3 C<isl> is a thread-safe C library for manipulating
4 sets and relations of integer points bounded by affine constraints.
5 The descriptions of the sets and relations may involve
6 both parameters and existentially quantified variables.
7 All computations are performed in exact integer arithmetic
9 The C<isl> library offers functionality that is similar
10 to that offered by the C<Omega> and C<Omega+> libraries,
11 but the underlying algorithms are in most cases completely different.
13 The library is by no means complete and some fairly basic
14 functionality is still missing.
15 Still, even in its current form, the library has been successfully
16 used as a backend polyhedral library for the polyhedral
17 scanner C<CLooG> and as part of an equivalence checker of
18 static affine programs.
19 For bug reports, feature requests and questions,
20 visit the the discussion group at
21 L<http://groups.google.com/group/isl-development>.
23 =head2 Backward Incompatible Changes
25 =head3 Changes since isl-0.02
29 =item * The old printing functions have been deprecated
30 and replaced by C<isl_printer> functions, see L<Input and Output>.
32 =item * Most functions related to dependence analysis have acquired
33 an extra C<must> argument. To obtain the old behavior, this argument
34 should be given the value 1. See L<Dependence Analysis>.
38 =head3 Changes since isl-0.03
42 =item * The function C<isl_pw_qpolynomial_fold_add> has been
43 renamed to C<isl_pw_qpolynomial_fold_fold>.
44 Similarly, C<isl_union_pw_qpolynomial_fold_add> has been
45 renamed to C<isl_union_pw_qpolynomial_fold_fold>.
49 =head3 Changes since isl-0.04
53 =item * All header files have been renamed from C<isl_header.h>
58 =head3 Changes since isl-0.05
62 =item * The functions C<isl_printer_print_basic_set> and
63 C<isl_printer_print_basic_map> no longer print a newline.
65 =item * The functions C<isl_flow_get_no_source>
66 and C<isl_union_map_compute_flow> now return
67 the accesses for which no source could be found instead of
68 the iterations where those accesses occur.
70 =item * The functions C<isl_basic_map_identity> and
71 C<isl_map_identity> now take a B<map> space as input. An old call
72 C<isl_map_identity(space)> can be rewritten to
73 C<isl_map_identity(isl_space_map_from_set(space))>.
75 =item * The function C<isl_map_power> no longer takes
76 a parameter position as input. Instead, the exponent
77 is now expressed as the domain of the resulting relation.
81 =head3 Changes since isl-0.06
85 =item * The format of C<isl_printer_print_qpolynomial>'s
86 C<ISL_FORMAT_ISL> output has changed.
87 Use C<ISL_FORMAT_C> to obtain the old output.
89 =item * The C<*_fast_*> functions have been renamed to C<*_plain_*>.
90 Some of the old names have been kept for backward compatibility,
91 but they will be removed in the future.
95 =head3 Changes since isl-0.07
99 =item * The function C<isl_pw_aff_max> has been renamed to
100 C<isl_pw_aff_union_max>.
101 Similarly, the function C<isl_pw_aff_add> has been renamed to
102 C<isl_pw_aff_union_add>.
104 =item * The C<isl_dim> type has been renamed to C<isl_space>
105 along with the associated functions.
106 Some of the old names have been kept for backward compatibility,
107 but they will be removed in the future.
109 =item * Spaces of maps, sets and parameter domains are now
110 treated differently. The distinction between map spaces and set spaces
111 has always been made on a conceptual level, but proper use of such spaces
112 was never checked. Furthermore, up until isl-0.07 there was no way
113 of explicitly creating a parameter space. These can now be created
114 directly using C<isl_space_params_alloc> or from other spaces using
117 =item * The space in which C<isl_aff>, C<isl_pw_aff>, C<isl_qpolynomial>,
118 C<isl_pw_qpolynomial>, C<isl_qpolynomial_fold> and C<isl_pw_qpolynomial_fold>
119 objects live is now a map space
120 instead of a set space. This means, for example, that the dimensions
121 of the domain of an C<isl_aff> are now considered to be of type
122 C<isl_dim_in> instead of C<isl_dim_set>. Extra functions have been
123 added to obtain the domain space. Some of the constructors still
124 take a domain space and have therefore been renamed.
126 =item * The functions C<isl_equality_alloc> and C<isl_inequality_alloc>
127 now take an C<isl_local_space> instead of an C<isl_space>.
128 An C<isl_local_space> can be created from an C<isl_space>
129 using C<isl_local_space_from_space>.
131 =item * The C<isl_div> type has been removed. Functions that used
132 to return an C<isl_div> now return an C<isl_aff>.
133 Note that the space of an C<isl_aff> is that of relation.
134 When replacing a call to C<isl_div_get_coefficient> by a call to
135 C<isl_aff_get_coefficient> any C<isl_dim_set> argument needs
136 to be replaced by C<isl_dim_in>.
137 A call to C<isl_aff_from_div> can be replaced by a call
139 A call to C<isl_qpolynomial_div(div)> call be replaced by
142 isl_qpolynomial_from_aff(isl_aff_floor(div))
144 The function C<isl_constraint_div> has also been renamed
145 to C<isl_constraint_get_div>.
147 =item * The C<nparam> argument has been removed from
148 C<isl_map_read_from_str> and similar functions.
149 When reading input in the original PolyLib format,
150 the result will have no parameters.
151 If parameters are expected, the caller may want to perform
152 dimension manipulation on the result.
156 =head3 Changes since isl-0.09
160 =item * The C<schedule_split_parallel> option has been replaced
161 by the C<schedule_split_scaled> option.
163 =item * The first argument of C<isl_pw_aff_cond> is now
164 an C<isl_pw_aff> instead of an C<isl_set>.
165 A call C<isl_pw_aff_cond(a, b, c)> can be replaced by
167 isl_pw_aff_cond(isl_set_indicator_function(a), b, c)
171 =head3 Changes since isl-0.10
175 =item * The functions C<isl_set_dim_has_lower_bound> and
176 C<isl_set_dim_has_upper_bound> have been renamed to
177 C<isl_set_dim_has_any_lower_bound> and
178 C<isl_set_dim_has_any_upper_bound>.
179 The new C<isl_set_dim_has_lower_bound> and
180 C<isl_set_dim_has_upper_bound> have slightly different meanings.
186 C<isl> is released under the MIT license.
190 Permission is hereby granted, free of charge, to any person obtaining a copy of
191 this software and associated documentation files (the "Software"), to deal in
192 the Software without restriction, including without limitation the rights to
193 use, copy, modify, merge, publish, distribute, sublicense, and/or sell copies
194 of the Software, and to permit persons to whom the Software is furnished to do
195 so, subject to the following conditions:
197 The above copyright notice and this permission notice shall be included in all
198 copies or substantial portions of the Software.
200 THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
201 IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
202 FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
203 AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
204 LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
205 OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
210 Note that C<isl> currently requires C<GMP>, which is released
211 under the GNU Lesser General Public License (LGPL). This means
212 that code linked against C<isl> is also linked against LGPL code.
216 The source of C<isl> can be obtained either as a tarball
217 or from the git repository. Both are available from
218 L<http://freshmeat.net/projects/isl/>.
219 The installation process depends on how you obtained
222 =head2 Installation from the git repository
226 =item 1 Clone or update the repository
228 The first time the source is obtained, you need to clone
231 git clone git://repo.or.cz/isl.git
233 To obtain updates, you need to pull in the latest changes
237 =item 2 Generate C<configure>
243 After performing the above steps, continue
244 with the L<Common installation instructions>.
246 =head2 Common installation instructions
250 =item 1 Obtain C<GMP>
252 Building C<isl> requires C<GMP>, including its headers files.
253 Your distribution may not provide these header files by default
254 and you may need to install a package called C<gmp-devel> or something
255 similar. Alternatively, C<GMP> can be built from
256 source, available from L<http://gmplib.org/>.
260 C<isl> uses the standard C<autoconf> C<configure> script.
265 optionally followed by some configure options.
266 A complete list of options can be obtained by running
270 Below we discuss some of the more common options.
272 C<isl> can optionally use C<piplib>, but no
273 C<piplib> functionality is currently used by default.
274 The C<--with-piplib> option can
275 be used to specify which C<piplib>
276 library to use, either an installed version (C<system>),
277 an externally built version (C<build>)
278 or no version (C<no>). The option C<build> is mostly useful
279 in C<configure> scripts of larger projects that bundle both C<isl>
286 Installation prefix for C<isl>
288 =item C<--with-gmp-prefix>
290 Installation prefix for C<GMP> (architecture-independent files).
292 =item C<--with-gmp-exec-prefix>
294 Installation prefix for C<GMP> (architecture-dependent files).
296 =item C<--with-piplib>
298 Which copy of C<piplib> to use, either C<no> (default), C<system> or C<build>.
300 =item C<--with-piplib-prefix>
302 Installation prefix for C<system> C<piplib> (architecture-independent files).
304 =item C<--with-piplib-exec-prefix>
306 Installation prefix for C<system> C<piplib> (architecture-dependent files).
308 =item C<--with-piplib-builddir>
310 Location where C<build> C<piplib> was built.
318 =item 4 Install (optional)
324 =head1 Integer Set Library
326 =head2 Initialization
328 All manipulations of integer sets and relations occur within
329 the context of an C<isl_ctx>.
330 A given C<isl_ctx> can only be used within a single thread.
331 All arguments of a function are required to have been allocated
332 within the same context.
333 There are currently no functions available for moving an object
334 from one C<isl_ctx> to another C<isl_ctx>. This means that
335 there is currently no way of safely moving an object from one
336 thread to another, unless the whole C<isl_ctx> is moved.
338 An C<isl_ctx> can be allocated using C<isl_ctx_alloc> and
339 freed using C<isl_ctx_free>.
340 All objects allocated within an C<isl_ctx> should be freed
341 before the C<isl_ctx> itself is freed.
343 isl_ctx *isl_ctx_alloc();
344 void isl_ctx_free(isl_ctx *ctx);
348 An C<isl_val> represents an integer value, a rational value
349 or one of three special values, infinity, negative infinity and NaN.
350 Some predefined values can be created using the following functions.
353 __isl_give isl_val *isl_val_zero(isl_ctx *ctx);
354 __isl_give isl_val *isl_val_one(isl_ctx *ctx);
355 __isl_give isl_val *isl_val_nan(isl_ctx *ctx);
356 __isl_give isl_val *isl_val_infty(isl_ctx *ctx);
357 __isl_give isl_val *isl_val_neginfty(isl_ctx *ctx);
359 Specific integer values can be created using the following functions.
362 __isl_give isl_val *isl_val_int_from_si(isl_ctx *ctx,
364 __isl_give isl_val *isl_val_int_from_ui(isl_ctx *ctx,
367 They can be copied and freed using the following functions.
370 __isl_give isl_val *isl_val_copy(__isl_keep isl_val *v);
371 void *isl_val_free(__isl_take isl_val *v);
373 They can be inspected using the following functions.
376 isl_ctx *isl_val_get_ctx(__isl_keep isl_val *val);
377 long isl_val_get_num_si(__isl_keep isl_val *v);
378 long isl_val_get_den_si(__isl_keep isl_val *v);
379 double isl_val_get_d(__isl_keep isl_val *v);
381 Note that C<isl_val_get_num_si>, C<isl_val_get_den_si> and
382 C<isl_val_get_d> can only be applied to rational values.
384 An C<isl_val> can be modified using the following function.
387 __isl_give isl_val *isl_val_set_si(__isl_take isl_val *v,
390 The following unary properties are defined on C<isl_val>s.
393 int isl_val_sgn(__isl_keep isl_val *v);
394 int isl_val_is_zero(__isl_keep isl_val *v);
395 int isl_val_is_one(__isl_keep isl_val *v);
396 int isl_val_is_negone(__isl_keep isl_val *v);
397 int isl_val_is_nonneg(__isl_keep isl_val *v);
398 int isl_val_is_nonpos(__isl_keep isl_val *v);
399 int isl_val_is_pos(__isl_keep isl_val *v);
400 int isl_val_is_neg(__isl_keep isl_val *v);
401 int isl_val_is_int(__isl_keep isl_val *v);
402 int isl_val_is_rat(__isl_keep isl_val *v);
403 int isl_val_is_nan(__isl_keep isl_val *v);
404 int isl_val_is_infty(__isl_keep isl_val *v);
405 int isl_val_is_neginfty(__isl_keep isl_val *v);
407 Note that the sign of NaN is undefined.
409 The following binary properties are defined on pairs of C<isl_val>s.
412 int isl_val_lt(__isl_keep isl_val *v1,
413 __isl_keep isl_val *v2);
414 int isl_val_le(__isl_keep isl_val *v1,
415 __isl_keep isl_val *v2);
416 int isl_val_gt(__isl_keep isl_val *v1,
417 __isl_keep isl_val *v2);
418 int isl_val_ge(__isl_keep isl_val *v1,
419 __isl_keep isl_val *v2);
420 int isl_val_eq(__isl_keep isl_val *v1,
421 __isl_keep isl_val *v2);
422 int isl_val_ne(__isl_keep isl_val *v1,
423 __isl_keep isl_val *v2);
425 For integer C<isl_val>s we additionally have the following binary property.
428 int isl_val_is_divisible_by(__isl_keep isl_val *v1,
429 __isl_keep isl_val *v2);
431 An C<isl_val> can also be compared to an integer using the following
432 function. The result is undefined for NaN.
435 int isl_val_cmp_si(__isl_keep isl_val *v, long i);
437 The following unary operations are available on C<isl_val>s.
440 __isl_give isl_val *isl_val_abs(__isl_take isl_val *v);
441 __isl_give isl_val *isl_val_neg(__isl_take isl_val *v);
442 __isl_give isl_val *isl_val_floor(__isl_take isl_val *v);
443 __isl_give isl_val *isl_val_ceil(__isl_take isl_val *v);
444 __isl_give isl_val *isl_val_trunc(__isl_take isl_val *v);
446 The following binary operations are available on C<isl_val>s.
449 __isl_give isl_val *isl_val_abs(__isl_take isl_val *v);
450 __isl_give isl_val *isl_val_neg(__isl_take isl_val *v);
451 __isl_give isl_val *isl_val_floor(__isl_take isl_val *v);
452 __isl_give isl_val *isl_val_ceil(__isl_take isl_val *v);
453 __isl_give isl_val *isl_val_trunc(__isl_take isl_val *v);
454 __isl_give isl_val *isl_val_2exp(__isl_take isl_val *v);
455 __isl_give isl_val *isl_val_min(__isl_take isl_val *v1,
456 __isl_take isl_val *v2);
457 __isl_give isl_val *isl_val_max(__isl_take isl_val *v1,
458 __isl_take isl_val *v2);
459 __isl_give isl_val *isl_val_add(__isl_take isl_val *v1,
460 __isl_take isl_val *v2);
461 __isl_give isl_val *isl_val_add_ui(__isl_take isl_val *v1,
463 __isl_give isl_val *isl_val_sub(__isl_take isl_val *v1,
464 __isl_take isl_val *v2);
465 __isl_give isl_val *isl_val_sub_ui(__isl_take isl_val *v1,
467 __isl_give isl_val *isl_val_mul(__isl_take isl_val *v1,
468 __isl_take isl_val *v2);
469 __isl_give isl_val *isl_val_mul_ui(__isl_take isl_val *v1,
471 __isl_give isl_val *isl_val_div(__isl_take isl_val *v1,
472 __isl_take isl_val *v2);
474 On integer values, we additionally have the following operations.
477 __isl_give isl_val *isl_val_2exp(__isl_take isl_val *v);
478 __isl_give isl_val *isl_val_mod(__isl_take isl_val *v1,
479 __isl_take isl_val *v2);
480 __isl_give isl_val *isl_val_gcd(__isl_take isl_val *v1,
481 __isl_take isl_val *v2);
482 __isl_give isl_val *isl_val_gcdext(__isl_take isl_val *v1,
483 __isl_take isl_val *v2, __isl_give isl_val **x,
484 __isl_give isl_val **y);
486 The function C<isl_val_gcdext> returns the greatest common divisor g
487 of C<v1> and C<v2> as well as two integers C<*x> and C<*y> such
488 that C<*x> * C<v1> + C<*y> * C<v2> = g.
490 A value can be read from input using
493 __isl_give isl_val *isl_val_read_from_str(isl_ctx *ctx,
496 A value can be printed using
499 __isl_give isl_printer *isl_printer_print_val(
500 __isl_take isl_printer *p, __isl_keep isl_val *v);
502 =head3 GMP specific functions
504 These functions are only available if C<isl> has been compiled with C<GMP>
507 Specific integer and rational values can be created from C<GMP> values using
508 the following functions.
510 #include <isl/val_gmp.h>
511 __isl_give isl_val *isl_val_int_from_gmp(isl_ctx *ctx,
513 __isl_give isl_val *isl_val_from_gmp(isl_ctx *ctx,
514 const mpz_t n, const mpz_t d);
516 The numerator and denominator of a rational value can be extracted as
517 C<GMP> values using the following functions.
519 #include <isl/val_gmp.h>
520 int isl_val_get_num_gmp(__isl_keep isl_val *v, mpz_t z);
521 int isl_val_get_den_gmp(__isl_keep isl_val *v, mpz_t z);
523 =head2 Integers (obsolescent)
525 All operations on integers, mainly the coefficients
526 of the constraints describing the sets and relations,
527 are performed in exact integer arithmetic using C<GMP>.
528 However, to allow future versions of C<isl> to optionally
529 support fixed integer arithmetic, all calls to C<GMP>
530 are wrapped inside C<isl> specific macros.
531 The basic type is C<isl_int> and the operations below
532 are available on this type.
533 The meanings of these operations are essentially the same
534 as their C<GMP> C<mpz_> counterparts.
535 As always with C<GMP> types, C<isl_int>s need to be
536 initialized with C<isl_int_init> before they can be used
537 and they need to be released with C<isl_int_clear>
539 The user should not assume that an C<isl_int> is represented
540 as a C<mpz_t>, but should instead explicitly convert between
541 C<mpz_t>s and C<isl_int>s using C<isl_int_set_gmp> and
542 C<isl_int_get_gmp> whenever a C<mpz_t> is required.
546 =item isl_int_init(i)
548 =item isl_int_clear(i)
550 =item isl_int_set(r,i)
552 =item isl_int_set_si(r,i)
554 =item isl_int_set_gmp(r,g)
556 =item isl_int_get_gmp(i,g)
558 =item isl_int_abs(r,i)
560 =item isl_int_neg(r,i)
562 =item isl_int_swap(i,j)
564 =item isl_int_swap_or_set(i,j)
566 =item isl_int_add_ui(r,i,j)
568 =item isl_int_sub_ui(r,i,j)
570 =item isl_int_add(r,i,j)
572 =item isl_int_sub(r,i,j)
574 =item isl_int_mul(r,i,j)
576 =item isl_int_mul_ui(r,i,j)
578 =item isl_int_addmul(r,i,j)
580 =item isl_int_submul(r,i,j)
582 =item isl_int_gcd(r,i,j)
584 =item isl_int_lcm(r,i,j)
586 =item isl_int_divexact(r,i,j)
588 =item isl_int_cdiv_q(r,i,j)
590 =item isl_int_fdiv_q(r,i,j)
592 =item isl_int_fdiv_r(r,i,j)
594 =item isl_int_fdiv_q_ui(r,i,j)
596 =item isl_int_read(r,s)
598 =item isl_int_print(out,i,width)
602 =item isl_int_cmp(i,j)
604 =item isl_int_cmp_si(i,si)
606 =item isl_int_eq(i,j)
608 =item isl_int_ne(i,j)
610 =item isl_int_lt(i,j)
612 =item isl_int_le(i,j)
614 =item isl_int_gt(i,j)
616 =item isl_int_ge(i,j)
618 =item isl_int_abs_eq(i,j)
620 =item isl_int_abs_ne(i,j)
622 =item isl_int_abs_lt(i,j)
624 =item isl_int_abs_gt(i,j)
626 =item isl_int_abs_ge(i,j)
628 =item isl_int_is_zero(i)
630 =item isl_int_is_one(i)
632 =item isl_int_is_negone(i)
634 =item isl_int_is_pos(i)
636 =item isl_int_is_neg(i)
638 =item isl_int_is_nonpos(i)
640 =item isl_int_is_nonneg(i)
642 =item isl_int_is_divisible_by(i,j)
646 =head2 Sets and Relations
648 C<isl> uses six types of objects for representing sets and relations,
649 C<isl_basic_set>, C<isl_basic_map>, C<isl_set>, C<isl_map>,
650 C<isl_union_set> and C<isl_union_map>.
651 C<isl_basic_set> and C<isl_basic_map> represent sets and relations that
652 can be described as a conjunction of affine constraints, while
653 C<isl_set> and C<isl_map> represent unions of
654 C<isl_basic_set>s and C<isl_basic_map>s, respectively.
655 However, all C<isl_basic_set>s or C<isl_basic_map>s in the union need
656 to live in the same space. C<isl_union_set>s and C<isl_union_map>s
657 represent unions of C<isl_set>s or C<isl_map>s in I<different> spaces,
658 where spaces are considered different if they have a different number
659 of dimensions and/or different names (see L<"Spaces">).
660 The difference between sets and relations (maps) is that sets have
661 one set of variables, while relations have two sets of variables,
662 input variables and output variables.
664 =head2 Memory Management
666 Since a high-level operation on sets and/or relations usually involves
667 several substeps and since the user is usually not interested in
668 the intermediate results, most functions that return a new object
669 will also release all the objects passed as arguments.
670 If the user still wants to use one or more of these arguments
671 after the function call, she should pass along a copy of the
672 object rather than the object itself.
673 The user is then responsible for making sure that the original
674 object gets used somewhere else or is explicitly freed.
676 The arguments and return values of all documented functions are
677 annotated to make clear which arguments are released and which
678 arguments are preserved. In particular, the following annotations
685 C<__isl_give> means that a new object is returned.
686 The user should make sure that the returned pointer is
687 used exactly once as a value for an C<__isl_take> argument.
688 In between, it can be used as a value for as many
689 C<__isl_keep> arguments as the user likes.
690 There is one exception, and that is the case where the
691 pointer returned is C<NULL>. Is this case, the user
692 is free to use it as an C<__isl_take> argument or not.
696 C<__isl_take> means that the object the argument points to
697 is taken over by the function and may no longer be used
698 by the user as an argument to any other function.
699 The pointer value must be one returned by a function
700 returning an C<__isl_give> pointer.
701 If the user passes in a C<NULL> value, then this will
702 be treated as an error in the sense that the function will
703 not perform its usual operation. However, it will still
704 make sure that all the other C<__isl_take> arguments
709 C<__isl_keep> means that the function will only use the object
710 temporarily. After the function has finished, the user
711 can still use it as an argument to other functions.
712 A C<NULL> value will be treated in the same way as
713 a C<NULL> value for an C<__isl_take> argument.
717 =head2 Error Handling
719 C<isl> supports different ways to react in case a runtime error is triggered.
720 Runtime errors arise, e.g., if a function such as C<isl_map_intersect> is called
721 with two maps that have incompatible spaces. There are three possible ways
722 to react on error: to warn, to continue or to abort.
724 The default behavior is to warn. In this mode, C<isl> prints a warning, stores
725 the last error in the corresponding C<isl_ctx> and the function in which the
726 error was triggered returns C<NULL>. An error does not corrupt internal state,
727 such that isl can continue to be used. C<isl> also provides functions to
728 read the last error and to reset the memory that stores the last error. The
729 last error is only stored for information purposes. Its presence does not
730 change the behavior of C<isl>. Hence, resetting an error is not required to
731 continue to use isl, but only to observe new errors.
734 enum isl_error isl_ctx_last_error(isl_ctx *ctx);
735 void isl_ctx_reset_error(isl_ctx *ctx);
737 Another option is to continue on error. This is similar to warn on error mode,
738 except that C<isl> does not print any warning. This allows a program to
739 implement its own error reporting.
741 The last option is to directly abort the execution of the program from within
742 the isl library. This makes it obviously impossible to recover from an error,
743 but it allows to directly spot the error location. By aborting on error,
744 debuggers break at the location the error occurred and can provide a stack
745 trace. Other tools that automatically provide stack traces on abort or that do
746 not want to continue execution after an error was triggered may also prefer to
749 The on error behavior of isl can be specified by calling
750 C<isl_options_set_on_error> or by setting the command line option
751 C<--isl-on-error>. Valid arguments for the function call are
752 C<ISL_ON_ERROR_WARN>, C<ISL_ON_ERROR_CONTINUE> and C<ISL_ON_ERROR_ABORT>. The
753 choices for the command line option are C<warn>, C<continue> and C<abort>.
754 It is also possible to query the current error mode.
756 #include <isl/options.h>
757 int isl_options_set_on_error(isl_ctx *ctx, int val);
758 int isl_options_get_on_error(isl_ctx *ctx);
762 Identifiers are used to identify both individual dimensions
763 and tuples of dimensions. They consist of an optional name and an optional
764 user pointer. The name and the user pointer cannot both be C<NULL>, however.
765 Identifiers with the same name but different pointer values
766 are considered to be distinct.
767 Similarly, identifiers with different names but the same pointer value
768 are also considered to be distinct.
769 Equal identifiers are represented using the same object.
770 Pairs of identifiers can therefore be tested for equality using the
772 Identifiers can be constructed, copied, freed, inspected and printed
773 using the following functions.
776 __isl_give isl_id *isl_id_alloc(isl_ctx *ctx,
777 __isl_keep const char *name, void *user);
778 __isl_give isl_id *isl_id_set_free_user(
779 __isl_take isl_id *id,
780 __isl_give void (*free_user)(void *user));
781 __isl_give isl_id *isl_id_copy(isl_id *id);
782 void *isl_id_free(__isl_take isl_id *id);
784 isl_ctx *isl_id_get_ctx(__isl_keep isl_id *id);
785 void *isl_id_get_user(__isl_keep isl_id *id);
786 __isl_keep const char *isl_id_get_name(__isl_keep isl_id *id);
788 __isl_give isl_printer *isl_printer_print_id(
789 __isl_take isl_printer *p, __isl_keep isl_id *id);
791 The callback set by C<isl_id_set_free_user> is called on the user
792 pointer when the last reference to the C<isl_id> is freed.
793 Note that C<isl_id_get_name> returns a pointer to some internal
794 data structure, so the result can only be used while the
795 corresponding C<isl_id> is alive.
799 Whenever a new set, relation or similiar object is created from scratch,
800 the space in which it lives needs to be specified using an C<isl_space>.
801 Each space involves zero or more parameters and zero, one or two
802 tuples of set or input/output dimensions. The parameters and dimensions
803 are identified by an C<isl_dim_type> and a position.
804 The type C<isl_dim_param> refers to parameters,
805 the type C<isl_dim_set> refers to set dimensions (for spaces
806 with a single tuple of dimensions) and the types C<isl_dim_in>
807 and C<isl_dim_out> refer to input and output dimensions
808 (for spaces with two tuples of dimensions).
809 Local spaces (see L</"Local Spaces">) also contain dimensions
810 of type C<isl_dim_div>.
811 Note that parameters are only identified by their position within
812 a given object. Across different objects, parameters are (usually)
813 identified by their names or identifiers. Only unnamed parameters
814 are identified by their positions across objects. The use of unnamed
815 parameters is discouraged.
817 #include <isl/space.h>
818 __isl_give isl_space *isl_space_alloc(isl_ctx *ctx,
819 unsigned nparam, unsigned n_in, unsigned n_out);
820 __isl_give isl_space *isl_space_params_alloc(isl_ctx *ctx,
822 __isl_give isl_space *isl_space_set_alloc(isl_ctx *ctx,
823 unsigned nparam, unsigned dim);
824 __isl_give isl_space *isl_space_copy(__isl_keep isl_space *space);
825 void *isl_space_free(__isl_take isl_space *space);
826 unsigned isl_space_dim(__isl_keep isl_space *space,
827 enum isl_dim_type type);
829 The space used for creating a parameter domain
830 needs to be created using C<isl_space_params_alloc>.
831 For other sets, the space
832 needs to be created using C<isl_space_set_alloc>, while
833 for a relation, the space
834 needs to be created using C<isl_space_alloc>.
835 C<isl_space_dim> can be used
836 to find out the number of dimensions of each type in
837 a space, where type may be
838 C<isl_dim_param>, C<isl_dim_in> (only for relations),
839 C<isl_dim_out> (only for relations), C<isl_dim_set>
840 (only for sets) or C<isl_dim_all>.
842 To check whether a given space is that of a set or a map
843 or whether it is a parameter space, use these functions:
845 #include <isl/space.h>
846 int isl_space_is_params(__isl_keep isl_space *space);
847 int isl_space_is_set(__isl_keep isl_space *space);
848 int isl_space_is_map(__isl_keep isl_space *space);
850 Spaces can be compared using the following functions:
852 #include <isl/space.h>
853 int isl_space_is_equal(__isl_keep isl_space *space1,
854 __isl_keep isl_space *space2);
855 int isl_space_is_domain(__isl_keep isl_space *space1,
856 __isl_keep isl_space *space2);
857 int isl_space_is_range(__isl_keep isl_space *space1,
858 __isl_keep isl_space *space2);
860 C<isl_space_is_domain> checks whether the first argument is equal
861 to the domain of the second argument. This requires in particular that
862 the first argument is a set space and that the second argument
865 It is often useful to create objects that live in the
866 same space as some other object. This can be accomplished
867 by creating the new objects
868 (see L<Creating New Sets and Relations> or
869 L<Creating New (Piecewise) Quasipolynomials>) based on the space
870 of the original object.
873 __isl_give isl_space *isl_basic_set_get_space(
874 __isl_keep isl_basic_set *bset);
875 __isl_give isl_space *isl_set_get_space(__isl_keep isl_set *set);
877 #include <isl/union_set.h>
878 __isl_give isl_space *isl_union_set_get_space(
879 __isl_keep isl_union_set *uset);
882 __isl_give isl_space *isl_basic_map_get_space(
883 __isl_keep isl_basic_map *bmap);
884 __isl_give isl_space *isl_map_get_space(__isl_keep isl_map *map);
886 #include <isl/union_map.h>
887 __isl_give isl_space *isl_union_map_get_space(
888 __isl_keep isl_union_map *umap);
890 #include <isl/constraint.h>
891 __isl_give isl_space *isl_constraint_get_space(
892 __isl_keep isl_constraint *constraint);
894 #include <isl/polynomial.h>
895 __isl_give isl_space *isl_qpolynomial_get_domain_space(
896 __isl_keep isl_qpolynomial *qp);
897 __isl_give isl_space *isl_qpolynomial_get_space(
898 __isl_keep isl_qpolynomial *qp);
899 __isl_give isl_space *isl_qpolynomial_fold_get_space(
900 __isl_keep isl_qpolynomial_fold *fold);
901 __isl_give isl_space *isl_pw_qpolynomial_get_domain_space(
902 __isl_keep isl_pw_qpolynomial *pwqp);
903 __isl_give isl_space *isl_pw_qpolynomial_get_space(
904 __isl_keep isl_pw_qpolynomial *pwqp);
905 __isl_give isl_space *isl_pw_qpolynomial_fold_get_domain_space(
906 __isl_keep isl_pw_qpolynomial_fold *pwf);
907 __isl_give isl_space *isl_pw_qpolynomial_fold_get_space(
908 __isl_keep isl_pw_qpolynomial_fold *pwf);
909 __isl_give isl_space *isl_union_pw_qpolynomial_get_space(
910 __isl_keep isl_union_pw_qpolynomial *upwqp);
911 __isl_give isl_space *isl_union_pw_qpolynomial_fold_get_space(
912 __isl_keep isl_union_pw_qpolynomial_fold *upwf);
915 __isl_give isl_space *isl_multi_val_get_space(
916 __isl_keep isl_multi_val *mv);
919 __isl_give isl_space *isl_aff_get_domain_space(
920 __isl_keep isl_aff *aff);
921 __isl_give isl_space *isl_aff_get_space(
922 __isl_keep isl_aff *aff);
923 __isl_give isl_space *isl_pw_aff_get_domain_space(
924 __isl_keep isl_pw_aff *pwaff);
925 __isl_give isl_space *isl_pw_aff_get_space(
926 __isl_keep isl_pw_aff *pwaff);
927 __isl_give isl_space *isl_multi_aff_get_domain_space(
928 __isl_keep isl_multi_aff *maff);
929 __isl_give isl_space *isl_multi_aff_get_space(
930 __isl_keep isl_multi_aff *maff);
931 __isl_give isl_space *isl_pw_multi_aff_get_domain_space(
932 __isl_keep isl_pw_multi_aff *pma);
933 __isl_give isl_space *isl_pw_multi_aff_get_space(
934 __isl_keep isl_pw_multi_aff *pma);
935 __isl_give isl_space *isl_union_pw_multi_aff_get_space(
936 __isl_keep isl_union_pw_multi_aff *upma);
937 __isl_give isl_space *isl_multi_pw_aff_get_domain_space(
938 __isl_keep isl_multi_pw_aff *mpa);
939 __isl_give isl_space *isl_multi_pw_aff_get_space(
940 __isl_keep isl_multi_pw_aff *mpa);
942 #include <isl/point.h>
943 __isl_give isl_space *isl_point_get_space(
944 __isl_keep isl_point *pnt);
946 The identifiers or names of the individual dimensions may be set or read off
947 using the following functions.
949 #include <isl/space.h>
950 __isl_give isl_space *isl_space_set_dim_id(
951 __isl_take isl_space *space,
952 enum isl_dim_type type, unsigned pos,
953 __isl_take isl_id *id);
954 int isl_space_has_dim_id(__isl_keep isl_space *space,
955 enum isl_dim_type type, unsigned pos);
956 __isl_give isl_id *isl_space_get_dim_id(
957 __isl_keep isl_space *space,
958 enum isl_dim_type type, unsigned pos);
959 __isl_give isl_space *isl_space_set_dim_name(
960 __isl_take isl_space *space,
961 enum isl_dim_type type, unsigned pos,
962 __isl_keep const char *name);
963 int isl_space_has_dim_name(__isl_keep isl_space *space,
964 enum isl_dim_type type, unsigned pos);
965 __isl_keep const char *isl_space_get_dim_name(
966 __isl_keep isl_space *space,
967 enum isl_dim_type type, unsigned pos);
969 Note that C<isl_space_get_name> returns a pointer to some internal
970 data structure, so the result can only be used while the
971 corresponding C<isl_space> is alive.
972 Also note that every function that operates on two sets or relations
973 requires that both arguments have the same parameters. This also
974 means that if one of the arguments has named parameters, then the
975 other needs to have named parameters too and the names need to match.
976 Pairs of C<isl_set>, C<isl_map>, C<isl_union_set> and/or C<isl_union_map>
977 arguments may have different parameters (as long as they are named),
978 in which case the result will have as parameters the union of the parameters of
981 Given the identifier or name of a dimension (typically a parameter),
982 its position can be obtained from the following function.
984 #include <isl/space.h>
985 int isl_space_find_dim_by_id(__isl_keep isl_space *space,
986 enum isl_dim_type type, __isl_keep isl_id *id);
987 int isl_space_find_dim_by_name(__isl_keep isl_space *space,
988 enum isl_dim_type type, const char *name);
990 The identifiers or names of entire spaces may be set or read off
991 using the following functions.
993 #include <isl/space.h>
994 __isl_give isl_space *isl_space_set_tuple_id(
995 __isl_take isl_space *space,
996 enum isl_dim_type type, __isl_take isl_id *id);
997 __isl_give isl_space *isl_space_reset_tuple_id(
998 __isl_take isl_space *space, enum isl_dim_type type);
999 int isl_space_has_tuple_id(__isl_keep isl_space *space,
1000 enum isl_dim_type type);
1001 __isl_give isl_id *isl_space_get_tuple_id(
1002 __isl_keep isl_space *space, enum isl_dim_type type);
1003 __isl_give isl_space *isl_space_set_tuple_name(
1004 __isl_take isl_space *space,
1005 enum isl_dim_type type, const char *s);
1006 int isl_space_has_tuple_name(__isl_keep isl_space *space,
1007 enum isl_dim_type type);
1008 const char *isl_space_get_tuple_name(__isl_keep isl_space *space,
1009 enum isl_dim_type type);
1011 The C<type> argument needs to be one of C<isl_dim_in>, C<isl_dim_out>
1012 or C<isl_dim_set>. As with C<isl_space_get_name>,
1013 the C<isl_space_get_tuple_name> function returns a pointer to some internal
1015 Binary operations require the corresponding spaces of their arguments
1016 to have the same name.
1018 Spaces can be nested. In particular, the domain of a set or
1019 the domain or range of a relation can be a nested relation.
1020 The following functions can be used to construct and deconstruct
1023 #include <isl/space.h>
1024 int isl_space_is_wrapping(__isl_keep isl_space *space);
1025 __isl_give isl_space *isl_space_wrap(__isl_take isl_space *space);
1026 __isl_give isl_space *isl_space_unwrap(__isl_take isl_space *space);
1028 The input to C<isl_space_is_wrapping> and C<isl_space_unwrap> should
1029 be the space of a set, while that of
1030 C<isl_space_wrap> should be the space of a relation.
1031 Conversely, the output of C<isl_space_unwrap> is the space
1032 of a relation, while that of C<isl_space_wrap> is the space of a set.
1034 Spaces can be created from other spaces
1035 using the following functions.
1037 __isl_give isl_space *isl_space_domain(__isl_take isl_space *space);
1038 __isl_give isl_space *isl_space_from_domain(__isl_take isl_space *space);
1039 __isl_give isl_space *isl_space_range(__isl_take isl_space *space);
1040 __isl_give isl_space *isl_space_from_range(__isl_take isl_space *space);
1041 __isl_give isl_space *isl_space_params(
1042 __isl_take isl_space *space);
1043 __isl_give isl_space *isl_space_set_from_params(
1044 __isl_take isl_space *space);
1045 __isl_give isl_space *isl_space_reverse(__isl_take isl_space *space);
1046 __isl_give isl_space *isl_space_join(__isl_take isl_space *left,
1047 __isl_take isl_space *right);
1048 __isl_give isl_space *isl_space_align_params(
1049 __isl_take isl_space *space1, __isl_take isl_space *space2)
1050 __isl_give isl_space *isl_space_insert_dims(__isl_take isl_space *space,
1051 enum isl_dim_type type, unsigned pos, unsigned n);
1052 __isl_give isl_space *isl_space_add_dims(__isl_take isl_space *space,
1053 enum isl_dim_type type, unsigned n);
1054 __isl_give isl_space *isl_space_drop_dims(__isl_take isl_space *space,
1055 enum isl_dim_type type, unsigned first, unsigned n);
1056 __isl_give isl_space *isl_space_move_dims(__isl_take isl_space *space,
1057 enum isl_dim_type dst_type, unsigned dst_pos,
1058 enum isl_dim_type src_type, unsigned src_pos,
1060 __isl_give isl_space *isl_space_map_from_set(
1061 __isl_take isl_space *space);
1062 __isl_give isl_space *isl_space_map_from_domain_and_range(
1063 __isl_take isl_space *domain,
1064 __isl_take isl_space *range);
1065 __isl_give isl_space *isl_space_zip(__isl_take isl_space *space);
1066 __isl_give isl_space *isl_space_curry(
1067 __isl_take isl_space *space);
1068 __isl_give isl_space *isl_space_uncurry(
1069 __isl_take isl_space *space);
1071 Note that if dimensions are added or removed from a space, then
1072 the name and the internal structure are lost.
1076 A local space is essentially a space with
1077 zero or more existentially quantified variables.
1078 The local space of a (constraint of a) basic set or relation can be obtained
1079 using the following functions.
1081 #include <isl/constraint.h>
1082 __isl_give isl_local_space *isl_constraint_get_local_space(
1083 __isl_keep isl_constraint *constraint);
1085 #include <isl/set.h>
1086 __isl_give isl_local_space *isl_basic_set_get_local_space(
1087 __isl_keep isl_basic_set *bset);
1089 #include <isl/map.h>
1090 __isl_give isl_local_space *isl_basic_map_get_local_space(
1091 __isl_keep isl_basic_map *bmap);
1093 A new local space can be created from a space using
1095 #include <isl/local_space.h>
1096 __isl_give isl_local_space *isl_local_space_from_space(
1097 __isl_take isl_space *space);
1099 They can be inspected, modified, copied and freed using the following functions.
1101 #include <isl/local_space.h>
1102 isl_ctx *isl_local_space_get_ctx(
1103 __isl_keep isl_local_space *ls);
1104 int isl_local_space_is_set(__isl_keep isl_local_space *ls);
1105 int isl_local_space_dim(__isl_keep isl_local_space *ls,
1106 enum isl_dim_type type);
1107 int isl_local_space_has_dim_id(
1108 __isl_keep isl_local_space *ls,
1109 enum isl_dim_type type, unsigned pos);
1110 __isl_give isl_id *isl_local_space_get_dim_id(
1111 __isl_keep isl_local_space *ls,
1112 enum isl_dim_type type, unsigned pos);
1113 int isl_local_space_has_dim_name(
1114 __isl_keep isl_local_space *ls,
1115 enum isl_dim_type type, unsigned pos)
1116 const char *isl_local_space_get_dim_name(
1117 __isl_keep isl_local_space *ls,
1118 enum isl_dim_type type, unsigned pos);
1119 __isl_give isl_local_space *isl_local_space_set_dim_name(
1120 __isl_take isl_local_space *ls,
1121 enum isl_dim_type type, unsigned pos, const char *s);
1122 __isl_give isl_local_space *isl_local_space_set_dim_id(
1123 __isl_take isl_local_space *ls,
1124 enum isl_dim_type type, unsigned pos,
1125 __isl_take isl_id *id);
1126 __isl_give isl_space *isl_local_space_get_space(
1127 __isl_keep isl_local_space *ls);
1128 __isl_give isl_aff *isl_local_space_get_div(
1129 __isl_keep isl_local_space *ls, int pos);
1130 __isl_give isl_local_space *isl_local_space_copy(
1131 __isl_keep isl_local_space *ls);
1132 void *isl_local_space_free(__isl_take isl_local_space *ls);
1134 Note that C<isl_local_space_get_div> can only be used on local spaces
1137 Two local spaces can be compared using
1139 int isl_local_space_is_equal(__isl_keep isl_local_space *ls1,
1140 __isl_keep isl_local_space *ls2);
1142 Local spaces can be created from other local spaces
1143 using the following functions.
1145 __isl_give isl_local_space *isl_local_space_domain(
1146 __isl_take isl_local_space *ls);
1147 __isl_give isl_local_space *isl_local_space_range(
1148 __isl_take isl_local_space *ls);
1149 __isl_give isl_local_space *isl_local_space_from_domain(
1150 __isl_take isl_local_space *ls);
1151 __isl_give isl_local_space *isl_local_space_intersect(
1152 __isl_take isl_local_space *ls1,
1153 __isl_take isl_local_space *ls2);
1154 __isl_give isl_local_space *isl_local_space_add_dims(
1155 __isl_take isl_local_space *ls,
1156 enum isl_dim_type type, unsigned n);
1157 __isl_give isl_local_space *isl_local_space_insert_dims(
1158 __isl_take isl_local_space *ls,
1159 enum isl_dim_type type, unsigned first, unsigned n);
1160 __isl_give isl_local_space *isl_local_space_drop_dims(
1161 __isl_take isl_local_space *ls,
1162 enum isl_dim_type type, unsigned first, unsigned n);
1164 =head2 Input and Output
1166 C<isl> supports its own input/output format, which is similar
1167 to the C<Omega> format, but also supports the C<PolyLib> format
1170 =head3 C<isl> format
1172 The C<isl> format is similar to that of C<Omega>, but has a different
1173 syntax for describing the parameters and allows for the definition
1174 of an existentially quantified variable as the integer division
1175 of an affine expression.
1176 For example, the set of integers C<i> between C<0> and C<n>
1177 such that C<i % 10 <= 6> can be described as
1179 [n] -> { [i] : exists (a = [i/10] : 0 <= i and i <= n and
1182 A set or relation can have several disjuncts, separated
1183 by the keyword C<or>. Each disjunct is either a conjunction
1184 of constraints or a projection (C<exists>) of a conjunction
1185 of constraints. The constraints are separated by the keyword
1188 =head3 C<PolyLib> format
1190 If the represented set is a union, then the first line
1191 contains a single number representing the number of disjuncts.
1192 Otherwise, a line containing the number C<1> is optional.
1194 Each disjunct is represented by a matrix of constraints.
1195 The first line contains two numbers representing
1196 the number of rows and columns,
1197 where the number of rows is equal to the number of constraints
1198 and the number of columns is equal to two plus the number of variables.
1199 The following lines contain the actual rows of the constraint matrix.
1200 In each row, the first column indicates whether the constraint
1201 is an equality (C<0>) or inequality (C<1>). The final column
1202 corresponds to the constant term.
1204 If the set is parametric, then the coefficients of the parameters
1205 appear in the last columns before the constant column.
1206 The coefficients of any existentially quantified variables appear
1207 between those of the set variables and those of the parameters.
1209 =head3 Extended C<PolyLib> format
1211 The extended C<PolyLib> format is nearly identical to the
1212 C<PolyLib> format. The only difference is that the line
1213 containing the number of rows and columns of a constraint matrix
1214 also contains four additional numbers:
1215 the number of output dimensions, the number of input dimensions,
1216 the number of local dimensions (i.e., the number of existentially
1217 quantified variables) and the number of parameters.
1218 For sets, the number of ``output'' dimensions is equal
1219 to the number of set dimensions, while the number of ``input''
1224 #include <isl/set.h>
1225 __isl_give isl_basic_set *isl_basic_set_read_from_file(
1226 isl_ctx *ctx, FILE *input);
1227 __isl_give isl_basic_set *isl_basic_set_read_from_str(
1228 isl_ctx *ctx, const char *str);
1229 __isl_give isl_set *isl_set_read_from_file(isl_ctx *ctx,
1231 __isl_give isl_set *isl_set_read_from_str(isl_ctx *ctx,
1234 #include <isl/map.h>
1235 __isl_give isl_basic_map *isl_basic_map_read_from_file(
1236 isl_ctx *ctx, FILE *input);
1237 __isl_give isl_basic_map *isl_basic_map_read_from_str(
1238 isl_ctx *ctx, const char *str);
1239 __isl_give isl_map *isl_map_read_from_file(
1240 isl_ctx *ctx, FILE *input);
1241 __isl_give isl_map *isl_map_read_from_str(isl_ctx *ctx,
1244 #include <isl/union_set.h>
1245 __isl_give isl_union_set *isl_union_set_read_from_file(
1246 isl_ctx *ctx, FILE *input);
1247 __isl_give isl_union_set *isl_union_set_read_from_str(
1248 isl_ctx *ctx, const char *str);
1250 #include <isl/union_map.h>
1251 __isl_give isl_union_map *isl_union_map_read_from_file(
1252 isl_ctx *ctx, FILE *input);
1253 __isl_give isl_union_map *isl_union_map_read_from_str(
1254 isl_ctx *ctx, const char *str);
1256 The input format is autodetected and may be either the C<PolyLib> format
1257 or the C<isl> format.
1261 Before anything can be printed, an C<isl_printer> needs to
1264 __isl_give isl_printer *isl_printer_to_file(isl_ctx *ctx,
1266 __isl_give isl_printer *isl_printer_to_str(isl_ctx *ctx);
1267 void *isl_printer_free(__isl_take isl_printer *printer);
1268 __isl_give char *isl_printer_get_str(
1269 __isl_keep isl_printer *printer);
1271 The printer can be inspected using the following functions.
1273 FILE *isl_printer_get_file(
1274 __isl_keep isl_printer *printer);
1275 int isl_printer_get_output_format(
1276 __isl_keep isl_printer *p);
1278 The behavior of the printer can be modified in various ways
1280 __isl_give isl_printer *isl_printer_set_output_format(
1281 __isl_take isl_printer *p, int output_format);
1282 __isl_give isl_printer *isl_printer_set_indent(
1283 __isl_take isl_printer *p, int indent);
1284 __isl_give isl_printer *isl_printer_indent(
1285 __isl_take isl_printer *p, int indent);
1286 __isl_give isl_printer *isl_printer_set_prefix(
1287 __isl_take isl_printer *p, const char *prefix);
1288 __isl_give isl_printer *isl_printer_set_suffix(
1289 __isl_take isl_printer *p, const char *suffix);
1291 The C<output_format> may be either C<ISL_FORMAT_ISL>, C<ISL_FORMAT_OMEGA>,
1292 C<ISL_FORMAT_POLYLIB>, C<ISL_FORMAT_EXT_POLYLIB> or C<ISL_FORMAT_LATEX>
1293 and defaults to C<ISL_FORMAT_ISL>.
1294 Each line in the output is indented by C<indent> (set by
1295 C<isl_printer_set_indent>) spaces
1296 (default: 0), prefixed by C<prefix> and suffixed by C<suffix>.
1297 In the C<PolyLib> format output,
1298 the coefficients of the existentially quantified variables
1299 appear between those of the set variables and those
1301 The function C<isl_printer_indent> increases the indentation
1302 by the specified amount (which may be negative).
1304 To actually print something, use
1306 #include <isl/printer.h>
1307 __isl_give isl_printer *isl_printer_print_double(
1308 __isl_take isl_printer *p, double d);
1310 #include <isl/set.h>
1311 __isl_give isl_printer *isl_printer_print_basic_set(
1312 __isl_take isl_printer *printer,
1313 __isl_keep isl_basic_set *bset);
1314 __isl_give isl_printer *isl_printer_print_set(
1315 __isl_take isl_printer *printer,
1316 __isl_keep isl_set *set);
1318 #include <isl/map.h>
1319 __isl_give isl_printer *isl_printer_print_basic_map(
1320 __isl_take isl_printer *printer,
1321 __isl_keep isl_basic_map *bmap);
1322 __isl_give isl_printer *isl_printer_print_map(
1323 __isl_take isl_printer *printer,
1324 __isl_keep isl_map *map);
1326 #include <isl/union_set.h>
1327 __isl_give isl_printer *isl_printer_print_union_set(
1328 __isl_take isl_printer *p,
1329 __isl_keep isl_union_set *uset);
1331 #include <isl/union_map.h>
1332 __isl_give isl_printer *isl_printer_print_union_map(
1333 __isl_take isl_printer *p,
1334 __isl_keep isl_union_map *umap);
1336 When called on a file printer, the following function flushes
1337 the file. When called on a string printer, the buffer is cleared.
1339 __isl_give isl_printer *isl_printer_flush(
1340 __isl_take isl_printer *p);
1342 =head2 Creating New Sets and Relations
1344 C<isl> has functions for creating some standard sets and relations.
1348 =item * Empty sets and relations
1350 __isl_give isl_basic_set *isl_basic_set_empty(
1351 __isl_take isl_space *space);
1352 __isl_give isl_basic_map *isl_basic_map_empty(
1353 __isl_take isl_space *space);
1354 __isl_give isl_set *isl_set_empty(
1355 __isl_take isl_space *space);
1356 __isl_give isl_map *isl_map_empty(
1357 __isl_take isl_space *space);
1358 __isl_give isl_union_set *isl_union_set_empty(
1359 __isl_take isl_space *space);
1360 __isl_give isl_union_map *isl_union_map_empty(
1361 __isl_take isl_space *space);
1363 For C<isl_union_set>s and C<isl_union_map>s, the space
1364 is only used to specify the parameters.
1366 =item * Universe sets and relations
1368 __isl_give isl_basic_set *isl_basic_set_universe(
1369 __isl_take isl_space *space);
1370 __isl_give isl_basic_map *isl_basic_map_universe(
1371 __isl_take isl_space *space);
1372 __isl_give isl_set *isl_set_universe(
1373 __isl_take isl_space *space);
1374 __isl_give isl_map *isl_map_universe(
1375 __isl_take isl_space *space);
1376 __isl_give isl_union_set *isl_union_set_universe(
1377 __isl_take isl_union_set *uset);
1378 __isl_give isl_union_map *isl_union_map_universe(
1379 __isl_take isl_union_map *umap);
1381 The sets and relations constructed by the functions above
1382 contain all integer values, while those constructed by the
1383 functions below only contain non-negative values.
1385 __isl_give isl_basic_set *isl_basic_set_nat_universe(
1386 __isl_take isl_space *space);
1387 __isl_give isl_basic_map *isl_basic_map_nat_universe(
1388 __isl_take isl_space *space);
1389 __isl_give isl_set *isl_set_nat_universe(
1390 __isl_take isl_space *space);
1391 __isl_give isl_map *isl_map_nat_universe(
1392 __isl_take isl_space *space);
1394 =item * Identity relations
1396 __isl_give isl_basic_map *isl_basic_map_identity(
1397 __isl_take isl_space *space);
1398 __isl_give isl_map *isl_map_identity(
1399 __isl_take isl_space *space);
1401 The number of input and output dimensions in C<space> needs
1404 =item * Lexicographic order
1406 __isl_give isl_map *isl_map_lex_lt(
1407 __isl_take isl_space *set_space);
1408 __isl_give isl_map *isl_map_lex_le(
1409 __isl_take isl_space *set_space);
1410 __isl_give isl_map *isl_map_lex_gt(
1411 __isl_take isl_space *set_space);
1412 __isl_give isl_map *isl_map_lex_ge(
1413 __isl_take isl_space *set_space);
1414 __isl_give isl_map *isl_map_lex_lt_first(
1415 __isl_take isl_space *space, unsigned n);
1416 __isl_give isl_map *isl_map_lex_le_first(
1417 __isl_take isl_space *space, unsigned n);
1418 __isl_give isl_map *isl_map_lex_gt_first(
1419 __isl_take isl_space *space, unsigned n);
1420 __isl_give isl_map *isl_map_lex_ge_first(
1421 __isl_take isl_space *space, unsigned n);
1423 The first four functions take a space for a B<set>
1424 and return relations that express that the elements in the domain
1425 are lexicographically less
1426 (C<isl_map_lex_lt>), less or equal (C<isl_map_lex_le>),
1427 greater (C<isl_map_lex_gt>) or greater or equal (C<isl_map_lex_ge>)
1428 than the elements in the range.
1429 The last four functions take a space for a map
1430 and return relations that express that the first C<n> dimensions
1431 in the domain are lexicographically less
1432 (C<isl_map_lex_lt_first>), less or equal (C<isl_map_lex_le_first>),
1433 greater (C<isl_map_lex_gt_first>) or greater or equal (C<isl_map_lex_ge_first>)
1434 than the first C<n> dimensions in the range.
1438 A basic set or relation can be converted to a set or relation
1439 using the following functions.
1441 __isl_give isl_set *isl_set_from_basic_set(
1442 __isl_take isl_basic_set *bset);
1443 __isl_give isl_map *isl_map_from_basic_map(
1444 __isl_take isl_basic_map *bmap);
1446 Sets and relations can be converted to union sets and relations
1447 using the following functions.
1449 __isl_give isl_union_set *isl_union_set_from_basic_set(
1450 __isl_take isl_basic_set *bset);
1451 __isl_give isl_union_map *isl_union_map_from_basic_map(
1452 __isl_take isl_basic_map *bmap);
1453 __isl_give isl_union_set *isl_union_set_from_set(
1454 __isl_take isl_set *set);
1455 __isl_give isl_union_map *isl_union_map_from_map(
1456 __isl_take isl_map *map);
1458 The inverse conversions below can only be used if the input
1459 union set or relation is known to contain elements in exactly one
1462 __isl_give isl_set *isl_set_from_union_set(
1463 __isl_take isl_union_set *uset);
1464 __isl_give isl_map *isl_map_from_union_map(
1465 __isl_take isl_union_map *umap);
1467 A zero-dimensional (basic) set can be constructed on a given parameter domain
1468 using the following function.
1470 __isl_give isl_basic_set *isl_basic_set_from_params(
1471 __isl_take isl_basic_set *bset);
1472 __isl_give isl_set *isl_set_from_params(
1473 __isl_take isl_set *set);
1475 Sets and relations can be copied and freed again using the following
1478 __isl_give isl_basic_set *isl_basic_set_copy(
1479 __isl_keep isl_basic_set *bset);
1480 __isl_give isl_set *isl_set_copy(__isl_keep isl_set *set);
1481 __isl_give isl_union_set *isl_union_set_copy(
1482 __isl_keep isl_union_set *uset);
1483 __isl_give isl_basic_map *isl_basic_map_copy(
1484 __isl_keep isl_basic_map *bmap);
1485 __isl_give isl_map *isl_map_copy(__isl_keep isl_map *map);
1486 __isl_give isl_union_map *isl_union_map_copy(
1487 __isl_keep isl_union_map *umap);
1488 void *isl_basic_set_free(__isl_take isl_basic_set *bset);
1489 void *isl_set_free(__isl_take isl_set *set);
1490 void *isl_union_set_free(__isl_take isl_union_set *uset);
1491 void *isl_basic_map_free(__isl_take isl_basic_map *bmap);
1492 void *isl_map_free(__isl_take isl_map *map);
1493 void *isl_union_map_free(__isl_take isl_union_map *umap);
1495 Other sets and relations can be constructed by starting
1496 from a universe set or relation, adding equality and/or
1497 inequality constraints and then projecting out the
1498 existentially quantified variables, if any.
1499 Constraints can be constructed, manipulated and
1500 added to (or removed from) (basic) sets and relations
1501 using the following functions.
1503 #include <isl/constraint.h>
1504 __isl_give isl_constraint *isl_equality_alloc(
1505 __isl_take isl_local_space *ls);
1506 __isl_give isl_constraint *isl_inequality_alloc(
1507 __isl_take isl_local_space *ls);
1508 __isl_give isl_constraint *isl_constraint_set_constant(
1509 __isl_take isl_constraint *constraint, isl_int v);
1510 __isl_give isl_constraint *isl_constraint_set_constant_si(
1511 __isl_take isl_constraint *constraint, int v);
1512 __isl_give isl_constraint *isl_constraint_set_constant_val(
1513 __isl_take isl_constraint *constraint,
1514 __isl_take isl_val *v);
1515 __isl_give isl_constraint *isl_constraint_set_coefficient(
1516 __isl_take isl_constraint *constraint,
1517 enum isl_dim_type type, int pos, isl_int v);
1518 __isl_give isl_constraint *isl_constraint_set_coefficient_si(
1519 __isl_take isl_constraint *constraint,
1520 enum isl_dim_type type, int pos, int v);
1521 __isl_give isl_constraint *
1522 isl_constraint_set_coefficient_val(
1523 __isl_take isl_constraint *constraint,
1524 enum isl_dim_type type, int pos, isl_val *v);
1525 __isl_give isl_basic_map *isl_basic_map_add_constraint(
1526 __isl_take isl_basic_map *bmap,
1527 __isl_take isl_constraint *constraint);
1528 __isl_give isl_basic_set *isl_basic_set_add_constraint(
1529 __isl_take isl_basic_set *bset,
1530 __isl_take isl_constraint *constraint);
1531 __isl_give isl_map *isl_map_add_constraint(
1532 __isl_take isl_map *map,
1533 __isl_take isl_constraint *constraint);
1534 __isl_give isl_set *isl_set_add_constraint(
1535 __isl_take isl_set *set,
1536 __isl_take isl_constraint *constraint);
1537 __isl_give isl_basic_set *isl_basic_set_drop_constraint(
1538 __isl_take isl_basic_set *bset,
1539 __isl_take isl_constraint *constraint);
1541 For example, to create a set containing the even integers
1542 between 10 and 42, you would use the following code.
1545 isl_local_space *ls;
1547 isl_basic_set *bset;
1549 space = isl_space_set_alloc(ctx, 0, 2);
1550 bset = isl_basic_set_universe(isl_space_copy(space));
1551 ls = isl_local_space_from_space(space);
1553 c = isl_equality_alloc(isl_local_space_copy(ls));
1554 c = isl_constraint_set_coefficient_si(c, isl_dim_set, 0, -1);
1555 c = isl_constraint_set_coefficient_si(c, isl_dim_set, 1, 2);
1556 bset = isl_basic_set_add_constraint(bset, c);
1558 c = isl_inequality_alloc(isl_local_space_copy(ls));
1559 c = isl_constraint_set_constant_si(c, -10);
1560 c = isl_constraint_set_coefficient_si(c, isl_dim_set, 0, 1);
1561 bset = isl_basic_set_add_constraint(bset, c);
1563 c = isl_inequality_alloc(ls);
1564 c = isl_constraint_set_constant_si(c, 42);
1565 c = isl_constraint_set_coefficient_si(c, isl_dim_set, 0, -1);
1566 bset = isl_basic_set_add_constraint(bset, c);
1568 bset = isl_basic_set_project_out(bset, isl_dim_set, 1, 1);
1572 isl_basic_set *bset;
1573 bset = isl_basic_set_read_from_str(ctx,
1574 "{[i] : exists (a : i = 2a and i >= 10 and i <= 42)}");
1576 A basic set or relation can also be constructed from two matrices
1577 describing the equalities and the inequalities.
1579 __isl_give isl_basic_set *isl_basic_set_from_constraint_matrices(
1580 __isl_take isl_space *space,
1581 __isl_take isl_mat *eq, __isl_take isl_mat *ineq,
1582 enum isl_dim_type c1,
1583 enum isl_dim_type c2, enum isl_dim_type c3,
1584 enum isl_dim_type c4);
1585 __isl_give isl_basic_map *isl_basic_map_from_constraint_matrices(
1586 __isl_take isl_space *space,
1587 __isl_take isl_mat *eq, __isl_take isl_mat *ineq,
1588 enum isl_dim_type c1,
1589 enum isl_dim_type c2, enum isl_dim_type c3,
1590 enum isl_dim_type c4, enum isl_dim_type c5);
1592 The C<isl_dim_type> arguments indicate the order in which
1593 different kinds of variables appear in the input matrices
1594 and should be a permutation of C<isl_dim_cst>, C<isl_dim_param>,
1595 C<isl_dim_set> and C<isl_dim_div> for sets and
1596 of C<isl_dim_cst>, C<isl_dim_param>,
1597 C<isl_dim_in>, C<isl_dim_out> and C<isl_dim_div> for relations.
1599 A (basic or union) set or relation can also be constructed from a
1600 (union) (piecewise) (multiple) affine expression
1601 or a list of affine expressions
1602 (See L<"Piecewise Quasi Affine Expressions"> and
1603 L<"Piecewise Multiple Quasi Affine Expressions">).
1605 __isl_give isl_basic_map *isl_basic_map_from_aff(
1606 __isl_take isl_aff *aff);
1607 __isl_give isl_map *isl_map_from_aff(
1608 __isl_take isl_aff *aff);
1609 __isl_give isl_set *isl_set_from_pw_aff(
1610 __isl_take isl_pw_aff *pwaff);
1611 __isl_give isl_map *isl_map_from_pw_aff(
1612 __isl_take isl_pw_aff *pwaff);
1613 __isl_give isl_basic_map *isl_basic_map_from_aff_list(
1614 __isl_take isl_space *domain_space,
1615 __isl_take isl_aff_list *list);
1616 __isl_give isl_basic_map *isl_basic_map_from_multi_aff(
1617 __isl_take isl_multi_aff *maff)
1618 __isl_give isl_map *isl_map_from_multi_aff(
1619 __isl_take isl_multi_aff *maff)
1620 __isl_give isl_set *isl_set_from_pw_multi_aff(
1621 __isl_take isl_pw_multi_aff *pma);
1622 __isl_give isl_map *isl_map_from_pw_multi_aff(
1623 __isl_take isl_pw_multi_aff *pma);
1624 __isl_give isl_union_map *
1625 isl_union_map_from_union_pw_multi_aff(
1626 __isl_take isl_union_pw_multi_aff *upma);
1628 The C<domain_dim> argument describes the domain of the resulting
1629 basic relation. It is required because the C<list> may consist
1630 of zero affine expressions.
1632 =head2 Inspecting Sets and Relations
1634 Usually, the user should not have to care about the actual constraints
1635 of the sets and maps, but should instead apply the abstract operations
1636 explained in the following sections.
1637 Occasionally, however, it may be required to inspect the individual
1638 coefficients of the constraints. This section explains how to do so.
1639 In these cases, it may also be useful to have C<isl> compute
1640 an explicit representation of the existentially quantified variables.
1642 __isl_give isl_set *isl_set_compute_divs(
1643 __isl_take isl_set *set);
1644 __isl_give isl_map *isl_map_compute_divs(
1645 __isl_take isl_map *map);
1646 __isl_give isl_union_set *isl_union_set_compute_divs(
1647 __isl_take isl_union_set *uset);
1648 __isl_give isl_union_map *isl_union_map_compute_divs(
1649 __isl_take isl_union_map *umap);
1651 This explicit representation defines the existentially quantified
1652 variables as integer divisions of the other variables, possibly
1653 including earlier existentially quantified variables.
1654 An explicitly represented existentially quantified variable therefore
1655 has a unique value when the values of the other variables are known.
1656 If, furthermore, the same existentials, i.e., existentials
1657 with the same explicit representations, should appear in the
1658 same order in each of the disjuncts of a set or map, then the user should call
1659 either of the following functions.
1661 __isl_give isl_set *isl_set_align_divs(
1662 __isl_take isl_set *set);
1663 __isl_give isl_map *isl_map_align_divs(
1664 __isl_take isl_map *map);
1666 Alternatively, the existentially quantified variables can be removed
1667 using the following functions, which compute an overapproximation.
1669 __isl_give isl_basic_set *isl_basic_set_remove_divs(
1670 __isl_take isl_basic_set *bset);
1671 __isl_give isl_basic_map *isl_basic_map_remove_divs(
1672 __isl_take isl_basic_map *bmap);
1673 __isl_give isl_set *isl_set_remove_divs(
1674 __isl_take isl_set *set);
1675 __isl_give isl_map *isl_map_remove_divs(
1676 __isl_take isl_map *map);
1678 It is also possible to only remove those divs that are defined
1679 in terms of a given range of dimensions or only those for which
1680 no explicit representation is known.
1682 __isl_give isl_basic_set *
1683 isl_basic_set_remove_divs_involving_dims(
1684 __isl_take isl_basic_set *bset,
1685 enum isl_dim_type type,
1686 unsigned first, unsigned n);
1687 __isl_give isl_basic_map *
1688 isl_basic_map_remove_divs_involving_dims(
1689 __isl_take isl_basic_map *bmap,
1690 enum isl_dim_type type,
1691 unsigned first, unsigned n);
1692 __isl_give isl_set *isl_set_remove_divs_involving_dims(
1693 __isl_take isl_set *set, enum isl_dim_type type,
1694 unsigned first, unsigned n);
1695 __isl_give isl_map *isl_map_remove_divs_involving_dims(
1696 __isl_take isl_map *map, enum isl_dim_type type,
1697 unsigned first, unsigned n);
1699 __isl_give isl_basic_set *
1700 isl_basic_set_remove_unknown_divs(
1701 __isl_take isl_basic_set *bset);
1702 __isl_give isl_set *isl_set_remove_unknown_divs(
1703 __isl_take isl_set *set);
1704 __isl_give isl_map *isl_map_remove_unknown_divs(
1705 __isl_take isl_map *map);
1707 To iterate over all the sets or maps in a union set or map, use
1709 int isl_union_set_foreach_set(__isl_keep isl_union_set *uset,
1710 int (*fn)(__isl_take isl_set *set, void *user),
1712 int isl_union_map_foreach_map(__isl_keep isl_union_map *umap,
1713 int (*fn)(__isl_take isl_map *map, void *user),
1716 The number of sets or maps in a union set or map can be obtained
1719 int isl_union_set_n_set(__isl_keep isl_union_set *uset);
1720 int isl_union_map_n_map(__isl_keep isl_union_map *umap);
1722 To extract the set or map in a given space from a union, use
1724 __isl_give isl_set *isl_union_set_extract_set(
1725 __isl_keep isl_union_set *uset,
1726 __isl_take isl_space *space);
1727 __isl_give isl_map *isl_union_map_extract_map(
1728 __isl_keep isl_union_map *umap,
1729 __isl_take isl_space *space);
1731 To iterate over all the basic sets or maps in a set or map, use
1733 int isl_set_foreach_basic_set(__isl_keep isl_set *set,
1734 int (*fn)(__isl_take isl_basic_set *bset, void *user),
1736 int isl_map_foreach_basic_map(__isl_keep isl_map *map,
1737 int (*fn)(__isl_take isl_basic_map *bmap, void *user),
1740 The callback function C<fn> should return 0 if successful and
1741 -1 if an error occurs. In the latter case, or if any other error
1742 occurs, the above functions will return -1.
1744 It should be noted that C<isl> does not guarantee that
1745 the basic sets or maps passed to C<fn> are disjoint.
1746 If this is required, then the user should call one of
1747 the following functions first.
1749 __isl_give isl_set *isl_set_make_disjoint(
1750 __isl_take isl_set *set);
1751 __isl_give isl_map *isl_map_make_disjoint(
1752 __isl_take isl_map *map);
1754 The number of basic sets in a set can be obtained
1757 int isl_set_n_basic_set(__isl_keep isl_set *set);
1759 To iterate over the constraints of a basic set or map, use
1761 #include <isl/constraint.h>
1763 int isl_basic_set_n_constraint(
1764 __isl_keep isl_basic_set *bset);
1765 int isl_basic_set_foreach_constraint(
1766 __isl_keep isl_basic_set *bset,
1767 int (*fn)(__isl_take isl_constraint *c, void *user),
1769 int isl_basic_map_foreach_constraint(
1770 __isl_keep isl_basic_map *bmap,
1771 int (*fn)(__isl_take isl_constraint *c, void *user),
1773 void *isl_constraint_free(__isl_take isl_constraint *c);
1775 Again, the callback function C<fn> should return 0 if successful and
1776 -1 if an error occurs. In the latter case, or if any other error
1777 occurs, the above functions will return -1.
1778 The constraint C<c> represents either an equality or an inequality.
1779 Use the following function to find out whether a constraint
1780 represents an equality. If not, it represents an inequality.
1782 int isl_constraint_is_equality(
1783 __isl_keep isl_constraint *constraint);
1785 The coefficients of the constraints can be inspected using
1786 the following functions.
1788 int isl_constraint_is_lower_bound(
1789 __isl_keep isl_constraint *constraint,
1790 enum isl_dim_type type, unsigned pos);
1791 int isl_constraint_is_upper_bound(
1792 __isl_keep isl_constraint *constraint,
1793 enum isl_dim_type type, unsigned pos);
1794 void isl_constraint_get_constant(
1795 __isl_keep isl_constraint *constraint, isl_int *v);
1796 __isl_give isl_val *isl_constraint_get_constant_val(
1797 __isl_keep isl_constraint *constraint);
1798 void isl_constraint_get_coefficient(
1799 __isl_keep isl_constraint *constraint,
1800 enum isl_dim_type type, int pos, isl_int *v);
1801 __isl_give isl_val *isl_constraint_get_coefficient_val(
1802 __isl_keep isl_constraint *constraint,
1803 enum isl_dim_type type, int pos);
1804 int isl_constraint_involves_dims(
1805 __isl_keep isl_constraint *constraint,
1806 enum isl_dim_type type, unsigned first, unsigned n);
1808 The explicit representations of the existentially quantified
1809 variables can be inspected using the following function.
1810 Note that the user is only allowed to use this function
1811 if the inspected set or map is the result of a call
1812 to C<isl_set_compute_divs> or C<isl_map_compute_divs>.
1813 The existentially quantified variable is equal to the floor
1814 of the returned affine expression. The affine expression
1815 itself can be inspected using the functions in
1816 L<"Piecewise Quasi Affine Expressions">.
1818 __isl_give isl_aff *isl_constraint_get_div(
1819 __isl_keep isl_constraint *constraint, int pos);
1821 To obtain the constraints of a basic set or map in matrix
1822 form, use the following functions.
1824 __isl_give isl_mat *isl_basic_set_equalities_matrix(
1825 __isl_keep isl_basic_set *bset,
1826 enum isl_dim_type c1, enum isl_dim_type c2,
1827 enum isl_dim_type c3, enum isl_dim_type c4);
1828 __isl_give isl_mat *isl_basic_set_inequalities_matrix(
1829 __isl_keep isl_basic_set *bset,
1830 enum isl_dim_type c1, enum isl_dim_type c2,
1831 enum isl_dim_type c3, enum isl_dim_type c4);
1832 __isl_give isl_mat *isl_basic_map_equalities_matrix(
1833 __isl_keep isl_basic_map *bmap,
1834 enum isl_dim_type c1,
1835 enum isl_dim_type c2, enum isl_dim_type c3,
1836 enum isl_dim_type c4, enum isl_dim_type c5);
1837 __isl_give isl_mat *isl_basic_map_inequalities_matrix(
1838 __isl_keep isl_basic_map *bmap,
1839 enum isl_dim_type c1,
1840 enum isl_dim_type c2, enum isl_dim_type c3,
1841 enum isl_dim_type c4, enum isl_dim_type c5);
1843 The C<isl_dim_type> arguments dictate the order in which
1844 different kinds of variables appear in the resulting matrix
1845 and should be a permutation of C<isl_dim_cst>, C<isl_dim_param>,
1846 C<isl_dim_in>, C<isl_dim_out> and C<isl_dim_div>.
1848 The number of parameters, input, output or set dimensions can
1849 be obtained using the following functions.
1851 unsigned isl_basic_set_dim(__isl_keep isl_basic_set *bset,
1852 enum isl_dim_type type);
1853 unsigned isl_basic_map_dim(__isl_keep isl_basic_map *bmap,
1854 enum isl_dim_type type);
1855 unsigned isl_set_dim(__isl_keep isl_set *set,
1856 enum isl_dim_type type);
1857 unsigned isl_map_dim(__isl_keep isl_map *map,
1858 enum isl_dim_type type);
1860 To check whether the description of a set or relation depends
1861 on one or more given dimensions, it is not necessary to iterate over all
1862 constraints. Instead the following functions can be used.
1864 int isl_basic_set_involves_dims(
1865 __isl_keep isl_basic_set *bset,
1866 enum isl_dim_type type, unsigned first, unsigned n);
1867 int isl_set_involves_dims(__isl_keep isl_set *set,
1868 enum isl_dim_type type, unsigned first, unsigned n);
1869 int isl_basic_map_involves_dims(
1870 __isl_keep isl_basic_map *bmap,
1871 enum isl_dim_type type, unsigned first, unsigned n);
1872 int isl_map_involves_dims(__isl_keep isl_map *map,
1873 enum isl_dim_type type, unsigned first, unsigned n);
1875 Similarly, the following functions can be used to check whether
1876 a given dimension is involved in any lower or upper bound.
1878 int isl_set_dim_has_any_lower_bound(__isl_keep isl_set *set,
1879 enum isl_dim_type type, unsigned pos);
1880 int isl_set_dim_has_any_upper_bound(__isl_keep isl_set *set,
1881 enum isl_dim_type type, unsigned pos);
1883 Note that these functions return true even if there is a bound on
1884 the dimension on only some of the basic sets of C<set>.
1885 To check if they have a bound for all of the basic sets in C<set>,
1886 use the following functions instead.
1888 int isl_set_dim_has_lower_bound(__isl_keep isl_set *set,
1889 enum isl_dim_type type, unsigned pos);
1890 int isl_set_dim_has_upper_bound(__isl_keep isl_set *set,
1891 enum isl_dim_type type, unsigned pos);
1893 The identifiers or names of the domain and range spaces of a set
1894 or relation can be read off or set using the following functions.
1896 __isl_give isl_set *isl_set_set_tuple_id(
1897 __isl_take isl_set *set, __isl_take isl_id *id);
1898 __isl_give isl_set *isl_set_reset_tuple_id(
1899 __isl_take isl_set *set);
1900 int isl_set_has_tuple_id(__isl_keep isl_set *set);
1901 __isl_give isl_id *isl_set_get_tuple_id(
1902 __isl_keep isl_set *set);
1903 __isl_give isl_map *isl_map_set_tuple_id(
1904 __isl_take isl_map *map, enum isl_dim_type type,
1905 __isl_take isl_id *id);
1906 __isl_give isl_map *isl_map_reset_tuple_id(
1907 __isl_take isl_map *map, enum isl_dim_type type);
1908 int isl_map_has_tuple_id(__isl_keep isl_map *map,
1909 enum isl_dim_type type);
1910 __isl_give isl_id *isl_map_get_tuple_id(
1911 __isl_keep isl_map *map, enum isl_dim_type type);
1913 const char *isl_basic_set_get_tuple_name(
1914 __isl_keep isl_basic_set *bset);
1915 __isl_give isl_basic_set *isl_basic_set_set_tuple_name(
1916 __isl_take isl_basic_set *set, const char *s);
1917 int isl_set_has_tuple_name(__isl_keep isl_set *set);
1918 const char *isl_set_get_tuple_name(
1919 __isl_keep isl_set *set);
1920 const char *isl_basic_map_get_tuple_name(
1921 __isl_keep isl_basic_map *bmap,
1922 enum isl_dim_type type);
1923 __isl_give isl_basic_map *isl_basic_map_set_tuple_name(
1924 __isl_take isl_basic_map *bmap,
1925 enum isl_dim_type type, const char *s);
1926 int isl_map_has_tuple_name(__isl_keep isl_map *map,
1927 enum isl_dim_type type);
1928 const char *isl_map_get_tuple_name(
1929 __isl_keep isl_map *map,
1930 enum isl_dim_type type);
1932 As with C<isl_space_get_tuple_name>, the value returned points to
1933 an internal data structure.
1934 The identifiers, positions or names of individual dimensions can be
1935 read off using the following functions.
1937 __isl_give isl_id *isl_basic_set_get_dim_id(
1938 __isl_keep isl_basic_set *bset,
1939 enum isl_dim_type type, unsigned pos);
1940 __isl_give isl_set *isl_set_set_dim_id(
1941 __isl_take isl_set *set, enum isl_dim_type type,
1942 unsigned pos, __isl_take isl_id *id);
1943 int isl_set_has_dim_id(__isl_keep isl_set *set,
1944 enum isl_dim_type type, unsigned pos);
1945 __isl_give isl_id *isl_set_get_dim_id(
1946 __isl_keep isl_set *set, enum isl_dim_type type,
1948 int isl_basic_map_has_dim_id(
1949 __isl_keep isl_basic_map *bmap,
1950 enum isl_dim_type type, unsigned pos);
1951 __isl_give isl_map *isl_map_set_dim_id(
1952 __isl_take isl_map *map, enum isl_dim_type type,
1953 unsigned pos, __isl_take isl_id *id);
1954 int isl_map_has_dim_id(__isl_keep isl_map *map,
1955 enum isl_dim_type type, unsigned pos);
1956 __isl_give isl_id *isl_map_get_dim_id(
1957 __isl_keep isl_map *map, enum isl_dim_type type,
1960 int isl_set_find_dim_by_id(__isl_keep isl_set *set,
1961 enum isl_dim_type type, __isl_keep isl_id *id);
1962 int isl_map_find_dim_by_id(__isl_keep isl_map *map,
1963 enum isl_dim_type type, __isl_keep isl_id *id);
1964 int isl_set_find_dim_by_name(__isl_keep isl_set *set,
1965 enum isl_dim_type type, const char *name);
1966 int isl_map_find_dim_by_name(__isl_keep isl_map *map,
1967 enum isl_dim_type type, const char *name);
1969 const char *isl_constraint_get_dim_name(
1970 __isl_keep isl_constraint *constraint,
1971 enum isl_dim_type type, unsigned pos);
1972 const char *isl_basic_set_get_dim_name(
1973 __isl_keep isl_basic_set *bset,
1974 enum isl_dim_type type, unsigned pos);
1975 int isl_set_has_dim_name(__isl_keep isl_set *set,
1976 enum isl_dim_type type, unsigned pos);
1977 const char *isl_set_get_dim_name(
1978 __isl_keep isl_set *set,
1979 enum isl_dim_type type, unsigned pos);
1980 const char *isl_basic_map_get_dim_name(
1981 __isl_keep isl_basic_map *bmap,
1982 enum isl_dim_type type, unsigned pos);
1983 int isl_map_has_dim_name(__isl_keep isl_map *map,
1984 enum isl_dim_type type, unsigned pos);
1985 const char *isl_map_get_dim_name(
1986 __isl_keep isl_map *map,
1987 enum isl_dim_type type, unsigned pos);
1989 These functions are mostly useful to obtain the identifiers, positions
1990 or names of the parameters. Identifiers of individual dimensions are
1991 essentially only useful for printing. They are ignored by all other
1992 operations and may not be preserved across those operations.
1996 =head3 Unary Properties
2002 The following functions test whether the given set or relation
2003 contains any integer points. The ``plain'' variants do not perform
2004 any computations, but simply check if the given set or relation
2005 is already known to be empty.
2007 int isl_basic_set_plain_is_empty(__isl_keep isl_basic_set *bset);
2008 int isl_basic_set_is_empty(__isl_keep isl_basic_set *bset);
2009 int isl_set_plain_is_empty(__isl_keep isl_set *set);
2010 int isl_set_is_empty(__isl_keep isl_set *set);
2011 int isl_union_set_is_empty(__isl_keep isl_union_set *uset);
2012 int isl_basic_map_plain_is_empty(__isl_keep isl_basic_map *bmap);
2013 int isl_basic_map_is_empty(__isl_keep isl_basic_map *bmap);
2014 int isl_map_plain_is_empty(__isl_keep isl_map *map);
2015 int isl_map_is_empty(__isl_keep isl_map *map);
2016 int isl_union_map_is_empty(__isl_keep isl_union_map *umap);
2018 =item * Universality
2020 int isl_basic_set_is_universe(__isl_keep isl_basic_set *bset);
2021 int isl_basic_map_is_universe(__isl_keep isl_basic_map *bmap);
2022 int isl_set_plain_is_universe(__isl_keep isl_set *set);
2024 =item * Single-valuedness
2026 int isl_basic_map_is_single_valued(
2027 __isl_keep isl_basic_map *bmap);
2028 int isl_map_plain_is_single_valued(
2029 __isl_keep isl_map *map);
2030 int isl_map_is_single_valued(__isl_keep isl_map *map);
2031 int isl_union_map_is_single_valued(__isl_keep isl_union_map *umap);
2035 int isl_map_plain_is_injective(__isl_keep isl_map *map);
2036 int isl_map_is_injective(__isl_keep isl_map *map);
2037 int isl_union_map_plain_is_injective(
2038 __isl_keep isl_union_map *umap);
2039 int isl_union_map_is_injective(
2040 __isl_keep isl_union_map *umap);
2044 int isl_map_is_bijective(__isl_keep isl_map *map);
2045 int isl_union_map_is_bijective(__isl_keep isl_union_map *umap);
2049 int isl_basic_map_plain_is_fixed(
2050 __isl_keep isl_basic_map *bmap,
2051 enum isl_dim_type type, unsigned pos,
2053 int isl_set_plain_is_fixed(__isl_keep isl_set *set,
2054 enum isl_dim_type type, unsigned pos,
2056 int isl_map_plain_is_fixed(__isl_keep isl_map *map,
2057 enum isl_dim_type type, unsigned pos,
2060 Check if the relation obviously lies on a hyperplane where the given dimension
2061 has a fixed value and if so, return that value in C<*val>.
2065 To check whether a set is a parameter domain, use this function:
2067 int isl_set_is_params(__isl_keep isl_set *set);
2068 int isl_union_set_is_params(
2069 __isl_keep isl_union_set *uset);
2073 The following functions check whether the domain of the given
2074 (basic) set is a wrapped relation.
2076 int isl_basic_set_is_wrapping(
2077 __isl_keep isl_basic_set *bset);
2078 int isl_set_is_wrapping(__isl_keep isl_set *set);
2080 =item * Internal Product
2082 int isl_basic_map_can_zip(
2083 __isl_keep isl_basic_map *bmap);
2084 int isl_map_can_zip(__isl_keep isl_map *map);
2086 Check whether the product of domain and range of the given relation
2088 i.e., whether both domain and range are nested relations.
2092 int isl_basic_map_can_curry(
2093 __isl_keep isl_basic_map *bmap);
2094 int isl_map_can_curry(__isl_keep isl_map *map);
2096 Check whether the domain of the (basic) relation is a wrapped relation.
2098 int isl_basic_map_can_uncurry(
2099 __isl_keep isl_basic_map *bmap);
2100 int isl_map_can_uncurry(__isl_keep isl_map *map);
2102 Check whether the range of the (basic) relation is a wrapped relation.
2106 =head3 Binary Properties
2112 int isl_set_plain_is_equal(__isl_keep isl_set *set1,
2113 __isl_keep isl_set *set2);
2114 int isl_set_is_equal(__isl_keep isl_set *set1,
2115 __isl_keep isl_set *set2);
2116 int isl_union_set_is_equal(
2117 __isl_keep isl_union_set *uset1,
2118 __isl_keep isl_union_set *uset2);
2119 int isl_basic_map_is_equal(
2120 __isl_keep isl_basic_map *bmap1,
2121 __isl_keep isl_basic_map *bmap2);
2122 int isl_map_is_equal(__isl_keep isl_map *map1,
2123 __isl_keep isl_map *map2);
2124 int isl_map_plain_is_equal(__isl_keep isl_map *map1,
2125 __isl_keep isl_map *map2);
2126 int isl_union_map_is_equal(
2127 __isl_keep isl_union_map *umap1,
2128 __isl_keep isl_union_map *umap2);
2130 =item * Disjointness
2132 int isl_set_plain_is_disjoint(__isl_keep isl_set *set1,
2133 __isl_keep isl_set *set2);
2134 int isl_set_is_disjoint(__isl_keep isl_set *set1,
2135 __isl_keep isl_set *set2);
2136 int isl_map_is_disjoint(__isl_keep isl_map *map1,
2137 __isl_keep isl_map *map2);
2141 int isl_basic_set_is_subset(
2142 __isl_keep isl_basic_set *bset1,
2143 __isl_keep isl_basic_set *bset2);
2144 int isl_set_is_subset(__isl_keep isl_set *set1,
2145 __isl_keep isl_set *set2);
2146 int isl_set_is_strict_subset(
2147 __isl_keep isl_set *set1,
2148 __isl_keep isl_set *set2);
2149 int isl_union_set_is_subset(
2150 __isl_keep isl_union_set *uset1,
2151 __isl_keep isl_union_set *uset2);
2152 int isl_union_set_is_strict_subset(
2153 __isl_keep isl_union_set *uset1,
2154 __isl_keep isl_union_set *uset2);
2155 int isl_basic_map_is_subset(
2156 __isl_keep isl_basic_map *bmap1,
2157 __isl_keep isl_basic_map *bmap2);
2158 int isl_basic_map_is_strict_subset(
2159 __isl_keep isl_basic_map *bmap1,
2160 __isl_keep isl_basic_map *bmap2);
2161 int isl_map_is_subset(
2162 __isl_keep isl_map *map1,
2163 __isl_keep isl_map *map2);
2164 int isl_map_is_strict_subset(
2165 __isl_keep isl_map *map1,
2166 __isl_keep isl_map *map2);
2167 int isl_union_map_is_subset(
2168 __isl_keep isl_union_map *umap1,
2169 __isl_keep isl_union_map *umap2);
2170 int isl_union_map_is_strict_subset(
2171 __isl_keep isl_union_map *umap1,
2172 __isl_keep isl_union_map *umap2);
2174 Check whether the first argument is a (strict) subset of the
2179 int isl_set_plain_cmp(__isl_keep isl_set *set1,
2180 __isl_keep isl_set *set2);
2182 This function is useful for sorting C<isl_set>s.
2183 The order depends on the internal representation of the inputs.
2184 The order is fixed over different calls to the function (assuming
2185 the internal representation of the inputs has not changed), but may
2186 change over different versions of C<isl>.
2190 =head2 Unary Operations
2196 __isl_give isl_set *isl_set_complement(
2197 __isl_take isl_set *set);
2198 __isl_give isl_map *isl_map_complement(
2199 __isl_take isl_map *map);
2203 __isl_give isl_basic_map *isl_basic_map_reverse(
2204 __isl_take isl_basic_map *bmap);
2205 __isl_give isl_map *isl_map_reverse(
2206 __isl_take isl_map *map);
2207 __isl_give isl_union_map *isl_union_map_reverse(
2208 __isl_take isl_union_map *umap);
2212 __isl_give isl_basic_set *isl_basic_set_project_out(
2213 __isl_take isl_basic_set *bset,
2214 enum isl_dim_type type, unsigned first, unsigned n);
2215 __isl_give isl_basic_map *isl_basic_map_project_out(
2216 __isl_take isl_basic_map *bmap,
2217 enum isl_dim_type type, unsigned first, unsigned n);
2218 __isl_give isl_set *isl_set_project_out(__isl_take isl_set *set,
2219 enum isl_dim_type type, unsigned first, unsigned n);
2220 __isl_give isl_map *isl_map_project_out(__isl_take isl_map *map,
2221 enum isl_dim_type type, unsigned first, unsigned n);
2222 __isl_give isl_basic_set *isl_basic_set_params(
2223 __isl_take isl_basic_set *bset);
2224 __isl_give isl_basic_set *isl_basic_map_domain(
2225 __isl_take isl_basic_map *bmap);
2226 __isl_give isl_basic_set *isl_basic_map_range(
2227 __isl_take isl_basic_map *bmap);
2228 __isl_give isl_set *isl_set_params(__isl_take isl_set *set);
2229 __isl_give isl_set *isl_map_params(__isl_take isl_map *map);
2230 __isl_give isl_set *isl_map_domain(
2231 __isl_take isl_map *bmap);
2232 __isl_give isl_set *isl_map_range(
2233 __isl_take isl_map *map);
2234 __isl_give isl_set *isl_union_set_params(
2235 __isl_take isl_union_set *uset);
2236 __isl_give isl_set *isl_union_map_params(
2237 __isl_take isl_union_map *umap);
2238 __isl_give isl_union_set *isl_union_map_domain(
2239 __isl_take isl_union_map *umap);
2240 __isl_give isl_union_set *isl_union_map_range(
2241 __isl_take isl_union_map *umap);
2243 __isl_give isl_basic_map *isl_basic_map_domain_map(
2244 __isl_take isl_basic_map *bmap);
2245 __isl_give isl_basic_map *isl_basic_map_range_map(
2246 __isl_take isl_basic_map *bmap);
2247 __isl_give isl_map *isl_map_domain_map(__isl_take isl_map *map);
2248 __isl_give isl_map *isl_map_range_map(__isl_take isl_map *map);
2249 __isl_give isl_union_map *isl_union_map_domain_map(
2250 __isl_take isl_union_map *umap);
2251 __isl_give isl_union_map *isl_union_map_range_map(
2252 __isl_take isl_union_map *umap);
2254 The functions above construct a (basic, regular or union) relation
2255 that maps (a wrapped version of) the input relation to its domain or range.
2259 __isl_give isl_basic_set *isl_basic_set_eliminate(
2260 __isl_take isl_basic_set *bset,
2261 enum isl_dim_type type,
2262 unsigned first, unsigned n);
2263 __isl_give isl_set *isl_set_eliminate(
2264 __isl_take isl_set *set, enum isl_dim_type type,
2265 unsigned first, unsigned n);
2266 __isl_give isl_basic_map *isl_basic_map_eliminate(
2267 __isl_take isl_basic_map *bmap,
2268 enum isl_dim_type type,
2269 unsigned first, unsigned n);
2270 __isl_give isl_map *isl_map_eliminate(
2271 __isl_take isl_map *map, enum isl_dim_type type,
2272 unsigned first, unsigned n);
2274 Eliminate the coefficients for the given dimensions from the constraints,
2275 without removing the dimensions.
2279 __isl_give isl_basic_set *isl_basic_set_fix(
2280 __isl_take isl_basic_set *bset,
2281 enum isl_dim_type type, unsigned pos,
2283 __isl_give isl_basic_set *isl_basic_set_fix_si(
2284 __isl_take isl_basic_set *bset,
2285 enum isl_dim_type type, unsigned pos, int value);
2286 __isl_give isl_set *isl_set_fix(__isl_take isl_set *set,
2287 enum isl_dim_type type, unsigned pos,
2289 __isl_give isl_set *isl_set_fix_si(__isl_take isl_set *set,
2290 enum isl_dim_type type, unsigned pos, int value);
2291 __isl_give isl_basic_map *isl_basic_map_fix_si(
2292 __isl_take isl_basic_map *bmap,
2293 enum isl_dim_type type, unsigned pos, int value);
2294 __isl_give isl_map *isl_map_fix(__isl_take isl_map *map,
2295 enum isl_dim_type type, unsigned pos,
2297 __isl_give isl_map *isl_map_fix_si(__isl_take isl_map *map,
2298 enum isl_dim_type type, unsigned pos, int value);
2300 Intersect the set or relation with the hyperplane where the given
2301 dimension has the fixed given value.
2303 __isl_give isl_basic_map *isl_basic_map_lower_bound_si(
2304 __isl_take isl_basic_map *bmap,
2305 enum isl_dim_type type, unsigned pos, int value);
2306 __isl_give isl_basic_map *isl_basic_map_upper_bound_si(
2307 __isl_take isl_basic_map *bmap,
2308 enum isl_dim_type type, unsigned pos, int value);
2309 __isl_give isl_set *isl_set_lower_bound(
2310 __isl_take isl_set *set,
2311 enum isl_dim_type type, unsigned pos,
2313 __isl_give isl_set *isl_set_lower_bound_si(
2314 __isl_take isl_set *set,
2315 enum isl_dim_type type, unsigned pos, int value);
2316 __isl_give isl_map *isl_map_lower_bound_si(
2317 __isl_take isl_map *map,
2318 enum isl_dim_type type, unsigned pos, int value);
2319 __isl_give isl_set *isl_set_upper_bound(
2320 __isl_take isl_set *set,
2321 enum isl_dim_type type, unsigned pos,
2323 __isl_give isl_set *isl_set_upper_bound_si(
2324 __isl_take isl_set *set,
2325 enum isl_dim_type type, unsigned pos, int value);
2326 __isl_give isl_map *isl_map_upper_bound_si(
2327 __isl_take isl_map *map,
2328 enum isl_dim_type type, unsigned pos, int value);
2330 Intersect the set or relation with the half-space where the given
2331 dimension has a value bounded by the fixed given value.
2333 __isl_give isl_set *isl_set_equate(__isl_take isl_set *set,
2334 enum isl_dim_type type1, int pos1,
2335 enum isl_dim_type type2, int pos2);
2336 __isl_give isl_basic_map *isl_basic_map_equate(
2337 __isl_take isl_basic_map *bmap,
2338 enum isl_dim_type type1, int pos1,
2339 enum isl_dim_type type2, int pos2);
2340 __isl_give isl_map *isl_map_equate(__isl_take isl_map *map,
2341 enum isl_dim_type type1, int pos1,
2342 enum isl_dim_type type2, int pos2);
2344 Intersect the set or relation with the hyperplane where the given
2345 dimensions are equal to each other.
2347 __isl_give isl_map *isl_map_oppose(__isl_take isl_map *map,
2348 enum isl_dim_type type1, int pos1,
2349 enum isl_dim_type type2, int pos2);
2351 Intersect the relation with the hyperplane where the given
2352 dimensions have opposite values.
2354 __isl_give isl_basic_map *isl_basic_map_order_ge(
2355 __isl_take isl_basic_map *bmap,
2356 enum isl_dim_type type1, int pos1,
2357 enum isl_dim_type type2, int pos2);
2358 __isl_give isl_map *isl_map_order_lt(__isl_take isl_map *map,
2359 enum isl_dim_type type1, int pos1,
2360 enum isl_dim_type type2, int pos2);
2361 __isl_give isl_basic_map *isl_basic_map_order_gt(
2362 __isl_take isl_basic_map *bmap,
2363 enum isl_dim_type type1, int pos1,
2364 enum isl_dim_type type2, int pos2);
2365 __isl_give isl_map *isl_map_order_gt(__isl_take isl_map *map,
2366 enum isl_dim_type type1, int pos1,
2367 enum isl_dim_type type2, int pos2);
2369 Intersect the relation with the half-space where the given
2370 dimensions satisfy the given ordering.
2374 __isl_give isl_map *isl_set_identity(
2375 __isl_take isl_set *set);
2376 __isl_give isl_union_map *isl_union_set_identity(
2377 __isl_take isl_union_set *uset);
2379 Construct an identity relation on the given (union) set.
2383 __isl_give isl_basic_set *isl_basic_map_deltas(
2384 __isl_take isl_basic_map *bmap);
2385 __isl_give isl_set *isl_map_deltas(__isl_take isl_map *map);
2386 __isl_give isl_union_set *isl_union_map_deltas(
2387 __isl_take isl_union_map *umap);
2389 These functions return a (basic) set containing the differences
2390 between image elements and corresponding domain elements in the input.
2392 __isl_give isl_basic_map *isl_basic_map_deltas_map(
2393 __isl_take isl_basic_map *bmap);
2394 __isl_give isl_map *isl_map_deltas_map(
2395 __isl_take isl_map *map);
2396 __isl_give isl_union_map *isl_union_map_deltas_map(
2397 __isl_take isl_union_map *umap);
2399 The functions above construct a (basic, regular or union) relation
2400 that maps (a wrapped version of) the input relation to its delta set.
2404 Simplify the representation of a set or relation by trying
2405 to combine pairs of basic sets or relations into a single
2406 basic set or relation.
2408 __isl_give isl_set *isl_set_coalesce(__isl_take isl_set *set);
2409 __isl_give isl_map *isl_map_coalesce(__isl_take isl_map *map);
2410 __isl_give isl_union_set *isl_union_set_coalesce(
2411 __isl_take isl_union_set *uset);
2412 __isl_give isl_union_map *isl_union_map_coalesce(
2413 __isl_take isl_union_map *umap);
2415 One of the methods for combining pairs of basic sets or relations
2416 can result in coefficients that are much larger than those that appear
2417 in the constraints of the input. By default, the coefficients are
2418 not allowed to grow larger, but this can be changed by unsetting
2419 the following option.
2421 int isl_options_set_coalesce_bounded_wrapping(
2422 isl_ctx *ctx, int val);
2423 int isl_options_get_coalesce_bounded_wrapping(
2426 =item * Detecting equalities
2428 __isl_give isl_basic_set *isl_basic_set_detect_equalities(
2429 __isl_take isl_basic_set *bset);
2430 __isl_give isl_basic_map *isl_basic_map_detect_equalities(
2431 __isl_take isl_basic_map *bmap);
2432 __isl_give isl_set *isl_set_detect_equalities(
2433 __isl_take isl_set *set);
2434 __isl_give isl_map *isl_map_detect_equalities(
2435 __isl_take isl_map *map);
2436 __isl_give isl_union_set *isl_union_set_detect_equalities(
2437 __isl_take isl_union_set *uset);
2438 __isl_give isl_union_map *isl_union_map_detect_equalities(
2439 __isl_take isl_union_map *umap);
2441 Simplify the representation of a set or relation by detecting implicit
2444 =item * Removing redundant constraints
2446 __isl_give isl_basic_set *isl_basic_set_remove_redundancies(
2447 __isl_take isl_basic_set *bset);
2448 __isl_give isl_set *isl_set_remove_redundancies(
2449 __isl_take isl_set *set);
2450 __isl_give isl_basic_map *isl_basic_map_remove_redundancies(
2451 __isl_take isl_basic_map *bmap);
2452 __isl_give isl_map *isl_map_remove_redundancies(
2453 __isl_take isl_map *map);
2457 __isl_give isl_basic_set *isl_set_convex_hull(
2458 __isl_take isl_set *set);
2459 __isl_give isl_basic_map *isl_map_convex_hull(
2460 __isl_take isl_map *map);
2462 If the input set or relation has any existentially quantified
2463 variables, then the result of these operations is currently undefined.
2467 __isl_give isl_basic_set *
2468 isl_set_unshifted_simple_hull(
2469 __isl_take isl_set *set);
2470 __isl_give isl_basic_map *
2471 isl_map_unshifted_simple_hull(
2472 __isl_take isl_map *map);
2473 __isl_give isl_basic_set *isl_set_simple_hull(
2474 __isl_take isl_set *set);
2475 __isl_give isl_basic_map *isl_map_simple_hull(
2476 __isl_take isl_map *map);
2477 __isl_give isl_union_map *isl_union_map_simple_hull(
2478 __isl_take isl_union_map *umap);
2480 These functions compute a single basic set or relation
2481 that contains the whole input set or relation.
2482 In particular, the output is described by translates
2483 of the constraints describing the basic sets or relations in the input.
2484 In case of C<isl_set_unshifted_simple_hull>, only the original
2485 constraints are used, without any translation.
2489 (See \autoref{s:simple hull}.)
2495 __isl_give isl_basic_set *isl_basic_set_affine_hull(
2496 __isl_take isl_basic_set *bset);
2497 __isl_give isl_basic_set *isl_set_affine_hull(
2498 __isl_take isl_set *set);
2499 __isl_give isl_union_set *isl_union_set_affine_hull(
2500 __isl_take isl_union_set *uset);
2501 __isl_give isl_basic_map *isl_basic_map_affine_hull(
2502 __isl_take isl_basic_map *bmap);
2503 __isl_give isl_basic_map *isl_map_affine_hull(
2504 __isl_take isl_map *map);
2505 __isl_give isl_union_map *isl_union_map_affine_hull(
2506 __isl_take isl_union_map *umap);
2508 In case of union sets and relations, the affine hull is computed
2511 =item * Polyhedral hull
2513 __isl_give isl_basic_set *isl_set_polyhedral_hull(
2514 __isl_take isl_set *set);
2515 __isl_give isl_basic_map *isl_map_polyhedral_hull(
2516 __isl_take isl_map *map);
2517 __isl_give isl_union_set *isl_union_set_polyhedral_hull(
2518 __isl_take isl_union_set *uset);
2519 __isl_give isl_union_map *isl_union_map_polyhedral_hull(
2520 __isl_take isl_union_map *umap);
2522 These functions compute a single basic set or relation
2523 not involving any existentially quantified variables
2524 that contains the whole input set or relation.
2525 In case of union sets and relations, the polyhedral hull is computed
2528 =item * Other approximations
2530 __isl_give isl_basic_set *
2531 isl_basic_set_drop_constraints_involving_dims(
2532 __isl_take isl_basic_set *bset,
2533 enum isl_dim_type type,
2534 unsigned first, unsigned n);
2535 __isl_give isl_basic_map *
2536 isl_basic_map_drop_constraints_involving_dims(
2537 __isl_take isl_basic_map *bmap,
2538 enum isl_dim_type type,
2539 unsigned first, unsigned n);
2540 __isl_give isl_basic_set *
2541 isl_basic_set_drop_constraints_not_involving_dims(
2542 __isl_take isl_basic_set *bset,
2543 enum isl_dim_type type,
2544 unsigned first, unsigned n);
2545 __isl_give isl_set *
2546 isl_set_drop_constraints_involving_dims(
2547 __isl_take isl_set *set,
2548 enum isl_dim_type type,
2549 unsigned first, unsigned n);
2550 __isl_give isl_map *
2551 isl_map_drop_constraints_involving_dims(
2552 __isl_take isl_map *map,
2553 enum isl_dim_type type,
2554 unsigned first, unsigned n);
2556 These functions drop any constraints (not) involving the specified dimensions.
2557 Note that the result depends on the representation of the input.
2561 __isl_give isl_basic_set *isl_basic_set_sample(
2562 __isl_take isl_basic_set *bset);
2563 __isl_give isl_basic_set *isl_set_sample(
2564 __isl_take isl_set *set);
2565 __isl_give isl_basic_map *isl_basic_map_sample(
2566 __isl_take isl_basic_map *bmap);
2567 __isl_give isl_basic_map *isl_map_sample(
2568 __isl_take isl_map *map);
2570 If the input (basic) set or relation is non-empty, then return
2571 a singleton subset of the input. Otherwise, return an empty set.
2573 =item * Optimization
2575 #include <isl/ilp.h>
2576 enum isl_lp_result isl_basic_set_max(
2577 __isl_keep isl_basic_set *bset,
2578 __isl_keep isl_aff *obj, isl_int *opt)
2579 enum isl_lp_result isl_set_min(__isl_keep isl_set *set,
2580 __isl_keep isl_aff *obj, isl_int *opt);
2581 enum isl_lp_result isl_set_max(__isl_keep isl_set *set,
2582 __isl_keep isl_aff *obj, isl_int *opt);
2584 Compute the minimum or maximum of the integer affine expression C<obj>
2585 over the points in C<set>, returning the result in C<opt>.
2586 The return value may be one of C<isl_lp_error>,
2587 C<isl_lp_ok>, C<isl_lp_unbounded> or C<isl_lp_empty>.
2589 =item * Parametric optimization
2591 __isl_give isl_pw_aff *isl_set_dim_min(
2592 __isl_take isl_set *set, int pos);
2593 __isl_give isl_pw_aff *isl_set_dim_max(
2594 __isl_take isl_set *set, int pos);
2595 __isl_give isl_pw_aff *isl_map_dim_max(
2596 __isl_take isl_map *map, int pos);
2598 Compute the minimum or maximum of the given set or output dimension
2599 as a function of the parameters (and input dimensions), but independently
2600 of the other set or output dimensions.
2601 For lexicographic optimization, see L<"Lexicographic Optimization">.
2605 The following functions compute either the set of (rational) coefficient
2606 values of valid constraints for the given set or the set of (rational)
2607 values satisfying the constraints with coefficients from the given set.
2608 Internally, these two sets of functions perform essentially the
2609 same operations, except that the set of coefficients is assumed to
2610 be a cone, while the set of values may be any polyhedron.
2611 The current implementation is based on the Farkas lemma and
2612 Fourier-Motzkin elimination, but this may change or be made optional
2613 in future. In particular, future implementations may use different
2614 dualization algorithms or skip the elimination step.
2616 __isl_give isl_basic_set *isl_basic_set_coefficients(
2617 __isl_take isl_basic_set *bset);
2618 __isl_give isl_basic_set *isl_set_coefficients(
2619 __isl_take isl_set *set);
2620 __isl_give isl_union_set *isl_union_set_coefficients(
2621 __isl_take isl_union_set *bset);
2622 __isl_give isl_basic_set *isl_basic_set_solutions(
2623 __isl_take isl_basic_set *bset);
2624 __isl_give isl_basic_set *isl_set_solutions(
2625 __isl_take isl_set *set);
2626 __isl_give isl_union_set *isl_union_set_solutions(
2627 __isl_take isl_union_set *bset);
2631 __isl_give isl_map *isl_map_fixed_power(
2632 __isl_take isl_map *map, isl_int exp);
2633 __isl_give isl_union_map *isl_union_map_fixed_power(
2634 __isl_take isl_union_map *umap, isl_int exp);
2636 Compute the given power of C<map>, where C<exp> is assumed to be non-zero.
2637 If the exponent C<exp> is negative, then the -C<exp> th power of the inverse
2638 of C<map> is computed.
2640 __isl_give isl_map *isl_map_power(__isl_take isl_map *map,
2642 __isl_give isl_union_map *isl_union_map_power(
2643 __isl_take isl_union_map *umap, int *exact);
2645 Compute a parametric representation for all positive powers I<k> of C<map>.
2646 The result maps I<k> to a nested relation corresponding to the
2647 I<k>th power of C<map>.
2648 The result may be an overapproximation. If the result is known to be exact,
2649 then C<*exact> is set to C<1>.
2651 =item * Transitive closure
2653 __isl_give isl_map *isl_map_transitive_closure(
2654 __isl_take isl_map *map, int *exact);
2655 __isl_give isl_union_map *isl_union_map_transitive_closure(
2656 __isl_take isl_union_map *umap, int *exact);
2658 Compute the transitive closure of C<map>.
2659 The result may be an overapproximation. If the result is known to be exact,
2660 then C<*exact> is set to C<1>.
2662 =item * Reaching path lengths
2664 __isl_give isl_map *isl_map_reaching_path_lengths(
2665 __isl_take isl_map *map, int *exact);
2667 Compute a relation that maps each element in the range of C<map>
2668 to the lengths of all paths composed of edges in C<map> that
2669 end up in the given element.
2670 The result may be an overapproximation. If the result is known to be exact,
2671 then C<*exact> is set to C<1>.
2672 To compute the I<maximal> path length, the resulting relation
2673 should be postprocessed by C<isl_map_lexmax>.
2674 In particular, if the input relation is a dependence relation
2675 (mapping sources to sinks), then the maximal path length corresponds
2676 to the free schedule.
2677 Note, however, that C<isl_map_lexmax> expects the maximum to be
2678 finite, so if the path lengths are unbounded (possibly due to
2679 the overapproximation), then you will get an error message.
2683 __isl_give isl_basic_set *isl_basic_map_wrap(
2684 __isl_take isl_basic_map *bmap);
2685 __isl_give isl_set *isl_map_wrap(
2686 __isl_take isl_map *map);
2687 __isl_give isl_union_set *isl_union_map_wrap(
2688 __isl_take isl_union_map *umap);
2689 __isl_give isl_basic_map *isl_basic_set_unwrap(
2690 __isl_take isl_basic_set *bset);
2691 __isl_give isl_map *isl_set_unwrap(
2692 __isl_take isl_set *set);
2693 __isl_give isl_union_map *isl_union_set_unwrap(
2694 __isl_take isl_union_set *uset);
2698 Remove any internal structure of domain (and range) of the given
2699 set or relation. If there is any such internal structure in the input,
2700 then the name of the space is also removed.
2702 __isl_give isl_basic_set *isl_basic_set_flatten(
2703 __isl_take isl_basic_set *bset);
2704 __isl_give isl_set *isl_set_flatten(
2705 __isl_take isl_set *set);
2706 __isl_give isl_basic_map *isl_basic_map_flatten_domain(
2707 __isl_take isl_basic_map *bmap);
2708 __isl_give isl_basic_map *isl_basic_map_flatten_range(
2709 __isl_take isl_basic_map *bmap);
2710 __isl_give isl_map *isl_map_flatten_range(
2711 __isl_take isl_map *map);
2712 __isl_give isl_map *isl_map_flatten_domain(
2713 __isl_take isl_map *map);
2714 __isl_give isl_basic_map *isl_basic_map_flatten(
2715 __isl_take isl_basic_map *bmap);
2716 __isl_give isl_map *isl_map_flatten(
2717 __isl_take isl_map *map);
2719 __isl_give isl_map *isl_set_flatten_map(
2720 __isl_take isl_set *set);
2722 The function above constructs a relation
2723 that maps the input set to a flattened version of the set.
2727 Lift the input set to a space with extra dimensions corresponding
2728 to the existentially quantified variables in the input.
2729 In particular, the result lives in a wrapped map where the domain
2730 is the original space and the range corresponds to the original
2731 existentially quantified variables.
2733 __isl_give isl_basic_set *isl_basic_set_lift(
2734 __isl_take isl_basic_set *bset);
2735 __isl_give isl_set *isl_set_lift(
2736 __isl_take isl_set *set);
2737 __isl_give isl_union_set *isl_union_set_lift(
2738 __isl_take isl_union_set *uset);
2740 Given a local space that contains the existentially quantified
2741 variables of a set, a basic relation that, when applied to
2742 a basic set, has essentially the same effect as C<isl_basic_set_lift>,
2743 can be constructed using the following function.
2745 #include <isl/local_space.h>
2746 __isl_give isl_basic_map *isl_local_space_lifting(
2747 __isl_take isl_local_space *ls);
2749 =item * Internal Product
2751 __isl_give isl_basic_map *isl_basic_map_zip(
2752 __isl_take isl_basic_map *bmap);
2753 __isl_give isl_map *isl_map_zip(
2754 __isl_take isl_map *map);
2755 __isl_give isl_union_map *isl_union_map_zip(
2756 __isl_take isl_union_map *umap);
2758 Given a relation with nested relations for domain and range,
2759 interchange the range of the domain with the domain of the range.
2763 __isl_give isl_basic_map *isl_basic_map_curry(
2764 __isl_take isl_basic_map *bmap);
2765 __isl_give isl_basic_map *isl_basic_map_uncurry(
2766 __isl_take isl_basic_map *bmap);
2767 __isl_give isl_map *isl_map_curry(
2768 __isl_take isl_map *map);
2769 __isl_give isl_map *isl_map_uncurry(
2770 __isl_take isl_map *map);
2771 __isl_give isl_union_map *isl_union_map_curry(
2772 __isl_take isl_union_map *umap);
2773 __isl_give isl_union_map *isl_union_map_uncurry(
2774 __isl_take isl_union_map *umap);
2776 Given a relation with a nested relation for domain,
2777 the C<curry> functions
2778 move the range of the nested relation out of the domain
2779 and use it as the domain of a nested relation in the range,
2780 with the original range as range of this nested relation.
2781 The C<uncurry> functions perform the inverse operation.
2783 =item * Aligning parameters
2785 __isl_give isl_basic_set *isl_basic_set_align_params(
2786 __isl_take isl_basic_set *bset,
2787 __isl_take isl_space *model);
2788 __isl_give isl_set *isl_set_align_params(
2789 __isl_take isl_set *set,
2790 __isl_take isl_space *model);
2791 __isl_give isl_basic_map *isl_basic_map_align_params(
2792 __isl_take isl_basic_map *bmap,
2793 __isl_take isl_space *model);
2794 __isl_give isl_map *isl_map_align_params(
2795 __isl_take isl_map *map,
2796 __isl_take isl_space *model);
2798 Change the order of the parameters of the given set or relation
2799 such that the first parameters match those of C<model>.
2800 This may involve the introduction of extra parameters.
2801 All parameters need to be named.
2803 =item * Dimension manipulation
2805 __isl_give isl_basic_set *isl_basic_set_add_dims(
2806 __isl_take isl_basic_set *bset,
2807 enum isl_dim_type type, unsigned n);
2808 __isl_give isl_set *isl_set_add_dims(
2809 __isl_take isl_set *set,
2810 enum isl_dim_type type, unsigned n);
2811 __isl_give isl_map *isl_map_add_dims(
2812 __isl_take isl_map *map,
2813 enum isl_dim_type type, unsigned n);
2814 __isl_give isl_basic_set *isl_basic_set_insert_dims(
2815 __isl_take isl_basic_set *bset,
2816 enum isl_dim_type type, unsigned pos,
2818 __isl_give isl_basic_map *isl_basic_map_insert_dims(
2819 __isl_take isl_basic_map *bmap,
2820 enum isl_dim_type type, unsigned pos,
2822 __isl_give isl_set *isl_set_insert_dims(
2823 __isl_take isl_set *set,
2824 enum isl_dim_type type, unsigned pos, unsigned n);
2825 __isl_give isl_map *isl_map_insert_dims(
2826 __isl_take isl_map *map,
2827 enum isl_dim_type type, unsigned pos, unsigned n);
2828 __isl_give isl_basic_set *isl_basic_set_move_dims(
2829 __isl_take isl_basic_set *bset,
2830 enum isl_dim_type dst_type, unsigned dst_pos,
2831 enum isl_dim_type src_type, unsigned src_pos,
2833 __isl_give isl_basic_map *isl_basic_map_move_dims(
2834 __isl_take isl_basic_map *bmap,
2835 enum isl_dim_type dst_type, unsigned dst_pos,
2836 enum isl_dim_type src_type, unsigned src_pos,
2838 __isl_give isl_set *isl_set_move_dims(
2839 __isl_take isl_set *set,
2840 enum isl_dim_type dst_type, unsigned dst_pos,
2841 enum isl_dim_type src_type, unsigned src_pos,
2843 __isl_give isl_map *isl_map_move_dims(
2844 __isl_take isl_map *map,
2845 enum isl_dim_type dst_type, unsigned dst_pos,
2846 enum isl_dim_type src_type, unsigned src_pos,
2849 It is usually not advisable to directly change the (input or output)
2850 space of a set or a relation as this removes the name and the internal
2851 structure of the space. However, the above functions can be useful
2852 to add new parameters, assuming
2853 C<isl_set_align_params> and C<isl_map_align_params>
2858 =head2 Binary Operations
2860 The two arguments of a binary operation not only need to live
2861 in the same C<isl_ctx>, they currently also need to have
2862 the same (number of) parameters.
2864 =head3 Basic Operations
2868 =item * Intersection
2870 __isl_give isl_basic_set *isl_basic_set_intersect_params(
2871 __isl_take isl_basic_set *bset1,
2872 __isl_take isl_basic_set *bset2);
2873 __isl_give isl_basic_set *isl_basic_set_intersect(
2874 __isl_take isl_basic_set *bset1,
2875 __isl_take isl_basic_set *bset2);
2876 __isl_give isl_set *isl_set_intersect_params(
2877 __isl_take isl_set *set,
2878 __isl_take isl_set *params);
2879 __isl_give isl_set *isl_set_intersect(
2880 __isl_take isl_set *set1,
2881 __isl_take isl_set *set2);
2882 __isl_give isl_union_set *isl_union_set_intersect_params(
2883 __isl_take isl_union_set *uset,
2884 __isl_take isl_set *set);
2885 __isl_give isl_union_map *isl_union_map_intersect_params(
2886 __isl_take isl_union_map *umap,
2887 __isl_take isl_set *set);
2888 __isl_give isl_union_set *isl_union_set_intersect(
2889 __isl_take isl_union_set *uset1,
2890 __isl_take isl_union_set *uset2);
2891 __isl_give isl_basic_map *isl_basic_map_intersect_domain(
2892 __isl_take isl_basic_map *bmap,
2893 __isl_take isl_basic_set *bset);
2894 __isl_give isl_basic_map *isl_basic_map_intersect_range(
2895 __isl_take isl_basic_map *bmap,
2896 __isl_take isl_basic_set *bset);
2897 __isl_give isl_basic_map *isl_basic_map_intersect(
2898 __isl_take isl_basic_map *bmap1,
2899 __isl_take isl_basic_map *bmap2);
2900 __isl_give isl_map *isl_map_intersect_params(
2901 __isl_take isl_map *map,
2902 __isl_take isl_set *params);
2903 __isl_give isl_map *isl_map_intersect_domain(
2904 __isl_take isl_map *map,
2905 __isl_take isl_set *set);
2906 __isl_give isl_map *isl_map_intersect_range(
2907 __isl_take isl_map *map,
2908 __isl_take isl_set *set);
2909 __isl_give isl_map *isl_map_intersect(
2910 __isl_take isl_map *map1,
2911 __isl_take isl_map *map2);
2912 __isl_give isl_union_map *isl_union_map_intersect_domain(
2913 __isl_take isl_union_map *umap,
2914 __isl_take isl_union_set *uset);
2915 __isl_give isl_union_map *isl_union_map_intersect_range(
2916 __isl_take isl_union_map *umap,
2917 __isl_take isl_union_set *uset);
2918 __isl_give isl_union_map *isl_union_map_intersect(
2919 __isl_take isl_union_map *umap1,
2920 __isl_take isl_union_map *umap2);
2922 The second argument to the C<_params> functions needs to be
2923 a parametric (basic) set. For the other functions, a parametric set
2924 for either argument is only allowed if the other argument is
2925 a parametric set as well.
2929 __isl_give isl_set *isl_basic_set_union(
2930 __isl_take isl_basic_set *bset1,
2931 __isl_take isl_basic_set *bset2);
2932 __isl_give isl_map *isl_basic_map_union(
2933 __isl_take isl_basic_map *bmap1,
2934 __isl_take isl_basic_map *bmap2);
2935 __isl_give isl_set *isl_set_union(
2936 __isl_take isl_set *set1,
2937 __isl_take isl_set *set2);
2938 __isl_give isl_map *isl_map_union(
2939 __isl_take isl_map *map1,
2940 __isl_take isl_map *map2);
2941 __isl_give isl_union_set *isl_union_set_union(
2942 __isl_take isl_union_set *uset1,
2943 __isl_take isl_union_set *uset2);
2944 __isl_give isl_union_map *isl_union_map_union(
2945 __isl_take isl_union_map *umap1,
2946 __isl_take isl_union_map *umap2);
2948 =item * Set difference
2950 __isl_give isl_set *isl_set_subtract(
2951 __isl_take isl_set *set1,
2952 __isl_take isl_set *set2);
2953 __isl_give isl_map *isl_map_subtract(
2954 __isl_take isl_map *map1,
2955 __isl_take isl_map *map2);
2956 __isl_give isl_map *isl_map_subtract_domain(
2957 __isl_take isl_map *map,
2958 __isl_take isl_set *dom);
2959 __isl_give isl_map *isl_map_subtract_range(
2960 __isl_take isl_map *map,
2961 __isl_take isl_set *dom);
2962 __isl_give isl_union_set *isl_union_set_subtract(
2963 __isl_take isl_union_set *uset1,
2964 __isl_take isl_union_set *uset2);
2965 __isl_give isl_union_map *isl_union_map_subtract(
2966 __isl_take isl_union_map *umap1,
2967 __isl_take isl_union_map *umap2);
2968 __isl_give isl_union_map *isl_union_map_subtract_domain(
2969 __isl_take isl_union_map *umap,
2970 __isl_take isl_union_set *dom);
2971 __isl_give isl_union_map *isl_union_map_subtract_range(
2972 __isl_take isl_union_map *umap,
2973 __isl_take isl_union_set *dom);
2977 __isl_give isl_basic_set *isl_basic_set_apply(
2978 __isl_take isl_basic_set *bset,
2979 __isl_take isl_basic_map *bmap);
2980 __isl_give isl_set *isl_set_apply(
2981 __isl_take isl_set *set,
2982 __isl_take isl_map *map);
2983 __isl_give isl_union_set *isl_union_set_apply(
2984 __isl_take isl_union_set *uset,
2985 __isl_take isl_union_map *umap);
2986 __isl_give isl_basic_map *isl_basic_map_apply_domain(
2987 __isl_take isl_basic_map *bmap1,
2988 __isl_take isl_basic_map *bmap2);
2989 __isl_give isl_basic_map *isl_basic_map_apply_range(
2990 __isl_take isl_basic_map *bmap1,
2991 __isl_take isl_basic_map *bmap2);
2992 __isl_give isl_map *isl_map_apply_domain(
2993 __isl_take isl_map *map1,
2994 __isl_take isl_map *map2);
2995 __isl_give isl_union_map *isl_union_map_apply_domain(
2996 __isl_take isl_union_map *umap1,
2997 __isl_take isl_union_map *umap2);
2998 __isl_give isl_map *isl_map_apply_range(
2999 __isl_take isl_map *map1,
3000 __isl_take isl_map *map2);
3001 __isl_give isl_union_map *isl_union_map_apply_range(
3002 __isl_take isl_union_map *umap1,
3003 __isl_take isl_union_map *umap2);
3007 __isl_give isl_basic_set *
3008 isl_basic_set_preimage_multi_aff(
3009 __isl_take isl_basic_set *bset,
3010 __isl_take isl_multi_aff *ma);
3011 __isl_give isl_set *isl_set_preimage_multi_aff(
3012 __isl_take isl_set *set,
3013 __isl_take isl_multi_aff *ma);
3014 __isl_give isl_set *isl_set_preimage_pw_multi_aff(
3015 __isl_take isl_set *set,
3016 __isl_take isl_pw_multi_aff *pma);
3017 __isl_give isl_map *isl_map_preimage_domain_multi_aff(
3018 __isl_take isl_map *map,
3019 __isl_take isl_multi_aff *ma);
3020 __isl_give isl_union_map *
3021 isl_union_map_preimage_domain_multi_aff(
3022 __isl_take isl_union_map *umap,
3023 __isl_take isl_multi_aff *ma);
3025 These functions compute the preimage of the given set or map domain under
3026 the given function. In other words, the expression is plugged
3027 into the set description or into the domain of the map.
3028 Objects of types C<isl_multi_aff> and C<isl_pw_multi_aff> are described in
3029 L</"Piecewise Multiple Quasi Affine Expressions">.
3031 =item * Cartesian Product
3033 __isl_give isl_set *isl_set_product(
3034 __isl_take isl_set *set1,
3035 __isl_take isl_set *set2);
3036 __isl_give isl_union_set *isl_union_set_product(
3037 __isl_take isl_union_set *uset1,
3038 __isl_take isl_union_set *uset2);
3039 __isl_give isl_basic_map *isl_basic_map_domain_product(
3040 __isl_take isl_basic_map *bmap1,
3041 __isl_take isl_basic_map *bmap2);
3042 __isl_give isl_basic_map *isl_basic_map_range_product(
3043 __isl_take isl_basic_map *bmap1,
3044 __isl_take isl_basic_map *bmap2);
3045 __isl_give isl_basic_map *isl_basic_map_product(
3046 __isl_take isl_basic_map *bmap1,
3047 __isl_take isl_basic_map *bmap2);
3048 __isl_give isl_map *isl_map_domain_product(
3049 __isl_take isl_map *map1,
3050 __isl_take isl_map *map2);
3051 __isl_give isl_map *isl_map_range_product(
3052 __isl_take isl_map *map1,
3053 __isl_take isl_map *map2);
3054 __isl_give isl_union_map *isl_union_map_domain_product(
3055 __isl_take isl_union_map *umap1,
3056 __isl_take isl_union_map *umap2);
3057 __isl_give isl_union_map *isl_union_map_range_product(
3058 __isl_take isl_union_map *umap1,
3059 __isl_take isl_union_map *umap2);
3060 __isl_give isl_map *isl_map_product(
3061 __isl_take isl_map *map1,
3062 __isl_take isl_map *map2);
3063 __isl_give isl_union_map *isl_union_map_product(
3064 __isl_take isl_union_map *umap1,
3065 __isl_take isl_union_map *umap2);
3067 The above functions compute the cross product of the given
3068 sets or relations. The domains and ranges of the results
3069 are wrapped maps between domains and ranges of the inputs.
3070 To obtain a ``flat'' product, use the following functions
3073 __isl_give isl_basic_set *isl_basic_set_flat_product(
3074 __isl_take isl_basic_set *bset1,
3075 __isl_take isl_basic_set *bset2);
3076 __isl_give isl_set *isl_set_flat_product(
3077 __isl_take isl_set *set1,
3078 __isl_take isl_set *set2);
3079 __isl_give isl_basic_map *isl_basic_map_flat_range_product(
3080 __isl_take isl_basic_map *bmap1,
3081 __isl_take isl_basic_map *bmap2);
3082 __isl_give isl_map *isl_map_flat_domain_product(
3083 __isl_take isl_map *map1,
3084 __isl_take isl_map *map2);
3085 __isl_give isl_map *isl_map_flat_range_product(
3086 __isl_take isl_map *map1,
3087 __isl_take isl_map *map2);
3088 __isl_give isl_union_map *isl_union_map_flat_range_product(
3089 __isl_take isl_union_map *umap1,
3090 __isl_take isl_union_map *umap2);
3091 __isl_give isl_basic_map *isl_basic_map_flat_product(
3092 __isl_take isl_basic_map *bmap1,
3093 __isl_take isl_basic_map *bmap2);
3094 __isl_give isl_map *isl_map_flat_product(
3095 __isl_take isl_map *map1,
3096 __isl_take isl_map *map2);
3098 =item * Simplification
3100 __isl_give isl_basic_set *isl_basic_set_gist(
3101 __isl_take isl_basic_set *bset,
3102 __isl_take isl_basic_set *context);
3103 __isl_give isl_set *isl_set_gist(__isl_take isl_set *set,
3104 __isl_take isl_set *context);
3105 __isl_give isl_set *isl_set_gist_params(
3106 __isl_take isl_set *set,
3107 __isl_take isl_set *context);
3108 __isl_give isl_union_set *isl_union_set_gist(
3109 __isl_take isl_union_set *uset,
3110 __isl_take isl_union_set *context);
3111 __isl_give isl_union_set *isl_union_set_gist_params(
3112 __isl_take isl_union_set *uset,
3113 __isl_take isl_set *set);
3114 __isl_give isl_basic_map *isl_basic_map_gist(
3115 __isl_take isl_basic_map *bmap,
3116 __isl_take isl_basic_map *context);
3117 __isl_give isl_map *isl_map_gist(__isl_take isl_map *map,
3118 __isl_take isl_map *context);
3119 __isl_give isl_map *isl_map_gist_params(
3120 __isl_take isl_map *map,
3121 __isl_take isl_set *context);
3122 __isl_give isl_map *isl_map_gist_domain(
3123 __isl_take isl_map *map,
3124 __isl_take isl_set *context);
3125 __isl_give isl_map *isl_map_gist_range(
3126 __isl_take isl_map *map,
3127 __isl_take isl_set *context);
3128 __isl_give isl_union_map *isl_union_map_gist(
3129 __isl_take isl_union_map *umap,
3130 __isl_take isl_union_map *context);
3131 __isl_give isl_union_map *isl_union_map_gist_params(
3132 __isl_take isl_union_map *umap,
3133 __isl_take isl_set *set);
3134 __isl_give isl_union_map *isl_union_map_gist_domain(
3135 __isl_take isl_union_map *umap,
3136 __isl_take isl_union_set *uset);
3137 __isl_give isl_union_map *isl_union_map_gist_range(
3138 __isl_take isl_union_map *umap,
3139 __isl_take isl_union_set *uset);
3141 The gist operation returns a set or relation that has the
3142 same intersection with the context as the input set or relation.
3143 Any implicit equality in the intersection is made explicit in the result,
3144 while all inequalities that are redundant with respect to the intersection
3146 In case of union sets and relations, the gist operation is performed
3151 =head3 Lexicographic Optimization
3153 Given a (basic) set C<set> (or C<bset>) and a zero-dimensional domain C<dom>,
3154 the following functions
3155 compute a set that contains the lexicographic minimum or maximum
3156 of the elements in C<set> (or C<bset>) for those values of the parameters
3157 that satisfy C<dom>.
3158 If C<empty> is not C<NULL>, then C<*empty> is assigned a set
3159 that contains the parameter values in C<dom> for which C<set> (or C<bset>)
3161 In other words, the union of the parameter values
3162 for which the result is non-empty and of C<*empty>
3165 __isl_give isl_set *isl_basic_set_partial_lexmin(
3166 __isl_take isl_basic_set *bset,
3167 __isl_take isl_basic_set *dom,
3168 __isl_give isl_set **empty);
3169 __isl_give isl_set *isl_basic_set_partial_lexmax(
3170 __isl_take isl_basic_set *bset,
3171 __isl_take isl_basic_set *dom,
3172 __isl_give isl_set **empty);
3173 __isl_give isl_set *isl_set_partial_lexmin(
3174 __isl_take isl_set *set, __isl_take isl_set *dom,
3175 __isl_give isl_set **empty);
3176 __isl_give isl_set *isl_set_partial_lexmax(
3177 __isl_take isl_set *set, __isl_take isl_set *dom,
3178 __isl_give isl_set **empty);
3180 Given a (basic) set C<set> (or C<bset>), the following functions simply
3181 return a set containing the lexicographic minimum or maximum
3182 of the elements in C<set> (or C<bset>).
3183 In case of union sets, the optimum is computed per space.
3185 __isl_give isl_set *isl_basic_set_lexmin(
3186 __isl_take isl_basic_set *bset);
3187 __isl_give isl_set *isl_basic_set_lexmax(
3188 __isl_take isl_basic_set *bset);
3189 __isl_give isl_set *isl_set_lexmin(
3190 __isl_take isl_set *set);
3191 __isl_give isl_set *isl_set_lexmax(
3192 __isl_take isl_set *set);
3193 __isl_give isl_union_set *isl_union_set_lexmin(
3194 __isl_take isl_union_set *uset);
3195 __isl_give isl_union_set *isl_union_set_lexmax(
3196 __isl_take isl_union_set *uset);
3198 Given a (basic) relation C<map> (or C<bmap>) and a domain C<dom>,
3199 the following functions
3200 compute a relation that maps each element of C<dom>
3201 to the single lexicographic minimum or maximum
3202 of the elements that are associated to that same
3203 element in C<map> (or C<bmap>).
3204 If C<empty> is not C<NULL>, then C<*empty> is assigned a set
3205 that contains the elements in C<dom> that do not map
3206 to any elements in C<map> (or C<bmap>).
3207 In other words, the union of the domain of the result and of C<*empty>
3210 __isl_give isl_map *isl_basic_map_partial_lexmax(
3211 __isl_take isl_basic_map *bmap,
3212 __isl_take isl_basic_set *dom,
3213 __isl_give isl_set **empty);
3214 __isl_give isl_map *isl_basic_map_partial_lexmin(
3215 __isl_take isl_basic_map *bmap,
3216 __isl_take isl_basic_set *dom,
3217 __isl_give isl_set **empty);
3218 __isl_give isl_map *isl_map_partial_lexmax(
3219 __isl_take isl_map *map, __isl_take isl_set *dom,
3220 __isl_give isl_set **empty);
3221 __isl_give isl_map *isl_map_partial_lexmin(
3222 __isl_take isl_map *map, __isl_take isl_set *dom,
3223 __isl_give isl_set **empty);
3225 Given a (basic) map C<map> (or C<bmap>), the following functions simply
3226 return a map mapping each element in the domain of
3227 C<map> (or C<bmap>) to the lexicographic minimum or maximum
3228 of all elements associated to that element.
3229 In case of union relations, the optimum is computed per space.
3231 __isl_give isl_map *isl_basic_map_lexmin(
3232 __isl_take isl_basic_map *bmap);
3233 __isl_give isl_map *isl_basic_map_lexmax(
3234 __isl_take isl_basic_map *bmap);
3235 __isl_give isl_map *isl_map_lexmin(
3236 __isl_take isl_map *map);
3237 __isl_give isl_map *isl_map_lexmax(
3238 __isl_take isl_map *map);
3239 __isl_give isl_union_map *isl_union_map_lexmin(
3240 __isl_take isl_union_map *umap);
3241 __isl_give isl_union_map *isl_union_map_lexmax(
3242 __isl_take isl_union_map *umap);
3244 The following functions return their result in the form of
3245 a piecewise multi-affine expression
3246 (See L<"Piecewise Multiple Quasi Affine Expressions">),
3247 but are otherwise equivalent to the corresponding functions
3248 returning a basic set or relation.
3250 __isl_give isl_pw_multi_aff *
3251 isl_basic_map_lexmin_pw_multi_aff(
3252 __isl_take isl_basic_map *bmap);
3253 __isl_give isl_pw_multi_aff *
3254 isl_basic_set_partial_lexmin_pw_multi_aff(
3255 __isl_take isl_basic_set *bset,
3256 __isl_take isl_basic_set *dom,
3257 __isl_give isl_set **empty);
3258 __isl_give isl_pw_multi_aff *
3259 isl_basic_set_partial_lexmax_pw_multi_aff(
3260 __isl_take isl_basic_set *bset,
3261 __isl_take isl_basic_set *dom,
3262 __isl_give isl_set **empty);
3263 __isl_give isl_pw_multi_aff *
3264 isl_basic_map_partial_lexmin_pw_multi_aff(
3265 __isl_take isl_basic_map *bmap,
3266 __isl_take isl_basic_set *dom,
3267 __isl_give isl_set **empty);
3268 __isl_give isl_pw_multi_aff *
3269 isl_basic_map_partial_lexmax_pw_multi_aff(
3270 __isl_take isl_basic_map *bmap,
3271 __isl_take isl_basic_set *dom,
3272 __isl_give isl_set **empty);
3273 __isl_give isl_pw_multi_aff *isl_set_lexmin_pw_multi_aff(
3274 __isl_take isl_set *set);
3275 __isl_give isl_pw_multi_aff *isl_set_lexmax_pw_multi_aff(
3276 __isl_take isl_set *set);
3277 __isl_give isl_pw_multi_aff *isl_map_lexmin_pw_multi_aff(
3278 __isl_take isl_map *map);
3279 __isl_give isl_pw_multi_aff *isl_map_lexmax_pw_multi_aff(
3280 __isl_take isl_map *map);
3284 Lists are defined over several element types, including
3285 C<isl_val>, C<isl_id>, C<isl_aff>, C<isl_pw_aff>, C<isl_constraint>,
3286 C<isl_basic_set>, C<isl_set>, C<isl_ast_expr> and C<isl_ast_node>.
3287 Here we take lists of C<isl_set>s as an example.
3288 Lists can be created, copied, modified and freed using the following functions.
3290 #include <isl/list.h>
3291 __isl_give isl_set_list *isl_set_list_from_set(
3292 __isl_take isl_set *el);
3293 __isl_give isl_set_list *isl_set_list_alloc(
3294 isl_ctx *ctx, int n);
3295 __isl_give isl_set_list *isl_set_list_copy(
3296 __isl_keep isl_set_list *list);
3297 __isl_give isl_set_list *isl_set_list_insert(
3298 __isl_take isl_set_list *list, unsigned pos,
3299 __isl_take isl_set *el);
3300 __isl_give isl_set_list *isl_set_list_add(
3301 __isl_take isl_set_list *list,
3302 __isl_take isl_set *el);
3303 __isl_give isl_set_list *isl_set_list_drop(
3304 __isl_take isl_set_list *list,
3305 unsigned first, unsigned n);
3306 __isl_give isl_set_list *isl_set_list_set_set(
3307 __isl_take isl_set_list *list, int index,
3308 __isl_take isl_set *set);
3309 __isl_give isl_set_list *isl_set_list_concat(
3310 __isl_take isl_set_list *list1,
3311 __isl_take isl_set_list *list2);
3312 __isl_give isl_set_list *isl_set_list_sort(
3313 __isl_take isl_set_list *list,
3314 int (*cmp)(__isl_keep isl_set *a,
3315 __isl_keep isl_set *b, void *user),
3317 void *isl_set_list_free(__isl_take isl_set_list *list);
3319 C<isl_set_list_alloc> creates an empty list with a capacity for
3320 C<n> elements. C<isl_set_list_from_set> creates a list with a single
3323 Lists can be inspected using the following functions.
3325 #include <isl/list.h>
3326 isl_ctx *isl_set_list_get_ctx(__isl_keep isl_set_list *list);
3327 int isl_set_list_n_set(__isl_keep isl_set_list *list);
3328 __isl_give isl_set *isl_set_list_get_set(
3329 __isl_keep isl_set_list *list, int index);
3330 int isl_set_list_foreach(__isl_keep isl_set_list *list,
3331 int (*fn)(__isl_take isl_set *el, void *user),
3333 int isl_set_list_foreach_scc(__isl_keep isl_set_list *list,
3334 int (*follows)(__isl_keep isl_set *a,
3335 __isl_keep isl_set *b, void *user),
3337 int (*fn)(__isl_take isl_set *el, void *user),
3340 The function C<isl_set_list_foreach_scc> calls C<fn> on each of the
3341 strongly connected components of the graph with as vertices the elements
3342 of C<list> and a directed edge from vertex C<b> to vertex C<a>
3343 iff C<follows(a, b)> returns C<1>. The callbacks C<follows> and C<fn>
3344 should return C<-1> on error.
3346 Lists can be printed using
3348 #include <isl/list.h>
3349 __isl_give isl_printer *isl_printer_print_set_list(
3350 __isl_take isl_printer *p,
3351 __isl_keep isl_set_list *list);
3353 =head2 Multiple Values
3355 An C<isl_multi_val> object represents a sequence of zero or more values,
3356 living in a set space.
3358 An C<isl_multi_val> can be constructed from an C<isl_val_list>
3359 using the following function
3361 #include <isl/val.h>
3362 __isl_give isl_multi_val *isl_multi_val_from_val_list(
3363 __isl_take isl_space *space,
3364 __isl_take isl_val_list *list);
3366 The zero multiple value (with value zero for each set dimension)
3367 can be created using the following function.
3369 #include <isl/val.h>
3370 __isl_give isl_multi_val *isl_multi_val_zero(
3371 __isl_take isl_space *space);
3373 Multiple values can be copied and freed using
3375 #include <isl/val.h>
3376 __isl_give isl_multi_val *isl_multi_val_copy(
3377 __isl_keep isl_multi_val *mv);
3378 void *isl_multi_val_free(__isl_take isl_multi_val *mv);
3380 They can be inspected using
3382 #include <isl/val.h>
3383 isl_ctx *isl_multi_val_get_ctx(
3384 __isl_keep isl_multi_val *mv);
3385 unsigned isl_multi_val_dim(__isl_keep isl_multi_val *mv,
3386 enum isl_dim_type type);
3387 __isl_give isl_val *isl_multi_val_get_val(
3388 __isl_keep isl_multi_val *mv, int pos);
3389 const char *isl_multi_val_get_tuple_name(
3390 __isl_keep isl_multi_val *mv,
3391 enum isl_dim_type type);
3393 They can be modified using
3395 #include <isl/val.h>
3396 __isl_give isl_multi_val *isl_multi_val_set_val(
3397 __isl_take isl_multi_val *mv, int pos,
3398 __isl_take isl_val *val);
3399 __isl_give isl_multi_val *isl_multi_val_set_dim_name(
3400 __isl_take isl_multi_val *mv,
3401 enum isl_dim_type type, unsigned pos, const char *s);
3402 __isl_give isl_multi_val *isl_multi_val_set_tuple_name(
3403 __isl_take isl_multi_val *mv,
3404 enum isl_dim_type type, const char *s);
3405 __isl_give isl_multi_val *isl_multi_val_set_tuple_id(
3406 __isl_take isl_multi_val *mv,
3407 enum isl_dim_type type, __isl_take isl_id *id);
3409 __isl_give isl_multi_val *isl_multi_val_insert_dims(
3410 __isl_take isl_multi_val *mv,
3411 enum isl_dim_type type, unsigned first, unsigned n);
3412 __isl_give isl_multi_val *isl_multi_val_add_dims(
3413 __isl_take isl_multi_val *mv,
3414 enum isl_dim_type type, unsigned n);
3415 __isl_give isl_multi_val *isl_multi_val_drop_dims(
3416 __isl_take isl_multi_val *mv,
3417 enum isl_dim_type type, unsigned first, unsigned n);
3421 #include <isl/val.h>
3422 __isl_give isl_multi_val *isl_multi_val_align_params(
3423 __isl_take isl_multi_val *mv,
3424 __isl_take isl_space *model);
3425 __isl_give isl_multi_val *isl_multi_val_range_splice(
3426 __isl_take isl_multi_val *mv1, unsigned pos,
3427 __isl_take isl_multi_val *mv2);
3428 __isl_give isl_multi_val *isl_multi_val_range_product(
3429 __isl_take isl_multi_val *mv1,
3430 __isl_take isl_multi_val *mv2);
3431 __isl_give isl_multi_val *isl_multi_val_flat_range_product(
3432 __isl_take isl_multi_val *mv1,
3433 __isl_take isl_multi_aff *mv2);
3434 __isl_give isl_multi_val *isl_multi_val_add_val(
3435 __isl_take isl_multi_val *mv,
3436 __isl_take isl_val *v);
3437 __isl_give isl_multi_val *isl_multi_val_mod_val(
3438 __isl_take isl_multi_val *mv,
3439 __isl_take isl_val *v);
3443 Vectors can be created, copied and freed using the following functions.
3445 #include <isl/vec.h>
3446 __isl_give isl_vec *isl_vec_alloc(isl_ctx *ctx,
3448 __isl_give isl_vec *isl_vec_copy(__isl_keep isl_vec *vec);
3449 void *isl_vec_free(__isl_take isl_vec *vec);
3451 Note that the elements of a newly created vector may have arbitrary values.
3452 The elements can be changed and inspected using the following functions.
3454 isl_ctx *isl_vec_get_ctx(__isl_keep isl_vec *vec);
3455 int isl_vec_size(__isl_keep isl_vec *vec);
3456 int isl_vec_get_element(__isl_keep isl_vec *vec,
3457 int pos, isl_int *v);
3458 __isl_give isl_val *isl_vec_get_element_val(
3459 __isl_keep isl_vec *vec, int pos);
3460 __isl_give isl_vec *isl_vec_set_element(
3461 __isl_take isl_vec *vec, int pos, isl_int v);
3462 __isl_give isl_vec *isl_vec_set_element_si(
3463 __isl_take isl_vec *vec, int pos, int v);
3464 __isl_give isl_vec *isl_vec_set_element_val(
3465 __isl_take isl_vec *vec, int pos,
3466 __isl_take isl_val *v);
3467 __isl_give isl_vec *isl_vec_set(__isl_take isl_vec *vec,
3469 __isl_give isl_vec *isl_vec_set_si(__isl_take isl_vec *vec,
3471 __isl_give isl_vec *isl_vec_set_val(
3472 __isl_take isl_vec *vec, __isl_take isl_val *v);
3473 __isl_give isl_vec *isl_vec_fdiv_r(__isl_take isl_vec *vec,
3476 C<isl_vec_get_element> will return a negative value if anything went wrong.
3477 In that case, the value of C<*v> is undefined.
3479 The following function can be used to concatenate two vectors.
3481 __isl_give isl_vec *isl_vec_concat(__isl_take isl_vec *vec1,
3482 __isl_take isl_vec *vec2);
3486 Matrices can be created, copied and freed using the following functions.
3488 #include <isl/mat.h>
3489 __isl_give isl_mat *isl_mat_alloc(isl_ctx *ctx,
3490 unsigned n_row, unsigned n_col);
3491 __isl_give isl_mat *isl_mat_copy(__isl_keep isl_mat *mat);
3492 void *isl_mat_free(__isl_take isl_mat *mat);
3494 Note that the elements of a newly created matrix may have arbitrary values.
3495 The elements can be changed and inspected using the following functions.
3497 isl_ctx *isl_mat_get_ctx(__isl_keep isl_mat *mat);
3498 int isl_mat_rows(__isl_keep isl_mat *mat);
3499 int isl_mat_cols(__isl_keep isl_mat *mat);
3500 int isl_mat_get_element(__isl_keep isl_mat *mat,
3501 int row, int col, isl_int *v);
3502 __isl_give isl_val *isl_mat_get_element_val(
3503 __isl_keep isl_mat *mat, int row, int col);
3504 __isl_give isl_mat *isl_mat_set_element(__isl_take isl_mat *mat,
3505 int row, int col, isl_int v);
3506 __isl_give isl_mat *isl_mat_set_element_si(__isl_take isl_mat *mat,
3507 int row, int col, int v);
3508 __isl_give isl_mat *isl_mat_set_element_val(
3509 __isl_take isl_mat *mat, int row, int col,
3510 __isl_take isl_val *v);
3512 C<isl_mat_get_element> will return a negative value if anything went wrong.
3513 In that case, the value of C<*v> is undefined.
3515 The following function can be used to compute the (right) inverse
3516 of a matrix, i.e., a matrix such that the product of the original
3517 and the inverse (in that order) is a multiple of the identity matrix.
3518 The input matrix is assumed to be of full row-rank.
3520 __isl_give isl_mat *isl_mat_right_inverse(__isl_take isl_mat *mat);
3522 The following function can be used to compute the (right) kernel
3523 (or null space) of a matrix, i.e., a matrix such that the product of
3524 the original and the kernel (in that order) is the zero matrix.
3526 __isl_give isl_mat *isl_mat_right_kernel(__isl_take isl_mat *mat);
3528 =head2 Piecewise Quasi Affine Expressions
3530 The zero quasi affine expression or the quasi affine expression
3531 that is equal to a specified dimension on a given domain can be created using
3533 __isl_give isl_aff *isl_aff_zero_on_domain(
3534 __isl_take isl_local_space *ls);
3535 __isl_give isl_pw_aff *isl_pw_aff_zero_on_domain(
3536 __isl_take isl_local_space *ls);
3537 __isl_give isl_aff *isl_aff_var_on_domain(
3538 __isl_take isl_local_space *ls,
3539 enum isl_dim_type type, unsigned pos);
3540 __isl_give isl_pw_aff *isl_pw_aff_var_on_domain(
3541 __isl_take isl_local_space *ls,
3542 enum isl_dim_type type, unsigned pos);
3544 Note that the space in which the resulting objects live is a map space
3545 with the given space as domain and a one-dimensional range.
3547 An empty piecewise quasi affine expression (one with no cells)
3548 or a piecewise quasi affine expression with a single cell can
3549 be created using the following functions.
3551 #include <isl/aff.h>
3552 __isl_give isl_pw_aff *isl_pw_aff_empty(
3553 __isl_take isl_space *space);
3554 __isl_give isl_pw_aff *isl_pw_aff_alloc(
3555 __isl_take isl_set *set, __isl_take isl_aff *aff);
3556 __isl_give isl_pw_aff *isl_pw_aff_from_aff(
3557 __isl_take isl_aff *aff);
3559 A piecewise quasi affine expression that is equal to 1 on a set
3560 and 0 outside the set can be created using the following function.
3562 #include <isl/aff.h>
3563 __isl_give isl_pw_aff *isl_set_indicator_function(
3564 __isl_take isl_set *set);
3566 Quasi affine expressions can be copied and freed using
3568 #include <isl/aff.h>
3569 __isl_give isl_aff *isl_aff_copy(__isl_keep isl_aff *aff);
3570 void *isl_aff_free(__isl_take isl_aff *aff);
3572 __isl_give isl_pw_aff *isl_pw_aff_copy(
3573 __isl_keep isl_pw_aff *pwaff);
3574 void *isl_pw_aff_free(__isl_take isl_pw_aff *pwaff);
3576 A (rational) bound on a dimension can be extracted from an C<isl_constraint>
3577 using the following function. The constraint is required to have
3578 a non-zero coefficient for the specified dimension.
3580 #include <isl/constraint.h>
3581 __isl_give isl_aff *isl_constraint_get_bound(
3582 __isl_keep isl_constraint *constraint,
3583 enum isl_dim_type type, int pos);
3585 The entire affine expression of the constraint can also be extracted
3586 using the following function.
3588 #include <isl/constraint.h>
3589 __isl_give isl_aff *isl_constraint_get_aff(
3590 __isl_keep isl_constraint *constraint);
3592 Conversely, an equality constraint equating
3593 the affine expression to zero or an inequality constraint enforcing
3594 the affine expression to be non-negative, can be constructed using
3596 __isl_give isl_constraint *isl_equality_from_aff(
3597 __isl_take isl_aff *aff);
3598 __isl_give isl_constraint *isl_inequality_from_aff(
3599 __isl_take isl_aff *aff);
3601 The expression can be inspected using
3603 #include <isl/aff.h>
3604 isl_ctx *isl_aff_get_ctx(__isl_keep isl_aff *aff);
3605 int isl_aff_dim(__isl_keep isl_aff *aff,
3606 enum isl_dim_type type);
3607 __isl_give isl_local_space *isl_aff_get_domain_local_space(
3608 __isl_keep isl_aff *aff);
3609 __isl_give isl_local_space *isl_aff_get_local_space(
3610 __isl_keep isl_aff *aff);
3611 const char *isl_aff_get_dim_name(__isl_keep isl_aff *aff,
3612 enum isl_dim_type type, unsigned pos);
3613 const char *isl_pw_aff_get_dim_name(
3614 __isl_keep isl_pw_aff *pa,
3615 enum isl_dim_type type, unsigned pos);
3616 int isl_pw_aff_has_dim_id(__isl_keep isl_pw_aff *pa,
3617 enum isl_dim_type type, unsigned pos);
3618 __isl_give isl_id *isl_pw_aff_get_dim_id(
3619 __isl_keep isl_pw_aff *pa,
3620 enum isl_dim_type type, unsigned pos);
3621 __isl_give isl_id *isl_pw_aff_get_tuple_id(
3622 __isl_keep isl_pw_aff *pa,
3623 enum isl_dim_type type);
3624 int isl_aff_get_constant(__isl_keep isl_aff *aff,
3626 int isl_aff_get_coefficient(__isl_keep isl_aff *aff,
3627 enum isl_dim_type type, int pos, isl_int *v);
3628 int isl_aff_get_denominator(__isl_keep isl_aff *aff,
3630 __isl_give isl_aff *isl_aff_get_div(
3631 __isl_keep isl_aff *aff, int pos);
3633 int isl_pw_aff_n_piece(__isl_keep isl_pw_aff *pwaff);
3634 int isl_pw_aff_foreach_piece(__isl_keep isl_pw_aff *pwaff,
3635 int (*fn)(__isl_take isl_set *set,
3636 __isl_take isl_aff *aff,
3637 void *user), void *user);
3639 int isl_aff_is_cst(__isl_keep isl_aff *aff);
3640 int isl_pw_aff_is_cst(__isl_keep isl_pw_aff *pwaff);
3642 int isl_aff_involves_dims(__isl_keep isl_aff *aff,
3643 enum isl_dim_type type, unsigned first, unsigned n);
3644 int isl_pw_aff_involves_dims(__isl_keep isl_pw_aff *pwaff,
3645 enum isl_dim_type type, unsigned first, unsigned n);
3647 isl_ctx *isl_pw_aff_get_ctx(__isl_keep isl_pw_aff *pwaff);
3648 unsigned isl_pw_aff_dim(__isl_keep isl_pw_aff *pwaff,
3649 enum isl_dim_type type);
3650 int isl_pw_aff_is_empty(__isl_keep isl_pw_aff *pwaff);
3652 It can be modified using
3654 #include <isl/aff.h>
3655 __isl_give isl_pw_aff *isl_pw_aff_set_tuple_id(
3656 __isl_take isl_pw_aff *pwaff,
3657 enum isl_dim_type type, __isl_take isl_id *id);
3658 __isl_give isl_aff *isl_aff_set_dim_name(
3659 __isl_take isl_aff *aff, enum isl_dim_type type,
3660 unsigned pos, const char *s);
3661 __isl_give isl_aff *isl_aff_set_dim_id(
3662 __isl_take isl_aff *aff, enum isl_dim_type type,
3663 unsigned pos, __isl_take isl_id *id);
3664 __isl_give isl_pw_aff *isl_pw_aff_set_dim_id(
3665 __isl_take isl_pw_aff *pma,
3666 enum isl_dim_type type, unsigned pos,
3667 __isl_take isl_id *id);
3668 __isl_give isl_aff *isl_aff_set_constant(
3669 __isl_take isl_aff *aff, isl_int v);
3670 __isl_give isl_aff *isl_aff_set_constant_si(
3671 __isl_take isl_aff *aff, int v);
3672 __isl_give isl_aff *isl_aff_set_constant_val(
3673 __isl_take isl_aff *aff, __isl_take isl_val *v);
3674 __isl_give isl_aff *isl_aff_set_coefficient(
3675 __isl_take isl_aff *aff,
3676 enum isl_dim_type type, int pos, isl_int v);
3677 __isl_give isl_aff *isl_aff_set_coefficient_si(
3678 __isl_take isl_aff *aff,
3679 enum isl_dim_type type, int pos, int v);
3680 __isl_give isl_aff *isl_aff_set_denominator(
3681 __isl_take isl_aff *aff, isl_int v);
3683 __isl_give isl_aff *isl_aff_add_constant(
3684 __isl_take isl_aff *aff, isl_int v);
3685 __isl_give isl_aff *isl_aff_add_constant_si(
3686 __isl_take isl_aff *aff, int v);
3687 __isl_give isl_aff *isl_aff_add_constant_num(
3688 __isl_take isl_aff *aff, isl_int v);
3689 __isl_give isl_aff *isl_aff_add_constant_num_si(
3690 __isl_take isl_aff *aff, int v);
3691 __isl_give isl_aff *isl_aff_add_coefficient(
3692 __isl_take isl_aff *aff,
3693 enum isl_dim_type type, int pos, isl_int v);
3694 __isl_give isl_aff *isl_aff_add_coefficient_si(
3695 __isl_take isl_aff *aff,
3696 enum isl_dim_type type, int pos, int v);
3698 __isl_give isl_aff *isl_aff_insert_dims(
3699 __isl_take isl_aff *aff,
3700 enum isl_dim_type type, unsigned first, unsigned n);
3701 __isl_give isl_pw_aff *isl_pw_aff_insert_dims(
3702 __isl_take isl_pw_aff *pwaff,
3703 enum isl_dim_type type, unsigned first, unsigned n);
3704 __isl_give isl_aff *isl_aff_add_dims(
3705 __isl_take isl_aff *aff,
3706 enum isl_dim_type type, unsigned n);
3707 __isl_give isl_pw_aff *isl_pw_aff_add_dims(
3708 __isl_take isl_pw_aff *pwaff,
3709 enum isl_dim_type type, unsigned n);
3710 __isl_give isl_aff *isl_aff_drop_dims(
3711 __isl_take isl_aff *aff,
3712 enum isl_dim_type type, unsigned first, unsigned n);
3713 __isl_give isl_pw_aff *isl_pw_aff_drop_dims(
3714 __isl_take isl_pw_aff *pwaff,
3715 enum isl_dim_type type, unsigned first, unsigned n);
3717 Note that C<isl_aff_set_constant>, C<isl_aff_set_constant_si>,
3718 C<isl_aff_set_coefficient> and C<isl_aff_set_coefficient_si>
3719 set the I<numerator> of the constant or coefficient, while
3720 C<isl_aff_set_constant_val> sets the constant as a whole.
3721 C<add_constant> and C<add_coefficient> add an integer value to
3722 the possibly rational constant or coefficient.
3723 The C<add_constant_num> functions add an integer value to
3726 To check whether an affine expressions is obviously zero
3727 or obviously equal to some other affine expression, use
3729 #include <isl/aff.h>
3730 int isl_aff_plain_is_zero(__isl_keep isl_aff *aff);
3731 int isl_aff_plain_is_equal(__isl_keep isl_aff *aff1,
3732 __isl_keep isl_aff *aff2);
3733 int isl_pw_aff_plain_is_equal(
3734 __isl_keep isl_pw_aff *pwaff1,
3735 __isl_keep isl_pw_aff *pwaff2);
3739 #include <isl/aff.h>
3740 __isl_give isl_aff *isl_aff_add(__isl_take isl_aff *aff1,
3741 __isl_take isl_aff *aff2);
3742 __isl_give isl_pw_aff *isl_pw_aff_add(
3743 __isl_take isl_pw_aff *pwaff1,
3744 __isl_take isl_pw_aff *pwaff2);
3745 __isl_give isl_pw_aff *isl_pw_aff_min(
3746 __isl_take isl_pw_aff *pwaff1,
3747 __isl_take isl_pw_aff *pwaff2);
3748 __isl_give isl_pw_aff *isl_pw_aff_max(
3749 __isl_take isl_pw_aff *pwaff1,
3750 __isl_take isl_pw_aff *pwaff2);
3751 __isl_give isl_aff *isl_aff_sub(__isl_take isl_aff *aff1,
3752 __isl_take isl_aff *aff2);
3753 __isl_give isl_pw_aff *isl_pw_aff_sub(
3754 __isl_take isl_pw_aff *pwaff1,
3755 __isl_take isl_pw_aff *pwaff2);
3756 __isl_give isl_aff *isl_aff_neg(__isl_take isl_aff *aff);
3757 __isl_give isl_pw_aff *isl_pw_aff_neg(
3758 __isl_take isl_pw_aff *pwaff);
3759 __isl_give isl_aff *isl_aff_ceil(__isl_take isl_aff *aff);
3760 __isl_give isl_pw_aff *isl_pw_aff_ceil(
3761 __isl_take isl_pw_aff *pwaff);
3762 __isl_give isl_aff *isl_aff_floor(__isl_take isl_aff *aff);
3763 __isl_give isl_pw_aff *isl_pw_aff_floor(
3764 __isl_take isl_pw_aff *pwaff);
3765 __isl_give isl_aff *isl_aff_mod(__isl_take isl_aff *aff,
3767 __isl_give isl_pw_aff *isl_pw_aff_mod(
3768 __isl_take isl_pw_aff *pwaff, isl_int mod);
3769 __isl_give isl_aff *isl_aff_scale(__isl_take isl_aff *aff,
3771 __isl_give isl_pw_aff *isl_pw_aff_scale(
3772 __isl_take isl_pw_aff *pwaff, isl_int f);
3773 __isl_give isl_aff *isl_aff_scale_down(__isl_take isl_aff *aff,
3775 __isl_give isl_aff *isl_aff_scale_down_ui(
3776 __isl_take isl_aff *aff, unsigned f);
3777 __isl_give isl_pw_aff *isl_pw_aff_scale_down(
3778 __isl_take isl_pw_aff *pwaff, isl_int f);
3780 __isl_give isl_pw_aff *isl_pw_aff_list_min(
3781 __isl_take isl_pw_aff_list *list);
3782 __isl_give isl_pw_aff *isl_pw_aff_list_max(
3783 __isl_take isl_pw_aff_list *list);
3785 __isl_give isl_pw_aff *isl_pw_aff_coalesce(
3786 __isl_take isl_pw_aff *pwqp);
3788 __isl_give isl_aff *isl_aff_align_params(
3789 __isl_take isl_aff *aff,
3790 __isl_take isl_space *model);
3791 __isl_give isl_pw_aff *isl_pw_aff_align_params(
3792 __isl_take isl_pw_aff *pwaff,
3793 __isl_take isl_space *model);
3795 __isl_give isl_aff *isl_aff_project_domain_on_params(
3796 __isl_take isl_aff *aff);
3798 __isl_give isl_aff *isl_aff_gist_params(
3799 __isl_take isl_aff *aff,
3800 __isl_take isl_set *context);
3801 __isl_give isl_aff *isl_aff_gist(__isl_take isl_aff *aff,
3802 __isl_take isl_set *context);
3803 __isl_give isl_pw_aff *isl_pw_aff_gist_params(
3804 __isl_take isl_pw_aff *pwaff,
3805 __isl_take isl_set *context);
3806 __isl_give isl_pw_aff *isl_pw_aff_gist(
3807 __isl_take isl_pw_aff *pwaff,
3808 __isl_take isl_set *context);
3810 __isl_give isl_set *isl_pw_aff_domain(
3811 __isl_take isl_pw_aff *pwaff);
3812 __isl_give isl_pw_aff *isl_pw_aff_intersect_domain(
3813 __isl_take isl_pw_aff *pa,
3814 __isl_take isl_set *set);
3815 __isl_give isl_pw_aff *isl_pw_aff_intersect_params(
3816 __isl_take isl_pw_aff *pa,
3817 __isl_take isl_set *set);
3819 __isl_give isl_aff *isl_aff_mul(__isl_take isl_aff *aff1,
3820 __isl_take isl_aff *aff2);
3821 __isl_give isl_aff *isl_aff_div(__isl_take isl_aff *aff1,
3822 __isl_take isl_aff *aff2);
3823 __isl_give isl_pw_aff *isl_pw_aff_mul(
3824 __isl_take isl_pw_aff *pwaff1,
3825 __isl_take isl_pw_aff *pwaff2);
3826 __isl_give isl_pw_aff *isl_pw_aff_div(
3827 __isl_take isl_pw_aff *pa1,
3828 __isl_take isl_pw_aff *pa2);
3829 __isl_give isl_pw_aff *isl_pw_aff_tdiv_q(
3830 __isl_take isl_pw_aff *pa1,
3831 __isl_take isl_pw_aff *pa2);
3832 __isl_give isl_pw_aff *isl_pw_aff_tdiv_r(
3833 __isl_take isl_pw_aff *pa1,
3834 __isl_take isl_pw_aff *pa2);
3836 When multiplying two affine expressions, at least one of the two needs
3837 to be a constant. Similarly, when dividing an affine expression by another,
3838 the second expression needs to be a constant.
3839 C<isl_pw_aff_tdiv_q> computes the quotient of an integer division with
3840 rounding towards zero. C<isl_pw_aff_tdiv_r> computes the corresponding
3843 #include <isl/aff.h>
3844 __isl_give isl_aff *isl_aff_pullback_multi_aff(
3845 __isl_take isl_aff *aff,
3846 __isl_take isl_multi_aff *ma);
3847 __isl_give isl_pw_aff *isl_pw_aff_pullback_multi_aff(
3848 __isl_take isl_pw_aff *pa,
3849 __isl_take isl_multi_aff *ma);
3850 __isl_give isl_pw_aff *isl_pw_aff_pullback_pw_multi_aff(
3851 __isl_take isl_pw_aff *pa,
3852 __isl_take isl_pw_multi_aff *pma);
3854 These functions precompose the input expression by the given
3855 C<isl_multi_aff> or C<isl_pw_multi_aff>. In other words,
3856 the C<isl_multi_aff> or C<isl_pw_multi_aff> is plugged
3857 into the (piecewise) affine expression.
3858 Objects of type C<isl_multi_aff> are described in
3859 L</"Piecewise Multiple Quasi Affine Expressions">.
3861 #include <isl/aff.h>
3862 __isl_give isl_basic_set *isl_aff_zero_basic_set(
3863 __isl_take isl_aff *aff);
3864 __isl_give isl_basic_set *isl_aff_neg_basic_set(
3865 __isl_take isl_aff *aff);
3866 __isl_give isl_basic_set *isl_aff_le_basic_set(
3867 __isl_take isl_aff *aff1, __isl_take isl_aff *aff2);
3868 __isl_give isl_basic_set *isl_aff_ge_basic_set(
3869 __isl_take isl_aff *aff1, __isl_take isl_aff *aff2);
3870 __isl_give isl_set *isl_pw_aff_eq_set(
3871 __isl_take isl_pw_aff *pwaff1,
3872 __isl_take isl_pw_aff *pwaff2);
3873 __isl_give isl_set *isl_pw_aff_ne_set(
3874 __isl_take isl_pw_aff *pwaff1,
3875 __isl_take isl_pw_aff *pwaff2);
3876 __isl_give isl_set *isl_pw_aff_le_set(
3877 __isl_take isl_pw_aff *pwaff1,
3878 __isl_take isl_pw_aff *pwaff2);
3879 __isl_give isl_set *isl_pw_aff_lt_set(
3880 __isl_take isl_pw_aff *pwaff1,
3881 __isl_take isl_pw_aff *pwaff2);
3882 __isl_give isl_set *isl_pw_aff_ge_set(
3883 __isl_take isl_pw_aff *pwaff1,
3884 __isl_take isl_pw_aff *pwaff2);
3885 __isl_give isl_set *isl_pw_aff_gt_set(
3886 __isl_take isl_pw_aff *pwaff1,
3887 __isl_take isl_pw_aff *pwaff2);
3889 __isl_give isl_set *isl_pw_aff_list_eq_set(
3890 __isl_take isl_pw_aff_list *list1,
3891 __isl_take isl_pw_aff_list *list2);
3892 __isl_give isl_set *isl_pw_aff_list_ne_set(
3893 __isl_take isl_pw_aff_list *list1,
3894 __isl_take isl_pw_aff_list *list2);
3895 __isl_give isl_set *isl_pw_aff_list_le_set(
3896 __isl_take isl_pw_aff_list *list1,
3897 __isl_take isl_pw_aff_list *list2);
3898 __isl_give isl_set *isl_pw_aff_list_lt_set(
3899 __isl_take isl_pw_aff_list *list1,
3900 __isl_take isl_pw_aff_list *list2);
3901 __isl_give isl_set *isl_pw_aff_list_ge_set(
3902 __isl_take isl_pw_aff_list *list1,
3903 __isl_take isl_pw_aff_list *list2);
3904 __isl_give isl_set *isl_pw_aff_list_gt_set(
3905 __isl_take isl_pw_aff_list *list1,
3906 __isl_take isl_pw_aff_list *list2);
3908 The function C<isl_aff_neg_basic_set> returns a basic set
3909 containing those elements in the domain space
3910 of C<aff> where C<aff> is negative.
3911 The function C<isl_aff_ge_basic_set> returns a basic set
3912 containing those elements in the shared space
3913 of C<aff1> and C<aff2> where C<aff1> is greater than or equal to C<aff2>.
3914 The function C<isl_pw_aff_ge_set> returns a set
3915 containing those elements in the shared domain
3916 of C<pwaff1> and C<pwaff2> where C<pwaff1> is greater than or equal to C<pwaff2>.
3917 The functions operating on C<isl_pw_aff_list> apply the corresponding
3918 C<isl_pw_aff> function to each pair of elements in the two lists.
3920 #include <isl/aff.h>
3921 __isl_give isl_set *isl_pw_aff_nonneg_set(
3922 __isl_take isl_pw_aff *pwaff);
3923 __isl_give isl_set *isl_pw_aff_zero_set(
3924 __isl_take isl_pw_aff *pwaff);
3925 __isl_give isl_set *isl_pw_aff_non_zero_set(
3926 __isl_take isl_pw_aff *pwaff);
3928 The function C<isl_pw_aff_nonneg_set> returns a set
3929 containing those elements in the domain
3930 of C<pwaff> where C<pwaff> is non-negative.
3932 #include <isl/aff.h>
3933 __isl_give isl_pw_aff *isl_pw_aff_cond(
3934 __isl_take isl_pw_aff *cond,
3935 __isl_take isl_pw_aff *pwaff_true,
3936 __isl_take isl_pw_aff *pwaff_false);
3938 The function C<isl_pw_aff_cond> performs a conditional operator
3939 and returns an expression that is equal to C<pwaff_true>
3940 for elements where C<cond> is non-zero and equal to C<pwaff_false> for elements
3941 where C<cond> is zero.
3943 #include <isl/aff.h>
3944 __isl_give isl_pw_aff *isl_pw_aff_union_min(
3945 __isl_take isl_pw_aff *pwaff1,
3946 __isl_take isl_pw_aff *pwaff2);
3947 __isl_give isl_pw_aff *isl_pw_aff_union_max(
3948 __isl_take isl_pw_aff *pwaff1,
3949 __isl_take isl_pw_aff *pwaff2);
3950 __isl_give isl_pw_aff *isl_pw_aff_union_add(
3951 __isl_take isl_pw_aff *pwaff1,
3952 __isl_take isl_pw_aff *pwaff2);
3954 The function C<isl_pw_aff_union_max> computes a piecewise quasi-affine
3955 expression with a domain that is the union of those of C<pwaff1> and
3956 C<pwaff2> and such that on each cell, the quasi-affine expression is
3957 the maximum of those of C<pwaff1> and C<pwaff2>. If only one of
3958 C<pwaff1> or C<pwaff2> is defined on a given cell, then the
3959 associated expression is the defined one.
3961 An expression can be read from input using
3963 #include <isl/aff.h>
3964 __isl_give isl_aff *isl_aff_read_from_str(
3965 isl_ctx *ctx, const char *str);
3966 __isl_give isl_pw_aff *isl_pw_aff_read_from_str(
3967 isl_ctx *ctx, const char *str);
3969 An expression can be printed using
3971 #include <isl/aff.h>
3972 __isl_give isl_printer *isl_printer_print_aff(
3973 __isl_take isl_printer *p, __isl_keep isl_aff *aff);
3975 __isl_give isl_printer *isl_printer_print_pw_aff(
3976 __isl_take isl_printer *p,
3977 __isl_keep isl_pw_aff *pwaff);
3979 =head2 Piecewise Multiple Quasi Affine Expressions
3981 An C<isl_multi_aff> object represents a sequence of
3982 zero or more affine expressions, all defined on the same domain space.
3983 Similarly, an C<isl_multi_pw_aff> object represents a sequence of
3984 zero or more piecewise affine expressions.
3986 An C<isl_multi_aff> can be constructed from a single
3987 C<isl_aff> or an C<isl_aff_list> using the
3988 following functions. Similarly for C<isl_multi_pw_aff>.
3990 #include <isl/aff.h>
3991 __isl_give isl_multi_aff *isl_multi_aff_from_aff(
3992 __isl_take isl_aff *aff);
3993 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_from_pw_aff(
3994 __isl_take isl_pw_aff *pa);
3995 __isl_give isl_multi_aff *isl_multi_aff_from_aff_list(
3996 __isl_take isl_space *space,
3997 __isl_take isl_aff_list *list);
3999 An empty piecewise multiple quasi affine expression (one with no cells),
4000 the zero piecewise multiple quasi affine expression (with value zero
4001 for each output dimension),
4002 a piecewise multiple quasi affine expression with a single cell (with
4003 either a universe or a specified domain) or
4004 a zero-dimensional piecewise multiple quasi affine expression
4006 can be created using the following functions.
4008 #include <isl/aff.h>
4009 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_empty(
4010 __isl_take isl_space *space);
4011 __isl_give isl_multi_aff *isl_multi_aff_zero(
4012 __isl_take isl_space *space);
4013 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_zero(
4014 __isl_take isl_space *space);
4015 __isl_give isl_multi_aff *isl_multi_aff_identity(
4016 __isl_take isl_space *space);
4017 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_identity(
4018 __isl_take isl_space *space);
4019 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_identity(
4020 __isl_take isl_space *space);
4021 __isl_give isl_pw_multi_aff *
4022 isl_pw_multi_aff_from_multi_aff(
4023 __isl_take isl_multi_aff *ma);
4024 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_alloc(
4025 __isl_take isl_set *set,
4026 __isl_take isl_multi_aff *maff);
4027 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_from_domain(
4028 __isl_take isl_set *set);
4030 __isl_give isl_union_pw_multi_aff *
4031 isl_union_pw_multi_aff_empty(
4032 __isl_take isl_space *space);
4033 __isl_give isl_union_pw_multi_aff *
4034 isl_union_pw_multi_aff_add_pw_multi_aff(
4035 __isl_take isl_union_pw_multi_aff *upma,
4036 __isl_take isl_pw_multi_aff *pma);
4037 __isl_give isl_union_pw_multi_aff *
4038 isl_union_pw_multi_aff_from_domain(
4039 __isl_take isl_union_set *uset);
4041 A piecewise multiple quasi affine expression can also be initialized
4042 from an C<isl_set> or C<isl_map>, provided the C<isl_set> is a singleton
4043 and the C<isl_map> is single-valued.
4044 In case of a conversion from an C<isl_union_set> or an C<isl_union_map>
4045 to an C<isl_union_pw_multi_aff>, these properties need to hold in each space.
4047 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_from_set(
4048 __isl_take isl_set *set);
4049 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_from_map(
4050 __isl_take isl_map *map);
4052 __isl_give isl_union_pw_multi_aff *
4053 isl_union_pw_multi_aff_from_union_set(
4054 __isl_take isl_union_set *uset);
4055 __isl_give isl_union_pw_multi_aff *
4056 isl_union_pw_multi_aff_from_union_map(
4057 __isl_take isl_union_map *umap);
4059 Multiple quasi affine expressions can be copied and freed using
4061 #include <isl/aff.h>
4062 __isl_give isl_multi_aff *isl_multi_aff_copy(
4063 __isl_keep isl_multi_aff *maff);
4064 void *isl_multi_aff_free(__isl_take isl_multi_aff *maff);
4066 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_copy(
4067 __isl_keep isl_pw_multi_aff *pma);
4068 void *isl_pw_multi_aff_free(
4069 __isl_take isl_pw_multi_aff *pma);
4071 __isl_give isl_union_pw_multi_aff *
4072 isl_union_pw_multi_aff_copy(
4073 __isl_keep isl_union_pw_multi_aff *upma);
4074 void *isl_union_pw_multi_aff_free(
4075 __isl_take isl_union_pw_multi_aff *upma);
4077 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_copy(
4078 __isl_keep isl_multi_pw_aff *mpa);
4079 void *isl_multi_pw_aff_free(
4080 __isl_take isl_multi_pw_aff *mpa);
4082 The expression can be inspected using
4084 #include <isl/aff.h>
4085 isl_ctx *isl_multi_aff_get_ctx(
4086 __isl_keep isl_multi_aff *maff);
4087 isl_ctx *isl_pw_multi_aff_get_ctx(
4088 __isl_keep isl_pw_multi_aff *pma);
4089 isl_ctx *isl_union_pw_multi_aff_get_ctx(
4090 __isl_keep isl_union_pw_multi_aff *upma);
4091 isl_ctx *isl_multi_pw_aff_get_ctx(
4092 __isl_keep isl_multi_pw_aff *mpa);
4093 unsigned isl_multi_aff_dim(__isl_keep isl_multi_aff *maff,
4094 enum isl_dim_type type);
4095 unsigned isl_pw_multi_aff_dim(
4096 __isl_keep isl_pw_multi_aff *pma,
4097 enum isl_dim_type type);
4098 unsigned isl_multi_pw_aff_dim(
4099 __isl_keep isl_multi_pw_aff *mpa,
4100 enum isl_dim_type type);
4101 __isl_give isl_aff *isl_multi_aff_get_aff(
4102 __isl_keep isl_multi_aff *multi, int pos);
4103 __isl_give isl_pw_aff *isl_pw_multi_aff_get_pw_aff(
4104 __isl_keep isl_pw_multi_aff *pma, int pos);
4105 __isl_give isl_pw_aff *isl_multi_pw_aff_get_pw_aff(
4106 __isl_keep isl_multi_pw_aff *mpa, int pos);
4107 const char *isl_pw_multi_aff_get_dim_name(
4108 __isl_keep isl_pw_multi_aff *pma,
4109 enum isl_dim_type type, unsigned pos);
4110 __isl_give isl_id *isl_pw_multi_aff_get_dim_id(
4111 __isl_keep isl_pw_multi_aff *pma,
4112 enum isl_dim_type type, unsigned pos);
4113 const char *isl_multi_aff_get_tuple_name(
4114 __isl_keep isl_multi_aff *multi,
4115 enum isl_dim_type type);
4116 int isl_pw_multi_aff_has_tuple_name(
4117 __isl_keep isl_pw_multi_aff *pma,
4118 enum isl_dim_type type);
4119 const char *isl_pw_multi_aff_get_tuple_name(
4120 __isl_keep isl_pw_multi_aff *pma,
4121 enum isl_dim_type type);
4122 int isl_pw_multi_aff_has_tuple_id(
4123 __isl_keep isl_pw_multi_aff *pma,
4124 enum isl_dim_type type);
4125 __isl_give isl_id *isl_pw_multi_aff_get_tuple_id(
4126 __isl_keep isl_pw_multi_aff *pma,
4127 enum isl_dim_type type);
4129 int isl_pw_multi_aff_foreach_piece(
4130 __isl_keep isl_pw_multi_aff *pma,
4131 int (*fn)(__isl_take isl_set *set,
4132 __isl_take isl_multi_aff *maff,
4133 void *user), void *user);
4135 int isl_union_pw_multi_aff_foreach_pw_multi_aff(
4136 __isl_keep isl_union_pw_multi_aff *upma,
4137 int (*fn)(__isl_take isl_pw_multi_aff *pma,
4138 void *user), void *user);
4140 It can be modified using
4142 #include <isl/aff.h>
4143 __isl_give isl_multi_aff *isl_multi_aff_set_aff(
4144 __isl_take isl_multi_aff *multi, int pos,
4145 __isl_take isl_aff *aff);
4146 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_set_pw_aff(
4147 __isl_take isl_pw_multi_aff *pma, unsigned pos,
4148 __isl_take isl_pw_aff *pa);
4149 __isl_give isl_multi_aff *isl_multi_aff_set_dim_name(
4150 __isl_take isl_multi_aff *maff,
4151 enum isl_dim_type type, unsigned pos, const char *s);
4152 __isl_give isl_multi_aff *isl_multi_aff_set_tuple_name(
4153 __isl_take isl_multi_aff *maff,
4154 enum isl_dim_type type, const char *s);
4155 __isl_give isl_multi_aff *isl_multi_aff_set_tuple_id(
4156 __isl_take isl_multi_aff *maff,
4157 enum isl_dim_type type, __isl_take isl_id *id);
4158 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_set_tuple_id(
4159 __isl_take isl_pw_multi_aff *pma,
4160 enum isl_dim_type type, __isl_take isl_id *id);
4162 __isl_give isl_multi_pw_aff *
4163 isl_multi_pw_aff_set_dim_name(
4164 __isl_take isl_multi_pw_aff *mpa,
4165 enum isl_dim_type type, unsigned pos, const char *s);
4166 __isl_give isl_multi_pw_aff *
4167 isl_multi_pw_aff_set_tuple_name(
4168 __isl_take isl_multi_pw_aff *mpa,
4169 enum isl_dim_type type, const char *s);
4171 __isl_give isl_multi_aff *isl_multi_aff_insert_dims(
4172 __isl_take isl_multi_aff *ma,
4173 enum isl_dim_type type, unsigned first, unsigned n);
4174 __isl_give isl_multi_aff *isl_multi_aff_add_dims(
4175 __isl_take isl_multi_aff *ma,
4176 enum isl_dim_type type, unsigned n);
4177 __isl_give isl_multi_aff *isl_multi_aff_drop_dims(
4178 __isl_take isl_multi_aff *maff,
4179 enum isl_dim_type type, unsigned first, unsigned n);
4180 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_drop_dims(
4181 __isl_take isl_pw_multi_aff *pma,
4182 enum isl_dim_type type, unsigned first, unsigned n);
4184 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_insert_dims(
4185 __isl_take isl_multi_pw_aff *mpa,
4186 enum isl_dim_type type, unsigned first, unsigned n);
4187 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_add_dims(
4188 __isl_take isl_multi_pw_aff *mpa,
4189 enum isl_dim_type type, unsigned n);
4191 To check whether two multiple affine expressions are
4192 obviously equal to each other, use
4194 int isl_multi_aff_plain_is_equal(__isl_keep isl_multi_aff *maff1,
4195 __isl_keep isl_multi_aff *maff2);
4196 int isl_pw_multi_aff_plain_is_equal(
4197 __isl_keep isl_pw_multi_aff *pma1,
4198 __isl_keep isl_pw_multi_aff *pma2);
4202 #include <isl/aff.h>
4203 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_union_lexmin(
4204 __isl_take isl_pw_multi_aff *pma1,
4205 __isl_take isl_pw_multi_aff *pma2);
4206 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_union_lexmax(
4207 __isl_take isl_pw_multi_aff *pma1,
4208 __isl_take isl_pw_multi_aff *pma2);
4209 __isl_give isl_multi_aff *isl_multi_aff_add(
4210 __isl_take isl_multi_aff *maff1,
4211 __isl_take isl_multi_aff *maff2);
4212 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_add(
4213 __isl_take isl_pw_multi_aff *pma1,
4214 __isl_take isl_pw_multi_aff *pma2);
4215 __isl_give isl_union_pw_multi_aff *isl_union_pw_multi_aff_add(
4216 __isl_take isl_union_pw_multi_aff *upma1,
4217 __isl_take isl_union_pw_multi_aff *upma2);
4218 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_union_add(
4219 __isl_take isl_pw_multi_aff *pma1,
4220 __isl_take isl_pw_multi_aff *pma2);
4221 __isl_give isl_multi_aff *isl_multi_aff_sub(
4222 __isl_take isl_multi_aff *ma1,
4223 __isl_take isl_multi_aff *ma2);
4224 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_sub(
4225 __isl_take isl_pw_multi_aff *pma1,
4226 __isl_take isl_pw_multi_aff *pma2);
4227 __isl_give isl_union_pw_multi_aff *isl_union_pw_multi_aff_sub(
4228 __isl_take isl_union_pw_multi_aff *upma1,
4229 __isl_take isl_union_pw_multi_aff *upma2);
4231 C<isl_multi_aff_sub> subtracts the second argument from the first.
4233 __isl_give isl_multi_aff *isl_multi_aff_scale(
4234 __isl_take isl_multi_aff *maff,
4236 __isl_give isl_multi_aff *isl_multi_aff_scale_vec(
4237 __isl_take isl_multi_aff *ma,
4238 __isl_take isl_vec *v);
4239 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_scale_vec(
4240 __isl_take isl_pw_multi_aff *pma,
4241 __isl_take isl_vec *v);
4242 __isl_give isl_union_pw_multi_aff *isl_union_pw_multi_aff_scale_vec(
4243 __isl_take isl_union_pw_multi_aff *upma,
4244 __isl_take isl_vec *v);
4246 C<isl_multi_aff_scale_vec> scales the first elements of C<ma>
4247 by the corresponding elements of C<v>.
4249 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_intersect_params(
4250 __isl_take isl_pw_multi_aff *pma,
4251 __isl_take isl_set *set);
4252 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_intersect_domain(
4253 __isl_take isl_pw_multi_aff *pma,
4254 __isl_take isl_set *set);
4255 __isl_give isl_union_pw_multi_aff *
4256 isl_union_pw_multi_aff_intersect_domain(
4257 __isl_take isl_union_pw_multi_aff *upma,
4258 __isl_take isl_union_set *uset);
4259 __isl_give isl_multi_aff *isl_multi_aff_lift(
4260 __isl_take isl_multi_aff *maff,
4261 __isl_give isl_local_space **ls);
4262 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_coalesce(
4263 __isl_take isl_pw_multi_aff *pma);
4264 __isl_give isl_multi_aff *isl_multi_aff_align_params(
4265 __isl_take isl_multi_aff *multi,
4266 __isl_take isl_space *model);
4267 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_align_params(
4268 __isl_take isl_pw_multi_aff *pma,
4269 __isl_take isl_space *model);
4270 __isl_give isl_pw_multi_aff *
4271 isl_pw_multi_aff_project_domain_on_params(
4272 __isl_take isl_pw_multi_aff *pma);
4273 __isl_give isl_multi_aff *isl_multi_aff_gist_params(
4274 __isl_take isl_multi_aff *maff,
4275 __isl_take isl_set *context);
4276 __isl_give isl_multi_aff *isl_multi_aff_gist(
4277 __isl_take isl_multi_aff *maff,
4278 __isl_take isl_set *context);
4279 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_gist_params(
4280 __isl_take isl_pw_multi_aff *pma,
4281 __isl_take isl_set *set);
4282 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_gist(
4283 __isl_take isl_pw_multi_aff *pma,
4284 __isl_take isl_set *set);
4285 __isl_give isl_set *isl_pw_multi_aff_domain(
4286 __isl_take isl_pw_multi_aff *pma);
4287 __isl_give isl_union_set *isl_union_pw_multi_aff_domain(
4288 __isl_take isl_union_pw_multi_aff *upma);
4289 __isl_give isl_multi_aff *isl_multi_aff_range_splice(
4290 __isl_take isl_multi_aff *ma1, unsigned pos,
4291 __isl_take isl_multi_aff *ma2);
4292 __isl_give isl_multi_aff *isl_multi_aff_splice(
4293 __isl_take isl_multi_aff *ma1,
4294 unsigned in_pos, unsigned out_pos,
4295 __isl_take isl_multi_aff *ma2);
4296 __isl_give isl_multi_aff *isl_multi_aff_range_product(
4297 __isl_take isl_multi_aff *ma1,
4298 __isl_take isl_multi_aff *ma2);
4299 __isl_give isl_multi_aff *isl_multi_aff_flat_range_product(
4300 __isl_take isl_multi_aff *ma1,
4301 __isl_take isl_multi_aff *ma2);
4302 __isl_give isl_multi_aff *isl_multi_aff_product(
4303 __isl_take isl_multi_aff *ma1,
4304 __isl_take isl_multi_aff *ma2);
4305 __isl_give isl_pw_multi_aff *
4306 isl_pw_multi_aff_range_product(
4307 __isl_take isl_pw_multi_aff *pma1,
4308 __isl_take isl_pw_multi_aff *pma2);
4309 __isl_give isl_pw_multi_aff *
4310 isl_pw_multi_aff_flat_range_product(
4311 __isl_take isl_pw_multi_aff *pma1,
4312 __isl_take isl_pw_multi_aff *pma2);
4313 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_product(
4314 __isl_take isl_pw_multi_aff *pma1,
4315 __isl_take isl_pw_multi_aff *pma2);
4316 __isl_give isl_union_pw_multi_aff *
4317 isl_union_pw_multi_aff_flat_range_product(
4318 __isl_take isl_union_pw_multi_aff *upma1,
4319 __isl_take isl_union_pw_multi_aff *upma2);
4320 __isl_give isl_multi_pw_aff *
4321 isl_multi_pw_aff_range_splice(
4322 __isl_take isl_multi_pw_aff *mpa1, unsigned pos,
4323 __isl_take isl_multi_pw_aff *mpa2);
4324 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_splice(
4325 __isl_take isl_multi_pw_aff *mpa1,
4326 unsigned in_pos, unsigned out_pos,
4327 __isl_take isl_multi_pw_aff *mpa2);
4328 __isl_give isl_multi_pw_aff *
4329 isl_multi_pw_aff_range_product(
4330 __isl_take isl_multi_pw_aff *mpa1,
4331 __isl_take isl_multi_pw_aff *mpa2);
4332 __isl_give isl_multi_pw_aff *
4333 isl_multi_pw_aff_flat_range_product(
4334 __isl_take isl_multi_pw_aff *mpa1,
4335 __isl_take isl_multi_pw_aff *mpa2);
4337 If the C<ls> argument of C<isl_multi_aff_lift> is not C<NULL>,
4338 then it is assigned the local space that lies at the basis of
4339 the lifting applied.
4341 #include <isl/aff.h>
4342 __isl_give isl_multi_aff *isl_multi_aff_pullback_multi_aff(
4343 __isl_take isl_multi_aff *ma1,
4344 __isl_take isl_multi_aff *ma2);
4345 __isl_give isl_pw_multi_aff *
4346 isl_pw_multi_aff_pullback_multi_aff(
4347 __isl_take isl_pw_multi_aff *pma,
4348 __isl_take isl_multi_aff *ma);
4349 __isl_give isl_pw_multi_aff *
4350 isl_pw_multi_aff_pullback_pw_multi_aff(
4351 __isl_take isl_pw_multi_aff *pma1,
4352 __isl_take isl_pw_multi_aff *pma2);
4354 The function C<isl_multi_aff_pullback_multi_aff> precomposes C<ma1> by C<ma2>.
4355 In other words, C<ma2> is plugged
4358 __isl_give isl_set *isl_multi_aff_lex_le_set(
4359 __isl_take isl_multi_aff *ma1,
4360 __isl_take isl_multi_aff *ma2);
4361 __isl_give isl_set *isl_multi_aff_lex_ge_set(
4362 __isl_take isl_multi_aff *ma1,
4363 __isl_take isl_multi_aff *ma2);
4365 The function C<isl_multi_aff_lex_le_set> returns a set
4366 containing those elements in the shared domain space
4367 where C<ma1> is lexicographically smaller than or
4370 An expression can be read from input using
4372 #include <isl/aff.h>
4373 __isl_give isl_multi_aff *isl_multi_aff_read_from_str(
4374 isl_ctx *ctx, const char *str);
4375 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_read_from_str(
4376 isl_ctx *ctx, const char *str);
4377 __isl_give isl_union_pw_multi_aff *
4378 isl_union_pw_multi_aff_read_from_str(
4379 isl_ctx *ctx, const char *str);
4381 An expression can be printed using
4383 #include <isl/aff.h>
4384 __isl_give isl_printer *isl_printer_print_multi_aff(
4385 __isl_take isl_printer *p,
4386 __isl_keep isl_multi_aff *maff);
4387 __isl_give isl_printer *isl_printer_print_pw_multi_aff(
4388 __isl_take isl_printer *p,
4389 __isl_keep isl_pw_multi_aff *pma);
4390 __isl_give isl_printer *isl_printer_print_union_pw_multi_aff(
4391 __isl_take isl_printer *p,
4392 __isl_keep isl_union_pw_multi_aff *upma);
4393 __isl_give isl_printer *isl_printer_print_multi_pw_aff(
4394 __isl_take isl_printer *p,
4395 __isl_keep isl_multi_pw_aff *mpa);
4399 Points are elements of a set. They can be used to construct
4400 simple sets (boxes) or they can be used to represent the
4401 individual elements of a set.
4402 The zero point (the origin) can be created using
4404 __isl_give isl_point *isl_point_zero(__isl_take isl_space *space);
4406 The coordinates of a point can be inspected, set and changed
4409 int isl_point_get_coordinate(__isl_keep isl_point *pnt,
4410 enum isl_dim_type type, int pos, isl_int *v);
4411 __isl_give isl_val *isl_point_get_coordinate_val(
4412 __isl_keep isl_point *pnt,
4413 enum isl_dim_type type, int pos);
4414 __isl_give isl_point *isl_point_set_coordinate(
4415 __isl_take isl_point *pnt,
4416 enum isl_dim_type type, int pos, isl_int v);
4417 __isl_give isl_point *isl_point_set_coordinate_val(
4418 __isl_take isl_point *pnt,
4419 enum isl_dim_type type, int pos,
4420 __isl_take isl_val *v);
4422 __isl_give isl_point *isl_point_add_ui(
4423 __isl_take isl_point *pnt,
4424 enum isl_dim_type type, int pos, unsigned val);
4425 __isl_give isl_point *isl_point_sub_ui(
4426 __isl_take isl_point *pnt,
4427 enum isl_dim_type type, int pos, unsigned val);
4429 Other properties can be obtained using
4431 isl_ctx *isl_point_get_ctx(__isl_keep isl_point *pnt);
4433 Points can be copied or freed using
4435 __isl_give isl_point *isl_point_copy(
4436 __isl_keep isl_point *pnt);
4437 void isl_point_free(__isl_take isl_point *pnt);
4439 A singleton set can be created from a point using
4441 __isl_give isl_basic_set *isl_basic_set_from_point(
4442 __isl_take isl_point *pnt);
4443 __isl_give isl_set *isl_set_from_point(
4444 __isl_take isl_point *pnt);
4446 and a box can be created from two opposite extremal points using
4448 __isl_give isl_basic_set *isl_basic_set_box_from_points(
4449 __isl_take isl_point *pnt1,
4450 __isl_take isl_point *pnt2);
4451 __isl_give isl_set *isl_set_box_from_points(
4452 __isl_take isl_point *pnt1,
4453 __isl_take isl_point *pnt2);
4455 All elements of a B<bounded> (union) set can be enumerated using
4456 the following functions.
4458 int isl_set_foreach_point(__isl_keep isl_set *set,
4459 int (*fn)(__isl_take isl_point *pnt, void *user),
4461 int isl_union_set_foreach_point(__isl_keep isl_union_set *uset,
4462 int (*fn)(__isl_take isl_point *pnt, void *user),
4465 The function C<fn> is called for each integer point in
4466 C<set> with as second argument the last argument of
4467 the C<isl_set_foreach_point> call. The function C<fn>
4468 should return C<0> on success and C<-1> on failure.
4469 In the latter case, C<isl_set_foreach_point> will stop
4470 enumerating and return C<-1> as well.
4471 If the enumeration is performed successfully and to completion,
4472 then C<isl_set_foreach_point> returns C<0>.
4474 To obtain a single point of a (basic) set, use
4476 __isl_give isl_point *isl_basic_set_sample_point(
4477 __isl_take isl_basic_set *bset);
4478 __isl_give isl_point *isl_set_sample_point(
4479 __isl_take isl_set *set);
4481 If C<set> does not contain any (integer) points, then the
4482 resulting point will be ``void'', a property that can be
4485 int isl_point_is_void(__isl_keep isl_point *pnt);
4487 =head2 Piecewise Quasipolynomials
4489 A piecewise quasipolynomial is a particular kind of function that maps
4490 a parametric point to a rational value.
4491 More specifically, a quasipolynomial is a polynomial expression in greatest
4492 integer parts of affine expressions of parameters and variables.
4493 A piecewise quasipolynomial is a subdivision of a given parametric
4494 domain into disjoint cells with a quasipolynomial associated to
4495 each cell. The value of the piecewise quasipolynomial at a given
4496 point is the value of the quasipolynomial associated to the cell
4497 that contains the point. Outside of the union of cells,
4498 the value is assumed to be zero.
4499 For example, the piecewise quasipolynomial
4501 [n] -> { [x] -> ((1 + n) - x) : x <= n and x >= 0 }
4503 maps C<x> to C<1 + n - x> for values of C<x> between C<0> and C<n>.
4504 A given piecewise quasipolynomial has a fixed domain dimension.
4505 Union piecewise quasipolynomials are used to contain piecewise quasipolynomials
4506 defined over different domains.
4507 Piecewise quasipolynomials are mainly used by the C<barvinok>
4508 library for representing the number of elements in a parametric set or map.
4509 For example, the piecewise quasipolynomial above represents
4510 the number of points in the map
4512 [n] -> { [x] -> [y] : x,y >= 0 and 0 <= x + y <= n }
4514 =head3 Input and Output
4516 Piecewise quasipolynomials can be read from input using
4518 __isl_give isl_union_pw_qpolynomial *
4519 isl_union_pw_qpolynomial_read_from_str(
4520 isl_ctx *ctx, const char *str);
4522 Quasipolynomials and piecewise quasipolynomials can be printed
4523 using the following functions.
4525 __isl_give isl_printer *isl_printer_print_qpolynomial(
4526 __isl_take isl_printer *p,
4527 __isl_keep isl_qpolynomial *qp);
4529 __isl_give isl_printer *isl_printer_print_pw_qpolynomial(
4530 __isl_take isl_printer *p,
4531 __isl_keep isl_pw_qpolynomial *pwqp);
4533 __isl_give isl_printer *isl_printer_print_union_pw_qpolynomial(
4534 __isl_take isl_printer *p,
4535 __isl_keep isl_union_pw_qpolynomial *upwqp);
4537 The output format of the printer
4538 needs to be set to either C<ISL_FORMAT_ISL> or C<ISL_FORMAT_C>.
4539 For C<isl_printer_print_union_pw_qpolynomial>, only C<ISL_FORMAT_ISL>
4541 In case of printing in C<ISL_FORMAT_C>, the user may want
4542 to set the names of all dimensions
4544 __isl_give isl_qpolynomial *isl_qpolynomial_set_dim_name(
4545 __isl_take isl_qpolynomial *qp,
4546 enum isl_dim_type type, unsigned pos,
4548 __isl_give isl_pw_qpolynomial *
4549 isl_pw_qpolynomial_set_dim_name(
4550 __isl_take isl_pw_qpolynomial *pwqp,
4551 enum isl_dim_type type, unsigned pos,
4554 =head3 Creating New (Piecewise) Quasipolynomials
4556 Some simple quasipolynomials can be created using the following functions.
4557 More complicated quasipolynomials can be created by applying
4558 operations such as addition and multiplication
4559 on the resulting quasipolynomials
4561 __isl_give isl_qpolynomial *isl_qpolynomial_zero_on_domain(
4562 __isl_take isl_space *domain);
4563 __isl_give isl_qpolynomial *isl_qpolynomial_one_on_domain(
4564 __isl_take isl_space *domain);
4565 __isl_give isl_qpolynomial *isl_qpolynomial_infty_on_domain(
4566 __isl_take isl_space *domain);
4567 __isl_give isl_qpolynomial *isl_qpolynomial_neginfty_on_domain(
4568 __isl_take isl_space *domain);
4569 __isl_give isl_qpolynomial *isl_qpolynomial_nan_on_domain(
4570 __isl_take isl_space *domain);
4571 __isl_give isl_qpolynomial *isl_qpolynomial_rat_cst_on_domain(
4572 __isl_take isl_space *domain,
4573 const isl_int n, const isl_int d);
4574 __isl_give isl_qpolynomial *isl_qpolynomial_var_on_domain(
4575 __isl_take isl_space *domain,
4576 enum isl_dim_type type, unsigned pos);
4577 __isl_give isl_qpolynomial *isl_qpolynomial_from_aff(
4578 __isl_take isl_aff *aff);
4580 Note that the space in which a quasipolynomial lives is a map space
4581 with a one-dimensional range. The C<domain> argument in some of
4582 the functions above corresponds to the domain of this map space.
4584 The zero piecewise quasipolynomial or a piecewise quasipolynomial
4585 with a single cell can be created using the following functions.
4586 Multiple of these single cell piecewise quasipolynomials can
4587 be combined to create more complicated piecewise quasipolynomials.
4589 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_zero(
4590 __isl_take isl_space *space);
4591 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_alloc(
4592 __isl_take isl_set *set,
4593 __isl_take isl_qpolynomial *qp);
4594 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_from_qpolynomial(
4595 __isl_take isl_qpolynomial *qp);
4596 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_from_pw_aff(
4597 __isl_take isl_pw_aff *pwaff);
4599 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_zero(
4600 __isl_take isl_space *space);
4601 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_from_pw_qpolynomial(
4602 __isl_take isl_pw_qpolynomial *pwqp);
4603 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_add_pw_qpolynomial(
4604 __isl_take isl_union_pw_qpolynomial *upwqp,
4605 __isl_take isl_pw_qpolynomial *pwqp);
4607 Quasipolynomials can be copied and freed again using the following
4610 __isl_give isl_qpolynomial *isl_qpolynomial_copy(
4611 __isl_keep isl_qpolynomial *qp);
4612 void *isl_qpolynomial_free(__isl_take isl_qpolynomial *qp);
4614 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_copy(
4615 __isl_keep isl_pw_qpolynomial *pwqp);
4616 void *isl_pw_qpolynomial_free(
4617 __isl_take isl_pw_qpolynomial *pwqp);
4619 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_copy(
4620 __isl_keep isl_union_pw_qpolynomial *upwqp);
4621 void *isl_union_pw_qpolynomial_free(
4622 __isl_take isl_union_pw_qpolynomial *upwqp);
4624 =head3 Inspecting (Piecewise) Quasipolynomials
4626 To iterate over all piecewise quasipolynomials in a union
4627 piecewise quasipolynomial, use the following function
4629 int isl_union_pw_qpolynomial_foreach_pw_qpolynomial(
4630 __isl_keep isl_union_pw_qpolynomial *upwqp,
4631 int (*fn)(__isl_take isl_pw_qpolynomial *pwqp, void *user),
4634 To extract the piecewise quasipolynomial in a given space from a union, use
4636 __isl_give isl_pw_qpolynomial *
4637 isl_union_pw_qpolynomial_extract_pw_qpolynomial(
4638 __isl_keep isl_union_pw_qpolynomial *upwqp,
4639 __isl_take isl_space *space);
4641 To iterate over the cells in a piecewise quasipolynomial,
4642 use either of the following two functions
4644 int isl_pw_qpolynomial_foreach_piece(
4645 __isl_keep isl_pw_qpolynomial *pwqp,
4646 int (*fn)(__isl_take isl_set *set,
4647 __isl_take isl_qpolynomial *qp,
4648 void *user), void *user);
4649 int isl_pw_qpolynomial_foreach_lifted_piece(
4650 __isl_keep isl_pw_qpolynomial *pwqp,
4651 int (*fn)(__isl_take isl_set *set,
4652 __isl_take isl_qpolynomial *qp,
4653 void *user), void *user);
4655 As usual, the function C<fn> should return C<0> on success
4656 and C<-1> on failure. The difference between
4657 C<isl_pw_qpolynomial_foreach_piece> and
4658 C<isl_pw_qpolynomial_foreach_lifted_piece> is that
4659 C<isl_pw_qpolynomial_foreach_lifted_piece> will first
4660 compute unique representations for all existentially quantified
4661 variables and then turn these existentially quantified variables
4662 into extra set variables, adapting the associated quasipolynomial
4663 accordingly. This means that the C<set> passed to C<fn>
4664 will not have any existentially quantified variables, but that
4665 the dimensions of the sets may be different for different
4666 invocations of C<fn>.
4668 To iterate over all terms in a quasipolynomial,
4671 int isl_qpolynomial_foreach_term(
4672 __isl_keep isl_qpolynomial *qp,
4673 int (*fn)(__isl_take isl_term *term,
4674 void *user), void *user);
4676 The terms themselves can be inspected and freed using
4679 unsigned isl_term_dim(__isl_keep isl_term *term,
4680 enum isl_dim_type type);
4681 void isl_term_get_num(__isl_keep isl_term *term,
4683 void isl_term_get_den(__isl_keep isl_term *term,
4685 int isl_term_get_exp(__isl_keep isl_term *term,
4686 enum isl_dim_type type, unsigned pos);
4687 __isl_give isl_aff *isl_term_get_div(
4688 __isl_keep isl_term *term, unsigned pos);
4689 void isl_term_free(__isl_take isl_term *term);
4691 Each term is a product of parameters, set variables and
4692 integer divisions. The function C<isl_term_get_exp>
4693 returns the exponent of a given dimensions in the given term.
4694 The C<isl_int>s in the arguments of C<isl_term_get_num>
4695 and C<isl_term_get_den> need to have been initialized
4696 using C<isl_int_init> before calling these functions.
4698 =head3 Properties of (Piecewise) Quasipolynomials
4700 To check whether a quasipolynomial is actually a constant,
4701 use the following function.
4703 int isl_qpolynomial_is_cst(__isl_keep isl_qpolynomial *qp,
4704 isl_int *n, isl_int *d);
4706 If C<qp> is a constant and if C<n> and C<d> are not C<NULL>
4707 then the numerator and denominator of the constant
4708 are returned in C<*n> and C<*d>, respectively.
4710 To check whether two union piecewise quasipolynomials are
4711 obviously equal, use
4713 int isl_union_pw_qpolynomial_plain_is_equal(
4714 __isl_keep isl_union_pw_qpolynomial *upwqp1,
4715 __isl_keep isl_union_pw_qpolynomial *upwqp2);
4717 =head3 Operations on (Piecewise) Quasipolynomials
4719 __isl_give isl_qpolynomial *isl_qpolynomial_scale(
4720 __isl_take isl_qpolynomial *qp, isl_int v);
4721 __isl_give isl_qpolynomial *isl_qpolynomial_neg(
4722 __isl_take isl_qpolynomial *qp);
4723 __isl_give isl_qpolynomial *isl_qpolynomial_add(
4724 __isl_take isl_qpolynomial *qp1,
4725 __isl_take isl_qpolynomial *qp2);
4726 __isl_give isl_qpolynomial *isl_qpolynomial_sub(
4727 __isl_take isl_qpolynomial *qp1,
4728 __isl_take isl_qpolynomial *qp2);
4729 __isl_give isl_qpolynomial *isl_qpolynomial_mul(
4730 __isl_take isl_qpolynomial *qp1,
4731 __isl_take isl_qpolynomial *qp2);
4732 __isl_give isl_qpolynomial *isl_qpolynomial_pow(
4733 __isl_take isl_qpolynomial *qp, unsigned exponent);
4735 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_add(
4736 __isl_take isl_pw_qpolynomial *pwqp1,
4737 __isl_take isl_pw_qpolynomial *pwqp2);
4738 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_sub(
4739 __isl_take isl_pw_qpolynomial *pwqp1,
4740 __isl_take isl_pw_qpolynomial *pwqp2);
4741 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_add_disjoint(
4742 __isl_take isl_pw_qpolynomial *pwqp1,
4743 __isl_take isl_pw_qpolynomial *pwqp2);
4744 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_neg(
4745 __isl_take isl_pw_qpolynomial *pwqp);
4746 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_mul(
4747 __isl_take isl_pw_qpolynomial *pwqp1,
4748 __isl_take isl_pw_qpolynomial *pwqp2);
4749 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_pow(
4750 __isl_take isl_pw_qpolynomial *pwqp, unsigned exponent);
4752 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_add(
4753 __isl_take isl_union_pw_qpolynomial *upwqp1,
4754 __isl_take isl_union_pw_qpolynomial *upwqp2);
4755 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_sub(
4756 __isl_take isl_union_pw_qpolynomial *upwqp1,
4757 __isl_take isl_union_pw_qpolynomial *upwqp2);
4758 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_mul(
4759 __isl_take isl_union_pw_qpolynomial *upwqp1,
4760 __isl_take isl_union_pw_qpolynomial *upwqp2);
4762 __isl_give isl_qpolynomial *isl_pw_qpolynomial_eval(
4763 __isl_take isl_pw_qpolynomial *pwqp,
4764 __isl_take isl_point *pnt);
4766 __isl_give isl_qpolynomial *isl_union_pw_qpolynomial_eval(
4767 __isl_take isl_union_pw_qpolynomial *upwqp,
4768 __isl_take isl_point *pnt);
4770 __isl_give isl_set *isl_pw_qpolynomial_domain(
4771 __isl_take isl_pw_qpolynomial *pwqp);
4772 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_intersect_domain(
4773 __isl_take isl_pw_qpolynomial *pwpq,
4774 __isl_take isl_set *set);
4775 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_intersect_params(
4776 __isl_take isl_pw_qpolynomial *pwpq,
4777 __isl_take isl_set *set);
4779 __isl_give isl_union_set *isl_union_pw_qpolynomial_domain(
4780 __isl_take isl_union_pw_qpolynomial *upwqp);
4781 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_intersect_domain(
4782 __isl_take isl_union_pw_qpolynomial *upwpq,
4783 __isl_take isl_union_set *uset);
4784 __isl_give isl_union_pw_qpolynomial *
4785 isl_union_pw_qpolynomial_intersect_params(
4786 __isl_take isl_union_pw_qpolynomial *upwpq,
4787 __isl_take isl_set *set);
4789 __isl_give isl_qpolynomial *isl_qpolynomial_align_params(
4790 __isl_take isl_qpolynomial *qp,
4791 __isl_take isl_space *model);
4793 __isl_give isl_qpolynomial *isl_qpolynomial_project_domain_on_params(
4794 __isl_take isl_qpolynomial *qp);
4795 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_project_domain_on_params(
4796 __isl_take isl_pw_qpolynomial *pwqp);
4798 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_coalesce(
4799 __isl_take isl_union_pw_qpolynomial *upwqp);
4801 __isl_give isl_qpolynomial *isl_qpolynomial_gist_params(
4802 __isl_take isl_qpolynomial *qp,
4803 __isl_take isl_set *context);
4804 __isl_give isl_qpolynomial *isl_qpolynomial_gist(
4805 __isl_take isl_qpolynomial *qp,
4806 __isl_take isl_set *context);
4808 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_gist_params(
4809 __isl_take isl_pw_qpolynomial *pwqp,
4810 __isl_take isl_set *context);
4811 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_gist(
4812 __isl_take isl_pw_qpolynomial *pwqp,
4813 __isl_take isl_set *context);
4815 __isl_give isl_union_pw_qpolynomial *
4816 isl_union_pw_qpolynomial_gist_params(
4817 __isl_take isl_union_pw_qpolynomial *upwqp,
4818 __isl_take isl_set *context);
4819 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_gist(
4820 __isl_take isl_union_pw_qpolynomial *upwqp,
4821 __isl_take isl_union_set *context);
4823 The gist operation applies the gist operation to each of
4824 the cells in the domain of the input piecewise quasipolynomial.
4825 The context is also exploited
4826 to simplify the quasipolynomials associated to each cell.
4828 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_to_polynomial(
4829 __isl_take isl_pw_qpolynomial *pwqp, int sign);
4830 __isl_give isl_union_pw_qpolynomial *
4831 isl_union_pw_qpolynomial_to_polynomial(
4832 __isl_take isl_union_pw_qpolynomial *upwqp, int sign);
4834 Approximate each quasipolynomial by a polynomial. If C<sign> is positive,
4835 the polynomial will be an overapproximation. If C<sign> is negative,
4836 it will be an underapproximation. If C<sign> is zero, the approximation
4837 will lie somewhere in between.
4839 =head2 Bounds on Piecewise Quasipolynomials and Piecewise Quasipolynomial Reductions
4841 A piecewise quasipolynomial reduction is a piecewise
4842 reduction (or fold) of quasipolynomials.
4843 In particular, the reduction can be maximum or a minimum.
4844 The objects are mainly used to represent the result of
4845 an upper or lower bound on a quasipolynomial over its domain,
4846 i.e., as the result of the following function.
4848 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_bound(
4849 __isl_take isl_pw_qpolynomial *pwqp,
4850 enum isl_fold type, int *tight);
4852 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_bound(
4853 __isl_take isl_union_pw_qpolynomial *upwqp,
4854 enum isl_fold type, int *tight);
4856 The C<type> argument may be either C<isl_fold_min> or C<isl_fold_max>.
4857 If C<tight> is not C<NULL>, then C<*tight> is set to C<1>
4858 is the returned bound is known be tight, i.e., for each value
4859 of the parameters there is at least
4860 one element in the domain that reaches the bound.
4861 If the domain of C<pwqp> is not wrapping, then the bound is computed
4862 over all elements in that domain and the result has a purely parametric
4863 domain. If the domain of C<pwqp> is wrapping, then the bound is
4864 computed over the range of the wrapped relation. The domain of the
4865 wrapped relation becomes the domain of the result.
4867 A (piecewise) quasipolynomial reduction can be copied or freed using the
4868 following functions.
4870 __isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_copy(
4871 __isl_keep isl_qpolynomial_fold *fold);
4872 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_copy(
4873 __isl_keep isl_pw_qpolynomial_fold *pwf);
4874 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_copy(
4875 __isl_keep isl_union_pw_qpolynomial_fold *upwf);
4876 void isl_qpolynomial_fold_free(
4877 __isl_take isl_qpolynomial_fold *fold);
4878 void *isl_pw_qpolynomial_fold_free(
4879 __isl_take isl_pw_qpolynomial_fold *pwf);
4880 void *isl_union_pw_qpolynomial_fold_free(
4881 __isl_take isl_union_pw_qpolynomial_fold *upwf);
4883 =head3 Printing Piecewise Quasipolynomial Reductions
4885 Piecewise quasipolynomial reductions can be printed
4886 using the following function.
4888 __isl_give isl_printer *isl_printer_print_pw_qpolynomial_fold(
4889 __isl_take isl_printer *p,
4890 __isl_keep isl_pw_qpolynomial_fold *pwf);
4891 __isl_give isl_printer *isl_printer_print_union_pw_qpolynomial_fold(
4892 __isl_take isl_printer *p,
4893 __isl_keep isl_union_pw_qpolynomial_fold *upwf);
4895 For C<isl_printer_print_pw_qpolynomial_fold>,
4896 output format of the printer
4897 needs to be set to either C<ISL_FORMAT_ISL> or C<ISL_FORMAT_C>.
4898 For C<isl_printer_print_union_pw_qpolynomial_fold>,
4899 output format of the printer
4900 needs to be set to C<ISL_FORMAT_ISL>.
4901 In case of printing in C<ISL_FORMAT_C>, the user may want
4902 to set the names of all dimensions
4904 __isl_give isl_pw_qpolynomial_fold *
4905 isl_pw_qpolynomial_fold_set_dim_name(
4906 __isl_take isl_pw_qpolynomial_fold *pwf,
4907 enum isl_dim_type type, unsigned pos,
4910 =head3 Inspecting (Piecewise) Quasipolynomial Reductions
4912 To iterate over all piecewise quasipolynomial reductions in a union
4913 piecewise quasipolynomial reduction, use the following function
4915 int isl_union_pw_qpolynomial_fold_foreach_pw_qpolynomial_fold(
4916 __isl_keep isl_union_pw_qpolynomial_fold *upwf,
4917 int (*fn)(__isl_take isl_pw_qpolynomial_fold *pwf,
4918 void *user), void *user);
4920 To iterate over the cells in a piecewise quasipolynomial reduction,
4921 use either of the following two functions
4923 int isl_pw_qpolynomial_fold_foreach_piece(
4924 __isl_keep isl_pw_qpolynomial_fold *pwf,
4925 int (*fn)(__isl_take isl_set *set,
4926 __isl_take isl_qpolynomial_fold *fold,
4927 void *user), void *user);
4928 int isl_pw_qpolynomial_fold_foreach_lifted_piece(
4929 __isl_keep isl_pw_qpolynomial_fold *pwf,
4930 int (*fn)(__isl_take isl_set *set,
4931 __isl_take isl_qpolynomial_fold *fold,
4932 void *user), void *user);
4934 See L<Inspecting (Piecewise) Quasipolynomials> for an explanation
4935 of the difference between these two functions.
4937 To iterate over all quasipolynomials in a reduction, use
4939 int isl_qpolynomial_fold_foreach_qpolynomial(
4940 __isl_keep isl_qpolynomial_fold *fold,
4941 int (*fn)(__isl_take isl_qpolynomial *qp,
4942 void *user), void *user);
4944 =head3 Properties of Piecewise Quasipolynomial Reductions
4946 To check whether two union piecewise quasipolynomial reductions are
4947 obviously equal, use
4949 int isl_union_pw_qpolynomial_fold_plain_is_equal(
4950 __isl_keep isl_union_pw_qpolynomial_fold *upwf1,
4951 __isl_keep isl_union_pw_qpolynomial_fold *upwf2);
4953 =head3 Operations on Piecewise Quasipolynomial Reductions
4955 __isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_scale(
4956 __isl_take isl_qpolynomial_fold *fold, isl_int v);
4958 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_add(
4959 __isl_take isl_pw_qpolynomial_fold *pwf1,
4960 __isl_take isl_pw_qpolynomial_fold *pwf2);
4962 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_fold(
4963 __isl_take isl_pw_qpolynomial_fold *pwf1,
4964 __isl_take isl_pw_qpolynomial_fold *pwf2);
4966 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_fold(
4967 __isl_take isl_union_pw_qpolynomial_fold *upwf1,
4968 __isl_take isl_union_pw_qpolynomial_fold *upwf2);
4970 __isl_give isl_qpolynomial *isl_pw_qpolynomial_fold_eval(
4971 __isl_take isl_pw_qpolynomial_fold *pwf,
4972 __isl_take isl_point *pnt);
4974 __isl_give isl_qpolynomial *isl_union_pw_qpolynomial_fold_eval(
4975 __isl_take isl_union_pw_qpolynomial_fold *upwf,
4976 __isl_take isl_point *pnt);
4978 __isl_give isl_pw_qpolynomial_fold *
4979 isl_pw_qpolynomial_fold_intersect_params(
4980 __isl_take isl_pw_qpolynomial_fold *pwf,
4981 __isl_take isl_set *set);
4983 __isl_give isl_union_set *isl_union_pw_qpolynomial_fold_domain(
4984 __isl_take isl_union_pw_qpolynomial_fold *upwf);
4985 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_intersect_domain(
4986 __isl_take isl_union_pw_qpolynomial_fold *upwf,
4987 __isl_take isl_union_set *uset);
4988 __isl_give isl_union_pw_qpolynomial_fold *
4989 isl_union_pw_qpolynomial_fold_intersect_params(
4990 __isl_take isl_union_pw_qpolynomial_fold *upwf,
4991 __isl_take isl_set *set);
4993 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_project_domain_on_params(
4994 __isl_take isl_pw_qpolynomial_fold *pwf);
4996 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_coalesce(
4997 __isl_take isl_pw_qpolynomial_fold *pwf);
4999 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_coalesce(
5000 __isl_take isl_union_pw_qpolynomial_fold *upwf);
5002 __isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_gist_params(
5003 __isl_take isl_qpolynomial_fold *fold,
5004 __isl_take isl_set *context);
5005 __isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_gist(
5006 __isl_take isl_qpolynomial_fold *fold,
5007 __isl_take isl_set *context);
5009 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_gist(
5010 __isl_take isl_pw_qpolynomial_fold *pwf,
5011 __isl_take isl_set *context);
5012 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_gist_params(
5013 __isl_take isl_pw_qpolynomial_fold *pwf,
5014 __isl_take isl_set *context);
5016 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_gist(
5017 __isl_take isl_union_pw_qpolynomial_fold *upwf,
5018 __isl_take isl_union_set *context);
5019 __isl_give isl_union_pw_qpolynomial_fold *
5020 isl_union_pw_qpolynomial_fold_gist_params(
5021 __isl_take isl_union_pw_qpolynomial_fold *upwf,
5022 __isl_take isl_set *context);
5024 The gist operation applies the gist operation to each of
5025 the cells in the domain of the input piecewise quasipolynomial reduction.
5026 In future, the operation will also exploit the context
5027 to simplify the quasipolynomial reductions associated to each cell.
5029 __isl_give isl_pw_qpolynomial_fold *
5030 isl_set_apply_pw_qpolynomial_fold(
5031 __isl_take isl_set *set,
5032 __isl_take isl_pw_qpolynomial_fold *pwf,
5034 __isl_give isl_pw_qpolynomial_fold *
5035 isl_map_apply_pw_qpolynomial_fold(
5036 __isl_take isl_map *map,
5037 __isl_take isl_pw_qpolynomial_fold *pwf,
5039 __isl_give isl_union_pw_qpolynomial_fold *
5040 isl_union_set_apply_union_pw_qpolynomial_fold(
5041 __isl_take isl_union_set *uset,
5042 __isl_take isl_union_pw_qpolynomial_fold *upwf,
5044 __isl_give isl_union_pw_qpolynomial_fold *
5045 isl_union_map_apply_union_pw_qpolynomial_fold(
5046 __isl_take isl_union_map *umap,
5047 __isl_take isl_union_pw_qpolynomial_fold *upwf,
5050 The functions taking a map
5051 compose the given map with the given piecewise quasipolynomial reduction.
5052 That is, compute a bound (of the same type as C<pwf> or C<upwf> itself)
5053 over all elements in the intersection of the range of the map
5054 and the domain of the piecewise quasipolynomial reduction
5055 as a function of an element in the domain of the map.
5056 The functions taking a set compute a bound over all elements in the
5057 intersection of the set and the domain of the
5058 piecewise quasipolynomial reduction.
5060 =head2 Parametric Vertex Enumeration
5062 The parametric vertex enumeration described in this section
5063 is mainly intended to be used internally and by the C<barvinok>
5066 #include <isl/vertices.h>
5067 __isl_give isl_vertices *isl_basic_set_compute_vertices(
5068 __isl_keep isl_basic_set *bset);
5070 The function C<isl_basic_set_compute_vertices> performs the
5071 actual computation of the parametric vertices and the chamber
5072 decomposition and store the result in an C<isl_vertices> object.
5073 This information can be queried by either iterating over all
5074 the vertices or iterating over all the chambers or cells
5075 and then iterating over all vertices that are active on the chamber.
5077 int isl_vertices_foreach_vertex(
5078 __isl_keep isl_vertices *vertices,
5079 int (*fn)(__isl_take isl_vertex *vertex, void *user),
5082 int isl_vertices_foreach_cell(
5083 __isl_keep isl_vertices *vertices,
5084 int (*fn)(__isl_take isl_cell *cell, void *user),
5086 int isl_cell_foreach_vertex(__isl_keep isl_cell *cell,
5087 int (*fn)(__isl_take isl_vertex *vertex, void *user),
5090 Other operations that can be performed on an C<isl_vertices> object are
5093 isl_ctx *isl_vertices_get_ctx(
5094 __isl_keep isl_vertices *vertices);
5095 int isl_vertices_get_n_vertices(
5096 __isl_keep isl_vertices *vertices);
5097 void isl_vertices_free(__isl_take isl_vertices *vertices);
5099 Vertices can be inspected and destroyed using the following functions.
5101 isl_ctx *isl_vertex_get_ctx(__isl_keep isl_vertex *vertex);
5102 int isl_vertex_get_id(__isl_keep isl_vertex *vertex);
5103 __isl_give isl_basic_set *isl_vertex_get_domain(
5104 __isl_keep isl_vertex *vertex);
5105 __isl_give isl_basic_set *isl_vertex_get_expr(
5106 __isl_keep isl_vertex *vertex);
5107 void isl_vertex_free(__isl_take isl_vertex *vertex);
5109 C<isl_vertex_get_expr> returns a singleton parametric set describing
5110 the vertex, while C<isl_vertex_get_domain> returns the activity domain
5112 Note that C<isl_vertex_get_domain> and C<isl_vertex_get_expr> return
5113 B<rational> basic sets, so they should mainly be used for inspection
5114 and should not be mixed with integer sets.
5116 Chambers can be inspected and destroyed using the following functions.
5118 isl_ctx *isl_cell_get_ctx(__isl_keep isl_cell *cell);
5119 __isl_give isl_basic_set *isl_cell_get_domain(
5120 __isl_keep isl_cell *cell);
5121 void isl_cell_free(__isl_take isl_cell *cell);
5123 =head1 Polyhedral Compilation Library
5125 This section collects functionality in C<isl> that has been specifically
5126 designed for use during polyhedral compilation.
5128 =head2 Dependence Analysis
5130 C<isl> contains specialized functionality for performing
5131 array dataflow analysis. That is, given a I<sink> access relation
5132 and a collection of possible I<source> access relations,
5133 C<isl> can compute relations that describe
5134 for each iteration of the sink access, which iteration
5135 of which of the source access relations was the last
5136 to access the same data element before the given iteration
5138 The resulting dependence relations map source iterations
5139 to the corresponding sink iterations.
5140 To compute standard flow dependences, the sink should be
5141 a read, while the sources should be writes.
5142 If any of the source accesses are marked as being I<may>
5143 accesses, then there will be a dependence from the last
5144 I<must> access B<and> from any I<may> access that follows
5145 this last I<must> access.
5146 In particular, if I<all> sources are I<may> accesses,
5147 then memory based dependence analysis is performed.
5148 If, on the other hand, all sources are I<must> accesses,
5149 then value based dependence analysis is performed.
5151 #include <isl/flow.h>
5153 typedef int (*isl_access_level_before)(void *first, void *second);
5155 __isl_give isl_access_info *isl_access_info_alloc(
5156 __isl_take isl_map *sink,
5157 void *sink_user, isl_access_level_before fn,
5159 __isl_give isl_access_info *isl_access_info_add_source(
5160 __isl_take isl_access_info *acc,
5161 __isl_take isl_map *source, int must,
5163 void *isl_access_info_free(__isl_take isl_access_info *acc);
5165 __isl_give isl_flow *isl_access_info_compute_flow(
5166 __isl_take isl_access_info *acc);
5168 int isl_flow_foreach(__isl_keep isl_flow *deps,
5169 int (*fn)(__isl_take isl_map *dep, int must,
5170 void *dep_user, void *user),
5172 __isl_give isl_map *isl_flow_get_no_source(
5173 __isl_keep isl_flow *deps, int must);
5174 void isl_flow_free(__isl_take isl_flow *deps);
5176 The function C<isl_access_info_compute_flow> performs the actual
5177 dependence analysis. The other functions are used to construct
5178 the input for this function or to read off the output.
5180 The input is collected in an C<isl_access_info>, which can
5181 be created through a call to C<isl_access_info_alloc>.
5182 The arguments to this functions are the sink access relation
5183 C<sink>, a token C<sink_user> used to identify the sink
5184 access to the user, a callback function for specifying the
5185 relative order of source and sink accesses, and the number
5186 of source access relations that will be added.
5187 The callback function has type C<int (*)(void *first, void *second)>.
5188 The function is called with two user supplied tokens identifying
5189 either a source or the sink and it should return the shared nesting
5190 level and the relative order of the two accesses.
5191 In particular, let I<n> be the number of loops shared by
5192 the two accesses. If C<first> precedes C<second> textually,
5193 then the function should return I<2 * n + 1>; otherwise,
5194 it should return I<2 * n>.
5195 The sources can be added to the C<isl_access_info> by performing
5196 (at most) C<max_source> calls to C<isl_access_info_add_source>.
5197 C<must> indicates whether the source is a I<must> access
5198 or a I<may> access. Note that a multi-valued access relation
5199 should only be marked I<must> if every iteration in the domain
5200 of the relation accesses I<all> elements in its image.
5201 The C<source_user> token is again used to identify
5202 the source access. The range of the source access relation
5203 C<source> should have the same dimension as the range
5204 of the sink access relation.
5205 The C<isl_access_info_free> function should usually not be
5206 called explicitly, because it is called implicitly by
5207 C<isl_access_info_compute_flow>.
5209 The result of the dependence analysis is collected in an
5210 C<isl_flow>. There may be elements of
5211 the sink access for which no preceding source access could be
5212 found or for which all preceding sources are I<may> accesses.
5213 The relations containing these elements can be obtained through
5214 calls to C<isl_flow_get_no_source>, the first with C<must> set
5215 and the second with C<must> unset.
5216 In the case of standard flow dependence analysis,
5217 with the sink a read and the sources I<must> writes,
5218 the first relation corresponds to the reads from uninitialized
5219 array elements and the second relation is empty.
5220 The actual flow dependences can be extracted using
5221 C<isl_flow_foreach>. This function will call the user-specified
5222 callback function C<fn> for each B<non-empty> dependence between
5223 a source and the sink. The callback function is called
5224 with four arguments, the actual flow dependence relation
5225 mapping source iterations to sink iterations, a boolean that
5226 indicates whether it is a I<must> or I<may> dependence, a token
5227 identifying the source and an additional C<void *> with value
5228 equal to the third argument of the C<isl_flow_foreach> call.
5229 A dependence is marked I<must> if it originates from a I<must>
5230 source and if it is not followed by any I<may> sources.
5232 After finishing with an C<isl_flow>, the user should call
5233 C<isl_flow_free> to free all associated memory.
5235 A higher-level interface to dependence analysis is provided
5236 by the following function.
5238 #include <isl/flow.h>
5240 int isl_union_map_compute_flow(__isl_take isl_union_map *sink,
5241 __isl_take isl_union_map *must_source,
5242 __isl_take isl_union_map *may_source,
5243 __isl_take isl_union_map *schedule,
5244 __isl_give isl_union_map **must_dep,
5245 __isl_give isl_union_map **may_dep,
5246 __isl_give isl_union_map **must_no_source,
5247 __isl_give isl_union_map **may_no_source);
5249 The arrays are identified by the tuple names of the ranges
5250 of the accesses. The iteration domains by the tuple names
5251 of the domains of the accesses and of the schedule.
5252 The relative order of the iteration domains is given by the
5253 schedule. The relations returned through C<must_no_source>
5254 and C<may_no_source> are subsets of C<sink>.
5255 Any of C<must_dep>, C<may_dep>, C<must_no_source>
5256 or C<may_no_source> may be C<NULL>, but a C<NULL> value for
5257 any of the other arguments is treated as an error.
5259 =head3 Interaction with Dependence Analysis
5261 During the dependence analysis, we frequently need to perform
5262 the following operation. Given a relation between sink iterations
5263 and potential source iterations from a particular source domain,
5264 what is the last potential source iteration corresponding to each
5265 sink iteration. It can sometimes be convenient to adjust
5266 the set of potential source iterations before or after each such operation.
5267 The prototypical example is fuzzy array dataflow analysis,
5268 where we need to analyze if, based on data-dependent constraints,
5269 the sink iteration can ever be executed without one or more of
5270 the corresponding potential source iterations being executed.
5271 If so, we can introduce extra parameters and select an unknown
5272 but fixed source iteration from the potential source iterations.
5273 To be able to perform such manipulations, C<isl> provides the following
5276 #include <isl/flow.h>
5278 typedef __isl_give isl_restriction *(*isl_access_restrict)(
5279 __isl_keep isl_map *source_map,
5280 __isl_keep isl_set *sink, void *source_user,
5282 __isl_give isl_access_info *isl_access_info_set_restrict(
5283 __isl_take isl_access_info *acc,
5284 isl_access_restrict fn, void *user);
5286 The function C<isl_access_info_set_restrict> should be called
5287 before calling C<isl_access_info_compute_flow> and registers a callback function
5288 that will be called any time C<isl> is about to compute the last
5289 potential source. The first argument is the (reverse) proto-dependence,
5290 mapping sink iterations to potential source iterations.
5291 The second argument represents the sink iterations for which
5292 we want to compute the last source iteration.
5293 The third argument is the token corresponding to the source
5294 and the final argument is the token passed to C<isl_access_info_set_restrict>.
5295 The callback is expected to return a restriction on either the input or
5296 the output of the operation computing the last potential source.
5297 If the input needs to be restricted then restrictions are needed
5298 for both the source and the sink iterations. The sink iterations
5299 and the potential source iterations will be intersected with these sets.
5300 If the output needs to be restricted then only a restriction on the source
5301 iterations is required.
5302 If any error occurs, the callback should return C<NULL>.
5303 An C<isl_restriction> object can be created, freed and inspected
5304 using the following functions.
5306 #include <isl/flow.h>
5308 __isl_give isl_restriction *isl_restriction_input(
5309 __isl_take isl_set *source_restr,
5310 __isl_take isl_set *sink_restr);
5311 __isl_give isl_restriction *isl_restriction_output(
5312 __isl_take isl_set *source_restr);
5313 __isl_give isl_restriction *isl_restriction_none(
5314 __isl_take isl_map *source_map);
5315 __isl_give isl_restriction *isl_restriction_empty(
5316 __isl_take isl_map *source_map);
5317 void *isl_restriction_free(
5318 __isl_take isl_restriction *restr);
5319 isl_ctx *isl_restriction_get_ctx(
5320 __isl_keep isl_restriction *restr);
5322 C<isl_restriction_none> and C<isl_restriction_empty> are special
5323 cases of C<isl_restriction_input>. C<isl_restriction_none>
5324 is essentially equivalent to
5326 isl_restriction_input(isl_set_universe(
5327 isl_space_range(isl_map_get_space(source_map))),
5329 isl_space_domain(isl_map_get_space(source_map))));
5331 whereas C<isl_restriction_empty> is essentially equivalent to
5333 isl_restriction_input(isl_set_empty(
5334 isl_space_range(isl_map_get_space(source_map))),
5336 isl_space_domain(isl_map_get_space(source_map))));
5340 B<The functionality described in this section is fairly new
5341 and may be subject to change.>
5343 The following function can be used to compute a schedule
5344 for a union of domains.
5345 By default, the algorithm used to construct the schedule is similar
5346 to that of C<Pluto>.
5347 Alternatively, Feautrier's multi-dimensional scheduling algorithm can
5349 The generated schedule respects all C<validity> dependences.
5350 That is, all dependence distances over these dependences in the
5351 scheduled space are lexicographically positive.
5352 The default algorithm tries to minimize the dependence distances over
5353 C<proximity> dependences.
5354 Moreover, it tries to obtain sequences (bands) of schedule dimensions
5355 for groups of domains where the dependence distances have only
5356 non-negative values.
5357 When using Feautrier's algorithm, the C<proximity> dependence
5358 distances are only minimized during the extension to a
5359 full-dimensional schedule.
5361 #include <isl/schedule.h>
5362 __isl_give isl_schedule *isl_union_set_compute_schedule(
5363 __isl_take isl_union_set *domain,
5364 __isl_take isl_union_map *validity,
5365 __isl_take isl_union_map *proximity);
5366 void *isl_schedule_free(__isl_take isl_schedule *sched);
5368 A mapping from the domains to the scheduled space can be obtained
5369 from an C<isl_schedule> using the following function.
5371 __isl_give isl_union_map *isl_schedule_get_map(
5372 __isl_keep isl_schedule *sched);
5374 A representation of the schedule can be printed using
5376 __isl_give isl_printer *isl_printer_print_schedule(
5377 __isl_take isl_printer *p,
5378 __isl_keep isl_schedule *schedule);
5380 A representation of the schedule as a forest of bands can be obtained
5381 using the following function.
5383 __isl_give isl_band_list *isl_schedule_get_band_forest(
5384 __isl_keep isl_schedule *schedule);
5386 The individual bands can be visited in depth-first post-order
5387 using the following function.
5389 #include <isl/schedule.h>
5390 int isl_schedule_foreach_band(
5391 __isl_keep isl_schedule *sched,
5392 int (*fn)(__isl_keep isl_band *band, void *user),
5395 The list can be manipulated as explained in L<"Lists">.
5396 The bands inside the list can be copied and freed using the following
5399 #include <isl/band.h>
5400 __isl_give isl_band *isl_band_copy(
5401 __isl_keep isl_band *band);
5402 void *isl_band_free(__isl_take isl_band *band);
5404 Each band contains zero or more scheduling dimensions.
5405 These are referred to as the members of the band.
5406 The section of the schedule that corresponds to the band is
5407 referred to as the partial schedule of the band.
5408 For those nodes that participate in a band, the outer scheduling
5409 dimensions form the prefix schedule, while the inner scheduling
5410 dimensions form the suffix schedule.
5411 That is, if we take a cut of the band forest, then the union of
5412 the concatenations of the prefix, partial and suffix schedules of
5413 each band in the cut is equal to the entire schedule (modulo
5414 some possible padding at the end with zero scheduling dimensions).
5415 The properties of a band can be inspected using the following functions.
5417 #include <isl/band.h>
5418 isl_ctx *isl_band_get_ctx(__isl_keep isl_band *band);
5420 int isl_band_has_children(__isl_keep isl_band *band);
5421 __isl_give isl_band_list *isl_band_get_children(
5422 __isl_keep isl_band *band);
5424 __isl_give isl_union_map *isl_band_get_prefix_schedule(
5425 __isl_keep isl_band *band);
5426 __isl_give isl_union_map *isl_band_get_partial_schedule(
5427 __isl_keep isl_band *band);
5428 __isl_give isl_union_map *isl_band_get_suffix_schedule(
5429 __isl_keep isl_band *band);
5431 int isl_band_n_member(__isl_keep isl_band *band);
5432 int isl_band_member_is_zero_distance(
5433 __isl_keep isl_band *band, int pos);
5435 int isl_band_list_foreach_band(
5436 __isl_keep isl_band_list *list,
5437 int (*fn)(__isl_keep isl_band *band, void *user),
5440 Note that a scheduling dimension is considered to be ``zero
5441 distance'' if it does not carry any proximity dependences
5443 That is, if the dependence distances of the proximity
5444 dependences are all zero in that direction (for fixed
5445 iterations of outer bands).
5446 Like C<isl_schedule_foreach_band>,
5447 the function C<isl_band_list_foreach_band> calls C<fn> on the bands
5448 in depth-first post-order.
5450 A band can be tiled using the following function.
5452 #include <isl/band.h>
5453 int isl_band_tile(__isl_keep isl_band *band,
5454 __isl_take isl_vec *sizes);
5456 int isl_options_set_tile_scale_tile_loops(isl_ctx *ctx,
5458 int isl_options_get_tile_scale_tile_loops(isl_ctx *ctx);
5459 int isl_options_set_tile_shift_point_loops(isl_ctx *ctx,
5461 int isl_options_get_tile_shift_point_loops(isl_ctx *ctx);
5463 The C<isl_band_tile> function tiles the band using the given tile sizes
5464 inside its schedule.
5465 A new child band is created to represent the point loops and it is
5466 inserted between the modified band and its children.
5467 The C<tile_scale_tile_loops> option specifies whether the tile
5468 loops iterators should be scaled by the tile sizes.
5469 If the C<tile_shift_point_loops> option is set, then the point loops
5470 are shifted to start at zero.
5472 A band can be split into two nested bands using the following function.
5474 int isl_band_split(__isl_keep isl_band *band, int pos);
5476 The resulting outer band contains the first C<pos> dimensions of C<band>
5477 while the inner band contains the remaining dimensions.
5479 A representation of the band can be printed using
5481 #include <isl/band.h>
5482 __isl_give isl_printer *isl_printer_print_band(
5483 __isl_take isl_printer *p,
5484 __isl_keep isl_band *band);
5488 #include <isl/schedule.h>
5489 int isl_options_set_schedule_max_coefficient(
5490 isl_ctx *ctx, int val);
5491 int isl_options_get_schedule_max_coefficient(
5493 int isl_options_set_schedule_max_constant_term(
5494 isl_ctx *ctx, int val);
5495 int isl_options_get_schedule_max_constant_term(
5497 int isl_options_set_schedule_fuse(isl_ctx *ctx, int val);
5498 int isl_options_get_schedule_fuse(isl_ctx *ctx);
5499 int isl_options_set_schedule_maximize_band_depth(
5500 isl_ctx *ctx, int val);
5501 int isl_options_get_schedule_maximize_band_depth(
5503 int isl_options_set_schedule_outer_zero_distance(
5504 isl_ctx *ctx, int val);
5505 int isl_options_get_schedule_outer_zero_distance(
5507 int isl_options_set_schedule_split_scaled(
5508 isl_ctx *ctx, int val);
5509 int isl_options_get_schedule_split_scaled(
5511 int isl_options_set_schedule_algorithm(
5512 isl_ctx *ctx, int val);
5513 int isl_options_get_schedule_algorithm(
5515 int isl_options_set_schedule_separate_components(
5516 isl_ctx *ctx, int val);
5517 int isl_options_get_schedule_separate_components(
5522 =item * schedule_max_coefficient
5524 This option enforces that the coefficients for variable and parameter
5525 dimensions in the calculated schedule are not larger than the specified value.
5526 This option can significantly increase the speed of the scheduling calculation
5527 and may also prevent fusing of unrelated dimensions. A value of -1 means that
5528 this option does not introduce bounds on the variable or parameter
5531 =item * schedule_max_constant_term
5533 This option enforces that the constant coefficients in the calculated schedule
5534 are not larger than the maximal constant term. This option can significantly
5535 increase the speed of the scheduling calculation and may also prevent fusing of
5536 unrelated dimensions. A value of -1 means that this option does not introduce
5537 bounds on the constant coefficients.
5539 =item * schedule_fuse
5541 This option controls the level of fusion.
5542 If this option is set to C<ISL_SCHEDULE_FUSE_MIN>, then loops in the
5543 resulting schedule will be distributed as much as possible.
5544 If this option is set to C<ISL_SCHEDULE_FUSE_MAX>, then C<isl> will
5545 try to fuse loops in the resulting schedule.
5547 =item * schedule_maximize_band_depth
5549 If this option is set, we do not split bands at the point
5550 where we detect splitting is necessary. Instead, we
5551 backtrack and split bands as early as possible. This
5552 reduces the number of splits and maximizes the width of
5553 the bands. Wider bands give more possibilities for tiling.
5554 Note that if the C<schedule_fuse> option is set to C<ISL_SCHEDULE_FUSE_MIN>,
5555 then bands will be split as early as possible, even if there is no need.
5556 The C<schedule_maximize_band_depth> option therefore has no effect in this case.
5558 =item * schedule_outer_zero_distance
5560 If this option is set, then we try to construct schedules
5561 where the outermost scheduling dimension in each band
5562 results in a zero dependence distance over the proximity
5565 =item * schedule_split_scaled
5567 If this option is set, then we try to construct schedules in which the
5568 constant term is split off from the linear part if the linear parts of
5569 the scheduling rows for all nodes in the graphs have a common non-trivial
5571 The constant term is then placed in a separate band and the linear
5574 =item * schedule_algorithm
5576 Selects the scheduling algorithm to be used.
5577 Available scheduling algorithms are C<ISL_SCHEDULE_ALGORITHM_ISL>
5578 and C<ISL_SCHEDULE_ALGORITHM_FEAUTRIER>.
5580 =item * schedule_separate_components
5582 If at any point the dependence graph contains any (weakly connected) components,
5583 then these components are scheduled separately.
5584 If this option is not set, then some iterations of the domains
5585 in these components may be scheduled together.
5586 If this option is set, then the components are given consecutive
5591 =head2 AST Generation
5593 This section describes the C<isl> functionality for generating
5594 ASTs that visit all the elements
5595 in a domain in an order specified by a schedule.
5596 In particular, given a C<isl_union_map>, an AST is generated
5597 that visits all the elements in the domain of the C<isl_union_map>
5598 according to the lexicographic order of the corresponding image
5599 element(s). If the range of the C<isl_union_map> consists of
5600 elements in more than one space, then each of these spaces is handled
5601 separately in an arbitrary order.
5602 It should be noted that the image elements only specify the I<order>
5603 in which the corresponding domain elements should be visited.
5604 No direct relation between the image elements and the loop iterators
5605 in the generated AST should be assumed.
5607 Each AST is generated within a build. The initial build
5608 simply specifies the constraints on the parameters (if any)
5609 and can be created, inspected, copied and freed using the following functions.
5611 #include <isl/ast_build.h>
5612 __isl_give isl_ast_build *isl_ast_build_from_context(
5613 __isl_take isl_set *set);
5614 isl_ctx *isl_ast_build_get_ctx(
5615 __isl_keep isl_ast_build *build);
5616 __isl_give isl_ast_build *isl_ast_build_copy(
5617 __isl_keep isl_ast_build *build);
5618 void *isl_ast_build_free(
5619 __isl_take isl_ast_build *build);
5621 The C<set> argument is usually a parameter set with zero or more parameters.
5622 More C<isl_ast_build> functions are described in L</"Nested AST Generation">
5623 and L</"Fine-grained Control over AST Generation">.
5624 Finally, the AST itself can be constructed using the following
5627 #include <isl/ast_build.h>
5628 __isl_give isl_ast_node *isl_ast_build_ast_from_schedule(
5629 __isl_keep isl_ast_build *build,
5630 __isl_take isl_union_map *schedule);
5632 =head3 Inspecting the AST
5634 The basic properties of an AST node can be obtained as follows.
5636 #include <isl/ast.h>
5637 isl_ctx *isl_ast_node_get_ctx(
5638 __isl_keep isl_ast_node *node);
5639 enum isl_ast_node_type isl_ast_node_get_type(
5640 __isl_keep isl_ast_node *node);
5642 The type of an AST node is one of
5643 C<isl_ast_node_for>,
5645 C<isl_ast_node_block> or
5646 C<isl_ast_node_user>.
5647 An C<isl_ast_node_for> represents a for node.
5648 An C<isl_ast_node_if> represents an if node.
5649 An C<isl_ast_node_block> represents a compound node.
5650 An C<isl_ast_node_user> represents an expression statement.
5651 An expression statement typically corresponds to a domain element, i.e.,
5652 one of the elements that is visited by the AST.
5654 Each type of node has its own additional properties.
5656 #include <isl/ast.h>
5657 __isl_give isl_ast_expr *isl_ast_node_for_get_iterator(
5658 __isl_keep isl_ast_node *node);
5659 __isl_give isl_ast_expr *isl_ast_node_for_get_init(
5660 __isl_keep isl_ast_node *node);
5661 __isl_give isl_ast_expr *isl_ast_node_for_get_cond(
5662 __isl_keep isl_ast_node *node);
5663 __isl_give isl_ast_expr *isl_ast_node_for_get_inc(
5664 __isl_keep isl_ast_node *node);
5665 __isl_give isl_ast_node *isl_ast_node_for_get_body(
5666 __isl_keep isl_ast_node *node);
5667 int isl_ast_node_for_is_degenerate(
5668 __isl_keep isl_ast_node *node);
5670 An C<isl_ast_for> is considered degenerate if it is known to execute
5673 #include <isl/ast.h>
5674 __isl_give isl_ast_expr *isl_ast_node_if_get_cond(
5675 __isl_keep isl_ast_node *node);
5676 __isl_give isl_ast_node *isl_ast_node_if_get_then(
5677 __isl_keep isl_ast_node *node);
5678 int isl_ast_node_if_has_else(
5679 __isl_keep isl_ast_node *node);
5680 __isl_give isl_ast_node *isl_ast_node_if_get_else(
5681 __isl_keep isl_ast_node *node);
5683 __isl_give isl_ast_node_list *
5684 isl_ast_node_block_get_children(
5685 __isl_keep isl_ast_node *node);
5687 __isl_give isl_ast_expr *isl_ast_node_user_get_expr(
5688 __isl_keep isl_ast_node *node);
5690 Each of the returned C<isl_ast_expr>s can in turn be inspected using
5691 the following functions.
5693 #include <isl/ast.h>
5694 isl_ctx *isl_ast_expr_get_ctx(
5695 __isl_keep isl_ast_expr *expr);
5696 enum isl_ast_expr_type isl_ast_expr_get_type(
5697 __isl_keep isl_ast_expr *expr);
5699 The type of an AST expression is one of
5701 C<isl_ast_expr_id> or
5702 C<isl_ast_expr_int>.
5703 An C<isl_ast_expr_op> represents the result of an operation.
5704 An C<isl_ast_expr_id> represents an identifier.
5705 An C<isl_ast_expr_int> represents an integer value.
5707 Each type of expression has its own additional properties.
5709 #include <isl/ast.h>
5710 enum isl_ast_op_type isl_ast_expr_get_op_type(
5711 __isl_keep isl_ast_expr *expr);
5712 int isl_ast_expr_get_op_n_arg(__isl_keep isl_ast_expr *expr);
5713 __isl_give isl_ast_expr *isl_ast_expr_get_op_arg(
5714 __isl_keep isl_ast_expr *expr, int pos);
5715 int isl_ast_node_foreach_ast_op_type(
5716 __isl_keep isl_ast_node *node,
5717 int (*fn)(enum isl_ast_op_type type, void *user),
5720 C<isl_ast_expr_get_op_type> returns the type of the operation
5721 performed. C<isl_ast_expr_get_op_n_arg> returns the number of
5722 arguments. C<isl_ast_expr_get_op_arg> returns the specified
5724 C<isl_ast_node_foreach_ast_op_type> calls C<fn> for each distinct
5725 C<isl_ast_op_type> that appears in C<node>.
5726 The operation type is one of the following.
5730 =item C<isl_ast_op_and>
5732 Logical I<and> of two arguments.
5733 Both arguments can be evaluated.
5735 =item C<isl_ast_op_and_then>
5737 Logical I<and> of two arguments.
5738 The second argument can only be evaluated if the first evaluates to true.
5740 =item C<isl_ast_op_or>
5742 Logical I<or> of two arguments.
5743 Both arguments can be evaluated.
5745 =item C<isl_ast_op_or_else>
5747 Logical I<or> of two arguments.
5748 The second argument can only be evaluated if the first evaluates to false.
5750 =item C<isl_ast_op_max>
5752 Maximum of two or more arguments.
5754 =item C<isl_ast_op_min>
5756 Minimum of two or more arguments.
5758 =item C<isl_ast_op_minus>
5762 =item C<isl_ast_op_add>
5764 Sum of two arguments.
5766 =item C<isl_ast_op_sub>
5768 Difference of two arguments.
5770 =item C<isl_ast_op_mul>
5772 Product of two arguments.
5774 =item C<isl_ast_op_div>
5776 Exact division. That is, the result is known to be an integer.
5778 =item C<isl_ast_op_fdiv_q>
5780 Result of integer division, rounded towards negative
5783 =item C<isl_ast_op_pdiv_q>
5785 Result of integer division, where dividend is known to be non-negative.
5787 =item C<isl_ast_op_pdiv_r>
5789 Remainder of integer division, where dividend is known to be non-negative.
5791 =item C<isl_ast_op_cond>
5793 Conditional operator defined on three arguments.
5794 If the first argument evaluates to true, then the result
5795 is equal to the second argument. Otherwise, the result
5796 is equal to the third argument.
5797 The second and third argument may only be evaluated if
5798 the first argument evaluates to true and false, respectively.
5799 Corresponds to C<a ? b : c> in C.
5801 =item C<isl_ast_op_select>
5803 Conditional operator defined on three arguments.
5804 If the first argument evaluates to true, then the result
5805 is equal to the second argument. Otherwise, the result
5806 is equal to the third argument.
5807 The second and third argument may be evaluated independently
5808 of the value of the first argument.
5809 Corresponds to C<a * b + (1 - a) * c> in C.
5811 =item C<isl_ast_op_eq>
5815 =item C<isl_ast_op_le>
5817 Less than or equal relation.
5819 =item C<isl_ast_op_lt>
5823 =item C<isl_ast_op_ge>
5825 Greater than or equal relation.
5827 =item C<isl_ast_op_gt>
5829 Greater than relation.
5831 =item C<isl_ast_op_call>
5834 The number of arguments of the C<isl_ast_expr> is one more than
5835 the number of arguments in the function call, the first argument
5836 representing the function being called.
5840 #include <isl/ast.h>
5841 __isl_give isl_id *isl_ast_expr_get_id(
5842 __isl_keep isl_ast_expr *expr);
5844 Return the identifier represented by the AST expression.
5846 #include <isl/ast.h>
5847 int isl_ast_expr_get_int(__isl_keep isl_ast_expr *expr,
5850 Return the integer represented by the AST expression.
5851 Note that the integer is returned through the C<v> argument.
5852 The return value of the function itself indicates whether the
5853 operation was performed successfully.
5855 =head3 Manipulating and printing the AST
5857 AST nodes can be copied and freed using the following functions.
5859 #include <isl/ast.h>
5860 __isl_give isl_ast_node *isl_ast_node_copy(
5861 __isl_keep isl_ast_node *node);
5862 void *isl_ast_node_free(__isl_take isl_ast_node *node);
5864 AST expressions can be copied and freed using the following functions.
5866 #include <isl/ast.h>
5867 __isl_give isl_ast_expr *isl_ast_expr_copy(
5868 __isl_keep isl_ast_expr *expr);
5869 void *isl_ast_expr_free(__isl_take isl_ast_expr *expr);
5871 New AST expressions can be created either directly or within
5872 the context of an C<isl_ast_build>.
5874 #include <isl/ast.h>
5875 __isl_give isl_ast_expr *isl_ast_expr_from_id(
5876 __isl_take isl_id *id);
5877 __isl_give isl_ast_expr *isl_ast_expr_neg(
5878 __isl_take isl_ast_expr *expr);
5879 __isl_give isl_ast_expr *isl_ast_expr_add(
5880 __isl_take isl_ast_expr *expr1,
5881 __isl_take isl_ast_expr *expr2);
5882 __isl_give isl_ast_expr *isl_ast_expr_sub(
5883 __isl_take isl_ast_expr *expr1,
5884 __isl_take isl_ast_expr *expr2);
5885 __isl_give isl_ast_expr *isl_ast_expr_mul(
5886 __isl_take isl_ast_expr *expr1,
5887 __isl_take isl_ast_expr *expr2);
5888 __isl_give isl_ast_expr *isl_ast_expr_div(
5889 __isl_take isl_ast_expr *expr1,
5890 __isl_take isl_ast_expr *expr2);
5891 __isl_give isl_ast_expr *isl_ast_expr_and(
5892 __isl_take isl_ast_expr *expr1,
5893 __isl_take isl_ast_expr *expr2)
5894 __isl_give isl_ast_expr *isl_ast_expr_or(
5895 __isl_take isl_ast_expr *expr1,
5896 __isl_take isl_ast_expr *expr2)
5898 #include <isl/ast_build.h>
5899 __isl_give isl_ast_expr *isl_ast_build_expr_from_pw_aff(
5900 __isl_keep isl_ast_build *build,
5901 __isl_take isl_pw_aff *pa);
5902 __isl_give isl_ast_expr *
5903 isl_ast_build_call_from_pw_multi_aff(
5904 __isl_keep isl_ast_build *build,
5905 __isl_take isl_pw_multi_aff *pma);
5907 The domains of C<pa> and C<pma> should correspond
5908 to the schedule space of C<build>.
5909 The tuple id of C<pma> is used as the function being called.
5911 User specified data can be attached to an C<isl_ast_node> and obtained
5912 from the same C<isl_ast_node> using the following functions.
5914 #include <isl/ast.h>
5915 __isl_give isl_ast_node *isl_ast_node_set_annotation(
5916 __isl_take isl_ast_node *node,
5917 __isl_take isl_id *annotation);
5918 __isl_give isl_id *isl_ast_node_get_annotation(
5919 __isl_keep isl_ast_node *node);
5921 Basic printing can be performed using the following functions.
5923 #include <isl/ast.h>
5924 __isl_give isl_printer *isl_printer_print_ast_expr(
5925 __isl_take isl_printer *p,
5926 __isl_keep isl_ast_expr *expr);
5927 __isl_give isl_printer *isl_printer_print_ast_node(
5928 __isl_take isl_printer *p,
5929 __isl_keep isl_ast_node *node);
5931 More advanced printing can be performed using the following functions.
5933 #include <isl/ast.h>
5934 __isl_give isl_printer *isl_ast_op_type_print_macro(
5935 enum isl_ast_op_type type,
5936 __isl_take isl_printer *p);
5937 __isl_give isl_printer *isl_ast_node_print_macros(
5938 __isl_keep isl_ast_node *node,
5939 __isl_take isl_printer *p);
5940 __isl_give isl_printer *isl_ast_node_print(
5941 __isl_keep isl_ast_node *node,
5942 __isl_take isl_printer *p,
5943 __isl_take isl_ast_print_options *options);
5944 __isl_give isl_printer *isl_ast_node_for_print(
5945 __isl_keep isl_ast_node *node,
5946 __isl_take isl_printer *p,
5947 __isl_take isl_ast_print_options *options);
5948 __isl_give isl_printer *isl_ast_node_if_print(
5949 __isl_keep isl_ast_node *node,
5950 __isl_take isl_printer *p,
5951 __isl_take isl_ast_print_options *options);
5953 While printing an C<isl_ast_node> in C<ISL_FORMAT_C>,
5954 C<isl> may print out an AST that makes use of macros such
5955 as C<floord>, C<min> and C<max>.
5956 C<isl_ast_op_type_print_macro> prints out the macro
5957 corresponding to a specific C<isl_ast_op_type>.
5958 C<isl_ast_node_print_macros> scans the C<isl_ast_node>
5959 for expressions where these macros would be used and prints
5960 out the required macro definitions.
5961 Essentially, C<isl_ast_node_print_macros> calls
5962 C<isl_ast_node_foreach_ast_op_type> with C<isl_ast_op_type_print_macro>
5963 as function argument.
5964 C<isl_ast_node_print>, C<isl_ast_node_for_print> and
5965 C<isl_ast_node_if_print> print an C<isl_ast_node>
5966 in C<ISL_FORMAT_C>, but allow for some extra control
5967 through an C<isl_ast_print_options> object.
5968 This object can be created using the following functions.
5970 #include <isl/ast.h>
5971 __isl_give isl_ast_print_options *
5972 isl_ast_print_options_alloc(isl_ctx *ctx);
5973 __isl_give isl_ast_print_options *
5974 isl_ast_print_options_copy(
5975 __isl_keep isl_ast_print_options *options);
5976 void *isl_ast_print_options_free(
5977 __isl_take isl_ast_print_options *options);
5979 __isl_give isl_ast_print_options *
5980 isl_ast_print_options_set_print_user(
5981 __isl_take isl_ast_print_options *options,
5982 __isl_give isl_printer *(*print_user)(
5983 __isl_take isl_printer *p,
5984 __isl_take isl_ast_print_options *options,
5985 __isl_keep isl_ast_node *node, void *user),
5987 __isl_give isl_ast_print_options *
5988 isl_ast_print_options_set_print_for(
5989 __isl_take isl_ast_print_options *options,
5990 __isl_give isl_printer *(*print_for)(
5991 __isl_take isl_printer *p,
5992 __isl_take isl_ast_print_options *options,
5993 __isl_keep isl_ast_node *node, void *user),
5996 The callback set by C<isl_ast_print_options_set_print_user>
5997 is called whenever a node of type C<isl_ast_node_user> needs to
5999 The callback set by C<isl_ast_print_options_set_print_for>
6000 is called whenever a node of type C<isl_ast_node_for> needs to
6002 Note that C<isl_ast_node_for_print> will I<not> call the
6003 callback set by C<isl_ast_print_options_set_print_for> on the node
6004 on which C<isl_ast_node_for_print> is called, but only on nested
6005 nodes of type C<isl_ast_node_for>. It is therefore safe to
6006 call C<isl_ast_node_for_print> from within the callback set by
6007 C<isl_ast_print_options_set_print_for>.
6009 The following option determines the type to be used for iterators
6010 while printing the AST.
6012 int isl_options_set_ast_iterator_type(
6013 isl_ctx *ctx, const char *val);
6014 const char *isl_options_get_ast_iterator_type(
6019 #include <isl/ast_build.h>
6020 int isl_options_set_ast_build_atomic_upper_bound(
6021 isl_ctx *ctx, int val);
6022 int isl_options_get_ast_build_atomic_upper_bound(
6024 int isl_options_set_ast_build_prefer_pdiv(isl_ctx *ctx,
6026 int isl_options_get_ast_build_prefer_pdiv(isl_ctx *ctx);
6027 int isl_options_set_ast_build_exploit_nested_bounds(
6028 isl_ctx *ctx, int val);
6029 int isl_options_get_ast_build_exploit_nested_bounds(
6031 int isl_options_set_ast_build_group_coscheduled(
6032 isl_ctx *ctx, int val);
6033 int isl_options_get_ast_build_group_coscheduled(
6035 int isl_options_set_ast_build_scale_strides(
6036 isl_ctx *ctx, int val);
6037 int isl_options_get_ast_build_scale_strides(
6039 int isl_options_set_ast_build_allow_else(isl_ctx *ctx,
6041 int isl_options_get_ast_build_allow_else(isl_ctx *ctx);
6042 int isl_options_set_ast_build_allow_or(isl_ctx *ctx,
6044 int isl_options_get_ast_build_allow_or(isl_ctx *ctx);
6048 =item * ast_build_atomic_upper_bound
6050 Generate loop upper bounds that consist of the current loop iterator,
6051 an operator and an expression not involving the iterator.
6052 If this option is not set, then the current loop iterator may appear
6053 several times in the upper bound.
6054 For example, when this option is turned off, AST generation
6057 [n] -> { A[i] -> [i] : 0 <= i <= 100, n }
6061 for (int c0 = 0; c0 <= 100 && n >= c0; c0 += 1)
6064 When the option is turned on, the following AST is generated
6066 for (int c0 = 0; c0 <= min(100, n); c0 += 1)
6069 =item * ast_build_prefer_pdiv
6071 If this option is turned off, then the AST generation will
6072 produce ASTs that may only contain C<isl_ast_op_fdiv_q>
6073 operators, but no C<isl_ast_op_pdiv_q> or
6074 C<isl_ast_op_pdiv_r> operators.
6075 If this options is turned on, then C<isl> will try to convert
6076 some of the C<isl_ast_op_fdiv_q> operators to (expressions containing)
6077 C<isl_ast_op_pdiv_q> or C<isl_ast_op_pdiv_r> operators.
6079 =item * ast_build_exploit_nested_bounds
6081 Simplify conditions based on bounds of nested for loops.
6082 In particular, remove conditions that are implied by the fact
6083 that one or more nested loops have at least one iteration,
6084 meaning that the upper bound is at least as large as the lower bound.
6085 For example, when this option is turned off, AST generation
6088 [N,M] -> { A[i,j] -> [i,j] : 0 <= i <= N and
6094 for (int c0 = 0; c0 <= N; c0 += 1)
6095 for (int c1 = 0; c1 <= M; c1 += 1)
6098 When the option is turned on, the following AST is generated
6100 for (int c0 = 0; c0 <= N; c0 += 1)
6101 for (int c1 = 0; c1 <= M; c1 += 1)
6104 =item * ast_build_group_coscheduled
6106 If two domain elements are assigned the same schedule point, then
6107 they may be executed in any order and they may even appear in different
6108 loops. If this options is set, then the AST generator will make
6109 sure that coscheduled domain elements do not appear in separate parts
6110 of the AST. This is useful in case of nested AST generation
6111 if the outer AST generation is given only part of a schedule
6112 and the inner AST generation should handle the domains that are
6113 coscheduled by this initial part of the schedule together.
6114 For example if an AST is generated for a schedule
6116 { A[i] -> [0]; B[i] -> [0] }
6118 then the C<isl_ast_build_set_create_leaf> callback described
6119 below may get called twice, once for each domain.
6120 Setting this option ensures that the callback is only called once
6121 on both domains together.
6123 =item * ast_build_separation_bounds
6125 This option specifies which bounds to use during separation.
6126 If this option is set to C<ISL_AST_BUILD_SEPARATION_BOUNDS_IMPLICIT>
6127 then all (possibly implicit) bounds on the current dimension will
6128 be used during separation.
6129 If this option is set to C<ISL_AST_BUILD_SEPARATION_BOUNDS_EXPLICIT>
6130 then only those bounds that are explicitly available will
6131 be used during separation.
6133 =item * ast_build_scale_strides
6135 This option specifies whether the AST generator is allowed
6136 to scale down iterators of strided loops.
6138 =item * ast_build_allow_else
6140 This option specifies whether the AST generator is allowed
6141 to construct if statements with else branches.
6143 =item * ast_build_allow_or
6145 This option specifies whether the AST generator is allowed
6146 to construct if conditions with disjunctions.
6150 =head3 Fine-grained Control over AST Generation
6152 Besides specifying the constraints on the parameters,
6153 an C<isl_ast_build> object can be used to control
6154 various aspects of the AST generation process.
6155 The most prominent way of control is through ``options'',
6156 which can be set using the following function.
6158 #include <isl/ast_build.h>
6159 __isl_give isl_ast_build *
6160 isl_ast_build_set_options(
6161 __isl_take isl_ast_build *control,
6162 __isl_take isl_union_map *options);
6164 The options are encoded in an <isl_union_map>.
6165 The domain of this union relation refers to the schedule domain,
6166 i.e., the range of the schedule passed to C<isl_ast_build_ast_from_schedule>.
6167 In the case of nested AST generation (see L</"Nested AST Generation">),
6168 the domain of C<options> should refer to the extra piece of the schedule.
6169 That is, it should be equal to the range of the wrapped relation in the
6170 range of the schedule.
6171 The range of the options can consist of elements in one or more spaces,
6172 the names of which determine the effect of the option.
6173 The values of the range typically also refer to the schedule dimension
6174 to which the option applies. In case of nested AST generation
6175 (see L</"Nested AST Generation">), these values refer to the position
6176 of the schedule dimension within the innermost AST generation.
6177 The constraints on the domain elements of
6178 the option should only refer to this dimension and earlier dimensions.
6179 We consider the following spaces.
6183 =item C<separation_class>
6185 This space is a wrapped relation between two one dimensional spaces.
6186 The input space represents the schedule dimension to which the option
6187 applies and the output space represents the separation class.
6188 While constructing a loop corresponding to the specified schedule
6189 dimension(s), the AST generator will try to generate separate loops
6190 for domain elements that are assigned different classes.
6191 If only some of the elements are assigned a class, then those elements
6192 that are not assigned any class will be treated as belonging to a class
6193 that is separate from the explicitly assigned classes.
6194 The typical use case for this option is to separate full tiles from
6196 The other options, described below, are applied after the separation
6199 As an example, consider the separation into full and partial tiles
6200 of a tiling of a triangular domain.
6201 Take, for example, the domain
6203 { A[i,j] : 0 <= i,j and i + j <= 100 }
6205 and a tiling into tiles of 10 by 10. The input to the AST generator
6206 is then the schedule
6208 { A[i,j] -> [([i/10]),[j/10],i,j] : 0 <= i,j and
6211 Without any options, the following AST is generated
6213 for (int c0 = 0; c0 <= 10; c0 += 1)
6214 for (int c1 = 0; c1 <= -c0 + 10; c1 += 1)
6215 for (int c2 = 10 * c0;
6216 c2 <= min(-10 * c1 + 100, 10 * c0 + 9);
6218 for (int c3 = 10 * c1;
6219 c3 <= min(10 * c1 + 9, -c2 + 100);
6223 Separation into full and partial tiles can be obtained by assigning
6224 a class, say C<0>, to the full tiles. The full tiles are represented by those
6225 values of the first and second schedule dimensions for which there are
6226 values of the third and fourth dimensions to cover an entire tile.
6227 That is, we need to specify the following option
6229 { [a,b,c,d] -> separation_class[[0]->[0]] :
6230 exists b': 0 <= 10a,10b' and
6231 10a+9+10b'+9 <= 100;
6232 [a,b,c,d] -> separation_class[[1]->[0]] :
6233 0 <= 10a,10b and 10a+9+10b+9 <= 100 }
6237 { [a, b, c, d] -> separation_class[[1] -> [0]] :
6238 a >= 0 and b >= 0 and b <= 8 - a;
6239 [a, b, c, d] -> separation_class[[0] -> [0]] :
6242 With this option, the generated AST is as follows
6245 for (int c0 = 0; c0 <= 8; c0 += 1) {
6246 for (int c1 = 0; c1 <= -c0 + 8; c1 += 1)
6247 for (int c2 = 10 * c0;
6248 c2 <= 10 * c0 + 9; c2 += 1)
6249 for (int c3 = 10 * c1;
6250 c3 <= 10 * c1 + 9; c3 += 1)
6252 for (int c1 = -c0 + 9; c1 <= -c0 + 10; c1 += 1)
6253 for (int c2 = 10 * c0;
6254 c2 <= min(-10 * c1 + 100, 10 * c0 + 9);
6256 for (int c3 = 10 * c1;
6257 c3 <= min(-c2 + 100, 10 * c1 + 9);
6261 for (int c0 = 9; c0 <= 10; c0 += 1)
6262 for (int c1 = 0; c1 <= -c0 + 10; c1 += 1)
6263 for (int c2 = 10 * c0;
6264 c2 <= min(-10 * c1 + 100, 10 * c0 + 9);
6266 for (int c3 = 10 * c1;
6267 c3 <= min(10 * c1 + 9, -c2 + 100);
6274 This is a single-dimensional space representing the schedule dimension(s)
6275 to which ``separation'' should be applied. Separation tries to split
6276 a loop into several pieces if this can avoid the generation of guards
6278 See also the C<atomic> option.
6282 This is a single-dimensional space representing the schedule dimension(s)
6283 for which the domains should be considered ``atomic''. That is, the
6284 AST generator will make sure that any given domain space will only appear
6285 in a single loop at the specified level.
6287 Consider the following schedule
6289 { a[i] -> [i] : 0 <= i < 10;
6290 b[i] -> [i+1] : 0 <= i < 10 }
6292 If the following option is specified
6294 { [i] -> separate[x] }
6296 then the following AST will be generated
6300 for (int c0 = 1; c0 <= 9; c0 += 1) {
6307 If, on the other hand, the following option is specified
6309 { [i] -> atomic[x] }
6311 then the following AST will be generated
6313 for (int c0 = 0; c0 <= 10; c0 += 1) {
6320 If neither C<atomic> nor C<separate> is specified, then the AST generator
6321 may produce either of these two results or some intermediate form.
6325 This is a single-dimensional space representing the schedule dimension(s)
6326 that should be I<completely> unrolled.
6327 To obtain a partial unrolling, the user should apply an additional
6328 strip-mining to the schedule and fully unroll the inner loop.
6332 Additional control is available through the following functions.
6334 #include <isl/ast_build.h>
6335 __isl_give isl_ast_build *
6336 isl_ast_build_set_iterators(
6337 __isl_take isl_ast_build *control,
6338 __isl_take isl_id_list *iterators);
6340 The function C<isl_ast_build_set_iterators> allows the user to
6341 specify a list of iterator C<isl_id>s to be used as iterators.
6342 If the input schedule is injective, then
6343 the number of elements in this list should be as large as the dimension
6344 of the schedule space, but no direct correspondence should be assumed
6345 between dimensions and elements.
6346 If the input schedule is not injective, then an additional number
6347 of C<isl_id>s equal to the largest dimension of the input domains
6349 If the number of provided C<isl_id>s is insufficient, then additional
6350 names are automatically generated.
6352 #include <isl/ast_build.h>
6353 __isl_give isl_ast_build *
6354 isl_ast_build_set_create_leaf(
6355 __isl_take isl_ast_build *control,
6356 __isl_give isl_ast_node *(*fn)(
6357 __isl_take isl_ast_build *build,
6358 void *user), void *user);
6361 C<isl_ast_build_set_create_leaf> function allows for the
6362 specification of a callback that should be called whenever the AST
6363 generator arrives at an element of the schedule domain.
6364 The callback should return an AST node that should be inserted
6365 at the corresponding position of the AST. The default action (when
6366 the callback is not set) is to continue generating parts of the AST to scan
6367 all the domain elements associated to the schedule domain element
6368 and to insert user nodes, ``calling'' the domain element, for each of them.
6369 The C<build> argument contains the current state of the C<isl_ast_build>.
6370 To ease nested AST generation (see L</"Nested AST Generation">),
6371 all control information that is
6372 specific to the current AST generation such as the options and
6373 the callbacks has been removed from this C<isl_ast_build>.
6374 The callback would typically return the result of a nested
6376 user defined node created using the following function.
6378 #include <isl/ast.h>
6379 __isl_give isl_ast_node *isl_ast_node_alloc_user(
6380 __isl_take isl_ast_expr *expr);
6382 #include <isl/ast_build.h>
6383 __isl_give isl_ast_build *
6384 isl_ast_build_set_at_each_domain(
6385 __isl_take isl_ast_build *build,
6386 __isl_give isl_ast_node *(*fn)(
6387 __isl_take isl_ast_node *node,
6388 __isl_keep isl_ast_build *build,
6389 void *user), void *user);
6390 __isl_give isl_ast_build *
6391 isl_ast_build_set_before_each_for(
6392 __isl_take isl_ast_build *build,
6393 __isl_give isl_id *(*fn)(
6394 __isl_keep isl_ast_build *build,
6395 void *user), void *user);
6396 __isl_give isl_ast_build *
6397 isl_ast_build_set_after_each_for(
6398 __isl_take isl_ast_build *build,
6399 __isl_give isl_ast_node *(*fn)(
6400 __isl_take isl_ast_node *node,
6401 __isl_keep isl_ast_build *build,
6402 void *user), void *user);
6404 The callback set by C<isl_ast_build_set_at_each_domain> will
6405 be called for each domain AST node.
6406 The callbacks set by C<isl_ast_build_set_before_each_for>
6407 and C<isl_ast_build_set_after_each_for> will be called
6408 for each for AST node. The first will be called in depth-first
6409 pre-order, while the second will be called in depth-first post-order.
6410 Since C<isl_ast_build_set_before_each_for> is called before the for
6411 node is actually constructed, it is only passed an C<isl_ast_build>.
6412 The returned C<isl_id> will be added as an annotation (using
6413 C<isl_ast_node_set_annotation>) to the constructed for node.
6414 In particular, if the user has also specified an C<after_each_for>
6415 callback, then the annotation can be retrieved from the node passed to
6416 that callback using C<isl_ast_node_get_annotation>.
6417 All callbacks should C<NULL> on failure.
6418 The given C<isl_ast_build> can be used to create new
6419 C<isl_ast_expr> objects using C<isl_ast_build_expr_from_pw_aff>
6420 or C<isl_ast_build_call_from_pw_multi_aff>.
6422 =head3 Nested AST Generation
6424 C<isl> allows the user to create an AST within the context
6425 of another AST. These nested ASTs are created using the
6426 same C<isl_ast_build_ast_from_schedule> function that is used to create the
6427 outer AST. The C<build> argument should be an C<isl_ast_build>
6428 passed to a callback set by
6429 C<isl_ast_build_set_create_leaf>.
6430 The space of the range of the C<schedule> argument should refer
6431 to this build. In particular, the space should be a wrapped
6432 relation and the domain of this wrapped relation should be the
6433 same as that of the range of the schedule returned by
6434 C<isl_ast_build_get_schedule> below.
6435 In practice, the new schedule is typically
6436 created by calling C<isl_union_map_range_product> on the old schedule
6437 and some extra piece of the schedule.
6438 The space of the schedule domain is also available from
6439 the C<isl_ast_build>.
6441 #include <isl/ast_build.h>
6442 __isl_give isl_union_map *isl_ast_build_get_schedule(
6443 __isl_keep isl_ast_build *build);
6444 __isl_give isl_space *isl_ast_build_get_schedule_space(
6445 __isl_keep isl_ast_build *build);
6446 __isl_give isl_ast_build *isl_ast_build_restrict(
6447 __isl_take isl_ast_build *build,
6448 __isl_take isl_set *set);
6450 The C<isl_ast_build_get_schedule> function returns a (partial)
6451 schedule for the domains elements for which part of the AST still needs to
6452 be generated in the current build.
6453 In particular, the domain elements are mapped to those iterations of the loops
6454 enclosing the current point of the AST generation inside which
6455 the domain elements are executed.
6456 No direct correspondence between
6457 the input schedule and this schedule should be assumed.
6458 The space obtained from C<isl_ast_build_get_schedule_space> can be used
6459 to create a set for C<isl_ast_build_restrict> to intersect
6460 with the current build. In particular, the set passed to
6461 C<isl_ast_build_restrict> can have additional parameters.
6462 The ids of the set dimensions in the space returned by
6463 C<isl_ast_build_get_schedule_space> correspond to the
6464 iterators of the already generated loops.
6465 The user should not rely on the ids of the output dimensions
6466 of the relations in the union relation returned by
6467 C<isl_ast_build_get_schedule> having any particular value.
6471 Although C<isl> is mainly meant to be used as a library,
6472 it also contains some basic applications that use some
6473 of the functionality of C<isl>.
6474 The input may be specified in either the L<isl format>
6475 or the L<PolyLib format>.
6477 =head2 C<isl_polyhedron_sample>
6479 C<isl_polyhedron_sample> takes a polyhedron as input and prints
6480 an integer element of the polyhedron, if there is any.
6481 The first column in the output is the denominator and is always
6482 equal to 1. If the polyhedron contains no integer points,
6483 then a vector of length zero is printed.
6487 C<isl_pip> takes the same input as the C<example> program
6488 from the C<piplib> distribution, i.e., a set of constraints
6489 on the parameters, a line containing only -1 and finally a set
6490 of constraints on a parametric polyhedron.
6491 The coefficients of the parameters appear in the last columns
6492 (but before the final constant column).
6493 The output is the lexicographic minimum of the parametric polyhedron.
6494 As C<isl> currently does not have its own output format, the output
6495 is just a dump of the internal state.
6497 =head2 C<isl_polyhedron_minimize>
6499 C<isl_polyhedron_minimize> computes the minimum of some linear
6500 or affine objective function over the integer points in a polyhedron.
6501 If an affine objective function
6502 is given, then the constant should appear in the last column.
6504 =head2 C<isl_polytope_scan>
6506 Given a polytope, C<isl_polytope_scan> prints
6507 all integer points in the polytope.
6509 =head2 C<isl_codegen>
6511 Given a schedule, a context set and an options relation,
6512 C<isl_codegen> prints out an AST that scans the domain elements
6513 of the schedule in the order of their image(s) taking into account
6514 the constraints in the context set.