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 =head3 Conversion from C<isl_int>
525 The following functions are only temporarily available to ease
526 the transition from C<isl_int> to C<isl_val>. They will be removed
529 #include <isl/val_int.h>
530 __isl_give isl_val *isl_val_int_from_isl_int(isl_ctx *ctx,
532 int isl_val_get_num_isl_int(__isl_keep isl_val *v,
535 =head2 Integers (obsolescent)
537 All operations on integers, mainly the coefficients
538 of the constraints describing the sets and relations,
539 are performed in exact integer arithmetic using C<GMP>.
540 However, to allow future versions of C<isl> to optionally
541 support fixed integer arithmetic, all calls to C<GMP>
542 are wrapped inside C<isl> specific macros.
543 The basic type is C<isl_int> and the operations below
544 are available on this type.
545 The meanings of these operations are essentially the same
546 as their C<GMP> C<mpz_> counterparts.
547 As always with C<GMP> types, C<isl_int>s need to be
548 initialized with C<isl_int_init> before they can be used
549 and they need to be released with C<isl_int_clear>
551 The user should not assume that an C<isl_int> is represented
552 as a C<mpz_t>, but should instead explicitly convert between
553 C<mpz_t>s and C<isl_int>s using C<isl_int_set_gmp> and
554 C<isl_int_get_gmp> whenever a C<mpz_t> is required.
558 =item isl_int_init(i)
560 =item isl_int_clear(i)
562 =item isl_int_set(r,i)
564 =item isl_int_set_si(r,i)
566 =item isl_int_set_gmp(r,g)
568 =item isl_int_get_gmp(i,g)
570 =item isl_int_abs(r,i)
572 =item isl_int_neg(r,i)
574 =item isl_int_swap(i,j)
576 =item isl_int_swap_or_set(i,j)
578 =item isl_int_add_ui(r,i,j)
580 =item isl_int_sub_ui(r,i,j)
582 =item isl_int_add(r,i,j)
584 =item isl_int_sub(r,i,j)
586 =item isl_int_mul(r,i,j)
588 =item isl_int_mul_ui(r,i,j)
590 =item isl_int_addmul(r,i,j)
592 =item isl_int_submul(r,i,j)
594 =item isl_int_gcd(r,i,j)
596 =item isl_int_lcm(r,i,j)
598 =item isl_int_divexact(r,i,j)
600 =item isl_int_cdiv_q(r,i,j)
602 =item isl_int_fdiv_q(r,i,j)
604 =item isl_int_fdiv_r(r,i,j)
606 =item isl_int_fdiv_q_ui(r,i,j)
608 =item isl_int_read(r,s)
610 =item isl_int_print(out,i,width)
614 =item isl_int_cmp(i,j)
616 =item isl_int_cmp_si(i,si)
618 =item isl_int_eq(i,j)
620 =item isl_int_ne(i,j)
622 =item isl_int_lt(i,j)
624 =item isl_int_le(i,j)
626 =item isl_int_gt(i,j)
628 =item isl_int_ge(i,j)
630 =item isl_int_abs_eq(i,j)
632 =item isl_int_abs_ne(i,j)
634 =item isl_int_abs_lt(i,j)
636 =item isl_int_abs_gt(i,j)
638 =item isl_int_abs_ge(i,j)
640 =item isl_int_is_zero(i)
642 =item isl_int_is_one(i)
644 =item isl_int_is_negone(i)
646 =item isl_int_is_pos(i)
648 =item isl_int_is_neg(i)
650 =item isl_int_is_nonpos(i)
652 =item isl_int_is_nonneg(i)
654 =item isl_int_is_divisible_by(i,j)
658 =head2 Sets and Relations
660 C<isl> uses six types of objects for representing sets and relations,
661 C<isl_basic_set>, C<isl_basic_map>, C<isl_set>, C<isl_map>,
662 C<isl_union_set> and C<isl_union_map>.
663 C<isl_basic_set> and C<isl_basic_map> represent sets and relations that
664 can be described as a conjunction of affine constraints, while
665 C<isl_set> and C<isl_map> represent unions of
666 C<isl_basic_set>s and C<isl_basic_map>s, respectively.
667 However, all C<isl_basic_set>s or C<isl_basic_map>s in the union need
668 to live in the same space. C<isl_union_set>s and C<isl_union_map>s
669 represent unions of C<isl_set>s or C<isl_map>s in I<different> spaces,
670 where spaces are considered different if they have a different number
671 of dimensions and/or different names (see L<"Spaces">).
672 The difference between sets and relations (maps) is that sets have
673 one set of variables, while relations have two sets of variables,
674 input variables and output variables.
676 =head2 Memory Management
678 Since a high-level operation on sets and/or relations usually involves
679 several substeps and since the user is usually not interested in
680 the intermediate results, most functions that return a new object
681 will also release all the objects passed as arguments.
682 If the user still wants to use one or more of these arguments
683 after the function call, she should pass along a copy of the
684 object rather than the object itself.
685 The user is then responsible for making sure that the original
686 object gets used somewhere else or is explicitly freed.
688 The arguments and return values of all documented functions are
689 annotated to make clear which arguments are released and which
690 arguments are preserved. In particular, the following annotations
697 C<__isl_give> means that a new object is returned.
698 The user should make sure that the returned pointer is
699 used exactly once as a value for an C<__isl_take> argument.
700 In between, it can be used as a value for as many
701 C<__isl_keep> arguments as the user likes.
702 There is one exception, and that is the case where the
703 pointer returned is C<NULL>. Is this case, the user
704 is free to use it as an C<__isl_take> argument or not.
708 C<__isl_take> means that the object the argument points to
709 is taken over by the function and may no longer be used
710 by the user as an argument to any other function.
711 The pointer value must be one returned by a function
712 returning an C<__isl_give> pointer.
713 If the user passes in a C<NULL> value, then this will
714 be treated as an error in the sense that the function will
715 not perform its usual operation. However, it will still
716 make sure that all the other C<__isl_take> arguments
721 C<__isl_keep> means that the function will only use the object
722 temporarily. After the function has finished, the user
723 can still use it as an argument to other functions.
724 A C<NULL> value will be treated in the same way as
725 a C<NULL> value for an C<__isl_take> argument.
729 =head2 Error Handling
731 C<isl> supports different ways to react in case a runtime error is triggered.
732 Runtime errors arise, e.g., if a function such as C<isl_map_intersect> is called
733 with two maps that have incompatible spaces. There are three possible ways
734 to react on error: to warn, to continue or to abort.
736 The default behavior is to warn. In this mode, C<isl> prints a warning, stores
737 the last error in the corresponding C<isl_ctx> and the function in which the
738 error was triggered returns C<NULL>. An error does not corrupt internal state,
739 such that isl can continue to be used. C<isl> also provides functions to
740 read the last error and to reset the memory that stores the last error. The
741 last error is only stored for information purposes. Its presence does not
742 change the behavior of C<isl>. Hence, resetting an error is not required to
743 continue to use isl, but only to observe new errors.
746 enum isl_error isl_ctx_last_error(isl_ctx *ctx);
747 void isl_ctx_reset_error(isl_ctx *ctx);
749 Another option is to continue on error. This is similar to warn on error mode,
750 except that C<isl> does not print any warning. This allows a program to
751 implement its own error reporting.
753 The last option is to directly abort the execution of the program from within
754 the isl library. This makes it obviously impossible to recover from an error,
755 but it allows to directly spot the error location. By aborting on error,
756 debuggers break at the location the error occurred and can provide a stack
757 trace. Other tools that automatically provide stack traces on abort or that do
758 not want to continue execution after an error was triggered may also prefer to
761 The on error behavior of isl can be specified by calling
762 C<isl_options_set_on_error> or by setting the command line option
763 C<--isl-on-error>. Valid arguments for the function call are
764 C<ISL_ON_ERROR_WARN>, C<ISL_ON_ERROR_CONTINUE> and C<ISL_ON_ERROR_ABORT>. The
765 choices for the command line option are C<warn>, C<continue> and C<abort>.
766 It is also possible to query the current error mode.
768 #include <isl/options.h>
769 int isl_options_set_on_error(isl_ctx *ctx, int val);
770 int isl_options_get_on_error(isl_ctx *ctx);
774 Identifiers are used to identify both individual dimensions
775 and tuples of dimensions. They consist of an optional name and an optional
776 user pointer. The name and the user pointer cannot both be C<NULL>, however.
777 Identifiers with the same name but different pointer values
778 are considered to be distinct.
779 Similarly, identifiers with different names but the same pointer value
780 are also considered to be distinct.
781 Equal identifiers are represented using the same object.
782 Pairs of identifiers can therefore be tested for equality using the
784 Identifiers can be constructed, copied, freed, inspected and printed
785 using the following functions.
788 __isl_give isl_id *isl_id_alloc(isl_ctx *ctx,
789 __isl_keep const char *name, void *user);
790 __isl_give isl_id *isl_id_set_free_user(
791 __isl_take isl_id *id,
792 __isl_give void (*free_user)(void *user));
793 __isl_give isl_id *isl_id_copy(isl_id *id);
794 void *isl_id_free(__isl_take isl_id *id);
796 isl_ctx *isl_id_get_ctx(__isl_keep isl_id *id);
797 void *isl_id_get_user(__isl_keep isl_id *id);
798 __isl_keep const char *isl_id_get_name(__isl_keep isl_id *id);
800 __isl_give isl_printer *isl_printer_print_id(
801 __isl_take isl_printer *p, __isl_keep isl_id *id);
803 The callback set by C<isl_id_set_free_user> is called on the user
804 pointer when the last reference to the C<isl_id> is freed.
805 Note that C<isl_id_get_name> returns a pointer to some internal
806 data structure, so the result can only be used while the
807 corresponding C<isl_id> is alive.
811 Whenever a new set, relation or similiar object is created from scratch,
812 the space in which it lives needs to be specified using an C<isl_space>.
813 Each space involves zero or more parameters and zero, one or two
814 tuples of set or input/output dimensions. The parameters and dimensions
815 are identified by an C<isl_dim_type> and a position.
816 The type C<isl_dim_param> refers to parameters,
817 the type C<isl_dim_set> refers to set dimensions (for spaces
818 with a single tuple of dimensions) and the types C<isl_dim_in>
819 and C<isl_dim_out> refer to input and output dimensions
820 (for spaces with two tuples of dimensions).
821 Local spaces (see L</"Local Spaces">) also contain dimensions
822 of type C<isl_dim_div>.
823 Note that parameters are only identified by their position within
824 a given object. Across different objects, parameters are (usually)
825 identified by their names or identifiers. Only unnamed parameters
826 are identified by their positions across objects. The use of unnamed
827 parameters is discouraged.
829 #include <isl/space.h>
830 __isl_give isl_space *isl_space_alloc(isl_ctx *ctx,
831 unsigned nparam, unsigned n_in, unsigned n_out);
832 __isl_give isl_space *isl_space_params_alloc(isl_ctx *ctx,
834 __isl_give isl_space *isl_space_set_alloc(isl_ctx *ctx,
835 unsigned nparam, unsigned dim);
836 __isl_give isl_space *isl_space_copy(__isl_keep isl_space *space);
837 void *isl_space_free(__isl_take isl_space *space);
838 unsigned isl_space_dim(__isl_keep isl_space *space,
839 enum isl_dim_type type);
841 The space used for creating a parameter domain
842 needs to be created using C<isl_space_params_alloc>.
843 For other sets, the space
844 needs to be created using C<isl_space_set_alloc>, while
845 for a relation, the space
846 needs to be created using C<isl_space_alloc>.
847 C<isl_space_dim> can be used
848 to find out the number of dimensions of each type in
849 a space, where type may be
850 C<isl_dim_param>, C<isl_dim_in> (only for relations),
851 C<isl_dim_out> (only for relations), C<isl_dim_set>
852 (only for sets) or C<isl_dim_all>.
854 To check whether a given space is that of a set or a map
855 or whether it is a parameter space, use these functions:
857 #include <isl/space.h>
858 int isl_space_is_params(__isl_keep isl_space *space);
859 int isl_space_is_set(__isl_keep isl_space *space);
860 int isl_space_is_map(__isl_keep isl_space *space);
862 Spaces can be compared using the following functions:
864 #include <isl/space.h>
865 int isl_space_is_equal(__isl_keep isl_space *space1,
866 __isl_keep isl_space *space2);
867 int isl_space_is_domain(__isl_keep isl_space *space1,
868 __isl_keep isl_space *space2);
869 int isl_space_is_range(__isl_keep isl_space *space1,
870 __isl_keep isl_space *space2);
872 C<isl_space_is_domain> checks whether the first argument is equal
873 to the domain of the second argument. This requires in particular that
874 the first argument is a set space and that the second argument
877 It is often useful to create objects that live in the
878 same space as some other object. This can be accomplished
879 by creating the new objects
880 (see L<Creating New Sets and Relations> or
881 L<Creating New (Piecewise) Quasipolynomials>) based on the space
882 of the original object.
885 __isl_give isl_space *isl_basic_set_get_space(
886 __isl_keep isl_basic_set *bset);
887 __isl_give isl_space *isl_set_get_space(__isl_keep isl_set *set);
889 #include <isl/union_set.h>
890 __isl_give isl_space *isl_union_set_get_space(
891 __isl_keep isl_union_set *uset);
894 __isl_give isl_space *isl_basic_map_get_space(
895 __isl_keep isl_basic_map *bmap);
896 __isl_give isl_space *isl_map_get_space(__isl_keep isl_map *map);
898 #include <isl/union_map.h>
899 __isl_give isl_space *isl_union_map_get_space(
900 __isl_keep isl_union_map *umap);
902 #include <isl/constraint.h>
903 __isl_give isl_space *isl_constraint_get_space(
904 __isl_keep isl_constraint *constraint);
906 #include <isl/polynomial.h>
907 __isl_give isl_space *isl_qpolynomial_get_domain_space(
908 __isl_keep isl_qpolynomial *qp);
909 __isl_give isl_space *isl_qpolynomial_get_space(
910 __isl_keep isl_qpolynomial *qp);
911 __isl_give isl_space *isl_qpolynomial_fold_get_space(
912 __isl_keep isl_qpolynomial_fold *fold);
913 __isl_give isl_space *isl_pw_qpolynomial_get_domain_space(
914 __isl_keep isl_pw_qpolynomial *pwqp);
915 __isl_give isl_space *isl_pw_qpolynomial_get_space(
916 __isl_keep isl_pw_qpolynomial *pwqp);
917 __isl_give isl_space *isl_pw_qpolynomial_fold_get_domain_space(
918 __isl_keep isl_pw_qpolynomial_fold *pwf);
919 __isl_give isl_space *isl_pw_qpolynomial_fold_get_space(
920 __isl_keep isl_pw_qpolynomial_fold *pwf);
921 __isl_give isl_space *isl_union_pw_qpolynomial_get_space(
922 __isl_keep isl_union_pw_qpolynomial *upwqp);
923 __isl_give isl_space *isl_union_pw_qpolynomial_fold_get_space(
924 __isl_keep isl_union_pw_qpolynomial_fold *upwf);
927 __isl_give isl_space *isl_multi_val_get_space(
928 __isl_keep isl_multi_val *mv);
931 __isl_give isl_space *isl_aff_get_domain_space(
932 __isl_keep isl_aff *aff);
933 __isl_give isl_space *isl_aff_get_space(
934 __isl_keep isl_aff *aff);
935 __isl_give isl_space *isl_pw_aff_get_domain_space(
936 __isl_keep isl_pw_aff *pwaff);
937 __isl_give isl_space *isl_pw_aff_get_space(
938 __isl_keep isl_pw_aff *pwaff);
939 __isl_give isl_space *isl_multi_aff_get_domain_space(
940 __isl_keep isl_multi_aff *maff);
941 __isl_give isl_space *isl_multi_aff_get_space(
942 __isl_keep isl_multi_aff *maff);
943 __isl_give isl_space *isl_pw_multi_aff_get_domain_space(
944 __isl_keep isl_pw_multi_aff *pma);
945 __isl_give isl_space *isl_pw_multi_aff_get_space(
946 __isl_keep isl_pw_multi_aff *pma);
947 __isl_give isl_space *isl_union_pw_multi_aff_get_space(
948 __isl_keep isl_union_pw_multi_aff *upma);
949 __isl_give isl_space *isl_multi_pw_aff_get_domain_space(
950 __isl_keep isl_multi_pw_aff *mpa);
951 __isl_give isl_space *isl_multi_pw_aff_get_space(
952 __isl_keep isl_multi_pw_aff *mpa);
954 #include <isl/point.h>
955 __isl_give isl_space *isl_point_get_space(
956 __isl_keep isl_point *pnt);
958 The identifiers or names of the individual dimensions may be set or read off
959 using the following functions.
961 #include <isl/space.h>
962 __isl_give isl_space *isl_space_set_dim_id(
963 __isl_take isl_space *space,
964 enum isl_dim_type type, unsigned pos,
965 __isl_take isl_id *id);
966 int isl_space_has_dim_id(__isl_keep isl_space *space,
967 enum isl_dim_type type, unsigned pos);
968 __isl_give isl_id *isl_space_get_dim_id(
969 __isl_keep isl_space *space,
970 enum isl_dim_type type, unsigned pos);
971 __isl_give isl_space *isl_space_set_dim_name(
972 __isl_take isl_space *space,
973 enum isl_dim_type type, unsigned pos,
974 __isl_keep const char *name);
975 int isl_space_has_dim_name(__isl_keep isl_space *space,
976 enum isl_dim_type type, unsigned pos);
977 __isl_keep const char *isl_space_get_dim_name(
978 __isl_keep isl_space *space,
979 enum isl_dim_type type, unsigned pos);
981 Note that C<isl_space_get_name> returns a pointer to some internal
982 data structure, so the result can only be used while the
983 corresponding C<isl_space> is alive.
984 Also note that every function that operates on two sets or relations
985 requires that both arguments have the same parameters. This also
986 means that if one of the arguments has named parameters, then the
987 other needs to have named parameters too and the names need to match.
988 Pairs of C<isl_set>, C<isl_map>, C<isl_union_set> and/or C<isl_union_map>
989 arguments may have different parameters (as long as they are named),
990 in which case the result will have as parameters the union of the parameters of
993 Given the identifier or name of a dimension (typically a parameter),
994 its position can be obtained from the following function.
996 #include <isl/space.h>
997 int isl_space_find_dim_by_id(__isl_keep isl_space *space,
998 enum isl_dim_type type, __isl_keep isl_id *id);
999 int isl_space_find_dim_by_name(__isl_keep isl_space *space,
1000 enum isl_dim_type type, const char *name);
1002 The identifiers or names of entire spaces may be set or read off
1003 using the following functions.
1005 #include <isl/space.h>
1006 __isl_give isl_space *isl_space_set_tuple_id(
1007 __isl_take isl_space *space,
1008 enum isl_dim_type type, __isl_take isl_id *id);
1009 __isl_give isl_space *isl_space_reset_tuple_id(
1010 __isl_take isl_space *space, enum isl_dim_type type);
1011 int isl_space_has_tuple_id(__isl_keep isl_space *space,
1012 enum isl_dim_type type);
1013 __isl_give isl_id *isl_space_get_tuple_id(
1014 __isl_keep isl_space *space, enum isl_dim_type type);
1015 __isl_give isl_space *isl_space_set_tuple_name(
1016 __isl_take isl_space *space,
1017 enum isl_dim_type type, const char *s);
1018 int isl_space_has_tuple_name(__isl_keep isl_space *space,
1019 enum isl_dim_type type);
1020 const char *isl_space_get_tuple_name(__isl_keep isl_space *space,
1021 enum isl_dim_type type);
1023 The C<type> argument needs to be one of C<isl_dim_in>, C<isl_dim_out>
1024 or C<isl_dim_set>. As with C<isl_space_get_name>,
1025 the C<isl_space_get_tuple_name> function returns a pointer to some internal
1027 Binary operations require the corresponding spaces of their arguments
1028 to have the same name.
1030 Spaces can be nested. In particular, the domain of a set or
1031 the domain or range of a relation can be a nested relation.
1032 The following functions can be used to construct and deconstruct
1035 #include <isl/space.h>
1036 int isl_space_is_wrapping(__isl_keep isl_space *space);
1037 __isl_give isl_space *isl_space_wrap(__isl_take isl_space *space);
1038 __isl_give isl_space *isl_space_unwrap(__isl_take isl_space *space);
1040 The input to C<isl_space_is_wrapping> and C<isl_space_unwrap> should
1041 be the space of a set, while that of
1042 C<isl_space_wrap> should be the space of a relation.
1043 Conversely, the output of C<isl_space_unwrap> is the space
1044 of a relation, while that of C<isl_space_wrap> is the space of a set.
1046 Spaces can be created from other spaces
1047 using the following functions.
1049 __isl_give isl_space *isl_space_domain(__isl_take isl_space *space);
1050 __isl_give isl_space *isl_space_from_domain(__isl_take isl_space *space);
1051 __isl_give isl_space *isl_space_range(__isl_take isl_space *space);
1052 __isl_give isl_space *isl_space_from_range(__isl_take isl_space *space);
1053 __isl_give isl_space *isl_space_params(
1054 __isl_take isl_space *space);
1055 __isl_give isl_space *isl_space_set_from_params(
1056 __isl_take isl_space *space);
1057 __isl_give isl_space *isl_space_reverse(__isl_take isl_space *space);
1058 __isl_give isl_space *isl_space_join(__isl_take isl_space *left,
1059 __isl_take isl_space *right);
1060 __isl_give isl_space *isl_space_align_params(
1061 __isl_take isl_space *space1, __isl_take isl_space *space2)
1062 __isl_give isl_space *isl_space_insert_dims(__isl_take isl_space *space,
1063 enum isl_dim_type type, unsigned pos, unsigned n);
1064 __isl_give isl_space *isl_space_add_dims(__isl_take isl_space *space,
1065 enum isl_dim_type type, unsigned n);
1066 __isl_give isl_space *isl_space_drop_dims(__isl_take isl_space *space,
1067 enum isl_dim_type type, unsigned first, unsigned n);
1068 __isl_give isl_space *isl_space_move_dims(__isl_take isl_space *space,
1069 enum isl_dim_type dst_type, unsigned dst_pos,
1070 enum isl_dim_type src_type, unsigned src_pos,
1072 __isl_give isl_space *isl_space_map_from_set(
1073 __isl_take isl_space *space);
1074 __isl_give isl_space *isl_space_map_from_domain_and_range(
1075 __isl_take isl_space *domain,
1076 __isl_take isl_space *range);
1077 __isl_give isl_space *isl_space_zip(__isl_take isl_space *space);
1078 __isl_give isl_space *isl_space_curry(
1079 __isl_take isl_space *space);
1080 __isl_give isl_space *isl_space_uncurry(
1081 __isl_take isl_space *space);
1083 Note that if dimensions are added or removed from a space, then
1084 the name and the internal structure are lost.
1088 A local space is essentially a space with
1089 zero or more existentially quantified variables.
1090 The local space of a (constraint of a) basic set or relation can be obtained
1091 using the following functions.
1093 #include <isl/constraint.h>
1094 __isl_give isl_local_space *isl_constraint_get_local_space(
1095 __isl_keep isl_constraint *constraint);
1097 #include <isl/set.h>
1098 __isl_give isl_local_space *isl_basic_set_get_local_space(
1099 __isl_keep isl_basic_set *bset);
1101 #include <isl/map.h>
1102 __isl_give isl_local_space *isl_basic_map_get_local_space(
1103 __isl_keep isl_basic_map *bmap);
1105 A new local space can be created from a space using
1107 #include <isl/local_space.h>
1108 __isl_give isl_local_space *isl_local_space_from_space(
1109 __isl_take isl_space *space);
1111 They can be inspected, modified, copied and freed using the following functions.
1113 #include <isl/local_space.h>
1114 isl_ctx *isl_local_space_get_ctx(
1115 __isl_keep isl_local_space *ls);
1116 int isl_local_space_is_set(__isl_keep isl_local_space *ls);
1117 int isl_local_space_dim(__isl_keep isl_local_space *ls,
1118 enum isl_dim_type type);
1119 int isl_local_space_has_dim_id(
1120 __isl_keep isl_local_space *ls,
1121 enum isl_dim_type type, unsigned pos);
1122 __isl_give isl_id *isl_local_space_get_dim_id(
1123 __isl_keep isl_local_space *ls,
1124 enum isl_dim_type type, unsigned pos);
1125 int isl_local_space_has_dim_name(
1126 __isl_keep isl_local_space *ls,
1127 enum isl_dim_type type, unsigned pos)
1128 const char *isl_local_space_get_dim_name(
1129 __isl_keep isl_local_space *ls,
1130 enum isl_dim_type type, unsigned pos);
1131 __isl_give isl_local_space *isl_local_space_set_dim_name(
1132 __isl_take isl_local_space *ls,
1133 enum isl_dim_type type, unsigned pos, const char *s);
1134 __isl_give isl_local_space *isl_local_space_set_dim_id(
1135 __isl_take isl_local_space *ls,
1136 enum isl_dim_type type, unsigned pos,
1137 __isl_take isl_id *id);
1138 __isl_give isl_space *isl_local_space_get_space(
1139 __isl_keep isl_local_space *ls);
1140 __isl_give isl_aff *isl_local_space_get_div(
1141 __isl_keep isl_local_space *ls, int pos);
1142 __isl_give isl_local_space *isl_local_space_copy(
1143 __isl_keep isl_local_space *ls);
1144 void *isl_local_space_free(__isl_take isl_local_space *ls);
1146 Note that C<isl_local_space_get_div> can only be used on local spaces
1149 Two local spaces can be compared using
1151 int isl_local_space_is_equal(__isl_keep isl_local_space *ls1,
1152 __isl_keep isl_local_space *ls2);
1154 Local spaces can be created from other local spaces
1155 using the following functions.
1157 __isl_give isl_local_space *isl_local_space_domain(
1158 __isl_take isl_local_space *ls);
1159 __isl_give isl_local_space *isl_local_space_range(
1160 __isl_take isl_local_space *ls);
1161 __isl_give isl_local_space *isl_local_space_from_domain(
1162 __isl_take isl_local_space *ls);
1163 __isl_give isl_local_space *isl_local_space_intersect(
1164 __isl_take isl_local_space *ls1,
1165 __isl_take isl_local_space *ls2);
1166 __isl_give isl_local_space *isl_local_space_add_dims(
1167 __isl_take isl_local_space *ls,
1168 enum isl_dim_type type, unsigned n);
1169 __isl_give isl_local_space *isl_local_space_insert_dims(
1170 __isl_take isl_local_space *ls,
1171 enum isl_dim_type type, unsigned first, unsigned n);
1172 __isl_give isl_local_space *isl_local_space_drop_dims(
1173 __isl_take isl_local_space *ls,
1174 enum isl_dim_type type, unsigned first, unsigned n);
1176 =head2 Input and Output
1178 C<isl> supports its own input/output format, which is similar
1179 to the C<Omega> format, but also supports the C<PolyLib> format
1182 =head3 C<isl> format
1184 The C<isl> format is similar to that of C<Omega>, but has a different
1185 syntax for describing the parameters and allows for the definition
1186 of an existentially quantified variable as the integer division
1187 of an affine expression.
1188 For example, the set of integers C<i> between C<0> and C<n>
1189 such that C<i % 10 <= 6> can be described as
1191 [n] -> { [i] : exists (a = [i/10] : 0 <= i and i <= n and
1194 A set or relation can have several disjuncts, separated
1195 by the keyword C<or>. Each disjunct is either a conjunction
1196 of constraints or a projection (C<exists>) of a conjunction
1197 of constraints. The constraints are separated by the keyword
1200 =head3 C<PolyLib> format
1202 If the represented set is a union, then the first line
1203 contains a single number representing the number of disjuncts.
1204 Otherwise, a line containing the number C<1> is optional.
1206 Each disjunct is represented by a matrix of constraints.
1207 The first line contains two numbers representing
1208 the number of rows and columns,
1209 where the number of rows is equal to the number of constraints
1210 and the number of columns is equal to two plus the number of variables.
1211 The following lines contain the actual rows of the constraint matrix.
1212 In each row, the first column indicates whether the constraint
1213 is an equality (C<0>) or inequality (C<1>). The final column
1214 corresponds to the constant term.
1216 If the set is parametric, then the coefficients of the parameters
1217 appear in the last columns before the constant column.
1218 The coefficients of any existentially quantified variables appear
1219 between those of the set variables and those of the parameters.
1221 =head3 Extended C<PolyLib> format
1223 The extended C<PolyLib> format is nearly identical to the
1224 C<PolyLib> format. The only difference is that the line
1225 containing the number of rows and columns of a constraint matrix
1226 also contains four additional numbers:
1227 the number of output dimensions, the number of input dimensions,
1228 the number of local dimensions (i.e., the number of existentially
1229 quantified variables) and the number of parameters.
1230 For sets, the number of ``output'' dimensions is equal
1231 to the number of set dimensions, while the number of ``input''
1236 #include <isl/set.h>
1237 __isl_give isl_basic_set *isl_basic_set_read_from_file(
1238 isl_ctx *ctx, FILE *input);
1239 __isl_give isl_basic_set *isl_basic_set_read_from_str(
1240 isl_ctx *ctx, const char *str);
1241 __isl_give isl_set *isl_set_read_from_file(isl_ctx *ctx,
1243 __isl_give isl_set *isl_set_read_from_str(isl_ctx *ctx,
1246 #include <isl/map.h>
1247 __isl_give isl_basic_map *isl_basic_map_read_from_file(
1248 isl_ctx *ctx, FILE *input);
1249 __isl_give isl_basic_map *isl_basic_map_read_from_str(
1250 isl_ctx *ctx, const char *str);
1251 __isl_give isl_map *isl_map_read_from_file(
1252 isl_ctx *ctx, FILE *input);
1253 __isl_give isl_map *isl_map_read_from_str(isl_ctx *ctx,
1256 #include <isl/union_set.h>
1257 __isl_give isl_union_set *isl_union_set_read_from_file(
1258 isl_ctx *ctx, FILE *input);
1259 __isl_give isl_union_set *isl_union_set_read_from_str(
1260 isl_ctx *ctx, const char *str);
1262 #include <isl/union_map.h>
1263 __isl_give isl_union_map *isl_union_map_read_from_file(
1264 isl_ctx *ctx, FILE *input);
1265 __isl_give isl_union_map *isl_union_map_read_from_str(
1266 isl_ctx *ctx, const char *str);
1268 The input format is autodetected and may be either the C<PolyLib> format
1269 or the C<isl> format.
1273 Before anything can be printed, an C<isl_printer> needs to
1276 __isl_give isl_printer *isl_printer_to_file(isl_ctx *ctx,
1278 __isl_give isl_printer *isl_printer_to_str(isl_ctx *ctx);
1279 void *isl_printer_free(__isl_take isl_printer *printer);
1280 __isl_give char *isl_printer_get_str(
1281 __isl_keep isl_printer *printer);
1283 The printer can be inspected using the following functions.
1285 FILE *isl_printer_get_file(
1286 __isl_keep isl_printer *printer);
1287 int isl_printer_get_output_format(
1288 __isl_keep isl_printer *p);
1290 The behavior of the printer can be modified in various ways
1292 __isl_give isl_printer *isl_printer_set_output_format(
1293 __isl_take isl_printer *p, int output_format);
1294 __isl_give isl_printer *isl_printer_set_indent(
1295 __isl_take isl_printer *p, int indent);
1296 __isl_give isl_printer *isl_printer_indent(
1297 __isl_take isl_printer *p, int indent);
1298 __isl_give isl_printer *isl_printer_set_prefix(
1299 __isl_take isl_printer *p, const char *prefix);
1300 __isl_give isl_printer *isl_printer_set_suffix(
1301 __isl_take isl_printer *p, const char *suffix);
1303 The C<output_format> may be either C<ISL_FORMAT_ISL>, C<ISL_FORMAT_OMEGA>,
1304 C<ISL_FORMAT_POLYLIB>, C<ISL_FORMAT_EXT_POLYLIB> or C<ISL_FORMAT_LATEX>
1305 and defaults to C<ISL_FORMAT_ISL>.
1306 Each line in the output is indented by C<indent> (set by
1307 C<isl_printer_set_indent>) spaces
1308 (default: 0), prefixed by C<prefix> and suffixed by C<suffix>.
1309 In the C<PolyLib> format output,
1310 the coefficients of the existentially quantified variables
1311 appear between those of the set variables and those
1313 The function C<isl_printer_indent> increases the indentation
1314 by the specified amount (which may be negative).
1316 To actually print something, use
1318 #include <isl/printer.h>
1319 __isl_give isl_printer *isl_printer_print_double(
1320 __isl_take isl_printer *p, double d);
1322 #include <isl/set.h>
1323 __isl_give isl_printer *isl_printer_print_basic_set(
1324 __isl_take isl_printer *printer,
1325 __isl_keep isl_basic_set *bset);
1326 __isl_give isl_printer *isl_printer_print_set(
1327 __isl_take isl_printer *printer,
1328 __isl_keep isl_set *set);
1330 #include <isl/map.h>
1331 __isl_give isl_printer *isl_printer_print_basic_map(
1332 __isl_take isl_printer *printer,
1333 __isl_keep isl_basic_map *bmap);
1334 __isl_give isl_printer *isl_printer_print_map(
1335 __isl_take isl_printer *printer,
1336 __isl_keep isl_map *map);
1338 #include <isl/union_set.h>
1339 __isl_give isl_printer *isl_printer_print_union_set(
1340 __isl_take isl_printer *p,
1341 __isl_keep isl_union_set *uset);
1343 #include <isl/union_map.h>
1344 __isl_give isl_printer *isl_printer_print_union_map(
1345 __isl_take isl_printer *p,
1346 __isl_keep isl_union_map *umap);
1348 When called on a file printer, the following function flushes
1349 the file. When called on a string printer, the buffer is cleared.
1351 __isl_give isl_printer *isl_printer_flush(
1352 __isl_take isl_printer *p);
1354 =head2 Creating New Sets and Relations
1356 C<isl> has functions for creating some standard sets and relations.
1360 =item * Empty sets and relations
1362 __isl_give isl_basic_set *isl_basic_set_empty(
1363 __isl_take isl_space *space);
1364 __isl_give isl_basic_map *isl_basic_map_empty(
1365 __isl_take isl_space *space);
1366 __isl_give isl_set *isl_set_empty(
1367 __isl_take isl_space *space);
1368 __isl_give isl_map *isl_map_empty(
1369 __isl_take isl_space *space);
1370 __isl_give isl_union_set *isl_union_set_empty(
1371 __isl_take isl_space *space);
1372 __isl_give isl_union_map *isl_union_map_empty(
1373 __isl_take isl_space *space);
1375 For C<isl_union_set>s and C<isl_union_map>s, the space
1376 is only used to specify the parameters.
1378 =item * Universe sets and relations
1380 __isl_give isl_basic_set *isl_basic_set_universe(
1381 __isl_take isl_space *space);
1382 __isl_give isl_basic_map *isl_basic_map_universe(
1383 __isl_take isl_space *space);
1384 __isl_give isl_set *isl_set_universe(
1385 __isl_take isl_space *space);
1386 __isl_give isl_map *isl_map_universe(
1387 __isl_take isl_space *space);
1388 __isl_give isl_union_set *isl_union_set_universe(
1389 __isl_take isl_union_set *uset);
1390 __isl_give isl_union_map *isl_union_map_universe(
1391 __isl_take isl_union_map *umap);
1393 The sets and relations constructed by the functions above
1394 contain all integer values, while those constructed by the
1395 functions below only contain non-negative values.
1397 __isl_give isl_basic_set *isl_basic_set_nat_universe(
1398 __isl_take isl_space *space);
1399 __isl_give isl_basic_map *isl_basic_map_nat_universe(
1400 __isl_take isl_space *space);
1401 __isl_give isl_set *isl_set_nat_universe(
1402 __isl_take isl_space *space);
1403 __isl_give isl_map *isl_map_nat_universe(
1404 __isl_take isl_space *space);
1406 =item * Identity relations
1408 __isl_give isl_basic_map *isl_basic_map_identity(
1409 __isl_take isl_space *space);
1410 __isl_give isl_map *isl_map_identity(
1411 __isl_take isl_space *space);
1413 The number of input and output dimensions in C<space> needs
1416 =item * Lexicographic order
1418 __isl_give isl_map *isl_map_lex_lt(
1419 __isl_take isl_space *set_space);
1420 __isl_give isl_map *isl_map_lex_le(
1421 __isl_take isl_space *set_space);
1422 __isl_give isl_map *isl_map_lex_gt(
1423 __isl_take isl_space *set_space);
1424 __isl_give isl_map *isl_map_lex_ge(
1425 __isl_take isl_space *set_space);
1426 __isl_give isl_map *isl_map_lex_lt_first(
1427 __isl_take isl_space *space, unsigned n);
1428 __isl_give isl_map *isl_map_lex_le_first(
1429 __isl_take isl_space *space, unsigned n);
1430 __isl_give isl_map *isl_map_lex_gt_first(
1431 __isl_take isl_space *space, unsigned n);
1432 __isl_give isl_map *isl_map_lex_ge_first(
1433 __isl_take isl_space *space, unsigned n);
1435 The first four functions take a space for a B<set>
1436 and return relations that express that the elements in the domain
1437 are lexicographically less
1438 (C<isl_map_lex_lt>), less or equal (C<isl_map_lex_le>),
1439 greater (C<isl_map_lex_gt>) or greater or equal (C<isl_map_lex_ge>)
1440 than the elements in the range.
1441 The last four functions take a space for a map
1442 and return relations that express that the first C<n> dimensions
1443 in the domain are lexicographically less
1444 (C<isl_map_lex_lt_first>), less or equal (C<isl_map_lex_le_first>),
1445 greater (C<isl_map_lex_gt_first>) or greater or equal (C<isl_map_lex_ge_first>)
1446 than the first C<n> dimensions in the range.
1450 A basic set or relation can be converted to a set or relation
1451 using the following functions.
1453 __isl_give isl_set *isl_set_from_basic_set(
1454 __isl_take isl_basic_set *bset);
1455 __isl_give isl_map *isl_map_from_basic_map(
1456 __isl_take isl_basic_map *bmap);
1458 Sets and relations can be converted to union sets and relations
1459 using the following functions.
1461 __isl_give isl_union_set *isl_union_set_from_basic_set(
1462 __isl_take isl_basic_set *bset);
1463 __isl_give isl_union_map *isl_union_map_from_basic_map(
1464 __isl_take isl_basic_map *bmap);
1465 __isl_give isl_union_set *isl_union_set_from_set(
1466 __isl_take isl_set *set);
1467 __isl_give isl_union_map *isl_union_map_from_map(
1468 __isl_take isl_map *map);
1470 The inverse conversions below can only be used if the input
1471 union set or relation is known to contain elements in exactly one
1474 __isl_give isl_set *isl_set_from_union_set(
1475 __isl_take isl_union_set *uset);
1476 __isl_give isl_map *isl_map_from_union_map(
1477 __isl_take isl_union_map *umap);
1479 A zero-dimensional (basic) set can be constructed on a given parameter domain
1480 using the following function.
1482 __isl_give isl_basic_set *isl_basic_set_from_params(
1483 __isl_take isl_basic_set *bset);
1484 __isl_give isl_set *isl_set_from_params(
1485 __isl_take isl_set *set);
1487 Sets and relations can be copied and freed again using the following
1490 __isl_give isl_basic_set *isl_basic_set_copy(
1491 __isl_keep isl_basic_set *bset);
1492 __isl_give isl_set *isl_set_copy(__isl_keep isl_set *set);
1493 __isl_give isl_union_set *isl_union_set_copy(
1494 __isl_keep isl_union_set *uset);
1495 __isl_give isl_basic_map *isl_basic_map_copy(
1496 __isl_keep isl_basic_map *bmap);
1497 __isl_give isl_map *isl_map_copy(__isl_keep isl_map *map);
1498 __isl_give isl_union_map *isl_union_map_copy(
1499 __isl_keep isl_union_map *umap);
1500 void *isl_basic_set_free(__isl_take isl_basic_set *bset);
1501 void *isl_set_free(__isl_take isl_set *set);
1502 void *isl_union_set_free(__isl_take isl_union_set *uset);
1503 void *isl_basic_map_free(__isl_take isl_basic_map *bmap);
1504 void *isl_map_free(__isl_take isl_map *map);
1505 void *isl_union_map_free(__isl_take isl_union_map *umap);
1507 Other sets and relations can be constructed by starting
1508 from a universe set or relation, adding equality and/or
1509 inequality constraints and then projecting out the
1510 existentially quantified variables, if any.
1511 Constraints can be constructed, manipulated and
1512 added to (or removed from) (basic) sets and relations
1513 using the following functions.
1515 #include <isl/constraint.h>
1516 __isl_give isl_constraint *isl_equality_alloc(
1517 __isl_take isl_local_space *ls);
1518 __isl_give isl_constraint *isl_inequality_alloc(
1519 __isl_take isl_local_space *ls);
1520 __isl_give isl_constraint *isl_constraint_set_constant(
1521 __isl_take isl_constraint *constraint, isl_int v);
1522 __isl_give isl_constraint *isl_constraint_set_constant_si(
1523 __isl_take isl_constraint *constraint, int v);
1524 __isl_give isl_constraint *isl_constraint_set_constant_val(
1525 __isl_take isl_constraint *constraint,
1526 __isl_take isl_val *v);
1527 __isl_give isl_constraint *isl_constraint_set_coefficient(
1528 __isl_take isl_constraint *constraint,
1529 enum isl_dim_type type, int pos, isl_int v);
1530 __isl_give isl_constraint *isl_constraint_set_coefficient_si(
1531 __isl_take isl_constraint *constraint,
1532 enum isl_dim_type type, int pos, int v);
1533 __isl_give isl_constraint *
1534 isl_constraint_set_coefficient_val(
1535 __isl_take isl_constraint *constraint,
1536 enum isl_dim_type type, int pos, isl_val *v);
1537 __isl_give isl_basic_map *isl_basic_map_add_constraint(
1538 __isl_take isl_basic_map *bmap,
1539 __isl_take isl_constraint *constraint);
1540 __isl_give isl_basic_set *isl_basic_set_add_constraint(
1541 __isl_take isl_basic_set *bset,
1542 __isl_take isl_constraint *constraint);
1543 __isl_give isl_map *isl_map_add_constraint(
1544 __isl_take isl_map *map,
1545 __isl_take isl_constraint *constraint);
1546 __isl_give isl_set *isl_set_add_constraint(
1547 __isl_take isl_set *set,
1548 __isl_take isl_constraint *constraint);
1549 __isl_give isl_basic_set *isl_basic_set_drop_constraint(
1550 __isl_take isl_basic_set *bset,
1551 __isl_take isl_constraint *constraint);
1553 For example, to create a set containing the even integers
1554 between 10 and 42, you would use the following code.
1557 isl_local_space *ls;
1559 isl_basic_set *bset;
1561 space = isl_space_set_alloc(ctx, 0, 2);
1562 bset = isl_basic_set_universe(isl_space_copy(space));
1563 ls = isl_local_space_from_space(space);
1565 c = isl_equality_alloc(isl_local_space_copy(ls));
1566 c = isl_constraint_set_coefficient_si(c, isl_dim_set, 0, -1);
1567 c = isl_constraint_set_coefficient_si(c, isl_dim_set, 1, 2);
1568 bset = isl_basic_set_add_constraint(bset, c);
1570 c = isl_inequality_alloc(isl_local_space_copy(ls));
1571 c = isl_constraint_set_constant_si(c, -10);
1572 c = isl_constraint_set_coefficient_si(c, isl_dim_set, 0, 1);
1573 bset = isl_basic_set_add_constraint(bset, c);
1575 c = isl_inequality_alloc(ls);
1576 c = isl_constraint_set_constant_si(c, 42);
1577 c = isl_constraint_set_coefficient_si(c, isl_dim_set, 0, -1);
1578 bset = isl_basic_set_add_constraint(bset, c);
1580 bset = isl_basic_set_project_out(bset, isl_dim_set, 1, 1);
1584 isl_basic_set *bset;
1585 bset = isl_basic_set_read_from_str(ctx,
1586 "{[i] : exists (a : i = 2a and i >= 10 and i <= 42)}");
1588 A basic set or relation can also be constructed from two matrices
1589 describing the equalities and the inequalities.
1591 __isl_give isl_basic_set *isl_basic_set_from_constraint_matrices(
1592 __isl_take isl_space *space,
1593 __isl_take isl_mat *eq, __isl_take isl_mat *ineq,
1594 enum isl_dim_type c1,
1595 enum isl_dim_type c2, enum isl_dim_type c3,
1596 enum isl_dim_type c4);
1597 __isl_give isl_basic_map *isl_basic_map_from_constraint_matrices(
1598 __isl_take isl_space *space,
1599 __isl_take isl_mat *eq, __isl_take isl_mat *ineq,
1600 enum isl_dim_type c1,
1601 enum isl_dim_type c2, enum isl_dim_type c3,
1602 enum isl_dim_type c4, enum isl_dim_type c5);
1604 The C<isl_dim_type> arguments indicate the order in which
1605 different kinds of variables appear in the input matrices
1606 and should be a permutation of C<isl_dim_cst>, C<isl_dim_param>,
1607 C<isl_dim_set> and C<isl_dim_div> for sets and
1608 of C<isl_dim_cst>, C<isl_dim_param>,
1609 C<isl_dim_in>, C<isl_dim_out> and C<isl_dim_div> for relations.
1611 A (basic or union) set or relation can also be constructed from a
1612 (union) (piecewise) (multiple) affine expression
1613 or a list of affine expressions
1614 (See L<"Piecewise Quasi Affine Expressions"> and
1615 L<"Piecewise Multiple Quasi Affine Expressions">).
1617 __isl_give isl_basic_map *isl_basic_map_from_aff(
1618 __isl_take isl_aff *aff);
1619 __isl_give isl_map *isl_map_from_aff(
1620 __isl_take isl_aff *aff);
1621 __isl_give isl_set *isl_set_from_pw_aff(
1622 __isl_take isl_pw_aff *pwaff);
1623 __isl_give isl_map *isl_map_from_pw_aff(
1624 __isl_take isl_pw_aff *pwaff);
1625 __isl_give isl_basic_map *isl_basic_map_from_aff_list(
1626 __isl_take isl_space *domain_space,
1627 __isl_take isl_aff_list *list);
1628 __isl_give isl_basic_map *isl_basic_map_from_multi_aff(
1629 __isl_take isl_multi_aff *maff)
1630 __isl_give isl_map *isl_map_from_multi_aff(
1631 __isl_take isl_multi_aff *maff)
1632 __isl_give isl_set *isl_set_from_pw_multi_aff(
1633 __isl_take isl_pw_multi_aff *pma);
1634 __isl_give isl_map *isl_map_from_pw_multi_aff(
1635 __isl_take isl_pw_multi_aff *pma);
1636 __isl_give isl_union_map *
1637 isl_union_map_from_union_pw_multi_aff(
1638 __isl_take isl_union_pw_multi_aff *upma);
1640 The C<domain_dim> argument describes the domain of the resulting
1641 basic relation. It is required because the C<list> may consist
1642 of zero affine expressions.
1644 =head2 Inspecting Sets and Relations
1646 Usually, the user should not have to care about the actual constraints
1647 of the sets and maps, but should instead apply the abstract operations
1648 explained in the following sections.
1649 Occasionally, however, it may be required to inspect the individual
1650 coefficients of the constraints. This section explains how to do so.
1651 In these cases, it may also be useful to have C<isl> compute
1652 an explicit representation of the existentially quantified variables.
1654 __isl_give isl_set *isl_set_compute_divs(
1655 __isl_take isl_set *set);
1656 __isl_give isl_map *isl_map_compute_divs(
1657 __isl_take isl_map *map);
1658 __isl_give isl_union_set *isl_union_set_compute_divs(
1659 __isl_take isl_union_set *uset);
1660 __isl_give isl_union_map *isl_union_map_compute_divs(
1661 __isl_take isl_union_map *umap);
1663 This explicit representation defines the existentially quantified
1664 variables as integer divisions of the other variables, possibly
1665 including earlier existentially quantified variables.
1666 An explicitly represented existentially quantified variable therefore
1667 has a unique value when the values of the other variables are known.
1668 If, furthermore, the same existentials, i.e., existentials
1669 with the same explicit representations, should appear in the
1670 same order in each of the disjuncts of a set or map, then the user should call
1671 either of the following functions.
1673 __isl_give isl_set *isl_set_align_divs(
1674 __isl_take isl_set *set);
1675 __isl_give isl_map *isl_map_align_divs(
1676 __isl_take isl_map *map);
1678 Alternatively, the existentially quantified variables can be removed
1679 using the following functions, which compute an overapproximation.
1681 __isl_give isl_basic_set *isl_basic_set_remove_divs(
1682 __isl_take isl_basic_set *bset);
1683 __isl_give isl_basic_map *isl_basic_map_remove_divs(
1684 __isl_take isl_basic_map *bmap);
1685 __isl_give isl_set *isl_set_remove_divs(
1686 __isl_take isl_set *set);
1687 __isl_give isl_map *isl_map_remove_divs(
1688 __isl_take isl_map *map);
1690 It is also possible to only remove those divs that are defined
1691 in terms of a given range of dimensions or only those for which
1692 no explicit representation is known.
1694 __isl_give isl_basic_set *
1695 isl_basic_set_remove_divs_involving_dims(
1696 __isl_take isl_basic_set *bset,
1697 enum isl_dim_type type,
1698 unsigned first, unsigned n);
1699 __isl_give isl_basic_map *
1700 isl_basic_map_remove_divs_involving_dims(
1701 __isl_take isl_basic_map *bmap,
1702 enum isl_dim_type type,
1703 unsigned first, unsigned n);
1704 __isl_give isl_set *isl_set_remove_divs_involving_dims(
1705 __isl_take isl_set *set, enum isl_dim_type type,
1706 unsigned first, unsigned n);
1707 __isl_give isl_map *isl_map_remove_divs_involving_dims(
1708 __isl_take isl_map *map, enum isl_dim_type type,
1709 unsigned first, unsigned n);
1711 __isl_give isl_basic_set *
1712 isl_basic_set_remove_unknown_divs(
1713 __isl_take isl_basic_set *bset);
1714 __isl_give isl_set *isl_set_remove_unknown_divs(
1715 __isl_take isl_set *set);
1716 __isl_give isl_map *isl_map_remove_unknown_divs(
1717 __isl_take isl_map *map);
1719 To iterate over all the sets or maps in a union set or map, use
1721 int isl_union_set_foreach_set(__isl_keep isl_union_set *uset,
1722 int (*fn)(__isl_take isl_set *set, void *user),
1724 int isl_union_map_foreach_map(__isl_keep isl_union_map *umap,
1725 int (*fn)(__isl_take isl_map *map, void *user),
1728 The number of sets or maps in a union set or map can be obtained
1731 int isl_union_set_n_set(__isl_keep isl_union_set *uset);
1732 int isl_union_map_n_map(__isl_keep isl_union_map *umap);
1734 To extract the set or map in a given space from a union, use
1736 __isl_give isl_set *isl_union_set_extract_set(
1737 __isl_keep isl_union_set *uset,
1738 __isl_take isl_space *space);
1739 __isl_give isl_map *isl_union_map_extract_map(
1740 __isl_keep isl_union_map *umap,
1741 __isl_take isl_space *space);
1743 To iterate over all the basic sets or maps in a set or map, use
1745 int isl_set_foreach_basic_set(__isl_keep isl_set *set,
1746 int (*fn)(__isl_take isl_basic_set *bset, void *user),
1748 int isl_map_foreach_basic_map(__isl_keep isl_map *map,
1749 int (*fn)(__isl_take isl_basic_map *bmap, void *user),
1752 The callback function C<fn> should return 0 if successful and
1753 -1 if an error occurs. In the latter case, or if any other error
1754 occurs, the above functions will return -1.
1756 It should be noted that C<isl> does not guarantee that
1757 the basic sets or maps passed to C<fn> are disjoint.
1758 If this is required, then the user should call one of
1759 the following functions first.
1761 __isl_give isl_set *isl_set_make_disjoint(
1762 __isl_take isl_set *set);
1763 __isl_give isl_map *isl_map_make_disjoint(
1764 __isl_take isl_map *map);
1766 The number of basic sets in a set can be obtained
1769 int isl_set_n_basic_set(__isl_keep isl_set *set);
1771 To iterate over the constraints of a basic set or map, use
1773 #include <isl/constraint.h>
1775 int isl_basic_set_n_constraint(
1776 __isl_keep isl_basic_set *bset);
1777 int isl_basic_set_foreach_constraint(
1778 __isl_keep isl_basic_set *bset,
1779 int (*fn)(__isl_take isl_constraint *c, void *user),
1781 int isl_basic_map_foreach_constraint(
1782 __isl_keep isl_basic_map *bmap,
1783 int (*fn)(__isl_take isl_constraint *c, void *user),
1785 void *isl_constraint_free(__isl_take isl_constraint *c);
1787 Again, the callback function C<fn> should return 0 if successful and
1788 -1 if an error occurs. In the latter case, or if any other error
1789 occurs, the above functions will return -1.
1790 The constraint C<c> represents either an equality or an inequality.
1791 Use the following function to find out whether a constraint
1792 represents an equality. If not, it represents an inequality.
1794 int isl_constraint_is_equality(
1795 __isl_keep isl_constraint *constraint);
1797 The coefficients of the constraints can be inspected using
1798 the following functions.
1800 int isl_constraint_is_lower_bound(
1801 __isl_keep isl_constraint *constraint,
1802 enum isl_dim_type type, unsigned pos);
1803 int isl_constraint_is_upper_bound(
1804 __isl_keep isl_constraint *constraint,
1805 enum isl_dim_type type, unsigned pos);
1806 void isl_constraint_get_constant(
1807 __isl_keep isl_constraint *constraint, isl_int *v);
1808 __isl_give isl_val *isl_constraint_get_constant_val(
1809 __isl_keep isl_constraint *constraint);
1810 void isl_constraint_get_coefficient(
1811 __isl_keep isl_constraint *constraint,
1812 enum isl_dim_type type, int pos, isl_int *v);
1813 __isl_give isl_val *isl_constraint_get_coefficient_val(
1814 __isl_keep isl_constraint *constraint,
1815 enum isl_dim_type type, int pos);
1816 int isl_constraint_involves_dims(
1817 __isl_keep isl_constraint *constraint,
1818 enum isl_dim_type type, unsigned first, unsigned n);
1820 The explicit representations of the existentially quantified
1821 variables can be inspected using the following function.
1822 Note that the user is only allowed to use this function
1823 if the inspected set or map is the result of a call
1824 to C<isl_set_compute_divs> or C<isl_map_compute_divs>.
1825 The existentially quantified variable is equal to the floor
1826 of the returned affine expression. The affine expression
1827 itself can be inspected using the functions in
1828 L<"Piecewise Quasi Affine Expressions">.
1830 __isl_give isl_aff *isl_constraint_get_div(
1831 __isl_keep isl_constraint *constraint, int pos);
1833 To obtain the constraints of a basic set or map in matrix
1834 form, use the following functions.
1836 __isl_give isl_mat *isl_basic_set_equalities_matrix(
1837 __isl_keep isl_basic_set *bset,
1838 enum isl_dim_type c1, enum isl_dim_type c2,
1839 enum isl_dim_type c3, enum isl_dim_type c4);
1840 __isl_give isl_mat *isl_basic_set_inequalities_matrix(
1841 __isl_keep isl_basic_set *bset,
1842 enum isl_dim_type c1, enum isl_dim_type c2,
1843 enum isl_dim_type c3, enum isl_dim_type c4);
1844 __isl_give isl_mat *isl_basic_map_equalities_matrix(
1845 __isl_keep isl_basic_map *bmap,
1846 enum isl_dim_type c1,
1847 enum isl_dim_type c2, enum isl_dim_type c3,
1848 enum isl_dim_type c4, enum isl_dim_type c5);
1849 __isl_give isl_mat *isl_basic_map_inequalities_matrix(
1850 __isl_keep isl_basic_map *bmap,
1851 enum isl_dim_type c1,
1852 enum isl_dim_type c2, enum isl_dim_type c3,
1853 enum isl_dim_type c4, enum isl_dim_type c5);
1855 The C<isl_dim_type> arguments dictate the order in which
1856 different kinds of variables appear in the resulting matrix
1857 and should be a permutation of C<isl_dim_cst>, C<isl_dim_param>,
1858 C<isl_dim_in>, C<isl_dim_out> and C<isl_dim_div>.
1860 The number of parameters, input, output or set dimensions can
1861 be obtained using the following functions.
1863 unsigned isl_basic_set_dim(__isl_keep isl_basic_set *bset,
1864 enum isl_dim_type type);
1865 unsigned isl_basic_map_dim(__isl_keep isl_basic_map *bmap,
1866 enum isl_dim_type type);
1867 unsigned isl_set_dim(__isl_keep isl_set *set,
1868 enum isl_dim_type type);
1869 unsigned isl_map_dim(__isl_keep isl_map *map,
1870 enum isl_dim_type type);
1872 To check whether the description of a set or relation depends
1873 on one or more given dimensions, it is not necessary to iterate over all
1874 constraints. Instead the following functions can be used.
1876 int isl_basic_set_involves_dims(
1877 __isl_keep isl_basic_set *bset,
1878 enum isl_dim_type type, unsigned first, unsigned n);
1879 int isl_set_involves_dims(__isl_keep isl_set *set,
1880 enum isl_dim_type type, unsigned first, unsigned n);
1881 int isl_basic_map_involves_dims(
1882 __isl_keep isl_basic_map *bmap,
1883 enum isl_dim_type type, unsigned first, unsigned n);
1884 int isl_map_involves_dims(__isl_keep isl_map *map,
1885 enum isl_dim_type type, unsigned first, unsigned n);
1887 Similarly, the following functions can be used to check whether
1888 a given dimension is involved in any lower or upper bound.
1890 int isl_set_dim_has_any_lower_bound(__isl_keep isl_set *set,
1891 enum isl_dim_type type, unsigned pos);
1892 int isl_set_dim_has_any_upper_bound(__isl_keep isl_set *set,
1893 enum isl_dim_type type, unsigned pos);
1895 Note that these functions return true even if there is a bound on
1896 the dimension on only some of the basic sets of C<set>.
1897 To check if they have a bound for all of the basic sets in C<set>,
1898 use the following functions instead.
1900 int isl_set_dim_has_lower_bound(__isl_keep isl_set *set,
1901 enum isl_dim_type type, unsigned pos);
1902 int isl_set_dim_has_upper_bound(__isl_keep isl_set *set,
1903 enum isl_dim_type type, unsigned pos);
1905 The identifiers or names of the domain and range spaces of a set
1906 or relation can be read off or set using the following functions.
1908 __isl_give isl_set *isl_set_set_tuple_id(
1909 __isl_take isl_set *set, __isl_take isl_id *id);
1910 __isl_give isl_set *isl_set_reset_tuple_id(
1911 __isl_take isl_set *set);
1912 int isl_set_has_tuple_id(__isl_keep isl_set *set);
1913 __isl_give isl_id *isl_set_get_tuple_id(
1914 __isl_keep isl_set *set);
1915 __isl_give isl_map *isl_map_set_tuple_id(
1916 __isl_take isl_map *map, enum isl_dim_type type,
1917 __isl_take isl_id *id);
1918 __isl_give isl_map *isl_map_reset_tuple_id(
1919 __isl_take isl_map *map, enum isl_dim_type type);
1920 int isl_map_has_tuple_id(__isl_keep isl_map *map,
1921 enum isl_dim_type type);
1922 __isl_give isl_id *isl_map_get_tuple_id(
1923 __isl_keep isl_map *map, enum isl_dim_type type);
1925 const char *isl_basic_set_get_tuple_name(
1926 __isl_keep isl_basic_set *bset);
1927 __isl_give isl_basic_set *isl_basic_set_set_tuple_name(
1928 __isl_take isl_basic_set *set, const char *s);
1929 int isl_set_has_tuple_name(__isl_keep isl_set *set);
1930 const char *isl_set_get_tuple_name(
1931 __isl_keep isl_set *set);
1932 const char *isl_basic_map_get_tuple_name(
1933 __isl_keep isl_basic_map *bmap,
1934 enum isl_dim_type type);
1935 __isl_give isl_basic_map *isl_basic_map_set_tuple_name(
1936 __isl_take isl_basic_map *bmap,
1937 enum isl_dim_type type, const char *s);
1938 int isl_map_has_tuple_name(__isl_keep isl_map *map,
1939 enum isl_dim_type type);
1940 const char *isl_map_get_tuple_name(
1941 __isl_keep isl_map *map,
1942 enum isl_dim_type type);
1944 As with C<isl_space_get_tuple_name>, the value returned points to
1945 an internal data structure.
1946 The identifiers, positions or names of individual dimensions can be
1947 read off using the following functions.
1949 __isl_give isl_id *isl_basic_set_get_dim_id(
1950 __isl_keep isl_basic_set *bset,
1951 enum isl_dim_type type, unsigned pos);
1952 __isl_give isl_set *isl_set_set_dim_id(
1953 __isl_take isl_set *set, enum isl_dim_type type,
1954 unsigned pos, __isl_take isl_id *id);
1955 int isl_set_has_dim_id(__isl_keep isl_set *set,
1956 enum isl_dim_type type, unsigned pos);
1957 __isl_give isl_id *isl_set_get_dim_id(
1958 __isl_keep isl_set *set, enum isl_dim_type type,
1960 int isl_basic_map_has_dim_id(
1961 __isl_keep isl_basic_map *bmap,
1962 enum isl_dim_type type, unsigned pos);
1963 __isl_give isl_map *isl_map_set_dim_id(
1964 __isl_take isl_map *map, enum isl_dim_type type,
1965 unsigned pos, __isl_take isl_id *id);
1966 int isl_map_has_dim_id(__isl_keep isl_map *map,
1967 enum isl_dim_type type, unsigned pos);
1968 __isl_give isl_id *isl_map_get_dim_id(
1969 __isl_keep isl_map *map, enum isl_dim_type type,
1972 int isl_set_find_dim_by_id(__isl_keep isl_set *set,
1973 enum isl_dim_type type, __isl_keep isl_id *id);
1974 int isl_map_find_dim_by_id(__isl_keep isl_map *map,
1975 enum isl_dim_type type, __isl_keep isl_id *id);
1976 int isl_set_find_dim_by_name(__isl_keep isl_set *set,
1977 enum isl_dim_type type, const char *name);
1978 int isl_map_find_dim_by_name(__isl_keep isl_map *map,
1979 enum isl_dim_type type, const char *name);
1981 const char *isl_constraint_get_dim_name(
1982 __isl_keep isl_constraint *constraint,
1983 enum isl_dim_type type, unsigned pos);
1984 const char *isl_basic_set_get_dim_name(
1985 __isl_keep isl_basic_set *bset,
1986 enum isl_dim_type type, unsigned pos);
1987 int isl_set_has_dim_name(__isl_keep isl_set *set,
1988 enum isl_dim_type type, unsigned pos);
1989 const char *isl_set_get_dim_name(
1990 __isl_keep isl_set *set,
1991 enum isl_dim_type type, unsigned pos);
1992 const char *isl_basic_map_get_dim_name(
1993 __isl_keep isl_basic_map *bmap,
1994 enum isl_dim_type type, unsigned pos);
1995 int isl_map_has_dim_name(__isl_keep isl_map *map,
1996 enum isl_dim_type type, unsigned pos);
1997 const char *isl_map_get_dim_name(
1998 __isl_keep isl_map *map,
1999 enum isl_dim_type type, unsigned pos);
2001 These functions are mostly useful to obtain the identifiers, positions
2002 or names of the parameters. Identifiers of individual dimensions are
2003 essentially only useful for printing. They are ignored by all other
2004 operations and may not be preserved across those operations.
2008 =head3 Unary Properties
2014 The following functions test whether the given set or relation
2015 contains any integer points. The ``plain'' variants do not perform
2016 any computations, but simply check if the given set or relation
2017 is already known to be empty.
2019 int isl_basic_set_plain_is_empty(__isl_keep isl_basic_set *bset);
2020 int isl_basic_set_is_empty(__isl_keep isl_basic_set *bset);
2021 int isl_set_plain_is_empty(__isl_keep isl_set *set);
2022 int isl_set_is_empty(__isl_keep isl_set *set);
2023 int isl_union_set_is_empty(__isl_keep isl_union_set *uset);
2024 int isl_basic_map_plain_is_empty(__isl_keep isl_basic_map *bmap);
2025 int isl_basic_map_is_empty(__isl_keep isl_basic_map *bmap);
2026 int isl_map_plain_is_empty(__isl_keep isl_map *map);
2027 int isl_map_is_empty(__isl_keep isl_map *map);
2028 int isl_union_map_is_empty(__isl_keep isl_union_map *umap);
2030 =item * Universality
2032 int isl_basic_set_is_universe(__isl_keep isl_basic_set *bset);
2033 int isl_basic_map_is_universe(__isl_keep isl_basic_map *bmap);
2034 int isl_set_plain_is_universe(__isl_keep isl_set *set);
2036 =item * Single-valuedness
2038 int isl_basic_map_is_single_valued(
2039 __isl_keep isl_basic_map *bmap);
2040 int isl_map_plain_is_single_valued(
2041 __isl_keep isl_map *map);
2042 int isl_map_is_single_valued(__isl_keep isl_map *map);
2043 int isl_union_map_is_single_valued(__isl_keep isl_union_map *umap);
2047 int isl_map_plain_is_injective(__isl_keep isl_map *map);
2048 int isl_map_is_injective(__isl_keep isl_map *map);
2049 int isl_union_map_plain_is_injective(
2050 __isl_keep isl_union_map *umap);
2051 int isl_union_map_is_injective(
2052 __isl_keep isl_union_map *umap);
2056 int isl_map_is_bijective(__isl_keep isl_map *map);
2057 int isl_union_map_is_bijective(__isl_keep isl_union_map *umap);
2061 int isl_basic_map_plain_is_fixed(
2062 __isl_keep isl_basic_map *bmap,
2063 enum isl_dim_type type, unsigned pos,
2065 int isl_set_plain_is_fixed(__isl_keep isl_set *set,
2066 enum isl_dim_type type, unsigned pos,
2068 int isl_map_plain_is_fixed(__isl_keep isl_map *map,
2069 enum isl_dim_type type, unsigned pos,
2072 Check if the relation obviously lies on a hyperplane where the given dimension
2073 has a fixed value and if so, return that value in C<*val>.
2075 __isl_give isl_val *
2076 isl_basic_map_plain_get_val_if_fixed(
2077 __isl_keep isl_basic_map *bmap,
2078 enum isl_dim_type type, unsigned pos);
2079 __isl_give isl_val *isl_set_plain_get_val_if_fixed(
2080 __isl_keep isl_set *set,
2081 enum isl_dim_type type, unsigned pos);
2082 __isl_give isl_val *isl_map_plain_get_val_if_fixed(
2083 __isl_keep isl_map *map,
2084 enum isl_dim_type type, unsigned pos);
2086 If the set or relation obviously lies on a hyperplane where the given dimension
2087 has a fixed value, then return that value.
2088 Otherwise return NaN.
2092 int isl_set_dim_residue_class_val(
2093 __isl_keep isl_set *set,
2094 int pos, __isl_give isl_val **modulo,
2095 __isl_give isl_val **residue);
2097 Check if the values of the given set dimension are equal to a fixed
2098 value modulo some integer value. If so, assign the modulo to C<*modulo>
2099 and the fixed value to C<*residue>. If the given dimension attains only
2100 a single value, then assign C<0> to C<*modulo> and the fixed value to
2102 If the dimension does not attain only a single value and if no modulo
2103 can be found then assign C<1> to C<*modulo> and C<1> to C<*residue>.
2107 To check whether a set is a parameter domain, use this function:
2109 int isl_set_is_params(__isl_keep isl_set *set);
2110 int isl_union_set_is_params(
2111 __isl_keep isl_union_set *uset);
2115 The following functions check whether the domain of the given
2116 (basic) set is a wrapped relation.
2118 int isl_basic_set_is_wrapping(
2119 __isl_keep isl_basic_set *bset);
2120 int isl_set_is_wrapping(__isl_keep isl_set *set);
2122 =item * Internal Product
2124 int isl_basic_map_can_zip(
2125 __isl_keep isl_basic_map *bmap);
2126 int isl_map_can_zip(__isl_keep isl_map *map);
2128 Check whether the product of domain and range of the given relation
2130 i.e., whether both domain and range are nested relations.
2134 int isl_basic_map_can_curry(
2135 __isl_keep isl_basic_map *bmap);
2136 int isl_map_can_curry(__isl_keep isl_map *map);
2138 Check whether the domain of the (basic) relation is a wrapped relation.
2140 int isl_basic_map_can_uncurry(
2141 __isl_keep isl_basic_map *bmap);
2142 int isl_map_can_uncurry(__isl_keep isl_map *map);
2144 Check whether the range of the (basic) relation is a wrapped relation.
2148 =head3 Binary Properties
2154 int isl_set_plain_is_equal(__isl_keep isl_set *set1,
2155 __isl_keep isl_set *set2);
2156 int isl_set_is_equal(__isl_keep isl_set *set1,
2157 __isl_keep isl_set *set2);
2158 int isl_union_set_is_equal(
2159 __isl_keep isl_union_set *uset1,
2160 __isl_keep isl_union_set *uset2);
2161 int isl_basic_map_is_equal(
2162 __isl_keep isl_basic_map *bmap1,
2163 __isl_keep isl_basic_map *bmap2);
2164 int isl_map_is_equal(__isl_keep isl_map *map1,
2165 __isl_keep isl_map *map2);
2166 int isl_map_plain_is_equal(__isl_keep isl_map *map1,
2167 __isl_keep isl_map *map2);
2168 int isl_union_map_is_equal(
2169 __isl_keep isl_union_map *umap1,
2170 __isl_keep isl_union_map *umap2);
2172 =item * Disjointness
2174 int isl_set_plain_is_disjoint(__isl_keep isl_set *set1,
2175 __isl_keep isl_set *set2);
2176 int isl_set_is_disjoint(__isl_keep isl_set *set1,
2177 __isl_keep isl_set *set2);
2178 int isl_map_is_disjoint(__isl_keep isl_map *map1,
2179 __isl_keep isl_map *map2);
2183 int isl_basic_set_is_subset(
2184 __isl_keep isl_basic_set *bset1,
2185 __isl_keep isl_basic_set *bset2);
2186 int isl_set_is_subset(__isl_keep isl_set *set1,
2187 __isl_keep isl_set *set2);
2188 int isl_set_is_strict_subset(
2189 __isl_keep isl_set *set1,
2190 __isl_keep isl_set *set2);
2191 int isl_union_set_is_subset(
2192 __isl_keep isl_union_set *uset1,
2193 __isl_keep isl_union_set *uset2);
2194 int isl_union_set_is_strict_subset(
2195 __isl_keep isl_union_set *uset1,
2196 __isl_keep isl_union_set *uset2);
2197 int isl_basic_map_is_subset(
2198 __isl_keep isl_basic_map *bmap1,
2199 __isl_keep isl_basic_map *bmap2);
2200 int isl_basic_map_is_strict_subset(
2201 __isl_keep isl_basic_map *bmap1,
2202 __isl_keep isl_basic_map *bmap2);
2203 int isl_map_is_subset(
2204 __isl_keep isl_map *map1,
2205 __isl_keep isl_map *map2);
2206 int isl_map_is_strict_subset(
2207 __isl_keep isl_map *map1,
2208 __isl_keep isl_map *map2);
2209 int isl_union_map_is_subset(
2210 __isl_keep isl_union_map *umap1,
2211 __isl_keep isl_union_map *umap2);
2212 int isl_union_map_is_strict_subset(
2213 __isl_keep isl_union_map *umap1,
2214 __isl_keep isl_union_map *umap2);
2216 Check whether the first argument is a (strict) subset of the
2221 int isl_set_plain_cmp(__isl_keep isl_set *set1,
2222 __isl_keep isl_set *set2);
2224 This function is useful for sorting C<isl_set>s.
2225 The order depends on the internal representation of the inputs.
2226 The order is fixed over different calls to the function (assuming
2227 the internal representation of the inputs has not changed), but may
2228 change over different versions of C<isl>.
2232 =head2 Unary Operations
2238 __isl_give isl_set *isl_set_complement(
2239 __isl_take isl_set *set);
2240 __isl_give isl_map *isl_map_complement(
2241 __isl_take isl_map *map);
2245 __isl_give isl_basic_map *isl_basic_map_reverse(
2246 __isl_take isl_basic_map *bmap);
2247 __isl_give isl_map *isl_map_reverse(
2248 __isl_take isl_map *map);
2249 __isl_give isl_union_map *isl_union_map_reverse(
2250 __isl_take isl_union_map *umap);
2254 __isl_give isl_basic_set *isl_basic_set_project_out(
2255 __isl_take isl_basic_set *bset,
2256 enum isl_dim_type type, unsigned first, unsigned n);
2257 __isl_give isl_basic_map *isl_basic_map_project_out(
2258 __isl_take isl_basic_map *bmap,
2259 enum isl_dim_type type, unsigned first, unsigned n);
2260 __isl_give isl_set *isl_set_project_out(__isl_take isl_set *set,
2261 enum isl_dim_type type, unsigned first, unsigned n);
2262 __isl_give isl_map *isl_map_project_out(__isl_take isl_map *map,
2263 enum isl_dim_type type, unsigned first, unsigned n);
2264 __isl_give isl_basic_set *isl_basic_set_params(
2265 __isl_take isl_basic_set *bset);
2266 __isl_give isl_basic_set *isl_basic_map_domain(
2267 __isl_take isl_basic_map *bmap);
2268 __isl_give isl_basic_set *isl_basic_map_range(
2269 __isl_take isl_basic_map *bmap);
2270 __isl_give isl_set *isl_set_params(__isl_take isl_set *set);
2271 __isl_give isl_set *isl_map_params(__isl_take isl_map *map);
2272 __isl_give isl_set *isl_map_domain(
2273 __isl_take isl_map *bmap);
2274 __isl_give isl_set *isl_map_range(
2275 __isl_take isl_map *map);
2276 __isl_give isl_set *isl_union_set_params(
2277 __isl_take isl_union_set *uset);
2278 __isl_give isl_set *isl_union_map_params(
2279 __isl_take isl_union_map *umap);
2280 __isl_give isl_union_set *isl_union_map_domain(
2281 __isl_take isl_union_map *umap);
2282 __isl_give isl_union_set *isl_union_map_range(
2283 __isl_take isl_union_map *umap);
2285 __isl_give isl_basic_map *isl_basic_map_domain_map(
2286 __isl_take isl_basic_map *bmap);
2287 __isl_give isl_basic_map *isl_basic_map_range_map(
2288 __isl_take isl_basic_map *bmap);
2289 __isl_give isl_map *isl_map_domain_map(__isl_take isl_map *map);
2290 __isl_give isl_map *isl_map_range_map(__isl_take isl_map *map);
2291 __isl_give isl_union_map *isl_union_map_domain_map(
2292 __isl_take isl_union_map *umap);
2293 __isl_give isl_union_map *isl_union_map_range_map(
2294 __isl_take isl_union_map *umap);
2296 The functions above construct a (basic, regular or union) relation
2297 that maps (a wrapped version of) the input relation to its domain or range.
2301 __isl_give isl_basic_set *isl_basic_set_eliminate(
2302 __isl_take isl_basic_set *bset,
2303 enum isl_dim_type type,
2304 unsigned first, unsigned n);
2305 __isl_give isl_set *isl_set_eliminate(
2306 __isl_take isl_set *set, enum isl_dim_type type,
2307 unsigned first, unsigned n);
2308 __isl_give isl_basic_map *isl_basic_map_eliminate(
2309 __isl_take isl_basic_map *bmap,
2310 enum isl_dim_type type,
2311 unsigned first, unsigned n);
2312 __isl_give isl_map *isl_map_eliminate(
2313 __isl_take isl_map *map, enum isl_dim_type type,
2314 unsigned first, unsigned n);
2316 Eliminate the coefficients for the given dimensions from the constraints,
2317 without removing the dimensions.
2321 __isl_give isl_basic_set *isl_basic_set_fix(
2322 __isl_take isl_basic_set *bset,
2323 enum isl_dim_type type, unsigned pos,
2325 __isl_give isl_basic_set *isl_basic_set_fix_si(
2326 __isl_take isl_basic_set *bset,
2327 enum isl_dim_type type, unsigned pos, int value);
2328 __isl_give isl_basic_set *isl_basic_set_fix_val(
2329 __isl_take isl_basic_set *bset,
2330 enum isl_dim_type type, unsigned pos,
2331 __isl_take isl_val *v);
2332 __isl_give isl_set *isl_set_fix(__isl_take isl_set *set,
2333 enum isl_dim_type type, unsigned pos,
2335 __isl_give isl_set *isl_set_fix_si(__isl_take isl_set *set,
2336 enum isl_dim_type type, unsigned pos, int value);
2337 __isl_give isl_set *isl_set_fix_val(
2338 __isl_take isl_set *set,
2339 enum isl_dim_type type, unsigned pos,
2340 __isl_take isl_val *v);
2341 __isl_give isl_basic_map *isl_basic_map_fix_si(
2342 __isl_take isl_basic_map *bmap,
2343 enum isl_dim_type type, unsigned pos, int value);
2344 __isl_give isl_basic_map *isl_basic_map_fix_val(
2345 __isl_take isl_basic_map *bmap,
2346 enum isl_dim_type type, unsigned pos,
2347 __isl_take isl_val *v);
2348 __isl_give isl_map *isl_map_fix(__isl_take isl_map *map,
2349 enum isl_dim_type type, unsigned pos,
2351 __isl_give isl_map *isl_map_fix_si(__isl_take isl_map *map,
2352 enum isl_dim_type type, unsigned pos, int value);
2353 __isl_give isl_map *isl_map_fix_val(
2354 __isl_take isl_map *map,
2355 enum isl_dim_type type, unsigned pos,
2356 __isl_take isl_val *v);
2358 Intersect the set or relation with the hyperplane where the given
2359 dimension has the fixed given value.
2361 __isl_give isl_basic_map *isl_basic_map_lower_bound_si(
2362 __isl_take isl_basic_map *bmap,
2363 enum isl_dim_type type, unsigned pos, int value);
2364 __isl_give isl_basic_map *isl_basic_map_upper_bound_si(
2365 __isl_take isl_basic_map *bmap,
2366 enum isl_dim_type type, unsigned pos, int value);
2367 __isl_give isl_set *isl_set_lower_bound(
2368 __isl_take isl_set *set,
2369 enum isl_dim_type type, unsigned pos,
2371 __isl_give isl_set *isl_set_lower_bound_si(
2372 __isl_take isl_set *set,
2373 enum isl_dim_type type, unsigned pos, int value);
2374 __isl_give isl_set *isl_set_lower_bound_val(
2375 __isl_take isl_set *set,
2376 enum isl_dim_type type, unsigned pos,
2377 __isl_take isl_val *value);
2378 __isl_give isl_map *isl_map_lower_bound_si(
2379 __isl_take isl_map *map,
2380 enum isl_dim_type type, unsigned pos, int value);
2381 __isl_give isl_set *isl_set_upper_bound(
2382 __isl_take isl_set *set,
2383 enum isl_dim_type type, unsigned pos,
2385 __isl_give isl_set *isl_set_upper_bound_si(
2386 __isl_take isl_set *set,
2387 enum isl_dim_type type, unsigned pos, int value);
2388 __isl_give isl_set *isl_set_upper_bound_val(
2389 __isl_take isl_set *set,
2390 enum isl_dim_type type, unsigned pos,
2391 __isl_take isl_val *value);
2392 __isl_give isl_map *isl_map_upper_bound_si(
2393 __isl_take isl_map *map,
2394 enum isl_dim_type type, unsigned pos, int value);
2396 Intersect the set or relation with the half-space where the given
2397 dimension has a value bounded by the fixed given integer value.
2399 __isl_give isl_set *isl_set_equate(__isl_take isl_set *set,
2400 enum isl_dim_type type1, int pos1,
2401 enum isl_dim_type type2, int pos2);
2402 __isl_give isl_basic_map *isl_basic_map_equate(
2403 __isl_take isl_basic_map *bmap,
2404 enum isl_dim_type type1, int pos1,
2405 enum isl_dim_type type2, int pos2);
2406 __isl_give isl_map *isl_map_equate(__isl_take isl_map *map,
2407 enum isl_dim_type type1, int pos1,
2408 enum isl_dim_type type2, int pos2);
2410 Intersect the set or relation with the hyperplane where the given
2411 dimensions are equal to each other.
2413 __isl_give isl_map *isl_map_oppose(__isl_take isl_map *map,
2414 enum isl_dim_type type1, int pos1,
2415 enum isl_dim_type type2, int pos2);
2417 Intersect the relation with the hyperplane where the given
2418 dimensions have opposite values.
2420 __isl_give isl_basic_map *isl_basic_map_order_ge(
2421 __isl_take isl_basic_map *bmap,
2422 enum isl_dim_type type1, int pos1,
2423 enum isl_dim_type type2, int pos2);
2424 __isl_give isl_map *isl_map_order_lt(__isl_take isl_map *map,
2425 enum isl_dim_type type1, int pos1,
2426 enum isl_dim_type type2, int pos2);
2427 __isl_give isl_basic_map *isl_basic_map_order_gt(
2428 __isl_take isl_basic_map *bmap,
2429 enum isl_dim_type type1, int pos1,
2430 enum isl_dim_type type2, int pos2);
2431 __isl_give isl_map *isl_map_order_gt(__isl_take isl_map *map,
2432 enum isl_dim_type type1, int pos1,
2433 enum isl_dim_type type2, int pos2);
2435 Intersect the relation with the half-space where the given
2436 dimensions satisfy the given ordering.
2440 __isl_give isl_map *isl_set_identity(
2441 __isl_take isl_set *set);
2442 __isl_give isl_union_map *isl_union_set_identity(
2443 __isl_take isl_union_set *uset);
2445 Construct an identity relation on the given (union) set.
2449 __isl_give isl_basic_set *isl_basic_map_deltas(
2450 __isl_take isl_basic_map *bmap);
2451 __isl_give isl_set *isl_map_deltas(__isl_take isl_map *map);
2452 __isl_give isl_union_set *isl_union_map_deltas(
2453 __isl_take isl_union_map *umap);
2455 These functions return a (basic) set containing the differences
2456 between image elements and corresponding domain elements in the input.
2458 __isl_give isl_basic_map *isl_basic_map_deltas_map(
2459 __isl_take isl_basic_map *bmap);
2460 __isl_give isl_map *isl_map_deltas_map(
2461 __isl_take isl_map *map);
2462 __isl_give isl_union_map *isl_union_map_deltas_map(
2463 __isl_take isl_union_map *umap);
2465 The functions above construct a (basic, regular or union) relation
2466 that maps (a wrapped version of) the input relation to its delta set.
2470 Simplify the representation of a set or relation by trying
2471 to combine pairs of basic sets or relations into a single
2472 basic set or relation.
2474 __isl_give isl_set *isl_set_coalesce(__isl_take isl_set *set);
2475 __isl_give isl_map *isl_map_coalesce(__isl_take isl_map *map);
2476 __isl_give isl_union_set *isl_union_set_coalesce(
2477 __isl_take isl_union_set *uset);
2478 __isl_give isl_union_map *isl_union_map_coalesce(
2479 __isl_take isl_union_map *umap);
2481 One of the methods for combining pairs of basic sets or relations
2482 can result in coefficients that are much larger than those that appear
2483 in the constraints of the input. By default, the coefficients are
2484 not allowed to grow larger, but this can be changed by unsetting
2485 the following option.
2487 int isl_options_set_coalesce_bounded_wrapping(
2488 isl_ctx *ctx, int val);
2489 int isl_options_get_coalesce_bounded_wrapping(
2492 =item * Detecting equalities
2494 __isl_give isl_basic_set *isl_basic_set_detect_equalities(
2495 __isl_take isl_basic_set *bset);
2496 __isl_give isl_basic_map *isl_basic_map_detect_equalities(
2497 __isl_take isl_basic_map *bmap);
2498 __isl_give isl_set *isl_set_detect_equalities(
2499 __isl_take isl_set *set);
2500 __isl_give isl_map *isl_map_detect_equalities(
2501 __isl_take isl_map *map);
2502 __isl_give isl_union_set *isl_union_set_detect_equalities(
2503 __isl_take isl_union_set *uset);
2504 __isl_give isl_union_map *isl_union_map_detect_equalities(
2505 __isl_take isl_union_map *umap);
2507 Simplify the representation of a set or relation by detecting implicit
2510 =item * Removing redundant constraints
2512 __isl_give isl_basic_set *isl_basic_set_remove_redundancies(
2513 __isl_take isl_basic_set *bset);
2514 __isl_give isl_set *isl_set_remove_redundancies(
2515 __isl_take isl_set *set);
2516 __isl_give isl_basic_map *isl_basic_map_remove_redundancies(
2517 __isl_take isl_basic_map *bmap);
2518 __isl_give isl_map *isl_map_remove_redundancies(
2519 __isl_take isl_map *map);
2523 __isl_give isl_basic_set *isl_set_convex_hull(
2524 __isl_take isl_set *set);
2525 __isl_give isl_basic_map *isl_map_convex_hull(
2526 __isl_take isl_map *map);
2528 If the input set or relation has any existentially quantified
2529 variables, then the result of these operations is currently undefined.
2533 __isl_give isl_basic_set *
2534 isl_set_unshifted_simple_hull(
2535 __isl_take isl_set *set);
2536 __isl_give isl_basic_map *
2537 isl_map_unshifted_simple_hull(
2538 __isl_take isl_map *map);
2539 __isl_give isl_basic_set *isl_set_simple_hull(
2540 __isl_take isl_set *set);
2541 __isl_give isl_basic_map *isl_map_simple_hull(
2542 __isl_take isl_map *map);
2543 __isl_give isl_union_map *isl_union_map_simple_hull(
2544 __isl_take isl_union_map *umap);
2546 These functions compute a single basic set or relation
2547 that contains the whole input set or relation.
2548 In particular, the output is described by translates
2549 of the constraints describing the basic sets or relations in the input.
2550 In case of C<isl_set_unshifted_simple_hull>, only the original
2551 constraints are used, without any translation.
2555 (See \autoref{s:simple hull}.)
2561 __isl_give isl_basic_set *isl_basic_set_affine_hull(
2562 __isl_take isl_basic_set *bset);
2563 __isl_give isl_basic_set *isl_set_affine_hull(
2564 __isl_take isl_set *set);
2565 __isl_give isl_union_set *isl_union_set_affine_hull(
2566 __isl_take isl_union_set *uset);
2567 __isl_give isl_basic_map *isl_basic_map_affine_hull(
2568 __isl_take isl_basic_map *bmap);
2569 __isl_give isl_basic_map *isl_map_affine_hull(
2570 __isl_take isl_map *map);
2571 __isl_give isl_union_map *isl_union_map_affine_hull(
2572 __isl_take isl_union_map *umap);
2574 In case of union sets and relations, the affine hull is computed
2577 =item * Polyhedral hull
2579 __isl_give isl_basic_set *isl_set_polyhedral_hull(
2580 __isl_take isl_set *set);
2581 __isl_give isl_basic_map *isl_map_polyhedral_hull(
2582 __isl_take isl_map *map);
2583 __isl_give isl_union_set *isl_union_set_polyhedral_hull(
2584 __isl_take isl_union_set *uset);
2585 __isl_give isl_union_map *isl_union_map_polyhedral_hull(
2586 __isl_take isl_union_map *umap);
2588 These functions compute a single basic set or relation
2589 not involving any existentially quantified variables
2590 that contains the whole input set or relation.
2591 In case of union sets and relations, the polyhedral hull is computed
2594 =item * Other approximations
2596 __isl_give isl_basic_set *
2597 isl_basic_set_drop_constraints_involving_dims(
2598 __isl_take isl_basic_set *bset,
2599 enum isl_dim_type type,
2600 unsigned first, unsigned n);
2601 __isl_give isl_basic_map *
2602 isl_basic_map_drop_constraints_involving_dims(
2603 __isl_take isl_basic_map *bmap,
2604 enum isl_dim_type type,
2605 unsigned first, unsigned n);
2606 __isl_give isl_basic_set *
2607 isl_basic_set_drop_constraints_not_involving_dims(
2608 __isl_take isl_basic_set *bset,
2609 enum isl_dim_type type,
2610 unsigned first, unsigned n);
2611 __isl_give isl_set *
2612 isl_set_drop_constraints_involving_dims(
2613 __isl_take isl_set *set,
2614 enum isl_dim_type type,
2615 unsigned first, unsigned n);
2616 __isl_give isl_map *
2617 isl_map_drop_constraints_involving_dims(
2618 __isl_take isl_map *map,
2619 enum isl_dim_type type,
2620 unsigned first, unsigned n);
2622 These functions drop any constraints (not) involving the specified dimensions.
2623 Note that the result depends on the representation of the input.
2627 __isl_give isl_basic_set *isl_basic_set_sample(
2628 __isl_take isl_basic_set *bset);
2629 __isl_give isl_basic_set *isl_set_sample(
2630 __isl_take isl_set *set);
2631 __isl_give isl_basic_map *isl_basic_map_sample(
2632 __isl_take isl_basic_map *bmap);
2633 __isl_give isl_basic_map *isl_map_sample(
2634 __isl_take isl_map *map);
2636 If the input (basic) set or relation is non-empty, then return
2637 a singleton subset of the input. Otherwise, return an empty set.
2639 =item * Optimization
2641 #include <isl/ilp.h>
2642 enum isl_lp_result isl_basic_set_max(
2643 __isl_keep isl_basic_set *bset,
2644 __isl_keep isl_aff *obj, isl_int *opt)
2645 __isl_give isl_val *isl_basic_set_max_val(
2646 __isl_keep isl_basic_set *bset,
2647 __isl_keep isl_aff *obj);
2648 enum isl_lp_result isl_set_min(__isl_keep isl_set *set,
2649 __isl_keep isl_aff *obj, isl_int *opt);
2650 __isl_give isl_val *isl_set_min_val(
2651 __isl_keep isl_set *set,
2652 __isl_keep isl_aff *obj);
2653 enum isl_lp_result isl_set_max(__isl_keep isl_set *set,
2654 __isl_keep isl_aff *obj, isl_int *opt);
2655 __isl_give isl_val *isl_set_max_val(
2656 __isl_keep isl_set *set,
2657 __isl_keep isl_aff *obj);
2659 Compute the minimum or maximum of the integer affine expression C<obj>
2660 over the points in C<set>, returning the result in C<opt>.
2661 The return value may be one of C<isl_lp_error>,
2662 C<isl_lp_ok>, C<isl_lp_unbounded> or C<isl_lp_empty>, in case of
2663 an C<isl_lp_result>. If the result is an C<isl_val> then
2664 the result is C<NULL> in case of an error, the optimal value in case
2665 there is one, negative infinity or infinity if the problem is unbounded and
2666 NaN if the problem is empty.
2668 =item * Parametric optimization
2670 __isl_give isl_pw_aff *isl_set_dim_min(
2671 __isl_take isl_set *set, int pos);
2672 __isl_give isl_pw_aff *isl_set_dim_max(
2673 __isl_take isl_set *set, int pos);
2674 __isl_give isl_pw_aff *isl_map_dim_max(
2675 __isl_take isl_map *map, int pos);
2677 Compute the minimum or maximum of the given set or output dimension
2678 as a function of the parameters (and input dimensions), but independently
2679 of the other set or output dimensions.
2680 For lexicographic optimization, see L<"Lexicographic Optimization">.
2684 The following functions compute either the set of (rational) coefficient
2685 values of valid constraints for the given set or the set of (rational)
2686 values satisfying the constraints with coefficients from the given set.
2687 Internally, these two sets of functions perform essentially the
2688 same operations, except that the set of coefficients is assumed to
2689 be a cone, while the set of values may be any polyhedron.
2690 The current implementation is based on the Farkas lemma and
2691 Fourier-Motzkin elimination, but this may change or be made optional
2692 in future. In particular, future implementations may use different
2693 dualization algorithms or skip the elimination step.
2695 __isl_give isl_basic_set *isl_basic_set_coefficients(
2696 __isl_take isl_basic_set *bset);
2697 __isl_give isl_basic_set *isl_set_coefficients(
2698 __isl_take isl_set *set);
2699 __isl_give isl_union_set *isl_union_set_coefficients(
2700 __isl_take isl_union_set *bset);
2701 __isl_give isl_basic_set *isl_basic_set_solutions(
2702 __isl_take isl_basic_set *bset);
2703 __isl_give isl_basic_set *isl_set_solutions(
2704 __isl_take isl_set *set);
2705 __isl_give isl_union_set *isl_union_set_solutions(
2706 __isl_take isl_union_set *bset);
2710 __isl_give isl_map *isl_map_fixed_power(
2711 __isl_take isl_map *map, isl_int exp);
2712 __isl_give isl_map *isl_map_fixed_power_val(
2713 __isl_take isl_map *map,
2714 __isl_take isl_val *exp);
2715 __isl_give isl_union_map *isl_union_map_fixed_power(
2716 __isl_take isl_union_map *umap, isl_int exp);
2717 __isl_give isl_union_map *
2718 isl_union_map_fixed_power_val(
2719 __isl_take isl_union_map *umap,
2720 __isl_take isl_val *exp);
2722 Compute the given power of C<map>, where C<exp> is assumed to be non-zero.
2723 If the exponent C<exp> is negative, then the -C<exp> th power of the inverse
2724 of C<map> is computed.
2726 __isl_give isl_map *isl_map_power(__isl_take isl_map *map,
2728 __isl_give isl_union_map *isl_union_map_power(
2729 __isl_take isl_union_map *umap, int *exact);
2731 Compute a parametric representation for all positive powers I<k> of C<map>.
2732 The result maps I<k> to a nested relation corresponding to the
2733 I<k>th power of C<map>.
2734 The result may be an overapproximation. If the result is known to be exact,
2735 then C<*exact> is set to C<1>.
2737 =item * Transitive closure
2739 __isl_give isl_map *isl_map_transitive_closure(
2740 __isl_take isl_map *map, int *exact);
2741 __isl_give isl_union_map *isl_union_map_transitive_closure(
2742 __isl_take isl_union_map *umap, int *exact);
2744 Compute the transitive closure of C<map>.
2745 The result may be an overapproximation. If the result is known to be exact,
2746 then C<*exact> is set to C<1>.
2748 =item * Reaching path lengths
2750 __isl_give isl_map *isl_map_reaching_path_lengths(
2751 __isl_take isl_map *map, int *exact);
2753 Compute a relation that maps each element in the range of C<map>
2754 to the lengths of all paths composed of edges in C<map> that
2755 end up in the given element.
2756 The result may be an overapproximation. If the result is known to be exact,
2757 then C<*exact> is set to C<1>.
2758 To compute the I<maximal> path length, the resulting relation
2759 should be postprocessed by C<isl_map_lexmax>.
2760 In particular, if the input relation is a dependence relation
2761 (mapping sources to sinks), then the maximal path length corresponds
2762 to the free schedule.
2763 Note, however, that C<isl_map_lexmax> expects the maximum to be
2764 finite, so if the path lengths are unbounded (possibly due to
2765 the overapproximation), then you will get an error message.
2769 __isl_give isl_basic_set *isl_basic_map_wrap(
2770 __isl_take isl_basic_map *bmap);
2771 __isl_give isl_set *isl_map_wrap(
2772 __isl_take isl_map *map);
2773 __isl_give isl_union_set *isl_union_map_wrap(
2774 __isl_take isl_union_map *umap);
2775 __isl_give isl_basic_map *isl_basic_set_unwrap(
2776 __isl_take isl_basic_set *bset);
2777 __isl_give isl_map *isl_set_unwrap(
2778 __isl_take isl_set *set);
2779 __isl_give isl_union_map *isl_union_set_unwrap(
2780 __isl_take isl_union_set *uset);
2784 Remove any internal structure of domain (and range) of the given
2785 set or relation. If there is any such internal structure in the input,
2786 then the name of the space is also removed.
2788 __isl_give isl_basic_set *isl_basic_set_flatten(
2789 __isl_take isl_basic_set *bset);
2790 __isl_give isl_set *isl_set_flatten(
2791 __isl_take isl_set *set);
2792 __isl_give isl_basic_map *isl_basic_map_flatten_domain(
2793 __isl_take isl_basic_map *bmap);
2794 __isl_give isl_basic_map *isl_basic_map_flatten_range(
2795 __isl_take isl_basic_map *bmap);
2796 __isl_give isl_map *isl_map_flatten_range(
2797 __isl_take isl_map *map);
2798 __isl_give isl_map *isl_map_flatten_domain(
2799 __isl_take isl_map *map);
2800 __isl_give isl_basic_map *isl_basic_map_flatten(
2801 __isl_take isl_basic_map *bmap);
2802 __isl_give isl_map *isl_map_flatten(
2803 __isl_take isl_map *map);
2805 __isl_give isl_map *isl_set_flatten_map(
2806 __isl_take isl_set *set);
2808 The function above constructs a relation
2809 that maps the input set to a flattened version of the set.
2813 Lift the input set to a space with extra dimensions corresponding
2814 to the existentially quantified variables in the input.
2815 In particular, the result lives in a wrapped map where the domain
2816 is the original space and the range corresponds to the original
2817 existentially quantified variables.
2819 __isl_give isl_basic_set *isl_basic_set_lift(
2820 __isl_take isl_basic_set *bset);
2821 __isl_give isl_set *isl_set_lift(
2822 __isl_take isl_set *set);
2823 __isl_give isl_union_set *isl_union_set_lift(
2824 __isl_take isl_union_set *uset);
2826 Given a local space that contains the existentially quantified
2827 variables of a set, a basic relation that, when applied to
2828 a basic set, has essentially the same effect as C<isl_basic_set_lift>,
2829 can be constructed using the following function.
2831 #include <isl/local_space.h>
2832 __isl_give isl_basic_map *isl_local_space_lifting(
2833 __isl_take isl_local_space *ls);
2835 =item * Internal Product
2837 __isl_give isl_basic_map *isl_basic_map_zip(
2838 __isl_take isl_basic_map *bmap);
2839 __isl_give isl_map *isl_map_zip(
2840 __isl_take isl_map *map);
2841 __isl_give isl_union_map *isl_union_map_zip(
2842 __isl_take isl_union_map *umap);
2844 Given a relation with nested relations for domain and range,
2845 interchange the range of the domain with the domain of the range.
2849 __isl_give isl_basic_map *isl_basic_map_curry(
2850 __isl_take isl_basic_map *bmap);
2851 __isl_give isl_basic_map *isl_basic_map_uncurry(
2852 __isl_take isl_basic_map *bmap);
2853 __isl_give isl_map *isl_map_curry(
2854 __isl_take isl_map *map);
2855 __isl_give isl_map *isl_map_uncurry(
2856 __isl_take isl_map *map);
2857 __isl_give isl_union_map *isl_union_map_curry(
2858 __isl_take isl_union_map *umap);
2859 __isl_give isl_union_map *isl_union_map_uncurry(
2860 __isl_take isl_union_map *umap);
2862 Given a relation with a nested relation for domain,
2863 the C<curry> functions
2864 move the range of the nested relation out of the domain
2865 and use it as the domain of a nested relation in the range,
2866 with the original range as range of this nested relation.
2867 The C<uncurry> functions perform the inverse operation.
2869 =item * Aligning parameters
2871 __isl_give isl_basic_set *isl_basic_set_align_params(
2872 __isl_take isl_basic_set *bset,
2873 __isl_take isl_space *model);
2874 __isl_give isl_set *isl_set_align_params(
2875 __isl_take isl_set *set,
2876 __isl_take isl_space *model);
2877 __isl_give isl_basic_map *isl_basic_map_align_params(
2878 __isl_take isl_basic_map *bmap,
2879 __isl_take isl_space *model);
2880 __isl_give isl_map *isl_map_align_params(
2881 __isl_take isl_map *map,
2882 __isl_take isl_space *model);
2884 Change the order of the parameters of the given set or relation
2885 such that the first parameters match those of C<model>.
2886 This may involve the introduction of extra parameters.
2887 All parameters need to be named.
2889 =item * Dimension manipulation
2891 __isl_give isl_basic_set *isl_basic_set_add_dims(
2892 __isl_take isl_basic_set *bset,
2893 enum isl_dim_type type, unsigned n);
2894 __isl_give isl_set *isl_set_add_dims(
2895 __isl_take isl_set *set,
2896 enum isl_dim_type type, unsigned n);
2897 __isl_give isl_map *isl_map_add_dims(
2898 __isl_take isl_map *map,
2899 enum isl_dim_type type, unsigned n);
2900 __isl_give isl_basic_set *isl_basic_set_insert_dims(
2901 __isl_take isl_basic_set *bset,
2902 enum isl_dim_type type, unsigned pos,
2904 __isl_give isl_basic_map *isl_basic_map_insert_dims(
2905 __isl_take isl_basic_map *bmap,
2906 enum isl_dim_type type, unsigned pos,
2908 __isl_give isl_set *isl_set_insert_dims(
2909 __isl_take isl_set *set,
2910 enum isl_dim_type type, unsigned pos, unsigned n);
2911 __isl_give isl_map *isl_map_insert_dims(
2912 __isl_take isl_map *map,
2913 enum isl_dim_type type, unsigned pos, unsigned n);
2914 __isl_give isl_basic_set *isl_basic_set_move_dims(
2915 __isl_take isl_basic_set *bset,
2916 enum isl_dim_type dst_type, unsigned dst_pos,
2917 enum isl_dim_type src_type, unsigned src_pos,
2919 __isl_give isl_basic_map *isl_basic_map_move_dims(
2920 __isl_take isl_basic_map *bmap,
2921 enum isl_dim_type dst_type, unsigned dst_pos,
2922 enum isl_dim_type src_type, unsigned src_pos,
2924 __isl_give isl_set *isl_set_move_dims(
2925 __isl_take isl_set *set,
2926 enum isl_dim_type dst_type, unsigned dst_pos,
2927 enum isl_dim_type src_type, unsigned src_pos,
2929 __isl_give isl_map *isl_map_move_dims(
2930 __isl_take isl_map *map,
2931 enum isl_dim_type dst_type, unsigned dst_pos,
2932 enum isl_dim_type src_type, unsigned src_pos,
2935 It is usually not advisable to directly change the (input or output)
2936 space of a set or a relation as this removes the name and the internal
2937 structure of the space. However, the above functions can be useful
2938 to add new parameters, assuming
2939 C<isl_set_align_params> and C<isl_map_align_params>
2944 =head2 Binary Operations
2946 The two arguments of a binary operation not only need to live
2947 in the same C<isl_ctx>, they currently also need to have
2948 the same (number of) parameters.
2950 =head3 Basic Operations
2954 =item * Intersection
2956 __isl_give isl_basic_set *isl_basic_set_intersect_params(
2957 __isl_take isl_basic_set *bset1,
2958 __isl_take isl_basic_set *bset2);
2959 __isl_give isl_basic_set *isl_basic_set_intersect(
2960 __isl_take isl_basic_set *bset1,
2961 __isl_take isl_basic_set *bset2);
2962 __isl_give isl_set *isl_set_intersect_params(
2963 __isl_take isl_set *set,
2964 __isl_take isl_set *params);
2965 __isl_give isl_set *isl_set_intersect(
2966 __isl_take isl_set *set1,
2967 __isl_take isl_set *set2);
2968 __isl_give isl_union_set *isl_union_set_intersect_params(
2969 __isl_take isl_union_set *uset,
2970 __isl_take isl_set *set);
2971 __isl_give isl_union_map *isl_union_map_intersect_params(
2972 __isl_take isl_union_map *umap,
2973 __isl_take isl_set *set);
2974 __isl_give isl_union_set *isl_union_set_intersect(
2975 __isl_take isl_union_set *uset1,
2976 __isl_take isl_union_set *uset2);
2977 __isl_give isl_basic_map *isl_basic_map_intersect_domain(
2978 __isl_take isl_basic_map *bmap,
2979 __isl_take isl_basic_set *bset);
2980 __isl_give isl_basic_map *isl_basic_map_intersect_range(
2981 __isl_take isl_basic_map *bmap,
2982 __isl_take isl_basic_set *bset);
2983 __isl_give isl_basic_map *isl_basic_map_intersect(
2984 __isl_take isl_basic_map *bmap1,
2985 __isl_take isl_basic_map *bmap2);
2986 __isl_give isl_map *isl_map_intersect_params(
2987 __isl_take isl_map *map,
2988 __isl_take isl_set *params);
2989 __isl_give isl_map *isl_map_intersect_domain(
2990 __isl_take isl_map *map,
2991 __isl_take isl_set *set);
2992 __isl_give isl_map *isl_map_intersect_range(
2993 __isl_take isl_map *map,
2994 __isl_take isl_set *set);
2995 __isl_give isl_map *isl_map_intersect(
2996 __isl_take isl_map *map1,
2997 __isl_take isl_map *map2);
2998 __isl_give isl_union_map *isl_union_map_intersect_domain(
2999 __isl_take isl_union_map *umap,
3000 __isl_take isl_union_set *uset);
3001 __isl_give isl_union_map *isl_union_map_intersect_range(
3002 __isl_take isl_union_map *umap,
3003 __isl_take isl_union_set *uset);
3004 __isl_give isl_union_map *isl_union_map_intersect(
3005 __isl_take isl_union_map *umap1,
3006 __isl_take isl_union_map *umap2);
3008 The second argument to the C<_params> functions needs to be
3009 a parametric (basic) set. For the other functions, a parametric set
3010 for either argument is only allowed if the other argument is
3011 a parametric set as well.
3015 __isl_give isl_set *isl_basic_set_union(
3016 __isl_take isl_basic_set *bset1,
3017 __isl_take isl_basic_set *bset2);
3018 __isl_give isl_map *isl_basic_map_union(
3019 __isl_take isl_basic_map *bmap1,
3020 __isl_take isl_basic_map *bmap2);
3021 __isl_give isl_set *isl_set_union(
3022 __isl_take isl_set *set1,
3023 __isl_take isl_set *set2);
3024 __isl_give isl_map *isl_map_union(
3025 __isl_take isl_map *map1,
3026 __isl_take isl_map *map2);
3027 __isl_give isl_union_set *isl_union_set_union(
3028 __isl_take isl_union_set *uset1,
3029 __isl_take isl_union_set *uset2);
3030 __isl_give isl_union_map *isl_union_map_union(
3031 __isl_take isl_union_map *umap1,
3032 __isl_take isl_union_map *umap2);
3034 =item * Set difference
3036 __isl_give isl_set *isl_set_subtract(
3037 __isl_take isl_set *set1,
3038 __isl_take isl_set *set2);
3039 __isl_give isl_map *isl_map_subtract(
3040 __isl_take isl_map *map1,
3041 __isl_take isl_map *map2);
3042 __isl_give isl_map *isl_map_subtract_domain(
3043 __isl_take isl_map *map,
3044 __isl_take isl_set *dom);
3045 __isl_give isl_map *isl_map_subtract_range(
3046 __isl_take isl_map *map,
3047 __isl_take isl_set *dom);
3048 __isl_give isl_union_set *isl_union_set_subtract(
3049 __isl_take isl_union_set *uset1,
3050 __isl_take isl_union_set *uset2);
3051 __isl_give isl_union_map *isl_union_map_subtract(
3052 __isl_take isl_union_map *umap1,
3053 __isl_take isl_union_map *umap2);
3054 __isl_give isl_union_map *isl_union_map_subtract_domain(
3055 __isl_take isl_union_map *umap,
3056 __isl_take isl_union_set *dom);
3057 __isl_give isl_union_map *isl_union_map_subtract_range(
3058 __isl_take isl_union_map *umap,
3059 __isl_take isl_union_set *dom);
3063 __isl_give isl_basic_set *isl_basic_set_apply(
3064 __isl_take isl_basic_set *bset,
3065 __isl_take isl_basic_map *bmap);
3066 __isl_give isl_set *isl_set_apply(
3067 __isl_take isl_set *set,
3068 __isl_take isl_map *map);
3069 __isl_give isl_union_set *isl_union_set_apply(
3070 __isl_take isl_union_set *uset,
3071 __isl_take isl_union_map *umap);
3072 __isl_give isl_basic_map *isl_basic_map_apply_domain(
3073 __isl_take isl_basic_map *bmap1,
3074 __isl_take isl_basic_map *bmap2);
3075 __isl_give isl_basic_map *isl_basic_map_apply_range(
3076 __isl_take isl_basic_map *bmap1,
3077 __isl_take isl_basic_map *bmap2);
3078 __isl_give isl_map *isl_map_apply_domain(
3079 __isl_take isl_map *map1,
3080 __isl_take isl_map *map2);
3081 __isl_give isl_union_map *isl_union_map_apply_domain(
3082 __isl_take isl_union_map *umap1,
3083 __isl_take isl_union_map *umap2);
3084 __isl_give isl_map *isl_map_apply_range(
3085 __isl_take isl_map *map1,
3086 __isl_take isl_map *map2);
3087 __isl_give isl_union_map *isl_union_map_apply_range(
3088 __isl_take isl_union_map *umap1,
3089 __isl_take isl_union_map *umap2);
3093 __isl_give isl_basic_set *
3094 isl_basic_set_preimage_multi_aff(
3095 __isl_take isl_basic_set *bset,
3096 __isl_take isl_multi_aff *ma);
3097 __isl_give isl_set *isl_set_preimage_multi_aff(
3098 __isl_take isl_set *set,
3099 __isl_take isl_multi_aff *ma);
3100 __isl_give isl_set *isl_set_preimage_pw_multi_aff(
3101 __isl_take isl_set *set,
3102 __isl_take isl_pw_multi_aff *pma);
3103 __isl_give isl_map *isl_map_preimage_domain_multi_aff(
3104 __isl_take isl_map *map,
3105 __isl_take isl_multi_aff *ma);
3106 __isl_give isl_union_map *
3107 isl_union_map_preimage_domain_multi_aff(
3108 __isl_take isl_union_map *umap,
3109 __isl_take isl_multi_aff *ma);
3111 These functions compute the preimage of the given set or map domain under
3112 the given function. In other words, the expression is plugged
3113 into the set description or into the domain of the map.
3114 Objects of types C<isl_multi_aff> and C<isl_pw_multi_aff> are described in
3115 L</"Piecewise Multiple Quasi Affine Expressions">.
3117 =item * Cartesian Product
3119 __isl_give isl_set *isl_set_product(
3120 __isl_take isl_set *set1,
3121 __isl_take isl_set *set2);
3122 __isl_give isl_union_set *isl_union_set_product(
3123 __isl_take isl_union_set *uset1,
3124 __isl_take isl_union_set *uset2);
3125 __isl_give isl_basic_map *isl_basic_map_domain_product(
3126 __isl_take isl_basic_map *bmap1,
3127 __isl_take isl_basic_map *bmap2);
3128 __isl_give isl_basic_map *isl_basic_map_range_product(
3129 __isl_take isl_basic_map *bmap1,
3130 __isl_take isl_basic_map *bmap2);
3131 __isl_give isl_basic_map *isl_basic_map_product(
3132 __isl_take isl_basic_map *bmap1,
3133 __isl_take isl_basic_map *bmap2);
3134 __isl_give isl_map *isl_map_domain_product(
3135 __isl_take isl_map *map1,
3136 __isl_take isl_map *map2);
3137 __isl_give isl_map *isl_map_range_product(
3138 __isl_take isl_map *map1,
3139 __isl_take isl_map *map2);
3140 __isl_give isl_union_map *isl_union_map_domain_product(
3141 __isl_take isl_union_map *umap1,
3142 __isl_take isl_union_map *umap2);
3143 __isl_give isl_union_map *isl_union_map_range_product(
3144 __isl_take isl_union_map *umap1,
3145 __isl_take isl_union_map *umap2);
3146 __isl_give isl_map *isl_map_product(
3147 __isl_take isl_map *map1,
3148 __isl_take isl_map *map2);
3149 __isl_give isl_union_map *isl_union_map_product(
3150 __isl_take isl_union_map *umap1,
3151 __isl_take isl_union_map *umap2);
3153 The above functions compute the cross product of the given
3154 sets or relations. The domains and ranges of the results
3155 are wrapped maps between domains and ranges of the inputs.
3156 To obtain a ``flat'' product, use the following functions
3159 __isl_give isl_basic_set *isl_basic_set_flat_product(
3160 __isl_take isl_basic_set *bset1,
3161 __isl_take isl_basic_set *bset2);
3162 __isl_give isl_set *isl_set_flat_product(
3163 __isl_take isl_set *set1,
3164 __isl_take isl_set *set2);
3165 __isl_give isl_basic_map *isl_basic_map_flat_range_product(
3166 __isl_take isl_basic_map *bmap1,
3167 __isl_take isl_basic_map *bmap2);
3168 __isl_give isl_map *isl_map_flat_domain_product(
3169 __isl_take isl_map *map1,
3170 __isl_take isl_map *map2);
3171 __isl_give isl_map *isl_map_flat_range_product(
3172 __isl_take isl_map *map1,
3173 __isl_take isl_map *map2);
3174 __isl_give isl_union_map *isl_union_map_flat_range_product(
3175 __isl_take isl_union_map *umap1,
3176 __isl_take isl_union_map *umap2);
3177 __isl_give isl_basic_map *isl_basic_map_flat_product(
3178 __isl_take isl_basic_map *bmap1,
3179 __isl_take isl_basic_map *bmap2);
3180 __isl_give isl_map *isl_map_flat_product(
3181 __isl_take isl_map *map1,
3182 __isl_take isl_map *map2);
3184 =item * Simplification
3186 __isl_give isl_basic_set *isl_basic_set_gist(
3187 __isl_take isl_basic_set *bset,
3188 __isl_take isl_basic_set *context);
3189 __isl_give isl_set *isl_set_gist(__isl_take isl_set *set,
3190 __isl_take isl_set *context);
3191 __isl_give isl_set *isl_set_gist_params(
3192 __isl_take isl_set *set,
3193 __isl_take isl_set *context);
3194 __isl_give isl_union_set *isl_union_set_gist(
3195 __isl_take isl_union_set *uset,
3196 __isl_take isl_union_set *context);
3197 __isl_give isl_union_set *isl_union_set_gist_params(
3198 __isl_take isl_union_set *uset,
3199 __isl_take isl_set *set);
3200 __isl_give isl_basic_map *isl_basic_map_gist(
3201 __isl_take isl_basic_map *bmap,
3202 __isl_take isl_basic_map *context);
3203 __isl_give isl_map *isl_map_gist(__isl_take isl_map *map,
3204 __isl_take isl_map *context);
3205 __isl_give isl_map *isl_map_gist_params(
3206 __isl_take isl_map *map,
3207 __isl_take isl_set *context);
3208 __isl_give isl_map *isl_map_gist_domain(
3209 __isl_take isl_map *map,
3210 __isl_take isl_set *context);
3211 __isl_give isl_map *isl_map_gist_range(
3212 __isl_take isl_map *map,
3213 __isl_take isl_set *context);
3214 __isl_give isl_union_map *isl_union_map_gist(
3215 __isl_take isl_union_map *umap,
3216 __isl_take isl_union_map *context);
3217 __isl_give isl_union_map *isl_union_map_gist_params(
3218 __isl_take isl_union_map *umap,
3219 __isl_take isl_set *set);
3220 __isl_give isl_union_map *isl_union_map_gist_domain(
3221 __isl_take isl_union_map *umap,
3222 __isl_take isl_union_set *uset);
3223 __isl_give isl_union_map *isl_union_map_gist_range(
3224 __isl_take isl_union_map *umap,
3225 __isl_take isl_union_set *uset);
3227 The gist operation returns a set or relation that has the
3228 same intersection with the context as the input set or relation.
3229 Any implicit equality in the intersection is made explicit in the result,
3230 while all inequalities that are redundant with respect to the intersection
3232 In case of union sets and relations, the gist operation is performed
3237 =head3 Lexicographic Optimization
3239 Given a (basic) set C<set> (or C<bset>) and a zero-dimensional domain C<dom>,
3240 the following functions
3241 compute a set that contains the lexicographic minimum or maximum
3242 of the elements in C<set> (or C<bset>) for those values of the parameters
3243 that satisfy C<dom>.
3244 If C<empty> is not C<NULL>, then C<*empty> is assigned a set
3245 that contains the parameter values in C<dom> for which C<set> (or C<bset>)
3247 In other words, the union of the parameter values
3248 for which the result is non-empty and of C<*empty>
3251 __isl_give isl_set *isl_basic_set_partial_lexmin(
3252 __isl_take isl_basic_set *bset,
3253 __isl_take isl_basic_set *dom,
3254 __isl_give isl_set **empty);
3255 __isl_give isl_set *isl_basic_set_partial_lexmax(
3256 __isl_take isl_basic_set *bset,
3257 __isl_take isl_basic_set *dom,
3258 __isl_give isl_set **empty);
3259 __isl_give isl_set *isl_set_partial_lexmin(
3260 __isl_take isl_set *set, __isl_take isl_set *dom,
3261 __isl_give isl_set **empty);
3262 __isl_give isl_set *isl_set_partial_lexmax(
3263 __isl_take isl_set *set, __isl_take isl_set *dom,
3264 __isl_give isl_set **empty);
3266 Given a (basic) set C<set> (or C<bset>), the following functions simply
3267 return a set containing the lexicographic minimum or maximum
3268 of the elements in C<set> (or C<bset>).
3269 In case of union sets, the optimum is computed per space.
3271 __isl_give isl_set *isl_basic_set_lexmin(
3272 __isl_take isl_basic_set *bset);
3273 __isl_give isl_set *isl_basic_set_lexmax(
3274 __isl_take isl_basic_set *bset);
3275 __isl_give isl_set *isl_set_lexmin(
3276 __isl_take isl_set *set);
3277 __isl_give isl_set *isl_set_lexmax(
3278 __isl_take isl_set *set);
3279 __isl_give isl_union_set *isl_union_set_lexmin(
3280 __isl_take isl_union_set *uset);
3281 __isl_give isl_union_set *isl_union_set_lexmax(
3282 __isl_take isl_union_set *uset);
3284 Given a (basic) relation C<map> (or C<bmap>) and a domain C<dom>,
3285 the following functions
3286 compute a relation that maps each element of C<dom>
3287 to the single lexicographic minimum or maximum
3288 of the elements that are associated to that same
3289 element in C<map> (or C<bmap>).
3290 If C<empty> is not C<NULL>, then C<*empty> is assigned a set
3291 that contains the elements in C<dom> that do not map
3292 to any elements in C<map> (or C<bmap>).
3293 In other words, the union of the domain of the result and of C<*empty>
3296 __isl_give isl_map *isl_basic_map_partial_lexmax(
3297 __isl_take isl_basic_map *bmap,
3298 __isl_take isl_basic_set *dom,
3299 __isl_give isl_set **empty);
3300 __isl_give isl_map *isl_basic_map_partial_lexmin(
3301 __isl_take isl_basic_map *bmap,
3302 __isl_take isl_basic_set *dom,
3303 __isl_give isl_set **empty);
3304 __isl_give isl_map *isl_map_partial_lexmax(
3305 __isl_take isl_map *map, __isl_take isl_set *dom,
3306 __isl_give isl_set **empty);
3307 __isl_give isl_map *isl_map_partial_lexmin(
3308 __isl_take isl_map *map, __isl_take isl_set *dom,
3309 __isl_give isl_set **empty);
3311 Given a (basic) map C<map> (or C<bmap>), the following functions simply
3312 return a map mapping each element in the domain of
3313 C<map> (or C<bmap>) to the lexicographic minimum or maximum
3314 of all elements associated to that element.
3315 In case of union relations, the optimum is computed per space.
3317 __isl_give isl_map *isl_basic_map_lexmin(
3318 __isl_take isl_basic_map *bmap);
3319 __isl_give isl_map *isl_basic_map_lexmax(
3320 __isl_take isl_basic_map *bmap);
3321 __isl_give isl_map *isl_map_lexmin(
3322 __isl_take isl_map *map);
3323 __isl_give isl_map *isl_map_lexmax(
3324 __isl_take isl_map *map);
3325 __isl_give isl_union_map *isl_union_map_lexmin(
3326 __isl_take isl_union_map *umap);
3327 __isl_give isl_union_map *isl_union_map_lexmax(
3328 __isl_take isl_union_map *umap);
3330 The following functions return their result in the form of
3331 a piecewise multi-affine expression
3332 (See L<"Piecewise Multiple Quasi Affine Expressions">),
3333 but are otherwise equivalent to the corresponding functions
3334 returning a basic set or relation.
3336 __isl_give isl_pw_multi_aff *
3337 isl_basic_map_lexmin_pw_multi_aff(
3338 __isl_take isl_basic_map *bmap);
3339 __isl_give isl_pw_multi_aff *
3340 isl_basic_set_partial_lexmin_pw_multi_aff(
3341 __isl_take isl_basic_set *bset,
3342 __isl_take isl_basic_set *dom,
3343 __isl_give isl_set **empty);
3344 __isl_give isl_pw_multi_aff *
3345 isl_basic_set_partial_lexmax_pw_multi_aff(
3346 __isl_take isl_basic_set *bset,
3347 __isl_take isl_basic_set *dom,
3348 __isl_give isl_set **empty);
3349 __isl_give isl_pw_multi_aff *
3350 isl_basic_map_partial_lexmin_pw_multi_aff(
3351 __isl_take isl_basic_map *bmap,
3352 __isl_take isl_basic_set *dom,
3353 __isl_give isl_set **empty);
3354 __isl_give isl_pw_multi_aff *
3355 isl_basic_map_partial_lexmax_pw_multi_aff(
3356 __isl_take isl_basic_map *bmap,
3357 __isl_take isl_basic_set *dom,
3358 __isl_give isl_set **empty);
3359 __isl_give isl_pw_multi_aff *isl_set_lexmin_pw_multi_aff(
3360 __isl_take isl_set *set);
3361 __isl_give isl_pw_multi_aff *isl_set_lexmax_pw_multi_aff(
3362 __isl_take isl_set *set);
3363 __isl_give isl_pw_multi_aff *isl_map_lexmin_pw_multi_aff(
3364 __isl_take isl_map *map);
3365 __isl_give isl_pw_multi_aff *isl_map_lexmax_pw_multi_aff(
3366 __isl_take isl_map *map);
3370 Lists are defined over several element types, including
3371 C<isl_val>, C<isl_id>, C<isl_aff>, C<isl_pw_aff>, C<isl_constraint>,
3372 C<isl_basic_set>, C<isl_set>, C<isl_ast_expr> and C<isl_ast_node>.
3373 Here we take lists of C<isl_set>s as an example.
3374 Lists can be created, copied, modified and freed using the following functions.
3376 #include <isl/list.h>
3377 __isl_give isl_set_list *isl_set_list_from_set(
3378 __isl_take isl_set *el);
3379 __isl_give isl_set_list *isl_set_list_alloc(
3380 isl_ctx *ctx, int n);
3381 __isl_give isl_set_list *isl_set_list_copy(
3382 __isl_keep isl_set_list *list);
3383 __isl_give isl_set_list *isl_set_list_insert(
3384 __isl_take isl_set_list *list, unsigned pos,
3385 __isl_take isl_set *el);
3386 __isl_give isl_set_list *isl_set_list_add(
3387 __isl_take isl_set_list *list,
3388 __isl_take isl_set *el);
3389 __isl_give isl_set_list *isl_set_list_drop(
3390 __isl_take isl_set_list *list,
3391 unsigned first, unsigned n);
3392 __isl_give isl_set_list *isl_set_list_set_set(
3393 __isl_take isl_set_list *list, int index,
3394 __isl_take isl_set *set);
3395 __isl_give isl_set_list *isl_set_list_concat(
3396 __isl_take isl_set_list *list1,
3397 __isl_take isl_set_list *list2);
3398 __isl_give isl_set_list *isl_set_list_sort(
3399 __isl_take isl_set_list *list,
3400 int (*cmp)(__isl_keep isl_set *a,
3401 __isl_keep isl_set *b, void *user),
3403 void *isl_set_list_free(__isl_take isl_set_list *list);
3405 C<isl_set_list_alloc> creates an empty list with a capacity for
3406 C<n> elements. C<isl_set_list_from_set> creates a list with a single
3409 Lists can be inspected using the following functions.
3411 #include <isl/list.h>
3412 isl_ctx *isl_set_list_get_ctx(__isl_keep isl_set_list *list);
3413 int isl_set_list_n_set(__isl_keep isl_set_list *list);
3414 __isl_give isl_set *isl_set_list_get_set(
3415 __isl_keep isl_set_list *list, int index);
3416 int isl_set_list_foreach(__isl_keep isl_set_list *list,
3417 int (*fn)(__isl_take isl_set *el, void *user),
3419 int isl_set_list_foreach_scc(__isl_keep isl_set_list *list,
3420 int (*follows)(__isl_keep isl_set *a,
3421 __isl_keep isl_set *b, void *user),
3423 int (*fn)(__isl_take isl_set *el, void *user),
3426 The function C<isl_set_list_foreach_scc> calls C<fn> on each of the
3427 strongly connected components of the graph with as vertices the elements
3428 of C<list> and a directed edge from vertex C<b> to vertex C<a>
3429 iff C<follows(a, b)> returns C<1>. The callbacks C<follows> and C<fn>
3430 should return C<-1> on error.
3432 Lists can be printed using
3434 #include <isl/list.h>
3435 __isl_give isl_printer *isl_printer_print_set_list(
3436 __isl_take isl_printer *p,
3437 __isl_keep isl_set_list *list);
3439 =head2 Multiple Values
3441 An C<isl_multi_val> object represents a sequence of zero or more values,
3442 living in a set space.
3444 An C<isl_multi_val> can be constructed from an C<isl_val_list>
3445 using the following function
3447 #include <isl/val.h>
3448 __isl_give isl_multi_val *isl_multi_val_from_val_list(
3449 __isl_take isl_space *space,
3450 __isl_take isl_val_list *list);
3452 The zero multiple value (with value zero for each set dimension)
3453 can be created using the following function.
3455 #include <isl/val.h>
3456 __isl_give isl_multi_val *isl_multi_val_zero(
3457 __isl_take isl_space *space);
3459 Multiple values can be copied and freed using
3461 #include <isl/val.h>
3462 __isl_give isl_multi_val *isl_multi_val_copy(
3463 __isl_keep isl_multi_val *mv);
3464 void *isl_multi_val_free(__isl_take isl_multi_val *mv);
3466 They can be inspected using
3468 #include <isl/val.h>
3469 isl_ctx *isl_multi_val_get_ctx(
3470 __isl_keep isl_multi_val *mv);
3471 unsigned isl_multi_val_dim(__isl_keep isl_multi_val *mv,
3472 enum isl_dim_type type);
3473 __isl_give isl_val *isl_multi_val_get_val(
3474 __isl_keep isl_multi_val *mv, int pos);
3475 const char *isl_multi_val_get_tuple_name(
3476 __isl_keep isl_multi_val *mv,
3477 enum isl_dim_type type);
3479 They can be modified using
3481 #include <isl/val.h>
3482 __isl_give isl_multi_val *isl_multi_val_set_val(
3483 __isl_take isl_multi_val *mv, int pos,
3484 __isl_take isl_val *val);
3485 __isl_give isl_multi_val *isl_multi_val_set_dim_name(
3486 __isl_take isl_multi_val *mv,
3487 enum isl_dim_type type, unsigned pos, const char *s);
3488 __isl_give isl_multi_val *isl_multi_val_set_tuple_name(
3489 __isl_take isl_multi_val *mv,
3490 enum isl_dim_type type, const char *s);
3491 __isl_give isl_multi_val *isl_multi_val_set_tuple_id(
3492 __isl_take isl_multi_val *mv,
3493 enum isl_dim_type type, __isl_take isl_id *id);
3495 __isl_give isl_multi_val *isl_multi_val_insert_dims(
3496 __isl_take isl_multi_val *mv,
3497 enum isl_dim_type type, unsigned first, unsigned n);
3498 __isl_give isl_multi_val *isl_multi_val_add_dims(
3499 __isl_take isl_multi_val *mv,
3500 enum isl_dim_type type, unsigned n);
3501 __isl_give isl_multi_val *isl_multi_val_drop_dims(
3502 __isl_take isl_multi_val *mv,
3503 enum isl_dim_type type, unsigned first, unsigned n);
3507 #include <isl/val.h>
3508 __isl_give isl_multi_val *isl_multi_val_align_params(
3509 __isl_take isl_multi_val *mv,
3510 __isl_take isl_space *model);
3511 __isl_give isl_multi_val *isl_multi_val_range_splice(
3512 __isl_take isl_multi_val *mv1, unsigned pos,
3513 __isl_take isl_multi_val *mv2);
3514 __isl_give isl_multi_val *isl_multi_val_range_product(
3515 __isl_take isl_multi_val *mv1,
3516 __isl_take isl_multi_val *mv2);
3517 __isl_give isl_multi_val *isl_multi_val_flat_range_product(
3518 __isl_take isl_multi_val *mv1,
3519 __isl_take isl_multi_aff *mv2);
3520 __isl_give isl_multi_val *isl_multi_val_add_val(
3521 __isl_take isl_multi_val *mv,
3522 __isl_take isl_val *v);
3523 __isl_give isl_multi_val *isl_multi_val_mod_val(
3524 __isl_take isl_multi_val *mv,
3525 __isl_take isl_val *v);
3526 __isl_give isl_multi_val *isl_multi_val_scale_val(
3527 __isl_take isl_multi_val *mv,
3528 __isl_take isl_val *v);
3532 Vectors can be created, copied and freed using the following functions.
3534 #include <isl/vec.h>
3535 __isl_give isl_vec *isl_vec_alloc(isl_ctx *ctx,
3537 __isl_give isl_vec *isl_vec_copy(__isl_keep isl_vec *vec);
3538 void *isl_vec_free(__isl_take isl_vec *vec);
3540 Note that the elements of a newly created vector may have arbitrary values.
3541 The elements can be changed and inspected using the following functions.
3543 isl_ctx *isl_vec_get_ctx(__isl_keep isl_vec *vec);
3544 int isl_vec_size(__isl_keep isl_vec *vec);
3545 int isl_vec_get_element(__isl_keep isl_vec *vec,
3546 int pos, isl_int *v);
3547 __isl_give isl_val *isl_vec_get_element_val(
3548 __isl_keep isl_vec *vec, int pos);
3549 __isl_give isl_vec *isl_vec_set_element(
3550 __isl_take isl_vec *vec, int pos, isl_int v);
3551 __isl_give isl_vec *isl_vec_set_element_si(
3552 __isl_take isl_vec *vec, int pos, int v);
3553 __isl_give isl_vec *isl_vec_set_element_val(
3554 __isl_take isl_vec *vec, int pos,
3555 __isl_take isl_val *v);
3556 __isl_give isl_vec *isl_vec_set(__isl_take isl_vec *vec,
3558 __isl_give isl_vec *isl_vec_set_si(__isl_take isl_vec *vec,
3560 __isl_give isl_vec *isl_vec_set_val(
3561 __isl_take isl_vec *vec, __isl_take isl_val *v);
3562 int isl_vec_cmp_element(__isl_keep isl_vec *vec1,
3563 __isl_keep isl_vec *vec2, int pos);
3564 __isl_give isl_vec *isl_vec_fdiv_r(__isl_take isl_vec *vec,
3567 C<isl_vec_get_element> will return a negative value if anything went wrong.
3568 In that case, the value of C<*v> is undefined.
3570 The following function can be used to concatenate two vectors.
3572 __isl_give isl_vec *isl_vec_concat(__isl_take isl_vec *vec1,
3573 __isl_take isl_vec *vec2);
3577 Matrices can be created, copied and freed using the following functions.
3579 #include <isl/mat.h>
3580 __isl_give isl_mat *isl_mat_alloc(isl_ctx *ctx,
3581 unsigned n_row, unsigned n_col);
3582 __isl_give isl_mat *isl_mat_copy(__isl_keep isl_mat *mat);
3583 void *isl_mat_free(__isl_take isl_mat *mat);
3585 Note that the elements of a newly created matrix may have arbitrary values.
3586 The elements can be changed and inspected using the following functions.
3588 isl_ctx *isl_mat_get_ctx(__isl_keep isl_mat *mat);
3589 int isl_mat_rows(__isl_keep isl_mat *mat);
3590 int isl_mat_cols(__isl_keep isl_mat *mat);
3591 int isl_mat_get_element(__isl_keep isl_mat *mat,
3592 int row, int col, isl_int *v);
3593 __isl_give isl_val *isl_mat_get_element_val(
3594 __isl_keep isl_mat *mat, int row, int col);
3595 __isl_give isl_mat *isl_mat_set_element(__isl_take isl_mat *mat,
3596 int row, int col, isl_int v);
3597 __isl_give isl_mat *isl_mat_set_element_si(__isl_take isl_mat *mat,
3598 int row, int col, int v);
3599 __isl_give isl_mat *isl_mat_set_element_val(
3600 __isl_take isl_mat *mat, int row, int col,
3601 __isl_take isl_val *v);
3603 C<isl_mat_get_element> will return a negative value if anything went wrong.
3604 In that case, the value of C<*v> is undefined.
3606 The following function can be used to compute the (right) inverse
3607 of a matrix, i.e., a matrix such that the product of the original
3608 and the inverse (in that order) is a multiple of the identity matrix.
3609 The input matrix is assumed to be of full row-rank.
3611 __isl_give isl_mat *isl_mat_right_inverse(__isl_take isl_mat *mat);
3613 The following function can be used to compute the (right) kernel
3614 (or null space) of a matrix, i.e., a matrix such that the product of
3615 the original and the kernel (in that order) is the zero matrix.
3617 __isl_give isl_mat *isl_mat_right_kernel(__isl_take isl_mat *mat);
3619 =head2 Piecewise Quasi Affine Expressions
3621 The zero quasi affine expression or the quasi affine expression
3622 that is equal to a specified dimension on a given domain can be created using
3624 __isl_give isl_aff *isl_aff_zero_on_domain(
3625 __isl_take isl_local_space *ls);
3626 __isl_give isl_pw_aff *isl_pw_aff_zero_on_domain(
3627 __isl_take isl_local_space *ls);
3628 __isl_give isl_aff *isl_aff_var_on_domain(
3629 __isl_take isl_local_space *ls,
3630 enum isl_dim_type type, unsigned pos);
3631 __isl_give isl_pw_aff *isl_pw_aff_var_on_domain(
3632 __isl_take isl_local_space *ls,
3633 enum isl_dim_type type, unsigned pos);
3635 Note that the space in which the resulting objects live is a map space
3636 with the given space as domain and a one-dimensional range.
3638 An empty piecewise quasi affine expression (one with no cells)
3639 or a piecewise quasi affine expression with a single cell can
3640 be created using the following functions.
3642 #include <isl/aff.h>
3643 __isl_give isl_pw_aff *isl_pw_aff_empty(
3644 __isl_take isl_space *space);
3645 __isl_give isl_pw_aff *isl_pw_aff_alloc(
3646 __isl_take isl_set *set, __isl_take isl_aff *aff);
3647 __isl_give isl_pw_aff *isl_pw_aff_from_aff(
3648 __isl_take isl_aff *aff);
3650 A piecewise quasi affine expression that is equal to 1 on a set
3651 and 0 outside the set can be created using the following function.
3653 #include <isl/aff.h>
3654 __isl_give isl_pw_aff *isl_set_indicator_function(
3655 __isl_take isl_set *set);
3657 Quasi affine expressions can be copied and freed using
3659 #include <isl/aff.h>
3660 __isl_give isl_aff *isl_aff_copy(__isl_keep isl_aff *aff);
3661 void *isl_aff_free(__isl_take isl_aff *aff);
3663 __isl_give isl_pw_aff *isl_pw_aff_copy(
3664 __isl_keep isl_pw_aff *pwaff);
3665 void *isl_pw_aff_free(__isl_take isl_pw_aff *pwaff);
3667 A (rational) bound on a dimension can be extracted from an C<isl_constraint>
3668 using the following function. The constraint is required to have
3669 a non-zero coefficient for the specified dimension.
3671 #include <isl/constraint.h>
3672 __isl_give isl_aff *isl_constraint_get_bound(
3673 __isl_keep isl_constraint *constraint,
3674 enum isl_dim_type type, int pos);
3676 The entire affine expression of the constraint can also be extracted
3677 using the following function.
3679 #include <isl/constraint.h>
3680 __isl_give isl_aff *isl_constraint_get_aff(
3681 __isl_keep isl_constraint *constraint);
3683 Conversely, an equality constraint equating
3684 the affine expression to zero or an inequality constraint enforcing
3685 the affine expression to be non-negative, can be constructed using
3687 __isl_give isl_constraint *isl_equality_from_aff(
3688 __isl_take isl_aff *aff);
3689 __isl_give isl_constraint *isl_inequality_from_aff(
3690 __isl_take isl_aff *aff);
3692 The expression can be inspected using
3694 #include <isl/aff.h>
3695 isl_ctx *isl_aff_get_ctx(__isl_keep isl_aff *aff);
3696 int isl_aff_dim(__isl_keep isl_aff *aff,
3697 enum isl_dim_type type);
3698 __isl_give isl_local_space *isl_aff_get_domain_local_space(
3699 __isl_keep isl_aff *aff);
3700 __isl_give isl_local_space *isl_aff_get_local_space(
3701 __isl_keep isl_aff *aff);
3702 const char *isl_aff_get_dim_name(__isl_keep isl_aff *aff,
3703 enum isl_dim_type type, unsigned pos);
3704 const char *isl_pw_aff_get_dim_name(
3705 __isl_keep isl_pw_aff *pa,
3706 enum isl_dim_type type, unsigned pos);
3707 int isl_pw_aff_has_dim_id(__isl_keep isl_pw_aff *pa,
3708 enum isl_dim_type type, unsigned pos);
3709 __isl_give isl_id *isl_pw_aff_get_dim_id(
3710 __isl_keep isl_pw_aff *pa,
3711 enum isl_dim_type type, unsigned pos);
3712 __isl_give isl_id *isl_pw_aff_get_tuple_id(
3713 __isl_keep isl_pw_aff *pa,
3714 enum isl_dim_type type);
3715 int isl_aff_get_constant(__isl_keep isl_aff *aff,
3717 __isl_give isl_val *isl_aff_get_constant_val(
3718 __isl_keep isl_aff *aff);
3719 int isl_aff_get_coefficient(__isl_keep isl_aff *aff,
3720 enum isl_dim_type type, int pos, isl_int *v);
3721 __isl_give isl_val *isl_aff_get_coefficient_val(
3722 __isl_keep isl_aff *aff,
3723 enum isl_dim_type type, int pos);
3724 int isl_aff_get_denominator(__isl_keep isl_aff *aff,
3726 __isl_give isl_val *isl_aff_get_denominator_val(
3727 __isl_keep isl_aff *aff);
3728 __isl_give isl_aff *isl_aff_get_div(
3729 __isl_keep isl_aff *aff, int pos);
3731 int isl_pw_aff_n_piece(__isl_keep isl_pw_aff *pwaff);
3732 int isl_pw_aff_foreach_piece(__isl_keep isl_pw_aff *pwaff,
3733 int (*fn)(__isl_take isl_set *set,
3734 __isl_take isl_aff *aff,
3735 void *user), void *user);
3737 int isl_aff_is_cst(__isl_keep isl_aff *aff);
3738 int isl_pw_aff_is_cst(__isl_keep isl_pw_aff *pwaff);
3740 int isl_aff_involves_dims(__isl_keep isl_aff *aff,
3741 enum isl_dim_type type, unsigned first, unsigned n);
3742 int isl_pw_aff_involves_dims(__isl_keep isl_pw_aff *pwaff,
3743 enum isl_dim_type type, unsigned first, unsigned n);
3745 isl_ctx *isl_pw_aff_get_ctx(__isl_keep isl_pw_aff *pwaff);
3746 unsigned isl_pw_aff_dim(__isl_keep isl_pw_aff *pwaff,
3747 enum isl_dim_type type);
3748 int isl_pw_aff_is_empty(__isl_keep isl_pw_aff *pwaff);
3750 It can be modified using
3752 #include <isl/aff.h>
3753 __isl_give isl_pw_aff *isl_pw_aff_set_tuple_id(
3754 __isl_take isl_pw_aff *pwaff,
3755 enum isl_dim_type type, __isl_take isl_id *id);
3756 __isl_give isl_aff *isl_aff_set_dim_name(
3757 __isl_take isl_aff *aff, enum isl_dim_type type,
3758 unsigned pos, const char *s);
3759 __isl_give isl_aff *isl_aff_set_dim_id(
3760 __isl_take isl_aff *aff, enum isl_dim_type type,
3761 unsigned pos, __isl_take isl_id *id);
3762 __isl_give isl_pw_aff *isl_pw_aff_set_dim_id(
3763 __isl_take isl_pw_aff *pma,
3764 enum isl_dim_type type, unsigned pos,
3765 __isl_take isl_id *id);
3766 __isl_give isl_aff *isl_aff_set_constant(
3767 __isl_take isl_aff *aff, isl_int v);
3768 __isl_give isl_aff *isl_aff_set_constant_si(
3769 __isl_take isl_aff *aff, int v);
3770 __isl_give isl_aff *isl_aff_set_constant_val(
3771 __isl_take isl_aff *aff, __isl_take isl_val *v);
3772 __isl_give isl_aff *isl_aff_set_coefficient(
3773 __isl_take isl_aff *aff,
3774 enum isl_dim_type type, int pos, isl_int v);
3775 __isl_give isl_aff *isl_aff_set_coefficient_si(
3776 __isl_take isl_aff *aff,
3777 enum isl_dim_type type, int pos, int v);
3778 __isl_give isl_aff *isl_aff_set_coefficient_val(
3779 __isl_take isl_aff *aff,
3780 enum isl_dim_type type, int pos,
3781 __isl_take isl_val *v);
3782 __isl_give isl_aff *isl_aff_set_denominator(
3783 __isl_take isl_aff *aff, isl_int v);
3785 __isl_give isl_aff *isl_aff_add_constant(
3786 __isl_take isl_aff *aff, isl_int v);
3787 __isl_give isl_aff *isl_aff_add_constant_si(
3788 __isl_take isl_aff *aff, int v);
3789 __isl_give isl_aff *isl_aff_add_constant_val(
3790 __isl_take isl_aff *aff, __isl_take isl_val *v);
3791 __isl_give isl_aff *isl_aff_add_constant_num(
3792 __isl_take isl_aff *aff, isl_int v);
3793 __isl_give isl_aff *isl_aff_add_constant_num_si(
3794 __isl_take isl_aff *aff, int v);
3795 __isl_give isl_aff *isl_aff_add_coefficient(
3796 __isl_take isl_aff *aff,
3797 enum isl_dim_type type, int pos, isl_int v);
3798 __isl_give isl_aff *isl_aff_add_coefficient_si(
3799 __isl_take isl_aff *aff,
3800 enum isl_dim_type type, int pos, int v);
3801 __isl_give isl_aff *isl_aff_add_coefficient_val(
3802 __isl_take isl_aff *aff,
3803 enum isl_dim_type type, int pos,
3804 __isl_take isl_val *v);
3806 __isl_give isl_aff *isl_aff_insert_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_insert_dims(
3810 __isl_take isl_pw_aff *pwaff,
3811 enum isl_dim_type type, unsigned first, unsigned n);
3812 __isl_give isl_aff *isl_aff_add_dims(
3813 __isl_take isl_aff *aff,
3814 enum isl_dim_type type, unsigned n);
3815 __isl_give isl_pw_aff *isl_pw_aff_add_dims(
3816 __isl_take isl_pw_aff *pwaff,
3817 enum isl_dim_type type, unsigned n);
3818 __isl_give isl_aff *isl_aff_drop_dims(
3819 __isl_take isl_aff *aff,
3820 enum isl_dim_type type, unsigned first, unsigned n);
3821 __isl_give isl_pw_aff *isl_pw_aff_drop_dims(
3822 __isl_take isl_pw_aff *pwaff,
3823 enum isl_dim_type type, unsigned first, unsigned n);
3825 Note that C<isl_aff_set_constant>, C<isl_aff_set_constant_si>,
3826 C<isl_aff_set_coefficient> and C<isl_aff_set_coefficient_si>
3827 set the I<numerator> of the constant or coefficient, while
3828 C<isl_aff_set_constant_val> and C<isl_aff_set_coefficient_val> set
3829 the constant or coefficient as a whole.
3830 The C<add_constant> and C<add_coefficient> functions add an integer
3831 or rational value to
3832 the possibly rational constant or coefficient.
3833 The C<add_constant_num> functions add an integer value to
3836 To check whether an affine expressions is obviously zero
3837 or obviously equal to some other affine expression, use
3839 #include <isl/aff.h>
3840 int isl_aff_plain_is_zero(__isl_keep isl_aff *aff);
3841 int isl_aff_plain_is_equal(__isl_keep isl_aff *aff1,
3842 __isl_keep isl_aff *aff2);
3843 int isl_pw_aff_plain_is_equal(
3844 __isl_keep isl_pw_aff *pwaff1,
3845 __isl_keep isl_pw_aff *pwaff2);
3849 #include <isl/aff.h>
3850 __isl_give isl_aff *isl_aff_add(__isl_take isl_aff *aff1,
3851 __isl_take isl_aff *aff2);
3852 __isl_give isl_pw_aff *isl_pw_aff_add(
3853 __isl_take isl_pw_aff *pwaff1,
3854 __isl_take isl_pw_aff *pwaff2);
3855 __isl_give isl_pw_aff *isl_pw_aff_min(
3856 __isl_take isl_pw_aff *pwaff1,
3857 __isl_take isl_pw_aff *pwaff2);
3858 __isl_give isl_pw_aff *isl_pw_aff_max(
3859 __isl_take isl_pw_aff *pwaff1,
3860 __isl_take isl_pw_aff *pwaff2);
3861 __isl_give isl_aff *isl_aff_sub(__isl_take isl_aff *aff1,
3862 __isl_take isl_aff *aff2);
3863 __isl_give isl_pw_aff *isl_pw_aff_sub(
3864 __isl_take isl_pw_aff *pwaff1,
3865 __isl_take isl_pw_aff *pwaff2);
3866 __isl_give isl_aff *isl_aff_neg(__isl_take isl_aff *aff);
3867 __isl_give isl_pw_aff *isl_pw_aff_neg(
3868 __isl_take isl_pw_aff *pwaff);
3869 __isl_give isl_aff *isl_aff_ceil(__isl_take isl_aff *aff);
3870 __isl_give isl_pw_aff *isl_pw_aff_ceil(
3871 __isl_take isl_pw_aff *pwaff);
3872 __isl_give isl_aff *isl_aff_floor(__isl_take isl_aff *aff);
3873 __isl_give isl_pw_aff *isl_pw_aff_floor(
3874 __isl_take isl_pw_aff *pwaff);
3875 __isl_give isl_aff *isl_aff_mod(__isl_take isl_aff *aff,
3877 __isl_give isl_aff *isl_aff_mod_val(__isl_take isl_aff *aff,
3878 __isl_take isl_val *mod);
3879 __isl_give isl_pw_aff *isl_pw_aff_mod(
3880 __isl_take isl_pw_aff *pwaff, isl_int mod);
3881 __isl_give isl_pw_aff *isl_pw_aff_mod_val(
3882 __isl_take isl_pw_aff *pa,
3883 __isl_take isl_val *mod);
3884 __isl_give isl_aff *isl_aff_scale(__isl_take isl_aff *aff,
3886 __isl_give isl_aff *isl_aff_scale_val(__isl_take isl_aff *aff,
3887 __isl_take isl_val *v);
3888 __isl_give isl_pw_aff *isl_pw_aff_scale(
3889 __isl_take isl_pw_aff *pwaff, isl_int f);
3890 __isl_give isl_pw_aff *isl_pw_aff_scale_val(
3891 __isl_take isl_pw_aff *pa, __isl_take isl_val *v);
3892 __isl_give isl_aff *isl_aff_scale_down(__isl_take isl_aff *aff,
3894 __isl_give isl_aff *isl_aff_scale_down_ui(
3895 __isl_take isl_aff *aff, unsigned f);
3896 __isl_give isl_aff *isl_aff_scale_down_val(
3897 __isl_take isl_aff *aff, __isl_take isl_val *v);
3898 __isl_give isl_pw_aff *isl_pw_aff_scale_down(
3899 __isl_take isl_pw_aff *pwaff, isl_int f);
3900 __isl_give isl_pw_aff *isl_pw_aff_scale_down_val(
3901 __isl_take isl_pw_aff *pa,
3902 __isl_take isl_val *f);
3904 __isl_give isl_pw_aff *isl_pw_aff_list_min(
3905 __isl_take isl_pw_aff_list *list);
3906 __isl_give isl_pw_aff *isl_pw_aff_list_max(
3907 __isl_take isl_pw_aff_list *list);
3909 __isl_give isl_pw_aff *isl_pw_aff_coalesce(
3910 __isl_take isl_pw_aff *pwqp);
3912 __isl_give isl_aff *isl_aff_align_params(
3913 __isl_take isl_aff *aff,
3914 __isl_take isl_space *model);
3915 __isl_give isl_pw_aff *isl_pw_aff_align_params(
3916 __isl_take isl_pw_aff *pwaff,
3917 __isl_take isl_space *model);
3919 __isl_give isl_aff *isl_aff_project_domain_on_params(
3920 __isl_take isl_aff *aff);
3922 __isl_give isl_aff *isl_aff_gist_params(
3923 __isl_take isl_aff *aff,
3924 __isl_take isl_set *context);
3925 __isl_give isl_aff *isl_aff_gist(__isl_take isl_aff *aff,
3926 __isl_take isl_set *context);
3927 __isl_give isl_pw_aff *isl_pw_aff_gist_params(
3928 __isl_take isl_pw_aff *pwaff,
3929 __isl_take isl_set *context);
3930 __isl_give isl_pw_aff *isl_pw_aff_gist(
3931 __isl_take isl_pw_aff *pwaff,
3932 __isl_take isl_set *context);
3934 __isl_give isl_set *isl_pw_aff_domain(
3935 __isl_take isl_pw_aff *pwaff);
3936 __isl_give isl_pw_aff *isl_pw_aff_intersect_domain(
3937 __isl_take isl_pw_aff *pa,
3938 __isl_take isl_set *set);
3939 __isl_give isl_pw_aff *isl_pw_aff_intersect_params(
3940 __isl_take isl_pw_aff *pa,
3941 __isl_take isl_set *set);
3943 __isl_give isl_aff *isl_aff_mul(__isl_take isl_aff *aff1,
3944 __isl_take isl_aff *aff2);
3945 __isl_give isl_aff *isl_aff_div(__isl_take isl_aff *aff1,
3946 __isl_take isl_aff *aff2);
3947 __isl_give isl_pw_aff *isl_pw_aff_mul(
3948 __isl_take isl_pw_aff *pwaff1,
3949 __isl_take isl_pw_aff *pwaff2);
3950 __isl_give isl_pw_aff *isl_pw_aff_div(
3951 __isl_take isl_pw_aff *pa1,
3952 __isl_take isl_pw_aff *pa2);
3953 __isl_give isl_pw_aff *isl_pw_aff_tdiv_q(
3954 __isl_take isl_pw_aff *pa1,
3955 __isl_take isl_pw_aff *pa2);
3956 __isl_give isl_pw_aff *isl_pw_aff_tdiv_r(
3957 __isl_take isl_pw_aff *pa1,
3958 __isl_take isl_pw_aff *pa2);
3960 When multiplying two affine expressions, at least one of the two needs
3961 to be a constant. Similarly, when dividing an affine expression by another,
3962 the second expression needs to be a constant.
3963 C<isl_pw_aff_tdiv_q> computes the quotient of an integer division with
3964 rounding towards zero. C<isl_pw_aff_tdiv_r> computes the corresponding
3967 #include <isl/aff.h>
3968 __isl_give isl_aff *isl_aff_pullback_multi_aff(
3969 __isl_take isl_aff *aff,
3970 __isl_take isl_multi_aff *ma);
3971 __isl_give isl_pw_aff *isl_pw_aff_pullback_multi_aff(
3972 __isl_take isl_pw_aff *pa,
3973 __isl_take isl_multi_aff *ma);
3974 __isl_give isl_pw_aff *isl_pw_aff_pullback_pw_multi_aff(
3975 __isl_take isl_pw_aff *pa,
3976 __isl_take isl_pw_multi_aff *pma);
3978 These functions precompose the input expression by the given
3979 C<isl_multi_aff> or C<isl_pw_multi_aff>. In other words,
3980 the C<isl_multi_aff> or C<isl_pw_multi_aff> is plugged
3981 into the (piecewise) affine expression.
3982 Objects of type C<isl_multi_aff> are described in
3983 L</"Piecewise Multiple Quasi Affine Expressions">.
3985 #include <isl/aff.h>
3986 __isl_give isl_basic_set *isl_aff_zero_basic_set(
3987 __isl_take isl_aff *aff);
3988 __isl_give isl_basic_set *isl_aff_neg_basic_set(
3989 __isl_take isl_aff *aff);
3990 __isl_give isl_basic_set *isl_aff_le_basic_set(
3991 __isl_take isl_aff *aff1, __isl_take isl_aff *aff2);
3992 __isl_give isl_basic_set *isl_aff_ge_basic_set(
3993 __isl_take isl_aff *aff1, __isl_take isl_aff *aff2);
3994 __isl_give isl_set *isl_pw_aff_eq_set(
3995 __isl_take isl_pw_aff *pwaff1,
3996 __isl_take isl_pw_aff *pwaff2);
3997 __isl_give isl_set *isl_pw_aff_ne_set(
3998 __isl_take isl_pw_aff *pwaff1,
3999 __isl_take isl_pw_aff *pwaff2);
4000 __isl_give isl_set *isl_pw_aff_le_set(
4001 __isl_take isl_pw_aff *pwaff1,
4002 __isl_take isl_pw_aff *pwaff2);
4003 __isl_give isl_set *isl_pw_aff_lt_set(
4004 __isl_take isl_pw_aff *pwaff1,
4005 __isl_take isl_pw_aff *pwaff2);
4006 __isl_give isl_set *isl_pw_aff_ge_set(
4007 __isl_take isl_pw_aff *pwaff1,
4008 __isl_take isl_pw_aff *pwaff2);
4009 __isl_give isl_set *isl_pw_aff_gt_set(
4010 __isl_take isl_pw_aff *pwaff1,
4011 __isl_take isl_pw_aff *pwaff2);
4013 __isl_give isl_set *isl_pw_aff_list_eq_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_ne_set(
4017 __isl_take isl_pw_aff_list *list1,
4018 __isl_take isl_pw_aff_list *list2);
4019 __isl_give isl_set *isl_pw_aff_list_le_set(
4020 __isl_take isl_pw_aff_list *list1,
4021 __isl_take isl_pw_aff_list *list2);
4022 __isl_give isl_set *isl_pw_aff_list_lt_set(
4023 __isl_take isl_pw_aff_list *list1,
4024 __isl_take isl_pw_aff_list *list2);
4025 __isl_give isl_set *isl_pw_aff_list_ge_set(
4026 __isl_take isl_pw_aff_list *list1,
4027 __isl_take isl_pw_aff_list *list2);
4028 __isl_give isl_set *isl_pw_aff_list_gt_set(
4029 __isl_take isl_pw_aff_list *list1,
4030 __isl_take isl_pw_aff_list *list2);
4032 The function C<isl_aff_neg_basic_set> returns a basic set
4033 containing those elements in the domain space
4034 of C<aff> where C<aff> is negative.
4035 The function C<isl_aff_ge_basic_set> returns a basic set
4036 containing those elements in the shared space
4037 of C<aff1> and C<aff2> where C<aff1> is greater than or equal to C<aff2>.
4038 The function C<isl_pw_aff_ge_set> returns a set
4039 containing those elements in the shared domain
4040 of C<pwaff1> and C<pwaff2> where C<pwaff1> is greater than or equal to C<pwaff2>.
4041 The functions operating on C<isl_pw_aff_list> apply the corresponding
4042 C<isl_pw_aff> function to each pair of elements in the two lists.
4044 #include <isl/aff.h>
4045 __isl_give isl_set *isl_pw_aff_nonneg_set(
4046 __isl_take isl_pw_aff *pwaff);
4047 __isl_give isl_set *isl_pw_aff_zero_set(
4048 __isl_take isl_pw_aff *pwaff);
4049 __isl_give isl_set *isl_pw_aff_non_zero_set(
4050 __isl_take isl_pw_aff *pwaff);
4052 The function C<isl_pw_aff_nonneg_set> returns a set
4053 containing those elements in the domain
4054 of C<pwaff> where C<pwaff> is non-negative.
4056 #include <isl/aff.h>
4057 __isl_give isl_pw_aff *isl_pw_aff_cond(
4058 __isl_take isl_pw_aff *cond,
4059 __isl_take isl_pw_aff *pwaff_true,
4060 __isl_take isl_pw_aff *pwaff_false);
4062 The function C<isl_pw_aff_cond> performs a conditional operator
4063 and returns an expression that is equal to C<pwaff_true>
4064 for elements where C<cond> is non-zero and equal to C<pwaff_false> for elements
4065 where C<cond> is zero.
4067 #include <isl/aff.h>
4068 __isl_give isl_pw_aff *isl_pw_aff_union_min(
4069 __isl_take isl_pw_aff *pwaff1,
4070 __isl_take isl_pw_aff *pwaff2);
4071 __isl_give isl_pw_aff *isl_pw_aff_union_max(
4072 __isl_take isl_pw_aff *pwaff1,
4073 __isl_take isl_pw_aff *pwaff2);
4074 __isl_give isl_pw_aff *isl_pw_aff_union_add(
4075 __isl_take isl_pw_aff *pwaff1,
4076 __isl_take isl_pw_aff *pwaff2);
4078 The function C<isl_pw_aff_union_max> computes a piecewise quasi-affine
4079 expression with a domain that is the union of those of C<pwaff1> and
4080 C<pwaff2> and such that on each cell, the quasi-affine expression is
4081 the maximum of those of C<pwaff1> and C<pwaff2>. If only one of
4082 C<pwaff1> or C<pwaff2> is defined on a given cell, then the
4083 associated expression is the defined one.
4085 An expression can be read from input using
4087 #include <isl/aff.h>
4088 __isl_give isl_aff *isl_aff_read_from_str(
4089 isl_ctx *ctx, const char *str);
4090 __isl_give isl_pw_aff *isl_pw_aff_read_from_str(
4091 isl_ctx *ctx, const char *str);
4093 An expression can be printed using
4095 #include <isl/aff.h>
4096 __isl_give isl_printer *isl_printer_print_aff(
4097 __isl_take isl_printer *p, __isl_keep isl_aff *aff);
4099 __isl_give isl_printer *isl_printer_print_pw_aff(
4100 __isl_take isl_printer *p,
4101 __isl_keep isl_pw_aff *pwaff);
4103 =head2 Piecewise Multiple Quasi Affine Expressions
4105 An C<isl_multi_aff> object represents a sequence of
4106 zero or more affine expressions, all defined on the same domain space.
4107 Similarly, an C<isl_multi_pw_aff> object represents a sequence of
4108 zero or more piecewise affine expressions.
4110 An C<isl_multi_aff> can be constructed from a single
4111 C<isl_aff> or an C<isl_aff_list> using the
4112 following functions. Similarly for C<isl_multi_pw_aff>.
4114 #include <isl/aff.h>
4115 __isl_give isl_multi_aff *isl_multi_aff_from_aff(
4116 __isl_take isl_aff *aff);
4117 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_from_pw_aff(
4118 __isl_take isl_pw_aff *pa);
4119 __isl_give isl_multi_aff *isl_multi_aff_from_aff_list(
4120 __isl_take isl_space *space,
4121 __isl_take isl_aff_list *list);
4123 An empty piecewise multiple quasi affine expression (one with no cells),
4124 the zero piecewise multiple quasi affine expression (with value zero
4125 for each output dimension),
4126 a piecewise multiple quasi affine expression with a single cell (with
4127 either a universe or a specified domain) or
4128 a zero-dimensional piecewise multiple quasi affine expression
4130 can be created using the following functions.
4132 #include <isl/aff.h>
4133 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_empty(
4134 __isl_take isl_space *space);
4135 __isl_give isl_multi_aff *isl_multi_aff_zero(
4136 __isl_take isl_space *space);
4137 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_zero(
4138 __isl_take isl_space *space);
4139 __isl_give isl_multi_aff *isl_multi_aff_identity(
4140 __isl_take isl_space *space);
4141 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_identity(
4142 __isl_take isl_space *space);
4143 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_identity(
4144 __isl_take isl_space *space);
4145 __isl_give isl_pw_multi_aff *
4146 isl_pw_multi_aff_from_multi_aff(
4147 __isl_take isl_multi_aff *ma);
4148 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_alloc(
4149 __isl_take isl_set *set,
4150 __isl_take isl_multi_aff *maff);
4151 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_from_domain(
4152 __isl_take isl_set *set);
4154 __isl_give isl_union_pw_multi_aff *
4155 isl_union_pw_multi_aff_empty(
4156 __isl_take isl_space *space);
4157 __isl_give isl_union_pw_multi_aff *
4158 isl_union_pw_multi_aff_add_pw_multi_aff(
4159 __isl_take isl_union_pw_multi_aff *upma,
4160 __isl_take isl_pw_multi_aff *pma);
4161 __isl_give isl_union_pw_multi_aff *
4162 isl_union_pw_multi_aff_from_domain(
4163 __isl_take isl_union_set *uset);
4165 A piecewise multiple quasi affine expression can also be initialized
4166 from an C<isl_set> or C<isl_map>, provided the C<isl_set> is a singleton
4167 and the C<isl_map> is single-valued.
4168 In case of a conversion from an C<isl_union_set> or an C<isl_union_map>
4169 to an C<isl_union_pw_multi_aff>, these properties need to hold in each space.
4171 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_from_set(
4172 __isl_take isl_set *set);
4173 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_from_map(
4174 __isl_take isl_map *map);
4176 __isl_give isl_union_pw_multi_aff *
4177 isl_union_pw_multi_aff_from_union_set(
4178 __isl_take isl_union_set *uset);
4179 __isl_give isl_union_pw_multi_aff *
4180 isl_union_pw_multi_aff_from_union_map(
4181 __isl_take isl_union_map *umap);
4183 Multiple quasi affine expressions can be copied and freed using
4185 #include <isl/aff.h>
4186 __isl_give isl_multi_aff *isl_multi_aff_copy(
4187 __isl_keep isl_multi_aff *maff);
4188 void *isl_multi_aff_free(__isl_take isl_multi_aff *maff);
4190 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_copy(
4191 __isl_keep isl_pw_multi_aff *pma);
4192 void *isl_pw_multi_aff_free(
4193 __isl_take isl_pw_multi_aff *pma);
4195 __isl_give isl_union_pw_multi_aff *
4196 isl_union_pw_multi_aff_copy(
4197 __isl_keep isl_union_pw_multi_aff *upma);
4198 void *isl_union_pw_multi_aff_free(
4199 __isl_take isl_union_pw_multi_aff *upma);
4201 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_copy(
4202 __isl_keep isl_multi_pw_aff *mpa);
4203 void *isl_multi_pw_aff_free(
4204 __isl_take isl_multi_pw_aff *mpa);
4206 The expression can be inspected using
4208 #include <isl/aff.h>
4209 isl_ctx *isl_multi_aff_get_ctx(
4210 __isl_keep isl_multi_aff *maff);
4211 isl_ctx *isl_pw_multi_aff_get_ctx(
4212 __isl_keep isl_pw_multi_aff *pma);
4213 isl_ctx *isl_union_pw_multi_aff_get_ctx(
4214 __isl_keep isl_union_pw_multi_aff *upma);
4215 isl_ctx *isl_multi_pw_aff_get_ctx(
4216 __isl_keep isl_multi_pw_aff *mpa);
4217 unsigned isl_multi_aff_dim(__isl_keep isl_multi_aff *maff,
4218 enum isl_dim_type type);
4219 unsigned isl_pw_multi_aff_dim(
4220 __isl_keep isl_pw_multi_aff *pma,
4221 enum isl_dim_type type);
4222 unsigned isl_multi_pw_aff_dim(
4223 __isl_keep isl_multi_pw_aff *mpa,
4224 enum isl_dim_type type);
4225 __isl_give isl_aff *isl_multi_aff_get_aff(
4226 __isl_keep isl_multi_aff *multi, int pos);
4227 __isl_give isl_pw_aff *isl_pw_multi_aff_get_pw_aff(
4228 __isl_keep isl_pw_multi_aff *pma, int pos);
4229 __isl_give isl_pw_aff *isl_multi_pw_aff_get_pw_aff(
4230 __isl_keep isl_multi_pw_aff *mpa, int pos);
4231 const char *isl_pw_multi_aff_get_dim_name(
4232 __isl_keep isl_pw_multi_aff *pma,
4233 enum isl_dim_type type, unsigned pos);
4234 __isl_give isl_id *isl_pw_multi_aff_get_dim_id(
4235 __isl_keep isl_pw_multi_aff *pma,
4236 enum isl_dim_type type, unsigned pos);
4237 const char *isl_multi_aff_get_tuple_name(
4238 __isl_keep isl_multi_aff *multi,
4239 enum isl_dim_type type);
4240 int isl_pw_multi_aff_has_tuple_name(
4241 __isl_keep isl_pw_multi_aff *pma,
4242 enum isl_dim_type type);
4243 const char *isl_pw_multi_aff_get_tuple_name(
4244 __isl_keep isl_pw_multi_aff *pma,
4245 enum isl_dim_type type);
4246 int isl_pw_multi_aff_has_tuple_id(
4247 __isl_keep isl_pw_multi_aff *pma,
4248 enum isl_dim_type type);
4249 __isl_give isl_id *isl_pw_multi_aff_get_tuple_id(
4250 __isl_keep isl_pw_multi_aff *pma,
4251 enum isl_dim_type type);
4253 int isl_pw_multi_aff_foreach_piece(
4254 __isl_keep isl_pw_multi_aff *pma,
4255 int (*fn)(__isl_take isl_set *set,
4256 __isl_take isl_multi_aff *maff,
4257 void *user), void *user);
4259 int isl_union_pw_multi_aff_foreach_pw_multi_aff(
4260 __isl_keep isl_union_pw_multi_aff *upma,
4261 int (*fn)(__isl_take isl_pw_multi_aff *pma,
4262 void *user), void *user);
4264 It can be modified using
4266 #include <isl/aff.h>
4267 __isl_give isl_multi_aff *isl_multi_aff_set_aff(
4268 __isl_take isl_multi_aff *multi, int pos,
4269 __isl_take isl_aff *aff);
4270 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_set_pw_aff(
4271 __isl_take isl_pw_multi_aff *pma, unsigned pos,
4272 __isl_take isl_pw_aff *pa);
4273 __isl_give isl_multi_aff *isl_multi_aff_set_dim_name(
4274 __isl_take isl_multi_aff *maff,
4275 enum isl_dim_type type, unsigned pos, const char *s);
4276 __isl_give isl_multi_aff *isl_multi_aff_set_tuple_name(
4277 __isl_take isl_multi_aff *maff,
4278 enum isl_dim_type type, const char *s);
4279 __isl_give isl_multi_aff *isl_multi_aff_set_tuple_id(
4280 __isl_take isl_multi_aff *maff,
4281 enum isl_dim_type type, __isl_take isl_id *id);
4282 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_set_tuple_id(
4283 __isl_take isl_pw_multi_aff *pma,
4284 enum isl_dim_type type, __isl_take isl_id *id);
4286 __isl_give isl_multi_pw_aff *
4287 isl_multi_pw_aff_set_dim_name(
4288 __isl_take isl_multi_pw_aff *mpa,
4289 enum isl_dim_type type, unsigned pos, const char *s);
4290 __isl_give isl_multi_pw_aff *
4291 isl_multi_pw_aff_set_tuple_name(
4292 __isl_take isl_multi_pw_aff *mpa,
4293 enum isl_dim_type type, const char *s);
4295 __isl_give isl_multi_aff *isl_multi_aff_insert_dims(
4296 __isl_take isl_multi_aff *ma,
4297 enum isl_dim_type type, unsigned first, unsigned n);
4298 __isl_give isl_multi_aff *isl_multi_aff_add_dims(
4299 __isl_take isl_multi_aff *ma,
4300 enum isl_dim_type type, unsigned n);
4301 __isl_give isl_multi_aff *isl_multi_aff_drop_dims(
4302 __isl_take isl_multi_aff *maff,
4303 enum isl_dim_type type, unsigned first, unsigned n);
4304 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_drop_dims(
4305 __isl_take isl_pw_multi_aff *pma,
4306 enum isl_dim_type type, unsigned first, unsigned n);
4308 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_insert_dims(
4309 __isl_take isl_multi_pw_aff *mpa,
4310 enum isl_dim_type type, unsigned first, unsigned n);
4311 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_add_dims(
4312 __isl_take isl_multi_pw_aff *mpa,
4313 enum isl_dim_type type, unsigned n);
4315 To check whether two multiple affine expressions are
4316 obviously equal to each other, use
4318 int isl_multi_aff_plain_is_equal(__isl_keep isl_multi_aff *maff1,
4319 __isl_keep isl_multi_aff *maff2);
4320 int isl_pw_multi_aff_plain_is_equal(
4321 __isl_keep isl_pw_multi_aff *pma1,
4322 __isl_keep isl_pw_multi_aff *pma2);
4326 #include <isl/aff.h>
4327 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_union_lexmin(
4328 __isl_take isl_pw_multi_aff *pma1,
4329 __isl_take isl_pw_multi_aff *pma2);
4330 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_union_lexmax(
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_add(
4334 __isl_take isl_multi_aff *maff1,
4335 __isl_take isl_multi_aff *maff2);
4336 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_add(
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_add(
4340 __isl_take isl_union_pw_multi_aff *upma1,
4341 __isl_take isl_union_pw_multi_aff *upma2);
4342 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_union_add(
4343 __isl_take isl_pw_multi_aff *pma1,
4344 __isl_take isl_pw_multi_aff *pma2);
4345 __isl_give isl_multi_aff *isl_multi_aff_sub(
4346 __isl_take isl_multi_aff *ma1,
4347 __isl_take isl_multi_aff *ma2);
4348 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_sub(
4349 __isl_take isl_pw_multi_aff *pma1,
4350 __isl_take isl_pw_multi_aff *pma2);
4351 __isl_give isl_union_pw_multi_aff *isl_union_pw_multi_aff_sub(
4352 __isl_take isl_union_pw_multi_aff *upma1,
4353 __isl_take isl_union_pw_multi_aff *upma2);
4355 C<isl_multi_aff_sub> subtracts the second argument from the first.
4357 __isl_give isl_multi_aff *isl_multi_aff_scale(
4358 __isl_take isl_multi_aff *maff,
4360 __isl_give isl_multi_aff *isl_multi_aff_scale_val(
4361 __isl_take isl_multi_aff *ma,
4362 __isl_take isl_val *v);
4363 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_scale_val(
4364 __isl_take isl_pw_multi_aff *pma,
4365 __isl_take isl_val *v);
4366 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_scale_val(
4367 __isl_take isl_multi_pw_aff *mpa,
4368 __isl_take isl_val *v);
4369 __isl_give isl_multi_aff *isl_multi_aff_scale_vec(
4370 __isl_take isl_multi_aff *ma,
4371 __isl_take isl_vec *v);
4372 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_scale_vec(
4373 __isl_take isl_pw_multi_aff *pma,
4374 __isl_take isl_vec *v);
4375 __isl_give isl_union_pw_multi_aff *isl_union_pw_multi_aff_scale_vec(
4376 __isl_take isl_union_pw_multi_aff *upma,
4377 __isl_take isl_vec *v);
4379 C<isl_multi_aff_scale_vec> scales the first elements of C<ma>
4380 by the corresponding elements of C<v>.
4382 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_intersect_params(
4383 __isl_take isl_pw_multi_aff *pma,
4384 __isl_take isl_set *set);
4385 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_intersect_domain(
4386 __isl_take isl_pw_multi_aff *pma,
4387 __isl_take isl_set *set);
4388 __isl_give isl_union_pw_multi_aff *
4389 isl_union_pw_multi_aff_intersect_domain(
4390 __isl_take isl_union_pw_multi_aff *upma,
4391 __isl_take isl_union_set *uset);
4392 __isl_give isl_multi_aff *isl_multi_aff_lift(
4393 __isl_take isl_multi_aff *maff,
4394 __isl_give isl_local_space **ls);
4395 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_coalesce(
4396 __isl_take isl_pw_multi_aff *pma);
4397 __isl_give isl_multi_aff *isl_multi_aff_align_params(
4398 __isl_take isl_multi_aff *multi,
4399 __isl_take isl_space *model);
4400 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_align_params(
4401 __isl_take isl_pw_multi_aff *pma,
4402 __isl_take isl_space *model);
4403 __isl_give isl_pw_multi_aff *
4404 isl_pw_multi_aff_project_domain_on_params(
4405 __isl_take isl_pw_multi_aff *pma);
4406 __isl_give isl_multi_aff *isl_multi_aff_gist_params(
4407 __isl_take isl_multi_aff *maff,
4408 __isl_take isl_set *context);
4409 __isl_give isl_multi_aff *isl_multi_aff_gist(
4410 __isl_take isl_multi_aff *maff,
4411 __isl_take isl_set *context);
4412 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_gist_params(
4413 __isl_take isl_pw_multi_aff *pma,
4414 __isl_take isl_set *set);
4415 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_gist(
4416 __isl_take isl_pw_multi_aff *pma,
4417 __isl_take isl_set *set);
4418 __isl_give isl_set *isl_pw_multi_aff_domain(
4419 __isl_take isl_pw_multi_aff *pma);
4420 __isl_give isl_union_set *isl_union_pw_multi_aff_domain(
4421 __isl_take isl_union_pw_multi_aff *upma);
4422 __isl_give isl_multi_aff *isl_multi_aff_range_splice(
4423 __isl_take isl_multi_aff *ma1, unsigned pos,
4424 __isl_take isl_multi_aff *ma2);
4425 __isl_give isl_multi_aff *isl_multi_aff_splice(
4426 __isl_take isl_multi_aff *ma1,
4427 unsigned in_pos, unsigned out_pos,
4428 __isl_take isl_multi_aff *ma2);
4429 __isl_give isl_multi_aff *isl_multi_aff_range_product(
4430 __isl_take isl_multi_aff *ma1,
4431 __isl_take isl_multi_aff *ma2);
4432 __isl_give isl_multi_aff *isl_multi_aff_flat_range_product(
4433 __isl_take isl_multi_aff *ma1,
4434 __isl_take isl_multi_aff *ma2);
4435 __isl_give isl_multi_aff *isl_multi_aff_product(
4436 __isl_take isl_multi_aff *ma1,
4437 __isl_take isl_multi_aff *ma2);
4438 __isl_give isl_pw_multi_aff *
4439 isl_pw_multi_aff_range_product(
4440 __isl_take isl_pw_multi_aff *pma1,
4441 __isl_take isl_pw_multi_aff *pma2);
4442 __isl_give isl_pw_multi_aff *
4443 isl_pw_multi_aff_flat_range_product(
4444 __isl_take isl_pw_multi_aff *pma1,
4445 __isl_take isl_pw_multi_aff *pma2);
4446 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_product(
4447 __isl_take isl_pw_multi_aff *pma1,
4448 __isl_take isl_pw_multi_aff *pma2);
4449 __isl_give isl_union_pw_multi_aff *
4450 isl_union_pw_multi_aff_flat_range_product(
4451 __isl_take isl_union_pw_multi_aff *upma1,
4452 __isl_take isl_union_pw_multi_aff *upma2);
4453 __isl_give isl_multi_pw_aff *
4454 isl_multi_pw_aff_range_splice(
4455 __isl_take isl_multi_pw_aff *mpa1, unsigned pos,
4456 __isl_take isl_multi_pw_aff *mpa2);
4457 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_splice(
4458 __isl_take isl_multi_pw_aff *mpa1,
4459 unsigned in_pos, unsigned out_pos,
4460 __isl_take isl_multi_pw_aff *mpa2);
4461 __isl_give isl_multi_pw_aff *
4462 isl_multi_pw_aff_range_product(
4463 __isl_take isl_multi_pw_aff *mpa1,
4464 __isl_take isl_multi_pw_aff *mpa2);
4465 __isl_give isl_multi_pw_aff *
4466 isl_multi_pw_aff_flat_range_product(
4467 __isl_take isl_multi_pw_aff *mpa1,
4468 __isl_take isl_multi_pw_aff *mpa2);
4470 If the C<ls> argument of C<isl_multi_aff_lift> is not C<NULL>,
4471 then it is assigned the local space that lies at the basis of
4472 the lifting applied.
4474 #include <isl/aff.h>
4475 __isl_give isl_multi_aff *isl_multi_aff_pullback_multi_aff(
4476 __isl_take isl_multi_aff *ma1,
4477 __isl_take isl_multi_aff *ma2);
4478 __isl_give isl_pw_multi_aff *
4479 isl_pw_multi_aff_pullback_multi_aff(
4480 __isl_take isl_pw_multi_aff *pma,
4481 __isl_take isl_multi_aff *ma);
4482 __isl_give isl_pw_multi_aff *
4483 isl_pw_multi_aff_pullback_pw_multi_aff(
4484 __isl_take isl_pw_multi_aff *pma1,
4485 __isl_take isl_pw_multi_aff *pma2);
4487 The function C<isl_multi_aff_pullback_multi_aff> precomposes C<ma1> by C<ma2>.
4488 In other words, C<ma2> is plugged
4491 __isl_give isl_set *isl_multi_aff_lex_le_set(
4492 __isl_take isl_multi_aff *ma1,
4493 __isl_take isl_multi_aff *ma2);
4494 __isl_give isl_set *isl_multi_aff_lex_ge_set(
4495 __isl_take isl_multi_aff *ma1,
4496 __isl_take isl_multi_aff *ma2);
4498 The function C<isl_multi_aff_lex_le_set> returns a set
4499 containing those elements in the shared domain space
4500 where C<ma1> is lexicographically smaller than or
4503 An expression can be read from input using
4505 #include <isl/aff.h>
4506 __isl_give isl_multi_aff *isl_multi_aff_read_from_str(
4507 isl_ctx *ctx, const char *str);
4508 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_read_from_str(
4509 isl_ctx *ctx, const char *str);
4510 __isl_give isl_union_pw_multi_aff *
4511 isl_union_pw_multi_aff_read_from_str(
4512 isl_ctx *ctx, const char *str);
4514 An expression can be printed using
4516 #include <isl/aff.h>
4517 __isl_give isl_printer *isl_printer_print_multi_aff(
4518 __isl_take isl_printer *p,
4519 __isl_keep isl_multi_aff *maff);
4520 __isl_give isl_printer *isl_printer_print_pw_multi_aff(
4521 __isl_take isl_printer *p,
4522 __isl_keep isl_pw_multi_aff *pma);
4523 __isl_give isl_printer *isl_printer_print_union_pw_multi_aff(
4524 __isl_take isl_printer *p,
4525 __isl_keep isl_union_pw_multi_aff *upma);
4526 __isl_give isl_printer *isl_printer_print_multi_pw_aff(
4527 __isl_take isl_printer *p,
4528 __isl_keep isl_multi_pw_aff *mpa);
4532 Points are elements of a set. They can be used to construct
4533 simple sets (boxes) or they can be used to represent the
4534 individual elements of a set.
4535 The zero point (the origin) can be created using
4537 __isl_give isl_point *isl_point_zero(__isl_take isl_space *space);
4539 The coordinates of a point can be inspected, set and changed
4542 int isl_point_get_coordinate(__isl_keep isl_point *pnt,
4543 enum isl_dim_type type, int pos, isl_int *v);
4544 __isl_give isl_val *isl_point_get_coordinate_val(
4545 __isl_keep isl_point *pnt,
4546 enum isl_dim_type type, int pos);
4547 __isl_give isl_point *isl_point_set_coordinate(
4548 __isl_take isl_point *pnt,
4549 enum isl_dim_type type, int pos, isl_int v);
4550 __isl_give isl_point *isl_point_set_coordinate_val(
4551 __isl_take isl_point *pnt,
4552 enum isl_dim_type type, int pos,
4553 __isl_take isl_val *v);
4555 __isl_give isl_point *isl_point_add_ui(
4556 __isl_take isl_point *pnt,
4557 enum isl_dim_type type, int pos, unsigned val);
4558 __isl_give isl_point *isl_point_sub_ui(
4559 __isl_take isl_point *pnt,
4560 enum isl_dim_type type, int pos, unsigned val);
4562 Other properties can be obtained using
4564 isl_ctx *isl_point_get_ctx(__isl_keep isl_point *pnt);
4566 Points can be copied or freed using
4568 __isl_give isl_point *isl_point_copy(
4569 __isl_keep isl_point *pnt);
4570 void isl_point_free(__isl_take isl_point *pnt);
4572 A singleton set can be created from a point using
4574 __isl_give isl_basic_set *isl_basic_set_from_point(
4575 __isl_take isl_point *pnt);
4576 __isl_give isl_set *isl_set_from_point(
4577 __isl_take isl_point *pnt);
4579 and a box can be created from two opposite extremal points using
4581 __isl_give isl_basic_set *isl_basic_set_box_from_points(
4582 __isl_take isl_point *pnt1,
4583 __isl_take isl_point *pnt2);
4584 __isl_give isl_set *isl_set_box_from_points(
4585 __isl_take isl_point *pnt1,
4586 __isl_take isl_point *pnt2);
4588 All elements of a B<bounded> (union) set can be enumerated using
4589 the following functions.
4591 int isl_set_foreach_point(__isl_keep isl_set *set,
4592 int (*fn)(__isl_take isl_point *pnt, void *user),
4594 int isl_union_set_foreach_point(__isl_keep isl_union_set *uset,
4595 int (*fn)(__isl_take isl_point *pnt, void *user),
4598 The function C<fn> is called for each integer point in
4599 C<set> with as second argument the last argument of
4600 the C<isl_set_foreach_point> call. The function C<fn>
4601 should return C<0> on success and C<-1> on failure.
4602 In the latter case, C<isl_set_foreach_point> will stop
4603 enumerating and return C<-1> as well.
4604 If the enumeration is performed successfully and to completion,
4605 then C<isl_set_foreach_point> returns C<0>.
4607 To obtain a single point of a (basic) set, use
4609 __isl_give isl_point *isl_basic_set_sample_point(
4610 __isl_take isl_basic_set *bset);
4611 __isl_give isl_point *isl_set_sample_point(
4612 __isl_take isl_set *set);
4614 If C<set> does not contain any (integer) points, then the
4615 resulting point will be ``void'', a property that can be
4618 int isl_point_is_void(__isl_keep isl_point *pnt);
4620 =head2 Piecewise Quasipolynomials
4622 A piecewise quasipolynomial is a particular kind of function that maps
4623 a parametric point to a rational value.
4624 More specifically, a quasipolynomial is a polynomial expression in greatest
4625 integer parts of affine expressions of parameters and variables.
4626 A piecewise quasipolynomial is a subdivision of a given parametric
4627 domain into disjoint cells with a quasipolynomial associated to
4628 each cell. The value of the piecewise quasipolynomial at a given
4629 point is the value of the quasipolynomial associated to the cell
4630 that contains the point. Outside of the union of cells,
4631 the value is assumed to be zero.
4632 For example, the piecewise quasipolynomial
4634 [n] -> { [x] -> ((1 + n) - x) : x <= n and x >= 0 }
4636 maps C<x> to C<1 + n - x> for values of C<x> between C<0> and C<n>.
4637 A given piecewise quasipolynomial has a fixed domain dimension.
4638 Union piecewise quasipolynomials are used to contain piecewise quasipolynomials
4639 defined over different domains.
4640 Piecewise quasipolynomials are mainly used by the C<barvinok>
4641 library for representing the number of elements in a parametric set or map.
4642 For example, the piecewise quasipolynomial above represents
4643 the number of points in the map
4645 [n] -> { [x] -> [y] : x,y >= 0 and 0 <= x + y <= n }
4647 =head3 Input and Output
4649 Piecewise quasipolynomials can be read from input using
4651 __isl_give isl_union_pw_qpolynomial *
4652 isl_union_pw_qpolynomial_read_from_str(
4653 isl_ctx *ctx, const char *str);
4655 Quasipolynomials and piecewise quasipolynomials can be printed
4656 using the following functions.
4658 __isl_give isl_printer *isl_printer_print_qpolynomial(
4659 __isl_take isl_printer *p,
4660 __isl_keep isl_qpolynomial *qp);
4662 __isl_give isl_printer *isl_printer_print_pw_qpolynomial(
4663 __isl_take isl_printer *p,
4664 __isl_keep isl_pw_qpolynomial *pwqp);
4666 __isl_give isl_printer *isl_printer_print_union_pw_qpolynomial(
4667 __isl_take isl_printer *p,
4668 __isl_keep isl_union_pw_qpolynomial *upwqp);
4670 The output format of the printer
4671 needs to be set to either C<ISL_FORMAT_ISL> or C<ISL_FORMAT_C>.
4672 For C<isl_printer_print_union_pw_qpolynomial>, only C<ISL_FORMAT_ISL>
4674 In case of printing in C<ISL_FORMAT_C>, the user may want
4675 to set the names of all dimensions
4677 __isl_give isl_qpolynomial *isl_qpolynomial_set_dim_name(
4678 __isl_take isl_qpolynomial *qp,
4679 enum isl_dim_type type, unsigned pos,
4681 __isl_give isl_pw_qpolynomial *
4682 isl_pw_qpolynomial_set_dim_name(
4683 __isl_take isl_pw_qpolynomial *pwqp,
4684 enum isl_dim_type type, unsigned pos,
4687 =head3 Creating New (Piecewise) Quasipolynomials
4689 Some simple quasipolynomials can be created using the following functions.
4690 More complicated quasipolynomials can be created by applying
4691 operations such as addition and multiplication
4692 on the resulting quasipolynomials
4694 __isl_give isl_qpolynomial *isl_qpolynomial_zero_on_domain(
4695 __isl_take isl_space *domain);
4696 __isl_give isl_qpolynomial *isl_qpolynomial_one_on_domain(
4697 __isl_take isl_space *domain);
4698 __isl_give isl_qpolynomial *isl_qpolynomial_infty_on_domain(
4699 __isl_take isl_space *domain);
4700 __isl_give isl_qpolynomial *isl_qpolynomial_neginfty_on_domain(
4701 __isl_take isl_space *domain);
4702 __isl_give isl_qpolynomial *isl_qpolynomial_nan_on_domain(
4703 __isl_take isl_space *domain);
4704 __isl_give isl_qpolynomial *isl_qpolynomial_rat_cst_on_domain(
4705 __isl_take isl_space *domain,
4706 const isl_int n, const isl_int d);
4707 __isl_give isl_qpolynomial *isl_qpolynomial_val_on_domain(
4708 __isl_take isl_space *domain,
4709 __isl_take isl_val *val);
4710 __isl_give isl_qpolynomial *isl_qpolynomial_var_on_domain(
4711 __isl_take isl_space *domain,
4712 enum isl_dim_type type, unsigned pos);
4713 __isl_give isl_qpolynomial *isl_qpolynomial_from_aff(
4714 __isl_take isl_aff *aff);
4716 Note that the space in which a quasipolynomial lives is a map space
4717 with a one-dimensional range. The C<domain> argument in some of
4718 the functions above corresponds to the domain of this map space.
4720 The zero piecewise quasipolynomial or a piecewise quasipolynomial
4721 with a single cell can be created using the following functions.
4722 Multiple of these single cell piecewise quasipolynomials can
4723 be combined to create more complicated piecewise quasipolynomials.
4725 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_zero(
4726 __isl_take isl_space *space);
4727 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_alloc(
4728 __isl_take isl_set *set,
4729 __isl_take isl_qpolynomial *qp);
4730 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_from_qpolynomial(
4731 __isl_take isl_qpolynomial *qp);
4732 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_from_pw_aff(
4733 __isl_take isl_pw_aff *pwaff);
4735 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_zero(
4736 __isl_take isl_space *space);
4737 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_from_pw_qpolynomial(
4738 __isl_take isl_pw_qpolynomial *pwqp);
4739 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_add_pw_qpolynomial(
4740 __isl_take isl_union_pw_qpolynomial *upwqp,
4741 __isl_take isl_pw_qpolynomial *pwqp);
4743 Quasipolynomials can be copied and freed again using the following
4746 __isl_give isl_qpolynomial *isl_qpolynomial_copy(
4747 __isl_keep isl_qpolynomial *qp);
4748 void *isl_qpolynomial_free(__isl_take isl_qpolynomial *qp);
4750 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_copy(
4751 __isl_keep isl_pw_qpolynomial *pwqp);
4752 void *isl_pw_qpolynomial_free(
4753 __isl_take isl_pw_qpolynomial *pwqp);
4755 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_copy(
4756 __isl_keep isl_union_pw_qpolynomial *upwqp);
4757 void *isl_union_pw_qpolynomial_free(
4758 __isl_take isl_union_pw_qpolynomial *upwqp);
4760 =head3 Inspecting (Piecewise) Quasipolynomials
4762 To iterate over all piecewise quasipolynomials in a union
4763 piecewise quasipolynomial, use the following function
4765 int isl_union_pw_qpolynomial_foreach_pw_qpolynomial(
4766 __isl_keep isl_union_pw_qpolynomial *upwqp,
4767 int (*fn)(__isl_take isl_pw_qpolynomial *pwqp, void *user),
4770 To extract the piecewise quasipolynomial in a given space from a union, use
4772 __isl_give isl_pw_qpolynomial *
4773 isl_union_pw_qpolynomial_extract_pw_qpolynomial(
4774 __isl_keep isl_union_pw_qpolynomial *upwqp,
4775 __isl_take isl_space *space);
4777 To iterate over the cells in a piecewise quasipolynomial,
4778 use either of the following two functions
4780 int isl_pw_qpolynomial_foreach_piece(
4781 __isl_keep isl_pw_qpolynomial *pwqp,
4782 int (*fn)(__isl_take isl_set *set,
4783 __isl_take isl_qpolynomial *qp,
4784 void *user), void *user);
4785 int isl_pw_qpolynomial_foreach_lifted_piece(
4786 __isl_keep isl_pw_qpolynomial *pwqp,
4787 int (*fn)(__isl_take isl_set *set,
4788 __isl_take isl_qpolynomial *qp,
4789 void *user), void *user);
4791 As usual, the function C<fn> should return C<0> on success
4792 and C<-1> on failure. The difference between
4793 C<isl_pw_qpolynomial_foreach_piece> and
4794 C<isl_pw_qpolynomial_foreach_lifted_piece> is that
4795 C<isl_pw_qpolynomial_foreach_lifted_piece> will first
4796 compute unique representations for all existentially quantified
4797 variables and then turn these existentially quantified variables
4798 into extra set variables, adapting the associated quasipolynomial
4799 accordingly. This means that the C<set> passed to C<fn>
4800 will not have any existentially quantified variables, but that
4801 the dimensions of the sets may be different for different
4802 invocations of C<fn>.
4804 The constant term of a quasipolynomial can be extracted using
4806 __isl_give isl_val *isl_qpolynomial_get_constant_val(
4807 __isl_keep isl_qpolynomial *qp);
4809 To iterate over all terms in a quasipolynomial,
4812 int isl_qpolynomial_foreach_term(
4813 __isl_keep isl_qpolynomial *qp,
4814 int (*fn)(__isl_take isl_term *term,
4815 void *user), void *user);
4817 The terms themselves can be inspected and freed using
4820 unsigned isl_term_dim(__isl_keep isl_term *term,
4821 enum isl_dim_type type);
4822 void isl_term_get_num(__isl_keep isl_term *term,
4824 void isl_term_get_den(__isl_keep isl_term *term,
4826 __isl_give isl_val *isl_term_get_coefficient_val(
4827 __isl_keep isl_term *term);
4828 int isl_term_get_exp(__isl_keep isl_term *term,
4829 enum isl_dim_type type, unsigned pos);
4830 __isl_give isl_aff *isl_term_get_div(
4831 __isl_keep isl_term *term, unsigned pos);
4832 void isl_term_free(__isl_take isl_term *term);
4834 Each term is a product of parameters, set variables and
4835 integer divisions. The function C<isl_term_get_exp>
4836 returns the exponent of a given dimensions in the given term.
4837 The C<isl_int>s in the arguments of C<isl_term_get_num>
4838 and C<isl_term_get_den> need to have been initialized
4839 using C<isl_int_init> before calling these functions.
4841 =head3 Properties of (Piecewise) Quasipolynomials
4843 To check whether a quasipolynomial is actually a constant,
4844 use the following function.
4846 int isl_qpolynomial_is_cst(__isl_keep isl_qpolynomial *qp,
4847 isl_int *n, isl_int *d);
4849 If C<qp> is a constant and if C<n> and C<d> are not C<NULL>
4850 then the numerator and denominator of the constant
4851 are returned in C<*n> and C<*d>, respectively.
4853 To check whether two union piecewise quasipolynomials are
4854 obviously equal, use
4856 int isl_union_pw_qpolynomial_plain_is_equal(
4857 __isl_keep isl_union_pw_qpolynomial *upwqp1,
4858 __isl_keep isl_union_pw_qpolynomial *upwqp2);
4860 =head3 Operations on (Piecewise) Quasipolynomials
4862 __isl_give isl_qpolynomial *isl_qpolynomial_scale(
4863 __isl_take isl_qpolynomial *qp, isl_int v);
4864 __isl_give isl_qpolynomial *isl_qpolynomial_scale_val(
4865 __isl_take isl_qpolynomial *qp,
4866 __isl_take isl_val *v);
4867 __isl_give isl_qpolynomial *isl_qpolynomial_neg(
4868 __isl_take isl_qpolynomial *qp);
4869 __isl_give isl_qpolynomial *isl_qpolynomial_add(
4870 __isl_take isl_qpolynomial *qp1,
4871 __isl_take isl_qpolynomial *qp2);
4872 __isl_give isl_qpolynomial *isl_qpolynomial_sub(
4873 __isl_take isl_qpolynomial *qp1,
4874 __isl_take isl_qpolynomial *qp2);
4875 __isl_give isl_qpolynomial *isl_qpolynomial_mul(
4876 __isl_take isl_qpolynomial *qp1,
4877 __isl_take isl_qpolynomial *qp2);
4878 __isl_give isl_qpolynomial *isl_qpolynomial_pow(
4879 __isl_take isl_qpolynomial *qp, unsigned exponent);
4881 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_fix_val(
4882 __isl_take isl_pw_qpolynomial *pwqp,
4883 enum isl_dim_type type, unsigned n,
4884 __isl_take isl_val *v);
4885 __isl_give isl_pw_qpolynomial *
4886 isl_pw_qpolynomial_scale_val(
4887 __isl_take isl_pw_qpolynomial *pwqp,
4888 __isl_take isl_val *v);
4889 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_add(
4890 __isl_take isl_pw_qpolynomial *pwqp1,
4891 __isl_take isl_pw_qpolynomial *pwqp2);
4892 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_sub(
4893 __isl_take isl_pw_qpolynomial *pwqp1,
4894 __isl_take isl_pw_qpolynomial *pwqp2);
4895 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_add_disjoint(
4896 __isl_take isl_pw_qpolynomial *pwqp1,
4897 __isl_take isl_pw_qpolynomial *pwqp2);
4898 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_neg(
4899 __isl_take isl_pw_qpolynomial *pwqp);
4900 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_mul(
4901 __isl_take isl_pw_qpolynomial *pwqp1,
4902 __isl_take isl_pw_qpolynomial *pwqp2);
4903 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_pow(
4904 __isl_take isl_pw_qpolynomial *pwqp, unsigned exponent);
4906 __isl_give isl_union_pw_qpolynomial *
4907 isl_union_pw_qpolynomial_scale_val(
4908 __isl_take isl_union_pw_qpolynomial *upwqp,
4909 __isl_take isl_val *v);
4910 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_add(
4911 __isl_take isl_union_pw_qpolynomial *upwqp1,
4912 __isl_take isl_union_pw_qpolynomial *upwqp2);
4913 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_sub(
4914 __isl_take isl_union_pw_qpolynomial *upwqp1,
4915 __isl_take isl_union_pw_qpolynomial *upwqp2);
4916 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_mul(
4917 __isl_take isl_union_pw_qpolynomial *upwqp1,
4918 __isl_take isl_union_pw_qpolynomial *upwqp2);
4920 __isl_give isl_qpolynomial *isl_pw_qpolynomial_eval(
4921 __isl_take isl_pw_qpolynomial *pwqp,
4922 __isl_take isl_point *pnt);
4924 __isl_give isl_qpolynomial *isl_union_pw_qpolynomial_eval(
4925 __isl_take isl_union_pw_qpolynomial *upwqp,
4926 __isl_take isl_point *pnt);
4928 __isl_give isl_set *isl_pw_qpolynomial_domain(
4929 __isl_take isl_pw_qpolynomial *pwqp);
4930 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_intersect_domain(
4931 __isl_take isl_pw_qpolynomial *pwpq,
4932 __isl_take isl_set *set);
4933 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_intersect_params(
4934 __isl_take isl_pw_qpolynomial *pwpq,
4935 __isl_take isl_set *set);
4937 __isl_give isl_union_set *isl_union_pw_qpolynomial_domain(
4938 __isl_take isl_union_pw_qpolynomial *upwqp);
4939 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_intersect_domain(
4940 __isl_take isl_union_pw_qpolynomial *upwpq,
4941 __isl_take isl_union_set *uset);
4942 __isl_give isl_union_pw_qpolynomial *
4943 isl_union_pw_qpolynomial_intersect_params(
4944 __isl_take isl_union_pw_qpolynomial *upwpq,
4945 __isl_take isl_set *set);
4947 __isl_give isl_qpolynomial *isl_qpolynomial_align_params(
4948 __isl_take isl_qpolynomial *qp,
4949 __isl_take isl_space *model);
4951 __isl_give isl_qpolynomial *isl_qpolynomial_project_domain_on_params(
4952 __isl_take isl_qpolynomial *qp);
4953 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_project_domain_on_params(
4954 __isl_take isl_pw_qpolynomial *pwqp);
4956 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_coalesce(
4957 __isl_take isl_union_pw_qpolynomial *upwqp);
4959 __isl_give isl_qpolynomial *isl_qpolynomial_gist_params(
4960 __isl_take isl_qpolynomial *qp,
4961 __isl_take isl_set *context);
4962 __isl_give isl_qpolynomial *isl_qpolynomial_gist(
4963 __isl_take isl_qpolynomial *qp,
4964 __isl_take isl_set *context);
4966 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_gist_params(
4967 __isl_take isl_pw_qpolynomial *pwqp,
4968 __isl_take isl_set *context);
4969 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_gist(
4970 __isl_take isl_pw_qpolynomial *pwqp,
4971 __isl_take isl_set *context);
4973 __isl_give isl_union_pw_qpolynomial *
4974 isl_union_pw_qpolynomial_gist_params(
4975 __isl_take isl_union_pw_qpolynomial *upwqp,
4976 __isl_take isl_set *context);
4977 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_gist(
4978 __isl_take isl_union_pw_qpolynomial *upwqp,
4979 __isl_take isl_union_set *context);
4981 The gist operation applies the gist operation to each of
4982 the cells in the domain of the input piecewise quasipolynomial.
4983 The context is also exploited
4984 to simplify the quasipolynomials associated to each cell.
4986 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_to_polynomial(
4987 __isl_take isl_pw_qpolynomial *pwqp, int sign);
4988 __isl_give isl_union_pw_qpolynomial *
4989 isl_union_pw_qpolynomial_to_polynomial(
4990 __isl_take isl_union_pw_qpolynomial *upwqp, int sign);
4992 Approximate each quasipolynomial by a polynomial. If C<sign> is positive,
4993 the polynomial will be an overapproximation. If C<sign> is negative,
4994 it will be an underapproximation. If C<sign> is zero, the approximation
4995 will lie somewhere in between.
4997 =head2 Bounds on Piecewise Quasipolynomials and Piecewise Quasipolynomial Reductions
4999 A piecewise quasipolynomial reduction is a piecewise
5000 reduction (or fold) of quasipolynomials.
5001 In particular, the reduction can be maximum or a minimum.
5002 The objects are mainly used to represent the result of
5003 an upper or lower bound on a quasipolynomial over its domain,
5004 i.e., as the result of the following function.
5006 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_bound(
5007 __isl_take isl_pw_qpolynomial *pwqp,
5008 enum isl_fold type, int *tight);
5010 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_bound(
5011 __isl_take isl_union_pw_qpolynomial *upwqp,
5012 enum isl_fold type, int *tight);
5014 The C<type> argument may be either C<isl_fold_min> or C<isl_fold_max>.
5015 If C<tight> is not C<NULL>, then C<*tight> is set to C<1>
5016 is the returned bound is known be tight, i.e., for each value
5017 of the parameters there is at least
5018 one element in the domain that reaches the bound.
5019 If the domain of C<pwqp> is not wrapping, then the bound is computed
5020 over all elements in that domain and the result has a purely parametric
5021 domain. If the domain of C<pwqp> is wrapping, then the bound is
5022 computed over the range of the wrapped relation. The domain of the
5023 wrapped relation becomes the domain of the result.
5025 A (piecewise) quasipolynomial reduction can be copied or freed using the
5026 following functions.
5028 __isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_copy(
5029 __isl_keep isl_qpolynomial_fold *fold);
5030 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_copy(
5031 __isl_keep isl_pw_qpolynomial_fold *pwf);
5032 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_copy(
5033 __isl_keep isl_union_pw_qpolynomial_fold *upwf);
5034 void isl_qpolynomial_fold_free(
5035 __isl_take isl_qpolynomial_fold *fold);
5036 void *isl_pw_qpolynomial_fold_free(
5037 __isl_take isl_pw_qpolynomial_fold *pwf);
5038 void *isl_union_pw_qpolynomial_fold_free(
5039 __isl_take isl_union_pw_qpolynomial_fold *upwf);
5041 =head3 Printing Piecewise Quasipolynomial Reductions
5043 Piecewise quasipolynomial reductions can be printed
5044 using the following function.
5046 __isl_give isl_printer *isl_printer_print_pw_qpolynomial_fold(
5047 __isl_take isl_printer *p,
5048 __isl_keep isl_pw_qpolynomial_fold *pwf);
5049 __isl_give isl_printer *isl_printer_print_union_pw_qpolynomial_fold(
5050 __isl_take isl_printer *p,
5051 __isl_keep isl_union_pw_qpolynomial_fold *upwf);
5053 For C<isl_printer_print_pw_qpolynomial_fold>,
5054 output format of the printer
5055 needs to be set to either C<ISL_FORMAT_ISL> or C<ISL_FORMAT_C>.
5056 For C<isl_printer_print_union_pw_qpolynomial_fold>,
5057 output format of the printer
5058 needs to be set to C<ISL_FORMAT_ISL>.
5059 In case of printing in C<ISL_FORMAT_C>, the user may want
5060 to set the names of all dimensions
5062 __isl_give isl_pw_qpolynomial_fold *
5063 isl_pw_qpolynomial_fold_set_dim_name(
5064 __isl_take isl_pw_qpolynomial_fold *pwf,
5065 enum isl_dim_type type, unsigned pos,
5068 =head3 Inspecting (Piecewise) Quasipolynomial Reductions
5070 To iterate over all piecewise quasipolynomial reductions in a union
5071 piecewise quasipolynomial reduction, use the following function
5073 int isl_union_pw_qpolynomial_fold_foreach_pw_qpolynomial_fold(
5074 __isl_keep isl_union_pw_qpolynomial_fold *upwf,
5075 int (*fn)(__isl_take isl_pw_qpolynomial_fold *pwf,
5076 void *user), void *user);
5078 To iterate over the cells in a piecewise quasipolynomial reduction,
5079 use either of the following two functions
5081 int isl_pw_qpolynomial_fold_foreach_piece(
5082 __isl_keep isl_pw_qpolynomial_fold *pwf,
5083 int (*fn)(__isl_take isl_set *set,
5084 __isl_take isl_qpolynomial_fold *fold,
5085 void *user), void *user);
5086 int isl_pw_qpolynomial_fold_foreach_lifted_piece(
5087 __isl_keep isl_pw_qpolynomial_fold *pwf,
5088 int (*fn)(__isl_take isl_set *set,
5089 __isl_take isl_qpolynomial_fold *fold,
5090 void *user), void *user);
5092 See L<Inspecting (Piecewise) Quasipolynomials> for an explanation
5093 of the difference between these two functions.
5095 To iterate over all quasipolynomials in a reduction, use
5097 int isl_qpolynomial_fold_foreach_qpolynomial(
5098 __isl_keep isl_qpolynomial_fold *fold,
5099 int (*fn)(__isl_take isl_qpolynomial *qp,
5100 void *user), void *user);
5102 =head3 Properties of Piecewise Quasipolynomial Reductions
5104 To check whether two union piecewise quasipolynomial reductions are
5105 obviously equal, use
5107 int isl_union_pw_qpolynomial_fold_plain_is_equal(
5108 __isl_keep isl_union_pw_qpolynomial_fold *upwf1,
5109 __isl_keep isl_union_pw_qpolynomial_fold *upwf2);
5111 =head3 Operations on Piecewise Quasipolynomial Reductions
5113 __isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_scale(
5114 __isl_take isl_qpolynomial_fold *fold, isl_int v);
5115 __isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_scale_val(
5116 __isl_take isl_qpolynomial_fold *fold,
5117 __isl_take isl_val *v);
5118 __isl_give isl_pw_qpolynomial_fold *
5119 isl_pw_qpolynomial_fold_scale_val(
5120 __isl_take isl_pw_qpolynomial_fold *pwf,
5121 __isl_take isl_val *v);
5122 __isl_give isl_union_pw_qpolynomial_fold *
5123 isl_union_pw_qpolynomial_fold_scale_val(
5124 __isl_take isl_union_pw_qpolynomial_fold *upwf,
5125 __isl_take isl_val *v);
5127 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_add(
5128 __isl_take isl_pw_qpolynomial_fold *pwf1,
5129 __isl_take isl_pw_qpolynomial_fold *pwf2);
5131 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_fold(
5132 __isl_take isl_pw_qpolynomial_fold *pwf1,
5133 __isl_take isl_pw_qpolynomial_fold *pwf2);
5135 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_fold(
5136 __isl_take isl_union_pw_qpolynomial_fold *upwf1,
5137 __isl_take isl_union_pw_qpolynomial_fold *upwf2);
5139 __isl_give isl_qpolynomial *isl_pw_qpolynomial_fold_eval(
5140 __isl_take isl_pw_qpolynomial_fold *pwf,
5141 __isl_take isl_point *pnt);
5143 __isl_give isl_qpolynomial *isl_union_pw_qpolynomial_fold_eval(
5144 __isl_take isl_union_pw_qpolynomial_fold *upwf,
5145 __isl_take isl_point *pnt);
5147 __isl_give isl_pw_qpolynomial_fold *
5148 isl_pw_qpolynomial_fold_intersect_params(
5149 __isl_take isl_pw_qpolynomial_fold *pwf,
5150 __isl_take isl_set *set);
5152 __isl_give isl_union_set *isl_union_pw_qpolynomial_fold_domain(
5153 __isl_take isl_union_pw_qpolynomial_fold *upwf);
5154 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_intersect_domain(
5155 __isl_take isl_union_pw_qpolynomial_fold *upwf,
5156 __isl_take isl_union_set *uset);
5157 __isl_give isl_union_pw_qpolynomial_fold *
5158 isl_union_pw_qpolynomial_fold_intersect_params(
5159 __isl_take isl_union_pw_qpolynomial_fold *upwf,
5160 __isl_take isl_set *set);
5162 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_project_domain_on_params(
5163 __isl_take isl_pw_qpolynomial_fold *pwf);
5165 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_coalesce(
5166 __isl_take isl_pw_qpolynomial_fold *pwf);
5168 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_coalesce(
5169 __isl_take isl_union_pw_qpolynomial_fold *upwf);
5171 __isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_gist_params(
5172 __isl_take isl_qpolynomial_fold *fold,
5173 __isl_take isl_set *context);
5174 __isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_gist(
5175 __isl_take isl_qpolynomial_fold *fold,
5176 __isl_take isl_set *context);
5178 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_gist(
5179 __isl_take isl_pw_qpolynomial_fold *pwf,
5180 __isl_take isl_set *context);
5181 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_gist_params(
5182 __isl_take isl_pw_qpolynomial_fold *pwf,
5183 __isl_take isl_set *context);
5185 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_gist(
5186 __isl_take isl_union_pw_qpolynomial_fold *upwf,
5187 __isl_take isl_union_set *context);
5188 __isl_give isl_union_pw_qpolynomial_fold *
5189 isl_union_pw_qpolynomial_fold_gist_params(
5190 __isl_take isl_union_pw_qpolynomial_fold *upwf,
5191 __isl_take isl_set *context);
5193 The gist operation applies the gist operation to each of
5194 the cells in the domain of the input piecewise quasipolynomial reduction.
5195 In future, the operation will also exploit the context
5196 to simplify the quasipolynomial reductions associated to each cell.
5198 __isl_give isl_pw_qpolynomial_fold *
5199 isl_set_apply_pw_qpolynomial_fold(
5200 __isl_take isl_set *set,
5201 __isl_take isl_pw_qpolynomial_fold *pwf,
5203 __isl_give isl_pw_qpolynomial_fold *
5204 isl_map_apply_pw_qpolynomial_fold(
5205 __isl_take isl_map *map,
5206 __isl_take isl_pw_qpolynomial_fold *pwf,
5208 __isl_give isl_union_pw_qpolynomial_fold *
5209 isl_union_set_apply_union_pw_qpolynomial_fold(
5210 __isl_take isl_union_set *uset,
5211 __isl_take isl_union_pw_qpolynomial_fold *upwf,
5213 __isl_give isl_union_pw_qpolynomial_fold *
5214 isl_union_map_apply_union_pw_qpolynomial_fold(
5215 __isl_take isl_union_map *umap,
5216 __isl_take isl_union_pw_qpolynomial_fold *upwf,
5219 The functions taking a map
5220 compose the given map with the given piecewise quasipolynomial reduction.
5221 That is, compute a bound (of the same type as C<pwf> or C<upwf> itself)
5222 over all elements in the intersection of the range of the map
5223 and the domain of the piecewise quasipolynomial reduction
5224 as a function of an element in the domain of the map.
5225 The functions taking a set compute a bound over all elements in the
5226 intersection of the set and the domain of the
5227 piecewise quasipolynomial reduction.
5229 =head2 Parametric Vertex Enumeration
5231 The parametric vertex enumeration described in this section
5232 is mainly intended to be used internally and by the C<barvinok>
5235 #include <isl/vertices.h>
5236 __isl_give isl_vertices *isl_basic_set_compute_vertices(
5237 __isl_keep isl_basic_set *bset);
5239 The function C<isl_basic_set_compute_vertices> performs the
5240 actual computation of the parametric vertices and the chamber
5241 decomposition and store the result in an C<isl_vertices> object.
5242 This information can be queried by either iterating over all
5243 the vertices or iterating over all the chambers or cells
5244 and then iterating over all vertices that are active on the chamber.
5246 int isl_vertices_foreach_vertex(
5247 __isl_keep isl_vertices *vertices,
5248 int (*fn)(__isl_take isl_vertex *vertex, void *user),
5251 int isl_vertices_foreach_cell(
5252 __isl_keep isl_vertices *vertices,
5253 int (*fn)(__isl_take isl_cell *cell, void *user),
5255 int isl_cell_foreach_vertex(__isl_keep isl_cell *cell,
5256 int (*fn)(__isl_take isl_vertex *vertex, void *user),
5259 Other operations that can be performed on an C<isl_vertices> object are
5262 isl_ctx *isl_vertices_get_ctx(
5263 __isl_keep isl_vertices *vertices);
5264 int isl_vertices_get_n_vertices(
5265 __isl_keep isl_vertices *vertices);
5266 void isl_vertices_free(__isl_take isl_vertices *vertices);
5268 Vertices can be inspected and destroyed using the following functions.
5270 isl_ctx *isl_vertex_get_ctx(__isl_keep isl_vertex *vertex);
5271 int isl_vertex_get_id(__isl_keep isl_vertex *vertex);
5272 __isl_give isl_basic_set *isl_vertex_get_domain(
5273 __isl_keep isl_vertex *vertex);
5274 __isl_give isl_basic_set *isl_vertex_get_expr(
5275 __isl_keep isl_vertex *vertex);
5276 void isl_vertex_free(__isl_take isl_vertex *vertex);
5278 C<isl_vertex_get_expr> returns a singleton parametric set describing
5279 the vertex, while C<isl_vertex_get_domain> returns the activity domain
5281 Note that C<isl_vertex_get_domain> and C<isl_vertex_get_expr> return
5282 B<rational> basic sets, so they should mainly be used for inspection
5283 and should not be mixed with integer sets.
5285 Chambers can be inspected and destroyed using the following functions.
5287 isl_ctx *isl_cell_get_ctx(__isl_keep isl_cell *cell);
5288 __isl_give isl_basic_set *isl_cell_get_domain(
5289 __isl_keep isl_cell *cell);
5290 void isl_cell_free(__isl_take isl_cell *cell);
5292 =head1 Polyhedral Compilation Library
5294 This section collects functionality in C<isl> that has been specifically
5295 designed for use during polyhedral compilation.
5297 =head2 Dependence Analysis
5299 C<isl> contains specialized functionality for performing
5300 array dataflow analysis. That is, given a I<sink> access relation
5301 and a collection of possible I<source> access relations,
5302 C<isl> can compute relations that describe
5303 for each iteration of the sink access, which iteration
5304 of which of the source access relations was the last
5305 to access the same data element before the given iteration
5307 The resulting dependence relations map source iterations
5308 to the corresponding sink iterations.
5309 To compute standard flow dependences, the sink should be
5310 a read, while the sources should be writes.
5311 If any of the source accesses are marked as being I<may>
5312 accesses, then there will be a dependence from the last
5313 I<must> access B<and> from any I<may> access that follows
5314 this last I<must> access.
5315 In particular, if I<all> sources are I<may> accesses,
5316 then memory based dependence analysis is performed.
5317 If, on the other hand, all sources are I<must> accesses,
5318 then value based dependence analysis is performed.
5320 #include <isl/flow.h>
5322 typedef int (*isl_access_level_before)(void *first, void *second);
5324 __isl_give isl_access_info *isl_access_info_alloc(
5325 __isl_take isl_map *sink,
5326 void *sink_user, isl_access_level_before fn,
5328 __isl_give isl_access_info *isl_access_info_add_source(
5329 __isl_take isl_access_info *acc,
5330 __isl_take isl_map *source, int must,
5332 void *isl_access_info_free(__isl_take isl_access_info *acc);
5334 __isl_give isl_flow *isl_access_info_compute_flow(
5335 __isl_take isl_access_info *acc);
5337 int isl_flow_foreach(__isl_keep isl_flow *deps,
5338 int (*fn)(__isl_take isl_map *dep, int must,
5339 void *dep_user, void *user),
5341 __isl_give isl_map *isl_flow_get_no_source(
5342 __isl_keep isl_flow *deps, int must);
5343 void isl_flow_free(__isl_take isl_flow *deps);
5345 The function C<isl_access_info_compute_flow> performs the actual
5346 dependence analysis. The other functions are used to construct
5347 the input for this function or to read off the output.
5349 The input is collected in an C<isl_access_info>, which can
5350 be created through a call to C<isl_access_info_alloc>.
5351 The arguments to this functions are the sink access relation
5352 C<sink>, a token C<sink_user> used to identify the sink
5353 access to the user, a callback function for specifying the
5354 relative order of source and sink accesses, and the number
5355 of source access relations that will be added.
5356 The callback function has type C<int (*)(void *first, void *second)>.
5357 The function is called with two user supplied tokens identifying
5358 either a source or the sink and it should return the shared nesting
5359 level and the relative order of the two accesses.
5360 In particular, let I<n> be the number of loops shared by
5361 the two accesses. If C<first> precedes C<second> textually,
5362 then the function should return I<2 * n + 1>; otherwise,
5363 it should return I<2 * n>.
5364 The sources can be added to the C<isl_access_info> by performing
5365 (at most) C<max_source> calls to C<isl_access_info_add_source>.
5366 C<must> indicates whether the source is a I<must> access
5367 or a I<may> access. Note that a multi-valued access relation
5368 should only be marked I<must> if every iteration in the domain
5369 of the relation accesses I<all> elements in its image.
5370 The C<source_user> token is again used to identify
5371 the source access. The range of the source access relation
5372 C<source> should have the same dimension as the range
5373 of the sink access relation.
5374 The C<isl_access_info_free> function should usually not be
5375 called explicitly, because it is called implicitly by
5376 C<isl_access_info_compute_flow>.
5378 The result of the dependence analysis is collected in an
5379 C<isl_flow>. There may be elements of
5380 the sink access for which no preceding source access could be
5381 found or for which all preceding sources are I<may> accesses.
5382 The relations containing these elements can be obtained through
5383 calls to C<isl_flow_get_no_source>, the first with C<must> set
5384 and the second with C<must> unset.
5385 In the case of standard flow dependence analysis,
5386 with the sink a read and the sources I<must> writes,
5387 the first relation corresponds to the reads from uninitialized
5388 array elements and the second relation is empty.
5389 The actual flow dependences can be extracted using
5390 C<isl_flow_foreach>. This function will call the user-specified
5391 callback function C<fn> for each B<non-empty> dependence between
5392 a source and the sink. The callback function is called
5393 with four arguments, the actual flow dependence relation
5394 mapping source iterations to sink iterations, a boolean that
5395 indicates whether it is a I<must> or I<may> dependence, a token
5396 identifying the source and an additional C<void *> with value
5397 equal to the third argument of the C<isl_flow_foreach> call.
5398 A dependence is marked I<must> if it originates from a I<must>
5399 source and if it is not followed by any I<may> sources.
5401 After finishing with an C<isl_flow>, the user should call
5402 C<isl_flow_free> to free all associated memory.
5404 A higher-level interface to dependence analysis is provided
5405 by the following function.
5407 #include <isl/flow.h>
5409 int isl_union_map_compute_flow(__isl_take isl_union_map *sink,
5410 __isl_take isl_union_map *must_source,
5411 __isl_take isl_union_map *may_source,
5412 __isl_take isl_union_map *schedule,
5413 __isl_give isl_union_map **must_dep,
5414 __isl_give isl_union_map **may_dep,
5415 __isl_give isl_union_map **must_no_source,
5416 __isl_give isl_union_map **may_no_source);
5418 The arrays are identified by the tuple names of the ranges
5419 of the accesses. The iteration domains by the tuple names
5420 of the domains of the accesses and of the schedule.
5421 The relative order of the iteration domains is given by the
5422 schedule. The relations returned through C<must_no_source>
5423 and C<may_no_source> are subsets of C<sink>.
5424 Any of C<must_dep>, C<may_dep>, C<must_no_source>
5425 or C<may_no_source> may be C<NULL>, but a C<NULL> value for
5426 any of the other arguments is treated as an error.
5428 =head3 Interaction with Dependence Analysis
5430 During the dependence analysis, we frequently need to perform
5431 the following operation. Given a relation between sink iterations
5432 and potential source iterations from a particular source domain,
5433 what is the last potential source iteration corresponding to each
5434 sink iteration. It can sometimes be convenient to adjust
5435 the set of potential source iterations before or after each such operation.
5436 The prototypical example is fuzzy array dataflow analysis,
5437 where we need to analyze if, based on data-dependent constraints,
5438 the sink iteration can ever be executed without one or more of
5439 the corresponding potential source iterations being executed.
5440 If so, we can introduce extra parameters and select an unknown
5441 but fixed source iteration from the potential source iterations.
5442 To be able to perform such manipulations, C<isl> provides the following
5445 #include <isl/flow.h>
5447 typedef __isl_give isl_restriction *(*isl_access_restrict)(
5448 __isl_keep isl_map *source_map,
5449 __isl_keep isl_set *sink, void *source_user,
5451 __isl_give isl_access_info *isl_access_info_set_restrict(
5452 __isl_take isl_access_info *acc,
5453 isl_access_restrict fn, void *user);
5455 The function C<isl_access_info_set_restrict> should be called
5456 before calling C<isl_access_info_compute_flow> and registers a callback function
5457 that will be called any time C<isl> is about to compute the last
5458 potential source. The first argument is the (reverse) proto-dependence,
5459 mapping sink iterations to potential source iterations.
5460 The second argument represents the sink iterations for which
5461 we want to compute the last source iteration.
5462 The third argument is the token corresponding to the source
5463 and the final argument is the token passed to C<isl_access_info_set_restrict>.
5464 The callback is expected to return a restriction on either the input or
5465 the output of the operation computing the last potential source.
5466 If the input needs to be restricted then restrictions are needed
5467 for both the source and the sink iterations. The sink iterations
5468 and the potential source iterations will be intersected with these sets.
5469 If the output needs to be restricted then only a restriction on the source
5470 iterations is required.
5471 If any error occurs, the callback should return C<NULL>.
5472 An C<isl_restriction> object can be created, freed and inspected
5473 using the following functions.
5475 #include <isl/flow.h>
5477 __isl_give isl_restriction *isl_restriction_input(
5478 __isl_take isl_set *source_restr,
5479 __isl_take isl_set *sink_restr);
5480 __isl_give isl_restriction *isl_restriction_output(
5481 __isl_take isl_set *source_restr);
5482 __isl_give isl_restriction *isl_restriction_none(
5483 __isl_take isl_map *source_map);
5484 __isl_give isl_restriction *isl_restriction_empty(
5485 __isl_take isl_map *source_map);
5486 void *isl_restriction_free(
5487 __isl_take isl_restriction *restr);
5488 isl_ctx *isl_restriction_get_ctx(
5489 __isl_keep isl_restriction *restr);
5491 C<isl_restriction_none> and C<isl_restriction_empty> are special
5492 cases of C<isl_restriction_input>. C<isl_restriction_none>
5493 is essentially equivalent to
5495 isl_restriction_input(isl_set_universe(
5496 isl_space_range(isl_map_get_space(source_map))),
5498 isl_space_domain(isl_map_get_space(source_map))));
5500 whereas C<isl_restriction_empty> is essentially equivalent to
5502 isl_restriction_input(isl_set_empty(
5503 isl_space_range(isl_map_get_space(source_map))),
5505 isl_space_domain(isl_map_get_space(source_map))));
5509 B<The functionality described in this section is fairly new
5510 and may be subject to change.>
5512 The following function can be used to compute a schedule
5513 for a union of domains.
5514 By default, the algorithm used to construct the schedule is similar
5515 to that of C<Pluto>.
5516 Alternatively, Feautrier's multi-dimensional scheduling algorithm can
5518 The generated schedule respects all C<validity> dependences.
5519 That is, all dependence distances over these dependences in the
5520 scheduled space are lexicographically positive.
5521 The default algorithm tries to minimize the dependence distances over
5522 C<proximity> dependences.
5523 Moreover, it tries to obtain sequences (bands) of schedule dimensions
5524 for groups of domains where the dependence distances have only
5525 non-negative values.
5526 When using Feautrier's algorithm, the C<proximity> dependence
5527 distances are only minimized during the extension to a
5528 full-dimensional schedule.
5530 #include <isl/schedule.h>
5531 __isl_give isl_schedule *isl_union_set_compute_schedule(
5532 __isl_take isl_union_set *domain,
5533 __isl_take isl_union_map *validity,
5534 __isl_take isl_union_map *proximity);
5535 void *isl_schedule_free(__isl_take isl_schedule *sched);
5537 A mapping from the domains to the scheduled space can be obtained
5538 from an C<isl_schedule> using the following function.
5540 __isl_give isl_union_map *isl_schedule_get_map(
5541 __isl_keep isl_schedule *sched);
5543 A representation of the schedule can be printed using
5545 __isl_give isl_printer *isl_printer_print_schedule(
5546 __isl_take isl_printer *p,
5547 __isl_keep isl_schedule *schedule);
5549 A representation of the schedule as a forest of bands can be obtained
5550 using the following function.
5552 __isl_give isl_band_list *isl_schedule_get_band_forest(
5553 __isl_keep isl_schedule *schedule);
5555 The individual bands can be visited in depth-first post-order
5556 using the following function.
5558 #include <isl/schedule.h>
5559 int isl_schedule_foreach_band(
5560 __isl_keep isl_schedule *sched,
5561 int (*fn)(__isl_keep isl_band *band, void *user),
5564 The list can be manipulated as explained in L<"Lists">.
5565 The bands inside the list can be copied and freed using the following
5568 #include <isl/band.h>
5569 __isl_give isl_band *isl_band_copy(
5570 __isl_keep isl_band *band);
5571 void *isl_band_free(__isl_take isl_band *band);
5573 Each band contains zero or more scheduling dimensions.
5574 These are referred to as the members of the band.
5575 The section of the schedule that corresponds to the band is
5576 referred to as the partial schedule of the band.
5577 For those nodes that participate in a band, the outer scheduling
5578 dimensions form the prefix schedule, while the inner scheduling
5579 dimensions form the suffix schedule.
5580 That is, if we take a cut of the band forest, then the union of
5581 the concatenations of the prefix, partial and suffix schedules of
5582 each band in the cut is equal to the entire schedule (modulo
5583 some possible padding at the end with zero scheduling dimensions).
5584 The properties of a band can be inspected using the following functions.
5586 #include <isl/band.h>
5587 isl_ctx *isl_band_get_ctx(__isl_keep isl_band *band);
5589 int isl_band_has_children(__isl_keep isl_band *band);
5590 __isl_give isl_band_list *isl_band_get_children(
5591 __isl_keep isl_band *band);
5593 __isl_give isl_union_map *isl_band_get_prefix_schedule(
5594 __isl_keep isl_band *band);
5595 __isl_give isl_union_map *isl_band_get_partial_schedule(
5596 __isl_keep isl_band *band);
5597 __isl_give isl_union_map *isl_band_get_suffix_schedule(
5598 __isl_keep isl_band *band);
5600 int isl_band_n_member(__isl_keep isl_band *band);
5601 int isl_band_member_is_zero_distance(
5602 __isl_keep isl_band *band, int pos);
5604 int isl_band_list_foreach_band(
5605 __isl_keep isl_band_list *list,
5606 int (*fn)(__isl_keep isl_band *band, void *user),
5609 Note that a scheduling dimension is considered to be ``zero
5610 distance'' if it does not carry any proximity dependences
5612 That is, if the dependence distances of the proximity
5613 dependences are all zero in that direction (for fixed
5614 iterations of outer bands).
5615 Like C<isl_schedule_foreach_band>,
5616 the function C<isl_band_list_foreach_band> calls C<fn> on the bands
5617 in depth-first post-order.
5619 A band can be tiled using the following function.
5621 #include <isl/band.h>
5622 int isl_band_tile(__isl_keep isl_band *band,
5623 __isl_take isl_vec *sizes);
5625 int isl_options_set_tile_scale_tile_loops(isl_ctx *ctx,
5627 int isl_options_get_tile_scale_tile_loops(isl_ctx *ctx);
5628 int isl_options_set_tile_shift_point_loops(isl_ctx *ctx,
5630 int isl_options_get_tile_shift_point_loops(isl_ctx *ctx);
5632 The C<isl_band_tile> function tiles the band using the given tile sizes
5633 inside its schedule.
5634 A new child band is created to represent the point loops and it is
5635 inserted between the modified band and its children.
5636 The C<tile_scale_tile_loops> option specifies whether the tile
5637 loops iterators should be scaled by the tile sizes.
5638 If the C<tile_shift_point_loops> option is set, then the point loops
5639 are shifted to start at zero.
5641 A band can be split into two nested bands using the following function.
5643 int isl_band_split(__isl_keep isl_band *band, int pos);
5645 The resulting outer band contains the first C<pos> dimensions of C<band>
5646 while the inner band contains the remaining dimensions.
5648 A representation of the band can be printed using
5650 #include <isl/band.h>
5651 __isl_give isl_printer *isl_printer_print_band(
5652 __isl_take isl_printer *p,
5653 __isl_keep isl_band *band);
5657 #include <isl/schedule.h>
5658 int isl_options_set_schedule_max_coefficient(
5659 isl_ctx *ctx, int val);
5660 int isl_options_get_schedule_max_coefficient(
5662 int isl_options_set_schedule_max_constant_term(
5663 isl_ctx *ctx, int val);
5664 int isl_options_get_schedule_max_constant_term(
5666 int isl_options_set_schedule_fuse(isl_ctx *ctx, int val);
5667 int isl_options_get_schedule_fuse(isl_ctx *ctx);
5668 int isl_options_set_schedule_maximize_band_depth(
5669 isl_ctx *ctx, int val);
5670 int isl_options_get_schedule_maximize_band_depth(
5672 int isl_options_set_schedule_outer_zero_distance(
5673 isl_ctx *ctx, int val);
5674 int isl_options_get_schedule_outer_zero_distance(
5676 int isl_options_set_schedule_split_scaled(
5677 isl_ctx *ctx, int val);
5678 int isl_options_get_schedule_split_scaled(
5680 int isl_options_set_schedule_algorithm(
5681 isl_ctx *ctx, int val);
5682 int isl_options_get_schedule_algorithm(
5684 int isl_options_set_schedule_separate_components(
5685 isl_ctx *ctx, int val);
5686 int isl_options_get_schedule_separate_components(
5691 =item * schedule_max_coefficient
5693 This option enforces that the coefficients for variable and parameter
5694 dimensions in the calculated schedule are not larger than the specified value.
5695 This option can significantly increase the speed of the scheduling calculation
5696 and may also prevent fusing of unrelated dimensions. A value of -1 means that
5697 this option does not introduce bounds on the variable or parameter
5700 =item * schedule_max_constant_term
5702 This option enforces that the constant coefficients in the calculated schedule
5703 are not larger than the maximal constant term. This option can significantly
5704 increase the speed of the scheduling calculation and may also prevent fusing of
5705 unrelated dimensions. A value of -1 means that this option does not introduce
5706 bounds on the constant coefficients.
5708 =item * schedule_fuse
5710 This option controls the level of fusion.
5711 If this option is set to C<ISL_SCHEDULE_FUSE_MIN>, then loops in the
5712 resulting schedule will be distributed as much as possible.
5713 If this option is set to C<ISL_SCHEDULE_FUSE_MAX>, then C<isl> will
5714 try to fuse loops in the resulting schedule.
5716 =item * schedule_maximize_band_depth
5718 If this option is set, we do not split bands at the point
5719 where we detect splitting is necessary. Instead, we
5720 backtrack and split bands as early as possible. This
5721 reduces the number of splits and maximizes the width of
5722 the bands. Wider bands give more possibilities for tiling.
5723 Note that if the C<schedule_fuse> option is set to C<ISL_SCHEDULE_FUSE_MIN>,
5724 then bands will be split as early as possible, even if there is no need.
5725 The C<schedule_maximize_band_depth> option therefore has no effect in this case.
5727 =item * schedule_outer_zero_distance
5729 If this option is set, then we try to construct schedules
5730 where the outermost scheduling dimension in each band
5731 results in a zero dependence distance over the proximity
5734 =item * schedule_split_scaled
5736 If this option is set, then we try to construct schedules in which the
5737 constant term is split off from the linear part if the linear parts of
5738 the scheduling rows for all nodes in the graphs have a common non-trivial
5740 The constant term is then placed in a separate band and the linear
5743 =item * schedule_algorithm
5745 Selects the scheduling algorithm to be used.
5746 Available scheduling algorithms are C<ISL_SCHEDULE_ALGORITHM_ISL>
5747 and C<ISL_SCHEDULE_ALGORITHM_FEAUTRIER>.
5749 =item * schedule_separate_components
5751 If at any point the dependence graph contains any (weakly connected) components,
5752 then these components are scheduled separately.
5753 If this option is not set, then some iterations of the domains
5754 in these components may be scheduled together.
5755 If this option is set, then the components are given consecutive
5760 =head2 AST Generation
5762 This section describes the C<isl> functionality for generating
5763 ASTs that visit all the elements
5764 in a domain in an order specified by a schedule.
5765 In particular, given a C<isl_union_map>, an AST is generated
5766 that visits all the elements in the domain of the C<isl_union_map>
5767 according to the lexicographic order of the corresponding image
5768 element(s). If the range of the C<isl_union_map> consists of
5769 elements in more than one space, then each of these spaces is handled
5770 separately in an arbitrary order.
5771 It should be noted that the image elements only specify the I<order>
5772 in which the corresponding domain elements should be visited.
5773 No direct relation between the image elements and the loop iterators
5774 in the generated AST should be assumed.
5776 Each AST is generated within a build. The initial build
5777 simply specifies the constraints on the parameters (if any)
5778 and can be created, inspected, copied and freed using the following functions.
5780 #include <isl/ast_build.h>
5781 __isl_give isl_ast_build *isl_ast_build_from_context(
5782 __isl_take isl_set *set);
5783 isl_ctx *isl_ast_build_get_ctx(
5784 __isl_keep isl_ast_build *build);
5785 __isl_give isl_ast_build *isl_ast_build_copy(
5786 __isl_keep isl_ast_build *build);
5787 void *isl_ast_build_free(
5788 __isl_take isl_ast_build *build);
5790 The C<set> argument is usually a parameter set with zero or more parameters.
5791 More C<isl_ast_build> functions are described in L</"Nested AST Generation">
5792 and L</"Fine-grained Control over AST Generation">.
5793 Finally, the AST itself can be constructed using the following
5796 #include <isl/ast_build.h>
5797 __isl_give isl_ast_node *isl_ast_build_ast_from_schedule(
5798 __isl_keep isl_ast_build *build,
5799 __isl_take isl_union_map *schedule);
5801 =head3 Inspecting the AST
5803 The basic properties of an AST node can be obtained as follows.
5805 #include <isl/ast.h>
5806 isl_ctx *isl_ast_node_get_ctx(
5807 __isl_keep isl_ast_node *node);
5808 enum isl_ast_node_type isl_ast_node_get_type(
5809 __isl_keep isl_ast_node *node);
5811 The type of an AST node is one of
5812 C<isl_ast_node_for>,
5814 C<isl_ast_node_block> or
5815 C<isl_ast_node_user>.
5816 An C<isl_ast_node_for> represents a for node.
5817 An C<isl_ast_node_if> represents an if node.
5818 An C<isl_ast_node_block> represents a compound node.
5819 An C<isl_ast_node_user> represents an expression statement.
5820 An expression statement typically corresponds to a domain element, i.e.,
5821 one of the elements that is visited by the AST.
5823 Each type of node has its own additional properties.
5825 #include <isl/ast.h>
5826 __isl_give isl_ast_expr *isl_ast_node_for_get_iterator(
5827 __isl_keep isl_ast_node *node);
5828 __isl_give isl_ast_expr *isl_ast_node_for_get_init(
5829 __isl_keep isl_ast_node *node);
5830 __isl_give isl_ast_expr *isl_ast_node_for_get_cond(
5831 __isl_keep isl_ast_node *node);
5832 __isl_give isl_ast_expr *isl_ast_node_for_get_inc(
5833 __isl_keep isl_ast_node *node);
5834 __isl_give isl_ast_node *isl_ast_node_for_get_body(
5835 __isl_keep isl_ast_node *node);
5836 int isl_ast_node_for_is_degenerate(
5837 __isl_keep isl_ast_node *node);
5839 An C<isl_ast_for> is considered degenerate if it is known to execute
5842 #include <isl/ast.h>
5843 __isl_give isl_ast_expr *isl_ast_node_if_get_cond(
5844 __isl_keep isl_ast_node *node);
5845 __isl_give isl_ast_node *isl_ast_node_if_get_then(
5846 __isl_keep isl_ast_node *node);
5847 int isl_ast_node_if_has_else(
5848 __isl_keep isl_ast_node *node);
5849 __isl_give isl_ast_node *isl_ast_node_if_get_else(
5850 __isl_keep isl_ast_node *node);
5852 __isl_give isl_ast_node_list *
5853 isl_ast_node_block_get_children(
5854 __isl_keep isl_ast_node *node);
5856 __isl_give isl_ast_expr *isl_ast_node_user_get_expr(
5857 __isl_keep isl_ast_node *node);
5859 Each of the returned C<isl_ast_expr>s can in turn be inspected using
5860 the following functions.
5862 #include <isl/ast.h>
5863 isl_ctx *isl_ast_expr_get_ctx(
5864 __isl_keep isl_ast_expr *expr);
5865 enum isl_ast_expr_type isl_ast_expr_get_type(
5866 __isl_keep isl_ast_expr *expr);
5868 The type of an AST expression is one of
5870 C<isl_ast_expr_id> or
5871 C<isl_ast_expr_int>.
5872 An C<isl_ast_expr_op> represents the result of an operation.
5873 An C<isl_ast_expr_id> represents an identifier.
5874 An C<isl_ast_expr_int> represents an integer value.
5876 Each type of expression has its own additional properties.
5878 #include <isl/ast.h>
5879 enum isl_ast_op_type isl_ast_expr_get_op_type(
5880 __isl_keep isl_ast_expr *expr);
5881 int isl_ast_expr_get_op_n_arg(__isl_keep isl_ast_expr *expr);
5882 __isl_give isl_ast_expr *isl_ast_expr_get_op_arg(
5883 __isl_keep isl_ast_expr *expr, int pos);
5884 int isl_ast_node_foreach_ast_op_type(
5885 __isl_keep isl_ast_node *node,
5886 int (*fn)(enum isl_ast_op_type type, void *user),
5889 C<isl_ast_expr_get_op_type> returns the type of the operation
5890 performed. C<isl_ast_expr_get_op_n_arg> returns the number of
5891 arguments. C<isl_ast_expr_get_op_arg> returns the specified
5893 C<isl_ast_node_foreach_ast_op_type> calls C<fn> for each distinct
5894 C<isl_ast_op_type> that appears in C<node>.
5895 The operation type is one of the following.
5899 =item C<isl_ast_op_and>
5901 Logical I<and> of two arguments.
5902 Both arguments can be evaluated.
5904 =item C<isl_ast_op_and_then>
5906 Logical I<and> of two arguments.
5907 The second argument can only be evaluated if the first evaluates to true.
5909 =item C<isl_ast_op_or>
5911 Logical I<or> of two arguments.
5912 Both arguments can be evaluated.
5914 =item C<isl_ast_op_or_else>
5916 Logical I<or> of two arguments.
5917 The second argument can only be evaluated if the first evaluates to false.
5919 =item C<isl_ast_op_max>
5921 Maximum of two or more arguments.
5923 =item C<isl_ast_op_min>
5925 Minimum of two or more arguments.
5927 =item C<isl_ast_op_minus>
5931 =item C<isl_ast_op_add>
5933 Sum of two arguments.
5935 =item C<isl_ast_op_sub>
5937 Difference of two arguments.
5939 =item C<isl_ast_op_mul>
5941 Product of two arguments.
5943 =item C<isl_ast_op_div>
5945 Exact division. That is, the result is known to be an integer.
5947 =item C<isl_ast_op_fdiv_q>
5949 Result of integer division, rounded towards negative
5952 =item C<isl_ast_op_pdiv_q>
5954 Result of integer division, where dividend is known to be non-negative.
5956 =item C<isl_ast_op_pdiv_r>
5958 Remainder of integer division, where dividend is known to be non-negative.
5960 =item C<isl_ast_op_cond>
5962 Conditional operator defined on three arguments.
5963 If the first argument evaluates to true, then the result
5964 is equal to the second argument. Otherwise, the result
5965 is equal to the third argument.
5966 The second and third argument may only be evaluated if
5967 the first argument evaluates to true and false, respectively.
5968 Corresponds to C<a ? b : c> in C.
5970 =item C<isl_ast_op_select>
5972 Conditional operator defined on three arguments.
5973 If the first argument evaluates to true, then the result
5974 is equal to the second argument. Otherwise, the result
5975 is equal to the third argument.
5976 The second and third argument may be evaluated independently
5977 of the value of the first argument.
5978 Corresponds to C<a * b + (1 - a) * c> in C.
5980 =item C<isl_ast_op_eq>
5984 =item C<isl_ast_op_le>
5986 Less than or equal relation.
5988 =item C<isl_ast_op_lt>
5992 =item C<isl_ast_op_ge>
5994 Greater than or equal relation.
5996 =item C<isl_ast_op_gt>
5998 Greater than relation.
6000 =item C<isl_ast_op_call>
6003 The number of arguments of the C<isl_ast_expr> is one more than
6004 the number of arguments in the function call, the first argument
6005 representing the function being called.
6009 #include <isl/ast.h>
6010 __isl_give isl_id *isl_ast_expr_get_id(
6011 __isl_keep isl_ast_expr *expr);
6013 Return the identifier represented by the AST expression.
6015 #include <isl/ast.h>
6016 int isl_ast_expr_get_int(__isl_keep isl_ast_expr *expr,
6018 __isl_give isl_val *isl_ast_expr_get_val(
6019 __isl_keep isl_ast_expr *expr);
6021 Return the integer represented by the AST expression.
6022 Note that the integer is returned by C<isl_ast_expr_get_int>
6023 through the C<v> argument.
6024 The return value of this function itself indicates whether the
6025 operation was performed successfully.
6027 =head3 Manipulating and printing the AST
6029 AST nodes can be copied and freed using the following functions.
6031 #include <isl/ast.h>
6032 __isl_give isl_ast_node *isl_ast_node_copy(
6033 __isl_keep isl_ast_node *node);
6034 void *isl_ast_node_free(__isl_take isl_ast_node *node);
6036 AST expressions can be copied and freed using the following functions.
6038 #include <isl/ast.h>
6039 __isl_give isl_ast_expr *isl_ast_expr_copy(
6040 __isl_keep isl_ast_expr *expr);
6041 void *isl_ast_expr_free(__isl_take isl_ast_expr *expr);
6043 New AST expressions can be created either directly or within
6044 the context of an C<isl_ast_build>.
6046 #include <isl/ast.h>
6047 __isl_give isl_ast_expr *isl_ast_expr_from_val(
6048 __isl_take isl_val *v);
6049 __isl_give isl_ast_expr *isl_ast_expr_from_id(
6050 __isl_take isl_id *id);
6051 __isl_give isl_ast_expr *isl_ast_expr_neg(
6052 __isl_take isl_ast_expr *expr);
6053 __isl_give isl_ast_expr *isl_ast_expr_add(
6054 __isl_take isl_ast_expr *expr1,
6055 __isl_take isl_ast_expr *expr2);
6056 __isl_give isl_ast_expr *isl_ast_expr_sub(
6057 __isl_take isl_ast_expr *expr1,
6058 __isl_take isl_ast_expr *expr2);
6059 __isl_give isl_ast_expr *isl_ast_expr_mul(
6060 __isl_take isl_ast_expr *expr1,
6061 __isl_take isl_ast_expr *expr2);
6062 __isl_give isl_ast_expr *isl_ast_expr_div(
6063 __isl_take isl_ast_expr *expr1,
6064 __isl_take isl_ast_expr *expr2);
6065 __isl_give isl_ast_expr *isl_ast_expr_and(
6066 __isl_take isl_ast_expr *expr1,
6067 __isl_take isl_ast_expr *expr2)
6068 __isl_give isl_ast_expr *isl_ast_expr_or(
6069 __isl_take isl_ast_expr *expr1,
6070 __isl_take isl_ast_expr *expr2)
6072 #include <isl/ast_build.h>
6073 __isl_give isl_ast_expr *isl_ast_build_expr_from_pw_aff(
6074 __isl_keep isl_ast_build *build,
6075 __isl_take isl_pw_aff *pa);
6076 __isl_give isl_ast_expr *
6077 isl_ast_build_call_from_pw_multi_aff(
6078 __isl_keep isl_ast_build *build,
6079 __isl_take isl_pw_multi_aff *pma);
6081 The domains of C<pa> and C<pma> should correspond
6082 to the schedule space of C<build>.
6083 The tuple id of C<pma> is used as the function being called.
6085 User specified data can be attached to an C<isl_ast_node> and obtained
6086 from the same C<isl_ast_node> using the following functions.
6088 #include <isl/ast.h>
6089 __isl_give isl_ast_node *isl_ast_node_set_annotation(
6090 __isl_take isl_ast_node *node,
6091 __isl_take isl_id *annotation);
6092 __isl_give isl_id *isl_ast_node_get_annotation(
6093 __isl_keep isl_ast_node *node);
6095 Basic printing can be performed using the following functions.
6097 #include <isl/ast.h>
6098 __isl_give isl_printer *isl_printer_print_ast_expr(
6099 __isl_take isl_printer *p,
6100 __isl_keep isl_ast_expr *expr);
6101 __isl_give isl_printer *isl_printer_print_ast_node(
6102 __isl_take isl_printer *p,
6103 __isl_keep isl_ast_node *node);
6105 More advanced printing can be performed using the following functions.
6107 #include <isl/ast.h>
6108 __isl_give isl_printer *isl_ast_op_type_print_macro(
6109 enum isl_ast_op_type type,
6110 __isl_take isl_printer *p);
6111 __isl_give isl_printer *isl_ast_node_print_macros(
6112 __isl_keep isl_ast_node *node,
6113 __isl_take isl_printer *p);
6114 __isl_give isl_printer *isl_ast_node_print(
6115 __isl_keep isl_ast_node *node,
6116 __isl_take isl_printer *p,
6117 __isl_take isl_ast_print_options *options);
6118 __isl_give isl_printer *isl_ast_node_for_print(
6119 __isl_keep isl_ast_node *node,
6120 __isl_take isl_printer *p,
6121 __isl_take isl_ast_print_options *options);
6122 __isl_give isl_printer *isl_ast_node_if_print(
6123 __isl_keep isl_ast_node *node,
6124 __isl_take isl_printer *p,
6125 __isl_take isl_ast_print_options *options);
6127 While printing an C<isl_ast_node> in C<ISL_FORMAT_C>,
6128 C<isl> may print out an AST that makes use of macros such
6129 as C<floord>, C<min> and C<max>.
6130 C<isl_ast_op_type_print_macro> prints out the macro
6131 corresponding to a specific C<isl_ast_op_type>.
6132 C<isl_ast_node_print_macros> scans the C<isl_ast_node>
6133 for expressions where these macros would be used and prints
6134 out the required macro definitions.
6135 Essentially, C<isl_ast_node_print_macros> calls
6136 C<isl_ast_node_foreach_ast_op_type> with C<isl_ast_op_type_print_macro>
6137 as function argument.
6138 C<isl_ast_node_print>, C<isl_ast_node_for_print> and
6139 C<isl_ast_node_if_print> print an C<isl_ast_node>
6140 in C<ISL_FORMAT_C>, but allow for some extra control
6141 through an C<isl_ast_print_options> object.
6142 This object can be created using the following functions.
6144 #include <isl/ast.h>
6145 __isl_give isl_ast_print_options *
6146 isl_ast_print_options_alloc(isl_ctx *ctx);
6147 __isl_give isl_ast_print_options *
6148 isl_ast_print_options_copy(
6149 __isl_keep isl_ast_print_options *options);
6150 void *isl_ast_print_options_free(
6151 __isl_take isl_ast_print_options *options);
6153 __isl_give isl_ast_print_options *
6154 isl_ast_print_options_set_print_user(
6155 __isl_take isl_ast_print_options *options,
6156 __isl_give isl_printer *(*print_user)(
6157 __isl_take isl_printer *p,
6158 __isl_take isl_ast_print_options *options,
6159 __isl_keep isl_ast_node *node, void *user),
6161 __isl_give isl_ast_print_options *
6162 isl_ast_print_options_set_print_for(
6163 __isl_take isl_ast_print_options *options,
6164 __isl_give isl_printer *(*print_for)(
6165 __isl_take isl_printer *p,
6166 __isl_take isl_ast_print_options *options,
6167 __isl_keep isl_ast_node *node, void *user),
6170 The callback set by C<isl_ast_print_options_set_print_user>
6171 is called whenever a node of type C<isl_ast_node_user> needs to
6173 The callback set by C<isl_ast_print_options_set_print_for>
6174 is called whenever a node of type C<isl_ast_node_for> needs to
6176 Note that C<isl_ast_node_for_print> will I<not> call the
6177 callback set by C<isl_ast_print_options_set_print_for> on the node
6178 on which C<isl_ast_node_for_print> is called, but only on nested
6179 nodes of type C<isl_ast_node_for>. It is therefore safe to
6180 call C<isl_ast_node_for_print> from within the callback set by
6181 C<isl_ast_print_options_set_print_for>.
6183 The following option determines the type to be used for iterators
6184 while printing the AST.
6186 int isl_options_set_ast_iterator_type(
6187 isl_ctx *ctx, const char *val);
6188 const char *isl_options_get_ast_iterator_type(
6193 #include <isl/ast_build.h>
6194 int isl_options_set_ast_build_atomic_upper_bound(
6195 isl_ctx *ctx, int val);
6196 int isl_options_get_ast_build_atomic_upper_bound(
6198 int isl_options_set_ast_build_prefer_pdiv(isl_ctx *ctx,
6200 int isl_options_get_ast_build_prefer_pdiv(isl_ctx *ctx);
6201 int isl_options_set_ast_build_exploit_nested_bounds(
6202 isl_ctx *ctx, int val);
6203 int isl_options_get_ast_build_exploit_nested_bounds(
6205 int isl_options_set_ast_build_group_coscheduled(
6206 isl_ctx *ctx, int val);
6207 int isl_options_get_ast_build_group_coscheduled(
6209 int isl_options_set_ast_build_scale_strides(
6210 isl_ctx *ctx, int val);
6211 int isl_options_get_ast_build_scale_strides(
6213 int isl_options_set_ast_build_allow_else(isl_ctx *ctx,
6215 int isl_options_get_ast_build_allow_else(isl_ctx *ctx);
6216 int isl_options_set_ast_build_allow_or(isl_ctx *ctx,
6218 int isl_options_get_ast_build_allow_or(isl_ctx *ctx);
6222 =item * ast_build_atomic_upper_bound
6224 Generate loop upper bounds that consist of the current loop iterator,
6225 an operator and an expression not involving the iterator.
6226 If this option is not set, then the current loop iterator may appear
6227 several times in the upper bound.
6228 For example, when this option is turned off, AST generation
6231 [n] -> { A[i] -> [i] : 0 <= i <= 100, n }
6235 for (int c0 = 0; c0 <= 100 && n >= c0; c0 += 1)
6238 When the option is turned on, the following AST is generated
6240 for (int c0 = 0; c0 <= min(100, n); c0 += 1)
6243 =item * ast_build_prefer_pdiv
6245 If this option is turned off, then the AST generation will
6246 produce ASTs that may only contain C<isl_ast_op_fdiv_q>
6247 operators, but no C<isl_ast_op_pdiv_q> or
6248 C<isl_ast_op_pdiv_r> operators.
6249 If this options is turned on, then C<isl> will try to convert
6250 some of the C<isl_ast_op_fdiv_q> operators to (expressions containing)
6251 C<isl_ast_op_pdiv_q> or C<isl_ast_op_pdiv_r> operators.
6253 =item * ast_build_exploit_nested_bounds
6255 Simplify conditions based on bounds of nested for loops.
6256 In particular, remove conditions that are implied by the fact
6257 that one or more nested loops have at least one iteration,
6258 meaning that the upper bound is at least as large as the lower bound.
6259 For example, when this option is turned off, AST generation
6262 [N,M] -> { A[i,j] -> [i,j] : 0 <= i <= N and
6268 for (int c0 = 0; c0 <= N; c0 += 1)
6269 for (int c1 = 0; c1 <= M; c1 += 1)
6272 When the option is turned on, the following AST is generated
6274 for (int c0 = 0; c0 <= N; c0 += 1)
6275 for (int c1 = 0; c1 <= M; c1 += 1)
6278 =item * ast_build_group_coscheduled
6280 If two domain elements are assigned the same schedule point, then
6281 they may be executed in any order and they may even appear in different
6282 loops. If this options is set, then the AST generator will make
6283 sure that coscheduled domain elements do not appear in separate parts
6284 of the AST. This is useful in case of nested AST generation
6285 if the outer AST generation is given only part of a schedule
6286 and the inner AST generation should handle the domains that are
6287 coscheduled by this initial part of the schedule together.
6288 For example if an AST is generated for a schedule
6290 { A[i] -> [0]; B[i] -> [0] }
6292 then the C<isl_ast_build_set_create_leaf> callback described
6293 below may get called twice, once for each domain.
6294 Setting this option ensures that the callback is only called once
6295 on both domains together.
6297 =item * ast_build_separation_bounds
6299 This option specifies which bounds to use during separation.
6300 If this option is set to C<ISL_AST_BUILD_SEPARATION_BOUNDS_IMPLICIT>
6301 then all (possibly implicit) bounds on the current dimension will
6302 be used during separation.
6303 If this option is set to C<ISL_AST_BUILD_SEPARATION_BOUNDS_EXPLICIT>
6304 then only those bounds that are explicitly available will
6305 be used during separation.
6307 =item * ast_build_scale_strides
6309 This option specifies whether the AST generator is allowed
6310 to scale down iterators of strided loops.
6312 =item * ast_build_allow_else
6314 This option specifies whether the AST generator is allowed
6315 to construct if statements with else branches.
6317 =item * ast_build_allow_or
6319 This option specifies whether the AST generator is allowed
6320 to construct if conditions with disjunctions.
6324 =head3 Fine-grained Control over AST Generation
6326 Besides specifying the constraints on the parameters,
6327 an C<isl_ast_build> object can be used to control
6328 various aspects of the AST generation process.
6329 The most prominent way of control is through ``options'',
6330 which can be set using the following function.
6332 #include <isl/ast_build.h>
6333 __isl_give isl_ast_build *
6334 isl_ast_build_set_options(
6335 __isl_take isl_ast_build *control,
6336 __isl_take isl_union_map *options);
6338 The options are encoded in an <isl_union_map>.
6339 The domain of this union relation refers to the schedule domain,
6340 i.e., the range of the schedule passed to C<isl_ast_build_ast_from_schedule>.
6341 In the case of nested AST generation (see L</"Nested AST Generation">),
6342 the domain of C<options> should refer to the extra piece of the schedule.
6343 That is, it should be equal to the range of the wrapped relation in the
6344 range of the schedule.
6345 The range of the options can consist of elements in one or more spaces,
6346 the names of which determine the effect of the option.
6347 The values of the range typically also refer to the schedule dimension
6348 to which the option applies. In case of nested AST generation
6349 (see L</"Nested AST Generation">), these values refer to the position
6350 of the schedule dimension within the innermost AST generation.
6351 The constraints on the domain elements of
6352 the option should only refer to this dimension and earlier dimensions.
6353 We consider the following spaces.
6357 =item C<separation_class>
6359 This space is a wrapped relation between two one dimensional spaces.
6360 The input space represents the schedule dimension to which the option
6361 applies and the output space represents the separation class.
6362 While constructing a loop corresponding to the specified schedule
6363 dimension(s), the AST generator will try to generate separate loops
6364 for domain elements that are assigned different classes.
6365 If only some of the elements are assigned a class, then those elements
6366 that are not assigned any class will be treated as belonging to a class
6367 that is separate from the explicitly assigned classes.
6368 The typical use case for this option is to separate full tiles from
6370 The other options, described below, are applied after the separation
6373 As an example, consider the separation into full and partial tiles
6374 of a tiling of a triangular domain.
6375 Take, for example, the domain
6377 { A[i,j] : 0 <= i,j and i + j <= 100 }
6379 and a tiling into tiles of 10 by 10. The input to the AST generator
6380 is then the schedule
6382 { A[i,j] -> [([i/10]),[j/10],i,j] : 0 <= i,j and
6385 Without any options, the following AST is generated
6387 for (int c0 = 0; c0 <= 10; c0 += 1)
6388 for (int c1 = 0; c1 <= -c0 + 10; c1 += 1)
6389 for (int c2 = 10 * c0;
6390 c2 <= min(-10 * c1 + 100, 10 * c0 + 9);
6392 for (int c3 = 10 * c1;
6393 c3 <= min(10 * c1 + 9, -c2 + 100);
6397 Separation into full and partial tiles can be obtained by assigning
6398 a class, say C<0>, to the full tiles. The full tiles are represented by those
6399 values of the first and second schedule dimensions for which there are
6400 values of the third and fourth dimensions to cover an entire tile.
6401 That is, we need to specify the following option
6403 { [a,b,c,d] -> separation_class[[0]->[0]] :
6404 exists b': 0 <= 10a,10b' and
6405 10a+9+10b'+9 <= 100;
6406 [a,b,c,d] -> separation_class[[1]->[0]] :
6407 0 <= 10a,10b and 10a+9+10b+9 <= 100 }
6411 { [a, b, c, d] -> separation_class[[1] -> [0]] :
6412 a >= 0 and b >= 0 and b <= 8 - a;
6413 [a, b, c, d] -> separation_class[[0] -> [0]] :
6416 With this option, the generated AST is as follows
6419 for (int c0 = 0; c0 <= 8; c0 += 1) {
6420 for (int c1 = 0; c1 <= -c0 + 8; c1 += 1)
6421 for (int c2 = 10 * c0;
6422 c2 <= 10 * c0 + 9; c2 += 1)
6423 for (int c3 = 10 * c1;
6424 c3 <= 10 * c1 + 9; c3 += 1)
6426 for (int c1 = -c0 + 9; c1 <= -c0 + 10; c1 += 1)
6427 for (int c2 = 10 * c0;
6428 c2 <= min(-10 * c1 + 100, 10 * c0 + 9);
6430 for (int c3 = 10 * c1;
6431 c3 <= min(-c2 + 100, 10 * c1 + 9);
6435 for (int c0 = 9; c0 <= 10; c0 += 1)
6436 for (int c1 = 0; c1 <= -c0 + 10; c1 += 1)
6437 for (int c2 = 10 * c0;
6438 c2 <= min(-10 * c1 + 100, 10 * c0 + 9);
6440 for (int c3 = 10 * c1;
6441 c3 <= min(10 * c1 + 9, -c2 + 100);
6448 This is a single-dimensional space representing the schedule dimension(s)
6449 to which ``separation'' should be applied. Separation tries to split
6450 a loop into several pieces if this can avoid the generation of guards
6452 See also the C<atomic> option.
6456 This is a single-dimensional space representing the schedule dimension(s)
6457 for which the domains should be considered ``atomic''. That is, the
6458 AST generator will make sure that any given domain space will only appear
6459 in a single loop at the specified level.
6461 Consider the following schedule
6463 { a[i] -> [i] : 0 <= i < 10;
6464 b[i] -> [i+1] : 0 <= i < 10 }
6466 If the following option is specified
6468 { [i] -> separate[x] }
6470 then the following AST will be generated
6474 for (int c0 = 1; c0 <= 9; c0 += 1) {
6481 If, on the other hand, the following option is specified
6483 { [i] -> atomic[x] }
6485 then the following AST will be generated
6487 for (int c0 = 0; c0 <= 10; c0 += 1) {
6494 If neither C<atomic> nor C<separate> is specified, then the AST generator
6495 may produce either of these two results or some intermediate form.
6499 This is a single-dimensional space representing the schedule dimension(s)
6500 that should be I<completely> unrolled.
6501 To obtain a partial unrolling, the user should apply an additional
6502 strip-mining to the schedule and fully unroll the inner loop.
6506 Additional control is available through the following functions.
6508 #include <isl/ast_build.h>
6509 __isl_give isl_ast_build *
6510 isl_ast_build_set_iterators(
6511 __isl_take isl_ast_build *control,
6512 __isl_take isl_id_list *iterators);
6514 The function C<isl_ast_build_set_iterators> allows the user to
6515 specify a list of iterator C<isl_id>s to be used as iterators.
6516 If the input schedule is injective, then
6517 the number of elements in this list should be as large as the dimension
6518 of the schedule space, but no direct correspondence should be assumed
6519 between dimensions and elements.
6520 If the input schedule is not injective, then an additional number
6521 of C<isl_id>s equal to the largest dimension of the input domains
6523 If the number of provided C<isl_id>s is insufficient, then additional
6524 names are automatically generated.
6526 #include <isl/ast_build.h>
6527 __isl_give isl_ast_build *
6528 isl_ast_build_set_create_leaf(
6529 __isl_take isl_ast_build *control,
6530 __isl_give isl_ast_node *(*fn)(
6531 __isl_take isl_ast_build *build,
6532 void *user), void *user);
6535 C<isl_ast_build_set_create_leaf> function allows for the
6536 specification of a callback that should be called whenever the AST
6537 generator arrives at an element of the schedule domain.
6538 The callback should return an AST node that should be inserted
6539 at the corresponding position of the AST. The default action (when
6540 the callback is not set) is to continue generating parts of the AST to scan
6541 all the domain elements associated to the schedule domain element
6542 and to insert user nodes, ``calling'' the domain element, for each of them.
6543 The C<build> argument contains the current state of the C<isl_ast_build>.
6544 To ease nested AST generation (see L</"Nested AST Generation">),
6545 all control information that is
6546 specific to the current AST generation such as the options and
6547 the callbacks has been removed from this C<isl_ast_build>.
6548 The callback would typically return the result of a nested
6550 user defined node created using the following function.
6552 #include <isl/ast.h>
6553 __isl_give isl_ast_node *isl_ast_node_alloc_user(
6554 __isl_take isl_ast_expr *expr);
6556 #include <isl/ast_build.h>
6557 __isl_give isl_ast_build *
6558 isl_ast_build_set_at_each_domain(
6559 __isl_take isl_ast_build *build,
6560 __isl_give isl_ast_node *(*fn)(
6561 __isl_take isl_ast_node *node,
6562 __isl_keep isl_ast_build *build,
6563 void *user), void *user);
6564 __isl_give isl_ast_build *
6565 isl_ast_build_set_before_each_for(
6566 __isl_take isl_ast_build *build,
6567 __isl_give isl_id *(*fn)(
6568 __isl_keep isl_ast_build *build,
6569 void *user), void *user);
6570 __isl_give isl_ast_build *
6571 isl_ast_build_set_after_each_for(
6572 __isl_take isl_ast_build *build,
6573 __isl_give isl_ast_node *(*fn)(
6574 __isl_take isl_ast_node *node,
6575 __isl_keep isl_ast_build *build,
6576 void *user), void *user);
6578 The callback set by C<isl_ast_build_set_at_each_domain> will
6579 be called for each domain AST node.
6580 The callbacks set by C<isl_ast_build_set_before_each_for>
6581 and C<isl_ast_build_set_after_each_for> will be called
6582 for each for AST node. The first will be called in depth-first
6583 pre-order, while the second will be called in depth-first post-order.
6584 Since C<isl_ast_build_set_before_each_for> is called before the for
6585 node is actually constructed, it is only passed an C<isl_ast_build>.
6586 The returned C<isl_id> will be added as an annotation (using
6587 C<isl_ast_node_set_annotation>) to the constructed for node.
6588 In particular, if the user has also specified an C<after_each_for>
6589 callback, then the annotation can be retrieved from the node passed to
6590 that callback using C<isl_ast_node_get_annotation>.
6591 All callbacks should C<NULL> on failure.
6592 The given C<isl_ast_build> can be used to create new
6593 C<isl_ast_expr> objects using C<isl_ast_build_expr_from_pw_aff>
6594 or C<isl_ast_build_call_from_pw_multi_aff>.
6596 =head3 Nested AST Generation
6598 C<isl> allows the user to create an AST within the context
6599 of another AST. These nested ASTs are created using the
6600 same C<isl_ast_build_ast_from_schedule> function that is used to create the
6601 outer AST. The C<build> argument should be an C<isl_ast_build>
6602 passed to a callback set by
6603 C<isl_ast_build_set_create_leaf>.
6604 The space of the range of the C<schedule> argument should refer
6605 to this build. In particular, the space should be a wrapped
6606 relation and the domain of this wrapped relation should be the
6607 same as that of the range of the schedule returned by
6608 C<isl_ast_build_get_schedule> below.
6609 In practice, the new schedule is typically
6610 created by calling C<isl_union_map_range_product> on the old schedule
6611 and some extra piece of the schedule.
6612 The space of the schedule domain is also available from
6613 the C<isl_ast_build>.
6615 #include <isl/ast_build.h>
6616 __isl_give isl_union_map *isl_ast_build_get_schedule(
6617 __isl_keep isl_ast_build *build);
6618 __isl_give isl_space *isl_ast_build_get_schedule_space(
6619 __isl_keep isl_ast_build *build);
6620 __isl_give isl_ast_build *isl_ast_build_restrict(
6621 __isl_take isl_ast_build *build,
6622 __isl_take isl_set *set);
6624 The C<isl_ast_build_get_schedule> function returns a (partial)
6625 schedule for the domains elements for which part of the AST still needs to
6626 be generated in the current build.
6627 In particular, the domain elements are mapped to those iterations of the loops
6628 enclosing the current point of the AST generation inside which
6629 the domain elements are executed.
6630 No direct correspondence between
6631 the input schedule and this schedule should be assumed.
6632 The space obtained from C<isl_ast_build_get_schedule_space> can be used
6633 to create a set for C<isl_ast_build_restrict> to intersect
6634 with the current build. In particular, the set passed to
6635 C<isl_ast_build_restrict> can have additional parameters.
6636 The ids of the set dimensions in the space returned by
6637 C<isl_ast_build_get_schedule_space> correspond to the
6638 iterators of the already generated loops.
6639 The user should not rely on the ids of the output dimensions
6640 of the relations in the union relation returned by
6641 C<isl_ast_build_get_schedule> having any particular value.
6645 Although C<isl> is mainly meant to be used as a library,
6646 it also contains some basic applications that use some
6647 of the functionality of C<isl>.
6648 The input may be specified in either the L<isl format>
6649 or the L<PolyLib format>.
6651 =head2 C<isl_polyhedron_sample>
6653 C<isl_polyhedron_sample> takes a polyhedron as input and prints
6654 an integer element of the polyhedron, if there is any.
6655 The first column in the output is the denominator and is always
6656 equal to 1. If the polyhedron contains no integer points,
6657 then a vector of length zero is printed.
6661 C<isl_pip> takes the same input as the C<example> program
6662 from the C<piplib> distribution, i.e., a set of constraints
6663 on the parameters, a line containing only -1 and finally a set
6664 of constraints on a parametric polyhedron.
6665 The coefficients of the parameters appear in the last columns
6666 (but before the final constant column).
6667 The output is the lexicographic minimum of the parametric polyhedron.
6668 As C<isl> currently does not have its own output format, the output
6669 is just a dump of the internal state.
6671 =head2 C<isl_polyhedron_minimize>
6673 C<isl_polyhedron_minimize> computes the minimum of some linear
6674 or affine objective function over the integer points in a polyhedron.
6675 If an affine objective function
6676 is given, then the constant should appear in the last column.
6678 =head2 C<isl_polytope_scan>
6680 Given a polytope, C<isl_polytope_scan> prints
6681 all integer points in the polytope.
6683 =head2 C<isl_codegen>
6685 Given a schedule, a context set and an options relation,
6686 C<isl_codegen> prints out an AST that scans the domain elements
6687 of the schedule in the order of their image(s) taking into account
6688 the constraints in the context set.