multi_aff *
4499 isl_union_pw_multi_aff_read_from_str(
4500 isl_ctx *ctx, const char *str);
4502 An expression can be printed using
4504 #include <isl/aff.h>
4505 __isl_give isl_printer *isl_printer_print_multi_aff(
4506 __isl_take isl_printer *p,
4507 __isl_keep isl_multi_aff *maff);
4508 __isl_give isl_printer *isl_printer_print_pw_multi_aff(
4509 __isl_take isl_printer *p,
4510 __isl_keep isl_pw_multi_aff *pma);
4511 __isl_give isl_printer *isl_printer_print_union_pw_multi_aff(
4512 __isl_take isl_printer *p,
4513 __isl_keep isl_union_pw_multi_aff *upma);
4514 __isl_give isl_printer *isl_printer_print_multi_pw_aff(
4515 __isl_take isl_printer *p,
4516 __isl_keep isl_multi_pw_aff *mpa);
4520 Points are elements of a set. They can be used to construct
4521 simple sets (boxes) or they can be used to represent the
4522 individual elements of a set.
4523 The zero point (the origin) can be created using
4525 __isl_give isl_point *isl_point_zero(__isl_take isl_space *space);
4527 The coordinates of a point can be inspected, set and changed
4530 int isl_point_get_coordinate(__isl_keep isl_point *pnt,
4531 enum isl_dim_type type, int pos, isl_int *v);
4532 __isl_give isl_val *isl_point_get_coordinate_val(
4533 __isl_keep isl_point *pnt,
4534 enum isl_dim_type type, int pos);
4535 __isl_give isl_point *isl_point_set_coordinate(
4536 __isl_take isl_point *pnt,
4537 enum isl_dim_type type, int pos, isl_int v);
4538 __isl_give isl_point *isl_point_set_coordinate_val(
4539 __isl_take isl_point *pnt,
4540 enum isl_dim_type type, int pos,
4541 __isl_take isl_val *v);
4543 __isl_give isl_point *isl_point_add_ui(
4544 __isl_take isl_point *pnt,
4545 enum isl_dim_type type, int pos, unsigned val);
4546 __isl_give isl_point *isl_point_sub_ui(
4547 __isl_take isl_point *pnt,
4548 enum isl_dim_type type, int pos, unsigned val);
4550 Other properties can be obtained using
4552 isl_ctx *isl_point_get_ctx(__isl_keep isl_point *pnt);
4554 Points can be copied or freed using
4556 __isl_give isl_point *isl_point_copy(
4557 __isl_keep isl_point *pnt);
4558 void isl_point_free(__isl_take isl_point *pnt);
4560 A singleton set can be created from a point using
4562 __isl_give isl_basic_set *isl_basic_set_from_point(
4563 __isl_take isl_point *pnt);
4564 __isl_give isl_set *isl_set_from_point(
4565 __isl_take isl_point *pnt);
4567 and a box can be created from two opposite extremal points using
4569 __isl_give isl_basic_set *isl_basic_set_box_from_points(
4570 __isl_take isl_point *pnt1,
4571 __isl_take isl_point *pnt2);
4572 __isl_give isl_set *isl_set_box_from_points(
4573 __isl_take isl_point *pnt1,
4574 __isl_take isl_point *pnt2);
4576 All elements of a B<bounded> (union) set can be enumerated using
4577 the following functions.
4579 int isl_set_foreach_point(__isl_keep isl_set *set,
4580 int (*fn)(__isl_take isl_point *pnt, void *user),
4582 int isl_union_set_foreach_point(__isl_keep isl_union_set *uset,
4583 int (*fn)(__isl_take isl_point *pnt, void *user),
4586 The function C<fn> is called for each integer point in
4587 C<set> with as second argument the last argument of
4588 the C<isl_set_foreach_point> call. The function C<fn>
4589 should return C<0> on success and C<-1> on failure.
4590 In the latter case, C<isl_set_foreach_point> will stop
4591 enumerating and return C<-1> as well.
4592 If the enumeration is performed successfully and to completion,
4593 then C<isl_set_foreach_point> returns C<0>.
4595 To obtain a single point of a (basic) set, use
4597 __isl_give isl_point *isl_basic_set_sample_point(
4598 __isl_take isl_basic_set *bset);
4599 __isl_give isl_point *isl_set_sample_point(
4600 __isl_take isl_set *set);
4602 If C<set> does not contain any (integer) points, then the
4603 resulting point will be ``void'', a property that can be
4606 int isl_point_is_void(__isl_keep isl_point *pnt);
4608 =head2 Piecewise Quasipolynomials
4610 A piecewise quasipolynomial is a particular kind of function that maps
4611 a parametric point to a rational value.
4612 More specifically, a quasipolynomial is a polynomial expression in greatest
4613 integer parts of affine expressions of parameters and variables.
4614 A piecewise quasipolynomial is a subdivision of a given parametric
4615 domain into disjoint cells with a quasipolynomial associated to
4616 each cell. The value of the piecewise quasipolynomial at a given
4617 point is the value of the quasipolynomial associated to the cell
4618 that contains the point. Outside of the union of cells,
4619 the value is assumed to be zero.
4620 For example, the piecewise quasipolynomial
4622 [n] -> { [x] -> ((1 + n) - x) : x <= n and x >= 0 }
4624 maps C<x> to C<1 + n - x> for values of C<x> between C<0> and C<n>.
4625 A given piecewise quasipolynomial has a fixed domain dimension.
4626 Union piecewise quasipolynomials are used to contain piecewise quasipolynomials
4627 defined over different domains.
4628 Piecewise quasipolynomials are mainly used by the C<barvinok>
4629 library for representing the number of elements in a parametric set or map.
4630 For example, the piecewise quasipolynomial above represents
4631 the number of points in the map
4633 [n] -> { [x] -> [y] : x,y >= 0 and 0 <= x + y <= n }
4635 =head3 Input and Output
4637 Piecewise quasipolynomials can be read from input using
4639 __isl_give isl_union_pw_qpolynomial *
4640 isl_union_pw_qpolynomial_read_from_str(
4641 isl_ctx *ctx, const char *str);
4643 Quasipolynomials and piecewise quasipolynomials can be printed
4644 using the following functions.
4646 __isl_give isl_printer *isl_printer_print_qpolynomial(
4647 __isl_take isl_printer *p,
4648 __isl_keep isl_qpolynomial *qp);
4650 __isl_give isl_printer *isl_printer_print_pw_qpolynomial(
4651 __isl_take isl_printer *p,
4652 __isl_keep isl_pw_qpolynomial *pwqp);
4654 __isl_give isl_printer *isl_printer_print_union_pw_qpolynomial(
4655 __isl_take isl_printer *p,
4656 __isl_keep isl_union_pw_qpolynomial *upwqp);
4658 The output format of the printer
4659 needs to be set to either C<ISL_FORMAT_ISL> or C<ISL_FORMAT_C>.
4660 For C<isl_printer_print_union_pw_qpolynomial>, only C<ISL_FORMAT_ISL>
4662 In case of printing in C<ISL_FORMAT_C>, the user may want
4663 to set the names of all dimensions
4665 __isl_give isl_qpolynomial *isl_qpolynomial_set_dim_name(
4666 __isl_take isl_qpolynomial *qp,
4667 enum isl_dim_type type, unsigned pos,
4669 __isl_give isl_pw_qpolynomial *
4670 isl_pw_qpolynomial_set_dim_name(
4671 __isl_take isl_pw_qpolynomial *pwqp,
4672 enum isl_dim_type type, unsigned pos,
4675 =head3 Creating New (Piecewise) Quasipolynomials
4677 Some simple quasipolynomials can be created using the following functions.
4678 More complicated quasipolynomials can be created by applying
4679 operations such as addition and multiplication
4680 on the resulting quasipolynomials
4682 __isl_give isl_qpolynomial *isl_qpolynomial_zero_on_domain(
4683 __isl_take isl_space *domain);
4684 __isl_give isl_qpolynomial *isl_qpolynomial_one_on_domain(
4685 __isl_take isl_space *domain);
4686 __isl_give isl_qpolynomial *isl_qpolynomial_infty_on_domain(
4687 __isl_take isl_space *domain);
4688 __isl_give isl_qpolynomial *isl_qpolynomial_neginfty_on_domain(
4689 __isl_take isl_space *domain);
4690 __isl_give isl_qpolynomial *isl_qpolynomial_nan_on_domain(
4691 __isl_take isl_space *domain);
4692 __isl_give isl_qpolynomial *isl_qpolynomial_rat_cst_on_domain(
4693 __isl_take isl_space *domain,
4694 const isl_int n, const isl_int d);
4695 __isl_give isl_qpolynomial *isl_qpolynomial_val_on_domain(
4696 __isl_take isl_space *domain,
4697 __isl_take isl_val *val);
4698 __isl_give isl_qpolynomial *isl_qpolynomial_var_on_domain(
4699 __isl_take isl_space *domain,
4700 enum isl_dim_type type, unsigned pos);
4701 __isl_give isl_qpolynomial *isl_qpolynomial_from_aff(
4702 __isl_take isl_aff *aff);
4704 Note that the space in which a quasipolynomial lives is a map space
4705 with a one-dimensional range. The C<domain> argument in some of
4706 the functions above corresponds to the domain of this map space.
4708 The zero piecewise quasipolynomial or a piecewise quasipolynomial
4709 with a single cell can be created using the following functions.
4710 Multiple of these single cell piecewise quasipolynomials can
4711 be combined to create more complicated piecewise quasipolynomials.
4713 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_zero(
4714 __isl_take isl_space *space);
4715 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_alloc(
4716 __isl_take isl_set *set,
4717 __isl_take isl_qpolynomial *qp);
4718 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_from_qpolynomial(
4719 __isl_take isl_qpolynomial *qp);
4720 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_from_pw_aff(
4721 __isl_take isl_pw_aff *pwaff);
4723 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_zero(
4724 __isl_take isl_space *space);
4725 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_from_pw_qpolynomial(
4726 __isl_take isl_pw_qpolynomial *pwqp);
4727 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_add_pw_qpolynomial(
4728 __isl_take isl_union_pw_qpolynomial *upwqp,
4729 __isl_take isl_pw_qpolynomial *pwqp);
4731 Quasipolynomials can be copied and freed again using the following
4734 __isl_give isl_qpolynomial *isl_qpolynomial_copy(
4735 __isl_keep isl_qpolynomial *qp);
4736 void *isl_qpolynomial_free(__isl_take isl_qpolynomial *qp);
4738 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_copy(
4739 __isl_keep isl_pw_qpolynomial *pwqp);
4740 void *isl_pw_qpolynomial_free(
4741 __isl_take isl_pw_qpolynomial *pwqp);
4743 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_copy(
4744 __isl_keep isl_union_pw_qpolynomial *upwqp);
4745 void *isl_union_pw_qpolynomial_free(
4746 __isl_take isl_union_pw_qpolynomial *upwqp);
4748 =head3 Inspecting (Piecewise) Quasipolynomials
4750 To iterate over all piecewise quasipolynomials in a union
4751 piecewise quasipolynomial, use the following function
4753 int isl_union_pw_qpolynomial_foreach_pw_qpolynomial(
4754 __isl_keep isl_union_pw_qpolynomial *upwqp,
4755 int (*fn)(__isl_take isl_pw_qpolynomial *pwqp, void *user),
4758 To extract the piecewise quasipolynomial in a given space from a union, use
4760 __isl_give isl_pw_qpolynomial *
4761 isl_union_pw_qpolynomial_extract_pw_qpolynomial(
4762 __isl_keep isl_union_pw_qpolynomial *upwqp,
4763 __isl_take isl_space *space);
4765 To iterate over the cells in a piecewise quasipolynomial,
4766 use either of the following two functions
4768 int isl_pw_qpolynomial_foreach_piece(
4769 __isl_keep isl_pw_qpolynomial *pwqp,
4770 int (*fn)(__isl_take isl_set *set,
4771 __isl_take isl_qpolynomial *qp,
4772 void *user), void *user);
4773 int isl_pw_qpolynomial_foreach_lifted_piece(
4774 __isl_keep isl_pw_qpolynomial *pwqp,
4775 int (*fn)(__isl_take isl_set *set,
4776 __isl_take isl_qpolynomial *qp,
4777 void *user), void *user);
4779 As usual, the function C<fn> should return C<0> on success
4780 and C<-1> on failure. The difference between
4781 C<isl_pw_qpolynomial_foreach_piece> and
4782 C<isl_pw_qpolynomial_foreach_lifted_piece> is that
4783 C<isl_pw_qpolynomial_foreach_lifted_piece> will first
4784 compute unique representations for all existentially quantified
4785 variables and then turn these existentially quantified variables
4786 into extra set variables, adapting the associated quasipolynomial
4787 accordingly. This means that the C<set> passed to C<fn>
4788 will not have any existentially quantified variables, but that
4789 the dimensions of the sets may be different for different
4790 invocations of C<fn>.
4792 The constant term of a quasipolynomial can be extracted using
4794 __isl_give isl_val *isl_qpolynomial_get_constant_val(
4795 __isl_keep isl_qpolynomial *qp);
4797 To iterate over all terms in a quasipolynomial,
4800 int isl_qpolynomial_foreach_term(
4801 __isl_keep isl_qpolynomial *qp,
4802 int (*fn)(__isl_take isl_term *term,
4803 void *user), void *user);
4805 The terms themselves can be inspected and freed using
4808 unsigned isl_term_dim(__isl_keep isl_term *term,
4809 enum isl_dim_type type);
4810 void isl_term_get_num(__isl_keep isl_term *term,
4812 void isl_term_get_den(__isl_keep isl_term *term,
4814 __isl_give isl_val *isl_term_get_coefficient_val(
4815 __isl_keep isl_term *term);
4816 int isl_term_get_exp(__isl_keep isl_term *term,
4817 enum isl_dim_type type, unsigned pos);
4818 __isl_give isl_aff *isl_term_get_div(
4819 __isl_keep isl_term *term, unsigned pos);
4820 void isl_term_free(__isl_take isl_term *term);
4822 Each term is a product of parameters, set variables and
4823 integer divisions. The function C<isl_term_get_exp>
4824 returns the exponent of a given dimensions in the given term.
4825 The C<isl_int>s in the arguments of C<isl_term_get_num>
4826 and C<isl_term_get_den> need to have been initialized
4827 using C<isl_int_init> before calling these functions.
4829 =head3 Properties of (Piecewise) Quasipolynomials
4831 To check whether a quasipolynomial is actually a constant,
4832 use the following function.
4834 int isl_qpolynomial_is_cst(__isl_keep isl_qpolynomial *qp,
4835 isl_int *n, isl_int *d);
4837 If C<qp> is a constant and if C<n> and C<d> are not C<NULL>
4838 then the numerator and denominator of the constant
4839 are returned in C<*n> and C<*d>, respectively.
4841 To check whether two union piecewise quasipolynomials are
4842 obviously equal, use
4844 int isl_union_pw_qpolynomial_plain_is_equal(
4845 __isl_keep isl_union_pw_qpolynomial *upwqp1,
4846 __isl_keep isl_union_pw_qpolynomial *upwqp2);
4848 =head3 Operations on (Piecewise) Quasipolynomials
4850 __isl_give isl_qpolynomial *isl_qpolynomial_scale(
4851 __isl_take isl_qpolynomial *qp, isl_int v);
4852 __isl_give isl_qpolynomial *isl_qpolynomial_scale_val(
4853 __isl_take isl_qpolynomial *qp,
4854 __isl_take isl_val *v);
4855 __isl_give isl_qpolynomial *isl_qpolynomial_neg(
4856 __isl_take isl_qpolynomial *qp);
4857 __isl_give isl_qpolynomial *isl_qpolynomial_add(
4858 __isl_take isl_qpolynomial *qp1,
4859 __isl_take isl_qpolynomial *qp2);
4860 __isl_give isl_qpolynomial *isl_qpolynomial_sub(
4861 __isl_take isl_qpolynomial *qp1,
4862 __isl_take isl_qpolynomial *qp2);
4863 __isl_give isl_qpolynomial *isl_qpolynomial_mul(
4864 __isl_take isl_qpolynomial *qp1,
4865 __isl_take isl_qpolynomial *qp2);
4866 __isl_give isl_qpolynomial *isl_qpolynomial_pow(
4867 __isl_take isl_qpolynomial *qp, unsigned exponent);
4869 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_fix_val(
4870 __isl_take isl_pw_qpolynomial *pwqp,
4871 enum isl_dim_type type, unsigned n,
4872 __isl_take isl_val *v);
4873 __isl_give isl_pw_qpolynomial *
4874 isl_pw_qpolynomial_scale_val(
4875 __isl_take isl_pw_qpolynomial *pwqp,
4876 __isl_take isl_val *v);
4877 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_add(
4878 __isl_take isl_pw_qpolynomial *pwqp1,
4879 __isl_take isl_pw_qpolynomial *pwqp2);
4880 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_sub(
4881 __isl_take isl_pw_qpolynomial *pwqp1,
4882 __isl_take isl_pw_qpolynomial *pwqp2);
4883 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_add_disjoint(
4884 __isl_take isl_pw_qpolynomial *pwqp1,
4885 __isl_take isl_pw_qpolynomial *pwqp2);
4886 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_neg(
4887 __isl_take isl_pw_qpolynomial *pwqp);
4888 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_mul(
4889 __isl_take isl_pw_qpolynomial *pwqp1,
4890 __isl_take isl_pw_qpolynomial *pwqp2);
4891 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_pow(
4892 __isl_take isl_pw_qpolynomial *pwqp, unsigned exponent);
4894 __isl_give isl_union_pw_qpolynomial *
4895 isl_union_pw_qpolynomial_scale_val(
4896 __isl_take isl_union_pw_qpolynomial *upwqp,
4897 __isl_take isl_val *v);
4898 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_add(
4899 __isl_take isl_union_pw_qpolynomial *upwqp1,
4900 __isl_take isl_union_pw_qpolynomial *upwqp2);
4901 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_sub(
4902 __isl_take isl_union_pw_qpolynomial *upwqp1,
4903 __isl_take isl_union_pw_qpolynomial *upwqp2);
4904 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_mul(
4905 __isl_take isl_union_pw_qpolynomial *upwqp1,
4906 __isl_take isl_union_pw_qpolynomial *upwqp2);
4908 __isl_give isl_qpolynomial *isl_pw_qpolynomial_eval(
4909 __isl_take isl_pw_qpolynomial *pwqp,
4910 __isl_take isl_point *pnt);
4912 __isl_give isl_qpolynomial *isl_union_pw_qpolynomial_eval(
4913 __isl_take isl_union_pw_qpolynomial *upwqp,
4914 __isl_take isl_point *pnt);
4916 __isl_give isl_set *isl_pw_qpolynomial_domain(
4917 __isl_take isl_pw_qpolynomial *pwqp);
4918 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_intersect_domain(
4919 __isl_take isl_pw_qpolynomial *pwpq,
4920 __isl_take isl_set *set);
4921 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_intersect_params(
4922 __isl_take isl_pw_qpolynomial *pwpq,
4923 __isl_take isl_set *set);
4925 __isl_give isl_union_set *isl_union_pw_qpolynomial_domain(
4926 __isl_take isl_union_pw_qpolynomial *upwqp);
4927 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_intersect_domain(
4928 __isl_take isl_union_pw_qpolynomial *upwpq,
4929 __isl_take isl_union_set *uset);
4930 __isl_give isl_union_pw_qpolynomial *
4931 isl_union_pw_qpolynomial_intersect_params(
4932 __isl_take isl_union_pw_qpolynomial *upwpq,
4933 __isl_take isl_set *set);
4935 __isl_give isl_qpolynomial *isl_qpolynomial_align_params(
4936 __isl_take isl_qpolynomial *qp,
4937 __isl_take isl_space *model);
4939 __isl_give isl_qpolynomial *isl_qpolynomial_project_domain_on_params(
4940 __isl_take isl_qpolynomial *qp);
4941 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_project_domain_on_params(
4942 __isl_take isl_pw_qpolynomial *pwqp);
4944 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_coalesce(
4945 __isl_take isl_union_pw_qpolynomial *upwqp);
4947 __isl_give isl_qpolynomial *isl_qpolynomial_gist_params(
4948 __isl_take isl_qpolynomial *qp,
4949 __isl_take isl_set *context);
4950 __isl_give isl_qpolynomial *isl_qpolynomial_gist(
4951 __isl_take isl_qpolynomial *qp,
4952 __isl_take isl_set *context);
4954 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_gist_params(
4955 __isl_take isl_pw_qpolynomial *pwqp,
4956 __isl_take isl_set *context);
4957 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_gist(
4958 __isl_take isl_pw_qpolynomial *pwqp,
4959 __isl_take isl_set *context);
4961 __isl_give isl_union_pw_qpolynomial *
4962 isl_union_pw_qpolynomial_gist_params(
4963 __isl_take isl_union_pw_qpolynomial *upwqp,
4964 __isl_take isl_set *context);
4965 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_gist(
4966 __isl_take isl_union_pw_qpolynomial *upwqp,
4967 __isl_take isl_union_set *context);
4969 The gist operation applies the gist operation to each of
4970 the cells in the domain of the input piecewise quasipolynomial.
4971 The context is also exploited
4972 to simplify the quasipolynomials associated to each cell.
4974 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_to_polynomial(
4975 __isl_take isl_pw_qpolynomial *pwqp, int sign);
4976 __isl_give isl_union_pw_qpolynomial *
4977 isl_union_pw_qpolynomial_to_polynomial(
4978 __isl_take isl_union_pw_qpolynomial *upwqp, int sign);
4980 Approximate each quasipolynomial by a polynomial. If C<sign> is positive,
4981 the polynomial will be an overapproximation. If C<sign> is negative,
4982 it will be an underapproximation. If C<sign> is zero, the approximation
4983 will lie somewhere in between.
4985 =head2 Bounds on Piecewise Quasipolynomials and Piecewise Quasipolynomial Reductions
4987 A piecewise quasipolynomial reduction is a piecewise
4988 reduction (or fold) of quasipolynomials.
4989 In particular, the reduction can be maximum or a minimum.
4990 The objects are mainly used to represent the result of
4991 an upper or lower bound on a quasipolynomial over its domain,
4992 i.e., as the result of the following function.
4994 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_bound(
4995 __isl_take isl_pw_qpolynomial *pwqp,
4996 enum isl_fold type, int *tight);
4998 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_bound(
4999 __isl_take isl_union_pw_qpolynomial *upwqp,
5000 enum isl_fold type, int *tight);
5002 The C<type> argument may be either C<isl_fold_min> or C<isl_fold_max>.
5003 If C<tight> is not C<NULL>, then C<*tight> is set to C<1>
5004 is the returned bound is known be tight, i.e., for each value
5005 of the parameters there is at least
5006 one element in the domain that reaches the bound.
5007 If the domain of C<pwqp> is not wrapping, then the bound is computed
5008 over all elements in that domain and the result has a purely parametric
5009 domain. If the domain of C<pwqp> is wrapping, then the bound is
5010 computed over the range of the wrapped relation. The domain of the
5011 wrapped relation becomes the domain of the result.
5013 A (piecewise) quasipolynomial reduction can be copied or freed using the
5014 following functions.
5016 __isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_copy(
5017 __isl_keep isl_qpolynomial_fold *fold);
5018 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_copy(
5019 __isl_keep isl_pw_qpolynomial_fold *pwf);
5020 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_copy(
5021 __isl_keep isl_union_pw_qpolynomial_fold *upwf);
5022 void isl_qpolynomial_fold_free(
5023 __isl_take isl_qpolynomial_fold *fold);
5024 void *isl_pw_qpolynomial_fold_free(
5025 __isl_take isl_pw_qpolynomial_fold *pwf);
5026 void *isl_union_pw_qpolynomial_fold_free(
5027 __isl_take isl_union_pw_qpolynomial_fold *upwf);
5029 =head3 Printing Piecewise Quasipolynomial Reductions
5031 Piecewise quasipolynomial reductions can be printed
5032 using the following function.
5034 __isl_give isl_printer *isl_printer_print_pw_qpolynomial_fold(
5035 __isl_take isl_printer *p,
5036 __isl_keep isl_pw_qpolynomial_fold *pwf);
5037 __isl_give isl_printer *isl_printer_print_union_pw_qpolynomial_fold(
5038 __isl_take isl_printer *p,
5039 __isl_keep isl_union_pw_qpolynomial_fold *upwf);
5041 For C<isl_printer_print_pw_qpolynomial_fold>,
5042 output format of the printer
5043 needs to be set to either C<ISL_FORMAT_ISL> or C<ISL_FORMAT_C>.
5044 For C<isl_printer_print_union_pw_qpolynomial_fold>,
5045 output format of the printer
5046 needs to be set to C<ISL_FORMAT_ISL>.
5047 In case of printing in C<ISL_FORMAT_C>, the user may want
5048 to set the names of all dimensions
5050 __isl_give isl_pw_qpolynomial_fold *
5051 isl_pw_qpolynomial_fold_set_dim_name(
5052 __isl_take isl_pw_qpolynomial_fold *pwf,
5053 enum isl_dim_type type, unsigned pos,
5056 =head3 Inspecting (Piecewise) Quasipolynomial Reductions
5058 To iterate over all piecewise quasipolynomial reductions in a union
5059 piecewise quasipolynomial reduction, use the following function
5061 int isl_union_pw_qpolynomial_fold_foreach_pw_qpolynomial_fold(
5062 __isl_keep isl_union_pw_qpolynomial_fold *upwf,
5063 int (*fn)(__isl_take isl_pw_qpolynomial_fold *pwf,
5064 void *user), void *user);
5066 To iterate over the cells in a piecewise quasipolynomial reduction,
5067 use either of the following two functions
5069 int isl_pw_qpolynomial_fold_foreach_piece(
5070 __isl_keep isl_pw_qpolynomial_fold *pwf,
5071 int (*fn)(__isl_take isl_set *set,
5072 __isl_take isl_qpolynomial_fold *fold,
5073 void *user), void *user);
5074 int isl_pw_qpolynomial_fold_foreach_lifted_piece(
5075 __isl_keep isl_pw_qpolynomial_fold *pwf,
5076 int (*fn)(__isl_take isl_set *set,
5077 __isl_take isl_qpolynomial_fold *fold,
5078 void *user), void *user);
5080 See L<Inspecting (Piecewise) Quasipolynomials> for an explanation
5081 of the difference between these two functions.
5083 To iterate over all quasipolynomials in a reduction, use
5085 int isl_qpolynomial_fold_foreach_qpolynomial(
5086 __isl_keep isl_qpolynomial_fold *fold,
5087 int (*fn)(__isl_take isl_qpolynomial *qp,
5088 void *user), void *user);
5090 =head3 Properties of Piecewise Quasipolynomial Reductions
5092 To check whether two union piecewise quasipolynomial reductions are
5093 obviously equal, use
5095 int isl_union_pw_qpolynomial_fold_plain_is_equal(
5096 __isl_keep isl_union_pw_qpolynomial_fold *upwf1,
5097 __isl_keep isl_union_pw_qpolynomial_fold *upwf2);
5099 =head3 Operations on Piecewise Quasipolynomial Reductions
5101 __isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_scale(
5102 __isl_take isl_qpolynomial_fold *fold, isl_int v);
5103 __isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_scale_val(
5104 __isl_take isl_qpolynomial_fold *fold,
5105 __isl_take isl_val *v);
5106 __isl_give isl_pw_qpolynomial_fold *
5107 isl_pw_qpolynomial_fold_scale_val(
5108 __isl_take isl_pw_qpolynomial_fold *pwf,
5109 __isl_take isl_val *v);
5110 __isl_give isl_union_pw_qpolynomial_fold *
5111 isl_union_pw_qpolynomial_fold_scale_val(
5112 __isl_take isl_union_pw_qpolynomial_fold *upwf,
5113 __isl_take isl_val *v);
5115 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_add(
5116 __isl_take isl_pw_qpolynomial_fold *pwf1,
5117 __isl_take isl_pw_qpolynomial_fold *pwf2);
5119 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_fold(
5120 __isl_take isl_pw_qpolynomial_fold *pwf1,
5121 __isl_take isl_pw_qpolynomial_fold *pwf2);
5123 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_fold(
5124 __isl_take isl_union_pw_qpolynomial_fold *upwf1,
5125 __isl_take isl_union_pw_qpolynomial_fold *upwf2);
5127 __isl_give isl_qpolynomial *isl_pw_qpolynomial_fold_eval(
5128 __isl_take isl_pw_qpolynomial_fold *pwf,
5129 __isl_take isl_point *pnt);
5131 __isl_give isl_qpolynomial *isl_union_pw_qpolynomial_fold_eval(
5132 __isl_take isl_union_pw_qpolynomial_fold *upwf,
5133 __isl_take isl_point *pnt);
5135 __isl_give isl_pw_qpolynomial_fold *
5136 isl_pw_qpolynomial_fold_intersect_params(
5137 __isl_take isl_pw_qpolynomial_fold *pwf,
5138 __isl_take isl_set *set);
5140 __isl_give isl_union_set *isl_union_pw_qpolynomial_fold_domain(
5141 __isl_take isl_union_pw_qpolynomial_fold *upwf);
5142 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_intersect_domain(
5143 __isl_take isl_union_pw_qpolynomial_fold *upwf,
5144 __isl_take isl_union_set *uset);
5145 __isl_give isl_union_pw_qpolynomial_fold *
5146 isl_union_pw_qpolynomial_fold_intersect_params(
5147 __isl_take isl_union_pw_qpolynomial_fold *upwf,
5148 __isl_take isl_set *set);
5150 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_project_domain_on_params(
5151 __isl_take isl_pw_qpolynomial_fold *pwf);
5153 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_coalesce(
5154 __isl_take isl_pw_qpolynomial_fold *pwf);
5156 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_coalesce(
5157 __isl_take isl_union_pw_qpolynomial_fold *upwf);
5159 __isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_gist_params(
5160 __isl_take isl_qpolynomial_fold *fold,
5161 __isl_take isl_set *context);
5162 __isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_gist(
5163 __isl_take isl_qpolynomial_fold *fold,
5164 __isl_take isl_set *context);
5166 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_gist(
5167 __isl_take isl_pw_qpolynomial_fold *pwf,
5168 __isl_take isl_set *context);
5169 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_gist_params(
5170 __isl_take isl_pw_qpolynomial_fold *pwf,
5171 __isl_take isl_set *context);
5173 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_gist(
5174 __isl_take isl_union_pw_qpolynomial_fold *upwf,
5175 __isl_take isl_union_set *context);
5176 __isl_give isl_union_pw_qpolynomial_fold *
5177 isl_union_pw_qpolynomial_fold_gist_params(
5178 __isl_take isl_union_pw_qpolynomial_fold *upwf,
5179 __isl_take isl_set *context);
5181 The gist operation applies the gist operation to each of
5182 the cells in the domain of the input piecewise quasipolynomial reduction.
5183 In future, the operation will also exploit the context
5184 to simplify the quasipolynomial reductions associated to each cell.
5186 __isl_give isl_pw_qpolynomial_fold *
5187 isl_set_apply_pw_qpolynomial_fold(
5188 __isl_take isl_set *set,
5189 __isl_take isl_pw_qpolynomial_fold *pwf,
5191 __isl_give isl_pw_qpolynomial_fold *
5192 isl_map_apply_pw_qpolynomial_fold(
5193 __isl_take isl_map *map,
5194 __isl_take isl_pw_qpolynomial_fold *pwf,
5196 __isl_give isl_union_pw_qpolynomial_fold *
5197 isl_union_set_apply_union_pw_qpolynomial_fold(
5198 __isl_take isl_union_set *uset,
5199 __isl_take isl_union_pw_qpolynomial_fold *upwf,
5201 __isl_give isl_union_pw_qpolynomial_fold *
5202 isl_union_map_apply_union_pw_qpolynomial_fold(
5203 __isl_take isl_union_map *umap,
5204 __isl_take isl_union_pw_qpolynomial_fold *upwf,
5207 The functions taking a map
5208 compose the given map with the given piecewise quasipolynomial reduction.
5209 That is, compute a bound (of the same type as C<pwf> or C<upwf> itself)
5210 over all elements in the intersection of the range of the map
5211 and the domain of the piecewise quasipolynomial reduction
5212 as a function of an element in the domain of the map.
5213 The functions taking a set compute a bound over all elements in the
5214 intersection of the set and the domain of the
5215 piecewise quasipolynomial reduction.
5217 =head2 Parametric Vertex Enumeration
5219 The parametric vertex enumeration described in this section
5220 is mainly intended to be used internally and by the C<barvinok>
5223 #include <isl/vertices.h>
5224 __isl_give isl_vertices *isl_basic_set_compute_vertices(
5225 __isl_keep isl_basic_set *bset);
5227 The function C<isl_basic_set_compute_vertices> performs the
5228 actual computation of the parametric vertices and the chamber
5229 decomposition and store the result in an C<isl_vertices> object.
5230 This information can be queried by either iterating over all
5231 the vertices or iterating over all the chambers or cells
5232 and then iterating over all vertices that are active on the chamber.
5234 int isl_vertices_foreach_vertex(
5235 __isl_keep isl_vertices *vertices,
5236 int (*fn)(__isl_take isl_vertex *vertex, void *user),
5239 int isl_vertices_foreach_cell(
5240 __isl_keep isl_vertices *vertices,
5241 int (*fn)(__isl_take isl_cell *cell, void *user),
5243 int isl_cell_foreach_vertex(__isl_keep isl_cell *cell,
5244 int (*fn)(__isl_take isl_vertex *vertex, void *user),
5247 Other operations that can be performed on an C<isl_vertices> object are
5250 isl_ctx *isl_vertices_get_ctx(
5251 __isl_keep isl_vertices *vertices);
5252 int isl_vertices_get_n_vertices(
5253 __isl_keep isl_vertices *vertices);
5254 void isl_vertices_free(__isl_take isl_vertices *vertices);
5256 Vertices can be inspected and destroyed using the following functions.
5258 isl_ctx *isl_vertex_get_ctx(__isl_keep isl_vertex *vertex);
5259 int isl_vertex_get_id(__isl_keep isl_vertex *vertex);
5260 __isl_give isl_basic_set *isl_vertex_get_domain(
5261 __isl_keep isl_vertex *vertex);
5262 __isl_give isl_basic_set *isl_vertex_get_expr(
5263 __isl_keep isl_vertex *vertex);
5264 void isl_vertex_free(__isl_take isl_vertex *vertex);
5266 C<isl_vertex_get_expr> returns a singleton parametric set describing
5267 the vertex, while C<isl_vertex_get_domain> returns the activity domain
5269 Note that C<isl_vertex_get_domain> and C<isl_vertex_get_expr> return
5270 B<rational> basic sets, so they should mainly be used for inspection
5271 and should not be mixed with integer sets.
5273 Chambers can be inspected and destroyed using the following functions.
5275 isl_ctx *isl_cell_get_ctx(__isl_keep isl_cell *cell);
5276 __isl_give isl_basic_set *isl_cell_get_domain(
5277 __isl_keep isl_cell *cell);
5278 void isl_cell_free(__isl_take isl_cell *cell);
5280 =head1 Polyhedral Compilation Library
5282 This section collects functionality in C<isl> that has been specifically
5283 designed for use during polyhedral compilation.
5285 =head2 Dependence Analysis
5287 C<isl> contains specialized functionality for performing
5288 array dataflow analysis. That is, given a I<sink> access relation
5289 and a collection of possible I<source> access relations,
5290 C<isl> can compute relations that describe
5291 for each iteration of the sink access, which iteration
5292 of which of the source access relations was the last
5293 to access the same data element before the given iteration
5295 The resulting dependence relations map source iterations
5296 to the corresponding sink iterations.
5297 To compute standard flow dependences, the sink should be
5298 a read, while the sources should be writes.
5299 If any of the source accesses are marked as being I<may>
5300 accesses, then there will be a dependence from the last
5301 I<must> access B<and> from any I<may> access that follows
5302 this last I<must> access.
5303 In particular, if I<all> sources are I<may> accesses,
5304 then memory based dependence analysis is performed.
5305 If, on the other hand, all sources are I<must> accesses,
5306 then value based dependence analysis is performed.
5308 #include <isl/flow.h>
5310 typedef int (*isl_access_level_before)(void *first, void *second);
5312 __isl_give isl_access_info *isl_access_info_alloc(
5313 __isl_take isl_map *sink,
5314 void *sink_user, isl_access_level_before fn,
5316 __isl_give isl_access_info *isl_access_info_add_source(
5317 __isl_take isl_access_info *acc,
5318 __isl_take isl_map *source, int must,
5320 void *isl_access_info_free(__isl_take isl_access_info *acc);
5322 __isl_give isl_flow *isl_access_info_compute_flow(
5323 __isl_take isl_access_info *acc);
5325 int isl_flow_foreach(__isl_keep isl_flow *deps,
5326 int (*fn)(__isl_take isl_map *dep, int must,
5327 void *dep_user, void *user),
5329 __isl_give isl_map *isl_flow_get_no_source(
5330 __isl_keep isl_flow *deps, int must);
5331 void isl_flow_free(__isl_take isl_flow *deps);
5333 The function C<isl_access_info_compute_flow> performs the actual
5334 dependence analysis. The other functions are used to construct
5335 the input for this function or to read off the output.
5337 The input is collected in an C<isl_access_info>, which can
5338 be created through a call to C<isl_access_info_alloc>.
5339 The arguments to this functions are the sink access relation
5340 C<sink>, a token C<sink_user> used to identify the sink
5341 access to the user, a callback function for specifying the
5342 relative order of source and sink accesses, and the number
5343 of source access relations that will be added.
5344 The callback function has type C<int (*)(void *first, void *second)>.
5345 The function is called with two user supplied tokens identifying
5346 either a source or the sink and it should return the shared nesting
5347 level and the relative order of the two accesses.
5348 In particular, let I<n> be the number of loops shared by
5349 the two accesses. If C<first> precedes C<second> textually,
5350 then the function should return I<2 * n + 1>; otherwise,
5351 it should return I<2 * n>.
5352 The sources can be added to the C<isl_access_info> by performing
5353 (at most) C<max_source> calls to C<isl_access_info_add_source>.
5354 C<must> indicates whether the source is a I<must> access
5355 or a I<may> access. Note that a multi-valued access relation
5356 should only be marked I<must> if every iteration in the domain
5357 of the relation accesses I<all> elements in its image.
5358 The C<source_user> token is again used to identify
5359 the source access. The range of the source access relation
5360 C<source> should have the same dimension as the range
5361 of the sink access relation.
5362 The C<isl_access_info_free> function should usually not be
5363 called explicitly, because it is called implicitly by
5364 C<isl_access_info_compute_flow>.
5366 The result of the dependence analysis is collected in an
5367 C<isl_flow>. There may be elements of
5368 the sink access for which no preceding source access could be
5369 found or for which all preceding sources are I<may> accesses.
5370 The relations containing these elements can be obtained through
5371 calls to C<isl_flow_get_no_source>, the first with C<must> set
5372 and the second with C<must> unset.
5373 In the case of standard flow dependence analysis,
5374 with the sink a read and the sources I<must> writes,
5375 the first relation corresponds to the reads from uninitialized
5376 array elements and the second relation is empty.
5377 The actual flow dependences can be extracted using
5378 C<isl_flow_foreach>. This function will call the user-specified
5379 callback function C<fn> for each B<non-empty> dependence between
5380 a source and the sink. The callback function is called
5381 with four arguments, the actual flow dependence relation
5382 mapping source iterations to sink iterations, a boolean that
5383 indicates whether it is a I<must> or I<may> dependence, a token
5384 identifying the source and an additional C<void *> with value
5385 equal to the third argument of the C<isl_flow_foreach> call.
5386 A dependence is marked I<must> if it originates from a I<must>
5387 source and if it is not followed by any I<may> sources.
5389 After finishing with an C<isl_flow>, the user should call
5390 C<isl_flow_free> to free all associated memory.
5392 A higher-level interface to dependence analysis is provided
5393 by the following function.
5395 #include <isl/flow.h>
5397 int isl_union_map_compute_flow(__isl_take isl_union_map *sink,
5398 __isl_take isl_union_map *must_source,
5399 __isl_take isl_union_map *may_source,
5400 __isl_take isl_union_map *schedule,
5401 __isl_give isl_union_map **must_dep,
5402 __isl_give isl_union_map **may_dep,
5403 __isl_give isl_union_map **must_no_source,
5404 __isl_give isl_union_map **may_no_source);
5406 The arrays are identified by the tuple names of the ranges
5407 of the accesses. The iteration domains by the tuple names
5408 of the domains of the accesses and of the schedule.
5409 The relative order of the iteration domains is given by the
5410 schedule. The relations returned through C<must_no_source>
5411 and C<may_no_source> are subsets of C<sink>.
5412 Any of C<must_dep>, C<may_dep>, C<must_no_source>
5413 or C<may_no_source> may be C<NULL>, but a C<NULL> value for
5414 any of the other arguments is treated as an error.
5416 =head3 Interaction with Dependence Analysis
5418 During the dependence analysis, we frequently need to perform
5419 the following operation. Given a relation between sink iterations
5420 and potential source iterations from a particular source domain,
5421 what is the last potential source iteration corresponding to each
5422 sink iteration. It can sometimes be convenient to adjust
5423 the set of potential source iterations before or after each such operation.
5424 The prototypical example is fuzzy array dataflow analysis,
5425 where we need to analyze if, based on data-dependent constraints,
5426 the sink iteration can ever be executed without one or more of
5427 the corresponding potential source iterations being executed.
5428 If so, we can introduce extra parameters and select an unknown
5429 but fixed source iteration from the potential source iterations.
5430 To be able to perform such manipulations, C<isl> provides the following
5433 #include <isl/flow.h>
5435 typedef __isl_give isl_restriction *(*isl_access_restrict)(
5436 __isl_keep isl_map *source_map,
5437 __isl_keep isl_set *sink, void *source_user,
5439 __isl_give isl_access_info *isl_access_info_set_restrict(
5440 __isl_take isl_access_info *acc,
5441 isl_access_restrict fn, void *user);
5443 The function C<isl_access_info_set_restrict> should be called
5444 before calling C<isl_access_info_compute_flow> and registers a callback function
5445 that will be called any time C<isl> is about to compute the last
5446 potential source. The first argument is the (reverse) proto-dependence,
5447 mapping sink iterations to potential source iterations.
5448 The second argument represents the sink iterations for which
5449 we want to compute the last source iteration.
5450 The third argument is the token corresponding to the source
5451 and the final argument is the token passed to C<isl_access_info_set_restrict>.
5452 The callback is expected to return a restriction on either the input or
5453 the output of the operation computing the last potential source.
5454 If the input needs to be restricted then restrictions are needed
5455 for both the source and the sink iterations. The sink iterations
5456 and the potential source iterations will be intersected with these sets.
5457 If the output needs to be restricted then only a restriction on the source
5458 iterations is required.
5459 If any error occurs, the callback should return C<NULL>.
5460 An C<isl_restriction> object can be created, freed and inspected
5461 using the following functions.
5463 #include <isl/flow.h>
5465 __isl_give isl_restriction *isl_restriction_input(
5466 __isl_take isl_set *source_restr,
5467 __isl_take isl_set *sink_restr);
5468 __isl_give isl_restriction *isl_restriction_output(
5469 __isl_take isl_set *source_restr);
5470 __isl_give isl_restriction *isl_restriction_none(
5471 __isl_take isl_map *source_map);
5472 __isl_give isl_restriction *isl_restriction_empty(
5473 __isl_take isl_map *source_map);
5474 void *isl_restriction_free(
5475 __isl_take isl_restriction *restr);
5476 isl_ctx *isl_restriction_get_ctx(
5477 __isl_keep isl_restriction *restr);
5479 C<isl_restriction_none> and C<isl_restriction_empty> are special
5480 cases of C<isl_restriction_input>. C<isl_restriction_none>
5481 is essentially equivalent to
5483 isl_restriction_input(isl_set_universe(
5484 isl_space_range(isl_map_get_space(source_map))),
5486 isl_space_domain(isl_map_get_space(source_map))));
5488 whereas C<isl_restriction_empty> is essentially equivalent to
5490 isl_restriction_input(isl_set_empty(
5491 isl_space_range(isl_map_get_space(source_map))),
5493 isl_space_domain(isl_map_get_space(source_map))));
5497 B<The functionality described in this section is fairly new
5498 and may be subject to change.>
5500 The following function can be used to compute a schedule
5501 for a union of domains.
5502 By default, the algorithm used to construct the schedule is similar
5503 to that of C<Pluto>.
5504 Alternatively, Feautrier's multi-dimensional scheduling algorithm can
5506 The generated schedule respects all C<validity> dependences.
5507 That is, all dependence distances over these dependences in the
5508 scheduled space are lexicographically positive.
5509 The default algorithm tries to minimize the dependence distances over
5510 C<proximity> dependences.
5511 Moreover, it tries to obtain sequences (bands) of schedule dimensions
5512 for groups of domains where the dependence distances have only
5513 non-negative values.
5514 When using Feautrier's algorithm, the C<proximity> dependence
5515 distances are only minimized during the extension to a
5516 full-dimensional schedule.
5518 #include <isl/schedule.h>
5519 __isl_give isl_schedule *isl_union_set_compute_schedule(
5520 __isl_take isl_union_set *domain,
5521 __isl_take isl_union_map *validity,
5522 __isl_take isl_union_map *proximity);
5523 void *isl_schedule_free(__isl_take isl_schedule *sched);
5525 A mapping from the domains to the scheduled space can be obtained
5526 from an C<isl_schedule> using the following function.
5528 __isl_give isl_union_map *isl_schedule_get_map(
5529 __isl_keep isl_schedule *sched);
5531 A representation of the schedule can be printed using
5533 __isl_give isl_printer *isl_printer_print_schedule(
5534 __isl_take isl_printer *p,
5535 __isl_keep isl_schedule *schedule);
5537 A representation of the schedule as a forest of bands can be obtained
5538 using the following function.
5540 __isl_give isl_band_list *isl_schedule_get_band_forest(
5541 __isl_keep isl_schedule *schedule);
5543 The individual bands can be visited in depth-first post-order
5544 using the following function.
5546 #include <isl/schedule.h>
5547 int isl_schedule_foreach_band(
5548 __isl_keep isl_schedule *sched,
5549 int (*fn)(__isl_keep isl_band *band, void *user),
5552 The list can be manipulated as explained in L<"Lists">.
5553 The bands inside the list can be copied and freed using the following
5556 #include <isl/band.h>
5557 __isl_give isl_band *isl_band_copy(
5558 __isl_keep isl_band *band);
5559 void *isl_band_free(__isl_take isl_band *band);
5561 Each band contains zero or more scheduling dimensions.
5562 These are referred to as the members of the band.
5563 The section of the schedule that corresponds to the band is
5564 referred to as the partial schedule of the band.
5565 For those nodes that participate in a band, the outer scheduling
5566 dimensions form the prefix schedule, while the inner scheduling
5567 dimensions form the suffix schedule.
5568 That is, if we take a cut of the band forest, then the union of
5569 the concatenations of the prefix, partial and suffix schedules of
5570 each band in the cut is equal to the entire schedule (modulo
5571 some possible padding at the end with zero scheduling dimensions).
5572 The properties of a band can be inspected using the following functions.
5574 #include <isl/band.h>
5575 isl_ctx *isl_band_get_ctx(__isl_keep isl_band *band);
5577 int isl_band_has_children(__isl_keep isl_band *band);
5578 __isl_give isl_band_list *isl_band_get_children(
5579 __isl_keep isl_band *band);
5581 __isl_give isl_union_map *isl_band_get_prefix_schedule(
5582 __isl_keep isl_band *band);
5583 __isl_give isl_union_map *isl_band_get_partial_schedule(
5584 __isl_keep isl_band *band);
5585 __isl_give isl_union_map *isl_band_get_suffix_schedule(
5586 __isl_keep isl_band *band);
5588 int isl_band_n_member(__isl_keep isl_band *band);
5589 int isl_band_member_is_zero_distance(
5590 __isl_keep isl_band *band, int pos);
5592 int isl_band_list_foreach_band(
5593 __isl_keep isl_band_list *list,
5594 int (*fn)(__isl_keep isl_band *band, void *user),
5597 Note that a scheduling dimension is considered to be ``zero
5598 distance'' if it does not carry any proximity dependences
5600 That is, if the dependence distances of the proximity
5601 dependences are all zero in that direction (for fixed
5602 iterations of outer bands).
5603 Like C<isl_schedule_foreach_band>,
5604 the function C<isl_band_list_foreach_band> calls C<fn> on the bands
5605 in depth-first post-order.
5607 A band can be tiled using the following function.
5609 #include <isl/band.h>
5610 int isl_band_tile(__isl_keep isl_band *band,
5611 __isl_take isl_vec *sizes);
5613 int isl_options_set_tile_scale_tile_loops(isl_ctx *ctx,
5615 int isl_options_get_tile_scale_tile_loops(isl_ctx *ctx);
5616 int isl_options_set_tile_shift_point_loops(isl_ctx *ctx,
5618 int isl_options_get_tile_shift_point_loops(isl_ctx *ctx);
5620 The C<isl_band_tile> function tiles the band using the given tile sizes
5621 inside its schedule.
5622 A new child band is created to represent the point loops and it is
5623 inserted between the modified band and its children.
5624 The C<tile_scale_tile_loops> option specifies whether the tile
5625 loops iterators should be scaled by the tile sizes.
5626 If the C<tile_shift_point_loops> option is set, then the point loops
5627 are shifted to start at zero.
5629 A band can be split into two nested bands using the following function.
5631 int isl_band_split(__isl_keep isl_band *band, int pos);
5633 The resulting outer band contains the first C<pos> dimensions of C<band>
5634 while the inner band contains the remaining dimensions.
5636 A representation of the band can be printed using
5638 #include <isl/band.h>
5639 __isl_give isl_printer *isl_printer_print_band(
5640 __isl_take isl_printer *p,
5641 __isl_keep isl_band *band);
5645 #include <isl/schedule.h>
5646 int isl_options_set_schedule_max_coefficient(
5647 isl_ctx *ctx, int val);
5648 int isl_options_get_schedule_max_coefficient(
5650 int isl_options_set_schedule_max_constant_term(
5651 isl_ctx *ctx, int val);
5652 int isl_options_get_schedule_max_constant_term(
5654 int isl_options_set_schedule_fuse(isl_ctx *ctx, int val);
5655 int isl_options_get_schedule_fuse(isl_ctx *ctx);
5656 int isl_options_set_schedule_maximize_band_depth(
5657 isl_ctx *ctx, int val);
5658 int isl_options_get_schedule_maximize_band_depth(
5660 int isl_options_set_schedule_outer_zero_distance(
5661 isl_ctx *ctx, int val);
5662 int isl_options_get_schedule_outer_zero_distance(
5664 int isl_options_set_schedule_split_scaled(
5665 isl_ctx *ctx, int val);
5666 int isl_options_get_schedule_split_scaled(
5668 int isl_options_set_schedule_algorithm(
5669 isl_ctx *ctx, int val);
5670 int isl_options_get_schedule_algorithm(
5672 int isl_options_set_schedule_separate_components(
5673 isl_ctx *ctx, int val);
5674 int isl_options_get_schedule_separate_components(
5679 =item * schedule_max_coefficient
5681 This option enforces that the coefficients for variable and parameter
5682 dimensions in the calculated schedule are not larger than the specified value.
5683 This option can significantly increase the speed of the scheduling calculation
5684 and may also prevent fusing of unrelated dimensions. A value of -1 means that
5685 this option does not introduce bounds on the variable or parameter
5688 =item * schedule_max_constant_term
5690 This option enforces that the constant coefficients in the calculated schedule
5691 are not larger than the maximal constant term. This option can significantly
5692 increase the speed of the scheduling calculation and may also prevent fusing of
5693 unrelated dimensions. A value of -1 means that this option does not introduce
5694 bounds on the constant coefficients.
5696 =item * schedule_fuse
5698 This option controls the level of fusion.
5699 If this option is set to C<ISL_SCHEDULE_FUSE_MIN>, then loops in the
5700 resulting schedule will be distributed as much as possible.
5701 If this option is set to C<ISL_SCHEDULE_FUSE_MAX>, then C<isl> will
5702 try to fuse loops in the resulting schedule.
5704 =item * schedule_maximize_band_depth
5706 If this option is set, we do not split bands at the point
5707 where we detect splitting is necessary. Instead, we
5708 backtrack and split bands as early as possible. This
5709 reduces the number of splits and maximizes the width of
5710 the bands. Wider bands give more possibilities for tiling.
5711 Note that if the C<schedule_fuse> option is set to C<ISL_SCHEDULE_FUSE_MIN>,
5712 then bands will be split as early as possible, even if there is no need.
5713 The C<schedule_maximize_band_depth> option therefore has no effect in this case.
5715 =item * schedule_outer_zero_distance
5717 If this option is set, then we try to construct schedules
5718 where the outermost scheduling dimension in each band
5719 results in a zero dependence distance over the proximity
5722 =item * schedule_split_scaled
5724 If this option is set, then we try to construct schedules in which the
5725 constant term is split off from the linear part if the linear parts of
5726 the scheduling rows for all nodes in the graphs have a common non-trivial
5728 The constant term is then placed in a separate band and the linear
5731 =item * schedule_algorithm
5733 Selects the scheduling algorithm to be used.
5734 Available scheduling algorithms are C<ISL_SCHEDULE_ALGORITHM_ISL>
5735 and C<ISL_SCHEDULE_ALGORITHM_FEAUTRIER>.
5737 =item * schedule_separate_components
5739 If at any point the dependence graph contains any (weakly connected) components,
5740 then these components are scheduled separately.
5741 If this option is not set, then some iterations of the domains
5742 in these components may be scheduled together.
5743 If this option is set, then the components are given consecutive
5748 =head2 AST Generation
5750 This section describes the C<isl> functionality for generating
5751 ASTs that visit all the elements
5752 in a domain in an order specified by a schedule.
5753 In particular, given a C<isl_union_map>, an AST is generated
5754 that visits all the elements in the domain of the C<isl_union_map>
5755 according to the lexicographic order of the corresponding image
5756 element(s). If the range of the C<isl_union_map> consists of
5757 elements in more than one space, then each of these spaces is handled
5758 separately in an arbitrary order.
5759 It should be noted that the image elements only specify the I<order>
5760 in which the corresponding domain elements should be visited.
5761 No direct relation between the image elements and the loop iterators
5762 in the generated AST should be assumed.
5764 Each AST is generated within a build. The initial build
5765 simply specifies the constraints on the parameters (if any)
5766 and can be created, inspected, copied and freed using the following functions.
5768 #include <isl/ast_build.h>
5769 __isl_give isl_ast_build *isl_ast_build_from_context(
5770 __isl_take isl_set *set);
5771 isl_ctx *isl_ast_build_get_ctx(
5772 __isl_keep isl_ast_build *build);
5773 __isl_give isl_ast_build *isl_ast_build_copy(
5774 __isl_keep isl_ast_build *build);
5775 void *isl_ast_build_free(
5776 __isl_take isl_ast_build *build);
5778 The C<set> argument is usually a parameter set with zero or more parameters.
5779 More C<isl_ast_build> functions are described in L</"Nested AST Generation">
5780 and L</"Fine-grained Control over AST Generation">.
5781 Finally, the AST itself can be constructed using the following
5784 #include <isl/ast_build.h>
5785 __isl_give isl_ast_node *isl_ast_build_ast_from_schedule(
5786 __isl_keep isl_ast_build *build,
5787 __isl_take isl_union_map *schedule);
5789 =head3 Inspecting the AST
5791 The basic properties of an AST node can be obtained as follows.
5793 #include <isl/ast.h>
5794 isl_ctx *isl_ast_node_get_ctx(
5795 __isl_keep isl_ast_node *node);
5796 enum isl_ast_node_type isl_ast_node_get_type(
5797 __isl_keep isl_ast_node *node);
5799 The type of an AST node is one of
5800 C<isl_ast_node_for>,
5802 C<isl_ast_node_block> or
5803 C<isl_ast_node_user>.
5804 An C<isl_ast_node_for> represents a for node.
5805 An C<isl_ast_node_if> represents an if node.
5806 An C<isl_ast_node_block> represents a compound node.
5807 An C<isl_ast_node_user> represents an expression statement.
5808 An expression statement typically corresponds to a domain element, i.e.,
5809 one of the elements that is visited by the AST.
5811 Each type of node has its own additional properties.
5813 #include <isl/ast.h>
5814 __isl_give isl_ast_expr *isl_ast_node_for_get_iterator(
5815 __isl_keep isl_ast_node *node);
5816 __isl_give isl_ast_expr *isl_ast_node_for_get_init(
5817 __isl_keep isl_ast_node *node);
5818 __isl_give isl_ast_expr *isl_ast_node_for_get_cond(
5819 __isl_keep isl_ast_node *node);
5820 __isl_give isl_ast_expr *isl_ast_node_for_get_inc(
5821 __isl_keep isl_ast_node *node);
5822 __isl_give isl_ast_node *isl_ast_node_for_get_body(
5823 __isl_keep isl_ast_node *node);
5824 int isl_ast_node_for_is_degenerate(
5825 __isl_keep isl_ast_node *node);
5827 An C<isl_ast_for> is considered degenerate if it is known to execute
5830 #include <isl/ast.h>
5831 __isl_give isl_ast_expr *isl_ast_node_if_get_cond(
5832 __isl_keep isl_ast_node *node);
5833 __isl_give isl_ast_node *isl_ast_node_if_get_then(
5834 __isl_keep isl_ast_node *node);
5835 int isl_ast_node_if_has_else(
5836 __isl_keep isl_ast_node *node);
5837 __isl_give isl_ast_node *isl_ast_node_if_get_else(
5838 __isl_keep isl_ast_node *node);
5840 __isl_give isl_ast_node_list *
5841 isl_ast_node_block_get_children(
5842 __isl_keep isl_ast_node *node);
5844 __isl_give isl_ast_expr *isl_ast_node_user_get_expr(
5845 __isl_keep isl_ast_node *node);
5847 Each of the returned C<isl_ast_expr>s can in turn be inspected using
5848 the following functions.
5850 #include <isl/ast.h>
5851 isl_ctx *isl_ast_expr_get_ctx(
5852 __isl_keep isl_ast_expr *expr);
5853 enum isl_ast_expr_type isl_ast_expr_get_type(
5854 __isl_keep isl_ast_expr *expr);
5856 The type of an AST expression is one of
5858 C<isl_ast_expr_id> or
5859 C<isl_ast_expr_int>.
5860 An C<isl_ast_expr_op> represents the result of an operation.
5861 An C<isl_ast_expr_id> represents an identifier.
5862 An C<isl_ast_expr_int> represents an integer value.
5864 Each type of expression has its own additional properties.
5866 #include <isl/ast.h>
5867 enum isl_ast_op_type isl_ast_expr_get_op_type(
5868 __isl_keep isl_ast_expr *expr);
5869 int isl_ast_expr_get_op_n_arg(__isl_keep isl_ast_expr *expr);
5870 __isl_give isl_ast_expr *isl_ast_expr_get_op_arg(
5871 __isl_keep isl_ast_expr *expr, int pos);
5872 int isl_ast_node_foreach_ast_op_type(
5873 __isl_keep isl_ast_node *node,
5874 int (*fn)(enum isl_ast_op_type type, void *user),
5877 C<isl_ast_expr_get_op_type> returns the type of the operation
5878 performed. C<isl_ast_expr_get_op_n_arg> returns the number of
5879 arguments. C<isl_ast_expr_get_op_arg> returns the specified
5881 C<isl_ast_node_foreach_ast_op_type> calls C<fn> for each distinct
5882 C<isl_ast_op_type> that appears in C<node>.
5883 The operation type is one of the following.
5887 =item C<isl_ast_op_and>
5889 Logical I<and> of two arguments.
5890 Both arguments can be evaluated.
5892 =item C<isl_ast_op_and_then>
5894 Logical I<and> of two arguments.
5895 The second argument can only be evaluated if the first evaluates to true.
5897 =item C<isl_ast_op_or>
5899 Logical I<or> of two arguments.
5900 Both arguments can be evaluated.
5902 =item C<isl_ast_op_or_else>
5904 Logical I<or> of two arguments.
5905 The second argument can only be evaluated if the first evaluates to false.
5907 =item C<isl_ast_op_max>
5909 Maximum of two or more arguments.
5911 =item C<isl_ast_op_min>
5913 Minimum of two or more arguments.
5915 =item C<isl_ast_op_minus>
5919 =item C<isl_ast_op_add>
5921 Sum of two arguments.
5923 =item C<isl_ast_op_sub>
5925 Difference of two arguments.
5927 =item C<isl_ast_op_mul>
5929 Product of two arguments.
5931 =item C<isl_ast_op_div>
5933 Exact division. That is, the result is known to be an integer.
5935 =item C<isl_ast_op_fdiv_q>
5937 Result of integer division, rounded towards negative
5940 =item C<isl_ast_op_pdiv_q>
5942 Result of integer division, where dividend is known to be non-negative.
5944 =item C<isl_ast_op_pdiv_r>
5946 Remainder of integer division, where dividend is known to be non-negative.
5948 =item C<isl_ast_op_cond>
5950 Conditional operator defined on three arguments.
5951 If the first argument evaluates to true, then the result
5952 is equal to the second argument. Otherwise, the result
5953 is equal to the third argument.
5954 The second and third argument may only be evaluated if
5955 the first argument evaluates to true and false, respectively.
5956 Corresponds to C<a ? b : c> in C.
5958 =item C<isl_ast_op_select>
5960 Conditional operator defined on three arguments.
5961 If the first argument evaluates to true, then the result
5962 is equal to the second argument. Otherwise, the result
5963 is equal to the third argument.
5964 The second and third argument may be evaluated independently
5965 of the value of the first argument.
5966 Corresponds to C<a * b + (1 - a) * c> in C.
5968 =item C<isl_ast_op_eq>
5972 =item C<isl_ast_op_le>
5974 Less than or equal relation.
5976 =item C<isl_ast_op_lt>
5980 =item C<isl_ast_op_ge>
5982 Greater than or equal relation.
5984 =item C<isl_ast_op_gt>
5986 Greater than relation.
5988 =item C<isl_ast_op_call>
5991 The number of arguments of the C<isl_ast_expr> is one more than
5992 the number of arguments in the function call, the first argument
5993 representing the function being called.
5997 #include <isl/ast.h>
5998 __isl_give isl_id *isl_ast_expr_get_id(
5999 __isl_keep isl_ast_expr *expr);
6001 Return the identifier represented by the AST expression.
6003 #include <isl/ast.h>
6004 int isl_ast_expr_get_int(__isl_keep isl_ast_expr *expr,
6007 Return the integer represented by the AST expression.
6008 Note that the integer is returned through the C<v> argument.
6009 The return value of the function itself indicates whether the
6010 operation was performed successfully.
6012 =head3 Manipulating and printing the AST
6014 AST nodes can be copied and freed using the following functions.
6016 #include <isl/ast.h>
6017 __isl_give isl_ast_node *isl_ast_node_copy(
6018 __isl_keep isl_ast_node *node);
6019 void *isl_ast_node_free(__isl_take isl_ast_node *node);
6021 AST expressions can be copied and freed using the following functions.
6023 #include <isl/ast.h>
6024 __isl_give isl_ast_expr *isl_ast_expr_copy(
6025 __isl_keep isl_ast_expr *expr);
6026 void *isl_ast_expr_free(__isl_take isl_ast_expr *expr);
6028 New AST expressions can be created either directly or within
6029 the context of an C<isl_ast_build>.
6031 #include <isl/ast.h>
6032 __isl_give isl_ast_expr *isl_ast_expr_from_id(
6033 __isl_take isl_id *id);
6034 __isl_give isl_ast_expr *isl_ast_expr_neg(
6035 __isl_take isl_ast_expr *expr);
6036 __isl_give isl_ast_expr *isl_ast_expr_add(
6037 __isl_take isl_ast_expr *expr1,
6038 __isl_take isl_ast_expr *expr2);
6039 __isl_give isl_ast_expr *isl_ast_expr_sub(
6040 __isl_take isl_ast_expr *expr1,
6041 __isl_take isl_ast_expr *expr2);
6042 __isl_give isl_ast_expr *isl_ast_expr_mul(
6043 __isl_take isl_ast_expr *expr1,
6044 __isl_take isl_ast_expr *expr2);
6045 __isl_give isl_ast_expr *isl_ast_expr_div(
6046 __isl_take isl_ast_expr *expr1,
6047 __isl_take isl_ast_expr *expr2);
6048 __isl_give isl_ast_expr *isl_ast_expr_and(
6049 __isl_take isl_ast_expr *expr1,
6050 __isl_take isl_ast_expr *expr2)
6051 __isl_give isl_ast_expr *isl_ast_expr_or(
6052 __isl_take isl_ast_expr *expr1,
6053 __isl_take isl_ast_expr *expr2)
6055 #include <isl/ast_build.h>
6056 __isl_give isl_ast_expr *isl_ast_build_expr_from_pw_aff(
6057 __isl_keep isl_ast_build *build,
6058 __isl_take isl_pw_aff *pa);
6059 __isl_give isl_ast_expr *
6060 isl_ast_build_call_from_pw_multi_aff(
6061 __isl_keep isl_ast_build *build,
6062 __isl_take isl_pw_multi_aff *pma);
6064 The domains of C<pa> and C<pma> should correspond
6065 to the schedule space of C<build>.
6066 The tuple id of C<pma> is used as the function being called.
6068 User specified data can be attached to an C<isl_ast_node> and obtained
6069 from the same C<isl_ast_node> using the following functions.
6071 #include <isl/ast.h>
6072 __isl_give isl_ast_node *isl_ast_node_set_annotation(
6073 __isl_take isl_ast_node *node,
6074 __isl_take isl_id *annotation);
6075 __isl_give isl_id *isl_ast_node_get_annotation(
6076 __isl_keep isl_ast_node *node);
6078 Basic printing can be performed using the following functions.
6080 #include <isl/ast.h>
6081 __isl_give isl_printer *isl_printer_print_ast_expr(
6082 __isl_take isl_printer *p,
6083 __isl_keep isl_ast_expr *expr);
6084 __isl_give isl_printer *isl_printer_print_ast_node(
6085 __isl_take isl_printer *p,
6086 __isl_keep isl_ast_node *node);
6088 More advanced printing can be performed using the following functions.
6090 #include <isl/ast.h>
6091 __isl_give isl_printer *isl_ast_op_type_print_macro(
6092 enum isl_ast_op_type type,
6093 __isl_take isl_printer *p);
6094 __isl_give isl_printer *isl_ast_node_print_macros(
6095 __isl_keep isl_ast_node *node,
6096 __isl_take isl_printer *p);
6097 __isl_give isl_printer *isl_ast_node_print(
6098 __isl_keep isl_ast_node *node,
6099 __isl_take isl_printer *p,
6100 __isl_take isl_ast_print_options *options);
6101 __isl_give isl_printer *isl_ast_node_for_print(
6102 __isl_keep isl_ast_node *node,
6103 __isl_take isl_printer *p,
6104 __isl_take isl_ast_print_options *options);
6105 __isl_give isl_printer *isl_ast_node_if_print(
6106 __isl_keep isl_ast_node *node,
6107 __isl_take isl_printer *p,
6108 __isl_take isl_ast_print_options *options);
6110 While printing an C<isl_ast_node> in C<ISL_FORMAT_C>,
6111 C<isl> may print out an AST that makes use of macros such
6112 as C<floord>, C<min> and C<max>.
6113 C<isl_ast_op_type_print_macro> prints out the macro
6114 corresponding to a specific C<isl_ast_op_type>.
6115 C<isl_ast_node_print_macros> scans the C<isl_ast_node>
6116 for expressions where these macros would be used and prints
6117 out the required macro definitions.
6118 Essentially, C<isl_ast_node_print_macros> calls
6119 C<isl_ast_node_foreach_ast_op_type> with C<isl_ast_op_type_print_macro>
6120 as function argument.
6121 C<isl_ast_node_print>, C<isl_ast_node_for_print> and
6122 C<isl_ast_node_if_print> print an C<isl_ast_node>
6123 in C<ISL_FORMAT_C>, but allow for some extra control
6124 through an C<isl_ast_print_options> object.
6125 This object can be created using the following functions.
6127 #include <isl/ast.h>
6128 __isl_give isl_ast_print_options *
6129 isl_ast_print_options_alloc(isl_ctx *ctx);
6130 __isl_give isl_ast_print_options *
6131 isl_ast_print_options_copy(
6132 __isl_keep isl_ast_print_options *options);
6133 void *isl_ast_print_options_free(
6134 __isl_take isl_ast_print_options *options);
6136 __isl_give isl_ast_print_options *
6137 isl_ast_print_options_set_print_user(
6138 __isl_take isl_ast_print_options *options,
6139 __isl_give isl_printer *(*print_user)(
6140 __isl_take isl_printer *p,
6141 __isl_take isl_ast_print_options *options,
6142 __isl_keep isl_ast_node *node, void *user),
6144 __isl_give isl_ast_print_options *
6145 isl_ast_print_options_set_print_for(
6146 __isl_take isl_ast_print_options *options,
6147 __isl_give isl_printer *(*print_for)(
6148 __isl_take isl_printer *p,
6149 __isl_take isl_ast_print_options *options,
6150 __isl_keep isl_ast_node *node, void *user),
6153 The callback set by C<isl_ast_print_options_set_print_user>
6154 is called whenever a node of type C<isl_ast_node_user> needs to
6156 The callback set by C<isl_ast_print_options_set_print_for>
6157 is called whenever a node of type C<isl_ast_node_for> needs to
6159 Note that C<isl_ast_node_for_print> will I<not> call the
6160 callback set by C<isl_ast_print_options_set_print_for> on the node
6161 on which C<isl_ast_node_for_print> is called, but only on nested
6162 nodes of type C<isl_ast_node_for>. It is therefore safe to
6163 call C<isl_ast_node_for_print> from within the callback set by
6164 C<isl_ast_print_options_set_print_for>.
6166 The following option determines the type to be used for iterators
6167 while printing the AST.
6169 int isl_options_set_ast_iterator_type(
6170 isl_ctx *ctx, const char *val);
6171 const char *isl_options_get_ast_iterator_type(
6176 #include <isl/ast_build.h>
6177 int isl_options_set_ast_build_atomic_upper_bound(
6178 isl_ctx *ctx, int val);
6179 int isl_options_get_ast_build_atomic_upper_bound(
6181 int isl_options_set_ast_build_prefer_pdiv(isl_ctx *ctx,
6183 int isl_options_get_ast_build_prefer_pdiv(isl_ctx *ctx);
6184 int isl_options_set_ast_build_exploit_nested_bounds(
6185 isl_ctx *ctx, int val);
6186 int isl_options_get_ast_build_exploit_nested_bounds(
6188 int isl_options_set_ast_build_group_coscheduled(
6189 isl_ctx *ctx, int val);
6190 int isl_options_get_ast_build_group_coscheduled(
6192 int isl_options_set_ast_build_scale_strides(
6193 isl_ctx *ctx, int val);
6194 int isl_options_get_ast_build_scale_strides(
6196 int isl_options_set_ast_build_allow_else(isl_ctx *ctx,
6198 int isl_options_get_ast_build_allow_else(isl_ctx *ctx);
6199 int isl_options_set_ast_build_allow_or(isl_ctx *ctx,
6201 int isl_options_get_ast_build_allow_or(isl_ctx *ctx);
6205 =item * ast_build_atomic_upper_bound
6207 Generate loop upper bounds that consist of the current loop iterator,
6208 an operator and an expression not involving the iterator.
6209 If this option is not set, then the current loop iterator may appear
6210 several times in the upper bound.
6211 For example, when this option is turned off, AST generation
6214 [n] -> { A[i] -> [i] : 0 <= i <= 100, n }
6218 for (int c0 = 0; c0 <= 100 && n >= c0; c0 += 1)
6221 When the option is turned on, the following AST is generated
6223 for (int c0 = 0; c0 <= min(100, n); c0 += 1)
6226 =item * ast_build_prefer_pdiv
6228 If this option is turned off, then the AST generation will
6229 produce ASTs that may only contain C<isl_ast_op_fdiv_q>
6230 operators, but no C<isl_ast_op_pdiv_q> or
6231 C<isl_ast_op_pdiv_r> operators.
6232 If this options is turned on, then C<isl> will try to convert
6233 some of the C<isl_ast_op_fdiv_q> operators to (expressions containing)
6234 C<isl_ast_op_pdiv_q> or C<isl_ast_op_pdiv_r> operators.
6236 =item * ast_build_exploit_nested_bounds
6238 Simplify conditions based on bounds of nested for loops.
6239 In particular, remove conditions that are implied by the fact
6240 that one or more nested loops have at least one iteration,
6241 meaning that the upper bound is at least as large as the lower bound.
6242 For example, when this option is turned off, AST generation
6245 [N,M] -> { A[i,j] -> [i,j] : 0 <= i <= N and
6251 for (int c0 = 0; c0 <= N; c0 += 1)
6252 for (int c1 = 0; c1 <= M; c1 += 1)
6255 When the option is turned on, the following AST is generated
6257 for (int c0 = 0; c0 <= N; c0 += 1)
6258 for (int c1 = 0; c1 <= M; c1 += 1)
6261 =item * ast_build_group_coscheduled
6263 If two domain elements are assigned the same schedule point, then
6264 they may be executed in any order and they may even appear in different
6265 loops. If this options is set, then the AST generator will make
6266 sure that coscheduled domain elements do not appear in separate parts
6267 of the AST. This is useful in case of nested AST generation
6268 if the outer AST generation is given only part of a schedule
6269 and the inner AST generation should handle the domains that are
6270 coscheduled by this initial part of the schedule together.
6271 For example if an AST is generated for a schedule
6273 { A[i] -> [0]; B[i] -> [0] }
6275 then the C<isl_ast_build_set_create_leaf> callback described
6276 below may get called twice, once for each domain.
6277 Setting this option ensures that the callback is only called once
6278 on both domains together.
6280 =item * ast_build_separation_bounds
6282 This option specifies which bounds to use during separation.
6283 If this option is set to C<ISL_AST_BUILD_SEPARATION_BOUNDS_IMPLICIT>
6284 then all (possibly implicit) bounds on the current dimension will
6285 be used during separation.
6286 If this option is set to C<ISL_AST_BUILD_SEPARATION_BOUNDS_EXPLICIT>
6287 then only those bounds that are explicitly available will
6288 be used during separation.
6290 =item * ast_build_scale_strides
6292 This option specifies whether the AST generator is allowed
6293 to scale down iterators of strided loops.
6295 =item * ast_build_allow_else
6297 This option specifies whether the AST generator is allowed
6298 to construct if statements with else branches.
6300 =item * ast_build_allow_or
6302 This option specifies whether the AST generator is allowed
6303 to construct if conditions with disjunctions.
6307 =head3 Fine-grained Control over AST Generation
6309 Besides specifying the constraints on the parameters,
6310 an C<isl_ast_build> object can be used to control
6311 various aspects of the AST generation process.
6312 The most prominent way of control is through ``options'',
6313 which can be set using the following function.
6315 #include <isl/ast_build.h>
6316 __isl_give isl_ast_build *
6317 isl_ast_build_set_options(
6318 __isl_take isl_ast_build *control,
6319 __isl_take isl_union_map *options);
6321 The options are encoded in an <isl_union_map>.
6322 The domain of this union relation refers to the schedule domain,
6323 i.e., the range of the schedule passed to C<isl_ast_build_ast_from_schedule>.
6324 In the case of nested AST generation (see L</"Nested AST Generation">),
6325 the domain of C<options> should refer to the extra piece of the schedule.
6326 That is, it should be equal to the range of the wrapped relation in the
6327 range of the schedule.
6328 The range of the options can consist of elements in one or more spaces,
6329 the names of which determine the effect of the option.
6330 The values of the range typically also refer to the schedule dimension
6331 to which the option applies. In case of nested AST generation
6332 (see L</"Nested AST Generation">), these values refer to the position
6333 of the schedule dimension within the innermost AST generation.
6334 The constraints on the domain elements of
6335 the option should only refer to this dimension and earlier dimensions.
6336 We consider the following spaces.
6340 =item C<separation_class>
6342 This space is a wrapped relation between two one dimensional spaces.
6343 The input space represents the schedule dimension to which the option
6344 applies and the output space represents the separation class.
6345 While constructing a loop corresponding to the specified schedule
6346 dimension(s), the AST generator will try to generate separate loops
6347 for domain elements that are assigned different classes.
6348 If only some of the elements are assigned a class, then those elements
6349 that are not assigned any class will be treated as belonging to a class
6350 that is separate from the explicitly assigned classes.
6351 The typical use case for this option is to separate full tiles from
6353 The other options, described below, are applied after the separation
6356 As an example, consider the separation into full and partial tiles
6357 of a tiling of a triangular domain.
6358 Take, for example, the domain
6360 { A[i,j] : 0 <= i,j and i + j <= 100 }
6362 and a tiling into tiles of 10 by 10. The input to the AST generator
6363 is then the schedule
6365 { A[i,j] -> [([i/10]),[j/10],i,j] : 0 <= i,j and
6368 Without any options, the following AST is generated
6370 for (int c0 = 0; c0 <= 10; c0 += 1)
6371 for (int c1 = 0; c1 <= -c0 + 10; c1 += 1)
6372 for (int c2 = 10 * c0;
6373 c2 <= min(-10 * c1 + 100, 10 * c0 + 9);
6375 for (int c3 = 10 * c1;
6376 c3 <= min(10 * c1 + 9, -c2 + 100);
6380 Separation into full and partial tiles can be obtained by assigning
6381 a class, say C<0>, to the full tiles. The full tiles are represented by those
6382 values of the first and second schedule dimensions for which there are
6383 values of the third and fourth dimensions to cover an entire tile.
6384 That is, we need to specify the following option
6386 { [a,b,c,d] -> separation_class[[0]->[0]] :
6387 exists b': 0 <= 10a,10b' and
6388 10a+9+10b'+9 <= 100;
6389 [a,b,c,d] -> separation_class[[1]->[0]] :
6390 0 <= 10a,10b and 10a+9+10b+9 <= 100 }
6394 { [a, b, c, d] -> separation_class[[1] -> [0]] :
6395 a >= 0 and b >= 0 and b <= 8 - a;
6396 [a, b, c, d] -> separation_class[[0] -> [0]] :
6399 With this option, the generated AST is as follows
6402 for (int c0 = 0; c0 <= 8; c0 += 1) {
6403 for (int c1 = 0; c1 <= -c0 + 8; c1 += 1)
6404 for (int c2 = 10 * c0;
6405 c2 <= 10 * c0 + 9; c2 += 1)
6406 for (int c3 = 10 * c1;
6407 c3 <= 10 * c1 + 9; c3 += 1)
6409 for (int c1 = -c0 + 9; c1 <= -c0 + 10; c1 += 1)
6410 for (int c2 = 10 * c0;
6411 c2 <= min(-10 * c1 + 100, 10 * c0 + 9);
6413 for (int c3 = 10 * c1;
6414 c3 <= min(-c2 + 100, 10 * c1 + 9);
6418 for (int c0 = 9; c0 <= 10; c0 += 1)
6419 for (int c1 = 0; c1 <= -c0 + 10; c1 += 1)
6420 for (int c2 = 10 * c0;
6421 c2 <= min(-10 * c1 + 100, 10 * c0 + 9);
6423 for (int c3 = 10 * c1;
6424 c3 <= min(10 * c1 + 9, -c2 + 100);
6431 This is a single-dimensional space representing the schedule dimension(s)
6432 to which ``separation'' should be applied. Separation tries to split
6433 a loop into several pieces if this can avoid the generation of guards
6435 See also the C<atomic> option.
6439 This is a single-dimensional space representing the schedule dimension(s)
6440 for which the domains should be considered ``atomic''. That is, the
6441 AST generator will make sure that any given domain space will only appear
6442 in a single loop at the specified level.
6444 Consider the following schedule
6446 { a[i] -> [i] : 0 <= i < 10;
6447 b[i] -> [i+1] : 0 <= i < 10 }
6449 If the following option is specified
6451 { [i] -> separate[x] }
6453 then the following AST will be generated
6457 for (int c0 = 1; c0 <= 9; c0 += 1) {
6464 If, on the other hand, the following option is specified
6466 { [i] -> atomic[x] }
6468 then the following AST will be generated
6470 for (int c0 = 0; c0 <= 10; c0 += 1) {
6477 If neither C<atomic> nor C<separate> is specified, then the AST generator
6478 may produce either of these two results or some intermediate form.
6482 This is a single-dimensional space representing the schedule dimension(s)
6483 that should be I<completely> unrolled.
6484 To obtain a partial unrolling, the user should apply an additional
6485 strip-mining to the schedule and fully unroll the inner loop.
6489 Additional control is available through the following functions.
6491 #include <isl/ast_build.h>
6492 __isl_give isl_ast_build *
6493 isl_ast_build_set_iterators(
6494 __isl_take isl_ast_build *control,
6495 __isl_take isl_id_list *iterators);
6497 The function C<isl_ast_build_set_iterators> allows the user to
6498 specify a list of iterator C<isl_id>s to be used as iterators.
6499 If the input schedule is injective, then
6500 the number of elements in this list should be as large as the dimension
6501 of the schedule space, but no direct correspondence should be assumed
6502 between dimensions and elements.
6503 If the input schedule is not injective, then an additional number
6504 of C<isl_id>s equal to the largest dimension of the input domains
6506 If the number of provided C<isl_id>s is insufficient, then additional
6507 names are automatically generated.
6509 #include <isl/ast_build.h>
6510 __isl_give isl_ast_build *
6511 isl_ast_build_set_create_leaf(
6512 __isl_take isl_ast_build *control,
6513 __isl_give isl_ast_node *(*fn)(
6514 __isl_take isl_ast_build *build,
6515 void *user), void *user);
6518 C<isl_ast_build_set_create_leaf> function allows for the
6519 specification of a callback that should be called whenever the AST
6520 generator arrives at an element of the schedule domain.
6521 The callback should return an AST node that should be inserted
6522 at the corresponding position of the AST. The default action (when
6523 the callback is not set) is to continue generating parts of the AST to scan
6524 all the domain elements associated to the schedule domain element
6525 and to insert user nodes, ``calling'' the domain element, for each of them.
6526 The C<build> argument contains the current state of the C<isl_ast_build>.
6527 To ease nested AST generation (see L</"Nested AST Generation">),
6528 all control information that is
6529 specific to the current AST generation such as the options and
6530 the callbacks has been removed from this C<isl_ast_build>.
6531 The callback would typically return the result of a nested
6533 user defined node created using the following function.
6535 #include <isl/ast.h>
6536 __isl_give isl_ast_node *isl_ast_node_alloc_user(
6537 __isl_take isl_ast_expr *expr);
6539 #include <isl/ast_build.h>
6540 __isl_give isl_ast_build *
6541 isl_ast_build_set_at_each_domain(
6542 __isl_take isl_ast_build *build,
6543 __isl_give isl_ast_node *(*fn)(
6544 __isl_take isl_ast_node *node,
6545 __isl_keep isl_ast_build *build,
6546 void *user), void *user);
6547 __isl_give isl_ast_build *
6548 isl_ast_build_set_before_each_for(
6549 __isl_take isl_ast_build *build,
6550 __isl_give isl_id *(*fn)(
6551 __isl_keep isl_ast_build *build,
6552 void *user), void *user);
6553 __isl_give isl_ast_build *
6554 isl_ast_build_set_after_each_for(
6555 __isl_take isl_ast_build *build,
6556 __isl_give isl_ast_node *(*fn)(
6557 __isl_take isl_ast_node *node,
6558 __isl_keep isl_ast_build *build,
6559 void *user), void *user);
6561 The callback set by C<isl_ast_build_set_at_each_domain> will
6562 be called for each domain AST node.
6563 The callbacks set by C<isl_ast_build_set_before_each_for>
6564 and C<isl_ast_build_set_after_each_for> will be called
6565 for each for AST node. The first will be called in depth-first
6566 pre-order, while the second will be called in depth-first post-order.
6567 Since C<isl_ast_build_set_before_each_for> is called before the for
6568 node is actually constructed, it is only passed an C<isl_ast_build>.
6569 The returned C<isl_id> will be added as an annotation (using
6570 C<isl_ast_node_set_annotation>) to the constructed for node.
6571 In particular, if the user has also specified an C<after_each_for>
6572 callback, then the annotation can be retrieved from the node passed to
6573 that callback using C<isl_ast_node_get_annotation>.
6574 All callbacks should C<NULL> on failure.
6575 The given C<isl_ast_build> can be used to create new
6576 C<isl_ast_expr> objects using C<isl_ast_build_expr_from_pw_aff>
6577 or C<isl_ast_build_call_from_pw_multi_aff>.
6579 =head3 Nested AST Generation
6581 C<isl> allows the user to create an AST within the context
6582 of another AST. These nested ASTs are created using the
6583 same C<isl_ast_build_ast_from_schedule> function that is used to create the
6584 outer AST. The C<build> argument should be an C<isl_ast_build>
6585 passed to a callback set by
6586 C<isl_ast_build_set_create_leaf>.
6587 The space of the range of the C<schedule> argument should refer
6588 to this build. In particular, the space should be a wrapped
6589 relation and the domain of this wrapped relation should be the
6590 same as that of the range of the schedule returned by
6591 C<isl_ast_build_get_schedule> below.
6592 In practice, the new schedule is typically
6593 created by calling C<isl_union_map_range_product> on the old schedule
6594 and some extra piece of the schedule.
6595 The space of the schedule domain is also available from
6596 the C<isl_ast_build>.
6598 #include <isl/ast_build.h>
6599 __isl_give isl_union_map *isl_ast_build_get_schedule(
6600 __isl_keep isl_ast_build *build);
6601 __isl_give isl_space *isl_ast_build_get_schedule_space(
6602 __isl_keep isl_ast_build *build);
6603 __isl_give isl_ast_build *isl_ast_build_restrict(
6604 __isl_take isl_ast_build *build,
6605 __isl_take isl_set *set);
6607 The C<isl_ast_build_get_schedule> function returns a (partial)
6608 schedule for the domains elements for which part of the AST still needs to
6609 be generated in the current build.
6610 In particular, the domain elements are mapped to those iterations of the loops
6611 enclosing the current point of the AST generation inside which
6612 the domain elements are executed.
6613 No direct correspondence between
6614 the input schedule and this schedule should be assumed.
6615 The space obtained from C<isl_ast_build_get_schedule_space> can be used
6616 to create a set for C<isl_ast_build_restrict> to intersect
6617 with the current build. In particular, the set passed to
6618 C<isl_ast_build_restrict> can have additional parameters.
6619 The ids of the set dimensions in the space returned by
6620 C<isl_ast_build_get_schedule_space> correspond to the
6621 iterators of the already generated loops.
6622 The user should not rely on the ids of the output dimensions
6623 of the relations in the union relation returned by
6624 C<isl_ast_build_get_schedule> having any particular value.
6628 Although C<isl> is mainly meant to be used as a library,
6629 it also contains some basic applications that use some
6630 of the functionality of C<isl>.
6631 The input may be specified in either the L<isl format>
6632 or the L<PolyLib format>.
6634 =head2 C<isl_polyhedron_sample>
6636 C<isl_polyhedron_sample> takes a polyhedron as input and prints
6637 an integer element of the polyhedron, if there is any.
6638 The first column in the output is the denominator and is always
6639 equal to 1. If the polyhedron contains no integer points,
6640 then a vector of length zero is printed.
6644 C<isl_pip> takes the same input as the C<example> program
6645 from the C<piplib> distribution, i.e., a set of constraints
6646 on the parameters, a line containing only -1 and finally a set
6647 of constraints on a parametric polyhedron.
6648 The coefficients of the parameters appear in the last columns
6649 (but before the final constant column).
6650 The output is the lexicographic minimum of the parametric polyhedron.
6651 As C<isl> currently does not have its own output format, the output
6652 is just a dump of the internal state.
6654 =head2 C<isl_polyhedron_minimize>
6656 C<isl_polyhedron_minimize> computes the minimum of some linear
6657 or affine objective function over the integer points in a polyhedron.
6658 If an affine objective function
6659 is given, then the constant should appear in the last column.
6661 =head2 C<isl_polytope_scan>
6663 Given a polytope, C<isl_polytope_scan> prints
6664 all integer points in the polytope.
6666 =head2 C<isl_codegen>
6668 Given a schedule, a context set and an options relation,
6669 C<isl_codegen> prints out an AST that scans the domain elements
6670 of the schedule in the order of their image(s) taking into account
6671 the constraints in the context set.